LMFDB - Embedded newform 720.2.by.c.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(49,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

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

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

chi := DirichletCharacter("720.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.by (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.1
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	720.529
Dual form			720.2.by.c.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.57313 + 0.724745i) q^{3} +(-1.81431 + 1.30701i) q^{5} +(3.85337 + 2.22474i) q^{7} +(1.94949 - 2.28024i) q^{9} +(0.724745 - 1.25529i) q^{11} +(2.12132 - 1.22474i) q^{13} +(1.90691 - 3.37101i) q^{15} +3.89898i q^{17} -0.550510 q^{19} +(-7.67423 - 0.707107i) q^{21} +(-2.51059 + 1.44949i) q^{23} +(1.58346 - 4.74264i) q^{25} +(-1.41421 + 5.00000i) q^{27} +(-3.00000 + 5.19615i) q^{29} +(3.22474 + 5.58542i) q^{31} +(-0.230351 + 2.50000i) q^{33} +(-9.89898 + 1.00000i) q^{35} +8.00000i q^{37} +(-2.44949 + 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{41} +(-6.45145 - 3.72474i) q^{43} +(-0.556696 + 6.68506i) q^{45} +(0.389270 + 0.224745i) q^{47} +(6.39898 + 11.0834i) q^{49} +(-2.82577 - 6.13361i) q^{51} -8.44949i q^{53} +(0.325765 + 3.22474i) q^{55} +(0.866025 - 0.398979i) q^{57} +(5.62372 + 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +(12.5851 - 4.44949i) q^{63} +(-2.24799 + 4.99465i) q^{65} +(-8.18350 + 4.72474i) q^{67} +(2.89898 - 4.09978i) q^{69} -2.44949 q^{71} +4.79796i q^{73} +(0.946206 + 8.60841i) q^{75} +(5.58542 - 3.22474i) q^{77} +(3.67423 - 6.36396i) q^{79} +(-1.39898 - 8.89060i) q^{81} +(3.46410 + 2.00000i) q^{83} +(-5.09599 - 7.07397i) q^{85} +(0.953512 - 10.3485i) q^{87} -12.8990 q^{89} +10.8990 q^{91} +(-9.12096 - 6.44949i) q^{93} +(0.998798 - 0.719521i) q^{95} +(-11.2583 - 6.50000i) q^{97} +(-1.44949 - 4.09978i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{5} - 4 q^{9} - 4 q^{11} + 8 q^{15} - 24 q^{19} - 32 q^{21} - 24 q^{29} + 16 q^{31} - 40 q^{35} + 4 q^{41} + 20 q^{45} + 12 q^{49} - 52 q^{51} + 32 q^{55} - 4 q^{59} - 8 q^{61} - 12 q^{65} - 16 q^{69}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q - 4 * q^5 - 4 * q^9 - 4 * q^11 + 8 * q^15 - 24 * q^19 - 32 * q^21 - 24 * q^29 + 16 * q^31 - 40 * q^35 + 4 * q^41 + 20 * q^45 + 12 * q^49 - 52 * q^51 + 32 * q^55 - 4 * q^59 - 8 * q^61 - 12 * q^65 - 16 * q^69 + 4 * q^75 + 28 * q^81 - 20 * q^85 - 64 * q^89 + 48 * q^91 + 24 * q^95 + 8 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.57313	+	0.724745i	−0.908248	+	0.418432i
$3$	−1.57313	+	0.724745i	−0.908248	+	0.418432i
$4$		0			0
$5$	−1.81431	+	1.30701i	−0.811386	+	0.584511i
$5$	−1.81431	+	1.30701i	−0.811386	+	0.584511i
$6$		0			0
$7$	3.85337	+	2.22474i	1.45644	+	0.840875i	0.998834	−	0.0482818i	$-0.0153745\pi$
$7$	3.85337	+	2.22474i	1.45644	+	0.840875i	0.457604	+	0.889156i	$0.348708\pi$
$8$		0			0
$9$	1.94949	−	2.28024i	0.649830	−	0.760080i
$10$		0			0
$11$	0.724745	−	1.25529i	0.218519	−	0.378486i	−0.735837	−	0.677159i	$-0.763211\pi$
$11$	0.724745	−	1.25529i	0.218519	−	0.378486i	0.954355	+	0.298674i	$0.0965442\pi$
$12$		0			0
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$		0			0
$15$	1.90691	−	3.37101i	0.492361	−	0.870391i
$16$		0			0
$17$			3.89898i			0.945641i	0.881159	+	0.472821i	$0.156764\pi$
$17$			3.89898i			0.945641i	−0.881159	+	0.472821i	$0.843236\pi$
$18$		0			0
$19$	−0.550510			−0.126296			−0.0631479	−	0.998004i	$-0.520114\pi$
$19$	−0.550510			−0.126296			−0.0631479	+	0.998004i	$0.520114\pi$
$20$		0			0
$21$	−7.67423	−	0.707107i	−1.67466	−	0.154303i
$22$		0			0
$23$	−2.51059	+	1.44949i	−0.523494	+	0.302240i	−0.738363	−	0.674403i	$-0.764401\pi$
$23$	−2.51059	+	1.44949i	−0.523494	+	0.302240i	0.214869	+	0.976643i	$0.431068\pi$
$24$		0			0
$25$	1.58346	−	4.74264i	0.316693	−	0.948528i
$26$		0			0
$27$	−1.41421	+	5.00000i	−0.272166	+	0.962250i
$28$		0			0
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	0.995573	+	0.0939863i	$0.0299610\pi$
$31$	3.22474	+	5.58542i	0.579181	+	1.00317i	−0.416392	+	0.909185i	$0.636706\pi$
$32$		0			0
$33$	−0.230351	+	2.50000i	−0.0400989	+	0.435194i
$34$		0			0
$35$	−9.89898	+	1.00000i	−1.67323	+	0.169031i
$36$		0			0
$37$			8.00000i			1.31519i	0.753371	+	0.657596i	$0.228427\pi$
$37$			8.00000i			1.31519i	−0.753371	+	0.657596i	$0.771573\pi$
$38$		0			0
$39$	−2.44949	+	3.46410i	−0.392232	+	0.554700i
$40$		0			0
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	0.902424	−	0.430848i	$-0.141786\pi$
$41$	0.500000	+	0.866025i	0.0780869	+	0.135250i	−0.824338	+	0.566099i	$0.808452\pi$
$42$		0			0
$43$	−6.45145	−	3.72474i	−0.983836	−	0.568018i	−0.0804103	−	0.996762i	$-0.525623\pi$
$43$	−6.45145	−	3.72474i	−0.983836	−	0.568018i	−0.903426	+	0.428744i	$0.858956\pi$
$44$		0			0
$45$	−0.556696	+	6.68506i	−0.0829874	+	0.996551i
$46$		0			0
$47$	0.389270	+	0.224745i	0.0567808	+	0.0327824i	0.528122	−	0.849169i	$-0.322896\pi$
$47$	0.389270	+	0.224745i	0.0567808	+	0.0327824i	−0.471341	+	0.881951i	$0.656230\pi$
$48$		0			0
$49$	6.39898	+	11.0834i	0.914140	+	1.58334i
$50$		0			0
$51$	−2.82577	−	6.13361i	−0.395686	−	0.858877i
$52$		0			0
$53$		−	8.44949i		−	1.16063i	−0.814393	−	0.580313i	$-0.802930\pi$
$53$		−	8.44949i		−	1.16063i	0.814393	−	0.580313i	$-0.197070\pi$
$54$		0			0
$55$	0.325765	+	3.22474i	0.0439262	+	0.434825i
$56$		0			0
$57$	0.866025	−	0.398979i	0.114708	−	0.0528461i
$58$		0			0
$59$	5.62372	+	9.74058i	0.732147	+	1.26812i	0.955964	+	0.293484i	$0.0948147\pi$
$59$	5.62372	+	9.74058i	0.732147	+	1.26812i	−0.223817	+	0.974631i	$0.571852\pi$
$60$		0			0
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	−0.851279	−	0.524713i	$-0.824173\pi$
$61$	0.224745	−	0.389270i	0.0287756	−	0.0498409i	0.880055	+	0.474873i	$0.157506\pi$
$62$		0			0
$63$	12.5851	−	4.44949i	1.58557	−	0.560583i
$64$		0			0
$65$	−2.24799	+	4.99465i	−0.278829	+	0.619510i
$66$		0			0
$67$	−8.18350	+	4.72474i	−0.999773	+	0.577219i	−0.908181	−	0.418577i	$-0.862529\pi$
$67$	−8.18350	+	4.72474i	−0.999773	+	0.577219i	−0.0915922	+	0.995797i	$0.529196\pi$
$68$		0			0
$69$	2.89898	−	4.09978i	0.348996	−	0.493555i
$70$		0			0
$71$	−2.44949			−0.290701			−0.145350	−	0.989380i	$-0.546431\pi$
$71$	−2.44949			−0.290701			−0.145350	+	0.989380i	$0.546431\pi$
$72$		0			0
$73$			4.79796i			0.561559i	0.959772	+	0.280779i	$0.0905929\pi$
$73$			4.79796i			0.561559i	−0.959772	+	0.280779i	$0.909407\pi$
$74$		0			0
$75$	0.946206	+	8.60841i	0.109258	+	0.994013i
$76$		0			0
$77$	5.58542	−	3.22474i	0.636518	−	0.367494i
$78$		0			0
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	−0.581874	−	0.813279i	$-0.697680\pi$
$79$	3.67423	−	6.36396i	0.413384	−	0.716002i	0.995257	+	0.0972777i	$0.0310135\pi$
$80$		0			0
