LMFDB - Embedded newform 720.2.q.l.481.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(241,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [8,0,0,0,-4,0,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.856615824.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 $ x^8 + 11x^6 + 36x^4 + 32*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 360)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			481.3
Root			$-2.06288i$ of defining polynomial
Character	$\chi$	$=$	720.481
Dual form			720.2.q.l.241.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.574618 + 1.63396i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.28651 - 3.96035i) q^{7} +(-2.33963 + 1.87780i) q^{9} +(-2.29604 - 3.97686i) q^{11} +(1.83963 - 3.18633i) q^{13} +(-1.70236 - 0.319344i) q^{15} -2.55395 q^{17} -4.76643 q^{19} +(5.15716 - 6.01174i) q^{21} +(-1.28651 + 2.22830i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.41264 - 2.74383i) q^{27} +(-0.956412 - 1.65655i) q^{29} +(1.73339 - 3.00231i) q^{31} +(5.17866 - 6.03680i) q^{33} +4.57301 q^{35} +5.46677 q^{37} +(6.26340 + 1.17495i) q^{39} +(-3.32056 + 5.75139i) q^{41} +(-3.27698 - 5.67589i) q^{43} +(-0.456412 - 2.96508i) q^{45} +(5.01989 + 8.69471i) q^{47} +(-6.95623 + 12.0485i) q^{49} +(-1.46755 - 4.17304i) q^{51} +4.03813 q^{53} +4.59208 q^{55} +(-2.73888 - 7.78814i) q^{57} +(6.13567 - 10.6273i) q^{59} +(-4.79604 - 8.30698i) q^{61} +(12.7863 + 4.97212i) q^{63} +(1.83963 + 3.18633i) q^{65} +(-5.66972 + 9.82025i) q^{67} +(-4.38019 - 0.821677i) q^{69} +1.67925 q^{71} +3.12530 q^{73} +(1.12774 - 1.31461i) q^{75} +(-10.4998 + 18.1862i) q^{77} +(-6.64113 - 11.5028i) q^{79} +(1.94771 - 8.78672i) q^{81} +(5.39275 + 9.34051i) q^{83} +(1.27698 - 2.21179i) q^{85} +(2.15716 - 2.51462i) q^{87} +4.04905 q^{89} -16.8253 q^{91} +(5.90169 + 1.10709i) q^{93} +(2.38322 - 4.12785i) q^{95} +(-8.68962 - 15.0509i) q^{97} +(12.8396 + 4.99285i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - q^{7} + q^{11} - 4 q^{13} - 3 q^{15} + 10 q^{17} - 2 q^{19} + 7 q^{23} - 4 q^{25} + 18 q^{27} - 7 q^{29} - 2 q^{31} - 3 q^{33} + 2 q^{35} + 12 q^{37} + 6 q^{39} - 12 q^{41} - 11 q^{43}+ \cdots + 84 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - q^7 + q^11 - 4 * q^13 - 3 * q^15 + 10 * q^17 - 2 * q^19 + 7 * q^23 - 4 * q^25 + 18 * q^27 - 7 * q^29 - 2 * q^31 - 3 * q^33 + 2 * q^35 + 12 * q^37 + 6 * q^39 - 12 * q^41 - 11 * q^43 - 3 * q^45 + 7 * q^47 - 3 * q^49 - 39 * q^51 + 24 * q^53 - 2 * q^55 + 27 * q^57 + 11 * q^59 - 19 * q^61 + 33 * q^63 - 4 * q^65 - 10 * q^67 - 9 * q^69 - 24 * q^71 + 18 * q^73 + 3 * q^75 - 32 * q^77 - 24 * q^79 - 12 * q^81 + 23 * q^83 - 5 * q^85 - 24 * q^87 + 42 * q^89 - 28 * q^91 + 18 * q^93 + q^95 - q^97 + 84 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.574618	+	1.63396i	0.331756	+	0.943365i
$3$	0.574618	+	1.63396i	0.331756	+	0.943365i
$4$		0			0
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	−2.28651	−	3.96035i	−0.864218	−	1.49687i	−0.867821	−	0.496877i	$-0.834480\pi$
$7$	−2.28651	−	3.96035i	−0.864218	−	1.49687i	0.00360263	−	0.999994i	$-0.498853\pi$
$8$		0			0
$9$	−2.33963	+	1.87780i	−0.779876	+	0.625934i
$10$		0			0
$11$	−2.29604	−	3.97686i	−0.692282	−	1.19907i	−0.971088	−	0.238720i	$-0.923272\pi$
$11$	−2.29604	−	3.97686i	−0.692282	−	1.19907i	0.278807	−	0.960347i	$-0.410061\pi$
$12$		0			0
$13$	1.83963	−	3.18633i	0.510221	−	0.883728i	−0.489709	−	0.871886i	$-0.662897\pi$
$13$	1.83963	−	3.18633i	0.510221	−	0.883728i	0.999930	−	0.0118424i	$-0.00376965\pi$
$14$		0			0
$15$	−1.70236	−	0.319344i	−0.439547	−	0.0824543i
$16$		0			0
$17$	−2.55395			−0.619424			−0.309712	−	0.950830i	$-0.600233\pi$
$17$	−2.55395			−0.619424			−0.309712	+	0.950830i	$0.600233\pi$
$18$		0			0
$19$	−4.76643			−1.09349			−0.546747	−	0.837298i	$-0.684134\pi$
$19$	−4.76643			−1.09349			−0.546747	+	0.837298i	$0.684134\pi$
$20$		0			0
$21$	5.15716	−	6.01174i	1.12539	−	1.31187i
$22$		0			0
$23$	−1.28651	+	2.22830i	−0.268255	+	0.464632i	−0.968411	−	0.249358i	$-0.919780\pi$
$23$	−1.28651	+	2.22830i	−0.268255	+	0.464632i	0.700156	+	0.713990i	$0.253114\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	−4.41264	−	2.74383i	−0.849213	−	0.528050i
$28$		0			0
$29$	−0.956412	−	1.65655i	−0.177601	−	0.307614i	0.763457	−	0.645858i	$-0.223500\pi$
$29$	−0.956412	−	1.65655i	−0.177601	−	0.307614i	−0.941058	+	0.338244i	$0.890167\pi$
$30$		0			0
$31$	1.73339	−	3.00231i	0.311326	−	0.539232i	−0.667324	−	0.744767i	$-0.732560\pi$
$31$	1.73339	−	3.00231i	0.311326	−	0.539232i	0.978650	+	0.205536i	$0.0658937\pi$
$32$		0			0
$33$	5.17866	−	6.03680i	0.901489	−	1.05087i
$34$		0			0
$35$	4.57301			0.772980
$36$		0			0
$37$	5.46677			0.898732			0.449366	−	0.893348i	$-0.351650\pi$
$37$	5.46677			0.898732			0.449366	+	0.893348i	$0.351650\pi$
$38$		0			0
$39$	6.26340	+	1.17495i	1.00295	+	0.188142i
$40$		0			0
$41$	−3.32056	+	5.75139i	−0.518585	+	0.898215i	0.481182	+	0.876621i	$0.340208\pi$
$41$	−3.32056	+	5.75139i	−0.518585	+	0.898215i	−0.999767	+	0.0215947i	$0.993126\pi$
$42$		0			0
$43$	−3.27698	−	5.67589i	−0.499734	−	0.865565i	0.500266	−	0.865872i	$-0.333236\pi$
$43$	−3.27698	−	5.67589i	−0.499734	−	0.865565i	−1.00000		0.000307033i	$0.999902\pi$
$44$		0			0
$45$	−0.456412	−	2.96508i	−0.0680378	−	0.442008i
$46$		0			0
$47$	5.01989	+	8.69471i	0.732227	+	1.26825i	0.955929	+	0.293597i	$0.0948522\pi$
$47$	5.01989	+	8.69471i	0.732227	+	1.26825i	−0.223703	+	0.974657i	$0.571814\pi$
$48$		0			0
$49$	−6.95623	+	12.0485i	−0.993747	+	1.72122i
$50$		0			0
$51$	−1.46755	−	4.17304i	−0.205498	−	0.584343i
$52$		0			0
$53$	4.03813			0.554679			0.277340	−	0.960772i	$-0.410547\pi$
$53$	4.03813			0.554679			0.277340	+	0.960772i	$0.410547\pi$
$54$		0			0
$55$	4.59208			0.619196
$56$		0			0
$57$	−2.73888	−	7.78814i	−0.362773	−	1.03156i
$58$		0			0
$59$	6.13567	−	10.6273i	0.798796	−	1.38355i	−0.121605	−	0.992579i	$-0.538804\pi$
$59$	6.13567	−	10.6273i	0.798796	−	1.38355i	0.920401	−	0.390976i	$-0.127863\pi$
$60$		0			0
$61$	−4.79604	−	8.30698i	−0.614070	−	1.06360i	−0.990547	−	0.137174i	$-0.956198\pi$
$61$	−4.79604	−	8.30698i	−0.614070	−	1.06360i	0.376477	−	0.926426i	$-0.377135\pi$
$62$		0			0
$63$	12.7863	+	4.97212i	1.61093	+	0.626429i
$64$		0			0
$65$	1.83963	+	3.18633i	0.228178	+	0.395215i
$66$		0			0
$67$	−5.66972	+	9.82025i	−0.692667	+	1.19973i	0.278294	+	0.960496i	$0.410231\pi$
$67$	−5.66972	+	9.82025i	−0.692667	+	1.19973i	−0.970961	+	0.239238i	$0.923102\pi$
$68$		0			0
$69$	−4.38019	−	0.821677i	−0.527313	−	0.0989183i
$70$		0			0
$71$	1.67925			0.199291			0.0996454	−	0.995023i	$-0.468229\pi$
