LMFDB - Embedded newform 297.2.n.b.91.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(37,297)] 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("297.37"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			91.3
Character	$\chi$	$=$	297.91
Dual form			297.2.n.b.235.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31425 - 0.585142i) q^{2} +(0.0466010 + 0.0517556i) q^{4} +(3.18694 - 1.41892i) q^{5} +(0.330459 - 0.0702413i) q^{7} +(0.858159 + 2.64114i) q^{8} -5.01870 q^{10} +(3.01538 + 1.38112i) q^{11} +(-0.120893 - 1.15022i) q^{13} +(-0.475408 - 0.101051i) q^{14} +(0.432166 - 4.11179i) q^{16} +(-3.32650 - 2.41684i) q^{17} +(1.38230 + 4.25428i) q^{19} +(0.221951 + 0.0988191i) q^{20} +(-3.15481 - 3.57956i) q^{22} +(2.64122 - 4.57472i) q^{23} +(4.79760 - 5.32827i) q^{25} +(-0.514156 + 1.58241i) q^{26} +(0.0190351 + 0.0138298i) q^{28} +(5.16281 - 1.09739i) q^{29} +(-0.591027 - 5.62325i) q^{31} +(-0.196895 + 0.341031i) q^{32} +(2.95766 + 5.12281i) q^{34} +(0.953487 - 0.692749i) q^{35} +(1.10852 - 3.41166i) q^{37} +(0.672671 - 6.40003i) q^{38} +(6.48246 + 7.19950i) q^{40} +(-10.9211 - 2.32135i) q^{41} +(0.753935 + 1.30585i) q^{43} +(0.0690391 + 0.220424i) q^{44} +(-6.14808 + 4.46684i) q^{46} +(-5.90260 + 6.55551i) q^{47} +(-6.29055 + 2.80073i) q^{49} +(-9.42304 + 4.19541i) q^{50} +(0.0538964 - 0.0598580i) q^{52} +(1.63163 - 1.18545i) q^{53} +(11.5695 + 0.122962i) q^{55} +(0.469104 + 0.812512i) q^{56} +(-7.42735 - 1.57873i) q^{58} +(7.72787 + 8.58266i) q^{59} +(-0.823304 + 7.83322i) q^{61} +(-2.51364 + 7.73619i) q^{62} +(-6.23134 + 4.52733i) q^{64} +(-2.01734 - 3.49413i) q^{65} +(2.09211 - 3.62364i) q^{67} +(-0.0299329 - 0.284792i) q^{68} +(-1.65848 + 0.352520i) q^{70} +(1.95860 + 1.42300i) q^{71} +(-1.04183 + 3.20643i) q^{73} +(-3.45317 + 3.83514i) q^{74} +(-0.155767 + 0.269796i) q^{76} +(1.09347 + 0.244599i) q^{77} +(7.79960 + 3.47260i) q^{79} +(-4.45700 - 13.7172i) q^{80} +(12.9947 + 9.44124i) q^{82} +(-1.18499 + 11.2744i) q^{83} +(-14.0306 - 2.98231i) q^{85} +(-0.226749 - 2.15738i) q^{86} +(-1.06005 + 9.14926i) q^{88} +3.45994 q^{89} +(-0.120743 - 0.371608i) q^{91} +(0.359851 - 0.0764886i) q^{92} +(11.5934 - 5.16171i) q^{94} +(10.4418 + 11.5968i) q^{95} +(-11.9111 - 5.30317i) q^{97} +9.90618 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.31425	−	0.585142i	−0.929315	−	0.413758i	−0.114464	−	0.993427i	$-0.536515\pi$
$2$	−1.31425	−	0.585142i	−0.929315	−	0.413758i	−0.814852	+	0.579670i	$0.803182\pi$
$3$		0			0
$3$		0			0
$4$	0.0466010	+	0.0517556i	0.0233005	+	0.0258778i
$5$	3.18694	−	1.41892i	1.42524	−	0.634559i	0.458124	−	0.888888i	$-0.348521\pi$
$5$	3.18694	−	1.41892i	1.42524	−	0.634559i	0.967118	+	0.254329i	$0.0818547\pi$
$6$		0			0
$7$	0.330459	−	0.0702413i	0.124902	−	0.0265487i	−0.145037	−	0.989426i	$-0.546330\pi$
$7$	0.330459	−	0.0702413i	0.124902	−	0.0265487i	0.269938	+	0.962878i	$0.412997\pi$
$8$	0.858159	+	2.64114i	0.303405	+	0.933784i
$9$		0			0
$10$	−5.01870			−1.58705
$11$	3.01538	+	1.38112i	0.909171	+	0.416422i
$11$	3.01538	+	1.38112i	0.909171	+	0.416422i
$12$		0			0
$13$	−0.120893	−	1.15022i	−0.0335296	−	0.319013i	−0.998412	−	0.0563310i	$-0.982060\pi$
$13$	−0.120893	−	1.15022i	−0.0335296	−	0.319013i	0.964883	−	0.262682i	$-0.0846069\pi$
$14$	−0.475408	−	0.101051i	−0.127058	−	0.0270070i
$15$		0			0
$16$	0.432166	−	4.11179i	0.108042	−	1.02795i
$17$	−3.32650	−	2.41684i	−0.806795	−	0.586171i	0.106105	−	0.994355i	$-0.466162\pi$
$17$	−3.32650	−	2.41684i	−0.806795	−	0.586171i	−0.912900	+	0.408184i	$0.866162\pi$
$18$		0			0
$19$	1.38230	+	4.25428i	0.317121	+	0.976000i	0.974872	+	0.222764i	$0.0715080\pi$
$19$	1.38230	+	4.25428i	0.317121	+	0.976000i	−0.657751	+	0.753236i	$0.728492\pi$
$20$	0.221951	+	0.0988191i	0.0496298	+	0.0220966i
$21$		0			0
$22$	−3.15481	−	3.57956i	−0.672609	−	0.763164i
$23$	2.64122	−	4.57472i	0.550731	−	0.953895i	−0.447491	−	0.894289i	$-0.647682\pi$
$23$	2.64122	−	4.57472i	0.550731	−	0.953895i	0.998222	−	0.0596062i	$-0.0189845\pi$
$24$		0			0
$25$	4.79760	−	5.32827i	0.959520	−	1.06565i
$26$	−0.514156	+	1.58241i	−0.100834	+	0.310336i
$27$		0			0
$28$	0.0190351	+	0.0138298i	0.00359730	+	0.00261359i
$29$	5.16281	−	1.09739i	0.958710	−	0.203780i	0.298121	−	0.954528i	$-0.403640\pi$
$29$	5.16281	−	1.09739i	0.958710	−	0.203780i	0.660589	+	0.750748i	$0.270307\pi$
$30$		0			0
$31$	−0.591027	−	5.62325i	−0.106152	−	1.00996i	−0.909853	−	0.414932i	$-0.863806\pi$
$31$	−0.591027	−	5.62325i	−0.106152	−	1.00996i	0.803701	−	0.595033i	$-0.202861\pi$
$32$	−0.196895	+	0.341031i	−0.0348064	+	0.0602864i
$33$		0			0
$34$	2.95766	+	5.12281i	0.507234	+	0.878555i
$35$	0.953487	−	0.692749i	0.161169	−	0.117096i
$36$		0			0
$37$	1.10852	−	3.41166i	0.182239	−	0.560874i	−0.817651	−	0.575714i	$-0.804724\pi$
$37$	1.10852	−	3.41166i	0.182239	−	0.560874i	0.999890	+	0.0148406i	$0.00472409\pi$
$38$	0.672671	−	6.40003i	0.109122	−	1.03822i
$39$		0			0
$40$	6.48246	+	7.19950i	1.02497	+	1.13834i
$41$	−10.9211	−	2.32135i	−1.70559	−	0.362535i	−0.750965	−	0.660342i	$-0.770411\pi$
$41$	−10.9211	−	2.32135i	−1.70559	−	0.362535i	−0.954626	+	0.297808i	$0.903745\pi$
$42$		0			0
$43$	0.753935	+	1.30585i	0.114974	+	0.199141i	0.917769	−	0.397114i	$-0.129988\pi$
$43$	0.753935	+	1.30585i	0.114974	+	0.199141i	−0.802795	+	0.596255i	$0.796655\pi$
$44$	0.0690391	+	0.220424i	0.0104080	+	0.0332302i
$45$		0			0
$46$	−6.14808	+	4.46684i	−0.906484	+	0.658599i
$47$	−5.90260	+	6.55551i	−0.860983	+	0.956219i	−0.999417	−	0.0341530i	$-0.989127\pi$
$47$	−5.90260	+	6.55551i	−0.860983	+	0.956219i	0.138433	+	0.990372i	$0.455793\pi$
$48$		0			0
$49$	−6.29055	+	2.80073i	−0.898650	+	0.400105i
$50$	−9.42304	+	4.19541i	−1.33262	+	0.593320i
$51$		0			0
$52$	0.0538964	−	0.0598580i	0.00747409	−	0.00830082i
$53$	1.63163	−	1.18545i	0.224122	−	0.162834i	−0.470058	−	0.882635i	$-0.655767\pi$
$53$	1.63163	−	1.18545i	0.224122	−	0.162834i	0.694180	+	0.719801i	$0.255767\pi$
$54$		0			0
$55$	11.5695	+	0.122962i	1.56003	+	0.0165802i
$56$	0.469104	+	0.812512i	0.0626866	+	0.108576i
$57$		0			0
$58$	−7.42735	−	1.57873i	−0.975259	−	0.207298i
$59$	7.72787	+	8.58266i	1.00608	+	1.11737i	0.993079	+	0.117452i	$0.0374727\pi$
$59$	7.72787	+	8.58266i	1.00608	+	1.11737i	0.0130039	+	0.999915i	$0.495861\pi$
$60$		0			0
$61$	−0.823304	+	7.83322i	−0.105413	+	1.00294i	0.806131	+	0.591738i	$0.201558\pi$
$61$	−0.823304	+	7.83322i	−0.105413	+	1.00294i	−0.911544	+	0.411203i	$0.865109\pi$
$62$	−2.51364	+	7.73619i	−0.319233	+	0.982497i
$63$		0			0
$64$	−6.23134	+	4.52733i	−0.778918	+	0.565917i
$65$	−2.01734	−	3.49413i	−0.250220	−	0.433394i
$66$		0			0
$67$	2.09211	−	3.62364i	0.255592	−	0.442698i	−0.709464	−	0.704741i	$-0.751063\pi$
$67$	2.09211	−	3.62364i	0.255592	−	0.442698i	0.965056	+	0.262043i	$0.0843963\pi$
$68$	−0.0299329	−	0.284792i	−0.00362989	−	0.0345361i
$69$		0			0
$70$	−1.65848	+	0.352520i	−0.198226	+	0.0421342i
$71$	1.95860	+	1.42300i	0.232442	+	0.168879i	0.697910	−	0.716186i	$-0.254114\pi$
$71$	1.95860	+	1.42300i	0.232442	+	0.168879i	−0.465467	+	0.885065i	$0.654114\pi$
$72$		0			0
$73$	−1.04183	+	3.20643i	−0.121937	+	0.375284i	−0.993331	−	0.115301i	$-0.963217\pi$
$73$	−1.04183	+	3.20643i	−0.121937	+	0.375284i	0.871394	+	0.490585i	$0.163217\pi$
$74$	−3.45317	+	3.83514i	−0.401423	+	0.445826i
$75$		0			0
$76$	−0.155767	+	0.269796i	−0.0178676	+	0.0309477i
$77$	1.09347	+	0.244599i	0.124613	+	0.0278746i
$78$		0			0
$79$	7.79960	+	3.47260i	0.877523	+	0.390699i	0.795516	−	0.605933i	$-0.207200\pi$
$79$	7.79960	+	3.47260i	0.877523	+	0.390699i	0.0820077	+	0.996632i	$0.473867\pi$
$80$	−4.45700	−	13.7172i	−0.498307	−	1.53363i
$81$		0			0
$82$	12.9947	+	9.44124i	1.43503	+	1.04261i
$83$	−1.18499	+	11.2744i	−0.130069	+	1.23753i	0.713557	+	0.700597i	$0.247083\pi$