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$		0			0
$83$	3.46410	+	2.00000i	0.380235	+	0.219529i	0.677920	−	0.735135i	$-0.262881\pi$
$83$	3.46410	+	2.00000i	0.380235	+	0.219529i	−0.297686	+	0.954664i	$0.596215\pi$
$84$		0			0
$85$	−5.09599	−	7.07397i	−0.552738	−	0.767280i
$86$		0			0
$87$	0.953512	−	10.3485i	0.102227	−	1.10947i
$88$		0			0
$89$	−12.8990			−1.36729			−0.683645	−	0.729815i	$-0.739606\pi$
$89$	−12.8990			−1.36729			−0.683645	+	0.729815i	$0.739606\pi$
$90$		0			0
$91$	10.8990			1.14252
$92$		0			0
$93$	−9.12096	−	6.44949i	−0.945799	−	0.668781i
$94$		0			0
$95$	0.998798	−	0.719521i	0.102475	−	0.0738213i
$96$		0			0
$97$	−11.2583	−	6.50000i	−1.14311	−	0.659975i	−0.195911	−	0.980622i	$-0.562766\pi$
$97$	−11.2583	−	6.50000i	−1.14311	−	0.659975i	−0.947199	+	0.320647i	$0.896100\pi$
$98$		0			0
$99$	−1.44949	−	4.09978i	−0.145679	−	0.412043i
$100$		0			0
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	−0.595466	−	0.803380i	$-0.703033\pi$
$101$	4.00000	−	6.92820i	0.398015	−	0.689382i	0.993481	+	0.113998i	$0.0363659\pi$
$102$		0			0
$103$	8.87455	−	5.12372i	0.874435	−	0.504856i	0.00561582	−	0.999984i	$-0.498212\pi$
$103$	8.87455	−	5.12372i	0.874435	−	0.504856i	0.868820	+	0.495129i	$0.164879\pi$
$104$		0			0
$105$	14.8477	−	8.74737i	1.44898	−	0.853656i
$106$		0			0
$107$		−	1.65153i		−	0.159660i	−0.996809	−	0.0798298i	$-0.974562\pi$
$107$		−	1.65153i		−	0.159660i	0.996809	−	0.0798298i	$-0.0254377\pi$
$108$		0			0
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$		0			0
$111$	−5.79796	−	12.5851i	−0.550318	−	1.19452i
$112$		0			0
$113$	−4.24264	+	2.44949i	−0.399114	+	0.230429i	−0.686102	−	0.727506i	$-0.740679\pi$
$113$	−4.24264	+	2.44949i	−0.399114	+	0.230429i	0.286988	+	0.957934i	$0.407346\pi$
$114$		0			0
$115$	2.66050	−	5.91119i	0.248093	−	0.551221i
$116$		0			0
$117$	1.34278	−	7.22474i	0.124140	−	0.667928i
$118$		0			0
$119$	−8.67423	+	15.0242i	−0.795166	+	1.37727i
$120$		0			0
$121$	4.44949	+	7.70674i	0.404499	+	0.700613i
$122$		0			0
$123$	−1.41421	−	1.00000i	−0.127515	−	0.0901670i
$124$		0			0
$125$	3.32577	+	10.6742i	0.297465	+	0.954733i
$126$		0			0
$127$			2.89898i			0.257243i	0.991694	+	0.128621i	$0.0410552\pi$
$127$			2.89898i			0.257243i	−0.991694	+	0.128621i	$0.958945\pi$
$128$		0			0
$129$	12.8485	+	1.18386i	1.13124	+	0.104233i
$130$		0			0
$131$	−2.44949	−	4.24264i	−0.214013	−	0.370681i	0.738954	−	0.673756i	$-0.235320\pi$
$131$	−2.44949	−	4.24264i	−0.214013	−	0.370681i	−0.952967	+	0.303075i	$0.901987\pi$
$132$		0			0
$133$	−2.12132	−	1.22474i	−0.183942	−	0.106199i
$134$		0			0
$135$	−3.96921	−	10.9200i	−0.341615	−	0.939840i
$136$		0			0
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	0.384893	−	0.922961i	$-0.374238\pi$
$137$	−2.59808	−	1.50000i	−0.221969	−	0.128154i	−0.606861	+	0.794808i	$0.707572\pi$
$138$		0			0
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	0.999653	−	0.0263597i	$-0.00839153\pi$
$139$	5.62372	+	9.74058i	0.476998	+	0.826185i	−0.522654	+	0.852545i	$0.675058\pi$
$140$		0			0
$141$	−0.775255	−	0.0714323i	−0.0652883	−	0.00601568i
$142$		0			0
$143$		−	3.55051i		−	0.296909i
$144$		0			0
$145$	−1.34847	−	13.3485i	−0.111984	−	1.10853i
$146$		0			0
$147$	−18.0990	−	12.7980i	−1.49278	−	1.05556i
$148$		0			0
$149$	8.12372	+	14.0707i	0.665521	+	1.15272i	0.979144	+	0.203169i	$0.0651241\pi$
$149$	8.12372	+	14.0707i	0.665521	+	1.15272i	−0.313622	+	0.949548i	$0.601543\pi$
$150$		0			0
$151$	−3.44949	+	5.97469i	−0.280715	+	0.486213i	−0.971561	−	0.236789i	$-0.923905\pi$
$151$	−3.44949	+	5.97469i	−0.280715	+	0.486213i	0.690846	+	0.723002i	$0.257238\pi$
$152$		0			0
$153$	8.89060	+	7.60102i	0.718763	+	0.614506i
$154$		0			0
$155$	−13.1509	−	5.91894i	−1.05630	−	0.475421i
$156$		0			0
$157$	13.8564	−	8.00000i	1.10586	−	0.638470i	0.168107	−	0.985769i	$-0.446235\pi$
$157$	13.8564	−	8.00000i	1.10586	−	0.638470i	0.937754	+	0.347299i	$0.112901\pi$
$158$		0			0
$159$	6.12372	+	13.2922i	0.485643	+	1.05414i
$160$		0			0
$161$	−12.8990			−1.01658
$162$		0			0
$163$		−	0.898979i		−	0.0704135i	−0.999380	−	0.0352068i	$-0.988791\pi$
$163$		−	0.898979i		−	0.0704135i	0.999380	−	0.0352068i	$-0.0112090\pi$
$164$		0			0
$165$	−2.84959	−	4.83685i	−0.221840	−	0.376549i
$166$		0			0
$167$	20.9989	−	12.1237i	1.62494	−	0.938162i	0.639374	−	0.768896i	$-0.279194\pi$
$167$	20.9989	−	12.1237i	1.62494	−	0.938162i	0.985570	−	0.169266i	$-0.0541397\pi$
$168$		0			0
$169$	−3.50000	+	6.06218i	−0.269231	+	0.466321i
$170$		0			0
$171$	−1.07321	+	1.25529i	−0.0820707	+	0.0959948i
$172$		0			0
$173$	6.75323	+	3.89898i	0.513439	+	0.296434i	0.734246	−	0.678884i	$-0.237536\pi$
$173$	6.75323	+	3.89898i	0.513439	+	0.296434i	−0.220807	+	0.975317i	$0.570869\pi$
$174$		0			0
$175$	16.6528	−	14.7524i	1.25884	−	1.11517i
$176$		0			0
$177$	−15.9063	−	11.2474i	−1.19559	−	0.845410i
$178$		0			0
$179$	8.89898			0.665141			0.332570	−	0.943078i	$-0.392084\pi$
$179$	8.89898			0.665141			0.332570	+	0.943078i	$0.392084\pi$
$180$		0			0
$181$	10.4495			0.776704			0.388352	−	0.921511i	$-0.373044\pi$
$181$	10.4495			0.776704			0.388352	+	0.921511i	$0.373044\pi$
$182$		0			0
$183$	−0.0714323	+	0.775255i	−0.00528043	+	0.0573085i
$184$		0			0
$185$	−10.4561	−	14.5145i	−0.768745	−	1.06713i
$186$		0			0
$187$	4.89437	+	2.82577i	0.357912	+	0.206640i
$188$		0			0
$189$	−16.5732	+	16.1206i	−1.20552	+	1.17260i
$190$		0			0
$191$	−3.12372	+	5.41045i	−0.226025	+	0.391486i	−0.956626	−	0.291318i	$-0.905906\pi$
$191$	−3.12372	+	5.41045i	−0.226025	+	0.391486i	0.730602	+	0.682804i	$0.239240\pi$
$192$		0			0
$193$	13.5939	−	7.84847i	0.978514	−	0.564945i	0.0766927	−	0.997055i	$-0.475564\pi$
$193$	13.5939	−	7.84847i	0.978514	−	0.564945i	0.901821	+	0.432110i	$0.142231\pi$
$194$		0			0
$195$	−0.0834643	−	9.48647i	−0.00597701	−	0.679340i
$196$		0			0
$197$		−	8.00000i		−	0.569976i	−0.958531	−	0.284988i	$-0.908010\pi$
$197$		−	8.00000i		−	0.569976i	0.958531	−	0.284988i	$-0.0919897\pi$
$198$		0			0
$199$	20.4495			1.44963			0.724813	−	0.688946i	$-0.241926\pi$
$199$	20.4495			1.44963			0.724813	+	0.688946i	$0.241926\pi$
$200$		0			0
$201$	9.44949	−	13.3636i	0.666516	−	0.942595i
$202$		0			0
$203$	−23.1202	+	13.3485i	−1.62272	+	0.936879i
$204$		0			0
$205$	−2.03906	−	0.917738i	−0.142414	−	0.0640976i
$206$		0			0
$207$	−1.58919	+	8.55051i	−0.110456	+	0.594302i
$208$		0			0
$209$	−0.398979	+	0.691053i	−0.0275980	+	0.0478011i
$210$		0			0
$211$	−7.89898	−	13.6814i	−0.543788	−	0.941869i	−0.998682	−	0.0513231i	$-0.983656\pi$
$211$	−7.89898	−	13.6814i	−0.543788	−	0.941869i	0.454894	−	0.890546i	$-0.349677\pi$
$212$		0			0
$213$	3.85337	−	1.77526i	0.264029	−	0.121638i
$214$		0			0
$215$	16.5732	−	1.67423i	1.13028	−	0.114182i
$216$		0			0
$217$			28.6969i			1.94808i
$218$		0			0
$219$	−3.47730	−	7.54782i	−0.234974	−	0.510035i
