LMFDB - Embedded newform 684.2.cf.b.127.9

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			127.9
Character	$\chi$	$=$	684.127
Dual form			684.2.cf.b.307.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.11501 + 0.869917i) q^{2} +(0.486490 + 1.93993i) q^{4} +(0.379809 + 2.15400i) q^{5} +(3.95398 + 2.28283i) q^{7} +(-1.14514 + 2.58625i) q^{8} +(-1.45031 + 2.73213i) q^{10} +(0.901599 - 0.520538i) q^{11} +(-2.14406 - 5.89076i) q^{13} +(2.42285 + 5.98501i) q^{14} +(-3.52665 + 1.88751i) q^{16} +(-3.60831 + 3.02773i) q^{17} +(0.405875 - 4.33996i) q^{19} +(-3.99384 + 1.78470i) q^{20} +(1.45812 + 0.203911i) q^{22} +(0.497757 + 0.0877679i) q^{23} +(0.202995 - 0.0738841i) q^{25} +(2.73382 - 8.43340i) q^{26} +(-2.50496 + 8.78101i) q^{28} +(1.64993 - 1.96631i) q^{29} +(1.70726 - 2.95706i) q^{31} +(-5.57423 - 0.963299i) q^{32} +(-6.65717 + 0.237020i) q^{34} +(-3.41546 + 9.38391i) q^{35} +5.34518i q^{37} +(4.22796 - 4.48602i) q^{38} +(-6.00571 - 1.48435i) q^{40} +(-1.36033 + 3.73748i) q^{41} +(-1.90224 + 0.335417i) q^{43} +(1.44843 + 1.49580i) q^{44} +(0.478652 + 0.530869i) q^{46} +(2.10734 - 2.51143i) q^{47} +(6.92262 + 11.9903i) q^{49} +(0.290614 + 0.0942071i) q^{50} +(10.3846 - 7.02513i) q^{52} +(-13.2697 - 2.33980i) q^{53} +(1.46367 + 1.74434i) q^{55} +(-10.4318 + 7.61181i) q^{56} +(3.55022 - 0.757153i) q^{58} +(11.0231 - 9.24945i) q^{59} +(0.482765 - 2.73790i) q^{61} +(4.47600 - 1.81197i) q^{62} +(-5.37733 - 5.92320i) q^{64} +(11.8744 - 6.85567i) q^{65} +(10.5415 + 8.84536i) q^{67} +(-7.62899 - 5.52690i) q^{68} +(-11.9715 + 7.49198i) q^{70} +(1.19674 + 6.78706i) q^{71} +(-0.635538 - 0.231317i) q^{73} +(-4.64986 + 5.95993i) q^{74} +(8.61667 - 1.32398i) q^{76} +4.75320 q^{77} +(-6.33497 - 2.30574i) q^{79} +(-5.40516 - 6.87952i) q^{80} +(-4.76808 + 2.98395i) q^{82} +(-5.05030 - 2.91579i) q^{83} +(-7.89220 - 6.62234i) q^{85} +(-2.41280 - 1.28080i) q^{86} +(0.313787 + 2.92784i) q^{88} +(0.179291 + 0.492599i) q^{89} +(4.97003 - 28.1865i) q^{91} +(0.0718903 + 1.00831i) q^{92} +(4.53444 - 0.967059i) q^{94} +(9.50244 - 0.774100i) q^{95} +(-1.40922 - 1.67944i) q^{97} +(-2.71180 + 19.3914i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) $ 60 * q - 3 * q^2 - 3 * q^4 + 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 + 21 * q^16 + 18 * q^19 - 30 * q^20 - 12 * q^22 - 18 * q^28 - 12 * q^31 - 33 * q^32 - 15 * q^34 + 84 * q^38 - 87 * q^40 + 12 * q^41 - 18 * q^43 + 51 * q^44 - 21 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 - 42 * q^56 - 36 * q^58 - 105 * q^62 + 21 * q^64 + 36 * q^65 + 42 * q^67 + 15 * q^68 - 96 * q^70 - 24 * q^71 + 18 * q^73 - 69 * q^74 + 54 * q^76 + 72 * q^77 + 12 * q^79 + 12 * q^80 + 75 * q^82 - 60 * q^85 - 21 * q^86 + 36 * q^88 + 12 * q^89 - 84 * q^91 - 99 * q^92 + 24 * q^95 + 12 * q^97 + 105 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.11501	+	0.869917i	0.788430	+	0.615124i
$2$	1.11501	+	0.869917i	0.788430	+	0.615124i
$3$		0			0
$3$		0			0
$4$	0.486490	+	1.93993i	0.243245	+	0.969965i
$5$	0.379809	+	2.15400i	0.169856	+	0.963299i	0.943916	+	0.330187i	$0.107112\pi$
$5$	0.379809	+	2.15400i	0.169856	+	0.963299i	−0.774060	+	0.633112i	$0.781777\pi$
$6$		0			0
$7$	3.95398	+	2.28283i	1.49446	+	0.862829i	0.999980	−	0.00635858i	$-0.00202401\pi$
$7$	3.95398	+	2.28283i	1.49446	+	0.862829i	0.494483	+	0.869187i	$0.335357\pi$
$8$	−1.14514	+	2.58625i	−0.404867	+	0.914376i
$9$		0			0
$10$	−1.45031	+	2.73213i	−0.458629	+	0.863976i
$11$	0.901599	−	0.520538i	0.271842	−	0.156948i	−0.357882	−	0.933767i	$-0.616501\pi$
$11$	0.901599	−	0.520538i	0.271842	−	0.156948i	0.629725	+	0.776819i	$0.283168\pi$
$12$		0			0
$13$	−2.14406	−	5.89076i	−0.594656	−	1.63380i	−0.761757	−	0.647863i	$-0.775663\pi$
$13$	−2.14406	−	5.89076i	−0.594656	−	1.63380i	0.167101	−	0.985940i	$-0.446559\pi$
$14$	2.42285	+	5.98501i	0.647534	+	1.59956i
$15$		0			0
$16$	−3.52665	+	1.88751i	−0.881663	+	0.471879i
$17$	−3.60831	+	3.02773i	−0.875143	+	0.734332i	−0.965175	−	0.261607i	$-0.915748\pi$
$17$	−3.60831	+	3.02773i	−0.875143	+	0.734332i	0.0900314	+	0.995939i	$0.471303\pi$
$18$		0			0
$19$	0.405875	−	4.33996i	0.0931140	−	0.995655i
$19$	0.405875	−	4.33996i	0.0931140	−	0.995655i
$20$	−3.99384	+	1.78470i	−0.893049	+	0.399072i
$21$		0			0
$22$	1.45812	+	0.203911i	0.310871	+	0.0434739i
$23$	0.497757	+	0.0877679i	0.103789	+	0.0183009i	0.225302	−	0.974289i	$-0.427663\pi$
$23$	0.497757	+	0.0877679i	0.103789	+	0.0183009i	−0.121512	+	0.992590i	$0.538774\pi$
$24$		0			0
$25$	0.202995	−	0.0738841i	0.0405990	−	0.0147768i
$26$	2.73382	−	8.43340i	0.536146	−	1.65393i
$27$		0			0
$28$	−2.50496	+	8.78101i	−0.473392	+	1.65946i
$29$	1.64993	−	1.96631i	0.306385	−	0.365135i	−0.590779	−	0.806834i	$-0.701179\pi$
$29$	1.64993	−	1.96631i	0.306385	−	0.365135i	0.897164	+	0.441698i	$0.145624\pi$
$30$		0			0
$31$	1.70726	−	2.95706i	0.306632	−	0.531103i	−0.670991	−	0.741465i	$-0.734131\pi$
$31$	1.70726	−	2.95706i	0.306632	−	0.531103i	0.977623	+	0.210363i	$0.0674645\pi$
$32$	−5.57423	−	0.963299i	−0.985394	−	0.170289i
$33$		0			0
$34$	−6.65717	+	0.237020i	−1.14169	+	0.0406485i
$35$	−3.41546	+	9.38391i	−0.577319	+	1.58617i
$36$		0			0
$37$			5.34518i			0.878743i	0.898306	+	0.439371i	$0.144799\pi$
$37$			5.34518i			0.878743i	−0.898306	+	0.439371i	$0.855201\pi$
$38$	4.22796	−	4.48602i	0.685865	−	0.727728i
$39$		0			0
$40$	−6.00571	−	1.48435i	−0.949586	−	0.234696i
$41$	−1.36033	+	3.73748i	−0.212448	+	0.583696i	−0.999447	−	0.0332582i	$-0.989412\pi$
$41$	−1.36033	+	3.73748i	−0.212448	+	0.583696i	0.786999	+	0.616955i	$0.211634\pi$
$42$		0			0
$43$	−1.90224	+	0.335417i	−0.290089	+	0.0511505i	−0.316799	−	0.948493i	$-0.602608\pi$
$43$	−1.90224	+	0.335417i	−0.290089	+	0.0511505i	0.0267099	+	0.999643i	$0.491497\pi$
$44$	1.44843	+	1.49580i	0.218359	+	0.225500i
$45$		0			0
$46$	0.478652	+	0.530869i	0.0705734	+	0.0782723i
$47$	2.10734	−	2.51143i	0.307388	−	0.366330i	−0.590131	−	0.807308i	$-0.700924\pi$
$47$	2.10734	−	2.51143i	0.307388	−	0.366330i	0.897518	+	0.440978i	$0.145368\pi$
$48$		0			0
$49$	6.92262	+	11.9903i	0.988946	+	1.71291i
$50$	0.290614	+	0.0942071i	0.0410990	+	0.0133229i
$51$		0			0
$52$	10.3846	−	7.02513i	1.44008	−	0.974210i
$53$	−13.2697	−	2.33980i	−1.82273	−	0.321396i	−0.845562	−	0.533878i	$-0.820734\pi$
$53$	−13.2697	−	2.33980i	−1.82273	−	0.321396i	−0.977165	+	0.212482i	$0.931845\pi$
$54$		0			0
$55$	1.46367	+	1.74434i	0.197362	+	0.235207i
$56$	−10.4318	+	7.61181i	−1.39401	+	1.01717i
$57$		0			0
$58$	3.55022	−	0.757153i	0.466166	−	0.0994191i
$59$	11.0231	−	9.24945i	1.43508	−	1.20418i	0.492450	−	0.870341i	$-0.336102\pi$
$59$	11.0231	−	9.24945i	1.43508	−	1.20418i	0.942631	−	0.333835i	$-0.108343\pi$
$60$		0			0
$61$	0.482765	−	2.73790i	0.0618118	−	0.350552i	−0.938179	−	0.346152i	$-0.887488\pi$
$61$	0.482765	−	2.73790i	0.0618118	−	0.350552i	0.999990	−	0.00440026i	$-0.00140065\pi$
$62$	4.47600	−	1.81197i	0.568452	−	0.230121i
$63$		0			0
$64$	−5.37733	−	5.92320i	−0.672166	−	0.740400i
$65$	11.8744	−	6.85567i	1.47283	−	0.850341i
$66$		0			0
$67$	10.5415	+	8.84536i	1.28785	+	1.08063i	0.992111	+	0.125364i	$0.0400097\pi$
$67$	10.5415	+	8.84536i	1.28785	+	1.08063i	0.295737	+	0.955269i	$0.404435\pi$
$68$	−7.62899	−	5.52690i	−0.925151	−	0.670235i
$69$		0			0
$70$	−11.9715	+	7.49198i	−1.43087	+	0.895463i
$71$	1.19674	+	6.78706i	0.142027	+	0.805476i	0.969706	+	0.244274i	$0.0785497\pi$
$71$	1.19674	+	6.78706i	0.142027	+	0.805476i	−0.827679	+	0.561202i	$0.810339\pi$
$72$		0			0
$73$	−0.635538	−	0.231317i	−0.0743841	−	0.0270736i	0.304560	−	0.952493i	$-0.401491\pi$
$73$	−0.635538	−	0.231317i	−0.0743841	−	0.0270736i	−0.378944	+	0.925420i	$0.623713\pi$
$74$	−4.64986	+	5.95993i	−0.540536	+	0.692828i
