LMFDB - Embedded newform 560.2.q.i.81.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [560,2,Mod(81,560)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(560, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("560.81");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 560 = 2^{4} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	560.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:	$4.47162251319$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			81.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	560.81
Dual form			560.2.q.i.401.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})$	\(q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-7.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +9.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.00000 + 5.19615i) q^{33} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} -7.00000 q^{41} +5.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(4.00000 + 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(1.00000 - 1.73205i) q^{53} -2.00000 q^{55} -18.0000 q^{57} +(5.00000 - 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-12.0000 + 10.3923i) q^{63} +(-4.50000 + 7.79423i) q^{67} +9.00000 q^{69} -2.00000 q^{71} +(2.00000 - 3.46410i) q^{73} +(1.50000 + 2.59808i) q^{75} +(5.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{83} +4.00000 q^{85} +(13.5000 - 23.3827i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(6.00000 + 10.3923i) q^{93} +(3.00000 - 5.19615i) q^{95} +14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 3 q^{3} + q^{5} - q^{7} - 6 q^{9}+O(q^{10}) $ 2 * q + 3 * q^3 + q^5 - q^7 - 6 * q^9	$ 2 q + 3 q^{3} + q^{5} - q^{7} - 6 q^{9} - 2 q^{11} + 6 q^{15} + 4 q^{17} - 6 q^{19} - 15 q^{21} + 3 q^{23} - q^{25} - 18 q^{27} + 18 q^{29} - 4 q^{31} + 6 q^{33} + 4 q^{35} + 4 q^{37} - 14 q^{41} + 10 q^{43} + 6 q^{45} + 8 q^{47} - 13 q^{49} - 12 q^{51} + 2 q^{53} - 4 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} - 24 q^{63} - 9 q^{67} + 18 q^{69} - 4 q^{71} + 4 q^{73} + 3 q^{75} + 10 q^{77} + 10 q^{79} - 9 q^{81} + 14 q^{83} + 8 q^{85} + 27 q^{87} - q^{89} + 12 q^{93} + 6 q^{95} + 28 q^{97} + 24 q^{99}+O(q^{100}) $ 2 * q + 3 * q^3 + q^5 - q^7 - 6 * q^9 - 2 * q^11 + 6 * q^15 + 4 * q^17 - 6 * q^19 - 15 * q^21 + 3 * q^23 - q^25 - 18 * q^27 + 18 * q^29 - 4 * q^31 + 6 * q^33 + 4 * q^35 + 4 * q^37 - 14 * q^41 + 10 * q^43 + 6 * q^45 + 8 * q^47 - 13 * q^49 - 12 * q^51 + 2 * q^53 - 4 * q^55 - 36 * q^57 + 10 * q^59 - q^61 - 24 * q^63 - 9 * q^67 + 18 * q^69 - 4 * q^71 + 4 * q^73 + 3 * q^75 + 10 * q^77 + 10 * q^79 - 9 * q^81 + 14 * q^83 + 8 * q^85 + 27 * q^87 - q^89 + 12 * q^93 + 6 * q^95 + 28 * q^97 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/560\mathbb{Z}\right)^\times$.

$n$	$241$	$337$	$351$	$421$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i		−	1.00000i	$-0.5\pi$
$3$	1.50000	−	2.59808i	0.866025	−	1.50000i	0.866025	−	0.500000i	$-0.166667\pi$
$4$		0			0
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$		0			0
$9$	−3.00000	−	5.19615i	−1.00000	−	1.73205i
$10$		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
$13$		0			0			−	1.00000i	$-0.5\pi$
$13$		0			0				1.00000i	$0.5\pi$
$14$		0			0
$15$	3.00000			0.774597
$16$		0			0
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$		0			0
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$		0			0
$21$	−7.50000	−	2.59808i	−1.63663	−	0.566947i
$22$		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
$27$	−9.00000			−1.73205
$28$		0			0
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$		0			0
$35$	2.00000	−	1.73205i	0.338062	−	0.292770i
$36$		0			0
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$		0			0
$45$	3.00000	−	5.19615i	0.447214	−	0.774597i
$46$		0			0
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	0.995066	+	0.0992202i	$0.0316348\pi$
$47$	4.00000	+	6.92820i	0.583460	+	1.01058i	−0.411606	+	0.911362i	$0.635032\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$		0			0
$51$	−6.00000	−	10.3923i	−0.840168	−	1.45521i
$52$		0			0
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$	−18.0000			−2.38416
$58$		0			0
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	−0.331949	−	0.943297i	$-0.607706\pi$
$59$	5.00000	−	8.66025i	0.650945	−	1.12747i	0.982894	−	0.184172i	$-0.0589603\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$		0			0
$63$	−12.0000	+	10.3923i	−1.51186	+	1.30931i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	0.448528	+	0.893769i	$0.351948\pi$
$67$	−4.50000	+	7.79423i	−0.549762	+	0.952217i	−0.998290	+	0.0584478i	$0.981385\pi$
$68$		0			0
$69$	9.00000			1.08347
$70$		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
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	−0.724923	−	0.688830i	$-0.758125\pi$
$73$	2.00000	−	3.46410i	0.234082	−	0.405442i	0.959006	+	0.283387i	$0.0914581\pi$
$74$		0			0
$75$	1.50000	+	2.59808i	0.173205	+	0.300000i
$76$		0			0
$77$	5.00000	+	1.73205i	0.569803	+	0.197386i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	7.00000			0.768350			0.384175	−	0.923260i	$-0.374486\pi$
$83$	7.00000			0.768350			0.384175	+	0.923260i	$0.374486\pi$
$84$		0			0
$85$	4.00000			0.433861
$86$		0			0
$87$	13.5000	−	23.3827i	1.44735	−	2.50689i
$88$		0			0
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	0.838308	−	0.545197i	$-0.183545\pi$
$89$	−0.500000	−	0.866025i	−0.0529999	−	0.0917985i	−0.891308	+	0.453398i	$0.850212\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	6.00000	+	10.3923i	0.622171	+	1.07763i
