LMFDB - Embedded newform 882.2.bl.a.395.10

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			395.10
Character	$\chi$	$=$	882.395
Dual form			882.2.bl.a.719.10

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

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

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	0.999834	+	0.0181934i	$0.00579145\pi$
$5$	3.09036	+	2.10697i	1.38205	+	0.942266i	0.382216	+	0.924073i	$0.375161\pi$
$6$		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	0.998645	+	0.0520356i	$0.0165709\pi$
$11$	0.198018	+	1.31377i	0.0597048	+	0.396115i	−0.938940	+	0.344080i	$0.888191\pi$
$12$		0			0
$13$	5.18974	−	4.13868i	1.43938	−	1.14786i	0.476087	−	0.879398i	$-0.342055\pi$
$13$	5.18974	−	4.13868i	1.43938	−	1.14786i	0.963289	−	0.268466i	$-0.0865166\pi$
$14$	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	$-0.548026\pi$
$17$	−3.42802	−	1.05740i	−0.831418	−	0.256458i	−0.681110	+	0.732181i	$0.738503\pi$
$18$		0			0
$19$	6.36887	−	3.67707i	1.46112	−	0.843578i	0.462056	−	0.886851i	$-0.347112\pi$
$19$	6.36887	−	3.67707i	1.46112	−	0.843578i	0.999063	+	0.0432727i	$0.0137784\pi$
$20$	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	0.945064	+	0.326886i	$0.105999\pi$
$23$	1.67066	+	5.41615i	0.348357	+	1.12934i	−0.596707	+	0.802459i	$0.703525\pi$
$24$		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	$-0.783322\pi$
$29$	−6.48494	+	1.48014i	−1.20422	+	0.274856i	−0.427100	+	0.904205i	$0.640465\pi$
$30$		0			0
$31$	−0.438536	−	0.253189i	−0.0787634	−	0.0454741i	0.460101	−	0.887867i	$-0.347813\pi$
$31$	−0.438536	−	0.253189i	−0.0787634	−	0.0454741i	−0.538864	+	0.842392i	$0.681147\pi$
$32$	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	−0.822970	−	0.568085i	$-0.807684\pi$
$37$	−1.93416	+	1.79464i	−0.317974	+	0.295037i	0.504996	+	0.863122i	$0.331494\pi$
$38$	−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	$-0.466838\pi$
$41$	6.06006	−	2.91837i	0.946423	−	0.455773i	0.842431	+	0.538805i	$0.181124\pi$
$42$		0			0
$43$	−0.521418	−	0.251102i	−0.0795156	−	0.0382927i	0.393703	−	0.919238i	$-0.371194\pi$
$43$	−0.521418	−	0.251102i	−0.0795156	−	0.0382927i	−0.473219	+	0.880945i	$0.656908\pi$
$44$	−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	0.544472	+	0.838779i	$0.316730\pi$
$47$	−2.91481	+	7.42682i	−0.425169	+	1.08331i	−0.969641	+	0.244534i	$0.921365\pi$
$48$		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	$-0.591818\pi$
$53$	5.04360	−	5.43570i	0.692791	−	0.746651i	0.977262	+	0.212033i	$0.0680085\pi$
$54$		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	−0.393814	+	0.919190i	$0.628844\pi$
$59$	−10.7024	+	7.29681i	−1.39334	+	0.949963i	−0.999526	+	0.0307729i	$0.990203\pi$
$60$		0			0
$61$	−2.41389	−	2.60156i	−0.309067	−	0.333095i	0.559348	−	0.828933i	$-0.311052\pi$
$61$	−2.41389	−	2.60156i	−0.309067	−	0.333095i	−0.868415	+	0.495838i	$0.834861\pi$
$62$	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	0.445144	+	0.895459i	$0.353152\pi$
$67$	−4.52583	+	7.83896i	−0.552918	+	0.957682i	−0.998062	+	0.0622230i	$0.980181\pi$
$68$	−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	$-0.327275\pi$
$71$	5.14067	+	1.17332i	0.610086	+	0.139248i	0.0936946	+	0.995601i	$0.470132\pi$
$72$		0			0
$73$	5.00623	−	1.96480i	0.585935	−	0.229962i	−0.0538085	−	0.998551i	$-0.517136\pi$
$73$	5.00623	−	1.96480i	0.585935	−	0.229962i	0.639743	+	0.768589i	$0.279041\pi$
$74$	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	0.882961	−	0.469447i	$-0.155547\pi$
$79$	0.310444	+	0.537704i	0.0349277	+	0.0604965i	−0.848033	+	0.529943i	$0.822213\pi$
