LMFDB - Embedded newform 864.2.bn.a.35.10

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			35.10
Character	$\chi$	$=$	864.35
Dual form			864.2.bn.a.395.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.07440 + 0.919596i) q^{2} +(0.308687 - 1.97603i) q^{4} +(-1.05601 - 0.810304i) q^{5} +(-0.165787 + 0.0444224i) q^{7} +(1.48550 + 2.40693i) q^{8} +(1.87973 - 0.100507i) q^{10} +(-0.144412 + 1.09692i) q^{11} +(-4.15071 + 0.546451i) q^{13} +(0.137271 - 0.200184i) q^{14} +(-3.80942 - 1.21995i) q^{16} +1.67770 q^{17} +(3.90182 + 1.61619i) q^{19} +(-1.92716 + 1.83658i) q^{20} +(-0.853565 - 1.31133i) q^{22} +(-0.443260 + 1.65427i) q^{23} +(-0.835534 - 3.11825i) q^{25} +(3.95702 - 4.40408i) q^{26} +(0.0366040 + 0.341313i) q^{28} +(3.97106 + 5.17518i) q^{29} +(-3.09485 + 1.78681i) q^{31} +(5.21472 - 2.19241i) q^{32} +(-1.80253 + 1.54281i) q^{34} +(0.211068 + 0.0874271i) q^{35} +(3.58091 + 8.64508i) q^{37} +(-5.67837 + 1.85166i) q^{38} +(0.381642 - 3.74544i) q^{40} +(2.94866 + 0.790091i) q^{41} +(8.75033 + 1.15200i) q^{43} +(2.12297 + 0.623968i) q^{44} +(-1.04502 - 2.18497i) q^{46} +(0.598230 + 0.345388i) q^{47} +(-6.03667 + 3.48527i) q^{49} +(3.76523 + 2.58191i) q^{50} +(-0.201463 + 8.37063i) q^{52} +(4.43574 + 10.7088i) q^{53} +(1.04134 - 1.04134i) q^{55} +(-0.353197 - 0.333047i) q^{56} +(-9.02560 - 1.90847i) q^{58} +(-1.99344 + 2.59791i) q^{59} +(-7.81078 + 5.99342i) q^{61} +(1.68197 - 4.76576i) q^{62} +(-3.58659 + 7.15097i) q^{64} +(4.82597 + 2.78628i) q^{65} +(9.46982 - 1.24673i) q^{67} +(0.517885 - 3.31520i) q^{68} +(-0.307169 + 0.100165i) q^{70} +(0.107240 - 0.107240i) q^{71} +(3.93478 + 3.93478i) q^{73} +(-11.7973 - 5.99532i) q^{74} +(4.39808 - 7.21123i) q^{76} +(-0.0247862 - 0.188270i) q^{77} +(0.777341 - 1.34639i) q^{79} +(3.03425 + 4.37507i) q^{80} +(-3.89461 + 1.86270i) q^{82} +(-2.96167 - 3.85972i) q^{83} +(-1.77167 - 1.35945i) q^{85} +(-10.4608 + 6.80905i) q^{86} +(-2.85473 + 1.28188i) q^{88} +(-10.7307 - 10.7307i) q^{89} +(0.663857 - 0.274979i) q^{91} +(3.13206 + 1.38655i) q^{92} +(-0.960358 + 0.179043i) q^{94} +(-2.81075 - 4.86836i) q^{95} +(-6.90201 + 11.9546i) q^{97} +(3.28078 - 9.29588i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/864\mathbb{Z}\right)^\times$.

$n$	$325$	$353$	$703$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−1.07440	+	0.919596i	−0.759718	+	0.650252i
$2$	−1.07440	+	0.919596i	−0.759718	+	0.650252i
$3$		0			0
$3$		0			0
$4$	0.308687	−	1.97603i	0.154344	−	0.988017i
$5$	−1.05601	−	0.810304i	−0.472261	−	0.362379i	0.345041	−	0.938587i	$-0.387865\pi$
$5$	−1.05601	−	0.810304i	−0.472261	−	0.362379i	−0.817303	+	0.576209i	$0.804532\pi$
$6$		0			0
$7$	−0.165787	+	0.0444224i	−0.0626615	+	0.0167901i	−0.290014	−	0.957023i	$-0.593660\pi$
$7$	−0.165787	+	0.0444224i	−0.0626615	+	0.0167901i	0.227352	+	0.973813i	$0.426993\pi$
$8$	1.48550	+	2.40693i	0.525203	+	0.850977i
$9$		0			0
$10$	1.87973	−	0.100507i	0.594423	−	0.0317833i
$11$	−0.144412	+	1.09692i	−0.0435419	+	0.330733i	0.955786	+	0.294064i	$0.0950080\pi$
$11$	−0.144412	+	1.09692i	−0.0435419	+	0.330733i	−0.999327	+	0.0366690i	$0.988325\pi$
$12$		0			0
$13$	−4.15071	+	0.546451i	−1.15120	+	0.151558i	−0.681876	−	0.731468i	$-0.738836\pi$
$13$	−4.15071	+	0.546451i	−1.15120	+	0.151558i	−0.469324	+	0.883026i	$0.655502\pi$
$14$	0.137271	−	0.200184i	0.0366873	−	0.0535015i
$15$		0			0
$16$	−3.80942	−	1.21995i	−0.952356	−	0.304988i
$17$	1.67770			0.406902			0.203451	−	0.979085i	$-0.434784\pi$
$17$	1.67770			0.406902			0.203451	+	0.979085i	$0.434784\pi$
$18$		0			0
$19$	3.90182	+	1.61619i	0.895139	+	0.370779i	0.782349	−	0.622840i	$-0.214021\pi$
$19$	3.90182	+	1.61619i	0.895139	+	0.370779i	0.112790	+	0.993619i	$0.464021\pi$
$20$	−1.92716	+	1.83658i	−0.430927	+	0.410671i
$21$		0			0
$22$	−0.853565	−	1.31133i	−0.181981	−	0.279577i
$23$	−0.443260	+	1.65427i	−0.0924261	+	0.344939i	−0.996617	−	0.0821905i	$-0.973808\pi$
$23$	−0.443260	+	1.65427i	−0.0924261	+	0.344939i	0.904191	+	0.427129i	$0.140475\pi$
$24$		0			0
$25$	−0.835534	−	3.11825i	−0.167107	−	0.623651i
$26$	3.95702	−	4.40408i	0.776036	−	0.863712i
$27$		0			0
$28$	0.0366040	+	0.341313i	0.00691751	+	0.0645020i
$29$	3.97106	+	5.17518i	0.737407	+	0.961008i	0.999992	−	0.00390119i	$-0.00124179\pi$
$29$	3.97106	+	5.17518i	0.737407	+	0.961008i	−0.262585	+	0.964909i	$0.584575\pi$
$30$		0			0
$31$	−3.09485	+	1.78681i	−0.555851	+	0.320920i	−0.751478	−	0.659758i	$-0.770659\pi$
$31$	−3.09485	+	1.78681i	−0.555851	+	0.320920i	0.195628	+	0.980678i	$0.437326\pi$
$32$	5.21472	−	2.19241i	0.921842	−	0.387567i
$33$		0			0
$34$	−1.80253	+	1.54281i	−0.309131	+	0.264589i
$35$	0.211068	+	0.0874271i	0.0356769	+	0.0147779i
$36$		0			0
$37$	3.58091	+	8.64508i	0.588698	+	1.42124i	0.884748	+	0.466070i	$0.154331\pi$
$37$	3.58091	+	8.64508i	0.588698	+	1.42124i	−0.296050	+	0.955173i	$0.595669\pi$
$38$	−5.67837	+	1.85166i	−0.921153	+	0.300379i
$39$		0			0
$40$	0.381642	−	3.74544i	0.0603429	−	0.592206i
$41$	2.94866	+	0.790091i	0.460503	+	0.123391i	0.481610	−	0.876386i	$-0.340052\pi$
$41$	2.94866	+	0.790091i	0.460503	+	0.123391i	−0.0211066	+	0.999777i	$0.506719\pi$
$42$		0			0
$43$	8.75033	+	1.15200i	1.33441	+	0.175679i	0.763754	−	0.645508i	$-0.223354\pi$
$43$	8.75033	+	1.15200i	1.33441	+	0.175679i	0.570660	+	0.821187i	$0.306688\pi$
$44$	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
$50$	3.76523	+	2.58191i	0.532485	+	0.365137i
$51$		0			0
$52$	−0.201463	+	8.37063i	−0.0279380	+	1.16080i
$53$	4.43574	+	10.7088i	0.609296	+	1.47097i	0.863768	+	0.503891i	$0.168099\pi$
$53$	4.43574	+	10.7088i	0.609296	+	1.47097i	−0.254471	+	0.967080i	$0.581901\pi$
$54$		0			0
$55$	1.04134	−	1.04134i	0.140414	−	0.140414i
$56$	−0.353197	−	0.333047i	−0.0471980	−	0.0445052i
$57$		0			0
$58$	−9.02560	−	1.90847i	−1.18512	−	0.250594i
$59$	−1.99344	+	2.59791i	−0.259524	+	0.338219i	−0.904882	−	0.425661i	$-0.860041\pi$
$59$	−1.99344	+	2.59791i	−0.259524	+	0.338219i	0.645358	+	0.763880i	$0.276708\pi$
$60$		0			0
$61$	−7.81078	+	5.99342i	−1.00007	+	0.767379i	−0.972657	−	0.232245i	$-0.925393\pi$
$61$	−7.81078	+	5.99342i	−1.00007	+	0.767379i	−0.0274104	+	0.999624i	$0.508726\pi$
$62$	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
$67$	9.46982	−	1.24673i	1.15692	−	0.152312i	0.472455	−	0.881355i	$-0.343368\pi$
$67$	9.46982	−	1.24673i	1.15692	−	0.152312i	0.684468	+	0.729043i	$0.260035\pi$
$68$	0.517885	−	3.31520i	0.0628027	−	0.402027i
$69$		0			0
$70$	−0.307169	+	0.100165i	−0.0367138	+	0.0119720i
$71$	0.107240	−	0.107240i	0.0127271	−	0.0127271i	−0.700715	−	0.713442i	$-0.747135\pi$
$71$	0.107240	−	0.107240i	0.0127271	−	0.0127271i	0.713442	+	0.700715i	$0.247135\pi$
$72$		0			0
$73$	3.93478	+	3.93478i	0.460532	+	0.460532i	0.898830	−	0.438298i	$-0.144419\pi$
$73$	3.93478	+	3.93478i	0.460532	+	0.460532i	−0.438298	+	0.898830i	$0.644419\pi$
$74$	−11.7973	−	5.99532i	−1.37141	−	0.696942i
$75$		0			0
$76$	4.39808	−	7.21123i	0.504495	−	0.827185i
$77$	−0.0247862	−	0.188270i	−0.00282465	−	0.0214553i
