LMFDB - Embedded newform 2646.2.h.n.361.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(361,2646)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2646, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("2646.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			361.2
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2646.361
Dual form			2646.2.h.n.667.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.44949 q^{5} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.44949 q^{5} -1.00000 q^{8} +(1.72474 - 2.98735i) q^{10} -2.00000 q^{11} +(-2.44949 + 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.72474 + 6.45145i) q^{19} +(-1.72474 - 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +1.00000 q^{23} +6.89898 q^{25} +(2.44949 + 4.24264i) q^{26} +(1.44949 + 2.51059i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} +(3.89898 + 6.75323i) q^{37} +7.44949 q^{38} -3.44949 q^{40} +(4.89898 - 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(1.00000 + 1.73205i) q^{44} +(0.500000 - 0.866025i) q^{46} +(4.89898 - 8.48528i) q^{47} +(3.44949 - 5.97469i) q^{50} +4.89898 q^{52} +(-0.550510 + 0.953512i) q^{53} -6.89898 q^{55} +2.89898 q^{58} +(1.00000 + 1.73205i) q^{59} +(5.72474 - 9.91555i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-8.44949 + 14.6349i) q^{65} +(1.55051 + 2.68556i) q^{67} +2.00000 q^{68} -9.89898 q^{71} +(1.44949 - 2.51059i) q^{73} +7.79796 q^{74} +(3.72474 - 6.45145i) q^{76} +(-3.94949 + 6.84072i) q^{79} +(-1.72474 + 2.98735i) q^{80} +(-4.89898 - 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +2.89898 q^{86} +2.00000 q^{88} +(3.55051 + 6.14966i) q^{89} +(-0.500000 - 0.866025i) q^{92} +(-4.89898 - 8.48528i) q^{94} +(12.8485 + 22.2542i) q^{95} +(-3.44949 - 5.97469i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 8 q^{11} - 2 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} - 4 q^{37} + 20 q^{38} - 4 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} - 8 q^{55} - 8 q^{58} + 4 q^{59} + 18 q^{61} + 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} + 8 q^{68} - 20 q^{71} - 4 q^{73} - 8 q^{74} + 10 q^{76} - 6 q^{79} - 2 q^{80} - 4 q^{83} - 4 q^{85} - 8 q^{86} + 8 q^{88} + 24 q^{89} - 2 q^{92} + 22 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 8 * q^11 - 2 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 - 4 * q^37 + 20 * q^38 - 4 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 + 8 * q^68 - 20 * q^71 - 4 * q^73 - 8 * q^74 + 10 * q^76 - 6 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 - 8 * q^86 + 8 * q^88 + 24 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times$.

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.44949			1.54266			0.771329	−	0.636436i	$-0.219592\pi$
$5$	3.44949			1.54266			0.771329	+	0.636436i	$0.219592\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.72474	−	2.98735i	0.545412	−	0.944682i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$		0			0
$19$	3.72474	+	6.45145i	0.854515	+	1.48006i	0.877094	+	0.480318i	$0.159479\pi$
$19$	3.72474	+	6.45145i	0.854515	+	1.48006i	−0.0225791	+	0.999745i	$0.507188\pi$
$20$	−1.72474	−	2.98735i	−0.385665	−	0.667991i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$		0			0
$25$	6.89898			1.37980
$26$	2.44949	+	4.24264i	0.480384	+	0.832050i
$27$		0			0
$28$		0			0
$29$	1.44949	+	2.51059i	0.269163	+	0.466205i	0.968646	−	0.248445i	$-0.0799195\pi$
$29$	1.44949	+	2.51059i	0.269163	+	0.466205i	−0.699483	+	0.714650i	$0.746586\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$		0			0
$37$	3.89898	+	6.75323i	0.640988	+	1.11022i	0.985213	+	0.171337i	$0.0548086\pi$
$37$	3.89898	+	6.75323i	0.640988	+	1.11022i	−0.344224	+	0.938887i	$0.611858\pi$
$38$	7.44949			1.20847
$39$		0			0
$40$	−3.44949			−0.545412
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	−0.175106	−	0.984550i	$-0.556027\pi$
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	0.940198	−	0.340629i	$-0.110640\pi$
$42$		0			0
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	0.955126	−	0.296201i	$-0.0957199\pi$
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	−0.734080	+	0.679062i	$0.762387\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	−0.248528	−	0.968625i	$-0.579947\pi$
$47$	4.89898	−	8.48528i	0.714590	−	1.23771i	0.963118	−	0.269081i	$-0.0867199\pi$
$48$		0			0
$49$		0			0
$50$	3.44949	−	5.97469i	0.487832	−	0.844949i
$51$		0			0
$52$	4.89898			0.679366
$53$	−0.550510	+	0.953512i	−0.0756184	+	0.130975i	−0.901355	−	0.433081i	$-0.857426\pi$
$53$	−0.550510	+	0.953512i	−0.0756184	+	0.130975i	0.825737	+	0.564056i	$0.190760\pi$
$54$		0			0
$55$	−6.89898			−0.930258
$56$		0			0
$57$		0			0
$58$	2.89898			0.380655
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$		0			0
$61$	5.72474	−	9.91555i	0.732978	−	1.26956i	−0.222626	−	0.974904i	$-0.571463\pi$
$61$	5.72474	−	9.91555i	0.732978	−	1.26956i	0.955605	−	0.294652i	$-0.0952037\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−8.44949	+	14.6349i	−1.04803	+	1.81524i
$66$		0			0
$67$	1.55051	+	2.68556i	0.189425	+	0.328094i	0.945059	−	0.326901i	$-0.106004\pi$
$67$	1.55051	+	2.68556i	0.189425	+	0.328094i	−0.755634	+	0.654994i	$0.772671\pi$
$68$	2.00000			0.242536
$69$		0			0
$70$		0			0
$71$	−9.89898			−1.17479			−0.587396	−	0.809299i	$-0.699847\pi$
$71$	−9.89898			−1.17479			−0.587396	+	0.809299i	$0.699847\pi$
$72$		0			0
$73$	1.44949	−	2.51059i	0.169650	−	0.293842i	−0.768647	−	0.639673i	$-0.779070\pi$
$73$	1.44949	−	2.51059i	0.169650	−	0.293842i	0.938297	+	0.345831i	$0.112403\pi$
$74$	7.79796			0.906494
$75$		0			0
$76$	3.72474	−	6.45145i	0.427258	−	0.740032i
$77$		0			0
$78$		0			0
$79$	−3.94949	+	6.84072i	−0.444352	+	0.769641i	−0.998007	−	0.0631057i	$-0.979899\pi$
$79$	−3.94949	+	6.84072i	−0.444352	+	0.769641i	0.553655	+	0.832746i	$0.313233\pi$
$80$	−1.72474	+	2.98735i	−0.192832	+	0.333995i
$81$		0			0
$82$	−4.89898	−	8.48528i	−0.541002	−	0.937043i
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$		0			0
$85$	−3.44949	+	5.97469i	−0.374150	+	0.648046i
$86$	2.89898			0.312605
$87$		0			0
$88$	2.00000			0.213201
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	0.990529	−	0.137307i	$-0.0438445\pi$
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	−0.614175	+	0.789170i	$0.710511\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$		0			0
$94$	−4.89898	−	8.48528i	−0.505291	−	0.875190i
$95$	12.8485	+	22.2542i	1.31823	+	2.28323i
$96$		0			0
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	0.636049	−	0.771649i	$-0.280568\pi$