$80$	−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	$-0.872666\pi$
$83$	−3.06487	+	3.84322i	−0.336413	+	0.421848i	0.584636	+	0.811296i	$0.301237\pi$
$84$		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	$-0.354606\pi$
$89$	5.64124	+	0.850280i	0.597970	+	0.0901295i	0.156919	+	0.987611i	$0.449844\pi$
$90$		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	$0.327822\pi$
$97$			16.8856i			1.71448i	−0.514919	+	0.857239i	$0.672178\pi$
$98$	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	−0.622907	−	0.782296i	$-0.714048\pi$
$101$	1.10185	−	14.7031i	0.109638	−	1.46302i	0.732544	−	0.680719i	$-0.238333\pi$
$102$		0			0
$103$	8.58036	−	12.5851i	0.845448	−	1.24005i	−0.123392	−	0.992358i	$-0.539377\pi$
$103$	8.58036	−	12.5851i	0.845448	−	1.24005i	0.968840	−	0.247687i	$-0.0796705\pi$
$104$	−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	−0.938860	−	0.344299i	$-0.888117\pi$
$107$	0.618296	−	4.10213i	0.0597729	−	0.396567i	0.998633	−	0.0522687i	$-0.0166452\pi$
$108$		0			0
$109$	2.43855	−	0.367552i	0.233570	−	0.0352051i	−0.0312139	−	0.999513i	$-0.509937\pi$
$109$	2.43855	−	0.367552i	0.233570	−	0.0352051i	0.264784	+	0.964308i	$0.414699\pi$
$110$	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	$-0.339504\pi$
$113$	−2.79551	−	2.22934i	−0.262979	−	0.209719i	−0.746098	+	0.665836i	$0.768075\pi$
$114$		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	0.997190	+	0.0749114i	$0.0238674\pi$
$127$	1.47918	+	6.48070i	0.131256	+	0.575069i	−0.865934	+	0.500157i	$0.833275\pi$
$128$	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	−0.953792	−	0.300467i	$-0.902858\pi$
$131$	−0.634486	−	8.46663i	−0.0554353	−	0.739733i	0.898357	−	0.439266i	$-0.144761\pi$
$132$		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	$-0.379467\pi$
$137$	−7.37758	−	10.8209i	−0.630309	−	0.924493i	−0.999989	+	0.00466562i	$0.998515\pi$
$138$		0			0
$139$	−2.70819	−	5.62362i	−0.229706	−	0.476989i	0.753977	−	0.656901i	$-0.228133\pi$
$139$	−2.70819	−	5.62362i	−0.229706	−	0.476989i	−0.983683	+	0.179912i	$0.942419\pi$
$140$	−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	$-0.650661\pi$
$149$	−17.0329	−	6.68493i	−1.39539	−	0.547651i	−0.939550	+	0.342411i	$0.888757\pi$
$150$		0			0
$151$	−11.4737	−	10.6460i	−0.933717	−	0.866363i	0.0575354	−	0.998343i	$-0.481676\pi$
$151$	−11.4737	−	10.6460i	−0.933717	−	0.866363i	−0.991252	+	0.131981i	$0.957866\pi$
$152$	−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	−0.904608	−	0.426245i	$-0.859836\pi$
$157$	−12.1653	−	17.8432i	−0.970898	−	1.42405i	−0.0662902	−	0.997800i	$-0.521116\pi$
$158$	−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	−0.912799	−	0.408410i	$-0.866083\pi$
$163$	−0.907304	−	12.1071i	−0.0710655	−	0.948304i	0.841733	−	0.539894i	$-0.181536\pi$
$164$	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	0.883692	+	0.468069i	$0.155050\pi$
$167$	3.75539	+	16.4534i	0.290601	+	1.27320i	−0.593091	+	0.805135i	$0.702093\pi$
$168$		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	$-0.413768\pi$
$173$	13.5671	−	4.18488i	1.03148	−	0.318171i	0.763880	+	0.645358i	$0.223292\pi$
$174$		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	0.803248	+	0.595645i	$0.203104\pi$
$179$	−2.62184	+	8.49980i	−0.195966	+	0.635305i	−0.999213	+	0.0396597i	$0.987373\pi$
$180$		0			0
$181$	−3.67499	−	2.93070i	−0.273160	−	0.217837i	0.477323	−	0.878728i	$-0.341607\pi$
$181$	−3.67499	−	2.93070i	−0.273160	−	0.217837i	−0.750482	+	0.660891i	$0.770179\pi$
$182$	−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	$-0.729968\pi$
$191$	3.85118	−	5.64865i	0.278662	−	0.408722i	0.939898	+	0.341456i	$0.110920\pi$
