LMFDB - Embedded newform 684.2.cf.b.91.4

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)

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);

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")

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			91.4
Character	$\chi$	$=$	684.91
Dual form			684.2.cf.b.451.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.578232 - 1.29060i) q^{2} +(-1.33130 + 1.49253i) q^{4} +(-3.00606 + 2.52238i) q^{5} +(3.14549 + 1.81605i) q^{7} +(2.69606 + 0.855142i) q^{8} +(4.99358 + 2.42109i) q^{10} +(-0.114858 + 0.0663132i) q^{11} +(-6.41015 - 1.13028i) q^{13} +(0.524971 - 5.10966i) q^{14} +(-0.455300 - 3.97400i) q^{16} +(-2.07248 - 0.754320i) q^{17} +(-3.51706 - 2.57494i) q^{19} +(0.237219 - 7.84467i) q^{20} +(0.151998 + 0.109891i) q^{22} +(3.26515 - 3.89125i) q^{23} +(1.80573 - 10.2408i) q^{25} +(2.24781 + 8.92650i) q^{26} +(-6.89809 + 2.27704i) q^{28} +(-0.208018 - 0.571524i) q^{29} +(-0.726976 + 1.25916i) q^{31} +(-4.86558 + 2.88551i) q^{32} +(0.224847 + 3.11091i) q^{34} +(-14.0363 + 2.47497i) q^{35} -2.84148i q^{37} +(-1.28954 + 6.02802i) q^{38} +(-10.2615 + 4.22988i) q^{40} +(-8.74416 + 1.54183i) q^{41} +(-0.382981 - 0.456418i) q^{43} +(0.0539353 - 0.259712i) q^{44} +(-6.91006 - 1.96395i) q^{46} +(1.54735 + 4.25131i) q^{47} +(3.09606 + 5.36254i) q^{49} +(-14.2609 + 3.59108i) q^{50} +(10.2208 - 8.06261i) q^{52} +(0.676498 - 0.806218i) q^{53} +(0.178002 - 0.489057i) q^{55} +(6.92744 + 7.58601i) q^{56} +(-0.617326 + 0.598941i) q^{58} +(-5.41120 - 1.96952i) q^{59} +(5.10087 + 4.28014i) q^{61} +(2.04543 + 0.210149i) q^{62} +(6.53746 + 4.61103i) q^{64} +(22.1203 - 12.7711i) q^{65} +(-13.3272 + 4.85072i) q^{67} +(3.88493 - 2.08901i) q^{68} +(11.3104 + 16.6841i) q^{70} +(2.03061 - 1.70388i) q^{71} +(-0.940394 - 5.33324i) q^{73} +(-3.66721 + 1.64303i) q^{74} +(8.52542 - 1.82131i) q^{76} -0.481712 q^{77} +(-2.11318 - 11.9844i) q^{79} +(11.3926 + 10.7976i) q^{80} +(7.04604 + 10.3937i) q^{82} +(1.92603 + 1.11199i) q^{83} +(8.13266 - 2.96005i) q^{85} +(-0.367602 + 0.758190i) q^{86} +(-0.366371 + 0.0805646i) q^{88} +(-5.86514 - 1.03418i) q^{89} +(-18.1104 - 15.1964i) q^{91} +(1.46094 + 10.0537i) q^{92} +(4.59201 - 4.45525i) q^{94} +(17.0674 - 1.13095i) q^{95} +(-4.42348 + 12.1534i) q^{97} +(5.13065 - 7.09657i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$-1$	$1$

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 $

$2$	−0.578232	−	1.29060i	−0.408872	−	0.912592i
$2$	−0.578232	−	1.29060i	−0.408872	−	0.912592i
$3$		0			0
$3$		0			0
$4$	−1.33130	+	1.49253i	−0.665648	+	0.746266i
$5$	−3.00606	+	2.52238i	−1.34435	+	1.12804i	−0.363863	+	0.931452i	$0.618542\pi$
$5$	−3.00606	+	2.52238i	−1.34435	+	1.12804i	−0.980486	+	0.196590i	$0.937013\pi$
$6$		0			0
$7$	3.14549	+	1.81605i	1.18888	+	0.686402i	0.958053	−	0.286592i	$-0.0925225\pi$
$7$	3.14549	+	1.81605i	1.18888	+	0.686402i	0.230830	+	0.972994i	$0.425856\pi$
$8$	2.69606	+	0.855142i	0.953201	+	0.302338i
$9$		0			0
$10$	4.99358	+	2.42109i	1.57911	+	0.765617i
$11$	−0.114858	+	0.0663132i	−0.0346310	+	0.0199942i	−0.517216	−	0.855855i	$-0.673031\pi$
$11$	−0.114858	+	0.0663132i	−0.0346310	+	0.0199942i	0.482585	+	0.875849i	$0.339698\pi$
$12$		0			0
$13$	−6.41015	−	1.13028i	−1.77786	−	0.313484i	−0.814191	−	0.580598i	$-0.802819\pi$
$13$	−6.41015	−	1.13028i	−1.77786	−	0.313484i	−0.963665	+	0.267114i	$0.913930\pi$
$14$	0.524971	−	5.10966i	0.140304	−	1.36562i
$15$		0			0
$16$	−0.455300	−	3.97400i	−0.113825	−	0.993501i
$17$	−2.07248	−	0.754320i	−0.502650	−	0.182950i	0.0782357	−	0.996935i	$-0.475071\pi$
$17$	−2.07248	−	0.754320i	−0.502650	−	0.182950i	−0.580885	+	0.813985i	$0.697294\pi$
$18$		0			0
$19$	−3.51706	−	2.57494i	−0.806868	−	0.590731i
$19$	−3.51706	−	2.57494i	−0.806868	−	0.590731i
$20$	0.237219	−	7.84467i	0.0530437	−	1.75412i
$21$		0			0
$22$	0.151998	+	0.109891i	0.0324062	+	0.0234289i
$23$	3.26515	−	3.89125i	0.680830	−	0.811382i	−0.309384	−	0.950937i	$-0.600123\pi$
$23$	3.26515	−	3.89125i	0.680830	−	0.811382i	0.990214	+	0.139555i	$0.0445673\pi$
$24$		0			0
$25$	1.80573	−	10.2408i	0.361146	−	2.04816i
$26$	2.24781	+	8.92650i	0.440832	+	1.75063i
$27$		0			0
$28$	−6.89809	+	2.27704i	−1.30362	+	0.430320i
$29$	−0.208018	−	0.571524i	−0.0386279	−	0.106129i	0.918879	−	0.394539i	$-0.129096\pi$
$29$	−0.208018	−	0.571524i	−0.0386279	−	0.106129i	−0.957507	+	0.288410i	$0.906873\pi$
$30$		0			0
$31$	−0.726976	+	1.25916i	−0.130569	+	0.226152i	−0.923896	−	0.382644i	$-0.875014\pi$
$31$	−0.726976	+	1.25916i	−0.130569	+	0.226152i	0.793327	+	0.608795i	$0.208347\pi$
$32$	−4.86558	+	2.88551i	−0.860121	+	0.510090i
$33$		0			0
$34$	0.224847	+	3.11091i	0.0385609	+	0.533517i
$35$	−14.0363	+	2.47497i	−2.37256	+	0.418347i
$36$		0			0
$37$		−	2.84148i		−	0.467136i	−0.972340	−	0.233568i	$-0.924960\pi$
$37$		−	2.84148i		−	0.467136i	0.972340	−	0.233568i	$-0.0750402\pi$
$38$	−1.28954	+	6.02802i	−0.209191	+	0.977875i
$39$		0			0
$40$	−10.2615	+	4.22988i	−1.62248	+	0.668803i
$41$	−8.74416	+	1.54183i	−1.36561	+	0.240794i	−0.807938	−	0.589268i	$-0.799416\pi$
$41$	−8.74416	+	1.54183i	−1.36561	+	0.240794i	−0.557671	+	0.830062i	$0.688305\pi$
$42$		0			0
$43$	−0.382981	−	0.456418i	−0.0584040	−	0.0696032i	0.736052	−	0.676926i	$-0.236688\pi$
$43$	−0.382981	−	0.456418i	−0.0584040	−	0.0696032i	−0.794456	+	0.607322i	$0.792244\pi$
$44$	0.0539353	−	0.259712i	0.00813105	−	0.0391530i
$45$		0			0
$46$	−6.91006	−	1.96395i	−1.01883	−	0.289569i
$47$	1.54735	+	4.25131i	0.225704	+	0.620117i	0.999918	−	0.0128071i	$-0.00407674\pi$
$47$	1.54735	+	4.25131i	0.225704	+	0.620117i	−0.774214	+	0.632924i	$0.781855\pi$
$48$		0			0
$49$	3.09606	+	5.36254i	0.442295	+	0.766077i
$50$	−14.2609	+	3.59108i	−2.01679	+	0.507855i
$51$		0			0
$52$	10.2208	−	8.06261i	1.41737	−	1.11808i
$53$	0.676498	−	0.806218i	0.0929241	−	0.110743i	−0.717579	−	0.696478i	$-0.754750\pi$
$53$	0.676498	−	0.806218i	0.0929241	−	0.110743i	0.810503	+	0.585735i	$0.199194\pi$
$54$		0			0
$55$	0.178002	−	0.489057i	0.0240018	−	0.0659444i
$56$	6.92744	+	7.58601i	0.925718	+	1.01372i
$57$		0			0
$58$	−0.617326	+	0.598941i	−0.0810589	+	0.0786448i
$59$	−5.41120	−	1.96952i	−0.704478	−	0.256409i	−0.0351565	−	0.999382i	$-0.511193\pi$
$59$	−5.41120	−	1.96952i	−0.704478	−	0.256409i	−0.669322	+	0.742973i	$0.733415\pi$
$60$		0			0
$61$	5.10087	+	4.28014i	0.653099	+	0.548015i	0.908010	−	0.418949i	$-0.137602\pi$
$61$	5.10087	+	4.28014i	0.653099	+	0.548015i	−0.254911	+	0.966965i	$0.582046\pi$
$62$	2.04543	+	0.210149i	0.259770	+	0.0266890i
$63$		0			0
$64$	6.53746	+	4.61103i	0.817183	+	0.576378i
$65$	22.1203	−	12.7711i	2.74368	−	1.58407i
$66$		0			0
$67$	−13.3272	+	4.85072i	−1.62818	+	0.592610i	−0.984916	−	0.173034i	$-0.944643\pi$
$67$	−13.3272	+	4.85072i	−1.62818	+	0.592610i	−0.643266	+	0.765643i	$0.722421\pi$
$68$	3.88493	−	2.08901i	0.471117	−	0.253330i
$69$		0			0
$70$	11.3104	+	16.6841i	1.35185	+	1.99413i
$71$	2.03061	−	1.70388i	0.240989	−	0.202214i	−0.514292	−	0.857615i	$-0.671945\pi$
$71$	2.03061	−	1.70388i	0.240989	−	0.202214i	0.755280	+	0.655402i	$0.227501\pi$
$72$		0			0
$73$	−0.940394	−	5.33324i	−0.110065	−	0.624208i	−0.989076	−	0.147407i	$-0.952907\pi$
$73$	−0.940394	−	5.33324i	−0.110065	−	0.624208i	0.879011	−	0.476801i	$-0.158204\pi$
$74$	−3.66721	+	1.64303i	−0.426305	+	0.190999i
$75$		0			0
$76$	8.52542	−	1.82131i	0.977933	−	0.208919i
$77$	−0.481712			−0.0548962
$78$		0			0
$79$	−2.11318	−	11.9844i	−0.237751	−	1.34835i	−0.836742	−	0.547597i	$-0.815543\pi$
$79$	−2.11318	−	11.9844i	−0.237751	−	1.34835i	0.598991	−	0.800756i	$-0.295568\pi$
$80$	11.3926	+	10.7976i	1.27373	+	1.20721i
