LMFDB - Embedded newform 882.2.bl.a.719.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [882,2,Mod(17,882)] 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("882.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(882, base_ring=CyclotomicField(42)) chi = DirichletCharacter(H, H._module([21, 25])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.bl (of order $42$, degree $12$, 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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$20$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			719.11
Character	$\chi$	$=$	882.719
Dual form			882.2.bl.a.395.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.930874 - 0.365341i) q^{2} +(0.733052 - 0.680173i) q^{4} +(-3.09036 + 2.10697i) q^{5} +(-0.605636 - 2.57550i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.10697 + 3.09036i) q^{10} +(-0.198018 + 1.31377i) q^{11} +(5.18974 + 4.13868i) q^{13} +(-1.50471 - 2.17620i) q^{14} +(0.0747301 - 0.997204i) q^{16} +(3.42802 - 1.05740i) q^{17} +(6.36887 + 3.67707i) q^{19} +(-0.832289 + 3.64650i) q^{20} +(0.295642 + 1.29529i) q^{22} +(-1.67066 + 5.41615i) q^{23} +(3.28429 - 8.36823i) q^{25} +(6.34303 + 1.95656i) q^{26} +(-2.19575 - 1.47604i) q^{28} +(6.48494 + 1.48014i) q^{29} +(-0.438536 + 0.253189i) q^{31} +(-0.294755 - 0.955573i) q^{32} +(2.80474 - 2.23671i) q^{34} +(7.29814 + 6.68316i) q^{35} +(-1.93416 - 1.79464i) q^{37} +(7.27200 + 1.09608i) q^{38} +(0.557459 + 3.69850i) q^{40} +(-6.06006 - 2.91837i) q^{41} +(-0.521418 + 0.251102i) q^{43} +(0.748430 + 1.09775i) q^{44} +(0.423567 + 5.65211i) q^{46} +(2.91481 + 7.42682i) q^{47} +(-6.26641 + 3.11963i) q^{49} -8.98965i q^{50} +(6.61937 - 0.496053i) q^{52} +(-5.04360 - 5.43570i) q^{53} +(-2.15612 - 4.47723i) q^{55} +(-2.58322 - 0.571808i) q^{56} +(6.57742 - 0.991386i) q^{58} +(10.7024 + 7.29681i) q^{59} +(-2.41389 + 2.60156i) q^{61} +(-0.315721 + 0.395902i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-24.7583 - 1.85538i) q^{65} +(-4.52583 - 7.83896i) q^{67} +(1.79370 - 3.10678i) q^{68} +(9.23528 + 3.55487i) q^{70} +(-5.14067 + 1.17332i) q^{71} +(5.00623 + 1.96480i) q^{73} +(-2.45611 - 0.963954i) q^{74} +(7.16976 - 1.63645i) q^{76} +(3.50353 - 0.285668i) q^{77} +(0.310444 - 0.537704i) q^{79} +(1.87014 + 3.23917i) q^{80} +(-6.70735 - 0.502647i) q^{82} +(3.06487 + 3.84322i) q^{83} +(-8.36590 + 10.4905i) q^{85} +(-0.393637 + 0.424240i) q^{86} +(1.09775 + 0.748430i) q^{88} +(-5.64124 + 0.850280i) q^{89} +(7.51608 - 15.8727i) q^{91} +(2.45924 + 5.10666i) q^{92} +(5.42664 + 5.84853i) q^{94} +(-27.4296 + 2.05556i) q^{95} -16.8856i q^{97} +(-4.69351 + 5.19336i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) $ 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

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 $

$2$	0.930874	−	0.365341i	0.658227	−	0.258335i
$2$	0.930874	−	0.365341i	0.658227	−	0.258335i
$3$		0			0
$3$		0			0
$4$	0.733052	−	0.680173i	0.366526	−	0.340086i
$5$	−3.09036	+	2.10697i	−1.38205	+	0.942266i	−0.382216	+	0.924073i	$0.624839\pi$
$5$	−3.09036	+	2.10697i	−1.38205	+	0.942266i	−0.999834	+	0.0181934i	$0.994209\pi$
$6$		0			0
$7$	−0.605636	−	2.57550i	−0.228909	−	0.973448i
$7$	−0.605636	−	2.57550i	−0.228909	−	0.973448i
$8$	0.433884	−	0.900969i	0.153401	−	0.318541i
$9$		0			0
$10$	−2.10697	+	3.09036i	−0.666283	+	0.977257i
$11$	−0.198018	+	1.31377i	−0.0597048	+	0.396115i	0.938940	+	0.344080i	$0.111809\pi$
$11$	−0.198018	+	1.31377i	−0.0597048	+	0.396115i	−0.998645	+	0.0520356i	$0.983429\pi$
$12$		0			0
$13$	5.18974	+	4.13868i	1.43938	+	1.14786i	0.963289	+	0.268466i	$0.0865166\pi$
$13$	5.18974	+	4.13868i	1.43938	+	1.14786i	0.476087	+	0.879398i	$0.342055\pi$
$14$	−1.50471	−	2.17620i	−0.402150	−	0.581615i
$15$		0			0
$16$	0.0747301	−	0.997204i	0.0186825	−	0.249301i
$17$	3.42802	−	1.05740i	0.831418	−	0.256458i	0.150307	−	0.988639i	$-0.451974\pi$
$17$	3.42802	−	1.05740i	0.831418	−	0.256458i	0.681110	+	0.732181i	$0.261497\pi$
$18$		0			0
$19$	6.36887	+	3.67707i	1.46112	+	0.843578i	0.999063	−	0.0432727i	$-0.0137784\pi$
$19$	6.36887	+	3.67707i	1.46112	+	0.843578i	0.462056	+	0.886851i	$0.347112\pi$
$20$	−0.832289	+	3.64650i	−0.186106	+	0.815382i
$21$		0			0
$22$	0.295642	+	1.29529i	0.0630312	+	0.276158i
$23$	−1.67066	+	5.41615i	−0.348357	+	1.12934i	0.596707	+	0.802459i	$0.296475\pi$
$23$	−1.67066	+	5.41615i	−0.348357	+	1.12934i	−0.945064	+	0.326886i	$0.894001\pi$
$24$		0			0
$25$	3.28429	−	8.36823i	0.656858	−	1.67365i
$26$	6.34303	+	1.95656i	1.24397	+	0.383714i
$27$		0			0
$28$	−2.19575	−	1.47604i	−0.414957	−	0.278945i
$29$	6.48494	+	1.48014i	1.20422	+	0.274856i	0.777123	−	0.629349i	$-0.216678\pi$
$29$	6.48494	+	1.48014i	1.20422	+	0.274856i	0.427100	+	0.904205i	$0.359535\pi$
$30$		0			0
$31$	−0.438536	+	0.253189i	−0.0787634	+	0.0454741i	−0.538864	−	0.842392i	$-0.681147\pi$
$31$	−0.438536	+	0.253189i	−0.0787634	+	0.0454741i	0.460101	+	0.887867i	$0.347813\pi$
$32$	−0.294755	−	0.955573i	−0.0521058	−	0.168923i
$33$		0			0
$34$	2.80474	−	2.23671i	0.481009	−	0.383592i
$35$	7.29814	+	6.68316i	1.23361	+	1.12966i
$36$		0			0
$37$	−1.93416	−	1.79464i	−0.317974	−	0.295037i	0.504996	−	0.863122i	$-0.331494\pi$
$37$	−1.93416	−	1.79464i	−0.317974	−	0.295037i	−0.822970	+	0.568085i	$0.807684\pi$
$38$	7.27200	+	1.09608i	1.17967	+	0.177807i
$39$		0			0
$40$	0.557459	+	3.69850i	0.0881420	+	0.584784i
$41$	−6.06006	−	2.91837i	−0.946423	−	0.455773i	−0.103992	−	0.994578i	$-0.533162\pi$
$41$	−6.06006	−	2.91837i	−0.946423	−	0.455773i	−0.842431	+	0.538805i	$0.818876\pi$
$42$		0			0
$43$	−0.521418	+	0.251102i	−0.0795156	+	0.0382927i	−0.473219	−	0.880945i	$-0.656908\pi$
$43$	−0.521418	+	0.251102i	−0.0795156	+	0.0382927i	0.393703	+	0.919238i	$0.371194\pi$
$44$	0.748430	+	1.09775i	0.112830	+	0.165491i
$45$		0			0
$46$	0.423567	+	5.65211i	0.0624516	+	0.833358i
$47$	2.91481	+	7.42682i	0.425169	+	1.08331i	0.969641	+	0.244534i	$0.0786349\pi$
$47$	2.91481	+	7.42682i	0.425169	+	1.08331i	−0.544472	+	0.838779i	$0.683270\pi$
$48$		0			0
$49$	−6.26641	+	3.11963i	−0.895201	+	0.445662i
$50$		−	8.98965i		−	1.27133i
$51$		0			0
$52$	6.61937	−	0.496053i	0.917942	−	0.0687902i
$53$	−5.04360	−	5.43570i	−0.692791	−	0.746651i	0.284471	−	0.958685i	$-0.408182\pi$
$53$	−5.04360	−	5.43570i	−0.692791	−	0.746651i	−0.977262	+	0.212033i	$0.931991\pi$
$54$		0			0
$55$	−2.15612	−	4.47723i	−0.290731	−	0.603709i
$56$	−2.58322	−	0.571808i	−0.345198	−	0.0764111i
$57$		0			0
$58$	6.57742	−	0.991386i	0.863657	−	0.130175i
$59$	10.7024	+	7.29681i	1.39334	+	0.949963i	0.999526	+	0.0307729i	$0.00979688\pi$
$59$	10.7024	+	7.29681i	1.39334	+	0.949963i	0.393814	+	0.919190i	$0.371156\pi$
$60$		0			0
$61$	−2.41389	+	2.60156i	−0.309067	+	0.333095i	−0.868415	−	0.495838i	$-0.834861\pi$
$61$	−2.41389	+	2.60156i	−0.309067	+	0.333095i	0.559348	+	0.828933i	$0.311052\pi$
$62$	−0.315721	+	0.395902i	−0.0400967	+	0.0502796i
$63$		0			0
$64$	−0.623490	−	0.781831i	−0.0779362	−	0.0977289i
$65$	−24.7583	−	1.85538i	−3.07088	−	0.230131i
$66$		0			0
$67$	−4.52583	−	7.83896i	−0.552918	−	0.957682i	−0.998062	−	0.0622230i	$-0.980181\pi$
$67$	−4.52583	−	7.83896i	−0.552918	−	0.957682i	0.445144	−	0.895459i	$-0.353152\pi$
$68$	1.79370	−	3.10678i	0.217518	−	0.376752i
$69$		0			0
$70$	9.23528	+	3.55487i	1.10383	+	0.424889i
$71$	−5.14067	+	1.17332i	−0.610086	+	0.139248i	−0.516391	−	0.856353i	$-0.672725\pi$
$71$	−5.14067	+	1.17332i	−0.610086	+	0.139248i	−0.0936946	+	0.995601i	$0.529868\pi$
$72$		0			0
$73$	5.00623	+	1.96480i	0.585935	+	0.229962i	0.639743	−	0.768589i	$-0.279041\pi$
$73$	5.00623	+	1.96480i	0.585935	+	0.229962i	−0.0538085	+	0.998551i	$0.517136\pi$
$74$	−2.45611	−	0.963954i	−0.285517	−	0.112057i
$75$		0			0
$76$	7.16976	−	1.63645i	0.822428	−	0.187714i
