LMFDB - Embedded newform 864.2.bn.a.683.25

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [864,2,Mod(35,864)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(864, base_ring=CyclotomicField(24)) chi = DirichletCharacter(H, H._module([12, 9, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("864.35"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 864 = 2^{5} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	864.bn (of order $24$, degree $8$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$6.89907473464$
Analytic rank:	$0$
Dimension:	$368$
Relative dimension:	$46$ over $\Q(\zeta_{24})$
Twist minimal:	no (minimal twist has level 288)
Sato-Tate group:	$\mathrm{SU}(2)[C_{24}]$

Embedding invariants

Embedding label			683.25
Character	$\chi$	$=$	864.683
Dual form			864.2.bn.a.611.25

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.259191 - 1.39026i) q^{2} +(-1.86564 - 0.720686i) q^{4} +(0.173739 + 1.31968i) q^{5} +(0.0444224 + 0.165787i) q^{7} +(-1.48550 + 2.40693i) q^{8} +(1.87973 + 0.100507i) q^{10} +(0.877753 - 0.673524i) q^{11} +(2.54859 - 3.32139i) q^{13} +(0.242000 - 0.0187881i) q^{14} +(2.96122 + 2.68908i) q^{16} -1.67770 q^{17} +(3.90182 - 1.61619i) q^{19} +(0.626942 - 2.58726i) q^{20} +(-0.708866 - 1.39488i) q^{22} +(-1.65427 - 0.443260i) q^{23} +(3.11825 - 0.835534i) q^{25} +(-3.95702 - 4.40408i) q^{26} +(0.0366040 - 0.341313i) q^{28} +(6.46737 + 0.851445i) q^{29} +(3.09485 - 1.78681i) q^{31} +(4.50604 - 3.41988i) q^{32} +(-0.434846 + 2.33244i) q^{34} +(-0.211068 + 0.0874271i) q^{35} +(3.58091 - 8.64508i) q^{37} +(-1.23560 - 5.84344i) q^{38} +(-3.43447 - 1.54221i) q^{40} +(0.790091 - 2.94866i) q^{41} +(-5.37283 - 7.00201i) q^{43} +(-2.12297 + 0.623968i) q^{44} +(-1.04502 + 2.18497i) q^{46} +(0.598230 + 0.345388i) q^{47} +(6.03667 - 3.48527i) q^{49} +(-0.353383 - 4.55174i) q^{50} +(-7.14844 + 4.35979i) q^{52} +(-4.43574 + 10.7088i) q^{53} +(1.04134 + 1.04134i) q^{55} +(-0.465026 - 0.139354i) q^{56} +(2.86002 - 8.77063i) q^{58} +(-3.24657 + 0.427420i) q^{59} +(-1.28507 + 9.76104i) q^{61} +(-1.68197 - 4.76576i) q^{62} +(-3.58659 - 7.15097i) q^{64} +(4.82597 + 2.78628i) q^{65} +(-5.81460 + 7.57774i) q^{67} +(3.12999 + 1.20910i) q^{68} +(0.0668394 + 0.316099i) q^{70} +(-0.107240 - 0.107240i) q^{71} +(3.93478 - 3.93478i) q^{73} +(-11.0908 - 7.21912i) q^{74} +(-8.44415 + 0.203233i) q^{76} +(0.150653 + 0.115600i) q^{77} +(0.777341 - 1.34639i) q^{79} +(-3.03425 + 4.37507i) q^{80} +(-3.89461 - 1.86270i) q^{82} +(-4.82345 - 0.635020i) q^{83} +(-0.291483 - 2.21403i) q^{85} +(-11.1272 + 5.65476i) q^{86} +(0.317221 + 3.11321i) q^{88} +(10.7307 - 10.7307i) q^{89} +(0.663857 + 0.274979i) q^{91} +(2.76682 + 2.01917i) q^{92} +(0.635235 - 0.742173i) q^{94} +(2.81075 + 4.86836i) q^{95} +(-6.90201 + 11.9546i) q^{97} +(-3.28078 - 9.29588i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) $ 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.259191	−	1.39026i	0.183276	−	0.983061i
$2$	0.259191	−	1.39026i	0.183276	−	0.983061i
$3$		0			0
$3$		0			0
$4$	−1.86564	−	0.720686i	−0.932820	−	0.360343i
$5$	0.173739	+	1.31968i	0.0776986	+	0.590180i	0.985361	+	0.170479i	$0.0545315\pi$
$5$	0.173739	+	1.31968i	0.0776986	+	0.590180i	−0.907663	+	0.419700i	$0.862135\pi$
$6$		0			0
$7$	0.0444224	+	0.165787i	0.0167901	+	0.0626615i	0.973813	−	0.227352i	$-0.0730068\pi$
$7$	0.0444224	+	0.165787i	0.0167901	+	0.0626615i	−0.957023	+	0.290014i	$0.906340\pi$
$8$	−1.48550	+	2.40693i	−0.525203	+	0.850977i
$9$		0			0
$10$	1.87973	+	0.100507i	0.594423	+	0.0317833i
$11$	0.877753	−	0.673524i	0.264653	−	0.203075i	−0.467907	−	0.883777i	$-0.654992\pi$
$11$	0.877753	−	0.673524i	0.264653	−	0.203075i	0.732560	+	0.680702i	$0.238325\pi$
$12$		0			0
$13$	2.54859	−	3.32139i	0.706853	−	0.921189i	−0.292532	−	0.956256i	$-0.594498\pi$
$13$	2.54859	−	3.32139i	0.706853	−	0.921189i	0.999385	+	0.0350670i	$0.0111645\pi$
$14$	0.242000	−	0.0187881i	0.0646773	−	0.00502134i
$15$		0			0
$16$	2.96122	+	2.68908i	0.740306	+	0.672271i
$17$	−1.67770			−0.406902			−0.203451	−	0.979085i	$-0.565216\pi$
$17$	−1.67770			−0.406902			−0.203451	+	0.979085i	$0.565216\pi$
$18$		0			0
$19$	3.90182	−	1.61619i	0.895139	−	0.370779i	0.112790	−	0.993619i	$-0.464021\pi$
$19$	3.90182	−	1.61619i	0.895139	−	0.370779i	0.782349	+	0.622840i	$0.214021\pi$
$20$	0.626942	−	2.58726i	0.140188	−	0.578529i
$21$		0			0
$22$	−0.708866	−	1.39488i	−0.151131	−	0.297389i
$23$	−1.65427	−	0.443260i	−0.344939	−	0.0924261i	0.0821905	−	0.996617i	$-0.473808\pi$
$23$	−1.65427	−	0.443260i	−0.344939	−	0.0924261i	−0.427129	+	0.904191i	$0.640475\pi$
$24$		0			0
$25$	3.11825	−	0.835534i	0.623651	−	0.167107i
$26$	−3.95702	−	4.40408i	−0.776036	−	0.863712i
$27$		0			0
$28$	0.0366040	−	0.341313i	0.00691751	−	0.0645020i
$29$	6.46737	+	0.851445i	1.20096	+	0.158109i	0.704343	−	0.709860i	$-0.251242\pi$
$29$	6.46737	+	0.851445i	1.20096	+	0.158109i	0.496618	+	0.867969i	$0.334575\pi$
$30$		0			0
$31$	3.09485	−	1.78681i	0.555851	−	0.320920i	−0.195628	−	0.980678i	$-0.562674\pi$
$31$	3.09485	−	1.78681i	0.555851	−	0.320920i	0.751478	+	0.659758i	$0.229341\pi$
$32$	4.50604	−	3.41988i	0.796564	−	0.604555i
$33$		0			0
$34$	−0.434846	+	2.33244i	−0.0745755	+	0.400010i
$35$	−0.211068	+	0.0874271i	−0.0356769	+	0.0147779i
$36$		0			0
$37$	3.58091	−	8.64508i	0.588698	−	1.42124i	−0.296050	−	0.955173i	$-0.595669\pi$
$37$	3.58091	−	8.64508i	0.588698	−	1.42124i	0.884748	−	0.466070i	$-0.154331\pi$
$38$	−1.23560	−	5.84344i	−0.200441	−	0.947931i
$39$		0			0
$40$	−3.43447	−	1.54221i	−0.543037	−	0.243844i
$41$	0.790091	−	2.94866i	0.123391	−	0.460503i	−0.876386	−	0.481610i	$-0.840052\pi$
$41$	0.790091	−	2.94866i	0.123391	−	0.460503i	0.999777	+	0.0211066i	$0.00671894\pi$
$42$		0			0
$43$	−5.37283	−	7.00201i	−0.819349	−	1.06780i	−0.996498	−	0.0836124i	$-0.973354\pi$
$43$	−5.37283	−	7.00201i	−0.819349	−	1.06780i	0.177149	−	0.984184i	$-0.443312\pi$
$44$	−2.12297	+	0.623968i	−0.320050	+	0.0940667i
$45$		0			0
$46$	−1.04502	+	2.18497i	−0.154080	+	0.322157i
$47$	0.598230	+	0.345388i	0.0872608	+	0.0503801i	0.542995	−	0.839736i	$-0.317290\pi$
$47$	0.598230	+	0.345388i	0.0872608	+	0.0503801i	−0.455735	+	0.890116i	$0.650623\pi$
$48$		0			0
$49$	6.03667	−	3.48527i	0.862381	−	0.497896i
$50$	−0.353383	−	4.55174i	−0.0499760	−	0.643714i
$51$		0			0
$52$	−7.14844	+	4.35979i	−0.991311	+	0.604593i
$53$	−4.43574	+	10.7088i	−0.609296	+	1.47097i	0.254471	+	0.967080i	$0.418099\pi$
$53$	−4.43574	+	10.7088i	−0.609296	+	1.47097i	−0.863768	+	0.503891i	$0.831901\pi$
$54$		0			0
$55$	1.04134	+	1.04134i	0.140414	+	0.140414i
$56$	−0.465026	−	0.139354i	−0.0621417	−	0.0186220i
$57$		0			0
$58$	2.86002	−	8.77063i	0.375539	−	1.15164i
$59$	−3.24657	+	0.427420i	−0.422668	+	0.0556453i	−0.338860	−	0.940837i	$-0.610041\pi$
$59$	−3.24657	+	0.427420i	−0.422668	+	0.0556453i	−0.0838076	+	0.996482i	$0.526708\pi$
$60$		0			0
$61$	−1.28507	+	9.76104i	−0.164536	+	1.24977i	0.687459	+	0.726223i	$0.258726\pi$
$61$	−1.28507	+	9.76104i	−0.164536	+	1.24977i	−0.851995	+	0.523550i	$0.824607\pi$
$62$	−1.68197	−	4.76576i	−0.213610	−	0.605252i
$63$		0			0
$64$	−3.58659	−	7.15097i	−0.448323	−	0.893871i
$65$	4.82597	+	2.78628i	0.598588	+	0.345595i
$66$		0			0
$67$	−5.81460	+	7.57774i	−0.710367	+	0.925768i	−0.999503	−	0.0315197i	$-0.989965\pi$
$67$	−5.81460	+	7.57774i	−0.710367	+	0.925768i	0.289136	+	0.957288i	$0.406632\pi$
$68$	3.12999	+	1.20910i	0.379567	+	0.146625i
$69$		0			0
$70$	0.0668394	+	0.316099i	0.00798883	+	0.0377811i
$71$	−0.107240	−	0.107240i	−0.0127271	−	0.0127271i	0.700715	−	0.713442i	$-0.252865\pi$
$71$	−0.107240	−	0.107240i	−0.0127271	−	0.0127271i	−0.713442	+	0.700715i	$0.752865\pi$
$72$		0			0
$73$	3.93478	−	3.93478i	0.460532	−	0.460532i	−0.438298	−	0.898830i	$-0.644419\pi$
$73$	3.93478	−	3.93478i	0.460532	−	0.460532i	0.898830	+	0.438298i	$0.144419\pi$