$94$		0			0
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	14.0000			1.42148			0.710742	−	0.703452i	$-0.248359\pi$
$97$	14.0000			1.42148			0.710742	+	0.703452i	$0.248359\pi$
$98$		0			0
$99$	12.0000			1.20605
$100$		0			0
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	−0.930953	−	0.365140i	$-0.881021\pi$
$101$	−1.50000	+	2.59808i	−0.149256	+	0.258518i	0.781697	+	0.623658i	$0.214354\pi$
$102$		0			0
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$	−1.50000	−	7.79423i	−0.146385	−	0.760639i
$106$		0			0
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	0.929377	−	0.369132i	$-0.120345\pi$
$107$	1.50000	+	2.59808i	0.145010	+	0.251166i	−0.784366	+	0.620298i	$0.787012\pi$
$108$		0			0
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	−0.565940	−	0.824447i	$-0.691487\pi$
$109$	4.50000	−	7.79423i	0.431022	−	0.746552i	0.996962	+	0.0778949i	$0.0248199\pi$
$110$		0			0
$111$	12.0000			1.13899
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$	−1.50000	+	2.59808i	−0.139876	+	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−10.0000	−	3.46410i	−0.916698	−	0.317554i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$		0			0
$123$	−10.5000	+	18.1865i	−0.946753	+	1.63982i
$124$		0			0
$125$	−1.00000			−0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	7.50000	−	12.9904i	0.660338	−	1.14374i
$130$		0			0
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$		0			0
$133$	−12.0000	+	10.3923i	−1.04053	+	0.901127i
$134$		0			0
$135$	−4.50000	−	7.79423i	−0.387298	−	0.670820i
$136$		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
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$		0			0
$141$	24.0000			2.02116
$142$		0			0
$143$		0			0
$144$		0			0
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$		0			0
$147$	−3.00000	+	20.7846i	−0.247436	+	1.71429i
$148$		0			0
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	0.798019	−	0.602632i	$-0.205881\pi$
$149$	−1.50000	−	2.59808i	−0.122885	−	0.212843i	−0.920904	+	0.389789i	$0.872548\pi$
$150$		0			0
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	0.331842	+	0.943335i	$0.392330\pi$
$151$	−8.00000	+	13.8564i	−0.651031	+	1.12762i	−0.982873	+	0.184284i	$0.941004\pi$
$152$		0			0
$153$	−24.0000			−1.94029
$154$		0			0
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	−0.993608	−	0.112884i	$-0.963991\pi$
$157$	−5.00000	+	8.66025i	−0.399043	+	0.691164i	0.594565	+	0.804048i	$0.297324\pi$
$158$		0			0
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	6.00000	−	5.19615i	0.472866	−	0.409514i
$162$		0			0
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$		0			0
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$		0			0
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	−13.0000			−1.00000
$170$		0			0
$171$	−18.0000	+	31.1769i	−1.37649	+	2.38416i
$172$		0			0
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	0.672949	−	0.739689i	$-0.265027\pi$
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	−0.977064	+	0.212947i	$0.931694\pi$
$174$		0			0
$175$	2.50000	+	0.866025i	0.188982	+	0.0654654i
$176$		0			0
$177$	−15.0000	−	25.9808i	−1.12747	−	1.95283i
$178$		0			0
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−3.00000			−0.221766
$184$		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
$189$	4.50000	+	23.3827i	0.327327	+	1.70084i
$190$		0			0
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	−0.982828	−	0.184525i	$-0.940925\pi$
$191$	−9.00000	−	15.5885i	−0.651217	−	1.12794i	0.331611	−	0.943416i	$-0.392408\pi$
$192$		0			0
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.162488	+	0.986710i	$0.551952\pi$
$193$	−13.0000	+	22.5167i	−0.935760	+	1.62078i	−0.773272	+	0.634074i	$0.781381\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	−0.928166	−	0.372168i	$-0.878615\pi$
$199$	−2.00000	+	3.46410i	−0.141776	+	0.245564i	0.786389	+	0.617731i	$0.211948\pi$
$200$		0			0
$201$	13.5000	+	23.3827i	0.952217	+	1.64929i
$202$		0			0
$203$	−4.50000	−	23.3827i	−0.315838	−	1.64114i
$204$		0			0
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$		0			0
$207$	9.00000	−	15.5885i	0.625543	−	1.08347i
$208$		0			0
$209$	12.0000			0.830057
$210$		0			0
$211$	26.0000			1.78991			0.894957	−	0.446153i	$-0.147206\pi$
$211$	26.0000			1.78991			0.894957	+	0.446153i	$0.147206\pi$
$212$		0			0
$213$	−3.00000	+	5.19615i	−0.205557	+	0.356034i
$214$		0			0
$215$	2.50000	+	4.33013i	0.170499	+	0.295312i
$216$		0			0
$217$	10.0000	+	3.46410i	0.678844	+	0.235159i
$218$		0			0
$219$	−6.00000	−	10.3923i	−0.405442	−	0.702247i
$220$		0			0
$221$		0			0
$222$		0			0
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$		0			0
$225$	6.00000			0.400000
$226$		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
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	−0.958187	−	0.286143i	$-0.907627\pi$
$229$	−11.0000	−	19.0526i	−0.726900	−	1.25903i	0.231287	−	0.972886i	$-0.425707\pi$
$230$		0			0
$231$	12.0000	−	10.3923i	0.789542	−	0.683763i
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$		0			0
$237$	30.0000			1.94871
$238$		0			0
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−5.50000	−	4.33013i	−0.351382	−	0.276642i
$246$		0			0
$247$		0			0
$248$		0			0
$249$	10.5000	−	18.1865i	0.665410	−	1.15252i
$250$		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	−	10.3923i	0.375735	−	0.650791i
$256$		0			0
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	0.713878	−	0.700270i	$-0.246937\pi$
