LMFDB - Embedded newform 2646.2.e.p.1549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(1549,2646)]

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, 2]))

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.309123.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 $ x^6 - 3x^5 + 10x^4 - 15x^3 + 19x^2 - 12*x + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1549.2
Root			$0.500000 + 2.05195i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.p.2125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(-0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +(-0.296790 - 0.514055i) q^{10} +(-0.296790 + 0.514055i) q^{11} +(1.25729 - 2.17770i) q^{13} +1.00000 q^{16} +(1.46050 + 2.52967i) q^{17} +(-2.69076 + 4.66053i) q^{19} +(-0.296790 - 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(2.23025 + 3.86291i) q^{23} +(2.32383 - 4.02499i) q^{25} +(1.25729 - 2.17770i) q^{26} +(3.09718 + 5.36447i) q^{29} +7.86693 q^{31} +1.00000 q^{32} +(1.46050 + 2.52967i) q^{34} +(0.500000 - 0.866025i) q^{37} +(-2.69076 + 4.66053i) q^{38} +(-0.296790 - 0.514055i) q^{40} +(-0.136673 + 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(-0.296790 + 0.514055i) q^{44} +(2.23025 + 3.86291i) q^{46} +12.1623 q^{47} +(2.32383 - 4.02499i) q^{50} +(1.25729 - 2.17770i) q^{52} +(-4.02704 - 6.97504i) q^{53} +0.352336 q^{55} +(3.09718 + 5.36447i) q^{58} +8.64766 q^{59} +6.64766 q^{61} +7.86693 q^{62} +1.00000 q^{64} -1.49261 q^{65} -1.91381 q^{67} +(1.46050 + 2.52967i) q^{68} +14.4107 q^{71} +(-3.95691 - 6.85356i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-2.69076 + 4.66053i) q^{76} -9.24844 q^{79} +(-0.296790 - 0.514055i) q^{80} +(-0.136673 + 0.236725i) q^{82} +(3.85087 + 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-5.58113 - 9.66679i) q^{86} +(-0.296790 + 0.514055i) q^{88} +(-6.21780 + 10.7695i) q^{89} +(2.23025 + 3.86291i) q^{92} +12.1623 q^{94} +3.19436 q^{95} +(-5.86693 - 10.1618i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	$ 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−0.296790	−	0.514055i	−0.132728	−	0.229892i	0.791999	−	0.610522i	$-0.209040\pi$
$5$	−0.296790	−	0.514055i	−0.132728	−	0.229892i	−0.924727	+	0.380630i	$0.875707\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.296790	−	0.514055i	−0.0938531	−	0.162558i
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	−0.907294	−	0.420497i	$-0.861856\pi$
$11$	−0.296790	+	0.514055i	−0.0894855	+	0.154993i	0.817808	+	0.575491i	$0.195189\pi$
$12$		0			0
$13$	1.25729	−	2.17770i	0.348711	−	0.603985i	−0.637310	−	0.770608i	$-0.719953\pi$
$13$	1.25729	−	2.17770i	0.348711	−	0.603985i	0.986021	+	0.166623i	$0.0532862\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	1.46050	+	2.52967i	0.354224	+	0.613535i	0.986985	−	0.160813i	$-0.0514116\pi$
$17$	1.46050	+	2.52967i	0.354224	+	0.613535i	−0.632760	+	0.774348i	$0.718078\pi$
$18$		0			0
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	0.372674	+	0.927962i	$0.378441\pi$
$19$	−2.69076	+	4.66053i	−0.617302	+	1.06920i	−0.989976	+	0.141236i	$0.954892\pi$
$20$	−0.296790	−	0.514055i	−0.0663642	−	0.114946i
$21$		0			0
$22$	−0.296790	+	0.514055i	−0.0632758	+	0.109597i
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	0.999203	−	0.0399086i	$-0.0127067\pi$
$23$	2.23025	+	3.86291i	0.465040	+	0.805473i	−0.534164	+	0.845381i	$0.679373\pi$
$24$		0			0
$25$	2.32383	−	4.02499i	0.464766	−	0.804999i
$26$	1.25729	−	2.17770i	0.246576	−	0.427082i
$27$		0			0
$28$		0			0
$29$	3.09718	+	5.36447i	0.575132	+	0.996157i	0.996027	+	0.0890480i	$0.0283825\pi$
$29$	3.09718	+	5.36447i	0.575132	+	0.996157i	−0.420896	+	0.907109i	$0.638284\pi$
$30$		0			0
$31$	7.86693			1.41294			0.706471	−	0.707742i	$-0.250286\pi$
$31$	7.86693			1.41294			0.706471	+	0.707742i	$0.250286\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	1.46050	+	2.52967i	0.250475	+	0.433835i
$35$		0			0
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	−2.69076	+	4.66053i	−0.436498	+	0.756038i
$39$		0			0
$40$	−0.296790	−	0.514055i	−0.0469266	−	0.0812792i
$41$	−0.136673	+	0.236725i	−0.0213448	+	0.0369702i	−0.876500	−	0.481401i	$-0.840128\pi$
$41$	−0.136673	+	0.236725i	−0.0213448	+	0.0369702i	0.855156	+	0.518371i	$0.173461\pi$
$42$		0			0
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	−0.880204	−	0.474596i	$-0.842594\pi$
$43$	−5.58113	−	9.66679i	−0.851114	−	1.47417i	0.0290902	−	0.999577i	$-0.490739\pi$
$44$	−0.296790	+	0.514055i	−0.0447427	+	0.0774967i
$45$		0			0
$46$	2.23025	+	3.86291i	0.328833	+	0.569555i
$47$	12.1623			1.77405			0.887023	−	0.461724i	$-0.152769\pi$
$47$	12.1623			1.77405			0.887023	+	0.461724i	$0.152769\pi$
$48$		0			0
$49$		0			0
$50$	2.32383	−	4.02499i	0.328639	−	0.569220i
$51$		0			0
$52$	1.25729	−	2.17770i	0.174355	−	0.301992i
$53$	−4.02704	−	6.97504i	−0.553157	−	0.958096i	−0.998044	−	0.0625092i	$-0.980090\pi$
$53$	−4.02704	−	6.97504i	−0.553157	−	0.958096i	0.444888	−	0.895586i	$-0.353244\pi$
$54$		0			0
$55$	0.352336			0.0475090
$56$		0			0
$57$		0			0
$58$	3.09718	+	5.36447i	0.406679	+	0.704389i
$59$	8.64766			1.12583			0.562915	−	0.826515i	$-0.309680\pi$
$59$	8.64766			1.12583			0.562915	+	0.826515i	$0.309680\pi$
$60$		0			0
$61$	6.64766			0.851146			0.425573	−	0.904924i	$-0.360073\pi$
$61$	6.64766			0.851146			0.425573	+	0.904924i	$0.360073\pi$
$62$	7.86693			0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.49261			−0.185135
$66$		0			0
$67$	−1.91381			−0.233809			−0.116905	−	0.993143i	$-0.537297\pi$
$67$	−1.91381			−0.233809			−0.116905	+	0.993143i	$0.537297\pi$
$68$	1.46050	+	2.52967i	0.177112	+	0.306767i
$69$		0			0
$70$		0			0
$71$	14.4107			1.71023			0.855117	−	0.518435i	$-0.173485\pi$
$71$	14.4107			1.71023			0.855117	+	0.518435i	$0.173485\pi$
$72$		0			0
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	0.535994	−	0.844222i	$-0.319937\pi$
$73$	−3.95691	−	6.85356i	−0.463121	−	0.802149i	−0.999115	+	0.0420732i	$0.986604\pi$
$74$	0.500000	−	0.866025i	0.0581238	−	0.100673i
$75$		0			0
$76$	−2.69076	+	4.66053i	−0.308651	+	0.534599i
$77$		0			0
$78$		0			0
$79$	−9.24844			−1.04053			−0.520265	−	0.854005i	$-0.674167\pi$
$79$	−9.24844			−1.04053			−0.520265	+	0.854005i	$0.674167\pi$
$80$	−0.296790	−	0.514055i	−0.0331821	−	0.0574731i
$81$		0			0
$82$	−0.136673	+	0.236725i	−0.0150930	+	0.0261419i
$83$	3.85087	+	6.66991i	0.422688	+	0.732118i	0.996201	−	0.0870787i	$-0.0277532\pi$
$83$	3.85087	+	6.66991i	0.422688	+	0.732118i	−0.573513	+	0.819196i	$0.694420\pi$
$84$		0			0
$85$	0.866926	−	1.50156i	0.0940313	−	0.162867i
$86$	−5.58113	−	9.66679i	−0.601828	−	1.04240i
$87$		0			0
$88$	−0.296790	+	0.514055i	−0.0316379	+	0.0547984i
$89$	−6.21780	+	10.7695i	−0.659085	+	1.14157i	0.321767	+	0.946819i	$0.395723\pi$
$89$	−6.21780	+	10.7695i	−0.659085	+	1.14157i	−0.980853	+	0.194751i	$0.937610\pi$
$90$		0			0
$91$		0			0
$92$	2.23025	+	3.86291i	0.232520	+	0.402736i
$93$		0			0
$94$	12.1623			1.25444
$95$	3.19436			0.327734
$96$		0			0
