LMFDB - Embedded newform 740.2.bp.a.169.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(169,740)] 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("740.169"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 11])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.bp (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$20$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			169.8
Character	$\chi$	$=$	740.169
Dual form			740.2.bp.a.289.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.324044 - 0.890304i) q^{3} +(-0.350865 - 2.20837i) q^{5} +(4.31890 + 0.761538i) q^{7} +(1.61050 - 1.35137i) q^{9} +(-0.398930 - 0.690967i) q^{11} +(4.54857 + 3.81671i) q^{13} +(-1.85242 + 1.02799i) q^{15} +(-3.51825 + 2.95216i) q^{17} +(-0.565183 - 1.55283i) q^{19} +(-0.721513 - 4.09190i) q^{21} +(0.646500 - 1.11977i) q^{23} +(-4.75379 + 1.54968i) q^{25} +(-4.18653 - 2.41709i) q^{27} +(6.97099 - 4.02470i) q^{29} +2.11192i q^{31} +(-0.485900 + 0.579073i) q^{33} +(0.166405 - 9.80491i) q^{35} +(5.80584 - 1.81445i) q^{37} +(1.92409 - 5.28639i) q^{39} +(-8.72727 - 7.32305i) q^{41} +1.78254 q^{43} +(-3.54938 - 3.08242i) q^{45} +(-0.367788 - 0.212342i) q^{47} +(11.4951 + 4.18386i) q^{49} +(3.76839 + 2.17568i) q^{51} +(3.92991 - 0.692949i) q^{53} +(-1.38594 + 1.12342i) q^{55} +(-1.19935 + 1.00637i) q^{57} +(-4.42906 + 0.780963i) q^{59} +(-0.130492 + 0.155514i) q^{61} +(7.98468 - 4.60996i) q^{63} +(6.83276 - 11.3841i) q^{65} +(-5.03707 - 0.888171i) q^{67} +(-1.20643 - 0.212726i) q^{69} +(-14.7335 + 5.36254i) q^{71} -0.313499i q^{73} +(2.92012 + 3.73015i) q^{75} +(-1.19674 - 3.28802i) q^{77} +(-13.1703 - 2.32228i) q^{79} +(0.299882 - 1.70072i) q^{81} +(6.49696 + 7.74277i) q^{83} +(7.75389 + 6.73378i) q^{85} +(-5.84212 - 4.90212i) q^{87} +(-6.41911 + 1.13186i) q^{89} +(16.7382 + 19.9479i) q^{91} +(1.88025 - 0.684354i) q^{93} +(-3.23092 + 1.79297i) q^{95} +(0.185715 - 0.321668i) q^{97} +(-1.57623 - 0.573699i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q + 3 q^{5} + 6 q^{9} + 12 q^{11} + 3 q^{15} + 6 q^{19} - 12 q^{21} - 33 q^{25} - 48 q^{35} + 24 q^{39} + 30 q^{41} - 27 q^{45} + 6 q^{49} - 3 q^{55} - 42 q^{59} + 48 q^{61} - 18 q^{65} - 108 q^{69}+ \cdots + 90 q^{99}+O(q^{100}) $ 120 * q + 3 * q^5 + 6 * q^9 + 12 * q^11 + 3 * q^15 + 6 * q^19 - 12 * q^21 - 33 * q^25 - 48 * q^35 + 24 * q^39 + 30 * q^41 - 27 * q^45 + 6 * q^49 - 3 * q^55 - 42 * q^59 + 48 * q^61 - 18 * q^65 - 108 * q^69 - 18 * q^71 - 12 * q^75 - 48 * q^79 + 108 * q^81 - 33 * q^85 - 84 * q^89 - 30 * q^91 + 99 * q^95 + 90 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.324044	−	0.890304i	−0.187087	−	0.514017i	0.810320	−	0.585988i	$-0.199293\pi$
$3$	−0.324044	−	0.890304i	−0.187087	−	0.514017i	−0.997407	+	0.0719706i	$0.977071\pi$
$4$		0			0
$5$	−0.350865	−	2.20837i	−0.156912	−	0.987613i
$5$	−0.350865	−	2.20837i	−0.156912	−	0.987613i
$6$		0			0
$7$	4.31890	+	0.761538i	1.63239	+	0.287834i	0.913362	−	0.407148i	$-0.133477\pi$
$7$	4.31890	+	0.761538i	1.63239	+	0.287834i	0.719027	+	0.694982i	$0.244588\pi$
$8$		0			0
$9$	1.61050	−	1.35137i	0.536832	−	0.450456i
$10$		0			0
$11$	−0.398930	−	0.690967i	−0.120282	−	0.208334i	0.799597	−	0.600537i	$-0.205047\pi$
$11$	−0.398930	−	0.690967i	−0.120282	−	0.208334i	−0.919879	+	0.392203i	$0.871713\pi$
$12$		0			0
$13$	4.54857	+	3.81671i	1.26155	+	1.05856i	0.995515	+	0.0945992i	$0.0301570\pi$
$13$	4.54857	+	3.81671i	1.26155	+	1.05856i	0.266032	+	0.963964i	$0.414287\pi$
$14$		0			0
$15$	−1.85242	+	1.02799i	−0.478294	+	0.265425i
$16$		0			0
$17$	−3.51825	+	2.95216i	−0.853300	+	0.716004i	−0.960514	−	0.278232i	$-0.910252\pi$
$17$	−3.51825	+	2.95216i	−0.853300	+	0.716004i	0.107214	+	0.994236i	$0.465807\pi$
$18$		0			0
$19$	−0.565183	−	1.55283i	−0.129662	−	0.356243i	0.857825	−	0.513941i	$-0.171815\pi$
$19$	−0.565183	−	1.55283i	−0.129662	−	0.356243i	−0.987487	+	0.157698i	$0.949593\pi$
$20$		0			0
$21$	−0.721513	−	4.09190i	−0.157447	−	0.892926i
$22$		0			0
$23$	0.646500	−	1.11977i	0.134805	−	0.233488i	−0.790718	−	0.612180i	$-0.790293\pi$
$23$	0.646500	−	1.11977i	0.134805	−	0.233488i	0.925523	+	0.378692i	$0.123626\pi$
$24$		0			0
$25$	−4.75379	+	1.54968i	−0.950757	+	0.309936i
$26$		0			0
$27$	−4.18653	−	2.41709i	−0.805697	−	0.465170i
$28$		0			0
$29$	6.97099	−	4.02470i	1.29448	−	0.747368i	0.315035	−	0.949080i	$-0.397984\pi$
$29$	6.97099	−	4.02470i	1.29448	−	0.747368i	0.979445	+	0.201712i	$0.0646504\pi$
$30$		0			0
$31$			2.11192i			0.379311i	0.981851	+	0.189656i	$0.0607372\pi$
$31$			2.11192i			0.379311i	−0.981851	+	0.189656i	$0.939263\pi$
$32$		0			0
$33$	−0.485900	+	0.579073i	−0.0845844	+	0.100804i
$34$		0			0
$35$	0.166405	−	9.80491i	0.0281276	−	1.65733i
$36$		0			0
$37$	5.80584	−	1.81445i	0.954474	−	0.298294i
$37$	5.80584	−	1.81445i	0.954474	−	0.298294i
$38$		0			0
$39$	1.92409	−	5.28639i	0.308101	−	0.846501i
$40$		0			0
$41$	−8.72727	−	7.32305i	−1.36297	−	1.14367i	−0.975052	−	0.221974i	$-0.928750\pi$
$41$	−8.72727	−	7.32305i	−1.36297	−	1.14367i	−0.387918	−	0.921694i	$-0.626806\pi$
$42$		0			0
$43$	1.78254			0.271835			0.135918	−	0.990720i	$-0.456602\pi$
$43$	1.78254			0.271835			0.135918	+	0.990720i	$0.456602\pi$
$44$		0			0
$45$	−3.54938	−	3.08242i	−0.529111	−	0.459500i
$46$		0			0
$47$	−0.367788	−	0.212342i	−0.0536473	−	0.0309733i	0.472936	−	0.881097i	$-0.343194\pi$
$47$	−0.367788	−	0.212342i	−0.0536473	−	0.0309733i	−0.526584	+	0.850123i	$0.676527\pi$
$48$		0			0
$49$	11.4951	+	4.18386i	1.64215	+	0.597695i
$50$		0			0
$51$	3.76839	+	2.17568i	0.527680	+	0.304656i
$52$		0			0
$53$	3.92991	−	0.692949i	0.539815	−	0.0951839i	0.102908	−	0.994691i	$-0.467185\pi$
$53$	3.92991	−	0.692949i	0.539815	−	0.0951839i	0.436906	+	0.899507i	$0.356074\pi$
$54$		0			0
$55$	−1.38594	+	1.12342i	−0.186880	+	0.151482i
$56$		0			0
$57$	−1.19935	+	1.00637i	−0.158857	+	0.133297i
$58$		0			0
$59$	−4.42906	+	0.780963i	−0.576615	+	0.101673i	−0.454348	−	0.890824i	$-0.650128\pi$
$59$	−4.42906	+	0.780963i	−0.576615	+	0.101673i	−0.122267	+	0.992497i	$0.539017\pi$
$60$		0			0
$61$	−0.130492	+	0.155514i	−0.0167077	+	0.0199115i	−0.774334	−	0.632778i	$-0.781915\pi$
$61$	−0.130492	+	0.155514i	−0.0167077	+	0.0199115i	0.757626	+	0.652689i	$0.226359\pi$
$62$		0			0
$63$	7.98468	−	4.60996i	1.00598	−	0.580800i
$64$		0			0
$65$	6.83276	−	11.3841i	0.847499	−	1.41202i
$66$		0			0
$67$	−5.03707	−	0.888171i	−0.615376	−	0.108507i	−0.142733	−	0.989761i	$-0.545589\pi$
$67$	−5.03707	−	0.888171i	−0.615376	−	0.108507i	−0.472643	+	0.881254i	$0.656700\pi$
$68$		0			0
$69$	−1.20643	−	0.212726i	−0.145237	−	0.0256092i
$70$		0			0
$71$	−14.7335	+	5.36254i	−1.74854	+	0.636417i	−0.999655	−	0.0262828i	$-0.991633\pi$
$71$	−14.7335	+	5.36254i	−1.74854	+	0.636417i	−0.748886	+	0.662699i	$0.769411\pi$
$72$		0			0
$73$		−	0.313499i		−	0.0366923i	−0.999832	−	0.0183461i	$-0.994160\pi$
