LMFDB - Embedded newform 684.2.cf.c.523.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			523.10
Character	$\chi$	$=$	684.523
Dual form			684.2.cf.c.667.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37612 + 0.326044i) q^{2} +(1.78739 + 0.897349i) q^{4} +(1.25586 + 0.457097i) q^{5} +(-1.18216 - 0.682521i) q^{7} +(2.16708 + 1.81762i) q^{8} +(1.57918 + 1.03849i) q^{10} +(1.56682 - 0.904604i) q^{11} +(3.73606 - 4.45246i) q^{13} +(-1.40426 - 1.32467i) q^{14} +(2.38953 + 3.20783i) q^{16} +(0.927369 + 5.25937i) q^{17} +(-4.15334 - 1.32280i) q^{19} +(1.83454 + 1.94396i) q^{20} +(2.45107 - 0.733988i) q^{22} +(2.07944 + 5.71321i) q^{23} +(-2.46197 - 2.06583i) q^{25} +(6.59294 - 4.90898i) q^{26} +(-1.50052 - 2.28074i) q^{28} +(-0.589123 - 0.103878i) q^{29} +(-0.450194 + 0.779760i) q^{31} +(2.24238 + 5.19343i) q^{32} +(-0.438619 + 7.53987i) q^{34} +(-1.17266 - 1.39752i) q^{35} +7.89511i q^{37} +(-5.28418 - 3.17450i) q^{38} +(1.89073 + 3.27326i) q^{40} +(0.449691 + 0.535921i) q^{41} +(2.55877 - 7.03016i) q^{43} +(3.61227 - 0.210897i) q^{44} +(0.998791 + 8.54003i) q^{46} +(-6.84854 - 1.20758i) q^{47} +(-2.56833 - 4.44848i) q^{49} +(-2.71440 - 3.64554i) q^{50} +(10.6732 - 4.60574i) q^{52} +(-3.67511 - 10.0973i) q^{53} +(2.38121 - 0.419871i) q^{55} +(-1.32127 - 3.62780i) q^{56} +(-0.776832 - 0.335028i) q^{58} +(-1.38285 - 7.84254i) q^{59} +(-9.66972 + 3.51949i) q^{61} +(-0.873756 + 0.926257i) q^{62} +(1.39249 + 7.87788i) q^{64} +(6.72719 - 3.88394i) q^{65} +(0.147890 - 0.838725i) q^{67} +(-3.06192 + 10.2327i) q^{68} +(-1.15806 - 2.30548i) q^{70} +(-0.630487 - 0.229479i) q^{71} +(-2.99543 + 2.51346i) q^{73} +(-2.57415 + 10.8646i) q^{74} +(-6.23662 - 6.09135i) q^{76} -2.46965 q^{77} +(2.83807 - 2.38143i) q^{79} +(1.53464 + 5.12084i) q^{80} +(0.444093 + 0.884109i) q^{82} +(8.34975 + 4.82073i) q^{83} +(-1.23939 + 7.02896i) q^{85} +(5.81331 - 8.84005i) q^{86} +(5.03966 + 0.887540i) q^{88} +(-2.69672 + 3.21383i) q^{89} +(-7.45552 + 2.71359i) q^{91} +(-1.40997 + 12.0777i) q^{92} +(-9.03066 - 3.89470i) q^{94} +(-4.61138 - 3.55973i) q^{95} +(7.53165 - 1.32803i) q^{97} +(-2.08392 - 6.95901i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 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 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	1.37612	+	0.326044i	0.973061	+	0.230548i
$2$	1.37612	+	0.326044i	0.973061	+	0.230548i
$3$		0			0
$3$		0			0
$4$	1.78739	+	0.897349i	0.893695	+	0.448674i
$5$	1.25586	+	0.457097i	0.561640	+	0.204420i	0.607210	−	0.794541i	$-0.292288\pi$
$5$	1.25586	+	0.457097i	0.561640	+	0.204420i	−0.0455709	+	0.998961i	$0.514511\pi$
$6$		0			0
$7$	−1.18216	−	0.682521i	−0.446815	−	0.257969i	0.259669	−	0.965698i	$-0.416387\pi$
$7$	−1.18216	−	0.682521i	−0.446815	−	0.257969i	−0.706484	+	0.707729i	$0.749720\pi$
$8$	2.16708	+	1.81762i	0.766179	+	0.642627i
$9$		0			0
$10$	1.57918	+	1.03849i	0.499381	+	0.328398i
$11$	1.56682	−	0.904604i	0.472414	−	0.272748i	−0.244836	−	0.969565i	$-0.578734\pi$
$11$	1.56682	−	0.904604i	0.472414	−	0.272748i	0.717250	+	0.696816i	$0.245401\pi$
$12$		0			0
$13$	3.73606	−	4.45246i	1.03620	−	1.23489i	0.0646821	−	0.997906i	$-0.479397\pi$
$13$	3.73606	−	4.45246i	1.03620	−	1.23489i	0.971514	−	0.236984i	$-0.0761589\pi$
$14$	−1.40426	−	1.32467i	−0.375304	−	0.354032i
$15$		0			0
$16$	2.38953	+	3.20783i	0.597383	+	0.801956i
$17$	0.927369	+	5.25937i	0.224920	+	1.27559i	0.862838	+	0.505481i	$0.168685\pi$
$17$	0.927369	+	5.25937i	0.224920	+	1.27559i	−0.637918	+	0.770104i	$0.720204\pi$
$18$		0			0
$19$	−4.15334	−	1.32280i	−0.952841	−	0.303471i
$19$	−4.15334	−	1.32280i	−0.952841	−	0.303471i
$20$	1.83454	+	1.94396i	0.410217	+	0.434683i
$21$		0			0
$22$	2.45107	−	0.733988i	0.522569	−	0.156487i
$23$	2.07944	+	5.71321i	0.433593	+	1.19129i	0.943591	+	0.331112i	$0.107424\pi$
$23$	2.07944	+	5.71321i	0.433593	+	1.19129i	−0.509998	+	0.860175i	$0.670354\pi$
$24$		0			0
$25$	−2.46197	−	2.06583i	−0.492393	−	0.413167i
$26$	6.59294	−	4.90898i	1.29298	−	0.962730i
$27$		0			0
$28$	−1.50052	−	2.28074i	−0.283572	−	0.431020i
$29$	−0.589123	−	0.103878i	−0.109397	−	0.0192897i	0.118681	−	0.992932i	$-0.462133\pi$
$29$	−0.589123	−	0.103878i	−0.109397	−	0.0192897i	−0.228079	+	0.973643i	$0.573244\pi$
$30$		0			0
$31$	−0.450194	+	0.779760i	−0.0808573	+	0.140049i	−0.903618	−	0.428338i	$-0.859099\pi$
$31$	−0.450194	+	0.779760i	−0.0808573	+	0.140049i	0.822761	+	0.568387i	$0.192432\pi$
$32$	2.24238	+	5.19343i	0.396400	+	0.918078i
$33$		0			0
$34$	−0.438619	+	7.53987i	−0.0752226	+	1.29308i
$35$	−1.17266	−	1.39752i	−0.198215	−	0.236223i
$36$		0			0
$37$			7.89511i			1.29795i	0.760811	+	0.648974i	$0.224802\pi$
$37$			7.89511i			1.29795i	−0.760811	+	0.648974i	$0.775198\pi$
$38$	−5.28418	−	3.17450i	−0.857208	−	0.514971i
$39$		0			0
$40$	1.89073	+	3.27326i	0.298951	+	0.517547i
$41$	0.449691	+	0.535921i	0.0702300	+	0.0836968i	0.800015	−	0.599979i	$-0.204825\pi$
$41$	0.449691	+	0.535921i	0.0702300	+	0.0836968i	−0.729786	+	0.683676i	$0.760380\pi$
$42$		0			0
$43$	2.55877	−	7.03016i	0.390209	−	1.07209i	−0.576697	−	0.816958i	$-0.695659\pi$
$43$	2.55877	−	7.03016i	0.390209	−	1.07209i	0.966906	−	0.255132i	$-0.0821189\pi$
$44$	3.61227	−	0.210897i	0.544570	−	0.0317939i
$45$		0			0
$46$	0.998791	+	8.54003i	0.147264	+	1.25916i
$47$	−6.84854	−	1.20758i	−0.998962	−	0.176144i	−0.349824	−	0.936815i	$-0.613759\pi$
$47$	−6.84854	−	1.20758i	−0.998962	−	0.176144i	−0.649137	+	0.760671i	$0.724870\pi$
$48$		0			0
$49$	−2.56833	−	4.44848i	−0.366904	−	0.635497i
$50$	−2.71440	−	3.64554i	−0.383874	−	0.515557i
$51$		0			0
$52$	10.6732	−	4.60574i	1.48011	−	0.638701i
$53$	−3.67511	−	10.0973i	−0.504815	−	1.38697i	−0.886522	−	0.462686i	$-0.846886\pi$
$53$	−3.67511	−	10.0973i	−0.504815	−	1.38697i	0.381707	−	0.924283i	$-0.375336\pi$
$54$		0			0
$55$	2.38121	−	0.419871i	0.321082	−	0.0566154i
$56$	−1.32127	−	3.62780i	−0.176563	−	0.484786i
$57$		0			0
$58$	−0.776832	−	0.335028i	−0.102003	−	0.0439914i
$59$	−1.38285	−	7.84254i	−0.180032	−	1.02101i	−0.932174	−	0.362011i	$-0.882090\pi$
$59$	−1.38285	−	7.84254i	−0.180032	−	1.02101i	0.752142	−	0.659001i	$-0.229021\pi$
$60$		0			0
$61$	−9.66972	+	3.51949i	−1.23808	+	0.450624i	−0.876357	−	0.481661i	$-0.840034\pi$
$61$	−9.66972	+	3.51949i	−1.23808	+	0.450624i	−0.361723	+	0.932286i	$0.617811\pi$
$62$	−0.873756	+	0.926257i	−0.110967	+	0.117635i
$63$		0			0
$64$	1.39249	+	7.87788i	0.174061	+	0.984735i
$65$	6.72719	−	3.88394i	0.834405	−	0.481744i
$66$		0			0
$67$	0.147890	−	0.838725i	0.0180676	−	0.102467i	−0.974440	−	0.224646i	$-0.927877\pi$
$67$	0.147890	−	0.838725i	0.0180676	−	0.102467i	0.992508	+	0.122180i	$0.0389884\pi$
$68$	−3.06192	+	10.2327i	−0.371312	+	1.24090i
$69$		0			0
$70$	−1.15806	−	2.30548i	−0.138414	−	0.275558i
$71$	−0.630487	−	0.229479i	−0.0748251	−	0.0272341i	0.304336	−	0.952565i	$-0.401565\pi$
$71$	−0.630487	−	0.229479i	−0.0748251	−	0.0272341i	−0.379162	+	0.925331i	$0.623788\pi$
$72$		0			0
$73$	−2.99543	+	2.51346i	−0.350588	+	0.294178i	−0.801026	−	0.598629i	$-0.795712\pi$
$73$	−2.99543	+	2.51346i	−0.350588	+	0.294178i	0.450438	+	0.892808i	$0.351268\pi$
$74$	−2.57415	+	10.8646i	−0.299239	+	1.26298i
$75$		0			0
$76$	−6.23662	−	6.09135i	−0.715390	−	0.698726i
$77$	−2.46965			−0.281442
$78$		0			0
$79$	2.83807	−	2.38143i	0.319308	−	0.267932i	−0.469018	−	0.883188i	$-0.655392\pi$
$79$	2.83807	−	2.38143i	0.319308	−	0.267932i	0.788327	+	0.615257i	$0.210948\pi$
$80$	1.53464	+	5.12084i	0.171578	+	0.572527i
$81$		0			0
$82$	0.444093	+	0.884109i	0.0490419	+	0.0976335i
$83$	8.34975	+	4.82073i	0.916504	+	0.529144i	0.882518	−	0.470278i	$-0.155847\pi$
$83$	8.34975	+	4.82073i	0.916504	+	0.529144i	0.0339859	+	0.999422i	$0.489180\pi$
