LMFDB - Embedded newform 2646.2.e.k.1549.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("2646.1549");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
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			1549.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2646.1549
Dual form			2646.2.e.k.2125.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.724745 + 1.25529i) q^{5} -1.00000 q^{8} +(-0.724745 - 1.25529i) q^{10} +(1.00000 - 1.73205i) q^{11} +(2.44949 - 4.24264i) q^{13} +1.00000 q^{16} +(-1.00000 - 1.73205i) q^{17} +(1.27526 - 2.20881i) q^{19} +(0.724745 + 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.44949 - 2.51059i) q^{25} +(-2.44949 + 4.24264i) q^{26} +(-3.44949 - 5.97469i) q^{29} -6.00000 q^{31} -1.00000 q^{32} +(1.00000 + 1.73205i) q^{34} +(-5.89898 + 10.2173i) q^{37} +(-1.27526 + 2.20881i) q^{38} +(-0.724745 - 1.25529i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(1.00000 - 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} +9.79796 q^{47} +(-1.44949 + 2.51059i) q^{50} +(2.44949 - 4.24264i) q^{52} +(-5.44949 - 9.43879i) q^{53} +2.89898 q^{55} +(3.44949 + 5.97469i) q^{58} -2.00000 q^{59} -6.55051 q^{61} +6.00000 q^{62} +1.00000 q^{64} +7.10102 q^{65} -12.8990 q^{67} +(-1.00000 - 1.73205i) q^{68} -0.101021 q^{71} +(-3.44949 - 5.97469i) q^{73} +(5.89898 - 10.2173i) q^{74} +(1.27526 - 2.20881i) q^{76} -1.89898 q^{79} +(0.724745 + 1.25529i) q^{80} +(4.89898 - 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(3.44949 + 5.97469i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(8.44949 - 14.6349i) q^{89} +(-0.500000 - 0.866025i) q^{92} -9.79796 q^{94} +3.69694 q^{95} +(1.44949 + 2.51059i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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}+ \cdots - 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

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	1.00000			0.500000
$5$	0.724745	+	1.25529i	0.324116	+	0.561385i	0.981333	−	0.192316i	$-0.0615999\pi$
$5$	0.724745	+	1.25529i	0.324116	+	0.561385i	−0.657217	+	0.753701i	$0.728267\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$		0			0
$10$	−0.724745	−	1.25529i	−0.229184	−	0.396959i
$11$	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	$-0.595588\pi$
$13$	2.44949	−	4.24264i	0.679366	−	1.17670i	0.975172	−	0.221449i	$-0.0710785\pi$
$14$		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
$19$	1.27526	−	2.20881i	0.292564	−	0.506735i	−0.681852	−	0.731491i	$-0.738825\pi$
$19$	1.27526	−	2.20881i	0.292564	−	0.506735i	0.974415	+	0.224756i	$0.0721584\pi$
$20$	0.724745	+	1.25529i	0.162058	+	0.280692i
$21$		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
$25$	1.44949	−	2.51059i	0.289898	−	0.502118i
$26$	−2.44949	+	4.24264i	−0.480384	+	0.832050i
$27$		0			0
$28$		0			0
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	−0.985309	−	0.170780i	$-0.945371\pi$
$29$	−3.44949	−	5.97469i	−0.640554	−	1.10947i	0.344755	−	0.938693i	$-0.387962\pi$
$30$		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
$37$	−5.89898	+	10.2173i	−0.969786	+	1.67972i	−0.273621	+	0.961838i	$0.588221\pi$
$37$	−5.89898	+	10.2173i	−0.969786	+	1.67972i	−0.696165	+	0.717881i	$0.745112\pi$
$38$	−1.27526	+	2.20881i	−0.206874	+	0.358316i
$39$		0			0
$40$	−0.724745	−	1.25529i	−0.114592	−	0.198480i
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	0.175106	+	0.984550i	$0.443973\pi$
$41$	−4.89898	+	8.48528i	−0.765092	+	1.32518i	−0.940198	+	0.340629i	$0.889360\pi$
$42$		0			0
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	−0.999540	−	0.0303367i	$-0.990342\pi$
$43$	−3.44949	−	5.97469i	−0.526042	−	0.911132i	0.473497	−	0.880795i	$-0.342991\pi$
$44$	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	$-0.246613\pi$
$47$	9.79796			1.42918			0.714590	+	0.699544i	$0.246613\pi$
$48$		0			0
$49$		0			0
$50$	−1.44949	+	2.51059i	−0.204989	+	0.355051i
$51$		0			0
$52$	2.44949	−	4.24264i	0.339683	−	0.588348i
$53$	−5.44949	−	9.43879i	−0.748545	−	1.29652i	−0.948520	−	0.316717i	$-0.897419\pi$
$53$	−5.44949	−	9.43879i	−0.748545	−	1.29652i	0.199975	−	0.979801i	$-0.435914\pi$
$54$		0			0
$55$	2.89898			0.390898
$56$		0			0
$57$		0			0
$58$	3.44949	+	5.97469i	0.452940	+	0.784515i
$59$	−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
$61$	−6.55051			−0.838707			−0.419353	−	0.907823i	$-0.637743\pi$
$61$	−6.55051			−0.838707			−0.419353	+	0.907823i	$0.637743\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	7.10102			0.880773
$66$		0			0
$67$	−12.8990			−1.57586			−0.787931	−	0.615764i	$-0.788847\pi$
$67$	−12.8990			−1.57586			−0.787931	+	0.615764i	$0.788847\pi$
$68$	−1.00000	−	1.73205i	−0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−0.101021			−0.0119889			−0.00599446	−	0.999982i	$-0.501908\pi$
$71$	−0.101021			−0.0119889			−0.00599446	+	0.999982i	$0.501908\pi$
$72$		0			0
$73$	−3.44949	−	5.97469i	−0.403732	−	0.699285i	0.590441	−	0.807081i	$-0.298954\pi$
$73$	−3.44949	−	5.97469i	−0.403732	−	0.699285i	−0.994173	+	0.107796i	$0.965621\pi$
$74$	5.89898	−	10.2173i	0.685742	−	1.18774i
$75$		0			0
$76$	1.27526	−	2.20881i	0.146282	−	0.253368i
$77$		0			0
$78$		0			0
$79$	−1.89898			−0.213652			−0.106826	−	0.994278i	$-0.534069\pi$
$79$	−1.89898			−0.213652			−0.106826	+	0.994278i	$0.534069\pi$
$80$	0.724745	+	1.25529i	0.0810289	+	0.140346i
$81$		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
$85$	1.44949	−	2.51059i	0.157219	−	0.272312i
$86$	3.44949	+	5.97469i	0.371968	+	0.644268i
$87$		0			0
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	8.44949	−	14.6349i	0.895644	−	1.55130i	0.0626387	−	0.998036i	$-0.480048\pi$
$89$	8.44949	−	14.6349i	0.895644	−	1.55130i	0.833005	−	0.553265i	$-0.186618\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$		0			0
$94$	−9.79796			−1.01058
$95$	3.69694			0.379298
$96$		0			0
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	0.930182	−	0.367099i	$-0.119649\pi$
$97$	1.44949	+	2.51059i	0.147173	+	0.254912i	−0.783008	+	0.622011i	$0.786316\pi$
$98$		0			0
$99$		0			0
$100$	1.44949	−	2.51059i	0.144949	−	0.251059i
$101$	8.62372	−	14.9367i	0.858093	−	1.48626i	−0.0156533	−	0.999877i	$-0.504983\pi$
$101$	8.62372	−	14.9367i	0.858093	−	1.48626i	0.873746	−	0.486383i	$-0.161684\pi$
