LMFDB - Embedded newform 720.2.q.h.481.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(241,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 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("720.241");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.q (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:	$5.74922894553$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.h.241.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.86603 + 3.23205i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.86603 + 3.23205i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(2.73205 + 4.73205i) q^{11} +(-0.732051 + 1.26795i) q^{13} +(-0.866025 - 1.50000i) q^{15} +7.46410 q^{17} +2.00000 q^{19} +6.46410 q^{21} +(0.133975 - 0.232051i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.19615 q^{27} +(-4.23205 - 7.33013i) q^{29} +(-1.00000 + 1.73205i) q^{31} +9.46410 q^{33} +3.73205 q^{35} -10.3923 q^{37} +(1.26795 + 2.19615i) q^{39} +(1.96410 - 3.40192i) q^{41} +(-5.73205 - 9.92820i) q^{43} -3.00000 q^{45} +(1.86603 + 3.23205i) q^{47} +(-3.46410 + 6.00000i) q^{49} +(6.46410 - 11.1962i) q^{51} +6.00000 q^{53} +5.46410 q^{55} +(1.73205 - 3.00000i) q^{57} +(-3.19615 + 5.53590i) q^{59} +(0.767949 + 1.33013i) q^{61} +(5.59808 - 9.69615i) q^{63} +(0.732051 + 1.26795i) q^{65} +(4.86603 - 8.42820i) q^{67} +(-0.232051 - 0.401924i) q^{69} -2.53590 q^{71} -6.92820 q^{73} -1.73205 q^{75} +(-10.1962 + 17.6603i) q^{77} +(4.26795 + 7.39230i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.40192 - 2.42820i) q^{83} +(3.73205 - 6.46410i) q^{85} -14.6603 q^{87} +3.92820 q^{89} -5.46410 q^{91} +(1.73205 + 3.00000i) q^{93} +(1.00000 - 1.73205i) q^{95} +(-2.46410 - 4.26795i) q^{97} +(8.19615 - 14.1962i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q + 2 * q^5 + 4 * q^7 - 6 * q^9	$ 4 q + 2 q^{5} + 4 q^{7} - 6 q^{9} + 4 q^{11} + 4 q^{13} + 16 q^{17} + 8 q^{19} + 12 q^{21} + 4 q^{23} - 2 q^{25} - 10 q^{29} - 4 q^{31} + 24 q^{33} + 8 q^{35} + 12 q^{39} - 6 q^{41} - 16 q^{43} - 12 q^{45} + 4 q^{47} + 12 q^{51} + 24 q^{53} + 8 q^{55} + 8 q^{59} + 10 q^{61} + 12 q^{63} - 4 q^{65} + 16 q^{67} + 6 q^{69} - 24 q^{71} - 20 q^{77} + 24 q^{79} - 18 q^{81} - 16 q^{83} + 8 q^{85} - 24 q^{87} - 12 q^{89} - 8 q^{91} + 4 q^{95} + 4 q^{97} + 12 q^{99}+O(q^{100}) $ 4 * q + 2 * q^5 + 4 * q^7 - 6 * q^9 + 4 * q^11 + 4 * q^13 + 16 * q^17 + 8 * q^19 + 12 * q^21 + 4 * q^23 - 2 * q^25 - 10 * q^29 - 4 * q^31 + 24 * q^33 + 8 * q^35 + 12 * q^39 - 6 * q^41 - 16 * q^43 - 12 * q^45 + 4 * q^47 + 12 * q^51 + 24 * q^53 + 8 * q^55 + 8 * q^59 + 10 * q^61 + 12 * q^63 - 4 * q^65 + 16 * q^67 + 6 * q^69 - 24 * q^71 - 20 * q^77 + 24 * q^79 - 18 * q^81 - 16 * q^83 + 8 * q^85 - 24 * q^87 - 12 * q^89 - 8 * q^91 + 4 * q^95 + 4 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$		0			0
$7$	1.86603	+	3.23205i	0.705291	+	1.22160i	0.966586	+	0.256341i	$0.0825171\pi$
$7$	1.86603	+	3.23205i	0.705291	+	1.22160i	−0.261295	+	0.965259i	$0.584150\pi$
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	2.73205	+	4.73205i	0.823744	+	1.42677i	0.902875	+	0.429903i	$0.141452\pi$
$11$	2.73205	+	4.73205i	0.823744	+	1.42677i	−0.0791309	+	0.996864i	$0.525215\pi$
$12$		0			0
$13$	−0.732051	+	1.26795i	−0.203034	+	0.351666i	−0.949505	−	0.313753i	$-0.898414\pi$
$13$	−0.732051	+	1.26795i	−0.203034	+	0.351666i	0.746470	+	0.665419i	$0.231747\pi$
$14$		0			0
$15$	−0.866025	−	1.50000i	−0.223607	−	0.387298i
$16$		0			0
$17$	7.46410			1.81031			0.905155	−	0.425081i	$-0.139754\pi$
$17$	7.46410			1.81031			0.905155	+	0.425081i	$0.139754\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$		0			0
$21$	6.46410			1.41058
$22$		0			0
$23$	0.133975	−	0.232051i	0.0279356	−	0.0483859i	−0.851720	−	0.523998i	$-0.824440\pi$
$23$	0.133975	−	0.232051i	0.0279356	−	0.0483859i	0.879655	+	0.475612i	$0.157773\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$	−4.23205	−	7.33013i	−0.785872	−	1.36117i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−4.23205	−	7.33013i	−0.785872	−	1.36117i	0.142605	−	0.989780i	$-0.454452\pi$
$30$		0			0
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$		0			0
$33$	9.46410			1.64749
$34$		0			0
$35$	3.73205			0.630832
$36$		0			0
$37$	−10.3923			−1.70848			−0.854242	−	0.519875i	$-0.825978\pi$
$37$	−10.3923			−1.70848			−0.854242	+	0.519875i	$0.825978\pi$
$38$		0			0
$39$	1.26795	+	2.19615i	0.203034	+	0.351666i
$40$		0			0
$41$	1.96410	−	3.40192i	0.306741	−	0.531291i	−0.670906	−	0.741542i	$-0.734095\pi$
$41$	1.96410	−	3.40192i	0.306741	−	0.531291i	0.977647	+	0.210251i	$0.0674281\pi$
$42$		0			0
$43$	−5.73205	−	9.92820i	−0.874130	−	1.51404i	−0.857687	−	0.514172i	$-0.828099\pi$
$43$	−5.73205	−	9.92820i	−0.874130	−	1.51404i	−0.0164424	−	0.999865i	$-0.505234\pi$
$44$		0			0
$45$	−3.00000			−0.447214
$46$		0			0
$47$	1.86603	+	3.23205i	0.272188	+	0.471443i	0.969422	−	0.245401i	$-0.0789195\pi$
$47$	1.86603	+	3.23205i	0.272188	+	0.471443i	−0.697234	+	0.716844i	$0.745586\pi$
$48$		0			0
$49$	−3.46410	+	6.00000i	−0.494872	+	0.857143i
$50$		0			0
$51$	6.46410	−	11.1962i	0.905155	−	1.56777i
$52$		0			0
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	5.46410			0.736779
$56$		0			0
$57$	1.73205	−	3.00000i	0.229416	−	0.397360i
$58$		0			0
$59$	−3.19615	+	5.53590i	−0.416104	+	0.720713i	−0.995544	−	0.0943023i	$-0.969938\pi$
$59$	−3.19615	+	5.53590i	−0.416104	+	0.720713i	0.579440	+	0.815015i	$0.303271\pi$
$60$		0			0
$61$	0.767949	+	1.33013i	0.0983258	+	0.170305i	0.910992	−	0.412424i	$-0.135318\pi$
$61$	0.767949	+	1.33013i	0.0983258	+	0.170305i	−0.812666	+	0.582730i	$0.801985\pi$
$62$		0			0
$63$	5.59808	−	9.69615i	0.705291	−	1.22160i
$64$		0			0
$65$	0.732051	+	1.26795i	0.0907997	+	0.157270i
$66$		0			0
$67$	4.86603	−	8.42820i	0.594480	−	1.02967i	−0.399140	−	0.916890i	$-0.630691\pi$
$67$	4.86603	−	8.42820i	0.594480	−	1.02967i	0.993620	−	0.112779i	$-0.0359752\pi$
$68$		0			0
$69$	−0.232051	−	0.401924i	−0.0279356	−	0.0483859i
$70$		0			0
$71$	−2.53590			−0.300956			−0.150478	−	0.988613i	$-0.548081\pi$
$71$	−2.53590			−0.300956			−0.150478	+	0.988613i	$0.548081\pi$
$72$		0			0
$73$	−6.92820			−0.810885			−0.405442	−	0.914121i	$-0.632883\pi$
$73$	−6.92820			−0.810885			−0.405442	+	0.914121i	$0.632883\pi$
$74$		0			0
$75$	−1.73205			−0.200000
$76$		0			0
$77$	−10.1962	+	17.6603i	−1.16196	+	2.01257i
$78$		0			0
