LMFDB - Embedded newform 2646.2.f.k.883.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("2646.883");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$21.1284163748$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			883.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	2646.883
Dual form			2646.2.f.k.1765.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.724745 + 1.25529i) q^{5} -1.00000 q^{8} +1.44949 q^{10} +(1.00000 - 1.73205i) q^{11} +(2.44949 + 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +2.00000 q^{17} -2.55051 q^{19} +(0.724745 - 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.44949 - 2.51059i) q^{25} +4.89898 q^{26} +(-3.44949 + 5.97469i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +11.7980 q^{37} +(-1.27526 + 2.20881i) q^{38} +(-0.724745 - 1.25529i) q^{40} +(-4.89898 - 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} -2.00000 q^{44} -1.00000 q^{46} +(-4.89898 + 8.48528i) q^{47} +(-1.44949 - 2.51059i) q^{50} +(2.44949 - 4.24264i) q^{52} +10.8990 q^{53} +2.89898 q^{55} +(3.44949 + 5.97469i) q^{58} +(1.00000 + 1.73205i) q^{59} +(3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-3.55051 + 6.14966i) q^{65} +(6.44949 + 11.1708i) q^{67} +(-1.00000 - 1.73205i) q^{68} -0.101021 q^{71} +6.89898 q^{73} +(5.89898 - 10.2173i) q^{74} +(1.27526 + 2.20881i) q^{76} +(0.949490 - 1.64456i) q^{79} -1.44949 q^{80} -9.79796 q^{82} +(-1.00000 + 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(3.44949 + 5.97469i) q^{86} +(-1.00000 + 1.73205i) q^{88} -16.8990 q^{89} +(-0.500000 + 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(-1.84847 - 3.20164i) q^{95} +(1.44949 - 2.51059i) q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 4 q^{10} + 4 q^{11} - 2 q^{16} + 8 q^{17} - 20 q^{19} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} + 8 q^{37} - 10 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 4 * q^10 + 4 * q^11 - 2 * q^16 + 8 * q^17 - 20 * q^19 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 + 8 * q^37 - 10 * q^38 + 2 * q^40 - 4 * q^43 - 8 * q^44 - 4 * q^46 + 4 * q^50 + 24 * q^53 - 8 * q^55 + 4 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 - 4 * q^68 - 20 * q^71 + 8 * q^73 + 4 * q^74 + 10 * q^76 - 6 * q^79 + 4 * q^80 - 4 * q^83 - 4 * q^85 + 4 * q^86 - 4 * q^88 - 48 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

Character values

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

$n$	$785$	$1081$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.724745	+	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
$10$	1.44949			0.458369
$11$	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	0.975172	+	0.221449i	$0.0710785\pi$
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	−0.295806	+	0.955248i	$0.595588\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$		0			0
$19$	−2.55051			−0.585127			−0.292564	−	0.956246i	$-0.594508\pi$
$19$	−2.55051			−0.585127			−0.292564	+	0.956246i	$0.594508\pi$
$20$	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
$26$	4.89898			0.960769
$27$		0			0
$28$		0			0
$29$	−3.44949	+	5.97469i	−0.640554	+	1.10947i	0.344755	+	0.938693i	$0.387962\pi$
$29$	−3.44949	+	5.97469i	−0.640554	+	1.10947i	−0.985309	+	0.170780i	$0.945371\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$		0			0
$36$		0			0
$37$	11.7980			1.93957			0.969786	−	0.243956i	$-0.0784453\pi$
$37$	11.7980			1.93957			0.969786	+	0.243956i	$0.0784453\pi$
$38$	−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	−0.940198	−	0.340629i	$-0.889360\pi$
$41$	−4.89898	−	8.48528i	−0.765092	−	1.32518i	0.175106	−	0.984550i	$-0.443973\pi$
$42$		0			0
$43$	−3.44949	+	5.97469i	−0.526042	+	0.911132i	0.473497	+	0.880795i	$0.342991\pi$
$43$	−3.44949	+	5.97469i	−0.526042	+	0.911132i	−0.999540	+	0.0303367i	$0.990342\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	−1.00000			−0.147442
$47$	−4.89898	+	8.48528i	−0.714590	+	1.23771i	0.248528	+	0.968625i	$0.420053\pi$
$47$	−4.89898	+	8.48528i	−0.714590	+	1.23771i	−0.963118	+	0.269081i	$0.913280\pi$
$48$		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
$53$	10.8990			1.49709			0.748545	−	0.663084i	$-0.230753\pi$
$53$	10.8990			1.49709			0.748545	+	0.663084i	$0.230753\pi$
$54$		0			0
$55$	2.89898			0.390898
$56$		0			0
$57$		0			0
$58$	3.44949	+	5.97469i	0.452940	+	0.784515i
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$		0			0
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	−0.576521	−	0.817082i	$-0.695590\pi$
$61$	3.27526	−	5.67291i	0.419353	−	0.726341i	0.995875	+	0.0907408i	$0.0289235\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.55051	+	6.14966i	−0.440387	+	0.762772i
$66$		0			0
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	0.927233	+	0.374486i	$0.122181\pi$
$67$	6.44949	+	11.1708i	0.787931	+	1.36474i	−0.139302	+	0.990250i	$0.544486\pi$
$68$	−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
$73$	6.89898			0.807464			0.403732	−	0.914877i	$-0.367713\pi$
$73$	6.89898			0.807464			0.403732	+	0.914877i	$0.367713\pi$
$74$	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