$83$	−1.18499	+	11.2744i	−0.130069	+	1.23753i	−0.843626	+	0.536931i	$0.819584\pi$
$84$		0			0
$85$	−14.0306	−	2.98231i	−1.52184	−	0.323477i
$86$	−0.226749	−	2.15738i	−0.0244510	−	0.232636i
$87$		0			0
$88$	−1.06005	+	9.14926i	−0.113002	+	0.975314i
$89$	3.45994			0.366753			0.183376	−	0.983043i	$-0.441297\pi$
$89$	3.45994			0.366753			0.183376	+	0.983043i	$0.441297\pi$
$90$		0			0
$91$	−0.120743	−	0.371608i	−0.0126573	−	0.0389551i
$92$	0.359851	−	0.0764886i	0.0375170	−	0.00797449i
$93$		0			0
$94$	11.5934	−	5.16171i	1.19577	−	0.532390i
$95$	10.4418	+	11.5968i	1.07130	+	1.18980i
$96$		0			0
$97$	−11.9111	−	5.30317i	−1.20939	−	0.538456i	−0.299817	−	0.953997i	$-0.596926\pi$
$97$	−11.9111	−	5.30317i	−1.20939	−	0.538456i	−0.909574	+	0.415541i	$0.863592\pi$
$98$	9.90618			1.00068
$99$		0			0
$100$	0.499341			0.0499341
$101$	1.99464	+	0.888070i	0.198474	+	0.0883663i	0.503567	−	0.863956i	$-0.332021\pi$
$101$	1.99464	+	0.888070i	0.198474	+	0.0883663i	−0.305093	+	0.952323i	$0.598687\pi$
$102$		0			0
$103$	0.583179	+	0.647686i	0.0574624	+	0.0638184i	0.771191	−	0.636604i	$-0.219662\pi$
$103$	0.583179	+	0.647686i	0.0574624	+	0.0638184i	−0.713728	+	0.700423i	$0.752995\pi$
$104$	2.93414	−	1.30636i	0.287716	−	0.128099i
$105$		0			0
$106$	−2.83803	+	0.603242i	−0.275654	+	0.0585920i
$107$	−1.90401	−	5.85995i	−0.184068	−	0.566502i	0.815863	−	0.578245i	$-0.196262\pi$
$107$	−1.90401	−	5.85995i	−0.184068	−	0.566502i	−0.999931	+	0.0117425i	$0.996262\pi$
$108$		0			0
$109$	−11.7010			−1.12075			−0.560376	−	0.828238i	$-0.689343\pi$
$109$	−11.7010			−1.12075			−0.560376	+	0.828238i	$0.689343\pi$
$110$	−15.1333	−	6.93141i	−1.44290	−	0.660884i
$111$		0			0
$112$	−0.146004	−	1.38914i	−0.0137961	−	0.131261i
$113$	−0.409378	−	0.0870160i	−0.0385110	−	0.00818577i	0.188616	−	0.982051i	$-0.439600\pi$
$113$	−0.409378	−	0.0870160i	−0.0385110	−	0.00818577i	−0.227127	+	0.973865i	$0.572933\pi$
$114$		0			0
$115$	1.92625	−	18.3270i	0.179623	−	1.70900i
$116$	0.297388	+	0.216065i	0.0276118	+	0.0200611i
$117$		0			0
$118$	−5.13427	−	15.8017i	−0.472648	−	1.45466i
$119$	−1.26904	−	0.565011i	−0.116332	−	0.0517945i
$120$		0			0
$121$	7.18503	+	8.32918i	0.653185	+	0.757198i
$122$	5.66557	−	9.81305i	0.512937	−	0.888432i
$123$		0			0
$124$	0.263492	−	0.292638i	0.0236623	−	0.0262796i
$125$	2.33919	−	7.19928i	0.209223	−	0.643924i
$126$		0			0
$127$	−7.46315	−	5.42229i	−0.662247	−	0.481151i	0.205174	−	0.978726i	$-0.434224\pi$
$127$	−7.46315	−	5.42229i	−0.662247	−	0.481151i	−0.867421	+	0.497575i	$0.834224\pi$
$128$	11.6090	−	2.46758i	1.02610	−	0.218105i
$129$		0			0
$130$	0.606724	+	5.77259i	0.0532132	+	0.506290i
$131$	−7.68773	+	13.3155i	−0.671680	+	1.16338i	0.305747	+	0.952113i	$0.401094\pi$
$131$	−7.68773	+	13.3155i	−0.671680	+	1.16338i	−0.977427	+	0.211272i	$0.932239\pi$
$132$		0			0
$133$	0.755621	+	1.30877i	0.0655206	+	0.113485i
$134$	−4.86990	+	3.53819i	−0.420695	+	0.305653i
$135$		0			0
$136$	3.52856	−	10.8598i	0.302571	−	0.931219i
$137$	0.205037	−	1.95080i	0.0175175	−	0.166668i	−0.982266	−	0.187495i	$-0.939963\pi$
$137$	0.205037	−	1.95080i	0.0175175	−	0.166668i	0.999783	+	0.0208268i	$0.00662984\pi$
$138$		0			0
$139$	11.8080	+	13.1141i	1.00154	+	1.11232i	0.993668	+	0.112356i	$0.0358397\pi$
$139$	11.8080	+	13.1141i	1.00154	+	1.11232i	0.00787377	+	0.999969i	$0.497494\pi$
$140$	0.0802871	+	0.0170655i	0.00678550	+	0.00144230i
$141$		0			0
$142$	−1.74143	−	3.01624i	−0.146137	−	0.253117i
$143$	1.22405	−	3.63531i	0.102360	−	0.304000i
$144$		0			0
$145$	14.8965	−	10.8229i	1.23708	−	0.898794i
$146$	3.24544	−	3.60443i	0.268595	−	0.298304i
$147$		0			0
$148$	0.228231	−	0.101615i	0.0187604	−	0.00835268i
$149$	−0.616240	+	0.274368i	−0.0504844	+	0.0224771i	−0.431824	−	0.901958i	$-0.642130\pi$
$149$	−0.616240	+	0.274368i	−0.0504844	+	0.0224771i	0.381339	+	0.924435i	$0.375463\pi$
$150$		0			0
$151$	3.69632	−	4.10518i	0.300802	−	0.334075i	−0.573728	−	0.819046i	$-0.694503\pi$
$151$	3.69632	−	4.10518i	0.300802	−	0.334075i	0.874530	+	0.484971i	$0.161170\pi$
$152$	−10.0499	+	7.30170i	−0.815157	+	0.592246i
$153$		0			0
$154$	−1.29397	−	0.961300i	−0.104271	−	0.0774638i
$155$	−9.86248	−	17.0823i	−0.792174	−	1.37209i
$156$		0			0
$157$	−0.777453	−	0.165253i	−0.0620475	−	0.0131886i	0.176783	−	0.984250i	$-0.443431\pi$
$157$	−0.777453	−	0.165253i	−0.0620475	−	0.0131886i	−0.238831	+	0.971061i	$0.576764\pi$
$158$	−8.21866	−	9.12774i	−0.653841	−	0.726164i
$159$		0			0
$160$	−0.143596	+	1.36622i	−0.0113522	+	0.108009i
$161$	0.551480	−	1.69728i	0.0434627	−	0.133765i
$162$		0			0
$163$	−11.6538	+	8.46700i	−0.912799	+	0.663187i	−0.941721	−	0.336395i	$-0.890792\pi$
$163$	−11.6538	+	8.46700i	−0.912799	+	0.663187i	0.0289225	+	0.999582i	$0.490792\pi$
$164$	−0.388791	−	0.673406i	−0.0303595	−	0.0525842i
$165$		0			0
$166$	8.15450	−	14.1240i	0.632912	−	1.09624i
$167$	−1.41854	−	13.4965i	−0.109770	−	1.04439i	−0.901280	−	0.433236i	$-0.857372\pi$
$167$	−1.41854	−	13.4965i	−0.109770	−	1.04439i	0.791510	−	0.611156i	$-0.209295\pi$
$168$		0			0
$169$	11.4075	−	2.42475i	0.877503	−	0.186519i
$170$	16.6947	+	12.1294i	1.28043	+	0.930284i
$171$		0			0
$172$	−0.0324512	+	0.0998744i	−0.00247438	+	0.00761535i
$173$	11.7677	−	13.0693i	0.894681	−	0.993644i	−0.105319	−	0.994439i	$-0.533586\pi$
$173$	11.7677	−	13.0693i	0.894681	−	0.993644i	1.00000		0.000794492i	$0.000252895\pi$
$174$		0			0
$175$	1.21115	−	2.09777i	0.0915541	−	0.158576i
$176$	6.98201	−	11.8017i	0.526289	−	0.889589i
$177$		0			0
$178$	−4.54722	−	2.02455i	−0.340829	−	0.151747i
$179$	4.96972	+	15.2952i	0.371454	+	1.14322i	0.945840	+	0.324634i	$0.105241\pi$
$179$	4.96972	+	15.2952i	0.371454	+	1.14322i	−0.574386	+	0.818585i	$0.694759\pi$
$180$		0			0
$181$	12.0200	+	8.73306i	0.893441	+	0.649123i	0.936773	−	0.349938i	$-0.113797\pi$
$181$	12.0200	+	8.73306i	0.893441	+	0.649123i	−0.0433317	+	0.999061i	$0.513797\pi$
$182$	−0.0587572	+	0.559038i	−0.00435538	+	0.0414386i
$183$		0			0
$184$	14.3491	+	3.04999i	1.05783	+	0.224848i
$185$	−1.30809	−	12.4456i	−0.0961727	−	0.915022i
$186$		0			0
$187$	−6.69272	−	11.8820i	−0.489420	−	0.868897i
$188$	−0.614351			−0.0448062
$189$		0			0
$190$	−6.93735	−	21.3510i	−0.503288	−	1.54896i
$191$	−1.32489	+	0.281614i	−0.0958655	+	0.0203768i	−0.255595	−	0.966784i	$-0.582271\pi$
$191$	−1.32489	+	0.281614i	−0.0958655	+	0.0203768i	0.159729	+	0.987161i	$0.448938\pi$
$192$		0			0
$193$	−20.4072	+	9.08585i	−1.46894	+	0.654014i	−0.976340	−	0.216242i	$-0.930620\pi$
$193$	−20.4072	+	9.08585i	−1.46894	+	0.654014i	−0.492600	+	0.870256i	$0.663953\pi$
$194$	12.5511	+	13.9394i	0.901116	+	1.00079i
$195$		0			0
$196$	−0.438099	−	0.195054i	−0.0312928	−	0.0139325i
$197$	−8.74655			−0.623166			−0.311583	−	0.950219i	$-0.600859\pi$
$197$	−8.74655			−0.623166			−0.311583	+	0.950219i	$0.600859\pi$
$198$		0			0
$199$	6.39133			0.453070			0.226535	−	0.974003i	$-0.427260\pi$
$199$	6.39133			0.453070			0.226535	+	0.974003i	$0.427260\pi$
$200$	18.1898	+	8.09863i	1.28621	+	0.572660i
$201$		0			0
$202$	−2.10181	−	2.33429i	−0.147883	−	0.164240i
$203$	1.62902	−	0.725285i	0.114335	−	0.0509051i
$204$		0			0
$205$	−38.0987	+	8.09813i	−2.66093	+	0.565598i
$206$	−0.387455	−	1.19246i	−0.0269953	−	0.0830829i
$207$		0			0
$208$	−4.78169			−0.331551
$209$	−1.70750	+	14.7374i	−0.118110	+	1.01941i
$210$		0			0
$211$	−0.689268	−	6.55795i	−0.0474512	−	0.451468i	−0.992291	−	0.123934i	$-0.960449\pi$
$211$	−0.689268	−	6.55795i	−0.0474512	−	0.451468i	0.944839	−	0.327534i	$-0.106218\pi$
$212$	0.137389	+	0.0292030i	0.00943594	+	0.00200567i
$213$		0			0
$214$	−0.926552	+	8.81555i	−0.0633378	+	0.602619i
$215$	4.25564	+	3.09190i	0.290232	+	0.210866i
$216$		0			0
$217$	−0.590295	−	1.81674i	−0.0400718	−	0.123328i
