LMFDB - Embedded newform 2646.2.m.a.1763.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2646,2,Mod(881,2646)]

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([5, 3]))

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

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

chi := DirichletCharacter("2646.881");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2646 = 2 \cdot 3^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2646.m (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 23 x^{14} - 8 x^{13} - 131 x^{12} + 380 x^{11} - 289 x^{10} - 880 x^{9} + \cdots + 6561 $ x^16 - 8x^15 + 23x^14 - 8x^13 - 131x^12 + 380x^11 - 289x^10 - 880x^9 + 2785x^8 - 2640x^7 - 2601x^6 + 10260x^5 - 10611x^4 - 1944x^3 + 16767x^2 - 17496*x + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3^{4} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1763.2
Root			$1.58110 - 0.707199i$ of defining polynomial
Character	$\chi$	$=$	2646.1763
Dual form			2646.2.m.a.881.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} -1.00000i q^{8} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} -1.00000i q^{8} +0.900258i q^{10} +(-2.70900 - 1.56404i) q^{11} +(1.99033 - 1.14912i) q^{13} +(-0.500000 + 0.866025i) q^{16} +5.15276 q^{17} -2.74947i q^{19} +(0.450129 - 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +(-1.48584 + 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} -2.29824 q^{26} +(1.85590 + 1.07151i) q^{29} +(-8.66298 + 5.00158i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.46242 - 2.57638i) q^{34} +9.47403 q^{37} +(-1.37474 + 2.38111i) q^{38} +(-0.779646 + 0.450129i) q^{40} +(1.22134 + 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} -3.12809i q^{44} +1.71570 q^{46} +(-3.93034 + 6.80755i) q^{47} +(-3.62824 + 2.09477i) q^{50} +(1.99033 + 1.14912i) q^{52} -13.9411i q^{53} +2.81608i q^{55} +(-1.07151 - 1.85590i) q^{58} +(-3.99222 - 6.91472i) q^{59} +(-6.28224 - 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 - 1.03450i) q^{65} +(-1.83525 - 3.17875i) q^{67} +(2.57638 + 4.46242i) q^{68} +14.1484i q^{71} -12.6082i q^{73} +(-8.20475 - 4.73701i) q^{74} +(2.38111 - 1.37474i) q^{76} +(3.27402 - 5.67077i) q^{79} +0.900258 q^{80} -2.44268i q^{82} +(0.184437 - 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(0.473119 - 0.273155i) q^{86} +(-1.56404 + 2.70900i) q^{88} -12.0049 q^{89} +(-1.48584 - 0.857850i) q^{92} +(6.80755 - 3.93034i) q^{94} +(-2.14361 + 1.23762i) q^{95} +(-8.86815 - 5.12003i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4}+O(q^{10}) $ 16 * q + 8 * q^4	$ 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) $ 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	0.747645	−	0.664099i	$-0.231185\pi$
$5$	−0.450129	−	0.779646i	−0.201304	−	0.348668i	−0.948949	+	0.315430i	$0.897851\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$			0.900258i			0.284687i
$11$	−2.70900	−	1.56404i	−0.816795	−	0.471577i	0.0325150	−	0.999471i	$-0.489648\pi$
$11$	−2.70900	−	1.56404i	−0.816795	−	0.471577i	−0.849310	+	0.527894i	$0.822982\pi$
$12$		0			0
$13$	1.99033	−	1.14912i	0.552019	−	0.318708i	−0.197917	−	0.980219i	$-0.563418\pi$
$13$	1.99033	−	1.14912i	0.552019	−	0.318708i	0.749936	+	0.661511i	$0.230084\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	5.15276			1.24973			0.624863	−	0.780734i	$-0.285155\pi$
$17$	5.15276			1.24973			0.624863	+	0.780734i	$0.285155\pi$
$18$		0			0
$19$		−	2.74947i		−	0.630772i	−0.948964	−	0.315386i	$-0.897866\pi$
$19$		−	2.74947i		−	0.630772i	0.948964	−	0.315386i	$-0.102134\pi$
$20$	0.450129	−	0.779646i	0.100652	−	0.174334i
$21$		0			0
$22$	1.56404	+	2.70900i	0.333455	+	0.577561i
$23$	−1.48584	+	0.857850i	−0.309819	+	0.178874i	−0.646845	−	0.762621i	$-0.723912\pi$
$23$	−1.48584	+	0.857850i	−0.309819	+	0.178874i	0.337027	+	0.941495i	$0.390579\pi$
$24$		0			0
$25$	2.09477	−	3.62824i	0.418954	−	0.725649i
$26$	−2.29824			−0.450722
$27$		0			0
$28$		0			0
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	0.662319	−	0.749222i	$-0.269572\pi$
$29$	1.85590	+	1.07151i	0.344633	+	0.198974i	−0.317686	+	0.948196i	$0.602906\pi$
$30$		0			0
$31$	−8.66298	+	5.00158i	−1.55592	+	0.898309i	−0.558277	+	0.829655i	$0.688537\pi$
$31$	−8.66298	+	5.00158i	−1.55592	+	0.898309i	−0.997640	+	0.0686548i	$0.978129\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$		0			0
$34$	−4.46242	−	2.57638i	−0.765298	−	0.441845i
$35$		0			0
$36$		0			0
$37$	9.47403			1.55752			0.778760	−	0.627321i	$-0.215849\pi$
$37$	9.47403			1.55752			0.778760	+	0.627321i	$0.215849\pi$
$38$	−1.37474	+	2.38111i	−0.223012	+	0.386267i
$39$		0			0
$40$	−0.779646	+	0.450129i	−0.123273	+	0.0711716i
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	0.945496	−	0.325634i	$-0.105578\pi$
$41$	1.22134	+	2.11542i	0.190741	+	0.330373i	−0.754755	+	0.656007i	$0.772244\pi$
$42$		0			0
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	−0.886102	−	0.463491i	$-0.846597\pi$
$43$	−0.273155	+	0.473119i	−0.0416558	+	0.0721499i	0.844446	+	0.535641i	$0.179930\pi$
$44$		−	3.12809i		−	0.471577i
$45$		0			0
$46$	1.71570			0.252966
$47$	−3.93034	+	6.80755i	−0.573299	+	0.992983i	0.422925	+	0.906165i	$0.361003\pi$
$47$	−3.93034	+	6.80755i	−0.573299	+	0.992983i	−0.996224	+	0.0868184i	$0.972330\pi$
$48$		0			0
$49$		0			0
$50$	−3.62824	+	2.09477i	−0.513111	+	0.296245i
$51$		0			0
$52$	1.99033	+	1.14912i	0.276009	+	0.159354i
$53$		−	13.9411i		−	1.91496i	−0.288507	−	0.957478i	$-0.593159\pi$
$53$		−	13.9411i		−	1.91496i	0.288507	−	0.957478i	$-0.406841\pi$
$54$		0			0
$55$			2.81608i			0.379721i
$56$		0			0
$57$		0			0
$58$	−1.07151	−	1.85590i	−0.140696	−	0.243692i
$59$	−3.99222	−	6.91472i	−0.519742	−	0.900220i	−0.999737	−	0.0229484i	$-0.992695\pi$
$59$	−3.99222	−	6.91472i	−0.519742	−	0.900220i	0.479994	−	0.877272i	$-0.340639\pi$
$60$		0			0
$61$	−6.28224	−	3.62705i	−0.804359	−	0.464397i	0.0406343	−	0.999174i	$-0.487062\pi$
$61$	−6.28224	−	3.62705i	−0.804359	−	0.464397i	−0.844993	+	0.534777i	$0.820395\pi$
$62$	10.0032			1.27040
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−1.79181	−	1.03450i	−0.222247	−	0.128314i
$66$		0			0
$67$	−1.83525	−	3.17875i	−0.224212	−	0.388346i	0.731871	−	0.681443i	$-0.238647\pi$
$67$	−1.83525	−	3.17875i	−0.224212	−	0.388346i	−0.956083	+	0.293097i	$0.905314\pi$
$68$	2.57638	+	4.46242i	0.312432	+	0.541148i
$69$		0			0
$70$		0			0
$71$			14.1484i			1.67911i	0.543275	+	0.839555i	$0.317184\pi$
$71$			14.1484i			1.67911i	−0.543275	+	0.839555i	$0.682816\pi$
$72$		0			0
$73$		−	12.6082i		−	1.47568i	−0.674978	−	0.737838i	$-0.735847\pi$
$73$		−	12.6082i		−	1.47568i	0.674978	−	0.737838i	$-0.264153\pi$
$74$	−8.20475	−	4.73701i	−0.953783	−	0.550667i
$75$		0			0
$76$	2.38111	−	1.37474i	0.273132	−	0.157693i
$77$		0			0
$78$		0			0
$79$	3.27402	−	5.67077i	0.368356	−	0.638011i	−0.620953	−	0.783848i	$-0.713254\pi$
$79$	3.27402	−	5.67077i	0.368356	−	0.638011i	0.989309	+	0.145837i	$0.0465875\pi$
$80$	0.900258			0.100652
$81$		0			0
$82$		−	2.44268i		−	0.269748i
