LMFDB - Embedded newform 567.2.be.a.503.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [567,2,Mod(62,567)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("567.62"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(567, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.be (of order $18$, degree $6$, 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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			503.5
Character	$\chi$	$=$	567.503
Dual form			567.2.be.a.62.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.492726 + 1.35375i) q^{2} +(-0.0577819 - 0.0484848i) q^{4} +(-0.440273 + 2.49691i) q^{5} +(-1.60923 + 2.10009i) q^{7} +(-2.40115 + 1.38630i) q^{8} +(-3.16327 - 1.82631i) q^{10} +(-2.06906 + 0.364832i) q^{11} +(0.0331071 + 0.0909611i) q^{13} +(-2.05009 - 3.21327i) q^{14} +(-0.719801 - 4.08219i) q^{16} +(3.94280 - 6.82913i) q^{17} +(1.53773 - 0.887809i) q^{19} +(0.146502 - 0.122930i) q^{20} +(0.525589 - 2.98077i) q^{22} +(-3.82906 + 4.56329i) q^{23} +(-1.34226 - 0.488541i) q^{25} -0.139452 q^{26} +(0.194807 - 0.0433240i) q^{28} +(-0.573096 + 1.57457i) q^{29} +(0.916092 - 1.09176i) q^{31} +(0.419987 + 0.0740550i) q^{32} +(7.30224 + 8.70247i) q^{34} +(-4.53523 - 4.94272i) q^{35} +(-1.88241 + 3.26042i) q^{37} +(0.444195 + 2.51916i) q^{38} +(-2.40431 - 6.60580i) q^{40} +(-2.60026 + 0.946417i) q^{41} +(1.03518 + 5.87080i) q^{43} +(0.137243 + 0.0792375i) q^{44} +(-4.29090 - 7.43206i) q^{46} +(-3.23438 + 2.71396i) q^{47} +(-1.82075 - 6.75906i) q^{49} +(1.32273 - 1.57637i) q^{50} +(0.00249724 - 0.00686110i) q^{52} -9.25188i q^{53} -5.32689i q^{55} +(0.952641 - 7.27350i) q^{56} +(-1.84920 - 1.55166i) q^{58} +(-1.28271 + 7.27458i) q^{59} +(7.80852 + 9.30583i) q^{61} +(1.02659 + 1.77810i) q^{62} +(3.83798 - 6.64757i) q^{64} +(-0.241698 + 0.0426179i) q^{65} +(-10.6299 + 3.86898i) q^{67} +(-0.558931 + 0.203434i) q^{68} +(8.92585 - 3.70418i) q^{70} +(11.9234 + 6.88396i) q^{71} +(-12.0252 + 6.94274i) q^{73} +(-3.48630 - 4.15481i) q^{74} +(-0.131898 - 0.0232572i) q^{76} +(2.56342 - 4.93232i) q^{77} +(-5.82433 - 2.11988i) q^{79} +10.5098 q^{80} -3.98644i q^{82} +(8.67692 + 3.15814i) q^{83} +(15.3158 + 12.8515i) q^{85} +(-8.45769 - 1.49132i) q^{86} +(4.46236 - 3.74436i) q^{88} +(-6.28476 - 10.8855i) q^{89} +(-0.244303 - 0.0768495i) q^{91} +(0.442501 - 0.0780248i) q^{92} +(-2.08038 - 5.71579i) q^{94} +(1.53976 + 4.23045i) q^{95} +(-15.0854 + 2.65997i) q^{97} +(10.0472 + 0.865519i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) $ 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{11}{18}\right)$

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 $

$2$	−0.492726	+	1.35375i	−0.348410	+	0.957249i	0.634461	+	0.772955i	$0.281222\pi$
$2$	−0.492726	+	1.35375i	−0.348410	+	0.957249i	−0.982871	+	0.184294i	$0.941000\pi$
$3$		0			0
$3$		0			0
$4$	−0.0577819	−	0.0484848i	−0.0288910	−	0.0242424i
$5$	−0.440273	+	2.49691i	−0.196896	+	1.11665i	0.712797	+	0.701370i	$0.247428\pi$
$5$	−0.440273	+	2.49691i	−0.196896	+	1.11665i	−0.909693	+	0.415282i	$0.863683\pi$
$6$		0			0
$7$	−1.60923	+	2.10009i	−0.608232	+	0.793759i
$7$	−1.60923	+	2.10009i	−0.608232	+	0.793759i
$8$	−2.40115	+	1.38630i	−0.848933	+	0.490132i
$9$		0			0
$10$	−3.16327	−	1.82631i	−1.00031	−	0.577531i
$11$	−2.06906	+	0.364832i	−0.623846	+	0.110001i	−0.476631	−	0.879104i	$-0.658142\pi$
$11$	−2.06906	+	0.364832i	−0.623846	+	0.110001i	−0.147215	+	0.989104i	$0.547031\pi$
$12$		0			0
$13$	0.0331071	+	0.0909611i	0.00918227	+	0.0252281i	0.944199	−	0.329375i	$-0.106838\pi$
$13$	0.0331071	+	0.0909611i	0.00918227	+	0.0252281i	−0.935017	+	0.354603i	$0.884616\pi$
$14$	−2.05009	−	3.21327i	−0.547911	−	0.858783i
$15$		0			0
$16$	−0.719801	−	4.08219i	−0.179950	−	1.02055i
$17$	3.94280	−	6.82913i	0.956269	−	1.65631i	0.224831	−	0.974398i	$-0.427817\pi$
$17$	3.94280	−	6.82913i	0.956269	−	1.65631i	0.731438	−	0.681908i	$-0.238850\pi$
$18$		0			0
$19$	1.53773	−	0.887809i	0.352780	−	0.203677i	−0.313129	−	0.949711i	$-0.601377\pi$
$19$	1.53773	−	0.887809i	0.352780	−	0.203677i	0.665909	+	0.746033i	$0.268044\pi$
$20$	0.146502	−	0.122930i	0.0327588	−	0.0274879i
$21$		0			0
$22$	0.525589	−	2.98077i	0.112056	−	0.635501i
$23$	−3.82906	+	4.56329i	−0.798414	+	0.951513i	−0.999607	−	0.0280391i	$-0.991074\pi$
$23$	−3.82906	+	4.56329i	−0.798414	+	0.951513i	0.201193	+	0.979552i	$0.435518\pi$
$24$		0			0
$25$	−1.34226	−	0.488541i	−0.268451	−	0.0977083i
$26$	−0.139452			−0.0273487
$27$		0			0
$28$	0.194807	−	0.0433240i	0.0368150	−	0.00818746i
$29$	−0.573096	+	1.57457i	−0.106421	+	0.292390i	−0.981461	−	0.191661i	$-0.938613\pi$
$29$	−0.573096	+	1.57457i	−0.106421	+	0.292390i	0.875040	+	0.484051i	$0.160835\pi$
$30$		0			0
$31$	0.916092	−	1.09176i	0.164535	−	0.196085i	−0.677477	−	0.735544i	$-0.736927\pi$
$31$	0.916092	−	1.09176i	0.164535	−	0.196085i	0.842012	+	0.539459i	$0.181371\pi$
$32$	0.419987	+	0.0740550i	0.0742439	+	0.0130912i
$33$		0			0
$34$	7.30224	+	8.70247i	1.25232	+	1.49246i
$35$	−4.53523	−	4.94272i	−0.766594	−	0.835472i
$36$		0			0
$37$	−1.88241	+	3.26042i	−0.309466	+	0.536010i	−0.978246	−	0.207450i	$-0.933483\pi$
$37$	−1.88241	+	3.26042i	−0.309466	+	0.536010i	0.668780	+	0.743460i	$0.266817\pi$
$38$	0.444195	+	2.51916i	0.0720580	+	0.408661i
$39$		0			0
$40$	−2.40431	−	6.60580i	−0.380155	−	1.04447i
$41$	−2.60026	+	0.946417i	−0.406092	+	0.147806i	−0.536987	−	0.843591i	$-0.680437\pi$
$41$	−2.60026	+	0.946417i	−0.406092	+	0.147806i	0.130894	+	0.991396i	$0.458215\pi$
$42$		0			0
$43$	1.03518	+	5.87080i	0.157864	+	0.895289i	0.956121	+	0.292973i	$0.0946445\pi$
$43$	1.03518	+	5.87080i	0.157864	+	0.895289i	−0.798257	+	0.602317i	$0.794244\pi$
$44$	0.137243	+	0.0792375i	0.0206902	+	0.0119455i
$45$		0			0
$46$	−4.29090	−	7.43206i	−0.632659	−	1.09580i
$47$	−3.23438	+	2.71396i	−0.471782	+	0.395872i	−0.847444	−	0.530885i	$-0.821860\pi$
$47$	−3.23438	+	2.71396i	−0.471782	+	0.395872i	0.375662	+	0.926757i	$0.377415\pi$
$48$		0			0
$49$	−1.82075	−	6.75906i	−0.260107	−	0.965580i
$50$	1.32273	−	1.57637i	0.187062	−	0.222932i
$51$		0			0
$52$	0.00249724	−	0.00686110i	0.000346304	−	0.000951464i
$53$		−	9.25188i		−	1.27084i	−0.772165	−	0.635422i	$-0.780826\pi$
$53$		−	9.25188i		−	1.27084i	0.772165	−	0.635422i	$-0.219174\pi$
$54$		0			0
$55$		−	5.32689i		−	0.718278i
$56$	0.952641	−	7.27350i	0.127302	−	0.971962i
$57$		0			0
$58$	−1.84920	−	1.55166i	−0.242812	−	0.203743i
$59$	−1.28271	+	7.27458i	−0.166994	+	0.947070i	0.779991	+	0.625791i	$0.215224\pi$
$59$	−1.28271	+	7.27458i	−0.166994	+	0.947070i	−0.946985	+	0.321279i	$0.895887\pi$
$60$		0			0
$61$	7.80852	+	9.30583i	0.999778	+	1.19149i	0.981462	+	0.191657i	$0.0613861\pi$
$61$	7.80852	+	9.30583i	0.999778	+	1.19149i	0.0183160	+	0.999832i	$0.494169\pi$
$62$	1.02659	+	1.77810i	0.130377	+	0.225819i
$63$		0			0
$64$	3.83798	−	6.64757i	0.479747	−	0.830947i
$65$	−0.241698	+	0.0426179i	−0.0299789	+	0.00528609i
$66$		0			0
$67$	−10.6299	+	3.86898i	−1.29865	+	0.472671i	−0.896558	−	0.442926i	$-0.853940\pi$
$67$	−10.6299	+	3.86898i	−1.29865	+	0.472671i	−0.402096	+	0.915597i	$0.631718\pi$
$68$	−0.558931	+	0.203434i	−0.0677804	+	0.0246700i
$69$		0			0
$70$	8.92585	−	3.70418i	1.06684	−	0.442735i
$71$	11.9234	+	6.88396i	1.41504	+	0.816976i	0.995858	−	0.0909251i	$-0.0289824\pi$
$71$	11.9234	+	6.88396i	1.41504	+	0.816976i	0.419185	+	0.907901i	$0.362316\pi$
$72$		0			0
$73$	−12.0252	+	6.94274i	−1.40744	+	0.812587i	−0.995141	−	0.0984612i	$-0.968608\pi$
$73$	−12.0252	+	6.94274i	−1.40744	+	0.812587i	−0.412301	+	0.911048i	$0.635275\pi$
$74$	−3.48630	−	4.15481i	−0.405274	−	0.482987i
$75$		0			0
$76$	−0.131898	−	0.0232572i	−0.0151298	−	0.00266779i
$77$	2.56342	−	4.93232i	0.292129	−	0.562090i
$78$		0			0