$74$	−11.0908	−	7.21912i	−1.28927	−	0.839206i
$75$		0			0
$76$	−8.44415	+	0.203233i	−0.968611	+	0.0233124i
$77$	0.150653	+	0.115600i	0.0171685	+	0.0131739i
$78$		0			0
$79$	0.777341	−	1.34639i	0.0874576	−	0.151481i	−0.818978	−	0.573825i	$-0.805459\pi$
$79$	0.777341	−	1.34639i	0.0874576	−	0.151481i	0.906436	+	0.422344i	$0.138792\pi$
$80$	−3.03425	+	4.37507i	−0.339240	+	0.489148i
$81$		0			0
$82$	−3.89461	−	1.86270i	−0.430088	−	0.205701i
$83$	−4.82345	−	0.635020i	−0.529443	−	0.0697025i	−0.138934	−	0.990302i	$-0.544368\pi$
$83$	−4.82345	−	0.635020i	−0.529443	−	0.0697025i	−0.390509	+	0.920599i	$0.627701\pi$
$84$		0			0
$85$	−0.291483	−	2.21403i	−0.0316158	−	0.240146i
$86$	−11.1272	+	5.65476i	−1.19988	+	0.609769i
$87$		0			0
$88$	0.317221	+	3.11321i	0.0338159	+	0.331869i
$89$	10.7307	−	10.7307i	1.13745	−	1.13745i	0.148546	−	0.988905i	$-0.452541\pi$
$89$	10.7307	−	10.7307i	1.13745	−	1.13745i	0.988905	−	0.148546i	$-0.0474594\pi$
$90$		0			0
$91$	0.663857	+	0.274979i	0.0695912	+	0.0288256i
$92$	2.76682	+	2.01917i	0.288461	+	0.210513i
$93$		0			0
$94$	0.635235	−	0.742173i	0.0655195	−	0.0765493i
$95$	2.81075	+	4.86836i	0.288377	+	0.499484i
$96$		0			0
$97$	−6.90201	+	11.9546i	−0.700793	+	1.21381i	0.267396	+	0.963587i	$0.413837\pi$
$97$	−6.90201	+	11.9546i	−0.700793	+	1.21381i	−0.968189	+	0.250222i	$0.919496\pi$
$98$	−3.28078	−	9.29588i	−0.331408	−	0.939026i
$99$		0			0
$100$	−6.41970	−	0.688479i	−0.641970	−	0.0688479i
$101$	2.41616	−	1.85399i	0.240417	−	0.184479i	−0.481524	−	0.876433i	$-0.659917\pi$
$101$	2.41616	−	1.85399i	0.240417	−	0.184479i	0.721941	+	0.691954i	$0.243250\pi$
$102$		0			0
$103$	−0.0714267	−	0.0191387i	−0.00703788	−	0.00188579i	0.255298	−	0.966862i	$-0.417826\pi$
$103$	−0.0714267	−	0.0191387i	−0.00703788	−	0.00188579i	−0.262336	+	0.964977i	$0.584493\pi$
$104$	4.20841	+	11.0682i	0.412669	+	1.08533i
$105$		0			0
$106$	13.7383	+	8.94247i	1.33439	+	0.868569i
$107$	10.4670	+	4.33555i	1.01188	+	0.419134i	0.826140	−	0.563465i	$-0.190532\pi$
$107$	10.4670	+	4.33555i	1.01188	+	0.419134i	0.185739	+	0.982599i	$0.440532\pi$
$108$		0			0
$109$	4.40564	+	10.6362i	0.421984	+	1.01876i	0.981762	+	0.190116i	$0.0608866\pi$
$109$	4.40564	+	10.6362i	0.421984	+	1.01876i	−0.559778	+	0.828643i	$0.689113\pi$
$110$	1.71763	−	1.17782i	0.163770	−	0.112301i
$111$		0			0
$112$	−0.314269	+	0.610386i	−0.0296957	+	0.0576761i
$113$	−2.75339	−	4.76900i	−0.259017	−	0.448630i	0.706962	−	0.707251i	$-0.250065\pi$
$113$	−2.75339	−	4.76900i	−0.259017	−	0.448630i	−0.965979	+	0.258621i	$0.916732\pi$
$114$		0			0
$115$	0.297550	−	2.26012i	0.0277467	−	0.210757i
$116$	−11.4522	−	6.24944i	−1.06331	−	0.580246i
$117$		0			0
$118$	−0.247260	+	4.62436i	−0.0227622	+	0.425707i
$119$	−0.0745275	−	0.278141i	−0.00683193	−	0.0254971i
$120$		0			0
$121$	−2.53019	+	9.44281i	−0.230018	+	0.858437i
$122$	13.2373	+	4.31655i	1.19845	+	0.390802i
$123$		0			0
$124$	−7.06159	+	1.10313i	−0.634150	+	0.0990640i
$125$	4.19129	+	10.1187i	0.374881	+	0.905042i
$126$		0			0
$127$		−	10.3560i		−	0.918945i	−0.888192	−	0.459473i	$-0.848038\pi$
$127$		−	10.3560i		−	0.918945i	0.888192	−	0.459473i	$-0.151962\pi$
$128$	−10.8713	+	3.13281i	−0.960897	+	0.276904i
$129$		0			0
$130$	5.12450	−	5.98717i	0.449448	−	0.525110i
$131$	−12.5469	−	9.62756i	−1.09623	−	0.841163i	−0.107997	−	0.994151i	$-0.534444\pi$
$131$	−12.5469	−	9.62756i	−1.09623	−	0.841163i	−0.988228	+	0.152988i	$0.951110\pi$
$132$		0			0
$133$	0.441270	+	0.575075i	0.0382630	+	0.0498653i
$134$	9.02793	+	10.0479i	0.779894	+	0.868006i
$135$		0			0
$136$	2.49222	−	4.03810i	0.213706	−	0.346265i
$137$	13.6981	−	3.67040i	1.17031	−	0.313584i	0.379234	−	0.925301i	$-0.376188\pi$
$137$	13.6981	−	3.67040i	1.17031	−	0.313584i	0.791077	+	0.611717i	$0.209521\pi$
$138$		0			0
$139$	−22.2942	+	2.93509i	−1.89097	+	0.248951i	−0.984765	−	0.173891i	$-0.944366\pi$
$139$	−22.2942	+	2.93509i	−1.89097	+	0.248951i	−0.906203	+	0.422842i	$0.861032\pi$
$140$	0.456784	−	0.0109938i	0.0386053	−	0.000929148i
$141$		0			0
$142$	−0.176887	+	0.121296i	−0.0148441	+	0.0101789i
$143$		−	4.63190i		−	0.387339i
$144$		0			0
$145$			8.68280i			0.721067i
$146$	−4.45051	−	6.49023i	−0.368326	−	0.537135i
$147$		0			0
$148$	−12.9111	+	13.5479i	−1.06128	+	1.11363i
$149$	−14.4913	+	1.90781i	−1.18717	+	0.156294i	−0.698132	−	0.715969i	$-0.745985\pi$
$149$	−14.4913	+	1.90781i	−1.18717	+	0.156294i	−0.489038	+	0.872263i	$0.662652\pi$
$150$		0			0
$151$	22.3710	−	5.99430i	1.82053	−	0.487809i	0.823673	−	0.567065i	$-0.191921\pi$
$151$	22.3710	−	5.99430i	1.82053	−	0.487809i	0.996854	+	0.0792562i	$0.0252545\pi$
$152$	−1.90611	+	11.7922i	−0.154606	+	0.956476i
$153$		0			0
$154$	0.199762	−	0.179484i	0.0160973	−	0.0144633i
$155$	2.89572	+	3.77377i	0.232590	+	0.303117i
$156$		0			0
$157$	10.1020	+	7.75154i	0.806227	+	0.618640i	0.927434	−	0.373987i	$-0.122010\pi$
$157$	10.1020	+	7.75154i	0.806227	+	0.618640i	−0.121206	+	0.992627i	$0.538676\pi$
$158$	−1.67036	−	1.42968i	−0.132886	−	0.113739i
$159$		0			0
$160$	5.29603	+	5.35238i	0.418688	+	0.423143i
$161$		−	0.293946i		−	0.0231662i
$162$		0			0
$163$	0.0659393	+	0.159192i	0.00516477	+	0.0124689i	0.926441	−	0.376440i	$-0.122852\pi$
$163$	0.0659393	+	0.159192i	0.00516477	+	0.0124689i	−0.921276	+	0.388909i	$0.872852\pi$
$164$	−3.59908	+	4.93173i	−0.281041	+	0.385103i
$165$		0			0
$166$	−2.13304	+	6.54126i	−0.165556	+	0.507700i
$167$	−3.69073	+	13.7740i	−0.285598	+	1.06586i	0.662804	+	0.748793i	$0.269366\pi$
$167$	−3.69073	+	13.7740i	−0.285598	+	1.06586i	−0.948402	+	0.317072i	$0.897300\pi$
$168$		0			0
$169$	−1.17167	−	4.37274i	−0.0901285	−	0.336364i
$170$	−3.15363	−	0.168622i	−0.241872	−	0.0129327i
$171$		0			0
$172$	4.97751	+	16.9354i	0.379532	+	1.29131i
$173$	−0.461232	+	3.50340i	−0.0350668	+	0.266359i	0.964926	+	0.262523i	$0.0845544\pi$
$173$	−0.461232	+	3.50340i	−0.0350668	+	0.266359i	−0.999993	+	0.00383618i	$0.998779\pi$
$174$		0			0
$175$	0.277041	+	0.479849i	0.0209423	+	0.0362731i
$176$	4.41038	+	0.365897i	0.332445	+	0.0275806i
$177$		0			0
$178$	−12.1371	−	17.6998i	−0.909717	−	1.32665i
$179$	−8.74430	−	21.1106i	−0.653580	−	1.57788i	−0.807546	−	0.589805i	$-0.799205\pi$
$179$	−8.74430	−	21.1106i	−0.653580	−	1.57788i	0.153966	−	0.988076i	$-0.450795\pi$
$180$		0			0
$181$	13.6633	+	5.65954i	1.01559	+	0.420670i	0.827490	−	0.561480i	$-0.189768\pi$
$181$	13.6633	+	5.65954i	1.01559	+	0.420670i	0.188098	+	0.982150i	$0.439768\pi$
$182$	0.554358	−	0.851661i	0.0410917	−	0.0631293i
$183$		0			0
$184$	3.52431	−	3.32324i	0.259815	−	0.244993i
$185$	12.0309	+	3.22367i	0.884530	+	0.237009i
$186$		0			0
$187$	−1.47261	+	1.12997i	−0.107688	+	0.0826318i
$188$	−0.867165	−	1.07551i	−0.0632445	−	0.0784394i
$189$		0			0
$190$	7.49681	−	2.64583i	0.543876	−	0.191949i
$191$	−10.9654	+	18.9927i	−0.793431	+	1.37426i	0.130400	+	0.991461i	$0.458374\pi$
$191$	−10.9654	+	18.9927i	−0.793431	+	1.37426i	−0.923831	+	0.382801i	$0.874960\pi$
$192$		0			0
$193$	−6.84398	−	11.8541i	−0.492641	−	0.853278i	0.507324	−	0.861756i	$-0.330635\pi$
$193$	−6.84398	−	11.8541i	−0.492641	−	0.853278i	−0.999964	+	0.00847726i	$0.997302\pi$
$194$	14.8311	+	12.6941i	1.06481	+	0.911384i
$195$		0			0
$196$	−13.7740	+	2.15172i	−0.983859	+	0.153694i
$197$	16.7997	+	6.95868i	1.19693	+	0.495785i	0.890006	−	0.455948i	$-0.150700\pi$
$197$	16.7997	+	6.95868i	1.19693	+	0.495785i	0.306926	+	0.951734i	$0.400700\pi$
$198$		0			0
$199$	3.67634	−	3.67634i	0.260609	−	0.260609i	−0.564693	−	0.825301i	$-0.691005\pi$
$199$	3.67634	−	3.67634i	0.260609	−	0.260609i	0.825301	+	0.564693i	$0.191005\pi$
$200$	−2.62109	+	8.74659i	−0.185339	+	0.618478i
$201$		0			0
$202$	−1.95127	−	3.83963i	−0.137291	−	0.270155i
$203$	0.146138	+	1.11003i	0.0102569	+	0.0779086i
$204$		0			0
$205$	4.02856	+	0.530370i	0.281367	+	0.0370427i