$73$		−	0.313499i		−	0.0366923i	0.999832	−	0.0183461i	$-0.00584009\pi$
$74$		0			0
$75$	2.92012	+	3.73015i	0.337187	+	0.430721i
$76$		0			0
$77$	−1.19674	−	3.28802i	−0.136381	−	0.374704i
$78$		0			0
$79$	−13.1703	−	2.32228i	−1.48178	−	0.261277i	−0.626488	−	0.779431i	$-0.715508\pi$
$79$	−13.1703	−	2.32228i	−1.48178	−	0.261277i	−0.855287	+	0.518154i	$0.826619\pi$
$80$		0			0
$81$	0.299882	−	1.70072i	0.0333202	−	0.188968i
$82$		0			0
$83$	6.49696	+	7.74277i	0.713134	+	0.849880i	0.993944	−	0.109883i	$-0.0350477\pi$
$83$	6.49696	+	7.74277i	0.713134	+	0.849880i	−0.280811	+	0.959763i	$0.590603\pi$
$84$		0			0
$85$	7.75389	+	6.73378i	0.841027	+	0.730381i
$86$		0			0
$87$	−5.84212	−	4.90212i	−0.626341	−	0.525562i
$88$		0			0
$89$	−6.41911	+	1.13186i	−0.680424	+	0.119977i	−0.503169	−	0.864188i	$-0.667833\pi$
$89$	−6.41911	+	1.13186i	−0.680424	+	0.119977i	−0.177255	+	0.984165i	$0.556722\pi$
$90$		0			0
$91$	16.7382	+	19.9479i	1.75464	+	2.09110i
$92$		0			0
$93$	1.88025	−	0.684354i	0.194973	−	0.0709642i
$94$		0			0
$95$	−3.23092	+	1.79297i	−0.331485	+	0.183955i
$96$		0			0
$97$	0.185715	−	0.321668i	0.0188565	−	0.0326604i	−0.856443	−	0.516241i	$-0.827331\pi$
$97$	0.185715	−	0.321668i	0.0188565	−	0.0326604i	0.875300	+	0.483581i	$0.160664\pi$
$98$		0			0
$99$	−1.57623	−	0.573699i	−0.158417	−	0.0576590i
$100$		0			0
$101$	−0.868722	+	1.50467i	−0.0864411	+	0.149720i	−0.906004	−	0.423268i	$-0.860883\pi$
$101$	−0.868722	+	1.50467i	−0.0864411	+	0.149720i	0.819563	+	0.572989i	$0.194216\pi$
$102$		0			0
$103$	8.01418	+	13.8810i	0.789661	+	1.36773i	0.926175	+	0.377095i	$0.123077\pi$
$103$	8.01418	+	13.8810i	0.789661	+	1.36773i	−0.136514	+	0.990638i	$0.543590\pi$
$104$		0			0
$105$	−8.78328	+	3.02907i	−0.857160	+	0.295607i
$106$		0			0
$107$	−2.28730	+	2.72590i	−0.221122	+	0.263523i	−0.865189	−	0.501446i	$-0.832801\pi$
$107$	−2.28730	+	2.72590i	−0.221122	+	0.263523i	0.644067	+	0.764969i	$0.277246\pi$
$108$		0			0
$109$	3.37384	−	9.26956i	0.323156	−	0.887863i	−0.666641	−	0.745379i	$-0.732269\pi$
$109$	3.37384	−	9.26956i	0.323156	−	0.887863i	0.989797	−	0.142484i	$-0.0455090\pi$
$110$		0			0
$111$	−3.49676	−	4.58100i	−0.331898	−	0.434809i
$112$		0			0
$113$	13.2781	+	4.83284i	1.24910	+	0.454635i	0.880098	−	0.474793i	$-0.157477\pi$
$113$	13.2781	+	4.83284i	1.24910	+	0.454635i	0.369003	+	0.929428i	$0.379699\pi$
$114$		0			0
$115$	−2.69970	−	1.03482i	−0.251748	−	0.0964976i
$116$		0			0
$117$	12.4832			1.15407
$118$		0			0
$119$	−17.4431	+	10.0708i	−1.59901	+	0.923188i
$120$		0			0
$121$	5.18171	−	8.97498i	0.471064	−	0.815908i
$122$		0			0
$123$	−3.69172	+	10.1429i	−0.332871	+	0.914556i
$124$		0			0
$125$	5.09021	+	9.95439i	0.455282	+	0.890347i
$126$		0			0
$127$	−18.0242	+	3.17816i	−1.59939	+	0.282016i	−0.901039	−	0.433739i	$-0.857194\pi$
$127$	−18.0242	+	3.17816i	−1.59939	+	0.282016i	−0.698352	+	0.715755i	$0.746083\pi$
$128$		0			0
$129$	−0.577623	−	1.58701i	−0.0508569	−	0.139728i
$130$		0			0
$131$	8.38240	+	9.98976i	0.732374	+	0.872809i	0.995770	−	0.0918783i	$-0.0292871\pi$
$131$	8.38240	+	9.98976i	0.732374	+	0.872809i	−0.263396	+	0.964688i	$0.584843\pi$
$132$		0			0
$133$	−1.25843	−	7.13691i	−0.109120	−	0.618849i
$134$		0			0
$135$	−3.86892	+	10.0935i	−0.332984	+	0.868707i
$136$		0			0
$137$	−8.39094	+	4.84451i	−0.716886	+	0.413894i	−0.813605	−	0.581417i	$-0.802498\pi$
$137$	−8.39094	+	4.84451i	−0.716886	+	0.413894i	0.0967195	+	0.995312i	$0.469165\pi$
$138$		0			0
$139$	−10.6628	+	8.94714i	−0.904405	+	0.758886i	−0.971046	−	0.238891i	$-0.923216\pi$
$139$	−10.6628	+	8.94714i	−0.904405	+	0.758886i	0.0666412	+	0.997777i	$0.478772\pi$
$140$		0			0
$141$	−0.0698698	+	0.396251i	−0.00588410	+	0.0333704i
$142$		0			0
$143$	0.822656	−	4.66551i	0.0687939	−	0.390150i
$144$		0			0
$145$	−11.3339	−	13.9824i	−0.941230	−	1.16117i
$146$		0			0
$147$		−	11.5899i		−	0.955916i
$148$		0			0
$149$	11.8863			0.973766			0.486883	−	0.873467i	$-0.338134\pi$
$149$	11.8863			0.973766			0.486883	+	0.873467i	$0.338134\pi$
$150$		0			0
$151$	0.575189	−	0.209352i	0.0468082	−	0.0170368i	−0.318510	−	0.947920i	$-0.603182\pi$
$151$	0.575189	−	0.209352i	0.0468082	−	0.0170368i	0.365318	+	0.930883i	$0.380960\pi$
$152$		0			0
$153$	−1.67667	+	9.50889i	−0.135551	+	0.768748i
$154$		0			0
$155$	4.66389	−	0.740998i	0.374613	−	0.0595184i
$156$		0			0
$157$	−7.48889	−	8.92491i	−0.597678	−	0.712285i	0.379384	−	0.925239i	$-0.376136\pi$
$157$	−7.48889	−	8.92491i	−0.597678	−	0.712285i	−0.977062	+	0.212954i	$0.931691\pi$
$158$		0			0
$159$	−1.89040	−	3.27427i	−0.149919	−	0.259666i
$160$		0			0
$161$	3.64491	−	4.34384i	0.287259	−	0.342342i
$162$		0			0
$163$	−4.03275	−	22.8708i	−0.315869	−	1.79138i	−0.567305	−	0.823508i	$-0.692014\pi$
$163$	−4.03275	−	22.8708i	−0.315869	−	1.79138i	0.251436	−	0.967874i	$-0.419097\pi$
$164$		0			0
$165$	1.44929	+	0.869870i	0.112827	+	0.0677193i
$166$		0			0
$167$	3.65419	−	1.33002i	0.282769	−	0.102920i	−0.196742	−	0.980455i	$-0.563036\pi$
$167$	3.65419	−	1.33002i	0.282769	−	0.102920i	0.479511	+	0.877536i	$0.340814\pi$
$168$		0			0
$169$	3.86484	+	21.9186i	0.297296	+	1.68605i
$170$		0			0
$171$	−3.00867	−	1.73705i	−0.230079	−	0.132836i
$172$		0			0
$173$	3.98194	−	10.9403i	0.302741	−	0.831775i	−0.691280	−	0.722587i	$-0.742953\pi$
$173$	3.98194	−	10.9403i	0.302741	−	0.831775i	0.994021	−	0.109188i	$-0.0348250\pi$
$174$		0			0
$175$	−21.7113	+	3.07272i	−1.64122	+	0.232276i
$176$		0			0
$177$	2.13051	+	3.69015i	0.160139	+	0.277368i
$178$		0			0
$179$			13.4118i			1.00245i	0.865318	+	0.501224i	$0.167117\pi$
$179$			13.4118i			1.00245i	−0.865318	+	0.501224i	$0.832883\pi$
$180$		0			0
$181$	15.6557	+	13.1367i	1.16368	+	0.976445i	0.999949	−	0.0100599i	$-0.00320221\pi$
$181$	15.6557	+	13.1367i	1.16368	+	0.976445i	0.163732	+	0.986505i	$0.447647\pi$
$182$		0			0
$183$	0.180740	+	0.0657839i	0.0133607	+	0.00486288i
$184$		0			0
$185$	−6.04404	−	12.1848i	−0.444367	−	0.895845i
$186$		0			0
$187$	3.44338	+	1.25329i	0.251805	+	0.0916495i
$188$		0			0
$189$	−16.2405	−	13.6274i	−1.18132	−	0.991245i
$190$		0			0
$191$		−	1.03076i		−	0.0745829i	−0.999304	−	0.0372914i	$-0.988127\pi$
$191$		−	1.03076i		−	0.0745829i	0.999304	−	0.0372914i	$-0.0118730\pi$
$192$		0			0
$193$	7.82817	+	13.5588i	0.563484	+	0.975984i	0.997189	+	0.0749284i	$0.0238728\pi$
$193$	7.82817	+	13.5588i	0.563484	+	0.975984i	−0.433705	+	0.901055i	$0.642794\pi$
$194$		0			0
$195$	−12.3494	−	2.39429i	−0.884359	−	0.171459i
$196$		0			0
$197$	−5.61287	+	15.4212i	−0.399900	+	1.09872i	0.562433	+	0.826843i	$0.309865\pi$
$197$	−5.61287	+	15.4212i	−0.399900	+	1.09872i	−0.962333	+	0.271874i	$0.912357\pi$
$198$		0			0
$199$	15.7156	+	9.07343i	1.11405	+	0.643198i	0.939876	−	0.341516i	$-0.110940\pi$
$199$	15.7156	+	9.07343i	1.11405	+	0.643198i	0.174176	+	0.984715i	$0.444274\pi$
$200$		0			0
$201$	0.841491	+	4.77233i	0.0593542	+	0.336614i
$202$		0			0
