LMFDB - Embedded newform 720.2.q.d.241.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			241.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	720.241
Dual form			720.2.q.d.481.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{13} +(1.50000 + 0.866025i) q^{15} +4.00000 q^{17} +8.00000 q^{19} +5.19615i q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +3.46410i q^{33} -3.00000 q^{35} -4.00000 q^{37} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{45} +(3.50000 - 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(6.00000 - 3.46410i) q^{51} -2.00000 q^{53} -2.00000 q^{55} +(12.0000 - 6.92820i) q^{57} +(-7.00000 - 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(4.50000 + 2.59808i) q^{69} -2.00000 q^{71} +4.00000 q^{73} +1.73205i q^{75} +(-3.00000 - 5.19615i) q^{77} +(-3.00000 + 5.19615i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{83} +(2.00000 + 3.46410i) q^{85} -1.73205i q^{87} -15.0000 q^{89} -6.00000 q^{91} +(4.00000 + 6.92820i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + q^5 - 3 * q^7 + 3 * q^9	$ 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9} - 2 q^{11} + 2 q^{13} + 3 q^{15} + 8 q^{17} + 16 q^{19} + 3 q^{23} - q^{25} + q^{29} - 6 q^{35} - 8 q^{37} + 6 q^{39} - 5 q^{41} - 8 q^{43} + 6 q^{45} + 7 q^{47} - 2 q^{49} + 12 q^{51} - 4 q^{53} - 4 q^{55} + 24 q^{57} - 14 q^{59} - 7 q^{61} + 9 q^{63} - 2 q^{65} - 3 q^{67} + 9 q^{69} - 4 q^{71} + 8 q^{73} - 6 q^{77} - 6 q^{79} - 9 q^{81} + 9 q^{83} + 4 q^{85} - 30 q^{89} - 12 q^{91} + 8 q^{95} - 2 q^{97} + 6 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + q^5 - 3 * q^7 + 3 * q^9 - 2 * q^11 + 2 * q^13 + 3 * q^15 + 8 * q^17 + 16 * q^19 + 3 * q^23 - q^25 + q^29 - 6 * q^35 - 8 * q^37 + 6 * q^39 - 5 * q^41 - 8 * q^43 + 6 * q^45 + 7 * q^47 - 2 * q^49 + 12 * q^51 - 4 * q^53 - 4 * q^55 + 24 * q^57 - 14 * q^59 - 7 * q^61 + 9 * q^63 - 2 * q^65 - 3 * q^67 + 9 * q^69 - 4 * q^71 + 8 * q^73 - 6 * q^77 - 6 * q^79 - 9 * q^81 + 9 * q^83 + 4 * q^85 - 30 * q^89 - 12 * q^91 + 8 * q^95 - 2 * q^97 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	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
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	−0.976478	−	0.215615i	$-0.930824\pi$
$11$	−1.00000	+	1.73205i	−0.301511	+	0.522233i	0.674967	+	0.737848i	$0.264158\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	1.50000	+	0.866025i	0.387298	+	0.223607i
$16$		0			0
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$		0			0
$19$	8.00000			1.83533			0.917663	−	0.397360i	$-0.130073\pi$
$19$	8.00000			1.83533			0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$			5.19615i			1.13389i
$22$		0			0
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	0.978961	−	0.204046i	$-0.0654092\pi$
$23$	1.50000	+	2.59808i	0.312772	+	0.541736i	−0.666190	+	0.745782i	$0.732076\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$		−	5.19615i		−	1.00000i
$28$		0			0
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$		0			0
$33$			3.46410i			0.603023i
$34$		0			0
$35$	−3.00000			−0.507093
$36$		0			0
$37$	−4.00000			−0.657596			−0.328798	−	0.944400i	$-0.606644\pi$
$37$	−4.00000			−0.657596			−0.328798	+	0.944400i	$0.606644\pi$
$38$		0			0
$39$	3.00000	+	1.73205i	0.480384	+	0.277350i
$40$		0			0
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	0.602072	−	0.798441i	$-0.294342\pi$
$41$	−2.50000	−	4.33013i	−0.390434	−	0.676252i	−0.992507	+	0.122189i	$0.961009\pi$
$42$		0			0
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$	3.00000			0.447214
$46$		0			0
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	−0.489398	−	0.872060i	$-0.662783\pi$
$47$	3.50000	−	6.06218i	0.510527	−	0.884260i	0.999926	−	0.0121990i	$-0.00388317\pi$
$48$		0			0
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$		0			0
$51$	6.00000	−	3.46410i	0.840168	−	0.485071i
$52$		0			0
$53$	−2.00000			−0.274721			−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000			−0.274721			−0.137361	+	0.990521i	$0.543862\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$	12.0000	−	6.92820i	1.58944	−	0.917663i
$58$		0			0
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.812198	−	0.583382i	$-0.801729\pi$
$59$	−7.00000	−	12.1244i	−0.911322	−	1.57846i	−0.0991242	−	0.995075i	$-0.531604\pi$
$60$		0			0
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	−0.998264	−	0.0588933i	$-0.981243\pi$
$61$	−3.50000	+	6.06218i	−0.448129	+	0.776182i	0.550135	+	0.835076i	$0.314576\pi$
$62$		0			0
$63$	4.50000	+	7.79423i	0.566947	+	0.981981i
$64$		0			0
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	0.759733	−	0.650236i	$-0.225330\pi$
$67$	−1.50000	−	2.59808i	−0.183254	−	0.317406i	−0.942987	+	0.332830i	$0.891996\pi$
$68$		0			0
$69$	4.50000	+	2.59808i	0.541736	+	0.312772i
$70$		0			0
$71$	−2.00000			−0.237356			−0.118678	−	0.992933i	$-0.537866\pi$
$71$	−2.00000			−0.237356			−0.118678	+	0.992933i	$0.537866\pi$
$72$		0			0
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$		0			0
$75$			1.73205i			0.200000i
$76$		0			0
$77$	−3.00000	−	5.19615i	−0.341882	−	0.592157i
$78$		0			0
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	−0.983967	−	0.178352i	$-0.942924\pi$
$79$	−3.00000	+	5.19615i	−0.337526	+	0.584613i	0.646440	+	0.762964i	$0.276257\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	−0.506036	−	0.862512i	$-0.668890\pi$
$83$	4.50000	−	7.79423i	0.493939	−	0.855528i	0.999976	+	0.00698436i	$0.00222321\pi$
$84$		0			0
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$		0			0
$87$		−	1.73205i		−	0.185695i
$88$		0			0
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$		0			0
$93$		0			0
$94$		0			0
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$		0			0