$71$	1.67925			0.199291			0.0996454	+	0.995023i	$0.468229\pi$
$72$		0			0
$73$	3.12530			0.365789			0.182895	−	0.983133i	$-0.441453\pi$
$73$	3.12530			0.365789			0.182895	+	0.983133i	$0.441453\pi$
$74$		0			0
$75$	1.12774	−	1.31461i	0.130220	−	0.151798i
$76$		0			0
$77$	−10.4998	+	18.1862i	−1.19657	+	2.07251i
$78$		0			0
$79$	−6.64113	−	11.5028i	−0.747185	−	1.29416i	−0.949167	−	0.314773i	$-0.898071\pi$
$79$	−6.64113	−	11.5028i	−0.747185	−	1.29416i	0.201982	−	0.979389i	$-0.435262\pi$
$80$		0			0
$81$	1.94771	−	8.78672i	0.216412	−	0.976302i
$82$		0			0
$83$	5.39275	+	9.34051i	0.591931	+	1.02525i	0.993972	+	0.109633i	$0.0349675\pi$
$83$	5.39275	+	9.34051i	0.591931	+	1.02525i	−0.402041	+	0.915622i	$0.631699\pi$
$84$		0			0
$85$	1.27698	−	2.21179i	0.138507	−	0.239902i
$86$		0			0
$87$	2.15716	−	2.51462i	0.231272	−	0.269596i
$88$		0			0
$89$	4.04905			0.429198			0.214599	−	0.976702i	$-0.431155\pi$
$89$	4.04905			0.429198			0.214599	+	0.976702i	$0.431155\pi$
$90$		0			0
$91$	−16.8253			−1.76377
$92$		0			0
$93$	5.90169	+	1.10709i	0.611976	+	0.114800i
$94$		0			0
$95$	2.38322	−	4.12785i	0.244513	−	0.423509i
$96$		0			0
$97$	−8.68962	−	15.0509i	−0.882297	−	1.52818i	−0.848781	−	0.528745i	$-0.822663\pi$
$97$	−8.68962	−	15.0509i	−0.882297	−	1.52818i	−0.0335162	−	0.999438i	$-0.510671\pi$
$98$		0			0
$99$	12.8396	+	4.99285i	1.29043	+	0.501800i
$100$		0			0
$101$	−6.57301	−	11.3848i	−0.654039	−	1.13283i	−0.982134	−	0.188184i	$-0.939740\pi$
$101$	−6.57301	−	11.3848i	−0.654039	−	1.13283i	0.328094	−	0.944645i	$-0.393594\pi$
$102$		0			0
$103$	−5.75245	+	9.96354i	−0.566806	+	0.981736i	0.430073	+	0.902794i	$0.358488\pi$
$103$	−5.75245	+	9.96354i	−0.566806	+	0.981736i	−0.996879	+	0.0789425i	$0.974846\pi$
$104$		0			0
$105$	2.62774	+	7.47211i	0.256441	+	0.729203i
$106$		0			0
$107$	−5.52396			−0.534022			−0.267011	−	0.963694i	$-0.586036\pi$
$107$	−5.52396			−0.534022			−0.267011	+	0.963694i	$0.586036\pi$
$108$		0			0
$109$	−16.7381			−1.60322			−0.801610	−	0.597847i	$-0.796023\pi$
$109$	−16.7381			−1.60322			−0.801610	+	0.597847i	$0.796023\pi$
$110$		0			0
$111$	3.14131	+	8.93247i	0.298160	+	0.847833i
$112$		0			0
$113$	−1.89376	+	3.28009i	−0.178150	+	0.308565i	−0.941247	−	0.337719i	$-0.890345\pi$
$113$	−1.89376	+	3.28009i	−0.178150	+	0.308565i	0.763097	+	0.646284i	$0.223678\pi$
$114$		0			0
$115$	−1.28651	−	2.22830i	−0.119967	−	0.207790i
$116$		0			0
$117$	1.67925	+	10.9093i	0.155247	+	1.00856i
$118$		0			0
$119$	5.83963	+	10.1145i	0.535318	+	0.927198i
$120$		0			0
$121$	−5.04359	+	8.73575i	−0.458508	+	0.794159i
$122$		0			0
$123$	−11.3056	−	2.12080i	−1.01939	−	0.191226i
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	11.1444			0.988903			0.494451	−	0.869205i	$-0.335369\pi$
$127$	11.1444			0.988903			0.494451	+	0.869205i	$0.335369\pi$
$128$		0			0
$129$	7.39114	−	8.61591i	0.650754	−	0.758588i
$130$		0			0
$131$	−10.9125	+	18.9009i	−0.953426	+	1.65138i	−0.215496	+	0.976505i	$0.569137\pi$
$131$	−10.9125	+	18.9009i	−0.953426	+	1.65138i	−0.737930	+	0.674878i	$0.764196\pi$
$132$		0			0
$133$	10.8985	+	18.8767i	0.945018	+	1.63682i
$134$		0			0
$135$	4.58255	−	2.44955i	0.394403	−	0.210823i
$136$		0			0
$137$	2.22284	+	3.85008i	0.189910	+	0.328934i	0.945220	−	0.326434i	$-0.105847\pi$
$137$	2.22284	+	3.85008i	0.189910	+	0.328934i	−0.755310	+	0.655368i	$0.772514\pi$
$138$		0			0
$139$	5.58338	−	9.67069i	0.473576	−	0.820257i	−0.525967	−	0.850505i	$-0.676296\pi$
$139$	5.58338	−	9.67069i	0.473576	−	0.820257i	0.999542	+	0.0302478i	$0.00962964\pi$
$140$		0			0
$141$	−11.3223	+	13.1984i	−0.953506	+	1.11151i
$142$		0			0
$143$	−16.8954			−1.41287
$144$		0			0
$145$	1.91282			0.158851
$146$		0			0
$147$	−23.6840	−	4.44286i	−1.95342	−	0.366441i
$148$		0			0
$149$	6.54341	−	11.3335i	0.536057	−	0.928478i	−0.463055	−	0.886330i	$-0.653247\pi$
$149$	6.54341	−	11.3335i	0.536057	−	0.928478i	0.999111	−	0.0421478i	$-0.0134200\pi$
$150$		0			0
$151$	−0.179436	−	0.310792i	−0.0146023	−	0.0252919i	0.858632	−	0.512593i	$-0.171315\pi$
$151$	−0.179436	−	0.310792i	−0.0146023	−	0.0252919i	−0.873234	+	0.487301i	$0.837982\pi$
$152$		0			0
$153$	5.97529	−	4.79582i	0.483074	−	0.387719i
$154$		0			0
$155$	1.73339	+	3.00231i	0.139229	+	0.241152i
$156$		0			0
$157$	6.53489	−	11.3188i	0.521541	−	0.903335i	−0.478145	−	0.878281i	$-0.658691\pi$
$157$	6.53489	−	11.3188i	0.521541	−	0.903335i	0.999686	−	0.0250544i	$-0.00797591\pi$
$158$		0			0
$159$	2.32038	+	6.59812i	0.184018	+	0.523265i
$160$		0			0
$161$	11.7664			0.927325
$162$		0			0
$163$	18.7872			1.47152			0.735762	−	0.677240i	$-0.236824\pi$
$163$	18.7872			1.47152			0.735762	+	0.677240i	$0.236824\pi$
$164$		0			0
$165$	2.63869	+	7.50325i	0.205422	+	0.584128i
$166$		0			0
$167$	7.12613	−	12.3428i	0.551437	−	0.955117i	−0.446734	−	0.894667i	$-0.647413\pi$
$167$	7.12613	−	12.3428i	0.551437	−	0.955117i	0.998171	−	0.0604500i	$-0.0192536\pi$
$168$		0			0
$169$	−0.268456	−	0.464980i	−0.0206505	−	0.0357677i
$170$		0			0
$171$	11.1517	−	8.95042i	0.852790	−	0.684456i
$172$		0			0
$173$	4.59208	+	7.95371i	0.349129	+	0.604710i	0.986095	−	0.166183i	$-0.0531441\pi$
$173$	4.59208	+	7.95371i	0.349129	+	0.604710i	−0.636966	+	0.770892i	$0.719811\pi$
$174$		0			0
$175$	−2.28651	+	3.96035i	−0.172844	+	0.299374i
$176$		0			0
$177$	20.8902	+	3.91878i	1.57020	+	0.294553i
$178$		0			0
$179$	−18.7872			−1.40422			−0.702109	−	0.712069i	$-0.747758\pi$
$179$	−18.7872			−1.40422			−0.702109	+	0.712069i	$0.747758\pi$
$180$		0			0
$181$	11.9128			0.885473			0.442737	−	0.896652i	$-0.354008\pi$
$181$	11.9128			0.885473			0.442737	+	0.896652i	$0.354008\pi$
$182$		0			0
$183$	10.8174	−	12.6099i	0.799642	−	0.932148i
$184$		0			0
$185$	−2.73339	+	4.73437i	−0.200963	+	0.348077i
$186$		0			0
$187$	5.86397	+	10.1567i	0.428816	+	0.742731i
$188$		0			0
$189$	−0.776975	+	23.7494i	−0.0565167	+	1.72751i
$190$		0			0
$191$	2.37285	+	4.10990i	0.171694	+	0.297382i	0.939012	−	0.343884i	$-0.111743\pi$
$191$	2.37285	+	4.10990i	0.171694	+	0.297382i	−0.767318	+	0.641266i	$0.778409\pi$
$192$		0			0
$193$	−4.27698	+	7.40794i	−0.307863	+	0.533235i	−0.977895	−	0.209098i	$-0.932947\pi$
$193$	−4.27698	+	7.40794i	−0.307863	+	0.533235i	0.670031	+	0.742333i	$0.266281\pi$
$194$		0			0
$195$	−4.14924	+	4.83679i	−0.297133	+	0.346370i
$196$		0			0
$197$	−12.2539			−0.873056			−0.436528	−	0.899691i	$-0.643792\pi$
$197$	−12.2539			−0.873056			−0.436528	+	0.899691i	$0.643792\pi$
$198$		0			0
$199$	−1.71738			−0.121742			−0.0608710	−	0.998146i	$-0.519388\pi$
$199$	−1.71738			−0.121742			−0.0608710	+	0.998146i	$0.519388\pi$
$200$		0			0
$201$	−19.3038	−	3.62118i	−1.36158	−	0.255419i