$75$		0			0
$76$	8.61667	−	1.32398i	0.988400	−	0.151871i
$77$	4.75320			0.541677
$78$		0			0
$79$	−6.33497	−	2.30574i	−0.712740	−	0.259416i	−0.0398996	−	0.999204i	$-0.512704\pi$
$79$	−6.33497	−	2.30574i	−0.712740	−	0.259416i	−0.672841	+	0.739787i	$0.734926\pi$
$80$	−5.40516	−	6.87952i	−0.604316	−	0.769154i
$81$		0			0
$82$	−4.76808	+	2.98395i	−0.526546	+	0.329522i
$83$	−5.05030	−	2.91579i	−0.554342	−	0.320049i	0.196529	−	0.980498i	$-0.437033\pi$
$83$	−5.05030	−	2.91579i	−0.554342	−	0.320049i	−0.750871	+	0.660448i	$0.770366\pi$
$84$		0			0
$85$	−7.89220	−	6.62234i	−0.856029	−	0.718294i
$86$	−2.41280	−	1.28080i	−0.260179	−	0.138112i
$87$		0			0
$88$	0.313787	+	2.92784i	0.0334498	+	0.312109i
$89$	0.179291	+	0.492599i	0.0190049	+	0.0522154i	0.948832	−	0.315780i	$-0.102266\pi$
$89$	0.179291	+	0.492599i	0.0190049	+	0.0522154i	−0.929827	+	0.367996i	$0.880044\pi$
$90$		0			0
$91$	4.97003	−	28.1865i	0.521001	−	2.95474i
$92$	0.0718903	+	1.00831i	0.00749508	+	0.105124i
$93$		0			0
$94$	4.53444	−	0.967059i	0.467692	−	0.0997445i
$95$	9.50244	−	0.774100i	0.974930	−	0.0794210i
$96$		0			0
$97$	−1.40922	−	1.67944i	−0.143085	−	0.170522i	0.689743	−	0.724055i	$-0.257724\pi$
$97$	−1.40922	−	1.67944i	−0.143085	−	0.170522i	−0.832827	+	0.553533i	$0.813279\pi$
$98$	−2.71180	+	19.3914i	−0.273934	+	1.95883i
$99$		0			0
$100$	0.242085	+	0.357852i	0.0242085	+	0.0357852i
$101$	10.3581	−	3.77002i	1.03066	−	0.375131i	0.229331	−	0.973349i	$-0.426346\pi$
$101$	10.3581	−	3.77002i	1.03066	−	0.375131i	0.801334	+	0.598217i	$0.204124\pi$
$102$		0			0
$103$	−4.32112	−	7.48441i	−0.425773	−	0.737461i	0.570719	−	0.821145i	$-0.306664\pi$
$103$	−4.32112	−	7.48441i	−0.425773	−	0.737461i	−0.996492	+	0.0836847i	$0.973331\pi$
$104$	17.6902	+	1.20065i	1.73467	+	0.117733i
$105$		0			0
$106$	−12.7604	−	14.1524i	−1.23940	−	1.37460i
$107$	8.20469	−	14.2109i	0.793178	−	1.37382i	−0.130812	−	0.991407i	$-0.541759\pi$
$107$	8.20469	−	14.2109i	0.793178	−	1.37382i	0.923990	−	0.382417i	$-0.124908\pi$
$108$		0			0
$109$	2.84292	−	0.501284i	0.272302	−	0.0480143i	−0.0358294	−	0.999358i	$-0.511407\pi$
$109$	2.84292	−	0.501284i	0.272302	−	0.0480143i	0.308132	+	0.951344i	$0.400296\pi$
$110$	0.114581	+	3.21823i	0.0109248	+	0.306846i
$111$		0			0
$112$	−18.2532	−	0.587561i	−1.72476	−	0.0555193i
$113$		−	11.8084i		−	1.11084i	−0.831571	−	0.555419i	$-0.812558\pi$
$113$		−	11.8084i		−	1.11084i	0.831571	−	0.555419i	$-0.187442\pi$
$114$		0			0
$115$			1.10550i			0.103089i
$116$	4.61718	+	2.24416i	0.428695	+	0.208365i
$117$		0			0
$118$	20.3371	−	0.724074i	1.87218	−	0.0666564i
$119$	−21.1790	+	3.73442i	−1.94147	+	0.342334i
$120$		0			0
$121$	−4.95808	+	8.58765i	−0.450735	+	0.780695i
$122$	2.92003	−	2.63282i	0.264367	−	0.238364i
$123$		0			0
$124$	6.56704	+	1.87338i	0.589738	+	0.168234i
$125$	5.70432	+	9.88018i	0.510210	+	0.883710i
$126$		0			0
$127$	5.90524	−	2.14933i	0.524005	−	0.190722i	−0.0664543	−	0.997789i	$-0.521169\pi$
$127$	5.90524	−	2.14933i	0.524005	−	0.190722i	0.590460	+	0.807067i	$0.298946\pi$
$128$	−0.843079	−	11.2823i	−0.0745184	−	0.997220i
$129$		0			0
$130$	19.2039	+	2.68558i	1.68429	+	0.235541i
$131$	−7.92435	−	9.44388i	−0.692354	−	0.825115i	0.299284	−	0.954164i	$-0.403252\pi$
$131$	−7.92435	−	9.44388i	−0.692354	−	0.825115i	−0.991638	+	0.129049i	$0.958808\pi$
$132$		0			0
$133$	11.5122	−	16.2336i	0.998235	−	1.40763i
$134$	4.05913	+	19.0329i	0.350656	+	1.64419i
$135$		0			0
$136$	−3.69845	−	12.7991i	−0.317139	−	1.09752i
$137$	−0.610044	+	3.45973i	−0.0521196	+	0.295585i	−0.999715	−	0.0238893i	$-0.992395\pi$
$137$	−0.610044	+	3.45973i	−0.0521196	+	0.295585i	0.947595	+	0.319474i	$0.103506\pi$
$138$		0			0
$139$	6.13717	+	16.8617i	0.520548	+	1.43019i	0.869912	+	0.493207i	$0.164176\pi$
$139$	6.13717	+	16.8617i	0.520548	+	1.43019i	−0.349363	+	0.936987i	$0.613602\pi$
$140$	−19.8657	−	2.06058i	−1.67896	−	0.174151i
$141$		0			0
$142$	−4.56980	+	8.60870i	−0.383489	+	0.722426i
$143$	−4.99945	−	4.19503i	−0.418075	−	0.350806i
$144$		0			0
$145$	4.86210	+	2.80713i	0.403775	+	0.233120i
$146$	−0.507404	−	0.810786i	−0.0419931	−	0.0671011i
$147$		0			0
$148$	−10.3693	+	2.60038i	−0.852350	+	0.213750i
$149$	1.75739	+	0.639638i	0.143971	+	0.0524012i	0.413001	−	0.910731i	$-0.364481\pi$
$149$	1.75739	+	0.639638i	0.143971	+	0.0524012i	−0.269030	+	0.963132i	$0.586703\pi$
$150$		0			0
$151$	−21.2101			−1.72605			−0.863025	−	0.505162i	$-0.831433\pi$
$151$	−21.2101			−1.72605			−0.863025	+	0.505162i	$0.831433\pi$
$152$	10.7594	+	6.01954i	0.872704	+	0.488249i
$153$		0			0
$154$	5.29986	+	4.13489i	0.427075	+	0.333199i
$155$	7.01793	+	2.55432i	0.563694	+	0.205168i
$156$		0			0
$157$	1.75129	+	9.93209i	0.139769	+	0.792667i	0.971420	+	0.237368i	$0.0762848\pi$
$157$	1.75129	+	9.93209i	0.139769	+	0.792667i	−0.831651	+	0.555298i	$0.812604\pi$
$158$	−5.05775	−	8.08182i	−0.402373	−	0.642955i
$159$		0			0
$160$	−0.0421943	−	12.3728i	−0.00333575	−	0.978154i
$161$	1.76776	+	1.48333i	0.139319	+	0.116902i
$162$		0			0
$163$	5.03257	−	2.90555i	0.394181	−	0.227581i	−0.289789	−	0.957091i	$-0.593585\pi$
$163$	5.03257	−	2.90555i	0.394181	−	0.227581i	0.683970	+	0.729510i	$0.260252\pi$
$164$	−7.91224	−	0.820699i	−0.617842	−	0.0640858i
$165$		0			0
$166$	−3.09463	−	7.64447i	−0.240190	−	0.593326i
$167$	−0.882661	+	5.00582i	−0.0683024	+	0.387362i	0.931423	+	0.363938i	$0.118568\pi$
$167$	−0.882661	+	5.00582i	−0.0683024	+	0.387362i	−0.999726	+	0.0234242i	$0.992543\pi$
$168$		0			0
$169$	−20.1455	+	16.9041i	−1.54965	+	1.30031i
$170$	−3.03899	−	14.2495i	−0.233080	−	1.09289i
$171$		0			0
$172$	−1.57611	−	3.52704i	−0.120177	−	0.268934i
$173$	−8.40343	−	10.0148i	−0.638901	−	0.761412i	0.345296	−	0.938494i	$-0.387779\pi$
$173$	−8.40343	−	10.0148i	−0.638901	−	0.761412i	−0.984196	+	0.177082i	$0.943334\pi$
$174$		0			0
$175$	0.971302	+	0.171267i	0.0734235	+	0.0129465i
$176$	−2.19710	+	3.53754i	−0.165613	+	0.266652i
$177$		0			0
$178$	−0.228609	+	0.705221i	−0.0171349	+	0.0528586i
$179$	3.17645	+	5.50178i	0.237419	+	0.411222i	0.959973	−	0.280092i	$-0.0903651\pi$
$179$	3.17645	+	5.50178i	0.237419	+	0.411222i	−0.722554	+	0.691315i	$0.757032\pi$
$180$		0			0
$181$	3.64638	−	4.34559i	0.271034	−	0.323005i	−0.613310	−	0.789843i	$-0.710162\pi$
$181$	3.64638	−	4.34559i	0.271034	−	0.323005i	0.884343	+	0.466837i	$0.154607\pi$
$182$	30.0615	−	27.1046i	2.22831	−	2.00913i
$183$		0			0
$184$	−0.796988	+	1.18681i	−0.0587547	+	0.0874931i
$185$	−11.5135	+	2.03015i	−0.846492	+	0.149259i
$186$		0			0
$187$	−1.67720	+	4.60806i	−0.122649	+	0.336975i
$188$	5.89721	+	2.86631i	0.430098	+	0.209047i
$189$		0			0
$190$	11.2687	+	7.40320i	0.817518	+	0.537085i
$191$		−	8.11075i		−	0.586874i	−0.955978	−	0.293437i	$-0.905201\pi$
$191$		−	8.11075i		−	0.586874i	0.955978	−	0.293437i	$-0.0947990\pi$
$192$		0			0
$193$	−0.572488	+	1.57290i	−0.0412086	+	0.113220i	−0.958590	−	0.284789i	$-0.908076\pi$
$193$	−0.572488	+	1.57290i	−0.0412086	+	0.113220i	0.917382	+	0.398009i	$0.130299\pi$
$194$	−0.110318	−	3.09850i	−0.00792037	−	0.222459i
$195$		0			0
$196$	−19.8926	+	19.2626i	−1.42090	+	1.37590i
$197$	−9.18287	+	15.9052i	−0.654253	+	1.13320i	0.327828	+	0.944737i	$0.393683\pi$
$197$	−9.18287	+	15.9052i	−0.654253	+	1.13320i	−0.982081	+	0.188461i	$0.939650\pi$
$198$		0			0
$199$	1.01983	−	1.21539i	0.0722939	−	0.0861565i	−0.728685	−	0.684849i	$-0.759868\pi$
$199$	1.01983	−	1.21539i	0.0722939	−	0.0861565i	0.800979	+	0.598692i	$0.204313\pi$
$200$	−0.0413743	+	0.609602i	−0.00292560	+	0.0431054i
$201$		0			0
$202$	14.8289	+	4.80703i	1.04336	+	0.338222i
$203$	11.0126	−	4.00824i	0.772930	−	0.281323i
$204$		0			0
$205$	−8.56721	−	1.51063i	−0.598360	−	0.105507i