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	−0.986292	+	0.165011i	$0.947234\pi$
$98$		0			0
$99$		0			0
$100$	−3.44949	−	5.97469i	−0.344949	−	0.597469i
$101$	7.24745			0.721148			0.360574	−	0.932731i	$-0.382581\pi$
$101$	7.24745			0.721148			0.360574	+	0.932731i	$0.382581\pi$
$102$		0			0
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	2.44949	−	4.24264i	0.240192	−	0.416025i
$105$		0			0
$106$	0.550510	+	0.953512i	0.0534703	+	0.0926132i
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$		0			0
$109$	8.34847	−	14.4600i	0.799638	−	1.38501i	−0.120213	−	0.992748i	$-0.538358\pi$
$109$	8.34847	−	14.4600i	0.799638	−	1.38501i	0.919852	−	0.392266i	$-0.128309\pi$
$110$	−3.44949	+	5.97469i	−0.328896	+	0.569664i
$111$		0			0
$112$		0			0
$113$	−7.94949	+	13.7689i	−0.747825	+	1.29527i	0.201038	+	0.979583i	$0.435569\pi$
$113$	−7.94949	+	13.7689i	−0.747825	+	1.29527i	−0.948863	+	0.315688i	$0.897765\pi$
$114$		0			0
$115$	3.44949			0.321667
$116$	1.44949	−	2.51059i	0.134582	−	0.233102i
$117$		0			0
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−5.72474	−	9.91555i	−0.518294	−	0.897712i
$123$		0			0
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	6.55051			0.585895
$126$		0			0
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	8.44949	+	14.6349i	0.741069	+	1.28357i
$131$	−13.4495			−1.17509			−0.587544	−	0.809192i	$-0.699905\pi$
$131$	−13.4495			−1.17509			−0.587544	+	0.809192i	$0.699905\pi$
$132$		0			0
$133$		0			0
$134$	3.10102			0.267887
$135$		0			0
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	11.7980			1.00797			0.503984	−	0.863713i	$-0.331867\pi$
$137$	11.7980			1.00797			0.503984	+	0.863713i	$0.331867\pi$
$138$		0			0
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	−0.593069	−	0.805152i	$-0.702084\pi$
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	0.993816	+	0.111037i	$0.0354171\pi$
$140$		0			0
$141$		0			0
$142$	−4.94949	+	8.57277i	−0.415352	+	0.719411i
$143$	4.89898	−	8.48528i	0.409673	−	0.709575i
$144$		0			0
$145$	5.00000	+	8.66025i	0.415227	+	0.719195i
$146$	−1.44949	−	2.51059i	−0.119961	−	0.207778i
$147$		0			0
$148$	3.89898	−	6.75323i	0.320494	−	0.555112i
$149$	6.00000			0.491539			0.245770	−	0.969328i	$-0.420959\pi$
$149$	6.00000			0.491539			0.245770	+	0.969328i	$0.420959\pi$
$150$		0			0
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	−3.72474	−	6.45145i	−0.302117	−	0.523281i
$153$		0			0
$154$		0			0
$155$	10.3485	+	17.9241i	0.831209	+	1.43970i
$156$		0			0
$157$	3.17423	+	5.49794i	0.253332	+	0.438783i	0.964441	−	0.264298i	$-0.0851403\pi$
$157$	3.17423	+	5.49794i	0.253332	+	0.438783i	−0.711109	+	0.703081i	$0.751807\pi$
$158$	3.94949	+	6.84072i	0.314205	+	0.544218i
$159$		0			0
$160$	1.72474	+	2.98735i	0.136353	+	0.236170i
$161$		0			0
$162$		0			0
$163$	0.101021	+	0.174973i	0.00791254	+	0.0137049i	0.869955	−	0.493132i	$-0.164148\pi$
$163$	0.101021	+	0.174973i	0.00791254	+	0.0137049i	−0.862042	+	0.506837i	$0.830815\pi$
$164$	−9.79796			−0.765092
$165$		0			0
$166$	−2.00000			−0.155230
$167$	−9.34847	+	16.1920i	−0.723406	+	1.25298i	0.236220	+	0.971700i	$0.424091\pi$
$167$	−9.34847	+	16.1920i	−0.723406	+	1.25298i	−0.959627	+	0.281277i	$0.909242\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	3.44949	+	5.97469i	0.264564	+	0.458238i
$171$		0			0
$172$	1.44949	−	2.51059i	0.110523	−	0.191431i
$173$	6.44949	−	11.1708i	0.490346	−	0.849304i	−0.509593	−	0.860416i	$-0.670204\pi$
$173$	6.44949	−	11.1708i	0.490346	−	0.849304i	0.999938	+	0.0111123i	$0.00353722\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	7.10102			0.532244
$179$	−4.34847	+	7.53177i	−0.325020	+	0.562951i	−0.981516	−	0.191378i	$-0.938704\pi$
$179$	−4.34847	+	7.53177i	−0.325020	+	0.562951i	0.656497	+	0.754329i	$0.272038\pi$
$180$		0			0
$181$	−4.34847			−0.323219			−0.161610	−	0.986855i	$-0.551669\pi$
$181$	−4.34847			−0.323219			−0.161610	+	0.986855i	$0.551669\pi$
$182$		0			0
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	13.4495	+	23.2952i	0.988826	+	1.71270i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	−9.79796			−0.714590
$189$		0			0
$190$	25.6969			1.86425
$191$	6.94949	−	12.0369i	0.502847	−	0.870957i	−0.497147	−	0.867666i	$-0.665619\pi$
$191$	6.94949	−	12.0369i	0.502847	−	0.870957i	0.999995	−	0.00329106i	$-0.00104758\pi$
$192$		0			0
$193$	4.05051	+	7.01569i	0.291562	+	0.505000i	0.974179	−	0.225776i	$-0.0724917\pi$
$193$	4.05051	+	7.01569i	0.291562	+	0.505000i	−0.682617	+	0.730776i	$0.739158\pi$
$194$	−6.89898			−0.495318
$195$		0			0
$196$		0			0
$197$	12.6969			0.904619			0.452310	−	0.891861i	$-0.350600\pi$
$197$	12.6969			0.904619			0.452310	+	0.891861i	$0.350600\pi$
$198$		0			0
$199$	3.44949	−	5.97469i	0.244528	−	0.423535i	−0.717471	−	0.696588i	$-0.754700\pi$
$199$	3.44949	−	5.97469i	0.244528	−	0.423535i	0.961999	+	0.273054i	$0.0880337\pi$
$200$	−6.89898			−0.487832
$201$		0			0
$202$	3.62372	−	6.27647i	0.254964	−	0.441611i
$203$		0			0
$204$		0			0
$205$	16.8990	−	29.2699i	1.18028	−	2.04430i
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$		0			0
$208$	−2.44949	−	4.24264i	−0.169842	−	0.294174i
$209$	−7.44949	−	12.9029i	−0.515292	−	0.892512i
$210$		0			0
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	−0.914448	−	0.404703i	$-0.867375\pi$
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	0.807707	+	0.589584i	$0.200708\pi$
$212$	1.10102			0.0756184
$213$		0			0
$214$	−12.0000			−0.820303
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$	−8.34847	−	14.4600i	−0.565430	−	0.979353i
$219$		0			0
$220$	3.44949	+	5.97469i	0.232565	+	0.402814i
$221$	−4.89898	−	8.48528i	−0.329541	−	0.570782i
$222$		0			0
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	−0.968553	−	0.248807i	$-0.919962\pi$
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	0.268804	−	0.963195i	$-0.413372\pi$
$224$		0			0
$225$		0			0
$226$	7.94949	+	13.7689i	0.528792	+	0.915895i
$227$	−0.550510			−0.0365386			−0.0182693	−	0.999833i	$-0.505816\pi$
$227$	−0.550510			−0.0365386			−0.0182693	+	0.999833i	$0.505816\pi$
$228$		0			0
$229$	23.2474			1.53623			0.768117	−	0.640309i	$-0.221194\pi$
$229$	23.2474			1.53623			0.768117	+	0.640309i	$0.221194\pi$
$230$	1.72474	−	2.98735i	0.113726	−	0.196980i
$231$		0			0
$232$	−1.44949	−	2.51059i	−0.0951637	−	0.164828i
$233$	−3.50000	−	6.06218i	−0.229293	−	0.397146i	0.728306	−	0.685252i	$-0.240308\pi$
$233$	−3.50000	−	6.06218i	−0.229293	−	0.397146i	−0.957599	+	0.288106i	$0.906975\pi$
$234$		0			0
$235$	16.8990	−	29.2699i	1.10237	−	1.90936i
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$		0			0