$99$	3.00000	+	5.19615i	0.301511	+	0.522233i
$100$		0			0
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.0623905	−	0.998052i	$-0.480128\pi$
$101$	9.00000	−	15.5885i	0.895533	−	1.55111i	0.833143	−	0.553058i	$-0.186539\pi$
$102$		0			0
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	0.992990	−	0.118199i	$-0.0377120\pi$
$103$	4.00000	+	6.92820i	0.394132	+	0.682656i	−0.598858	+	0.800855i	$0.704379\pi$
$104$		0			0
$105$	−4.50000	+	2.59808i	−0.439155	+	0.253546i
$106$		0			0
$107$	−3.00000			−0.290021			−0.145010	−	0.989430i	$-0.546322\pi$
$107$	−3.00000			−0.290021			−0.145010	+	0.989430i	$0.546322\pi$
$108$		0			0
$109$	5.00000			0.478913			0.239457	−	0.970907i	$-0.423031\pi$
$109$	5.00000			0.478913			0.239457	+	0.970907i	$0.423031\pi$
$110$		0			0
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$		0			0
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	0.990519	−	0.137376i	$-0.0438669\pi$
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	−0.614231	+	0.789127i	$0.710534\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$		0			0
$117$	6.00000			0.554700
$118$		0			0
$119$	−6.00000	+	10.3923i	−0.550019	+	0.952661i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−7.50000	−	4.33013i	−0.676252	−	0.390434i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$		0			0
$129$			13.8564i			1.21999i
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$		0			0
$133$	−12.0000	+	20.7846i	−1.04053	+	1.80225i
$134$		0			0
$135$	4.50000	−	2.59808i	0.387298	−	0.223607i
$136$		0			0
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$		0			0
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$		−	12.1244i		−	1.02105i
$142$		0			0
$143$	−4.00000			−0.334497
$144$		0			0
$145$	1.00000			0.0830455
$146$		0			0
$147$	−3.00000	−	1.73205i	−0.247436	−	0.142857i
$148$		0			0
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	−0.969724	−	0.244202i	$-0.921474\pi$
$149$	−8.50000	−	14.7224i	−0.696347	−	1.20611i	0.273377	−	0.961907i	$-0.411859\pi$
$150$		0			0
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	−0.903842	−	0.427865i	$-0.859266\pi$
$151$	−1.00000	+	1.73205i	−0.0813788	+	0.140952i	0.822464	+	0.568818i	$0.192599\pi$
$152$		0			0
$153$	6.00000	−	10.3923i	0.485071	−	0.840168i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$	−3.00000	+	1.73205i	−0.237915	+	0.137361i
$160$		0			0
$161$	−9.00000			−0.709299
$162$		0			0
$163$	4.00000			0.313304			0.156652	−	0.987654i	$-0.449930\pi$
$163$	4.00000			0.313304			0.156652	+	0.987654i	$0.449930\pi$
$164$		0			0
$165$	−3.00000	+	1.73205i	−0.233550	+	0.134840i
$166$		0			0
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	0.637713	−	0.770274i	$-0.279881\pi$
$167$	−4.50000	−	7.79423i	−0.348220	−	0.603136i	−0.985933	+	0.167139i	$0.946547\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$		0			0
$171$	12.0000	−	20.7846i	0.917663	−	1.58944i
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−1.50000	−	2.59808i	−0.113389	−	0.196396i
$176$		0			0
$177$	−21.0000	−	12.1244i	−1.57846	−	0.911322i
$178$		0			0
$179$	2.00000			0.149487			0.0747435	−	0.997203i	$-0.476186\pi$
$179$	2.00000			0.149487			0.0747435	+	0.997203i	$0.476186\pi$
$180$		0			0
$181$	−7.00000			−0.520306			−0.260153	−	0.965567i	$-0.583773\pi$
$181$	−7.00000			−0.520306			−0.260153	+	0.965567i	$0.583773\pi$
$182$		0			0
$183$			12.1244i			0.896258i
$184$		0			0
$185$	−2.00000	−	3.46410i	−0.147043	−	0.254686i
$186$		0			0
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$		0			0
$189$	13.5000	+	7.79423i	0.981981	+	0.566947i
$190$		0			0
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	−0.684244	−	0.729253i	$-0.739868\pi$
$191$	4.00000	−	6.92820i	0.289430	−	0.501307i	0.973674	+	0.227946i	$0.0732010\pi$
$192$		0			0
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	0.987945	−	0.154805i	$-0.0494748\pi$
$193$	5.00000	+	8.66025i	0.359908	+	0.623379i	−0.628037	+	0.778183i	$0.716141\pi$
$194$		0			0
$195$			3.46410i			0.248069i
$196$		0			0
$197$	−12.0000			−0.854965			−0.427482	−	0.904024i	$-0.640599\pi$
$197$	−12.0000			−0.854965			−0.427482	+	0.904024i	$0.640599\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$		0			0
$201$	−4.50000	−	2.59808i	−0.317406	−	0.183254i
$202$		0			0
$203$	1.50000	+	2.59808i	0.105279	+	0.182349i
$204$		0			0
$205$	2.50000	−	4.33013i	0.174608	−	0.302429i
$206$		0			0
$207$	9.00000			0.625543
$208$		0			0
$209$	−8.00000	+	13.8564i	−0.553372	+	0.958468i
$210$		0			0
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	−0.944237	−	0.329266i	$-0.893199\pi$
$211$	−11.0000	−	19.0526i	−0.757271	−	1.31163i	0.186966	−	0.982366i	$-0.440135\pi$
$212$		0			0
$213$	−3.00000	+	1.73205i	−0.205557	+	0.118678i
$214$		0			0
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$		0			0
$219$	6.00000	−	3.46410i	0.405442	−	0.234082i
$220$		0			0
$221$	4.00000	+	6.92820i	0.269069	+	0.466041i
$222$		0			0
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$		0			0
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$		0			0
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	−0.924734	−	0.380615i	$-0.875712\pi$
$227$	−2.00000	+	3.46410i	−0.132745	+	0.229920i	0.791989	+	0.610535i	$0.209046\pi$
$228$		0			0
$229$	−7.50000	−	12.9904i	−0.495614	−	0.858429i	0.504373	−	0.863486i	$-0.331724\pi$
$229$	−7.50000	−	12.9904i	−0.495614	−	0.858429i	−0.999987	+	0.00505719i	$0.998390\pi$
$230$		0			0
$231$	−9.00000	−	5.19615i	−0.592157	−	0.341882i
$232$		0			0
$233$	24.0000			1.57229			0.786146	−	0.618041i	$-0.212073\pi$
$233$	24.0000			1.57229			0.786146	+	0.618041i	$0.212073\pi$
$234$		0			0
$235$	7.00000			0.456630
$236$		0			0
$237$			10.3923i			0.675053i
$238$		0			0