$79$	4.26795	+	7.39230i	0.480182	+	0.831699i	0.999742	−	0.0227349i	$-0.00723735\pi$
$79$	4.26795	+	7.39230i	0.480182	+	0.831699i	−0.519560	+	0.854434i	$0.673904\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−1.40192	−	2.42820i	−0.153881	−	0.266530i	0.778770	−	0.627310i	$-0.215844\pi$
$83$	−1.40192	−	2.42820i	−0.153881	−	0.266530i	−0.932651	+	0.360780i	$0.882511\pi$
$84$		0			0
$85$	3.73205	−	6.46410i	0.404798	−	0.701130i
$86$		0			0
$87$	−14.6603			−1.57174
$88$		0			0
$89$	3.92820			0.416389			0.208194	−	0.978087i	$-0.433241\pi$
$89$	3.92820			0.416389			0.208194	+	0.978087i	$0.433241\pi$
$90$		0			0
$91$	−5.46410			−0.572793
$92$		0			0
$93$	1.73205	+	3.00000i	0.179605	+	0.311086i
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	−2.46410	−	4.26795i	−0.250192	−	0.433345i	0.713387	−	0.700770i	$-0.247160\pi$
$97$	−2.46410	−	4.26795i	−0.250192	−	0.433345i	−0.963578	+	0.267426i	$0.913827\pi$
$98$		0			0
$99$	8.19615	−	14.1962i	0.823744	−	1.42677i
$100$		0			0
$101$	6.46410	+	11.1962i	0.643202	+	1.11406i	0.984714	+	0.174181i	$0.0557278\pi$
$101$	6.46410	+	11.1962i	0.643202	+	1.11406i	−0.341511	+	0.939878i	$0.610939\pi$
$102$		0			0
$103$	−3.19615	+	5.53590i	−0.314926	+	0.545468i	−0.979422	−	0.201824i	$-0.935313\pi$
$103$	−3.19615	+	5.53590i	−0.314926	+	0.545468i	0.664496	+	0.747292i	$0.268646\pi$
$104$		0			0
$105$	3.23205	−	5.59808i	0.315416	−	0.546316i
$106$		0			0
$107$	5.19615			0.502331			0.251166	−	0.967944i	$-0.419186\pi$
$107$	5.19615			0.502331			0.251166	+	0.967944i	$0.419186\pi$
$108$		0			0
$109$	3.39230			0.324924			0.162462	−	0.986715i	$-0.448057\pi$
$109$	3.39230			0.324924			0.162462	+	0.986715i	$0.448057\pi$
$110$		0			0
$111$	−9.00000	+	15.5885i	−0.854242	+	1.47959i
$112$		0			0
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	−0.330947	−	0.943649i	$-0.607368\pi$
$113$	6.92820	−	12.0000i	0.651751	−	1.12887i	0.982698	−	0.185216i	$-0.0592984\pi$
$114$		0			0
$115$	−0.133975	−	0.232051i	−0.0124932	−	0.0216388i
$116$		0			0
$117$	4.39230			0.406069
$118$		0			0
$119$	13.9282	+	24.1244i	1.27680	+	2.21148i
$120$		0			0
$121$	−9.42820	+	16.3301i	−0.857109	+	1.48456i
$122$		0			0
$123$	−3.40192	−	5.89230i	−0.306741	−	0.531291i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−19.7321			−1.75094			−0.875468	−	0.483276i	$-0.839447\pi$
$127$	−19.7321			−1.75094			−0.875468	+	0.483276i	$0.839447\pi$
$128$		0			0
$129$	−19.8564			−1.74826
$130$		0			0
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	−0.780387	−	0.625297i	$-0.784978\pi$
$131$	1.73205	−	3.00000i	0.151330	−	0.262111i	0.931717	+	0.363186i	$0.118311\pi$
$132$		0			0
$133$	3.73205	+	6.46410i	0.323610	+	0.560509i
$134$		0			0
$135$	−2.59808	+	4.50000i	−0.223607	+	0.387298i
$136$		0			0
$137$	2.92820	+	5.07180i	0.250173	+	0.433313i	0.963573	−	0.267444i	$-0.0861791\pi$
$137$	2.92820	+	5.07180i	0.250173	+	0.433313i	−0.713400	+	0.700757i	$0.752846\pi$
$138$		0			0
$139$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$139$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$140$		0			0
$141$	6.46410			0.544376
$142$		0			0
$143$	−8.00000			−0.668994
$144$		0			0
$145$	−8.46410			−0.702905
$146$		0			0
$147$	6.00000	+	10.3923i	0.494872	+	0.857143i
$148$		0			0
$149$	−2.23205	+	3.86603i	−0.182857	+	0.316717i	−0.942852	−	0.333211i	$-0.891868\pi$
$149$	−2.23205	+	3.86603i	−0.182857	+	0.316717i	0.759995	+	0.649928i	$0.225201\pi$
$150$		0			0
$151$	−0.732051	−	1.26795i	−0.0595734	−	0.103184i	0.834701	−	0.550704i	$-0.185641\pi$
$151$	−0.732051	−	1.26795i	−0.0595734	−	0.103184i	−0.894274	+	0.447520i	$0.852307\pi$
$152$		0			0
$153$	−11.1962	−	19.3923i	−0.905155	−	1.56777i
$154$		0			0
$155$	1.00000	+	1.73205i	0.0803219	+	0.139122i
$156$		0			0
$157$	4.46410	−	7.73205i	0.356274	−	0.617085i	−0.631061	−	0.775733i	$-0.717380\pi$
$157$	4.46410	−	7.73205i	0.356274	−	0.617085i	0.987335	+	0.158648i	$0.0507136\pi$
$158$		0			0
$159$	5.19615	−	9.00000i	0.412082	−	0.713746i
$160$		0			0
$161$	1.00000			0.0788110
$162$		0			0
$163$	−21.3205			−1.66995			−0.834976	−	0.550287i	$-0.814518\pi$
$163$	−21.3205			−1.66995			−0.834976	+	0.550287i	$0.814518\pi$
$164$		0			0
$165$	4.73205	−	8.19615i	0.368390	−	0.638070i
$166$		0			0
$167$	4.79423	−	8.30385i	0.370989	−	0.642571i	−0.618729	−	0.785604i	$-0.712352\pi$
$167$	4.79423	−	8.30385i	0.370989	−	0.642571i	0.989718	+	0.143033i	$0.0456856\pi$
$168$		0			0
$169$	5.42820	+	9.40192i	0.417554	+	0.723225i
$170$		0			0
$171$	−3.00000	−	5.19615i	−0.229416	−	0.397360i
$172$		0			0
$173$	−11.4641	−	19.8564i	−0.871600	−	1.50965i	−0.860342	−	0.509718i	$-0.829750\pi$
$173$	−11.4641	−	19.8564i	−0.871600	−	1.50965i	−0.0112580	−	0.999937i	$-0.503584\pi$
$174$		0			0
$175$	1.86603	−	3.23205i	0.141058	−	0.244320i
$176$		0			0
$177$	5.53590	+	9.58846i	0.416104	+	0.720713i
$178$		0			0
$179$	−6.53590			−0.488516			−0.244258	−	0.969710i	$-0.578544\pi$
$179$	−6.53590			−0.488516			−0.244258	+	0.969710i	$0.578544\pi$
$180$		0			0
$181$	−16.4641			−1.22377			−0.611884	−	0.790948i	$-0.709588\pi$
$181$	−16.4641			−1.22377			−0.611884	+	0.790948i	$0.709588\pi$
$182$		0			0
$183$	2.66025			0.196652
$184$		0			0
$185$	−5.19615	+	9.00000i	−0.382029	+	0.661693i
$186$		0			0
$187$	20.3923	+	35.3205i	1.49123	+	2.58289i
$188$		0			0
$189$	−9.69615	−	16.7942i	−0.705291	−	1.22160i
$190$		0			0
$191$	1.53590	+	2.66025i	0.111134	+	0.192489i	0.916228	−	0.400658i	$-0.131218\pi$
$191$	1.53590	+	2.66025i	0.111134	+	0.192489i	−0.805094	+	0.593147i	$0.797885\pi$
$192$		0			0
$193$	5.26795	−	9.12436i	0.379195	−	0.656785i	−0.611750	−	0.791051i	$-0.709534\pi$
$193$	5.26795	−	9.12436i	0.379195	−	0.656785i	0.990945	+	0.134266i	$0.0428675\pi$
$194$		0			0
$195$	2.53590			0.181599
$196$		0			0
$197$	1.07180			0.0763624			0.0381812	−	0.999271i	$-0.487844\pi$
$197$	1.07180			0.0763624			0.0381812	+	0.999271i	$0.487844\pi$
$198$		0			0
$199$	−20.9282			−1.48356			−0.741780	−	0.670643i	$-0.766018\pi$
$199$	−20.9282			−1.48356			−0.741780	+	0.670643i	$0.766018\pi$
$200$		0			0
$201$	−8.42820	−	14.5981i	−0.594480	−	1.02967i
$202$		0			0
$203$	15.7942	−	27.3564i	1.10854	−	1.92004i
$204$		0			0
$205$	−1.96410	−	3.40192i	−0.137179	−	0.237601i
$206$		0			0
$207$	−0.803848			−0.0558713
$208$		0			0
$209$	5.46410	+	9.46410i	0.377960	+	0.654646i
$210$		0			0
$211$	−10.1962	+	17.6603i	−0.701932	+	1.21578i	0.265855	+	0.964013i	$0.414346\pi$
