LMFDB - Embedded newform 720.2.bm.h.109.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(109,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("720.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.bm (of order $4$, degree $2$, 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:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.15
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.h.469.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.456856 - 1.33839i) q^{2} +(-1.58257 - 1.22290i) q^{4} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} +O(q^{10})$	\(q+(0.456856 - 1.33839i) q^{2} +(-1.58257 - 1.22290i) q^{4} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} +(2.90411 - 1.25146i) q^{10} +(-4.39624 + 4.39624i) q^{11} +(-0.417468 + 0.417468i) q^{13} +(-1.18315 + 3.46612i) q^{14} +(1.00903 + 3.87064i) q^{16} +4.40417i q^{17} +(-4.53682 - 4.53682i) q^{19} +(-0.348184 - 4.45856i) q^{20} +(3.87543 + 7.89232i) q^{22} +0.281063 q^{23} +(-0.494901 + 4.97545i) q^{25} +(0.368012 + 0.749457i) q^{26} +(4.09849 + 3.16704i) q^{28} +(-3.73710 - 3.73710i) q^{29} -3.05233 q^{31} +(5.64140 + 0.417848i) q^{32} +(5.89449 + 2.01207i) q^{34} +(-3.88686 - 4.29266i) q^{35} +(5.26234 + 5.26234i) q^{37} +(-8.14471 + 3.99936i) q^{38} +(-6.12636 - 1.57091i) q^{40} -5.16508i q^{41} +(2.66933 + 2.66933i) q^{43} +(12.3335 - 1.58118i) q^{44} +(0.128405 - 0.376171i) q^{46} +7.45202i q^{47} -0.293066 q^{49} +(6.43298 + 2.93543i) q^{50} +(1.17119 - 0.150149i) q^{52} +(-2.89462 - 2.89462i) q^{53} +(-13.8850 - 0.688864i) q^{55} +(6.11114 - 4.03849i) q^{56} +(-6.70900 + 3.29437i) q^{58} +(4.60721 - 4.60721i) q^{59} +(-0.211318 - 0.211318i) q^{61} +(-1.39447 + 4.08520i) q^{62} +(3.13655 - 7.35949i) q^{64} +(-1.31853 - 0.0654147i) q^{65} +(7.17140 - 7.17140i) q^{67} +(5.38586 - 6.96989i) q^{68} +(-7.52099 + 3.24100i) q^{70} +15.9477i q^{71} +10.5662 q^{73} +(9.44719 - 4.63893i) q^{74} +(1.63174 + 12.7279i) q^{76} +(11.3853 - 11.3853i) q^{77} +4.53907 q^{79} +(-4.90135 + 7.48176i) q^{80} +(-6.91288 - 2.35969i) q^{82} +(-4.56660 + 4.56660i) q^{83} +(-7.30010 + 6.61000i) q^{85} +(4.79209 - 2.35310i) q^{86} +(3.51840 - 17.2294i) q^{88} -10.2745i q^{89} +(1.08115 - 1.08115i) q^{91} +(-0.444800 - 0.343712i) q^{92} +(9.97370 + 3.40450i) q^{94} +(0.710893 - 14.3291i) q^{95} +6.78053i q^{97} +(-0.133889 + 0.392236i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) $ 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.456856	−	1.33839i	0.323046	−	0.946383i
$2$	0.456856	−	1.33839i	0.323046	−	0.946383i
$3$		0			0
$3$		0			0
$4$	−1.58257	−	1.22290i	−0.791283	−	0.611450i
$5$	1.50085	+	1.65754i	0.671200	+	0.741276i
$5$	1.50085	+	1.65754i	0.671200	+	0.741276i
$6$		0			0
$7$	−2.58977			−0.978843			−0.489421	−	0.872047i	$-0.662792\pi$
$7$	−2.58977			−0.978843			−0.489421	+	0.872047i	$0.662792\pi$
$8$	−2.35972	+	1.55940i	−0.834287	+	0.551331i
$9$		0			0
$10$	2.90411	−	1.25146i	0.918360	−	0.395747i
$11$	−4.39624	+	4.39624i	−1.32552	+	1.32552i	−0.416278	+	0.909237i	$0.636666\pi$
$11$	−4.39624	+	4.39624i	−1.32552	+	1.32552i	−0.909237	+	0.416278i	$0.863334\pi$
$12$		0			0
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	−0.762625	−	0.646840i	$-0.776090\pi$
$13$	−0.417468	+	0.417468i	−0.115785	+	0.115785i	0.646840	+	0.762625i	$0.276090\pi$
$14$	−1.18315	+	3.46612i	−0.316211	+	0.926361i
$15$		0			0
$16$	1.00903	+	3.87064i	0.252258	+	0.967660i
$17$			4.40417i			1.06817i	0.845431	+	0.534084i	$0.179343\pi$
$17$			4.40417i			1.06817i	−0.845431	+	0.534084i	$0.820657\pi$
$18$		0			0
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.999131	−	0.0416882i	$-0.986726\pi$
$19$	−4.53682	−	4.53682i	−1.04082	−	1.04082i	−0.0416882	−	0.999131i	$-0.513274\pi$
$20$	−0.348184	−	4.45856i	−0.0778562	−	0.996965i
$21$		0			0
$22$	3.87543	+	7.89232i	0.826244	+	1.68265i
$23$	0.281063			0.0586056			0.0293028	−	0.999571i	$-0.490671\pi$
$23$	0.281063			0.0586056			0.0293028	+	0.999571i	$0.490671\pi$
$24$		0			0
$25$	−0.494901	+	4.97545i	−0.0989802	+	0.995089i
$26$	0.368012	+	0.749457i	0.0721731	+	0.146981i
$27$		0			0
$28$	4.09849	+	3.16704i	0.774542	+	0.598514i
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	0.269140	−	0.963101i	$-0.413261\pi$
$29$	−3.73710	−	3.73710i	−0.693962	−	0.693962i	−0.963101	+	0.269140i	$0.913261\pi$
$30$		0			0
$31$	−3.05233			−0.548214			−0.274107	−	0.961699i	$-0.588382\pi$
$31$	−3.05233			−0.548214			−0.274107	+	0.961699i	$0.588382\pi$
$32$	5.64140	+	0.417848i	0.997268	+	0.0738659i
$33$		0			0
$34$	5.89449	+	2.01207i	1.01090	+	0.345067i
$35$	−3.88686	−	4.29266i	−0.657000	−	0.725593i
$36$		0			0
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	0.991928	−	0.126804i	$-0.0404719\pi$
$37$	5.26234	+	5.26234i	0.865124	+	0.865124i	−0.126804	+	0.991928i	$0.540472\pi$
$38$	−8.14471	+	3.99936i	−1.32125	+	0.648782i
$39$		0			0
$40$	−6.12636	−	1.57091i	−0.968662	−	0.248383i
$41$		−	5.16508i		−	0.806649i	−0.915057	−	0.403325i	$-0.867855\pi$
$41$		−	5.16508i		−	0.806649i	0.915057	−	0.403325i	$-0.132145\pi$
$42$		0			0
$43$	2.66933	+	2.66933i	0.407069	+	0.407069i	0.880715	−	0.473647i	$-0.157063\pi$
$43$	2.66933	+	2.66933i	0.407069	+	0.407069i	−0.473647	+	0.880715i	$0.657063\pi$
$44$	12.3335	−	1.58118i	1.85934	−	0.238371i
$45$		0			0
$46$	0.128405	−	0.376171i	0.0189323	−	0.0554634i
$47$			7.45202i			1.08699i	0.839413	+	0.543495i	$0.182899\pi$
$47$			7.45202i			1.08699i	−0.839413	+	0.543495i	$0.817101\pi$
$48$		0			0
$49$	−0.293066			−0.0418665
$50$	6.43298	+	2.93543i	0.909761	+	0.415132i
$51$		0			0
$52$	1.17119	−	0.150149i	0.162415	−	0.0208219i
$53$	−2.89462	−	2.89462i	−0.397606	−	0.397606i	0.479782	−	0.877388i	$-0.340716\pi$
$53$	−2.89462	−	2.89462i	−0.397606	−	0.397606i	−0.877388	+	0.479782i	$0.840716\pi$
$54$		0			0
$55$	−13.8850	−	0.688864i	−1.87226	−	0.0928863i
$56$	6.11114	−	4.03849i	0.816636	−	0.539666i
$57$		0			0
$58$	−6.70900	+	3.29437i	−0.880935	+	0.432573i
$59$	4.60721	−	4.60721i	0.599808	−	0.599808i	−0.340453	−	0.940261i	$-0.610580\pi$
$59$	4.60721	−	4.60721i	0.599808	−	0.599808i	0.940261	+	0.340453i	$0.110580\pi$
$60$		0			0
$61$	−0.211318	−	0.211318i	−0.0270564	−	0.0270564i	0.693449	−	0.720506i	$-0.256090\pi$
$61$	−0.211318	−	0.211318i	−0.0270564	−	0.0270564i	−0.720506	+	0.693449i	$0.756090\pi$
$62$	−1.39447	+	4.08520i	−0.177098	+	0.518821i
$63$		0			0
$64$	3.13655	−	7.35949i	0.392069	−	0.919936i
$65$	−1.31853	−	0.0654147i	−0.163543	−	0.00811370i
$66$		0			0
$67$	7.17140	−	7.17140i	0.876126	−	0.876126i	−0.117005	−	0.993131i	$-0.537329\pi$
$67$	7.17140	−	7.17140i	0.876126	−	0.876126i	0.993131	+	0.117005i	$0.0373294\pi$
$68$	5.38586	−	6.96989i	0.653132	−	0.845223i
$69$		0			0
$70$	−7.52099	+	3.24100i	−0.898930	+	0.387374i
$71$			15.9477i			1.89265i	0.323222	+	0.946323i	$0.395234\pi$
$71$			15.9477i			1.89265i	−0.323222	+	0.946323i	$0.604766\pi$
$72$		0			0
$73$	10.5662			1.23668			0.618339	−	0.785912i	$-0.287806\pi$
$73$	10.5662			1.23668			0.618339	+	0.785912i	$0.287806\pi$
$74$	9.44719	−	4.63893i	1.09821	−	0.539264i
$75$		0			0
$76$	1.63174	+	12.7279i	0.187174	+	1.45999i
$77$	11.3853	−	11.3853i	1.29747	−	1.29747i
$78$		0			0
$79$	4.53907			0.510685			0.255342	−	0.966851i	$-0.417812\pi$
$79$	4.53907			0.510685			0.255342	+	0.966851i	$0.417812\pi$
$80$	−4.90135	+	7.48176i	−0.547988	+	0.836486i
$81$		0			0
$82$	−6.91288	−	2.35969i	−0.763400	−	0.260585i