$220$		0			0
$221$	4.77526	+	8.27098i	0.321218	+	0.556367i
$222$		0			0
$223$	−16.3670	−	9.44949i	−1.09602	−	0.632785i	−0.160844	−	0.986980i	$-0.551421\pi$
$223$	−16.3670	−	9.44949i	−1.09602	−	0.632785i	−0.935171	+	0.354195i	$0.884755\pi$
$224$		0			0
$225$	−7.72741	−	12.8564i	−0.515160	−	0.857094i
$226$		0			0
$227$	1.25529	+	0.724745i	0.0833169	+	0.0481030i	0.541080	−	0.840971i	$-0.318016\pi$
$227$	1.25529	+	0.724745i	0.0833169	+	0.0481030i	−0.457763	+	0.889074i	$0.651349\pi$
$228$		0			0
$229$	−6.77526	−	11.7351i	−0.447721	−	0.775476i	0.550516	−	0.834825i	$-0.314431\pi$
$229$	−6.77526	−	11.7351i	−0.447721	−	0.775476i	−0.998237	+	0.0593484i	$0.981098\pi$
$230$		0			0
$231$	−6.44949	+	9.12096i	−0.424345	+	0.600115i
$232$		0			0
$233$		−	15.6969i		−	1.02834i	−0.857688	−	0.514170i	$-0.828100\pi$
$233$		−	15.6969i		−	1.02834i	0.857688	−	0.514170i	$-0.171900\pi$
$234$		0			0
$235$	−1.00000	+	0.101021i	−0.0652328	+	0.00658985i
$236$		0			0
$237$	−1.16781	+	12.6742i	−0.0758573	+	0.823280i
$238$		0			0
$239$	−14.3485	−	24.8523i	−0.928125	−	1.60756i	−0.786456	−	0.617646i	$-0.788086\pi$
$239$	−14.3485	−	24.8523i	−0.928125	−	1.60756i	−0.141669	−	0.989914i	$-0.545247\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$		0			0
$243$	8.64420	+	12.9722i	0.554526	+	0.832167i
$244$		0			0
$245$	−26.0958	−	11.7452i	−1.66720	−	0.750371i
$246$		0			0
$247$	−1.16781	+	0.674235i	−0.0743059	+	0.0429005i
$248$		0			0
$249$	−6.89898	−	0.635674i	−0.437205	−	0.0402842i
$250$		0			0
$251$	−11.4495			−0.722685			−0.361343	−	0.932433i	$-0.617682\pi$
$251$	−11.4495			−0.722685			−0.361343	+	0.932433i	$0.617682\pi$
$252$		0			0
$253$			4.20204i			0.264180i
$254$		0			0
$255$	13.1435	+	7.43499i	0.823078	+	0.465597i
$256$		0			0
$257$	17.2330	−	9.94949i	1.07497	−	0.620632i	0.145432	−	0.989368i	$-0.453543\pi$
$257$	17.2330	−	9.94949i	1.07497	−	0.620632i	0.929534	+	0.368736i	$0.120209\pi$
$258$		0			0
$259$	−17.7980	+	30.8270i	−1.10591	+	1.91549i
$260$		0			0
$261$	6.00000	+	16.9706i	0.371391	+	1.05045i
$262$		0			0
$263$	6.53893	+	3.77526i	0.403208	+	0.232792i	0.687867	−	0.725837i	$-0.258547\pi$
$263$	6.53893	+	3.77526i	0.403208	+	0.232792i	−0.284659	+	0.958629i	$0.591880\pi$
$264$		0			0
$265$	11.0435	+	15.3300i	0.678400	+	0.941716i
$266$		0			0
$267$	20.2918	−	9.34847i	1.24184	−	0.572117i
$268$		0			0
$269$	28.0454			1.70996			0.854979	−	0.518662i	$-0.173570\pi$
$269$	28.0454			1.70996			0.854979	+	0.518662i	$0.173570\pi$
$270$		0			0
$271$	−23.5959			−1.43335			−0.716675	−	0.697407i	$-0.754337\pi$
$271$	−23.5959			−1.43335			−0.716675	+	0.697407i	$0.754337\pi$
$272$		0			0
$273$	−17.1455	+	7.89898i	−1.03770	+	0.478068i
$274$		0			0
$275$	−4.80581	−	5.42492i	−0.289801	−	0.327135i
$276$		0			0
$277$	−8.31031	−	4.79796i	−0.499318	−	0.288281i	0.229114	−	0.973400i	$-0.426417\pi$
$277$	−8.31031	−	4.79796i	−0.499318	−	0.288281i	−0.728432	+	0.685118i	$0.759751\pi$
$278$		0			0
$279$	19.0227	+	3.53553i	1.13886	+	0.211667i
$280$		0			0
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	−0.987615	−	0.156898i	$-0.949851\pi$
$281$	−6.00000	+	10.3923i	−0.357930	+	0.619953i	0.629685	+	0.776851i	$0.283184\pi$
$282$		0			0
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	−0.393494	−	0.919327i	$-0.628734\pi$
$283$	3.46410	−	2.00000i	0.205919	−	0.118888i	0.599414	+	0.800439i	$0.295400\pi$
$284$		0			0
$285$	−1.04977	+	1.85578i	−0.0621831	+	0.109927i
$286$		0			0
$287$			4.44949i			0.262645i
$288$		0			0
$289$	1.79796			0.105762
$290$		0			0
$291$	22.4217	+	2.06594i	1.31438	+	0.121108i
$292$		0			0
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.880652	−	0.473763i	$-0.842895\pi$
$293$	−15.5885	+	9.00000i	−0.910687	+	0.525786i	−0.0300351	+	0.999549i	$0.509562\pi$
$294$		0			0
$295$	−22.9342	−	10.3222i	−1.33528	−	0.600982i
$296$		0			0
$297$	5.25153	+	5.39898i	0.304725	+	0.313281i
$298$		0			0
$299$	−3.55051	+	6.14966i	−0.205331	+	0.355644i
$300$		0			0
$301$	−16.5732	−	28.7056i	−0.955264	−	1.65457i
$302$		0			0
$303$	−1.27135	+	13.7980i	−0.0730371	+	0.792672i
$304$		0			0
$305$	0.101021	+	1.00000i	0.00578442	+	0.0572598i
$306$		0			0
$307$			23.9444i			1.36658i	0.730148	+	0.683289i	$0.239451\pi$
$307$			23.9444i			1.36658i	−0.730148	+	0.683289i	$0.760549\pi$
$308$		0			0
$309$	−10.2474	+	14.4921i	−0.582957	+	0.824426i
$310$		0			0
$311$	11.4495	+	19.8311i	0.649241	+	1.12452i	0.983304	+	0.181968i	$0.0582467\pi$
$311$	11.4495	+	19.8311i	0.649241	+	1.12452i	−0.334063	+	0.942551i	$0.608420\pi$
$312$		0			0
$313$	6.66574	+	3.84847i	0.376770	+	0.217528i	0.676412	−	0.736523i	$-0.263534\pi$
$313$	6.66574	+	3.84847i	0.376770	+	0.217528i	−0.299642	+	0.954052i	$0.596867\pi$
$314$		0			0
$315$	−17.0177	+	24.5215i	−0.958840	+	1.38163i
$316$		0			0
$317$	26.7986	+	15.4722i	1.50516	+	0.869005i	0.999982	+	0.00599020i	$0.00190675\pi$
$317$	26.7986	+	15.4722i	1.50516	+	0.869005i	0.505179	+	0.863015i	$0.331427\pi$
$318$		0			0
$319$	4.34847	+	7.53177i	0.243468	+	0.421698i
$320$		0			0
$321$	1.19694	+	2.59808i	0.0668066	+	0.145010i
$322$		0			0
$323$		−	2.14643i		−	0.119430i
$324$		0			0
$325$	−2.44949	−	12.0000i	−0.135873	−	0.665640i
$326$		0			0
$327$	−12.5851	+	5.79796i	−0.695955	+	0.320628i
$328$		0			0
$329$	1.00000	+	1.73205i	0.0551318	+	0.0954911i
$330$		0			0
$331$	16.6969	−	28.9199i	0.917747	−	1.58958i	0.114917	−	0.993375i	$-0.463340\pi$
$331$	16.6969	−	28.9199i	0.917747	−	1.58958i	0.802829	−	0.596209i	$-0.203327\pi$
$332$		0			0
$333$	18.2419	+	15.5959i	0.999651	+	0.854651i
$334$		0			0
$335$	8.67215	−	19.2681i	0.473810	−	1.05273i
$336$		0			0
$337$	−17.8366	+	10.2980i	−0.971621	+	0.560966i	−0.899730	−	0.436447i	$-0.856237\pi$
$337$	−17.8366	+	10.2980i	−0.971621	+	0.560966i	−0.0718909	+	0.997413i	$0.522903\pi$
$338$		0			0
$339$	4.89898	−	6.92820i	0.266076	−	0.376288i
$340$		0			0
$341$	9.34847			0.506248
$342$		0			0
$343$			25.7980i			1.39296i
$344$		0			0
$345$	0.0987803	+	11.2273i	0.00531815	+	0.604456i
$346$		0			0
$347$	13.2047	−	7.62372i	0.708864	−	0.409263i	−0.101776	−	0.994807i	$-0.532453\pi$
$347$	13.2047	−	7.62372i	0.708864	−	0.409263i	0.810640	+	0.585544i	$0.199119\pi$
$348$		0			0
$349$	5.79796	−	10.0424i	0.310358	−	0.537555i	−0.668082	−	0.744088i	$-0.732885\pi$
$349$	5.79796	−	10.0424i	0.310358	−	0.537555i	0.978440	+	0.206532i	$0.0662179\pi$
$350$		0			0
$351$	3.12372	+	12.3387i	0.166732	+	0.658589i
$352$		0			0
$353$	−5.71223	−	3.29796i	−0.304031	−	0.175533i	0.340221	−	0.940345i	$-0.389498\pi$
$353$	−5.71223	−	3.29796i	−0.304031	−	0.175533i	−0.644253	+	0.764813i	$0.722831\pi$
$354$		0			0
$355$	4.44414	−	3.20150i	0.235871	−	0.169918i
$356$		0			0
$357$	2.75699	−	29.9217i	0.145916	−	1.58362i
$358$		0			0
$359$	8.44949			0.445947			0.222974	−	0.974825i	$-0.428424\pi$