$257$	−4.00000	−	6.92820i	−0.249513	−	0.432169i	−0.963391	+	0.268101i	$0.913604\pi$
$258$		0			0
$259$	8.00000	−	6.92820i	0.497096	−	0.430498i
$260$		0			0
$261$	−27.0000	−	46.7654i	−1.67126	−	2.89470i
$262$		0			0
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	−0.778595	−	0.627527i	$-0.784067\pi$
$263$	2.50000	−	4.33013i	0.154157	−	0.267007i	0.932752	+	0.360520i	$0.117401\pi$
$264$		0			0
$265$	2.00000			0.122859
$266$		0			0
$267$	−3.00000			−0.183597
$268$		0			0
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	−0.908124	−	0.418701i	$-0.862486\pi$
$269$	−1.50000	+	2.59808i	−0.0914566	+	0.158408i	0.816668	+	0.577108i	$0.195819\pi$
$270$		0			0
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	0.760405	−	0.649449i	$-0.225000\pi$
$271$	−3.00000	−	5.19615i	−0.182237	−	0.315644i	−0.942642	+	0.333805i	$0.891667\pi$
$272$		0			0
$273$		0			0
$274$		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
$279$	24.0000			1.43684
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$		0			0
$285$	−9.00000	−	15.5885i	−0.533114	−	0.923381i
$286$		0			0
$287$	3.50000	+	18.1865i	0.206598	+	1.07352i
$288$		0			0
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	21.0000	−	36.3731i	1.23104	−	2.13223i
$292$		0			0
$293$	28.0000			1.63578			0.817889	−	0.575376i	$-0.195144\pi$
$293$	28.0000			1.63578			0.817889	+	0.575376i	$0.195144\pi$
$294$		0			0
$295$	10.0000			0.582223
$296$		0			0
$297$	9.00000	−	15.5885i	0.522233	−	0.904534i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−2.50000	−	12.9904i	−0.144098	−	0.748753i
$302$		0			0
$303$	4.50000	+	7.79423i	0.258518	+	0.447767i
$304$		0			0
$305$	0.500000	−	0.866025i	0.0286299	−	0.0495885i
$306$		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
$309$	3.00000			0.170664
$310$		0			0
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		0			0
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	0.730554	−	0.682855i	$-0.239262\pi$
$313$	−4.00000	−	6.92820i	−0.226093	−	0.391605i	−0.956647	+	0.291250i	$0.905929\pi$
$314$		0			0
$315$	−15.0000	−	5.19615i	−0.845154	−	0.292770i
$316$		0			0
$317$	16.0000	+	27.7128i	0.898650	+	1.55651i	0.829222	+	0.558920i	$0.188784\pi$
$317$	16.0000	+	27.7128i	0.898650	+	1.55651i	0.0694277	+	0.997587i	$0.477883\pi$
$318$		0			0
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$		0			0
$321$	9.00000			0.502331
$322$		0			0
$323$	−24.0000			−1.33540
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−13.5000	−	23.3827i	−0.746552	−	1.29307i
$328$		0			0
$329$	16.0000	−	13.8564i	0.882109	−	0.763928i
$330$		0			0
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.851957	−	0.523612i	$-0.824584\pi$
$331$	−16.0000	−	27.7128i	−0.879440	−	1.52323i	−0.0274825	−	0.999622i	$-0.508749\pi$
$332$		0			0
$333$	12.0000	−	20.7846i	0.657596	−	1.13899i
$334$		0			0
$335$	−9.00000			−0.491723
$336$		0			0
$337$	−26.0000			−1.41631			−0.708155	−	0.706057i	$-0.750472\pi$
$337$	−26.0000			−1.41631			−0.708155	+	0.706057i	$0.750472\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$		0			0
$341$	−4.00000	−	6.92820i	−0.216612	−	0.375183i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$	4.50000	+	7.79423i	0.242272	+	0.419627i
$346$		0			0
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	−0.489946	−	0.871753i	$-0.662984\pi$
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	0.999933	−	0.0115703i	$-0.00368303\pi$
$348$		0			0
$349$	−35.0000			−1.87351			−0.936754	−	0.349990i	$-0.886185\pi$
$349$	−35.0000			−1.87351			−0.936754	+	0.349990i	$0.886185\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	−1.00000	−	1.73205i	−0.0530745	−	0.0919277i
$356$		0			0
$357$	−24.0000	+	20.7846i	−1.27021	+	1.10004i
$358$		0			0
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	0.808409	−	0.588621i	$-0.200329\pi$
$359$	−2.00000	−	3.46410i	−0.105556	−	0.182828i	−0.913965	+	0.405793i	$0.866996\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$		0			0
$363$	21.0000			1.10221
$364$		0			0
$365$	4.00000			0.209370
$366$		0			0
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	−0.973116	−	0.230317i	$-0.926024\pi$
$367$	−5.50000	+	9.52628i	−0.287098	+	0.497268i	0.686018	+	0.727585i	$0.259357\pi$
$368$		0			0
$369$	21.0000	+	36.3731i	1.09322	+	1.89351i
$370$		0			0
$371$	−5.00000	−	1.73205i	−0.259587	−	0.0899236i
$372$		0			0
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−30.0000			−1.54100			−0.770498	−	0.637442i	$-0.779993\pi$
$379$	−30.0000			−1.54100			−0.770498	+	0.637442i	$0.779993\pi$
$380$		0			0
$381$	−24.0000	+	41.5692i	−1.22956	+	2.12966i
$382$		0			0
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	0.991522	−	0.129937i	$-0.0414776\pi$
$383$	7.50000	+	12.9904i	0.383232	+	0.663777i	−0.608290	+	0.793715i	$0.708144\pi$
$384$		0			0
$385$	1.00000	+	5.19615i	0.0509647	+	0.264820i
$386$		0			0
$387$	−15.0000	−	25.9808i	−0.762493	−	1.32068i
$388$		0			0
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$		0			0
$393$	24.0000			1.21064
$394$		0			0
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$		0			0
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	−0.998125	−	0.0612128i	$-0.980503\pi$
$397$	−11.0000	−	19.0526i	−0.552074	−	0.956221i	0.446051	−	0.895008i	$-0.352830\pi$
$398$		0			0
$399$	9.00000	+	46.7654i	0.450564	+	2.34120i
$400$		0			0
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	−0.935336	−	0.353760i	$-0.884903\pi$