$97$	−5.86693	−	10.1618i	−0.595696	−	1.03178i	−0.993448	−	0.114283i	$-0.963543\pi$
$97$	−5.86693	−	10.1618i	−0.595696	−	1.03178i	0.397752	−	0.917493i	$-0.369790\pi$
$98$		0			0
$99$		0			0
$100$	2.32383	−	4.02499i	0.232383	−	0.402499i
$101$	0.811379	−	1.40535i	0.0807352	−	0.139837i	−0.822831	−	0.568287i	$-0.807607\pi$
$101$	0.811379	−	1.40535i	0.0807352	−	0.139837i	0.903566	+	0.428449i	$0.140940\pi$
$102$		0			0
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	0.979309	−	0.202372i	$-0.0648651\pi$
$103$	3.19076	+	5.52655i	0.314395	+	0.544548i	−0.664914	+	0.746920i	$0.731532\pi$
$104$	1.25729	−	2.17770i	0.123288	−	0.213541i
$105$		0			0
$106$	−4.02704	−	6.97504i	−0.391141	−	0.677476i
$107$	−9.35447	+	16.2024i	−0.904331	+	1.56635i	−0.0825182	+	0.996590i	$0.526296\pi$
$107$	−9.35447	+	16.2024i	−0.904331	+	1.56635i	−0.821813	+	0.569758i	$0.807037\pi$
$108$		0			0
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	0.789173	−	0.614171i	$-0.210509\pi$
$109$	−1.43346	−	2.48283i	−0.137301	−	0.237812i	−0.926474	+	0.376359i	$0.877176\pi$
$110$	0.352336			0.0335940
$111$		0			0
$112$		0			0
$113$	6.16012	−	10.6696i	0.579495	−	1.00371i	−0.416042	−	0.909345i	$-0.636583\pi$
$113$	6.16012	−	10.6696i	0.579495	−	1.00371i	0.995537	−	0.0943695i	$-0.0300835\pi$
$114$		0			0
$115$	1.32383	−	2.29294i	0.123448	−	0.213818i
$116$	3.09718	+	5.36447i	0.287566	+	0.498078i
$117$		0			0
$118$	8.64766			0.796082
$119$		0			0
$120$		0			0
$121$	5.32383	+	9.22115i	0.483985	+	0.838286i
$122$	6.64766			0.601851
$123$		0			0
$124$	7.86693			0.706471
$125$	−5.72665			−0.512207
$126$		0			0
$127$	12.3346			1.09452			0.547261	−	0.836962i	$-0.315671\pi$
$127$	12.3346			1.09452			0.547261	+	0.836962i	$0.315671\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−1.49261			−0.130910
$131$	0.593579	+	1.02811i	0.0518613	+	0.0898264i	0.890791	−	0.454414i	$-0.150151\pi$
$131$	0.593579	+	1.02811i	0.0518613	+	0.0898264i	−0.838929	+	0.544240i	$0.816818\pi$
$132$		0			0
$133$		0			0
$134$	−1.91381			−0.165328
$135$		0			0
$136$	1.46050	+	2.52967i	0.125237	+	0.216917i
$137$	1.26089	−	2.18393i	0.107725	−	0.186586i	−0.807123	−	0.590383i	$-0.798977\pi$
$137$	1.26089	−	2.18393i	0.107725	−	0.186586i	0.914848	+	0.403797i	$0.132310\pi$
$138$		0			0
$139$	−2.45691	+	4.25549i	−0.208392	+	0.360946i	−0.951208	−	0.308550i	$-0.900156\pi$
$139$	−2.45691	+	4.25549i	−0.208392	+	0.360946i	0.742816	+	0.669496i	$0.233490\pi$
$140$		0			0
$141$		0			0
$142$	14.4107			1.20932
$143$	0.746304	+	1.29264i	0.0624091	+	0.108096i
$144$		0			0
$145$	1.83842	−	3.18424i	0.152673	−	0.264437i
$146$	−3.95691	−	6.85356i	−0.327476	−	0.567205i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	9.02558	+	15.6328i	0.739404	+	1.28069i	0.952764	+	0.303712i	$0.0982261\pi$
$149$	9.02558	+	15.6328i	0.739404	+	1.28069i	−0.213360	+	0.976974i	$0.568441\pi$
$150$		0			0
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	−0.897598	−	0.440815i	$-0.854690\pi$
$151$	−0.823832	+	1.42692i	−0.0670425	+	0.116121i	0.830556	+	0.556936i	$0.188023\pi$
$152$	−2.69076	+	4.66053i	−0.218249	+	0.378019i
$153$		0			0
$154$		0			0
$155$	−2.33482	−	4.04403i	−0.187537	−	0.324824i
$156$		0			0
$157$	6.60078			0.526799			0.263400	−	0.964687i	$-0.415156\pi$
$157$	6.60078			0.526799			0.263400	+	0.964687i	$0.415156\pi$
$158$	−9.24844			−0.735766
$159$		0			0
$160$	−0.296790	−	0.514055i	−0.0234633	−	0.0406396i
$161$		0			0
$162$		0			0
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	−0.959065	−	0.283188i	$-0.908608\pi$
$163$	−2.99115	+	5.18082i	−0.234285	+	0.405793i	0.724780	+	0.688980i	$0.241941\pi$
$164$	−0.136673	+	0.236725i	−0.0106724	+	0.0184851i
$165$		0			0
$166$	3.85087	+	6.66991i	0.298886	+	0.517685i
$167$	3.73025	−	6.46099i	0.288656	−	0.499966i	−0.684833	−	0.728700i	$-0.740125\pi$
$167$	3.73025	−	6.46099i	0.288656	−	0.499966i	0.973489	+	0.228733i	$0.0734584\pi$
$168$		0			0
$169$	3.33842	+	5.78231i	0.256802	+	0.444793i
$170$	0.866926	−	1.50156i	0.0664902	−	0.115164i
$171$		0			0
$172$	−5.58113	−	9.66679i	−0.425557	−	0.737086i
$173$	−25.6591			−1.95083			−0.975414	−	0.220381i	$-0.929270\pi$
$173$	−25.6591			−1.95083			−0.975414	+	0.220381i	$0.929270\pi$
$174$		0			0
$175$		0			0
$176$	−0.296790	+	0.514055i	−0.0223714	+	0.0387483i
$177$		0			0
$178$	−6.21780	+	10.7695i	−0.466044	+	0.807211i
$179$	−7.51819	−	13.0219i	−0.561936	−	0.973301i	−0.997328	−	0.0730602i	$-0.976723\pi$
$179$	−7.51819	−	13.0219i	−0.561936	−	0.973301i	0.435392	−	0.900241i	$-0.356610\pi$
$180$		0			0
$181$	0.0861875			0.00640627			0.00320313	−	0.999995i	$-0.498980\pi$
$181$	0.0861875			0.00640627			0.00320313	+	0.999995i	$0.498980\pi$
$182$		0			0
$183$		0			0
$184$	2.23025	+	3.86291i	0.164416	+	0.284778i
$185$	−0.593579			−0.0436408
$186$		0			0
$187$	−1.73385			−0.126792
$188$	12.1623			0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	−3.98229			−0.288148			−0.144074	−	0.989567i	$-0.546020\pi$
$191$	−3.98229			−0.288148			−0.144074	+	0.989567i	$0.546020\pi$
$192$		0			0
$193$	6.78074			0.488088			0.244044	−	0.969764i	$-0.421526\pi$
$193$	6.78074			0.488088			0.244044	+	0.969764i	$0.421526\pi$
$194$	−5.86693	−	10.1618i	−0.421221	−	0.729576i
$195$		0			0
$196$		0			0
$197$	−11.0584			−0.787875			−0.393938	−	0.919137i	$-0.628887\pi$
$197$	−11.0584			−0.787875			−0.393938	+	0.919137i	$0.628887\pi$
$198$		0			0
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	0.749109	−	0.662447i	$-0.230482\pi$
$199$	−2.80924	−	4.86575i	−0.199142	−	0.344924i	−0.948250	+	0.317523i	$0.897149\pi$
$200$	2.32383	−	4.02499i	0.164320	−	0.284610i
$201$		0			0
$202$	0.811379	−	1.40535i	0.0570884	−	0.0988800i
$203$		0			0
$204$		0			0
$205$	0.162253			0.0113322
$206$	3.19076	+	5.52655i	0.222311	+	0.385053i
$207$		0			0
$208$	1.25729	−	2.17770i	0.0871777	−	0.150996i
$209$	−1.59718	−	2.76639i	−0.110479	−	0.191355i
$210$		0			0
$211$	9.66225	−	16.7355i	0.665177	−	1.15212i	−0.314060	−	0.949403i	$-0.601689\pi$
$211$	9.66225	−	16.7355i	0.665177	−	1.15212i	0.979237	−	0.202717i	$-0.0649772\pi$
$212$	−4.02704	−	6.97504i	−0.276578	−	0.479048i
$213$		0			0
$214$	−9.35447	+	16.2024i	−0.639459	+	1.10757i
$215$	−3.31284	+	5.73801i	−0.225934	+	0.391329i
$216$		0			0
$217$		0			0
$218$	−1.43346	−	2.48283i	−0.0970863	−	0.168158i
$219$		0			0
$220$	0.352336			0.0237545
$221$	7.34514			0.494088
$222$		0			0
$223$	−12.6623	−	21.9317i	−0.847927	−	1.46865i	−0.883055	−	0.469270i	$-0.844517\pi$
$223$	−12.6623	−	21.9317i	−0.847927	−	1.46865i	0.0351275	−	0.999383i	$-0.488816\pi$
$224$		0			0
$225$		0			0
$226$	6.16012	−	10.6696i	0.409765	−	0.709734i
$227$	−2.40856	+	4.17174i	−0.159862	+	0.276888i	−0.934819	−	0.355126i	$-0.884438\pi$
$227$	−2.40856	+	4.17174i	−0.159862	+	0.276888i	0.774957	+	0.632014i	$0.217771\pi$
$228$		0			0
$229$	−4.64766	−	8.04999i	−0.307126	−	0.531958i	0.670606	−	0.741814i	$-0.266034\pi$
$229$	−4.64766	−	8.04999i	−0.307126	−	0.531958i	−0.977732	+	0.209855i	$0.932701\pi$
$230$	1.32383	−	2.29294i	0.0872909	−	0.151192i