$83$	0.184437	−	0.319454i	0.0202446	−	0.0350646i	−0.855726	−	0.517430i	$-0.826889\pi$
$83$	0.184437	−	0.319454i	0.0202446	−	0.0350646i	0.875970	+	0.482365i	$0.160222\pi$
$84$		0			0
$85$	−2.31940	−	4.01733i	−0.251575	−	0.435740i
$86$	0.473119	−	0.273155i	0.0510177	−	0.0294551i
$87$		0			0
$88$	−1.56404	+	2.70900i	−0.166728	+	0.288781i
$89$	−12.0049			−1.27252			−0.636258	−	0.771477i	$-0.719518\pi$
$89$	−12.0049			−1.27252			−0.636258	+	0.771477i	$0.719518\pi$
$90$		0			0
$91$		0			0
$92$	−1.48584	−	0.857850i	−0.154909	−	0.0894370i
$93$		0			0
$94$	6.80755	−	3.93034i	0.702145	−	0.405384i
$95$	−2.14361	+	1.23762i	−0.219930	+	0.126977i
$96$		0			0
$97$	−8.86815	−	5.12003i	−0.900424	−	0.519860i	−0.0230864	−	0.999733i	$-0.507349\pi$
$97$	−8.86815	−	5.12003i	−0.900424	−	0.519860i	−0.877338	+	0.479873i	$0.840683\pi$
$98$		0			0
$99$		0			0
$100$	4.18954			0.418954
$101$	−1.35969	+	2.35506i	−0.135294	+	0.234337i	−0.925710	−	0.378234i	$-0.876531\pi$
$101$	−1.35969	+	2.35506i	−0.135294	+	0.234337i	0.790415	+	0.612571i	$0.209865\pi$
$102$		0			0
$103$	1.18861	−	0.686242i	0.117117	−	0.0676174i	−0.440297	−	0.897852i	$-0.645127\pi$
$103$	1.18861	−	0.686242i	0.117117	−	0.0676174i	0.557414	+	0.830235i	$0.311794\pi$
$104$	−1.14912	−	1.99033i	−0.112680	−	0.195168i
$105$		0			0
$106$	−6.97054	+	12.0733i	−0.677039	+	1.17267i
$107$		−	14.2704i		−	1.37957i	−0.724014	−	0.689785i	$-0.757705\pi$
$107$		−	14.2704i		−	1.37957i	0.724014	−	0.689785i	$-0.242295\pi$
$108$		0			0
$109$	5.29166			0.506849			0.253425	−	0.967355i	$-0.418443\pi$
$109$	5.29166			0.506849			0.253425	+	0.967355i	$0.418443\pi$
$110$	1.40804	−	2.43880i	0.134252	−	0.232531i
$111$		0			0
$112$		0			0
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	−0.387713	−	0.921780i	$-0.626735\pi$
$113$	2.30371	−	1.33005i	0.216715	−	0.125121i	0.604428	+	0.796659i	$0.293402\pi$
$114$		0			0
$115$	1.33764	+	0.772286i	0.124735	+	0.0720160i
$116$			2.14301i			0.198974i
$117$		0			0
$118$			7.98443i			0.735026i
$119$		0			0
$120$		0			0
$121$	−0.607537	−	1.05229i	−0.0552307	−	0.0956623i
$122$	3.62705	+	6.28224i	0.328378	+	0.568767i
$123$		0			0
$124$	−8.66298	−	5.00158i	−0.777959	−	0.449155i
$125$	−8.27295			−0.739955
$126$		0			0
$127$	6.10587			0.541808			0.270904	−	0.962606i	$-0.412677\pi$
$127$	6.10587			0.541808			0.270904	+	0.962606i	$0.412677\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$		0			0
$130$	1.03450	+	1.79181i	0.0907320	+	0.157152i
$131$	−3.97879	−	6.89147i	−0.347629	−	0.602111i	0.638199	−	0.769871i	$-0.279680\pi$
$131$	−3.97879	−	6.89147i	−0.347629	−	0.602111i	−0.985828	+	0.167761i	$0.946346\pi$
$132$		0			0
$133$		0			0
$134$			3.67050i			0.317083i
$135$		0			0
$136$		−	5.15276i		−	0.441845i
$137$	18.9140	+	10.9200i	1.61593	+	0.932957i	0.987958	+	0.154719i	$0.0494473\pi$
$137$	18.9140	+	10.9200i	1.61593	+	0.932957i	0.627970	+	0.778237i	$0.283886\pi$
$138$		0			0
$139$	11.7109	−	6.76127i	0.993302	−	0.573483i	0.0870425	−	0.996205i	$-0.472258\pi$
$139$	11.7109	−	6.76127i	0.993302	−	0.573483i	0.906260	+	0.422721i	$0.138925\pi$
$140$		0			0
$141$		0			0
$142$	7.07421	−	12.2529i	0.593655	−	1.02824i
$143$	−7.18909			−0.601182
$144$		0			0
$145$		−	1.92926i		−	0.160217i
$146$	−6.30409	+	10.9190i	−0.521730	+	0.903663i
$147$		0			0
$148$	4.73701	+	8.20475i	0.389380	+	0.674426i
$149$	−4.41192	+	2.54722i	−0.361438	+	0.208676i	−0.669711	−	0.742621i	$-0.733582\pi$
$149$	−4.41192	+	2.54722i	−0.361438	+	0.208676i	0.308273	+	0.951298i	$0.400249\pi$
$150$		0			0
$151$	10.5877	−	18.3385i	0.861618	−	1.49237i	−0.00874783	−	0.999962i	$-0.502785\pi$
$151$	10.5877	−	18.3385i	0.861618	−	1.49237i	0.870366	−	0.492405i	$-0.163882\pi$
$152$	−2.74947			−0.223012
$153$		0			0
$154$		0			0
$155$	7.79892	+	4.50271i	0.626424	+	0.361666i
$156$		0			0
$157$	0.311703	−	0.179962i	0.0248766	−	0.0143625i	−0.487510	−	0.873117i	$-0.662095\pi$
$157$	0.311703	−	0.179962i	0.0248766	−	0.0143625i	0.512387	+	0.858755i	$0.328761\pi$
$158$	−5.67077	+	3.27402i	−0.451142	+	0.260467i
$159$		0			0
$160$	−0.779646	−	0.450129i	−0.0616364	−	0.0355858i
$161$		0			0
$162$		0			0
$163$	−12.3728			−0.969113			−0.484557	−	0.874760i	$-0.661019\pi$
$163$	−12.3728			−0.969113			−0.484557	+	0.874760i	$0.661019\pi$
$164$	−1.22134	+	2.11542i	−0.0953705	+	0.165186i
$165$		0			0
$166$	−0.319454	+	0.184437i	−0.0247944	+	0.0143151i
$167$	−7.40866	−	12.8322i	−0.573299	−	0.992984i	−0.996224	−	0.0868188i	$-0.972330\pi$
$167$	−7.40866	−	12.8322i	−0.573299	−	0.992984i	0.422925	−	0.906165i	$-0.361003\pi$
$168$		0			0
$169$	−3.85905	+	6.68407i	−0.296850	+	0.514159i
$170$			4.63881i			0.355780i
$171$		0			0
$172$	−0.546311			−0.0416558
$173$	−2.31772	+	4.01441i	−0.176213	+	0.305210i	−0.940580	−	0.339571i	$-0.889718\pi$
$173$	−2.31772	+	4.01441i	−0.176213	+	0.305210i	0.764367	+	0.644781i	$0.223051\pi$
$174$		0			0
$175$		0			0
$176$	2.70900	−	1.56404i	0.204199	−	0.117894i
$177$		0			0
$178$	10.3965	+	6.00244i	0.779253	+	0.449902i
$179$		−	6.07205i		−	0.453846i	−0.973913	−	0.226923i	$-0.927133\pi$
$179$		−	6.07205i		−	0.453846i	0.973913	−	0.226923i	$-0.0728666\pi$
$180$		0			0
$181$		−	7.12701i		−	0.529746i	−0.964283	−	0.264873i	$-0.914670\pi$
$181$		−	7.12701i		−	0.529746i	0.964283	−	0.264873i	$-0.0853301\pi$
$182$		0			0
$183$		0			0
$184$	0.857850	+	1.48584i	0.0632415	+	0.109538i
$185$	−4.26453	−	7.38639i	−0.313535	−	0.543058i
$186$		0			0
$187$	−13.9588	−	8.05913i	−1.02077	−	0.589342i
$188$	−7.86068			−0.573299
$189$		0			0
$190$	2.47523			0.179572
$191$	−12.4713	−	7.20032i	−0.902394	−	0.520997i	−0.0244176	−	0.999702i	$-0.507773\pi$
$191$	−12.4713	−	7.20032i	−0.902394	−	0.520997i	−0.877976	+	0.478705i	$0.841106\pi$
$192$		0			0
$193$	−8.90573	−	15.4252i	−0.641048	−	1.11033i	−0.985199	−	0.171414i	$-0.945166\pi$
$193$	−8.90573	−	15.4252i	−0.641048	−	1.11033i	0.344151	−	0.938914i	$-0.388167\pi$
$194$	5.12003	+	8.86815i	0.367597	+	0.636696i
$195$		0			0
$196$		0			0
$197$		−	19.1025i		−	1.36100i	−0.732750	−	0.680498i	$-0.761764\pi$
$197$		−	19.1025i		−	1.36100i	0.732750	−	0.680498i	$-0.238236\pi$
$198$		0			0
$199$			13.3954i			0.949576i	0.880100	+	0.474788i	$0.157475\pi$
$199$			13.3954i			0.949576i	−0.880100	+	0.474788i	$0.842525\pi$
$200$	−3.62824	−	2.09477i	−0.256556	−	0.148122i
$201$		0			0
$202$	2.35506	−	1.35969i	0.165701	−	0.0956677i
$203$		0			0
$204$		0			0
$205$	1.09952	−	1.90442i	0.0767937	−	0.133011i
$206$	−1.37248			−0.0956254
$207$		0			0
$208$			2.29824i			0.159354i
$209$	−4.30029	+	7.44832i	−0.297457	+	0.515211i
$210$		0			0
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	−0.984258	−	0.176740i	$-0.943445\pi$
$211$	−9.37193	−	16.2327i	−0.645190	−	1.11750i	0.339067	−	0.940762i	$-0.389889\pi$
$212$	12.0733	−	6.97054i	0.829200	−	0.478739i
$213$		0			0
$214$	−7.13519	+	12.3585i	−0.487752	+	0.844810i
$215$	0.491820			0.0335419
$216$		0			0
$217$		0			0
$218$	−4.58271	−	2.64583i	−0.310380	−	0.179198i
$219$		0			0
$220$	−2.43880	+	1.40804i	−0.164424	+	0.0949302i
