LMFDB - Embedded newform 2646.2.e.k.1549.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1549.1
Root			$-1.22474 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.k.2125.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{4} +(-1.72474 - 2.98735i) q^{5} -1.00000 q^{8} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.72474 - 2.98735i) q^{5} -1.00000 q^{8} +(1.72474 + 2.98735i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} +1.00000 q^{16} +(-1.00000 - 1.73205i) q^{17} +(3.72474 - 6.45145i) q^{19} +(-1.72474 - 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-3.44949 + 5.97469i) q^{25} +(2.44949 - 4.24264i) q^{26} +(1.44949 + 2.51059i) q^{29} -6.00000 q^{31} -1.00000 q^{32} +(1.00000 + 1.73205i) q^{34} +(3.89898 - 6.75323i) q^{37} +(-3.72474 + 6.45145i) q^{38} +(1.72474 + 2.98735i) q^{40} +(4.89898 - 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(1.00000 - 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} -9.79796 q^{47} +(3.44949 - 5.97469i) q^{50} +(-2.44949 + 4.24264i) q^{52} +(-0.550510 - 0.953512i) q^{53} -6.89898 q^{55} +(-1.44949 - 2.51059i) q^{58} -2.00000 q^{59} -11.4495 q^{61} +6.00000 q^{62} +1.00000 q^{64} +16.8990 q^{65} -3.10102 q^{67} +(-1.00000 - 1.73205i) q^{68} -9.89898 q^{71} +(1.44949 + 2.51059i) q^{73} +(-3.89898 + 6.75323i) q^{74} +(3.72474 - 6.45145i) q^{76} +7.89898 q^{79} +(-1.72474 - 2.98735i) q^{80} +(-4.89898 + 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(-1.44949 - 2.51059i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(3.55051 - 6.14966i) q^{89} +(-0.500000 - 0.866025i) q^{92} +9.79796 q^{94} -25.6969 q^{95} +(-3.44949 - 5.97469i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^8	$ 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 4 q^{11} + 4 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{29} - 24 q^{31} - 4 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38} + 2 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} - 8 q^{55} + 4 q^{58} - 8 q^{59} - 36 q^{61} + 24 q^{62} + 4 q^{64} + 48 q^{65} - 32 q^{67} - 4 q^{68} - 20 q^{71} - 4 q^{73} + 4 q^{74} + 10 q^{76} + 12 q^{79} - 2 q^{80} - 4 q^{83} - 4 q^{85} + 4 q^{86} - 4 q^{88} + 24 q^{89} - 2 q^{92} - 44 q^{95} - 4 q^{97}+O(q^{100}) $ 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^8 + 2 * q^10 + 4 * q^11 + 4 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^29 - 24 * q^31 - 4 * q^32 + 4 * q^34 - 4 * q^37 - 10 * q^38 + 2 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 + 4 * q^58 - 8 * q^59 - 36 * q^61 + 24 * q^62 + 4 * q^64 + 48 * q^65 - 32 * q^67 - 4 * q^68 - 20 * q^71 - 4 * q^73 + 4 * q^74 + 10 * q^76 + 12 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 + 4 * q^86 - 4 * q^88 + 24 * q^89 - 2 * q^92 - 44 * q^95 - 4 * q^97

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	−1.72474	−	2.98735i	−0.771329	−	1.33598i	−0.936835	−	0.349773i	$-0.886259\pi$
$5$	−1.72474	−	2.98735i	−0.771329	−	1.33598i	0.165505	−	0.986209i	$-0.447075\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	1.72474	+	2.98735i	0.545412	+	0.944682i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	0.295806	+	0.955248i	$0.404412\pi$
$13$	−2.44949	+	4.24264i	−0.679366	+	1.17670i	−0.975172	+	0.221449i	$0.928921\pi$
$14$		0			0
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	3.72474	−	6.45145i	0.854515	−	1.48006i	−0.0225791	−	0.999745i	$-0.507188\pi$
$19$	3.72474	−	6.45145i	0.854515	−	1.48006i	0.877094	−	0.480318i	$-0.159479\pi$
$20$	−1.72474	−	2.98735i	−0.385665	−	0.667991i
$21$		0			0
$22$	−1.00000	+	1.73205i	−0.213201	+	0.369274i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	0.809177	−	0.587565i	$-0.199913\pi$
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i	−0.913434	+	0.406986i	$0.866580\pi$
$24$		0			0
$25$	−3.44949	+	5.97469i	−0.689898	+	1.19494i
$26$	2.44949	−	4.24264i	0.480384	−	0.832050i
$27$		0			0
$28$		0			0
$29$	1.44949	+	2.51059i	0.269163	+	0.466205i	0.968646	−	0.248445i	$-0.0799195\pi$
$29$	1.44949	+	2.51059i	0.269163	+	0.466205i	−0.699483	+	0.714650i	$0.746586\pi$
$30$		0			0
$31$	−6.00000			−1.07763			−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000			−1.07763			−0.538816	+	0.842424i	$0.681128\pi$
$32$	−1.00000			−0.176777
$33$		0			0
$34$	1.00000	+	1.73205i	0.171499	+	0.297044i
$35$		0			0
$36$		0			0
$37$	3.89898	−	6.75323i	0.640988	−	1.11022i	−0.344224	−	0.938887i	$-0.611858\pi$
$37$	3.89898	−	6.75323i	0.640988	−	1.11022i	0.985213	−	0.171337i	$-0.0548086\pi$
$38$	−3.72474	+	6.45145i	−0.604233	+	1.04656i
$39$		0			0
$40$	1.72474	+	2.98735i	0.272706	+	0.472341i
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	−0.175106	−	0.984550i	$-0.556027\pi$
$41$	4.89898	−	8.48528i	0.765092	−	1.32518i	0.940198	−	0.340629i	$-0.110640\pi$
$42$		0			0
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	0.955126	−	0.296201i	$-0.0957199\pi$
$43$	1.44949	+	2.51059i	0.221045	+	0.382861i	−0.734080	+	0.679062i	$0.762387\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−9.79796			−1.42918			−0.714590	−	0.699544i	$-0.753387\pi$
$47$	−9.79796			−1.42918			−0.714590	+	0.699544i	$0.753387\pi$
$48$		0			0
$49$		0			0
$50$	3.44949	−	5.97469i	0.487832	−	0.844949i
$51$		0			0
$52$	−2.44949	+	4.24264i	−0.339683	+	0.588348i
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	0.825737	−	0.564056i	$-0.190760\pi$
$53$	−0.550510	−	0.953512i	−0.0756184	−	0.130975i	−0.901355	+	0.433081i	$0.857426\pi$
$54$		0			0
$55$	−6.89898			−0.930258
$56$		0			0
$57$		0			0
$58$	−1.44949	−	2.51059i	−0.190327	−	0.329657i
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$		0			0
$61$	−11.4495			−1.46596			−0.732978	−	0.680252i	$-0.761870\pi$
$61$	−11.4495			−1.46596			−0.732978	+	0.680252i	$0.761870\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	16.8990			2.09606
$66$		0			0
$67$	−3.10102			−0.378850			−0.189425	−	0.981895i	$-0.560662\pi$
$67$	−3.10102			−0.378850			−0.189425	+	0.981895i	$0.560662\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−9.89898			−1.17479			−0.587396	−	0.809299i	$-0.699847\pi$
$71$	−9.89898			−1.17479			−0.587396	+	0.809299i	$0.699847\pi$
$72$		0			0
$73$	1.44949	+	2.51059i	0.169650	+	0.293842i	0.938297	−	0.345831i	$-0.112403\pi$
$73$	1.44949	+	2.51059i	0.169650	+	0.293842i	−0.768647	+	0.639673i	$0.779070\pi$
$74$	−3.89898	+	6.75323i	−0.453247	+	0.785047i
$75$		0			0
$76$	3.72474	−	6.45145i	0.427258	−	0.740032i
$77$		0			0
$78$		0			0
$79$	7.89898			0.888705			0.444352	−	0.895852i	$-0.353434\pi$
$79$	7.89898			0.888705			0.444352	+	0.895852i	$0.353434\pi$
