LMFDB - Embedded newform 1680.2.bg.o.1201.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1680,2,Mod(961,1680)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1680, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 0, 2]))

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

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

chi := DirichletCharacter("1680.961");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1680.bg (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:	$13.4148675396$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1201.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1680.1201
Dual form			1680.2.bg.o.961.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{11} +5.73205 q^{13} +1.00000 q^{15} +(-3.36603 + 5.83013i) q^{17} +(-1.23205 - 2.13397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(-0.633975 - 1.09808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +6.19615 q^{29} +(3.23205 - 5.59808i) q^{31} +(-1.36603 - 2.36603i) q^{33} +(-2.59808 + 0.500000i) q^{35} +(-3.59808 - 6.23205i) q^{37} +(-2.86603 + 4.96410i) q^{39} +2.73205 q^{41} +7.19615 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-3.36603 - 5.83013i) q^{51} +(4.19615 - 7.26795i) q^{53} +2.73205 q^{55} +2.46410 q^{57} +(5.09808 - 8.83013i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(-2.59808 + 0.500000i) q^{63} +(-2.86603 - 4.96410i) q^{65} +(1.33013 - 2.30385i) q^{67} +1.26795 q^{69} +4.19615 q^{71} +(2.33013 - 4.03590i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(4.73205 + 5.46410i) q^{77} +(6.69615 + 11.5981i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.12436 q^{83} +6.73205 q^{85} +(-3.09808 + 5.36603i) q^{87} +(4.56218 + 7.90192i) q^{89} +(4.96410 - 14.3301i) q^{91} +(3.23205 + 5.59808i) q^{93} +(-1.23205 + 2.13397i) q^{95} +1.07180 q^{97} +2.73205 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 16 q^{13} + 4 q^{15} - 10 q^{17} + 2 q^{19} - 6 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 6 q^{31} - 2 q^{33} - 4 q^{37} - 8 q^{39} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 4 q^{47} - 22 q^{49} - 10 q^{51} - 4 q^{53} + 4 q^{55} - 4 q^{57} + 10 q^{59} - 8 q^{61} - 8 q^{65} - 12 q^{67} + 12 q^{69} - 4 q^{71} - 8 q^{73} - 2 q^{75} + 12 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 20 q^{85} - 2 q^{87} - 6 q^{89} + 6 q^{91} + 6 q^{93} + 2 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 16 * q^13 + 4 * q^15 - 10 * q^17 + 2 * q^19 - 6 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 6 * q^31 - 2 * q^33 - 4 * q^37 - 8 * q^39 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 4 * q^47 - 22 * q^49 - 10 * q^51 - 4 * q^53 + 4 * q^55 - 4 * q^57 + 10 * q^59 - 8 * q^61 - 8 * q^65 - 12 * q^67 + 12 * q^69 - 4 * q^71 - 8 * q^73 - 2 * q^75 + 12 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 20 * q^85 - 2 * q^87 - 6 * q^89 + 6 * q^91 + 6 * q^93 + 2 * q^95 + 32 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1680\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$421$	$1121$	$1471$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$	$1$

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			0
$2$		0			0
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$		0			0
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$		0			0
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	−0.995094	−	0.0989291i	$-0.968458\pi$
$11$	−1.36603	+	2.36603i	−0.411872	+	0.713384i	0.583222	+	0.812313i	$0.301792\pi$
$12$		0			0
$13$	5.73205			1.58978			0.794892	−	0.606750i	$-0.207527\pi$
$13$	5.73205			1.58978			0.794892	+	0.606750i	$0.207527\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$		0			0
$17$	−3.36603	+	5.83013i	−0.816381	+	1.41401i	0.0919509	+	0.995764i	$0.470690\pi$
$17$	−3.36603	+	5.83013i	−0.816381	+	1.41401i	−0.908332	+	0.418250i	$0.862644\pi$
$18$		0			0
$19$	−1.23205	−	2.13397i	−0.282652	−	0.489567i	0.689385	−	0.724395i	$-0.257881\pi$
$19$	−1.23205	−	2.13397i	−0.282652	−	0.489567i	−0.972037	+	0.234828i	$0.924547\pi$
$20$		0			0
$21$	1.73205	+	2.00000i	0.377964	+	0.436436i
$22$		0			0
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	6.19615			1.15060			0.575298	−	0.817944i	$-0.304886\pi$
$29$	6.19615			1.15060			0.575298	+	0.817944i	$0.304886\pi$
$30$		0			0
$31$	3.23205	−	5.59808i	0.580493	−	1.00544i	−0.414927	−	0.909855i	$-0.636193\pi$
$31$	3.23205	−	5.59808i	0.580493	−	1.00544i	0.995421	−	0.0955896i	$-0.0304737\pi$
$32$		0			0
$33$	−1.36603	−	2.36603i	−0.237795	−	0.411872i
$34$		0			0
$35$	−2.59808	+	0.500000i	−0.439155	+	0.0845154i
$36$		0			0
$37$	−3.59808	−	6.23205i	−0.591520	−	1.02454i	−0.994028	−	0.109126i	$-0.965195\pi$
$37$	−3.59808	−	6.23205i	−0.591520	−	1.02454i	0.402508	−	0.915417i	$-0.368139\pi$
$38$		0			0
$39$	−2.86603	+	4.96410i	−0.458931	+	0.794892i
$40$		0			0
$41$	2.73205			0.426675			0.213337	−	0.976979i	$-0.431567\pi$
$41$	2.73205			0.426675			0.213337	+	0.976979i	$0.431567\pi$
$42$		0			0
$43$	7.19615			1.09740			0.548701	−	0.836018i	$-0.315122\pi$
$43$	7.19615			1.09740			0.548701	+	0.836018i	$0.315122\pi$
$44$		0			0
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$		0			0
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	0.929695	−	0.368329i	$-0.120070\pi$
$47$	1.00000	+	1.73205i	0.145865	+	0.252646i	−0.783830	+	0.620975i	$0.786737\pi$
$48$		0			0
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$		0			0
$51$	−3.36603	−	5.83013i	−0.471338	−	0.816381i
$52$		0			0
$53$	4.19615	−	7.26795i	0.576386	−	0.998330i	−0.419504	−	0.907754i	$-0.637796\pi$
$53$	4.19615	−	7.26795i	0.576386	−	0.998330i	0.995890	−	0.0905760i	$-0.0288708\pi$
$54$		0			0
$55$	2.73205			0.368390
$56$		0			0
$57$	2.46410			0.326378
$58$		0			0
$59$	5.09808	−	8.83013i	0.663713	−	1.14958i	−0.315920	−	0.948786i	$-0.602313\pi$
$59$	5.09808	−	8.83013i	0.663713	−	1.14958i	0.979633	−	0.200799i	$-0.0643537\pi$
$60$		0			0
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	0.709113	−	0.705095i	$-0.249096\pi$
$61$	−2.00000	−	3.46410i	−0.256074	−	0.443533i	−0.965187	+	0.261562i	$0.915762\pi$
$62$		0			0
$63$	−2.59808	+	0.500000i	−0.327327	+	0.0629941i
$64$		0			0
$65$	−2.86603	−	4.96410i	−0.355487	−	0.615721i
$66$		0			0
$67$	1.33013	−	2.30385i	0.162501	−	0.281460i	−0.773264	−	0.634084i	$-0.781377\pi$
$67$	1.33013	−	2.30385i	0.162501	−	0.281460i	0.935765	+	0.352624i	$0.114711\pi$
$68$		0			0
$69$	1.26795			0.152643
$70$		0			0
$71$	4.19615			0.497992			0.248996	−	0.968505i	$-0.419899\pi$
$71$	4.19615			0.497992			0.248996	+	0.968505i	$0.419899\pi$
$72$		0			0
$73$	2.33013	−	4.03590i	0.272721	−	0.472366i	−0.696837	−	0.717230i	$-0.745410\pi$