$102$		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
$106$	5.44949	+	9.43879i	0.529301	+	0.916777i
$107$	−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
$109$	−6.34847	−	10.9959i	−0.608073	−	1.05321i	−0.991558	−	0.129666i	$-0.958609\pi$
$109$	−6.34847	−	10.9959i	−0.608073	−	1.05321i	0.383485	−	0.923547i	$-0.374724\pi$
$110$	−2.89898			−0.276407
$111$		0			0
$112$		0			0
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	−0.973084	−	0.230449i	$-0.925981\pi$
$113$	−3.05051	+	5.28364i	−0.286968	+	0.497043i	0.686117	+	0.727492i	$0.259314\pi$
$114$		0			0
$115$	0.724745	−	1.25529i	0.0675828	−	0.117057i
$116$	−3.44949	−	5.97469i	−0.320277	−	0.554736i
$117$		0			0
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	6.55051			0.593055
$123$		0			0
$124$	−6.00000			−0.538816
$125$	11.4495			1.02407
$126$		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
$130$	−7.10102			−0.622801
$131$	4.27526	+	7.40496i	0.373531	+	0.646974i	0.990106	−	0.140322i	$-0.0448137\pi$
$131$	4.27526	+	7.40496i	0.373531	+	0.646974i	−0.616575	+	0.787296i	$0.711480\pi$
$132$		0			0
$133$		0			0
$134$	12.8990			1.11430
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	3.89898	−	6.75323i	0.333112	−	0.576967i	−0.650008	−	0.759927i	$-0.725235\pi$
$137$	3.89898	−	6.75323i	0.333112	−	0.576967i	0.983120	+	0.182960i	$0.0585678\pi$
$138$		0			0
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	−0.753253	−	0.657730i	$-0.771517\pi$
$139$	2.27526	−	3.94086i	0.192985	−	0.334259i	0.946238	+	0.323471i	$0.104850\pi$
$140$		0			0
$141$		0			0
$142$	0.101021			0.00847745
$143$	−4.89898	−	8.48528i	−0.409673	−	0.709575i
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	3.44949	+	5.97469i	0.285482	+	0.494469i
$147$		0			0
$148$	−5.89898	+	10.2173i	−0.484893	+	0.839860i
$149$	−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	$0.101452\pi$
$152$	−1.27526	+	2.20881i	−0.103437	+	0.179158i
$153$		0			0
$154$		0			0
$155$	−4.34847	−	7.53177i	−0.349277	−	0.604966i
$156$		0			0
$157$	8.34847			0.666280			0.333140	−	0.942877i	$-0.391892\pi$
$157$	8.34847			0.666280			0.333140	+	0.942877i	$0.391892\pi$
$158$	1.89898			0.151075
$159$		0			0
$160$	−0.724745	−	1.25529i	−0.0572961	−	0.0992398i
$161$		0			0
$162$		0			0
$163$	9.89898	−	17.1455i	0.775348	−	1.34294i	−0.159251	−	0.987238i	$-0.550908\pi$
$163$	9.89898	−	17.1455i	0.775348	−	1.34294i	0.934599	−	0.355704i	$-0.115759\pi$
$164$	−4.89898	+	8.48528i	−0.382546	+	0.662589i
$165$		0			0
$166$	1.00000	+	1.73205i	0.0776151	+	0.134433i
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	−0.581433	−	0.813594i	$-0.697508\pi$
$167$	5.34847	−	9.26382i	0.413877	−	0.716856i	0.995310	+	0.0967384i	$0.0308410\pi$
$168$		0			0
$169$	−5.50000	−	9.52628i	−0.423077	−	0.732791i
$170$	−1.44949	+	2.51059i	−0.111171	+	0.192553i
$171$		0			0
$172$	−3.44949	−	5.97469i	−0.263021	−	0.455566i
$173$	−3.10102			−0.235766			−0.117883	−	0.993027i	$-0.537611\pi$
$173$	−3.10102			−0.235766			−0.117883	+	0.993027i	$0.537611\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	−	1.73205i	0.0753778	−	0.130558i
$177$		0			0
$178$	−8.44949	+	14.6349i	−0.633316	+	1.09694i
$179$	10.3485	+	17.9241i	0.773481	+	1.33971i	0.935644	+	0.352944i	$0.114819\pi$
$179$	10.3485	+	17.9241i	0.773481	+	1.33971i	−0.162163	+	0.986764i	$0.551847\pi$
$180$		0			0
$181$	10.3485			0.769196			0.384598	−	0.923084i	$-0.374340\pi$
$181$	10.3485			0.769196			0.384598	+	0.923084i	$0.374340\pi$
$182$		0			0
$183$		0			0
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−17.1010			−1.25729
$186$		0			0
$187$	−4.00000			−0.292509
$188$	9.79796			0.714590
$189$		0			0
$190$	−3.69694			−0.268204
$191$	−4.10102			−0.296739			−0.148370	−	0.988932i	$-0.547403\pi$
$191$	−4.10102			−0.296739			−0.148370	+	0.988932i	$0.547403\pi$
$192$		0			0
$193$	−17.8990			−1.28840			−0.644198	−	0.764858i	$-0.722809\pi$
$193$	−17.8990			−1.28840			−0.644198	+	0.764858i	$0.722809\pi$
$194$	−1.44949	−	2.51059i	−0.104067	−	0.180250i
$195$		0			0
$196$		0			0
$197$	−16.6969			−1.18961			−0.594804	−	0.803871i	$-0.702770\pi$
$197$	−16.6969			−1.18961			−0.594804	+	0.803871i	$0.702770\pi$
$198$		0			0
$199$	−1.44949	−	2.51059i	−0.102752	−	0.177971i	0.810066	−	0.586339i	$-0.199431\pi$
$199$	−1.44949	−	2.51059i	−0.102752	−	0.177971i	−0.912817	+	0.408368i	$0.866098\pi$
$200$	−1.44949	+	2.51059i	−0.102494	+	0.177526i
$201$		0			0
$202$	−8.62372	+	14.9367i	−0.606763	+	1.05094i
$203$		0			0
$204$		0			0
$205$	−14.2020			−0.991914
$206$	−7.00000	−	12.1244i	−0.487713	−	0.844744i
$207$		0			0
$208$	2.44949	−	4.24264i	0.169842	−	0.294174i
$209$	−2.55051	−	4.41761i	−0.176422	−	0.305573i
$210$		0			0
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	−0.997982	−	0.0634968i	$-0.979775\pi$
$211$	−6.44949	+	11.1708i	−0.444001	+	0.769033i	0.553981	+	0.832529i	$0.313108\pi$
$212$	−5.44949	−	9.43879i	−0.374272	−	0.648259i
$213$		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
$218$	6.34847	+	10.9959i	0.429973	+	0.744734i
$219$		0			0
$220$	2.89898			0.195449
$221$	−9.79796			−0.659082
$222$		0			0
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	0.618136	−	0.786071i	$-0.287888\pi$
$223$	−5.55051	−	9.61377i	−0.371690	−	0.643785i	−0.989826	+	0.142286i	$0.954555\pi$
$224$		0			0
$225$		0			0
$226$	3.05051	−	5.28364i	0.202917	−	0.351462i
$227$	2.72474	−	4.71940i	0.180848	−	0.313237i	−0.761322	−	0.648374i	$-0.775449\pi$
$227$	2.72474	−	4.71940i	0.180848	−	0.313237i	0.942169	+	0.335137i	$0.108783\pi$
$228$		0			0
$229$	0.623724	+	1.08032i	0.0412169	+	0.0713897i	0.885898	−	0.463880i	$-0.153543\pi$
$229$	0.623724	+	1.08032i	0.0412169	+	0.0713897i	−0.844681	+	0.535270i	$0.820210\pi$
$230$	−0.724745	+	1.25529i	−0.0477883	+	0.0827717i
$231$		0			0
$232$	3.44949	+	5.97469i	0.226470	+	0.392258i
$233$	−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
$235$	7.10102	+	12.2993i	0.463220	+	0.802320i
$236$	−2.00000			−0.130189
$237$		0			0
$238$		0			0
$239$	3.39898	−	5.88721i	0.219862	−	0.380812i	−0.734904	−	0.678171i	$-0.762773\pi$
$239$	3.39898	−	5.88721i	0.219862	−	0.380812i	0.954766	+	0.297360i	$0.0961061\pi$
$240$		0			0
$241$	0.449490	−	0.778539i	0.0289542	−	0.0501501i	−0.851185	−	0.524865i	$-0.824116\pi$
