LMFDB - Embedded newform 720.2.bm.g.109.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [720,2,Mod(109,720)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("720.109"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [32,0,0,16,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.11
Character	$\chi$	$=$	720.109
Dual form			720.2.bm.g.469.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.903873 + 1.08766i) q^{2} +(-0.366025 + 1.96622i) q^{4} +(0.466314 + 2.18690i) q^{5} +4.79660 q^{7} +(-2.46943 + 1.37910i) q^{8} +(-1.95713 + 2.48388i) q^{10} +(2.09858 - 2.09858i) q^{11} +(1.75568 - 1.75568i) q^{13} +(4.33552 + 5.21709i) q^{14} +(-3.73205 - 1.43937i) q^{16} +0.0807527i q^{17} +(2.73205 + 2.73205i) q^{19} +(-4.47062 + 0.116414i) q^{20} +(4.17940 + 0.385699i) q^{22} -6.53131 q^{23} +(-4.56510 + 2.03957i) q^{25} +(3.49650 + 0.322676i) q^{26} +(-1.75568 + 9.43117i) q^{28} +(-4.01284 - 4.01284i) q^{29} +2.90771 q^{31} +(-1.80775 - 5.36023i) q^{32} +(-0.0878318 + 0.0729902i) q^{34} +(2.23672 + 10.4897i) q^{35} +(-3.86318 - 3.86318i) q^{37} +(-0.502125 + 5.44098i) q^{38} +(-4.16750 - 4.75731i) q^{40} +5.96030i q^{41} +(-7.67549 - 7.67549i) q^{43} +(3.35814 + 4.89441i) q^{44} +(-5.90348 - 7.10387i) q^{46} +2.39062i q^{47} +16.0073 q^{49} +(-6.34464 - 3.12178i) q^{50} +(2.80943 + 4.09467i) q^{52} +(-0.693188 - 0.693188i) q^{53} +(5.56800 + 3.61080i) q^{55} +(-11.8449 + 6.61500i) q^{56} +(0.737521 - 7.99172i) q^{58} +(-0.839022 + 0.839022i) q^{59} +(-5.95717 - 5.95717i) q^{61} +(2.62821 + 3.16262i) q^{62} +(4.19615 - 6.81119i) q^{64} +(4.65819 + 3.02080i) q^{65} +(-2.73995 + 2.73995i) q^{67} +(-0.158778 - 0.0295575i) q^{68} +(-9.38755 + 11.9142i) q^{70} +13.1449i q^{71} +9.73214 q^{73} +(0.710014 - 7.69366i) q^{74} +(-6.37182 + 4.37182i) q^{76} +(10.0660 - 10.0660i) q^{77} +4.50693 q^{79} +(1.40746 - 8.83284i) q^{80} +(-6.48280 + 5.38736i) q^{82} +(-6.08297 + 6.08297i) q^{83} +(-0.176598 + 0.0376561i) q^{85} +(1.41068 - 15.2860i) q^{86} +(-2.28814 + 8.07645i) q^{88} -11.4669i q^{89} +(8.42127 - 8.42127i) q^{91} +(2.39062 - 12.8420i) q^{92} +(-2.60020 + 2.16082i) q^{94} +(-4.70074 + 7.24873i) q^{95} -7.62464i q^{97} +(14.4686 + 17.4106i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) $ 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

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 $

$2$	0.903873	+	1.08766i	0.639135	+	0.769095i
$2$	0.903873	+	1.08766i	0.639135	+	0.769095i
$3$		0			0
$3$		0			0
$4$	−0.366025	+	1.96622i	−0.183013	+	0.983111i
$5$	0.466314	+	2.18690i	0.208542	+	0.978013i
$5$	0.466314	+	2.18690i	0.208542	+	0.978013i
$6$		0			0
$7$	4.79660			1.81294			0.906472	−	0.422267i	$-0.138765\pi$
$7$	4.79660			1.81294			0.906472	+	0.422267i	$0.138765\pi$
$8$	−2.46943	+	1.37910i	−0.873075	+	0.487586i
$9$		0			0
$10$	−1.95713	+	2.48388i	−0.618898	+	0.785471i
$11$	2.09858	−	2.09858i	0.632746	−	0.632746i	−0.316010	−	0.948756i	$-0.602343\pi$
$11$	2.09858	−	2.09858i	0.632746	−	0.632746i	0.948756	+	0.316010i	$0.102343\pi$
$12$		0			0
$13$	1.75568	−	1.75568i	0.486937	−	0.486937i	−0.420401	−	0.907338i	$-0.638111\pi$
$13$	1.75568	−	1.75568i	0.486937	−	0.486937i	0.907338	+	0.420401i	$0.138111\pi$
$14$	4.33552	+	5.21709i	1.15872	+	1.39432i
$15$		0			0
$16$	−3.73205	−	1.43937i	−0.933013	−	0.359843i
$17$			0.0807527i			0.0195854i	0.999952	+	0.00979270i	$0.00311716\pi$
$17$			0.0807527i			0.0195854i	−0.999952	+	0.00979270i	$0.996883\pi$
$18$		0			0
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	0.947255	−	0.320480i	$-0.103844\pi$
$19$	2.73205	+	2.73205i	0.626775	+	0.626775i	−0.320480	+	0.947255i	$0.603844\pi$
$20$	−4.47062	+	0.116414i	−0.999661	+	0.0260310i
$21$		0			0
$22$	4.17940	+	0.385699i	0.891052	+	0.0822313i
$23$	−6.53131			−1.36187			−0.680936	−	0.732343i	$-0.738427\pi$
$23$	−6.53131			−1.36187			−0.680936	+	0.732343i	$0.738427\pi$
$24$		0			0
$25$	−4.56510	+	2.03957i	−0.913020	+	0.407914i
$26$	3.49650	+	0.322676i	0.685719	+	0.0632821i
$27$		0			0
$28$	−1.75568	+	9.43117i	−0.331792	+	1.78232i
$29$	−4.01284	−	4.01284i	−0.745166	−	0.745166i	0.228401	−	0.973567i	$-0.426650\pi$
$29$	−4.01284	−	4.01284i	−0.745166	−	0.745166i	−0.973567	+	0.228401i	$0.926650\pi$
$30$		0			0
$31$	2.90771			0.522241			0.261120	−	0.965306i	$-0.415908\pi$
$31$	2.90771			0.522241			0.261120	+	0.965306i	$0.415908\pi$
$32$	−1.80775	−	5.36023i	−0.319568	−	0.947564i
$33$		0			0
$34$	−0.0878318	+	0.0729902i	−0.0150630	+	0.0125177i
$35$	2.23672	+	10.4897i	0.378075	+	1.77308i
$36$		0			0
$37$	−3.86318	−	3.86318i	−0.635102	−	0.635102i	0.314241	−	0.949343i	$-0.398250\pi$
$37$	−3.86318	−	3.86318i	−0.635102	−	0.635102i	−0.949343	+	0.314241i	$0.898250\pi$
$38$	−0.502125	+	5.44098i	−0.0814554	+	0.882644i
$39$		0			0
$40$	−4.16750	−	4.75731i	−0.658939	−	0.752197i
$41$			5.96030i			0.930842i	0.885089	+	0.465421i	$0.154097\pi$
$41$			5.96030i			0.930842i	−0.885089	+	0.465421i	$0.845903\pi$
$42$		0			0
$43$	−7.67549	−	7.67549i	−1.17050	−	1.17050i	−0.982090	−	0.188412i	$-0.939666\pi$
$43$	−7.67549	−	7.67549i	−1.17050	−	1.17050i	−0.188412	−	0.982090i	$-0.560334\pi$
$44$	3.35814	+	4.89441i	0.506259	+	0.737860i
$45$		0			0
$46$	−5.90348	−	7.10387i	−0.870420	−	1.04741i
$47$			2.39062i			0.348708i	0.984683	+	0.174354i	$0.0557838\pi$
$47$			2.39062i			0.348708i	−0.984683	+	0.174354i	$0.944216\pi$
$48$		0			0
$49$	16.0073			2.28676
$50$	−6.34464	−	3.12178i	−0.897268	−	0.441487i
$51$		0			0
$52$	2.80943	+	4.09467i	0.389597	+	0.567829i
$53$	−0.693188	−	0.693188i	−0.0952166	−	0.0952166i	0.657894	−	0.753111i	$-0.271447\pi$
$53$	−0.693188	−	0.693188i	−0.0952166	−	0.0952166i	−0.753111	+	0.657894i	$0.771447\pi$
$54$		0			0
$55$	5.56800	+	3.61080i	0.750788	+	0.486880i
$56$	−11.8449	+	6.61500i	−1.58283	+	0.883966i
$57$		0			0
$58$	0.737521	−	7.99172i	0.0968413	−	1.04936i
$59$	−0.839022	+	0.839022i	−0.109231	+	0.109231i	−0.759610	−	0.650379i	$-0.774610\pi$
$59$	−0.839022	+	0.839022i	−0.109231	+	0.109231i	0.650379	+	0.759610i	$0.274610\pi$
$60$		0			0
$61$	−5.95717	−	5.95717i	−0.762737	−	0.762737i	0.214079	−	0.976816i	$-0.431325\pi$
$61$	−5.95717	−	5.95717i	−0.762737	−	0.762737i	−0.976816	+	0.214079i	$0.931325\pi$
$62$	2.62821	+	3.16262i	0.333782	+	0.401653i
$63$		0			0
$64$	4.19615	−	6.81119i	0.524519	−	0.851399i
$65$	4.65819	+	3.02080i	0.577778	+	0.374684i
$66$		0			0
$67$	−2.73995	+	2.73995i	−0.334739	+	0.334739i	−0.854383	−	0.519644i	$-0.826065\pi$
$67$	−2.73995	+	2.73995i	−0.334739	+	0.334739i	0.519644	+	0.854383i	$0.326065\pi$
$68$	−0.158778	−	0.0295575i	−0.0192546	−	0.00358438i
$69$		0			0
$70$	−9.38755	+	11.9142i	−1.12203	+	1.42401i
$71$			13.1449i			1.56001i	0.625771	+	0.780007i	$0.284784\pi$
$71$			13.1449i			1.56001i	−0.625771	+	0.780007i	$0.715216\pi$
$72$		0			0
$73$	9.73214			1.13906			0.569530	−	0.821970i	$-0.307125\pi$
$73$	9.73214			1.13906			0.569530	+	0.821970i	$0.307125\pi$
$74$	0.710014	−	7.69366i	0.0825375	−	0.894370i
$75$		0			0
$76$	−6.37182	+	4.37182i	−0.730897	+	0.501482i
$77$	10.0660	−	10.0660i	1.14713	−	1.14713i
$78$		0			0
$79$	4.50693			0.507069			0.253535	−	0.967326i	$-0.418407\pi$
$79$	4.50693			0.507069			0.253535	+	0.967326i	$0.418407\pi$
$80$	1.40746	−	8.83284i	0.157359	−	0.987541i