$239$	−4.00000	−	6.92820i	−0.258738	−	0.448148i	0.707166	−	0.707048i	$-0.249973\pi$
$239$	−4.00000	−	6.92820i	−0.258738	−	0.448148i	−0.965904	+	0.258900i	$0.916640\pi$
$240$		0			0
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	−0.632709	−	0.774389i	$-0.718057\pi$
$241$	5.50000	−	9.52628i	0.354286	−	0.613642i	0.986996	+	0.160748i	$0.0513906\pi$
$242$		0			0
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$		0			0
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$		0			0
$247$	8.00000	+	13.8564i	0.509028	+	0.881662i
$248$		0			0
$249$		−	15.5885i		−	0.987878i
$250$		0			0
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−6.00000			−0.377217
$254$		0			0
$255$	6.00000	+	3.46410i	0.375735	+	0.216930i
$256$		0			0
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	6.00000	−	10.3923i	0.372822	−	0.645746i
$260$		0			0
$261$	−1.50000	−	2.59808i	−0.0928477	−	0.160817i
$262$		0			0
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	−0.999970	−	0.00771799i	$-0.997543\pi$
$263$	−8.00000	+	13.8564i	−0.493301	+	0.854423i	0.506669	+	0.862141i	$0.330877\pi$
$264$		0			0
$265$	−1.00000	−	1.73205i	−0.0614295	−	0.106399i
$266$		0			0
$267$	−22.5000	+	12.9904i	−1.37698	+	0.794998i
$268$		0			0
$269$	25.0000			1.52428			0.762138	−	0.647414i	$-0.224150\pi$
$269$	25.0000			1.52428			0.762138	+	0.647414i	$0.224150\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$	−9.00000	+	5.19615i	−0.544705	+	0.314485i
$274$		0			0
$275$	−1.00000	−	1.73205i	−0.0603023	−	0.104447i
$276$		0			0
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	−0.988044	−	0.154172i	$-0.950729\pi$
$277$	−6.00000	+	10.3923i	−0.360505	+	0.624413i	0.627539	+	0.778585i	$0.284062\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	−0.550804	−	0.834634i	$-0.685679\pi$
$281$	7.50000	−	12.9904i	0.447412	−	0.774941i	0.998217	+	0.0596933i	$0.0190123\pi$
$282$		0			0
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	0.988703	+	0.149890i	$0.0478921\pi$
$283$	10.5000	+	18.1865i	0.624160	+	1.08108i	−0.364542	+	0.931187i	$0.618775\pi$
$284$		0			0
$285$	12.0000	+	6.92820i	0.710819	+	0.410391i
$286$		0			0
$287$	15.0000			0.885422
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$			3.46410i			0.203069i
$292$		0			0
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$		0			0
$295$	7.00000	−	12.1244i	0.407556	−	0.705907i
$296$		0			0
$297$	9.00000	+	5.19615i	0.522233	+	0.301511i
$298$		0			0
$299$	−3.00000	+	5.19615i	−0.173494	+	0.300501i
$300$		0			0
$301$	−12.0000	−	20.7846i	−0.691669	−	1.19800i
$302$		0			0
$303$		−	31.1769i		−	1.79107i
$304$		0			0
$305$	−7.00000			−0.400819
$306$		0			0
$307$	−7.00000			−0.399511			−0.199756	−	0.979846i	$-0.564015\pi$
$307$	−7.00000			−0.399511			−0.199756	+	0.979846i	$0.564015\pi$
$308$		0			0
$309$	12.0000	+	6.92820i	0.682656	+	0.394132i
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$		0			0
$315$	−4.50000	+	7.79423i	−0.253546	+	0.439155i
$316$		0			0
$317$	17.0000	−	29.4449i	0.954815	−	1.65379i	0.220024	−	0.975494i	$-0.429386\pi$
$317$	17.0000	−	29.4449i	0.954815	−	1.65379i	0.734791	−	0.678294i	$-0.237280\pi$
$318$		0			0
$319$	1.00000	+	1.73205i	0.0559893	+	0.0969762i
$320$		0			0
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$		0			0
$323$	32.0000			1.78053
$324$		0			0
$325$	−2.00000			−0.110940
$326$		0			0
$327$	7.50000	−	4.33013i	0.414751	−	0.239457i
$328$		0			0
$329$	10.5000	+	18.1865i	0.578884	+	1.00266i
$330$		0			0
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	−0.936618	−	0.350352i	$-0.886062\pi$
$331$	−3.00000	+	5.19615i	−0.164895	+	0.285606i	0.771723	+	0.635959i	$0.219395\pi$
$332$		0			0
$333$	−6.00000	+	10.3923i	−0.328798	+	0.569495i
$334$		0			0
$335$	1.50000	−	2.59808i	0.0819538	−	0.141948i
$336$		0			0
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	0.954164	−	0.299285i	$-0.0967480\pi$
$337$	4.00000	+	6.92820i	0.217894	+	0.377403i	−0.736270	+	0.676688i	$0.763415\pi$
$338$		0			0
$339$	12.0000	+	6.92820i	0.651751	+	0.376288i
$340$		0			0
$341$		0			0
$342$		0			0
$343$	−15.0000			−0.809924
$344$		0			0
$345$			5.19615i			0.279751i
$346$		0			0
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	0.914702	−	0.404128i	$-0.132425\pi$
$347$	2.00000	+	3.46410i	0.107366	+	0.185963i	−0.807337	+	0.590091i	$0.799092\pi$
$348$		0			0
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	−0.791325	−	0.611396i	$-0.790608\pi$
$349$	2.50000	−	4.33013i	0.133822	−	0.231786i	0.925147	+	0.379610i	$0.123942\pi$
$350$		0			0
$351$	9.00000	−	5.19615i	0.480384	−	0.277350i
$352$		0			0
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$		0			0
$357$			20.7846i			1.10004i
$358$		0			0
$359$	−24.0000			−1.26667			−0.633336	−	0.773877i	$-0.718315\pi$
$359$	−24.0000			−1.26667			−0.633336	+	0.773877i	$0.718315\pi$
$360$		0			0
$361$	45.0000			2.36842
$362$		0			0
$363$	10.5000	+	6.06218i	0.551107	+	0.318182i
$364$		0			0
$365$	2.00000	+	3.46410i	0.104685	+	0.181319i
$366$		0			0
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	−0.361874	−	0.932227i	$-0.617863\pi$
$367$	12.0000	−	20.7846i	0.626395	−	1.08495i	0.988269	−	0.152721i	$-0.0488036\pi$
$368$		0			0
$369$	−15.0000			−0.780869
$370$		0			0
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$		0			0
$375$	−1.50000	+	0.866025i	−0.0774597	+	0.0447214i
$376$		0			0
$377$	2.00000			0.103005
$378$		0			0
$379$	26.0000			1.33553			0.667765	−	0.744372i	$-0.267251\pi$
$379$	26.0000			1.33553			0.667765	+	0.744372i	$0.267251\pi$
$380$		0			0
$381$	7.50000	−	4.33013i	0.384237	−	0.221839i
$382$		0			0
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$		0			0
$385$	3.00000	−	5.19615i	0.152894	−	0.264820i
$386$		0			0
$387$	12.0000	+	20.7846i	0.609994	+	1.05654i