$79$	−5.82433	−	2.11988i	−0.655288	−	0.238505i	−0.00708756	−	0.999975i	$-0.502256\pi$
$79$	−5.82433	−	2.11988i	−0.655288	−	0.238505i	−0.648201	+	0.761469i	$0.724478\pi$
$80$	10.5098			1.17503
$81$		0			0
$82$		−	3.98644i		−	0.440228i
$83$	8.67692	+	3.15814i	0.952416	+	0.346651i	0.771057	−	0.636766i	$-0.219728\pi$
$83$	8.67692	+	3.15814i	0.952416	+	0.346651i	0.181359	+	0.983417i	$0.441951\pi$
$84$		0			0
$85$	15.3158	+	12.8515i	1.66123	+	1.39394i
$86$	−8.45769	−	1.49132i	−0.912016	−	0.160813i
$87$		0			0
$88$	4.46236	−	3.74436i	0.475689	−	0.399150i
$89$	−6.28476	−	10.8855i	−0.666183	−	1.15386i	−0.978963	−	0.204037i	$-0.934594\pi$
$89$	−6.28476	−	10.8855i	−0.666183	−	1.15386i	0.312781	−	0.949825i	$-0.398740\pi$
$90$		0			0
$91$	−0.244303	−	0.0768495i	−0.0256100	−	0.00805602i
$92$	0.442501	−	0.0780248i	0.0461339	−	0.00813465i
$93$		0			0
$94$	−2.08038	−	5.71579i	−0.214575	−	0.589539i
$95$	1.53976	+	4.23045i	0.157976	+	0.434035i
$96$		0			0
$97$	−15.0854	+	2.65997i	−1.53169	+	0.270079i	−0.875016	−	0.484094i	$-0.839149\pi$
$97$	−15.0854	+	2.65997i	−1.53169	+	0.270079i	−0.656676	+	0.754172i	$0.728038\pi$
$98$	10.0472	+	0.865519i	1.01492	+	0.0874306i
$99$		0			0
$100$	0.0538713	+	0.0933079i	0.00538713	+	0.00933079i
$101$	8.06029	−	6.76338i	0.802028	−	0.672982i	−0.146662	−	0.989187i	$-0.546853\pi$
$101$	8.06029	−	6.76338i	0.802028	−	0.672982i	0.948691	+	0.316205i	$0.102409\pi$
$102$		0			0
$103$	8.05199	+	1.41978i	0.793386	+	0.139895i	0.555630	−	0.831429i	$-0.312477\pi$
$103$	8.05199	+	1.41978i	0.793386	+	0.139895i	0.237756	+	0.971325i	$0.423588\pi$
$104$	−0.205595	−	0.172514i	−0.0201602	−	0.0169164i
$105$		0			0
$106$	12.5248	+	4.55864i	1.21651	+	0.442774i
$107$			8.64958i			0.836187i	0.908404	+	0.418093i	$0.137302\pi$
$107$			8.64958i			0.836187i	−0.908404	+	0.418093i	$0.862698\pi$
$108$		0			0
$109$	−2.35627			−0.225690			−0.112845	−	0.993613i	$-0.535996\pi$
$109$	−2.35627			−0.225690			−0.112845	+	0.993613i	$0.535996\pi$
$110$	7.21130	+	2.62470i	0.687570	+	0.250255i
$111$		0			0
$112$	9.73130	+	5.05755i	0.919521	+	0.477893i
$113$	9.10544	+	1.60554i	0.856568	+	0.151036i	0.584651	−	0.811285i	$-0.301231\pi$
$113$	9.10544	+	1.60554i	0.856568	+	0.151036i	0.271917	+	0.962321i	$0.412342\pi$
$114$		0			0
$115$	−9.70830	−	11.5699i	−0.905304	−	1.07890i
$116$	0.109457	−	0.0631952i	0.0101629	−	0.00586753i
$117$		0			0
$118$	−9.21597	−	5.32084i	−0.848399	−	0.489823i
$119$	7.99690	+	19.2699i	0.733075	+	1.76647i
$120$		0			0
$121$	−6.18870	+	2.25250i	−0.562609	+	0.204773i
$122$	−16.4453	+	5.98559i	−1.48888	+	0.541909i
$123$		0			0
$124$	−0.105867	+	0.0186672i	−0.00950715	+	0.00167637i
$125$	−4.52777	+	7.84233i	−0.404976	+	0.701439i
$126$		0			0
$127$	9.01241	+	15.6100i	0.799722	+	1.38516i	0.919797	+	0.392394i	$0.128353\pi$
$127$	9.01241	+	15.6100i	0.799722	+	1.38516i	−0.120075	+	0.992765i	$0.538314\pi$
$128$	7.65636	+	9.12449i	0.676733	+	0.806499i
$129$		0			0
$130$	0.0613968	−	0.348198i	0.00538485	−	0.0305390i
$131$	−1.18288	−	0.992556i	−0.103349	−	0.0867200i	0.589649	−	0.807660i	$-0.299266\pi$
$131$	−1.18288	−	0.992556i	−0.103349	−	0.0867200i	−0.692998	+	0.720940i	$0.743711\pi$
$132$		0			0
$133$	−0.610086	+	4.65806i	−0.0529011	+	0.403905i
$134$		−	16.2967i		−	1.40782i
$135$		0			0
$136$			21.8636i			1.87479i
$137$	−4.78721	+	13.1528i	−0.408999	+	1.12372i	0.548718	+	0.836007i	$0.315116\pi$
$137$	−4.78721	+	13.1528i	−0.408999	+	1.12372i	−0.957718	+	0.287709i	$0.907106\pi$
$138$		0			0
$139$	11.1981	−	13.3454i	0.949810	−	1.13194i	−0.0413335	−	0.999145i	$-0.513161\pi$
$139$	11.1981	−	13.3454i	0.949810	−	1.13194i	0.991144	−	0.132794i	$-0.0423949\pi$
$140$	0.0224079	+	0.505490i	0.00189381	+	0.0427217i
$141$		0			0
$142$	−15.1941	+	12.7494i	−1.27506	+	1.06991i
$143$	−0.101686	−	0.176126i	−0.00850343	−	0.0147284i
$144$		0			0
$145$	−3.67924	−	2.12421i	−0.305544	−	0.176406i
$146$	−3.47364	−	19.7000i	−0.287481	−	1.63038i
$147$		0			0
$148$	0.266850	−	0.0971254i	0.0219349	−	0.00798366i
$149$	−1.16714	−	3.20670i	−0.0956160	−	0.262703i	0.882659	−	0.470014i	$-0.155751\pi$
$149$	−1.16714	−	3.20670i	−0.0956160	−	0.262703i	−0.978275	+	0.207311i	$0.933529\pi$
$150$		0			0
$151$	2.20278	+	12.4926i	0.179260	+	1.01663i	0.933111	+	0.359587i	$0.117083\pi$
$151$	2.20278	+	12.4926i	0.179260	+	1.01663i	−0.753852	+	0.657044i	$0.771806\pi$
$152$	−2.46154	+	4.26352i	−0.199658	+	0.345817i
$153$		0			0
$154$	5.41408	+	5.90053i	0.436279	+	0.475478i
$155$	2.32268	+	2.76807i	0.186563	+	0.222337i
$156$		0			0
$157$	14.4524	+	2.54834i	1.15343	+	0.203380i	0.717471	−	0.696589i	$-0.245300\pi$
$157$	14.4524	+	2.54834i	1.15343	+	0.203380i	0.435955	+	0.899969i	$0.356411\pi$
$158$	5.73960	−	6.84019i	0.456618	−	0.544176i
$159$		0			0
$160$	−0.369817	+	1.01607i	−0.0292366	+	0.0803270i
$161$	−3.42148	−	15.3848i	−0.269651	−	1.21249i
$162$		0			0
$163$	1.55651			0.121915			0.0609577	−	0.998140i	$-0.480585\pi$
$163$	1.55651			0.121915			0.0609577	+	0.998140i	$0.480585\pi$
$164$	0.196135	+	0.0713873i	0.0153156	+	0.00557441i
$165$		0			0
$166$	−8.55069	+	10.1903i	−0.663662	+	0.790922i
$167$	0.221778	−	1.25777i	0.0171617	−	0.0973290i	−0.975024	−	0.222101i	$-0.928709\pi$
$167$	0.221778	−	1.25777i	0.0171617	−	0.0973290i	0.992186	+	0.124772i	$0.0398198\pi$
$168$		0			0
$169$	9.95140	−	8.35022i	0.765492	−	0.642324i
$170$	−24.9442	+	14.4016i	−1.91314	+	1.10455i
$171$		0			0
$172$	0.224830	−	0.389417i	0.0171431	−	0.0296928i
$173$	1.16666	+	6.61644i	0.0886992	+	0.503038i	0.996497	+	0.0836300i	$0.0266514\pi$
$173$	1.16666	+	6.61644i	0.0886992	+	0.503038i	−0.907798	+	0.419408i	$0.862238\pi$
$174$		0			0
$175$	3.18598	−	2.03268i	0.240838	−	0.153656i
$176$	2.97863	+	8.18371i	0.224523	+	0.616871i
$177$		0			0
$178$	17.8330	−	3.14443i	1.33664	−	0.235685i
$179$	2.71116	+	1.56529i	0.202642	+	0.116995i	0.597887	−	0.801580i	$-0.296007\pi$
$179$	2.71116	+	1.56529i	0.202642	+	0.116995i	−0.395245	+	0.918576i	$0.629340\pi$
$180$		0			0
$181$	−3.24378	+	1.87280i	−0.241108	+	0.139204i	−0.615686	−	0.787992i	$-0.711121\pi$
$181$	−3.24378	+	1.87280i	−0.241108	+	0.139204i	0.374578	+	0.927196i	$0.377788\pi$
$182$	0.224410	−	0.292861i	0.0166344	−	0.0217083i
$183$		0			0
$184$	2.86802	−	16.2654i	0.211433	−	1.19910i
$185$	−7.31221	−	6.13567i	−0.537604	−	0.451104i
$186$		0			0
$187$	−5.66642	+	15.5684i	−0.414369	+	1.13847i
$188$	0.318474			0.0232271
$189$		0			0
$190$	−6.48567			−0.470520
$191$	0.477709	−	1.31249i	0.0345658	−	0.0949687i	−0.921209	−	0.389068i	$-0.872797\pi$
$191$	0.477709	−	1.31249i	0.0345658	−	0.0949687i	0.955775	+	0.294099i	$0.0950195\pi$
$192$		0			0
$193$	0.851514	+	0.714505i	0.0612933	+	0.0514312i	0.672920	−	0.739716i	$-0.265040\pi$
$193$	0.851514	+	0.714505i	0.0612933	+	0.0514312i	−0.611626	+	0.791147i	$0.709484\pi$
$194$	3.83204	−	21.7326i	0.275125	−	1.56031i
$195$		0			0
$196$	−0.222505	+	0.478830i	−0.0158932	+	0.0342022i
$197$	−3.19302	+	1.84349i	−0.227493	+	0.131343i	−0.609415	−	0.792851i	$-0.708596\pi$
$197$	−3.19302	+	1.84349i	−0.227493	+	0.131343i	0.381922	+	0.924195i	$0.375262\pi$
$198$		0			0
$199$	15.0783	+	8.70545i	1.06887	+	0.617113i	0.927873	−	0.372897i	$-0.121636\pi$
$199$	15.0783	+	8.70545i	1.06887	+	0.617113i	0.140998	+	0.990010i	$0.454969\pi$
$200$	3.90022	−	0.687714i	0.275787	−	0.0486287i
$201$		0			0
$202$	5.18444	+	14.2441i	0.364776	+	1.00221i
$203$	−2.38449	−	3.73740i	−0.167358	−	0.262314i
$204$		0			0
$205$	−1.21830	−	6.90930i	−0.0850894	−	0.482566i
$206$	−5.88947	+	10.2009i	−0.410338	+	0.710727i
$207$		0			0
$208$	0.347490	−	0.200624i	0.0240941	−	0.0139107i
$209$	−2.85776	+	2.39795i	−0.197675	+	0.165869i
$210$		0			0
$211$	−0.368145	+	2.08786i	−0.0253442	+	0.143734i	−0.994854	−	0.101318i	$-0.967694\pi$