$211$	−10.1962	+	17.6603i	−0.701932	+	1.21578i	−0.967787	+	0.251769i	$0.918988\pi$
$212$		0			0
$213$	−2.19615	+	3.80385i	−0.150478	+	0.260635i
$214$		0			0
$215$	−11.4641			−0.781845
$216$		0			0
$217$	−7.46410			−0.506696
$218$		0			0
$219$	−6.00000	+	10.3923i	−0.405442	+	0.702247i
$220$		0			0
$221$	−5.46410	+	9.46410i	−0.367555	+	0.636624i
$222$		0			0
$223$	2.66987	+	4.62436i	0.178788	+	0.309670i	0.941466	−	0.337109i	$-0.109449\pi$
$223$	2.66987	+	4.62436i	0.178788	+	0.309670i	−0.762678	+	0.646779i	$0.776116\pi$
$224$		0			0
$225$	−1.50000	+	2.59808i	−0.100000	+	0.173205i
$226$		0			0
$227$	−12.1244	−	21.0000i	−0.804722	−	1.39382i	−0.916479	−	0.400083i	$-0.868981\pi$
$227$	−12.1244	−	21.0000i	−0.804722	−	1.39382i	0.111757	−	0.993736i	$-0.464352\pi$
$228$		0			0
$229$	11.6244	−	20.1340i	0.768159	−	1.33049i	−0.170401	−	0.985375i	$-0.554506\pi$
$229$	11.6244	−	20.1340i	0.768159	−	1.33049i	0.938560	−	0.345116i	$-0.112160\pi$
$230$		0			0
$231$	17.6603	+	30.5885i	1.16196	+	2.01257i
$232$		0			0
$233$	10.3923			0.680823			0.340411	−	0.940277i	$-0.389434\pi$
$233$	10.3923			0.680823			0.340411	+	0.940277i	$0.389434\pi$
$234$		0			0
$235$	3.73205			0.243452
$236$		0			0
$237$	14.7846			0.960364
$238$		0			0
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	0.305050	+	0.952336i	$0.401327\pi$
$239$	−10.3923	+	18.0000i	−0.672222	+	1.16432i	−0.977273	+	0.211987i	$0.932007\pi$
$240$		0			0
$241$	9.96410	+	17.2583i	0.641844	+	1.11171i	0.985021	+	0.172436i	$0.0551638\pi$
$241$	9.96410	+	17.2583i	0.641844	+	1.11171i	−0.343177	+	0.939271i	$0.611503\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	3.46410	+	6.00000i	0.221313	+	0.383326i
$246$		0			0
$247$	−1.46410	+	2.53590i	−0.0931586	+	0.161355i
$248$		0			0
$249$	−4.85641			−0.307762
$250$		0			0
$251$	−19.8564			−1.25333			−0.626663	−	0.779291i	$-0.715580\pi$
$251$	−19.8564			−1.25333			−0.626663	+	0.779291i	$0.715580\pi$
$252$		0			0
$253$	1.46410			0.0920473
$254$		0			0
$255$	−6.46410	−	11.1962i	−0.404798	−	0.701130i
$256$		0			0
$257$	−6.46410	+	11.1962i	−0.403220	+	0.698397i	−0.994112	−	0.108353i	$-0.965442\pi$
$257$	−6.46410	+	11.1962i	−0.403220	+	0.698397i	0.590893	+	0.806750i	$0.298776\pi$
$258$		0			0
$259$	−19.3923	−	33.5885i	−1.20498	−	2.08709i
$260$		0			0
$261$	−12.6962	+	21.9904i	−0.785872	+	1.36117i
$262$		0			0
$263$	0.803848	+	1.39230i	0.0495674	+	0.0858532i	0.889745	−	0.456459i	$-0.150882\pi$
$263$	0.803848	+	1.39230i	0.0495674	+	0.0858532i	−0.840177	+	0.542312i	$0.817549\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$		0			0
$267$	3.40192	−	5.89230i	0.208194	−	0.360603i
$268$		0			0
$269$	−9.39230			−0.572659			−0.286329	−	0.958131i	$-0.592435\pi$
$269$	−9.39230			−0.572659			−0.286329	+	0.958131i	$0.592435\pi$
$270$		0			0
$271$	−7.85641			−0.477243			−0.238621	−	0.971113i	$-0.576695\pi$
$271$	−7.85641			−0.477243			−0.238621	+	0.971113i	$0.576695\pi$
$272$		0			0
$273$	−4.73205	+	8.19615i	−0.286397	+	0.496054i
$274$		0			0
$275$	2.73205	−	4.73205i	0.164749	−	0.285353i
$276$		0			0
$277$	−3.19615	−	5.53590i	−0.192038	−	0.332620i	0.753887	−	0.657004i	$-0.228176\pi$
$277$	−3.19615	−	5.53590i	−0.192038	−	0.332620i	−0.945926	+	0.324384i	$0.894843\pi$
$278$		0			0
$279$	6.00000			0.359211
$280$		0			0
$281$	−6.42820	−	11.1340i	−0.383474	−	0.664197i	0.608082	−	0.793874i	$-0.291939\pi$
$281$	−6.42820	−	11.1340i	−0.383474	−	0.664197i	−0.991556	+	0.129677i	$0.958606\pi$
$282$		0			0
$283$	9.13397	−	15.8205i	0.542958	−	0.940432i	−0.455774	−	0.890096i	$-0.650637\pi$
$283$	9.13397	−	15.8205i	0.542958	−	0.940432i	0.998732	−	0.0503360i	$-0.0160292\pi$
$284$		0			0
$285$	−1.73205	−	3.00000i	−0.102598	−	0.177705i
$286$		0			0
$287$	14.6603			0.865367
$288$		0			0
$289$	38.7128			2.27722
$290$		0			0
$291$	−8.53590			−0.500383
$292$		0			0
$293$	0.267949	−	0.464102i	0.0156538	−	0.0271131i	−0.858092	−	0.513495i	$-0.828350\pi$
$293$	0.267949	−	0.464102i	0.0156538	−	0.0271131i	0.873746	+	0.486382i	$0.161684\pi$
$294$		0			0
$295$	3.19615	+	5.53590i	0.186087	+	0.322312i
$296$		0			0
$297$	−14.1962	−	24.5885i	−0.823744	−	1.42677i
$298$		0			0
$299$	0.196152	+	0.339746i	0.0113438	+	0.0196480i
$300$		0			0
$301$	21.3923	−	37.0526i	1.23303	−	2.13567i
$302$		0			0
$303$	22.3923			1.28640
$304$		0			0
$305$	1.53590			0.0879453
$306$		0			0
$307$	20.1244			1.14856			0.574279	−	0.818660i	$-0.305283\pi$
$307$	20.1244			1.14856			0.574279	+	0.818660i	$0.305283\pi$
$308$		0			0
$309$	5.53590	+	9.58846i	0.314926	+	0.545468i
$310$		0			0
$311$	8.46410	−	14.6603i	0.479955	−	0.831307i	−0.519780	−	0.854300i	$-0.673986\pi$
$311$	8.46410	−	14.6603i	0.479955	−	0.831307i	0.999736	+	0.0229931i	$0.00731959\pi$
$312$		0			0
$313$	4.19615	+	7.26795i	0.237181	+	0.410809i	0.959904	−	0.280328i	$-0.0904434\pi$
$313$	4.19615	+	7.26795i	0.237181	+	0.410809i	−0.722724	+	0.691137i	$0.757110\pi$
$314$		0			0
$315$	−5.59808	−	9.69615i	−0.315416	−	0.546316i
$316$		0			0
$317$	−4.73205	−	8.19615i	−0.265778	−	0.460342i	0.701989	−	0.712188i	$-0.252296\pi$
$317$	−4.73205	−	8.19615i	−0.265778	−	0.460342i	−0.967767	+	0.251846i	$0.918962\pi$
$318$		0			0
$319$	23.1244	−	40.0526i	1.29472	−	2.24251i
$320$		0			0
$321$	4.50000	−	7.79423i	0.251166	−	0.435031i
$322$		0			0
$323$	14.9282			0.830627
$324$		0			0
$325$	1.46410			0.0812137
$326$		0			0
$327$	2.93782	−	5.08846i	0.162462	−	0.281392i
$328$		0			0
$329$	−6.96410	+	12.0622i	−0.383943	+	0.665009i
$330$		0			0
$331$	1.73205	+	3.00000i	0.0952021	+	0.164895i	0.909693	−	0.415282i	$-0.136317\pi$
$331$	1.73205	+	3.00000i	0.0952021	+	0.164895i	−0.814491	+	0.580176i	$0.802984\pi$
$332$		0			0
$333$	15.5885	+	27.0000i	0.854242	+	1.47959i
$334$		0			0
$335$	−4.86603	−	8.42820i	−0.265859	−	0.460482i
$336$		0			0
$337$	−11.4641	+	19.8564i	−0.624489	+	1.08165i	0.364150	+	0.931340i	$0.381360\pi$
$337$	−11.4641	+	19.8564i	−0.624489	+	1.08165i	−0.988639	+	0.150307i	$0.951974\pi$
$338$		0			0
$339$	−12.0000	−	20.7846i	−0.651751	−	1.12887i
$340$		0			0
$341$	−10.9282			−0.591795
$342$		0			0
$343$	0.267949			0.0144679
$344$		0			0
$345$	−0.464102			−0.0249864
$346$		0			0
$347$	1.19615	−	2.07180i	0.0642128	−	0.111220i	−0.832132	−	0.554578i	$-0.812880\pi$
$347$	1.19615	−	2.07180i	0.0642128	−	0.111220i	0.896345	+	0.443358i	$0.146213\pi$
$348$		0			0
$349$	3.23205	+	5.59808i	0.173008	+	0.299658i	0.939470	−	0.342631i	$-0.111318\pi$
$349$	3.23205	+	5.59808i	0.173008	+	0.299658i	−0.766462	+	0.642289i	$0.777985\pi$