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	−0.911826	−	0.410577i	$-0.865327\pi$
$83$	−4.56660	+	4.56660i	−0.501249	+	0.501249i	0.410577	+	0.911826i	$0.365327\pi$
$84$		0			0
$85$	−7.30010	+	6.61000i	−0.791807	+	0.716955i
$86$	4.79209	−	2.35310i	0.516745	−	0.253741i
$87$		0			0
$88$	3.51840	−	17.2294i	0.375062	−	1.83666i
$89$		−	10.2745i		−	1.08910i	−0.838730	−	0.544548i	$-0.816701\pi$
$89$		−	10.2745i		−	1.08910i	0.838730	−	0.544548i	$-0.183299\pi$
$90$		0			0
$91$	1.08115	−	1.08115i	0.113335	−	0.113335i
$92$	−0.444800	−	0.343712i	−0.0463737	−	0.0358344i
$93$		0			0
$94$	9.97370	+	3.40450i	1.02871	+	0.351147i
$95$	0.710893	−	14.3291i	0.0729361	−	1.47013i
$96$		0			0
$97$			6.78053i			0.688459i	0.938886	+	0.344229i	$0.111860\pi$
$97$			6.78053i			0.688459i	−0.938886	+	0.344229i	$0.888140\pi$
$98$	−0.133889	+	0.392236i	−0.0135248	+	0.0396218i
$99$		0			0
$100$	6.86769	−	7.26876i	0.686769	−	0.726876i
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.00264739	+	0.999996i	$0.500843\pi$
$101$	−10.0764	+	10.0764i	−1.00264	+	1.00264i	−0.999996	+	0.00264739i	$0.999157\pi$
$102$		0			0
$103$	−4.71475			−0.464558			−0.232279	−	0.972649i	$-0.574618\pi$
$103$	−4.71475			−0.464558			−0.232279	+	0.972649i	$0.574618\pi$
$104$	0.334108	−	1.63611i	0.0327620	−	0.160434i
$105$		0			0
$106$	−5.19654	+	2.55170i	−0.504733	+	0.247843i
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.954035	−	0.299696i	$-0.903115\pi$
$107$	−12.9687	−	12.9687i	−1.25373	−	1.25373i	−0.299696	−	0.954035i	$-0.596885\pi$
$108$		0			0
$109$	−0.382902	−	0.382902i	−0.0366754	−	0.0366754i	0.688531	−	0.725207i	$-0.258256\pi$
$109$	−0.382902	−	0.382902i	−0.0366754	−	0.0366754i	−0.725207	+	0.688531i	$0.758256\pi$
$110$	−7.26543	+	18.2689i	−0.692731	+	1.74187i
$111$		0			0
$112$	−2.61316	−	10.0241i	−0.246921	−	0.947187i
$113$			12.1861i			1.14637i	0.819424	+	0.573187i	$0.194293\pi$
$113$			12.1861i			1.14637i	−0.819424	+	0.573187i	$0.805707\pi$
$114$		0			0
$115$	0.421833	+	0.465874i	0.0393361	+	0.0434430i
$116$	1.34411	+	10.4843i	0.124797	+	0.973443i
$117$		0			0
$118$	−4.06141	−	8.27107i	−0.373883	−	0.761414i
$119$		−	11.4058i		−	1.04557i
$120$		0			0
$121$		−	27.6538i		−	2.51398i
$122$	−0.379366	+	0.186283i	−0.0343462	+	0.0168653i
$123$		0			0
$124$	4.83051	+	3.73269i	0.433793	+	0.335206i
$125$	−8.98979	+	6.64708i	−0.804071	+	0.594533i
$126$		0			0
$127$		−	6.75303i		−	0.599234i	−0.954060	−	0.299617i	$-0.903141\pi$
$127$		−	6.75303i		−	0.599234i	0.954060	−	0.299617i	$-0.0968589\pi$
$128$	−8.41690	−	7.56014i	−0.743956	−	0.668228i
$129$		0			0
$130$	−0.689928	+	1.73482i	−0.0605107	+	0.152154i
$131$	−3.95303	−	3.95303i	−0.345378	−	0.345378i	0.513007	−	0.858385i	$-0.328532\pi$
$131$	−3.95303	−	3.95303i	−0.345378	−	0.345378i	−0.858385	+	0.513007i	$0.828532\pi$
$132$		0			0
$133$	11.7494	+	11.7494i	1.01880	+	1.01880i
$134$	−6.32183	−	12.8744i	−0.546123	−	1.11218i
$135$		0			0
$136$	−6.86786	−	10.3926i	−0.588914	−	0.891159i
$137$	5.19519			0.443855			0.221927	−	0.975063i	$-0.428765\pi$
$137$	5.19519			0.443855			0.221927	+	0.975063i	$0.428765\pi$
$138$		0			0
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	−0.664457	−	0.747327i	$-0.731337\pi$
$139$	0.977024	−	0.977024i	0.0828701	−	0.0828701i	0.747327	+	0.664457i	$0.231337\pi$
$140$	0.901717	+	11.5467i	0.0762090	+	0.975872i
$141$		0			0
$142$	21.3442	+	7.28580i	1.79117	+	0.611411i
$143$		−	3.67058i		−	0.306949i
$144$		0			0
$145$	0.585580	−	11.8032i	0.0486298	−	0.980204i
$146$	4.82722	−	14.1416i	0.399503	−	1.17037i
$147$		0			0
$148$	−1.89269	−	14.7633i	−0.155578	−	1.21354i
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	−0.997455	−	0.0713047i	$-0.977284\pi$
$149$	−11.3051	+	11.3051i	−0.926150	+	0.926150i	0.0713047	+	0.997455i	$0.477284\pi$
$150$		0			0
$151$			2.87287i			0.233791i	0.993144	+	0.116895i	$0.0372942\pi$
$151$			2.87287i			0.233791i	−0.993144	+	0.116895i	$0.962706\pi$
$152$	17.7804	+	3.63091i	1.44218	+	0.294506i
$153$		0			0
$154$	−10.0365	−	20.4393i	−0.808763	−	1.64705i
$155$	−4.58109	−	5.05937i	−0.367962	−	0.406378i
$156$		0			0
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	−0.897905	−	0.440189i	$-0.854911\pi$
$157$	−5.73516	+	5.73516i	−0.457716	+	0.457716i	0.440189	+	0.897905i	$0.354911\pi$
$158$	2.07370	−	6.07503i	0.164975	−	0.483304i
$159$		0			0
$160$	7.77429	+	9.97799i	0.614612	+	0.788830i
$161$	−0.727889			−0.0573657
$162$		0			0
$163$	−11.9561	+	11.9561i	−0.936474	+	0.936474i	−0.998099	−	0.0616255i	$-0.980372\pi$
$163$	−11.9561	+	11.9561i	−0.936474	+	0.936474i	0.0616255	+	0.998099i	$0.480372\pi$
$164$	−6.31637	+	8.17407i	−0.493226	+	0.638288i
$165$		0			0
$166$	4.02560	+	8.19815i	0.312447	+	0.636300i
$167$	9.23665			0.714754			0.357377	−	0.933960i	$-0.383671\pi$
$167$	9.23665			0.714754			0.357377	+	0.933960i	$0.383671\pi$
$168$		0			0
$169$			12.6514i			0.973188i
$170$	5.51165	+	12.7902i	0.422724	+	0.980963i
$171$		0			0
$172$	−0.960066	−	7.48871i	−0.0732044	−	0.571008i
$173$	2.36187	−	2.36187i	0.179570	−	0.179570i	−0.611598	−	0.791168i	$-0.709473\pi$
$173$	2.36187	−	2.36187i	0.179570	−	0.179570i	0.791168	+	0.611598i	$0.209473\pi$
$174$		0			0
$175$	1.28168	−	12.8853i	0.0968861	−	0.974036i
$176$	−21.4522	−	12.5803i	−1.61702	−	0.948277i
$177$		0			0
$178$	−13.7513	−	4.69397i	−1.03070	−	0.351828i
$179$	−9.27202	−	9.27202i	−0.693023	−	0.693023i	0.269873	−	0.962896i	$-0.413018\pi$
$179$	−9.27202	−	9.27202i	−0.693023	−	0.693023i	−0.962896	+	0.269873i	$0.913018\pi$
$180$		0			0
$181$	−10.5707	+	10.5707i	−0.785715	+	0.785715i	−0.980789	−	0.195074i	$-0.937505\pi$
$181$	−10.5707	+	10.5707i	−0.785715	+	0.785715i	0.195074	+	0.980789i	$0.437505\pi$
$182$	−0.953068	−	1.94093i	−0.0706461	−	0.143871i
$183$		0			0
$184$	−0.663229	+	0.438289i	−0.0488939	+	0.0323111i
$185$	−0.824577	+	16.6206i	−0.0606241	+	1.22197i
$186$		0			0
$187$	−19.3618	−	19.3618i	−1.41587	−	1.41587i
$188$	9.11308	−	11.7933i	0.664640	−	0.860116i
$189$		0			0
$190$	−18.8531	−	7.49777i	−1.36775	−	0.543945i
$191$	8.32988			0.602729			0.301364	−	0.953509i	$-0.402558\pi$
$191$	8.32988			0.602729			0.301364	+	0.953509i	$0.402558\pi$
$192$		0			0
$193$		−	5.73404i		−	0.412745i	−0.978473	−	0.206373i	$-0.933834\pi$
$193$		−	5.73404i		−	0.412745i	0.978473	−	0.206373i	$-0.0661659\pi$
$194$	9.07499	+	3.09772i	0.651546	+	0.222404i
$195$		0			0
$196$	0.463796	+	0.358390i	0.0331283	+	0.0255993i
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	0.582519	−	0.812817i	$-0.302067\pi$
$197$	−3.23239	−	3.23239i	−0.230298	−	0.230298i	−0.812817	+	0.582519i	$0.802067\pi$
$198$		0			0
$199$			19.0599i			1.35112i	0.737303	+	0.675562i	$0.236099\pi$
$199$			19.0599i			1.35112i	−0.737303	+	0.675562i	$0.763901\pi$
$200$	−6.59088	−	12.5124i	−0.466046	−	0.884761i
$201$		0			0
$202$	8.88272	+	18.0897i	0.624986	+	1.27279i
$203$	9.67824	+	9.67824i	0.679279	+	0.679279i
$204$		0			0
$205$	8.56134	−	7.75200i	0.597950	−	0.541423i
$206$	−2.15396	+	6.31016i	−0.150073	+	0.439650i
$207$		0			0
$208$	−2.03711	−	1.19463i	−0.141248	−	0.0828328i
$209$	39.8899			2.75924
$210$		0			0
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	0.843149	−	0.537680i	$-0.180699\pi$
$211$	4.43719	+	4.43719i	0.305469	+	0.305469i	−0.537680	+	0.843149i	$0.680699\pi$
$212$	1.04110	+	8.12075i	0.0715027	+	0.557735i
$213$		0			0
$214$	−23.2820	+	11.4323i	−1.59152	+	0.781498i
$215$	−0.418267	+	8.43078i	−0.0285256	+	0.574975i
$216$		0			0
$217$	7.90485			0.536616