$359$	8.44949			0.445947			0.222974	+	0.974825i	$0.428424\pi$
$360$		0			0
$361$	−18.6969			−0.984049
$362$		0			0
$363$	−12.5851	−	8.89898i	−0.660544	−	0.467075i
$364$		0			0
$365$	−6.27097	−	8.70500i	−0.328237	−	0.455641i
$366$		0			0
$367$	−10.0424	−	5.79796i	−0.524207	−	0.302651i	0.214447	−	0.976736i	$-0.431205\pi$
$367$	−10.0424	−	5.79796i	−0.524207	−	0.302651i	−0.738654	+	0.674085i	$0.764538\pi$
$368$		0			0
$369$	2.94949	+	0.548188i	0.153544	+	0.0285375i
$370$		0			0
$371$	18.7980	−	32.5590i	0.975941	−	1.69038i
$372$		0			0
$373$	−22.1667	+	12.7980i	−1.14775	+	0.662653i	−0.948338	−	0.317263i	$-0.897236\pi$
$373$	−22.1667	+	12.7980i	−1.14775	+	0.662653i	−0.199411	+	0.979916i	$0.563903\pi$
$374$		0			0
$375$	−12.9680	−	14.3817i	−0.669663	−	0.742665i
$376$		0			0
$377$			14.6969i			0.756931i
$378$		0			0
$379$	−30.1464			−1.54852			−0.774259	−	0.632869i	$-0.781877\pi$
$379$	−30.1464			−1.54852			−0.774259	+	0.632869i	$0.781877\pi$
$380$		0			0
$381$	−2.10102	−	4.56048i	−0.107639	−	0.233640i
$382$		0			0
$383$	1.55708	−	0.898979i	0.0795630	−	0.0459357i	−0.459691	−	0.888079i	$-0.652040\pi$
$383$	1.55708	−	0.898979i	0.0795630	−	0.0459357i	0.539254	+	0.842143i	$0.318706\pi$
$384$		0			0
$385$	−5.91894	+	13.1509i	−0.301657	+	0.670231i
$386$		0			0
$387$	−21.0703	+	7.44949i	−1.07107	+	0.378679i
$388$		0			0
$389$	11.2247	−	19.4418i	0.569117	−	0.985740i	−0.427536	−	0.903998i	$-0.640618\pi$
$389$	11.2247	−	19.4418i	0.569117	−	0.985740i	0.996654	−	0.0817417i	$-0.0260483\pi$
$390$		0			0
$391$	−5.65153	−	9.78874i	−0.285810	−	0.495038i
$392$		0			0
$393$	6.92820	+	4.89898i	0.349482	+	0.247121i
$394$		0			0
$395$	1.65153	+	16.3485i	0.0830975	+	0.822581i
$396$		0			0
$397$			17.7980i			0.893254i	0.894720	+	0.446627i	$0.147375\pi$
$397$			17.7980i			0.893254i	−0.894720	+	0.446627i	$0.852625\pi$
$398$		0			0
$399$	4.22474	+	0.389270i	0.211502	+	0.0194879i
$400$		0			0
$401$	−14.3990	−	24.9398i	−0.719051	−	1.24543i	−0.961376	−	0.275237i	$-0.911244\pi$
$401$	−14.3990	−	24.9398i	−0.719051	−	1.24543i	0.242326	−	0.970195i	$-0.422090\pi$
$402$		0			0
$403$	13.6814	+	7.89898i	0.681521	+	0.393476i
$404$		0			0
$405$	14.1583	+	14.3019i	0.703530	+	0.710665i
$406$		0			0
$407$	10.0424	+	5.79796i	0.497781	+	0.287394i
$408$		0			0
$409$	3.05051	+	5.28364i	0.150838	+	0.261259i	0.931536	−	0.363650i	$-0.118469\pi$
$409$	3.05051	+	5.28364i	0.150838	+	0.261259i	−0.780698	+	0.624909i	$0.785136\pi$
$410$		0			0
$411$	5.17423	+	0.476756i	0.255226	+	0.0235166i
$412$		0			0
$413$			50.0454i			2.46257i
$414$		0			0
$415$	−8.89898	+	0.898979i	−0.436834	+	0.0441292i
$416$		0			0
$417$	−15.9063	−	11.2474i	−0.778935	−	0.550790i
$418$		0			0
$419$	−0.449490	−	0.778539i	−0.0219590	−	0.0380341i	0.854837	−	0.518896i	$-0.173657\pi$
$419$	−0.449490	−	0.778539i	−0.0219590	−	0.0380341i	−0.876796	+	0.480862i	$0.840324\pi$
$420$		0			0
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	−0.592979	−	0.805218i	$-0.702048\pi$
$421$	8.22474	−	14.2457i	0.400850	−	0.694292i	0.993829	+	0.110926i	$0.0353817\pi$
$422$		0			0
$423$	1.27135	−	0.449490i	0.0618151	−	0.0218549i
$424$		0			0
$425$	18.4915	+	6.17389i	0.896968	+	0.299478i
$426$		0			0
$427$	1.73205	−	1.00000i	0.0838198	−	0.0483934i
$428$		0			0
$429$	2.57321	+	5.58542i	0.124236	+	0.269667i
$430$		0			0
$431$	−13.7526			−0.662437			−0.331219	−	0.943554i	$-0.607460\pi$
$431$	−13.7526			−0.662437			−0.331219	+	0.943554i	$0.607460\pi$
$432$		0			0
$433$		−	23.0000i		−	1.10531i	−0.833410	−	0.552655i	$-0.813615\pi$
$433$		−	23.0000i		−	1.10531i	0.833410	−	0.552655i	$-0.186385\pi$
$434$		0			0
$435$	11.7956	+	20.0216i	0.565554	+	0.959963i
$436$		0			0
$437$	1.38211	−	0.797959i	0.0661151	−	0.0381716i
$438$		0			0
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	−0.473453	−	0.880819i	$-0.656993\pi$
$439$	11.0227	−	19.0919i	0.526085	−	0.911206i	0.999538	−	0.0303869i	$-0.00967395\pi$
$440$		0			0
$441$	37.7474	+	7.01569i	1.79750	+	0.334080i
$442$		0			0
$443$	2.81237	+	1.62372i	0.133620	+	0.0771455i	0.565320	−	0.824872i	$-0.308753\pi$
$443$	2.81237	+	1.62372i	0.133620	+	0.0771455i	−0.431700	+	0.902017i	$0.642086\pi$
$444$		0			0
$445$	23.4028	−	16.8591i	1.10940	−	0.799196i
$446$		0			0
$447$	−22.9774	−	16.2474i	−1.08679	−	0.768478i
$448$		0			0
$449$	0.797959			0.0376580			0.0188290	−	0.999823i	$-0.494006\pi$
$449$	0.797959			0.0376580			0.0188290	+	0.999823i	$0.494006\pi$
$450$		0			0
$451$	1.44949			0.0682538
$452$		0			0
$453$	1.09638	−	11.8990i	0.0515123	−	0.559063i
$454$		0			0
$455$	−19.7742	+	14.2450i	−0.927027	+	0.667818i
$456$		0			0
$457$	7.01569	+	4.05051i	0.328180	+	0.189475i	0.655033	−	0.755600i	$-0.272655\pi$
$457$	7.01569	+	4.05051i	0.328180	+	0.189475i	−0.326853	+	0.945075i	$0.605988\pi$
$458$		0			0
$459$	−19.4949	−	5.51399i	−0.909944	−	0.257371i
$460$		0			0
$461$	−1.22474	+	2.12132i	−0.0570421	+	0.0987997i	−0.893136	−	0.449786i	$-0.851500\pi$
$461$	−1.22474	+	2.12132i	−0.0570421	+	0.0987997i	0.836094	+	0.548586i	$0.184834\pi$
$462$		0			0
$463$	20.7846	−	12.0000i	0.965943	−	0.557687i	0.0679458	−	0.997689i	$-0.478356\pi$
$463$	20.7846	−	12.0000i	0.965943	−	0.557687i	0.897997	+	0.440002i	$0.145022\pi$
$464$		0			0
$465$	24.9778	−	0.219761i	1.15832	−	0.0101912i
$466$		0			0
$467$		−	4.34847i		−	0.201223i	−0.994926	−	0.100612i	$-0.967920\pi$
$467$		−	4.34847i		−	0.201223i	0.994926	−	0.100612i	$-0.0320799\pi$
$468$		0			0
$469$	−42.0454			−1.94148
$470$		0			0
$471$	−16.0000	+	22.6274i	−0.737241	+	1.04262i
$472$		0			0
$473$	−9.35131	+	5.39898i	−0.429974	+	0.248245i
$474$		0			0
$475$	−0.871713	+	2.61087i	−0.0399970	+	0.119795i
$476$		0			0
$477$	−19.2669	−	16.4722i	−0.882169	−	0.754210i
$478$		0			0
$479$	6.34847	−	10.9959i	0.290069	−	0.502414i	−0.683757	−	0.729710i	$-0.739655\pi$
$479$	6.34847	−	10.9959i	0.290069	−	0.502414i	0.973826	+	0.227296i	$0.0729884\pi$
$480$		0			0
$481$	9.79796	+	16.9706i	0.446748	+	0.773791i
$482$		0			0
$483$	20.2918	−	9.34847i	0.923309	−	0.425370i
$484$		0			0
$485$	28.9217	−	2.92168i	1.31327	−	0.132667i
$486$		0			0
$487$			34.8990i			1.58142i	0.612188	+	0.790712i	$0.290289\pi$
$487$			34.8990i			1.58142i	−0.612188	+	0.790712i	$0.709711\pi$
$488$		0			0
$489$	0.651531	+	1.41421i	0.0294632	+	0.0639529i
$490$		0			0
$491$	11.7247	+	20.3079i	0.529130	+	0.916481i	0.999423	+	0.0339700i	$0.0108151\pi$
$491$	11.7247	+	20.3079i	0.529130	+	0.916481i	−0.470293	+	0.882511i	$0.655852\pi$
$492$		0			0
$493$	−20.2597	−	11.6969i	−0.912451	−	0.526804i
$494$		0			0
$495$	7.98827	+	5.54378i	0.359046	+	0.249175i
$496$		0			0
$497$	−9.43879	−	5.44949i	−0.423388	−	0.244443i
$498$		0			0
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	0.827391	−	0.561627i	$-0.189824\pi$
$499$	−1.62372	−	2.81237i	−0.0726879	−	0.125899i	−0.900078	+	0.435728i	$0.856491\pi$