$202$		0			0
$203$	−4.37368	+	7.57544i	−0.306972	+	0.531692i
$204$		0			0
$205$	−3.32056	−	5.75139i	−0.231918	−	0.401694i
$206$		0			0
$207$	−1.17435	−	7.62919i	−0.0816232	−	0.530265i
$208$		0			0
$209$	10.9439	+	18.9554i	0.757006	+	1.31117i
$210$		0			0
$211$	1.26661	−	2.19384i	0.0871972	−	0.151030i	−0.819128	−	0.573611i	$-0.805542\pi$
$211$	1.26661	−	2.19384i	0.0871972	−	0.151030i	0.906325	+	0.422581i	$0.138876\pi$
$212$		0			0
$213$	0.964931	+	2.74383i	0.0661160	+	0.188004i
$214$		0			0
$215$	6.55395			0.446976
$216$		0			0
$217$	−15.8536			−1.07621
$218$		0			0
$219$	1.79586	+	5.10661i	0.121353	+	0.345073i
$220$		0			0
$221$	−4.69832	+	8.13772i	−0.316043	+	0.547403i
$222$		0			0
$223$	11.1659	+	19.3399i	0.747725	+	1.29510i	0.948911	+	0.315545i	$0.102187\pi$
$223$	11.1659	+	19.3399i	0.747725	+	1.29510i	−0.201185	+	0.979553i	$0.564479\pi$
$224$		0			0
$225$	2.79604	+	1.08728i	0.186403	+	0.0724850i
$226$		0			0
$227$	−5.20886	−	9.02201i	−0.345724	−	0.598812i	0.639761	−	0.768574i	$-0.279033\pi$
$227$	−5.20886	−	9.02201i	−0.345724	−	0.598812i	−0.985485	+	0.169762i	$0.945700\pi$
$228$		0			0
$229$	8.78169	−	15.2103i	0.580311	−	1.00513i	−0.415132	−	0.909761i	$-0.636264\pi$
$229$	8.78169	−	15.2103i	0.580311	−	1.00513i	0.995442	−	0.0953662i	$-0.0304022\pi$
$230$		0			0
$231$	−35.7489	−	6.70611i	−2.35210	−	0.441230i
$232$		0			0
$233$	19.2328			1.25999			0.629993	−	0.776601i	$-0.283058\pi$
$233$	19.2328			1.25999			0.629993	+	0.776601i	$0.283058\pi$
$234$		0			0
$235$	−10.0398			−0.654924
$236$		0			0
$237$	14.9789	−	17.4610i	0.972985	−	1.13422i
$238$		0			0
$239$	−5.25227	+	9.09720i	−0.339741	+	0.588449i	−0.984384	−	0.176035i	$-0.943673\pi$
$239$	−5.25227	+	9.09720i	−0.339741	+	0.588449i	0.644643	+	0.764484i	$0.277006\pi$
$240$		0			0
$241$	−4.66037	−	8.07200i	−0.300201	−	0.519963i	0.675980	−	0.736920i	$-0.263720\pi$
$241$	−4.66037	−	8.07200i	−0.300201	−	0.519963i	−0.976181	+	0.216956i	$0.930387\pi$
$242$		0			0
$243$	15.4763	−	1.86654i	0.992805	−	0.119738i
$244$		0			0
$245$	−6.95623	−	12.0485i	−0.444417	−	0.769753i
$246$		0			0
$247$	−8.76846	+	15.1874i	−0.557924	+	0.966352i
$248$		0			0
$249$	−12.1632	+	14.1787i	−0.770813	+	0.898541i
$250$		0			0
$251$	−19.9125			−1.25686			−0.628432	−	0.777865i	$-0.716303\pi$
$251$	−19.9125			−1.25686			−0.628432	+	0.777865i	$0.716303\pi$
$252$		0			0
$253$	11.8155			0.742833
$254$		0			0
$255$	4.34774	+	0.815589i	0.272266	+	0.0510742i
$256$		0			0
$257$	5.70868	−	9.88772i	0.356098	−	0.616779i	−0.631207	−	0.775614i	$-0.717440\pi$
$257$	5.70868	−	9.88772i	0.356098	−	0.616779i	0.987305	+	0.158835i	$0.0507737\pi$
$258$		0			0
$259$	−12.4998	−	21.6503i	−0.776701	−	1.34529i
$260$		0			0
$261$	5.34833	+	2.07976i	0.331053	+	0.128734i
$262$		0			0
$263$	2.28568	+	3.95891i	0.140941	+	0.244117i	0.927851	−	0.372951i	$-0.121654\pi$
$263$	2.28568	+	3.95891i	0.140941	+	0.244117i	−0.786910	+	0.617067i	$0.788321\pi$
$264$		0			0
$265$	−2.01906	+	3.49712i	−0.124030	+	0.214826i
$266$		0			0
$267$	2.32666	+	6.61597i	0.142389	+	0.404891i
$268$		0			0
$269$	17.5954			1.07281			0.536405	−	0.843961i	$-0.319782\pi$
$269$	17.5954			1.07281			0.536405	+	0.843961i	$0.319782\pi$
$270$		0			0
$271$	9.64113			0.585657			0.292828	−	0.956165i	$-0.405404\pi$
$271$	9.64113			0.585657			0.292828	+	0.956165i	$0.405404\pi$
$272$		0			0
$273$	−9.66812	−	27.4918i	−0.585141	−	1.66388i
$274$		0			0
$275$	−2.29604	+	3.97686i	−0.138456	+	0.239813i
$276$		0			0
$277$	−7.05211	−	12.2146i	−0.423720	−	0.733905i	0.572580	−	0.819849i	$-0.305943\pi$
$277$	−7.05211	−	12.2146i	−0.423720	−	0.733905i	−0.996300	+	0.0859443i	$0.972609\pi$
$278$		0			0
$279$	1.58228	+	10.2793i	0.0947284	+	0.615403i
$280$		0			0
$281$	−1.72793	−	2.99285i	−0.103079	−	0.178539i	0.809873	−	0.586606i	$-0.199536\pi$
$281$	−1.72793	−	2.99285i	−0.103079	−	0.178539i	−0.912952	+	0.408067i	$0.866203\pi$
$282$		0			0
$283$	12.0911	−	20.9423i	0.718739	−	1.24489i	−0.242760	−	0.970086i	$-0.578053\pi$
$283$	12.0911	−	20.9423i	0.718739	−	1.24489i	0.961500	−	0.274807i	$-0.0886138\pi$
$284$		0			0
$285$	8.11417	+	1.52213i	0.480642	+	0.0901633i
$286$		0			0
$287$	30.3700			1.79268
$288$		0			0
$289$	−10.4773			−0.616314
$290$		0			0
$291$	19.5992	−	22.8470i	1.14893	−	1.33931i
$292$		0			0
$293$	2.62715	−	4.55035i	0.153480	−	0.265834i	−0.779025	−	0.626993i	$-0.784285\pi$
$293$	2.62715	−	4.55035i	0.153480	−	0.265834i	0.932504	+	0.361159i	$0.117619\pi$
$294$		0			0
$295$	6.13567	+	10.6273i	0.357232	+	0.618744i
$296$		0			0
$297$	−0.780214	+	23.8484i	−0.0452726	+	1.38382i
$298$		0			0
$299$	4.73339	+	8.19847i	0.273739	+	0.474130i
$300$		0			0
$301$	−14.9857	+	25.9559i	−0.863759	+	1.49607i
$302$		0			0
$303$	14.8253	−	17.2819i	0.851690	−	0.992821i
$304$		0			0
$305$	9.59208			0.549241
$306$		0			0
$307$	−1.31148			−0.0748503			−0.0374252	−	0.999299i	$-0.511916\pi$
$307$	−1.31148			−0.0748503			−0.0374252	+	0.999299i	$0.511916\pi$
$308$		0			0
$309$	−19.5854	−	3.67402i	−1.11418	−	0.209008i
$310$		0			0
$311$	4.43170	−	7.67594i	0.251299	−	0.435263i	−0.712585	−	0.701586i	$-0.752476\pi$
$311$	4.43170	−	7.67594i	0.251299	−	0.435263i	0.963884	+	0.266324i	$0.0858089\pi$
$312$		0			0
$313$	−1.12169	−	1.94282i	−0.0634014	−	0.109814i	0.832582	−	0.553901i	$-0.186862\pi$
$313$	−1.12169	−	1.94282i	−0.0634014	−	0.109814i	−0.895984	+	0.444087i	$0.853528\pi$
$314$		0			0
$315$	−10.6991	+	8.58722i	−0.602829	+	0.483835i
$316$		0			0
$317$	−10.2873	−	17.8182i	−0.577794	−	1.00077i	−0.995732	−	0.0922935i	$-0.970580\pi$
$317$	−10.2873	−	17.8182i	−0.577794	−	1.00077i	0.417937	−	0.908476i	$-0.362753\pi$
$318$		0			0
$319$	−4.39192	+	7.60702i	−0.245900	+	0.425911i
$320$		0			0
$321$	−3.17417	−	9.02592i	−0.177165	−	0.503778i
$322$		0			0
$323$	12.1732			0.677337
$324$		0			0
$325$	−3.67925			−0.204088
$326$		0			0
$327$	−9.61803	−	27.3493i	−0.531878	−	1.51242i
$328$		0			0
$329$	22.9560	−	39.7610i	1.26561	−	2.19210i
$330$		0			0
$331$	10.8938	+	18.8685i	0.598775	+	1.03711i	0.993002	+	0.118096i	$0.0376790\pi$
$331$	10.8938	+	18.8685i	0.598775	+	1.03711i	−0.394227	+	0.919013i	$0.628988\pi$
$332$		0			0
$333$	−12.7902	+	10.2655i	−0.700899	+	0.562547i
$334$		0			0
$335$	−5.66972	−	9.82025i	−0.309770	−	0.536537i
$336$		0			0
$337$	−6.22284	+	10.7783i	−0.338980	+	0.587130i	−0.984241	−	0.176832i	$-0.943415\pi$
$337$	−6.22284	+	10.7783i	−0.338980	+	0.587130i	0.645261	+	0.763962i	$0.276749\pi$
$338$		0			0
$339$	−6.44771	−	1.20952i	−0.350192	−	0.0656922i
$340$		0			0
$341$	−15.9197			−0.862100
$342$		0			0
$343$	31.6108			1.70682
$344$		0			0