$218$	−0.687402	+	0.337541i	−0.0465568	+	0.0228611i
$219$		0			0
$220$	21.1316	+	18.0702i	1.42469	+	1.21829i
$221$	−1.83860	−	1.83860i	−0.123678	−	0.123678i
$222$		0			0
$223$			5.10536i			0.341880i	0.985281	+	0.170940i	$0.0546805\pi$
$223$			5.10536i			0.341880i	−0.985281	+	0.170940i	$0.945320\pi$
$224$	−14.6100	−	1.08213i	−0.976169	−	0.0723031i
$225$		0			0
$226$	16.3098	+	5.56730i	1.08491	+	0.370331i
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	−1.00000		0.000680242i	$-0.999783\pi$
$227$	−15.0563	+	15.0563i	−0.999320	+	0.999320i	0.000680242		1.00000i	$0.499783\pi$
$228$		0			0
$229$	17.5250	−	17.5250i	1.15809	−	1.15809i	0.173200	−	0.984887i	$-0.444589\pi$
$229$	17.5250	−	17.5250i	1.15809	−	1.15809i	0.984887	−	0.173200i	$-0.0554108\pi$
$230$	0.816237	−	0.351739i	0.0538211	−	0.0231930i
$231$		0			0
$232$	14.6461	+	2.99087i	0.961565	+	0.196360i
$233$	9.15254			0.599603			0.299802	−	0.954002i	$-0.403080\pi$
$233$	9.15254			0.599603			0.299802	+	0.954002i	$0.403080\pi$
$234$		0			0
$235$	−12.3521	+	11.1844i	−0.805759	+	0.729588i
$236$	−12.9254	+	1.65706i	−0.841371	+	0.107865i
$237$		0			0
$238$	−15.2654	−	5.21081i	−0.989509	−	0.337766i
$239$	12.9198			0.835713			0.417857	−	0.908513i	$-0.362781\pi$
$239$	12.9198			0.835713			0.417857	+	0.908513i	$0.362781\pi$
$240$		0			0
$241$	10.7071			0.689703			0.344851	−	0.938657i	$-0.387929\pi$
$241$	10.7071			0.689703			0.344851	+	0.938657i	$0.387929\pi$
$242$	−37.0115	−	12.6338i	−2.37919	−	0.812131i
$243$		0			0
$244$	0.0760037	+	0.592844i	0.00486564	+	0.0379530i
$245$	−0.439847	−	0.485769i	−0.0281008	−	0.0310346i
$246$		0			0
$247$	3.78796			0.241022
$248$	7.20264	−	4.75980i	0.457368	−	0.302248i
$249$		0			0
$250$	4.78933	+	15.0686i	0.302904	+	0.953021i
$251$	4.48257	−	4.48257i	0.282937	−	0.282937i	−0.551342	−	0.834279i	$-0.685884\pi$
$251$	4.48257	−	4.48257i	0.282937	−	0.282937i	0.834279	+	0.551342i	$0.185884\pi$
$252$		0			0
$253$	−1.23562	+	1.23562i	−0.0776827	+	0.0776827i
$254$	−9.03817	−	3.08516i	−0.567105	−	0.193580i
$255$		0			0
$256$	−13.9637	+	7.81119i	−0.872732	+	0.488199i
$257$		−	16.9307i		−	1.05610i	−0.849212	−	0.528052i	$-0.822922\pi$
$257$		−	16.9307i		−	1.05610i	0.849212	−	0.528052i	$-0.177078\pi$
$258$		0			0
$259$	−13.6283	−	13.6283i	−0.846821	−	0.846821i
$260$	2.00666	+	1.71595i	0.124448	+	0.106419i
$261$		0			0
$262$	−7.09666	+	3.48473i	−0.438433	+	0.215287i
$263$	−2.07893			−0.128192			−0.0640962	−	0.997944i	$-0.520416\pi$
$263$	−2.07893			−0.128192			−0.0640962	+	0.997944i	$0.520416\pi$
$264$		0			0
$265$	0.453569	−	9.14234i	0.0278625	−	0.561609i
$266$	21.0930	−	10.3574i	1.29329	−	0.635055i
$267$		0			0
$268$	−20.1191	+	2.57931i	−1.22897	+	0.157556i
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	0.999801	−	0.0199408i	$-0.00634778\pi$
$269$	16.0709	+	16.0709i	0.979860	+	0.979860i	−0.0199408	+	0.999801i	$0.506348\pi$
$270$		0			0
$271$	4.18571			0.254264			0.127132	−	0.991886i	$-0.459423\pi$
$271$	4.18571			0.254264			0.127132	+	0.991886i	$0.459423\pi$
$272$	−17.0470	+	4.44394i	−1.03362	+	0.269454i
$273$		0			0
$274$	2.37345	−	6.95318i	0.143385	−	0.420057i
$275$	−19.6975	−	24.0489i	−1.18781	−	1.45021i
$276$		0			0
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	0.0480985	−	0.998843i	$-0.484684\pi$
$277$	−15.8235	−	15.8235i	−0.950744	−	0.950744i	−0.998843	+	0.0480985i	$0.984684\pi$
$278$	−0.861278	−	1.75400i	−0.0516560	−	0.105198i
$279$		0			0
$280$	15.8659	+	4.06831i	0.948168	+	0.243128i
$281$		−	12.6546i		−	0.754911i	−0.926028	−	0.377455i	$-0.876799\pi$
$281$		−	12.6546i		−	0.754911i	0.926028	−	0.377455i	$-0.123201\pi$
$282$		0			0
$283$	1.54865	+	1.54865i	0.0920579	+	0.0920579i	0.751636	−	0.659578i	$-0.229265\pi$
$283$	1.54865	+	1.54865i	0.0920579	+	0.0920579i	−0.659578	+	0.751636i	$0.729265\pi$
$284$	19.5025	−	25.2383i	1.15726	−	1.49762i
$285$		0			0
$286$	−4.91266	−	1.67692i	−0.290492	−	0.0991586i
$287$			13.3764i			0.789583i
$288$		0			0
$289$	−2.39672			−0.140983
$290$	−15.5298	−	6.17610i	−0.911940	−	0.362673i
$291$		0			0
$292$	−16.7217	−	12.9214i	−0.978562	−	0.756166i
$293$	21.2881	+	21.2881i	1.24366	+	1.24366i	0.958470	+	0.285194i	$0.0920582\pi$
$293$	21.2881	+	21.2881i	1.24366	+	1.24366i	0.285194	+	0.958470i	$0.407942\pi$
$294$		0			0
$295$	14.5514	+	0.721922i	0.847215	+	0.0420319i
$296$	−20.6237	−	4.21156i	−1.19873	−	0.244792i
$297$		0			0
$298$	9.96582	+	20.2954i	0.577304	+	1.17568i
$299$	−0.117335	+	0.117335i	−0.00678565	+	0.00678565i
$300$		0			0
$301$	−6.91296	−	6.91296i	−0.398456	−	0.398456i
$302$	3.84501	+	1.31249i	0.221256	+	0.0755251i
$303$		0			0
$304$	12.9826	−	22.1382i	0.744604	−	1.26971i
$305$	0.0331122	−	0.667424i	0.00189600	−	0.0382166i
$306$		0			0
$307$	12.2344	−	12.2344i	0.698255	−	0.698255i	−0.265779	−	0.964034i	$-0.585629\pi$
$307$	12.2344	−	12.2344i	0.698255	−	0.698255i	0.964034	+	0.265779i	$0.0856291\pi$
$308$	−31.9410	+	4.09489i	−1.82001	+	0.233328i
$309$		0			0
$310$	−8.86429	+	3.81987i	−0.503458	+	0.216954i
$311$			19.4874i			1.10503i	0.833503	+	0.552515i	$0.186332\pi$
$311$			19.4874i			1.10503i	−0.833503	+	0.552515i	$0.813668\pi$
$312$		0			0
$313$	−9.73432			−0.550217			−0.275108	−	0.961413i	$-0.588714\pi$
$313$	−9.73432			−0.550217			−0.275108	+	0.961413i	$0.588714\pi$
$314$	5.05573	+	10.2960i	0.285311	+	0.581037i
$315$		0			0
$316$	−7.18337	−	5.55083i	−0.404096	−	0.312258i
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	−0.903699	−	0.428168i	$-0.859159\pi$
$317$	−8.46658	+	8.46658i	−0.475530	+	0.475530i	0.428168	+	0.903699i	$0.359159\pi$
$318$		0			0
$319$	32.8583			1.83971
$320$	16.9062	−	5.84652i	0.945083	−	0.326830i
$321$		0			0
$322$	−0.332540	+	0.974199i	−0.0185317	+	0.0542900i
$323$	19.9809	−	19.9809i	1.11177	−	1.11177i
$324$		0			0
$325$	−1.87049	−	2.28370i	−0.103756	−	0.126677i
$326$	10.5397	+	21.4641i	0.583739	+	1.18879i
$327$		0			0
$328$	8.05442	+	12.1881i	0.444731	+	0.672977i
$329$		−	19.2991i		−	1.06399i
$330$		0			0
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	−0.483975	−	0.875082i	$-0.660808\pi$
$331$	7.11555	−	7.11555i	0.391106	−	0.391106i	0.875082	+	0.483975i	$0.160808\pi$
$332$	12.8114	−	1.64245i	0.703119	−	0.0901411i
$333$		0			0
$334$	4.21982	−	12.3622i	0.230898	−	0.676431i
$335$	22.6501	+	1.12371i	1.23751	+	0.0613951i
$336$		0			0
$337$			15.8355i			0.862613i	0.902205	+	0.431307i	$0.141947\pi$
$337$			15.8355i			0.862613i	−0.902205	+	0.431307i	$0.858053\pi$
$338$	16.9325	+	5.77988i	0.921009	+	0.314384i
$339$		0			0
$340$	19.6363	−	1.53346i	1.06493	−	0.0831635i
$341$	13.4188	−	13.4188i	0.726667	−	0.726667i
$342$		0			0
$343$	18.8874			1.01982
$344$	−10.4614	−	2.13632i	−0.564041	−	0.115182i
$345$		0			0
$346$	−2.08207	−	4.24014i	−0.111933	−	0.227951i
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	0.912541	−	0.408986i	$-0.134117\pi$
$347$	9.38020	+	9.38020i	0.503555	+	0.503555i	−0.408986	+	0.912541i	$0.634117\pi$
$348$		0			0
$349$	0.479184	+	0.479184i	0.0256501	+	0.0256501i	0.719816	−	0.694165i	$-0.244226\pi$
$349$	0.479184	+	0.479184i	0.0256501	+	0.0256501i	−0.694165	+	0.719816i	$0.744226\pi$
$350$	−16.6600	−	7.60210i	−0.890513	−	0.406350i
$351$		0			0
$352$	−26.6379	+	22.9640i	−1.41980	+	1.22398i
$353$		−	8.95345i		−	0.476544i	−0.971198	−	0.238272i	$-0.923419\pi$
$353$		−	8.95345i		−	0.476544i	0.971198	−	0.238272i	$-0.0765810\pi$
$354$		0			0
$355$	−26.4340	+	23.9351i	−1.40297	+	1.27034i
$356$	−12.5647	+	16.2601i	−0.665928	+	0.861783i
