LMFDB - Embedded newform 684.2.cf.b.523.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(91,684)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			523.3
Character	$\chi$	$=$	684.523
Dual form			684.2.cf.b.667.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.814750 - 1.15593i) q^{2} +(-0.672365 + 1.88359i) q^{4} +(-3.29537 - 1.19942i) q^{5} +(-2.21173 - 1.27694i) q^{7} +(2.72512 - 0.757450i) q^{8} +O(q^{10})$	\(q+(-0.814750 - 1.15593i) q^{2} +(-0.672365 + 1.88359i) q^{4} +(-3.29537 - 1.19942i) q^{5} +(-2.21173 - 1.27694i) q^{7} +(2.72512 - 0.757450i) q^{8} +(1.29846 + 4.78645i) q^{10} +(-0.00324770 + 0.00187506i) q^{11} +(0.382681 - 0.456062i) q^{13} +(0.325947 + 3.59701i) q^{14} +(-3.09585 - 2.53292i) q^{16} +(0.634319 + 3.59740i) q^{17} +(-2.19475 + 3.76604i) q^{19} +(4.47490 - 5.40069i) q^{20} +(0.00481351 + 0.00222642i) q^{22} +(-0.471769 - 1.29618i) q^{23} +(5.59064 + 4.69110i) q^{25} +(-0.838966 - 0.0707777i) q^{26} +(3.89234 - 3.30743i) q^{28} +(4.56231 + 0.804457i) q^{29} +(4.50482 - 7.80257i) q^{31} +(-0.405545 + 5.64230i) q^{32} +(3.64155 - 3.66421i) q^{34} +(5.75689 + 6.86079i) q^{35} +11.9654i q^{37} +(6.14147 - 0.531404i) q^{38} +(-9.88877 - 0.772475i) q^{40} +(6.76233 + 8.05903i) q^{41} +(1.12571 - 3.09286i) q^{43} +(-0.00134821 - 0.00737807i) q^{44} +(-1.11392 + 1.60139i) q^{46} +(-1.35380 - 0.238711i) q^{47} +(-0.238826 - 0.413659i) q^{49} +(0.867630 - 10.2845i) q^{50} +(0.601734 + 1.02746i) q^{52} +(2.00076 + 5.49705i) q^{53} +(0.0129513 - 0.00228367i) q^{55} +(-6.99445 - 1.80455i) q^{56} +(-2.78724 - 5.92915i) q^{58} +(1.05912 + 6.00657i) q^{59} +(10.1552 - 3.69618i) q^{61} +(-12.6896 + 1.14988i) q^{62} +(6.85254 - 4.12828i) q^{64} +(-1.80808 + 1.04390i) q^{65} +(-2.79523 + 15.8525i) q^{67} +(-7.20254 - 1.22397i) q^{68} +(3.24019 - 12.2444i) q^{70} +(-9.17413 - 3.33911i) q^{71} +(-8.53345 + 7.16041i) q^{73} +(13.8312 - 9.74884i) q^{74} +(-5.61803 - 6.66617i) q^{76} +0.00957739 q^{77} +(-1.45560 + 1.22139i) q^{79} +(7.16395 + 12.0601i) q^{80} +(3.80609 - 14.3829i) q^{82} +(-6.90065 - 3.98409i) q^{83} +(2.22447 - 12.6156i) q^{85} +(-4.49232 + 1.21866i) q^{86} +(-0.00743010 + 0.00756973i) q^{88} +(9.76573 - 11.6383i) q^{89} +(-1.42875 + 0.520024i) q^{91} +(2.75867 - 0.0171194i) q^{92} +(0.827074 + 1.75939i) q^{94} +(11.7496 - 9.77809i) q^{95} +(1.06007 - 0.186919i) q^{97} +(-0.283579 + 0.613096i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8}+O(q^{10}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$-1$	$1$

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 $

$2$	−0.814750	−	1.15593i	−0.576115	−	0.817368i
$2$	−0.814750	−	1.15593i	−0.576115	−	0.817368i
$3$		0			0
$3$		0			0
$4$	−0.672365	+	1.88359i	−0.336182	+	0.941797i
$5$	−3.29537	−	1.19942i	−1.47373	−	0.536395i	−0.524622	−	0.851335i	$-0.675793\pi$
$5$	−3.29537	−	1.19942i	−1.47373	−	0.536395i	−0.949112	+	0.314940i	$0.898016\pi$
$6$		0			0
$7$	−2.21173	−	1.27694i	−0.835956	−	0.482640i	0.0199314	−	0.999801i	$-0.493655\pi$
$7$	−2.21173	−	1.27694i	−0.835956	−	0.482640i	−0.855888	+	0.517162i	$0.826989\pi$
$8$	2.72512	−	0.757450i	0.963475	−	0.267799i
$9$		0			0
$10$	1.29846	+	4.78645i	0.410608	+	1.51361i
$11$	−0.00324770	+	0.00187506i	−0.000979218	+	0.000565352i	−0.500490	−	0.865743i	$-0.666847\pi$
$11$	−0.00324770	+	0.00187506i	−0.000979218	+	0.000565352i	0.499510	+	0.866308i	$0.333513\pi$
$12$		0			0
$13$	0.382681	−	0.456062i	0.106137	−	0.126489i	−0.710361	−	0.703838i	$-0.751468\pi$
$13$	0.382681	−	0.456062i	0.106137	−	0.126489i	0.816498	+	0.577349i	$0.195913\pi$
$14$	0.325947	+	3.59701i	0.0871129	+	0.961340i
$15$		0			0
$16$	−3.09585	−	2.53292i	−0.773963	−	0.633231i
$17$	0.634319	+	3.59740i	0.153845	+	0.872498i	0.959834	+	0.280568i	$0.0905228\pi$
$17$	0.634319	+	3.59740i	0.153845	+	0.872498i	−0.805989	+	0.591930i	$0.798366\pi$
$18$		0			0
$19$	−2.19475	+	3.76604i	−0.503509	+	0.863990i
$19$	−2.19475	+	3.76604i	−0.503509	+	0.863990i
$20$	4.47490	−	5.40069i	1.00062	−	1.20763i
$21$		0			0
$22$	0.00481351	+	0.00222642i	0.00102624	+	0.000474674i
$23$	−0.471769	−	1.29618i	−0.0983707	−	0.270271i	0.880740	−	0.473601i	$-0.157046\pi$
$23$	−0.471769	−	1.29618i	−0.0983707	−	0.270271i	−0.979110	+	0.203329i	$0.934824\pi$
$24$		0			0
$25$	5.59064	+	4.69110i	1.11813	+	0.938221i
$26$	−0.838966	−	0.0707777i	−0.164535	−	0.0138806i
$27$		0			0
$28$	3.89234	−	3.30743i	0.735582	−	0.625046i
$29$	4.56231	+	0.804457i	0.847199	+	0.149384i	0.580363	−	0.814358i	$-0.302911\pi$
$29$	4.56231	+	0.804457i	0.847199	+	0.149384i	0.266836	+	0.963742i	$0.414022\pi$
$30$		0			0
$31$	4.50482	−	7.80257i	0.809089	−	1.40138i	−0.104407	−	0.994535i	$-0.533294\pi$
$31$	4.50482	−	7.80257i	0.809089	−	1.40138i	0.913496	−	0.406848i	$-0.133372\pi$
$32$	−0.405545	+	5.64230i	−0.0716910	+	0.997427i
$33$		0			0
$34$	3.64155	−	3.66421i	0.624520	−	0.628408i
$35$	5.75689	+	6.86079i	0.973092	+	1.15969i
$36$		0			0
$37$			11.9654i			1.96711i	0.180622	+	0.983553i	$0.442189\pi$
$37$			11.9654i			1.96711i	−0.180622	+	0.983553i	$0.557811\pi$
$38$	6.14147	−	0.531404i	0.996277	−	0.0862051i
$39$		0			0
$40$	−9.88877	−	0.772475i	−1.56355	−	0.122139i
$41$	6.76233	+	8.05903i	1.05610	+	1.25861i	0.964856	+	0.262780i	$0.0846392\pi$
$41$	6.76233	+	8.05903i	1.05610	+	1.25861i	0.0912419	+	0.995829i	$0.470916\pi$
$42$		0			0
$43$	1.12571	−	3.09286i	0.171669	−	0.471657i	−0.823785	−	0.566903i	$-0.808141\pi$
$43$	1.12571	−	3.09286i	0.171669	−	0.471657i	0.995454	+	0.0952458i	$0.0303637\pi$
$44$	−0.00134821	−	0.00737807i	−0.000203251	−	0.00111229i
$45$		0			0
$46$	−1.11392	+	1.60139i	−0.164238	+	0.236112i
$47$	−1.35380	−	0.238711i	−0.197472	−	0.0348196i	0.0740373	−	0.997255i	$-0.476412\pi$
$47$	−1.35380	−	0.238711i	−0.197472	−	0.0348196i	−0.271509	+	0.962436i	$0.587523\pi$
$48$		0			0
$49$	−0.238826	−	0.413659i	−0.0341180	−	0.0590942i
$50$	0.867630	−	10.2845i	0.122701	−	1.45445i
$51$		0			0
$52$	0.601734	+	1.02746i	0.0834455	+	0.142482i
$53$	2.00076	+	5.49705i	0.274826	+	0.755078i	0.997928	+	0.0643373i	$0.0204934\pi$
$53$	2.00076	+	5.49705i	0.274826	+	0.755078i	−0.723102	+	0.690741i	$0.757284\pi$
$54$		0			0
$55$	0.0129513	−	0.00228367i	0.00174636	−	0.000307930i
$56$	−6.99445	−	1.80455i	−0.934673	−	0.241143i
$57$		0			0
$58$	−2.78724	−	5.92915i	−0.365982	−	0.778536i
$59$	1.05912	+	6.00657i	0.137886	+	0.781989i	0.972807	+	0.231619i	$0.0744022\pi$
$59$	1.05912	+	6.00657i	0.137886	+	0.781989i	−0.834921	+	0.550370i	$0.814487\pi$
$60$		0			0
$61$	10.1552	−	3.69618i	1.30024	−	0.473248i	0.403164	−	0.915128i	$-0.367911\pi$
$61$	10.1552	−	3.69618i	1.30024	−	0.473248i	0.897074	+	0.441880i	$0.145688\pi$
$62$	−12.6896	+	1.14988i	−1.61157	+	0.146035i
$63$		0			0
$64$	6.85254	−	4.12828i	0.856568	−	0.516035i
$65$	−1.80808	+	1.04390i	−0.224265	+	0.129480i
$66$		0			0
$67$	−2.79523	+	15.8525i	−0.341492	+	1.93670i	0.00855120	+	0.999963i	$0.497278\pi$
$67$	−2.79523	+	15.8525i	−0.341492	+	1.93670i	−0.350043	+	0.936734i	$0.613833\pi$
$68$	−7.20254	−	1.22397i	−0.873436	−	0.148428i
$69$		0			0
$70$	3.24019	−	12.2444i	0.387277	−	1.46349i
$71$	−9.17413	−	3.33911i	−1.08877	−	0.396279i	−0.265604	−	0.964082i	$-0.585571\pi$
$71$	−9.17413	−	3.33911i	−1.08877	−	0.396279i	−0.823165	+	0.567803i	$0.807794\pi$
$72$		0			0
$73$	−8.53345	+	7.16041i	−0.998764	+	0.838063i	−0.986813	−	0.161866i	$-0.948249\pi$
$73$	−8.53345	+	7.16041i	−0.998764	+	0.838063i	−0.0119514	+	0.999929i	$0.503804\pi$
$74$	13.8312	−	9.74884i	1.60785	−	1.13328i
$75$		0			0
$76$	−5.61803	−	6.66617i	−0.644432	−	0.764662i
$77$	0.00957739			0.00109144
$78$		0			0
$79$	−1.45560	+	1.22139i	−0.163767	+	0.137417i	−0.720989	−	0.692947i	$-0.756312\pi$
$79$	−1.45560	+	1.22139i	−0.163767	+	0.137417i	0.557221	+	0.830364i	$0.311868\pi$