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	−0.807657	−	0.589653i	$-0.799265\pi$
$79$	0.949490	−	1.64456i	0.106826	−	0.185028i	0.914483	+	0.404625i	$0.132598\pi$
$80$	−1.44949			−0.162058
$81$		0			0
$82$	−9.79796			−1.08200
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		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
$89$	−16.8990			−1.79129			−0.895644	−	0.444771i	$-0.853285\pi$
$89$	−16.8990			−1.79129			−0.895644	+	0.444771i	$0.853285\pi$
$90$		0			0
$91$		0			0
$92$	−0.500000	+	0.866025i	−0.0521286	+	0.0902894i
$93$		0			0
$94$	4.89898	+	8.48528i	0.505291	+	0.875190i
$95$	−1.84847	−	3.20164i	−0.189649	−	0.328482i
$96$		0			0
$97$	1.44949	−	2.51059i	0.147173	−	0.254912i	−0.783008	−	0.622011i	$-0.786316\pi$
$97$	1.44949	−	2.51059i	0.147173	−	0.254912i	0.930182	+	0.367099i	$0.119649\pi$
$98$		0			0
$99$		0			0
$100$	−2.89898			−0.289898
$101$	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
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	12.6969			1.21615			0.608073	−	0.793881i	$-0.291943\pi$
$109$	12.6969			1.21615			0.608073	+	0.793881i	$0.291943\pi$
$110$	1.44949	−	2.51059i	0.138203	−	0.239375i
$111$		0			0
$112$		0			0
$113$	−3.05051	−	5.28364i	−0.286968	−	0.497043i	0.686117	−	0.727492i	$-0.259314\pi$
$113$	−3.05051	−	5.28364i	−0.286968	−	0.497043i	−0.973084	+	0.230449i	$0.925981\pi$
$114$		0			0
$115$	0.724745	−	1.25529i	0.0675828	−	0.117057i
$116$	6.89898			0.640554
$117$		0			0
$118$	2.00000			0.184115
$119$		0			0
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−3.27526	−	5.67291i	−0.296528	−	0.513601i
$123$		0			0
$124$	3.00000	−	5.19615i	0.269408	−	0.466628i
$125$	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	$0.542494\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	3.55051	+	6.14966i	0.311400	+	0.539361i
$131$	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
$136$	−2.00000			−0.171499
$137$	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	0.946238	−	0.323471i	$-0.104850\pi$
$139$	2.27526	+	3.94086i	0.192985	+	0.334259i	−0.753253	+	0.657730i	$0.771517\pi$
$140$		0			0
$141$		0			0
$142$	−0.0505103	+	0.0874863i	−0.00423873	+	0.00734169i
$143$	9.79796			0.819346
$144$		0			0
$145$	−10.0000			−0.830455
$146$	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	$0.101452\pi$
$152$	2.55051			0.206874
$153$		0			0
$154$		0			0
$155$	−4.34847	+	7.53177i	−0.349277	+	0.604966i
$156$		0			0
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	0.649986	−	0.759947i	$-0.274775\pi$
$157$	−4.17423	−	7.22999i	−0.333140	−	0.577016i	−0.983126	+	0.182931i	$0.941442\pi$
$158$	−0.949490	−	1.64456i	−0.0755373	−	0.130835i
$159$		0			0
$160$	−0.724745	+	1.25529i	−0.0572961	+	0.0992398i
$161$		0			0
$162$		0			0
$163$	−19.7980			−1.55070			−0.775348	−	0.631534i	$-0.782425\pi$
$163$	−19.7980			−1.55070			−0.775348	+	0.631534i	$0.782425\pi$
$164$	−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	0.995310	−	0.0967384i	$-0.0308410\pi$
$167$	5.34847	+	9.26382i	0.413877	+	0.716856i	−0.581433	+	0.813594i	$0.697508\pi$
$168$		0			0
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$	2.89898			0.222342
$171$		0			0
$172$	6.89898			0.526042
$173$	1.55051	−	2.68556i	0.117883	−	0.204180i	−0.801045	−	0.598604i	$-0.795723\pi$
$173$	1.55051	−	2.68556i	0.117883	−	0.204180i	0.918929	+	0.394424i	$0.129056\pi$
$174$		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
$179$	−20.6969			−1.54696			−0.773481	−	0.633820i	$-0.781486\pi$
$179$	−20.6969			−1.54696			−0.773481	+	0.633820i	$0.781486\pi$
$180$		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
$185$	8.55051	+	14.8099i	0.628646	+	1.08885i
$186$		0			0
$187$	2.00000	−	3.46410i	0.146254	−	0.253320i
$188$	9.79796			0.714590
$189$		0			0
$190$	−3.69694			−0.268204
$191$	2.05051	−	3.55159i	0.148370	−	0.256984i	−0.782255	−	0.622958i	$-0.785931\pi$
$191$	2.05051	−	3.55159i	0.148370	−	0.256984i	0.930625	+	0.365974i	$0.119264\pi$
$192$		0			0
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	0.984486	+	0.175463i	$0.0561422\pi$
$193$	8.94949	+	15.5010i	0.644198	+	1.11578i	−0.340288	+	0.940321i	$0.610524\pi$
$194$	−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
$199$	2.89898			0.205503			0.102752	−	0.994707i	$-0.467235\pi$
$199$	2.89898			0.205503			0.102752	+	0.994707i	$0.467235\pi$
$200$	−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
$205$	7.10102	−	12.2993i	0.495957	−	0.859022i
$206$	14.0000			0.975426
$207$		0			0
$208$	−4.89898			−0.339683
$209$	−2.55051	+	4.41761i	−0.176422	+	0.305573i
$210$		0			0
$211$	−6.44949	−	11.1708i	−0.444001	−	0.769033i	0.553981	−	0.832529i	$-0.313108\pi$
$211$	−6.44949	−	11.1708i	−0.444001	−	0.769033i	−0.997982	+	0.0634968i	$0.979775\pi$
$212$	−5.44949	−	9.43879i	−0.374272	−	0.648259i
$213$		0			0
$214$	6.00000	−	10.3923i	0.410152	−	0.710403i
$215$	−10.0000			−0.681994
$216$		0			0
$217$		0			0
$218$	6.34847	−	10.9959i	0.429973	−	0.744734i
$219$		0			0
$220$	−1.44949	−	2.51059i	−0.0977246	−	0.169264i
$221$	4.89898	+	8.48528i	0.329541	+	0.570782i
$222$		0			0
$223$	−5.55051	+	9.61377i	−0.371690	+	0.643785i	−0.989826	−	0.142286i	$-0.954555\pi$
