LMFDB - Embedded newform 972.2.l.d.107.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [972,2,Mod(107,972)] 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("972.107"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(972, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 972 = 2^{2} \cdot 3^{5} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	972.l (of order $18$, degree $6$, not minimal)

Newform invariants

comment:select newform

sage:traces = [96,3,0,3,6,0,0,-9,0,-3,0,0,6,33] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$7.76145907647$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 108)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			107.12
Character	$\chi$	$=$	972.107
Dual form			972.2.l.d.863.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.816016 + 1.15504i) q^{2} +(-0.668236 + 1.88506i) q^{4} +(-0.103444 + 0.284210i) q^{5} +(-0.478118 - 0.0843052i) q^{7} +(-2.72261 + 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(-0.0391221 + 0.0142393i) q^{11} +(-3.30779 + 2.77557i) q^{13} +(-0.292776 - 0.621040i) q^{14} +(-3.10692 - 2.51933i) q^{16} +(-2.14427 + 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.466628 - 0.384917i) q^{20} +(-0.0483712 - 0.0335681i) q^{22} +(1.14066 + 6.46900i) q^{23} +(3.76015 + 3.15514i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(-4.51541 + 5.38126i) q^{29} +(3.53661 - 0.623599i) q^{31} +(0.374633 - 5.64444i) q^{32} +(-3.17970 - 1.46650i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-0.977440 - 10.6567i) q^{38} +(0.0638189 - 0.853073i) q^{40} +(4.06534 + 4.84488i) q^{41} +(-0.827261 - 2.27288i) q^{43} +(-0.000699143 - 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(1.24905 - 7.08373i) q^{47} +(-6.35636 - 2.31353i) q^{49} +(-0.575971 + 6.91777i) q^{50} +(-3.02173 - 8.09012i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(1.36634 - 0.136900i) q^{56} +(-9.90022 - 0.824289i) q^{58} +(4.09063 + 1.48887i) q^{59} +(-1.30827 + 7.41960i) q^{61} +(3.60621 + 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-0.446672 - 1.22722i) q^{65} +(-7.15980 - 8.53272i) q^{67} +(-0.900820 - 4.86936i) q^{68} +(0.206792 - 0.0189671i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(3.98034 - 8.63027i) q^{74} +(11.5113 - 9.82502i) q^{76} +(0.0199054 - 0.00350987i) q^{77} +(1.94606 - 2.31923i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(4.41076 + 3.70106i) q^{83} +(-0.130039 - 0.737486i) q^{85} +(1.95021 - 2.81023i) q^{86} +(0.0956014 - 0.0687513i) q^{88} +(9.00521 + 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(-12.9567 - 2.17260i) q^{92} +(9.20124 - 4.33773i) q^{94} +(1.75321 - 1.47112i) q^{95} +(3.13032 - 1.13934i) q^{97} +(-2.51468 - 9.22972i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) $ 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/972\mathbb{Z}\right)^\times$.

$n$	$245$	$487$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	0.816016	+	1.15504i	0.577010	+	0.816737i
$2$	0.816016	+	1.15504i	0.577010	+	0.816737i
$3$		0			0
$3$		0			0
$4$	−0.668236	+	1.88506i	−0.334118	+	0.942531i
$5$	−0.103444	+	0.284210i	−0.0462615	+	0.127102i	−0.960672	−	0.277686i	$-0.910433\pi$
$5$	−0.103444	+	0.284210i	−0.0462615	+	0.127102i	0.914410	+	0.404788i	$0.132655\pi$
$6$		0			0
$7$	−0.478118	−	0.0843052i	−0.180712	−	0.0318644i	0.0825599	−	0.996586i	$-0.473690\pi$
$7$	−0.478118	−	0.0843052i	−0.180712	−	0.0318644i	−0.263272	+	0.964722i	$0.584802\pi$
$8$	−2.72261	+	0.766402i	−0.962589	+	0.270964i
$9$		0			0
$10$	−0.412685	+	0.112438i	−0.130503	+	0.0355559i
$11$	−0.0391221	+	0.0142393i	−0.0117958	+	0.00429331i	−0.347911	−	0.937527i	$-0.613109\pi$
$11$	−0.0391221	+	0.0142393i	−0.0117958	+	0.00429331i	0.336116	+	0.941821i	$0.390887\pi$
$12$		0			0
$13$	−3.30779	+	2.77557i	−0.917416	+	0.769803i	−0.973515	−	0.228622i	$-0.926578\pi$
$13$	−3.30779	+	2.77557i	−0.917416	+	0.769803i	0.0560994	+	0.998425i	$0.482134\pi$
$14$	−0.292776	−	0.621040i	−0.0782478	−	0.165980i
$15$		0			0
$16$	−3.10692	−	2.51933i	−0.776730	−	0.629833i
$17$	−2.14427	+	1.23800i	−0.520062	+	0.300258i	−0.736960	−	0.675936i	$-0.763739\pi$
$17$	−2.14427	+	1.23800i	−0.520062	+	0.300258i	0.216898	+	0.976194i	$0.430406\pi$
$18$		0			0
$19$	−6.55326	−	3.78353i	−1.50342	−	0.868001i	−0.999992	−	0.00396479i	$-0.998738\pi$
$19$	−6.55326	−	3.78353i	−1.50342	−	0.868001i	−0.503430	−	0.864036i	$-0.667929\pi$
$20$	−0.466628	−	0.384917i	−0.104341	−	0.0860701i
$21$		0			0
$22$	−0.0483712	−	0.0335681i	−0.0103128	−	0.00715675i
$23$	1.14066	+	6.46900i	0.237844	+	1.34888i	0.836541	+	0.547904i	$0.184574\pi$
$23$	1.14066	+	6.46900i	0.237844	+	1.34888i	−0.598697	+	0.800975i	$0.704315\pi$
$24$		0			0
$25$	3.76015	+	3.15514i	0.752030	+	0.631028i
$26$	−5.90510	−	1.55572i	−1.15809	−	0.305103i
$27$		0			0
$28$	0.478416	−	0.844947i	0.0904122	−	0.159680i
$29$	−4.51541	+	5.38126i	−0.838491	+	0.999274i	0.161432	+	0.986884i	$0.448389\pi$
$29$	−4.51541	+	5.38126i	−0.838491	+	0.999274i	−0.999923	+	0.0123907i	$0.996056\pi$
$30$		0			0
$31$	3.53661	−	0.623599i	0.635193	−	0.112002i	0.153226	−	0.988191i	$-0.451034\pi$
$31$	3.53661	−	0.623599i	0.635193	−	0.112002i	0.481967	+	0.876189i	$0.339923\pi$
$32$	0.374633	−	5.64444i	0.0662264	−	0.997805i
$33$		0			0
$34$	−3.17970	−	1.46650i	−0.545313	−	0.251502i
$35$	0.0734187	−	0.127165i	0.0124100	−	0.0214948i
$36$		0			0
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	−0.998100	−	0.0616082i	$-0.980377\pi$
$37$	−3.36015	−	5.81994i	−0.552405	−	0.956793i	0.445696	−	0.895184i	$-0.352956\pi$
$38$	−0.977440	−	10.6567i	−0.158562	−	1.72875i
$39$		0			0
$40$	0.0638189	−	0.853073i	0.0100907	−	0.134883i
$41$	4.06534	+	4.84488i	0.634899	+	0.756643i	0.983555	−	0.180608i	$-0.0578064\pi$
$41$	4.06534	+	4.84488i	0.634899	+	0.756643i	−0.348656	+	0.937251i	$0.613362\pi$
$42$		0			0
$43$	−0.827261	−	2.27288i	−0.126156	−	0.346611i	0.860495	−	0.509459i	$-0.170154\pi$
$43$	−0.827261	−	2.27288i	−0.126156	−	0.346611i	−0.986651	+	0.162848i	$0.947932\pi$
$44$	−0.000699143	−	0.0832628i	−0.000105400	−	0.0125523i
$45$		0			0
$46$	−6.54116	+	6.59631i	−0.964441	+	0.972573i
$47$	1.24905	−	7.08373i	0.182193	−	1.03327i	−0.747316	−	0.664469i	$-0.768658\pi$
$47$	1.24905	−	7.08373i	0.182193	−	1.03327i	0.929509	−	0.368799i	$-0.120231\pi$
$48$		0			0
$49$	−6.35636	−	2.31353i	−0.908051	−	0.330504i
$50$	−0.575971	+	6.91777i	−0.0814547	+	0.978320i
$51$		0			0
$52$	−3.02173	−	8.09012i	−0.419039	−	1.12190i
$53$			9.90799i			1.36097i	0.732763	+	0.680484i	$0.238230\pi$
$53$			9.90799i			1.36097i	−0.732763	+	0.680484i	$0.761770\pi$
$54$		0			0
$55$		−	0.0125918i		−	0.00169788i
$56$	1.36634	−	0.136900i	0.182585	−	0.0182941i
$57$		0			0
$58$	−9.90022	−	0.824289i	−1.29996	−	0.108235i
$59$	4.09063	+	1.48887i	0.532555	+	0.193834i	0.594279	−	0.804259i	$-0.297438\pi$
$59$	4.09063	+	1.48887i	0.532555	+	0.193834i	−0.0617238	+	0.998093i	$0.519660\pi$
$60$		0			0
$61$	−1.30827	+	7.41960i	−0.167507	+	0.949982i	0.778934	+	0.627106i	$0.215761\pi$
$61$	−1.30827	+	7.41960i	−0.167507	+	0.949982i	−0.946441	+	0.322876i	$0.895350\pi$
$62$	3.60621	+	3.57605i	0.457989	+	0.454159i
$63$		0			0
$64$	6.82526	−	4.17323i	0.853157	−	0.521654i
$65$	−0.446672	−	1.22722i	−0.0554028	−	0.152218i
$66$		0			0
$67$	−7.15980	−	8.53272i	−0.874709	−	1.04244i	−0.998741	−	0.0501590i	$-0.984027\pi$
$67$	−7.15980	−	8.53272i	−0.874709	−	1.04244i	0.124033	−	0.992278i	$-0.460417\pi$
$68$	−0.900820	−	4.86936i	−0.109241	−	0.590497i
$69$		0			0
$70$	0.206792	−	0.0189671i	0.0247163	−	0.00226700i
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	0.748200	−	0.663473i	$-0.230918\pi$
$71$	−1.68932	−	2.92598i	−0.200485	−	0.347250i	−0.948685	+	0.316223i	$0.897585\pi$
$72$		0			0
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	−0.846973	−	0.531636i	$-0.821577\pi$
$73$	0.315477	−	0.546421i	0.0369237	−	0.0639538i	0.883897	+	0.467682i	$0.154911\pi$
$74$	3.98034	−	8.63027i	0.462705	−	1.00325i
$75$		0			0
$76$	11.5113	−	9.82502i	1.32044	−	1.12701i