$84$		0			0
$85$	−1.23939	+	7.02896i	−0.134431	+	0.762397i
$86$	5.81331	−	8.84005i	0.626865	−	0.953247i
$87$		0			0
$88$	5.03966	+	0.887540i	0.537229	+	0.0946120i
$89$	−2.69672	+	3.21383i	−0.285852	+	0.340665i	−0.889793	−	0.456363i	$-0.849152\pi$
$89$	−2.69672	+	3.21383i	−0.285852	+	0.340665i	0.603941	+	0.797029i	$0.293596\pi$
$90$		0			0
$91$	−7.45552	+	2.71359i	−0.781551	+	0.284461i
$92$	−1.40997	+	12.0777i	−0.147000	+	1.25919i
$93$		0			0
$94$	−9.03066	−	3.89470i	−0.931441	−	0.401707i
$95$	−4.61138	−	3.55973i	−0.473117	−	0.365221i
$96$		0			0
$97$	7.53165	−	1.32803i	0.764723	−	0.134841i	0.222336	−	0.974970i	$-0.428632\pi$
$97$	7.53165	−	1.32803i	0.764723	−	0.134841i	0.542387	+	0.840129i	$0.317521\pi$
$98$	−2.08392	−	6.95901i	−0.210508	−	0.702966i
$99$		0			0
$100$	−2.54672	−	5.90169i	−0.254672	−	0.590169i
$101$	−0.403018	−	0.338172i	−0.0401018	−	0.0336494i	0.622517	−	0.782607i	$-0.286110\pi$
$101$	−0.403018	−	0.338172i	−0.0401018	−	0.0336494i	−0.662618	+	0.748957i	$0.730555\pi$
$102$		0			0
$103$	−8.31062	−	14.3944i	−0.818870	−	1.41832i	−0.906515	−	0.422173i	$-0.861268\pi$
$103$	−8.31062	−	14.3944i	−0.818870	−	1.41832i	0.0876453	−	0.996152i	$-0.472066\pi$
$104$	16.1892	−	2.85810i	1.58749	−	0.280259i
$105$		0			0
$106$	−1.76522	−	15.0933i	−0.171453	−	1.46599i
$107$	2.53421	−	4.38938i	0.244991	−	0.424337i	−0.717138	−	0.696931i	$-0.754548\pi$
$107$	2.53421	−	4.38938i	0.244991	−	0.424337i	0.962129	+	0.272594i	$0.0878816\pi$
$108$		0			0
$109$	−0.783126	+	2.15162i	−0.0750099	+	0.206088i	−0.971531	−	0.236914i	$-0.923864\pi$
$109$	−0.783126	+	2.15162i	−0.0750099	+	0.206088i	0.896521	+	0.443002i	$0.146086\pi$
$110$	3.41371	+	0.198587i	0.325485	+	0.0189345i
$111$		0			0
$112$	−0.635402	−	5.42307i	−0.0600398	−	0.512432i
$113$			11.5712i			1.08852i	0.838915	+	0.544262i	$0.183190\pi$
$113$			11.5712i			1.08852i	−0.838915	+	0.544262i	$0.816810\pi$
$114$		0			0
$115$			8.12553i			0.757709i
$116$	−0.959777	−	0.714319i	−0.0891131	−	0.0663229i
$117$		0			0
$118$	0.654049	−	11.2431i	0.0602101	−	1.03501i
$119$	2.49333	−	6.85038i	0.228563	−	0.627973i
$120$		0			0
$121$	−3.86338	+	6.69157i	−0.351217	+	0.608325i
$122$	−14.4542	+	1.69047i	−1.30862	+	0.153048i
$123$		0			0
$124$	−1.50439	+	0.989754i	−0.135098	+	0.0888825i
$125$	−5.48876	−	9.50682i	−0.490930	−	0.850316i
$126$		0			0
$127$	−7.85651	−	6.59239i	−0.697153	−	0.584980i	0.223809	−	0.974633i	$-0.428151\pi$
$127$	−7.85651	−	6.59239i	−0.697153	−	0.584980i	−0.920962	+	0.389652i	$0.872595\pi$
$128$	−0.652313	+	11.2949i	−0.0576569	+	0.998336i
$129$		0			0
$130$	10.5237	−	3.15140i	0.922992	−	0.276396i
$131$	−16.8151	+	2.96495i	−1.46914	+	0.259049i	−0.850229	−	0.526413i	$-0.823536\pi$
$131$	−16.8151	+	2.96495i	−1.46914	+	0.259049i	−0.618910	+	0.785462i	$0.712425\pi$
$132$		0			0
$133$	4.00708	+	4.39850i	0.347458	+	0.381398i
$134$	0.476975	−	1.10596i	0.0412043	−	0.0955407i
$135$		0			0
$136$	−7.54988	+	13.0831i	−0.647397	+	1.12187i
$137$	1.40505	−	0.511397i	0.120042	−	0.0436916i	−0.281301	−	0.959620i	$-0.590766\pi$
$137$	1.40505	−	0.511397i	0.120042	−	0.0436916i	0.401343	+	0.915928i	$0.368544\pi$
$138$		0			0
$139$	11.9953	−	14.2955i	1.01743	−	1.21253i	0.0404549	−	0.999181i	$-0.487119\pi$
$139$	11.9953	−	14.2955i	1.01743	−	1.21253i	0.976977	−	0.213346i	$-0.0684363\pi$
$140$	−0.841934	−	3.55019i	−0.0711564	−	0.300046i
$141$		0			0
$142$	−0.792804	−	0.521356i	−0.0665306	−	0.0437512i
$143$	1.82602	−	10.3559i	0.152699	−	0.866000i
$144$		0			0
$145$	−0.692376	−	0.399743i	−0.0574987	−	0.0331969i
$146$	−4.94155	+	2.48217i	−0.408966	+	0.205426i
$147$		0			0
$148$	−7.08467	+	14.1116i	−0.582356	+	1.15997i
$149$	−9.83882	+	8.25575i	−0.806028	+	0.676337i	−0.949656	−	0.313294i	$-0.898567\pi$
$149$	−9.83882	+	8.25575i	−0.806028	+	0.676337i	0.143629	+	0.989632i	$0.454123\pi$
$150$		0			0
$151$	12.7827			1.04024			0.520122	−	0.854092i	$-0.325887\pi$
$151$	12.7827			1.04024			0.520122	+	0.854092i	$0.325887\pi$
$152$	−6.59627	−	10.4158i	−0.535028	−	0.844834i
$153$		0			0
$154$	−3.39852	−	0.805214i	−0.273861	−	0.0648860i
$155$	−0.921809	+	0.773490i	−0.0740415	+	0.0621282i
$156$		0			0
$157$	−13.2613	−	4.82672i	−1.05837	−	0.385214i	−0.246553	−	0.969129i	$-0.579298\pi$
$157$	−13.2613	−	4.82672i	−1.05837	−	0.385214i	−0.811815	+	0.583915i	$0.801520\pi$
$158$	4.68197	−	2.35178i	0.372478	−	0.187098i
$159$		0			0
$160$	0.442220	+	7.54723i	0.0349605	+	0.596661i
$161$	1.44116	−	8.17320i	0.113579	−	0.644139i
$162$		0			0
$163$	−15.4400	+	8.91427i	−1.20935	+	0.698219i	−0.962618	−	0.270864i	$-0.912691\pi$
$163$	−15.4400	+	8.91427i	−1.20935	+	0.698219i	−0.246734	+	0.969083i	$0.579357\pi$
$164$	0.322866	+	1.36143i	0.0252116	+	0.106310i
$165$		0			0
$166$	9.91845	+	9.35627i	0.769821	+	0.726187i
$167$	−9.72858	+	3.54091i	−0.752820	+	0.274004i	−0.689792	−	0.724008i	$-0.742298\pi$
$167$	−9.72858	+	3.54091i	−0.752820	+	0.274004i	−0.0630280	+	0.998012i	$0.520076\pi$
$168$		0			0
$169$	−3.60884	−	20.4668i	−0.277603	−	1.57437i
$170$	−3.99730	+	9.26856i	−0.306579	+	0.710866i
$171$		0			0
$172$	10.8820	−	10.2695i	0.829747	−	0.783045i
$173$	−14.4030	+	2.53963i	−1.09504	+	0.193085i	−0.691856	−	0.722035i	$-0.743207\pi$
$173$	−14.4030	+	2.53963i	−1.09504	+	0.193085i	−0.403182	+	0.915120i	$0.632096\pi$
$174$		0			0
$175$	1.50046	+	4.12249i	0.113424	+	0.311631i
$176$	6.64578	+	2.86451i	0.500944	+	0.215920i
$177$		0			0
$178$	−4.75885	+	3.54335i	−0.356691	+	0.265585i
$179$	11.7089	+	20.2804i	0.875164	+	1.51583i	0.856588	+	0.516001i	$0.172580\pi$
$179$	11.7089	+	20.2804i	0.875164	+	1.51583i	0.0185761	+	0.999827i	$0.494087\pi$
$180$		0			0
$181$	11.7776	+	2.07670i	0.875420	+	0.154360i	0.593264	−	0.805008i	$-0.297839\pi$
$181$	11.7776	+	2.07670i	0.875420	+	0.154360i	0.282156	+	0.959368i	$0.408950\pi$
$182$	−11.1444	+	1.30338i	−0.826079	+	0.0966132i
$183$		0			0
$184$	−5.87816	+	16.1606i	−0.433344	+	1.19138i
$185$	−3.60883	+	9.91518i	−0.265327	+	0.728979i
$186$		0			0
$187$	6.21067	+	7.40159i	0.454169	+	0.541258i
$188$	−11.1574	−	8.30395i	−0.813736	−	0.605627i
$189$		0			0
$190$	−5.18516	−	6.40212i	−0.376171	−	0.464459i
$191$		−	24.0981i		−	1.74368i	−0.489792	−	0.871839i	$-0.662927\pi$
$191$		−	24.0981i		−	1.74368i	0.489792	−	0.871839i	$-0.337073\pi$
$192$		0			0
$193$	−0.142369	−	0.169668i	−0.0102479	−	0.0122130i	0.760896	−	0.648874i	$-0.224760\pi$
$193$	−0.142369	−	0.169668i	−0.0102479	−	0.0122130i	−0.771144	+	0.636661i	$0.780315\pi$
$194$	10.7974	+	0.628121i	0.775209	+	0.0450965i
$195$		0			0
$196$	−0.598772	−	10.2559i	−0.0427695	−	0.732561i
$197$	10.6034	−	18.3656i	0.755458	−	1.30849i	−0.189688	−	0.981844i	$-0.560748\pi$
$197$	10.6034	−	18.3656i	0.755458	−	1.30849i	0.945146	−	0.326648i	$-0.105919\pi$
$198$		0			0
$199$	9.96742	+	1.75752i	0.706572	+	0.124588i	0.515376	−	0.856964i	$-0.327652\pi$
$199$	9.96742	+	1.75752i	0.706572	+	0.124588i	0.191196	+	0.981552i	$0.438763\pi$
$200$	−1.58037	−	8.95176i	−0.111749	−	0.632985i
$201$		0			0
$202$	−0.444340	−	0.596765i	−0.0312637	−	0.0419883i
$203$	0.625539	+	0.524890i	0.0439042	+	0.0368400i
$204$		0			0
$205$	0.319783	+	0.878597i	0.0223346	+	0.0613638i
$206$	−6.74317	−	22.5180i	−0.469819	−	1.56891i
$207$		0			0
$208$	23.2101	+	1.34533i	1.60933	+	0.0932820i
$209$	−7.70414	+	1.68454i	−0.532907	+	0.116522i
$210$		0			0
$211$	4.68568	+	26.5738i	0.322576	+	1.82942i	0.526191	+	0.850367i	$0.323620\pi$
$211$	4.68568	+	26.5738i	0.322576	+	1.82942i	−0.203615	+	0.979051i	$0.565269\pi$
$212$	2.49193	−	21.3457i	0.171146	−	1.46603i
$213$		0			0
$214$	4.91850	−	5.21403i	0.336221	−	0.356424i
$215$	6.42694	−	7.65932i	0.438313	−	0.522362i
$216$		0			0
$217$	1.06441	−	0.614535i	0.0722565	−	0.0417173i