$203$	33.1719	−	12.0736i	2.32821	−	0.847400i
$204$		0			0
$205$	−13.1099	+	21.8424i	−0.915635	+	1.52554i
$206$		0			0
$207$	−0.472035	−	2.67704i	−0.0328087	−	0.186067i
$208$		0			0
$209$	−0.847485	+	1.00999i	−0.0586218	+	0.0698627i
$210$		0			0
$211$	−5.10808	−	8.84745i	−0.351655	−	0.609084i	0.634885	−	0.772607i	$-0.281048\pi$
$211$	−5.10808	−	8.84745i	−0.351655	−	0.609084i	−0.986540	+	0.163523i	$0.947714\pi$
$212$		0			0
$213$	9.54859	+	11.3796i	0.654258	+	0.779715i
$214$		0			0
$215$	−0.625433	−	3.93652i	−0.0426542	−	0.268468i
$216$		0			0
$217$	−1.60830	+	9.12115i	−0.109179	+	0.619184i
$218$		0			0
$219$	−0.279110	+	0.101588i	−0.0188605	+	0.00686465i
$220$		0			0
$221$	−27.2705			−1.83441
$222$		0			0
$223$			20.7185i			1.38741i	0.720258	+	0.693707i	$0.244024\pi$
$223$			20.7185i			1.38741i	−0.720258	+	0.693707i	$0.755976\pi$
$224$		0			0
$225$	−5.56177	+	8.91987i	−0.370785	+	0.594658i
$226$		0			0
$227$	2.01576	−	11.4319i	0.133791	−	0.758764i	−0.841904	−	0.539628i	$-0.818565\pi$
$227$	2.01576	−	11.4319i	0.133791	−	0.758764i	0.975694	−	0.219136i	$-0.0703239\pi$
$228$		0			0
$229$	−2.81923	+	15.9887i	−0.186300	+	1.05656i	0.737974	+	0.674830i	$0.235783\pi$
$229$	−2.81923	+	15.9887i	−0.186300	+	1.05656i	−0.924274	+	0.381730i	$0.875328\pi$
$230$		0			0
$231$	−2.53954	+	2.13093i	−0.167089	+	0.140205i
$232$		0			0
$233$	−19.5600	+	11.2930i	−1.28142	+	0.739828i	−0.977108	−	0.212744i	$-0.931760\pi$
$233$	−19.5600	+	11.2930i	−1.28142	+	0.739828i	−0.304312	+	0.952572i	$0.598426\pi$
$234$		0			0
$235$	−0.339886	+	0.886714i	−0.0221717	+	0.0578429i
$236$		0			0
$237$	2.20023	+	12.4781i	0.142920	+	0.810540i
$238$		0			0
$239$	7.64751	+	9.11394i	0.494676	+	0.589532i	0.954400	−	0.298530i	$-0.0964962\pi$
$239$	7.64751	+	9.11394i	0.494676	+	0.589532i	−0.459724	+	0.888062i	$0.652052\pi$
$240$		0			0
$241$	4.10427	+	11.2764i	0.264379	+	0.726375i	0.998860	+	0.0477455i	$0.0152037\pi$
$241$	4.10427	+	11.2764i	0.264379	+	0.726375i	−0.734481	+	0.678630i	$0.762574\pi$
$242$		0			0
$243$	−15.8936	+	2.80246i	−1.01957	+	0.179778i
$244$		0			0
$245$	5.20629	−	26.8533i	0.332618	−	1.71560i
$246$		0			0
$247$	3.35591	−	9.22029i	0.213532	−	0.586673i
$248$		0			0
$249$	4.78812	−	8.29327i	0.303435	−	0.525565i
$250$		0			0
$251$	7.37319	−	4.25691i	0.465392	−	0.268694i	−0.248917	−	0.968525i	$-0.580075\pi$
$251$	7.37319	−	4.25691i	0.465392	−	0.268694i	0.714309	+	0.699831i	$0.246741\pi$
$252$		0			0
$253$	−1.03163			−0.0648582
$254$		0			0
$255$	3.48251	−	9.08536i	0.218083	−	0.568947i
$256$		0			0
$257$	12.0026	+	4.36860i	0.748703	+	0.272506i	0.688060	−	0.725654i	$-0.258463\pi$
$257$	12.0026	+	4.36860i	0.748703	+	0.272506i	0.0606433	+	0.998159i	$0.480685\pi$
$258$		0			0
$259$	26.4566	−	3.41505i	1.64393	−	0.212201i
$260$		0			0
$261$	5.78790	−	15.9021i	0.358262	−	0.984317i
$262$		0			0
$263$	1.69791	−	2.02349i	0.104698	−	0.124774i	−0.711151	−	0.703039i	$-0.751826\pi$
$263$	1.69791	−	2.02349i	0.104698	−	0.124774i	0.815849	+	0.578265i	$0.196270\pi$
$264$		0			0
$265$	−2.90916	−	8.43556i	−0.178708	−	0.518192i
$266$		0			0
$267$	3.08778	+	5.34819i	0.188969	+	0.327304i
$268$		0			0
$269$	12.9649	−	22.4558i	0.790482	−	1.36916i	−0.135186	−	0.990820i	$-0.543163\pi$
$269$	12.9649	−	22.4558i	0.790482	−	1.36916i	0.925669	−	0.378335i	$-0.123503\pi$
$270$		0			0
$271$	−19.3375	−	7.03827i	−1.17467	−	0.427544i	−0.320352	−	0.947298i	$-0.603801\pi$
$271$	−19.3375	−	7.03827i	−1.17467	−	0.427544i	−0.854316	+	0.519754i	$0.826023\pi$
$272$		0			0
$273$	12.3357	−	21.3661i	0.746593	−	1.29314i
$274$		0			0
$275$	2.96721	+	2.66650i	0.178929	+	0.160796i
$276$		0			0
$277$	−8.30075	+	3.02123i	−0.498744	+	0.181528i	−0.579129	−	0.815236i	$-0.696607\pi$
$277$	−8.30075	+	3.02123i	−0.498744	+	0.181528i	0.0803851	+	0.996764i	$0.474385\pi$
$278$		0			0
$279$	2.85397	+	3.40123i	0.170863	+	0.203627i
$280$		0			0
$281$	−7.87777	+	1.38906i	−0.469948	+	0.0828646i	−0.403607	−	0.914932i	$-0.632244\pi$
$281$	−7.87777	+	1.38906i	−0.469948	+	0.0828646i	−0.0663413	+	0.997797i	$0.521133\pi$
$282$		0			0
$283$	−2.41869	−	2.02952i	−0.143776	−	0.120642i	0.568063	−	0.822985i	$-0.307693\pi$
$283$	−2.41869	−	2.02952i	−0.143776	−	0.120642i	−0.711839	+	0.702343i	$0.752137\pi$
$284$		0			0
$285$	2.64325	+	2.29550i	0.156572	+	0.135973i
$286$		0			0
$287$	−32.1154	−	38.2736i	−1.89571	−	2.25922i
$288$		0			0
$289$	0.710796	−	4.03113i	0.0418115	−	0.237125i
$290$		0			0
$291$	−0.346562	−	0.0611083i	−0.0203158	−	0.00358223i
$292$		0			0
$293$	3.97588	+	10.9237i	0.232274	+	0.638167i	0.999997	−	0.00261540i	$-0.000832507\pi$
$293$	3.97588	+	10.9237i	0.232274	+	0.638167i	−0.767723	+	0.640782i	$0.778610\pi$
$294$		0			0
$295$	3.27866	+	9.50699i	0.190891	+	0.553519i
$296$		0			0
$297$			3.85700i			0.223806i
$298$		0			0
$299$	7.21449	−	2.62586i	0.417224	−	0.151857i
$300$		0			0
$301$	7.69862	+	1.35748i	0.443741	+	0.0782436i
$302$		0			0
$303$	1.62112	+	0.285847i	0.0931309	+	0.0164215i
$304$		0			0
$305$	0.389217	+	0.233609i	0.0222865	+	0.0133764i
$306$		0			0
$307$	−0.972631	+	0.561549i	−0.0555110	+	0.0320493i	−0.527499	−	0.849556i	$-0.676870\pi$
$307$	−0.972631	+	0.561549i	−0.0555110	+	0.0320493i	0.471988	+	0.881605i	$0.343537\pi$
$308$		0			0
$309$	9.76134	−	11.6331i	0.555303	−	0.661785i
$310$		0			0
$311$	−16.1237	+	2.84304i	−0.914291	+	0.161214i	−0.610951	−	0.791668i	$-0.709213\pi$
$311$	−16.1237	+	2.84304i	−0.914291	+	0.161214i	−0.303340	+	0.952882i	$0.598102\pi$
$312$		0			0
$313$	7.60981	−	6.38538i	0.430132	−	0.360923i	−0.401870	−	0.915697i	$-0.631640\pi$
$313$	7.60981	−	6.38538i	0.430132	−	0.360923i	0.832001	+	0.554774i	$0.187195\pi$
$314$		0			0
$315$	−12.9820	−	16.0157i	−0.731455	−	0.902380i
$316$		0			0
$317$	−14.5263	+	2.56139i	−0.815880	+	0.143862i	−0.565990	−	0.824412i	$-0.691506\pi$
$317$	−14.5263	+	2.56139i	−0.815880	+	0.143862i	−0.249891	+	0.968274i	$0.580395\pi$
$318$		0			0
$319$	−5.56187	−	3.21115i	−0.311405	−	0.179790i
$320$		0			0
$321$	3.16807	+	1.15308i	0.176824	+	0.0643588i
$322$		0			0
$323$	6.57265	+	3.79472i	0.365712	+	0.211144i
$324$		0			0
$325$	−27.5376	−	11.0950i	−1.52751	−	0.615438i
$326$		0			0
$327$	−9.34600			−0.516835
$328$		0			0
$329$	−1.42673	−	1.19717i	−0.0786581	−	0.0660020i
$330$		0			0
$331$	9.78702	−	26.8896i	0.537943	−	1.47799i	−0.311469	−	0.950256i	$-0.600821\pi$
$331$	9.78702	−	26.8896i	0.537943	−	1.47799i	0.849412	−	0.527730i	$-0.176957\pi$
$332$		0			0
$333$	6.89830	−	10.7680i	0.378024	−	0.590082i
$334$		0			0
$335$	−0.194076	+	11.4353i	−0.0106035	+	0.624779i
$336$		0			0
$337$	12.6152	−	15.0342i	0.687193	−	0.818965i	−0.303820	−	0.952730i	$-0.598262\pi$
$337$	12.6152	−	15.0342i	0.687193	−	0.818965i	0.991013	+	0.133764i	$0.0427065\pi$
$338$		0			0
$339$		−	13.3876i		−	0.727116i
$340$		0			0
$341$	1.45927	−	0.842507i	0.0790237	−	0.0456243i
$342$		0			0
$343$	19.8740	+	11.4743i	1.07310	+	0.619553i