$73$	2.33013	−	4.03590i	0.272721	−	0.472366i	0.969558	+	0.244864i	$0.0787432\pi$
$74$		0			0
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$		0			0
$77$	4.73205	+	5.46410i	0.539267	+	0.622692i
$78$		0			0
$79$	6.69615	+	11.5981i	0.753376	+	1.30489i	0.946178	+	0.323648i	$0.104909\pi$
$79$	6.69615	+	11.5981i	0.753376	+	1.30489i	−0.192802	+	0.981238i	$0.561757\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	9.12436			1.00153			0.500764	−	0.865584i	$-0.333052\pi$
$83$	9.12436			1.00153			0.500764	+	0.865584i	$0.333052\pi$
$84$		0			0
$85$	6.73205			0.730193
$86$		0			0
$87$	−3.09808	+	5.36603i	−0.332149	+	0.575298i
$88$		0			0
$89$	4.56218	+	7.90192i	0.483590	+	0.837602i	0.999822	−	0.0188462i	$-0.00599930\pi$
$89$	4.56218	+	7.90192i	0.483590	+	0.837602i	−0.516233	+	0.856448i	$0.672666\pi$
$90$		0			0
$91$	4.96410	−	14.3301i	0.520379	−	1.50221i
$92$		0			0
$93$	3.23205	+	5.59808i	0.335148	+	0.580493i
$94$		0			0
$95$	−1.23205	+	2.13397i	−0.126406	+	0.218941i
$96$		0			0
$97$	1.07180			0.108824			0.0544122	−	0.998519i	$-0.482671\pi$
$97$	1.07180			0.108824			0.0544122	+	0.998519i	$0.482671\pi$
$98$		0			0
$99$	2.73205			0.274581
$100$		0			0
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	−0.465274	−	0.885167i	$-0.654044\pi$
$101$	5.36603	−	9.29423i	0.533939	−	0.924810i	0.999214	−	0.0396438i	$-0.0126223\pi$
$102$		0			0
$103$	0.598076	+	1.03590i	0.0589302	+	0.102070i	0.893985	−	0.448096i	$-0.147898\pi$
$103$	0.598076	+	1.03590i	0.0589302	+	0.102070i	−0.835055	+	0.550166i	$0.814564\pi$
$104$		0			0
$105$	0.866025	−	2.50000i	0.0845154	−	0.243975i
$106$		0			0
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	0.597075	−	0.802186i	$-0.296330\pi$
$107$	−4.09808	−	7.09808i	−0.396176	−	0.686197i	−0.993251	+	0.115989i	$0.962996\pi$
$108$		0			0
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		0			0
$111$	7.19615			0.683029
$112$		0			0
$113$	−4.92820			−0.463606			−0.231803	−	0.972763i	$-0.574463\pi$
$113$	−4.92820			−0.463606			−0.231803	+	0.972763i	$0.574463\pi$
$114$		0			0
$115$	−0.633975	+	1.09808i	−0.0591184	+	0.102396i
$116$		0			0
$117$	−2.86603	−	4.96410i	−0.264964	−	0.458931i
$118$		0			0
$119$	11.6603	+	13.4641i	1.06889	+	1.23425i
$120$		0			0
$121$	1.76795	+	3.06218i	0.160723	+	0.278380i
$122$		0			0
$123$	−1.36603	+	2.36603i	−0.123170	+	0.213337i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	−15.1962			−1.34844			−0.674220	−	0.738530i	$-0.735520\pi$
$127$	−15.1962			−1.34844			−0.674220	+	0.738530i	$0.735520\pi$
$128$		0			0
$129$	−3.59808	+	6.23205i	−0.316793	+	0.548701i
$130$		0			0
$131$	4.26795	+	7.39230i	0.372892	+	0.645869i	0.990009	−	0.141003i	$-0.0450327\pi$
$131$	4.26795	+	7.39230i	0.372892	+	0.645869i	−0.617117	+	0.786872i	$0.711699\pi$
$132$		0			0
$133$	−6.40192	+	1.23205i	−0.555117	+	0.106832i
$134$		0			0
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$		0			0
$137$	4.09808	−	7.09808i	0.350122	−	0.606430i	−0.636148	−	0.771567i	$-0.719473\pi$
$137$	4.09808	−	7.09808i	0.350122	−	0.606430i	0.986271	+	0.165137i	$0.0528067\pi$
$138$		0			0
$139$	7.92820			0.672461			0.336231	−	0.941780i	$-0.390848\pi$
$139$	7.92820			0.672461			0.336231	+	0.941780i	$0.390848\pi$
$140$		0			0
$141$	−2.00000			−0.168430
$142$		0			0
$143$	−7.83013	+	13.5622i	−0.654788	+	1.13413i
$144$		0			0
$145$	−3.09808	−	5.36603i	−0.257281	−	0.445624i
$146$		0			0
$147$	6.50000	−	2.59808i	0.536111	−	0.214286i
$148$		0			0
$149$	10.9282	+	18.9282i	0.895273	+	1.55066i	0.833466	+	0.552571i	$0.186353\pi$
$149$	10.9282	+	18.9282i	0.895273	+	1.55066i	0.0618073	+	0.998088i	$0.480314\pi$
$150$		0			0
$151$	2.46410	−	4.26795i	0.200526	−	0.347321i	−0.748172	−	0.663505i	$-0.769068\pi$
$151$	2.46410	−	4.26795i	0.200526	−	0.347321i	0.948698	+	0.316184i	$0.102402\pi$
$152$		0			0
$153$	6.73205			0.544254
$154$		0			0
$155$	−6.46410			−0.519209
$156$		0			0
$157$	7.19615	−	12.4641i	0.574315	−	0.994744i	−0.421800	−	0.906689i	$-0.638602\pi$
$157$	7.19615	−	12.4641i	0.574315	−	0.994744i	0.996116	−	0.0880548i	$-0.0280651\pi$
$158$		0			0
$159$	4.19615	+	7.26795i	0.332777	+	0.576386i
$160$		0			0
$161$	−3.29423	+	0.633975i	−0.259622	+	0.0499642i
$162$		0			0
$163$	−2.92820	−	5.07180i	−0.229355	−	0.397254i	0.728262	−	0.685298i	$-0.240328\pi$
$163$	−2.92820	−	5.07180i	−0.229355	−	0.397254i	−0.957617	+	0.288045i	$0.906995\pi$
$164$		0			0
$165$	−1.36603	+	2.36603i	−0.106345	+	0.184195i
$166$		0			0
$167$	0.339746			0.0262903			0.0131452	−	0.999914i	$-0.495816\pi$
$167$	0.339746			0.0262903			0.0131452	+	0.999914i	$0.495816\pi$
$168$		0			0
$169$	19.8564			1.52742
$170$		0			0
$171$	−1.23205	+	2.13397i	−0.0942173	+	0.163189i
$172$		0			0
$173$	−10.7321	−	18.5885i	−0.815943	−	1.41325i	−0.908649	−	0.417561i	$-0.862885\pi$
$173$	−10.7321	−	18.5885i	−0.815943	−	1.41325i	0.0927063	−	0.995693i	$-0.470448\pi$
$174$		0			0
$175$	1.73205	+	2.00000i	0.130931	+	0.151186i
$176$		0			0
$177$	5.09808	+	8.83013i	0.383195	+	0.663713i
$178$		0			0
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	−0.990134	−	0.140122i	$-0.955250\pi$
$179$	−5.00000	+	8.66025i	−0.373718	+	0.647298i	0.616417	+	0.787420i	$0.288584\pi$
$180$		0			0
$181$	10.3205			0.767117			0.383559	−	0.923517i	$-0.374698\pi$
$181$	10.3205			0.767117			0.383559	+	0.923517i	$0.374698\pi$
$182$		0			0
$183$	4.00000			0.295689
$184$		0			0
$185$	−3.59808	+	6.23205i	−0.264536	+	0.458189i
$186$		0			0
$187$	−9.19615	−	15.9282i	−0.672489	−	1.16479i
$188$		0			0
$189$	0.866025	−	2.50000i	0.0629941	−	0.181848i
$190$		0			0
$191$	2.46410	+	4.26795i	0.178296	+	0.308818i	0.941297	−	0.337579i	$-0.109608\pi$
$191$	2.46410	+	4.26795i	0.178296	+	0.308818i	−0.763001	+	0.646397i	$0.776275\pi$
$192$		0			0
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	−0.651727	−	0.758454i	$-0.725955\pi$
$193$	4.59808	−	7.96410i	0.330977	−	0.573269i	0.982704	+	0.185185i	$0.0592885\pi$
$194$		0			0
$195$	5.73205			0.410481
$196$		0			0
$197$	−17.6603			−1.25824			−0.629121	−	0.777308i	$-0.716585\pi$
$197$	−17.6603			−1.25824			−0.629121	+	0.777308i	$0.716585\pi$
$198$		0			0
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	−0.152305	−	0.988334i	$-0.548670\pi$
$199$	11.0000	−	19.0526i	0.779769	−	1.35060i	0.932075	−	0.362267i	$-0.117997\pi$
$200$		0			0
$201$	1.33013	+	2.30385i	0.0938199	+	0.162501i
$202$		0			0
$203$	5.36603	−	15.4904i	0.376621	−	1.08721i
$204$		0			0
$205$	−1.36603	−	2.36603i	−0.0954074	−	0.165250i
$206$		0			0
$207$	−0.633975	+	1.09808i	−0.0440643	+	0.0763216i
$208$		0			0
$209$	6.73205			0.465666
$210$		0			0