$206$	−0.0451210	+	0.0943410i	−0.00314373	+	0.00657305i
$207$		0			0
$208$	16.4785	−	2.98200i	1.14258	−	0.206765i
$209$	2.33630	−	4.04658i	0.161605	−	0.279908i
$210$		0			0
$211$	−4.84408	−	3.71699i	−0.333480	−	0.255888i	0.428424	−	0.903578i	$-0.359069\pi$
$211$	−4.84408	−	3.71699i	−0.333480	−	0.255888i	−0.761905	+	0.647689i	$0.775735\pi$
$212$	15.9932	−	16.7820i	1.09842	−	1.15259i
$213$		0			0
$214$	8.74049	−	13.4280i	0.597487	−	0.917921i
$215$	8.30695	−	8.30695i	0.566529	−	0.566529i
$216$		0			0
$217$	0.433710	+	0.433710i	0.0294421	+	0.0294421i
$218$	15.9289	−	3.36818i	1.07884	−	0.228122i
$219$		0			0
$220$	−1.19228	−	2.69324i	−0.0803837	−	0.181578i
$221$	−4.27578	+	5.57231i	−0.287620	+	0.374834i
$222$		0			0
$223$	−9.14774	−	5.28145i	−0.612578	−	0.353672i	0.161396	−	0.986890i	$-0.448400\pi$
$223$	−9.14774	−	5.28145i	−0.612578	−	0.353672i	−0.773974	+	0.633218i	$0.781734\pi$
$224$	0.767139	+	0.595123i	0.0512567	+	0.0397633i
$225$		0			0
$226$	−7.34380	+	2.59183i	−0.488503	+	0.172406i
$227$	−2.88471	+	21.9116i	−0.191465	+	1.45432i	0.578211	+	0.815887i	$0.303751\pi$
$227$	−2.88471	+	21.9116i	−0.191465	+	1.45432i	−0.769676	+	0.638435i	$0.779582\pi$
$228$		0			0
$229$	1.03165	−	0.135820i	0.0681735	−	0.00897521i	−0.0963623	−	0.995346i	$-0.530721\pi$
$229$	1.03165	−	0.135820i	0.0681735	−	0.00897521i	0.164536	+	0.986371i	$0.447387\pi$
$230$	−3.06503	−	0.999476i	−0.202102	−	0.0659035i
$231$		0			0
$232$	−11.6566	+	14.3017i	−0.765296	+	0.938950i
$233$	−14.9180	−	14.9180i	−0.977311	−	0.977311i	0.0224377	−	0.999748i	$-0.492857\pi$
$233$	−14.9180	−	14.9180i	−0.977311	−	0.977311i	−0.999748	+	0.0224377i	$0.992857\pi$
$234$		0			0
$235$	−0.351866	+	0.849481i	−0.0229532	+	0.0554140i
$236$	6.36497	+	1.54235i	0.414324	+	0.100399i
$237$		0			0
$238$	−0.406004	+	0.0315209i	−0.0263173	+	0.00204320i
$239$	11.0919	−	6.40393i	0.717477	−	0.414236i	−0.0963462	−	0.995348i	$-0.530716\pi$
$239$	11.0919	−	6.40393i	0.717477	−	0.414236i	0.813823	+	0.581112i	$0.197382\pi$
$240$		0			0
$241$	5.66423	+	3.27024i	0.364865	+	0.210655i	0.671213	−	0.741265i	$-0.265774\pi$
$241$	5.66423	+	3.27024i	0.364865	+	0.210655i	−0.306348	+	0.951920i	$0.599107\pi$
$242$	12.4721	+	5.96512i	0.801740	+	0.383452i
$243$		0			0
$244$	9.43212	−	17.2845i	0.603830	−	1.10652i
$245$	5.64825	+	7.36095i	0.360854	+	0.470274i
$246$		0			0
$247$	4.57617	−	17.0785i	0.291174	−	1.08668i
$248$	−0.296669	+	10.1034i	−0.0188385	+	0.641564i
$249$		0			0
$250$	15.1539	−	3.20431i	0.958419	−	0.202658i
$251$	−3.69201	+	8.91330i	−0.233038	+	0.562603i	−0.996532	−	0.0832121i	$-0.973482\pi$
$251$	−3.69201	+	8.91330i	−0.233038	+	0.562603i	0.763494	+	0.645815i	$0.223482\pi$
$252$		0			0
$253$	−1.75059	+	0.725116i	−0.110058	+	0.0455877i
$254$	−14.3975	−	2.68418i	−0.903380	−	0.168421i
$255$		0			0
$256$	1.53767	+	15.9259i	0.0961045	+	0.995371i
$257$	−0.809834	+	0.467558i	−0.0505160	+	0.0291654i	−0.525045	−	0.851074i	$-0.675952\pi$
$257$	−0.809834	+	0.467558i	−0.0505160	+	0.0291654i	0.474529	+	0.880240i	$0.342618\pi$
$258$		0			0
$259$	1.59231	+	0.209632i	0.0989414	+	0.0130259i
$260$	−6.99549	−	8.67620i	−0.433842	−	0.538075i
$261$		0			0
$262$	−16.6368	+	14.9480i	−1.02783	+	0.923492i
$263$	−6.76551	+	1.81281i	−0.417179	+	0.111783i	−0.461302	−	0.887243i	$-0.652617\pi$
$263$	−6.76551	+	1.81281i	−0.417179	+	0.111783i	0.0441227	+	0.999026i	$0.485951\pi$
$264$		0			0
$265$	−14.9029	−	3.99322i	−0.915478	−	0.245302i
$266$	0.913876	−	0.464425i	0.0560333	−	0.0284758i
$267$		0			0
$268$	16.3091	−	9.94683i	0.996239	−	0.607599i
$269$	25.5646	−	10.5892i	1.55870	−	0.645634i	0.573836	−	0.818970i	$-0.305455\pi$
$269$	25.5646	−	10.5892i	1.55870	−	0.645634i	0.984863	+	0.173336i	$0.0554548\pi$
$270$		0			0
$271$	−24.4270			−1.48383			−0.741917	−	0.670492i	$-0.766083\pi$
$271$	−24.4270			−1.48383			−0.741917	+	0.670492i	$0.766083\pi$
$272$	−4.96805	−	4.51148i	−0.301232	−	0.273549i
$273$		0			0
$274$	−1.55237	−	19.9953i	−0.0937822	−	1.20796i
$275$	2.17431	−	2.83361i	0.131116	−	0.170873i
$276$		0			0
$277$	−20.3161	+	15.5891i	−1.22068	+	0.936658i	−0.999258	−	0.0385209i	$-0.987735\pi$
$277$	−20.3161	+	15.5891i	−1.22068	+	0.936658i	−0.221419	+	0.975179i	$0.571069\pi$
$278$	−1.69793	+	31.7554i	−0.101835	+	1.90456i
$279$		0			0
$280$	0.103110	−	0.637897i	0.00616201	−	0.0381216i
$281$	2.17463	+	8.11585i	0.129728	+	0.484151i	0.999964	−	0.00848391i	$-0.00270054\pi$
$281$	2.17463	+	8.11585i	0.129728	+	0.484151i	−0.870236	+	0.492635i	$0.836034\pi$
$282$		0			0
$283$	2.46841	+	18.7494i	0.146732	+	1.11454i	0.893375	+	0.449312i	$0.148331\pi$
$283$	2.46841	+	18.7494i	0.146732	+	1.11454i	−0.746643	+	0.665224i	$0.768336\pi$
$284$	0.122785	+	0.277358i	0.00728595	+	0.0164582i
$285$		0			0
$286$	−6.43955	−	1.20055i	−0.380778	−	0.0709900i
$287$	0.523946			0.0309276
$288$		0			0
$289$	−14.1853			−0.834430
$290$	12.0713	+	2.25051i	0.708853	+	0.132154i
$291$		0			0
$292$	−10.1766	+	4.50514i	−0.595542	+	0.263644i
$293$	−3.14809	−	23.9121i	−0.183913	−	1.39696i	−0.795581	−	0.605847i	$-0.792835\pi$
$293$	−3.14809	−	23.9121i	−0.183913	−	1.39696i	0.611668	−	0.791115i	$-0.290499\pi$
$294$		0			0
$295$	−1.12812	−	4.21019i	−0.0656814	−	0.245126i
$296$	15.4886	+	21.4612i	0.900259	+	1.24741i
$297$		0			0
$298$	−1.10366	+	20.6411i	−0.0639333	+	1.19571i
$299$	−5.68830	+	4.36479i	−0.328963	+	0.252422i
$300$		0			0
$301$	0.922166	−	1.20179i	0.0531527	−	0.0692700i
$302$	−2.53525	−	32.6552i	−0.145887	−	1.87909i
$303$		0			0
$304$	15.9002	+	5.70643i	0.911940	+	0.327286i
$305$	−13.1047			−0.750375
$306$		0			0
$307$	−0.622170	+	0.257711i	−0.0355091	+	0.0147083i	−0.400367	−	0.916355i	$-0.631117\pi$
$307$	−0.622170	+	0.257711i	−0.0355091	+	0.0147083i	0.364858	+	0.931063i	$0.381117\pi$
$308$	−0.197753	−	0.324242i	−0.0112680	−	0.0184754i
$309$		0			0
$310$	5.99706	−	3.04767i	0.340610	−	0.173096i
$311$	16.3916	+	4.39213i	0.929485	+	0.249055i	0.691635	−	0.722247i	$-0.256891\pi$
$311$	16.3916	+	4.39213i	0.929485	+	0.249055i	0.237850	+	0.971302i	$0.423557\pi$
$312$		0			0
$313$	−2.49387	+	0.668229i	−0.140962	+	0.0377706i	−0.328610	−	0.944466i	$-0.606580\pi$
$313$	−2.49387	+	0.668229i	−0.140962	+	0.0377706i	0.187648	+	0.982236i	$0.439913\pi$
$314$	13.3950	−	12.0353i	0.755923	−	0.679189i
$315$		0			0
$316$	−2.42056	+	1.95167i	−0.136167	+	0.109790i
$317$	−13.1996	−	1.73775i	−0.741361	−	0.0976020i	−0.249620	−	0.968344i	$-0.580306\pi$
$317$	−13.1996	−	1.73775i	−0.741361	−	0.0976020i	−0.491740	+	0.870742i	$0.663639\pi$
$318$		0			0
$319$	6.25023	−	3.60857i	0.349945	−	0.202041i
$320$	8.81387	−	5.97556i	0.492711	−	0.334044i
$321$		0			0
$322$	−0.408661	−	0.0761884i	−0.0227738	−	0.00424581i
$323$	−6.54609	+	2.71148i	−0.364234	+	0.150871i
$324$		0			0
$325$	5.17203	−	12.4864i	0.286893	−	0.692620i
$326$	0.238409	−	0.0504116i	0.0132042	−	0.00279204i
$327$		0			0
$328$	5.92353	+	6.28192i	0.327072	+	0.346861i
$329$	−0.0306859	+	0.114522i	−0.00169177	+	0.00631377i
$330$		0			0
$331$	5.84491	+	7.61723i	0.321265	+	0.418681i	0.925869	−	0.377846i	$-0.123335\pi$
$331$	5.84491	+	7.61723i	0.321265	+	0.418681i	−0.604603	+	0.796527i	$0.706668\pi$
$332$	8.54117	+	4.66091i	0.468758	+	0.255801i
$333$		0			0
$334$	18.1928	+	8.70118i	0.995468	+	0.476108i
$335$	−11.0104	−	6.35688i	−0.601564	−	0.347313i
$336$		0			0
$337$	−0.454491	+	0.262401i	−0.0247577	+	0.0142939i	−0.512328	−	0.858790i	$-0.671217\pi$
$337$	−0.454491	+	0.262401i	−0.0247577	+	0.0142939i	0.487570	+	0.873084i	$0.337883\pi$
$338$	−6.38292	+	0.495550i	−0.347185	+	0.0269544i
$339$		0			0
$340$	−1.05182	+	4.34065i	−0.0570430	+	0.235405i
$341$	1.51305	−	3.65283i	0.0819364	−	0.197812i
$342$		0			0
$343$	1.69552	+	1.69552i	0.0915497	+	0.0915497i
$344$	24.8347	−	2.53053i	1.33899	−	0.136437i
$345$		0			0
$346$	4.75109	+	1.54928i	0.255420	+	0.0832900i