$350$		0			0
$351$	3.80385	−	6.58846i	0.203034	−	0.351666i
$352$		0			0
$353$	−2.92820	−	5.07180i	−0.155853	−	0.269945i	0.777517	−	0.628862i	$-0.216479\pi$
$353$	−2.92820	−	5.07180i	−0.155853	−	0.269945i	−0.933369	+	0.358918i	$0.883146\pi$
$354$		0			0
$355$	−1.26795	+	2.19615i	−0.0672958	+	0.116560i
$356$		0			0
$357$	48.2487			2.55359
$358$		0			0
$359$	−0.928203			−0.0489887			−0.0244943	−	0.999700i	$-0.507798\pi$
$359$	−0.928203			−0.0489887			−0.0244943	+	0.999700i	$0.507798\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$		0			0
$363$	16.3301	+	28.2846i	0.857109	+	1.48456i
$364$		0			0
$365$	−3.46410	+	6.00000i	−0.181319	+	0.314054i
$366$		0			0
$367$	3.19615	+	5.53590i	0.166838	+	0.288972i	0.937306	−	0.348506i	$-0.113311\pi$
$367$	3.19615	+	5.53590i	0.166838	+	0.288972i	−0.770469	+	0.637478i	$0.779978\pi$
$368$		0			0
$369$	−11.7846			−0.613482
$370$		0			0
$371$	11.1962	+	19.3923i	0.581275	+	1.00680i
$372$		0			0
$373$	−2.46410	+	4.26795i	−0.127586	+	0.220986i	−0.922741	−	0.385421i	$-0.874056\pi$
$373$	−2.46410	+	4.26795i	−0.127586	+	0.220986i	0.795155	+	0.606407i	$0.207390\pi$
$374$		0			0
$375$	−0.866025	+	1.50000i	−0.0447214	+	0.0774597i
$376$		0			0
$377$	12.3923			0.638236
$378$		0			0
$379$	27.1769			1.39598			0.697992	−	0.716105i	$-0.254077\pi$
$379$	27.1769			1.39598			0.697992	+	0.716105i	$0.254077\pi$
$380$		0			0
$381$	−17.0885	+	29.5981i	−0.875468	+	1.51636i
$382$		0			0
$383$	−1.73205	+	3.00000i	−0.0885037	+	0.153293i	−0.906879	−	0.421392i	$-0.861542\pi$
$383$	−1.73205	+	3.00000i	−0.0885037	+	0.153293i	0.818375	+	0.574684i	$0.194875\pi$
$384$		0			0
$385$	10.1962	+	17.6603i	0.519644	+	0.900050i
$386$		0			0
$387$	−17.1962	+	29.7846i	−0.874130	+	1.51404i
$388$		0			0
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	0.936302	+	0.351196i	$0.114225\pi$
$389$	15.2321	+	26.3827i	0.772296	+	1.33766i	−0.164006	+	0.986459i	$0.552442\pi$
$390$		0			0
$391$	1.00000	−	1.73205i	0.0505722	−	0.0875936i
$392$		0			0
$393$	−3.00000	−	5.19615i	−0.151330	−	0.262111i
$394$		0			0
$395$	8.53590			0.429488
$396$		0			0
$397$	10.0000			0.501886			0.250943	−	0.968002i	$-0.419259\pi$
$397$	10.0000			0.501886			0.250943	+	0.968002i	$0.419259\pi$
$398$		0			0
$399$	12.9282			0.647220
$400$		0			0
$401$	13.3923	−	23.1962i	0.668780	−	1.15836i	−0.309466	−	0.950911i	$-0.600150\pi$
$401$	13.3923	−	23.1962i	0.668780	−	1.15836i	0.978246	−	0.207450i	$-0.0665164\pi$
$402$		0			0
$403$	−1.46410	−	2.53590i	−0.0729321	−	0.126322i
$404$		0			0
$405$	4.50000	+	7.79423i	0.223607	+	0.387298i
$406$		0			0
$407$	−28.3923	−	49.1769i	−1.40735	−	2.43761i
$408$		0			0
$409$	4.46410	−	7.73205i	0.220736	−	0.382325i	−0.734296	−	0.678829i	$-0.762488\pi$
$409$	4.46410	−	7.73205i	0.220736	−	0.382325i	0.955032	+	0.296504i	$0.0958209\pi$
$410$		0			0
$411$	10.1436			0.500347
$412$		0			0
$413$	−23.8564			−1.17390
$414$		0			0
$415$	−2.80385			−0.137635
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−9.12436	+	15.8038i	−0.445754	+	0.772068i	−0.998104	−	0.0615435i	$-0.980398\pi$
$419$	−9.12436	+	15.8038i	−0.445754	+	0.772068i	0.552350	+	0.833612i	$0.313731\pi$
$420$		0			0
$421$	11.5359	+	19.9808i	0.562225	+	0.973803i	0.997302	+	0.0734093i	$0.0233880\pi$
$421$	11.5359	+	19.9808i	0.562225	+	0.973803i	−0.435077	+	0.900393i	$0.643279\pi$
$422$		0			0
$423$	5.59808	−	9.69615i	0.272188	−	0.471443i
$424$		0			0
$425$	−3.73205	−	6.46410i	−0.181031	−	0.313555i
$426$		0			0
$427$	−2.86603	+	4.96410i	−0.138697	+	0.240230i
$428$		0			0
$429$	−6.92820	+	12.0000i	−0.334497	+	0.579365i
$430$		0			0
$431$	11.4641			0.552206			0.276103	−	0.961128i	$-0.410957\pi$
$431$	11.4641			0.552206			0.276103	+	0.961128i	$0.410957\pi$
$432$		0			0
$433$	−19.4641			−0.935385			−0.467693	−	0.883891i	$-0.654915\pi$
$433$	−19.4641			−0.935385			−0.467693	+	0.883891i	$0.654915\pi$
$434$		0			0
$435$	−7.33013	+	12.6962i	−0.351453	+	0.608734i
$436$		0			0
$437$	0.267949	−	0.464102i	0.0128177	−	0.0222010i
$438$		0			0
$439$	17.4641	+	30.2487i	0.833516	+	1.44369i	0.895233	+	0.445599i	$0.147009\pi$
$439$	17.4641	+	30.2487i	0.833516	+	1.44369i	−0.0617168	+	0.998094i	$0.519658\pi$
$440$		0			0
$441$	20.7846			0.989743
$442$		0			0
$443$	−5.25833	−	9.10770i	−0.249831	−	0.432720i	0.713648	−	0.700505i	$-0.247042\pi$
$443$	−5.25833	−	9.10770i	−0.249831	−	0.432720i	−0.963479	+	0.267785i	$0.913708\pi$
$444$		0			0
$445$	1.96410	−	3.40192i	0.0931073	−	0.161267i
$446$		0			0
$447$	3.86603	+	6.69615i	0.182857	+	0.316717i
$448$		0			0
$449$	31.8564			1.50340			0.751698	−	0.659507i	$-0.229235\pi$
$449$	31.8564			1.50340			0.751698	+	0.659507i	$0.229235\pi$
$450$		0			0
$451$	21.4641			1.01071
$452$		0			0
$453$	−2.53590			−0.119147
$454$		0			0
$455$	−2.73205	+	4.73205i	−0.128081	+	0.221842i
$456$		0			0
$457$	−13.1962	−	22.8564i	−0.617290	−	1.06918i	−0.989978	−	0.141221i	$-0.954897\pi$
$457$	−13.1962	−	22.8564i	−0.617290	−	1.06918i	0.372688	−	0.927957i	$-0.378436\pi$
$458$		0			0
$459$	−38.7846			−1.81031
$460$		0			0
$461$	−12.6962	−	21.9904i	−0.591319	−	1.02419i	−0.994055	−	0.108878i	$-0.965274\pi$
$461$	−12.6962	−	21.9904i	−0.591319	−	1.02419i	0.402736	−	0.915316i	$-0.368059\pi$
$462$		0			0
$463$	1.73205	−	3.00000i	0.0804952	−	0.139422i	−0.822968	−	0.568088i	$-0.807683\pi$
$463$	1.73205	−	3.00000i	0.0804952	−	0.139422i	0.903463	+	0.428667i	$0.141016\pi$
$464$		0			0
$465$	3.46410			0.160644
$466$		0			0
$467$	9.60770			0.444591			0.222296	−	0.974979i	$-0.428645\pi$
$467$	9.60770			0.444591			0.222296	+	0.974979i	$0.428645\pi$
$468$		0			0
$469$	36.3205			1.67713
$470$		0			0
$471$	−7.73205	−	13.3923i	−0.356274	−	0.617085i
$472$		0			0
$473$	31.3205	−	54.2487i	1.44012	−	2.49436i
$474$		0			0
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$		0			0
$477$	−9.00000	−	15.5885i	−0.412082	−	0.713746i
$478$		0			0
$479$	3.19615	+	5.53590i	0.146036	+	0.252942i	0.929759	−	0.368169i	$-0.120015\pi$
$479$	3.19615	+	5.53590i	0.146036	+	0.252942i	−0.783723	+	0.621110i	$0.786682\pi$
$480$		0			0
$481$	7.60770	−	13.1769i	0.346881	−	0.600816i
$482$		0			0
$483$	0.866025	−	1.50000i	0.0394055	−	0.0682524i
$484$		0			0
$485$	−4.92820			−0.223778
$486$		0			0
$487$	8.24871			0.373785			0.186892	−	0.982380i	$-0.440158\pi$
$487$	8.24871			0.373785			0.186892	+	0.982380i	$0.440158\pi$
$488$		0			0
$489$	−18.4641	+	31.9808i	−0.834976	+	1.44622i