$80$	7.16395	+	12.0601i	0.800954	+	1.34836i
$81$		0			0
$82$	3.80609	−	14.3829i	0.420313	−	1.58832i
$83$	−6.90065	−	3.98409i	−0.757445	−	0.437311i	0.0709327	−	0.997481i	$-0.477402\pi$
$83$	−6.90065	−	3.98409i	−0.757445	−	0.437311i	−0.828378	+	0.560170i	$0.810736\pi$
$84$		0			0
$85$	2.22447	−	12.6156i	0.241277	−	1.36835i
$86$	−4.49232	+	1.21866i	−0.484419	+	0.131412i
$87$		0			0
$88$	−0.00743010	+	0.00756973i	−0.000792051	+	0.000806936i
$89$	9.76573	−	11.6383i	1.03517	−	1.23366i	0.0633322	−	0.997993i	$-0.479827\pi$
$89$	9.76573	−	11.6383i	1.03517	−	1.23366i	0.971833	−	0.235670i	$-0.0757283\pi$
$90$		0			0
$91$	−1.42875	+	0.520024i	−0.149774	+	0.0545133i
$92$	2.75867	−	0.0171194i	0.287611	−	0.00178482i
$93$		0			0
$94$	0.827074	+	1.75939i	0.0853061	+	0.181467i
$95$	11.7496	−	9.77809i	1.20548	−	1.00321i
$96$		0			0
$97$	1.06007	−	0.186919i	0.107634	−	0.0189788i	−0.119572	−	0.992826i	$-0.538152\pi$
$97$	1.06007	−	0.186919i	0.107634	−	0.0189788i	0.227206	+	0.973847i	$0.427041\pi$
$98$	−0.283579	+	0.613096i	−0.0286458	+	0.0619320i
$99$		0			0
$100$	−12.5951	+	7.37636i	−1.25951	+	0.737636i
$101$	−4.30721	−	3.61418i	−0.428583	−	0.359624i	0.402834	−	0.915273i	$-0.368025\pi$
$101$	−4.30721	−	3.61418i	−0.428583	−	0.359624i	−0.831417	+	0.555649i	$0.812470\pi$
$102$		0			0
$103$	4.25392	+	7.36801i	0.419151	+	0.725992i	0.995854	−	0.0909623i	$-0.0289943\pi$
$103$	4.25392	+	7.36801i	0.419151	+	0.725992i	−0.576703	+	0.816954i	$0.695661\pi$
$104$	0.697408	−	1.53268i	0.0683865	−	0.150292i
$105$		0			0
$106$	4.72411	−	6.79148i	0.458846	−	0.659646i
$107$	4.01613	−	6.95614i	0.388254	−	0.672475i	−0.603961	−	0.797014i	$-0.706412\pi$
$107$	4.01613	−	6.95614i	0.388254	−	0.672475i	0.992215	+	0.124539i	$0.0397451\pi$
$108$		0			0
$109$	−1.20572	+	3.31268i	−0.115487	+	0.317298i	−0.983947	−	0.178462i	$-0.942888\pi$
$109$	−1.20572	+	3.31268i	−0.115487	+	0.317298i	0.868460	+	0.495759i	$0.165110\pi$
$110$	−0.0131919	−	0.0131103i	−0.00125780	−	0.00125002i
$111$		0			0
$112$	3.61279	+	9.55538i	0.341377	+	0.902899i
$113$		−	0.762117i		−	0.0716939i	−0.999357	−	0.0358470i	$-0.988587\pi$
$113$		−	0.762117i		−	0.0716939i	0.999357	−	0.0358470i	$-0.0114129\pi$
$114$		0			0
$115$			4.83722i			0.451074i
$116$	−4.58280	+	8.05264i	−0.425503	+	0.747669i
$117$		0			0
$118$	6.08028	−	6.11813i	0.559735	−	0.563219i
$119$	3.19074	−	8.76648i	0.292495	−	0.803622i
$120$		0			0
$121$	−5.49999	+	9.52627i	−0.499999	+	0.866024i
$122$	−12.5465	−	8.72725i	−1.13590	−	0.790128i
$123$		0			0
$124$	11.6680	+	13.7314i	1.04782	+	1.23312i
$125$	−4.02949	−	6.97928i	−0.360408	−	0.624246i
$126$		0			0
$127$	−8.71951	−	7.31654i	−0.773731	−	0.649237i	0.167930	−	0.985799i	$-0.446292\pi$
$127$	−8.71951	−	7.31654i	−0.773731	−	0.649237i	−0.941662	+	0.336561i	$0.890736\pi$
$128$	−10.3551	−	4.55756i	−0.915272	−	0.402836i
$129$		0			0
$130$	2.67981	+	1.23951i	0.235035	+	0.108712i
$131$	−9.96414	+	1.75695i	−0.870571	+	0.153505i	−0.591051	−	0.806635i	$-0.701287\pi$
$131$	−9.96414	+	1.75695i	−0.870571	+	0.153505i	−0.279521	+	0.960140i	$0.590176\pi$
$132$		0			0
$133$	9.66322	−	5.52691i	0.837908	−	0.479244i
$134$	20.6019	−	9.68476i	1.77973	−	0.836636i
$135$		0			0
$136$	4.45345	+	9.32288i	0.381880	+	0.799431i
$137$	−9.14251	+	3.32760i	−0.781097	+	0.284296i	−0.701630	−	0.712541i	$-0.747544\pi$
$137$	−9.14251	+	3.32760i	−0.781097	+	0.284296i	−0.0794670	+	0.996837i	$0.525322\pi$
$138$		0			0
$139$	−2.45569	+	2.92658i	−0.208289	+	0.248229i	−0.860068	−	0.510180i	$-0.829579\pi$
$139$	−2.45569	+	2.92658i	−0.208289	+	0.248229i	0.651778	+	0.758409i	$0.274023\pi$
$140$	−16.7937	+	6.23069i	−1.41932	+	0.526589i
$141$		0			0
$142$	3.61483	+	13.3252i	0.303350	+	1.11823i
$143$	−0.000387690		0.00219870i	−3.24203e−5		0.000183865i
$144$		0			0
$145$	−14.0696	−	8.12309i	−1.16842	−	0.674586i
$146$	15.2296	+	4.03015i	1.26041	+	0.333538i
$147$		0			0
$148$	−22.5380	−	8.04513i	−1.85261	−	0.661306i
$149$	−4.17418	+	3.50256i	−0.341962	+	0.286941i	−0.797553	−	0.603249i	$-0.793873\pi$
$149$	−4.17418	+	3.50256i	−0.341962	+	0.286941i	0.455591	+	0.890189i	$0.349428\pi$
$150$		0			0
$151$	2.19768			0.178844			0.0894222	−	0.995994i	$-0.471498\pi$
$151$	2.19768			0.178844			0.0894222	+	0.995994i	$0.471498\pi$
$152$	−3.12836	+	11.9253i	−0.253743	+	0.967272i
$153$		0			0
$154$	−0.00780318	−	0.0110708i	−0.000628798	−	0.000892112i
$155$	−24.2036	+	20.3092i	−1.94408	+	1.63127i
$156$		0			0
$157$	10.0294	+	3.65039i	0.800431	+	0.291333i	0.709665	−	0.704539i	$-0.248846\pi$
$157$	10.0294	+	3.65039i	0.800431	+	0.291333i	0.0907657	+	0.995872i	$0.471069\pi$
$158$	2.59779	+	0.687445i	0.206669	+	0.0546902i
$159$		0			0
$160$	8.10389	−	18.1070i	0.640669	−	1.43149i
$161$	−0.611716	+	3.46922i	−0.0482100	+	0.273413i
$162$		0			0
$163$	−9.37371	+	5.41192i	−0.734206	+	0.423894i	−0.819959	−	0.572422i	$-0.806004\pi$
$163$	−9.37371	+	5.41192i	−0.734206	+	0.423894i	0.0857529	+	0.996316i	$0.472670\pi$
$164$	−19.7267	+	7.31887i	−1.54039	+	0.571508i
$165$		0			0
$166$	1.01696	+	11.2227i	0.0789314	+	0.871053i
$167$	9.25815	−	3.36969i	0.716417	−	0.260755i	0.0420132	−	0.999117i	$-0.486623\pi$
$167$	9.25815	−	3.36969i	0.716417	−	0.260755i	0.674404	+	0.738362i	$0.264401\pi$
$168$		0			0
$169$	2.19588	+	12.4534i	0.168914	+	0.957958i
$170$	−16.3952	+	7.70721i	−1.25745	+	0.591116i
$171$		0			0
$172$	5.06881	+	4.19991i	0.386493	+	0.320240i
$173$	−21.2004	+	3.73820i	−1.61184	+	0.284210i	−0.905717	−	0.423882i	$-0.860667\pi$
$173$	−21.2004	+	3.73820i	−1.61184	+	0.284210i	−0.706120	+	0.708093i	$0.749556\pi$
$174$		0			0
$175$	−6.37472	−	17.5144i	−0.481884	−	1.32396i
$176$	0.0148038	+	0.00242126i	0.00111588	+	0.000182510i
$177$		0			0
$178$	−21.4098	−	1.80619i	−1.60473	−	0.135380i
$179$	10.0713	+	17.4439i	0.752762	+	1.30382i	0.946480	+	0.322764i	$0.104612\pi$
$179$	10.0713	+	17.4439i	0.752762	+	1.30382i	−0.193718	+	0.981057i	$0.562055\pi$
$180$		0			0
$181$	−7.45770	−	1.31499i	−0.554327	−	0.0977428i	−0.110534	−	0.993872i	$-0.535256\pi$
$181$	−7.45770	−	1.31499i	−0.554327	−	0.0977428i	−0.443793	+	0.896130i	$0.646367\pi$
$182$	1.76519	+	1.22785i	0.130845	+	0.0910147i
$183$		0			0
$184$	−2.26741	−	3.17489i	−0.167156	−	0.234056i
$185$	14.3515	−	39.4305i	1.05515	−	2.89899i
$186$		0			0
$187$	−0.00880542	−	0.0104939i	−0.000643916	−	0.000767389i
$188$	1.35988	−	2.38951i	0.0991796	−	0.174273i
$189$		0			0
$190$	−20.8758	−	5.61500i	−1.51449	−	0.407355i
$191$		−	8.80175i		−	0.636872i	−0.947944	−	0.318436i	$-0.896842\pi$
$191$		−	8.80175i		−	0.636872i	0.947944	−	0.318436i	$-0.103158\pi$
$192$		0			0
$193$	−2.08205	−	2.48129i	−0.149869	−	0.178607i	0.685887	−	0.727708i	$-0.259415\pi$
$193$	−2.08205	−	2.48129i	−0.149869	−	0.178607i	−0.835756	+	0.549101i	$0.814970\pi$
$194$	−1.07976	−	1.07308i	−0.0775222	−	0.0770426i
$195$		0			0
$196$	0.939744	−	0.171722i	0.0671246	−	0.0122658i
$197$	−8.33206	+	14.4315i	−0.593634	+	1.02821i	0.400104	+	0.916470i	$0.368974\pi$
$197$	−8.33206	+	14.4315i	−0.593634	+	1.02821i	−0.993738	+	0.111735i	$0.964359\pi$
$198$		0			0
$199$	24.7689	+	4.36743i	1.75582	+	0.309599i	0.956593	−	0.291426i	$-0.0941298\pi$
$199$	24.7689	+	4.36743i	1.75582	+	0.309599i	0.799230	+	0.601025i	$0.205241\pi$
$200$	18.7884	+	8.54918i	1.32854	+	0.604519i
$201$		0			0
$202$	−0.668450	+	7.92349i	−0.0470319	+	0.557495i
$203$	−9.06335	−	7.60505i	−0.636123	−	0.533770i
$204$		0			0
$205$	−12.6182	−	34.6683i	−0.881296	−	2.42134i
$206$	5.05105	−	10.9203i	0.351923	−	0.760856i
$207$		0			0
$208$	−2.33989	+	0.442597i	−0.162242	+	0.0306886i
$209$	6.63182e−5	−	0.0163463i	4.58732e−6	−	0.00113069i
$210$		0			0
$211$	0.195718	+	1.10997i	0.0134738	+	0.0764136i	0.990803	−	0.135311i	$-0.0432032\pi$
$211$	0.195718	+	1.10997i	0.0134738	+	0.0764136i	−0.977329	+	0.211724i	$0.932092\pi$