$77$	3.50353	−	0.285668i	0.399265	−	0.0325549i
$78$		0			0
$79$	0.310444	−	0.537704i	0.0349277	−	0.0604965i	−0.848033	−	0.529943i	$-0.822213\pi$
$79$	0.310444	−	0.537704i	0.0349277	−	0.0604965i	0.882961	+	0.469447i	$0.155547\pi$
$80$	1.87014	+	3.23917i	0.209088	+	0.362150i
$81$		0			0
$82$	−6.70735	−	0.502647i	−0.740703	−	0.0555080i
$83$	3.06487	+	3.84322i	0.336413	+	0.421848i	0.921049	−	0.389448i	$-0.127334\pi$
$83$	3.06487	+	3.84322i	0.336413	+	0.421848i	−0.584636	+	0.811296i	$0.698763\pi$
$84$		0			0
$85$	−8.36590	+	10.4905i	−0.907409	+	1.13786i
$86$	−0.393637	+	0.424240i	−0.0424470	+	0.0457469i
$87$		0			0
$88$	1.09775	+	0.748430i	0.117020	+	0.0797829i
$89$	−5.64124	+	0.850280i	−0.597970	+	0.0901295i	−0.441051	−	0.897482i	$-0.645394\pi$
$89$	−5.64124	+	0.850280i	−0.597970	+	0.0901295i	−0.156919	+	0.987611i	$0.550156\pi$
$90$		0			0
$91$	7.51608	−	15.8727i	0.787900	−	1.66391i
$92$	2.45924	+	5.10666i	0.256393	+	0.532406i
$93$		0			0
$94$	5.42664	+	5.84853i	0.559715	+	0.603230i
$95$	−27.4296	+	2.05556i	−2.81422	+	0.210896i
$96$		0			0
$97$		−	16.8856i		−	1.71448i	−0.514919	−	0.857239i	$-0.672178\pi$
$97$		−	16.8856i		−	1.71448i	0.514919	−	0.857239i	$-0.327822\pi$
$98$	−4.69351	+	5.19336i	−0.474116	+	0.524609i
$99$		0			0
$100$	−3.28429	−	8.36823i	−0.328429	−	0.836823i
$101$	−1.10185	−	14.7031i	−0.109638	−	1.46302i	−0.732544	−	0.680719i	$-0.761667\pi$
$101$	−1.10185	−	14.7031i	−0.109638	−	1.46302i	0.622907	−	0.782296i	$-0.285952\pi$
$102$		0			0
$103$	8.58036	+	12.5851i	0.845448	+	1.24005i	0.968840	+	0.247687i	$0.0796705\pi$
$103$	8.58036	+	12.5851i	0.845448	+	1.24005i	−0.123392	+	0.992358i	$0.539377\pi$
$104$	5.98057	−	2.88009i	0.586443	−	0.282416i
$105$		0			0
$106$	−6.68084	−	3.21732i	−0.648900	−	0.312494i
$107$	−0.618296	−	4.10213i	−0.0597729	−	0.396567i	−0.998633	−	0.0522687i	$-0.983355\pi$
$107$	−0.618296	−	4.10213i	−0.0597729	−	0.396567i	0.938860	−	0.344299i	$-0.111883\pi$
$108$		0			0
$109$	2.43855	+	0.367552i	0.233570	+	0.0352051i	0.264784	−	0.964308i	$-0.414699\pi$
$109$	2.43855	+	0.367552i	0.233570	+	0.0352051i	−0.0312139	+	0.999513i	$0.509937\pi$
$110$	−3.64279	−	3.38001i	−0.347326	−	0.322272i
$111$		0			0
$112$	−2.61356	+	0.411475i	−0.246958	+	0.0388808i
$113$	2.79551	−	2.22934i	0.262979	−	0.209719i	−0.483119	−	0.875555i	$-0.660496\pi$
$113$	2.79551	−	2.22934i	0.262979	−	0.209719i	0.746098	+	0.665836i	$0.231925\pi$
$114$		0			0
$115$	−6.24873	−	20.2579i	−0.582697	−	1.88906i
$116$	5.76055	−	3.32586i	0.534854	−	0.308798i
$117$		0			0
$118$	12.6285	+	2.88236i	1.16254	+	0.265343i
$119$	−4.79948	−	8.18847i	−0.439968	−	0.750636i
$120$		0			0
$121$	8.82453	+	2.72201i	0.802230	+	0.247455i
$122$	−1.29657	+	3.30361i	−0.117386	+	0.299095i
$123$		0			0
$124$	−0.149257	+	0.483881i	−0.0134037	+	0.0434538i
$125$	3.32054	+	14.5483i	0.296998	+	1.30124i
$126$		0			0
$127$	1.47918	−	6.48070i	0.131256	−	0.575069i	−0.865934	−	0.500157i	$-0.833275\pi$
$127$	1.47918	−	6.48070i	0.131256	−	0.575069i	0.997190	−	0.0749114i	$-0.0238674\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−23.7247	+	7.31809i	−2.08079	+	0.641839i
$131$	0.634486	−	8.46663i	0.0554353	−	0.739733i	−0.898357	−	0.439266i	$-0.855239\pi$
$131$	0.634486	−	8.46663i	0.0554353	−	0.739733i	0.953792	−	0.300467i	$-0.0971424\pi$
$132$		0			0
$133$	5.61308	−	18.6300i	0.486715	−	1.61543i
$134$	−7.07687	−	5.64361i	−0.611348	−	0.487534i
$135$		0			0
$136$	0.534674	−	3.54733i	0.0458479	−	0.304181i
$137$	7.37758	−	10.8209i	0.630309	−	0.924493i	−0.369680	−	0.929159i	$-0.620533\pi$
$137$	7.37758	−	10.8209i	0.630309	−	0.924493i	0.999989	+	0.00466562i	$0.00148512\pi$
$138$		0			0
$139$	−2.70819	+	5.62362i	−0.229706	+	0.476989i	−0.983683	−	0.179912i	$-0.942419\pi$
$139$	−2.70819	+	5.62362i	−0.229706	+	0.476989i	0.753977	+	0.656901i	$0.228133\pi$
$140$	9.89562	−	0.0648899i	0.836333	−	0.00548420i
$141$		0			0
$142$	−4.35665	+	2.97032i	−0.365602	+	0.249263i
$143$	−6.46492	+	5.99857i	−0.540624	+	0.501626i
$144$		0			0
$145$	−23.1594	+	9.08940i	−1.92328	+	0.754834i
$146$	5.37799			0.445085
$147$		0			0
$148$	−2.63850			−0.216884
$149$	17.0329	−	6.68493i	1.39539	−	0.547651i	0.455841	−	0.890061i	$-0.349339\pi$
$149$	17.0329	−	6.68493i	1.39539	−	0.547651i	0.939550	+	0.342411i	$0.111243\pi$
$150$		0			0
$151$	−11.4737	+	10.6460i	−0.933717	+	0.866363i	−0.991252	−	0.131981i	$-0.957866\pi$
$151$	−11.4737	+	10.6460i	−0.933717	+	0.866363i	0.0575354	+	0.998343i	$0.481676\pi$
$152$	6.07628	−	4.14274i	0.492851	−	0.336020i
$153$		0			0
$154$	3.15698	−	1.54590i	0.254397	−	0.124573i
$155$	0.821772	−	1.70643i	0.0660063	−	0.137064i
$156$		0			0
$157$	−12.1653	+	17.8432i	−0.970898	+	1.42405i	−0.0662902	+	0.997800i	$0.521116\pi$
$157$	−12.1653	+	17.8432i	−0.970898	+	1.42405i	−0.904608	+	0.426245i	$0.859836\pi$
$158$	0.0925385	−	0.613953i	0.00736197	−	0.0488435i
$159$		0			0
$160$	2.92426	+	2.33202i	0.231183	+	0.184363i
$161$	14.9611	+	1.02257i	1.17910	+	0.0805899i
$162$		0			0
$163$	−0.907304	+	12.1071i	−0.0710655	+	0.948304i	0.841733	+	0.539894i	$0.181536\pi$
$163$	−0.907304	+	12.1071i	−0.0710655	+	0.948304i	−0.912799	+	0.408410i	$0.866083\pi$
$164$	−6.42734	+	1.98257i	−0.501891	+	0.154813i
$165$		0			0
$166$	4.25709	+	2.45783i	0.330414	+	0.190765i
$167$	−3.75539	+	16.4534i	−0.290601	+	1.27320i	0.593091	+	0.805135i	$0.297907\pi$
$167$	−3.75539	+	16.4534i	−0.290601	+	1.27320i	−0.883692	+	0.468069i	$0.844950\pi$
$168$		0			0
$169$	6.91198	+	30.2833i	0.531690	+	2.32949i
$170$	−3.95498	+	12.8217i	−0.303333	+	0.983383i
$171$		0			0
$172$	−0.211434	+	0.538725i	−0.0161217	+	0.0410774i
$173$	−13.5671	−	4.18488i	−1.03148	−	0.318171i	−0.267604	−	0.963529i	$-0.586232\pi$
$173$	−13.5671	−	4.18488i	−1.03148	−	0.318171i	−0.763880	+	0.645358i	$0.776708\pi$
$174$		0			0
$175$	−23.5415	−	3.39058i	−1.77957	−	0.256304i
$176$	1.29529	+	0.295642i	0.0976365	+	0.0222849i
$177$		0			0
$178$	−4.94064	+	2.85248i	−0.370317	+	0.213802i
$179$	2.62184	+	8.49980i	0.195966	+	0.635305i	0.999213	+	0.0396597i	$0.0126274\pi$
$179$	2.62184	+	8.49980i	0.195966	+	0.635305i	−0.803248	+	0.595645i	$0.796896\pi$
$180$		0			0
$181$	−3.67499	+	2.93070i	−0.273160	+	0.217837i	−0.750482	−	0.660891i	$-0.770179\pi$
$181$	−3.67499	+	2.93070i	−0.273160	+	0.217837i	0.477323	+	0.878728i	$0.341607\pi$
$182$	1.19757	−	17.5214i	0.0887695	−	1.29878i
$183$		0			0
$184$	4.15491	+	3.85519i	0.306304	+	0.284208i
$185$	9.75850	+	1.47086i	0.717459	+	0.108140i
$186$		0			0
$187$	0.710371	+	4.71300i	0.0519475	+	0.344649i
$188$	7.18823	+	3.46167i	0.524255	+	0.252468i
$189$		0			0
$190$	−24.7825	+	11.9346i	−1.79791	+	0.865829i
$191$	−3.85118	−	5.64865i	−0.278662	−	0.408722i	0.661236	−	0.750178i	$-0.270032\pi$
$191$	−3.85118	−	5.64865i	−0.278662	−	0.408722i	−0.939898	+	0.341456i	$0.889080\pi$
$192$		0			0
$193$	−1.56213	−	20.8451i	−0.112444	−	1.50047i	−0.713159	−	0.701003i	$-0.752736\pi$
$193$	−1.56213	−	20.8451i	−0.112444	−	1.50047i	0.600714	−	0.799464i	$-0.294883\pi$
$194$	−6.16902	−	15.7184i	−0.442910	−	1.12852i
$195$		0			0
$196$	−2.47171	+	6.54909i	−0.176551	+	0.467792i
$197$			9.48752i			0.675958i	0.941154	+	0.337979i	$0.109743\pi$
$197$			9.48752i			0.675958i	−0.941154	+	0.337979i	$0.890257\pi$
$198$		0			0
$199$	17.6915	−	1.32579i	1.25411	−	0.0939829i	0.568951	−	0.822372i	$-0.307349\pi$
$199$	17.6915	−	1.32579i	1.25411	−	0.0939829i	0.685164	+	0.728389i	$0.259730\pi$
$200$	−6.11452	−	6.58988i	−0.432362	−	0.465975i
$201$		0			0
$202$	−6.39733	−	13.2842i	−0.450115	−	0.934673i
$203$	−0.115400	−	17.5984i	−0.00809952	−	1.23517i
$204$		0			0
$205$	24.8767	−	3.74956i	1.73746	−	0.261881i
$206$	12.5851	+	8.58036i	0.876844	+	0.597822i
$207$		0			0
$208$	4.51494	−	4.86595i	0.313055	−	0.337393i