$231$		0			0
$232$	3.09718	+	5.36447i	0.203340	+	0.352195i
$233$	−0.0971780	+	0.168317i	−0.00636634	+	0.0110268i	−0.869191	−	0.494476i	$-0.835360\pi$
$233$	−0.0971780	+	0.168317i	−0.00636634	+	0.0110268i	0.862825	+	0.505503i	$0.168693\pi$
$234$		0			0
$235$	−3.60963	−	6.25206i	−0.235466	−	0.407840i
$236$	8.64766			0.562915
$237$		0			0
$238$		0			0
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	−0.556181	−	0.831061i	$-0.687734\pi$
$239$	6.82743	−	11.8255i	0.441630	−	0.764925i	0.997811	+	0.0661361i	$0.0210672\pi$
$240$		0			0
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	−0.995809	−	0.0914555i	$-0.970848\pi$
$241$	−6.50000	+	11.2583i	−0.418702	+	0.725213i	0.577107	+	0.816668i	$0.304181\pi$
$242$	5.32383	+	9.22115i	0.342229	+	0.592758i
$243$		0			0
$244$	6.64766			0.425573
$245$		0			0
$246$		0			0
$247$	6.76615	+	11.7193i	0.430520	+	0.745682i
$248$	7.86693			0.499550
$249$		0			0
$250$	−5.72665			−0.362185
$251$	−19.5438			−1.23359			−0.616796	−	0.787123i	$-0.711570\pi$
$251$	−19.5438			−1.23359			−0.616796	+	0.787123i	$0.711570\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$	12.3346			0.773943
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.16372	−	7.21177i	−0.259725	−	0.449858i	0.706443	−	0.707770i	$-0.250299\pi$
$257$	−4.16372	−	7.21177i	−0.259725	−	0.449858i	−0.966168	+	0.257912i	$0.916965\pi$
$258$		0			0
$259$		0			0
$260$	−1.49261			−0.0925676
$261$		0			0
$262$	0.593579	+	1.02811i	0.0366715	+	0.0635168i
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	0.472586	+	0.881284i	$0.343320\pi$
$263$	−8.54523	+	14.8008i	−0.526921	+	0.912655i	−0.999508	+	0.0313704i	$0.990013\pi$
$264$		0			0
$265$	−2.39037	+	4.14024i	−0.146839	+	0.254333i
$266$		0			0
$267$		0			0
$268$	−1.91381			−0.116905
$269$	−5.00720	−	8.67272i	−0.305294	−	0.528785i	0.672033	−	0.740522i	$-0.265421\pi$
$269$	−5.00720	−	8.67272i	−0.305294	−	0.528785i	−0.977327	+	0.211737i	$0.932088\pi$
$270$		0			0
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	−0.978380	−	0.206818i	$-0.933689\pi$
$271$	−5.10457	+	8.84137i	−0.310081	+	0.537075i	0.668299	+	0.743893i	$0.267023\pi$
$272$	1.46050	+	2.52967i	0.0885561	+	0.153384i
$273$		0			0
$274$	1.26089	−	2.18393i	0.0761733	−	0.131936i
$275$	1.37938	+	2.38915i	0.0831797	+	0.144071i
$276$		0			0
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	0.414271	+	0.910154i	$0.364037\pi$
$277$	−9.67111	+	16.7508i	−0.581081	+	1.00646i	−0.995352	+	0.0963074i	$0.969297\pi$
$278$	−2.45691	+	4.25549i	−0.147355	+	0.255227i
$279$		0			0
$280$		0			0
$281$	6.40136	+	11.0875i	0.381873	+	0.661424i	0.991330	−	0.131396i	$-0.0419458\pi$
$281$	6.40136	+	11.0875i	0.381873	+	0.661424i	−0.609457	+	0.792819i	$0.708612\pi$
$282$		0			0
$283$	16.3523			0.972046			0.486023	−	0.873946i	$-0.338447\pi$
$283$	16.3523			0.972046			0.486023	+	0.873946i	$0.338447\pi$
$284$	14.4107			0.855117
$285$		0			0
$286$	0.746304	+	1.29264i	0.0441299	+	0.0764352i
$287$		0			0
$288$		0			0
$289$	4.23385	−	7.33325i	0.249050	−	0.431367i
$290$	1.83842	−	3.18424i	0.107956	−	0.186985i
$291$		0			0
$292$	−3.95691	−	6.85356i	−0.231560	−	0.401074i
$293$	−10.3889	+	17.9941i	−0.606926	+	1.05123i	0.384817	+	0.922993i	$0.374264\pi$
$293$	−10.3889	+	17.9941i	−0.606926	+	1.05123i	−0.991744	+	0.128235i	$0.959069\pi$
$294$		0			0
$295$	−2.56654	−	4.44537i	−0.149430	−	0.258820i
$296$	0.500000	−	0.866025i	0.0290619	−	0.0503367i
$297$		0			0
$298$	9.02558	+	15.6328i	0.522838	+	0.905582i
$299$	11.2163			0.648658
$300$		0			0
$301$		0			0
$302$	−0.823832	+	1.42692i	−0.0474062	+	0.0821099i
$303$		0			0
$304$	−2.69076	+	4.66053i	−0.154326	+	0.267300i
$305$	−1.97296	−	3.41726i	−0.112971	−	0.195672i
$306$		0			0
$307$	22.6768			1.29424			0.647118	−	0.762390i	$-0.275974\pi$
$307$	22.6768			1.29424			0.647118	+	0.762390i	$0.275974\pi$
$308$		0			0
$309$		0			0
$310$	−2.33482	−	4.04403i	−0.132609	−	0.229686i
$311$	−6.51459			−0.369408			−0.184704	−	0.982794i	$-0.559133\pi$
$311$	−6.51459			−0.369408			−0.184704	+	0.982794i	$0.559133\pi$
$312$		0			0
$313$	−0.266149			−0.0150436			−0.00752181	−	0.999972i	$-0.502394\pi$
$313$	−0.266149			−0.0150436			−0.00752181	+	0.999972i	$0.502394\pi$
$314$	6.60078			0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	−15.7237			−0.883133			−0.441566	−	0.897229i	$-0.645577\pi$
$317$	−15.7237			−0.883133			−0.441566	+	0.897229i	$0.645577\pi$
$318$		0			0
$319$	−3.67684			−0.205864
$320$	−0.296790	−	0.514055i	−0.0165910	−	0.0287365i
$321$		0			0
$322$		0			0
$323$	−15.7195			−0.874654
$324$		0			0
$325$	−5.84348	−	10.1212i	−0.324138	−	0.561424i
$326$	−2.99115	+	5.18082i	−0.165664	+	0.286939i
$327$		0			0
$328$	−0.136673	+	0.236725i	−0.00754651	+	0.0130709i
$329$		0			0
$330$		0			0
$331$	−25.1623			−1.38304			−0.691521	−	0.722356i	$-0.743059\pi$
$331$	−25.1623			−1.38304			−0.691521	+	0.722356i	$0.743059\pi$
$332$	3.85087	+	6.66991i	0.211344	+	0.366059i
$333$		0			0
$334$	3.73025	−	6.46099i	0.204110	−	0.353529i
$335$	0.568000	+	0.983804i	0.0310331	+	0.0537510i
$336$		0			0
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	0.489681	+	0.871902i	$0.337113\pi$
$337$	−9.36693	+	16.2240i	−0.510249	+	0.883777i	−0.999929	+	0.0118752i	$0.996220\pi$
$338$	3.33842	+	5.78231i	0.181586	+	0.314516i
$339$		0			0
$340$	0.866926	−	1.50156i	0.0470156	−	0.0814335i
$341$	−2.33482	+	4.04403i	−0.126438	+	0.218997i
$342$		0			0
$343$		0			0
$344$	−5.58113	−	9.66679i	−0.300914	−	0.521199i
$345$		0			0
$346$	−25.6591			−1.37944
$347$	−22.5438			−1.21021			−0.605106	−	0.796145i	$-0.706869\pi$
$347$	−22.5438			−1.21021			−0.605106	+	0.796145i	$0.706869\pi$
$348$		0			0
$349$	−1.89543	−	3.28298i	−0.101460	−	0.175734i	0.810826	−	0.585287i	$-0.199018\pi$
$349$	−1.89543	−	3.28298i	−0.101460	−	0.175734i	−0.912286	+	0.409553i	$0.865685\pi$
$350$		0			0
$351$		0			0
$352$	−0.296790	+	0.514055i	−0.0158189	+	0.0273992i
$353$	−3.41741	+	5.91913i	−0.181890	+	0.315043i	−0.942524	−	0.334138i	$-0.891555\pi$
$353$	−3.41741	+	5.91913i	−0.181890	+	0.315043i	0.760634	+	0.649181i	$0.224888\pi$
$354$		0			0
$355$	−4.27694	−	7.40789i	−0.226997	−	0.393170i
$356$	−6.21780	+	10.7695i	−0.329543	+	0.570785i
$357$		0			0
$358$	−7.51819	−	13.0219i	−0.397349	−	0.688228i
$359$	6.32237	−	10.9507i	0.333682	−	0.577954i	−0.649549	−	0.760320i	$-0.725042\pi$
$359$	6.32237	−	10.9507i	0.333682	−	0.577954i	0.983231	+	0.182366i	$0.0583755\pi$
$360$		0			0
$361$	−4.98035	−	8.62622i	−0.262124	−	0.454012i
$362$	0.0861875			0.00452991
$363$		0			0
$364$		0			0
$365$	−2.34874	+	4.06813i	−0.122939	+	0.212936i
$366$		0			0
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	−0.767906	−	0.640563i	$-0.778701\pi$
$367$	3.27188	−	5.66707i	0.170791	−	0.295819i	0.938697	+	0.344744i	$0.112034\pi$
$368$	2.23025	+	3.86291i	0.116260	+	0.201368i
$369$		0			0
$370$	−0.593579			−0.0308587
$371$		0			0
$372$		0			0
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	0.717784	−	0.696266i	$-0.245157\pi$
