LMFDB - Embedded newform 2646.2.f.l.1765.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(883,2646)]

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([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.f (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1765.2
Root			$0.500000 - 2.05195i$ of defining polynomial
Character	$\chi$	$=$	2646.1765
Dual form			2646.2.f.l.883.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +1.00000 q^{8} -0.593579 q^{10} +(-0.296790 - 0.514055i) q^{11} +(-1.25729 + 2.17770i) q^{13} +(-0.500000 - 0.866025i) q^{16} +2.92101 q^{17} -5.38151 q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(2.23025 - 3.86291i) q^{23} +(2.32383 + 4.02499i) q^{25} +2.51459 q^{26} +(3.09718 + 5.36447i) q^{29} +(3.93346 - 6.81296i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.46050 - 2.52967i) q^{34} -1.00000 q^{37} +(2.69076 + 4.66053i) q^{38} +(0.296790 - 0.514055i) q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +0.593579 q^{44} -4.46050 q^{46} +(6.08113 + 10.5328i) q^{47} +(2.32383 - 4.02499i) q^{50} +(-1.25729 - 2.17770i) q^{52} +8.05408 q^{53} -0.352336 q^{55} +(3.09718 - 5.36447i) q^{58} +(4.32383 - 7.48910i) q^{59} +(3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 + 1.29264i) q^{65} +(0.956906 - 1.65741i) q^{67} +(-1.46050 + 2.52967i) q^{68} +14.4107 q^{71} -7.91381 q^{73} +(0.500000 + 0.866025i) q^{74} +(2.69076 - 4.66053i) q^{76} +(4.62422 + 8.00938i) q^{79} -0.593579 q^{80} -0.273346 q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-5.58113 + 9.66679i) q^{86} +(-0.296790 - 0.514055i) q^{88} -12.4356 q^{89} +(2.23025 + 3.86291i) q^{92} +(6.08113 - 10.5328i) q^{94} +(-1.59718 + 2.76639i) q^{95} +(5.86693 + 10.1618i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8}+O(q^{10}) $ 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8	$ 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} + 2 q^{10} + q^{11} + 8 q^{13} - 3 q^{16} - 8 q^{17} + 6 q^{19} - q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 16 q^{26} + 5 q^{29} + 20 q^{31} - 3 q^{32} + 4 q^{34} - 6 q^{37} - 3 q^{38} - q^{40} - 6 q^{43} - 2 q^{44} - 14 q^{46} + 9 q^{47} + 2 q^{50} + 8 q^{52} + 30 q^{53} - 26 q^{55} + 5 q^{58} + 14 q^{59} + 8 q^{61} - 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 4 q^{68} - 14 q^{71} - 38 q^{73} + 3 q^{74} - 3 q^{76} + 5 q^{79} + 2 q^{80} - 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 18 q^{89} + 7 q^{92} + 9 q^{94} + 4 q^{95} + 28 q^{97}+O(q^{100}) $ 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 + 2 * q^10 + q^11 + 8 * q^13 - 3 * q^16 - 8 * q^17 + 6 * q^19 - q^20 + q^22 + 7 * q^23 + 2 * q^25 - 16 * q^26 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 - 6 * q^37 - 3 * q^38 - q^40 - 6 * q^43 - 2 * q^44 - 14 * q^46 + 9 * q^47 + 2 * q^50 + 8 * q^52 + 30 * q^53 - 26 * q^55 + 5 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 4 * q^68 - 14 * q^71 - 38 * q^73 + 3 * q^74 - 3 * q^76 + 5 * q^79 + 2 * q^80 - 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 18 * q^89 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.296790	−	0.514055i	0.132728	−	0.229892i	−0.791999	−	0.610522i	$-0.790960\pi$
$5$	0.296790	−	0.514055i	0.132728	−	0.229892i	0.924727	+	0.380630i	$0.124293\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$		0			0
$10$	−0.593579			−0.187706
$11$	−0.296790	−	0.514055i	−0.0894855	−	0.154993i	0.817808	−	0.575491i	$-0.195189\pi$
$11$	−0.296790	−	0.514055i	−0.0894855	−	0.154993i	−0.907294	+	0.420497i	$0.861856\pi$
$12$		0			0
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	−0.986021	−	0.166623i	$-0.946714\pi$
$13$	−1.25729	+	2.17770i	−0.348711	+	0.603985i	0.637310	+	0.770608i	$0.280047\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.92101			0.708449			0.354224	−	0.935160i	$-0.384745\pi$
$17$	2.92101			0.708449			0.354224	+	0.935160i	$0.384745\pi$
$18$		0			0
$19$	−5.38151			−1.23460			−0.617302	−	0.786726i	$-0.711774\pi$
$19$	−5.38151			−1.23460			−0.617302	+	0.786726i	$0.711774\pi$
$20$	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	−0.534164	−	0.845381i	$-0.679373\pi$
$23$	2.23025	−	3.86291i	0.465040	−	0.805473i	0.999203	+	0.0399086i	$0.0127067\pi$
$24$		0			0
$25$	2.32383	+	4.02499i	0.464766	+	0.804999i
$26$	2.51459			0.493151
$27$		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
$31$	3.93346	−	6.81296i	0.706471	−	1.22364i	−0.259687	−	0.965693i	$-0.583620\pi$
$31$	3.93346	−	6.81296i	0.706471	−	1.22364i	0.966158	−	0.257951i	$-0.0830472\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.46050	−	2.52967i	−0.250475	−	0.433835i
$35$		0			0
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	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	−0.855156	−	0.518371i	$-0.826539\pi$
$41$	0.136673	−	0.236725i	0.0213448	−	0.0369702i	0.876500	+	0.481401i	$0.159872\pi$
$42$		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	$-0.490739\pi$
$44$	0.593579			0.0894855
$45$		0			0
$46$	−4.46050			−0.657666
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.843377	+	0.537323i	$0.180564\pi$
$47$	6.08113	+	10.5328i	0.887023	+	1.53637i	0.0436467	+	0.999047i	$0.486102\pi$
$48$		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
$53$	8.05408			1.10631			0.553157	−	0.833077i	$-0.313423\pi$
$53$	8.05408			1.10631			0.553157	+	0.833077i	$0.313423\pi$
$54$		0			0
$55$	−0.352336			−0.0475090
$56$		0			0
$57$		0			0
$58$	3.09718	−	5.36447i	0.406679	−	0.704389i
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	−0.434325	−	0.900756i	$-0.643013\pi$
$59$	4.32383	−	7.48910i	0.562915	−	0.974997i	0.997240	−	0.0742412i	$-0.0236535\pi$
$60$		0			0
$61$	3.32383	+	5.75705i	0.425573	+	0.737114i	0.996474	−	0.0839050i	$-0.0267392\pi$
$61$	3.32383	+	5.75705i	0.425573	+	0.737114i	−0.570901	+	0.821019i	$0.693406\pi$
$62$	−7.86693			−0.999101
$63$		0			0
$64$	1.00000			0.125000
$65$	0.746304	+	1.29264i	0.0925676	+	0.160332i
$66$		0			0