$209$	−6.09196	+	7.63908i	−0.421390	+	0.528406i
$210$		0			0
$211$	−5.16103	−	6.47172i	−0.355300	−	0.445532i	0.571774	−	0.820411i	$-0.306255\pi$
$211$	−5.16103	−	6.47172i	−0.355300	−	0.445532i	−0.927074	+	0.374880i	$0.877684\pi$
$212$	−7.39443	−	0.554136i	−0.507852	−	0.0380582i
$213$		0			0
$214$	−2.07423	−	3.59267i	−0.141791	−	0.245590i
$215$	1.08231	−	1.87461i	0.0738126	−	0.127847i
$216$		0			0
$217$	0.917682	+	0.976110i	0.0622963	+	0.0662626i
$218$	2.40426	−	0.548757i	0.162837	−	0.0371665i
$219$		0			0
$220$	−4.62584	−	1.81551i	−0.311874	−	0.122401i
$221$	22.1668	+	8.69984i	1.49110	+	0.585214i
$222$		0			0
$223$	−23.3539	+	5.33037i	−1.56389	+	0.356948i	−0.914847	−	0.403802i	$-0.867689\pi$
$223$	−23.3539	+	5.33037i	−1.56389	+	0.356948i	−0.649045	+	0.760750i	$0.724831\pi$
$224$	−2.28256	+	1.33787i	−0.152510	+	0.0893903i
$225$		0			0
$226$	1.78779	−	3.09655i	0.118922	−	0.205979i
$227$	−1.11398	−	1.92946i	−0.0739372	−	0.128063i	0.826686	−	0.562663i	$-0.190223\pi$
$227$	−1.11398	−	1.92946i	−0.0739372	−	0.128063i	−0.900624	+	0.434600i	$0.856890\pi$
$228$		0			0
$229$	13.0762	+	0.979928i	0.864102	+	0.0647555i	0.499403	−	0.866370i	$-0.333553\pi$
$229$	13.0762	+	0.979928i	0.864102	+	0.0647555i	0.364699	+	0.931125i	$0.381172\pi$
$230$	−13.2178	−	16.5746i	−0.871557	−	1.09290i
$231$		0			0
$232$	4.14727	−	5.20052i	0.272282	−	0.341431i
$233$	−4.53465	+	4.88719i	−0.297075	+	0.320171i	−0.863896	−	0.503670i	$-0.831983\pi$
$233$	−4.53465	+	4.88719i	−0.297075	+	0.320171i	0.566821	+	0.823841i	$0.308173\pi$
$234$		0			0
$235$	−24.6559	−	16.8101i	−1.60837	−	1.09657i
$236$	12.8085	−	1.93058i	0.833765	−	0.125670i
$237$		0			0
$238$	−7.45930	−	5.86899i	−0.483514	−	0.380430i
$239$	−3.51602	−	7.30108i	−0.227432	−	0.472268i	0.755758	−	0.654851i	$-0.227269\pi$
$239$	−3.51602	−	7.30108i	−0.227432	−	0.472268i	−0.983190	+	0.182583i	$0.941554\pi$
$240$		0			0
$241$	−14.1078	−	15.2046i	−0.908766	−	0.979417i	0.0910989	−	0.995842i	$-0.470962\pi$
$241$	−14.1078	−	15.2046i	−0.908766	−	0.979417i	−0.999865	+	0.0164248i	$0.994772\pi$
$242$	9.20899	−	0.690118i	0.591976	−	0.0443625i
$243$		0			0
$244$			3.54894i			0.227197i
$245$	12.7925	−	22.8439i	0.817281	−	1.45945i
$246$		0			0
$247$	17.8346	+	45.4418i	1.13479	+	2.89139i
$248$	0.0378417	+	0.504962i	0.00240295	+	0.0320651i
$249$		0			0
$250$	8.40608	+	12.3295i	0.531647	+	0.779783i
$251$	−13.5118	+	6.50696i	−0.852859	+	0.410715i	−0.808638	−	0.588306i	$-0.799795\pi$
$251$	−13.5118	+	6.50696i	−0.852859	+	0.410715i	−0.0442213	+	0.999022i	$0.514081\pi$
$252$		0			0
$253$	−6.78473	−	3.26735i	−0.426552	−	0.205417i
$254$	−0.990738	−	6.57312i	−0.0621644	−	0.412434i
$255$		0			0
$256$	−0.988831	−	0.149042i	−0.0618019	−	0.00931514i
$257$	−9.60367	−	8.91091i	−0.599061	−	0.555847i	0.321270	−	0.946988i	$-0.395890\pi$
$257$	−9.60367	−	8.91091i	−0.599061	−	0.555847i	−0.920331	+	0.391140i	$0.872081\pi$
$258$		0			0
$259$	−3.45069	+	6.06833i	−0.214416	+	0.377068i
$260$	−19.4111	+	15.4798i	−1.20382	+	0.960017i
$261$		0			0
$262$	−2.50258	−	8.11316i	−0.154610	−	0.501233i
$263$	23.4562	−	13.5424i	1.44637	−	0.835062i	0.448107	−	0.893980i	$-0.352098\pi$
$263$	23.4562	−	13.5424i	1.44637	−	0.835062i	0.998263	+	0.0589181i	$0.0187651\pi$
$264$		0			0
$265$	27.0394	+	6.17157i	1.66102	+	0.379116i
$266$	−1.58124	−	19.3929i	−0.0969520	−	1.18905i
$267$		0			0
$268$	−8.64952	−	2.66802i	−0.528353	−	0.162975i
$269$	8.80775	−	22.4418i	0.537018	−	1.36830i	−0.362732	−	0.931894i	$-0.618156\pi$
$269$	8.80775	−	22.4418i	0.537018	−	1.36830i	0.899750	−	0.436406i	$-0.143749\pi$
$270$		0			0
$271$	−0.209571	+	0.679413i	−0.0127305	+	0.0412714i	−0.961715	−	0.274051i	$-0.911636\pi$
$271$	−0.209571	+	0.679413i	−0.0127305	+	0.0412714i	0.948985	+	0.315322i	$0.102113\pi$
$272$	−0.798272	−	3.49746i	−0.0484023	−	0.212064i
$273$		0			0
$274$	2.91427	−	12.7682i	0.176057	−	0.771358i
$275$	10.3435	+	5.97185i	0.623739	+	0.360116i
$276$		0			0
$277$	−12.3609	+	3.81284i	−0.742696	+	0.229091i	−0.642936	−	0.765920i	$-0.722284\pi$
$277$	−12.3609	+	3.81284i	−0.742696	+	0.229091i	−0.0997604	+	0.995011i	$0.531808\pi$
$278$	−0.466446	+	6.22429i	−0.0279756	+	0.373308i
$279$		0			0
$280$	9.18787	−	3.67568i	0.549080	−	0.219664i
$281$	−11.5083	−	9.17758i	−0.686529	−	0.547489i	0.216917	−	0.976190i	$-0.430400\pi$
$281$	−11.5083	−	9.17758i	−0.686529	−	0.547489i	−0.903446	+	0.428701i	$0.858971\pi$
$282$		0			0
$283$	3.44972	−	22.8874i	0.205065	−	1.36052i	−0.615128	−	0.788427i	$-0.710896\pi$
$283$	3.44972	−	22.8874i	0.205065	−	1.36052i	0.820192	−	0.572088i	$-0.193866\pi$
$284$	−2.97032	+	4.35665i	−0.176256	+	0.258520i
$285$		0			0
$286$	−3.82650	+	7.94582i	−0.226266	+	0.469846i
$287$	−3.84608	+	17.3752i	−0.227027	+	1.02562i
$288$		0			0
$289$	−3.41283	+	2.32683i	−0.200755	+	0.136872i
$290$	−18.2378	+	16.9222i	−1.07096	+	0.993704i
$291$		0			0
$292$	5.00623	−	1.96480i	0.292967	−	0.114981i
$293$	−9.28442			−0.542401			−0.271201	−	0.962523i	$-0.587421\pi$
$293$	−9.28442			−0.542401			−0.271201	+	0.962523i	$0.587421\pi$
$294$		0			0
$295$	−48.4486			−2.82079
$296$	−2.45611	+	0.963954i	−0.142759	+	0.0560287i
$297$		0			0
$298$	13.4132	−	12.4456i	0.777007	−	0.720957i
$299$	−31.0860	+	21.1941i	−1.79775	+	1.22569i
$300$		0			0
$301$	0.962503	+	1.19084i	0.0554777	+	0.0686387i
$302$	−6.79113	+	14.1019i	−0.390786	+	0.811475i
$303$		0			0
$304$	4.14274	−	6.07628i	0.237602	−	0.348498i
$305$	1.97839	−	13.1257i	0.113282	−	0.751578i
$306$		0			0
$307$	−15.5409	−	12.3935i	−0.886968	−	0.707334i	0.0699936	−	0.997547i	$-0.477702\pi$
$307$	−15.5409	−	12.3935i	−0.886968	−	0.707334i	−0.956962	+	0.290214i	$0.906274\pi$
$308$	2.37397	−	2.59242i	0.135269	−	0.147717i
$309$		0			0
$310$	0.141538	−	1.88870i	0.00803883	−	0.107271i
$311$	9.41517	−	2.90419i	0.533885	−	0.164682i	−0.0160780	−	0.999871i	$-0.505118\pi$
$311$	9.41517	−	2.90419i	0.533885	−	0.164682i	0.549963	+	0.835189i	$0.314642\pi$
$312$		0			0
$313$	1.03887	+	0.599790i	0.0587202	+	0.0339021i	0.529073	−	0.848577i	$-0.322540\pi$
$313$	1.03887	+	0.599790i	0.0587202	+	0.0339021i	−0.470352	+	0.882479i	$0.655873\pi$
$314$	−4.80550	+	21.0543i	−0.271190	+	1.18816i
$315$		0			0
$316$	−0.138161	−	0.605321i	−0.00777214	−	0.0340520i
$317$	6.04233	−	19.5887i	0.339371	−	1.10021i	−0.611661	−	0.791120i	$-0.709498\pi$
$317$	6.04233	−	19.5887i	0.339371	−	1.10021i	0.951032	−	0.309094i	$-0.100026\pi$
$318$		0			0
$319$	−3.22870	+	8.22659i	−0.180773	+	0.460601i
$320$	3.57410	+	1.10247i	0.199799	+	0.0616297i
$321$		0			0
$322$	14.3005	−	4.51402i	0.796935	−	0.251557i
$323$	25.7208	+	5.87060i	1.43114	+	0.326649i
$324$		0			0
$325$	51.6781	−	29.8363i	2.86658	−	1.65502i
$326$	3.57865	+	11.6017i	0.198203	+	0.642558i
$327$		0			0
$328$	−5.25872	+	4.19369i	−0.290365	+	0.231558i
$329$	17.3625	−	12.0050i	0.957223	−	0.661860i
$330$		0			0
$331$	11.8142	+	10.9620i	0.649370	+	0.602527i	0.934501	−	0.355962i	$-0.115847\pi$
$331$	11.8142	+	10.9620i	0.649370	+	0.602527i	−0.285131	+	0.958489i	$0.592037\pi$
$332$	4.86076	+	0.732642i	0.266769	+	0.0402089i
$333$		0			0
$334$	2.51532	+	16.6881i	0.137632	+	0.913130i
$335$	30.5029	+	14.6894i	1.66655	+	0.802569i
$336$		0			0
$337$	9.56292	−	4.60526i	0.520925	−	0.250864i	−0.154895	−	0.987931i	$-0.549504\pi$
$337$	9.56292	−	4.60526i	0.520925	−	0.250864i	0.675820	+	0.737067i	$0.263790\pi$
$338$	17.4979	+	25.6647i	0.951762	+	1.39598i
$339$		0			0
$340$	1.00272	+	13.3803i	0.0543800	+	0.725651i
$341$	−0.245793	−	0.626270i	−0.0133104	−	0.0339144i
$342$		0			0
$343$	11.8298	+	14.2498i	0.638748	+	0.769416i
$344$			0.578731i			0.0312031i
$345$		0			0
$346$	−14.1581	+	1.06100i	−0.761146	+	0.0570400i
$347$	−19.5687	−	21.0900i	−1.05050	−	1.13217i	−0.990989	−	0.133942i	$-0.957236\pi$