$345$	2.90169	−	3.38252i	0.156222	−	0.182109i
$346$		0			0
$347$	8.59736	−	14.8911i	0.461530	−	0.799394i	−0.537507	−	0.843259i	$-0.680634\pi$
$347$	8.59736	−	14.8911i	0.461530	−	0.799394i	0.999037	+	0.0438652i	$0.0139672\pi$
$348$		0			0
$349$	−4.74191	−	8.21322i	−0.253828	−	0.439644i	0.710748	−	0.703446i	$-0.248357\pi$
$349$	−4.74191	−	8.21322i	−0.253828	−	0.439644i	−0.964577	+	0.263803i	$0.915023\pi$
$350$		0			0
$351$	−16.8604	+	9.01250i	−0.899939	+	0.481052i
$352$		0			0
$353$	−6.70868	−	11.6198i	−0.357067	−	0.618458i	0.630402	−	0.776268i	$-0.282890\pi$
$353$	−6.70868	−	11.6198i	−0.357067	−	0.618458i	−0.987469	+	0.157810i	$0.949557\pi$
$354$		0			0
$355$	−0.839627	+	1.45428i	−0.0445628	+	0.0771850i
$356$		0			0
$357$	−13.1711	+	15.3537i	−0.697091	+	0.812604i
$358$		0			0
$359$	−12.3970			−0.654289			−0.327144	−	0.944974i	$-0.606086\pi$
$359$	−12.3970			−0.654289			−0.327144	+	0.944974i	$0.606086\pi$
$360$		0			0
$361$	3.71887			0.195730
$362$		0			0
$363$	−17.1720	−	3.22128i	−0.901295	−	0.169073i
$364$		0			0
$365$	−1.56265	+	2.70659i	−0.0817929	+	0.141670i
$366$		0			0
$367$	−10.2857	−	17.8153i	−0.536908	−	0.929952i	−0.999068	−	0.0431555i	$-0.986259\pi$
$367$	−10.2857	−	17.8153i	−0.536908	−	0.929952i	0.462160	−	0.886796i	$-0.347074\pi$
$368$		0			0
$369$	−3.03109	−	19.6915i	−0.157792	−	1.02510i
$370$		0			0
$371$	−9.23321	−	15.9924i	−0.479364	−	0.830283i
$372$		0			0
$373$	2.23154	−	3.86515i	0.115545	−	0.200130i	−0.802453	−	0.596716i	$-0.796472\pi$
$373$	2.23154	−	3.86515i	0.115545	−	0.200130i	0.917997	+	0.396586i	$0.129805\pi$
$374$		0			0
$375$	0.574618	+	1.63396i	0.0296732	+	0.0843771i
$376$		0			0
$377$	−7.03776			−0.362463
$378$		0			0
$379$	8.77660			0.450823			0.225412	−	0.974264i	$-0.427627\pi$
$379$	8.77660			0.450823			0.225412	+	0.974264i	$0.427627\pi$
$380$		0			0
$381$	6.40376	+	18.2094i	0.328075	+	0.932896i
$382$		0			0
$383$	−1.60606	+	2.78177i	−0.0820658	+	0.142142i	−0.904137	−	0.427242i	$-0.859485\pi$
$383$	−1.60606	+	2.78177i	−0.0820658	+	0.142142i	0.822071	+	0.569384i	$0.192818\pi$
$384$		0			0
$385$	−10.4998	−	18.1862i	−0.535120	−	0.926856i
$386$		0			0
$387$	18.3251	+	7.12595i	0.931517	+	0.362232i
$388$		0			0
$389$	−12.7957	−	22.1628i	−0.648766	−	1.12370i	−0.983418	−	0.181354i	$-0.941952\pi$
$389$	−12.7957	−	22.1628i	−0.648766	−	1.12370i	0.334651	−	0.942342i	$-0.391381\pi$
$390$		0			0
$391$	3.28568	−	5.69096i	0.166164	−	0.287804i
$392$		0			0
$393$	−37.1538	−	6.96966i	−1.87416	−	0.351573i
$394$		0			0
$395$	13.2823			0.668303
$396$		0			0
$397$	14.3902			0.722221			0.361111	−	0.932523i	$-0.382398\pi$
$397$	14.3902			0.722221			0.361111	+	0.932523i	$0.382398\pi$
$398$		0			0
$399$	−24.5813	+	28.6546i	−1.23060	+	1.43452i
$400$		0			0
$401$	−13.0692	+	22.6365i	−0.652645	+	1.13042i	0.329833	+	0.944039i	$0.393008\pi$
$401$	−13.0692	+	22.6365i	−0.652645	+	1.13042i	−0.982479	+	0.186376i	$0.940326\pi$
$402$		0			0
$403$	−6.37757	−	11.0463i	−0.317689	−	0.550254i
$404$		0			0
$405$	6.63567	+	6.08013i	0.329729	+	0.302124i
$406$		0			0
$407$	−12.5519	−	21.7406i	−0.622176	−	1.07764i
$408$		0			0
$409$	−3.29096	+	5.70010i	−0.162727	+	0.281852i	−0.935846	−	0.352410i	$-0.885362\pi$
$409$	−3.29096	+	5.70010i	−0.162727	+	0.281852i	0.773119	+	0.634262i	$0.218696\pi$
$410$		0			0
$411$	−5.01357	+	5.84435i	−0.247301	+	0.288281i
$412$		0			0
$413$	−56.1170			−2.76134
$414$		0			0
$415$	−10.7855			−0.529439
$416$		0			0
$417$	19.0098	+	3.56604i	0.930914	+	0.174630i
$418$		0			0
$419$	6.37451	−	11.0410i	0.311415	−	0.539387i	−0.667254	−	0.744831i	$-0.732530\pi$
$419$	6.37451	−	11.0410i	0.311415	−	0.539387i	0.978669	+	0.205443i	$0.0658636\pi$
$420$		0			0
$421$	0.641128	+	1.11047i	0.0312467	+	0.0541208i	0.881226	−	0.472695i	$-0.156719\pi$
$421$	0.641128	+	1.11047i	0.0312467	+	0.0541208i	−0.849979	+	0.526816i	$0.823386\pi$
$422$		0			0
$423$	−28.0716	−	10.9160i	−1.36489	−	0.530755i
$424$		0			0
$425$	1.27698	+	2.21179i	0.0619424	+	0.107287i
$426$		0			0
$427$	−21.9324	+	37.9880i	−1.06138	+	1.83837i
$428$		0			0
$429$	−9.70842	−	27.6064i	−0.468727	−	1.33285i
$430$		0			0
$431$	−6.89137			−0.331946			−0.165973	−	0.986130i	$-0.553076\pi$
$431$	−6.89137			−0.331946			−0.165973	+	0.986130i	$0.553076\pi$
$432$		0			0
$433$	30.4551			1.46358			0.731790	−	0.681530i	$-0.238685\pi$
$433$	30.4551			1.46358			0.731790	+	0.681530i	$0.238685\pi$
$434$		0			0
$435$	1.09914	+	3.12547i	0.0526999	+	0.149855i
$436$		0			0
$437$	6.13205	−	10.6210i	0.293336	−	0.508072i
$438$		0			0
$439$	−14.8654	−	25.7477i	−0.709488	−	1.22887i	−0.965047	−	0.262077i	$-0.915593\pi$
$439$	−14.8654	−	25.7477i	−0.709488	−	1.22887i	0.255559	−	0.966794i	$-0.417741\pi$
$440$		0			0
$441$	−6.34981	−	41.2515i	−0.302372	−	1.96436i
$442$		0			0
$443$	−3.16482	−	5.48163i	−0.150365	−	0.260440i	0.780997	−	0.624535i	$-0.214712\pi$
$443$	−3.16482	−	5.48163i	−0.150365	−	0.260440i	−0.931362	+	0.364095i	$0.881378\pi$
$444$		0			0
$445$	−2.02453	+	3.50658i	−0.0959717	+	0.166228i
$446$		0			0
$447$	22.2784	+	4.17920i	1.05373	+	0.197669i
$448$		0			0
$449$	25.8456			1.21973			0.609866	−	0.792505i	$-0.291223\pi$
$449$	25.8456			1.21973			0.609866	+	0.792505i	$0.291223\pi$
$450$		0			0
$451$	30.4966			1.43603
$452$		0			0
$453$	0.404714	−	0.471778i	0.0190151	−	0.0221661i
$454$		0			0
$455$	8.41264	−	14.5711i	0.394391	−	0.683105i
$456$		0			0
$457$	17.6545	+	30.5786i	0.825845	+	1.43041i	0.901272	+	0.433254i	$0.142635\pi$
$457$	17.6545	+	30.5786i	0.825845	+	1.43041i	−0.0754270	+	0.997151i	$0.524032\pi$
$458$		0			0
$459$	11.2697	+	7.00760i	0.526023	+	0.327087i
$460$		0			0
$461$	−1.55941	−	2.70098i	−0.0726291	−	0.125797i	0.827424	−	0.561578i	$-0.189806\pi$
$461$	−1.55941	−	2.70098i	−0.0726291	−	0.125797i	−0.900053	+	0.435781i	$0.856472\pi$
$462$		0			0
$463$	−1.58736	+	2.74939i	−0.0737708	+	0.127775i	−0.900551	−	0.434750i	$-0.856837\pi$
$463$	−1.58736	+	2.74939i	−0.0737708	+	0.127775i	0.826780	+	0.562525i	$0.190170\pi$
$464$		0			0
$465$	−3.90961	+	4.55746i	−0.181304	+	0.211347i
$466$		0			0
$467$	−20.2808			−0.938482			−0.469241	−	0.883070i	$-0.655472\pi$
$467$	−20.2808			−0.938482			−0.469241	+	0.883070i	$0.655472\pi$
$468$		0			0
$469$	51.8554			2.39446
$470$		0			0
$471$	22.2494	+	4.17375i	1.02520	+	0.192316i
$472$		0			0
$473$	−15.0481	+	26.0641i	−0.691914	+	1.19843i
$474$		0			0
$475$	2.38322	+	4.12785i	0.109349	+	0.189399i
$476$		0			0
$477$	−9.44771	+	7.58281i	−0.432581	+	0.347193i
$478$		0			0
$479$	−5.03813	−	8.72629i	−0.230198	−	0.398714i	0.727668	−	0.685929i	$-0.240604\pi$
$479$	−5.03813	−	8.72629i	−0.230198	−	0.398714i	−0.957866	+	0.287215i	$0.907271\pi$