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	−0.801635	−	0.597814i	$-0.796036\pi$
$67$	0.956906	−	1.65741i	0.116905	−	0.202485i	0.918540	+	0.395329i	$0.129369\pi$
$68$	−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
$73$	−7.91381			−0.926242			−0.463121	−	0.886295i	$-0.653270\pi$
$73$	−7.91381			−0.926242			−0.463121	+	0.886295i	$0.653270\pi$
$74$	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
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	0.999722	+	0.0235607i	$0.00750031\pi$
$79$	4.62422	+	8.00938i	0.520265	+	0.901126i	−0.479457	+	0.877565i	$0.659166\pi$
$80$	−0.593579			−0.0663642
$81$		0			0
$82$	−0.273346			−0.0301860
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	0.573513	−	0.819196i	$-0.305580\pi$
$83$	−3.85087	−	6.66991i	−0.422688	−	0.732118i	−0.996201	+	0.0870787i	$0.972247\pi$
$84$		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
$89$	−12.4356			−1.31817			−0.659085	−	0.752068i	$-0.729056\pi$
$89$	−12.4356			−1.31817			−0.659085	+	0.752068i	$0.729056\pi$
$90$		0			0
$91$		0			0
$92$	2.23025	+	3.86291i	0.232520	+	0.402736i
$93$		0			0
$94$	6.08113	−	10.5328i	0.627220	−	1.08638i
$95$	−1.59718	+	2.76639i	−0.163867	+	0.283826i
$96$		0			0
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	0.993448	+	0.114283i	$0.0364570\pi$
$97$	5.86693	+	10.1618i	0.595696	+	1.03178i	−0.397752	+	0.917493i	$0.630210\pi$
$98$		0			0
$99$		0			0
$100$	−4.64766			−0.464766
$101$	−0.811379	−	1.40535i	−0.0807352	−	0.139837i	0.822831	−	0.568287i	$-0.192393\pi$
$101$	−0.811379	−	1.40535i	−0.0807352	−	0.139837i	−0.903566	+	0.428449i	$0.859060\pi$
$102$		0			0
$103$	−3.19076	+	5.52655i	−0.314395	+	0.544548i	−0.979309	−	0.202372i	$-0.935135\pi$
$103$	−3.19076	+	5.52655i	−0.314395	+	0.544548i	0.664914	+	0.746920i	$0.268468\pi$
$104$	−1.25729	+	2.17770i	−0.123288	+	0.213541i
$105$		0			0
$106$	−4.02704	−	6.97504i	−0.391141	−	0.677476i
$107$	18.7089			1.80866			0.904331	−	0.426832i	$-0.140370\pi$
$107$	18.7089			1.80866			0.904331	+	0.426832i	$0.140370\pi$
$108$		0			0
$109$	2.86693			0.274602			0.137301	−	0.990529i	$-0.456157\pi$
$109$	2.86693			0.274602			0.137301	+	0.990529i	$0.456157\pi$
$110$	0.176168	+	0.305132i	0.0167970	+	0.0290932i
$111$		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
$116$	−6.19436			−0.575132
$117$		0			0
$118$	−8.64766			−0.796082
$119$		0			0
$120$		0			0
$121$	5.32383	−	9.22115i	0.483985	−	0.838286i
$122$	3.32383	−	5.75705i	0.300926	−	0.521218i
$123$		0			0
$124$	3.93346	+	6.81296i	0.353235	+	0.611822i
$125$	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	$0.315671\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	0.746304	−	1.29264i	0.0654552	−	0.113372i
$131$	−0.593579	+	1.02811i	−0.0518613	+	0.0898264i	−0.890791	−	0.454414i	$-0.849849\pi$
$131$	−0.593579	+	1.02811i	−0.0518613	+	0.0898264i	0.838929	+	0.544240i	$0.183182\pi$
$132$		0			0
$133$		0			0
$134$	−1.91381			−0.165328
$135$		0			0
$136$	2.92101			0.250475
$137$	1.26089	+	2.18393i	0.107725	+	0.186586i	0.914848	−	0.403797i	$-0.132310\pi$
$137$	1.26089	+	2.18393i	0.107725	+	0.186586i	−0.807123	+	0.590383i	$0.798977\pi$
$138$		0			0
$139$	2.45691	−	4.25549i	0.208392	−	0.360946i	−0.742816	−	0.669496i	$-0.766510\pi$
$139$	2.45691	−	4.25549i	0.208392	−	0.360946i	0.951208	+	0.308550i	$0.0998437\pi$
$140$		0			0
$141$		0			0
$142$	−7.20535	−	12.4800i	−0.604659	−	1.04730i
$143$	1.49261			0.124818
$144$		0			0
$145$	3.67684			0.305345
$146$	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	−0.213360	−	0.976974i	$-0.568441\pi$
$149$	9.02558	−	15.6328i	0.739404	−	1.28069i	0.952764	−	0.303712i	$-0.0982261\pi$
$150$		0			0
$151$	−0.823832	−	1.42692i	−0.0670425	−	0.116121i	0.830556	−	0.556936i	$-0.188023\pi$
$151$	−0.823832	−	1.42692i	−0.0670425	−	0.116121i	−0.897598	+	0.440815i	$0.854690\pi$
$152$	−5.38151			−0.436498
$153$		0			0
$154$		0			0
$155$	−2.33482	−	4.04403i	−0.187537	−	0.324824i
$156$		0			0
$157$	3.30039	−	5.71644i	0.263400	−	0.456222i	−0.703743	−	0.710454i	$-0.748490\pi$
$157$	3.30039	−	5.71644i	0.263400	−	0.456222i	0.967143	+	0.254233i	$0.0818229\pi$
$158$	4.62422	−	8.00938i	0.367883	−	0.637192i
$159$		0			0
$160$	0.296790	+	0.514055i	0.0234633	+	0.0406396i
$161$		0			0
$162$		0			0
$163$	5.98229			0.468569			0.234285	−	0.972168i	$-0.424725\pi$
$163$	5.98229			0.468569			0.234285	+	0.972168i	$0.424725\pi$
$164$	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	−0.973489	−	0.228733i	$-0.926542\pi$
$167$	−3.73025	+	6.46099i	−0.288656	+	0.499966i	0.684833	+	0.728700i	$0.259875\pi$
$168$		0			0
$169$	3.33842	+	5.78231i	0.256802	+	0.444793i
$170$	−1.73385			−0.132980
$171$		0			0
$172$	11.1623			0.851114
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.678562	−	0.734543i	$-0.737397\pi$
$173$	−12.8296	−	22.2215i	−0.975414	−	1.68947i	−0.296851	−	0.954924i	$-0.595937\pi$
$174$		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
$179$	15.0364			1.12387			0.561936	−	0.827181i	$-0.310057\pi$
$179$	15.0364			1.12387			0.561936	+	0.827181i	$0.310057\pi$
$180$		0			0
$181$	−0.0861875			−0.00640627			−0.00320313	−	0.999995i	$-0.501020\pi$
$181$	−0.0861875			−0.00640627			−0.00320313	+	0.999995i	$0.501020\pi$
$182$		0			0
$183$		0			0
$184$	2.23025	−	3.86291i	0.164416	−	0.284778i
$185$	−0.296790	+	0.514055i	−0.0218204	+	0.0377941i
$186$		0			0
$187$	−0.866926	−	1.50156i	−0.0633959	−	0.109805i
$188$	−12.1623			−0.887023
$189$		0			0
$190$	3.19436			0.231743
$191$	1.99115	+	3.44877i	0.144074	+	0.249544i	0.929027	−	0.370011i	$-0.120646\pi$
$191$	1.99115	+	3.44877i	0.144074	+	0.249544i	−0.784953	+	0.619555i	$0.787313\pi$
$192$		0			0
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	−0.961862	−	0.273534i	$-0.911808\pi$
$193$	−3.39037	+	5.87229i	−0.244044	+	0.422697i	0.717818	+	0.696230i	$0.245141\pi$
$194$	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
$199$	−5.61849			−0.398284			−0.199142	−	0.979971i	$-0.563815\pi$