$223$	−5.55051	+	9.61377i	−0.371690	+	0.643785i	0.618136	+	0.786071i	$0.287888\pi$
$224$		0			0
$225$		0			0
$226$	−6.10102			−0.405834
$227$	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
$233$	7.00000			0.458585			0.229293	−	0.973358i	$-0.426359\pi$
$233$	7.00000			0.458585			0.229293	+	0.973358i	$0.426359\pi$
$234$		0			0
$235$	−14.2020			−0.926439
$236$	1.00000	−	1.73205i	0.0650945	−	0.112747i
$237$		0			0
$238$		0			0
$239$	3.39898	+	5.88721i	0.219862	+	0.380812i	0.954766	−	0.297360i	$-0.0961061\pi$
$239$	3.39898	+	5.88721i	0.219862	+	0.380812i	−0.734904	+	0.678171i	$0.762773\pi$
$240$		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	$0.157449\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	−6.55051			−0.419353
$245$		0			0
$246$		0			0
$247$	−6.24745	−	10.8209i	−0.397516	−	0.688517i
$248$	−3.00000	−	5.19615i	−0.190500	−	0.329956i
$249$		0			0
$250$	5.72474	−	9.91555i	0.362065	−	0.627114i
$251$	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
$254$	−1.50000	+	2.59808i	−0.0941184	+	0.163018i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−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
$262$	8.55051			0.528252
$263$	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
$268$	6.44949	−	11.1708i	0.393965	−	0.682368i
$269$	−18.3485			−1.11873			−0.559363	−	0.828923i	$-0.688954\pi$
$269$	−18.3485			−1.11873			−0.559363	+	0.828923i	$0.688954\pi$
$270$		0			0
$271$	−7.10102			−0.431356			−0.215678	−	0.976465i	$-0.569196\pi$
$271$	−7.10102			−0.431356			−0.215678	+	0.976465i	$0.569196\pi$
$272$	−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	$-0.0231839\pi$
$278$	4.55051			0.272921
$279$		0			0
$280$		0			0
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	0.430165	+	0.902750i	$0.358455\pi$
$281$	−9.50000	+	16.4545i	−0.566722	+	0.981592i	−0.996887	+	0.0788417i	$0.974878\pi$
$282$		0			0
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	−0.944672	−	0.328018i	$-0.893619\pi$
$283$	−12.7247	−	22.0399i	−0.756408	−	1.31014i	0.188264	−	0.982118i	$-0.439714\pi$
$284$	0.0505103	+	0.0874863i	0.00299723	+	0.00519136i
$285$		0			0
$286$	4.89898	−	8.48528i	0.289683	−	0.501745i
$287$		0			0
$288$		0			0
$289$	−13.0000			−0.764706
$290$	−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	0.823020	−	0.568012i	$-0.192287\pi$
$293$	−1.37628	−	2.38378i	−0.0804029	−	0.139262i	−0.903423	+	0.428750i	$0.858954\pi$
$294$		0			0
$295$	−1.44949	+	2.51059i	−0.0843926	+	0.146172i
$296$	−11.7980			−0.685742
$297$		0			0
$298$	−6.00000			−0.347571
$299$	2.44949	−	4.24264i	0.141658	−	0.245358i
$300$		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
$305$	9.49490			0.543676
$306$		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
$311$	−15.3485	−	26.5843i	−0.870332	−	1.50746i	−0.861654	−	0.507497i	$-0.830571\pi$
$311$	−15.3485	−	26.5843i	−0.870332	−	1.50746i	−0.00867810	−	0.999962i	$-0.502762\pi$
$312$		0			0
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	−0.924733	−	0.380616i	$-0.875712\pi$
$313$	−2.34847	+	4.06767i	−0.132743	+	0.229918i	0.791990	+	0.610534i	$0.209045\pi$
$314$	−8.34847			−0.471131
$315$		0			0
$316$	−1.89898			−0.106826
$317$	10.3485	−	17.9241i	0.581228	−	1.00672i	−0.414106	−	0.910229i	$-0.635906\pi$
$317$	10.3485	−	17.9241i	0.581228	−	1.00672i	0.995334	−	0.0964878i	$-0.0307609\pi$
$318$		0			0
$319$	6.89898	+	11.9494i	0.386269	+	0.669037i
$320$	0.724745	+	1.25529i	0.0405145	+	0.0701731i
$321$		0			0
$322$		0			0
$323$	−5.10102			−0.283828
$324$		0			0
$325$	14.2020			0.787787
$326$	−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
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	−0.923322	−	0.384027i	$-0.874537\pi$
$331$	−2.34847	+	4.06767i	−0.129084	+	0.223579i	0.794238	+	0.607606i	$0.207870\pi$
$332$	2.00000			0.109764
$333$		0			0
$334$	10.6969			0.585310
$335$	−9.34847	+	16.1920i	−0.510761	+	0.884665i
$336$		0			0
$337$	11.6969	+	20.2597i	0.637173	+	1.10362i	0.986050	+	0.166447i	$0.0532296\pi$
$337$	11.6969	+	20.2597i	0.637173	+	1.10362i	−0.348877	+	0.937168i	$0.613437\pi$
$338$	5.50000	+	9.52628i	0.299161	+	0.518161i
$339$		0			0
$340$	1.44949	−	2.51059i	0.0786096	−	0.136156i
$341$	12.0000			0.649836
$342$		0			0
$343$		0			0
$344$	3.44949	−	5.97469i	0.185984	−	0.322134i
$345$		0			0
$346$	−1.55051	−	2.68556i	−0.0833559	−	0.144377i
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	0.999542	+	0.0302659i	$0.00963541\pi$
$347$	9.79796	+	16.9706i	0.525982	+	0.911028i	−0.473560	+	0.880762i	$0.657031\pi$
$348$		0			0
$349$	5.55051	−	9.61377i	0.297112	−	0.514613i	−0.678362	−	0.734728i	$-0.737310\pi$
$349$	5.55051	−	9.61377i	0.297112	−	0.514613i	0.975474	+	0.220115i	$0.0706432\pi$
$350$		0			0
$351$		0			0
$352$	2.00000			0.106600
$353$	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
$359$	8.79796			0.464339			0.232169	−	0.972675i	$-0.425418\pi$
$359$	8.79796			0.464339			0.232169	+	0.972675i	$0.425418\pi$
$360$		0			0
$361$	−12.4949			−0.657626
$362$	5.17423	−	8.96204i	0.271952	−	0.471034i
$363$		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	$0.283932\pi$
$368$	1.00000			0.0521286