$211$	−0.368145	+	2.08786i	−0.0253442	+	0.143734i	0.969510	+	0.245052i	$0.0788051\pi$
$212$	−0.448576	+	0.534591i	−0.0308083	+	0.0367159i
$213$		0			0
$214$	−11.7094	−	4.26188i	−0.800439	−	0.291336i
$215$	−15.1146			−1.03081
$216$		0			0
$217$	0.818580	+	3.68076i	0.0555689	+	0.249866i
$218$	1.16099	−	3.18981i	0.0786325	−	0.216041i
$219$		0			0
$220$	−0.258273	+	0.307798i	−0.0174128	+	0.0207517i
$221$	0.751719	+	0.132548i	0.0505661	+	0.00891617i
$222$		0			0
$223$	−15.8310	−	18.8667i	−1.06012	−	1.26341i	−0.963392	−	0.268096i	$-0.913605\pi$
$223$	−15.8310	−	18.8667i	−1.06012	−	1.26341i	−0.0967321	−	0.995310i	$-0.530839\pi$
$224$	−0.831378	+	0.762838i	−0.0555488	+	0.0509693i
$225$		0			0
$226$	−6.65999	+	11.5354i	−0.443016	+	0.767326i
$227$	−0.274602	−	1.55735i	−0.0182260	−	0.103365i	0.974338	−	0.225091i	$-0.0722680\pi$
$227$	−0.274602	−	1.55735i	−0.0182260	−	0.103365i	−0.992564	+	0.121727i	$0.961157\pi$
$228$		0			0
$229$	−4.53395	−	12.4569i	−0.299612	−	0.823176i	−0.994565	−	0.104121i	$-0.966797\pi$
$229$	−4.53395	−	12.4569i	−0.299612	−	0.823176i	0.694953	−	0.719055i	$-0.255425\pi$
$230$	20.4463	−	7.44186i	1.34819	−	0.490702i
$231$		0			0
$232$	−0.806741	−	4.57526i	−0.0529651	−	0.300380i
$233$	13.6803	+	7.89830i	0.896223	+	0.517435i	0.875973	−	0.482360i	$-0.160220\pi$
$233$	13.6803	+	7.89830i	0.896223	+	0.517435i	0.0202503	+	0.999795i	$0.493554\pi$
$234$		0			0
$235$	−5.35251	−	9.27083i	−0.349160	−	0.604762i
$236$	0.426824	−	0.358148i	0.0277839	−	0.0233134i
$237$		0			0
$238$	−30.0269	+	1.33107i	−1.94636	+	0.0862802i
$239$	2.51826	−	3.00115i	0.162893	−	0.194128i	−0.678424	−	0.734671i	$-0.737337\pi$
$239$	2.51826	−	3.00115i	0.162893	−	0.194128i	0.841317	+	0.540543i	$0.181781\pi$
$240$		0			0
$241$	8.25538	−	22.6815i	0.531776	−	1.46104i	−0.325180	−	0.945652i	$-0.605425\pi$
$241$	8.25538	−	22.6815i	0.531776	−	1.46104i	0.856956	−	0.515390i	$-0.172353\pi$
$242$		−	9.48784i		−	0.609901i
$243$		0			0
$244$		−	0.916303i		−	0.0586603i
$245$	17.6784	−	1.57042i	1.12943	−	0.100330i
$246$		0			0
$247$	0.131666	+	0.110481i	0.00837770	+	0.00702973i
$248$	−0.686166	+	3.89144i	−0.0435716	+	0.247107i
$249$		0			0
$250$	−8.38563	−	9.99361i	−0.530354	−	0.632051i
$251$	3.34189	+	5.78833i	0.210938	+	0.365356i	0.952008	−	0.306072i	$-0.0990147\pi$
$251$	3.34189	+	5.78833i	0.210938	+	0.365356i	−0.741070	+	0.671428i	$0.765681\pi$
$252$		0			0
$253$	6.25773	−	10.8387i	0.393420	−	0.681424i
$254$	−25.5727	+	4.50915i	−1.60457	+	0.282929i
$255$		0			0
$256$	−1.69873	+	0.618288i	−0.106171	+	0.0386430i
$257$	19.9314	−	7.25443i	1.24329	−	0.452519i	0.365158	−	0.930945i	$-0.381015\pi$
$257$	19.9314	−	7.25443i	1.24329	−	0.452519i	0.878128	+	0.478426i	$0.158793\pi$
$258$		0			0
$259$	−3.81795	−	9.19999i	−0.237236	−	0.571660i
$260$	0.0160321	+	0.00925613i	0.000994268	+	0.000574041i
$261$		0			0
$262$	1.92651	−	1.11227i	0.119020	−	0.0687165i
$263$	−7.88441	−	9.39628i	−0.486174	−	0.579399i	0.466066	−	0.884750i	$-0.345671\pi$
$263$	−7.88441	−	9.39628i	−0.486174	−	0.579399i	−0.952240	+	0.305350i	$0.901226\pi$
$264$		0			0
$265$	23.1011	+	4.07335i	1.41909	+	0.250224i
$266$	−6.00526	−	3.12105i	−0.368206	−	0.191364i
$267$		0			0
$268$	0.801806	+	0.291833i	0.0489781	+	0.0178266i
$269$	12.8959			0.786276			0.393138	−	0.919480i	$-0.371390\pi$
$269$	12.8959			0.786276			0.393138	+	0.919480i	$0.371390\pi$
$270$		0			0
$271$		−	15.7114i		−	0.954402i	−0.878794	−	0.477201i	$-0.841651\pi$
$271$		−	15.7114i		−	0.954402i	0.878794	−	0.477201i	$-0.158349\pi$
$272$	−30.7158	−	11.1797i	−1.86242	−	0.677866i
$273$		0			0
$274$	−15.4468	−	12.9614i	−0.933177	−	0.783028i
$275$	2.95545	+	0.521125i	0.178220	+	0.0314250i
$276$		0			0
$277$	10.1616	−	8.52659i	0.610551	−	0.512313i	−0.284267	−	0.958745i	$-0.591750\pi$
$277$	10.1616	−	8.52659i	0.610551	−	0.512313i	0.894817	+	0.446432i	$0.147306\pi$
$278$	12.5488	+	21.7351i	0.752624	+	1.30358i
$279$		0			0
$280$	17.7419	+	5.58098i	1.06028	+	0.333527i
$281$	13.8620	−	2.44425i	0.826938	−	0.145811i	0.255867	−	0.966712i	$-0.417639\pi$
$281$	13.8620	−	2.44425i	0.826938	−	0.145811i	0.571071	+	0.820901i	$0.306528\pi$
$282$		0			0
$283$	2.86418	+	7.86927i	0.170258	+	0.467779i	0.995249	−	0.0973668i	$-0.0310420\pi$
$283$	2.86418	+	7.86927i	0.170258	+	0.467779i	−0.824991	+	0.565146i	$0.808820\pi$
$284$	−0.355188	−	0.975871i	−0.0210765	−	0.0579073i
$285$		0			0
$286$	0.288534	−	0.0508764i	0.0170614	−	0.00300838i
$287$	2.19686	−	6.98378i	0.129676	−	0.412240i
$288$		0			0
$289$	−22.5913	−	39.1293i	−1.32890	−	2.30172i
$290$	4.68851	−	3.93413i	0.275319	−	0.231020i
$291$		0			0
$292$	1.03146	+	0.181874i	0.0603614	+	0.0106433i
$293$	13.8218	+	11.5979i	0.807477	+	0.677554i	0.950004	−	0.312237i	$-0.101078\pi$
$293$	13.8218	+	11.5979i	0.807477	+	0.677554i	−0.142527	+	0.989791i	$0.545523\pi$
$294$		0			0
$295$	−17.5992	−	6.40560i	−1.02467	−	0.372948i
$296$		−	10.4383i		−	0.606716i
$297$		0			0
$298$	4.91616			0.284785
$299$	−0.541851	−	0.197218i	−0.0313361	−	0.0114054i
$300$		0			0
$301$	−13.9951	−	7.27351i	−0.806662	−	0.419238i
$302$	−17.9972	−	3.17340i	−1.03563	−	0.182609i
$303$		0			0
$304$	−4.73107	−	5.63827i	−0.271345	−	0.323377i
$305$	−26.6737	+	15.4001i	−1.52733	+	0.881805i
$306$		0			0
$307$	−1.13352	−	0.654438i	−0.0646934	−	0.0373507i	0.467304	−	0.884096i	$-0.345225\pi$
$307$	−1.13352	−	0.654438i	−0.0646934	−	0.0373507i	−0.531998	+	0.846746i	$0.678559\pi$
$308$	−0.387262	+	0.160712i	−0.0220663	+	0.00915740i
$309$		0			0
$310$	−4.89173	+	1.78044i	−0.277832	+	0.101122i
$311$	−22.9897	+	8.36756i	−1.30363	+	0.474481i	−0.898176	−	0.439637i	$-0.855107\pi$
$311$	−22.9897	+	8.36756i	−1.30363	+	0.474481i	−0.405450	+	0.914117i	$0.632885\pi$
$312$		0			0
$313$	0.0802239	−	0.0141456i	0.00453453	−	0.000799559i	−0.171380	−	0.985205i	$-0.554823\pi$
$313$	0.0802239	−	0.0141456i	0.00453453	−	0.000799559i	0.175915	+	0.984405i	$0.443712\pi$
$314$	−10.5709	+	18.3093i	−0.596550	+	1.03326i
$315$		0			0
$316$	0.233759	+	0.404882i	0.0131500	+	0.0227764i
$317$	−8.06845	−	9.61560i	−0.453169	−	0.540066i	0.490288	−	0.871560i	$-0.336892\pi$
$317$	−8.06845	−	9.61560i	−0.453169	−	0.540066i	−0.943457	+	0.331495i	$0.892447\pi$
$318$		0			0
$319$	0.611320	−	3.46697i	0.0342273	−	0.194113i
$320$	14.9086	+	12.5098i	0.833418	+	0.699321i
$321$		0			0
$322$	22.5130	+	2.94863i	1.25460	+	0.164321i
$323$		−	14.0018i		−	0.779081i
$324$		0			0
$325$		−	0.138267i		−	0.00766969i
$326$	−0.766934	+	2.10713i	−0.0424765	+	0.116703i
$327$		0			0
$328$	4.93158	−	5.87723i	0.272301	−	0.324516i
$329$	−0.494706	−	11.1599i	−0.0272741	−	0.615264i
$330$		0			0
$331$	8.49272	−	7.12624i	0.466802	−	0.391693i	−0.378824	−	0.925469i	$-0.623672\pi$
$331$	8.49272	−	7.12624i	0.466802	−	0.391693i	0.845626	+	0.533775i	$0.179227\pi$
$332$	−0.348247	−	0.603182i	−0.0191126	−	0.0331039i
$333$		0			0
$334$	1.59343	+	0.919969i	0.0871888	+	0.0503385i
$335$	−4.98043	−	28.2454i	−0.272110	−	1.54321i
$336$		0			0
$337$	−0.468324	+	0.170456i	−0.0255113	+	0.00928534i	−0.354744	−	0.934963i	$-0.615432\pi$
$337$	−0.468324	+	0.170456i	−0.0255113	+	0.00928534i	0.329233	+	0.944249i	$0.393210\pi$
$338$	6.40082	+	17.5861i	0.348159	+	0.956559i
$339$		0			0
$340$	−0.261875	−	1.48517i	−0.0142022	−	0.0805445i
$341$	−1.49714	+	2.59313i	−0.0810749	+	0.140426i
$342$		0			0
$343$	17.1246	+	7.05315i	0.924643	+	0.380835i
$344$	−10.6243	−	12.6616i	−0.572825	−	0.682667i
$345$		0			0
$346$	−9.53187	−	1.68073i	−0.512437	−	0.0903564i
$347$	−23.1420	+	27.5795i	−1.24233	+	1.48055i	−0.424136	+	0.905599i	$0.639422\pi$
$347$	−23.1420	+	27.5795i	−1.24233	+	1.48055i	−0.818190	+	0.574948i	$0.805022\pi$
$348$		0			0
$349$	−8.71674	+	23.9491i	−0.466597	+	1.28196i	0.453844	+	0.891081i	$0.350052\pi$