$388$		0			0
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	0.0561516	+	0.998422i	$0.482117\pi$
$389$	−16.5000	+	28.5788i	−0.836583	+	1.44900i	−0.892735	+	0.450582i	$0.851216\pi$
$390$		0			0
$391$	6.00000	+	10.3923i	0.303433	+	0.525561i
$392$		0			0
$393$	−9.00000	−	5.19615i	−0.453990	−	0.262111i
$394$		0			0
$395$	−6.00000			−0.301893
$396$		0			0
$397$	34.0000			1.70641			0.853206	−	0.521575i	$-0.174655\pi$
$397$	34.0000			1.70641			0.853206	+	0.521575i	$0.174655\pi$
$398$		0			0
$399$			41.5692i			2.08106i
$400$		0			0
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$		0			0
$407$	4.00000	−	6.92820i	0.198273	−	0.343418i
$408$		0			0
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	0.639430	−	0.768849i	$-0.279170\pi$
$409$	−7.00000	−	12.1244i	−0.346128	−	0.599511i	−0.985558	+	0.169338i	$0.945837\pi$
$410$		0			0
$411$			20.7846i			1.02523i
$412$		0			0
$413$	42.0000			2.06668
$414$		0			0
$415$	9.00000			0.441793
$416$		0			0
$417$	−24.0000	−	13.8564i	−1.17529	−	0.678551i
$418$		0			0
$419$	13.0000	+	22.5167i	0.635092	+	1.10001i	0.986496	+	0.163787i	$0.0523710\pi$
$419$	13.0000	+	22.5167i	0.635092	+	1.10001i	−0.351404	+	0.936224i	$0.614296\pi$
$420$		0			0
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	0.0706626	+	0.997500i	$0.477489\pi$
$421$	−17.0000	+	29.4449i	−0.828529	+	1.43505i	−0.899192	+	0.437555i	$0.855845\pi$
$422$		0			0
$423$	−10.5000	−	18.1865i	−0.510527	−	0.884260i
$424$		0			0
$425$	−2.00000	+	3.46410i	−0.0970143	+	0.168034i
$426$		0			0
$427$	−10.5000	−	18.1865i	−0.508131	−	0.880108i
$428$		0			0
$429$	−6.00000	+	3.46410i	−0.289683	+	0.167248i
$430$		0			0
$431$	30.0000			1.44505			0.722525	−	0.691345i	$-0.242982\pi$
$431$	30.0000			1.44505			0.722525	+	0.691345i	$0.242982\pi$
$432$		0			0
$433$	28.0000			1.34559			0.672797	−	0.739827i	$-0.265093\pi$
$433$	28.0000			1.34559			0.672797	+	0.739827i	$0.265093\pi$
$434$		0			0
$435$	1.50000	−	0.866025i	0.0719195	−	0.0415227i
$436$		0			0
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$	−6.00000			−0.285714
$442$		0			0
$443$	7.50000	−	12.9904i	0.356336	−	0.617192i	−0.631010	−	0.775775i	$-0.717359\pi$
$443$	7.50000	−	12.9904i	0.356336	−	0.617192i	0.987346	+	0.158583i	$0.0506926\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$		0			0
$447$	−25.5000	−	14.7224i	−1.20611	−	0.696347i
$448$		0			0
$449$	−26.0000			−1.22702			−0.613508	−	0.789689i	$-0.710242\pi$
$449$	−26.0000			−1.22702			−0.613508	+	0.789689i	$0.710242\pi$
$450$		0			0
$451$	10.0000			0.470882
$452$		0			0
$453$			3.46410i			0.162758i
$454$		0			0
$455$	−3.00000	−	5.19615i	−0.140642	−	0.243599i
$456$		0			0
$457$	10.0000	−	17.3205i	0.467780	−	0.810219i	−0.531542	−	0.847032i	$-0.678387\pi$
$457$	10.0000	−	17.3205i	0.467780	−	0.810219i	0.999322	+	0.0368128i	$0.0117205\pi$
$458$		0			0
$459$		−	20.7846i		−	0.970143i
$460$		0			0
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$		0			0
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	−0.892778	−	0.450497i	$-0.851247\pi$
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	0.0562469	−	0.998417i	$-0.482087\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	9.00000			0.415581
$470$		0			0
$471$	−21.0000	−	12.1244i	−0.967629	−	0.558661i
$472$		0			0
$473$	−8.00000	−	13.8564i	−0.367840	−	0.637118i
$474$		0			0
$475$	−4.00000	+	6.92820i	−0.183533	+	0.317888i
$476$		0			0
$477$	−3.00000	+	5.19615i	−0.137361	+	0.237915i
$478$		0			0
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$		0			0
$481$	−4.00000	−	6.92820i	−0.182384	−	0.315899i
$482$		0			0
$483$	−13.5000	+	7.79423i	−0.614271	+	0.354650i
$484$		0			0
$485$	−2.00000			−0.0908153
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$		0			0
$489$	6.00000	−	3.46410i	0.271329	−	0.156652i
$490$		0			0
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	0.998467	−	0.0553560i	$-0.0176294\pi$
$491$	10.0000	+	17.3205i	0.451294	+	0.781664i	−0.547173	+	0.837020i	$0.684296\pi$
$492$		0			0
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$		0			0
$495$	−3.00000	+	5.19615i	−0.134840	+	0.233550i
$496$		0			0
$497$	3.00000	−	5.19615i	0.134568	−	0.233079i
$498$		0			0
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	−0.962472	−	0.271380i	$-0.912520\pi$
$499$	−16.0000	−	27.7128i	−0.716258	−	1.24060i	0.246214	−	0.969216i	$-0.420813\pi$
$500$		0			0
$501$	−13.5000	−	7.79423i	−0.603136	−	0.348220i
$502$		0			0
$503$	7.00000			0.312115			0.156057	−	0.987748i	$-0.450122\pi$
$503$	7.00000			0.312115			0.156057	+	0.987748i	$0.450122\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		−	15.5885i		−	0.692308i
$508$		0			0
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.738945	−	0.673766i	$-0.764676\pi$
$509$	−21.5000	−	37.2391i	−0.952971	−	1.65059i	−0.214026	−	0.976828i	$-0.568658\pi$
$510$		0			0
$511$	−6.00000	+	10.3923i	−0.265424	+	0.459728i
$512$		0			0
$513$		−	41.5692i		−	1.83533i
$514$		0			0
$515$	−4.00000	+	6.92820i	−0.176261	+	0.305293i
$516$		0			0
$517$	7.00000	+	12.1244i	0.307860	+	0.533229i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.0000			0.481919			0.240959	−	0.970535i	$-0.422538\pi$
$521$	11.0000			0.481919			0.240959	+	0.970535i	$0.422538\pi$
$522$		0			0
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$		0			0
$525$	−4.50000	−	2.59808i	−0.196396	−	0.113389i
$526$		0			0
$527$		0			0
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−42.0000			−1.82264
$532$		0			0
$533$	5.00000	−	8.66025i	0.216574	−	0.375117i
$534$		0			0
$535$	−1.50000	−	2.59808i	−0.0648507	−	0.112325i
$536$		0			0
$537$	3.00000	−	1.73205i	0.129460	−	0.0747435i
$538$		0			0
$539$	4.00000			0.172292
$540$		0			0
$541$	−39.0000			−1.67674			−0.838370	−	0.545101i	$-0.816491\pi$