$199$	−5.61849			−0.398284			−0.199142	+	0.979971i	$0.563815\pi$
$200$	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
$205$	−0.0811263	−	0.140515i	−0.00566611	−	0.00981399i
$206$	6.38151			0.444621
$207$		0			0
$208$	2.51459			0.174355
$209$	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
$215$	−6.62568			−0.451868
$216$		0			0
$217$		0			0
$218$	−1.43346	−	2.48283i	−0.0970863	−	0.168158i
$219$		0			0
$220$	0.176168	−	0.305132i	0.0118773	−	0.0205720i
$221$	−3.67257	+	6.36108i	−0.247044	+	0.427892i
$222$		0			0
$223$	12.6623	+	21.9317i	0.847927	+	1.46865i	0.883055	+	0.469270i	$0.155483\pi$
$223$	12.6623	+	21.9317i	0.847927	+	1.46865i	−0.0351275	+	0.999383i	$0.511184\pi$
$224$		0			0
$225$		0			0
$226$	−12.3202			−0.819530
$227$	2.40856	+	4.17174i	0.159862	+	0.276888i	0.934819	−	0.355126i	$-0.115562\pi$
$227$	2.40856	+	4.17174i	0.159862	+	0.276888i	−0.774957	+	0.632014i	$0.782229\pi$
$228$		0			0
$229$	4.64766	−	8.04999i	0.307126	−	0.531958i	−0.670606	−	0.741814i	$-0.733966\pi$
$229$	4.64766	−	8.04999i	0.307126	−	0.531958i	0.977732	+	0.209855i	$0.0672993\pi$
$230$	−1.32383	+	2.29294i	−0.0872909	+	0.151192i
$231$		0			0
$232$	3.09718	+	5.36447i	0.203340	+	0.352195i
$233$	0.194356			0.0127327			0.00636634	−	0.999980i	$-0.497974\pi$
$233$	0.194356			0.0127327			0.00636634	+	0.999980i	$0.497974\pi$
$234$		0			0
$235$	7.21926			0.470933
$236$	4.32383	+	7.48910i	0.281457	+	0.487499i
$237$		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	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	−10.6477			−0.684458
$243$		0			0
$244$	−6.64766			−0.425573
$245$		0			0
$246$		0			0
$247$	6.76615	−	11.7193i	0.430520	−	0.745682i
$248$	3.93346	−	6.81296i	0.249775	−	0.432623i
$249$		0			0
$250$	−2.86333	−	4.95943i	−0.181093	−	0.313662i
$251$	19.5438			1.23359			0.616796	−	0.787123i	$-0.288430\pi$
$251$	19.5438			1.23359			0.616796	+	0.787123i	$0.288430\pi$
$252$		0			0
$253$	−2.64766			−0.166457
$254$	−6.16731	−	10.6821i	−0.386972	−	0.670255i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.16372	−	7.21177i	0.259725	−	0.449858i	−0.706443	−	0.707770i	$-0.749701\pi$
$257$	4.16372	−	7.21177i	0.259725	−	0.449858i	0.966168	+	0.257912i	$0.0830346\pi$
$258$		0			0
$259$		0			0
$260$	−1.49261			−0.0925676
$261$		0			0
$262$	1.18716			0.0733429
$263$	−8.54523	−	14.8008i	−0.526921	−	0.912655i	−0.999508	−	0.0313704i	$-0.990013\pi$
$263$	−8.54523	−	14.8008i	−0.526921	−	0.912655i	0.472586	−	0.881284i	$-0.343320\pi$
$264$		0			0
$265$	2.39037	−	4.14024i	0.146839	−	0.254333i
$266$		0			0
$267$		0			0
$268$	0.956906	+	1.65741i	0.0584524	+	0.101242i
$269$	−10.0144			−0.610588			−0.305294	−	0.952258i	$-0.598755\pi$
$269$	−10.0144			−0.610588			−0.305294	+	0.952258i	$0.598755\pi$
$270$		0			0
$271$	−10.2091			−0.620161			−0.310081	−	0.950710i	$-0.600356\pi$
$271$	−10.2091			−0.620161			−0.310081	+	0.950710i	$0.600356\pi$
$272$	−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	−0.995352	−	0.0963074i	$-0.969297\pi$
$277$	−9.67111	−	16.7508i	−0.581081	−	1.00646i	0.414271	−	0.910154i	$-0.364037\pi$
$278$	−4.91381			−0.294711
$279$		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
$283$	8.17617	−	14.1615i	0.486023	−	0.841816i	−0.513848	−	0.857881i	$-0.671781\pi$
$283$	8.17617	−	14.1615i	0.486023	−	0.841816i	0.999871	+	0.0160650i	$0.00511388\pi$
$284$	−7.20535	+	12.4800i	−0.427559	+	0.740553i
$285$		0			0
$286$	−0.746304	−	1.29264i	−0.0441299	−	0.0764352i
$287$		0			0
$288$		0			0
$289$	−8.46770			−0.498100
$290$	−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	$-0.625736\pi$
$293$	10.3889	−	17.9941i	0.606926	−	1.05123i	0.991744	−	0.128235i	$-0.0409311\pi$
$294$		0			0
$295$	−2.56654	−	4.44537i	−0.149430	−	0.258820i
$296$	−1.00000			−0.0581238
$297$		0			0
$298$	−18.0512			−1.04568
$299$	5.60817	+	9.71363i	0.324329	+	0.561754i
$300$		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
$305$	3.94592			0.225942
$306$		0			0
$307$	−22.6768			−1.29424			−0.647118	−	0.762390i	$-0.724026\pi$
$307$	−22.6768			−1.29424			−0.647118	+	0.762390i	$0.724026\pi$
$308$		0			0
$309$		0			0
$310$	−2.33482	+	4.04403i	−0.132609	+	0.229686i
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	−0.943477	−	0.331439i	$-0.892466\pi$
$311$	−3.25729	+	5.64180i	−0.184704	+	0.319917i	0.758773	+	0.651356i	$0.225799\pi$
$312$		0			0
$313$	−0.133074	−	0.230492i	−0.00752181	−	0.0130282i	0.862240	−	0.506500i	$-0.169061\pi$
$313$	−0.133074	−	0.230492i	−0.00752181	−	0.0130282i	−0.869762	+	0.493472i	$0.835728\pi$
$314$	−6.60078			−0.372503
$315$		0			0
$316$	−9.24844			−0.520265
$317$	7.86186	+	13.6171i	0.441566	+	0.764815i	0.997806	−	0.0662067i	$-0.0210897\pi$
$317$	7.86186	+	13.6171i	0.441566	+	0.764815i	−0.556240	+	0.831022i	$0.687756\pi$
$318$		0			0
$319$	1.83842	−	3.18424i	0.102932	−	0.178283i
$320$	0.296790	−	0.514055i	0.0165910	−	0.0287365i
$321$		0			0
$322$		0			0
$323$	−15.7195			−0.874654
$324$		0			0
$325$	−11.6870			−0.648276
$326$	−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
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	0.971339	+	0.237697i	$0.0763925\pi$
$331$	12.5811	+	21.7912i	0.691521	+	1.19775i	−0.279818	+	0.960053i	$0.590274\pi$
$332$	7.70175			0.422688
$333$		0			0
$334$	7.46050			0.408221
$335$	−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
$341$	−4.66964			−0.252875
$342$		0			0
$343$		0			0
$344$	−5.58113	−	9.66679i	−0.300914	−	0.521199i
$345$		0			0
$346$	−12.8296	+	22.2215i	−0.689722	+	1.19463i
$347$	11.2719	−	19.5235i	0.605106	−	1.04808i	−0.386928	−	0.922110i	$-0.626464\pi$
$347$	11.2719	−	19.5235i	0.605106	−	1.04808i	0.992035	−	0.125965i	$-0.0402028\pi$
$348$		0			0
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	0.912286	−	0.409553i	$-0.134315\pi$
$349$	1.89543	+	3.28298i	0.101460	+	0.175734i	−0.810826	+	0.585287i	$0.800982\pi$
$350$		0			0
$351$		0			0
$352$	0.593579			0.0316379
$353$	3.41741	+	5.91913i	0.181890	+	0.315043i	0.942524	−	0.334138i	$-0.108445\pi$