$344$		0			0
$345$	−0.0464833	+	2.73888i	−0.00250258	+	0.147457i
$346$		0			0
$347$	−3.05122	+	5.28487i	−0.163798	+	0.283707i	−0.936228	−	0.351393i	$-0.885708\pi$
$347$	−3.05122	+	5.28487i	−0.163798	+	0.283707i	0.772430	+	0.635100i	$0.219041\pi$
$348$		0			0
$349$	2.41356	+	13.6880i	0.129195	+	0.732702i	0.978727	+	0.205165i	$0.0657731\pi$
$349$	2.41356	+	13.6880i	0.129195	+	0.732702i	−0.849532	+	0.527537i	$0.823116\pi$
$350$		0			0
$351$	−9.81739	−	26.9731i	−0.524013	−	1.43972i
$352$		0			0
$353$	2.14425	−	1.79924i	0.114127	−	0.0957638i	−0.583938	−	0.811798i	$-0.698489\pi$
$353$	2.14425	−	1.79924i	0.114127	−	0.0957638i	0.698065	+	0.716034i	$0.254045\pi$
$354$		0			0
$355$	17.0119	+	30.6554i	0.902900	+	1.62702i
$356$		0			0
$357$	14.6184	+	12.2663i	0.773688	+	0.649202i
$358$		0			0
$359$	−4.27001	−	7.39587i	−0.225362	−	0.390339i	0.731066	−	0.682307i	$-0.239023\pi$
$359$	−4.27001	−	7.39587i	−0.225362	−	0.390339i	−0.956428	+	0.291968i	$0.905690\pi$
$360$		0			0
$361$	12.4630	−	10.4577i	0.655947	−	0.550405i
$362$		0			0
$363$	−9.66957	−	1.70501i	−0.507521	−	0.0894896i
$364$		0			0
$365$	−0.692322	+	0.109996i	−0.0362378	+	0.00575745i
$366$		0			0
$367$	6.60737	+	18.1536i	0.344902	+	0.947610i	0.983950	+	0.178443i	$0.0571062\pi$
$367$	6.60737	+	18.1536i	0.344902	+	0.947610i	−0.639048	+	0.769167i	$0.720672\pi$
$368$		0			0
$369$	−23.9514			−1.24686
$370$		0			0
$371$	17.5006			0.908585
$372$		0			0
$373$	−3.62155	−	9.95012i	−0.187517	−	0.515198i	0.809937	−	0.586517i	$-0.199501\pi$
$373$	−3.62155	−	9.95012i	−0.187517	−	0.515198i	−0.997454	+	0.0713194i	$0.977279\pi$
$374$		0			0
$375$	7.21298	−	7.75749i	0.372477	−	0.400595i
$376$		0			0
$377$	47.0691	+	8.29956i	2.42418	+	0.427449i
$378$		0			0
$379$	14.1433	−	11.8677i	0.726494	−	0.609601i	−0.202679	−	0.979245i	$-0.564965\pi$
$379$	14.1433	−	11.8677i	0.726494	−	0.609601i	0.929173	+	0.369644i	$0.120521\pi$
$380$		0			0
$381$	8.67017	+	15.0172i	0.444186	+	0.769353i
$382$		0			0
$383$	14.4442	+	12.1201i	0.738064	+	0.619309i	0.932317	−	0.361642i	$-0.117784\pi$
$383$	14.4442	+	12.1201i	0.738064	+	0.619309i	−0.194253	+	0.980952i	$0.562228\pi$
$384$		0			0
$385$	−6.84126	+	3.79650i	−0.348663	+	0.193487i
$386$		0			0
$387$	2.87078	−	2.40887i	0.145930	−	0.122450i
$388$		0			0
$389$	−9.23959	−	25.3856i	−0.468466	−	1.28710i	−0.918971	−	0.394326i	$-0.870978\pi$
$389$	−9.23959	−	25.3856i	−0.468466	−	1.28710i	0.450505	−	0.892774i	$-0.351244\pi$
$390$		0			0
$391$	1.03120	+	5.84820i	0.0521498	+	0.295756i
$392$		0			0
$393$	6.17766	−	10.7000i	0.311622	−	0.539744i
$394$		0			0
$395$	−0.507447	+	29.8997i	−0.0255324	+	1.50442i
$396$		0			0
$397$	−12.7543	−	7.36371i	−0.640121	−	0.369574i	0.144540	−	0.989499i	$-0.453830\pi$
$397$	−12.7543	−	7.36371i	−0.640121	−	0.369574i	−0.784661	+	0.619925i	$0.787163\pi$
$398$		0			0
$399$	−5.94624	+	3.43306i	−0.297684	+	0.171868i
$400$		0			0
$401$		−	5.67411i		−	0.283352i	−0.989913	−	0.141676i	$-0.954751\pi$
$401$		−	5.67411i		−	0.283352i	0.989913	−	0.141676i	$-0.0452490\pi$
$402$		0			0
$403$	−8.06056	+	9.60620i	−0.401525	+	0.478519i
$404$		0			0
$405$	−3.86103	−	0.0655279i	−0.191856	−	0.00325611i
$406$		0			0
$407$	−3.56985	−	3.28781i	−0.176951	−	0.162971i
$408$		0			0
$409$	−9.32479	+	25.6197i	−0.461081	+	1.26681i	0.463592	+	0.886049i	$0.346560\pi$
$409$	−9.32479	+	25.6197i	−0.461081	+	1.26681i	−0.924673	+	0.380762i	$0.875662\pi$
$410$		0			0
$411$	7.03212	+	5.90065i	0.346869	+	0.291058i
$412$		0			0
$413$	−19.7234			−0.970525
$414$		0			0
$415$	14.8193	−	17.0644i	0.727453	−	0.837656i
$416$		0			0
$417$	11.4209	+	6.59385i	0.559283	+	0.322902i
$418$		0			0
$419$	−32.5941	−	11.8633i	−1.59232	−	0.579558i	−0.614487	−	0.788927i	$-0.710637\pi$
$419$	−32.5941	−	11.8633i	−1.59232	−	0.579558i	−0.977837	+	0.209368i	$0.932859\pi$
$420$		0			0
$421$	−12.9180	−	7.45819i	−0.629583	−	0.363490i	0.151007	−	0.988533i	$-0.451748\pi$
$421$	−12.9180	−	7.45819i	−0.629583	−	0.363490i	−0.780591	+	0.625043i	$0.785082\pi$
$422$		0			0
$423$	−0.879273	+	0.155040i	−0.0427517	+	0.00753828i
$424$		0			0
$425$	12.1501	−	19.4861i	0.589366	−	0.945215i
$426$		0			0
$427$	−0.682010	+	0.572274i	−0.0330048	+	0.0276943i
$428$		0			0
$429$	−4.42030	+	0.779419i	−0.213414	+	0.0376307i
$430$		0			0
$431$	24.8086	−	29.5657i	1.19499	−	1.42413i	0.315027	−	0.949083i	$-0.397986\pi$
$431$	24.8086	−	29.5657i	1.19499	−	1.42413i	0.879960	−	0.475048i	$-0.157569\pi$
$432$		0			0
$433$	26.8761	−	15.5169i	1.29158	−	0.745695i	0.312646	−	0.949870i	$-0.398784\pi$
$433$	26.8761	−	15.5169i	1.29158	−	0.745695i	0.978934	+	0.204175i	$0.0654512\pi$
$434$		0			0
$435$	−8.77589	+	14.6215i	−0.420772	+	0.701049i
$436$		0			0
$437$	−2.10420	−	0.371028i	−0.100658	−	0.0177487i
$438$		0			0
$439$	−23.9885	−	4.22981i	−1.14491	−	0.201878i	−0.431156	−	0.902278i	$-0.641894\pi$
$439$	−23.9885	−	4.22981i	−1.14491	−	0.201878i	−0.713751	+	0.700400i	$0.753005\pi$
$440$		0			0
$441$	24.1667	−	8.79596i	1.15080	−	0.418855i
$442$		0			0
$443$			29.9783i			1.42431i	0.702022	+	0.712155i	$0.252281\pi$
$443$			29.9783i			1.42431i	−0.702022	+	0.712155i	$0.747719\pi$
$444$		0			0
$445$	4.75181	+	13.7786i	0.225257	+	0.653170i
$446$		0			0
$447$	−3.85169	−	10.5824i	−0.182179	−	0.500532i
$448$		0			0
$449$	33.4009	+	5.88948i	1.57629	+	0.277942i	0.892263	−	0.451517i	$-0.149117\pi$
$449$	33.4009	+	5.88948i	1.57629	+	0.277942i	0.684025	+	0.729459i	$0.260228\pi$
$450$		0			0
$451$	−1.57842	+	8.95164i	−0.0743247	+	0.421516i
$452$		0			0
$453$	−0.372773	−	0.444254i	−0.0175144	−	0.0208729i
$454$		0			0
$455$	38.1794	−	43.9632i	1.78988	−	2.06103i
$456$		0			0
$457$	−9.91966	−	8.32358i	−0.464022	−	0.389361i	0.380586	−	0.924745i	$-0.375722\pi$
$457$	−9.91966	−	8.32358i	−0.464022	−	0.389361i	−0.844608	+	0.535385i	$0.820167\pi$
$458$		0			0
$459$	21.8649	−	3.85537i	1.02057	−	0.179953i
$460$		0			0
$461$	−10.5826	−	12.6119i	−0.492882	−	0.587394i	0.461066	−	0.887366i	$-0.347467\pi$
$461$	−10.5826	−	12.6119i	−0.492882	−	0.587394i	−0.953948	+	0.299972i	$0.903023\pi$
$462$		0			0
$463$	−26.7562	+	9.73847i	−1.24347	+	0.452585i	−0.878189	−	0.478313i	$-0.841248\pi$
$463$	−26.7562	+	9.73847i	−1.24347	+	0.452585i	−0.365278	+	0.930898i	$0.619026\pi$
$464$		0			0
$465$	−2.17102	−	3.91217i	−0.100679	−	0.181422i
$466$		0			0
$467$	−1.24778	+	2.16122i	−0.0577404	+	0.100009i	−0.893451	−	0.449161i	$-0.851723\pi$
$467$	−1.24778	+	2.16122i	−0.0577404	+	0.100009i	0.835710	+	0.549170i	$0.185056\pi$
$468$		0			0
$469$	−21.0782	−	7.67184i	−0.973301	−	0.354253i
$470$		0			0
$471$	−5.51915	+	9.55945i	−0.254309	+	0.440476i
$472$		0			0
$473$	−0.711111	−	1.23168i	−0.0326969	−	0.0566327i
$474$		0			0
$475$	5.09315	+	6.50596i	0.233690	+	0.298514i
$476$		0			0
$477$	5.39268	−	6.42674i	0.246914	−	0.294260i
$478$		0			0
$479$	−4.57919	+	12.5812i	−0.209228	+	0.574850i	−0.999270	−	0.0382029i	$-0.987837\pi$