$206$	1.69272	−	12.1042i	0.117937	−	0.843340i
$207$		0			0
$208$	18.6803	+	16.7277i	1.29524	+	1.15986i
$209$	−1.89318	−	4.12418i	−0.130954	−	0.285275i
$210$		0			0
$211$	6.13391	−	5.14697i	0.422276	−	0.354332i	−0.406752	−	0.913539i	$-0.633339\pi$
$211$	6.13391	−	5.14697i	0.422276	−	0.354332i	0.829028	+	0.559207i	$0.188894\pi$
$212$	−1.91652	−	26.8805i	−0.131627	−	1.84616i
$213$		0			0
$214$	21.5106	−	8.70793i	1.47044	−	0.595262i
$215$	−1.44498	−	3.97004i	−0.0985465	−	0.270754i
$216$		0			0
$217$	13.5009	−	7.79475i	0.916501	−	0.529142i
$218$	3.60596	+	1.91417i	0.244226	+	0.129644i
$219$		0			0
$220$	−2.67183	+	3.68803i	−0.180135	+	0.248647i
$221$	25.5721	+	14.7640i	1.72016	+	0.993137i
$222$		0			0
$223$	3.42104	+	19.4017i	0.229090	+	1.29923i	0.854710	+	0.519106i	$0.173735\pi$
$223$	3.42104	+	19.4017i	0.229090	+	1.29923i	−0.625620	+	0.780128i	$0.715154\pi$
$224$	−19.8413	−	16.5339i	−1.32571	−	1.10472i
$225$		0			0
$226$	10.2723	−	13.1664i	0.683303	−	0.875819i
$227$	−1.77593			−0.117873			−0.0589365	−	0.998262i	$-0.518771\pi$
$227$	−1.77593			−0.117873			−0.0589365	+	0.998262i	$0.518771\pi$
$228$		0			0
$229$	10.0690			0.665376			0.332688	−	0.943037i	$-0.392044\pi$
$229$	10.0690			0.665376			0.332688	+	0.943037i	$0.392044\pi$
$230$	−0.961696	+	1.23265i	−0.0634123	+	0.0812783i
$231$		0			0
$232$	3.19597	+	6.51882i	0.209826	+	0.427982i
$233$	−2.37508	−	13.4697i	−0.155596	−	0.882431i	−0.958238	−	0.285970i	$-0.907684\pi$
$233$	−2.37508	−	13.4697i	−0.155596	−	0.882431i	0.802642	−	0.596461i	$-0.203427\pi$
$234$		0			0
$235$	6.21002	+	3.58536i	0.405097	+	0.233883i
$236$	23.3059	+	16.8842i	1.51709	+	1.09907i
$237$		0			0
$238$	−26.8634	−	14.2600i	−1.74129	−	0.924339i
$239$	−3.98234	+	2.29921i	−0.257596	+	0.148723i	−0.623238	−	0.782033i	$-0.714183\pi$
$239$	−3.98234	+	2.29921i	−0.257596	+	0.148723i	0.365641	+	0.930756i	$0.380850\pi$
$240$		0			0
$241$	3.28305	+	9.02009i	0.211480	+	0.581035i	0.999396	−	0.0347466i	$-0.0110624\pi$
$241$	3.28305	+	9.02009i	0.211480	+	0.581035i	−0.787917	+	0.615782i	$0.788840\pi$
$242$	−12.9988	+	5.26219i	−0.835597	+	0.338266i
$243$		0			0
$244$	5.54619	−	0.395431i	0.355059	−	0.0253149i
$245$	−23.1979	+	19.4654i	−1.48206	+	1.24360i
$246$		0			0
$247$	−26.4359	+	6.91423i	−1.68208	+	0.439942i
$248$	5.69263	+	7.80161i	0.361482	+	0.495403i
$249$		0			0
$250$	−2.23456	+	15.9788i	−0.141326	+	1.01059i
$251$	−2.12807	−	0.375237i	−0.134323	−	0.0236847i	0.106083	−	0.994357i	$-0.466169\pi$
$251$	−2.12807	−	0.375237i	−0.134323	−	0.0236847i	−0.240405	+	0.970673i	$0.577280\pi$
$252$		0			0
$253$	0.494463	−	0.179970i	0.0310866	−	0.0113146i
$254$	8.45414	+	2.74054i	0.530460	+	0.171957i
$255$		0			0
$256$	8.87458	−	13.3132i	0.554661	−	0.832076i
$257$	5.70179	−	6.79513i	0.355668	−	0.423868i	−0.558310	−	0.829632i	$-0.688550\pi$
$257$	5.70179	−	6.79513i	0.355668	−	0.423868i	0.913978	+	0.405764i	$0.132995\pi$
$258$		0			0
$259$	−12.2021	+	21.1347i	−0.758204	+	1.31325i
$260$	19.0763	+	19.7002i	1.18306	+	1.22176i
$261$		0			0
$262$	−0.620342	−	17.4235i	−0.0383248	−	1.07643i
$263$	−8.48870	+	23.3225i	−0.523435	+	1.43813i	0.343237	+	0.939249i	$0.388477\pi$
$263$	−8.48870	+	23.3225i	−0.523435	+	1.43813i	−0.866672	+	0.498878i	$0.833745\pi$
$264$		0			0
$265$		−	29.4715i		−	1.81042i
$266$	26.9581	−	8.08591i	1.65291	−	0.495779i
$267$		0			0
$268$	−12.0310	+	24.7529i	−0.734913	+	1.51203i
$269$	5.11352	−	14.0493i	0.311777	−	0.856600i	−0.680521	−	0.732728i	$-0.738247\pi$
$269$	5.11352	−	14.0493i	0.311777	−	0.856600i	0.992298	−	0.123872i	$-0.0395311\pi$
$270$		0			0
$271$	6.23726	−	1.09980i	0.378886	−	0.0668079i	0.0190382	−	0.999819i	$-0.493940\pi$
$271$	6.23726	−	1.09980i	0.378886	−	0.0668079i	0.359848	+	0.933011i	$0.382828\pi$
$272$	7.01037	−	17.4885i	0.425066	−	1.06040i
$273$		0			0
$274$	−3.68988	+	3.32694i	−0.222914	+	0.200988i
$275$	0.144560	−	0.172280i	0.00871732	−	0.0103889i
$276$		0			0
$277$	−8.61464	−	14.9210i	−0.517604	−	0.896516i	−0.999791	−	0.0204477i	$-0.993491\pi$
$277$	−8.61464	−	14.9210i	−0.517604	−	0.896516i	0.482187	−	0.876068i	$-0.339842\pi$
$278$	−7.82531	+	24.1398i	−0.469331	+	1.44781i
$279$		0			0
$280$	−20.3579	−	19.5791i	−1.21662	−	1.17007i
$281$	−3.72582	−	0.656962i	−0.222264	−	0.0391911i	0.0614071	−	0.998113i	$-0.480441\pi$
$281$	−3.72582	−	0.656962i	−0.222264	−	0.0391911i	−0.283671	+	0.958922i	$0.591552\pi$
$282$		0			0
$283$	−16.6311	−	19.8202i	−0.988617	−	1.17819i	−0.983995	−	0.178198i	$-0.942973\pi$
$283$	−16.6311	−	19.8202i	−0.988617	−	1.17819i	−0.00462198	−	0.999989i	$-0.501471\pi$
$284$	−12.5842	+	5.62344i	−0.746736	+	0.333689i
$285$		0			0
$286$	−1.92510	−	9.02660i	−0.113834	−	0.533754i
$287$	−13.9108	+	11.6725i	−0.821126	+	0.689006i
$288$		0			0
$289$	0.900718	−	5.10823i	0.0529834	−	0.300484i
$290$	2.97931	+	7.35960i	0.174951	+	0.432171i
$291$		0			0
$292$	0.139555	−	1.34543i	0.00816686	−	0.0787355i
$293$	−21.7865	+	12.5785i	−1.27278	+	0.734841i	−0.975511	−	0.219952i	$-0.929410\pi$
$293$	−21.7865	+	12.5785i	−1.27278	+	0.734841i	−0.297272	+	0.954793i	$0.596077\pi$
$294$		0			0
$295$	24.1100	+	20.2307i	1.40374	+	1.17788i
$296$	−13.8240	−	6.12096i	−0.803501	−	0.355774i
$297$		0			0
$298$	1.40308	+	2.24199i	0.0812780	+	0.129875i
$299$	−0.550201	−	3.12034i	−0.0318189	−	0.180454i
$300$		0			0
$301$	−8.28712	−	3.01626i	−0.477662	−	0.173855i
$302$	−23.6494	−	18.4510i	−1.36087	−	1.06173i
$303$		0			0
$304$	6.76036	+	16.0716i	0.387733	+	0.921772i
$305$	6.08080			0.348185
$306$		0			0
$307$	−25.3745	−	9.23556i	−1.44820	−	0.527101i	−0.506111	−	0.862468i	$-0.668917\pi$
$307$	−25.3745	−	9.23556i	−1.44820	−	0.527101i	−0.942088	+	0.335367i	$0.891140\pi$
$308$	2.31239	+	9.22087i	0.131760	+	0.525408i
$309$		0			0
$310$	5.60301	+	8.95310i	0.318230	+	0.508502i
$311$	27.1216	+	15.6587i	1.53793	+	0.887922i	0.998960	+	0.0455941i	$0.0145181\pi$
$311$	27.1216	+	15.6587i	1.53793	+	0.887922i	0.538966	+	0.842328i	$0.318815\pi$
$312$		0			0
$313$	−4.88055	−	4.09527i	−0.275865	−	0.231478i	0.494349	−	0.869263i	$-0.335406\pi$
$313$	−4.88055	−	4.09527i	−0.275865	−	0.231478i	−0.770214	+	0.637785i	$0.779851\pi$
$314$	−6.68738	+	12.5978i	−0.377390	+	0.710938i
$315$		0			0
$316$	1.39107	−	13.4111i	0.0782539	−	0.754435i
$317$	5.71877	+	15.7122i	0.321198	+	0.882484i	0.990254	+	0.139272i	$0.0444763\pi$
$317$	5.71877	+	15.7122i	0.321198	+	0.882484i	−0.669056	+	0.743212i	$0.733301\pi$
$318$		0			0
$319$	0.464036	−	2.63168i	0.0259810	−	0.147346i
$320$	10.7162	−	13.8325i	0.599056	−	0.773258i
$321$		0			0
$322$	0.680698	+	3.19172i	0.0379338	+	0.177868i
$323$	11.6757	+	16.8888i	0.649654	+	0.939718i
$324$		0			0
$325$	−0.870467	−	1.03738i	−0.0482848	−	0.0575436i
$326$	8.13895	+	1.13819i	0.450775	+	0.0630388i
$327$		0			0
$328$	−8.10828	−	7.79807i	−0.447705	−	0.430577i
$329$	14.0656	−	5.11945i	0.775460	−	0.282244i
$330$		0			0
$331$	4.21082	+	7.29336i	0.231448	+	0.400879i	0.958234	−	0.285984i	$-0.0923205\pi$
$331$	4.21082	+	7.29336i	0.231448	+	0.400879i	−0.726787	+	0.686863i	$0.758987\pi$
$332$	3.19951	−	11.2157i	0.175596	−	0.615543i
$333$		0			0
$334$	−5.33882	+	4.81369i	−0.292127	+	0.263394i
$335$	−15.0492	+	26.0659i	−0.822224	+	1.42413i
$336$		0			0
$337$	27.0560	−	4.77070i	1.47383	−	0.259877i	0.621723	−	0.783237i	$-0.286433\pi$
$337$	27.0560	−	4.77070i	1.47383	−	0.259877i	0.852111	+	0.523360i	$0.175322\pi$
$338$	−37.1675	+	1.32330i	−2.02165	+	0.0719780i
$339$		0			0
$340$	9.00740	−	18.5320i	0.488495	−	1.00504i
$341$		−	3.55477i		−	0.192502i
$342$		0			0
$343$			31.2531i			1.68751i
$344$	1.31086	−	5.30376i	0.0706766	−	0.285960i
$345$		0			0
$346$	−0.657845	−	18.4769i	−0.0353660	−	0.993323i
$347$	−16.5281	+	2.91434i	−0.887273	+	0.156450i	−0.598667	−	0.800998i	$-0.704303\pi$