$373$	−4.71420	−	8.16524i	−0.244092	−	0.422780i	−0.961876	+	0.273486i	$0.911823\pi$
$374$	−1.73385			−0.0896553
$375$		0			0
$376$	12.1623			0.627220
$377$	15.5763			0.802218
$378$		0			0
$379$	−7.27762			−0.373826			−0.186913	−	0.982376i	$-0.559848\pi$
$379$	−7.27762			−0.373826			−0.186913	+	0.982376i	$0.559848\pi$
$380$	3.19436			0.163867
$381$		0			0
$382$	−3.98229			−0.203752
$383$	12.0416	+	20.8567i	0.615299	+	1.06573i	0.990332	+	0.138717i	$0.0442979\pi$
$383$	12.0416	+	20.8567i	0.615299	+	1.06573i	−0.375033	+	0.927011i	$0.622369\pi$
$384$		0			0
$385$		0			0
$386$	6.78074			0.345130
$387$		0			0
$388$	−5.86693	−	10.1618i	−0.297848	−	0.515888i
$389$	−8.14913	+	14.1147i	−0.413177	+	0.715644i	−0.995235	−	0.0975035i	$-0.968914\pi$
$389$	−8.14913	+	14.1147i	−0.413177	+	0.715644i	0.582058	+	0.813147i	$0.302248\pi$
$390$		0			0
$391$	−6.51459	+	11.2836i	−0.329457	+	0.570636i
$392$		0			0
$393$		0			0
$394$	−11.0584			−0.557112
$395$	2.74484	+	4.75420i	0.138108	+	0.239210i
$396$		0			0
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	−0.671906	−	0.740636i	$-0.734524\pi$
$397$	6.08619	−	10.5416i	0.305457	−	0.529067i	0.977363	+	0.211569i	$0.0678574\pi$
$398$	−2.80924	−	4.86575i	−0.140815	−	0.243898i
$399$		0			0
$400$	2.32383	−	4.02499i	0.116192	−	0.201250i
$401$	−16.6804	−	28.8914i	−0.832981	−	1.44277i	−0.895663	−	0.444733i	$-0.853299\pi$
$401$	−16.6804	−	28.8914i	−0.832981	−	1.44277i	0.0626819	−	0.998034i	$-0.480035\pi$
$402$		0			0
$403$	9.89104	−	17.1318i	0.492708	−	0.853395i
$404$	0.811379	−	1.40535i	0.0403676	−	0.0699187i
$405$		0			0
$406$		0			0
$407$	0.296790	+	0.514055i	0.0147113	+	0.0254808i
$408$		0			0
$409$	5.78074			0.285839			0.142920	−	0.989734i	$-0.454351\pi$
$409$	5.78074			0.285839			0.142920	+	0.989734i	$0.454351\pi$
$410$	0.162253			0.00801309
$411$		0			0
$412$	3.19076	+	5.52655i	0.157197	+	0.272274i
$413$		0			0
$414$		0			0
$415$	2.28580	−	3.95912i	0.112205	−	0.194346i
$416$	1.25729	−	2.17770i	0.0616439	−	0.106770i
$417$		0			0
$418$	−1.59718	−	2.76639i	−0.0781205	−	0.135309i
$419$	15.4356	−	26.7352i	0.754078	−	1.30610i	−0.191753	−	0.981443i	$-0.561417\pi$
$419$	15.4356	−	26.7352i	0.754078	−	1.30610i	0.945831	−	0.324659i	$-0.105249\pi$
$420$		0			0
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	0.816939	−	0.576724i	$-0.195669\pi$
$421$	−1.86693	−	3.23361i	−0.0909884	−	0.157597i	−0.907927	+	0.419128i	$0.862336\pi$
$422$	9.66225	−	16.7355i	0.470351	−	0.814672i
$423$		0			0
$424$	−4.02704	−	6.97504i	−0.195570	−	0.338738i
$425$	13.5759			0.658526
$426$		0			0
$427$		0			0
$428$	−9.35447	+	16.2024i	−0.452165	+	0.783174i
$429$		0			0
$430$	−3.31284	+	5.73801i	−0.159759	+	0.276711i
$431$	14.0979	+	24.4182i	0.679070	+	1.17618i	0.975261	+	0.221055i	$0.0709499\pi$
$431$	14.0979	+	24.4182i	0.679070	+	1.17618i	−0.296192	+	0.955128i	$0.595717\pi$
$432$		0			0
$433$	−12.5438			−0.602815			−0.301407	−	0.953495i	$-0.597456\pi$
$433$	−12.5438			−0.602815			−0.301407	+	0.953495i	$0.597456\pi$
$434$		0			0
$435$		0			0
$436$	−1.43346	−	2.48283i	−0.0686504	−	0.118906i
$437$	−24.0043			−1.14828
$438$		0			0
$439$	−26.0406			−1.24285			−0.621426	−	0.783473i	$-0.713446\pi$
$439$	−26.0406			−1.24285			−0.621426	+	0.783473i	$0.713446\pi$
$440$	0.352336			0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	23.5729			1.11998			0.559992	−	0.828498i	$-0.310804\pi$
$443$	23.5729			1.11998			0.559992	+	0.828498i	$0.310804\pi$
$444$		0			0
$445$	7.38151			0.349917
$446$	−12.6623	−	21.9317i	−0.599575	−	1.03849i
$447$		0			0
$448$		0			0
$449$	−13.6870			−0.645928			−0.322964	−	0.946411i	$-0.604679\pi$
$449$	−13.6870			−0.645928			−0.322964	+	0.946411i	$0.604679\pi$
$450$		0			0
$451$	−0.0811263	−	0.140515i	−0.00382009	−	0.00661659i
$452$	6.16012	−	10.6696i	0.289748	−	0.501857i
$453$		0			0
$454$	−2.40856	+	4.17174i	−0.113039	+	0.195790i
$455$		0			0
$456$		0			0
$457$	−22.3523			−1.04560			−0.522799	−	0.852456i	$-0.675112\pi$
$457$	−22.3523			−1.04560			−0.522799	+	0.852456i	$0.675112\pi$
$458$	−4.64766	−	8.04999i	−0.217171	−	0.376151i
$459$		0			0
$460$	1.32383	−	2.29294i	0.0617240	−	0.106909i
$461$	−3.98755	−	6.90663i	−0.185719	−	0.321674i	0.758100	−	0.652138i	$-0.226128\pi$
$461$	−3.98755	−	6.90663i	−0.185719	−	0.321674i	−0.943818	+	0.330464i	$0.892795\pi$
$462$		0			0
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	0.310821	+	0.950468i	$0.399396\pi$
$463$	−14.3676	+	24.8854i	−0.667719	+	1.15652i	−0.978540	+	0.206055i	$0.933937\pi$
$464$	3.09718	+	5.36447i	0.143783	+	0.249039i
$465$		0			0
$466$	−0.0971780	+	0.168317i	−0.00450168	+	0.00779714i
$467$	16.7829	−	29.0688i	0.776619	−	1.34514i	−0.157261	−	0.987557i	$-0.550267\pi$
$467$	16.7829	−	29.0688i	0.776619	−	1.34514i	0.933880	−	0.357586i	$-0.116400\pi$
$468$		0			0
$469$		0			0
$470$	−3.60963	−	6.25206i	−0.166500	−	0.288386i
$471$		0			0
$472$	8.64766			0.398041
$473$	6.62568			0.304649
$474$		0			0
$475$	12.5057	+	21.6606i	0.573802	+	0.993855i
$476$		0			0
$477$		0			0
$478$	6.82743	−	11.8255i	0.312279	−	0.540884i
$479$	−0.183560	+	0.317935i	−0.00838707	+	0.0145268i	−0.870188	−	0.492719i	$-0.836003\pi$
$479$	−0.183560	+	0.317935i	−0.00838707	+	0.0145268i	0.861801	+	0.507246i	$0.169336\pi$
$480$		0			0
$481$	−1.25729	−	2.17770i	−0.0573277	−	0.0992945i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$		0			0
$484$	5.32383	+	9.22115i	0.241992	+	0.419143i
$485$	−3.48249	+	6.03184i	−0.158132	+	0.273892i
$486$		0			0
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	−0.975695	−	0.219131i	$-0.929678\pi$
$487$	−14.9538	−	25.9007i	−0.677621	−	1.17367i	0.298075	−	0.954543i	$-0.403656\pi$
$488$	6.64766			0.300926
$489$		0			0
$490$		0			0
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	−0.860210	−	0.509939i	$-0.829668\pi$
$491$	0.255158	−	0.441947i	0.0115151	−	0.0199448i	0.871726	+	0.489994i	$0.163001\pi$
$492$		0			0
$493$	−9.04689	+	15.6697i	−0.407451	+	0.705726i
$494$	6.76615	+	11.7193i	0.304423	+	0.527277i
$495$		0			0
$496$	7.86693			0.353235
$497$		0			0
$498$		0			0
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	0.996486	−	0.0837597i	$-0.0266928\pi$
$499$	9.50953	+	16.4710i	0.425705	+	0.737343i	−0.570781	+	0.821102i	$0.693359\pi$
$500$	−5.72665			−0.256104
$501$		0			0
$502$	−19.5438			−0.872281
$503$	−37.7807			−1.68456			−0.842280	−	0.539040i	$-0.818787\pi$
$503$	−37.7807			−1.68456			−0.842280	+	0.539040i	$0.818787\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$	−2.64766			−0.117703
$507$		0			0
$508$	12.3346			0.547261
$509$	5.60817	+	9.71363i	0.248578	+	0.430549i	0.963131	−	0.269031i	$-0.0867035\pi$
$509$	5.60817	+	9.71363i	0.248578	+	0.430549i	−0.714554	+	0.699581i	$0.753370\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−4.16372	−	7.21177i	−0.183654	−	0.318097i
$515$	1.89397	−	3.28045i	0.0834582	−	0.144554i
$516$		0			0
$517$	−3.60963	+	6.25206i	−0.158751	+	0.274965i
$518$		0			0
$519$		0			0
$520$	−1.49261			−0.0654552