$347$	−19.5687	−	21.0900i	−1.05050	−	1.13217i	−0.0595111	−	0.998228i	$-0.518954\pi$
$348$		0			0
$349$	11.3948	+	23.6615i	0.609949	+	1.26657i	0.945828	+	0.324668i	$0.105252\pi$
$349$	11.3948	+	23.6615i	0.609949	+	1.26657i	−0.335879	+	0.941905i	$0.609033\pi$
$350$	−23.1529	+	5.44446i	−1.23757	+	0.291019i
$351$		0			0
$352$	1.31377	−	0.198018i	0.0700240	−	0.0105544i
$353$	10.1099	+	6.89285i	0.538098	+	0.366869i	0.801666	−	0.597772i	$-0.203947\pi$
$353$	10.1099	+	6.89285i	0.538098	+	0.366869i	−0.263568	+	0.964641i	$0.584899\pi$
$354$		0			0
$355$	13.4144	−	14.4572i	0.711961	−	0.767311i
$356$	−3.55698	+	4.46032i	−0.188520	+	0.236396i
$357$		0			0
$358$	5.54593	+	6.95437i	0.293111	+	0.367550i
$359$	−19.5910	−	1.46814i	−1.03397	−	0.0774855i	−0.453083	−	0.891468i	$-0.649676\pi$
$359$	−19.5910	−	1.46814i	−1.03397	−	0.0774855i	−0.580889	+	0.813983i	$0.697295\pi$
$360$		0			0
$361$	17.5417	+	30.3831i	0.923247	+	1.59911i
$362$	−2.35024	+	4.07074i	−0.123526	+	0.213953i
$363$		0			0
$364$	−5.28652	−	16.7478i	−0.277089	−	0.877822i
$365$	−19.6108	+	4.47604i	−1.02648	+	0.234287i
$366$		0			0
$367$	7.84582	+	3.07926i	0.409548	+	0.160736i	0.561166	−	0.827703i	$-0.310353\pi$
$367$	7.84582	+	3.07926i	0.409548	+	0.160736i	−0.151618	+	0.988439i	$0.548448\pi$
$368$	5.27615	+	2.07074i	0.275039	+	0.107945i
$369$		0			0
$370$	9.62130	−	2.19600i	0.500187	−	0.114165i
$371$	−10.9451	+	16.2818i	−0.568240	+	0.845311i
$372$		0			0
$373$	8.62849	−	14.9450i	0.446766	−	0.773822i	−0.551407	−	0.834236i	$-0.685909\pi$
$373$	8.62849	−	14.9450i	0.446766	−	0.773822i	0.998173	+	0.0604144i	$0.0192422\pi$
$374$	2.38312	+	4.12768i	0.123228	+	0.213437i
$375$		0			0
$376$	7.95602	+	0.596221i	0.410300	+	0.0307478i
$377$	27.5293	+	34.5207i	1.41783	+	1.77791i
$378$		0			0
$379$	−13.4120	+	16.8181i	−0.688928	+	0.863888i	−0.996142	−	0.0877521i	$-0.972032\pi$
$379$	−13.4120	+	16.8181i	−0.688928	+	0.863888i	0.307214	+	0.951640i	$0.400603\pi$
$380$	−18.7092	+	20.1637i	−0.959760	+	1.03438i
$381$		0			0
$382$	−5.64865	−	3.85118i	−0.289010	−	0.197044i
$383$	−2.61513	+	0.394167i	−0.133627	+	0.0201410i	−0.215515	−	0.976501i	$-0.569143\pi$
$383$	−2.61513	+	0.394167i	−0.133627	+	0.0201410i	0.0818882	+	0.996642i	$0.473905\pi$
$384$		0			0
$385$	−10.2253	+	8.26466i	−0.521128	+	0.421206i
$386$	−9.06973	−	18.8335i	−0.461637	−	0.958599i
$387$		0			0
$388$	−11.4852	−	12.3781i	−0.583071	−	0.628401i
$389$	3.99786	−	0.299598i	0.202700	−	0.0151902i	0.0270067	−	0.999635i	$-0.491402\pi$
$389$	3.99786	−	0.299598i	0.202700	−	0.0151902i	0.175693	+	0.984445i	$0.443783\pi$
$390$		0			0
$391$			20.3332i			1.02830i
$392$	0.0918002	+	6.99940i	0.00463661	+	0.353523i
$393$		0			0
$394$	3.46618	+	8.83168i	0.174624	+	0.444934i
$395$	0.173545	+	2.31580i	0.00873199	+	0.116520i
$396$		0			0
$397$	−2.60404	−	3.81943i	−0.130693	−	0.191692i	0.755314	−	0.655363i	$-0.227484\pi$
$397$	−2.60404	−	3.81943i	−0.130693	−	0.191692i	−0.886007	+	0.463671i	$0.846532\pi$
$398$	15.9842	−	7.69756i	0.801213	−	0.385844i
$399$		0			0
$400$	−8.09940	−	3.90046i	−0.404970	−	0.195023i
$401$	0.0188342	+	0.124956i	0.000940533	+	0.00624003i	0.989296	−	0.145922i	$-0.0466147\pi$
$401$	0.0188342	+	0.124956i	0.000940533	+	0.00624003i	−0.988356	+	0.152162i	$0.951377\pi$
$402$		0			0
$403$	−3.32376	−	0.500976i	−0.165568	−	0.0249554i
$404$	−10.8084	−	10.0287i	−0.537737	−	0.498947i
$405$		0			0
$406$	−6.53684	−	16.3397i	−0.324418	−	0.810927i
$407$	2.74073	−	2.18566i	0.135853	−	0.108339i
$408$		0			0
$409$	2.93224	+	9.50610i	0.144990	+	0.470046i	0.998715	−	0.0506778i	$-0.0161382\pi$
$409$	2.93224	+	9.50610i	0.144990	+	0.470046i	−0.853725	+	0.520724i	$0.825662\pi$
$410$	21.7872	−	12.5788i	1.07599	−	0.621225i
$411$		0			0
$412$	14.8499	+	3.38939i	0.731601	+	0.166983i
$413$	12.3111	−	31.9834i	0.605791	−	1.57380i
$414$		0			0
$415$	−17.5691	−	5.41935i	−0.862433	−	0.266025i
$416$	2.42511	−	6.17908i	0.118901	−	0.302954i
$417$		0			0
$418$	−2.87998	+	9.33666i	−0.140864	+	0.456671i
$419$	−4.19165	−	18.3648i	−0.204775	−	0.897179i	−0.967981	−	0.251024i	$-0.919233\pi$
$419$	−4.19165	−	18.3648i	−0.204775	−	0.897179i	0.763206	−	0.646156i	$-0.223624\pi$
$420$		0			0
$421$	−1.34951	+	5.91260i	−0.0657712	+	0.288162i	−0.997108	−	0.0759963i	$-0.975786\pi$
$421$	−1.34951	+	5.91260i	−0.0657712	+	0.288162i	0.931337	+	0.364159i	$0.118643\pi$
$422$	−7.16865	−	4.13882i	−0.348964	−	0.201475i
$423$		0			0
$424$	−7.08573	+	2.18566i	−0.344114	+	0.106145i
$425$	2.41001	−	32.1593i	0.116902	−	1.55996i
$426$		0			0
$427$	8.16225	+	4.64138i	0.394999	+	0.224612i
$428$	−3.24340	−	2.58652i	−0.156776	−	0.125024i
$429$		0			0
$430$	0.322619	−	2.14043i	0.0155581	−	0.103221i
$431$	−12.2849	+	18.0186i	−0.591743	+	0.867928i	−0.998969	−	0.0453999i	$-0.985544\pi$
$431$	−12.2849	+	18.0186i	−0.591743	+	0.867928i	0.407226	+	0.913327i	$0.366496\pi$
$432$		0			0
$433$	17.4808	−	36.2993i	0.840075	−	1.74443i	0.194242	−	0.980954i	$-0.437775\pi$
$433$	17.4808	−	36.2993i	0.840075	−	1.74443i	0.645832	−	0.763479i	$-0.276511\pi$
$434$	1.21086	+	0.573368i	0.0581231	+	0.0275225i
$435$		0			0
$436$	2.03758	−	1.38920i	0.0975824	−	0.0665305i
$437$	−30.5558	+	28.3516i	−1.46168	+	1.35624i
$438$		0			0
$439$	−23.2885	+	9.14008i	−1.11150	+	0.436232i	−0.848837	−	0.528655i	$-0.822696\pi$
$439$	−23.2885	+	9.14008i	−1.11150	+	0.436232i	−0.262664	+	0.964887i	$0.584601\pi$
$440$	−4.96935			−0.236904
$441$		0			0
$442$	23.8129			1.13267
$443$	29.9855	−	11.7684i	1.42465	−	0.559135i	0.477132	−	0.878831i	$-0.341676\pi$
$443$	29.9855	−	11.7684i	1.42465	−	0.559135i	0.947520	+	0.319697i	$0.103581\pi$
$444$		0			0
$445$	15.6419	−	14.5136i	0.741499	−	0.688011i
$446$	−19.7921	+	13.4940i	−0.937184	+	0.638961i
$447$		0			0
$448$	−1.63600	+	2.07930i	−0.0772937	+	0.0982379i
$449$	5.30712	−	11.0203i	0.250458	−	0.520082i	−0.737397	−	0.675460i	$-0.763945\pi$
$449$	5.30712	−	11.0203i	0.250458	−	0.520082i	0.987855	+	0.155378i	$0.0496594\pi$
$450$		0			0
$451$	5.03406	−	7.38361i	0.237045	−	0.347681i
$452$	0.532913	−	3.53565i	0.0250661	−	0.166303i
$453$		0			0
$454$	−1.74188	−	1.38911i	−0.0817507	−	0.0651940i
$455$	10.2160	+	64.8886i	0.478933	+	3.04202i
$456$		0			0
$457$	2.37584	−	31.7034i	0.111137	−	1.48302i	−0.611196	−	0.791479i	$-0.709311\pi$
$457$	2.37584	−	31.7034i	0.111137	−	1.48302i	0.722333	−	0.691545i	$-0.243070\pi$
$458$	12.5303	−	3.86509i	0.585504	−	0.180604i
$459$		0			0
$460$	−18.3595	−	10.5999i	−0.856016	−	0.494221i
$461$	−0.633408	+	2.77514i	−0.0295008	+	0.129251i	−0.987534	−	0.157406i	$-0.949687\pi$
$461$	−0.633408	+	2.77514i	−0.0295008	+	0.129251i	0.958033	+	0.286657i	$0.0925441\pi$
$462$		0			0
$463$	0.253492	+	1.11062i	0.0117808	+	0.0516149i	0.980477	−	0.196636i	$-0.0630016\pi$
$463$	0.253492	+	1.11062i	0.0117808	+	0.0516149i	−0.968696	+	0.248250i	$0.920144\pi$
$464$	1.96063	−	6.35619i	0.0910198	−	0.295079i
$465$		0			0
$466$	−2.43570	+	6.20605i	−0.112831	+	0.287490i
$467$	−11.3387	−	3.49754i	−0.524694	−	0.161847i	0.0210819	−	0.999778i	$-0.493289\pi$
$467$	−11.3387	−	3.49754i	−0.524694	−	0.161847i	−0.545776	+	0.837931i	$0.683765\pi$
$468$		0			0
$469$	−17.4483	+	16.4038i	−0.805685	+	0.757459i
$470$	−29.0930	−	6.64028i	−1.34196	−	0.306293i
$471$		0			0
$472$	11.2178	−	6.47661i	0.516342	−	0.298110i
$473$	−0.226639	−	0.734744i	−0.0104209	−	0.0337836i
$474$		0			0
$475$	51.6878	−	41.2196i	2.37160	−	1.89129i
$476$	−9.08784	−	2.73810i	−0.416541	−	0.125500i
$477$		0			0
$478$	−5.94035	−	5.51184i	−0.271705	−	0.252106i
$479$	−3.16546	−	0.477117i	−0.144634	−	0.0218000i	0.0763263	−	0.997083i	$-0.475681\pi$
$479$	−3.16546	−	0.477117i	−0.144634	−	0.0218000i	−0.220960	+	0.975283i	$0.570919\pi$
$480$		0			0
$481$	−2.61036	−	17.3186i	−0.119022	−	0.789660i
$482$	−18.6875	−	8.99943i	−0.851192	−	0.409913i
$483$		0			0