$218$	15.3780	+	6.84674i	1.04153	+	0.463720i
$219$		0			0
$220$	0.532787	+	0.604518i	0.0359205	+	0.0407566i
$221$	−2.37774	+	4.11837i	−0.159944	+	0.277032i
$222$		0			0
$223$	−4.48111	+	4.97678i	−0.300078	+	0.333270i	−0.874260	−	0.485457i	$-0.838653\pi$
$223$	−4.48111	+	4.97678i	−0.300078	+	0.333270i	0.574183	+	0.818727i	$0.305320\pi$
$224$	−0.0411112	+	0.126527i	−0.00274686	+	0.00845395i
$225$		0			0
$226$	0.487108	+	0.353905i	0.0324020	+	0.0235414i
$227$	−6.01302	+	1.27811i	−0.399098	+	0.0848310i	−0.403088	−	0.915161i	$-0.632063\pi$
$227$	−6.01302	+	1.27811i	−0.399098	+	0.0848310i	0.00399006	+	0.999992i	$0.498730\pi$
$228$		0			0
$229$	2.39535	+	22.7902i	0.158289	+	1.50602i	0.728798	+	0.684729i	$0.240079\pi$
$229$	2.39535	+	22.7902i	0.158289	+	1.50602i	−0.570509	+	0.821291i	$0.693254\pi$
$230$	−13.2555	+	22.9591i	−0.874040	+	1.51388i
$231$		0			0
$232$	7.32887	+	12.6940i	0.481164	+	0.833400i
$233$	−9.54280	+	6.93325i	−0.625170	+	0.454212i	−0.854724	−	0.519084i	$-0.826273\pi$
$233$	−9.54280	+	6.93325i	−0.625170	+	0.454212i	0.229554	+	0.973296i	$0.426273\pi$
$234$		0			0
$235$	−9.50952	+	29.2673i	−0.620333	+	1.90919i
$236$	−0.0840751	+	0.799921i	−0.00547282	+	0.0520704i
$237$		0			0
$238$	1.33722	+	1.48513i	0.0866790	+	0.0962668i
$239$	−9.44182	−	2.00692i	−0.610740	−	0.129817i	−0.107850	−	0.994167i	$-0.534397\pi$
$239$	−9.44182	−	2.00692i	−0.610740	−	0.129817i	−0.502890	+	0.864350i	$0.667730\pi$
$240$		0			0
$241$	3.63345	+	6.29331i	0.234051	+	0.405388i	0.958996	−	0.283418i	$-0.0914685\pi$
$241$	3.63345	+	6.29331i	0.234051	+	0.405388i	−0.724946	+	0.688806i	$0.758135\pi$
$242$	−4.56918	−	15.1509i	−0.293718	−	0.973936i
$243$		0			0
$244$	−0.443780	+	0.322425i	−0.0284101	+	0.0206411i
$245$	−16.0736	+	17.8515i	−1.02690	+	1.14049i
$246$		0			0
$247$	4.72624	−	2.10426i	0.300723	−	0.133891i
$248$	14.3446	−	6.38662i	0.910882	−	0.405551i
$249$		0			0
$250$	−7.28688	+	8.09290i	−0.460863	+	0.511840i
$251$	−10.6325	+	7.72498i	−0.671119	+	0.487597i	−0.870400	−	0.492346i	$-0.836140\pi$
$251$	−10.6325	+	7.72498i	−0.671119	+	0.487597i	0.199280	+	0.979943i	$0.436140\pi$
$252$		0			0
$253$	14.2825	−	10.1467i	0.897932	−	0.637917i
$254$	6.63563	+	11.4932i	0.416356	+	0.721150i
$255$		0			0
$256$	−1.63297	−	0.347099i	−0.102061	−	0.0216937i
$257$	1.22201	+	1.35718i	0.0762271	+	0.0846588i	0.780052	−	0.625715i	$-0.215193\pi$
$257$	1.22201	+	1.35718i	0.0762271	+	0.0846588i	−0.703825	+	0.710374i	$0.748526\pi$
$258$		0			0
$259$	0.126680	−	1.20528i	0.00787151	−	0.0748924i
$260$	0.0868310	−	0.267238i	0.00538503	−	0.0165734i
$261$		0			0
$262$	17.8951	−	13.0015i	1.10556	−	0.803238i
$263$	2.63718	+	4.56773i	0.162616	+	0.281658i	0.935806	−	0.352516i	$-0.114674\pi$
$263$	2.63718	+	4.56773i	0.162616	+	0.281658i	−0.773190	+	0.634174i	$0.781340\pi$
$264$		0			0
$265$	3.51786	−	6.09311i	0.216100	−	0.374297i
$266$	−0.227256	−	2.16220i	−0.0139340	−	0.132573i
$267$		0			0
$268$	0.285038	−	0.0605867i	0.0174115	−	0.00370092i
$269$	−14.0391	−	10.2000i	−0.855982	−	0.621907i	0.0708069	−	0.997490i	$-0.477443\pi$
$269$	−14.0391	−	10.2000i	−0.855982	−	0.621907i	−0.926789	+	0.375583i	$0.877443\pi$
$270$		0			0
$271$	2.50681	−	7.71516i	0.152278	−	0.468662i	−0.845597	−	0.533821i	$-0.820755\pi$
$271$	2.50681	−	7.71516i	0.152278	−	0.468662i	0.997875	+	0.0651590i	$0.0207555\pi$
$272$	−11.3752	+	12.6334i	−0.689720	+	0.766012i
$273$		0			0
$274$	−1.41097	+	2.44386i	−0.0852396	+	0.147639i
$275$	21.8256	−	9.44072i	1.31613	−	0.569297i
$276$		0			0
$277$	−17.7796	−	7.91601i	−1.06828	−	0.475627i	−0.204169	−	0.978936i	$-0.565449\pi$
$277$	−17.7796	−	7.91601i	−1.06828	−	0.475627i	−0.864107	+	0.503309i	$0.832116\pi$
$278$	−7.84505	−	24.1446i	−0.470515	−	1.44810i
$279$		0			0
$280$	2.64789	+	1.92381i	0.158242	+	0.114969i
$281$	3.03018	−	28.8302i	0.180765	−	1.71987i	−0.409206	−	0.912442i	$-0.634194\pi$
$281$	3.03018	−	28.8302i	0.180765	−	1.71987i	0.589971	−	0.807424i	$-0.299139\pi$
$282$		0			0
$283$	−9.56153	−	2.03237i	−0.568374	−	0.120812i	−0.0852437	−	0.996360i	$-0.527167\pi$
$283$	−9.56153	−	2.03237i	−0.568374	−	0.120812i	−0.483130	+	0.875549i	$0.660500\pi$
$284$	0.0176240	+	0.167682i	0.00104579	+	0.00995007i
$285$		0			0
$286$	−3.73587	+	4.06146i	−0.220907	+	0.240159i
$287$	−3.77204			−0.222656
$288$		0			0
$289$	−0.0288211	−	0.0887023i	−0.00169536	−	0.00521778i
$290$	−25.9106	+	5.50747i	−1.52152	+	0.323410i
$291$		0			0
$292$	−0.214501	+	0.0955019i	−0.0125527	+	0.00558883i
$293$	−16.8680	−	18.7338i	−0.985440	−	1.09444i	−0.995526	−	0.0944929i	$-0.969877\pi$
$293$	−16.8680	−	18.7338i	−0.985440	−	1.09444i	0.0100855	−	0.999949i	$-0.496790\pi$
$294$		0			0
$295$	36.8063	+	16.3872i	2.14295	+	0.954101i
$296$	9.96196			0.579027
$297$		0			0
$298$	0.970438			0.0562159
$299$	−5.58122	−	2.48492i	−0.322770	−	0.143707i
$300$		0			0
$301$	0.340870	+	0.378574i	0.0196474	+	0.0218207i
$302$	−7.26000	+	3.23236i	−0.417766	+	0.186001i
$303$		0			0
$304$	18.0901	−	3.84517i	1.03754	−	0.220536i
$305$	8.49086	+	26.1322i	0.486185	+	1.49632i
$306$		0			0
$307$	4.47659			0.255492			0.127746	−	0.991807i	$-0.459226\pi$
$307$	4.47659			0.255492			0.127746	+	0.991807i	$0.459226\pi$
$308$	0.0382975	+	0.0679919i	0.00218220	+	0.00387420i
$309$		0			0
$310$	2.96619	+	28.2214i	0.168468	+	1.60287i
$311$	−22.1664	−	4.71160i	−1.25694	−	0.267171i	−0.469151	−	0.883118i	$-0.655440\pi$
$311$	−22.1664	−	4.71160i	−1.25694	−	0.267171i	−0.787787	+	0.615947i	$0.788773\pi$
$312$		0			0
$313$	−1.74382	+	16.5913i	−0.0985664	+	0.937797i	0.827762	+	0.561080i	$0.189614\pi$
$313$	−1.74382	+	16.5913i	−0.0985664	+	0.937797i	−0.926328	+	0.376717i	$0.877053\pi$
$314$	0.925071	+	0.672104i	0.0522048	+	0.0379290i
$315$		0			0
$316$	0.183742	+	0.565500i	0.0103363	+	0.0318118i
$317$	23.1745	+	10.3180i	1.30161	+	0.579515i	0.936245	−	0.351348i	$-0.114277\pi$
$317$	23.1745	+	10.3180i	1.30161	+	0.579515i	0.365367	+	0.930863i	$0.380943\pi$
$318$		0			0
$319$	17.0835	+	3.82140i	0.956490	+	0.213957i
$320$	−13.4350	+	23.2701i	−0.751039	+	1.30084i
$321$		0			0
$322$	−1.71793	+	1.90796i	−0.0957367	+	0.106326i
$323$	5.68372	−	17.4927i	0.316250	−	0.973319i
$324$		0			0
$325$	−6.70866	−	4.87413i	−0.372129	−	0.270368i
$326$	20.2704	−	4.30862i	1.12268	−	0.238632i
$327$		0			0
$328$	−3.24102	−	30.8363i	−0.178956	−	1.70265i
$329$	−1.49010	+	2.58094i	−0.0821521	+	0.142292i
$330$		0			0
$331$	−3.79418	−	6.57172i	−0.208547	−	0.361214i	0.742710	−	0.669613i	$-0.233540\pi$
$331$	−3.79418	−	6.57172i	−0.208547	−	0.361214i	−0.951257	+	0.308399i	$0.900207\pi$
$332$	−0.638736	+	0.464069i	−0.0350552	+	0.0254691i
$333$		0			0
$334$	−6.03306	+	18.5678i	−0.330114	+	1.01599i
$335$	1.52578	−	14.5168i	0.0833624	−	0.793140i
$336$		0			0
$337$	−9.64234	−	10.7089i	−0.525252	−	0.583351i	0.420887	−	0.907113i	$-0.361719\pi$
$337$	−9.64234	−	10.7089i	−0.525252	−	0.583351i	−0.946139	+	0.323762i	$0.895052\pi$
$338$	−16.4112	−	3.48830i	−0.892650	−	0.189739i
$339$		0			0
$340$	−0.499491	−	0.865143i	−0.0270887	−	0.0469190i
$341$	5.98419	−	17.7725i	0.324062	−	0.962435i
$342$		0			0
$343$	−3.79528	+	2.75744i	−0.204926	+	0.148888i
$344$	−2.80195	+	3.11188i	−0.151071	+	0.167781i
$345$		0			0
$346$	−23.1131	+	10.2906i	−1.24257	+	0.553227i
$347$	15.3861	−	6.85035i	0.825971	−	0.367746i	0.0501836	−	0.998740i	$-0.484019\pi$
$347$	15.3861	−	6.85035i	0.825971	−	0.367746i	0.775788	+	0.630994i	$0.217353\pi$
$348$		0			0
$349$	20.4612	−	22.7245i	1.09526	−	1.21641i	0.120609	−	0.992700i	$-0.461515\pi$
$349$	20.4612	−	22.7245i	1.09526	−	1.21641i	0.974655	−	0.223714i	$-0.0718181\pi$
$350$	−2.81924	+	2.04830i	−0.150695	+	0.109486i
$351$		0			0
$352$	−1.06472	+	0.756405i	−0.0567496	+	0.0403165i
$353$	0.243243	+	0.421309i	0.0129465	+	0.0224240i	0.872426	−	0.488746i	$-0.162546\pi$