$353$	3.41741	+	5.91913i	0.181890	+	0.315043i	−0.760634	+	0.649181i	$0.775112\pi$
$354$		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
$359$	−12.6447			−0.667364			−0.333682	−	0.942686i	$-0.608291\pi$
$359$	−12.6447			−0.667364			−0.333682	+	0.942686i	$0.608291\pi$
$360$		0			0
$361$	9.96070			0.524247
$362$	0.0430937	+	0.0746406i	0.00226496	+	0.00392302i
$363$		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	$-0.221299\pi$
$367$	−3.27188	−	5.66707i	−0.170791	−	0.295819i	−0.938697	+	0.344744i	$0.887966\pi$
$368$	−4.46050			−0.232520
$369$		0			0
$370$	0.593579			0.0308587
$371$		0			0
$372$		0			0
$373$	−4.71420	+	8.16524i	−0.244092	+	0.422780i	−0.961876	−	0.273486i	$-0.911823\pi$
$373$	−4.71420	+	8.16524i	−0.244092	+	0.422780i	0.717784	+	0.696266i	$0.245157\pi$
$374$	−0.866926	+	1.50156i	−0.0448277	+	0.0776438i
$375$		0			0
$376$	6.08113	+	10.5328i	0.313610	+	0.543189i
$377$	−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	$0.559848\pi$
$380$	−1.59718	−	2.76639i	−0.0819335	−	0.141913i
$381$		0			0
$382$	1.99115	−	3.44877i	0.101876	−	0.176454i
$383$	−12.0416	+	20.8567i	−0.615299	+	1.06573i	0.375033	+	0.927011i	$0.377631\pi$
$383$	−12.0416	+	20.8567i	−0.615299	+	1.06573i	−0.990332	+	0.138717i	$0.955702\pi$
$384$		0			0
$385$		0			0
$386$	6.78074			0.345130
$387$		0			0
$388$	−11.7339			−0.595696
$389$	−8.14913	−	14.1147i	−0.413177	−	0.715644i	0.582058	−	0.813147i	$-0.302248\pi$
$389$	−8.14913	−	14.1147i	−0.413177	−	0.715644i	−0.995235	+	0.0975035i	$0.968914\pi$
$390$		0			0
$391$	6.51459	−	11.2836i	0.329457	−	0.570636i
$392$		0			0
$393$		0			0
$394$	5.52918	+	9.57682i	0.278556	+	0.482473i
$395$	5.48968			0.276216
$396$		0			0
$397$	12.1724			0.610914			0.305457	−	0.952206i	$-0.401191\pi$
$397$	12.1724			0.610914			0.305457	+	0.952206i	$0.401191\pi$
$398$	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	0.0626819	+	0.998034i	$0.480035\pi$
$401$	−16.6804	+	28.8914i	−0.832981	+	1.44277i	−0.895663	+	0.444733i	$0.853299\pi$
$402$		0			0
$403$	9.89104	+	17.1318i	0.492708	+	0.853395i
$404$	1.62276			0.0807352
$405$		0			0
$406$		0			0
$407$	0.296790	+	0.514055i	0.0147113	+	0.0254808i
$408$		0			0
$409$	2.89037	−	5.00627i	0.142920	−	0.247544i	−0.785675	−	0.618639i	$-0.787684\pi$
$409$	2.89037	−	5.00627i	0.142920	−	0.247544i	0.928595	+	0.371095i	$0.121018\pi$
$410$	−0.0811263	+	0.140515i	−0.00400654	+	0.00693954i
$411$		0			0
$412$	−3.19076	−	5.52655i	−0.157197	−	0.272274i
$413$		0			0
$414$		0			0
$415$	−4.57160			−0.224411
$416$	−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	$0.438583\pi$
$419$	−15.4356	+	26.7352i	−0.754078	+	1.30610i	−0.945831	+	0.324659i	$0.894751\pi$
$420$		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	$0.862336\pi$
$422$	−19.3245			−0.940702
$423$		0			0
$424$	8.05408			0.391141
$425$	6.78794	+	11.7570i	0.329263	+	0.570301i
$426$		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
$431$	−28.1957			−1.35814			−0.679070	−	0.734074i	$-0.737617\pi$
$431$	−28.1957			−1.35814			−0.679070	+	0.734074i	$0.737617\pi$
$432$		0			0
$433$	12.5438			0.602815			0.301407	−	0.953495i	$-0.402544\pi$
$433$	12.5438			0.602815			0.301407	+	0.953495i	$0.402544\pi$
$434$		0			0
$435$		0			0
$436$	−1.43346	+	2.48283i	−0.0686504	+	0.118906i
$437$	−12.0021	+	20.7883i	−0.574140	+	0.994440i
$438$		0			0
$439$	−13.0203	−	22.5519i	−0.621426	−	1.07634i	−0.989220	−	0.146434i	$-0.953220\pi$
$439$	−13.0203	−	22.5519i	−0.621426	−	1.07634i	0.367794	−	0.929907i	$-0.380113\pi$
$440$	−0.352336			−0.0167970
$441$		0			0
$442$	7.34514			0.349373
$443$	−11.7865	−	20.4148i	−0.559992	−	0.969935i	−0.997496	−	0.0707186i	$-0.977471\pi$
$443$	−11.7865	−	20.4148i	−0.559992	−	0.969935i	0.437504	−	0.899216i	$-0.355863\pi$
$444$		0			0
$445$	−3.69076	+	6.39258i	−0.174959	+	0.303037i
$446$	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
$451$	−0.162253			−0.00764018
$452$	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
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	0.999648	+	0.0265293i	$0.00844554\pi$
$457$	11.1762	+	19.3577i	0.522799	+	0.905515i	−0.476849	+	0.878985i	$0.658221\pi$
$458$	−9.29533			−0.434342
$459$		0			0
$460$	2.64766			0.123448
$461$	3.98755	+	6.90663i	0.185719	+	0.321674i	0.943818	−	0.330464i	$-0.107205\pi$
$461$	3.98755	+	6.90663i	0.185719	+	0.321674i	−0.758100	+	0.652138i	$0.773872\pi$
$462$		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
$467$	33.5657			1.55324			0.776619	−	0.629971i	$-0.216933\pi$
$467$	33.5657			1.55324			0.776619	+	0.629971i	$0.216933\pi$
$468$		0			0
$469$		0			0
$470$	−3.60963	−	6.25206i	−0.166500	−	0.288386i
$471$		0			0
$472$	4.32383	−	7.48910i	0.199020	−	0.344714i
$473$	−3.31284	+	5.73801i	−0.152325	+	0.263834i
$474$		0			0
$475$	−12.5057	−	21.6606i	−0.573802	−	0.993855i
$476$		0			0
$477$		0			0
$478$	−13.6549			−0.624559
$479$	0.183560	+	0.317935i	0.00838707	+	0.0145268i	0.870188	−	0.492719i	$-0.163997\pi$
$479$	0.183560	+	0.317935i	0.00838707	+	0.0145268i	−0.861801	+	0.507246i	$0.830664\pi$
$480$		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
$485$	6.96497			0.316263
$486$		0			0
$487$	29.9076			1.35524			0.677621	−	0.735412i	$-0.263011\pi$
$487$	29.9076			1.35524			0.677621	+	0.735412i	$0.263011\pi$
$488$	3.32383	+	5.75705i	0.150463	+	0.260609i
$489$		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
$494$	−13.5323			−0.608847
$495$		0			0
$496$	−7.86693			−0.353235
$497$		0			0
$498$		0			0
$499$	9.50953	−	16.4710i	0.425705	−	0.737343i	−0.570781	−	0.821102i	$-0.693359\pi$
$499$	9.50953	−	16.4710i	0.425705	−	0.737343i	0.996486	+	0.0837597i	$0.0266928\pi$
$500$	−2.86333	+	4.95943i	−0.128052	+	0.221792i
$501$		0			0
$502$	−9.77188	−	16.9254i	−0.436141	−	0.755418i
$503$	37.7807			1.68456			0.842280	−	0.539040i	$-0.181213\pi$
$503$	37.7807			1.68456			0.842280	+	0.539040i	$0.181213\pi$
$504$		0			0
$505$	−0.963235			−0.0428634
$506$	1.32383	+	2.29294i	0.0588515	+	0.101934i