$480$		0			0
$481$	10.0568	−	17.4189i	0.458552	−	0.794235i
$482$		0			0
$483$	6.76121	+	19.2258i	0.307646	+	0.874806i
$484$		0			0
$485$	17.3792			0.789150
$486$		0			0
$487$	28.3589			1.28506			0.642532	−	0.766259i	$-0.277884\pi$
$487$	28.3589			1.28506			0.642532	+	0.766259i	$0.277884\pi$
$488$		0			0
$489$	10.7954	+	30.6974i	0.488187	+	1.38818i
$490$		0			0
$491$	16.4560	−	28.5027i	0.742651	−	1.28631i	−0.208633	−	0.977994i	$-0.566901\pi$
$491$	16.4560	−	28.5027i	0.742651	−	1.28631i	0.951284	−	0.308315i	$-0.0997652\pi$
$492$		0			0
$493$	2.44263	+	4.23076i	0.110010	+	0.190544i
$494$		0			0
$495$	−10.7437	+	8.62302i	−0.482896	+	0.387576i
$496$		0			0
$497$	−3.83963	−	6.65043i	−0.172231	−	0.298313i
$498$		0			0
$499$	2.50546	−	4.33959i	0.112160	−	0.194267i	−0.804481	−	0.593978i	$-0.797556\pi$
$499$	2.50546	−	4.33959i	0.112160	−	0.194267i	0.916641	+	0.399712i	$0.130890\pi$
$500$		0			0
$501$	24.2624	+	4.55138i	1.08397	+	0.203341i
$502$		0			0
$503$	−42.1916			−1.88123			−0.940615	−	0.339477i	$-0.889750\pi$
$503$	−42.1916			−1.88123			−0.940615	+	0.339477i	$0.889750\pi$
$504$		0			0
$505$	13.1460			0.584991
$506$		0			0
$507$	0.605497	−	0.705832i	0.0268911	−	0.0313471i
$508$		0			0
$509$	8.61660	−	14.9244i	0.381924	−	0.661512i	−0.609413	−	0.792853i	$-0.708595\pi$
$509$	8.61660	−	14.9244i	0.381924	−	0.661512i	0.991337	+	0.131341i	$0.0419282\pi$
$510$		0			0
$511$	−7.14603	−	12.3773i	−0.316122	−	0.547539i
$512$		0			0
$513$	21.0326	+	13.0783i	0.928610	+	0.577420i
$514$		0			0
$515$	−5.75245	−	9.96354i	−0.253483	−	0.439046i
$516$		0			0
$517$	23.0517	−	39.9268i	1.01381	−	1.75598i
$518$		0			0
$519$	−10.3573	+	12.0736i	−0.454636	+	0.529972i
$520$		0			0
$521$	−5.42901			−0.237849			−0.118925	−	0.992903i	$-0.537945\pi$
$521$	−5.42901			−0.237849			−0.118925	+	0.992903i	$0.537945\pi$
$522$		0			0
$523$	−6.68128			−0.292152			−0.146076	−	0.989273i	$-0.546664\pi$
$523$	−6.68128			−0.292152			−0.146076	+	0.989273i	$0.546664\pi$
$524$		0			0
$525$	−7.78490	−	1.46036i	−0.339761	−	0.0637355i
$526$		0			0
$527$	−4.42699	+	7.66776i	−0.192843	+	0.334013i
$528$		0			0
$529$	8.18980	+	14.1851i	0.356078	+	0.616746i
$530$		0			0
$531$	5.60078	+	36.3855i	0.243053	+	1.57899i
$532$		0			0
$533$	12.2172	+	21.1608i	0.529186	+	0.916576i
$534$		0			0
$535$	2.76198	−	4.78389i	0.119411	−	0.206826i
$536$		0			0
$537$	−10.7954	−	30.6974i	−0.465858	−	1.32469i
$538$		0			0
$539$	63.8871			2.75181
$540$		0			0
$541$	35.3087			1.51804			0.759020	−	0.651067i	$-0.225678\pi$
$541$	35.3087			1.51804			0.759020	+	0.651067i	$0.225678\pi$
$542$		0			0
$543$	6.84533	+	19.4650i	0.293761	+	0.835325i
$544$		0			0
$545$	8.36905	−	14.4956i	0.358491	−	0.620924i
$546$		0			0
$547$	5.78105	+	10.0131i	0.247180	+	0.428128i	0.962742	−	0.270421i	$-0.0871629\pi$
$547$	5.78105	+	10.0131i	0.247180	+	0.428128i	−0.715563	+	0.698549i	$0.753830\pi$
$548$		0			0
$549$	26.8198	+	10.4292i	1.14464	+	0.445109i
$550$		0			0
$551$	4.55867	+	7.89585i	0.194206	+	0.336374i
$552$		0			0
$553$	−30.3700	+	52.6023i	−1.29146	+	2.23688i
$554$		0			0
$555$	−9.30640	−	1.74578i	−0.395035	−	0.0741043i
$556$		0			0
$557$	−18.0415			−0.764441			−0.382220	−	0.924071i	$-0.624840\pi$
$557$	−18.0415			−0.764441			−0.382220	+	0.924071i	$0.624840\pi$
$558$		0			0
$559$	−24.1137			−1.01990
$560$		0			0
$561$	−13.2261	+	15.4177i	−0.558404	+	0.650936i
$562$		0			0
$563$	1.28086	−	2.21852i	0.0539820	−	0.0934995i	−0.837772	−	0.546021i	$-0.816142\pi$
$563$	1.28086	−	2.21852i	0.0539820	−	0.0934995i	0.891754	+	0.452521i	$0.149475\pi$
$564$		0			0
$565$	−1.89376	−	3.28009i	−0.0796711	−	0.137994i
$566$		0			0
$567$	−39.2519	+	12.3773i	−1.64843	+	0.519797i
$568$		0			0
$569$	10.3502	+	17.9270i	0.433902	+	0.751540i	0.997205	−	0.0747101i	$-0.0238032\pi$
$569$	10.3502	+	17.9270i	0.433902	+	0.751540i	−0.563304	+	0.826250i	$0.690470\pi$
$570$		0			0
$571$	−3.58338	+	6.20659i	−0.149960	+	0.259738i	−0.931212	−	0.364477i	$-0.881248\pi$
$571$	−3.58338	+	6.20659i	−0.149960	+	0.259738i	0.781253	+	0.624215i	$0.214581\pi$
$572$		0			0
$573$	−5.35192	+	6.23876i	−0.223579	+	0.260628i
$574$		0			0
$575$	2.57301			0.107302
$576$		0			0
$577$	−27.2463			−1.13428			−0.567140	−	0.823622i	$-0.691950\pi$
$577$	−27.2463			−1.13428			−0.567140	+	0.823622i	$0.691950\pi$
$578$		0			0
$579$	−14.5619	−	2.73165i	−0.605171	−	0.113524i
$580$		0			0
$581$	24.6611	−	42.7143i	1.02312	−	1.77209i
$582$		0			0
$583$	−9.27170	−	16.0590i	−0.383994	−	0.665098i
$584$		0			0
$585$	−10.2873	−	4.00036i	−0.425329	−	0.165395i
$586$		0			0
$587$	8.24746	+	14.2850i	0.340409	+	0.589606i	0.984509	−	0.175336i	$-0.0561012\pi$
$587$	8.24746	+	14.2850i	0.340409	+	0.589606i	−0.644100	+	0.764942i	$0.722768\pi$
$588$		0			0
$589$	−8.26207	+	14.3103i	−0.340433	+	0.589647i
$590$		0			0
$591$	−7.04133	−	20.0224i	−0.289642	−	0.823611i
$592$		0			0
$593$	−14.2819			−0.586487			−0.293244	−	0.956038i	$-0.594735\pi$
$593$	−14.2819			−0.586487			−0.293244	+	0.956038i	$0.594735\pi$
$594$		0			0
$595$	−11.6793			−0.478803
$596$		0			0
$597$	−0.986839	−	2.80613i	−0.0403886	−	0.114847i
$598$		0			0
$599$	11.1951	−	19.3904i	0.457419	−	0.792272i	−0.541405	−	0.840762i	$-0.682107\pi$
$599$	11.1951	−	19.3904i	0.457419	−	0.792272i	0.998824	+	0.0484897i	$0.0154408\pi$
$600$		0			0
$601$	6.05015	+	10.4792i	0.246791	+	0.427454i	0.962634	−	0.270807i	$-0.0872906\pi$
$601$	6.05015	+	10.4792i	0.246791	+	0.427454i	−0.715843	+	0.698262i	$0.753957\pi$
$602$		0			0
$603$	−5.17545	−	33.6223i	−0.210761	−	1.36921i
$604$		0			0
$605$	−5.04359	−	8.73575i	−0.205051	−	0.355159i
$606$		0			0
$607$	10.1659	−	17.6079i	0.412622	−	0.714682i	−0.582554	−	0.812792i	$-0.697946\pi$
$607$	10.1659	−	17.6079i	0.412622	−	0.714682i	0.995176	+	0.0981100i	$0.0312797\pi$
$608$		0			0
$609$	−14.8911	−	2.79342i	−0.603420	−	0.113195i
$610$		0			0
$611$	36.9389			1.49439
$612$		0			0
$613$	24.8853			1.00511			0.502553	−	0.864546i	$-0.332394\pi$
$613$	24.8853			1.00511			0.502553	+	0.864546i	$0.332394\pi$
$614$		0			0
$615$	7.48946	−	8.73051i	0.302004	−	0.352048i
$616$		0			0
$617$	−22.6994	+	39.3165i	−0.913844	+	1.58282i	−0.105259	+	0.994445i	$0.533567\pi$
$617$	−22.6994	+	39.3165i	−0.913844	+	1.58282i	−0.808585	+	0.588380i	$0.799766\pi$
$618$		0			0
$619$	9.71376	+	16.8247i	0.390429	+	0.676243i	0.992506	−	0.122195i	$-0.0389933\pi$
$619$	9.71376	+	16.8247i	0.390429	+	0.676243i	−0.602077	+	0.798438i	$0.705660\pi$
$620$		0			0
$621$	11.7910	−	6.30272i	0.473155	−	0.252919i
$622$		0			0
$623$	−9.25818	−	16.0356i	−0.370921	−	0.642454i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$	−24.6837	+	28.7740i	−0.985774	+	1.14912i