$353$	0.243243	+	0.421309i	0.0129465	+	0.0224240i	−0.859480	+	0.511170i	$0.829212\pi$
$354$		0			0
$355$	8.26104	+	1.75594i	0.438451	+	0.0931956i
$356$	0.161236	+	0.179071i	0.00854552	+	0.00949076i
$357$		0			0
$358$	2.41842	−	23.0097i	0.127817	−	1.21610i
$359$	−10.5622	+	32.5072i	−0.557453	+	1.71566i	0.131924	+	0.991260i	$0.457884\pi$
$359$	−10.5622	+	32.5072i	−0.557453	+	1.71566i	−0.689377	+	0.724403i	$0.742116\pi$
$360$		0			0
$361$	−0.816851	+	0.593477i	−0.0429921	+	0.0312356i
$362$	−10.6872	−	18.5108i	−0.561709	−	0.972908i
$363$		0			0
$364$	0.0136061	−	0.0235664i	0.000713152	−	0.00123522i
$365$	1.22940	+	11.6970i	0.0643497	+	0.612246i
$366$		0			0
$367$	2.31194	−	0.491418i	0.120682	−	0.0256518i	−0.147175	−	0.989111i	$-0.547018\pi$
$367$	2.31194	−	0.491418i	0.120682	−	0.0256518i	0.267857	+	0.963459i	$0.413685\pi$
$368$	−17.6688	−	12.8372i	−0.921052	−	0.669183i
$369$		0			0
$370$	−5.56331	+	17.1221i	−0.289223	+	0.890136i
$371$	0.455921	−	0.506351i	0.0236702	−	0.0262885i
$372$		0			0
$373$	11.4332	−	19.8028i	0.591987	−	1.02535i	−0.401978	−	0.915649i	$-0.631677\pi$
$373$	11.4332	−	19.8028i	0.591987	−	1.02535i	0.993965	−	0.109701i	$-0.0349895\pi$
$374$	1.84326	+	19.5321i	0.0953126	+	1.00998i
$375$		0			0
$376$	−22.3794	−	9.96394i	−1.15413	−	0.513851i
$377$	−1.88638	−	5.80568i	−0.0971535	−	0.299008i
$378$		0			0
$379$	−21.9257	−	15.9299i	−1.12625	−	0.818266i	−0.141102	−	0.989995i	$-0.545065\pi$
$379$	−21.9257	−	15.9299i	−1.12625	−	0.818266i	−0.985144	+	0.171729i	$0.945065\pi$
$380$	−0.113601	+	1.08084i	−0.00582761	+	0.0554460i
$381$		0			0
$382$	1.90602	+	0.405136i	0.0975203	+	0.0207286i
$383$	2.19467	+	20.8808i	0.112142	+	1.06696i	0.895399	+	0.445264i	$0.146890\pi$
$383$	2.19467	+	20.8808i	0.112142	+	1.06696i	−0.783257	+	0.621698i	$0.786443\pi$
$384$		0			0
$385$	3.83189	−	0.772025i	0.195291	−	0.0393460i
$386$	32.1366			1.63571
$387$		0			0
$388$	−0.280601	−	0.863601i	−0.0142454	−	0.0438427i
$389$	6.90000	−	1.46664i	0.349844	−	0.0743616i	−0.0296383	−	0.999561i	$-0.509436\pi$
$389$	6.90000	−	1.46664i	0.349844	−	0.0743616i	0.379482	+	0.925199i	$0.376102\pi$
$390$		0			0
$391$	−19.8424	+	8.83440i	−1.00347	+	0.446775i
$392$	−12.7954	−	14.2108i	−0.646266	−	0.717751i
$393$		0			0
$394$	11.4952	+	5.11797i	0.579118	+	0.257840i
$395$	29.7842			1.49860
$396$		0			0
$397$	1.54426			0.0775042			0.0387521	−	0.999249i	$-0.487662\pi$
$397$	1.54426			0.0775042			0.0387521	+	0.999249i	$0.487662\pi$
$398$	−8.39981	−	3.73984i	−0.421044	−	0.187461i
$399$		0			0
$400$	−19.8354	−	22.0294i	−0.991769	−	1.10147i
$401$	−20.2465	+	9.01430i	−1.01106	+	0.450153i	−0.844315	−	0.535847i	$-0.819992\pi$
$401$	−20.2465	+	9.01430i	−1.01106	+	0.450153i	−0.166745	+	0.986000i	$0.553326\pi$
$402$		0			0
$403$	−6.39650	+	1.35962i	−0.318632	+	0.0677274i
$404$	0.0469894	+	0.144619i	0.00233781	+	0.00719505i
$405$		0			0
$406$	−2.56533			−0.127315
$407$	8.05450	−	8.75646i	0.399247	−	0.434042i
$408$		0			0
$409$	0.495068	+	4.71026i	0.0244796	+	0.232907i	0.999920	+	0.0126443i	$0.00402493\pi$
$409$	0.495068	+	4.71026i	0.0244796	+	0.232907i	−0.975440	+	0.220263i	$0.929308\pi$
$410$	54.8098	+	11.6502i	2.70686	+	0.575361i
$411$		0			0
$412$	−0.00634468	+	0.0603656i	−0.000312580	+	0.00297400i
$413$	3.15660	+	2.29341i	0.155326	+	0.112851i
$414$		0			0
$415$	12.2210	+	37.6123i	0.599904	+	1.84631i
$416$	0.416063	+	0.185243i	0.0203992	+	0.00908229i
$417$		0			0
$418$	10.8676	−	18.3695i	0.531549	−	0.898482i
$419$	20.1474	−	34.8963i	0.984265	−	1.70480i	0.339109	−	0.940747i	$-0.389875\pi$
$419$	20.1474	−	34.8963i	0.984265	−	1.70480i	0.645157	−	0.764050i	$-0.276792\pi$
$420$		0			0
$421$	−9.10282	+	10.1097i	−0.443644	+	0.492717i	−0.922944	−	0.384934i	$-0.874224\pi$
$421$	−9.10282	+	10.1097i	−0.443644	+	0.492717i	0.479300	+	0.877651i	$0.340891\pi$
$422$	−2.93146	+	9.02210i	−0.142701	+	0.439189i
$423$		0			0
$424$	4.53114	+	3.29207i	0.220052	+	0.159877i
$425$	−28.8368	+	6.12945i	−1.39879	+	0.297322i
$426$		0			0
$427$	0.278147	+	2.64639i	0.0134605	+	0.128068i
$428$	0.214556	−	0.371622i	0.0103710	−	0.0179630i
$429$		0			0
$430$	−3.78377	−	6.55369i	−0.182470	−	0.316047i
$431$	6.35439	−	4.61673i	0.306080	−	0.222380i	−0.424133	−	0.905600i	$-0.639421\pi$
$431$	6.35439	−	4.61673i	0.306080	−	0.222380i	0.730213	+	0.683220i	$0.239421\pi$
$432$		0			0
$433$	0.426664	−	1.31314i	0.0205041	−	0.0631053i	−0.940281	−	0.340400i	$-0.889438\pi$
$433$	0.426664	−	1.31314i	0.0205041	−	0.0631053i	0.960785	+	0.277294i	$0.0894377\pi$
$434$	−0.287256	+	2.73306i	−0.0137887	+	0.131191i
$435$		0			0
$436$	−0.545277	−	0.605592i	−0.0261141	−	0.0290026i
$437$	23.1131	+	4.91284i	1.10565	+	0.235013i
$438$		0			0
$439$	2.75465	+	4.77119i	0.131472	+	0.227717i	0.924244	−	0.381802i	$-0.124696\pi$
$439$	2.75465	+	4.77119i	0.131472	+	0.227717i	−0.792772	+	0.609518i	$0.791363\pi$
$440$	9.60372	+	30.6622i	0.457840	+	1.46177i
$441$		0			0
$442$	5.53478	−	4.02125i	0.263263	−	0.191272i
$443$	−0.738277	+	0.819940i	−0.0350766	+	0.0389565i	−0.760428	−	0.649422i	$-0.775011\pi$
$443$	−0.738277	+	0.819940i	−0.0350766	+	0.0389565i	0.725351	+	0.688379i	$0.241677\pi$
$444$		0			0
$445$	11.0266	−	4.90936i	0.522711	−	0.232726i
$446$	8.80143	−	3.91865i	0.416760	−	0.185553i
$447$		0			0
$448$	−1.74120	+	1.93380i	−0.0822639	+	0.0913634i
$449$	1.16721	−	0.848031i	0.0550843	−	0.0400211i	−0.559902	−	0.828559i	$-0.689161\pi$
$449$	1.16721	−	0.848031i	0.0550843	−	0.0400211i	0.614987	+	0.788538i	$0.289161\pi$
$450$		0			0
$451$	−29.7252	−	22.0831i	−1.39971	−	1.03985i
$452$	−0.0145738	−	0.0252426i	−0.000685496	−	0.00118731i
$453$		0			0
$454$	8.65049	+	1.83872i	0.405987	+	0.0862953i
$455$	−0.912081	−	1.01297i	−0.0427590	−	0.0474887i
$456$		0			0
$457$	3.15336	−	30.0022i	0.147508	−	1.40344i	−0.630988	−	0.775793i	$-0.717350\pi$
$457$	3.15336	−	30.0022i	0.147508	−	1.40344i	0.778496	−	0.627650i	$-0.215983\pi$
$458$	10.1874	−	31.3537i	0.476027	−	1.46506i
$459$		0			0
$460$	1.03829	−	0.754362i	0.0484105	−	0.0351723i
$461$	−13.3385	−	23.1030i	−0.621237	−	1.07601i	−0.989256	−	0.146195i	$-0.953297\pi$
$461$	−13.3385	−	23.1030i	−0.621237	−	1.07601i	0.368019	−	0.929818i	$-0.380036\pi$
$462$		0			0
$463$	−0.348740	+	0.604035i	−0.0162073	+	0.0280719i	−0.874015	−	0.485898i	$-0.838493\pi$
$463$	−0.348740	+	0.604035i	−0.0162073	+	0.0280719i	0.857808	+	0.513970i	$0.171826\pi$
$464$	−2.28104	−	21.7026i	−0.105895	−	1.00752i
$465$		0			0
$466$	16.5986	−	3.52813i	0.768914	−	0.163438i
$467$	25.9087	+	18.8238i	1.19891	+	0.871061i	0.994177	−	0.107756i	$-0.0343666\pi$
$467$	25.9087	+	18.8238i	1.19891	+	0.871061i	0.204736	+	0.978817i	$0.434367\pi$
$468$		0			0
$469$	0.436828	−	1.34442i	0.0201709	−	0.0620795i
$470$	29.6234	−	32.9001i	1.36643	−	1.51757i
$471$		0			0
$472$	−16.0363	+	27.7757i	−0.738130	+	1.27848i
$473$	0.469864	+	4.97892i	0.0216044	+	0.228931i
$474$		0			0
$475$	29.2997	+	13.0451i	1.34436	+	0.598549i
$476$	−0.0298958	−	0.0920098i	−0.00137027	−	0.00421726i
$477$		0			0
$478$	11.2346	+	8.16240i	0.513858	+	0.373339i
$479$	−2.29842	+	21.8680i	−0.105017	+	0.999174i	0.807426	+	0.589969i	$0.200860\pi$
$479$	−2.29842	+	21.8680i	−0.105017	+	0.999174i	−0.912443	+	0.409204i	$0.865806\pi$
$480$		0			0
$481$	−4.05816	−	0.862588i	−0.185036	−	0.0393306i
$482$	−1.09278	−	10.3971i	−0.0497746	−	0.473573i
$483$		0			0
$484$	−0.0962525	+	0.760014i	−0.00437511	+	0.0345461i
$485$	−45.4848			−2.06536
$486$		0			0
$487$	5.41429	+	16.6635i	0.245345	+	0.755094i	0.995580	+	0.0939221i	$0.0299405\pi$
$487$	5.41429	+	16.6635i	0.245345	+	0.755094i	−0.750235	+	0.661172i	$0.770060\pi$
$488$	−21.3952	+	4.54768i	−0.968513	+	0.205864i
$489$		0			0
$490$	31.5704	−	14.0560i	1.42620	−	0.634987i