$80$	−1.72474	−	2.98735i	−0.192832	−	0.333995i
$81$		0			0
$82$	−4.89898	+	8.48528i	−0.541002	+	0.937043i
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	0.805910	−	0.592037i	$-0.201676\pi$
$83$	−1.00000	−	1.73205i	−0.109764	−	0.190117i	−0.915675	+	0.401920i	$0.868343\pi$
$84$		0			0
$85$	−3.44949	+	5.97469i	−0.374150	+	0.648046i
$86$	−1.44949	−	2.51059i	−0.156302	−	0.270724i
$87$		0			0
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	3.55051	−	6.14966i	0.376353	−	0.651863i	−0.614175	−	0.789170i	$-0.710511\pi$
$89$	3.55051	−	6.14966i	0.376353	−	0.651863i	0.990529	+	0.137307i	$0.0438445\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$		0			0
$94$	9.79796			1.01058
$95$	−25.6969			−2.63645
$96$		0			0
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	0.636049	−	0.771649i	$-0.280568\pi$
$97$	−3.44949	−	5.97469i	−0.350243	−	0.606638i	−0.986292	+	0.165011i	$0.947234\pi$
$98$		0			0
$99$		0			0
$100$	−3.44949	+	5.97469i	−0.344949	+	0.597469i
$101$	−3.62372	+	6.27647i	−0.360574	+	0.624533i	−0.988055	−	0.154099i	$-0.950753\pi$
$101$	−3.62372	+	6.27647i	−0.360574	+	0.624533i	0.627481	+	0.778632i	$0.284086\pi$
$102$		0			0
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	0.971925	+	0.235291i	$0.0756043\pi$
$103$	7.00000	+	12.1244i	0.689730	+	1.19465i	−0.282194	+	0.959357i	$0.591062\pi$
$104$	2.44949	−	4.24264i	0.240192	−	0.416025i
$105$		0			0
$106$	0.550510	+	0.953512i	0.0534703	+	0.0926132i
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	8.34847	+	14.4600i	0.799638	+	1.38501i	0.919852	+	0.392266i	$0.128309\pi$
$109$	8.34847	+	14.4600i	0.799638	+	1.38501i	−0.120213	+	0.992748i	$0.538358\pi$
$110$	6.89898			0.657792
$111$		0			0
$112$		0			0
$113$	−7.94949	+	13.7689i	−0.747825	+	1.29527i	0.201038	+	0.979583i	$0.435569\pi$
$113$	−7.94949	+	13.7689i	−0.747825	+	1.29527i	−0.948863	+	0.315688i	$0.897765\pi$
$114$		0			0
$115$	−1.72474	+	2.98735i	−0.160833	+	0.278571i
$116$	1.44949	+	2.51059i	0.134582	+	0.233102i
$117$		0			0
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	11.4495			1.03659
$123$		0			0
$124$	−6.00000			−0.538816
$125$	6.55051			0.585895
$126$		0			0
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	−1.00000			−0.0883883
$129$		0			0
$130$	−16.8990			−1.48214
$131$	6.72474	+	11.6476i	0.587544	+	1.01766i	0.994553	+	0.104232i	$0.0332383\pi$
$131$	6.72474	+	11.6476i	0.587544	+	1.01766i	−0.407009	+	0.913424i	$0.633428\pi$
$132$		0			0
$133$		0			0
$134$	3.10102			0.267887
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−5.89898	+	10.2173i	−0.503984	+	0.872926i	0.496006	+	0.868319i	$0.334800\pi$
$137$	−5.89898	+	10.2173i	−0.503984	+	0.872926i	−0.999989	+	0.00460626i	$0.998534\pi$
$138$		0			0
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	−0.593069	−	0.805152i	$-0.702084\pi$
$139$	4.72474	−	8.18350i	0.400748	−	0.694115i	0.993816	+	0.111037i	$0.0354171\pi$
$140$		0			0
$141$		0			0
$142$	9.89898			0.830704
$143$	4.89898	+	8.48528i	0.409673	+	0.709575i
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	−1.44949	−	2.51059i	−0.119961	−	0.207778i
$147$		0			0
$148$	3.89898	−	6.75323i	0.320494	−	0.555112i
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$		0			0
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	−0.746190	−	0.665733i	$-0.768119\pi$
$151$	2.50000	−	4.33013i	0.203447	−	0.352381i	0.949637	+	0.313353i	$0.101452\pi$
$152$	−3.72474	+	6.45145i	−0.302117	+	0.523281i
$153$		0			0
$154$		0			0
$155$	10.3485	+	17.9241i	0.831209	+	1.43970i
$156$		0			0
$157$	−6.34847			−0.506663			−0.253332	−	0.967380i	$-0.581526\pi$
$157$	−6.34847			−0.506663			−0.253332	+	0.967380i	$0.581526\pi$
$158$	−7.89898			−0.628409
$159$		0			0
$160$	1.72474	+	2.98735i	0.136353	+	0.236170i
$161$		0			0
$162$		0			0
$163$	0.101021	−	0.174973i	0.00791254	−	0.0137049i	−0.862042	−	0.506837i	$-0.830815\pi$
$163$	0.101021	−	0.174973i	0.00791254	−	0.0137049i	0.869955	+	0.493132i	$0.164148\pi$
$164$	4.89898	−	8.48528i	0.382546	−	0.662589i
$165$		0			0
$166$	1.00000	+	1.73205i	0.0776151	+	0.134433i
$167$	−9.34847	+	16.1920i	−0.723406	+	1.25298i	0.236220	+	0.971700i	$0.424091\pi$
$167$	−9.34847	+	16.1920i	−0.723406	+	1.25298i	−0.959627	+	0.281277i	$0.909242\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	3.44949	−	5.97469i	0.264564	−	0.458238i
$171$		0			0
$172$	1.44949	+	2.51059i	0.110523	+	0.191431i
$173$	−12.8990			−0.980691			−0.490346	−	0.871528i	$-0.663129\pi$
$173$	−12.8990			−0.980691			−0.490346	+	0.871528i	$0.663129\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	−3.55051	+	6.14966i	−0.266122	+	0.460937i
$179$	−4.34847	−	7.53177i	−0.325020	−	0.562951i	0.656497	−	0.754329i	$-0.272038\pi$
$179$	−4.34847	−	7.53177i	−0.325020	−	0.562951i	−0.981516	+	0.191378i	$0.938704\pi$
$180$		0			0
$181$	−4.34847			−0.323219			−0.161610	−	0.986855i	$-0.551669\pi$
$181$	−4.34847			−0.323219			−0.161610	+	0.986855i	$0.551669\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−26.8990			−1.97765
$186$		0			0
$187$	−4.00000			−0.292509
$188$	−9.79796			−0.714590
$189$		0			0
$190$	25.6969			1.86425
$191$	−13.8990			−1.00569			−0.502847	−	0.864375i	$-0.667714\pi$
$191$	−13.8990			−1.00569			−0.502847	+	0.864375i	$0.667714\pi$
$192$		0			0
$193$	−8.10102			−0.583124			−0.291562	−	0.956552i	$-0.594175\pi$
$193$	−8.10102			−0.583124			−0.291562	+	0.956552i	$0.594175\pi$
$194$	3.44949	+	5.97469i	0.247659	+	0.428958i
$195$		0			0
$196$		0			0
$197$	12.6969			0.904619			0.452310	−	0.891861i	$-0.350600\pi$
$197$	12.6969			0.904619			0.452310	+	0.891861i	$0.350600\pi$
$198$		0			0
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	0.961999	−	0.273054i	$-0.0880337\pi$
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	−0.717471	+	0.696588i	$0.754700\pi$
$200$	3.44949	−	5.97469i	0.243916	−	0.422474i
$201$		0			0
$202$	3.62372	−	6.27647i	0.254964	−	0.441611i
$203$		0			0
$204$		0			0
$205$	−33.7980			−2.36055
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$		0			0
$208$	−2.44949	+	4.24264i	−0.169842	+	0.294174i
$209$	−7.44949	−	12.9029i	−0.515292	−	0.892512i
$210$		0			0
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	−0.914448	−	0.404703i	$-0.867375\pi$
$211$	−1.55051	+	2.68556i	−0.106742	+	0.184882i	0.807707	+	0.589584i	$0.200708\pi$
$212$	−0.550510	−	0.953512i	−0.0378092	−	0.0654875i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$		0			0
$218$	−8.34847	−	14.4600i	−0.565430	−	0.979353i
$219$		0			0
$220$	−6.89898			−0.465129
$221$	9.79796			0.659082
$222$		0			0
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	−0.968553	−	0.248807i	$-0.919962\pi$