$212$	−11.6995	+	0.0726028i	−0.803522	+	0.00498638i
$213$		0			0
$214$	−11.3130	+	1.02514i	−0.773339	+	0.0700769i
$215$	−7.41926	+	8.84193i	−0.505989	+	0.603015i
$216$		0			0
$217$	−19.9269	+	11.5048i	−1.35273	+	0.780997i
$218$	4.81160	−	1.30528i	0.325883	−	0.0884047i
$219$		0			0
$220$	−0.00440651	+	0.0259305i	−0.000297087	+	0.00174824i
$221$	1.88338	+	1.08737i	0.126690	+	0.0731444i
$222$		0			0
$223$	−18.9083	−	6.88205i	−1.26619	−	0.460856i	−0.380350	−	0.924843i	$-0.624196\pi$
$223$	−18.9083	−	6.88205i	−1.26619	−	0.460856i	−0.885842	+	0.463987i	$0.846419\pi$
$224$	8.10186	−	11.9614i	0.541328	−	0.799204i
$225$		0			0
$226$	−0.880957	+	0.620935i	−0.0586004	+	0.0413040i
$227$	16.1679			1.07310			0.536552	−	0.843867i	$-0.319726\pi$
$227$	16.1679			1.07310			0.536552	+	0.843867i	$0.319726\pi$
$228$		0			0
$229$	10.8224			0.715167			0.357583	−	0.933881i	$-0.383601\pi$
$229$	10.8224			0.715167			0.357583	+	0.933881i	$0.383601\pi$
$230$	5.59151	−	3.94113i	0.368693	−	0.259870i
$231$		0			0
$232$	13.0422	−	1.26347i	0.856260	−	0.0829512i
$233$	13.5192	+	4.92057i	0.885669	+	0.322357i	0.744495	−	0.667628i	$-0.232690\pi$
$233$	13.5192	+	4.92057i	0.885669	+	0.322357i	0.141174	+	0.989985i	$0.454912\pi$
$234$		0			0
$235$	4.17495	+	2.41041i	0.272344	+	0.157238i
$236$	−12.0261	−	2.04365i	−0.782829	−	0.133030i
$237$		0			0
$238$	−12.7331	+	3.45421i	−0.825366	+	0.223903i
$239$	−17.1433	+	9.89769i	−1.10891	+	0.640228i	−0.938546	−	0.345153i	$-0.887827\pi$
$239$	−17.1433	+	9.89769i	−1.10891	+	0.640228i	−0.170362	+	0.985382i	$0.554494\pi$
$240$		0			0
$241$	11.2387	−	13.3938i	0.723951	−	0.862771i	−0.271057	−	0.962563i	$-0.587373\pi$
$241$	11.2387	−	13.3938i	0.723951	−	0.862771i	0.995008	+	0.0997922i	$0.0318178\pi$
$242$	15.4929	−	1.40390i	0.995918	−	0.0902462i
$243$		0			0
$244$	0.134125	+	21.6134i	0.00858650	+	1.38366i
$245$	0.290871	+	1.64961i	0.0185831	+	0.105390i
$246$		0			0
$247$	0.877660	+	2.44213i	0.0558442	+	0.155389i
$248$	6.36610	−	24.6751i	0.404248	−	1.56687i
$249$		0			0
$250$	−4.78456	+	10.3442i	−0.302602	+	0.654224i
$251$	8.15333	+	22.4011i	0.514634	+	1.41394i	0.876359	+	0.481659i	$0.159966\pi$
$251$	8.15333	+	22.4011i	0.514634	+	1.41394i	−0.361725	+	0.932285i	$0.617812\pi$
$252$		0			0
$253$	0.00396257	+	0.00332499i	0.000249125	+	0.000209040i
$254$	−1.35321	+	16.0403i	−0.0849079	+	1.00646i
$255$		0			0
$256$	3.16860	+	15.6831i	0.198037	+	0.980194i
$257$	17.1342	+	3.02122i	1.06880	+	0.188458i	0.680259	−	0.732972i	$-0.261868\pi$
$257$	17.1342	+	3.02122i	1.06880	+	0.188458i	0.388543	+	0.921431i	$0.372979\pi$
$258$		0			0
$259$	15.2792	−	26.4643i	0.949403	−	1.64441i
$260$	−0.750588	−	4.10758i	−0.0465495	−	0.254741i
$261$		0			0
$262$	10.1492	+	10.0864i	0.627020	+	0.623141i
$263$	12.8586	+	15.3242i	0.792892	+	0.944932i	0.999439	−	0.0335045i	$-0.0106668\pi$
$263$	12.8586	+	15.3242i	0.792892	+	0.944932i	−0.206546	+	0.978437i	$0.566222\pi$
$264$		0			0
$265$		−	20.5146i		−	1.26020i
$266$	−14.2619	−	6.66699i	−0.874450	−	0.408779i
$267$		0			0
$268$	−27.9803	−	15.9238i	−1.70917	−	0.972699i
$269$	−5.35478	−	6.38158i	−0.326487	−	0.389092i	0.577686	−	0.816259i	$-0.303956\pi$
$269$	−5.35478	−	6.38158i	−0.326487	−	0.389092i	−0.904172	+	0.427168i	$0.859511\pi$
$270$		0			0
$271$	6.32735	−	17.3842i	0.384359	−	1.05602i	−0.585142	−	0.810931i	$-0.698961\pi$
$271$	6.32735	−	17.3842i	0.384359	−	1.05602i	0.969501	−	0.245087i	$-0.0788164\pi$
$272$	7.14819	−	12.7437i	0.433423	−	0.772701i
$273$		0			0
$274$	11.2953	+	7.85697i	0.682377	+	0.474657i
$275$	−0.0269528	−	0.00475251i	−0.00162532	−	0.000286587i
$276$		0			0
$277$	9.63808	+	16.6936i	0.579096	+	1.00302i	0.995583	+	0.0938823i	$0.0299277\pi$
$277$	9.63808	+	16.6936i	0.579096	+	1.00302i	−0.416487	+	0.909142i	$0.636739\pi$
$278$	5.38371	+	0.454185i	0.322893	+	0.0272402i
$279$		0			0
$280$	20.8849	+	14.3359i	1.24811	+	0.856735i
$281$	3.74181	+	10.2805i	0.223218	+	0.613286i	0.999861	−	0.0166547i	$-0.00530159\pi$
$281$	3.74181	+	10.2805i	0.223218	+	0.613286i	−0.776644	+	0.629940i	$0.783079\pi$
$282$		0			0
$283$	8.46982	−	1.49346i	0.503479	−	0.0887769i	0.0838603	−	0.996478i	$-0.473275\pi$
$283$	8.46982	−	1.49346i	0.503479	−	0.0887769i	0.419618	+	0.907701i	$0.362164\pi$
$284$	12.4579	−	15.0352i	0.739239	−	0.892177i
$285$		0			0
$286$	0.00285742	−	0.00134325i	0.000168963	−	7.94279e-5i
$287$	−4.66553	−	26.4595i	−0.275397	−	1.56186i
$288$		0			0
$289$	3.43583	−	1.25054i	0.202108	−	0.0735612i
$290$	2.07346	+	22.8818i	0.121758	+	1.34367i
$291$		0			0
$292$	−7.74972	−	20.8880i	−0.453518	−	1.22237i
$293$	11.0763	−	6.39490i	0.647084	−	0.373594i	−0.140254	−	0.990116i	$-0.544792\pi$
$293$	11.0763	−	6.39490i	0.647084	−	0.373594i	0.787338	+	0.616522i	$0.211459\pi$
$294$		0			0
$295$	3.71419	−	21.0642i	0.216248	−	1.22640i
$296$	9.06321	+	32.6072i	0.526789	+	1.89526i
$297$		0			0
$298$	7.44964	+	1.97137i	0.431546	+	0.114198i
$299$	−0.771673	−	0.280866i	−0.0446270	−	0.0162429i
$300$		0			0
$301$	−6.43918	+	5.40312i	−0.371148	+	0.311430i
$302$	−1.79056	−	2.54037i	−0.103035	−	0.146182i
$303$		0			0
$304$	16.3337	−	6.09999i	0.936803	−	0.349858i
$305$	−37.8983			−2.17005
$306$		0			0
$307$	−14.4522	+	12.1269i	−0.824833	+	0.692117i	−0.954098	−	0.299493i	$-0.903182\pi$
$307$	−14.4522	+	12.1269i	−0.824833	+	0.692117i	0.129266	+	0.991610i	$0.458738\pi$
$308$	−0.00643950	+	0.0180399i	−0.000366924	+	0.00102792i
$309$		0			0
$310$	43.1959	+	11.4308i	2.45336	+	0.649225i
$311$	17.5045	+	10.1062i	0.992587	+	0.573070i	0.906047	−	0.423178i	$-0.139086\pi$
$311$	17.5045	+	10.1062i	0.992587	+	0.573070i	0.0865403	+	0.996248i	$0.472419\pi$
$312$		0			0
$313$	0.692923	−	3.92976i	0.0391664	−	0.222123i	−0.958942	−	0.283602i	$-0.908471\pi$
$313$	0.692923	−	3.92976i	0.0391664	−	0.222123i	0.998108	+	0.0614787i	$0.0195816\pi$
$314$	−3.95182	−	14.5674i	−0.223014	−	0.822088i
$315$		0			0
$316$	−1.32191	−	3.56297i	−0.0743634	−	0.200433i
$317$	−11.1384	+	13.2743i	−0.625596	+	0.745557i	−0.982022	−	0.188767i	$-0.939551\pi$
$317$	−11.1384	+	13.2743i	−0.625596	+	0.745557i	0.356425	+	0.934324i	$0.383995\pi$
$318$		0			0
$319$	−0.0163254	+	0.00594196i	−0.000914047	+	0.000332686i
$320$	−27.5332	+	5.38516i	−1.53915	+	0.301040i
$321$		0			0
$322$	4.50858	−	2.11944i	0.251253	−	0.118112i
$323$	−14.9401	−	5.50651i	−0.831292	−	0.306391i
$324$		0			0
$325$	4.27886	−	0.754479i	0.237349	−	0.0418510i
$326$	13.8931	+	6.42603i	0.769465	+	0.355905i
$327$		0			0
$328$	24.5324	+	16.8397i	1.35458	+	0.929816i
$329$	2.68942	+	2.25669i	0.148273	+	0.124415i
$330$		0			0
$331$	−2.53054	−	4.38302i	−0.139091	−	0.240913i	0.788062	−	0.615596i	$-0.211085\pi$
$331$	−2.53054	−	4.38302i	−0.139091	−	0.240913i	−0.927153	+	0.374683i	$0.877751\pi$
$332$	12.1442	−	10.3193i	0.666498	−	0.566343i
$333$		0			0
$334$	−11.4382	−	7.95635i	−0.625872	−	0.435352i
$335$	28.2251	−	48.8874i	1.54210	−	2.67100i
$336$		0			0
$337$	1.59075	−	4.37055i	0.0866537	−	0.238079i	−0.888795	−	0.458304i	$-0.848457\pi$
$337$	1.59075	−	4.37055i	0.0866537	−	0.238079i	0.975449	+	0.220225i	$0.0706792\pi$
$338$	12.6063	−	12.6847i	0.685690	−	0.689959i
$339$		0			0
$340$	22.2670	+	12.6723i	1.20760	+	0.687250i
$341$			0.0337872i			0.00182968i
$342$		0			0
$343$			19.0971i			1.03115i
$344$	0.725005	−	9.28108i	0.0390897	−	0.500403i
$345$		0			0
$346$	21.5941	+	21.4606i	1.16091	+	1.15373i
$347$	6.38901	−	17.5537i	0.342980	−	0.942330i	−0.641545	−	0.767086i	$-0.721706\pi$
$347$	6.38901	−	17.5537i	0.342980	−	0.942330i	0.984525	−	0.175245i	$-0.0560717\pi$
$348$		0			0
$349$	−13.3174	+	23.0664i	−0.712865	+	1.23472i	0.250912	+	0.968010i	$0.419269\pi$
$349$	−13.3174	+	23.0664i	−0.712865	+	1.23472i	−0.963777	+	0.266708i	$0.914064\pi$