$401$	−15.5000	−	26.8468i	−0.774033	−	1.34066i	0.161303	−	0.986905i	$-0.448430\pi$
$402$		0			0
$403$		0			0
$404$		0			0
$405$	−9.00000			−0.447214
$406$		0			0
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	−0.900725	−	0.434389i	$-0.856964\pi$
$409$	−1.50000	+	2.59808i	−0.0741702	+	0.128467i	0.826555	+	0.562856i	$0.190297\pi$
$410$		0			0
$411$	18.0000	+	31.1769i	0.887875	+	1.53784i
$412$		0			0
$413$	−25.0000	−	8.66025i	−1.23017	−	0.426143i
$414$		0			0
$415$	3.50000	+	6.06218i	0.171808	+	0.297581i
$416$		0			0
$417$	21.0000	−	36.3731i	1.02837	−	1.78120i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	−19.0000			−0.926003			−0.463002	−	0.886357i	$-0.653228\pi$
$421$	−19.0000			−0.926003			−0.463002	+	0.886357i	$0.653228\pi$
$422$		0			0
$423$	24.0000	−	41.5692i	1.16692	−	2.02116i
$424$		0			0
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$		0			0
$427$	−2.00000	+	1.73205i	−0.0967868	+	0.0838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$		0			0
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$		0			0
$435$	27.0000			1.29455
$436$		0			0
$437$	9.00000	−	15.5885i	0.430528	−	0.745697i
$438$		0			0
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	0.522387	−	0.852709i	$-0.325042\pi$
$439$	−10.0000	−	17.3205i	−0.477274	−	0.826663i	−0.999661	+	0.0260459i	$0.991708\pi$
$440$		0			0
$441$	33.0000	+	25.9808i	1.57143	+	1.23718i
$442$		0			0
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	0.954094	+	0.299506i	$0.0968220\pi$
$443$	15.5000	+	26.8468i	0.736427	+	1.27553i	−0.217667	+	0.976023i	$0.569845\pi$
$444$		0			0
$445$	0.500000	−	0.866025i	0.0237023	−	0.0410535i
$446$		0			0
$447$	−9.00000			−0.425685
$448$		0			0
$449$	−33.0000			−1.55737			−0.778683	−	0.627417i	$-0.784112\pi$
$449$	−33.0000			−1.55737			−0.778683	+	0.627417i	$0.784112\pi$
$450$		0			0
$451$	7.00000	−	12.1244i	0.329617	−	0.570914i
$452$		0			0
$453$	24.0000	+	41.5692i	1.12762	+	1.95309i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	0.948566	+	0.316579i	$0.102534\pi$
$457$	16.0000	+	27.7128i	0.748448	+	1.29635i	−0.200118	+	0.979772i	$0.564132\pi$
$458$		0			0
$459$	−18.0000	+	31.1769i	−0.840168	+	1.45521i
$460$		0			0
$461$	−14.0000			−0.652045			−0.326023	−	0.945362i	$-0.605709\pi$
$461$	−14.0000			−0.652045			−0.326023	+	0.945362i	$0.605709\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$		0			0
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$		0			0
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$	22.5000	+	7.79423i	1.03895	+	0.359904i
$470$		0			0
$471$	15.0000	+	25.9808i	0.691164	+	1.19713i
$472$		0			0
$473$	−5.00000	+	8.66025i	−0.229900	+	0.398199i
$474$		0			0
$475$	6.00000			0.275299
$476$		0			0
$477$	−12.0000			−0.549442
$478$		0			0
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	−0.450098	−	0.892979i	$-0.648611\pi$
$479$	12.0000	−	20.7846i	0.548294	−	0.949673i	0.998392	−	0.0566937i	$-0.0180558\pi$
$480$		0			0
$481$		0			0
$482$		0			0
$483$	−4.50000	−	23.3827i	−0.204757	−	1.06395i
$484$		0			0
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$		0			0
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	−0.988374	−	0.152042i	$-0.951415\pi$
$487$	−8.00000	+	13.8564i	−0.362515	+	0.627894i	0.625859	+	0.779936i	$0.284748\pi$
$488$		0			0
$489$	−12.0000			−0.542659
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$		0			0
$495$	6.00000	+	10.3923i	0.269680	+	0.467099i
$496$		0			0
$497$	1.00000	+	5.19615i	0.0448561	+	0.233079i
$498$		0			0
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	0.591179	−	0.806541i	$-0.298663\pi$
$499$	−9.00000	−	15.5885i	−0.402895	−	0.697835i	−0.994074	+	0.108705i	$0.965329\pi$
$500$		0			0
$501$	31.5000	−	54.5596i	1.40732	−	2.43754i
$502$		0			0
$503$	21.0000			0.936344			0.468172	−	0.883637i	$-0.344913\pi$
$503$	21.0000			0.936344			0.468172	+	0.883637i	$0.344913\pi$
$504$		0			0
$505$	−3.00000			−0.133498
$506$		0			0
$507$	−19.5000	+	33.7750i	−0.866025	+	1.50000i
$508$		0			0
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	0.854732	−	0.519070i	$-0.173722\pi$
$509$	−0.500000	−	0.866025i	−0.0221621	−	0.0383859i	−0.876894	+	0.480684i	$0.840388\pi$
$510$		0			0
$511$	−10.0000	−	3.46410i	−0.442374	−	0.153243i
$512$		0			0
$513$	27.0000	+	46.7654i	1.19208	+	2.06474i
$514$		0			0
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$		0			0
$517$	−16.0000			−0.703679
$518$		0			0
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	0.0637207	+	0.997968i	$0.479703\pi$
$521$	−19.0000	+	32.9090i	−0.832405	+	1.44177i	−0.896126	+	0.443800i	$0.853630\pi$
$522$		0			0
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$		0			0
$525$	6.00000	−	5.19615i	0.261861	−	0.226779i
$526$		0			0
$527$	8.00000	+	13.8564i	0.348485	+	0.603595i
$528$		0			0
$529$	7.00000	−	12.1244i	0.304348	−	0.527146i
$530$		0			0
$531$	−60.0000			−2.60378
$532$		0			0
$533$		0			0
$534$		0			0
$535$	−1.50000	+	2.59808i	−0.0648507	+	0.112325i
$536$		0			0
$537$	−18.0000	−	31.1769i	−0.776757	−	1.34538i
$538$		0			0
$539$	2.00000	−	13.8564i	0.0861461	−	0.596838i
$540$		0			0
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	0.831978	−	0.554809i	$-0.187209\pi$
$541$	−1.50000	−	2.59808i	−0.0644900	−	0.111700i	−0.896468	+	0.443109i	$0.853875\pi$
$542$		0			0
$543$	10.5000	−	18.1865i	0.450598	−	0.780459i
$544$		0			0
$545$	9.00000			0.385518
$546$		0			0
$547$	33.0000			1.41098			0.705489	−	0.708721i	$-0.250727\pi$
$547$	33.0000			1.41098			0.705489	+	0.708721i	$0.250727\pi$
$548$		0			0