$78$		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
$83$	−2.96167	−	3.85972i	−0.325085	−	0.423660i	0.602008	−	0.798490i	$-0.294368\pi$
$83$	−2.96167	−	3.85972i	−0.325085	−	0.423660i	−0.927093	+	0.374831i	$0.877701\pi$
$84$		0			0
$85$	−1.77167	−	1.35945i	−0.192164	−	0.147453i
$86$	−10.4608	+	6.80905i	−1.12801	+	0.734239i
$87$		0			0
$88$	−2.85473	+	1.28188i	−0.304315	+	0.136649i
$89$	−10.7307	−	10.7307i	−1.13745	−	1.13745i	−0.988905	−	0.148546i	$-0.952541\pi$
$89$	−10.7307	−	10.7307i	−1.13745	−	1.13745i	−0.148546	−	0.988905i	$-0.547459\pi$
$90$		0			0
$91$	0.663857	−	0.274979i	0.0695912	−	0.0288256i
$92$	3.13206	+	1.38655i	0.326540	+	0.144558i
$93$		0			0
$94$	−0.960358	+	0.179043i	−0.0990534	+	0.0184669i
$95$	−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
$101$	−0.397518	+	3.01945i	−0.0395545	+	0.300447i	0.960221	+	0.279242i	$0.0900833\pi$
$101$	−0.397518	+	3.01945i	−0.0395545	+	0.300447i	−0.999775	+	0.0212041i	$0.993250\pi$
$102$		0			0
$103$	0.0191387	−	0.0714267i	0.00188579	−	0.00703788i	−0.964977	−	0.262336i	$-0.915507\pi$
$103$	0.0191387	−	0.0714267i	0.00188579	−	0.00703788i	0.966862	+	0.255298i	$0.0821737\pi$
$104$	−7.48114	−	9.17870i	−0.733586	−	0.900045i
$105$		0			0
$106$	−14.6136	−	7.42652i	−1.41940	−	0.721327i
$107$	−10.4670	+	4.33555i	−1.01188	+	0.419134i	−0.826140	−	0.563465i	$-0.809468\pi$
$107$	−10.4670	+	4.33555i	−1.01188	+	0.419134i	−0.185739	+	0.982599i	$0.559468\pi$
$108$		0			0
$109$	4.40564	−	10.6362i	0.421984	−	1.01876i	−0.559778	−	0.828643i	$-0.689113\pi$
$109$	4.40564	−	10.6362i	0.421984	−	1.01876i	0.981762	−	0.190116i	$-0.0608866\pi$
$110$	−0.161207	+	2.07643i	−0.0153705	+	0.197980i
$111$		0			0
$112$	0.685745	+	0.0330280i	0.0647968	+	0.00312085i
$113$	2.75339	+	4.76900i	0.259017	+	0.448630i	0.965979	−	0.258621i	$-0.0832682\pi$
$113$	2.75339	+	4.76900i	0.259017	+	0.448630i	−0.706962	+	0.707251i	$0.749935\pi$
$114$		0			0
$115$	1.80855	−	1.38775i	0.168648	−	0.129408i
$116$	11.4522	−	6.24944i	1.06331	−	0.580246i
$117$		0			0
$118$	−0.247260	−	4.62436i	−0.0227622	−	0.425707i
$119$	−0.278141	+	0.0745275i	−0.0254971	+	0.00683193i
$120$		0			0
$121$	9.44281	+	2.53019i	0.858437	+	0.230018i
$122$	2.88040	−	13.6221i	0.260780	−	1.23329i
$123$		0			0
$124$	2.57546	+	6.66709i	0.231283	+	0.598722i
$125$	−4.19129	+	10.1187i	−0.374881	+	0.905042i
$126$		0			0
$127$			10.3560i			0.918945i	0.888192	+	0.459473i	$0.151962\pi$
$127$			10.3560i			0.918945i	−0.888192	+	0.459473i	$0.848038\pi$
$128$	−2.72256	−	10.9812i	−0.240643	−	0.970614i
$129$		0			0
$130$	−7.74729	+	1.44436i	−0.679483	+	0.126679i
$131$	2.06427	+	15.6797i	0.180356	+	1.36994i	0.806961	+	0.590604i	$0.201110\pi$
$131$	2.06427	+	15.6797i	0.180356	+	1.36994i	−0.626605	+	0.779337i	$0.715556\pi$
$132$		0			0
$133$	−0.718664	−	0.0946140i	−0.0623161	−	0.00820407i
$134$	−9.02793	+	10.0479i	−0.779894	+	0.868006i
$135$		0			0
$136$	2.49222	+	4.03810i	0.213706	+	0.346265i
$137$	3.67040	+	13.6981i	0.313584	+	1.17031i	0.925301	+	0.379234i	$0.123812\pi$
$137$	3.67040	+	13.6981i	0.313584	+	1.17031i	−0.611717	+	0.791077i	$0.709521\pi$
$138$		0			0
$139$	13.6890	−	17.8398i	1.16108	−	1.51315i	0.341788	−	0.939777i	$-0.388968\pi$
$139$	13.6890	−	17.8398i	1.16108	−	1.51315i	0.819294	−	0.573374i	$-0.194366\pi$
$140$	0.237913	−	0.390089i	0.0201073	−	0.0329686i
$141$		0			0
$142$	−0.0166016	+	0.213837i	−0.00139318	+	0.0179448i
$143$		−	4.63190i		−	0.387339i
$144$		0			0
$145$		−	8.68280i		−	0.721067i
$146$	−7.84596	−	0.609136i	−0.649336	−	0.0504124i
$147$		0			0
$148$	18.1884	−	4.40738i	1.49507	−	0.362284i
$149$	−8.89784	+	11.5959i	−0.728939	+	0.949972i	−0.999920	−	0.0126123i	$-0.995985\pi$
$149$	−8.89784	+	11.5959i	−0.728939	+	0.949972i	0.270981	+	0.962585i	$0.412652\pi$
$150$		0			0
$151$	−5.99430	−	22.3710i	−0.487809	−	1.82053i	−0.567065	−	0.823673i	$-0.691921\pi$
$151$	−5.99430	−	22.3710i	−0.487809	−	1.82053i	0.0792562	−	0.996854i	$-0.474745\pi$
$152$	1.90611	+	11.7922i	0.154606	+	0.956476i
$153$		0			0
$154$	0.199762	+	0.179484i	0.0160973	+	0.0144633i
$155$	4.71604	+	0.620878i	0.378801	+	0.0498702i
$156$		0			0
$157$	1.66203	+	12.6244i	0.132644	+	1.00753i	0.920244	+	0.391346i	$0.127990\pi$
$157$	1.66203	+	12.6244i	0.132644	+	1.00753i	−0.787599	+	0.616188i	$0.788676\pi$
$158$	0.402960	+	2.16141i	0.0320578	+	0.171952i
$159$		0			0
$160$	−7.28331	−	1.91031i	−0.575796	−	0.151023i
$161$		−	0.293946i		−	0.0231662i
$162$		0			0
$163$	0.0659393	−	0.159192i	0.00516477	−	0.0124689i	−0.921276	−	0.388909i	$-0.872852\pi$
$163$	0.0659393	−	0.159192i	0.00516477	−	0.0124689i	0.926441	+	0.376440i	$0.122852\pi$
$164$	2.47146	−	5.58276i	0.192989	−	0.435940i
$165$		0			0
$166$	6.73141	+	1.42336i	0.522459	+	0.110474i
$167$	−13.7740	−	3.69073i	−1.06586	−	0.285598i	−0.317072	−	0.948402i	$-0.602700\pi$
$167$	−13.7740	−	3.69073i	−1.06586	−	0.285598i	−0.748793	+	0.662804i	$0.769366\pi$
$168$		0			0
$169$	4.37274	−	1.17167i	0.336364	−	0.0901285i
$170$	3.15363	−	0.168622i	0.241872	−	0.0129327i
$171$		0			0
$172$	4.97751	−	16.9354i	0.379532	−	1.29131i
$173$	2.80342	−	2.15114i	0.213140	−	0.163548i	−0.496674	−	0.867937i	$-0.665446\pi$
$173$	2.80342	−	2.15114i	0.213140	−	0.163548i	0.709814	+	0.704389i	$0.248779\pi$
$174$		0			0
$175$	0.277041	+	0.479849i	0.0209423	+	0.0362731i
$176$	1.88832	−	4.00245i	0.142337	−	0.301696i
$177$		0			0
$178$	21.3970	+	1.66120i	1.60377	+	0.124512i
$179$	8.74430	−	21.1106i	0.653580	−	1.57788i	−0.153966	−	0.988076i	$-0.549205\pi$
$179$	8.74430	−	21.1106i	0.653580	−	1.57788i	0.807546	−	0.589805i	$-0.200795\pi$
$180$		0			0
$181$	13.6633	−	5.65954i	1.01559	−	0.420670i	0.188098	−	0.982150i	$-0.439768\pi$
$181$	13.6633	−	5.65954i	1.01559	−	0.420670i	0.827490	+	0.561480i	$0.189768\pi$
$182$	−0.460382	+	0.905919i	−0.0341257	+	0.0671511i
$183$		0			0
$184$	−4.64016	+	1.39052i	−0.342077	+	0.102510i
$185$	3.22367	−	12.0309i	0.237009	−	0.884530i
$186$		0			0
$187$	−0.242280	+	1.84030i	−0.0177173	+	0.134576i
$188$	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	$-0.541626\pi$
$191$	10.9654	−	18.9927i	0.793431	−	1.37426i	0.923831	−	0.382801i	$-0.125040\pi$
$192$		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	$0.997302\pi$
$194$	−3.57788	−	19.1912i	−0.256877	−	1.37784i
$195$		0			0
$196$	5.02357	+	13.0045i	0.358827	+	0.928894i
$197$	−16.7997	+	6.95868i	−1.19693	+	0.495785i	−0.890006	−	0.455948i	$-0.849300\pi$
$197$	−16.7997	+	6.95868i	−1.19693	+	0.495785i	−0.306926	+	0.951734i	$0.599300\pi$
$198$		0			0
$199$	3.67634	+	3.67634i	0.260609	+	0.260609i	0.825301	−	0.564693i	$-0.191005\pi$
$199$	3.67634	+	3.67634i	0.260609	+	0.260609i	−0.564693	+	0.825301i	$0.691005\pi$
$200$	6.26422	−	6.64323i	0.442948	−	0.469747i
$201$		0			0
$202$	−2.34958	−	3.60967i	−0.165316	−	0.253975i
$203$	−0.888242	−	0.681572i	−0.0623424	−	0.0478370i
$204$		0			0
$205$	−2.47359	−	3.22365i	−0.172763	−	0.225150i
$206$	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
$211$	−0.796970	−	6.05359i	−0.0548657	−	0.416746i	−0.996733	−	0.0807624i	$-0.974265\pi$