$221$	10.2557	−	5.92113i	0.689873	−	0.398298i
$222$		0			0
$223$	−2.21609	−	1.27946i	−0.148400	−	0.0856789i	0.423961	−	0.905680i	$-0.360639\pi$
$223$	−2.21609	−	1.27946i	−0.148400	−	0.0856789i	−0.572362	+	0.820001i	$0.693973\pi$
$224$		0			0
$225$		0			0
$226$	−2.66010			−0.176947
$227$	−4.36455	+	7.55962i	−0.289685	+	0.501749i	−0.973735	−	0.227686i	$-0.926884\pi$
$227$	−4.36455	+	7.55962i	−0.289685	+	0.501749i	0.684049	+	0.729436i	$0.260217\pi$
$228$		0			0
$229$	−3.40979	+	1.96865i	−0.225325	+	0.130092i	−0.608414	−	0.793620i	$-0.708194\pi$
$229$	−3.40979	+	1.96865i	−0.225325	+	0.130092i	0.383088	+	0.923712i	$0.374861\pi$
$230$	−0.772286	−	1.33764i	−0.0509230	−	0.0882013i
$231$		0			0
$232$	1.07151	−	1.85590i	0.0703478	−	0.121846i
$233$			4.52812i			0.296647i	0.988939	+	0.148324i	$0.0473877\pi$
$233$			4.52812i			0.296647i	−0.988939	+	0.148324i	$0.952612\pi$
$234$		0			0
$235$	7.07664			0.461629
$236$	3.99222	−	6.91472i	0.259871	−	0.450110i
$237$		0			0
$238$		0			0
$239$	7.55315	−	4.36081i	0.488573	−	0.282078i	−0.235409	−	0.971896i	$-0.575643\pi$
$239$	7.55315	−	4.36081i	0.488573	−	0.282078i	0.723982	+	0.689819i	$0.242310\pi$
$240$		0			0
$241$	−17.1314	−	9.89079i	−1.10353	−	0.637122i	−0.166382	−	0.986061i	$-0.553209\pi$
$241$	−17.1314	−	9.89079i	−1.10353	−	0.637122i	−0.937145	+	0.348939i	$0.886542\pi$
$242$			1.21507i			0.0781079i
$243$		0			0
$244$		−	7.25411i		−	0.464397i
$245$		0			0
$246$		0			0
$247$	−3.15947	−	5.47236i	−0.201032	−	0.348198i
$248$	5.00158	+	8.66298i	0.317600	+	0.550100i
$249$		0			0
$250$	7.16459	+	4.13648i	0.453128	+	0.261614i
$251$	3.80791			0.240353			0.120176	−	0.992753i	$-0.461654\pi$
$251$	3.80791			0.240353			0.120176	+	0.992753i	$0.461654\pi$
$252$		0			0
$253$	5.36686			0.337411
$254$	−5.28784	−	3.05293i	−0.331788	−	0.191558i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	0.529230	−	0.848479i	$-0.322481\pi$
$257$	−7.53771	−	13.0557i	−0.470189	−	0.814392i	−0.999419	+	0.0340869i	$0.989148\pi$
$258$		0			0
$259$		0			0
$260$		−	2.06901i		−	0.128314i
$261$		0			0
$262$			7.95758i			0.491621i
$263$	−6.59852	−	3.80965i	−0.406882	−	0.234913i	0.282567	−	0.959248i	$-0.408814\pi$
$263$	−6.59852	−	3.80965i	−0.406882	−	0.234913i	−0.689449	+	0.724334i	$0.742147\pi$
$264$		0			0
$265$	−10.8691	+	6.27529i	−0.667684	+	0.385488i
$266$		0			0
$267$		0			0
$268$	1.83525	−	3.17875i	0.112106	−	0.194173i
$269$	8.65440			0.527668			0.263834	−	0.964568i	$-0.415013\pi$
$269$	8.65440			0.527668			0.263834	+	0.964568i	$0.415013\pi$
$270$		0			0
$271$			18.0839i			1.09852i	0.835653	+	0.549258i	$0.185090\pi$
$271$			18.0839i			1.09852i	−0.835653	+	0.549258i	$0.814910\pi$
$272$	−2.57638	+	4.46242i	−0.156216	+	0.270574i
$273$		0			0
$274$	−10.9200	−	18.9140i	−0.659700	−	1.14263i
$275$	−11.3495	+	6.55262i	−0.684398	+	0.395138i
$276$		0			0
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	−0.976105	−	0.217301i	$-0.930275\pi$
$277$	−4.99073	+	8.64419i	−0.299864	+	0.519379i	0.676241	+	0.736681i	$0.263608\pi$
$278$	−13.5225			−0.811028
$279$		0			0
$280$		0			0
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	0.835469	−	0.549538i	$-0.185196\pi$
$281$	13.0297	+	7.52272i	0.777289	+	0.448768i	−0.0581797	+	0.998306i	$0.518530\pi$
$282$		0			0
$283$	3.48950	−	2.01467i	0.207429	−	0.119759i	−0.392687	−	0.919672i	$-0.628454\pi$
$283$	3.48950	−	2.01467i	0.207429	−	0.119759i	0.600116	+	0.799913i	$0.295121\pi$
$284$	−12.2529	+	7.07421i	−0.727076	+	0.419777i
$285$		0			0
$286$	6.22593	+	3.59454i	0.368147	+	0.212550i
$287$		0			0
$288$		0			0
$289$	9.55089			0.561817
$290$	−0.964632	+	1.67079i	−0.0566451	+	0.0981123i
$291$		0			0
$292$	10.9190	−	6.30409i	0.638987	−	0.368919i
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	0.991817	−	0.127665i	$-0.0407483\pi$
$293$	6.59608	+	11.4248i	0.385347	+	0.667441i	−0.606470	+	0.795106i	$0.707415\pi$
$294$		0			0
$295$	−3.59402	+	6.22503i	−0.209252	+	0.362435i
$296$		−	9.47403i		−	0.550667i
$297$		0			0
$298$	5.09444			0.295113
$299$	−1.97154	+	3.41481i	−0.114017	+	0.197484i
$300$		0			0
$301$		0			0
$302$	−18.3385	+	10.5877i	−1.05526	+	0.609256i
$303$		0			0
$304$	2.38111	+	1.37474i	0.136566	+	0.0788465i
$305$			6.53057i			0.373939i
$306$		0			0
$307$			28.7690i			1.64194i	0.570974	+	0.820968i	$0.306566\pi$
$307$			28.7690i			1.64194i	−0.570974	+	0.820968i	$0.693434\pi$
$308$		0			0
$309$		0			0
$310$	−4.50271	−	7.79892i	−0.255737	−	0.442949i
$311$	−15.4228	−	26.7132i	−0.874550	−	1.51476i	−0.857242	−	0.514914i	$-0.827824\pi$
$311$	−15.4228	−	26.7132i	−0.874550	−	1.51476i	−0.0173077	−	0.999850i	$-0.505509\pi$
$312$		0			0
$313$	−15.9055	−	9.18304i	−0.899032	−	0.519056i	−0.0221460	−	0.999755i	$-0.507050\pi$
$313$	−15.9055	−	9.18304i	−0.899032	−	0.519056i	−0.876886	+	0.480698i	$0.840383\pi$
$314$	−0.359924			−0.0203117
$315$		0			0
$316$	6.54804			0.368356
$317$	15.1173	+	8.72800i	0.849074	+	0.490213i	0.860338	−	0.509723i	$-0.170252\pi$
$317$	15.1173	+	8.72800i	0.849074	+	0.490213i	−0.0112642	+	0.999937i	$0.503586\pi$
$318$		0			0
$319$	−3.35176	−	5.80543i	−0.187663	−	0.325042i
$320$	0.450129	+	0.779646i	0.0251630	+	0.0435835i
$321$		0			0
$322$		0			0
$323$		−	14.1673i		−	0.788292i
$324$		0			0
$325$		−	9.62855i		−	0.534096i
$326$	10.7152	+	6.18640i	0.593458	+	0.342633i
$327$		0			0
$328$	2.11542	−	1.22134i	0.116804	−	0.0674371i
$329$		0			0
$330$		0			0
$331$	−5.21472	+	9.03216i	−0.286627	+	0.496452i	−0.973002	−	0.230795i	$-0.925867\pi$
$331$	−5.21472	+	9.03216i	−0.286627	+	0.496452i	0.686375	+	0.727247i	$0.259201\pi$
$332$	0.368874			0.0202446
$333$		0			0
$334$			14.8173i			0.810768i
$335$	−1.65220	+	2.86169i	−0.0902693	+	0.156351i
$336$		0			0
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	−0.869626	−	0.493712i	$-0.835640\pi$
$337$	−15.8312	−	27.4204i	−0.862380	−	1.49369i	0.00724616	−	0.999974i	$-0.497693\pi$
$338$	6.68407	−	3.85905i	0.363566	−	0.209905i
$339$		0			0
$340$	2.31940	−	4.01733i	0.125787	−	0.217870i
$341$	31.2907			1.69449
$342$		0			0
$343$		0			0
$344$	0.473119	+	0.273155i	0.0255089	+	0.0147275i
$345$		0			0
$346$	4.01441	−	2.31772i	0.215816	−	0.124601i
$347$	−10.8472	+	6.26261i	−0.582306	+	0.336195i	−0.762049	−	0.647519i	$-0.775807\pi$
$347$	−10.8472	+	6.26261i	−0.582306	+	0.336195i	0.179743	+	0.983714i	$0.442473\pi$
$348$		0			0
$349$	−12.2560	−	7.07599i	−0.656047	−	0.378769i	0.134722	−	0.990883i	$-0.456986\pi$
$349$	−12.2560	−	7.07599i	−0.656047	−	0.378769i	−0.790769	+	0.612115i	$0.790319\pi$
$350$		0			0
$351$		0			0
$352$	−3.12809			−0.166728
$353$	−2.48267	+	4.30012i	−0.132139	+	0.228872i	−0.924501	−	0.381180i	$-0.875518\pi$
$353$	−2.48267	+	4.30012i	−0.132139	+	0.228872i	0.792362	+	0.610052i	$0.208851\pi$
$354$		0			0
$355$	11.0308	−	6.36862i	0.585452	−	0.338011i
$356$	−6.00244	−	10.3965i	−0.318129	−	0.551015i
$357$		0			0
$358$	−3.03602	+	5.25855i	−0.160459	+	0.277923i
$359$		−	17.3220i		−	0.914218i	−0.889411	−	0.457109i	$-0.848885\pi$
$359$		−	17.3220i		−	0.914218i	0.889411	−	0.457109i	$-0.151115\pi$