$541$	−39.0000			−1.67674			−0.838370	+	0.545101i	$0.816491\pi$
$542$		0			0
$543$	−10.5000	+	6.06218i	−0.450598	+	0.260153i
$544$		0			0
$545$	2.50000	+	4.33013i	0.107088	+	0.185482i
$546$		0			0
$547$	−14.5000	+	25.1147i	−0.619975	+	1.07383i	0.369514	+	0.929225i	$0.379524\pi$
$547$	−14.5000	+	25.1147i	−0.619975	+	1.07383i	−0.989490	+	0.144604i	$0.953809\pi$
$548$		0			0
$549$	10.5000	+	18.1865i	0.448129	+	0.776182i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$	−9.00000	−	15.5885i	−0.382719	−	0.662889i
$554$		0			0
$555$	−6.00000	−	3.46410i	−0.254686	−	0.147043i
$556$		0			0
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	−16.0000			−0.676728
$560$		0			0
$561$			13.8564i			0.585018i
$562$		0			0
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$		0			0
$565$	−4.00000	+	6.92820i	−0.168281	+	0.291472i
$566$		0			0
$567$	27.0000			1.13389
$568$		0			0
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	0.978022	+	0.208502i	$0.0668588\pi$
$571$	16.0000	+	27.7128i	0.669579	+	1.15975i	−0.308443	+	0.951243i	$0.599808\pi$
$572$		0			0
$573$		−	13.8564i		−	0.578860i
$574$		0			0
$575$	−3.00000			−0.125109
$576$		0			0
$577$	−10.0000			−0.416305			−0.208153	−	0.978096i	$-0.566745\pi$
$577$	−10.0000			−0.416305			−0.208153	+	0.978096i	$0.566745\pi$
$578$		0			0
$579$	15.0000	+	8.66025i	0.623379	+	0.359908i
$580$		0			0
$581$	13.5000	+	23.3827i	0.560074	+	0.970077i
$582$		0			0
$583$	2.00000	−	3.46410i	0.0828315	−	0.143468i
$584$		0			0
$585$	3.00000	+	5.19615i	0.124035	+	0.214834i
$586$		0			0
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	0.293640	+	0.955916i	$0.405133\pi$
$587$	−16.5000	+	28.5788i	−0.681028	+	1.17957i	−0.974668	+	0.223659i	$0.928200\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$		0			0
$593$	20.0000			0.821302			0.410651	−	0.911793i	$-0.365302\pi$
$593$	20.0000			0.821302			0.410651	+	0.911793i	$0.365302\pi$
$594$		0			0
$595$	−12.0000			−0.491952
$596$		0			0
$597$	−6.00000	+	3.46410i	−0.245564	+	0.141776i
$598$		0			0
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	0.745613	−	0.666379i	$-0.232157\pi$
$599$	−5.00000	−	8.66025i	−0.204294	−	0.353848i	−0.949908	+	0.312531i	$0.898823\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$		0			0
$603$	−9.00000			−0.366508
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	−20.5000	−	35.5070i	−0.832069	−	1.44119i	−0.896394	−	0.443257i	$-0.853823\pi$
$607$	−20.5000	−	35.5070i	−0.832069	−	1.44119i	0.0643251	−	0.997929i	$-0.479511\pi$
$608$		0			0
$609$	4.50000	+	2.59808i	0.182349	+	0.105279i
$610$		0			0
$611$	14.0000			0.566379
$612$		0			0
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$		0			0
$615$		−	8.66025i		−	0.349215i
$616$		0			0
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	0.959117	+	0.283011i	$0.0913331\pi$
$617$	18.0000	+	31.1769i	0.724653	+	1.25514i	−0.234464	+	0.972125i	$0.575334\pi$
$618$		0			0
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	−0.903416	−	0.428765i	$-0.858949\pi$
$619$	−2.00000	+	3.46410i	−0.0803868	+	0.139234i	0.823029	+	0.567999i	$0.192282\pi$
$620$		0			0
$621$	13.5000	−	7.79423i	0.541736	−	0.312772i
$622$		0			0
$623$	22.5000	−	38.9711i	0.901443	−	1.56135i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$			27.7128i			1.10674i
$628$		0			0
$629$	−16.0000			−0.637962
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$		0			0
$633$	−33.0000	−	19.0526i	−1.31163	−	0.757271i
$634$		0			0
$635$	2.50000	+	4.33013i	0.0992095	+	0.171836i
$636$		0			0
$637$	2.00000	−	3.46410i	0.0792429	−	0.137253i
$638$		0			0
$639$	−3.00000	+	5.19615i	−0.118678	+	0.205557i
$640$		0			0
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	0.330997	+	0.943632i	$0.392615\pi$
$641$	−16.5000	+	28.5788i	−0.651711	+	1.12880i	−0.982708	+	0.185164i	$0.940718\pi$
$642$		0			0
$643$	−4.50000	−	7.79423i	−0.177463	−	0.307374i	0.763548	−	0.645751i	$-0.223456\pi$
$643$	−4.50000	−	7.79423i	−0.177463	−	0.307374i	−0.941011	+	0.338377i	$0.890122\pi$
$644$		0			0
$645$	−12.0000	+	6.92820i	−0.472500	+	0.272798i
$646$		0			0
$647$	17.0000			0.668339			0.334169	−	0.942513i	$-0.391544\pi$
$647$	17.0000			0.668339			0.334169	+	0.942513i	$0.391544\pi$
$648$		0			0
$649$	28.0000			1.09910
$650$		0			0
$651$		0			0
$652$		0			0
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	0.902502	−	0.430686i	$-0.141728\pi$
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	−0.824236	+	0.566247i	$0.808395\pi$
$654$		0			0
$655$	3.00000	−	5.19615i	0.117220	−	0.203030i
$656$		0			0
$657$	6.00000	−	10.3923i	0.234082	−	0.405442i
$658$		0			0
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	−0.933357	−	0.358951i	$-0.883135\pi$
$659$	−4.00000	+	6.92820i	−0.155818	+	0.269884i	0.777539	+	0.628835i	$0.216468\pi$
$660$		0			0
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	0.969442	−	0.245319i	$-0.0788928\pi$
$661$	7.00000	+	12.1244i	0.272268	+	0.471583i	−0.697174	+	0.716902i	$0.745559\pi$
$662$		0			0
$663$	12.0000	+	6.92820i	0.466041	+	0.269069i
$664$		0			0
$665$	−24.0000			−0.930680
$666$		0			0
$667$	3.00000			0.116160
$668$		0			0
$669$			32.9090i			1.27233i
$670$		0			0
$671$	−7.00000	−	12.1244i	−0.270232	−	0.468056i
$672$		0			0
$673$	−3.00000	+	5.19615i	−0.115642	+	0.200297i	−0.918036	−	0.396497i	$-0.870226\pi$
$673$	−3.00000	+	5.19615i	−0.115642	+	0.200297i	0.802395	+	0.596794i	$0.203559\pi$
$674$		0			0
$675$	4.50000	+	2.59808i	0.173205	+	0.100000i
$676$		0			0
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	−0.107772	−	0.994176i	$-0.534372\pi$
$677$	21.0000	−	36.3731i	0.807096	−	1.39793i	0.914867	−	0.403755i	$-0.132295\pi$
$678$		0			0
$679$	−3.00000	−	5.19615i	−0.115129	−	0.199410i
$680$		0			0
