LMFDB - Embedded newform 531.2.i.b.64.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [531,2,Mod(19,531)] 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("531.19"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(531, base_ring=CyclotomicField(58)) chi = DirichletCharacter(H, H._module([0, 38])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 531 = 3^{2} \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	531.i (of order $29$, degree $28$, minimal)

Newform invariants

comment:select newform

sage:traces = [140,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.24005634733$
Analytic rank:	$0$
Dimension:	$140$
Relative dimension:	$5$ over $\Q(\zeta_{29})$
Twist minimal:	no (minimal twist has level 177)
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			64.5
Character	$\chi$	$=$	531.64
Dual form			531.2.i.b.307.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89244 + 0.637637i) q^{2} +(1.58256 + 1.20303i) q^{4} +(-1.39663 + 3.50528i) q^{5} +(-2.04500 + 0.946119i) q^{7} +(-0.0135559 - 0.0199934i) q^{8} +(-4.87813 + 5.74298i) q^{10} +(-1.04248 + 3.75469i) q^{11} +(0.590330 - 1.11348i) q^{13} +(-4.47332 + 0.486503i) q^{14} +(-1.07655 - 3.87737i) q^{16} +(2.37714 + 1.09978i) q^{17} +(3.41192 - 0.751019i) q^{19} +(-6.42719 + 3.86711i) q^{20} +(-4.36697 + 6.44080i) q^{22} +(-0.813834 + 4.96417i) q^{23} +(-6.70642 - 6.35266i) q^{25} +(1.82716 - 1.73078i) q^{26} +(-4.37454 - 0.962909i) q^{28} +(5.12456 - 1.72667i) q^{29} +(9.66316 + 2.12702i) q^{31} +(0.432440 - 7.97589i) q^{32} +(3.79734 + 3.59703i) q^{34} +(-0.460297 - 8.48968i) q^{35} +(-0.253768 + 0.374280i) q^{37} +(6.93572 + 0.754305i) q^{38} +(0.0890149 - 0.0195937i) q^{40} +(0.226879 + 1.38390i) q^{41} +(2.43261 + 8.76146i) q^{43} +(-6.16679 + 4.68787i) q^{44} +(-4.70547 + 8.87545i) q^{46} +(-4.79757 - 12.0410i) q^{47} +(-1.24481 + 1.46550i) q^{49} +(-8.64080 - 16.2983i) q^{50} +(2.27378 - 1.05196i) q^{52} +(-1.37012 - 1.61303i) q^{53} +(-11.7053 - 8.89812i) q^{55} +(0.0466379 + 0.0280611i) q^{56} +10.7989 q^{58} +(7.45440 + 1.85253i) q^{59} +(1.71930 + 0.579299i) q^{61} +(16.9307 + 10.1868i) q^{62} +(2.92518 - 7.34165i) q^{64} +(3.07859 + 3.62439i) q^{65} +(3.88818 + 5.73464i) q^{67} +(2.43889 + 4.60024i) q^{68} +(4.54225 - 16.3597i) q^{70} +(0.829739 + 2.08249i) q^{71} +(-14.2116 + 1.54561i) q^{73} +(-0.718896 + 0.546491i) q^{74} +(6.30305 + 2.91610i) q^{76} +(-1.42050 - 8.66467i) q^{77} +(11.3641 - 6.83755i) q^{79} +(15.0948 + 1.64166i) q^{80} +(-0.453072 + 2.76362i) q^{82} +(-0.668692 - 12.3333i) q^{83} +(-7.17504 + 6.79656i) q^{85} +(-0.983070 + 18.1317i) q^{86} +(0.0892008 - 0.0300553i) q^{88} +(-10.4224 + 3.51170i) q^{89} +(-0.153741 + 2.83559i) q^{91} +(-7.25997 + 6.87701i) q^{92} +(-1.40133 - 25.8459i) q^{94} +(-2.13265 + 13.0086i) q^{95} +(-4.46533 - 0.485634i) q^{97} +(-3.29018 + 1.97963i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29}+ \cdots + 143 q^{98}+O(q^{100}) $ 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/531\mathbb{Z}\right)^\times$.

$n$	$119$	$415$
$\chi(n)$	$1$	$e\left(\frac{3}{29}\right)$

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 $

$2$	1.89244	+	0.637637i	1.33816	+	0.450877i	0.895199	−	0.445666i	$-0.147033\pi$
$2$	1.89244	+	0.637637i	1.33816	+	0.450877i	0.442957	+	0.896543i	$0.353930\pi$
$3$		0			0
$3$		0			0
$4$	1.58256	+	1.20303i	0.791278	+	0.601514i
$5$	−1.39663	+	3.50528i	−0.624592	+	1.56761i	0.186351	+	0.982483i	$0.440334\pi$
$5$	−1.39663	+	3.50528i	−0.624592	+	1.56761i	−0.810943	+	0.585125i	$0.801046\pi$
$6$		0			0
$7$	−2.04500	+	0.946119i	−0.772939	+	0.357599i	−0.766387	−	0.642379i	$-0.777948\pi$
$7$	−2.04500	+	0.946119i	−0.772939	+	0.357599i	−0.00655155	+	0.999979i	$0.502085\pi$
$8$	−0.0135559	−	0.0199934i	−0.00479272	−	0.00706873i
$9$		0			0
$10$	−4.87813	+	5.74298i	−1.54260	+	1.81609i
$11$	−1.04248	+	3.75469i	−0.314321	+	1.13208i	0.622600	+	0.782540i	$0.286076\pi$
$11$	−1.04248	+	3.75469i	−0.314321	+	1.13208i	−0.936921	+	0.349542i	$0.886337\pi$
$12$		0			0
$13$	0.590330	−	1.11348i	0.163728	−	0.308824i	−0.788050	−	0.615611i	$-0.788909\pi$
$13$	0.590330	−	1.11348i	0.163728	−	0.308824i	0.951778	+	0.306787i	$0.0992540\pi$
$14$	−4.47332	+	0.486503i	−1.19555	+	0.130023i
$15$		0			0
$16$	−1.07655	−	3.87737i	−0.269137	−	0.969342i
$17$	2.37714	+	1.09978i	0.576542	+	0.266737i	0.686416	−	0.727209i	$-0.259183\pi$
$17$	2.37714	+	1.09978i	0.576542	+	0.266737i	−0.109874	+	0.993946i	$0.535045\pi$
$18$		0			0
$19$	3.41192	−	0.751019i	0.782747	−	0.172296i	0.194420	−	0.980918i	$-0.437718\pi$
$19$	3.41192	−	0.751019i	0.782747	−	0.172296i	0.588328	+	0.808623i	$0.299787\pi$
$20$	−6.42719	+	3.86711i	−1.43716	+	0.864713i
$21$		0			0
$22$	−4.36697	+	6.44080i	−0.931041	+	1.37318i
$23$	−0.813834	+	4.96417i	−0.169696	+	1.03510i	0.755371	+	0.655297i	$0.227457\pi$
$23$	−0.813834	+	4.96417i	−0.169696	+	1.03510i	−0.925067	+	0.379803i	$0.875992\pi$
$24$		0			0
$25$	−6.70642	−	6.35266i	−1.34128	−	1.27053i
$26$	1.82716	−	1.73078i	0.358335	−	0.339433i
$27$		0			0
$28$	−4.37454	−	0.962909i	−0.826711	−	0.181973i
$29$	5.12456	−	1.72667i	0.951607	−	0.320634i	0.199666	−	0.979864i	$-0.436014\pi$
$29$	5.12456	−	1.72667i	0.951607	−	0.320634i	0.751941	+	0.659230i	$0.229118\pi$
$30$		0			0
$31$	9.66316	+	2.12702i	1.73556	+	0.382025i	0.966401	−	0.257038i	$-0.0827467\pi$
$31$	9.66316	+	2.12702i	1.73556	+	0.382025i	0.769154	+	0.639063i	$0.220678\pi$
$32$	0.432440	−	7.97589i	0.0764453	−	1.40995i
$33$		0			0
$34$	3.79734	+	3.59703i	0.651238	+	0.616885i
$35$	−0.460297	−	8.48968i	−0.0778044	−	1.43502i
$36$		0			0
$37$	−0.253768	+	0.374280i	−0.0417193	+	0.0615313i	−0.847977	−	0.530034i	$-0.822179\pi$
$37$	−0.253768	+	0.374280i	−0.0417193	+	0.0615313i	0.806257	+	0.591565i	$0.201490\pi$
$38$	6.93572	+	0.754305i	1.12512	+	0.122364i
$39$		0			0
$40$	0.0890149	−	0.0195937i	0.0140745	−	0.00309803i
$41$	0.226879	+	1.38390i	0.0354326	+	0.216129i	0.998608	−	0.0527443i	$-0.0167968\pi$
$41$	0.226879	+	1.38390i	0.0354326	+	0.216129i	−0.963175	+	0.268874i	$0.913349\pi$
$42$		0			0
$43$	2.43261	+	8.76146i	0.370969	+	1.33611i	0.879841	+	0.475268i	$0.157649\pi$
$43$	2.43261	+	8.76146i	0.370969	+	1.33611i	−0.508872	+	0.860842i	$0.669937\pi$
$44$	−6.16679	+	4.68787i	−0.929679	+	0.706723i
$45$		0			0
$46$	−4.70547	+	8.87545i	−0.693783	+	1.30861i
$47$	−4.79757	−	12.0410i	−0.699797	−	1.75636i	−0.652881	−	0.757460i	$-0.726440\pi$
$47$	−4.79757	−	12.0410i	−0.699797	−	1.75636i	−0.0469161	−	0.998899i	$-0.514939\pi$
$48$		0			0
$49$	−1.24481	+	1.46550i	−0.177830	+	0.209357i
$50$	−8.64080	−	16.2983i	−1.22199	−	2.30492i
$51$		0			0
$52$	2.27378	−	1.05196i	0.315316	−	0.145881i
$53$	−1.37012	−	1.61303i	−0.188201	−	0.221567i	0.659967	−	0.751294i	$-0.270570\pi$
$53$	−1.37012	−	1.61303i	−0.188201	−	0.221567i	−0.848168	+	0.529727i	$0.822294\pi$
$54$		0			0
$55$	−11.7053	−	8.89812i	−1.57834	−	1.19982i
$56$	0.0466379	+	0.0280611i	0.00623225	+	0.00374982i
$57$		0			0
$58$	10.7989			1.41797
$59$	7.45440	+	1.85253i	0.970481	+	0.241179i
$59$	7.45440	+	1.85253i	0.970481	+	0.241179i
$60$		0			0
$61$	1.71930	+	0.579299i	0.220134	+	0.0741717i	0.427207	−	0.904154i	$-0.359497\pi$
$61$	1.71930	+	0.579299i	0.220134	+	0.0741717i	−0.207074	+	0.978325i	$0.566394\pi$
$62$	16.9307	+	10.1868i	2.15020	+	1.29373i
$63$		0			0
$64$	2.92518	−	7.34165i	0.365647	−	0.917706i
$65$	3.07859	+	3.62439i	0.381852	+	0.449550i
$66$		0			0
$67$	3.88818	+	5.73464i	0.475017	+	0.700598i	0.987415	−	0.158150i	$-0.0505530\pi$
$67$	3.88818	+	5.73464i	0.475017	+	0.700598i	−0.512398	+	0.858748i	$0.671243\pi$
$68$	2.43889	+	4.60024i	0.295759	+	0.557861i
$69$		0			0
$70$	4.54225	−	16.3597i	0.542903	−	1.95536i
$71$	0.829739	+	2.08249i	0.0984719	+	0.247146i	0.969957	−	0.243276i	$-0.0782221\pi$
$71$	0.829739	+	2.08249i	0.0984719	+	0.247146i	−0.871485	+	0.490422i	$0.836843\pi$
$72$		0			0