$238$		0			0
$239$	−6.39898	+	11.0834i	−0.413916	+	0.716923i	−0.995314	−	0.0966962i	$-0.969172\pi$
$239$	−6.39898	+	11.0834i	−0.413916	+	0.716923i	0.581398	+	0.813619i	$0.302506\pi$
$240$		0			0
$241$	8.89898			0.573234			0.286617	−	0.958045i	$-0.407469\pi$
$241$	8.89898			0.573234			0.286617	+	0.958045i	$0.407469\pi$
$242$	−3.50000	+	6.06218i	−0.224989	+	0.389692i
$243$		0			0
$244$	−11.4495			−0.732978
$245$		0			0
$246$		0			0
$247$	−36.4949			−2.32211
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$	3.27526	−	5.67291i	0.207145	−	0.358786i
$251$	12.5505			0.792181			0.396091	−	0.918211i	$-0.370367\pi$
$251$	12.5505			0.792181			0.396091	+	0.918211i	$0.370367\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	−1.50000	+	2.59808i	−0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	27.7980			1.73399			0.866995	−	0.498318i	$-0.166049\pi$
$257$	27.7980			1.73399			0.866995	+	0.498318i	$0.166049\pi$
$258$		0			0
$259$		0			0
$260$	16.8990			1.04803
$261$		0			0
$262$	−6.72474	+	11.6476i	−0.415456	+	0.719591i
$263$	−16.1010			−0.992831			−0.496416	−	0.868085i	$-0.665351\pi$
$263$	−16.1010			−0.992831			−0.496416	+	0.868085i	$0.665351\pi$
$264$		0			0
$265$	−1.89898	+	3.28913i	−0.116653	+	0.202050i
$266$		0			0
$267$		0			0
$268$	1.55051	−	2.68556i	0.0947125	−	0.164047i
$269$	1.82577	−	3.16232i	0.111319	−	0.192810i	−0.804983	−	0.593297i	$-0.797826\pi$
$269$	1.82577	−	3.16232i	0.111319	−	0.192810i	0.916302	+	0.400487i	$0.131159\pi$
$270$		0			0
$271$	8.44949	+	14.6349i	0.513270	+	0.889010i	0.999882	+	0.0153912i	$0.00489937\pi$
$271$	8.44949	+	14.6349i	0.513270	+	0.889010i	−0.486612	+	0.873618i	$0.661767\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	5.89898	−	10.2173i	0.356370	−	0.617252i
$275$	−13.7980			−0.832048
$276$		0			0
$277$	10.6969			0.642717			0.321358	−	0.946958i	$-0.395861\pi$
$277$	10.6969			0.642717			0.321358	+	0.946958i	$0.395861\pi$
$278$	−4.72474	−	8.18350i	−0.283371	−	0.490814i
$279$		0			0
$280$		0			0
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	−0.996887	−	0.0788417i	$-0.974878\pi$
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	0.430165	−	0.902750i	$-0.358455\pi$
$282$		0			0
$283$	−10.2753	−	17.7973i	−0.610801	−	1.05794i	−0.991106	−	0.133077i	$-0.957514\pi$
$283$	−10.2753	−	17.7973i	−0.610801	−	1.05794i	0.380305	−	0.924861i	$-0.375819\pi$
$284$	4.94949	+	8.57277i	0.293698	+	0.508700i
$285$		0			0
$286$	−4.89898	−	8.48528i	−0.289683	−	0.501745i
$287$		0			0
$288$		0			0
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	10.0000			0.587220
$291$		0			0
$292$	−2.89898			−0.169650
$293$	−13.6237	+	23.5970i	−0.795906	+	1.37855i	0.126356	+	0.991985i	$0.459672\pi$
$293$	−13.6237	+	23.5970i	−0.795906	+	1.37855i	−0.922262	+	0.386565i	$0.873661\pi$
$294$		0			0
$295$	3.44949	+	5.97469i	0.200837	+	0.347860i
$296$	−3.89898	−	6.75323i	−0.226624	−	0.392524i
$297$		0			0
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	−2.44949	+	4.24264i	−0.141658	+	0.245358i
$300$		0			0
$301$		0			0
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$		0			0
$304$	−7.44949			−0.427258
$305$	19.7474	−	34.2036i	1.13074	−	1.95849i
$306$		0			0
$307$	−0.752551			−0.0429504			−0.0214752	−	0.999769i	$-0.506836\pi$
$307$	−0.752551			−0.0429504			−0.0214752	+	0.999769i	$0.506836\pi$
$308$		0			0
$309$		0			0
$310$	20.6969			1.17551
$311$	−0.651531	−	1.12848i	−0.0369449	−	0.0639905i	0.846962	−	0.531654i	$-0.178429\pi$
$311$	−0.651531	−	1.12848i	−0.0369449	−	0.0639905i	−0.883907	+	0.467663i	$0.845096\pi$
$312$		0			0
$313$	12.3485	−	21.3882i	0.697977	−	1.20893i	−0.271190	−	0.962526i	$-0.587417\pi$
$313$	12.3485	−	21.3882i	0.697977	−	1.20893i	0.969167	−	0.246405i	$-0.0792495\pi$
$314$	6.34847			0.358265
$315$		0			0
$316$	7.89898			0.444352
$317$	−4.34847	+	7.53177i	−0.244234	+	0.423026i	−0.961916	−	0.273345i	$-0.911870\pi$
$317$	−4.34847	+	7.53177i	−0.244234	+	0.423026i	0.717682	+	0.696371i	$0.245203\pi$
$318$		0			0
$319$	−2.89898	−	5.02118i	−0.162312	−	0.281132i
$320$	3.44949			0.192832
$321$		0			0
$322$		0			0
$323$	−14.8990			−0.829001
$324$		0			0
$325$	−16.8990	+	29.2699i	−0.937387	+	1.62360i
$326$	0.202041			0.0111900
$327$		0			0
$328$	−4.89898	+	8.48528i	−0.270501	+	0.468521i
$329$		0			0
$330$		0			0
$331$	12.3485	−	21.3882i	0.678733	−	1.17560i	−0.296629	−	0.954993i	$-0.595863\pi$
$331$	12.3485	−	21.3882i	0.678733	−	1.17560i	0.975363	−	0.220608i	$-0.0708041\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$		0			0
$334$	9.34847	+	16.1920i	0.511525	+	0.885988i
$335$	5.34847	+	9.26382i	0.292218	+	0.506137i
$336$		0			0
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.251772	+	0.967787i	$0.581013\pi$
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.712242	+	0.701934i	$0.752320\pi$
$338$	−11.0000			−0.598321
$339$		0			0
$340$	6.89898			0.374150
$341$	−6.00000	−	10.3923i	−0.324918	−	0.562775i
$342$		0			0
$343$		0			0
$344$	−1.44949	−	2.51059i	−0.0781512	−	0.135362i
$345$		0			0
$346$	−6.44949	−	11.1708i	−0.346727	−	0.600548i
$347$	−9.79796	−	16.9706i	−0.525982	−	0.911028i	−0.999542	−	0.0302659i	$-0.990365\pi$
$347$	−9.79796	−	16.9706i	−0.525982	−	0.911028i	0.473560	−	0.880762i	$-0.342969\pi$
$348$		0			0
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	0.997551	+	0.0699435i	$0.0222819\pi$
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	−0.438203	+	0.898876i	$0.644385\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$		0			0
$355$	−34.1464			−1.81230
$356$	3.55051	−	6.14966i	0.188177	−	0.325932i
$357$		0			0
$358$	4.34847	+	7.53177i	0.229824	+	0.398066i
$359$	5.39898	+	9.35131i	0.284947	+	0.493543i	0.972596	−	0.232500i	$-0.0746906\pi$
$359$	5.39898	+	9.35131i	0.284947	+	0.493543i	−0.687649	+	0.726043i	$0.741357\pi$
$360$		0			0
$361$	−18.2474	+	31.6055i	−0.960392	+	1.66345i
$362$	−2.17423	+	3.76588i	−0.114275	+	0.197931i
$363$		0			0
$364$		0			0
$365$	5.00000	−	8.66025i	0.261712	−	0.453298i
$366$		0			0
$367$	−5.79796			−0.302651			−0.151325	−	0.988484i	$-0.548354\pi$
$367$	−5.79796			−0.302651			−0.151325	+	0.988484i	$0.548354\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$		0			0
$370$	26.8990			1.39841
$371$		0			0
$372$		0			0
$373$	2.89898			0.150103			0.0750517	−	0.997180i	$-0.476088\pi$
$373$	2.89898			0.150103			0.0750517	+	0.997180i	$0.476088\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	−4.89898	+	8.48528i	−0.252646	+	0.437595i
$377$	−14.2020			−0.731442
$378$		0			0
$379$	−26.4949			−1.36095			−0.680476	−	0.732771i	$-0.738227\pi$