$360$		0			0
$361$	11.4404			0.602127
$362$	−3.56350	+	6.17217i	−0.187294	+	0.324402i
$363$		0			0
$364$		0			0
$365$	−9.82992	+	5.67531i	−0.514522	+	0.297059i
$366$		0			0
$367$	1.18799	+	0.685884i	0.0620124	+	0.0358029i	0.530686	−	0.847569i	$-0.321934\pi$
$367$	1.18799	+	0.685884i	0.0620124	+	0.0358029i	−0.468673	+	0.883372i	$0.655268\pi$
$368$		−	1.71570i		−	0.0894370i
$369$		0			0
$370$			8.52907i			0.443405i
$371$		0			0
$372$		0			0
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	0.921545	−	0.388271i	$-0.126928\pi$
$373$	2.40488	+	4.16537i	0.124520	+	0.215675i	−0.797025	+	0.603946i	$0.793594\pi$
$374$	8.05913	+	13.9588i	0.416728	+	0.721794i
$375$		0			0
$376$	6.80755	+	3.93034i	0.351073	+	0.202692i
$377$	4.92515			0.253658
$378$		0			0
$379$	19.5669			1.00508			0.502542	−	0.864553i	$-0.332398\pi$
$379$	19.5669			1.00508			0.502542	+	0.864553i	$0.332398\pi$
$380$	−2.14361	−	1.23762i	−0.109965	−	0.0634884i
$381$		0			0
$382$	7.20032	+	12.4713i	0.368401	+	0.638089i
$383$	15.7349	+	27.2536i	0.804014	+	1.39259i	0.916955	+	0.398992i	$0.130640\pi$
$383$	15.7349	+	27.2536i	0.804014	+	1.39259i	−0.112940	+	0.993602i	$0.536027\pi$
$384$		0			0
$385$		0			0
$386$			17.8115i			0.906579i
$387$		0			0
$388$		−	10.2401i		−	0.519860i
$389$	3.52130	+	2.03303i	0.178537	+	0.103078i	0.586605	−	0.809873i	$-0.300464\pi$
$389$	3.52130	+	2.03303i	0.178537	+	0.103078i	−0.408068	+	0.912952i	$0.633797\pi$
$390$		0			0
$391$	−7.65617	+	4.42029i	−0.387189	+	0.223544i
$392$		0			0
$393$		0			0
$394$	−9.55124	+	16.5432i	−0.481185	+	0.833436i
$395$	−5.89492			−0.296606
$396$		0			0
$397$			4.40740i			0.221201i	0.993865	+	0.110601i	$0.0352774\pi$
$397$			4.40740i			0.221201i	−0.993865	+	0.110601i	$0.964723\pi$
$398$	6.69771	−	11.6008i	0.335726	−	0.581494i
$399$		0			0
$400$	2.09477	+	3.62824i	0.104738	+	0.181412i
$401$	16.0586	−	9.27141i	0.801926	−	0.462992i	−0.0422180	−	0.999108i	$-0.513442\pi$
$401$	16.0586	−	9.27141i	0.801926	−	0.462992i	0.844144	+	0.536116i	$0.180109\pi$
$402$		0			0
$403$	−11.4948	+	19.9096i	−0.572597	+	0.991768i
$404$	−2.71939			−0.135294
$405$		0			0
$406$		0			0
$407$	−25.6652	−	14.8178i	−1.27218	−	0.734491i
$408$		0			0
$409$	−21.5555	+	12.4451i	−1.06585	+	0.615370i	−0.927045	−	0.374949i	$-0.877660\pi$
$409$	−21.5555	+	12.4451i	−1.06585	+	0.615370i	−0.138807	+	0.990319i	$0.544327\pi$
$410$	−1.90442	+	1.09952i	−0.0940527	+	0.0543014i
$411$		0			0
$412$	1.18861	+	0.686242i	0.0585584	+	0.0338087i
$413$		0			0
$414$		0			0
$415$	−0.332081			−0.0163012
$416$	1.14912	−	1.99033i	0.0563402	−	0.0975841i
$417$		0			0
$418$	7.44832	−	4.30029i	0.364309	−	0.210334i
$419$	−2.57422	−	4.45869i	−0.125759	−	0.217821i	0.796270	−	0.604941i	$-0.206803\pi$
$419$	−2.57422	−	4.45869i	−0.125759	−	0.217821i	−0.922029	+	0.387120i	$0.873470\pi$
$420$		0			0
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	0.323063	+	0.946377i	$0.395287\pi$
$421$	−13.5022	+	23.3864i	−0.658055	+	1.13978i	−0.981119	+	0.193408i	$0.938046\pi$
$422$			18.7439i			0.912437i
$423$		0			0
$424$	−13.9411			−0.677039
$425$	10.7938	−	18.6955i	0.523577	−	0.906863i
$426$		0			0
$427$		0			0
$428$	12.3585	−	7.13519i	0.597371	−	0.344892i
$429$		0			0
$430$	−0.425929	−	0.245910i	−0.0205401	−	0.0118588i
$431$		−	9.36317i		−	0.451008i	−0.974242	−	0.225504i	$-0.927597\pi$
$431$		−	9.36317i		−	0.451008i	0.974242	−	0.225504i	$-0.0724029\pi$
$432$		0			0
$433$			21.0373i			1.01099i	0.862830	+	0.505494i	$0.168690\pi$
$433$			21.0373i			1.01099i	−0.862830	+	0.505494i	$0.831310\pi$
$434$		0			0
$435$		0			0
$436$	2.64583	+	4.58271i	0.126712	+	0.219472i
$437$	2.35863	+	4.08527i	0.112829	+	0.195425i
$438$		0			0
$439$	17.6867	+	10.2114i	0.844141	+	0.487365i	0.858670	−	0.512530i	$-0.171292\pi$
$439$	17.6867	+	10.2114i	0.844141	+	0.487365i	−0.0145289	+	0.999894i	$0.504625\pi$
$440$	2.81608			0.134252
$441$		0			0
$442$	−11.8423			−0.563279
$443$	28.0288	+	16.1825i	1.33169	+	0.768852i	0.985559	−	0.169334i	$-0.0541618\pi$
$443$	28.0288	+	16.1825i	1.33169	+	0.768852i	0.346131	+	0.938186i	$0.387495\pi$
$444$		0			0
$445$	5.40375	+	9.35956i	0.256162	+	0.443686i
$446$	1.27946	+	2.21609i	0.0605841	+	0.104935i
$447$		0			0
$448$		0			0
$449$		−	21.5693i		−	1.01792i	−0.860791	−	0.508958i	$-0.830031\pi$
$449$		−	21.5693i		−	1.01792i	0.860791	−	0.508958i	$-0.169969\pi$
$450$		0			0
$451$		−	7.64090i		−	0.359796i
$452$	2.30371	+	1.33005i	0.108358	+	0.0625603i
$453$		0			0
$454$	7.55962	−	4.36455i	0.354790	−	0.204838i
$455$		0			0
$456$		0			0
$457$	−10.5350	+	18.2471i	−0.492806	+	0.853564i	−0.999966	−	0.00828760i	$-0.997362\pi$
$457$	−10.5350	+	18.2471i	−0.492806	+	0.853564i	0.507160	+	0.861852i	$0.330695\pi$
$458$	3.93729			0.183977
$459$		0			0
$460$			1.54457i			0.0720160i
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	−0.215684	−	0.976463i	$-0.569198\pi$
$461$	15.8412	−	27.4378i	0.737800	−	1.27791i	0.953484	−	0.301444i	$-0.0974687\pi$
$462$		0			0
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	0.949977	−	0.312319i	$-0.101106\pi$
$463$	4.40058	+	7.62202i	0.204512	+	0.354225i	−0.745465	+	0.666545i	$0.767773\pi$
$464$	−1.85590	+	1.07151i	−0.0861582	+	0.0497434i
$465$		0			0
$466$	2.26406	−	3.92147i	0.104881	−	0.181658i
$467$	−18.9889			−0.878701			−0.439350	−	0.898316i	$-0.644791\pi$
$467$	−18.9889			−0.878701			−0.439350	+	0.898316i	$0.644791\pi$
$468$		0			0
$469$		0			0
$470$	−6.12855	−	3.53832i	−0.282689	−	0.163211i
$471$		0			0
$472$	−6.91472	+	3.99222i	−0.318276	+	0.183757i
$473$	1.47996	−	0.854453i	0.0680485	−	0.0392878i
$474$		0			0
$475$	−9.97575	−	5.75950i	−0.457719	−	0.264264i
$476$		0			0
$477$		0			0
$478$	−8.72163			−0.398918
$479$	12.0701	−	20.9060i	0.551495	−	0.955218i	−0.446672	−	0.894698i	$-0.647391\pi$
$479$	12.0701	−	20.9060i	0.551495	−	0.955218i	0.998167	−	0.0605197i	$-0.0192758\pi$
$480$		0			0
$481$	18.8565	−	10.8868i	0.859781	−	0.496395i
$482$	9.89079	+	17.1314i	0.450513	+	0.780312i
$483$		0			0
$484$	0.607537	−	1.05229i	0.0276153	−	0.0478312i
$485$			9.21869i			0.418599i
$486$		0			0
$487$	−14.1108			−0.639424			−0.319712	−	0.947515i	$-0.603586\pi$
$487$	−14.1108			−0.639424			−0.319712	+	0.947515i	$0.603586\pi$
$488$	−3.62705	+	6.28224i	−0.164189	+	0.284384i
$489$		0			0
$490$		0			0
$491$	18.8344	−	10.8740i	0.849982	−	0.490738i	−0.0106626	−	0.999943i	$-0.503394\pi$
$491$	18.8344	−	10.8740i	0.849982	−	0.490738i	0.860645	+	0.509206i	$0.170061\pi$
$492$		0			0
$493$	9.56302	+	5.52121i	0.430697	+	0.248663i
$494$			6.31894i			0.284302i
$495$		0			0
$496$		−	10.0032i		−	0.449155i
$497$		0			0
$498$		0			0
$499$	4.21233	+	7.29596i	0.188570	+	0.326612i	0.944774	−	0.327724i	$-0.106282\pi$
$499$	4.21233	+	7.29596i	0.188570	+	0.326612i	−0.756204	+	0.654336i	$0.772948\pi$
$500$	−4.13648	−	7.16459i	−0.184989	−	0.320410i
$501$		0			0
$502$	−3.29774	−	1.90395i	−0.147186	−	0.0849776i
$503$	−8.71316			−0.388501			−0.194250	−	0.980952i	$-0.562227\pi$
$503$	−8.71316			−0.388501			−0.194250	+	0.980952i	$0.562227\pi$