$211$	−0.796970	−	6.05359i	−0.0548657	−	0.416746i	0.941868	−	0.335984i	$-0.109069\pi$
$212$	22.5303	−	5.45950i	1.54739	−	0.374960i
$213$		0			0
$214$	7.25878	−	14.2835i	0.496200	−	0.976400i
$215$	−8.30695	−	8.30695i	−0.566529	−	0.566529i
$216$		0			0
$217$	0.433710	−	0.433710i	0.0294421	−	0.0294421i
$218$	5.04753	+	15.4789i	0.341862	+	1.04837i
$219$		0			0
$220$	−1.73627	−	2.37917i	−0.117059	−	0.160403i
$221$	−6.96365	+	0.916782i	−0.468426	+	0.0616694i
$222$		0			0
$223$	9.14774	+	5.28145i	0.612578	+	0.353672i	0.773974	−	0.633218i	$-0.218266\pi$
$223$	9.14774	+	5.28145i	0.612578	+	0.353672i	−0.161396	+	0.986890i	$0.551600\pi$
$224$	−0.767139	+	0.595123i	−0.0512567	+	0.0397633i
$225$		0			0
$226$	−7.34380	−	2.59183i	−0.488503	−	0.172406i
$227$	17.5336	−	13.4540i	1.16375	−	0.892975i	0.168063	−	0.985776i	$-0.446249\pi$
$227$	17.5336	−	13.4540i	1.16375	−	0.892975i	0.995685	+	0.0928016i	$0.0295822\pi$
$228$		0			0
$229$	−0.633449	+	0.825527i	−0.0418595	+	0.0545523i	−0.813814	−	0.581125i	$-0.802613\pi$
$229$	−0.633449	+	0.825527i	−0.0418595	+	0.0545523i	0.771955	+	0.635678i	$0.219279\pi$
$230$	−0.666943	+	3.15413i	−0.0439769	+	0.207977i
$231$		0			0
$232$	−6.55728	+	17.2458i	−0.430507	+	1.13224i
$233$	14.9180	−	14.9180i	0.977311	−	0.977311i	−0.0224377	−	0.999748i	$-0.507143\pi$
$233$	14.9180	−	14.9180i	0.977311	−	0.977311i	0.999748	+	0.0224377i	$0.00714273\pi$
$234$		0			0
$235$	−0.351866	−	0.849481i	−0.0229532	−	0.0554140i
$236$	4.51820	+	4.74105i	0.294110	+	0.308616i
$237$		0			0
$238$	0.230300	−	0.335850i	0.0149281	−	0.0217699i
$239$	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	0.306348	−	0.951920i	$-0.400893\pi$
$241$	−5.66423	−	3.27024i	−0.364865	−	0.210655i	−0.671213	+	0.741265i	$0.734226\pi$
$242$	−12.4721	+	5.96512i	−0.801740	+	0.383452i
$243$		0			0
$244$	9.43212	+	17.2845i	0.603830	+	1.10652i
$245$	9.19890	+	1.21106i	0.587696	+	0.0773716i
$246$		0			0
$247$	−17.0785	−	4.57617i	−1.08668	−	0.291174i
$248$	−8.89811	−	4.79476i	−0.565030	−	0.304468i
$249$		0			0
$250$	−4.80195	−	14.7258i	−0.303702	−	0.931344i
$251$	3.69201	+	8.91330i	0.233038	+	0.562603i	0.996532	−	0.0832121i	$-0.0265179\pi$
$251$	3.69201	+	8.91330i	0.233038	+	0.562603i	−0.763494	+	0.645815i	$0.776518\pi$
$252$		0			0
$253$	−1.75059	−	0.725116i	−0.110058	−	0.0455877i
$254$	−9.52333	−	11.1265i	−0.597547	−	0.698140i
$255$		0			0
$256$	13.0234	+	9.29463i	0.813965	+	0.580915i
$257$	−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
$259$	−0.977702	−	1.27417i	−0.0607515	−	0.0791729i
$260$	6.99549	−	8.67620i	0.433842	−	0.538075i
$261$		0			0
$262$	−16.6368	−	14.9480i	−1.02783	−	0.923492i
$263$	−1.81281	−	6.76551i	−0.111783	−	0.417179i	0.887243	−	0.461302i	$-0.152617\pi$
$263$	−1.81281	−	6.76551i	−0.111783	−	0.417179i	−0.999026	+	0.0441227i	$0.985951\pi$
$264$		0			0
$265$	3.99322	−	14.9029i	0.245302	−	0.915478i
$266$	0.859142	−	0.559227i	0.0526774	−	0.0342884i
$267$		0			0
$268$	0.459638	−	19.0975i	0.0280768	−	1.16657i
$269$	−25.5646	−	10.5892i	−1.55870	−	0.645634i	−0.573836	−	0.818970i	$-0.694545\pi$
$269$	−25.5646	−	10.5892i	−1.55870	−	0.645634i	−0.984863	+	0.173336i	$0.944545\pi$
$270$		0			0
$271$	−24.4270			−1.48383			−0.741917	−	0.670492i	$-0.766083\pi$
$271$	−24.4270			−1.48383			−0.741917	+	0.670492i	$0.766083\pi$
$272$	−6.39108	−	2.04672i	−0.387516	−	0.124100i
$273$		0			0
$274$	−16.5402	−	11.3420i	−0.999232	−	0.685197i
$275$	3.54113	−	0.466199i	0.213538	−	0.0281129i
$276$		0			0
$277$	−3.34250	+	25.3888i	−0.200831	+	1.52547i	0.532989	+	0.846122i	$0.321069\pi$
$277$	−3.34250	+	25.3888i	−0.200831	+	1.52547i	−0.733820	+	0.679344i	$0.762265\pi$
$278$	1.69793	+	31.7554i	0.101835	+	1.90456i
$279$		0			0
$280$	0.103110	+	0.637897i	0.00616201	+	0.0381216i
$281$	8.11585	−	2.17463i	0.484151	−	0.129728i	−0.00848391	−	0.999964i	$-0.502701\pi$
$281$	8.11585	−	2.17463i	0.484151	−	0.129728i	0.492635	+	0.870236i	$0.336034\pi$
$282$		0			0
$283$	15.0033	+	11.5124i	0.891851	+	0.684341i	0.949423	−	0.314000i	$-0.101669\pi$
$283$	15.0033	+	11.5124i	0.891851	+	0.684341i	−0.0575719	+	0.998341i	$0.518336\pi$
$284$	−0.178807	−	0.245014i	−0.0106102	−	0.0145389i
$285$		0			0
$286$	4.25948	+	4.97654i	0.251868	+	0.294269i
$287$	−0.523946			−0.0309276
$288$		0			0
$289$	−14.1853			−0.834430
$290$	7.98467	+	9.32883i	0.468876	+	0.547808i
$291$		0			0
$292$	8.98988	−	6.56065i	0.526093	−	0.383933i
$293$	19.1345	+	14.6824i	1.11785	+	0.857754i	0.990959	−	0.134163i	$-0.0428345\pi$
$293$	19.1345	+	14.6824i	1.11785	+	0.857754i	0.126888	+	0.991917i	$0.459501\pi$
$294$		0			0
$295$	4.21019	−	1.12812i	0.245126	−	0.0656814i
$296$	−15.4886	+	21.4612i	−0.900259	+	1.24741i
$297$		0			0
$298$	−1.10366	−	20.6411i	−0.0639333	−	1.19571i
$299$	0.935866	−	7.10861i	0.0541225	−	0.411101i
$300$		0			0
$301$	−1.50186	+	0.197724i	−0.0865659	+	0.0113966i
$302$	27.0126	+	18.5232i	1.55440	+	1.06589i
$303$		0			0
$304$	−12.8920	−	10.9168i	−0.739408	−	0.626120i
$305$	13.1047			0.750375
$306$		0			0
$307$	−0.622170	−	0.257711i	−0.0355091	−	0.0147083i	0.364858	−	0.931063i	$-0.381117\pi$
$307$	−0.622170	−	0.257711i	−0.0355091	−	0.0147083i	−0.400367	+	0.916355i	$0.631117\pi$
$308$	−0.379678	−	0.00913806i	−0.0216342	−	0.000520690i
$309$		0			0
$310$	−5.63789	+	3.66978i	−0.320211	+	0.208429i
$311$	4.39213	−	16.3916i	0.249055	−	0.929485i	−0.722247	−	0.691635i	$-0.756891\pi$
$311$	4.39213	−	16.3916i	0.249055	−	0.929485i	0.971302	−	0.237850i	$-0.0764426\pi$
$312$		0			0
$313$	0.668229	+	2.49387i	0.0377706	+	0.140962i	0.982236	−	0.187648i	$-0.0600865\pi$
$313$	0.668229	+	2.49387i	0.0377706	+	0.140962i	−0.944466	+	0.328610i	$0.893420\pi$
$314$	−13.3950	−	12.0353i	−0.755923	−	0.679189i
$315$		0			0
$316$	−2.42056	−	1.95167i	−0.136167	−	0.109790i
$317$	−8.10471	−	10.5623i	−0.455206	−	0.593236i	0.508214	−	0.861231i	$-0.330306\pi$
$317$	−8.10471	−	10.5623i	−0.455206	−	0.593236i	−0.963420	+	0.267994i	$0.913639\pi$
$318$		0			0
$319$	−6.25023	+	3.60857i	−0.349945	+	0.202041i
$320$	9.58192	−	4.64526i	0.535646	−	0.259678i
$321$		0			0
$322$	0.270312	+	0.315817i	0.0150639	+	0.0175998i
$323$	6.54609	+	2.71148i	0.364234	+	0.150871i
$324$		0			0
$325$	5.17203	+	12.4864i	0.286893	+	0.692620i
$326$	0.0755465	+	0.231674i	0.00418413	+	0.0128312i
$327$		0			0
$328$	2.47854	+	8.27088i	0.136854	+	0.456683i
$329$	−0.114522	−	0.0306859i	−0.00631377	−	0.00169177i
$330$		0			0
$331$	−9.51917	−	1.25322i	−0.523221	−	0.0688833i	−0.135710	−	0.990749i	$-0.543332\pi$
$331$	−9.51917	−	1.25322i	−0.523221	−	0.0688833i	−0.387511	+	0.921865i	$0.626665\pi$
$332$	−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	−0.487570	−	0.873084i	$-0.662117\pi$
$337$	0.454491	−	0.262401i	0.0247577	−	0.0142939i	0.512328	+	0.858790i	$0.328783\pi$
$338$	−3.62062	+	5.28000i	−0.196936	+	0.287194i
$339$		0			0
$340$	−3.23321	+	3.08123i	−0.175345	+	0.167103i
$341$	−1.51305	−	3.65283i	−0.0819364	−	0.197812i
$342$		0			0
$343$	1.69552	−	1.69552i	0.0915497	−	0.0915497i
$344$	10.2258	+	22.7727i	0.551339	+	1.22782i