$81$		0			0
$82$	−6.48280	+	5.38736i	−0.715906	+	0.594934i
$83$	−6.08297	+	6.08297i	−0.667693	+	0.667693i	−0.957182	−	0.289488i	$-0.906515\pi$
$83$	−6.08297	+	6.08297i	−0.667693	+	0.667693i	0.289488	+	0.957182i	$0.406515\pi$
$84$		0			0
$85$	−0.176598	+	0.0376561i	−0.0191548	+	0.00408438i
$86$	1.41068	−	15.2860i	0.152118	−	1.64834i
$87$		0			0
$88$	−2.28814	+	8.07645i	−0.243916	+	0.860953i
$89$		−	11.4669i		−	1.21548i	−0.794134	−	0.607742i	$-0.792075\pi$
$89$		−	11.4669i		−	1.21548i	0.794134	−	0.607742i	$-0.207925\pi$
$90$		0			0
$91$	8.42127	−	8.42127i	0.882789	−	0.882789i
$92$	2.39062	−	12.8420i	0.249240	−	1.33887i
$93$		0			0
$94$	−2.60020	+	2.16082i	−0.268190	+	0.222872i
$95$	−4.70074	+	7.24873i	−0.482286	+	0.743704i
$96$		0			0
$97$		−	7.62464i		−	0.774165i	−0.922045	−	0.387082i	$-0.873483\pi$
$97$		−	7.62464i		−	0.774165i	0.922045	−	0.387082i	$-0.126517\pi$
$98$	14.4686	+	17.4106i	1.46155	+	1.75874i
$99$		0			0
$100$	−2.33930	−	9.72253i	−0.233930	−	0.972253i
$101$	13.1875	−	13.1875i	1.31220	−	1.31220i	0.392410	−	0.919790i	$-0.371641\pi$
$101$	13.1875	−	13.1875i	1.31220	−	1.31220i	0.919790	−	0.392410i	$-0.128359\pi$
$102$		0			0
$103$	−6.44111			−0.634661			−0.317331	−	0.948315i	$-0.602786\pi$
$103$	−6.44111			−0.634661			−0.317331	+	0.948315i	$0.602786\pi$
$104$	−1.91426	+	6.75677i	−0.187709	+	0.662556i
$105$		0			0
$106$	0.127401	−	1.38051i	0.0123743	−	0.134087i
$107$	1.65546	+	1.65546i	0.160040	+	0.160040i	0.782584	−	0.622545i	$-0.213901\pi$
$107$	1.65546	+	1.65546i	0.160040	+	0.160040i	−0.622545	+	0.782584i	$0.713901\pi$
$108$		0			0
$109$	1.82858	+	1.82858i	0.175146	+	0.175146i	0.789236	−	0.614090i	$-0.210477\pi$
$109$	1.82858	+	1.82858i	0.175146	+	0.175146i	−0.614090	+	0.789236i	$0.710477\pi$
$110$	1.10543	+	9.31981i	0.105398	+	0.888609i
$111$		0			0
$112$	−17.9011	−	6.90410i	−1.69150	−	0.652376i
$113$		−	17.9731i		−	1.69077i	−0.534161	−	0.845383i	$-0.679372\pi$
$113$		−	17.9731i		−	1.69077i	0.534161	−	0.845383i	$-0.320628\pi$
$114$		0			0
$115$	−3.04564	−	14.2833i	−0.284008	−	1.33193i
$116$	9.35893	−	6.42133i	0.868955	−	0.596206i
$117$		0			0
$118$	−1.67094	−	0.154204i	−0.153823	−	0.0141956i
$119$			0.387338i			0.0355072i
$120$		0			0
$121$			2.19191i			0.199265i
$122$	1.09487	−	11.8639i	0.0991249	−	1.07411i
$123$		0			0
$124$	−1.06430	+	5.71721i	−0.0955767	+	0.513421i
$125$	−6.58912	−	9.03236i	−0.589348	−	0.807879i
$126$		0			0
$127$		−	7.70602i		−	0.683798i	−0.939737	−	0.341899i	$-0.888930\pi$
$127$		−	7.70602i		−	0.683798i	0.939737	−	0.341899i	$-0.111070\pi$
$128$	11.2011	−	1.59245i	0.990045	−	0.140754i
$129$		0			0
$130$	0.924803	+	7.79697i	0.0811106	+	0.683839i
$131$	−10.2405	−	10.2405i	−0.894717	−	0.894717i	0.100246	−	0.994963i	$-0.468037\pi$
$131$	−10.2405	−	10.2405i	−0.894717	−	0.894717i	−0.994963	+	0.100246i	$0.968037\pi$
$132$		0			0
$133$	13.1045	+	13.1045i	1.13631	+	1.13631i
$134$	−5.45672	−	0.503577i	−0.471389	−	0.0435025i
$135$		0			0
$136$	−0.111366	−	0.199413i	−0.00954957	−	0.0170995i
$137$	21.6832			1.85252			0.926259	−	0.376887i	$-0.123006\pi$
$137$	21.6832			1.85252			0.926259	+	0.376887i	$0.123006\pi$
$138$		0			0
$139$	15.4467	−	15.4467i	1.31017	−	1.31017i	0.388889	−	0.921285i	$-0.372859\pi$
$139$	15.4467	−	15.4467i	1.31017	−	1.31017i	0.921285	−	0.388889i	$-0.127141\pi$
$140$	−21.4438	+	0.558393i	−1.81233	+	0.0471928i
$141$		0			0
$142$	−14.2972	+	11.8813i	−1.19980	+	0.997059i
$143$		−	7.36886i		−	0.616215i
$144$		0			0
$145$	6.90445	−	10.6469i	0.573384	−	0.884181i
$146$	8.79662	+	10.5853i	0.728013	+	0.876045i
$147$		0			0
$148$	9.00988	−	6.18184i	0.740607	−	0.508144i
$149$	−9.97314	+	9.97314i	−0.817031	+	0.817031i	−0.985677	−	0.168645i	$-0.946061\pi$
$149$	−9.97314	+	9.97314i	−0.817031	+	0.817031i	0.168645	+	0.985677i	$0.446061\pi$
$150$		0			0
$151$			21.1154i			1.71835i	0.511681	+	0.859175i	$0.329023\pi$
$151$			21.1154i			1.71835i	−0.511681	+	0.859175i	$0.670977\pi$
$152$	−10.5144	−	2.97883i	−0.852829	−	0.241615i
$153$		0			0
$154$	20.0469	+	1.85004i	1.61543	+	0.149081i
$155$	1.35591	+	6.35889i	0.108909	+	0.510759i
$156$		0			0
$157$	−11.4878	+	11.4878i	−0.916827	+	0.916827i	−0.996797	−	0.0799700i	$-0.974518\pi$
$157$	−11.4878	+	11.4878i	−0.916827	+	0.916827i	0.0799700	+	0.996797i	$0.474518\pi$
$158$	4.07370	+	4.90203i	0.324086	+	0.389984i
$159$		0			0
$160$	10.8793	−	6.45292i	0.860087	−	0.510148i
$161$	−31.3280			−2.46900
$162$		0			0
$163$	−6.20045	+	6.20045i	−0.485657	+	0.485657i	−0.906933	−	0.421276i	$-0.861582\pi$
$163$	−6.20045	+	6.20045i	−0.485657	+	0.485657i	0.421276	+	0.906933i	$0.361582\pi$
$164$	−11.7193	−	2.18162i	−0.915121	−	0.170356i
$165$		0			0
$166$	−12.1145	−	1.11799i	−0.940265	−	0.0867730i
$167$	−13.5417			−1.04789			−0.523943	−	0.851753i	$-0.675540\pi$
$167$	−13.5417			−1.04789			−0.523943	+	0.851753i	$0.675540\pi$
$168$		0			0
$169$			6.83520i			0.525785i
$170$	−0.200580	−	0.158043i	−0.0153838	−	0.0121214i
$171$		0			0
$172$	17.9011	−	12.2823i	1.36495	−	0.936516i
$173$	7.13309	−	7.13309i	0.542319	−	0.542319i	−0.381889	−	0.924208i	$-0.624726\pi$
$173$	7.13309	−	7.13309i	0.542319	−	0.542319i	0.924208	+	0.381889i	$0.124726\pi$
$174$		0			0
$175$	−21.8970	+	9.78299i	−1.65525	+	0.739525i
$176$	−10.8527	+	4.81137i	−0.818050	+	0.362671i
$177$		0			0
$178$	12.4721	−	10.3646i	0.934823	−	0.776859i
$179$	12.3059	+	12.3059i	0.919785	+	0.919785i	0.997013	−	0.0772285i	$-0.0246071\pi$
$179$	12.3059	+	12.3059i	0.919785	+	0.919785i	−0.0772285	+	0.997013i	$0.524607\pi$
$180$		0			0
$181$	−14.9151	+	14.9151i	−1.10863	+	1.10863i	−0.115296	+	0.993331i	$0.536782\pi$
$181$	−14.9151	+	14.9151i	−1.10863	+	1.10863i	−0.993331	+	0.115296i	$0.963218\pi$
$182$	16.7713	+	1.54775i	1.24317	+	0.114727i
$183$		0			0
$184$	16.1286	−	9.00734i	1.18902	−	0.664030i
$185$	6.64694	−	10.2498i	0.488693	−	0.753584i
$186$		0			0
$187$	0.169466	+	0.169466i	0.0123926	+	0.0123926i
$188$	−4.70050	−	0.875029i	−0.342819	−	0.0638181i
$189$		0			0
$190$	−12.1331	+	1.43911i	−0.880224	+	0.104404i
$191$	19.1903			1.38856			0.694281	−	0.719704i	$-0.255723\pi$
$191$	19.1903			1.38856			0.694281	+	0.719704i	$0.255723\pi$
$192$		0			0
$193$		−	17.0789i		−	1.22937i	−0.788775	−	0.614683i	$-0.789284\pi$
$193$		−	17.0789i		−	1.22937i	0.788775	−	0.614683i	$-0.210716\pi$
$194$	8.29304	−	6.89171i	0.595406	−	0.494796i
$195$		0			0
$196$	−5.85909	+	31.4740i	−0.418507	+	2.24814i
$197$	−3.05153	−	3.05153i	−0.217412	−	0.217412i	0.589995	−	0.807407i	$-0.299130\pi$
$197$	−3.05153	−	3.05153i	−0.217412	−	0.217412i	−0.807407	+	0.589995i	$0.799130\pi$
$198$		0			0
$199$			21.3495i			1.51342i	0.653748	+	0.756712i	$0.273196\pi$
$199$			21.3495i			1.51342i	−0.653748	+	0.756712i	$0.726804\pi$
$200$	8.46042	−	11.3323i	0.598242	−	0.801316i
$201$		0			0
$202$	26.2633	+	2.42373i	1.84788	+	0.170533i
$203$	−19.2480	−	19.2480i	−1.35094	−	1.35094i
$204$		0			0
$205$	−13.0346	+	2.77937i	−0.910376	+	0.194120i
$206$	−5.82194	−	7.00576i	−0.405634	−	0.488114i
$207$		0			0
$208$	−9.07935	+	4.02520i	−0.629539	+	0.279097i
$209$	11.4669			0.793179
$210$		0			0
$211$	2.62590	+	2.62590i	0.180775	+	0.180775i	0.791693	−	0.610919i	$-0.209200\pi$
$211$	2.62590	+	2.62590i	0.180775	+	0.180775i	−0.610919	+	0.791693i	$0.709200\pi$