$218$	−1.77920	+	2.70555i	−0.120502	+	0.183243i
$219$		0			0
$220$	4.63292	+	1.38630i	0.312351	+	0.0934643i
$221$	26.8818	+	15.5202i	1.80827	+	1.04400i
$222$		0			0
$223$	0.0346307	+	0.0126046i	0.00231905	+	0.000844064i	0.343179	−	0.939270i	$-0.388496\pi$
$223$	0.0346307	+	0.0126046i	0.00231905	+	0.000844064i	−0.340860	+	0.940114i	$0.610718\pi$
$224$	0.893774	−	7.66995i	0.0597178	−	0.512470i
$225$		0			0
$226$	−3.77271	+	15.9233i	−0.250957	+	1.05920i
$227$	13.2865			0.881859			0.440929	−	0.897542i	$-0.354649\pi$
$227$	13.2865			0.881859			0.440929	+	0.897542i	$0.354649\pi$
$228$		0			0
$229$	28.8285			1.90504			0.952520	−	0.304477i	$-0.0984816\pi$
$229$	28.8285			1.90504			0.952520	+	0.304477i	$0.0984816\pi$
$230$	−2.64928	+	11.1817i	−0.174688	+	0.737297i
$231$		0			0
$232$	−1.08787	−	1.29592i	−0.0714219	−	0.0850811i
$233$	14.3124	+	5.20928i	0.937636	+	0.341272i	0.765232	−	0.643755i	$-0.222624\pi$
$233$	14.3124	+	5.20928i	0.937636	+	0.341272i	0.172404	+	0.985026i	$0.444847\pi$
$234$		0			0
$235$	−8.04885	−	4.64701i	−0.525049	−	0.303137i
$236$	4.56580	−	15.2586i	0.297208	−	0.993249i
$237$		0			0
$238$	5.66464	−	8.61398i	0.367184	−	0.558361i
$239$	−18.8499	+	10.8830i	−1.21930	+	0.703964i	−0.964768	−	0.263100i	$-0.915255\pi$
$239$	−18.8499	+	10.8830i	−1.21930	+	0.703964i	−0.254533	+	0.967064i	$0.581922\pi$
$240$		0			0
$241$	4.70691	−	5.60947i	0.303198	−	0.361338i	−0.592835	−	0.805324i	$-0.701992\pi$
$241$	4.70691	−	5.60947i	0.303198	−	0.361338i	0.896034	+	0.443986i	$0.146436\pi$
$242$	−7.49821	+	7.94875i	−0.482003	+	0.510965i
$243$		0			0
$244$	−20.4418	−	2.38641i	−1.30865	−	0.152774i
$245$	−1.19209	−	6.76066i	−0.0761596	−	0.431923i
$246$		0			0
$247$	−21.4068	+	13.5505i	−1.36208	+	0.862198i
$248$	−2.39292	+	0.871519i	−0.151950	+	0.0553415i
$249$		0			0
$250$	−4.45353	−	14.8721i	−0.281666	−	0.940592i
$251$	10.3774	+	28.5117i	0.655017	+	1.79964i	0.598327	+	0.801252i	$0.295833\pi$
$251$	10.3774	+	28.5117i	0.655017	+	1.79964i	0.0566903	+	0.998392i	$0.481945\pi$
$252$		0			0
$253$	8.42631	+	7.07051i	0.529757	+	0.444519i
$254$	−8.66206	−	11.6335i	−0.543506	−	0.729949i
$255$		0			0
$256$	−4.58029	+	15.3304i	−0.286268	+	0.958150i
$257$	−13.8423	−	2.44078i	−0.863461	−	0.152251i	−0.275658	−	0.961256i	$-0.588896\pi$
$257$	−13.8423	−	2.44078i	−0.863461	−	0.152251i	−0.587803	+	0.809004i	$0.700007\pi$
$258$		0			0
$259$	5.38858	−	9.33329i	0.334830	−	0.579943i
$260$	15.5094	−	0.905490i	0.961850	−	0.0561561i
$261$		0			0
$262$	−24.1062	−	1.40234i	−1.48928	−	0.0866366i
$263$	10.9130	+	13.0056i	0.672925	+	0.801961i	0.989179	−	0.146713i	$-0.0468695\pi$
$263$	10.9130	+	13.0056i	0.672925	+	0.801961i	−0.316254	+	0.948675i	$0.602425\pi$
$264$		0			0
$265$		−	14.3607i		−	0.882171i
$266$	4.08010	+	7.35933i	0.250167	+	0.451230i
$267$		0			0
$268$	1.01697	−	1.36642i	0.0621210	−	0.0834674i
$269$	2.93895	+	3.50250i	0.179191	+	0.213551i	0.848162	−	0.529737i	$-0.177709\pi$
$269$	2.93895	+	3.50250i	0.179191	+	0.213551i	−0.668971	+	0.743288i	$0.733265\pi$
$270$		0			0
$271$	−7.27616	+	19.9911i	−0.441995	+	1.21437i	0.496183	+	0.868218i	$0.334735\pi$
$271$	−7.27616	+	19.9911i	−0.441995	+	1.21437i	−0.938178	+	0.346153i	$0.887488\pi$
$272$	−14.6552	+	15.5423i	−0.888600	+	0.942389i
$273$		0			0
$274$	2.10025	−	0.245633i	0.126881	−	0.0148392i
$275$	−5.72622	−	1.00969i	−0.345304	−	0.0608864i
$276$		0			0
$277$	−2.28795	−	3.96285i	−0.137470	−	0.238104i	0.789069	−	0.614305i	$-0.210564\pi$
$277$	−2.28795	−	3.96285i	−0.137470	−	0.238104i	−0.926538	+	0.376201i	$0.877230\pi$
$278$	21.1679	−	15.7612i	1.26957	−	0.945297i
$279$		0			0
$280$	−0.00108081	−	5.15998i	−6.45910e−5	−	0.308368i
$281$	6.42344	+	17.6482i	0.383190	+	1.05281i	0.970005	+	0.243085i	$0.0781594\pi$
$281$	6.42344	+	17.6482i	0.383190	+	1.05281i	−0.586815	+	0.809721i	$0.699618\pi$
$282$		0			0
$283$	24.9211	−	4.39427i	1.48141	−	0.261212i	0.626268	−	0.779608i	$-0.284582\pi$
$283$	24.9211	−	4.39427i	1.48141	−	0.261212i	0.855141	+	0.518396i	$0.173471\pi$
$284$	−0.921005	−	0.975935i	−0.0546516	−	0.0579111i
$285$		0			0
$286$	5.88928	−	13.6555i	0.348240	−	0.807467i
$287$	−0.165830	−	0.940469i	−0.00978864	−	0.0555141i
$288$		0			0
$289$	−10.8262	+	3.94042i	−0.636836	+	0.231789i
$290$	−0.822455	−	0.775838i	−0.0482962	−	0.0455588i
$291$		0			0
$292$	−7.60945	+	1.80459i	−0.445309	+	0.105606i
$293$	−0.535807	+	0.309349i	−0.0313022	+	0.0180723i	−0.515569	−	0.856848i	$-0.672420\pi$
$293$	−0.535807	+	0.309349i	−0.0313022	+	0.0180723i	0.484267	+	0.874920i	$0.339086\pi$
$294$		0			0
$295$	1.84813	−	10.4813i	0.107602	−	0.610242i
$296$	−14.3503	+	17.1093i	−0.834097	+	0.994460i
$297$		0			0
$298$	−16.2311	+	8.15298i	−0.940242	+	0.472290i
$299$	33.2068	+	12.0863i	1.92040	+	0.698967i
$300$		0			0
$301$	−7.82312	+	6.56437i	−0.450917	+	0.378364i
$302$	17.5905	+	4.16773i	1.01222	+	0.239826i
$303$		0			0
$304$	−5.68121	−	16.4840i	−0.325840	−	0.945425i
$305$	−13.7526			−0.787472
$306$		0			0
$307$	14.7710	−	12.3943i	0.843024	−	0.707381i	−0.115218	−	0.993340i	$-0.536757\pi$
$307$	14.7710	−	12.3943i	0.843024	−	0.707381i	0.958242	+	0.285959i	$0.0923122\pi$
$308$	−4.41422	−	2.21613i	−0.251524	−	0.126276i
$309$		0			0
$310$	−1.52071	+	0.763861i	−0.0863704	+	0.0433844i
$311$	−7.47317	−	4.31464i	−0.423765	−	0.244661i	0.272922	−	0.962036i	$-0.412010\pi$
$311$	−7.47317	−	4.31464i	−0.423765	−	0.244661i	−0.696687	+	0.717375i	$0.745343\pi$
$312$		0			0
$313$	5.84370	−	33.1413i	0.330305	−	1.87326i	−0.139109	−	0.990277i	$-0.544424\pi$
$313$	5.84370	−	33.1413i	0.330305	−	1.87326i	0.469414	−	0.882978i	$-0.344465\pi$
$314$	−16.6754	−	10.9659i	−0.941046	−	0.618841i
$315$		0			0
$316$	7.20972	−	1.70980i	0.405578	−	0.0961837i
$317$	15.3580	−	18.3030i	0.862592	−	1.02800i	−0.136709	−	0.990611i	$-0.543653\pi$
$317$	15.3580	−	18.3030i	0.862592	−	1.02800i	0.999301	−	0.0373855i	$-0.0119030\pi$
$318$		0			0
$319$	−1.01702	+	0.370164i	−0.0569421	+	0.0207252i
$320$	−1.85218	+	10.5300i	−0.103540	+	0.588648i
$321$		0			0
$322$	4.64802	−	10.7774i	0.259024	−	0.600601i
$323$	3.10542	−	23.0707i	0.172790	−	1.28369i
$324$		0			0
$325$	−18.3961	+	3.24373i	−1.02043	+	0.179930i
$326$	−24.1536	+	7.23296i	−1.33775	+	0.400596i
$327$		0			0
$328$	0.000414471		1.97875i	2.28854e−5		0.109258i
$329$	7.27187	+	6.10183i	0.400911	+	0.336405i
$330$		0			0
$331$	11.1872	+	19.3767i	0.614902	+	1.06504i	0.990402	+	0.138219i	$0.0441379\pi$
$331$	11.1872	+	19.3767i	0.614902	+	1.06504i	−0.375499	+	0.926823i	$0.622529\pi$
$332$	10.5984	+	16.1092i	0.581662	+	0.884105i
$333$		0			0
$334$	−14.5421	+	1.70076i	−0.795711	+	0.0930615i
$335$	0.569108	−	0.985724i	0.0310937	−	0.0538559i
$336$		0			0
$337$	−7.67933	+	21.0988i	−0.418320	+	1.14932i	0.534336	+	0.845272i	$0.320562\pi$
$337$	−7.67933	+	21.0988i	−0.418320	+	1.14932i	−0.952656	+	0.304051i	$0.901661\pi$
$338$	1.70688	−	29.3413i	0.0928421	−	1.59596i
$339$		0			0
$340$	−8.52271	+	11.4513i	−0.462209	+	0.621035i
$341$			1.62899i			0.0882148i
$342$		0			0
$343$			16.5671i			0.894537i
$344$	18.3233	−	10.5841i	0.987924	−	0.570654i
$345$		0			0
$346$	−20.6482	−	1.20117i	−1.11005	−	0.0645755i
$347$	−6.73751	+	18.5112i	−0.361689	+	0.993731i	0.616744	+	0.787164i	$0.288451\pi$
$347$	−6.73751	+	18.5112i	−0.361689	+	0.993731i	−0.978432	+	0.206567i	$0.933771\pi$
$348$		0			0
$349$	11.0085	−	19.0672i	0.589270	−	1.02064i	−0.405059	−	0.914291i	$-0.632749\pi$
$349$	11.0085	−	19.0672i	0.589270	−	1.02064i	0.994328	−	0.106354i	$-0.0339177\pi$
$350$	0.720699	+	6.16225i	0.0385230	+	0.329386i
$351$		0			0
$352$	8.21141	+	6.10871i	0.437669	+	0.325595i
$353$	−10.2460	−	17.7465i	−0.545338	−	0.944553i	−0.998586	−	0.0531686i	$-0.983068\pi$