$345$		0			0
$346$	−1.03383	+	4.88921i	−0.0555788	+	0.262845i
$347$	−21.8742	+	28.5070i	−1.17427	+	1.53034i	−0.377544	+	0.925992i	$0.623231\pi$
$347$	−21.8742	+	28.5070i	−1.17427	+	1.53034i	−0.796724	+	0.604344i	$0.793435\pi$
$348$		0			0
$349$	−22.9357	+	17.5992i	−1.22772	+	0.942062i	−0.999502	−	0.0315480i	$-0.989956\pi$
$349$	−22.9357	+	17.5992i	−1.22772	+	0.942062i	−0.228217	+	0.973610i	$0.573290\pi$
$350$	−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
$355$	−0.200144	+	0.0263494i	−0.0106225	+	0.00139848i
$356$	−24.5167	+	17.8918i	−1.29938	+	0.948264i
$357$		0			0
$358$	10.0183	+	30.7225i	0.529485	+	1.62374i
$359$	6.44282	−	6.44282i	0.340039	−	0.340039i	−0.516343	−	0.856382i	$-0.672707\pi$
$359$	6.44282	−	6.44282i	0.340039	−	0.340039i	0.856382	+	0.516343i	$0.172707\pi$
$360$		0			0
$361$	−0.822894	−	0.822894i	−0.0433102	−	0.0433102i
$362$	−9.47545	+	18.6454i	−0.498019	+	0.979980i
$363$		0			0
$364$	−0.338443	−	1.39669i	−0.0177392	−	0.0732063i
$365$	−0.966794	−	7.34353i	−0.0506043	−	0.384378i
$366$		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
$371$	−1.21110	−	1.57833i	−0.0628771	−	0.0819430i
$372$		0			0
$373$	−9.61261	−	7.37602i	−0.497722	−	0.381916i	0.329175	−	0.944269i	$-0.393229\pi$
$373$	−9.61261	−	7.37602i	−0.497722	−	0.381916i	−0.826897	+	0.562353i	$0.809896\pi$
$374$	−1.43203	−	2.20003i	−0.0740484	−	0.113761i
$375$		0			0
$376$	0.0573458	+	1.95297i	0.00295738	+	0.100717i
$377$	−19.3107	−	19.3107i	−0.994551	−	0.994551i
$378$		0			0
$379$	−28.0488	+	11.6182i	−1.44077	+	0.596786i	−0.959985	−	0.280053i	$-0.909648\pi$
$379$	−28.0488	+	11.6182i	−1.44077	+	0.596786i	−0.480784	+	0.876839i	$0.659648\pi$
$380$	−10.4877	+	4.05134i	−0.538008	+	0.207829i
$381$		0			0
$382$	5.68429	+	30.4896i	0.290834	+	1.55998i
$383$	1.29677	+	2.24608i	0.0662620	+	0.114769i	0.897253	−	0.441517i	$-0.145559\pi$
$383$	1.29677	+	2.24608i	0.0662620	+	0.114769i	−0.830991	+	0.556286i	$0.812226\pi$
$384$		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
$389$	4.52357	−	34.3599i	0.229354	−	1.74212i	−0.358841	−	0.933399i	$-0.616828\pi$
$389$	4.52357	−	34.3599i	0.229354	−	1.74212i	0.588195	−	0.808719i	$-0.299839\pi$
$390$		0			0
$391$	−0.743658	+	2.77537i	−0.0376084	+	0.140356i
$392$	−17.3562	−	9.35244i	−0.876623	−	0.472370i
$393$		0			0
$394$	11.6505	−	22.9254i	0.586945	−	1.15497i
$395$	−1.91187	+	0.791921i	−0.0961964	+	0.0398458i
$396$		0			0
$397$	7.92586	−	19.1347i	0.397788	−	0.960344i	−0.590402	−	0.807109i	$-0.701031\pi$
$397$	7.92586	−	19.1347i	0.397788	−	0.960344i	0.988190	−	0.153235i	$-0.0489691\pi$
$398$	−7.33061	−	0.569126i	−0.367451	−	0.0285277i
$399$		0			0
$400$	−0.621219	+	12.8981i	−0.0310609	+	0.644903i
$401$	9.24072	+	16.0054i	0.461460	+	0.799271i	0.999034	−	0.0439449i	$-0.0139926\pi$
$401$	9.24072	+	16.0054i	0.461460	+	0.799271i	−0.537574	+	0.843216i	$0.680659\pi$
$402$		0			0
$403$	11.8694	−	9.10771i	0.591257	−	0.453687i
$404$	5.84383	+	1.71758i	0.290741	+	0.0854526i
$405$		0			0
$406$	1.58110	−	0.0845401i	0.0784688	−	0.00419565i
$407$	−10.0001	+	2.67951i	−0.495686	+	0.132819i
$408$		0			0
$409$	−23.1765	−	6.21012i	−1.14600	−	0.307071i	−0.364641	−	0.931148i	$-0.618808\pi$
$409$	−23.1765	−	6.21012i	−1.14600	−	0.307071i	−0.781362	+	0.624078i	$0.785475\pi$
$410$	5.62210	+	1.18880i	0.277656	+	0.0587104i
$411$		0			0
$412$	−0.135234	−	0.0598673i	−0.00666249	−	0.00294945i
$413$	0.215081	−	0.519252i	0.0105834	−	0.0255507i
$414$		0			0
$415$			6.47575i			0.317882i
$416$	−20.4468	+	11.9496i	−1.00248	+	0.585880i
$417$		0			0
$418$	−1.21110	−	6.49611i	−0.0592366	−	0.317735i
$419$	4.37862	+	33.2589i	0.213910	+	1.62480i	0.675255	+	0.737584i	$0.264033\pi$
$419$	4.37862	+	33.2589i	0.213910	+	1.62480i	−0.461346	+	0.887220i	$0.652633\pi$
$420$		0			0
$421$	3.33774	+	0.439422i	0.162672	+	0.0214161i	0.211422	−	0.977395i	$-0.432191\pi$
$421$	3.33774	+	0.439422i	0.162672	+	0.0214161i	−0.0487505	+	0.998811i	$0.515524\pi$
$422$	6.42313	+	5.77111i	0.312673	+	0.280933i
$423$		0			0
$424$	−19.1861	+	26.5845i	−0.931758	+	1.29106i
$425$	−1.40178	−	5.23150i	−0.0679962	−	0.253765i
$426$		0			0
$427$	1.02868	−	1.34060i	0.0497813	−	0.0648763i
$428$	5.33619	+	22.0214i	0.257935	+	1.06444i
$429$		0			0
$430$	16.5641	+	1.28598i	0.798790	+	0.0620156i
$431$			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	$-0.984666\pi$
$433$		−	2.00407i		−	0.0963096i	0.998840	−	0.0481548i	$-0.0153341\pi$
$434$	−0.0671417	+	0.864817i	−0.00322290	+	0.0415125i
$435$		0			0
$436$	−19.6575	−	11.9889i	−0.941421	−	0.574166i
$437$	−4.40313	+	5.73827i	−0.210630	+	0.274498i
$438$		0			0
$439$	−3.96881	−	14.8118i	−0.189421	−	0.706928i	−0.993641	−	0.112597i	$-0.964083\pi$
$439$	−3.96881	−	14.8118i	−0.189421	−	0.706928i	0.804220	−	0.594332i	$-0.202583\pi$
$440$	4.05333	+	0.959517i	0.193235	+	0.0457432i
$441$		0			0
$442$	6.63870	−	7.38874i	0.315771	−	0.351446i
$443$	5.26299	+	0.692885i	0.250052	+	0.0329200i	0.254510	−	0.967070i	$-0.418086\pi$
$443$	5.26299	+	0.692885i	0.250052	+	0.0329200i	−0.00445816	+	0.999990i	$0.501419\pi$
$444$		0			0
$445$	2.63658	+	20.0268i	0.124986	+	0.949363i
$446$	−14.6852	+	2.73781i	−0.695363	+	0.129639i
$447$		0			0
$448$	0.276945	−	1.34486i	0.0130844	−	0.0635387i
$449$			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
$452$	10.2737	−	3.96866i	0.483232	−	0.186670i
$453$		0			0
$454$	−6.46593	+	30.5789i	−0.303461	+	1.43514i
$455$	−0.923855	−	0.247546i	−0.0433110	−	0.0116051i
$456$		0			0
$457$	23.7493	−	6.36361i	1.11095	−	0.297677i	0.343731	−	0.939068i	$-0.388309\pi$
$457$	23.7493	−	6.36361i	1.11095	−	0.297677i	0.767214	+	0.641391i	$0.221642\pi$
$458$	−0.0785710	−	1.46947i	−0.00367138	−	0.0686636i
$459$		0			0
$460$	−2.18396	−	4.00213i	−0.101828	−	0.186600i
$461$	−14.3124	+	10.9823i	−0.666596	+	0.511497i	−0.885732	−	0.464197i	$-0.846343\pi$
$461$	−14.3124	+	10.9823i	−0.666596	+	0.511497i	0.219136	+	0.975694i	$0.429676\pi$
$462$		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	$0.651696\pi$
$464$	−8.81397	−	24.5590i	−0.409178	−	1.14012i
$465$		0			0
$466$	−2.30942	+	29.7465i	−0.106982	+	1.37798i
$467$	12.3974	−	29.9300i	0.573683	−	1.38499i	−0.324715	−	0.945812i	$-0.605269\pi$
$467$	12.3974	−	29.9300i	0.573683	−	1.38499i	0.898398	−	0.439181i	$-0.144731\pi$
$468$		0			0
$469$	−1.51459	+	0.627362i	−0.0699371	+	0.0289689i
$470$	1.15923	+	0.589110i	0.0534711	+	0.0271736i
$471$		0			0
$472$	−9.21423	−	0.938885i	−0.424119	−	0.0432157i
$473$	−2.52731	+	9.43204i	−0.116206	+	0.433686i
$474$		0			0
$475$	1.77958	−	13.5172i	0.0816527	−	0.620214i
$476$	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	$0.583576\pi$
$479$	−21.1446	+	36.6236i	−0.966123	+	1.67337i	−0.706568	+	0.707645i	$0.749758\pi$
$480$		0			0
$481$	−19.5874	−	33.9264i	−0.893110	−	1.54691i
$482$	9.09297	−	1.69524i	0.414174	−	0.0772160i
$483$		0			0
$484$	7.91462	−	17.8783i	0.359755	−	0.812649i
$485$	16.9755	−	7.03146i	0.770816	−	0.319282i
$486$		0			0
$487$	−8.93552	−	8.93552i	−0.404907	−	0.404907i	0.475051	−	0.879958i	$-0.342430\pi$