$212$	1.61668	−	1.10924i	0.111034	−	0.0761826i
$213$		0			0
$214$	−0.304258	+	3.29692i	−0.0207987	+	0.225373i
$215$	13.2064	−	20.3648i	0.900668	−	1.38887i
$216$		0			0
$217$	13.9471			0.946793
$218$	−0.336075	+	3.64168i	−0.0227618	+	0.246645i
$219$		0			0
$220$	−9.13766	+	9.62627i	−0.616061	+	0.649003i
$221$	0.141776	+	0.141776i	0.00953686	+	0.00953686i
$222$		0			0
$223$			3.53169i			0.236499i	0.992984	+	0.118250i	$0.0377283\pi$
$223$			3.53169i			0.236499i	−0.992984	+	0.118250i	$0.962272\pi$
$224$	−8.67103	−	25.7109i	−0.579358	−	1.71788i
$225$		0			0
$226$	19.5487	−	16.2454i	1.30036	−	1.08063i
$227$	6.02386	−	6.02386i	0.399818	−	0.399818i	−0.478351	−	0.878169i	$-0.658765\pi$
$227$	6.02386	−	6.02386i	0.399818	−	0.399818i	0.878169	+	0.478351i	$0.158765\pi$
$228$		0			0
$229$	7.09963	−	7.09963i	0.469157	−	0.469157i	−0.432485	−	0.901641i	$-0.642363\pi$
$229$	7.09963	−	7.09963i	0.469157	−	0.469157i	0.901641	+	0.432485i	$0.142363\pi$
$230$	12.7826	−	16.2230i	0.842860	−	1.06971i
$231$		0			0
$232$	15.4435	+	4.37530i	1.01392	+	0.287253i
$233$	−6.56359			−0.429995			−0.214998	−	0.976615i	$-0.568974\pi$
$233$	−6.56359			−0.429995			−0.214998	+	0.976615i	$0.568974\pi$
$234$		0			0
$235$	−5.22807	+	1.11478i	−0.341041	+	0.0727204i
$236$	−1.34260	−	1.95681i	−0.0873958	−	0.127377i
$237$		0			0
$238$	−0.421294	+	0.350105i	−0.0273084	+	0.0226939i
$239$	8.78166			0.568039			0.284019	−	0.958819i	$-0.408332\pi$
$239$	8.78166			0.568039			0.284019	+	0.958819i	$0.408332\pi$
$240$		0			0
$241$	−11.3869			−0.733496			−0.366748	−	0.930320i	$-0.619529\pi$
$241$	−11.3869			−0.733496			−0.366748	+	0.930320i	$0.619529\pi$
$242$	−2.38407	+	1.98121i	−0.153254	+	0.127357i
$243$		0			0
$244$	13.8936	−	9.53264i	0.889446	−	0.610265i
$245$	7.46445	+	35.0065i	0.476886	+	2.23649i
$246$		0			0
$247$	9.59319			0.610400
$248$	−7.18039	+	4.01004i	−0.455955	+	0.254638i
$249$		0			0
$250$	3.86845	−	15.3309i	0.244662	−	0.969608i
$251$	−0.420538	+	0.420538i	−0.0265441	+	0.0265441i	−0.720254	−	0.693710i	$-0.755975\pi$
$251$	−0.420538	+	0.420538i	−0.0265441	+	0.0265441i	0.693710	+	0.720254i	$0.255975\pi$
$252$		0			0
$253$	−13.7065	+	13.7065i	−0.861719	+	0.861719i
$254$	8.38156	−	6.96527i	0.525906	−	0.437040i
$255$		0			0
$256$	11.8564	+	10.7436i	0.741025	+	0.671477i
$257$			16.0615i			1.00189i	0.865479	+	0.500945i	$0.167014\pi$
$257$			16.0615i			1.00189i	−0.865479	+	0.500945i	$0.832986\pi$
$258$		0			0
$259$	−18.5301	−	18.5301i	−1.15140	−	1.15140i
$260$	−7.64458	+	8.05335i	−0.474097	+	0.499447i
$261$		0			0
$262$	1.88211	−	20.3943i	0.116277	−	1.25997i
$263$	−9.23715			−0.569587			−0.284793	−	0.958589i	$-0.591925\pi$
$263$	−9.23715			−0.569587			−0.284793	+	0.958589i	$0.591925\pi$
$264$		0			0
$265$	1.19269	−	1.83918i	0.0732665	−	0.112980i
$266$	−2.40849	+	26.0982i	−0.147674	+	1.60018i
$267$		0			0
$268$	−4.38446	−	6.39025i	−0.267824	−	0.390347i
$269$	9.97314	+	9.97314i	0.608073	+	0.608073i	0.942442	−	0.334369i	$-0.108523\pi$
$269$	9.97314	+	9.97314i	0.608073	+	0.608073i	−0.334369	+	0.942442i	$0.608523\pi$
$270$		0			0
$271$	1.01510			0.0616632			0.0308316	−	0.999525i	$-0.490184\pi$
$271$	1.01510			0.0616632			0.0308316	+	0.999525i	$0.490184\pi$
$272$	0.116233	−	0.301373i	0.00704768	−	0.0182734i
$273$		0			0
$274$	19.5988	+	23.5840i	1.18401	+	1.42476i
$275$	−5.30004	+	13.8604i	−0.319604	+	0.835816i
$276$		0			0
$277$	11.3489	+	11.3489i	0.681888	+	0.681888i	0.960425	−	0.278538i	$-0.0898497\pi$
$277$	11.3489	+	11.3489i	0.681888	+	0.681888i	−0.278538	+	0.960425i	$0.589850\pi$
$278$	30.7627	+	2.83896i	1.84502	+	0.170269i
$279$		0			0
$280$	−19.9898	−	22.8189i	−1.19462	−	1.36369i
$281$		−	12.9788i		−	0.774252i	−0.922027	−	0.387126i	$-0.873468\pi$
$281$		−	12.9788i		−	0.774252i	0.922027	−	0.387126i	$-0.126532\pi$
$282$		0			0
$283$	4.38446	+	4.38446i	0.260629	+	0.260629i	0.825310	−	0.564680i	$-0.191001\pi$
$283$	4.38446	+	4.38446i	0.260629	+	0.260629i	−0.564680	+	0.825310i	$0.691001\pi$
$284$	−25.8458	−	4.81137i	−1.53367	−	0.285502i
$285$		0			0
$286$	8.01484	−	6.66052i	0.473928	−	0.393845i
$287$			28.5892i			1.68756i
$288$		0			0
$289$	16.9935			0.999616
$290$	17.8210	−	2.11376i	1.04649	−	0.124125i
$291$		0			0
$292$	−3.56221	+	19.1355i	−0.208463	+	1.11982i
$293$	−16.8008	−	16.8008i	−0.981515	−	0.981515i	0.0183170	−	0.999832i	$-0.494169\pi$
$293$	−16.8008	−	16.8008i	−0.981515	−	0.981515i	−0.999832	+	0.0183170i	$0.994169\pi$
$294$		0			0
$295$	−2.22611	−	1.44361i	−0.129609	−	0.0840504i
$296$	14.8675	+	4.21212i	0.864159	+	0.244824i
$297$		0			0
$298$	−19.8619	−	1.83297i	−1.15057	−	0.106181i
$299$	−11.4669	+	11.4669i	−0.663146	+	0.663146i
$300$		0			0
$301$	−36.8162	−	36.8162i	−2.12205	−	2.12205i
$302$	−22.9665	+	19.0857i	−1.32157	+	1.09826i
$303$		0			0
$304$	−6.26371	−	14.1286i	−0.359248	−	0.810330i
$305$	10.2498	−	15.8057i	0.586905	−	0.905030i
$306$		0			0
$307$	−5.37820	+	5.37820i	−0.306950	+	0.306950i	−0.843725	−	0.536775i	$-0.819642\pi$
$307$	−5.37820	+	5.37820i	−0.306950	+	0.306950i	0.536775	+	0.843725i	$0.319642\pi$
$308$	16.1076	+	23.4765i	0.917818	+	1.33770i
$309$		0			0
$310$	−5.69077	+	7.22241i	−0.323214	+	0.410205i
$311$			18.1831i			1.03107i	0.856868	+	0.515536i	$0.172407\pi$
$311$			18.1831i			1.03107i	−0.856868	+	0.515536i	$0.827593\pi$
$312$		0			0
$313$	−24.1016			−1.36230			−0.681151	−	0.732143i	$-0.738520\pi$
$313$	−24.1016			−1.36230			−0.681151	+	0.732143i	$0.738520\pi$
$314$	−22.8784	−	2.11135i	−1.29110	−	0.119150i
$315$		0			0
$316$	−1.64965	+	8.86162i	−0.0928001	+	0.498505i
$317$	−14.9248	+	14.9248i	−0.838258	+	0.838258i	−0.988629	−	0.150372i	$-0.951953\pi$
$317$	−14.9248	+	14.9248i	−0.838258	+	0.838258i	0.150372	+	0.988629i	$0.451953\pi$
$318$		0			0
$319$	−16.8425			−0.943001
$320$	16.8521	+	6.00043i	0.942064	+	0.335434i
$321$		0			0
$322$	−28.3166	−	34.0744i	−1.57802	−	1.89889i
$323$	−0.220620	+	0.220620i	−0.0122756	+	0.0122756i
$324$		0			0
$325$	−4.43402	+	11.5957i	−0.245955	+	0.643212i
$326$	−12.3484	−	1.13958i	−0.683916	−	0.0631157i
$327$		0			0
$328$	−8.21986	−	14.7185i	−0.453866	−	0.812695i
$329$			11.4669i			0.632189i
$330$		0			0
$331$	12.7757	−	12.7757i	0.702216	−	0.702216i	−0.262670	−	0.964886i	$-0.584603\pi$
$331$	12.7757	−	12.7757i	0.702216	−	0.702216i	0.964886	+	0.262670i	$0.0846030\pi$
$332$	−9.73395	−	14.1870i	−0.534220	−	0.778612i
$333$		0			0
$334$	−12.2400	−	14.7288i	−0.669741	−	0.805924i
$335$	−7.26970	−	4.71434i	−0.397186	−	0.257572i
$336$		0			0
$337$			1.78345i			0.0971508i	0.998820	+	0.0485754i	$0.0154681\pi$
$337$			1.78345i			0.0971508i	−0.998820	+	0.0485754i	$0.984532\pi$
$338$	−7.43440	+	6.17816i	−0.404378	+	0.336047i
$339$		0			0
$340$	−0.00940077	−	0.361015i	−0.000509828	−	0.0195788i
$341$	6.10207	−	6.10207i	0.330446	−	0.330446i
$342$		0			0
$343$	43.2046			2.33283
$344$	29.5394	+	8.36879i	1.59266	+	0.451215i
$345$		0			0
$346$	14.2058	+	1.31099i	0.763710	+	0.0704795i
$347$	17.3955	+	17.3955i	0.933841	+	0.933841i	0.997943	−	0.0641024i	$-0.0204184\pi$
$347$	17.3955	+	17.3955i	0.933841	+	0.933841i	−0.0641024	+	0.997943i	$0.520418\pi$
$348$		0			0
$349$	−11.0996	−	11.0996i	−0.594149	−	0.594149i	0.344600	−	0.938750i	$-0.388015\pi$
$349$	−11.0996	−	11.0996i	−0.594149	−	0.594149i	−0.938750	+	0.344600i	$0.888015\pi$