$77$	0.0199054	−	0.00350987i	0.00226844	−	0.000399987i
$78$		0			0
$79$	1.94606	−	2.31923i	0.218949	−	0.260934i	−0.645378	−	0.763863i	$-0.723300\pi$
$79$	1.94606	−	2.31923i	0.218949	−	0.260934i	0.864327	+	0.502930i	$0.167745\pi$
$80$	1.03741	−	0.622407i	0.115986	−	0.0695873i
$81$		0			0
$82$	−2.27865	+	8.64913i	−0.251635	+	0.955136i
$83$	4.41076	+	3.70106i	0.484143	+	0.406245i	0.851922	−	0.523669i	$-0.175437\pi$
$83$	4.41076	+	3.70106i	0.484143	+	0.406245i	−0.367778	+	0.929913i	$0.619882\pi$
$84$		0			0
$85$	−0.130039	−	0.737486i	−0.0141047	−	0.0799915i
$86$	1.95021	−	2.81023i	0.210297	−	0.303034i
$87$		0			0
$88$	0.0956014	−	0.0687513i	0.0101911	−	0.00732892i
$89$	9.00521	+	5.19916i	0.954550	+	0.551110i	0.894491	−	0.447085i	$-0.147538\pi$
$89$	9.00521	+	5.19916i	0.954550	+	0.551110i	0.0600588	+	0.998195i	$0.480871\pi$
$90$		0			0
$91$	1.81551	−	1.04819i	0.190317	−	0.109880i
$92$	−12.9567	−	2.17260i	−1.35083	−	0.226510i
$93$		0			0
$94$	9.20124	−	4.33773i	0.949035	−	0.447403i
$95$	1.75321	−	1.47112i	0.179876	−	0.150933i
$96$		0			0
$97$	3.13032	−	1.13934i	0.317836	−	0.115683i	−0.178176	−	0.983999i	$-0.557020\pi$
$97$	3.13032	−	1.13934i	0.317836	−	0.115683i	0.496012	+	0.868316i	$0.334797\pi$
$98$	−2.51468	−	9.22972i	−0.254021	−	0.932343i
$99$		0			0
$100$	−8.46030	+	4.97974i	−0.846030	+	0.497974i
$101$	16.4460	+	2.89987i	1.63644	+	0.288548i	0.914855	−	0.403782i	$-0.132304\pi$
$101$	16.4460	+	2.89987i	1.63644	+	0.288548i	0.721581	+	0.692330i	$0.243416\pi$
$102$		0			0
$103$	−5.43561	+	14.9342i	−0.535587	+	1.47151i	0.316745	+	0.948511i	$0.397410\pi$
$103$	−5.43561	+	14.9342i	−0.535587	+	1.47151i	−0.852332	+	0.523001i	$0.824812\pi$
$104$	6.87864	−	10.0919i	0.674506	−	0.989591i
$105$		0			0
$106$	−11.4441	+	8.08508i	−1.11155	+	0.785293i
$107$	1.00162			0.0968302			0.0484151	−	0.998827i	$-0.484583\pi$
$107$	1.00162			0.0968302			0.0484151	+	0.998827i	$0.484583\pi$
$108$		0			0
$109$	7.26618			0.695973			0.347987	−	0.937499i	$-0.386865\pi$
$109$	7.26618			0.695973			0.347987	+	0.937499i	$0.386865\pi$
$110$	0.0145441	−	0.0102751i	0.00138672	−	0.000979697i
$111$		0			0
$112$	1.27308	+	1.46647i	0.120295	+	0.138568i
$113$	−4.94870	+	13.5964i	−0.465534	+	1.27905i	0.455733	+	0.890116i	$0.349377\pi$
$113$	−4.94870	+	13.5964i	−0.465534	+	1.27905i	−0.921268	+	0.388929i	$0.872845\pi$
$114$		0			0
$115$	−1.95655	−	0.344992i	−0.182449	−	0.0321706i
$116$	−7.12665	−	12.1078i	−0.661693	−	1.12418i
$117$		0			0
$118$	1.61832	+	5.93979i	0.148978	+	0.546802i
$119$	1.12959	−	0.411135i	0.103549	−	0.0376887i
$120$		0			0
$121$	−8.42516	+	7.06955i	−0.765924	+	0.642686i
$122$	−9.63750	+	4.54340i	−0.872539	+	0.411340i
$123$		0			0
$124$	−1.18776	+	7.08343i	−0.106664	+	0.636111i
$125$	−2.59533	+	1.49841i	−0.232133	+	0.134022i
$126$		0			0
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	0.801200	−	0.598397i	$-0.204195\pi$
$127$	7.70348	+	4.44760i	0.683573	+	0.394661i	−0.117627	+	0.993058i	$0.537529\pi$
$128$	10.3898	+	4.47802i	0.918335	+	0.395805i
$129$		0			0
$130$	1.05300	−	1.51736i	0.0923540	−	0.133081i
$131$	−3.37461	−	19.1384i	−0.294841	−	1.67213i	−0.667848	−	0.744298i	$-0.732784\pi$
$131$	−3.37461	−	19.1384i	−0.294841	−	1.67213i	0.373007	−	0.927829i	$-0.378327\pi$
$132$		0			0
$133$	2.81427	+	2.36145i	0.244028	+	0.204764i
$134$	4.01312	−	15.2327i	0.346681	−	1.31590i
$135$		0			0
$136$	4.88922	−	5.01396i	0.419247	−	0.429943i
$137$	−9.85858	+	11.7490i	−0.842275	+	1.00378i	0.157592	+	0.987504i	$0.449627\pi$
$137$	−9.85858	+	11.7490i	−0.842275	+	1.00378i	−0.999867	+	0.0162805i	$0.994818\pi$
$138$		0			0
$139$	8.79915	−	1.55153i	0.746334	−	0.131599i	0.212468	−	0.977168i	$-0.431850\pi$
$139$	8.79915	−	1.55153i	0.746334	−	0.131599i	0.533866	+	0.845569i	$0.320739\pi$
$140$	0.190653	+	0.223375i	0.0161131	+	0.0188786i
$141$		0			0
$142$	2.00112	−	4.33888i	0.167930	−	0.364110i
$143$	0.0898857	−	0.155687i	0.00751662	−	0.0130192i
$144$		0			0
$145$	−1.06231	−	1.83998i	−0.0882203	−	0.152802i
$146$	0.888573	−	0.0815005i	0.0735388	−	0.00674503i
$147$		0			0
$148$	13.2163	−	2.44499i	1.08638	−	0.200977i
$149$	1.10684	+	1.31908i	0.0906760	+	0.108063i	0.809475	−	0.587155i	$-0.199752\pi$
$149$	1.10684	+	1.31908i	0.0906760	+	0.108063i	−0.718799	+	0.695218i	$0.755308\pi$
$150$		0			0
$151$	0.206273	+	0.566731i	0.0167863	+	0.0461199i	0.947803	−	0.318857i	$-0.103299\pi$
$151$	0.206273	+	0.566731i	0.0167863	+	0.0461199i	−0.931016	+	0.364977i	$0.881077\pi$
$152$	20.7417	+	5.27866i	1.68238	+	0.428155i
$153$		0			0
$154$	0.0202972	+	0.0201275i	0.00163560	+	0.00162192i
$155$	−0.188607	+	1.06964i	−0.0151493	+	0.0859159i
$156$		0			0
$157$	9.74784	+	3.54792i	0.777962	+	0.283155i	0.700323	−	0.713826i	$-0.253039\pi$
$157$	9.74784	+	3.54792i	0.777962	+	0.283155i	0.0776395	+	0.996981i	$0.475262\pi$
$158$	4.26682	+	0.355255i	0.339450	+	0.0282625i
$159$		0			0
$160$	1.56545	+	0.690356i	0.123760	+	0.0545775i
$161$		−	3.18911i		−	0.251337i
$162$		0			0
$163$			5.70430i			0.446795i	0.974727	+	0.223397i	$0.0717148\pi$
$163$			5.70430i			0.446795i	−0.974727	+	0.223397i	$0.928285\pi$
$164$	−11.8495	+	4.42589i	−0.925291	+	0.345604i
$165$		0			0
$166$	−0.675630	+	8.11473i	−0.0524391	+	0.629825i
$167$	−4.93392	−	1.79580i	−0.381798	−	0.138963i	0.143989	−	0.989579i	$-0.454007\pi$
$167$	−4.93392	−	1.79580i	−0.381798	−	0.138963i	−0.525787	+	0.850616i	$0.676229\pi$
$168$		0			0
$169$	0.980286	−	5.55948i	0.0754066	−	0.427652i
$170$	0.745712	−	0.752000i	0.0571935	−	0.0576758i
$171$		0			0
$172$	4.83733	−	0.0406182i	0.368843	−	0.00309711i
$173$	0.474467	+	1.30359i	0.0360730	+	0.0991099i	0.956422	−	0.291989i	$-0.0943172\pi$
$173$	0.474467	+	1.30359i	0.0360730	+	0.0991099i	−0.920349	+	0.391099i	$0.872095\pi$
$174$		0			0
$175$	−1.53180	−	1.82553i	−0.115793	−	0.137997i
$176$	0.157423	+	0.0543213i	0.0118662	+	0.00409462i
$177$		0			0
$178$	1.34316	+	14.6440i	0.100674	+	1.09761i
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	0.996994	−	0.0774732i	$-0.0246852\pi$
$179$	5.77179	+	9.99703i	0.431403	+	0.747213i	−0.565591	+	0.824686i	$0.691352\pi$
$180$		0			0
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	−0.348814	−	0.937192i	$-0.613416\pi$
$181$	8.57298	−	14.8488i	0.637225	−	1.10371i	0.986039	−	0.166514i	$-0.0532510\pi$
$182$	2.69218	+	1.24165i	0.199558	+	0.0920373i
$183$		0			0
$184$	−8.06343	−	16.7384i	−0.594444	−	1.23397i
$185$	2.00167	−	0.352948i	0.147166	−	0.0259493i
$186$		0			0
$187$	0.0662603	−	0.0789659i	0.00484543	−	0.00577456i
$188$	12.5186	+	7.08814i	0.913014	+	0.516956i
$189$		0			0
$190$	3.12985	+	0.824572i	0.227063	+	0.0598208i
$191$	12.6819	+	10.6414i	0.917630	+	0.769983i	0.973555	−	0.228452i	$-0.0733663\pi$
$191$	12.6819	+	10.6414i	0.917630	+	0.769983i	−0.0559250	+	0.998435i	$0.517811\pi$
$192$		0			0
$193$	−1.52864	−	8.66934i	−0.110034	−	0.624033i	−0.989090	−	0.147314i	$-0.952937\pi$
$193$	−1.52864	−	8.66934i	−0.110034	−	0.624033i	0.879056	−	0.476719i	$-0.158174\pi$
$194$	3.87038	+	2.68592i	0.277877	+	0.192838i
$195$		0			0
$196$	8.60869	−	10.4362i	0.614906	−	0.745439i
$197$	−10.8232	−	6.24879i	−0.771122	−	0.445208i	0.0621526	−	0.998067i	$-0.480203\pi$
$197$	−10.8232	−	6.24879i	−0.771122	−	0.445208i	−0.833275	+	0.552859i	$0.813537\pi$
$198$		0			0
$199$	3.88531	−	2.24318i	0.275422	−	0.159015i	−0.355927	−	0.934514i	$-0.615835\pi$
$199$	3.88531	−	2.24318i	0.275422	−	0.159015i	0.631349	+	0.775499i	$0.282501\pi$
$200$	−12.6555	−	5.70844i	−0.894882	−	0.403648i
$201$		0			0
$202$	10.0707	+	21.3621i	0.708573	+	1.50303i
$203$	2.61257	−	2.19221i	0.183366	−	0.153863i
$204$		0			0
$205$	−1.79750	+	0.654235i	−0.125543	+	0.0456937i
$206$	−21.6852	+	5.90821i	−1.51088	+	0.411644i
$207$		0			0
$208$	17.2696	−	0.290040i	1.19743	−	0.0201107i
$209$	0.310252	+	0.0547058i	0.0214606	+	0.00378408i
$210$		0			0
$211$	−7.67638	+	21.0907i	−0.528464	+	1.45194i	0.332415	+	0.943133i	$0.392137\pi$
$211$	−7.67638	+	21.0907i	−0.528464	+	1.45194i	−0.860879	+	0.508810i	$0.830086\pi$