$500$		0			0
$501$	−24.2474	+	34.2911i	−1.08330	+	1.53201i
$502$		0			0
$503$			9.55051i			0.425836i	0.977070	+	0.212918i	$0.0682968\pi$
$503$			9.55051i			0.425836i	−0.977070	+	0.212918i	$0.931703\pi$
$504$		0			0
$505$	1.79796	+	17.7980i	0.0800081	+	0.791999i
$506$		0			0
$507$	1.11243	−	12.0732i	0.0494048	−	0.536190i
$508$		0			0
$509$	−3.79796	−	6.57826i	−0.168342	−	0.291576i	0.769495	−	0.638652i	$-0.220508\pi$
$509$	−3.79796	−	6.57826i	−0.168342	−	0.291576i	−0.937837	+	0.347076i	$0.887174\pi$
$510$		0			0
$511$	−10.6742	+	18.4883i	−0.472200	+	0.817875i
$512$		0			0
$513$	0.778539	−	2.75255i	0.0343733	−	0.121528i
$514$		0			0
$515$	−9.40447	+	20.8951i	−0.414410	+	0.920750i
$516$		0			0
$517$	0.564242	−	0.325765i	0.0248153	−	0.0143271i
$518$		0			0
$519$	−13.4495	−	1.23924i	−0.590367	−	0.0543966i
$520$		0			0
$521$	−7.69694			−0.337209			−0.168604	−	0.985684i	$-0.553926\pi$
$521$	−7.69694			−0.337209			−0.168604	+	0.985684i	$0.553926\pi$
$522$		0			0
$523$		−	29.7980i		−	1.30297i	−0.758660	−	0.651487i	$-0.774146\pi$
$523$		−	29.7980i		−	1.30297i	0.758660	−	0.651487i	$-0.225854\pi$
$524$		0			0
$525$	−15.5054	+	35.2765i	−0.676712	+	1.53959i
$526$		0			0
$527$	−21.7774	+	12.5732i	−0.948640	+	0.547698i
$528$		0			0
$529$	−7.29796	+	12.6404i	−0.317303	+	0.549584i
$530$		0			0
$531$	33.1742	+	6.16572i	1.43964	+	0.267569i
$532$		0			0
$533$	2.12132	+	1.22474i	0.0918846	+	0.0530496i
$534$		0			0
$535$	2.15856	+	2.99639i	0.0933228	+	0.129545i
$536$		0			0
$537$	−13.9993	+	6.44949i	−0.604113	+	0.278316i
$538$		0			0
$539$	18.5505			0.799027
$540$		0			0
$541$	−39.5959			−1.70236			−0.851181	−	0.524873i	$-0.824113\pi$
$541$	−39.5959			−1.70236			−0.851181	+	0.524873i	$0.824113\pi$
$542$		0			0
$543$	−16.4384	+	7.57321i	−0.705440	+	0.324998i
$544$		0			0
$545$	−14.5145	+	10.4561i	−0.621733	+	0.447888i
$546$		0			0
$547$	−6.27647	−	3.62372i	−0.268363	−	0.154939i	0.359781	−	0.933037i	$-0.382852\pi$
$547$	−6.27647	−	3.62372i	−0.268363	−	0.154939i	−0.628143	+	0.778098i	$0.716185\pi$
$548$		0			0
$549$	−0.449490	−	1.27135i	−0.0191838	−	0.0542599i
$550$		0			0
$551$	1.65153	−	2.86054i	0.0703576	−	0.121863i
$552$		0			0
$553$	28.3164	−	16.3485i	1.20413	−	0.695208i
$554$		0			0
$555$	26.9681	+	15.2553i	1.14473	+	0.647550i
$556$		0			0
$557$		−	38.9444i		−	1.65013i	−0.565040	−	0.825063i	$-0.691139\pi$
$557$		−	38.9444i		−	1.65013i	0.565040	−	0.825063i	$-0.308861\pi$
$558$		0			0
$559$	−18.2474			−0.771785
$560$		0			0
$561$	−9.74745	−	0.898133i	−0.411538	−	0.0379192i
$562$		0			0
$563$	31.3037	−	18.0732i	1.31929	−	0.761695i	0.335680	−	0.941976i	$-0.391034\pi$
$563$	31.3037	−	18.0732i	1.31929	−	0.761695i	0.983615	+	0.180281i	$0.0577007\pi$
$564$		0			0
$565$	4.49598	−	9.98930i	0.189147	−	0.420253i
$566$		0			0
$567$	14.3885	−	37.3712i	0.604262	−	1.56944i
$568$		0			0
$569$	8.74745	−	15.1510i	0.366712	−	0.635164i	−0.622337	−	0.782749i	$-0.713817\pi$
$569$	8.74745	−	15.1510i	0.366712	−	0.635164i	0.989049	+	0.147585i	$0.0471501\pi$
$570$		0			0
$571$	6.37628	+	11.0440i	0.266839	+	0.462178i	0.968044	−	0.250781i	$-0.0806875\pi$
$571$	6.37628	+	11.0440i	0.266839	+	0.462178i	−0.701205	+	0.712960i	$0.747354\pi$
$572$		0			0
$573$	0.992836	−	10.7753i	0.0414763	−	0.450143i
$574$		0			0
$575$	2.89898	+	14.2020i	0.120896	+	0.592266i
$576$		0			0
$577$			13.6969i			0.570211i	0.958496	+	0.285106i	$0.0920286\pi$
$577$			13.6969i			0.570211i	−0.958496	+	0.285106i	$0.907971\pi$
$578$		0			0
$579$	−15.6969	+	22.1988i	−0.652343	+	0.922552i
$580$		0			0
$581$	8.89898	+	15.4135i	0.369192	+	0.639459i
$582$		0			0
$583$	−10.6066	−	6.12372i	−0.439281	−	0.253619i
$584$		0			0
$585$	7.00657	+	14.8630i	0.289686	+	0.614508i
$586$		0			0
$587$	25.9326	+	14.9722i	1.07035	+	0.617969i	0.928278	−	0.371887i	$-0.121289\pi$
$587$	25.9326	+	14.9722i	1.07035	+	0.617969i	0.142075	+	0.989856i	$0.454623\pi$
$588$		0			0
$589$	−1.77526	−	3.07483i	−0.0731481	−	0.126696i
$590$		0			0
$591$	5.79796	+	12.5851i	0.238496	+	0.517680i
$592$		0			0
$593$		−	41.3939i		−	1.69984i	−0.526910	−	0.849921i	$-0.676649\pi$
$593$		−	41.3939i		−	1.69984i	0.526910	−	0.849921i	$-0.323351\pi$
$594$		0			0
$595$	−3.89898	−	38.5959i	−0.159843	−	1.58228i
$596$		0			0
$597$	−32.1698	+	14.8207i	−1.31662	+	0.606569i
$598$		0			0
$599$	−7.10102	−	12.2993i	−0.290140	−	0.502537i	0.683703	−	0.729761i	$-0.260368\pi$
$599$	−7.10102	−	12.2993i	−0.290140	−	0.502537i	−0.973843	+	0.227224i	$0.927035\pi$
$600$		0			0
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	−0.992665	−	0.120896i	$-0.961423\pi$
$601$	−9.60102	+	16.6295i	−0.391634	+	0.678330i	0.601031	+	0.799225i	$0.294757\pi$
$602$		0			0
$603$	−5.18010	+	27.8712i	−0.210950	+	1.13500i
$604$		0			0
$605$	−18.1455	−	8.16693i	−0.737721	−	0.332033i
$606$		0			0
$607$	−10.0424	+	5.79796i	−0.407607	+	0.235332i	−0.689761	−	0.724037i	$-0.742284\pi$
$607$	−10.0424	+	5.79796i	−0.407607	+	0.235332i	0.282154	+	0.959369i	$0.408951\pi$
$608$		0			0
$609$	26.6969	−	37.7552i	1.08181	−	1.52992i
$610$		0			0
$611$	1.10102			0.0445425
$612$		0			0
$613$		−	16.9444i		−	0.684377i	−0.939631	−	0.342189i	$-0.888832\pi$
$613$		−	16.9444i		−	0.684377i	0.939631	−	0.342189i	$-0.111168\pi$
$614$		0			0
$615$	3.87283	−	0.0340742i	0.156168	−	0.00137400i
$616$		0			0
$617$	32.6465	−	18.8485i	1.31430	−	0.758811i	0.331494	−	0.943457i	$-0.392447\pi$
$617$	32.6465	−	18.8485i	1.31430	−	0.758811i	0.982805	+	0.184647i	$0.0591140\pi$
$618$		0			0
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	−0.305048	−	0.952337i	$-0.598672\pi$
$619$	16.7247	−	28.9681i	0.672224	−	1.16433i	0.977272	−	0.211989i	$-0.0679943\pi$
$620$		0			0
$621$	−3.69694	−	14.6028i	−0.148353	−	0.585992i
$622$		0			0
$623$	−49.7046	−	28.6969i	−1.99137	−	1.14972i
$624$		0			0
$625$	−19.9853	−	15.0196i	−0.799411	−	0.600784i
$626$		0			0
$627$	0.126811	−	1.37628i	0.00506433	−	0.0549632i
$628$		0			0
$629$	−31.1918			−1.24370
$630$		0			0
$631$	−3.34847			−0.133300			−0.0666502	−	0.997776i	$-0.521231\pi$
$631$	−3.34847			−0.133300			−0.0666502	+	0.997776i	$0.521231\pi$
$632$		0			0
$633$	22.3417	+	15.7980i	0.888002	+	0.627912i
$634$		0			0
$635$	−3.78899	−	5.25966i	−0.150361	−	0.208723i
$636$		0			0
$637$	27.1486	+	15.6742i	1.07567	+	0.621036i
$638$		0			0
$639$	−4.77526	+	5.58542i	−0.188906	+	0.220956i
$640$		0			0
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	−0.225876	−	0.974156i	$-0.572524\pi$
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	0.956582	−	0.291464i	$-0.0941423\pi$
$642$		0			0
$643$	−8.00853	+	4.62372i	−0.315825	+	0.182342i	−0.649530	−	0.760336i	$-0.725034\pi$
$643$	−8.00853	+	4.62372i	−0.315825	+	0.182342i	0.333705	+	0.942678i	$0.391701\pi$
$644$		0			0
$645$	−24.8585	+	14.6451i	−0.978801	+	0.576652i
$646$		0			0