$350$	−15.0517	+	21.6386i	−0.804546	+	1.15663i
$351$		0			0
$352$	−0.00926256	−	0.0190849i	−0.000493696	−	0.00101723i
$353$	−14.4069	−	24.9535i	−0.766802	−	1.32814i	−0.939289	−	0.343128i	$-0.888514\pi$
$353$	−14.4069	−	24.9535i	−0.766802	−	1.32814i	0.172487	−	0.985012i	$-0.444820\pi$
$354$		0			0
$355$	26.2272	+	22.0072i	1.39199	+	1.16802i
$356$	15.3558	+	26.2199i	0.813855	+	1.38965i
$357$		0			0
$358$	11.9585	−	25.8542i	0.632025	−	1.36643i
$359$	5.54418	−	0.977588i	0.292610	−	0.0515951i	−0.0254160	−	0.999677i	$-0.508091\pi$
$359$	5.54418	−	0.977588i	0.292610	−	0.0515951i	0.318026	+	0.948082i	$0.396980\pi$
$360$		0			0
$361$	−9.36617	−	16.5310i	−0.492957	−	0.870054i
$362$	4.55612	+	9.69200i	0.239464	+	0.509400i
$363$		0			0
$364$	−0.0188704	−	3.04084i	−0.000989078	−	0.159383i
$365$	36.7092	−	13.3610i	1.92145	−	0.699349i
$366$		0			0
$367$	−0.856254	+	1.02044i	−0.0446961	+	0.0532667i	−0.787929	−	0.615766i	$-0.788847\pi$
$367$	−0.856254	+	1.02044i	−0.0446961	+	0.0532667i	0.743233	+	0.669032i	$0.233291\pi$
$368$	−1.82259	+	5.20772i	−0.0950088	+	0.271471i
$369$		0			0
$370$	−57.2720	+	15.5366i	−2.97743	+	0.807709i
$371$	2.59428	−	14.7129i	0.134688	−	0.763855i
$372$		0			0
$373$	2.69212	+	1.55430i	0.139393	+	0.0804785i	0.568075	−	0.822977i	$-0.307689\pi$
$373$	2.69212	+	1.55430i	0.139393	+	0.0804785i	−0.428682	+	0.903456i	$0.641022\pi$
$374$	−0.00495602	+	0.0187284i	−0.000256270	+	0.000968422i
$375$		0			0
$376$	−3.87007	+	0.374918i	−0.199584	+	0.0193349i
$377$	2.11279	−	1.77284i	0.108814	−	0.0913060i
$378$		0			0
$379$	25.2168			1.29530			0.647650	−	0.761938i	$-0.275752\pi$
$379$	25.2168			1.29530			0.647650	+	0.761938i	$0.275752\pi$
$380$	10.5180	+	28.7058i	0.539560	+	1.47258i
$381$		0			0
$382$	−10.1742	+	7.17122i	−0.520559	+	0.366912i
$383$	−0.227120	+	0.190577i	−0.0116053	+	0.00973802i	−0.648572	−	0.761153i	$-0.724633\pi$
$383$	−0.227120	+	0.190577i	−0.0116053	+	0.00973802i	0.636967	+	0.770891i	$0.280189\pi$
$384$		0			0
$385$	−0.0315610	−	0.0114873i	−0.00160850	−	0.000585446i
$386$	−1.17186	+	4.42835i	−0.0596460	+	0.225397i
$387$		0			0
$388$	−0.360675	+	2.12242i	−0.0183105	+	0.107750i
$389$	−5.15872	+	29.2565i	−0.261557	+	1.48336i	0.517105	+	0.855922i	$0.327010\pi$
$389$	−5.15872	+	29.2565i	−0.261557	+	1.48336i	−0.778663	+	0.627443i	$0.784102\pi$
$390$		0			0
$391$	4.36361	−	2.51933i	0.220677	−	0.127408i
$392$	−0.964156	−	0.946371i	−0.0486972	−	0.0477990i
$393$		0			0
$394$	23.4705	−	2.12680i	1.18242	−	0.107147i
$395$	6.26169	−	2.27907i	0.315060	−	0.114672i
$396$		0			0
$397$	−2.71559	−	15.4009i	−0.136291	−	0.772947i	−0.973952	−	0.226755i	$-0.927188\pi$
$397$	−2.71559	−	15.4009i	−0.136291	−	0.772947i	0.837660	−	0.546191i	$-0.183923\pi$
$398$	−15.1320	−	32.1896i	−0.758500	−	1.61352i
$399$		0			0
$400$	−5.42559	−	28.6836i	−0.271279	−	1.43418i
$401$	−7.90035	+	1.39304i	−0.394525	+	0.0695653i	−0.367391	−	0.930066i	$-0.619749\pi$
$401$	−7.90035	+	1.39304i	−0.394525	+	0.0695653i	−0.0271334	+	0.999632i	$0.508638\pi$
$402$		0			0
$403$	−1.83454	−	5.04037i	−0.0913852	−	0.251079i
$404$	9.70365	−	5.68299i	0.482775	−	0.282739i
$405$		0			0
$406$	−1.40657	+	16.6729i	−0.0698069	+	0.827460i
$407$	−0.0224359	−	0.0388601i	−0.00111211	−	0.00192622i
$408$		0			0
$409$	−7.37540	−	1.30048i	−0.364690	−	0.0643047i	−0.0116995	−	0.999932i	$-0.503724\pi$
$409$	−7.37540	−	1.30048i	−0.364690	−	0.0643047i	−0.352991	+	0.935627i	$0.614835\pi$
$410$	−29.7936	+	42.8319i	−1.47140	+	2.11531i
$411$		0			0
$412$	−16.7385	+	3.05867i	−0.824648	+	0.150690i
$413$	5.32756	−	14.6374i	0.262152	−	0.720257i
$414$		0			0
$415$	17.9616	+	21.4058i	0.881701	+	1.05077i
$416$	2.41804	+	2.34416i	0.118554	+	0.114932i
$417$		0			0
$418$	−0.0189492	+	0.0132415i	−0.000926837	+	0.000647661i
$419$			15.6423i			0.764176i	0.924126	+	0.382088i	$0.124795\pi$
$419$			15.6423i			0.764176i	−0.924126	+	0.382088i	$0.875205\pi$
$420$		0			0
$421$	−16.8520	−	20.0835i	−0.821318	−	0.978808i	0.178669	−	0.983909i	$-0.442821\pi$
$421$	−16.8520	−	20.0835i	−0.821318	−	0.978808i	−0.999987	+	0.00510082i	$0.998376\pi$
$422$	1.12359	−	1.13059i	0.0546956	−	0.0550361i
$423$		0			0
$424$	9.61606	+	13.4646i	0.466997	+	0.653901i
$425$	−13.3295	+	23.0874i	−0.646578	+	1.11991i
$426$		0			0
$427$	−27.1804	−	4.79263i	−1.31535	−	0.231932i
$428$	10.4022	+	12.2418i	0.502811	+	0.591730i
$429$		0			0
$430$	16.2655	+	1.37221i	0.784393	+	0.0661737i
$431$	3.64600	+	3.05936i	0.175622	+	0.147364i	0.726361	−	0.687313i	$-0.241210\pi$
$431$	3.64600	+	3.05936i	0.175622	+	0.147364i	−0.550740	+	0.834677i	$0.685654\pi$
$432$		0			0
$433$	1.71821	+	4.72075i	0.0825720	+	0.226865i	0.974107	−	0.226087i	$-0.0725933\pi$
$433$	1.71821	+	4.72075i	0.0825720	+	0.226865i	−0.891535	+	0.452952i	$0.850371\pi$
$434$	29.5342	+	13.6606i	1.41769	+	0.655731i
$435$		0			0
$436$	−5.42907	−	4.49842i	−0.260005	−	0.215435i
$437$	5.91687	+	1.06807i	0.283042	+	0.0510928i
$438$		0			0
$439$	1.33326	+	7.56129i	0.0636330	+	0.360881i	0.999953	+	0.00973175i	$0.00309776\pi$
$439$	1.33326	+	7.56129i	0.0636330	+	0.360881i	−0.936320	+	0.351149i	$0.885791\pi$
$440$	0.0335642	−	0.0160333i	0.00160011	−	0.000764356i
$441$		0			0
$442$	−0.277557	−	3.06300i	−0.0132020	−	0.145692i
$443$	−10.1596	+	12.1078i	−0.482698	+	0.575258i	−0.951345	−	0.308128i	$-0.900297\pi$
$443$	−10.1596	+	12.1078i	−0.482698	+	0.575258i	0.468646	+	0.883386i	$0.344742\pi$
$444$		0			0
$445$	−46.1409	+	26.6395i	−2.18729	+	1.26283i
$446$	7.45033	+	27.4639i	0.352783	+	1.30045i
$447$		0			0
$448$	−20.4276	+	0.380339i	−0.965112	+	0.0179693i
$449$	0.961162	+	0.554927i	0.0453600	+	0.0261886i	0.522509	−	0.852634i	$-0.324996\pi$
$449$	0.961162	+	0.554927i	0.0453600	+	0.0261886i	−0.477148	+	0.878823i	$0.658330\pi$
$450$		0			0
$451$	−0.0370731	−	0.0134935i	−0.00174571	−	0.000635385i
$452$	1.43552	+	0.512420i	0.0675211	+	0.0241022i
$453$		0			0
$454$	−13.1728	−	18.6891i	−0.618232	−	0.877122i
$455$	5.33200			0.249968
$456$		0			0
$457$	−2.71901			−0.127190			−0.0635949	−	0.997976i	$-0.520257\pi$
$457$	−2.71901			−0.127190			−0.0635949	+	0.997976i	$0.520257\pi$
$458$	−8.81758	−	12.5100i	−0.412019	−	0.584555i
$459$		0			0
$460$	−9.11137	−	3.25238i	−0.424820	−	0.151643i
$461$	−9.32484	−	3.39396i	−0.434301	−	0.158073i	0.115612	−	0.993294i	$-0.463117\pi$
$461$	−9.32484	−	3.39396i	−0.434301	−	0.158073i	−0.549913	+	0.835222i	$0.685339\pi$
$462$		0			0
$463$	−9.46007	−	5.46177i	−0.439647	−	0.253830i	0.263801	−	0.964577i	$-0.415024\pi$
$463$	−9.46007	−	5.46177i	−0.439647	−	0.253830i	−0.703448	+	0.710747i	$0.748357\pi$
$464$	−12.0866	−	14.0465i	−0.561106	−	0.652090i
$465$		0			0
$466$	−5.32688	−	19.6363i	−0.246763	−	0.909633i
$467$	−2.92071	+	1.68627i	−0.135154	+	0.0780314i	−0.566053	−	0.824369i	$-0.691530\pi$
$467$	−2.92071	+	1.68627i	−0.135154	+	0.0780314i	0.430898	+	0.902400i	$0.358197\pi$
$468$		0			0
$469$	26.4251	−	31.4922i	1.22020	−	1.45418i
$470$	−0.615270	−	6.78985i	−0.0283803	−	0.313193i
$471$		0			0
$472$	7.43590	+	15.5664i	0.342265	+	0.716501i
$473$	0.00214334	+	0.0121555i	9.85507e−5	+	0.000558909i
$474$		0			0
$475$	−29.9369	+	10.7588i	−1.37360	+	0.493648i
$476$	14.3672	+	11.9043i	0.658517	+	0.545634i
$477$		0			0
$478$	25.4086	+	11.7524i	1.16216	+	0.537541i
$479$	−8.89289	−	24.4330i	−0.406326	−	1.11637i	−0.959106	−	0.283046i	$-0.908655\pi$
$479$	−8.89289	−	24.4330i	−0.406326	−	1.11637i	0.552780	−	0.833327i	$-0.313567\pi$
$480$		0			0
$481$	5.45698	+	4.57895i	0.248817	+	0.208782i
$482$	−24.6391	−	2.07863i	−1.12228	−	0.0946789i
$483$		0			0
$484$	−14.2456	−	16.7649i	−0.647528	−	0.762040i
$485$	−3.71752	−	0.655499i	−0.168804	−	0.0297647i
$486$		0			0
$487$	−18.5458	+	32.1223i	−0.840392	+	1.45560i	0.0491719	+	0.998790i	$0.484342\pi$