$507$		0			0
$508$	−6.16731	+	10.6821i	−0.273630	+	0.473942i
$509$	−5.60817	+	9.71363i	−0.248578	+	0.430549i	−0.963131	−	0.269031i	$-0.913296\pi$
$509$	−5.60817	+	9.71363i	−0.248578	+	0.430549i	0.714554	+	0.699581i	$0.246630\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−8.32743			−0.367307
$515$	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
$520$	0.746304	+	1.29264i	0.0327276	+	0.0566859i
$521$	−27.4720			−1.20357			−0.601785	−	0.798658i	$-0.705543\pi$
$521$	−27.4720			−1.20357			−0.601785	+	0.798658i	$0.705543\pi$
$522$		0			0
$523$	−22.1838			−0.970032			−0.485016	−	0.874505i	$-0.661186\pi$
$523$	−22.1838			−0.970032			−0.485016	+	0.874505i	$0.661186\pi$
$524$	−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
$530$	−4.78074			−0.207662
$531$		0			0
$532$		0			0
$533$	0.343677	+	0.595265i	0.0148863	+	0.0257838i
$534$		0			0
$535$	5.55262	−	9.61742i	0.240061	−	0.415797i
$536$	0.956906	−	1.65741i	0.0413321	−	0.0715892i
$537$		0			0
$538$	5.00720	+	8.67272i	0.215876	+	0.373908i
$539$		0			0
$540$		0			0
$541$	−29.8492			−1.28332			−0.641659	−	0.766990i	$-0.721754\pi$
$541$	−29.8492			−1.28332			−0.641659	+	0.766990i	$0.721754\pi$
$542$	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	$0.709904\pi$
$548$	−2.52179			−0.107725
$549$		0			0
$550$	−2.75876			−0.117634
$551$	−16.6675	−	28.8690i	−0.710060	−	1.22986i
$552$		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
$557$	30.1301			1.27666			0.638328	−	0.769765i	$-0.279626\pi$
$557$	30.1301			1.27666			0.638328	+	0.769765i	$0.279626\pi$
$558$		0			0
$559$	28.0685			1.18717
$560$		0			0
$561$		0			0
$562$	6.40136	−	11.0875i	0.270025	−	0.467697i
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	−0.819617	−	0.572912i	$-0.805814\pi$
$563$	2.04883	−	3.54867i	0.0863478	−	0.149559i	0.905965	+	0.423353i	$0.139147\pi$
$564$		0			0
$565$	−3.65652	−	6.33327i	−0.153831	−	0.266443i
$566$	−16.3523			−0.687340
$567$		0			0
$568$	14.4107			0.604659
$569$	3.11849	+	5.40138i	0.130734	+	0.226437i	0.923960	−	0.382490i	$-0.124933\pi$
$569$	3.11849	+	5.40138i	0.130734	+	0.226437i	−0.793226	+	0.608927i	$0.791600\pi$
$570$		0			0
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	0.205266	+	0.978706i	$0.434194\pi$
$571$	−17.8011	+	30.8323i	−0.744951	+	1.29029i	−0.950218	+	0.311587i	$0.899139\pi$
$572$	−0.746304	+	1.29264i	−0.0312045	+	0.0540479i
$573$		0			0
$574$		0			0
$575$	20.7309			0.864539
$576$		0			0
$577$	−46.2776			−1.92656			−0.963281	−	0.268494i	$-0.913474\pi$
$577$	−46.2776			−1.92656			−0.963281	+	0.268494i	$0.913474\pi$
$578$	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
$583$	−2.39037	−	4.14024i	−0.0989990	−	0.171471i
$584$	−7.91381			−0.327476
$585$		0			0
$586$	−20.7778			−0.858324
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	0.841727	−	0.539903i	$-0.181539\pi$
$587$	−1.13161	−	1.96001i	−0.0467066	−	0.0808982i	−0.888434	+	0.459005i	$0.848206\pi$
$588$		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
$593$	46.1957			1.89703			0.948515	−	0.316732i	$-0.102586\pi$
$593$	46.1957			1.89703			0.948515	+	0.316732i	$0.102586\pi$
$594$		0			0
$595$		0			0
$596$	9.02558	+	15.6328i	0.369702	+	0.640343i
$597$		0			0
$598$	5.60817	−	9.71363i	0.229335	−	0.397220i
$599$	−8.39037	+	14.5325i	−0.342821	+	0.593784i	−0.984955	−	0.172808i	$-0.944716\pi$
$599$	−8.39037	+	14.5325i	−0.342821	+	0.593784i	0.642134	+	0.766592i	$0.278049\pi$
$600$		0			0
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	0.726049	−	0.687643i	$-0.241355\pi$
$601$	−5.69961	−	9.87202i	−0.232492	−	0.402688i	−0.958541	+	0.284955i	$0.908021\pi$
$602$		0			0
$603$		0			0
$604$	1.64766			0.0670425
$605$	−3.16012	−	5.47348i	−0.128477	−	0.222529i
$606$		0			0
$607$	7.21420	−	12.4954i	0.292815	−	0.507171i	−0.681659	−	0.731670i	$-0.738741\pi$
$607$	7.21420	−	12.4954i	0.292815	−	0.507171i	0.974474	+	0.224499i	$0.0720745\pi$
$608$	2.69076	−	4.66053i	0.109125	−	0.189009i
$609$		0			0
$610$	−1.97296	−	3.41726i	−0.0798827	−	0.138361i
$611$	−30.5831			−1.23726
$612$		0			0
$613$	−24.4107			−0.985939			−0.492969	−	0.870047i	$-0.664089\pi$
$613$	−24.4107			−0.985939			−0.492969	+	0.870047i	$0.664089\pi$
$614$	11.3384	+	19.6387i	0.457581	+	0.792554i
$615$		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	0.830678	+	0.556753i	$0.187953\pi$
$619$	22.3296	+	38.6759i	0.897501	+	1.55452i	0.0668227	+	0.997765i	$0.478714\pi$
$620$	4.66964			0.187537
$621$		0			0
$622$	6.51459			0.261211
$623$		0			0
$624$		0			0
$625$	−9.91955	+	17.1812i	−0.396782	+	0.687246i
$626$	−0.133074	+	0.230492i	−0.00531873	+	0.00921230i
$627$		0			0
$628$	3.30039	+	5.71644i	0.131700	+	0.228111i
$629$	−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	$0.269482\pi$
$632$	4.62422	+	8.00938i	0.183942	+	0.318596i
$633$		0			0
$634$	7.86186	−	13.6171i	0.312235	−	0.540806i
$635$	3.66079	−	6.34067i	0.145274	−	0.251622i
$636$		0			0
$637$		0			0
$638$	−3.67684			−0.145568
$639$		0			0
$640$	−0.593579			−0.0234633
$641$	15.3940	+	26.6631i	0.608025	+	1.05313i	0.991566	+	0.129606i	$0.0413714\pi$
$641$	15.3940	+	26.6631i	0.608025	+	1.05313i	−0.383540	+	0.923524i	$0.625295\pi$
$642$		0			0
$643$	−13.7345	+	23.7889i	−0.541637	+	0.938142i	0.457174	+	0.889378i	$0.348862\pi$
$643$	−13.7345	+	23.7889i	−0.541637	+	0.938142i	−0.998810	+	0.0487649i	$0.984471\pi$
$644$		0			0
$645$		0			0
$646$	7.85973	+	13.6134i	0.309237	+	0.535614i
$647$	−13.2704			−0.521714			−0.260857	−	0.965377i	$-0.584005\pi$
$647$	−13.2704			−0.521714			−0.260857	+	0.965377i	$0.584005\pi$
$648$		0			0
$649$	−5.13307			−0.201491
$650$	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	−0.983562	−	0.180571i	$-0.942205\pi$
$653$	−8.57081	+	14.8451i	−0.335402	+	0.580933i	0.648160	+	0.761504i	$0.275539\pi$
$654$		0			0
$655$	0.352336	+	0.610265i	0.0137669	+	0.0238450i
$656$	−0.273346			−0.0106724
$657$		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