$347$	−16.5281	+	2.91434i	−0.887273	+	0.156450i	−0.288606	+	0.957448i	$0.593192\pi$
$348$		0			0
$349$	6.24129	−	10.8102i	0.334089	−	0.578659i	−0.649221	−	0.760600i	$-0.724905\pi$
$349$	6.24129	−	10.8102i	0.334089	−	0.578659i	0.983309	+	0.181941i	$0.0582381\pi$
$350$	0.934023	+	1.03592i	0.0499256	+	0.0553720i
$351$		0			0
$352$	−5.52715	+	2.03309i	−0.294598	+	0.108364i
$353$	−8.01687	−	13.8856i	−0.426695	−	0.739058i	0.569882	−	0.821727i	$-0.306989\pi$
$353$	−8.01687	−	13.8856i	−0.426695	−	0.739058i	−0.996577	+	0.0826690i	$0.973656\pi$
$354$		0			0
$355$	−14.1648	+	5.15557i	−0.751790	+	0.273629i
$356$	−0.868384	+	0.587458i	−0.0460243	+	0.0311352i
$357$		0			0
$358$	−1.24431	+	8.89778i	−0.0657640	+	0.470262i
$359$	3.75196	+	4.47141i	0.198021	+	0.235992i	0.855913	−	0.517120i	$-0.172996\pi$
$359$	3.75196	+	4.47141i	0.198021	+	0.235992i	−0.657892	+	0.753112i	$0.728552\pi$
$360$		0			0
$361$	−18.6705	−	3.52296i	−0.982660	−	0.185419i
$362$	7.84605	−	1.67332i	0.412379	−	0.0879480i
$363$		0			0
$364$	57.0976	−	4.07093i	2.99273	−	0.213375i
$365$	0.256874	−	1.45681i	0.0134454	−	0.0762527i
$366$		0			0
$367$	−4.68850	−	12.8815i	−0.244737	−	0.672411i	−0.999858	−	0.0168252i	$-0.994644\pi$
$367$	−4.68850	−	12.8815i	−0.244737	−	0.672411i	0.755121	−	0.655585i	$-0.227578\pi$
$368$	−1.92108	+	0.629996i	−0.100143	+	0.0328408i
$369$		0			0
$370$	−14.6038	−	7.75218i	−0.759213	−	0.403017i
$371$	−47.1265	−	39.5439i	−2.44669	−	2.05302i
$372$		0			0
$373$	−5.91807	−	3.41680i	−0.306426	−	0.176915i	0.338900	−	0.940822i	$-0.389945\pi$
$373$	−5.91807	−	3.41680i	−0.306426	−	0.176915i	−0.645326	+	0.763907i	$0.723279\pi$
$374$	−5.87872	+	3.67901i	−0.303981	+	0.190237i
$375$		0			0
$376$	4.08199	+	8.32604i	0.210513	+	0.429383i
$377$	−15.1206	−	5.50346i	−0.778752	−	0.283443i
$378$		0			0
$379$	2.41729			0.124168			0.0620839	−	0.998071i	$-0.480225\pi$
$379$	2.41729			0.124168			0.0620839	+	0.998071i	$0.480225\pi$
$380$	6.12455	+	18.0575i	0.314183	+	0.926329i
$381$		0			0
$382$	7.05568	−	9.04356i	0.361000	−	0.462709i
$383$	8.88806	+	3.23499i	0.454159	+	0.165300i	0.558963	−	0.829193i	$-0.311199\pi$
$383$	8.88806	+	3.23499i	0.454159	+	0.165300i	−0.104804	+	0.994493i	$0.533422\pi$
$384$		0			0
$385$	1.80531	+	10.2384i	0.0920069	+	0.521797i
$386$	−2.00662	+	1.25578i	−0.102134	+	0.0639175i
$387$		0			0
$388$	2.57243	−	3.55082i	0.130595	−	0.180266i
$389$	−17.4074	−	14.6065i	−0.882589	−	0.740580i	0.0841207	−	0.996456i	$-0.473192\pi$
$389$	−17.4074	−	14.6065i	−0.882589	−	0.740580i	−0.966710	+	0.255875i	$0.917636\pi$
$390$		0			0
$391$	−2.06180	+	1.19038i	−0.104270	+	0.0602000i
$392$	−38.9373	+	4.17304i	−1.96663	+	0.210771i
$393$		0			0
$394$	−24.0752	+	9.74611i	−1.21289	+	0.491002i
$395$	2.56049	−	14.5213i	0.128832	−	0.730645i
$396$		0			0
$397$	−21.0054	+	17.6256i	−1.05423	+	0.884604i	−0.993532	−	0.113552i	$-0.963777\pi$
$397$	−21.0054	+	17.6256i	−1.05423	+	0.884604i	−0.0606979	+	0.998156i	$0.519333\pi$
$398$	2.19441	−	0.468000i	0.109996	−	0.0234587i
$399$		0			0
$400$	−0.576435	+	0.643719i	−0.0288218	+	0.0321860i
$401$	−0.797085	−	0.949929i	−0.0398045	−	0.0474372i	0.745775	−	0.666198i	$-0.232079\pi$
$401$	−0.797085	−	0.949929i	−0.0398045	−	0.0474372i	−0.785579	+	0.618761i	$0.787635\pi$
$402$		0			0
$403$	−21.0798	−	3.71693i	−1.05006	−	0.185154i
$404$	12.3527	+	18.2598i	0.614568	+	0.908460i
$405$		0			0
$406$	15.7659	+	5.11078i	0.782450	+	0.253644i
$407$	2.78237	+	4.81921i	0.137917	+	0.238879i
$408$		0			0
$409$	−19.5574	+	23.3076i	−0.967053	+	1.15249i	0.0212179	+	0.999775i	$0.493246\pi$
$409$	−19.5574	+	23.3076i	−0.967053	+	1.15249i	−0.988270	+	0.152714i	$0.951199\pi$
$410$	−8.23839	−	9.13712i	−0.406865	−	0.451250i
$411$		0			0
$412$	12.4170	−	12.0238i	0.611744	−	0.592369i
$413$	64.6999	−	11.4083i	3.18367	−	0.561367i
$414$		0			0
$415$	4.36247	−	11.9858i	0.214145	−	0.588359i
$416$	6.27693	+	34.9018i	0.307752	+	1.71120i
$417$		0			0
$418$	1.47678	−	6.24540i	0.0722315	−	0.305473i
$419$		−	14.2671i		−	0.696992i	−0.937310	−	0.348496i	$-0.886693\pi$
$419$		−	14.2671i		−	0.696992i	0.937310	−	0.348496i	$-0.113307\pi$
$420$		0			0
$421$	−7.36725	+	20.2414i	−0.359058	+	0.986503i	0.620299	+	0.784365i	$0.287011\pi$
$421$	−7.36725	+	20.2414i	−0.359058	+	0.986503i	−0.979357	+	0.202138i	$0.935211\pi$
$422$	11.3168	−	0.402920i	0.550893	−	0.0196138i
$423$		0			0
$424$	21.2468	−	31.6392i	1.03184	−	1.53653i
$425$	−0.508767	+	0.881210i	−0.0246788	+	0.0427450i
$426$		0			0
$427$	8.15900	−	9.72352i	0.394842	−	0.470554i
$428$	31.5597	+	9.00304i	1.52550	+	0.435178i
$429$		0			0
$430$	1.84244	−	5.68364i	0.0888504	−	0.274089i
$431$	−27.6536	+	10.0651i	−1.33203	+	0.484819i	−0.907293	−	0.420498i	$-0.861855\pi$
$431$	−27.6536	+	10.0651i	−1.33203	+	0.484819i	−0.424736	+	0.905317i	$0.639633\pi$
$432$		0			0
$433$	−0.0332873	−	0.00586945i	−0.00159969	−	0.000282068i	0.172848	−	0.984948i	$-0.444703\pi$
$433$	−0.0332873	−	0.00586945i	−0.00159969	−	0.000282068i	−0.174448	+	0.984666i	$0.555814\pi$
$434$	21.8344	+	3.05344i	1.04809	+	0.146570i
$435$		0			0
$436$	2.35551	+	5.27120i	0.112808	+	0.252445i
$437$	0.582936	−	2.12462i	0.0278856	−	0.101634i
$438$		0			0
$439$	−3.39127	+	2.84561i	−0.161857	+	0.135814i	−0.720119	−	0.693851i	$-0.755913\pi$
$439$	−3.39127	+	2.84561i	−0.161857	+	0.135814i	0.558262	+	0.829665i	$0.311468\pi$
$440$	−6.18740	+	1.78792i	−0.294973	+	0.0852356i
$441$		0			0
$442$	15.6696	+	38.7076i	0.745327	+	1.84113i
$443$	9.63658	+	26.4763i	0.457848	+	1.25793i	0.927084	+	0.374854i	$0.122307\pi$
$443$	9.63658	+	26.4763i	0.457848	+	1.25793i	−0.469236	+	0.883073i	$0.655471\pi$
$444$		0			0
$445$	−0.992963	+	0.573288i	−0.0470710	+	0.0271764i
$446$	−13.0634	+	24.6091i	−0.618568	+	1.16527i
$447$		0			0
$448$	−7.74017	−	35.6957i	−0.365689	−	1.68647i
$449$	−32.9679	−	19.0340i	−1.55585	−	0.898272i	−0.997646	−	0.0685703i	$-0.978156\pi$
$449$	−32.9679	−	19.0340i	−1.55585	−	0.898272i	−0.558207	−	0.829702i	$-0.688510\pi$
$450$		0			0
$451$	0.719028	+	4.07781i	0.0338577	+	0.192017i
$452$	22.9074	−	5.74466i	1.07747	−	0.270206i
$453$		0			0
$454$	−1.98018	−	1.54491i	−0.0929346	−	0.0725065i
$455$	62.6013			2.93480
$456$		0			0
$457$	−14.5559			−0.680897			−0.340449	−	0.940263i	$-0.610579\pi$
$457$	−14.5559			−0.680897			−0.340449	+	0.940263i	$0.610579\pi$
$458$	11.2270	+	8.75916i	0.524603	+	0.409289i
$459$		0			0
$460$	−2.14460	+	0.537817i	−0.0999924	+	0.0250758i
$461$	4.10390	+	23.2744i	0.191138	+	1.08400i	0.917813	+	0.397014i	$0.129953\pi$
$461$	4.10390	+	23.2744i	0.191138	+	1.08400i	−0.726675	+	0.686981i	$0.758935\pi$
$462$		0			0
$463$	−2.29455	−	1.32476i	−0.106637	−	0.0615668i	0.445733	−	0.895166i	$-0.352943\pi$
$463$	−2.29455	−	1.32476i	−0.106637	−	0.0615668i	−0.552370	+	0.833599i	$0.686276\pi$
$464$	−2.10730	+	10.0488i	−0.0978288	+	0.466503i
$465$		0			0
$466$	9.06931	−	17.0850i	0.420128	−	0.791447i
$467$	−2.86057	+	1.65155i	−0.132371	+	0.0764246i	−0.564723	−	0.825280i	$-0.691017\pi$
$467$	−2.86057	+	1.65155i	−0.132371	+	0.0764246i	0.432352	+	0.901705i	$0.357684\pi$
$468$		0			0
$469$	21.4884	+	59.0388i	0.992240	+	2.72616i
$470$	3.80527	+	9.39990i	0.175524	+	0.433585i
$471$		0			0
$472$	11.2984	+	39.1002i	0.520053	+	1.79973i
$473$	−1.54046	+	1.29260i	−0.0708305	+	0.0594338i
$474$		0			0
$475$	−0.238264	−	0.910977i	−0.0109323	−	0.0417985i
$476$	−17.5479	−	39.2689i	−0.804306	−	1.79989i
$477$		0			0
$478$	−6.44047	−	0.900669i	−0.294580	−	0.0411957i
$479$	−4.28953	−	0.756360i	−0.195994	−	0.0345590i	0.0747895	−	0.997199i	$-0.476172\pi$
$479$	−4.28953	−	0.756360i	−0.195994	−	0.0345590i	−0.270783	+	0.962640i	$0.587283\pi$
$480$		0			0
$481$	31.4872	−	11.4604i	1.43569	−	0.522549i
