LMFDB - Embedded newform 684.2.cf.b.127.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [684,2,Mod(91,684)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(684, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 0, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("684.91"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.cf (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [60,-3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$10$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			127.10
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.b.307.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37514 + 0.330144i) q^{2} +(1.78201 + 0.907986i) q^{4} +(-0.432248 - 2.45140i) q^{5} +(-1.95860 - 1.13080i) q^{7} +(2.15074 + 1.83693i) q^{8} +(0.214913 - 3.51371i) q^{10} +(3.50932 - 2.02611i) q^{11} +(-0.674540 - 1.85328i) q^{13} +(-2.32002 - 2.20162i) q^{14} +(2.35112 + 3.23608i) q^{16} +(4.59329 - 3.85423i) q^{17} +(-1.31039 + 4.15727i) q^{19} +(1.45557 - 4.76089i) q^{20} +(5.49471 - 1.62760i) q^{22} +(-2.40556 - 0.424166i) q^{23} +(-1.12405 + 0.409121i) q^{25} +(-0.315736 - 2.77122i) q^{26} +(-2.46349 - 3.79347i) q^{28} +(6.27599 - 7.47944i) q^{29} +(-2.39881 + 4.15486i) q^{31} +(2.16474 + 5.22627i) q^{32} +(7.58886 - 3.78365i) q^{34} +(-1.92543 + 5.29009i) q^{35} -1.46248i q^{37} +(-3.17447 + 5.28420i) q^{38} +(3.57338 - 6.06634i) q^{40} +(-3.98615 + 10.9519i) q^{41} +(-1.50372 + 0.265146i) q^{43} +(8.09332 - 0.424128i) q^{44} +(-3.16795 - 1.37747i) q^{46} +(-0.929224 + 1.10741i) q^{47} +(-0.942596 - 1.63262i) q^{49} +(-1.68079 + 0.191500i) q^{50} +(0.480719 - 3.91504i) q^{52} +(-2.26529 - 0.399432i) q^{53} +(-6.48369 - 7.72696i) q^{55} +(-2.13525 - 6.02986i) q^{56} +(11.0996 - 8.21328i) q^{58} +(-8.73918 + 7.33304i) q^{59} +(-1.80322 + 10.2266i) q^{61} +(-4.67039 + 4.92155i) q^{62} +(1.25140 + 7.90152i) q^{64} +(-4.25157 + 2.45464i) q^{65} +(8.48745 + 7.12181i) q^{67} +(11.6849 - 2.69763i) q^{68} +(-4.39423 + 6.63893i) q^{70} +(-1.05276 - 5.97051i) q^{71} +(-3.23920 - 1.17897i) q^{73} +(0.482829 - 2.01111i) q^{74} +(-6.10988 + 6.21847i) q^{76} -9.16447 q^{77} +(5.12059 + 1.86374i) q^{79} +(6.91666 - 7.16232i) q^{80} +(-9.09719 + 13.7443i) q^{82} +(6.35421 + 3.66861i) q^{83} +(-11.4337 - 9.59400i) q^{85} +(-2.15536 - 0.131830i) q^{86} +(11.2695 + 2.08873i) q^{88} +(4.28998 + 11.7866i) q^{89} +(-0.774535 + 4.39260i) q^{91} +(-3.90160 - 2.94009i) q^{92} +(-1.64342 + 1.21606i) q^{94} +(10.7575 + 1.41532i) q^{95} +(-3.13752 - 3.73916i) q^{97} +(-0.757199 - 2.55628i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37514	+	0.330144i	0.972370	+	0.233447i
$2$	1.37514	+	0.330144i	0.972370	+	0.233447i
$3$		0			0
$3$		0			0
$4$	1.78201	+	0.907986i	0.891005	+	0.453993i
$5$	−0.432248	−	2.45140i	−0.193307	−	1.09630i	−0.914809	−	0.403886i	$-0.867659\pi$
$5$	−0.432248	−	2.45140i	−0.193307	−	1.09630i	0.721502	−	0.692412i	$-0.243452\pi$
$6$		0			0
$7$	−1.95860	−	1.13080i	−0.740280	−	0.427401i	0.0818908	−	0.996641i	$-0.473904\pi$
$7$	−1.95860	−	1.13080i	−0.740280	−	0.427401i	−0.822171	+	0.569240i	$0.807237\pi$
$8$	2.15074	+	1.83693i	0.760403	+	0.649452i
$9$		0			0
$10$	0.214913	−	3.51371i	0.0679616	−	1.11113i
$11$	3.50932	−	2.02611i	1.05810	−	0.610894i	0.133194	−	0.991090i	$-0.457477\pi$
$11$	3.50932	−	2.02611i	1.05810	−	0.610894i	0.924906	+	0.380196i	$0.124143\pi$
$12$		0			0
$13$	−0.674540	−	1.85328i	−0.187084	−	0.514008i	0.810323	−	0.585984i	$-0.199292\pi$
$13$	−0.674540	−	1.85328i	−0.187084	−	0.514008i	−0.997406	+	0.0719757i	$0.977070\pi$
$14$	−2.32002	−	2.20162i	−0.620051	−	0.588408i
$15$		0			0
$16$	2.35112	+	3.23608i	0.587780	+	0.809021i
$17$	4.59329	−	3.85423i	1.11404	−	0.934788i	0.115749	−	0.993279i	$-0.463073\pi$
$17$	4.59329	−	3.85423i	1.11404	−	0.934788i	0.998288	+	0.0584910i	$0.0186289\pi$
$18$		0			0
$19$	−1.31039	+	4.15727i	−0.300625	+	0.953743i
$19$	−1.31039	+	4.15727i	−0.300625	+	0.953743i
$20$	1.45557	−	4.76089i	0.325475	−	1.06457i
$21$		0			0
$22$	5.49471	−	1.62760i	1.17148	−	0.347005i
$23$	−2.40556	−	0.424166i	−0.501595	−	0.0884447i	−0.0828746	−	0.996560i	$-0.526410\pi$
$23$	−2.40556	−	0.424166i	−0.501595	−	0.0884447i	−0.418720	+	0.908115i	$0.637521\pi$
$24$		0			0
$25$	−1.12405	+	0.409121i	−0.224810	+	0.0818242i
$26$	−0.315736	−	2.77122i	−0.0619209	−	0.543480i
$27$		0			0
$28$	−2.46349	−	3.79347i	−0.465556	−	0.716899i
$29$	6.27599	−	7.47944i	1.16542	−	1.38890i	0.259346	−	0.965785i	$-0.416493\pi$
$29$	6.27599	−	7.47944i	1.16542	−	1.38890i	0.906077	−	0.423112i	$-0.139062\pi$
$30$		0			0
$31$	−2.39881	+	4.15486i	−0.430839	+	0.746235i	−0.996946	−	0.0780971i	$-0.975116\pi$
$31$	−2.39881	+	4.15486i	−0.430839	+	0.746235i	0.566107	+	0.824332i	$0.308449\pi$
$32$	2.16474	+	5.22627i	0.382676	+	0.923882i
$33$		0			0
$34$	7.58886	−	3.78365i	1.30148	−	0.648891i
$35$	−1.92543	+	5.29009i	−0.325458	+	0.894188i
$36$		0			0
$37$		−	1.46248i		−	0.240430i	−0.992748	−	0.120215i	$-0.961642\pi$
$37$		−	1.46248i		−	0.240430i	0.992748	−	0.120215i	$-0.0383584\pi$
$38$	−3.17447	+	5.28420i	−0.514966	+	0.857210i
$39$		0			0
$40$	3.57338	−	6.06634i	0.565002	−	0.959172i
$41$	−3.98615	+	10.9519i	−0.622532	+	1.71039i	0.0781722	+	0.996940i	$0.475092\pi$
$41$	−3.98615	+	10.9519i	−0.622532	+	1.71039i	−0.700704	+	0.713452i	$0.747131\pi$
$42$		0			0
$43$	−1.50372	+	0.265146i	−0.229315	+	0.0404344i	−0.287125	−	0.957893i	$-0.592699\pi$
$43$	−1.50372	+	0.265146i	−0.229315	+	0.0404344i	0.0578099	+	0.998328i	$0.481588\pi$
$44$	8.09332	−	0.424128i	1.22011	−	0.0639397i
$45$		0			0
$46$	−3.16795	−	1.37747i	−0.467088	−	0.203097i
$47$	−0.929224	+	1.10741i	−0.135541	+	0.161532i	−0.829546	−	0.558439i	$-0.811400\pi$
$47$	−0.929224	+	1.10741i	−0.135541	+	0.161532i	0.694004	+	0.719971i	$0.255845\pi$
$48$		0			0
$49$	−0.942596	−	1.63262i	−0.134657	−	0.233232i
$50$	−1.68079	+	0.191500i	−0.237700	+	0.0270821i
$51$		0			0
$52$	0.480719	−	3.91504i	0.0666637	−	0.542919i
$53$	−2.26529	−	0.399432i	−0.311162	−	0.0548662i	0.0158867	−	0.999874i	$-0.494943\pi$
$53$	−2.26529	−	0.399432i	−0.311162	−	0.0548662i	−0.327048	+	0.945008i	$0.606054\pi$
$54$		0			0
$55$	−6.48369	−	7.72696i	−0.874261	−	1.04190i
$56$	−2.13525	−	6.02986i	−0.285335	−	0.805773i
$57$		0			0
$58$	11.0996	−	8.21328i	1.45746	−	1.07846i
$59$	−8.73918	+	7.33304i	−1.13774	+	0.954681i	−0.999363	−	0.0356984i	$-0.988634\pi$
$59$	−8.73918	+	7.33304i	−1.13774	+	0.954681i	−0.138381	+	0.990379i	$0.544190\pi$
$60$		0			0
$61$	−1.80322	+	10.2266i	−0.230879	+	1.30938i	0.620241	+	0.784411i	$0.287035\pi$
$61$	−1.80322	+	10.2266i	−0.230879	+	1.30938i	−0.851121	+	0.524970i	$0.824076\pi$
$62$	−4.67039	+	4.92155i	−0.593141	+	0.625038i
$63$		0			0
$64$	1.25140	+	7.90152i	0.156425	+	0.987690i
$65$	−4.25157	+	2.45464i	−0.527342	+	0.304461i
$66$		0			0
$67$	8.48745	+	7.12181i	1.03691	+	0.870068i	0.991657	−	0.128908i	$-0.0411471\pi$
$67$	8.48745	+	7.12181i	1.03691	+	0.870068i	0.0452501	+	0.998976i	$0.485592\pi$
$68$	11.6849	−	2.69763i	1.41700	−	0.327136i
$69$		0			0
$70$	−4.39423	+	6.63893i	−0.525211	+	0.793504i
$71$	−1.05276	−	5.97051i	−0.124940	−	0.708569i	−0.981344	−	0.192262i	$-0.938418\pi$
$71$	−1.05276	−	5.97051i	−0.124940	−	0.708569i	0.856404	−	0.516307i	$-0.172694\pi$
$72$		0			0
$73$	−3.23920	−	1.17897i	−0.379120	−	0.137988i	0.145429	−	0.989369i	$-0.453544\pi$
$73$	−3.23920	−	1.17897i	−0.379120	−	0.137988i	−0.524549	+	0.851380i	$0.675766\pi$
$74$	0.482829	−	2.01111i	0.0561277	−	0.233787i
$75$		0			0
$76$	−6.10988	+	6.21847i	−0.700851	+	0.713308i
$77$	−9.16447			−1.04439
$78$		0			0