$484$	8.32027	−	4.00683i	0.378194	−	0.182129i
$485$	35.5776	+	52.1827i	1.61549	+	2.36950i
$486$		0			0
$487$	−2.32075	−	30.9683i	−0.105163	−	1.40331i	−0.761170	−	0.648553i	$-0.775375\pi$
$487$	−2.32075	−	30.9683i	−0.105163	−	1.40331i	0.656006	−	0.754756i	$-0.272245\pi$
$488$	1.29657	+	3.30361i	0.0586931	+	0.149548i
$489$		0			0
$490$	3.56235	−	25.9384i	0.160931	−	1.17178i
$491$		−	25.2042i		−	1.13745i	−0.822528	−	0.568725i	$-0.807437\pi$
$491$		−	25.2042i		−	1.13745i	0.822528	−	0.568725i	$-0.192563\pi$
$492$		0			0
$493$	23.7956	−	1.78324i	1.07170	−	0.0803129i
$494$	33.2035	+	35.7849i	1.49390	+	1.61004i
$495$		0			0
$496$	0.219709	+	0.456231i	0.00986523	+	0.0204854i
$497$	6.13528	+	12.5292i	0.275205	+	0.562011i
$498$		0			0
$499$	35.6741	−	5.37700i	1.59699	−	0.240708i	0.710583	−	0.703613i	$-0.248431\pi$
$499$	35.6741	−	5.37700i	1.59699	−	0.240708i	0.886408	+	0.462906i	$0.153193\pi$
$500$	12.3295	+	8.40608i	0.551390	+	0.375931i
$501$		0			0
$502$	−10.2006	+	10.9936i	−0.455273	+	0.490668i
$503$	6.61094	−	8.28985i	0.294767	−	0.369626i	−0.612290	−	0.790633i	$-0.709752\pi$
$503$	6.61094	−	8.28985i	0.294767	−	0.369626i	0.907058	+	0.421007i	$0.138323\pi$
$504$		0			0
$505$	34.3842	+	43.1164i	1.53008	+	1.91865i
$506$	−7.50942	−	0.562754i	−0.333835	−	0.0250174i
$507$		0			0
$508$	−3.32368	−	5.75678i	−0.147464	−	0.255416i
$509$	−4.75038	+	8.22790i	−0.210557	+	0.364695i	−0.951889	−	0.306443i	$-0.900861\pi$
$509$	−4.75038	+	8.22790i	−0.210557	+	0.364695i	0.741332	+	0.671138i	$0.234194\pi$
$510$		0			0
$511$	2.02839	−	14.0835i	0.0897306	−	0.623017i
$512$	−0.974928	+	0.222521i	−0.0430861	+	0.00983413i
$513$		0			0
$514$	−12.1953	−	4.78631i	−0.537913	−	0.211115i
$515$	−53.0328	−	20.8138i	−2.33691	−	0.917168i
$516$		0			0
$517$	−10.3343	+	2.35873i	−0.454501	+	0.103737i
$518$	−0.995152	+	6.90953i	−0.0437244	+	0.303587i
$519$		0			0
$520$	−12.4138	+	21.5014i	−0.544383	+	0.942899i
$521$	10.2133	+	17.6900i	0.447454	+	0.775013i	0.998220	−	0.0596472i	$-0.0189976\pi$
$521$	10.2133	+	17.6900i	0.447454	+	0.775013i	−0.550766	+	0.834660i	$0.685664\pi$
$522$		0			0
$523$	−7.69803	−	0.576887i	−0.336611	−	0.0252255i	−0.0946476	−	0.995511i	$-0.530172\pi$
$523$	−7.69803	−	0.576887i	−0.336611	−	0.0252255i	−0.241964	+	0.970285i	$0.577791\pi$
$524$	−5.29366	−	6.63804i	−0.231255	−	0.289984i
$525$		0			0
$526$	16.8871	−	21.1758i	0.736314	−	0.923308i
$527$	−1.23559	+	1.33165i	−0.0538231	+	0.0580075i
$528$		0			0
$529$	−7.54006	−	5.14073i	−0.327829	−	0.223510i
$530$	27.4250	−	4.13365i	1.19127	−	0.179554i
$531$		0			0
$532$	−8.55695	−	17.4746i	−0.370991	−	0.757621i
$533$	−19.3720	−	40.2263i	−0.839093	−	1.74239i
$534$		0			0
$535$	10.5538	+	11.3743i	0.456281	+	0.491754i
$536$	−9.02634	+	0.676431i	−0.389879	+	0.0292174i
$537$		0			0
$538$		−	24.1083i		−	1.03938i
$539$	−2.85760	−	8.85034i	−0.123086	−	0.381211i
$540$		0			0
$541$	7.28404	+	18.5594i	0.313165	+	0.797932i	0.997625	+	0.0688812i	$0.0219429\pi$
$541$	7.28404	+	18.5594i	0.313165	+	0.797932i	−0.684460	+	0.729051i	$0.739962\pi$
$542$	0.0531332	+	0.709013i	0.00228227	+	0.0304547i
$543$		0			0
$544$	−2.02085	−	2.96405i	−0.0866434	−	0.127083i
$545$	−8.31041	+	4.00208i	−0.355979	+	0.171430i
$546$		0			0
$547$	25.0455	+	12.0613i	1.07087	+	0.515703i	0.884386	−	0.466756i	$-0.154577\pi$
$547$	25.0455	+	12.0613i	1.07087	+	0.515703i	0.186482	+	0.982458i	$0.440292\pi$
$548$	−1.95195	−	12.9503i	−0.0833830	−	0.553210i
$549$		0			0
$550$	11.8103	+	1.78012i	0.503593	+	0.0759044i
$551$	35.8592	+	33.2724i	1.52765	+	1.41745i
$552$		0			0
$553$	−1.57287	−	0.473895i	−0.0668854	−	0.0201521i
$554$	−10.1135	+	8.06523i	−0.429680	+	0.342659i
$555$		0			0
$556$	1.83979	+	5.96444i	0.0780243	+	0.252949i
$557$	−13.8945	+	8.02197i	−0.588727	+	0.339902i	−0.764594	−	0.644512i	$-0.777061\pi$
$557$	−13.8945	+	8.02197i	−0.588727	+	0.339902i	0.175867	+	0.984414i	$0.443727\pi$
$558$		0			0
$559$	−3.74526	−	0.854831i	−0.158408	−	0.0361555i
$560$	7.20987	−	6.77830i	0.304673	−	0.286435i
$561$		0			0
$562$	−14.0657	−	4.33871i	−0.593327	−	0.183017i
$563$	10.1007	−	25.7361i	0.425693	−	1.08465i	−0.543732	−	0.839259i	$-0.682989\pi$
$563$	10.1007	−	25.7361i	0.425693	−	1.08465i	0.969425	−	0.245389i	$-0.0789157\pi$
$564$		0			0
$565$	−3.94196	+	12.7795i	−0.165839	+	0.537638i
$566$	−5.15045	−	22.5656i	−0.216490	−	0.948503i
$567$		0			0
$568$	−1.17332	+	5.14067i	−0.0492316	+	0.215698i
$569$	−28.3717	−	16.3804i	−1.18941	−	0.686703i	−0.231234	−	0.972898i	$-0.574276\pi$
$569$	−28.3717	−	16.3804i	−1.18941	−	0.686703i	−0.958171	+	0.286195i	$0.907610\pi$
$570$		0			0
$571$	−3.97586	+	1.22639i	−0.166385	+	0.0513229i	−0.376828	−	0.926283i	$-0.622985\pi$
$571$	−3.97586	+	1.22639i	−0.166385	+	0.0513229i	0.210444	+	0.977606i	$0.432509\pi$
$572$	−0.659059	+	8.79453i	−0.0275566	+	0.367718i
$573$		0			0
$574$	2.76765	+	17.5792i	0.115520	+	0.733742i
$575$	39.8366	+	31.7687i	1.66130	+	1.32484i
$576$		0			0
$577$	−4.63913	+	30.7786i	−0.193129	+	1.28133i	0.656652	+	0.754194i	$0.271972\pi$
$577$	−4.63913	+	30.7786i	−0.193129	+	1.28133i	−0.849781	+	0.527136i	$0.823266\pi$
$578$	−2.32683	+	3.41283i	−0.0967832	+	0.141955i
$579$		0			0
$580$	−10.7947	+	22.4154i	−0.448225	+	0.930749i
$581$	8.04202	−	10.2212i	0.333639	−	0.424045i
$582$		0			0
$583$	8.13996	−	5.54973i	0.337123	−	0.229846i
$584$	3.94234	−	3.65796i	0.163135	−	0.151367i
$585$		0			0
$586$	−8.64262	+	3.39198i	−0.357023	+	0.140121i
$587$	13.5513			0.559322			0.279661	−	0.960099i	$-0.409778\pi$
$587$	13.5513			0.559322			0.279661	+	0.960099i	$0.409778\pi$
$588$		0			0
$589$	−3.72397			−0.153444
$590$	−45.0995	+	17.7003i	−1.85672	+	0.728708i
$591$		0			0
$592$	−1.93416	+	1.79464i	−0.0794935	+	0.0737592i
$593$	0.752150	−	0.512807i	0.0308871	−	0.0210585i	−0.547778	−	0.836624i	$-0.684526\pi$
$593$	0.752150	−	0.512807i	0.0308871	−	0.0210585i	0.578665	+	0.815565i	$0.303574\pi$
$594$		0			0
$595$	32.0850	+	15.1929i	1.31536	+	0.622850i
$596$	7.93911	−	16.4857i	0.325199	−	0.675282i
$597$		0			0
$598$	−21.1941	+	31.0860i	−0.866691	+	1.27120i
$599$	6.45742	−	42.8422i	0.263843	−	1.75048i	−0.328229	−	0.944598i	$-0.606452\pi$
$599$	6.45742	−	42.8422i	0.263843	−	1.75048i	0.592072	−	0.805885i	$-0.298310\pi$
$600$		0			0
$601$	−7.37638	−	5.88246i	−0.300889	−	0.239951i	0.461393	−	0.887196i	$-0.347350\pi$
$601$	−7.37638	−	5.88246i	−0.300889	−	0.239951i	−0.762282	+	0.647245i	$0.775921\pi$
$602$	1.33103	+	0.756877i	0.0542487	+	0.0308480i
$603$		0			0
$604$	−1.16967	+	15.6082i	−0.0475933	+	0.635089i
$605$	−33.0062	+	10.1811i	−1.34189	+	0.413919i
$606$		0			0
$607$	−12.5949	−	7.27168i	−0.511212	−	0.295148i	0.222120	−	0.975019i	$-0.428702\pi$
$607$	−12.5949	−	7.27168i	−0.511212	−	0.295148i	−0.733332	+	0.679871i	$0.762036\pi$
$608$	1.63645	−	7.16976i	0.0663668	−	0.290772i
$609$		0			0
$610$	−2.95374	−	12.9412i	−0.119594	−	0.523974i
$611$	−15.6101	+	50.6068i	−0.631518	+	2.04733i
$612$		0			0
$613$	1.07936	−	2.75015i	0.0435948	−	0.111078i	−0.907418	−	0.420229i	$-0.861950\pi$
$613$	1.07936	−	2.75015i	0.0435948	−	0.111078i	0.951013	+	0.309151i	$0.100045\pi$
$614$	−18.9945	−	5.85903i	−0.766556	−	0.236451i
$615$		0			0
$616$	1.26275	−	3.28052i	0.0508775	−	0.132176i
$617$	9.05445	+	2.06662i	0.364519	+	0.0831990i	0.400857	−	0.916141i	$-0.368712\pi$
$617$	9.05445	+	2.06662i	0.364519	+	0.0831990i	−0.0363386	+	0.999340i	$0.511569\pi$
$618$		0			0
$619$	20.3634	−	11.7568i	0.818476	−	0.472547i	−0.0314146	−	0.999506i	$-0.510001\pi$
$619$	20.3634	−	11.7568i	0.818476	−	0.472547i	0.849891	+	0.526959i	$0.176668\pi$
$620$	−0.558264	−	1.80985i	−0.0224204	−	0.0726852i
$621$		0			0
$622$	7.70331	−	6.14318i	0.308875	−	0.246319i
$623$	5.60644	+	14.0141i	0.224617	+	0.561461i
$624$		0			0
$625$	−7.96502	−	7.39046i	−0.318601	−	0.295618i