$353$	−10.2460	−	17.7465i	−0.545338	−	0.944553i	0.453247	−	0.891385i	$-0.350265\pi$
$354$		0			0
$355$	−0.686912	−	0.576388i	−0.0364575	−	0.0305915i
$356$	−7.70402	+	3.32447i	−0.408312	+	0.176196i
$357$		0			0
$358$	9.50050	+	31.7258i	0.502117	+	1.67676i
$359$	−11.1171	+	1.96024i	−0.586738	+	0.103458i	−0.459133	−	0.888367i	$-0.651840\pi$
$359$	−11.1171	+	1.96024i	−0.586738	+	0.103458i	−0.127605	+	0.991825i	$0.540729\pi$
$360$		0			0
$361$	15.5004	+	10.9881i	0.815811	+	0.578319i
$362$	15.5302	+	6.69779i	0.816249	+	0.352028i
$363$		0			0
$364$	−15.7610	−	1.83996i	−0.826099	−	0.0964402i
$365$	−4.91074	+	1.78736i	−0.257040	+	0.0935549i
$366$		0			0
$367$	4.93537	−	5.88174i	0.257624	−	0.307025i	−0.621693	−	0.783261i	$-0.713555\pi$
$367$	4.93537	−	5.88174i	0.257624	−	0.307025i	0.879317	+	0.476236i	$0.157999\pi$
$368$	−13.3581	+	20.3224i	−0.696340	+	1.05938i
$369$		0			0
$370$	−8.19896	+	12.4678i	−0.426244	+	0.648170i
$371$	−2.54704	+	14.4450i	−0.132236	+	0.749945i
$372$		0			0
$373$	10.6167	+	6.12955i	0.549711	+	0.317376i	0.749005	−	0.662564i	$-0.230532\pi$
$373$	10.6167	+	6.12955i	0.549711	+	0.317376i	−0.199294	+	0.979940i	$0.563865\pi$
$374$	6.13336	+	12.2104i	0.317149	+	0.631385i
$375$		0			0
$376$	−12.6464	−	15.0650i	−0.652189	−	0.776918i
$377$	−2.66351	+	2.23495i	−0.137178	+	0.115106i
$378$		0			0
$379$	−8.64524			−0.444076			−0.222038	−	0.975038i	$-0.571271\pi$
$379$	−8.64524			−0.444076			−0.222038	+	0.975038i	$0.571271\pi$
$380$	−5.04801	−	10.5007i	−0.258958	−	0.538672i
$381$		0			0
$382$	7.85705	−	33.1618i	0.402001	−	1.69671i
$383$	−14.4544	+	12.1287i	−0.738584	+	0.619745i	−0.932457	−	0.361281i	$-0.882339\pi$
$383$	−14.4544	+	12.1287i	−0.738584	+	0.619745i	0.193873	+	0.981027i	$0.437895\pi$
$384$		0			0
$385$	−3.10154	−	1.12887i	−0.158069	−	0.0575325i
$386$	−0.140596	−	0.279902i	−0.00715617	−	0.0142466i
$387$		0			0
$388$	14.6537	+	4.38480i	0.743929	+	0.222605i
$389$	−0.467114	+	2.64914i	−0.0236836	+	0.134317i	−0.994357	−	0.106086i	$-0.966168\pi$
$389$	−0.467114	+	2.64914i	−0.0236836	+	0.134317i	0.970673	+	0.240402i	$0.0772793\pi$
$390$		0			0
$391$	−28.1195	+	16.2348i	−1.42206	+	0.821030i
$392$	2.51988	−	14.3085i	0.127273	−	0.722687i
$393$		0			0
$394$	20.5794	−	21.8160i	1.03678	−	1.09907i
$395$	4.65278	−	1.69347i	0.234107	−	0.0852079i
$396$		0			0
$397$	−0.105492	−	0.598277i	−0.00529451	−	0.0300267i	0.982046	−	0.188641i	$-0.0604084\pi$
$397$	−0.105492	−	0.598277i	−0.00529451	−	0.0300267i	−0.987341	+	0.158615i	$0.949297\pi$
$398$	13.1433	+	5.66838i	0.658814	+	0.284130i
$399$		0			0
$400$	0.743895	−	12.8339i	0.0371947	−	0.641696i
$401$	37.4771	−	6.60822i	1.87152	−	0.329999i	0.881639	−	0.471924i	$-0.156440\pi$
$401$	37.4771	−	6.60822i	1.87152	−	0.329999i	0.989877	+	0.141925i	$0.0453293\pi$
$402$		0			0
$403$	1.78990	+	4.91770i	0.0891611	+	0.244968i
$404$	−0.416892	−	0.966093i	−0.0207411	−	0.0480649i
$405$		0			0
$406$	0.689677	+	0.926262i	0.0342281	+	0.0459696i
$407$	7.14195	+	12.3702i	0.354013	+	0.613169i
$408$		0			0
$409$	−8.87907	−	1.56562i	−0.439042	−	0.0774149i	−0.0502417	−	0.998737i	$-0.515999\pi$
$409$	−8.87907	−	1.56562i	−0.439042	−	0.0774149i	−0.388800	+	0.921322i	$0.627110\pi$
$410$	0.153597	+	1.31331i	0.00758563	+	0.0648600i
$411$		0			0
$412$	−1.93751	−	33.1860i	−0.0954544	−	1.63496i
$413$	−3.71795	+	10.2150i	−0.182948	+	0.502646i
$414$		0			0
$415$	8.28261	+	9.87083i	0.406577	+	0.484540i
$416$	31.5012	+	9.41886i	1.54447	+	0.461797i
$417$		0			0
$418$	−11.1510	−	0.193771i	−0.545415	−	0.00947765i
$419$		−	8.75167i		−	0.427547i	−0.976883	−	0.213774i	$-0.931425\pi$
$419$		−	8.75167i		−	0.427547i	0.976883	−	0.213774i	$-0.0685755\pi$
$420$		0			0
$421$	8.76572	+	10.4466i	0.427215	+	0.509135i	0.936117	−	0.351690i	$-0.114393\pi$
$421$	8.76572	+	10.4466i	0.427215	+	0.509135i	−0.508902	+	0.860825i	$0.669948\pi$
$422$	−2.21619	+	38.0964i	−0.107883	+	1.85450i
$423$		0			0
$424$	10.3888	−	28.5616i	0.504525	−	1.38707i
$425$	8.58184	−	14.8642i	0.416280	−	0.721019i
$426$		0			0
$427$	13.8333	+	2.43918i	0.669440	+	0.118040i
$428$	8.46843	−	5.57147i	0.409337	−	0.269307i
$429$		0			0
$430$	11.3415	−	8.44465i	0.546935	−	0.407237i
$431$	2.79520	+	2.34545i	0.134640	+	0.112977i	0.707621	−	0.706592i	$-0.249769\pi$
$431$	2.79520	+	2.34545i	0.134640	+	0.112977i	−0.572981	+	0.819569i	$0.694213\pi$
$432$		0			0
$433$	4.79840	+	13.1835i	0.230596	+	0.633558i	0.999986	−	0.00522103i	$-0.00166191\pi$
$433$	4.79840	+	13.1835i	0.230596	+	0.633558i	−0.769390	+	0.638779i	$0.779440\pi$
$434$	1.66511	−	0.498628i	0.0799278	−	0.0239349i
$435$		0			0
$436$	−3.33051	+	3.14305i	−0.159502	+	0.150525i
$437$	−1.07918	−	26.4796i	−0.0516241	−	1.26669i
$438$		0			0
$439$	−0.314211	−	1.78198i	−0.0149965	−	0.0850492i	0.976391	−	0.216011i	$-0.0693046\pi$
$439$	−0.314211	−	1.78198i	−0.0149965	−	0.0850492i	−0.991387	+	0.130962i	$0.958194\pi$
$440$	5.92344	+	3.41824i	0.282389	+	0.162958i
$441$		0			0
$442$	31.9323	+	30.1223i	1.51886	+	1.43277i
$443$	7.88486	−	9.39682i	0.374621	−	0.446456i	−0.545488	−	0.838119i	$-0.683656\pi$
$443$	7.88486	−	9.39682i	0.374621	−	0.446456i	0.920109	+	0.391663i	$0.128100\pi$
$444$		0			0
$445$	−4.85575	+	2.80347i	−0.230185	+	0.132897i
$446$	0.0435463	+	0.0286365i	0.00206198	+	0.00135598i
$447$		0			0
$448$	3.73068	−	10.2633i	0.176258	−	0.484897i
$449$	−5.13353	−	2.96384i	−0.242266	−	0.139872i	0.373952	−	0.927448i	$-0.378003\pi$
$449$	−5.13353	−	2.96384i	−0.242266	−	0.139872i	−0.616218	+	0.787576i	$0.711336\pi$
$450$		0			0
$451$	1.18938	+	0.432900i	0.0560058	+	0.0203844i
$452$	−10.3834	+	20.6822i	−0.488393	+	0.972809i
$453$		0			0
$454$	18.2838	+	4.33200i	0.858102	+	0.203311i
$455$	−10.6035			−0.497099
$456$		0			0
$457$	−19.0703			−0.892069			−0.446034	−	0.895016i	$-0.647164\pi$
$457$	−19.0703			−0.892069			−0.446034	+	0.895016i	$0.647164\pi$
$458$	39.6713	+	9.39935i	1.85372	+	0.439203i
$459$		0			0
$460$	−7.29143	+	14.5235i	−0.339965	+	0.677161i
$461$	−19.6569	−	7.15452i	−0.915512	−	0.333219i	−0.159060	−	0.987269i	$-0.550846\pi$
$461$	−19.6569	−	7.15452i	−0.915512	−	0.333219i	−0.756451	+	0.654050i	$0.773069\pi$
$462$		0			0
$463$	−8.52005	−	4.91905i	−0.395960	−	0.228608i	0.288779	−	0.957396i	$-0.406751\pi$
$463$	−8.52005	−	4.91905i	−0.395960	−	0.228608i	−0.684740	+	0.728788i	$0.740084\pi$
$464$	−1.07450	−	2.13802i	−0.0498826	−	0.0992552i
$465$		0			0
$466$	17.9971	+	11.8350i	0.833698	+	0.548248i
$467$	3.88633	−	2.24377i	0.179838	−	0.103829i	−0.407379	−	0.913259i	$-0.633557\pi$
$467$	3.88633	−	2.24377i	0.179838	−	0.103829i	0.587216	+	0.809430i	$0.300224\pi$
$468$		0			0
$469$	−0.747277	+	0.890570i	−0.0345060	+	0.0411227i
$470$	−9.56102	−	9.01910i	−0.441017	−	0.416020i
$471$		0			0
$472$	11.2580	−	19.5089i	0.518193	−	0.897971i
$473$	−2.35038	−	13.3297i	−0.108071	−	0.612899i
$474$		0			0
$475$	7.49269	+	11.8368i	0.343788	+	0.543109i
$476$	10.6037	−	10.0069i	0.486022	−	0.458666i
$477$		0			0
$478$	−29.4880	+	8.83038i	−1.34875	+	0.403892i
$479$	−7.66192	−	21.0509i	−0.350082	−	0.961842i	−0.982343	−	0.187087i	$-0.940095\pi$
$479$	−7.66192	−	21.0509i	−0.350082	−	0.961842i	0.632261	−	0.774755i	$-0.282127\pi$
$480$		0			0
$481$	35.1526	+	29.4966i	1.60282	+	1.34493i
$482$	8.30618	−	6.18463i	0.378336	−	0.281702i
$483$		0			0
$484$	−12.9100	+	8.49365i	−0.586820	+	0.386075i
$485$	10.0658	+	1.77487i	0.457063	+	0.0805925i
$486$		0			0
$487$	16.6226	−	28.7912i	0.753242	−	1.30465i	−0.193001	−	0.981199i	$-0.561822\pi$
$487$	16.6226	−	28.7912i	0.753242	−	1.30465i	0.946243	−	0.323455i	$-0.104845\pi$
$488$	−27.3522	−	9.94889i	−1.23817	−	0.450365i
$489$		0			0
$490$	0.563823	−	9.69212i	0.0254709	−	0.437846i
$491$	16.0502	+	19.1279i	0.724335	+	0.863228i	0.995044	−	0.0994326i	$-0.0317028\pi$