$79$	5.12059	+	1.86374i	0.576112	+	0.209688i	0.613610	−	0.789609i	$-0.289717\pi$
$79$	5.12059	+	1.86374i	0.576112	+	0.209688i	−0.0374984	+	0.999297i	$0.511939\pi$
$80$	6.91666	−	7.16232i	0.773306	−	0.800772i
$81$		0			0
$82$	−9.09719	+	13.7443i	−1.00462	+	1.51781i
$83$	6.35421	+	3.66861i	0.697466	+	0.402682i	0.806403	−	0.591367i	$-0.201411\pi$
$83$	6.35421	+	3.66861i	0.697466	+	0.402682i	−0.108937	+	0.994049i	$0.534745\pi$
$84$		0			0
$85$	−11.4337	−	9.59400i	−1.24016	−	1.04062i
$86$	−2.15536	−	0.131830i	−0.232418	−	0.0142156i
$87$		0			0
$88$	11.2695	+	2.08873i	1.20133	+	0.222659i
$89$	4.28998	+	11.7866i	0.454737	+	1.24938i	0.929355	+	0.369187i	$0.120364\pi$
$89$	4.28998	+	11.7866i	0.454737	+	1.24938i	−0.474618	+	0.880192i	$0.657414\pi$
$90$		0			0
$91$	−0.774535	+	4.39260i	−0.0811933	+	0.460470i
$92$	−3.90160	−	2.94009i	−0.406770	−	0.306525i
$93$		0			0
$94$	−1.64342	+	1.21606i	−0.169505	+	0.125427i
$95$	10.7575	+	1.41532i	1.10370	+	0.145209i
$96$		0			0
$97$	−3.13752	−	3.73916i	−0.318567	−	0.379654i	0.582868	−	0.812567i	$-0.301930\pi$
$97$	−3.13752	−	3.73916i	−0.318567	−	0.379654i	−0.901436	+	0.432913i	$0.857486\pi$
$98$	−0.757199	−	2.55628i	−0.0764886	−	0.258223i
$99$		0			0
$100$	−2.37455	−	0.291565i	−0.237455	−	0.0291565i
$101$	−1.91216	+	0.695968i	−0.190267	+	0.0692514i	−0.435396	−	0.900239i	$-0.643392\pi$
$101$	−1.91216	+	0.695968i	−0.190267	+	0.0692514i	0.245130	+	0.969490i	$0.421169\pi$
$102$		0			0
$103$	0.520359	+	0.901288i	0.0512725	+	0.0888065i	0.890523	−	0.454939i	$-0.150339\pi$
$103$	0.520359	+	0.901288i	0.0512725	+	0.0888065i	−0.839250	+	0.543746i	$0.817006\pi$
$104$	1.95358	−	5.22502i	0.191564	−	0.512355i
$105$		0			0
$106$	−2.98322	−	1.29715i	−0.289756	−	0.125990i
$107$	1.97600	−	3.42253i	0.191027	−	0.330868i	−0.754564	−	0.656227i	$-0.772152\pi$
$107$	1.97600	−	3.42253i	0.191027	−	0.330868i	0.945591	+	0.325358i	$0.105485\pi$
$108$		0			0
$109$	13.0850	−	2.30724i	1.25331	−	0.220993i	0.492701	−	0.870198i	$-0.336009\pi$
$109$	13.0850	−	2.30724i	1.25331	−	0.220993i	0.760613	+	0.649205i	$0.224898\pi$
$110$	−6.36496	−	12.7662i	−0.606875	−	1.21721i
$111$		0			0
$112$	−0.945549	−	8.99683i	−0.0893459	−	0.850120i
$113$		−	7.56376i		−	0.711539i	−0.934574	−	0.355770i	$-0.884219\pi$
$113$		−	7.56376i		−	0.711539i	0.934574	−	0.355770i	$-0.115781\pi$
$114$		0			0
$115$			6.08034i			0.566995i
$116$	17.9751	−	7.62992i	1.66895	−	0.708420i
$117$		0			0
$118$	−14.4385	+	7.19876i	−1.32917	+	0.662700i
$119$	−13.3548	+	2.35480i	−1.22423	+	0.215865i
$120$		0			0
$121$	2.71022	−	4.69424i	0.246384	−	0.426749i
$122$	−5.85593	+	13.4677i	−0.530171	+	1.21930i
$123$		0			0
$124$	−8.04726	+	5.22592i	−0.722665	+	0.469301i
$125$	−4.73425	−	8.19996i	−0.423444	−	0.733427i
$126$		0			0
$127$	−11.6296	+	4.23284i	−1.03196	+	0.375604i	−0.801828	−	0.597554i	$-0.796139\pi$
$127$	−11.6296	+	4.23284i	−1.03196	+	0.375604i	−0.230136	+	0.973159i	$0.573917\pi$
$128$	−0.887785	+	11.2788i	−0.0784698	+	0.996916i
$129$		0			0
$130$	−6.65688	+	1.97185i	−0.583847	+	0.172942i
$131$	−11.1257	−	13.2590i	−0.972054	−	1.15845i	−0.987348	−	0.158566i	$-0.949313\pi$
$131$	−11.1257	−	13.2590i	−0.972054	−	1.15845i	0.0152947	−	0.999883i	$-0.495131\pi$
$132$		0			0
$133$	7.26756	−	6.66063i	0.630177	−	0.577550i
$134$	9.32019	+	12.5956i	0.805142	+	1.08809i
$135$		0			0
$136$	16.9589	+	0.148077i	1.45422	+	0.0126975i
$137$	−0.619278	+	3.51210i	−0.0529085	+	0.300059i	−0.999767	−	0.0215919i	$-0.993127\pi$
$137$	−0.619278	+	3.51210i	−0.0529085	+	0.300059i	0.946858	+	0.321651i	$0.104238\pi$
$138$		0			0
$139$	2.32823	+	6.39676i	0.197478	+	0.542566i	0.998421	−	0.0561742i	$-0.0178902\pi$
$139$	2.32823	+	6.39676i	0.197478	+	0.542566i	−0.800943	+	0.598741i	$0.795668\pi$
$140$	−8.23447	+	7.67872i	−0.695940	+	0.648970i
$141$		0			0
$142$	0.523433	−	8.55784i	0.0439255	−	0.718158i
$143$	−6.12213	−	5.13707i	−0.511958	−	0.429584i
$144$		0			0
$145$	−21.0479	−	12.1520i	−1.74793	−	1.00917i
$146$	−4.06512	−	2.69065i	−0.336432	−	0.222680i
$147$		0			0
$148$	1.32791	−	2.60615i	0.109154	−	0.214225i
$149$	−11.8357	−	4.30783i	−0.969617	−	0.352912i	−0.191822	−	0.981430i	$-0.561440\pi$
$149$	−11.8357	−	4.30783i	−0.969617	−	0.352912i	−0.777795	+	0.628518i	$0.783662\pi$
$150$		0			0
$151$	−16.1180			−1.31166			−0.655830	−	0.754908i	$-0.727681\pi$
$151$	−16.1180			−1.31166			−0.655830	+	0.754908i	$0.727681\pi$
$152$	−10.4549	+	6.53412i	−0.848005	+	0.529988i
$153$		0			0
$154$	−12.6024	−	3.02559i	−1.01553	−	0.243809i
$155$	11.2221	+	4.08451i	0.901380	+	0.328076i
$156$		0			0
$157$	3.72999	+	21.1538i	0.297686	+	1.68826i	0.656081	+	0.754690i	$0.272213\pi$
$157$	3.72999	+	21.1538i	0.297686	+	1.68826i	−0.358396	+	0.933570i	$0.616676\pi$
$158$	6.42622	+	4.25344i	0.511243	+	0.338385i
$159$		0			0
$160$	11.8760	−	7.56569i	0.938877	−	0.598120i
$161$	4.23189	+	3.55098i	0.333519	+	0.279856i
$162$		0			0
$163$	15.0288	−	8.67686i	1.17714	−	0.679624i	0.221792	−	0.975094i	$-0.428810\pi$
$163$	15.0288	−	8.67686i	1.17714	−	0.679624i	0.955352	+	0.295470i	$0.0954762\pi$
$164$	−17.0475	+	15.8969i	−1.33119	+	1.24134i
$165$		0			0
$166$	7.52675	+	7.14265i	0.584189	+	0.554377i
$167$	−0.162857	+	0.923607i	−0.0126022	+	0.0714709i	−0.990460	−	0.137798i	$-0.955997\pi$
$167$	−0.162857	+	0.923607i	−0.0126022	+	0.0714709i	0.977858	+	0.209269i	$0.0671085\pi$
$168$		0			0
$169$	6.97892	−	5.85601i	0.536840	−	0.450462i
$170$	−12.5555	−	16.9678i	−0.962963	−	1.30137i
$171$		0			0
$172$	−2.92039	−	0.892862i	−0.222678	−	0.0680801i
$173$	7.00083	+	8.34327i	0.532264	+	0.634327i	0.963435	−	0.267943i	$-0.0863439\pi$
$173$	7.00083	+	8.34327i	0.532264	+	0.634327i	−0.431171	+	0.902270i	$0.641900\pi$
$174$		0			0
$175$	2.66420	+	0.469770i	0.201394	+	0.0355113i
$176$	14.8075	+	6.59283i	1.11616	+	0.496953i
$177$		0			0
$178$	2.00804	+	17.6245i	0.150509	+	1.32102i
$179$	11.1484	+	19.3096i	0.833271	+	1.44327i	0.895431	+	0.445201i	$0.146868\pi$
$179$	11.1484	+	19.3096i	0.833271	+	1.44327i	−0.0621601	+	0.998066i	$0.519799\pi$
$180$		0			0
$181$	−13.8765	+	16.5374i	−1.03143	+	1.22922i	−0.0584634	+	0.998290i	$0.518620\pi$
$181$	−13.8765	+	16.5374i	−1.03143	+	1.22922i	−0.972971	+	0.230926i	$0.925824\pi$
$182$	−2.51528	+	5.78473i	−0.186445	+	0.428793i
$183$		0			0
$184$	−4.39459	−	5.33112i	−0.323974	−	0.393015i
$185$	−3.58512	+	0.632154i	−0.263583	+	0.0464769i
$186$		0			0
$187$	8.31025	−	22.8322i	0.607706	−	1.66966i
$188$	−2.66140	+	1.12969i	−0.194102	+	0.0823909i
$189$		0			0
$190$	14.3258	+	5.49780i	1.03931	+	0.398852i
$191$		−	7.01677i		−	0.507716i	−0.967242	−	0.253858i	$-0.918300\pi$
$191$		−	7.01677i		−	0.507716i	0.967242	−	0.253858i	$-0.0816996\pi$
$192$		0			0
$193$	−1.55617	+	4.27555i	−0.112016	+	0.307761i	−0.983015	−	0.183523i	$-0.941250\pi$
$193$	−1.55617	+	4.27555i	−0.112016	+	0.307761i	0.871000	+	0.491284i	$0.163472\pi$
$194$	−3.08007	−	6.17769i	−0.221136	−	0.443532i
$195$		0			0
$196$	−0.197315	−	3.76522i	−0.0140939	−	0.268944i
$197$	5.76009	−	9.97676i	0.410389	−	0.710815i	−0.584543	−	0.811363i	$-0.698726\pi$
$197$	5.76009	−	9.97676i	0.410389	−	0.710815i	0.994932	+	0.100548i	$0.0320595\pi$
$198$		0			0
$199$	10.6595	−	12.7035i	0.755633	−	0.900528i	−0.241931	−	0.970294i	$-0.577781\pi$
$199$	10.6595	−	12.7035i	0.755633	−	0.900528i	0.997563	+	0.0697654i	$0.0222251\pi$
$200$	−3.16907	−	1.18488i	−0.224087	−	0.0837839i
$201$		0			0
$202$	−2.85925	+	0.325766i	−0.201176	+	0.0229208i
$203$	−20.7499	+	7.55234i	−1.45636	+	0.530070i
$204$		0			0
$205$	28.5704	+	5.03772i	1.99544	+	0.351850i
$206$	0.418011	+	1.41119i	0.0291242	+	0.0983221i
$207$		0			0
$208$	4.41145	−	6.54016i	0.305879	−	0.453478i