$211$	−20.9282			−1.44076			−0.720378	−	0.693581i	$-0.756032\pi$
$211$	−20.9282			−1.44076			−0.720378	+	0.693581i	$0.756032\pi$
$212$		0			0
$213$	−2.09808	+	3.63397i	−0.143758	+	0.248996i
$214$		0			0
$215$	−3.59808	−	6.23205i	−0.245387	−	0.425022i
$216$		0			0
$217$	−11.1962	−	12.9282i	−0.760044	−	0.877624i
$218$		0			0
$219$	2.33013	+	4.03590i	0.157455	+	0.272721i
$220$		0			0
$221$	−19.2942	+	33.4186i	−1.29787	+	2.24798i
$222$		0			0
$223$	−0.392305			−0.0262707			−0.0131353	−	0.999914i	$-0.504181\pi$
$223$	−0.392305			−0.0262707			−0.0131353	+	0.999914i	$0.504181\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$		0			0
$227$	7.83013	−	13.5622i	0.519704	−	0.900153i	−0.480034	−	0.877250i	$-0.659376\pi$
$227$	7.83013	−	13.5622i	0.519704	−	0.900153i	0.999738	−	0.0229034i	$-0.00729102\pi$
$228$		0			0
$229$	1.50000	+	2.59808i	0.0991228	+	0.171686i	0.911322	−	0.411695i	$-0.135063\pi$
$229$	1.50000	+	2.59808i	0.0991228	+	0.171686i	−0.812199	+	0.583380i	$0.801730\pi$
$230$		0			0
$231$	−7.09808	+	1.36603i	−0.467019	+	0.0898779i
$232$		0			0
$233$	8.66025	+	15.0000i	0.567352	+	0.982683i	0.996827	+	0.0796037i	$0.0253655\pi$
$233$	8.66025	+	15.0000i	0.567352	+	0.982683i	−0.429474	+	0.903079i	$0.641301\pi$
$234$		0			0
$235$	1.00000	−	1.73205i	0.0652328	−	0.112987i
$236$		0			0
$237$	−13.3923			−0.869924
$238$		0			0
$239$	−20.9282			−1.35373			−0.676866	−	0.736106i	$-0.736663\pi$
$239$	−20.9282			−1.35373			−0.676866	+	0.736106i	$0.736663\pi$
$240$		0			0
$241$	−3.26795	+	5.66025i	−0.210507	+	0.364609i	−0.951873	−	0.306492i	$-0.900845\pi$
$241$	−3.26795	+	5.66025i	−0.210507	+	0.364609i	0.741366	+	0.671101i	$0.234178\pi$
$242$		0			0
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$		0			0
$245$	−1.00000	+	6.92820i	−0.0638877	+	0.442627i
$246$		0			0
$247$	−7.06218	−	12.2321i	−0.449356	−	0.778307i
$248$		0			0
$249$	−4.56218	+	7.90192i	−0.289116	+	0.500764i
$250$		0			0
$251$	−6.58846			−0.415860			−0.207930	−	0.978144i	$-0.566673\pi$
$251$	−6.58846			−0.415860			−0.207930	+	0.978144i	$0.566673\pi$
$252$		0			0
$253$	3.46410			0.217786
$254$		0			0
$255$	−3.36603	+	5.83013i	−0.210789	+	0.365097i
$256$		0			0
$257$	−5.83013	−	10.0981i	−0.363673	−	0.629901i	0.624889	−	0.780714i	$-0.285144\pi$
$257$	−5.83013	−	10.0981i	−0.363673	−	0.629901i	−0.988562	+	0.150813i	$0.951811\pi$
$258$		0			0
$259$	−18.6962	+	3.59808i	−1.16172	+	0.223574i
$260$		0			0
$261$	−3.09808	−	5.36603i	−0.191766	−	0.332149i
$262$		0			0
$263$	−6.19615	+	10.7321i	−0.382071	+	0.661767i	−0.991358	−	0.131183i	$-0.958122\pi$
$263$	−6.19615	+	10.7321i	−0.382071	+	0.661767i	0.609287	+	0.792950i	$0.291456\pi$
$264$		0			0
$265$	−8.39230			−0.515535
$266$		0			0
$267$	−9.12436			−0.558401
$268$		0			0
$269$	9.73205	−	16.8564i	0.593374	−	1.02775i	−0.400401	−	0.916340i	$-0.631129\pi$
$269$	9.73205	−	16.8564i	0.593374	−	1.02775i	0.993774	−	0.111413i	$-0.0355377\pi$
$270$		0			0
$271$	8.46410	+	14.6603i	0.514158	+	0.890547i	0.999865	+	0.0164256i	$0.00522868\pi$
$271$	8.46410	+	14.6603i	0.514158	+	0.890547i	−0.485708	+	0.874121i	$0.661438\pi$
$272$		0			0
$273$	9.92820	+	11.4641i	0.600882	+	0.693839i
$274$		0			0
$275$	−1.36603	−	2.36603i	−0.0823744	−	0.142677i
$276$		0			0
$277$	−1.33013	+	2.30385i	−0.0799196	+	0.138425i	−0.903215	−	0.429188i	$-0.858800\pi$
$277$	−1.33013	+	2.30385i	−0.0799196	+	0.138425i	0.823295	+	0.567613i	$0.192133\pi$
$278$		0			0
$279$	−6.46410			−0.386996
$280$		0			0
$281$	−13.8564			−0.826604			−0.413302	−	0.910594i	$-0.635625\pi$
$281$	−13.8564			−0.826604			−0.413302	+	0.910594i	$0.635625\pi$
$282$		0			0
$283$	0.0621778	−	0.107695i	0.00369609	−	0.00640181i	−0.864171	−	0.503197i	$-0.832157\pi$
$283$	0.0621778	−	0.107695i	0.00369609	−	0.00640181i	0.867868	+	0.496796i	$0.165490\pi$
$284$		0			0
$285$	−1.23205	−	2.13397i	−0.0729804	−	0.126406i
$286$		0			0
$287$	2.36603	−	6.83013i	0.139662	−	0.403170i
$288$		0			0
$289$	−14.1603	−	24.5263i	−0.832956	−	1.44272i
$290$		0			0
$291$	−0.535898	+	0.928203i	−0.0314149	+	0.0544122i
$292$		0			0
$293$	5.07180			0.296298			0.148149	−	0.988965i	$-0.452669\pi$
$293$	5.07180			0.296298			0.148149	+	0.988965i	$0.452669\pi$
$294$		0			0
$295$	−10.1962			−0.593643
$296$		0			0
$297$	−1.36603	+	2.36603i	−0.0792648	+	0.137291i
$298$		0			0
$299$	−3.63397	−	6.29423i	−0.210158	−	0.364005i
$300$		0			0
$301$	6.23205	−	17.9904i	0.359209	−	1.03695i
$302$		0			0
$303$	5.36603	+	9.29423i	0.308270	+	0.533939i
$304$		0			0
$305$	−2.00000	+	3.46410i	−0.114520	+	0.198354i
$306$		0			0
$307$	7.87564			0.449487			0.224743	−	0.974418i	$-0.427846\pi$
$307$	7.87564			0.449487			0.224743	+	0.974418i	$0.427846\pi$
$308$		0			0
$309$	−1.19615			−0.0680467
$310$		0			0
$311$	−7.56218	+	13.0981i	−0.428812	+	0.742724i	−0.996768	−	0.0803351i	$-0.974401\pi$
$311$	−7.56218	+	13.0981i	−0.428812	+	0.742724i	0.567956	+	0.823059i	$0.307734\pi$
$312$		0			0
$313$	−2.33013	−	4.03590i	−0.131707	−	0.228122i	0.792628	−	0.609706i	$-0.208712\pi$
$313$	−2.33013	−	4.03590i	−0.131707	−	0.228122i	−0.924335	+	0.381583i	$0.875379\pi$
$314$		0			0
$315$	1.73205	+	2.00000i	0.0975900	+	0.112687i
$316$		0			0
$317$	−15.2224	−	26.3660i	−0.854977	−	1.48086i	−0.876666	−	0.481099i	$-0.840238\pi$
$317$	−15.2224	−	26.3660i	−0.854977	−	1.48086i	0.0216894	−	0.999765i	$-0.493095\pi$
$318$		0			0
$319$	−8.46410	+	14.6603i	−0.473899	+	0.820817i
$320$		0			0
$321$	8.19615			0.457465
$322$		0			0
$323$	16.5885			0.923006
$324$		0			0
$325$	−2.86603	+	4.96410i	−0.158978	+	0.275359i
$326$		0			0
$327$	−5.50000	−	9.52628i	−0.304151	−	0.526804i
$328$		0			0
$329$	5.19615	−	1.00000i	0.286473	−	0.0551318i
$330$		0			0
$331$	10.9641	+	18.9904i	0.602642	+	1.04381i	0.992419	+	0.122897i	$0.0392184\pi$
$331$	10.9641	+	18.9904i	0.602642	+	1.04381i	−0.389778	+	0.920909i	$0.627448\pi$
$332$		0			0
$333$	−3.59808	+	6.23205i	−0.197173	+	0.341514i
$334$		0			0
$335$	−2.66025			−0.145345
$336$		0			0
$337$	−33.9808			−1.85105			−0.925525	−	0.378686i	$-0.876376\pi$
$337$	−33.9808			−1.85105			−0.925525	+	0.378686i	$0.876376\pi$
$338$		0			0
$339$	2.46410	−	4.26795i	0.133832	−	0.231803i
$340$		0			0
$341$	8.83013	+	15.2942i	0.478178	+	0.828229i
$342$		0			0
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$	−0.633975	−	1.09808i	−0.0341320	−	0.0591184i
$346$		0			0
$347$	−17.4641	+	30.2487i	−0.937522	+	1.62384i	−0.167449	+	0.985881i	$0.553553\pi$
$347$	−17.4641	+	30.2487i	−0.937522	+	1.62384i	−0.770074	+	0.637955i	$0.779781\pi$
$348$		0			0
$349$	22.0000			1.17763			0.588817	−	0.808267i	$-0.299594\pi$
$349$	22.0000			1.17763			0.588817	+	0.808267i	$0.299594\pi$
$350$		0			0