$491$	0.134679	+	0.149576i	0.00607798	+	0.00675028i	0.746176	−	0.665749i	$-0.231888\pi$
$491$	0.134679	+	0.149576i	0.00607798	+	0.00675028i	−0.740098	+	0.672499i	$0.765221\pi$
$492$		0			0
$493$	−19.8263	−	8.82724i	−0.892932	−	0.397559i
$494$	−7.44274			−0.334865
$495$		0			0
$496$	−23.3770			−1.04966
$497$	0.747190	+	0.332670i	0.0335161	+	0.0149223i
$498$		0			0
$499$	−16.3288	−	18.1349i	−0.730976	−	0.811831i	0.257004	−	0.966410i	$-0.417264\pi$
$499$	−16.3288	−	18.1349i	−0.730976	−	0.811831i	−0.987980	+	0.154579i	$0.950598\pi$
$500$	0.481612	−	0.214427i	0.0215383	−	0.00958948i
$501$		0			0
$502$	18.4940	−	3.93102i	0.825428	−	0.175450i
$503$	5.13640	+	15.8082i	0.229021	+	0.704853i	0.997859	+	0.0654093i	$0.0208353\pi$
$503$	5.13640	+	15.8082i	0.229021	+	0.704853i	−0.768838	+	0.639444i	$0.779165\pi$
$504$		0			0
$505$	7.61689			0.338947
$506$	−24.7080	+	4.97801i	−1.09841	+	0.221299i
$507$		0			0
$508$	−0.0671557	−	0.638944i	−0.00297955	−	0.0283485i
$509$	16.5182	+	3.51105i	0.732157	+	0.155625i	0.558880	−	0.829249i	$-0.311231\pi$
$509$	16.5182	+	3.51105i	0.732157	+	0.155625i	0.173277	+	0.984873i	$0.444565\pi$
$510$		0			0
$511$	−0.119059	+	1.13277i	−0.00526687	+	0.0501109i
$512$	−17.2604	−	12.5404i	−0.762810	−	0.554214i
$513$		0			0
$514$	−0.811886	−	2.49873i	−0.0358108	−	0.110214i
$515$	2.77757	+	1.23665i	0.122394	+	0.0544935i
$516$		0			0
$517$	−26.8525	+	11.6152i	−1.18097	+	0.510834i
$518$	−0.871748	+	1.50991i	−0.0383024	+	0.0663418i
$519$		0			0
$520$	7.49730	−	8.32659i	0.328778	−	0.365145i
$521$	5.89465	−	18.1419i	0.258249	−	0.794809i	−0.734923	−	0.678151i	$-0.762782\pi$
$521$	5.89465	−	18.1419i	0.258249	−	0.794809i	0.993172	−	0.116658i	$-0.0372183\pi$
$522$		0			0
$523$	12.1874	+	8.85469i	0.532919	+	0.387189i	0.821449	−	0.570283i	$-0.193166\pi$
$523$	12.1874	+	8.85469i	0.532919	+	0.387189i	−0.288529	+	0.957471i	$0.593166\pi$
$524$	−1.04741	+	0.222634i	−0.0457563	+	0.00972581i
$525$		0			0
$526$	−0.793144	−	7.54626i	−0.0345827	−	0.329033i
$527$	−11.6245	+	20.1341i	−0.506369	+	0.877057i
$528$		0			0
$529$	−2.45203	−	4.24705i	−0.106610	−	0.184654i
$530$	−8.18868	+	5.94942i	−0.355693	+	0.258426i
$531$		0			0
$532$	−0.0325237	+	0.100098i	−0.00141008	+	0.00433979i
$533$	−1.34978	+	12.8423i	−0.0584653	+	0.556261i
$534$		0			0
$535$	−14.3827	−	15.9737i	−0.621820	−	0.690601i
$536$	11.3659	+	2.41590i	0.490932	+	0.104351i
$537$		0			0
$538$	12.4825	+	21.6203i	0.538158	+	0.932117i
$539$	−22.8365	−	0.242708i	−0.983639	−	0.0104542i
$540$		0			0
$541$	5.44671	−	3.95727i	0.234172	−	0.170136i	−0.464511	−	0.885568i	$-0.653770\pi$
$541$	5.44671	−	3.95727i	0.234172	−	0.170136i	0.698683	+	0.715431i	$0.253770\pi$
$542$	−7.80903	+	8.67281i	−0.335427	+	0.372529i
$543$		0			0
$544$	1.47919	−	0.658577i	0.0634197	−	0.0282363i
$545$	−37.2903	+	16.6027i	−1.59734	+	0.711183i
$546$		0			0
$547$	6.21789	−	6.90567i	0.265858	−	0.295265i	−0.595404	−	0.803426i	$-0.703008\pi$
$547$	6.21789	−	6.90567i	0.265858	−	0.295265i	0.861262	+	0.508161i	$0.169675\pi$
$548$	0.110520	−	0.0802974i	0.00472117	−	0.00343013i
$549$		0			0
$550$	−34.2084	−	0.363569i	−1.45865	−	0.0155027i
$551$	11.8052	+	20.4471i	0.502917	+	0.871077i
$552$		0			0
$553$	2.82137	+	0.599701i	0.119977	+	0.0255019i
$554$	18.7349	+	20.8072i	0.795970	+	0.884014i
$555$		0			0
$556$	−0.128465	+	1.22226i	−0.00544812	+	0.0518354i
$557$	10.5763	−	32.5504i	0.448131	−	1.37921i	−0.430882	−	0.902408i	$-0.641797\pi$
$557$	10.5763	−	32.5504i	0.448131	−	1.37921i	0.879013	−	0.476798i	$-0.158203\pi$
$558$		0			0
$559$	1.41087	−	1.02506i	0.0596734	−	0.0433553i
$560$	−2.43637	−	4.21992i	−0.102956	−	0.178324i
$561$		0			0
$562$	−20.8522	+	36.1170i	−0.879596	+	1.52350i
$563$	−1.08683	−	10.3405i	−0.0458044	−	0.435799i	−0.993260	−	0.115911i	$-0.963021\pi$
$563$	−1.08683	−	10.3405i	−0.0458044	−	0.435799i	0.947455	−	0.319888i	$-0.103645\pi$
$564$		0			0
$565$	−1.42813	+	0.303558i	−0.0600819	+	0.0127708i
$566$	11.3770	+	8.26589i	0.478212	+	0.347441i
$567$		0			0
$568$	−2.07757	+	6.39409i	−0.0871727	+	0.268290i
$569$	12.7246	−	14.1321i	0.533443	−	0.592449i	−0.414832	−	0.909898i	$-0.636160\pi$
$569$	12.7246	−	14.1321i	0.533443	−	0.592449i	0.948275	+	0.317449i	$0.102826\pi$
$570$		0			0
$571$	15.5552	−	26.9425i	0.650966	−	1.12751i	−0.331922	−	0.943307i	$-0.607697\pi$
$571$	15.5552	−	26.9425i	0.650966	−	1.12751i	0.982889	−	0.184200i	$-0.0589694\pi$
$572$	0.245189	−	0.106058i	0.0102519	−	0.00443449i
$573$		0			0
$574$	4.95740	+	2.20718i	0.206918	+	0.0921258i
$575$	−11.7039	−	36.0208i	−0.488085	−	1.50217i
$576$		0			0
$577$	−8.81901	−	6.40738i	−0.367140	−	0.266743i	0.388884	−	0.921287i	$-0.372861\pi$
$577$	−8.81901	−	6.40738i	−0.367140	−	0.266743i	−0.756024	+	0.654544i	$0.772861\pi$
$578$	−0.0140253	+	0.133441i	−0.000583374	+	0.00555043i
$579$		0			0
$580$	1.25434	+	0.266617i	0.0520834	+	0.0110707i
$581$	0.400339	+	3.80897i	0.0166089	+	0.158023i
$582$		0			0
$583$	6.55724	−	1.32111i	0.271573	−	0.0547147i
$584$	−9.36268			−0.387430
$585$		0			0
$586$	11.2068	+	34.4911i	0.462950	+	1.42482i
$587$	22.0454	−	4.68590i	0.909912	−	0.193408i	0.270902	−	0.962607i	$-0.412678\pi$
$587$	22.0454	−	4.68590i	0.909912	−	0.193408i	0.639009	+	0.769199i	$0.279345\pi$
$588$		0			0
$589$	23.1059	−	10.2874i	0.952062	−	0.423885i
$590$	−38.7838	−	43.0738i	−1.59671	−	1.77332i
$591$		0			0
$592$	−13.5490	−	6.03239i	−0.556859	−	0.247930i
$593$	39.7293			1.63148			0.815742	−	0.578415i	$-0.196329\pi$
$593$	39.7293			1.63148			0.815742	+	0.578415i	$0.196329\pi$
$594$		0			0
$595$	−4.84604			−0.198668
$596$	−0.0429174	−	0.0191081i	−0.00175797	−	0.000782697i
$597$		0			0
$598$	5.88109	+	6.53161i	0.240496	+	0.267097i
$599$	−7.51680	+	3.34669i	−0.307128	+	0.136742i	−0.554513	−	0.832175i	$-0.687095\pi$
$599$	−7.51680	+	3.34669i	−0.307128	+	0.136742i	0.247385	+	0.968917i	$0.420429\pi$
$600$		0			0
$601$	22.4921	−	4.78084i	0.917471	−	0.195015i	0.275107	−	0.961414i	$-0.411287\pi$
$601$	22.4921	−	4.78084i	0.917471	−	0.195015i	0.642365	+	0.766399i	$0.277953\pi$
$602$	−0.226469	−	0.696998i	−0.00923017	−	0.0284075i
$603$		0			0
$604$	0.384718			0.0156539
$605$	34.7167	+	16.3496i	1.41143	+	0.664707i
$606$		0			0
$607$	−0.00457413	−	0.0435199i	−0.000185658	−	0.00176642i	0.994429	−	0.105412i	$-0.0336160\pi$
$607$	−0.00457413	−	0.0435199i	−0.000185658	−	0.00176642i	−0.994614	+	0.103645i	$0.966949\pi$
$608$	−1.72301	−	0.366237i	−0.0698773	−	0.0148529i
$609$		0			0
$610$	4.13192	−	39.3126i	0.167296	−	1.59172i
$611$	8.25383	+	5.99676i	0.333914	+	0.242603i
$612$		0			0
$613$	−9.45678	−	29.1050i	−0.381956	−	1.17554i	−0.938665	−	0.344832i	$-0.887936\pi$
$613$	−9.45678	−	29.1050i	−0.381956	−	1.17554i	0.556709	−	0.830708i	$-0.312064\pi$
$614$	−5.88336	−	2.61944i	−0.237433	−	0.105712i
$615$		0			0
$616$	0.292353	+	3.09792i	0.0117792	+	0.124819i
$617$	−4.32264	+	7.48703i	−0.174023	+	0.301416i	−0.939823	−	0.341663i	$-0.889010\pi$
$617$	−4.32264	+	7.48703i	−0.174023	+	0.301416i	0.765800	+	0.643079i	$0.222343\pi$
$618$		0			0
$619$	−22.5537	+	25.0484i	−0.906508	+	1.00678i	0.0934301	+	0.995626i	$0.470217\pi$
$619$	−22.5537	+	25.0484i	−0.906508	+	1.00678i	−0.999938	+	0.0111530i	$0.996450\pi$
$620$	0.424505	−	1.30649i	0.0170485	−	0.0524700i
$621$		0			0
$622$	26.3752	+	19.1627i	1.05755	+	0.768354i
$623$	1.14337	−	0.243031i	0.0458081	−	0.00973682i
$624$		0			0
$625$	0.986962	+	9.39032i	0.0394785	+	0.375613i
$626$	12.0001	−	20.7848i	0.479620	−	0.830726i
$627$		0			0
$628$	−0.0276773	−	0.0479385i	−0.00110444	−	0.00191295i
$629$	−11.9329	+	8.66978i	−0.475797	+	0.345687i
$630$		0			0
$631$	4.15555	−	12.7895i	0.165430	−	0.509140i	−0.833638	−	0.552311i	$-0.813746\pi$
$631$	4.15555	−	12.7895i	0.165430	−	0.509140i	0.999068	+	0.0431710i	$0.0137460\pi$