$209$	3.82448	+	17.2442i	0.264545	+	1.19280i
$210$		0			0
$211$	−13.2623	+	11.1284i	−0.913013	+	0.766109i	−0.972690	−	0.232109i	$-0.925437\pi$
$211$	−13.2623	+	11.1284i	−0.913013	+	0.766109i	0.0596769	+	0.998218i	$0.480993\pi$
$212$	−3.67409	−	2.76865i	−0.252338	−	0.190151i
$213$		0			0
$214$	3.84720	−	4.05409i	0.262989	−	0.277132i
$215$	1.29996	+	3.57160i	0.0886563	+	0.243581i
$216$		0			0
$217$	9.39661	−	5.42513i	0.637883	−	0.368282i
$218$	18.7554	+	1.14716i	1.27028	+	0.0776953i
$219$		0			0
$220$	−4.53803	−	19.6566i	−0.305954	−	1.32525i
$221$	−10.2413	−	5.91284i	−0.688907	−	0.397740i
$222$		0			0
$223$	−1.26802	−	7.19130i	−0.0849129	−	0.481565i	−0.997375	−	0.0724046i	$-0.976933\pi$
$223$	−1.26802	−	7.19130i	−0.0849129	−	0.481565i	0.912462	−	0.409161i	$-0.134178\pi$
$224$	1.66999	−	12.6840i	0.111581	−	0.847488i
$225$		0			0
$226$	2.49713	−	10.4012i	0.166107	−	0.691879i
$227$	22.5097			1.49402			0.747009	−	0.664814i	$-0.231489\pi$
$227$	22.5097			1.49402			0.747009	+	0.664814i	$0.231489\pi$
$228$		0			0
$229$	−19.8331			−1.31061			−0.655303	−	0.755366i	$-0.727459\pi$
$229$	−19.8331			−1.31061			−0.655303	+	0.755366i	$0.727459\pi$
$230$	−2.00739	+	8.36131i	−0.132363	+	0.551328i
$231$		0			0
$232$	27.2372	−	4.55782i	1.78821	−	0.299236i
$233$	−0.592771	−	3.36177i	−0.0388337	−	0.220237i	0.959215	−	0.282678i	$-0.0912227\pi$
$233$	−0.592771	−	3.36177i	−0.0388337	−	0.220237i	−0.998049	+	0.0624407i	$0.980112\pi$
$234$		0			0
$235$	3.11635	+	1.79922i	0.203288	+	0.117368i
$236$	−22.2316	+	5.13250i	−1.44715	+	0.334097i
$237$		0			0
$238$	−19.1421	−	1.17081i	−1.24080	−	0.0758922i
$239$	9.19023	−	5.30598i	0.594467	−	0.343215i	−0.172395	−	0.985028i	$-0.555151\pi$
$239$	9.19023	−	5.30598i	0.594467	−	0.343215i	0.766862	+	0.641812i	$0.221817\pi$
$240$		0			0
$241$	2.64845	+	7.27656i	0.170602	+	0.468725i	0.995299	−	0.0968500i	$-0.0308767\pi$
$241$	2.64845	+	7.27656i	0.170602	+	0.468725i	−0.824697	+	0.565574i	$0.808654\pi$
$242$	5.27670	−	5.56047i	0.339199	−	0.357440i
$243$		0			0
$244$	−12.4990	+	16.5866i	−0.800165	+	1.06185i
$245$	−3.59478	+	3.01637i	−0.229662	+	0.192709i
$246$		0			0
$247$	8.58851	−	0.375715i	0.546474	−	0.0239061i
$248$	−12.7914	+	4.52960i	−0.812254	+	0.287630i
$249$		0			0
$250$	−3.80308	−	12.8391i	−0.240528	−	0.812014i
$251$	4.52615	+	0.798083i	0.285688	+	0.0503745i	0.314656	−	0.949206i	$-0.398111\pi$
$251$	4.52615	+	0.798083i	0.285688	+	0.0503745i	−0.0289677	+	0.999580i	$0.509222\pi$
$252$		0			0
$253$	−9.30130	+	3.38540i	−0.584768	+	0.212838i
$254$	−17.3898	+	1.98129i	−1.09113	+	0.124317i
$255$		0			0
$256$	−4.94446	+	15.2168i	−0.309029	+	0.951053i
$257$	18.5753	−	22.1372i	1.15869	−	1.38088i	0.247508	−	0.968886i	$-0.420388\pi$
$257$	18.5753	−	22.1372i	1.15869	−	1.38088i	0.911187	−	0.411993i	$-0.135167\pi$
$258$		0			0
$259$	−1.65377	+	2.86441i	−0.102760	+	0.177986i
$260$	−9.80512	+	0.513834i	−0.608088	+	0.0318666i
$261$		0			0
$262$	−10.9219	−	21.9061i	−0.674759	−	1.35336i
$263$	5.38375	−	14.7917i	0.331976	−	0.912097i	−0.655622	−	0.755090i	$-0.727593\pi$
$263$	5.38375	−	14.7917i	0.331976	−	0.912097i	0.987598	−	0.157007i	$-0.0501845\pi$
$264$		0			0
$265$			5.72578i			0.351732i
$266$	12.1929	−	6.75995i	0.747592	−	0.414479i
$267$		0			0
$268$	8.65821	+	20.3976i	0.528884	+	1.24598i
$269$	−0.00677455	+	0.0186129i	−0.000413051	+	0.00113485i	−0.939899	−	0.341453i	$-0.889081\pi$
$269$	−0.00677455	+	0.0186129i	−0.000413051	+	0.00113485i	0.939486	+	0.342588i	$0.111303\pi$
$270$		0			0
$271$	15.6646	−	2.76209i	0.951556	−	0.167785i	0.323739	−	0.946146i	$-0.395060\pi$
$271$	15.6646	−	2.76209i	0.951556	−	0.167785i	0.627817	+	0.778361i	$0.283949\pi$
$272$	23.2720	+	5.80251i	1.41107	+	0.351829i
$273$		0			0
$274$	−2.01109	+	4.62517i	−0.121494	+	0.279417i
$275$	−3.11573	+	3.71318i	−0.187886	+	0.223913i
$276$		0			0
$277$	9.76647	+	16.9160i	0.586810	+	1.01639i	0.994647	+	0.103330i	$0.0329499\pi$
$277$	9.76647	+	16.9160i	0.586810	+	1.01639i	−0.407837	+	0.913055i	$0.633717\pi$
$278$	1.08979	+	9.56509i	0.0653612	+	0.573676i
$279$		0			0
$280$	−13.8586	+	7.84074i	−0.828211	+	0.468574i
$281$	−19.9458	−	3.51698i	−1.18987	−	0.209805i	−0.456552	−	0.889697i	$-0.650916\pi$
$281$	−19.9458	−	3.51698i	−1.18987	−	0.209805i	−0.733313	+	0.679891i	$0.762027\pi$
$282$		0			0
$283$	−16.4205	−	19.5692i	−0.976098	−	1.16327i	−0.986573	−	0.163323i	$-0.947779\pi$
$283$	−16.4205	−	19.5692i	−0.976098	−	1.16327i	0.0104743	−	0.999945i	$-0.496666\pi$
$284$	3.54511	−	11.5954i	0.210364	−	0.688060i
$285$		0			0
$286$	−6.72280	−	9.08537i	−0.397527	−	0.537229i
$287$	20.1916	−	16.9428i	1.19187	−	1.00010i
$288$		0			0
$289$	3.29122	−	18.6654i	0.193601	−	1.09797i
$290$	−24.9318	−	23.6595i	−1.46405	−	1.38933i
$291$		0			0
$292$	−4.70180	−	5.04210i	−0.275152	−	0.295066i
$293$	19.0136	−	10.9775i	1.11078	−	0.641312i	0.171752	−	0.985140i	$-0.445057\pi$
$293$	19.0136	−	10.9775i	1.11078	−	0.641312i	0.939032	+	0.343829i	$0.111724\pi$
$294$		0			0
$295$	21.7537	+	18.2535i	1.26655	+	1.06276i
$296$	2.68647	−	3.14542i	0.156148	−	0.182824i
$297$		0			0
$298$	−14.8535	−	9.83134i	−0.860440	−	0.569514i
$299$	0.836550	+	4.74431i	0.0483789	+	0.274370i
$300$		0			0
$301$	3.24500	+	1.18108i	0.187039	+	0.0680766i
$302$	−22.1644	−	5.32124i	−1.27542	−	0.306203i
$303$		0			0
$304$	−16.5342	+	5.53370i	−0.948299	+	0.317380i
$305$	25.8489			1.48010
$306$		0			0
$307$	−25.5611	−	9.30349i	−1.45885	−	0.530978i	−0.513802	−	0.857909i	$-0.671763\pi$
$307$	−25.5611	−	9.30349i	−1.45885	−	0.530978i	−0.945048	+	0.326931i	$0.893986\pi$
$308$	−16.3312	−	8.32121i	−0.930555	−	0.474145i
$309$		0			0
$310$	14.0835	+	9.32167i	0.799886	+	0.529435i
$311$	−6.39367	−	3.69139i	−0.362552	−	0.209319i	0.307648	−	0.951500i	$-0.400458\pi$
$311$	−6.39367	−	3.69139i	−0.362552	−	0.209319i	−0.670199	+	0.742181i	$0.733791\pi$
$312$		0			0
$313$	20.4596	+	17.1676i	1.15644	+	0.970371i	0.999850	−	0.0172922i	$-0.00550456\pi$
$313$	20.4596	+	17.1676i	1.15644	+	0.970371i	0.156593	+	0.987663i	$0.449949\pi$
$314$	−1.85455	+	30.3209i	−0.104658	+	1.71111i
$315$		0			0
$316$	7.43270	+	7.97064i	0.418122	+	0.448383i
$317$	3.01956	+	8.29617i	0.169595	+	0.465959i	0.995151	−	0.0983617i	$-0.0313602\pi$
$317$	3.01956	+	8.29617i	0.169595	+	0.465959i	−0.825555	+	0.564321i	$0.809138\pi$
$318$		0			0
$319$	6.87033	−	38.9636i	0.384665	−	2.18154i
$320$	18.8288	−	6.48310i	1.05256	−	0.362416i
$321$		0			0
$322$	4.64710	+	6.28021i	0.258973	+	0.349983i
$323$	10.0040	+	24.1461i	0.556640	+	1.34352i
$324$		0			0
$325$	1.51643	+	1.80722i	0.0841166	+	0.100246i
$326$	23.5312	−	6.97023i	1.30327	−	0.386045i
$327$		0			0
$328$	−28.6909	+	16.2324i	−1.58419	+	0.896283i
$329$	3.07223	−	1.11820i	0.169377	−	0.0616484i
$330$		0			0
$331$	11.7362	+	20.3277i	0.645081	+	1.11731i	0.984283	+	0.176600i	$0.0565098\pi$
$331$	11.7362	+	20.3277i	0.645081	+	1.11731i	−0.339201	+	0.940714i	$0.610157\pi$
$332$	7.99223	+	12.3070i	0.438631	+	0.675436i
$333$		0			0
$334$	−0.528874	+	1.21632i	−0.0289387	+	0.0665541i
$335$	13.7897	−	23.8845i	0.753413	−	1.30495i
$336$		0			0
$337$	4.11975	−	0.726423i	0.224417	−	0.0395708i	−0.0603088	−	0.998180i	$-0.519209\pi$
$337$	4.11975	−	0.726423i	0.224417	−	0.0395708i	0.284726	+	0.958609i	$0.408097\pi$
$338$	11.5303	−	5.74878i	0.627166	−	0.312692i
$339$		0			0
$340$	−11.6637	−	27.4782i	−0.632554	−	1.49022i
$341$			19.4410i			1.05279i
$342$		0			0
$343$			20.0947i			1.08501i
$344$	−3.72116	−	2.19196i	−0.200632	−	0.118182i
$345$		0			0
$346$	6.87264	+	13.7844i	0.369475	+	0.741055i
$347$	−28.3131	+	4.99237i	−1.51993	+	0.268005i	−0.870405	−	0.492336i	$-0.836143\pi$