$73$	−14.2116	+	1.54561i	−1.66334	+	0.180899i	−0.890905	−	0.454190i	$-0.849929\pi$
$73$	−14.2116	+	1.54561i	−1.66334	+	0.180899i	−0.772438	+	0.635090i	$0.780963\pi$
$74$	−0.718896	+	0.546491i	−0.0835700	+	0.0635283i
$75$		0			0
$76$	6.30305	+	2.91610i	0.723009	+	0.334500i
$77$	−1.42050	−	8.66467i	−0.161881	−	0.987431i
$78$		0			0
$79$	11.3641	−	6.83755i	1.27856	−	0.769284i	0.295993	−	0.955190i	$-0.404350\pi$
$79$	11.3641	−	6.83755i	1.27856	−	0.769284i	0.982568	+	0.185906i	$0.0595221\pi$
$80$	15.0948	+	1.64166i	1.68765	+	0.183543i
$81$		0			0
$82$	−0.453072	+	2.76362i	−0.0500335	+	0.305191i
$83$	−0.668692	−	12.3333i	−0.0733985	−	1.35376i	−0.770801	−	0.637076i	$-0.780144\pi$
$83$	−0.668692	−	12.3333i	−0.0733985	−	1.35376i	0.697402	−	0.716680i	$-0.254339\pi$
$84$		0			0
$85$	−7.17504	+	6.79656i	−0.778243	+	0.737191i
$86$	−0.983070	+	18.1317i	−0.106007	+	1.95519i
$87$		0			0
$88$	0.0892008	−	0.0300553i	0.00950884	−	0.00320390i
$89$	−10.4224	+	3.51170i	−1.10477	+	0.372240i	−0.811831	−	0.583892i	$-0.801529\pi$
$89$	−10.4224	+	3.51170i	−1.10477	+	0.372240i	−0.292937	+	0.956132i	$0.594632\pi$
$90$		0			0
$91$	−0.153741	+	2.83559i	−0.0161165	+	0.297251i
$92$	−7.25997	+	6.87701i	−0.756904	+	0.716978i
$93$		0			0
$94$	−1.40133	−	25.8459i	−0.144536	−	2.66581i
$95$	−2.13265	+	13.0086i	−0.218806	+	1.33466i
$96$		0			0
$97$	−4.46533	−	0.485634i	−0.453385	−	0.0493086i	−0.121422	−	0.992601i	$-0.538745\pi$
$97$	−4.46533	−	0.485634i	−0.453385	−	0.0493086i	−0.331963	+	0.943292i	$0.607711\pi$
$98$	−3.29018	+	1.97963i	−0.332358	+	0.199973i
$99$		0			0
$100$	−2.97086	−	18.1215i	−0.297086	−	1.81215i
$101$	−12.7655	−	5.90594i	−1.27021	−	0.587663i	−0.335157	−	0.942162i	$-0.608789\pi$
$101$	−12.7655	−	5.90594i	−1.27021	−	0.587663i	−0.935056	+	0.354499i	$0.884651\pi$
$102$		0			0
$103$	10.6838	−	8.12161i	1.05271	−	0.800246i	0.0723292	−	0.997381i	$-0.476957\pi$
$103$	10.6838	−	8.12161i	1.05271	−	0.800246i	0.980376	+	0.197135i	$0.0631637\pi$
$104$	−0.0302647	+	0.00329148i	−0.00296770	+	0.000322756i
$105$		0			0
$106$	−1.56434	−	3.92621i	−0.151943	−	0.381347i
$107$	3.73112	−	13.4383i	0.360701	−	1.29913i	−0.531333	−	0.847163i	$-0.678309\pi$
$107$	3.73112	−	13.4383i	0.360701	−	1.29913i	0.892035	−	0.451966i	$-0.149277\pi$
$108$		0			0
$109$	−0.499968	−	0.943040i	−0.0478883	−	0.0903269i	0.858413	−	0.512959i	$-0.171451\pi$
$109$	−0.499968	−	0.943040i	−0.0478883	−	0.0903269i	−0.906301	+	0.422633i	$0.861106\pi$
$110$	−16.4777	−	24.3028i	−1.57109	−	2.31719i
$111$		0			0
$112$	5.87000	+	6.91069i	0.554662	+	0.652999i
$113$	−7.15200	+	17.9502i	−0.672804	+	1.68861i	0.0510850	+	0.998694i	$0.483732\pi$
$113$	−7.15200	+	17.9502i	−0.672804	+	1.68861i	−0.723889	+	0.689916i	$0.757647\pi$
$114$		0			0
$115$	−16.2642	−	9.78582i	−1.51664	−	0.912533i
$116$	10.1871	+	3.43244i	0.945852	+	0.318695i
$117$		0			0
$118$	12.9258	+	8.25901i	1.18991	+	0.760303i
$119$	−5.90180			−0.541017
$120$		0			0
$121$	−3.58550	−	2.15733i	−0.325955	−	0.196121i
$122$	2.88429	+	2.19258i	0.261131	+	0.198507i
$123$		0			0
$124$	12.7336	+	14.9912i	1.14351	+	1.34625i
$125$	14.5116	−	6.71378i	1.29796	−	0.600499i
$126$		0			0
$127$	−1.29228	−	2.43750i	−0.114671	−	0.216293i	0.819533	−	0.573033i	$-0.194233\pi$
$127$	−1.29228	−	2.43750i	−0.114671	−	0.216293i	−0.934204	+	0.356740i	$0.883888\pi$
$128$	−0.125102	+	0.147282i	−0.0110576	+	0.0130180i
$129$		0			0
$130$	3.51499	+	8.82196i	0.308285	+	0.773737i
$131$	3.25437	−	6.13840i	0.284336	−	0.536315i	−0.699666	−	0.714470i	$-0.746668\pi$
$131$	3.25437	−	6.13840i	0.284336	−	0.536315i	0.984002	+	0.178155i	$0.0570129\pi$
$132$		0			0
$133$	−6.26683	+	4.76392i	−0.543403	+	0.413084i
$134$	3.70153	+	13.3317i	0.319763	+	1.15168i
$135$		0			0
$136$	−0.0102358	−	0.0624357i	−0.000877714	−	0.00535382i
$137$	21.9646	−	4.83477i	1.87656	−	0.413063i	0.878639	−	0.477486i	$-0.158452\pi$
$137$	21.9646	−	4.83477i	1.87656	−	0.413063i	0.997923	+	0.0644236i	$0.0205209\pi$
$138$		0			0
$139$	−9.25621	−	1.00667i	−0.785101	−	0.0853849i	−0.293218	−	0.956046i	$-0.594726\pi$
$139$	−9.25621	−	1.00667i	−0.785101	−	0.0853849i	−0.491884	+	0.870661i	$0.663692\pi$
$140$	9.48488	−	13.9892i	0.801619	−	1.18230i
$141$		0			0
$142$	0.242359	+	4.47005i	0.0203383	+	0.375118i
$143$	3.56537	+	3.37729i	0.298151	+	0.282423i
$144$		0			0
$145$	−1.10467	+	20.3745i	−0.0917382	+	1.69201i
$146$	−27.8801	−	6.13688i	−2.30738	−	0.507892i
$147$		0			0
$148$	−0.851873	+	0.287029i	−0.0700235	+	0.0235937i
$149$	3.05154	+	0.671694i	0.249992	+	0.0550273i	0.338198	−	0.941075i	$-0.390183\pi$
$149$	3.05154	+	0.671694i	0.249992	+	0.0550273i	−0.0882067	+	0.996102i	$0.528114\pi$
$150$		0			0
$151$	−0.301845	+	0.285923i	−0.0245638	+	0.0232681i	−0.699883	−	0.714258i	$-0.746765\pi$
$151$	−0.301845	+	0.285923i	−0.0245638	+	0.0232681i	0.675319	+	0.737526i	$0.264006\pi$
$152$	−0.0612669	−	0.0580351i	−0.00496940	−	0.00470727i
$153$		0			0
$154$	2.83670	−	17.3031i	0.228588	−	1.39433i
$155$	−20.9517	+	30.9014i	−1.68288	+	2.48206i
$156$		0			0
$157$	9.26144	−	5.57243i	0.739144	−	0.444728i	−0.0955626	−	0.995423i	$-0.530465\pi$
$157$	9.26144	−	5.57243i	0.739144	−	0.444728i	0.834706	+	0.550695i	$0.185637\pi$
$158$	25.8657	−	5.69347i	2.05777	−	0.452948i
$159$		0			0
$160$	27.3537	+	12.6552i	2.16250	+	1.00048i
$161$	−3.03240	−	10.9217i	−0.238987	−	0.860752i
$162$		0			0
$163$	−1.06904	+	0.116266i	−0.0837341	+	0.00910663i	−0.149890	−	0.988703i	$-0.547892\pi$
$163$	−1.06904	+	0.116266i	−0.0837341	+	0.00910663i	0.0661561	+	0.997809i	$0.478926\pi$
$164$	−1.30583	+	2.46305i	−0.101968	+	0.192332i
$165$		0			0
$166$	6.59871	−	23.7664i	0.512159	−	1.84463i
$167$	1.80147	−	2.12086i	0.139402	−	0.164117i	−0.688031	−	0.725682i	$-0.741525\pi$
$167$	1.80147	−	2.12086i	0.139402	−	0.164117i	0.827433	+	0.561565i	$0.189800\pi$
$168$		0			0
$169$	6.40408	+	9.44532i	0.492622	+	0.726563i
$170$	−17.9121	+	8.28700i	−1.37379	+	0.635584i
$171$		0			0
$172$	−6.69055	+	16.7920i	−0.510149	+	1.28038i
$173$	5.51537	+	4.19268i	0.419326	+	0.318763i	0.793472	−	0.608606i	$-0.208271\pi$
$173$	5.51537	+	4.19268i	0.419326	+	0.318763i	−0.374146	+	0.927370i	$0.622064\pi$
$174$		0			0
$175$	19.7250	+	6.64614i	1.49107	+	0.502401i
$176$	15.6806			1.18197
$177$		0			0
$178$	−21.9629			−1.64619
$179$	12.7811	+	4.30645i	0.955303	+	0.321879i	0.753427	−	0.657532i	$-0.228400\pi$
$179$	12.7811	+	4.30645i	0.955303	+	0.321879i	0.201876	+	0.979411i	$0.435296\pi$
$180$		0			0
$181$	−11.4991	−	8.74140i	−0.854722	−	0.649743i	0.0832211	−	0.996531i	$-0.473479\pi$
$181$	−11.4991	−	8.74140i	−0.854722	−	0.649743i	−0.937944	+	0.346788i	$0.887272\pi$
$182$	−2.09903	+	5.26816i	−0.155590	+	0.390502i
$183$		0			0
$184$	0.110283	−	0.0510223i	0.00813016	−	0.00376141i
$185$	−0.957536	−	1.41226i	−0.0703995	−	0.103831i
$186$		0			0
$187$	−6.60749	+	7.77894i	−0.483187	+	0.568852i
$188$	6.89323	−	24.8272i	0.502740	−	1.81071i
$189$		0			0
$190$	−12.3307	+	23.2581i	−0.894562	+	1.68732i
$191$	2.26749	−	0.246605i	0.164070	−	0.0178437i	−0.0257152	−	0.999669i	$-0.508186\pi$
$191$	2.26749	−	0.246605i	0.164070	−	0.0178437i	0.189785	+	0.981826i	$0.439221\pi$
$192$		0			0
$193$	1.40196	+	5.04942i	0.100916	+	0.363465i	0.996715	−	0.0809943i	$-0.0258096\pi$
$193$	1.40196	+	5.04942i	0.100916	+	0.363465i	−0.895799	+	0.444460i	$0.853396\pi$
$194$	−8.14070	−	3.76629i	−0.584468	−	0.270404i
$195$		0			0
$196$	−3.73301	+	0.821699i	−0.266644	+	0.0586928i
$197$	−16.8541	+	10.1408i	−1.20081	+	0.722502i	−0.968226	−	0.250075i	$-0.919545\pi$
$197$	−16.8541	+	10.1408i	−1.20081	+	0.722502i	−0.232581	+	0.972577i	$0.574717\pi$
$198$		0			0
$199$	8.30546	−	12.2496i	0.588758	−	0.868353i	−0.410291	−	0.911955i	$-0.634573\pi$
$199$	8.30546	−	12.2496i	0.588758	−	0.868353i	0.999049	+	0.0436015i	$0.0138832\pi$
$200$	−0.0360999	+	0.220200i	−0.00255265	+	0.0155705i
$201$		0			0
$202$	−20.3921	−	19.3164i	−1.43478	−	1.35910i