$487$	−18.5458	+	32.1223i	−0.840392	+	1.45560i	−0.889564	+	0.456811i	$0.848992\pi$
$488$	24.8744	−	17.7646i	1.12601	−	0.804165i
$489$		0			0
$490$	1.66985	−	1.68025i	0.0754363	−	0.0759059i
$491$	4.42577	+	5.27443i	0.199732	+	0.238032i	0.856609	−	0.515967i	$-0.172567\pi$
$491$	4.42577	+	5.27443i	0.199732	+	0.238032i	−0.656876	+	0.753998i	$0.728123\pi$
$492$		0			0
$493$			16.9227i			0.762161i
$494$	2.10787	−	3.00425i	0.0948376	−	0.135167i
$495$		0			0
$496$	−33.7096	+	12.7452i	−1.51360	+	0.572279i
$497$	16.0269	+	19.1001i	0.718903	+	0.856755i
$498$		0			0
$499$	13.7848	−	37.8735i	0.617093	−	1.69545i	−0.0968973	−	0.995294i	$-0.530892\pi$
$499$	13.7848	−	37.8735i	0.617093	−	1.69545i	0.713991	−	0.700155i	$-0.246886\pi$
$500$	15.8554	−	2.89730i	0.709076	−	0.129571i
$501$		0			0
$502$	19.2512	−	27.6760i	0.859225	−	1.23524i
$503$	−25.1210	−	4.42950i	−1.12009	−	0.197502i	−0.417209	−	0.908811i	$-0.636992\pi$
$503$	−25.1210	−	4.42950i	−1.12009	−	0.197502i	−0.702879	+	0.711309i	$0.748103\pi$
$504$		0			0
$505$	9.85894	+	17.0762i	0.438717	+	0.759880i
$506$	0.000614964	−	0.00728950i	2.73385e−5	−	0.000324058i
$507$		0			0
$508$	19.6441	−	11.5046i	0.871565	−	0.510435i
$509$	−9.28177	−	25.5015i	−0.411407	−	1.13033i	−0.956443	−	0.291919i	$-0.905706\pi$
$509$	−9.28177	−	25.5015i	−0.411407	−	1.13033i	0.545036	−	0.838413i	$-0.316516\pi$
$510$		0			0
$511$	28.0171	−	4.94018i	1.23941	−	0.218541i
$512$	15.5470	−	16.4405i	0.687088	−	0.726575i
$513$		0			0
$514$	−10.4678	−	22.2675i	−0.461713	−	0.982178i
$515$	−5.18094	−	29.3825i	−0.228299	−	1.29475i
$516$		0			0
$517$	0.00484433	−	0.00176319i	0.000213053	−	7.75451e-5i
$518$	−43.0397	+	3.90009i	−1.89106	+	0.171360i
$519$		0			0
$520$	−4.13654	+	4.21428i	−0.181399	+	0.184808i
$521$	13.1732	−	7.60552i	0.577126	−	0.333204i	−0.182864	−	0.983138i	$-0.558537\pi$
$521$	13.1732	−	7.60552i	0.577126	−	0.333204i	0.759990	+	0.649934i	$0.225204\pi$
$522$		0			0
$523$	5.85798	−	33.2223i	0.256152	−	1.45271i	−0.536947	−	0.843616i	$-0.680423\pi$
$523$	5.85798	−	33.2223i	0.256152	−	1.45271i	0.793099	−	0.609093i	$-0.208466\pi$
$524$	3.39016	−	19.9497i	0.148100	−	0.871507i
$525$		0			0
$526$	7.23728	−	27.3490i	0.315560	−	1.19248i
$527$	30.9265	+	11.2563i	1.34718	+	0.490333i
$528$		0			0
$529$	16.1615	−	13.5611i	0.702675	−	0.589614i
$530$	−23.7135	+	16.7143i	−1.03005	+	0.726021i
$531$		0			0
$532$	3.91325	+	21.9177i	0.169661	+	0.950252i
$533$	6.26323			0.271290
$534$		0			0
$535$	−21.5779	+	18.1060i	−0.932895	+	0.782792i
$536$	4.39017	+	45.3173i	0.189626	+	1.95741i
$537$		0			0
$538$	−3.01387	+	11.3892i	−0.129937	+	0.491022i
$539$	0.00155127		0.000895627i	6.68180e−5		3.85774e-5i
$540$		0			0
$541$	−1.62382	+	9.20914i	−0.0698135	+	0.395932i	0.929798	+	0.368069i	$0.119981\pi$
$541$	−1.62382	+	9.20914i	−0.0698135	+	0.395932i	−0.999612	+	0.0278624i	$0.991130\pi$
$542$	−25.2502	+	6.84982i	−1.08459	+	0.294225i
$543$		0			0
$544$	−20.5549	+	2.12011i	−0.881283	+	0.0908989i
$545$	7.94658	−	9.47036i	0.340394	−	0.405666i
$546$		0			0
$547$	−16.5137	+	6.01049i	−0.706074	+	0.256990i	−0.670002	−	0.742359i	$-0.733707\pi$
$547$	−16.5137	+	6.01049i	−0.706074	+	0.256990i	−0.0360723	+	0.999349i	$0.511485\pi$
$548$	−0.120750	−	19.4581i	−0.00515821	−	0.831210i
$549$		0			0
$550$	0.0164662	+	0.0350278i	0.000702122	+	0.00149359i
$551$	−13.0427	+	15.4163i	−0.555639	+	0.656755i
$552$		0			0
$553$	4.77904	−	0.842674i	0.203225	−	0.0358341i
$554$	11.4441	−	24.7421i	0.486214	−	1.05119i
$555$		0			0
$556$	−3.86137	−	6.59326i	−0.163758	−	0.279616i
$557$	24.6228	+	20.6610i	1.04330	+	0.875436i	0.992374	−	0.123267i	$-0.0393370\pi$
$557$	24.6228	+	20.6610i	1.04330	+	0.875436i	0.0509300	+	0.998702i	$0.483781\pi$
$558$		0			0
$559$	−0.979748	−	1.69697i	−0.0414389	−	0.0717743i
$560$	−0.444612	−	35.8218i	−0.0187883	−	1.51375i
$561$		0			0
$562$	8.83498	−	12.7014i	0.372681	−	0.535774i
$563$	−21.8457	+	37.8379i	−0.920688	+	1.59468i	−0.122334	+	0.992489i	$0.539038\pi$
$563$	−21.8457	+	37.8379i	−0.920688	+	1.59468i	−0.798354	+	0.602189i	$0.794295\pi$
$564$		0			0
$565$	−0.914096	+	2.51146i	−0.0384563	+	0.105658i
$566$	−8.62713	−	8.57376i	−0.362625	−	0.360382i
$567$		0			0
$568$	−27.5298	−	2.15053i	−1.15512	−	0.0902341i
$569$		−	21.4379i		−	0.898726i	−0.893349	−	0.449363i	$-0.851651\pi$
$569$		−	21.4379i		−	0.898726i	0.893349	−	0.449363i	$-0.148349\pi$
$570$		0			0
$571$		−	3.00361i		−	0.125697i	−0.998023	−	0.0628487i	$-0.979981\pi$
$571$		−	3.00361i		−	0.125697i	0.998023	−	0.0628487i	$-0.0200185\pi$
$572$	−0.00388079	−	0.00220858i	−0.000162264	−	9.23453e-5i
$573$		0			0
$574$	−26.7842	+	26.9509i	−1.11795	+	1.12491i
$575$	3.44300	−	9.45957i	0.143583	−	0.394491i
$576$		0			0
$577$	−1.51128	+	2.61761i	−0.0629154	+	0.108973i	−0.895767	−	0.444523i	$-0.853373\pi$
$577$	−1.51128	+	2.61761i	−0.0629154	+	0.108973i	0.832852	+	0.553496i	$0.186707\pi$
$578$	−4.24488	−	2.95271i	−0.176564	−	0.122817i
$579$		0			0
$580$	24.7605	−	21.0397i	1.02812	−	0.873628i
$581$	10.1749	+	17.6235i	0.422127	+	0.731146i
$582$		0			0
$583$	−0.0168052	−	0.0141012i	−0.000696000	−	0.000584013i
$584$	−17.8310	+	25.9766i	−0.737852	+	1.07492i
$585$		0			0
$586$	−16.4165	−	7.59321i	−0.678159	−	0.313673i
$587$	−39.0655	+	6.88830i	−1.61241	+	0.284311i	−0.905930	−	0.423427i	$-0.860827\pi$
$587$	−39.0655	+	6.88830i	−1.61241	+	0.284311i	−0.706475	+	0.707738i	$0.749716\pi$
$588$		0			0
$589$	19.4979	+	34.0900i	0.803397	+	1.40465i
$590$	−27.3749	+	12.8687i	−1.12701	+	0.529796i
$591$		0			0
$592$	30.3075	−	37.0432i	1.24563	−	1.52247i
$593$	2.55640	−	0.930453i	0.104979	−	0.0382091i	−0.288997	−	0.957330i	$-0.593322\pi$
$593$	2.55640	−	0.930453i	0.104979	−	0.0382091i	0.393975	+	0.919121i	$0.371099\pi$
$594$		0			0
$595$	−21.0293	+	25.0618i	−0.862118	+	1.02743i
$596$	−3.79082	−	10.2175i	−0.155278	−	0.418524i
$597$		0			0
$598$	0.304058	+	1.12084i	0.0124339	+	0.0458345i
$599$	−5.56492	+	31.5602i	−0.227376	+	1.28952i	0.630713	+	0.776016i	$0.282762\pi$
$599$	−5.56492	+	31.5602i	−0.227376	+	1.28952i	−0.858090	+	0.513500i	$0.828349\pi$
$600$		0			0
$601$	27.9203	+	16.1198i	1.13889	+	0.657540i	0.946156	−	0.323710i	$-0.104930\pi$
$601$	27.9203	+	16.1198i	1.13889	+	0.657540i	0.192737	+	0.981250i	$0.438264\pi$
$602$	11.4920	+	3.04108i	0.468378	+	0.123945i
$603$		0			0
$604$	−1.47764	+	4.13953i	−0.0601243	+	0.168435i
$605$	29.5505	−	24.7958i	1.20140	−	1.00809i
$606$		0			0
$607$	−6.79373			−0.275749			−0.137874	−	0.990450i	$-0.544027\pi$
$607$	−6.79373			−0.275749			−0.137874	+	0.990450i	$0.544027\pi$
$608$	−20.3591	−	13.9107i	−0.825670	−	0.564154i
$609$		0			0
$610$	30.8777	+	43.8080i	1.25020	+	1.77373i
$611$	−0.626941	+	0.526066i	−0.0253633	+	0.0212823i
$612$		0			0
$613$	14.5217	+	5.28548i	0.586528	+	0.213479i	0.618201	−	0.786020i	$-0.287862\pi$
$613$	14.5217	+	5.28548i	0.586528	+	0.213479i	−0.0316739	+	0.999498i	$0.510084\pi$
$614$	25.7928	+	6.82546i	1.04091	+	0.275453i
$615$		0			0
$616$	0.0260995	−	0.00725439i	0.00105158	−	0.000292288i
$617$	−3.54117	+	20.0829i	−0.142562	+	0.808509i	0.826731	+	0.562598i	$0.190198\pi$
$617$	−3.54117	+	20.0829i	−0.142562	+	0.808509i	−0.969292	+	0.245911i	$0.920913\pi$
$618$		0			0
$619$	−30.5054	+	17.6123i	−1.22611	+	0.707897i	−0.966215	−	0.257738i	$-0.917023\pi$
$619$	−30.5054	+	17.6123i	−1.22611	+	0.707897i	−0.259899	+	0.965636i	$0.583689\pi$
$620$	−21.9807	−	59.2449i	−0.882765	−	2.37933i
$621$		0			0
$622$	−2.57966	−	28.4680i	−0.103435	−	1.14146i
$623$	−36.4607	+	13.2706i	−1.46077	+	0.531676i
$624$		0			0
$625$	−1.42888	−	8.10360i	−0.0571553	−	0.324144i
$626$	−5.10711	+	2.40080i	−0.204121	+	0.0959554i
$627$		0			0
$628$	−13.6192	+	16.4369i	−0.543467	+	0.655902i
$629$	−43.0445	+	7.58990i	−1.71630	+	0.302629i
$630$		0			0
$631$	−0.387450	−	1.06451i	−0.0154241	−	0.0423774i	0.931742	−	0.363122i	$-0.118289\pi$