$549$	−3.00000	+	5.19615i	−0.128037	+	0.221766i
$550$		0			0
$551$	−27.0000	−	46.7654i	−1.15024	−	1.99227i
$552$		0			0
$553$	20.0000	−	17.3205i	0.850487	−	0.736543i
$554$		0			0
$555$	6.00000	+	10.3923i	0.254686	+	0.441129i
$556$		0			0
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	−0.844062	−	0.536246i	$-0.819842\pi$
$557$	1.00000	−	1.73205i	0.0423714	−	0.0733893i	0.886433	+	0.462856i	$0.153175\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$	24.0000			1.01328
$562$		0			0
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	−0.629433	−	0.777055i	$-0.716713\pi$
$563$	8.50000	−	14.7224i	0.358232	−	0.620477i	0.987666	+	0.156578i	$0.0500463\pi$
$564$		0			0
$565$	1.00000	+	1.73205i	0.0420703	+	0.0728679i
$566$		0			0
$567$	22.5000	+	7.79423i	0.944911	+	0.327327i
$568$		0			0
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	0.990668	−	0.136295i	$-0.0435194\pi$
$569$	9.00000	+	15.5885i	0.377300	+	0.653502i	−0.613369	+	0.789797i	$0.710186\pi$
$570$		0			0
$571$	−15.0000	+	25.9808i	−0.627730	+	1.08726i	0.360276	+	0.932846i	$0.382683\pi$
$571$	−15.0000	+	25.9808i	−0.627730	+	1.08726i	−0.988006	+	0.154415i	$0.950651\pi$
$572$		0			0
$573$	−54.0000			−2.25588
$574$		0			0
$575$	−3.00000			−0.125109
$576$		0			0
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	−0.951133	−	0.308783i	$-0.900078\pi$
$577$	−5.00000	+	8.66025i	−0.208153	+	0.360531i	0.742980	+	0.669314i	$0.233412\pi$
$578$		0			0
$579$	39.0000	+	67.5500i	1.62078	+	2.80728i
$580$		0			0
$581$	−3.50000	−	18.1865i	−0.145204	−	0.754505i
$582$		0			0
$583$	2.00000	+	3.46410i	0.0828315	+	0.143468i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	28.0000			1.15568			0.577842	−	0.816149i	$-0.303895\pi$
$587$	28.0000			1.15568			0.577842	+	0.816149i	$0.303895\pi$
$588$		0			0
$589$	24.0000			0.988903
$590$		0			0
$591$	3.00000	−	5.19615i	0.123404	−	0.213741i
$592$		0			0
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$		0			0
$595$	−2.00000	−	10.3923i	−0.0819920	−	0.426043i
$596$		0			0
$597$	6.00000	+	10.3923i	0.245564	+	0.425329i
$598$		0			0
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	−0.717021	−	0.697051i	$-0.754495\pi$
$599$	6.00000	−	10.3923i	0.245153	−	0.424618i	0.962175	+	0.272433i	$0.0878284\pi$
$600$		0			0
$601$	42.0000			1.71322			0.856608	−	0.515968i	$-0.172568\pi$
$601$	42.0000			1.71322			0.856608	+	0.515968i	$0.172568\pi$
$602$		0			0
$603$	54.0000			2.19905
$604$		0			0
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	0.875994	−	0.482322i	$-0.160206\pi$
$607$	0.500000	+	0.866025i	0.0202944	+	0.0351509i	−0.855700	+	0.517472i	$0.826873\pi$
$608$		0			0
$609$	−67.5000	−	23.3827i	−2.73524	−	0.947514i
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$		0			0
$615$	−21.0000			−0.846802
$616$		0			0
$617$	44.0000			1.77137			0.885687	−	0.464283i	$-0.153688\pi$
$617$	44.0000			1.77137			0.885687	+	0.464283i	$0.153688\pi$
$618$		0			0
$619$	−23.0000	+	39.8372i	−0.924448	+	1.60119i	−0.132002	+	0.991250i	$0.542140\pi$
$619$	−23.0000	+	39.8372i	−0.924448	+	1.60119i	−0.792446	+	0.609941i	$0.791193\pi$
$620$		0			0
$621$	−13.5000	−	23.3827i	−0.541736	−	0.938315i
$622$		0			0
$623$	−2.00000	+	1.73205i	−0.0801283	+	0.0693932i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	18.0000	−	31.1769i	0.718851	−	1.24509i
$628$		0			0
$629$	16.0000			0.637962
$630$		0			0
$631$	−2.00000			−0.0796187			−0.0398094	−	0.999207i	$-0.512675\pi$
$631$	−2.00000			−0.0796187			−0.0398094	+	0.999207i	$0.512675\pi$
$632$		0			0
$633$	39.0000	−	67.5500i	1.55011	−	2.68487i
$634$		0			0
$635$	−8.00000	−	13.8564i	−0.317470	−	0.549875i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	−0.911165	−	0.412042i	$-0.864816\pi$
$641$	−2.50000	+	4.33013i	−0.0987441	+	0.171030i	0.812421	+	0.583071i	$0.198149\pi$
$642$		0			0
$643$	−28.0000			−1.10421			−0.552106	−	0.833774i	$-0.686176\pi$
$643$	−28.0000			−1.10421			−0.552106	+	0.833774i	$0.686176\pi$
$644$		0			0
$645$	15.0000			0.590624
$646$		0			0
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	−0.953652	−	0.300913i	$-0.902709\pi$
$647$	−5.50000	+	9.52628i	−0.216227	+	0.374517i	0.737424	+	0.675430i	$0.236042\pi$
$648$		0			0
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$		0			0
$651$	24.0000	−	20.7846i	0.940634	−	0.814613i
$652$		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
$655$	−4.00000	+	6.92820i	−0.156293	+	0.270707i
$656$		0			0
$657$	−24.0000			−0.936329
$658$		0			0
$659$	26.0000			1.01282			0.506408	−	0.862294i	$-0.330973\pi$
$659$	26.0000			1.01282			0.506408	+	0.862294i	$0.330973\pi$
$660$		0			0
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	−0.739014	−	0.673690i	$-0.764708\pi$
$661$	5.50000	−	9.52628i	0.213925	−	0.370529i	0.952940	+	0.303160i	$0.0980418\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−15.0000	−	5.19615i	−0.581675	−	0.201498i
$666$		0			0
$667$	13.5000	+	23.3827i	0.522722	+	0.905381i
$668$		0			0
$669$	−42.0000	+	72.7461i	−1.62381	+	2.81253i
$670$		0			0
$671$	2.00000			0.0772091
$672$		0			0
$673$	16.0000			0.616755			0.308377	−	0.951264i	$-0.400214\pi$
$673$	16.0000			0.616755			0.308377	+	0.951264i	$0.400214\pi$
$674$		0			0
$675$	4.50000	−	7.79423i	0.173205	−	0.300000i
$676$		0			0
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.795698	+	0.605693i	$0.207104\pi$
$677$	24.0000	+	41.5692i	0.922395	+	1.59763i	0.126697	+	0.991941i	$0.459562\pi$
$678$		0			0
$679$	−7.00000	−	36.3731i	−0.268635	−	1.39587i
$680$		0			0