$490$		0			0
$491$	0.928203	−	1.60770i	0.0418892	−	0.0725543i	−0.844321	−	0.535838i	$-0.819996\pi$
$491$	0.928203	−	1.60770i	0.0418892	−	0.0725543i	0.886210	+	0.463284i	$0.153329\pi$
$492$		0			0
$493$	−31.5885	−	54.7128i	−1.42267	−	2.46414i
$494$		0			0
$495$	−8.19615	−	14.1962i	−0.368390	−	0.638070i
$496$		0			0
$497$	−4.73205	−	8.19615i	−0.212261	−	0.367648i
$498$		0			0
$499$	4.92820	−	8.53590i	0.220617	−	0.382119i	−0.734379	−	0.678740i	$-0.762526\pi$
$499$	4.92820	−	8.53590i	0.220617	−	0.382119i	0.954995	+	0.296621i	$0.0958597\pi$
$500$		0			0
$501$	−8.30385	−	14.3827i	−0.370989	−	0.642571i
$502$		0			0
$503$	−6.12436			−0.273072			−0.136536	−	0.990635i	$-0.543597\pi$
$503$	−6.12436			−0.273072			−0.136536	+	0.990635i	$0.543597\pi$
$504$		0			0
$505$	12.9282			0.575297
$506$		0			0
$507$	18.8038			0.835108
$508$		0			0
$509$	20.6962	−	35.8468i	0.917341	−	1.58888i	0.113903	−	0.993492i	$-0.463665\pi$
$509$	20.6962	−	35.8468i	0.917341	−	1.58888i	0.803438	−	0.595389i	$-0.203002\pi$
$510$		0			0
$511$	−12.9282	−	22.3923i	−0.571910	−	0.990577i
$512$		0			0
$513$	−10.3923			−0.458831
$514$		0			0
$515$	3.19615	+	5.53590i	0.140839	+	0.243941i
$516$		0			0
$517$	−10.1962	+	17.6603i	−0.448426	+	0.776697i
$518$		0			0
$519$	−39.7128			−1.74320
$520$		0			0
$521$	−13.0000			−0.569540			−0.284770	−	0.958596i	$-0.591917\pi$
$521$	−13.0000			−0.569540			−0.284770	+	0.958596i	$0.591917\pi$
$522$		0			0
$523$	−21.1962			−0.926843			−0.463422	−	0.886138i	$-0.653378\pi$
$523$	−21.1962			−0.926843			−0.463422	+	0.886138i	$0.653378\pi$
$524$		0			0
$525$	−3.23205	−	5.59808i	−0.141058	−	0.244320i
$526$		0			0
$527$	−7.46410	+	12.9282i	−0.325141	+	0.563161i
$528$		0			0
$529$	11.4641	+	19.8564i	0.498439	+	0.863322i
$530$		0			0
$531$	19.1769			0.832207
$532$		0			0
$533$	2.87564	+	4.98076i	0.124558	+	0.215741i
$534$		0			0
$535$	2.59808	−	4.50000i	0.112325	−	0.194552i
$536$		0			0
$537$	−5.66025	+	9.80385i	−0.244258	+	0.423067i
$538$		0			0
$539$	−37.8564			−1.63059
$540$		0			0
$541$	−39.3923			−1.69361			−0.846804	−	0.531905i	$-0.821476\pi$
$541$	−39.3923			−1.69361			−0.846804	+	0.531905i	$0.821476\pi$
$542$		0			0
$543$	−14.2583	+	24.6962i	−0.611884	+	1.05981i
$544$		0			0
$545$	1.69615	−	2.93782i	0.0726552	−	0.125842i
$546$		0			0
$547$	−2.99038	−	5.17949i	−0.127859	−	0.221459i	0.794988	−	0.606626i	$-0.207477\pi$
$547$	−2.99038	−	5.17949i	−0.127859	−	0.221459i	−0.922847	+	0.385167i	$0.874144\pi$
$548$		0			0
$549$	2.30385	−	3.99038i	0.0983258	−	0.170305i
$550$		0			0
$551$	−8.46410	−	14.6603i	−0.360583	−	0.624548i
$552$		0			0
$553$	−15.9282	+	27.5885i	−0.677336	+	1.17318i
$554$		0			0
$555$	9.00000	+	15.5885i	0.382029	+	0.661693i
$556$		0			0
$557$	−36.6410			−1.55253			−0.776265	−	0.630407i	$-0.782888\pi$
$557$	−36.6410			−1.55253			−0.776265	+	0.630407i	$0.782888\pi$
$558$		0			0
$559$	16.7846			0.709913
$560$		0			0
$561$	70.6410			2.98247
$562$		0			0
$563$	−21.7942	+	37.7487i	−0.918517	+	1.59092i	−0.116849	+	0.993150i	$0.537279\pi$
$563$	−21.7942	+	37.7487i	−0.918517	+	1.59092i	−0.801669	+	0.597769i	$0.796054\pi$
$564$		0			0
$565$	−6.92820	−	12.0000i	−0.291472	−	0.504844i
$566$		0			0
$567$	−33.5885			−1.41058
$568$		0			0
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	0.741981	−	0.670421i	$-0.233886\pi$
$569$	−5.00000	−	8.66025i	−0.209611	−	0.363057i	−0.951592	+	0.307364i	$0.900553\pi$
$570$		0			0
$571$	0.392305	−	0.679492i	0.0164174	−	0.0284359i	−0.857700	−	0.514151i	$-0.828107\pi$
$571$	0.392305	−	0.679492i	0.0164174	−	0.0284359i	0.874117	+	0.485715i	$0.161441\pi$
$572$		0			0
$573$	5.32051			0.222267
$574$		0			0
$575$	−0.267949			−0.0111743
$576$		0			0
$577$	19.0718			0.793969			0.396985	−	0.917825i	$-0.370057\pi$
$577$	19.0718			0.793969			0.396985	+	0.917825i	$0.370057\pi$
$578$		0			0
$579$	−9.12436	−	15.8038i	−0.379195	−	0.656785i
$580$		0			0
$581$	5.23205	−	9.06218i	0.217062	−	0.375962i
$582$		0			0
$583$	16.3923	+	28.3923i	0.678900	+	1.17589i
$584$		0			0
$585$	2.19615	−	3.80385i	0.0907997	−	0.157270i
$586$		0			0
$587$	19.7942	+	34.2846i	0.816995	+	1.41508i	0.907886	+	0.419216i	$0.137695\pi$
$587$	19.7942	+	34.2846i	0.816995	+	1.41508i	−0.0908911	+	0.995861i	$0.528972\pi$
$588$		0			0
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$	0.928203	−	1.60770i	0.0381812	−	0.0661317i
$592$		0			0
$593$	−32.5359			−1.33609			−0.668045	−	0.744121i	$-0.732868\pi$
$593$	−32.5359			−1.33609			−0.668045	+	0.744121i	$0.732868\pi$
$594$		0			0
$595$	27.8564			1.14200
$596$		0			0
$597$	−18.1244	+	31.3923i	−0.741780	+	1.28480i
$598$		0			0
$599$	11.1962	−	19.3923i	0.457462	−	0.792348i	−0.541364	−	0.840789i	$-0.682092\pi$
$599$	11.1962	−	19.3923i	0.457462	−	0.792348i	0.998826	+	0.0484404i	$0.0154251\pi$
$600$		0			0
$601$	5.39230	+	9.33975i	0.219957	+	0.380976i	0.954794	−	0.297267i	$-0.0960751\pi$
$601$	5.39230	+	9.33975i	0.219957	+	0.380976i	−0.734838	+	0.678243i	$0.762742\pi$
$602$		0			0
$603$	−29.1962			−1.18896
$604$		0			0
$605$	9.42820	+	16.3301i	0.383311	+	0.663914i
$606$		0			0
$607$	21.8660	−	37.8731i	0.887515	−	1.53722i	0.0447105	−	0.999000i	$-0.485763\pi$
$607$	21.8660	−	37.8731i	0.887515	−	1.53722i	0.842804	−	0.538220i	$-0.180903\pi$
$608$		0			0
$609$	−27.3564	−	47.3827i	−1.10854	−	1.92004i
$610$		0			0
$611$	−5.46410			−0.221054
$612$		0			0
$613$	1.60770			0.0649342			0.0324671	−	0.999473i	$-0.489664\pi$
$613$	1.60770			0.0649342			0.0324671	+	0.999473i	$0.489664\pi$
$614$		0			0
$615$	−6.80385			−0.274358
$616$		0			0
$617$	−8.53590	+	14.7846i	−0.343642	+	0.595206i	−0.985106	−	0.171947i	$-0.944994\pi$
$617$	−8.53590	+	14.7846i	−0.343642	+	0.595206i	0.641464	+	0.767153i	$0.278327\pi$
$618$		0			0
$619$	8.85641	+	15.3397i	0.355969	+	0.616556i	0.987283	−	0.158971i	$-0.0508175\pi$
$619$	8.85641	+	15.3397i	0.355969	+	0.616556i	−0.631314	+	0.775527i	$0.717484\pi$
$620$		0			0
$621$	−0.696152	+	1.20577i	−0.0279356	+	0.0483859i
$622$		0			0
$623$	7.33013	+	12.6962i	0.293675	+	0.508661i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	18.9282			0.755920
$628$		0			0
$629$	−77.5692			−3.09289
$630$		0			0
$631$	23.7128			0.943992			0.471996	−	0.881601i	$-0.343534\pi$
$631$	23.7128			0.943992			0.471996	+	0.881601i	$0.343534\pi$
$632$		0			0
$633$	17.6603	+	30.5885i	0.701932	+	1.21578i
$634$		0			0
$635$	−9.86603	+	17.0885i	−0.391521	+	0.678135i
$636$		0			0