$212$	−18.6772	−	6.62088i	−1.28275	−	0.454724i
$213$		0			0
$214$	0.817337	+	1.15691i	0.0558720	+	0.0790848i
$215$	0.731549			0.0498912
$216$		0			0
$217$	−1.74349			−0.118356
$218$	5.92932	+	8.39273i	0.401584	+	0.568427i
$219$		0			0
$220$	0.0237364	+	0.00841432i	0.00160031	+	0.000567293i
$221$	3.65666	−	10.0466i	0.245974	−	0.675807i
$222$		0			0
$223$	18.0384	+	3.18066i	1.20794	+	0.212993i	0.741128	−	0.671363i	$-0.234291\pi$
$223$	18.0384	+	3.18066i	1.20794	+	0.212993i	0.466813	+	0.884356i	$0.345402\pi$
$224$	−0.654974	+	2.66712i	−0.0437623	+	0.178205i
$225$		0			0
$226$	−19.7426	+	5.37896i	−1.31326	+	0.357803i
$227$	−18.4210	+	6.70470i	−1.22264	+	0.445006i	−0.871073	−	0.491154i	$-0.836575\pi$
$227$	−18.4210	+	6.70470i	−1.22264	+	0.445006i	−0.351572	+	0.936161i	$0.614353\pi$
$228$		0			0
$229$	4.34201	−	3.64338i	0.286928	−	0.240761i	−0.487951	−	0.872871i	$-0.662255\pi$
$229$	4.34201	−	3.64338i	0.286928	−	0.240761i	0.774879	+	0.632110i	$0.217811\pi$
$230$	−1.19809	−	2.54141i	−0.0789999	−	0.167575i
$231$		0			0
$232$	8.16952	−	18.1117i	0.536355	−	1.18909i
$233$	6.50499	−	3.75566i	0.426156	−	0.246041i	−0.271552	−	0.962424i	$-0.587537\pi$
$233$	6.50499	−	3.75566i	0.426156	−	0.246041i	0.697708	+	0.716383i	$0.254203\pi$
$234$		0			0
$235$	1.88406	+	1.08776i	0.122902	+	0.0709577i
$236$	−5.54012	+	6.71618i	−0.360631	+	0.437186i
$237$		0			0
$238$	1.39664	+	0.969223i	0.0905306	+	0.0628254i
$239$	1.12380	+	6.37337i	0.0726924	+	0.412259i	0.999340	+	0.0363276i	$0.0115660\pi$
$239$	1.12380	+	6.37337i	0.0726924	+	0.412259i	−0.926648	+	0.375931i	$0.877323\pi$
$240$		0			0
$241$	−0.531573	−	0.446043i	−0.0342416	−	0.0287322i	0.625506	−	0.780219i	$-0.284892\pi$
$241$	−0.531573	−	0.446043i	−0.0342416	−	0.0287322i	−0.659748	+	0.751487i	$0.729337\pi$
$242$	−15.0407	−	3.96253i	−0.966852	−	0.254721i
$243$		0			0
$244$	−13.1122	−	7.42422i	−0.839420	−	0.475287i
$245$	1.31505	−	1.56722i	0.0840156	−	0.100126i
$246$		0			0
$247$	32.1783	−	5.67389i	2.04745	−	0.361021i
$248$	−9.15088	+	4.40828i	−0.581082	+	0.279926i
$249$		0			0
$250$	−3.84856	−	1.77498i	−0.243404	−	0.112260i
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	−0.898405	−	0.439168i	$-0.855273\pi$
$251$	−1.09113	+	1.88989i	−0.0688715	+	0.119289i	0.829533	+	0.558457i	$0.188607\pi$
$252$		0			0
$253$	−0.136739	−	0.236839i	−0.00859670	−	0.0148899i
$254$	1.14900	+	12.5271i	0.0720945	+	0.786023i
$255$		0			0
$256$	3.30592	+	15.6547i	0.206620	+	0.978421i
$257$	−9.24962	−	11.0233i	−0.576975	−	0.687612i	0.396072	−	0.918220i	$-0.370373\pi$
$257$	−9.24962	−	11.0233i	−0.576975	−	0.687612i	−0.973047	+	0.230607i	$0.925929\pi$
$258$		0			0
$259$	1.11590	+	3.06590i	0.0693384	+	0.190506i
$260$	2.61187	−	0.0219314i	0.161981	−	0.00136013i
$261$		0			0
$262$	19.3518	−	19.5150i	1.19556	−	1.20564i
$263$	−1.77884	+	10.0883i	−0.109688	+	0.622073i	0.879555	+	0.475796i	$0.157840\pi$
$263$	−1.77884	+	10.0883i	−0.109688	+	0.622073i	−0.989244	+	0.146277i	$0.953271\pi$
$264$		0			0
$265$	−2.81595	−	1.02492i	−0.172982	−	0.0629604i
$266$	−0.431083	+	5.17757i	−0.0264314	+	0.317457i
$267$		0			0
$268$	20.8691	−	7.79480i	1.27479	−	0.476143i
$269$		−	3.15222i		−	0.192194i	−0.995372	−	0.0960971i	$-0.969364\pi$
$269$		−	3.15222i		−	0.192194i	0.995372	−	0.0960971i	$-0.0306359\pi$
$270$		0			0
$271$			3.33151i			0.202375i	0.994867	+	0.101188i	$0.0322642\pi$
$271$			3.33151i			0.202375i	−0.994867	+	0.101188i	$0.967736\pi$
$272$	9.78101	+	1.55578i	0.593061	+	0.0943329i
$273$		0			0
$274$	−21.6153	−	1.79969i	−1.30583	−	0.108723i
$275$	−0.192032	−	0.0698939i	−0.0115800	−	0.00421476i
$276$		0			0
$277$	0.725065	−	4.11205i	0.0435649	−	0.247069i	−0.955246	−	0.295811i	$-0.904410\pi$
$277$	0.725065	−	4.11205i	0.0435649	−	0.247069i	0.998811	+	0.0487421i	$0.0155212\pi$
$278$	8.97233	+	8.89730i	0.538124	+	0.533625i
$279$		0			0
$280$	−0.102431	+	0.402489i	−0.00612145	+	0.0240533i
$281$	−6.71308	−	18.4440i	−0.400469	−	1.10028i	−0.962054	−	0.272860i	$-0.912031\pi$
$281$	−6.71308	−	18.4440i	−0.400469	−	1.10028i	0.561585	−	0.827419i	$-0.310192\pi$
$282$		0			0
$283$	−9.89761	−	11.7955i	−0.588352	−	0.701170i	0.386937	−	0.922106i	$-0.373533\pi$
$283$	−9.89761	−	11.7955i	−0.588352	−	0.701170i	−0.975288	+	0.220936i	$0.929089\pi$
$284$	6.64452	−	1.22922i	0.394280	−	0.0729409i
$285$		0			0
$286$	0.253172	−	0.0232211i	0.0149704	−	0.00137310i
$287$	−1.53526	−	2.65916i	−0.0906238	−	0.156965i
$288$		0			0
$289$	−5.43473	+	9.41323i	−0.319690	+	0.553720i
$290$	1.25839	−	2.72847i	0.0738950	−	0.160221i
$291$		0			0
$292$	0.819226	+	0.959831i	0.0479416	+	0.0561699i
$293$	−18.3390	+	3.23366i	−1.07138	+	0.188912i	−0.681399	−	0.731913i	$-0.738628\pi$
$293$	−18.3390	+	3.23366i	−1.07138	+	0.188912i	−0.389976	+	0.920825i	$0.627517\pi$
$294$		0			0
$295$	−0.846301	+	1.00858i	−0.0492736	+	0.0587219i
$296$	13.6088	+	13.2702i	0.790995	+	0.771317i
$297$		0			0
$298$	−0.620393	+	2.35484i	−0.0359384	+	0.136412i
$299$	−21.7282	−	18.2321i	−1.25657	−	1.05439i
$300$		0			0
$301$	0.203913	+	1.15645i	0.0117534	+	0.0666566i
$302$	−0.486275	+	0.700716i	−0.0279820	+	0.0403217i
$303$		0			0
$304$	10.8285	+	28.2650i	0.621058	+	1.62111i
$305$	−1.97339	−	1.13934i	−0.112996	−	0.0652382i
$306$		0			0
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.912136	−	0.409887i	$-0.865568\pi$
$307$	−17.7533	+	10.2499i	−1.01323	+	0.584990i	−0.101096	+	0.994877i	$0.532235\pi$
$308$	−0.00668521	+	0.0398684i	−0.000380925	+	0.00227171i
$309$		0			0
$310$	−1.38939	+	0.654998i	−0.0789120	+	0.0372014i
$311$	−15.3427	+	12.8740i	−0.870002	+	0.730018i	−0.964099	−	0.265545i	$-0.914448\pi$
$311$	−15.3427	+	12.8740i	−0.870002	+	0.730018i	0.0940965	+	0.995563i	$0.470004\pi$
$312$		0			0
$313$	16.5775	−	6.03372i	0.937017	−	0.341046i	0.172030	−	0.985092i	$-0.444968\pi$
$313$	16.5775	−	6.03372i	0.937017	−	0.341046i	0.764987	+	0.644046i	$0.222745\pi$
$314$	3.85640	+	14.1543i	0.217629	+	0.798774i
$315$		0			0
$316$	3.07146	+	5.21825i	0.172783	+	0.293549i
$317$	−4.23145	−	0.746120i	−0.237662	−	0.0419063i	0.0535483	−	0.998565i	$-0.482947\pi$
$317$	−4.23145	−	0.746120i	−0.237662	−	0.0419063i	−0.291210	+	0.956659i	$0.594058\pi$
$318$		0			0
$319$	0.100027	−	0.274822i	0.00560045	−	0.0153871i
$320$	0.480042	+	2.37150i	0.0268352	+	0.132571i
$321$		0			0
$322$	3.68355	−	2.60236i	0.205276	−	0.145024i
$323$	18.7360			1.04250
$324$		0			0
$325$	−21.1951			−1.17569
$326$	−6.58869	+	4.65480i	−0.364914	+	0.257805i
$327$		0			0
$328$	−14.7815	−	10.0751i	−0.816170	−	0.556302i
$329$	−1.19439	+	3.28156i	−0.0658489	+	0.180918i
$330$		0			0
$331$	−19.8236	−	3.49544i	−1.08961	−	0.192127i	−0.400146	−	0.916451i	$-0.631041\pi$
$331$	−19.8236	−	3.49544i	−1.08961	−	0.192127i	−0.689459	+	0.724324i	$0.742152\pi$
$332$	−9.92416	+	5.84137i	−0.544659	+	0.320587i
$333$		0			0
$334$	−1.95194	−	7.16428i	−0.106805	−	0.392012i
$335$	3.16572	−	1.15223i	0.172962	−	0.0629529i
$336$		0			0
$337$	10.1185	−	8.49041i	0.551189	−	0.462502i	−0.324155	−	0.946004i	$-0.605080\pi$
$337$	10.1185	−	8.49041i	0.551189	−	0.462502i	0.875343	+	0.483502i	$0.160635\pi$
$338$	7.22135	−	3.40435i	0.392789	−	0.185172i
$339$		0			0
$340$	1.47710	+	0.247683i	0.0801072	+	0.0134325i
$341$	−0.129480	+	0.0747552i	−0.00701173	+	0.00404822i
$342$		0			0
$343$	5.78720	+	3.34124i	0.312480	+	0.180410i
$344$	3.99425	+	5.55416i	0.215356	+	0.299460i
$345$		0			0
$346$	−1.11852	+	1.61178i	−0.0601322	+	0.0866496i
$347$	3.10029	+	17.5826i	0.166433	+	0.943886i	0.947575	+	0.319533i	$0.103526\pi$
$347$	3.10029	+	17.5826i	0.166433	+	0.943886i	−0.781143	+	0.624353i	$0.785363\pi$
$348$		0			0
$349$	−10.0141	−	8.40283i	−0.536043	−	0.449793i	0.334139	−	0.942524i	$-0.391554\pi$
$349$	−10.0141	−	8.40283i	−0.536043	−	0.449793i	−0.870182	+	0.492730i	$0.835999\pi$
$350$	0.858586	−	3.25895i	0.0458933	−	0.174198i
$351$		0			0
$352$	0.0657163	+	0.226157i	0.00350269	+	0.0120542i
$353$	13.8117	−	16.4601i	0.735120	−	0.876082i	−0.260886	−	0.965370i	$-0.584015\pi$