$192$		0			0
$193$	−1.56213	+	20.8451i	−0.112444	+	1.50047i	0.600714	+	0.799464i	$0.294883\pi$
$193$	−1.56213	+	20.8451i	−0.112444	+	1.50047i	−0.713159	+	0.701003i	$0.752736\pi$
$194$	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	0.685164	−	0.728389i	$-0.259730\pi$
$199$	17.6915	+	1.32579i	1.25411	+	0.0939829i	0.568951	+	0.822372i	$0.307349\pi$
$200$	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	−0.927074	−	0.374880i	$-0.877684\pi$
$211$	−5.16103	+	6.47172i	−0.355300	+	0.445532i	0.571774	+	0.820411i	$0.306255\pi$
$212$	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	−0.649045	−	0.760750i	$-0.724831\pi$
$223$	−23.3539	−	5.33037i	−1.56389	−	0.356948i	−0.914847	+	0.403802i	$0.867689\pi$
$224$	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	$-0.809777\pi$
$227$	1.11398	−	1.92946i	0.0739372	−	0.128063i	0.900624	+	0.434600i	$0.143110\pi$
$228$		0			0
$229$	13.0762	−	0.979928i	0.864102	−	0.0647555i	0.364699	−	0.931125i	$-0.381172\pi$
$229$	13.0762	−	0.979928i	0.864102	−	0.0647555i	0.499403	+	0.866370i	$0.333553\pi$
$230$	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	$-0.168017\pi$
$233$	4.53465	+	4.88719i	0.297075	+	0.320171i	−0.566821	+	0.823841i	$0.691827\pi$
$234$		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	$-0.772731\pi$
$239$	3.51602	−	7.30108i	0.227432	−	0.472268i	0.983190	+	0.182583i	$0.0584458\pi$
$240$		0			0
$241$	−14.1078	+	15.2046i	−0.908766	+	0.979417i	−0.999865	−	0.0164248i	$-0.994772\pi$
$241$	−14.1078	+	15.2046i	−0.908766	+	0.979417i	0.0910989	+	0.995842i	$0.470962\pi$
$242$	−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	$-0.200205\pi$
$251$	13.5118	+	6.50696i	0.852859	+	0.410715i	0.0442213	+	0.999022i	$0.485919\pi$
$252$		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	$-0.604110\pi$
$257$	9.60367	−	8.91091i	0.599061	−	0.555847i	0.920331	+	0.391140i	$0.127919\pi$
$258$		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	$-0.647902\pi$
$263$	−23.4562	−	13.5424i	−1.44637	−	0.835062i	−0.998263	+	0.0589181i	$0.981235\pi$
$264$		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	−0.899750	−	0.436406i	$-0.856251\pi$
$269$	−8.80775	−	22.4418i	−0.537018	−	1.36830i	0.362732	−	0.931894i	$-0.381844\pi$
$270$		0			0
$271$	−0.209571	−	0.679413i	−0.0127305	−	0.0412714i	0.948985	−	0.315322i	$-0.102113\pi$
$271$	−0.209571	−	0.679413i	−0.0127305	−	0.0412714i	−0.961715	+	0.274051i	$0.911636\pi$
$272$	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	−0.0997604	−	0.995011i	$-0.531808\pi$
$277$	−12.3609	−	3.81284i	−0.742696	−	0.229091i	−0.642936	+	0.765920i	$0.722284\pi$
$278$	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	$-0.569600\pi$
$281$	11.5083	−	9.17758i	0.686529	−	0.547489i	0.903446	+	0.428701i	$0.141029\pi$
$282$		0			0
$283$	3.44972	+	22.8874i	0.205065	+	1.36052i	0.820192	+	0.572088i	$0.193866\pi$
$283$	3.44972	+	22.8874i	0.205065	+	1.36052i	−0.615128	+	0.788427i	$0.710896\pi$
$284$	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	$-0.412579\pi$
$293$	9.28442			0.542401			0.271201	+	0.962523i	$0.412579\pi$
$294$		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	−0.956962	−	0.290214i	$-0.906274\pi$
$307$	−15.5409	+	12.3935i	−0.886968	+	0.707334i	0.0699936	+	0.997547i	$0.477702\pi$
$308$	−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	$-0.494882\pi$
$311$	−9.41517	−	2.90419i	−0.533885	−	0.164682i	−0.549963	+	0.835189i	$0.685358\pi$
$312$		0			0
$313$	1.03887	−	0.599790i	0.0587202	−	0.0339021i	−0.470352	−	0.882479i	$-0.655873\pi$
$313$	1.03887	−	0.599790i	0.0587202	−	0.0339021i	0.529073	+	0.848577i	$0.322540\pi$