$491$	16.0502	+	19.1279i	0.724335	+	0.863228i	−0.270710	+	0.962661i	$0.587258\pi$
$492$		0			0
$493$		−	3.19475i		−	0.143884i
$494$	−33.8763	+	11.6675i	−1.52417	+	0.524946i
$495$		0			0
$496$	−3.57709	+	0.419114i	−0.160616	+	0.0188188i
$497$	0.588714	+	0.701602i	0.0264074	+	0.0314711i
$498$		0			0
$499$	−1.81073	+	4.97495i	−0.0810595	+	0.222709i	−0.973601	−	0.228256i	$-0.926698\pi$
$499$	−1.81073	+	4.97495i	−0.0810595	+	0.222709i	0.892542	+	0.450965i	$0.148920\pi$
$500$	−1.27963	−	21.9177i	−0.0572270	−	0.980191i
$501$		0			0
$502$	4.98446	+	42.6189i	0.222467	+	1.90218i
$503$	−36.9767	−	6.52000i	−1.64871	−	0.290712i	−0.729354	−	0.684136i	$-0.760179\pi$
$503$	−36.9767	−	6.52000i	−1.64871	−	0.290712i	−0.919357	+	0.393424i	$0.871290\pi$
$504$		0			0
$505$	−0.351558	−	0.608916i	−0.0156441	−	0.0270964i
$506$	9.29028	+	12.4772i	0.413003	+	0.554679i
$507$		0			0
$508$	−8.12697	−	18.8332i	−0.360576	−	0.835589i
$509$	5.95327	+	16.3565i	0.263874	+	0.724988i	0.998897	+	0.0469459i	$0.0149488\pi$
$509$	5.95327	+	16.3565i	0.263874	+	0.724988i	−0.735024	+	0.678042i	$0.762829\pi$
$510$		0			0
$511$	5.25657	−	0.926874i	0.232537	−	0.0410025i
$512$	−11.3014	+	19.6030i	−0.499456	+	0.866339i
$513$		0			0
$514$	−18.2529	−	7.87200i	−0.805099	−	0.347219i
$515$	−3.85736	−	21.8762i	−0.169976	−	0.963981i
$516$		0			0
$517$	−11.8228	+	4.30315i	−0.519967	+	0.189252i
$518$	10.4584	−	11.0868i	0.459515	−	0.487125i
$519$		0			0
$520$	21.6379	+	3.81067i	0.948885	+	0.167109i
$521$	20.0104	−	11.5530i	0.876671	−	0.506146i	0.00711171	−	0.999975i	$-0.497736\pi$
$521$	20.0104	−	11.5530i	0.876671	−	0.506146i	0.869559	+	0.493828i	$0.164403\pi$
$522$		0			0
$523$	−3.96812	+	22.5043i	−0.173514	+	0.984046i	0.766331	+	0.642446i	$0.222080\pi$
$523$	−3.96812	+	22.5043i	−0.173514	+	0.984046i	−0.939845	+	0.341601i	$0.889031\pi$
$524$	−32.7157	−	9.78945i	−1.42919	−	0.427654i
$525$		0			0
$526$	10.7772	+	21.4554i	0.469907	+	0.935499i
$527$	−4.51854	−	1.64462i	−0.196831	−	0.0716406i
$528$		0			0
$529$	−10.6977	+	8.97645i	−0.465118	+	0.390281i
$530$	4.68222	−	19.7620i	0.203383	−	0.858406i
$531$		0			0
$532$	3.21522	+	11.4576i	0.139397	+	0.496749i
$533$	4.06624			0.176128
$534$		0			0
$535$	5.18900	−	4.35408i	0.224340	−	0.188243i
$536$	1.84498	−	1.54878i	0.0796908	−	0.0668970i
$537$		0			0
$538$	2.90236	+	5.77807i	0.125130	+	0.249110i
$539$	−8.04822	−	4.64664i	−0.346662	−	0.200145i
$540$		0			0
$541$	4.71561	−	26.7436i	0.202740	−	1.14980i	−0.698217	−	0.715886i	$-0.746023\pi$
$541$	4.71561	−	26.7436i	0.202740	−	1.14980i	0.900957	−	0.433909i	$-0.142866\pi$
$542$	−16.5308	+	25.1377i	−0.710059	+	1.07976i
$543$		0			0
$544$	−25.2347	+	16.6097i	−1.08193	+	0.712137i
$545$	−1.96700	+	2.34418i	−0.0842571	+	0.100414i
$546$		0			0
$547$	20.4989	−	7.46099i	0.876469	−	0.319009i	0.135685	−	0.990752i	$-0.456676\pi$
$547$	20.4989	−	7.46099i	0.876469	−	0.319009i	0.740784	+	0.671743i	$0.234454\pi$
$548$	2.97028	+	0.346755i	0.126884	+	0.0148126i
$549$		0			0
$550$	−7.55074	−	3.25645i	−0.321965	−	0.138855i
$551$	2.30941	+	1.21073i	0.0983844	+	0.0515789i
$552$		0			0
$553$	−4.98044	+	0.878185i	−0.211790	+	0.0373442i
$554$	−1.85642	−	6.19931i	−0.0788719	−	0.263383i
$555$		0			0
$556$	34.2684	−	14.7876i	1.45330	−	0.627135i
$557$	25.3187	+	21.2449i	1.07279	+	0.900176i	0.995302	−	0.0968178i	$-0.0308664\pi$
$557$	25.3187	+	21.2449i	1.07279	+	0.900176i	0.0774855	+	0.996993i	$0.475311\pi$
$558$		0			0
$559$	−21.7418	−	37.6579i	−0.919580	−	1.59276i
$560$	1.68089	−	7.10108i	0.0710307	−	0.300076i
$561$		0			0
$562$	3.08529	+	26.3804i	0.130145	+	1.11279i
$563$	6.93499	−	12.0118i	0.292275	−	0.506235i	−0.682072	−	0.731285i	$-0.738921\pi$
$563$	6.93499	−	12.0118i	0.292275	−	0.506235i	0.974347	+	0.225049i	$0.0722544\pi$
$564$		0			0
$565$	−5.28915	+	14.5318i	−0.222516	+	0.611359i
$566$	35.7271	+	2.07836i	1.50172	+	0.0873602i
$567$		0			0
$568$	−0.949212	−	1.64329i	−0.0398280	−	0.0689508i
$569$		−	3.92803i		−	0.164672i	−0.996605	−	0.0823358i	$-0.973762\pi$
$569$		−	3.92803i		−	0.164672i	0.996605	−	0.0823358i	$-0.0262380\pi$
$570$		0			0
$571$		−	10.5601i		−	0.441928i	−0.975282	−	0.220964i	$-0.929080\pi$
$571$		−	10.5601i		−	0.441928i	0.975282	−	0.220964i	$-0.0709203\pi$
$572$	12.5566	−	16.8714i	0.525019	−	0.705428i
$573$		0			0
$574$	0.0784329	−	1.34826i	0.00327373	−	0.0562754i
$575$	6.68304	−	18.3615i	0.278702	−	0.765728i
$576$		0			0
$577$	8.16413	−	14.1407i	0.339877	−	0.588685i	−0.644532	−	0.764577i	$-0.722948\pi$
$577$	8.16413	−	14.1407i	0.339877	−	0.588685i	0.984409	+	0.175893i	$0.0562811\pi$
$578$	−16.1829	+	1.89265i	−0.673119	+	0.0787239i
$579$		0			0
$580$	−0.878837	−	1.33580i	−0.0364917	−	0.0554661i
$581$	−6.58050	−	11.3978i	−0.273005	−	0.472859i
$582$		0			0
$583$	−14.8923	−	12.4961i	−0.616776	−	0.517536i
$584$	−11.0599	+	0.00231661i	−0.457660	+	9.58619e-5i
$585$		0			0
$586$	−0.838194	+	0.251003i	−0.0346255	+	0.0103688i
$587$	29.6611	−	5.23004i	1.22424	−	0.215867i	0.476092	−	0.879396i	$-0.342053\pi$
$587$	29.6611	−	5.23004i	1.22424	−	0.215867i	0.748151	+	0.663529i	$0.230942\pi$
$588$		0			0
$589$	2.90127	−	2.64309i	0.119545	−	0.108907i
$590$	5.96059	−	13.8209i	0.245394	−	0.568996i
$591$		0			0
$592$	−25.3261	+	18.8656i	−1.04090	+	0.775371i
$593$	−40.3277	+	14.6781i	−1.65606	+	0.602756i	−0.989736	−	0.142907i	$-0.954355\pi$
$593$	−40.3277	+	14.6781i	−1.65606	+	0.602756i	−0.666323	+	0.745663i	$0.732133\pi$
$594$		0			0
$595$	6.26258	−	7.46345i	0.256741	−	0.305972i
$596$	−24.9941	+	5.92740i	−1.02380	+	0.242796i
$597$		0			0
$598$	41.7557	+	27.4590i	1.70752	+	1.12288i
$599$	−3.44329	+	19.5279i	−0.140689	+	0.797887i	0.830039	+	0.557705i	$0.188318\pi$
$599$	−3.44329	+	19.5279i	−0.140689	+	0.797887i	−0.970728	+	0.240182i	$0.922793\pi$
$600$		0			0
$601$	23.4312	+	13.5280i	0.955778	+	0.551819i	0.894871	−	0.446325i	$-0.147267\pi$
$601$	23.4312	+	13.5280i	0.955778	+	0.551819i	0.0609068	+	0.998143i	$0.480601\pi$
$602$	−12.9058	+	6.48266i	−0.526001	+	0.264213i
$603$		0			0
$604$	22.8477	+	11.4706i	0.929661	+	0.466731i
$605$	−7.91058	+	6.63777i	−0.321611	+	0.269864i
$606$		0			0
$607$	−5.36045			−0.217574			−0.108787	−	0.994065i	$-0.534697\pi$
$607$	−5.36045			−0.217574			−0.108787	+	0.994065i	$0.534697\pi$
$608$	−2.44349	−	24.5363i	−0.0990964	−	0.995078i
$609$		0			0
$610$	−18.9252	−	4.48395i	−0.766258	−	0.181550i
$611$	−30.9632	+	25.9812i	−1.25264	+	1.05109i
$612$		0			0
$613$	−13.2066	−	4.80681i	−0.533410	−	0.194145i	0.0612502	−	0.998122i	$-0.480491\pi$
$613$	−13.2066	−	4.80681i	−0.533410	−	0.194145i	−0.594660	+	0.803977i	$0.702713\pi$
$614$	24.3677	−	12.2400i	0.983399	−	0.493967i
$615$		0			0
$616$	−5.35193	−	4.48889i	−0.215635	−	0.180863i
$617$	−4.11256	+	23.3235i	−0.165565	+	0.938967i	0.782914	+	0.622129i	$0.213732\pi$
$617$	−4.11256	+	23.3235i	−0.165565	+	0.938967i	−0.948480	+	0.316838i	$0.897379\pi$
$618$		0			0
$619$	−17.2160	+	9.93966i	−0.691969	+	0.399509i	−0.804349	−	0.594157i	$-0.797486\pi$
$619$	−17.2160	+	9.93966i	−0.691969	+	0.399509i	0.112380	+	0.993665i	$0.464153\pi$
$620$	−2.34172	+	0.555344i	−0.0940459	+	0.0223031i
$621$		0			0
$622$	−8.87719	−	8.37403i	−0.355943	−	0.335768i
$623$	5.38147	−	1.95869i	0.215604	−	0.0784734i
$624$		0			0
$625$	0.242809	+	1.37704i	0.00971235	+	0.0550815i
$626$	18.8471	−	43.7009i	0.753282	−	1.74664i
$627$		0			0
$628$	−19.3719	−	20.5273i	−0.773022	−	0.819127i
$629$	−41.5233	+	7.32168i	−1.65564	+	0.291935i
$630$		0			0
$631$	−0.440226	−	1.20951i	−0.0175251	−	0.0481499i	0.930622	−	0.365983i	$-0.119267\pi$
$631$	−0.440226	−	1.20951i	−0.0175251	−	0.0481499i	−0.948147	+	0.317833i	$0.897045\pi$
$632$	10.4789	−	0.00219491i	0.416827	−	8.73090e-5i
$633$		0			0