$357$		0			0
$358$	−16.6455	+	8.17359i	−0.879744	+	0.431988i
$359$			3.47704i			0.183511i	0.995782	+	0.0917556i	$0.0292478\pi$
$359$			3.47704i			0.183511i	−0.995782	+	0.0917556i	$0.970752\pi$
$360$		0			0
$361$			22.1655i			1.16661i
$362$	9.31843	+	18.9770i	0.489766	+	0.997409i
$363$		0			0
$364$	−3.03313	+	0.388853i	−0.158979	+	0.0203814i
$365$	15.8582	+	17.5139i	0.830058	+	0.916719i
$366$		0			0
$367$			15.1190i			0.789206i	0.918852	+	0.394603i	$0.129118\pi$
$367$			15.1190i			0.789206i	−0.918852	+	0.394603i	$0.870882\pi$
$368$	0.283601	+	1.08789i	0.0147837	+	0.0567103i
$369$		0			0
$370$	21.8680	+	8.69679i	1.13687	+	0.452125i
$371$	7.49640	+	7.49640i	0.389194	+	0.389194i
$372$		0			0
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	0.999909	−	0.0135107i	$-0.00430073\pi$
$373$	19.0505	+	19.0505i	0.986398	+	0.986398i	−0.0135107	+	0.999909i	$0.504301\pi$
$374$	−34.7591	+	17.0680i	−1.79735	+	0.882567i
$375$		0			0
$376$	−11.6207	−	17.5847i	−0.599291	−	0.906861i
$377$	3.12024			0.160701
$378$		0			0
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	−0.610660	−	0.791893i	$-0.709096\pi$
$379$	3.52823	−	3.52823i	0.181233	−	0.181233i	0.791893	+	0.610660i	$0.209096\pi$
$380$	−18.6481	+	21.8074i	−0.956625	+	1.11869i
$381$		0			0
$382$	3.80555	−	11.1486i	0.194709	−	0.570413i
$383$		−	3.20268i		−	0.163649i	−0.996647	−	0.0818246i	$-0.973925\pi$
$383$		−	3.20268i		−	0.163649i	0.996647	−	0.0818246i	$-0.0260747\pi$
$384$		0			0
$385$	35.9591	+	1.78400i	1.83265	+	0.0909211i
$386$	−7.67438	−	2.61963i	−0.390615	−	0.133336i
$387$		0			0
$388$	8.29192	−	10.7306i	0.420958	−	0.544766i
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	−0.991324	−	0.131441i	$-0.958039\pi$
$389$	−16.9595	+	16.9595i	−0.859882	+	0.859882i	0.131441	+	0.991324i	$0.458039\pi$
$390$		0			0
$391$			1.23785i			0.0626007i
$392$	0.691553	−	0.457006i	0.0349287	−	0.0230823i
$393$		0			0
$394$	−5.80292	+	2.84945i	−0.292347	+	0.143553i
$395$	6.81246	+	7.52370i	0.342772	+	0.378558i
$396$		0			0
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	−0.982294	−	0.187348i	$-0.940011\pi$
$397$	−15.8392	+	15.8392i	−0.794946	+	0.794946i	0.187348	+	0.982294i	$0.440011\pi$
$398$	25.5096	+	8.70764i	1.27868	+	0.436475i
$399$		0			0
$400$	−19.7575	+	3.10480i	−0.987877	+	0.155240i
$401$	10.8608			0.542364			0.271182	−	0.962528i	$-0.412586\pi$
$401$	10.8608			0.542364			0.271182	+	0.962528i	$0.412586\pi$
$402$		0			0
$403$	1.27425	−	1.27425i	0.0634750	−	0.0634750i
$404$	28.2691	−	3.62416i	1.40644	−	0.180308i
$405$		0			0
$406$	17.3748	−	8.53169i	0.862297	−	0.423421i
$407$	−46.2690			−2.29347
$408$		0			0
$409$		−	12.5363i		−	0.619880i	−0.950756	−	0.309940i	$-0.899691\pi$
$409$		−	12.5363i		−	0.619880i	0.950756	−	0.309940i	$-0.100309\pi$
$410$	−6.46389	−	14.9999i	−0.319229	−	0.740794i
$411$		0			0
$412$	7.46140	+	5.76566i	0.367597	+	0.284054i
$413$	−11.9316	+	11.9316i	−0.587118	+	0.587118i
$414$		0			0
$415$	−14.4231	−	0.715558i	−0.708002	−	0.0351253i
$416$	−2.52954	+	2.18067i	−0.124021	+	0.106916i
$417$		0			0
$418$	18.2239	−	53.3882i	0.891361	−	2.61130i
$419$	21.6745	+	21.6745i	1.05887	+	1.05887i	0.998155	+	0.0607123i	$0.0193372\pi$
$419$	21.6745	+	21.6745i	1.05887	+	1.05887i	0.0607123	+	0.998155i	$0.480663\pi$
$420$		0			0
$421$	−9.02933	+	9.02933i	−0.440063	+	0.440063i	−0.892033	−	0.451970i	$-0.850721\pi$
$421$	−9.02933	+	9.02933i	−0.440063	+	0.440063i	0.451970	+	0.892033i	$0.350721\pi$
$422$	7.96585	−	3.91153i	0.387771	−	0.190410i
$423$		0			0
$424$	11.3443	+	2.31662i	0.550930	+	0.112505i
$425$	−21.9127	−	2.17963i	−1.06292	−	0.105727i
$426$		0			0
$427$	0.547265	+	0.547265i	0.0264840	+	0.0264840i
$428$	4.66440	+	36.3832i	0.225462	+	1.75865i
$429$		0			0
$430$	11.0926	+	4.41145i	0.534931	+	0.212739i
$431$	22.1994			1.06931			0.534653	−	0.845072i	$-0.320442\pi$
$431$	22.1994			1.06931			0.534653	+	0.845072i	$0.320442\pi$
$432$		0			0
$433$			31.1117i			1.49513i	0.664187	+	0.747566i	$0.268778\pi$
$433$			31.1117i			1.49513i	−0.664187	+	0.747566i	$0.731222\pi$
$434$	3.61137	−	10.5798i	0.173351	−	0.507844i
$435$		0			0
$436$	0.137717	+	1.07422i	0.00659544	+	0.0514457i
$437$	−1.27513	−	1.27513i	−0.0609979	−	0.0609979i
$438$		0			0
$439$			0.460911i			0.0219981i	0.999940	+	0.0109990i	$0.00350117\pi$
$439$			0.460911i			0.0219981i	−0.999940	+	0.0109990i	$0.996499\pi$
$440$	33.8390	−	20.0268i	1.61321	−	0.954740i
$441$		0			0
$442$	−3.30074	+	1.62079i	−0.157000	+	0.0770930i
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	0.635247	−	0.772309i	$-0.280898\pi$
$443$	−2.88482	−	2.88482i	−0.137062	−	0.137062i	−0.772309	+	0.635247i	$0.780898\pi$
$444$		0			0
$445$	17.0304	−	15.4205i	0.807321	−	0.731001i
$446$	6.83295	+	2.33241i	0.323550	+	0.110443i
$447$		0			0
$448$	−8.12295	+	19.0594i	−0.383774	+	0.900473i
$449$	−3.02196			−0.142615			−0.0713075	−	0.997454i	$-0.522717\pi$
$449$	−3.02196			−0.142615			−0.0713075	+	0.997454i	$0.522717\pi$
$450$		0			0
$451$	22.7069	+	22.7069i	1.06923	+	1.06923i
$452$	14.9024	−	19.2854i	0.700951	−	0.907107i
$453$		0			0
$454$	13.2726	+	27.0297i	0.622914	+	1.26857i
$455$	3.41469	+	0.169409i	0.160083	+	0.00794204i
$456$		0			0
$457$	4.69013			0.219395			0.109698	−	0.993965i	$-0.465012\pi$
$457$	4.69013			0.219395			0.109698	+	0.993965i	$0.465012\pi$
$458$	−15.4489	−	31.4617i	−0.721879	−	1.47011i
$459$		0			0
$460$	−0.0978615	−	1.25314i	−0.00456281	−	0.0584278i
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	0.0248664	−	0.999691i	$-0.492084\pi$
$461$	−20.9304	−	20.9304i	−0.974824	−	0.974824i	−0.999691	+	0.0248664i	$0.992084\pi$
$462$		0			0
$463$			25.5190i			1.18597i	0.805215	+	0.592983i	$0.202050\pi$
$463$			25.5190i			1.18597i	−0.805215	+	0.592983i	$0.797950\pi$
$464$	10.6941	−	18.2358i	0.496462	−	0.846576i
$465$		0			0
$466$	4.18139	−	12.2497i	0.193699	−	0.567454i
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	−0.0456227	−	0.998959i	$-0.514527\pi$
$467$	20.6018	−	20.6018i	0.953336	−	0.953336i	0.998959	+	0.0456227i	$0.0145272\pi$
$468$		0			0
$469$	−18.5723	+	18.5723i	−0.857590	+	0.857590i
$470$	9.32592	+	21.6415i	0.430173	+	0.998247i
$471$		0			0
$472$	−3.68725	+	18.0562i	−0.169719	+	0.831105i
$473$	−23.4700			−1.07915
$474$		0			0
$475$	24.8180	−	20.3275i	1.13873	−	0.932687i
$476$	−13.9482	+	18.0504i	−0.639313	+	0.827341i
$477$		0			0
$478$	5.90249	−	17.2917i	0.269973	−	0.790905i
$479$	−30.6830			−1.40194			−0.700972	−	0.713189i	$-0.747250\pi$
$479$	−30.6830			−1.40194			−0.700972	+	0.713189i	$0.747250\pi$
$480$		0			0
$481$	−4.39372			−0.200337
$482$	4.89158	−	14.3302i	0.222806	−	0.652723i
$483$		0			0
$484$	−33.8178	+	43.7640i	−1.53717	+	1.98927i
$485$	−11.2390	+	10.1766i	−0.510338	+	0.462094i
$486$		0			0
$487$	4.53105			0.205322			0.102661	−	0.994716i	$-0.467264\pi$
$487$	4.53105			0.205322			0.102661	+	0.994716i	$0.467264\pi$
$488$	0.828178	+	0.169122i	0.0374899	+	0.00765578i
$489$		0			0
$490$	−0.851094	+	0.366760i	−0.0384485	+	0.0165685i
$491$	−2.06787	+	2.06787i	−0.0933215	+	0.0933215i	−0.752226	−	0.658905i	$-0.771020\pi$
$491$	−2.06787	+	2.06787i	−0.0933215	+	0.0933215i	0.658905	+	0.752226i	$0.271020\pi$
$492$		0			0
$493$	16.4588	−	16.4588i	0.741268	−	0.741268i
$494$	1.73055	−	5.06976i	0.0778612	−	0.228099i
$495$		0			0
$496$	−3.07989	−	11.8145i	−0.138291	−	0.530485i
$497$		−	41.3010i		−	1.85260i
$498$		0			0
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.970549	−	0.240906i	$-0.922556\pi$