$626$	1.18618	+	0.178788i	0.0474094	+	0.00714581i
$627$		0			0
$628$	3.21868	+	21.3545i	0.128439	+	0.852139i
$629$	−8.52800	−	4.10687i	−0.340034	−	0.163752i
$630$		0			0
$631$	−28.9687	+	13.9506i	−1.15323	+	0.555365i	−0.910001	−	0.414605i	$-0.863920\pi$
$631$	−28.9687	+	13.9506i	−1.15323	+	0.555365i	−0.243225	+	0.969970i	$0.578205\pi$
$632$	−0.349758	−	0.513001i	−0.0139126	−	0.0204061i
$633$		0			0
$634$	−1.53193	−	20.4422i	−0.0608406	−	0.811862i
$635$	9.08346	+	23.1443i	0.360466	+	0.918452i
$636$		0			0
$637$	−45.4322	−	9.74458i	−1.80009	−	0.386094i
$638$			8.83750i			0.349880i
$639$		0			0
$640$	3.72982	−	0.279511i	0.147434	−	0.0110486i
$641$	−16.4880	−	17.7698i	−0.651236	−	0.701866i	0.317974	−	0.948099i	$-0.396997\pi$
$641$	−16.4880	−	17.7698i	−0.651236	−	0.701866i	−0.969211	+	0.246233i	$0.920807\pi$
$642$		0			0
$643$	14.1789	+	29.4429i	0.559163	+	1.16111i	0.968565	+	0.248760i	$0.0800230\pi$
$643$	14.1789	+	29.4429i	0.559163	+	1.16111i	−0.409402	+	0.912354i	$0.634263\pi$
$644$	11.6628	−	9.42654i	0.459578	−	0.371458i
$645$		0			0
$646$	26.0876	−	3.93207i	1.02640	−	0.154705i
$647$	−0.981216	−	0.668982i	−0.0385756	−	0.0263004i	0.543879	−	0.839164i	$-0.316955\pi$
$647$	−0.981216	−	0.668982i	−0.0385756	−	0.0263004i	−0.582454	+	0.812863i	$0.697908\pi$
$648$		0			0
$649$	−11.7056	+	12.6156i	−0.459484	+	0.495206i
$650$	37.2053	−	46.6540i	1.45931	−	1.82992i
$651$		0			0
$652$	7.56984	+	9.49228i	0.296458	+	0.371746i
$653$	28.8985	+	2.16564i	1.13089	+	0.0847481i	0.626998	−	0.779021i	$-0.284284\pi$
$653$	28.8985	+	2.16564i	1.13089	+	0.0847481i	0.503888	+	0.863769i	$0.331903\pi$
$654$		0			0
$655$	15.8782	+	27.5018i	0.620411	+	1.07458i
$656$	−3.36308	+	5.82503i	−0.131306	+	0.227429i
$657$		0			0
$658$	11.7763	−	17.5184i	0.459089	−	0.682939i
$659$	31.9926	−	7.30209i	1.24625	−	0.284449i	0.451990	−	0.892023i	$-0.350714\pi$
$659$	31.9926	−	7.30209i	1.24625	−	0.284449i	0.794263	+	0.607574i	$0.207857\pi$
$660$		0			0
$661$	−31.3265	−	12.2947i	−1.21846	−	0.478210i	−0.333000	−	0.942927i	$-0.608061\pi$
$661$	−31.3265	−	12.2947i	−1.21846	−	0.478210i	−0.885460	+	0.464716i	$0.846156\pi$
$662$	15.0024	+	5.88802i	0.583086	+	0.228845i
$663$		0			0
$664$	4.79242	−	1.09384i	0.185982	−	0.0424491i
$665$	21.9065	+	69.4000i	0.849496	+	2.69122i
$666$		0			0
$667$	−18.8508	+	32.6506i	−0.729906	+	1.26424i
$668$	8.43828	+	14.6155i	0.326487	+	0.565492i
$669$		0			0
$670$	33.7610	+	2.53004i	1.30430	+	0.0977439i
$671$	−2.93984	−	3.68644i	−0.113491	−	0.142314i
$672$		0			0
$673$	21.9469	−	27.5205i	0.845989	−	1.06084i	−0.151389	−	0.988474i	$-0.548375\pi$
$673$	21.9469	−	27.5205i	0.845989	−	1.06084i	0.997378	−	0.0723624i	$-0.0230538\pi$
$674$	7.21938	−	7.78064i	0.278080	−	0.299699i
$675$		0			0
$676$	25.6647	+	17.4979i	0.987106	+	0.672997i
$677$	−10.9637	+	1.65252i	−0.421370	+	0.0635113i	−0.356305	−	0.934370i	$-0.615964\pi$
$677$	−10.9637	+	1.65252i	−0.421370	+	0.0635113i	−0.0650652	+	0.997881i	$0.520726\pi$
$678$		0			0
$679$	−43.4890	+	10.2266i	−1.66895	+	0.392459i
$680$	5.82179	+	12.0891i	0.223256	+	0.463595i
$681$		0			0
$682$	−0.457604	−	0.493180i	−0.0175226	−	0.0188848i
$683$	6.49205	−	0.486512i	0.248411	−	0.0186159i	0.0500575	−	0.998746i	$-0.484060\pi$
$683$	6.49205	−	0.486512i	0.248411	−	0.0186159i	0.198354	+	0.980130i	$0.436441\pi$
$684$		0			0
$685$			48.9849i			1.87162i
$686$	16.2181	+	8.94284i	0.619209	+	0.341439i
$687$		0			0
$688$	0.211434	+	0.538725i	0.00806085	+	0.0205387i
$689$	−3.67832	−	49.0837i	−0.140133	−	1.86994i
$690$		0			0
$691$	−26.5003	−	38.8688i	−1.00812	−	1.47864i	−0.872945	−	0.487819i	$-0.837793\pi$
$691$	−26.5003	−	38.8688i	−1.00812	−	1.47864i	−0.135175	−	0.990822i	$-0.543160\pi$
$692$	−12.7918	+	6.16021i	−0.486271	+	0.234176i
$693$		0			0
$694$	−25.9210	−	12.4829i	−0.983947	−	0.473844i
$695$	−3.47952	−	23.0851i	−0.131986	−	0.875667i
$696$		0			0
$697$	−23.8599	−	3.59631i	−0.903759	−	0.136220i
$698$	19.2516	+	17.8629i	0.728686	+	0.676121i
$699$		0			0
$700$	−19.5633	+	13.5268i	−0.739423	+	0.511265i
$701$	16.7997	−	13.3973i	0.634515	−	0.506009i	−0.252592	−	0.967573i	$-0.581283\pi$
$701$	16.7997	−	13.3973i	0.634515	−	0.506009i	0.887107	+	0.461564i	$0.152712\pi$
$702$		0			0
$703$	−5.71941	−	18.5419i	−0.215712	−	0.699320i
$704$	1.15061	−	0.664303i	0.0433651	−	0.0250368i
$705$		0			0
$706$	11.9293	+	2.72279i	0.448966	+	0.102474i
$707$	−37.2006	+	11.7426i	−1.39907	+	0.441624i
$708$		0			0
$709$	−21.3249	−	6.57785i	−0.800872	−	0.247036i	−0.132810	−	0.991142i	$-0.542400\pi$
$709$	−21.3249	−	6.57785i	−0.800872	−	0.247036i	−0.668063	+	0.744105i	$0.732876\pi$
$710$	7.20525	−	18.3587i	0.270408	−	0.688989i
$711$		0			0
$712$	−1.68157	+	5.45150i	−0.0630194	+	0.204304i
$713$	−0.638664	−	2.79817i	−0.0239181	−	0.104792i
$714$		0			0
$715$	7.34012	−	32.1592i	0.274505	−	1.20268i
$716$	7.70328	+	4.44749i	0.287885	+	0.166210i
$717$		0			0
$718$	−18.7731	+	5.79073i	−0.700606	+	0.216108i
$719$	−3.82393	+	51.0268i	−0.142608	+	1.90298i	0.227165	+	0.973856i	$0.427054\pi$
$719$	−3.82393	+	51.0268i	−0.142608	+	1.90298i	−0.369774	+	0.929122i	$0.620565\pi$
$720$		0			0
$721$	27.2163	−	29.7207i	1.01359	−	1.10686i
$722$	27.4293	+	21.8741i	1.02081	+	0.814071i
$723$		0			0
$724$	−0.700571	+	4.64798i	−0.0260365	+	0.172741i
$725$	33.6846	−	49.4062i	1.25101	−	1.83490i
$726$		0			0
$727$	9.03038	−	18.7518i	0.334918	−	0.695465i	−0.663701	−	0.747998i	$-0.731015\pi$
$727$	9.03038	−	18.7518i	0.334918	−	0.695465i	0.998619	+	0.0525333i	$0.0167296\pi$
$728$	−11.0397	−	13.6587i	−0.409160	−	0.506224i
$729$		0			0
$730$	−16.6199	+	11.3313i	−0.615131	+	0.419389i
$731$	−1.52192	+	1.41213i	−0.0562902	+	0.0522296i
$732$		0			0
$733$	22.4476	−	8.81002i	0.829120	−	0.325406i	0.0874487	−	0.996169i	$-0.472129\pi$
$733$	22.4476	−	8.81002i	0.829120	−	0.325406i	0.741671	+	0.670763i	$0.234033\pi$
$734$	8.42844			0.311100
$735$		0			0
$736$	5.66796			0.208924
$737$	11.1948	−	4.39362i	0.412364	−	0.161841i
$738$		0			0
$739$	−26.3373	+	24.4374i	−0.968832	+	0.898945i	−0.994915	−	0.100715i	$-0.967887\pi$
$739$	−26.3373	+	24.4374i	−0.968832	+	0.898945i	0.0260835	+	0.999660i	$0.491696\pi$
$740$	8.15393	−	5.55925i	0.299744	−	0.204362i
$741$		0			0
$742$	−4.24006	+	19.1550i	−0.155657	+	0.703203i
$743$	−5.84926	+	12.1461i	−0.214588	+	0.445597i	−0.980281	−	0.197609i	$-0.936682\pi$
$743$	−5.84926	+	12.1461i	−0.214588	+	0.445597i	0.765692	+	0.643207i	$0.222396\pi$
$744$		0			0
$745$	−38.5529	+	56.5467i	−1.41247	+	2.07171i
$746$	2.57202	−	17.0642i	0.0941683	−	0.624766i
$747$		0			0
$748$	3.72640	+	2.97170i	0.136251	+	0.108656i
$749$	−10.1906	+	4.07682i	−0.372355	+	0.148964i
$750$		0			0
$751$	−1.47508	+	19.6836i	−0.0538264	+	0.718264i	0.903377	+	0.428848i	$0.141080\pi$
$751$	−1.47508	+	19.6836i	−0.0538264	+	0.718264i	−0.957203	+	0.289416i	$0.906539\pi$
$752$	7.62388	−	2.35165i	0.278014	−	0.0857560i
$753$		0			0
$754$	38.2381	+	22.0768i	1.39255	+	0.803990i
$755$	13.0270	−	57.0749i	0.474100	−	2.07717i
$756$		0			0
$757$	−7.45750	−	32.6734i	−0.271047	−	1.18754i	−0.908779	−	0.417277i	$-0.862984\pi$
$757$	−7.45750	−	32.6734i	−0.271047	−	1.18754i	0.637732	−	0.770258i	$-0.279873\pi$
$758$	−6.34053	+	20.5555i	−0.230298	+	0.746609i
$759$		0			0
$760$	−10.0493	+	25.6051i	−0.364525	+	0.928794i
$761$	10.0095	+	3.08751i	0.362843	+	0.111922i	0.470816	−	0.882232i	$-0.343960\pi$
$761$	10.0095	+	3.08751i	0.362843	+	0.111922i	−0.107973	+	0.994154i	$0.534436\pi$
$762$		0			0
$763$	−0.530243	−	6.50308i	−0.0191961	−	0.235427i
$764$	−6.66517	−	1.52128i	−0.241137	−	0.0550381i
$765$		0			0
$766$	−2.29035	+	1.32233i	−0.0827537	+	0.0477779i
$767$	25.3438	+	82.1626i	0.915112	+	2.96672i
$768$		0			0
$769$	13.1951	−	10.5228i	0.475829	−	0.379461i	−0.356006	−	0.934484i	$-0.615862\pi$