$350$	−30.4327	−	14.9739i	−1.62670	−	0.800391i
$351$		0			0
$352$	−15.0426	−	7.45517i	−0.801772	−	0.397362i
$353$		−	6.98354i		−	0.371696i	−0.982578	−	0.185848i	$-0.940497\pi$
$353$		−	6.98354i		−	0.371696i	0.982578	−	0.185848i	$-0.0595032\pi$
$354$		0			0
$355$	−28.7467	+	6.12966i	−1.52571	+	0.325328i
$356$	22.5464	+	4.19716i	1.19496	+	0.222449i
$357$		0			0
$358$	−2.26170	+	24.5076i	−0.119535	+	1.29527i
$359$		−	9.16900i		−	0.483921i	−0.970286	−	0.241961i	$-0.922209\pi$
$359$		−	9.16900i		−	0.483921i	0.970286	−	0.241961i	$-0.0777905\pi$
$360$		0			0
$361$		−	4.07180i		−	0.214305i
$362$	−29.7039	−	2.74124i	−1.56120	−	0.144077i
$363$		0			0
$364$	13.4757	+	19.6405i	0.706318	+	1.02944i
$365$	4.53823	+	21.2833i	0.237542	+	1.11402i
$366$		0			0
$367$			28.8148i			1.50412i	0.659095	+	0.752060i	$0.270940\pi$
$367$			28.8148i			1.50412i	−0.659095	+	0.752060i	$0.729060\pi$
$368$	24.3752	+	9.40099i	1.27064	+	0.490061i
$369$		0			0
$370$	17.1564	−	2.03493i	0.891918	−	0.105791i
$371$	−3.32494	−	3.32494i	−0.172622	−	0.172622i
$372$		0			0
$373$	−23.1885	−	23.1885i	−1.20066	−	1.20066i	−0.973967	−	0.226688i	$-0.927210\pi$
$373$	−23.1885	−	23.1885i	−1.20066	−	1.20066i	−0.226688	−	0.973967i	$-0.572790\pi$
$374$	−0.0311462	+	0.337498i	−0.00161053	+	0.0174516i
$375$		0			0
$376$	−3.29692	−	5.90348i	−0.170025	−	0.304448i
$377$	−14.0905			−0.725698
$378$		0			0
$379$	−8.54748	+	8.54748i	−0.439055	+	0.439055i	−0.891694	−	0.452639i	$-0.850483\pi$
$379$	−8.54748	+	8.54748i	−0.439055	+	0.439055i	0.452639	+	0.891694i	$0.350483\pi$
$380$	−12.5320	−	11.8959i	−0.642879	−	0.610247i
$381$		0			0
$382$	17.3456	+	20.8726i	0.887478	+	1.06793i
$383$		−	15.3296i		−	0.783304i	−0.920114	−	0.391652i	$-0.871904\pi$
$383$		−	15.3296i		−	0.783304i	0.920114	−	0.391652i	$-0.128096\pi$
$384$		0			0
$385$	26.7074	+	17.3195i	1.36114	+	0.882686i
$386$	18.5761	−	15.4372i	0.945498	−	0.785731i
$387$		0			0
$388$	14.9917	+	2.79081i	0.761089	+	0.141682i
$389$	12.2654	−	12.2654i	0.621880	−	0.621880i	−0.324132	−	0.946012i	$-0.605072\pi$
$389$	12.2654	−	12.2654i	0.621880	−	0.621880i	0.946012	+	0.324132i	$0.105072\pi$
$390$		0			0
$391$		−	0.527420i		−	0.0266728i
$392$	−39.5290	+	22.0758i	−1.99652	+	1.11499i
$393$		0			0
$394$	0.560841	−	6.07723i	0.0282548	−	0.306166i
$395$	2.10165	+	9.85623i	0.105745	+	0.495921i
$396$		0			0
$397$	1.29269	−	1.29269i	0.0648781	−	0.0648781i	−0.673923	−	0.738801i	$-0.735392\pi$
$397$	1.29269	−	1.29269i	0.0648781	−	0.0648781i	0.738801	+	0.673923i	$0.235392\pi$
$398$	−23.2211	+	19.2972i	−1.16397	+	0.967282i
$399$		0			0
$400$	19.9729	−	1.04089i	0.998645	−	0.0520444i
$401$	18.9391			0.945775			0.472887	−	0.881123i	$-0.343212\pi$
$401$	18.9391			0.945775			0.472887	+	0.881123i	$0.343212\pi$
$402$		0			0
$403$	5.10501	−	5.10501i	0.254298	−	0.254298i
$404$	21.1025	+	30.7564i	1.04989	+	1.53019i
$405$		0			0
$406$	3.53759	−	38.3331i	0.175568	−	1.90244i
$407$	−16.2144			−0.803717
$408$		0			0
$409$			5.06528i			0.250462i	0.992128	+	0.125231i	$0.0399672\pi$
$409$			5.06528i			0.250462i	−0.992128	+	0.125231i	$0.960033\pi$
$410$	−14.8047	−	11.6651i	−0.731150	−	0.576097i
$411$		0			0
$412$	2.35761	−	12.6646i	0.116151	−	0.623942i
$413$	−4.02445	+	4.02445i	−0.198030	+	0.198030i
$414$		0			0
$415$	−16.1395	−	10.4663i	−0.792255	−	0.513771i
$416$	−12.5846	−	6.23701i	−0.617013	−	0.305794i
$417$		0			0
$418$	10.3646	+	12.4721i	0.506949	+	0.610030i
$419$	−11.0463	−	11.0463i	−0.539648	−	0.539648i	0.383777	−	0.923426i	$-0.374623\pi$
$419$	−11.0463	−	11.0463i	−0.539648	−	0.539648i	−0.923426	+	0.383777i	$0.874623\pi$
$420$		0			0
$421$	−19.8136	+	19.8136i	−0.965655	+	0.965655i	−0.999429	−	0.0337748i	$-0.989247\pi$
$421$	−19.8136	+	19.8136i	−0.965655	+	0.965655i	0.0337748	+	0.999429i	$0.489247\pi$
$422$	−0.482616	+	5.22958i	−0.0234934	+	0.254572i
$423$		0			0
$424$	2.66775	+	0.755800i	0.129558	+	0.0367049i
$425$	−0.164701	−	0.368644i	−0.00798916	−	0.0178819i
$426$		0			0
$427$	−28.5741	−	28.5741i	−1.38280	−	1.38280i
$428$	−3.86095	+	2.64906i	−0.186626	+	0.128047i
$429$		0			0
$430$	34.0869	−	4.04307i	1.64382	−	0.194974i
$431$	−9.40148			−0.452853			−0.226427	−	0.974028i	$-0.572704\pi$
$431$	−9.40148			−0.452853			−0.226427	+	0.974028i	$0.572704\pi$
$432$		0			0
$433$			18.5845i			0.893112i	0.894756	+	0.446556i	$0.147350\pi$
$433$			18.5845i			0.893112i	−0.894756	+	0.446556i	$0.852650\pi$
$434$	12.6064	+	15.1698i	0.605129	+	0.728173i
$435$		0			0
$436$	−4.26469	+	2.92608i	−0.204242	+	0.140134i
$437$	−17.8439	−	17.8439i	−0.853588	−	0.853588i
$438$		0			0
$439$			2.71467i			0.129564i	0.997899	+	0.0647819i	$0.0206352\pi$
$439$			2.71467i			0.129564i	−0.997899	+	0.0647819i	$0.979365\pi$
$440$	−18.7294	−	1.23777i	−0.892890	−	0.0590084i
$441$		0			0
$442$	−0.0260570	+	0.282351i	−0.00123940	+	0.0134301i
$443$	−9.96756	−	9.96756i	−0.473573	−	0.473573i	0.429496	−	0.903069i	$-0.358691\pi$
$443$	−9.96756	−	9.96756i	−0.473573	−	0.473573i	−0.903069	+	0.429496i	$0.858691\pi$
$444$		0			0
$445$	25.0769	−	5.34716i	1.18876	−	0.253480i
$446$	−3.84129	+	3.19220i	−0.181890	+	0.151155i
$447$		0			0
$448$	20.1273	−	32.6705i	0.950923	−	1.54354i
$449$	−13.6173			−0.642642			−0.321321	−	0.946970i	$-0.604127\pi$
$449$	−13.6173			−0.642642			−0.321321	+	0.946970i	$0.604127\pi$
$450$		0			0
$451$	12.5082	+	12.5082i	0.588987	+	0.588987i
$452$	35.3391	+	6.57860i	1.66221	+	0.309432i
$453$		0			0
$454$	11.9967	+	1.10713i	0.563035	+	0.0519601i
$455$	22.3435	+	14.4896i	1.04748	+	0.679281i
$456$		0			0
$457$	−18.5845			−0.869344			−0.434672	−	0.900589i	$-0.643136\pi$
$457$	−18.5845			−0.869344			−0.434672	+	0.900589i	$0.643136\pi$
$458$	14.1392	+	1.30484i	0.660680	+	0.0609713i
$459$		0			0
$460$	29.1990	−	0.760338i	1.36141	−	0.0354509i
$461$	7.08538	+	7.08538i	0.329999	+	0.329999i	0.852586	−	0.522587i	$-0.175033\pi$
$461$	7.08538	+	7.08538i	0.329999	+	0.329999i	−0.522587	+	0.852586i	$0.675033\pi$
$462$		0			0
$463$			14.6677i			0.681665i	0.940124	+	0.340832i	$0.110709\pi$
$463$			14.6677i			0.681665i	−0.940124	+	0.340832i	$0.889291\pi$
$464$	9.20015	+	20.7521i	0.427106	+	0.963392i
$465$		0			0
$466$	−5.93266	−	7.13898i	−0.274825	−	0.330707i
$467$	14.5282	−	14.5282i	0.672284	−	0.672284i	−0.285958	−	0.958242i	$-0.592312\pi$
$467$	14.5282	−	14.5282i	0.672284	−	0.672284i	0.958242	+	0.285958i	$0.0923118\pi$
$468$		0			0
$469$	−13.1425	+	13.1425i	−0.606862	+	0.606862i
$470$	−5.93802	−	4.67876i	−0.273900	−	0.215815i
$471$		0			0
$472$	0.914807	−	3.22900i	0.0421074	−	0.148627i
$473$	−32.2153			−1.48126
$474$		0			0
$475$	−18.0443	−	6.89988i	−0.827929	−	0.316588i
$476$	−0.761592	−	0.141776i	−0.0349075	−	0.00649827i
$477$		0			0
$478$	7.93751	+	9.55150i	0.363053	+	0.436875i
$479$	−27.3521			−1.24975			−0.624876	−	0.780724i	$-0.714850\pi$
$479$	−27.3521			−1.24975			−0.624876	+	0.780724i	$0.714850\pi$
$480$		0			0
$481$	−13.5650			−0.618509
$482$	−10.2923	−	12.3851i	−0.468803	−	0.564128i
$483$		0			0
$484$	−4.30979	−	0.802296i	−0.195899	−	0.0364680i
$485$	16.6744	−	3.55548i	0.757143	−	0.161446i
$486$		0			0
$487$	−4.89831			−0.221964			−0.110982	−	0.993822i	$-0.535400\pi$
$487$	−4.89831			−0.221964			−0.110982	+	0.993822i	$0.535400\pi$