$504$		0			0
$505$	2.44815			0.108941
$506$	−4.64783	−	2.68343i	−0.206621	−	0.119293i
$507$		0			0
$508$	3.05293	+	5.28784i	0.135452	+	0.234610i
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	−0.980297	−	0.197530i	$-0.936708\pi$
$509$	−14.9177	−	25.8382i	−0.661214	−	1.14526i	0.319082	−	0.947727i	$-0.396625\pi$
$510$		0			0
$511$		0			0
$512$			1.00000i			0.0441942i
$513$		0			0
$514$			15.0754i			0.664948i
$515$	−1.07005	−	0.617794i	−0.0471521	−	0.0272233i
$516$		0			0
$517$	21.2946	−	12.2944i	0.936536	−	0.540709i
$518$		0			0
$519$		0			0
$520$	−1.03450	+	1.79181i	−0.0453660	+	0.0785762i
$521$	19.7801			0.866581			0.433291	−	0.901254i	$-0.357352\pi$
$521$	19.7801			0.866581			0.433291	+	0.901254i	$0.357352\pi$
$522$		0			0
$523$			12.2319i			0.534865i	0.963577	+	0.267433i	$0.0861752\pi$
$523$			12.2319i			0.534865i	−0.963577	+	0.267433i	$0.913825\pi$
$524$	3.97879	−	6.89147i	0.173814	−	0.301055i
$525$		0			0
$526$	3.80965	+	6.59852i	0.166109	+	0.287709i
$527$	−44.6382	+	25.7719i	−1.94447	+	1.12264i
$528$		0			0
$529$	−10.0282	+	17.3693i	−0.436008	+	0.755188i
$530$	12.5506			0.545162
$531$		0			0
$532$		0			0
$533$	4.86174	+	2.80693i	0.210585	+	0.121581i
$534$		0			0
$535$	−11.1258	+	6.42351i	−0.481012	+	0.277713i
$536$	−3.17875	+	1.83525i	−0.137301	+	0.0792708i
$537$		0			0
$538$	−7.49493	−	4.32720i	−0.323129	−	0.186559i
$539$		0			0
$540$		0			0
$541$	0.697888			0.0300046			0.0150023	−	0.999887i	$-0.495224\pi$
$541$	0.697888			0.0300046			0.0150023	+	0.999887i	$0.495224\pi$
$542$	9.04193	−	15.6611i	0.388384	−	0.672701i
$543$		0			0
$544$	4.46242	−	2.57638i	0.191325	−	0.110461i
$545$	−2.38193	−	4.12562i	−0.102031	−	0.176722i
$546$		0			0
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.0681854	−	0.997673i	$-0.478279\pi$
$547$	21.0049	−	36.3815i	0.898103	−	1.55556i	0.829917	−	0.557887i	$-0.188388\pi$
$548$			21.8400i			0.932957i
$549$		0			0
$550$	13.1052			0.558809
$551$	2.94608	−	5.10275i	0.125507	−	0.217385i
$552$		0			0
$553$		0			0
$554$	8.64419	−	4.99073i	0.367257	−	0.212036i
$555$		0			0
$556$	11.7109	+	6.76127i	0.496651	+	0.286742i
$557$			5.60737i			0.237592i	0.992919	+	0.118796i	$0.0379034\pi$
$557$			5.60737i			0.237592i	−0.992919	+	0.118796i	$0.962097\pi$
$558$		0			0
$559$			1.25555i			0.0531042i
$560$		0			0
$561$		0			0
$562$	−7.52272	−	13.0297i	−0.317327	−	0.549626i
$563$	17.5948	+	30.4751i	0.741532	+	1.28437i	0.951798	+	0.306727i	$0.0992338\pi$
$563$	17.5948	+	30.4751i	0.741532	+	1.28437i	−0.210266	+	0.977644i	$0.567433\pi$
$564$		0			0
$565$	−2.07394	−	1.19739i	−0.0872512	−	0.0503745i
$566$	−4.02933			−0.169365
$567$		0			0
$568$	14.1484			0.593655
$569$	7.63608	+	4.40869i	0.320121	+	0.184822i	0.651447	−	0.758695i	$-0.274162\pi$
$569$	7.63608	+	4.40869i	0.320121	+	0.184822i	−0.331325	+	0.943517i	$0.607496\pi$
$570$		0			0
$571$	5.94140	+	10.2908i	0.248640	+	0.430657i	0.963149	−	0.268970i	$-0.0866831\pi$
$571$	5.94140	+	10.2908i	0.248640	+	0.430657i	−0.714509	+	0.699626i	$0.753350\pi$
$572$	−3.59454	−	6.22593i	−0.150295	−	0.260319i
$573$		0			0
$574$		0			0
$575$			7.18799i			0.299760i
$576$		0			0
$577$			18.2806i			0.761030i	0.924775	+	0.380515i	$0.124253\pi$
$577$			18.2806i			0.761030i	−0.924775	+	0.380515i	$0.875747\pi$
$578$	−8.27131	−	4.77544i	−0.344041	−	0.198632i
$579$		0			0
$580$	1.67079	−	0.964632i	0.0693758	−	0.0400542i
$581$		0			0
$582$		0			0
$583$	−21.8045	+	37.7664i	−0.903049	+	1.56413i
$584$	−12.6082			−0.521730
$585$		0			0
$586$		−	13.1922i		−	0.544963i
$587$	−1.75389	+	3.03782i	−0.0723907	+	0.125384i	−0.899949	−	0.435996i	$-0.856396\pi$
$587$	−1.75389	+	3.03782i	−0.0723907	+	0.125384i	0.827558	+	0.561380i	$0.189730\pi$
$588$		0			0
$589$	13.7517	+	23.8186i	0.566628	+	0.981429i
$590$	6.22503	−	3.59402i	0.256280	−	0.147964i
$591$		0			0
$592$	−4.73701	+	8.20475i	−0.194690	+	0.337213i
$593$	48.4672			1.99031			0.995155	−	0.0983219i	$-0.0313475\pi$
$593$	48.4672			1.99031			0.995155	+	0.0983219i	$0.0313475\pi$
$594$		0			0
$595$		0			0
$596$	−4.41192	−	2.54722i	−0.180719	−	0.104338i
$597$		0			0
$598$	3.41481	−	1.97154i	0.139642	−	0.0806224i
$599$	21.7773	−	12.5731i	0.889796	−	0.513724i	0.0159203	−	0.999873i	$-0.494932\pi$
$599$	21.7773	−	12.5731i	0.889796	−	0.513724i	0.873876	+	0.486149i	$0.161599\pi$
$600$		0			0
$601$	−11.2731	−	6.50854i	−0.459840	−	0.265489i	0.252137	−	0.967692i	$-0.418867\pi$
$601$	−11.2731	−	6.50854i	−0.459840	−	0.265489i	−0.711977	+	0.702203i	$0.752200\pi$
$602$		0			0
$603$		0			0
$604$	21.1755			0.861618
$605$	−0.546940	+	0.947328i	−0.0222363	+	0.0385144i
$606$		0			0
$607$	−7.10546	+	4.10234i	−0.288402	+	0.166509i	−0.637221	−	0.770681i	$-0.719916\pi$
$607$	−7.10546	+	4.10234i	−0.288402	+	0.166509i	0.348819	+	0.937190i	$0.386583\pi$
$608$	−1.37474	−	2.38111i	−0.0557529	−	0.0965668i
$609$		0			0
$610$	3.26528	−	5.65564i	0.132207	−	0.228990i
$611$			18.0657i			0.730861i
$612$		0			0
$613$	−4.70101			−0.189872			−0.0949361	−	0.995483i	$-0.530265\pi$
$613$	−4.70101			−0.189872			−0.0949361	+	0.995483i	$0.530265\pi$
$614$	14.3845	−	24.9147i	0.580512	−	1.00548i
$615$		0			0
$616$		0			0
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	−0.801777	−	0.597623i	$-0.796112\pi$
$617$	−17.0178	+	9.82521i	−0.685109	+	0.395548i	0.116668	+	0.993171i	$0.462779\pi$
$618$		0			0
$619$	30.0586	+	17.3544i	1.20816	+	0.697531i	0.962357	−	0.271789i	$-0.0876153\pi$
$619$	30.0586	+	17.3544i	1.20816	+	0.697531i	0.245802	+	0.969320i	$0.420949\pi$
$620$			9.00541i			0.361666i
$621$		0			0
$622$			30.8457i			1.23680i
$623$		0			0
$624$		0			0
$625$	−6.74995	−	11.6912i	−0.269998	−	0.467650i
$626$	9.18304	+	15.9055i	0.367028	+	0.635712i
$627$		0			0
$628$	0.311703	+	0.179962i	0.0124383	+	0.00718126i
$629$	48.8174			1.94648
$630$		0			0
$631$	22.9139			0.912188			0.456094	−	0.889932i	$-0.349248\pi$
$631$	22.9139			0.912188			0.456094	+	0.889932i	$0.349248\pi$
$632$	−5.67077	−	3.27402i	−0.225571	−	0.130233i
$633$		0			0
$634$	−8.72800	−	15.1173i	−0.346633	−	0.600386i
$635$	−2.74843	−	4.76041i	−0.109068	−	0.188911i
$636$		0			0
$637$		0			0
$638$			6.70353i			0.265395i
$639$		0			0
$640$		−	0.900258i		−	0.0355858i
$641$	11.9968	+	6.92634i	0.473844	+	0.273574i	0.717848	−	0.696200i	$-0.245127\pi$
$641$	11.9968	+	6.92634i	0.473844	+	0.273574i	−0.244003	+	0.969774i	$0.578461\pi$
$642$		0			0
$643$	27.9684	−	16.1476i	1.10297	−	0.636797i	0.165967	−	0.986131i	$-0.446925\pi$
$643$	27.9684	−	16.1476i	1.10297	−	0.636797i	0.936998	+	0.349334i	$0.113592\pi$
$644$		0			0
$645$		0			0
$646$	−7.08367	+	12.2693i	−0.278703	+	0.482729i
$647$	17.9343			0.705070			0.352535	−	0.935799i	$-0.385320\pi$
$647$	17.9343			0.705070			0.352535	+	0.935799i	$0.385320\pi$
$648$		0			0
$649$			24.9760i			0.980393i
$650$	−4.81428	+	8.33857i	−0.188831	+	0.327066i
$651$		0			0
$652$	−6.18640	−	10.7152i	−0.242278	−	0.419638i
$653$	6.49080	−	3.74747i	0.254005	−	0.146650i	−0.367592	−	0.929987i	$-0.619818\pi$