$661$	−17.1680	+	29.7358i	−0.667757	+	1.15659i	0.310773	+	0.950484i	$0.399412\pi$
$661$	−17.1680	+	29.7358i	−0.667757	+	1.15659i	−0.978530	+	0.206105i	$0.933921\pi$
$662$	12.5811	−	21.7912i	0.488979	−	0.846937i
$663$		0			0
$664$	−3.85087	−	6.66991i	−0.149443	−	0.258843i
$665$		0			0
$666$		0			0
$667$	27.6300			1.06984
$668$	−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	$0.929277\pi$
$674$	18.7339			0.721601
$675$		0			0
$676$	−6.67684			−0.256802
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	0.786345	−	0.617788i	$-0.211971\pi$
$677$	−3.69076	−	6.39258i	−0.141847	−	0.245687i	−0.928192	+	0.372101i	$0.878638\pi$
$678$		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
$683$	9.59785			0.367252			0.183626	−	0.982996i	$-0.441217\pi$
$683$	9.59785			0.367252			0.183626	+	0.982996i	$0.441217\pi$
$684$		0			0
$685$	1.49688			0.0571929
$686$		0			0
$687$		0			0
$688$	−5.58113	+	9.66679i	−0.212778	+	0.368543i
$689$	−10.1264	+	17.5394i	−0.385783	+	0.668197i
$690$		0			0
$691$	7.07227	+	12.2495i	0.269042	+	0.465994i	0.968615	−	0.248567i	$-0.0799597\pi$
$691$	7.07227	+	12.2495i	0.269042	+	0.465994i	−0.699573	+	0.714561i	$0.746626\pi$
$692$	25.6591			0.975414
$693$		0			0
$694$	−22.5438			−0.855750
$695$	−1.45837	−	2.52597i	−0.0553191	−	0.0958155i
$696$		0			0
$697$	0.399223	−	0.691475i	0.0151217	−	0.0261915i
$698$	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
$703$	5.38151			0.202968
$704$	−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
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	0.947528	−	0.319673i	$-0.103573\pi$
$709$	5.24338	+	9.08180i	0.196919	+	0.341074i	−0.750609	+	0.660747i	$0.770240\pi$
$710$	−8.55389			−0.321022
$711$		0			0
$712$	−12.4356			−0.466044
$713$	−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
$719$	2.23990			0.0835340			0.0417670	−	0.999127i	$-0.486701\pi$
$719$	2.23990			0.0835340			0.0417670	+	0.999127i	$0.486701\pi$
$720$		0			0
$721$		0			0
$722$	−4.98035	−	8.62622i	−0.185349	−	0.321035i
$723$		0			0
$724$	0.0430937	−	0.0746406i	0.00160157	−	0.00277399i
$725$	−14.3946	+	24.9322i	−0.534604	+	0.925961i
$726$		0			0
$727$	0.185023	+	0.320469i	0.00686211	+	0.0118855i	0.869436	−	0.494045i	$-0.164482\pi$
$727$	0.185023	+	0.320469i	0.00686211	+	0.0118855i	−0.862574	+	0.505931i	$0.831149\pi$
$728$		0			0
$729$		0			0
$730$	4.69748			0.173861
$731$	−16.3025	−	28.2368i	−0.602971	−	1.04438i
$732$		0			0
$733$	−7.00953	+	12.1409i	−0.258903	+	0.448433i	−0.965948	−	0.258735i	$-0.916694\pi$
$733$	−7.00953	+	12.1409i	−0.258903	+	0.448433i	0.707045	+	0.707168i	$0.250028\pi$
$734$	−3.27188	+	5.66707i	−0.120767	+	0.209175i
$735$		0			0
$736$	2.23025	+	3.86291i	0.0822082	+	0.142389i
$737$	−1.13600			−0.0418451
$738$		0			0
$739$	−26.7745			−0.984916			−0.492458	−	0.870336i	$-0.663901\pi$
$739$	−26.7745			−0.984916			−0.492458	+	0.870336i	$0.663901\pi$
$740$	−0.296790	−	0.514055i	−0.0109102	−	0.0188970i
$741$		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
$746$	9.42840			0.345198
$747$		0			0
$748$	1.73385			0.0633959
$749$		0			0
$750$		0			0
$751$	−5.75729	+	9.97193i	−0.210087	+	0.363881i	−0.951741	−	0.306901i	$-0.900708\pi$
$751$	−5.75729	+	9.97193i	−0.210087	+	0.363881i	0.741655	+	0.670782i	$0.234041\pi$
$752$	6.08113	−	10.5328i	0.221756	−	0.384092i
$753$		0			0
$754$	7.78813	+	13.4894i	0.283627	+	0.491256i
$755$	−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	$0.589376\pi$
$758$	3.63881	+	6.30260i	0.132168	+	0.228921i
$759$		0			0
$760$	−1.59718	+	2.76639i	−0.0579357	+	0.100348i
$761$	−0.850874	+	1.47376i	−0.0308442	+	0.0534236i	−0.881035	−	0.473050i	$-0.843153\pi$
$761$	−0.850874	+	1.47376i	−0.0308442	+	0.0534236i	0.850191	+	0.526474i	$0.176486\pi$
$762$		0			0
$763$		0			0
$764$	−3.98229			−0.144074
$765$		0			0
$766$	24.0833			0.870164
$767$	10.8727	+	18.8320i	0.392589	+	0.679984i
$768$		0			0
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.00765823	−	0.999971i	$-0.497562\pi$
$769$	24.1211	−	41.7790i	0.869829	−	1.50659i	0.862171	−	0.506618i	$-0.169104\pi$
$770$		0			0
$771$		0			0
$772$	−3.39037	−	5.87229i	−0.122022	−	0.211348i
$773$	6.20487			0.223174			0.111587	−	0.993755i	$-0.464407\pi$
$773$	6.20487			0.223174			0.111587	+	0.993755i	$0.464407\pi$
$774$		0			0
$775$	36.5628			1.31338
$776$	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
$782$	−13.0292			−0.465922
$783$		0			0
$784$		0			0
$785$	−1.95904	−	3.39316i	−0.0699212	−	0.121107i
$786$		0			0
$787$	−3.04883	+	5.28073i	−0.108679	+	0.188238i	−0.915235	−	0.402920i	$-0.867995\pi$
$787$	−3.04883	+	5.28073i	−0.108679	+	0.188238i	0.806556	+	0.591157i	$0.201329\pi$
$788$	5.52918	−	9.57682i	0.196969	−	0.341160i
$789$		0			0
$790$	−2.74484	−	4.75420i	−0.0976571	−	0.169147i
$791$		0			0
$792$		0			0
$793$	−16.7161			−0.593608
$794$	−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	−0.734371	−	0.678749i	$-0.762523\pi$
$797$	6.22860	−	10.7882i	0.220628	−	0.382139i	0.954999	+	0.296609i	$0.0958559\pi$
$798$		0			0
$799$	17.7630	+	30.7665i	0.628411	+	1.08844i
$800$	−4.64766			−0.164320
$801$		0			0
$802$	33.3609			1.17801
$803$	2.34874	+	4.06813i	0.0828852	+	0.143561i
$804$		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
$809$	−5.63288			−0.198042			−0.0990208	−	0.995085i	$-0.531571\pi$
$809$	−5.63288			−0.198042			−0.0990208	+	0.995085i	$0.531571\pi$
$810$		0			0
$811$	−45.6414			−1.60269			−0.801344	−	0.598204i	$-0.795881\pi$
$811$	−45.6414			−1.60269			−0.801344	+	0.598204i	$0.795881\pi$
$812$		0			0
$813$		0			0
$814$	0.296790	−	0.514055i	0.0104025	−	0.0180176i
$815$	1.77548	−	3.07523i	0.0621924	−	0.107720i
$816$		0			0
$817$	30.0349	+	52.0220i	1.05079	+	1.82002i
$818$	−5.78074			−0.202119
$819$		0			0
$820$	0.162253			0.00566611
$821$	16.3473	+	28.3143i	0.570524	+	0.988176i	0.996512	+	0.0834476i	$0.0265931\pi$
$821$	16.3473	+	28.3143i	0.570524	+	0.988176i	−0.425988	+	0.904729i	$0.640074\pi$
$822$		0			0