$351$	5.73205			0.305954
$352$		0			0
$353$	−10.5622	+	18.2942i	−0.562168	+	0.973704i	0.435139	+	0.900363i	$0.356699\pi$
$353$	−10.5622	+	18.2942i	−0.562168	+	0.973704i	−0.997307	+	0.0733402i	$0.976634\pi$
$354$		0			0
$355$	−2.09808	−	3.63397i	−0.111354	−	0.192871i
$356$		0			0
$357$	−17.4904	+	3.36603i	−0.925689	+	0.178149i
$358$		0			0
$359$	−2.36603	−	4.09808i	−0.124874	−	0.216288i	0.796810	−	0.604230i	$-0.206519\pi$
$359$	−2.36603	−	4.09808i	−0.124874	−	0.216288i	−0.921684	+	0.387942i	$0.873186\pi$
$360$		0			0
$361$	6.46410	−	11.1962i	0.340216	−	0.589271i
$362$		0			0
$363$	−3.53590			−0.185587
$364$		0			0
$365$	−4.66025			−0.243929
$366$		0			0
$367$	0.401924	−	0.696152i	0.0209803	−	0.0363389i	−0.855345	−	0.518059i	$-0.826655\pi$
$367$	0.401924	−	0.696152i	0.0209803	−	0.0363389i	0.876325	+	0.481721i	$0.159988\pi$
$368$		0			0
$369$	−1.36603	−	2.36603i	−0.0711124	−	0.123170i
$370$		0			0
$371$	−14.5359	−	16.7846i	−0.754666	−	0.871414i
$372$		0			0
$373$	9.25833	+	16.0359i	0.479378	+	0.830307i	0.999720	−	0.0236505i	$-0.00752890\pi$
$373$	9.25833	+	16.0359i	0.479378	+	0.830307i	−0.520342	+	0.853958i	$0.674196\pi$
$374$		0			0
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$		0			0
$377$	35.5167			1.82920
$378$		0			0
$379$	28.3205			1.45473			0.727363	−	0.686253i	$-0.240745\pi$
$379$	28.3205			1.45473			0.727363	+	0.686253i	$0.240745\pi$
$380$		0			0
$381$	7.59808	−	13.1603i	0.389261	−	0.674220i
$382$		0			0
$383$	5.66025	+	9.80385i	0.289225	+	0.500953i	0.973625	−	0.228154i	$-0.0732689\pi$
$383$	5.66025	+	9.80385i	0.289225	+	0.500953i	−0.684400	+	0.729107i	$0.739936\pi$
$384$		0			0
$385$	2.36603	−	6.83013i	0.120584	−	0.348096i
$386$		0			0
$387$	−3.59808	−	6.23205i	−0.182900	−	0.316793i
$388$		0			0
$389$	−18.2942	+	31.6865i	−0.927554	+	1.60657i	−0.140153	+	0.990130i	$0.544760\pi$
$389$	−18.2942	+	31.6865i	−0.927554	+	1.60657i	−0.787401	+	0.616441i	$0.788574\pi$
$390$		0			0
$391$	8.53590			0.431679
$392$		0			0
$393$	−8.53590			−0.430579
$394$		0			0
$395$	6.69615	−	11.5981i	0.336920	−	0.583563i
$396$		0			0
$397$	10.4019	+	18.0167i	0.522058	+	0.904230i	0.999671	+	0.0256600i	$0.00816873\pi$
$397$	10.4019	+	18.0167i	0.522058	+	0.904230i	−0.477613	+	0.878570i	$0.658498\pi$
$398$		0			0
$399$	2.13397	−	6.16025i	0.106832	−	0.308398i
$400$		0			0
$401$	−2.19615	−	3.80385i	−0.109671	−	0.189955i	0.805966	−	0.591962i	$-0.201646\pi$
$401$	−2.19615	−	3.80385i	−0.109671	−	0.189955i	−0.915637	+	0.402006i	$0.868313\pi$
$402$		0			0
$403$	18.5263	−	32.0885i	0.922860	−	1.59844i
$404$		0			0
$405$	1.00000			0.0496904
$406$		0			0
$407$	19.6603			0.974523
$408$		0			0
$409$	−15.4282	+	26.7224i	−0.762876	+	1.32134i	0.178487	+	0.983942i	$0.442880\pi$
$409$	−15.4282	+	26.7224i	−0.762876	+	1.32134i	−0.941362	+	0.337397i	$0.890454\pi$
$410$		0			0
$411$	4.09808	+	7.09808i	0.202143	+	0.350122i
$412$		0			0
$413$	−17.6603	−	20.3923i	−0.869004	−	1.00344i
$414$		0			0
$415$	−4.56218	−	7.90192i	−0.223949	−	0.387890i
$416$		0			0
$417$	−3.96410	+	6.86603i	−0.194123	+	0.336231i
$418$		0			0
$419$	28.5359			1.39407			0.697035	−	0.717037i	$-0.254502\pi$
$419$	28.5359			1.39407			0.697035	+	0.717037i	$0.254502\pi$
$420$		0			0
$421$	13.9282			0.678819			0.339410	−	0.940639i	$-0.389773\pi$
$421$	13.9282			0.678819			0.339410	+	0.940639i	$0.389773\pi$
$422$		0			0
$423$	1.00000	−	1.73205i	0.0486217	−	0.0842152i
$424$		0			0
$425$	−3.36603	−	5.83013i	−0.163276	−	0.282803i
$426$		0			0
$427$	−10.3923	+	2.00000i	−0.502919	+	0.0967868i
$428$		0			0
$429$	−7.83013	−	13.5622i	−0.378042	−	0.654788i
$430$		0			0
$431$	−8.66025	+	15.0000i	−0.417150	+	0.722525i	−0.995651	−	0.0931566i	$-0.970304\pi$
$431$	−8.66025	+	15.0000i	−0.417150	+	0.722525i	0.578502	+	0.815681i	$0.303638\pi$
$432$		0			0
$433$	4.80385			0.230858			0.115429	−	0.993316i	$-0.463176\pi$
$433$	4.80385			0.230858			0.115429	+	0.993316i	$0.463176\pi$
$434$		0			0
$435$	6.19615			0.297083
$436$		0			0
$437$	−1.56218	+	2.70577i	−0.0747291	+	0.129435i
$438$		0			0
$439$	3.73205	+	6.46410i	0.178121	+	0.308515i	0.941237	−	0.337747i	$-0.109665\pi$
$439$	3.73205	+	6.46410i	0.178121	+	0.308515i	−0.763116	+	0.646262i	$0.776331\pi$
$440$		0			0
$441$	−1.00000	+	6.92820i	−0.0476190	+	0.329914i
$442$		0			0
$443$	1.26795	+	2.19615i	0.0602421	+	0.104342i	0.894574	−	0.446921i	$-0.147479\pi$
$443$	1.26795	+	2.19615i	0.0602421	+	0.104342i	−0.834331	+	0.551263i	$0.814146\pi$
$444$		0			0
$445$	4.56218	−	7.90192i	0.216268	−	0.374587i
$446$		0			0
$447$	−21.8564			−1.03377
$448$		0			0
$449$	−8.14359			−0.384320			−0.192160	−	0.981364i	$-0.561549\pi$
$449$	−8.14359			−0.384320			−0.192160	+	0.981364i	$0.561549\pi$
$450$		0			0
$451$	−3.73205	+	6.46410i	−0.175735	+	0.304383i
$452$		0			0
$453$	2.46410	+	4.26795i	0.115774	+	0.200526i
$454$		0			0
$455$	−14.8923	+	2.86603i	−0.698162	+	0.134361i
$456$		0			0
$457$	−0.330127	−	0.571797i	−0.0154427	−	0.0267475i	0.858201	−	0.513314i	$-0.171582\pi$
$457$	−0.330127	−	0.571797i	−0.0154427	−	0.0267475i	−0.873643	+	0.486567i	$0.838249\pi$
$458$		0			0
$459$	−3.36603	+	5.83013i	−0.157113	+	0.272127i
$460$		0			0
$461$	−34.9808			−1.62922			−0.814608	−	0.580012i	$-0.803048\pi$
$461$	−34.9808			−1.62922			−0.814608	+	0.580012i	$0.803048\pi$
$462$		0			0
$463$	−22.2679			−1.03488			−0.517440	−	0.855720i	$-0.673115\pi$
$463$	−22.2679			−1.03488			−0.517440	+	0.855720i	$0.673115\pi$
$464$		0			0
$465$	3.23205	−	5.59808i	0.149883	−	0.259605i
$466$		0			0
$467$	−13.9282	−	24.1244i	−0.644520	−	1.11634i	−0.984412	−	0.175877i	$-0.943724\pi$
$467$	−13.9282	−	24.1244i	−0.644520	−	1.11634i	0.339892	−	0.940465i	$-0.389610\pi$
$468$		0			0
$469$	−4.60770	−	5.32051i	−0.212764	−	0.245678i
$470$		0			0
$471$	7.19615	+	12.4641i	0.331581	+	0.574315i
$472$		0			0
$473$	−9.83013	+	17.0263i	−0.451990	+	0.782869i
$474$		0			0
$475$	2.46410			0.113061
$476$		0			0
$477$	−8.39230			−0.384257
$478$		0			0
$479$	−16.3923	+	28.3923i	−0.748984	+	1.29728i	0.199327	+	0.979933i	$0.436124\pi$
$479$	−16.3923	+	28.3923i	−0.748984	+	1.29728i	−0.948310	+	0.317344i	$0.897209\pi$
$480$		0			0
$481$	−20.6244	−	35.7224i	−0.940390	−	1.62880i
$482$		0			0
$483$	1.09808	−	3.16987i	0.0499642	−	0.144234i
$484$		0			0
$485$	−0.535898	−	0.928203i	−0.0243339	−	0.0421475i
$486$		0			0
$487$	−15.7942	+	27.3564i	−0.715705	+	1.23964i	0.246982	+	0.969020i	$0.420561\pi$
$487$	−15.7942	+	27.3564i	−0.715705	+	1.23964i	−0.962687	+	0.270617i	$0.912772\pi$
$488$		0			0
$489$	5.85641			0.264836
$490$		0			0
$491$	−10.2487			−0.462518			−0.231259	−	0.972892i	$-0.574284\pi$
$491$	−10.2487			−0.462518			−0.231259	+	0.972892i	$0.574284\pi$