$653$	6.49080	−	3.74747i	0.254005	−	0.146650i	0.621597	+	0.783338i	$0.286484\pi$
$654$		0			0
$655$	−3.58194	+	6.20410i	−0.139958	+	0.242414i
$656$	−2.44268			−0.0953705
$657$		0			0
$658$		0			0
$659$	9.32497	+	5.38377i	0.363249	+	0.209722i	0.670505	−	0.741905i	$-0.266077\pi$
$659$	9.32497	+	5.38377i	0.363249	+	0.209722i	−0.307256	+	0.951627i	$0.599411\pi$
$660$		0			0
$661$	10.0813	−	5.82044i	0.392117	−	0.226389i	−0.290960	−	0.956735i	$-0.593975\pi$
$661$	10.0813	−	5.82044i	0.392117	−	0.226389i	0.683077	+	0.730346i	$0.260641\pi$
$662$	9.03216	−	5.21472i	0.351045	−	0.202676i
$663$		0			0
$664$	−0.319454	−	0.184437i	−0.0123972	−	0.00715754i
$665$		0			0
$666$		0			0
$667$	−3.67677			−0.142365
$668$	7.40866	−	12.8322i	0.286650	−	0.496492i
$669$		0			0
$670$	2.86169	−	1.65220i	0.110557	−	0.0638301i
$671$	11.3457	+	19.6514i	0.437997	+	0.758634i
$672$		0			0
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	−0.876449	−	0.481496i	$-0.840094\pi$
$673$	−0.550931	+	0.954241i	−0.0212368	+	0.0367833i	0.855212	+	0.518279i	$0.173427\pi$
$674$			31.6624i			1.21959i
$675$		0			0
$676$	−7.71810			−0.296850
$677$	5.61618	−	9.72751i	0.215847	−	0.373859i	−0.737687	−	0.675143i	$-0.764082\pi$
$677$	5.61618	−	9.72751i	0.215847	−	0.373859i	0.953534	+	0.301284i	$0.0974153\pi$
$678$		0			0
$679$		0			0
$680$	−4.01733	+	2.31940i	−0.154057	+	0.0889451i
$681$		0			0
$682$	−27.0986	−	15.6454i	−1.03766	−	0.599092i
$683$			43.5081i			1.66479i	0.554181	+	0.832396i	$0.313032\pi$
$683$			43.5081i			1.66479i	−0.554181	+	0.832396i	$0.686968\pi$
$684$		0			0
$685$		−	19.6616i		−	0.751231i
$686$		0			0
$687$		0			0
$688$	−0.273155	−	0.473119i	−0.0104139	−	0.0180375i
$689$	−16.0200	−	27.7474i	−0.610312	−	1.05709i
$690$		0			0
$691$	27.9085	+	16.1130i	1.06169	+	0.612967i	0.925899	−	0.377770i	$-0.123309\pi$
$691$	27.9085	+	16.1130i	1.06169	+	0.612967i	0.135791	+	0.990738i	$0.456642\pi$
$692$	−4.63544			−0.176213
$693$		0			0
$694$	12.5252			0.475451
$695$	−10.5428	−	6.08689i	−0.399911	−	0.230889i
$696$		0			0
$697$	6.29326	+	10.9002i	0.238374	+	0.412876i
$698$	7.07599	+	12.2560i	0.267830	+	0.463895i
$699$		0			0
$700$		0			0
$701$			21.8995i			0.827133i	0.910474	+	0.413566i	$0.135717\pi$
$701$			21.8995i			0.827133i	−0.910474	+	0.413566i	$0.864283\pi$
$702$		0			0
$703$		−	26.0486i		−	0.982440i
$704$	2.70900	+	1.56404i	0.102099	+	0.0589471i
$705$		0			0
$706$	4.30012	−	2.48267i	0.161837	−	0.0934366i
$707$		0			0
$708$		0			0
$709$	9.02351	−	15.6292i	0.338885	−	0.586966i	−0.645338	−	0.763897i	$-0.723284\pi$
$709$	9.02351	−	15.6292i	0.338885	−	0.586966i	0.984223	+	0.176931i	$0.0566168\pi$
$710$	−12.7372			−0.478020
$711$		0			0
$712$			12.0049i			0.449902i
$713$	8.58120	−	14.8631i	0.321369	−	0.556627i
$714$		0			0
$715$	3.23602	+	5.60494i	0.121020	+	0.209613i
$716$	5.25855	−	3.03602i	0.196521	−	0.113462i
$717$		0			0
$718$	−8.66098	+	15.0013i	−0.323225	+	0.559842i
$719$	9.31888			0.347536			0.173768	−	0.984787i	$-0.444406\pi$
$719$	9.31888			0.347536			0.173768	+	0.984787i	$0.444406\pi$
$720$		0			0
$721$		0			0
$722$	−9.90769	−	5.72021i	−0.368726	−	0.212884i
$723$		0			0
$724$	6.17217	−	3.56350i	0.229387	−	0.132437i
$725$	7.77537	−	4.48911i	0.288770	−	0.166722i
$726$		0			0
$727$	6.73516	+	3.88855i	0.249793	+	0.144218i	0.619670	−	0.784863i	$-0.287267\pi$
$727$	6.73516	+	3.88855i	0.249793	+	0.144218i	−0.369876	+	0.929081i	$0.620600\pi$
$728$		0			0
$729$		0			0
$730$	11.3506			0.420105
$731$	−1.40750	+	2.43787i	−0.0520583	+	0.0901677i
$732$		0			0
$733$	31.2841	−	18.0619i	1.15550	−	0.667131i	0.205282	−	0.978703i	$-0.434189\pi$
$733$	31.2841	−	18.0619i	1.15550	−	0.667131i	0.950222	+	0.311572i	$0.100856\pi$
$734$	−0.685884	−	1.18799i	−0.0253164	−	0.0438494i
$735$		0			0
$736$	−0.857850	+	1.48584i	−0.0316208	+	0.0547688i
$737$			11.4817i			0.422932i
$738$		0			0
$739$	−24.1385			−0.887949			−0.443975	−	0.896039i	$-0.646432\pi$
$739$	−24.1385			−0.887949			−0.443975	+	0.896039i	$0.646432\pi$
$740$	4.26453	−	7.38639i	0.156767	−	0.271529i
$741$		0			0
$742$		0			0
$743$	−10.5762	+	6.10618i	−0.388003	+	0.224014i	−0.681295	−	0.732009i	$-0.738583\pi$
$743$	−10.5762	+	6.10618i	−0.388003	+	0.224014i	0.293291	+	0.956023i	$0.405249\pi$
$744$		0			0
$745$	3.97186	+	2.29316i	0.145518	+	0.0840147i
$746$		−	4.80975i		−	0.176098i
$747$		0			0
$748$		−	16.1183i		−	0.589342i
$749$		0			0
$750$		0			0
$751$	11.7190	+	20.2980i	0.427634	+	0.740684i	0.996662	−	0.0816339i	$-0.0260138\pi$
$751$	11.7190	+	20.2980i	0.427634	+	0.740684i	−0.569028	+	0.822318i	$0.692680\pi$
$752$	−3.93034	−	6.80755i	−0.143325	−	0.248246i
$753$		0			0
$754$	−4.26531	−	2.46258i	−0.155333	−	0.0896818i
$755$	−19.0634			−0.693788
$756$		0			0
$757$	3.52341			0.128060			0.0640302	−	0.997948i	$-0.479605\pi$
$757$	3.52341			0.128060			0.0640302	+	0.997948i	$0.479605\pi$
$758$	−16.9454	−	9.78346i	−0.615486	−	0.355351i
$759$		0			0
$760$	1.23762	+	2.14361i	0.0448931	+	0.0777571i
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	0.992174	−	0.124866i	$-0.0398500\pi$
$761$	10.7021	+	18.5365i	0.387950	+	0.671949i	−0.604224	+	0.796815i	$0.706517\pi$
$762$		0			0
$763$		0			0
$764$		−	14.4006i		−	0.520997i
$765$		0			0
$766$		−	31.4697i		−	1.13705i
$767$	−15.8917	−	9.17506i	−0.573815	−	0.331292i
$768$		0			0
$769$	23.4043	−	13.5125i	0.843982	−	0.487273i	−0.0146339	−	0.999893i	$-0.504658\pi$
$769$	23.4043	−	13.5125i	0.843982	−	0.487273i	0.858616	+	0.512620i	$0.171325\pi$
$770$		0			0
$771$		0			0
$772$	8.90573	−	15.4252i	0.320524	−	0.555164i
$773$	−16.2056			−0.582875			−0.291437	−	0.956590i	$-0.594134\pi$
$773$	−16.2056			−0.582875			−0.291437	+	0.956590i	$0.594134\pi$
$774$		0			0
$775$			41.9086i			1.50540i
$776$	−5.12003	+	8.86815i	−0.183798	+	0.318348i
$777$		0			0
$778$	−2.03303	−	3.52130i	−0.0728875	−	0.126245i
$779$	5.81628	−	3.35803i	0.208390	−	0.120314i
$780$		0			0
$781$	22.1288	−	38.3281i	0.791829	−	1.37149i
$782$	8.84058			0.316139
$783$		0			0
$784$		0			0
$785$	−0.280613	−	0.162012i	−0.0100155	−	0.00578246i
$786$		0			0
$787$	33.1317	−	19.1286i	1.18102	−	0.681860i	0.224767	−	0.974413i	$-0.427838\pi$
$787$	33.1317	−	19.1286i	1.18102	−	0.681860i	0.956249	+	0.292553i	$0.0945047\pi$
$788$	16.5432	−	9.55124i	0.589328	−	0.340249i
$789$		0			0
$790$	5.10515	+	2.94746i	0.181633	+	0.104866i
$791$		0			0
$792$		0			0
$793$	−16.6717			−0.592028
$794$	2.20370	−	3.81692i	0.0782064	−	0.135457i
$795$		0			0
$796$	−11.6008	+	6.69771i	−0.411179	+	0.237394i
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	0.933204	−	0.359347i	$-0.117000\pi$
$797$	4.38709	+	7.59866i	0.155399	+	0.269158i	−0.777805	+	0.628505i	$0.783667\pi$
$798$		0			0
$799$	−20.2521	+	35.0776i	−0.716467	+	1.24096i
$800$		−	4.18954i		−	0.148122i
$801$		0			0
$802$	−18.5428			−0.654770
$803$	−19.7197	+	34.1556i	−0.695895	+	1.20532i
$804$		0			0
$805$		0			0
$806$	19.9096	−	11.4948i	0.701286	−	0.404887i
$807$		0			0
$808$	2.35506	+	1.35969i	0.0828506	+	0.0478338i
$809$			30.7212i			1.08010i	0.841633	+	0.540050i	$0.181595\pi$