$203$	−8.84611	+	8.37948i	−0.620875	+	0.588124i
$204$		0			0
$205$	−5.16783	−	1.13753i	−0.360937	−	0.0794483i
$206$	25.3971	−	8.55727i	1.76950	−	0.596213i
$207$		0			0
$208$	−4.95289	−	1.09021i	−0.343421	−	0.0755928i
$209$	−0.737025	+	13.5936i	−0.0509811	+	0.940290i
$210$		0			0
$211$	8.58272	+	8.12998i	0.590859	+	0.559691i	0.923615	−	0.383322i	$-0.125220\pi$
$211$	8.58272	+	8.12998i	0.590859	+	0.559691i	−0.332756	+	0.943013i	$0.607979\pi$
$212$	−0.227772	−	4.20101i	−0.0156435	−	0.288527i
$213$		0			0
$214$	15.6297	−	23.0520i	1.06842	−	1.57581i
$215$	−34.1088	−	3.70956i	−2.32620	−	0.252990i
$216$		0			0
$217$	−21.7736	+	4.79274i	−1.47809	+	0.325352i
$218$	−0.344842	−	2.10344i	−0.0233557	−	0.142463i
$219$		0			0
$220$	−7.81957	−	28.1635i	−0.527195	−	1.89879i
$221$	2.62789	−	1.99767i	0.176771	−	0.134378i
$222$		0			0
$223$	−12.5687	+	23.7072i	−0.841665	+	1.58755i	−0.0328691	+	0.999460i	$0.510464\pi$
$223$	−12.5687	+	23.7072i	−0.841665	+	1.58755i	−0.808796	+	0.588089i	$0.799880\pi$
$224$	6.66180	+	16.7199i	0.445110	+	1.11714i
$225$		0			0
$226$	−24.9804	+	29.4092i	−1.66167	+	1.95627i
$227$	4.45936	+	8.41124i	0.295978	+	0.558274i	0.986247	−	0.165279i	$-0.0528525\pi$
$227$	4.45936	+	8.41124i	0.295978	+	0.558274i	−0.690269	+	0.723553i	$0.742508\pi$
$228$		0			0
$229$	5.20272	−	2.40704i	0.343806	−	0.159061i	−0.240386	−	0.970677i	$-0.577274\pi$
$229$	5.20272	−	2.40704i	0.343806	−	0.159061i	0.584191	+	0.811616i	$0.301412\pi$
$230$	−24.5391	−	28.8897i	−1.61806	−	1.90493i
$231$		0			0
$232$	−0.103990	−	0.0790509i	−0.00682726	−	0.00518995i
$233$	2.49256	+	1.49972i	0.163293	+	0.0982501i	0.594855	−	0.803833i	$-0.297210\pi$
$233$	2.49256	+	1.49972i	0.163293	+	0.0982501i	−0.431562	+	0.902083i	$0.642037\pi$
$234$		0			0
$235$	48.9075			3.19037
$236$	9.56836	+	11.8996i	0.622847	+	0.774598i
$237$		0			0
$238$	−11.1688	−	3.76320i	−0.723965	−	0.243932i
$239$	−5.93983	−	3.57388i	−0.384216	−	0.231175i	0.310322	−	0.950632i	$-0.399563\pi$
$239$	−5.93983	−	3.57388i	−0.384216	−	0.231175i	−0.694537	+	0.719457i	$0.744391\pi$
$240$		0			0
$241$	−2.84994	+	7.15282i	−0.183581	+	0.460754i	−0.991748	−	0.128199i	$-0.959080\pi$
$241$	−2.84994	+	7.15282i	−0.183581	+	0.460754i	0.808167	+	0.588953i	$0.200460\pi$
$242$	−5.40976	−	6.36886i	−0.347752	−	0.409406i
$243$		0			0
$244$	2.02397	+	2.98514i	0.129572	+	0.191104i
$245$	−3.39845	−	6.41016i	−0.217119	−	0.409530i
$246$		0			0
$247$	1.17791	−	4.24245i	0.0749487	−	0.269941i
$248$	−0.0884661	−	0.222033i	−0.00561760	−	0.0140991i
$249$		0			0
$250$	31.7433	−	3.45229i	2.00762	−	0.218342i
$251$	5.16866	−	3.92911i	0.326243	−	0.248003i	−0.429213	−	0.903204i	$-0.641209\pi$
$251$	5.16866	−	3.92911i	0.326243	−	0.248003i	0.755455	+	0.655200i	$0.227416\pi$
$252$		0			0
$253$	−17.7905	−	8.23077i	−1.11848	−	0.517464i
$254$	−0.891322	−	5.43682i	−0.0559265	−	0.341137i
$255$		0			0
$256$	−13.8740	+	8.34773i	−0.867128	+	0.521733i
$257$	16.4415	+	1.78812i	1.02559	+	0.111540i	0.605422	−	0.795904i	$-0.293004\pi$
$257$	16.4415	+	1.78812i	1.02559	+	0.111540i	0.420172	+	0.907444i	$0.361970\pi$
$258$		0			0
$259$	0.164843	−	1.00550i	0.0102429	−	0.0624787i
$260$	0.511791	+	9.43943i	0.0317399	+	0.585409i
$261$		0			0
$262$	10.0728	−	9.54144i	0.622298	−	0.589472i
$263$	0.196976	−	3.63302i	0.0121461	−	0.224021i	−0.986158	−	0.165808i	$-0.946977\pi$
$263$	0.196976	−	3.63302i	0.0121461	−	0.224021i	0.998304	−	0.0582135i	$-0.0185404\pi$
$264$		0			0
$265$	7.56769	−	2.54985i	0.464879	−	0.156636i
$266$	−14.8972	+	5.01946i	−0.913408	+	0.307763i
$267$		0			0
$268$	−0.745665	+	13.7530i	−0.0455488	+	0.840097i
$269$	22.3727	−	21.1926i	1.36409	−	1.29213i	0.446401	−	0.894833i	$-0.352705\pi$
$269$	22.3727	−	21.1926i	1.36409	−	1.29213i	0.917688	−	0.397302i	$-0.130053\pi$
$270$		0			0
$271$	−0.453772	−	8.36933i	−0.0275647	−	0.508401i	−0.979417	−	0.201845i	$-0.935306\pi$
$271$	−0.453772	−	8.36933i	−0.0275647	−	0.508401i	0.951853	−	0.306556i	$-0.0991765\pi$
$272$	1.70516	−	10.4010i	0.103391	−	0.630656i
$273$		0			0
$274$	44.6495	+	4.85592i	2.69737	+	0.293357i
$275$	30.8436	−	18.5580i	1.85994	−	1.11909i
$276$		0			0
$277$	−3.13922	−	19.1484i	−0.188617	−	1.15052i	−0.896122	−	0.443807i	$-0.853627\pi$
$277$	−3.13922	−	19.1484i	−0.188617	−	1.15052i	0.707505	−	0.706709i	$-0.249821\pi$
$278$	−16.8749	−	7.80717i	−1.01209	−	0.468243i
$279$		0			0
$280$	−0.163498	+	0.124288i	−0.00977087	+	0.00742762i
$281$	−26.6284	+	2.89601i	−1.58852	+	0.172761i	−0.859282	−	0.511503i	$-0.829089\pi$
$281$	−26.6284	+	2.89601i	−1.58852	+	0.172761i	−0.729234	+	0.684264i	$0.760123\pi$
$282$		0			0
$283$	−3.55017	−	8.91026i	−0.211036	−	0.529660i	0.784911	−	0.619609i	$-0.212709\pi$
$283$	−3.55017	−	8.91026i	−0.211036	−	0.529660i	−0.995946	+	0.0899493i	$0.971330\pi$
$284$	−1.19218	+	4.29385i	−0.0707430	+	0.254793i
$285$		0			0
$286$	4.59375	+	8.66473i	0.271634	+	0.512356i
$287$	−1.77331	−	2.61543i	−0.104675	−	0.154384i
$288$		0			0
$289$	−6.56428	−	7.72806i	−0.386134	−	0.454592i
$290$	−15.0821	+	37.8532i	−0.885650	+	2.22281i
$291$		0			0
$292$	−24.3501	−	14.6510i	−1.42498	−	0.857382i
$293$	−15.0095	−	5.05730i	−0.876865	−	0.295450i	−0.155359	−	0.987858i	$-0.549653\pi$
$293$	−15.0095	−	5.05730i	−0.876865	−	0.295450i	−0.721506	+	0.692408i	$0.756550\pi$
$294$		0			0
$295$	−16.9047	+	23.5424i	−0.984229	+	1.37069i
$296$	0.0109232			0.000634897
$297$		0			0
$298$	5.34655	+	3.21691i	0.309717	+	0.186351i
$299$	5.04707	+	3.83669i	0.291880	+	0.221881i
$300$		0			0
$301$	−13.2641	−	15.6157i	−0.764529	−	0.900073i
$302$	−0.753538	+	0.348624i	−0.0433612	+	0.0200610i
$303$		0			0
$304$	−6.58507	−	12.4208i	−0.377679	−	0.712379i
$305$	−4.43183	+	5.21756i	−0.253766	+	0.298756i
$306$		0			0
$307$	−1.20686	−	3.02898i	−0.0688789	−	0.172873i	0.890507	−	0.454969i	$-0.150350\pi$
$307$	−1.20686	−	3.02898i	−0.0688789	−	0.172873i	−0.959386	+	0.282096i	$0.908970\pi$
$308$	8.17582	−	15.4212i	0.465861	−	0.878706i
$309$		0			0
$310$	−59.3536	+	45.1195i	−3.37106	+	2.56261i
$311$	3.06115	+	11.0253i	0.173582	+	0.625186i	0.998226	+	0.0595342i	$0.0189615\pi$
$311$	3.06115	+	11.0253i	0.173582	+	0.625186i	−0.824644	+	0.565652i	$0.808625\pi$
$312$		0			0
$313$	1.32351	+	8.07303i	0.0748090	+	0.456315i	0.997493	+	0.0707587i	$0.0225420\pi$
$313$	1.32351	+	8.07303i	0.0748090	+	0.456315i	−0.922684	+	0.385556i	$0.874010\pi$
$314$	21.0799	−	4.64004i	1.18961	−	0.261852i
$315$		0			0
$316$	26.2101	+	2.85052i	1.47443	+	0.160354i
$317$	−3.09509	+	4.56491i	−0.173837	+	0.256391i	−0.904620	−	0.426220i	$-0.859845\pi$
$317$	−3.09509	+	4.56491i	−0.173837	+	0.256391i	0.730782	+	0.682611i	$0.239155\pi$
$318$		0			0
$319$	1.14082	+	21.0412i	0.0638736	+	1.17808i
$320$	21.6491	+	20.5071i	1.21022	+	1.14638i
$321$		0			0
$322$	1.22546	−	22.6023i	0.0682922	−	1.25957i
$323$	8.93658	+	1.96709i	0.497244	+	0.109452i
$324$		0			0
$325$	−11.0326	+	3.71730i	−0.611977	+	0.206199i
$326$	−2.09724	−	0.461637i	−0.116155	−	0.0255677i
$327$		0			0
$328$	0.0245934	−	0.0232961i	0.00135794	−	0.00128631i
$329$	21.2033	+	20.0848i	1.16897	+	1.10731i
$330$		0			0
$331$	0.535117	−	3.26407i	0.0294127	−	0.179410i	−0.968035	−	0.250817i	$-0.919301\pi$
$331$	0.535117	−	3.26407i	0.0294127	−	0.179410i	0.997447	+	0.0714074i	$0.0227490\pi$
$332$	13.7791	−	20.3226i	0.756225	−	1.11535i
$333$		0			0
$334$	4.76151	−	2.86491i	0.260538	−	0.156761i
$335$	−25.5319	+	5.61999i	−1.39495	+	0.307053i
$336$		0			0
$337$	−11.3663	−	5.25860i	−0.619161	−	0.286454i	0.0851255	−	0.996370i	$-0.472871\pi$
$337$	−11.3663	−	5.25860i	−0.619161	−	0.286454i	−0.704287	+	0.709916i	$0.748733\pi$
$338$	6.09665	+	21.9582i	0.331614	+	1.19437i
$339$		0			0
$340$	−19.5314	+	2.12416i	−1.05924	+	0.115199i
$341$	−18.0600	+	34.0648i	−0.978005	+	1.84471i
$342$		0			0
$343$	5.37877	−	19.3726i	0.290426	−	1.04602i
$344$	0.142195	−	0.167405i	0.00766666	−	0.00902589i
$345$		0			0
$346$	7.76410	+	11.4512i	0.417400	+	0.615620i