$499$	−27.0618	−	27.0618i	−1.21145	−	1.21145i	−0.240906	−	0.970549i	$-0.577444\pi$
$500$	22.3557	+	0.474177i	0.999775	+	0.0212058i
$501$		0			0
$502$	−3.95153	−	8.04730i	−0.176365	−	0.359169i
$503$	8.42170			0.375505			0.187753	−	0.982216i	$-0.439880\pi$
$503$	8.42170			0.375505			0.187753	+	0.982216i	$0.439880\pi$
$504$		0			0
$505$	−31.8254	−	1.57892i	−1.41621	−	0.0702609i
$506$	1.08924	+	2.21824i	0.0484225	+	0.0986126i
$507$		0			0
$508$	−8.25828	+	10.6871i	−0.366402	+	0.474164i
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.999999	−	0.00112047i	$-0.999643\pi$
$509$	−22.5863	−	22.5863i	−1.00112	−	1.00112i	−0.00112047	−	0.999999i	$-0.500357\pi$
$510$		0			0
$511$	−27.3640			−1.21051
$512$	4.07501	+	22.2575i	0.180092	+	0.983650i
$513$		0			0
$514$	−22.6598	−	7.73486i	−0.999480	−	0.341170i
$515$	−7.07612	−	7.81490i	−0.311811	−	0.344365i
$516$		0			0
$517$	−32.7609	−	32.7609i	−1.44082	−	1.44082i
$518$	−24.4661	+	12.0138i	−1.07498	+	0.527855i
$519$		0			0
$520$	3.21337	−	1.90175i	0.140915	−	0.0833974i
$521$		−	30.9260i		−	1.35489i	−0.735572	−	0.677447i	$-0.763086\pi$
$521$		−	30.9260i		−	1.35489i	0.735572	−	0.677447i	$-0.236914\pi$
$522$		0			0
$523$	26.4425	+	26.4425i	1.15625	+	1.15625i	0.985276	+	0.170974i	$0.0546913\pi$
$523$	26.4425	+	26.4425i	1.15625	+	1.15625i	0.170974	+	0.985276i	$0.445309\pi$
$524$	1.42177	+	11.0901i	0.0621104	+	0.484473i
$525$		0			0
$526$	−0.949771	+	2.78242i	−0.0414120	+	0.121319i
$527$		−	13.4430i		−	0.585585i
$528$		0			0
$529$	−22.9210			−0.996565
$530$	−12.0288	−	4.78378i	−0.522497	−	0.207794i
$531$		0			0
$532$	−4.22584	−	32.9624i	−0.183214	−	1.42910i
$533$	2.15626	+	2.15626i	0.0933978	+	0.0933978i
$534$		0			0
$535$	2.03211	−	40.9602i	0.0878560	−	1.77086i
$536$	−5.73942	+	28.1056i	−0.247905	+	1.21398i
$537$		0			0
$538$	28.8512	−	14.1670i	1.24386	−	0.610784i
$539$	1.28839	−	1.28839i	0.0554947	−	0.0554947i
$540$		0			0
$541$	21.6730	+	21.6730i	0.931794	+	0.931794i	0.997818	−	0.0660242i	$-0.0210315\pi$
$541$	21.6730	+	21.6730i	0.931794	+	0.931794i	−0.0660242	+	0.997818i	$0.521031\pi$
$542$	1.91227	−	5.60211i	0.0821389	−	0.240631i
$543$		0			0
$544$	−1.84028	+	24.8457i	−0.0789012	+	1.06525i
$545$	0.0599984	−	1.20935i	0.00257005	−	0.0518031i
$546$		0			0
$547$	−2.92159	+	2.92159i	−0.124918	+	0.124918i	−0.766802	−	0.641884i	$-0.778153\pi$
$547$	−2.92159	+	2.92159i	−0.124918	+	0.124918i	0.641884	+	0.766802i	$0.278153\pi$
$548$	−8.22173	−	6.35320i	−0.351215	−	0.271395i
$549$		0			0
$550$	−41.1858	+	15.3761i	−1.75617	+	0.655638i
$551$			33.9091i			1.44458i
$552$		0			0
$553$	−11.7552			−0.499880
$554$	−28.4071	+	13.9490i	−1.20690	+	0.592635i
$555$		0			0
$556$	−2.74101	+	0.351402i	−0.116245	+	0.0149028i
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.0861022	+	0.996286i	$0.527441\pi$
$557$	−25.5453	+	25.5453i	−1.08239	+	1.08239i	−0.996286	+	0.0861022i	$0.972559\pi$
$558$		0			0
$559$	−2.22872			−0.0942648
$560$	12.6934	−	19.3761i	0.536394	−	0.818789i
$561$		0			0
$562$	−16.9368	−	5.78133i	−0.714435	−	0.243871i
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	−0.908223	−	0.418487i	$-0.862561\pi$
$563$	−11.6203	+	11.6203i	−0.489736	+	0.489736i	0.418487	+	0.908223i	$0.362561\pi$
$564$		0			0
$565$	−20.1990	+	18.2895i	−0.849780	+	0.769447i
$566$	2.78021	−	1.36519i	0.116861	−	0.0573832i
$567$		0			0
$568$	−24.8689	−	37.6321i	−1.04347	−	1.57901i
$569$			13.3498i			0.559654i	0.960050	+	0.279827i	$0.0902771\pi$
$569$			13.3498i			0.559654i	−0.960050	+	0.279827i	$0.909723\pi$
$570$		0			0
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	−0.999893	−	0.0146492i	$-0.995337\pi$
$571$	−23.5430	+	23.5430i	−0.985244	+	0.985244i	0.0146492	+	0.999893i	$0.495337\pi$
$572$	−4.48875	+	5.80893i	−0.187684	+	0.242884i
$573$		0			0
$574$	17.9028	+	6.11108i	0.747248	+	0.255071i
$575$	−0.139098	+	1.39841i	−0.00580080	+	0.0583179i
$576$		0			0
$577$		−	34.7117i		−	1.44507i	−0.691335	−	0.722534i	$-0.742977\pi$
$577$		−	34.7117i		−	1.44507i	0.691335	−	0.722534i	$-0.257023\pi$
$578$	−1.09495	+	3.20774i	−0.0455441	+	0.133424i
$579$		0			0
$580$	−15.3609	+	17.9633i	−0.637826	+	0.745884i
$581$	11.8265	−	11.8265i	0.490644	−	0.490644i
$582$		0			0
$583$	25.4508			1.05407
$584$	−24.9332	+	16.4769i	−1.03174	+	0.681818i
$585$		0			0
$586$	38.2173	−	18.7662i	1.57874	−	0.775223i
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.993140	+	0.116931i	$0.0373057\pi$
$587$	26.8949	+	26.8949i	1.11007	+	1.11007i	0.116931	+	0.993140i	$0.462694\pi$
$588$		0			0
$589$	13.8479	+	13.8479i	0.570592	+	0.570592i
$590$	7.61410	−	19.1456i	0.313467	−	0.788212i
$591$		0			0
$592$	−15.0588	+	25.6785i	−0.618912	+	1.05538i
$593$			8.25028i			0.338798i	0.985548	+	0.169399i	$0.0541827\pi$
$593$			8.25028i			0.338798i	−0.985548	+	0.169399i	$0.945817\pi$
$594$		0			0
$595$	18.9056	−	17.1184i	0.775055	−	0.701786i
$596$	31.7161	−	4.06606i	1.29914	−	0.166552i
$597$		0			0
$598$	0.103434	+	0.210645i	0.00422975	+	0.00861390i
$599$		−	19.6734i		−	0.803832i	−0.915677	−	0.401916i	$-0.868344\pi$
$599$		−	19.6734i		−	0.803832i	0.915677	−	0.401916i	$-0.131656\pi$
$600$		0			0
$601$		−	30.0313i		−	1.22500i	−0.790470	−	0.612501i	$-0.790164\pi$
$601$		−	30.0313i		−	1.22500i	0.790470	−	0.612501i	$-0.209836\pi$
$602$	−12.4104	+	6.09400i	−0.505812	+	0.248373i
$603$		0			0
$604$	3.51323	−	4.54651i	0.142951	−	0.184995i
$605$	45.8374	−	41.5042i	1.86355	−	1.68739i
$606$		0			0
$607$			5.52944i			0.224433i	0.993684	+	0.112217i	$0.0357950\pi$
$607$			5.52944i			0.224433i	−0.993684	+	0.112217i	$0.964205\pi$
$608$	−23.6983	−	27.4897i	−0.961095	−	1.11486i
$609$		0			0
$610$	−0.878145	−	0.349233i	−0.0355550	−	0.0141400i
$611$	−3.11098	−	3.11098i	−0.125857	−	0.125857i
$612$		0			0
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.982044	−	0.188653i	$-0.939588\pi$
$613$	−28.9851	−	28.9851i	−1.17070	−	1.17070i	−0.188653	−	0.982044i	$-0.560412\pi$
$614$	−10.7850	−	21.9638i	−0.435249	−	0.886385i
$615$		0			0
$616$	−9.11185	+	44.6202i	−0.367127	+	1.79780i
$617$	26.5578			1.06918			0.534588	−	0.845113i	$-0.320467\pi$
$617$	26.5578			1.06918			0.534588	+	0.845113i	$0.320467\pi$
$618$		0			0
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	−0.578234	−	0.815871i	$-0.696258\pi$
$619$	5.91235	−	5.91235i	0.237638	−	0.237638i	0.815871	+	0.578234i	$0.196258\pi$
$620$	1.06277	+	13.6090i	0.0426819	+	0.546550i
$621$		0			0
$622$	26.0817	+	8.90293i	1.04578	+	0.356975i
$623$			26.6087i			1.06605i
$624$		0			0
$625$	−24.5101	−	4.92471i	−0.980406	−	0.196988i
$626$	−4.44718	+	13.0283i	−0.177745	+	0.520716i
$627$		0			0
$628$	16.0898	−	2.06274i	0.642053	−	0.0823124i
$629$	−23.1763	+	23.1763i	−0.924098	+	0.924098i
$630$		0			0
$631$			37.6881i			1.50034i	0.661246	+	0.750169i	$0.270028\pi$
$631$			37.6881i			1.50034i	−0.661246	+	0.750169i	$0.729972\pi$
$632$	−10.7109	+	7.07822i	−0.426058	+	0.281556i
$633$		0			0
$634$	7.46357	+	15.1996i	0.296416	+	0.603652i
$635$	11.1934	−	10.1353i	0.444198	−	0.402206i
$636$		0			0
$637$	0.122346	−	0.122346i	0.00484751	−	0.00484751i
$638$	15.0115	−	43.9772i	0.594311	−	1.74107i
$639$		0			0
$640$	−0.101240	−	25.2980i	−0.00400188	−	0.999992i
$641$	−36.5113			−1.44211			−0.721055	−	0.692878i	$-0.756343\pi$
$641$	−36.5113			−1.44211			−0.721055	+	0.692878i	$0.756343\pi$
$642$		0			0
$643$	12.1973	−	12.1973i	0.481014	−	0.481014i	−0.424441	−	0.905455i	$-0.639529\pi$