$809$			30.7212i			1.08010i	−0.841633	+	0.540050i	$0.818405\pi$
$810$		0			0
$811$			8.70634i			0.305721i	0.988248	+	0.152861i	$0.0488485\pi$
$811$			8.70634i			0.305721i	−0.988248	+	0.152861i	$0.951151\pi$
$812$		0			0
$813$		0			0
$814$	14.8178	+	25.6652i	0.519363	+	0.899564i
$815$	5.56936	+	9.64641i	0.195086	+	0.337899i
$816$		0			0
$817$	1.30083	+	0.751032i	0.0455101	+	0.0262753i
$818$	24.8902			0.870265
$819$		0			0
$820$	2.19904			0.0767937
$821$	45.4098	+	26.2173i	1.58481	+	0.914992i	0.994142	+	0.108078i	$0.0344697\pi$
$821$	45.4098	+	26.2173i	1.58481	+	0.914992i	0.590670	+	0.806914i	$0.298864\pi$
$822$		0			0
$823$	−4.18199	−	7.24342i	−0.145775	−	0.252490i	0.783887	−	0.620904i	$-0.213234\pi$
$823$	−4.18199	−	7.24342i	−0.145775	−	0.252490i	−0.929662	+	0.368414i	$0.879901\pi$
$824$	−0.686242	−	1.18861i	−0.0239064	−	0.0414070i
$825$		0			0
$826$		0			0
$827$			26.4934i			0.921267i	0.887590	+	0.460634i	$0.152378\pi$
$827$			26.4934i			0.921267i	−0.887590	+	0.460634i	$0.847622\pi$
$828$		0			0
$829$		−	5.93671i		−	0.206190i	−0.994671	−	0.103095i	$-0.967125\pi$
$829$		−	5.93671i		−	0.206190i	0.994671	−	0.103095i	$-0.0328746\pi$
$830$	0.287591	+	0.166041i	0.00998243	+	0.00576336i
$831$		0			0
$832$	−1.99033	+	1.14912i	−0.0690024	+	0.0398385i
$833$		0			0
$834$		0			0
$835$	−6.66970	+	11.5523i	−0.230815	+	0.399783i
$836$	−8.60058			−0.297457
$837$		0			0
$838$			5.14845i			0.177850i
$839$	−3.80537	+	6.59110i	−0.131376	+	0.227550i	−0.924207	−	0.381891i	$-0.875273\pi$
$839$	−3.80537	+	6.59110i	−0.131376	+	0.227550i	0.792831	+	0.609441i	$0.208606\pi$
$840$		0			0
$841$	−12.2037	−	21.1375i	−0.420819	−	0.728880i
$842$	23.3864	−	13.5022i	0.805950	−	0.465315i
$843$		0			0
$844$	9.37193	−	16.2327i	0.322595	−	0.558751i
$845$	6.94828			0.239028
$846$		0			0
$847$		0			0
$848$	12.0733	+	6.97054i	0.414600	+	0.239369i
$849$		0			0
$850$	−18.6955	+	10.7938i	−0.641249	+	0.370225i
$851$	−14.0769	+	8.12730i	−0.482550	+	0.278600i
$852$		0			0
$853$	24.8764	+	14.3624i	0.851751	+	0.491759i	0.861241	−	0.508196i	$-0.169688\pi$
$853$	24.8764	+	14.3624i	0.851751	+	0.491759i	−0.00949029	+	0.999955i	$0.503021\pi$
$854$		0			0
$855$		0			0
$856$	−14.2704			−0.487752
$857$	−20.1198	+	34.8486i	−0.687280	+	1.19040i	0.285434	+	0.958398i	$0.407862\pi$
$857$	−20.1198	+	34.8486i	−0.687280	+	1.19040i	−0.972714	+	0.232006i	$0.925471\pi$
$858$		0			0
$859$	−13.3256	+	7.69355i	−0.454664	+	0.262501i	−0.709798	−	0.704405i	$-0.751214\pi$
$859$	−13.3256	+	7.69355i	−0.454664	+	0.262501i	0.255134	+	0.966906i	$0.417881\pi$
$860$	0.245910	+	0.425929i	0.00838547	+	0.0145241i
$861$		0			0
$862$	−4.68159	+	8.10874i	−0.159455	+	0.276185i
$863$		−	19.2250i		−	0.654428i	−0.944950	−	0.327214i	$-0.893890\pi$
$863$		−	19.2250i		−	0.654428i	0.944950	−	0.327214i	$-0.106110\pi$
$864$		0			0
$865$	4.17309			0.141889
$866$	10.5186	−	18.2188i	0.357438	−	0.619101i
$867$		0			0
$868$		0			0
$869$	−17.7386	+	10.2414i	−0.601742	+	0.347416i
$870$		0			0
$871$	−7.30552	−	4.21785i	−0.247538	−	0.142916i
$872$		−	5.29166i		−	0.179198i
$873$		0			0
$874$		−	4.71727i		−	0.159564i
$875$		0			0
$876$		0			0
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	0.942568	−	0.334014i	$-0.108403\pi$
$877$	5.39035	+	9.33636i	0.182019	+	0.315267i	−0.760549	+	0.649281i	$0.775070\pi$
$878$	−10.2114	−	17.6867i	−0.344619	−	0.596898i
$879$		0			0
$880$	−2.43880	−	1.40804i	−0.0822120	−	0.0474651i
$881$	−44.2875			−1.49208			−0.746041	−	0.665900i	$-0.768048\pi$
$881$	−44.2875			−1.49208			−0.746041	+	0.665900i	$0.768048\pi$
$882$		0			0
$883$	−47.6098			−1.60220			−0.801098	−	0.598533i	$-0.795751\pi$
$883$	−47.6098			−1.60220			−0.801098	+	0.598533i	$0.795751\pi$
$884$	10.2557	+	5.92113i	0.344936	+	0.199149i
$885$		0			0
$886$	−16.1825	−	28.0288i	−0.543660	−	0.941647i
$887$	0.989965	+	1.71467i	0.0332398	+	0.0575730i	0.882167	−	0.470937i	$-0.156084\pi$
$887$	0.989965	+	1.71467i	0.0332398	+	0.0575730i	−0.848927	+	0.528510i	$0.822751\pi$
$888$		0			0
$889$		0			0
$890$		−	10.8075i		−	0.362268i
$891$		0			0
$892$		−	2.55892i		−	0.0856789i
$893$	18.7172	+	10.8064i	0.626346	+	0.361621i
$894$		0			0
$895$	−4.73405	+	2.73320i	−0.158242	+	0.0913609i
$896$		0			0
$897$		0			0
$898$	−10.7846	+	18.6795i	−0.359888	+	0.623344i
$899$	−21.4369			−0.714960
$900$		0			0
$901$		−	71.8350i		−	2.39317i
$902$	−3.82045	+	6.61721i	−0.127207	+	0.220329i
$903$		0			0
$904$	−1.33005	−	2.30371i	−0.0442368	−	0.0766204i
$905$	−5.55654	+	3.20807i	−0.184706	+	0.106640i
$906$		0			0
$907$	−17.0252	+	29.4886i	−0.565314	+	0.979152i	0.431707	+	0.902014i	$0.357912\pi$
$907$	−17.0252	+	29.4886i	−0.565314	+	0.979152i	−0.997020	+	0.0771381i	$0.975422\pi$
$908$	−8.72909			−0.289685
$909$		0			0
$910$		0			0
$911$	6.58371	+	3.80111i	0.218128	+	0.125936i	0.605083	−	0.796162i	$-0.293140\pi$
$911$	6.58371	+	3.80111i	0.218128	+	0.125936i	−0.386955	+	0.922099i	$0.626473\pi$
$912$		0			0
$913$	−0.999280	+	0.576934i	−0.0330713	+	0.0190937i
$914$	18.2471	−	10.5350i	0.603561	−	0.348466i
$915$		0			0
$916$	−3.40979	−	1.96865i	−0.112663	−	0.0650459i
$917$		0			0
$918$		0			0
$919$	8.22273			0.271243			0.135621	−	0.990761i	$-0.456697\pi$
$919$	8.22273			0.271243			0.135621	+	0.990761i	$0.456697\pi$
$920$	0.772286	−	1.33764i	0.0254615	−	0.0441006i
$921$		0			0
$922$	−27.4378	+	15.8412i	−0.903617	+	0.521704i
$923$	16.2582	+	28.1601i	0.535146	+	0.926900i
$924$		0			0
$925$	19.8459	−	34.3741i	0.652529	−	1.13021i
$926$		−	8.80115i		−	0.289224i
$927$		0			0
$928$	2.14301			0.0703478
$929$	−2.53982	+	4.39909i	−0.0833287	+	0.144329i	−0.904678	−	0.426096i	$-0.859888\pi$
$929$	−2.53982	+	4.39909i	−0.0833287	+	0.144329i	0.821349	+	0.570426i	$0.193222\pi$
$930$		0			0
$931$		0			0
$932$	−3.92147	+	2.26406i	−0.128452	+	0.0741618i
$933$		0			0
$934$	16.4449	+	9.49444i	0.538092	+	0.310668i
$935$			14.5106i			0.474547i
$936$		0			0
$937$		−	10.8127i		−	0.353236i	−0.984280	−	0.176618i	$-0.943484\pi$
$937$		−	10.8127i		−	0.353236i	0.984280	−	0.176618i	$-0.0565157\pi$
$938$		0			0
$939$		0			0
$940$	3.53832	+	6.12855i	0.115407	+	0.199891i
$941$	9.58193	+	16.5964i	0.312362	+	0.541027i	0.978873	−	0.204468i	$-0.0655464\pi$
$941$	9.58193	+	16.5964i	0.312362	+	0.541027i	−0.666511	+	0.745495i	$0.732213\pi$
$942$		0			0
$943$	−3.62942	−	2.09545i	−0.118190	−	0.0682372i
$944$	7.98443			0.259871
$945$		0			0
$946$	−1.70891			−0.0555613
$947$	−21.9930	−	12.6977i	−0.714676	−	0.412618i	0.0981139	−	0.995175i	$-0.468719\pi$
$947$	−21.9930	−	12.6977i	−0.714676	−	0.412618i	−0.812790	+	0.582557i	$0.802052\pi$
$948$		0			0
$949$	−14.4883	−	25.0945i	−0.470310	−	0.814601i
$950$	5.75950	+	9.97575i	0.186863	+	0.323656i
$951$		0			0
$952$		0			0
$953$		−	18.4818i		−	0.598686i	−0.954146	−	0.299343i	$-0.903233\pi$
$953$		−	18.4818i		−	0.598686i	0.954146	−	0.299343i	$-0.0967674\pi$
$954$		0			0
$955$			12.9643i			0.419515i
$956$	7.55315	+	4.36081i	0.244286	+	0.141039i
$957$		0			0
$958$	−20.9060	+	12.0701i	−0.675441	+	0.389966i