$347$	0.765300	−	0.354065i	0.0410834	−	0.0190072i	−0.399240	−	0.916847i	$-0.630726\pi$
$347$	0.765300	−	0.354065i	0.0410834	−	0.0190072i	0.440323	+	0.897839i	$0.354864\pi$
$348$		0			0
$349$	4.35996	−	10.9427i	0.233383	−	0.585748i	−0.764911	−	0.644136i	$-0.777217\pi$
$349$	4.35996	−	10.9427i	0.233383	−	0.585748i	0.998294	+	0.0583884i	$0.0185962\pi$
$350$	33.0906	+	25.1548i	1.76877	+	1.34458i
$351$		0			0
$352$	29.4962	+	9.93842i	1.57215	+	0.529720i
$353$	−30.1631			−1.60542			−0.802709	−	0.596370i	$-0.796609\pi$
$353$	−30.1631			−1.60542			−0.802709	+	0.596370i	$0.796609\pi$
$354$		0			0
$355$	−8.45854			−0.448933
$356$	−20.7186	−	6.98092i	−1.09809	−	0.369988i
$357$		0			0
$358$	21.4415	+	16.2994i	1.13322	+	0.861449i
$359$	−2.98682	+	7.49636i	−0.157638	+	0.395643i	−0.986489	−	0.163827i	$-0.947616\pi$
$359$	−2.98682	+	7.49636i	−0.157638	+	0.395643i	0.828851	+	0.559470i	$0.188995\pi$
$360$		0			0
$361$	−6.16679	+	2.85306i	−0.324568	+	0.150161i
$362$	−16.1875	−	23.8748i	−0.850798	−	1.25483i
$363$		0			0
$364$	−3.65460	+	4.30253i	−0.191553	+	0.225514i
$365$	14.4306	−	51.9743i	0.755332	−	2.72046i
$366$		0			0
$367$	3.18754	−	6.01235i	0.166388	−	0.313842i	−0.786271	−	0.617882i	$-0.787991\pi$
$367$	3.18754	−	6.01235i	0.166388	−	0.313842i	0.952659	+	0.304040i	$0.0983357\pi$
$368$	20.1240	−	2.18862i	1.04904	−	0.114090i
$369$		0			0
$370$	−0.911569	−	3.28318i	−0.0473902	−	0.170684i
$371$	4.32803	+	2.00236i	0.224700	+	0.103957i
$372$		0			0
$373$	14.8644	−	3.27190i	0.769650	−	0.169413i	0.187247	−	0.982313i	$-0.440044\pi$
$373$	14.8644	−	3.27190i	0.769650	−	0.169413i	0.582403	+	0.812900i	$0.302113\pi$
$374$	−17.4644	+	10.5080i	−0.903063	+	0.543355i
$375$		0			0
$376$	−0.175705	+	0.259146i	−0.00906130	+	0.0133644i
$377$	1.10257	−	6.72540i	0.0567854	−	0.346376i
$378$		0			0
$379$	21.5063	+	20.3718i	1.10470	+	1.04643i	0.998643	+	0.0520694i	$0.0165817\pi$
$379$	21.5063	+	20.3718i	1.10470	+	1.04643i	0.106059	+	0.994360i	$0.466177\pi$
$380$	−19.0248	+	18.0212i	−0.975950	+	0.924469i
$381$		0			0
$382$	4.44834	+	0.979153i	0.227597	+	0.0500978i
$383$	5.77316	−	1.94521i	0.294995	−	0.0993953i	−0.167913	−	0.985802i	$-0.553703\pi$
$383$	5.77316	−	1.94521i	0.294995	−	0.0993953i	0.462908	+	0.886407i	$0.346806\pi$
$384$		0			0
$385$	32.3560	+	7.12209i	1.64901	+	0.362976i
$386$	−0.566564	+	10.4497i	−0.0288374	+	0.531874i
$387$		0			0
$388$	−6.48240	−	6.14046i	−0.329094	−	0.311735i
$389$	−1.43779	−	26.5186i	−0.0728991	−	1.34454i	−0.774771	−	0.632242i	$-0.782135\pi$
$389$	−1.43779	−	26.5186i	−0.0728991	−	1.34454i	0.701872	−	0.712303i	$-0.252348\pi$
$390$		0			0
$391$	−7.39411	+	10.9055i	−0.373936	+	0.551515i
$392$	0.0461748	+	0.00502181i	0.00233218	+	0.000253640i
$393$		0			0
$394$	−38.3615	+	8.44401i	−1.93263	+	0.425403i
$395$	8.09607	+	49.3838i	0.407357	+	2.48477i
$396$		0			0
$397$	1.76146	+	6.34420i	0.0884050	+	0.318406i	0.994509	−	0.104648i	$-0.0333717\pi$
$397$	1.76146	+	6.34420i	0.0884050	+	0.318406i	−0.906104	+	0.423054i	$0.860958\pi$
$398$	23.5284	−	17.8858i	1.17937	−	0.896535i
$399$		0			0
$400$	−17.4118	+	32.8422i	−0.870592	+	1.64211i
$401$	−1.93786	−	4.86365i	−0.0967719	−	0.242879i	0.872619	−	0.488402i	$-0.162420\pi$
$401$	−1.93786	−	4.86365i	−0.0967719	−	0.242879i	−0.969391	+	0.245522i	$0.921041\pi$
$402$		0			0
$403$	8.07285	−	9.50410i	0.402138	−	0.473433i
$404$	−13.0971	−	24.7037i	−0.651605	−	1.22906i
$405$		0			0
$406$	−22.0838	+	10.2170i	−1.09600	+	0.507064i
$407$	−1.14076	−	1.34300i	−0.0565453	−	0.0665702i
$408$		0			0
$409$	15.3235	+	11.6487i	0.757701	+	0.575989i	0.911105	−	0.412174i	$-0.135231\pi$
$409$	15.3235	+	11.6487i	0.757701	+	0.575989i	−0.153404	+	0.988164i	$0.549024\pi$
$410$	−9.05448	−	5.44790i	−0.447169	−	0.269053i
$411$		0			0
$412$	26.6782			1.31434
$413$	−16.9970	+	3.26432i	−0.836368	+	0.160626i
$414$		0			0
$415$	44.1656	+	14.8811i	2.16800	+	0.730485i
$416$	−8.62571	−	5.18992i	−0.422910	−	0.254457i
$417$		0			0
$418$	−10.0626	+	25.2551i	−0.492176	+	1.23527i
$419$	6.98672	+	8.22541i	0.341324	+	0.401837i	0.905864	−	0.423568i	$-0.139223\pi$
$419$	6.98672	+	8.22541i	0.341324	+	0.401837i	−0.564541	+	0.825405i	$0.690947\pi$
$420$		0			0
$421$	−3.92220	−	5.78481i	−0.191156	−	0.281934i	0.720018	−	0.693955i	$-0.244133\pi$
$421$	−3.92220	−	5.78481i	−0.191156	−	0.281934i	−0.911174	+	0.412021i	$0.864823\pi$
$422$	11.0583	+	20.8582i	0.538309	+	1.01536i
$423$		0			0
$424$	−0.0136768	+	0.0492595i	−0.000664206	+	0.00239225i
$425$	−8.95558	−	22.4768i	−0.434409	−	1.09029i
$426$		0			0
$427$	−4.06406	+	0.441993i	−0.196674	+	0.0213895i
$428$	22.0714	−	16.7782i	1.06686	−	0.811006i
$429$		0			0
$430$	−62.1835	−	28.7692i	−2.99875	−	1.38737i
$431$	−2.22019	−	13.5426i	−0.106943	−	0.652323i	−0.984839	−	0.173472i	$-0.944502\pi$
$431$	−2.22019	−	13.5426i	−0.106943	−	0.652323i	0.877896	−	0.478851i	$-0.158947\pi$
$432$		0			0
$433$	27.7657	−	16.7061i	1.33433	−	0.802843i	0.343661	−	0.939094i	$-0.388333\pi$
$433$	27.7657	−	16.7061i	1.33433	−	0.802843i	0.990674	+	0.136251i	$0.0435054\pi$
$434$	−44.2613	−	4.81370i	−2.12461	−	0.231065i
$435$		0			0
$436$	0.343276	−	2.09389i	0.0164399	−	0.100279i
$437$	0.951454	+	17.5485i	0.0455142	+	0.839460i
$438$		0			0
$439$	−7.98199	+	7.56095i	−0.380960	+	0.360864i	−0.854087	−	0.520130i	$-0.825884\pi$
$439$	−7.98199	+	7.56095i	−0.380960	+	0.360864i	0.473128	+	0.880994i	$0.343125\pi$
$440$	−0.0192286	+	0.354650i	−0.000916685	+	0.0169073i
$441$		0			0
$442$	6.24690	−	2.10483i	0.297135	−	0.100116i
$443$	25.4524	−	8.57592i	1.20928	−	0.407454i	0.358777	−	0.933423i	$-0.383194\pi$
$443$	25.4524	−	8.57592i	1.20928	−	0.407454i	0.850504	+	0.525969i	$0.176297\pi$
$444$		0			0
$445$	2.24669	−	41.4378i	0.106503	−	1.96434i
$446$	−38.9021	+	36.8501i	−1.84207	+	1.74490i
$447$		0			0
$448$	0.964072	+	17.7813i	0.0455481	+	0.840086i
$449$	1.12554	−	6.86546i	0.0531173	−	0.324001i	−0.946880	−	0.321588i	$-0.895783\pi$
$449$	1.12554	−	6.86546i	0.0531173	−	0.324001i	0.999997	−	0.00241348i	$-0.000768235\pi$
$450$		0			0
$451$	−5.43265	−	0.590836i	−0.255813	−	0.0278214i
$452$	−32.9130	+	19.8031i	−1.54810	+	0.931460i
$453$		0			0
$454$	3.07574	+	18.7612i	0.144352	+	0.880507i
$455$	−9.72483	−	4.49918i	−0.455907	−	0.210925i
$456$		0			0
$457$	−20.0120	+	15.2127i	−0.936123	+	0.711622i	−0.957586	−	0.288147i	$-0.906961\pi$
$457$	−20.0120	+	15.2127i	−0.936123	+	0.711622i	0.0214630	+	0.999770i	$0.493168\pi$
$458$	11.3806	−	1.23772i	0.531783	−	0.0578348i
$459$		0			0
$460$	−13.9663	−	35.0529i	−0.651184	−	1.63435i
$461$	3.31204	−	11.9289i	0.154257	−	0.555584i	−0.845509	−	0.533961i	$-0.820703\pi$
$461$	3.31204	−	11.9289i	0.154257	−	0.555584i	0.999766	−	0.0216232i	$-0.00688340\pi$
$462$		0			0
$463$	4.04503	+	7.62973i	0.187988	+	0.354584i	0.959535	−	0.281589i	$-0.0908614\pi$
$463$	4.04503	+	7.62973i	0.187988	+	0.354584i	−0.771547	+	0.636173i	$0.780517\pi$
$464$	−12.2117	−	18.0110i	−0.566916	−	0.836139i
$465$		0			0
$466$	3.76073	+	4.42748i	0.174213	+	0.205099i
$467$	−1.06323	+	2.66852i	−0.0492006	+	0.123484i	−0.951523	−	0.307578i	$-0.900482\pi$
$467$	−1.06323	+	2.66852i	−0.0492006	+	0.123484i	0.902322	+	0.431062i	$0.141861\pi$
$468$		0			0
$469$	−13.3770	−	8.04867i	−0.617693	−	0.371653i
$470$	92.5543	+	31.1852i	4.26921	+	1.43847i
$471$		0			0
$472$	−0.0640124	−	0.174152i	−0.00294641	−	0.00801597i
$473$	−35.4326			−1.62919
$474$		0			0
$475$	−27.6527	−	16.6381i	−1.26879	−	0.763408i
$476$	−9.33993	−	7.10003i	−0.428095	−	0.325429i
$477$		0			0
$478$	−8.96193	−	10.5508i	−0.409909	−	0.482582i
$479$	34.9759	−	16.1816i	1.59809	−	0.739356i	0.599935	−	0.800049i	$-0.295193\pi$
$479$	34.9759	−	16.1816i	1.59809	−	0.739356i	0.998156	+	0.0606930i	$0.0193311\pi$
$480$		0			0
$481$	0.266947	+	0.503515i	0.0121717	+	0.0229583i
$482$	−9.95424	+	11.7190i	−0.453403	+	0.533788i
$483$		0			0
$484$	−3.07894	−	7.72755i	−0.139952	−	0.351252i