$487$	−8.93552	−	8.93552i	−0.404907	−	0.404907i	−0.879958	+	0.475051i	$0.842430\pi$
$488$	−26.0286	−	9.89675i	−1.17826	−	0.448005i
$489$		0			0
$490$	−10.9970	+	7.15810i	−0.496794	+	0.323370i
$491$	−5.13704	−	3.94179i	−0.231832	−	0.177891i	0.486313	−	0.873785i	$-0.338342\pi$
$491$	−5.13704	−	3.94179i	−0.231832	−	0.177891i	−0.718144	+	0.695894i	$0.755008\pi$
$492$		0			0
$493$	6.66225	+	8.68242i	0.300053	+	0.391036i
$494$	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
$499$	4.32559	+	32.8562i	0.193640	+	1.47084i	0.761740	+	0.647883i	$0.224346\pi$
$499$	4.32559	+	32.8562i	0.193640	+	1.47084i	−0.568099	+	0.822960i	$0.692321\pi$
$500$	18.7011	+	11.4056i	0.836337	+	0.510076i
$501$		0			0
$502$	−12.1633	−	6.18133i	−0.542877	−	0.275886i
$503$	−14.8092	−	14.8092i	−0.660309	−	0.660309i	0.295144	−	0.955453i	$-0.404632\pi$
$503$	−14.8092	−	14.8092i	−0.660309	−	0.660309i	−0.955453	+	0.295144i	$0.904632\pi$
$504$		0			0
$505$	2.86645	−	2.86645i	0.127556	−	0.127556i
$506$	2.54765	−	0.830764i	0.113257	−	0.0369319i
$507$		0			0
$508$	20.4638	+	3.19676i	0.907934	+	0.141833i
$509$	2.82141	−	0.371446i	0.125057	−	0.0164640i	−0.0677379	−	0.997703i	$-0.521578\pi$
$509$	2.82141	−	0.371446i	0.125057	−	0.0164640i	0.192795	+	0.981239i	$0.438245\pi$
$510$		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
$515$	−0.0780879	+	0.0599190i	−0.00344097	+	0.00264035i
$516$		0			0
$517$	−0.465254	+	0.606331i	−0.0204619	+	0.0266664i
$518$	2.22217	+	0.469878i	0.0976363	+	0.0206453i
$519$		0			0
$520$	0.462613	+	15.7548i	0.0202869	+	0.690892i
$521$	17.3570	−	17.3570i	0.760426	−	0.760426i	−0.215973	−	0.976399i	$-0.569292\pi$
$521$	17.3570	−	17.3570i	0.760426	−	0.760426i	0.976399	+	0.215973i	$0.0692925\pi$
$522$		0			0
$523$	−11.8890	−	28.7025i	−0.519868	−	1.25507i	−0.937984	−	0.346679i	$-0.887309\pi$
$523$	−11.8890	−	28.7025i	−0.519868	−	1.25507i	0.418115	−	0.908394i	$-0.362691\pi$
$524$	31.6208	+	0.761047i	1.38136	+	0.0332465i
$525$		0			0
$526$	8.16922	+	5.60183i	0.356195	+	0.244251i
$527$	−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
$533$	−12.6708	−	1.66814i	−0.548832	−	0.0722551i
$534$		0			0
$535$	14.5663	+	3.90303i	0.629756	+	0.168743i
$536$	17.0682	+	20.9411i	0.737233	+	0.904520i
$537$		0			0
$538$	37.2044	−	12.1320i	1.60400	−	0.523048i
$539$	−2.95129	−	7.12505i	−0.127121	−	0.306898i
$540$		0			0
$541$	−21.3742	−	8.85350i	−0.918950	−	0.380642i	−0.127474	−	0.991842i	$-0.540687\pi$
$541$	−21.3742	−	8.85350i	−0.918950	−	0.380642i	−0.791476	+	0.611200i	$0.790687\pi$
$542$	26.2444	−	22.4629i	1.12730	−	0.964866i
$543$		0			0
$544$	8.74875	−	3.67821i	0.375100	−	0.157702i
$545$	−13.2709	+	7.66197i	−0.568463	+	0.328203i
$546$		0			0
$547$	16.0779	+	20.9532i	0.687443	+	0.895893i	0.998514	−	0.0544935i	$-0.0173544\pi$
$547$	16.0779	+	20.9532i	0.687443	+	0.895893i	−0.311071	+	0.950387i	$0.600688\pi$
$548$	28.2010	−	3.02441i	1.20469	−	0.129196i
$549$		0			0
$550$	−3.37589	+	3.75730i	−0.143949	+	0.160212i
$551$	7.13029	+	26.6106i	0.303761	+	1.13365i
$552$		0			0
$553$	−0.0690627	+	0.257745i	−0.00293684	+	0.0109604i
$554$	−19.7562	−	30.3516i	−0.839363	−	1.28952i
$555$		0			0
$556$	−31.0264	−	32.5568i	−1.31581	−	1.38071i
$557$	4.58647	+	1.89978i	0.194335	+	0.0804962i	0.477728	−	0.878508i	$-0.341460\pi$
$557$	4.58647	+	1.89978i	0.194335	+	0.0804962i	−0.283394	+	0.959004i	$0.591460\pi$
$558$		0			0
$559$	−36.9496			−1.56280
$560$	−0.697389	−	0.590539i	−0.0294701	−	0.0249548i
$561$		0			0
$562$	−6.71991	+	9.79973i	−0.283462	+	0.413377i
$563$	25.4583	−	3.35165i	1.07294	−	0.141255i	0.426703	−	0.904392i	$-0.359675\pi$
$563$	25.4583	−	3.35165i	1.07294	−	0.141255i	0.646237	+	0.763136i	$0.276342\pi$
$564$		0			0
$565$	0.956743	−	7.26719i	0.0402505	−	0.305733i
$566$	−26.7063	+	1.42796i	−1.12255	+	0.0600217i
$567$		0			0
$568$	0.417424	+	0.0988141i	0.0175147	+	0.00414615i
$569$	−6.41471	+	1.71882i	−0.268919	+	0.0720566i	−0.390759	−	0.920493i	$-0.627787\pi$
$569$	−6.41471	+	1.71882i	−0.268919	+	0.0720566i	0.121840	+	0.992550i	$0.461121\pi$
$570$		0			0
$571$	9.90036	+	7.59681i	0.414317	+	0.317917i	0.794800	−	0.606871i	$-0.207576\pi$
$571$	9.90036	+	7.59681i	0.414317	+	0.317917i	−0.380483	+	0.924788i	$0.624242\pi$
$572$	−9.15280	−	1.42981i	−0.382698	−	0.0597833i
$573$		0			0
$574$	0.562930	−	0.481819i	0.0234962	−	0.0201107i
$575$	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	$0.468340\pi$
$578$	15.2408	−	13.0448i	0.633932	−	0.542590i
$579$		0			0
$580$	−17.1575	−	2.68027i	−0.712427	−	0.111292i
$581$	0.662463	+	0.508326i	0.0274836	+	0.0210889i
$582$		0			0
$583$	−12.3873	+	3.31916i	−0.513029	+	0.137466i
$584$	−3.62562	+	15.3158i	−0.150029	+	0.633774i
$585$		0			0
$586$	−34.0600	+	1.82116i	−1.40701	+	0.0752313i
$587$	−2.57596	+	19.5663i	−0.106321	+	0.807589i	0.852330	+	0.523005i	$0.175189\pi$
$587$	−2.57596	+	19.5663i	−0.106321	+	0.807589i	−0.958651	+	0.284585i	$0.908144\pi$
$588$		0			0
$589$	−14.9633	+	1.96996i	−0.616554	+	0.0811709i
$590$	−3.48603	+	5.08372i	−0.143518	+	0.209293i
$591$		0			0
$592$	−3.09462	−	37.3013i	−0.127188	−	1.53308i
$593$	15.1394			0.621700			0.310850	−	0.950459i	$-0.399386\pi$
$593$	15.1394			0.621700			0.310850	+	0.950459i	$0.399386\pi$
$594$		0			0
$595$	0.354109	+	0.146677i	0.0145170	+	0.00601315i
$596$	20.1672	+	21.1619i	0.826082	+	0.866827i
$597$		0			0
$598$	5.53155	+	8.49813i	0.226202	+	0.347514i
$599$	12.0858	−	45.1048i	0.493812	−	1.84293i	−0.0427730	−	0.999085i	$-0.513619\pi$
$599$	12.0858	−	45.1048i	0.493812	−	1.84293i	0.536585	−	0.843846i	$-0.319714\pi$
$600$		0			0
$601$	−10.6746	−	39.8381i	−0.435426	−	1.62503i	−0.740045	−	0.672557i	$-0.765196\pi$
$601$	−10.6746	−	39.8381i	−0.435426	−	1.62503i	0.304619	−	0.952474i	$-0.401471\pi$
$602$	1.43178	−	1.59354i	0.0583550	−	0.0649479i
$603$		0			0
$604$	−46.0563	+	4.93929i	−1.87400	+	0.200977i
$605$	−7.92146	−	10.3234i	−0.322053	−	0.419708i
$606$		0			0
$607$	10.2159	−	5.89815i	0.414651	−	0.239399i	−0.278135	−	0.960542i	$-0.589716\pi$
$607$	10.2159	−	5.89815i	0.414651	−	0.239399i	0.692786	+	0.721143i	$0.256383\pi$
$608$	23.8903	−	0.126421i	0.968878	−	0.00512705i
$609$		0			0
$610$	−14.0798	+	12.0511i	−0.570074	+	0.487933i
$611$	−2.67182	−	1.10670i	−0.108090	−	0.0447724i
$612$		0			0
$613$	9.99410	+	24.1279i	0.403658	+	0.974516i	0.986770	+	0.162125i	$0.0518347\pi$
$613$	9.99410	+	24.1279i	0.403658	+	0.974516i	−0.583113	+	0.812391i	$0.698165\pi$
$614$	0.905451	−	0.295259i	0.0365410	−	0.0119157i
$615$		0			0
$616$	0.416331	−	0.339333i	0.0167745	−	0.0136721i
$617$	−3.50208	−	0.938379i	−0.140988	−	0.0377777i	0.187635	−	0.982239i	$-0.439918\pi$
$617$	−3.50208	−	0.938379i	−0.140988	−	0.0377777i	−0.328623	+	0.944461i	$0.606585\pi$
$618$		0			0
$619$	−48.6247	−	6.40156i	−1.95439	−	0.257300i	−0.955145	−	0.296137i	$-0.904301\pi$
$619$	−48.6247	−	6.40156i	−1.95439	−	0.257300i	−0.999246	+	0.0388370i	$0.987635\pi$
$620$	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
$626$	−3.01130	−	2.06492i	−0.120356	−	0.0825307i