$347$	−28.3131	+	4.99237i	−1.51993	+	0.268005i	−0.649524	+	0.760341i	$0.725032\pi$
$348$		0			0
$349$	8.81928	−	15.2754i	0.472085	−	0.817676i	−0.527404	−	0.849614i	$-0.676835\pi$
$349$	8.81928	−	15.2754i	0.472085	−	0.817676i	0.999490	+	0.0319385i	$0.0101681\pi$
$350$	3.50855	+	1.52557i	0.187540	+	0.0815449i
$351$		0			0
$352$	18.1858	+	13.9546i	0.969304	+	0.743785i
$353$	6.17019	+	10.6871i	0.328406	+	0.568816i	0.982196	−	0.187861i	$-0.0601553\pi$
$353$	6.17019	+	10.6871i	0.328406	+	0.568816i	−0.653790	+	0.756676i	$0.726822\pi$
$354$		0			0
$355$	−14.1810	+	5.16148i	−0.752651	+	0.273943i
$356$	−3.05731	+	24.8991i	−0.162037	+	1.31965i
$357$		0			0
$358$	8.95565	+	30.2339i	0.473321	+	1.59791i
$359$	−16.2599	−	19.3778i	−0.858166	−	1.02272i	−0.999463	−	0.0327557i	$-0.989572\pi$
$359$	−16.2599	−	19.3778i	−0.858166	−	1.02272i	0.141297	−	0.989967i	$-0.454873\pi$
$360$		0			0
$361$	−15.5657	−	10.8953i	−0.819250	−	0.573437i
$362$	−24.5419	+	18.1600i	−1.28989	+	0.954467i
$363$		0			0
$364$	−5.36865	+	7.12440i	−0.281394	+	0.373420i
$365$	−1.49000	+	8.45019i	−0.0779899	+	0.442303i
$366$		0			0
$367$	−10.2694	−	28.2149i	−0.536058	−	1.47281i	−0.851751	−	0.523946i	$-0.824459\pi$
$367$	−10.2694	−	28.2149i	−0.536058	−	1.47281i	0.315693	−	0.948861i	$-0.397763\pi$
$368$	−4.28314	−	8.78187i	−0.223274	−	0.457787i
$369$		0			0
$370$	−5.13874	−	0.314307i	−0.267150	−	0.0163400i
$371$	3.98512	+	3.34391i	0.206897	+	0.173607i
$372$		0			0
$373$	10.3596	+	5.98112i	0.536400	+	0.309690i	0.743618	−	0.668604i	$-0.233108\pi$
$373$	10.3596	+	5.98112i	0.536400	+	0.309690i	−0.207219	+	0.978295i	$0.566441\pi$
$374$	18.9657	−	28.6539i	0.980691	−	1.48166i
$375$		0			0
$376$	−4.03275	+	0.674832i	−0.207973	+	0.0348018i
$377$	−18.0949	−	6.58601i	−0.931936	−	0.339197i
$378$		0			0
$379$	−4.07439			−0.209287			−0.104644	−	0.994510i	$-0.533370\pi$
$379$	−4.07439			−0.209287			−0.104644	+	0.994510i	$0.533370\pi$
$380$	17.8849	+	12.2898i	0.917478	+	0.630454i
$381$		0			0
$382$	2.31654	−	9.64903i	0.118525	−	0.493687i
$383$	−25.4516	−	9.26361i	−1.30051	−	0.473348i	−0.403350	−	0.915046i	$-0.632154\pi$
$383$	−25.4516	−	9.26361i	−1.30051	−	0.473348i	−0.897164	+	0.441697i	$0.854376\pi$
$384$		0			0
$385$	3.96132	+	22.4658i	0.201887	+	1.14496i
$386$	−3.55150	+	5.36571i	−0.180766	+	0.273107i
$387$		0			0
$388$	−2.19600	−	9.51204i	−0.111485	−	0.482901i
$389$	15.4284	+	12.9460i	0.782250	+	0.656386i	0.943814	−	0.330476i	$-0.107209\pi$
$389$	15.4284	+	12.9460i	0.782250	+	0.656386i	−0.161564	+	0.986862i	$0.551654\pi$
$390$		0			0
$391$	−12.6843	+	7.32328i	−0.641472	+	0.370354i
$392$	0.971727	−	5.24284i	0.0490796	−	0.264803i
$393$		0			0
$394$	11.2147	−	11.8178i	0.564987	−	0.595371i
$395$	2.35541	−	13.3582i	0.118514	−	0.672124i
$396$		0			0
$397$	−18.8533	+	15.8198i	−0.946219	+	0.793972i	−0.978657	−	0.205502i	$-0.934117\pi$
$397$	−18.8533	+	15.8198i	−0.946219	+	0.793972i	0.0324379	+	0.999474i	$0.489673\pi$
$398$	18.8523	−	13.9499i	0.944980	−	0.699246i
$399$		0			0
$400$	−3.96673	−	2.67563i	−0.198336	−	0.133781i
$401$	0.321043	+	0.382604i	0.0160321	+	0.0191063i	0.774001	−	0.633184i	$-0.218253\pi$
$401$	0.321043	+	0.382604i	0.0160321	+	0.0191063i	−0.757969	+	0.652291i	$0.773808\pi$
$402$		0			0
$403$	9.31822	+	1.64305i	0.464174	+	0.0818464i
$404$	−4.03941	−	0.495990i	−0.200968	−	0.0246764i
$405$		0			0
$406$	−31.0273	+	3.53507i	−1.53986	+	0.175442i
$407$	−2.96314	−	5.13231i	−0.146877	−	0.254399i
$408$		0			0
$409$	19.0013	−	22.6449i	0.939555	−	1.11972i	−0.0530814	−	0.998590i	$-0.516904\pi$
$409$	19.0013	−	22.6449i	0.939555	−	1.11972i	0.992637	−	0.121128i	$-0.0386513\pi$
$410$	37.6250	+	16.3599i	1.85817	+	0.807957i
$411$		0			0
$412$	0.108927	+	2.07858i	0.00536647	+	0.102404i
$413$	25.4087	−	4.48024i	1.25028	−	0.220458i
$414$		0			0
$415$	6.24662	−	17.1625i	0.306635	−	0.842472i
$416$	8.22555	−	7.53721i	0.403291	−	0.369542i
$417$		0			0
$418$	−0.433866	+	24.9758i	−0.0212211	+	1.22160i
$419$			1.30584i			0.0637944i	0.999491	+	0.0318972i	$0.0101549\pi$
$419$			1.30584i			0.0637944i	−0.999491	+	0.0318972i	$0.989845\pi$
$420$		0			0
$421$	−3.72752	+	10.2413i	−0.181668	+	0.499129i	−0.996781	−	0.0801730i	$-0.974453\pi$
$421$	−3.72752	+	10.2413i	−0.181668	+	0.499129i	0.815113	+	0.579302i	$0.196675\pi$
$422$	−21.9114	+	10.9246i	−1.06663	+	0.531801i
$423$		0			0
$424$	−4.13834	−	5.02025i	−0.200975	−	0.243805i
$425$	−3.58625	+	6.21156i	−0.173958	+	0.301305i
$426$		0			0
$427$	15.0960	−	17.9907i	0.730546	−	0.870631i
$428$	6.62886	−	4.30480i	0.320418	−	0.208081i
$429$		0			0
$430$	0.608478	+	5.34062i	0.0293434	+	0.257547i
$431$	−2.24231	+	0.816132i	−0.108008	+	0.0393117i	−0.395459	−	0.918484i	$-0.629414\pi$
$431$	−2.24231	+	0.816132i	−0.108008	+	0.0393117i	0.287451	+	0.957795i	$0.407192\pi$
$432$		0			0
$433$	2.57802	+	0.454574i	0.123892	+	0.0218454i	0.235250	−	0.971935i	$-0.424409\pi$
$433$	2.57802	+	0.454574i	0.123892	+	0.0218454i	−0.111358	+	0.993780i	$0.535520\pi$
$434$	14.7127	−	4.35808i	0.706232	−	0.209194i
$435$		0			0
$436$	25.4125	+	7.76947i	1.21704	+	0.372090i
$437$	4.91560	−	9.44475i	0.235145	−	0.451804i
$438$		0			0
$439$	23.4760	−	19.6987i	1.12045	−	0.940168i	0.121822	−	0.992552i	$-0.461126\pi$
$439$	23.4760	−	19.6987i	1.12045	−	0.940168i	0.998627	+	0.0523836i	$0.0166819\pi$
$440$	0.249099	−	28.5288i	0.0118753	−	1.36006i
$441$		0			0
$442$	−12.1312	−	11.5121i	−0.577021	−	0.547574i
$443$	−7.62297	−	20.9440i	−0.362178	−	0.995077i	−0.978258	−	0.207393i	$-0.933502\pi$
$443$	−7.62297	−	20.9440i	−0.362178	−	0.995077i	0.616079	−	0.787684i	$-0.288720\pi$
$444$		0			0
$445$	27.0394	−	15.6112i	1.28179	−	0.740041i
$446$	0.630460	−	10.3077i	0.0298531	−	0.488082i
$447$		0			0
$448$	6.48402	−	16.8910i	0.306341	−	0.798024i
$449$	−11.1844	−	6.45731i	−0.527824	−	0.304739i	0.212306	−	0.977203i	$-0.431903\pi$
$449$	−11.1844	−	6.45731i	−0.527824	−	0.304739i	−0.740130	+	0.672464i	$0.765236\pi$
$450$		0			0
$451$	8.20095	+	46.5099i	0.386168	+	2.19007i
$452$	6.86780	−	13.4787i	0.323034	−	0.633985i
$453$		0			0
$454$	30.9539	+	7.43142i	1.45274	+	0.348774i
$455$	11.1028			0.520508
$456$		0			0
$457$	3.99249			0.186761			0.0933805	−	0.995630i	$-0.470233\pi$
$457$	3.99249			0.186761			0.0933805	+	0.995630i	$0.470233\pi$
$458$	−27.2732	−	6.54776i	−1.27439	−	0.305957i
$459$		0			0
$460$	−5.52087	+	10.8352i	−0.257412	+	0.505195i
$461$	−1.62577	−	9.22018i	−0.0757195	−	0.429427i	−0.998976	−	0.0452425i	$-0.985594\pi$
$461$	−1.62577	−	9.22018i	−0.0757195	−	0.429427i	0.923257	−	0.384184i	$-0.125517\pi$
$462$		0			0
$463$	9.62591	+	5.55752i	0.447354	+	0.258280i	0.706712	−	0.707501i	$-0.250178\pi$
$463$	9.62591	+	5.55752i	0.447354	+	0.258280i	−0.259358	+	0.965781i	$0.583511\pi$
$464$	38.9597	+	2.72457i	1.80866	+	0.126485i
$465$		0			0
$466$	0.294726	−	4.81860i	0.0136529	−	0.223217i
$467$	−18.0455	+	10.4186i	−0.835048	+	0.482115i	−0.855578	−	0.517674i	$-0.826798\pi$
$467$	−18.0455	+	10.4186i	−0.835048	+	0.482115i	0.0205298	+	0.999789i	$0.493465\pi$
$468$		0			0
$469$	−8.57017	−	23.5464i	−0.395734	−	1.08727i
$470$	3.69141	+	3.50303i	0.170272	+	0.161583i
$471$		0			0
$472$	−32.2660	−	0.281730i	−1.48516	−	0.0129677i
$473$	−4.73981	+	3.97717i	−0.217937	+	0.182871i
$474$		0			0
$475$	−0.227878	−	5.20909i	−0.0104558	−	0.239009i
$476$	−25.9364	−	7.92965i	−1.18880	−	0.363455i
$477$		0			0
$478$	14.3896	−	4.26236i	0.658164	−	0.194956i
$479$	10.6190	+	1.87242i	0.485196	+	0.0855532i	0.410895	−	0.911683i	$-0.365216\pi$
$479$	10.6190	+	1.87242i	0.485196	+	0.0855532i	0.0743012	+	0.997236i	$0.476327\pi$
$480$		0			0