$81$		0			0
$82$	7.04604	+	10.3937i	0.778105	+	1.14779i
$83$	1.92603	+	1.11199i	0.211409	+	0.122057i	0.601966	−	0.798522i	$-0.294384\pi$
$83$	1.92603	+	1.11199i	0.211409	+	0.122057i	−0.390557	+	0.920579i	$0.627718\pi$
$84$		0			0
$85$	8.13266	−	2.96005i	0.882111	−	0.321062i
$86$	−0.367602	+	0.758190i	−0.0396396	+	0.0817578i
$87$		0			0
$88$	−0.366371	+	0.0805646i	−0.0390553	+	0.00858821i
$89$	−5.86514	−	1.03418i	−0.621703	−	0.109623i	−0.146081	−	0.989273i	$-0.546666\pi$
$89$	−5.86514	−	1.03418i	−0.621703	−	0.109623i	−0.475622	+	0.879650i	$0.657777\pi$
$90$		0			0
$91$	−18.1104	−	15.1964i	−1.89849	−	1.59302i
$92$	1.46094	+	10.0537i	0.152313	+	1.04818i
$93$		0			0
$94$	4.59201	−	4.45525i	0.473630	−	0.459524i
$95$	17.0674	−	1.13095i	1.75108	−	0.116033i
$96$		0			0
$97$	−4.42348	+	12.1534i	−0.449136	+	1.23399i	0.484190	+	0.874963i	$0.339114\pi$
$97$	−4.42348	+	12.1534i	−0.449136	+	1.23399i	−0.933327	+	0.359029i	$0.883108\pi$
$98$	5.13065	−	7.09657i	0.518274	−	0.716862i
$99$		0			0
$100$	12.8807	+	16.3286i	1.28807	+	1.63286i
$101$	−0.763578	+	4.33046i	−0.0759788	+	0.430897i	0.922962	+	0.384890i	$0.125761\pi$
$101$	−0.763578	+	4.33046i	−0.0759788	+	0.430897i	−0.998941	+	0.0460069i	$0.985350\pi$
$102$		0			0
$103$	3.16703	+	5.48546i	0.312057	+	0.540498i	0.978807	−	0.204783i	$-0.0656487\pi$
$103$	3.16703	+	5.48546i	0.312057	+	0.540498i	−0.666751	+	0.745281i	$0.732315\pi$
$104$	−16.3156	−	8.52889i	−1.59987	−	0.836327i
$105$		0			0
$106$	−1.43168	−	0.406907i	−0.139057	−	0.0395223i
$107$	−2.76186	+	4.78368i	−0.266999	+	0.462456i	−0.968085	−	0.250620i	$-0.919365\pi$
$107$	−2.76186	+	4.78368i	−0.266999	+	0.462456i	0.701086	+	0.713076i	$0.252699\pi$
$108$		0			0
$109$	−7.83434	−	9.33660i	−0.750394	−	0.894285i	0.246806	−	0.969065i	$-0.420619\pi$
$109$	−7.83434	−	9.33660i	−0.750394	−	0.894285i	−0.997200	+	0.0747803i	$0.976174\pi$
$110$	−0.734103	+	0.0530586i	−0.0699939	+	0.00505894i
$111$		0			0
$112$	5.78484	−	13.3270i	0.546616	−	1.25929i
$113$		−	11.9979i		−	1.12867i	−0.825546	−	0.564336i	$-0.809132\pi$
$113$		−	11.9979i		−	1.12867i	0.825546	−	0.564336i	$-0.190868\pi$
$114$		0			0
$115$			19.9333i			1.85879i
$116$	1.12995	+	0.450395i	0.104913	+	0.0418181i
$117$		0			0
$118$	0.587070	+	8.12253i	0.0540442	+	0.747740i
$119$	−5.14907	−	6.13643i	−0.472015	−	0.562525i
$120$		0			0
$121$	−5.49121	+	9.51105i	−0.499200	+	0.864641i
$122$	2.57446	−	9.05809i	0.233081	−	0.820081i
$123$		0			0
$124$	−0.911514	−	2.76135i	−0.0818564	−	0.247976i
$125$	10.5927	+	18.3471i	0.947443	+	1.64102i
$126$		0			0
$127$	−2.37797	+	13.4861i	−0.211011	+	1.19670i	0.676686	+	0.736272i	$0.263416\pi$
$127$	−2.37797	+	13.4861i	−0.211011	+	1.19670i	−0.887697	+	0.460429i	$0.847696\pi$
$128$	2.17082	−	11.1035i	0.191875	−	0.981419i
$129$		0			0
$130$	−29.2731	−	21.1637i	−2.56742	−	1.85618i
$131$	0.715663	−	1.96627i	0.0625278	−	0.171794i	−0.904495	−	0.426485i	$-0.859752\pi$
$131$	0.715663	−	1.96627i	0.0625278	−	0.171794i	0.967022	+	0.254691i	$0.0819739\pi$
$132$		0			0
$133$	−6.38665	−	14.4866i	−0.553793	−	1.25615i
$134$	13.9666	+	14.3953i	1.20653	+	1.24356i
$135$		0			0
$136$	−4.94247	−	3.80595i	−0.423813	−	0.326358i
$137$	−16.8320	−	14.1237i	−1.43806	−	1.20667i	−0.940751	−	0.339098i	$-0.889878\pi$
$137$	−16.8320	−	14.1237i	−1.43806	−	1.20667i	−0.497306	−	0.867575i	$-0.665677\pi$
$138$		0			0
$139$	11.8412	+	2.08792i	1.00436	+	0.177095i	0.651554	−	0.758602i	$-0.274117\pi$
$139$	11.8412	+	2.08792i	1.00436	+	0.177095i	0.352803	+	0.935697i	$0.385228\pi$
$140$	14.9925	−	24.2445i	1.26709	−	2.04904i
$141$		0			0
$142$	−3.37319	−	1.63546i	−0.283072	−	0.137245i
$143$	0.811209	−	0.295256i	0.0678367	−	0.0246905i
$144$		0			0
$145$	2.06691	+	1.19333i	0.171648	+	0.0991009i
$146$	−6.33931	+	4.29752i	−0.524645	+	0.355665i
$147$		0			0
$148$	4.24100	+	3.78285i	0.348608	+	0.310948i
$149$	0.139687	+	0.792202i	0.0114436	+	0.0648997i	0.989995	−	0.141104i	$-0.0450652\pi$
$149$	0.139687	+	0.792202i	0.0114436	+	0.0648997i	−0.978551	+	0.206004i	$0.933954\pi$
$150$		0			0
$151$	−3.81184			−0.310203			−0.155102	−	0.987899i	$-0.549571\pi$
$151$	−3.81184			−0.310203			−0.155102	+	0.987899i	$0.549571\pi$
$152$	−7.28026	−	9.94977i	−0.590507	−	0.807033i
$153$		0			0
$154$	0.278541	+	0.621698i	0.0224455	+	0.0500978i
$155$	−0.990748	−	5.61881i	−0.0795788	−	0.451314i
$156$		0			0
$157$	−5.09012	+	4.27111i	−0.406236	+	0.340872i	−0.822898	−	0.568189i	$-0.807644\pi$
$157$	−5.09012	+	4.27111i	−0.406236	+	0.340872i	0.416662	+	0.909061i	$0.363200\pi$
$158$	−14.2452	+	9.65704i	−1.13329	+	0.768273i
$159$		0			0
$160$	7.34786	−	20.9468i	0.580899	−	1.65599i
$161$	17.3372	−	6.31022i	1.36636	−	0.497315i
$162$		0			0
$163$	12.2112	−	7.05013i	0.956454	−	0.552209i	0.0613741	−	0.998115i	$-0.480452\pi$
$163$	12.2112	−	7.05013i	0.956454	−	0.552209i	0.895080	+	0.445906i	$0.147118\pi$
$164$	9.33984	−	15.1036i	0.729319	−	1.17939i
$165$		0			0
$166$	0.321447	−	3.12872i	0.0249491	−	0.242835i
$167$	0.530626	+	0.445248i	0.0410611	+	0.0344543i	0.663087	−	0.748542i	$-0.269246\pi$
$167$	0.530626	+	0.445248i	0.0410611	+	0.0344543i	−0.622026	+	0.782996i	$0.713690\pi$
$168$		0			0
$169$	27.5965	+	10.0443i	2.12281	+	0.772638i
$170$	−8.52280	−	8.78442i	−0.653669	−	0.673734i
$171$		0			0
$172$	1.19108	+	0.0360177i	0.0908190	+	0.00274632i
$173$	−0.212455	+	0.583714i	−0.0161526	+	0.0443790i	−0.947507	−	0.319735i	$-0.896406\pi$
$173$	−0.212455	+	0.583714i	−0.0161526	+	0.0443790i	0.931354	+	0.364114i	$0.118628\pi$
$174$		0			0
$175$	24.2777	−	28.9330i	1.83522	−	2.18713i
$176$	0.315824	+	0.426253i	0.0238061	+	0.0321300i
$177$		0			0
$178$	2.05669	+	8.16754i	0.154156	+	0.612183i
$179$	3.49386	+	6.05155i	0.261143	+	0.452314i	0.966546	−	0.256493i	$-0.0825671\pi$
$179$	3.49386	+	6.05155i	0.261143	+	0.452314i	−0.705403	+	0.708807i	$0.749234\pi$
$180$		0			0
$181$	1.45869	+	4.00773i	0.108424	+	0.297892i	0.982025	−	0.188750i	$-0.0604437\pi$
$181$	1.45869	+	4.00773i	0.108424	+	0.297892i	−0.873601	+	0.486642i	$0.838221\pi$
$182$	−9.14051	+	32.1603i	−0.677539	+	2.38388i
$183$		0			0
$184$	12.1306	−	7.69888i	0.894280	−	0.567569i
$185$	7.16729	+	8.54164i	0.526950	+	0.627994i
$186$		0			0
$187$	0.288062	−	0.0507931i	0.0210652	−	0.00371436i
$188$	−8.40519	−	3.35028i	−0.613012	−	0.244344i
$189$		0			0
$190$	−11.3285	−	21.3733i	−0.821859	−	1.55058i
$191$			22.8590i			1.65402i	0.562187	+	0.827010i	$0.309960\pi$
$191$			22.8590i			1.65402i	−0.562187	+	0.827010i	$0.690040\pi$
$192$		0			0
$193$	−11.0749	+	1.95280i	−0.797186	+	0.140565i	−0.557382	−	0.830256i	$-0.688194\pi$
$193$	−11.0749	+	1.95280i	−0.797186	+	0.140565i	−0.239804	+	0.970821i	$0.577083\pi$
$194$	18.2430	−	1.31854i	1.30977	−	0.0946659i
$195$		0			0
$196$	−12.1255	−	2.51816i	−0.866110	−	0.179868i
$197$	−5.43953	+	9.42154i	−0.387550	+	0.671257i	−0.992119	−	0.125296i	$-0.960012\pi$
$197$	−5.43953	+	9.42154i	−0.387550	+	0.671257i	0.604569	+	0.796553i	$0.293345\pi$
$198$		0			0
$199$	5.97342	+	16.4118i	0.423444	+	1.16340i	0.949723	+	0.313091i	$0.101365\pi$
$199$	5.97342	+	16.4118i	0.423444	+	1.16340i	−0.526279	+	0.850312i	$0.676413\pi$
$200$	13.6257	−	26.0656i	0.963481	−	1.84312i
$201$		0			0
$202$	6.03042	−	1.51854i	0.424299	−	0.106844i
$203$	0.383598	−	2.17549i	0.0269233	−	0.152690i
$204$		0			0
$205$	22.3964	−	26.6909i	1.56423	−	1.86418i
$206$	5.24825	−	7.25924i	0.365663	−	0.505775i
$207$		0			0
$208$	−1.57320	+	25.9886i	−0.109082	+	1.80198i
$209$	0.574714	+	0.0625245i	0.0397538	+	0.00432491i
$210$		0			0
$211$	−10.3242	−	3.75769i	−0.710745	−	0.258690i	−0.0387534	−	0.999249i	$-0.512339\pi$