$347$	−35.6249	+	4.69010i	−1.91244	+	0.251778i	−0.990704	−	0.136033i	$-0.956565\pi$
$347$	−35.6249	+	4.69010i	−1.91244	+	0.251778i	−0.921739	+	0.387811i	$0.873231\pi$
$348$		0			0
$349$	−3.77349	+	28.6625i	−0.201990	+	1.53427i	0.527073	+	0.849820i	$0.323290\pi$
$349$	−3.77349	+	28.6625i	−0.201990	+	1.53427i	−0.729063	+	0.684447i	$0.760044\pi$
$350$	0.738920	−	0.260786i	0.0394969	−	0.0139396i
$351$		0			0
$352$	1.65183	−	6.03674i	0.0880426	−	0.321759i
$353$	1.05732	+	0.610443i	0.0562754	+	0.0324906i	0.527874	−	0.849323i	$-0.322989\pi$
$353$	1.05732	+	0.610443i	0.0562754	+	0.0324906i	−0.471598	+	0.881813i	$0.656323\pi$
$354$		0			0
$355$	0.122891	−	0.160155i	0.00652238	−	0.00850013i
$356$	−27.7531	+	12.2861i	−1.47091	+	0.651165i
$357$		0			0
$358$	−31.6157	+	6.68515i	−1.67094	+	0.353321i
$359$	−6.44282	−	6.44282i	−0.340039	−	0.340039i	0.516343	−	0.856382i	$-0.327293\pi$
$359$	−6.44282	−	6.44282i	−0.340039	−	0.340039i	−0.856382	+	0.516343i	$0.827293\pi$
$360$		0			0
$361$	−0.822894	+	0.822894i	−0.0433102	+	0.0433102i
$362$	11.4096	−	17.5287i	0.599678	−	0.921287i
$363$		0			0
$364$	−1.04034	−	0.991444i	−0.0545289	−	0.0519658i
$365$	5.87629	+	4.50903i	0.307579	+	0.236014i
$366$		0			0
$367$	−0.917382	+	1.58895i	−0.0478869	+	0.0829426i	−0.888975	−	0.457955i	$-0.848582\pi$
$367$	−0.917382	+	1.58895i	−0.0478869	+	0.0829426i	0.841088	+	0.540898i	$0.181915\pi$
$368$	−3.70669	−	5.76105i	−0.193225	−	0.300316i
$369$		0			0
$370$	7.60004	−	15.8905i	0.395107	−	0.826109i
$371$	−1.97243	−	0.259675i	−0.102403	−	0.0134817i
$372$		0			0
$373$	−1.58151	−	12.0128i	−0.0818876	−	0.621998i	−0.982348	−	0.187061i	$-0.940104\pi$
$373$	−1.58151	−	12.0128i	−0.0818876	−	0.621998i	0.900461	−	0.434937i	$-0.143229\pi$
$374$	1.18927	+	2.34019i	0.0614955	+	0.121008i
$375$		0			0
$376$	−1.71999	+	0.926822i	−0.0887019	+	0.0477972i
$377$	19.3107	−	19.3107i	0.994551	−	0.994551i
$378$		0			0
$379$	−28.0488	−	11.6182i	−1.44077	−	0.596786i	−0.480784	−	0.876839i	$-0.659648\pi$
$379$	−28.0488	−	11.6182i	−1.44077	−	0.596786i	−0.959985	+	0.280053i	$0.909648\pi$
$380$	−1.73528	−	11.1083i	−0.0890182	−	0.569843i
$381$		0			0
$382$	23.5626	+	20.1675i	1.20557	+	1.03186i
$383$	−1.29677	−	2.24608i	−0.0662620	−	0.114769i	0.830991	−	0.556286i	$-0.187774\pi$
$383$	−1.29677	−	2.24608i	−0.0662620	−	0.114769i	−0.897253	+	0.441517i	$0.854441\pi$
$384$		0			0
$385$	−0.126381	+	0.218899i	−0.00644098	+	0.0111561i
$386$	−18.2542	+	6.44242i	−0.929114	+	0.327910i
$387$		0			0
$388$	21.4922	−	17.3288i	1.09110	−	0.879739i
$389$	−27.4948	+	21.0975i	−1.39404	+	1.06969i	−0.406274	+	0.913751i	$0.633172\pi$
$389$	−27.4948	+	21.0975i	−1.39404	+	1.06969i	−0.987767	+	0.155934i	$0.950161\pi$
$390$		0			0
$391$	2.77537	+	0.743658i	0.140356	+	0.0376084i
$392$	−0.578669	+	19.7072i	−0.0292272	+	0.995363i
$393$		0			0
$394$	14.0287	−	21.5524i	0.706757	−	1.08579i
$395$	1.91187	+	0.791921i	0.0961964	+	0.0398458i
$396$		0			0
$397$	7.92586	+	19.1347i	0.397788	+	0.960344i	0.988190	+	0.153235i	$0.0489691\pi$
$397$	7.92586	+	19.1347i	0.397788	+	0.960344i	−0.590402	+	0.807109i	$0.701031\pi$
$398$	−4.15818	−	6.06394i	−0.208431	−	0.303958i
$399$		0			0
$400$	11.4807	+	5.91104i	0.574033	+	0.295552i
$401$	−9.24072	−	16.0054i	−0.461460	−	0.799271i	0.537574	−	0.843216i	$-0.319341\pi$
$401$	−9.24072	−	16.0054i	−0.461460	−	0.799271i	−0.999034	+	0.0439449i	$0.986007\pi$
$402$		0			0
$403$	1.95281	−	14.8331i	0.0972763	−	0.738887i
$404$	−5.84383	+	1.71758i	−0.290741	+	0.0854526i
$405$		0			0
$406$	1.58110	+	0.0845401i	0.0784688	+	0.00419565i
$407$	−2.67951	−	10.0001i	−0.132819	−	0.495686i
$408$		0			0
$409$	6.21012	−	23.1765i	0.307071	−	1.14600i	−0.624078	−	0.781362i	$-0.714525\pi$
$409$	6.21012	−	23.1765i	0.307071	−	1.14600i	0.931148	−	0.364641i	$-0.118808\pi$
$410$	1.78152	−	5.46328i	0.0879830	−	0.269812i
$411$		0			0
$412$	0.119463	+	0.0871822i	0.00588554	+	0.00429516i
$413$	−0.215081	−	0.519252i	−0.0105834	−	0.0255507i
$414$		0			0
$415$		−	6.47575i		−	0.317882i
$416$	0.125320	−	23.6822i	0.00614432	−	1.16112i
$417$		0			0
$418$	−5.02025	−	4.29689i	−0.245548	−	0.210168i
$419$	−26.6138	−	20.4215i	−1.30017	−	0.997653i	−0.999028	−	0.0440730i	$-0.985967\pi$
$419$	−26.6138	−	20.4215i	−1.30017	−	0.997653i	−0.301139	−	0.953580i	$-0.597367\pi$
$420$		0			0
$421$	−2.04942	−	2.67086i	−0.0998826	−	0.130170i	0.740738	−	0.671794i	$-0.234476\pi$
$421$	−2.04942	−	2.67086i	−0.0998826	−	0.130170i	−0.840620	+	0.541625i	$0.817809\pi$
$422$	−6.42313	+	5.77111i	−0.312673	+	0.280933i
$423$		0			0
$424$	−19.1861	−	26.5845i	−0.931758	−	1.29106i
$425$	−5.23150	+	1.40178i	−0.253765	+	0.0679962i
$426$		0			0
$427$	−1.67534	+	0.220562i	−0.0810752	+	0.0106738i
$428$	−16.4030	−	15.6320i	−0.792868	−	0.755600i
$429$		0			0
$430$	−9.39572	−	13.7019i	−0.453102	−	0.660764i
$431$			20.6971i			0.996944i	0.866906	+	0.498472i	$0.166105\pi$
$431$			20.6971i			0.996944i	−0.866906	+	0.498472i	$0.833895\pi$
$432$		0			0
$433$			2.00407i			0.0963096i	0.998840	+	0.0481548i	$0.0153341\pi$
$433$			2.00407i			0.0963096i	−0.998840	+	0.0481548i	$0.984666\pi$
$434$	0.715382	−	0.490555i	0.0343395	−	0.0235474i
$435$		0			0
$436$	−0.554003	−	23.0183i	−0.0265319	−	1.10238i
$437$	−7.17105	+	0.944086i	−0.343038	+	0.0451618i
$438$		0			0
$439$	14.8118	−	3.96881i	0.706928	−	0.189421i	0.112597	−	0.993641i	$-0.464083\pi$
$439$	14.8118	−	3.96881i	0.706928	−	0.189421i	0.594332	+	0.804220i	$0.297417\pi$
$440$	−4.05333	+	0.959517i	−0.193235	+	0.0457432i
$441$		0			0
$442$	6.63870	+	7.38874i	0.315771	+	0.351446i
$443$	3.23155	+	4.21144i	0.153536	+	0.200091i	0.863788	−	0.503856i	$-0.168086\pi$
$443$	3.23155	+	4.21144i	0.153536	+	0.200091i	−0.710252	+	0.703947i	$0.751419\pi$
$444$		0			0
$445$	16.0255	+	12.2968i	0.759679	+	0.582922i
$446$	−9.71360	+	11.3488i	−0.459952	+	0.537382i
$447$		0			0
$448$	1.02621	−	0.912272i	0.0484839	−	0.0431008i
$449$			12.3646i			0.583520i	0.956492	+	0.291760i	$0.0942408\pi$
$449$			12.3646i			0.583520i	−0.956492	+	0.291760i	$0.905759\pi$
$450$		0			0
$451$	−1.29249	−	3.12034i	−0.0608609	−	0.146931i
$452$	1.69987	+	10.8816i	0.0799551	+	0.511826i
$453$		0			0
$454$	29.7151	+	9.68979i	1.39460	+	0.454764i
$455$	−0.247546	+	0.923855i	−0.0116051	+	0.0433110i
$456$		0			0
$457$	−6.36361	−	23.7493i	−0.297677	−	1.11095i	−0.939068	−	0.343731i	$-0.888309\pi$
$457$	−6.36361	−	23.7493i	−0.297677	−	1.11095i	0.641391	−	0.767214i	$-0.278358\pi$
$458$	0.0785710	−	1.46947i	0.00367138	−	0.0686636i
$459$		0			0
$460$	−2.18396	+	4.00213i	−0.101828	+	0.186600i
$461$	2.35475	−	17.8861i	0.109672	−	0.833038i	−0.844872	−	0.534968i	$-0.820324\pi$
$461$	2.35475	−	17.8861i	0.109672	−	0.833038i	0.954544	−	0.298070i	$-0.0963429\pi$
$462$		0			0
$463$	11.6229	+	20.1315i	0.540164	+	0.935592i	0.998894	+	0.0470159i	$0.0149711\pi$
$463$	11.6229	+	20.1315i	0.540164	+	0.935592i	−0.458730	+	0.888576i	$0.651696\pi$
$464$	16.8617	+	19.9126i	0.782785	+	0.924420i
$465$		0			0
$466$	−24.6065	+	16.8733i	−1.13987	+	0.781639i
$467$	−12.3974	−	29.9300i	−0.573683	−	1.38499i	−0.898398	−	0.439181i	$-0.855269\pi$
$467$	−12.3974	−	29.9300i	−0.573683	−	1.38499i	0.324715	−	0.945812i	$-0.394731\pi$
$468$		0			0
$469$	−1.51459	−	0.627362i	−0.0699371	−	0.0289689i
$470$	1.08980	+	0.709364i	0.0502686	+	0.0327205i
$471$		0			0
$472$	3.79401	−	8.44920i	0.174634	−	0.388906i
$473$	−9.43204	−	2.52731i	−0.433686	−	0.116206i
$474$		0			0
$475$	10.8165	−	8.29978i	0.496294	−	0.380820i
$476$	−0.0614106	+	0.572621i	−0.00281475	+	0.0262460i
$477$		0			0
$478$	−6.02818	−	17.0805i	−0.275723	−	0.781244i
$479$	21.1446	−	36.6236i	0.966123	−	1.67337i	0.259554	−	0.965729i	$-0.416424\pi$
$479$	21.1446	−	36.6236i	0.966123	−	1.67337i	0.706568	−	0.707645i	$-0.250242\pi$
$480$		0			0
$481$	−19.5874	−	33.9264i	−0.893110	−	1.54691i
$482$	6.01461	−	7.02713i	0.273958	−	0.320077i
$483$		0			0