$521$	−13.7360	−	23.7914i	−0.601785	−	1.04232i	−0.992551	−	0.121831i	$-0.961123\pi$
$521$	−13.7360	−	23.7914i	−0.601785	−	1.04232i	0.390766	−	0.920490i	$-0.372210\pi$
$522$		0			0
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	−0.999852	−	0.0172166i	$-0.994520\pi$
$523$	−11.0919	+	19.2118i	−0.485016	+	0.840072i	0.514836	+	0.857289i	$0.327853\pi$
$524$	0.593579	+	1.02811i	0.0259306	+	0.0449132i
$525$		0			0
$526$	−8.54523	+	14.8008i	−0.372590	+	0.645344i
$527$	11.4897	+	19.9007i	0.500498	+	0.866889i
$528$		0			0
$529$	1.55195	−	2.68805i	0.0674760	−	0.116872i
$530$	−2.39037	+	4.14024i	−0.103831	+	0.179841i
$531$		0			0
$532$		0			0
$533$	0.343677	+	0.595265i	0.0148863	+	0.0257838i
$534$		0			0
$535$	11.1052			0.480122
$536$	−1.91381			−0.0826641
$537$		0			0
$538$	−5.00720	−	8.67272i	−0.215876	−	0.373908i
$539$		0			0
$540$		0			0
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	−0.343403	−	0.939188i	$-0.611580\pi$
$541$	14.9246	−	25.8502i	0.641659	−	1.11139i	0.985062	−	0.172198i	$-0.0550869\pi$
$542$	−5.10457	+	8.84137i	−0.219260	+	0.379770i
$543$		0			0
$544$	1.46050	+	2.52967i	0.0626186	+	0.108459i
$545$	−0.850874	+	1.47376i	−0.0364474	+	0.0631288i
$546$		0			0
$547$	8.84348	+	15.3174i	0.378120	+	0.654923i	0.990789	−	0.135417i	$-0.0432373\pi$
$547$	8.84348	+	15.3174i	0.378120	+	0.654923i	−0.612669	+	0.790340i	$0.709904\pi$
$548$	1.26089	−	2.18393i	0.0538627	−	0.0932929i
$549$		0			0
$550$	1.37938	+	2.38915i	0.0588169	+	0.101874i
$551$	−33.3350			−1.42012
$552$		0			0
$553$		0			0
$554$	−9.67111	+	16.7508i	−0.410886	+	0.711675i
$555$		0			0
$556$	−2.45691	+	4.25549i	−0.104196	+	0.180473i
$557$	−15.0651	−	26.0935i	−0.638328	−	1.10562i	−0.985800	−	0.167926i	$-0.946293\pi$
$557$	−15.0651	−	26.0935i	−0.638328	−	1.10562i	0.347472	−	0.937690i	$-0.387040\pi$
$558$		0			0
$559$	−28.0685			−1.18717
$560$		0			0
$561$		0			0
$562$	6.40136	+	11.0875i	0.270025	+	0.467697i
$563$	4.09766			0.172696			0.0863478	−	0.996265i	$-0.472480\pi$
$563$	4.09766			0.172696			0.0863478	+	0.996265i	$0.472480\pi$
$564$		0			0
$565$	−7.31304			−0.307662
$566$	16.3523			0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	−6.23697			−0.261467			−0.130734	−	0.991418i	$-0.541733\pi$
$569$	−6.23697			−0.261467			−0.130734	+	0.991418i	$0.541733\pi$
$570$		0			0
$571$	35.6021			1.48990			0.744951	−	0.667119i	$-0.232473\pi$
$571$	35.6021			1.48990			0.744951	+	0.667119i	$0.232473\pi$
$572$	0.746304	+	1.29264i	0.0312045	+	0.0540479i
$573$		0			0
$574$		0			0
$575$	20.7309			0.864539
$576$		0			0
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.714164	−	0.699979i	$-0.753193\pi$
$577$	−23.1388	−	40.0776i	−0.963281	−	1.66845i	−0.249118	−	0.968473i	$-0.580141\pi$
$578$	4.23385	−	7.33325i	0.176105	−	0.305023i
$579$		0			0
$580$	1.83842	−	3.18424i	0.0763363	−	0.132218i
$581$		0			0
$582$		0			0
$583$	4.78074			0.197998
$584$	−3.95691	−	6.85356i	−0.163738	−	0.283602i
$585$		0			0
$586$	−10.3889	+	17.9941i	−0.429162	+	0.743330i
$587$	1.13161	+	1.96001i	0.0467066	+	0.0808982i	0.888434	−	0.459005i	$-0.151794\pi$
$587$	1.13161	+	1.96001i	0.0467066	+	0.0808982i	−0.841727	+	0.539903i	$0.818461\pi$
$588$		0			0
$589$	−21.1680	+	36.6640i	−0.872212	+	1.51072i
$590$	−2.56654	−	4.44537i	−0.105663	−	0.183013i
$591$		0			0
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	23.0979	−	40.0067i	0.948515	−	1.64288i	0.199960	−	0.979804i	$-0.435919\pi$
$593$	23.0979	−	40.0067i	0.948515	−	1.64288i	0.748555	−	0.663072i	$-0.230748\pi$
$594$		0			0
$595$		0			0
$596$	9.02558	+	15.6328i	0.369702	+	0.640343i
$597$		0			0
$598$	11.2163			0.458670
$599$	16.7807			0.685642			0.342821	−	0.939401i	$-0.388618\pi$
$599$	16.7807			0.685642			0.342821	+	0.939401i	$0.388618\pi$
$600$		0			0
$601$	5.69961	+	9.87202i	0.232492	+	0.402688i	0.958541	−	0.284955i	$-0.0919787\pi$
$601$	5.69961	+	9.87202i	0.232492	+	0.402688i	−0.726049	+	0.687643i	$0.758645\pi$
$602$		0			0
$603$		0			0
$604$	−0.823832	+	1.42692i	−0.0335212	+	0.0580605i
$605$	3.16012	−	5.47348i	0.128477	−	0.222529i
$606$		0			0
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	0.681659	−	0.731670i	$-0.261259\pi$
$607$	−7.21420	−	12.4954i	−0.292815	−	0.507171i	−0.974474	+	0.224499i	$0.927925\pi$
$608$	−2.69076	+	4.66053i	−0.109125	+	0.189009i
$609$		0			0
$610$	−1.97296	−	3.41726i	−0.0798827	−	0.138361i
$611$	15.2915	−	26.4857i	0.618629	−	1.07150i
$612$		0			0
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	0.999967	−	0.00809942i	$-0.00257815\pi$
$613$	12.2053	+	21.1403i	0.492969	+	0.853848i	−0.506998	+	0.861947i	$0.669245\pi$
$614$	22.6768			0.915163
$615$		0			0
$616$		0			0
$617$	−24.4698	+	42.3830i	−0.985119	+	1.70628i	−0.343710	+	0.939076i	$0.611684\pi$
$617$	−24.4698	+	42.3830i	−0.985119	+	1.70628i	−0.641408	+	0.767200i	$0.721650\pi$
$618$		0			0
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.0668227	+	0.997765i	$0.521286\pi$
$619$	−22.3296	+	38.6759i	−0.897501	+	1.55452i	−0.830678	+	0.556753i	$0.812047\pi$
$620$	−2.33482	−	4.04403i	−0.0937687	−	0.162412i
$621$		0			0
$622$	−6.51459			−0.261211
$623$		0			0
$624$		0			0
$625$	−9.91955	−	17.1812i	−0.396782	−	0.687246i
$626$	−0.266149			−0.0106375
$627$		0			0
$628$	6.60078			0.263400
$629$	2.92101			0.116468
$630$		0			0
$631$	33.2852			1.32506			0.662532	−	0.749034i	$-0.269482\pi$
$631$	33.2852			1.32506			0.662532	+	0.749034i	$0.269482\pi$
$632$	−9.24844			−0.367883
$633$		0			0
$634$	−15.7237			−0.624469
$635$	−3.66079	−	6.34067i	−0.145274	−	0.251622i
$636$		0			0
$637$		0			0
$638$	−3.67684			−0.145568
$639$		0			0
$640$	−0.296790	−	0.514055i	−0.0117316	−	0.0203198i
$641$	15.3940	−	26.6631i	0.608025	−	1.05313i	−0.383540	−	0.923524i	$-0.625295\pi$
$641$	15.3940	−	26.6631i	0.608025	−	1.05313i	0.991566	−	0.129606i	$-0.0413714\pi$
$642$		0			0
$643$	13.7345	−	23.7889i	0.541637	−	0.938142i	−0.457174	−	0.889378i	$-0.651138\pi$
$643$	13.7345	−	23.7889i	0.541637	−	0.938142i	0.998810	−	0.0487649i	$-0.0155285\pi$
$644$		0			0
$645$		0			0
$646$	−15.7195			−0.618474
$647$	−6.63521	−	11.4925i	−0.260857	−	0.451818i	0.705613	−	0.708598i	$-0.250672\pi$
$647$	−6.63521	−	11.4925i	−0.260857	−	0.451818i	−0.966470	+	0.256780i	$0.917338\pi$
$648$		0			0
$649$	−2.56654	+	4.44537i	−0.100745	+	0.174496i
$650$	−5.84348	−	10.1212i	−0.229200	−	0.396986i
$651$		0			0
$652$	−2.99115	+	5.18082i	−0.117142	+	0.202896i
$653$	−8.57081	−	14.8451i	−0.335402	−	0.580933i	0.648160	−	0.761504i	$-0.275539\pi$
$653$	−8.57081	−	14.8451i	−0.335402	−	0.580933i	−0.983562	+	0.180571i	$0.942205\pi$
$654$		0			0
$655$	0.352336	−	0.610265i	0.0137669	−	0.0238450i
$656$	−0.136673	+	0.236725i	−0.00533619	+	0.00924255i
$657$		0			0
$658$		0			0
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	0.771022	−	0.636808i	$-0.219746\pi$
$659$	−4.26089	−	7.38008i	−0.165981	−	0.287487i	−0.937003	+	0.349321i	$0.886412\pi$
$660$		0			0
$661$	−34.3360			−1.33551			−0.667757	−	0.744379i	$-0.732746\pi$
$661$	−34.3360			−1.33551			−0.667757	+	0.744379i	$0.732746\pi$