$482$	−4.18610	+	12.9135i	−0.190672	+	0.588192i
$483$		0			0
$484$	−19.0715	−	5.44052i	−0.866886	−	0.247296i
$485$	3.08229	−	3.67333i	0.139960	−	0.166797i
$486$		0			0
$487$	−8.14968	+	14.1157i	−0.369297	+	0.639642i	−0.989456	−	0.144835i	$-0.953735\pi$
$487$	−8.14968	+	14.1157i	−0.369297	+	0.639642i	0.620159	+	0.784476i	$0.287068\pi$
$488$	6.52805	+	4.38381i	0.295511	+	0.198446i
$489$		0			0
$490$	−42.7992	+	1.52381i	−1.93347	+	0.0688386i
$491$	9.70159	−	26.6549i	0.437826	−	1.20292i	−0.503077	−	0.864242i	$-0.667799\pi$
$491$	9.70159	−	26.6549i	0.437826	−	1.20292i	0.940903	−	0.338676i	$-0.109979\pi$
$492$		0			0
$493$			12.0906i			0.544534i
$494$	−35.4911	−	15.2876i	−1.59682	−	0.687821i
$495$		0			0
$496$	−0.439418	+	13.6510i	−0.0197305	+	0.612947i
$497$	−10.7618	+	29.5678i	−0.482733	+	1.32630i
$498$		0			0
$499$	23.7613	−	4.18976i	1.06370	−	0.187559i	0.385703	−	0.922623i	$-0.373959\pi$
$499$	23.7613	−	4.18976i	1.06370	−	0.187559i	0.677998	+	0.735064i	$0.262848\pi$
$500$	−16.3917	+	15.8726i	−0.733061	+	0.709844i
$501$		0			0
$502$	−2.04640	−	2.26964i	−0.0913351	−	0.101299i
$503$	−10.7567	+	12.8194i	−0.479619	+	0.571587i	−0.950546	−	0.310585i	$-0.899475\pi$
$503$	−10.7567	+	12.8194i	−0.479619	+	0.571587i	0.470927	+	0.882172i	$0.343920\pi$
$504$		0			0
$505$	12.0547	+	20.8794i	0.536428	+	0.929120i
$506$	0.707890	+	0.229474i	0.0314695	+	0.0102013i
$507$		0			0
$508$	7.04240	+	10.4101i	0.312456	+	0.461874i
$509$	−26.6274	−	4.69514i	−1.18024	−	0.208108i	−0.451101	−	0.892473i	$-0.648969\pi$
$509$	−26.6274	−	4.69514i	−1.18024	−	0.208108i	−0.729140	+	0.684365i	$0.760080\pi$
$510$		0			0
$511$	−1.98485	−	2.36545i	−0.0878044	−	0.104641i
$512$	21.4766	−	7.12422i	0.949142	−	0.314849i
$513$		0			0
$514$	12.2687	−	2.61655i	0.541151	−	0.115411i
$515$	14.4802	−	12.1504i	0.638075	−	0.535408i
$516$		0			0
$517$	0.592680	−	3.36126i	0.0260661	−	0.147828i
$518$	−31.9910	+	12.9506i	−1.40560	+	0.569016i
$519$		0			0
$520$	4.13268	+	38.5607i	0.181230	+	1.69100i
$521$	24.3436	−	14.0548i	1.06651	−	0.615752i	0.139287	−	0.990252i	$-0.455519\pi$
$521$	24.3436	−	14.0548i	1.06651	−	0.615752i	0.927227	+	0.374500i	$0.122186\pi$
$522$		0			0
$523$	10.3904	+	8.71855i	0.454339	+	0.381236i	0.841043	−	0.540968i	$-0.181942\pi$
$523$	10.3904	+	8.71855i	0.454339	+	0.381236i	−0.386704	+	0.922204i	$0.626387\pi$
$524$	14.4653	−	19.9670i	0.631921	−	0.872264i
$525$		0			0
$526$	−29.7536	+	18.6203i	−1.29732	+	0.811886i
$527$	2.79286	+	15.8391i	0.121659	+	0.689961i
$528$		0			0
$529$	−21.3729	−	7.77909i	−0.929255	−	0.338221i
$530$	25.6378	−	32.8610i	1.11363	−	1.42739i
$531$		0			0
$532$	37.0926	+	14.4354i	1.60817	+	0.625854i
$533$	24.9332			1.07998
$534$		0			0
$535$	33.7266	+	12.2755i	1.45813	+	0.530715i
$536$	−34.9477	+	17.1337i	−1.50951	+	0.740065i
$537$		0			0
$538$	17.9233	−	11.2167i	0.772729	−	0.483588i
$539$	12.4829	+	7.20698i	0.537675	+	0.310427i
$540$		0			0
$541$	−19.6708	−	16.5058i	−0.845714	−	0.709638i	0.113128	−	0.993580i	$-0.463913\pi$
$541$	−19.6708	−	16.5058i	−0.845714	−	0.709638i	−0.958841	+	0.283943i	$0.908357\pi$
$542$	7.91133	+	4.19961i	0.339821	+	0.180389i
$543$		0			0
$544$	23.0301	−	13.4014i	0.987410	−	0.574580i
$545$	2.15953	+	5.93326i	0.0925042	+	0.254153i
$546$		0			0
$547$	−1.86933	+	10.6015i	−0.0799270	+	0.453288i	0.918409	+	0.395631i	$0.129474\pi$
$547$	−1.86933	+	10.6015i	−0.0799270	+	0.453288i	−0.998336	+	0.0576571i	$0.981637\pi$
$548$	−7.00841	+	0.499684i	−0.299385	+	0.0213454i
$549$		0			0
$550$	0.311056	−	0.0663387i	0.0132635	−	0.00282869i
$551$	−7.86406	−	7.95872i	−0.335020	−	0.339053i
$552$		0			0
$553$	−19.7847	−	23.5785i	−0.841332	−	1.00266i
$554$	3.37462	−	24.1311i	0.143374	−	1.02523i
$555$		0			0
$556$	−29.7249	+	20.1088i	−1.26062	+	0.852802i
$557$	5.88826	−	2.14315i	0.249493	−	0.0908082i	−0.214246	−	0.976780i	$-0.568730\pi$
$557$	5.88826	−	2.14315i	0.249493	−	0.0908082i	0.463740	+	0.885971i	$0.346507\pi$
$558$		0			0
$559$	6.05438	+	10.4865i	0.256073	+	0.443531i
$560$	−5.66711	−	39.5406i	−0.239479	−	1.67089i
$561$		0			0
$562$	−3.58282	−	3.97367i	−0.151132	−	0.167619i
$563$	14.8489	−	25.7190i	0.625806	−	1.08393i	−0.362579	−	0.931953i	$-0.618104\pi$
$563$	14.8489	−	25.7190i	0.625806	−	1.08393i	0.988384	−	0.151974i	$-0.0485631\pi$
$564$		0			0
$565$	25.4353	−	4.48492i	1.07007	−	0.188682i
$566$	−1.30193	−	36.5674i	−0.0547243	−	1.53704i
$567$		0			0
$568$	−18.9234	−	4.67704i	−0.794010	−	0.196244i
$569$		−	21.3074i		−	0.893254i	−0.894720	−	0.446627i	$-0.852625\pi$
$569$		−	21.3074i		−	0.893254i	0.894720	−	0.446627i	$-0.147375\pi$
$570$		0			0
$571$		−	19.0626i		−	0.797744i	−0.917007	−	0.398872i	$-0.869402\pi$
$571$		−	19.0626i		−	0.797744i	0.917007	−	0.398872i	$-0.130598\pi$
$572$	5.70589	−	11.7394i	0.238575	−	0.490850i
$573$		0			0
$574$	−25.6647	+	0.913758i	−1.07123	+	0.0381395i
$575$	0.107527	−	0.0189599i	0.00448417	−	0.000790681i
$576$		0			0
$577$	20.8821	−	36.1689i	0.869334	−	1.50573i	0.00665563	−	0.999978i	$-0.497881\pi$
$577$	20.8821	−	36.1689i	0.869334	−	1.50573i	0.862678	−	0.505753i	$-0.168785\pi$
$578$	5.44804	−	4.91217i	0.226609	−	0.204319i
$579$		0			0
$580$	−3.08028	+	10.7978i	−0.127902	+	0.448353i
$581$	−13.3125	−	23.0579i	−0.552296	−	0.956604i
$582$		0			0
$583$	−13.1819	+	4.79780i	−0.545937	+	0.198705i
$584$	1.32602	−	1.37877i	0.0548711	−	0.0570538i
$585$		0			0
$586$	−35.2344	−	4.92736i	−1.45552	−	0.203548i
$587$	−25.3752	−	30.2410i	−1.04735	−	1.24818i	−0.967898	−	0.251342i	$-0.919128\pi$
$587$	−25.3752	−	30.2410i	−1.04735	−	1.24818i	−0.0794499	−	0.996839i	$-0.525316\pi$
$588$		0			0
$589$	−12.1406	−	8.60962i	−0.500244	−	0.354753i
$590$	9.28385	+	43.5311i	0.382210	+	1.79215i
$591$		0			0
$592$	−10.0891	−	18.8506i	−0.414660	−	0.774755i
$593$	−5.32452	+	30.1969i	−0.218652	+	1.24004i	0.655804	+	0.754931i	$0.272330\pi$
$593$	−5.32452	+	30.1969i	−0.218652	+	1.24004i	−0.874456	+	0.485105i	$0.838781\pi$
$594$		0			0
$595$	−16.0879	−	44.2011i	−0.659540	−	1.81207i
$596$	−0.385899	+	3.72039i	−0.0158070	+	0.152393i
$597$		0			0
$598$	2.10096	−	3.95784i	0.0859146	−	0.161848i
$599$	24.9871	+	20.9666i	1.02094	+	0.856673i	0.989746	−	0.142840i	$-0.0456234\pi$
$599$	24.9871	+	20.9666i	1.02094	+	0.856673i	0.0311976	+	0.999513i	$0.490068\pi$
$600$		0			0
$601$	13.2788	+	7.66652i	0.541654	+	0.312724i	0.745749	−	0.666227i	$-0.232092\pi$
$601$	13.2788	+	7.66652i	0.541654	+	0.312724i	−0.204095	+	0.978951i	$0.565425\pi$
$602$	−6.61631	−	10.5723i	−0.269661	−	0.430893i
$603$		0			0
$604$	−10.3185	−	41.1460i	−0.419853	−	1.67421i
$605$	−20.3809	−	7.41805i	−0.828602	−	0.301587i
$606$		0			0
$607$	−0.899795			−0.0365216			−0.0182608	−	0.999833i	$-0.505813\pi$
$607$	−0.899795			−0.0365216			−0.0182608	+	0.999833i	$0.505813\pi$
$608$	−6.44312	+	23.8010i	−0.261303	+	0.965257i
$609$		0			0
$610$	6.78014	+	5.28979i	0.274520	+	0.214177i
$611$	−19.3125	−	7.02918i	−0.781301	−	0.284370i
$612$		0			0
$613$	2.77080	+	15.7140i	0.111912	+	0.634683i	0.988233	+	0.152956i	$0.0488793\pi$
$613$	2.77080	+	15.7140i	0.111912	+	0.634683i	−0.876321	+	0.481727i	$0.840010\pi$
$614$	−20.2586	−	32.3714i	−0.817571	−	1.30640i
$615$		0			0
$616$	−5.44306	+	12.2929i	−0.219307	+	0.495297i
$617$	20.8388	+	17.4858i	0.838938	+	0.703952i	0.957324	−	0.289015i	$-0.0933279\pi$
$617$	20.8388	+	17.4858i	0.838938	+	0.703952i	−0.118387	+	0.992968i	$0.537772\pi$
$618$		0			0
$619$	35.9416	−	20.7509i	1.44462	−	0.834049i	0.446462	−	0.894802i	$-0.352684\pi$
$619$	35.9416	−	20.7509i	1.44462	−	0.834049i	0.998153	+	0.0607533i	$0.0193503\pi$
$620$	−1.54104	+	14.8569i	−0.0618897	+	0.596669i
$621$		0			0
$622$	16.6191	+	41.0531i	0.666366	+	1.64608i