$631$	−0.387450	−	1.06451i	−0.0154241	−	0.0423774i	−0.947166	+	0.320744i	$0.896067\pi$
$632$	−3.04153	+	4.43098i	−0.120986	+	0.176255i
$633$		0			0
$634$	24.4192	+	2.06008i	0.969810	+	0.0818161i
$635$	19.9584	+	34.5690i	0.792026	+	1.37183i
$636$		0			0
$637$	−0.280048	−	0.0493801i	−0.0110959	−	0.00195651i
$638$	0.0201696	+	0.0140299i	0.000798523	+	0.000555448i
$639$		0			0
$640$	28.6575	+	27.4390i	1.13279	+	1.08462i
$641$	−7.36003	+	20.2215i	−0.290704	+	0.798702i	0.705260	+	0.708949i	$0.250830\pi$
$641$	−7.36003	+	20.2215i	−0.290704	+	0.798702i	−0.995964	+	0.0897537i	$0.971392\pi$
$642$		0			0
$643$	−11.3370	−	13.5109i	−0.447088	−	0.532819i	0.494683	−	0.869074i	$-0.335284\pi$
$643$	−11.3370	−	13.5109i	−0.447088	−	0.532819i	−0.941771	+	0.336254i	$0.890840\pi$
$644$	−6.12330	−	3.48480i	−0.241292	−	0.137320i
$645$		0			0
$646$	5.80732	+	21.7562i	0.228486	+	0.855988i
$647$		−	28.7307i		−	1.12952i	−0.825255	−	0.564760i	$-0.808969\pi$
$647$		−	28.7307i		−	1.12952i	0.825255	−	0.564760i	$-0.191031\pi$
$648$		0			0
$649$	−0.0147024	−	0.0175216i	−0.000577119	−	0.000687783i
$650$	−4.35833	−	4.33137i	−0.170948	−	0.169890i
$651$		0			0
$652$	−3.89130	−	21.2951i	−0.152395	−	0.833979i
$653$	16.1978	−	28.0554i	0.633868	−	1.09789i	−0.352886	−	0.935666i	$-0.614800\pi$
$653$	16.1978	−	28.0554i	0.633868	−	1.09789i	0.986754	−	0.162225i	$-0.0518670\pi$
$654$		0			0
$655$	34.9428	+	6.16137i	1.36533	+	0.240744i
$656$	−0.522263	−	42.0780i	−0.0203910	−	1.64287i
$657$		0			0
$658$	0.417380	−	4.94743i	0.0162712	−	0.192871i
$659$	20.9657	+	17.5923i	0.816707	+	0.685298i	0.952198	−	0.305480i	$-0.0988169\pi$
$659$	20.9657	+	17.5923i	0.816707	+	0.685298i	−0.135492	+	0.990778i	$0.543261\pi$
$660$		0			0
$661$	−8.14296	−	22.3726i	−0.316724	−	0.870193i	−0.991257	−	0.131948i	$-0.957877\pi$
$661$	−8.14296	−	22.3726i	−0.316724	−	0.870193i	0.674532	−	0.738245i	$-0.264345\pi$
$662$	−3.00473	+	6.49620i	−0.116782	+	0.252482i
$663$		0			0
$664$	−21.8228	−	5.63023i	−0.846890	−	0.218495i
$665$	−38.4730	+	6.62299i	−1.49192	+	0.256829i
$666$		0			0
$667$	−1.10964	−	6.29307i	−0.0429653	−	0.243668i
$668$	0.122278	+	19.7043i	0.00473107	+	0.762381i
$669$		0			0
$670$	−79.5070	+	7.20461i	−3.07162	+	0.278338i
$671$	−0.0260504	+	0.0310457i	−0.00100566	+	0.00119850i
$672$		0			0
$673$	12.0059	−	6.93159i	0.462792	−	0.267193i	−0.250425	−	0.968136i	$-0.580570\pi$
$673$	12.0059	−	6.93159i	0.462792	−	0.267193i	0.713218	+	0.700943i	$0.247237\pi$
$674$	−6.34813	+	1.72211i	−0.244521	+	0.0663330i
$675$		0			0
$676$	−24.9337	−	4.23711i	−0.958987	−	0.162966i
$677$	−27.0022	−	15.5897i	−1.03778	−	0.599162i	−0.118576	−	0.992945i	$-0.537833\pi$
$677$	−27.0022	−	15.5897i	−1.03778	−	0.599162i	−0.919203	+	0.393783i	$0.871166\pi$
$678$		0			0
$679$	−2.58328	−	0.940237i	−0.0991372	−	0.0360830i
$680$	−3.49373	−	36.0639i	−0.133978	−	1.38299i
$681$		0			0
$682$	0.0390558	−	0.0275281i	0.00149552	−	0.00105411i
$683$	13.4184			0.513441			0.256720	−	0.966486i	$-0.417358\pi$
$683$	13.4184			0.513441			0.256720	+	0.966486i	$0.417358\pi$
$684$		0			0
$685$	34.1191			1.30362
$686$	22.0750	−	15.5594i	0.842826	−	0.594059i
$687$		0			0
$688$	−11.3190	+	6.72371i	−0.431533	+	0.256339i
$689$	3.27265	+	1.19115i	0.124678	+	0.0453791i
$690$		0			0
$691$	23.7827	+	13.7310i	0.904738	+	0.522351i	0.878734	−	0.477311i	$-0.158389\pi$
$691$	23.7827	+	13.7310i	0.904738	+	0.522351i	0.0260037	+	0.999662i	$0.491722\pi$
$692$	7.21314	−	42.4464i	0.274203	−	1.61357i
$693$		0			0
$694$	−25.4963	+	6.91658i	−0.967827	+	0.262550i
$695$	11.6026	−	6.69877i	0.440112	−	0.254099i
$696$		0			0
$697$	−24.7021	+	29.4388i	−0.935658	+	1.11507i
$698$	37.5136	−	3.39934i	1.41991	−	0.128667i
$699$		0			0
$700$	37.2762	−	0.231323i	1.40891	−	0.00874319i
$701$	3.07645	+	17.4474i	0.116196	+	0.658980i	0.986151	+	0.165849i	$0.0530365\pi$
$701$	3.07645	+	17.4474i	0.116196	+	0.658980i	−0.869955	+	0.493131i	$0.835852\pi$
$702$		0			0
$703$	−45.0623	−	26.2611i	−1.69956	−	0.990456i
$704$	−0.0145142	+	0.0262563i	−0.000547025	+	0.000989573i
$705$		0			0
$706$	−17.1065	+	36.9843i	−0.643813	+	1.39192i
$707$	4.91129	+	13.4937i	0.184708	+	0.507481i
$708$		0			0
$709$	−1.95002	−	1.63626i	−0.0732344	−	0.0614509i	0.605436	−	0.795894i	$-0.292999\pi$
$709$	−1.95002	−	1.63626i	−0.0732344	−	0.0614509i	−0.678670	+	0.734443i	$0.737443\pi$
$710$	4.07028	−	48.2472i	0.152755	−	1.81069i
$711$		0			0
$712$	17.7973	−	39.1129i	0.666982	−	1.46582i
$713$	−12.2387	−	2.15802i	−0.458344	−	0.0808184i
$714$		0			0
$715$	0.00391474	−	0.00678053i	0.000146403	−	0.000253577i
$716$	−39.6289	+	7.24148i	−1.48100	+	0.270627i
$717$		0			0
$718$	−5.64715	−	5.61221i	−0.210750	−	0.209446i
$719$	−18.2917	−	21.7992i	−0.682164	−	0.812971i	0.308220	−	0.951315i	$-0.400267\pi$
$719$	−18.2917	−	21.7992i	−0.682164	−	0.812971i	−0.990384	+	0.138344i	$0.955822\pi$
$720$		0			0
$721$		−	21.7281i		−	0.809196i
$722$	−11.4777	+	24.2953i	−0.427155	+	0.904179i
$723$		0			0
$724$	7.49121	−	13.1631i	0.278409	−	0.489204i
$725$	21.7324	+	25.8997i	0.807121	+	0.961890i
$726$		0			0
$727$	4.78434	−	13.1449i	0.177441	−	0.487516i	−0.818806	−	0.574071i	$-0.805363\pi$
$727$	4.78434	−	13.1449i	0.177441	−	0.487516i	0.996247	+	0.0865544i	$0.0275857\pi$
$728$	−3.49963	+	2.49934i	−0.129705	+	0.0926315i
$729$		0			0
$730$	−45.3533	−	31.5474i	−1.67860	−	1.16762i
$731$	11.8403	+	2.08777i	0.437930	+	0.0772190i
$732$		0			0
$733$	7.51394	+	13.0145i	0.277534	+	0.480702i	0.970771	−	0.240007i	$-0.0771497\pi$
$733$	7.51394	+	13.0145i	0.277534	+	0.480702i	−0.693238	+	0.720709i	$0.743816\pi$
$734$	1.87720	+	0.158366i	0.0692886	+	0.00584539i
$735$		0			0
$736$	7.50473	−	2.13621i	0.276628	−	0.0787416i
$737$	−0.0206464	−	0.0567255i	−0.000760520	−	0.00208951i
$738$		0			0
$739$	−6.78203	+	1.19586i	−0.249481	+	0.0439902i	−0.296990	−	0.954881i	$-0.595983\pi$
$739$	−6.78203	+	1.19586i	−0.249481	+	0.0439902i	0.0475090	+	0.998871i	$0.484872\pi$
$740$	64.6216	+	53.5442i	2.37554	+	1.96832i
$741$		0			0
$742$	−19.1208	+	8.98851i	−0.701946	+	0.329978i
$743$	−1.26270	−	7.16110i	−0.0463238	−	0.262715i	0.952846	−	0.303454i	$-0.0981399\pi$
$743$	−1.26270	−	7.16110i	−0.0463238	−	0.262715i	−0.999170	+	0.0407388i	$0.987029\pi$
$744$		0			0
$745$	17.9565	−	6.53563i	0.657875	−	0.239447i
$746$	−0.396742	−	4.37828i	−0.0145258	−	0.160300i
$747$		0			0
$748$	0.0256867	−	0.00953012i	0.000939198	−	0.000348456i
$749$	−17.7652	+	10.2567i	−0.649126	+	0.374773i
$750$		0			0
$751$	−0.615511	+	3.49074i	−0.0224603	+	0.127379i	−0.993976	−	0.109595i	$-0.965045\pi$
$751$	−0.615511	+	3.49074i	−0.0224603	+	0.127379i	0.971516	+	0.236974i	$0.0761556\pi$
$752$	3.58652	+	4.16808i	0.130787	+	0.151994i
$753$		0			0
$754$	−3.77068	−	0.997822i	−0.137320	−	0.0363385i
$755$	−7.24215	−	2.63593i	−0.263569	−	0.0959313i
$756$		0			0
$757$	−10.4718	+	8.78689i	−0.380604	+	0.319365i	−0.812940	−	0.582348i	$-0.802134\pi$
$757$	−10.4718	+	8.78689i	−0.380604	+	0.319365i	0.432335	+	0.901713i	$0.357690\pi$
$758$	−20.5454	−	29.1489i	−0.746242	−	1.05874i
$759$		0			0
$760$	24.6125	−	35.5462i	0.892790	−	1.28939i
$761$	−4.54239			−0.164662			−0.0823308	−	0.996605i	$-0.526236\pi$
$761$	−4.54239			−0.164662			−0.0823308	+	0.996605i	$0.526236\pi$
$762$		0			0
$763$	6.89684	−	5.78714i	0.249682	−	0.209508i
$764$	16.5789	+	5.91798i	0.599804	+	0.214105i
$765$		0			0
$766$	0.405340	+	0.107264i	0.0146455	+	0.00387560i
$767$	3.14467	+	1.81558i	0.113547	+	0.0655567i
$768$		0			0
$769$	−7.07178	+	40.1061i	−0.255015	+	1.44626i	0.541019	+	0.841010i	$0.318039\pi$
$769$	−7.07178	+	40.1061i	−0.255015	+	1.44626i	−0.796034	+	0.605252i	$0.793073\pi$
$770$	0.0124358	+	0.0458417i	0.000448156	+	0.00165202i
$771$		0			0