$379$	−26.4949			−1.36095			−0.680476	+	0.732771i	$0.738227\pi$
$380$	12.8485	−	22.2542i	0.659113	−	1.14162i
$381$		0			0
$382$	−6.94949	−	12.0369i	−0.355567	−	0.615860i
$383$	6.89898			0.352521			0.176261	−	0.984344i	$-0.443600\pi$
$383$	6.89898			0.352521			0.176261	+	0.984344i	$0.443600\pi$
$384$		0			0
$385$		0			0
$386$	8.10102			0.412331
$387$		0			0
$388$	−3.44949	+	5.97469i	−0.175121	+	0.303319i
$389$	15.1010			0.765652			0.382826	−	0.923820i	$-0.374951\pi$
$389$	15.1010			0.765652			0.382826	+	0.923820i	$0.374951\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$	6.34847	−	10.9959i	0.319831	−	0.553964i
$395$	−13.6237	+	23.5970i	−0.685484	+	1.18729i
$396$		0			0
$397$	4.65153	+	8.05669i	0.233454	+	0.404354i	0.958822	−	0.284007i	$-0.0916640\pi$
$397$	4.65153	+	8.05669i	0.233454	+	0.404354i	−0.725369	+	0.688361i	$0.758331\pi$
$398$	−3.44949	−	5.97469i	−0.172907	−	0.299484i
$399$		0			0
$400$	−3.44949	+	5.97469i	−0.172474	+	0.298735i
$401$	10.1010			0.504421			0.252210	−	0.967672i	$-0.418842\pi$
$401$	10.1010			0.504421			0.252210	+	0.967672i	$0.418842\pi$
$402$		0			0
$403$	−29.3939			−1.46421
$404$	−3.62372	−	6.27647i	−0.180287	−	0.312266i
$405$		0			0
$406$		0			0
$407$	−7.79796	−	13.5065i	−0.386530	−	0.669490i
$408$		0			0
$409$	2.89898	+	5.02118i	0.143345	+	0.248281i	0.928754	−	0.370696i	$-0.120881\pi$
$409$	2.89898	+	5.02118i	0.143345	+	0.248281i	−0.785409	+	0.618977i	$0.787547\pi$
$410$	−16.8990	−	29.2699i	−0.834581	−	1.44554i
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$		0			0
$415$	−3.44949	−	5.97469i	−0.169329	−	0.293286i
$416$	−4.89898			−0.240192
$417$		0			0
$418$	−14.8990			−0.728733
$419$	−12.2753	+	21.2614i	−0.599685	+	1.03869i	0.393182	+	0.919461i	$0.371374\pi$
$419$	−12.2753	+	21.2614i	−0.599685	+	1.03869i	−0.992867	+	0.119225i	$0.961959\pi$
$420$		0			0
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	0.661080	−	0.750316i	$-0.270098\pi$
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	−0.980332	+	0.197354i	$0.936765\pi$
$422$	1.55051	+	2.68556i	0.0754777	+	0.130731i
$423$		0			0
$424$	0.550510	−	0.953512i	0.0267351	−	0.0463066i
$425$	−6.89898	+	11.9494i	−0.334650	+	0.579630i
$426$		0			0
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	10.0000			0.482243
$431$	−3.79796	+	6.57826i	−0.182941	+	0.316864i	−0.942881	−	0.333130i	$-0.891895\pi$
$431$	−3.79796	+	6.57826i	−0.182941	+	0.316864i	0.759940	+	0.649994i	$0.225228\pi$
$432$		0			0
$433$	−11.7980			−0.566974			−0.283487	−	0.958976i	$-0.591491\pi$
$433$	−11.7980			−0.566974			−0.283487	+	0.958976i	$0.591491\pi$
$434$		0			0
$435$		0			0
$436$	−16.6969			−0.799638
$437$	3.72474	+	6.45145i	0.178179	+	0.308615i
$438$		0			0
$439$	10.8990	−	18.8776i	0.520180	−	0.900978i	−0.479545	−	0.877517i	$-0.659198\pi$
$439$	10.8990	−	18.8776i	0.520180	−	0.900978i	0.999725	−	0.0234607i	$-0.00746845\pi$
$440$	6.89898			0.328896
$441$		0			0
$442$	−9.79796			−0.466041
$443$	−2.55051	+	4.41761i	−0.121178	+	0.209887i	−0.920233	−	0.391372i	$-0.872001\pi$
$443$	−2.55051	+	4.41761i	−0.121178	+	0.209887i	0.799054	+	0.601259i	$0.205334\pi$
$444$		0			0
$445$	12.2474	+	21.2132i	0.580585	+	1.00560i
$446$	−20.8990			−0.989595
$447$		0			0
$448$		0			0
$449$	18.5959			0.877596			0.438798	−	0.898586i	$-0.355404\pi$
$449$	18.5959			0.877596			0.438798	+	0.898586i	$0.355404\pi$
$450$		0			0
$451$	−9.79796	+	16.9706i	−0.461368	+	0.799113i
$452$	15.8990			0.747825
$453$		0			0
$454$	−0.275255	+	0.476756i	−0.0129184	+	0.0223753i
$455$		0			0
$456$		0			0
$457$	−15.7474	+	27.2754i	−0.736635	+	1.27589i	0.217368	+	0.976090i	$0.430253\pi$
$457$	−15.7474	+	27.2754i	−0.736635	+	1.27589i	−0.954002	+	0.299799i	$0.903080\pi$
$458$	11.6237	−	20.1329i	0.543141	−	0.940748i
$459$		0			0
$460$	−1.72474	−	2.98735i	−0.0804166	−	0.139286i
$461$	−10.1742	−	17.6223i	−0.473861	−	0.820752i	0.525691	−	0.850676i	$-0.323807\pi$
$461$	−10.1742	−	17.6223i	−0.473861	−	0.820752i	−0.999552	+	0.0299238i	$0.990474\pi$
$462$		0			0
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	−0.396125	−	0.918197i	$-0.629645\pi$
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	0.993244	−	0.116044i	$-0.0370213\pi$
$464$	−2.89898			−0.134582
$465$		0			0
$466$	−7.00000			−0.324269
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	0.726840	−	0.686807i	$-0.240988\pi$
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	−0.958212	+	0.286058i	$0.907655\pi$
$468$		0			0
$469$		0			0
$470$	−16.8990	−	29.2699i	−0.779492	−	1.35012i
$471$		0			0
$472$	−1.00000	−	1.73205i	−0.0460287	−	0.0797241i
$473$	−2.89898	−	5.02118i	−0.133295	−	0.230874i
$474$		0			0
$475$	25.6969	+	44.5084i	1.17906	+	2.04219i
$476$		0			0
$477$		0			0
$478$	6.39898	+	11.0834i	0.292683	+	0.506941i
$479$	−29.5959			−1.35227			−0.676136	−	0.736777i	$-0.736347\pi$
$479$	−29.5959			−1.35227			−0.676136	+	0.736777i	$0.736347\pi$
$480$		0			0
$481$	−38.2020			−1.74186
$482$	4.44949	−	7.70674i	0.202669	−	0.351032i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−11.8990	−	20.6096i	−0.540305	−	0.935835i
$486$		0			0
$487$	−11.1969	+	19.3937i	−0.507382	+	0.878811i	0.492582	+	0.870266i	$0.336053\pi$
$487$	−11.1969	+	19.3937i	−0.507382	+	0.878811i	−0.999963	+	0.00854475i	$0.997280\pi$
$488$	−5.72474	+	9.91555i	−0.259147	+	0.448856i
$489$		0			0
$490$		0			0
$491$	−1.89898	+	3.28913i	−0.0856997	+	0.148436i	−0.905689	−	0.423942i	$-0.860646\pi$
$491$	−1.89898	+	3.28913i	−0.0856997	+	0.148436i	0.819989	+	0.572379i	$0.193979\pi$
$492$		0			0
$493$	−5.79796			−0.261127
$494$	−18.2474	+	31.6055i	−0.820992	+	1.42200i
$495$		0			0
$496$	−6.00000			−0.269408
$497$		0			0
$498$		0			0
$499$	33.3939			1.49492			0.747458	−	0.664309i	$-0.231274\pi$
$499$	33.3939			1.49492			0.747458	+	0.664309i	$0.231274\pi$
$500$	−3.27526	−	5.67291i	−0.146474	−	0.253700i
$501$		0			0
$502$	6.27526	−	10.8691i	0.280078	−	0.485110i
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$		0			0
$508$	1.50000	+	2.59808i	0.0665517	+	0.115271i
$509$	−16.8990			−0.749034			−0.374517	−	0.927220i	$-0.622191\pi$
$509$	−16.8990			−0.749034			−0.374517	+	0.927220i	$0.622191\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	13.8990	−	24.0737i	0.613058	−	1.06185i
$515$	−48.2929			−2.12804
$516$		0			0
$517$	−9.79796	+	16.9706i	−0.430914	+	0.746364i
$518$		0			0
$519$		0			0
$520$	8.44949	−	14.6349i	0.370535	−	0.641785i
$521$	19.3485	−	33.5125i	0.847672	−	1.46821i	−0.0356087	−	0.999366i	$-0.511337\pi$
$521$	19.3485	−	33.5125i	0.847672	−	1.46821i	0.883281	−	0.468845i	$-0.155330\pi$
$522$		0			0