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	−0.760591	−	0.649231i	$-0.775091\pi$
$823$	5.21994	−	9.04119i	0.181956	−	0.315156i	0.942546	+	0.334075i	$0.108424\pi$
$824$	−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
$829$	26.2091			0.910281			0.455141	−	0.890420i	$-0.349589\pi$
$829$	26.2091			0.910281			0.455141	+	0.890420i	$0.349589\pi$
$830$	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
$835$	2.21420	+	3.83511i	0.0766256	+	0.132719i
$836$	−3.19436			−0.110479
$837$		0			0
$838$	30.8712			1.06643
$839$	−11.1886	−	19.3793i	−0.386274	−	0.669046i	0.605671	−	0.795715i	$-0.292905\pi$
$839$	−11.1886	−	19.3793i	−0.386274	−	0.669046i	−0.991945	+	0.126669i	$0.959571\pi$
$840$		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
$845$	3.96324			0.136339
$846$		0			0
$847$		0			0
$848$	−4.02704	−	6.97504i	−0.138289	−	0.239524i
$849$		0			0
$850$	6.78794	−	11.7570i	0.232824	−	0.403263i
$851$	−2.23025	+	3.86291i	−0.0764521	+	0.132419i
$852$		0			0
$853$	4.96264	+	8.59555i	0.169918	+	0.294306i	0.938391	−	0.345576i	$-0.112317\pi$
$853$	4.96264	+	8.59555i	0.169918	+	0.294306i	−0.768473	+	0.639882i	$0.778983\pi$
$854$		0			0
$855$		0			0
$856$	18.7089			0.639459
$857$	3.89776	+	6.75112i	0.133145	+	0.230614i	0.924887	−	0.380241i	$-0.124159\pi$
$857$	3.89776	+	6.75112i	0.133145	+	0.230614i	−0.791742	+	0.610855i	$0.790826\pi$
$858$		0			0
$859$	−8.17111	+	14.1528i	−0.278795	+	0.482886i	−0.971085	−	0.238732i	$-0.923268\pi$
$859$	−8.17111	+	14.1528i	−0.278795	+	0.482886i	0.692291	+	0.721619i	$0.256602\pi$
$860$	3.31284	−	5.73801i	0.112967	−	0.195664i
$861$		0			0
$862$	14.0979	+	24.4182i	0.480175	+	0.831687i
$863$	1.46050			0.0497162			0.0248581	−	0.999691i	$-0.492087\pi$
$863$	1.46050			0.0497162			0.0248581	+	0.999691i	$0.492087\pi$
$864$		0			0
$865$	−15.2307			−0.517860
$866$	−6.27188	−	10.8632i	−0.213127	−	0.369147i
$867$		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
$872$	2.86693			0.0970863
$873$		0			0
$874$	24.0043			0.811957
$875$		0			0
$876$		0			0
$877$	1.20467	−	2.08655i	0.0406789	−	0.0704579i	−0.844969	−	0.534815i	$-0.820381\pi$
$877$	1.20467	−	2.08655i	0.0406789	−	0.0704579i	0.885648	+	0.464357i	$0.153715\pi$
$878$	−13.0203	+	22.5519i	−0.439415	+	0.761088i
$879$		0			0
$880$	0.176168	+	0.305132i	0.00593863	+	0.0102860i
$881$	18.9607			0.638802			0.319401	−	0.947620i	$-0.396518\pi$
$881$	18.9607			0.638802			0.319401	+	0.947620i	$0.396518\pi$
$882$		0			0
$883$	3.64008			0.122498			0.0612492	−	0.998123i	$-0.480492\pi$
$883$	3.64008			0.122498			0.0612492	+	0.998123i	$0.480492\pi$
$884$	−3.67257	−	6.36108i	−0.123522	−	0.213946i
$885$		0			0
$886$	−11.7865	+	20.4148i	−0.395974	+	0.685848i
$887$	−12.2286	+	21.1805i	−0.410596	+	0.711173i	−0.994955	−	0.100322i	$-0.968013\pi$
$887$	−12.2286	+	21.1805i	−0.410596	+	0.711173i	0.584359	+	0.811495i	$0.301346\pi$
$888$		0			0
$889$		0			0
$890$	7.38151			0.247429
$891$		0			0
$892$	−25.3245			−0.847927
$893$	−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
$898$	6.84348	+	11.8533i	0.228370	+	0.395548i
$899$	48.7305			1.62525
$900$		0			0
$901$	23.5261			0.783767
$902$	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	0.770601	−	0.637318i	$-0.219956\pi$
$907$	−5.01838	−	8.69209i	−0.166633	−	0.288616i	−0.937234	+	0.348701i	$0.886623\pi$
$908$	−4.81711			−0.159862
$909$		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
$913$	−2.28580	+	3.95912i	−0.0756489	+	0.131028i
$914$	11.1762	−	19.3577i	0.369675	−	0.640296i
$915$		0			0
$916$	4.64766	+	8.04999i	0.153563	+	0.265979i
$917$		0			0
$918$		0			0
$919$	−21.7821			−0.718525			−0.359262	−	0.933237i	$-0.616972\pi$
$919$	−21.7821			−0.718525			−0.359262	+	0.933237i	$0.616972\pi$
$920$	−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
$926$	28.7352			0.944297
$927$		0			0
$928$	−6.19436			−0.203340
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	−0.998975	−	0.0452622i	$-0.985588\pi$
$929$	−16.4189	−	28.4383i	−0.538686	−	0.933031i	0.460289	−	0.887769i	$-0.347746\pi$
$930$		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
$935$	−1.02918			−0.0336577
$936$		0			0
$937$	−8.78074			−0.286854			−0.143427	−	0.989661i	$-0.545812\pi$
$937$	−8.78074			−0.286854			−0.143427	+	0.989661i	$0.545812\pi$
$938$		0			0
$939$		0			0
$940$	−3.60963	+	6.25206i	−0.117733	+	0.203920i
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	−0.829161	−	0.559010i	$-0.811181\pi$
$941$	2.13307	−	3.69459i	0.0695362	−	0.120440i	0.898697	+	0.438570i	$0.144515\pi$
$942$		0			0
$943$	−0.609631	−	1.05591i	−0.0198523	−	0.0343852i
$944$	−8.64766			−0.281457
$945$		0			0
$946$	6.62568			0.215420
$947$	−11.5292	−	19.9691i	−0.374648	−	0.648909i	0.615626	−	0.788038i	$-0.288903\pi$
$947$	−11.5292	−	19.9691i	−0.374648	−	0.648909i	−0.990274	+	0.139129i	$0.955570\pi$
$948$		0			0
$949$	9.94999	−	17.2339i	0.322990	−	0.559436i
$950$	−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
$955$	2.36381			0.0764910
$956$	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
$961$	−15.4443	−	26.7502i	−0.498202	−	0.862911i
$962$	−2.51459			−0.0810736
$963$		0			0
$964$	−13.0000			−0.418702
$965$	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
$971$	−31.9794			−1.02627			−0.513133	−	0.858309i	$-0.671515\pi$
$971$	−31.9794			−1.02627			−0.513133	+	0.858309i	$0.671515\pi$
$972$		0			0
$973$		0			0
$974$	−14.9538	−	25.9007i	−0.479150	−	0.829913i
$975$		0			0
$976$	3.32383	−	5.75705i	0.106393	−	0.184279i
$977$	−13.7104	+	23.7471i	−0.438635	+	0.759738i	−0.997584	−	0.0694638i	$-0.977871\pi$
$977$	−13.7104	+	23.7471i	−0.438635	+	0.759738i	0.558950	+	0.829202i	$0.311204\pi$
$978$		0			0
$979$	3.69076	+	6.39258i	0.117957	+	0.204308i
$980$		0			0
$981$		0			0
$982$	−0.510317			−0.0162849
$983$	−29.5782	−	51.2309i	−0.943398	−	1.63401i	−0.758927	−	0.651175i	$-0.774276\pi$
$983$	−29.5782	−	51.2309i	−0.943398	−	1.63401i	−0.184471	−	0.982838i	$-0.559057\pi$
$984$		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