$492$		0			0
$493$	−20.8564	+	36.1244i	−0.939325	+	1.62696i
$494$		0			0
$495$	−1.36603	−	2.36603i	−0.0613983	−	0.106345i
$496$		0			0
$497$	3.63397	−	10.4904i	0.163006	−	0.470558i
$498$		0			0
$499$	−10.2321	−	17.7224i	−0.458050	−	0.793365i	0.540808	−	0.841146i	$-0.318118\pi$
$499$	−10.2321	−	17.7224i	−0.458050	−	0.793365i	−0.998858	+	0.0477808i	$0.984785\pi$
$500$		0			0
$501$	−0.169873	+	0.294229i	−0.00758937	+	0.0131452i
$502$		0			0
$503$	6.39230			0.285019			0.142509	−	0.989793i	$-0.454483\pi$
$503$	6.39230			0.285019			0.142509	+	0.989793i	$0.454483\pi$
$504$		0			0
$505$	−10.7321			−0.477570
$506$		0			0
$507$	−9.92820	+	17.1962i	−0.440927	+	0.763708i
$508$		0			0
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	0.710573	−	0.703623i	$-0.248436\pi$
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	−0.964642	+	0.263563i	$0.915102\pi$
$510$		0			0
$511$	−8.07180	−	9.32051i	−0.357075	−	0.412315i
$512$		0			0
$513$	−1.23205	−	2.13397i	−0.0543964	−	0.0942173i
$514$		0			0
$515$	0.598076	−	1.03590i	0.0263544	−	0.0456471i
$516$		0			0
$517$	−5.46410			−0.240311
$518$		0			0
$519$	21.4641			0.942169
$520$		0			0
$521$	−0.732051	+	1.26795i	−0.0320717	+	0.0555499i	−0.881616	−	0.471968i	$-0.843544\pi$
$521$	−0.732051	+	1.26795i	−0.0320717	+	0.0555499i	0.849544	+	0.527518i	$0.176877\pi$
$522$		0			0
$523$	−12.1340	−	21.0167i	−0.530582	−	0.918994i	−0.999363	−	0.0356803i	$-0.988640\pi$
$523$	−12.1340	−	21.0167i	−0.530582	−	0.918994i	0.468782	−	0.883314i	$-0.344693\pi$
$524$		0			0
$525$	−2.59808	+	0.500000i	−0.113389	+	0.0218218i
$526$		0			0
$527$	21.7583	+	37.6865i	0.947808	+	1.64165i
$528$		0			0
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$		0			0
$531$	−10.1962			−0.442475
$532$		0			0
$533$	15.6603			0.678321
$534$		0			0
$535$	−4.09808	+	7.09808i	−0.177175	+	0.306877i
$536$		0			0
$537$	−5.00000	−	8.66025i	−0.215766	−	0.373718i
$538$		0			0
$539$	17.7583	−	7.09808i	0.764905	−	0.305736i
$540$		0			0
$541$	17.8923	+	30.9904i	0.769250	+	1.33238i	0.937970	+	0.346716i	$0.112703\pi$
$541$	17.8923	+	30.9904i	0.769250	+	1.33238i	−0.168720	+	0.985664i	$0.553963\pi$
$542$		0			0
$543$	−5.16025	+	8.93782i	−0.221448	+	0.383559i
$544$		0			0
$545$	11.0000			0.471188
$546$		0			0
$547$	−22.2487			−0.951286			−0.475643	−	0.879638i	$-0.657785\pi$
$547$	−22.2487			−0.951286			−0.475643	+	0.879638i	$0.657785\pi$
$548$		0			0
$549$	−2.00000	+	3.46410i	−0.0853579	+	0.147844i
$550$		0			0
$551$	−7.63397	−	13.2224i	−0.325218	−	0.563295i
$552$		0			0
$553$	34.7942	−	6.69615i	1.47960	−	0.284749i
$554$		0			0
$555$	−3.59808	−	6.23205i	−0.152730	−	0.264536i
$556$		0			0
$557$	13.3923	−	23.1962i	0.567450	−	0.982853i	−0.429367	−	0.903130i	$-0.641263\pi$
$557$	13.3923	−	23.1962i	0.567450	−	0.982853i	0.996817	−	0.0797224i	$-0.0254034\pi$
$558$		0			0
$559$	41.2487			1.74463
$560$		0			0
$561$	18.3923			0.776524
$562$		0			0
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$		0			0
$565$	2.46410	+	4.26795i	0.103666	+	0.179554i
$566$		0			0
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$		0			0
$569$	13.2224	+	22.9019i	0.554313	+	0.960099i	0.997957	+	0.0638952i	$0.0203523\pi$
$569$	13.2224	+	22.9019i	0.554313	+	0.960099i	−0.443643	+	0.896203i	$0.646314\pi$
$570$		0			0
$571$	19.6962	−	34.1147i	0.824258	−	1.42766i	−0.0782265	−	0.996936i	$-0.524926\pi$
$571$	19.6962	−	34.1147i	0.824258	−	1.42766i	0.902485	−	0.430722i	$-0.141741\pi$
$572$		0			0
$573$	−4.92820			−0.205879
$574$		0			0
$575$	1.26795			0.0528771
$576$		0			0
$577$	−5.66987	+	9.82051i	−0.236040	+	0.408833i	−0.959574	−	0.281455i	$-0.909183\pi$
$577$	−5.66987	+	9.82051i	−0.236040	+	0.408833i	0.723534	+	0.690288i	$0.242516\pi$
$578$		0			0
$579$	4.59808	+	7.96410i	0.191090	+	0.330977i
$580$		0			0
$581$	7.90192	−	22.8109i	0.327827	−	0.946355i
$582$		0			0
$583$	11.4641	+	19.8564i	0.474795	+	0.822368i
$584$		0			0
$585$	−2.86603	+	4.96410i	−0.118496	+	0.205240i
$586$		0			0
$587$	−37.2679			−1.53821			−0.769106	−	0.639121i	$-0.779298\pi$
$587$	−37.2679			−1.53821			−0.769106	+	0.639121i	$0.779298\pi$
$588$		0			0
$589$	−15.9282			−0.656310
$590$		0			0
$591$	8.83013	−	15.2942i	0.363223	−	0.629121i
$592$		0			0
$593$	18.9545	+	32.8301i	0.778367	+	1.34817i	0.932882	+	0.360181i	$0.117285\pi$
$593$	18.9545	+	32.8301i	0.778367	+	1.34817i	−0.154515	+	0.987990i	$0.549381\pi$
$594$		0			0
$595$	5.83013	−	16.8301i	0.239012	−	0.689968i
$596$		0			0
$597$	11.0000	+	19.0526i	0.450200	+	0.779769i
$598$		0			0
$599$	5.12436	−	8.87564i	0.209375	−	0.362649i	−0.742142	−	0.670242i	$-0.766190\pi$
$599$	5.12436	−	8.87564i	0.209375	−	0.362649i	0.951518	+	0.307593i	$0.0995236\pi$
$600$		0			0
$601$	−13.9282			−0.568143			−0.284072	−	0.958803i	$-0.591685\pi$
$601$	−13.9282			−0.568143			−0.284072	+	0.958803i	$0.591685\pi$
$602$		0			0
$603$	−2.66025			−0.108334
$604$		0			0
$605$	1.76795	−	3.06218i	0.0718774	−	0.124495i
$606$		0			0
$607$	−3.59808	−	6.23205i	−0.146041	−	0.252951i	0.783720	−	0.621115i	$-0.213320\pi$
$607$	−3.59808	−	6.23205i	−0.146041	−	0.252951i	−0.929761	+	0.368164i	$0.879987\pi$
$608$		0			0
$609$	10.7321	+	12.3923i	0.434885	+	0.502162i
$610$		0			0
$611$	5.73205	+	9.92820i	0.231894	+	0.401652i
$612$		0			0
$613$	6.53590	−	11.3205i	0.263982	−	0.457231i	−0.703314	−	0.710879i	$-0.748297\pi$
$613$	6.53590	−	11.3205i	0.263982	−	0.457231i	0.967297	+	0.253648i	$0.0816306\pi$
$614$		0			0
$615$	2.73205			0.110167
$616$		0			0
$617$	12.2487			0.493115			0.246557	−	0.969128i	$-0.420701\pi$
$617$	12.2487			0.493115			0.246557	+	0.969128i	$0.420701\pi$
$618$		0			0
$619$	−21.9641	+	38.0429i	−0.882812	+	1.52907i	−0.0346105	+	0.999401i	$0.511019\pi$
$619$	−21.9641	+	38.0429i	−0.882812	+	1.52907i	−0.848201	+	0.529674i	$0.822314\pi$
$620$		0			0
$621$	−0.633975	−	1.09808i	−0.0254405	−	0.0440643i
$622$		0			0
$623$	23.7058	−	4.56218i	0.949752	−	0.182780i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	−3.36603	+	5.83013i	−0.134426	+	0.232833i
$628$		0			0
$629$	48.4449			1.93162
$630$		0			0
$631$	−7.21539			−0.287240			−0.143620	−	0.989633i	$-0.545874\pi$
$631$	−7.21539			−0.287240			−0.143620	+	0.989633i	$0.545874\pi$
$632$		0			0
$633$	10.4641	−	18.1244i	0.415911	−	0.720378i
$634$		0			0
$635$	7.59808	+	13.1603i	0.301520	+	0.522249i
$636$		0			0
$637$	−31.5263	−	24.8205i	−1.24912	−	0.983424i
$638$		0			0
$639$	−2.09808	−	3.63397i	−0.0829986	−	0.143758i
$640$		0			0
$641$	−7.09808	+	12.2942i	−0.280357	+	0.485593i	−0.971473	−	0.237151i	$-0.923786\pi$
$641$	−7.09808	+	12.2942i	−0.280357	+	0.485593i	0.691116	+	0.722744i	$0.257120\pi$