$223$	−10.4495	−	18.0990i	−0.699750	−	1.21200i	0.268804	−	0.963195i	$-0.413372\pi$
$224$		0			0
$225$		0			0
$226$	7.94949	−	13.7689i	0.528792	−	0.915895i
$227$	0.275255	−	0.476756i	0.0182693	−	0.0316434i	−0.856746	−	0.515738i	$-0.827518\pi$
$227$	0.275255	−	0.476756i	0.0182693	−	0.0316434i	0.875016	+	0.484095i	$0.160851\pi$
$228$		0			0
$229$	−11.6237	−	20.1329i	−0.768117	−	1.33042i	−0.938583	−	0.345055i	$-0.887860\pi$
$229$	−11.6237	−	20.1329i	−0.768117	−	1.33042i	0.170465	−	0.985364i	$-0.445473\pi$
$230$	1.72474	−	2.98735i	0.113726	−	0.196980i
$231$		0			0
$232$	−1.44949	−	2.51059i	−0.0951637	−	0.164828i
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	−0.957599	−	0.288106i	$-0.906975\pi$
$233$	−3.50000	+	6.06218i	−0.229293	+	0.397146i	0.728306	+	0.685252i	$0.240308\pi$
$234$		0			0
$235$	16.8990	+	29.2699i	1.10237	+	1.90936i
$236$	−2.00000			−0.130189
$237$		0			0
$238$		0			0
$239$	−6.39898	+	11.0834i	−0.413916	+	0.716923i	−0.995314	−	0.0966962i	$-0.969172\pi$
$239$	−6.39898	+	11.0834i	−0.413916	+	0.716923i	0.581398	+	0.813619i	$0.302506\pi$
$240$		0			0
$241$	−4.44949	+	7.70674i	−0.286617	+	0.496435i	−0.973000	−	0.230805i	$-0.925864\pi$
$241$	−4.44949	+	7.70674i	−0.286617	+	0.496435i	0.686383	+	0.727240i	$0.259197\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−11.4495			−0.732978
$245$		0			0
$246$		0			0
$247$	18.2474	+	31.6055i	1.16106	+	2.01101i
$248$	6.00000			0.381000
$249$		0			0
$250$	−6.55051			−0.414291
$251$	12.5505			0.792181			0.396091	−	0.918211i	$-0.370367\pi$
$251$	12.5505			0.792181			0.396091	+	0.918211i	$0.370367\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	3.00000			0.188237
$255$		0			0
$256$	1.00000			0.0625000
$257$	−13.8990	−	24.0737i	−0.866995	−	1.50168i	−0.865053	−	0.501680i	$-0.832715\pi$
$257$	−13.8990	−	24.0737i	−0.866995	−	1.50168i	−0.00194150	−	0.999998i	$-0.500618\pi$
$258$		0			0
$259$		0			0
$260$	16.8990			1.04803
$261$		0			0
$262$	−6.72474	−	11.6476i	−0.415456	−	0.719591i
$263$	8.05051	−	13.9439i	0.496416	−	0.859817i	−0.503576	−	0.863951i	$-0.667983\pi$
$263$	8.05051	−	13.9439i	0.496416	−	0.859817i	0.999991	+	0.00413383i	$0.00131584\pi$
$264$		0			0
$265$	−1.89898	+	3.28913i	−0.116653	+	0.202050i
$266$		0			0
$267$		0			0
$268$	−3.10102			−0.189425
$269$	1.82577	+	3.16232i	0.111319	+	0.192810i	0.916302	−	0.400487i	$-0.131159\pi$
$269$	1.82577	+	3.16232i	0.111319	+	0.192810i	−0.804983	+	0.593297i	$0.797826\pi$
$270$		0			0
$271$	8.44949	−	14.6349i	0.513270	−	0.889010i	−0.486612	−	0.873618i	$-0.661767\pi$
$271$	8.44949	−	14.6349i	0.513270	−	0.889010i	0.999882	−	0.0153912i	$-0.00489937\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	5.89898	−	10.2173i	0.356370	−	0.617252i
$275$	6.89898	+	11.9494i	0.416024	+	0.720575i
$276$		0			0
$277$	−5.34847	+	9.26382i	−0.321358	+	0.556609i	−0.980769	−	0.195174i	$-0.937473\pi$
$277$	−5.34847	+	9.26382i	−0.321358	+	0.556609i	0.659410	+	0.751783i	$0.270806\pi$
$278$	−4.72474	+	8.18350i	−0.283371	+	0.490814i
$279$		0			0
$280$		0			0
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	−0.996887	−	0.0788417i	$-0.974878\pi$
$281$	−9.50000	−	16.4545i	−0.566722	−	0.981592i	0.430165	−	0.902750i	$-0.358455\pi$
$282$		0			0
$283$	20.5505			1.22160			0.610801	−	0.791785i	$-0.290848\pi$
$283$	20.5505			1.22160			0.610801	+	0.791785i	$0.290848\pi$
$284$	−9.89898			−0.587396
$285$		0			0
$286$	−4.89898	−	8.48528i	−0.289683	−	0.501745i
$287$		0			0
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−5.00000	+	8.66025i	−0.293610	+	0.508548i
$291$		0			0
$292$	1.44949	+	2.51059i	0.0848250	+	0.146921i
$293$	−13.6237	+	23.5970i	−0.795906	+	1.37855i	0.126356	+	0.991985i	$0.459672\pi$
$293$	−13.6237	+	23.5970i	−0.795906	+	1.37855i	−0.922262	+	0.386565i	$0.873661\pi$
$294$		0			0
$295$	3.44949	+	5.97469i	0.200837	+	0.347860i
$296$	−3.89898	+	6.75323i	−0.226624	+	0.392524i
$297$		0			0
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	4.89898			0.283315
$300$		0			0
$301$		0			0
$302$	−2.50000	+	4.33013i	−0.143859	+	0.249171i
$303$		0			0
$304$	3.72474	−	6.45145i	0.213629	−	0.370016i
$305$	19.7474	+	34.2036i	1.13074	+	1.95849i
$306$		0			0
$307$	−0.752551			−0.0429504			−0.0214752	−	0.999769i	$-0.506836\pi$
$307$	−0.752551			−0.0429504			−0.0214752	+	0.999769i	$0.506836\pi$
$308$		0			0
$309$		0			0
$310$	−10.3485	−	17.9241i	−0.587754	−	1.01802i
$311$	1.30306			0.0738898			0.0369449	−	0.999317i	$-0.488237\pi$
$311$	1.30306			0.0738898			0.0369449	+	0.999317i	$0.488237\pi$
$312$		0			0
$313$	−24.6969			−1.39595			−0.697977	−	0.716120i	$-0.745916\pi$
$313$	−24.6969			−1.39595			−0.697977	+	0.716120i	$0.745916\pi$
$314$	6.34847			0.358265
$315$		0			0
$316$	7.89898			0.444352
$317$	8.69694			0.488469			0.244234	−	0.969716i	$-0.421463\pi$
$317$	8.69694			0.488469			0.244234	+	0.969716i	$0.421463\pi$
$318$		0			0
$319$	5.79796			0.324623
$320$	−1.72474	−	2.98735i	−0.0964162	−	0.166998i
$321$		0			0
$322$		0			0
$323$	−14.8990			−0.829001
$324$		0			0
$325$	−16.8990	−	29.2699i	−0.937387	−	1.62360i
$326$	−0.101021	+	0.174973i	−0.00559501	+	0.00969084i
$327$		0			0
$328$	−4.89898	+	8.48528i	−0.270501	+	0.468521i
$329$		0			0
$330$		0			0
$331$	−24.6969			−1.35747			−0.678733	−	0.734385i	$-0.737471\pi$
$331$	−24.6969			−1.35747			−0.678733	+	0.734385i	$0.737471\pi$
$332$	−1.00000	−	1.73205i	−0.0548821	−	0.0950586i
$333$		0			0
$334$	9.34847	−	16.1920i	0.511525	−	0.885988i
$335$	5.34847	+	9.26382i	0.292218	+	0.506137i
$336$		0			0
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.251772	+	0.967787i	$0.581013\pi$
$337$	−17.6969	+	30.6520i	−0.964014	+	1.66972i	−0.712242	+	0.701934i	$0.752320\pi$
$338$	5.50000	+	9.52628i	0.299161	+	0.518161i
$339$		0			0
$340$	−3.44949	+	5.97469i	−0.187075	+	0.324023i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$		0			0
$344$	−1.44949	−	2.51059i	−0.0781512	−	0.135362i
$345$		0			0
$346$	12.8990			0.693453
$347$	19.5959			1.05196			0.525982	−	0.850496i	$-0.323698\pi$
$347$	19.5959			1.05196			0.525982	+	0.850496i	$0.323698\pi$
$348$		0			0
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	0.997551	+	0.0699435i	$0.0222819\pi$
$349$	10.4495	+	18.0990i	0.559348	+	0.968820i	−0.438203	+	0.898876i	$0.644385\pi$
$350$		0			0
$351$		0			0
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	17.0732	+	29.5717i	0.906152	+	1.56950i
$356$	3.55051	−	6.14966i	0.188177	−	0.325932i
$357$		0			0
$358$	4.34847	+	7.53177i	0.229824	+	0.398066i
$359$	5.39898	−	9.35131i	0.284947	−	0.493543i	−0.687649	−	0.726043i	$-0.741357\pi$