$662$	−25.1623			−0.977959
$663$		0			0
$664$	3.85087	+	6.66991i	0.149443	+	0.258843i
$665$		0			0
$666$		0			0
$667$	−13.8150	+	23.9282i	−0.534918	+	0.926505i
$668$	3.73025	−	6.46099i	0.144328	−	0.249983i
$669$		0			0
$670$	0.568000	+	0.983804i	0.0219437	+	0.0380077i
$671$	−1.97296	+	3.41726i	−0.0761652	+	0.131922i
$672$		0			0
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	0.678546	−	0.734558i	$-0.262610\pi$
$673$	−7.70155	−	13.3395i	−0.296873	−	0.514199i	−0.975419	+	0.220359i	$0.929277\pi$
$674$	−9.36693	+	16.2240i	−0.360800	+	0.624925i
$675$		0			0
$676$	3.33842	+	5.78231i	0.128401	+	0.222397i
$677$	−7.38151			−0.283695			−0.141847	−	0.989889i	$-0.545304\pi$
$677$	−7.38151			−0.283695			−0.141847	+	0.989889i	$0.545304\pi$
$678$		0			0
$679$		0			0
$680$	0.866926	−	1.50156i	0.0332451	−	0.0575822i
$681$		0			0
$682$	−2.33482	+	4.04403i	−0.0894050	+	0.154854i
$683$	−4.79893	−	8.31198i	−0.183626	−	0.318049i	0.759487	−	0.650523i	$-0.225450\pi$
$683$	−4.79893	−	8.31198i	−0.183626	−	0.318049i	−0.943113	+	0.332474i	$0.892117\pi$
$684$		0			0
$685$	−1.49688			−0.0571929
$686$		0			0
$687$		0			0
$688$	−5.58113	−	9.66679i	−0.212778	−	0.368543i
$689$	−20.2527			−0.771567
$690$		0			0
$691$	14.1445			0.538084			0.269042	−	0.963128i	$-0.413293\pi$
$691$	14.1445			0.538084			0.269042	+	0.963128i	$0.413293\pi$
$692$	−25.6591			−0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	2.91674			0.110638
$696$		0			0
$697$	−0.798447			−0.0302433
$698$	−1.89543	−	3.28298i	−0.0717431	−	0.124263i
$699$		0			0
$700$		0			0
$701$	−37.3753			−1.41164			−0.705822	−	0.708389i	$-0.749422\pi$
$701$	−37.3753			−1.41164			−0.705822	+	0.708389i	$0.749422\pi$
$702$		0			0
$703$	2.69076	+	4.66053i	0.101484	+	0.175775i
$704$	−0.296790	+	0.514055i	−0.0111857	+	0.0193742i
$705$		0			0
$706$	−3.41741	+	5.91913i	−0.128616	+	0.222769i
$707$		0			0
$708$		0			0
$709$	−10.4868			−0.393838			−0.196919	−	0.980420i	$-0.563094\pi$
$709$	−10.4868			−0.393838			−0.196919	+	0.980420i	$0.563094\pi$
$710$	−4.27694	−	7.40789i	−0.160511	−	0.278013i
$711$		0			0
$712$	−6.21780	+	10.7695i	−0.233022	+	0.403606i
$713$	17.5452	+	30.3892i	0.657074	+	1.13809i
$714$		0			0
$715$	0.442991	−	0.767282i	0.0165669	−	0.0286947i
$716$	−7.51819	−	13.0219i	−0.280968	−	0.486651i
$717$		0			0
$718$	6.32237	−	10.9507i	0.235949	−	0.408675i
$719$	1.11995	−	1.93981i	0.0417670	−	0.0723426i	−0.844386	−	0.535735i	$-0.820035\pi$
$719$	1.11995	−	1.93981i	0.0417670	−	0.0723426i	0.886153	+	0.463392i	$0.153368\pi$
$720$		0			0
$721$		0			0
$722$	−4.98035	−	8.62622i	−0.185349	−	0.321035i
$723$		0			0
$724$	0.0861875			0.00320313
$725$	28.7893			1.06921
$726$		0			0
$727$	−0.185023	−	0.320469i	−0.00686211	−	0.0118855i	0.862574	−	0.505931i	$-0.168851\pi$
$727$	−0.185023	−	0.320469i	−0.00686211	−	0.0118855i	−0.869436	+	0.494045i	$0.835518\pi$
$728$		0			0
$729$		0			0
$730$	−2.34874	+	4.06813i	−0.0869307	+	0.150568i
$731$	16.3025	−	28.2368i	0.602971	−	1.04438i
$732$		0			0
$733$	7.00953	+	12.1409i	0.258903	+	0.448433i	0.965948	−	0.258735i	$-0.0833057\pi$
$733$	7.00953	+	12.1409i	0.258903	+	0.448433i	−0.707045	+	0.707168i	$0.749972\pi$
$734$	3.27188	−	5.66707i	0.120767	−	0.209175i
$735$		0			0
$736$	2.23025	+	3.86291i	0.0822082	+	0.142389i
$737$	0.568000	−	0.983804i	0.0209225	−	0.0362389i
$738$		0			0
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	0.999962	−	0.00868705i	$-0.00276521\pi$
$739$	13.3872	+	23.1874i	0.492458	+	0.852962i	−0.507504	+	0.861649i	$0.669432\pi$
$740$	−0.593579			−0.0218204
$741$		0			0
$742$		0			0
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	−0.758480	−	0.651696i	$-0.774058\pi$
$743$	5.04669	−	8.74113i	0.185145	−	0.320681i	0.943625	+	0.331015i	$0.107391\pi$
$744$		0			0
$745$	5.35740	−	9.27928i	0.196280	−	0.339967i
$746$	−4.71420	−	8.16524i	−0.172599	−	0.298951i
$747$		0			0
$748$	−1.73385			−0.0633959
$749$		0			0
$750$		0			0
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	0.741655	−	0.670782i	$-0.234041\pi$
$751$	−5.75729	−	9.97193i	−0.210087	−	0.363881i	−0.951741	+	0.306901i	$0.900708\pi$
$752$	12.1623			0.443512
$753$		0			0
$754$	15.5763			0.567254
$755$	0.978019			0.0355938
$756$		0			0
$757$	−15.2484			−0.554214			−0.277107	−	0.960839i	$-0.589376\pi$
$757$	−15.2484			−0.554214			−0.277107	+	0.960839i	$0.589376\pi$
$758$	−7.27762			−0.264335
$759$		0			0
$760$	3.19436			0.115871
$761$	0.850874	+	1.47376i	0.0308442	+	0.0534236i	0.881035	−	0.473050i	$-0.156847\pi$
$761$	0.850874	+	1.47376i	0.0308442	+	0.0534236i	−0.850191	+	0.526474i	$0.823514\pi$
$762$		0			0
$763$		0			0
$764$	−3.98229			−0.144074
$765$		0			0
$766$	12.0416	+	20.8567i	0.435082	+	0.753584i
$767$	10.8727	−	18.8320i	0.392589	−	0.679984i
$768$		0			0
$769$	−24.1211	+	41.7790i	−0.869829	+	1.50659i	−0.00765823	+	0.999971i	$0.502438\pi$
$769$	−24.1211	+	41.7790i	−0.869829	+	1.50659i	−0.862171	+	0.506618i	$0.830896\pi$
$770$		0			0
$771$		0			0
$772$	6.78074			0.244044
$773$	3.10243	+	5.37357i	0.111587	+	0.193274i	0.916410	−	0.400240i	$-0.131073\pi$
$773$	3.10243	+	5.37357i	0.111587	+	0.193274i	−0.804823	+	0.593514i	$0.797740\pi$
$774$		0			0
$775$	18.2814	−	31.6643i	0.656688	−	1.13742i
$776$	−5.86693	−	10.1618i	−0.210610	−	0.364788i
$777$		0			0
$778$	−8.14913	+	14.1147i	−0.292160	+	0.506037i
$779$	−0.735508	−	1.27394i	−0.0263523	−	0.0456436i
$780$		0			0
$781$	−4.27694	+	7.40789i	−0.153041	+	0.265075i
$782$	−6.51459	+	11.2836i	−0.232961	+	0.403501i
$783$		0			0
$784$		0			0
$785$	−1.95904	−	3.39316i	−0.0699212	−	0.121107i
$786$		0			0
$787$	−6.09766			−0.217358			−0.108679	−	0.994077i	$-0.534662\pi$
$787$	−6.09766			−0.217358			−0.108679	+	0.994077i	$0.534662\pi$
$788$	−11.0584			−0.393938
$789$		0			0
$790$	2.74484	+	4.75420i	0.0976571	+	0.169147i
$791$		0			0
$792$		0			0
$793$	8.35807	−	14.4766i	0.296804	−	0.514079i
$794$	6.08619	−	10.5416i	0.215991	−	0.374107i
$795$		0			0
$796$	−2.80924	−	4.86575i	−0.0995710	−	0.172462i
$797$	−6.22860	+	10.7882i	−0.220628	+	0.382139i	−0.954999	−	0.296609i	$-0.904144\pi$
$797$	−6.22860	+	10.7882i	−0.220628	+	0.382139i	0.734371	+	0.678749i	$0.237477\pi$
$798$		0			0
$799$	17.7630	+	30.7665i	0.628411	+	1.08844i
$800$	2.32383	−	4.02499i	0.0821599	−	0.142305i
$801$		0			0
$802$	−16.6804	−	28.8914i	−0.589007	−	1.02019i
$803$	4.69748			0.165770
$804$		0			0
$805$		0			0
$806$	9.89104	−	17.1318i	0.348397	−	0.603442i
$807$		0			0
$808$	0.811379	−	1.40535i	0.0285442	−	0.0494400i
$809$	2.81644	+	4.87822i	0.0990208	+	0.171509i	0.911280	−	0.411788i	$-0.135096\pi$
$809$	2.81644	+	4.87822i	0.0990208	+	0.171509i	−0.812259	+	0.583297i	$0.801762\pi$
$810$		0			0
$811$	45.6414			1.60269			0.801344	−	0.598204i	$-0.204119\pi$
$811$	45.6414			1.60269			0.801344	+	0.598204i	$0.204119\pi$
$812$		0			0
$813$		0			0
$814$	0.296790	+	0.514055i	0.0104025	+	0.0180176i
$815$	3.55096			0.124385
$816$		0			0
$817$	60.0698			2.10158
$818$	5.78074			0.202119
$819$		0			0