$643$	12.1973	−	12.1973i	0.481014	−	0.481014i	0.905455	+	0.424441i	$0.139529\pi$
$644$	1.15193	+	0.890136i	0.0453925	+	0.0350763i
$645$		0			0
$646$	−17.6139	−	35.8707i	−0.693008	−	1.41131i
$647$	16.5371			0.650142			0.325071	−	0.945690i	$-0.394612\pi$
$647$	16.5371			0.650142			0.325071	+	0.945690i	$0.394612\pi$
$648$		0			0
$649$			40.5088i			1.59011i
$650$	−3.91102	+	1.46012i	−0.153403	+	0.0572705i
$651$		0			0
$652$	33.5424	−	4.30020i	1.31362	−	0.168409i
$653$	−2.73228	+	2.73228i	−0.106923	+	0.106923i	−0.758544	−	0.651622i	$-0.774089\pi$
$653$	−2.73228	+	2.73228i	−0.106923	+	0.106923i	0.651622	+	0.758544i	$0.274089\pi$
$654$		0			0
$655$	0.619416	−	12.4852i	0.0242026	−	0.487838i
$656$	19.9922	−	5.21172i	0.780562	−	0.203484i
$657$		0			0
$658$	−25.8296	−	8.81688i	−1.00694	−	0.343718i
$659$	−14.1442	−	14.1442i	−0.550982	−	0.550982i	0.375743	−	0.926724i	$-0.377388\pi$
$659$	−14.1442	−	14.1442i	−0.550982	−	0.550982i	−0.926724	+	0.375743i	$0.877388\pi$
$660$		0			0
$661$	14.2173	−	14.2173i	0.552991	−	0.552991i	−0.374312	−	0.927303i	$-0.622121\pi$
$661$	14.2173	−	14.2173i	0.552991	−	0.552991i	0.927303	+	0.374312i	$0.122121\pi$
$662$	−6.27259	−	12.7742i	−0.243791	−	0.496481i
$663$		0			0
$664$	3.65474	−	17.8970i	0.141831	−	0.694539i
$665$	−1.84105	+	37.1091i	−0.0713929	+	1.43903i
$666$		0			0
$667$	−1.05036	−	1.05036i	−0.0406701	−	0.0406701i
$668$	−14.6176	−	11.2955i	−0.565572	−	0.437036i
$669$		0			0
$670$	11.8518	−	29.8013i	0.457875	−	1.15132i
$671$	1.85800			0.0717274
$672$		0			0
$673$			17.6236i			0.679341i	0.940545	+	0.339670i	$0.110316\pi$
$673$			17.6236i			0.679341i	−0.940545	+	0.339670i	$0.889684\pi$
$674$	21.1940	+	7.23453i	0.816363	+	0.278663i
$675$		0			0
$676$	15.4714	−	20.0217i	0.595056	−	0.770067i
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.936525	−	0.350601i	$-0.885977\pi$
$677$	−33.4900	−	33.4900i	−1.28713	−	1.28713i	−0.350601	−	0.936525i	$-0.614023\pi$
$678$		0			0
$679$		−	17.5601i		−	0.673893i
$680$	6.91857	−	26.9815i	0.265315	−	1.03469i
$681$		0			0
$682$	−11.8291	−	24.0899i	−0.452959	−	0.922452i
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	0.695476	−	0.718549i	$-0.255193\pi$
$683$	−0.602993	−	0.602993i	−0.0230729	−	0.0230729i	−0.718549	+	0.695476i	$0.755193\pi$
$684$		0			0
$685$	7.79720	+	8.61125i	0.297916	+	0.329019i
$686$	8.62881	−	25.2787i	0.329450	−	0.965144i
$687$		0			0
$688$	−7.63857	+	13.0254i	−0.291218	+	0.496590i
$689$	2.41682			0.0920736
$690$		0			0
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	0.386192	−	0.922418i	$-0.373790\pi$
$691$	−14.0957	−	14.0957i	−0.536226	−	0.536226i	−0.922418	+	0.386192i	$0.873790\pi$
$692$	−6.62616	+	0.849486i	−0.251889	+	0.0322926i
$693$		0			0
$694$	16.8397	−	8.26895i	0.639228	−	0.313885i
$695$	3.08582	+	0.153094i	0.117052	+	0.00580717i
$696$		0			0
$697$	22.7479			0.861637
$698$	0.860252	−	0.422416i	0.0325610	−	0.0159887i
$699$		0			0
$700$	−17.7858	+	18.8245i	−0.672239	+	0.711497i
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	0.0928282	−	0.995682i	$-0.470409\pi$
$701$	−23.9043	−	23.9043i	−0.902854	−	0.902854i	−0.995682	+	0.0928282i	$0.970409\pi$
$702$		0			0
$703$		−	47.7487i		−	1.80087i
$704$	18.5650	+	46.1431i	0.699696	+	1.73908i
$705$		0			0
$706$	−11.9832	−	4.09043i	−0.450993	−	0.153945i
$707$	26.0957	−	26.0957i	0.981431	−	0.981431i
$708$		0			0
$709$	30.0855	−	30.0855i	1.12989	−	1.12989i	0.139691	−	0.990195i	$-0.455389\pi$
$709$	30.0855	−	30.0855i	1.12989	−	1.12989i	0.990195	−	0.139691i	$-0.0446110\pi$
$710$	19.9580	+	46.3139i	0.749009	+	1.73813i
$711$		0			0
$712$	16.0221	+	24.2450i	0.600452	+	0.908618i
$713$	−0.857896			−0.0321285
$714$		0			0
$715$	6.08415	−	5.50899i	0.227534	−	0.206024i
$716$	3.33483	+	26.0123i	0.124628	+	0.972127i
$717$		0			0
$718$	4.65363	+	1.58850i	0.173672	+	0.0592825i
$719$	−20.9727			−0.782148			−0.391074	−	0.920359i	$-0.627896\pi$
$719$	−20.9727			−0.782148			−0.391074	+	0.920359i	$0.627896\pi$
$720$		0			0
$721$	12.2101			0.454729
$722$	29.6661	+	10.1265i	1.10406	+	0.376868i
$723$		0			0
$724$	29.6558	−	3.80193i	1.10215	−	0.141297i
$725$	20.4432	−	16.7442i	0.759242	−	0.621865i
$726$		0			0
$727$	−19.5823			−0.726269			−0.363134	−	0.931737i	$-0.618293\pi$
$727$	−19.5823			−0.726269			−0.363134	+	0.931737i	$0.618293\pi$
$728$	−0.865265	+	4.23715i	−0.0320689	+	0.157039i
$729$		0			0
$730$	30.6853	−	13.2232i	1.13571	−	0.489411i
$731$	−11.7562	+	11.7562i	−0.434818	+	0.434818i
$732$		0			0
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	−0.630232	−	0.776407i	$-0.717040\pi$
$733$	3.95752	−	3.95752i	0.146174	−	0.146174i	0.776407	+	0.630232i	$0.217040\pi$
$734$	20.2351	+	6.90721i	0.746892	+	0.254950i
$735$		0			0
$736$	1.58559	+	0.117442i	0.0584455	+	0.00432896i
$737$			63.0544i			2.32264i
$738$		0			0
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	0.670392	−	0.742007i	$-0.266126\pi$
$739$	−1.94684	−	1.94684i	−0.0716155	−	0.0716155i	−0.742007	+	0.670392i	$0.766126\pi$
$740$	21.6302	−	25.2947i	0.795143	−	0.929853i
$741$		0			0
$742$	13.4579	−	6.60833i	0.494054	−	0.242599i
$743$	10.5553			0.387238			0.193619	−	0.981077i	$-0.437977\pi$
$743$	10.5553			0.387238			0.193619	+	0.981077i	$0.437977\pi$
$744$		0			0
$745$	−35.7060	−	1.77144i	−1.30816	−	0.0649006i
$746$	34.2003	−	16.7936i	1.25216	−	0.614859i
$747$		0			0
$748$	6.96377	+	54.3188i	0.254621	+	1.98609i
$749$	33.5860	+	33.5860i	1.22721	+	1.22721i
$750$		0			0
$751$	49.4390			1.80405			0.902027	−	0.431680i	$-0.142079\pi$
$751$	49.4390			1.80405			0.902027	+	0.431680i	$0.142079\pi$
$752$	−28.8441	+	7.51932i	−1.05184	+	0.274201i
$753$		0			0
$754$	1.42550	−	4.17609i	0.0519136	−	0.152084i
$755$	−4.76191	+	4.31174i	−0.173304	+	0.156920i
$756$		0			0
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	0.628321	−	0.777954i	$-0.283742\pi$
$757$	−4.11693	−	4.11693i	−0.149632	−	0.149632i	−0.777954	+	0.628321i	$0.783742\pi$
$758$	−3.11025	−	6.33403i	−0.112969	−	0.230063i
$759$		0			0
$760$	20.6672	+	34.9212i	0.749680	+	1.26672i
$761$		−	14.6496i		−	0.531049i	−0.964104	−	0.265525i	$-0.914455\pi$
$761$		−	14.6496i		−	0.531049i	0.964104	−	0.265525i	$-0.0855452\pi$
$762$		0			0
$763$	0.991630	+	0.991630i	0.0358994	+	0.0358994i
$764$	−13.1826	−	10.1866i	−0.476929	−	0.368539i
$765$		0			0
$766$	−4.28643	−	1.46316i	−0.154875	−	0.0528662i
$767$			3.84673i			0.138897i
$768$		0			0
$769$	2.44453			0.0881520			0.0440760	−	0.999028i	$-0.485966\pi$
$769$	2.44453			0.0881520			0.0440760	+	0.999028i	$0.485966\pi$
$770$	18.8158	−	47.3123i	0.678075	−	1.70502i
$771$		0			0
$772$	−7.01216	+	9.07450i	−0.252373	+	0.326598i
$773$	−12.2398	−	12.2398i	−0.440234	−	0.440234i	0.451857	−	0.892091i	$-0.350762\pi$
$773$	−12.2398	−	12.2398i	−0.440234	−	0.440234i	−0.892091	+	0.451857i	$0.850762\pi$
$774$		0			0
$775$	1.51060	−	15.1867i	0.0542624	−	0.545522i
$776$	−10.5736	−	16.0002i	−0.379569	−	0.574372i
$777$		0			0
$778$	14.9504	+	30.4465i	0.535997	+	1.09156i
$779$	−23.4330	+	23.4330i	−0.839576	+	0.839576i
$780$		0			0
$781$	−70.1100	−	70.1100i	−2.50873	−	2.50873i
$782$	1.65672	+	0.565518i	0.0592442	+	0.0202229i
$783$		0			0
$784$	−0.295712	−	1.13435i	−0.0105612	−	0.0405126i
$785$	−18.1139	−	0.898665i	−0.646512	−	0.0320747i
$786$		0			0
$787$	18.2070	−	18.2070i	0.649009	−	0.649009i	−0.303745	−	0.952753i	$-0.598237\pi$
$787$	18.2070	−	18.2070i	0.649009	−	0.649009i	0.952753	+	0.303745i	$0.0982370\pi$
$788$	1.16258	+	9.06835i	0.0414152	+	0.323046i