$353$	13.8117	−	16.4601i	0.735120	−	0.876082i	0.996006	+	0.0892874i	$0.0284590\pi$
$354$		0			0
$355$	1.00634	−	0.177445i	0.0534111	−	0.00941781i
$356$	−15.8183	+	13.5011i	−0.838371	+	0.715558i
$357$		0			0
$358$	−6.83710	+	14.8244i	−0.361352	+	0.783493i
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	−0.500353	−	0.865821i	$-0.666797\pi$
$359$	9.46695	−	16.3972i	0.499647	−	0.865413i	1.00000		0.000407927i	$0.000129847\pi$
$360$		0			0
$361$	19.1302	+	33.1344i	1.00685	+	1.74392i
$362$	24.1467	−	2.21475i	1.26912	−	0.116405i
$363$		0			0
$364$	0.762706	+	4.12278i	0.0399766	+	0.216093i
$365$	0.122664	+	0.146185i	0.00642053	+	0.00765169i
$366$		0			0
$367$	8.14687	+	22.3833i	0.425263	+	1.16840i	0.948656	+	0.316309i	$0.102444\pi$
$367$	8.14687	+	22.3833i	0.425263	+	1.16840i	−0.523393	+	0.852091i	$0.675334\pi$
$368$	12.7536	−	22.9724i	0.664828	−	1.19752i
$369$		0			0
$370$	2.04106	+	2.02400i	0.106110	+	0.105223i
$371$	0.835295	−	4.73719i	0.0433664	−	0.245943i
$372$		0			0
$373$	20.3677	+	7.41323i	1.05460	+	0.383843i	0.810397	−	0.585882i	$-0.199252\pi$
$373$	20.3677	+	7.41323i	1.05460	+	0.383843i	0.244202	+	0.969724i	$0.421474\pi$
$374$	0.145278	+	0.0120958i	0.00751216	+	0.000625460i
$375$		0			0
$376$	2.02829	+	20.2435i	0.104601	+	1.04398i
$377$		−	30.3329i		−	1.56222i
$378$		0			0
$379$		−	33.6783i		−	1.72994i	−0.501825	−	0.864969i	$-0.667338\pi$
$379$		−	33.6783i		−	1.72994i	0.501825	−	0.864969i	$-0.332662\pi$
$380$	1.60159	+	4.28796i	0.0821599	+	0.219968i
$381$		0			0
$382$	−1.94259	+	23.3316i	−0.0993914	+	1.19375i
$383$	−1.41277	−	0.514205i	−0.0721889	−	0.0262746i	0.305673	−	0.952136i	$-0.401118\pi$
$383$	−1.41277	−	0.514205i	−0.0721889	−	0.0262746i	−0.377862	+	0.925862i	$0.623341\pi$
$384$		0			0
$385$	−0.00106156	+	0.00602039i	−5.41020e−5	+	0.000306828i
$386$	8.76604	−	8.83996i	0.446180	−	0.449942i
$387$		0			0
$388$	0.0559413	+	6.66219i	0.00283999	+	0.338222i
$389$	1.32077	+	3.62877i	0.0669655	+	0.183986i	0.968662	−	0.248384i	$-0.0798996\pi$
$389$	1.32077	+	3.62877i	0.0669655	+	0.183986i	−0.901696	+	0.432370i	$0.857677\pi$
$390$		0			0
$391$	−10.4545	−	12.4592i	−0.528706	−	0.630087i
$392$	19.0790	+	1.42731i	0.963635	+	0.0720901i
$393$		0			0
$394$	−1.61432	−	17.6004i	−0.0813281	−	0.886693i
$395$	0.457839	+	0.793000i	0.0230364	+	0.0399002i
$396$		0			0
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	−0.999958	−	0.00913954i	$-0.997091\pi$
$397$	−9.80431	+	16.9816i	−0.492064	+	0.852280i	0.507894	+	0.861419i	$0.330424\pi$
$398$	5.76144	+	2.65721i	0.288795	+	0.133194i
$399$		0			0
$400$	−3.73364	−	19.2758i	−0.186682	−	0.963792i
$401$	21.3630	−	3.76688i	1.06682	−	0.188109i	0.387439	−	0.921896i	$-0.373360\pi$
$401$	21.3630	−	3.76688i	1.06682	−	0.188109i	0.679380	+	0.733787i	$0.262249\pi$
$402$		0			0
$403$	−9.96751	+	11.8788i	−0.496517	+	0.591726i
$404$	−16.4562	+	29.0639i	−0.818728	+	1.44598i
$405$		0			0
$406$	4.66398	+	1.22875i	0.231470	+	0.0609817i
$407$	0.214328	+	0.179842i	0.0106238	+	0.00891446i
$408$		0			0
$409$	−1.90971	−	10.8305i	−0.0944288	−	0.535533i	−0.994921	−	0.100660i	$-0.967905\pi$
$409$	−1.90971	−	10.8305i	−0.0944288	−	0.535533i	0.900492	−	0.434873i	$-0.143207\pi$
$410$	−2.22245	−	1.54231i	−0.109759	−	0.0761694i
$411$		0			0
$412$	−24.5197	−	20.2260i	−1.20800	−	0.996466i
$413$	−1.83029	−	1.05672i	−0.0900626	−	0.0519976i
$414$		0			0
$415$	−1.50814	+	0.870727i	−0.0740319	+	0.0427423i
$416$	14.4273	+	19.7104i	0.707356	+	0.966383i
$417$		0			0
$418$	0.189983	+	0.402995i	0.00929239	+	0.0197111i
$419$	18.5516	−	15.5667i	0.906306	−	0.760481i	−0.0651068	−	0.997878i	$-0.520739\pi$
$419$	18.5516	−	15.5667i	0.906306	−	0.760481i	0.971413	+	0.237397i	$0.0762944\pi$
$420$		0			0
$421$	−34.4045	+	12.5222i	−1.67677	+	0.610296i	−0.992862	−	0.119269i	$-0.961945\pi$
$421$	−34.4045	+	12.5222i	−1.67677	+	0.610296i	−0.683912	+	0.729565i	$0.739723\pi$
$422$	−30.6247	+	8.34381i	−1.49078	+	0.406170i
$423$		0			0
$424$	−7.59351	−	26.9756i	−0.368773	−	1.31005i
$425$	−11.9688	−	2.11043i	−0.580573	−	0.102371i
$426$		0			0
$427$	1.25102	−	3.43715i	0.0605411	−	0.166335i
$428$	−0.669318	+	1.88812i	−0.0323527	+	0.0912655i
$429$		0			0
$430$	0.596956	+	0.844969i	0.0287878	+	0.0407480i
$431$	−38.5608			−1.85741			−0.928705	−	0.370820i	$-0.879077\pi$
$431$	−38.5608			−1.85741			−0.928705	+	0.370820i	$0.879077\pi$
$432$		0			0
$433$	−6.56251			−0.315374			−0.157687	−	0.987489i	$-0.550404\pi$
$433$	−6.56251			−0.315374			−0.157687	+	0.987489i	$0.550404\pi$
$434$	−1.42271	−	2.01380i	−0.0682925	−	0.0966655i
$435$		0			0
$436$	−4.85552	+	13.6972i	−0.232537	+	0.655977i
$437$	17.0006	−	46.7088i	0.813249	−	2.23438i
$438$		0			0
$439$	1.79682	+	0.316828i	0.0857577	+	0.0151214i	0.216362	−	0.976313i	$-0.430581\pi$
$439$	1.79682	+	0.316828i	0.0857577	+	0.0151214i	−0.130605	+	0.991435i	$0.541692\pi$
$440$	0.00965041	+	0.0342827i	0.000460065	+	0.00163437i
$441$		0			0
$442$	14.5881	−	3.97459i	0.693886	−	0.189052i
$443$	1.63953	−	0.596740i	0.0778964	−	0.0283520i	−0.302778	−	0.953061i	$-0.597914\pi$
$443$	1.63953	−	0.596740i	0.0778964	−	0.0283520i	0.380674	+	0.924709i	$0.375692\pi$
$444$		0			0
$445$	−2.40918	+	2.02155i	−0.114206	+	0.0958304i
$446$	11.0458	+	23.4306i	0.523036	+	1.10947i
$447$		0			0
$448$	−3.61511	+	1.41990i	−0.170798	+	0.0670837i
$449$	8.00158	−	4.61971i	0.377618	−	0.218018i	−0.299164	−	0.954202i	$-0.596708\pi$
$449$	8.00158	−	4.61971i	0.377618	−	0.218018i	0.676781	+	0.736184i	$0.263374\pi$
$450$		0			0
$451$	−0.228032	−	0.131654i	−0.0107376	−	0.00619937i
$452$	−22.3232	−	18.4142i	−1.05000	−	0.866133i
$453$		0			0
$454$	−22.7760	−	15.8059i	−1.06893	−	0.741806i
$455$	0.110101	+	0.624414i	0.00516161	+	0.0292730i
$456$		0			0
$457$	−21.1294	−	17.7297i	−0.988391	−	0.829359i	−0.00305718	−	0.999995i	$-0.500973\pi$
$457$	−21.1294	−	17.7297i	−0.988391	−	0.829359i	−0.985334	+	0.170637i	$0.945418\pi$
$458$	7.75140	+	2.04214i	0.362199	+	0.0954229i
$459$		0			0
$460$	1.95776	−	3.45767i	0.0912812	−	0.161215i
$461$	13.3282	−	15.8839i	0.620755	−	0.739787i	−0.360445	−	0.932780i	$-0.617375\pi$
$461$	13.3282	−	15.8839i	0.620755	−	0.739787i	0.981200	+	0.192994i	$0.0618197\pi$
$462$		0			0
$463$	9.44034	−	1.66459i	0.438730	−	0.0773599i	0.0500796	−	0.998745i	$-0.484053\pi$
$463$	9.44034	−	1.66459i	0.438730	−	0.0773599i	0.388650	+	0.921385i	$0.372941\pi$
$464$	27.5862	−	5.34332i	1.28066	−	0.248058i
$465$		0			0
$466$	9.64611	+	4.44885i	0.446848	+	0.206089i
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	−0.994296	−	0.106657i	$-0.965985\pi$
$467$	−8.74737	+	15.1509i	−0.404780	+	0.701099i	0.589516	+	0.807757i	$0.299319\pi$
$468$		0			0
$469$	2.70388	+	4.68326i	0.124854	+	0.216253i
$470$	0.281013	+	3.06379i	0.0129622	+	0.141322i
$471$		0			0
$472$	−12.2783	−	0.918546i	−0.565154	−	0.0422795i
$473$	0.0647284	+	0.0771403i	0.00297621	+	0.00354691i
$474$		0			0
$475$	−12.7037	−	34.9031i	−0.582885	−	1.60146i
$476$	0.0201866	+	2.40407i	0.000925251	+	0.110191i
$477$		0			0
$478$	−6.44446	+	6.49880i	−0.294763	+	0.297248i
$479$	4.54899	−	25.7986i	0.207849	−	1.17877i	−0.685045	−	0.728501i	$-0.740217\pi$
$479$	4.54899	−	25.7986i	0.207849	−	1.17877i	0.892894	−	0.450268i	$-0.148671\pi$
$480$		0			0
$481$	27.2683	+	9.92485i	1.24333	+	0.452534i
$482$	0.0814253	−	0.977967i	0.00370882	−	0.0445452i
$483$		0			0
$484$	−7.69655	−	20.6061i	−0.349843	−	0.936640i
$485$			1.00752i			0.0457493i
$486$		0			0
$487$			7.10957i			0.322166i	0.986941	+	0.161083i	$0.0514986\pi$
$487$			7.10957i			0.322166i	−0.986941	+	0.161083i	$0.948501\pi$
$488$	−2.12446	−	21.2034i	−0.0961700	−	0.959831i
$489$		0			0
$490$	2.88330	+	0.240063i	0.130254	+	0.0108449i
$491$	−18.5617	−	6.75592i	−0.837679	−	0.304890i	−0.112673	−	0.993632i	$-0.535941\pi$
$491$	−18.5617	−	6.75592i	−0.837679	−	0.304890i	−0.725007	+	0.688742i	$0.758163\pi$
$492$		0			0
$493$	3.02029	−	17.1289i	0.136027	−	0.771449i
$494$	32.8115	+	32.5372i	1.47626	+	1.46392i
$495$		0			0
$496$	−12.5590	−	6.97241i	−0.563916	−	0.313071i