$769$	13.1951	−	10.5228i	0.475829	−	0.379461i	0.831835	+	0.555023i	$0.187290\pi$
$770$	−6.49902	+	11.4291i	−0.234209	+	0.411875i
$771$		0			0
$772$	−15.3234	−	14.2181i	−0.551502	−	0.511719i
$773$	−9.77021	−	1.47262i	−0.351410	−	0.0529665i	−0.0290345	−	0.999578i	$-0.509243\pi$
$773$	−9.77021	−	1.47262i	−0.351410	−	0.0529665i	−0.322376	+	0.946612i	$0.604481\pi$
$774$		0			0
$775$	0.678464	+	4.50132i	0.0243712	+	0.161692i
$776$	−15.2134	−	7.32641i	−0.546131	−	0.263003i
$777$		0			0
$778$	3.61205	−	1.73947i	0.129498	−	0.0623631i
$779$	−27.8647	−	40.8700i	−0.998357	−	1.46432i
$780$		0			0
$781$	−0.523527	−	6.98598i	−0.0187333	−	0.249978i
$782$	7.42857	+	18.9277i	0.265645	+	0.676852i
$783$		0			0
$784$	2.64262	+	6.48202i	0.0943793	+	0.231501i
$785$		−	80.7740i		−	2.88295i
$786$		0			0
$787$	−7.10004	+	0.532074i	−0.253089	+	0.0189664i	−0.200670	−	0.979659i	$-0.564312\pi$
$787$	−7.10004	+	0.532074i	−0.253089	+	0.0189664i	−0.0524186	+	0.998625i	$0.516693\pi$
$788$	6.45315	+	6.95484i	0.229884	+	0.247756i
$789$		0			0
$790$	1.00760	+	2.09231i	0.0358489	+	0.0744411i
$791$	−7.43473	−	5.84966i	−0.264349	−	0.207990i
$792$		0			0
$793$	−23.2945	+	3.51108i	−0.827212	+	0.124682i
$794$	−3.81943	−	2.60404i	−0.135547	−	0.0924141i
$795$		0			0
$796$	12.0670	−	13.0051i	0.427703	−	0.460955i
$797$	−16.7160	+	20.9612i	−0.592112	+	0.742485i	−0.984125	−	0.177475i	$-0.943207\pi$
$797$	−16.7160	+	20.9612i	−0.592112	+	0.742485i	0.392014	+	0.919959i	$0.371779\pi$
$798$		0			0
$799$	17.8452	+	22.3772i	0.631317	+	0.791647i
$800$	−8.96451	−	0.671797i	−0.316943	−	0.0237516i
$801$		0			0
$802$	0.0631840	+	0.109438i	0.00223110	+	0.00386438i
$803$	−3.57261	+	6.18794i	−0.126075	+	0.218368i
$804$		0			0
$805$	−48.3897	+	28.3625i	−1.70551	+	0.999647i
$806$	−3.27703	+	0.747960i	−0.115428	+	0.0263458i
$807$		0			0
$808$	−13.7251	−	5.38672i	−0.482848	−	0.189504i
$809$	−43.1255	−	16.9255i	−1.51621	−	0.595069i	−0.546097	−	0.837722i	$-0.683887\pi$
$809$	−43.1255	−	16.9255i	−1.51621	−	0.595069i	−0.970113	+	0.242653i	$0.921982\pi$
$810$		0			0
$811$	−2.76664	+	0.631468i	−0.0971500	+	0.0221738i	−0.270820	−	0.962630i	$-0.587295\pi$
$811$	−2.76664	+	0.631468i	−0.0971500	+	0.0221738i	0.173670	+	0.984804i	$0.444438\pi$
$812$	−12.0545	−	12.8220i	−0.423032	−	0.449966i
$813$		0			0
$814$	1.75276	−	3.03588i	0.0614344	−	0.106407i
$815$	−22.7055	−	39.3271i	−0.795338	−	1.37757i
$816$		0			0
$817$	−4.24417	−	0.318056i	−0.148485	−	0.0111274i
$818$	6.20252	+	7.77771i	0.216866	+	0.271941i
$819$		0			0
$820$	15.6856	−	19.6691i	0.547764	−	0.686874i
$821$	16.1136	−	17.3663i	0.562367	−	0.606087i	−0.386297	−	0.922375i	$-0.626246\pi$
$821$	16.1136	−	17.3663i	0.562367	−	0.606087i	0.948663	+	0.316287i	$0.102436\pi$
$822$		0			0
$823$	8.16626	+	5.56766i	0.284658	+	0.194076i	0.697228	−	0.716849i	$-0.254416\pi$
$823$	8.16626	+	5.56766i	0.284658	+	0.194076i	−0.412570	+	0.910926i	$0.635369\pi$
$824$	15.0616	−	2.27018i	0.524697	−	0.0790854i
$825$		0			0
$826$	−0.224725	−	34.2702i	−0.00781918	−	1.19241i
$827$	−0.416708	−	0.865304i	−0.0144904	−	0.0300896i	0.893598	−	0.448868i	$-0.148173\pi$
$827$	−0.416708	−	0.865304i	−0.0144904	−	0.0300896i	−0.908088	+	0.418778i	$0.862458\pi$
$828$		0			0
$829$	22.8857	+	24.6650i	0.794855	+	0.856650i	0.992325	−	0.123659i	$-0.0394630\pi$
$829$	22.8857	+	24.6650i	0.794855	+	0.856650i	−0.197470	+	0.980309i	$0.563273\pi$
$830$	−18.3345	+	1.37398i	−0.636400	+	0.0476916i
$831$		0			0
$832$		−	6.63793i		−	0.230129i
$833$	−18.1827	+	17.3203i	−0.629992	+	0.600113i
$834$		0			0
$835$	−23.0614	−	58.7595i	−0.798073	−	2.03346i
$836$	0.730169	+	9.74343i	0.0252534	+	0.336984i
$837$		0			0
$838$	−10.6113	−	15.5639i	−0.366562	−	0.537647i
$839$	−27.9737	+	13.4714i	−0.965760	+	0.465085i	−0.849184	−	0.528097i	$-0.822906\pi$
$839$	−27.9737	+	13.4714i	−0.965760	+	0.465085i	−0.116575	+	0.993182i	$0.537192\pi$
$840$		0			0
$841$	13.7355	+	6.61467i	0.473638	+	0.228092i
$842$	0.903890	+	5.99692i	0.0311501	+	0.206667i
$843$		0			0
$844$	−8.18519	−	1.23372i	−0.281746	−	0.0424663i
$845$	−85.1666	−	79.0231i	−2.92982	−	2.71848i
$846$		0			0
$847$	1.66608	−	24.3761i	0.0572470	−	0.837574i
$848$	−5.79741	+	4.62328i	−0.199084	+	0.158764i
$849$		0			0
$850$	−9.50570	−	30.8167i	−0.326043	−	1.05700i
$851$	12.9514	−	7.47747i	0.443967	−	0.256324i
$852$		0			0
$853$	−54.5429	−	12.4491i	−1.86751	−	0.426248i	−0.869775	−	0.493448i	$-0.835736\pi$
$853$	−54.5429	−	12.4491i	−1.86751	−	0.426248i	−0.997740	+	0.0671998i	$0.978594\pi$
$854$	9.29371	+	1.33854i	0.318024	+	0.0458037i
$855$		0			0
$856$	−3.96416	−	1.22278i	−0.135492	−	0.0417938i
$857$	7.11942	−	18.1400i	0.243195	−	0.619650i	−0.756204	−	0.654337i	$-0.772948\pi$
$857$	7.11942	−	18.1400i	0.243195	−	0.619650i	0.999398	+	0.0346864i	$0.0110432\pi$
$858$		0			0
$859$	−6.59084	+	21.3670i	−0.224877	+	0.729032i	0.770878	+	0.636983i	$0.219818\pi$
$859$	−6.59084	+	21.3670i	−0.224877	+	0.729032i	−0.995754	+	0.0920489i	$0.970658\pi$
$860$	−0.481671	−	2.11034i	−0.0164249	−	0.0719620i
$861$		0			0
$862$	−4.85274	+	21.2613i	−0.165285	+	0.724161i
$863$	15.1729	+	8.76009i	0.516492	+	0.298197i	0.735498	−	0.677526i	$-0.236948\pi$
$863$	15.1729	+	8.76009i	0.516492	+	0.298197i	−0.219006	+	0.975724i	$0.570281\pi$
$864$		0			0
$865$	50.7445	−	15.6526i	1.72537	−	0.532205i
$866$	3.01081	−	40.1765i	0.102312	−	1.36525i
$867$		0			0
$868$	1.33663	+	0.0913569i	0.0453682	+	0.00310086i
$869$	0.644944	+	0.514326i	0.0218782	+	0.0174473i
$870$		0			0
$871$	8.95510	−	59.4132i	0.303432	−	2.01314i
$872$	1.38920	−	2.03758i	0.0470442	−	0.0690012i
$873$		0			0
$874$	−18.0856	+	37.5551i	−0.611753	+	1.27032i
$875$	35.4580	−	17.3630i	1.19870	−	0.586977i
$876$		0			0
$877$	2.04296	−	1.39287i	0.0689860	−	0.0470339i	−0.528336	−	0.849035i	$-0.677184\pi$
$877$	2.04296	−	1.39287i	0.0689860	−	0.0470339i	0.597322	+	0.802002i	$0.296231\pi$
$878$	−18.3394	+	17.0165i	−0.618926	+	0.574280i
$879$		0			0
$880$	−4.62584	+	1.81551i	−0.155937	+	0.0612007i
$881$	−12.7838			−0.430698			−0.215349	−	0.976537i	$-0.569089\pi$
$881$	−12.7838			−0.430698			−0.215349	+	0.976537i	$0.569089\pi$
$882$		0			0
$883$	−46.7814			−1.57432			−0.787160	−	0.616749i	$-0.788449\pi$
$883$	−46.7814			−1.57432			−0.787160	+	0.616749i	$0.788449\pi$
$884$	22.1668	−	8.69984i	0.745551	−	0.292607i
$885$		0			0
$886$	23.6132	−	21.9098i	0.793301	−	0.736075i
$887$	−4.62581	+	3.15383i	−0.155320	+	0.105895i	−0.638486	−	0.769633i	$-0.720439\pi$
$887$	−4.62581	+	3.15383i	−0.155320	+	0.105895i	0.483166	+	0.875529i	$0.339487\pi$
$888$		0			0
$889$	−17.5869	+	0.115325i	−0.589845	+	0.00386787i
$890$	9.25826	−	19.2250i	0.310338	−	0.644423i
$891$		0			0
$892$	−13.4940	+	19.7921i	−0.451814	+	0.662689i
$893$	−8.74487	+	58.0184i	−0.292636	+	1.94151i
$894$		0			0
$895$	−26.0113	−	20.7433i	−0.869461	−	0.693372i
$896$	−0.763254	+	2.53327i	−0.0254985	+	0.0846305i
$897$		0			0
$898$	0.914073	−	12.1975i	0.0305030	−	0.407034i
$899$	−3.21864	+	0.992818i	−0.107348	+	0.0331123i
$900$		0			0
$901$	−23.0373	−	13.3006i	−0.767484	−	0.443107i
$902$	1.98854	−	8.71236i	0.0662111	−	0.290090i
$903$		0			0
$904$	−0.795643	−	3.48594i	−0.0264627	−	0.115941i
$905$	5.18212	−	16.8000i	0.172259	−	0.558451i
$906$		0			0
$907$	10.1464	−	25.8527i	0.336907	−	0.858426i	−0.657562	−	0.753400i	$-0.728412\pi$
$907$	10.1464	−	25.8527i	0.336907	−	0.858426i	0.994470	−	0.105026i	$-0.0334925\pi$
$908$	−2.12897	−	0.656701i	−0.0706524	−	0.0217934i
$909$		0			0
$910$	33.2163	+	56.6708i	1.10111	+	1.87862i
$911$	−10.4482	−	2.38474i	−0.346165	−	0.0790098i	0.0459038	−	0.998946i	$-0.485383\pi$
$911$	−10.4482	−	2.38474i	−0.346165	−	0.0790098i	−0.392068	+	0.919936i	$0.628240\pi$
$912$		0			0
$913$	−5.65599	+	3.26549i	−0.187186	+	0.108072i