$989$	−49.7893			−1.58321
$990$		0			0
$991$	−12.8377			−0.407804			−0.203902	−	0.978991i	$-0.565362\pi$
$991$	−12.8377			−0.407804			−0.203902	+	0.978991i	$0.565362\pi$
$992$	3.93346	+	6.81296i	0.124888	+	0.216312i
$993$		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	$-0.137488\pi$
$997$	2.89037	+	5.00627i	0.0915389	+	0.158550i	−0.816620	+	0.577176i	$0.804155\pi$
$998$	−19.0191			−0.602038
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.l.1765.2		6
3.2	odd	2		882.2.f.n.589.1		6
7.2	even	3		378.2.h.c.361.2		6
7.3	odd	6		2646.2.e.p.1549.2		6
7.4	even	3		378.2.e.d.37.2		6
7.5	odd	6		2646.2.h.o.361.2		6
7.6	odd	2		2646.2.f.m.1765.2		6
9.2	odd	6		882.2.f.n.295.1		6
9.4	even	3		7938.2.a.ca.1.2		3
9.5	odd	6		7938.2.a.bv.1.2		3
9.7	even	3	inner	2646.2.f.l.883.2		6
21.2	odd	6		126.2.h.d.67.2	yes	6
21.5	even	6		882.2.h.p.67.2		6
21.11	odd	6		126.2.e.c.121.2	yes	6
21.17	even	6		882.2.e.o.373.2		6
21.20	even	2		882.2.f.o.589.3		6
28.11	odd	6		3024.2.q.g.2305.2		6
28.23	odd	6		3024.2.t.h.1873.2		6
63.2	odd	6		126.2.e.c.25.2	✓	6
63.4	even	3		1134.2.g.l.163.2		6
63.11	odd	6		126.2.h.d.79.2	yes	6
63.13	odd	6		7938.2.a.bz.1.2		3
63.16	even	3		378.2.e.d.235.2		6
63.20	even	6		882.2.f.o.295.3		6
63.23	odd	6		1134.2.g.m.487.2		6
63.25	even	3		378.2.h.c.289.2		6
63.32	odd	6		1134.2.g.m.163.2		6
63.34	odd	6		2646.2.f.m.883.2		6
63.38	even	6		882.2.h.p.79.2		6
63.41	even	6		7938.2.a.bw.1.2		3
63.47	even	6		882.2.e.o.655.2		6
63.52	odd	6		2646.2.h.o.667.2		6
63.58	even	3		1134.2.g.l.487.2		6
63.61	odd	6		2646.2.e.p.2125.2		6
84.11	even	6		1008.2.q.g.625.2		6
84.23	even	6		1008.2.t.h.193.2		6
252.11	even	6		1008.2.t.h.961.2		6
252.79	odd	6		3024.2.q.g.2881.2		6
252.151	odd	6		3024.2.t.h.289.2		6
252.191	even	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	63.2	odd	6
126.2.e.c.121.2	yes	6	21.11	odd	6
126.2.h.d.67.2	yes	6	21.2	odd	6
126.2.h.d.79.2	yes	6	63.11	odd	6
378.2.e.d.37.2		6	7.4	even	3
378.2.e.d.235.2		6	63.16	even	3
378.2.h.c.289.2		6	63.25	even	3
378.2.h.c.361.2		6	7.2	even	3
882.2.e.o.373.2		6	21.17	even	6
882.2.e.o.655.2		6	63.47	even	6
882.2.f.n.295.1		6	9.2	odd	6
882.2.f.n.589.1		6	3.2	odd	2
882.2.f.o.295.3		6	63.20	even	6
882.2.f.o.589.3		6	21.20	even	2
882.2.h.p.67.2		6	21.5	even	6
882.2.h.p.79.2		6	63.38	even	6
1008.2.q.g.529.2		6	252.191	even	6
1008.2.q.g.625.2		6	84.11	even	6
1008.2.t.h.193.2		6	84.23	even	6
1008.2.t.h.961.2		6	252.11	even	6
1134.2.g.l.163.2		6	63.4	even	3
1134.2.g.l.487.2		6	63.58	even	3
1134.2.g.m.163.2		6	63.32	odd	6
1134.2.g.m.487.2		6	63.23	odd	6
2646.2.e.p.1549.2		6	7.3	odd	6
2646.2.e.p.2125.2		6	63.61	odd	6
2646.2.f.l.883.2		6	9.7	even	3	inner
2646.2.f.l.1765.2		6	1.1	even	1	trivial
2646.2.f.m.883.2		6	63.34	odd	6
2646.2.f.m.1765.2		6	7.6	odd	2
2646.2.h.o.361.2		6	7.5	odd	6
2646.2.h.o.667.2		6	63.52	odd	6
3024.2.q.g.2305.2		6	28.11	odd	6
3024.2.q.g.2881.2		6	252.79	odd	6
3024.2.t.h.289.2		6	252.151	odd	6
3024.2.t.h.1873.2		6	28.23	odd	6
7938.2.a.bv.1.2		3	9.5	odd	6
7938.2.a.bw.1.2		3	63.41	even	6
7938.2.a.bz.1.2		3	63.13	odd	6
7938.2.a.ca.1.2		3	9.4	even	3

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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.296790 - 0.514055i) q^{5} +1.00000 q^{8} -0.593579 q^{10} +(-0.296790 - 0.514055i) q^{11} +(-1.25729 + 2.17770i) q^{13} +(-0.500000 - 0.866025i) q^{16} +2.92101 q^{17} -5.38151 q^{19} +(0.296790 + 0.514055i) q^{20} +(-0.296790 + 0.514055i) q^{22} +(2.23025 - 3.86291i) q^{23} +(2.32383 + 4.02499i) q^{25} +2.51459 q^{26} +(3.09718 + 5.36447i) q^{29} +(3.93346 - 6.81296i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.46050 - 2.52967i) q^{34} -1.00000 q^{37} +(2.69076 + 4.66053i) q^{38} +(0.296790 - 0.514055i) q^{40} +(0.136673 - 0.236725i) q^{41} +(-5.58113 - 9.66679i) q^{43} +0.593579 q^{44} -4.46050 q^{46} +(6.08113 + 10.5328i) q^{47} +(2.32383 - 4.02499i) q^{50} +(-1.25729 - 2.17770i) q^{52} +8.05408 q^{53} -0.352336 q^{55} +(3.09718 - 5.36447i) q^{58} +(4.32383 - 7.48910i) q^{59} +(3.32383 + 5.75705i) q^{61} -7.86693 q^{62} +1.00000 q^{64} +(0.746304 + 1.29264i) q^{65} +(0.956906 - 1.65741i) q^{67} +(-1.46050 + 2.52967i) q^{68} +14.4107 q^{71} -7.91381 q^{73} +(0.500000 + 0.866025i) q^{74} +(2.69076 - 4.66053i) q^{76} +(4.62422 + 8.00938i) q^{79} -0.593579 q^{80} -0.273346 q^{82} +(-3.85087 - 6.66991i) q^{83} +(0.866926 - 1.50156i) q^{85} +(-5.58113 + 9.66679i) q^{86} +(-0.296790 - 0.514055i) q^{88} -12.4356 q^{89} +(2.23025 + 3.86291i) q^{92} +(6.08113 - 10.5328i) q^{94} +(-1.59718 + 2.76639i) q^{95} +(5.86693 + 10.1618i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8}+O(q^{10}) \) 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8	\( 6 q - 3 q^{2} - 3 q^{4} - q^{5} + 6 q^{8} + 2 q^{10} + q^{11} + 8 q^{13} - 3 q^{16} - 8 q^{17} + 6 q^{19} - q^{20} + q^{22} + 7 q^{23} + 2 q^{25} - 16 q^{26} + 5 q^{29} + 20 q^{31} - 3 q^{32} + 4 q^{34} - 6 q^{37} - 3 q^{38} - q^{40} - 6 q^{43} - 2 q^{44} - 14 q^{46} + 9 q^{47} + 2 q^{50} + 8 q^{52} + 30 q^{53} - 26 q^{55} + 5 q^{58} + 14 q^{59} + 8 q^{61} - 40 q^{62} + 6 q^{64} + 12 q^{65} + q^{67} + 4 q^{68} - 14 q^{71} - 38 q^{73} + 3 q^{74} - 3 q^{76} + 5 q^{79} + 2 q^{80} - 2 q^{83} - 2 q^{85} - 6 q^{86} + q^{88} - 18 q^{89} + 7 q^{92} + 9 q^{94} + 4 q^{95} + 28 q^{97}+O(q^{100}) \) 6 * q - 3 * q^2 - 3 * q^4 - q^5 + 6 * q^8 + 2 * q^10 + q^11 + 8 * q^13 - 3 * q^16 - 8 * q^17 + 6 * q^19 - q^20 + q^22 + 7 * q^23 + 2 * q^25 - 16 * q^26 + 5 * q^29 + 20 * q^31 - 3 * q^32 + 4 * q^34 - 6 * q^37 - 3 * q^38 - q^40 - 6 * q^43 - 2 * q^44 - 14 * q^46 + 9 * q^47 + 2 * q^50 + 8 * q^52 + 30 * q^53 - 26 * q^55 + 5 * q^58 + 14 * q^59 + 8 * q^61 - 40 * q^62 + 6 * q^64 + 12 * q^65 + q^67 + 4 * q^68 - 14 * q^71 - 38 * q^73 + 3 * q^74 - 3 * q^76 + 5 * q^79 + 2 * q^80 - 2 * q^83 - 2 * q^85 - 6 * q^86 + q^88 - 18 * q^89 + 7 * q^92 + 9 * q^94 + 4 * q^95 + 28 * q^97

Introduction

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