$623$	−0.415606	+	2.35702i	−0.0166509	+	0.0944319i
$624$		0			0
$625$	−18.2879	+	15.3454i	−0.731518	+	0.613816i
$626$	−1.87932	−	8.81193i	−0.0751126	−	0.352196i
$627$		0			0
$628$	−18.4156	+	8.22925i	−0.734861	+	0.328383i
$629$	−16.1838	−	19.2871i	−0.645289	−	0.769026i
$630$		0			0
$631$	23.4291	+	4.13118i	0.932697	+	0.164460i	0.619293	−	0.785160i	$-0.287419\pi$
$631$	23.4291	+	4.13118i	0.932697	+	0.164460i	0.313404	+	0.949620i	$0.398531\pi$
$632$	13.2176	−	13.7434i	0.525769	−	0.546683i
$633$		0			0
$634$	−7.29181	+	22.4941i	−0.289595	+	0.893354i
$635$	6.87253	+	11.9036i	0.272728	+	0.472379i
$636$		0			0
$637$	55.7897	−	66.4875i	2.21047	−	2.63433i
$638$	2.80674	−	2.53067i	0.111120	−	0.100190i
$639$		0			0
$640$	23.9818	−	6.10109i	0.947963	−	0.241167i
$641$	8.89546	−	1.56851i	0.351350	−	0.0619524i	0.00481186	−	0.999988i	$-0.498468\pi$
$641$	8.89546	−	1.56851i	0.351350	−	0.0619524i	0.346538	+	0.938036i	$0.387357\pi$
$642$		0			0
$643$	11.7470	−	32.2747i	0.463258	−	1.27279i	−0.459763	−	0.888042i	$-0.652066\pi$
$643$	11.7470	−	32.2747i	0.463258	−	1.27279i	0.923021	−	0.384749i	$-0.125712\pi$
$644$	−2.01755	+	4.15095i	−0.0795026	+	0.163570i
$645$		0			0
$646$	−1.67332	+	28.9881i	−0.0658359	+	1.14052i
$647$		−	41.3144i		−	1.62424i	−0.583493	−	0.812118i	$-0.698315\pi$
$647$		−	41.3144i		−	1.62424i	0.583493	−	0.812118i	$-0.301685\pi$
$648$		0			0
$649$	5.12369	−	14.0772i	0.201122	−	0.552579i
$650$	−0.0681427	−	1.91392i	−0.00267278	−	0.0750703i
$651$		0			0
$652$	8.08487	+	8.34930i	0.316628	+	0.326984i
$653$	−0.0166961	+	0.0289185i	−0.000653369	+	0.00113167i	−0.866352	−	0.499434i	$-0.833541\pi$
$653$	−0.0166961	+	0.0289185i	−0.000653369	+	0.00113167i	0.865699	+	0.500566i	$0.166875\pi$
$654$		0			0
$655$	17.3324	−	20.6559i	0.677232	−	0.807094i
$656$	−2.25713	−	15.7484i	−0.0881261	−	0.614874i
$657$		0			0
$658$	20.1367	+	6.52764i	0.785011	+	0.254474i
$659$	5.07881	−	1.84854i	0.197842	−	0.0720087i	−0.241199	−	0.970476i	$-0.577541\pi$
$659$	5.07881	−	1.84854i	0.197842	−	0.0720087i	0.439041	+	0.898467i	$0.355318\pi$
$660$		0			0
$661$	20.3678	+	3.59139i	0.792216	+	0.139689i	0.555090	−	0.831790i	$-0.312684\pi$
$661$	20.3678	+	3.59139i	0.792216	+	0.139689i	0.237125	+	0.971479i	$0.423795\pi$
$662$	−1.64951	+	11.7952i	−0.0641099	+	0.458434i
$663$		0			0
$664$	13.3242	−	9.72233i	0.517080	−	0.377300i
$665$	39.3396	+	18.6317i	1.52552	+	0.722505i
$666$		0			0
$667$	0.993844	−	0.833934i	0.0384818	−	0.0322901i
$668$	−10.1403	+	0.722984i	−0.392342	+	0.0279731i
$669$		0			0
$670$	−39.4552	+	15.9722i	−1.52429	+	0.617061i
$671$	−0.989920	−	2.71978i	−0.0382154	−	0.104996i
$672$		0			0
$673$	−5.25004	+	3.03111i	−0.202374	+	0.116841i	−0.597762	−	0.801673i	$-0.703943\pi$
$673$	−5.25004	+	3.03111i	−0.202374	+	0.116841i	0.395388	+	0.918514i	$0.370610\pi$
$674$	34.3178	+	18.2171i	1.32187	+	0.701696i
$675$		0			0
$676$	−42.5933	−	30.8571i	−1.63820	−	1.18681i
$677$	−20.8614	−	12.0443i	−0.801768	−	0.462901i	0.0423209	−	0.999104i	$-0.486525\pi$
$677$	−20.8614	−	12.0443i	−0.801768	−	0.462901i	−0.844089	+	0.536203i	$0.819858\pi$
$678$		0			0
$679$	−1.73814	−	9.85750i	−0.0667038	−	0.378296i
$680$	26.1646	−	12.8277i	1.00337	−	0.491919i
$681$		0			0
$682$	3.09235	−	3.96360i	0.118412	−	0.151774i
$683$	−10.2979			−0.394038			−0.197019	−	0.980400i	$-0.563126\pi$
$683$	−10.2979			−0.394038			−0.197019	+	0.980400i	$0.563126\pi$
$684$		0			0
$685$	−7.68396			−0.293589
$686$	−27.1876	+	34.8475i	−1.03803	+	1.33048i
$687$		0			0
$688$	6.07544	−	4.77341i	0.231624	−	0.181984i
$689$	14.6678	+	83.1850i	0.558797	+	3.16910i
$690$		0			0
$691$	−37.1904	−	21.4719i	−1.41479	−	0.816830i	−0.418956	−	0.908007i	$-0.637604\pi$
$691$	−37.1904	−	21.4719i	−1.41479	−	0.816830i	−0.995835	+	0.0911772i	$0.970937\pi$
$692$	15.3398	−	21.1742i	0.583133	−	0.804921i
$693$		0			0
$694$	−20.9642	−	11.1285i	−0.795789	−	0.422432i
$695$	−33.9893	+	19.6237i	−1.28929	+	0.744370i
$696$		0			0
$697$	−6.40759	−	17.6047i	−0.242705	−	0.666826i
$698$	16.3631	−	6.62411i	0.619353	−	0.250726i
$699$		0			0
$700$	0.140284	+	1.96758i	0.00530223	+	0.0743674i
$701$	−36.7078	+	30.8015i	−1.38644	+	1.16336i	−0.419675	+	0.907675i	$0.637856\pi$
$701$	−36.7078	+	30.8015i	−1.38644	+	1.16336i	−0.966761	+	0.255683i	$0.917700\pi$
$702$		0			0
$703$	23.1979	+	2.16947i	0.874925	+	0.0818233i
$704$	−7.93145	−	2.54125i	−0.298928	−	0.0957768i
$705$		0			0
$706$	3.14045	−	22.4566i	0.118193	−	0.845166i
$707$	49.5618	+	8.73909i	1.86396	+	0.328667i
$708$		0			0
$709$	−34.5018	+	12.5576i	−1.29574	+	0.471612i	−0.895608	−	0.444844i	$-0.853259\pi$
$709$	−34.5018	+	12.5576i	−1.29574	+	0.471612i	−0.400135	+	0.916456i	$0.631037\pi$
$710$	−20.2788	−	6.57369i	−0.761050	−	0.246706i
$711$		0			0
$712$	−1.47930	−	0.100401i	−0.0554389	−	0.00376269i
$713$	1.10933	−	1.32205i	0.0415448	−	0.0495112i
$714$		0			0
$715$	7.13728	−	12.3621i	0.266919	−	0.462317i
$716$	−9.12775	+	8.83866i	−0.341120	+	0.330316i
$717$		0			0
$718$	0.293714	+	8.24956i	0.0109613	+	0.307871i
$719$	9.85308	−	27.0711i	0.367458	−	1.00958i	−0.608867	−	0.793273i	$-0.708376\pi$
$719$	9.85308	−	27.0711i	0.367458	−	1.00958i	0.976325	−	0.216310i	$-0.0694022\pi$
$720$		0			0
$721$		−	39.4576i		−	1.46948i
$722$	−17.7531	−	20.1699i	−0.660703	−	0.750647i
$723$		0			0
$724$	10.2041	+	4.95964i	0.379231	+	0.184324i
$725$	0.189649	−	0.521055i	0.00704337	−	0.0193515i
$726$		0			0
$727$	−2.54121	+	0.448083i	−0.0942482	+	0.0166185i	−0.220573	−	0.975370i	$-0.570793\pi$
$727$	−2.54121	+	0.448083i	−0.0942482	+	0.0166185i	0.126325	+	0.991989i	$0.459682\pi$
$728$	67.2057	+	45.1310i	2.49081	+	1.67267i
$729$		0			0
$730$	1.55372	−	1.40089i	0.0575057	−	0.0518494i
$731$	5.84832	−	6.96976i	0.216308	−	0.257786i
$732$		0			0
$733$	23.1144	+	40.0353i	0.853749	+	1.47874i	0.877801	+	0.479026i	$0.159010\pi$
$733$	23.1144	+	40.0353i	0.853749	+	1.47874i	−0.0240517	+	0.999711i	$0.507657\pi$
$734$	5.97815	−	18.4416i	0.220657	−	0.680693i
$735$		0			0
$736$	−2.69006	−	0.968727i	−0.0991571	−	0.0357077i
$737$	14.1085	+	2.48772i	0.519695	+	0.0916362i
$738$		0			0
$739$	6.09276	+	7.26107i	0.224126	+	0.267103i	0.866376	−	0.499392i	$-0.166443\pi$
$739$	6.09276	+	7.26107i	0.224126	+	0.267103i	−0.642250	+	0.766495i	$0.721999\pi$
$740$	−9.53957	−	21.3478i	−0.350681	−	0.784761i
$741$		0			0
$742$	−18.1467	−	85.0879i	−0.666185	−	3.12368i
$743$	−28.6241	+	24.0185i	−1.05012	+	0.881152i	−0.993106	−	0.117221i	$-0.962601\pi$
$743$	−28.6241	+	24.0185i	−1.05012	+	0.881152i	−0.0570104	+	0.998374i	$0.518157\pi$
$744$		0			0
$745$	−0.710309	+	4.02836i	−0.0260237	+	0.147588i
$746$	−3.62637	−	8.95799i	−0.132771	−	0.327975i
$747$		0			0
$748$	−9.75525	−	1.01187i	−0.356687	−	0.0369975i
$749$	64.8823	−	37.4598i	2.37075	−	1.36875i
$750$		0			0
$751$	−27.1350	−	22.7690i	−0.990169	−	0.830851i	−0.00457720	−	0.999990i	$-0.501457\pi$
$751$	−27.1350	−	22.7690i	−0.990169	−	0.830851i	−0.985592	+	0.169139i	$0.945901\pi$
$752$	−2.69150	+	12.8346i	−0.0981490	+	0.468030i
$753$		0			0
$754$	−12.0721	−	19.2901i	−0.439640	−	0.702504i
$755$	−8.05576	−	45.6865i	−0.293179	−	1.66270i
$756$		0			0
$757$	−9.01300	−	3.28047i	−0.327583	−	0.119231i	0.172993	−	0.984923i	$-0.444656\pi$
$757$	−9.01300	−	3.28047i	−0.327583	−	0.119231i	−0.500576	+	0.865693i	$0.666878\pi$
$758$	2.69530	+	2.10284i	0.0978977	+	0.0763786i
$759$		0			0
$760$	−8.87957	+	25.4621i	−0.322096	+	0.923607i
$761$	−11.6152			−0.421049			−0.210525	−	0.977589i	$-0.567517\pi$
$761$	−11.6152			−0.421049			−0.210525	+	0.977589i	$0.567517\pi$
$762$		0			0
$763$	12.3852	+	4.50784i	0.448374	+	0.163195i
$764$	15.7343	−	3.94580i	0.569247	−	0.142754i
$765$		0			0
$766$	7.09610	+	11.3389i	0.256392	+	0.409692i