$241$	0.449490	−	0.778539i	0.0289542	−	0.0501501i	0.880139	+	0.474715i	$0.157449\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	−6.55051			−0.419353
$245$		0			0
$246$		0			0
$247$	−6.24745	−	10.8209i	−0.397516	−	0.688517i
$248$	6.00000			0.381000
$249$		0			0
$250$	−11.4495			−0.724129
$251$	17.4495			1.10140			0.550701	−	0.834703i	$-0.314360\pi$
$251$	17.4495			1.10140			0.550701	+	0.834703i	$0.314360\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	3.00000			0.188237
$255$		0			0
$256$	1.00000			0.0625000
$257$	−4.10102	−	7.10318i	−0.255815	−	0.443084i	0.709302	−	0.704905i	$-0.249010\pi$
$257$	−4.10102	−	7.10318i	−0.255815	−	0.443084i	−0.965116	+	0.261821i	$0.915677\pi$
$258$		0			0
$259$		0			0
$260$	7.10102			0.440387
$261$		0			0
$262$	−4.27526	−	7.40496i	−0.264126	−	0.457480i
$263$	12.9495	−	22.4292i	0.798500	−	1.38304i	−0.122093	−	0.992519i	$-0.538961\pi$
$263$	12.9495	−	22.4292i	0.798500	−	1.38304i	0.920593	−	0.390523i	$-0.127706\pi$
$264$		0			0
$265$	7.89898	−	13.6814i	0.485230	−	0.840444i
$266$		0			0
$267$		0			0
$268$	−12.8990			−0.787931
$269$	9.17423	+	15.8902i	0.559363	+	0.968845i	0.997550	+	0.0699611i	$0.0222875\pi$
$269$	9.17423	+	15.8902i	0.559363	+	0.968845i	−0.438187	+	0.898884i	$0.644379\pi$
$270$		0			0
$271$	3.55051	−	6.14966i	0.215678	−	0.373565i	−0.737804	−	0.675015i	$-0.764137\pi$
$271$	3.55051	−	6.14966i	0.215678	−	0.373565i	0.953482	+	0.301450i	$0.0974705\pi$
$272$	−1.00000	−	1.73205i	−0.0606339	−	0.105021i
$273$		0			0
$274$	−3.89898	+	6.75323i	−0.235546	+	0.407978i
$275$	−2.89898	−	5.02118i	−0.174815	−	0.302789i
$276$		0			0
$277$	9.34847	−	16.1920i	0.561695	−	0.972884i	−0.435654	−	0.900114i	$-0.643483\pi$
$277$	9.34847	−	16.1920i	0.561695	−	0.972884i	0.997349	−	0.0727700i	$-0.0231839\pi$
$278$	−2.27526	+	3.94086i	−0.136461	+	0.236357i
$279$		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
$283$	25.4495			1.51282			0.756408	−	0.654101i	$-0.226953\pi$
$283$	25.4495			1.51282			0.756408	+	0.654101i	$0.226953\pi$
$284$	−0.101021			−0.00599446
$285$		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
$292$	−3.44949	−	5.97469i	−0.201866	−	0.349642i
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	−0.903423	−	0.428750i	$-0.858954\pi$
$293$	−1.37628	+	2.38378i	−0.0804029	+	0.139262i	0.823020	+	0.568012i	$0.192287\pi$
$294$		0			0
$295$	−1.44949	−	2.51059i	−0.0843926	−	0.146172i
$296$	5.89898	−	10.2173i	0.342871	−	0.593870i
$297$		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
$304$	1.27526	−	2.20881i	0.0731409	−	0.126684i
$305$	−4.74745	−	8.22282i	−0.271838	−	0.470837i
$306$		0			0
$307$	−25.2474			−1.44095			−0.720474	−	0.693482i	$-0.756076\pi$
$307$	−25.2474			−1.44095			−0.720474	+	0.693482i	$0.756076\pi$
$308$		0			0
$309$		0			0
$310$	4.34847	+	7.53177i	0.246976	+	0.427776i
$311$	30.6969			1.74066			0.870332	−	0.492466i	$-0.163904\pi$
$311$	30.6969			1.74066			0.870332	+	0.492466i	$0.163904\pi$
$312$		0			0
$313$	4.69694			0.265487			0.132743	−	0.991150i	$-0.457621\pi$
$313$	4.69694			0.265487			0.132743	+	0.991150i	$0.457621\pi$
$314$	−8.34847			−0.471131
$315$		0			0
$316$	−1.89898			−0.106826
$317$	−20.6969			−1.16246			−0.581228	−	0.813741i	$-0.697428\pi$
$317$	−20.6969			−1.16246			−0.581228	+	0.813741i	$0.697428\pi$
$318$		0			0
$319$	−13.7980			−0.772537
$320$	0.724745	+	1.25529i	0.0405145	+	0.0701731i
$321$		0			0
$322$		0			0
$323$	−5.10102			−0.283828
$324$		0			0
$325$	−7.10102	−	12.2993i	−0.393894	−	0.682244i
$326$	−9.89898	+	17.1455i	−0.548254	+	0.949603i
$327$		0			0
$328$	4.89898	−	8.48528i	0.270501	−	0.468521i
$329$		0			0
$330$		0			0
$331$	4.69694			0.258167			0.129084	−	0.991634i	$-0.458796\pi$
$331$	4.69694			0.258167			0.129084	+	0.991634i	$0.458796\pi$
$332$	−1.00000	−	1.73205i	−0.0548821	−	0.0950586i
$333$		0			0
$334$	−5.34847	+	9.26382i	−0.292655	+	0.506894i
$335$	−9.34847	−	16.1920i	−0.510761	−	0.884665i
$336$		0			0
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	−0.348877	−	0.937168i	$-0.613437\pi$
$337$	11.6969	−	20.2597i	0.637173	−	1.10362i	0.986050	−	0.166447i	$-0.0532296\pi$
$338$	5.50000	+	9.52628i	0.299161	+	0.518161i
$339$		0			0
$340$	1.44949	−	2.51059i	0.0786096	−	0.136156i
$341$	−6.00000	+	10.3923i	−0.324918	+	0.562775i
$342$		0			0
$343$		0			0
$344$	3.44949	+	5.97469i	0.185984	+	0.322134i
$345$		0			0
$346$	3.10102			0.166712
$347$	−19.5959			−1.05196			−0.525982	−	0.850496i	$-0.676302\pi$
$347$	−19.5959			−1.05196			−0.525982	+	0.850496i	$0.676302\pi$
$348$		0			0
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	0.975474	−	0.220115i	$-0.0706432\pi$
$349$	5.55051	+	9.61377i	0.297112	+	0.514613i	−0.678362	+	0.734728i	$0.737310\pi$
$350$		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
$355$	−0.0732141	−	0.126811i	−0.00388580	−	0.00673040i
$356$	8.44949	−	14.6349i	0.447822	−	0.775651i
$357$		0			0
$358$	−10.3485	−	17.9241i	−0.546934	−	0.947317i
$359$	−4.39898	+	7.61926i	−0.232169	+	0.402129i	−0.958446	−	0.285273i	$-0.907916\pi$
$359$	−4.39898	+	7.61926i	−0.232169	+	0.402129i	0.726277	+	0.687402i	$0.241249\pi$
$360$		0			0
$361$	6.24745	+	10.8209i	0.328813	+	0.569521i
$362$	−10.3485			−0.543903
$363$		0			0
$364$		0			0
$365$	5.00000	−	8.66025i	0.261712	−	0.453298i
$366$		0			0
$367$	−6.89898	+	11.9494i	−0.360124	+	0.623753i	−0.987981	−	0.154576i	$-0.950599\pi$
$367$	−6.89898	+	11.9494i	−0.360124	+	0.623753i	0.627857	+	0.778329i	$0.283932\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$		0			0
$370$	17.1010			0.889040
$371$		0			0
$372$		0			0
$373$	3.44949	+	5.97469i	0.178608	+	0.309358i	0.941404	−	0.337281i	$-0.109507\pi$
$373$	3.44949	+	5.97469i	0.178608	+	0.309358i	−0.762796	+	0.646639i	$0.776174\pi$
$374$	4.00000			0.206835
$375$		0			0
$376$	−9.79796			−0.505291
$377$	−33.7980			−1.74068
$378$		0			0
$379$	22.4949			1.15549			0.577743	−	0.816219i	$-0.303934\pi$
$379$	22.4949			1.15549			0.577743	+	0.816219i	$0.303934\pi$
$380$	3.69694			0.189649
$381$		0			0
$382$	4.10102			0.209826
$383$	1.44949	+	2.51059i	0.0740655	+	0.128285i	0.900679	−	0.434484i	$-0.143069\pi$
$383$	1.44949	+	2.51059i	0.0740655	+	0.128285i	−0.826614	+	0.562769i	$0.809736\pi$
$384$		0			0
$385$		0			0
$386$	17.8990			0.911034