$369$		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	$0.776174\pi$
$374$	−2.00000	−	3.46410i	−0.103418	−	0.179124i
$375$		0			0
$376$	4.89898	−	8.48528i	0.252646	−	0.437595i
$377$	−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	$0.303934\pi$
$380$	−1.84847	+	3.20164i	−0.0948245	+	0.164241i
$381$		0			0
$382$	−2.05051	−	3.55159i	−0.104913	−	0.181715i
$383$	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
$388$	−2.89898			−0.147173
$389$	−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
$394$	−8.34847	+	14.4600i	−0.420590	+	0.728483i
$395$	2.75255			0.138496
$396$		0			0
$397$	−38.6969			−1.94214			−0.971072	−	0.238788i	$-0.923250\pi$
$397$	−38.6969			−1.94214			−0.971072	+	0.238788i	$0.923250\pi$
$398$	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
$404$	−17.2474			−0.858093
$405$		0			0
$406$		0			0
$407$	11.7980	−	20.4347i	0.584803	−	1.01291i
$408$		0			0
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	0.643511	−	0.765437i	$-0.277477\pi$
$409$	−6.89898	−	11.9494i	−0.341133	−	0.590859i	−0.984643	+	0.174578i	$0.944144\pi$
$410$	−7.10102	−	12.2993i	−0.350694	−	0.607421i
$411$		0			0
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$		0			0
$415$	−2.89898			−0.142305
$416$	−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	−0.961257	−	0.275653i	$-0.911106\pi$
$419$	−14.7247	−	25.5040i	−0.719351	−	1.24595i	0.241906	−	0.970300i	$-0.422227\pi$
$420$		0			0
$421$	−11.4495	+	19.8311i	−0.558014	+	0.966509i	0.439648	+	0.898170i	$0.355103\pi$
$421$	−11.4495	+	19.8311i	−0.558014	+	0.966509i	−0.997662	+	0.0683385i	$0.978230\pi$
$422$	−12.8990			−0.627912
$423$		0			0
$424$	−10.8990			−0.529301
$425$	2.89898	−	5.02118i	0.140621	−	0.243563i
$426$		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
$431$	−31.5959			−1.52192			−0.760961	−	0.648798i	$-0.775272\pi$
$431$	−31.5959			−1.52192			−0.760961	+	0.648798i	$0.775272\pi$
$432$		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
$437$	1.27526	+	2.20881i	0.0610037	+	0.105662i
$438$		0			0
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	−0.838554	−	0.544818i	$-0.816599\pi$
$439$	1.10102	−	1.90702i	0.0525488	−	0.0910173i	0.891103	+	0.453801i	$0.149932\pi$
$440$	−2.89898			−0.138203
$441$		0			0
$442$	9.79796			0.466041
$443$	−7.44949	+	12.9029i	−0.353936	+	0.613035i	−0.986935	−	0.161117i	$-0.948490\pi$
$443$	−7.44949	+	12.9029i	−0.353936	+	0.613035i	0.632999	+	0.774152i	$0.281824\pi$
$444$		0			0
$445$	−12.2474	−	21.2132i	−0.580585	−	1.00560i
$446$	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
$451$	−19.5959			−0.922736
$452$	−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
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	−0.585611	−	0.810593i	$-0.699145\pi$
$457$	8.74745	−	15.1510i	0.409188	−	0.708735i	0.994799	+	0.101857i	$0.0324785\pi$
$458$	1.24745			0.0582895
$459$		0			0
$460$	−1.44949			−0.0675828
$461$	−2.82577	+	4.89437i	−0.131609	+	0.227954i	−0.924297	−	0.381674i	$-0.875348\pi$
$461$	−2.82577	+	4.89437i	−0.131609	+	0.227954i	0.792688	+	0.609628i	$0.208681\pi$
$462$		0			0
$463$	−1.84847	−	3.20164i	−0.0859057	−	0.148793i	0.819871	−	0.572548i	$-0.194045\pi$
$463$	−1.84847	−	3.20164i	−0.0859057	−	0.148793i	−0.905777	+	0.423755i	$0.860712\pi$
$464$	−3.44949	−	5.97469i	−0.160139	−	0.277368i
$465$		0			0
$466$	3.50000	−	6.06218i	0.162134	−	0.280825i
$467$	10.0000			0.462745			0.231372	−	0.972865i	$-0.425678\pi$
$467$	10.0000			0.462745			0.231372	+	0.972865i	$0.425678\pi$
$468$		0			0
$469$		0			0
$470$	−7.10102	+	12.2993i	−0.327546	+	0.567326i
$471$		0			0
$472$	−1.00000	−	1.73205i	−0.0460287	−	0.0797241i
$473$	6.89898	+	11.9494i	0.317215	+	0.549433i
$474$		0			0
$475$	−3.69694	+	6.40329i	−0.169627	+	0.293803i
$476$		0			0
$477$		0			0
$478$	6.79796			0.310931
$479$	−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
$485$	4.20204			0.190805
$486$		0			0
$487$	−36.3939			−1.64916			−0.824582	−	0.565742i	$-0.808590\pi$
$487$	−36.3939			−1.64916			−0.824582	+	0.565742i	$0.808590\pi$
$488$	−3.27526	+	5.67291i	−0.148264	+	0.256800i
$489$		0			0
$490$		0			0
$491$	7.89898	+	13.6814i	0.356476	+	0.617434i	0.987369	−	0.158435i	$-0.0506448\pi$
$491$	7.89898	+	13.6814i	0.356476	+	0.617434i	−0.630893	+	0.775869i	$0.717312\pi$
$492$		0			0
$493$	−6.89898	+	11.9494i	−0.310714	+	0.538173i
$494$	−12.4949			−0.562172
$495$		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	$0.640899\pi$
$500$	−5.72474	−	9.91555i	−0.256018	−	0.443437i
$501$		0			0
$502$	8.72474	−	15.1117i	0.389404	−	0.674468i
$503$	−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
$506$	−1.00000	+	1.73205i	−0.0444554	+	0.0769991i
$507$		0			0
$508$	1.50000	+	2.59808i	0.0665517	+	0.115271i
$509$	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
$514$	−8.20204			−0.361777
$515$	−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
$520$	3.55051	−	6.14966i	0.155700	−	0.269681i
$521$	−9.30306			−0.407575			−0.203787	−	0.979015i	$-0.565325\pi$
$521$	−9.30306			−0.407575			−0.203787	+	0.979015i	$0.565325\pi$
$522$		0			0
$523$	14.3485			0.627415			0.313707	−	0.949520i	$-0.398429\pi$