$634$	27.1020	−	20.1796i	1.07636	−	0.801435i
$635$	−6.85334	−	11.8703i	−0.271967	−	0.471060i
$636$		0			0
$637$	−29.4021	−	5.18438i	−1.16495	−	0.205413i
$638$	−1.52023	+	0.177796i	−0.0601863	+	0.00703903i
$639$		0			0
$640$	−5.98208	+	13.8867i	−0.236462	+	0.548919i
$641$	−1.62727	+	4.47089i	−0.0642733	+	0.176590i	−0.967672	−	0.252212i	$-0.918842\pi$
$641$	−1.62727	+	4.47089i	−0.0642733	+	0.176590i	0.903399	+	0.428802i	$0.141064\pi$
$642$		0			0
$643$	−13.4534	−	16.0331i	−0.530550	−	0.632285i	0.432492	−	0.901638i	$-0.357635\pi$
$643$	−13.4534	−	16.0331i	−0.530550	−	0.632285i	−0.963041	+	0.269353i	$0.913190\pi$
$644$	9.91012	−	13.3155i	0.390514	−	0.524704i
$645$		0			0
$646$	11.7955	−	30.7354i	0.464086	−	1.20927i
$647$		−	33.1116i		−	1.30175i	−0.759184	−	0.650875i	$-0.774402\pi$
$647$		−	33.1116i		−	1.30175i	0.759184	−	0.650875i	$-0.225598\pi$
$648$		0			0
$649$	−9.26107	−	11.0369i	−0.363529	−	0.433237i
$650$	−26.3727	−	1.53419i	−1.03442	−	0.0601759i
$651$		0			0
$652$	−35.5964	+	2.07824i	−1.39406	+	0.0813903i
$653$	−8.60908	+	14.9114i	−0.336899	+	0.583527i	−0.983848	−	0.179007i	$-0.942712\pi$
$653$	−8.60908	+	14.9114i	−0.336899	+	0.583527i	0.646949	+	0.762534i	$0.276045\pi$
$654$		0			0
$655$	−22.4727	−	3.96254i	−0.878081	−	0.154829i
$656$	−0.644591	+	2.72313i	−0.0251670	+	0.106320i
$657$		0			0
$658$	8.01748	+	10.7678i	0.312554	+	0.419772i
$659$	−0.609150	−	0.511137i	−0.0237291	−	0.0199111i	0.630846	−	0.775908i	$-0.282708\pi$
$659$	−0.609150	−	0.511137i	−0.0237291	−	0.0199111i	−0.654575	+	0.755997i	$0.727152\pi$
$660$		0			0
$661$	−15.1036	−	41.4969i	−0.587463	−	1.61404i	−0.775125	−	0.631808i	$-0.782313\pi$
$661$	−15.1036	−	41.4969i	−0.587463	−	1.61404i	0.187662	−	0.982234i	$-0.439909\pi$
$662$	9.07717	+	30.3122i	0.352794	+	1.17812i
$663$		0			0
$664$	9.33231	+	25.6236i	0.362164	+	0.994389i
$665$	3.02180	+	7.35554i	0.117180	+	0.285236i
$666$		0			0
$667$	−0.631567	−	3.58179i	−0.0244544	−	0.138688i
$668$	−20.5662	−	2.40093i	−0.795730	−	0.0928949i
$669$		0			0
$670$	1.10455	−	1.17092i	0.0426724	−	0.0452365i
$671$	−11.9670	+	14.2617i	−0.461980	+	0.550566i
$672$		0			0
$673$	12.4476	−	7.18661i	0.479819	−	0.277024i	−0.240522	−	0.970644i	$-0.577319\pi$
$673$	12.4476	−	7.18661i	0.479819	−	0.277024i	0.720341	+	0.693620i	$0.243985\pi$
$674$	−17.4468	+	26.5306i	−0.672025	+	1.02192i
$675$		0			0
$676$	11.9154	−	39.8205i	0.458285	−	1.53156i
$677$	15.3724	+	8.87525i	0.590809	+	0.341104i	0.765417	−	0.643534i	$-0.222533\pi$
$677$	15.3724	+	8.87525i	0.590809	+	0.341104i	−0.174609	+	0.984638i	$0.555866\pi$
$678$		0			0
$679$	−9.81003	−	3.57056i	−0.376474	−	0.137025i
$680$	−15.4619	+	12.9796i	−0.592936	+	0.497744i
$681$		0			0
$682$	−0.531123	+	2.24168i	−0.0203377	+	0.0858384i
$683$	16.5441			0.633042			0.316521	−	0.948585i	$-0.397485\pi$
$683$	16.5441			0.633042			0.316521	+	0.948585i	$0.397485\pi$
$684$		0			0
$685$	1.99831			0.0763515
$686$	−5.40159	+	22.7982i	−0.206234	+	0.870439i
$687$		0			0
$688$	28.6658	−	8.59070i	1.09287	−	0.327517i
$689$	−58.6882	−	21.3608i	−2.23584	−	0.813780i
$690$		0			0
$691$	−19.6705	−	11.3568i	−0.748302	−	0.432032i	0.0767783	−	0.997048i	$-0.475537\pi$
$691$	−19.6705	−	11.3568i	−0.748302	−	0.432032i	−0.825080	+	0.565016i	$0.808870\pi$
$692$	−28.0227	−	8.38518i	−1.06526	−	0.318757i
$693$		0			0
$694$	−15.3071	+	23.2768i	−0.581048	+	0.883575i
$695$	21.5989	−	12.4702i	0.819295	−	0.473020i
$696$		0			0
$697$	−2.40158	+	2.86209i	−0.0909663	+	0.108409i
$698$	21.3657	−	22.6495i	0.808703	−	0.857295i
$699$		0			0
$700$	−1.01740	+	8.71494i	−0.0384540	+	0.329394i
$701$	5.86111	+	33.2400i	0.221371	+	1.25546i	0.869503	+	0.493928i	$0.164440\pi$
$701$	5.86111	+	33.2400i	0.221371	+	1.25546i	−0.648132	+	0.761528i	$0.724449\pi$
$702$		0			0
$703$	10.4436	−	32.7910i	0.393889	−	1.23674i
$704$	9.30814	+	11.0836i	0.350814	+	0.417728i
$705$		0			0
$706$	−8.31349	−	27.7619i	−0.312882	−	1.04483i
$707$	0.245622	+	0.674842i	0.00923758	+	0.0253800i
$708$		0			0
$709$	−2.99281	−	2.51127i	−0.112397	−	0.0943126i	0.584857	−	0.811137i	$-0.301151\pi$
$709$	−2.99281	−	2.51127i	−0.112397	−	0.0943126i	−0.697254	+	0.716824i	$0.745595\pi$
$710$	−0.757343	−	1.01714i	−0.0284226	−	0.0381726i
$711$		0			0
$712$	−11.6856	+	2.06300i	−0.437935	+	0.0773143i
$713$	−5.39109	−	0.950594i	−0.201898	−	0.0356000i
$714$		0			0
$715$	7.02686	−	12.1709i	0.262790	−	0.455165i
$716$	2.72978	+	46.7560i	0.102017	+	1.74735i
$717$		0			0
$718$	−15.9375	−	0.927140i	−0.594784	−	0.0346005i
$719$	10.7238	+	12.7801i	0.399930	+	0.476619i	0.927999	−	0.372583i	$-0.121528\pi$
$719$	10.7238	+	12.7801i	0.399930	+	0.476619i	−0.528068	+	0.849202i	$0.677083\pi$
$720$		0			0
$721$			22.6887i			0.844972i
$722$	17.7478	+	20.1747i	0.660503	+	0.750823i
$723$		0			0
$724$	19.1876	+	14.2805i	0.713101	+	0.530729i
$725$	1.23580	+	1.47277i	0.0458966	+	0.0546975i
$726$		0			0
$727$	−5.04395	+	13.8581i	−0.187070	+	0.513970i	−0.997405	−	0.0719967i	$-0.977063\pi$
$727$	−5.04395	+	13.8581i	−0.187070	+	0.513970i	0.810335	+	0.585967i	$0.199285\pi$
$728$	−21.0890	−	7.67077i	−0.781610	−	0.284298i
$729$		0			0
$730$	−7.34051	+	0.858502i	−0.271685	+	0.0317746i
$731$	39.3472	+	6.93797i	1.45531	+	0.256610i
$732$		0			0
$733$	−21.8482	−	37.8423i	−0.806983	−	1.39774i	−0.914944	−	0.403581i	$-0.867765\pi$
$733$	−21.8482	−	37.8423i	−0.806983	−	1.39774i	0.107961	−	0.994155i	$-0.465568\pi$
$734$	8.70935	−	6.48482i	0.321468	−	0.239359i
$735$		0			0
$736$	−25.0083	+	23.6106i	−0.921818	+	0.870299i
$737$	−0.526997	−	1.44791i	−0.0194122	−	0.0533346i
$738$		0			0
$739$	−40.8384	+	7.20091i	−1.50227	+	0.264890i	−0.863436	−	0.504458i	$-0.831692\pi$
$739$	−40.8384	+	7.20091i	−1.50227	+	0.264890i	−0.638829	+	0.769348i	$0.720581\pi$
$740$	−15.3478	+	14.4839i	−0.564195	+	0.532440i
$741$		0			0
$742$	−8.21471	+	19.0475i	−0.301572	+	0.699256i
$743$	−8.77287	−	49.7534i	−0.321845	−	1.82528i	−0.530975	−	0.847387i	$-0.678174\pi$
$743$	−8.77287	−	49.7534i	−0.321845	−	1.82528i	0.209130	−	0.977888i	$-0.432937\pi$
$744$		0			0
$745$	−16.1299	+	5.87080i	−0.590954	+	0.215090i
$746$	12.6113	+	11.8965i	0.461732	+	0.435561i
$747$		0			0
$748$	4.45909	+	18.8027i	0.163040	+	0.687494i
$749$	−5.99169	+	3.45930i	−0.218932	+	0.126400i
$750$		0			0
$751$	3.78440	−	21.4624i	0.138095	−	0.783174i	−0.834560	−	0.550917i	$-0.814278\pi$
$751$	3.78440	−	21.4624i	0.138095	−	0.783174i	0.972655	−	0.232256i	$-0.0746109\pi$
$752$	−12.4911	−	24.8545i	−0.455503	−	0.906349i
$753$		0			0
$754$	−4.39399	+	2.20713i	−0.160020	+	0.0803789i
$755$	16.0534	+	5.84295i	0.584242	+	0.212647i
$756$		0			0
$757$	0.0722766	−	0.0606473i	0.00262694	−	0.00220426i	−0.641473	−	0.767145i	$-0.721676\pi$
$757$	0.0722766	−	0.0606473i	0.00262694	−	0.00220426i	0.644100	+	0.764941i	$0.277232\pi$
$758$	−11.8969	−	2.81873i	−0.432113	−	0.102381i
$759$		0			0
$760$	−3.52298	−	16.0960i	−0.127792	−	0.583863i
$761$	3.56523			0.129240			0.0646198	−	0.997910i	$-0.479417\pi$
$761$	3.56523			0.129240			0.0646198	+	0.997910i	$0.479417\pi$
$762$		0			0
$763$	2.39431	−	2.00906i	0.0866798	−	0.0727330i
$764$	21.6244	−	43.0727i	0.782344	−	1.55832i
$765$		0			0
$766$	−23.8454	+	11.9777i	−0.861568	+	0.432771i
$767$	−40.0850	−	23.1431i	−1.44738	−	0.835648i
$768$		0			0
$769$	3.64181	−	20.6537i	0.131327	−	0.744793i	−0.846020	−	0.533151i	$-0.821008\pi$
$769$	3.64181	−	20.6537i	0.131327	−	0.744793i	0.977347	−	0.211642i	$-0.0678811\pi$
$770$	−3.90002	−	2.56469i	−0.140547	−	0.0924251i
$771$		0			0
$772$	−0.102217	−	0.431018i	−0.00367886	−	0.0155127i
$773$	−14.7529	+	17.5818i	−0.530625	+	0.632375i	−0.963059	−	0.269291i	$-0.913211\pi$
$773$	−14.7529	+	17.5818i	−0.530625	+	0.632375i	0.432433	+	0.901666i	$0.357655\pi$