$211$	−10.3242	−	3.75769i	−0.710745	−	0.258690i	−0.671992	+	0.740559i	$0.734561\pi$
$212$	0.302688	+	2.08301i	0.0207887	+	0.143062i
$213$		0			0
$214$	7.77081	+	0.798380i	0.531202	+	0.0545761i
$215$	2.30252	+	0.405997i	0.157031	+	0.0276887i
$216$		0			0
$217$	−4.57339	+	2.64045i	−0.310462	+	0.179245i
$218$	−7.51976	+	15.5097i	−0.509302	+	1.05045i
$219$		0			0
$220$	0.492959	+	0.916753i	0.0332353	+	0.0618075i
$221$	12.4323	+	7.17779i	0.836287	+	0.482830i
$222$		0			0
$223$	3.16227	−	2.65346i	0.211761	−	0.177689i	−0.530737	−	0.847536i	$-0.678085\pi$
$223$	3.16227	−	2.65346i	0.211761	−	0.177689i	0.742499	+	0.669847i	$0.233641\pi$
$224$	−20.5448	+	0.240195i	−1.37271	+	0.0160487i
$225$		0			0
$226$	−15.4845	+	6.93759i	−1.03002	+	0.461481i
$227$	−22.7323			−1.50880			−0.754399	−	0.656416i	$-0.772072\pi$
$227$	−22.7323			−1.50880			−0.754399	+	0.656416i	$0.772072\pi$
$228$		0			0
$229$	−4.30789			−0.284673			−0.142337	−	0.989818i	$-0.545462\pi$
$229$	−4.30789			−0.284673			−0.142337	+	0.989818i	$0.545462\pi$
$230$	25.7259	−	11.5260i	1.69631	−	0.760005i
$231$		0			0
$232$	−0.0720939	−	1.71875i	−0.00473319	−	0.112841i
$233$	2.82584	−	2.37116i	0.185127	−	0.155340i	−0.545514	−	0.838101i	$-0.683666\pi$
$233$	2.82584	−	2.37116i	0.185127	−	0.155340i	0.730641	+	0.682762i	$0.239221\pi$
$234$		0			0
$235$	−15.3748	−	8.87666i	−1.00294	−	0.579050i
$236$	10.1435	−	5.45438i	0.660284	−	0.355050i
$237$		0			0
$238$	−4.94231	+	10.1937i	−0.320363	+	0.660757i
$239$	15.7598	−	9.09895i	1.01942	−	0.588562i	0.105484	−	0.994421i	$-0.466361\pi$
$239$	15.7598	−	9.09895i	1.01942	−	0.588562i	0.913936	+	0.405859i	$0.133028\pi$
$240$		0			0
$241$	0.688871	+	0.121467i	0.0443741	+	0.00782435i	0.195791	−	0.980646i	$-0.437273\pi$
$241$	0.688871	+	0.121467i	0.0443741	+	0.00782435i	−0.151417	+	0.988470i	$0.548384\pi$
$242$	15.4501	+	1.58736i	0.993173	+	0.102039i
$243$		0			0
$244$	−13.1790	+	1.91508i	−0.843699	+	0.122600i
$245$	−22.8333	−	8.31065i	−1.45877	−	0.530948i
$246$		0			0
$247$	19.6345	+	20.4810i	1.24931	+	1.30318i
$248$	−3.03673	+	2.77310i	−0.192832	+	0.176092i
$249$		0			0
$250$	17.5538	−	24.2799i	1.11020	−	1.53559i
$251$	17.6189	−	20.9974i	1.11209	−	1.32534i	0.171742	−	0.985142i	$-0.445061\pi$
$251$	17.6189	−	20.9974i	1.11209	−	1.32534i	0.940353	−	0.340201i	$-0.110495\pi$
$252$		0			0
$253$	−0.116987	+	0.663463i	−0.00735488	+	0.0417116i
$254$	18.7802	−	4.72910i	1.17838	−	0.296730i
$255$		0			0
$256$	−15.5854	+	3.61873i	−0.974088	+	0.226171i
$257$	5.12241	+	14.0737i	0.319527	+	0.877894i	0.990635	+	0.136535i	$0.0435965\pi$
$257$	5.12241	+	14.0737i	0.319527	+	0.877894i	−0.671108	+	0.741360i	$0.734181\pi$
$258$		0			0
$259$	5.16026	−	8.93784i	0.320643	−	0.555370i
$260$	−10.3873	+	50.0174i	−0.644193	+	3.10195i
$261$		0			0
$262$	−2.95148	+	0.213324i	−0.182343	+	0.0131792i
$263$	−1.54112	+	0.271742i	−0.0950297	+	0.0167563i	−0.220961	−	0.975283i	$-0.570919\pi$
$263$	−1.54112	+	0.271742i	−0.0950297	+	0.0167563i	0.125931	+	0.992039i	$0.459808\pi$
$264$		0			0
$265$			4.12992i			0.253699i
$266$	−15.0034	+	16.6192i	−0.919919	+	1.01899i
$267$		0			0
$268$	10.5027	−	26.3491i	0.641552	−	1.60953i
$269$	18.7970	−	3.31442i	1.14607	−	0.202084i	0.431813	−	0.901963i	$-0.357874\pi$
$269$	18.7970	−	3.31442i	1.14607	−	0.202084i	0.714261	+	0.699879i	$0.246763\pi$
$270$		0			0
$271$	−0.812187	−	0.967927i	−0.0493369	−	0.0587974i	0.740812	−	0.671713i	$-0.234441\pi$
$271$	−0.812187	−	0.967927i	−0.0493369	−	0.0587974i	−0.790149	+	0.612915i	$0.789997\pi$
$272$	−2.05407	+	8.57948i	−0.124546	+	0.520207i
$273$		0			0
$274$	−8.49530	+	29.8902i	−0.513220	+	1.80573i
$275$	0.471698	+	1.29598i	0.0284444	+	0.0781505i
$276$		0			0
$277$	−2.57753	−	4.46441i	−0.154869	−	0.268240i	0.778143	−	0.628088i	$-0.216162\pi$
$277$	−2.57753	−	4.46441i	−0.154869	−	0.268240i	−0.933011	+	0.359847i	$0.882829\pi$
$278$	−4.15228	−	16.4896i	−0.249037	−	0.988978i
$279$		0			0
$280$	−39.9591	−	5.33033i	−2.38801	−	0.318548i
$281$	−16.3514	+	19.4869i	−0.975443	+	1.16249i	0.0112566	+	0.999937i	$0.496417\pi$
$281$	−16.3514	+	19.4869i	−0.975443	+	1.16249i	−0.986700	+	0.162552i	$0.948028\pi$
$282$		0			0
$283$	−0.410271	+	1.12721i	−0.0243881	+	0.0670057i	−0.951289	−	0.308300i	$-0.900240\pi$
$283$	−0.410271	+	1.12721i	−0.0243881	+	0.0670057i	0.926901	+	0.375306i	$0.122462\pi$
$284$	−0.160243	+	5.29912i	−0.00950865	+	0.314445i
$285$		0			0
$286$	−0.850124	−	0.876220i	−0.0502689	−	0.0518120i
$287$	−30.3047	−	11.0300i	−1.78883	−	0.651081i
$288$		0			0
$289$	−9.29659	−	7.80077i	−0.546858	−	0.458869i
$290$	0.344961	−	3.35758i	0.0202568	−	0.197164i
$291$		0			0
$292$	9.21197	+	5.69655i	0.539090	+	0.333366i
$293$	2.26935	−	1.31021i	0.132577	−	0.0765433i	−0.432245	−	0.901756i	$-0.642278\pi$
$293$	2.26935	−	1.31021i	0.132577	−	0.0765433i	0.564822	+	0.825213i	$0.308945\pi$
$294$		0			0
$295$	21.2342	−	7.72863i	1.23630	−	0.449978i
$296$	2.42987	−	7.66079i	0.141233	−	0.445275i
$297$		0			0
$298$	0.941645	−	0.638356i	0.0545480	−	0.0369790i
$299$	−25.3283	+	21.2530i	−1.46477	+	1.22909i
$300$		0			0
$301$	−0.375783	−	2.13117i	−0.0216598	−	0.122839i
$302$	2.20413	+	4.91956i	0.126833	+	0.283089i
$303$		0			0
$304$	−8.63149	+	15.1492i	−0.495050	+	0.868864i
$305$	−26.1296			−1.49618
$306$		0			0
$307$	3.60419	+	20.4404i	0.205702	+	1.16659i	0.896332	+	0.443384i	$0.146222\pi$
$307$	3.60419	+	20.4404i	0.205702	+	1.16659i	−0.690630	+	0.723208i	$0.742667\pi$
$308$	0.641302	−	0.718971i	0.0365416	−	0.0409672i
$309$		0			0
$310$	−6.67875	+	4.52763i	−0.379328	+	0.257152i
$311$	7.49584	+	4.32773i	0.425050	+	0.245403i	0.697236	−	0.716842i	$-0.254413\pi$
$311$	7.49584	+	4.32773i	0.425050	+	0.245403i	−0.272186	+	0.962245i	$0.587746\pi$
$312$		0			0
$313$	−16.3293	+	5.94338i	−0.922987	+	0.335940i	−0.759426	−	0.650594i	$-0.774520\pi$
$313$	−16.3293	+	5.94338i	−0.922987	+	0.335940i	−0.163561	+	0.986533i	$0.552298\pi$
$314$	8.45557	+	4.09961i	0.477175	+	0.231354i
$315$		0			0
$316$	20.7004	+	12.8008i	1.16449	+	0.720103i
$317$	−18.3187	−	3.23007i	−1.02888	−	0.181419i	−0.366366	−	0.930471i	$-0.619398\pi$
$317$	−18.3187	−	3.23007i	−1.02888	−	0.181419i	−0.662512	+	0.749052i	$0.730509\pi$
$318$		0			0
$319$	0.0617921	+	0.0518497i	0.00345969	+	0.00290303i
$320$	−31.2827	+	2.62897i	−1.74876	+	0.146964i
$321$		0			0
$322$	−18.1689	−	18.7266i	−1.01251	−	1.04359i
$323$	5.34670	+	7.98949i	0.297498	+	0.444547i
$324$		0			0
$325$	−23.1500	+	63.6040i	−1.28413	+	3.52812i
$326$	−16.1598	−	11.6831i	−0.895008	−	0.647070i
$327$		0			0
$328$	−24.8933	−	3.32063i	−1.37450	−	0.183351i
$329$	−2.85341	+	16.1825i	−0.157314	+	0.892170i
$330$		0			0
$331$	1.69965	+	2.94388i	0.0934212	+	0.161810i	0.908949	−	0.416908i	$-0.136886\pi$
$331$	1.69965	+	2.94388i	0.0934212	+	0.161810i	−0.815527	+	0.578718i	$0.803553\pi$
$332$	−4.22379	+	1.39426i	−0.231811	+	0.0765202i
$333$		0			0
$334$	0.267812	−	0.942283i	0.0146540	−	0.0515594i
$335$	27.8271	−	48.1979i	1.52036	−	2.63333i
$336$		0			0
$337$	14.9862	+	17.8599i	0.816351	+	0.972889i	0.999949	−	0.0101120i	$-0.00321881\pi$
$337$	14.9862	+	17.8599i	0.816351	+	0.972889i	−0.183598	+	0.983001i	$0.558774\pi$
$338$	−2.99399	−	41.4239i	−0.162852	−	2.25316i
$339$		0			0
$340$	−6.40902	+	16.0790i	−0.347578	+	0.872004i
$341$		−	0.192832i		−	0.0104425i
$342$		0			0
$343$		−	2.93426i		−	0.158435i
$344$	−0.642236	−	1.55803i	−0.0346270	−	0.0840035i
$345$		0			0
$346$	0.876190	−	0.0633282i	0.0471042	−	0.00340454i
$347$	3.20788	+	3.82300i	0.172208	+	0.205229i	0.845244	−	0.534380i	$-0.179455\pi$
$347$	3.20788	+	3.82300i	0.172208	+	0.205229i	−0.673037	+	0.739609i	$0.735010\pi$
$348$		0			0