$481$	−2.71039	+	0.986501i	−0.123583	+	0.0449806i
$482$	1.23968	+	10.8806i	0.0564657	+	0.495600i
$483$		0			0
$484$	9.09195	−	5.90434i	0.413270	−	0.268379i
$485$	−7.80997	+	9.30756i	−0.354633	+	0.422635i
$486$		0			0
$487$	−7.31947	+	12.6777i	−0.331677	+	0.574481i	−0.982841	−	0.184456i	$-0.940948\pi$
$487$	−7.31947	+	12.6777i	−0.331677	+	0.574481i	0.651164	+	0.758937i	$0.274281\pi$
$488$	−22.6638	+	18.6824i	−1.02594	+	0.845712i
$489$		0			0
$490$	−5.93915	+	2.96114i	−0.268303	+	0.133771i
$491$	−11.8169	+	32.4667i	−0.533290	+	1.46520i	0.321844	+	0.946793i	$0.395697\pi$
$491$	−11.8169	+	32.4667i	−0.533290	+	1.46520i	−0.855133	+	0.518408i	$0.826525\pi$
$492$		0			0
$493$		−	58.5443i		−	2.63670i
$494$	11.9344	+	2.31878i	0.536955	+	0.104327i
$495$		0			0
$496$	−19.0854	+	2.00583i	−0.856958	+	0.0900646i
$497$	−4.68950	+	12.8843i	−0.210353	+	0.577939i
$498$		0			0
$499$	−3.46259	+	0.610547i	−0.155007	+	0.0273319i	−0.250613	−	0.968087i	$-0.580632\pi$
$499$	−3.46259	+	0.610547i	−0.155007	+	0.0273319i	0.0956063	+	0.995419i	$0.469521\pi$
$500$	−0.991028	−	18.9111i	−0.0443201	−	0.845728i
$501$		0			0
$502$	5.96060	+	2.59176i	0.266035	+	0.115676i
$503$	−2.89245	+	3.44708i	−0.128968	+	0.153698i	−0.826664	−	0.562696i	$-0.809764\pi$
$503$	−2.89245	+	3.44708i	−0.128968	+	0.153698i	0.697696	+	0.716394i	$0.254209\pi$
$504$		0			0
$505$	2.53262	+	4.38662i	0.112700	+	0.195202i
$506$	−13.9082	+	1.58462i	−0.618297	+	0.0704451i
$507$		0			0
$508$	−24.5675	−	3.01659i	−1.09001	−	0.133839i
$509$	4.85022	+	0.855225i	0.214982	+	0.0379072i	0.280102	−	0.959970i	$-0.409632\pi$
$509$	4.85022	+	0.855225i	0.214982	+	0.0379072i	−0.0651195	+	0.997877i	$0.520743\pi$
$510$		0			0
$511$	5.01112	+	5.97202i	0.221679	+	0.264187i
$512$	−11.8231	+	19.2929i	−0.522510	+	0.852633i
$513$		0			0
$514$	32.8520	−	24.3092i	1.44904	−	1.07223i
$515$	1.98449	−	1.66519i	0.0874471	−	0.0733768i
$516$		0			0
$517$	−1.01722	+	5.76895i	−0.0447374	+	0.253718i
$518$	−3.21983	+	3.39298i	−0.141471	+	0.149079i
$519$		0			0
$520$	−13.6530	−	2.53050i	−0.598725	−	0.110970i
$521$	10.5634	−	6.09880i	0.462793	−	0.267193i	−0.250425	−	0.968136i	$-0.580570\pi$
$521$	10.5634	−	6.09880i	0.462793	−	0.267193i	0.713218	+	0.700943i	$0.247237\pi$
$522$		0			0
$523$	−1.21616	−	1.02048i	−0.0531791	−	0.0446226i	0.615811	−	0.787894i	$-0.288829\pi$
$523$	−1.21616	−	1.02048i	−0.0531791	−	0.0446226i	−0.668990	+	0.743272i	$0.733273\pi$
$524$	−7.78701	−	33.7297i	−0.340177	−	1.47349i
$525$		0			0
$526$	12.2868	−	18.5633i	0.535729	−	0.809396i
$527$	4.99535	+	28.3300i	0.217601	+	1.23408i
$528$		0			0
$529$	−16.0061	−	5.82575i	−0.695918	−	0.253293i
$530$	−1.89033	+	7.87374i	−0.0821108	+	0.342014i
$531$		0			0
$532$	18.9986	−	5.27046i	0.823695	−	0.228504i
$533$	22.9857			0.995621
$534$		0			0
$535$	−9.24410	−	3.36458i	−0.399657	−	0.145463i
$536$	5.17208	+	30.9080i	0.223400	+	1.33502i
$537$		0			0
$538$	−0.0154609	+	0.0233588i	−0.000666566	+	0.00100707i
$539$	−6.61574	−	3.81960i	−0.284960	−	0.164522i
$540$		0			0
$541$	10.6180	+	8.90954i	0.456502	+	0.383051i	0.841842	−	0.539724i	$-0.181471\pi$
$541$	10.6180	+	8.90954i	0.456502	+	0.383051i	−0.385340	+	0.922775i	$0.625916\pi$
$542$	22.4529	+	1.37331i	0.964433	+	0.0589887i
$543$		0			0
$544$	30.0865	+	15.6623i	1.28995	+	0.671518i
$545$	−11.3119	−	31.0792i	−0.484549	−	1.33129i
$546$		0			0
$547$	3.81045	−	21.6102i	0.162923	−	0.923984i	−0.788257	−	0.615347i	$-0.789016\pi$
$547$	3.81045	−	21.6102i	0.162923	−	0.923984i	0.951180	−	0.308637i	$-0.0998728\pi$
$548$	−4.29250	+	5.69630i	−0.183366	+	0.243334i
$549$		0			0
$550$	−5.51045	+	4.07750i	−0.234966	+	0.173865i
$551$	22.8700	+	35.8920i	0.974295	+	1.52905i
$552$		0			0
$553$	−7.92167	−	9.44068i	−0.336864	−	0.401458i
$554$	7.84553	+	26.4862i	0.333325	+	1.12529i
$555$		0			0
$556$	−1.65924	+	13.5131i	−0.0703676	+	0.573083i
$557$	−36.9095	+	13.4340i	−1.56391	+	0.569216i	−0.971627	−	0.236517i	$-0.923994\pi$
$557$	−36.9095	+	13.4340i	−1.56391	+	0.569216i	−0.592280	+	0.805732i	$0.701772\pi$
$558$		0			0
$559$	1.50571	+	2.60796i	0.0636846	+	0.110305i
$560$	−21.6461	+	6.20677i	−0.914714	+	0.262284i
$561$		0			0
$562$	−26.2671	−	11.4213i	−1.10801	−	0.481779i
$563$	8.94085	−	15.4860i	0.376812	−	0.652657i	−0.613785	−	0.789474i	$-0.710354\pi$
$563$	8.94085	−	15.4860i	0.376812	−	0.652657i	0.990596	+	0.136816i	$0.0436870\pi$
$564$		0			0
$565$	−18.5418	+	3.26942i	−0.780059	+	0.137545i
$566$	−16.1198	−	32.3315i	−0.677567	−	1.35899i
$567$		0			0
$568$	8.70316	−	14.7749i	0.365177	−	0.619940i
$569$			9.37031i			0.392824i	0.980521	+	0.196412i	$0.0629290\pi$
$569$			9.37031i			0.392824i	−0.980521	+	0.196412i	$0.937071\pi$
$570$		0			0
$571$			4.40498i			0.184343i	0.995743	+	0.0921714i	$0.0293808\pi$
$571$			4.40498i			0.184343i	−0.995743	+	0.0921714i	$0.970619\pi$
$572$	−6.24530	−	14.7131i	−0.261129	−	0.615187i
$573$		0			0
$574$	33.3598	−	16.6325i	1.39241	−	0.694227i
$575$	2.87751	−	0.507383i	0.120001	−	0.0211593i
$576$		0			0
$577$	−4.73531	+	8.20180i	−0.197134	+	0.341445i	−0.947598	−	0.319466i	$-0.896497\pi$
$577$	−4.73531	+	8.20180i	−0.197134	+	0.341445i	0.750464	+	0.660911i	$0.229830\pi$
$578$	10.6882	−	24.5810i	0.444569	−	1.02243i
$579$		0			0
$580$	−26.4737	−	40.7661i	−1.09926	−	1.69272i
$581$	−8.29690	−	14.3707i	−0.344213	−	0.596195i
$582$		0			0
$583$	−8.75893	+	3.18799i	−0.362758	+	0.132033i
$584$	−4.80101	−	8.48585i	−0.198667	−	0.351147i
$585$		0			0
$586$	29.7704	−	8.81835i	1.22980	−	0.364283i
$587$	11.9820	+	14.2796i	0.494549	+	0.589381i	0.954368	−	0.298632i	$-0.0965302\pi$
$587$	11.9820	+	14.2796i	0.494549	+	0.589381i	−0.459819	+	0.888013i	$0.652086\pi$
$588$		0			0
$589$	−14.1295	−	15.4170i	−0.582195	−	0.635246i
$590$	23.8880	+	32.2829i	0.983455	+	1.32907i
$591$		0			0
$592$	4.73271	−	3.43847i	0.194513	−	0.141320i
$593$	−3.78045	+	21.4400i	−0.155244	+	0.880435i	0.803318	+	0.595551i	$0.203066\pi$
$593$	−3.78045	+	21.4400i	−0.155244	+	0.880435i	−0.958562	+	0.284884i	$0.908045\pi$
$594$		0			0
$595$	11.5451	+	31.7200i	0.473304	+	1.30039i
$596$	−17.1798	−	18.4232i	−0.703714	−	0.754645i
$597$		0			0
$598$	−0.415932	+	6.80026i	−0.0170087	+	0.278083i
$599$	−21.8252	−	18.3135i	−0.891752	−	0.748269i	0.0768090	−	0.997046i	$-0.475527\pi$
$599$	−21.8252	−	18.3135i	−0.891752	−	0.748269i	−0.968561	+	0.248777i	$0.919971\pi$
$600$		0			0
$601$	−14.9421	−	8.62681i	−0.609500	−	0.351895i	0.163270	−	0.986581i	$-0.447796\pi$
$601$	−14.9421	−	8.62681i	−0.609500	−	0.351895i	−0.772770	+	0.634686i	$0.781129\pi$
$602$	4.07240	+	2.69547i	0.165979	+	0.109859i
$603$		0			0
$604$	−28.7224	−	14.6349i	−1.16870	−	0.595485i
$605$	−12.6789	−	4.61476i	−0.515472	−	0.187617i
$606$		0			0
$607$	26.6273			1.08077			0.540384	−	0.841418i	$-0.318279\pi$
$607$	26.6273			1.08077			0.540384	+	0.841418i	$0.318279\pi$
$608$	−24.5637	+	2.15096i	−0.996188	+	0.0872329i
$609$		0			0
$610$	35.5458	+	8.53385i	1.43921	+	0.345525i
$611$	2.67914	+	0.975126i	0.108386	+	0.0394494i
$612$		0			0
$613$	−0.471362	−	2.67323i	−0.0190381	−	0.107971i	0.973808	−	0.227372i	$-0.0730135\pi$
$613$	−0.471362	−	2.67323i	−0.0190381	−	0.107971i	−0.992846	+	0.119402i	$0.961902\pi$
$614$	−32.0786	−	21.2324i	−1.29459	−	0.856871i
$615$		0			0
$616$	−19.7104	−	16.8344i	−0.794156	−	0.678279i
$617$	−29.3580	−	24.6343i	−1.18191	−	0.991740i	−0.999964	−	0.00843082i	$-0.997316\pi$
$617$	−29.3580	−	24.6343i	−1.18191	−	0.991740i	−0.181945	−	0.983309i	$-0.558239\pi$
$618$		0			0
$619$	−2.88998	+	1.66853i	−0.116158	+	0.0670639i	−0.556953	−	0.830544i	$-0.688030\pi$
$619$	−2.88998	+	1.66853i	−0.116158	+	0.0670639i	0.440795	+	0.897608i	$0.354696\pi$