$772$	6.07365	−	2.25341i	0.218595	−	0.0811019i
$773$	11.1116	−	13.2423i	0.399658	−	0.476294i	−0.528258	−	0.849084i	$-0.677154\pi$
$773$	11.1116	−	13.2423i	0.399658	−	0.476294i	0.927916	+	0.372790i	$0.121599\pi$
$774$		0			0
$775$	61.7875	−	22.4888i	2.21947	−	0.807821i
$776$	2.74724	−	1.31233i	0.0986201	−	0.0471098i
$777$		0			0
$778$	38.0217	−	17.8736i	1.36314	−	0.640801i
$779$	−45.1922	+	7.77970i	−1.61918	+	0.278737i
$780$		0			0
$781$	0.0360558	−	0.00635761i	0.00129018	−	0.000227493i
$782$	−6.46743	−	2.99142i	−0.231275	−	0.106973i
$783$		0			0
$784$	−0.308396	+	1.88556i	−0.0110142	+	0.0673413i
$785$	−28.6721	−	24.0588i	−1.02335	−	0.858694i
$786$		0			0
$787$	16.5763	+	28.7110i	0.590882	+	1.02344i	0.994114	+	0.108340i	$0.0345534\pi$
$787$	16.5763	+	28.7110i	0.590882	+	1.02344i	−0.403232	+	0.915098i	$0.632113\pi$
$788$	−21.5810	−	25.3975i	−0.768791	−	0.904747i
$789$		0			0
$790$	−7.73616	−	5.38122i	−0.275240	−	0.191455i
$791$	−0.973181	+	1.68560i	−0.0346023	+	0.0599330i
$792$		0			0
$793$	2.20051	−	6.04585i	0.0781424	−	0.214694i
$794$	−15.5898	+	15.6869i	−0.553263	+	0.556707i
$795$		0			0
$796$	−24.8802	+	43.7181i	−0.881856	+	1.54955i
$797$		−	20.7949i		−	0.736592i	−0.929709	−	0.368296i	$-0.879941\pi$
$797$		−	20.7949i		−	0.736592i	0.929709	−	0.368296i	$-0.120059\pi$
$798$		0			0
$799$		−	5.02158i		−	0.177651i
$800$	−28.7359	+	29.6416i	−1.01597	+	1.04799i
$801$		0			0
$802$	8.04708	+	7.99729i	0.284152	+	0.282394i
$803$	0.0142879	−	0.0392556i	0.000504208	−	0.00138530i
$804$		0			0
$805$	6.17687	−	10.6986i	0.217706	−	0.377078i
$806$	−4.33164	+	6.22725i	−0.152575	+	0.219346i
$807$		0			0
$808$	−14.4752	−	6.58656i	−0.509236	−	0.231715i
$809$	17.4247	+	30.1805i	0.612621	+	1.06109i	0.990797	+	0.135357i	$0.0432182\pi$
$809$	17.4247	+	30.1805i	0.612621	+	1.06109i	−0.378176	+	0.925734i	$0.623448\pi$
$810$		0			0
$811$	14.3667	+	12.0551i	0.504484	+	0.423312i	0.859183	−	0.511668i	$-0.170972\pi$
$811$	14.3667	+	12.0551i	0.504484	+	0.423312i	−0.354699	+	0.934980i	$0.615417\pi$
$812$	20.4187	−	11.9583i	0.716556	−	0.419654i
$813$		0			0
$814$	−0.0266401	+	0.0575957i	−0.000933734	+	0.00201873i
$815$	37.3810	−	6.59128i	1.30940	−	0.230882i
$816$		0			0
$817$	9.17721	+	11.0275i	0.321070	+	0.385804i
$818$	4.50584	+	9.58504i	0.157543	+	0.335133i
$819$		0			0
$820$	73.7851	−	0.457885i	2.57669	−	0.0159900i
$821$	−5.25655	+	1.91323i	−0.183455	+	0.0667721i	−0.432114	−	0.901819i	$-0.642232\pi$
$821$	−5.25655	+	1.91323i	−0.183455	+	0.0667721i	0.248659	+	0.968591i	$0.420010\pi$
$822$		0			0
$823$	−16.6976	+	19.8994i	−0.582040	+	0.693648i	−0.974055	−	0.226310i	$-0.927334\pi$
$823$	−16.6976	+	19.8994i	−0.582040	+	0.693648i	0.392015	+	0.919959i	$0.371778\pi$
$824$	17.1733	+	16.8566i	0.598262	+	0.587226i
$825$		0			0
$826$	−21.2604	+	5.76748i	−0.739746	+	0.200676i
$827$	2.26042	−	12.8195i	0.0786025	−	0.445777i	−0.919952	−	0.392031i	$-0.871773\pi$
$827$	2.26042	−	12.8195i	0.0786025	−	0.445777i	0.998555	−	0.0537463i	$-0.0171162\pi$
$828$		0			0
$829$	−36.0310	−	20.8025i	−1.25141	−	0.722502i	−0.280020	−	0.959994i	$-0.590341\pi$
$829$	−36.0310	−	20.8025i	−1.25141	−	0.722502i	−0.971389	+	0.237492i	$0.923675\pi$
$830$	10.1095	−	38.2028i	0.350905	−	1.32604i
$831$		0			0
$832$	0.739588	−	4.70500i	0.0256406	−	0.163116i
$833$	1.33661	−	1.12155i	0.0463107	−	0.0388593i
$834$		0			0
$835$	−34.5507			−1.19568
$836$	0.0307451	+	0.0111156i	0.00106334	+	0.000384440i
$837$		0			0
$838$	18.0815	−	12.7446i	0.624613	−	0.440254i
$839$	−8.14585	+	6.83518i	−0.281226	+	0.235977i	−0.772479	−	0.635040i	$-0.780984\pi$
$839$	−8.14585	+	6.83518i	−0.281226	+	0.235977i	0.491253	+	0.871017i	$0.336539\pi$
$840$		0			0
$841$	−7.08361	−	2.57822i	−0.244262	−	0.0889043i
$842$	−9.48496	+	35.8428i	−0.326873	+	1.23523i
$843$		0			0
$844$	−2.22233	−	0.377653i	−0.0764958	−	0.0129993i
$845$	7.70064	−	43.6725i	0.264910	−	1.50238i
$846$		0			0
$847$	24.3290	−	14.0464i	0.835955	−	0.482639i
$848$	7.72955	−	22.0858i	0.265434	−	0.758431i
$849$		0			0
$850$	37.5478	−	3.40243i	1.28788	−	0.116702i
$851$	15.5093	−	5.64492i	0.531652	−	0.193505i
$852$		0			0
$853$	−3.43498	−	19.4807i	−0.117612	−	0.667008i	−0.985424	−	0.170116i	$-0.945586\pi$
$853$	−3.43498	−	19.4807i	−0.117612	−	0.667008i	0.867812	−	0.496892i	$-0.165525\pi$
$854$	16.6052	+	35.3235i	0.568220	+	1.20874i
$855$		0			0
$856$	5.67550	−	21.9983i	0.193985	−	0.751887i
$857$	−4.78136	+	0.843082i	−0.163328	+	0.0287991i	−0.254714	−	0.967016i	$-0.581981\pi$
$857$	−4.78136	+	0.843082i	−0.163328	+	0.0287991i	0.0913861	+	0.995816i	$0.470870\pi$
$858$		0			0
$859$	9.60567	+	26.3914i	0.327741	+	0.900462i	0.988682	+	0.150024i	$0.0479350\pi$
$859$	9.60567	+	26.3914i	0.327741	+	0.900462i	−0.660941	+	0.750438i	$0.729843\pi$
$860$	−11.6662	−	19.9199i	−0.397813	−	0.679262i
$861$		0			0
$862$	0.565835	−	6.70715i	0.0192724	−	0.228446i
$863$	−17.5382	−	30.3771i	−0.597007	−	1.03405i	−0.993260	−	0.115906i	$-0.963023\pi$
$863$	−17.5382	−	30.3771i	−0.597007	−	1.03405i	0.396253	−	0.918141i	$-0.370310\pi$
$864$		0			0
$865$	74.3468	+	13.1094i	2.52787	+	0.445731i
$866$	4.05696	−	5.83237i	0.137861	−	0.198192i
$867$		0			0
$868$	−8.27223	−	45.2696i	−0.280778	−	1.53655i
$869$	0.00243716	−	0.00669604i	8.26750e−5	−	0.000227148i
$870$		0			0
$871$	6.16006	+	7.34127i	0.208726	+	0.248749i
$872$	−0.776534	+	9.94073i	−0.0262968	+	0.336636i
$873$		0			0
$874$	−3.58615	−	7.70972i	−0.121303	−	0.260785i
$875$			20.5817i			0.695789i
$876$		0			0
$877$	−5.71112	−	6.80625i	−0.192851	−	0.229831i	0.660951	−	0.750429i	$-0.270153\pi$
$877$	−5.71112	−	6.80625i	−0.192851	−	0.229831i	−0.853802	+	0.520599i	$0.825709\pi$
$878$	7.65407	−	7.70172i	0.258312	−	0.259920i
$879$		0			0
$880$	−0.0458798	−	0.0257349i	−0.00154661	−	0.000867522i
$881$	7.40571	−	12.8271i	0.249505	−	0.432155i	−0.713884	−	0.700264i	$-0.753066\pi$
$881$	7.40571	−	12.8271i	0.249505	−	0.432155i	0.963388	+	0.268109i	$0.0863989\pi$
$882$		0			0
$883$	45.1226	+	7.95634i	1.51850	+	0.267752i	0.869842	−	0.493330i	$-0.164221\pi$
$883$	45.1226	+	7.95634i	1.51850	+	0.267752i	0.648655	+	0.761082i	$0.275332\pi$
$884$	−3.31448	+	2.81641i	−0.111478	+	0.0947262i
$885$		0			0
$886$	22.2733	+	1.87904i	0.748287	+	0.0631277i
$887$	39.4359	+	33.0906i	1.32413	+	1.11107i	0.985412	+	0.170185i	$0.0544365\pi$
$887$	39.4359	+	33.0906i	1.32413	+	1.11107i	0.338715	+	0.940889i	$0.390008\pi$
$888$		0			0
$889$	9.94241	+	27.3165i	0.333458	+	0.916167i
$890$	68.3868	+	31.6313i	2.29233	+	1.06028i
$891$		0			0
$892$	25.6762	−	30.9883i	0.859704	−	1.03756i
$893$	3.87024	−	4.57456i	0.129513	−	0.153082i
$894$		0			0
$895$	−12.2660	−	69.5639i	−0.410007	−	2.32526i
$896$	17.0830	+	23.3030i	0.570703	+	0.778500i
$897$		0			0
$898$	−0.141648	−	1.56317i	−0.00472685	−	0.0521635i
$899$	26.8292	−	31.9738i	0.894803	−	1.06639i
$900$		0			0
$901$	−18.5060	+	10.6844i	−0.616524	+	0.355950i
$902$	0.0146077	+	0.0538479i	0.000486384	+	0.00179294i
$903$		0			0
$904$	−0.577265	−	2.07686i	−0.0191996	−	0.0690753i
$905$	22.9987	+	13.2783i	0.764502	+	0.441385i
$906$		0			0
$907$	−40.5085	−	14.7439i	−1.34506	−	0.489562i	−0.433659	−	0.901077i	$-0.642778\pi$
$907$	−40.5085	−	14.7439i	−1.34506	−	0.489562i	−0.911403	+	0.411515i	$0.865000\pi$
$908$	−10.8708	+	30.4538i	−0.360759	+	1.01065i
$909$		0			0
$910$	−4.34425	−	6.16343i	−0.144010	−	0.204316i
$911$	5.19556			0.172137			0.0860684	−	0.996289i	$-0.472570\pi$
$911$	5.19556			0.172137			0.0860684	+	0.996289i	$0.472570\pi$
$912$		0			0
$913$	0.0298816			0.000988938
$914$	2.21531	+	3.14299i	0.0732759	+	0.103961i
$915$		0			0
$916$	−7.27662	+	20.3851i	−0.240426	+	0.673542i
$917$	24.2815	+	8.83776i	0.801847	+	0.291848i
$918$		0			0
$919$	−31.3210	−	18.0832i	−1.03318	−	0.596510i	−0.115290	−	0.993332i	$-0.536780\pi$