$349$	−1.36711	+	2.36790i	−0.0731797	+	0.126751i	−0.900293	−	0.435284i	$-0.856648\pi$
$349$	−1.36711	+	2.36790i	−0.0731797	+	0.126751i	0.827114	+	0.562035i	$0.189981\pi$
$350$	−51.3790	−	14.6028i	−2.74633	−	0.780551i
$351$		0			0
$352$	0.367503	−	0.654075i	0.0195880	−	0.0348623i
$353$	−14.1040	−	24.4289i	−0.750681	−	1.30022i	−0.947493	−	0.319776i	$-0.896392\pi$
$353$	−14.1040	−	24.4289i	−0.750681	−	1.30022i	0.196812	−	0.980441i	$-0.436941\pi$
$354$		0			0
$355$	−1.80628	+	10.2439i	−0.0958674	+	0.543691i
$356$	9.35178	−	7.37710i	0.495643	−	0.390985i
$357$		0			0
$358$	5.78986	−	8.00837i	0.306004	−	0.423256i
$359$	−9.54210	+	26.2167i	−0.503613	+	1.38367i	0.384110	+	0.923287i	$0.374508\pi$
$359$	−9.54210	+	26.2167i	−0.503613	+	1.38367i	−0.887723	+	0.460378i	$0.847714\pi$
$360$		0			0
$361$	5.73939	+	18.1124i	0.302073	+	0.953285i
$362$	4.32891	−	4.19999i	0.227523	−	0.220746i
$363$		0			0
$364$	46.7915	−	6.79939i	2.45254	−	0.356385i
$365$	16.2793	+	13.6600i	0.852099	+	0.714996i
$366$		0			0
$367$	−36.8532	−	6.49822i	−1.92372	−	0.339204i	−0.924595	−	0.380952i	$-0.875596\pi$
$367$	−36.8532	−	6.49822i	−1.92372	−	0.339204i	−0.999128	+	0.0417476i	$0.986707\pi$
$368$	−16.9505	−	11.2040i	−0.883604	−	0.584050i
$369$		0			0
$370$	6.87949	−	14.1892i	0.357648	−	0.737659i
$371$	3.59205	−	1.30740i	0.186490	−	0.0678767i
$372$		0			0
$373$	−5.83655	−	3.36973i	−0.302205	−	0.174478i	0.341228	−	0.939981i	$-0.389157\pi$
$373$	−5.83655	−	3.36973i	−0.302205	−	0.174478i	−0.643433	+	0.765502i	$0.722491\pi$
$374$	−0.232120	−	0.342402i	−0.0120026	−	0.0177052i
$375$		0			0
$376$	0.536274	+	12.7850i	0.0276562	+	0.659335i
$377$	0.687441	+	3.89867i	0.0354050	+	0.200792i
$378$		0			0
$379$	30.6964			1.57677			0.788384	−	0.615183i	$-0.210918\pi$
$379$	30.6964			1.57677			0.788384	+	0.615183i	$0.210918\pi$
$380$	−21.0338	+	26.9793i	−1.07901	+	1.38401i
$381$		0			0
$382$	29.5018	−	13.2178i	1.50945	−	0.676282i
$383$	−4.69272	−	26.6138i	−0.239787	−	1.35990i	−0.832294	−	0.554334i	$-0.812973\pi$
$383$	−4.69272	−	26.6138i	−0.239787	−	1.35990i	0.592507	−	0.805565i	$-0.298138\pi$
$384$		0			0
$385$	1.44805	−	1.21506i	0.0737996	−	0.0619253i
$386$	8.92411	+	13.1640i	0.454225	+	0.670032i
$387$		0			0
$388$	−12.2504	−	22.7820i	−0.621919	−	1.15658i
$389$	34.4298	−	12.5314i	1.74566	−	0.635368i	0.746124	−	0.665807i	$-0.231913\pi$
$389$	34.4298	−	12.5314i	1.74566	−	0.635368i	0.999537	+	0.0304389i	$0.00969050\pi$
$390$		0			0
$391$	−9.70220	+	5.60157i	−0.490661	+	0.283283i
$392$	3.76144	+	17.1053i	0.189981	+	0.863948i
$393$		0			0
$394$	15.3047	+	1.57242i	0.771042	+	0.0792175i
$395$	36.5816	+	30.6956i	1.84062	+	1.54446i
$396$		0			0
$397$	12.0237	+	4.37627i	0.603453	+	0.219639i	0.625636	−	0.780115i	$-0.284839\pi$
$397$	12.0237	+	4.37627i	0.603453	+	0.219639i	−0.0221832	+	0.999754i	$0.507062\pi$
$398$	17.7271	−	17.1991i	0.888578	−	0.862114i
$399$		0			0
$400$	−41.5191	−	2.51333i	−2.07595	−	0.125667i
$401$	−4.52331	+	12.4277i	−0.225883	+	0.620610i	−0.999922	−	0.0125293i	$-0.996012\pi$
$401$	−4.52331	+	12.4277i	−0.225883	+	0.620610i	0.774038	+	0.633139i	$0.218234\pi$
$402$		0			0
$403$	6.08323	−	7.24971i	0.303027	−	0.361134i
$404$	−5.44681	−	6.90479i	−0.270989	−	0.343526i
$405$		0			0
$406$	−3.02950	+	0.762867i	−0.150352	+	0.0378605i
$407$	0.188428	+	0.326366i	0.00934001	+	0.0161774i
$408$		0			0
$409$	−8.83683	−	24.2790i	−0.436953	−	1.20052i	−0.941464	−	0.337113i	$-0.890549\pi$
$409$	−8.83683	−	24.2790i	−0.436953	−	1.20052i	0.504511	−	0.863405i	$-0.331673\pi$
$410$	−47.3976	−	13.4712i	−2.34080	−	0.665295i
$411$		0			0
$412$	−12.4035	−	2.57588i	−0.611075	−	0.126904i
$413$	−13.4441	−	16.0221i	−0.661542	−	0.788396i
$414$		0			0
$415$	−8.59460	+	1.51546i	−0.421892	+	0.0743910i
$416$	34.4505	−	12.9970i	1.68908	−	0.637232i
$417$		0			0
$418$	−0.251624	−	0.777880i	−0.0123073	−	0.0380473i
$419$			19.8048i			0.967529i	0.875198	+	0.483765i	$0.160731\pi$
$419$			19.8048i			0.967529i	−0.875198	+	0.483765i	$0.839269\pi$
$420$		0			0
$421$	17.6581	−	3.11360i	0.860603	−	0.151748i	0.274107	−	0.961699i	$-0.411618\pi$
$421$	17.6581	−	3.11360i	0.860603	−	0.151748i	0.586496	+	0.809952i	$0.300507\pi$
$422$	1.12009	+	15.4972i	0.0545250	+	0.754391i
$423$		0			0
$424$	2.51331	−	1.59511i	0.122057	−	0.0774654i
$425$	−11.4672	+	19.8617i	−0.556239	+	0.963434i
$426$		0			0
$427$	8.27178	+	22.7265i	0.400300	+	1.09981i
$428$	−3.46294	−	10.4907i	−0.167388	−	0.507085i
$429$		0			0
$430$	−0.807412	−	3.20639i	−0.0389368	−	0.154626i
$431$	−0.459335	+	2.60502i	−0.0221254	+	0.125479i	−0.993870	−	0.110556i	$-0.964737\pi$
$431$	−0.459335	+	2.60502i	−0.0221254	+	0.125479i	0.971745	+	0.236035i	$0.0758480\pi$
$432$		0			0
$433$	−5.16377	+	6.15394i	−0.248155	+	0.295739i	−0.875715	−	0.482829i	$-0.839609\pi$
$433$	−5.16377	+	6.15394i	−0.248155	+	0.295739i	0.627560	+	0.778568i	$0.284054\pi$
$434$	6.05224	+	4.37562i	0.290517	+	0.210037i
$435$		0			0
$436$	24.3650	+	0.736786i	1.16687	+	0.0352856i
$437$	−21.5034	+	5.27820i	−1.02865	+	0.252491i
$438$		0			0
$439$	16.0502	+	5.84179i	0.766034	+	0.278814i	0.695337	−	0.718684i	$-0.255255\pi$
$439$	16.0502	+	5.84179i	0.766034	+	0.278814i	0.0706975	+	0.997498i	$0.477477\pi$
$440$	0.898117	−	1.16631i	0.0428160	−	0.0556016i
$441$		0			0
$442$	2.07491	−	20.1955i	0.0986933	−	0.960604i
$443$	−27.7191	−	4.88763i	−1.31698	−	0.232218i	−0.529366	−	0.848393i	$-0.677570\pi$
$443$	−27.7191	−	4.88763i	−1.31698	−	0.232218i	−0.787609	+	0.616175i	$0.788681\pi$
$444$		0			0
$445$	20.2395	−	11.6853i	0.959445	−	0.553936i
$446$	−5.25308	−	2.54691i	−0.248741	−	0.120600i
$447$		0			0
$448$	12.1897	+	26.3763i	0.575908	+	1.24616i
$449$	2.80954	+	1.62209i	0.132590	+	0.0765510i	0.564828	−	0.825209i	$-0.308943\pi$
$449$	2.80954	+	1.62209i	0.132590	+	0.0765510i	−0.432238	+	0.901760i	$0.642276\pi$
$450$		0			0
$451$	0.902092	−	0.756945i	0.0424779	−	0.0356432i
$452$	17.9073	+	15.9728i	0.842289	+	0.751298i
$453$		0			0
$454$	13.1446	+	29.3384i	0.616905	+	1.37692i
$455$	92.7721			4.34922
$456$		0			0
$457$	7.67802			0.359162			0.179581	−	0.983743i	$-0.442526\pi$
$457$	7.67802			0.359162			0.179581	+	0.983743i	$0.442526\pi$
$458$	2.49096	+	5.55976i	0.116395	+	0.259791i
$459$		0			0
$460$	−29.7510	−	26.5371i	−1.38715	−	1.23730i
$461$	−12.9525	+	10.8684i	−0.603258	+	0.506193i	−0.892491	−	0.451065i	$-0.851044\pi$
$461$	−12.9525	+	10.8684i	−0.603258	+	0.506193i	0.289233	+	0.957259i	$0.406600\pi$
$462$		0			0
$463$	−33.0367	−	19.0738i	−1.53535	−	0.886433i	−0.999102	−	0.0423700i	$-0.986509\pi$
$463$	−33.0367	−	19.0738i	−1.53535	−	0.886433i	−0.536244	−	0.844063i	$-0.680157\pi$
$464$	−2.17653	+	1.08688i	−0.101043	+	0.0504571i
$465$		0			0
$466$	−4.69421	−	2.27595i	−0.217455	−	0.105431i
$467$	4.70600	−	2.71701i	0.217768	−	0.125728i	−0.387148	−	0.922017i	$-0.626540\pi$
$467$	4.70600	−	2.71701i	0.217768	−	0.125728i	0.604916	+	0.796289i	$0.293207\pi$
$468$		0			0
$469$	−50.7298	−	8.94504i	−2.34249	−	0.413043i
$470$	−2.56601	+	24.9755i	−0.118361	+	1.15204i
$471$		0			0
$472$	−12.9047	−	9.93727i	−0.593987	−	0.457400i
$473$	0.0742549	+	0.0270266i	0.00341425	+	0.00124268i
$474$		0			0
$475$	−32.7202	+	31.3678i	−1.50131	+	1.43925i
$476$	16.0137	+	0.484248i	0.733989	+	0.0221955i
$477$		0			0
$478$	−20.8559	−	15.0783i	−0.953928	−	0.689668i
$479$	−12.7757	+	15.2254i	−0.583735	+	0.695668i	−0.974389	−	0.224869i	$-0.927805\pi$
$479$	−12.7757	+	15.2254i	−0.583735	+	0.695668i	0.390654	+	0.920538i	$0.372249\pi$
$480$		0			0
$481$	−3.21167	+	18.2143i	−0.146440	+	0.830501i
$482$	−0.241562	−	0.959293i	−0.0110029	−	0.0436946i
$483$		0			0
$484$	−6.88512	−	20.8578i	−0.312960	−	0.948083i