$620$	16.2892	+	17.4681i	0.654190	+	0.701538i
$621$		0			0
$622$	−7.57349	−	7.18699i	−0.303669	−	0.288172i
$623$	4.92593	−	27.9363i	0.197353	−	1.11925i
$624$		0			0
$625$	−22.6367	+	18.9944i	−0.905467	+	0.759777i
$626$	22.4670	+	30.3624i	0.897960	+	1.21353i
$627$		0			0
$628$	−12.5605	+	41.0831i	−0.501219	+	1.63940i
$629$	−5.63673	−	6.71760i	−0.224751	−	0.267848i
$630$		0			0
$631$	−37.2451	−	6.56731i	−1.48270	−	0.261441i	−0.627045	−	0.778983i	$-0.715736\pi$
$631$	−37.2451	−	6.56731i	−1.48270	−	0.261441i	−0.855658	+	0.517542i	$0.826847\pi$
$632$	7.58953	+	13.4146i	0.301895	+	0.533604i
$633$		0			0
$634$	1.41338	+	12.4053i	0.0561326	+	0.492676i
$635$	15.4033	+	26.6792i	0.611260	+	1.05873i
$636$		0			0
$637$	−2.38990	+	2.84817i	−0.0946911	+	0.112848i
$638$	22.3112	−	51.3121i	0.883310	−	2.03147i
$639$		0			0
$640$	28.0326	−	2.69893i	1.10809	−	0.106685i
$641$	−11.1604	+	1.96789i	−0.440811	+	0.0777269i	−0.389649	−	0.920963i	$-0.627404\pi$
$641$	−11.1604	+	1.96789i	−0.440811	+	0.0777269i	−0.0511622	+	0.998690i	$0.516293\pi$
$642$		0			0
$643$	−7.33180	+	20.1439i	−0.289138	+	0.794400i	0.707050	+	0.707164i	$0.250026\pi$
$643$	−7.33180	+	20.1439i	−0.289138	+	0.794400i	−0.996188	+	0.0872359i	$0.972197\pi$
$644$	4.31703	+	10.1704i	0.170115	+	0.400769i
$645$		0			0
$646$	5.78526	+	36.5070i	0.227618	+	1.43635i
$647$		−	31.6669i		−	1.24495i	−0.782638	−	0.622477i	$-0.786127\pi$
$647$		−	31.6669i		−	1.24495i	0.782638	−	0.622477i	$-0.213873\pi$
$648$		0			0
$649$	−15.8111	+	43.4405i	−0.620638	+	1.70519i
$650$	1.48867	+	2.98581i	0.0583903	+	0.117113i
$651$		0			0
$652$	34.6599	−	1.81634i	1.35739	−	0.0711334i
$653$	3.45916	−	5.99144i	0.135367	−	0.234463i	−0.790370	−	0.612629i	$-0.790112\pi$
$653$	3.45916	−	5.99144i	0.135367	−	0.234463i	0.925738	+	0.378166i	$0.123445\pi$
$654$		0			0
$655$	−27.6942	+	33.0046i	−1.08210	+	1.28960i
$656$	−44.8130	+	12.8496i	−1.74965	+	0.501694i
$657$		0			0
$658$	4.59391	−	0.523402i	0.179089	−	0.0204043i
$659$	−25.2667	+	9.19631i	−0.984249	+	0.358237i	−0.783491	−	0.621403i	$-0.786563\pi$
$659$	−25.2667	+	9.19631i	−0.984249	+	0.358237i	−0.200758	+	0.979641i	$0.564341\pi$
$660$		0			0
$661$	−23.4306	−	4.13145i	−0.911346	−	0.160695i	−0.301731	−	0.953393i	$-0.597565\pi$
$661$	−23.4306	−	4.13145i	−0.911346	−	0.160695i	−0.609614	+	0.792698i	$0.708676\pi$
$662$	9.42786	+	31.8281i	0.366424	+	1.23703i
$663$		0			0
$664$	6.92733	+	19.5625i	0.268832	+	0.759171i
$665$	−19.4692	−	14.9366i	−0.754985	−	0.579218i
$666$		0			0
$667$	−18.2698	+	15.3302i	−0.707411	+	0.593588i
$668$	−1.12884	+	1.49801i	−0.0436760	+	0.0579596i
$669$		0			0
$670$	26.8481	−	28.2919i	1.03723	−	1.09301i
$671$	14.3921	+	39.5419i	0.555600	+	1.52650i
$672$		0			0
$673$	−20.2132	+	11.6701i	−0.779161	+	0.449849i	−0.836133	−	0.548527i	$-0.815189\pi$
$673$	−20.2132	+	11.6701i	−0.779161	+	0.449849i	0.0569720	+	0.998376i	$0.481855\pi$
$674$	5.90505	+	0.361177i	0.227454	+	0.0139120i
$675$		0			0
$676$	17.7537	−	4.09871i	0.682834	−	0.157643i
$677$	11.0256	+	6.36563i	0.423748	+	0.244651i	0.696680	−	0.717382i	$-0.254660\pi$
$677$	11.0256	+	6.36563i	0.423748	+	0.244651i	−0.272932	+	0.962033i	$0.587993\pi$
$678$		0			0
$679$	1.91692	+	10.8714i	0.0735647	+	0.417206i
$680$	−6.96746	−	41.6371i	−0.267190	−	1.59671i
$681$		0			0
$682$	−6.41832	+	26.7340i	−0.245770	+	1.02370i
$683$	31.4554			1.20361			0.601804	−	0.798644i	$-0.294449\pi$
$683$	31.4554			1.20361			0.601804	+	0.798644i	$0.294449\pi$
$684$		0			0
$685$	8.87723			0.339182
$686$	−6.63414	+	27.6330i	−0.253293	+	1.05503i
$687$		0			0
$688$	−4.39345	−	4.24276i	−0.167499	−	0.161754i
$689$	0.787769	+	4.46766i	0.0300116	+	0.170204i
$690$		0			0
$691$	−28.7335	−	16.5893i	−1.09308	−	0.631087i	−0.158682	−	0.987330i	$-0.550724\pi$
$691$	−28.7335	−	16.5893i	−1.09308	−	0.631087i	−0.934394	+	0.356242i	$0.884058\pi$
$692$	4.89998	+	21.2245i	0.186269	+	0.806833i
$693$		0			0
$694$	−40.5827	−	2.48221i	−1.54050	−	0.0942233i
$695$	14.6746	−	8.47241i	0.556641	−	0.321377i
$696$		0			0
$697$	23.9014	+	65.6686i	0.905330	+	2.48737i
$698$	17.1708	−	18.0942i	0.649925	−	0.684876i
$699$		0			0
$700$	4.32108	+	3.25619i	0.163322	+	0.123072i
$701$	−40.4379	+	33.9314i	−1.52732	+	1.28157i	−0.712965	+	0.701200i	$0.752648\pi$
$701$	−40.4379	+	33.9314i	−1.52732	+	1.28157i	−0.814352	+	0.580371i	$0.802908\pi$
$702$		0			0
$703$	6.07992	+	1.91642i	0.229309	+	0.0722793i
$704$	20.4009	+	25.1935i	0.768888	+	0.949515i
$705$		0			0
$706$	4.95659	+	16.7333i	0.186544	+	0.629764i
$707$	4.53214	+	0.799139i	0.170449	+	0.0300547i
$708$		0			0
$709$	28.2332	−	10.2761i	1.06032	−	0.385926i	0.247773	−	0.968818i	$-0.420301\pi$
$709$	28.2332	−	10.2761i	1.06032	−	0.385926i	0.812549	+	0.582893i	$0.198079\pi$
$710$	−21.2049	+	2.41596i	−0.795806	+	0.0906694i
$711$		0			0
$712$	−12.4245	+	33.2304i	−0.465628	+	1.24536i
$713$	7.53284	−	8.97729i	0.282107	−	0.336202i
$714$		0			0
$715$	−9.94674	+	17.2283i	−0.371987	+	0.644300i
$716$	2.33371	+	44.5325i	0.0872149	+	1.66426i
$717$		0			0
$718$	−15.9622	−	32.0153i	−0.595703	−	1.19480i
$719$	9.63485	−	26.4715i	0.359319	−	0.987222i	−0.619947	−	0.784644i	$-0.712846\pi$
$719$	9.63485	−	26.4715i	0.359319	−	0.987222i	0.979266	−	0.202578i	$-0.0649319\pi$
$720$		0			0
$721$		−	2.35368i		−	0.0876556i
$722$	−17.8080	−	20.1215i	−0.662746	−	0.748844i
$723$		0			0
$724$	−39.7439	+	16.8701i	−1.47707	+	0.626973i
$725$	−3.99454	+	10.9749i	−0.148354	+	0.407598i
$726$		0			0
$727$	−39.3678	+	6.94161i	−1.46007	+	0.257450i	−0.846584	−	0.532255i	$-0.821345\pi$
$727$	−39.3678	+	6.94161i	−1.46007	+	0.257450i	−0.613487	+	0.789705i	$0.710234\pi$
$728$	−9.73472	+	8.02461i	−0.360793	+	0.297412i
$729$		0			0
$730$	−4.83873	+	11.1283i	−0.179089	+	0.411875i
$731$	−5.88508	+	7.01356i	−0.217667	+	0.259406i
$732$		0			0
$733$	15.2457	+	26.4064i	0.563114	+	0.975342i	0.997222	+	0.0744815i	$0.0237302\pi$
$733$	15.2457	+	26.4064i	0.563114	+	0.975342i	−0.434108	+	0.900861i	$0.642936\pi$
$734$	−4.80686	−	42.1898i	−0.177424	−	1.55725i
$735$		0			0
$736$	−2.99063	−	13.4903i	−0.110236	−	0.497260i
$737$	44.2147	+	7.79625i	1.62867	+	0.287179i
$738$		0			0
$739$	1.68167	+	2.00414i	0.0618614	+	0.0737235i	0.796088	−	0.605181i	$-0.206899\pi$
$739$	1.68167	+	2.00414i	0.0618614	+	0.0737235i	−0.734226	+	0.678905i	$0.762455\pi$
$740$	−6.96271	−	2.12874i	−0.255954	−	0.0782539i
$741$		0			0
$742$	4.37612	+	5.91400i	0.160652	+	0.217110i
$743$	−32.3606	+	27.1537i	−1.18719	+	0.996174i	−0.187290	+	0.982305i	$0.559970\pi$
$743$	−32.3606	+	27.1537i	−1.18719	+	0.996174i	−0.999904	+	0.0138689i	$0.995585\pi$
$744$		0			0
$745$	−5.44427	+	30.8760i	−0.199463	+	1.13121i
$746$	12.2712	+	11.6450i	0.449282	+	0.426354i
$747$		0			0
$748$	35.5403	−	33.1417i	1.29948	−	1.21178i
$749$	−7.74037	+	4.46891i	−0.282827	+	0.163290i
$750$		0			0
$751$	13.8883	+	11.6537i	0.506791	+	0.425248i	0.859998	−	0.510297i	$-0.170465\pi$
$751$	13.8883	+	11.6537i	0.506791	+	0.425248i	−0.353208	+	0.935545i	$0.614909\pi$
$752$	−5.76838	−	0.403400i	−0.210351	−	0.0147105i
$753$		0			0
$754$	−22.7087	−	15.0306i	−0.827002	−	0.547382i
$755$	6.96695	+	39.5115i	0.253553	+	1.43797i
$756$		0			0
$757$	−24.4898	−	8.91355i	−0.890096	−	0.323968i	−0.143819	−	0.989604i	$-0.545938\pi$
$757$	−24.4898	−	8.91355i	−0.890096	−	0.323968i	−0.746277	+	0.665636i	$0.768161\pi$
$758$	−5.60285	−	1.34513i	−0.203505	−	0.0488574i
$759$		0			0
$760$	20.5369	+	22.8048i	0.744950	+	0.827217i
$761$	−0.510156			−0.0184931			−0.00924657	−	0.999957i	$-0.502943\pi$
$761$	−0.510156			−0.0184931			−0.00924657	+	0.999957i	$0.502943\pi$
$762$		0			0