$359$	5.39898	−	9.35131i	0.284947	−	0.493543i	0.972596	+	0.232500i	$0.0746906\pi$
$360$		0			0
$361$	−18.2474	−	31.6055i	−0.960392	−	1.66345i
$362$	4.34847			0.228550
$363$		0			0
$364$		0			0
$365$	5.00000	−	8.66025i	0.261712	−	0.453298i
$366$		0			0
$367$	2.89898	−	5.02118i	0.151325	−	0.262103i	−0.780389	−	0.625294i	$-0.784979\pi$
$367$	2.89898	−	5.02118i	0.151325	−	0.262103i	0.931715	+	0.363190i	$0.118313\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$		0			0
$370$	26.8990			1.39841
$371$		0			0
$372$		0			0
$373$	−1.44949	−	2.51059i	−0.0750517	−	0.129993i	0.826057	−	0.563587i	$-0.190579\pi$
$373$	−1.44949	−	2.51059i	−0.0750517	−	0.129993i	−0.901109	+	0.433593i	$0.857246\pi$
$374$	4.00000			0.206835
$375$		0			0
$376$	9.79796			0.505291
$377$	−14.2020			−0.731442
$378$		0			0
$379$	−26.4949			−1.36095			−0.680476	−	0.732771i	$-0.738227\pi$
$379$	−26.4949			−1.36095			−0.680476	+	0.732771i	$0.738227\pi$
$380$	−25.6969			−1.31823
$381$		0			0
$382$	13.8990			0.711134
$383$	−3.44949	−	5.97469i	−0.176261	−	0.305292i	0.764336	−	0.644818i	$-0.223067\pi$
$383$	−3.44949	−	5.97469i	−0.176261	−	0.305292i	−0.940597	+	0.339526i	$0.889734\pi$
$384$		0			0
$385$		0			0
$386$	8.10102			0.412331
$387$		0			0
$388$	−3.44949	−	5.97469i	−0.175121	−	0.303319i
$389$	−7.55051	+	13.0779i	−0.382826	+	0.663074i	−0.991465	−	0.130373i	$-0.958382\pi$
$389$	−7.55051	+	13.0779i	−0.382826	+	0.663074i	0.608639	+	0.793447i	$0.291716\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$	−12.6969			−0.639663
$395$	−13.6237	−	23.5970i	−0.685484	−	1.18729i
$396$		0			0
$397$	4.65153	−	8.05669i	0.233454	−	0.404354i	−0.725369	−	0.688361i	$-0.758331\pi$
$397$	4.65153	−	8.05669i	0.233454	−	0.404354i	0.958822	+	0.284007i	$0.0916640\pi$
$398$	−3.44949	−	5.97469i	−0.172907	−	0.299484i
$399$		0			0
$400$	−3.44949	+	5.97469i	−0.172474	+	0.298735i
$401$	−5.05051	−	8.74774i	−0.252210	−	0.436841i	0.711924	−	0.702257i	$-0.247824\pi$
$401$	−5.05051	−	8.74774i	−0.252210	−	0.436841i	−0.964134	+	0.265416i	$0.914491\pi$
$402$		0			0
$403$	14.6969	−	25.4558i	0.732107	−	1.26805i
$404$	−3.62372	+	6.27647i	−0.180287	+	0.312266i
$405$		0			0
$406$		0			0
$407$	−7.79796	−	13.5065i	−0.386530	−	0.669490i
$408$		0			0
$409$	−5.79796			−0.286691			−0.143345	−	0.989673i	$-0.545786\pi$
$409$	−5.79796			−0.286691			−0.143345	+	0.989673i	$0.545786\pi$
$410$	33.7980			1.66916
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$		0			0
$415$	−3.44949	+	5.97469i	−0.169329	+	0.293286i
$416$	2.44949	−	4.24264i	0.120096	−	0.208013i
$417$		0			0
$418$	7.44949	+	12.9029i	0.364366	+	0.631101i
$419$	−12.2753	+	21.2614i	−0.599685	+	1.03869i	0.393182	+	0.919461i	$0.371374\pi$
$419$	−12.2753	+	21.2614i	−0.599685	+	1.03869i	−0.992867	+	0.119225i	$0.961959\pi$
$420$		0			0
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	0.661080	−	0.750316i	$-0.270098\pi$
$421$	−6.55051	−	11.3458i	−0.319252	−	0.552961i	−0.980332	+	0.197354i	$0.936765\pi$
$422$	1.55051	−	2.68556i	0.0754777	−	0.130731i
$423$		0			0
$424$	0.550510	+	0.953512i	0.0267351	+	0.0463066i
$425$	13.7980			0.669299
$426$		0			0
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	−5.00000	+	8.66025i	−0.241121	+	0.417635i
$431$	−3.79796	−	6.57826i	−0.182941	−	0.316864i	0.759940	−	0.649994i	$-0.225228\pi$
$431$	−3.79796	−	6.57826i	−0.182941	−	0.316864i	−0.942881	+	0.333130i	$0.891895\pi$
$432$		0			0
$433$	−11.7980			−0.566974			−0.283487	−	0.958976i	$-0.591491\pi$
$433$	−11.7980			−0.566974			−0.283487	+	0.958976i	$0.591491\pi$
$434$		0			0
$435$		0			0
$436$	8.34847	+	14.4600i	0.399819	+	0.692507i
$437$	−7.44949			−0.356357
$438$		0			0
$439$	−21.7980			−1.04036			−0.520180	−	0.854057i	$-0.674135\pi$
$439$	−21.7980			−1.04036			−0.520180	+	0.854057i	$0.674135\pi$
$440$	6.89898			0.328896
$441$		0			0
$442$	−9.79796			−0.466041
$443$	5.10102			0.242357			0.121178	−	0.992631i	$-0.461333\pi$
$443$	5.10102			0.242357			0.121178	+	0.992631i	$0.461333\pi$
$444$		0			0
$445$	−24.4949			−1.16117
$446$	10.4495	+	18.0990i	0.494798	+	0.857015i
$447$		0			0
$448$		0			0
$449$	18.5959			0.877596			0.438798	−	0.898586i	$-0.355404\pi$
$449$	18.5959			0.877596			0.438798	+	0.898586i	$0.355404\pi$
$450$		0			0
$451$	−9.79796	−	16.9706i	−0.461368	−	0.799113i
$452$	−7.94949	+	13.7689i	−0.373913	+	0.647636i
$453$		0			0
$454$	−0.275255	+	0.476756i	−0.0129184	+	0.0223753i
$455$		0			0
$456$		0			0
$457$	31.4949			1.47327			0.736635	−	0.676291i	$-0.236414\pi$
$457$	31.4949			1.47327			0.736635	+	0.676291i	$0.236414\pi$
$458$	11.6237	+	20.1329i	0.543141	+	0.940748i
$459$		0			0
$460$	−1.72474	+	2.98735i	−0.0804166	+	0.139286i
$461$	−10.1742	−	17.6223i	−0.473861	−	0.820752i	0.525691	−	0.850676i	$-0.323807\pi$
$461$	−10.1742	−	17.6223i	−0.473861	−	0.820752i	−0.999552	+	0.0299238i	$0.990474\pi$
$462$		0			0
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	−0.396125	−	0.918197i	$-0.629645\pi$
$463$	12.8485	−	22.2542i	0.597119	−	1.03424i	0.993244	−	0.116044i	$-0.0370213\pi$
$464$	1.44949	+	2.51059i	0.0672909	+	0.116551i
$465$		0			0
$466$	3.50000	−	6.06218i	0.162134	−	0.280825i
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	−0.958212	−	0.286058i	$-0.907655\pi$
$467$	−5.00000	+	8.66025i	−0.231372	+	0.400749i	0.726840	+	0.686807i	$0.240988\pi$
$468$		0			0
$469$		0			0
$470$	−16.8990	−	29.2699i	−0.779492	−	1.35012i
$471$		0			0
$472$	2.00000			0.0920575
$473$	5.79796			0.266590
$474$		0			0
$475$	25.6969	+	44.5084i	1.17906	+	2.04219i
$476$		0			0
$477$		0			0
$478$	6.39898	−	11.0834i	0.292683	−	0.506941i
$479$	14.7980	−	25.6308i	0.676136	−	1.17110i	−0.299999	−	0.953939i	$-0.596987\pi$
$479$	14.7980	−	25.6308i	0.676136	−	1.17110i	0.976135	−	0.217163i	$-0.0696802\pi$
$480$		0			0
$481$	19.1010	+	33.0839i	0.870932	+	1.50850i
$482$	4.44949	−	7.70674i	0.202669	−	0.351032i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−11.8990	+	20.6096i	−0.540305	+	0.935835i
$486$		0			0
$487$	−11.1969	−	19.3937i	−0.507382	−	0.878811i	−0.999963	−	0.00854475i	$-0.997280\pi$
$487$	−11.1969	−	19.3937i	−0.507382	−	0.878811i	0.492582	−	0.870266i	$-0.336053\pi$
$488$	11.4495			0.518294
$489$		0			0
$490$		0			0
$491$	−1.89898	+	3.28913i	−0.0856997	+	0.148436i	−0.905689	−	0.423942i	$-0.860646\pi$
$491$	−1.89898	+	3.28913i	−0.0856997	+	0.148436i	0.819989	+	0.572379i	$0.193979\pi$
$492$		0			0
$493$	2.89898	−	5.02118i	0.130563	−	0.226143i
$494$	−18.2474	−	31.6055i	−0.820992	−	1.42200i
$495$		0			0
$496$	−6.00000			−0.269408
$497$		0			0
$498$		0			0
$499$	−16.6969	−	28.9199i	−0.747458	−	1.29463i	−0.949038	−	0.315163i	$-0.897941\pi$