$632$	−2.47835	+	23.5799i	−0.0985833	+	0.937957i
$633$		0			0
$634$	−24.4197	−	27.1208i	−0.969829	−	1.07710i
$635$	−31.4784	−	6.69093i	−1.24918	−	0.265522i
$636$		0			0
$637$	3.98193	+	6.89690i	0.157770	+	0.273265i
$638$	−20.2159	−	15.0185i	−0.800354	−	0.594589i
$639$		0			0
$640$	33.4960	−	24.3363i	1.32405	−	0.961976i
$641$	10.0567	−	11.1691i	0.397215	−	0.441152i	−0.511047	−	0.859553i	$-0.670742\pi$
$641$	10.0567	−	11.1691i	0.397215	−	0.441152i	0.908263	+	0.418400i	$0.137409\pi$
$642$		0			0
$643$	11.7551	−	5.23371i	0.463576	−	0.206397i	−0.161639	−	0.986850i	$-0.551678\pi$
$643$	11.7551	−	5.23371i	0.463576	−	0.206397i	0.625215	+	0.780453i	$0.285011\pi$
$644$	0.113543	−	0.0505528i	0.00447424	−	0.00199206i
$645$		0			0
$646$	−17.7055	+	19.6640i	−0.696614	+	0.773669i
$647$	−15.1827	+	11.0309i	−0.596894	+	0.433669i	−0.844775	−	0.535121i	$-0.820266\pi$
$647$	−15.1827	+	11.0309i	−0.596894	+	0.433669i	0.247881	+	0.968791i	$0.420266\pi$
$648$		0			0
$649$	11.4488	+	36.5531i	0.449404	+	1.43483i
$650$	5.96480	+	10.3313i	0.233959	+	0.405228i
$651$		0			0
$652$	−0.981295	−	0.208581i	−0.0384305	−	0.00816865i
$653$	11.4699	+	12.7386i	0.448850	+	0.498499i	0.924524	−	0.381123i	$-0.124462\pi$
$653$	11.4699	+	12.7386i	0.448850	+	0.498499i	−0.475674	+	0.879622i	$0.657796\pi$
$654$		0			0
$655$	−5.60669	+	53.3441i	−0.219071	+	2.08433i
$656$	−14.2647	+	43.9021i	−0.556941	+	1.71409i
$657$		0			0
$658$	3.46858	−	2.52007i	0.135219	−	0.0982427i
$659$	−20.2286	−	35.0370i	−0.787995	−	1.36485i	−0.927193	−	0.374583i	$-0.877786\pi$
$659$	−20.2286	−	35.0370i	−0.787995	−	1.36485i	0.139198	−	0.990265i	$-0.455548\pi$
$660$		0			0
$661$	−13.2018	+	22.8661i	−0.513489	+	0.889390i	0.486388	+	0.873743i	$0.338314\pi$
$661$	−13.2018	+	22.8661i	−0.513489	+	0.889390i	−0.999878	+	0.0156469i	$0.995019\pi$
$662$	1.14112	+	10.8570i	0.0443508	+	0.421970i
$663$		0			0
$664$	−30.7942	+	6.54551i	−1.19505	+	0.254015i
$665$	4.26516	+	3.09882i	0.165396	+	0.120167i
$666$		0			0
$667$	8.61585	−	26.5168i	0.333607	−	1.02674i
$668$	0.632415	−	0.702368i	0.0244689	−	0.0271754i
$669$		0			0
$670$	−10.4997	+	18.1860i	−0.405638	+	0.702585i
$671$	−13.3012	+	22.4830i	−0.513486	+	0.867948i
$672$		0			0
$673$	−20.2772	−	9.02800i	−0.781630	−	0.348004i	−0.0231764	−	0.999731i	$-0.507378\pi$
$673$	−20.2772	−	9.02800i	−0.781630	−	0.348004i	−0.758453	+	0.651727i	$0.774045\pi$
$674$	6.40622	+	19.7163i	0.246758	+	0.759444i
$675$		0			0
$676$	0.657096	+	0.477409i	0.0252729	+	0.0183619i
$677$	−3.87015	+	36.8221i	−0.148742	+	1.41519i	0.624475	+	0.781045i	$0.285313\pi$
$677$	−3.87015	+	36.8221i	−0.148742	+	1.41519i	−0.773217	+	0.634142i	$0.781354\pi$
$678$		0			0
$679$	−4.30865	−	0.915831i	−0.165351	−	0.0351464i
$680$	−4.16383	−	39.6162i	−0.159676	−	1.51921i
$681$		0			0
$682$	−18.2642	+	19.8559i	−0.699371	+	0.760322i
$683$	−27.2029			−1.04089			−0.520445	−	0.853895i	$-0.674234\pi$
$683$	−27.2029			−1.04089			−0.520445	+	0.853895i	$0.674234\pi$
$684$		0			0
$685$	−2.11458	−	6.50801i	−0.0807940	−	0.248658i
$686$	6.60144	−	1.40318i	0.252044	−	0.0535737i
$687$		0			0
$688$	5.69522	−	2.53567i	0.217128	−	0.0966717i
$689$	−1.56078	−	1.73342i	−0.0594609	−	0.0660380i
$690$		0			0
$691$	13.6125	+	6.06070i	0.517846	+	0.230560i	0.648981	−	0.760805i	$-0.275196\pi$
$691$	13.6125	+	6.06070i	0.517846	+	0.230560i	−0.131135	+	0.991364i	$0.541862\pi$
$692$	1.22480			0.0465598
$693$		0			0
$694$	−24.2297			−0.919746
$695$	56.2392	+	25.0393i	2.13327	+	0.949795i
$696$		0			0
$697$	30.7187	+	34.1166i	1.16355	+	1.29226i
$698$	−40.1882	+	17.8929i	−1.52115	+	0.677258i
$699$		0			0
$700$	0.165012	−	0.0350744i	0.00623686	−	0.00132569i
$701$	1.74688	+	5.37634i	0.0659787	+	0.203062i	0.978611	−	0.205720i	$-0.0659537\pi$
$701$	1.74688	+	5.37634i	0.0659787	+	0.203062i	−0.912632	+	0.408782i	$0.865954\pi$
$702$		0			0
$703$	16.0465			0.605204
$704$	−25.0426	+	5.04542i	−0.943830	+	0.190157i
$705$		0			0
$706$	−0.0731564	−	0.696037i	−0.00275328	−	0.0261957i
$707$	0.721526	+	0.153365i	0.0271358	+	0.00576789i
$708$		0			0
$709$	−4.95891	+	47.1808i	−0.186236	+	1.77191i	0.358716	+	0.933447i	$0.383215\pi$
$709$	−4.95891	+	47.1808i	−0.186236	+	1.77191i	−0.544952	+	0.838467i	$0.683452\pi$
$710$	−9.82960	−	7.14163i	−0.368898	−	0.268020i
$711$		0			0
$712$	2.96918	+	9.13819i	0.111275	+	0.342468i
$713$	−27.2858	−	12.1484i	−1.02186	−	0.454962i
$714$		0			0
$715$	−1.25724	−	13.3223i	−0.0470180	−	0.498226i
$716$	−0.560020	+	0.969983i	−0.0209289	+	0.0362500i
$717$		0			0
$718$	32.9027	−	36.5422i	1.22792	−	1.36374i
$719$	−6.92225	+	21.3045i	−0.258157	+	0.794524i	0.735035	+	0.678029i	$0.237166\pi$
$719$	−6.92225	+	21.3045i	−0.258157	+	0.794524i	−0.993191	+	0.116495i	$0.962834\pi$
$720$		0			0
$721$	0.238212	+	0.173071i	0.00887146	+	0.00644549i
$722$	1.42081	−	0.302003i	0.0528772	−	0.0112394i
$723$		0			0
$724$	0.108160	+	1.02907i	0.00401973	+	0.0382452i
$725$	18.9219	−	32.7737i	0.702742	−	1.21718i
$726$		0			0
$727$	−9.63134	−	16.6820i	−0.357207	−	0.618700i	0.630286	−	0.776363i	$-0.282937\pi$
$727$	−9.63134	−	16.6820i	−0.357207	−	0.618700i	−0.987493	+	0.157663i	$0.949604\pi$
$728$	0.877853	−	0.637798i	0.0325354	−	0.0236383i
$729$		0			0
$730$	5.22864	−	16.0921i	0.193521	−	0.595595i
$731$	0.648079	−	6.16606i	0.0239701	−	0.228060i
$732$		0			0
$733$	24.8205	+	27.5659i	0.916765	+	1.01817i	0.999766	+	0.0216214i	$0.00688283\pi$
$733$	24.8205	+	27.5659i	0.916765	+	1.01817i	−0.0830011	+	0.996549i	$0.526451\pi$
$734$	−3.32601	−	0.706966i	−0.122765	−	0.0260946i
$735$		0			0
$736$	1.04008	+	1.80147i	0.0383379	+	0.0664032i
$737$	11.3132	−	8.03721i	0.416726	−	0.296054i
$738$		0			0
$739$	−24.2184	+	17.5957i	−0.890888	+	0.647268i	−0.936109	−	0.351709i	$-0.885601\pi$
$739$	−24.2184	+	17.5957i	−0.890888	+	0.647268i	0.0452217	+	0.998977i	$0.485601\pi$
$740$	0.583174	−	0.647680i	0.0214379	−	0.0238092i
$741$		0			0
$742$	−0.895481	+	0.398694i	−0.0328742	+	0.0146365i
$743$	5.66871	−	2.52387i	0.207965	−	0.0925919i	−0.300111	−	0.953904i	$-0.597024\pi$
$743$	5.66871	−	2.52387i	0.207965	−	0.0925919i	0.508076	+	0.861312i	$0.330357\pi$
$744$		0			0
$745$	−1.57461	+	1.74879i	−0.0576894	+	0.0640706i
$746$	−26.6135	+	19.3358i	−0.974389	+	0.707935i
$747$		0			0
$748$	0.303072	−	0.900098i	0.0110814	−	0.0329108i
$749$	−1.04081	−	1.80273i	−0.0380303	−	0.0658705i
$750$		0			0
$751$	−0.470257	−	0.0999562i	−0.0171599	−	0.00364745i	0.199324	−	0.979934i	$-0.436125\pi$
$751$	−0.470257	−	0.0999562i	−0.0171599	−	0.00364745i	−0.216484	+	0.976286i	$0.569459\pi$
$752$	24.4039	+	27.1033i	0.889920	+	0.988357i
$753$		0			0
$754$	−0.917972	+	8.73392i	−0.0334306	+	0.318071i
$755$	5.95503	−	18.3277i	0.216726	−	0.667014i
$756$		0			0
$757$	−7.65001	+	5.55806i	−0.278045	+	0.202011i	−0.718064	−	0.695977i	$-0.754972\pi$
$757$	−7.65001	+	5.55806i	−0.278045	+	0.202011i	0.440020	+	0.897988i	$0.354972\pi$
$758$	19.4945	+	33.7655i	0.708074	+	1.22642i
$759$		0			0
$760$	−21.6680	+	37.5301i	−0.785981	+	1.36136i
$761$	0.0588940	+	0.560339i	0.00213491	+	0.0203123i	0.995537	−	0.0943669i	$-0.0300827\pi$
$761$	0.0588940	+	0.560339i	0.00213491	+	0.0203123i	−0.993403	+	0.114679i	$0.963416\pi$
$762$		0			0
$763$	−3.86670	+	0.821893i	−0.139984	+	0.0297545i
$764$	−0.0763161	−	0.0554469i	−0.00276102	−	0.00200600i
$765$		0			0
$766$	9.33392	−	28.7268i	0.337248	−	1.03794i
$767$	8.93768	−	9.92630i	0.322721	−	0.358418i
$768$		0			0
$769$	22.9258	−	39.7086i	0.826725	−	1.43193i	−0.0738688	−	0.997268i	$-0.523535\pi$
$769$	22.9258	−	39.7086i	0.826725	−	1.43193i	0.900594	−	0.434662i	$-0.143132\pi$
$770$	−5.48781	−	1.22757i	−0.197767	−	0.0442385i
$771$		0			0
$772$	−1.42124	−	0.632776i	−0.0511514	−	0.0227741i
$773$	14.6681	+	45.1438i	0.527575	+	1.62371i	0.759166	+	0.650897i	$0.225607\pi$