$637$	−5.07180	−	8.78461i	−0.200952	−	0.348059i
$638$		0			0
$639$	3.80385	+	6.58846i	0.150478	+	0.260635i
$640$		0			0
$641$	3.57180	+	6.18653i	0.141077	+	0.244353i	0.927903	−	0.372823i	$-0.121610\pi$
$641$	3.57180	+	6.18653i	0.141077	+	0.244353i	−0.786825	+	0.617176i	$0.788277\pi$
$642$		0			0
$643$	−18.8660	+	32.6769i	−0.744003	+	1.28865i	0.206656	+	0.978414i	$0.433742\pi$
$643$	−18.8660	+	32.6769i	−0.744003	+	1.28865i	−0.950659	+	0.310238i	$0.899591\pi$
$644$		0			0
$645$	−9.92820	+	17.1962i	−0.390923	+	0.677098i
$646$		0			0
$647$	−28.5167			−1.12111			−0.560553	−	0.828119i	$-0.689411\pi$
$647$	−28.5167			−1.12111			−0.560553	+	0.828119i	$0.689411\pi$
$648$		0			0
$649$	−34.9282			−1.37105
$650$		0			0
$651$	−6.46410	+	11.1962i	−0.253348	+	0.438812i
$652$		0			0
$653$	−12.2679	+	21.2487i	−0.480082	+	0.831526i	−0.999739	−	0.0228487i	$-0.992726\pi$
$653$	−12.2679	+	21.2487i	−0.480082	+	0.831526i	0.519657	+	0.854375i	$0.326060\pi$
$654$		0			0
$655$	−1.73205	−	3.00000i	−0.0676768	−	0.117220i
$656$		0			0
$657$	10.3923	+	18.0000i	0.405442	+	0.702247i
$658$		0			0
$659$	10.3923	+	18.0000i	0.404827	+	0.701180i	0.994301	−	0.106606i	$-0.0339985\pi$
$659$	10.3923	+	18.0000i	0.404827	+	0.701180i	−0.589475	+	0.807787i	$0.700665\pi$
$660$		0			0
$661$	16.8564	−	29.1962i	0.655638	−	1.13560i	−0.326095	−	0.945337i	$-0.605733\pi$
$661$	16.8564	−	29.1962i	0.655638	−	1.13560i	0.981733	−	0.190262i	$-0.0609337\pi$
$662$		0			0
$663$	9.46410	+	16.3923i	0.367555	+	0.636624i
$664$		0			0
$665$	7.46410			0.289445
$666$		0			0
$667$	−2.26795			−0.0878153
$668$		0			0
$669$	9.24871			0.357576
$670$		0			0
$671$	−4.19615	+	7.26795i	−0.161991	+	0.280576i
$672$		0			0
$673$	23.6603	+	40.9808i	0.912036	+	1.57969i	0.811184	+	0.584791i	$0.198823\pi$
$673$	23.6603	+	40.9808i	0.912036	+	1.57969i	0.100852	+	0.994901i	$0.467843\pi$
$674$		0			0
$675$	2.59808	+	4.50000i	0.100000	+	0.173205i
$676$		0			0
$677$	−22.5885	−	39.1244i	−0.868145	−	1.50367i	−0.863890	−	0.503680i	$-0.831979\pi$
$677$	−22.5885	−	39.1244i	−0.868145	−	1.50367i	−0.00425474	−	0.999991i	$-0.501354\pi$
$678$		0			0
$679$	9.19615	−	15.9282i	0.352916	−	0.611268i
$680$		0			0
$681$	−42.0000			−1.60944
$682$		0			0
$683$	−1.60770			−0.0615167			−0.0307584	−	0.999527i	$-0.509792\pi$
$683$	−1.60770			−0.0615167			−0.0307584	+	0.999527i	$0.509792\pi$
$684$		0			0
$685$	5.85641			0.223762
$686$		0			0
$687$	−20.1340	−	34.8731i	−0.768159	−	1.33049i
$688$		0			0
$689$	−4.39230	+	7.60770i	−0.167333	+	0.289830i
$690$		0			0
$691$	−14.8038	−	25.6410i	−0.563165	−	0.975430i	−0.997218	−	0.0745428i	$-0.976250\pi$
$691$	−14.8038	−	25.6410i	−0.563165	−	0.975430i	0.434053	−	0.900887i	$-0.357083\pi$
$692$		0			0
$693$	61.1769			2.32392
$694$		0			0
$695$		0			0
$696$		0			0
$697$	14.6603	−	25.3923i	0.555297	−	0.961802i
$698$		0			0
$699$	9.00000	−	15.5885i	0.340411	−	0.589610i
$700$		0			0
$701$	38.1769			1.44192			0.720961	−	0.692976i	$-0.243701\pi$
$701$	38.1769			1.44192			0.720961	+	0.692976i	$0.243701\pi$
$702$		0			0
$703$	−20.7846			−0.783906
$704$		0			0
$705$	3.23205	−	5.59808i	0.121726	−	0.210836i
$706$		0			0
$707$	−24.1244	+	41.7846i	−0.907290	+	1.57147i
$708$		0			0
$709$	2.69615	+	4.66987i	0.101256	+	0.175381i	0.912202	−	0.409740i	$-0.134381\pi$
$709$	2.69615	+	4.66987i	0.101256	+	0.175381i	−0.810946	+	0.585121i	$0.801047\pi$
$710$		0			0
$711$	12.8038	−	22.1769i	0.480182	−	0.831699i
$712$		0			0
$713$	0.267949	+	0.464102i	0.0100348	+	0.0173807i
$714$		0			0
$715$	−4.00000	+	6.92820i	−0.149592	+	0.259100i
$716$		0			0
$717$	18.0000	+	31.1769i	0.672222	+	1.16432i
$718$		0			0
$719$	−1.32051			−0.0492466			−0.0246233	−	0.999697i	$-0.507839\pi$
$719$	−1.32051			−0.0492466			−0.0246233	+	0.999697i	$0.507839\pi$
$720$		0			0
$721$	−23.8564			−0.888459
$722$		0			0
$723$	34.5167			1.28369
$724$		0			0
$725$	−4.23205	+	7.33013i	−0.157174	+	0.272234i
$726$		0			0
$727$	−17.9904	−	31.1603i	−0.667226	−	1.15567i	−0.978677	−	0.205407i	$-0.934148\pi$
$727$	−17.9904	−	31.1603i	−0.667226	−	1.15567i	0.311450	−	0.950262i	$-0.399185\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	−42.7846	−	74.1051i	−1.58245	−	2.74088i
$732$		0			0
$733$	−21.9282	+	37.9808i	−0.809937	+	1.40285i	0.102971	+	0.994684i	$0.467165\pi$
$733$	−21.9282	+	37.9808i	−0.809937	+	1.40285i	−0.912907	+	0.408167i	$0.866168\pi$
$734$		0			0
$735$	12.0000			0.442627
$736$		0			0
$737$	53.1769			1.95880
$738$		0			0
$739$	−48.2487			−1.77486			−0.887429	−	0.460945i	$-0.847511\pi$
$739$	−48.2487			−1.77486			−0.887429	+	0.460945i	$0.847511\pi$
$740$		0			0
$741$	2.53590	+	4.39230i	0.0931586	+	0.161355i
$742$		0			0
$743$	22.9186	−	39.6962i	0.840801	−	1.45631i	−0.0484169	−	0.998827i	$-0.515418\pi$
$743$	22.9186	−	39.6962i	0.840801	−	1.45631i	0.889218	−	0.457483i	$-0.151249\pi$
$744$		0			0
$745$	2.23205	+	3.86603i	0.0817760	+	0.141640i
$746$		0			0
$747$	−4.20577	+	7.28461i	−0.153881	+	0.266530i
$748$		0			0
$749$	9.69615	+	16.7942i	0.354290	+	0.613648i
$750$		0			0
$751$	−2.19615	+	3.80385i	−0.0801387	+	0.138804i	−0.903309	−	0.428990i	$-0.858870\pi$
$751$	−2.19615	+	3.80385i	−0.0801387	+	0.138804i	0.823171	+	0.567794i	$0.192203\pi$
$752$		0			0
$753$	−17.1962	+	29.7846i	−0.626663	+	1.08541i
$754$		0			0
$755$	−1.46410			−0.0532841
$756$		0			0
$757$	0.392305			0.0142586			0.00712928	−	0.999975i	$-0.497731\pi$
$757$	0.392305			0.0142586			0.00712928	+	0.999975i	$0.497731\pi$
$758$		0			0
$759$	1.26795	−	2.19615i	0.0460236	−	0.0797153i
$760$		0			0
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	−0.610527	−	0.791995i	$-0.709042\pi$
$761$	10.5000	−	18.1865i	0.380625	−	0.659261i	0.991152	+	0.132734i	$0.0423756\pi$
$762$		0			0
$763$	6.33013	+	10.9641i	0.229166	+	0.396927i
$764$		0			0
$765$	−22.3923			−0.809595
$766$		0			0
$767$	−4.67949	−	8.10512i	−0.168967	−	0.292659i
$768$		0			0
$769$	3.89230	−	6.74167i	0.140360	−	0.243111i	−0.787272	−	0.616606i	$-0.788507\pi$
$769$	3.89230	−	6.74167i	0.140360	−	0.243111i	0.927632	+	0.373495i	$0.121841\pi$
$770$		0			0
$771$	11.1962	+	19.3923i	0.403220	+	0.698397i
$772$		0			0
$773$	32.7846			1.17918			0.589590	−	0.807703i	$-0.299289\pi$
$773$	32.7846			1.17918			0.589590	+	0.807703i	$0.299289\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$		0			0
$777$	−67.1769			−2.40996
$778$		0			0
$779$	3.92820	−	6.80385i	0.140742	−	0.243773i
$780$		0			0
$781$	−6.92820	−	12.0000i	−0.247911	−	0.429394i