$349$	−8.71674	+	23.9491i	−0.466597	+	1.28196i	−0.920441	+	0.390882i	$0.872170\pi$
$350$	1.18193	+	5.31459i	0.0631771	+	0.284077i
$351$		0			0
$352$	−0.895997			−0.0477568
$353$	−14.7098	−	5.35392i	−0.782922	−	0.284960i	−0.0805314	−	0.996752i	$-0.525662\pi$
$353$	−14.7098	−	5.35392i	−0.782922	−	0.284960i	−0.702391	+	0.711792i	$0.747884\pi$
$354$		0			0
$355$	−22.4382	+	26.7408i	−1.19089	+	1.41925i
$356$	−0.164637	+	0.933701i	−0.00872573	+	0.0494861i
$357$		0			0
$358$	−3.45488	+	2.89899i	−0.182596	+	0.153216i
$359$	4.91929	−	2.84015i	0.259630	−	0.149898i	−0.364536	−	0.931189i	$-0.618772\pi$
$359$	4.91929	−	2.84015i	0.259630	−	0.149898i	0.624166	+	0.781292i	$0.285439\pi$
$360$		0			0
$361$	−7.92359	+	13.7241i	−0.417031	+	0.722319i
$362$	−0.937012	−	5.31406i	−0.0492482	−	0.279301i
$363$		0			0
$364$	0.0103903	+	0.0162855i	0.000544599	+	0.000853593i
$365$	−12.0410	−	33.0825i	−0.630257	−	1.73162i
$366$		0			0
$367$	−18.6146	+	3.28226i	−0.971675	+	0.171332i	−0.636884	−	0.770960i	$-0.719777\pi$
$367$	−18.6146	+	3.28226i	−0.971675	+	0.171332i	−0.334791	+	0.942292i	$0.608666\pi$
$368$	21.3844	+	12.3463i	1.11474	+	0.643595i
$369$		0			0
$370$	11.9091	−	6.87573i	0.619125	−	0.357452i
$371$	19.4298	+	14.8884i	1.00874	+	0.772968i
$372$		0			0
$373$	−2.60608	+	14.7798i	−0.134938	+	0.765269i	0.839966	+	0.542640i	$0.182575\pi$
$373$	−2.60608	+	14.7798i	−0.134938	+	0.765269i	−0.974903	+	0.222629i	$0.928536\pi$
$374$	−18.2837	−	15.3419i	−0.945429	−	0.793309i
$375$		0			0
$376$	4.00383	−	11.0004i	0.206482	−	0.567304i
$377$	−0.162198			−0.00835363
$378$		0			0
$379$	−2.87213			−0.147532			−0.0737658	−	0.997276i	$-0.523502\pi$
$379$	−2.87213			−0.147532			−0.0737658	+	0.997276i	$0.523502\pi$
$380$	0.116142	−	0.319099i	0.00595798	−	0.0163694i
$381$		0			0
$382$	1.54141	+	1.29340i	0.0788656	+	0.0661761i
$383$	−2.37952	+	13.4949i	−0.121588	+	0.689558i	0.861689	+	0.507438i	$0.169407\pi$
$383$	−2.37952	+	13.4949i	−0.121588	+	0.689558i	−0.983276	+	0.182121i	$0.941704\pi$
$384$		0			0
$385$	11.1869	+	8.57220i	0.570140	+	0.436880i
$386$	−1.38683	+	0.800685i	−0.0705876	+	0.0407538i
$387$		0			0
$388$	1.00063	+	0.577716i	0.0507994	+	0.0293291i
$389$	14.2770	−	2.51742i	0.723872	−	0.127638i	0.200440	−	0.979706i	$-0.435763\pi$
$389$	14.2770	−	2.51742i	0.723872	−	0.127638i	0.523432	+	0.852068i	$0.324652\pi$
$390$		0			0
$391$	16.0661	+	44.1413i	0.812498	+	2.23232i
$392$	13.7420	+	13.7054i	0.694075	+	0.692226i
$393$		0			0
$394$	−0.922349	−	5.23090i	−0.0464673	−	0.263529i
$395$	7.85745	−	13.6095i	0.395351	−	0.684768i
$396$		0			0
$397$	30.4332	−	17.5706i	1.52740	−	0.881845i	0.527931	−	0.849288i	$-0.322968\pi$
$397$	30.4332	−	17.5706i	1.52740	−	0.881845i	0.999470	−	0.0325575i	$-0.0103652\pi$
$398$	−19.2145	+	16.1229i	−0.963135	+	0.808167i
$399$		0			0
$400$	−1.02816	+	5.83100i	−0.0514082	+	0.291550i
$401$	−5.80377	+	6.91666i	−0.289826	+	0.345402i	−0.891237	−	0.453539i	$-0.850161\pi$
$401$	−5.80377	+	6.91666i	−0.289826	+	0.345402i	0.601410	+	0.798940i	$0.294606\pi$
$402$		0			0
$403$	0.129636	+	0.0471838i	0.00645765	+	0.00235039i
$404$	−0.793660			−0.0394861
$405$		0			0
$406$	6.23442	−	1.38650i	0.309409	−	0.0688108i
$407$	2.70531	−	7.43278i	0.134097	−	0.368429i
$408$		0			0
$409$	−7.60537	+	9.06373i	−0.376062	+	0.448173i	−0.920567	−	0.390585i	$-0.872273\pi$
$409$	−7.60537	+	9.06373i	−0.376062	+	0.448173i	0.544506	+	0.838757i	$0.316717\pi$
$410$	9.95377	+	1.75512i	0.491582	+	0.0866791i
$411$		0			0
$412$	−0.396422	−	0.472437i	−0.0195303	−	0.0232753i
$413$	−13.2131	−	14.4003i	−0.650174	−	0.708591i
$414$		0			0
$415$	−11.7058	+	20.2750i	−0.574615	+	0.995263i
$416$	0.00716844	+	0.0406542i	0.000351461	+	0.00199324i
$417$		0			0
$418$	−1.83814	−	5.05024i	−0.0899061	−	0.247015i
$419$	18.4999	−	6.73342i	0.903780	−	0.328949i	0.152014	−	0.988378i	$-0.451424\pi$
$419$	18.4999	−	6.73342i	0.903780	−	0.328949i	0.751767	+	0.659429i	$0.229202\pi$
$420$		0			0
$421$	2.28747	+	12.9729i	0.111485	+	0.632260i	0.988431	+	0.151672i	$0.0484657\pi$
$421$	2.28747	+	12.9729i	0.111485	+	0.632260i	−0.876946	+	0.480588i	$0.840423\pi$
$422$	−2.64505	−	1.52712i	−0.128759	−	0.0743390i
$423$		0			0
$424$	12.8259	+	22.2151i	0.622881	+	1.07886i
$425$	−8.62855	+	7.24022i	−0.418546	+	0.351202i
$426$		0			0
$427$	−32.1088	+	1.42335i	−1.55385	+	0.0688808i
$428$	0.419373	−	0.499790i	0.0202712	−	0.0241583i
$429$		0			0
$430$	7.44737	−	20.4615i	0.359144	−	0.986741i
$431$			18.5835i			0.895137i	0.894250	+	0.447568i	$0.147710\pi$
$431$			18.5835i			0.895137i	−0.894250	+	0.447568i	$0.852290\pi$
$432$		0			0
$433$		−	26.0198i		−	1.25043i	−0.780451	−	0.625217i	$-0.785010\pi$
$433$		−	26.0198i		−	1.25043i	0.780451	−	0.625217i	$-0.214990\pi$
$434$	−5.38618	−	0.705451i	−0.258545	−	0.0338627i
$435$		0			0
$436$	0.136150	+	0.114243i	0.00652039	+	0.00547126i
$437$	−1.83673	+	10.4166i	−0.0878625	+	0.498293i
$438$		0			0
$439$	8.67250	+	10.3355i	0.413916	+	0.493286i	0.932211	−	0.361916i	$-0.117877\pi$
$439$	8.67250	+	10.3355i	0.413916	+	0.493286i	−0.518295	+	0.855202i	$0.673433\pi$
$440$	7.38468	+	12.7906i	0.352051	+	0.609770i
$441$		0			0
$442$	−0.549830	+	0.952333i	−0.0261527	+	0.0452979i
$443$	−8.97414	+	1.58238i	−0.426374	+	0.0751813i	−0.382718	−	0.923865i	$-0.625012\pi$
$443$	−8.97414	+	1.58238i	−0.426374	+	0.0751813i	−0.0436564	+	0.999047i	$0.513901\pi$
$444$		0			0
$445$	29.9472	−	10.8999i	1.41963	−	0.516704i
$446$	33.3412	−	12.1352i	1.57875	−	0.574619i
$447$		0			0
$448$	7.78430	+	18.7576i	0.367774	+	0.886212i
$449$	−9.47386	−	5.46974i	−0.447099	−	0.258133i	0.259505	−	0.965742i	$-0.416441\pi$
$449$	−9.47386	−	5.46974i	−0.447099	−	0.258133i	−0.706604	+	0.707609i	$0.749774\pi$
$450$		0			0
$451$	5.03482	−	2.90685i	0.237080	−	0.136878i
$452$	−0.448286	−	0.534247i	−0.0210856	−	0.0251288i
$453$		0			0
$454$	2.24357	+	0.395601i	0.105296	+	0.0185665i
$455$	0.299446	−	0.576169i	0.0140383	−	0.0270112i
$456$		0			0
$457$	6.62792	+	2.41237i	0.310041	+	0.112846i	0.492355	−	0.870395i	$-0.336136\pi$
$457$	6.62792	+	2.41237i	0.310041	+	0.112846i	−0.182313	+	0.983240i	$0.558359\pi$
$458$	19.0976			0.892372
$459$		0			0
$460$			1.13924i			0.0531172i
$461$	−19.9750	−	7.27029i	−0.930327	−	0.338611i	−0.167988	−	0.985789i	$-0.553727\pi$
$461$	−19.9750	−	7.27029i	−0.930327	−	0.338611i	−0.762339	+	0.647178i	$0.775949\pi$
$462$		0			0
$463$	−16.3752	−	13.7404i	−0.761019	−	0.638570i	0.177373	−	0.984144i	$-0.443240\pi$
$463$	−16.3752	−	13.7404i	−0.761019	−	0.638570i	−0.938392	+	0.345573i	$0.887684\pi$
$464$	6.84021	+	1.20611i	0.317549	+	0.0559924i
$465$		0			0
$466$	−17.4330	+	14.6280i	−0.807567	+	0.677629i
$467$	−19.8901	−	34.4506i	−0.920403	−	1.59418i	−0.798792	−	0.601607i	$-0.794527\pi$
$467$	−19.8901	−	34.4506i	−0.920403	−	1.59418i	−0.121611	−	0.992578i	$-0.538806\pi$
$468$		0			0
$469$	8.98083	−	28.5499i	0.414696	−	1.31831i
$470$	15.1877	−	2.67801i	0.700558	−	0.123527i
$471$		0			0
$472$	−7.00481	−	19.2455i	−0.322422	−	0.885848i
$473$	−4.28371	−	11.7694i	−0.196965	−	0.541158i
$474$		0			0
$475$	−2.49776	+	0.440422i	−0.114605	+	0.0202080i
$476$	0.472219	−	1.50118i	0.0216441	−	0.0688064i
$477$		0			0
$478$	2.82200	+	4.88785i	0.129075	+	0.223565i
$479$	−5.68281	+	4.76844i	−0.259654	+	0.217876i	−0.763316	−	0.646025i	$-0.776430\pi$
$479$	−5.68281	+	4.76844i	−0.259654	+	0.217876i	0.503662	+	0.863901i	$0.331986\pi$
$480$		0			0
$481$	−0.358893	−	0.0632825i	−0.0163641	−	0.00288543i
$482$	26.6375	+	22.3515i	1.21330	+	1.01808i
$483$		0			0
$484$	0.466807	+	0.169904i	0.0212185	+	0.00772290i
$485$		−	38.8381i		−	1.76355i
$486$		0			0
$487$	21.2597			0.963370			0.481685	−	0.876345i	$-0.340025\pi$