$773$	14.6681	+	45.1438i	0.527575	+	1.62371i	−0.231591	+	0.972813i	$0.574393\pi$
$774$		0			0
$775$	−32.7977	−	23.8289i	−1.17813	−	0.855960i
$776$	3.78480	−	36.0099i	0.135866	−	1.29268i
$777$		0			0
$778$	−9.92651	−	2.10995i	−0.355883	−	0.0756452i
$779$	−5.22056	−	49.6703i	−0.187046	−	1.77962i
$780$		0			0
$781$	3.94058	+	6.99594i	0.141005	+	0.250335i
$782$	31.2472			1.11740
$783$		0			0
$784$	8.79746	+	27.0758i	0.314195	+	0.966993i
$785$	−2.71217	+	0.576490i	−0.0968017	+	0.0205758i
$786$		0			0
$787$	−22.5174	+	10.0254i	−0.802659	+	0.357367i	−0.766716	−	0.641987i	$-0.778110\pi$
$787$	−22.5174	+	10.0254i	−0.802659	+	0.357367i	−0.0359435	+	0.999354i	$0.511444\pi$
$788$	−0.407598	−	0.452683i	−0.0145201	−	0.0161262i
$789$		0			0
$790$	−39.1438	−	17.4280i	−1.39268	−	0.620059i
$791$	−0.141395			−0.00502742
$792$		0			0
$793$	9.10942			0.323485
$794$	−2.02954	−	0.903611i	−0.0720258	−	0.0320679i
$795$		0			0
$796$	0.297842	+	0.330787i	0.0105567	+	0.0117244i
$797$	36.9213	−	16.4384i	1.30782	−	0.582278i	0.369880	−	0.929080i	$-0.379399\pi$
$797$	36.9213	−	16.4384i	1.30782	−	0.582278i	0.937939	+	0.346801i	$0.112732\pi$
$798$		0			0
$799$	35.4786	−	7.54122i	1.25514	−	0.266789i
$800$	0.872487	+	2.68524i	0.0308471	+	0.0949376i
$801$		0			0
$802$	31.8835			1.12585
$803$	−7.56996	+	8.22970i	−0.267138	+	0.290420i
$804$		0			0
$805$	−0.650767	−	6.19164i	−0.0229365	−	0.218226i
$806$	9.20217	+	1.95598i	0.324132	+	0.0688965i
$807$		0			0
$808$	−0.633802	+	6.03023i	−0.0222971	+	0.212143i
$809$	10.3850	+	7.54517i	0.365119	+	0.265274i	0.755184	−	0.655513i	$-0.227548\pi$
$809$	10.3850	+	7.54517i	0.365119	+	0.265274i	−0.390065	+	0.920787i	$0.627548\pi$
$810$		0			0
$811$	11.5743	+	35.6220i	0.406428	+	1.25086i	0.919697	+	0.392629i	$0.128434\pi$
$811$	11.5743	+	35.6220i	0.406428	+	1.25086i	−0.513269	+	0.858228i	$0.671566\pi$
$812$	0.113451	+	0.0505118i	0.00398136	+	0.00177262i
$813$		0			0
$814$	−15.7094	+	6.79516i	−0.550614	+	0.238170i
$815$	−25.1261	+	43.5196i	−0.880128	+	1.52443i
$816$		0			0
$817$	−4.51331	+	5.01253i	−0.157901	+	0.175366i
$818$	2.10553	−	6.48015i	0.0736180	−	0.226573i
$819$		0			0
$820$	−2.19456	−	1.59444i	−0.0766374	−	0.0556803i
$821$	−46.5293	+	9.89011i	−1.62388	+	0.345167i	−0.927882	−	0.372873i	$-0.878373\pi$
$821$	−46.5293	+	9.89011i	−1.62388	+	0.345167i	−0.696002	+	0.718040i	$0.745039\pi$
$822$		0			0
$823$	−4.20257	−	39.9847i	−0.146492	−	1.39378i	−0.782765	−	0.622317i	$-0.786192\pi$
$823$	−4.20257	−	39.9847i	−0.146492	−	1.39378i	0.636273	−	0.771464i	$-0.280475\pi$
$824$	−1.21017	+	2.09608i	−0.0421583	+	0.0730203i
$825$		0			0
$826$	−2.80660	−	4.86117i	−0.0976541	−	0.169142i
$827$	22.4362	−	16.3008i	0.780182	−	0.566835i	−0.124852	−	0.992175i	$-0.539846\pi$
$827$	22.4362	−	16.3008i	0.780182	−	0.566835i	0.905034	+	0.425340i	$0.139846\pi$
$828$		0			0
$829$	15.8416	−	48.7555i	0.550202	−	1.69335i	−0.158087	−	0.987425i	$-0.550533\pi$
$829$	15.8416	−	48.7555i	0.550202	−	1.69335i	0.708289	−	0.705923i	$-0.249467\pi$
$830$	5.94710	−	56.5829i	0.206427	−	1.96402i
$831$		0			0
$832$	5.96074	+	6.62007i	0.206651	+	0.229510i
$833$	27.6944	+	5.88664i	0.959555	+	0.203960i
$834$		0			0
$835$	−23.6712	−	40.9998i	−0.819177	−	1.41886i
$836$	−0.842314	+	0.598404i	−0.0291320	+	0.0206962i
$837$		0			0
$838$	−46.8980	+	34.0734i	−1.62007	+	1.17705i
$839$	−0.0921287	+	0.102319i	−0.00318063	+	0.00353245i	−0.744733	−	0.667362i	$-0.767423\pi$
$839$	−0.0921287	+	0.102319i	−0.00318063	+	0.00353245i	0.741552	+	0.670895i	$0.234090\pi$
$840$		0			0
$841$	−1.04247	+	0.464137i	−0.0359472	+	0.0160047i
$842$	17.8790	−	7.96024i	0.616151	−	0.274328i
$843$		0			0
$844$	0.307290	−	0.341280i	0.0105774	−	0.0117474i
$845$	32.9146	−	23.9139i	1.13230	−	0.822662i
$846$		0			0
$847$	2.95942	+	2.24777i	0.101687	+	0.0772343i
$848$	−4.16919	−	7.22124i	−0.143170	−	0.247978i
$849$		0			0
$850$	41.4854	+	8.81799i	1.42294	+	0.302455i
$851$	−12.6796	−	14.0821i	−0.434650	−	0.482727i
$852$		0			0
$853$	−1.60566	+	15.2768i	−0.0549767	+	0.523068i	0.932029	+	0.362383i	$0.118037\pi$
$853$	−1.60566	+	15.2768i	−0.0549767	+	0.523068i	−0.987006	+	0.160685i	$0.948630\pi$
$854$	1.18296	−	3.64077i	0.0404800	−	0.124585i
$855$		0			0
$856$	13.8430	−	10.0575i	0.473144	−	0.343759i
$857$	−11.5275	−	19.9662i	−0.393773	−	0.682034i	0.599171	−	0.800621i	$-0.295497\pi$
$857$	−11.5275	−	19.9662i	−0.393773	−	0.682034i	−0.992944	+	0.118587i	$0.962164\pi$
$858$		0			0
$859$	27.0597	−	46.8688i	0.923265	−	1.59914i	0.128937	−	0.991653i	$-0.458844\pi$
$859$	27.0597	−	46.8688i	0.923265	−	1.59914i	0.794328	−	0.607489i	$-0.207823\pi$
$860$	0.0382936	+	0.364339i	0.00130580	+	0.0124239i
$861$		0			0
$862$	−11.0527	+	2.34932i	−0.376457	+	0.0800183i
$863$	−34.3062	−	24.9249i	−1.16780	−	0.848453i	−0.177052	−	0.984201i	$-0.556656\pi$
$863$	−34.3062	−	24.9249i	−1.16780	−	0.848453i	−0.990743	+	0.135748i	$0.956656\pi$
$864$		0			0
$865$	18.9586	−	58.3486i	0.644612	−	1.98391i
$866$	−1.32911	+	1.47613i	−0.0451651	+	0.0501609i
$867$		0			0
$868$	0.0665182	−	0.115213i	0.00225778	−	0.00391058i
$869$	18.7227	+	21.2434i	0.635123	+	0.720632i
$870$		0			0
$871$	−4.42089	−	1.96831i	−0.149796	−	0.0666935i
$872$	−10.0413	−	30.9040i	−0.340042	−	1.04654i
$873$		0			0
$874$	−27.5017	−	19.9811i	−0.930258	−	0.675872i
$875$	0.267320	−	2.54338i	0.00903706	−	0.0859819i
$876$		0			0
$877$	49.7123	+	10.5667i	1.67866	+	0.356811i	0.946097	−	0.323884i	$-0.104989\pi$
$877$	49.7123	+	10.5667i	1.67866	+	0.356811i	0.732567	+	0.680695i	$0.238322\pi$
$878$	−0.828474	−	7.88240i	−0.0279596	−	0.266018i
$879$		0			0
$880$	5.50555	−	47.5183i	0.185592	−	1.60184i
$881$	33.9359			1.14333			0.571665	−	0.820487i	$-0.306298\pi$
$881$	33.9359			1.14333			0.571665	+	0.820487i	$0.306298\pi$
$882$		0			0
$883$	−14.3560	−	44.1833i	−0.483119	−	1.48689i	−0.834687	−	0.550725i	$-0.814351\pi$
$883$	−14.3560	−	44.1833i	−0.483119	−	1.48689i	0.351568	−	0.936162i	$-0.385649\pi$
$884$	−0.323954	+	0.0688585i	−0.0108958	+	0.00231596i
$885$		0			0
$886$	1.45006	−	0.645609i	0.0487158	−	0.0216897i
$887$	16.3803	+	18.1922i	0.549997	+	0.610833i	0.952483	−	0.304593i	$-0.0985204\pi$
$887$	16.3803	+	18.1922i	0.549997	+	0.610833i	−0.402486	+	0.915426i	$0.631854\pi$
$888$		0			0
$889$	−2.84714	−	1.26763i	−0.0954899	−	0.0425148i
$890$	−17.3644			−0.582056
$891$		0			0
$892$	−0.466401			−0.0156162
$893$	−36.0482	−	16.0497i	−1.20631	−	0.537082i
$894$		0			0
$895$	37.5408	+	41.6933i	1.25485	+	1.39365i
$896$	3.66299	−	1.63087i	0.122372	−	0.0544835i
$897$		0			0
$898$	−2.03023	+	0.431539i	−0.0677497	+	0.0144006i
$899$	−9.22225	−	28.3832i	−0.307579	−	0.946632i
$900$		0			0
$901$	−8.29267			−0.276269
$902$	26.1447	+	46.4162i	0.870522	+	1.54549i
$903$		0			0
$904$	−0.121490	−	1.15590i	−0.00404069	−	0.0384446i
$905$	50.6985	+	10.7763i	1.68528	+	0.358217i
$906$		0			0
$907$	3.59491	−	34.2032i	0.119367	−	1.13570i	−0.756785	−	0.653664i	$-0.773231\pi$
$907$	3.59491	−	34.2032i	0.119367	−	1.13570i	0.876152	−	0.482036i	$-0.160102\pi$
$908$	−0.346362	−	0.251647i	−0.0114944	−	0.00835118i
$909$		0			0
$910$	0.605972	+	1.86499i	0.0200878	+	0.0618238i
$911$	14.4082	+	6.41493i	0.477364	+	0.212536i	0.631291	−	0.775546i	$-0.282525\pi$
$911$	14.4082	+	6.41493i	0.477364	+	0.212536i	−0.153927	+	0.988082i	$0.549192\pi$
$912$		0			0
$913$	−19.1445	+	32.3600i	−0.633590	+	1.07096i
$914$	−21.6998	+	37.5852i	−0.717767	+	1.24321i
$915$		0			0
$916$	−1.06790	+	1.18602i	−0.0352843	+	0.0391872i
$917$	−1.60518	+	4.94024i	−0.0530078	+	0.163141i
$918$		0			0
$919$	−24.4677	−	17.7768i	−0.807115	−	0.586403i	0.105878	−	0.994379i	$-0.466235\pi$
$919$	−24.4677	−	17.7768i	−0.807115	−	0.586403i	−0.912993	+	0.407976i	$0.866235\pi$
$920$	50.0572	−	10.6400i	1.65034	−	0.350790i