$485$	−17.3583	−	47.6915i	−0.788199	−	2.16556i
$486$		0			0
$487$	19.8885	−	34.4478i	0.901232	−	1.56098i	0.0753359	−	0.997158i	$-0.475997\pi$
$487$	19.8885	−	34.4478i	0.901232	−	1.56098i	0.825896	−	0.563822i	$-0.190670\pi$
$488$	10.0921	+	15.9015i	0.456848	+	0.719825i
$489$		0			0
$490$	2.47723	+	34.2741i	0.111910	+	1.54835i
$491$	−26.2474	+	4.62812i	−1.18453	+	0.208864i	−0.730999	−	0.682378i	$-0.760946\pi$
$491$	−26.2474	+	4.62812i	−1.18453	+	0.208864i	−0.453527	+	0.891242i	$0.649835\pi$
$492$		0			0
$493$			1.34138i			0.0604128i
$494$	15.0795	−	37.1830i	0.678460	−	1.67294i
$495$		0			0
$496$	5.33489	+	2.31571i	0.239544	+	0.103978i
$497$	9.48158	−	1.67186i	0.425307	−	0.0749931i
$498$		0			0
$499$	−1.58546	−	1.88948i	−0.0709748	−	0.0845845i	0.729389	−	0.684100i	$-0.239805\pi$
$499$	−1.58546	−	1.88948i	−0.0709748	−	0.0845845i	−0.800364	+	0.599515i	$0.795360\pi$
$500$	−41.4858	−	8.61550i	−1.85530	−	0.385297i
$501$		0			0
$502$	−37.2870	−	10.5976i	−1.66420	−	0.472994i
$503$	9.97372	+	27.4026i	0.444706	+	1.22182i	0.936364	+	0.351031i	$0.114169\pi$
$503$	9.97372	+	27.4026i	0.444706	+	1.22182i	−0.491657	+	0.870789i	$0.663609\pi$
$504$		0			0
$505$	−8.62772	−	14.9436i	−0.383928	−	0.664984i
$506$	0.923911	−	0.232653i	0.0410729	−	0.0103427i
$507$		0			0
$508$	−16.9627	−	21.5032i	−0.752598	−	0.954052i
$509$	−6.92417	+	8.25190i	−0.306908	+	0.365759i	−0.897349	−	0.441322i	$-0.854510\pi$
$509$	−6.92417	+	8.25190i	−0.306908	+	0.365759i	0.590440	+	0.807081i	$0.298954\pi$
$510$		0			0
$511$	6.72742	−	18.4834i	0.297604	−	0.817659i
$512$	13.6823	+	18.0221i	0.604678	+	0.796470i
$513$		0			0
$514$	15.2016	−	14.7489i	0.670514	−	0.650544i
$515$	−23.3567	−	8.50114i	−1.02922	−	0.374605i
$516$		0			0
$517$	−0.459643	−	0.385687i	−0.0202151	−	0.0169625i
$518$	−14.5190	−	1.49169i	−0.637928	−	0.0655413i
$519$		0			0
$520$	70.5587	−	15.5158i	3.09420	−	0.680412i
$521$	−3.43242	+	1.98171i	−0.150377	+	0.0868202i	−0.573300	−	0.819345i	$-0.694337\pi$
$521$	−3.43242	+	1.98171i	−0.150377	+	0.0868202i	0.422924	+	0.906165i	$0.361004\pi$
$522$		0			0
$523$	24.7336	−	9.00230i	1.08153	−	0.393643i	0.261050	−	0.965325i	$-0.415931\pi$
$523$	24.7336	−	9.00230i	1.08153	−	0.393643i	0.820475	+	0.571682i	$0.193709\pi$
$524$	1.98196	+	3.68584i	0.0865822	+	0.161016i
$525$		0			0
$526$	1.24184	+	1.83184i	0.0541466	+	0.0798722i
$527$	2.45645	−	2.06121i	0.107005	−	0.0897876i
$528$		0			0
$529$	−0.486741	−	2.76045i	−0.0211627	−	0.120019i
$530$	5.33008	−	2.38805i	0.231524	−	0.103730i
$531$		0			0
$532$	30.1242	+	9.75366i	1.30605	+	0.422875i
$533$	57.7941			2.50334
$534$		0			0
$535$	−3.76396	−	21.3465i	−0.162730	−	0.922888i
$536$	−40.0791	+	1.68114i	−1.73115	+	0.0726142i
$537$		0			0
$538$	−15.1466	−	22.3429i	−0.653017	−	0.963272i
$539$	−0.711215	−	0.410620i	−0.0306342	−	0.0176867i
$540$		0			0
$541$	−16.8842	+	6.14533i	−0.725907	+	0.264209i	−0.678431	−	0.734664i	$-0.737340\pi$
$541$	−16.8842	+	6.14533i	−0.725907	+	0.264209i	−0.0474757	+	0.998872i	$0.515118\pi$
$542$	−0.779574	+	1.60790i	−0.0334856	+	0.0690650i
$543$		0			0
$544$	12.2604	−	2.30994i	0.525660	−	0.0990379i
$545$	47.1009	+	8.30516i	2.01758	+	0.355754i
$546$		0			0
$547$	−6.45422	−	5.41574i	−0.275963	−	0.231560i	0.494293	−	0.869295i	$-0.335427\pi$
$547$	−6.45422	−	5.41574i	−0.275963	−	0.231560i	−0.770256	+	0.637735i	$0.779871\pi$
$548$	43.4886	−	6.31944i	1.85774	−	0.269953i
$549$		0			0
$550$	1.39984	−	1.35815i	0.0596894	−	0.0579117i
$551$	−0.740029	+	2.54572i	−0.0315263	+	0.108451i
$552$		0			0
$553$	15.1173	−	41.5345i	0.642854	−	1.76623i
$554$	−4.27136	+	5.90802i	−0.181473	+	0.251008i
$555$		0			0
$556$	−18.8804	+	14.8937i	−0.800709	+	0.631634i
$557$	3.70739	−	21.0256i	0.157087	−	0.890884i	−0.799766	−	0.600312i	$-0.795043\pi$
$557$	3.70739	−	21.0256i	0.157087	−	0.890884i	0.956853	−	0.290573i	$-0.0938458\pi$
$558$		0			0
$559$	1.93908	+	3.35859i	0.0820144	+	0.142053i
$560$	16.2263	+	54.6534i	0.685685	+	2.30953i
$561$		0			0
$562$	34.6046	+	9.83521i	1.45971	+	0.414874i
$563$	−17.4354	+	30.1990i	−0.734815	+	1.27274i	0.219990	+	0.975502i	$0.429398\pi$
$563$	−17.4354	+	30.1990i	−0.734815	+	1.27274i	−0.954804	+	0.297235i	$0.903936\pi$
$564$		0			0
$565$	30.2634	+	36.0665i	1.27319	+	1.51733i
$566$	1.69201	−	0.122293i	0.0711204	−	0.00514036i
$567$		0			0
$568$	6.93170	−	2.85731i	0.290847	−	0.119890i
$569$		−	24.0150i		−	1.00676i	−0.864064	−	0.503382i	$-0.832089\pi$
$569$		−	24.0150i		−	1.00676i	0.864064	−	0.503382i	$-0.167911\pi$
$570$		0			0
$571$		−	31.2136i		−	1.30625i	−0.757250	−	0.653125i	$-0.773458\pi$
$571$		−	31.2136i		−	1.30625i	0.757250	−	0.653125i	$-0.226542\pi$
$572$	−0.639281	+	1.60383i	−0.0267297	+	0.0670594i
$573$		0			0
$574$	3.28781	+	45.4892i	0.137231	+	1.89868i
$575$	−33.9535	−	40.4642i	−1.41596	−	1.68748i
$576$		0			0
$577$	9.86003	−	17.0781i	0.410478	−	0.710969i	−0.584464	−	0.811420i	$-0.698695\pi$
$577$	9.86003	−	17.0781i	0.410478	−	0.710969i	0.994942	+	0.100451i	$0.0320284\pi$
$578$	−4.69208	+	16.5088i	−0.195165	+	0.686677i
$579$		0			0
$580$	−4.53276	+	1.49625i	−0.188213	+	0.0621286i
$581$	4.03886	+	6.99551i	0.167560	+	0.290223i
$582$		0			0
$583$	−0.0242381	+	0.137461i	−0.00100384	+	0.00569307i
$584$	2.02532	−	15.1829i	0.0838083	−	0.628273i
$585$		0			0
$586$	−3.00317	−	2.17122i	−0.124060	−	0.0896922i
$587$	7.48674	−	20.5697i	0.309011	−	0.849000i	−0.683839	−	0.729633i	$-0.739691\pi$
$587$	7.48674	−	20.5697i	0.309011	−	0.849000i	0.992850	−	0.119368i	$-0.0380867\pi$
$588$		0			0
$589$	5.79907	−	2.55662i	0.238947	−	0.105344i
$590$	−22.2529	−	22.9360i	−0.916136	−	0.944259i
$591$		0			0
$592$	−11.2920	+	1.29373i	−0.464100	+	0.0531718i
$593$	−36.0079	−	30.2142i	−1.47867	−	1.24075i	−0.907592	−	0.419853i	$-0.862082\pi$
$593$	−36.0079	−	30.2142i	−1.47867	−	1.24075i	−0.571076	−	0.820897i	$-0.693474\pi$
$594$		0			0
$595$	30.9568	+	5.45852i	1.26910	+	0.223777i
$596$	−1.36835	−	0.846169i	−0.0560498	−	0.0346604i
$597$		0			0
$598$	42.0747	+	20.3996i	1.72056	+	0.834200i
$599$	26.9051	−	9.79267i	1.09931	−	0.400118i	0.272251	−	0.962226i	$-0.412232\pi$
$599$	26.9051	−	9.79267i	1.09931	−	0.400118i	0.827063	+	0.562109i	$0.190010\pi$
$600$		0			0
$601$	−18.3472	−	10.5928i	−0.748399	−	0.432089i	0.0767159	−	0.997053i	$-0.475557\pi$
$601$	−18.3472	−	10.5928i	−0.748399	−	0.432089i	−0.825115	+	0.564964i	$0.808890\pi$
$602$	−2.53320	+	1.71730i	−0.103245	+	0.0699917i
$603$		0			0
$604$	5.07469	−	5.68929i	0.206486	−	0.231494i
$605$	−7.48361	−	42.4416i	−0.304252	−	1.72550i
$606$		0			0
$607$	−21.9349			−0.890312			−0.445156	−	0.895453i	$-0.646852\pi$
$607$	−21.9349			−0.890312			−0.445156	+	0.895453i	$0.646852\pi$
$608$	24.5425	+	2.38008i	0.995331	+	0.0965248i
$609$		0			0
$610$	15.1090	+	33.7229i	0.611744	+	1.36540i
$611$	−5.11356	−	29.0005i	−0.206873	−	1.17323i
$612$		0			0
$613$	2.11675	−	1.77616i	0.0854947	−	0.0717385i	−0.599039	−	0.800720i	$-0.704450\pi$
$613$	2.11675	−	1.77616i	0.0854947	−	0.0717385i	0.684533	+	0.728982i	$0.260006\pi$
$614$	24.2963	−	16.4708i	0.980518	−	0.664708i
$615$		0			0
$616$	−1.29872	−	0.411932i	−0.0523271	−	0.0165972i
$617$	6.28411	−	2.28723i	0.252989	−	0.0920803i	−0.212413	−	0.977180i	$-0.568132\pi$
$617$	6.28411	−	2.28723i	0.252989	−	0.0920803i	0.465401	+	0.885100i	$0.345910\pi$
$618$		0			0
$619$	−22.3047	+	12.8776i	−0.896501	+	0.517595i	−0.876063	−	0.482196i	$-0.839839\pi$
$619$	−22.3047	+	12.8776i	−0.896501	+	0.517595i	−0.0204377	+	0.999791i	$0.506506\pi$
$620$	9.70523	+	6.00158i	0.389771	+	0.241029i
$621$		0			0
$622$	1.25103	−	12.1766i	0.0501617	−	0.488236i
$623$	−16.5706	−	13.9044i	−0.663887	−	0.557067i