$681$			6.92820i			0.265489i
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−22.5000	−	12.9904i	−0.858429	−	0.495614i
$688$		0			0
$689$	−2.00000	−	3.46410i	−0.0761939	−	0.131972i
$690$		0			0
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	−0.967901	−	0.251330i	$-0.919132\pi$
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	0.701609	+	0.712562i	$0.252465\pi$
$692$		0			0
$693$	−18.0000			−0.683763
$694$		0			0
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$		0			0
$697$	−10.0000	−	17.3205i	−0.378777	−	0.656061i
$698$		0			0
$699$	36.0000	−	20.7846i	1.36165	−	0.786146i
$700$		0			0
$701$	23.0000			0.868698			0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000			0.868698			0.434349	+	0.900745i	$0.356978\pi$
$702$		0			0
$703$	−32.0000			−1.20690
$704$		0			0
$705$	10.5000	−	6.06218i	0.395453	−	0.228315i
$706$		0			0
$707$	27.0000	+	46.7654i	1.01544	+	1.75879i
$708$		0			0
$709$	20.5000	−	35.5070i	0.769894	−	1.33349i	−0.167727	−	0.985834i	$-0.553643\pi$
$709$	20.5000	−	35.5070i	0.769894	−	1.33349i	0.937620	−	0.347661i	$-0.113024\pi$
$710$		0			0
$711$	9.00000	+	15.5885i	0.337526	+	0.584613i
$712$		0			0
$713$		0			0
$714$		0			0
$715$	−2.00000	−	3.46410i	−0.0747958	−	0.129550i
$716$		0			0
$717$	−12.0000	−	6.92820i	−0.448148	−	0.258738i
$718$		0			0
$719$	−6.00000			−0.223762			−0.111881	−	0.993722i	$-0.535688\pi$
$719$	−6.00000			−0.223762			−0.111881	+	0.993722i	$0.535688\pi$
$720$		0			0
$721$	−24.0000			−0.893807
$722$		0			0
$723$		−	19.0526i		−	0.708572i
$724$		0			0
$725$	0.500000	+	0.866025i	0.0185695	+	0.0321634i
$726$		0			0
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	−0.570049	−	0.821611i	$-0.693076\pi$
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	0.996560	+	0.0828714i	$0.0264091\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	−16.0000	+	27.7128i	−0.591781	+	1.02500i
$732$		0			0
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	0.987971	+	0.154642i	$0.0494225\pi$
$733$	17.0000	+	29.4449i	0.627909	+	1.08757i	−0.360061	+	0.932929i	$0.617244\pi$
$734$		0			0
$735$		−	3.46410i		−	0.127775i
$736$		0			0
$737$	6.00000			0.221013
$738$		0			0
$739$	2.00000			0.0735712			0.0367856	−	0.999323i	$-0.488288\pi$
$739$	2.00000			0.0735712			0.0367856	+	0.999323i	$0.488288\pi$
$740$		0			0
$741$	24.0000	+	13.8564i	0.881662	+	0.509028i
$742$		0			0
$743$	−14.5000	−	25.1147i	−0.531953	−	0.921370i	−0.999304	−	0.0372984i	$-0.988125\pi$
$743$	−14.5000	−	25.1147i	−0.531953	−	0.921370i	0.467351	−	0.884072i	$-0.345209\pi$
$744$		0			0
$745$	8.50000	−	14.7224i	0.311416	−	0.539388i
$746$		0			0
$747$	−13.5000	−	23.3827i	−0.493939	−	0.855528i
$748$		0			0
$749$	4.50000	−	7.79423i	0.164426	−	0.284795i
$750$		0			0
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	0.942715	−	0.333599i	$-0.108263\pi$
$751$	5.00000	+	8.66025i	0.182453	+	0.316017i	−0.760263	+	0.649616i	$0.774930\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−2.00000			−0.0727875
$756$		0			0
$757$	−26.0000			−0.944986			−0.472493	−	0.881334i	$-0.656646\pi$
$757$	−26.0000			−0.944986			−0.472493	+	0.881334i	$0.656646\pi$
$758$		0			0
$759$	−9.00000	+	5.19615i	−0.326679	+	0.188608i
$760$		0			0
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	0.697467	−	0.716617i	$-0.254310\pi$
$761$	−7.50000	−	12.9904i	−0.271875	−	0.470901i	−0.969342	+	0.245716i	$0.920977\pi$
$762$		0			0
$763$	−7.50000	+	12.9904i	−0.271518	+	0.470283i
$764$		0			0
$765$	12.0000			0.433861
$766$		0			0
$767$	14.0000	−	24.2487i	0.505511	−	0.875570i
$768$		0			0
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	0.817423	−	0.576038i	$-0.195402\pi$
$769$	−2.50000	−	4.33013i	−0.0901523	−	0.156148i	−0.907575	+	0.419890i	$0.862069\pi$
$770$		0			0
$771$	9.00000	+	5.19615i	0.324127	+	0.187135i
$772$		0			0
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$		−	20.7846i		−	0.745644i
$778$		0			0
$779$	−20.0000	−	34.6410i	−0.716574	−	1.24114i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$	−4.50000	−	2.59808i	−0.160817	−	0.0928477i
$784$		0			0
$785$	7.00000	−	12.1244i	0.249841	−	0.432737i
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$		0			0
$789$			27.7128i			0.986602i
$790$		0			0
$791$	−24.0000			−0.853342
$792$		0			0
$793$	−14.0000			−0.497155
$794$		0			0
$795$	−3.00000	−	1.73205i	−0.106399	−	0.0614295i
$796$		0			0
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	0.538501	−	0.842625i	$-0.318991\pi$
$797$	−13.0000	−	22.5167i	−0.460484	−	0.797581i	−0.998985	+	0.0450436i	$0.985657\pi$
$798$		0			0
$799$	14.0000	−	24.2487i	0.495284	−	0.857858i
$800$		0			0
$801$	−22.5000	+	38.9711i	−0.794998	+	1.37698i
$802$		0			0
$803$	−4.00000	+	6.92820i	−0.141157	+	0.244491i
$804$		0			0
$805$	−4.50000	−	7.79423i	−0.158604	−	0.274710i
$806$		0			0
$807$	37.5000	−	21.6506i	1.32006	−	0.762138i
$808$		0			0
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$		0			0
$811$	42.0000			1.47482			0.737410	−	0.675446i	$-0.236049\pi$
$811$	42.0000			1.47482			0.737410	+	0.675446i	$0.236049\pi$
$812$		0			0
$813$	12.0000	−	6.92820i	0.420858	−	0.242983i
$814$		0			0
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$	−32.0000	+	55.4256i	−1.11954	+	1.93910i
$818$		0			0
$819$	−9.00000	+	15.5885i	−0.314485	+	0.544705i
$820$		0			0
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	−0.966708	−	0.255884i	$-0.917634\pi$
$821$	−7.50000	+	12.9904i	−0.261752	+	0.453367i	0.704956	+	0.709251i	$0.250967\pi$
$822$		0			0
$823$	26.5000	+	45.8993i	0.923732	+	1.59995i	0.793588	+	0.608456i	$0.208211\pi$
$823$	26.5000	+	45.8993i	0.923732	+	1.59995i	0.130144	+	0.991495i	$0.458456\pi$
$824$		0			0
$825$	−3.00000	−	1.73205i	−0.104447	−	0.0603023i
$826$		0			0