$647$		−	25.1010i		−	0.986823i	−0.869796	−	0.493411i	$-0.835750\pi$
$647$		−	25.1010i		−	0.986823i	0.869796	−	0.493411i	$-0.164250\pi$
$648$		0			0
$649$	16.3031			0.639951
$650$		0			0
$651$	−20.7980	−	45.1441i	−0.815136	−	1.76934i
$652$		0			0
$653$	29.4449	−	17.0000i	1.15227	−	0.665261i	0.202828	−	0.979214i	$-0.434987\pi$
$653$	29.4449	−	17.0000i	1.15227	−	0.665261i	0.949439	+	0.313953i	$0.101653\pi$
$654$		0			0
$655$	9.98930	+	4.49598i	0.390314	+	0.175672i
$656$		0			0
$657$	10.9405	+	9.35357i	0.426829	+	0.364918i
$658$		0			0
$659$	8.10102	−	14.0314i	0.315571	−	0.546585i	−0.663988	−	0.747743i	$-0.731137\pi$
$659$	8.10102	−	14.0314i	0.315571	−	0.546585i	0.979559	+	0.201159i	$0.0644706\pi$
$660$		0			0
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	0.968433	−	0.249274i	$-0.0801919\pi$
$661$	6.89898	+	11.9494i	0.268339	+	0.464777i	−0.700094	+	0.714051i	$0.746859\pi$
$662$		0			0
$663$	−13.5065	−	9.55051i	−0.524547	−	0.370911i
$664$		0			0
$665$	5.44949	−	0.550510i	0.211322	−	0.0213479i
$666$		0			0
$667$		−	17.3939i		−	0.673494i
$668$		0			0
$669$	32.5959	+	3.00340i	1.26023	+	0.116118i
$670$		0			0
$671$	−0.325765	−	0.564242i	−0.0125760	−	0.0217823i
$672$		0			0
$673$	−16.5420	−	9.55051i	−0.637646	−	0.368145i	0.146061	−	0.989276i	$-0.453340\pi$
$673$	−16.5420	−	9.55051i	−0.637646	−	0.368145i	−0.783707	+	0.621130i	$0.786674\pi$
$674$		0			0
$675$	21.4738	+	14.6244i	0.826529	+	0.562895i
$676$		0			0
$677$	−0.349945	−	0.202041i	−0.0134495	−	0.00776507i	0.493260	−	0.869882i	$-0.335805\pi$
$677$	−0.349945	−	0.202041i	−0.0134495	−	0.00776507i	−0.506710	+	0.862117i	$0.669138\pi$
$678$		0			0
$679$	−28.9217	−	50.0938i	−1.10991	−	1.92242i
$680$		0			0
$681$	−2.50000	−	0.230351i	−0.0958002	−	0.00882707i
$682$		0			0
$683$		−	40.5505i		−	1.55162i	−0.630965	−	0.775811i	$-0.717341\pi$
$683$		−	40.5505i		−	1.55162i	0.630965	−	0.775811i	$-0.282659\pi$
$684$		0			0
$685$	6.67423	−	0.674235i	0.255009	−	0.0257612i
$686$		0			0
$687$	19.1633	+	13.5505i	0.731126	+	0.516984i
$688$		0			0
$689$	−10.3485	−	17.9241i	−0.394245	−	0.682853i
$690$		0			0
$691$	−10.7980	+	18.7026i	−0.410774	+	0.711481i	−0.994975	−	0.100128i	$-0.968075\pi$
$691$	−10.7980	+	18.7026i	−0.410774	+	0.711481i	0.584201	+	0.811609i	$0.301408\pi$
$692$		0			0
$693$	3.53553	−	19.0227i	0.134304	−	0.722613i
$694$		0			0
$695$	−22.9342	−	10.3222i	−0.869944	−	0.391544i
$696$		0			0
$697$	−3.37662	+	1.94949i	−0.127898	+	0.0738422i
$698$		0			0
$699$	11.3763	+	24.6934i	0.430290	+	0.933989i
$700$		0			0
$701$	19.3939			0.732497			0.366248	−	0.930517i	$-0.380642\pi$
$701$	19.3939			0.732497			0.366248	+	0.930517i	$0.380642\pi$
$702$		0			0
$703$		−	4.40408i		−	0.166103i
$704$		0			0
$705$	1.49992	−	0.883663i	0.0564902	−	0.0332807i
$706$		0			0
$707$	30.8270	−	17.7980i	1.15937	−	0.669361i
$708$		0			0
$709$	11.3258	−	19.6168i	0.425348	−	0.736724i	−0.571105	−	0.820877i	$-0.693485\pi$
$709$	11.3258	−	19.6168i	0.425348	−	0.736724i	0.996453	+	0.0841527i	$0.0268184\pi$
$710$		0			0
$711$	−7.34847	−	20.7846i	−0.275589	−	0.779484i
$712$		0			0
$713$	−16.1920	−	9.34847i	−0.606396	−	0.350103i
$714$		0			0
$715$	4.64054	+	6.44174i	0.173546	+	0.240907i
$716$		0			0
$717$	40.5836	+	28.6969i	1.51562	+	1.07171i
$718$		0			0
$719$	22.2020			0.827996			0.413998	−	0.910278i	$-0.364132\pi$
$719$	22.2020			0.827996			0.413998	+	0.910278i	$0.364132\pi$
$720$		0			0
$721$	45.5959			1.69808
$722$		0			0
$723$	0.158919	−	1.72474i	0.00591025	−	0.0641440i
$724$		0			0
$725$	19.8931	+	22.4558i	0.738811	+	0.833989i
$726$		0			0
$727$	−9.22450	−	5.32577i	−0.342118	−	0.197522i	0.319090	−	0.947724i	$-0.396623\pi$
$727$	−9.22450	−	5.32577i	−0.342118	−	0.197522i	−0.661208	+	0.750203i	$0.729956\pi$
$728$		0			0
$729$	−23.0000	−	14.1421i	−0.851852	−	0.523783i
$730$		0			0
$731$	14.5227	−	25.1541i	0.537142	−	0.930357i
$732$		0			0
$733$	11.3851	−	6.57321i	0.420520	−	0.242787i	−0.274780	−	0.961507i	$-0.588605\pi$
$733$	11.3851	−	6.57321i	0.420520	−	0.242787i	0.695300	+	0.718720i	$0.255272\pi$
$734$		0			0
$735$	49.5644	−	0.436080i	1.82821	−	0.0160850i
$736$		0			0
$737$			13.6969i			0.504533i
$738$		0			0
$739$	7.24745			0.266602			0.133301	−	0.991076i	$-0.457442\pi$
$739$	7.24745			0.266602			0.133301	+	0.991076i	$0.457442\pi$
$740$		0			0
$741$	1.34847	−	1.90702i	0.0495373	−	0.0700563i
$742$		0			0
$743$	−11.3458	+	6.55051i	−0.416238	+	0.240315i	−0.693466	−	0.720489i	$-0.743917\pi$
$743$	−11.3458	+	6.55051i	−0.416238	+	0.240315i	0.277229	+	0.960804i	$0.410584\pi$
$744$		0			0
$745$	−33.1295	−	14.9109i	−1.21377	−	0.546293i
$746$		0			0
$747$	11.3137	−	4.00000i	0.413947	−	0.146352i
$748$		0			0
$749$	3.67423	−	6.36396i	0.134254	−	0.232534i
$750$		0			0
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	0.905050	+	0.425306i	$0.139833\pi$
$751$	22.4949	+	38.9623i	0.820850	+	1.42175i	−0.0841993	+	0.996449i	$0.526833\pi$
$752$		0			0
$753$	18.0116	−	8.29796i	0.656378	−	0.302394i
$754$		0			0
$755$	−1.55051	−	15.3485i	−0.0564288	−	0.558588i
$756$		0			0
$757$		−	10.0000i		−	0.363456i	−0.983349	−	0.181728i	$-0.941831\pi$
$757$		−	10.0000i		−	0.363456i	0.983349	−	0.181728i	$-0.0581691\pi$
$758$		0			0
$759$	−3.04541	−	6.61037i	−0.110541	−	0.239941i
$760$		0			0
$761$	24.2474	+	41.9978i	0.878969	+	1.52242i	0.852473	+	0.522771i	$0.175102\pi$
$761$	24.2474	+	41.9978i	0.878969	+	1.52242i	0.0264959	+	0.999649i	$0.491565\pi$
$762$		0			0
$763$	30.8270	+	17.7980i	1.11601	+	0.644329i
$764$		0			0
$765$	−26.0649	−	2.17055i	−0.942380	−	0.0784763i
$766$		0			0
$767$	23.8594	+	13.7753i	0.861515	+	0.497396i
$768$		0			0
$769$	−12.2474	−	21.2132i	−0.441654	−	0.764968i	0.556158	−	0.831076i	$-0.312275\pi$
$769$	−12.2474	−	21.2132i	−0.441654	−	0.764968i	−0.997812	+	0.0661088i	$0.978942\pi$
$770$		0			0
$771$	−19.8990	+	28.1414i	−0.716644	+	1.01349i
$772$		0			0
$773$			23.3939i			0.841419i	0.907195	+	0.420710i	$0.138219\pi$
$773$			23.3939i			0.841419i	−0.907195	+	0.420710i	$0.861781\pi$
$774$		0			0
$775$	31.5959	−	6.44949i	1.13496	−	0.231673i
$776$		0			0
$777$	5.65685	−	61.3939i	0.202939	−	2.20249i
$778$		0			0
$779$	−0.275255	−	0.476756i	−0.00986204	−	0.0170816i
$780$		0			0
$781$	−1.77526	+	3.07483i	−0.0635236	+	0.110026i
$782$		0			0
$783$	−21.7381	−	22.3485i	−0.776857	−	0.798669i
$784$		0			0
$785$	−14.6838	+	32.6249i	−0.524087	+	1.16443i
$786$		0			0
$787$	−6.40329	+	3.69694i	−0.228252	+	0.131782i	−0.609766	−	0.792582i	$-0.708736\pi$
$787$	−6.40329	+	3.69694i	−0.228252	+	0.131782i	0.381513	+	0.924363i	$0.375403\pi$
$788$		0			0
$789$	−13.0227	−	1.19992i	−0.463621	−	0.0427182i
$790$		0			0
$791$	−21.7980			−0.775046
$792$		0			0
$793$		−	1.10102i		−	0.0390984i
$794$		0			0
$795$	−28.4833	−	16.1124i	−1.01020	−	0.571448i
$796$		0			0