$314$	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	−0.951032	−	0.309094i	$-0.899974\pi$
$317$	−6.04233	−	19.5887i	−0.339371	−	1.10021i	0.611661	−	0.791120i	$-0.290502\pi$
$318$		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	−0.285131	−	0.958489i	$-0.592037\pi$
$331$	11.8142	−	10.9620i	0.649370	−	0.602527i	0.934501	+	0.355962i	$0.115847\pi$
$332$	−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	0.675820	−	0.737067i	$-0.263790\pi$
$337$	9.56292	+	4.60526i	0.520925	+	0.250864i	−0.154895	+	0.987931i	$0.549504\pi$
$338$	−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	0.0595111	−	0.998228i	$-0.481046\pi$
$347$	19.5687	−	21.0900i	1.05050	−	1.13217i	0.990989	−	0.133942i	$-0.0427637\pi$
$348$		0			0
$349$	11.3948	−	23.6615i	0.609949	−	1.26657i	−0.335879	−	0.941905i	$-0.609033\pi$
$349$	11.3948	−	23.6615i	0.609949	−	1.26657i	0.945828	−	0.324668i	$-0.105252\pi$
$350$	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	$-0.796053\pi$
$353$	−10.1099	+	6.89285i	−0.538098	+	0.366869i	0.263568	+	0.964641i	$0.415101\pi$
$354$		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	$-0.350324\pi$
$359$	19.5910	−	1.46814i	1.03397	−	0.0774855i	0.580889	+	0.813983i	$0.302705\pi$
$360$		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	−0.151618	−	0.988439i	$-0.548448\pi$
$367$	7.84582	−	3.07926i	0.409548	−	0.160736i	0.561166	+	0.827703i	$0.310353\pi$
$368$	−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	0.998173	−	0.0604144i	$-0.0192422\pi$
$373$	8.62849	+	14.9450i	0.446766	+	0.773822i	−0.551407	+	0.834236i	$0.685909\pi$
$374$	−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	0.307214	−	0.951640i	$-0.400603\pi$
$379$	−13.4120	−	16.8181i	−0.688928	−	0.863888i	−0.996142	+	0.0877521i	$0.972032\pi$
$380$	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	$-0.430857\pi$
$383$	2.61513	+	0.394167i	0.133627	+	0.0201410i	−0.0818882	+	0.996642i	$0.526095\pi$
$384$		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	$-0.508598\pi$
$389$	−3.99786	−	0.299598i	−0.202700	−	0.0151902i	−0.175693	+	0.984445i	$0.556217\pi$
$390$		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	−0.886007	−	0.463671i	$-0.846532\pi$
$397$	−2.60404	+	3.81943i	−0.130693	+	0.191692i	0.755314	+	0.655363i	$0.227484\pi$
$398$	−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	$-0.953385\pi$
$401$	−0.0188342	+	0.124956i	−0.000940533	+	0.00624003i	0.988356	+	0.152162i	$0.0486234\pi$
$402$		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	−0.853725	−	0.520724i	$-0.825662\pi$
$409$	2.93224	−	9.50610i	0.144990	−	0.470046i	0.998715	+	0.0506778i	$0.0161382\pi$
$410$	−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	−0.763206	−	0.646156i	$-0.776376\pi$
$419$	4.19165	−	18.3648i	0.204775	−	0.897179i	0.967981	−	0.251024i	$-0.0807672\pi$
$420$		0			0
$421$	−1.34951	−	5.91260i	−0.0657712	−	0.288162i	0.931337	−	0.364159i	$-0.118643\pi$
$421$	−1.34951	−	5.91260i	−0.0657712	−	0.288162i	−0.997108	+	0.0759963i	$0.975786\pi$
$422$	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	$-0.0144562\pi$
$431$	12.2849	+	18.0186i	0.591743	+	0.867928i	−0.407226	+	0.913327i	$0.633504\pi$
$432$		0			0
$433$	17.4808	+	36.2993i	0.840075	+	1.74443i	0.645832	+	0.763479i	$0.276511\pi$
$433$	17.4808	+	36.2993i	0.840075	+	1.74443i	0.194242	+	0.980954i	$0.437775\pi$
$434$	−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	−0.262664	−	0.964887i	$-0.584601\pi$
$439$	−23.2885	−	9.14008i	−1.11150	−	0.436232i	−0.848837	+	0.528655i	$0.822696\pi$
$440$	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	$-0.658324\pi$