$774$		0			0
$775$	2.71922	−	0.989714i	0.0976772	−	0.0355516i
$776$	18.7356	+	10.8117i	0.672567	+	0.388119i
$777$		0			0
$778$	−1.50654	+	3.49322i	−0.0540120	+	0.125238i
$779$	−1.15880	−	2.82071i	−0.0415184	−	0.101062i
$780$		0			0
$781$	−1.19545	+	0.210790i	−0.0427765	+	0.00754265i
$782$	−43.9890	+	13.1728i	−1.57304	+	0.471058i
$783$		0			0
$784$	8.13284	−	18.8685i	0.290458	−	0.673876i
$785$	−14.4481	−	12.1234i	−0.515676	−	0.432703i
$786$		0			0
$787$	−19.7759	−	34.2528i	−0.704933	−	1.22098i	−0.966716	−	0.255853i	$-0.917644\pi$
$787$	−19.7759	−	34.2528i	−0.704933	−	1.22098i	0.261782	−	0.965127i	$-0.415690\pi$
$788$	35.4327	−	23.3115i	1.26224	−	0.830439i
$789$		0			0
$790$	6.95491	−	0.813405i	0.247445	−	0.0289396i
$791$	7.89757	−	13.6790i	0.280805	−	0.486369i
$792$		0			0
$793$	−20.4562	+	56.2030i	−0.726422	+	1.99583i
$794$	0.0498949	−	0.857694i	0.00177070	−	0.0304384i
$795$		0			0
$796$	16.2386	+	12.0856i	0.575560	+	0.428364i
$797$			13.4187i			0.475316i	0.971349	+	0.237658i	$0.0763798\pi$
$797$			13.4187i			0.475316i	−0.971349	+	0.237658i	$0.923620\pi$
$798$		0			0
$799$		−	37.1389i		−	1.31388i
$800$	5.20811	−	17.4184i	0.184135	−	0.615835i
$801$		0			0
$802$	53.7274	+	3.12550i	1.89718	+	0.110365i
$803$	−2.41961	+	6.64782i	−0.0853861	+	0.234596i
$804$		0			0
$805$	5.54584	−	9.60568i	0.195465	−	0.338556i
$806$	0.859718	+	7.35091i	0.0302823	+	0.258925i
$807$		0			0
$808$	−0.258703	−	1.46538i	−0.00910113	−	0.0515519i
$809$	4.70080	+	8.14202i	0.165271	+	0.286258i	0.936752	−	0.349995i	$-0.113817\pi$
$809$	4.70080	+	8.14202i	0.165271	+	0.286258i	−0.771480	+	0.636253i	$0.780483\pi$
$810$		0			0
$811$	19.1736	+	16.0885i	0.673275	+	0.564945i	0.914033	−	0.405640i	$-0.132951\pi$
$811$	19.1736	+	16.0885i	0.673275	+	0.564945i	−0.240758	+	0.970585i	$0.577396\pi$
$812$	0.647074	+	1.49951i	0.0227078	+	0.0526225i
$813$		0			0
$814$	5.79492	+	19.3514i	0.203112	+	0.678268i
$815$	−23.4652	+	4.13754i	−0.821949	+	0.144932i
$816$		0			0
$817$	−19.9269	+	25.8139i	−0.697155	+	0.903114i
$818$	−11.7082	−	5.04944i	−0.409366	−	0.176550i
$819$		0			0
$820$	−0.216830	+	1.85735i	−0.00757205	+	0.0648616i
$821$	−24.7423	+	9.00545i	−0.863511	+	0.314292i	−0.735537	−	0.677485i	$-0.763070\pi$
$821$	−24.7423	+	9.00545i	−0.863511	+	0.314292i	−0.127975	+	0.991777i	$0.540848\pi$
$822$		0			0
$823$	−5.76680	+	6.87260i	−0.201018	+	0.239564i	−0.857131	−	0.515099i	$-0.827755\pi$
$823$	−5.76680	+	6.87260i	−0.201018	+	0.239564i	0.656113	+	0.754663i	$0.272200\pi$
$824$	8.15385	−	46.2995i	0.284053	−	1.61292i
$825$		0			0
$826$	−8.44685	+	12.8448i	−0.293904	+	0.446927i
$827$	1.44344	−	8.18615i	0.0501933	−	0.284660i	−0.949372	−	0.314155i	$-0.898279\pi$
$827$	1.44344	−	8.18615i	0.0501933	−	0.284660i	0.999565	+	0.0294949i	$0.00938989\pi$
$828$		0			0
$829$	−20.1777	−	11.6496i	−0.700801	−	0.404608i	0.106845	−	0.994276i	$-0.465925\pi$
$829$	−20.1777	−	11.6496i	−0.700801	−	0.404608i	−0.807646	+	0.589668i	$0.799259\pi$
$830$	8.17951	+	16.2839i	0.283915	+	0.565222i
$831$		0			0
$832$	40.2783	+	23.2322i	1.39640	+	0.805432i
$833$	21.0144	−	17.6332i	0.728106	−	0.610954i
$834$		0			0
$835$	−13.8363			−0.478825
$836$	−15.2819	−	3.90238i	−0.528537	−	0.134967i
$837$		0			0
$838$	2.85343	−	12.0433i	0.0985701	−	0.416030i
$839$	−0.765232	+	0.642106i	−0.0264188	+	0.0221680i	−0.655901	−	0.754847i	$-0.727711\pi$
$839$	−0.765232	+	0.642106i	−0.0264188	+	0.0221680i	0.629483	+	0.777015i	$0.283267\pi$
$840$		0			0
$841$	−26.9148	−	9.79619i	−0.928097	−	0.337800i
$842$	8.65660	+	17.2337i	0.298326	+	0.593913i
$843$		0			0
$844$	−15.4708	+	51.7025i	−0.532529	+	1.77967i
$845$	4.82309	−	27.3531i	0.165919	−	0.940975i
$846$		0			0
$847$	9.13428	−	5.27368i	0.313858	−	0.181206i
$848$	23.6085	−	35.9169i	0.810721	−	1.23339i
$849$		0			0
$850$	16.6560	−	17.6568i	0.571296	−	0.605623i
$851$	−45.1064	+	16.4174i	−1.54623	+	0.562781i
$852$		0			0
$853$	4.28670	+	24.3111i	0.146774	+	0.832396i	0.965926	+	0.258820i	$0.0833335\pi$
$853$	4.28670	+	24.3111i	0.146774	+	0.832396i	−0.819152	+	0.573577i	$0.805555\pi$
$854$	18.2409	+	7.86686i	0.624192	+	0.269198i
$855$		0			0
$856$	13.4701	−	4.90590i	0.460398	−	0.167680i
$857$	28.8784	−	5.09204i	0.986467	−	0.173941i	0.342934	−	0.939359i	$-0.388579\pi$
$857$	28.8784	−	5.09204i	0.986467	−	0.173941i	0.643533	+	0.765419i	$0.277468\pi$
$858$		0			0
$859$	7.42637	+	20.4038i	0.253385	+	0.696168i	0.999538	+	0.0303943i	$0.00967631\pi$
$859$	7.42637	+	20.4038i	0.253385	+	0.696168i	−0.746153	+	0.665774i	$0.768101\pi$
$860$	18.3605	−	7.92300i	0.626089	−	0.270172i
$861$		0			0
$862$	3.08180	+	4.13898i	0.104967	+	0.140974i
$863$	−13.3261	−	23.0815i	−0.453626	−	0.785703i	0.544982	−	0.838448i	$-0.316536\pi$
$863$	−13.3261	−	23.0815i	−0.453626	−	0.785703i	−0.998608	+	0.0527447i	$0.983203\pi$
$864$		0			0
$865$	−19.2490	−	3.39413i	−0.654487	−	0.115404i
$866$	2.30475	+	19.7065i	0.0783188	+	0.669654i
$867$		0			0
$868$	2.45396	−	0.143271i	0.0832928	−	0.00486292i
$869$	2.29250	−	6.29860i	0.0777679	−	0.213666i
$870$		0			0
$871$	−3.18186	−	3.79200i	−0.107813	−	0.128487i
$872$	−5.60794	+	3.23931i	−0.189909	+	0.109697i
$873$		0			0
$874$	7.14843	−	36.7908i	0.241799	−	1.24447i
$875$			14.9848i			0.506578i
$876$		0			0
$877$	34.9016	+	41.5942i	1.17854	+	1.40454i	0.895286	+	0.445492i	$0.146971\pi$
$877$	34.9016	+	41.5942i	1.17854	+	1.40454i	0.283259	+	0.959044i	$0.408584\pi$
$878$	0.148613	−	2.55466i	0.00501544	−	0.0862155i
$879$		0			0
$880$	7.03684	+	6.63520i	0.237212	+	0.223673i
$881$	16.7722	−	29.0502i	0.565068	−	0.978727i	−0.431975	−	0.901886i	$-0.642183\pi$
$881$	16.7722	−	29.0502i	0.565068	−	0.978727i	0.997043	−	0.0768413i	$-0.0244835\pi$
$882$		0			0
$883$	36.0797	+	6.36182i	1.21418	+	0.214092i	0.743818	−	0.668383i	$-0.233013\pi$
$883$	36.0797	+	6.36182i	1.21418	+	0.214092i	0.470360	+	0.882475i	$0.344124\pi$
$884$	34.1213	+	51.8631i	1.14762	+	1.74435i
$885$		0			0
$886$	13.9143	−	10.3603i	0.467459	−	0.348061i
$887$	−20.9279	−	17.5606i	−0.702690	−	0.589627i	0.219848	−	0.975534i	$-0.429444\pi$
$887$	−20.9279	−	17.5606i	−0.702690	−	0.589627i	−0.922538	+	0.385907i	$0.873888\pi$
$888$		0			0
$889$	4.78821	+	13.1555i	0.160592	+	0.441222i
$890$	−7.59613	+	2.27471i	−0.254623	+	0.0762485i
$891$		0			0
$892$	0.0505880	+	0.0536051i	0.00169381	+	0.00179483i
$893$	26.8469	+	14.0747i	0.898397	+	0.470993i
$894$		0			0
$895$	5.43467	+	30.8215i	0.181661	+	1.03025i
$896$	8.48014	−	12.9072i	0.283302	−	0.431198i
$897$		0			0
$898$	−6.09798	−	5.75235i	−0.203492	−	0.191958i
$899$	0.346220	−	0.412609i	0.0115471	−	0.0137613i
$900$		0			0
$901$	49.6972	−	28.6927i	1.65565	−	0.955892i
$902$	1.49558	+	0.983511i	0.0497975	+	0.0327473i
$903$		0			0
$904$	−21.0320	+	25.0757i	−0.699516	+	0.834005i
$905$	13.8418	+	7.99155i	0.460116	+	0.265648i
$906$		0			0
$907$	23.1259	+	8.41712i	0.767882	+	0.279486i	0.696110	−	0.717935i	$-0.254913\pi$
$907$	23.1259	+	8.41712i	0.767882	+	0.279486i	0.0717715	+	0.997421i	$0.477135\pi$
$908$	23.7482	+	11.9227i	0.788113	+	0.395667i
$909$		0			0
$910$	−14.5916	−	3.45721i	−0.483708	−	0.114605i
$911$	−12.3194			−0.408160			−0.204080	−	0.978954i	$-0.565420\pi$
$911$	−12.3194			−0.408160			−0.204080	+	0.978954i	$0.565420\pi$
$912$		0			0
$913$	17.4434			0.577293
$914$	−26.2429	−	6.21774i	−0.868037	−	0.205665i
$915$		0			0
$916$	51.5278	+	25.8692i	1.70252	+	0.854742i
$917$	21.9018	+	7.97159i	0.723260	+	0.263245i
$918$		0			0
$919$	17.7965	+	10.2748i	0.587054	+	0.338936i	0.763932	−	0.645297i	$-0.223266\pi$
$919$	17.7965	+	10.2748i	0.587054	+	0.338936i	−0.176878	+	0.984233i	$0.556600\pi$
$920$	−14.7692	+	17.6087i	−0.486925	+	0.580541i
$921$		0			0
$922$	−24.7174	−	16.2544i	−0.814026	−	0.535312i