$485$	7.93870	−	14.9740i	0.360478	−	0.679933i
$486$		0			0
$487$	−2.44868	+	1.86144i	−0.110960	+	0.0843499i	−0.659183	−	0.751983i	$-0.729098\pi$
$487$	−2.44868	+	1.86144i	−0.110960	+	0.0843499i	0.548223	+	0.836332i	$0.315305\pi$
$488$	−0.0117244	−	0.0422275i	−0.000530739	−	0.00191155i
$489$		0			0
$490$	−2.34401	−	14.2978i	−0.105891	−	0.645909i
$491$	−9.66114	+	2.12658i	−0.436001	+	0.0959712i	−0.427547	−	0.903993i	$-0.640622\pi$
$491$	−9.66114	+	2.12658i	−0.436001	+	0.0959712i	−0.00845432	+	0.999964i	$0.502691\pi$
$492$		0			0
$493$	14.0808	+	1.53138i	0.634167	+	0.0689698i
$494$	4.93427	−	7.27750i	0.222003	−	0.327430i
$495$		0			0
$496$	−2.15559	−	39.7575i	−0.0967888	−	1.78516i
$497$	−3.66710	−	3.47366i	−0.164492	−	0.155815i
$498$		0			0
$499$	−0.0642414	+	1.18486i	−0.00287584	+	0.0530417i	−0.999619	−	0.0275989i	$-0.991214\pi$
$499$	−0.0642414	+	1.18486i	−0.00287584	+	0.0530417i	0.996743	+	0.0806407i	$0.0256966\pi$
$500$	31.0423	+	6.83293i	1.38825	+	0.305578i
$501$		0			0
$502$	12.2867	−	4.13987i	0.548383	−	0.184772i
$503$	15.6525	+	3.44538i	0.697911	+	0.153622i	0.549735	−	0.835339i	$-0.314729\pi$
$503$	15.6525	+	3.44538i	0.697911	+	0.153622i	0.148176	+	0.988961i	$0.452660\pi$
$504$		0			0
$505$	38.5306	−	36.4982i	1.71459	−	1.62415i
$506$	−28.4192	−	26.9201i	−1.26339	−	1.19674i
$507$		0			0
$508$	0.887274	−	5.41213i	0.0393664	−	0.240125i
$509$	15.1625	−	22.3631i	0.672067	−	0.991225i	−0.326867	−	0.945070i	$-0.605993\pi$
$509$	15.1625	−	22.3631i	0.672067	−	0.991225i	0.998934	−	0.0461548i	$-0.0146967\pi$
$510$		0			0
$511$	27.6005	−	16.6066i	1.22097	−	0.734635i
$512$	−31.2011	+	6.86789i	−1.37891	+	0.303521i
$513$		0			0
$514$	29.9744	+	13.8676i	1.32211	+	0.611675i
$515$	13.5472	+	48.7926i	0.596960	+	2.15006i
$516$		0			0
$517$	50.2116	−	5.46084i	2.20830	−	0.240167i
$518$	0.953100	−	1.79774i	0.0418768	−	0.0789880i
$519$		0			0
$520$	0.0307310	−	0.110683i	0.00134764	−	0.00485378i
$521$	−7.70492	+	9.07093i	−0.337558	+	0.397405i	−0.904584	−	0.426296i	$-0.859818\pi$
$521$	−7.70492	+	9.07093i	−0.337558	+	0.397405i	0.567025	+	0.823700i	$0.308094\pi$
$522$		0			0
$523$	−19.5869	−	28.8885i	−0.856475	−	1.26321i	−0.963164	−	0.268914i	$-0.913335\pi$
$523$	−19.5869	−	28.8885i	−0.856475	−	1.26321i	0.106689	−	0.994292i	$-0.465975\pi$
$524$	12.5349	−	5.79926i	0.547590	−	0.253342i
$525$		0			0
$526$	2.68931	−	6.74966i	0.117259	−	0.294299i
$527$	20.6315	+	15.6836i	0.898721	+	0.683190i
$528$		0			0
$529$	−2.18461	−	0.736082i	−0.0949832	−	0.0320036i
$530$	15.9473			0.692705
$531$		0			0
$532$	−15.6487			−0.678459
$533$	1.67488	+	0.564334i	0.0725473	+	0.0244440i
$534$		0			0
$535$	41.8940	+	31.8470i	1.81123	+	1.37686i
$536$	0.0619473	−	0.155476i	0.00267572	−	0.00671554i
$537$		0			0
$538$	55.8522	−	25.8400i	2.40796	−	1.11404i
$539$	−4.20481	−	6.20163i	−0.181114	−	0.267123i
$540$		0			0
$541$	−13.4966	+	15.8894i	−0.580265	+	0.683140i	−0.971470	−	0.237163i	$-0.923782\pi$
$541$	−13.4966	+	15.8894i	−0.580265	+	0.683140i	0.391205	+	0.920303i	$0.372058\pi$
$542$	4.47786	−	16.1278i	0.192340	−	0.692748i
$543$		0			0
$544$	9.79973	−	18.4842i	0.420160	−	0.792506i
$545$	4.00389	−	0.435449i	0.171508	−	0.0186526i
$546$		0			0
$547$	−6.54945	−	23.5890i	−0.280034	−	1.00859i	−0.961062	−	0.276334i	$-0.910880\pi$
$547$	−6.54945	−	23.5890i	−0.280034	−	1.00859i	0.681027	−	0.732258i	$-0.261533\pi$
$548$	40.5766	+	18.7727i	1.73335	+	0.801931i
$549$		0			0
$550$	70.2029	−	15.4528i	2.99346	−	0.658911i
$551$	16.1878	−	9.73988i	0.689624	−	0.414933i
$552$		0			0
$553$	−16.7705	+	24.7346i	−0.713153	+	1.05182i
$554$	6.26894	−	38.2388i	0.266342	−	1.62461i
$555$		0			0
$556$	−13.4374	−	12.7286i	−0.569873	−	0.539813i
$557$	10.0648	−	9.53389i	0.426459	−	0.403964i	−0.444139	−	0.895958i	$-0.646490\pi$
$557$	10.0648	−	9.53389i	0.426459	−	0.403964i	0.870599	+	0.491994i	$0.163732\pi$
$558$		0			0
$559$	11.1918	+	2.46349i	0.473361	+	0.104195i
$560$	−32.4221	+	10.9243i	−1.37008	+	0.461635i
$561$		0			0
$562$	−52.2392	−	11.4987i	−2.20358	−	0.485044i
$563$	0.901272	−	16.6230i	0.0379841	−	0.700576i	−0.916084	−	0.400986i	$-0.868668\pi$
$563$	0.901272	−	16.6230i	0.0379841	−	0.700576i	0.954068	−	0.299589i	$-0.0968497\pi$
$564$		0			0
$565$	−52.9317	−	50.1395i	−2.22685	−	2.10939i
$566$	−1.03697	−	19.1258i	−0.0435872	−	0.803919i
$567$		0			0
$568$	0.0303882	−	0.0448192i	0.00127506	−	0.00188057i
$569$	22.2417	+	2.41893i	0.932421	+	0.101407i	0.561704	−	0.827339i	$-0.310146\pi$
$569$	22.2417	+	2.41893i	0.932421	+	0.101407i	0.370718	+	0.928746i	$0.379112\pi$
$570$		0			0
$571$	−33.7250	+	7.42343i	−1.41135	+	0.310661i	−0.854283	−	0.519808i	$-0.826003\pi$
$571$	−33.7250	+	7.42343i	−1.41135	+	0.310661i	−0.557064	+	0.830469i	$0.688072\pi$
$572$	1.57941	+	9.63399i	0.0660386	+	0.402817i
$573$		0			0
$574$	−1.68818	−	6.08027i	−0.0704632	−	0.253786i
$575$	36.9936	−	28.1218i	1.54274	−	1.17276i
$576$		0			0
$577$	7.36745	−	13.8965i	0.306711	−	0.578518i	−0.681464	−	0.731852i	$-0.738656\pi$
$577$	7.36745	−	13.8965i	0.306711	−	0.578518i	0.988174	+	0.153334i	$0.0490011\pi$
$578$	−7.49479	−	18.8105i	−0.311742	−	0.782414i
$579$		0			0
$580$	−26.2593	+	30.9149i	−1.09036	+	1.28367i
$581$	13.0363	+	24.5890i	0.540835	+	1.02012i
$582$		0			0
$583$	7.48478	−	3.46283i	0.309988	−	0.143416i
$584$	0.223552	+	0.263186i	0.00925067	+	0.0108907i
$585$		0			0
$586$	−25.1799	−	19.1412i	−1.04017	−	0.790717i
$587$	9.69805	+	5.83512i	0.400281	+	0.240841i	0.701434	−	0.712735i	$-0.252544\pi$
$587$	9.69805	+	5.83512i	0.400281	+	0.240841i	−0.301152	+	0.953576i	$0.597371\pi$
$588$		0			0
$589$	34.5673			1.42432
$590$	−47.0026	+	33.7736i	−1.93507	+	1.39044i
$591$		0			0
$592$	1.72442	+	0.581024i	0.0708731	+	0.0238799i
$593$	−12.5877	−	7.57375i	−0.516914	−	0.311017i	0.233084	−	0.972456i	$-0.425118\pi$
$593$	−12.5877	−	7.57375i	−0.516914	−	0.311017i	−0.749998	+	0.661440i	$0.769946\pi$
$594$		0			0
$595$	8.24263	−	20.6874i	0.337915	−	0.848102i
$596$	4.02116	+	4.73408i	0.164713	+	0.193915i
$597$		0			0
$598$	7.10486	+	10.4789i	0.290540	+	0.428514i
$599$	1.86661	+	3.52080i	0.0762676	+	0.143856i	0.918713	−	0.394926i	$-0.129230\pi$
$599$	1.86661	+	3.52080i	0.0762676	+	0.143856i	−0.842446	+	0.538782i	$0.818885\pi$
$600$		0			0
$601$	6.63515	−	23.8977i	0.270653	−	0.974806i	−0.695857	−	0.718180i	$-0.744975\pi$
$601$	6.63515	−	23.8977i	0.270653	−	0.974806i	0.966511	−	0.256626i	$-0.0826107\pi$
$602$	−15.1443	−	38.0094i	−0.617237	−	1.54915i
$603$		0			0
$604$	−0.821660	+	0.0893609i	−0.0334329	+	0.00363604i
$605$	12.5697	−	9.55520i	0.511029	−	0.388474i
$606$		0			0
$607$	−4.15918	−	1.92424i	−0.168816	−	0.0781025i	0.333661	−	0.942693i	$-0.391716\pi$
$607$	−4.15918	−	1.92424i	−0.168816	−	0.0781025i	−0.502477	+	0.864591i	$0.667578\pi$
$608$	−4.51460	−	27.5378i	−0.183091	−	1.11681i
$609$		0			0
$610$	−11.7139	+	7.04800i	−0.474281	+	0.285365i
$611$	−16.2396	−	1.76616i	−0.656982	−	0.0714511i
$612$		0			0
$613$	2.32105	−	14.1578i	0.0937462	−	0.571827i	−0.897627	−	0.440756i	$-0.854710\pi$
$613$	2.32105	−	14.1578i	0.0937462	−	0.571827i	0.991373	−	0.131070i	$-0.0418414\pi$
$614$	−0.352512	−	6.50170i	−0.0142262	−	0.262387i
$615$		0			0
$616$	−0.153980	+	0.145858i	−0.00620404	+	0.00587677i
$617$	−1.66226	+	30.6586i	−0.0669202	+	1.23427i	0.751533	+	0.659696i	$0.229315\pi$
$617$	−1.66226	+	30.6586i	−0.0669202	+	1.23427i	−0.818453	+	0.574574i	$0.805168\pi$
$618$		0			0
$619$	−25.6455	+	8.64096i	−1.03078	+	0.347310i	−0.783340	−	0.621594i	$-0.786485\pi$
$619$	−25.6455	+	8.64096i	−1.03078	+	0.347310i	−0.247438	+	0.968904i	$0.579589\pi$
$620$	−70.3325	+	23.6978i	−2.82462	+	0.951725i
$621$		0			0
$622$	−1.23708	+	22.8166i	−0.0496023	+	0.914861i
$623$	17.9913	−	17.0422i	0.720805	−	0.682783i
$624$		0			0
$625$	0.765773	+	14.1239i	0.0306309	+	0.564954i
$626$	−2.64301	+	16.1216i	−0.105636	+	0.644350i
$627$		0			0
$628$	21.3605	+	2.32310i	0.852378	+	0.0927017i