$767$	−78.1204	−	45.1028i	−2.82077	−	1.62857i
$768$		0			0
$769$	33.0054	+	27.6948i	1.19021	+	0.998701i	0.999856	+	0.0169848i	$0.00540669\pi$
$769$	33.0054	+	27.6948i	1.19021	+	0.998701i	0.190350	+	0.981716i	$0.439038\pi$
$770$	−6.89362	+	12.9864i	−0.248429	+	0.467996i
$771$		0			0
$772$	−3.32982	−	0.345387i	−0.119843	−	0.0124307i
$773$	14.1204	+	38.7956i	0.507876	+	1.39538i	0.883423	+	0.468576i	$0.155233\pi$
$773$	14.1204	+	38.7956i	0.507876	+	1.39538i	−0.375547	+	0.926803i	$0.622545\pi$
$774$		0			0
$775$	0.128085	−	0.726406i	0.00460095	−	0.0260933i
$776$	5.95720	−	1.72140i	0.213851	−	0.0617947i
$777$		0			0
$778$	−6.70293	−	31.4294i	−0.240312	−	1.12680i
$779$	15.6684	+	7.42074i	0.561379	+	0.265875i
$780$		0			0
$781$	4.61190	+	5.49625i	0.165027	+	0.196671i
$782$	−3.33445	−	0.466308i	−0.119240	−	0.0166751i
$783$		0			0
$784$	−47.0456	−	29.2192i	−1.68020	−	1.04354i
$785$	−20.7286	+	7.54458i	−0.739834	+	0.269278i
$786$		0			0
$787$	12.9294	+	22.3943i	0.460882	+	0.798271i	0.999005	−	0.0445951i	$-0.0141998\pi$
$787$	12.9294	+	22.3943i	0.460882	+	0.798271i	−0.538123	+	0.842866i	$0.680866\pi$
$788$	−35.3224	−	10.0764i	−1.25831	−	0.358957i
$789$		0			0
$790$	15.4873	−	13.9639i	0.551013	−	0.496815i
$791$	26.9565	−	46.6900i	0.958463	−	1.66011i
$792$		0			0
$793$	−17.1634	+	3.02637i	−0.609490	+	0.107469i
$794$	−38.7540	+	1.37978i	−1.37533	+	0.0489667i
$795$		0			0
$796$	2.85390	+	1.38713i	0.101154	+	0.0491654i
$797$		−	13.1077i		−	0.464299i	−0.972680	−	0.232149i	$-0.925424\pi$
$797$		−	13.1077i		−	0.464299i	0.972680	−	0.232149i	$-0.0745758\pi$
$798$		0			0
$799$			15.4425i			0.546316i
$800$	−1.20271	+	0.216302i	−0.0425223	+	0.00764744i
$801$		0			0
$802$	−0.0623982	−	1.75258i	−0.00220336	−	0.0618857i
$803$	−0.693410	+	0.122267i	−0.0244699	+	0.00431470i
$804$		0			0
$805$	−2.52368	+	4.37114i	−0.0889479	+	0.154062i
$806$	−20.2707	−	22.4820i	−0.714005	−	0.791896i
$807$		0			0
$808$	−2.11117	+	31.1056i	−0.0742707	+	1.09429i
$809$	11.6463	+	20.1719i	0.409461	+	0.709207i	0.994829	−	0.101560i	$-0.0323834\pi$
$809$	11.6463	+	20.1719i	0.409461	+	0.709207i	−0.585368	+	0.810768i	$0.699050\pi$
$810$		0			0
$811$	8.28742	−	3.01638i	0.291011	−	0.105919i	−0.192390	−	0.981319i	$-0.561624\pi$
$811$	8.28742	−	3.01638i	0.291011	−	0.105919i	0.483400	+	0.875399i	$0.339402\pi$
$812$	13.1332	+	19.4136i	0.460885	+	0.681284i
$813$		0			0
$814$	−1.08994	+	7.79389i	−0.0382024	+	0.273176i
$815$	8.16998	+	9.73660i	0.286182	+	0.341058i
$816$		0			0
$817$	0.683623	+	8.39179i	0.0239169	+	0.293592i
$818$	−42.0824	+	8.97490i	−1.47138	+	0.313800i
$819$		0			0
$820$	−1.23735	−	17.3547i	−0.0432101	−	0.606052i
$821$	6.53533	−	37.0637i	0.228084	−	1.29353i	−0.628616	−	0.777716i	$-0.716378\pi$
$821$	6.53533	−	37.0637i	0.228084	−	1.29353i	0.856700	−	0.515815i	$-0.172511\pi$
$822$		0			0
$823$	8.74441	+	24.0251i	0.304811	+	0.837461i	0.993647	+	0.112544i	$0.0358998\pi$
$823$	8.74441	+	24.0251i	0.304811	+	0.837461i	−0.688836	+	0.724917i	$0.741878\pi$
$824$	24.3048	−	2.60483i	0.846697	−	0.0907435i
$825$		0			0
$826$	82.0653	+	43.5631i	2.85542	+	1.51575i
$827$	28.1487	+	23.6195i	0.978825	+	0.821332i	0.983912	−	0.178655i	$-0.0571746\pi$
$827$	28.1487	+	23.6195i	0.978825	+	0.821332i	−0.00508639	+	0.999987i	$0.501619\pi$
$828$		0			0
$829$	−38.9906	−	22.5112i	−1.35420	−	0.781847i	−0.365365	−	0.930865i	$-0.619056\pi$
$829$	−38.9906	−	22.5112i	−1.35420	−	0.781847i	−0.988835	+	0.149017i	$0.952389\pi$
$830$	15.2908	−	9.56928i	0.530752	−	0.332154i
$831$		0			0
$832$	−23.3628	+	44.3763i	−0.809961	+	1.53847i
$833$	−61.2825	−	22.3050i	−2.12331	−	0.772822i
$834$		0			0
$835$	−11.1178			−0.384747
$836$	7.07960	−	5.67901i	0.244853	−	0.196413i
$837$		0			0
$838$	12.4112	−	15.9079i	0.428736	−	0.549529i
$839$	20.7866	+	7.56569i	0.717632	+	0.261197i	0.674920	−	0.737891i	$-0.264178\pi$
$839$	20.7866	+	7.56569i	0.717632	+	0.261197i	0.0427119	+	0.999087i	$0.486400\pi$
$840$		0			0
$841$	3.89169	+	22.0709i	0.134196	+	0.761064i
$842$	−25.8228	+	16.1604i	−0.889914	+	0.556924i
$843$		0			0
$844$	12.9688	+	9.39541i	0.446406	+	0.323403i
$845$	−44.0628	−	36.9731i	−1.51581	−	1.27191i
$846$		0			0
$847$	−39.2083	+	22.6369i	−1.34721	+	0.777813i
$848$	51.2139	−	16.7950i	1.75869	−	0.576743i
$849$		0			0
$850$	−1.33386	+	0.539972i	−0.0457510	+	0.0185209i
$851$	−0.469136	+	2.66060i	−0.0160818	+	0.0912042i
$852$		0			0
$853$	−5.10458	+	4.28325i	−0.174778	+	0.146656i	−0.725980	−	0.687716i	$-0.758614\pi$
$853$	−5.10458	+	4.28325i	−0.174778	+	0.146656i	0.551203	+	0.834371i	$0.314169\pi$
$854$	17.5560	−	3.74416i	0.600754	−	0.128123i
$855$		0			0
$856$	27.3575	+	37.4928i	0.935060	+	1.28148i
$857$	25.0151	+	29.8119i	0.854501	+	1.01835i	0.999581	+	0.0289345i	$0.00921143\pi$
$857$	25.0151	+	29.8119i	0.854501	+	1.01835i	−0.145081	+	0.989420i	$0.546344\pi$
$858$		0			0
$859$	−27.8609	−	4.91263i	−0.950603	−	0.167617i	−0.323216	−	0.946325i	$-0.604764\pi$
$859$	−27.8609	−	4.91263i	−0.950603	−	0.167617i	−0.627386	+	0.778708i	$0.715875\pi$
$860$	6.99863	−	4.73454i	0.238651	−	0.161446i
$861$		0			0
$862$	−39.5899	−	12.8337i	−1.34844	−	0.437117i
$863$	−15.3191	−	26.5334i	−0.521467	−	0.903207i	−0.999688	−	0.0249679i	$-0.992052\pi$
$863$	−15.3191	−	26.5334i	−0.521467	−	0.903207i	0.478221	−	0.878239i	$-0.341282\pi$
$864$		0			0
$865$	18.3802	−	21.9047i	0.624947	−	0.744782i
$866$	−0.0320097	−	0.0355017i	−0.00108774	−	0.00120640i
$867$		0			0
$868$	21.6893	+	22.3987i	0.736184	+	0.760263i
$869$	−6.91183	+	1.21874i	−0.234468	+	0.0413430i
$870$		0			0
$871$	29.5043	−	81.0624i	0.999715	−	2.74669i
$872$	−1.95909	+	7.92653i	−0.0663431	+	0.268426i
$873$		0			0
$874$	2.49822	−	1.86187i	0.0845036	−	0.0629786i
$875$			52.0880i			1.76090i
$876$		0			0
$877$	−14.6867	+	40.3513i	−0.495934	+	1.36257i	0.399239	+	0.916847i	$0.369275\pi$
$877$	−14.6867	+	40.3513i	−0.495934	+	1.36257i	−0.895172	+	0.445720i	$0.852948\pi$
$878$	−6.25675	+	0.222763i	−0.211155	+	0.00751789i
$879$		0			0
$880$	−8.45434	−	3.38898i	−0.284996	−	0.114242i
$881$	0.482168	−	0.835140i	0.0162447	−	0.0281366i	−0.857789	−	0.514002i	$-0.828162\pi$
$881$	0.482168	−	0.835140i	0.0162447	−	0.0281366i	0.874033	+	0.485866i	$0.161496\pi$
$882$		0			0
$883$	1.59412	−	1.89979i	0.0536463	−	0.0639332i	−0.738554	−	0.674194i	$-0.764491\pi$
$883$	1.59412	−	1.89979i	0.0536463	−	0.0639332i	0.792200	+	0.610261i	$0.208935\pi$
$884$	−16.2006	+	56.7906i	−0.544886	+	1.91007i
$885$		0			0
$886$	−12.2873	+	37.9043i	−0.412799	+	1.27342i
$887$	−25.2499	+	9.19021i	−0.847808	+	0.308577i	−0.729146	−	0.684358i	$-0.760083\pi$
$887$	−25.2499	+	9.19021i	−0.847808	+	0.308577i	−0.118662	+	0.992935i	$0.537860\pi$
$888$		0			0
$889$	28.2557	+	4.98225i	0.947667	+	0.167099i
$890$	−1.60588	−	0.224574i	−0.0538291	−	0.00752775i
$891$		0			0
$892$	−35.9736	+	16.0753i	−1.20449	+	0.538242i
$893$	−10.0442	−	10.1651i	−0.336117	−	0.340163i
$894$		0			0
$895$	−10.6444	+	8.93171i	−0.355803	+	0.298554i
$896$	22.4219	−	46.5344i	0.749065	−	1.55460i
$897$		0			0
$898$	−20.2015	−	49.9025i	−0.674133	−	1.66527i
$899$	−2.99764	−	8.23594i	−0.0999768	−	0.274684i
$900$		0			0
$901$	54.9653	−	31.7342i	1.83116	−	1.05722i
$902$	−2.74563	+	5.17229i	−0.0914196	+	0.172218i
$903$		0			0
$904$	30.5393	+	13.5222i	1.01572	+	0.449741i
$905$	10.7453	+	6.20383i	0.357187	+	0.206222i
$906$		0			0
$907$	−1.65880	−	9.40750i	−0.0550794	−	0.312371i	0.944804	−	0.327636i	$-0.106252\pi$
$907$	−1.65880	−	9.40750i	−0.0550794	−	0.312371i	−0.999883	+	0.0152650i	$0.995141\pi$
$908$	−0.863975	−	3.44519i	−0.0286720	−	0.114333i
$909$		0			0
$910$	69.8011	+	54.4579i	2.31388	+	1.80526i
$911$	52.8625			1.75141			0.875706	−	0.482845i	$-0.160397\pi$
$911$	52.8625			1.75141			0.875706	+	0.482845i	$0.160397\pi$