$484$	11.5257	−	15.7934i	0.523897	−	0.717882i
$485$	−16.9755	−	7.03146i	−0.770816	−	0.319282i
$486$		0			0
$487$	−8.93552	+	8.93552i	−0.404907	+	0.404907i	−0.879958	−	0.475051i	$-0.842430\pi$
$487$	−8.93552	+	8.93552i	−0.404907	+	0.404907i	0.475051	+	0.879958i	$0.342430\pi$
$488$	−21.5851	−	17.5931i	−0.977114	−	0.796401i
$489$		0			0
$490$	11.6976	−	5.94464i	0.528444	−	0.268552i
$491$	0.845170	+	6.41971i	0.0381420	+	0.289717i	0.999876	+	0.0157332i	$0.00500824\pi$
$491$	0.845170	+	6.41971i	0.0381420	+	0.289717i	−0.961734	+	0.273984i	$0.911658\pi$
$492$		0			0
$493$	−10.8503	−	1.42847i	−0.488674	−	0.0643351i
$494$	−22.5574	−	10.7887i	−1.01491	−	0.485404i
$495$		0			0
$496$	13.9694	+	3.03115i	0.627245	+	0.136103i
$497$	0.0130151	−	0.0225429i	0.000583808	−	0.00101119i
$498$		0			0
$499$	26.2915	+	20.1742i	1.17697	+	0.903119i	0.996754	−	0.0805085i	$-0.0256544\pi$
$499$	26.2915	+	20.1742i	1.17697	+	0.903119i	0.180214	+	0.983627i	$0.442321\pi$
$500$	−0.527049	−	21.8984i	−0.0235703	−	0.979327i
$501$		0			0
$502$	11.4349	+	7.44310i	0.510363	+	0.332202i
$503$	14.8092	−	14.8092i	0.660309	−	0.660309i	−0.295144	−	0.955453i	$-0.595368\pi$
$503$	14.8092	−	14.8092i	0.660309	−	0.660309i	0.955453	+	0.295144i	$0.0953676\pi$
$504$		0			0
$505$	2.86645	+	2.86645i	0.127556	+	0.127556i
$506$	0.554363	+	2.62171i	0.0246444	+	0.116549i
$507$		0			0
$508$	−7.46342	+	19.3205i	−0.331136	+	0.857211i
$509$	1.73239	−	2.25769i	0.0767867	−	0.100070i	−0.753381	−	0.657585i	$-0.771578\pi$
$509$	1.73239	−	2.25769i	0.0767867	−	0.100070i	0.830167	+	0.557514i	$0.188245\pi$
$510$		0			0
$511$	0.827127	+	0.477542i	0.0365899	+	0.0211252i
$512$	22.5397	+	1.99011i	0.996125	+	0.0879511i
$513$		0			0
$514$	0.440124	+	1.24707i	0.0194130	+	0.0550057i
$515$	0.0128474	−	0.0975856i	0.000566124	−	0.00430014i
$516$		0			0
$517$	0.757726	−	0.0997565i	0.0333247	−	0.00438728i
$518$	0.704156	−	2.15939i	0.0309388	−	0.0948782i
$519$		0			0
$520$	−13.8753	+	7.47675i	−0.608474	+	0.327877i
$521$	−17.3570	−	17.3570i	−0.760426	−	0.760426i	0.215973	−	0.976399i	$-0.430708\pi$
$521$	−17.3570	−	17.3570i	−0.760426	−	0.760426i	−0.976399	+	0.215973i	$0.930708\pi$
$522$		0			0
$523$	−11.8890	+	28.7025i	−0.519868	+	1.25507i	0.418115	+	0.908394i	$0.362691\pi$
$523$	−11.8890	+	28.7025i	−0.519868	+	1.25507i	−0.937984	+	0.346679i	$0.887309\pi$
$524$	16.4695	+	27.0039i	0.719473	+	1.17967i
$525$		0			0
$526$	0.766717	+	9.87567i	0.0334304	+	0.430600i
$527$	−5.19223	+	2.99773i	−0.226177	+	0.130583i
$528$		0			0
$529$	−17.3785	−	10.0335i	−0.755585	−	0.436237i
$530$	−9.41432	+	19.6839i	−0.408932	+	0.855014i
$531$		0			0
$532$	−0.408803	−	1.39090i	−0.0177238	−	0.0603031i
$533$	−7.78004	−	10.1391i	−0.336991	−	0.439175i
$534$		0			0
$535$	−3.90303	+	14.5663i	−0.168743	+	0.629756i
$536$	−9.60147	−	25.2520i	−0.414721	−	1.09072i
$537$		0			0
$538$	−8.09560	−	38.2860i	−0.349026	−	1.65063i
$539$	2.95129	−	7.12505i	0.127121	−	0.306898i
$540$		0			0
$541$	−21.3742	+	8.85350i	−0.918950	+	0.380642i	−0.791476	−	0.611200i	$-0.790687\pi$
$541$	−21.3742	+	8.85350i	−0.918950	+	0.380642i	−0.127474	+	0.991842i	$0.540687\pi$
$542$	−6.33126	+	33.9598i	−0.271951	+	1.45870i
$543$		0			0
$544$	−7.55980	+	5.73754i	−0.324124	+	0.245995i
$545$	−13.2709	+	7.66197i	−0.568463	+	0.328203i
$546$		0			0
$547$	−26.1850	−	3.44731i	−1.11959	−	0.147397i	−0.452064	−	0.891985i	$-0.649312\pi$
$547$	−26.1850	−	3.44731i	−1.11959	−	0.147397i	−0.667523	+	0.744589i	$0.732646\pi$
$548$	−28.2010	−	3.02441i	−1.20469	−	0.129196i
$549$		0			0
$550$	−3.37589	−	3.75730i	−0.143949	−	0.160212i
$551$	26.6106	−	7.13029i	1.13365	−	0.303761i
$552$		0			0
$553$	0.257745	+	0.0690627i	0.0109604	+	0.00293684i
$554$	16.4071	+	32.2852i	0.697072	+	1.37167i
$555$		0			0
$556$	43.7082	+	10.5913i	1.85364	+	0.449171i
$557$	−4.58647	+	1.89978i	−0.194335	+	0.0804962i	−0.477728	−	0.878508i	$-0.658540\pi$
$557$	−4.58647	+	1.89978i	−0.194335	+	0.0804962i	0.283394	+	0.959004i	$0.408540\pi$
$558$		0			0
$559$	−36.9496			−1.56280
$560$	−0.860117	−	0.308687i	−0.0363466	−	0.0130444i
$561$		0			0
$562$	11.8468	−	0.919747i	0.499726	−	0.0387972i
$563$	15.6318	−	20.3717i	0.658801	−	0.858566i	−0.337777	−	0.941226i	$-0.609675\pi$
$563$	15.6318	−	20.3717i	0.658801	−	0.858566i	0.996578	+	0.0826601i	$0.0263416\pi$
$564$		0			0
$565$	5.81520	−	4.46216i	0.244647	−	0.187724i
$566$	26.7063	+	1.42796i	1.12255	+	0.0600217i
$567$		0			0
$568$	0.417424	−	0.0988141i	0.0175147	−	0.00414615i
$569$	−1.71882	−	6.41471i	−0.0720566	−	0.268919i	0.920493	−	0.390759i	$-0.127787\pi$
$569$	−1.71882	−	6.41471i	−0.0720566	−	0.268919i	−0.992550	+	0.121840i	$0.961121\pi$
$570$		0			0
$571$	1.62885	+	12.3724i	0.0681654	+	0.517767i	0.991131	+	0.132886i	$0.0424244\pi$
$571$	1.62885	+	12.3724i	0.0681654	+	0.517767i	−0.922966	+	0.384882i	$0.874242\pi$
$572$	−3.33815	+	8.64146i	−0.139575	+	0.361318i
$573$		0			0
$574$	0.135802	−	0.728421i	0.00566828	−	0.0304037i
$575$	−5.52879			−0.230566
$576$		0			0
$577$	4.77050			0.198599			0.0992993	−	0.995058i	$-0.468340\pi$
$577$	4.77050			0.198599			0.0992993	+	0.995058i	$0.468340\pi$
$578$	−3.67671	+	19.7213i	−0.152931	+	0.820296i
$579$		0			0
$580$	6.25758	−	16.1990i	0.259832	−	0.672626i
$581$	−0.108992	−	0.827873i	−0.00452173	−	0.0343460i
$582$		0			0
$583$	3.31916	+	12.3873i	0.137466	+	0.513029i
$584$	3.62562	+	15.3158i	0.150029	+	0.633774i
$585$		0			0
$586$	−34.0600	−	1.82116i	−1.40701	−	0.0752313i
$587$	15.6570	−	12.0140i	0.646232	−	0.495872i	−0.232868	−	0.972508i	$-0.574811\pi$
$587$	15.6570	−	12.0140i	0.646232	−	0.495872i	0.879100	+	0.476637i	$0.158144\pi$
$588$		0			0
$589$	9.18771	−	11.9737i	0.378573	−	0.493366i
$590$	−6.14565	+	0.477129i	−0.253012	+	0.0196431i
$591$		0			0
$592$	33.8512	−	15.9706i	1.39128	−	0.656389i
$593$	−15.1394			−0.621700			−0.310850	−	0.950459i	$-0.600614\pi$
$593$	−15.1394			−0.621700			−0.310850	+	0.950459i	$0.600614\pi$
$594$		0			0
$595$	0.354109	−	0.146677i	0.0145170	−	0.00601315i
$596$	28.4104	+	6.88437i	1.16374	+	0.281995i
$597$		0			0
$598$	4.59382	+	9.03953i	0.187855	+	0.369654i
$599$	45.1048	+	12.0858i	1.84293	+	0.493812i	0.999085	−	0.0427730i	$-0.0136192\pi$
$599$	45.1048	+	12.0858i	1.84293	+	0.493812i	0.843846	+	0.536585i	$0.180286\pi$
$600$		0			0
$601$	39.8381	−	10.6746i	1.62503	−	0.435426i	0.672557	−	0.740045i	$-0.265196\pi$
$601$	39.8381	−	10.6746i	1.62503	−	0.435426i	0.952474	+	0.304619i	$0.0985292\pi$
$602$	−1.43178	−	1.59354i	−0.0583550	−	0.0649479i
$603$		0			0
$604$	−46.0563	−	4.93929i	−1.87400	−	0.200977i
$605$	−12.9011	−	1.69846i	−0.524504	−	0.0690523i
$606$		0			0
$607$	−10.2159	+	5.89815i	−0.414651	+	0.239399i	−0.692786	−	0.721143i	$-0.743617\pi$
$607$	−10.2159	+	5.89815i	−0.414651	+	0.239399i	0.278135	+	0.960542i	$0.410284\pi$
$608$	12.0546	−	20.6264i	0.488879	−	0.836509i
$609$		0			0
$610$	−3.39664	+	18.2190i	−0.137526	+	0.737665i
$611$	2.67182	−	1.10670i	0.108090	−	0.0447724i
$612$		0			0
$613$	9.99410	−	24.1279i	0.403658	−	0.974516i	−0.583113	−	0.812391i	$-0.698165\pi$
$613$	9.99410	−	24.1279i	0.403658	−	0.974516i	0.986770	−	0.162125i	$-0.0518347\pi$
$614$	0.197024	+	0.931773i	0.00795125	+	0.0376033i
$615$		0			0
$616$	−0.502036	+	0.190887i	−0.0202276	+	0.00769106i
$617$	−0.938379	+	3.50208i	−0.0377777	+	0.140988i	−0.982239	−	0.187635i	$-0.939918\pi$
$617$	−0.938379	+	3.50208i	−0.0377777	+	0.140988i	0.944461	+	0.328623i	$0.106585\pi$
$618$		0			0
$619$	29.8563	+	38.9094i	1.20002	+	1.56390i	0.734035	+	0.679111i	$0.237635\pi$
$619$	29.8563	+	38.9094i	1.20002	+	1.56390i	0.465989	+	0.884791i	$0.345699\pi$
$620$	−2.68266	−	9.12740i	−0.107738	−	0.366565i
$621$		0			0
$622$	10.3548	−	21.6502i	0.415188	−	0.868095i
$623$	2.25569	+	1.30232i	0.0903723	+	0.0521765i
$624$		0			0
$625$	1.35351	−	0.781451i	0.0541405	−	0.0312581i
$626$	0.282623	+	3.64032i	0.0112959	+	0.145496i