$629$	−1.01487	+	0.610628i	−0.0404656	+	0.0243473i
$630$		0			0
$631$	6.60194	+	40.2701i	0.262819	+	1.60313i	0.707016	+	0.707197i	$0.250041\pi$
$631$	6.60194	+	40.2701i	0.262819	+	1.60313i	−0.444197	+	0.895929i	$0.646511\pi$
$632$	−0.290756	−	0.134518i	−0.0115656	−	0.00535084i
$633$		0			0
$634$	−8.76802	+	6.66527i	−0.348222	+	0.264712i
$635$	10.3490	−	1.12552i	0.410686	−	0.0446648i
$636$		0			0
$637$	0.896959	+	2.25120i	0.0355388	+	0.0891957i
$638$	−11.2577	+	40.5465i	−0.445696	+	1.60525i
$639$		0			0
$640$	−0.341542	−	0.644216i	−0.0135006	−	0.0254649i
$641$	3.36375	+	4.96116i	0.132860	+	0.195954i	0.888300	−	0.459264i	$-0.151887\pi$
$641$	3.36375	+	4.96116i	0.132860	+	0.195954i	−0.755440	+	0.655218i	$0.772577\pi$
$642$		0			0
$643$	−25.7711	−	30.3400i	−1.01631	−	1.19649i	−0.980375	−	0.197140i	$-0.936835\pi$
$643$	−25.7711	−	30.3400i	−1.01631	−	1.19649i	−0.0359359	−	0.999354i	$-0.511441\pi$
$644$	8.34019	−	20.9323i	0.328650	−	0.824849i
$645$		0			0
$646$	15.6576	+	9.42089i	0.616041	+	0.370660i
$647$	−33.4691	−	11.2770i	−1.31580	−	0.443346i	−0.428088	−	0.903737i	$-0.640813\pi$
$647$	−33.4691	−	11.2770i	−1.31580	−	0.443346i	−0.887716	+	0.460391i	$0.847709\pi$
$648$		0			0
$649$	−14.7268	+	26.0577i	−0.578077	+	1.02286i
$650$	−23.2487			−0.911890
$651$		0			0
$652$	−1.83169	−	1.10209i	−0.0717347	−	0.0431613i
$653$	−29.9430	−	22.7621i	−1.17176	−	0.890749i	−0.176151	−	0.984363i	$-0.556365\pi$
$653$	−29.9430	−	22.7621i	−1.17176	−	0.890749i	−0.995609	+	0.0936144i	$0.970158\pi$
$654$		0			0
$655$	16.9716	+	19.9806i	0.663137	+	0.780705i
$656$	5.12166	−	2.36953i	0.199967	−	0.0925147i
$657$		0			0
$658$	27.3191	+	51.5292i	1.06501	+	2.00882i
$659$	−0.572052	+	0.673471i	−0.0222840	+	0.0262347i	−0.773191	−	0.634173i	$-0.781341\pi$
$659$	−0.572052	+	0.673471i	−0.0222840	+	0.0262347i	0.750907	+	0.660408i	$0.229617\pi$
$660$		0			0
$661$	3.25167	+	8.16107i	0.126475	+	0.317429i	0.978556	−	0.205982i	$-0.0660387\pi$
$661$	3.25167	+	8.16107i	0.126475	+	0.317429i	−0.852081	+	0.523411i	$0.824659\pi$
$662$	3.09397	−	5.83584i	0.120251	−	0.226817i
$663$		0			0
$664$	−0.237520	+	0.180558i	−0.00921756	+	0.00700701i
$665$	−7.94641	−	28.6204i	−0.308149	−	1.10985i
$666$		0			0
$667$	4.40092	+	26.8444i	0.170404	+	1.03942i
$668$	5.40238	−	1.18915i	0.209024	−	0.0460098i
$669$		0			0
$670$	−51.9010	−	5.64457i	−2.00511	−	0.218069i
$671$	−3.96743	+	5.85153i	−0.153161	+	0.225896i
$672$		0			0
$673$	−1.14547	−	21.1269i	−0.0441544	−	0.814381i	−0.933815	−	0.357757i	$-0.883541\pi$
$673$	−1.14547	−	21.1269i	−0.0441544	−	0.814381i	0.889660	−	0.456623i	$-0.150941\pi$
$674$	−18.1569	−	17.1991i	−0.699378	−	0.662486i
$675$		0			0
$676$	−1.22816	+	22.6520i	−0.0472368	+	0.871232i
$677$	42.4580	+	9.34571i	1.63179	+	0.359185i	0.934044	−	0.357157i	$-0.116254\pi$
$677$	42.4580	+	9.34571i	1.63179	+	0.359185i	0.697749	+	0.716342i	$0.254185\pi$
$678$		0			0
$679$	9.59108	−	3.23161i	0.368072	−	0.124018i
$680$	0.233150	+	0.0513202i	0.00894090	+	0.00196804i
$681$		0			0
$682$	−55.8984	+	52.9498i	−2.14046	+	2.02755i
$683$	−27.2660	−	25.8277i	−1.04330	−	0.988269i	−0.0433615	−	0.999059i	$-0.513807\pi$
$683$	−27.2660	−	25.8277i	−1.04330	−	0.988269i	−0.999942	+	0.0107900i	$0.996565\pi$
$684$		0			0
$685$	−13.7292	+	83.7444i	−0.524566	+	3.19971i
$686$	22.5317	−	33.2317i	0.860263	−	1.26879i
$687$		0			0
$688$	31.3526	−	18.8642i	1.19531	−	0.719193i
$689$	−2.60491	+	0.573383i	−0.0992391	+	0.0218442i
$690$		0			0
$691$	12.7926	+	5.91849i	0.486654	+	0.225150i	0.647844	−	0.761773i	$-0.275671\pi$
$691$	12.7926	+	5.91849i	0.486654	+	0.225150i	−0.161190	+	0.986923i	$0.551533\pi$
$692$	3.68448	+	13.2703i	0.140063	+	0.504461i
$693$		0			0
$694$	1.67405	−	0.182064i	0.0635460	−	0.00691104i
$695$	16.4562	−	31.0396i	0.624218	−	1.17740i
$696$		0			0
$697$	−0.982670	+	3.53926i	−0.0372213	+	0.134059i
$698$	15.2284	−	17.9283i	0.576404	−	0.678595i
$699$		0			0
$700$	23.2205	+	34.2476i	0.877652	+	1.29444i
$701$	−11.2105	+	5.18652i	−0.423414	+	0.195892i	−0.620012	−	0.784592i	$-0.712872\pi$
$701$	−11.2105	+	5.18652i	−0.423414	+	0.195892i	0.196599	+	0.980484i	$0.437010\pi$
$702$		0			0
$703$	−0.584745	+	1.46760i	−0.0220541	+	0.0553515i
$704$	24.5162	+	18.6367i	0.923988	+	0.702397i
$705$		0			0
$706$	−57.0818	−	19.2331i	−2.14830	−	0.723847i
$707$	31.6932			1.19195
$708$		0			0
$709$	−10.7610			−0.404136			−0.202068	−	0.979371i	$-0.564766\pi$
$709$	−10.7610			−0.404136			−0.202068	+	0.979371i	$0.564766\pi$
$710$	−16.0073	−	5.39347i	−0.600742	−	0.202413i
$711$		0			0
$712$	0.211495	+	0.160774i	0.00792610	+	0.00602527i
$713$	−18.4231	+	46.2385i	−0.689951	+	1.73165i
$714$		0			0
$715$	−16.8179	+	7.78077i	−0.628952	+	0.290984i
$716$	15.0460	+	22.1912i	0.562296	+	0.829324i
$717$		0			0
$718$	−10.4323	+	12.2819i	−0.389331	+	0.458356i
$719$	10.0593	−	36.2303i	0.375148	−	1.35116i	−0.499462	−	0.866336i	$-0.666469\pi$
$719$	10.0593	−	36.2303i	0.375148	−	1.35116i	0.874611	−	0.484826i	$-0.161117\pi$
$720$		0			0
$721$	−14.1644	+	26.7169i	−0.527509	+	0.994988i
$722$	−13.4895	+	1.46707i	−0.502027	+	0.0545987i
$723$		0			0
$724$	−7.68185	−	27.6675i	−0.285494	−	1.02826i
$725$	−45.3364	−	20.9748i	−1.68375	−	0.778986i
$726$		0			0
$727$	11.1478	−	2.45382i	0.413450	−	0.0910072i	−0.00337439	−	0.999994i	$-0.501074\pi$
$727$	11.1478	−	2.45382i	0.413450	−	0.0910072i	0.416824	+	0.908987i	$0.363143\pi$
$728$	0.0587773	−	0.0353651i	0.00217843	−	0.00131072i
$729$		0			0
$730$	60.4497	−	89.1567i	2.23734	−	3.29984i
$731$	−3.85306	+	23.5026i	−0.142510	+	0.869276i
$732$		0			0
$733$	3.74693	+	3.54928i	0.138396	+	0.131096i	0.753767	−	0.657142i	$-0.228235\pi$
$733$	3.74693	+	3.54928i	0.138396	+	0.131096i	−0.615370	+	0.788238i	$0.710994\pi$
$734$	9.86592	−	9.34550i	0.364158	−	0.344949i
$735$		0			0
$736$	39.2417	+	8.63775i	1.44647	+	0.318392i
$737$	−25.5852	+	8.62065i	−0.942442	+	0.317546i
$738$		0			0
$739$	43.4204	+	9.55756i	1.59725	+	0.351580i	0.922357	−	0.386339i	$-0.126260\pi$
$739$	43.4204	+	9.55756i	1.59725	+	0.351580i	0.674889	+	0.737919i	$0.264192\pi$
$740$	0.183634	−	3.38693i	0.00675051	−	0.124506i
$741$		0			0
$742$	6.91375	+	6.54905i	0.253812	+	0.240423i
$743$	1.69336	+	31.2322i	0.0621233	+	1.14580i	0.848898	+	0.528557i	$0.177267\pi$
$743$	1.69336	+	31.2322i	0.0621233	+	1.14580i	−0.786775	+	0.617240i	$0.788251\pi$
$744$		0			0
$745$	−6.61634	+	9.75837i	−0.242404	+	0.357519i
$746$	30.2163	+	3.28622i	1.10630	+	0.120317i
$747$		0			0
$748$	−19.8150	+	4.36161i	−0.724508	+	0.159476i
$749$	5.08407	+	31.0115i	0.185768	+	1.13313i
$750$		0			0
$751$	6.64513	+	23.9336i	0.242484	+	0.873349i	0.980162	+	0.198197i	$0.0635085\pi$
$751$	6.64513	+	23.9336i	0.242484	+	0.873349i	−0.737678	+	0.675153i	$0.764078\pi$
$752$	−41.5226	+	31.5646i	−1.51417	+	1.15104i
$753$		0			0
$754$	6.37492	−	12.0244i	0.232161	−	0.437902i
$755$	−0.580673	−	1.45738i	−0.0211328	−	0.0530395i
$756$		0			0
$757$	−18.9780	+	22.3427i	−0.689768	+	0.812058i	−0.989889	−	0.141843i	$-0.954697\pi$
$757$	−18.9780	+	22.3427i	−0.689768	+	0.812058i	0.300121	+	0.953901i	$0.402973\pi$
$758$	27.7094	+	52.2656i	1.00645	+	1.89837i
$759$		0			0
$760$	0.288996	−	0.133704i	0.0104830	−	0.00484995i
$761$	1.56591	+	1.84353i	0.0567642	+	0.0668280i	0.789811	−	0.613350i	$-0.210178\pi$
$761$	1.56591	+	1.84353i	0.0567642	+	0.0668280i	−0.733047	+	0.680178i	$0.761903\pi$
$762$		0			0
$763$	1.91467	+	1.45549i	0.0693155	+	0.0526923i
$764$	3.88511	+	2.33759i	0.140558	+	0.0845712i
$765$		0			0
$766$	12.1657			0.439564
$767$	6.46332	−	7.20673i	0.233377	−	0.260220i
$768$		0			0
$769$	−35.7421	−	12.0429i	−1.28889	−	0.434279i	−0.410345	−	0.911930i	$-0.634592\pi$
$769$	−35.7421	−	12.0429i	−1.28889	−	0.434279i	−0.878550	+	0.477651i	$0.841488\pi$
$770$	56.6904	+	34.1095i	2.04298	+	1.22922i
$771$		0			0
$772$	−3.85591	+	9.67760i	−0.138777	+	0.348304i