$479$	−4.57919	+	12.5812i	−0.209228	+	0.574850i	0.790042	+	0.613053i	$0.210059\pi$
$480$		0			0
$481$	33.3335	+	13.9060i	1.51988	+	0.634060i
$482$		0			0
$483$	−5.04845	−	1.83749i	−0.229712	−	0.0836085i
$484$		0			0
$485$	−0.775523	−	0.297265i	−0.0352147	−	0.0134981i
$486$		0			0
$487$	42.0899			1.90727			0.953637	−	0.300958i	$-0.0973064\pi$
$487$	42.0899			1.90727			0.953637	+	0.300958i	$0.0973064\pi$
$488$		0			0
$489$	−19.0552	+	11.0015i	−0.861706	+	0.497506i
$490$		0			0
$491$	−9.47119	+	16.4046i	−0.427429	+	0.740328i	−0.996644	−	0.0818603i	$-0.973914\pi$
$491$	−9.47119	+	16.4046i	−0.427429	+	0.740328i	0.569215	+	0.822189i	$0.307247\pi$
$492$		0			0
$493$	−12.6441	+	34.7394i	−0.569461	+	1.56458i
$494$		0			0
$495$	−0.713897	+	3.68218i	−0.0320873	+	0.165502i
$496$		0			0
$497$	−67.7161	+	11.9402i	−3.03748	+	0.535590i
$498$		0			0
$499$	2.33240	+	6.40822i	0.104413	+	0.286871i	0.980887	−	0.194576i	$-0.0623332\pi$
$499$	2.33240	+	6.40822i	0.104413	+	0.286871i	−0.876475	+	0.481448i	$0.840111\pi$
$500$		0			0
$501$	−2.36824	−	2.82235i	−0.105805	−	0.126093i
$502$		0			0
$503$	−6.11462	−	34.6778i	−0.272638	−	1.54620i	−0.746367	−	0.665534i	$-0.768204\pi$
$503$	−6.11462	−	34.6778i	−0.272638	−	1.54620i	0.473730	−	0.880670i	$-0.342907\pi$
$504$		0			0
$505$	3.62767	+	1.39052i	0.161429	+	0.0618774i
$506$		0			0
$507$	18.2619	−	10.5435i	0.811038	−	0.468253i
$508$		0			0
$509$	16.7180	−	14.0281i	0.741013	−	0.621784i	−0.192096	−	0.981376i	$-0.561529\pi$
$509$	16.7180	−	14.0281i	0.741013	−	0.621784i	0.933110	+	0.359592i	$0.117084\pi$
$510$		0			0
$511$	0.238741	−	1.35397i	0.0105613	−	0.0598961i
$512$		0			0
$513$	−1.38717	+	7.86706i	−0.0612453	+	0.347339i
$514$		0			0
$515$	27.8424	−	22.5686i	1.22688	−	0.994492i
$516$		0			0
$517$			0.338839i			0.0149021i
$518$		0			0
$519$	−11.0305			−0.484186
$520$		0			0
$521$	−32.1815	+	11.7131i	−1.40990	+	0.513161i	−0.931100	−	0.364763i	$-0.881150\pi$
$521$	−32.1815	+	11.7131i	−1.40990	+	0.513161i	−0.478799	+	0.877925i	$0.658928\pi$
$522$		0			0
$523$	−2.49122	+	14.1284i	−0.108933	+	0.617791i	0.880643	+	0.473781i	$0.157111\pi$
$523$	−2.49122	+	14.1284i	−0.108933	+	0.617791i	−0.989576	+	0.144011i	$0.954000\pi$
$524$		0			0
$525$	9.77106	+	18.3339i	0.426444	+	0.800158i
$526$		0			0
$527$	−6.23472	−	7.43024i	−0.271588	−	0.323667i
$528$		0			0
$529$	10.6641	+	18.4707i	0.463655	+	0.803075i
$530$		0			0
$531$	−6.07762	+	7.24303i	−0.263746	+	0.314321i
$532$		0			0
$533$	−11.7467	−	66.6188i	−0.508806	−	2.88558i
$534$		0			0
$535$	6.82233	+	4.09478i	0.294955	+	0.177033i
$536$		0			0
$537$	11.9406	−	4.34603i	0.515276	−	0.187545i
$538$		0			0
$539$	−1.69482	−	9.61179i	−0.0730010	−	0.414009i
$540$		0			0
$541$	−4.47951	−	2.58624i	−0.192589	−	0.111191i	0.400605	−	0.916251i	$-0.368800\pi$
$541$	−4.47951	−	2.58624i	−0.192589	−	0.111191i	−0.593194	+	0.805060i	$0.702133\pi$
$542$		0			0
$543$	6.62253	−	18.1952i	0.284200	−	0.780833i
$544$		0			0
$545$	−21.6544	−	4.19832i	−0.927571	−	0.179836i
$546$		0			0
$547$	−15.4266	−	26.7197i	−0.659596	−	1.14245i	−0.980720	−	0.195416i	$-0.937394\pi$
$547$	−15.4266	−	26.7197i	−0.659596	−	1.14245i	0.321125	−	0.947037i	$-0.395939\pi$
$548$		0			0
$549$			0.426797i			0.0182152i
$550$		0			0
$551$	−10.1896	−	8.55006i	−0.434090	−	0.364245i
$552$		0			0
$553$	−55.1127	−	20.0594i	−2.34363	−	0.853012i
$554$		0			0
$555$	−8.88965	+	9.32945i	−0.377345	+	0.396013i
$556$		0			0
$557$	19.0747	+	6.94261i	0.808219	+	0.294168i	0.712888	−	0.701278i	$-0.247387\pi$
$557$	19.0747	+	6.94261i	0.808219	+	0.294168i	0.0953312	+	0.995446i	$0.469609\pi$
$558$		0			0
$559$	8.10803	+	6.80345i	0.342933	+	0.287755i
$560$		0			0
$561$		−	3.47178i		−	0.146579i
$562$		0			0
$563$	16.9432	+	29.3465i	0.714071	+	1.23681i	0.963317	+	0.268367i	$0.0864838\pi$
$563$	16.9432	+	29.3465i	0.714071	+	1.23681i	−0.249246	+	0.968440i	$0.580183\pi$
$564$		0			0
$565$	6.01386	−	31.0187i	0.253005	−	1.30497i
$566$		0			0
$567$	2.59032	−	7.11684i	0.108783	−	0.298879i
$568$		0			0
$569$	−12.1617	−	7.02157i	−0.509846	−	0.294359i	0.222925	−	0.974836i	$-0.428440\pi$
$569$	−12.1617	−	7.02157i	−0.509846	−	0.294359i	−0.732770	+	0.680476i	$0.761773\pi$
$570$		0			0
$571$	−3.86828	−	21.9381i	−0.161882	−	0.918081i	−0.952221	−	0.305410i	$-0.901206\pi$
$571$	−3.86828	−	21.9381i	−0.161882	−	0.918081i	0.790338	−	0.612671i	$-0.209905\pi$
$572$		0			0
$573$	−0.917686	+	0.334010i	−0.0383369	+	0.0139535i
$574$		0			0
$575$	−1.33804	+	6.32502i	−0.0557999	+	0.263772i
$576$		0			0
$577$	3.10096	+	17.5864i	0.129095	+	0.732133i	0.978791	+	0.204861i	$0.0656742\pi$
$577$	3.10096	+	17.5864i	0.129095	+	0.732133i	−0.849696	+	0.527272i	$0.823215\pi$
$578$		0			0
$579$	9.53478	−	11.3631i	0.396252	−	0.472235i
$580$		0			0
$581$	22.1633	+	38.3879i	0.919488	+	1.59260i
$582$		0			0
$583$	−2.04657	−	2.43900i	−0.0847601	−	0.101013i
$584$		0			0
$585$	−4.37993	−	27.5676i	−0.181088	−	1.13978i
$586$		0			0
$587$	−6.16682	+	34.9738i	−0.254532	+	1.44352i	0.542740	+	0.839901i	$0.317387\pi$
$587$	−6.16682	+	34.9738i	−0.254532	+	1.44352i	−0.797271	+	0.603621i	$0.793724\pi$
$588$		0			0
$589$	3.27944	−	1.19362i	0.135127	−	0.0491823i
$590$		0			0
$591$	15.5484			0.639575
$592$		0			0
$593$		−	12.4419i		−	0.510929i	−0.966818	−	0.255464i	$-0.917772\pi$
$593$		−	12.4419i		−	0.510929i	0.966818	−	0.255464i	$-0.0822283\pi$
$594$		0			0
$595$	28.3602	+	34.9874i	1.16266	+	1.43434i
$596$		0			0
$597$	2.98555	−	16.9319i	0.122190	−	0.692976i
$598$		0			0
$599$	8.18282	−	46.4071i	0.334341	−	1.89614i	−0.0993017	−	0.995057i	$-0.531661\pi$
$599$	8.18282	−	46.4071i	0.334341	−	1.89614i	0.433643	−	0.901085i	$-0.357228\pi$
$600$		0			0
$601$	−37.1341	+	31.1592i	−1.51473	+	1.27101i	−0.660889	+	0.750484i	$0.729820\pi$
$601$	−37.1341	+	31.1592i	−1.51473	+	1.27101i	−0.853845	+	0.520528i	$0.825735\pi$
$602$		0			0
$603$	−9.31243	+	5.37653i	−0.379231	+	0.218949i
$604$		0			0
$605$	−21.6382	−	8.29411i	−0.879716	−	0.337204i
$606$		0			0
$607$	0.0401154	+	0.227506i	0.00162823	+	0.00923417i	0.985611	−	0.169029i	$-0.0540632\pi$
$607$	0.0401154	+	0.227506i	0.00162823	+	0.00923417i	−0.983983	+	0.178263i	$0.942952\pi$
$608$		0			0
$609$	−21.4983	−	25.6207i	−0.871157	−	1.03820i
$610$		0			0
$611$	−0.862461	−	2.36959i	−0.0348914	−	0.0958634i
$612$		0			0
$613$	−46.9139	+	8.27219i	−1.89484	+	0.334111i	−0.994812	−	0.101731i	$-0.967562\pi$
$613$	−46.9139	+	8.27219i	−1.89484	+	0.334111i	−0.900023	+	0.435842i	$0.856451\pi$
$614$		0			0
$615$	23.6946	+	4.59388i	0.955459	+	0.185243i
$616$		0			0
$617$	−3.58282	+	9.84371i	−0.144239	+	0.396293i	−0.990684	−	0.136184i	$-0.956516\pi$
$617$	−3.58282	+	9.84371i	−0.144239	+	0.396293i	0.846445	+	0.532476i	$0.178738\pi$
$618$		0			0
$619$	−6.17060	+	10.6878i	−0.248017	+	0.429579i	−0.962976	−	0.269589i	$-0.913112\pi$