$681$	6.00000	+	10.3923i	0.229920	+	0.398234i
$682$		0			0
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	0.257758	+	0.966209i	$0.417016\pi$
$683$	−18.5000	+	32.0429i	−0.707883	+	1.22609i	−0.965641	+	0.259880i	$0.916317\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−66.0000			−2.51806
$688$		0			0
$689$		0			0
$690$		0			0
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	0.995785	−	0.0917209i	$-0.0292368\pi$
$691$	11.0000	+	19.0526i	0.418460	+	0.724793i	−0.577325	+	0.816514i	$0.695903\pi$
$692$		0			0
$693$	−6.00000	−	31.1769i	−0.227921	−	1.18431i
$694$		0			0
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$		0			0
$697$	−14.0000	+	24.2487i	−0.530288	+	0.918485i
$698$		0			0
$699$	−72.0000			−2.72329
$700$		0			0
$701$	−47.0000			−1.77517			−0.887583	−	0.460648i	$-0.847617\pi$
$701$	−47.0000			−1.77517			−0.887583	+	0.460648i	$0.847617\pi$
$702$		0			0
$703$	12.0000	−	20.7846i	0.452589	−	0.783906i
$704$		0			0
$705$	12.0000	+	20.7846i	0.451946	+	0.782794i
$706$		0			0
$707$	7.50000	+	2.59808i	0.282067	+	0.0977107i
$708$		0			0
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	0.950628	−	0.310334i	$-0.100441\pi$
$709$	5.50000	+	9.52628i	0.206557	+	0.357767i	−0.744071	+	0.668101i	$0.767108\pi$
$710$		0			0
$711$	30.0000	−	51.9615i	1.12509	−	1.94871i
$712$		0			0
$713$	−12.0000			−0.449404
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−24.0000	+	41.5692i	−0.896296	+	1.55243i
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	2.00000	−	1.73205i	0.0744839	−	0.0645049i
$722$		0			0
$723$	15.0000	+	25.9808i	0.557856	+	0.966235i
$724$		0			0
$725$	−4.50000	+	7.79423i	−0.167126	+	0.289470i
$726$		0			0
$727$	21.0000			0.778847			0.389423	−	0.921059i	$-0.372674\pi$
$727$	21.0000			0.778847			0.389423	+	0.921059i	$0.372674\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$		0			0
$735$	−19.5000	+	7.79423i	−0.719268	+	0.287494i
$736$		0			0
$737$	−9.00000	−	15.5885i	−0.331519	−	0.574208i
$738$		0			0
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	−0.883832	−	0.467804i	$-0.845045\pi$
$739$	−1.00000	+	1.73205i	−0.0367856	+	0.0637145i	0.847046	+	0.531519i	$0.178379\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−9.00000			−0.330178			−0.165089	−	0.986279i	$-0.552791\pi$
$743$	−9.00000			−0.330178			−0.165089	+	0.986279i	$0.552791\pi$
$744$		0			0
$745$	1.50000	−	2.59808i	0.0549557	−	0.0951861i
$746$		0			0
$747$	−21.0000	−	36.3731i	−0.768350	−	1.33082i
$748$		0			0
$749$	6.00000	−	5.19615i	0.219235	−	0.189863i
$750$		0			0
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	0.827225	−	0.561870i	$-0.189918\pi$
$751$	−2.00000	−	3.46410i	−0.0729810	−	0.126407i	−0.900207	+	0.435463i	$0.856585\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−16.0000			−0.582300
$756$		0			0
$757$	16.0000			0.581530			0.290765	−	0.956795i	$-0.406090\pi$
$757$	16.0000			0.581530			0.290765	+	0.956795i	$0.406090\pi$
$758$		0			0
$759$	−9.00000	+	15.5885i	−0.326679	+	0.565825i
$760$		0			0
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	0.915264	−	0.402854i	$-0.131982\pi$
$761$	3.00000	+	5.19615i	0.108750	+	0.188360i	−0.806514	+	0.591215i	$0.798649\pi$
$762$		0			0
$763$	−22.5000	−	7.79423i	−0.814555	−	0.282170i
$764$		0			0
$765$	−12.0000	−	20.7846i	−0.433861	−	0.751469i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	−24.0000			−0.864339
$772$		0			0
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	−0.997012	−	0.0772449i	$-0.975388\pi$
$773$	−12.0000	+	20.7846i	−0.431610	+	0.747570i	0.565402	+	0.824815i	$0.308721\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$		0			0
$777$	−6.00000	−	31.1769i	−0.215249	−	1.11847i
$778$		0			0
$779$	21.0000	+	36.3731i	0.752403	+	1.30320i
$780$		0			0
$781$	2.00000	−	3.46410i	0.0715656	−	0.123955i
$782$		0			0
$783$	−81.0000			−2.89470
$784$		0			0
$785$	−10.0000			−0.356915
$786$		0			0
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$		0			0
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$		0			0
$791$	−1.00000	−	5.19615i	−0.0355559	−	0.184754i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$		0			0
$797$		0			0			−	1.00000i	$-0.5\pi$
$797$		0			0				1.00000i	$0.5\pi$
$798$		0			0
$799$	32.0000			1.13208
$800$		0			0
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$		0			0
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$	7.50000	+	2.59808i	0.264340	+	0.0915702i
$806$		0			0
$807$	4.50000	+	7.79423i	0.158408	+	0.274370i
$808$		0			0
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.0646355	−	0.997909i	$-0.479412\pi$
$809$	25.5000	−	44.1673i	0.896532	−	1.55284i	0.831897	−	0.554930i	$-0.187255\pi$
$810$		0			0
$811$	28.0000			0.983213			0.491606	−	0.870817i	$-0.336410\pi$
$811$	28.0000			0.983213			0.491606	+	0.870817i	$0.336410\pi$
$812$		0			0
$813$	−18.0000			−0.631288
$814$		0			0
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−15.0000	−	25.9808i	−0.524784	−	0.908952i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$		0			0
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	−0.651588	−	0.758573i	$-0.725897\pi$
$823$	9.50000	−	16.4545i	0.331149	−	0.573567i	0.982737	+	0.185006i	$0.0592303\pi$
$824$		0			0
$825$	−6.00000			−0.208893
$826$		0			0
$827$	19.0000			0.660695			0.330347	−	0.943859i	$-0.392834\pi$
$827$	19.0000			0.660695			0.330347	+	0.943859i	$0.392834\pi$
$828$		0			0
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	−0.121560	−	0.992584i	$-0.538790\pi$