$624$		0			0
$625$	−29.2626	−	10.6507i	−1.17050	−	0.426028i
$626$	17.1126	+	17.6379i	0.683959	+	0.704954i
$627$		0			0
$628$	0.401680	−	13.2833i	0.0160288	−	0.530060i
$629$	−2.14338	+	5.88890i	−0.0854624	+	0.234806i
$630$		0			0
$631$	−15.7619	+	18.7844i	−0.627473	+	0.747793i	−0.982336	−	0.187125i	$-0.940083\pi$
$631$	−15.7619	+	18.7844i	−0.627473	+	0.747793i	0.354863	+	0.934918i	$0.384528\pi$
$632$	4.55113	−	34.1178i	0.181034	−	1.35713i
$633$		0			0
$634$	6.42369	+	25.5098i	0.255117	+	1.01312i
$635$	−26.8688	−	46.5382i	−1.06626	−	1.84681i
$636$		0			0
$637$	−13.7851	−	37.8741i	−0.546184	−	1.50063i
$638$	0.0311871	−	0.109730i	0.00123471	−	0.00434425i
$639$		0			0
$640$	21.4816	+	38.8533i	0.849136	+	1.53581i
$641$	16.9399	+	20.1881i	0.669084	+	0.797384i	0.988659	−	0.150177i	$-0.0479845\pi$
$641$	16.9399	+	20.1881i	0.669084	+	0.797384i	−0.319575	+	0.947561i	$0.603540\pi$
$642$		0			0
$643$	−14.9537	+	2.63675i	−0.589718	+	0.103983i	−0.460541	−	0.887638i	$-0.652345\pi$
$643$	−14.9537	+	2.63675i	−0.589718	+	0.103983i	−0.129177	+	0.991622i	$0.541234\pi$
$644$	−13.6627	+	34.2771i	−0.538387	+	1.35071i
$645$		0			0
$646$	7.21960	−	11.5202i	0.284052	−	0.453257i
$647$		−	32.4651i		−	1.27634i	−0.769897	−	0.638168i	$-0.779692\pi$
$647$		−	32.4651i		−	1.27634i	0.769897	−	0.638168i	$-0.220308\pi$
$648$		0			0
$649$	0.752124	−	0.132620i	0.0295235	−	0.00520578i
$650$	95.4734	−	6.90051i	3.74477	−	0.270660i
$651$		0			0
$652$	−5.73416	+	27.6114i	−0.224567	+	1.08135i
$653$	−19.3262	+	33.4739i	−0.756292	+	1.30994i	0.188437	+	0.982085i	$0.439658\pi$
$653$	−19.3262	+	33.4739i	−0.756292	+	1.30994i	−0.944729	+	0.327851i	$0.893676\pi$
$654$		0			0
$655$	2.80835	+	7.71589i	0.109731	+	0.301485i
$656$	10.1085	+	34.0473i	0.394669	+	1.32933i
$657$		0			0
$658$	22.5351	−	5.67462i	0.878508	−	0.221220i
$659$	−5.95369	+	33.7650i	−0.231923	+	1.31530i	0.617076	+	0.786904i	$0.288317\pi$
$659$	−5.95369	+	33.7650i	−0.231923	+	1.31530i	−0.848998	+	0.528396i	$0.822794\pi$
$660$		0			0
$661$	17.5522	−	20.9178i	0.682700	−	0.813610i	−0.307752	−	0.951466i	$-0.599577\pi$
$661$	17.5522	−	20.9178i	0.682700	−	0.813610i	0.990452	+	0.137857i	$0.0440213\pi$
$662$	2.81658	−	3.89581i	0.109469	−	0.151415i
$663$		0			0
$664$	4.24177	+	4.64502i	0.164612	+	0.180262i
$665$	55.7393	+	27.4379i	2.16148	+	1.06400i
$666$		0			0
$667$	−2.90315	−	1.05666i	−0.112411	−	0.0409141i
$668$	−1.37097	+	0.199219i	−0.0530443	+	0.00770801i
$669$		0			0
$670$	−78.2947	−	8.04406i	−3.02479	−	0.310769i
$671$	−0.869704	−	0.153352i	−0.0335746	−	0.00592010i
$672$		0			0
$673$	21.6909	−	12.5232i	0.836122	−	0.482735i	−0.0198220	−	0.999804i	$-0.506310\pi$
$673$	21.6909	−	12.5232i	0.836122	−	0.482735i	0.855944	+	0.517068i	$0.172977\pi$
$674$	14.3845	−	29.6684i	0.554068	−	1.14278i
$675$		0			0
$676$	−51.7305	+	27.8167i	−1.98963	+	1.06987i
$677$	−12.0827	−	6.97595i	−0.464376	−	0.268108i	0.249506	−	0.968373i	$-0.419732\pi$
$677$	−12.0827	−	6.97595i	−0.464376	−	0.268108i	−0.713883	+	0.700265i	$0.753065\pi$
$678$		0			0
$679$	−35.9852	+	30.1951i	−1.38098	+	1.15878i
$680$	24.4574	−	1.02588i	0.937899	−	0.0393407i
$681$		0			0
$682$	−0.248870	+	0.111502i	−0.00952971	+	0.00426963i
$683$	−37.7081			−1.44286			−0.721430	−	0.692487i	$-0.756515\pi$
$683$	−37.7081			−1.44286			−0.721430	+	0.692487i	$0.756515\pi$
$684$		0			0
$685$	86.2235			3.29443
$686$	−3.78696	+	1.69668i	−0.144587	+	0.0647797i
$687$		0			0
$688$	−1.63944	+	1.72977i	−0.0625030	+	0.0659470i
$689$	−5.24771	+	4.40335i	−0.199922	+	0.167754i
$690$		0			0
$691$	−4.34115	−	2.50636i	−0.165145	−	0.0953465i	0.415150	−	0.909753i	$-0.363729\pi$
$691$	−4.34115	−	2.50636i	−0.165145	−	0.0953465i	−0.580295	+	0.814407i	$0.697063\pi$
$692$	−0.588372	−	1.09419i	−0.0223665	−	0.0415949i
$693$		0			0
$694$	3.07907	−	6.35067i	0.116880	−	0.241068i
$695$	−40.8618	+	23.5916i	−1.54998	+	0.894880i
$696$		0			0
$697$	19.2851	+	3.40049i	0.730476	+	0.128803i
$698$	3.84652	+	0.395195i	0.145593	+	0.0149583i
$699$		0			0
$700$	10.8626	+	74.7536i	0.410569	+	2.82542i
$701$	43.1668	+	15.7114i	1.63039	+	0.593413i	0.985321	−	0.170713i	$-0.0546072\pi$
$701$	43.1668	+	15.7114i	1.63039	+	0.593413i	0.645067	+	0.764126i	$0.276829\pi$
$702$		0			0
$703$	−7.31663	+	9.99365i	−0.275952	+	0.376917i
$704$	−1.05665	−	0.0960922i	−0.0398240	−	0.00362161i
$705$		0			0
$706$	−23.3725	+	32.3282i	−0.879636	+	1.21669i
$707$	−10.2662	+	12.2347i	−0.386099	+	0.460134i
$708$		0			0
$709$	6.04085	−	34.2593i	0.226869	−	1.28664i	−0.632211	−	0.774796i	$-0.717853\pi$
$709$	6.04085	−	34.2593i	0.226869	−	1.28664i	0.859080	−	0.511841i	$-0.171036\pi$
$710$	14.2653	−	3.59218i	0.535366	−	0.134812i
$711$		0			0
$712$	−14.9284	−	7.80374i	−0.559465	−	0.292457i
$713$	2.52602	+	6.94019i	0.0946002	+	0.259912i
$714$		0			0
$715$	−1.69379	+	2.93373i	−0.0633442	+	0.109715i
$716$	−13.6835	−	2.84170i	−0.511376	−	0.106199i
$717$		0			0
$718$	39.3528	−	2.84430i	1.46863	−	0.106148i
$719$	−33.2913	+	5.87015i	−1.24156	+	0.218920i	−0.755582	−	0.655054i	$-0.772646\pi$
$719$	−33.2913	+	5.87015i	−1.24156	+	0.218920i	−0.485973	+	0.873974i	$0.661535\pi$
$720$		0			0
$721$			23.0059i			0.856785i
$722$	20.0572	−	17.8804i	0.746451	−	0.665440i
$723$		0			0
$724$	−7.92362	−	3.15833i	−0.294479	−	0.117378i
$725$	−6.22848	+	1.09825i	−0.231320	+	0.0407880i
$726$		0			0
$727$	14.3441	+	17.0946i	0.531993	+	0.634004i	0.963373	−	0.268166i	$-0.0864176\pi$
$727$	14.3441	+	17.0946i	0.531993	+	0.634004i	−0.431380	+	0.902170i	$0.641973\pi$
$728$	−35.8316	−	56.4574i	−1.32801	−	2.09245i
$729$		0			0
$730$	8.21635	−	28.9087i	0.304101	−	1.06996i
$731$	0.449433	+	1.23481i	0.0166229	+	0.0456710i
$732$		0			0
$733$	−7.18916	−	12.4520i	−0.265538	−	0.459925i	0.702167	−	0.712013i	$-0.252216\pi$
$733$	−7.18916	−	12.4520i	−0.265538	−	0.459925i	−0.967704	+	0.252088i	$0.918883\pi$
$734$	12.9231	+	51.3203i	0.477000	+	1.89427i
$735$		0			0
$736$	−4.65861	+	28.3548i	−0.171719	+	1.04517i
$737$	1.20907	−	1.44092i	0.0445367	−	0.0530768i
$738$		0			0
$739$	−17.1003	+	46.9828i	−0.629046	+	1.72829i	0.0546341	+	0.998506i	$0.482601\pi$
$739$	−17.1003	+	46.9828i	−0.629046	+	1.72829i	−0.683680	+	0.729782i	$0.739621\pi$
$740$	−22.2905	−	0.674052i	−0.819414	−	0.0247787i
$741$		0			0
$742$	−3.76436	−	3.87992i	−0.138194	−	0.142436i
$743$	22.4570	+	8.17366i	0.823866	+	0.299863i	0.719339	−	0.694659i	$-0.244445\pi$
$743$	22.4570	+	8.17366i	0.823866	+	0.299863i	0.104527	+	0.994522i	$0.466667\pi$
$744$		0			0
$745$	−2.41814	−	2.02906i	−0.0885938	−	0.0743390i
$746$	−0.974100	+	9.48114i	−0.0356643	+	0.347129i
$747$		0			0
$748$	−0.307685	+	0.497562i	−0.0112501	+	0.0181927i
$749$	−17.3748	+	10.0313i	−0.634861	+	0.366537i
$750$		0			0
$751$	37.5314	−	13.6603i	1.36954	−	0.498472i	0.450550	−	0.892751i	$-0.351228\pi$
$751$	37.5314	−	13.6603i	1.36954	−	0.498472i	0.918991	+	0.394280i	$0.129006\pi$
$752$	16.1902	−	8.08479i	0.590396	−	0.294822i
$753$		0			0
$754$	4.63413	−	3.14155i	0.168765	−	0.114408i
$755$	11.4586	−	9.61492i	0.417022	−	0.349923i
$756$		0			0
$757$	5.21920	+	29.5995i	0.189695	+	1.07581i	0.919773	+	0.392450i	$0.128372\pi$
$757$	5.21920	+	29.5995i	0.189695	+	1.07581i	−0.730078	+	0.683363i	$0.760517\pi$
$758$	−17.7496	−	39.6168i	−0.644696	−	1.43895i
$759$		0			0
$760$	46.9819	+	11.5460i	1.70421	+	0.418817i
$761$	9.55210			0.346263			0.173132	−	0.984899i	$-0.444611\pi$
$761$	9.55210			0.346263			0.173132	+	0.984899i	$0.444611\pi$
$762$		0			0
$763$	−7.68710	−	43.5957i	−0.278292	−	1.57827i
$764$	−34.1178	−	30.4321i	−1.23434	−	1.10100i
$765$		0			0
$766$	−31.6342	+	21.4453i	−1.14299	+	0.774852i