$619$	−6.17060	+	10.6878i	−0.248017	+	0.429579i	0.714958	+	0.699167i	$0.246446\pi$
$620$		0			0
$621$	−5.41318	+	3.12530i	−0.217223	+	0.125414i
$622$		0			0
$623$	−28.5854			−1.14525
$624$		0			0
$625$	20.1970	−	14.7337i	0.807879	−	0.589348i
$626$		0			0
$627$	1.17382	+	0.427237i	0.0468780	+	0.0170622i
$628$		0			0
$629$	−15.0698	+	23.5235i	−0.600874	+	0.937941i
$630$		0			0
$631$	−13.4759	+	37.0246i	−0.536466	+	1.47393i	0.314782	+	0.949164i	$0.398069\pi$
$631$	−13.4759	+	37.0246i	−0.536466	+	1.47393i	−0.851248	+	0.524764i	$0.824154\pi$
$632$		0			0
$633$	−6.22168	+	7.41471i	−0.247290	+	0.294708i
$634$		0			0
$635$	13.3426	+	38.6890i	0.529486	+	1.53533i
$636$		0			0
$637$	36.3176	+	62.9039i	1.43896	+	2.49234i
$638$		0			0
$639$	−16.4814	+	28.5467i	−0.651995	+	1.12929i
$640$		0			0
$641$	4.65455	+	1.69412i	0.183844	+	0.0669136i	0.432302	−	0.901729i	$-0.357702\pi$
$641$	4.65455	+	1.69412i	0.183844	+	0.0669136i	−0.248458	+	0.968643i	$0.579924\pi$
$642$		0			0
$643$	10.6324	−	18.4158i	0.419300	−	0.726249i	−0.576569	−	0.817049i	$-0.695609\pi$
$643$	10.6324	−	18.4158i	0.419300	−	0.726249i	0.995869	+	0.0907990i	$0.0289421\pi$
$644$		0			0
$645$	−3.30203	+	1.83243i	−0.130017	+	0.0721519i
$646$		0			0
$647$	−34.6354	+	12.6063i	−1.36166	+	0.495603i	−0.916566	−	0.399882i	$-0.869051\pi$
$647$	−34.6354	+	12.6063i	−1.36166	+	0.495603i	−0.445091	+	0.895485i	$0.646829\pi$
$648$		0			0
$649$	2.30651	+	2.74879i	0.0905383	+	0.107899i
$650$		0			0
$651$	8.64176	−	1.52378i	0.338697	−	0.0597215i
$652$		0			0
$653$	8.24845	+	6.92127i	0.322787	+	0.270850i	0.789753	−	0.613425i	$-0.210209\pi$
$653$	8.24845	+	6.92127i	0.322787	+	0.270850i	−0.466966	+	0.884275i	$0.654653\pi$
$654$		0			0
$655$	19.1200	−	22.0165i	0.747080	−	0.860256i
$656$		0			0
$657$	−0.423652	−	0.504889i	−0.0165283	−	0.0196976i
$658$		0			0
$659$	−2.70254	+	15.3269i	−0.105276	+	0.597051i	0.885833	+	0.464003i	$0.153587\pi$
$659$	−2.70254	+	15.3269i	−0.105276	+	0.597051i	−0.991110	+	0.133048i	$0.957524\pi$
$660$		0			0
$661$	−40.1443	−	7.07852i	−1.56143	−	0.275322i	−0.674871	−	0.737936i	$-0.735801\pi$
$661$	−40.1443	−	7.07852i	−1.56143	−	0.275322i	−0.886560	+	0.462613i	$0.846912\pi$
$662$		0			0
$663$	8.83686	+	24.2791i	0.343195	+	0.942921i
$664$		0			0
$665$	−15.3194	+	5.28318i	−0.594061	+	0.204873i
$666$		0			0
$667$		−	10.4079i		−	0.402995i
$668$		0			0
$669$	18.4458	−	6.71371i	0.713155	−	0.259567i
$670$		0			0
$671$	0.159512	+	0.0281263i	0.00615790	+	0.00108580i
$672$		0			0
$673$	−31.9457	−	5.63289i	−1.23142	−	0.217132i	−0.480182	−	0.877169i	$-0.659429\pi$
$673$	−31.9457	−	5.63289i	−1.23142	−	0.217132i	−0.751233	+	0.660037i	$0.770541\pi$
$674$		0			0
$675$	23.6476	+	5.00256i	0.910196	+	0.192549i
$676$		0			0
$677$	−13.5828	+	7.84204i	−0.522030	+	0.301394i	−0.737765	−	0.675058i	$-0.764119\pi$
$677$	−13.5828	+	7.84204i	−0.522030	+	0.301394i	0.215735	+	0.976452i	$0.430785\pi$
$678$		0			0
$679$	1.04705	−	1.24782i	0.0401820	−	0.0478870i
$680$		0			0
$681$	−10.8311	+	1.90981i	−0.415048	+	0.0731842i
$682$		0			0
$683$	7.90817	−	6.63574i	0.302598	−	0.253909i	−0.478827	−	0.877909i	$-0.658938\pi$
$683$	7.90817	−	6.63574i	0.302598	−	0.253909i	0.781424	+	0.624000i	$0.214493\pi$
$684$		0			0
$685$	13.6426	+	16.8305i	0.521255	+	0.643061i
$686$		0			0
$687$	15.1483	−	2.67106i	0.577945	−	0.101907i
$688$		0			0
$689$	20.5203	+	11.8474i	0.781760	+	0.451349i
$690$		0			0
$691$	9.87074	+	3.59266i	0.375501	+	0.136671i	0.522874	−	0.852410i	$-0.324860\pi$
$691$	9.87074	+	3.59266i	0.375501	+	0.136671i	−0.147374	+	0.989081i	$0.547082\pi$
$692$		0			0
$693$	−6.37066	−	3.67810i	−0.242001	−	0.139720i
$694$		0			0
$695$	23.4998	+	20.4081i	0.891397	+	0.774124i
$696$		0			0
$697$	52.3235			1.98189
$698$		0			0
$699$	16.3925	+	13.7549i	0.620021	+	0.520260i
$700$		0			0
$701$	−14.5985	+	40.1090i	−0.551378	+	1.51490i	0.280453	+	0.959868i	$0.409515\pi$
$701$	−14.5985	+	40.1090i	−0.551378	+	1.51490i	−0.831830	+	0.555030i	$0.812707\pi$
$702$		0			0
$703$	−6.09889	−	7.98998i	−0.230024	−	0.301348i
$704$		0			0
$705$	0.899584	+	0.0152674i	0.0338803	+	0.000575004i
$706$		0			0
$707$	−4.89778	+	5.83695i	−0.184200	+	0.219521i
$708$		0			0
$709$			36.5430i			1.37240i	0.727412	+	0.686201i	$0.240723\pi$
$709$			36.5430i			1.37240i	−0.727412	+	0.686201i	$0.759277\pi$
$710$		0			0
$711$	−24.3490	+	14.0579i	−0.913158	+	0.527212i
$712$		0			0
$713$	2.36486	+	1.36535i	0.0885648	+	0.0511329i
$714$		0			0
$715$	−10.5918	−	0.179760i	−0.396112	−	0.00672266i
$716$		0			0
$717$	5.63605	−	9.76193i	0.210482	−	0.364566i
$718$		0			0
$719$	−1.76717	−	10.0221i	−0.0659042	−	0.373761i	−0.999866	−	0.0163876i	$-0.994783\pi$
$719$	−1.76717	−	10.0221i	−0.0659042	−	0.373761i	0.933962	−	0.357374i	$-0.116328\pi$
$720$		0			0
$721$	24.0415	+	66.0536i	0.895354	+	2.45996i
$722$		0			0
$723$	8.70944	−	7.30809i	0.323908	−	0.271791i
$724$		0			0
$725$	−26.9016	+	29.9354i	−0.999100	+	1.11177i
$726$		0			0
$727$	0.212334	+	0.178169i	0.00787503	+	0.00660794i	0.646717	−	0.762730i	$-0.276142\pi$
$727$	0.212334	+	0.178169i	0.00787503	+	0.00660794i	−0.638842	+	0.769338i	$0.720586\pi$
$728$		0			0
$729$	5.05483	+	8.75522i	0.187216	+	0.324268i
$730$		0			0
$731$	−6.27143	+	5.26236i	−0.231957	+	0.194635i
$732$		0			0
$733$	−11.0400	−	1.94665i	−0.407772	−	0.0719013i	−0.0340003	−	0.999422i	$-0.510825\pi$
$733$	−11.0400	−	1.94665i	−0.407772	−	0.0719013i	−0.373772	+	0.927521i	$0.621936\pi$
$734$		0			0
$735$	−25.5947	+	4.06648i	−0.944075	+	0.149995i
$736$		0			0
$737$	1.39574	+	3.83477i	0.0514128	+	0.141256i
$738$		0			0
$739$	43.9151			1.61544			0.807722	−	0.589564i	$-0.200701\pi$
$739$	43.9151			1.61544			0.807722	+	0.589564i	$0.200701\pi$
$740$		0			0
$741$	−9.29633			−0.341509
$742$		0			0
$743$	−6.23262	−	17.1240i	−0.228653	−	0.628218i	0.771313	−	0.636455i	$-0.219600\pi$
$743$	−6.23262	−	17.1240i	−0.228653	−	0.628218i	−0.999966	+	0.00823752i	$0.997378\pi$
$744$		0			0
$745$	−4.17050	−	26.2494i	−0.152795	−	0.961703i
$746$		0			0
$747$	20.9267	+	3.68993i	0.765666	+	0.135008i
$748$		0			0
$749$	−11.9545	+	10.0310i	−0.436808	+	0.366525i
$750$		0			0
$751$	−14.4686	−	25.0604i	−0.527967	−	0.914465i	−0.999468	−	0.0326002i	$-0.989621\pi$
$751$	−14.4686	−	25.0604i	−0.527967	−	0.914465i	0.471502	−	0.881865i	$-0.343712\pi$
$752$		0			0
$753$	−6.17919	−	5.18496i	−0.225182	−	0.188950i
$754$		0			0
$755$	−0.664139	−	1.19677i	−0.0241705	−	0.0435551i
$756$		0			0
$757$	4.57235	−	3.83665i	0.166185	−	0.139446i	−0.555903	−	0.831247i	$-0.687627\pi$
$757$	4.57235	−	3.83665i	0.166185	−	0.139446i	0.722087	+	0.691802i	$0.243183\pi$
$758$		0			0
$759$	0.334295	+	0.918467i	0.0121341	+	0.0333383i
$760$		0			0
$761$	−7.05714	−	40.0230i	−0.255821	−	1.45083i	−0.793956	−	0.607975i	$-0.791982\pi$
$761$	−7.05714	−	40.0230i	−0.255821	−	1.45083i	0.538135	−	0.842858i	$-0.319129\pi$
$762$		0			0
$763$	21.6304	−	37.4650i	0.783073	−	1.35632i