$773$	17.2539	+	20.3129i	0.620580	+	0.730603i	0.979204	−	0.202879i	$-0.0650298\pi$
$773$	17.2539	+	20.3129i	0.620580	+	0.730603i	−0.358624	+	0.933482i	$0.616754\pi$
$774$		0			0
$775$	−51.2930	−	75.6515i	−1.84250	−	2.71748i
$776$	0.0508219	+	0.0958603i	0.00182440	+	0.00344118i
$777$		0			0
$778$	14.1883	−	51.1015i	0.508674	−	1.83208i
$779$	1.81343	+	4.55137i	0.0649730	+	0.163070i
$780$		0			0
$781$	−8.68409	+	0.944452i	−0.310741	+	0.0337951i
$782$	−20.9467	+	15.9232i	−0.749051	+	0.569414i
$783$		0			0
$784$	7.02238	+	3.24890i	0.250799	+	0.116032i
$785$	6.59809	+	40.2466i	0.235496	+	1.43646i
$786$		0			0
$787$	−45.9865	+	27.6692i	−1.63924	+	0.986299i	−0.669290	+	0.743001i	$0.733402\pi$
$787$	−45.9865	+	27.6692i	−1.63924	+	0.986299i	−0.969952	+	0.243298i	$0.921771\pi$
$788$	−38.8723	−	4.22761i	−1.38477	−	0.150603i
$789$		0			0
$790$	−16.1676	+	98.6182i	−0.575219	+	3.50868i
$791$	−2.35714	−	43.4748i	−0.0838101	−	1.54579i
$792$		0			0
$793$	1.65999	−	1.57243i	0.0589481	−	0.0558386i
$794$	−0.711843	+	13.1292i	−0.0252624	+	0.465937i
$795$		0			0
$796$	27.8805	−	9.39403i	0.988198	−	0.332963i
$797$	−29.3586	+	9.89206i	−1.03993	+	0.350395i	−0.786912	−	0.617066i	$-0.788321\pi$
$797$	−29.3586	+	9.89206i	−1.03993	+	0.350395i	−0.253023	+	0.967460i	$0.581425\pi$
$798$		0			0
$799$	1.83798	−	33.8995i	0.0650229	−	1.19928i
$800$	−53.5682	+	50.7425i	−1.89392	+	1.79402i
$801$		0			0
$802$	−0.566030	−	10.4398i	−0.0199872	−	0.368643i
$803$	9.01212	−	54.9715i	0.318031	−	1.93990i
$804$		0			0
$805$	42.5188	+	4.62420i	1.49859	+	0.162982i
$806$	21.3375	−	12.8384i	0.751583	−	0.452212i
$807$		0			0
$808$	0.0549673	+	0.335286i	0.00193374	+	0.0117953i
$809$	42.7209	+	19.7648i	1.50199	+	0.694893i	0.986764	−	0.162162i	$-0.0518468\pi$
$809$	42.7209	+	19.7648i	1.50199	+	0.694893i	0.515224	+	0.857056i	$0.327709\pi$
$810$		0			0
$811$	37.5884	−	28.5740i	1.31991	−	1.00337i	0.321503	−	0.946908i	$-0.395812\pi$
$811$	37.5884	−	28.5740i	1.31991	−	1.00337i	0.998405	−	0.0564598i	$-0.0179813\pi$
$812$	−24.0802	+	2.61888i	−0.845050	+	0.0919048i
$813$		0			0
$814$	−1.30247	−	3.26894i	−0.0456514	−	0.114576i
$815$	1.08552	−	3.90968i	0.0380240	−	0.136950i
$816$		0			0
$817$	14.8799	+	28.0664i	0.520581	+	0.981921i
$818$	21.5713	+	31.8152i	0.754221	+	1.11239i
$819$		0			0
$820$	−6.80991	−	8.01725i	−0.237812	−	0.279975i
$821$	4.07154	−	10.2188i	0.142098	−	0.356638i	−0.840653	−	0.541574i	$-0.817828\pi$
$821$	4.07154	−	10.2188i	0.142098	−	0.356638i	0.982751	+	0.184936i	$0.0592078\pi$
$822$		0			0
$823$	−16.1982	−	9.74612i	−0.564633	−	0.339728i	0.204450	−	0.978877i	$-0.434459\pi$
$823$	−16.1982	−	9.74612i	−0.564633	−	0.339728i	−0.769083	+	0.639149i	$0.779287\pi$
$824$	−0.307207	−	0.103510i	−0.0107020	−	0.00360594i
$825$		0			0
$826$	−34.2472	−	4.66039i	−1.19161	−	0.162156i
$827$	−14.1624			−0.492475			−0.246238	−	0.969209i	$-0.579194\pi$
$827$	−14.1624			−0.492475			−0.246238	+	0.969209i	$0.579194\pi$
$828$		0			0
$829$	−23.6175	−	14.2102i	−0.820270	−	0.493540i	0.0425245	−	0.999095i	$-0.486460\pi$
$829$	−23.6175	−	14.2102i	−0.820270	−	0.493540i	−0.862794	+	0.505556i	$0.831288\pi$
$830$	74.0919	+	56.3232i	2.57177	+	1.95501i
$831$		0			0
$832$	−6.44796	−	7.59113i	−0.223543	−	0.263175i
$833$	−4.57082	+	2.11469i	−0.158370	+	0.0732695i
$834$		0			0
$835$	4.91820	+	9.27671i	0.170201	+	0.321034i
$836$	−17.5199	+	20.6260i	−0.605938	+	0.713365i
$837$		0			0
$838$	7.97712	+	20.0211i	0.275565	+	0.691616i
$839$	5.98157	−	11.2824i	0.206507	−	0.389513i	−0.758526	−	0.651643i	$-0.774080\pi$
$839$	5.98157	−	11.2824i	0.206507	−	0.389513i	0.965033	+	0.262130i	$0.0844248\pi$
$840$		0			0
$841$	0.193049	−	0.146752i	0.00665685	−	0.00506040i
$842$	−3.73391	−	13.4483i	−0.128679	−	0.463460i
$843$		0			0
$844$	3.80204	+	23.1914i	0.130872	+	0.798281i
$845$	−42.0526	+	9.25648i	−1.44665	+	0.318432i
$846$		0			0
$847$	9.37346	+	1.01942i	0.322076	+	0.0350278i
$848$	−4.77933	+	7.04898i	−0.164123	+	0.242063i
$849$		0			0
$850$	−2.61584	−	48.2464i	−0.0897227	−	1.65484i
$851$	−1.65147	−	1.56435i	−0.0566115	−	0.0536253i
$852$		0			0
$853$	2.56575	−	47.3225i	0.0878496	−	1.62029i	−0.539799	−	0.841794i	$-0.681500\pi$
$853$	2.56575	−	47.3225i	0.0878496	−	1.62029i	0.627648	−	0.778497i	$-0.284018\pi$
$854$	−7.97281	−	1.75495i	−0.272824	−	0.0600531i
$855$		0			0
$856$	−0.319256	+	0.107570i	−0.0109119	+	0.00367666i
$857$	37.0782	+	8.16152i	1.26657	+	0.278792i	0.796932	−	0.604069i	$-0.206455\pi$
$857$	37.0782	+	8.16152i	1.26657	+	0.278792i	0.469634	+	0.882861i	$0.344386\pi$
$858$		0			0
$859$	−19.3486	+	18.3279i	−0.660164	+	0.625341i	−0.942592	−	0.333948i	$-0.891619\pi$
$859$	−19.3486	+	18.3279i	−0.660164	+	0.625341i	0.282427	+	0.959289i	$0.408860\pi$
$860$	−49.5164	−	46.9045i	−1.68850	−	1.59943i
$861$		0			0
$862$	4.43367	−	27.0442i	0.151011	−	0.921128i
$863$	−17.1221	+	25.2532i	−0.582843	+	0.859629i	−0.998761	−	0.0497735i	$-0.984150\pi$
$863$	−17.1221	+	25.2532i	−0.582843	+	0.859629i	0.415918	+	0.909402i	$0.363460\pi$
$864$		0			0
$865$	−22.3994	+	13.4773i	−0.761604	+	0.458242i
$866$	63.1973	−	13.9108i	2.14753	−	0.472708i
$867$		0			0
$868$	−40.2238	−	18.6095i	−1.36528	−	0.631648i
$869$	13.8260	+	49.7967i	0.469014	+	1.68924i
$870$		0			0
$871$	8.68072	−	0.944085i	0.294135	−	0.0319891i
$872$	−0.0120771	+	0.0227798i	−0.000408981	+	0.000771421i
$873$		0			0
$874$	−9.38902	+	33.8162i	−0.317588	+	1.14385i
$875$	−23.3242	+	27.4594i	−0.788503	+	0.928298i
$876$		0			0
$877$	−2.82642	−	4.16866i	−0.0954414	−	0.140766i	0.776970	−	0.629537i	$-0.216755\pi$
$877$	−2.82642	−	4.16866i	−0.0954414	−	0.140766i	−0.872412	+	0.488772i	$0.837445\pi$
$878$	−19.9266	+	9.21901i	−0.672489	+	0.311127i
$879$		0			0
$880$	−21.9000	+	54.9649i	−0.738249	+	1.85287i
$881$	−20.1135	−	15.2899i	−0.677642	−	0.515130i	0.208807	−	0.977957i	$-0.433042\pi$
$881$	−20.1135	−	15.2899i	−0.677642	−	0.515130i	−0.886449	+	0.462827i	$0.846835\pi$
$882$		0			0
$883$	−1.37681	−	0.463900i	−0.0463333	−	0.0156115i	0.296039	−	0.955176i	$-0.404334\pi$
$883$	−1.37681	−	0.463900i	−0.0463333	−	0.0156115i	−0.342373	+	0.939564i	$0.611231\pi$
$884$	6.56203			0.220705
$885$		0			0
$886$	53.6355			1.80192
$887$	−9.09037	−	3.06290i	−0.305225	−	0.102842i	0.162521	−	0.986705i	$-0.448037\pi$
$887$	−9.09037	−	3.06290i	−0.305225	−	0.102842i	−0.467746	+	0.883863i	$0.654934\pi$
$888$		0			0
$889$	4.94888	+	3.76204i	0.165980	+	0.126175i
$890$	30.6740	−	76.9859i	1.02819	−	2.58057i
$891$		0			0
$892$	−48.4111	+	22.3974i	−1.62092	+	0.749919i
$893$	−25.4119	−	37.4798i	−0.850378	−	1.25421i
$894$		0			0
$895$	−32.9458	+	38.7867i	−1.10126	+	1.29650i
$896$	0.116488	−	0.419553i	0.00389160	−	0.0140163i
$897$		0			0
$898$	6.50768	−	12.2748i	0.217164	−	0.409615i
$899$	53.1921	−	5.78499i	1.77406	−	0.192940i
$900$		0			0
$901$	−1.48299	−	5.34126i	−0.0494056	−	0.177943i
$902$	−9.90422	−	4.58218i	−0.329774	−	0.152570i
$903$		0			0
$904$	0.455837	−	0.100337i	0.0151609	−	0.00333717i
$905$	46.7011	−	28.0991i	1.55240	−	0.934045i
$906$		0			0
$907$	−13.8557	+	20.4356i	−0.460069	+	0.678552i	−0.984992	−	0.172598i	$-0.944784\pi$
$907$	−13.8557	+	20.4356i	−0.460069	+	0.678552i	0.524923	+	0.851150i	$0.324094\pi$
$908$	−3.06178	+	18.6760i	−0.101609	+	0.619785i
$909$		0			0
$910$	−15.5348	−	14.7153i	−0.514973	−	0.487809i
$911$	−25.1422	+	23.8160i	−0.832999	+	0.789058i	−0.979773	−	0.200112i	$-0.935870\pi$
$911$	−25.1422	+	23.8160i	−0.832999	+	0.789058i	0.146774	+	0.989170i	$0.453111\pi$
$912$		0			0
$913$	47.0049	+	10.3466i	1.55563	+	0.342421i
$914$	−47.5717	+	16.0288i	−1.57353	+	0.530185i
$915$		0			0
$916$	11.1293	+	2.44975i	0.367723	+	0.0809421i
$917$	−0.847547	+	15.6321i	−0.0279885	+	0.516217i
$918$		0			0
$919$	17.4876	+	16.5651i	0.576863	+	0.546434i	0.919528	−	0.393024i	$-0.128571\pi$
$919$	17.4876	+	16.5651i	0.576863	+	0.546434i	−0.342665	+	0.939458i	$0.611330\pi$
$920$	0.0248229	+	0.457831i	0.000818386	+	0.0150942i