$627$		0			0
$628$	−13.2603	−	21.7420i	−0.529142	−	0.867598i
$629$	−6.00770	+	14.5039i	−0.239543	+	0.578307i
$630$		0			0
$631$	22.5852	+	22.5852i	0.899104	+	0.899104i	0.995357	−	0.0962531i	$-0.0306858\pi$
$631$	22.5852	+	22.5852i	0.899104	+	0.899104i	−0.0962531	+	0.995357i	$0.530686\pi$
$632$	2.08593	+	3.87107i	0.0829739	+	0.153983i
$633$		0			0
$634$	−5.83714	+	17.9004i	−0.231822	+	0.710915i
$635$	13.6666	−	1.79924i	0.542343	−	0.0714008i
$636$		0			0
$637$	3.80906	−	28.9327i	0.150920	−	1.14635i
$638$	−3.39684	−	9.62474i	−0.134482	−	0.381047i
$639$		0			0
$640$	−6.02309	−	13.8024i	−0.238084	−	0.545587i
$641$	40.3410	+	23.2909i	1.59337	+	0.919935i	0.992723	+	0.120424i	$0.0384255\pi$
$641$	40.3410	+	23.2909i	1.59337	+	0.919935i	0.600652	+	0.799511i	$0.294908\pi$
$642$		0			0
$643$	5.47177	−	7.13095i	0.215786	−	0.281217i	−0.672901	−	0.739733i	$-0.734952\pi$
$643$	5.47177	−	7.13095i	0.215786	−	0.281217i	0.888686	+	0.458515i	$0.151619\pi$
$644$	−0.211843	+	0.548398i	−0.00834779	+	0.0216099i
$645$		0			0
$646$	2.07297	+	9.80355i	0.0815598	+	0.385716i
$647$	26.5185	+	26.5185i	1.04255	+	1.04255i	0.999054	+	0.0434948i	$0.0138492\pi$
$647$	26.5185	+	26.5185i	1.04255	+	1.04255i	0.0434948	+	0.999054i	$0.486151\pi$
$648$		0			0
$649$	−2.56181	+	2.56181i	−0.100560	+	0.100560i
$650$	−16.0188	−	10.4268i	−0.628308	−	0.408974i
$651$		0			0
$652$	−0.00829178	−	0.344516i	−0.000324731	−	0.0134923i
$653$	−0.0661667	−	0.0507715i	−0.00258930	−	0.00198684i	0.607466	−	0.794346i	$-0.292186\pi$
$653$	−0.0661667	−	0.0507715i	−0.00258930	−	0.00198684i	−0.610055	+	0.792359i	$0.708853\pi$
$654$		0			0
$655$	10.5254	−	18.2306i	0.411262	−	0.712327i
$656$	10.2688	−	6.60701i	0.400930	−	0.257961i
$657$		0			0
$658$	0.151261	+	0.0723444i	0.00589677	+	0.00282028i
$659$	25.0738	+	3.30103i	0.976738	+	0.128590i	0.601962	−	0.798525i	$-0.294386\pi$
$659$	25.0738	+	3.30103i	0.976738	+	0.128590i	0.374777	+	0.927115i	$0.377719\pi$
$660$		0			0
$661$	3.99309	+	30.3305i	0.155313	+	1.17972i	0.874543	+	0.484948i	$0.161161\pi$
$661$	3.99309	+	30.3305i	0.155313	+	1.17972i	−0.719230	+	0.694772i	$0.755505\pi$
$662$	12.1049	−	6.15161i	0.470469	−	0.239089i
$663$		0			0
$664$	8.69368	−	10.6664i	0.337380	−	0.413936i
$665$	−0.682249	+	0.682249i	−0.0264565	+	0.0264565i
$666$		0			0
$667$	−10.3214	−	4.27525i	−0.399644	−	0.165538i
$668$	16.8123	−	23.0375i	0.650488	−	0.891347i
$669$		0			0
$670$	−11.6915	+	13.6597i	−0.451683	+	0.527720i
$671$	5.44632	+	9.43331i	0.210253	+	0.364169i
$672$		0			0
$673$	−14.0254	+	24.2927i	−0.540640	+	0.936415i	0.458228	+	0.888835i	$0.348484\pi$
$673$	−14.0254	+	24.2927i	−0.540640	+	0.936415i	−0.998867	+	0.0475804i	$0.984849\pi$
$674$	0.247005	+	0.699873i	0.00951426	+	0.0269581i
$675$		0			0
$676$	−0.965456	+	9.00236i	−0.0371329	+	0.346244i
$677$	−28.7439	+	22.0560i	−1.10472	+	0.847679i	−0.989337	−	0.145642i	$-0.953475\pi$
$677$	−28.7439	+	22.0560i	−1.10472	+	0.847679i	−0.115380	+	0.993321i	$0.536809\pi$
$678$		0			0
$679$	−2.28852	−	0.613207i	−0.0878254	−	0.0235327i
$680$	5.76201	+	2.58736i	0.220963	+	0.0992209i
$681$		0			0
$682$	−4.68621	−	3.05032i	−0.179444	−	0.116803i
$683$	−2.07795	−	0.860717i	−0.0795107	−	0.0329344i	0.342574	−	0.939491i	$-0.388701\pi$
$683$	−2.07795	−	0.860717i	−0.0795107	−	0.0329344i	−0.422084	+	0.906557i	$0.638701\pi$
$684$		0			0
$685$	7.22367	+	17.4395i	0.276002	+	0.666328i
$686$	2.79668	−	1.91775i	0.106778	−	0.0732201i
$687$		0			0
$688$	2.91884	−	35.1825i	0.111280	−	1.34132i
$689$	24.2633	+	42.0253i	0.924359	+	1.60104i
$690$		0			0
$691$	4.92842	−	37.4350i	0.187486	−	1.42410i	−0.596149	−	0.802874i	$-0.703303\pi$
$691$	4.92842	−	37.4350i	0.187486	−	1.42410i	0.783634	−	0.621222i	$-0.213364\pi$
$692$	3.38535	−	6.20368i	0.128692	−	0.235829i
$693$		0			0
$694$	−2.71320	+	50.7434i	−0.102992	+	1.92619i
$695$	−7.74676	−	28.9113i	−0.293851	−	1.09667i
$696$		0			0
$697$	−1.32554	+	4.94697i	−0.0502083	+	0.187380i
$698$	38.8702	+	12.6752i	1.47126	+	0.479763i
$699$		0			0
$700$	−0.171038	−	1.09488i	−0.00646462	−	0.0413827i
$701$	17.1061	+	41.2978i	0.646089	+	1.55980i	0.818334	+	0.574743i	$0.194898\pi$
$701$	17.1061	+	41.2978i	0.646089	+	1.55980i	−0.172245	+	0.985054i	$0.555102\pi$
$702$		0			0
$703$		−	39.5190i		−	1.49049i
$704$	−7.96449	−	3.86114i	−0.300173	−	0.145522i
$705$		0			0
$706$	1.12272	−	1.31172i	0.0422542	−	0.0493674i
$707$	0.414698	+	0.318209i	0.0155963	+	0.0119675i
$708$		0			0
$709$	−12.8537	−	16.7512i	−0.482730	−	0.629106i	0.486966	−	0.873421i	$-0.338104\pi$
$709$	−12.8537	−	16.7512i	−0.482730	−	0.629106i	−0.969696	+	0.244315i	$0.921437\pi$
$710$	−0.190804	−	0.212361i	−0.00716076	−	0.00796977i
$711$		0			0
$712$	9.88756	+	41.7684i	0.370552	+	1.56534i
$713$	−5.91173	+	1.58404i	−0.221396	+	0.0593228i
$714$		0			0
$715$	6.11264	−	0.804744i	0.228600	−	0.0300957i
$716$	1.09958	+	45.6867i	0.0410934	+	1.70739i
$717$		0			0
$718$	−10.6271	+	7.28727i	−0.396600	+	0.271958i
$719$			24.2360i			0.903851i	0.892056	+	0.451926i	$0.149263\pi$
$719$			24.2360i			0.903851i	−0.892056	+	0.451926i	$0.850737\pi$
$720$		0			0
$721$		−	0.0126918i		−	0.000472666i
$722$	0.930748	+	1.35732i	0.0346389	+	0.0505143i
$723$		0			0
$724$	−21.4121	−	20.4056i	−0.795775	−	0.758370i
$725$	20.8783	−	2.74868i	0.775401	−	0.102084i
$726$		0			0
$727$	−5.52453	+	1.48029i	−0.204893	+	0.0549010i	−0.359806	−	0.933027i	$-0.617157\pi$
$727$	−5.52453	+	1.48029i	−0.204893	+	0.0549010i	0.154912	+	0.987928i	$0.450490\pi$
$728$	−1.64801	+	1.18938i	−0.0610794	+	0.0440812i
$729$		0			0
$730$	7.79181	−	7.00086i	0.288388	−	0.259113i
$731$	9.01401	+	11.7473i	0.333395	+	0.434489i
$732$		0			0
$733$	−14.8205	−	11.3722i	−0.547408	−	0.420041i	0.297682	−	0.954665i	$-0.403787\pi$
$733$	−14.8205	−	11.3722i	−0.547408	−	0.420041i	−0.845090	+	0.534624i	$0.820453\pi$
$734$	1.97128	+	1.68724i	0.0727612	+	0.0622772i
$735$		0			0
$736$	−8.97010	+	3.66005i	−0.330642	+	0.134911i
$737$			10.5677i			0.389265i
$738$		0			0
$739$	12.0562	+	29.1063i	0.443496	+	1.07069i	0.974714	+	0.223458i	$0.0717346\pi$
$739$	12.0562	+	29.1063i	0.443496	+	1.07069i	−0.531218	+	0.847235i	$0.678265\pi$
$740$	−20.1221	−	14.6847i	−0.739702	−	0.539821i
$741$		0			0
$742$	−0.872252	+	2.67488i	−0.0320214	+	0.0981979i
$743$	−2.55767	+	9.54537i	−0.0938319	+	0.350186i	−0.996840	−	0.0794385i	$-0.974687\pi$
$743$	−2.55767	+	9.54537i	−0.0938319	+	0.350186i	0.903008	+	0.429624i	$0.141354\pi$
$744$		0			0
$745$	−5.03540	−	18.7924i	−0.184483	−	0.688500i
$746$	−17.1108	−	0.914898i	−0.626470	−	0.0334968i
$747$		0			0
$748$	3.56171	−	1.04683i	0.130229	−	0.0382760i
$749$	−0.253810	+	1.92788i	−0.00927401	+	0.0704431i
$750$		0			0
$751$	3.85776	+	6.68183i	0.140772	+	0.243823i	0.927787	−	0.373109i	$-0.121708\pi$
$751$	3.85776	+	6.68183i	0.140772	+	0.243823i	−0.787016	+	0.616933i	$0.788375\pi$
$752$	0.842714	+	2.63146i	0.0307306	+	0.0959595i
$753$		0			0
$754$	−21.8417	−	31.8520i	−0.795428	−	1.15998i
$755$	11.7973	+	28.4812i	0.429347	+	1.03654i
$756$		0			0
$757$	−8.34229	−	3.45549i	−0.303206	−	0.125592i	0.225893	−	0.974152i	$-0.427470\pi$
$757$	−8.34229	−	3.45549i	−0.303206	−	0.125592i	−0.529099	+	0.848560i	$0.677470\pi$
$758$	−23.4223	+	35.9837i	−0.850736	+	1.30699i
$759$		0			0
$760$	−15.8932	−	0.466677i	−0.576506	−	0.0169282i
$761$	18.5256	+	4.96391i	0.671551	+	0.179942i	0.578454	−	0.815715i	$-0.303656\pi$
$761$	18.5256	+	4.96391i	0.671551	+	0.179942i	0.0930979	+	0.995657i	$0.470323\pi$
$762$		0			0
$763$	−1.56762	+	1.20288i	−0.0567518	+	0.0435472i
$764$	34.1453	−	27.5309i	1.23533	−	0.996032i
$765$		0			0
$766$	−3.45874	+	1.22069i	−0.124969	+	0.0441052i
$767$	−6.85457	+	11.8725i	−0.247504	+	0.428690i
$768$		0			0
$769$	−3.01344	−	5.21944i	−0.108668	−	0.188218i	0.806563	−	0.591148i	$-0.201325\pi$
$769$	−3.01344	−	5.21944i	−0.108668	−	0.188218i	−0.915231	+	0.402930i	$0.867992\pi$