$443$	−29.9855	−	11.7684i	−1.42465	−	0.559135i	−0.947520	+	0.319697i	$0.896419\pi$
$444$		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	$-0.236055\pi$
$449$	−5.30712	−	11.0203i	−0.250458	−	0.520082i	−0.987855	+	0.155378i	$0.950341\pi$
$450$		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	0.722333	+	0.691545i	$0.243070\pi$
$457$	2.37584	+	31.7034i	0.111137	+	1.48302i	−0.611196	+	0.791479i	$0.709311\pi$
$458$	−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	$-0.0503131\pi$
$461$	0.633408	+	2.77514i	0.0295008	+	0.129251i	−0.958033	+	0.286657i	$0.907456\pi$
$462$		0			0
$463$	0.253492	−	1.11062i	0.0117808	−	0.0516149i	−0.968696	−	0.248250i	$-0.920144\pi$
$463$	0.253492	−	1.11062i	0.0117808	−	0.0516149i	0.980477	+	0.196636i	$0.0630016\pi$
$464$	−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	$-0.506711\pi$
$467$	11.3387	−	3.49754i	0.524694	−	0.161847i	0.545776	+	0.837931i	$0.316235\pi$
$468$		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	$-0.524319\pi$
$479$	3.16546	−	0.477117i	0.144634	−	0.0218000i	0.220960	+	0.975283i	$0.429081\pi$
$480$		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	0.656006	+	0.754756i	$0.272245\pi$
$487$	−2.32075	+	30.9683i	−0.105163	+	1.40331i	−0.761170	+	0.648553i	$0.775375\pi$
$488$	−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	0.886408	−	0.462906i	$-0.153193\pi$
$499$	35.6741	+	5.37700i	1.59699	+	0.240708i	0.710583	+	0.703613i	$0.248431\pi$
$500$	−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	$-0.290248\pi$
$503$	−6.61094	−	8.28985i	−0.294767	−	0.369626i	−0.907058	+	0.421007i	$0.861677\pi$
$504$		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	$-0.0991390\pi$
$509$	4.75038	+	8.22790i	0.210557	+	0.364695i	−0.741332	+	0.671138i	$0.765806\pi$
$510$		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	$-0.981002\pi$
$521$	−10.2133	+	17.6900i	−0.447454	+	0.775013i	0.550766	+	0.834660i	$0.314336\pi$
$522$		0			0
$523$	−7.69803	+	0.576887i	−0.336611	+	0.0252255i	−0.241964	−	0.970285i	$-0.577791\pi$
$523$	−7.69803	+	0.576887i	−0.336611	+	0.0252255i	−0.0946476	+	0.995511i	$0.530172\pi$
$524$	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	−0.684460	−	0.729051i	$-0.739962\pi$
$541$	7.28404	−	18.5594i	0.313165	−	0.797932i	0.997625	−	0.0688812i	$-0.0219429\pi$
$542$	−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	0.186482	−	0.982458i	$-0.440292\pi$
$547$	25.0455	−	12.0613i	1.07087	−	0.515703i	0.884386	+	0.466756i	$0.154577\pi$
$548$	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	$-0.222939\pi$
$557$	13.8945	+	8.02197i	0.588727	+	0.339902i	−0.175867	+	0.984414i	$0.556273\pi$
$558$		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	−0.969425	−	0.245389i	$-0.921084\pi$
$563$	−10.1007	−	25.7361i	−0.425693	−	1.08465i	0.543732	−	0.839259i	$-0.317011\pi$
$564$		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	$-0.425724\pi$
$569$	28.3717	−	16.3804i	1.18941	−	0.686703i	0.958171	+	0.286195i	$0.0923905\pi$
$570$		0			0
$571$	−3.97586	−	1.22639i	−0.166385	−	0.0513229i	0.210444	−	0.977606i	$-0.432509\pi$
$571$	−3.97586	−	1.22639i	−0.166385	−	0.0513229i	−0.376828	+	0.926283i	$0.622985\pi$
$572$	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	−0.849781	−	0.527136i	$-0.823266\pi$
$577$	−4.63913	−	30.7786i	−0.193129	−	1.28133i	0.656652	−	0.754194i	$-0.271972\pi$
$578$	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	$-0.590222\pi$
$587$	−13.5513			−0.559322			−0.279661	+	0.960099i	$0.590222\pi$
$588$		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	$-0.315474\pi$
$593$	−0.752150	−	0.512807i	−0.0308871	−	0.0210585i	−0.578665	+	0.815565i	$0.696426\pi$