$763$	−28.2373	−	10.2775i	−1.02226	−	0.372071i
$764$	6.37114	−	12.5040i	0.230500	−	0.452377i
$765$		0			0
$766$	−31.9411	−	21.1414i	−1.15408	−	0.763870i
$767$	19.4851	+	11.2497i	0.703567	+	0.406205i
$768$		0			0
$769$	−21.8261	−	18.3143i	−0.787069	−	0.660429i	0.157949	−	0.987447i	$-0.449512\pi$
$769$	−21.8261	−	18.3143i	−0.787069	−	0.660429i	−0.945018	+	0.327018i	$0.893956\pi$
$770$	−1.96957	+	32.2013i	−0.0709783	+	1.16045i
$771$		0			0
$772$	−6.65526	+	6.20609i	−0.239528	+	0.223362i
$773$	−3.00658	−	8.26050i	−0.108139	−	0.297109i	0.873806	−	0.486274i	$-0.161644\pi$
$773$	−3.00658	−	8.26050i	−0.108139	−	0.297109i	−0.981945	+	0.189164i	$0.939422\pi$
$774$		0			0
$775$	0.996543	−	5.65168i	0.0357969	−	0.203014i
$776$	0.120541	−	13.8054i	0.00432718	−	0.495584i
$777$		0			0
$778$	16.9421	+	22.8961i	0.607405	+	0.820863i
$779$	−40.3064	−	30.9227i	−1.44413	−	1.10792i
$780$		0			0
$781$	−15.7914	−	18.8194i	−0.565060	−	0.673412i
$782$	−19.8604	+	5.88288i	−0.710206	+	0.210371i
$783$		0			0
$784$	3.06715	−	6.88881i	0.109541	−	0.246029i
$785$	50.2442	−	18.2874i	1.79329	−	0.652705i
$786$		0			0
$787$	−0.866337	−	1.50054i	−0.0308816	−	0.0534885i	0.850172	−	0.526506i	$-0.176498\pi$
$787$	−0.866337	−	1.50054i	−0.0308816	−	0.0534885i	−0.881053	+	0.473017i	$0.843165\pi$
$788$	19.3233	−	12.5486i	0.688364	−	0.447026i
$789$		0			0
$790$	7.64915	−	17.5918i	0.272144	−	0.625887i
$791$	−8.55308	+	14.8144i	−0.304113	+	0.526739i
$792$		0			0
$793$	20.1691	−	3.55636i	0.716227	−	0.126290i
$794$	−31.1487	+	15.5301i	−1.10542	+	0.551142i
$795$		0			0
$796$	30.5300	−	12.9591i	1.08211	−	0.459323i
$797$		−	6.82560i		−	0.241775i	−0.992666	−	0.120888i	$-0.961426\pi$
$797$		−	6.82560i		−	0.241775i	0.992666	−	0.120888i	$-0.0385741\pi$
$798$		0			0
$799$			8.66808i			0.306655i
$800$	−4.57146	−	4.98895i	−0.161625	−	0.176386i
$801$		0			0
$802$	0.315164	+	0.632123i	0.0111288	+	0.0223211i
$803$	−13.7561	+	2.42558i	−0.485443	+	0.0855968i
$804$		0			0
$805$	6.87563	−	11.9089i	0.242334	−	0.419735i
$806$	12.2714	+	5.33578i	0.432242	+	0.187945i
$807$		0			0
$808$	−5.39100	−	2.01564i	−0.189655	−	0.0709100i
$809$	−16.9821	−	29.4139i	−0.597059	−	1.03414i	−0.993253	−	0.115970i	$-0.963002\pi$
$809$	−16.9821	−	29.4139i	−0.597059	−	1.03414i	0.396193	−	0.918167i	$-0.370331\pi$
$810$		0			0
$811$	20.0616	−	7.30184i	0.704460	−	0.256402i	0.0351458	−	0.999382i	$-0.488810\pi$
$811$	20.0616	−	7.30184i	0.704460	−	0.256402i	0.669314	+	0.742980i	$0.266588\pi$
$812$	−43.8339	−	5.38226i	−1.53827	−	0.188880i
$813$		0			0
$814$	−2.38033	−	8.03590i	−0.0834305	−	0.281658i
$815$	−27.7666	−	33.0909i	−0.972621	−	1.15912i
$816$		0			0
$817$	0.868177	−	6.59880i	0.0303737	−	0.230863i
$818$	33.6055	−	24.8667i	1.17499	−	0.869444i
$819$		0			0
$820$	46.3385	+	34.9188i	1.61821	+	1.21942i
$821$	0.405861	−	2.30175i	0.0141647	−	0.0803317i	−0.976906	−	0.213670i	$-0.931458\pi$
$821$	0.405861	−	2.30175i	0.0141647	−	0.0803317i	0.991071	+	0.133338i	$0.0425695\pi$
$822$		0			0
$823$	−9.76490	−	26.8288i	−0.340383	−	0.935195i	−0.985284	−	0.170928i	$-0.945323\pi$
$823$	−9.76490	−	26.8288i	−0.340383	−	0.935195i	0.644901	−	0.764267i	$-0.276899\pi$
$824$	−0.536441	+	2.89430i	−0.0186878	+	0.100828i
$825$		0			0
$826$	36.4196	+	2.22758i	1.26720	+	0.0775073i
$827$	−10.2530	−	8.60330i	−0.356532	−	0.299166i	0.446875	−	0.894597i	$-0.352537\pi$
$827$	−10.2530	−	8.60330i	−0.356532	−	0.299166i	−0.803407	+	0.595431i	$0.796981\pi$
$828$		0			0
$829$	−33.8489	−	19.5427i	−1.17562	−	0.678746i	−0.220625	−	0.975359i	$-0.570810\pi$
$829$	−33.8489	−	19.5427i	−1.17562	−	0.678746i	−0.954998	+	0.296613i	$0.904143\pi$
$830$	14.2560	−	21.5385i	0.494835	−	0.747611i
$831$		0			0
$832$	13.7996	−	7.64909i	0.478416	−	0.265185i
$833$	−10.6221	−	3.86614i	−0.368035	−	0.133954i
$834$		0			0
$835$	2.33452			0.0807895
$836$	−8.84222	+	34.2019i	−0.305814	+	1.18290i
$837$		0			0
$838$	−0.431114	+	1.79571i	−0.0148926	+	0.0620317i
$839$	4.89669	+	1.78225i	0.169053	+	0.0615301i	0.425160	−	0.905118i	$-0.360218\pi$
$839$	4.89669	+	1.78225i	0.169053	+	0.0615301i	−0.256107	+	0.966648i	$0.582440\pi$
$840$		0			0
$841$	−11.5181	−	65.3224i	−0.397176	−	2.25250i
$842$	−8.50695	+	12.8526i	−0.293169	+	0.442928i
$843$		0			0
$844$	−33.7379	+	7.78891i	−1.16131	+	0.268105i
$845$	−17.3720	−	14.5769i	−0.597616	−	0.501460i
$846$		0			0
$847$	−10.6165	+	6.12942i	−0.364786	+	0.210609i
$848$	−4.03338	−	8.26978i	−0.138507	−	0.283985i
$849$		0			0
$850$	−6.98229	+	7.35778i	−0.239491	+	0.252370i
$851$	−0.620334	+	3.51809i	−0.0212648	+	0.120599i
$852$		0			0
$853$	−33.5818	+	28.1785i	−1.14982	+	0.964812i	−0.999715	−	0.0238580i	$-0.992405\pi$
$853$	−33.5818	+	28.1785i	−1.14982	+	0.964812i	−0.150103	+	0.988670i	$0.547961\pi$
$854$	26.6986	−	19.7559i	0.913607	−	0.676032i
$855$		0			0
$856$	10.5368	−	3.73122i	0.360141	−	0.127531i
$857$	−29.6672	−	35.3560i	−1.01341	−	1.20774i	−0.978052	−	0.208363i	$-0.933186\pi$
$857$	−29.6672	−	35.3560i	−1.01341	−	1.20774i	−0.0353606	−	0.999375i	$-0.511258\pi$
$858$		0			0
$859$	−10.4649	−	1.84524i	−0.357057	−	0.0629588i	−0.00775759	−	0.999970i	$-0.502469\pi$
$859$	−10.4649	−	1.84524i	−0.357057	−	0.0629588i	−0.349300	+	0.937011i	$0.613580\pi$
$860$	−0.926429	+	7.54497i	−0.0315910	+	0.257281i
$861$		0			0
$862$	−3.35292	+	0.382012i	−0.114201	+	0.0130114i
$863$	−12.8994	−	22.3425i	−0.439102	−	0.760547i	0.558519	−	0.829492i	$-0.311370\pi$
$863$	−12.8994	−	22.3425i	−0.439102	−	0.760547i	−0.997620	+	0.0689453i	$0.978037\pi$
$864$		0			0
$865$	17.4266	−	20.7682i	0.592521	−	0.706140i
$866$	3.39506	+	1.47622i	0.115369	+	0.0501640i
$867$		0			0
$868$	21.6708	−	1.13565i	0.735555	−	0.0385465i
$869$	21.7459	−	3.83440i	0.737681	−	0.130073i
$870$		0			0
$871$	7.47362	−	20.5336i	0.253234	−	0.695754i
$872$	32.3807	+	19.0739i	1.09655	+	0.645923i
$873$		0			0
$874$	9.87776	−	11.3650i	0.334120	−	0.384426i
$875$			21.4139i			0.723922i
$876$		0			0
$877$	8.46940	−	23.2695i	0.285991	−	0.785755i	−0.710626	−	0.703570i	$-0.751588\pi$
$877$	8.46940	−	23.2695i	0.285991	−	0.785755i	0.996617	−	0.0821845i	$-0.0261897\pi$
$878$	38.7862	−	19.3380i	1.30897	−	0.652626i
$879$		0			0
$880$	9.76114	−	39.1488i	0.329048	−	1.31971i
$881$	−16.7092	+	28.9413i	−0.562949	+	0.975056i	0.434288	+	0.900774i	$0.357000\pi$
$881$	−16.7092	+	28.9413i	−0.562949	+	0.975056i	−0.997237	+	0.0742821i	$0.976333\pi$
$882$		0			0
$883$	25.9883	−	30.9716i	0.874575	−	1.04228i	−0.124173	−	0.992261i	$-0.539628\pi$
$883$	25.9883	−	30.9716i	0.874575	−	1.04228i	0.998748	−	0.0500172i	$-0.0159276\pi$
$884$	−12.8814	−	19.8357i	−0.433248	−	0.667148i
$885$		0			0
$886$	−3.56813	−	31.3175i	−0.119874	−	1.05213i
$887$	30.6358	−	11.1505i	1.02865	−	0.374398i	0.228084	−	0.973642i	$-0.426754\pi$
$887$	30.6358	−	11.1505i	1.02865	−	0.374398i	0.800567	+	0.599243i	$0.204532\pi$
$888$		0			0
$889$	27.5643	+	4.86033i	0.924476	+	0.163010i
$890$	42.3368	−	12.5407i	1.41913	−	0.420364i
$891$		0			0
$892$	4.26998	−	13.9663i	0.142969	−	0.467627i
$893$	−3.38614	−	5.31417i	−0.113313	−	0.177832i
$894$		0			0
$895$	42.5166	−	35.6757i	1.42117	−	1.19251i
$896$	14.4929	−	21.0868i	0.484173	−	0.704460i
$897$		0			0
$898$	−13.2482	−	12.5722i	−0.442100	−	0.419538i
$899$	16.0211	+	44.0176i	0.534334	+	1.46807i
$900$		0			0
$901$	−11.9446	+	6.89624i	−0.397934	+	0.229747i
$902$	−4.07751	+	66.6651i	−0.135766	+	2.21970i
$903$		0			0
$904$	13.8941	−	16.2677i	0.462110	−	0.541056i
$905$	46.5379	+	26.8687i	1.54697	+	0.893144i
$906$		0			0
$907$	7.91708	+	44.9000i	0.262882	+	1.49088i	0.774999	+	0.631963i	$0.217751\pi$
$907$	7.91708	+	44.9000i	0.262882	+	1.49088i	−0.512116	+	0.858916i	$0.671138\pi$