$488$	22.9264	+	6.49526i	1.03783	+	0.294026i
$489$		0			0
$490$	−31.3284	+	39.7603i	−1.41527	+	1.79619i
$491$	3.74548	−	3.74548i	0.169031	−	0.169031i	−0.617522	−	0.786553i	$-0.711863\pi$
$491$	3.74548	−	3.74548i	0.169031	−	0.169031i	0.786553	+	0.617522i	$0.211863\pi$
$492$		0			0
$493$	0.324048	−	0.324048i	0.0145944	−	0.0145944i
$494$	8.67103	+	10.4342i	0.390128	+	0.469456i
$495$		0			0
$496$	−10.8517	−	4.18529i	−0.487257	−	0.187925i
$497$			63.0508i			2.82822i
$498$		0			0
$499$	−1.88227	−	1.88227i	−0.0842620	−	0.0842620i	0.663720	−	0.747982i	$-0.268977\pi$
$499$	−1.88227	−	1.88227i	−0.0842620	−	0.0842620i	−0.747982	+	0.663720i	$0.768977\pi$
$500$	20.1714	−	9.64958i	0.902093	−	0.431543i
$501$		0			0
$502$	−0.837516	−	0.0772908i	−0.0373802	−	0.00344966i
$503$	40.3375			1.79856			0.899280	−	0.437373i	$-0.144091\pi$
$503$	40.3375			1.79856			0.899280	+	0.437373i	$0.144091\pi$
$504$		0			0
$505$	34.9892	+	22.6902i	1.55700	+	1.00970i
$506$	−27.2970	−	2.51912i	−1.21350	−	0.111988i
$507$		0			0
$508$	15.1517	+	2.82060i	0.672250	+	0.125144i
$509$	−19.5164	−	19.5164i	−0.865049	−	0.865049i	0.126870	−	0.991919i	$-0.459507\pi$
$509$	−19.5164	−	19.5164i	−0.865049	−	0.865049i	−0.991919	+	0.126870i	$0.959507\pi$
$510$		0			0
$511$	46.6811			2.06505
$512$	−0.968769	+	22.6067i	−0.0428139	+	0.999083i
$513$		0			0
$514$	−17.4695	+	14.5176i	−0.770548	+	0.640343i
$515$	−3.00358	−	14.0861i	−0.132354	−	0.620707i
$516$		0			0
$517$	5.01692	+	5.01692i	0.220644	+	0.220644i
$518$	3.40565	−	36.9034i	0.149636	−	1.62144i
$519$		0			0
$520$	−15.6691	−	1.03552i	−0.687134	−	0.0454106i
$521$			38.3466i			1.67999i	0.542591	+	0.839997i	$0.317443\pi$
$521$			38.3466i			1.67999i	−0.542591	+	0.839997i	$0.682557\pi$
$522$		0			0
$523$	0.720542	+	0.720542i	0.0315071	+	0.0315071i	0.722685	−	0.691178i	$-0.242908\pi$
$523$	0.720542	+	0.720542i	0.0315071	+	0.0315071i	−0.691178	+	0.722685i	$0.742908\pi$
$524$	23.8834	−	16.3868i	1.04335	−	0.715861i
$525$		0			0
$526$	−8.34921	−	10.0469i	−0.364043	−	0.438066i
$527$			0.234806i			0.0102283i
$528$		0			0
$529$	19.6580			0.854694
$530$	3.07845	−	0.365137i	0.133719	−	0.0158605i
$531$		0			0
$532$	−30.5630	+	20.9698i	−1.32508	+	0.909158i
$533$	10.4644	+	10.4644i	0.453262	+	0.453262i
$534$		0			0
$535$	−2.84837	+	4.39230i	−0.123146	+	0.189896i
$536$	2.98744	−	10.5448i	0.129038	−	0.455466i
$537$		0			0
$538$	−1.83297	+	19.8619i	−0.0790248	+	0.856306i
$539$	33.5927	−	33.5927i	1.44694	−	1.44694i
$540$		0			0
$541$	−8.97299	−	8.97299i	−0.385779	−	0.385779i	0.487400	−	0.873179i	$-0.337945\pi$
$541$	−8.97299	−	8.97299i	−0.385779	−	0.385779i	−0.873179	+	0.487400i	$0.837945\pi$
$542$	0.917525	+	1.10409i	0.0394111	+	0.0474248i
$543$		0			0
$544$	0.432853	−	0.145980i	0.0185584	−	0.00625886i
$545$	−3.14623	+	4.85161i	−0.134770	+	0.207820i
$546$		0			0
$547$	−2.19558	+	2.19558i	−0.0938764	+	0.0938764i	−0.752485	−	0.658609i	$-0.771145\pi$
$547$	−2.19558	+	2.19558i	−0.0938764	+	0.0938764i	0.658609	+	0.752485i	$0.271145\pi$
$548$	−7.93659	+	42.6339i	−0.339034	+	1.82123i
$549$		0			0
$550$	−19.8661	+	6.76343i	−0.847092	+	0.288394i
$551$		−	21.9266i		−	0.934103i
$552$		0			0
$553$	21.6179			0.919288
$554$	−2.08581	+	22.6017i	−0.0886177	+	0.960254i
$555$		0			0
$556$	24.7178	+	36.0255i	1.04827	+	1.52782i
$557$	8.22555	−	8.22555i	0.348528	−	0.348528i	−0.511033	−	0.859561i	$-0.670737\pi$
$557$	8.22555	−	8.22555i	0.348528	−	0.348528i	0.859561	+	0.511033i	$0.170737\pi$
$558$		0			0
$559$	−26.9514			−1.13992
$560$	6.75104	−	42.3676i	0.285283	−	1.79036i
$561$		0			0
$562$	14.1166	−	11.7312i	0.595473	−	0.494851i
$563$	−1.97777	+	1.97777i	−0.0833531	+	0.0833531i	−0.747554	−	0.664201i	$-0.768772\pi$
$563$	−1.97777	+	1.97777i	−0.0833531	+	0.0833531i	0.664201	+	0.747554i	$0.268772\pi$
$564$		0			0
$565$	39.3054	−	8.38110i	1.65359	−	0.352596i
$566$	−0.805822	+	8.73182i	−0.0338712	+	0.367026i
$567$		0			0
$568$	−18.1282	−	32.4604i	−0.760641	−	1.36201i
$569$			13.9009i			0.582755i	0.956608	+	0.291378i	$0.0941137\pi$
$569$			13.9009i			0.582755i	−0.956608	+	0.291378i	$0.905886\pi$
$570$		0			0
$571$	20.0321	−	20.0321i	0.838316	−	0.838316i	−0.150321	−	0.988637i	$-0.548031\pi$
$571$	20.0321	−	20.0321i	0.838316	−	0.838316i	0.988637	+	0.150321i	$0.0480308\pi$
$572$	14.4888	+	2.69719i	0.605807	+	0.112775i
$573$		0			0
$574$	−31.0954	+	25.8410i	−1.29790	+	1.07858i
$575$	29.8161	−	13.3211i	1.24342	−	0.555526i
$576$		0			0
$577$		−	5.72056i		−	0.238150i	−0.992885	−	0.119075i	$-0.962007\pi$
$577$		−	5.72056i		−	0.238150i	0.992885	−	0.119075i	$-0.0379929\pi$
$578$	15.3600	+	18.4832i	0.638890	+	0.768799i
$579$		0			0
$580$	18.4070	+	17.4727i	0.764311	+	0.725516i
$581$	−29.1776	+	29.1776i	−1.21049	+	1.21049i
$582$		0			0
$583$	−2.90942			−0.120496
$584$	−24.0328	+	13.4216i	−0.994485	+	0.555390i
$585$		0			0
$586$	3.08783	−	33.4595i	0.127557	−	1.38220i
$587$	−2.20548	−	2.20548i	−0.0910301	−	0.0910301i	0.660125	−	0.751155i	$-0.270503\pi$
$587$	−2.20548	−	2.20548i	−0.0910301	−	0.0910301i	−0.751155	+	0.660125i	$0.770503\pi$
$588$		0			0
$589$	7.94402	+	7.94402i	0.327328	+	0.327328i
$590$	−0.441955	−	3.72610i	−0.0181950	−	0.153401i
$591$		0			0
$592$	8.85701	+	19.9781i	0.364021	+	0.821096i
$593$		−	25.9747i		−	1.06665i	−0.845909	−	0.533327i	$-0.820942\pi$
$593$		−	25.9747i		−	1.06665i	0.845909	−	0.533327i	$-0.179058\pi$
$594$		0			0
$595$	−0.847071	+	0.180621i	−0.0347265	+	0.00740475i
$596$	−15.9590	−	23.2598i	−0.653705	−	0.952759i
$597$		0			0
$598$	−22.8367	−	2.10750i	−0.933861	−	0.0861820i
$599$		−	15.5466i		−	0.635215i	−0.948222	−	0.317607i	$-0.897121\pi$
$599$		−	15.5466i		−	0.635215i	0.948222	−	0.317607i	$-0.102879\pi$
$600$		0			0
$601$		−	7.95250i		−	0.324389i	−0.986759	−	0.162195i	$-0.948143\pi$
$601$		−	7.95250i		−	0.324389i	0.986759	−	0.162195i	$-0.0518572\pi$
$602$	6.76647	−	73.3209i	0.275781	−	2.98834i
$603$		0			0
$604$	−41.5176	−	7.72879i	−1.68933	−	0.314480i
$605$	−4.79351	+	1.02212i	−0.194884	+	0.0415551i
$606$		0			0
$607$		−	19.1199i		−	0.776052i	−0.921648	−	0.388026i	$-0.873157\pi$
$607$		−	19.1199i		−	0.776052i	0.921648	−	0.388026i	$-0.126843\pi$
$608$	9.70556	−	19.5833i	0.393612	−	0.794207i
$609$		0			0
$610$	26.4558	−	3.13794i	1.07117	−	0.127052i
$611$	4.19716	+	4.19716i	0.169799	+	0.169799i
$612$		0			0
$613$	2.68166	+	2.68166i	0.108311	+	0.108311i	0.759185	−	0.650874i	$-0.225598\pi$
$613$	2.68166	+	2.68166i	0.108311	+	0.108311i	−0.650874	+	0.759185i	$0.725598\pi$
$614$	−10.7109	−	0.988461i	−0.432256	−	0.0398910i
$615$		0			0
$616$	−10.9753	+	38.7395i	−0.442206	+	1.56086i
$617$	21.0752			0.848457			0.424228	−	0.905555i	$-0.360545\pi$
$617$	21.0752			0.848457			0.424228	+	0.905555i	$0.360545\pi$
$618$		0			0
$619$	−10.5100	+	10.5100i	−0.422434	+	0.422434i	−0.886041	−	0.463607i	$-0.846555\pi$
$619$	−10.5100	+	10.5100i	−0.422434	+	0.422434i	0.463607	+	0.886041i	$0.346555\pi$
$620$	−12.9993	+	0.338500i	−0.522064	+	0.0135945i
$621$		0			0
$622$	−19.7771	+	16.4353i	−0.792991	+	0.658994i
$623$		−	55.0019i		−	2.20361i
$624$		0			0
$625$	16.6803	−	18.6217i	0.667213	−	0.744867i
$626$	−21.7848	−	26.2144i	−0.870695	−	1.04774i
$627$		0			0
$628$	−18.3827	−	26.7924i	−0.733552	−	1.06913i
$629$	0.311962	−	0.311962i	0.0124387	−	0.0124387i