$487$	21.2597			0.963370			0.481685	+	0.876345i	$0.340025\pi$
$488$	−31.6501	−	11.5197i	−1.43273	−	0.521472i
$489$		0			0
$490$	−6.58464	+	24.7060i	−0.297464	+	1.11610i
$491$	36.4703	+	6.43071i	1.64588	+	0.290214i	0.918324	−	0.395830i	$-0.129543\pi$
$491$	36.4703	+	6.43071i	1.64588	+	0.290214i	0.727560	+	0.686044i	$0.240654\pi$
$492$		0			0
$493$	8.49333	+	10.1220i	0.382520	+	0.455870i
$494$	−0.214439	+	0.123806i	−0.00964807	+	0.00557032i
$495$		0			0
$496$	−5.11616	−	2.95382i	−0.229722	−	0.132630i
$497$	−33.6444	+	13.9622i	−1.50916	+	0.626292i
$498$		0			0
$499$	−7.60426	+	2.76772i	−0.340413	+	0.123900i	−0.506569	−	0.862199i	$-0.669087\pi$
$499$	−7.60426	+	2.76772i	−0.340413	+	0.123900i	0.166156	+	0.986099i	$0.446864\pi$
$500$	0.641857	−	0.233617i	0.0287047	−	0.0104477i
$501$		0			0
$502$	−9.48261	+	1.67204i	−0.423229	+	0.0746268i
$503$	−10.5540	+	18.2800i	−0.470578	+	0.815065i	−0.999434	−	0.0336470i	$-0.989288\pi$
$503$	−10.5540	+	18.2800i	−0.470578	+	0.815065i	0.528856	+	0.848712i	$0.322621\pi$
$504$		0			0
$505$	13.3388	+	23.1035i	0.593570	+	1.02809i
$506$	11.5896	+	13.8119i	0.515220	+	0.614016i
$507$		0			0
$508$	0.236091	−	1.33894i	0.0104748	−	0.0594058i
$509$	6.24961	+	5.24405i	0.277009	+	0.232438i	0.770698	−	0.637200i	$-0.219908\pi$
$509$	6.24961	+	5.24405i	0.277009	+	0.232438i	−0.493689	+	0.869638i	$0.664352\pi$
$510$		0			0
$511$	4.77092	−	36.4264i	0.211053	−	1.61141i
$512$			21.2181i			0.937714i
$513$		0			0
$514$			30.5566i			1.34780i
$515$	−7.09014	+	19.4800i	−0.312429	+	0.858392i
$516$		0			0
$517$	5.70199	−	6.79536i	0.250773	−	0.298860i
$518$	14.3357	−	0.635489i	0.629876	−	0.0279218i
$519$		0			0
$520$	0.521271	−	0.437398i	0.0228592	−	0.0191812i
$521$	14.4293	+	24.9923i	0.632160	+	1.09493i	0.987109	+	0.160047i	$0.0511646\pi$
$521$	14.4293	+	24.9923i	0.632160	+	1.09493i	−0.354950	+	0.934885i	$0.615502\pi$
$522$		0			0
$523$	−4.15555	−	2.39921i	−0.181710	−	0.104910i	0.406386	−	0.913701i	$-0.366789\pi$
$523$	−4.15555	−	2.39921i	−0.181710	−	0.104910i	−0.588096	+	0.808791i	$0.700122\pi$
$524$	0.0202253	+	0.114704i	0.000883548	+	0.00501085i
$525$		0			0
$526$	16.6051	−	6.04377i	0.724017	−	0.263521i
$527$	−3.84377	−	10.5607i	−0.167437	−	0.460030i
$528$		0			0
$529$	−2.16806	−	12.2957i	−0.0942633	−	0.534594i
$530$	−16.8968	+	29.2662i	−0.733951	+	1.27124i
$531$		0			0
$532$	0.261097	−	0.239572i	0.0113200	−	0.0103868i
$533$	−0.172174	−	0.205189i	−0.00745770	−	0.00888774i
$534$		0			0
$535$	−21.5972	−	3.80818i	−0.933730	−	0.164642i
$536$	20.1605	−	24.0263i	0.870799	−	1.03778i
$537$		0			0
$538$	−6.35414	+	17.4578i	−0.273946	+	0.752661i
$539$	6.23316	+	13.3207i	0.268481	+	0.573761i
$540$		0			0
$541$	42.2221			1.81527			0.907635	−	0.419760i	$-0.137886\pi$
$541$	42.2221			1.81527			0.907635	+	0.419760i	$0.137886\pi$
$542$	21.2694	+	7.74144i	0.913600	+	0.332523i
$543$		0			0
$544$	2.16165	−	2.57616i	0.0926802	−	0.110452i
$545$	1.03740	−	5.88339i	0.0444373	−	0.252017i
$546$		0			0
$547$	−15.5394	+	13.0391i	−0.664418	+	0.557513i	−0.911407	−	0.411505i	$-0.865003\pi$
$547$	−15.5394	+	13.0391i	−0.664418	+	0.557513i	0.246989	+	0.969018i	$0.420559\pi$
$548$	0.914324	−	0.527885i	0.0390580	−	0.0225501i
$549$		0			0
$550$	−2.16170	+	3.74418i	−0.0921753	+	0.159652i
$551$	0.516649	+	2.93006i	0.0220100	+	0.124825i
$552$		0			0
$553$	13.8246	−	8.82023i	0.587883	−	0.375074i
$554$	6.53602	+	17.9576i	0.277689	+	0.762944i
$555$		0			0
$556$	−1.29410	+	0.228184i	−0.0548819	+	0.00967715i
$557$	1.84854	+	1.06725i	0.0783251	+	0.0452210i	0.538651	−	0.842529i	$-0.318934\pi$
$557$	1.84854	+	1.06725i	0.0783251	+	0.0452210i	−0.460326	+	0.887750i	$0.652267\pi$
$558$		0			0
$559$	−0.499743	+	0.288527i	−0.0211369	+	0.0122034i
$560$	−16.9127	+	22.0715i	−0.714691	+	0.932690i
$561$		0			0
$562$	−3.52127	+	19.9701i	−0.148536	+	0.842387i
$563$	6.73571	+	5.65193i	0.283876	+	0.238200i	0.773596	−	0.633680i	$-0.218456\pi$
$563$	6.73571	+	5.65193i	0.283876	+	0.238200i	−0.489719	+	0.871880i	$0.662901\pi$
$564$		0			0
$565$	−8.01775	+	22.0286i	−0.337309	+	0.926750i
$566$	−12.0643			−0.507101
$567$		0			0
$568$	−38.1730			−1.60170
$569$	12.2179	−	33.5684i	0.512202	−	1.40726i	−0.366736	−	0.930325i	$-0.619525\pi$
$569$	12.2179	−	33.5684i	0.512202	−	1.40726i	0.878937	−	0.476937i	$-0.158253\pi$
$570$		0			0
$571$	−5.96309	−	5.00363i	−0.249548	−	0.209395i	0.509430	−	0.860512i	$-0.329856\pi$
$571$	−5.96309	−	5.00363i	−0.249548	−	0.209395i	−0.758977	+	0.651117i	$0.774301\pi$
$572$	−0.00266379	+	0.0151071i	−0.000111379	+	0.000631661i
$573$		0			0
$574$	8.37187	+	6.41510i	0.349435	+	0.267761i
$575$	7.36893	−	4.25446i	0.307306	−	0.177423i
$576$		0			0
$577$	17.2269	+	9.94598i	0.717167	+	0.414056i	0.813709	−	0.581272i	$-0.197445\pi$
$577$	17.2269	+	9.94598i	0.717167	+	0.414056i	−0.0965422	+	0.995329i	$0.530778\pi$
$578$	64.1027	−	11.3030i	2.66632	−	0.470145i
$579$		0			0
$580$	0.109602	+	0.301128i	0.00455096	+	0.0125037i
$581$	−20.5956	+	13.1401i	−0.854447	+	0.545144i
$582$		0			0
$583$	3.37538	+	19.1427i	0.139794	+	0.792811i
$584$	19.2495	−	33.3411i	0.796549	−	1.37966i
$585$		0			0
$586$	−22.5110	+	12.9967i	−0.929921	+	0.536890i
$587$	33.1432	−	27.8104i	1.36796	−	1.14786i	0.394533	−	0.918882i	$-0.370907\pi$
$587$	33.1432	−	27.8104i	1.36796	−	1.14786i	0.973432	−	0.228977i	$-0.0735379\pi$
$588$		0			0
$589$	0.439431	−	2.49214i	0.0181065	−	0.102687i
$590$	17.3432	−	20.6688i	0.714009	−	0.850922i
$591$		0			0
$592$	14.6646	+	5.33749i	0.602713	+	0.219369i
$593$	34.6890			1.42451			0.712253	−	0.701923i	$-0.247675\pi$
$593$	34.6890			1.42451			0.712253	+	0.701923i	$0.247675\pi$
$594$		0			0
$595$	−51.6359	+	11.4835i	−2.11687	+	0.470779i
$596$	−0.0880363	+	0.241878i	−0.00360611	+	0.00990770i
$597$		0			0
$598$	0.533969	−	0.636359i	0.0218356	−	0.0260227i
$599$	−38.5459	−	6.79668i	−1.57494	−	0.277705i	−0.683194	−	0.730237i	$-0.739410\pi$
$599$	−38.5459	−	6.79668i	−1.57494	−	0.277705i	−0.891748	+	0.452532i	$0.850521\pi$
$600$		0			0
$601$	−5.30537	−	6.32270i	−0.216411	−	0.257908i	0.646907	−	0.762569i	$-0.276062\pi$
$601$	−5.30537	−	6.32270i	−0.216411	−	0.257908i	−0.863318	+	0.504660i	$0.831618\pi$
$602$	16.7423	−	15.3620i	0.682364	−	0.626109i
$603$		0			0
$604$	0.478419	−	0.828647i	0.0194666	−	0.0337172i
$605$	−2.89958	−	16.4443i	−0.117885	−	0.668557i
$606$		0			0
$607$	2.91471	+	8.00809i	0.118304	+	0.325038i	0.984684	−	0.174347i	$-0.0557814\pi$
$607$	2.91471	+	8.00809i	0.118304	+	0.325038i	−0.866380	+	0.499385i	$0.833559\pi$
$608$	0.711573	−	0.258992i	0.0288581	−	0.0105035i
$609$		0			0
$610$	−7.70507	−	43.6976i	−0.311969	−	1.76927i
$611$	−0.353946	−	0.204351i	−0.0143191	−	0.00826715i
$612$		0			0
$613$	8.90517	+	15.4242i	0.359677	+	0.622978i	0.987907	−	0.155049i	$-0.0495537\pi$
$613$	8.90517	+	15.4242i	0.359677	+	0.622978i	−0.628230	+	0.778028i	$0.716220\pi$
$614$	1.44446	−	1.21205i	0.0582938	−	0.0489143i
$615$		0			0
$616$	0.682529	+	15.3969i	0.0274999	+	0.620358i
$617$	−0.725589	+	0.864723i	−0.0292111	+	0.0348125i	−0.780452	−	0.625215i	$-0.785011\pi$
$617$	−0.725589	+	0.864723i	−0.0292111	+	0.0348125i	0.751241	+	0.660028i	$0.229456\pi$
$618$		0			0
$619$	11.5905	−	31.8445i	0.465860	−	1.27994i	−0.455155	−	0.890412i	$-0.650416\pi$
$619$	11.5905	−	31.8445i	0.465860	−	1.27994i	0.921015	−	0.389527i	$-0.127362\pi$
$620$		−	0.272559i		−	0.0109462i
$621$		0			0
$622$		−	35.2453i		−	1.41321i
$623$	32.9742	+	4.31877i	1.32108	+	0.173028i
$624$		0			0
$625$	−23.0592	−	19.3490i	−0.922369	−	0.773959i
$626$	−0.0203787	+	0.115573i	−0.000814497	+	0.00461924i
$627$		0			0
$628$	−0.711530	−	0.847969i	−0.0283932	−	0.0338376i
$629$	14.8439	+	25.7104i	0.591865	+	1.02514i
$630$		0			0
$631$	5.72941	−	9.92363i	0.228084	−	0.395054i	−0.729156	−	0.684347i	$-0.760087\pi$