$387$		0			0
$388$	1.44949	+	2.51059i	0.0735867	+	0.127456i
$389$	−12.4495	+	21.5631i	−0.631214	+	1.09330i	0.356090	+	0.934452i	$0.384110\pi$
$389$	−12.4495	+	21.5631i	−0.631214	+	1.09330i	−0.987304	+	0.158843i	$0.949224\pi$
$390$		0			0
$391$	−1.00000	+	1.73205i	−0.0505722	+	0.0875936i
$392$		0			0
$393$		0			0
$394$	16.6969			0.841180
$395$	−1.37628	−	2.38378i	−0.0692479	−	0.119941i
$396$		0			0
$397$	19.3485	−	33.5125i	0.971072	−	1.68195i	0.278740	−	0.960367i	$-0.410083\pi$
$397$	19.3485	−	33.5125i	0.971072	−	1.68195i	0.692332	−	0.721579i	$-0.256583\pi$
$398$	1.44949	+	2.51059i	0.0726564	+	0.125844i
$399$		0			0
$400$	1.44949	−	2.51059i	0.0724745	−	0.125529i
$401$	−9.94949	−	17.2330i	−0.496854	−	0.860576i	0.503140	−	0.864205i	$-0.332178\pi$
$401$	−9.94949	−	17.2330i	−0.496854	−	0.860576i	−0.999993	+	0.00362911i	$0.998845\pi$
$402$		0			0
$403$	−14.6969	+	25.4558i	−0.732107	+	1.26805i
$404$	8.62372	−	14.9367i	0.429046	−	0.743130i
$405$		0			0
$406$		0			0
$407$	11.7980	+	20.4347i	0.584803	+	1.01291i
$408$		0			0
$409$	13.7980			0.682265			0.341133	−	0.940015i	$-0.389189\pi$
$409$	13.7980			0.682265			0.341133	+	0.940015i	$0.389189\pi$
$410$	14.2020			0.701389
$411$		0			0
$412$	7.00000	+	12.1244i	0.344865	+	0.597324i
$413$		0			0
$414$		0			0
$415$	1.44949	−	2.51059i	0.0711527	−	0.123240i
$416$	−2.44949	+	4.24264i	−0.120096	+	0.208013i
$417$		0			0
$418$	2.55051	+	4.41761i	0.124750	+	0.216073i
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	0.241906	+	0.970300i	$0.422227\pi$
$419$	−14.7247	+	25.5040i	−0.719351	+	1.24595i	−0.961257	+	0.275653i	$0.911106\pi$
$420$		0			0
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	−0.997662	−	0.0683385i	$-0.978230\pi$
$421$	−11.4495	−	19.8311i	−0.558014	−	0.966509i	0.439648	−	0.898170i	$-0.355103\pi$
$422$	6.44949	−	11.1708i	0.313956	−	0.543788i
$423$		0			0
$424$	5.44949	+	9.43879i	0.264651	+	0.458388i
$425$	−5.79796			−0.281242
$426$		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
$431$	15.7980	+	27.3629i	0.760961	+	1.31802i	0.942356	+	0.334613i	$0.108605\pi$
$431$	15.7980	+	27.3629i	0.760961	+	1.31802i	−0.181395	+	0.983410i	$0.558061\pi$
$432$		0			0
$433$	7.79796			0.374746			0.187373	−	0.982289i	$-0.440003\pi$
$433$	7.79796			0.374746			0.187373	+	0.982289i	$0.440003\pi$
$434$		0			0
$435$		0			0
$436$	−6.34847	−	10.9959i	−0.304037	−	0.526607i
$437$	−2.55051			−0.122007
$438$		0			0
$439$	−2.20204			−0.105098			−0.0525488	−	0.998618i	$-0.516735\pi$
$439$	−2.20204			−0.105098			−0.0525488	+	0.998618i	$0.516735\pi$
$440$	−2.89898			−0.138203
$441$		0			0
$442$	9.79796			0.466041
$443$	14.8990			0.707872			0.353936	−	0.935270i	$-0.384843\pi$
$443$	14.8990			0.707872			0.353936	+	0.935270i	$0.384843\pi$
$444$		0			0
$445$	24.4949			1.16117
$446$	5.55051	+	9.61377i	0.262824	+	0.455225i
$447$		0			0
$448$		0			0
$449$	−20.5959			−0.971981			−0.485991	−	0.873964i	$-0.661541\pi$
$449$	−20.5959			−0.971981			−0.485991	+	0.873964i	$0.661541\pi$
$450$		0			0
$451$	9.79796	+	16.9706i	0.461368	+	0.799113i
$452$	−3.05051	+	5.28364i	−0.143484	+	0.248521i
$453$		0			0
$454$	−2.72474	+	4.71940i	−0.127879	+	0.221492i
$455$		0			0
$456$		0			0
$457$	−17.4949			−0.818377			−0.409188	−	0.912450i	$-0.634188\pi$
$457$	−17.4949			−0.818377			−0.409188	+	0.912450i	$0.634188\pi$
$458$	−0.623724	−	1.08032i	−0.0291447	−	0.0504801i
$459$		0			0
$460$	0.724745	−	1.25529i	0.0337914	−	0.0585284i
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	0.792688	−	0.609628i	$-0.208681\pi$
$461$	−2.82577	−	4.89437i	−0.131609	−	0.227954i	−0.924297	+	0.381674i	$0.875348\pi$
$462$		0			0
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	−0.905777	−	0.423755i	$-0.860712\pi$
$463$	−1.84847	+	3.20164i	−0.0859057	+	0.148793i	0.819871	+	0.572548i	$0.194045\pi$
$464$	−3.44949	−	5.97469i	−0.160139	−	0.277368i
$465$		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
$470$	−7.10102	−	12.2993i	−0.327546	−	0.567326i
$471$		0			0
$472$	2.00000			0.0920575
$473$	−13.7980			−0.634431
$474$		0			0
$475$	−3.69694	−	6.40329i	−0.169627	−	0.293803i
$476$		0			0
$477$		0			0
$478$	−3.39898	+	5.88721i	−0.155466	+	0.269274i
$479$	−4.79796	+	8.31031i	−0.219224	+	0.379708i	−0.954571	−	0.297983i	$-0.903686\pi$
$479$	−4.79796	+	8.31031i	−0.219224	+	0.379708i	0.735347	+	0.677691i	$0.237019\pi$
$480$		0			0
$481$	28.8990	+	50.0545i	1.31768	+	2.28229i
$482$	−0.449490	+	0.778539i	−0.0204737	+	0.0354615i
$483$		0			0
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−2.10102	+	3.63907i	−0.0954024	+	0.165242i
$486$		0			0
$487$	18.1969	+	31.5180i	0.824582	+	1.42822i	0.902238	+	0.431238i	$0.141923\pi$
$487$	18.1969	+	31.5180i	0.824582	+	1.42822i	−0.0776564	+	0.996980i	$0.524744\pi$
$488$	6.55051			0.296528
$489$		0			0
$490$		0			0
$491$	7.89898	−	13.6814i	0.356476	−	0.617434i	−0.630893	−	0.775869i	$-0.717312\pi$
$491$	7.89898	−	13.6814i	0.356476	−	0.617434i	0.987369	+	0.158435i	$0.0506448\pi$
$492$		0			0
$493$	−6.89898	+	11.9494i	−0.310714	+	0.538173i
$494$	6.24745	+	10.8209i	0.281086	+	0.486855i
$495$		0			0
$496$	−6.00000			−0.269408
$497$		0			0
$498$		0			0
$499$	12.6969	+	21.9917i	0.568393	+	0.984486i	0.996725	+	0.0808642i	$0.0257680\pi$
$499$	12.6969	+	21.9917i	0.568393	+	0.984486i	−0.428332	+	0.903621i	$0.640899\pi$
$500$	11.4495			0.512037
$501$		0			0
$502$	−17.4495			−0.778809
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	2.00000			0.0889108
$507$		0			0
$508$	−3.00000			−0.133103
$509$	3.55051	+	6.14966i	0.157374	+	0.272579i	0.933921	−	0.357480i	$-0.116364\pi$
$509$	3.55051	+	6.14966i	0.157374	+	0.272579i	−0.776547	+	0.630059i	$0.783031\pi$
$510$		0			0
$511$		0			0
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	4.10102	+	7.10318i	0.180888	+	0.313308i
$515$	−10.1464	+	17.5741i	−0.447105	+	0.774409i
$516$		0			0
$517$	9.79796	−	16.9706i	0.430914	−	0.746364i
$518$		0			0
$519$		0			0
$520$	−7.10102			−0.311400
$521$	4.65153	+	8.05669i	0.203787	+	0.352970i	0.949746	−	0.313023i	$-0.101342\pi$
$521$	4.65153	+	8.05669i	0.203787	+	0.352970i	−0.745958	+	0.665993i	$0.768008\pi$
$522$		0			0
$523$	−7.17423	+	12.4261i	−0.313707	+	0.543357i	−0.979162	−	0.203081i	$-0.934904\pi$