$499$	−16.6969	−	28.9199i	−0.747458	−	1.29463i	0.201580	−	0.979472i	$-0.435392\pi$
$500$	6.55051			0.292948
$501$		0			0
$502$	−12.5505			−0.560157
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	2.00000			0.0889108
$507$		0			0
$508$	−3.00000			−0.133103
$509$	8.44949	+	14.6349i	0.374517	+	0.648683i	0.990255	−	0.139269i	$-0.0444752\pi$
$509$	8.44949	+	14.6349i	0.374517	+	0.648683i	−0.615738	+	0.787951i	$0.711142\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	13.8990	+	24.0737i	0.613058	+	1.06185i
$515$	24.1464	−	41.8228i	1.06402	−	1.84293i
$516$		0			0
$517$	−9.79796	+	16.9706i	−0.430914	+	0.746364i
$518$		0			0
$519$		0			0
$520$	−16.8990			−0.741069
$521$	19.3485	+	33.5125i	0.847672	+	1.46821i	0.883281	+	0.468845i	$0.155330\pi$
$521$	19.3485	+	33.5125i	0.847672	+	1.46821i	−0.0356087	+	0.999366i	$0.511337\pi$
$522$		0			0
$523$	0.174235	−	0.301783i	0.00761875	−	0.0131961i	−0.862191	−	0.506584i	$-0.830908\pi$
$523$	0.174235	−	0.301783i	0.00761875	−	0.0131961i	0.869810	+	0.493387i	$0.164242\pi$
$524$	6.72474	+	11.6476i	0.293772	+	0.508828i
$525$		0			0
$526$	−8.05051	+	13.9439i	−0.351019	+	0.607983i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	1.89898	−	3.28913i	0.0824864	−	0.142871i
$531$		0			0
$532$		0			0
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		0			0
$535$	41.3939			1.78961
$536$	3.10102			0.133944
$537$		0			0
$538$	−1.82577	−	3.16232i	−0.0787143	−	0.136337i
$539$		0			0
$540$		0			0
$541$	−15.2474	+	26.4094i	−0.655539	+	1.13543i	0.326219	+	0.945294i	$0.394225\pi$
$541$	−15.2474	+	26.4094i	−0.655539	+	1.13543i	−0.981758	+	0.190133i	$0.939108\pi$
$542$	−8.44949	+	14.6349i	−0.362937	+	0.628625i
$543$		0			0
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	28.7980	−	49.8795i	1.23357	−	2.13660i
$546$		0			0
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	−0.976331	−	0.216283i	$-0.930607\pi$
$547$	−15.7980	−	27.3629i	−0.675472	−	1.16995i	0.300859	−	0.953669i	$-0.402727\pi$
$548$	−5.89898	+	10.2173i	−0.251992	+	0.436463i
$549$		0			0
$550$	−6.89898	−	11.9494i	−0.294173	−	0.509523i
$551$	21.5959			0.920017
$552$		0			0
$553$		0			0
$554$	5.34847	−	9.26382i	0.227235	−	0.393582i
$555$		0			0
$556$	4.72474	−	8.18350i	0.200374	−	0.347058i
$557$	−1.55051	−	2.68556i	−0.0656972	−	0.113791i	0.831306	−	0.555815i	$-0.187594\pi$
$557$	−1.55051	−	2.68556i	−0.0656972	−	0.113791i	−0.897003	+	0.442024i	$0.854260\pi$
$558$		0			0
$559$	−14.2020			−0.600682
$560$		0			0
$561$		0			0
$562$	9.50000	+	16.4545i	0.400733	+	0.694090i
$563$	13.9444			0.587686			0.293843	−	0.955854i	$-0.405066\pi$
$563$	13.9444			0.587686			0.293843	+	0.955854i	$0.405066\pi$
$564$		0			0
$565$	54.8434			2.30728
$566$	−20.5505			−0.863802
$567$		0			0
$568$	9.89898			0.415352
$569$	30.0000			1.25767			0.628833	−	0.777541i	$-0.283533\pi$
$569$	30.0000			1.25767			0.628833	+	0.777541i	$0.283533\pi$
$570$		0			0
$571$	14.2020			0.594337			0.297168	−	0.954825i	$-0.403958\pi$
$571$	14.2020			0.594337			0.297168	+	0.954825i	$0.403958\pi$
$572$	4.89898	+	8.48528i	0.204837	+	0.354787i
$573$		0			0
$574$		0			0
$575$	6.89898			0.287707
$576$		0			0
$577$	11.7980	+	20.4347i	0.491155	+	0.850706i	0.999948	−	0.0101829i	$-0.00324136\pi$
$577$	11.7980	+	20.4347i	0.491155	+	0.850706i	−0.508793	+	0.860889i	$0.669908\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$		0			0
$580$	5.00000	−	8.66025i	0.207614	−	0.359597i
$581$		0			0
$582$		0			0
$583$	−2.20204			−0.0911992
$584$	−1.44949	−	2.51059i	−0.0599803	−	0.103889i
$585$		0			0
$586$	13.6237	−	23.5970i	0.562791	−	0.974782i
$587$	9.07321	+	15.7153i	0.374492	+	0.648639i	0.990251	−	0.139296i	$-0.0444839\pi$
$587$	9.07321	+	15.7153i	0.374492	+	0.648639i	−0.615759	+	0.787934i	$0.711151\pi$
$588$		0			0
$589$	−22.3485	+	38.7087i	−0.920853	+	1.59496i
$590$	−3.44949	−	5.97469i	−0.142013	−	0.245974i
$591$		0			0
$592$	3.89898	−	6.75323i	0.160247	−	0.277556i
$593$	7.34847	−	12.7279i	0.301765	−	0.522673i	−0.674770	−	0.738028i	$-0.735757\pi$
$593$	7.34847	−	12.7279i	0.301765	−	0.522673i	0.976536	+	0.215355i	$0.0690907\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	−4.89898			−0.200334
$599$	14.2020			0.580280			0.290140	−	0.956984i	$-0.406298\pi$
$599$	14.2020			0.580280			0.290140	+	0.956984i	$0.406298\pi$
$600$		0			0
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	0.707004	−	0.707210i	$-0.250046\pi$
$601$	−6.34847	−	10.9959i	−0.258959	−	0.448531i	−0.965963	+	0.258679i	$0.916713\pi$
$602$		0			0
$603$		0			0
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	12.0732	−	20.9114i	0.490846	−	0.850170i
$606$		0			0
$607$	−4.34847	−	7.53177i	−0.176499	−	0.305705i	0.764180	−	0.645003i	$-0.223144\pi$
$607$	−4.34847	−	7.53177i	−0.176499	−	0.305705i	−0.940679	+	0.339298i	$0.889811\pi$
$608$	−3.72474	+	6.45145i	−0.151058	+	0.261641i
$609$		0			0
$610$	−19.7474	−	34.2036i	−0.799551	−	1.38486i
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$		0			0
$613$	−7.34847	−	12.7279i	−0.296802	−	0.514076i	0.678601	−	0.734508i	$-0.262587\pi$
$613$	−7.34847	−	12.7279i	−0.296802	−	0.514076i	−0.975402	+	0.220432i	$0.929253\pi$
$614$	0.752551			0.0303705
$615$		0			0
$616$		0			0
$617$	21.6969	−	37.5802i	0.873486	−	1.51292i	0.0151189	−	0.999886i	$-0.495187\pi$
$617$	21.6969	−	37.5802i	0.873486	−	1.51292i	0.858367	−	0.513036i	$-0.171479\pi$
$618$		0			0
$619$	−2.07321	+	3.59091i	−0.0833295	+	0.144331i	−0.904678	−	0.426096i	$-0.859889\pi$
$619$	−2.07321	+	3.59091i	−0.0833295	+	0.144331i	0.821349	+	0.570426i	$0.193222\pi$
$620$	10.3485	+	17.9241i	0.415605	+	0.719848i
$621$		0			0
$622$	−1.30306			−0.0522480
$623$		0			0
$624$		0			0
$625$	5.94949	+	10.3048i	0.237980	+	0.412193i
$626$	24.6969			0.987088
$627$		0			0
$628$	−6.34847			−0.253332
$629$	−15.5959			−0.621850
$630$		0			0
$631$	18.1010			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$631$	18.1010			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$632$	−7.89898			−0.314205
$633$		0			0
$634$	−8.69694			−0.345400
$635$	5.17423	+	8.96204i	0.205333	+	0.355648i
$636$		0			0
$637$		0			0
$638$	−5.79796			−0.229543
$639$		0			0
$640$	1.72474	+	2.98735i	0.0681765	+	0.118085i
$641$	20.7474	−	35.9356i	0.819475	−	1.41937i	−0.0865947	−	0.996244i	$-0.527599\pi$
$641$	20.7474	−	35.9356i	0.819475	−	1.41937i	0.906070	−	0.423129i	$-0.139068\pi$
$642$		0			0
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	−0.608996	−	0.793173i	$-0.708428\pi$
$643$	9.69694	−	16.7956i	0.382410	−	0.662353i	0.991406	+	0.130820i	$0.0417609\pi$
$644$		0			0
$645$		0			0
$646$	14.8990			0.586193