$908$	40.1124	+	20.4385i	1.33118	+	0.678274i
$909$		0			0
$910$	15.2679	+	3.66552i	0.506126	+	0.121511i
$911$	8.16448			0.270501			0.135251	−	0.990811i	$-0.456816\pi$
$911$	8.16448			0.270501			0.135251	+	0.990811i	$0.456816\pi$
$912$		0			0
$913$	29.7320			0.983984
$914$	5.49023	+	1.31810i	0.181601	+	0.0435987i
$915$		0			0
$916$	−35.3427	−	18.0082i	−1.16776	−	0.595006i
$917$	6.79741	+	38.5500i	0.224470	+	1.27303i
$918$		0			0
$919$	27.0189	+	15.5994i	0.891270	+	0.514575i	0.874358	−	0.485282i	$-0.161283\pi$
$919$	27.0189	+	15.5994i	0.891270	+	0.514575i	0.0169126	+	0.999857i	$0.494616\pi$
$920$	−11.1691	+	13.0773i	−0.368236	+	0.431144i
$921$		0			0
$922$	0.808331	−	13.2158i	0.0266210	−	0.435238i
$923$	−10.3549	+	5.97841i	−0.340836	+	0.196782i
$924$		0			0
$925$	0.598331	+	1.64390i	0.0196730	+	0.0540512i
$926$	11.4022	+	10.8203i	0.374699	+	0.355577i
$927$		0			0
$928$	52.6755	+	16.6090i	1.72916	+	0.545216i
$929$	1.58407	−	1.32920i	0.0519718	−	0.0436095i	−0.616432	−	0.787408i	$-0.711422\pi$
$929$	1.58407	−	1.32920i	0.0519718	−	0.0436095i	0.668404	+	0.743799i	$0.266978\pi$
$930$		0			0
$931$	8.02242	−	1.77924i	0.262924	−	0.0583124i
$932$	1.99612	−	6.52894i	0.0653851	−	0.213863i
$933$		0			0
$934$	−28.2548	+	8.36939i	−0.924524	+	0.273855i
$935$	−59.5629	−	10.5026i	−1.94792	−	0.343470i
$936$		0			0
$937$	41.4174	−	15.0747i	1.35305	−	0.492469i	0.439150	−	0.898414i	$-0.355280\pi$
$937$	41.4174	−	15.0747i	1.35305	−	0.492469i	0.913898	+	0.405945i	$0.133058\pi$
$938$	−4.01149	−	35.2089i	−0.130980	−	1.14961i
$939$		0			0
$940$	3.91969	+	6.03584i	0.127846	+	0.196867i
$941$	−10.0883	+	12.0228i	−0.328869	+	0.391931i	−0.904990	−	0.425434i	$-0.860122\pi$
$941$	−10.0883	+	12.0228i	−0.328869	+	0.391931i	0.576120	+	0.817365i	$0.304566\pi$
$942$		0			0
$943$	14.2343	−	24.6546i	0.463534	−	0.802864i
$944$	−44.2772	−	11.0398i	−1.44110	−	0.359316i
$945$		0			0
$946$	−7.83093	+	3.90435i	−0.254606	+	0.126941i
$947$	12.9798	−	35.6618i	0.421788	−	1.15885i	−0.528894	−	0.848688i	$-0.677393\pi$
$947$	12.9798	−	35.6618i	0.421788	−	1.15885i	0.950682	−	0.310166i	$-0.100385\pi$
$948$		0			0
$949$			6.79843i			0.220686i
$950$	1.40638	−	7.23845i	0.0456291	−	0.234846i
$951$		0			0
$952$	−33.0483	−	19.4671i	−1.07110	−	0.630933i
$953$	−2.21624	+	6.08908i	−0.0717912	+	0.197245i	−0.970399	−	0.241509i	$-0.922358\pi$
$953$	−2.21624	+	6.08908i	−0.0717912	+	0.197245i	0.898607	+	0.438754i	$0.144580\pi$
$954$		0			0
$955$	−17.2009	+	3.03298i	−0.556608	+	0.0981450i
$956$	21.1948	−	1.11071i	0.685490	−	0.0359229i
$957$		0			0
$958$	13.9845	+	6.08065i	0.451818	+	0.196457i
$959$	5.18439	−	6.17851i	0.167413	−	0.199515i
$960$		0			0
$961$	3.99143	+	6.91336i	0.128756	+	0.223012i
$962$	−4.05285	+	0.461757i	−0.130669	+	0.0148877i
$963$		0			0
$964$	−1.88745	+	15.3717i	−0.0607907	+	0.495088i
$965$	11.1537	+	1.96670i	0.359051	+	0.0633104i
$966$		0			0
$967$	−18.5789	−	22.1415i	−0.597458	−	0.712023i	0.379563	−	0.925166i	$-0.376074\pi$
$967$	−18.5789	−	22.1415i	−0.597458	−	0.712023i	−0.977021	+	0.213143i	$0.931630\pi$
$968$	14.4520	−	5.11764i	0.464504	−	0.164487i
$969$		0			0
$970$	−13.8126	+	10.2208i	−0.443497	+	0.328169i
$971$	15.3572	−	12.8863i	0.492837	−	0.413540i	−0.362204	−	0.932099i	$-0.617976\pi$
$971$	15.3572	−	12.8863i	0.492837	−	0.413540i	0.855042	+	0.518559i	$0.173531\pi$
$972$		0			0
$973$	2.67337	−	15.1614i	0.0857044	−	0.486054i
$974$	−14.2507	+	15.0171i	−0.456623	+	0.481179i
$975$		0			0
$976$	−37.3337	+	18.2086i	−1.19502	+	0.582842i
$977$	14.0909	−	8.13540i	0.450809	−	0.260275i	−0.257363	−	0.966315i	$-0.582854\pi$
$977$	14.0909	−	8.13540i	0.450809	−	0.260275i	0.708172	+	0.706040i	$0.249520\pi$
$978$		0			0
$979$	38.9359	+	32.6711i	1.24440	+	1.04417i
$980$	−9.14475	+	2.11120i	−0.292118	+	0.0674399i
$981$		0			0
$982$	−26.9686	+	40.7449i	−0.860601	+	1.30022i
$983$	−2.90923	−	16.4991i	−0.0927902	−	0.526239i	−0.995402	−	0.0957840i	$-0.969464\pi$
$983$	−2.90923	−	16.4991i	−0.0927902	−	0.526239i	0.902612	−	0.430455i	$-0.141647\pi$
$984$		0			0
$985$	−26.9468	−	9.80783i	−0.858596	−	0.312504i
$986$	19.3280	−	80.5066i	0.615530	−	2.56385i
$987$		0			0
$988$	15.6459	+	7.12872i	0.497764	+	0.226795i
$989$	3.72975			0.118599
$990$		0			0
$991$	−6.08761	−	2.21571i	−0.193379	−	0.0703843i	0.243515	−	0.969897i	$-0.421699\pi$
$991$	−6.08761	−	2.21571i	−0.193379	−	0.0703843i	−0.436894	+	0.899513i	$0.643922\pi$
$992$	−26.9072	−	3.54261i	−0.854305	−	0.112478i
$993$		0			0
$994$	−10.7024	+	16.1695i	−0.339459	+	0.512864i
$995$	−35.7489	−	20.6396i	−1.13332	−	0.654321i
$996$		0			0
$997$	−19.8420	−	16.6494i	−0.628403	−	0.527293i	0.272029	−	0.962289i	$-0.412305\pi$
$997$	−19.8420	−	16.6494i	−0.628403	−	0.527293i	−0.900432	+	0.434996i	$0.856750\pi$
$998$	−4.96310	−	0.303564i	−0.157104	−	0.00960915i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.127.10		60
3.2	odd	2		228.2.w.b.127.1	yes	60
4.3	odd	2		684.2.cf.c.127.5		60
12.11	even	2		228.2.w.a.127.6	yes	60
19.3	odd	18		684.2.cf.c.307.5		60
57.41	even	18		228.2.w.a.79.6	✓	60
76.3	even	18	inner	684.2.cf.b.307.10		60
228.155	odd	18		228.2.w.b.79.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.6	✓	60	57.41	even	18
228.2.w.a.127.6	yes	60	12.11	even	2
228.2.w.b.79.1	yes	60	228.155	odd	18
228.2.w.b.127.1	yes	60	3.2	odd	2
684.2.cf.b.127.10		60	1.1	even	1	trivial
684.2.cf.b.307.10		60	76.3	even	18	inner
684.2.cf.c.127.5		60	4.3	odd	2
684.2.cf.c.307.5		60	19.3	odd	18

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.cf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37514 + 0.330144i) q^{2} +(1.78201 + 0.907986i) q^{4} +(-0.432248 - 2.45140i) q^{5} +(-1.95860 - 1.13080i) q^{7} +(2.15074 + 1.83693i) q^{8} +(0.214913 - 3.51371i) q^{10} +(3.50932 - 2.02611i) q^{11} +(-0.674540 - 1.85328i) q^{13} +(-2.32002 - 2.20162i) q^{14} +(2.35112 + 3.23608i) q^{16} +(4.59329 - 3.85423i) q^{17} +(-1.31039 + 4.15727i) q^{19} +(1.45557 - 4.76089i) q^{20} +(5.49471 - 1.62760i) q^{22} +(-2.40556 - 0.424166i) q^{23} +(-1.12405 + 0.409121i) q^{25} +(-0.315736 - 2.77122i) q^{26} +(-2.46349 - 3.79347i) q^{28} +(6.27599 - 7.47944i) q^{29} +(-2.39881 + 4.15486i) q^{31} +(2.16474 + 5.22627i) q^{32} +(7.58886 - 3.78365i) q^{34} +(-1.92543 + 5.29009i) q^{35} -1.46248i q^{37} +(-3.17447 + 5.28420i) q^{38} +(3.57338 - 6.06634i) q^{40} +(-3.98615 + 10.9519i) q^{41} +(-1.50372 + 0.265146i) q^{43} +(8.09332 - 0.424128i) q^{44} +(-3.16795 - 1.37747i) q^{46} +(-0.929224 + 1.10741i) q^{47} +(-0.942596 - 1.63262i) q^{49} +(-1.68079 + 0.191500i) q^{50} +(0.480719 - 3.91504i) q^{52} +(-2.26529 - 0.399432i) q^{53} +(-6.48369 - 7.72696i) q^{55} +(-2.13525 - 6.02986i) q^{56} +(11.0996 - 8.21328i) q^{58} +(-8.73918 + 7.33304i) q^{59} +(-1.80322 + 10.2266i) q^{61} +(-4.67039 + 4.92155i) q^{62} +(1.25140 + 7.90152i) q^{64} +(-4.25157 + 2.45464i) q^{65} +(8.48745 + 7.12181i) q^{67} +(11.6849 - 2.69763i) q^{68} +(-4.39423 + 6.63893i) q^{70} +(-1.05276 - 5.97051i) q^{71} +(-3.23920 - 1.17897i) q^{73} +(0.482829 - 2.01111i) q^{74} +(-6.10988 + 6.21847i) q^{76} -9.16447 q^{77} +(5.12059 + 1.86374i) q^{79} +(6.91666 - 7.16232i) q^{80} +(-9.09719 + 13.7443i) q^{82} +(6.35421 + 3.66861i) q^{83} +(-11.4337 - 9.59400i) q^{85} +(-2.15536 - 0.131830i) q^{86} +(11.2695 + 2.08873i) q^{88} +(4.28998 + 11.7866i) q^{89} +(-0.774535 + 4.39260i) q^{91} +(-3.90160 - 2.94009i) q^{92} +(-1.64342 + 1.21606i) q^{94} +(10.7575 + 1.41532i) q^{95} +(-3.13752 - 3.73916i) q^{97} +(-0.757199 - 2.55628i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

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