$523$	−7.17423	+	12.4261i	−0.313707	+	0.543357i	0.665455	+	0.746438i	$0.268238\pi$
$524$	4.27526	+	7.40496i	0.186765	+	0.323487i
$525$		0			0
$526$	−12.9495	+	22.4292i	−0.564625	+	0.977958i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	−7.89898	+	13.6814i	−0.343110	+	0.594284i
$531$		0			0
$532$		0			0
$533$	24.0000	+	41.5692i	1.03956	+	1.80056i
$534$		0			0
$535$	−17.3939			−0.752003
$536$	12.8990			0.557151
$537$		0			0
$538$	−9.17423	−	15.8902i	−0.395529	−	0.685077i
$539$		0			0
$540$		0			0
$541$	9.24745	−	16.0171i	0.397579	−	0.688627i	−0.595848	−	0.803097i	$-0.703184\pi$
$541$	9.24745	−	16.0171i	0.397579	−	0.688627i	0.993427	+	0.114471i	$0.0365172\pi$
$542$	−3.55051	+	6.14966i	−0.152507	+	0.264151i
$543$		0			0
$544$	1.00000	+	1.73205i	0.0428746	+	0.0742611i
$545$	9.20204	−	15.9384i	0.394172	−	0.682726i
$546$		0			0
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	0.935725	−	0.352730i	$-0.114747\pi$
$547$	3.79796	+	6.57826i	0.162389	+	0.281266i	−0.773336	+	0.633996i	$0.781413\pi$
$548$	3.89898	−	6.75323i	0.166556	−	0.288484i
$549$		0			0
$550$	2.89898	+	5.02118i	0.123613	+	0.214104i
$551$	−17.5959			−0.749611
$552$		0			0
$553$		0			0
$554$	−9.34847	+	16.1920i	−0.397178	+	0.687933i
$555$		0			0
$556$	2.27526	−	3.94086i	0.0964923	−	0.167130i
$557$	−6.44949	−	11.1708i	−0.273274	−	0.473324i	0.696424	−	0.717630i	$-0.254773\pi$
$557$	−6.44949	−	11.1708i	−0.273274	−	0.473324i	−0.969698	+	0.244306i	$0.921440\pi$
$558$		0			0
$559$	−33.7980			−1.42950
$560$		0			0
$561$		0			0
$562$	9.50000	+	16.4545i	0.400733	+	0.694090i
$563$	−39.9444			−1.68346			−0.841728	−	0.539902i	$-0.818461\pi$
$563$	−39.9444			−1.68346			−0.841728	+	0.539902i	$0.818461\pi$
$564$		0			0
$565$	−8.84337			−0.372043
$566$	−25.4495			−1.06972
$567$		0			0
$568$	0.101021			0.00423873
$569$	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
$571$	33.7980			1.41440			0.707200	−	0.707013i	$-0.249958\pi$
$571$	33.7980			1.41440			0.707200	+	0.707013i	$0.249958\pi$
$572$	−4.89898	−	8.48528i	−0.204837	−	0.354787i
$573$		0			0
$574$		0			0
$575$	−2.89898			−0.120896
$576$		0			0
$577$	−7.79796	−	13.5065i	−0.324633	−	0.562281i	0.656805	−	0.754061i	$-0.271908\pi$
$577$	−7.79796	−	13.5065i	−0.324633	−	0.562281i	−0.981438	+	0.191779i	$0.938574\pi$
$578$	−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
$583$	−21.7980			−0.902779
$584$	3.44949	+	5.97469i	0.142741	+	0.247234i
$585$		0			0
$586$	1.37628	−	2.38378i	0.0568534	−	0.0984730i
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	0.649924	−	0.760000i	$-0.274801\pi$
$587$	−8.07321	−	13.9832i	−0.333217	−	0.577149i	−0.983141	+	0.182850i	$0.941468\pi$
$588$		0			0
$589$	−7.65153	+	13.2528i	−0.315276	+	0.546074i
$590$	1.44949	+	2.51059i	0.0596745	+	0.103359i
$591$		0			0
$592$	−5.89898	+	10.2173i	−0.242447	+	0.419930i
$593$	−7.34847	+	12.7279i	−0.301765	+	0.522673i	−0.976536	−	0.215355i	$-0.930909\pi$
$593$	−7.34847	+	12.7279i	−0.301765	+	0.522673i	0.674770	+	0.738028i	$0.264243\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$		0			0
$598$	4.89898			0.200334
$599$	33.7980			1.38095			0.690474	−	0.723358i	$-0.257402\pi$
$599$	33.7980			1.38095			0.690474	+	0.723358i	$0.257402\pi$
$600$		0			0
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	0.984533	−	0.175198i	$-0.0560564\pi$
$601$	8.34847	+	14.4600i	0.340541	+	0.589835i	−0.643992	+	0.765032i	$0.722723\pi$
$602$		0			0
$603$		0			0
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	−5.07321	+	8.78706i	−0.206255	+	0.357245i
$606$		0			0
$607$	10.3485	+	17.9241i	0.420031	+	0.727516i	0.995942	−	0.0899969i	$-0.0286857\pi$
$607$	10.3485	+	17.9241i	0.420031	+	0.727516i	−0.575911	+	0.817513i	$0.695352\pi$
$608$	−1.27526	+	2.20881i	−0.0517184	+	0.0895789i
$609$		0			0
$610$	4.74745	+	8.22282i	0.192219	+	0.332932i
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$		0			0
$613$	7.34847	+	12.7279i	0.296802	+	0.514076i	0.975402	−	0.220432i	$-0.0707466\pi$
$613$	7.34847	+	12.7279i	0.296802	+	0.514076i	−0.678601	+	0.734508i	$0.737413\pi$
$614$	25.2474			1.01890
$615$		0			0
$616$		0			0
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	−0.978333	−	0.207037i	$-0.933618\pi$
$617$	−7.69694	+	13.3315i	−0.309867	+	0.536706i	0.668466	+	0.743743i	$0.266951\pi$
$618$		0			0
$619$	15.0732	−	26.1076i	0.605844	−	1.04935i	−0.386074	−	0.922468i	$-0.626169\pi$
$619$	15.0732	−	26.1076i	0.605844	−	1.04935i	0.991918	−	0.126884i	$-0.0404976\pi$
$620$	−4.34847	−	7.53177i	−0.174639	−	0.302483i
$621$		0			0
$622$	−30.6969			−1.23084
$623$		0			0
$624$		0			0
$625$	1.05051	+	1.81954i	0.0420204	+	0.0727815i
$626$	−4.69694			−0.187727
$627$		0			0
$628$	8.34847			0.333140
$629$	23.5959			0.940831
$630$		0			0
$631$	27.8990			1.11064			0.555320	−	0.831636i	$-0.312596\pi$
$631$	27.8990			1.11064			0.555320	+	0.831636i	$0.312596\pi$
$632$	1.89898			0.0755373
$633$		0			0
$634$	20.6969			0.821980
$635$	−2.17423	−	3.76588i	−0.0862819	−	0.149445i
$636$		0			0
$637$		0			0
$638$	13.7980			0.546266
$639$		0			0
$640$	−0.724745	−	1.25529i	−0.0286481	−	0.0496199i
$641$	−3.74745	+	6.49077i	−0.148015	+	0.256370i	−0.930494	−	0.366308i	$-0.880622\pi$
$641$	−3.74745	+	6.49077i	−0.148015	+	0.256370i	0.782479	+	0.622678i	$0.213955\pi$
$642$		0			0
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	0.157022	+	0.987595i	$0.449811\pi$
$643$	−19.6969	+	34.1161i	−0.776771	+	1.34541i	−0.933793	+	0.357812i	$0.883523\pi$
$644$		0			0
$645$		0			0
$646$	5.10102			0.200697
$647$	25.3485	+	43.9048i	0.996551	+	1.72608i	0.570139	+	0.821548i	$0.306889\pi$
$647$	25.3485	+	43.9048i	0.996551	+	1.72608i	0.426412	+	0.904529i	$0.359777\pi$
$648$		0			0
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$	7.10102	+	12.2993i	0.278525	+	0.482419i
$651$		0			0
$652$	9.89898	−	17.1455i	0.387674	−	0.671471i
$653$	4.89898	+	8.48528i	0.191712	+	0.332055i	0.945818	−	0.324698i	$-0.105263\pi$
$653$	4.89898	+	8.48528i	0.191712	+	0.332055i	−0.754106	+	0.656753i	$0.771929\pi$
$654$		0			0
$655$	−6.19694	+	10.7334i	−0.242134	+	0.419389i
$656$	−4.89898	+	8.48528i	−0.191273	+	0.331295i
$657$		0			0
$658$		0			0
$659$	−12.3485	−	21.3882i	−0.481028	−	0.833165i	0.518735	−	0.854935i	$-0.326403\pi$
$659$	−12.3485	−	21.3882i	−0.481028	−	0.833165i	−0.999763	+	0.0217701i	$0.993070\pi$