$627$		0			0
$628$	25.4592	+	0.612750i	1.01593	+	0.0244514i
$629$	6.00770	+	14.5039i	0.239543	+	0.578307i
$630$		0			0
$631$	22.5852	−	22.5852i	0.899104	−	0.899104i	−0.0962531	−	0.995357i	$-0.530686\pi$
$631$	22.5852	−	22.5852i	0.899104	−	0.899104i	0.995357	+	0.0962531i	$0.0306858\pi$
$632$	4.39541	−	0.129064i	0.174840	−	0.00513389i
$633$		0			0
$634$	18.4208	+	3.89508i	0.731582	+	0.154693i
$635$	8.39150	−	10.9360i	0.333006	−	0.433982i
$636$		0			0
$637$	23.1519	−	17.7651i	0.917312	−	0.703878i
$638$	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
$643$	−8.91147	+	1.17322i	−0.351434	+	0.0462672i	−0.304177	−	0.952616i	$-0.598381\pi$
$643$	−8.91147	+	1.17322i	−0.351434	+	0.0462672i	−0.0472573	+	0.998883i	$0.515048\pi$
$644$	−0.580848	−	0.0907374i	−0.0228886	−	0.00357555i
$645$		0			0
$646$	−9.52661	+	3.10653i	−0.374819	+	0.122225i
$647$	−26.5185	+	26.5185i	−1.04255	+	1.04255i	−0.0434948	+	0.999054i	$0.513849\pi$
$647$	−26.5185	+	26.5185i	−1.04255	+	1.04255i	−0.999054	+	0.0434948i	$0.986151\pi$
$648$		0			0
$649$	−2.56181	−	2.56181i	−0.100560	−	0.100560i
$650$	−17.0393	−	8.65924i	−0.668336	−	0.339643i
$651$		0			0
$652$	−0.294214	−	0.179439i	−0.0115223	−	0.00702737i
$653$	0.0108861	+	0.0826878i	0.000426004	+	0.00323582i	0.991657	−	0.128908i	$-0.0411472\pi$
$653$	0.0108861	+	0.0826878i	0.000426004	+	0.00323582i	−0.991231	+	0.132144i	$0.957814\pi$
$654$		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
$659$	15.3957	+	20.0641i	0.599731	+	0.781585i	0.990294	−	0.138991i	$-0.0443860\pi$
$659$	15.3957	+	20.0641i	0.599731	+	0.781585i	−0.390562	+	0.920577i	$0.627719\pi$
$660$		0			0
$661$	24.2705	+	18.6234i	0.944011	+	0.724365i	0.961305	−	0.275485i	$-0.0888385\pi$
$661$	24.2705	+	18.6234i	0.944011	+	0.724365i	−0.0172941	+	0.999850i	$0.505505\pi$
$662$	11.3799	−	7.40732i	0.442292	−	0.287894i
$663$		0			0
$664$	4.89051	−	12.8621i	0.189789	−	0.499148i
$665$	0.682249	+	0.682249i	0.0264565	+	0.0264565i
$666$		0			0
$667$	−10.3214	+	4.27525i	−0.399644	+	0.165538i
$668$	−11.5449	+	26.0786i	−0.446685	+	1.00901i
$669$		0			0
$670$	17.6754	−	3.29530i	0.682860	−	0.127308i
$671$	−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
$677$	4.72908	−	35.9209i	0.181753	−	1.38055i	−0.620798	−	0.783970i	$-0.713191\pi$
$677$	4.72908	−	35.9209i	0.181753	−	1.38055i	0.802552	−	0.596583i	$-0.203475\pi$
$678$		0			0
$679$	0.613207	−	2.28852i	0.0235327	−	0.0878254i
$680$	0.640282	−	6.28373i	0.0245537	−	0.240970i
$681$		0			0
$682$	4.98476	+	2.53322i	0.190876	+	0.0970020i
$683$	2.07795	−	0.860717i	0.0795107	−	0.0329344i	−0.342574	−	0.939491i	$-0.611299\pi$
$683$	2.07795	−	0.860717i	0.0795107	−	0.0329344i	0.422084	+	0.906557i	$0.361299\pi$
$684$		0			0
$685$	7.22367	−	17.4395i	0.276002	−	0.666328i
$686$	−0.262481	+	3.38087i	−0.0100216	+	0.129082i
$687$		0			0
$688$	−31.9283	−	15.0635i	−1.21726	−	0.574289i
$689$	−24.2633	−	42.0253i	−0.924359	−	1.60104i
$690$		0			0
$691$	29.9555	−	22.9857i	1.13956	−	0.874416i	0.146177	−	0.989258i	$-0.453303\pi$
$691$	29.9555	−	22.9857i	1.13956	−	0.874416i	0.993384	+	0.114843i	$0.0366364\pi$
$692$	−3.38535	−	6.20368i	−0.128692	−	0.235829i
$693$		0			0
$694$	−2.71320	−	50.7434i	−0.102992	−	1.92619i
$695$	−28.9113	+	7.74676i	−1.09667	+	0.293851i
$696$		0			0
$697$	4.94697	+	1.32554i	0.187380	+	0.0502083i
$698$	8.45807	−	40.0002i	0.320143	−	1.51403i
$699$		0			0
$700$	1.03372	−	0.399319i	0.0390708	−	0.0150928i
$701$	−17.1061	+	41.2978i	−0.646089	+	1.55980i	0.172245	+	0.985054i	$0.444898\pi$
$701$	−17.1061	+	41.2978i	−0.646089	+	1.55980i	−0.818334	+	0.574743i	$0.805102\pi$
$702$		0			0
$703$			39.5190i			1.49049i
$704$	−7.32609	−	4.96688i	−0.276112	−	0.187196i
$705$		0			0
$706$	−1.69735	+	0.316443i	−0.0638805	+	0.0119095i
$707$	−0.0682280	−	0.518243i	−0.00256598	−	0.0194905i
$708$		0			0
$709$	20.9338	+	2.75599i	0.786186	+	0.103503i	0.512922	−	0.858435i	$-0.328563\pi$
$709$	20.9338	+	2.75599i	0.786186	+	0.103503i	0.273265	+	0.961939i	$0.411896\pi$
$710$	0.190804	−	0.212361i	0.00716076	−	0.00796977i
$711$		0			0
$712$	9.88756	−	41.7684i	0.370552	−	1.56534i
$713$	−1.58404	−	5.91173i	−0.0593228	−	0.221396i
$714$		0			0
$715$	−3.75325	+	4.89133i	−0.140364	+	0.182925i
$716$	−39.0160	−	23.7956i	−1.45810	−	0.889284i
$717$		0			0
$718$	−0.997400	+	12.8470i	−0.0372226	+	0.479445i
$719$			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
$722$	1.64085	+	0.127391i	0.0610661	+	0.00474098i
$723$		0			0
$724$	−6.96575	−	28.7463i	−0.258880	−	1.06835i
$725$	12.8196	−	16.7068i	0.476108	−	0.620475i
$726$		0			0
$727$	1.48029	+	5.52453i	0.0549010	+	0.204893i	0.987928	−	0.154912i	$-0.0495096\pi$
$727$	1.48029	+	5.52453i	0.0549010	+	0.204893i	−0.933027	+	0.359806i	$0.882843\pi$
$728$	1.64801	+	1.18938i	0.0610794	+	0.0440812i
$729$		0			0
$730$	7.79181	+	7.00086i	0.288388	+	0.259113i
$731$	14.6805	+	1.93272i	0.542976	+	0.0714842i
$732$		0			0
$733$	−2.43834	−	18.5210i	−0.0900622	−	0.684090i	−0.975605	−	0.219533i	$-0.929547\pi$
$733$	−2.43834	−	18.5210i	−0.0900622	−	0.684090i	0.885543	−	0.464557i	$-0.153787\pi$
$734$	−0.475555	−	2.55080i	−0.0175531	−	0.0941516i
$735$		0			0
$736$	1.31536	+	9.59836i	0.0484847	+	0.353800i
$737$			10.5677i			0.389265i
$738$		0			0
$739$	12.0562	−	29.1063i	0.443496	−	1.07069i	−0.531218	−	0.847235i	$-0.678265\pi$
$739$	12.0562	−	29.1063i	0.443496	−	1.07069i	0.974714	−	0.223458i	$-0.0717346\pi$
$740$	−22.7784	−	10.0839i	−0.837350	−	0.370690i
$741$		0			0
$742$	2.75264	+	0.582047i	0.101053	+	0.0213676i
$743$	−9.54537	−	2.55767i	−0.350186	−	0.0938319i	0.0794385	−	0.996840i	$-0.474687\pi$
$743$	−9.54537	−	2.55767i	−0.350186	−	0.0938319i	−0.429624	+	0.903008i	$0.641354\pi$
$744$		0			0
$745$	18.7924	−	5.03540i	0.688500	−	0.184483i
$746$	17.1108	−	0.914898i	0.626470	−	0.0334968i
$747$		0			0
$748$	3.56171	+	1.04683i	0.130229	+	0.0382760i
$749$	1.54268	−	1.18374i	0.0563685	−	0.0432531i
$750$		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	$0.788375\pi$
$752$	−1.85755	−	2.04554i	−0.0677381	−	0.0745933i
$753$		0			0
$754$	38.5055	+	2.98945i	1.40229	+	0.108869i
$755$	−11.7973	+	28.4812i	−0.429347	+	1.03654i
$756$		0			0
$757$	−8.34229	+	3.45549i	−0.303206	+	0.125592i	−0.529099	−	0.848560i	$-0.677470\pi$
$757$	−8.34229	+	3.45549i	−0.303206	+	0.125592i	0.225893	+	0.974152i	$0.427470\pi$
$758$	19.4517	−	38.2762i	0.706517	−	1.39025i
$759$		0			0
$760$	7.54243	−	13.9972i	0.273593	−	0.507733i
$761$	4.96391	−	18.5256i	0.179942	−	0.671551i	−0.815715	−	0.578454i	$-0.803656\pi$
$761$	4.96391	−	18.5256i	0.179942	−	0.671551i	0.995657	−	0.0930979i	$-0.0296769\pi$
$762$		0			0
$763$	−0.257913	+	1.95904i	−0.00933707	+	0.0709221i
$764$	−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	$0.867992\pi$
$770$	−0.0655138	−	0.351405i	−0.00236095	−	0.0126638i
$771$		0			0
$772$	−25.5368	+	9.86473i	−0.919090	+	0.355039i
$773$	24.7943	−	10.2701i	0.891790	−	0.369391i	0.110732	−	0.993850i	$-0.464680\pi$
$773$	24.7943	−	10.2701i	0.891790	−	0.369391i	0.781058	+	0.624459i	$0.214680\pi$