$594$		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	−0.592072	−	0.805885i	$-0.701690\pi$
$599$	−6.45742	−	42.8422i	−0.263843	−	1.75048i	0.328229	−	0.944598i	$-0.393548\pi$
$600$		0			0
$601$	−7.37638	+	5.88246i	−0.300889	+	0.239951i	−0.762282	−	0.647245i	$-0.775921\pi$
$601$	−7.37638	+	5.88246i	−0.300889	+	0.239951i	0.461393	+	0.887196i	$0.347350\pi$
$602$	−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	−0.733332	−	0.679871i	$-0.762036\pi$
$607$	−12.5949	+	7.27168i	−0.511212	+	0.295148i	0.222120	+	0.975019i	$0.428702\pi$
$608$	−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	0.951013	−	0.309151i	$-0.100045\pi$
$613$	1.07936	+	2.75015i	0.0435948	+	0.111078i	−0.907418	+	0.420229i	$0.861950\pi$
$614$	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	$-0.631288\pi$
$617$	−9.05445	+	2.06662i	−0.364519	+	0.0831990i	0.0363386	+	0.999340i	$0.488431\pi$
$618$		0			0
$619$	20.3634	+	11.7568i	0.818476	+	0.472547i	0.849891	−	0.526959i	$-0.176668\pi$
$619$	20.3634	+	11.7568i	0.818476	+	0.472547i	−0.0314146	+	0.999506i	$0.510001\pi$
$620$	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	−0.243225	−	0.969970i	$-0.578205\pi$
$631$	−28.9687	−	13.9506i	−1.15323	−	0.555365i	−0.910001	+	0.414605i	$0.863920\pi$
$632$	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	$-0.603003\pi$
$641$	16.4880	−	17.7698i	0.651236	−	0.701866i	0.969211	+	0.246233i	$0.0791930\pi$
$642$		0			0
$643$	14.1789	−	29.4429i	0.559163	−	1.16111i	−0.409402	−	0.912354i	$-0.634263\pi$
$643$	14.1789	−	29.4429i	0.559163	−	1.16111i	0.968565	−	0.248760i	$-0.0800230\pi$
$644$	−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	$-0.683045\pi$
$647$	0.981216	−	0.668982i	0.0385756	−	0.0263004i	0.582454	+	0.812863i	$0.302092\pi$
$648$		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	$-0.715716\pi$
$653$	−28.8985	+	2.16564i	−1.13089	+	0.0847481i	−0.503888	+	0.863769i	$0.668097\pi$
$654$		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	$-0.649286\pi$
$659$	−31.9926	−	7.30209i	−1.24625	−	0.284449i	−0.794263	+	0.607574i	$0.792143\pi$
$660$		0			0
$661$	−31.3265	+	12.2947i	−1.21846	+	0.478210i	−0.885460	−	0.464716i	$-0.846156\pi$
$661$	−31.3265	+	12.2947i	−1.21846	+	0.478210i	−0.333000	+	0.942927i	$0.608061\pi$
$662$	−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	0.997378	+	0.0723624i	$0.0230538\pi$
$673$	21.9469	+	27.5205i	0.845989	+	1.06084i	−0.151389	+	0.988474i	$0.548375\pi$
$674$	−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	$-0.384036\pi$
$677$	10.9637	+	1.65252i	0.421370	+	0.0635113i	0.0650652	+	0.997881i	$0.479274\pi$
$678$		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	$-0.515940\pi$
$683$	−6.49205	−	0.486512i	−0.248411	−	0.0186159i	−0.198354	+	0.980130i	$0.563559\pi$
$684$		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	−0.135175	+	0.990822i	$0.543160\pi$
$691$	−26.5003	+	38.8688i	−1.00812	+	1.47864i	−0.872945	+	0.487819i	$0.837793\pi$
$692$	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	$-0.418717\pi$
$701$	−16.7997	−	13.3973i	−0.634515	−	0.506009i	−0.887107	+	0.461564i	$0.847288\pi$
$702$		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	−0.668063	−	0.744105i	$-0.732876\pi$
$709$	−21.3249	+	6.57785i	−0.800872	+	0.247036i	−0.132810	+	0.991142i	$0.542400\pi$
$710$	−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	0.369774	+	0.929122i	$0.379435\pi$
$719$	3.82393	+	51.0268i	0.142608	+	1.90298i	−0.227165	+	0.973856i	$0.572946\pi$
$720$		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	0.998619	−	0.0525333i	$-0.0167296\pi$