$631$	5.72941	−	9.92363i	0.228084	−	0.395054i	0.957240	+	0.289294i	$0.0934205\pi$
$632$	16.9239	−	2.98413i	0.673195	−	0.118702i
$633$		0			0
$634$	16.9927	−	6.18483i	0.674866	−	0.245631i
$635$	−42.9446	+	15.6305i	−1.70420	+	0.620279i
$636$		0			0
$637$	0.554532	−	0.389390i	0.0219713	−	0.0154282i
$638$	4.39221	+	2.53584i	0.173889	+	0.100395i
$639$		0			0
$640$	−26.1539	+	15.1000i	−1.03382	+	0.596879i
$641$	−14.4774	−	17.2535i	−0.571824	−	0.681474i	0.400180	−	0.916437i	$-0.368948\pi$
$641$	−14.4774	−	17.2535i	−0.571824	−	0.681474i	−0.972004	+	0.234963i	$0.924503\pi$
$642$		0			0
$643$	−2.47158	−	0.435807i	−0.0974698	−	0.0171866i	0.124701	−	0.992194i	$-0.460203\pi$
$643$	−2.47158	−	0.435807i	−0.0974698	−	0.0171866i	−0.222170	+	0.975008i	$0.571314\pi$
$644$	−0.548227	+	1.05485i	−0.0216032	+	0.0415670i
$645$		0			0
$646$	18.9550	+	6.89906i	0.745774	+	0.271440i
$647$	−19.6391			−0.772091			−0.386045	−	0.922480i	$-0.626159\pi$
$647$	−19.6391			−0.772091			−0.386045	+	0.922480i	$0.626159\pi$
$648$		0			0
$649$		−	15.5195i		−	0.609195i
$650$	0.187180	+	0.0681279i	0.00734180	+	0.00267220i
$651$		0			0
$652$	−0.0899383	−	0.0754672i	−0.00352225	−	0.00295552i
$653$	11.3035	+	1.99311i	0.442340	+	0.0779965i	0.390382	−	0.920653i	$-0.372343\pi$
$653$	11.3035	+	1.99311i	0.442340	+	0.0779965i	0.0519576	+	0.998649i	$0.483454\pi$
$654$		0			0
$655$	2.99911	−	2.51655i	0.117185	−	0.0983299i
$656$	5.73513	+	9.93353i	0.223919	+	0.387839i
$657$		0			0
$658$	15.3515	+	4.82905i	0.598463	+	0.188256i
$659$	−29.2489	+	5.15736i	−1.13937	+	0.200902i	−0.711332	−	0.702856i	$-0.751908\pi$
$659$	−29.2489	+	5.15736i	−1.13937	+	0.200902i	−0.428042	+	0.903759i	$0.640797\pi$
$660$		0			0
$661$	3.15998	+	8.68198i	0.122909	+	0.337690i	0.985854	−	0.167609i	$-0.0536045\pi$
$661$	3.15998	+	8.68198i	0.122909	+	0.337690i	−0.862945	+	0.505299i	$0.831382\pi$
$662$	5.46259	+	15.0083i	0.212310	+	0.583316i
$663$		0			0
$664$	−25.2127	+	4.44568i	−0.978442	+	0.172526i
$665$	−11.3622	−	3.57415i	−0.440605	−	0.138599i
$666$		0			0
$667$	−4.99080	−	8.64432i	−0.193245	−	0.334710i
$668$	−0.0737974	+	0.0619234i	−0.00285531	+	0.00239589i
$669$		0			0
$670$	40.6913	+	7.17498i	1.57204	+	0.277194i
$671$	−19.5514	−	16.4056i	−0.754773	−	0.633329i
$672$		0			0
$673$	−0.574231	−	0.209003i	−0.0221350	−	0.00805648i	0.330929	−	0.943656i	$-0.392638\pi$
$673$	−0.574231	−	0.209003i	−0.0221350	−	0.00805648i	−0.353064	+	0.935599i	$0.614860\pi$
$674$		−	0.717984i		−	0.0276557i
$675$		0			0
$676$	−0.979870			−0.0376873
$677$	1.73677	+	0.632133i	0.0667495	+	0.0242948i	0.375179	−	0.926952i	$-0.377581\pi$
$677$	1.73677	+	0.632133i	0.0667495	+	0.0242948i	−0.308430	+	0.951247i	$0.599803\pi$
$678$		0			0
$679$	18.6898	−	35.9612i	0.717247	−	1.38007i
$680$	−54.5915	−	9.62596i	−2.09349	−	0.369139i
$681$		0			0
$682$	−2.77278	−	3.30447i	−0.106175	−	0.126535i
$683$	20.1934	−	11.6587i	0.772680	−	0.446107i	−0.0611497	−	0.998129i	$-0.519477\pi$
$683$	20.1934	−	11.6587i	0.772680	−	0.446107i	0.833830	+	0.552021i	$0.186143\pi$
$684$		0			0
$685$	−30.7336	−	17.7440i	−1.17427	−	0.677965i
$686$	−17.9860	+	19.7073i	−0.686708	+	0.752427i
$687$		0			0
$688$	23.2206	−	8.45162i	0.885279	−	0.322215i
$689$	0.841561	−	0.306303i	0.0320609	−	0.0116692i
$690$		0			0
$691$	5.95279	−	1.04964i	0.226455	−	0.0399301i	−0.0592693	−	0.998242i	$-0.518877\pi$
$691$	5.95279	−	1.04964i	0.226455	−	0.0399301i	0.285724	+	0.958312i	$0.407766\pi$
$692$	0.253385	−	0.438876i	0.00963225	−	0.0166836i
$693$		0			0
$694$	−25.9332	−	44.9177i	−0.984412	−	1.70505i
$695$	28.3920	+	33.8362i	1.07697	+	1.28348i
$696$		0			0
$697$	−3.78910	+	21.4890i	−0.143522	+	0.813955i
$698$	−28.1262	−	23.6007i	−1.06459	−	0.893298i
$699$		0			0
$700$	−0.282646	−	0.0370194i	−0.0106830	−	0.00139920i
$701$			5.95954i			0.225089i	0.993647	+	0.112544i	$0.0359001\pi$
$701$			5.95954i			0.225089i	−0.993647	+	0.112544i	$0.964100\pi$
$702$		0			0
$703$			6.68487i			0.252125i
$704$	−5.51577	+	15.1545i	−0.207884	+	0.571155i
$705$		0			0
$706$	14.4958	−	17.2754i	0.545556	−	0.650168i
$707$	1.23284	+	27.8112i	0.0463658	+	1.04595i
$708$		0			0
$709$	19.8453	−	16.6521i	0.745304	−	0.625384i	−0.188952	−	0.981986i	$-0.560509\pi$
$709$	19.8453	−	16.6521i	0.745304	−	0.625384i	0.934256	+	0.356602i	$0.116065\pi$
$710$	−25.1445	−	43.5516i	−0.943658	−	1.63446i
$711$		0			0
$712$	30.1812	+	17.4251i	1.13109	+	0.653035i
$713$	1.47423	+	8.36079i	0.0552104	+	0.313114i
$714$		0			0
$715$	0.484540	−	0.176358i	0.0181208	−	0.00659542i
$716$	−0.0807634	−	0.221896i	−0.00301827	−	0.00829263i
$717$		0			0
$718$	1.42101	+	8.05893i	0.0530315	+	0.300757i
$719$	19.3073	−	33.4412i	0.720040	−	1.24715i	−0.240943	−	0.970539i	$-0.577457\pi$
$719$	19.3073	−	33.4412i	0.720040	−	1.24715i	0.960983	−	0.276607i	$-0.0892099\pi$
$720$		0			0
$721$	−15.9392	+	14.6251i	−0.593606	+	0.544669i
$722$	−14.6748	−	17.4888i	−0.546141	−	0.650866i
$723$		0			0
$724$	0.278234	+	0.0490602i	0.0103405	+	0.00182331i
$725$	1.53848	−	1.83349i	0.0571379	−	0.0680943i
$726$		0			0
$727$	−8.28491	+	22.7626i	−0.307270	+	0.844218i	0.685916	+	0.727681i	$0.259402\pi$
$727$	−8.28491	+	22.7626i	−0.307270	+	0.844218i	−0.993186	+	0.116537i	$0.962821\pi$
$728$	0.693145	−	0.154152i	0.0256897	−	0.00571323i
$729$		0			0
$730$	50.7185			1.87718
$731$	44.1740	+	16.0780i	1.63383	+	0.594667i
$732$		0			0
$733$	27.7677	−	33.0923i	1.02562	−	1.22229i	0.0509402	−	0.998702i	$-0.483778\pi$
$733$	27.7677	−	33.0923i	1.02562	−	1.22229i	0.974684	−	0.223589i	$-0.0717773\pi$
$734$	4.72854	−	26.8169i	0.174533	−	0.989828i
$735$		0			0
$736$	−1.94609	+	1.63296i	−0.0717338	+	0.0601918i
$737$	20.5825	−	11.8833i	0.758166	−	0.437727i
$738$		0			0
$739$	1.55436	−	2.69223i	0.0571780	−	0.0990352i	−0.836020	−	0.548700i	$-0.815123\pi$
$739$	1.55436	−	2.69223i	0.0571780	−	0.0990352i	0.893198	+	0.449664i	$0.148456\pi$
$740$	0.125027	+	0.709062i	0.00459608	+	0.0260656i
$741$		0			0
$742$	−29.7288	+	18.9672i	−1.09138	+	0.696308i
$743$	4.69492	+	12.8992i	0.172240	+	0.473225i	0.995536	−	0.0943876i	$-0.0300893\pi$
$743$	4.69492	+	12.8992i	0.172240	+	0.473225i	−0.823296	+	0.567613i	$0.807867\pi$
$744$		0			0
$745$	8.52069	−	1.50243i	0.312174	−	0.0550447i
$746$	−18.7241	−	10.8104i	−0.685539	−	0.395796i
$747$		0			0
$748$	1.08225	−	0.624834i	0.0395708	−	0.0228462i
$749$	−18.1649	−	13.9192i	−0.663731	−	0.508596i
$750$		0			0
$751$	−2.41618	+	13.7028i	−0.0881677	+	0.500024i	0.908460	+	0.417971i	$0.137259\pi$
$751$	−2.41618	+	13.7028i	−0.0881677	+	0.500024i	−0.996628	+	0.0820528i	$0.973852\pi$
$752$	13.4070	+	11.2498i	0.488904	+	0.410239i
$753$		0			0
$754$	0.0799193	−	0.219576i	0.00291049	−	0.00799650i
$755$	−32.1627			−1.17052
$756$		0			0
$757$	−17.3160			−0.629361			−0.314681	−	0.949198i	$-0.601897\pi$
$757$	−17.3160			−0.629361			−0.314681	+	0.949198i	$0.601897\pi$
$758$	1.41518	−	3.88816i	0.0514015	−	0.141224i
$759$		0			0
$760$	−9.56187	−	8.02336i	−0.346845	−	0.291038i
$761$	3.29855	−	18.7070i	0.119572	−	0.678128i	−0.864812	−	0.502095i	$-0.832563\pi$
$761$	3.29855	−	18.7070i	0.119572	−	0.678128i	0.984384	−	0.176032i	$-0.0563263\pi$
$762$		0			0
$763$	3.79178	−	4.94837i	0.137272	−	0.179143i
$764$	−0.0912389	+	0.0526768i	−0.00330091	+	0.00190578i
$765$		0			0
$766$	−17.0963	−	9.87058i	−0.617716	−	0.356639i
$767$	−0.704171	+	0.124164i	−0.0254261	+	0.00448331i
$768$		0			0
$769$	−10.6489	−	29.2575i	−0.384008	−	1.05505i	−0.969653	−	0.244485i	$-0.921381\pi$
$769$	−10.6489	−	29.2575i	−0.384008	−	1.05505i	0.585645	−	0.810568i	$-0.300841\pi$
$770$	−17.1167	+	10.9206i	−0.616845	+	0.393552i
$771$		0			0
$772$	−0.0145595	−	0.0825710i	−0.000524007	−	0.00297179i