$642$		0			0
$643$	40.5167			1.59782			0.798911	−	0.601450i	$-0.205410\pi$
$643$	40.5167			1.59782			0.798911	+	0.601450i	$0.205410\pi$
$644$		0			0
$645$	7.19615			0.283348
$646$		0			0
$647$	18.9545	−	32.8301i	0.745178	−	1.29069i	−0.204934	−	0.978776i	$-0.565698\pi$
$647$	18.9545	−	32.8301i	0.745178	−	1.29069i	0.950112	−	0.311910i	$-0.100969\pi$
$648$		0			0
$649$	13.9282	+	24.1244i	0.546730	+	0.946964i
$650$		0			0
$651$	16.7942	−	3.23205i	0.658218	−	0.126674i
$652$		0			0
$653$	6.70577	+	11.6147i	0.262417	+	0.454520i	0.966884	−	0.255217i	$-0.0821470\pi$
$653$	6.70577	+	11.6147i	0.262417	+	0.454520i	−0.704467	+	0.709737i	$0.748814\pi$
$654$		0			0
$655$	4.26795	−	7.39230i	0.166763	−	0.288841i
$656$		0			0
$657$	−4.66025			−0.181814
$658$		0			0
$659$	10.9282			0.425702			0.212851	−	0.977085i	$-0.431725\pi$
$659$	10.9282			0.425702			0.212851	+	0.977085i	$0.431725\pi$
$660$		0			0
$661$	−1.76795	+	3.06218i	−0.0687653	+	0.119105i	−0.898358	−	0.439264i	$-0.855239\pi$
$661$	−1.76795	+	3.06218i	−0.0687653	+	0.119105i	0.829593	+	0.558369i	$0.188573\pi$
$662$		0			0
$663$	−19.2942	−	33.4186i	−0.749326	−	1.29787i
$664$		0			0
$665$	4.26795	+	4.92820i	0.165504	+	0.191108i
$666$		0			0
$667$	−3.92820	−	6.80385i	−0.152101	−	0.263446i
$668$		0			0
$669$	0.196152	−	0.339746i	0.00758369	−	0.0131353i
$670$		0			0
$671$	10.9282			0.421879
$672$		0			0
$673$	−44.6603			−1.72153			−0.860763	−	0.509006i	$-0.830013\pi$
$673$	−44.6603			−1.72153			−0.860763	+	0.509006i	$0.830013\pi$
$674$		0			0
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$		0			0
$677$	4.43782	+	7.68653i	0.170559	+	0.295417i	0.938616	−	0.344965i	$-0.112109\pi$
$677$	4.43782	+	7.68653i	0.170559	+	0.295417i	−0.768056	+	0.640382i	$0.778776\pi$
$678$		0			0
$679$	0.928203	−	2.67949i	0.0356212	−	0.102829i
$680$		0			0
$681$	7.83013	+	13.5622i	0.300051	+	0.519704i
$682$		0			0
$683$	5.02628	−	8.70577i	0.192325	−	0.333117i	−0.753695	−	0.657224i	$-0.771730\pi$
$683$	5.02628	−	8.70577i	0.192325	−	0.333117i	0.946020	+	0.324107i	$0.105064\pi$
$684$		0			0
$685$	−8.19615			−0.313159
$686$		0			0
$687$	−3.00000			−0.114457
$688$		0			0
$689$	24.0526	−	41.6603i	0.916330	−	1.58713i
$690$		0			0
$691$	−9.42820	−	16.3301i	−0.358666	−	0.621227i	0.629072	−	0.777347i	$-0.283435\pi$
$691$	−9.42820	−	16.3301i	−0.358666	−	0.621227i	−0.987738	+	0.156119i	$0.950102\pi$
$692$		0			0
$693$	2.36603	−	6.83013i	0.0898779	−	0.259455i
$694$		0			0
$695$	−3.96410	−	6.86603i	−0.150367	−	0.260443i
$696$		0			0
$697$	−9.19615	+	15.9282i	−0.348329	+	0.603324i
$698$		0			0
$699$	−17.3205			−0.655122
$700$		0			0
$701$	22.5885			0.853154			0.426577	−	0.904451i	$-0.359719\pi$
$701$	22.5885			0.853154			0.426577	+	0.904451i	$0.359719\pi$
$702$		0			0
$703$	−8.86603	+	15.3564i	−0.334388	+	0.579178i
$704$		0			0
$705$	1.00000	+	1.73205i	0.0376622	+	0.0652328i
$706$		0			0
$707$	−18.5885	−	21.4641i	−0.699091	−	0.807241i
$708$		0			0
$709$	7.46410	+	12.9282i	0.280320	+	0.485529i	0.971464	−	0.237189i	$-0.0762260\pi$
$709$	7.46410	+	12.9282i	0.280320	+	0.485529i	−0.691143	+	0.722718i	$0.742893\pi$
$710$		0			0
$711$	6.69615	−	11.5981i	0.251125	−	0.434962i
$712$		0			0
$713$	−8.19615			−0.306948
$714$		0			0
$715$	15.6603			0.585660
$716$		0			0
$717$	10.4641	−	18.1244i	0.390789	−	0.676866i
$718$		0			0
$719$	−13.7321	−	23.7846i	−0.512119	−	0.887016i	−0.999901	−	0.0140509i	$-0.995527\pi$
$719$	−13.7321	−	23.7846i	−0.512119	−	0.887016i	0.487782	−	0.872965i	$-0.337806\pi$
$720$		0			0
$721$	3.10770	−	0.598076i	0.115737	−	0.0222735i
$722$		0			0
$723$	−3.26795	−	5.66025i	−0.121536	−	0.210507i
$724$		0			0
$725$	−3.09808	+	5.36603i	−0.115060	+	0.199289i
$726$		0			0
$727$	30.6603			1.13713			0.568563	−	0.822640i	$-0.307500\pi$
$727$	30.6603			1.13713			0.568563	+	0.822640i	$0.307500\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−24.2224	+	41.9545i	−0.895899	+	1.55174i
$732$		0			0
$733$	9.33013	+	16.1603i	0.344616	+	0.596893i	0.985284	−	0.170926i	$-0.0546758\pi$
$733$	9.33013	+	16.1603i	0.344616	+	0.596893i	−0.640668	+	0.767818i	$0.721342\pi$
$734$		0			0
$735$	−5.50000	−	4.33013i	−0.202871	−	0.159719i
$736$		0			0
$737$	3.63397	+	6.29423i	0.133859	+	0.231851i
$738$		0			0
$739$	−6.89230	+	11.9378i	−0.253538	+	0.439140i	−0.964497	−	0.264093i	$-0.914927\pi$
$739$	−6.89230	+	11.9378i	−0.253538	+	0.439140i	0.710960	+	0.703233i	$0.248261\pi$
$740$		0			0
$741$	14.1244			0.518871
$742$		0			0
$743$	−49.9090			−1.83098			−0.915491	−	0.402338i	$-0.868198\pi$
$743$	−49.9090			−1.83098			−0.915491	+	0.402338i	$0.868198\pi$
$744$		0			0
$745$	10.9282	−	18.9282i	0.400378	−	0.693476i
$746$		0			0
$747$	−4.56218	−	7.90192i	−0.166921	−	0.289116i
$748$		0			0
$749$	−21.2942	+	4.09808i	−0.778074	+	0.149740i
$750$		0			0
$751$	15.9641	+	27.6506i	0.582538	+	1.00899i	0.995177	+	0.0980914i	$0.0312737\pi$
$751$	15.9641	+	27.6506i	0.582538	+	1.00899i	−0.412639	+	0.910895i	$0.635393\pi$
$752$		0			0
$753$	3.29423	−	5.70577i	0.120048	−	0.207930i
$754$		0			0
$755$	−4.92820			−0.179356
$756$		0			0
$757$	−0.143594			−0.00521900			−0.00260950	−	0.999997i	$-0.500831\pi$
$757$	−0.143594			−0.00521900			−0.00260950	+	0.999997i	$0.500831\pi$
$758$		0			0
$759$	−1.73205	+	3.00000i	−0.0628695	+	0.108893i
$760$		0			0
$761$	−21.6340	−	37.4711i	−0.784231	−	1.35833i	−0.929457	−	0.368929i	$-0.879724\pi$
$761$	−21.6340	−	37.4711i	−0.784231	−	1.35833i	0.145226	−	0.989398i	$-0.453609\pi$
$762$		0			0
$763$	19.0526	+	22.0000i	0.689749	+	0.796453i
$764$		0			0
$765$	−3.36603	−	5.83013i	−0.121699	−	0.210789i
$766$		0			0
$767$	29.2224	−	50.6147i	1.05516	−	1.82759i
$768$		0			0
$769$	17.6795			0.637539			0.318769	−	0.947832i	$-0.396730\pi$
$769$	17.6795			0.637539			0.318769	+	0.947832i	$0.396730\pi$
$770$		0			0
$771$	11.6603			0.419934
$772$		0			0
$773$	0.758330	−	1.31347i	0.0272752	−	0.0472421i	−0.852066	−	0.523435i	$-0.824650\pi$
$773$	0.758330	−	1.31347i	0.0272752	−	0.0472421i	0.879341	+	0.476193i	$0.157984\pi$
$774$		0			0
$775$	3.23205	+	5.59808i	0.116099	+	0.201089i
$776$		0			0
$777$	6.23205	−	17.9904i	0.223574	−	0.645401i
$778$		0			0
$779$	−3.36603	−	5.83013i	−0.120600	−	0.208886i
$780$		0			0
$781$	−5.73205	+	9.92820i	−0.205109	+	0.355259i
$782$		0			0
$783$	6.19615			0.221432
$784$		0			0
$785$	−14.3923			−0.513683
$786$		0			0
$787$	3.26795	−	5.66025i	0.116490	−	0.201766i	−0.801885	−	0.597479i	$-0.796169\pi$
$787$	3.26795	−	5.66025i	0.116490	−	0.201766i	0.918374	+	0.395713i	$0.129502\pi$
$788$		0			0
$789$	−6.19615	−	10.7321i	−0.220589	−	0.382071i
$790$		0			0
$791$	−4.26795	+	12.3205i	−0.151751	+	0.438067i
$792$		0			0