$829$	23.0000	−	39.8372i	0.798823	−	1.38360i	0.920383	−	0.391018i	$-0.127877\pi$
$830$		0			0
$831$	18.0000	+	31.1769i	0.624413	+	1.08152i
$832$		0			0
$833$	−4.00000	+	27.7128i	−0.138592	+	0.960192i
$834$		0			0
$835$	10.5000	+	18.1865i	0.363367	+	0.629371i
$836$		0			0
$837$	18.0000	−	31.1769i	0.622171	−	1.07763i
$838$		0			0
$839$	−14.0000			−0.483334			−0.241667	−	0.970359i	$-0.577694\pi$
$839$	−14.0000			−0.483334			−0.241667	+	0.970359i	$0.577694\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$		0			0
$843$	3.00000	−	5.19615i	0.103325	−	0.178965i
$844$		0			0
$845$	−6.50000	−	11.2583i	−0.223607	−	0.387298i
$846$		0			0
$847$	14.0000	−	12.1244i	0.481046	−	0.416598i
$848$		0			0
$849$	6.00000	+	10.3923i	0.205919	+	0.356663i
$850$		0			0
$851$	−6.00000	+	10.3923i	−0.205677	+	0.356244i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$		0			0
$855$	−36.0000			−1.23117
$856$		0			0
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	−0.670366	−	0.742030i	$-0.733863\pi$
$857$	9.00000	−	15.5885i	0.307434	−	0.532492i	0.977800	+	0.209539i	$0.0671963\pi$
$858$		0			0
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	−0.906516	−	0.422172i	$-0.861268\pi$
$859$	−24.0000	−	41.5692i	−0.818869	−	1.41832i	0.0876464	−	0.996152i	$-0.472065\pi$
$860$		0			0
$861$	52.5000	+	18.1865i	1.78920	+	0.619795i
$862$		0			0
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$		0			0
$865$	4.00000	−	6.92820i	0.136004	−	0.235566i
$866$		0			0
$867$	3.00000			0.101885
$868$		0			0
$869$	−20.0000			−0.678454
$870$		0			0
$871$		0			0
$872$		0			0
$873$	−42.0000	−	72.7461i	−1.42148	−	2.46208i
$874$		0			0
$875$	0.500000	+	2.59808i	0.0169031	+	0.0878310i
$876$		0			0
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	−0.985079	−	0.172102i	$-0.944944\pi$
$877$	−19.0000	−	32.9090i	−0.641584	−	1.11126i	0.343495	−	0.939155i	$-0.388389\pi$
$878$		0			0
$879$	42.0000	−	72.7461i	1.41662	−	2.45367i
$880$		0			0
$881$	−7.00000			−0.235836			−0.117918	−	0.993023i	$-0.537622\pi$
$881$	−7.00000			−0.235836			−0.117918	+	0.993023i	$0.537622\pi$
$882$		0			0
$883$	12.0000			0.403832			0.201916	−	0.979403i	$-0.435283\pi$
$883$	12.0000			0.403832			0.201916	+	0.979403i	$0.435283\pi$
$884$		0			0
$885$	15.0000	−	25.9808i	0.504219	−	0.873334i
$886$		0			0
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	0.999886	−	0.0151042i	$-0.00480800\pi$
$887$	14.5000	+	25.1147i	0.486862	+	0.843270i	−0.513024	+	0.858375i	$0.671475\pi$
$888$		0			0
$889$	8.00000	+	41.5692i	0.268311	+	1.39419i
$890$		0			0
$891$	−9.00000	−	15.5885i	−0.301511	−	0.522233i
$892$		0			0
$893$	24.0000	−	41.5692i	0.803129	−	1.39106i
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−4.00000	−	6.92820i	−0.133259	−	0.230812i
$902$		0			0
$903$	−37.5000	−	12.9904i	−1.24792	−	0.432293i
$904$		0			0
$905$	3.50000	+	6.06218i	0.116344	+	0.201514i
$906$		0			0
$907$	2.50000	−	4.33013i	0.0830111	−	0.143780i	−0.821531	−	0.570164i	$-0.806880\pi$
$907$	2.50000	−	4.33013i	0.0830111	−	0.143780i	0.904542	+	0.426385i	$0.140213\pi$
$908$		0			0
$909$	18.0000			0.597022
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−7.00000	+	12.1244i	−0.231666	+	0.401258i
$914$		0			0
$915$	−1.50000	−	2.59808i	−0.0495885	−	0.0858898i
$916$		0			0
$917$	16.0000	−	13.8564i	0.528367	−	0.457579i
$918$		0			0
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	0.988199	+	0.153174i	$0.0489495\pi$
$919$	19.0000	+	32.9090i	0.626752	+	1.08557i	−0.361447	+	0.932393i	$0.617717\pi$
$920$		0			0
$921$	−10.5000	+	18.1865i	−0.345987	+	0.599267i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−4.00000			−0.131519
$926$		0			0
$927$	3.00000	−	5.19615i	0.0985329	−	0.170664i
$928$		0			0
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	−0.966550	−	0.256479i	$-0.917438\pi$
$929$	−21.5000	−	37.2391i	−0.705392	−	1.22177i	0.261158	−	0.965296i	$-0.415896\pi$
$930$		0			0
$931$	33.0000	+	25.9808i	1.08153	+	0.851485i
$932$		0			0
$933$	27.0000	+	46.7654i	0.883940	+	1.53103i
$934$		0			0
$935$	−4.00000	+	6.92820i	−0.130814	+	0.226576i
$936$		0			0
$937$	−28.0000			−0.914720			−0.457360	−	0.889282i	$-0.651205\pi$
$937$	−28.0000			−0.914720			−0.457360	+	0.889282i	$0.651205\pi$
$938$		0			0
$939$	−24.0000			−0.783210
$940$		0			0
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	−0.198150	−	0.980172i	$-0.563493\pi$
$941$	23.0000	−	39.8372i	0.749779	−	1.29865i	0.947929	−	0.318483i	$-0.103173\pi$
$942$		0			0
$943$	−10.5000	−	18.1865i	−0.341927	−	0.592235i
$944$		0			0
$945$	−18.0000	+	15.5885i	−0.585540	+	0.507093i
$946$		0			0
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	0.588264	−	0.808669i	$-0.299811\pi$
$947$	−12.5000	−	21.6506i	−0.406195	−	0.703551i	−0.994460	+	0.105118i	$0.966478\pi$
$948$		0			0
$949$		0			0
$950$		0			0
$951$	96.0000			3.11301
$952$		0			0
$953$	−12.0000			−0.388718			−0.194359	−	0.980930i	$-0.562263\pi$
$953$	−12.0000			−0.388718			−0.194359	+	0.980930i	$0.562263\pi$
$954$		0			0
$955$	9.00000	−	15.5885i	0.291233	−	0.504431i
$956$		0			0
$957$	27.0000	+	46.7654i	0.872786	+	1.51171i
$958$		0			0
$959$	30.0000	+	10.3923i	0.968751	+	0.335585i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$		0			0
$965$	−26.0000			−0.836970
$966$		0			0
$967$	−37.0000			−1.18984			−0.594920	−	0.803785i	$-0.702816\pi$
$967$	−37.0000			−1.18984			−0.594920	+	0.803785i	$0.702816\pi$
$968$		0			0
$969$	−36.0000	+	62.3538i	−1.15649	+	2.00309i
$970$		0			0
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$		0			0