$630$		0			0
$631$			14.3803i			0.572470i	0.958159	+	0.286235i	$0.0924039\pi$
$631$			14.3803i			0.572470i	−0.958159	+	0.286235i	$0.907596\pi$
$632$	−11.1295	+	6.21552i	−0.442710	+	0.247240i
$633$		0			0
$634$	−29.7232	−	2.74303i	−1.18046	−	0.108939i
$635$	16.8523	−	3.59343i	0.668764	−	0.142601i
$636$		0			0
$637$	28.1037	−	28.1037i	1.11351	−	1.11351i
$638$	−15.2235	−	18.3190i	−0.602705	−	0.725257i
$639$		0			0
$640$	8.70576	+	23.7531i	0.344125	+	0.938924i
$641$	31.5128			1.24468			0.622341	−	0.782746i	$-0.286182\pi$
$641$	31.5128			1.24468			0.622341	+	0.782746i	$0.286182\pi$
$642$		0			0
$643$	3.29103	−	3.29103i	0.129786	−	0.129786i	−0.639230	−	0.769016i	$-0.720747\pi$
$643$	3.29103	−	3.29103i	0.129786	−	0.129786i	0.769016	+	0.639230i	$0.220747\pi$
$644$	11.4669	−	61.5979i	0.451858	−	2.42730i
$645$		0			0
$646$	−0.439374	−	0.0405479i	−0.0172869	−	0.00159534i
$647$	−25.3387			−0.996169			−0.498084	−	0.867129i	$-0.665963\pi$
$647$	−25.3387			−0.996169			−0.498084	+	0.867129i	$0.665963\pi$
$648$		0			0
$649$			3.52151i			0.138231i
$650$	−16.6200	+	5.65829i	−0.651889	+	0.221937i
$651$		0			0
$652$	−9.92193	−	14.4610i	−0.388573	−	0.566336i
$653$	−20.8253	+	20.8253i	−0.814956	+	0.814956i	−0.985372	−	0.170416i	$-0.945489\pi$
$653$	−20.8253	+	20.8253i	−0.814956	+	0.814956i	0.170416	+	0.985372i	$0.445489\pi$
$654$		0			0
$655$	17.6197	−	27.1703i	0.688459	−	1.06163i
$656$	8.57910	−	22.2441i	0.334958	−	0.868488i
$657$		0			0
$658$	−12.4721	+	10.3646i	−0.486213	+	0.404054i
$659$	−7.10157	−	7.10157i	−0.276638	−	0.276638i	0.555128	−	0.831765i	$-0.312669\pi$
$659$	−7.10157	−	7.10157i	−0.276638	−	0.276638i	−0.831765	+	0.555128i	$0.812669\pi$
$660$		0			0
$661$	19.3139	−	19.3139i	0.751223	−	0.751223i	−0.223485	−	0.974707i	$-0.571743\pi$
$661$	19.3139	−	19.3139i	0.751223	−	0.751223i	0.974707	+	0.223485i	$0.0717432\pi$
$662$	25.4433	+	2.34805i	0.988881	+	0.0912596i
$663$		0			0
$664$	6.63242	−	23.4105i	0.257388	−	0.908504i
$665$	−22.5476	+	34.7692i	−0.874357	+	1.34829i
$666$		0			0
$667$	26.2091	+	26.2091i	1.01482	+	1.01482i
$668$	4.95660	−	26.6259i	0.191776	−	1.03019i
$669$		0			0
$670$	−1.44327	−	12.1682i	−0.0557585	−	0.470097i
$671$	−25.0032			−0.965238
$672$		0			0
$673$		−	31.0260i		−	1.19597i	−0.801509	−	0.597983i	$-0.795969\pi$
$673$		−	31.0260i		−	1.19597i	0.801509	−	0.597983i	$-0.204031\pi$
$674$	−1.93980	+	1.61201i	−0.0747181	+	0.0620925i
$675$		0			0
$676$	−13.4395	−	2.50186i	−0.516904	−	0.0962253i
$677$	−17.0809	−	17.0809i	−0.656473	−	0.656473i	0.298071	−	0.954544i	$-0.403657\pi$
$677$	−17.0809	−	17.0809i	−0.656473	−	0.656473i	−0.954544	+	0.298071i	$0.903657\pi$
$678$		0			0
$679$		−	36.5723i		−	1.40352i
$680$	0.384165	−	0.336536i	0.0147321	−	0.0129056i
$681$		0			0
$682$	12.1525	+	1.12150i	0.465344	+	0.0429446i
$683$	7.45091	+	7.45091i	0.285101	+	0.285101i	0.835139	−	0.550038i	$-0.185387\pi$
$683$	7.45091	+	7.45091i	0.285101	+	0.285101i	−0.550038	+	0.835139i	$0.685387\pi$
$684$		0			0
$685$	10.1112	+	47.4190i	0.386328	+	1.81179i
$686$	39.0515	+	46.9921i	1.49099	+	1.79417i
$687$		0			0
$688$	17.5974	+	39.6932i	0.670896	+	1.51329i
$689$	−2.43403			−0.0927290
$690$		0			0
$691$	22.1699	+	22.1699i	0.843381	+	0.843381i	0.989297	−	0.145916i	$-0.0466129\pi$
$691$	22.1699	+	22.1699i	0.843381	+	0.843381i	−0.145916	+	0.989297i	$0.546613\pi$
$692$	11.4143	+	16.6361i	0.433908	+	0.632411i
$693$		0			0
$694$	−3.19713	+	34.6438i	−0.121361	+	1.31506i
$695$	40.9835	+	26.5775i	1.55459	+	1.00814i
$696$		0			0
$697$	−0.481310			−0.0182309
$698$	2.04000	−	22.1053i	0.0772153	−	0.836699i
$699$		0			0
$700$	−11.2207	−	46.6351i	−0.424102	−	1.76264i
$701$	3.31765	+	3.31765i	0.125306	+	0.125306i	0.766979	−	0.641673i	$-0.221759\pi$
$701$	3.31765	+	3.31765i	0.125306	+	0.125306i	−0.641673	+	0.766979i	$0.721759\pi$
$702$		0			0
$703$		−	21.1088i		−	0.796133i
$704$	−5.48787	−	23.0998i	−0.206832	−	0.870607i
$705$		0			0
$706$	7.59574	−	6.31223i	0.285870	−	0.237564i
$707$	63.2549	−	63.2549i	2.37894	−	2.37894i
$708$		0			0
$709$	−2.54396	+	2.54396i	−0.0955403	+	0.0955403i	−0.753261	−	0.657721i	$-0.771521\pi$
$709$	−2.54396	+	2.54396i	−0.0955403	+	0.0955403i	0.657721	+	0.753261i	$0.271521\pi$
$710$	−32.6503	−	25.7263i	−1.22535	−	0.965489i
$711$		0			0
$712$	15.8140	+	28.3166i	0.592654	+	1.06121i
$713$	−18.9912			−0.711225
$714$		0			0
$715$	16.1150	−	3.43620i	0.602666	−	0.128507i
$716$	−28.7004	+	19.6918i	−1.07258	+	0.735918i
$717$		0			0
$718$	9.97279	−	8.28762i	0.372181	−	0.309291i
$719$	−30.5534			−1.13945			−0.569724	−	0.821836i	$-0.692950\pi$
$719$	−30.5534			−1.13945			−0.569724	+	0.821836i	$0.692950\pi$
$720$		0			0
$721$	−30.8954			−1.15060
$722$	4.42875	−	3.68039i	0.164821	−	0.136970i
$723$		0			0
$724$	−23.8670	−	34.7856i	−0.887010	−	1.29280i
$725$	26.5035	+	10.1346i	0.984315	+	0.376388i
$726$		0			0
$727$	−17.2992			−0.641592			−0.320796	−	0.947148i	$-0.603950\pi$
$727$	−17.2992			−0.641592			−0.320796	+	0.947148i	$0.603950\pi$
$728$	−9.18193	+	32.4095i	−0.340305	+	1.20118i
$729$		0			0
$730$	−19.0470	+	24.1734i	−0.704962	+	0.894699i
$731$	0.619817	−	0.619817i	0.0229247	−	0.0229247i
$732$		0			0
$733$	−22.3087	+	22.3087i	−0.823990	+	0.823990i	−0.986678	−	0.162687i	$-0.947984\pi$
$733$	−22.3087	+	22.3087i	−0.823990	+	0.823990i	0.162687	+	0.986678i	$0.447984\pi$
$734$	−31.3408	+	26.0449i	−1.15681	+	0.961336i
$735$		0			0
$736$	11.8070	+	35.0093i	0.435210	+	1.29046i
$737$			11.5000i			0.423609i
$738$		0			0
$739$	4.81191	+	4.81191i	0.177009	+	0.177009i	0.790051	−	0.613042i	$-0.210054\pi$
$739$	4.81191	+	4.81191i	0.177009	+	0.177009i	−0.613042	+	0.790051i	$0.710054\pi$
$740$	17.7205	+	16.8211i	0.651419	+	0.618354i
$741$		0			0
$742$	0.611092	−	6.62174i	0.0224339	−	0.243092i
$743$	−15.8418			−0.581178			−0.290589	−	0.956848i	$-0.593851\pi$
$743$	−15.8418			−0.581178			−0.290589	+	0.956848i	$0.593851\pi$
$744$		0			0
$745$	−26.4609	−	17.1597i	−0.969453	−	0.628682i
$746$	4.26182	−	46.1808i	0.156036	−	1.69080i
$747$		0			0
$748$	−0.395237	+	0.271179i	−0.0144513	+	0.00991528i
$749$	7.94059	+	7.94059i	0.290143	+	0.290143i
$750$		0			0
$751$	31.4221			1.14661			0.573304	−	0.819343i	$-0.305661\pi$
$751$	31.4221			1.14661			0.573304	+	0.819343i	$0.305661\pi$
$752$	3.44100	−	8.92193i	0.125480	−	0.325349i
$753$		0			0
$754$	−12.7360	−	15.3257i	−0.463819	−	0.558130i
$755$	−46.1775	+	9.84643i	−1.68057	+	0.358348i
$756$		0			0
$757$	7.83752	+	7.83752i	0.284859	+	0.284859i	0.835043	−	0.550184i	$-0.185442\pi$
$757$	7.83752	+	7.83752i	0.284859	+	0.284859i	−0.550184	+	0.835043i	$0.685442\pi$
$758$	−17.0226	−	1.57094i	−0.618290	−	0.0570593i
$759$		0			0
$760$	1.61140	−	24.3830i	0.0584516	−	0.884465i
$761$		−	31.9292i		−	1.15743i	−0.815529	−	0.578716i	$-0.803554\pi$
$761$		−	31.9292i		−	1.15743i	0.815529	−	0.578716i	$-0.196446\pi$
$762$		0			0
$763$	8.77094	+	8.77094i	0.317529	+	0.317529i
$764$	−7.02414	+	37.7324i	−0.254124	+	1.36511i
$765$		0			0
$766$	16.6734	−	13.8560i	0.602434	−	0.500637i
$767$			2.94610i			0.106378i
$768$		0			0
$769$	−31.1063			−1.12172			−0.560860	−	0.827911i	$-0.689529\pi$
$769$	−31.1063			−1.12172			−0.560860	+	0.827911i	$0.689529\pi$
$770$	5.30229	+	44.7034i	0.191081	+	1.61100i
$771$		0			0