$523$	0.174235	+	0.301783i	0.00761875	+	0.0131961i	0.869810	−	0.493387i	$-0.164242\pi$
$523$	0.174235	+	0.301783i	0.00761875	+	0.0131961i	−0.862191	+	0.506584i	$0.830908\pi$
$524$	6.72474	+	11.6476i	0.293772	+	0.508828i
$525$		0			0
$526$	−8.05051	+	13.9439i	−0.351019	+	0.607983i
$527$	−12.0000			−0.522728
$528$		0			0
$529$	−22.0000			−0.956522
$530$	1.89898	+	3.28913i	0.0824864	+	0.142871i
$531$		0			0
$532$		0			0
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		0			0
$535$	−20.6969	−	35.8481i	−0.894807	−	1.54985i
$536$	−1.55051	−	2.68556i	−0.0669718	−	0.115999i
$537$		0			0
$538$	−1.82577	−	3.16232i	−0.0787143	−	0.136337i
$539$		0			0
$540$		0			0
$541$	−15.2474	−	26.4094i	−0.655539	−	1.13543i	−0.981758	−	0.190133i	$-0.939108\pi$
$541$	−15.2474	−	26.4094i	−0.655539	−	1.13543i	0.326219	−	0.945294i	$-0.394225\pi$
$542$	16.8990			0.725873
$543$		0			0
$544$	−2.00000			−0.0857493
$545$	28.7980	−	49.8795i	1.23357	−	2.13660i
$546$		0			0
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	−0.976331	−	0.216283i	$-0.930607\pi$
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	0.300859	−	0.953669i	$-0.402727\pi$
$548$	−5.89898	−	10.2173i	−0.251992	−	0.436463i
$549$		0			0
$550$	−6.89898	+	11.9494i	−0.294173	+	0.509523i
$551$	−10.7980	+	18.7026i	−0.460009	+	0.796758i
$552$		0			0
$553$		0			0
$554$	5.34847	−	9.26382i	0.227235	−	0.393582i
$555$		0			0
$556$	−9.44949			−0.400748
$557$	−1.55051	+	2.68556i	−0.0656972	+	0.113791i	−0.897003	−	0.442024i	$-0.854260\pi$
$557$	−1.55051	+	2.68556i	−0.0656972	+	0.113791i	0.831306	+	0.555815i	$0.187594\pi$
$558$		0			0
$559$	−14.2020			−0.600682
$560$		0			0
$561$		0			0
$562$	−19.0000			−0.801467
$563$	−6.97219	−	12.0762i	−0.293843	−	0.508951i	0.680872	−	0.732402i	$-0.261601\pi$
$563$	−6.97219	−	12.0762i	−0.293843	−	0.508951i	−0.974715	+	0.223451i	$0.928268\pi$
$564$		0			0
$565$	−27.4217	+	47.4957i	−1.15364	+	1.99816i
$566$	−20.5505			−0.863802
$567$		0			0
$568$	9.89898			0.415352
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−7.10102	−	12.2993i	−0.297168	−	0.514711i	0.678319	−	0.734768i	$-0.262709\pi$
$571$	−7.10102	−	12.2993i	−0.297168	−	0.514711i	−0.975487	+	0.220057i	$0.929376\pi$
$572$	−9.79796			−0.409673
$573$		0			0
$574$		0			0
$575$	6.89898			0.287707
$576$		0			0
$577$	11.7980	−	20.4347i	0.491155	−	0.850706i	−0.508793	−	0.860889i	$-0.669908\pi$
$577$	11.7980	−	20.4347i	0.491155	−	0.850706i	0.999948	+	0.0101829i	$0.00324136\pi$
$578$	13.0000			0.540729
$579$		0			0
$580$	5.00000	−	8.66025i	0.207614	−	0.359597i
$581$		0			0
$582$		0			0
$583$	1.10102	−	1.90702i	0.0455996	−	0.0789808i
$584$	−1.44949	+	2.51059i	−0.0599803	+	0.103889i
$585$		0			0
$586$	13.6237	+	23.5970i	0.562791	+	0.974782i
$587$	9.07321	+	15.7153i	0.374492	+	0.648639i	0.990251	−	0.139296i	$-0.0444839\pi$
$587$	9.07321	+	15.7153i	0.374492	+	0.648639i	−0.615759	+	0.787934i	$0.711151\pi$
$588$		0			0
$589$	−22.3485	+	38.7087i	−0.920853	+	1.59496i
$590$	6.89898			0.284026
$591$		0			0
$592$	−7.79796			−0.320494
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	0.976536	−	0.215355i	$-0.0690907\pi$
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	−0.674770	+	0.738028i	$0.735757\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	2.44949	+	4.24264i	0.100167	+	0.173494i
$599$	−7.10102	−	12.2993i	−0.290140	−	0.502537i	0.683703	−	0.729761i	$-0.260368\pi$
$599$	−7.10102	−	12.2993i	−0.290140	−	0.502537i	−0.973843	+	0.227224i	$0.927035\pi$
$600$		0			0
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	0.707004	−	0.707210i	$-0.250046\pi$
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	−0.965963	+	0.258679i	$0.916713\pi$
$602$		0			0
$603$		0			0
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	−24.1464			−0.981692
$606$		0			0
$607$	8.69694			0.352998			0.176499	−	0.984301i	$-0.443523\pi$
$607$	8.69694			0.352998			0.176499	+	0.984301i	$0.443523\pi$
$608$	−3.72474	+	6.45145i	−0.151058	+	0.261641i
$609$		0			0
$610$	−19.7474	−	34.2036i	−0.799551	−	1.38486i
$611$	24.0000	+	41.5692i	0.970936	+	1.68171i
$612$		0			0
$613$	−7.34847	+	12.7279i	−0.296802	+	0.514076i	−0.975402	−	0.220432i	$-0.929253\pi$
$613$	−7.34847	+	12.7279i	−0.296802	+	0.514076i	0.678601	+	0.734508i	$0.262587\pi$
$614$	−0.376276	+	0.651729i	−0.0151852	+	0.0263016i
$615$		0			0
$616$		0			0
$617$	21.6969	−	37.5802i	0.873486	−	1.51292i	0.0151189	−	0.999886i	$-0.495187\pi$
$617$	21.6969	−	37.5802i	0.873486	−	1.51292i	0.858367	−	0.513036i	$-0.171479\pi$
$618$		0			0
$619$	4.14643			0.166659			0.0833295	−	0.996522i	$-0.473445\pi$
$619$	4.14643			0.166659			0.0833295	+	0.996522i	$0.473445\pi$
$620$	10.3485	−	17.9241i	0.415605	−	0.719848i
$621$		0			0
$622$	−1.30306			−0.0522480
$623$		0			0
$624$		0			0
$625$	−11.8990			−0.475959
$626$	−12.3485	−	21.3882i	−0.493544	−	0.854843i
$627$		0			0
$628$	3.17423	−	5.49794i	0.126666	−	0.219392i
$629$	−15.5959			−0.621850
$630$		0			0
$631$	18.1010			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$631$	18.1010			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$632$	3.94949	−	6.84072i	0.157102	−	0.272109i
$633$		0			0
$634$	4.34847	+	7.53177i	0.172700	+	0.299125i
$635$	−10.3485			−0.410666
$636$		0			0
$637$		0			0
$638$	−5.79796			−0.229543
$639$		0			0
$640$	1.72474	−	2.98735i	0.0681765	−	0.118085i
$641$	−41.4949			−1.63895			−0.819475	−	0.573115i	$-0.805735\pi$
$641$	−41.4949			−1.63895			−0.819475	+	0.573115i	$0.805735\pi$
$642$		0			0
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	−0.608996	−	0.793173i	$-0.708428\pi$
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	0.991406	+	0.130820i	$0.0417609\pi$
$644$		0			0
$645$		0			0
$646$	−7.44949	+	12.9029i	−0.293096	+	0.507658i
$647$	10.6515	−	18.4490i	0.418755	−	0.725305i	−0.577060	−	0.816702i	$-0.695800\pi$
$647$	10.6515	−	18.4490i	0.418755	−	0.725305i	0.995815	+	0.0913973i	$0.0291333\pi$
$648$		0			0
$649$	−2.00000	−	3.46410i	−0.0785069	−	0.135978i
$650$	16.8990	+	29.2699i	0.662833	+	1.14806i
$651$		0			0
$652$	0.101021	−	0.174973i	0.00395627	−	0.00685246i
$653$	9.79796			0.383424			0.191712	−	0.981451i	$-0.438596\pi$
$653$	9.79796			0.383424			0.191712	+	0.981451i	$0.438596\pi$
$654$		0			0
$655$	−46.3939			−1.81276
$656$	4.89898	+	8.48528i	0.191273	+	0.331295i
$657$		0			0
$658$		0			0
$659$	2.34847	+	4.06767i	0.0914834	+	0.158454i	0.908136	−	0.418676i	$-0.137506\pi$
$659$	2.34847	+	4.06767i	0.0914834	+	0.158454i	−0.816652	+	0.577130i	$0.804172\pi$
$660$		0			0
$661$	4.72474	+	8.18350i	0.183771	+	0.318301i	0.943162	−	0.332334i	$-0.107836\pi$