$497$	0.561018	+	1.54138i	0.0251651	+	0.0691405i
$498$		0			0
$499$	−25.4073	−	30.2792i	−1.13739	−	1.35548i	−0.925750	−	0.378136i	$-0.876565\pi$
$499$	−25.4073	−	30.2792i	−1.13739	−	1.35548i	−0.211636	−	0.977349i	$-0.567879\pi$
$500$	−1.09031	−	5.89365i	−0.0487602	−	0.263572i
$501$		0			0
$502$	−3.07328	+	0.281884i	−0.137167	+	0.0125811i
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.860587	−	0.509304i	$-0.829903\pi$
$503$	−19.5426	−	33.8489i	−0.871364	−	1.50925i	−0.0107769	−	0.999942i	$-0.503430\pi$
$504$		0			0
$505$	−2.52541	+	4.37413i	−0.112379	+	0.194646i
$506$	0.161977	−	0.351203i	0.00720076	−	0.0156129i
$507$		0			0
$508$	−13.5317	+	11.5495i	−0.600374	+	0.512426i
$509$	14.5240	−	2.56097i	0.643764	−	0.113513i	0.157771	−	0.987476i	$-0.449569\pi$
$509$	14.5240	−	2.56097i	0.643764	−	0.113513i	0.485993	+	0.873963i	$0.338458\pi$
$510$		0			0
$511$	−0.196901	+	0.234658i	−0.00871040	+	0.0103807i
$512$	−15.3842	+	16.5930i	−0.679891	+	0.733314i
$513$		0			0
$514$	5.18448	−	19.6788i	0.228677	−	0.867996i
$515$	−3.68217	−	3.08970i	−0.162256	−	0.136149i
$516$		0			0
$517$	0.0520017	+	0.294916i	0.00228703	+	0.0129704i
$518$	−2.63065	+	3.79073i	−0.115584	+	0.166555i
$519$		0			0
$520$	2.15666	+	2.99892i	0.0945758	+	0.131511i
$521$	−10.1293	−	5.84816i	−0.443773	−	0.256213i	0.261424	−	0.965224i	$-0.415808\pi$
$521$	−10.1293	−	5.84816i	−0.443773	−	0.256213i	−0.705197	+	0.709012i	$0.749141\pi$
$522$		0			0
$523$	6.89969	−	3.98354i	0.301702	−	0.174188i	−0.341505	−	0.939880i	$-0.610937\pi$
$523$	6.89969	−	3.98354i	0.301702	−	0.174188i	0.643207	+	0.765692i	$0.277603\pi$
$524$	38.3320	+	6.42759i	1.67454	+	0.280791i
$525$		0			0
$526$	−13.1040	+	6.17760i	−0.571361	+	0.269356i
$527$	−6.81143	+	5.71547i	−0.296711	+	0.248970i
$528$		0			0
$529$	−18.9339	+	6.89137i	−0.823213	+	0.299625i
$530$	−1.11403	−	4.08888i	−0.0483905	−	0.177610i
$531$		0			0
$532$	−6.33207	+	3.72706i	−0.274530	+	0.161589i
$533$	−26.8946	−	4.74224i	−1.16493	−	0.205409i
$534$		0			0
$535$	−0.103611	+	0.284670i	−0.00447951	+	0.0123073i
$536$	26.0329	+	17.7440i	1.12445	+	0.766425i
$537$		0			0
$538$	3.64094	−	2.57226i	0.156972	−	0.110898i
$539$	0.281617			0.0121301
$540$		0			0
$541$	8.41220			0.361669			0.180834	−	0.983514i	$-0.442120\pi$
$541$	8.41220			0.361669			0.180834	+	0.983514i	$0.442120\pi$
$542$	−3.84803	+	2.71857i	−0.165287	+	0.116772i
$543$		0			0
$544$	6.18447	+	12.5670i	0.265157	+	0.538806i
$545$	−0.751641	+	2.06512i	−0.0321968	+	0.0884599i
$546$		0			0
$547$	−17.2159	−	3.03562i	−0.736097	−	0.129794i	−0.206983	−	0.978345i	$-0.566365\pi$
$547$	−17.2159	−	3.03562i	−0.736097	−	0.129794i	−0.529114	+	0.848551i	$0.677476\pi$
$548$	−15.5597	−	26.4351i	−0.664679	−	1.12925i
$549$		0			0
$550$	−0.0759708	−	0.278839i	−0.00323941	−	0.0118897i
$551$	49.9508	−	18.1806i	2.12798	−	0.774520i
$552$		0			0
$553$	−1.12597	+	0.944803i	−0.0478812	+	0.0401771i
$554$	5.34124	−	2.51802i	0.226928	−	0.106980i
$555$		0			0
$556$	−2.95518	+	17.6237i	−0.125328	+	0.747413i
$557$	0.688812	−	0.397686i	0.0291859	−	0.0168505i	−0.485336	−	0.874328i	$-0.661303\pi$
$557$	0.688812	−	0.397686i	0.0291859	−	0.0168505i	0.514522	+	0.857477i	$0.327969\pi$
$558$		0			0
$559$	9.04493	+	5.22209i	0.382560	+	0.220871i
$560$	−0.548477	+	0.210125i	−0.0231774	+	0.00887942i
$561$		0			0
$562$	15.8256	−	22.8045i	0.667563	−	0.961950i
$563$	−1.08802	−	6.17049i	−0.0458547	−	0.260055i	0.953259	−	0.302155i	$-0.0977062\pi$
$563$	−1.08802	−	6.17049i	−0.0458547	−	0.260055i	−0.999113	+	0.0421004i	$0.986595\pi$
$564$		0			0
$565$	−3.35233	−	2.81293i	−0.141033	−	0.118341i
$566$	5.54768	−	21.0575i	0.233187	−	0.885111i
$567$		0			0
$568$	6.84184	+	6.67163i	0.287077	+	0.279935i
$569$	3.48344	−	4.15140i	0.146033	−	0.174036i	−0.688069	−	0.725645i	$-0.741542\pi$
$569$	3.48344	−	4.15140i	0.146033	−	0.174036i	0.834103	+	0.551609i	$0.185986\pi$
$570$		0			0
$571$	−30.0214	+	5.29359i	−1.25636	+	0.221530i	−0.761913	−	0.647680i	$-0.775740\pi$
$571$	−30.0214	+	5.29359i	−1.25636	+	0.221530i	−0.494444	+	0.869209i	$0.664628\pi$
$572$	0.233414	+	0.273475i	0.00975953	+	0.0114346i
$573$		0			0
$574$	1.81863	−	3.94320i	0.0759082	−	0.164586i
$575$	−16.1215	+	27.9233i	−0.672315	+	1.16448i
$576$		0			0
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	0.591290	−	0.806459i	$-0.298619\pi$
$577$	−9.67484	−	16.7573i	−0.402769	−	0.697616i	−0.994059	+	0.108843i	$0.965286\pi$
$578$	−15.3075	+	1.40401i	−0.636708	+	0.0583993i
$579$		0			0
$580$	4.17835	−	0.772986i	0.173497	−	0.0320965i
$581$	−1.79685	−	2.14140i	−0.0745457	−	0.0888401i
$582$		0			0
$583$	−0.141083	−	0.387622i	−0.00584305	−	0.0160536i
$584$	−0.440143	+	1.72948i	−0.0182132	+	0.0715662i
$585$		0			0
$586$	−18.6999	−	18.5436i	−0.772486	−	0.766027i
$587$	−7.51168	+	42.6009i	−0.310040	+	1.75833i	0.288735	+	0.957409i	$0.406765\pi$
$587$	−7.51168	+	42.6009i	−0.310040	+	1.75833i	−0.598775	+	0.800917i	$0.704346\pi$
$588$		0			0
$589$	−25.5357	−	9.29424i	−1.05218	−	0.382962i
$590$	−1.85555	−	0.154493i	−0.0763917	−	0.00636036i
$591$		0			0
$592$	−4.22266	+	26.5474i	−0.173550	+	1.09109i
$593$			32.7916i			1.34659i	0.739375	+	0.673294i	$0.235121\pi$
$593$			32.7916i			1.34659i	−0.739375	+	0.673294i	$0.764879\pi$
$594$		0			0
$595$			0.363568i			0.0149048i
$596$	−3.22618	+	1.20501i	−0.132150	+	0.0493590i
$597$		0			0
$598$	3.32828	−	39.9746i	0.136103	−	1.63468i
$599$	35.3166	+	12.8542i	1.44300	+	0.525209i	0.940627	−	0.339443i	$-0.110238\pi$
$599$	35.3166	+	12.8542i	1.44300	+	0.525209i	0.502372	+	0.864651i	$0.332461\pi$
$600$		0			0
$601$	1.73419	−	9.83507i	0.0707390	−	0.401181i	−0.928793	−	0.370598i	$-0.879153\pi$
$601$	1.73419	−	9.83507i	0.0707390	−	0.401181i	0.999532	−	0.0305826i	$-0.00973627\pi$
$602$	−1.16935	+	1.17921i	−0.0476591	+	0.0480609i
$603$		0			0
$604$	−1.20616	+	0.0101279i	−0.0490781	+	0.000412100i
$605$	−1.13770	−	3.12581i	−0.0462542	−	0.127082i
$606$		0			0
$607$	18.6606	+	22.2388i	0.757409	+	0.902645i	0.997681	−	0.0680603i	$-0.0216810\pi$
$607$	18.6606	+	22.2388i	0.757409	+	0.902645i	−0.240272	+	0.970706i	$0.577237\pi$
$608$	−23.8110	+	35.5720i	−0.965662	+	1.44264i
$609$		0			0
$610$	−0.294337	−	3.20906i	−0.0119174	−	0.129931i
$611$	15.5298	+	26.8983i	0.628266	+	1.08819i
$612$		0			0
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	−0.996873	−	0.0790155i	$-0.974822\pi$
$613$	−10.6465	+	18.4402i	−0.430007	+	0.744794i	0.566866	+	0.823810i	$0.308156\pi$
$614$	−26.3259	−	12.1417i	−1.06243	−	0.489999i
$615$		0			0
$616$	−0.0515049	+	0.0248116i	−0.00207519	+	0.000999687i
$617$	−2.44862	+	0.431758i	−0.0985777	+	0.0173819i	−0.222719	−	0.974883i	$-0.571493\pi$
$617$	−2.44862	+	0.431758i	−0.0985777	+	0.0173819i	0.124142	+	0.992264i	$0.460382\pi$
$618$		0			0
$619$	8.57608	−	10.2206i	0.344702	−	0.410800i	−0.565643	−	0.824650i	$-0.691372\pi$
$619$	8.57608	−	10.2206i	0.344702	−	0.410800i	0.910345	+	0.413851i	$0.135816\pi$
$620$	−1.89031	−	1.07031i	−0.0759168	−	0.0429847i
$621$		0			0
$622$	−27.3899	−	7.21598i	−1.09823	−	0.289334i
$623$	−3.86724	−	3.24500i	−0.154938	−	0.130008i
$624$		0			0
$625$	4.10439	+	23.2771i	0.164176	+	0.931086i
$626$	20.4967	+	14.2241i	0.819213	+	0.568509i
$627$		0			0
$628$	−13.2019	+	16.0044i	−0.526814	+	0.638646i
$629$	14.4101	+	8.31969i	0.574570	+	0.331728i
$630$		0			0
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.335117	−	0.942176i	$-0.391224\pi$
$631$	33.1235	−	19.1238i	1.31862	−	0.761308i	0.983507	+	0.180868i	$0.0578908\pi$
$632$	−3.52092	+	7.80584i	−0.140055	+	0.310499i
$633$		0			0
$634$	−2.59114	−	5.49635i	−0.102907	−	0.218288i
$635$	−2.06093	+	1.72932i	−0.0817854	+	0.0686261i
$636$		0			0
$637$	27.4468	−	9.98983i	1.08748	−	0.395812i
$638$	0.399055	−	0.108724i	0.0157987	−	0.00430443i
$639$		0			0
$640$	−2.34745	+	2.48965i	−0.0927913	+	0.0984120i
$641$	−13.9978	−	2.46820i	−0.552881	−	0.0974879i	−0.109774	−	0.993957i	$-0.535013\pi$
$641$	−13.9978	−	2.46820i	−0.552881	−	0.0974879i	−0.443107	+	0.896469i	$0.646124\pi$
$642$		0			0