$660$		0			0
$661$	−4.55051			−0.176994			−0.0884972	−	0.996076i	$-0.528206\pi$
$661$	−4.55051			−0.176994			−0.0884972	+	0.996076i	$0.528206\pi$
$662$	−4.69694			−0.182552
$663$		0			0
$664$	1.00000	+	1.73205i	0.0388075	+	0.0672166i
$665$		0			0
$666$		0			0
$667$	−3.44949	+	5.97469i	−0.133565	+	0.231341i
$668$	5.34847	−	9.26382i	0.206938	−	0.358428i
$669$		0			0
$670$	9.34847	+	16.1920i	0.361163	+	0.625552i
$671$	−6.55051	+	11.3458i	−0.252880	+	0.438000i
$672$		0			0
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	0.936894	−	0.349612i	$-0.113687\pi$
$673$	4.29796	+	7.44428i	0.165674	+	0.286956i	−0.771220	+	0.636568i	$0.780353\pi$
$674$	−11.6969	+	20.2597i	−0.450549	+	0.780374i
$675$		0			0
$676$	−5.50000	−	9.52628i	−0.211538	−	0.366395i
$677$	14.6969			0.564849			0.282425	−	0.959289i	$-0.408861\pi$
$677$	14.6969			0.564849			0.282425	+	0.959289i	$0.408861\pi$
$678$		0			0
$679$		0			0
$680$	−1.44949	+	2.51059i	−0.0555854	+	0.0962767i
$681$		0			0
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	25.8990	+	44.8583i	0.990997	+	1.71646i	0.611446	+	0.791286i	$0.290588\pi$
$683$	25.8990	+	44.8583i	0.990997	+	1.71646i	0.379551	+	0.925171i	$0.376079\pi$
$684$		0			0
$685$	11.3031			0.431868
$686$		0			0
$687$		0			0
$688$	−3.44949	−	5.97469i	−0.131511	−	0.227783i
$689$	−53.3939			−2.03414
$690$		0			0
$691$	−51.0454			−1.94186			−0.970929	−	0.239366i	$-0.923060\pi$
$691$	−51.0454			−1.94186			−0.970929	+	0.239366i	$0.923060\pi$
$692$	−3.10102			−0.117883
$693$		0			0
$694$	19.5959			0.743851
$695$	6.59592			0.250197
$696$		0			0
$697$	19.5959			0.742248
$698$	−5.55051	−	9.61377i	−0.210090	−	0.363886i
$699$		0			0
$700$		0			0
$701$	7.39388			0.279263			0.139631	−	0.990204i	$-0.455408\pi$
$701$	7.39388			0.279263			0.139631	+	0.990204i	$0.455408\pi$
$702$		0			0
$703$	15.0454	+	26.0594i	0.567448	+	0.982849i
$704$	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
$709$	27.5959			1.03639			0.518193	−	0.855264i	$-0.326605\pi$
$709$	27.5959			1.03639			0.518193	+	0.855264i	$0.326605\pi$
$710$	0.0732141	+	0.126811i	0.00274768	+	0.00475911i
$711$		0			0
$712$	−8.44949	+	14.6349i	−0.316658	+	0.548468i
$713$	3.00000	+	5.19615i	0.112351	+	0.194597i
$714$		0			0
$715$	7.10102	−	12.2993i	0.265563	−	0.459969i
$716$	10.3485	+	17.9241i	0.386740	+	0.669854i
$717$		0			0
$718$	4.39898	−	7.61926i	0.164168	−	0.284348i
$719$	−4.89898	+	8.48528i	−0.182701	+	0.316448i	−0.942799	−	0.333360i	$-0.891817\pi$
$719$	−4.89898	+	8.48528i	−0.182701	+	0.316448i	0.760098	+	0.649808i	$0.225151\pi$
$720$		0			0
$721$		0			0
$722$	−6.24745	−	10.8209i	−0.232506	−	0.402712i
$723$		0			0
$724$	10.3485			0.384598
$725$	−20.0000			−0.742781
$726$		0			0
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	0.776448	−	0.630181i	$-0.217019\pi$
$727$	−4.24745	−	7.35680i	−0.157529	−	0.272848i	−0.933977	+	0.357333i	$0.883686\pi$
$728$		0			0
$729$		0			0
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	−6.89898	+	11.9494i	−0.255168	+	0.441964i
$732$		0			0
$733$	−8.72474	−	15.1117i	−0.322256	−	0.558163i	0.658697	−	0.752408i	$-0.271108\pi$
$733$	−8.72474	−	15.1117i	−0.322256	−	0.558163i	−0.980953	+	0.194245i	$0.937774\pi$
$734$	6.89898	−	11.9494i	0.254646	−	0.441060i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−12.8990	+	22.3417i	−0.475140	+	0.822967i
$738$		0			0
$739$	−6.79796	−	11.7744i	−0.250067	−	0.433129i	0.713477	−	0.700679i	$-0.247119\pi$
$739$	−6.79796	−	11.7744i	−0.250067	−	0.433129i	−0.963544	+	0.267550i	$0.913786\pi$
$740$	−17.1010			−0.628646
$741$		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
$745$	4.34847	−	7.53177i	0.159316	−	0.275943i
$746$	−3.44949	−	5.97469i	−0.126295	−	0.218749i
$747$		0			0
$748$	−4.00000			−0.146254
$749$		0			0
$750$		0			0
$751$	−0.702041	−	1.21597i	−0.0256178	−	0.0443714i	0.852932	−	0.522022i	$-0.174822\pi$
$751$	−0.702041	−	1.21597i	−0.0256178	−	0.0443714i	−0.878550	+	0.477650i	$0.841489\pi$
$752$	9.79796			0.357295
$753$		0			0
$754$	33.7980			1.23085
$755$	7.24745			0.263762
$756$		0			0
$757$	−35.3939			−1.28641			−0.643206	−	0.765693i	$-0.722396\pi$
$757$	−35.3939			−1.28641			−0.643206	+	0.765693i	$0.722396\pi$
$758$	−22.4949			−0.817051
$759$		0			0
$760$	−3.69694			−0.134102
$761$	−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
$764$	−4.10102			−0.148370
$765$		0			0
$766$	−1.44949	−	2.51059i	−0.0523722	−	0.0907113i
$767$	−4.89898	+	8.48528i	−0.176892	+	0.306386i
$768$		0			0
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	0.375769	+	0.926714i	$0.377379\pi$
$769$	−17.0454	+	29.5235i	−0.614673	+	1.06465i	−0.990442	+	0.137932i	$0.955955\pi$
$770$		0			0
$771$		0			0
$772$	−17.8990			−0.644198
$773$	−16.9722	−	29.3967i	−0.610447	−	1.05733i	−0.991165	−	0.132635i	$-0.957656\pi$
$773$	−16.9722	−	29.3967i	−0.610447	−	1.05733i	0.380718	−	0.924691i	$-0.375677\pi$
$774$		0			0
$775$	−8.69694	+	15.0635i	−0.312403	+	0.541098i
$776$	−1.44949	−	2.51059i	−0.0520336	−	0.0901249i
$777$		0			0
$778$	12.4495	−	21.5631i	0.446336	−	0.773076i
$779$	12.4949	+	21.6418i	0.447676	+	0.775398i
$780$		0			0
$781$	−0.101021	+	0.174973i	−0.00361480	+	0.00626101i
$782$	1.00000	−	1.73205i	0.0357599	−	0.0619380i
$783$		0			0
$784$		0			0
$785$	6.05051	+	10.4798i	0.215952	+	0.374040i
$786$		0			0
$787$	11.3939			0.406148			0.203074	−	0.979163i	$-0.434907\pi$
$787$	11.3939			0.406148			0.203074	+	0.979163i	$0.434907\pi$
$788$	−16.6969			−0.594804
$789$		0			0
$790$	1.37628	+	2.38378i	0.0489657	+	0.0848111i
$791$		0			0
$792$		0			0
$793$	−16.0454	+	27.7915i	−0.569789	+	0.986904i
$794$	−19.3485	+	33.5125i	−0.686651	+	1.18932i
$795$		0			0
$796$	−1.44949	−	2.51059i	−0.0513758	−	0.0889855i
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	−0.662220	−	0.749310i	$-0.730385\pi$
$797$	8.97219	−	15.5403i	0.317811	−	0.550465i	0.980031	+	0.198844i	$0.0637188\pi$
$798$		0			0
$799$	−9.79796	−	16.9706i	−0.346627	−	0.600375i
$800$	−1.44949	+	2.51059i	−0.0512472	+	0.0887628i
$801$		0			0
$802$	9.94949	+	17.2330i	0.351329	+	0.608519i
$803$	−13.7980			−0.486919
$804$		0			0
$805$		0			0
$806$	14.6969	−	25.4558i	0.517678	−	0.896644i
$807$		0			0
$808$	−8.62372	+	14.9367i	−0.303382	+	0.525472i