$770$	0.271569	+	0.232439i	0.00978666	+	0.00837652i
$771$		0			0
$772$	4.22530	+	27.0479i	0.152072	+	0.973475i
$773$	−24.7943	−	10.2701i	−0.891790	−	0.369391i	−0.110732	−	0.993850i	$-0.535320\pi$
$773$	−24.7943	−	10.2701i	−0.891790	−	0.369391i	−0.781058	+	0.624459i	$0.785320\pi$
$774$		0			0
$775$	8.15758	−	8.15758i	0.293029	−	0.293029i
$776$	−18.5210	−	34.3712i	−0.664865	−	1.23385i
$777$		0			0
$778$	22.2046	+	43.6932i	0.796072	+	1.56648i
$779$	−1.68279	−	12.7821i	−0.0602923	−	0.457965i
$780$		0			0
$781$	−0.166359	−	0.0219016i	−0.00595280	−	0.000783701i
$782$	1.75323	−	3.66573i	0.0626953	−	0.131086i
$783$		0			0
$784$	27.2481	+	5.91243i	0.973146	+	0.211158i
$785$	−8.47445	+	14.6782i	−0.302466	+	0.523886i
$786$		0			0
$787$	11.6629	+	8.94929i	0.415739	+	0.319008i	0.795363	−	0.606133i	$-0.207280\pi$
$787$	11.6629	+	8.94929i	0.415739	+	0.319008i	−0.379624	+	0.925141i	$0.623947\pi$
$788$	−26.3272	−	25.0897i	−0.937869	−	0.893785i
$789$		0			0
$790$	1.59651	−	2.45273i	0.0568014	−	0.0872642i
$791$	0.668325	−	0.668325i	0.0237629	−	0.0237629i
$792$		0			0
$793$	29.1451	+	29.1451i	1.03497	+	1.03497i
$794$	28.6565	−	6.05944i	1.01698	−	0.215042i
$795$		0			0
$796$	−9.50821	+	4.20923i	−0.337009	+	0.149192i
$797$	−3.11638	+	4.06134i	−0.110388	+	0.143860i	−0.845280	−	0.534324i	$-0.820566\pi$
$797$	−3.11638	+	4.06134i	−0.110388	+	0.143860i	0.734892	+	0.678184i	$0.237233\pi$
$798$		0			0
$799$	−1.00365	−	0.579458i	−0.0355066	−	0.0204998i
$800$	11.1936	−	14.4290i	0.395752	−	0.510142i
$801$		0			0
$802$	−24.6468	+	8.69853i	−0.870308	+	0.307156i
$803$	0.803599	−	6.10394i	0.0283584	−	0.215403i
$804$		0			0
$805$	0.387915	−	0.0510700i	0.0136722	−	0.00179998i
$806$	−20.1156	−	6.55951i	−0.708543	−	0.231049i
$807$		0			0
$808$	0.873203	+	8.56962i	0.0307192	+	0.301478i
$809$	−25.1234	−	25.1234i	−0.883292	−	0.883292i	0.110576	−	0.993868i	$-0.464731\pi$
$809$	−25.1234	−	25.1234i	−0.883292	−	0.883292i	−0.993868	+	0.110576i	$0.964731\pi$
$810$		0			0
$811$	9.44355	−	22.7987i	0.331608	−	0.800572i	−0.666857	−	0.745186i	$-0.732361\pi$
$811$	9.44355	−	22.7987i	0.331608	−	0.800572i	0.998465	−	0.0553866i	$-0.0176391\pi$
$812$	0.527341	−	2.17623i	0.0185060	−	0.0763707i
$813$		0			0
$814$	−14.5972	+	1.13328i	−0.511632	+	0.0397215i
$815$	−0.198626	+	0.114677i	−0.00695757	+	0.00401695i
$816$		0			0
$817$	−32.2804	−	18.6371i	−1.12935	−	0.652029i
$818$	−30.6117	−	14.6408i	−1.07031	−	0.511904i
$819$		0			0
$820$	−7.13361	−	3.89281i	−0.249117	−	0.135943i
$821$	−9.15110	−	11.9259i	−0.319375	−	0.416218i	0.605884	−	0.795553i	$-0.292820\pi$
$821$	−9.15110	−	11.9259i	−0.319375	−	0.416218i	−0.925259	+	0.379335i	$0.876153\pi$
$822$		0			0
$823$	−2.05496	+	7.66921i	−0.0716314	+	0.267332i	−0.992448	−	0.122663i	$-0.960857\pi$
$823$	−2.05496	+	7.66921i	−0.0716314	+	0.267332i	0.920817	+	0.389995i	$0.127523\pi$
$824$	0.152170	−	0.143488i	0.00530108	−	0.00499865i
$825$		0			0
$826$	−0.777641	+	0.164433i	−0.0270576	+	0.00572135i
$827$	−8.68350	+	20.9638i	−0.301955	+	0.728983i	0.697963	+	0.716134i	$0.254090\pi$
$827$	−8.68350	+	20.9638i	−0.301955	+	0.728983i	−0.999917	+	0.0128492i	$0.995910\pi$
$828$		0			0
$829$	12.1233	−	5.02164i	0.421060	−	0.174409i	−0.162085	−	0.986777i	$-0.551822\pi$
$829$	12.1233	−	5.02164i	0.421060	−	0.174409i	0.583145	+	0.812368i	$0.301822\pi$
$830$	−9.00297	−	1.67846i	−0.312498	−	0.0582602i
$831$		0			0
$832$	−32.8919	−	6.31246i	−1.14032	−	0.218845i
$833$	−10.1277	+	5.84724i	−0.350905	+	0.202595i
$834$		0			0
$835$	−18.8185	−	2.47751i	−0.651242	−	0.0857377i
$836$	−7.27500	+	5.86573i	−0.251611	+	0.202870i
$837$		0			0
$838$	−35.2892	+	31.7069i	−1.21904	+	1.09530i
$839$	13.2373	−	3.54691i	0.457001	−	0.122453i	−0.0229725	−	0.999736i	$-0.507313\pi$
$839$	13.2373	−	3.54691i	0.457001	−	0.122453i	0.479973	+	0.877283i	$0.340646\pi$
$840$		0			0
$841$	13.0901	+	3.50747i	0.451382	+	0.120947i
$842$	−4.24437	+	2.15696i	−0.146271	+	0.0743338i
$843$		0			0
$844$	6.35852	+	10.4256i	0.218869	+	0.358865i
$845$	5.56705	−	2.30595i	0.191512	−	0.0793271i
$846$		0			0
$847$	−1.67789			−0.0576529
$848$	−41.9321	+	19.7831i	−1.43996	+	0.679356i
$849$		0			0
$850$	0.592872	+	7.63647i	0.0203353	+	0.261929i
$851$	−9.75581	+	12.7140i	−0.334425	+	0.435831i
$852$		0			0
$853$	−6.40539	+	4.91503i	−0.219316	+	0.168287i	−0.712576	−	0.701595i	$-0.752472\pi$
$853$	−6.40539	+	4.91503i	−0.219316	+	0.168287i	0.493260	+	0.869882i	$0.335805\pi$
$854$	−0.127594	+	2.38632i	−0.00436619	+	0.0816581i
$855$		0			0
$856$	−25.9840	+	18.7527i	−0.888115	+	0.640955i
$857$	−5.49593	−	20.5111i	−0.187737	−	0.700645i	−0.994028	−	0.109126i	$-0.965195\pi$
$857$	−5.49593	−	20.5111i	−0.187737	−	0.700645i	0.806291	−	0.591520i	$-0.201472\pi$
$858$		0			0
$859$	3.90378	+	29.6522i	0.133195	+	1.01172i	0.919281	+	0.393602i	$0.128771\pi$
$859$	3.90378	+	29.6522i	0.133195	+	1.01172i	−0.786086	+	0.618117i	$0.787896\pi$
$860$	−21.4845	+	9.51107i	−0.732615	+	0.324325i
$861$		0			0
$862$	28.7743	+	5.36451i	0.980057	+	0.182716i
$863$	−50.2980			−1.71216			−0.856082	−	0.516840i	$-0.827108\pi$
$863$	−50.2980			−1.71216			−0.856082	+	0.516840i	$0.827108\pi$
$864$		0			0
$865$	−4.70351			−0.159924
$866$	2.78618	+	0.519438i	0.0946782	+	0.0176512i
$867$		0			0
$868$	−0.496577	−	1.12171i	−0.0168549	−	0.0380735i
$869$	−0.224515	−	1.70536i	−0.00761614	−	0.0578503i
$870$		0			0
$871$	10.3496	+	38.6252i	0.350682	+	1.30876i
$872$	−32.1450	−	5.19595i	−1.08857	−	0.175957i
$873$		0			0
$874$	−0.546150	+	10.2143i	−0.0184738	+	0.345504i
$875$	−1.49135	+	1.14436i	−0.0504170	+	0.0386863i
$876$		0			0
$877$	−14.9730	+	19.5132i	−0.505604	+	0.658916i	−0.974513	−	0.224331i	$-0.927980\pi$
$877$	−14.9730	+	19.5132i	−0.505604	+	0.658916i	0.468909	+	0.883246i	$0.344647\pi$
$878$	−1.67858	−	21.6209i	−0.0566494	−	0.729670i
$879$		0			0
$880$	0.283389	+	5.88387i	0.00955305	+	0.198345i
$881$	14.3584			0.483747			0.241873	−	0.970308i	$-0.422238\pi$
$881$	14.3584			0.483747			0.241873	+	0.970308i	$0.422238\pi$
$882$		0			0
$883$	38.1415	−	15.7987i	1.28357	−	0.531670i	0.366504	−	0.930417i	$-0.380555\pi$
$883$	38.1415	−	15.7987i	1.28357	−	0.531670i	0.917061	+	0.398746i	$0.130555\pi$
$884$	11.9930	−	7.31442i	0.403367	−	0.246011i
$885$		0			0
$886$	6.69258	−	3.40112i	0.224842	−	0.114263i
$887$	10.4313	+	2.79505i	0.350248	+	0.0938486i	0.429654	−	0.902994i	$-0.358636\pi$
$887$	10.4313	+	2.79505i	0.350248	+	0.0938486i	−0.0794060	+	0.996842i	$0.525302\pi$
$888$		0			0
$889$	1.71688	−	0.460038i	0.0575825	−	0.0154292i
$890$	21.2493	−	19.0923i	0.712280	−	0.639976i
$891$		0			0
$892$	13.2601	+	16.4459i	0.443981	+	0.550650i
$893$	2.89240	+	0.380791i	0.0967904	+	0.0127427i
$894$		0			0
$895$	26.3401	−	15.2074i	0.880451	−	0.508329i
$896$	−1.00231	−	1.66315i	−0.0334848	−	0.0555620i
$897$		0			0
$898$	17.1899	+	3.20479i	0.573636	+	0.106945i
$899$	21.5369	−	8.92087i	0.718295	−	0.297528i
$900$		0			0
$901$	7.44185	−	17.9662i	0.247924	−	0.598542i
$902$	−4.67308	+	0.988126i	−0.155597	+	0.0329010i
$903$		0			0
$904$	15.5688	+	0.457152i	0.517810	+	0.0152047i
$905$	−5.09493	+	19.0145i	−0.169361	+	0.632065i
$906$		0			0
$907$	23.6581	+	30.8319i	0.785556	+	1.02376i	0.998905	+	0.0467802i	$0.0148960\pi$
$907$	23.6581	+	30.8319i	0.785556	+	1.02376i	−0.213350	+	0.976976i	$0.568437\pi$
$908$	21.1732	−	38.8001i	0.702658	−	1.28763i
$909$		0			0
$910$	1.22024	+	0.583609i	0.0404504	+	0.0193464i
$911$	15.1765	+	8.76218i	0.502821	+	0.290304i	0.729878	−	0.683578i	$-0.239577\pi$
$911$	15.1765	+	8.76218i	0.502821	+	0.290304i	−0.227057	+	0.973882i	$0.572910\pi$
$912$		0			0
$913$	−4.66150	+	2.69132i	−0.154273	+	0.0890697i
$914$	−34.6671	+	2.69144i	−1.14668	+	0.0890251i
$915$		0			0
$916$	−2.02257	−	0.490107i	−0.0668277	−	0.0161936i
$917$	1.03876	−	2.50778i	0.0343028	−	0.0828143i
$918$		0			0