$643$	−0.217868	+	0.598587i	−0.00859187	+	0.0236060i	−0.943914	−	0.330190i	$-0.892887\pi$
$643$	−0.217868	+	0.598587i	−0.00859187	+	0.0236060i	0.935323	+	0.353796i	$0.115109\pi$
$644$	6.01167	+	2.13108i	0.236893	+	0.0839762i
$645$		0			0
$646$	15.2889	+	21.6408i	0.601532	+	0.851446i
$647$	−7.26586			−0.285650			−0.142825	−	0.989748i	$-0.545619\pi$
$647$	−7.26586			−0.285650			−0.142825	+	0.989748i	$0.545619\pi$
$648$		0			0
$649$	−0.181235			−0.00711408
$650$	−17.2955	−	24.4812i	−0.678386	−	0.960230i
$651$		0			0
$652$	−10.7530	−	3.81182i	−0.421118	−	0.149282i
$653$	−10.8936	+	29.9299i	−0.426300	+	1.17125i	0.521742	+	0.853103i	$0.325282\pi$
$653$	−10.8936	+	29.9299i	−0.426300	+	1.17125i	−0.948042	+	0.318146i	$0.896940\pi$
$654$		0			0
$655$	5.78839	+	1.02065i	0.226171	+	0.0398801i
$656$	−0.424819	−	25.2946i	−0.0165864	−	0.987588i
$657$		0			0
$658$	−4.76497	+	1.29824i	−0.185758	+	0.0506105i
$659$	−13.8732	+	5.04944i	−0.540424	+	0.196698i	−0.597787	−	0.801655i	$-0.703953\pi$
$659$	−13.8732	+	5.04944i	−0.540424	+	0.196698i	0.0573629	+	0.998353i	$0.481731\pi$
$660$		0			0
$661$	15.3510	−	12.8810i	0.597085	−	0.501014i	−0.293422	−	0.955983i	$-0.594794\pi$
$661$	15.3510	−	12.8810i	0.597085	−	0.501014i	0.890507	+	0.454969i	$0.150350\pi$
$662$	−12.1390	−	25.7494i	−0.471797	−	1.00078i
$663$		0			0
$664$	−14.8453	−	6.69616i	−0.576109	−	0.259861i
$665$	−0.962265	+	0.555564i	−0.0373150	+	0.0215438i
$666$		0			0
$667$	−39.9619	−	23.0720i	−1.54733	−	0.893352i
$668$	6.68222	−	8.10073i	0.258543	−	0.313427i
$669$		0			0
$670$	3.91414	+	2.71629i	0.151217	+	0.104940i
$671$	−0.0544673	−	0.308899i	−0.00210269	−	0.0119249i
$672$		0			0
$673$	26.6304	+	22.3456i	1.02653	+	0.861358i	0.990434	−	0.137991i	$-0.0440643\pi$
$673$	26.6304	+	22.3456i	1.02653	+	0.861358i	0.0360929	+	0.999348i	$0.488509\pi$
$674$	18.0636	+	4.75894i	0.695784	+	0.183307i
$675$		0			0
$676$	9.82490	+	5.56294i	0.377881	+	0.213959i
$677$	21.6005	−	25.7424i	0.830174	−	0.989362i	−0.169819	−	0.985475i	$-0.554318\pi$
$677$	21.6005	−	25.7424i	0.830174	−	0.989362i	0.999992	−	0.00388710i	$-0.00123731\pi$
$678$		0			0
$679$	−1.59272	+	0.280839i	−0.0611228	+	0.0107776i
$680$	0.919255	+	1.90823i	0.0352518	+	0.0731772i
$681$		0			0
$682$	−0.192003	−	0.0885530i	−0.00735217	−	0.00339087i
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	−0.528225	−	0.849104i	$-0.677142\pi$
$683$	12.3153	−	21.3308i	0.471233	−	0.816200i	0.999459	+	0.0329044i	$0.0104757\pi$
$684$		0			0
$685$	−2.31937	−	4.01726i	−0.0886185	−	0.153492i
$686$	0.863180	+	9.41096i	0.0329563	+	0.359312i
$687$		0			0
$688$	−3.15591	+	9.14581i	−0.120318	+	0.348681i
$689$	−27.5003	−	32.7736i	−1.04768	−	1.24857i
$690$		0			0
$691$	−5.02830	−	13.8151i	−0.191285	−	0.525552i	0.806561	−	0.591151i	$-0.201326\pi$
$691$	−5.02830	−	13.8151i	−0.191285	−	0.525552i	−0.997846	+	0.0655990i	$0.979104\pi$
$692$	−2.77440	+	0.0232961i	−0.105467	+	0.000885586i
$693$		0			0
$694$	−17.7788	+	17.9287i	−0.674873	+	0.680564i
$695$	−0.469259	+	2.66130i	−0.0178000	+	0.100949i
$696$		0			0
$697$	−14.7151	−	5.35587i	−0.557375	−	0.202868i
$698$	1.53394	−	18.4235i	0.0580604	−	0.697341i
$699$		0			0
$700$	4.46484	−	1.66766i	0.168755	−	0.0630315i
$701$		−	32.3443i		−	1.22163i	−0.791775	−	0.610813i	$-0.790843\pi$
$701$		−	32.3443i		−	1.22163i	0.791775	−	0.610813i	$-0.209157\pi$
$702$		0			0
$703$			50.8528i			1.91795i
$704$	−0.207595	+	0.260452i	−0.00782402	+	0.00981617i
$705$		0			0
$706$	30.2826	+	2.52132i	1.13970	+	0.0948912i
$707$	−7.61865	−	2.77296i	−0.286529	−	0.104288i
$708$		0			0
$709$	−6.81735	+	38.6631i	−0.256031	+	1.45202i	0.537381	+	0.843339i	$0.319414\pi$
$709$	−6.81735	+	38.6631i	−0.256031	+	1.45202i	−0.793412	+	0.608685i	$0.791698\pi$
$710$	1.02615	+	1.01757i	0.0385106	+	0.0381886i
$711$		0			0
$712$	−28.5024	−	7.25370i	−1.06817	−	0.271844i
$713$	8.06812	+	22.1670i	0.302153	+	0.830160i
$714$		0			0
$715$	0.0349495	+	0.0416512i	0.00130704	+	0.00155767i
$716$	−22.7019	+	4.19981i	−0.848411	+	0.156954i
$717$		0			0
$718$	26.6647	−	2.44570i	0.995116	−	0.0912728i
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	0.856893	−	0.515495i	$-0.172392\pi$
$719$	−0.482259	−	0.835298i	−0.0179852	−	0.0311514i	−0.874878	+	0.484343i	$0.839059\pi$
$720$		0			0
$721$	3.85790	−	6.68207i	0.143676	−	0.248853i
$722$	−22.6611	+	49.1344i	−0.843358	+	1.82859i
$723$		0			0
$724$	22.2622	+	26.0831i	0.827369	+	0.969372i
$725$	−33.9572	+	5.98758i	−1.26114	+	0.222373i
$726$		0			0
$727$	13.4718	−	16.0551i	0.499641	−	0.595449i	−0.456001	−	0.889979i	$-0.650719\pi$
$727$	13.4718	−	16.0551i	0.499641	−	0.595449i	0.955642	+	0.294530i	$0.0951631\pi$
$728$	−4.13960	+	4.24521i	−0.153424	+	0.157338i
$729$		0			0
$730$	−0.0687541	+	0.260972i	−0.00254470	+	0.00965899i
$731$	4.58769	+	3.84953i	0.169682	+	0.142380i
$732$		0			0
$733$	0.311702	+	1.76775i	0.0115130	+	0.0652934i	0.990023	−	0.140906i	$-0.0450016\pi$
$733$	0.311702	+	1.76775i	0.0115130	+	0.0652934i	−0.978510	+	0.206199i	$0.933890\pi$
$734$	−19.2057	+	27.6751i	−0.708895	+	1.02151i
$735$		0			0
$736$	36.9412	−	4.01487i	1.36167	−	0.147990i
$737$	0.401606	+	0.231867i	0.0147934	+	0.00854095i
$738$		0			0
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	−0.781017	−	0.624510i	$-0.785299\pi$
$739$	−17.1448	+	9.89858i	−0.630683	+	0.364125i	0.150333	+	0.988635i	$0.451965\pi$
$740$	−0.672258	+	4.00913i	−0.0247127	+	0.147378i
$741$		0			0
$742$	6.15326	−	2.90083i	0.225893	−	0.106493i
$743$	−29.6635	+	24.8906i	−1.08825	+	0.913149i	−0.996579	−	0.0826402i	$-0.973665\pi$
$743$	−29.6635	+	24.8906i	−1.08825	+	0.913149i	−0.0916695	+	0.995789i	$0.529220\pi$
$744$		0			0
$745$	−0.489392	+	0.178124i	−0.0179299	+	0.00652596i
$746$	8.05778	+	29.5748i	0.295016	+	1.08281i
$747$		0			0
$748$	0.104578	+	0.177673i	0.00382376	+	0.00649635i
$749$	−0.478893	−	0.0844417i	−0.0174984	−	0.00308543i
$750$		0			0
$751$	−7.88528	+	21.6646i	−0.287738	+	0.790553i	0.708644	+	0.705566i	$0.249307\pi$
$751$	−7.88528	+	21.6646i	−0.287738	+	0.790553i	−0.996382	+	0.0849873i	$0.972915\pi$
$752$	−21.7270	+	18.8618i	−0.792301	+	0.687820i
$753$		0			0
$754$	35.0357	−	24.7521i	1.27593	−	0.901419i
$755$	−0.182408			−0.00663851
$756$		0			0
$757$	33.3070			1.21056			0.605281	−	0.796012i	$-0.293061\pi$
$757$	33.3070			1.21056			0.605281	+	0.796012i	$0.293061\pi$
$758$	38.8998	−	27.4820i	1.41290	−	0.998192i
$759$		0			0
$760$	−3.64585	+	5.34895i	−0.132249	+	0.194027i
$761$	−5.43009	+	14.9191i	−0.196841	+	0.540815i	−0.998366	−	0.0571457i	$-0.981800\pi$
$761$	−5.43009	+	14.9191i	−0.196841	+	0.540815i	0.801525	+	0.597961i	$0.204022\pi$
$762$		0			0
$763$	−3.47409	−	0.612576i	−0.125771	−	0.0221768i
$764$	−28.5342	+	16.7952i	−1.03233	+	0.607630i
$765$		0			0
$766$	−0.558912	−	2.05140i	−0.0201943	−	0.0741201i
$767$	−17.6634	+	6.42895i	−0.637789	+	0.232136i
$768$		0			0
$769$	−16.8819	+	14.1656i	−0.608779	+	0.510826i	−0.894254	−	0.447560i	$-0.852293\pi$
$769$	−16.8819	+	14.1656i	−0.608779	+	0.510826i	0.285475	+	0.958386i	$0.407849\pi$
$770$	−0.00782004	+	0.00368659i	−0.000281815	+	0.000132856i
$771$		0			0
$772$	17.3637	+	2.91158i	0.624935	+	0.104790i
$773$	−18.9410	+	10.9356i	−0.681261	+	0.393326i	−0.800330	−	0.599560i	$-0.795342\pi$
$773$	−18.9410	+	10.9356i	−0.681261	+	0.393326i	0.119069	+	0.992886i	$0.462009\pi$
$774$		0			0
$775$	15.2657	+	8.81366i	0.548360	+	0.316596i
$776$	−7.64945	+	5.50107i	−0.274599	+	0.197477i
$777$		0			0
$778$	−3.11361	+	4.48667i	−0.111628	+	0.160855i
$779$	−8.31048	−	47.1311i	−0.297754	−	1.68865i
$780$		0			0
$781$	0.107754	+	0.0904159i	0.00385572	+	0.00323534i
$782$	5.85981	−	22.2422i	0.209546	−	0.795380i
$783$		0			0
$784$	13.9202	+	23.2017i	0.497149	+	0.828633i
$785$	−2.01671	+	2.40342i	−0.0719794	+	0.0857817i
$786$		0			0
$787$	−3.32977	+	0.587128i	−0.118693	+	0.0209288i	−0.232679	−	0.972554i	$-0.574749\pi$
$787$	−3.32977	+	0.587128i	−0.118693	+	0.0209288i	0.113986	+	0.993482i	$0.463638\pi$
$788$	19.0118	−	16.2268i	0.677268	−	0.578055i
$789$		0			0