$789$		0			0
$790$	13.1819	−	5.68047i	0.468992	−	0.202102i
$791$		−	31.5593i		−	1.12212i
$792$		0			0
$793$	0.176437			0.00626545
$794$	13.9628	+	28.4352i	0.495520	+	1.00913i
$795$		0			0
$796$	23.3084	−	30.1636i	0.826145	−	1.06912i
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	−0.790429	−	0.612553i	$-0.790142\pi$
$797$	−5.02164	+	5.02164i	−0.177876	+	0.177876i	0.612553	+	0.790429i	$0.290142\pi$
$798$		0			0
$799$	−32.8200			−1.16109
$800$	−4.87092	+	27.8617i	−0.172213	+	0.985060i
$801$		0			0
$802$	4.96183	−	14.5360i	0.175208	−	0.513284i
$803$	−46.4514	+	46.4514i	−1.63923	+	1.63923i
$804$		0			0
$805$	−1.09245	−	1.20651i	−0.0385039	−	0.0425238i
$806$	−1.12329	−	2.28759i	−0.0395663	−	0.0805769i
$807$		0			0
$808$	8.06438	−	39.4908i	0.283704	−	1.38928i
$809$			23.6476i			0.831404i	0.909501	+	0.415702i	$0.136464\pi$
$809$			23.6476i			0.831404i	−0.909501	+	0.415702i	$0.863536\pi$
$810$		0			0
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	−0.990371	−	0.138438i	$-0.955792\pi$
$811$	−24.2614	+	24.2614i	−0.851934	+	0.851934i	0.138438	+	0.990371i	$0.455792\pi$
$812$	−3.48093	−	27.1520i	−0.122157	−	0.952848i
$813$		0			0
$814$	−21.1383	+	61.9259i	−0.740896	+	2.17050i
$815$	−37.7621	−	1.87345i	−1.32275	−	0.0656240i
$816$		0			0
$817$		−	24.2205i		−	0.847369i
$818$	−16.7784	−	5.72728i	−0.586644	−	0.200250i
$819$		0			0
$820$	−23.0288	+	1.79839i	−0.804201	+	0.0628027i
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.482771	−	0.875746i	$-0.339630\pi$
$821$	38.9257	−	38.9257i	1.35852	−	1.35852i	0.875746	−	0.482771i	$-0.160370\pi$
$822$		0			0
$823$	−38.6799			−1.34830			−0.674148	−	0.738596i	$-0.735489\pi$
$823$	−38.6799			−1.34830			−0.674148	+	0.738596i	$0.735489\pi$
$824$	11.1255	−	7.35217i	0.387574	−	0.256125i
$825$		0			0
$826$	10.5181	+	21.4202i	0.365973	+	0.745305i
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	0.103658	−	0.994613i	$-0.466945\pi$
$827$	−25.6217	−	25.6217i	−0.890955	−	0.890955i	−0.994613	+	0.103658i	$0.966945\pi$
$828$		0			0
$829$	−14.8962	−	14.8962i	−0.517367	−	0.517367i	0.399407	−	0.916774i	$-0.369216\pi$
$829$	−14.8962	−	14.8962i	−0.517367	−	0.517367i	−0.916774	+	0.399407i	$0.869216\pi$
$830$	−7.54697	+	18.9768i	−0.261959	+	0.658695i
$831$		0			0
$832$	1.76294	+	4.38176i	0.0611191	+	0.151910i
$833$		−	1.29071i		−	0.0447205i
$834$		0			0
$835$	13.8628	+	15.3102i	0.479743	+	0.529830i
$836$	−63.1284	−	48.7814i	−2.18334	−	1.68714i
$837$		0			0
$838$	38.9110	−	19.1068i	1.34416	−	0.660032i
$839$		−	14.5709i		−	0.503045i	−0.967851	−	0.251522i	$-0.919069\pi$
$839$		−	14.5709i		−	0.503045i	0.967851	−	0.251522i	$-0.0809312\pi$
$840$		0			0
$841$		−	1.06820i		−	0.0368344i
$842$	7.95965	+	16.2098i	0.274308	+	0.558628i
$843$		0			0
$844$	−1.59591	−	12.4484i	−0.0549334	−	0.428492i
$845$	−20.9703	+	18.9879i	−0.721401	+	0.653204i
$846$		0			0
$847$			71.6171i			2.46079i
$848$	8.28326	−	14.1248i	0.284448	−	0.485047i
$849$		0			0
$850$	−12.9281	+	28.3319i	−0.443431	+	0.971778i
$851$	1.47905	+	1.47905i	0.0507011	+	0.0507011i
$852$		0			0
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	0.472344	−	0.881414i	$-0.343408\pi$
$853$	−11.9474	−	11.9474i	−0.409070	−	0.409070i	−0.881414	+	0.472344i	$0.843408\pi$
$854$	0.982474	−	0.482432i	0.0336196	−	0.0165085i
$855$		0			0
$856$	50.8258	+	10.3791i	1.73719	+	0.354750i
$857$	18.3405			0.626498			0.313249	−	0.949671i	$-0.398583\pi$
$857$	18.3405			0.626498			0.313249	+	0.949671i	$0.398583\pi$
$858$		0			0
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	−0.938832	−	0.344377i	$-0.888090\pi$
$859$	−17.4227	+	17.4227i	−0.594455	+	0.594455i	0.344377	+	0.938832i	$0.388090\pi$
$860$	10.9719	−	12.8308i	0.374140	−	0.437526i
$861$		0			0
$862$	10.1419	−	29.7114i	0.345435	−	1.01197i
$863$		−	40.5444i		−	1.38015i	−0.723740	−	0.690073i	$-0.757578\pi$
$863$		−	40.5444i		−	1.38015i	0.723740	−	0.690073i	$-0.242422\pi$
$864$		0			0
$865$	7.45973	+	0.370091i	0.253638	+	0.0125835i
$866$	41.6395	+	14.2135i	1.41497	+	0.482996i
$867$		0			0
$868$	−12.5099	−	9.66684i	−0.424615	−	0.328114i
$869$	−19.9548	+	19.9548i	−0.676921	+	0.676921i
$870$		0			0
$871$			5.98767i			0.202884i
$872$	1.50064	+	0.306444i	0.0508180	+	0.0103775i
$873$		0			0
$874$	−2.28917	+	1.12407i	−0.0774325	+	0.0380223i
$875$	23.2815	−	17.2144i	0.787060	−	0.581954i
$876$		0			0
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.0500546	+	0.998746i	$0.515940\pi$
$877$	−31.0594	+	31.0594i	−1.04880	+	1.04880i	−0.998746	+	0.0500546i	$0.984060\pi$
$878$	0.616878	+	0.210570i	0.0208186	+	0.00710638i
$879$		0			0
$880$	−11.3441	−	54.4391i	−0.382409	−	1.83514i
$881$	18.0615			0.608506			0.304253	−	0.952591i	$-0.401593\pi$
$881$	18.0615			0.608506			0.304253	+	0.952591i	$0.401593\pi$
$882$		0			0
$883$	−18.0110	+	18.0110i	−0.606117	+	0.606117i	−0.941929	−	0.335812i	$-0.890989\pi$
$883$	−18.0110	+	18.0110i	−0.606117	+	0.606117i	0.335812	+	0.941929i	$0.390989\pi$
$884$	0.661283	+	5.15814i	0.0222413	+	0.173487i
$885$		0			0
$886$	−5.17896	+	2.54307i	−0.173991	+	0.0854359i
$887$	37.8699			1.27155			0.635774	−	0.771876i	$-0.280681\pi$
$887$	37.8699			1.27155			0.635774	+	0.771876i	$0.280681\pi$
$888$		0			0
$889$			17.4888i			0.586556i
$890$	−12.8582	−	29.8383i	−0.431006	−	1.00018i
$891$		0			0
$892$	6.24334	−	8.07957i	0.209043	−	0.270524i
$893$	33.8085	−	33.8085i	1.13136	−	1.13136i
$894$		0			0
$895$	1.45287	−	29.2847i	0.0485641	−	0.978879i
$896$	21.7979	+	19.5791i	0.728216	+	0.654091i
$897$		0			0
$898$	−1.38060	+	4.04455i	−0.0460712	+	0.134968i
$899$	11.4069	+	11.4069i	0.380440	+	0.380440i
$900$		0			0
$901$	12.7484	−	12.7484i	0.424710	−	0.424710i
$902$	40.7644	−	20.0169i	1.35731	−	0.666489i
$903$		0			0
$904$	−19.0030	−	28.7558i	−0.632032	−	0.956405i
$905$	−33.3865	−	1.65637i	−1.10980	−	0.0550595i
$906$		0			0
$907$	13.1614	+	13.1614i	0.437018	+	0.437018i	0.891007	−	0.453989i	$-0.149999\pi$
$907$	13.1614	+	13.1614i	0.437018	+	0.437018i	−0.453989	+	0.891007i	$0.649999\pi$
$908$	42.2398	−	5.41523i	1.40178	−	0.179711i
$909$		0			0
$910$	1.78676	−	4.49279i	0.0592304	−	0.148935i
$911$	−4.85931			−0.160996			−0.0804981	−	0.996755i	$-0.525651\pi$
$911$	−4.85931			−0.160996			−0.0804981	+	0.996755i	$0.525651\pi$
$912$		0			0
$913$		−	40.1517i		−	1.32883i
$914$	2.14271	−	6.27722i	0.0708746	−	0.207632i
$915$		0			0
$916$	−49.1659	+	6.30316i	−1.62449	+	0.208262i
$917$	10.2375	+	10.2375i	0.338071	+	0.338071i
$918$		0			0
$919$			37.6319i			1.24136i	0.784063	+	0.620681i	$0.213144\pi$
$919$			37.6319i			1.24136i	−0.784063	+	0.620681i	$0.786856\pi$
$920$	−1.72189	−	0.441525i	−0.0567691	−	0.0145567i
$921$		0			0
$922$	−37.5751	+	18.4508i	−1.23747	+	0.607645i
$923$	−6.65767	−	6.65767i	−0.219140	−	0.219140i
$924$		0			0
$925$	−28.7869	+	23.5782i	−0.946506	+	0.775246i
$926$	34.1543	+	11.6585i	1.12238	+	0.383121i
$927$		0			0
$928$	−19.5209	−	22.6440i	−0.640806	−	0.743326i
$929$	−37.6717			−1.23597			−0.617984	−	0.786191i	$-0.712050\pi$
$929$	−37.6717			−1.23597			−0.617984	+	0.786191i	$0.712050\pi$
$930$		0			0
$931$	1.32959	+	1.32959i	0.0435755	+	0.0435755i
$932$	−14.4845	−	11.1926i	−0.474456	−	0.366627i
$933$		0			0
$934$	−18.1611	−	36.9852i	−0.594250	−	1.21019i
$935$	3.03387	−	61.1521i	0.0992182	−	1.99989i
$936$		0			0
$937$	22.1390			0.723251			0.361625	−	0.932323i	$-0.382222\pi$
$937$	22.1390			0.723251			0.361625	+	0.932323i	$0.382222\pi$
$938$	16.3721	+	33.3418i	0.534568	+	1.08865i