$820$	0.162253			0.00566611
$821$	−32.6946			−1.14105			−0.570524	−	0.821281i	$-0.693260\pi$
$821$	−32.6946			−1.14105			−0.570524	+	0.821281i	$0.693260\pi$
$822$		0			0
$823$	−10.4399			−0.363911			−0.181956	−	0.983307i	$-0.558243\pi$
$823$	−10.4399			−0.363911			−0.181956	+	0.983307i	$0.558243\pi$
$824$	3.19076	+	5.52655i	0.111155	+	0.192527i
$825$		0			0
$826$		0			0
$827$	−16.7060			−0.580925			−0.290463	−	0.956886i	$-0.593809\pi$
$827$	−16.7060			−0.580925			−0.290463	+	0.956886i	$0.593809\pi$
$828$		0			0
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	0.998696	−	0.0510466i	$-0.0162557\pi$
$829$	13.1046	+	22.6978i	0.455141	+	0.788327i	−0.543556	+	0.839373i	$0.682922\pi$
$830$	2.28580	−	3.95912i	0.0793412	−	0.137423i
$831$		0			0
$832$	1.25729	−	2.17770i	0.0435888	−	0.0754981i
$833$		0			0
$834$		0			0
$835$	−4.42840			−0.153251
$836$	−1.59718	−	2.76639i	−0.0552396	−	0.0956777i
$837$		0			0
$838$	15.4356	−	26.7352i	0.533214	−	0.923554i
$839$	11.1886	+	19.3793i	0.386274	+	0.669046i	0.991945	−	0.126669i	$-0.0404286\pi$
$839$	11.1886	+	19.3793i	0.386274	+	0.669046i	−0.605671	+	0.795715i	$0.707095\pi$
$840$		0			0
$841$	−4.68502	+	8.11470i	−0.161553	+	0.279817i
$842$	−1.86693	−	3.23361i	−0.0643385	−	0.111438i
$843$		0			0
$844$	9.66225	−	16.7355i	0.332588	−	0.576060i
$845$	1.98162	−	3.43226i	0.0681697	−	0.118073i
$846$		0			0
$847$		0			0
$848$	−4.02704	−	6.97504i	−0.138289	−	0.239524i
$849$		0			0
$850$	13.5759			0.465649
$851$	4.46050			0.152904
$852$		0			0
$853$	−4.96264	−	8.59555i	−0.169918	−	0.294306i	0.768473	−	0.639882i	$-0.221017\pi$
$853$	−4.96264	−	8.59555i	−0.169918	−	0.294306i	−0.938391	+	0.345576i	$0.887683\pi$
$854$		0			0
$855$		0			0
$856$	−9.35447	+	16.2024i	−0.319729	+	0.553787i
$857$	−3.89776	+	6.75112i	−0.133145	+	0.230614i	−0.924887	−	0.380241i	$-0.875841\pi$
$857$	−3.89776	+	6.75112i	−0.133145	+	0.230614i	0.791742	+	0.610855i	$0.209174\pi$
$858$		0			0
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	0.971085	−	0.238732i	$-0.0767318\pi$
$859$	8.17111	+	14.1528i	0.278795	+	0.482886i	−0.692291	+	0.721619i	$0.743398\pi$
$860$	−3.31284	+	5.73801i	−0.112967	+	0.195664i
$861$		0			0
$862$	14.0979	+	24.4182i	0.480175	+	0.831687i
$863$	−0.730252	+	1.26483i	−0.0248581	+	0.0430555i	−0.878187	−	0.478318i	$-0.841247\pi$
$863$	−0.730252	+	1.26483i	−0.0248581	+	0.0430555i	0.853329	+	0.521373i	$0.174580\pi$
$864$		0			0
$865$	7.61537	+	13.1902i	0.258930	+	0.448480i
$866$	−12.5438			−0.426255
$867$		0			0
$868$		0			0
$869$	2.74484	−	4.75420i	0.0931124	−	0.161275i
$870$		0			0
$871$	−2.40623	+	4.16771i	−0.0815319	+	0.141217i
$872$	−1.43346	−	2.48283i	−0.0485432	−	0.0840792i
$873$		0			0
$874$	−24.0043			−0.811957
$875$		0			0
$876$		0			0
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	0.885648	−	0.464357i	$-0.153715\pi$
$877$	1.20467	+	2.08655i	0.0406789	+	0.0704579i	−0.844969	+	0.534815i	$0.820381\pi$
$878$	−26.0406			−0.878829
$879$		0			0
$880$	0.352336			0.0118773
$881$	−18.9607			−0.638802			−0.319401	−	0.947620i	$-0.603482\pi$
$881$	−18.9607			−0.638802			−0.319401	+	0.947620i	$0.603482\pi$
$882$		0			0
$883$	3.64008			0.122498			0.0612492	−	0.998123i	$-0.480492\pi$
$883$	3.64008			0.122498			0.0612492	+	0.998123i	$0.480492\pi$
$884$	7.34514			0.247044
$885$		0			0
$886$	23.5729			0.791949
$887$	12.2286	+	21.1805i	0.410596	+	0.711173i	0.994955	−	0.100322i	$-0.0319873\pi$
$887$	12.2286	+	21.1805i	0.410596	+	0.711173i	−0.584359	+	0.811495i	$0.698654\pi$
$888$		0			0
$889$		0			0
$890$	7.38151			0.247429
$891$		0			0
$892$	−12.6623	−	21.9317i	−0.423964	−	0.734326i
$893$	−32.7257	+	56.6825i	−1.09512	+	1.89681i
$894$		0			0
$895$	−4.46264	+	7.72952i	−0.149170	+	0.258369i
$896$		0			0
$897$		0			0
$898$	−13.6870			−0.456740
$899$	24.3653	+	42.2019i	0.812627	+	1.40751i
$900$		0			0
$901$	11.7630	−	20.3742i	0.391883	−	0.678762i
$902$	−0.0811263	−	0.140515i	−0.00270121	−	0.00467863i
$903$		0			0
$904$	6.16012	−	10.6696i	0.204882	−	0.354867i
$905$	−0.0255796	−	0.0443051i	−0.000850293	−	0.00147275i
$906$		0			0
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	−0.937234	−	0.348701i	$-0.886623\pi$
$907$	−5.01838	+	8.69209i	−0.166633	+	0.288616i	0.770601	+	0.637318i	$0.219956\pi$
$908$	−2.40856	+	4.17174i	−0.0799308	+	0.138444i
$909$		0			0
$910$		0			0
$911$	−11.4459	−	19.8249i	−0.379220	−	0.656828i	0.611729	−	0.791067i	$-0.290474\pi$
$911$	−11.4459	−	19.8249i	−0.379220	−	0.656828i	−0.990949	+	0.134239i	$0.957141\pi$
$912$		0			0
$913$	−4.57160			−0.151298
$914$	−22.3523			−0.739350
$915$		0			0
$916$	−4.64766	−	8.04999i	−0.153563	−	0.265979i
$917$		0			0
$918$		0			0
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	−0.628575	−	0.777749i	$-0.716362\pi$
$919$	10.8910	−	18.8638i	0.359262	−	0.622261i	0.987838	+	0.155488i	$0.0496950\pi$
$920$	1.32383	−	2.29294i	0.0436454	−	0.0755961i
$921$		0			0
$922$	−3.98755	−	6.90663i	−0.131323	−	0.227458i
$923$	18.1185	−	31.3821i	0.596377	−	1.03296i
$924$		0			0
$925$	−2.32383	−	4.02499i	−0.0764071	−	0.132341i
$926$	−14.3676	+	24.8854i	−0.472149	+	0.817785i
$927$		0			0
$928$	3.09718	+	5.36447i	0.101670	+	0.176097i
$929$	−32.8377			−1.07737			−0.538686	−	0.842507i	$-0.681079\pi$
$929$	−32.8377			−1.07737			−0.538686	+	0.842507i	$0.681079\pi$
$930$		0			0
$931$		0			0
$932$	−0.0971780	+	0.168317i	−0.00318317	+	0.00551341i
$933$		0			0
$934$	16.7829	−	29.0688i	0.549152	−	0.951160i
$935$	0.514589	+	0.891294i	0.0168289	+	0.0291484i
$936$		0			0
$937$	8.78074			0.286854			0.143427	−	0.989661i	$-0.454188\pi$
$937$	8.78074			0.286854			0.143427	+	0.989661i	$0.454188\pi$
$938$		0			0
$939$		0			0
$940$	−3.60963	−	6.25206i	−0.117733	−	0.203920i
$941$	4.26615			0.139072			0.0695362	−	0.997579i	$-0.477848\pi$
$941$	4.26615			0.139072			0.0695362	+	0.997579i	$0.477848\pi$
$942$		0			0
$943$	−1.21926			−0.0397046
$944$	8.64766			0.281457
$945$		0			0
$946$	6.62568			0.215420
$947$	23.0584			0.749296			0.374648	−	0.927167i	$-0.377764\pi$
$947$	23.0584			0.749296			0.374648	+	0.927167i	$0.377764\pi$
$948$		0			0
$949$	−19.9000			−0.645981
$950$	12.5057	+	21.6606i	0.405740	+	0.702762i
$951$		0			0
$952$		0			0
$953$	36.5552			1.18414			0.592070	−	0.805886i	$-0.298311\pi$
$953$	36.5552			1.18414			0.592070	+	0.805886i	$0.298311\pi$
$954$		0			0
$955$	1.18190	+	2.04712i	0.0382455	+	0.0662431i
$956$	6.82743	−	11.8255i	0.220815	−	0.382463i
$957$		0			0
$958$	−0.183560	+	0.317935i	−0.00593056	+	0.0102720i
$959$		0			0
$960$		0			0
$961$	30.8885			0.996404
$962$	−1.25729	−	2.17770i	−0.0405368	−	0.0702118i
$963$		0			0
$964$	−6.50000	+	11.2583i	−0.209351	+	0.362606i
$965$	−2.01245	−	3.48567i	−0.0647832	−	0.112208i
$966$		0			0
$967$	26.7719	−	46.3703i	0.860926	−	1.49117i	−0.0101108	−	0.999949i	$-0.503218\pi$
$967$	26.7719	−	46.3703i	0.860926	−	1.49117i	0.871037	−	0.491218i	$-0.163448\pi$
$968$	5.32383	+	9.22115i	0.171114	+	0.296379i
$969$		0			0
$970$	−3.48249	+	6.03184i	−0.111816	+	0.193671i