$773$	1.63416	−	2.83045i	0.0587768	−	0.101804i	−0.835140	−	0.550038i	$-0.814613\pi$
$773$	1.63416	−	2.83045i	0.0587768	−	0.101804i	0.893917	+	0.448233i	$0.147947\pi$
$774$		0			0
$775$	−1.76300	+	1.01787i	−0.0633287	+	0.0365629i
$776$	32.5348	−	27.2999i	1.16793	−	0.980010i
$777$		0			0
$778$	−3.62668	+	20.5679i	−0.130023	+	0.737396i
$779$	−3.15826	+	3.76387i	−0.113156	+	0.134855i
$780$		0			0
$781$	−27.1817	−	9.89333i	−0.972637	−	0.354011i
$782$	−67.6726			−2.41997
$783$		0			0
$784$	−26.2812	+	12.2978i	−0.938615	+	0.439208i
$785$	−12.7260	+	34.9643i	−0.454209	+	1.24793i
$786$		0			0
$787$	−15.0442	+	17.9290i	−0.536269	+	0.639100i	−0.964347	−	0.264641i	$-0.914746\pi$
$787$	−15.0442	+	17.9290i	−0.536269	+	0.639100i	0.428078	+	0.903742i	$0.359191\pi$
$788$	0.273880	+	0.0482925i	0.00975658	+	0.00172035i
$789$		0			0
$790$	14.5523	+	17.3428i	0.517749	+	0.617030i
$791$	−18.0245	+	16.5386i	−0.640878	+	0.588044i
$792$		0			0
$793$	−0.587951	+	1.01836i	−0.0208787	+	0.0361630i
$794$	8.79107	+	49.8566i	0.311983	+	1.76935i
$795$		0			0
$796$	−0.449170	−	1.23408i	−0.0159204	−	0.0437410i
$797$	24.5022	−	8.91806i	0.867912	−	0.315894i	0.130590	−	0.991436i	$-0.458313\pi$
$797$	24.5022	−	8.91806i	0.867912	−	0.315894i	0.737321	+	0.675542i	$0.236090\pi$
$798$		0			0
$799$	5.78151	+	32.7886i	0.204535	+	1.15998i
$800$	−0.527551	−	0.304582i	−0.0186517	−	0.0107686i
$801$		0			0
$802$	−6.50379	−	11.2649i	−0.229657	−	0.397777i
$803$	22.3479	−	18.7521i	0.788642	−	0.661749i
$804$		0			0
$805$	39.9207	−	1.76965i	1.40702	−	0.0623719i
$806$	−0.127751	+	0.152247i	−0.00449982	+	0.00536268i
$807$		0			0
$808$	−9.97783	+	27.4139i	−0.351019	+	0.964416i
$809$			24.8140i			0.872412i	0.899847	+	0.436206i	$0.143678\pi$
$809$			24.8140i			0.872412i	−0.899847	+	0.436206i	$0.856322\pi$
$810$		0			0
$811$			27.0995i			0.951593i	0.879555	+	0.475797i	$0.157840\pi$
$811$			27.0995i			0.951593i	−0.879555	+	0.475797i	$0.842160\pi$
$812$	−0.0434266	+	0.331566i	−0.00152397	+	0.0116357i
$813$		0			0
$814$	8.72918	+	7.32465i	0.305958	+	0.256729i
$815$	−0.685289	+	3.88647i	−0.0240046	+	0.136137i
$816$		0			0
$817$	6.80398	+	8.10867i	0.238041	+	0.283687i
$818$	−8.52270	−	14.7617i	−0.297989	−	0.516132i
$819$		0			0
$820$	−0.264600	+	0.458301i	−0.00924025	+	0.0160046i
$821$	−18.1866	+	3.20679i	−0.634716	+	0.111918i	−0.481743	−	0.876313i	$-0.659996\pi$
$821$	−18.1866	+	3.20679i	−0.634716	+	0.111918i	−0.152973	+	0.988230i	$0.548885\pi$
$822$		0			0
$823$	−14.9272	+	5.43305i	−0.520329	+	0.189384i	−0.588815	−	0.808268i	$-0.700405\pi$
$823$	−14.9272	+	5.43305i	−0.520329	+	0.189384i	0.0684859	+	0.997652i	$0.478183\pi$
$824$	−21.3023	+	7.75339i	−0.742099	+	0.270102i
$825$		0			0
$826$	26.0049	−	10.7919i	0.904825	−	0.375498i
$827$	−6.41452	−	3.70343i	−0.223055	−	0.128781i	0.384309	−	0.923204i	$-0.374440\pi$
$827$	−6.41452	−	3.70343i	−0.223055	−	0.128781i	−0.607364	+	0.794424i	$0.707773\pi$
$828$		0			0
$829$	−6.47519	+	3.73846i	−0.224893	+	0.129842i	−0.608214	−	0.793773i	$-0.708114\pi$
$829$	−6.47519	+	3.73846i	−0.224893	+	0.129842i	0.383321	+	0.923615i	$0.374780\pi$
$830$	−21.6797	−	25.8368i	−0.752512	−	0.896809i
$831$		0			0
$832$	0.731735	+	0.129025i	0.0253683	+	0.00447312i
$833$	−53.3373	−	14.2155i	−1.84803	−	0.492537i
$834$		0			0
$835$	3.04289	+	1.10752i	0.105304	+	0.0383274i
$836$	0.281391			0.00973211
$837$		0			0
$838$			28.3621i			0.979752i
$839$	−15.2482	−	5.54991i	−0.526428	−	0.191604i	0.0651148	−	0.997878i	$-0.479259\pi$
$839$	−15.2482	−	5.54991i	−0.526428	−	0.191604i	−0.591543	+	0.806274i	$0.701481\pi$
$840$		0			0
$841$	20.0645	+	16.8361i	0.691878	+	0.580555i
$842$	−18.6892	−	3.29541i	−0.644073	−	0.113567i
$843$		0			0
$844$	0.122501	−	0.102791i	0.00421667	−	0.00353821i
$845$	16.4684	+	28.5241i	0.566530	+	0.981260i
$846$		0			0
$847$	5.22859	−	16.6216i	0.179657	−	0.571125i
$848$	−37.7680	+	6.65951i	−1.29696	+	0.228689i
$849$		0			0
$850$	−5.54996	−	15.2484i	−0.190362	−	0.523015i
$851$	−7.67042	−	21.0743i	−0.262939	−	0.722418i
$852$		0			0
$853$	4.14761	−	0.731336i	0.142012	−	0.0250405i	−0.102190	−	0.994765i	$-0.532585\pi$
$853$	4.14761	−	0.731336i	0.142012	−	0.0250405i	0.244202	+	0.969724i	$0.421474\pi$
$854$	13.8940	−	44.1687i	0.475442	−	1.51142i
$855$		0			0
$856$	−11.9909	−	20.7689i	−0.409842	−	0.709867i
$857$	−28.3201	+	23.7634i	−0.967397	+	0.811742i	−0.982140	−	0.188149i	$-0.939751\pi$
$857$	−28.3201	+	23.7634i	−0.967397	+	0.811742i	0.0147437	+	0.999891i	$0.495307\pi$
$858$		0			0
$859$	−15.3634	−	2.70898i	−0.524191	−	0.0924291i	−0.0947102	−	0.995505i	$-0.530192\pi$
$859$	−15.3634	−	2.70898i	−0.524191	−	0.0924291i	−0.429481	+	0.903076i	$0.641304\pi$
$860$	0.873353	+	0.732830i	0.0297811	+	0.0249893i
$861$		0			0
$862$	−25.1575	−	9.15659i	−0.856868	−	0.311875i
$863$			29.1929i			0.993737i	0.867826	+	0.496868i	$0.165517\pi$
$863$			29.1929i			0.993737i	−0.867826	+	0.496868i	$0.834483\pi$
$864$		0			0
$865$	−17.0343			−0.579183
$866$	35.2245	+	12.8207i	1.19698	+	0.435664i
$867$		0			0
$868$	0.131162	−	0.252370i	0.00445192	−	0.00856600i
$869$	12.8243	+	2.26127i	0.435035	+	0.0767084i
$870$		0			0
$871$	−0.703854	−	0.838820i	−0.0238492	−	0.0284223i
$872$	5.65774	−	3.26650i	0.191595	−	0.110618i
$873$		0			0
$874$	−13.1965	−	7.61900i	−0.446378	−	0.257717i
$875$	−9.18336	−	22.1288i	−0.310454	−	0.748091i
$876$		0			0
$877$	42.4663	−	15.4565i	1.43399	−	0.521928i	0.495914	−	0.868371i	$-0.334833\pi$
$877$	42.4663	−	15.4565i	1.43399	−	0.521928i	0.938071	+	0.346443i	$0.112611\pi$
$878$	−18.2649	+	6.64787i	−0.616410	+	0.224355i
$879$		0			0
$880$	−21.7454	+	3.83430i	−0.733037	+	0.129254i
$881$	−16.3257	+	28.2769i	−0.550025	+	0.952672i	0.448247	+	0.893910i	$0.352049\pi$
$881$	−16.3257	+	28.2769i	−0.550025	+	0.952672i	−0.998272	+	0.0587620i	$0.981285\pi$
$882$		0			0
$883$	16.0749	+	27.8425i	0.540963	+	0.936975i	0.998849	+	0.0479641i	$0.0152733\pi$
$883$	16.0749	+	27.8425i	0.540963	+	0.936975i	−0.457886	+	0.889011i	$0.651393\pi$
$884$	−0.0370092	−	0.0441059i	−0.00124475	−	0.00148344i
$885$		0			0
$886$	2.27964	−	12.9285i	0.0765858	−	0.434340i
$887$	9.21436	+	7.73177i	0.309388	+	0.259607i	0.784239	−	0.620459i	$-0.213054\pi$
$887$	9.21436	+	7.73177i	0.309388	+	0.259607i	−0.474851	+	0.880066i	$0.657498\pi$
$888$		0			0
$889$	−47.2853	−	6.19316i	−1.58590	−	0.207712i
$890$			45.9117i			1.53896i
$891$		0			0
$892$			1.85772i			0.0622010i
$893$	−2.56412	+	7.04485i	−0.0858049	+	0.235747i
$894$		0			0
$895$	−5.10204	+	6.08037i	−0.170542	+	0.203244i
$896$	−31.4831	+	1.39562i	−1.05178	+	0.0466243i
$897$		0			0
$898$	12.0727	−	10.1302i	0.402871	−	0.338049i
$899$	1.19404	+	2.06813i	0.0398233	+	0.0689760i
$900$		0			0
$901$	−63.1822	−	36.4783i	−2.10491	−	1.21527i
$902$	1.45438	+	8.24819i	0.0484255	+	0.274635i
$903$		0			0
$904$	−24.0892	+	8.76777i	−0.801197	+	0.291612i
$905$	−3.24806	−	8.92397i	−0.107969	−	0.296643i
$906$		0			0
$907$	−4.96322	−	28.1478i	−0.164801	−	0.934633i	−0.949269	−	0.314464i	$-0.898175\pi$
$907$	−4.96322	−	28.1478i	−0.164801	−	0.934633i	0.784468	−	0.620169i	$-0.212936\pi$
$908$	−0.0596405	+	0.103300i	−0.00197924	+	0.00342815i
$909$		0			0
$910$	0.632446	+	0.689270i	0.0209654	+	0.0228491i
$911$	22.1361	+	26.3808i	0.733403	+	0.874036i	0.995859	−	0.0909082i	$-0.0289770\pi$
$911$	22.1361	+	26.3808i	0.733403	+	0.874036i	−0.262456	+	0.964944i	$0.584533\pi$
$912$		0			0
$913$	−19.1053	−	3.36878i	−0.632293	−	0.111490i
$914$	−6.53150	+	7.78394i	−0.216043	+	0.257470i
$915$		0			0
$916$	−0.341991	+	0.939612i	−0.0112997	+	0.0310457i
$917$	3.98799	−	0.886906i	0.131695	−	0.0292882i
$918$		0			0
$919$	11.7323			0.387012			0.193506	−	0.981099i	$-0.438014\pi$
$919$	11.7323			0.387012			0.193506	+	0.981099i	$0.438014\pi$