$661$	4.72474	+	8.18350i	0.183771	+	0.318301i	−0.759391	+	0.650635i	$0.774503\pi$
$662$	−12.3485	−	21.3882i	−0.479937	−	0.831275i
$663$		0			0
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$		0			0
$667$	1.44949	+	2.51059i	0.0561245	+	0.0972104i
$668$	18.6969			0.723406
$669$		0			0
$670$	10.6969			0.413259
$671$	−11.4495	+	19.8311i	−0.442003	+	0.765571i
$672$		0			0
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	−0.994272	−	0.106875i	$-0.965915\pi$
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	0.404579	−	0.914503i	$-0.367418\pi$
$674$	17.6969	+	30.6520i	0.681661	+	1.18067i
$675$		0			0
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	−0.689557	−	0.724232i	$-0.742195\pi$
$677$	7.34847	−	12.7279i	0.282425	−	0.489174i	0.971981	+	0.235058i	$0.0755280\pi$
$678$		0			0
$679$		0			0
$680$	3.44949	−	5.97469i	0.132282	−	0.229119i
$681$		0			0
$682$	−12.0000			−0.459504
$683$	16.1010	−	27.8878i	0.616088	−	1.06710i	−0.374104	−	0.927387i	$-0.622050\pi$
$683$	16.1010	−	27.8878i	0.616088	−	1.06710i	0.990193	−	0.139710i	$-0.0446169\pi$
$684$		0			0
$685$	40.6969			1.55495
$686$		0			0
$687$		0			0
$688$	−2.89898			−0.110523
$689$	−2.69694	−	4.67123i	−0.102745	−	0.177960i
$690$		0			0
$691$	3.47730	−	6.02285i	0.132283	−	0.229120i	−0.792274	−	0.610166i	$-0.791103\pi$
$691$	3.47730	−	6.02285i	0.132283	−	0.229120i	0.924556	+	0.381046i	$0.124436\pi$
$692$	−12.8990			−0.490346
$693$		0			0
$694$	−19.5959			−0.743851
$695$	16.2980	−	28.2289i	0.618217	−	1.07078i
$696$		0			0
$697$	9.79796	+	16.9706i	0.371124	+	0.642806i
$698$	20.8990			0.791038
$699$		0			0
$700$		0			0
$701$	−51.3939			−1.94112			−0.970560	−	0.240860i	$-0.922571\pi$
$701$	−51.3939			−1.94112			−0.970560	+	0.240860i	$0.922571\pi$
$702$		0			0
$703$	−29.0454	+	50.3081i	−1.09547	+	1.89741i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$		0			0
$709$	5.79796	−	10.0424i	0.217747	−	0.377149i	−0.736372	−	0.676577i	$-0.763463\pi$
$709$	5.79796	−	10.0424i	0.217747	−	0.377149i	0.954119	+	0.299428i	$0.0967959\pi$
$710$	−17.0732	+	29.5717i	−0.640746	+	1.10981i
$711$		0			0
$712$	−3.55051	−	6.14966i	−0.133061	−	0.230468i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	16.8990	−	29.2699i	0.631986	−	1.09463i
$716$	8.69694			0.325020
$717$		0			0
$718$	10.7980			0.402976
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	0.942799	−	0.333360i	$-0.108183\pi$
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	−0.760098	+	0.649808i	$0.774849\pi$
$720$		0			0
$721$		0			0
$722$	18.2474	+	31.6055i	0.679100	+	1.17624i
$723$		0			0
$724$	2.17423	+	3.76588i	0.0808048	+	0.139958i
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	0.947369	+	0.320143i	$0.103731\pi$
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	−0.196433	+	0.980517i	$0.562936\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	−5.79796			−0.214445
$732$		0			0
$733$	12.5505			0.463564			0.231782	−	0.972768i	$-0.425544\pi$
$733$	12.5505			0.463564			0.231782	+	0.972768i	$0.425544\pi$
$734$	−2.89898	+	5.02118i	−0.107003	+	0.185335i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−3.10102	−	5.37113i	−0.114228	−	0.197848i
$738$		0			0
$739$	12.7980	−	22.1667i	0.470781	−	0.815416i	−0.528661	−	0.848833i	$-0.677306\pi$
$739$	12.7980	−	22.1667i	0.470781	−	0.815416i	0.999441	+	0.0334173i	$0.0106390\pi$
$740$	13.4495	−	23.2952i	0.494413	−	0.856349i
$741$		0			0
$742$		0			0
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	20.6969			0.758277
$746$	1.44949	−	2.51059i	0.0530696	−	0.0919192i
$747$		0			0
$748$	−4.00000			−0.146254
$749$		0			0
$750$		0			0
$751$	40.5959			1.48137			0.740683	−	0.671855i	$-0.234502\pi$
$751$	40.5959			1.48137			0.740683	+	0.671855i	$0.234502\pi$
$752$	4.89898	+	8.48528i	0.178647	+	0.309426i
$753$		0			0
$754$	−7.10102	+	12.2993i	−0.258604	+	0.447915i
$755$	−17.2474			−0.627699
$756$		0			0
$757$	23.3939			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$757$	23.3939			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$758$	−13.2474	+	22.9453i	−0.481169	+	0.833409i
$759$		0			0
$760$	−12.8485	−	22.2542i	−0.466063	−	0.807245i
$761$	2.00000			0.0724999			0.0362500	−	0.999343i	$-0.488459\pi$
$761$	2.00000			0.0724999			0.0362500	+	0.999343i	$0.488459\pi$
$762$		0			0
$763$		0			0
$764$	−13.8990			−0.502847
$765$		0			0
$766$	3.44949	−	5.97469i	0.124635	−	0.215874i
$767$	−9.79796			−0.353784
$768$		0			0
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.296282	−	0.955100i	$-0.404253\pi$
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.679000	−	0.734138i	$-0.262414\pi$
$770$		0			0
$771$		0			0
$772$	4.05051	−	7.01569i	0.145781	−	0.252500i
$773$	9.97219	−	17.2723i	0.358675	−	0.621243i	−0.629065	−	0.777353i	$-0.716562\pi$
$773$	9.97219	−	17.2723i	0.358675	−	0.621243i	0.987740	+	0.156110i	$0.0498953\pi$
$774$		0			0
$775$	20.6969	+	35.8481i	0.743456	+	1.28770i
$776$	3.44949	+	5.97469i	0.123829	+	0.214479i
$777$		0			0
$778$	7.55051	−	13.0779i	0.270699	−	0.468864i
$779$	72.9898			2.61513
$780$		0			0
$781$	19.7980			0.708427
$782$	1.00000	+	1.73205i	0.0357599	+	0.0619380i
$783$		0			0
$784$		0			0
$785$	10.9495	+	18.9651i	0.390804	+	0.676892i
$786$		0			0
$787$	23.6969	+	41.0443i	0.844705	+	1.46307i	0.885877	+	0.463919i	$0.153557\pi$
$787$	23.6969	+	41.0443i	0.844705	+	1.46307i	−0.0411728	+	0.999152i	$0.513109\pi$
$788$	−6.34847	−	10.9959i	−0.226155	−	0.391712i
$789$		0			0
$790$	13.6237	+	23.5970i	0.484710	+	0.839543i
$791$		0			0
$792$		0			0
$793$	28.0454	+	48.5761i	0.995922	+	1.72499i
$794$	9.30306			0.330153
$795$		0			0
$796$	−6.89898			−0.244528
$797$	−17.9722	+	31.1288i	−0.636608	+	1.10264i	0.349564	+	0.936912i	$0.386330\pi$
$797$	−17.9722	+	31.1288i	−0.636608	+	1.10264i	−0.986172	+	0.165725i	$0.947004\pi$
$798$		0			0
$799$	9.79796	+	16.9706i	0.346627	+	0.600375i
$800$	3.44949	+	5.97469i	0.121958	+	0.211237i
$801$		0			0
$802$	5.05051	−	8.74774i	0.178340	−	0.308893i
$803$	−2.89898	+	5.02118i	−0.102303	+	0.177194i
$804$		0			0
$805$		0			0
$806$	−14.6969	+	25.4558i	−0.517678	+	0.896644i
$807$		0			0
$808$	−7.24745			−0.254964
$809$	−17.8990	+	31.0019i	−0.629295	+	1.08997i	0.358399	+	0.933569i	$0.383323\pi$
$809$	−17.8990	+	31.0019i	−0.629295	+	1.08997i	−0.987694	+	0.156402i	$0.950011\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$	−15.5959			−0.546637
$815$	0.348469	+	0.603566i	0.0122063	+	0.0211420i
$816$		0			0
$817$	−10.7980	+	18.7026i	−0.377773	+	0.654322i
$818$	5.79796			0.202721
$819$		0			0
$820$	−33.7980			−1.18028