$827$	−37.0000			−1.28662			−0.643308	−	0.765607i	$-0.722439\pi$
$827$	−37.0000			−1.28662			−0.643308	+	0.765607i	$0.722439\pi$
$828$		0			0
$829$	−3.00000			−0.104194			−0.0520972	−	0.998642i	$-0.516591\pi$
$829$	−3.00000			−0.104194			−0.0520972	+	0.998642i	$0.516591\pi$
$830$		0			0
$831$			20.7846i			0.721010i
$832$		0			0
$833$	−4.00000	−	6.92820i	−0.138592	−	0.240048i
$834$		0			0
$835$	4.50000	−	7.79423i	0.155729	−	0.269730i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	0.281205	+	0.959648i	$0.409266\pi$
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	−0.971682	+	0.236293i	$0.924067\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$		0			0
$843$		−	25.9808i		−	0.894825i
$844$		0			0
$845$	9.00000			0.309609
$846$		0			0
$847$	−21.0000			−0.721569
$848$		0			0
$849$	31.5000	+	18.1865i	1.08108	+	0.624160i
$850$		0			0
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	27.0000	−	46.7654i	0.924462	−	1.60122i	0.132039	−	0.991245i	$-0.457848\pi$
$853$	27.0000	−	46.7654i	0.924462	−	1.60122i	0.792424	−	0.609971i	$-0.208819\pi$
$854$		0			0
$855$	24.0000			0.820783
$856$		0			0
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	−0.938699	−	0.344739i	$-0.887967\pi$
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	0.767902	+	0.640567i	$0.221301\pi$
$858$		0			0
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	0.990374	−	0.138416i	$-0.0442012\pi$
$859$	11.0000	+	19.0526i	0.375315	+	0.650065i	−0.615059	+	0.788481i	$0.710868\pi$
$860$		0			0
$861$	22.5000	−	12.9904i	0.766798	−	0.442711i
$862$		0			0
$863$	−17.0000			−0.578687			−0.289343	−	0.957225i	$-0.593437\pi$
$863$	−17.0000			−0.578687			−0.289343	+	0.957225i	$0.593437\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1.50000	+	0.866025i	−0.0509427	+	0.0294118i
$868$		0			0
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	3.00000	−	5.19615i	0.101651	−	0.176065i
$872$		0			0
$873$	3.00000	+	5.19615i	0.101535	+	0.175863i
$874$		0			0
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$		0			0
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	0.977018	−	0.213158i	$-0.0683750\pi$
$877$	9.00000	+	15.5885i	0.303908	+	0.526385i	−0.673109	+	0.739543i	$0.735042\pi$
$878$		0			0
$879$	−18.0000	−	10.3923i	−0.607125	−	0.350524i
$880$		0			0
$881$	−35.0000			−1.17918			−0.589590	−	0.807703i	$-0.700711\pi$
$881$	−35.0000			−1.17918			−0.589590	+	0.807703i	$0.700711\pi$
$882$		0			0
$883$	−23.0000			−0.774012			−0.387006	−	0.922077i	$-0.626491\pi$
$883$	−23.0000			−0.774012			−0.387006	+	0.922077i	$0.626491\pi$
$884$		0			0
$885$		−	24.2487i		−	0.815112i
$886$		0			0
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	0.992149	+	0.125061i	$0.0399128\pi$
$887$	18.0000	+	31.1769i	0.604381	+	1.04682i	−0.387768	+	0.921757i	$0.626754\pi$
$888$		0			0
$889$	−7.50000	+	12.9904i	−0.251542	+	0.435683i
$890$		0			0
$891$	18.0000			0.603023
$892$		0			0
$893$	28.0000	−	48.4974i	0.936984	−	1.62290i
$894$		0			0
$895$	1.00000	+	1.73205i	0.0334263	+	0.0578961i
$896$		0			0
$897$			10.3923i			0.346989i
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−8.00000			−0.266519
$902$		0			0
$903$	−36.0000	−	20.7846i	−1.19800	−	0.691669i
$904$		0			0
$905$	−3.50000	−	6.06218i	−0.116344	−	0.201514i
$906$		0			0
$907$	−25.5000	+	44.1673i	−0.846714	+	1.46655i	0.0374111	+	0.999300i	$0.488089\pi$
$907$	−25.5000	+	44.1673i	−0.846714	+	1.46655i	−0.884125	+	0.467251i	$0.845244\pi$
$908$		0			0
$909$	−27.0000	−	46.7654i	−0.895533	−	1.55111i
$910$		0			0
$911$	−25.0000	+	43.3013i	−0.828287	+	1.43464i	0.0710941	+	0.997470i	$0.477351\pi$
$911$	−25.0000	+	43.3013i	−0.828287	+	1.43464i	−0.899381	+	0.437165i	$0.855982\pi$
$912$		0			0
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$		0			0
$915$	−10.5000	+	6.06218i	−0.347119	+	0.200409i
$916$		0			0
$917$	18.0000			0.594412
$918$		0			0
$919$	−10.0000			−0.329870			−0.164935	−	0.986304i	$-0.552741\pi$
$919$	−10.0000			−0.329870			−0.164935	+	0.986304i	$0.552741\pi$
$920$		0			0
$921$	−10.5000	+	6.06218i	−0.345987	+	0.199756i
$922$		0			0
$923$	−2.00000	−	3.46410i	−0.0658308	−	0.114022i
$924$		0			0
$925$	2.00000	−	3.46410i	0.0657596	−	0.113899i
$926$		0			0
$927$	24.0000			0.788263
$928$		0			0
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$		0			0
$931$	−8.00000	−	13.8564i	−0.262189	−	0.454125i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−8.00000			−0.261628
$936$		0			0
$937$		0			0			−	1.00000i	$-0.5\pi$
$937$		0			0				1.00000i	$0.5\pi$
$938$		0			0
$939$			24.2487i			0.791327i
$940$		0			0
$941$	3.50000	+	6.06218i	0.114097	+	0.197621i	0.917418	−	0.397924i	$-0.130269\pi$
$941$	3.50000	+	6.06218i	0.114097	+	0.197621i	−0.803322	+	0.595545i	$0.796936\pi$
$942$		0			0
$943$	7.50000	−	12.9904i	0.244234	−	0.423025i
$944$		0			0
$945$			15.5885i			0.507093i
$946$		0			0
$947$	28.5000	−	49.3634i	0.926126	−	1.60410i	0.136385	−	0.990656i	$-0.456452\pi$
$947$	28.5000	−	49.3634i	0.926126	−	1.60410i	0.789741	−	0.613441i	$-0.210215\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$		0			0
$951$		−	58.8897i		−	1.90963i
$952$		0			0
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	8.00000			0.258874
$956$		0			0
$957$	3.00000	+	1.73205i	0.0969762	+	0.0559893i
$958$		0			0
$959$	−18.0000	−	31.1769i	−0.581250	−	1.00676i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$		0			0
$963$	−4.50000	+	7.79423i	−0.145010	+	0.251166i
$964$		0			0
$965$	−5.00000	+	8.66025i	−0.160956	+	0.278783i
$966$		0			0
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	0.980814	+	0.194946i	$0.0624533\pi$
$967$	20.5000	+	35.5070i	0.659236	+	1.14183i	−0.321578	+	0.946883i	$0.604213\pi$
$968$		0			0
$969$	48.0000	−	27.7128i	1.54198	−	0.890264i