$809$	−8.10102	−	14.0314i	−0.284817	−	0.493317i	0.687748	−	0.725950i	$-0.258599\pi$
$809$	−8.10102	−	14.0314i	−0.284817	−	0.493317i	−0.972565	+	0.232632i	$0.925266\pi$
$810$		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
$814$	−11.7980	−	20.4347i	−0.413518	−	0.716235i
$815$	28.6969			1.00521
$816$		0			0
$817$	−17.5959			−0.615603
$818$	−13.7980			−0.482434
$819$		0			0
$820$	−14.2020			−0.495957
$821$	−0.404082			−0.0141026			−0.00705128	−	0.999975i	$-0.502245\pi$
$821$	−0.404082			−0.0141026			−0.00705128	+	0.999975i	$0.502245\pi$
$822$		0			0
$823$	−13.3939			−0.466881			−0.233441	−	0.972371i	$-0.574998\pi$
$823$	−13.3939			−0.466881			−0.233441	+	0.972371i	$0.574998\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$		0			0
$826$		0			0
$827$	36.4949			1.26905			0.634526	−	0.772902i	$-0.281195\pi$
$827$	36.4949			1.26905			0.634526	+	0.772902i	$0.281195\pi$
$828$		0			0
$829$	0.651531	+	1.12848i	0.0226286	+	0.0391939i	0.877118	−	0.480275i	$-0.159463\pi$
$829$	0.651531	+	1.12848i	0.0226286	+	0.0391939i	−0.854489	+	0.519469i	$0.826130\pi$
$830$	−1.44949	+	2.51059i	−0.0503125	+	0.0871438i
$831$		0			0
$832$	2.44949	−	4.24264i	0.0849208	−	0.147087i
$833$		0			0
$834$		0			0
$835$	15.5051			0.536576
$836$	−2.55051	−	4.41761i	−0.0882112	−	0.152786i
$837$		0			0
$838$	14.7247	−	25.5040i	0.508658	−	0.881021i
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	0.991907	+	0.126968i	$0.0405245\pi$
$839$	17.5505	+	30.3984i	0.605911	+	1.04947i	−0.385996	+	0.922500i	$0.626142\pi$
$840$		0			0
$841$	−9.29796	+	16.1045i	−0.320619	+	0.555329i
$842$	11.4495	+	19.8311i	0.394575	+	0.683425i
$843$		0			0
$844$	−6.44949	+	11.1708i	−0.222001	+	0.384516i
$845$	7.97219	−	13.8082i	0.274252	−	0.475018i
$846$		0			0
$847$		0			0
$848$	−5.44949	−	9.43879i	−0.187136	−	0.324129i
$849$		0			0
$850$	5.79796			0.198868
$851$	11.7980			0.404429
$852$		0			0
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	0.996449	−	0.0841942i	$-0.0268316\pi$
$853$	12.4217	+	21.5150i	0.425310	+	0.736659i	−0.571139	+	0.820853i	$0.693498\pi$
$854$		0			0
$855$		0			0
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	17.4495	−	30.2234i	0.596063	−	1.03241i	−0.397333	−	0.917675i	$-0.630064\pi$
$857$	17.4495	−	30.2234i	0.596063	−	1.03241i	0.993396	−	0.114737i	$-0.0366026\pi$
$858$		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
$862$	−15.7980	−	27.3629i	−0.538081	−	0.931983i
$863$	5.94949	−	10.3048i	0.202523	−	0.350780i	−0.746818	−	0.665029i	$-0.768419\pi$
$863$	5.94949	−	10.3048i	0.202523	−	0.350780i	0.949341	+	0.314249i	$0.101753\pi$
$864$		0			0
$865$	−2.24745	−	3.89270i	−0.0764155	−	0.132356i
$866$	−7.79796			−0.264985
$867$		0			0
$868$		0			0
$869$	−1.89898	+	3.28913i	−0.0644185	+	0.111576i
$870$		0			0
$871$	−31.5959	+	54.7257i	−1.07059	+	1.85431i
$872$	6.34847	+	10.9959i	0.214986	+	0.372367i
$873$		0			0
$874$	2.55051			0.0862723
$875$		0			0
$876$		0			0
$877$	−11.2474	−	19.4812i	−0.379799	−	0.657832i	0.611233	−	0.791450i	$-0.290674\pi$
$877$	−11.2474	−	19.4812i	−0.379799	−	0.657832i	−0.991033	+	0.133619i	$0.957340\pi$
$878$	2.20204			0.0743153
$879$		0			0
$880$	2.89898			0.0977246
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$		0			0
$883$	−19.7980			−0.666254			−0.333127	−	0.942882i	$-0.608104\pi$
$883$	−19.7980			−0.666254			−0.333127	+	0.942882i	$0.608104\pi$
$884$	−9.79796			−0.329541
$885$		0			0
$886$	−14.8990			−0.500541
$887$	7.10102	+	12.2993i	0.238429	+	0.412971i	0.960264	−	0.279094i	$-0.0900343\pi$
$887$	7.10102	+	12.2993i	0.238429	+	0.412971i	−0.721835	+	0.692065i	$0.756701\pi$
$888$		0			0
$889$		0			0
$890$	−24.4949			−0.821071
$891$		0			0
$892$	−5.55051	−	9.61377i	−0.185845	−	0.321893i
$893$	12.4949	−	21.6418i	0.418126	−	0.724215i
$894$		0			0
$895$	−15.0000	+	25.9808i	−0.501395	+	0.868441i
$896$		0			0
$897$		0			0
$898$	20.5959			0.687295
$899$	20.6969	+	35.8481i	0.690282	+	1.19560i
$900$		0			0
$901$	−10.8990	+	18.8776i	−0.363098	+	0.628904i
$902$	−9.79796	−	16.9706i	−0.326236	−	0.565058i
$903$		0			0
$904$	3.05051	−	5.28364i	0.101458	−	0.175731i
$905$	7.50000	+	12.9904i	0.249308	+	0.431815i
$906$		0			0
$907$	−1.34847	+	2.33562i	−0.0447752	+	0.0775529i	−0.887544	−	0.460722i	$-0.847590\pi$
$907$	−1.34847	+	2.33562i	−0.0447752	+	0.0775529i	0.842769	+	0.538275i	$0.180924\pi$
$908$	2.72474	−	4.71940i	0.0904238	−	0.156619i
$909$		0			0
$910$		0			0
$911$	25.9949	+	45.0245i	0.861249	+	1.49173i	0.870724	+	0.491773i	$0.163651\pi$
$911$	25.9949	+	45.0245i	0.861249	+	1.49173i	−0.00947432	+	0.999955i	$0.503016\pi$
$912$		0			0
$913$	−4.00000			−0.132381
$914$	17.4949			0.578680
$915$		0			0
$916$	0.623724	+	1.08032i	0.0206084	+	0.0356949i
$917$		0			0
$918$		0			0
$919$	12.8485	−	22.2542i	0.423832	−	0.734098i	−0.572479	−	0.819920i	$-0.694018\pi$
$919$	12.8485	−	22.2542i	0.423832	−	0.734098i	0.996311	+	0.0858213i	$0.0273514\pi$
$920$	−0.724745	+	1.25529i	−0.0238941	+	0.0413858i
$921$		0			0
$922$	2.82577	+	4.89437i	0.0930616	+	0.161187i
$923$	−0.247449	+	0.428594i	−0.00814487	+	0.0141073i
$924$		0			0
$925$	17.1010	+	29.6198i	0.562278	+	0.973894i
$926$	1.84847	−	3.20164i	0.0607445	−	0.105213i
$927$		0			0
$928$	3.44949	+	5.97469i	0.113235	+	0.196129i
$929$	34.2929			1.12511			0.562556	−	0.826759i	$-0.309818\pi$
$929$	34.2929			1.12511			0.562556	+	0.826759i	$0.309818\pi$
$930$		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
$935$	−2.89898	−	5.02118i	−0.0948068	−	0.164210i
$936$		0			0
$937$	−45.5959			−1.48955			−0.744777	−	0.667314i	$-0.767444\pi$
$937$	−45.5959			−1.48955			−0.744777	+	0.667314i	$0.767444\pi$
$938$		0			0
$939$		0			0
$940$	7.10102	+	12.2993i	0.231610	+	0.401160i
$941$	−1.44949			−0.0472520			−0.0236260	−	0.999721i	$-0.507521\pi$
$941$	−1.44949			−0.0472520			−0.0236260	+	0.999721i	$0.507521\pi$
$942$		0			0
$943$	9.79796			0.319065
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	13.7980			0.448610
$947$	−52.4949			−1.70585			−0.852927	−	0.522029i	$-0.825175\pi$
$947$	−52.4949			−1.70585			−0.852927	+	0.522029i	$0.825175\pi$
$948$		0			0
$949$	−33.7980			−1.09713
$950$	3.69694	+	6.40329i	0.119945	+	0.207750i
$951$		0			0
$952$		0			0
$953$	3.39388			0.109938			0.0549692	−	0.998488i	$-0.482494\pi$