$647$	10.6515	+	18.4490i	0.418755	+	0.725305i	0.995815	−	0.0913973i	$-0.0291333\pi$
$647$	10.6515	+	18.4490i	0.418755	+	0.725305i	−0.577060	+	0.816702i	$0.695800\pi$
$648$		0			0
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$	16.8990	+	29.2699i	0.662833	+	1.14806i
$651$		0			0
$652$	0.101021	−	0.174973i	0.00395627	−	0.00685246i
$653$	−4.89898	−	8.48528i	−0.191712	−	0.332055i	0.754106	−	0.656753i	$-0.228071\pi$
$653$	−4.89898	−	8.48528i	−0.191712	−	0.332055i	−0.945818	+	0.324698i	$0.894737\pi$
$654$		0			0
$655$	23.1969	−	40.1783i	0.906379	−	1.56990i
$656$	4.89898	−	8.48528i	0.191273	−	0.331295i
$657$		0			0
$658$		0			0
$659$	2.34847	+	4.06767i	0.0914834	+	0.158454i	0.908136	−	0.418676i	$-0.137506\pi$
$659$	2.34847	+	4.06767i	0.0914834	+	0.158454i	−0.816652	+	0.577130i	$0.804172\pi$
$660$		0			0
$661$	−9.44949			−0.367543			−0.183771	−	0.982969i	$-0.558831\pi$
$661$	−9.44949			−0.367543			−0.183771	+	0.982969i	$0.558831\pi$
$662$	24.6969			0.959874
$663$		0			0
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$		0			0
$667$	1.44949	−	2.51059i	0.0561245	−	0.0972104i
$668$	−9.34847	+	16.1920i	−0.361703	+	0.626488i
$669$		0			0
$670$	−5.34847	−	9.26382i	−0.206629	−	0.357893i
$671$	−11.4495	+	19.8311i	−0.442003	+	0.765571i
$672$		0			0
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	−0.994272	−	0.106875i	$-0.965915\pi$
$673$	−15.2980	−	26.4968i	−0.589693	−	1.02138i	0.404579	−	0.914503i	$-0.367418\pi$
$674$	17.6969	−	30.6520i	0.681661	−	1.18067i
$675$		0			0
$676$	−5.50000	−	9.52628i	−0.211538	−	0.366395i
$677$	−14.6969			−0.564849			−0.282425	−	0.959289i	$-0.591139\pi$
$677$	−14.6969			−0.564849			−0.282425	+	0.959289i	$0.591139\pi$
$678$		0			0
$679$		0			0
$680$	3.44949	−	5.97469i	0.132282	−	0.229119i
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	16.1010	+	27.8878i	0.616088	+	1.06710i	0.990193	+	0.139710i	$0.0446169\pi$
$683$	16.1010	+	27.8878i	0.616088	+	1.06710i	−0.374104	+	0.927387i	$0.622050\pi$
$684$		0			0
$685$	40.6969			1.55495
$686$		0			0
$687$		0			0
$688$	1.44949	+	2.51059i	0.0552613	+	0.0957153i
$689$	5.39388			0.205490
$690$		0			0
$691$	−6.95459			−0.264565			−0.132283	−	0.991212i	$-0.542231\pi$
$691$	−6.95459			−0.264565			−0.132283	+	0.991212i	$0.542231\pi$
$692$	−12.8990			−0.490346
$693$		0			0
$694$	−19.5959			−0.743851
$695$	−32.5959			−1.23643
$696$		0			0
$697$	−19.5959			−0.742248
$698$	−10.4495	−	18.0990i	−0.395519	−	0.685059i
$699$		0			0
$700$		0			0
$701$	−51.3939			−1.94112			−0.970560	−	0.240860i	$-0.922571\pi$
$701$	−51.3939			−1.94112			−0.970560	+	0.240860i	$0.922571\pi$
$702$		0			0
$703$	−29.0454	−	50.3081i	−1.09547	−	1.89741i
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$		0			0
$706$	−3.00000	+	5.19615i	−0.112906	+	0.195560i
$707$		0			0
$708$		0			0
$709$	−11.5959			−0.435494			−0.217747	−	0.976005i	$-0.569871\pi$
$709$	−11.5959			−0.435494			−0.217747	+	0.976005i	$0.569871\pi$
$710$	−17.0732	−	29.5717i	−0.640746	−	1.10981i
$711$		0			0
$712$	−3.55051	+	6.14966i	−0.133061	+	0.230468i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	16.8990	−	29.2699i	0.631986	−	1.09463i
$716$	−4.34847	−	7.53177i	−0.162510	−	0.281475i
$717$		0			0
$718$	−5.39898	+	9.35131i	−0.201488	+	0.348988i
$719$	4.89898	−	8.48528i	0.182701	−	0.316448i	−0.760098	−	0.649808i	$-0.774849\pi$
$719$	4.89898	−	8.48528i	0.182701	−	0.316448i	0.942799	+	0.333360i	$0.108183\pi$
$720$		0			0
$721$		0			0
$722$	18.2474	+	31.6055i	0.679100	+	1.17624i
$723$		0			0
$724$	−4.34847			−0.161610
$725$	−20.0000			−0.742781
$726$		0			0
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	0.947369	+	0.320143i	$0.103731\pi$
$727$	20.2474	+	35.0696i	0.750936	+	1.30066i	−0.196433	+	0.980517i	$0.562936\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	2.89898	−	5.02118i	0.107223	−	0.185715i
$732$		0			0
$733$	−6.27526	−	10.8691i	−0.231782	−	0.401458i	0.726551	−	0.687113i	$-0.241122\pi$
$733$	−6.27526	−	10.8691i	−0.231782	−	0.401458i	−0.958333	+	0.285655i	$0.907789\pi$
$734$	−2.89898	+	5.02118i	−0.107003	+	0.185335i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−3.10102	+	5.37113i	−0.114228	+	0.197848i
$738$		0			0
$739$	12.7980	+	22.1667i	0.470781	+	0.815416i	0.999441	−	0.0334173i	$-0.0106390\pi$
$739$	12.7980	+	22.1667i	0.470781	+	0.815416i	−0.528661	+	0.848833i	$0.677306\pi$
$740$	−26.8990			−0.988826
$741$		0			0
$742$		0			0
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$		0			0
$745$	−10.3485	+	17.9241i	−0.379139	+	0.656687i
$746$	1.44949	+	2.51059i	0.0530696	+	0.0919192i
$747$		0			0
$748$	−4.00000			−0.146254
$749$		0			0
$750$		0			0
$751$	−20.2980	−	35.1571i	−0.740683	−	1.28290i	−0.952185	−	0.305523i	$-0.901169\pi$
$751$	−20.2980	−	35.1571i	−0.740683	−	1.28290i	0.211502	−	0.977378i	$-0.432165\pi$
$752$	−9.79796			−0.357295
$753$		0			0
$754$	14.2020			0.517208
$755$	−17.2474			−0.627699
$756$		0			0
$757$	23.3939			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$757$	23.3939			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$758$	26.4949			0.962338
$759$		0			0
$760$	25.6969			0.932126
$761$	−1.00000	−	1.73205i	−0.0362500	−	0.0627868i	0.847331	−	0.531065i	$-0.178208\pi$
$761$	−1.00000	−	1.73205i	−0.0362500	−	0.0627868i	−0.883581	+	0.468278i	$0.844875\pi$
$762$		0			0
$763$		0			0
$764$	−13.8990			−0.502847
$765$		0			0
$766$	3.44949	+	5.97469i	0.124635	+	0.215874i
$767$	4.89898	−	8.48528i	0.176892	−	0.306386i
$768$		0			0
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.296282	−	0.955100i	$-0.404253\pi$
$769$	27.0454	−	46.8440i	0.975282	−	1.68924i	0.679000	−	0.734138i	$-0.262414\pi$
$770$		0			0
$771$		0			0
$772$	−8.10102			−0.291562
$773$	9.97219	+	17.2723i	0.358675	+	0.621243i	0.987740	−	0.156110i	$-0.0498953\pi$
$773$	9.97219	+	17.2723i	0.358675	+	0.621243i	−0.629065	+	0.777353i	$0.716562\pi$
$774$		0			0
$775$	20.6969	−	35.8481i	0.743456	−	1.28770i
$776$	3.44949	+	5.97469i	0.123829	+	0.214479i
$777$		0			0
$778$	7.55051	−	13.0779i	0.270699	−	0.468864i
$779$	−36.4949	−	63.2110i	−1.30757	−	2.26477i
$780$		0			0
$781$	−9.89898	+	17.1455i	−0.354213	+	0.613515i
$782$	1.00000	−	1.73205i	0.0357599	−	0.0619380i
$783$		0			0
$784$		0			0
$785$	10.9495	+	18.9651i	0.390804	+	0.676892i
$786$		0			0
$787$	−47.3939			−1.68941			−0.844705	−	0.535233i	$-0.820224\pi$
$787$	−47.3939			−1.68941			−0.844705	+	0.535233i	$0.820224\pi$
$788$	12.6969			0.452310
$789$		0			0
$790$	13.6237	+	23.5970i	0.484710	+	0.839543i
$791$		0			0
$792$		0			0
$793$	28.0454	−	48.5761i	0.995922	−	1.72499i
$794$	−4.65153	+	8.05669i	−0.165077	+	0.285921i