$939$		0			0
$940$	33.2253	−	2.59467i	1.08369	−	0.0846289i
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	0.801599	−	0.597862i	$-0.203983\pi$
$941$	6.24976	+	6.24976i	0.203736	+	0.203736i	−0.597862	+	0.801599i	$0.703983\pi$
$942$		0			0
$943$		−	1.45171i		−	0.0472742i
$944$	22.4817	+	13.1840i	0.731717	+	0.429104i
$945$		0			0
$946$	−10.7224	+	31.4120i	−0.348615	+	1.02129i
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	−0.772503	−	0.635011i	$-0.780995\pi$
$947$	−4.23108	+	4.23108i	−0.137492	+	0.137492i	0.635011	+	0.772503i	$0.280995\pi$
$948$		0			0
$949$	−4.41104	+	4.41104i	−0.143189	+	0.143189i
$950$	−15.8678	−	42.5028i	−0.514819	−	1.37897i
$951$		0			0
$952$	17.7862	+	26.9145i	0.576454	+	0.872304i
$953$	−0.585699			−0.0189726			−0.00948632	−	0.999955i	$-0.503020\pi$
$953$	−0.585699			−0.0189726			−0.00948632	+	0.999955i	$0.503020\pi$
$954$		0			0
$955$	12.5019	+	13.8071i	0.404552	+	0.446789i
$956$	−20.4465	−	15.7996i	−0.661286	−	0.510997i
$957$		0			0
$958$	−14.0177	+	41.0658i	−0.452892	+	1.32678i
$959$	−13.4544			−0.434464
$960$		0			0
$961$	−21.6833			−0.699461
$962$	−2.00730	+	5.88051i	−0.0647179	+	0.189595i
$963$		0			0
$964$	−16.9446	−	13.0937i	−0.545750	−	0.421719i
$965$	9.50443	−	8.60594i	0.305958	−	0.277035i
$966$		0			0
$967$	41.5832			1.33722			0.668612	−	0.743611i	$-0.266889\pi$
$967$	41.5832			1.33722			0.668612	+	0.743611i	$0.266889\pi$
$968$	43.1233	+	65.2552i	1.38604	+	2.09738i
$969$		0			0
$970$	8.48558	+	19.6914i	0.272455	+	0.632253i
$971$	−18.8728	+	18.8728i	−0.605656	+	0.605656i	−0.941808	−	0.336152i	$-0.890874\pi$
$971$	−18.8728	+	18.8728i	−0.605656	+	0.605656i	0.336152	+	0.941808i	$0.390874\pi$
$972$		0			0
$973$	−2.53027	+	2.53027i	−0.0811168	+	0.0811168i
$974$	2.07004	−	6.06431i	0.0663283	−	0.194313i
$975$		0			0
$976$	0.604708	−	1.03116i	0.0193562	−	0.0330066i
$977$			17.3929i			0.556448i	0.960516	+	0.278224i	$0.0897457\pi$
$977$			17.3929i			0.556448i	−0.960516	+	0.278224i	$0.910254\pi$
$978$		0			0
$979$	45.1692	+	45.1692i	1.44361	+	1.44361i
$980$	0.102041	+	1.30665i	0.00325957	+	0.0417394i
$981$		0			0
$982$	1.82289	+	3.71232i	0.0581708	+	0.118465i
$983$	28.6927			0.915154			0.457577	−	0.889170i	$-0.348717\pi$
$983$	28.6927			0.915154			0.457577	+	0.889170i	$0.348717\pi$
$984$		0			0
$985$	0.506495	−	10.2091i	0.0161383	−	0.325290i
$986$	−14.5090	−	29.5476i	−0.462060	−	0.940987i
$987$		0			0
$988$	−5.99470	−	4.63230i	−0.190717	−	0.147373i
$989$	0.750248	+	0.750248i	0.0238565	+	0.0238565i
$990$		0			0
$991$	5.67944			0.180413			0.0902066	−	0.995923i	$-0.471247\pi$
$991$	5.67944			0.180413			0.0902066	+	0.995923i	$0.471247\pi$
$992$	−17.2194	−	1.27541i	−0.546717	−	0.0404943i
$993$		0			0
$994$	−55.2768	−	18.8686i	−1.75327	−	0.598475i
$995$	−31.5927	+	28.6061i	−1.00156	+	0.906875i
$996$		0			0
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	0.984135	−	0.177419i	$-0.0567747\pi$
$997$	25.4723	+	25.4723i	0.806717	+	0.806717i	−0.177419	+	0.984135i	$0.556775\pi$
$998$	−48.5826	+	23.8559i	−1.53786	+	0.755145i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.h.109.15		48
3.2	odd	2		240.2.bl.a.109.10	✓	48
5.4	even	2	inner	720.2.bm.h.109.10		48
12.11	even	2		960.2.bl.a.529.4		48
15.14	odd	2		240.2.bl.a.109.15	yes	48
16.5	even	4	inner	720.2.bm.h.469.10		48
24.5	odd	2		1920.2.bl.a.289.3		48
24.11	even	2		1920.2.bl.b.289.22		48
48.5	odd	4		240.2.bl.a.229.15	yes	48
48.11	even	4		960.2.bl.a.49.22		48
48.29	odd	4		1920.2.bl.a.1249.22		48
48.35	even	4		1920.2.bl.b.1249.3		48
60.59	even	2		960.2.bl.a.529.22		48
80.69	even	4	inner	720.2.bm.h.469.15		48
120.29	odd	2		1920.2.bl.a.289.22		48
120.59	even	2		1920.2.bl.b.289.3		48
240.29	odd	4		1920.2.bl.a.1249.3		48
240.59	even	4		960.2.bl.a.49.4		48
240.149	odd	4		240.2.bl.a.229.10	yes	48
240.179	even	4		1920.2.bl.b.1249.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.bl.a.109.10	✓	48	3.2	odd	2
240.2.bl.a.109.15	yes	48	15.14	odd	2
240.2.bl.a.229.10	yes	48	240.149	odd	4
240.2.bl.a.229.15	yes	48	48.5	odd	4
720.2.bm.h.109.10		48	5.4	even	2	inner
720.2.bm.h.109.15		48	1.1	even	1	trivial
720.2.bm.h.469.10		48	16.5	even	4	inner
720.2.bm.h.469.15		48	80.69	even	4	inner
960.2.bl.a.49.4		48	240.59	even	4
960.2.bl.a.49.22		48	48.11	even	4
960.2.bl.a.529.4		48	12.11	even	2
960.2.bl.a.529.22		48	60.59	even	2
1920.2.bl.a.289.3		48	24.5	odd	2
1920.2.bl.a.289.22		48	120.29	odd	2
1920.2.bl.a.1249.3		48	240.29	odd	4
1920.2.bl.a.1249.22		48	48.29	odd	4
1920.2.bl.b.289.3		48	120.59	even	2
1920.2.bl.b.289.22		48	24.11	even	2
1920.2.bl.b.1249.3		48	48.35	even	4
1920.2.bl.b.1249.22		48	240.179	even	4

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.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.456856 - 1.33839i) q^{2} +(-1.58257 - 1.22290i) q^{4} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} +O(q^{10})\)	\(q+(0.456856 - 1.33839i) q^{2} +(-1.58257 - 1.22290i) q^{4} +(1.50085 + 1.65754i) q^{5} -2.58977 q^{7} +(-2.35972 + 1.55940i) q^{8} +(2.90411 - 1.25146i) q^{10} +(-4.39624 + 4.39624i) q^{11} +(-0.417468 + 0.417468i) q^{13} +(-1.18315 + 3.46612i) q^{14} +(1.00903 + 3.87064i) q^{16} +4.40417i q^{17} +(-4.53682 - 4.53682i) q^{19} +(-0.348184 - 4.45856i) q^{20} +(3.87543 + 7.89232i) q^{22} +0.281063 q^{23} +(-0.494901 + 4.97545i) q^{25} +(0.368012 + 0.749457i) q^{26} +(4.09849 + 3.16704i) q^{28} +(-3.73710 - 3.73710i) q^{29} -3.05233 q^{31} +(5.64140 + 0.417848i) q^{32} +(5.89449 + 2.01207i) q^{34} +(-3.88686 - 4.29266i) q^{35} +(5.26234 + 5.26234i) q^{37} +(-8.14471 + 3.99936i) q^{38} +(-6.12636 - 1.57091i) q^{40} -5.16508i q^{41} +(2.66933 + 2.66933i) q^{43} +(12.3335 - 1.58118i) q^{44} +(0.128405 - 0.376171i) q^{46} +7.45202i q^{47} -0.293066 q^{49} +(6.43298 + 2.93543i) q^{50} +(1.17119 - 0.150149i) q^{52} +(-2.89462 - 2.89462i) q^{53} +(-13.8850 - 0.688864i) q^{55} +(6.11114 - 4.03849i) q^{56} +(-6.70900 + 3.29437i) q^{58} +(4.60721 - 4.60721i) q^{59} +(-0.211318 - 0.211318i) q^{61} +(-1.39447 + 4.08520i) q^{62} +(3.13655 - 7.35949i) q^{64} +(-1.31853 - 0.0654147i) q^{65} +(7.17140 - 7.17140i) q^{67} +(5.38586 - 6.96989i) q^{68} +(-7.52099 + 3.24100i) q^{70} +15.9477i q^{71} +10.5662 q^{73} +(9.44719 - 4.63893i) q^{74} +(1.63174 + 12.7279i) q^{76} +(11.3853 - 11.3853i) q^{77} +4.53907 q^{79} +(-4.90135 + 7.48176i) q^{80} +(-6.91288 - 2.35969i) q^{82} +(-4.56660 + 4.56660i) q^{83} +(-7.30010 + 6.61000i) q^{85} +(4.79209 - 2.35310i) q^{86} +(3.51840 - 17.2294i) q^{88} -10.2745i q^{89} +(1.08115 - 1.08115i) q^{91} +(-0.444800 - 0.343712i) q^{92} +(9.97370 + 3.40450i) q^{94} +(0.710893 - 14.3291i) q^{95} +6.78053i q^{97} +(-0.133889 + 0.392236i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 12 q^{10} + 16 q^{14} - 4 q^{16} + 8 q^{19} + 40 q^{26} - 48 q^{31} - 28 q^{34} - 24 q^{35} - 16 q^{40} + 40 q^{44} - 4 q^{46} + 48 q^{49} + 32 q^{50} - 48 q^{56} + 32 q^{59} + 16 q^{61} + 48 q^{64} - 16 q^{65} - 40 q^{74} + 60 q^{76} - 96 q^{79} - 72 q^{80} - 16 q^{86} - 32 q^{91} + 44 q^{94} + 48 q^{95}+O(q^{100}) \) 48 * q + 12 * q^10 + 16 * q^14 - 4 * q^16 + 8 * q^19 + 40 * q^26 - 48 * q^31 - 28 * q^34 - 24 * q^35 - 16 * q^40 + 40 * q^44 - 4 * q^46 + 48 * q^49 + 32 * q^50 - 48 * q^56 + 32 * q^59 + 16 * q^61 + 48 * q^64 - 16 * q^65 - 40 * q^74 + 60 * q^76 - 96 * q^79 - 72 * q^80 - 16 * q^86 - 32 * q^91 + 44 * q^94 + 48 * q^95

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