$523$	14.3485			0.627415			0.313707	+	0.949520i	$0.398429\pi$
$524$	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
$530$	15.7980			0.686219
$531$		0			0
$532$		0			0
$533$	24.0000	−	41.5692i	1.03956	−	1.80056i
$534$		0			0
$535$	8.69694	+	15.0635i	0.376001	+	0.651254i
$536$	−6.44949	−	11.1708i	−0.278576	−	0.482507i
$537$		0			0
$538$	−9.17423	+	15.8902i	−0.395529	+	0.685077i
$539$		0			0
$540$		0			0
$541$	−18.4949			−0.795158			−0.397579	−	0.917568i	$-0.630149\pi$
$541$	−18.4949			−0.795158			−0.397579	+	0.917568i	$0.630149\pi$
$542$	−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	−0.773336	−	0.633996i	$-0.781413\pi$
$547$	3.79796	−	6.57826i	0.162389	−	0.281266i	0.935725	+	0.352730i	$0.114747\pi$
$548$	−7.79796			−0.333112
$549$		0			0
$550$	−5.79796			−0.247226
$551$	8.79796	−	15.2385i	0.374806	−	0.649182i
$552$		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
$557$	12.8990			0.546547			0.273274	−	0.961936i	$-0.411894\pi$
$557$	12.8990			0.546547			0.273274	+	0.961936i	$0.411894\pi$
$558$		0			0
$559$	−33.7980			−1.42950
$560$		0			0
$561$		0			0
$562$	9.50000	+	16.4545i	0.400733	+	0.694090i
$563$	19.9722	+	34.5929i	0.841728	+	1.45791i	0.888433	+	0.459006i	$0.151794\pi$
$563$	19.9722	+	34.5929i	0.841728	+	1.45791i	−0.0467054	+	0.998909i	$0.514872\pi$
$564$		0			0
$565$	4.42168	−	7.65858i	0.186022	−	0.322199i
$566$	−25.4495			−1.06972
$567$		0			0
$568$	0.101021			0.00423873
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	0.358954	+	0.933355i	$0.383134\pi$
$569$	−15.0000	+	25.9808i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$570$		0			0
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	−0.965892	−	0.258947i	$-0.916625\pi$
$571$	−16.8990	−	29.2699i	−0.707200	−	1.22491i	0.258691	−	0.965960i	$-0.416709\pi$
$572$	−4.89898	−	8.48528i	−0.204837	−	0.354787i
$573$		0			0
$574$		0			0
$575$	−2.89898			−0.120896
$576$		0			0
$577$	15.5959			0.649267			0.324633	−	0.945840i	$-0.394759\pi$
$577$	15.5959			0.649267			0.324633	+	0.945840i	$0.394759\pi$
$578$	−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
$583$	10.8990	−	18.8776i	0.451390	−	0.781830i
$584$	−6.89898			−0.285482
$585$		0			0
$586$	−2.75255			−0.113707
$587$	−8.07321	+	13.9832i	−0.333217	+	0.577149i	−0.983141	−	0.182850i	$-0.941468\pi$
$587$	−8.07321	+	13.9832i	−0.333217	+	0.577149i	0.649924	+	0.760000i	$0.274801\pi$
$588$		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
$593$	14.6969			0.603531			0.301765	−	0.953382i	$-0.402424\pi$
$593$	14.6969			0.603531			0.301765	+	0.953382i	$0.402424\pi$
$594$		0			0
$595$		0			0
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$		0			0
$598$	−2.44949	−	4.24264i	−0.100167	−	0.173494i
$599$	−16.8990	−	29.2699i	−0.690474	−	1.19594i	−0.971683	−	0.236289i	$-0.924069\pi$
$599$	−16.8990	−	29.2699i	−0.690474	−	1.19594i	0.281209	−	0.959646i	$-0.409264\pi$
$600$		0			0
$601$	8.34847	−	14.4600i	0.340541	−	0.589835i	−0.643992	−	0.765032i	$-0.722723\pi$
$601$	8.34847	−	14.4600i	0.340541	−	0.589835i	0.984533	+	0.175198i	$0.0560564\pi$
$602$		0			0
$603$		0			0
$604$	−5.00000			−0.203447
$605$	−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
$611$	−48.0000			−1.94187
$612$		0			0
$613$	−14.6969			−0.593604			−0.296802	−	0.954939i	$-0.595920\pi$
$613$	−14.6969			−0.593604			−0.296802	+	0.954939i	$0.595920\pi$
$614$	−12.6237	+	21.8649i	−0.509452	+	0.882397i
$615$		0			0
$616$		0			0
$617$	−7.69694	−	13.3315i	−0.309867	−	0.536706i	0.668466	−	0.743743i	$-0.266951\pi$
$617$	−7.69694	−	13.3315i	−0.309867	−	0.536706i	−0.978333	+	0.207037i	$0.933618\pi$
$618$		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	$-0.0404976\pi$
$620$	8.69694			0.349277
$621$		0			0
$622$	−30.6969			−1.23084
$623$		0			0
$624$		0			0
$625$	1.05051	+	1.81954i	0.0420204	+	0.0727815i
$626$	2.34847	+	4.06767i	0.0938637	+	0.162577i
$627$		0			0
$628$	−4.17423	+	7.22999i	−0.166570	+	0.288508i
$629$	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	$0.312596\pi$
$632$	−0.949490	+	1.64456i	−0.0377687	+	0.0654173i
$633$		0			0
$634$	−10.3485	−	17.9241i	−0.410990	−	0.711856i
$635$	−2.17423	−	3.76588i	−0.0862819	−	0.149445i
$636$		0			0
$637$		0			0
$638$	13.7980			0.546266
$639$		0			0
$640$	1.44949			0.0572961
$641$	−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	−0.933793	−	0.357812i	$-0.883523\pi$
$643$	−19.6969	−	34.1161i	−0.776771	−	1.34541i	0.157022	−	0.987595i	$-0.449811\pi$
$644$		0			0
$645$		0			0
$646$	−2.55051	+	4.41761i	−0.100348	+	0.173809i
$647$	−50.6969			−1.99310			−0.996551	−	0.0829807i	$-0.973556\pi$
$647$	−50.6969			−1.99310			−0.996551	+	0.0829807i	$0.973556\pi$
$648$		0			0
$649$	4.00000			0.157014
$650$	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
$656$	9.79796			0.382546
$657$		0			0
$658$		0			0
$659$	−12.3485	+	21.3882i	−0.481028	+	0.833165i	−0.999763	−	0.0217701i	$-0.993070\pi$
$659$	−12.3485	+	21.3882i	−0.481028	+	0.833165i	0.518735	+	0.854935i	$0.326403\pi$
$660$		0			0
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	0.906876	−	0.421397i	$-0.138460\pi$