$971$	−15.9897	+	27.6949i	−0.513133	+	0.888773i	0.486751	+	0.873541i	$0.338182\pi$
$971$	−15.9897	+	27.6949i	−0.513133	+	0.888773i	−0.999884	+	0.0152321i	$0.995151\pi$
$972$		0			0
$973$		0			0
$974$	−14.9538	−	25.9007i	−0.479150	−	0.829913i
$975$		0			0
$976$	6.64766			0.212787
$977$	27.4208			0.877270			0.438635	−	0.898665i	$-0.355462\pi$
$977$	27.4208			0.877270			0.438635	+	0.898665i	$0.355462\pi$
$978$		0			0
$979$	−3.69076	−	6.39258i	−0.117957	−	0.204308i
$980$		0			0
$981$		0			0
$982$	0.255158	−	0.441947i	0.00814243	−	0.0141031i
$983$	29.5782	−	51.2309i	0.943398	−	1.63401i	0.184471	−	0.982838i	$-0.440943\pi$
$983$	29.5782	−	51.2309i	0.943398	−	1.63401i	0.758927	−	0.651175i	$-0.225724\pi$
$984$		0			0
$985$	3.28201	+	5.68460i	0.104573	+	0.181126i
$986$	−9.04689	+	15.6697i	−0.288112	+	0.499024i
$987$		0			0
$988$	6.76615	+	11.7193i	0.215260	+	0.372841i
$989$	24.8946	−	43.1188i	0.791604	−	1.37110i
$990$		0			0
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	0.949782	−	0.312911i	$-0.101304\pi$
$991$	6.41887	+	11.1178i	0.203902	+	0.353169i	−0.745880	+	0.666080i	$0.767971\pi$
$992$	7.86693			0.249775
$993$		0			0
$994$		0			0
$995$	−1.66751	+	2.88821i	−0.0528636	+	0.0915624i
$996$		0			0
$997$	−2.89037	+	5.00627i	−0.0915389	+	0.158550i	−0.908159	−	0.418626i	$-0.862512\pi$
$997$	−2.89037	+	5.00627i	−0.0915389	+	0.158550i	0.816620	+	0.577176i	$0.195845\pi$
$998$	9.50953	+	16.4710i	0.301019	+	0.521380i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.p.1549.2		6
3.2	odd	2		882.2.e.o.373.2		6
7.2	even	3		2646.2.f.m.1765.2		6
7.3	odd	6		378.2.h.c.361.2		6
7.4	even	3		2646.2.h.o.361.2		6
7.5	odd	6		2646.2.f.l.1765.2		6
7.6	odd	2		378.2.e.d.37.2		6
9.2	odd	6		882.2.h.p.79.2		6
9.7	even	3		2646.2.h.o.667.2		6
21.2	odd	6		882.2.f.o.589.3		6
21.5	even	6		882.2.f.n.589.1		6
21.11	odd	6		882.2.h.p.67.2		6
21.17	even	6		126.2.h.d.67.2	yes	6
21.20	even	2		126.2.e.c.121.2	yes	6
28.3	even	6		3024.2.t.h.1873.2		6
28.27	even	2		3024.2.q.g.2305.2		6
63.2	odd	6		882.2.f.o.295.3		6
63.5	even	6		7938.2.a.bv.1.2		3
63.11	odd	6		882.2.e.o.655.2		6
63.13	odd	6		1134.2.g.l.163.2		6
63.16	even	3		2646.2.f.m.883.2		6
63.20	even	6		126.2.h.d.79.2	yes	6
63.23	odd	6		7938.2.a.bw.1.2		3
63.25	even	3	inner	2646.2.e.p.2125.2		6
63.31	odd	6		1134.2.g.l.487.2		6
63.34	odd	6		378.2.h.c.289.2		6
63.38	even	6		126.2.e.c.25.2	✓	6
63.40	odd	6		7938.2.a.ca.1.2		3
63.41	even	6		1134.2.g.m.163.2		6
63.47	even	6		882.2.f.n.295.1		6
63.52	odd	6		378.2.e.d.235.2		6
63.58	even	3		7938.2.a.bz.1.2		3
63.59	even	6		1134.2.g.m.487.2		6
63.61	odd	6		2646.2.f.l.883.2		6
84.59	odd	6		1008.2.t.h.193.2		6
84.83	odd	2		1008.2.q.g.625.2		6
252.83	odd	6		1008.2.t.h.961.2		6
252.115	even	6		3024.2.q.g.2881.2		6
252.223	even	6		3024.2.t.h.289.2		6
252.227	odd	6		1008.2.q.g.529.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.c.25.2	✓	6	63.38	even	6
126.2.e.c.121.2	yes	6	21.20	even	2
126.2.h.d.67.2	yes	6	21.17	even	6
126.2.h.d.79.2	yes	6	63.20	even	6
378.2.e.d.37.2		6	7.6	odd	2
378.2.e.d.235.2		6	63.52	odd	6
378.2.h.c.289.2		6	63.34	odd	6
378.2.h.c.361.2		6	7.3	odd	6
882.2.e.o.373.2		6	3.2	odd	2
882.2.e.o.655.2		6	63.11	odd	6
882.2.f.n.295.1		6	63.47	even	6
882.2.f.n.589.1		6	21.5	even	6
882.2.f.o.295.3		6	63.2	odd	6
882.2.f.o.589.3		6	21.2	odd	6
882.2.h.p.67.2		6	21.11	odd	6
882.2.h.p.79.2		6	9.2	odd	6
1008.2.q.g.529.2		6	252.227	odd	6
1008.2.q.g.625.2		6	84.83	odd	2
1008.2.t.h.193.2		6	84.59	odd	6
1008.2.t.h.961.2		6	252.83	odd	6
1134.2.g.l.163.2		6	63.13	odd	6
1134.2.g.l.487.2		6	63.31	odd	6
1134.2.g.m.163.2		6	63.41	even	6
1134.2.g.m.487.2		6	63.59	even	6
2646.2.e.p.1549.2		6	1.1	even	1	trivial
2646.2.e.p.2125.2		6	63.25	even	3	inner
2646.2.f.l.883.2		6	63.61	odd	6
2646.2.f.l.1765.2		6	7.5	odd	6
2646.2.f.m.883.2		6	63.16	even	3
2646.2.f.m.1765.2		6	7.2	even	3
2646.2.h.o.361.2		6	7.4	even	3
2646.2.h.o.667.2		6	9.7	even	3
3024.2.q.g.2305.2		6	28.27	even	2
3024.2.q.g.2881.2		6	252.115	even	6
3024.2.t.h.289.2		6	252.223	even	6
3024.2.t.h.1873.2		6	28.3	even	6
7938.2.a.bv.1.2		3	63.5	even	6
7938.2.a.bw.1.2		3	63.23	odd	6
7938.2.a.bz.1.2		3	63.58	even	3
7938.2.a.ca.1.2		3	63.40	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(-0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +(-0.296790 - 0.514055i) q^{10} +(-0.296790 + 0.514055i) q^{11} +(1.25729 - 2.17770i) q^{13} +1.00000 q^{16} +(1.46050 + 2.52967i) q^{17} +(-2.69076 + 4.66053i) q^{19} +(-0.296790 - 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(2.23025 + 3.86291i) q^{23} +(2.32383 - 4.02499i) q^{25} +(1.25729 - 2.17770i) q^{26} +(3.09718 + 5.36447i) q^{29} +7.86693 q^{31} +1.00000 q^{32} +(1.46050 + 2.52967i) q^{34} +(0.500000 - 0.866025i) q^{37} +(-2.69076 + 4.66053i) q^{38} +(-0.296790 - 0.514055i) q^{40} +(-0.136673 + 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +(-0.296790 + 0.514055i) q^{44} +(2.23025 + 3.86291i) q^{46} +12.1623 q^{47} +(2.32383 - 4.02499i) q^{50} +(1.25729 - 2.17770i) q^{52} +(-4.02704 - 6.97504i) q^{53} +0.352336 q^{55} +(3.09718 + 5.36447i) q^{58} +8.64766 q^{59} +6.64766 q^{61} +7.86693 q^{62} +1.00000 q^{64} -1.49261 q^{65} -1.91381 q^{67} +(1.46050 + 2.52967i) q^{68} +14.4107 q^{71} +(-3.95691 - 6.85356i) q^{73} +(0.500000 - 0.866025i) q^{74} +(-2.69076 + 4.66053i) q^{76} -9.24844 q^{79} +(-0.296790 - 0.514055i) q^{80} +(-0.136673 + 0.236725i) q^{82} +(3.85087 + 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-5.58113 - 9.66679i) q^{86} +(-0.296790 + 0.514055i) q^{88} +(-6.21780 + 10.7695i) q^{89} +(2.23025 + 3.86291i) q^{92} +12.1623 q^{94} +3.19436 q^{95} +(-5.86693 - 10.1618i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8	\( 6 q + 6 q^{2} + 6 q^{4} + q^{5} + 6 q^{8} + q^{10} + q^{11} - 8 q^{13} + 6 q^{16} - 4 q^{17} + 3 q^{19} + q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 8 q^{26} + 5 q^{29} + 40 q^{31} + 6 q^{32} - 4 q^{34} + 3 q^{37} + 3 q^{38} + q^{40} - 6 q^{43} + q^{44} + 7 q^{46} + 18 q^{47} + 2 q^{50} - 8 q^{52} - 15 q^{53} + 26 q^{55} + 5 q^{58} + 28 q^{59} + 16 q^{61} + 40 q^{62} + 6 q^{64} - 24 q^{65} - 2 q^{67} - 4 q^{68} - 14 q^{71} - 19 q^{73} + 3 q^{74} + 3 q^{76} - 10 q^{79} + q^{80} + 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 9 q^{89} + 7 q^{92} + 18 q^{94} - 8 q^{95} - 28 q^{97}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 + q^5 + 6 * q^8 + q^10 + q^11 - 8 * q^13 + 6 * q^16 - 4 * q^17 + 3 * q^19 + q^20 + q^22 + 7 * q^23 + 2 * q^25 - 8 * q^26 + 5 * q^29 + 40 * q^31 + 6 * q^32 - 4 * q^34 + 3 * q^37 + 3 * q^38 + q^40 - 6 * q^43 + q^44 + 7 * q^46 + 18 * q^47 + 2 * q^50 - 8 * q^52 - 15 * q^53 + 26 * q^55 + 5 * q^58 + 28 * q^59 + 16 * q^61 + 40 * q^62 + 6 * q^64 - 24 * q^65 - 2 * q^67 - 4 * q^68 - 14 * q^71 - 19 * q^73 + 3 * q^74 + 3 * q^76 - 10 * q^79 + q^80 + 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 9 * q^89 + 7 * q^92 + 18 * q^94 - 8 * q^95 - 28 * q^97

Introduction

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