$727$	9.03038	+	18.7518i	0.334918	+	0.695465i	−0.663701	+	0.747998i	$0.731015\pi$
$728$	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	0.741671	−	0.670763i	$-0.234033\pi$
$733$	22.4476	+	8.81002i	0.829120	+	0.325406i	0.0874487	+	0.996169i	$0.472129\pi$
$734$	−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	0.0260835	−	0.999660i	$-0.491696\pi$
$739$	−26.3373	−	24.4374i	−0.968832	−	0.898945i	−0.994915	+	0.100715i	$0.967887\pi$
$740$	−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	$-0.0633178\pi$
$743$	5.84926	+	12.1461i	0.214588	+	0.445597i	−0.765692	+	0.643207i	$0.777604\pi$
$744$		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	−0.957203	−	0.289416i	$-0.906539\pi$
$751$	−1.47508	−	19.6836i	−0.0538264	−	0.718264i	0.903377	−	0.428848i	$-0.141080\pi$
$752$	−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	0.637732	+	0.770258i	$0.279873\pi$
$757$	−7.45750	+	32.6734i	−0.271047	+	1.18754i	−0.908779	+	0.417277i	$0.862984\pi$
$758$	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	$-0.656040\pi$
$761$	−10.0095	+	3.08751i	−0.362843	+	0.111922i	0.107973	+	0.994154i	$0.465564\pi$
$762$		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	0.831835	−	0.555023i	$-0.187290\pi$
$769$	13.1951	+	10.5228i	0.475829	+	0.379461i	−0.356006	+	0.934484i	$0.615862\pi$
$770$	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	$-0.490757\pi$
$773$	9.77021	−	1.47262i	0.351410	−	0.0529665i	0.322376	+	0.946612i	$0.395519\pi$
$774$		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	−0.0524186	−	0.998625i	$-0.516693\pi$
$787$	−7.10004	−	0.532074i	−0.253089	−	0.0189664i	−0.200670	+	0.979659i	$0.564312\pi$
$788$	−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	$-0.0567928\pi$
$797$	16.7160	+	20.9612i	0.592112	+	0.742485i	−0.392014	+	0.919959i	$0.628221\pi$
$798$		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	$-0.316113\pi$
$809$	43.1255	−	16.9255i	1.51621	−	0.595069i	0.970113	+	0.242653i	$0.0780176\pi$
$810$		0			0
$811$	−2.76664	−	0.631468i	−0.0971500	−	0.0221738i	0.173670	−	0.984804i	$-0.444438\pi$
$811$	−2.76664	−	0.631468i	−0.0971500	−	0.0221738i	−0.270820	+	0.962630i	$0.587295\pi$
$812$	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	$-0.373754\pi$
$821$	−16.1136	−	17.3663i	−0.562367	−	0.606087i	−0.948663	+	0.316287i	$0.897564\pi$
$822$		0			0
$823$	8.16626	−	5.56766i	0.284658	−	0.194076i	−0.412570	−	0.910926i	$-0.635369\pi$
$823$	8.16626	−	5.56766i	0.284658	−	0.194076i	0.697228	+	0.716849i	$0.254416\pi$
$824$	−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	$-0.851827\pi$
$827$	0.416708	−	0.865304i	0.0144904	−	0.0300896i	0.908088	+	0.418778i	$0.137542\pi$
$828$		0			0
$829$	22.8857	−	24.6650i	0.794855	−	0.856650i	−0.197470	−	0.980309i	$-0.563273\pi$
$829$	22.8857	−	24.6650i	0.794855	−	0.856650i	0.992325	+	0.123659i	$0.0394630\pi$
$830$	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	$-0.177094\pi$
$839$	27.9737	+	13.4714i	0.965760	+	0.465085i	0.116575	+	0.993182i	$0.462808\pi$
$840$		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	−0.997740	−	0.0671998i	$-0.978594\pi$
$853$	−54.5429	+	12.4491i	−1.86751	+	0.426248i	−0.869775	+	0.493448i	$0.835736\pi$
$854$	−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	$-0.227052\pi$
$857$	−7.11942	−	18.1400i	−0.243195	−	0.619650i	−0.999398	+	0.0346864i	$0.988957\pi$
$858$		0			0
$859$	−6.59084	−	21.3670i	−0.224877	−	0.729032i	−0.995754	−	0.0920489i	$-0.970658\pi$
$859$	−6.59084	−	21.3670i	−0.224877	−	0.729032i	0.770878	−	0.636983i	$-0.219818\pi$
$860$	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	$-0.763052\pi$