$793$	−11.4641	−	19.8564i	−0.407102	−	0.705122i
$794$		0			0
$795$	4.19615	−	7.26795i	0.148822	−	0.257768i
$796$		0			0
$797$	−42.0526			−1.48958			−0.744789	−	0.667300i	$-0.767450\pi$
$797$	−42.0526			−1.48958			−0.744789	+	0.667300i	$0.767450\pi$
$798$		0			0
$799$	−13.4641			−0.476326
$800$		0			0
$801$	4.56218	−	7.90192i	0.161197	−	0.279201i
$802$		0			0
$803$	6.36603	+	11.0263i	0.224652	+	0.389109i
$804$		0			0
$805$	2.19615	+	2.53590i	0.0774042	+	0.0893787i
$806$		0			0
$807$	9.73205	+	16.8564i	0.342584	+	0.593374i
$808$		0			0
$809$	14.8564	−	25.7321i	0.522323	−	0.904691i	−0.477339	−	0.878719i	$-0.658399\pi$
$809$	14.8564	−	25.7321i	0.522323	−	0.904691i	0.999663	−	0.0259716i	$-0.00826796\pi$
$810$		0			0
$811$	−3.46410			−0.121641			−0.0608205	−	0.998149i	$-0.519372\pi$
$811$	−3.46410			−0.121641			−0.0608205	+	0.998149i	$0.519372\pi$
$812$		0			0
$813$	−16.9282			−0.593698
$814$		0			0
$815$	−2.92820	+	5.07180i	−0.102570	+	0.177657i
$816$		0			0
$817$	−8.86603	−	15.3564i	−0.310183	−	0.537253i
$818$		0			0
$819$	−14.8923	+	2.86603i	−0.520379	+	0.100147i
$820$		0			0
$821$	−9.75833	−	16.9019i	−0.340568	−	0.589881i	0.643970	−	0.765051i	$-0.277286\pi$
$821$	−9.75833	−	16.9019i	−0.340568	−	0.589881i	−0.984538	+	0.175169i	$0.943953\pi$
$822$		0			0
$823$	−11.5885	+	20.0718i	−0.403948	+	0.699659i	−0.994198	−	0.107561i	$-0.965696\pi$
$823$	−11.5885	+	20.0718i	−0.403948	+	0.699659i	0.590250	+	0.807220i	$0.299029\pi$
$824$		0			0
$825$	2.73205			0.0951178
$826$		0			0
$827$	52.2487			1.81687			0.908433	−	0.418031i	$-0.137280\pi$
$827$	52.2487			1.81687			0.908433	+	0.418031i	$0.137280\pi$
$828$		0			0
$829$	12.6962	−	21.9904i	0.440956	−	0.763758i	−0.556805	−	0.830643i	$-0.687973\pi$
$829$	12.6962	−	21.9904i	0.440956	−	0.763758i	0.997761	+	0.0668857i	$0.0213063\pi$
$830$		0			0
$831$	−1.33013	−	2.30385i	−0.0461416	−	0.0799196i
$832$		0			0
$833$	43.7583	−	17.4904i	1.51614	−	0.606006i
$834$		0			0
$835$	−0.169873	−	0.294229i	−0.00587870	−	0.0101822i
$836$		0			0
$837$	3.23205	−	5.59808i	0.111716	−	0.193498i
$838$		0			0
$839$	40.4449			1.39631			0.698156	−	0.715946i	$-0.254004\pi$
$839$	40.4449			1.39631			0.698156	+	0.715946i	$0.254004\pi$
$840$		0			0
$841$	9.39230			0.323873
$842$		0			0
$843$	6.92820	−	12.0000i	0.238620	−	0.413302i
$844$		0			0
$845$	−9.92820	−	17.1962i	−0.341541	−	0.591566i
$846$		0			0
$847$	9.18653	−	1.76795i	0.315653	−	0.0607475i
$848$		0			0
$849$	0.0621778	+	0.107695i	0.00213394	+	0.00369609i
$850$		0			0
$851$	−4.56218	+	7.90192i	−0.156389	+	0.270874i
$852$		0			0
$853$	19.9808			0.684128			0.342064	−	0.939677i	$-0.388874\pi$
$853$	19.9808			0.684128			0.342064	+	0.939677i	$0.388874\pi$
$854$		0			0
$855$	2.46410			0.0842705
$856$		0			0
$857$	−2.43782	+	4.22243i	−0.0832744	+	0.144236i	−0.904655	−	0.426146i	$-0.859871\pi$
$857$	−2.43782	+	4.22243i	−0.0832744	+	0.144236i	0.821380	+	0.570381i	$0.193204\pi$
$858$		0			0
$859$	0.267949	+	0.464102i	0.00914231	+	0.0158349i	0.870560	−	0.492062i	$-0.163757\pi$
$859$	0.267949	+	0.464102i	0.00914231	+	0.0158349i	−0.861418	+	0.507897i	$0.830423\pi$
$860$		0			0
$861$	4.73205	+	5.46410i	0.161268	+	0.186216i
$862$		0			0
$863$	−3.19615	−	5.53590i	−0.108798	−	0.188444i	0.806485	−	0.591254i	$-0.201367\pi$
$863$	−3.19615	−	5.53590i	−0.108798	−	0.188444i	−0.915284	+	0.402810i	$0.868034\pi$
$864$		0			0
$865$	−10.7321	+	18.5885i	−0.364901	+	0.632027i
$866$		0			0
$867$	28.3205			0.961815
$868$		0			0
$869$	−36.5885			−1.24118
$870$		0			0
$871$	7.62436	−	13.2058i	0.258341	−	0.447460i
$872$		0			0
$873$	−0.535898	−	0.928203i	−0.0181374	−	0.0314149i
$874$		0			0
$875$	0.866025	−	2.50000i	0.0292770	−	0.0845154i
$876$		0			0
$877$	15.9282	+	27.5885i	0.537857	+	0.931596i	0.999019	+	0.0442800i	$0.0140994\pi$
$877$	15.9282	+	27.5885i	0.537857	+	0.931596i	−0.461162	+	0.887316i	$0.652567\pi$
$878$		0			0
$879$	−2.53590	+	4.39230i	−0.0855337	+	0.148149i
$880$		0			0
$881$	−17.8564			−0.601598			−0.300799	−	0.953688i	$-0.597253\pi$
$881$	−17.8564			−0.601598			−0.300799	+	0.953688i	$0.597253\pi$
$882$		0			0
$883$	−22.4115			−0.754208			−0.377104	−	0.926171i	$-0.623080\pi$
$883$	−22.4115			−0.754208			−0.377104	+	0.926171i	$0.623080\pi$
$884$		0			0
$885$	5.09808	−	8.83013i	0.171370	−	0.296821i
$886$		0			0
$887$	−14.3660	−	24.8827i	−0.482364	−	0.835479i	0.517431	−	0.855725i	$-0.326888\pi$
$887$	−14.3660	−	24.8827i	−0.482364	−	0.835479i	−0.999795	+	0.0202460i	$0.993555\pi$
$888$		0			0
$889$	−13.1603	+	37.9904i	−0.441381	+	1.27416i
$890$		0			0
$891$	−1.36603	−	2.36603i	−0.0457636	−	0.0792648i
$892$		0			0
$893$	2.46410	−	4.26795i	0.0824580	−	0.142821i
$894$		0			0
$895$	10.0000			0.334263
$896$		0			0
$897$	7.26795			0.242670
$898$		0			0
$899$	20.0263	−	34.6865i	0.667914	−	1.15686i
$900$		0			0
$901$	28.2487	+	48.9282i	0.941101	+	1.63003i
$902$		0			0
$903$	12.4641	+	14.3923i	0.414779	+	0.478946i
$904$		0			0
$905$	−5.16025	−	8.93782i	−0.171533	−	0.297103i
$906$		0			0
$907$	1.20577	−	2.08846i	0.0400370	−	0.0693461i	−0.845313	−	0.534272i	$-0.820586\pi$
$907$	1.20577	−	2.08846i	0.0400370	−	0.0693461i	0.885350	+	0.464926i	$0.153919\pi$
$908$		0			0
$909$	−10.7321			−0.355960
$910$		0			0
$911$	11.2679			0.373324			0.186662	−	0.982424i	$-0.440233\pi$
$911$	11.2679			0.373324			0.186662	+	0.982424i	$0.440233\pi$
$912$		0			0
$913$	−12.4641	+	21.5885i	−0.412502	+	0.714474i
$914$		0			0
$915$	−2.00000	−	3.46410i	−0.0661180	−	0.114520i
$916$		0			0
$917$	22.1769	−	4.26795i	0.732346	−	0.140940i
$918$		0			0
$919$	−1.57180	−	2.72243i	−0.0518488	−	0.0898047i	0.838936	−	0.544230i	$-0.183178\pi$
$919$	−1.57180	−	2.72243i	−0.0518488	−	0.0898047i	−0.890785	+	0.454425i	$0.849845\pi$
$920$		0			0
$921$	−3.93782	+	6.82051i	−0.129756	+	0.224743i
$922$		0			0
$923$	24.0526			0.791700
$924$		0			0
$925$	7.19615			0.236608
$926$		0			0
$927$	0.598076	−	1.03590i	0.0196434	−	0.0340234i
$928$		0			0
$929$	−3.22243	−	5.58142i	−0.105725	−	0.183120i	0.808309	−	0.588758i	$-0.200383\pi$
$929$	−3.22243	−	5.58142i	−0.105725	−	0.183120i	−0.914034	+	0.405638i	$0.867050\pi$
$930$		0			0
$931$	−2.46410	+	17.0718i	−0.0807577	+	0.559506i
$932$		0			0
$933$	−7.56218	−	13.0981i	−0.247575	−	0.428812i
$934$		0			0
$935$	−9.19615	+	15.9282i	−0.300746	+	0.520908i
$936$		0			0
$937$	28.2679			0.923474			0.461737	−	0.887017i	$-0.347226\pi$
$937$	28.2679			0.923474			0.461737	+	0.887017i	$0.347226\pi$
$938$		0			0
$939$	4.66025			0.152082
$940$		0			0
$941$	−4.02628	+	6.97372i	−0.131253	+	0.227337i	−0.924160	−	0.382006i	$-0.875233\pi$
$941$	−4.02628	+	6.97372i	−0.131253	+	0.227337i	0.792907	+	0.609343i	$0.208567\pi$