$970$		0			0
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$		0			0
$973$	48.0000			1.53881
$974$		0			0
$975$	−3.00000	+	1.73205i	−0.0960769	+	0.0554700i
$976$		0			0
$977$	19.0000	+	32.9090i	0.607864	+	1.05285i	0.991592	+	0.129405i	$0.0413067\pi$
$977$	19.0000	+	32.9090i	0.607864	+	1.05285i	−0.383728	+	0.923446i	$0.625360\pi$
$978$		0			0
$979$	15.0000	−	25.9808i	0.479402	−	0.830349i
$980$		0			0
$981$	7.50000	−	12.9904i	0.239457	−	0.414751i
$982$		0			0
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	−0.841112	−	0.540860i	$-0.818099\pi$
$983$	1.50000	−	2.59808i	0.0478426	−	0.0828658i	0.888955	+	0.457995i	$0.151432\pi$
$984$		0			0
$985$	−6.00000	−	10.3923i	−0.191176	−	0.331126i
$986$		0			0
$987$	31.5000	+	18.1865i	1.00266	+	0.578884i
$988$		0			0
$989$	−24.0000			−0.763156
$990$		0			0
$991$	−26.0000			−0.825917			−0.412959	−	0.910750i	$-0.635505\pi$
$991$	−26.0000			−0.825917			−0.412959	+	0.910750i	$0.635505\pi$
$992$		0			0
$993$			10.3923i			0.329790i
$994$		0			0
$995$	−2.00000	−	3.46410i	−0.0634043	−	0.109819i
$996$		0			0
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	−0.687584	−	0.726105i	$-0.741329\pi$
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	0.972617	+	0.232413i	$0.0746622\pi$
$998$		0			0
$999$			20.7846i			0.657596i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.d.241.1		2
3.2	odd	2		2160.2.q.a.721.1		2
4.3	odd	2		45.2.e.a.16.1	✓	2
9.2	odd	6		6480.2.a.x.1.1		1
9.4	even	3	inner	720.2.q.d.481.1		2
9.5	odd	6		2160.2.q.a.1441.1		2
9.7	even	3		6480.2.a.k.1.1		1
12.11	even	2		135.2.e.a.46.1		2
20.3	even	4		225.2.k.a.124.2		4
20.7	even	4		225.2.k.a.124.1		4
20.19	odd	2		225.2.e.a.151.1		2
36.7	odd	6		405.2.a.e.1.1		1
36.11	even	6		405.2.a.b.1.1		1
36.23	even	6		135.2.e.a.91.1		2
36.31	odd	6		45.2.e.a.31.1	yes	2
60.23	odd	4		675.2.k.a.424.1		4
60.47	odd	4		675.2.k.a.424.2		4
60.59	even	2		675.2.e.a.451.1		2
180.7	even	12		2025.2.b.c.649.2		2
180.23	odd	12		675.2.k.a.199.2		4
180.43	even	12		2025.2.b.c.649.1		2
180.47	odd	12		2025.2.b.d.649.1		2
180.59	even	6		675.2.e.a.226.1		2
180.67	even	12		225.2.k.a.49.2		4
180.79	odd	6		2025.2.a.b.1.1		1
180.83	odd	12		2025.2.b.d.649.2		2
180.103	even	12		225.2.k.a.49.1		4
180.119	even	6		2025.2.a.e.1.1		1
180.139	odd	6		225.2.e.a.76.1		2
180.167	odd	12		675.2.k.a.199.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.a.16.1	✓	2	4.3	odd	2
45.2.e.a.31.1	yes	2	36.31	odd	6
135.2.e.a.46.1		2	12.11	even	2
135.2.e.a.91.1		2	36.23	even	6
225.2.e.a.76.1		2	180.139	odd	6
225.2.e.a.151.1		2	20.19	odd	2
225.2.k.a.49.1		4	180.103	even	12
225.2.k.a.49.2		4	180.67	even	12
225.2.k.a.124.1		4	20.7	even	4
225.2.k.a.124.2		4	20.3	even	4
405.2.a.b.1.1		1	36.11	even	6
405.2.a.e.1.1		1	36.7	odd	6
675.2.e.a.226.1		2	180.59	even	6
675.2.e.a.451.1		2	60.59	even	2
675.2.k.a.199.1		4	180.167	odd	12
675.2.k.a.199.2		4	180.23	odd	12
675.2.k.a.424.1		4	60.23	odd	4
675.2.k.a.424.2		4	60.47	odd	4
720.2.q.d.241.1		2	1.1	even	1	trivial
720.2.q.d.481.1		2	9.4	even	3	inner
2025.2.a.b.1.1		1	180.79	odd	6
2025.2.a.e.1.1		1	180.119	even	6
2025.2.b.c.649.1		2	180.43	even	12
2025.2.b.c.649.2		2	180.7	even	12
2025.2.b.d.649.1		2	180.47	odd	12
2025.2.b.d.649.2		2	180.83	odd	12
2160.2.q.a.721.1		2	3.2	odd	2
2160.2.q.a.1441.1		2	9.5	odd	6
6480.2.a.k.1.1		1	9.7	even	3
6480.2.a.x.1.1		1	9.2	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)

\(f(q)\)	\(=\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 0.866025i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-1.50000 + 2.59808i) q^{7} +(1.50000 - 2.59808i) q^{9} +(-1.00000 + 1.73205i) q^{11} +(1.00000 + 1.73205i) q^{13} +(1.50000 + 0.866025i) q^{15} +4.00000 q^{17} +8.00000 q^{19} +5.19615i q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.19615i q^{27} +(0.500000 - 0.866025i) q^{29} +3.46410i q^{33} -3.00000 q^{35} -4.00000 q^{37} +(3.00000 + 1.73205i) q^{39} +(-2.50000 - 4.33013i) q^{41} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{45} +(3.50000 - 6.06218i) q^{47} +(-1.00000 - 1.73205i) q^{49} +(6.00000 - 3.46410i) q^{51} -2.00000 q^{53} -2.00000 q^{55} +(12.0000 - 6.92820i) q^{57} +(-7.00000 - 12.1244i) q^{59} +(-3.50000 + 6.06218i) q^{61} +(4.50000 + 7.79423i) q^{63} +(-1.00000 + 1.73205i) q^{65} +(-1.50000 - 2.59808i) q^{67} +(4.50000 + 2.59808i) q^{69} -2.00000 q^{71} +4.00000 q^{73} +1.73205i q^{75} +(-3.00000 - 5.19615i) q^{77} +(-3.00000 + 5.19615i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(4.50000 - 7.79423i) q^{83} +(2.00000 + 3.46410i) q^{85} -1.73205i q^{87} -15.0000 q^{89} -6.00000 q^{91} +(4.00000 + 6.92820i) q^{95} +(-1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + q^5 - 3 * q^7 + 3 * q^9	\( 2 q + 3 q^{3} + q^{5} - 3 q^{7} + 3 q^{9} - 2 q^{11} + 2 q^{13} + 3 q^{15} + 8 q^{17} + 16 q^{19} + 3 q^{23} - q^{25} + q^{29} - 6 q^{35} - 8 q^{37} + 6 q^{39} - 5 q^{41} - 8 q^{43} + 6 q^{45} + 7 q^{47} - 2 q^{49} + 12 q^{51} - 4 q^{53} - 4 q^{55} + 24 q^{57} - 14 q^{59} - 7 q^{61} + 9 q^{63} - 2 q^{65} - 3 q^{67} + 9 q^{69} - 4 q^{71} + 8 q^{73} - 6 q^{77} - 6 q^{79} - 9 q^{81} + 9 q^{83} + 4 q^{85} - 30 q^{89} - 12 q^{91} + 8 q^{95} - 2 q^{97} + 6 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + q^5 - 3 * q^7 + 3 * q^9 - 2 * q^11 + 2 * q^13 + 3 * q^15 + 8 * q^17 + 16 * q^19 + 3 * q^23 - q^25 + q^29 - 6 * q^35 - 8 * q^37 + 6 * q^39 - 5 * q^41 - 8 * q^43 + 6 * q^45 + 7 * q^47 - 2 * q^49 + 12 * q^51 - 4 * q^53 - 4 * q^55 + 24 * q^57 - 14 * q^59 - 7 * q^61 + 9 * q^63 - 2 * q^65 - 3 * q^67 + 9 * q^69 - 4 * q^71 + 8 * q^73 - 6 * q^77 - 6 * q^79 - 9 * q^81 + 9 * q^83 + 4 * q^85 - 30 * q^89 - 12 * q^91 + 8 * q^95 - 2 * q^97 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more