$782$		0			0
$783$	21.9904	+	38.0885i	0.785872	+	1.36117i
$784$		0			0
$785$	−4.46410	−	7.73205i	−0.159331	−	0.275969i
$786$		0			0
$787$	−16.6603	+	28.8564i	−0.593874	+	1.02862i	0.399831	+	0.916589i	$0.369069\pi$
$787$	−16.6603	+	28.8564i	−0.593874	+	1.02862i	−0.993705	+	0.112031i	$0.964264\pi$
$788$		0			0
$789$	2.78461			0.0991347
$790$		0			0
$791$	51.7128			1.83870
$792$		0			0
$793$	−2.24871			−0.0798541
$794$		0			0
$795$	−5.19615	−	9.00000i	−0.184289	−	0.319197i
$796$		0			0
$797$	14.1962	−	24.5885i	0.502854	−	0.870968i	−0.497141	−	0.867670i	$-0.665617\pi$
$797$	14.1962	−	24.5885i	0.502854	−	0.870968i	0.999995	−	0.00329810i	$-0.00104982\pi$
$798$		0			0
$799$	13.9282	+	24.1244i	0.492744	+	0.853458i
$800$		0			0
$801$	−5.89230	−	10.2058i	−0.208194	−	0.360603i
$802$		0			0
$803$	−18.9282	−	32.7846i	−0.667962	−	1.15694i
$804$		0			0
$805$	0.500000	−	0.866025i	0.0176227	−	0.0305234i
$806$		0			0
$807$	−8.13397	+	14.0885i	−0.286329	+	0.495937i
$808$		0			0
$809$	−35.0718			−1.23306			−0.616529	−	0.787332i	$-0.711462\pi$
$809$	−35.0718			−1.23306			−0.616529	+	0.787332i	$0.711462\pi$
$810$		0			0
$811$	29.6077			1.03967			0.519833	−	0.854268i	$-0.325994\pi$
$811$	29.6077			1.03967			0.519833	+	0.854268i	$0.325994\pi$
$812$		0			0
$813$	−6.80385	+	11.7846i	−0.238621	+	0.413304i
$814$		0			0
$815$	−10.6603	+	18.4641i	−0.373412	+	0.646769i
$816$		0			0
$817$	−11.4641	−	19.8564i	−0.401078	−	0.694688i
$818$		0			0
$819$	8.19615	+	14.1962i	0.286397	+	0.496054i
$820$		0			0
$821$	12.6244	+	21.8660i	0.440593	+	0.763130i	0.997734	−	0.0672887i	$-0.0214349\pi$
$821$	12.6244	+	21.8660i	0.440593	+	0.763130i	−0.557140	+	0.830418i	$0.688102\pi$
$822$		0			0
$823$	10.1340	−	17.5526i	0.353248	−	0.611844i	−0.633568	−	0.773687i	$-0.718410\pi$
$823$	10.1340	−	17.5526i	0.353248	−	0.611844i	0.986817	+	0.161843i	$0.0517438\pi$
$824$		0			0
$825$	−4.73205	−	8.19615i	−0.164749	−	0.285353i
$826$		0			0
$827$	55.0526			1.91437			0.957183	−	0.289485i	$-0.0934841\pi$
$827$	55.0526			1.91437			0.957183	+	0.289485i	$0.0934841\pi$
$828$		0			0
$829$	−9.39230			−0.326208			−0.163104	−	0.986609i	$-0.552151\pi$
$829$	−9.39230			−0.326208			−0.163104	+	0.986609i	$0.552151\pi$
$830$		0			0
$831$	−11.0718			−0.384076
$832$		0			0
$833$	−25.8564	+	44.7846i	−0.895871	+	1.55169i
$834$		0			0
$835$	−4.79423	−	8.30385i	−0.165911	−	0.287366i
$836$		0			0
$837$	5.19615	−	9.00000i	0.179605	−	0.311086i
$838$		0			0
$839$	4.07180	+	7.05256i	0.140574	+	0.243481i	0.927713	−	0.373294i	$-0.121772\pi$
$839$	4.07180	+	7.05256i	0.140574	+	0.243481i	−0.787139	+	0.616776i	$0.788439\pi$
$840$		0			0
$841$	−21.3205	+	36.9282i	−0.735190	+	1.27339i
$842$		0			0
$843$	−22.2679			−0.766949
$844$		0			0
$845$	10.8564			0.373472
$846$		0			0
$847$	−70.3731			−2.41805
$848$		0			0
$849$	−15.8205	−	27.4019i	−0.542958	−	0.940432i
$850$		0			0
$851$	−1.39230	+	2.41154i	−0.0477276	+	0.0826666i
$852$		0			0
$853$	21.2679	+	36.8372i	0.728201	+	1.26128i	0.957643	+	0.287958i	$0.0929765\pi$
$853$	21.2679	+	36.8372i	0.728201	+	1.26128i	−0.229442	+	0.973322i	$0.573690\pi$
$854$		0			0
$855$	−6.00000			−0.205196
$856$		0			0
$857$	15.1244	+	26.1962i	0.516638	+	0.894844i	0.999813	+	0.0193198i	$0.00615008\pi$
$857$	15.1244	+	26.1962i	0.516638	+	0.894844i	−0.483175	+	0.875524i	$0.660517\pi$
$858$		0			0
$859$	0.196152	−	0.339746i	0.00669263	−	0.0115920i	−0.862660	−	0.505785i	$-0.831203\pi$
$859$	0.196152	−	0.339746i	0.00669263	−	0.0115920i	0.869352	+	0.494193i	$0.164536\pi$
$860$		0			0
$861$	12.6962	−	21.9904i	0.432684	−	0.749430i
$862$		0			0
$863$	−9.33975			−0.317929			−0.158964	−	0.987284i	$-0.550815\pi$
$863$	−9.33975			−0.317929			−0.158964	+	0.987284i	$0.550815\pi$
$864$		0			0
$865$	−22.9282			−0.779582
$866$		0			0
$867$	33.5263	−	58.0692i	1.13861	−	1.97213i
$868$		0			0
$869$	−23.3205	+	40.3923i	−0.791094	+	1.37022i
$870$		0			0
$871$	7.12436	+	12.3397i	0.241400	+	0.418116i
$872$		0			0
$873$	−7.39230	+	12.8038i	−0.250192	+	0.433345i
$874$		0			0
$875$	−1.86603	−	3.23205i	−0.0630832	−	0.109263i
$876$		0			0
$877$	−16.1962	+	28.0526i	−0.546905	+	0.947268i	0.451579	+	0.892231i	$0.350861\pi$
$877$	−16.1962	+	28.0526i	−0.546905	+	0.947268i	−0.998484	+	0.0550365i	$0.982472\pi$
$878$		0			0
$879$	−0.464102	−	0.803848i	−0.0156538	−	0.0271131i
$880$		0			0
$881$	−31.6410			−1.06601			−0.533006	−	0.846111i	$-0.678938\pi$
$881$	−31.6410			−1.06601			−0.533006	+	0.846111i	$0.678938\pi$
$882$		0			0
$883$	−1.19615			−0.0402537			−0.0201269	−	0.999797i	$-0.506407\pi$
$883$	−1.19615			−0.0402537			−0.0201269	+	0.999797i	$0.506407\pi$
$884$		0			0
$885$	11.0718			0.372174
$886$		0			0
$887$	12.6603	−	21.9282i	0.425090	−	0.736277i	−0.571339	−	0.820714i	$-0.693576\pi$
$887$	12.6603	−	21.9282i	0.425090	−	0.736277i	0.996429	+	0.0844371i	$0.0269092\pi$
$888$		0			0
$889$	−36.8205	−	63.7750i	−1.23492	−	2.13894i
$890$		0			0
$891$	−49.1769			−1.64749
$892$		0			0
$893$	3.73205	+	6.46410i	0.124888	+	0.216313i
$894$		0			0
$895$	−3.26795	+	5.66025i	−0.109235	+	0.189201i
$896$		0			0
$897$	0.679492			0.0226876
$898$		0			0
$899$	16.9282			0.564587
$900$		0			0
$901$	44.7846			1.49199
$902$		0			0
$903$	−37.0526	−	64.1769i	−1.23303	−	2.13567i
$904$		0			0
$905$	−8.23205	+	14.2583i	−0.273643	+	0.473963i
$906$		0			0
$907$	−5.13397	−	8.89230i	−0.170471	−	0.295264i	0.768114	−	0.640313i	$-0.221196\pi$
$907$	−5.13397	−	8.89230i	−0.170471	−	0.295264i	−0.938585	+	0.345049i	$0.887862\pi$
$908$		0			0
$909$	19.3923	−	33.5885i	0.643202	−	1.11406i
$910$		0			0
$911$	−9.73205	−	16.8564i	−0.322437	−	0.558478i	0.658553	−	0.752534i	$-0.271169\pi$
$911$	−9.73205	−	16.8564i	−0.322437	−	0.558478i	−0.980990	+	0.194057i	$0.937835\pi$
$912$		0			0
$913$	7.66025	−	13.2679i	0.253517	−	0.439105i
$914$		0			0
$915$	1.33013	−	2.30385i	0.0439726	−	0.0761629i
$916$		0			0
$917$	12.9282			0.426927
$918$		0			0
$919$	38.3923			1.26645			0.633223	−	0.773970i	$-0.281732\pi$
$919$	38.3923			1.26645			0.633223	+	0.773970i	$0.281732\pi$
$920$		0			0
$921$	17.4282	−	30.1865i	0.574279	−	0.994680i
$922$		0			0
$923$	1.85641	−	3.21539i	0.0611044	−	0.105836i
$924$		0			0
$925$	5.19615	+	9.00000i	0.170848	+	0.295918i
$926$		0			0
$927$	19.1769			0.629853
$928$		0			0
$929$	22.3205	+	38.6603i	0.732312	+	1.26840i	0.955893	+	0.293716i	$0.0948921\pi$
$929$	22.3205	+	38.6603i	0.732312	+	1.26840i	−0.223581	+	0.974685i	$0.571775\pi$