$628$		0			0
$629$	−13.9619			−0.556696
$630$		0			0
$631$	−7.78752			−0.310016			−0.155008	−	0.987913i	$-0.549540\pi$
$631$	−7.78752			−0.310016			−0.155008	+	0.987913i	$0.549540\pi$
$632$		0			0
$633$	4.31245	+	0.808970i	0.171405	+	0.0321537i
$634$		0			0
$635$	−5.57218	+	9.65130i	−0.221125	+	0.383000i
$636$		0			0
$637$	25.5937	+	44.3297i	1.01406	+	1.75640i
$638$		0			0
$639$	−3.92883	+	3.15331i	−0.155422	+	0.124743i
$640$		0			0
$641$	14.6981	+	25.4579i	0.580541	+	1.00553i	0.995415	+	0.0956483i	$0.0304924\pi$
$641$	14.6981	+	25.4579i	0.580541	+	1.00553i	−0.414874	+	0.909879i	$0.636174\pi$
$642$		0			0
$643$	4.65066	−	8.05518i	0.183404	−	0.317665i	−0.759633	−	0.650351i	$-0.774622\pi$
$643$	4.65066	−	8.05518i	0.183404	−	0.317665i	0.943038	+	0.332686i	$0.107955\pi$
$644$		0			0
$645$	3.76602	+	10.7089i	0.148287	+	0.421661i
$646$		0			0
$647$	40.4647			1.59083			0.795417	−	0.606063i	$-0.207252\pi$
$647$	40.4647			1.59083			0.795417	+	0.606063i	$0.207252\pi$
$648$		0			0
$649$	−56.3509			−2.21197
$650$		0			0
$651$	−9.10978	−	25.9041i	−0.357040	−	1.01526i
$652$		0			0
$653$	7.32546	−	12.6881i	0.286668	−	0.496523i	−0.686345	−	0.727276i	$-0.740786\pi$
$653$	7.32546	−	12.6881i	0.286668	−	0.496523i	0.973012	+	0.230754i	$0.0741191\pi$
$654$		0			0
$655$	−10.9125	−	18.9009i	−0.426385	−	0.738521i
$656$		0			0
$657$	−7.31204	+	5.86870i	−0.285270	+	0.228960i
$658$		0			0
$659$	−2.51380	−	4.35403i	−0.0979237	−	0.169609i	0.812901	−	0.582401i	$-0.197887\pi$
$659$	−2.51380	−	4.35403i	−0.0979237	−	0.169609i	−0.910825	+	0.412793i	$0.864553\pi$
$660$		0			0
$661$	−15.9128	+	27.5618i	−0.618937	+	1.07203i	0.370743	+	0.928736i	$0.379103\pi$
$661$	−15.9128	+	27.5618i	−0.618937	+	1.07203i	−0.989680	+	0.143295i	$0.954230\pi$
$662$		0			0
$663$	−15.9964	−	3.00076i	−0.621250	−	0.116540i
$664$		0			0
$665$	−21.7970			−0.845250
$666$		0			0
$667$	4.92172			0.190570
$668$		0			0
$669$	−25.1845	+	29.3577i	−0.973688	+	1.13504i
$670$		0			0
$671$	−22.0238	+	38.1463i	−0.850219	+	1.47262i
$672$		0			0
$673$	−5.45077	−	9.44101i	−0.210112	−	0.363924i	0.741638	−	0.670801i	$-0.234049\pi$
$673$	−5.45077	−	9.44101i	−0.210112	−	0.363924i	−0.951749	+	0.306877i	$0.900716\pi$
$674$		0			0
$675$	−0.169904	+	5.19337i	−0.00653963	+	0.199893i
$676$		0			0
$677$	14.0047	+	24.2569i	0.538245	+	0.932268i	0.998999	+	0.0447397i	$0.0142459\pi$
$677$	14.0047	+	24.2569i	0.538245	+	0.932268i	−0.460754	+	0.887528i	$0.652421\pi$
$678$		0			0
$679$	−39.7377	+	68.8278i	−1.52499	+	2.64137i
$680$		0			0
$681$	11.7485	−	13.6953i	0.450202	−	0.524804i
$682$		0			0
$683$	7.19544			0.275326			0.137663	−	0.990479i	$-0.456041\pi$
$683$	7.19544			0.275326			0.137663	+	0.990479i	$0.456041\pi$
$684$		0			0
$685$	−4.44569			−0.169861
$686$		0			0
$687$	29.8992	+	5.60876i	1.14072	+	0.213988i
$688$		0			0
$689$	7.42865	−	12.8668i	0.283009	−	0.490186i
$690$		0			0
$691$	11.2713	+	19.5225i	0.428782	+	0.742672i	0.996765	−	0.0803682i	$-0.0256096\pi$
$691$	11.2713	+	19.5225i	0.428782	+	0.742672i	−0.567984	+	0.823040i	$0.692276\pi$
$692$		0			0
$693$	−9.58448	−	62.2656i	−0.364084	−	2.36527i
$694$		0			0
$695$	5.58338	+	9.67069i	0.211790	+	0.366830i
$696$		0			0
$697$	8.48056	−	14.6888i	0.321224	−	0.556376i
$698$		0			0
$699$	11.0515	+	31.4256i	0.418008	+	1.18863i
$700$		0			0
$701$	−19.7098			−0.744428			−0.372214	−	0.928147i	$-0.621401\pi$
$701$	−19.7098			−0.744428			−0.372214	+	0.928147i	$0.621401\pi$
$702$		0			0
$703$	−26.0570			−0.982758
$704$		0			0
$705$	−5.76905	−	16.4046i	−0.217275	−	0.617832i
$706$		0			0
$707$	−30.0585	+	52.0628i	−1.13047	+	1.95802i
$708$		0			0
$709$	−12.0643	−	20.8960i	−0.453085	−	0.784766i	0.545491	−	0.838117i	$-0.316343\pi$
$709$	−12.0643	−	20.8960i	−0.453085	−	0.784766i	−0.998576	+	0.0533508i	$0.983010\pi$
$710$		0			0
$711$	37.1377	+	14.4415i	1.39277	+	0.541597i
$712$		0			0
$713$	4.46003	+	7.72500i	0.167029	+	0.289303i
$714$		0			0
$715$	8.44771	−	14.6319i	0.315926	−	0.547201i
$716$		0			0
$717$	−17.8825	−	3.35456i	−0.667833	−	0.125278i
$718$		0			0
$719$	−8.79732			−0.328085			−0.164042	−	0.986453i	$-0.552453\pi$
$719$	−8.79732			−0.328085			−0.164042	+	0.986453i	$0.552453\pi$
$720$		0			0
$721$	52.6121			1.95938
$722$		0			0
$723$	10.5114	−	12.2532i	0.390922	−	0.455700i
$724$		0			0
$725$	−0.956412	+	1.65655i	−0.0355202	+	0.0615229i
$726$		0			0
$727$	−2.62123	−	4.54011i	−0.0972162	−	0.168383i	0.813315	−	0.581823i	$-0.197660\pi$
$727$	−2.62123	−	4.54011i	−0.0972162	−	0.168383i	−0.910531	+	0.413440i	$0.864327\pi$
$728$		0			0
$729$	11.9428	+	24.2151i	0.442326	+	0.896854i
$730$		0			0
$731$	8.36923	+	14.4959i	0.309547	+	0.536152i
$732$		0			0
$733$	17.0589	−	29.5468i	0.630083	−	1.09134i	−0.357451	−	0.933932i	$-0.616354\pi$
$733$	17.0589	−	29.5468i	0.630083	−	1.09134i	0.987534	−	0.157404i	$-0.0503125\pi$
$734$		0			0
$735$	15.6896	−	18.2895i	0.578720	−	0.674618i
$736$		0			0
$737$	52.0716			1.91808
$738$		0			0
$739$	5.53174			0.203488			0.101744	−	0.994811i	$-0.467558\pi$
$739$	5.53174			0.203488			0.101744	+	0.994811i	$0.467558\pi$
$740$		0			0
$741$	−29.8541	−	5.60031i	−1.09672	−	0.205732i
$742$		0			0
$743$	−7.77234	+	13.4621i	−0.285140	+	0.493876i	−0.972643	−	0.232305i	$-0.925373\pi$
$743$	−7.77234	+	13.4621i	−0.285140	+	0.493876i	0.687503	+	0.726181i	$0.258707\pi$
$744$		0			0
$745$	6.54341	+	11.3335i	0.239732	+	0.415228i
$746$		0			0
$747$	−30.1567	−	11.7268i	−1.10337	−	0.429061i
$748$		0			0
$749$	12.6306	+	21.8768i	0.461511	+	0.799361i
$750$		0			0
$751$	11.2472	−	19.4807i	0.410416	−	0.710861i	−0.584519	−	0.811380i	$-0.698717\pi$
$751$	11.2472	−	19.4807i	0.410416	−	0.710861i	0.994935	+	0.100519i	$0.0320503\pi$
$752$		0			0
$753$	−11.4421	−	32.5361i	−0.416972	−	1.18568i
$754$		0			0
$755$	0.358872			0.0130607
$756$		0			0
$757$	−14.5714			−0.529605			−0.264802	−	0.964303i	$-0.585307\pi$
$757$	−14.5714			−0.529605			−0.264802	+	0.964303i	$0.585307\pi$
$758$		0			0
$759$	6.78939	+	19.3060i	0.246439	+	0.700763i
$760$		0			0
$761$	6.90736	−	11.9639i	0.250392	−	0.433691i	−0.713242	−	0.700918i	$-0.752774\pi$
$761$	6.90736	−	11.9639i	0.250392	−	0.433691i	0.963634	+	0.267227i	$0.0861073\pi$
$762$		0			0
$763$	38.2718	+	66.2887i	1.38553	+	2.39981i
$764$		0			0
$765$	1.16565	+	7.57266i	0.0421443	+	0.273790i
$766$		0			0
$767$	−22.5747	−	39.1005i	−0.815124	−	1.41184i
$768$		0			0
$769$	0.0643136	−	0.111394i	0.00231921	−	0.00401698i	−0.864863	−	0.502007i	$-0.832595\pi$
$769$	0.0643136	−	0.111394i	0.00231921	−	0.00401698i	0.867183	+	0.497990i	$0.165928\pi$
$770$		0			0
$771$	19.4364	+	3.64607i	0.699986	+	0.131310i