$942$		0			0
$943$	−1.73205	−	3.00000i	−0.0564033	−	0.0976934i
$944$		0			0
$945$	−2.59808	+	0.500000i	−0.0845154	+	0.0162650i
$946$		0			0
$947$	5.83013	+	10.0981i	0.189454	+	0.328143i	0.945068	−	0.326873i	$-0.105995\pi$
$947$	5.83013	+	10.0981i	0.189454	+	0.328143i	−0.755615	+	0.655017i	$0.772662\pi$
$948$		0			0
$949$	13.3564	−	23.1340i	0.433567	−	0.750961i
$950$		0			0
$951$	30.4449			0.987242
$952$		0			0
$953$	40.1051			1.29913			0.649566	−	0.760305i	$-0.274951\pi$
$953$	40.1051			1.29913			0.649566	+	0.760305i	$0.274951\pi$
$954$		0			0
$955$	2.46410	−	4.26795i	0.0797365	−	0.138108i
$956$		0			0
$957$	−8.46410	−	14.6603i	−0.273606	−	0.473899i
$958$		0			0
$959$	−14.1962	−	16.3923i	−0.458418	−	0.529335i
$960$		0			0
$961$	−5.39230	−	9.33975i	−0.173945	−	0.301282i
$962$		0			0
$963$	−4.09808	+	7.09808i	−0.132059	+	0.228732i
$964$		0			0
$965$	−9.19615			−0.296035
$966$		0			0
$967$	−14.1244			−0.454209			−0.227104	−	0.973870i	$-0.572926\pi$
$967$	−14.1244			−0.454209			−0.227104	+	0.973870i	$0.572926\pi$
$968$		0			0
$969$	−8.29423	+	14.3660i	−0.266449	+	0.461503i
$970$		0			0
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	0.606685	−	0.794943i	$-0.292499\pi$
$971$	−12.0000	−	20.7846i	−0.385098	−	0.667010i	−0.991783	+	0.127933i	$0.959166\pi$
$972$		0			0
$973$	6.86603	−	19.8205i	0.220115	−	0.635416i
$974$		0			0
$975$	−2.86603	−	4.96410i	−0.0917863	−	0.158978i
$976$		0			0
$977$	−7.29423	+	12.6340i	−0.233363	+	0.404197i	−0.958796	−	0.284097i	$-0.908306\pi$
$977$	−7.29423	+	12.6340i	−0.233363	+	0.404197i	0.725433	+	0.688293i	$0.241640\pi$
$978$		0			0
$979$	−24.9282			−0.796709
$980$		0			0
$981$	11.0000			0.351203
$982$		0			0
$983$	10.0981	−	17.4904i	0.322079	−	0.557857i	−0.658838	−	0.752285i	$-0.728952\pi$
$983$	10.0981	−	17.4904i	0.322079	−	0.557857i	0.980917	+	0.194428i	$0.0622851\pi$
$984$		0			0
$985$	8.83013	+	15.2942i	0.281351	+	0.487315i
$986$		0			0
$987$	−1.73205	+	5.00000i	−0.0551318	+	0.159152i
$988$		0			0
$989$	−4.56218	−	7.90192i	−0.145069	−	0.251267i
$990$		0			0
$991$	27.5526	−	47.7224i	0.875236	−	1.51595i	0.0187246	−	0.999825i	$-0.494039\pi$
$991$	27.5526	−	47.7224i	0.875236	−	1.51595i	0.856511	−	0.516128i	$-0.172627\pi$
$992$		0			0
$993$	−21.9282			−0.695870
$994$		0			0
$995$	−22.0000			−0.697447
$996$		0			0
$997$	2.00962	−	3.48076i	0.0636453	−	0.110237i	−0.832447	−	0.554105i	$-0.813061\pi$
$997$	2.00962	−	3.48076i	0.0636453	−	0.110237i	0.896092	+	0.443868i	$0.146394\pi$
$998$		0			0
$999$	−3.59808	−	6.23205i	−0.113838	−	0.197173i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1680.2.bg.o.1201.2		4
4.3	odd	2		105.2.i.d.46.1	yes	4
7.2	even	3	inner	1680.2.bg.o.961.2		4
12.11	even	2		315.2.j.c.46.2		4
20.3	even	4		525.2.r.a.424.2		4
20.7	even	4		525.2.r.f.424.1		4
20.19	odd	2		525.2.i.f.151.2		4
28.3	even	6		735.2.a.h.1.2		2
28.11	odd	6		735.2.a.g.1.2		2
28.19	even	6		735.2.i.l.226.1		4
28.23	odd	6		105.2.i.d.16.1	✓	4
28.27	even	2		735.2.i.l.361.1		4
84.11	even	6		2205.2.a.z.1.1		2
84.23	even	6		315.2.j.c.226.2		4
84.59	odd	6		2205.2.a.ba.1.1		2
140.23	even	12		525.2.r.f.499.1		4
140.39	odd	6		3675.2.a.bg.1.1		2
140.59	even	6		3675.2.a.be.1.1		2
140.79	odd	6		525.2.i.f.226.2		4
140.107	even	12		525.2.r.a.499.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.d.16.1	✓	4	28.23	odd	6
105.2.i.d.46.1	yes	4	4.3	odd	2
315.2.j.c.46.2		4	12.11	even	2
315.2.j.c.226.2		4	84.23	even	6
525.2.i.f.151.2		4	20.19	odd	2
525.2.i.f.226.2		4	140.79	odd	6
525.2.r.a.424.2		4	20.3	even	4
525.2.r.a.499.2		4	140.107	even	12
525.2.r.f.424.1		4	20.7	even	4
525.2.r.f.499.1		4	140.23	even	12
735.2.a.g.1.2		2	28.11	odd	6
735.2.a.h.1.2		2	28.3	even	6
735.2.i.l.226.1		4	28.19	even	6
735.2.i.l.361.1		4	28.27	even	2
1680.2.bg.o.961.2		4	7.2	even	3	inner
1680.2.bg.o.1201.2		4	1.1	even	1	trivial
2205.2.a.z.1.1		2	84.11	even	6
2205.2.a.ba.1.1		2	84.59	odd	6
3675.2.a.be.1.1		2	140.59	even	6
3675.2.a.bg.1.1		2	140.39	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:	\( N \)	\(=\)	\( 1680 = 2^{4} \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1680.bg (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{5} +(0.866025 - 2.50000i) q^{7} +(-0.500000 - 0.866025i) q^{9} +(-1.36603 + 2.36603i) q^{11} +5.73205 q^{13} +1.00000 q^{15} +(-3.36603 + 5.83013i) q^{17} +(-1.23205 - 2.13397i) q^{19} +(1.73205 + 2.00000i) q^{21} +(-0.633975 - 1.09808i) q^{23} +(-0.500000 + 0.866025i) q^{25} +1.00000 q^{27} +6.19615 q^{29} +(3.23205 - 5.59808i) q^{31} +(-1.36603 - 2.36603i) q^{33} +(-2.59808 + 0.500000i) q^{35} +(-3.59808 - 6.23205i) q^{37} +(-2.86603 + 4.96410i) q^{39} +2.73205 q^{41} +7.19615 q^{43} +(-0.500000 + 0.866025i) q^{45} +(1.00000 + 1.73205i) q^{47} +(-5.50000 - 4.33013i) q^{49} +(-3.36603 - 5.83013i) q^{51} +(4.19615 - 7.26795i) q^{53} +2.73205 q^{55} +2.46410 q^{57} +(5.09808 - 8.83013i) q^{59} +(-2.00000 - 3.46410i) q^{61} +(-2.59808 + 0.500000i) q^{63} +(-2.86603 - 4.96410i) q^{65} +(1.33013 - 2.30385i) q^{67} +1.26795 q^{69} +4.19615 q^{71} +(2.33013 - 4.03590i) q^{73} +(-0.500000 - 0.866025i) q^{75} +(4.73205 + 5.46410i) q^{77} +(6.69615 + 11.5981i) q^{79} +(-0.500000 + 0.866025i) q^{81} +9.12436 q^{83} +6.73205 q^{85} +(-3.09808 + 5.36603i) q^{87} +(4.56218 + 7.90192i) q^{89} +(4.96410 - 14.3301i) q^{91} +(3.23205 + 5.59808i) q^{93} +(-1.23205 + 2.13397i) q^{95} +1.07180 q^{97} +2.73205 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{5} - 2 q^{9} - 2 q^{11} + 16 q^{13} + 4 q^{15} - 10 q^{17} + 2 q^{19} - 6 q^{23} - 2 q^{25} + 4 q^{27} + 4 q^{29} + 6 q^{31} - 2 q^{33} - 4 q^{37} - 8 q^{39} + 4 q^{41} + 8 q^{43} - 2 q^{45} + 4 q^{47} - 22 q^{49} - 10 q^{51} - 4 q^{53} + 4 q^{55} - 4 q^{57} + 10 q^{59} - 8 q^{61} - 8 q^{65} - 12 q^{67} + 12 q^{69} - 4 q^{71} - 8 q^{73} - 2 q^{75} + 12 q^{77} + 6 q^{79} - 2 q^{81} - 12 q^{83} + 20 q^{85} - 2 q^{87} - 6 q^{89} + 6 q^{91} + 6 q^{93} + 2 q^{95} + 32 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^5 - 2 * q^9 - 2 * q^11 + 16 * q^13 + 4 * q^15 - 10 * q^17 + 2 * q^19 - 6 * q^23 - 2 * q^25 + 4 * q^27 + 4 * q^29 + 6 * q^31 - 2 * q^33 - 4 * q^37 - 8 * q^39 + 4 * q^41 + 8 * q^43 - 2 * q^45 + 4 * q^47 - 22 * q^49 - 10 * q^51 - 4 * q^53 + 4 * q^55 - 4 * q^57 + 10 * q^59 - 8 * q^61 - 8 * q^65 - 12 * q^67 + 12 * q^69 - 4 * q^71 - 8 * q^73 - 2 * q^75 + 12 * q^77 + 6 * q^79 - 2 * q^81 - 12 * q^83 + 20 * q^85 - 2 * q^87 - 6 * q^89 + 6 * q^91 + 6 * q^93 + 2 * q^95 + 32 * q^97 + 4 * q^99

Introduction

L-functions

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Database

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