$767$	32.4605	+	18.7411i	1.17208	+	0.676701i
$768$		0			0
$769$	28.5462	−	10.3900i	1.02940	−	0.374671i	0.228548	−	0.973533i	$-0.426602\pi$
$769$	28.5462	−	10.3900i	1.02940	−	0.374671i	0.800853	+	0.598861i	$0.204380\pi$
$770$	−2.40547	−	1.16627i	−0.0866871	−	0.0420295i
$771$		0			0
$772$	11.8293	−	19.1293i	0.425746	−	0.688480i
$773$	−0.589119	−	0.103878i	−0.0211891	−	0.00373622i	0.163044	−	0.986619i	$-0.447869\pi$
$773$	−0.589119	−	0.103878i	−0.0211891	−	0.00373622i	−0.184233	+	0.982883i	$0.558980\pi$
$774$		0			0
$775$	11.5821	+	9.71850i	0.416040	+	0.349099i
$776$	−22.3188	+	28.9836i	−0.801200	+	1.04045i
$777$		0			0
$778$	−36.0815	−	37.1890i	−1.29358	−	1.33329i
$779$	34.7238	+	17.0930i	1.24411	+	0.612419i
$780$		0			0
$781$	−0.120241	+	0.330360i	−0.00430257	+	0.0118212i
$782$	12.8395	+	9.28265i	0.459139	+	0.331947i
$783$		0			0
$784$	19.9011	−	14.7453i	0.710754	−	0.526619i
$785$	4.52780	−	25.6784i	0.161604	−	0.916502i
$786$		0			0
$787$	−0.962577	−	1.66723i	−0.0343122	−	0.0594304i	0.848359	−	0.529421i	$-0.177591\pi$
$787$	−0.962577	−	1.66723i	−0.0343122	−	0.0594304i	−0.882672	+	0.469990i	$0.844257\pi$
$788$	−6.82032	−	20.6615i	−0.242964	−	0.736036i
$789$		0			0
$790$	18.4631	−	64.9614i	0.656888	−	2.31122i
$791$	21.7888	−	37.7394i	0.774722	−	1.34186i
$792$		0			0
$793$	−27.8596	−	33.2017i	−0.989322	−	1.17903i
$794$	−1.30447	−	18.0483i	−0.0462940	−	0.640510i
$795$		0			0
$796$	−32.4475	−	12.9335i	−1.15007	−	0.458415i
$797$			4.78646i			0.169545i	0.996400	+	0.0847726i	$0.0270164\pi$
$797$			4.78646i			0.169545i	−0.996400	+	0.0847726i	$0.972984\pi$
$798$		0			0
$799$		−	9.97794i		−	0.352994i
$800$	20.7639	+	55.0378i	0.734116	+	1.94588i
$801$		0			0
$802$	18.6547	−	1.34830i	0.658721	−	0.0476102i
$803$	0.461676	+	0.550204i	0.0162922	+	0.0194163i
$804$		0			0
$805$	−36.1998	+	62.6998i	−1.27587	+	2.20988i
$806$	−12.8740	−	3.65900i	−0.453467	−	0.128883i
$807$		0			0
$808$	−5.76181	+	11.0222i	−0.202700	+	0.387760i
$809$	2.53018	+	4.38240i	0.0889564	+	0.154077i	0.907070	−	0.420979i	$-0.138313\pi$
$809$	2.53018	+	4.38240i	0.0889564	+	0.154077i	−0.818114	+	0.575056i	$0.804980\pi$
$810$		0			0
$811$	−1.72377	+	9.77601i	−0.0605299	+	0.343282i	0.939470	+	0.342631i	$0.111318\pi$
$811$	−1.72377	+	9.77601i	−0.0605299	+	0.343282i	−1.00000		0.000650628i	$0.999793\pi$
$812$	2.73631	+	3.46876i	0.0960256	+	0.121730i
$813$		0			0
$814$	0.312253	−	0.431900i	0.0109445	−	0.0151381i
$815$	−18.9244	+	51.9943i	−0.662893	+	1.82128i
$816$		0			0
$817$	0.171715	+	2.59140i	0.00600756	+	0.0906617i
$818$	−26.2247	+	25.4437i	−0.916926	+	0.889618i
$819$		0			0
$820$	10.0209	+	68.9608i	0.349944	+	2.40822i
$821$	−3.44782	−	2.89307i	−0.120330	−	0.100969i	0.580637	−	0.814162i	$-0.302804\pi$
$821$	−3.44782	−	2.89307i	−0.120330	−	0.100969i	−0.700967	+	0.713194i	$0.747248\pi$
$822$		0			0
$823$	−15.1795	−	2.67655i	−0.529124	−	0.0932988i	−0.0972972	−	0.995255i	$-0.531020\pi$
$823$	−15.1795	−	2.67655i	−0.529124	−	0.0932988i	−0.431827	+	0.901957i	$0.642131\pi$
$824$	3.84766	+	17.4974i	0.134039	+	0.609550i
$825$		0			0
$826$	−12.9043	+	26.6155i	−0.448998	+	0.926071i
$827$	48.1339	−	17.5193i	1.67378	−	0.609206i	0.681344	−	0.731963i	$-0.261396\pi$
$827$	48.1339	−	17.5193i	1.67378	−	0.609206i	0.992437	+	0.122757i	$0.0391735\pi$
$828$		0			0
$829$	−26.3220	−	15.1970i	−0.914201	−	0.527814i	−0.0324208	−	0.999474i	$-0.510322\pi$
$829$	−26.3220	−	15.1970i	−0.914201	−	0.527814i	−0.881781	+	0.471660i	$0.843655\pi$
$830$	6.92552	+	10.2159i	0.240388	+	0.354599i
$831$		0			0
$832$	−36.6944	−	36.9465i	−1.27215	−	1.28089i
$833$	−2.37145	−	13.4492i	−0.0821659	−	0.465986i
$834$		0			0
$835$	−2.71818			−0.0940664
$836$	−0.858435	+	0.774541i	−0.0296896	+	0.0267880i
$837$		0			0
$838$	25.5601	−	11.4518i	0.882960	−	0.395595i
$839$	1.97933	+	11.2253i	0.0683340	+	0.387541i	0.999723	+	0.0235170i	$0.00748638\pi$
$839$	1.97933	+	11.2253i	0.0683340	+	0.387541i	−0.931389	+	0.364024i	$0.881403\pi$
$840$		0			0
$841$	21.9319	−	18.4031i	0.756273	−	0.634588i
$842$	−14.2289	−	20.9892i	−0.490360	−	0.723334i
$843$		0			0
$844$	19.3530	−	10.4065i	0.666158	−	0.358208i
$845$	−108.292	+	39.4151i	−3.72536	+	1.35592i
$846$		0			0
$847$	−34.5450	+	19.9446i	−1.18698	+	0.685304i
$848$	−3.51192	−	2.32133i	−0.120600	−	0.0797149i
$849$		0			0
$850$	32.2642	+	3.31485i	1.10665	+	0.113698i
$851$	−11.0569	−	9.27785i	−0.379026	−	0.318041i
$852$		0			0
$853$	−18.9117	−	6.88330i	−0.647525	−	0.235680i	−0.00268364	−	0.999996i	$-0.500854\pi$
$853$	−18.9117	−	6.88330i	−0.647525	−	0.235680i	−0.644841	+	0.764317i	$0.723076\pi$
$854$	24.5479	−	23.8168i	0.840010	−	0.814993i
$855$		0			0
$856$	−11.5369	+	10.5353i	−0.394322	+	0.360089i
$857$	3.92157	−	10.7744i	0.133958	−	0.368047i	−0.854518	−	0.519421i	$-0.826148\pi$
$857$	3.92157	−	10.7744i	0.133958	−	0.368047i	0.988477	+	0.151374i	$0.0483698\pi$
$858$		0			0
$859$	12.4652	−	14.8554i	0.425307	−	0.506861i	−0.510255	−	0.860023i	$-0.670449\pi$
$859$	12.4652	−	14.8554i	0.425307	−	0.506861i	0.935562	+	0.353162i	$0.114894\pi$
$860$	−3.67130	+	2.89608i	−0.125190	+	0.0987556i
$861$		0			0
$862$	3.62764	−	0.913486i	0.123558	−	0.0311135i
$863$	20.4555	+	35.4300i	0.696314	+	1.20605i	0.969736	+	0.244158i	$0.0785114\pi$
$863$	20.4555	+	35.4300i	0.696314	+	1.20605i	−0.273421	+	0.961894i	$0.588155\pi$
$864$		0			0
$865$	−0.833699	−	2.29057i	−0.0283466	−	0.0778817i
$866$	10.9281	+	3.10596i	0.371353	+	0.105545i
$867$		0			0
$868$	2.14758	−	10.3411i	0.0728938	−	0.351001i
$869$	1.03744	+	1.23637i	0.0351928	+	0.0419411i
$870$		0			0
$871$	90.9123	−	16.0303i	3.08045	−	0.543166i
$872$	−13.1377	−	31.8715i	−0.444899	−	1.07931i
$873$		0			0
$874$	19.2460	+	24.7003i	0.651006	+	0.835501i
$875$			76.9476i			2.60131i
$876$		0			0
$877$	−27.1451	+	4.78640i	−0.916623	+	0.161625i	−0.612009	−	0.790851i	$-0.709639\pi$
$877$	−27.1451	+	4.78640i	−0.916623	+	0.161625i	−0.304614	+	0.952476i	$0.598527\pi$
$878$	−1.74131	−	24.0923i	−0.0587665	−	0.813076i
$879$		0			0
$880$	−2.02456	−	0.484713i	−0.0682478	−	0.0163397i
$881$	23.1999	−	40.1834i	0.781625	−	1.35381i	−0.149370	−	0.988781i	$-0.547725\pi$
$881$	23.1999	−	40.1834i	0.781625	−	1.35381i	0.930995	−	0.365033i	$-0.118942\pi$
$882$		0			0
$883$	−6.23517	−	17.1310i	−0.209830	−	0.576504i	0.789475	−	0.613783i	$-0.210353\pi$
$883$	−6.23517	−	17.1310i	−0.209830	−	0.576504i	−0.999305	+	0.0372793i	$0.988131\pi$
$884$	−27.2641	+	8.99983i	−0.916992	+	0.302697i
$885$		0			0
$886$	9.72010	+	38.6005i	0.326553	+	1.29681i
$887$	2.78945	−	15.8197i	0.0936605	−	0.531175i	−0.901489	−	0.432802i	$-0.857525\pi$
$887$	2.78945	−	15.8197i	0.0936605	−	0.531175i	0.995150	−	0.0983733i	$-0.0313639\pi$
$888$		0			0
$889$	−31.9713	+	38.1020i	−1.07228	+	1.27790i
$890$	−26.7842	−	19.3643i	−0.897808	−	0.649093i
$891$		0			0
$892$	−0.249546	+	8.25233i	−0.00835543	+	0.276308i
$893$	5.50474	−	18.9364i	0.184209	−	0.633683i
$894$		0			0
$895$	−25.7670	−	9.37844i	−0.861297	−	0.313487i
$896$	26.9928	−	30.9836i	0.901765	−	1.03509i
$897$		0			0
$898$	0.468902	−	4.56393i	0.0156475	−	0.152300i
$899$	0.870863	+	0.153557i	0.0290449	+	0.00512140i
$900$		0			0
$901$	−2.01017	+	1.16057i	−0.0669686	+	0.0386643i
$902$	−1.49853	−	0.726550i	−0.0498957	−	0.0241915i
$903$		0			0
$904$	10.2599	−	32.3471i	0.341241	−	1.07585i
$905$	−14.4939	−	8.36808i	−0.481795	−	0.278164i
$906$		0			0
$907$	−15.3909	+	12.9145i	−0.511046	+	0.428819i	−0.861497	−	0.507762i	$-0.830473\pi$
$907$	−15.3909	+	12.9145i	−0.511046	+	0.428819i	0.350451	+	0.936581i	$0.386028\pi$
$908$	30.2635	−	33.9287i	1.00433	−	1.12596i
$909$		0			0
$910$	−53.6437	−	119.732i	−1.77827	−	3.96906i