$920$	39.3504	+	14.3224i	1.29735	+	0.472195i
$921$		0			0
$922$	19.6844	−	23.4589i	0.648271	−	0.772579i
$923$	−0.231424	+	1.31247i	−0.00761741	+	0.0432005i
$924$		0			0
$925$	4.11952	−	3.45669i	0.135449	−	0.113655i
$926$	26.6696	−	15.3977i	0.876417	−	0.506000i
$927$		0			0
$928$	−0.357298	+	0.618858i	−0.0117289	+	0.0203150i
$929$	−2.23489	−	12.6747i	−0.0733243	−	0.415843i	−0.999271	−	0.0381876i	$-0.987842\pi$
$929$	−2.23489	−	12.6747i	−0.0733243	−	0.415843i	0.925946	−	0.377655i	$-0.123270\pi$
$930$		0			0
$931$	−8.80057	−	8.77713i	−0.288427	−	0.287659i
$932$	−0.407524	−	1.11966i	−0.0133489	−	0.0366758i
$933$		0			0
$934$	56.4380	−	9.95155i	1.84671	−	0.325625i
$935$	−36.3780	−	21.0028i	−1.18969	−	0.686867i
$936$		0			0
$937$	3.62026	−	2.09016i	0.118269	−	0.0682824i	−0.439699	−	0.898145i	$-0.644915\pi$
$937$	3.62026	−	2.09016i	0.118269	−	0.0682824i	0.557967	+	0.829863i	$0.311581\pi$
$938$	34.2245	+	26.2251i	1.11747	+	0.856281i
$939$		0			0
$940$	−0.140216	+	0.795202i	−0.00457333	+	0.0259366i
$941$	−15.9401	−	13.3754i	−0.519633	−	0.436024i	0.344871	−	0.938650i	$-0.387923\pi$
$941$	−15.9401	−	13.3754i	−0.519633	−	0.436024i	−0.864504	+	0.502626i	$0.832367\pi$
$942$		0			0
$943$	5.63777	−	15.4896i	0.183591	−	0.504412i
$944$	30.6195			0.996581
$945$		0			0
$946$	18.0436			0.586647
$947$	12.6075	−	34.6388i	0.409688	−	1.12561i	−0.547667	−	0.836697i	$-0.684484\pi$
$947$	12.6075	−	34.6388i	0.409688	−	1.12561i	0.957355	−	0.288913i	$-0.0932939\pi$
$948$		0			0
$949$	−1.02964	−	0.863970i	−0.0334235	−	0.0280456i
$950$	0.634488	−	3.59836i	0.0205855	−	0.116746i
$951$		0			0
$952$	−45.9156	−	35.1836i	−1.48813	−	1.14031i
$953$	−20.4679	+	11.8171i	−0.663020	+	0.382795i	−0.793427	−	0.608666i	$-0.791705\pi$
$953$	−20.4679	+	11.8171i	−0.663020	+	0.382795i	0.130407	+	0.991461i	$0.458372\pi$
$954$		0			0
$955$	3.06686	+	1.77065i	0.0992412	+	0.0572969i
$956$	−0.291020	+	0.0513147i	−0.00941226	+	0.00165963i
$957$		0			0
$958$	−3.65523	−	10.0427i	−0.118095	−	0.324464i
$959$	−19.9182	−	31.2194i	−0.643194	−	1.00813i
$960$		0			0
$961$	5.03039	+	28.5287i	0.162271	+	0.920282i
$962$	0.262505	−	0.454671i	0.00846349	−	0.0146592i
$963$		0			0
$964$	−1.57672	+	0.910319i	−0.0507827	+	0.0293194i
$965$	−2.15895	+	1.81158i	−0.0694991	+	0.0583167i
$966$		0			0
$967$	7.67106	−	43.5048i	0.246685	−	1.39902i	−0.569862	−	0.821740i	$-0.693004\pi$
$967$	7.67106	−	43.5048i	0.246685	−	1.39902i	0.816547	−	0.577279i	$-0.195885\pi$
$968$	11.7373	−	13.9880i	0.377252	−	0.449591i
$969$		0			0
$970$	52.5772	+	19.1365i	1.68815	+	0.614437i
$971$	33.0944			1.06205			0.531025	−	0.847356i	$-0.321807\pi$
$971$	33.0944			1.06205			0.531025	+	0.847356i	$0.321807\pi$
$972$		0			0
$973$	10.0061	+	44.9928i	0.320782	+	1.44240i
$974$	−10.4752	+	28.7804i	−0.335648	+	0.922184i
$975$		0			0
$976$	32.3676	−	38.5742i	1.03606	−	1.23473i
$977$	48.6949	+	8.58623i	1.55789	+	0.274698i	0.885194	−	0.465222i	$-0.154026\pi$
$977$	48.6949	+	8.58623i	1.55789	+	0.274698i	0.672695	+	0.739920i	$0.265137\pi$
$978$		0			0
$979$	16.9749	+	20.2299i	0.542521	+	0.646552i
$980$	−1.09763	−	0.766391i	−0.0350626	−	0.0244815i
$981$		0			0
$982$	−26.6755	+	46.2033i	−0.851249	+	1.47441i
$983$	3.47841	+	19.7270i	0.110944	+	0.629194i	0.988679	+	0.150048i	$0.0479427\pi$
$983$	3.47841	+	19.7270i	0.110944	+	0.629194i	−0.877735	+	0.479147i	$0.840946\pi$
$984$		0			0
$985$	−3.19723	−	8.78432i	−0.101872	−	0.279892i
$986$	−17.8875	+	6.51053i	−0.569655	+	0.207337i
$987$		0			0
$988$	−0.00225127	−	0.0127676i	−7.16225e−5	−	0.000406191i
$989$	−30.7540	−	17.7558i	−0.977920	−	0.564602i
$990$		0			0
$991$	−30.2226	−	52.3470i	−0.960051	−	1.66286i	−0.722360	−	0.691517i	$-0.756943\pi$
$991$	−30.2226	−	52.3470i	−0.960051	−	1.66286i	−0.237691	−	0.971341i	$-0.576391\pi$
$992$	0.465596	−	0.390682i	0.0147827	−	0.0124042i
$993$		0			0
$994$	−2.32398	−	52.4258i	−0.0737123	−	1.66284i
$995$	−28.3753	+	33.8163i	−0.899556	+	1.07205i
$996$		0			0
$997$	−12.9226	+	35.5046i	−0.409264	+	1.12444i	0.548315	+	0.836272i	$0.315269\pi$
$997$	−12.9226	+	35.5046i	−0.409264	+	1.12444i	−0.957579	+	0.288171i	$0.906953\pi$
$998$		−	11.6580i		−	0.369028i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.be.a.503.5		132
3.2	odd	2		189.2.be.a.104.17	yes	132
7.6	odd	2	inner	567.2.be.a.503.6		132
21.20	even	2		189.2.be.a.104.18	yes	132
27.7	even	9		189.2.be.a.20.18	yes	132
27.20	odd	18	inner	567.2.be.a.62.6		132
189.20	even	18	inner	567.2.be.a.62.5		132
189.34	odd	18		189.2.be.a.20.17	✓	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.17	✓	132	189.34	odd	18
189.2.be.a.20.18	yes	132	27.7	even	9
189.2.be.a.104.17	yes	132	3.2	odd	2
189.2.be.a.104.18	yes	132	21.20	even	2
567.2.be.a.62.5		132	189.20	even	18	inner
567.2.be.a.62.6		132	27.20	odd	18	inner
567.2.be.a.503.5		132	1.1	even	1	trivial
567.2.be.a.503.6		132	7.6	odd	2	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.be (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.492726 + 1.35375i) q^{2} +(-0.0577819 - 0.0484848i) q^{4} +(-0.440273 + 2.49691i) q^{5} +(-1.60923 + 2.10009i) q^{7} +(-2.40115 + 1.38630i) q^{8} +(-3.16327 - 1.82631i) q^{10} +(-2.06906 + 0.364832i) q^{11} +(0.0331071 + 0.0909611i) q^{13} +(-2.05009 - 3.21327i) q^{14} +(-0.719801 - 4.08219i) q^{16} +(3.94280 - 6.82913i) q^{17} +(1.53773 - 0.887809i) q^{19} +(0.146502 - 0.122930i) q^{20} +(0.525589 - 2.98077i) q^{22} +(-3.82906 + 4.56329i) q^{23} +(-1.34226 - 0.488541i) q^{25} -0.139452 q^{26} +(0.194807 - 0.0433240i) q^{28} +(-0.573096 + 1.57457i) q^{29} +(0.916092 - 1.09176i) q^{31} +(0.419987 + 0.0740550i) q^{32} +(7.30224 + 8.70247i) q^{34} +(-4.53523 - 4.94272i) q^{35} +(-1.88241 + 3.26042i) q^{37} +(0.444195 + 2.51916i) q^{38} +(-2.40431 - 6.60580i) q^{40} +(-2.60026 + 0.946417i) q^{41} +(1.03518 + 5.87080i) q^{43} +(0.137243 + 0.0792375i) q^{44} +(-4.29090 - 7.43206i) q^{46} +(-3.23438 + 2.71396i) q^{47} +(-1.82075 - 6.75906i) q^{49} +(1.32273 - 1.57637i) q^{50} +(0.00249724 - 0.00686110i) q^{52} -9.25188i q^{53} -5.32689i q^{55} +(0.952641 - 7.27350i) q^{56} +(-1.84920 - 1.55166i) q^{58} +(-1.28271 + 7.27458i) q^{59} +(7.80852 + 9.30583i) q^{61} +(1.02659 + 1.77810i) q^{62} +(3.83798 - 6.64757i) q^{64} +(-0.241698 + 0.0426179i) q^{65} +(-10.6299 + 3.86898i) q^{67} +(-0.558931 + 0.203434i) q^{68} +(8.92585 - 3.70418i) q^{70} +(11.9234 + 6.88396i) q^{71} +(-12.0252 + 6.94274i) q^{73} +(-3.48630 - 4.15481i) q^{74} +(-0.131898 - 0.0232572i) q^{76} +(2.56342 - 4.93232i) q^{77} +(-5.82433 - 2.11988i) q^{79} +10.5098 q^{80} -3.98644i q^{82} +(8.67692 + 3.15814i) q^{83} +(15.3158 + 12.8515i) q^{85} +(-8.45769 - 1.49132i) q^{86} +(4.46236 - 3.74436i) q^{88} +(-6.28476 - 10.8855i) q^{89} +(-0.244303 - 0.0768495i) q^{91} +(0.442501 - 0.0780248i) q^{92} +(-2.08038 - 5.71579i) q^{94} +(1.53976 + 4.23045i) q^{95} +(-15.0854 + 2.65997i) q^{97} +(10.0472 + 0.865519i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q + 12 q^{2} - 12 q^{4} - 6 q^{7} + 18 q^{8} + 18 q^{11} - 3 q^{14} - 24 q^{16} - 12 q^{22} - 12 q^{23} - 12 q^{25} - 12 q^{28} + 48 q^{29} + 6 q^{32} + 36 q^{35} - 6 q^{37} - 12 q^{43} + 18 q^{44}+ \cdots - 126 q^{98}+O(q^{100}) \) 132 * q + 12 * q^2 - 12 * q^4 - 6 * q^7 + 18 * q^8 + 18 * q^11 - 3 * q^14 - 24 * q^16 - 12 * q^22 - 12 * q^23 - 12 * q^25 - 12 * q^28 + 48 * q^29 + 6 * q^32 + 36 * q^35 - 6 * q^37 - 12 * q^43 + 18 * q^44 - 6 * q^46 - 24 * q^49 - 18 * q^50 - 57 * q^56 - 12 * q^58 + 18 * q^64 - 78 * q^65 - 12 * q^67 - 69 * q^70 - 18 * q^71 + 6 * q^74 + 57 * q^77 + 24 * q^79 + 54 * q^85 + 42 * q^86 - 72 * q^88 + 6 * q^91 + 120 * q^92 - 126 * q^95 - 126 * q^98

Introduction

L-functions

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