$921$		0			0
$922$	13.8741	−	20.4628i	0.456921	−	0.673908i
$923$	2.80863	+	0.305457i	0.0924472	+	0.0100542i
$924$		0			0
$925$	4.07955	−	0.897978i	0.134135	−	0.0295253i
$926$	2.78997	+	17.0181i	0.0916841	+	0.559248i
$927$		0			0
$928$	−11.5556	−	41.6196i	−0.379332	−	1.36623i
$929$	−30.6302	+	23.2844i	−1.00494	+	0.763938i	−0.971871	−	0.235515i	$-0.924322\pi$
$929$	−30.6302	+	23.2844i	−1.00494	+	0.763938i	−0.0330720	+	0.999453i	$0.510529\pi$
$930$		0			0
$931$	−3.14656	+	5.93504i	−0.103124	+	0.194513i
$932$	2.14041	+	5.37201i	0.0701113	+	0.175966i
$933$		0			0
$934$	−3.71365	+	4.37205i	−0.121514	+	0.143058i
$935$	−18.0391	−	34.0254i	−0.589942	−	1.11275i
$936$		0			0
$937$	−35.8872	+	16.6032i	−1.17238	+	0.542402i	−0.906749	−	0.421671i	$-0.861444\pi$
$937$	−35.8872	+	16.6032i	−1.17238	+	0.542402i	−0.265635	+	0.964074i	$0.585582\pi$
$938$	−20.1830	−	23.7613i	−0.658999	−	0.775834i
$939$		0			0
$940$	77.3988	+	58.8370i	2.52447	+	1.91905i
$941$	5.05634	+	3.04230i	0.164832	+	0.0991762i	0.595580	−	0.803296i	$-0.296922\pi$
$941$	5.05634	+	3.04230i	0.164832	+	0.0991762i	−0.430747	+	0.902473i	$0.641750\pi$
$942$		0			0
$943$	−7.05457			−0.229728
$944$	−0.842049	−	30.8978i	−0.0274064	−	1.00564i
$945$		0			0
$946$	−67.0539	−	22.5931i	−2.18011	−	0.734565i
$947$	−9.71497	−	5.84530i	−0.315694	−	0.189947i	0.348883	−	0.937166i	$-0.386561\pi$
$947$	−9.71497	−	5.84530i	−0.315694	−	0.189947i	−0.664578	+	0.747219i	$0.731388\pi$
$948$		0			0
$949$	−6.66854	+	16.7368i	−0.216470	+	0.543298i
$950$	−41.7220	−	49.1189i	−1.35364	−	1.59363i
$951$		0			0
$952$	0.0800039	+	0.117997i	0.00259294	+	0.00382430i
$953$	−9.57381	−	18.0581i	−0.310126	−	0.584960i	0.678633	−	0.734478i	$-0.262573\pi$
$953$	−9.57381	−	18.0581i	−0.310126	−	0.584960i	−0.988759	+	0.149518i	$0.952228\pi$
$954$		0			0
$955$	−2.30243	+	8.29261i	−0.0745050	+	0.268343i
$956$	−5.10064	−	12.8016i	−0.164967	−	0.414035i
$957$		0			0
$958$	76.5078	−	8.32072i	2.47185	−	0.268830i
$959$	−40.3434	+	30.6683i	−1.30276	+	0.990330i
$960$		0			0
$961$	60.7177	+	28.0910i	1.95863	+	0.906161i
$962$	0.184121	+	1.12309i	0.00593629	+	0.0362098i
$963$		0			0
$964$	−13.1152	+	7.89118i	−0.422413	+	0.254158i
$965$	−19.6576	−	2.13790i	−0.632802	−	0.0688214i
$966$		0			0
$967$	−1.55902	+	9.50962i	−0.0501348	+	0.305809i	−0.999976	−	0.00692379i	$-0.997796\pi$
$967$	−1.55902	+	9.50962i	−0.0501348	+	0.305809i	0.949841	+	0.312733i	$0.101244\pi$
$968$	0.00547231	+	0.100931i	0.000175887	+	0.00324404i
$969$		0			0
$970$	24.5714	−	23.2753i	0.788942	−	0.747325i
$971$	−1.52121	+	28.0570i	−0.0488178	+	0.900392i	0.866878	+	0.498520i	$0.166123\pi$
$971$	−1.52121	+	28.0570i	−0.0488178	+	0.900392i	−0.915696	+	0.401872i	$0.868360\pi$
$972$		0			0
$973$	19.8814	−	6.69883i	0.637369	−	0.214755i
$974$	−5.82091	+	1.96129i	−0.186514	+	0.0628438i
$975$		0			0
$976$	0.395252	−	7.29000i	0.0126517	−	0.233347i
$977$	29.8468	−	28.2724i	0.954883	−	0.904514i	−0.0406262	−	0.999174i	$-0.512935\pi$
$977$	29.8468	−	28.2724i	0.954883	−	0.904514i	0.995510	+	0.0946608i	$0.0301767\pi$
$978$		0			0
$979$	−2.32020	−	42.7936i	−0.0741540	−	1.36769i
$980$	2.33336	−	14.2329i	0.0745364	−	0.454652i
$981$		0			0
$982$	−19.6391	−	2.13588i	−0.626709	−	0.0681587i
$983$	−48.8363	+	29.3838i	−1.55764	+	0.937199i	−0.563853	+	0.825875i	$0.690682\pi$
$983$	−48.8363	+	29.3838i	−1.55764	+	0.937199i	−0.993784	+	0.111324i	$0.964491\pi$
$984$		0			0
$985$	−12.0073	−	73.2414i	−0.382585	−	2.33366i
$986$	25.6706	+	11.8765i	0.817517	+	0.378224i
$987$		0			0
$988$	6.96790	−	5.29686i	0.221678	−	0.168516i
$989$	−45.4731	+	4.94550i	−1.44596	+	0.157258i
$990$		0			0
$991$	10.7756	+	27.0448i	0.342300	+	0.859108i	0.994850	+	0.101362i	$0.0323200\pi$
$991$	10.7756	+	27.0448i	0.342300	+	0.859108i	−0.652550	+	0.757746i	$0.726301\pi$
$992$	21.1436	−	76.1525i	0.671311	−	2.41784i
$993$		0			0
$994$	−4.72483	−	8.91197i	−0.149862	−	0.282671i
$995$	31.3387	+	46.2211i	0.993504	+	1.46531i
$996$		0			0
$997$	−32.2022	−	37.9114i	−1.01985	−	1.20066i	−0.979493	−	0.201480i	$-0.935425\pi$
$997$	−32.2022	−	37.9114i	−1.01985	−	1.20066i	−0.0403610	−	0.999185i	$-0.512851\pi$
$998$	−0.877085	+	2.20132i	−0.0277636	+	0.0696815i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	531.2.i.b.64.5		140
3.2	odd	2		177.2.e.b.64.1	✓	140
59.12	even	29	inner	531.2.i.b.307.5		140
177.71	odd	58		177.2.e.b.130.1	yes	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.2.e.b.64.1	✓	140	3.2	odd	2
177.2.e.b.130.1	yes	140	177.71	odd	58
531.2.i.b.64.5		140	1.1	even	1	trivial
531.2.i.b.307.5		140	59.12	even	29	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:	\( N \)	\(=\)	\( 531 = 3^{2} \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	531.i (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89244 + 0.637637i) q^{2} +(1.58256 + 1.20303i) q^{4} +(-1.39663 + 3.50528i) q^{5} +(-2.04500 + 0.946119i) q^{7} +(-0.0135559 - 0.0199934i) q^{8} +(-4.87813 + 5.74298i) q^{10} +(-1.04248 + 3.75469i) q^{11} +(0.590330 - 1.11348i) q^{13} +(-4.47332 + 0.486503i) q^{14} +(-1.07655 - 3.87737i) q^{16} +(2.37714 + 1.09978i) q^{17} +(3.41192 - 0.751019i) q^{19} +(-6.42719 + 3.86711i) q^{20} +(-4.36697 + 6.44080i) q^{22} +(-0.813834 + 4.96417i) q^{23} +(-6.70642 - 6.35266i) q^{25} +(1.82716 - 1.73078i) q^{26} +(-4.37454 - 0.962909i) q^{28} +(5.12456 - 1.72667i) q^{29} +(9.66316 + 2.12702i) q^{31} +(0.432440 - 7.97589i) q^{32} +(3.79734 + 3.59703i) q^{34} +(-0.460297 - 8.48968i) q^{35} +(-0.253768 + 0.374280i) q^{37} +(6.93572 + 0.754305i) q^{38} +(0.0890149 - 0.0195937i) q^{40} +(0.226879 + 1.38390i) q^{41} +(2.43261 + 8.76146i) q^{43} +(-6.16679 + 4.68787i) q^{44} +(-4.70547 + 8.87545i) q^{46} +(-4.79757 - 12.0410i) q^{47} +(-1.24481 + 1.46550i) q^{49} +(-8.64080 - 16.2983i) q^{50} +(2.27378 - 1.05196i) q^{52} +(-1.37012 - 1.61303i) q^{53} +(-11.7053 - 8.89812i) q^{55} +(0.0466379 + 0.0280611i) q^{56} +10.7989 q^{58} +(7.45440 + 1.85253i) q^{59} +(1.71930 + 0.579299i) q^{61} +(16.9307 + 10.1868i) q^{62} +(2.92518 - 7.34165i) q^{64} +(3.07859 + 3.62439i) q^{65} +(3.88818 + 5.73464i) q^{67} +(2.43889 + 4.60024i) q^{68} +(4.54225 - 16.3597i) q^{70} +(0.829739 + 2.08249i) q^{71} +(-14.2116 + 1.54561i) q^{73} +(-0.718896 + 0.546491i) q^{74} +(6.30305 + 2.91610i) q^{76} +(-1.42050 - 8.66467i) q^{77} +(11.3641 - 6.83755i) q^{79} +(15.0948 + 1.64166i) q^{80} +(-0.453072 + 2.76362i) q^{82} +(-0.668692 - 12.3333i) q^{83} +(-7.17504 + 6.79656i) q^{85} +(-0.983070 + 18.1317i) q^{86} +(0.0892008 - 0.0300553i) q^{88} +(-10.4224 + 3.51170i) q^{89} +(-0.153741 + 2.83559i) q^{91} +(-7.25997 + 6.87701i) q^{92} +(-1.40133 - 25.8459i) q^{94} +(-2.13265 + 13.0086i) q^{95} +(-4.46533 - 0.485634i) q^{97} +(-3.29018 + 1.97963i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - q^{2} - q^{4} - 2 q^{5} - 2 q^{7} + 3 q^{8} - 116 q^{10} - 2 q^{11} + 4 q^{13} + 43 q^{14} + 7 q^{16} - 2 q^{19} - 4 q^{20} + 6 q^{22} - 6 q^{23} - 57 q^{25} - 12 q^{26} - 10 q^{28} + 4 q^{29}+ \cdots + 143 q^{98}+O(q^{100}) \) 140 * q - q^2 - q^4 - 2 * q^5 - 2 * q^7 + 3 * q^8 - 116 * q^10 - 2 * q^11 + 4 * q^13 + 43 * q^14 + 7 * q^16 - 2 * q^19 - 4 * q^20 + 6 * q^22 - 6 * q^23 - 57 * q^25 - 12 * q^26 - 10 * q^28 + 4 * q^29 - 12 * q^31 + 150 * q^32 - 2 * q^34 - 6 * q^35 + 12 * q^37 + 12 * q^38 - 66 * q^40 + 4 * q^41 - 60 * q^43 - 20 * q^44 + 76 * q^46 + 25 * q^47 + 31 * q^49 - 137 * q^50 + 118 * q^52 - 48 * q^53 + 93 * q^55 - 228 * q^56 - 120 * q^58 - 57 * q^59 + 72 * q^61 + 179 * q^62 + 249 * q^64 + 39 * q^65 + 40 * q^67 - 94 * q^68 + 94 * q^70 - 30 * q^71 - 205 * q^73 - 66 * q^74 - 216 * q^76 + 46 * q^77 + 4 * q^79 + 356 * q^80 - 28 * q^82 - 4 * q^83 + 50 * q^85 + 18 * q^86 - 162 * q^88 - 26 * q^89 - 198 * q^91 - 10 * q^92 - 4 * q^94 + 326 * q^95 - 20 * q^97 + 143 * q^98

Introduction

L-functions

Modular forms

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