$923$	−3.37728	+	1.94987i	−0.111165	+	0.0641809i
$924$		0			0
$925$	16.3100	−	19.4375i	0.536269	−	0.639101i
$926$	−10.1208	−	9.54710i	−0.332589	−	0.313737i
$927$		0			0
$928$	−0.781552	−	3.29250i	−0.0256557	−	0.108082i
$929$	−8.88754	−	50.4037i	−0.291591	−	1.65369i	−0.680745	−	0.732521i	$-0.738344\pi$
$929$	−8.88754	−	50.4037i	−0.291591	−	1.65369i	0.389154	−	0.921173i	$-0.372767\pi$
$930$		0			0
$931$	4.78270	+	21.8734i	0.156747	+	0.716872i
$932$	20.9073	+	22.1542i	0.684841	+	0.725686i
$933$		0			0
$934$	6.07961	−	1.82058i	0.198931	−	0.0595711i
$935$	4.41652	+	12.1343i	0.144435	+	0.396833i
$936$		0			0
$937$	6.61304	+	5.54900i	0.216039	+	0.181278i	0.744384	−	0.667751i	$-0.232743\pi$
$937$	6.61304	+	5.54900i	0.216039	+	0.181278i	−0.528346	+	0.849029i	$0.677188\pi$
$938$	−1.31870	+	0.981883i	−0.0430572	+	0.0320596i
$939$		0			0
$940$	−10.2165	−	15.5286i	−0.333224	−	0.506488i
$941$	26.3412	+	4.64466i	0.858697	+	0.151412i	0.585625	−	0.810582i	$-0.300849\pi$
$941$	26.3412	+	4.64466i	0.858697	+	0.151412i	0.273072	+	0.961994i	$0.411960\pi$
$942$		0			0
$943$	−2.12673	+	3.68360i	−0.0692557	+	0.119954i
$944$	21.8531	−	23.1759i	0.711259	−	0.754312i
$945$		0			0
$946$	1.11166	−	19.1095i	0.0361433	−	0.621304i
$947$	−14.3653	−	17.1199i	−0.466809	−	0.556322i	0.480354	−	0.877075i	$-0.340508\pi$
$947$	−14.3653	−	17.1199i	−0.466809	−	0.556322i	−0.947163	+	0.320753i	$0.896064\pi$
$948$		0			0
$949$			22.7274i			0.737764i
$950$	6.45149	+	18.7317i	0.209314	+	0.607738i
$951$		0			0
$952$	17.8547	−	10.3134i	0.578673	−	0.334259i
$953$	−20.5766	−	24.5223i	−0.666542	−	0.794354i	0.321767	−	0.946819i	$-0.395723\pi$
$953$	−20.5766	−	24.5223i	−0.666542	−	0.794354i	−0.988309	+	0.152465i	$0.951279\pi$
$954$		0			0
$955$	11.0152	−	30.2640i	0.356443	−	0.979319i
$956$	−43.4581	+	2.53723i	−1.40553	+	0.0820600i
$957$		0			0
$958$	−3.68015	−	31.4667i	−0.118900	−	1.01664i
$959$	−2.01004	−	0.354424i	−0.0649074	−	0.0114449i
$960$		0			0
$961$	15.0946	+	26.1447i	0.486924	+	0.843377i
$962$	38.7569	+	52.0520i	1.24957	+	1.67822i
$963$		0			0
$964$	13.4467	−	5.80258i	0.433090	−	0.186889i
$965$	−0.101241	−	0.278157i	−0.00325905	−	0.00895418i
$966$		0			0
$967$	−0.553021	+	0.0975125i	−0.0177840	+	0.00313579i	−0.182533	−	0.983200i	$-0.558430\pi$
$967$	−0.553021	+	0.0975125i	−0.0177840	+	0.00313579i	0.164749	+	0.986336i	$0.447319\pi$
$968$	−20.5350	+	7.47901i	−0.660021	+	0.240385i
$969$		0			0
$970$	13.2730	+	5.72430i	0.426170	+	0.183796i
$971$	10.5773	+	59.9870i	0.339443	+	1.92508i	0.377970	+	0.925818i	$0.376622\pi$
$971$	10.5773	+	59.9870i	0.339443	+	1.92508i	−0.0385275	+	0.999258i	$0.512267\pi$
$972$		0			0
$973$	−23.9374	+	8.71250i	−0.767398	+	0.279310i
$974$	32.2618	−	34.2003i	1.03374	−	1.09585i
$975$		0			0
$976$	−34.3960	−	22.6088i	−1.10099	−	0.723691i
$977$	43.4749	−	25.1002i	1.39089	−	0.803028i	0.397472	−	0.917614i	$-0.369888\pi$
$977$	43.4749	−	25.1002i	1.39089	−	0.803028i	0.993413	+	0.114586i	$0.0365542\pi$
$978$		0			0
$979$	−1.31804	+	7.47496i	−0.0421247	+	0.238901i
$980$	3.93595	−	13.1537i	0.125729	−	0.420178i
$981$		0			0
$982$	15.8504	+	31.5552i	0.505806	+	1.00697i
$983$	49.1688	+	17.8960i	1.56824	+	0.570793i	0.972606	−	0.232462i	$-0.0746780\pi$
$983$	49.1688	+	17.8960i	1.56824	+	0.570793i	0.595636	+	0.803255i	$0.296900\pi$
$984$		0			0
$985$	21.7112	−	18.2179i	0.691777	−	0.580470i
$986$	1.04163	−	4.39635i	0.0331722	−	0.140008i
$987$		0			0
$988$	−50.4219	+	5.01068i	−1.60413	+	0.159411i
$989$	45.4856			1.44636
$990$		0			0
$991$	−41.7459	+	35.0290i	−1.32610	+	1.11273i	−0.341132	+	0.940015i	$0.610810\pi$
$991$	−41.7459	+	35.0290i	−1.32610	+	1.11273i	−0.984971	+	0.172718i	$0.944745\pi$
$992$	−5.05914	−	0.589538i	−0.160628	−	0.0187178i
$993$		0			0
$994$	0.581385	+	1.15743i	0.0184404	+	0.0367115i
$995$	11.7144	+	6.76329i	0.371370	+	0.214411i
$996$		0			0
$997$	−4.37523	+	24.8131i	−0.138565	+	0.785840i	0.833746	+	0.552148i	$0.186192\pi$
$997$	−4.37523	+	24.8131i	−0.138565	+	0.785840i	−0.972311	+	0.233692i	$0.924919\pi$
$998$	−4.11383	+	6.25573i	−0.130221	+	0.198022i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.cf.c.523.10		60
3.2	odd	2		228.2.w.a.67.1	✓	60
4.3	odd	2		684.2.cf.b.523.9		60
12.11	even	2		228.2.w.b.67.2	yes	60
19.2	odd	18		684.2.cf.b.667.9		60
57.2	even	18		228.2.w.b.211.2	yes	60
76.59	even	18	inner	684.2.cf.c.667.10		60
228.59	odd	18		228.2.w.a.211.1	yes	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.w.a.67.1	✓	60	3.2	odd	2
228.2.w.a.211.1	yes	60	228.59	odd	18
228.2.w.b.67.2	yes	60	12.11	even	2
228.2.w.b.211.2	yes	60	57.2	even	18
684.2.cf.b.523.9		60	4.3	odd	2
684.2.cf.b.667.9		60	19.2	odd	18
684.2.cf.c.523.10		60	1.1	even	1	trivial
684.2.cf.c.667.10		60	76.59	even	18	inner

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)

\(f(q)\)	\(=\)	\(q+(1.37612 + 0.326044i) q^{2} +(1.78739 + 0.897349i) q^{4} +(1.25586 + 0.457097i) q^{5} +(-1.18216 - 0.682521i) q^{7} +(2.16708 + 1.81762i) q^{8} +(1.57918 + 1.03849i) q^{10} +(1.56682 - 0.904604i) q^{11} +(3.73606 - 4.45246i) q^{13} +(-1.40426 - 1.32467i) q^{14} +(2.38953 + 3.20783i) q^{16} +(0.927369 + 5.25937i) q^{17} +(-4.15334 - 1.32280i) q^{19} +(1.83454 + 1.94396i) q^{20} +(2.45107 - 0.733988i) q^{22} +(2.07944 + 5.71321i) q^{23} +(-2.46197 - 2.06583i) q^{25} +(6.59294 - 4.90898i) q^{26} +(-1.50052 - 2.28074i) q^{28} +(-0.589123 - 0.103878i) q^{29} +(-0.450194 + 0.779760i) q^{31} +(2.24238 + 5.19343i) q^{32} +(-0.438619 + 7.53987i) q^{34} +(-1.17266 - 1.39752i) q^{35} +7.89511i q^{37} +(-5.28418 - 3.17450i) q^{38} +(1.89073 + 3.27326i) q^{40} +(0.449691 + 0.535921i) q^{41} +(2.55877 - 7.03016i) q^{43} +(3.61227 - 0.210897i) q^{44} +(0.998791 + 8.54003i) q^{46} +(-6.84854 - 1.20758i) q^{47} +(-2.56833 - 4.44848i) q^{49} +(-2.71440 - 3.64554i) q^{50} +(10.6732 - 4.60574i) q^{52} +(-3.67511 - 10.0973i) q^{53} +(2.38121 - 0.419871i) q^{55} +(-1.32127 - 3.62780i) q^{56} +(-0.776832 - 0.335028i) q^{58} +(-1.38285 - 7.84254i) q^{59} +(-9.66972 + 3.51949i) q^{61} +(-0.873756 + 0.926257i) q^{62} +(1.39249 + 7.87788i) q^{64} +(6.72719 - 3.88394i) q^{65} +(0.147890 - 0.838725i) q^{67} +(-3.06192 + 10.2327i) q^{68} +(-1.15806 - 2.30548i) q^{70} +(-0.630487 - 0.229479i) q^{71} +(-2.99543 + 2.51346i) q^{73} +(-2.57415 + 10.8646i) q^{74} +(-6.23662 - 6.09135i) q^{76} -2.46965 q^{77} +(2.83807 - 2.38143i) q^{79} +(1.53464 + 5.12084i) q^{80} +(0.444093 + 0.884109i) q^{82} +(8.34975 + 4.82073i) q^{83} +(-1.23939 + 7.02896i) q^{85} +(5.81331 - 8.84005i) q^{86} +(5.03966 + 0.887540i) q^{88} +(-2.69672 + 3.21383i) q^{89} +(-7.45552 + 2.71359i) q^{91} +(-1.40997 + 12.0777i) q^{92} +(-9.03066 - 3.89470i) q^{94} +(-4.61138 - 3.55973i) q^{95} +(7.53165 - 1.32803i) q^{97} +(-2.08392 - 6.95901i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 3 q^{2} - 3 q^{4} - 3 q^{8} - 6 q^{10} - 6 q^{13} + 9 q^{14} - 27 q^{16} - 18 q^{19} - 30 q^{20} + 12 q^{22} - 18 q^{28} + 12 q^{31} + 63 q^{32} - 39 q^{34} + 48 q^{38} + 33 q^{40} + 12 q^{41} + 18 q^{43}+ \cdots - 117 q^{98}+O(q^{100}) \) 60 * q + 3 * q^2 - 3 * q^4 - 3 * q^8 - 6 * q^10 - 6 * q^13 + 9 * q^14 - 27 * q^16 - 18 * q^19 - 30 * q^20 + 12 * q^22 - 18 * q^28 + 12 * q^31 + 63 * q^32 - 39 * q^34 + 48 * q^38 + 33 * q^40 + 12 * q^41 + 18 * q^43 + 9 * q^44 - 69 * q^46 + 30 * q^49 + 27 * q^50 - 3 * q^52 - 12 * q^53 + 42 * q^56 - 36 * q^58 - 27 * q^62 + 21 * q^64 + 36 * q^65 - 42 * q^67 - 93 * q^68 + 132 * q^70 + 24 * q^71 + 18 * q^73 - 27 * q^74 + 66 * q^76 + 72 * q^77 - 12 * q^79 - 6 * q^80 - 9 * q^82 - 60 * q^85 - 123 * q^86 + 36 * q^88 + 12 * q^89 + 84 * q^91 + 99 * q^92 - 24 * q^95 + 12 * q^97 - 117 * q^98

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