$764$		0			0
$765$	21.5874	+	0.366374i	0.780495	+	0.0132463i
$766$		0			0
$767$	−23.1266	−	13.3522i	−0.835054	−	0.482119i
$768$		0			0
$769$	−16.1199	+	9.30685i	−0.581300	+	0.335614i	−0.761650	−	0.647989i	$-0.775610\pi$
$769$	−16.1199	+	9.30685i	−0.581300	+	0.335614i	0.180350	+	0.983603i	$0.442277\pi$
$770$		0			0
$771$		−	12.1016i		−	0.435829i
$772$		0			0
$773$	8.34439	−	9.94446i	0.300127	−	0.357677i	−0.594813	−	0.803864i	$-0.702774\pi$
$773$	8.34439	−	9.94446i	0.300127	−	0.357677i	0.894940	+	0.446187i	$0.147218\pi$
$774$		0			0
$775$	−3.27280	−	10.0396i	−0.117562	−	0.360633i
$776$		0			0
$777$	−11.6135	−	22.4478i	−0.416633	−	0.805310i
$778$		0			0
$779$	−6.43893	+	17.6908i	−0.230699	+	0.633840i
$780$		0			0
$781$	9.58296	+	8.04106i	0.342905	+	0.287732i
$782$		0			0
$783$	−38.9123			−1.39061
$784$		0			0
$785$	−17.0819	+	19.6697i	−0.609679	+	0.702040i
$786$		0			0
$787$	0.705191	+	0.407142i	0.0251374	+	0.0145131i	0.512516	−	0.858678i	$-0.328714\pi$
$787$	0.705191	+	0.407142i	0.0251374	+	0.0145131i	−0.487379	+	0.873191i	$0.662047\pi$
$788$		0			0
$789$	−2.35172	−	0.855958i	−0.0837236	−	0.0304729i
$790$		0			0
$791$	53.6664	+	30.9843i	1.90816	+	1.10168i
$792$		0			0
$793$	−1.18710	+	0.209318i	−0.0421552	+	0.00743310i
$794$		0			0
$795$	−6.56752	+	5.32353i	−0.232926	+	0.188806i
$796$		0			0
$797$	30.5017	−	25.5940i	1.08043	−	0.906586i	0.0844706	−	0.996426i	$-0.473080\pi$
$797$	30.5017	−	25.5940i	1.08043	−	0.906586i	0.995956	+	0.0898403i	$0.0286357\pi$
$798$		0			0
$799$	1.92084	−	0.338695i	0.0679543	−	0.0119822i
$800$		0			0
$801$	−8.80839	+	10.4974i	−0.311229	+	0.370908i
$802$		0			0
$803$	−0.216618	+	0.125064i	−0.00764427	+	0.00441342i
$804$		0			0
$805$	−10.8717	−	6.52521i	−0.383176	−	0.229983i
$806$		0			0
$807$	−24.1937	−	4.26600i	−0.851659	−	0.150170i
$808$		0			0
$809$	35.2228	+	6.21073i	1.23837	+	0.218357i	0.754216	−	0.656627i	$-0.228017\pi$
$809$	35.2228	+	6.21073i	1.23837	+	0.218357i	0.484151	+	0.874984i	$0.339128\pi$
$810$		0			0
$811$	8.27790	−	3.01291i	0.290676	−	0.105798i	−0.192566	−	0.981284i	$-0.561681\pi$
$811$	8.27790	−	3.01291i	0.290676	−	0.105798i	0.483243	+	0.875486i	$0.339459\pi$
$812$		0			0
$813$			19.4969i			0.683788i
$814$		0			0
$815$	−49.0923	+	16.9304i	−1.71963	+	0.593045i
$816$		0			0
$817$	−1.00746	−	2.76799i	−0.0352467	−	0.0968396i
$818$		0			0
$819$	53.9138	+	9.50645i	1.88390	+	0.332182i
$820$		0			0
$821$	7.83242	−	44.4198i	0.273353	−	1.55026i	−0.470791	−	0.882245i	$-0.656031\pi$
$821$	7.83242	−	44.4198i	0.273353	−	1.55026i	0.744144	−	0.668019i	$-0.232857\pi$
$822$		0			0
$823$	−11.8439	−	14.1150i	−0.412851	−	0.492016i	0.519043	−	0.854748i	$-0.326289\pi$
$823$	−11.8439	−	14.1150i	−0.412851	−	0.492016i	−0.931894	+	0.362732i	$0.881844\pi$
$824$		0			0
$825$	1.41249	−	3.50578i	0.0491765	−	0.122056i
$826$		0			0
$827$	−20.8396	−	17.4865i	−0.724664	−	0.608065i	0.204007	−	0.978969i	$-0.434603\pi$
$827$	−20.8396	−	17.4865i	−0.724664	−	0.608065i	−0.928671	+	0.370904i	$0.879048\pi$
$828$		0			0
$829$	9.32783	−	1.64475i	0.323969	−	0.0571245i	−0.00929858	−	0.999957i	$-0.502960\pi$
$829$	9.32783	−	1.64475i	0.323969	−	0.0571245i	0.333268	+	0.942832i	$0.391849\pi$
$830$		0			0
$831$	5.37962	+	6.41118i	0.186617	+	0.222401i
$832$		0			0
$833$	−52.7939	+	19.2154i	−1.82920	+	0.665775i
$834$		0			0
$835$	−4.21929	−	7.60314i	−0.146015	−	0.263117i
$836$		0			0
$837$	5.10470	−	8.84159i	0.176444	−	0.305610i
$838$		0			0
$839$	−3.75024	−	1.36497i	−0.129473	−	0.0471242i	0.276471	−	0.961022i	$-0.410835\pi$
$839$	−3.75024	−	1.36497i	−0.129473	−	0.0471242i	−0.405944	+	0.913898i	$0.633057\pi$
$840$		0			0
$841$	17.8964	−	30.9976i	0.617119	−	1.06888i
$842$		0			0
$843$	3.78943	+	6.56349i	0.130515	+	0.226059i
$844$		0			0
$845$	47.0484	−	16.2255i	1.61851	−	0.558174i
$846$		0			0
$847$	29.2141	−	34.8160i	1.00381	−	1.19629i
$848$		0			0
$849$	−1.02313	+	2.81102i	−0.0351137	+	0.0964740i
$850$		0			0
$851$	1.72171	−	7.67425i	0.0590193	−	0.263070i
$852$		0			0
$853$	27.3895	+	9.96896i	0.937798	+	0.341331i	0.765296	−	0.643679i	$-0.222593\pi$
$853$	27.3895	+	9.96896i	0.937798	+	0.341331i	0.172502	+	0.985009i	$0.444815\pi$
$854$		0			0
$855$	−2.78042	+	7.25372i	−0.0950884	+	0.248072i
$856$		0			0
$857$	−11.3940			−0.389213			−0.194606	−	0.980881i	$-0.562343\pi$
$857$	−11.3940			−0.389213			−0.194606	+	0.980881i	$0.562343\pi$
$858$		0			0
$859$	39.9762	−	23.0803i	1.36397	−	0.787489i	0.373822	−	0.927501i	$-0.378047\pi$
$859$	39.9762	−	23.0803i	1.36397	−	0.787489i	0.990150	+	0.140011i	$0.0447138\pi$
$860$		0			0
$861$	−23.6684	+	40.9948i	−0.806616	+	1.39710i
$862$		0			0
$863$	−18.2906	+	50.2531i	−0.622620	+	1.71064i	0.0778601	+	0.996964i	$0.475191\pi$
$863$	−18.2906	+	50.2531i	−0.622620	+	1.71064i	−0.700481	+	0.713671i	$0.747031\pi$
$864$		0			0
$865$	−25.5573	−	4.95503i	−0.868975	−	0.168476i
$866$		0			0
$867$	−3.81926	+	0.673438i	−0.129709	+	0.0228712i
$868$		0			0
$869$	3.64941	+	10.0267i	0.123798	+	0.340132i
$870$		0			0
$871$	−19.5216	−	23.2649i	−0.661464	−	0.788302i
$872$		0			0
$873$	−0.135598	−	0.769015i	−0.00458930	−	0.0260272i
$874$		0			0
$875$	14.4034	+	46.8683i	0.486925	+	1.58444i
$876$		0			0
$877$	−21.1439	+	12.2074i	−0.713979	+	0.412216i	−0.812533	−	0.582916i	$-0.801912\pi$
$877$	−21.1439	+	12.2074i	−0.713979	+	0.412216i	0.0985535	+	0.995132i	$0.468578\pi$
$878$		0			0
$879$	8.43701	−	7.07949i	0.284573	−	0.238785i
$880$		0			0
$881$	4.29172	−	24.3396i	0.144592	−	0.820020i	−0.823102	−	0.567893i	$-0.807759\pi$
$881$	4.29172	−	24.3396i	0.144592	−	0.820020i	0.967694	−	0.252127i	$-0.0811302\pi$
$882$		0			0
$883$	5.73595	−	32.5302i	0.193030	−	1.09473i	−0.722166	−	0.691719i	$-0.756854\pi$
$883$	5.73595	−	32.5302i	0.193030	−	1.09473i	0.915196	−	0.403008i	$-0.132035\pi$
$884$		0			0
$885$	7.40169	−	5.99969i	0.248805	−	0.201677i
$886$		0			0
$887$			17.4414i			0.585623i	0.956170	+	0.292812i	$0.0945909\pi$
$887$			17.4414i			0.585623i	−0.956170	+	0.292812i	$0.905409\pi$
$888$		0			0
$889$	−80.2650			−2.69200
$890$		0			0
$891$	−1.29477	+	0.471258i	−0.0433765	+	0.0157877i
$892$		0			0
$893$	−0.121864	+	0.691123i	−0.00407801	+	0.0231276i
$894$		0			0
$895$	29.6183	−	4.70575i	0.990030	−	0.157296i
$896$		0			0
$897$	−4.67562	−	5.57219i	−0.156115	−	0.186050i
$898$		0			0
$899$	8.49983	+	14.7221i	0.283485	+	0.491011i
$900$		0			0
$901$	−11.7807	+	14.0397i	−0.392472	+	0.467730i
$902$		0			0
$903$	−1.28613	−	7.29400i	−0.0427997	−	0.242729i
$904$		0			0
$905$	23.5177	−	39.1829i	0.781754	−	1.30248i
$906$		0			0
$907$	−30.7961	+	11.2089i	−1.02257	+	0.372184i	−0.798246	−	0.602331i	$-0.794239\pi$
$907$	−30.7961	+	11.2089i	−1.02257	+	0.372184i	−0.224321	+	0.974515i	$0.572016\pi$
$908$		0			0
$909$	0.634289	+	3.59723i	0.0210380	+	0.119313i
$910$		0			0
$911$	4.69453	+	2.71039i	0.155537	+	0.0897992i	0.575748	−	0.817627i	$-0.304711\pi$