$921$		0			0
$922$	4.01162	+	38.1680i	0.132116	+	1.25700i
$923$	1.39998	−	2.42484i	0.0460809	−	0.0798145i
$924$		0			0
$925$	−12.8600	−	22.2743i	−0.422836	−	0.732373i
$926$	0.811777	−	0.589790i	0.0266766	−	0.0193817i
$927$		0			0
$928$	−0.642285	+	1.97675i	−0.0210840	+	0.0648900i
$929$	0.0320686	−	0.305112i	0.00105214	−	0.0100104i	−0.993983	−	0.109532i	$-0.965065\pi$
$929$	0.0320686	−	0.305112i	0.00105214	−	0.0100104i	0.995035	+	0.0995219i	$0.0317313\pi$
$930$		0			0
$931$	−20.6105	−	22.8903i	−0.675483	−	0.750200i
$932$	−0.803538	−	0.170797i	−0.0263208	−	0.00559465i
$933$		0			0
$934$	−23.0360	−	39.8994i	−0.753760	−	1.30555i
$935$	−38.1888	−	28.3707i	−1.24891	−	0.927823i
$936$		0			0
$937$	−11.1295	+	8.08603i	−0.363584	+	0.264159i	−0.754545	−	0.656248i	$-0.772143\pi$
$937$	−11.1295	+	8.08603i	−0.363584	+	0.264159i	0.390962	+	0.920407i	$0.372143\pi$
$938$	−1.36078	+	1.51130i	−0.0444309	+	0.0493456i
$939$		0			0
$940$	−1.95790	+	0.871713i	−0.0638596	+	0.0284321i
$941$	−2.27374	+	1.01233i	−0.0741216	+	0.0330011i	−0.443463	−	0.896293i	$-0.646250\pi$
$941$	−2.27374	+	1.01233i	−0.0741216	+	0.0330011i	0.369341	+	0.929294i	$0.379583\pi$
$942$		0			0
$943$	−39.4645	+	43.8298i	−1.28514	+	1.42730i
$944$	38.6298	−	28.0662i	1.25729	−	0.913477i
$945$		0			0
$946$	2.29585	−	6.81848i	0.0746446	−	0.221688i
$947$	−7.58098	−	13.1306i	−0.246349	−	0.426689i	0.716161	−	0.697935i	$-0.245898\pi$
$947$	−7.58098	−	13.1306i	−0.246349	−	0.426689i	−0.962510	+	0.271246i	$0.912564\pi$
$948$		0			0
$949$	3.81403	+	0.810698i	0.123809	+	0.0263164i
$950$	−30.8739	−	34.2890i	−1.00168	−	1.11248i
$951$		0			0
$952$	0.403240	−	3.83657i	0.0130691	−	0.124344i
$953$	−6.45470	+	19.8655i	−0.209088	+	0.643507i	0.790433	+	0.612549i	$0.209856\pi$
$953$	−6.45470	+	19.8655i	−0.209088	+	0.643507i	−0.999521	+	0.0309580i	$0.990144\pi$
$954$		0			0
$955$	−3.82275	+	2.77739i	−0.123701	+	0.0898742i
$956$	−0.336128	−	0.582191i	−0.0108712	−	0.0188294i
$957$		0			0
$958$	15.8166	−	27.3951i	0.511010	−	0.885095i
$959$	−0.0692703	−	0.659063i	−0.00223685	−	0.0212822i
$960$		0			0
$961$	−0.949012	+	0.201719i	−0.0306133	+	0.00650705i
$962$	4.82870	+	3.50825i	0.155683	+	0.113111i
$963$		0			0
$964$	−0.156392	+	0.481326i	−0.00503705	+	0.0155025i
$965$	−52.1443	+	57.9121i	−1.67858	+	1.86426i
$966$		0			0
$967$	−28.6868	+	49.6870i	−0.922505	+	1.59783i	−0.126980	+	0.991905i	$0.540528\pi$
$967$	−28.6868	+	49.6870i	−0.922505	+	1.59783i	−0.795525	+	0.605920i	$0.792805\pi$
$968$	−15.8326	+	26.1244i	−0.508881	+	0.839671i
$969$		0			0
$970$	59.7784	+	26.6150i	1.91937	+	0.854558i
$971$	−1.39820	−	4.30322i	−0.0448704	−	0.138097i	0.926111	−	0.377250i	$-0.123130\pi$
$971$	−1.39820	−	4.30322i	−0.0448704	−	0.138097i	−0.970982	+	0.239153i	$0.923130\pi$
$972$		0			0
$973$	4.82322	+	3.50427i	0.154625	+	0.112342i
$974$	2.63476	−	25.0681i	0.0844232	−	0.803233i
$975$		0			0
$976$	31.8527	+	6.77051i	1.01958	+	0.216719i
$977$	−1.87556	−	17.8447i	−0.0600043	−	0.570903i	−0.982678	−	0.185321i	$-0.940667\pi$
$977$	−1.87556	−	17.8447i	−0.0600043	−	0.570903i	0.922674	−	0.385582i	$-0.125999\pi$
$978$		0			0
$979$	10.4330	+	4.77858i	0.333441	+	0.152724i
$980$	−1.67296			−0.0534408
$981$		0			0
$982$	−0.0894786	−	0.275387i	−0.00285538	−	0.00878795i
$983$	−6.31572	+	1.34245i	−0.201440	+	0.0428175i	−0.307527	−	0.951539i	$-0.599501\pi$
$983$	−6.31572	+	1.34245i	−0.201440	+	0.0428175i	0.106086	+	0.994357i	$0.466168\pi$
$984$		0			0
$985$	−27.8747	+	12.4106i	−0.888162	+	0.395435i
$986$	20.8915	+	23.2024i	0.665322	+	0.738915i
$987$		0			0
$988$	0.329154	+	0.146549i	0.0104718	+	0.00466234i
$989$	7.96522			0.253279
$990$		0			0
$991$	12.2590			0.389420			0.194710	−	0.980861i	$-0.437623\pi$
$991$	12.2590			0.389420			0.194710	+	0.980861i	$0.437623\pi$
$992$	2.03407	+	0.905628i	0.0645819	+	0.0287537i
$993$		0			0
$994$	−0.787335	−	0.874424i	−0.0249728	−	0.0277351i
$995$	20.3688	−	9.06877i	0.645734	−	0.287499i
$996$		0			0
$997$	−11.9369	+	2.53726i	−0.378044	+	0.0803557i	−0.393015	−	0.919532i	$-0.628568\pi$
$997$	−11.9369	+	2.53726i	−0.378044	+	0.0803557i	0.0149707	+	0.999888i	$0.495234\pi$
$998$	10.8486	+	33.3885i	0.343406	+	1.05689i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.91.3		72
3.2	odd	2		99.2.m.b.58.7	yes	72
9.2	odd	6		99.2.m.b.25.3	yes	72
9.4	even	3		891.2.f.e.487.7		36
9.5	odd	6		891.2.f.f.487.3		36
9.7	even	3	inner	297.2.n.b.289.7		72
11.4	even	5	inner	297.2.n.b.37.7		72
33.2	even	10		1089.2.e.o.364.14		36
33.20	odd	10		1089.2.e.p.364.5		36
33.26	odd	10		99.2.m.b.4.3	✓	72
99.2	even	30		1089.2.e.o.727.14		36
99.4	even	15		891.2.f.e.730.7		36
99.13	odd	30		9801.2.a.cn.1.14		18
99.20	odd	30		1089.2.e.p.727.5		36
99.31	even	15		9801.2.a.cp.1.5		18
99.59	odd	30		891.2.f.f.730.3		36
99.68	even	30		9801.2.a.co.1.5		18
99.70	even	15	inner	297.2.n.b.235.3		72
99.86	odd	30		9801.2.a.cm.1.14		18
99.92	odd	30		99.2.m.b.70.7	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.3	✓	72	33.26	odd	10
99.2.m.b.25.3	yes	72	9.2	odd	6
99.2.m.b.58.7	yes	72	3.2	odd	2
99.2.m.b.70.7	yes	72	99.92	odd	30
297.2.n.b.37.7		72	11.4	even	5	inner
297.2.n.b.91.3		72	1.1	even	1	trivial
297.2.n.b.235.3		72	99.70	even	15	inner
297.2.n.b.289.7		72	9.7	even	3	inner
891.2.f.e.487.7		36	9.4	even	3
891.2.f.e.730.7		36	99.4	even	15
891.2.f.f.487.3		36	9.5	odd	6
891.2.f.f.730.3		36	99.59	odd	30
1089.2.e.o.364.14		36	33.2	even	10
1089.2.e.o.727.14		36	99.2	even	30
1089.2.e.p.364.5		36	33.20	odd	10
1089.2.e.p.727.5		36	99.20	odd	30
9801.2.a.cm.1.14		18	99.86	odd	30
9801.2.a.cn.1.14		18	99.13	odd	30
9801.2.a.co.1.5		18	99.68	even	30
9801.2.a.cp.1.5		18	99.31	even	15

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31425 - 0.585142i) q^{2} +(0.0466010 + 0.0517556i) q^{4} +(3.18694 - 1.41892i) q^{5} +(0.330459 - 0.0702413i) q^{7} +(0.858159 + 2.64114i) q^{8} -5.01870 q^{10} +(3.01538 + 1.38112i) q^{11} +(-0.120893 - 1.15022i) q^{13} +(-0.475408 - 0.101051i) q^{14} +(0.432166 - 4.11179i) q^{16} +(-3.32650 - 2.41684i) q^{17} +(1.38230 + 4.25428i) q^{19} +(0.221951 + 0.0988191i) q^{20} +(-3.15481 - 3.57956i) q^{22} +(2.64122 - 4.57472i) q^{23} +(4.79760 - 5.32827i) q^{25} +(-0.514156 + 1.58241i) q^{26} +(0.0190351 + 0.0138298i) q^{28} +(5.16281 - 1.09739i) q^{29} +(-0.591027 - 5.62325i) q^{31} +(-0.196895 + 0.341031i) q^{32} +(2.95766 + 5.12281i) q^{34} +(0.953487 - 0.692749i) q^{35} +(1.10852 - 3.41166i) q^{37} +(0.672671 - 6.40003i) q^{38} +(6.48246 + 7.19950i) q^{40} +(-10.9211 - 2.32135i) q^{41} +(0.753935 + 1.30585i) q^{43} +(0.0690391 + 0.220424i) q^{44} +(-6.14808 + 4.46684i) q^{46} +(-5.90260 + 6.55551i) q^{47} +(-6.29055 + 2.80073i) q^{49} +(-9.42304 + 4.19541i) q^{50} +(0.0538964 - 0.0598580i) q^{52} +(1.63163 - 1.18545i) q^{53} +(11.5695 + 0.122962i) q^{55} +(0.469104 + 0.812512i) q^{56} +(-7.42735 - 1.57873i) q^{58} +(7.72787 + 8.58266i) q^{59} +(-0.823304 + 7.83322i) q^{61} +(-2.51364 + 7.73619i) q^{62} +(-6.23134 + 4.52733i) q^{64} +(-2.01734 - 3.49413i) q^{65} +(2.09211 - 3.62364i) q^{67} +(-0.0299329 - 0.284792i) q^{68} +(-1.65848 + 0.352520i) q^{70} +(1.95860 + 1.42300i) q^{71} +(-1.04183 + 3.20643i) q^{73} +(-3.45317 + 3.83514i) q^{74} +(-0.155767 + 0.269796i) q^{76} +(1.09347 + 0.244599i) q^{77} +(7.79960 + 3.47260i) q^{79} +(-4.45700 - 13.7172i) q^{80} +(12.9947 + 9.44124i) q^{82} +(-1.18499 + 11.2744i) q^{83} +(-14.0306 - 2.98231i) q^{85} +(-0.226749 - 2.15738i) q^{86} +(-1.06005 + 9.14926i) q^{88} +3.45994 q^{89} +(-0.120743 - 0.371608i) q^{91} +(0.359851 - 0.0764886i) q^{92} +(11.5934 - 5.16171i) q^{94} +(10.4418 + 11.5968i) q^{95} +(-11.9111 - 5.30317i) q^{97} +9.90618 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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