$795$		0			0
$796$	3.44949	+	5.97469i	0.122264	+	0.211767i
$797$	−17.9722	+	31.1288i	−0.636608	+	1.10264i	0.349564	+	0.936912i	$0.386330\pi$
$797$	−17.9722	+	31.1288i	−0.636608	+	1.10264i	−0.986172	+	0.165725i	$0.947004\pi$
$798$		0			0
$799$	9.79796	+	16.9706i	0.346627	+	0.600375i
$800$	3.44949	−	5.97469i	0.121958	−	0.211237i
$801$		0			0
$802$	5.05051	+	8.74774i	0.178340	+	0.308893i
$803$	5.79796			0.204606
$804$		0			0
$805$		0			0
$806$	−14.6969	+	25.4558i	−0.517678	+	0.896644i
$807$		0			0
$808$	3.62372	−	6.27647i	0.127482	−	0.220806i
$809$	−17.8990	−	31.0019i	−0.629295	−	1.08997i	−0.987694	−	0.156402i	$-0.950011\pi$
$809$	−17.8990	−	31.0019i	−0.629295	−	1.08997i	0.358399	−	0.933569i	$-0.383323\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$	7.79796	+	13.5065i	0.273318	+	0.473401i
$815$	−0.696938			−0.0244127
$816$		0			0
$817$	21.5959			0.755546
$818$	5.79796			0.202721
$819$		0			0
$820$	−33.7980			−1.18028
$821$	−39.5959			−1.38191			−0.690954	−	0.722899i	$-0.742809\pi$
$821$	−39.5959			−1.38191			−0.690954	+	0.722899i	$0.742809\pi$
$822$		0			0
$823$	45.3939			1.58233			0.791166	−	0.611602i	$-0.209475\pi$
$823$	45.3939			1.58233			0.791166	+	0.611602i	$0.209475\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$		0			0
$826$		0			0
$827$	−12.4949			−0.434490			−0.217245	−	0.976117i	$-0.569707\pi$
$827$	−12.4949			−0.434490			−0.217245	+	0.976117i	$0.569707\pi$
$828$		0			0
$829$	15.3485	+	26.5843i	0.533074	+	0.923312i	0.999254	+	0.0386218i	$0.0122967\pi$
$829$	15.3485	+	26.5843i	0.533074	+	0.923312i	−0.466180	+	0.884690i	$0.654370\pi$
$830$	3.44949	−	5.97469i	0.119734	−	0.207385i
$831$		0			0
$832$	−2.44949	+	4.24264i	−0.0849208	+	0.147087i
$833$		0			0
$834$		0			0
$835$	64.4949			2.23194
$836$	−7.44949	−	12.9029i	−0.257646	−	0.446256i
$837$		0			0
$838$	12.2753	−	21.2614i	0.424042	−	0.734462i
$839$	22.4495	+	38.8837i	0.775042	+	1.34241i	0.934771	+	0.355252i	$0.115605\pi$
$839$	22.4495	+	38.8837i	0.775042	+	1.34241i	−0.159728	+	0.987161i	$0.551062\pi$
$840$		0			0
$841$	10.2980	−	17.8366i	0.355102	−	0.615055i
$842$	6.55051	+	11.3458i	0.225745	+	0.391003i
$843$		0			0
$844$	−1.55051	+	2.68556i	−0.0533708	+	0.0924409i
$845$	−18.9722	+	32.8608i	−0.652663	+	1.13045i
$846$		0			0
$847$		0			0
$848$	−0.550510	−	0.953512i	−0.0189046	−	0.0327437i
$849$		0			0
$850$	−13.7980			−0.473266
$851$	−7.79796			−0.267311
$852$		0			0
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	−0.979289	−	0.202467i	$-0.935104\pi$
$853$	−19.4217	−	33.6393i	−0.664986	−	1.15179i	0.314303	−	0.949323i	$-0.398229\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	12.5505	−	21.7381i	0.428717	−	0.742560i	−0.568042	−	0.822999i	$-0.692299\pi$
$857$	12.5505	−	21.7381i	0.428717	−	0.742560i	0.996760	+	0.0804393i	$0.0256323\pi$
$858$		0			0
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	0.768031	−	0.640412i	$-0.221237\pi$
$859$	−5.00000	−	8.66025i	−0.170598	−	0.295484i	−0.938629	+	0.344928i	$0.887903\pi$
$860$	5.00000	−	8.66025i	0.170499	−	0.295312i
$861$		0			0
$862$	3.79796	+	6.57826i	0.129359	+	0.224056i
$863$	1.05051	−	1.81954i	0.0357598	−	0.0619378i	−0.847592	−	0.530649i	$-0.821948\pi$
$863$	1.05051	−	1.81954i	0.0357598	−	0.0619378i	0.883351	+	0.468711i	$0.155282\pi$
$864$		0			0
$865$	22.2474	+	38.5337i	0.756436	+	1.31019i
$866$	11.7980			0.400911
$867$		0			0
$868$		0			0
$869$	7.89898	−	13.6814i	0.267955	−	0.464111i
$870$		0			0
$871$	7.59592	−	13.1565i	0.257378	−	0.445792i
$872$	−8.34847	−	14.4600i	−0.282715	−	0.489676i
$873$		0			0
$874$	7.44949			0.251983
$875$		0			0
$876$		0			0
$877$	13.2474	+	22.9453i	0.447335	+	0.774806i	0.998212	−	0.0597803i	$-0.0190400\pi$
$877$	13.2474	+	22.9453i	0.447335	+	0.774806i	−0.550877	+	0.834586i	$0.685707\pi$
$878$	21.7980			0.735645
$879$		0			0
$880$	−6.89898			−0.232565
$881$	−19.5959			−0.660203			−0.330102	−	0.943945i	$-0.607083\pi$
$881$	−19.5959			−0.660203			−0.330102	+	0.943945i	$0.607083\pi$
$882$		0			0
$883$	−0.202041			−0.00679922			−0.00339961	−	0.999994i	$-0.501082\pi$
$883$	−0.202041			−0.00679922			−0.00339961	+	0.999994i	$0.501082\pi$
$884$	9.79796			0.329541
$885$		0			0
$886$	−5.10102			−0.171372
$887$	16.8990	+	29.2699i	0.567412	+	0.982787i	0.996821	+	0.0796764i	$0.0253887\pi$
$887$	16.8990	+	29.2699i	0.567412	+	0.982787i	−0.429409	+	0.903110i	$0.641278\pi$
$888$		0			0
$889$		0			0
$890$	24.4949			0.821071
$891$		0			0
$892$	−10.4495	−	18.0990i	−0.349875	−	0.606001i
$893$	−36.4949	+	63.2110i	−1.22126	+	2.11528i
$894$		0			0
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$		0			0
$898$	−18.5959			−0.620554
$899$	−8.69694	−	15.0635i	−0.290059	−	0.502397i
$900$		0			0
$901$	−1.10102	+	1.90702i	−0.0366803	+	0.0635322i
$902$	9.79796	+	16.9706i	0.326236	+	0.565058i
$903$		0			0
$904$	7.94949	−	13.7689i	0.264396	−	0.457947i
$905$	7.50000	+	12.9904i	0.249308	+	0.431815i
$906$		0			0
$907$	13.3485	−	23.1202i	0.443229	−	0.767695i	−0.554698	−	0.832052i	$-0.687166\pi$
$907$	13.3485	−	23.1202i	0.443229	−	0.767695i	0.997927	+	0.0643570i	$0.0204996\pi$
$908$	0.275255	−	0.476756i	0.00913466	−	0.0158217i
$909$		0			0
$910$		0			0
$911$	−22.9949	−	39.8283i	−0.761855	−	1.31957i	−0.941893	−	0.335912i	$-0.890956\pi$
$911$	−22.9949	−	39.8283i	−0.761855	−	1.31957i	0.180038	−	0.983660i	$-0.442378\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$	−31.4949			−1.04176
$915$		0			0
$916$	−11.6237	−	20.1329i	−0.384059	−	0.665209i
$917$		0			0
$918$		0			0
$919$	−1.84847	+	3.20164i	−0.0609754	+	0.105612i	−0.894902	−	0.446263i	$-0.852754\pi$
$919$	−1.84847	+	3.20164i	−0.0609754	+	0.105612i	0.833926	+	0.551876i	$0.186088\pi$
$920$	1.72474	−	2.98735i	0.0568632	−	0.0984899i
$921$		0			0
$922$	10.1742	+	17.6223i	0.335071	+	0.580359i
$923$	24.2474	−	41.9978i	0.798114	−	1.38237i
$924$		0			0
$925$	26.8990	+	46.5904i	0.884433	+	1.53188i
$926$	−12.8485	+	22.2542i	−0.422227	+	0.731318i
$927$		0			0
$928$	−1.44949	−	2.51059i	−0.0475818	−	0.0824142i
$929$	−34.2929			−1.12511			−0.562556	−	0.826759i	$-0.690182\pi$
$929$	−34.2929			−1.12511			−0.562556	+	0.826759i	$0.690182\pi$
$930$		0			0
$931$		0			0
$932$	−3.50000	+	6.06218i	−0.114646	+	0.198573i
$933$		0			0
$934$	5.00000	−	8.66025i	0.163605	−	0.283372i
$935$	6.89898	+	11.9494i	0.225621	+	0.390787i
$936$		0			0
$937$	−6.40408			−0.209212			−0.104606	−	0.994514i	$-0.533358\pi$
$937$	−6.40408			−0.209212			−0.104606	+	0.994514i	$0.533358\pi$
$938$		0			0
$939$		0			0
$940$	16.8990	+	29.2699i	0.551184	+	0.954679i
$941$	3.44949			0.112450			0.0562251	−	0.998418i	$-0.482094\pi$