$774$		0			0
$775$	8.15758	+	8.15758i	0.293029	+	0.293029i
$776$	−39.0268	+	1.14596i	−1.40098	+	0.0411376i
$777$		0			0
$778$	26.7371	+	41.0763i	0.958572	+	1.47266i
$779$	10.2282	+	7.84837i	0.366463	+	0.281197i
$780$		0			0
$781$	0.102147	+	0.133121i	0.00365511	+	0.00476343i
$782$	−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
$787$	1.91884	+	14.5750i	0.0683993	+	0.519544i	0.991008	+	0.133806i	$0.0427199\pi$
$787$	1.91884	+	14.5750i	0.0683993	+	0.519544i	−0.922608	+	0.385738i	$0.873947\pi$
$788$	8.56473	+	35.3449i	0.305106	+	1.25911i
$789$		0			0
$790$	1.32587	−	2.60899i	0.0471723	−	0.0928236i
$791$	−0.668325	−	0.668325i	−0.0237629	−	0.0237629i
$792$		0			0
$793$	29.1451	−	29.1451i	1.03497	−	1.03497i
$794$	9.08063	+	27.8470i	0.322260	+	0.988253i
$795$		0			0
$796$	8.39941	−	6.12973i	0.297709	−	0.217263i
$797$	−5.07542	+	0.668191i	−0.179780	+	0.0236686i	−0.219879	−	0.975527i	$-0.570566\pi$
$797$	−5.07542	+	0.668191i	−0.179780	+	0.0236686i	0.0400984	+	0.999196i	$0.487233\pi$
$798$		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
$803$	−4.88437	+	3.74791i	−0.172366	+	0.132261i
$804$		0			0
$805$	−0.238186	+	0.310410i	−0.00839494	+	0.0109405i
$806$	−4.37711	+	20.7004i	−0.154177	+	0.729141i
$807$		0			0
$808$	−7.85811	+	3.52859i	−0.276447	+	0.124135i
$809$	25.1234	−	25.1234i	0.883292	−	0.883292i	−0.110576	−	0.993868i	$-0.535269\pi$
$809$	25.1234	−	25.1234i	0.883292	−	0.883292i	0.993868	+	0.110576i	$0.0352695\pi$
$810$		0			0
$811$	9.44355	+	22.7987i	0.331608	+	0.800572i	0.998465	+	0.0553866i	$0.0176391\pi$
$811$	9.44355	+	22.7987i	0.331608	+	0.800572i	−0.666857	+	0.745186i	$0.732361\pi$
$812$	−1.62100	+	1.54481i	−0.0568859	+	0.0542120i
$813$		0			0
$814$	8.28005	−	12.0749i	0.290216	−	0.423225i
$815$	−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
$821$	−14.9037	−	1.96211i	−0.520143	−	0.0684782i	−0.134116	−	0.990966i	$-0.542820\pi$
$821$	−14.9037	−	1.96211i	−0.520143	−	0.0684782i	−0.386027	+	0.922487i	$0.626153\pi$
$822$		0			0
$823$	7.66921	+	2.05496i	0.267332	+	0.0716314i	0.389995	−	0.920817i	$-0.372477\pi$
$823$	7.66921	+	2.05496i	0.267332	+	0.0716314i	−0.122663	+	0.992448i	$0.539143\pi$
$824$	0.200349	−	0.0600387i	0.00697950	−	0.00209155i
$825$		0			0
$826$	0.246418	+	0.755674i	0.00857397	+	0.0262932i
$827$	8.68350	+	20.9638i	0.301955	+	0.728983i	0.999917	+	0.0128492i	$0.00409015\pi$
$827$	8.68350	+	20.9638i	0.301955	+	0.728983i	−0.697963	+	0.716134i	$0.745910\pi$
$828$		0			0
$829$	12.1233	+	5.02164i	0.421060	+	0.174409i	0.583145	−	0.812368i	$-0.301822\pi$
$829$	12.1233	+	5.02164i	0.421060	+	0.174409i	−0.162085	+	0.986777i	$0.551822\pi$
$830$	−5.95507	−	6.95757i	−0.206704	−	0.241501i
$831$		0			0
$832$	10.9792	−	31.6415i	0.380636	−	1.09697i
$833$	−10.1277	+	5.84724i	−0.350905	+	0.202595i
$834$		0			0
$835$	11.5549	+	15.0586i	0.399872	+	0.521124i
$836$	7.27500	+	5.86573i	0.251611	+	0.202870i
$837$		0			0
$838$	−35.2892	−	31.7069i	−1.21904	−	1.09530i
$839$	3.54691	+	13.2373i	0.122453	+	0.457001i	0.999736	−	0.0229725i	$-0.00731301\pi$
$839$	3.54691	+	13.2373i	0.122453	+	0.457001i	−0.877283	+	0.479973i	$0.840646\pi$
$840$		0			0
$841$	−3.50747	+	13.0901i	−0.120947	+	0.451382i
$842$	−3.99017	+	2.59726i	−0.137510	+	0.0895073i
$843$		0			0
$844$	−12.2081	−	0.293824i	−0.420221	−	0.0101138i
$845$	−5.56705	−	2.30595i	−0.191512	−	0.0793271i
$846$		0			0
$847$	−1.67789			−0.0576529
$848$	−3.83337	−	46.2059i	−0.131638	−	1.58672i
$849$		0			0
$850$	6.31694	+	4.33168i	0.216669	+	0.148575i
$851$	−15.8886	+	2.09177i	−0.544653	+	0.0717049i
$852$		0			0
$853$	−1.05384	+	8.00474i	−0.0360829	+	0.274077i	0.963887	+	0.266312i	$0.0858051\pi$
$853$	−1.05384	+	8.00474i	−0.0360829	+	0.274077i	−0.999970	+	0.00776524i	$0.997528\pi$
$854$	0.127594	+	2.38632i	0.00436619	+	0.0816581i
$855$		0			0
$856$	−25.9840	−	18.7527i	−0.888115	−	0.640955i
$857$	−20.5111	+	5.49593i	−0.700645	+	0.187737i	−0.591520	−	0.806291i	$-0.701472\pi$
$857$	−20.5111	+	5.49593i	−0.700645	+	0.187737i	−0.109126	+	0.994028i	$0.534805\pi$
$858$		0			0
$859$	23.7276	+	18.2069i	0.809577	+	0.621210i	0.928348	−	0.371712i	$-0.121229\pi$
$859$	23.7276	+	18.2069i	0.809577	+	0.621210i	−0.118772	+	0.992922i	$0.537896\pi$
$860$	−18.9791	+	13.8506i	−0.647181	+	0.472301i
$861$		0			0
$862$	−19.0330	−	22.2370i	−0.648265	−	0.757396i
$863$	50.2980			1.71216			0.856082	−	0.516840i	$-0.172892\pi$
$863$	50.2980			1.71216			0.856082	+	0.516840i	$0.172892\pi$
$864$		0			0
$865$	−4.70351			−0.159924
$866$	1.84294	+	2.15318i	0.0626255	+	0.0731681i
$867$		0			0
$868$	−0.723145	−	0.990906i	−0.0245451	−	0.0336335i
$869$	1.36463	+	1.04711i	0.0462918	+	0.0355209i
$870$		0			0
$871$	−38.6252	+	10.3496i	−1.30876	+	0.350682i
$872$	32.1450	−	5.19595i	1.08857	−	0.175957i
$873$		0			0
$874$	−0.546150	−	10.2143i	−0.0184738	−	0.345504i
$875$	0.245365	−	1.86373i	0.00829483	−	0.0630055i
$876$		0			0
$877$	24.3855	−	3.21041i	0.823439	−	0.108408i	0.292980	−	0.956118i	$-0.405353\pi$
$877$	24.3855	−	3.21041i	0.823439	−	0.108408i	0.530459	+	0.847711i	$0.322020\pi$
$878$	17.8850	+	12.2641i	0.603588	+	0.413895i
$879$		0			0
$880$	−5.23728	+	2.69651i	−0.176549	+	0.0908995i
$881$	−14.3584			−0.483747			−0.241873	−	0.970308i	$-0.577762\pi$
$881$	−14.3584			−0.483747			−0.241873	+	0.970308i	$0.577762\pi$
$882$		0			0
$883$	38.1415	+	15.7987i	1.28357	+	0.531670i	0.917061	−	0.398746i	$-0.130555\pi$
$883$	38.1415	+	15.7987i	1.28357	+	0.531670i	0.366504	+	0.930417i	$0.380555\pi$
$884$	−0.337996	+	14.0434i	−0.0113680	+	0.472331i
$885$		0			0
$886$	−6.29175	+	4.09538i	−0.211375	+	0.137587i
$887$	2.79505	−	10.4313i	0.0938486	−	0.350248i	−0.902994	−	0.429654i	$-0.858636\pi$
$887$	2.79505	−	10.4313i	0.0938486	−	0.350248i	0.996842	+	0.0794060i	$0.0253023\pi$
$888$		0			0
$889$	−0.460038	−	1.71688i	−0.0154292	−	0.0575825i
$890$	−21.2493	−	19.0923i	−0.712280	−	0.639976i
$891$		0			0
$892$	13.2601	−	16.4459i	0.443981	−	0.550650i
$893$	1.77597	+	2.31449i	0.0594307	+	0.0774516i
$894$		0			0
$895$	−26.3401	+	15.2074i	−0.880451	+	0.508329i
$896$	0.939177	+	1.69960i	0.0313757	+	0.0567797i
$897$		0			0
$898$	−11.3704	−	13.2845i	−0.379435	−	0.443310i
$899$	−21.5369	−	8.92087i	−0.718295	−	0.297528i
$900$		0			0
$901$	7.44185	+	17.9662i	0.247924	+	0.598542i
$902$	−1.48080	−	4.54107i	−0.0493052	−	0.151201i
$903$		0			0
$904$	−7.38849	+	13.7115i	−0.245738	+	0.456039i
$905$	−19.0145	−	5.09493i	−0.632065	−	0.169361i
$906$		0			0
$907$	−38.5303	−	5.07261i	−1.27938	−	0.168433i	−0.539965	−	0.841687i	$-0.681563\pi$
$907$	−38.5303	−	5.07261i	−1.27938	−	0.168433i	−0.739411	+	0.673254i	$0.764896\pi$
$908$	−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
$914$	−19.6644	+	28.6768i	−0.650440	+	0.948546i
$915$		0			0
$916$	1.43573	+	1.50655i	0.0474379	+	0.0497777i
$917$	−1.03876	−	2.50778i	−0.0343028	−	0.0828143i
$918$		0			0
$919$	9.98940	−	9.98940i	0.329520	−	0.329520i	−0.522884	−	0.852404i	$-0.675144\pi$
$919$	9.98940	−	9.98940i	0.329520	−	0.329520i	0.852404	+	0.522884i	$0.175144\pi$