$772$		0			0
$773$	−44.5427			−1.60209			−0.801044	−	0.598605i	$-0.795722\pi$
$773$	−44.5427			−1.60209			−0.801044	+	0.598605i	$0.795722\pi$
$774$		0			0
$775$	−3.46677			−0.124530
$776$		0			0
$777$	28.1931	−	32.8648i	1.01142	−	1.17902i
$778$		0			0
$779$	15.8272	−	27.4136i	0.567070	−	0.982194i
$780$		0			0
$781$	−3.85563	−	6.67815i	−0.137965	−	0.238963i
$782$		0			0
$783$	−0.324997	+	9.93401i	−0.0116145	+	0.355012i
$784$		0			0
$785$	6.53489	+	11.3188i	0.233240	+	0.403984i
$786$		0			0
$787$	16.3932	−	28.3939i	0.584355	−	1.01213i	−0.410601	−	0.911815i	$-0.634681\pi$
$787$	16.3932	−	28.3939i	0.584355	−	1.01213i	0.994956	−	0.100317i	$-0.0319858\pi$
$788$		0			0
$789$	−5.15529	+	6.00956i	−0.183533	+	0.213946i
$790$		0			0
$791$	17.3204			0.615842
$792$		0			0
$793$	−35.2917			−1.25324
$794$		0			0
$795$	−6.87433	−	1.28955i	−0.243807	−	0.0457357i
$796$		0			0
$797$	−26.9383	+	46.6584i	−0.954202	+	1.65273i	−0.218019	+	0.975944i	$0.569960\pi$
$797$	−26.9383	+	46.6584i	−0.954202	+	1.65273i	−0.736183	+	0.676783i	$0.763374\pi$
$798$		0			0
$799$	−12.8206	−	22.2059i	−0.453559	−	0.785587i
$800$		0			0
$801$	−9.47327	+	7.60332i	−0.334721	+	0.268650i
$802$		0			0
$803$	−7.17582	−	12.4289i	−0.253229	−	0.438606i
$804$		0			0
$805$	−5.88322	+	10.1900i	−0.207356	+	0.359151i
$806$		0			0
$807$	10.1106	+	28.7501i	0.355911	+	1.01205i
$808$		0			0
$809$	−44.3890			−1.56064			−0.780318	−	0.625383i	$-0.784943\pi$
$809$	−44.3890			−1.56064			−0.780318	+	0.625383i	$0.784943\pi$
$810$		0			0
$811$	−23.6339			−0.829898			−0.414949	−	0.909845i	$-0.636201\pi$
$811$	−23.6339			−0.829898			−0.414949	+	0.909845i	$0.636201\pi$
$812$		0			0
$813$	5.53997	+	15.7532i	0.194295	+	0.552488i
$814$		0			0
$815$	−9.39358	+	16.2702i	−0.329043	+	0.569919i
$816$		0			0
$817$	15.6195	+	27.0537i	0.546456	+	0.946490i
$818$		0			0
$819$	39.3649	−	31.5946i	1.37552	−	1.10400i
$820$		0			0
$821$	3.40921	+	5.90492i	0.118982	+	0.206083i	0.919365	−	0.393407i	$-0.128704\pi$
$821$	3.40921	+	5.90492i	0.118982	+	0.206083i	−0.800382	+	0.599490i	$0.795370\pi$
$822$		0			0
$823$	−21.1656	+	36.6598i	−0.737785	+	1.27788i	0.215706	+	0.976458i	$0.430795\pi$
$823$	−21.1656	+	36.6598i	−0.737785	+	1.27788i	−0.953491	+	0.301423i	$0.902538\pi$
$824$		0			0
$825$	−7.81736	−	1.46645i	−0.272165	−	0.0510553i
$826$		0			0
$827$	30.3700			1.05607			0.528034	−	0.849223i	$-0.322929\pi$
$827$	30.3700			1.05607			0.528034	+	0.849223i	$0.322929\pi$
$828$		0			0
$829$	−45.8420			−1.59216			−0.796078	−	0.605193i	$-0.793096\pi$
$829$	−45.8420			−1.59216			−0.796078	+	0.605193i	$0.793096\pi$
$830$		0			0
$831$	15.9059	−	18.5416i	0.551768	−	0.643200i
$832$		0			0
$833$	17.7659	−	30.7714i	0.615551	−	1.06617i
$834$		0			0
$835$	7.12613	+	12.3428i	0.246610	+	0.427141i
$836$		0			0
$837$	−15.8867	+	8.49202i	−0.549123	+	0.293527i
$838$		0			0
$839$	−5.62512	−	9.74300i	−0.194201	−	0.336366i	0.752437	−	0.658664i	$-0.228878\pi$
$839$	−5.62512	−	9.74300i	−0.194201	−	0.336366i	−0.946638	+	0.322298i	$0.895545\pi$
$840$		0			0
$841$	12.6706	−	21.9460i	0.436916	−	0.756760i
$842$		0			0
$843$	3.89730	−	4.54310i	0.134230	−	0.156473i
$844$		0			0
$845$	0.536913			0.0184704
$846$		0			0
$847$	46.1288			1.58500
$848$		0			0
$849$	41.1666	+	7.72242i	1.41283	+	0.265033i
$850$		0			0
$851$	−7.03304	+	12.1816i	−0.241090	+	0.417580i
$852$		0			0
$853$	−2.67417	−	4.63180i	−0.0915619	−	0.158590i	0.816607	−	0.577195i	$-0.195853\pi$
$853$	−2.67417	−	4.63180i	−0.0915619	−	0.158590i	−0.908169	+	0.418605i	$0.862519\pi$
$854$		0			0
$855$	2.17545	+	14.1328i	0.0743990	+	0.483333i
$856$		0			0
$857$	−25.9646	−	44.9719i	−0.886933	−	1.53621i	−0.843482	−	0.537157i	$-0.819498\pi$
$857$	−25.9646	−	44.9719i	−0.886933	−	1.53621i	−0.0434504	−	0.999056i	$-0.513835\pi$
$858$		0			0
$859$	14.7117	−	25.4815i	0.501958	−	0.869417i	−0.498039	−	0.867154i	$-0.665947\pi$
$859$	14.7117	−	25.4815i	0.501958	−	0.869417i	0.999997	−	0.00226239i	$-0.000720142\pi$
$860$		0			0
$861$	17.4511	+	49.6232i	0.594734	+	1.69115i
$862$		0			0
$863$	−15.9635			−0.543405			−0.271703	−	0.962381i	$-0.587587\pi$
$863$	−15.9635			−0.543405			−0.271703	+	0.962381i	$0.587587\pi$
$864$		0			0
$865$	−9.18416			−0.312271
$866$		0			0
$867$	−6.02047	−	17.1195i	−0.204466	−	0.581409i
$868$		0			0
$869$	−30.4966	+	52.8216i	−1.03453	+	1.79185i
$870$		0			0
$871$	20.8604	+	36.1312i	0.706826	+	1.22426i
$872$		0			0
$873$	48.5930	+	18.8960i	1.64462	+	0.639533i
$874$		0			0
$875$	−2.28651	−	3.96035i	−0.0772980	−	0.133884i
$876$		0			0
$877$	−2.71432	+	4.70135i	−0.0916562	+	0.158753i	−0.908208	−	0.418519i	$-0.862549\pi$
$877$	−2.71432	+	4.70135i	−0.0916562	+	0.158753i	0.816552	+	0.577272i	$0.195883\pi$
$878$		0			0
$879$	8.94468	+	1.67793i	0.301697	+	0.0565951i
$880$		0			0
$881$	10.2676			0.345926			0.172963	−	0.984928i	$-0.444666\pi$
$881$	10.2676			0.345926			0.172963	+	0.984928i	$0.444666\pi$
$882$		0			0
$883$	−12.6184			−0.424642			−0.212321	−	0.977200i	$-0.568102\pi$
$883$	−12.6184			−0.424642			−0.212321	+	0.977200i	$0.568102\pi$
$884$		0			0
$885$	−13.8389	+	16.1320i	−0.465188	+	0.542273i
$886$		0			0
$887$	−18.8015	+	32.5652i	−0.631293	+	1.09343i	0.355995	+	0.934488i	$0.384142\pi$
$887$	−18.8015	+	32.5652i	−0.631293	+	1.09343i	−0.987288	+	0.158943i	$0.949191\pi$
$888$		0			0
$889$	−25.4817	−	44.1356i	−0.854628	−	1.48026i
$890$		0			0
$891$	−39.4155	+	12.4289i	−1.32047	+	0.416383i
$892$		0			0
$893$	−23.9270	−	41.4427i	−0.800686	−	1.38683i
$894$		0			0
$895$	9.39358	−	16.2702i	0.313993	−	0.543851i
$896$		0			0
$897$	−10.6760	+	12.4451i	−0.356463	+	0.415531i
$898$		0			0
$899$	−6.63133			−0.221167
$900$		0			0
$901$	−10.3132			−0.343582
$902$		0			0
$903$	−51.0219	−	9.57116i	−1.69790	−	0.318508i
$904$		0			0
$905$	−5.95641	+	10.3168i	−0.197998	+	0.342942i
$906$		0			0
$907$	−14.1556	−	24.5181i	−0.470028	−	0.814112i	0.529385	−	0.848382i	$-0.322423\pi$
$907$	−14.1556	−	24.5181i	−0.470028	−	0.814112i	−0.999413	+	0.0342699i	$0.989089\pi$
$908$		0			0
$909$	36.7568	+	14.2933i	1.21915	+	0.474080i
$910$		0			0
$911$	−3.80658	−	6.59320i	−0.126118	−	0.218442i	0.796052	−	0.605229i	$-0.206918\pi$
$911$	−3.80658	−	6.59320i	−0.126118	−	0.218442i	−0.922169	+	0.386786i	$0.873585\pi$
$912$		0			0
$913$	24.7639	−	42.8924i	0.819566	−	1.41953i
$914$		0			0
$915$	5.51179	+	15.6730i	0.182214	+	0.518135i
$916$		0			0
$917$	99.8057			3.29587
$918$		0			0
$919$	41.2182			1.35966			0.679832	−	0.733368i	$-0.262053\pi$
$919$	41.2182			1.35966			0.679832	+	0.733368i	$0.262053\pi$
$920$		0			0
$921$	−0.753603	−	2.14291i	−0.0248321	−	0.0706112i
$922$		0			0