$941$	3.44949			0.112450			0.0562251	+	0.998418i	$0.482094\pi$
$942$		0			0
$943$	−9.79796			−0.319065
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	−5.79796			−0.188508
$947$	−3.50510			−0.113901			−0.0569503	−	0.998377i	$-0.518138\pi$
$947$	−3.50510			−0.113901			−0.0569503	+	0.998377i	$0.518138\pi$
$948$		0			0
$949$	−14.2020			−0.461018
$950$	−25.6969	−	44.5084i	−0.833719	−	1.44404i
$951$		0			0
$952$		0			0
$953$	−55.3939			−1.79438			−0.897192	−	0.441641i	$-0.854396\pi$
$953$	−55.3939			−1.79438			−0.897192	+	0.441641i	$0.854396\pi$
$954$		0			0
$955$	23.9722	+	41.5211i	0.775722	+	1.34359i
$956$	−6.39898	+	11.0834i	−0.206958	+	0.358461i
$957$		0			0
$958$	−14.7980	+	25.6308i	−0.478100	+	0.828094i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−19.1010	−	33.0839i	−0.615842	−	1.06667i
$963$		0			0
$964$	−4.44949	+	7.70674i	−0.143308	+	0.248217i
$965$	13.9722	+	24.2005i	0.449781	+	0.779043i
$966$		0			0
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	−0.724495	−	0.689280i	$-0.757927\pi$
$967$	7.29796	−	12.6404i	0.234687	−	0.406489i	0.959182	+	0.282791i	$0.0912603\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	11.8990	−	20.6096i	0.382053	−	0.661736i
$971$	26.9722	−	46.7172i	0.865579	−	1.49923i	−0.000892350	−	1.00000i	$-0.500284\pi$
$971$	26.9722	−	46.7172i	0.865579	−	1.49923i	0.866471	−	0.499227i	$-0.166383\pi$
$972$		0			0
$973$		0			0
$974$	11.1969	+	19.3937i	0.358773	+	0.621413i
$975$		0			0
$976$	−11.4495			−0.366489
$977$	−1.59592			−0.0510579			−0.0255290	−	0.999674i	$-0.508127\pi$
$977$	−1.59592			−0.0510579			−0.0255290	+	0.999674i	$0.508127\pi$
$978$		0			0
$979$	−7.10102	−	12.2993i	−0.226950	−	0.393088i
$980$		0			0
$981$		0			0
$982$	1.89898	−	3.28913i	0.0605989	−	0.104960i
$983$	−22.5959	+	39.1373i	−0.720698	+	1.24829i	0.240023	+	0.970767i	$0.422845\pi$
$983$	−22.5959	+	39.1373i	−0.720698	+	1.24829i	−0.960720	+	0.277518i	$0.910488\pi$
$984$		0			0
$985$	−21.8990	−	37.9301i	−0.697760	−	1.20855i
$986$	−2.89898	+	5.02118i	−0.0923223	+	0.159907i
$987$		0			0
$988$	18.2474	+	31.6055i	0.580529	+	1.00551i
$989$	1.44949	−	2.51059i	0.0460911	−	0.0798321i
$990$		0			0
$991$	−8.89898	−	15.4135i	−0.282685	−	0.489625i	0.689360	−	0.724419i	$-0.257892\pi$
$991$	−8.89898	−	15.4135i	−0.282685	−	0.489625i	−0.972045	+	0.234794i	$0.924559\pi$
$992$	6.00000			0.190500
$993$		0			0
$994$		0			0
$995$	11.8990	−	20.6096i	0.377223	−	0.653369i
$996$		0			0
$997$	8.92679	−	15.4616i	0.282714	−	0.489675i	−0.689338	−	0.724440i	$-0.742099\pi$
$997$	8.92679	−	15.4616i	0.282714	−	0.489675i	0.972052	+	0.234764i	$0.0754319\pi$
$998$	16.6969	+	28.9199i	0.528532	+	0.915445i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.1	✓	4	63.47	even	6
126.2.f.c.85.2	yes	4	21.5	even	6
378.2.f.d.127.2		4	63.61	odd	6
378.2.f.d.253.2		4	7.5	odd	6
882.2.e.m.373.2		4	21.20	even	2
882.2.e.m.655.2		4	63.38	even	6
882.2.e.n.373.1		4	3.2	odd	2
882.2.e.n.655.1		4	63.11	odd	6
882.2.f.j.295.2		4	63.2	odd	6
882.2.f.j.589.1		4	21.2	odd	6
882.2.h.k.67.1		4	21.17	even	6
882.2.h.k.79.1		4	63.20	even	6
882.2.h.l.67.2		4	21.11	odd	6
882.2.h.l.79.2		4	9.2	odd	6
1008.2.r.e.337.1		4	84.47	odd	6
1008.2.r.e.673.2		4	252.47	odd	6
1134.2.a.i.1.1		2	63.40	odd	6
1134.2.a.p.1.2		2	63.5	even	6
2646.2.e.k.1549.1		4	1.1	even	1	trivial
2646.2.e.k.2125.1		4	63.25	even	3	inner
2646.2.e.l.1549.2		4	7.6	odd	2
2646.2.e.l.2125.2		4	63.52	odd	6
2646.2.f.k.883.1		4	63.16	even	3
2646.2.f.k.1765.1		4	7.2	even	3
2646.2.h.m.361.1		4	7.3	odd	6
2646.2.h.m.667.1		4	63.34	odd	6
2646.2.h.n.361.2		4	7.4	even	3
2646.2.h.n.667.2		4	9.7	even	3
3024.2.r.e.1009.2		4	28.19	even	6
3024.2.r.e.2017.2		4	252.187	even	6
7938.2.a.bm.1.2		2	63.58	even	3
7938.2.a.bn.1.1		2	63.23	odd	6
9072.2.a.bd.1.1		2	252.103	even	6
9072.2.a.bk.1.2		2	252.131	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.72474 - 2.98735i) q^{5} -1.00000 q^{8} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(-1.72474 - 2.98735i) q^{5} -1.00000 q^{8} +(1.72474 + 2.98735i) q^{10} +(1.00000 - 1.73205i) q^{11} +(-2.44949 + 4.24264i) q^{13} +1.00000 q^{16} +(-1.00000 - 1.73205i) q^{17} +(3.72474 - 6.45145i) q^{19} +(-1.72474 - 2.98735i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(-3.44949 + 5.97469i) q^{25} +(2.44949 - 4.24264i) q^{26} +(1.44949 + 2.51059i) q^{29} -6.00000 q^{31} -1.00000 q^{32} +(1.00000 + 1.73205i) q^{34} +(3.89898 - 6.75323i) q^{37} +(-3.72474 + 6.45145i) q^{38} +(1.72474 + 2.98735i) q^{40} +(4.89898 - 8.48528i) q^{41} +(1.44949 + 2.51059i) q^{43} +(1.00000 - 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} -9.79796 q^{47} +(3.44949 - 5.97469i) q^{50} +(-2.44949 + 4.24264i) q^{52} +(-0.550510 - 0.953512i) q^{53} -6.89898 q^{55} +(-1.44949 - 2.51059i) q^{58} -2.00000 q^{59} -11.4495 q^{61} +6.00000 q^{62} +1.00000 q^{64} +16.8990 q^{65} -3.10102 q^{67} +(-1.00000 - 1.73205i) q^{68} -9.89898 q^{71} +(1.44949 + 2.51059i) q^{73} +(-3.89898 + 6.75323i) q^{74} +(3.72474 - 6.45145i) q^{76} +7.89898 q^{79} +(-1.72474 - 2.98735i) q^{80} +(-4.89898 + 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(-3.44949 + 5.97469i) q^{85} +(-1.44949 - 2.51059i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(3.55051 - 6.14966i) q^{89} +(-0.500000 - 0.866025i) q^{92} +9.79796 q^{94} -25.6969 q^{95} +(-3.44949 - 5.97469i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{8}+O(q^{10}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^8	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 4 q^{11} + 4 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{29} - 24 q^{31} - 4 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38} + 2 q^{40} - 4 q^{43} + 4 q^{44} + 2 q^{46} + 4 q^{50} - 12 q^{53} - 8 q^{55} + 4 q^{58} - 8 q^{59} - 36 q^{61} + 24 q^{62} + 4 q^{64} + 48 q^{65} - 32 q^{67} - 4 q^{68} - 20 q^{71} - 4 q^{73} + 4 q^{74} + 10 q^{76} + 12 q^{79} - 2 q^{80} - 4 q^{83} - 4 q^{85} + 4 q^{86} - 4 q^{88} + 24 q^{89} - 2 q^{92} - 44 q^{95} - 4 q^{97}+O(q^{100}) \) 4 * q - 4 * q^2 + 4 * q^4 - 2 * q^5 - 4 * q^8 + 2 * q^10 + 4 * q^11 + 4 * q^16 - 4 * q^17 + 10 * q^19 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^29 - 24 * q^31 - 4 * q^32 + 4 * q^34 - 4 * q^37 - 10 * q^38 + 2 * q^40 - 4 * q^43 + 4 * q^44 + 2 * q^46 + 4 * q^50 - 12 * q^53 - 8 * q^55 + 4 * q^58 - 8 * q^59 - 36 * q^61 + 24 * q^62 + 4 * q^64 + 48 * q^65 - 32 * q^67 - 4 * q^68 - 20 * q^71 - 4 * q^73 + 4 * q^74 + 10 * q^76 + 12 * q^79 - 2 * q^80 - 4 * q^83 - 4 * q^85 + 4 * q^86 - 4 * q^88 + 24 * q^89 - 2 * q^92 - 44 * q^95 - 4 * q^97

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