$772$	33.5809	+	6.25131i	1.20860	+	0.224989i
$773$	9.09313	+	9.09313i	0.327057	+	0.327057i	0.851466	−	0.524409i	$-0.175714\pi$
$773$	9.09313	+	9.09313i	0.327057	+	0.327057i	−0.524409	+	0.851466i	$0.675714\pi$
$774$		0			0
$775$	−13.2740	+	5.93049i	−0.476817	+	0.213029i
$776$	10.5152	+	18.8285i	0.377472	+	0.675904i
$777$		0			0
$778$	24.4270	+	2.25426i	0.875750	+	0.0808192i
$779$	−16.2838	+	16.2838i	−0.583429	+	0.583429i
$780$		0			0
$781$	27.5857	+	27.5857i	0.987092	+	0.987092i
$782$	0.573656	−	0.476721i	0.0205139	−	0.0170475i
$783$		0			0
$784$	−59.7402	−	23.0405i	−2.13358	−	0.822877i
$785$	−30.4797	−	19.7658i	−1.08787	−	0.705472i
$786$		0			0
$787$	33.7151	−	33.7151i	1.20181	−	1.20181i	0.228200	−	0.973614i	$-0.426716\pi$
$787$	33.7151	−	33.7151i	1.20181	−	1.20181i	0.973614	−	0.228200i	$-0.0732840\pi$
$788$	7.11691	−	4.88304i	0.253529	−	0.173951i
$789$		0			0
$790$	−8.82064	+	11.1947i	−0.313824	+	0.398288i
$791$		−	86.2096i		−	3.06526i
$792$		0			0
$793$	−20.9177			−0.742810
$794$	2.57443	+	0.237583i	0.0913632	+	0.00843152i
$795$		0			0
$796$	−41.9778	−	7.81445i	−1.48786	−	0.276976i
$797$	11.4589	−	11.4589i	0.405896	−	0.405896i	−0.474409	−	0.880305i	$-0.657338\pi$
$797$	11.4589	−	11.4589i	0.405896	−	0.405896i	0.880305	+	0.474409i	$0.157338\pi$
$798$		0			0
$799$	−0.193049			−0.00682959
$800$	19.1851	+	20.7830i	0.678296	+	0.734789i
$801$		0			0
$802$	17.1186	+	20.5994i	0.604478	+	0.727390i
$803$	20.4237	−	20.4237i	0.720736	−	0.720736i
$804$		0			0
$805$	−14.6087	−	68.5114i	−0.514890	−	2.41471i
$806$	10.1668	+	0.938251i	0.358111	+	0.0330485i
$807$		0			0
$808$	−14.3786	+	50.7523i	−0.505838	+	1.78546i
$809$		−	6.24385i		−	0.219522i	−0.993958	−	0.109761i	$-0.964991\pi$
$809$		−	6.24385i		−	0.219522i	0.993958	−	0.109761i	$-0.0350086\pi$
$810$		0			0
$811$	7.76764	−	7.76764i	0.272759	−	0.272759i	−0.557451	−	0.830210i	$-0.688221\pi$
$811$	7.76764	−	7.76764i	0.272759	−	0.272759i	0.830210	+	0.557451i	$0.188221\pi$
$812$	44.8910	−	30.8005i	1.57537	−	1.08089i
$813$		0			0
$814$	−14.6557	−	17.6358i	−0.513684	−	0.618134i
$815$	−16.4512	−	10.6684i	−0.576259	−	0.373699i
$816$		0			0
$817$		−	41.9397i		−	1.46728i
$818$	−5.50932	+	4.57837i	−0.192629	+	0.160079i
$819$		0			0
$820$	−0.693864	−	26.6462i	−0.0242308	−	0.930527i
$821$	−8.46118	+	8.46118i	−0.295297	+	0.295297i	−0.839169	−	0.543871i	$-0.816958\pi$
$821$	−8.46118	+	8.46118i	−0.295297	+	0.295297i	0.543871	+	0.839169i	$0.316958\pi$
$822$		0			0
$823$	−43.8269			−1.52771			−0.763854	−	0.645389i	$-0.776695\pi$
$823$	−43.8269			−1.52771			−0.763854	+	0.645389i	$0.776695\pi$
$824$	15.9058	−	8.88295i	0.554107	−	0.309452i
$825$		0			0
$826$	−8.01484	−	0.739655i	−0.278872	−	0.0257359i
$827$	24.5603	+	24.5603i	0.854046	+	0.854046i	0.990629	−	0.136583i	$-0.0436120\pi$
$827$	24.5603	+	24.5603i	0.854046	+	0.854046i	−0.136583	+	0.990629i	$0.543612\pi$
$828$		0			0
$829$	9.18724	+	9.18724i	0.319086	+	0.319086i	0.848416	−	0.529330i	$-0.177557\pi$
$829$	9.18724	+	9.18724i	0.319086	+	0.319086i	−0.529330	+	0.848416i	$0.677557\pi$
$830$	−3.20421	−	27.0145i	−0.111220	−	0.937688i
$831$		0			0
$832$	−4.59116	−	19.3253i	−0.159170	−	0.669985i
$833$			1.29264i			0.0447872i
$834$		0			0
$835$	−6.31468	−	29.6143i	−0.218528	−	1.02485i
$836$	−4.19716	+	22.5464i	−0.145162	+	0.779783i
$837$		0			0
$838$	2.03021	−	21.9992i	0.0701324	−	0.759949i
$839$			41.7367i			1.44091i	0.693502	+	0.720455i	$0.256067\pi$
$839$			41.7367i			1.44091i	−0.693502	+	0.720455i	$0.743933\pi$
$840$		0			0
$841$			3.20578i			0.110544i
$842$	−39.4595	−	3.64154i	−1.35986	−	0.125496i
$843$		0			0
$844$	−6.12425	+	4.20196i	−0.210805	+	0.144637i
$845$	−14.9479	+	3.18735i	−0.514224	+	0.109648i
$846$		0			0
$847$			10.5137i			0.361256i
$848$	1.58926	+	3.58477i	0.0545752	+	0.123101i
$849$		0			0
$850$	0.252092	−	0.512347i	0.00864670	−	0.0175733i
$851$	25.2316	+	25.2316i	0.864928	+	0.864928i
$852$		0			0
$853$	−1.94078	−	1.94078i	−0.0664511	−	0.0664511i	0.673100	−	0.739551i	$-0.264962\pi$
$853$	−1.94078	−	1.94078i	−0.0664511	−	0.0664511i	−0.739551	+	0.673100i	$0.764962\pi$
$854$	5.25165	−	56.9065i	0.179708	−	1.94730i
$855$		0			0
$856$	−6.37110	−	1.80499i	−0.217760	−	0.0616934i
$857$	13.3372			0.455591			0.227796	−	0.973709i	$-0.426848\pi$
$857$	13.3372			0.455591			0.227796	+	0.973709i	$0.426848\pi$
$858$		0			0
$859$	−0.723573	+	0.723573i	−0.0246880	+	0.0246880i	−0.719343	−	0.694655i	$-0.755557\pi$
$859$	−0.723573	+	0.723573i	−0.0246880	+	0.0246880i	0.694655	+	0.719343i	$0.255557\pi$
$860$	35.2078	+	33.4207i	1.20057	+	1.13964i
$861$		0			0
$862$	−8.49775	−	10.2256i	−0.289434	−	0.348287i
$863$			50.6997i			1.72584i	0.505342	+	0.862919i	$0.331366\pi$
$863$			50.6997i			1.72584i	−0.505342	+	0.862919i	$0.668634\pi$
$864$		0			0
$865$	18.9257	+	12.2731i	0.643492	+	0.417299i
$866$	−20.2136	+	16.7980i	−0.686887	+	0.570819i
$867$		0			0
$868$	−5.10501	+	27.4231i	−0.173275	+	0.930802i
$869$	9.45816	−	9.45816i	0.320846	−	0.320846i
$870$		0			0
$871$			9.62095i			0.325993i
$872$	−7.03733	−	1.99374i	−0.238314	−	0.0675167i
$873$		0			0
$874$	3.27953	−	35.5367i	0.110932	−	1.20205i
$875$	−31.6053	−	43.3246i	−1.06846	−	1.46464i
$876$		0			0
$877$	−33.1206	+	33.1206i	−1.11840	+	1.11840i	−0.126429	+	0.991976i	$0.540351\pi$
$877$	−33.1206	+	33.1206i	−1.11840	+	1.11840i	−0.991976	+	0.126429i	$0.959649\pi$
$878$	−2.95264	+	2.45371i	−0.0996469	+	0.0828088i
$879$		0			0
$880$	−15.5828	−	21.4901i	−0.525294	−	0.724431i
$881$	38.9477			1.31218			0.656091	−	0.754682i	$-0.272209\pi$
$881$	38.9477			1.31218			0.656091	+	0.754682i	$0.272209\pi$
$882$		0			0
$883$	4.65765	−	4.65765i	0.156743	−	0.156743i	−0.624379	−	0.781122i	$-0.714648\pi$
$883$	4.65765	−	4.65765i	0.156743	−	0.156743i	0.781122	+	0.624379i	$0.214648\pi$
$884$	−0.330656	+	0.226869i	−0.0111211	+	0.00763042i
$885$		0			0
$886$	1.83194	−	19.8508i	0.0615453	−	0.666899i
$887$	25.1222			0.843520			0.421760	−	0.906707i	$-0.361412\pi$
$887$	25.1222			0.843520			0.421760	+	0.906707i	$0.361412\pi$
$888$		0			0
$889$		−	36.9627i		−	1.23969i
$890$	28.4823	+	22.4421i	0.954728	+	0.752261i
$891$		0			0
$892$	−6.94407	−	1.29269i	−0.232505	−	0.0432823i
$893$	−6.53131	+	6.53131i	−0.218562	+	0.218562i
$894$		0			0
$895$	−21.1734	+	32.6502i	−0.707748	+	1.09138i
$896$	53.7270	−	7.63834i	1.79489	−	0.255179i
$897$		0			0
$898$	−12.3083	−	14.8111i	−0.410735	−	0.494252i
$899$	−11.6682	−	11.6682i	−0.389156	−	0.389156i
$900$		0			0
$901$	0.0559767	−	0.0559767i	0.00186486	−	0.00186486i
$902$	−2.29888	+	24.9105i	−0.0765444	+	0.829429i
$903$		0			0
$904$	24.7867	+	44.3832i	0.824394	+	1.47616i
$905$	−39.5729	−	25.6627i	−1.31545	−	0.853057i
$906$		0			0
$907$	10.1443	+	10.1443i	0.336835	+	0.336835i	0.855175	−	0.518340i	$-0.173450\pi$
$907$	10.1443	+	10.1443i	0.336835	+	0.336835i	−0.518340	+	0.855175i	$0.673450\pi$
$908$	9.63935	+	14.0491i	0.319893	+	0.466237i
$909$		0			0
$910$	4.43591	+	37.3989i	0.147049	+	1.23976i
$911$	−41.0617			−1.36043			−0.680217	−	0.733011i	$-0.738115\pi$
$911$	−41.0617			−1.36043			−0.680217	+	0.733011i	$0.738115\pi$
$912$		0			0
$913$			25.5312i			0.844960i
$914$	−16.7980	−	20.2136i	−0.555628	−	0.668608i
$915$		0			0
$916$	11.3608	+	16.5581i	0.375371	+	0.547094i