$863$	−15.1729	+	8.76009i	−0.516492	+	0.298197i	0.219006	+	0.975724i	$0.429719\pi$
$864$		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	0.597322	−	0.802002i	$-0.296231\pi$
$877$	2.04296	+	1.39287i	0.0689860	+	0.0470339i	−0.528336	+	0.849035i	$0.677184\pi$
$878$	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	$-0.430911\pi$
$881$	12.7838			0.430698			0.215349	+	0.976537i	$0.430911\pi$
$882$		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	$-0.279561\pi$
$887$	4.62581	+	3.15383i	0.155320	+	0.105895i	−0.483166	+	0.875529i	$0.660513\pi$
$888$		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	0.994470	+	0.105026i	$0.0334925\pi$
$907$	10.1464	+	25.8527i	0.336907	+	0.858426i	−0.657562	+	0.753400i	$0.728412\pi$
$908$	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	$-0.514617\pi$
$911$	10.4482	−	2.38474i	0.346165	−	0.0790098i	0.392068	+	0.919936i	$0.371760\pi$
$912$		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	−0.877504	−	0.479570i	$-0.840793\pi$
$919$	−14.0920	+	13.0754i	−0.464851	+	0.431318i	0.412653	+	0.910888i	$0.364602\pi$
$920$	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	0.0983398	+	0.995153i	$0.468647\pi$
$929$	−19.8307	+	50.5278i	−0.650624	+	1.65776i	−0.748964	+	0.662611i	$0.769448\pi$
$930$		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	−0.750402	−	0.660981i	$-0.770140\pi$
$937$	7.17025	−	14.8892i	0.234242	−	0.486409i	0.984644	+	0.174573i	$0.0558545\pi$
$938$	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	$-0.715122\pi$
$941$	−3.92089	+	2.67322i	−0.127817	+	0.0871445i	0.497724	+	0.867336i	$0.334169\pi$
$942$		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	$-0.447714\pi$
$947$	14.5329	−	1.08909i	0.472255	−	0.0353906i	0.308732	+	0.951149i	$0.400095\pi$
$948$		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	$-0.242445\pi$
$953$	33.2254	+	7.58348i	1.07628	+	0.245653i	0.352587	+	0.935779i	$0.385302\pi$
$954$		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	0.999839	−	0.0179600i	$-0.00571716\pi$
$967$	23.6286	+	29.6293i	0.759844	+	0.952814i	−0.239995	+	0.970774i	$0.577146\pi$
$968$	−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	$-0.512491\pi$
$971$	−11.5685	−	1.74367i	−0.371251	−	0.0559570i	−0.332018	+	0.943273i	$0.607729\pi$
$972$		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	$-0.535348\pi$
$977$	−11.5190	−	0.863233i	−0.368527	−	0.0276173i	−0.257707	+	0.966223i	$0.582967\pi$
$978$		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	$-0.971224\pi$
$983$	0.0731088	−	0.975569i	0.00233181	−	0.0311158i	0.998248	+	0.0591631i	$0.0188432\pi$
$984$		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	−0.416289	−	0.909232i	$-0.636670\pi$
$991$	−17.1908	+	2.59109i	−0.546083	+	0.0823087i	−0.129794	+	0.991541i	$0.541431\pi$
$992$	−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	0.783765	+	0.621057i	$0.213296\pi$
$997$	−6.74656	+	21.8718i	−0.213666	+	0.692687i	−0.997431	+	0.0716305i	$0.977180\pi$
$998$	−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.395.10	✓	240
3.2	odd	2	inner	882.2.bl.a.395.11	yes	240
49.33	odd	42	inner	882.2.bl.a.719.11	yes	240
147.131	even	42	inner	882.2.bl.a.719.10	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.bl.a.395.10	✓	240	1.1	even	1	trivial
882.2.bl.a.395.11	yes	240	3.2	odd	2	inner
882.2.bl.a.719.10	yes	240	147.131	even	42	inner
882.2.bl.a.719.11	yes	240	49.33	odd	42	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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
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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