$790$	−0.542343	+	1.17592i	−0.0192957	+	0.0418375i
$791$	3.51231	−	6.08351i	0.124884	−	0.216305i
$792$		0			0
$793$	−16.2661	−	28.1737i	−0.577625	−	1.00048i
$794$	−27.6149	+	2.53285i	−0.980014	+	0.0898876i
$795$		0			0
$796$	1.63224	+	8.82302i	0.0578532	+	0.312724i
$797$	30.7576	+	36.6554i	1.08949	+	1.29840i	0.951392	+	0.307984i	$0.0996543\pi$
$797$	30.7576	+	36.6554i	1.08949	+	1.29840i	0.138098	+	0.990419i	$0.455901\pi$
$798$		0			0
$799$	6.09132	+	16.7358i	0.215495	+	0.592069i
$800$	19.2177	−	20.0419i	0.679447	−	0.708588i
$801$		0			0
$802$	21.7835	+	21.6013i	0.769201	+	0.762769i
$803$	−0.00456146	+	0.0258693i	−0.000160970	+	0.000912908i
$804$		0			0
$805$	0.906376	+	0.329894i	0.0319455	+	0.0116272i
$806$	−21.8542	−	1.81957i	−0.769780	−	0.0640917i
$807$		0			0
$808$	−46.9985	+	4.70900i	−1.65340	+	0.165662i
$809$			17.3637i			0.610473i	0.952277	+	0.305237i	$0.0987356\pi$
$809$			17.3637i			0.610473i	−0.952277	+	0.305237i	$0.901264\pi$
$810$		0			0
$811$			13.7618i			0.483242i	0.970371	+	0.241621i	$0.0776791\pi$
$811$			13.7618i			0.483242i	−0.970371	+	0.241621i	$0.922321\pi$
$812$	2.38663	+	6.38977i	0.0837544	+	0.224237i
$813$		0			0
$814$	−0.0328303	+	0.394312i	−0.00115070	+	0.0138206i
$815$	−1.62122	−	0.590074i	−0.0567887	−	0.0206694i
$816$		0			0
$817$	−3.17825	+	18.0247i	−0.111193	+	0.630606i
$818$	10.9513	−	11.0436i	0.382903	−	0.386131i
$819$		0			0
$820$	−0.0321227	−	3.82557i	−0.00112177	−	0.133595i
$821$	9.12358	+	25.0668i	0.318415	+	0.874839i	0.990885	+	0.134714i	$0.0430114\pi$
$821$	9.12358	+	25.0668i	0.318415	+	0.874839i	−0.672469	+	0.740125i	$0.734766\pi$
$822$		0			0
$823$	28.3560	+	33.7934i	0.988430	+	1.17796i	0.984035	+	0.177974i	$0.0569543\pi$
$823$	28.3560	+	33.7934i	0.988430	+	1.17796i	0.00439434	+	0.999990i	$0.498601\pi$
$824$	3.35346	−	44.8260i	0.116823	−	1.56159i
$825$		0			0
$826$	−0.272993	−	2.97635i	−0.00949865	−	0.103561i
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	0.947611	−	0.319426i	$-0.103490\pi$
$827$	5.67028	+	9.82121i	0.197175	+	0.341517i	−0.750436	+	0.660943i	$0.770157\pi$
$828$		0			0
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	−0.495238	−	0.868757i	$-0.664919\pi$
$829$	14.5329	−	25.1717i	0.504747	−	0.874248i	0.999985	−	0.00549015i	$-0.00174758\pi$
$830$	−2.23639	−	1.03144i	−0.0776264	−	0.0358018i
$831$		0			0
$832$	−10.9934	+	32.7481i	−0.381129	+	1.13534i
$833$	16.4939	−	2.90832i	0.571480	−	0.100767i
$834$		0			0
$835$	1.02077	−	1.21650i	0.0353251	−	0.0420988i
$836$	−0.310446	+	0.548289i	−0.0107370	+	0.0189630i
$837$		0			0
$838$	33.1185	+	8.72523i	1.14406	+	0.301408i
$839$	9.01496	+	7.56445i	0.311231	+	0.261154i	0.785001	−	0.619495i	$-0.212663\pi$
$839$	9.01496	+	7.56445i	0.311231	+	0.261154i	−0.473770	+	0.880649i	$0.657107\pi$
$840$		0			0
$841$	−3.53320	−	20.0378i	−0.121834	−	0.690957i
$842$	−42.5383	−	29.5203i	−1.46597	−	1.01734i
$843$		0			0
$844$	−34.6276	−	28.5640i	−1.19193	−	0.983214i
$845$	1.47865	+	0.853700i	0.0508672	+	0.0293682i
$846$		0			0
$847$	4.62422	−	2.66980i	0.158890	−	0.0917353i
$848$	24.9615	−	30.7834i	0.857183	−	1.05710i
$849$		0			0
$850$	−7.32913	−	15.5466i	−0.251387	−	0.533245i
$851$	33.8164	−	28.3753i	1.15921	−	0.972694i
$852$		0			0
$853$	41.0887	−	14.9551i	1.40685	−	0.512052i	0.476646	−	0.879095i	$-0.341852\pi$
$853$	41.0887	−	14.9551i	1.40685	−	0.512052i	0.930204	+	0.367044i	$0.119630\pi$
$854$	4.99090	−	1.35979i	0.170785	−	0.0465311i
$855$		0			0
$856$	−2.72702	+	0.767643i	−0.0932077	+	0.0262375i
$857$	4.01547	+	0.708036i	0.137166	+	0.0241860i	0.241810	−	0.970324i	$-0.422259\pi$
$857$	4.01547	+	0.708036i	0.137166	+	0.0241860i	−0.104644	+	0.994510i	$0.533370\pi$
$858$		0			0
$859$	13.3102	−	36.5694i	0.454137	−	1.24773i	−0.475650	−	0.879634i	$-0.657787\pi$
$859$	13.3102	−	36.5694i	0.454137	−	1.24773i	0.929787	−	0.368097i	$-0.119991\pi$
$860$	−0.488847	+	1.37902i	−0.0166696	+	0.0470241i
$861$		0			0
$862$	−31.4663	−	44.5393i	−1.07174	−	1.51701i
$863$	48.5663			1.65322			0.826608	−	0.562778i	$-0.190268\pi$
$863$	48.5663			1.65322			0.826608	+	0.562778i	$0.190268\pi$
$864$		0			0
$865$	−0.419573			−0.0142659
$866$	−5.35512	−	7.57997i	−0.181974	−	0.257578i
$867$		0			0
$868$	1.16506	−	3.28659i	0.0395448	−	0.111554i
$869$	−0.0431100	+	0.118444i	−0.00146241	+	0.00401793i
$870$		0			0
$871$	47.3662	+	8.35194i	1.60494	+	0.282995i
$872$	−19.7830	+	5.56881i	−0.669937	+	0.188584i
$873$		0			0
$874$	67.8233	−	18.4787i	2.29416	−	0.625052i
$875$	1.36720	−	0.497620i	0.0462198	−	0.0168226i
$876$		0			0
$877$	−13.0367	+	10.9391i	−0.440219	+	0.369387i	−0.835791	−	0.549047i	$-0.814991\pi$
$877$	−13.0367	+	10.9391i	−0.440219	+	0.369387i	0.395573	+	0.918435i	$0.370546\pi$
$878$	1.10029	+	2.33394i	0.0371329	+	0.0787667i
$879$		0			0
$880$	−0.0317230	+	0.0391219i	−0.00106938	+	0.00131880i
$881$	−2.59611	+	1.49886i	−0.0874651	+	0.0504980i	−0.543095	−	0.839672i	$-0.682748\pi$
$881$	−2.59611	+	1.49886i	−0.0874651	+	0.0504980i	0.455630	+	0.890169i	$0.349414\pi$
$882$		0			0
$883$	−17.0858	−	9.86450i	−0.574984	−	0.331967i	0.184154	−	0.982897i	$-0.441046\pi$
$883$	−17.0858	−	9.86450i	−0.574984	−	0.331967i	−0.759137	+	0.650931i	$0.774379\pi$
$884$	16.4950	+	13.6065i	0.554785	+	0.457637i
$885$		0			0
$886$	2.02714	+	1.40677i	0.0681031	+	0.0472615i
$887$	8.08090	+	45.8290i	0.271330	+	1.53879i	0.750383	+	0.661003i	$0.229869\pi$
$887$	8.08090	+	45.8290i	0.271330	+	1.53879i	−0.479053	+	0.877786i	$0.659020\pi$
$888$		0			0
$889$	−3.30822	−	2.77592i	−0.110954	−	0.0931015i
$890$	−4.30090	−	1.13309i	−0.144166	−	0.0379813i
$891$		0			0
$892$	−18.0497	+	31.8781i	−0.604347	+	1.06736i
$893$	−34.9869	+	41.6957i	−1.17079	+	1.39529i
$894$		0			0
$895$	−3.43831	+	0.606266i	−0.114930	+	0.0202652i
$896$	−4.59002	−	3.01694i	−0.153342	−	0.100789i
$897$		0			0
$898$	11.8654	+	5.47238i	0.395952	+	0.182616i
$899$	−12.6135	+	21.8472i	−0.420683	+	0.728645i
$900$		0			0
$901$	−12.2661	−	21.2454i	−0.408642	−	0.707788i
$902$	−0.0340117	−	0.370818i	−0.00113247	−	0.0123469i
$903$		0			0
$904$	3.05306	−	40.8105i	0.101543	−	1.35734i
$905$	3.33336	+	3.97254i	0.110805	+	0.132052i
$906$		0			0
$907$	11.8969	+	32.6863i	0.395028	+	1.08533i	0.964675	+	0.263442i	$0.0848578\pi$
$907$	11.8969	+	32.6863i	0.395028	+	1.08533i	−0.569647	+	0.821890i	$0.692920\pi$
$908$	−0.329198	−	39.2051i	−0.0109248	−	1.30107i
$909$		0			0
$910$	−0.631379	+	0.636702i	−0.0209300	+	0.0211065i
$911$	−5.19680	+	29.4725i	−0.172178	+	0.976468i	0.769174	+	0.639040i	$0.220668\pi$
$911$	−5.19680	+	29.4725i	−0.172178	+	0.976468i	−0.941351	+	0.337428i	$0.890443\pi$
$912$		0			0
$913$	−0.225259	−	0.0819874i	−0.00745497	−	0.00271339i
$914$	3.23655	−	38.8730i	0.107056	−	1.28580i
$915$		0			0
$916$	3.96651	+	10.6196i	0.131057	+	0.350881i
$917$			9.43490i			0.311568i
$918$		0			0
$919$		−	52.7647i		−	1.74055i	−0.492569	−	0.870273i	$-0.663942\pi$
$919$		−	52.7647i		−	1.74055i	0.492569	−	0.870273i	$-0.336058\pi$
$920$	5.59132	−	0.560220i	0.184340	−	0.0184699i
$921$		0			0
$922$	29.2225	+	2.43306i	0.962393	+	0.0801286i
$923$	13.7092	+	4.98973i	0.451242	+	0.164239i
$924$		0			0
$925$	5.72808	−	32.4856i	0.188338	−	1.06812i
$926$	9.62614	+	9.54565i	0.316334	+	0.313689i
$927$		0			0
$928$	28.6825	+	27.5029i	0.941550	+	0.902828i
$929$	19.0206	+	52.2588i	0.624047	+	1.71455i	0.696858	+	0.717209i	$0.254581\pi$
$929$	19.0206	+	52.2588i	0.624047	+	1.71455i	−0.0728110	+	0.997346i	$0.523197\pi$
$930$		0			0
$931$	32.9016	+	39.2106i	1.07831	+	1.28508i
$932$	2.73278	+	14.7720i	0.0895153	+	0.483872i
$933$		0			0
$934$	−24.6379	+	2.25980i	−0.806176	+	0.0739430i
$935$	0.0155887	+	0.0270003i	0.000509803	+	0.000883005i
$936$		0			0
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	−0.677715	−	0.735325i	$-0.737029\pi$
$937$	9.12048	−	15.7971i	0.297953	−	0.516070i	0.975667	+	0.219255i	$0.0703628\pi$
$938$	−3.20294	+	6.94470i	−0.104580	+	0.226753i
$939$		0			0
$940$	−3.30949	+	2.82468i	−0.107944	+	0.0921310i
$941$	−17.1627	+	3.02624i	−0.559487	+	0.0986527i	−0.446239	−	0.894914i	$-0.647237\pi$