$917$	−49.1196	−	49.1196i	−1.62207	−	1.62207i
$918$		0			0
$919$			13.0575i			0.430728i	0.976534	+	0.215364i	$0.0690937\pi$
$919$			13.0575i			0.430728i	−0.976534	+	0.215364i	$0.930906\pi$
$920$	27.2192	+	31.0714i	0.897390	+	1.02440i
$921$		0			0
$922$	−1.30222	+	14.1108i	−0.0428865	+	0.464714i
$923$	23.0782	+	23.0782i	0.759628	+	0.759628i
$924$		0			0
$925$	25.5150	+	9.75657i	0.838928	+	0.320794i
$926$	−15.9535	+	13.2577i	−0.524265	+	0.435676i
$927$		0			0
$928$	−14.2555	+	28.7639i	−0.467961	+	0.944223i
$929$	19.7138			0.646789			0.323394	−	0.946264i	$-0.395176\pi$
$929$	19.7138			0.646789			0.323394	+	0.946264i	$0.395176\pi$
$930$		0			0
$931$	43.7329	+	43.7329i	1.43329	+	1.43329i
$932$	2.40244	−	12.9055i	0.0786946	−	0.422733i
$933$		0			0
$934$	28.9334	+	2.67014i	0.946730	+	0.0873697i
$935$	−0.291582	+	0.449630i	−0.00953574	+	0.0147045i
$936$		0			0
$937$	−8.22657			−0.268750			−0.134375	−	0.990931i	$-0.542903\pi$
$937$	−8.22657			−0.268750			−0.134375	+	0.990931i	$0.542903\pi$
$938$	−26.1737	−	2.41546i	−0.854601	−	0.0788675i
$939$		0			0
$940$	−0.278303	−	10.6876i	−0.00907724	−	0.348590i
$941$	−20.5746	−	20.5746i	−0.670714	−	0.670714i	0.287167	−	0.957881i	$-0.407287\pi$
$941$	−20.5746	−	20.5746i	−0.670714	−	0.670714i	−0.957881	+	0.287167i	$0.907287\pi$
$942$		0			0
$943$		−	38.9285i		−	1.26769i
$944$	4.33894	−	1.92361i	0.141220	−	0.0626080i
$945$		0			0
$946$	−29.1186	−	35.0394i	−0.946726	−	1.13923i
$947$	3.82001	−	3.82001i	0.124134	−	0.124134i	−0.642311	−	0.766444i	$-0.722024\pi$
$947$	3.82001	−	3.82001i	0.124134	−	0.124134i	0.766444	+	0.642311i	$0.222024\pi$
$948$		0			0
$949$	17.0865	−	17.0865i	0.554651	−	0.554651i
$950$	−8.80501	−	25.8628i	−0.285672	−	0.839099i
$951$		0			0
$952$	−0.534179	−	0.956503i	−0.0173128	−	0.0310005i
$953$	27.9560			0.905585			0.452792	−	0.891616i	$-0.350428\pi$
$953$	27.9560			0.905585			0.452792	+	0.891616i	$0.350428\pi$
$954$		0			0
$955$	8.94871	+	41.9673i	0.289573	+	1.35803i
$956$	−3.21431	+	17.2667i	−0.103958	+	0.558445i
$957$		0			0
$958$	−24.7229	−	29.7499i	−0.798760	−	0.961177i
$959$	104.005			3.35851
$960$		0			0
$961$	−22.5452			−0.727264
$962$	−12.2610	−	14.7541i	−0.395311	−	0.475692i
$963$		0			0
$964$	4.16790	−	22.3892i	0.134239	−	0.721108i
$965$	37.3499	−	7.96413i	1.20234	−	0.256374i
$966$		0			0
$967$	1.02224			0.0328732			0.0164366	−	0.999865i	$-0.494768\pi$
$967$	1.02224			0.0328732			0.0164366	+	0.999865i	$0.494768\pi$
$968$	−3.02287	−	5.41277i	−0.0971588	−	0.173973i
$969$		0			0
$970$	18.9387	+	14.9224i	0.608084	+	0.479129i
$971$	−35.7245	+	35.7245i	−1.14645	+	1.14645i	−0.159208	+	0.987245i	$0.550894\pi$
$971$	−35.7245	+	35.7245i	−1.14645	+	1.14645i	−0.987245	+	0.159208i	$0.949106\pi$
$972$		0			0
$973$	74.0917	−	74.0917i	2.37527	−	2.37527i
$974$	−4.42745	−	5.32771i	−0.141865	−	0.170711i
$975$		0			0
$976$	13.6579	+	30.8071i	0.437178	+	0.986110i
$977$			8.80804i			0.281794i	0.990024	+	0.140897i	$0.0449987\pi$
$977$			8.80804i			0.281794i	−0.990024	+	0.140897i	$0.955001\pi$
$978$		0			0
$979$	−24.0641	−	24.0641i	−0.769093	−	0.769093i
$980$	−71.5628	+	1.86348i	−2.28599	+	0.0595268i
$981$		0			0
$982$	7.45926	+	0.688383i	0.238035	+	0.0219672i
$983$	20.3937			0.650457			0.325228	−	0.945636i	$-0.394559\pi$
$983$	20.3937			0.650457			0.325228	+	0.945636i	$0.394559\pi$
$984$		0			0
$985$	5.25043	−	8.09637i	0.167293	−	0.257972i
$986$	0.645353	+	0.0595568i	0.0205522	+	0.00189668i
$987$		0			0
$988$	−3.51135	+	18.8623i	−0.111711	+	0.600091i
$989$	50.1310	+	50.1310i	1.59407	+	1.59407i
$990$		0			0
$991$	48.0654			1.52685			0.763424	−	0.645898i	$-0.223517\pi$
$991$	48.0654			1.52685			0.763424	+	0.645898i	$0.223517\pi$
$992$	−5.25641	−	15.5860i	−0.166891	−	0.494856i
$993$		0			0
$994$	−68.5781	+	56.9900i	−2.17516	+	1.80761i
$995$	−46.6893	+	9.95556i	−1.48015	+	0.315613i
$996$		0			0
$997$	−34.3855	−	34.3855i	−1.08900	−	1.08900i	−0.995632	−	0.0933695i	$-0.970236\pi$
$997$	−34.3855	−	34.3855i	−1.08900	−	1.08900i	−0.0933695	−	0.995632i	$-0.529764\pi$
$998$	0.345943	−	3.74861i	0.0109506	−	0.118660i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.bm.g.109.11	yes	32
3.2	odd	2	inner	720.2.bm.g.109.6	yes	32
5.4	even	2	inner	720.2.bm.g.109.5	✓	32
15.14	odd	2	inner	720.2.bm.g.109.12	yes	32
16.5	even	4	inner	720.2.bm.g.469.7	yes	32
48.5	odd	4	inner	720.2.bm.g.469.10	yes	32
80.69	even	4	inner	720.2.bm.g.469.9	yes	32
240.149	odd	4	inner	720.2.bm.g.469.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
720.2.bm.g.109.5	✓	32	5.4	even	2	inner
720.2.bm.g.109.6	yes	32	3.2	odd	2	inner
720.2.bm.g.109.11	yes	32	1.1	even	1	trivial
720.2.bm.g.109.12	yes	32	15.14	odd	2	inner
720.2.bm.g.469.7	yes	32	16.5	even	4	inner
720.2.bm.g.469.8	yes	32	240.149	odd	4	inner
720.2.bm.g.469.9	yes	32	80.69	even	4	inner
720.2.bm.g.469.10	yes	32	48.5	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.bm (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.903873 + 1.08766i) q^{2} +(-0.366025 + 1.96622i) q^{4} +(0.466314 + 2.18690i) q^{5} +4.79660 q^{7} +(-2.46943 + 1.37910i) q^{8} +(-1.95713 + 2.48388i) q^{10} +(2.09858 - 2.09858i) q^{11} +(1.75568 - 1.75568i) q^{13} +(4.33552 + 5.21709i) q^{14} +(-3.73205 - 1.43937i) q^{16} +0.0807527i q^{17} +(2.73205 + 2.73205i) q^{19} +(-4.47062 + 0.116414i) q^{20} +(4.17940 + 0.385699i) q^{22} -6.53131 q^{23} +(-4.56510 + 2.03957i) q^{25} +(3.49650 + 0.322676i) q^{26} +(-1.75568 + 9.43117i) q^{28} +(-4.01284 - 4.01284i) q^{29} +2.90771 q^{31} +(-1.80775 - 5.36023i) q^{32} +(-0.0878318 + 0.0729902i) q^{34} +(2.23672 + 10.4897i) q^{35} +(-3.86318 - 3.86318i) q^{37} +(-0.502125 + 5.44098i) q^{38} +(-4.16750 - 4.75731i) q^{40} +5.96030i q^{41} +(-7.67549 - 7.67549i) q^{43} +(3.35814 + 4.89441i) q^{44} +(-5.90348 - 7.10387i) q^{46} +2.39062i q^{47} +16.0073 q^{49} +(-6.34464 - 3.12178i) q^{50} +(2.80943 + 4.09467i) q^{52} +(-0.693188 - 0.693188i) q^{53} +(5.56800 + 3.61080i) q^{55} +(-11.8449 + 6.61500i) q^{56} +(0.737521 - 7.99172i) q^{58} +(-0.839022 + 0.839022i) q^{59} +(-5.95717 - 5.95717i) q^{61} +(2.62821 + 3.16262i) q^{62} +(4.19615 - 6.81119i) q^{64} +(4.65819 + 3.02080i) q^{65} +(-2.73995 + 2.73995i) q^{67} +(-0.158778 - 0.0295575i) q^{68} +(-9.38755 + 11.9142i) q^{70} +13.1449i q^{71} +9.73214 q^{73} +(0.710014 - 7.69366i) q^{74} +(-6.37182 + 4.37182i) q^{76} +(10.0660 - 10.0660i) q^{77} +4.50693 q^{79} +(1.40746 - 8.83284i) q^{80} +(-6.48280 + 5.38736i) q^{82} +(-6.08297 + 6.08297i) q^{83} +(-0.176598 + 0.0376561i) q^{85} +(1.41068 - 15.2860i) q^{86} +(-2.28814 + 8.07645i) q^{88} -11.4669i q^{89} +(8.42127 - 8.42127i) q^{91} +(2.39062 - 12.8420i) q^{92} +(-2.60020 + 2.16082i) q^{94} +(-4.70074 + 7.24873i) q^{95} -7.62464i q^{97} +(14.4686 + 17.4106i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 16 q^{4} - 24 q^{10} - 64 q^{16} + 32 q^{19} + 32 q^{31} - 72 q^{40} - 32 q^{46} + 128 q^{49} - 32 q^{64} - 104 q^{70} - 32 q^{76} + 224 q^{79} - 48 q^{85} - 32 q^{91} - 48 q^{94}+O(q^{100}) \) 32 * q + 16 * q^4 - 24 * q^10 - 64 * q^16 + 32 * q^19 + 32 * q^31 - 72 * q^40 - 32 * q^46 + 128 * q^49 - 32 * q^64 - 104 * q^70 - 32 * q^76 + 224 * q^79 - 48 * q^85 - 32 * q^91 - 48 * q^94

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