$797$	−30.8270	+	17.7980i	−1.09195	+	0.630436i	−0.934094	−	0.357027i	$-0.883791\pi$
$797$	−30.8270	+	17.7980i	−1.09195	+	0.630436i	−0.157853	+	0.987463i	$0.550457\pi$
$798$		0			0
$799$	−0.876276	+	1.51775i	−0.0310004	+	0.0536943i
$800$		0			0
$801$	−25.1464	+	29.4128i	−0.888505	+	1.03925i
$802$		0			0
$803$	6.02285	+	3.47730i	0.212542	+	0.122711i
$804$		0			0
$805$	23.4028	−	16.8591i	0.824840	−	0.594204i
$806$		0			0
$807$	−44.1191	+	20.3258i	−1.55307	+	0.715501i
$808$		0			0
$809$	−47.0908			−1.65562			−0.827812	−	0.561005i	$-0.810415\pi$
$809$	−47.0908			−1.65562			−0.827812	+	0.561005i	$0.810415\pi$
$810$		0			0
$811$	17.2474			0.605640			0.302820	−	0.953048i	$-0.402072\pi$
$811$	17.2474			0.605640			0.302820	+	0.953048i	$0.402072\pi$
$812$		0			0
$813$	37.1195	−	17.1010i	1.30184	−	0.599759i
$814$		0			0
$815$	1.17497	+	1.63103i	0.0411575	+	0.0571325i
$816$		0			0
$817$	3.55159	+	2.05051i	0.124254	+	0.0717383i
$818$		0			0
$819$	21.2474	−	24.8523i	0.742446	−	0.868409i
$820$		0			0
$821$	21.0227	−	36.4124i	0.733697	−	1.27080i	−0.221595	−	0.975139i	$-0.571126\pi$
$821$	21.0227	−	36.4124i	0.733697	−	1.27080i	0.955292	−	0.295662i	$-0.0955404\pi$
$822$		0			0
$823$	6.57826	−	3.79796i	0.229304	−	0.132389i	−0.380947	−	0.924597i	$-0.624402\pi$
$823$	6.57826	−	3.79796i	0.229304	−	0.132389i	0.610251	+	0.792208i	$0.291069\pi$
$824$		0			0
$825$	11.4918	+	5.05113i	0.400095	+	0.175858i
$826$		0			0
$827$			13.7980i			0.479802i	0.970797	+	0.239901i	$0.0771150\pi$
$827$			13.7980i			0.479802i	−0.970797	+	0.239901i	$0.922885\pi$
$828$		0			0
$829$	21.5505			0.748480			0.374240	−	0.927332i	$-0.377904\pi$
$829$	21.5505			0.748480			0.374240	+	0.927332i	$0.377904\pi$
$830$		0			0
$831$	16.5505	+	1.52497i	0.574131	+	0.0529006i
$832$		0			0
$833$	−43.2138	+	24.9495i	−1.49727	+	0.864449i
$834$		0			0
$835$	−22.2528	+	49.4420i	−0.770090	+	1.71101i
$836$		0			0
$837$	−32.4876	+	8.22474i	−1.12294	+	0.284289i
$838$		0			0
$839$	−7.87628	+	13.6421i	−0.271919	+	0.470978i	−0.969353	−	0.245671i	$-0.920992\pi$
$839$	−7.87628	+	13.6421i	−0.271919	+	0.470978i	0.697434	+	0.716649i	$0.254325\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$		0			0
$843$	1.90702	−	20.6969i	0.0656814	−	0.712840i
$844$		0			0
$845$	−1.57321	−	15.5732i	−0.0541202	−	0.535735i
$846$		0			0
$847$			39.5959i			1.36053i
$848$		0			0
$849$	−4.00000	+	5.65685i	−0.137280	+	0.194143i
$850$		0			0
$851$	−11.5959	−	20.0847i	−0.397503	−	0.688495i
$852$		0			0
$853$	−21.7774	−	12.5732i	−0.745646	−	0.430499i	0.0784728	−	0.996916i	$-0.474996\pi$
$853$	−21.7774	−	12.5732i	−0.745646	−	0.430499i	−0.824118	+	0.566418i	$0.808329\pi$
$854$		0			0
$855$	0.306467	−	3.68020i	0.0104809	−	0.125860i
$856$		0			0
$857$	46.2405	+	26.6969i	1.57954	+	0.911950i	0.994923	+	0.100644i	$0.0320902\pi$
$857$	46.2405	+	26.6969i	1.57954	+	0.911950i	0.584621	+	0.811306i	$0.301243\pi$
$858$		0			0
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	−0.991280	−	0.131770i	$-0.957934\pi$
$859$	−17.8712	−	30.9538i	−0.609757	−	1.05613i	0.381524	−	0.924359i	$-0.375399\pi$
$860$		0			0
$861$	−3.22474	−	6.99964i	−0.109899	−	0.238547i
$862$		0			0
$863$			21.5505i			0.733588i	0.930302	+	0.366794i	$0.119545\pi$
$863$			21.5505i			0.733588i	−0.930302	+	0.366794i	$0.880455\pi$
$864$		0			0
$865$	−17.3485	+	1.75255i	−0.589866	+	0.0595885i
$866$		0			0
$867$	−2.82843	+	1.30306i	−0.0960584	+	0.0442543i
$868$		0			0
$869$	−5.32577	−	9.22450i	−0.180664	−	0.312920i
$870$		0			0
$871$	−11.5732	+	20.0454i	−0.392143	+	0.679212i
$872$		0			0
$873$	−36.7696	+	13.0000i	−1.24446	+	0.439983i
$874$		0			0
$875$	−10.9320	+	48.5308i	−0.369570	+	1.64064i
$876$		0			0
$877$	−47.7582	+	27.5732i	−1.61268	+	0.931081i	−0.623934	+	0.781477i	$0.714467\pi$
$877$	−47.7582	+	27.5732i	−1.61268	+	0.931081i	−0.988746	+	0.149604i	$0.952200\pi$
$878$		0			0
$879$	18.0000	−	25.4558i	0.607125	−	0.858604i
$880$		0			0
$881$	−30.0000			−1.01073			−0.505363	−	0.862907i	$-0.668641\pi$
$881$	−30.0000			−1.01073			−0.505363	+	0.862907i	$0.668641\pi$
$882$		0			0
$883$		−	11.4495i		−	0.385306i	−0.981267	−	0.192653i	$-0.938291\pi$
$883$		−	11.4495i		−	0.385306i	0.981267	−	0.192653i	$-0.0617092\pi$
$884$		0			0
$885$	43.5595	−	0.383248i	1.46424	−	0.0128827i
$886$		0			0
$887$	−4.02834	+	2.32577i	−0.135259	+	0.0780916i	−0.566102	−	0.824335i	$-0.691549\pi$
$887$	−4.02834	+	2.32577i	−0.135259	+	0.0780916i	0.430844	+	0.902427i	$0.358216\pi$
$888$		0			0
$889$	−6.44949	+	11.1708i	−0.216309	+	0.374658i
$890$		0			0
$891$	−12.1742	−	4.68729i	−0.407852	−	0.157030i
$892$		0			0
$893$	−0.214297	−	0.123724i	−0.00717117	−	0.00414028i
$894$		0			0
$895$	−16.1455	+	11.6310i	−0.539686	+	0.388782i
$896$		0			0
$897$	1.12848	−	12.2474i	0.0376790	−	0.408930i
$898$		0			0
$899$	−38.6969			−1.29062
$900$		0			0
$901$	32.9444			1.09754
$902$		0			0
$903$	46.8761	+	33.1464i	1.55994	+	1.10304i
$904$		0			0
$905$	−18.9586	+	13.6576i	−0.630207	+	0.453993i
$906$		0			0
$907$	29.2217	+	16.8712i	0.970292	+	0.560198i	0.899325	−	0.437281i	$-0.144058\pi$
$907$	29.2217	+	16.8712i	0.970292	+	0.560198i	0.0709665	+	0.997479i	$0.477392\pi$
$908$		0			0
$909$	−8.00000	−	22.6274i	−0.265343	−	0.750504i
$910$		0			0
$911$	−0.123724	+	0.214297i	−0.00409917	+	0.00709997i	−0.868068	−	0.496446i	$-0.834638\pi$
$911$	−0.123724	+	0.214297i	−0.00409917	+	0.00709997i	0.863969	+	0.503546i	$0.167971\pi$
$912$		0			0
$913$	5.02118	−	2.89898i	0.166177	−	0.0959422i
$914$		0			0
$915$	−0.883663	−	1.49992i	−0.0292130	−	0.0495858i
$916$		0			0
$917$		−	21.7980i		−	0.719832i
$918$		0			0
$919$	10.8990			0.359524			0.179762	−	0.983710i	$-0.442467\pi$
$919$	10.8990			0.359524			0.179762	+	0.983710i	$0.442467\pi$
$920$		0			0
$921$	−17.3536	−	37.6677i	−0.571820	−	1.24119i
$922$		0			0
$923$	−5.19615	+	3.00000i	−0.171033	+	0.0987462i
$924$		0			0
$925$	37.9411	+	12.6677i	1.24750	+	0.416512i
$926$		0			0
$927$	5.61753	−	30.2247i	0.184504	−	0.992711i
$928$		0			0
$929$	−27.7980	+	48.1475i	−0.912021	+	1.57967i	−0.100817	+	0.994905i	$0.532146\pi$
$929$	−27.7980	+	48.1475i	−0.912021	+	1.57967i	−0.811205	+	0.584762i	$0.801188\pi$
$930$		0			0
$931$	−3.52270	−	6.10150i	−0.115452	−	0.199969i
$932$		0			0
$933$	−32.3840	−	22.8990i	−1.06021	−	0.749679i
$934$		0			0
$935$	−12.5732	+	1.27015i	−0.411188	+	0.0415384i
$936$		0			0
$937$		−	39.5959i		−	1.29354i	−0.762684	−	0.646771i	$-0.776119\pi$
$937$		−	39.5959i		−	1.29354i	0.762684	−	0.646771i	$-0.223881\pi$
$938$		0			0
$939$	−13.2753	−	1.22319i	−0.433222	−	0.0399172i
$940$		0			0
$941$	24.8990	+	43.1263i	0.811684	+	1.40588i	0.911685	+	0.410890i	$0.134782\pi$
$941$	24.8990	+	43.1263i	0.811684	+	1.40588i	−0.100001	+	0.994987i	$0.531885\pi$
$942$		0			0
$943$	−2.51059	−	1.44949i	−0.0817561	−	0.0472019i
$944$		0			0
$945$	8.99927	−	50.9091i	0.292746	−	1.65607i