$912$		0			0
$913$	−6.07112			−0.200925
$914$	−16.2300	−	12.6624i	−0.536840	−	0.418836i
$915$		0			0
$916$	4.89846	+	19.5331i	0.161850	+	0.645392i
$917$	−9.77395	−	55.4308i	−0.322764	−	1.83049i
$918$		0			0
$919$	−27.7489	−	16.0208i	−0.915352	−	0.528479i	−0.0332027	−	0.999449i	$-0.510571\pi$
$919$	−27.7489	−	16.0208i	−0.915352	−	0.528479i	−0.882149	+	0.470970i	$0.843904\pi$
$920$	−2.85910	−	1.26595i	−0.0942618	−	0.0417372i
$921$		0			0
$922$	−15.6709	+	29.5212i	−0.516093	+	0.972228i
$923$	37.4151	−	21.6016i	1.23153	−	0.711025i
$924$		0			0
$925$	0.394924	+	1.08504i	0.0129850	+	0.0356761i
$926$	−1.40601	−	3.47319i	−0.0462045	−	0.114136i
$927$		0			0
$928$	−11.0913	+	9.37130i	−0.364088	+	0.307628i
$929$	30.5227	−	25.6116i	1.00142	−	0.840288i	0.0142362	−	0.999899i	$-0.495468\pi$
$929$	30.5227	−	25.6116i	1.00142	−	0.840288i	0.987180	+	0.159611i	$0.0510239\pi$
$930$		0			0
$931$	54.8473	−	25.1774i	1.79755	−	0.825154i
$932$	24.9749	−	11.1604i	0.818079	−	0.365570i
$933$		0			0
$934$	−4.62627	−	0.646962i	−0.151376	−	0.0211693i
$935$	−10.5628	−	1.86250i	−0.345440	−	0.0609104i
$936$		0			0
$937$	−0.987865	+	0.359553i	−0.0322721	+	0.0117461i	−0.358106	−	0.933681i	$-0.616577\pi$
$937$	−0.987865	+	0.359553i	−0.0322721	+	0.0117461i	0.325834	+	0.945427i	$0.394355\pi$
$938$	−27.3991	+	84.5219i	−0.894612	+	2.75974i
$939$		0			0
$940$	−3.93422	+	13.7912i	−0.128320	+	0.449821i
$941$	18.3607	−	21.8815i	0.598542	−	0.713315i	−0.378681	−	0.925527i	$-0.623622\pi$
$941$	18.3607	−	21.8815i	0.598542	−	0.713315i	0.977224	+	0.212212i	$0.0680668\pi$
$942$		0			0
$943$	−1.00515	+	1.74096i	−0.0327320	+	0.0566935i
$944$	−21.4161	+	53.4258i	−0.697034	+	1.73886i
$945$		0			0
$946$	−2.84208	+	0.101189i	−0.0924041	+	0.00328992i
$947$	−6.62594	+	18.2046i	−0.215314	+	0.591571i	−0.999584	−	0.0288495i	$-0.990816\pi$
$947$	−6.62594	+	18.2046i	−0.215314	+	0.591571i	0.784270	+	0.620420i	$0.213038\pi$
$948$		0			0
$949$			4.23976i			0.137628i
$950$	0.526808	−	1.22302i	0.0170919	−	0.0396799i
$951$		0			0
$952$	14.5946	−	59.0504i	0.473015	−	1.91383i
$953$	−7.47431	+	20.5355i	−0.242117	+	0.665210i	0.757802	+	0.652484i	$0.226273\pi$
$953$	−7.47431	+	20.5355i	−0.242117	+	0.665210i	−0.999919	+	0.0127259i	$0.995949\pi$
$954$		0			0
$955$	17.4706	−	3.08053i	0.565335	−	0.0996837i
$956$	−6.39767	−	6.60692i	−0.206915	−	0.213683i
$957$		0			0
$958$	−4.12490	−	4.57488i	−0.133269	−	0.147808i
$959$	−10.3101	+	12.2871i	−0.332930	+	0.396770i
$960$		0			0
$961$	9.67055	+	16.7499i	0.311953	+	0.540319i
$962$	45.0781	+	14.6128i	1.45338	+	0.471135i
$963$		0			0
$964$	−15.9012	+	10.7571i	−0.512142	+	0.346462i
$965$	−3.60546	−	0.635740i	−0.116064	−	0.0204652i
$966$		0			0
$967$	24.6769	+	29.4088i	0.793555	+	0.945722i	0.999460	−	0.0328496i	$-0.0104582\pi$
$967$	24.6769	+	29.4088i	0.793555	+	0.945722i	−0.205905	+	0.978572i	$0.566014\pi$
$968$	−16.5321	−	22.6568i	−0.531361	−	0.728218i
$969$		0			0
$970$	6.63228	−	1.41446i	0.212950	−	0.0454156i
$971$	−1.44887	+	1.21575i	−0.0464966	+	0.0390153i	−0.665740	−	0.746184i	$-0.731884\pi$
$971$	−1.44887	+	1.21575i	−0.0464966	+	0.0390153i	0.619243	+	0.785199i	$0.287439\pi$
$972$		0			0
$973$	−14.2263	+	80.6811i	−0.456073	+	2.58652i
$974$	−21.3664	+	8.64955i	−0.684624	+	0.277149i
$975$		0			0
$976$	3.46528	+	10.5668i	0.110921	+	0.338237i
$977$	10.0011	−	5.77416i	0.319965	−	0.184732i	−0.331412	−	0.943486i	$-0.607525\pi$
$977$	10.0011	−	5.77416i	0.319965	−	0.184732i	0.651377	+	0.758754i	$0.274192\pi$
$978$		0			0
$979$	0.418066	+	0.350799i	0.0133614	+	0.0112116i
$980$	−49.0470	−	35.5326i	−1.56675	−	1.13505i
$981$		0			0
$982$	34.0049	−	21.2809i	1.08514	−	0.679100i
$983$	9.07049	+	51.4413i	0.289304	+	1.64072i	0.689494	+	0.724291i	$0.257833\pi$
$983$	9.07049	+	51.4413i	0.289304	+	1.64072i	−0.400190	+	0.916432i	$0.631056\pi$
$984$		0			0
$985$	−37.7476	−	13.7390i	−1.20274	−	0.437761i
$986$	−10.5178	+	13.4811i	−0.334956	+	0.429327i
$987$		0			0
$988$	−26.2739	−	47.9201i	−0.835885	−	1.52454i
$989$	−0.976292			−0.0310443
$990$		0			0
$991$	−27.2851	−	9.93097i	−0.866740	−	0.315468i	−0.129894	−	0.991528i	$-0.541464\pi$
$991$	−27.2851	−	9.93097i	−0.866740	−	0.315468i	−0.736846	+	0.676060i	$0.763686\pi$
$992$	−12.3652	+	14.8387i	−0.392595	+	0.471130i
$993$		0			0
$994$	−37.7211	+	23.6065i	−1.19644	+	0.748754i
$995$	3.00528	+	1.73510i	0.0952739	+	0.0550064i
$996$		0			0
$997$	−20.7606	−	17.4202i	−0.657494	−	0.551703i	0.251841	−	0.967769i	$-0.418964\pi$
$997$	−20.7606	−	17.4202i	−0.657494	−	0.551703i	−0.909334	+	0.416066i	$0.863408\pi$
$998$	30.1388	+	15.9987i	0.954027	+	0.506431i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.b.127.9		60
3.2	odd	2		228.2.w.b.127.2	yes	60
4.3	odd	2		684.2.cf.c.127.8		60
12.11	even	2		228.2.w.a.127.3	yes	60
19.3	odd	18		684.2.cf.c.307.8		60
57.41	even	18		228.2.w.a.79.3	✓	60
76.3	even	18	inner	684.2.cf.b.307.9		60
228.155	odd	18		228.2.w.b.79.2	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.79.3	✓	60	57.41	even	18
228.2.w.a.127.3	yes	60	12.11	even	2
228.2.w.b.79.2	yes	60	228.155	odd	18
228.2.w.b.127.2	yes	60	3.2	odd	2
684.2.cf.b.127.9		60	1.1	even	1	trivial
684.2.cf.b.307.9		60	76.3	even	18	inner
684.2.cf.c.127.8		60	4.3	odd	2
684.2.cf.c.307.8		60	19.3	odd	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(1.11501 + 0.869917i) q^{2} +(0.486490 + 1.93993i) q^{4} +(0.379809 + 2.15400i) q^{5} +(3.95398 + 2.28283i) q^{7} +(-1.14514 + 2.58625i) q^{8} +(-1.45031 + 2.73213i) q^{10} +(0.901599 - 0.520538i) q^{11} +(-2.14406 - 5.89076i) q^{13} +(2.42285 + 5.98501i) q^{14} +(-3.52665 + 1.88751i) q^{16} +(-3.60831 + 3.02773i) q^{17} +(0.405875 - 4.33996i) q^{19} +(-3.99384 + 1.78470i) q^{20} +(1.45812 + 0.203911i) q^{22} +(0.497757 + 0.0877679i) q^{23} +(0.202995 - 0.0738841i) q^{25} +(2.73382 - 8.43340i) q^{26} +(-2.50496 + 8.78101i) q^{28} +(1.64993 - 1.96631i) q^{29} +(1.70726 - 2.95706i) q^{31} +(-5.57423 - 0.963299i) q^{32} +(-6.65717 + 0.237020i) q^{34} +(-3.41546 + 9.38391i) q^{35} +5.34518i q^{37} +(4.22796 - 4.48602i) q^{38} +(-6.00571 - 1.48435i) q^{40} +(-1.36033 + 3.73748i) q^{41} +(-1.90224 + 0.335417i) q^{43} +(1.44843 + 1.49580i) q^{44} +(0.478652 + 0.530869i) q^{46} +(2.10734 - 2.51143i) q^{47} +(6.92262 + 11.9903i) q^{49} +(0.290614 + 0.0942071i) q^{50} +(10.3846 - 7.02513i) q^{52} +(-13.2697 - 2.33980i) q^{53} +(1.46367 + 1.74434i) q^{55} +(-10.4318 + 7.61181i) q^{56} +(3.55022 - 0.757153i) q^{58} +(11.0231 - 9.24945i) q^{59} +(0.482765 - 2.73790i) q^{61} +(4.47600 - 1.81197i) q^{62} +(-5.37733 - 5.92320i) q^{64} +(11.8744 - 6.85567i) q^{65} +(10.5415 + 8.84536i) q^{67} +(-7.62899 - 5.52690i) q^{68} +(-11.9715 + 7.49198i) q^{70} +(1.19674 + 6.78706i) q^{71} +(-0.635538 - 0.231317i) q^{73} +(-4.64986 + 5.95993i) q^{74} +(8.61667 - 1.32398i) q^{76} +4.75320 q^{77} +(-6.33497 - 2.30574i) q^{79} +(-5.40516 - 6.87952i) q^{80} +(-4.76808 + 2.98395i) q^{82} +(-5.05030 - 2.91579i) q^{83} +(-7.89220 - 6.62234i) q^{85} +(-2.41280 - 1.28080i) q^{86} +(0.313787 + 2.92784i) q^{88} +(0.179291 + 0.492599i) q^{89} +(4.97003 - 28.1865i) q^{91} +(0.0718903 + 1.00831i) q^{92} +(4.53444 - 0.967059i) q^{94} +(9.50244 - 0.774100i) q^{95} +(-1.40922 - 1.67944i) q^{97} +(-2.71180 + 19.3914i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 3 q^{2} - 3 q^{4} + 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} + 21 q^{16} + 18 q^{19} - 30 q^{20} - 12 q^{22} - 18 q^{28} - 12 q^{31} - 33 q^{32} - 15 q^{34} + 84 q^{38} - 87 q^{40} + 12 q^{41} - 18 q^{43}+ \cdots + 105 q^{98}+O(q^{100}) \) 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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