$930$		0			0
$931$	−6.92820	+	12.0000i	−0.227063	+	0.393284i
$932$		0			0
$933$	−14.6603	−	25.3923i	−0.479955	−	0.831307i
$934$		0			0
$935$	40.7846			1.33380
$936$		0			0
$937$	43.7128			1.42804			0.714018	−	0.700128i	$-0.246874\pi$
$937$	43.7128			1.42804			0.714018	+	0.700128i	$0.246874\pi$
$938$		0			0
$939$	14.5359			0.474361
$940$		0			0
$941$	1.30385	−	2.25833i	0.0425042	−	0.0736195i	−0.843991	−	0.536358i	$-0.819800\pi$
$941$	1.30385	−	2.25833i	0.0425042	−	0.0736195i	0.886495	+	0.462738i	$0.153133\pi$
$942$		0			0
$943$	−0.526279	−	0.911543i	−0.0171380	−	0.0296839i
$944$		0			0
$945$	−19.3923			−0.630832
$946$		0			0
$947$	15.2583	+	26.4282i	0.495829	+	0.858801i	0.999988	−	0.00480945i	$-0.00153090\pi$
$947$	15.2583	+	26.4282i	0.495829	+	0.858801i	−0.504159	+	0.863611i	$0.668198\pi$
$948$		0			0
$949$	5.07180	−	8.78461i	0.164637	−	0.285160i
$950$		0			0
$951$	−16.3923			−0.531557
$952$		0			0
$953$	19.6077			0.635156			0.317578	−	0.948232i	$-0.397131\pi$
$953$	19.6077			0.635156			0.317578	+	0.948232i	$0.397131\pi$
$954$		0			0
$955$	3.07180			0.0994010
$956$		0			0
$957$	−40.0526	−	69.3731i	−1.29472	−	2.24251i
$958$		0			0
$959$	−10.9282	+	18.9282i	−0.352890	+	0.611224i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$		0			0
$963$	−7.79423	−	13.5000i	−0.251166	−	0.435031i
$964$		0			0
$965$	−5.26795	−	9.12436i	−0.169581	−	0.293723i
$966$		0			0
$967$	19.3301	−	33.4808i	0.621615	−	1.07667i	−0.367570	−	0.929996i	$-0.619810\pi$
$967$	19.3301	−	33.4808i	0.621615	−	1.07667i	0.989185	−	0.146673i	$-0.0468565\pi$
$968$		0			0
$969$	12.9282	−	22.3923i	0.415314	−	0.719344i
$970$		0			0
$971$	29.7128			0.953530			0.476765	−	0.879031i	$-0.341809\pi$
$971$	29.7128			0.953530			0.476765	+	0.879031i	$0.341809\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	1.26795	−	2.19615i	0.0406069	−	0.0703332i
$976$		0			0
$977$	22.5885	−	39.1244i	0.722669	−	1.25170i	−0.237258	−	0.971447i	$-0.576249\pi$
$977$	22.5885	−	39.1244i	0.722669	−	1.25170i	0.959926	−	0.280252i	$-0.0904181\pi$
$978$		0			0
$979$	10.7321	+	18.5885i	0.342998	+	0.594090i
$980$		0			0
$981$	−5.08846	−	8.81347i	−0.162462	−	0.281392i
$982$		0			0
$983$	−2.25833	−	3.91154i	−0.0720295	−	0.124759i	0.827761	−	0.561081i	$-0.189614\pi$
$983$	−2.25833	−	3.91154i	−0.0720295	−	0.124759i	−0.899791	+	0.436322i	$0.856281\pi$
$984$		0			0
$985$	0.535898	−	0.928203i	0.0170751	−	0.0295750i
$986$		0			0
$987$	12.0622	+	20.8923i	0.383943	+	0.665009i
$988$		0			0
$989$	−3.07180			−0.0976775
$990$		0			0
$991$	−53.0333			−1.68466			−0.842329	−	0.538963i	$-0.818816\pi$
$991$	−53.0333			−1.68466			−0.842329	+	0.538963i	$0.818816\pi$
$992$		0			0
$993$	6.00000			0.190404
$994$		0			0
$995$	−10.4641	+	18.1244i	−0.331734	+	0.574581i
$996$		0			0
$997$	17.7846	+	30.8038i	0.563244	+	0.975568i	0.997211	+	0.0746386i	$0.0237803\pi$
$997$	17.7846	+	30.8038i	0.563244	+	0.975568i	−0.433966	+	0.900929i	$0.642886\pi$
$998$		0			0
$999$	54.0000			1.70848

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.h.481.2		4
3.2	odd	2		2160.2.q.h.1441.2		4
4.3	odd	2		360.2.q.b.121.1	✓	4
9.2	odd	6		2160.2.q.h.721.2		4
9.4	even	3		6480.2.a.ba.1.1		2
9.5	odd	6		6480.2.a.bk.1.1		2
9.7	even	3	inner	720.2.q.h.241.2		4
12.11	even	2		1080.2.q.b.361.1		4
36.7	odd	6		360.2.q.b.241.1	yes	4
36.11	even	6		1080.2.q.b.721.1		4
36.23	even	6		3240.2.a.p.1.2		2
36.31	odd	6		3240.2.a.k.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.b.121.1	✓	4	4.3	odd	2
360.2.q.b.241.1	yes	4	36.7	odd	6
720.2.q.h.241.2		4	9.7	even	3	inner
720.2.q.h.481.2		4	1.1	even	1	trivial
1080.2.q.b.361.1		4	12.11	even	2
1080.2.q.b.721.1		4	36.11	even	6
2160.2.q.h.721.2		4	9.2	odd	6
2160.2.q.h.1441.2		4	3.2	odd	2
3240.2.a.k.1.2		2	36.31	odd	6
3240.2.a.p.1.2		2	36.23	even	6
6480.2.a.ba.1.1		2	9.4	even	3
6480.2.a.bk.1.1		2	9.5	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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.86603 + 3.23205i) q^{7} +(-1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{5} +(1.86603 + 3.23205i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(2.73205 + 4.73205i) q^{11} +(-0.732051 + 1.26795i) q^{13} +(-0.866025 - 1.50000i) q^{15} +7.46410 q^{17} +2.00000 q^{19} +6.46410 q^{21} +(0.133975 - 0.232051i) q^{23} +(-0.500000 - 0.866025i) q^{25} -5.19615 q^{27} +(-4.23205 - 7.33013i) q^{29} +(-1.00000 + 1.73205i) q^{31} +9.46410 q^{33} +3.73205 q^{35} -10.3923 q^{37} +(1.26795 + 2.19615i) q^{39} +(1.96410 - 3.40192i) q^{41} +(-5.73205 - 9.92820i) q^{43} -3.00000 q^{45} +(1.86603 + 3.23205i) q^{47} +(-3.46410 + 6.00000i) q^{49} +(6.46410 - 11.1962i) q^{51} +6.00000 q^{53} +5.46410 q^{55} +(1.73205 - 3.00000i) q^{57} +(-3.19615 + 5.53590i) q^{59} +(0.767949 + 1.33013i) q^{61} +(5.59808 - 9.69615i) q^{63} +(0.732051 + 1.26795i) q^{65} +(4.86603 - 8.42820i) q^{67} +(-0.232051 - 0.401924i) q^{69} -2.53590 q^{71} -6.92820 q^{73} -1.73205 q^{75} +(-10.1962 + 17.6603i) q^{77} +(4.26795 + 7.39230i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.40192 - 2.42820i) q^{83} +(3.73205 - 6.46410i) q^{85} -14.6603 q^{87} +3.92820 q^{89} -5.46410 q^{91} +(1.73205 + 3.00000i) q^{93} +(1.00000 - 1.73205i) q^{95} +(-2.46410 - 4.26795i) q^{97} +(8.19615 - 14.1962i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{5} + 4 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q + 2 * q^5 + 4 * q^7 - 6 * q^9	\( 4 q + 2 q^{5} + 4 q^{7} - 6 q^{9} + 4 q^{11} + 4 q^{13} + 16 q^{17} + 8 q^{19} + 12 q^{21} + 4 q^{23} - 2 q^{25} - 10 q^{29} - 4 q^{31} + 24 q^{33} + 8 q^{35} + 12 q^{39} - 6 q^{41} - 16 q^{43} - 12 q^{45} + 4 q^{47} + 12 q^{51} + 24 q^{53} + 8 q^{55} + 8 q^{59} + 10 q^{61} + 12 q^{63} - 4 q^{65} + 16 q^{67} + 6 q^{69} - 24 q^{71} - 20 q^{77} + 24 q^{79} - 18 q^{81} - 16 q^{83} + 8 q^{85} - 24 q^{87} - 12 q^{89} - 8 q^{91} + 4 q^{95} + 4 q^{97} + 12 q^{99}+O(q^{100}) \) 4 * q + 2 * q^5 + 4 * q^7 - 6 * q^9 + 4 * q^11 + 4 * q^13 + 16 * q^17 + 8 * q^19 + 12 * q^21 + 4 * q^23 - 2 * q^25 - 10 * q^29 - 4 * q^31 + 24 * q^33 + 8 * q^35 + 12 * q^39 - 6 * q^41 - 16 * q^43 - 12 * q^45 + 4 * q^47 + 12 * q^51 + 24 * q^53 + 8 * q^55 + 8 * q^59 + 10 * q^61 + 12 * q^63 - 4 * q^65 + 16 * q^67 + 6 * q^69 - 24 * q^71 - 20 * q^77 + 24 * q^79 - 18 * q^81 - 16 * q^83 + 8 * q^85 - 24 * q^87 - 12 * q^89 - 8 * q^91 + 4 * q^95 + 4 * q^97 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more