$953$	3.39388			0.109938			0.0549692	+	0.998488i	$0.482494\pi$
$954$		0			0
$955$	−2.97219	−	5.14799i	−0.0961779	−	0.166585i
$956$	3.39898	−	5.88721i	0.109931	−	0.190406i
$957$		0			0
$958$	4.79796	−	8.31031i	0.155015	−	0.268494i
$959$		0			0
$960$		0			0
$961$	5.00000			0.161290
$962$	−28.8990	−	50.0545i	−0.931740	−	1.61382i
$963$		0			0
$964$	0.449490	−	0.778539i	0.0144771	−	0.0250751i
$965$	−12.9722	−	22.4685i	−0.417590	−	0.723287i
$966$		0			0
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	−0.993162	−	0.116746i	$-0.962754\pi$
$967$	−12.2980	+	21.3007i	−0.395476	+	0.684984i	0.597686	+	0.801730i	$0.296087\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	2.10102	−	3.63907i	0.0674597	−	0.116844i
$971$	0.0278064	−	0.0481621i	0.000892350	−	0.00154560i	−0.865579	−	0.500773i	$-0.833049\pi$
$971$	0.0278064	−	0.0481621i	0.000892350	−	0.00154560i	0.866471	+	0.499227i	$0.166383\pi$
$972$		0			0
$973$		0			0
$974$	−18.1969	−	31.5180i	−0.583068	−	1.00990i
$975$		0			0
$976$	−6.55051			−0.209677
$977$	37.5959			1.20280			0.601400	−	0.798948i	$-0.294610\pi$
$977$	37.5959			1.20280			0.601400	+	0.798948i	$0.294610\pi$
$978$		0			0
$979$	−16.8990	−	29.2699i	−0.540094	−	0.935470i
$980$		0			0
$981$		0			0
$982$	−7.89898	+	13.6814i	−0.252067	+	0.436592i
$983$	16.5959	−	28.7450i	0.529328	−	0.916822i	−0.470087	−	0.882620i	$-0.655778\pi$
$983$	16.5959	−	28.7450i	0.529328	−	0.916822i	0.999415	−	0.0342024i	$-0.0108891\pi$
$984$		0			0
$985$	−12.1010	−	20.9596i	−0.385571	−	0.667828i
$986$	6.89898	−	11.9494i	0.219708	−	0.380546i
$987$		0			0
$988$	−6.24745	−	10.8209i	−0.198758	−	0.344259i
$989$	−3.44949	+	5.97469i	−0.109687	+	0.189984i
$990$		0			0
$991$	0.898979	+	1.55708i	0.0285570	+	0.0494622i	0.879951	−	0.475065i	$-0.157575\pi$
$991$	0.898979	+	1.55708i	0.0285570	+	0.0494622i	−0.851394	+	0.524527i	$0.824242\pi$
$992$	6.00000			0.190500
$993$		0			0
$994$		0			0
$995$	2.10102	−	3.63907i	0.0666068	−	0.115366i
$996$		0			0
$997$	26.0732	−	45.1601i	0.825747	−	1.43024i	−0.0756001	−	0.997138i	$-0.524087\pi$
$997$	26.0732	−	45.1601i	0.825747	−	1.43024i	0.901347	−	0.433097i	$-0.142579\pi$
$998$	−12.6969	−	21.9917i	−0.401915	−	0.696136i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.e.k.1549.2		4
3.2	odd	2		882.2.e.n.373.2		4
7.2	even	3		2646.2.f.k.1765.2		4
7.3	odd	6		2646.2.h.m.361.2		4
7.4	even	3		2646.2.h.n.361.1		4
7.5	odd	6		378.2.f.d.253.1		4
7.6	odd	2		2646.2.e.l.1549.1		4
9.2	odd	6		882.2.h.l.79.1		4
9.7	even	3		2646.2.h.n.667.1		4
21.2	odd	6		882.2.f.j.589.2		4
21.5	even	6		126.2.f.c.85.1	yes	4
21.11	odd	6		882.2.h.l.67.1		4
21.17	even	6		882.2.h.k.67.2		4
21.20	even	2		882.2.e.m.373.1		4
28.19	even	6		3024.2.r.e.1009.1		4
63.2	odd	6		882.2.f.j.295.1		4
63.5	even	6		1134.2.a.p.1.1		2
63.11	odd	6		882.2.e.n.655.2		4
63.16	even	3		2646.2.f.k.883.2		4
63.20	even	6		882.2.h.k.79.2		4
63.23	odd	6		7938.2.a.bn.1.2		2
63.25	even	3	inner	2646.2.e.k.2125.2		4
63.34	odd	6		2646.2.h.m.667.2		4
63.38	even	6		882.2.e.m.655.1		4
63.40	odd	6		1134.2.a.i.1.2		2
63.47	even	6		126.2.f.c.43.2	✓	4
63.52	odd	6		2646.2.e.l.2125.1		4
63.58	even	3		7938.2.a.bm.1.1		2
63.61	odd	6		378.2.f.d.127.1		4
84.47	odd	6		1008.2.r.e.337.2		4
252.47	odd	6		1008.2.r.e.673.1		4
252.103	even	6		9072.2.a.bd.1.2		2
252.131	odd	6		9072.2.a.bk.1.1		2
252.187	even	6		3024.2.r.e.2017.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	63.47	even	6
126.2.f.c.85.1	yes	4	21.5	even	6
378.2.f.d.127.1		4	63.61	odd	6
378.2.f.d.253.1		4	7.5	odd	6
882.2.e.m.373.1		4	21.20	even	2
882.2.e.m.655.1		4	63.38	even	6
882.2.e.n.373.2		4	3.2	odd	2
882.2.e.n.655.2		4	63.11	odd	6
882.2.f.j.295.1		4	63.2	odd	6
882.2.f.j.589.2		4	21.2	odd	6
882.2.h.k.67.2		4	21.17	even	6
882.2.h.k.79.2		4	63.20	even	6
882.2.h.l.67.1		4	21.11	odd	6
882.2.h.l.79.1		4	9.2	odd	6
1008.2.r.e.337.2		4	84.47	odd	6
1008.2.r.e.673.1		4	252.47	odd	6
1134.2.a.i.1.2		2	63.40	odd	6
1134.2.a.p.1.1		2	63.5	even	6
2646.2.e.k.1549.2		4	1.1	even	1	trivial
2646.2.e.k.2125.2		4	63.25	even	3	inner
2646.2.e.l.1549.1		4	7.6	odd	2
2646.2.e.l.2125.1		4	63.52	odd	6
2646.2.f.k.883.2		4	63.16	even	3
2646.2.f.k.1765.2		4	7.2	even	3
2646.2.h.m.361.2		4	7.3	odd	6
2646.2.h.m.667.2		4	63.34	odd	6
2646.2.h.n.361.1		4	7.4	even	3
2646.2.h.n.667.1		4	9.7	even	3
3024.2.r.e.1009.1		4	28.19	even	6
3024.2.r.e.2017.1		4	252.187	even	6
7938.2.a.bm.1.1		2	63.58	even	3
7938.2.a.bn.1.2		2	63.23	odd	6
9072.2.a.bd.1.2		2	252.103	even	6
9072.2.a.bk.1.1		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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{4} +(0.724745 + 1.25529i) q^{5} -1.00000 q^{8} +(-0.724745 - 1.25529i) q^{10} +(1.00000 - 1.73205i) q^{11} +(2.44949 - 4.24264i) q^{13} +1.00000 q^{16} +(-1.00000 - 1.73205i) q^{17} +(1.27526 - 2.20881i) q^{19} +(0.724745 + 1.25529i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.44949 - 2.51059i) q^{25} +(-2.44949 + 4.24264i) q^{26} +(-3.44949 - 5.97469i) q^{29} -6.00000 q^{31} -1.00000 q^{32} +(1.00000 + 1.73205i) q^{34} +(-5.89898 + 10.2173i) q^{37} +(-1.27526 + 2.20881i) q^{38} +(-0.724745 - 1.25529i) q^{40} +(-4.89898 + 8.48528i) q^{41} +(-3.44949 - 5.97469i) q^{43} +(1.00000 - 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} +9.79796 q^{47} +(-1.44949 + 2.51059i) q^{50} +(2.44949 - 4.24264i) q^{52} +(-5.44949 - 9.43879i) q^{53} +2.89898 q^{55} +(3.44949 + 5.97469i) q^{58} -2.00000 q^{59} -6.55051 q^{61} +6.00000 q^{62} +1.00000 q^{64} +7.10102 q^{65} -12.8990 q^{67} +(-1.00000 - 1.73205i) q^{68} -0.101021 q^{71} +(-3.44949 - 5.97469i) q^{73} +(5.89898 - 10.2173i) q^{74} +(1.27526 - 2.20881i) q^{76} -1.89898 q^{79} +(0.724745 + 1.25529i) q^{80} +(4.89898 - 8.48528i) q^{82} +(-1.00000 - 1.73205i) q^{83} +(1.44949 - 2.51059i) q^{85} +(3.44949 + 5.97469i) q^{86} +(-1.00000 + 1.73205i) q^{88} +(8.44949 - 14.6349i) q^{89} +(-0.500000 - 0.866025i) q^{92} -9.79796 q^{94} +3.69694 q^{95} +(1.44949 + 2.51059i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 4 q^{4} - 2 q^{5} - 4 q^{8} + 2 q^{10} + 4 q^{11} + 4 q^{16} - 4 q^{17} + 10 q^{19} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{29} - 24 q^{31} - 4 q^{32} + 4 q^{34} - 4 q^{37} - 10 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more