$821$	19.7980	−	34.2911i	0.690954	−	1.19677i	−0.280572	−	0.959833i	$-0.590524\pi$
$821$	19.7980	−	34.2911i	0.690954	−	1.19677i	0.971526	−	0.236934i	$-0.0761424\pi$
$822$		0			0
$823$	−22.6969	−	39.3123i	−0.791166	−	1.37034i	−0.925246	−	0.379368i	$-0.876141\pi$
$823$	−22.6969	−	39.3123i	−0.791166	−	1.37034i	0.134080	−	0.990970i	$-0.457192\pi$
$824$	14.0000			0.487713
$825$		0			0
$826$		0			0
$827$	−12.4949			−0.434490			−0.217245	−	0.976117i	$-0.569707\pi$
$827$	−12.4949			−0.434490			−0.217245	+	0.976117i	$0.569707\pi$
$828$		0			0
$829$	15.3485	−	26.5843i	0.533074	−	0.923312i	−0.466180	−	0.884690i	$-0.654370\pi$
$829$	15.3485	−	26.5843i	0.533074	−	0.923312i	0.999254	−	0.0386218i	$-0.0122967\pi$
$830$	−6.89898			−0.239467
$831$		0			0
$832$	−2.44949	+	4.24264i	−0.0849208	+	0.147087i
$833$		0			0
$834$		0			0
$835$	−32.2474	+	55.8542i	−1.11597	+	1.93291i
$836$	−7.44949	+	12.9029i	−0.257646	+	0.446256i
$837$		0			0
$838$	12.2753	+	21.2614i	0.424042	+	0.734462i
$839$	22.4495	+	38.8837i	0.775042	+	1.34241i	0.934771	+	0.355252i	$0.115605\pi$
$839$	22.4495	+	38.8837i	0.775042	+	1.34241i	−0.159728	+	0.987161i	$0.551062\pi$
$840$		0			0
$841$	10.2980	−	17.8366i	0.355102	−	0.615055i
$842$	−13.1010			−0.451491
$843$		0			0
$844$	3.10102			0.106742
$845$	−18.9722	−	32.8608i	−0.652663	−	1.13045i
$846$		0			0
$847$		0			0
$848$	−0.550510	−	0.953512i	−0.0189046	−	0.0327437i
$849$		0			0
$850$	6.89898	+	11.9494i	0.236633	+	0.409860i
$851$	3.89898	+	6.75323i	0.133655	+	0.231498i
$852$		0			0
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	−0.979289	−	0.202467i	$-0.935104\pi$
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	0.314303	−	0.949323i	$-0.398229\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	−25.1010			−0.857435			−0.428717	−	0.903439i	$-0.641034\pi$
$857$	−25.1010			−0.857435			−0.428717	+	0.903439i	$0.641034\pi$
$858$		0			0
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	3.79796	+	6.57826i	0.129359	+	0.224056i
$863$	1.05051	+	1.81954i	0.0357598	+	0.0619378i	0.883351	−	0.468711i	$-0.155282\pi$
$863$	1.05051	+	1.81954i	0.0357598	+	0.0619378i	−0.847592	+	0.530649i	$0.821948\pi$
$864$		0			0
$865$	22.2474	−	38.5337i	0.756436	−	1.31019i
$866$	−5.89898	+	10.2173i	−0.200455	+	0.347199i
$867$		0			0
$868$		0			0
$869$	7.89898	−	13.6814i	0.267955	−	0.464111i
$870$		0			0
$871$	−15.1918			−0.514756
$872$	−8.34847	+	14.4600i	−0.282715	+	0.489676i
$873$		0			0
$874$	7.44949			0.251983
$875$		0			0
$876$		0			0
$877$	−26.4949			−0.894669			−0.447335	−	0.894367i	$-0.647627\pi$
$877$	−26.4949			−0.894669			−0.447335	+	0.894367i	$0.647627\pi$
$878$	−10.8990	−	18.8776i	−0.367823	−	0.637088i
$879$		0			0
$880$	3.44949	−	5.97469i	0.116282	−	0.201407i
$881$	−19.5959			−0.660203			−0.330102	−	0.943945i	$-0.607083\pi$
$881$	−19.5959			−0.660203			−0.330102	+	0.943945i	$0.607083\pi$
$882$		0			0
$883$	−0.202041			−0.00679922			−0.00339961	−	0.999994i	$-0.501082\pi$
$883$	−0.202041			−0.00679922			−0.00339961	+	0.999994i	$0.501082\pi$
$884$	−4.89898	+	8.48528i	−0.164771	+	0.285391i
$885$		0			0
$886$	2.55051	+	4.41761i	0.0856861	+	0.148413i
$887$	−33.7980			−1.13482			−0.567412	−	0.823434i	$-0.692055\pi$
$887$	−33.7980			−1.13482			−0.567412	+	0.823434i	$0.692055\pi$
$888$		0			0
$889$		0			0
$890$	24.4949			0.821071
$891$		0			0
$892$	−10.4495	+	18.0990i	−0.349875	+	0.606001i
$893$	72.9898			2.44251
$894$		0			0
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$		0			0
$898$	9.29796	−	16.1045i	0.310277	−	0.537415i
$899$	−8.69694	+	15.0635i	−0.290059	+	0.502397i
$900$		0			0
$901$	−1.10102	−	1.90702i	−0.0366803	−	0.0635322i
$902$	9.79796	+	16.9706i	0.326236	+	0.565058i
$903$		0			0
$904$	7.94949	−	13.7689i	0.264396	−	0.457947i
$905$	−15.0000			−0.498617
$906$		0			0
$907$	−26.6969			−0.886457			−0.443229	−	0.896409i	$-0.646167\pi$
$907$	−26.6969			−0.886457			−0.443229	+	0.896409i	$0.646167\pi$
$908$	0.275255	+	0.476756i	0.00913466	+	0.0158217i
$909$		0			0
$910$		0			0
$911$	−22.9949	−	39.8283i	−0.761855	−	1.31957i	−0.941893	−	0.335912i	$-0.890956\pi$
$911$	−22.9949	−	39.8283i	−0.761855	−	1.31957i	0.180038	−	0.983660i	$-0.442378\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	15.7474	+	27.2754i	0.520879	+	0.902189i
$915$		0			0
$916$	−11.6237	−	20.1329i	−0.384059	−	0.665209i
$917$		0			0
$918$		0			0
$919$	−1.84847	−	3.20164i	−0.0609754	−	0.105612i	0.833926	−	0.551876i	$-0.186088\pi$
$919$	−1.84847	−	3.20164i	−0.0609754	−	0.105612i	−0.894902	+	0.446263i	$0.852754\pi$
$920$	−3.44949			−0.113726
$921$		0			0
$922$	−20.3485			−0.670141
$923$	24.2474	−	41.9978i	0.798114	−	1.38237i
$924$		0			0
$925$	26.8990	+	46.5904i	0.884433	+	1.53188i
$926$	−12.8485	−	22.2542i	−0.422227	−	0.731318i
$927$		0			0
$928$	−1.44949	+	2.51059i	−0.0475818	+	0.0824142i
$929$	17.1464	−	29.6985i	0.562556	−	0.974376i	−0.434716	−	0.900567i	$-0.643151\pi$
$929$	17.1464	−	29.6985i	0.562556	−	0.974376i	0.997272	−	0.0738083i	$-0.0235153\pi$
$930$		0			0
$931$		0			0
$932$	−3.50000	+	6.06218i	−0.114646	+	0.198573i
$933$		0			0
$934$	−10.0000			−0.327210
$935$	6.89898	−	11.9494i	0.225621	−	0.390787i
$936$		0			0
$937$	−6.40408			−0.209212			−0.104606	−	0.994514i	$-0.533358\pi$
$937$	−6.40408			−0.209212			−0.104606	+	0.994514i	$0.533358\pi$
$938$		0			0
$939$		0			0
$940$	−33.7980			−1.10237
$941$	−1.72474	−	2.98735i	−0.0562251	−	0.0973847i	0.836543	−	0.547901i	$-0.184573\pi$
$941$	−1.72474	−	2.98735i	−0.0562251	−	0.0973847i	−0.892768	+	0.450517i	$0.851240\pi$
$942$		0			0
$943$	4.89898	−	8.48528i	0.159533	−	0.276319i
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	−5.79796			−0.188508
$947$	1.75255	−	3.03551i	0.0569503	−	0.0986408i	−0.836145	−	0.548509i	$-0.815196\pi$
$947$	1.75255	−	3.03551i	0.0569503	−	0.0986408i	0.893095	+	0.449868i	$0.148529\pi$
$948$		0			0
$949$	7.10102	+	12.2993i	0.230509	+	0.399253i
$950$	51.3939			1.66744
$951$		0			0
$952$		0			0
$953$	−55.3939			−1.79438			−0.897192	−	0.441641i	$-0.854396\pi$
$953$	−55.3939			−1.79438			−0.897192	+	0.441641i	$0.854396\pi$
$954$		0			0
$955$	23.9722	−	41.5211i	0.775722	−	1.34359i
$956$	12.7980			0.413916
$957$		0			0
$958$	−14.7980	+	25.6308i	−0.478100	+	0.828094i
$959$		0			0
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	−19.1010	+	33.0839i	−0.615842	+	1.06667i
$963$		0			0
$964$	−4.44949	−	7.70674i	−0.143308	−	0.248217i
$965$	13.9722	+	24.2005i	0.449781	+	0.779043i
$966$		0			0
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	−0.724495	−	0.689280i	$-0.757927\pi$