$661$	2.27526	+	3.94086i	0.0884972	+	0.153282i	−0.818379	+	0.574679i	$0.805127\pi$
$662$	2.34847	+	4.06767i	0.0912758	+	0.158094i
$663$		0			0
$664$	1.00000	−	1.73205i	0.0388075	−	0.0672166i
$665$		0			0
$666$		0			0
$667$	6.89898			0.267130
$668$	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	−0.771220	−	0.636568i	$-0.780353\pi$
$673$	4.29796	−	7.44428i	0.165674	−	0.286956i	0.936894	+	0.349612i	$0.113687\pi$
$674$	23.3939			0.901098
$675$		0			0
$676$	11.0000			0.423077
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	−0.971981	−	0.235058i	$-0.924472\pi$
$677$	−7.34847	+	12.7279i	−0.282425	+	0.489174i	0.689557	+	0.724232i	$0.257805\pi$
$678$		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
$683$	−51.7980			−1.98199			−0.990997	−	0.133885i	$-0.957255\pi$
$683$	−51.7980			−1.98199			−0.990997	+	0.133885i	$0.957255\pi$
$684$		0			0
$685$	11.3031			0.431868
$686$		0			0
$687$		0			0
$688$	−3.44949	−	5.97469i	−0.131511	−	0.227783i
$689$	26.6969	+	46.2405i	1.01707	+	1.76162i
$690$		0			0
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.278168	−	0.960533i	$-0.410273\pi$
$691$	25.5227	−	44.2066i	0.970929	−	1.68170i	0.692762	−	0.721167i	$-0.256394\pi$
$692$	−3.10102			−0.117883
$693$		0			0
$694$	19.5959			0.743851
$695$	−3.29796	+	5.71223i	−0.125099	+	0.216677i
$696$		0			0
$697$	−9.79796	−	16.9706i	−0.371124	−	0.642806i
$698$	−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
$703$	−30.0908			−1.13490
$704$	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
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	0.481583	+	0.876400i	$0.340062\pi$
$709$	−13.7980	+	23.8988i	−0.518193	+	0.897537i	−0.999777	+	0.0211367i	$0.993271\pi$
$710$	−0.146428			−0.00549535
$711$		0			0
$712$	16.8990			0.633316
$713$	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
$719$	9.79796			0.365402			0.182701	−	0.983169i	$-0.441516\pi$
$719$	9.79796			0.365402			0.182701	+	0.983169i	$0.441516\pi$
$720$		0			0
$721$		0			0
$722$	−6.24745	+	10.8209i	−0.232506	+	0.402712i
$723$		0			0
$724$	−5.17423	−	8.96204i	−0.192299	−	0.333071i
$725$	10.0000	+	17.3205i	0.371391	+	0.643268i
$726$		0			0
$727$	−4.24745	+	7.35680i	−0.157529	+	0.272848i	−0.933977	−	0.357333i	$-0.883686\pi$
$727$	−4.24745	+	7.35680i	−0.157529	+	0.272848i	0.776448	+	0.630181i	$0.217019\pi$
$728$		0			0
$729$		0			0
$730$	10.0000			0.370117
$731$	−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
$737$	25.7980			0.950280
$738$		0			0
$739$	13.5959			0.500134			0.250067	−	0.968229i	$-0.419547\pi$
$739$	13.5959			0.500134			0.250067	+	0.968229i	$0.419547\pi$
$740$	8.55051	−	14.8099i	0.314323	−	0.544423i
$741$		0			0
$742$		0			0
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	0.980522	+	0.196409i	$0.0629279\pi$
$743$	18.0000	+	31.1769i	0.660356	+	1.14377i	−0.320166	+	0.947361i	$0.603739\pi$
$744$		0			0
$745$	4.34847	−	7.53177i	0.159316	−	0.275943i
$746$	6.89898			0.252590
$747$		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	$0.841489\pi$
$752$	−4.89898	−	8.48528i	−0.178647	−	0.309426i
$753$		0			0
$754$	−16.8990	+	29.2699i	−0.615425	+	1.06595i
$755$	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	$0.722396\pi$
$758$	11.2474	−	19.4812i	0.408526	−	0.707587i
$759$		0			0
$760$	1.84847	+	3.20164i	0.0670510	+	0.116136i
$761$	−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
$766$	2.89898			0.104744
$767$	−4.89898	+	8.48528i	−0.176892	+	0.306386i
$768$		0			0
$769$	−17.0454	−	29.5235i	−0.614673	−	1.06465i	−0.990442	−	0.137932i	$-0.955955\pi$
$769$	−17.0454	−	29.5235i	−0.614673	−	1.06465i	0.375769	−	0.926714i	$-0.377379\pi$
$770$		0			0
$771$		0			0
$772$	8.94949	−	15.5010i	0.322099	−	0.557892i
$773$	33.9444			1.22089			0.610447	−	0.792057i	$-0.290990\pi$
$773$	33.9444			1.22089			0.610447	+	0.792057i	$0.290990\pi$
$774$		0			0
$775$	17.3939			0.624807
$776$	−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
$782$	−2.00000			−0.0715199
$783$		0			0
$784$		0			0
$785$	6.05051	−	10.4798i	0.215952	−	0.374040i
$786$		0			0
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	0.746443	−	0.665449i	$-0.231760\pi$
$787$	−5.69694	−	9.86739i	−0.203074	−	0.351734i	−0.949517	+	0.313715i	$0.898427\pi$
$788$	8.34847	+	14.4600i	0.297402	+	0.515115i
$789$		0			0
$790$	1.37628	−	2.38378i	0.0489657	−	0.0848111i
$791$		0			0
$792$		0			0
$793$	32.0908			1.13958
$794$	−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	0.980031	−	0.198844i	$-0.0637188\pi$
$797$	8.97219	+	15.5403i	0.317811	+	0.550465i	−0.662220	+	0.749310i	$0.730385\pi$
$798$		0			0
$799$	−9.79796	+	16.9706i	−0.346627	+	0.600375i
$800$	2.89898			0.102494
$801$		0			0
$802$	−19.8990			−0.702657
$803$	6.89898	−	11.9494i	0.243460	−	0.421685i
$804$		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
$809$	16.2020			0.569633			0.284817	−	0.958582i	$-0.408067\pi$
$809$	16.2020			0.569633			0.284817	+	0.958582i	$0.408067\pi$
$810$		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
$815$	−14.3485	−	24.8523i	−0.502605	−	0.870537i
$816$		0			0
$817$	8.79796	−	15.2385i	0.307802	−	0.533128i
$818$	−13.7980			−0.482434
$819$		0			0
$820$	−14.2020			−0.495957