$946$		0			0
$947$	−18.4008	−	10.6237i	−0.597947	−	0.345225i	0.170287	−	0.985395i	$-0.445531\pi$
$947$	−18.4008	−	10.6237i	−0.597947	−	0.345225i	−0.768233	+	0.640170i	$0.778864\pi$
$948$		0			0
$949$	5.87628	+	10.1780i	0.190752	+	0.330392i
$950$		0			0
$951$	−53.3712	−	4.91764i	−1.73068	−	0.159465i
$952$		0			0
$953$			50.7980i			1.64551i	0.568398	+	0.822754i	$0.307563\pi$
$953$			50.7980i			1.64551i	−0.568398	+	0.822754i	$0.692437\pi$
$954$		0			0
$955$	−1.40408	−	13.8990i	−0.0454350	−	0.449760i
$956$		0			0
$957$	−12.2993	−	8.69694i	−0.397581	−	0.281132i
$958$		0			0
$959$	−6.67423	−	11.5601i	−0.215522	−	0.373296i
$960$		0			0
$961$	−5.29796	+	9.17633i	−0.170902	+	0.296011i
$962$		0			0
$963$	−3.76588	−	3.21964i	−0.121354	−	0.103752i
$964$		0			0
$965$	−14.4057	+	32.0070i	−0.463735	+	1.03034i
$966$		0			0
$967$	24.8523	−	14.3485i	0.799195	−	0.461416i	−0.0439944	−	0.999032i	$-0.514008\pi$
$967$	24.8523	−	14.3485i	0.799195	−	0.461416i	0.843190	+	0.537616i	$0.180675\pi$
$968$		0			0
$969$	1.55561	+	3.37662i	0.0499735	+	0.108473i
$970$		0			0
$971$	23.3939			0.750745			0.375373	−	0.926874i	$-0.377515\pi$
$971$	23.3939			0.750745			0.375373	+	0.926874i	$0.377515\pi$
$972$		0			0
$973$			50.0454i			1.60438i
$974$		0			0
$975$	12.5503	+	17.1023i	0.401932	+	0.547713i
$976$		0			0
$977$	32.8215	−	18.9495i	1.05005	−	0.606248i	0.127388	−	0.991853i	$-0.459341\pi$
$977$	32.8215	−	18.9495i	1.05005	−	0.606248i	0.922664	+	0.385605i	$0.126007\pi$
$978$		0			0
$979$	−9.34847	+	16.1920i	−0.298778	+	0.517499i
$980$		0			0
$981$	15.5959	−	18.2419i	0.497939	−	0.582419i
$982$		0			0
$983$	32.3840	+	18.6969i	1.03289	+	0.596340i	0.917811	−	0.397017i	$-0.129954\pi$
$983$	32.3840	+	18.6969i	1.03289	+	0.596340i	0.115079	+	0.993356i	$0.463288\pi$
$984$		0			0
$985$	10.4561	+	14.5145i	0.333158	+	0.462471i
$986$		0			0
$987$	−2.82843	−	2.00000i	−0.0900298	−	0.0636607i
$988$		0			0
$989$	21.5959			0.686710
$990$		0			0
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$		0			0
$993$	−5.30691	+	57.5959i	−0.168410	+	1.82775i
$994$		0			0
$995$	−37.1018	+	26.7276i	−1.17621	+	0.847323i
$996$		0			0
$997$	28.5307	+	16.4722i	0.903576	+	0.521680i	0.878359	−	0.478002i	$-0.158639\pi$
$997$	28.5307	+	16.4722i	0.903576	+	0.521680i	0.0252170	+	0.999682i	$0.491972\pi$
$998$		0			0
$999$	−40.0000	−	11.3137i	−1.26554	−	0.357950i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.by.c.529.1		8
3.2	odd	2		2160.2.by.d.289.4		8
4.3	odd	2		90.2.i.b.79.4	yes	8
5.4	even	2	inner	720.2.by.c.529.4		8
9.4	even	3	inner	720.2.by.c.49.4		8
9.5	odd	6		2160.2.by.d.1009.1		8
12.11	even	2		270.2.i.b.19.2		8
15.14	odd	2		2160.2.by.d.289.1		8
20.3	even	4		450.2.e.n.151.2		4
20.7	even	4		450.2.e.k.151.1		4
20.19	odd	2		90.2.i.b.79.1	yes	8
36.7	odd	6		810.2.c.f.649.1		4
36.11	even	6		810.2.c.e.649.4		4
36.23	even	6		270.2.i.b.199.3		8
36.31	odd	6		90.2.i.b.49.1	✓	8
45.4	even	6	inner	720.2.by.c.49.1		8
45.14	odd	6		2160.2.by.d.1009.4		8
60.23	odd	4		1350.2.e.j.451.1		4
60.47	odd	4		1350.2.e.m.451.2		4
60.59	even	2		270.2.i.b.19.3		8
180.7	even	12		4050.2.a.bs.1.1		2
180.23	odd	12		1350.2.e.j.901.1		4
180.43	even	12		4050.2.a.bq.1.2		2
180.47	odd	12		4050.2.a.bm.1.1		2
180.59	even	6		270.2.i.b.199.2		8
180.67	even	12		450.2.e.k.301.1		4
180.79	odd	6		810.2.c.f.649.3		4
180.83	odd	12		4050.2.a.bz.1.2		2
180.103	even	12		450.2.e.n.301.2		4
180.119	even	6		810.2.c.e.649.2		4
180.139	odd	6		90.2.i.b.49.4	yes	8
180.167	odd	12		1350.2.e.m.901.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.2.i.b.49.1	✓	8	36.31	odd	6
90.2.i.b.49.4	yes	8	180.139	odd	6
90.2.i.b.79.1	yes	8	20.19	odd	2
90.2.i.b.79.4	yes	8	4.3	odd	2
270.2.i.b.19.2		8	12.11	even	2
270.2.i.b.19.3		8	60.59	even	2
270.2.i.b.199.2		8	180.59	even	6
270.2.i.b.199.3		8	36.23	even	6
450.2.e.k.151.1		4	20.7	even	4
450.2.e.k.301.1		4	180.67	even	12
450.2.e.n.151.2		4	20.3	even	4
450.2.e.n.301.2		4	180.103	even	12
720.2.by.c.49.1		8	45.4	even	6	inner
720.2.by.c.49.4		8	9.4	even	3	inner
720.2.by.c.529.1		8	1.1	even	1	trivial
720.2.by.c.529.4		8	5.4	even	2	inner
810.2.c.e.649.2		4	180.119	even	6
810.2.c.e.649.4		4	36.11	even	6
810.2.c.f.649.1		4	36.7	odd	6
810.2.c.f.649.3		4	180.79	odd	6
1350.2.e.j.451.1		4	60.23	odd	4
1350.2.e.j.901.1		4	180.23	odd	12
1350.2.e.m.451.2		4	60.47	odd	4
1350.2.e.m.901.2		4	180.167	odd	12
2160.2.by.d.289.1		8	15.14	odd	2
2160.2.by.d.289.4		8	3.2	odd	2
2160.2.by.d.1009.1		8	9.5	odd	6
2160.2.by.d.1009.4		8	45.14	odd	6
4050.2.a.bm.1.1		2	180.47	odd	12
4050.2.a.bq.1.2		2	180.43	even	12
4050.2.a.bs.1.1		2	180.7	even	12
4050.2.a.bz.1.2		2	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.by (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.57313 + 0.724745i) q^{3} +(-1.81431 + 1.30701i) q^{5} +(3.85337 + 2.22474i) q^{7} +(1.94949 - 2.28024i) q^{9} +(0.724745 - 1.25529i) q^{11} +(2.12132 - 1.22474i) q^{13} +(1.90691 - 3.37101i) q^{15} +3.89898i q^{17} -0.550510 q^{19} +(-7.67423 - 0.707107i) q^{21} +(-2.51059 + 1.44949i) q^{23} +(1.58346 - 4.74264i) q^{25} +(-1.41421 + 5.00000i) q^{27} +(-3.00000 + 5.19615i) q^{29} +(3.22474 + 5.58542i) q^{31} +(-0.230351 + 2.50000i) q^{33} +(-9.89898 + 1.00000i) q^{35} +8.00000i q^{37} +(-2.44949 + 3.46410i) q^{39} +(0.500000 + 0.866025i) q^{41} +(-6.45145 - 3.72474i) q^{43} +(-0.556696 + 6.68506i) q^{45} +(0.389270 + 0.224745i) q^{47} +(6.39898 + 11.0834i) q^{49} +(-2.82577 - 6.13361i) q^{51} -8.44949i q^{53} +(0.325765 + 3.22474i) q^{55} +(0.866025 - 0.398979i) q^{57} +(5.62372 + 9.74058i) q^{59} +(0.224745 - 0.389270i) q^{61} +(12.5851 - 4.44949i) q^{63} +(-2.24799 + 4.99465i) q^{65} +(-8.18350 + 4.72474i) q^{67} +(2.89898 - 4.09978i) q^{69} -2.44949 q^{71} +4.79796i q^{73} +(0.946206 + 8.60841i) q^{75} +(5.58542 - 3.22474i) q^{77} +(3.67423 - 6.36396i) q^{79} +(-1.39898 - 8.89060i) q^{81} +(3.46410 + 2.00000i) q^{83} +(-5.09599 - 7.07397i) q^{85} +(0.953512 - 10.3485i) q^{87} -12.8990 q^{89} +10.8990 q^{91} +(-9.12096 - 6.44949i) q^{93} +(0.998798 - 0.719521i) q^{95} +(-11.2583 - 6.50000i) q^{97} +(-1.44949 - 4.09978i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{5} - 4 q^{9} - 4 q^{11} + 8 q^{15} - 24 q^{19} - 32 q^{21} - 24 q^{29} + 16 q^{31} - 40 q^{35} + 4 q^{41} + 20 q^{45} + 12 q^{49} - 52 q^{51} + 32 q^{55} - 4 q^{59} - 8 q^{61} - 12 q^{65} - 16 q^{69}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q - 4 * q^5 - 4 * q^9 - 4 * q^11 + 8 * q^15 - 24 * q^19 - 32 * q^21 - 24 * q^29 + 16 * q^31 - 40 * q^35 + 4 * q^41 + 20 * q^45 + 12 * q^49 - 52 * q^51 + 32 * q^55 - 4 * q^59 - 8 * q^61 - 12 * q^65 - 16 * q^69 + 4 * q^75 + 28 * q^81 - 20 * q^85 - 64 * q^89 + 48 * q^91 + 24 * q^95 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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