$919$	−31.3210	−	18.0832i	−1.03318	−	0.596510i	−0.917895	+	0.396822i	$0.870113\pi$
$920$	3.66395	+	13.1820i	0.120797	+	0.434598i
$921$		0			0
$922$	3.67422	+	13.5441i	0.121004	+	0.446052i
$923$	−5.03360	+	2.90615i	−0.165683	+	0.0956572i
$924$		0			0
$925$	−56.1311	+	66.8944i	−1.84558	+	2.19948i
$926$	1.39415	+	15.3852i	0.0458145	+	0.505589i
$927$		0			0
$928$	−6.38921	+	25.4156i	−0.209736	+	0.834309i
$929$	7.06350	+	40.0591i	0.231746	+	1.31430i	0.849360	+	0.527815i	$0.176988\pi$
$929$	7.06350	+	40.0591i	0.231746	+	1.31430i	−0.617614	+	0.786482i	$0.711900\pi$
$930$		0			0
$931$	2.08202	+	0.00844694i	0.0682355	+	0.000276837i
$932$	−18.3582	+	22.1562i	−0.601341	+	0.725750i
$933$		0			0
$934$	4.32887	+	2.00225i	0.141645	+	0.0655158i
$935$	0.0164306	+	0.0451426i	0.000537337	+	0.00147632i
$936$		0			0
$937$	−18.1313	−	15.2140i	−0.592324	−	0.497019i	0.296644	−	0.954988i	$-0.404133\pi$
$937$	−18.1313	−	15.2140i	−0.592324	−	0.497019i	−0.888968	+	0.457969i	$0.848577\pi$
$938$	−57.9328	−	4.88738i	−1.89157	−	0.159579i
$939$		0			0
$940$	−7.34733	+	6.24324i	−0.239643	+	0.203632i
$941$	13.1762	+	2.32332i	0.429532	+	0.0757382i	0.384235	−	0.923235i	$-0.374465\pi$
$941$	13.1762	+	2.32332i	0.429532	+	0.0757382i	0.0452976	+	0.998974i	$0.485576\pi$
$942$		0			0
$943$	7.25565	−	12.5672i	0.236277	−	0.409243i
$944$	11.9353	−	21.2781i	0.388461	−	0.692544i
$945$		0			0
$946$	0.0123046	−	0.0123812i	0.000400058	−	0.000402548i
$947$	3.99772	+	4.76429i	0.129908	+	0.154819i	0.827077	−	0.562088i	$-0.190002\pi$
$947$	3.99772	+	4.76429i	0.129908	+	0.154819i	−0.697169	+	0.716907i	$0.745557\pi$
$948$		0			0
$949$			6.63193i			0.215282i
$950$	36.8276	+	25.8394i	1.19484	+	0.838340i
$951$		0			0
$952$	2.05497	−	26.3065i	0.0666020	−	0.852599i
$953$	−4.71849	−	5.62328i	−0.152847	−	0.182156i	0.684187	−	0.729306i	$-0.260157\pi$
$953$	−4.71849	−	5.62328i	−0.152847	−	0.182156i	−0.837034	+	0.547150i	$0.815713\pi$
$954$		0			0
$955$	−10.5570	+	29.0050i	−0.341615	+	0.938580i
$956$	−7.11668	−	38.9459i	−0.230170	−	1.25960i
$957$		0			0
$958$	−20.9975	+	30.1864i	−0.678397	+	0.975278i
$959$	24.4699	+	4.31471i	0.790176	+	0.139329i
$960$		0			0
$961$	−25.0867	−	43.4515i	−0.809250	−	1.40166i
$962$	0.846886	−	10.0386i	0.0273047	−	0.323657i
$963$		0			0
$964$	17.6720	+	30.1747i	0.569176	+	0.971863i
$965$	3.88503	+	10.6740i	0.125063	+	0.343609i
$966$		0			0
$967$	−33.6281	+	5.92954i	−1.08141	+	0.190681i	−0.685837	−	0.727755i	$-0.740564\pi$
$967$	−33.6281	+	5.92954i	−1.08141	+	0.190681i	−0.395570	+	0.918436i	$0.629453\pi$
$968$	−7.77246	+	30.1262i	−0.249816	+	0.968292i
$969$		0			0
$970$	2.27114	+	4.83128i	0.0729218	+	0.155123i
$971$	1.61392	+	9.15301i	0.0517932	+	0.293734i	0.999691	−	0.0248393i	$-0.00790742\pi$
$971$	1.61392	+	9.15301i	0.0517932	+	0.293734i	−0.947898	+	0.318573i	$0.896796\pi$
$972$		0			0
$973$	9.16841	−	3.33703i	0.293926	−	0.106980i
$974$	52.2415	−	4.73392i	1.67393	−	0.151685i
$975$		0			0
$976$	−40.8011	−	14.2795i	−1.30601	−	0.457074i
$977$	1.71104	−	0.987869i	0.0547410	−	0.0316047i	−0.472380	−	0.881395i	$-0.656605\pi$
$977$	1.71104	−	0.987869i	0.0547410	−	0.0316047i	0.527121	+	0.849790i	$0.323272\pi$
$978$		0			0
$979$	−0.00989356	+	0.0561092i	−0.000316200	+	0.00179326i
$980$	−3.30277	−	0.561257i	−0.105503	−	0.0179287i
$981$		0			0
$982$	2.49099	−	9.41324i	0.0794907	−	0.300388i
$983$	−15.7370	−	5.72779i	−0.501931	−	0.182688i	0.0786313	−	0.996904i	$-0.474945\pi$
$983$	−15.7370	−	5.72779i	−0.501931	−	0.182688i	−0.580562	+	0.814216i	$0.697167\pi$
$984$		0			0
$985$	44.7666	−	37.5637i	1.42638	−	1.19688i
$986$	19.5616	−	13.7878i	0.622967	−	0.439093i
$987$		0			0
$988$	−5.19010	+	0.0111510i	−0.165119	+	0.000354761i
$989$	−4.53997			−0.144363
$990$		0			0
$991$	−32.4691	+	27.2448i	−1.03142	+	0.865460i	−0.991019	−	0.133723i	$-0.957307\pi$
$991$	−32.4691	+	27.2448i	−1.03142	+	0.865460i	−0.0403967	+	0.999184i	$0.512862\pi$
$992$	42.1975	+	28.5818i	1.33977	+	0.907473i
$993$		0			0
$994$	9.02052	−	34.0878i	0.286114	−	1.08120i
$995$	−76.3844	−	44.1006i	−2.42155	−	1.39808i
$996$		0			0
$997$	−2.18396	+	12.3859i	−0.0691668	+	0.392264i	0.930496	+	0.366302i	$0.119376\pi$
$997$	−2.18396	+	12.3859i	−0.0691668	+	0.392264i	−0.999663	+	0.0259626i	$0.991735\pi$
$998$	−55.0104	+	14.9231i	−1.74132	+	0.472382i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.523.3		60
3.2	odd	2		228.2.w.b.67.8	yes	60
4.3	odd	2		684.2.cf.c.523.5		60
12.11	even	2		228.2.w.a.67.6	✓	60
19.2	odd	18		684.2.cf.c.667.5		60
57.2	even	18		228.2.w.a.211.6	yes	60
76.59	even	18	inner	684.2.cf.b.667.3		60
228.59	odd	18		228.2.w.b.211.8	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.6	✓	60	12.11	even	2
228.2.w.a.211.6	yes	60	57.2	even	18
228.2.w.b.67.8	yes	60	3.2	odd	2
228.2.w.b.211.8	yes	60	228.59	odd	18
684.2.cf.b.523.3		60	1.1	even	1	trivial
684.2.cf.b.667.3		60	76.59	even	18	inner
684.2.cf.c.523.5		60	4.3	odd	2
684.2.cf.c.667.5		60	19.2	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.814750 - 1.15593i) q^{2} +(-0.672365 + 1.88359i) q^{4} +(-3.29537 - 1.19942i) q^{5} +(-2.21173 - 1.27694i) q^{7} +(2.72512 - 0.757450i) q^{8} +O(q^{10})\)	\(q+(-0.814750 - 1.15593i) q^{2} +(-0.672365 + 1.88359i) q^{4} +(-3.29537 - 1.19942i) q^{5} +(-2.21173 - 1.27694i) q^{7} +(2.72512 - 0.757450i) q^{8} +(1.29846 + 4.78645i) q^{10} +(-0.00324770 + 0.00187506i) q^{11} +(0.382681 - 0.456062i) q^{13} +(0.325947 + 3.59701i) q^{14} +(-3.09585 - 2.53292i) q^{16} +(0.634319 + 3.59740i) q^{17} +(-2.19475 + 3.76604i) q^{19} +(4.47490 - 5.40069i) q^{20} +(0.00481351 + 0.00222642i) q^{22} +(-0.471769 - 1.29618i) q^{23} +(5.59064 + 4.69110i) q^{25} +(-0.838966 - 0.0707777i) q^{26} +(3.89234 - 3.30743i) q^{28} +(4.56231 + 0.804457i) q^{29} +(4.50482 - 7.80257i) q^{31} +(-0.405545 + 5.64230i) q^{32} +(3.64155 - 3.66421i) q^{34} +(5.75689 + 6.86079i) q^{35} +11.9654i q^{37} +(6.14147 - 0.531404i) q^{38} +(-9.88877 - 0.772475i) q^{40} +(6.76233 + 8.05903i) q^{41} +(1.12571 - 3.09286i) q^{43} +(-0.00134821 - 0.00737807i) q^{44} +(-1.11392 + 1.60139i) q^{46} +(-1.35380 - 0.238711i) q^{47} +(-0.238826 - 0.413659i) q^{49} +(0.867630 - 10.2845i) q^{50} +(0.601734 + 1.02746i) q^{52} +(2.00076 + 5.49705i) q^{53} +(0.0129513 - 0.00228367i) q^{55} +(-6.99445 - 1.80455i) q^{56} +(-2.78724 - 5.92915i) q^{58} +(1.05912 + 6.00657i) q^{59} +(10.1552 - 3.69618i) q^{61} +(-12.6896 + 1.14988i) q^{62} +(6.85254 - 4.12828i) q^{64} +(-1.80808 + 1.04390i) q^{65} +(-2.79523 + 15.8525i) q^{67} +(-7.20254 - 1.22397i) q^{68} +(3.24019 - 12.2444i) q^{70} +(-9.17413 - 3.33911i) q^{71} +(-8.53345 + 7.16041i) q^{73} +(13.8312 - 9.74884i) q^{74} +(-5.61803 - 6.66617i) q^{76} +0.00957739 q^{77} +(-1.45560 + 1.22139i) q^{79} +(7.16395 + 12.0601i) q^{80} +(3.80609 - 14.3829i) q^{82} +(-6.90065 - 3.98409i) q^{83} +(2.22447 - 12.6156i) q^{85} +(-4.49232 + 1.21866i) q^{86} +(-0.00743010 + 0.00756973i) q^{88} +(9.76573 - 11.6383i) q^{89} +(-1.42875 + 0.520024i) q^{91} +(2.75867 - 0.0171194i) q^{92} +(0.827074 + 1.75939i) q^{94} +(11.7496 - 9.77809i) q^{95} +(1.06007 - 0.186919i) q^{97} +(-0.283579 + 0.613096i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8}+O(q^{10}) \) 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43} + 51 q^{44} - 21 q^{46} + 30 q^{49} + 27 q^{50} - 3 q^{52} - 12 q^{53} - 42 q^{56} - 36 q^{58} - 105 q^{62} + 21 q^{64} + 36 q^{65} + 42 q^{67} + 15 q^{68} - 96 q^{70} - 24 q^{71} + 18 q^{73} - 69 q^{74} + 54 q^{76} + 72 q^{77} + 12 q^{79} + 12 q^{80} + 75 q^{82} - 60 q^{85} - 21 q^{86} + 36 q^{88} + 12 q^{89} - 84 q^{91} - 99 q^{92} + 24 q^{95} + 12 q^{97} + 105 q^{98}+O(q^{100}) \) 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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