$914$	−9.37095	−	30.3799i	−0.309964	−	1.00488i
$915$		0			0
$916$	10.2521	−	8.17576i	0.338738	−	0.270135i
$917$	−22.1901	+	3.49358i	−0.732781	+	0.115368i
$918$		0			0
$919$	−14.0920	−	13.0754i	−0.464851	−	0.431318i	0.412653	−	0.910888i	$-0.364602\pi$
$919$	−14.0920	−	13.0754i	−0.464851	−	0.431318i	−0.877504	+	0.479570i	$0.840793\pi$
$920$	−20.9629	−	3.15965i	−0.691128	−	0.104171i
$921$		0			0
$922$	0.424251	+	2.81472i	0.0139719	+	0.0926978i
$923$	−31.5348	−	15.1864i	−1.03798	−	0.499865i
$924$		0			0
$925$	−21.3703	+	10.2914i	−0.702651	+	0.338379i
$926$	0.641724	+	0.941236i	0.0210884	+	0.0309309i
$927$		0			0
$928$	−0.497083	−	6.63311i	−0.0163175	−	0.217743i
$929$	19.8307	+	50.5278i	0.650624	+	1.65776i	0.748964	+	0.662611i	$0.230552\pi$
$929$	19.8307	+	50.5278i	0.650624	+	1.65776i	−0.0983398	+	0.995153i	$0.531353\pi$
$930$		0			0
$931$	−51.3811	−	3.17348i	−1.68395	−	0.104006i
$932$			6.66691i			0.218382i
$933$		0			0
$934$	−11.8327	+	0.886741i	−0.387179	+	0.0290150i
$935$	−12.1255	−	13.0681i	−0.396545	−	0.427374i
$936$		0			0
$937$	7.17025	+	14.8892i	0.234242	+	0.486409i	0.984644	−	0.174573i	$-0.0558545\pi$
$937$	7.17025	+	14.8892i	0.234242	+	0.486409i	−0.750402	+	0.660981i	$0.770140\pi$
$938$	−10.2491	+	21.6445i	−0.334646	+	0.706717i
$939$		0			0
$940$	−29.5078	+	4.44759i	−0.962440	+	0.145064i
$941$	3.92089	+	2.67322i	0.127817	+	0.0871445i	0.625541	−	0.780191i	$-0.284878\pi$
$941$	3.92089	+	2.67322i	0.127817	+	0.0871445i	−0.497724	+	0.867336i	$0.665831\pi$
$942$		0			0
$943$	25.9306	−	27.9466i	0.844418	−	0.910066i
$944$	8.07620	−	10.1272i	0.262858	−	0.329613i
$945$		0			0
$946$	−0.479404	−	0.601154i	−0.0155868	−	0.0195452i
$947$	−14.5329	−	1.08909i	−0.472255	−	0.0353906i	−0.163523	−	0.986540i	$-0.552286\pi$
$947$	−14.5329	−	1.08909i	−0.472255	−	0.0353906i	−0.308732	+	0.951149i	$0.599905\pi$
$948$		0			0
$949$	17.8494	+	30.9160i	0.579415	+	1.00358i
$950$	33.0556	−	57.2539i	1.07246	−	1.85756i
$951$		0			0
$952$	−9.45998	+	0.771339i	−0.306600	+	0.0249993i
$953$	−33.2254	+	7.58348i	−1.07628	+	0.245653i	−0.723689	−	0.690126i	$-0.757555\pi$
$953$	−33.2254	+	7.58348i	−1.07628	+	0.245653i	−0.352587	+	0.935779i	$0.614698\pi$
$954$		0			0
$955$	23.8031	+	9.34202i	0.770249	+	0.302301i
$956$	−7.54342	−	2.96057i	−0.243972	−	0.0957518i
$957$		0			0
$958$	−3.12096	+	0.712338i	−0.100834	+	0.0230146i
$959$	−32.3374	−	12.4474i	−1.04423	−	0.401948i
$960$		0			0
$961$	−15.3718	+	26.6247i	−0.495864	+	0.858862i
$962$	−8.75710	−	15.1678i	−0.282340	−	0.489028i
$963$		0			0
$964$	−20.6836	−	1.55002i	−0.666173	−	0.0499227i
$965$	48.7477	+	61.1276i	1.56924	+	1.96777i
$966$		0			0
$967$	23.6286	−	29.6293i	0.759844	−	0.952814i	−0.239995	−	0.970774i	$-0.577146\pi$
$967$	23.6286	−	29.6293i	0.759844	−	0.952814i	0.999839	+	0.0179600i	$0.00571716\pi$
$968$	6.28126	−	6.76959i	0.201887	−	0.217583i
$969$		0			0
$970$	52.1827	+	35.5776i	1.67549	+	1.14233i
$971$	11.5685	−	1.74367i	0.371251	−	0.0559570i	0.0392327	−	0.999230i	$-0.487509\pi$
$971$	11.5685	−	1.74367i	0.371251	−	0.0559570i	0.332018	+	0.943273i	$0.392271\pi$
$972$		0			0
$973$	16.1238	+	3.56908i	0.516906	+	0.114420i
$974$	−13.4743	−	27.9797i	−0.431745	−	0.896528i
$975$		0			0
$976$	2.41389	+	2.60156i	0.0772668	+	0.0832738i
$977$	11.5190	−	0.863233i	0.368527	−	0.0276173i	0.110820	−	0.993840i	$-0.464652\pi$
$977$	11.5190	−	0.863233i	0.368527	−	0.0276173i	0.257707	+	0.966223i	$0.417033\pi$
$978$		0			0
$979$		−	7.57964i		−	0.242246i
$980$	−6.16027	−	25.4469i	−0.196783	−	0.812871i
$981$		0			0
$982$	−9.20813	−	23.4619i	−0.293843	−	0.748700i
$983$	−0.0731088	−	0.975569i	−0.00233181	−	0.0311158i	0.995917	−	0.0902789i	$-0.0287758\pi$
$983$	−0.0731088	−	0.975569i	−0.00233181	−	0.0311158i	−0.998248	+	0.0591631i	$0.981157\pi$
$984$		0			0
$985$	−19.9899	−	29.3198i	−0.636932	−	0.934208i
$986$	21.4992	−	10.3535i	0.684675	−	0.329722i
$987$		0			0
$988$	43.9820	+	21.1806i	1.39925	+	0.673844i
$989$	−0.488892	−	3.24358i	−0.0155459	−	0.103140i
$990$		0			0
$991$	−17.1908	−	2.59109i	−0.546083	−	0.0823087i	−0.129794	−	0.991541i	$-0.541431\pi$
$991$	−17.1908	−	2.59109i	−0.546083	−	0.0823087i	−0.416289	+	0.909232i	$0.636670\pi$
$992$	0.371201	+	0.344424i	0.0117856	+	0.0109355i
$993$		0			0
$994$	10.2886	+	9.42163i	0.326335	+	0.298836i
$995$	−51.8796	+	41.3726i	−1.64469	+	1.31160i
$996$		0			0
$997$	−6.74656	−	21.8718i	−0.213666	−	0.692687i	−0.997431	−	0.0716305i	$-0.977180\pi$
$997$	−6.74656	−	21.8718i	−0.213666	−	0.692687i	0.783765	−	0.621057i	$-0.213296\pi$
$998$	31.2436	−	18.0385i	0.988999	−	0.570999i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.bl.a.719.11	yes	240
3.2	odd	2	inner	882.2.bl.a.719.10	yes	240
49.3	odd	42	inner	882.2.bl.a.395.10	✓	240
147.101	even	42	inner	882.2.bl.a.395.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.10	✓	240	49.3	odd	42	inner
882.2.bl.a.395.11	yes	240	147.101	even	42	inner
882.2.bl.a.719.10	yes	240	3.2	odd	2	inner
882.2.bl.a.719.11	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.bl (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.930874 - 0.365341i) q^{2} +(0.733052 - 0.680173i) q^{4} +(-3.09036 + 2.10697i) q^{5} +(-0.605636 - 2.57550i) q^{7} +(0.433884 - 0.900969i) q^{8} +(-2.10697 + 3.09036i) q^{10} +(-0.198018 + 1.31377i) q^{11} +(5.18974 + 4.13868i) q^{13} +(-1.50471 - 2.17620i) q^{14} +(0.0747301 - 0.997204i) q^{16} +(3.42802 - 1.05740i) q^{17} +(6.36887 + 3.67707i) q^{19} +(-0.832289 + 3.64650i) q^{20} +(0.295642 + 1.29529i) q^{22} +(-1.67066 + 5.41615i) q^{23} +(3.28429 - 8.36823i) q^{25} +(6.34303 + 1.95656i) q^{26} +(-2.19575 - 1.47604i) q^{28} +(6.48494 + 1.48014i) q^{29} +(-0.438536 + 0.253189i) q^{31} +(-0.294755 - 0.955573i) q^{32} +(2.80474 - 2.23671i) q^{34} +(7.29814 + 6.68316i) q^{35} +(-1.93416 - 1.79464i) q^{37} +(7.27200 + 1.09608i) q^{38} +(0.557459 + 3.69850i) q^{40} +(-6.06006 - 2.91837i) q^{41} +(-0.521418 + 0.251102i) q^{43} +(0.748430 + 1.09775i) q^{44} +(0.423567 + 5.65211i) q^{46} +(2.91481 + 7.42682i) q^{47} +(-6.26641 + 3.11963i) q^{49} -8.98965i q^{50} +(6.61937 - 0.496053i) q^{52} +(-5.04360 - 5.43570i) q^{53} +(-2.15612 - 4.47723i) q^{55} +(-2.58322 - 0.571808i) q^{56} +(6.57742 - 0.991386i) q^{58} +(10.7024 + 7.29681i) q^{59} +(-2.41389 + 2.60156i) q^{61} +(-0.315721 + 0.395902i) q^{62} +(-0.623490 - 0.781831i) q^{64} +(-24.7583 - 1.85538i) q^{65} +(-4.52583 - 7.83896i) q^{67} +(1.79370 - 3.10678i) q^{68} +(9.23528 + 3.55487i) q^{70} +(-5.14067 + 1.17332i) q^{71} +(5.00623 + 1.96480i) q^{73} +(-2.45611 - 0.963954i) q^{74} +(7.16976 - 1.63645i) q^{76} +(3.50353 - 0.285668i) q^{77} +(0.310444 - 0.537704i) q^{79} +(1.87014 + 3.23917i) q^{80} +(-6.70735 - 0.502647i) q^{82} +(3.06487 + 3.84322i) q^{83} +(-8.36590 + 10.4905i) q^{85} +(-0.393637 + 0.424240i) q^{86} +(1.09775 + 0.748430i) q^{88} +(-5.64124 + 0.850280i) q^{89} +(7.51608 - 15.8727i) q^{91} +(2.45924 + 5.10666i) q^{92} +(5.42664 + 5.84853i) q^{94} +(-27.4296 + 2.05556i) q^{95} -16.8856i q^{97} +(-4.69351 + 5.19336i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 20 q^{4} - 4 q^{7} - 12 q^{10} + 20 q^{16} + 24 q^{19} - 20 q^{22} + 24 q^{25} + 4 q^{28} + 12 q^{31} - 32 q^{37} + 44 q^{40} - 48 q^{43} + 204 q^{49} + 140 q^{55} + 136 q^{58} + 88 q^{61} + 40 q^{64}+ \cdots + 80 q^{94}+O(q^{100}) \) 240 * q - 20 * q^4 - 4 * q^7 - 12 * q^10 + 20 * q^16 + 24 * q^19 - 20 * q^22 + 24 * q^25 + 4 * q^28 + 12 * q^31 - 32 * q^37 + 44 * q^40 - 48 * q^43 + 204 * q^49 + 140 * q^55 + 136 * q^58 + 88 * q^61 + 40 * q^64 - 32 * q^67 - 16 * q^70 - 24 * q^73 - 28 * q^79 - 48 * q^82 - 112 * q^85 + 4 * q^88 + 80 * q^91 + 80 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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