$821$	0.202041	−	0.349945i	0.00705128	−	0.0122132i	−0.862478	−	0.506094i	$-0.831089\pi$
$821$	0.202041	−	0.349945i	0.00705128	−	0.0122132i	0.869530	+	0.493881i	$0.164422\pi$
$822$		0			0
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	0.958818	−	0.284020i	$-0.0916682\pi$
$823$	6.69694	+	11.5994i	0.233441	+	0.404331i	−0.725378	+	0.688351i	$0.758335\pi$
$824$	−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
$829$	−1.30306			−0.0452572			−0.0226286	−	0.999744i	$-0.507204\pi$
$829$	−1.30306			−0.0452572			−0.0226286	+	0.999744i	$0.507204\pi$
$830$	−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
$835$	−7.75255	+	13.4278i	−0.268288	+	0.464689i
$836$	5.10102			0.176422
$837$		0			0
$838$	−29.4495			−1.01732
$839$	17.5505	−	30.3984i	0.605911	−	1.04947i	−0.385996	−	0.922500i	$-0.626142\pi$
$839$	17.5505	−	30.3984i	0.605911	−	1.04947i	0.991907	−	0.126968i	$-0.0405245\pi$
$840$		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
$845$	−15.9444			−0.548504
$846$		0			0
$847$		0			0
$848$	−5.44949	+	9.43879i	−0.187136	+	0.324129i
$849$		0			0
$850$	−2.89898	−	5.02118i	−0.0994342	−	0.172225i
$851$	−5.89898	−	10.2173i	−0.202214	−	0.350246i
$852$		0			0
$853$	12.4217	−	21.5150i	0.425310	−	0.736659i	−0.571139	−	0.820853i	$-0.693498\pi$
$853$	12.4217	−	21.5150i	0.425310	−	0.736659i	0.996449	+	0.0841942i	$0.0268316\pi$
$854$		0			0
$855$		0			0
$856$	−12.0000			−0.410152
$857$	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
$863$	−11.8990			−0.405046			−0.202523	−	0.979278i	$-0.564914\pi$
$863$	−11.8990			−0.405046			−0.202523	+	0.979278i	$0.564914\pi$
$864$		0			0
$865$	4.49490			0.152831
$866$	3.89898	−	6.75323i	0.132493	−	0.229484i
$867$		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
$872$	−12.6969			−0.429973
$873$		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	$0.957340\pi$
$878$	−1.10102	−	1.90702i	−0.0371576	−	0.0643589i
$879$		0			0
$880$	−1.44949	+	2.51059i	−0.0488623	+	0.0846320i
$881$	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	$0.608104\pi$
$884$	4.89898	−	8.48528i	0.164771	−	0.285391i
$885$		0			0
$886$	7.44949	+	12.9029i	0.250271	+	0.433481i
$887$	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
$892$	11.1010			0.371690
$893$	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
$898$	−10.2980	+	17.8366i	−0.343647	+	0.595215i
$899$	−41.3939			−1.38056
$900$		0			0
$901$	21.7980			0.726195
$902$	−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	$0.180924\pi$
$908$	−5.44949			−0.180848
$909$		0			0
$910$		0			0
$911$	25.9949	−	45.0245i	0.861249	−	1.49173i	−0.00947432	−	0.999955i	$-0.503016\pi$
$911$	25.9949	−	45.0245i	0.861249	−	1.49173i	0.870724	−	0.491773i	$-0.163651\pi$
$912$		0			0
$913$	2.00000	+	3.46410i	0.0661903	+	0.114645i
$914$	−8.74745	−	15.1510i	−0.289340	−	0.501151i
$915$		0			0
$916$	0.623724	−	1.08032i	0.0206084	−	0.0356949i
$917$		0			0
$918$		0			0
$919$	−25.6969			−0.847664			−0.423832	−	0.905741i	$-0.639315\pi$
$919$	−25.6969			−0.847664			−0.423832	+	0.905741i	$0.639315\pi$
$920$	−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
$926$	−3.69694			−0.121489
$927$		0			0
$928$	−6.89898			−0.226470
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	0.434716	+	0.900567i	$0.356849\pi$
$929$	−17.1464	+	29.6985i	−0.562556	+	0.974376i	−0.997272	+	0.0738083i	$0.976485\pi$
$930$		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
$935$	5.79796			0.189614
$936$		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
$941$	0.724745	+	1.25529i	0.0236260	+	0.0409214i	0.877597	−	0.479400i	$-0.159146\pi$
$941$	0.724745	+	1.25529i	0.0236260	+	0.0409214i	−0.853971	+	0.520321i	$0.825812\pi$
$942$		0			0
$943$	−4.89898	+	8.48528i	−0.159533	+	0.276319i
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	13.7980			0.448610
$947$	26.2474	−	45.4619i	0.852927	−	1.47731i	−0.0256270	−	0.999672i	$-0.508158\pi$
$947$	26.2474	−	45.4619i	0.852927	−	1.47731i	0.878554	−	0.477642i	$-0.158508\pi$
$948$		0			0
$949$	16.8990	+	29.2699i	0.548564	+	0.950141i
$950$	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
$955$	5.94439			0.192356
$956$	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
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	57.7980			1.86348
$963$		0			0
$964$	−0.898979			−0.0289542
$965$	−12.9722	+	22.4685i	−0.417590	+	0.723287i
$966$		0			0
$967$	−12.2980	−	21.3007i	−0.395476	−	0.684984i	0.597686	−	0.801730i	$-0.296087\pi$
$967$	−12.2980	−	21.3007i	−0.395476	−	0.684984i	−0.993162	+	0.116746i	$0.962754\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	2.10102	−	3.63907i	0.0674597	−	0.116844i
$971$	−0.0556128			−0.00178470			−0.000892350	−	1.00000i	$-0.500284\pi$
$971$	−0.0556128			−0.00178470			−0.000892350		1.00000i	$0.500284\pi$
$972$		0			0
$973$		0			0
$974$	−18.1969	+	31.5180i	−0.583068	+	1.00990i
$975$		0			0
$976$	3.27526	+	5.67291i	0.104838	+	0.181585i
$977$	−18.7980	−	32.5590i	−0.601400	−	1.04166i	−0.992609	−	0.121354i	$-0.961276\pi$
$977$	−18.7980	−	32.5590i	−0.601400	−	1.04166i	0.391209	−	0.920302i	$-0.372057\pi$
$978$		0			0
$979$	−16.8990	+	29.2699i	−0.540094	+	0.935470i