$911$	4.69453	+	2.71039i	0.155537	+	0.0897992i	−0.420212	+	0.907426i	$0.638044\pi$
$912$		0			0
$913$	2.75817	−	7.57801i	0.0912821	−	0.250796i
$914$		0			0
$915$	0.0818598	−	0.422221i	0.00270620	−	0.0139582i
$916$		0			0
$917$	28.5952	+	49.5283i	0.944295	+	1.63557i
$918$		0			0
$919$		−	50.5550i		−	1.66766i	−0.552023	−	0.833829i	$-0.686144\pi$
$919$		−	50.5550i		−	1.66766i	0.552023	−	0.833829i	$-0.313856\pi$
$920$		0			0
$921$	0.815125	+	0.683971i	0.0268593	+	0.0225376i
$922$		0			0
$923$	−87.4834	−	31.8414i	−2.87955	−	1.04807i
$924$		0			0
$925$	−24.7879	+	17.6227i	−0.815021	+	0.579431i
$926$		0			0
$927$	31.6651	+	11.5252i	1.04002	+	0.378536i
$928$		0			0
$929$	4.57589	+	3.83963i	0.150130	+	0.125974i	0.714759	−	0.699371i	$-0.246536\pi$
$929$	4.57589	+	3.83963i	0.150130	+	0.125974i	−0.564629	+	0.825345i	$0.690981\pi$
$930$		0			0
$931$		−	20.2145i		−	0.662505i
$932$		0			0
$933$	7.75596	+	13.4337i	0.253919	+	0.439800i
$934$		0			0
$935$	1.55956	−	8.04399i	0.0510031	−	0.263067i
$936$		0			0
$937$	−11.2214	+	30.8307i	−0.366589	+	1.00719i	0.610061	+	0.792355i	$0.291145\pi$
$937$	−11.2214	+	30.8307i	−0.366589	+	1.00719i	−0.976649	+	0.214839i	$0.931077\pi$
$938$		0			0
$939$	−8.15085	−	4.70589i	−0.265993	−	0.153571i
$940$		0			0
$941$	−4.09873	−	23.2451i	−0.133615	−	0.757768i	−0.975814	−	0.218601i	$-0.929851\pi$
$941$	−4.09873	−	23.2451i	−0.133615	−	0.757768i	0.842199	−	0.539166i	$-0.181261\pi$
$942$		0			0
$943$	−13.8423	+	5.03819i	−0.450768	+	0.164066i
$944$		0			0
$945$	−24.3960	+	40.6463i	−0.793603	+	1.32222i
$946$		0			0
$947$	4.82434	+	27.3602i	0.156770	+	0.889086i	0.957150	+	0.289593i	$0.0935199\pi$
$947$	4.82434	+	27.3602i	0.156770	+	0.889086i	−0.800380	+	0.599493i	$0.795369\pi$
$948$		0			0
$949$	1.19653	−	1.42597i	0.0388411	−	0.0462891i
$950$		0			0
$951$	6.98759	+	12.1029i	0.226588	+	0.392462i
$952$		0			0
$953$	16.8182	+	20.0432i	0.544795	+	0.649261i	0.966256	−	0.257585i	$-0.0829268\pi$
$953$	16.8182	+	20.0432i	0.544795	+	0.649261i	−0.421461	+	0.906847i	$0.638482\pi$
$954$		0			0
$955$	−2.27629	+	0.361657i	−0.0736590	+	0.0117029i
$956$		0			0
$957$	−1.05661	+	5.99232i	−0.0341552	+	0.193704i
$958$		0			0
$959$	−39.9289	+	14.5329i	−1.28937	+	0.469292i
$960$		0			0
$961$	26.5398			0.856123
$962$		0			0
$963$			7.48104i			0.241073i
$964$		0			0
$965$	27.1962	−	22.0448i	0.875476	−	0.709648i
$966$		0			0
$967$	5.80155	−	32.9022i	0.186565	−	1.05806i	−0.737362	−	0.675497i	$-0.763929\pi$
$967$	5.80155	−	32.9022i	0.186565	−	1.05806i	0.923928	−	0.382567i	$-0.124960\pi$
$968$		0			0
$969$	1.24863	−	7.08132i	0.0401117	−	0.227485i
$970$		0			0
$971$	42.4349	−	35.6071i	1.36180	−	1.14269i	0.386381	−	0.922339i	$-0.373725\pi$
$971$	42.4349	−	35.6071i	1.36180	−	1.14269i	0.975421	−	0.220348i	$-0.0707194\pi$
$972$		0			0
$973$	−52.8650	+	30.5216i	−1.69477	+	0.978479i
$974$		0			0
$975$	−0.954492	+	28.1121i	−0.0305682	+	0.900308i
$976$		0			0
$977$	1.07411	+	6.09157i	0.0343638	+	0.194887i	0.997157	−	0.0753527i	$-0.0240083\pi$
$977$	1.07411	+	6.09157i	0.0343638	+	0.194887i	−0.962793	+	0.270239i	$0.912897\pi$
$978$		0			0
$979$	3.34286	+	3.98386i	0.106838	+	0.127325i
$980$		0			0
$981$	−7.09301	−	19.4879i	−0.226462	−	0.622201i
$982$		0			0
$983$	−38.1665	+	6.72979i	−1.21732	+	0.214647i	−0.745173	−	0.666871i	$-0.767633\pi$
$983$	−38.1665	+	6.72979i	−1.21732	+	0.214647i	−0.472150	+	0.881518i	$0.656522\pi$
$984$		0			0
$985$	36.0251	+	6.98450i	1.14786	+	0.222545i
$986$		0			0
$987$	−0.603520	+	1.65816i	−0.0192103	+	0.0527798i
$988$		0			0
$989$	1.15241	−	1.99604i	0.0366447	−	0.0634704i
$990$		0			0
$991$	18.0120	−	10.3992i	0.572170	−	0.330342i	−0.185846	−	0.982579i	$-0.559502\pi$
$991$	18.0120	−	10.3992i	0.572170	−	0.330342i	0.758015	+	0.652237i	$0.226169\pi$
$992$		0			0
$993$	−27.1114			−0.860353
$994$		0			0
$995$	14.5234	−	37.8895i	0.460423	−	1.20118i
$996$		0			0
$997$	23.6864	+	8.62113i	0.750155	+	0.273034i	0.688671	−	0.725074i	$-0.258195\pi$
$997$	23.6864	+	8.62113i	0.750155	+	0.273034i	0.0614837	+	0.998108i	$0.480417\pi$
$998$		0			0
$999$	−28.6920	−	6.43701i	−0.907774	−	0.203658i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.bp.a.169.8	✓	120
5.4	even	2	inner	740.2.bp.a.169.13	yes	120
37.30	even	18	inner	740.2.bp.a.289.13	yes	120
185.104	even	18	inner	740.2.bp.a.289.8	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.bp.a.169.8	✓	120	1.1	even	1	trivial
740.2.bp.a.169.13	yes	120	5.4	even	2	inner
740.2.bp.a.289.8	yes	120	185.104	even	18	inner
740.2.bp.a.289.13	yes	120	37.30	even	18	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:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.bp (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.324044 - 0.890304i) q^{3} +(-0.350865 - 2.20837i) q^{5} +(4.31890 + 0.761538i) q^{7} +(1.61050 - 1.35137i) q^{9} +(-0.398930 - 0.690967i) q^{11} +(4.54857 + 3.81671i) q^{13} +(-1.85242 + 1.02799i) q^{15} +(-3.51825 + 2.95216i) q^{17} +(-0.565183 - 1.55283i) q^{19} +(-0.721513 - 4.09190i) q^{21} +(0.646500 - 1.11977i) q^{23} +(-4.75379 + 1.54968i) q^{25} +(-4.18653 - 2.41709i) q^{27} +(6.97099 - 4.02470i) q^{29} +2.11192i q^{31} +(-0.485900 + 0.579073i) q^{33} +(0.166405 - 9.80491i) q^{35} +(5.80584 - 1.81445i) q^{37} +(1.92409 - 5.28639i) q^{39} +(-8.72727 - 7.32305i) q^{41} +1.78254 q^{43} +(-3.54938 - 3.08242i) q^{45} +(-0.367788 - 0.212342i) q^{47} +(11.4951 + 4.18386i) q^{49} +(3.76839 + 2.17568i) q^{51} +(3.92991 - 0.692949i) q^{53} +(-1.38594 + 1.12342i) q^{55} +(-1.19935 + 1.00637i) q^{57} +(-4.42906 + 0.780963i) q^{59} +(-0.130492 + 0.155514i) q^{61} +(7.98468 - 4.60996i) q^{63} +(6.83276 - 11.3841i) q^{65} +(-5.03707 - 0.888171i) q^{67} +(-1.20643 - 0.212726i) q^{69} +(-14.7335 + 5.36254i) q^{71} -0.313499i q^{73} +(2.92012 + 3.73015i) q^{75} +(-1.19674 - 3.28802i) q^{77} +(-13.1703 - 2.32228i) q^{79} +(0.299882 - 1.70072i) q^{81} +(6.49696 + 7.74277i) q^{83} +(7.75389 + 6.73378i) q^{85} +(-5.84212 - 4.90212i) q^{87} +(-6.41911 + 1.13186i) q^{89} +(16.7382 + 19.9479i) q^{91} +(1.88025 - 0.684354i) q^{93} +(-3.23092 + 1.79297i) q^{95} +(0.185715 - 0.321668i) q^{97} +(-1.57623 - 0.573699i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q + 3 q^{5} + 6 q^{9} + 12 q^{11} + 3 q^{15} + 6 q^{19} - 12 q^{21} - 33 q^{25} - 48 q^{35} + 24 q^{39} + 30 q^{41} - 27 q^{45} + 6 q^{49} - 3 q^{55} - 42 q^{59} + 48 q^{61} - 18 q^{65} - 108 q^{69}+ \cdots + 90 q^{99}+O(q^{100}) \) 120 * q + 3 * q^5 + 6 * q^9 + 12 * q^11 + 3 * q^15 + 6 * q^19 - 12 * q^21 - 33 * q^25 - 48 * q^35 + 24 * q^39 + 30 * q^41 - 27 * q^45 + 6 * q^49 - 3 * q^55 - 42 * q^59 + 48 * q^61 - 18 * q^65 - 108 * q^69 - 18 * q^71 - 12 * q^75 - 48 * q^79 + 108 * q^81 - 33 * q^85 - 84 * q^89 - 30 * q^91 + 99 * q^95 + 90 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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