$941$	−17.1627	+	3.02624i	−0.559487	+	0.0986527i	−0.113249	+	0.993567i	$0.536126\pi$
$942$		0			0
$943$	−26.7044	+	31.8250i	−0.869613	+	1.03636i
$944$	−8.95832	−	14.9315i	−0.291568	−	0.485978i
$945$		0			0
$946$	−0.0362807	+	0.137712i	−0.00117959	+	0.00447739i
$947$	−32.9582	−	27.6552i	−1.07100	−	0.898673i	−0.0758544	−	0.997119i	$-0.524168\pi$
$947$	−32.9582	−	27.6552i	−1.07100	−	0.898673i	−0.995142	+	0.0984459i	$0.968613\pi$
$948$		0			0
$949$	0.473098	+	2.68307i	0.0153574	+	0.0870962i
$950$	29.9481	−	43.1547i	0.971643	−	1.40012i
$951$		0			0
$952$	−2.76033	+	1.98508i	−0.0894628	+	0.0643368i
$953$	−17.5809	−	10.1503i	−0.569502	−	0.328802i	0.187449	−	0.982274i	$-0.439978\pi$
$953$	−17.5809	−	10.1503i	−0.569502	−	0.328802i	−0.756950	+	0.653472i	$0.773312\pi$
$954$		0			0
$955$	−4.33625	+	2.50353i	−0.140318	+	0.0810124i
$956$	−12.7652	−	2.14049i	−0.412855	−	0.0692283i
$957$		0			0
$958$	33.5105	−	15.7978i	1.08267	−	0.510404i
$959$	5.70407	−	4.78628i	0.184194	−	0.154557i
$960$		0			0
$961$	−17.0118	+	6.19178i	−0.548767	+	0.199735i
$962$	10.7878	+	39.5948i	0.347811	+	1.27659i
$963$		0			0
$964$	1.19604	−	0.703987i	0.0385217	−	0.0226739i
$965$	2.62204	+	0.462336i	0.0844064	+	0.0148831i
$966$		0			0
$967$	15.9777	−	43.8984i	0.513808	−	1.41168i	−0.363430	−	0.931621i	$-0.618394\pi$
$967$	15.9777	−	43.8984i	0.513808	−	1.41168i	0.877238	−	0.480055i	$-0.159383\pi$
$968$	17.5203	−	25.7047i	0.563125	−	0.826181i
$969$		0			0
$970$	−1.16373	+	0.822156i	−0.0373652	+	0.0263978i
$971$	29.3788			0.942809			0.471405	−	0.881917i	$-0.343747\pi$
$971$	29.3788			0.942809			0.471405	+	0.881917i	$0.343747\pi$
$972$		0			0
$973$	−4.33784			−0.139065
$974$	−8.21184	+	5.80153i	−0.263124	+	0.185893i
$975$		0			0
$976$	22.7571	−	19.7561i	0.728438	−	0.632378i
$977$	−6.38707	+	17.5483i	−0.204341	+	0.561421i	−0.998956	−	0.0456927i	$-0.985451\pi$
$977$	−6.38707	+	17.5483i	−0.204341	+	0.561421i	0.794615	+	0.607114i	$0.207673\pi$
$978$		0			0
$979$	−0.426335	−	0.0751744i	−0.0136257	−	0.00240258i
$980$	2.07554	+	3.52623i	0.0663007	+	0.112641i
$981$		0			0
$982$	−7.34331	−	26.9525i	−0.234335	−	0.860089i
$983$	24.5887	−	8.94954i	0.784257	−	0.285446i	0.0813102	−	0.996689i	$-0.474090\pi$
$983$	24.5887	−	8.94954i	0.784257	−	0.285446i	0.702946	+	0.711243i	$0.251867\pi$
$984$		0			0
$985$	2.89556	−	2.42966i	0.0922602	−	0.0774155i
$986$	22.2492	−	10.4889i	0.708560	−	0.334035i
$987$		0			0
$988$	−10.8070	+	64.4495i	−0.343817	+	2.05041i
$989$	13.7596	−	7.94413i	0.437531	−	0.252609i
$990$		0			0
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	0.847932	−	0.530105i	$-0.177847\pi$
$991$	25.5875	+	14.7730i	0.812815	+	0.469279i	−0.0351178	+	0.999383i	$0.511181\pi$
$992$	−2.19493	−	20.1958i	−0.0696892	−	0.641216i
$993$		0			0
$994$	−1.32256	+	1.90579i	−0.0419491	+	0.0604481i
$995$	0.235623	+	1.33629i	0.00746975	+	0.0423631i
$996$		0			0
$997$	30.3335	+	25.4528i	0.960670	+	0.806098i	0.981062	−	0.193694i	$-0.0620469\pi$
$997$	30.3335	+	25.4528i	0.960670	+	0.806098i	−0.0203917	+	0.999792i	$0.506491\pi$
$998$	14.2410	−	54.0548i	0.450790	−	1.71107i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	972.2.l.d.107.12		96
3.2	odd	2		972.2.l.a.107.5		96
4.3	odd	2	inner	972.2.l.d.107.3		96
9.2	odd	6		972.2.l.b.755.7		96
9.4	even	3		108.2.l.a.47.1	yes	96
9.5	odd	6		324.2.l.a.143.16		96
9.7	even	3		972.2.l.c.755.10		96
12.11	even	2		972.2.l.a.107.14		96
27.4	even	9		972.2.l.b.215.9		96
27.5	odd	18	inner	972.2.l.d.863.3		96
27.13	even	9		324.2.l.a.179.3		96
27.14	odd	18		108.2.l.a.23.14	yes	96
27.22	even	9		972.2.l.a.863.14		96
27.23	odd	18		972.2.l.c.215.8		96
36.7	odd	6		972.2.l.c.755.8		96
36.11	even	6		972.2.l.b.755.9		96
36.23	even	6		324.2.l.a.143.3		96
36.31	odd	6		108.2.l.a.47.14	yes	96
108.23	even	18		972.2.l.c.215.10		96
108.31	odd	18		972.2.l.b.215.7		96
108.59	even	18	inner	972.2.l.d.863.12		96
108.67	odd	18		324.2.l.a.179.16		96
108.95	even	18		108.2.l.a.23.1	✓	96
108.103	odd	18		972.2.l.a.863.5		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
108.2.l.a.23.1	✓	96	108.95	even	18
108.2.l.a.23.14	yes	96	27.14	odd	18
108.2.l.a.47.1	yes	96	9.4	even	3
108.2.l.a.47.14	yes	96	36.31	odd	6
324.2.l.a.143.3		96	36.23	even	6
324.2.l.a.143.16		96	9.5	odd	6
324.2.l.a.179.3		96	27.13	even	9
324.2.l.a.179.16		96	108.67	odd	18
972.2.l.a.107.5		96	3.2	odd	2
972.2.l.a.107.14		96	12.11	even	2
972.2.l.a.863.5		96	108.103	odd	18
972.2.l.a.863.14		96	27.22	even	9
972.2.l.b.215.7		96	108.31	odd	18
972.2.l.b.215.9		96	27.4	even	9
972.2.l.b.755.7		96	9.2	odd	6
972.2.l.b.755.9		96	36.11	even	6
972.2.l.c.215.8		96	27.23	odd	18
972.2.l.c.215.10		96	108.23	even	18
972.2.l.c.755.8		96	36.7	odd	6
972.2.l.c.755.10		96	9.7	even	3
972.2.l.d.107.3		96	4.3	odd	2	inner
972.2.l.d.107.12		96	1.1	even	1	trivial
972.2.l.d.863.3		96	27.5	odd	18	inner
972.2.l.d.863.12		96	108.59	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 972 = 2^{2} \cdot 3^{5} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	972.l (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.816016 + 1.15504i) q^{2} +(-0.668236 + 1.88506i) q^{4} +(-0.103444 + 0.284210i) q^{5} +(-0.478118 - 0.0843052i) q^{7} +(-2.72261 + 0.766402i) q^{8} +(-0.412685 + 0.112438i) q^{10} +(-0.0391221 + 0.0142393i) q^{11} +(-3.30779 + 2.77557i) q^{13} +(-0.292776 - 0.621040i) q^{14} +(-3.10692 - 2.51933i) q^{16} +(-2.14427 + 1.23800i) q^{17} +(-6.55326 - 3.78353i) q^{19} +(-0.466628 - 0.384917i) q^{20} +(-0.0483712 - 0.0335681i) q^{22} +(1.14066 + 6.46900i) q^{23} +(3.76015 + 3.15514i) q^{25} +(-5.90510 - 1.55572i) q^{26} +(0.478416 - 0.844947i) q^{28} +(-4.51541 + 5.38126i) q^{29} +(3.53661 - 0.623599i) q^{31} +(0.374633 - 5.64444i) q^{32} +(-3.17970 - 1.46650i) q^{34} +(0.0734187 - 0.127165i) q^{35} +(-3.36015 - 5.81994i) q^{37} +(-0.977440 - 10.6567i) q^{38} +(0.0638189 - 0.853073i) q^{40} +(4.06534 + 4.84488i) q^{41} +(-0.827261 - 2.27288i) q^{43} +(-0.000699143 - 0.0832628i) q^{44} +(-6.54116 + 6.59631i) q^{46} +(1.24905 - 7.08373i) q^{47} +(-6.35636 - 2.31353i) q^{49} +(-0.575971 + 6.91777i) q^{50} +(-3.02173 - 8.09012i) q^{52} +9.90799i q^{53} -0.0125918i q^{55} +(1.36634 - 0.136900i) q^{56} +(-9.90022 - 0.824289i) q^{58} +(4.09063 + 1.48887i) q^{59} +(-1.30827 + 7.41960i) q^{61} +(3.60621 + 3.57605i) q^{62} +(6.82526 - 4.17323i) q^{64} +(-0.446672 - 1.22722i) q^{65} +(-7.15980 - 8.53272i) q^{67} +(-0.900820 - 4.86936i) q^{68} +(0.206792 - 0.0189671i) q^{70} +(-1.68932 - 2.92598i) q^{71} +(0.315477 - 0.546421i) q^{73} +(3.98034 - 8.63027i) q^{74} +(11.5113 - 9.82502i) q^{76} +(0.0199054 - 0.00350987i) q^{77} +(1.94606 - 2.31923i) q^{79} +(1.03741 - 0.622407i) q^{80} +(-2.27865 + 8.64913i) q^{82} +(4.41076 + 3.70106i) q^{83} +(-0.130039 - 0.737486i) q^{85} +(1.95021 - 2.81023i) q^{86} +(0.0956014 - 0.0687513i) q^{88} +(9.00521 + 5.19916i) q^{89} +(1.81551 - 1.04819i) q^{91} +(-12.9567 - 2.17260i) q^{92} +(9.20124 - 4.33773i) q^{94} +(1.75321 - 1.47112i) q^{95} +(3.13032 - 1.13934i) q^{97} +(-2.51468 - 9.22972i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 3 q^{2} + 3 q^{4} + 6 q^{5} - 9 q^{8} - 3 q^{10} + 6 q^{13} + 33 q^{14} + 3 q^{16} - 18 q^{17} - 18 q^{20} + 3 q^{22} + 6 q^{25} - 12 q^{28} + 30 q^{29} + 33 q^{32} + 15 q^{34} - 6 q^{37} - 63 q^{38}+ \cdots - 180 q^{98}+O(q^{100}) \) 96 * q + 3 * q^2 + 3 * q^4 + 6 * q^5 - 9 * q^8 - 3 * q^10 + 6 * q^13 + 33 * q^14 + 3 * q^16 - 18 * q^17 - 18 * q^20 + 3 * q^22 + 6 * q^25 - 12 * q^28 + 30 * q^29 + 33 * q^32 + 15 * q^34 - 6 * q^37 - 63 * q^38 + 33 * q^40 - 24 * q^41 + 63 * q^44 - 3 * q^46 + 6 * q^49 - 21 * q^50 + 57 * q^52 - 18 * q^56 + 57 * q^58 + 6 * q^61 + 90 * q^62 - 3 * q^64 + 30 * q^65 - 102 * q^68 + 51 * q^70 - 6 * q^73 + 75 * q^74 + 27 * q^76 - 42 * q^77 - 12 * q^82 - 24 * q^85 - 111 * q^86 + 27 * q^88 + 147 * q^92 + 30 * q^94 - 12 * q^97 - 180 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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