$923$	3.08920	−	5.35065i	0.101682	−	0.176119i
$924$		0			0
$925$	−2.73339	−	4.73437i	−0.0898732	−	0.155665i
$926$		0			0
$927$	−5.25097	−	34.1129i	−0.172464	−	1.12042i
$928$		0			0
$929$	−17.6128	−	30.5063i	−0.577857	−	1.00088i	−0.995725	−	0.0923702i	$-0.970556\pi$
$929$	−17.6128	−	30.5063i	−0.577857	−	1.00088i	0.417867	−	0.908508i	$-0.362778\pi$
$930$		0			0
$931$	33.1564	−	57.4286i	1.08666	−	1.88214i
$932$		0			0
$933$	15.0887	+	2.83048i	0.493981	+	0.0926656i
$934$		0			0
$935$	−11.7279			−0.383545
$936$		0			0
$937$	−15.7113			−0.513265			−0.256632	−	0.966509i	$-0.582613\pi$
$937$	−15.7113			−0.513265			−0.256632	+	0.966509i	$0.582613\pi$
$938$		0			0
$939$	2.52994	−	2.94916i	0.0825613	−	0.0962423i
$940$		0			0
$941$	20.2594	−	35.0903i	0.660437	−	1.14391i	−0.320064	−	0.947396i	$-0.603704\pi$
$941$	20.2594	−	35.0903i	0.660437	−	1.14391i	0.980501	−	0.196515i	$-0.0629624\pi$
$942$		0			0
$943$	−8.54386	−	14.7984i	−0.278226	−	0.481902i
$944$		0			0
$945$	−20.1791	−	12.5476i	−0.656425	−	0.408172i
$946$		0			0
$947$	13.0266	+	22.5627i	0.423307	+	0.733189i	0.996261	−	0.0863989i	$-0.0275360\pi$
$947$	13.0266	+	22.5627i	0.423307	+	0.733189i	−0.572954	+	0.819588i	$0.694203\pi$
$948$		0			0
$949$	5.74939	−	9.95824i	0.186633	−	0.323258i
$950$		0			0
$951$	23.2029	−	27.0477i	0.752404	−	0.877083i
$952$		0			0
$953$	8.24264			0.267005			0.133503	−	0.991048i	$-0.457378\pi$
$953$	8.24264			0.267005			0.133503	+	0.991048i	$0.457378\pi$
$954$		0			0
$955$	−4.74571			−0.153567
$956$		0			0
$957$	−14.9532	−	2.80506i	−0.483369	−	0.0906749i
$958$		0			0
$959$	10.1651	−	17.6065i	0.328248	−	0.568542i
$960$		0			0
$961$	9.49074	+	16.4384i	0.306153	+	0.530272i
$962$		0			0
$963$	12.9240	−	10.3729i	0.416471	−	0.334263i
$964$		0			0
$965$	−4.27698	−	7.40794i	−0.137681	−	0.238470i
$966$		0			0
$967$	6.25818	−	10.8395i	0.201250	−	0.348574i	−0.747682	−	0.664057i	$-0.768833\pi$
$967$	6.25818	−	10.8395i	0.201250	−	0.348574i	0.948931	+	0.315483i	$0.102166\pi$
$968$		0			0
$969$	6.99496	+	19.8905i	0.224711	+	0.638976i
$970$		0			0
$971$	−34.5180			−1.10774			−0.553868	−	0.832604i	$-0.686849\pi$
$971$	−34.5180			−1.10774			−0.553868	+	0.832604i	$0.686849\pi$
$972$		0			0
$973$	−51.0657			−1.63709
$974$		0			0
$975$	−2.11417	−	6.01174i	−0.0677076	−	0.192530i
$976$		0			0
$977$	26.3164	−	45.5813i	0.841936	−	1.45828i	−0.0463193	−	0.998927i	$-0.514749\pi$
$977$	26.3164	−	45.5813i	0.841936	−	1.45828i	0.888256	−	0.459350i	$-0.151918\pi$
$978$		0			0
$979$	−9.29678	−	16.1025i	−0.297126	−	0.514638i
$980$		0			0
$981$	39.1609	−	31.4309i	1.25031	−	1.00351i
$982$		0			0
$983$	17.9082	+	31.0179i	0.571183	+	0.989318i	0.996445	+	0.0842478i	$0.0268487\pi$
$983$	17.9082	+	31.0179i	0.571183	+	0.989318i	−0.425262	+	0.905070i	$0.639818\pi$
$984$		0			0
$985$	6.12697	−	10.6122i	0.195221	−	0.338133i
$986$		0			0
$987$	78.1588	+	14.6618i	2.48782	+	0.466689i
$988$		0			0
$989$	16.8634			0.536225
$990$		0			0
$991$	−42.7203			−1.35706			−0.678528	−	0.734574i	$-0.737382\pi$
$991$	−42.7203			−1.35706			−0.678528	+	0.734574i	$0.737382\pi$
$992$		0			0
$993$	−24.5706	+	28.6421i	−0.779725	+	0.908931i
$994$		0			0
$995$	0.858691	−	1.48730i	0.0272223	−	0.0471504i
$996$		0			0
$997$	−23.4571	−	40.6290i	−0.742895	−	1.28673i	−0.951172	−	0.308662i	$-0.900119\pi$
$997$	−23.4571	−	40.6290i	−0.742895	−	1.28673i	0.208276	−	0.978070i	$-0.433215\pi$
$998$		0			0
$999$	−24.1229	−	14.9999i	−0.763215	−	0.474576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.q.l.481.3		8
3.2	odd	2		2160.2.q.l.1441.1		8
4.3	odd	2		360.2.q.e.121.2	✓	8
9.2	odd	6		2160.2.q.l.721.1		8
9.4	even	3		6480.2.a.cb.1.4		4
9.5	odd	6		6480.2.a.bz.1.4		4
9.7	even	3	inner	720.2.q.l.241.3		8
12.11	even	2		1080.2.q.e.361.4		8
36.7	odd	6		360.2.q.e.241.2	yes	8
36.11	even	6		1080.2.q.e.721.4		8
36.23	even	6		3240.2.a.s.1.1		4
36.31	odd	6		3240.2.a.u.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.q.e.121.2	✓	8	4.3	odd	2
360.2.q.e.241.2	yes	8	36.7	odd	6
720.2.q.l.241.3		8	9.7	even	3	inner
720.2.q.l.481.3		8	1.1	even	1	trivial
1080.2.q.e.361.4		8	12.11	even	2
1080.2.q.e.721.4		8	36.11	even	6
2160.2.q.l.721.1		8	9.2	odd	6
2160.2.q.l.1441.1		8	3.2	odd	2
3240.2.a.s.1.1		4	36.23	even	6
3240.2.a.u.1.1		4	36.31	odd	6
6480.2.a.bz.1.4		4	9.5	odd	6
6480.2.a.cb.1.4		4	9.4	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.574618 + 1.63396i) q^{3} +(-0.500000 + 0.866025i) q^{5} +(-2.28651 - 3.96035i) q^{7} +(-2.33963 + 1.87780i) q^{9} +(-2.29604 - 3.97686i) q^{11} +(1.83963 - 3.18633i) q^{13} +(-1.70236 - 0.319344i) q^{15} -2.55395 q^{17} -4.76643 q^{19} +(5.15716 - 6.01174i) q^{21} +(-1.28651 + 2.22830i) q^{23} +(-0.500000 - 0.866025i) q^{25} +(-4.41264 - 2.74383i) q^{27} +(-0.956412 - 1.65655i) q^{29} +(1.73339 - 3.00231i) q^{31} +(5.17866 - 6.03680i) q^{33} +4.57301 q^{35} +5.46677 q^{37} +(6.26340 + 1.17495i) q^{39} +(-3.32056 + 5.75139i) q^{41} +(-3.27698 - 5.67589i) q^{43} +(-0.456412 - 2.96508i) q^{45} +(5.01989 + 8.69471i) q^{47} +(-6.95623 + 12.0485i) q^{49} +(-1.46755 - 4.17304i) q^{51} +4.03813 q^{53} +4.59208 q^{55} +(-2.73888 - 7.78814i) q^{57} +(6.13567 - 10.6273i) q^{59} +(-4.79604 - 8.30698i) q^{61} +(12.7863 + 4.97212i) q^{63} +(1.83963 + 3.18633i) q^{65} +(-5.66972 + 9.82025i) q^{67} +(-4.38019 - 0.821677i) q^{69} +1.67925 q^{71} +3.12530 q^{73} +(1.12774 - 1.31461i) q^{75} +(-10.4998 + 18.1862i) q^{77} +(-6.64113 - 11.5028i) q^{79} +(1.94771 - 8.78672i) q^{81} +(5.39275 + 9.34051i) q^{83} +(1.27698 - 2.21179i) q^{85} +(2.15716 - 2.51462i) q^{87} +4.04905 q^{89} -16.8253 q^{91} +(5.90169 + 1.10709i) q^{93} +(2.38322 - 4.12785i) q^{95} +(-8.68962 - 15.0509i) q^{97} +(12.8396 + 4.99285i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - q^{7} + q^{11} - 4 q^{13} - 3 q^{15} + 10 q^{17} - 2 q^{19} + 7 q^{23} - 4 q^{25} + 18 q^{27} - 7 q^{29} - 2 q^{31} - 3 q^{33} + 2 q^{35} + 12 q^{37} + 6 q^{39} - 12 q^{41} - 11 q^{43}+ \cdots + 84 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - q^7 + q^11 - 4 * q^13 - 3 * q^15 + 10 * q^17 - 2 * q^19 + 7 * q^23 - 4 * q^25 + 18 * q^27 - 7 * q^29 - 2 * q^31 - 3 * q^33 + 2 * q^35 + 12 * q^37 + 6 * q^39 - 12 * q^41 - 11 * q^43 - 3 * q^45 + 7 * q^47 - 3 * q^49 - 39 * q^51 + 24 * q^53 - 2 * q^55 + 27 * q^57 + 11 * q^59 - 19 * q^61 + 33 * q^63 - 4 * q^65 - 10 * q^67 - 9 * q^69 - 24 * q^71 + 18 * q^73 + 3 * q^75 - 32 * q^77 - 24 * q^79 - 12 * q^81 + 23 * q^83 - 5 * q^85 - 24 * q^87 + 42 * q^89 - 28 * q^91 + 18 * q^93 + q^95 - q^97 + 84 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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