$920$	6.02679	+	2.29154i	0.198698	+	0.0755499i
$921$		0			0
$922$	5.27804	−	24.9611i	0.173823	−	0.822050i
$923$	−0.386521	+	0.503724i	−0.0127225	+	0.0165803i
$924$		0			0
$925$	23.9656	−	18.3894i	0.787984	−	0.604641i
$926$	−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
$931$	−29.1868	+	3.84252i	−0.956560	+	0.125933i
$932$	−24.8735	−	34.0835i	−0.814758	−	1.11644i
$933$		0			0
$934$	14.2037	+	43.5575i	0.464758	+	1.42524i
$935$	1.74705	−	1.74705i	0.0571348	−	0.0571348i
$936$		0			0
$937$	15.4659	+	15.4659i	0.505248	+	0.505248i	0.913064	−	0.407816i	$-0.133710\pi$
$937$	15.4659	+	15.4659i	0.505248	+	0.505248i	−0.407816	+	0.913064i	$0.633710\pi$
$938$	1.05036	−	2.06685i	0.0342954	−	0.0674850i
$939$		0			0
$940$	−1.78722	+	0.433077i	−0.0582927	+	0.0141254i
$941$	−3.30725	−	25.1210i	−0.107813	−	0.818922i	−0.956849	−	0.290586i	$-0.906150\pi$
$941$	−3.30725	−	25.1210i	−0.107813	−	0.818922i	0.849036	−	0.528336i	$-0.177184\pi$
$942$		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
$947$	−25.8695	−	33.7138i	−0.840645	−	1.09555i	−0.994215	−	0.107412i	$-0.965744\pi$
$947$	−25.8695	−	33.7138i	−0.840645	−	1.09555i	0.153569	−	0.988138i	$-0.450923\pi$
$948$		0			0
$949$	−18.4823	−	14.1820i	−0.599961	−	0.460366i
$950$	10.5184	+	16.1595i	0.341262	+	0.524283i
$951$		0			0
$952$	−0.592560	−	0.558753i	−0.0192050	−	0.0181093i
$953$	11.7909	+	11.7909i	0.381943	+	0.381943i	0.871802	−	0.489859i	$-0.162952\pi$
$953$	11.7909	+	11.7909i	0.381943	+	0.381943i	−0.489859	+	0.871802i	$0.662952\pi$
$954$		0			0
$955$	−26.9694	+	11.1711i	−0.872710	+	0.361488i
$956$	−9.23045	−	23.8948i	−0.298534	−	0.772814i
$957$		0			0
$958$	−10.9610	−	58.7930i	−0.354134	−	1.89952i
$959$	−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
$965$	−2.37814	+	18.0638i	−0.0765550	+	0.581493i
$966$		0			0
$967$	5.66820	−	21.1540i	0.182277	−	0.680267i	−0.812920	−	0.582375i	$-0.802123\pi$
$967$	5.66820	−	21.1540i	0.182277	−	0.680267i	0.995197	−	0.0978919i	$-0.0312099\pi$
$968$	7.93729	+	26.4867i	0.255114	+	0.851316i
$969$		0			0
$970$	−11.7724	+	23.1652i	−0.377989	+	0.743789i
$971$	−52.9107	+	21.9163i	−1.69798	+	0.703328i	−0.999919	−	0.0127064i	$-0.995955\pi$
$971$	−52.9107	+	21.9163i	−1.69798	+	0.703328i	−0.698065	+	0.716035i	$0.745955\pi$
$972$		0			0
$973$	−1.47696	+	3.56569i	−0.0473491	+	0.114311i
$974$	17.8174	+	1.38329i	0.570907	+	0.0443235i
$975$		0			0
$976$	37.0663	−	13.3027i	1.18646	−	0.425809i
$977$	−10.6302	−	18.4121i	−0.340091	−	0.589054i	0.644359	−	0.764723i	$-0.277124\pi$
$977$	−10.6302	−	18.4121i	−0.340091	−	0.589054i	−0.984449	+	0.175669i	$0.943791\pi$
$978$		0			0
$979$	13.3203	−	10.2211i	0.425720	−	0.326667i
$980$	5.23267	−	17.8035i	0.167152	−	0.568712i
$981$		0			0
$982$	9.14412	−	0.488927i	0.291800	−	0.0156023i
$983$	−10.1671	+	2.72427i	−0.324281	+	0.0868908i	−0.417287	−	0.908775i	$-0.637019\pi$
$983$	−10.1671	+	2.72427i	−0.324281	+	0.0868908i	0.0930062	+	0.995666i	$0.470352\pi$
$984$		0			0
$985$	23.3793	+	6.26447i	0.744927	+	0.199602i
$986$	−15.1423	−	3.20184i	−0.482228	−	0.101967i
$987$		0			0
$988$	−14.3146	+	32.3351i	−0.455407	+	1.02872i
$989$	−5.78439	+	13.9648i	−0.183933	+	0.444054i
$990$		0			0
$991$		−	28.2543i		−	0.897526i	−0.893651	−	0.448763i	$-0.851865\pi$
$991$		−	28.2543i		−	0.897526i	0.893651	−	0.448763i	$-0.148135\pi$
$992$	−12.2213	+	16.1029i	−0.388028	+	0.511267i
$993$		0			0
$994$	−0.00674682	−	0.0361888i	−0.000213996	−	0.00114784i
$995$	−0.903293	−	6.86119i	−0.0286363	−	0.217514i
$996$		0			0
$997$	−24.2150	−	3.18796i	−0.766897	−	0.100964i	−0.263079	−	0.964774i	$-0.584738\pi$
$997$	−24.2150	−	3.18796i	−0.766897	−	0.100964i	−0.503817	+	0.863810i	$0.668071\pi$
$998$	−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.35.10		368
3.2	odd	2		288.2.bf.a.227.37	yes	368
9.4	even	3		288.2.bf.a.131.22	yes	368
9.5	odd	6	inner	864.2.bn.a.611.25		368
32.11	odd	8	inner	864.2.bn.a.683.25		368
96.11	even	8		288.2.bf.a.11.22	✓	368
288.139	odd	24		288.2.bf.a.203.37	yes	368
288.203	even	24	inner	864.2.bn.a.395.10		368

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
288.2.bf.a.11.22	✓	368	96.11	even	8
288.2.bf.a.131.22	yes	368	9.4	even	3
288.2.bf.a.203.37	yes	368	288.139	odd	24
288.2.bf.a.227.37	yes	368	3.2	odd	2
864.2.bn.a.35.10		368	1.1	even	1	trivial
864.2.bn.a.395.10		368	288.203	even	24	inner
864.2.bn.a.611.25		368	9.5	odd	6	inner
864.2.bn.a.683.25		368	32.11	odd	8	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:	\( N \)	\(=\)	\( 864 = 2^{5} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	864.bn (of order \(24\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.07440 + 0.919596i) q^{2} +(0.308687 - 1.97603i) q^{4} +(-1.05601 - 0.810304i) q^{5} +(-0.165787 + 0.0444224i) q^{7} +(1.48550 + 2.40693i) q^{8} +(1.87973 - 0.100507i) q^{10} +(-0.144412 + 1.09692i) q^{11} +(-4.15071 + 0.546451i) q^{13} +(0.137271 - 0.200184i) q^{14} +(-3.80942 - 1.21995i) q^{16} +1.67770 q^{17} +(3.90182 + 1.61619i) q^{19} +(-1.92716 + 1.83658i) q^{20} +(-0.853565 - 1.31133i) q^{22} +(-0.443260 + 1.65427i) q^{23} +(-0.835534 - 3.11825i) q^{25} +(3.95702 - 4.40408i) q^{26} +(0.0366040 + 0.341313i) q^{28} +(3.97106 + 5.17518i) q^{29} +(-3.09485 + 1.78681i) q^{31} +(5.21472 - 2.19241i) q^{32} +(-1.80253 + 1.54281i) q^{34} +(0.211068 + 0.0874271i) q^{35} +(3.58091 + 8.64508i) q^{37} +(-5.67837 + 1.85166i) q^{38} +(0.381642 - 3.74544i) q^{40} +(2.94866 + 0.790091i) q^{41} +(8.75033 + 1.15200i) q^{43} +(2.12297 + 0.623968i) q^{44} +(-1.04502 - 2.18497i) q^{46} +(0.598230 + 0.345388i) q^{47} +(-6.03667 + 3.48527i) q^{49} +(3.76523 + 2.58191i) q^{50} +(-0.201463 + 8.37063i) q^{52} +(4.43574 + 10.7088i) q^{53} +(1.04134 - 1.04134i) q^{55} +(-0.353197 - 0.333047i) q^{56} +(-9.02560 - 1.90847i) q^{58} +(-1.99344 + 2.59791i) q^{59} +(-7.81078 + 5.99342i) q^{61} +(1.68197 - 4.76576i) q^{62} +(-3.58659 + 7.15097i) q^{64} +(4.82597 + 2.78628i) q^{65} +(9.46982 - 1.24673i) q^{67} +(0.517885 - 3.31520i) q^{68} +(-0.307169 + 0.100165i) q^{70} +(0.107240 - 0.107240i) q^{71} +(3.93478 + 3.93478i) q^{73} +(-11.7973 - 5.99532i) q^{74} +(4.39808 - 7.21123i) q^{76} +(-0.0247862 - 0.188270i) q^{77} +(0.777341 - 1.34639i) q^{79} +(3.03425 + 4.37507i) q^{80} +(-3.89461 + 1.86270i) q^{82} +(-2.96167 - 3.85972i) q^{83} +(-1.77167 - 1.35945i) q^{85} +(-10.4608 + 6.80905i) q^{86} +(-2.85473 + 1.28188i) q^{88} +(-10.7307 - 10.7307i) q^{89} +(0.663857 - 0.274979i) q^{91} +(3.13206 + 1.38655i) q^{92} +(-0.960358 + 0.179043i) q^{94} +(-2.81075 - 4.86836i) q^{95} +(-6.90201 + 11.9546i) q^{97} +(3.28078 - 9.29588i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 368 q + 12 q^{2} - 4 q^{4} + 12 q^{5} - 4 q^{7} - 16 q^{10} + 12 q^{11} - 4 q^{13} + 12 q^{14} - 4 q^{16} - 16 q^{19} + 12 q^{20} - 4 q^{22} + 12 q^{23} - 4 q^{25} - 16 q^{28} + 12 q^{29} + 12 q^{32} - 12 q^{34}+ \cdots - 8 q^{97}+O(q^{100}) \) 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

Modular forms

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