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	0.959182	+	0.282791i	$0.0912603\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	−23.7980			−0.764106
$971$	26.9722	+	46.7172i	0.865579	+	1.49923i	0.866471	+	0.499227i	$0.166383\pi$
$971$	26.9722	+	46.7172i	0.865579	+	1.49923i	−0.000892350		1.00000i	$0.500284\pi$
$972$		0			0
$973$		0			0
$974$	11.1969	+	19.3937i	0.358773	+	0.621413i
$975$		0			0
$976$	5.72474	+	9.91555i	0.183245	+	0.317389i
$977$	0.797959	+	1.38211i	0.0255290	+	0.0442175i	0.878508	−	0.477728i	$-0.158540\pi$
$977$	0.797959	+	1.38211i	0.0255290	+	0.0442175i	−0.852979	+	0.521946i	$0.825206\pi$
$978$		0			0
$979$	−7.10102	−	12.2993i	−0.226950	−	0.393088i
$980$		0			0
$981$		0			0
$982$	1.89898	+	3.28913i	0.0605989	+	0.104960i
$983$	45.1918			1.44140			0.720698	−	0.693249i	$-0.243822\pi$
$983$	45.1918			1.44140			0.720698	+	0.693249i	$0.243822\pi$
$984$		0			0
$985$	43.7980			1.39552
$986$	−2.89898	+	5.02118i	−0.0923223	+	0.159907i
$987$		0			0
$988$	18.2474	+	31.6055i	0.580529	+	1.00551i
$989$	1.44949	+	2.51059i	0.0460911	+	0.0798321i
$990$		0			0
$991$	−8.89898	+	15.4135i	−0.282685	+	0.489625i	−0.972045	−	0.234794i	$-0.924559\pi$
$991$	−8.89898	+	15.4135i	−0.282685	+	0.489625i	0.689360	+	0.724419i	$0.257892\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		0			0
$994$		0			0
$995$	11.8990	−	20.6096i	0.377223	−	0.653369i
$996$		0			0
$997$	−17.8536			−0.565428			−0.282714	−	0.959204i	$-0.591235\pi$
$997$	−17.8536			−0.565428			−0.282714	+	0.959204i	$0.591235\pi$
$998$	16.6969	−	28.9199i	0.528532	−	0.915445i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.h.n.361.2		4
3.2	odd	2		882.2.h.l.67.2		4
7.2	even	3		2646.2.e.k.1549.1		4
7.3	odd	6		378.2.f.d.253.2		4
7.4	even	3		2646.2.f.k.1765.1		4
7.5	odd	6		2646.2.e.l.1549.2		4
7.6	odd	2		2646.2.h.m.361.1		4
9.2	odd	6		882.2.e.n.655.1		4
9.7	even	3		2646.2.e.k.2125.1		4
21.2	odd	6		882.2.e.n.373.1		4
21.5	even	6		882.2.e.m.373.2		4
21.11	odd	6		882.2.f.j.589.1		4
21.17	even	6		126.2.f.c.85.2	yes	4
21.20	even	2		882.2.h.k.67.1		4
28.3	even	6		3024.2.r.e.1009.2		4
63.2	odd	6		882.2.h.l.79.2		4
63.4	even	3		7938.2.a.bm.1.2		2
63.11	odd	6		882.2.f.j.295.2		4
63.16	even	3	inner	2646.2.h.n.667.2		4
63.20	even	6		882.2.e.m.655.2		4
63.25	even	3		2646.2.f.k.883.1		4
63.31	odd	6		1134.2.a.i.1.1		2
63.32	odd	6		7938.2.a.bn.1.1		2
63.34	odd	6		2646.2.e.l.2125.2		4
63.38	even	6		126.2.f.c.43.1	✓	4
63.47	even	6		882.2.h.k.79.1		4
63.52	odd	6		378.2.f.d.127.2		4
63.59	even	6		1134.2.a.p.1.2		2
63.61	odd	6		2646.2.h.m.667.1		4
84.59	odd	6		1008.2.r.e.337.1		4
252.31	even	6		9072.2.a.bd.1.1		2
252.59	odd	6		9072.2.a.bk.1.2		2
252.115	even	6		3024.2.r.e.2017.2		4
252.227	odd	6		1008.2.r.e.673.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.1	✓	4	63.38	even	6
126.2.f.c.85.2	yes	4	21.17	even	6
378.2.f.d.127.2		4	63.52	odd	6
378.2.f.d.253.2		4	7.3	odd	6
882.2.e.m.373.2		4	21.5	even	6
882.2.e.m.655.2		4	63.20	even	6
882.2.e.n.373.1		4	21.2	odd	6
882.2.e.n.655.1		4	9.2	odd	6
882.2.f.j.295.2		4	63.11	odd	6
882.2.f.j.589.1		4	21.11	odd	6
882.2.h.k.67.1		4	21.20	even	2
882.2.h.k.79.1		4	63.47	even	6
882.2.h.l.67.2		4	3.2	odd	2
882.2.h.l.79.2		4	63.2	odd	6
1008.2.r.e.337.1		4	84.59	odd	6
1008.2.r.e.673.2		4	252.227	odd	6
1134.2.a.i.1.1		2	63.31	odd	6
1134.2.a.p.1.2		2	63.59	even	6
2646.2.e.k.1549.1		4	7.2	even	3
2646.2.e.k.2125.1		4	9.7	even	3
2646.2.e.l.1549.2		4	7.5	odd	6
2646.2.e.l.2125.2		4	63.34	odd	6
2646.2.f.k.883.1		4	63.25	even	3
2646.2.f.k.1765.1		4	7.4	even	3
2646.2.h.m.361.1		4	7.6	odd	2
2646.2.h.m.667.1		4	63.61	odd	6
2646.2.h.n.361.2		4	1.1	even	1	trivial
2646.2.h.n.667.2		4	63.16	even	3	inner
3024.2.r.e.1009.2		4	28.3	even	6
3024.2.r.e.2017.2		4	252.115	even	6
7938.2.a.bm.1.2		2	63.4	even	3
7938.2.a.bn.1.1		2	63.32	odd	6
9072.2.a.bd.1.1		2	252.31	even	6
9072.2.a.bk.1.2		2	252.59	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:	\( N \)	\(=\)	\( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2646.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.44949 q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +3.44949 q^{5} -1.00000 q^{8} +(1.72474 - 2.98735i) q^{10} -2.00000 q^{11} +(-2.44949 + 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +(-1.00000 + 1.73205i) q^{17} +(3.72474 + 6.45145i) q^{19} +(-1.72474 - 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +1.00000 q^{23} +6.89898 q^{25} +(2.44949 + 4.24264i) q^{26} +(1.44949 + 2.51059i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 + 1.73205i) q^{34} +(3.89898 + 6.75323i) q^{37} +7.44949 q^{38} -3.44949 q^{40} +(4.89898 - 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(1.00000 + 1.73205i) q^{44} +(0.500000 - 0.866025i) q^{46} +(4.89898 - 8.48528i) q^{47} +(3.44949 - 5.97469i) q^{50} +4.89898 q^{52} +(-0.550510 + 0.953512i) q^{53} -6.89898 q^{55} +2.89898 q^{58} +(1.00000 + 1.73205i) q^{59} +(5.72474 - 9.91555i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-8.44949 + 14.6349i) q^{65} +(1.55051 + 2.68556i) q^{67} +2.00000 q^{68} -9.89898 q^{71} +(1.44949 - 2.51059i) q^{73} +7.79796 q^{74} +(3.72474 - 6.45145i) q^{76} +(-3.94949 + 6.84072i) q^{79} +(-1.72474 + 2.98735i) q^{80} +(-4.89898 - 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +2.89898 q^{86} +2.00000 q^{88} +(3.55051 + 6.14966i) q^{89} +(-0.500000 - 0.866025i) q^{92} +(-4.89898 - 8.48528i) q^{94} +(12.8485 + 22.2542i) q^{95} +(-3.44949 - 5.97469i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} + 4 q^{5} - 4 q^{8} + 2 q^{10} - 8 q^{11} - 2 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} + 4 q^{23} + 8 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} - 4 q^{37} + 20 q^{38} - 4 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} - 8 q^{55} - 8 q^{58} + 4 q^{59} + 18 q^{61} + 24 q^{62} + 4 q^{64} - 24 q^{65} + 16 q^{67} + 8 q^{68} - 20 q^{71} - 4 q^{73} - 8 q^{74} + 10 q^{76} - 6 q^{79} - 2 q^{80} - 4 q^{83} - 4 q^{85} - 8 q^{86} + 8 q^{88} + 24 q^{89} - 2 q^{92} + 22 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 + 4 * q^5 - 4 * q^8 + 2 * q^10 - 8 * q^11 - 2 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 + 4 * q^23 + 8 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 - 4 * q^37 + 20 * q^38 - 4 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 - 8 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 + 8 * q^68 - 20 * q^71 - 4 * q^73 - 8 * q^74 + 10 * q^76 - 6 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 - 8 * q^86 + 8 * q^88 + 24 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

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