$919$	9.98940	+	9.98940i	0.329520	+	0.329520i	0.852404	−	0.522884i	$-0.175144\pi$
$919$	9.98940	+	9.98940i	0.329520	+	0.329520i	−0.522884	+	0.852404i	$0.675144\pi$
$920$	4.99793	+	4.07359i	0.164777	+	0.134302i
$921$		0			0
$922$	−24.2560	−	7.90963i	−0.798827	−	0.260490i
$923$	−0.629499	+	0.0828751i	−0.0207202	+	0.00272787i
$924$		0			0
$925$	3.94293	−	29.9495i	0.129643	−	0.984735i
$926$	31.0006	−	10.9410i	1.01874	−	0.359543i
$927$		0			0
$928$	32.0541	−	18.2810i	1.05223	−	0.600102i
$929$	−29.8614	−	17.2405i	−0.979720	−	0.565642i	−0.0775347	−	0.996990i	$-0.524705\pi$
$929$	−29.8614	−	17.2405i	−0.979720	−	0.565642i	−0.902186	+	0.431348i	$0.858038\pi$
$930$		0			0
$931$	17.9211	−	23.3553i	0.587341	−	0.765438i
$932$	17.0804	+	38.5828i	0.559487	+	1.26382i
$933$		0			0
$934$	−44.8237	+	9.47800i	−1.46668	+	0.310130i
$935$	−1.74705	−	1.74705i	−0.0571348	−	0.0571348i
$936$		0			0
$937$	15.4659	−	15.4659i	0.505248	−	0.505248i	−0.407816	−	0.913064i	$-0.633710\pi$
$937$	15.4659	−	15.4659i	0.505248	−	0.505248i	0.913064	+	0.407816i	$0.133710\pi$
$938$	−1.26476	+	1.94306i	−0.0412960	+	0.0634432i
$939$		0			0
$940$	1.26867	−	1.33124i	0.0413793	−	0.0434202i
$941$	20.1018	+	15.4247i	0.655301	+	0.502830i	0.882070	−	0.471119i	$-0.156150\pi$
$941$	20.1018	+	15.4247i	0.655301	+	0.502830i	−0.226769	+	0.973949i	$0.572816\pi$
$942$		0			0
$943$	−2.61404	+	4.52766i	−0.0851250	+	0.147441i
$944$	−10.7632	−	7.46462i	−0.350312	−	0.242953i
$945$		0			0
$946$	−5.95832	+	12.4579i	−0.193722	+	0.405042i
$947$	−42.1317	−	5.54675i	−1.36910	−	0.180245i	−0.590129	−	0.807309i	$-0.700923\pi$
$947$	−42.1317	−	5.54675i	−1.36910	−	0.180245i	−0.778968	+	0.627064i	$0.784256\pi$
$948$		0			0
$949$	−3.04080	−	23.0971i	−0.0987084	−	0.749765i
$950$	−8.73531	−	17.1890i	−0.283411	−	0.557683i
$951$		0			0
$952$	0.780174	+	0.233795i	0.0252856	+	0.00757734i
$953$	−11.7909	+	11.7909i	−0.381943	+	0.381943i	−0.871802	−	0.489859i	$-0.837048\pi$
$953$	−11.7909	+	11.7909i	−0.381943	+	0.381943i	0.489859	+	0.871802i	$0.337048\pi$
$954$		0			0
$955$	−26.9694	−	11.1711i	−0.872710	−	0.361488i
$956$	−25.3088	+	3.95362i	−0.818544	+	0.127869i
$957$		0			0
$958$	−45.4357	−	38.8890i	−1.46796	−	1.25645i
$959$	1.21701	+	2.10792i	0.0392992	+	0.0680682i
$960$		0			0
$961$	−9.11462	+	15.7870i	−0.294020	+	0.509258i
$962$	−52.2434	+	18.4382i	−1.68440	+	0.594470i
$963$		0			0
$964$	−8.21059	−	10.1832i	−0.264445	−	0.327980i
$965$	14.4546	−	11.0914i	0.465310	−	0.357045i
$966$		0			0
$967$	−21.1540	−	5.66820i	−0.680267	−	0.182277i	−0.0978919	−	0.995197i	$-0.531210\pi$
$967$	−21.1540	−	5.66820i	−0.680267	−	0.182277i	−0.582375	+	0.812920i	$0.697877\pi$
$968$	−18.9695	−	20.1173i	−0.609704	−	0.646593i
$969$		0			0
$970$	−14.1754	+	21.7778i	−0.455146	+	0.699242i
$971$	52.9107	+	21.9163i	1.69798	+	0.703328i	0.999919	−	0.0127064i	$-0.00404470\pi$
$971$	52.9107	+	21.9163i	1.69798	+	0.703328i	0.698065	+	0.716035i	$0.254045\pi$
$972$		0			0
$973$	−1.47696	−	3.56569i	−0.0473491	−	0.114311i
$974$	10.1067	+	14.7387i	0.323839	+	0.472258i
$975$		0			0
$976$	−30.0536	+	25.4490i	−0.961993	+	0.814602i
$977$	10.6302	+	18.4121i	0.340091	+	0.589054i	0.984449	−	0.175669i	$-0.0562089\pi$
$977$	10.6302	+	18.4121i	0.340091	+	0.589054i	−0.644359	+	0.764723i	$0.722876\pi$
$978$		0			0
$979$	2.19153	−	16.6463i	0.0700415	−	0.532018i
$980$	−5.23267	−	17.8035i	−0.167152	−	0.568712i
$981$		0			0
$982$	9.14412	+	0.488927i	0.291800	+	0.0156023i
$983$	−2.72427	−	10.1671i	−0.0868908	−	0.324281i	0.908775	−	0.417287i	$-0.137019\pi$
$983$	−2.72427	−	10.1671i	−0.0868908	−	0.324281i	−0.995666	+	0.0930062i	$0.970352\pi$
$984$		0			0
$985$	−6.26447	+	23.3793i	−0.199602	+	0.744927i
$986$	−4.79826	+	14.7145i	−0.152808	+	0.468605i
$987$		0			0
$988$	−20.8457	+	28.5643i	−0.663190	+	0.908752i
$989$	5.78439	+	13.9648i	0.183933	+	0.444054i
$990$		0			0
$991$			28.2543i			0.897526i	0.893651	+	0.448763i	$0.148135\pi$
$991$			28.2543i			0.897526i	−0.893651	+	0.448763i	$0.851865\pi$
$992$	7.83484	−	18.6354i	0.248756	−	0.591676i
$993$		0			0
$994$	−0.0279670	−	0.0239373i	−0.000887059	−	0.000759245i
$995$	5.49032	+	4.21287i	0.174055	+	0.133557i
$996$		0			0
$997$	14.8684	+	19.3768i	0.470886	+	0.613670i	0.967059	−	0.254554i	$-0.0819285\pi$
$997$	14.8684	+	19.3768i	0.470886	+	0.613670i	−0.496173	+	0.868224i	$0.665262\pi$
$998$	34.8618	−	31.3230i	1.10353	−	0.991511i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	864.2.bn.a.683.25		368
3.2	odd	2		288.2.bf.a.11.22	✓	368
9.4	even	3		288.2.bf.a.203.37	yes	368
9.5	odd	6	inner	864.2.bn.a.395.10		368
32.3	odd	8	inner	864.2.bn.a.35.10		368
96.35	even	8		288.2.bf.a.227.37	yes	368
288.67	odd	24		288.2.bf.a.131.22	yes	368
288.131	even	24	inner	864.2.bn.a.611.25		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.22	✓	368	3.2	odd	2
288.2.bf.a.131.22	yes	368	288.67	odd	24
288.2.bf.a.203.37	yes	368	9.4	even	3
288.2.bf.a.227.37	yes	368	96.35	even	8
864.2.bn.a.35.10		368	32.3	odd	8	inner
864.2.bn.a.395.10		368	9.5	odd	6	inner
864.2.bn.a.611.25		368	288.131	even	24	inner
864.2.bn.a.683.25		368	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.259191 - 1.39026i) q^{2} +(-1.86564 - 0.720686i) q^{4} +(0.173739 + 1.31968i) q^{5} +(0.0444224 + 0.165787i) q^{7} +(-1.48550 + 2.40693i) q^{8} +(1.87973 + 0.100507i) q^{10} +(0.877753 - 0.673524i) q^{11} +(2.54859 - 3.32139i) q^{13} +(0.242000 - 0.0187881i) q^{14} +(2.96122 + 2.68908i) q^{16} -1.67770 q^{17} +(3.90182 - 1.61619i) q^{19} +(0.626942 - 2.58726i) q^{20} +(-0.708866 - 1.39488i) q^{22} +(-1.65427 - 0.443260i) q^{23} +(3.11825 - 0.835534i) q^{25} +(-3.95702 - 4.40408i) q^{26} +(0.0366040 - 0.341313i) q^{28} +(6.46737 + 0.851445i) q^{29} +(3.09485 - 1.78681i) q^{31} +(4.50604 - 3.41988i) q^{32} +(-0.434846 + 2.33244i) q^{34} +(-0.211068 + 0.0874271i) q^{35} +(3.58091 - 8.64508i) q^{37} +(-1.23560 - 5.84344i) q^{38} +(-3.43447 - 1.54221i) q^{40} +(0.790091 - 2.94866i) q^{41} +(-5.37283 - 7.00201i) q^{43} +(-2.12297 + 0.623968i) q^{44} +(-1.04502 + 2.18497i) q^{46} +(0.598230 + 0.345388i) q^{47} +(6.03667 - 3.48527i) q^{49} +(-0.353383 - 4.55174i) q^{50} +(-7.14844 + 4.35979i) q^{52} +(-4.43574 + 10.7088i) q^{53} +(1.04134 + 1.04134i) q^{55} +(-0.465026 - 0.139354i) q^{56} +(2.86002 - 8.77063i) q^{58} +(-3.24657 + 0.427420i) q^{59} +(-1.28507 + 9.76104i) q^{61} +(-1.68197 - 4.76576i) q^{62} +(-3.58659 - 7.15097i) q^{64} +(4.82597 + 2.78628i) q^{65} +(-5.81460 + 7.57774i) q^{67} +(3.12999 + 1.20910i) q^{68} +(0.0668394 + 0.316099i) q^{70} +(-0.107240 - 0.107240i) q^{71} +(3.93478 - 3.93478i) q^{73} +(-11.0908 - 7.21912i) q^{74} +(-8.44415 + 0.203233i) q^{76} +(0.150653 + 0.115600i) q^{77} +(0.777341 - 1.34639i) q^{79} +(-3.03425 + 4.37507i) q^{80} +(-3.89461 - 1.86270i) q^{82} +(-4.82345 - 0.635020i) q^{83} +(-0.291483 - 2.21403i) q^{85} +(-11.1272 + 5.65476i) q^{86} +(0.317221 + 3.11321i) q^{88} +(10.7307 - 10.7307i) q^{89} +(0.663857 + 0.274979i) q^{91} +(2.76682 + 2.01917i) q^{92} +(0.635235 - 0.742173i) q^{94} +(2.81075 + 4.86836i) q^{95} +(-6.90201 + 11.9546i) q^{97} +(-3.28078 - 9.29588i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 368 * q + 12 * q^2 - 4 * q^4 + 12 * q^5 - 4 * q^7 - 16 * q^10 + 12 * q^11 - 4 * q^13 + 12 * q^14 - 4 * q^16 - 16 * q^19 + 12 * q^20 - 4 * q^22 + 12 * q^23 - 4 * q^25 - 16 * q^28 + 12 * q^29 + 12 * q^32 - 12 * q^34 - 16 * q^37 + 12 * q^38 - 4 * q^40 + 12 * q^41 - 4 * q^43 - 16 * q^46 + 24 * q^47 + 168 * q^50 - 4 * q^52 - 16 * q^55 + 12 * q^56 + 32 * q^58 + 12 * q^59 - 4 * q^61 - 16 * q^64 + 24 * q^65 - 4 * q^67 + 60 * q^68 - 4 * q^70 - 16 * q^73 + 12 * q^74 - 28 * q^76 + 12 * q^77 - 8 * q^79 - 16 * q^82 + 132 * q^83 - 24 * q^85 + 12 * q^86 - 4 * q^88 - 16 * q^91 - 216 * q^92 - 20 * q^94 - 8 * q^97

Introduction

L-functions

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