$973$	−7.00000	−	36.3731i	−0.224410	−	1.16607i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	−0.519841	−	0.854263i	$-0.674009\pi$
$977$	15.0000	−	25.9808i	0.479893	−	0.831198i	0.999734	+	0.0230645i	$0.00734232\pi$
$978$		0			0
$979$	2.00000			0.0639203
$980$		0			0
$981$	−54.0000			−1.72409
$982$		0			0
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	−0.698038	−	0.716061i	$-0.745943\pi$
$983$	8.50000	−	14.7224i	0.271108	−	0.469573i	0.969146	+	0.246488i	$0.0792766\pi$
$984$		0			0
$985$	1.00000	+	1.73205i	0.0318626	+	0.0551877i
$986$		0			0
$987$	−12.0000	−	62.3538i	−0.381964	−	1.98474i
$988$		0			0
$989$	7.50000	+	12.9904i	0.238486	+	0.413070i
$990$		0			0
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	−0.351126	−	0.936328i	$-0.614201\pi$
$991$	20.0000	−	34.6410i	0.635321	−	1.10041i	0.986447	−	0.164080i	$-0.0524655\pi$
$992$		0			0
$993$	−96.0000			−3.04647
$994$		0			0
$995$	−4.00000			−0.126809
$996$		0			0
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$		0			0
$999$	−18.0000	−	31.1769i	−0.569495	−	0.986394i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	560.2.q.i.81.1		2
4.3	odd	2		70.2.e.a.11.1	✓	2
7.2	even	3	inner	560.2.q.i.401.1		2
7.3	odd	6		3920.2.a.bk.1.1		1
7.4	even	3		3920.2.a.b.1.1		1
12.11	even	2		630.2.k.f.361.1		2
20.3	even	4		350.2.j.f.249.1		4
20.7	even	4		350.2.j.f.249.2		4
20.19	odd	2		350.2.e.l.151.1		2
28.3	even	6		490.2.a.e.1.1		1
28.11	odd	6		490.2.a.k.1.1		1
28.19	even	6		490.2.e.f.471.1		2
28.23	odd	6		70.2.e.a.51.1	yes	2
28.27	even	2		490.2.e.f.361.1		2
84.11	even	6		4410.2.a.r.1.1		1
84.23	even	6		630.2.k.f.541.1		2
84.59	odd	6		4410.2.a.h.1.1		1
140.3	odd	12		2450.2.c.a.99.1		2
140.23	even	12		350.2.j.f.149.2		4
140.39	odd	6		2450.2.a.b.1.1		1
140.59	even	6		2450.2.a.q.1.1		1
140.67	even	12		2450.2.c.s.99.2		2
140.79	odd	6		350.2.e.l.51.1		2
140.87	odd	12		2450.2.c.a.99.2		2
140.107	even	12		350.2.j.f.149.1		4
140.123	even	12		2450.2.c.s.99.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.e.a.11.1	✓	2	4.3	odd	2
70.2.e.a.51.1	yes	2	28.23	odd	6
350.2.e.l.51.1		2	140.79	odd	6
350.2.e.l.151.1		2	20.19	odd	2
350.2.j.f.149.1		4	140.107	even	12
350.2.j.f.149.2		4	140.23	even	12
350.2.j.f.249.1		4	20.3	even	4
350.2.j.f.249.2		4	20.7	even	4
490.2.a.e.1.1		1	28.3	even	6
490.2.a.k.1.1		1	28.11	odd	6
490.2.e.f.361.1		2	28.27	even	2
490.2.e.f.471.1		2	28.19	even	6
560.2.q.i.81.1		2	1.1	even	1	trivial
560.2.q.i.401.1		2	7.2	even	3	inner
630.2.k.f.361.1		2	12.11	even	2
630.2.k.f.541.1		2	84.23	even	6
2450.2.a.b.1.1		1	140.39	odd	6
2450.2.a.q.1.1		1	140.59	even	6
2450.2.c.a.99.1		2	140.3	odd	12
2450.2.c.a.99.2		2	140.87	odd	12
2450.2.c.s.99.1		2	140.123	even	12
2450.2.c.s.99.2		2	140.67	even	12
3920.2.a.b.1.1		1	7.4	even	3
3920.2.a.bk.1.1		1	7.3	odd	6
4410.2.a.h.1.1		1	84.59	odd	6
4410.2.a.r.1.1		1	84.11	even	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:	\( N \)	\(=\)	\( 560 = 2^{4} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	560.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +O(q^{10})\)	\(q+(1.50000 - 2.59808i) q^{3} +(0.500000 + 0.866025i) q^{5} +(-0.500000 - 2.59808i) q^{7} +(-3.00000 - 5.19615i) q^{9} +(-1.00000 + 1.73205i) q^{11} +3.00000 q^{15} +(2.00000 - 3.46410i) q^{17} +(-3.00000 - 5.19615i) q^{19} +(-7.50000 - 2.59808i) q^{21} +(1.50000 + 2.59808i) q^{23} +(-0.500000 + 0.866025i) q^{25} -9.00000 q^{27} +9.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(3.00000 + 5.19615i) q^{33} +(2.00000 - 1.73205i) q^{35} +(2.00000 + 3.46410i) q^{37} -7.00000 q^{41} +5.00000 q^{43} +(3.00000 - 5.19615i) q^{45} +(4.00000 + 6.92820i) q^{47} +(-6.50000 + 2.59808i) q^{49} +(-6.00000 - 10.3923i) q^{51} +(1.00000 - 1.73205i) q^{53} -2.00000 q^{55} -18.0000 q^{57} +(5.00000 - 8.66025i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(-12.0000 + 10.3923i) q^{63} +(-4.50000 + 7.79423i) q^{67} +9.00000 q^{69} -2.00000 q^{71} +(2.00000 - 3.46410i) q^{73} +(1.50000 + 2.59808i) q^{75} +(5.00000 + 1.73205i) q^{77} +(5.00000 + 8.66025i) q^{79} +(-4.50000 + 7.79423i) q^{81} +7.00000 q^{83} +4.00000 q^{85} +(13.5000 - 23.3827i) q^{87} +(-0.500000 - 0.866025i) q^{89} +(6.00000 + 10.3923i) q^{93} +(3.00000 - 5.19615i) q^{95} +14.0000 q^{97} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 3 q^{3} + q^{5} - q^{7} - 6 q^{9}+O(q^{10}) \) 2 * q + 3 * q^3 + q^5 - q^7 - 6 * q^9	\( 2 q + 3 q^{3} + q^{5} - q^{7} - 6 q^{9} - 2 q^{11} + 6 q^{15} + 4 q^{17} - 6 q^{19} - 15 q^{21} + 3 q^{23} - q^{25} - 18 q^{27} + 18 q^{29} - 4 q^{31} + 6 q^{33} + 4 q^{35} + 4 q^{37} - 14 q^{41} + 10 q^{43} + 6 q^{45} + 8 q^{47} - 13 q^{49} - 12 q^{51} + 2 q^{53} - 4 q^{55} - 36 q^{57} + 10 q^{59} - q^{61} - 24 q^{63} - 9 q^{67} + 18 q^{69} - 4 q^{71} + 4 q^{73} + 3 q^{75} + 10 q^{77} + 10 q^{79} - 9 q^{81} + 14 q^{83} + 8 q^{85} + 27 q^{87} - q^{89} + 12 q^{93} + 6 q^{95} + 28 q^{97} + 24 q^{99}+O(q^{100}) \) 2 * q + 3 * q^3 + q^5 - q^7 - 6 * q^9 - 2 * q^11 + 6 * q^15 + 4 * q^17 - 6 * q^19 - 15 * q^21 + 3 * q^23 - q^25 - 18 * q^27 + 18 * q^29 - 4 * q^31 + 6 * q^33 + 4 * q^35 + 4 * q^37 - 14 * q^41 + 10 * q^43 + 6 * q^45 + 8 * q^47 - 13 * q^49 - 12 * q^51 + 2 * q^53 - 4 * q^55 - 36 * q^57 + 10 * q^59 - q^61 - 24 * q^63 - 9 * q^67 + 18 * q^69 - 4 * q^71 + 4 * q^73 + 3 * q^75 + 10 * q^77 + 10 * q^79 - 9 * q^81 + 14 * q^83 + 8 * q^85 + 27 * q^87 - q^89 + 12 * q^93 + 6 * q^95 + 28 * q^97 + 24 * q^99

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