$959$		0			0
$960$		0			0
$961$	34.5315	−	59.8103i	1.11392	−	1.92937i
$962$	−21.7736			−0.702008
$963$		0			0
$964$		−	19.7816i		−	0.637122i
$965$	−8.01745	+	13.8866i	−0.258091	+	0.447026i
$966$		0			0
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	0.668222	−	0.743962i	$-0.267056\pi$
$967$	−9.64551	−	16.7065i	−0.310179	−	0.537245i	−0.978401	+	0.206717i	$0.933722\pi$
$968$	−1.05229	+	0.607537i	−0.0338217	+	0.0195270i
$969$		0			0
$970$	4.60935	−	7.98362i	0.147997	−	0.256339i
$971$	1.95089			0.0626070			0.0313035	−	0.999510i	$-0.490034\pi$
$971$	1.95089			0.0626070			0.0313035	+	0.999510i	$0.490034\pi$
$972$		0			0
$973$		0			0
$974$	12.2204	+	7.05542i	0.391565	+	0.226070i
$975$		0			0
$976$	6.28224	−	3.62705i	0.201090	−	0.116099i
$977$	−14.4856	+	8.36326i	−0.463435	+	0.267564i	−0.713488	−	0.700668i	$-0.752885\pi$
$977$	−14.4856	+	8.36326i	−0.463435	+	0.267564i	0.250052	+	0.968232i	$0.419552\pi$
$978$		0			0
$979$	32.5213	+	18.7762i	1.03938	+	0.600089i
$980$		0			0
$981$		0			0
$982$	−21.7480			−0.694008
$983$	−16.1458	+	27.9653i	−0.514970	+	0.891955i	0.484879	+	0.874581i	$0.338864\pi$
$983$	−16.1458	+	27.9653i	−0.514970	+	0.891955i	−0.999849	+	0.0173733i	$0.994470\pi$
$984$		0			0
$985$	−14.8932	+	8.59858i	−0.474536	+	0.273974i
$986$	−5.52121	−	9.56302i	−0.175831	−	0.304549i
$987$		0			0
$988$	3.15947	−	5.47236i	0.100516	−	0.174099i
$989$		−	0.937305i		−	0.0298046i
$990$		0			0
$991$	−8.50267			−0.270096			−0.135048	−	0.990839i	$-0.543119\pi$
$991$	−8.50267			−0.270096			−0.135048	+	0.990839i	$0.543119\pi$
$992$	−5.00158	+	8.66298i	−0.158800	+	0.275050i
$993$		0			0
$994$		0			0
$995$	10.4437	−	6.02967i	0.331087	−	0.191153i
$996$		0			0
$997$	9.78395	+	5.64877i	0.309861	+	0.178898i	0.646864	−	0.762605i	$-0.276080\pi$
$997$	9.78395	+	5.64877i	0.309861	+	0.178898i	−0.337003	+	0.941503i	$0.609413\pi$
$998$		−	8.42465i		−	0.266678i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.m.a.1763.2		16
3.2	odd	2		882.2.m.a.587.8		16
7.2	even	3		2646.2.l.a.521.6		16
7.3	odd	6		2646.2.t.b.1979.6		16
7.4	even	3		378.2.t.a.89.7		16
7.5	odd	6		378.2.l.a.143.7		16
7.6	odd	2		2646.2.m.b.1763.3		16
9.4	even	3		882.2.m.b.293.5		16
9.5	odd	6		2646.2.m.b.881.3		16
21.2	odd	6		882.2.l.b.227.1		16
21.5	even	6		126.2.l.a.101.4	yes	16
21.11	odd	6		126.2.t.a.47.3	yes	16
21.17	even	6		882.2.t.a.803.2		16
21.20	even	2		882.2.m.b.587.5		16
28.11	odd	6		3024.2.df.c.1601.6		16
28.19	even	6		3024.2.ca.c.2033.6		16
63.4	even	3		126.2.l.a.5.8	✓	16
63.5	even	6		378.2.t.a.17.7		16
63.11	odd	6		1134.2.k.b.971.7		16
63.13	odd	6		882.2.m.a.293.8		16
63.23	odd	6		2646.2.t.b.2285.6		16
63.25	even	3		1134.2.k.a.971.2		16
63.31	odd	6		882.2.l.b.509.5		16
63.32	odd	6		378.2.l.a.341.3		16
63.40	odd	6		126.2.t.a.59.3	yes	16
63.41	even	6	inner	2646.2.m.a.881.2		16
63.47	even	6		1134.2.k.a.647.2		16
63.58	even	3		882.2.t.a.815.2		16
63.59	even	6		2646.2.l.a.1097.2		16
63.61	odd	6		1134.2.k.b.647.7		16
84.11	even	6		1008.2.df.c.929.4		16
84.47	odd	6		1008.2.ca.c.353.1		16
252.67	odd	6		1008.2.ca.c.257.1		16
252.95	even	6		3024.2.ca.c.2609.6		16
252.103	even	6		1008.2.df.c.689.4		16
252.131	odd	6		3024.2.df.c.17.6		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.l.a.5.8	✓	16	63.4	even	3
126.2.l.a.101.4	yes	16	21.5	even	6
126.2.t.a.47.3	yes	16	21.11	odd	6
126.2.t.a.59.3	yes	16	63.40	odd	6
378.2.l.a.143.7		16	7.5	odd	6
378.2.l.a.341.3		16	63.32	odd	6
378.2.t.a.17.7		16	63.5	even	6
378.2.t.a.89.7		16	7.4	even	3
882.2.l.b.227.1		16	21.2	odd	6
882.2.l.b.509.5		16	63.31	odd	6
882.2.m.a.293.8		16	63.13	odd	6
882.2.m.a.587.8		16	3.2	odd	2
882.2.m.b.293.5		16	9.4	even	3
882.2.m.b.587.5		16	21.20	even	2
882.2.t.a.803.2		16	21.17	even	6
882.2.t.a.815.2		16	63.58	even	3
1008.2.ca.c.257.1		16	252.67	odd	6
1008.2.ca.c.353.1		16	84.47	odd	6
1008.2.df.c.689.4		16	252.103	even	6
1008.2.df.c.929.4		16	84.11	even	6
1134.2.k.a.647.2		16	63.47	even	6
1134.2.k.a.971.2		16	63.25	even	3
1134.2.k.b.647.7		16	63.61	odd	6
1134.2.k.b.971.7		16	63.11	odd	6
2646.2.l.a.521.6		16	7.2	even	3
2646.2.l.a.1097.2		16	63.59	even	6
2646.2.m.a.881.2		16	63.41	even	6	inner
2646.2.m.a.1763.2		16	1.1	even	1	trivial
2646.2.m.b.881.3		16	9.5	odd	6
2646.2.m.b.1763.3		16	7.6	odd	2
2646.2.t.b.1979.6		16	7.3	odd	6
2646.2.t.b.2285.6		16	63.23	odd	6
3024.2.ca.c.2033.6		16	28.19	even	6
3024.2.ca.c.2609.6		16	252.95	even	6
3024.2.df.c.17.6		16	252.131	odd	6
3024.2.df.c.1601.6		16	28.11	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.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} -1.00000i q^{8} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.450129 - 0.779646i) q^{5} -1.00000i q^{8} +0.900258i q^{10} +(-2.70900 - 1.56404i) q^{11} +(1.99033 - 1.14912i) q^{13} +(-0.500000 + 0.866025i) q^{16} +5.15276 q^{17} -2.74947i q^{19} +(0.450129 - 0.779646i) q^{20} +(1.56404 + 2.70900i) q^{22} +(-1.48584 + 0.857850i) q^{23} +(2.09477 - 3.62824i) q^{25} -2.29824 q^{26} +(1.85590 + 1.07151i) q^{29} +(-8.66298 + 5.00158i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-4.46242 - 2.57638i) q^{34} +9.47403 q^{37} +(-1.37474 + 2.38111i) q^{38} +(-0.779646 + 0.450129i) q^{40} +(1.22134 + 2.11542i) q^{41} +(-0.273155 + 0.473119i) q^{43} -3.12809i q^{44} +1.71570 q^{46} +(-3.93034 + 6.80755i) q^{47} +(-3.62824 + 2.09477i) q^{50} +(1.99033 + 1.14912i) q^{52} -13.9411i q^{53} +2.81608i q^{55} +(-1.07151 - 1.85590i) q^{58} +(-3.99222 - 6.91472i) q^{59} +(-6.28224 - 3.62705i) q^{61} +10.0032 q^{62} -1.00000 q^{64} +(-1.79181 - 1.03450i) q^{65} +(-1.83525 - 3.17875i) q^{67} +(2.57638 + 4.46242i) q^{68} +14.1484i q^{71} -12.6082i q^{73} +(-8.20475 - 4.73701i) q^{74} +(2.38111 - 1.37474i) q^{76} +(3.27402 - 5.67077i) q^{79} +0.900258 q^{80} -2.44268i q^{82} +(0.184437 - 0.319454i) q^{83} +(-2.31940 - 4.01733i) q^{85} +(0.473119 - 0.273155i) q^{86} +(-1.56404 + 2.70900i) q^{88} -12.0049 q^{89} +(-1.48584 - 0.857850i) q^{92} +(6.80755 - 3.93034i) q^{94} +(-2.14361 + 1.23762i) q^{95} +(-8.86815 - 5.12003i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4}+O(q^{10}) \) 16 * q + 8 * q^4	\( 16 q + 8 q^{4} + 12 q^{11} - 6 q^{13} - 8 q^{16} + 36 q^{17} - 6 q^{23} - 8 q^{25} - 24 q^{26} - 6 q^{29} - 6 q^{31} + 4 q^{37} - 6 q^{41} - 2 q^{43} - 12 q^{46} + 18 q^{47} + 12 q^{50} - 6 q^{52} + 6 q^{58} - 30 q^{59} + 60 q^{61} + 36 q^{62} - 16 q^{64} + 42 q^{65} + 14 q^{67} + 18 q^{68} + 18 q^{74} - 16 q^{79} - 12 q^{85} + 24 q^{86} + 48 q^{89} - 6 q^{92} - 66 q^{95} - 6 q^{97}+O(q^{100}) \) 16 * q + 8 * q^4 + 12 * q^11 - 6 * q^13 - 8 * q^16 + 36 * q^17 - 6 * q^23 - 8 * q^25 - 24 * q^26 - 6 * q^29 - 6 * q^31 + 4 * q^37 - 6 * q^41 - 2 * q^43 - 12 * q^46 + 18 * q^47 + 12 * q^50 - 6 * q^52 + 6 * q^58 - 30 * q^59 + 60 * q^61 + 36 * q^62 - 16 * q^64 + 42 * q^65 + 14 * q^67 + 18 * q^68 + 18 * q^74 - 16 * q^79 - 12 * q^85 + 24 * q^86 + 48 * q^89 - 6 * q^92 - 66 * q^95 - 6 * q^97

Introduction

L-functions

Modular forms

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