$980$		0			0
$981$		0			0
$982$	15.7980			0.504133
$983$	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
$989$	6.89898			0.219375
$990$		0			0
$991$	−1.79796			−0.0571140			−0.0285570	−	0.999592i	$-0.509091\pi$
$991$	−1.79796			−0.0571140			−0.0285570	+	0.999592i	$0.509091\pi$
$992$	−3.00000	+	5.19615i	−0.0952501	+	0.164978i
$993$		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	$-0.142579\pi$
$998$	25.3939			0.803829
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2646.2.f.k.883.2		4
3.2	odd	2		882.2.f.j.295.1		4
7.2	even	3		2646.2.e.k.2125.2		4
7.3	odd	6		2646.2.h.m.667.2		4
7.4	even	3		2646.2.h.n.667.1		4
7.5	odd	6		2646.2.e.l.2125.1		4
7.6	odd	2		378.2.f.d.127.1		4
9.2	odd	6		7938.2.a.bn.1.2		2
9.4	even	3	inner	2646.2.f.k.1765.2		4
9.5	odd	6		882.2.f.j.589.2		4
9.7	even	3		7938.2.a.bm.1.1		2
21.2	odd	6		882.2.e.n.655.2		4
21.5	even	6		882.2.e.m.655.1		4
21.11	odd	6		882.2.h.l.79.1		4
21.17	even	6		882.2.h.k.79.2		4
21.20	even	2		126.2.f.c.43.2	✓	4
28.27	even	2		3024.2.r.e.2017.1		4
63.4	even	3		2646.2.e.k.1549.2		4
63.5	even	6		882.2.h.k.67.2		4
63.13	odd	6		378.2.f.d.253.1		4
63.20	even	6		1134.2.a.p.1.1		2
63.23	odd	6		882.2.h.l.67.1		4
63.31	odd	6		2646.2.e.l.1549.1		4
63.32	odd	6		882.2.e.n.373.2		4
63.34	odd	6		1134.2.a.i.1.2		2
63.40	odd	6		2646.2.h.m.361.2		4
63.41	even	6		126.2.f.c.85.1	yes	4
63.58	even	3		2646.2.h.n.361.1		4
63.59	even	6		882.2.e.m.373.1		4
84.83	odd	2		1008.2.r.e.673.1		4
252.83	odd	6		9072.2.a.bk.1.1		2
252.139	even	6		3024.2.r.e.1009.1		4
252.167	odd	6		1008.2.r.e.337.2		4
252.223	even	6		9072.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.2	✓	4	21.20	even	2
126.2.f.c.85.1	yes	4	63.41	even	6
378.2.f.d.127.1		4	7.6	odd	2
378.2.f.d.253.1		4	63.13	odd	6
882.2.e.m.373.1		4	63.59	even	6
882.2.e.m.655.1		4	21.5	even	6
882.2.e.n.373.2		4	63.32	odd	6
882.2.e.n.655.2		4	21.2	odd	6
882.2.f.j.295.1		4	3.2	odd	2
882.2.f.j.589.2		4	9.5	odd	6
882.2.h.k.67.2		4	63.5	even	6
882.2.h.k.79.2		4	21.17	even	6
882.2.h.l.67.1		4	63.23	odd	6
882.2.h.l.79.1		4	21.11	odd	6
1008.2.r.e.337.2		4	252.167	odd	6
1008.2.r.e.673.1		4	84.83	odd	2
1134.2.a.i.1.2		2	63.34	odd	6
1134.2.a.p.1.1		2	63.20	even	6
2646.2.e.k.1549.2		4	63.4	even	3
2646.2.e.k.2125.2		4	7.2	even	3
2646.2.e.l.1549.1		4	63.31	odd	6
2646.2.e.l.2125.1		4	7.5	odd	6
2646.2.f.k.883.2		4	1.1	even	1	trivial
2646.2.f.k.1765.2		4	9.4	even	3	inner
2646.2.h.m.361.2		4	63.40	odd	6
2646.2.h.m.667.2		4	7.3	odd	6
2646.2.h.n.361.1		4	63.58	even	3
2646.2.h.n.667.1		4	7.4	even	3
3024.2.r.e.1009.1		4	252.139	even	6
3024.2.r.e.2017.1		4	28.27	even	2
7938.2.a.bm.1.1		2	9.7	even	3
7938.2.a.bn.1.2		2	9.2	odd	6
9072.2.a.bd.1.2		2	252.223	even	6
9072.2.a.bk.1.1		2	252.83	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.724745 + 1.25529i) q^{5} -1.00000 q^{8} +1.44949 q^{10} +(1.00000 - 1.73205i) q^{11} +(2.44949 + 4.24264i) q^{13} +(-0.500000 + 0.866025i) q^{16} +2.00000 q^{17} -2.55051 q^{19} +(0.724745 - 1.25529i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(-0.500000 - 0.866025i) q^{23} +(1.44949 - 2.51059i) q^{25} +4.89898 q^{26} +(-3.44949 + 5.97469i) q^{29} +(3.00000 + 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(1.00000 - 1.73205i) q^{34} +11.7980 q^{37} +(-1.27526 + 2.20881i) q^{38} +(-0.724745 - 1.25529i) q^{40} +(-4.89898 - 8.48528i) q^{41} +(-3.44949 + 5.97469i) q^{43} -2.00000 q^{44} -1.00000 q^{46} +(-4.89898 + 8.48528i) q^{47} +(-1.44949 - 2.51059i) q^{50} +(2.44949 - 4.24264i) q^{52} +10.8990 q^{53} +2.89898 q^{55} +(3.44949 + 5.97469i) q^{58} +(1.00000 + 1.73205i) q^{59} +(3.27526 - 5.67291i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-3.55051 + 6.14966i) q^{65} +(6.44949 + 11.1708i) q^{67} +(-1.00000 - 1.73205i) q^{68} -0.101021 q^{71} +6.89898 q^{73} +(5.89898 - 10.2173i) q^{74} +(1.27526 + 2.20881i) q^{76} +(0.949490 - 1.64456i) q^{79} -1.44949 q^{80} -9.79796 q^{82} +(-1.00000 + 1.73205i) q^{83} +(1.44949 + 2.51059i) q^{85} +(3.44949 + 5.97469i) q^{86} +(-1.00000 + 1.73205i) q^{88} -16.8990 q^{89} +(-0.500000 + 0.866025i) q^{92} +(4.89898 + 8.48528i) q^{94} +(-1.84847 - 3.20164i) q^{95} +(1.44949 - 2.51059i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{8} - 4 q^{10} + 4 q^{11} - 2 q^{16} + 8 q^{17} - 20 q^{19} - 2 q^{20} - 4 q^{22} - 2 q^{23} - 4 q^{25} - 4 q^{29} + 12 q^{31} + 2 q^{32} + 4 q^{34} + 8 q^{37} - 10 q^{38}+ \cdots - 4 q^{97}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^8 - 4 * q^10 + 4 * q^11 - 2 * q^16 + 8 * q^17 - 20 * q^19 - 2 * q^20 - 4 * q^22 - 2 * q^23 - 4 * q^25 - 4 * q^29 + 12 * q^31 + 2 * q^32 + 4 * q^34 + 8 * q^37 - 10 * q^38 + 2 * q^40 - 4 * q^43 - 8 * q^44 - 4 * q^46 + 4 * q^50 + 24 * q^53 - 8 * q^55 + 4 * q^58 + 4 * q^59 + 18 * q^61 + 24 * q^62 + 4 * q^64 - 24 * q^65 + 16 * q^67 - 4 * q^68 - 20 * q^71 + 8 * q^73 + 4 * q^74 + 10 * q^76 - 6 * q^79 + 4 * q^80 - 4 * q^83 - 4 * q^85 + 4 * q^86 - 4 * q^88 - 48 * q^89 - 2 * q^92 + 22 * q^95 - 4 * q^97

Introduction

L-functions

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Database

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