$911$	−47.7221			−1.58110			−0.790552	−	0.612395i	$-0.790206\pi$
$911$	−47.7221			−1.58110			−0.790552	+	0.612395i	$0.790206\pi$
$912$		0			0
$913$	−0.294959			−0.00976172
$914$	−4.43967	−	9.90925i	−0.146851	−	0.327769i
$915$		0			0
$916$	5.73508	−	6.42966i	0.189492	−	0.212442i
$917$	5.82195	−	4.88520i	0.192258	−	0.161323i
$918$		0			0
$919$	−10.5468	−	6.08921i	−0.347907	−	0.200864i	0.315856	−	0.948807i	$-0.397708\pi$
$919$	−10.5468	−	6.08921i	−0.347907	−	0.200864i	−0.663763	+	0.747943i	$0.731042\pi$
$920$	−17.0458	+	53.7412i	−0.561982	+	1.77180i
$921$		0			0
$922$	21.5163	+	10.4320i	0.708603	+	0.343560i
$923$	−14.9424	+	8.62698i	−0.491834	+	0.283960i
$924$		0			0
$925$	−29.0990	−	5.13094i	−0.956769	−	0.168704i
$926$	−5.51371	+	53.6662i	−0.181192	+	1.76358i
$927$		0			0
$928$	2.66126	+	2.18056i	0.0873602	+	0.0715804i
$929$	−3.57159	−	1.29995i	−0.117180	−	0.0426500i	0.282765	−	0.959189i	$-0.408748\pi$
$929$	−3.57159	−	1.29995i	−0.117180	−	0.0426500i	−0.399945	+	0.916539i	$0.630971\pi$
$930$		0			0
$931$	2.91917	−	26.8325i	0.0956720	−	0.879401i
$932$	−0.222997	+	7.37437i	−0.00730451	+	0.241555i
$933$		0			0
$934$	−6.22774	−	4.50251i	−0.203778	−	0.147327i
$935$	−0.737810	+	0.879288i	−0.0241290	+	0.0287558i
$936$		0			0
$937$	9.15393	−	51.9145i	0.299046	−	1.69597i	−0.351242	−	0.936285i	$-0.614240\pi$
$937$	9.15393	−	51.9145i	0.299046	−	1.69597i	0.650287	−	0.759688i	$-0.274648\pi$
$938$	17.7891	+	70.6442i	0.580836	+	2.30662i
$939$		0			0
$940$	33.7172	−	11.1300i	1.09973	−	0.363019i
$941$	9.21031	+	25.3051i	0.300247	+	0.824923i	0.994456	+	0.105149i	$0.0335321\pi$
$941$	9.21031	+	25.3051i	0.300247	+	0.824923i	−0.694209	+	0.719773i	$0.744246\pi$
$942$		0			0
$943$	−22.5513	+	39.0600i	−0.734372	+	1.27197i
$944$	−5.36314	+	22.4008i	−0.174555	+	0.729086i
$945$		0			0
$946$	−0.00805604	−	0.111461i	−0.000261925	−	0.00362391i
$947$	29.9433	−	5.27981i	0.973027	−	0.171571i	0.335535	−	0.942028i	$-0.391083\pi$
$947$	29.9433	−	5.27981i	0.973027	−	0.171571i	0.637492	+	0.770457i	$0.279972\pi$
$948$		0			0
$949$			35.2498i			1.14426i
$950$	59.4032	+	24.0909i	1.92729	+	0.781612i
$951$		0			0
$952$	−8.63469	−	20.9474i	−0.279852	−	0.678908i
$953$	−27.5664	+	4.86069i	−0.892962	+	0.157453i	−0.601258	−	0.799055i	$-0.705333\pi$
$953$	−27.5664	+	4.86069i	−0.892962	+	0.157453i	−0.291704	+	0.956509i	$0.594222\pi$
$954$		0			0
$955$	−57.6591	−	68.7155i	−1.86581	−	2.22358i
$956$	−7.40055	+	35.6355i	−0.239351	+	1.15253i
$957$		0			0
$958$	27.0373	+	7.68444i	0.873534	+	0.248273i
$959$	−27.2955	−	74.9939i	−0.881419	−	2.42168i
$960$		0			0
$961$	14.4430	+	25.0160i	0.465904	+	0.806969i
$962$	25.3645	−	6.38710i	0.817783	−	0.205928i
$963$		0			0
$964$	−1.09838	+	0.866454i	−0.0353766	+	0.0279066i
$965$	28.3659	−	33.8052i	0.913132	−	1.08823i
$966$		0			0
$967$	4.63867	−	12.7446i	0.149169	−	0.409840i	−0.842492	−	0.538709i	$-0.818912\pi$
$967$	4.63867	−	12.7446i	0.149169	−	0.409840i	0.991662	+	0.128869i	$0.0411346\pi$
$968$	−22.9379	+	20.9466i	−0.737252	+	0.673249i
$969$		0			0
$970$	−51.5135	+	49.9793i	−1.65400	+	1.60474i
$971$	9.79356	+	3.56457i	0.314290	+	0.114392i	0.494349	−	0.869264i	$-0.335406\pi$
$971$	9.79356	+	3.56457i	0.314290	+	0.114392i	−0.180059	+	0.983656i	$0.557629\pi$
$972$		0			0
$973$	33.4546	+	28.0717i	1.07250	+	0.899938i
$974$	−55.9585	−	5.74922i	−1.79303	−	0.184217i
$975$		0			0
$976$	14.6868	−	22.2196i	0.470114	−	0.711232i
$977$	−29.6369	+	17.1109i	−0.948168	+	0.547425i	−0.892511	−	0.451025i	$-0.851059\pi$
$977$	−29.6369	+	17.1109i	−0.948168	+	0.547425i	−0.0556569	+	0.998450i	$0.517725\pi$
$978$		0			0
$979$	0.742237	−	0.270152i	0.0237220	−	0.00863410i
$980$	42.8018	−	23.0155i	1.36725	−	0.735203i
$981$		0			0
$982$	21.1501	+	31.1987i	0.674927	+	0.995591i
$983$	32.8104	−	27.5312i	1.04649	−	0.878109i	0.0537697	−	0.998553i	$-0.482876\pi$
$983$	32.8104	−	27.5312i	1.04649	−	0.878109i	0.992720	+	0.120444i	$0.0384319\pi$
$984$		0			0
$985$	−7.41318	−	42.0422i	−0.236204	−	1.33958i
$986$	1.73119	−	0.775630i	0.0551323	−	0.0247011i
$987$		0			0
$988$	−56.7078	+	2.03876i	−1.80412	+	0.0648616i
$989$	−3.02653			−0.0962380
$990$		0			0
$991$	−6.48293	−	36.7665i	−0.205937	−	1.16793i	−0.895959	−	0.444138i	$-0.853510\pi$
$991$	−6.48293	−	36.7665i	−0.205937	−	1.16793i	0.690022	−	0.723789i	$-0.257601\pi$
$992$	−0.0961517	−	8.22423i	−0.00305282	−	0.261120i
$993$		0			0
$994$	−7.64025	−	11.2702i	−0.242334	−	0.357469i
$995$	−59.3533	−	34.2676i	−1.88163	−	1.08636i
$996$		0			0
$997$	−24.3330	+	8.85649i	−0.770634	+	0.280488i	−0.697262	−	0.716817i	$-0.745598\pi$
$997$	−24.3330	+	8.85649i	−0.770634	+	0.280488i	−0.0733724	+	0.997305i	$0.523376\pi$
$998$	−1.52179	+	3.13875i	−0.0481716	+	0.0993553i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.91.4		60
3.2	odd	2		228.2.w.b.91.7	yes	60
4.3	odd	2		684.2.cf.c.91.9		60
12.11	even	2		228.2.w.a.91.2	✓	60
19.14	odd	18		684.2.cf.c.451.9		60
57.14	even	18		228.2.w.a.223.2	yes	60
76.71	even	18	inner	684.2.cf.b.451.4		60
228.71	odd	18		228.2.w.b.223.7	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.91.2	✓	60	12.11	even	2
228.2.w.a.223.2	yes	60	57.14	even	18
228.2.w.b.91.7	yes	60	3.2	odd	2
228.2.w.b.223.7	yes	60	228.71	odd	18
684.2.cf.b.91.4		60	1.1	even	1	trivial
684.2.cf.b.451.4		60	76.71	even	18	inner
684.2.cf.c.91.9		60	4.3	odd	2
684.2.cf.c.451.9		60	19.14	odd	18

Overview	Random
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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)

\(f(q)\)	\(=\)	\(q+(-0.578232 - 1.29060i) q^{2} +(-1.33130 + 1.49253i) q^{4} +(-3.00606 + 2.52238i) q^{5} +(3.14549 + 1.81605i) q^{7} +(2.69606 + 0.855142i) q^{8} +(4.99358 + 2.42109i) q^{10} +(-0.114858 + 0.0663132i) q^{11} +(-6.41015 - 1.13028i) q^{13} +(0.524971 - 5.10966i) q^{14} +(-0.455300 - 3.97400i) q^{16} +(-2.07248 - 0.754320i) q^{17} +(-3.51706 - 2.57494i) q^{19} +(0.237219 - 7.84467i) q^{20} +(0.151998 + 0.109891i) q^{22} +(3.26515 - 3.89125i) q^{23} +(1.80573 - 10.2408i) q^{25} +(2.24781 + 8.92650i) q^{26} +(-6.89809 + 2.27704i) q^{28} +(-0.208018 - 0.571524i) q^{29} +(-0.726976 + 1.25916i) q^{31} +(-4.86558 + 2.88551i) q^{32} +(0.224847 + 3.11091i) q^{34} +(-14.0363 + 2.47497i) q^{35} -2.84148i q^{37} +(-1.28954 + 6.02802i) q^{38} +(-10.2615 + 4.22988i) q^{40} +(-8.74416 + 1.54183i) q^{41} +(-0.382981 - 0.456418i) q^{43} +(0.0539353 - 0.259712i) q^{44} +(-6.91006 - 1.96395i) q^{46} +(1.54735 + 4.25131i) q^{47} +(3.09606 + 5.36254i) q^{49} +(-14.2609 + 3.59108i) q^{50} +(10.2208 - 8.06261i) q^{52} +(0.676498 - 0.806218i) q^{53} +(0.178002 - 0.489057i) q^{55} +(6.92744 + 7.58601i) q^{56} +(-0.617326 + 0.598941i) q^{58} +(-5.41120 - 1.96952i) q^{59} +(5.10087 + 4.28014i) q^{61} +(2.04543 + 0.210149i) q^{62} +(6.53746 + 4.61103i) q^{64} +(22.1203 - 12.7711i) q^{65} +(-13.3272 + 4.85072i) q^{67} +(3.88493 - 2.08901i) q^{68} +(11.3104 + 16.6841i) q^{70} +(2.03061 - 1.70388i) q^{71} +(-0.940394 - 5.33324i) q^{73} +(-3.66721 + 1.64303i) q^{74} +(8.52542 - 1.82131i) q^{76} -0.481712 q^{77} +(-2.11318 - 11.9844i) q^{79} +(11.3926 + 10.7976i) q^{80} +(7.04604 + 10.3937i) q^{82} +(1.92603 + 1.11199i) q^{83} +(8.13266 - 2.96005i) q^{85} +(-0.367602 + 0.758190i) q^{86} +(-0.366371 + 0.0805646i) q^{88} +(-5.86514 - 1.03418i) q^{89} +(-18.1104 - 15.1964i) q^{91} +(1.46094 + 10.0537i) q^{92} +(4.59201 - 4.45525i) q^{94} +(17.0674 - 1.13095i) q^{95} +(-4.42348 + 12.1534i) q^{97} +(5.13065 - 7.09657i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 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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