LMFDB - Embedded newform 171.2.u.d.55.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [171,2,Mod(28,171)] 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("171.28"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(171, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 8])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	171.u (of order $9$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0] 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:	$1.36544187456$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 9x^{10} + 57x^{8} - 182x^{6} + 423x^{4} - 408x^{2} + 289 $ x^12 - 9x^10 + 57x^8 - 182x^6 + 423x^4 - 408*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.2
Root			$-1.58445 - 0.914781i$ of defining polynomial
Character	$\chi$	$=$	171.55
Dual form			171.2.u.d.28.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.408427 - 2.31631i) q^{2} +(-3.31908 - 1.20805i) q^{4} +(3.38621 - 1.23248i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(-1.80177 + 3.12075i) q^{8} +(-1.47178 - 8.34689i) q^{10} +(-1.58445 + 2.74434i) q^{11} +(-4.64543 + 3.89798i) q^{13} +(-0.408427 + 0.148655i) q^{14} +(1.08125 + 0.907278i) q^{16} +(0.576485 - 3.26941i) q^{17} +(2.77719 + 3.35965i) q^{19} -12.7280 q^{20} +(5.70961 + 4.79093i) q^{22} +(4.15381 + 1.51186i) q^{23} +(6.11721 - 5.13295i) q^{25} +(7.13159 + 12.3523i) q^{26} +(0.113341 + 0.642788i) q^{28} +(-1.31786 - 7.47398i) q^{29} +(3.70574 + 6.41852i) q^{31} +(-2.97779 + 2.49866i) q^{32} +(-7.33750 - 2.67063i) q^{34} +(-0.510114 - 0.428036i) q^{35} -1.77332 q^{37} +(8.91625 - 5.06065i) q^{38} +(-2.25490 + 12.7882i) q^{40} +(1.70008 + 1.42654i) q^{41} +(-6.35117 + 2.31164i) q^{43} +(8.57419 - 7.19460i) q^{44} +(5.19846 - 9.00400i) q^{46} +(-0.833963 - 4.72964i) q^{47} +(3.48293 - 6.03260i) q^{49} +(-9.39105 - 16.2658i) q^{50} +(20.1275 - 7.32580i) q^{52} +(0.141845 + 0.0516275i) q^{53} +(-1.98293 + 11.2457i) q^{55} +0.665906 q^{56} -17.8503 q^{58} +(-1.24239 + 7.04595i) q^{59} +(5.56418 + 2.02520i) q^{61} +(16.3808 - 5.96212i) q^{62} +(5.98293 + 10.3627i) q^{64} +(-10.9262 + 18.9248i) q^{65} +(0.241230 + 1.36808i) q^{67} +(-5.86299 + 10.1550i) q^{68} +(-1.19981 + 1.00676i) q^{70} +(-8.48161 + 3.08705i) q^{71} +(-6.66637 - 5.59375i) q^{73} +(-0.724272 + 4.10755i) q^{74} +(-5.15910 - 14.5059i) q^{76} +0.585588 q^{77} +(-2.19981 - 1.84586i) q^{79} +(4.77955 + 1.73961i) q^{80} +(3.99866 - 3.35527i) q^{82} +(-3.65280 - 6.32683i) q^{83} +(-2.07738 - 11.7814i) q^{85} +(2.76047 + 15.6554i) q^{86} +(-5.70961 - 9.88933i) q^{88} +(-5.62262 + 4.71794i) q^{89} +(1.05303 + 0.383273i) q^{91} +(-11.9604 - 10.0360i) q^{92} -11.2959 q^{94} +(13.5449 + 7.95365i) q^{95} +(-0.145430 + 0.824773i) q^{97} +(-12.5508 - 10.5314i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{4} + 6 q^{7} + 12 q^{10} - 24 q^{13} + 18 q^{16} + 12 q^{19} + 12 q^{25} - 12 q^{28} + 24 q^{31} - 78 q^{34} - 48 q^{37} - 30 q^{40} - 24 q^{43} + 6 q^{46} + 54 q^{52} + 18 q^{55} - 48 q^{58}+ \cdots + 30 q^{97}+O(q^{100}) $ 12 * q - 6 * q^4 + 6 * q^7 + 12 * q^10 - 24 * q^13 + 18 * q^16 + 12 * q^19 + 12 * q^25 - 12 * q^28 + 24 * q^31 - 78 * q^34 - 48 * q^37 - 30 * q^40 - 24 * q^43 + 6 * q^46 + 54 * q^52 + 18 * q^55 - 48 * q^58 + 30 * q^61 + 30 * q^64 + 48 * q^67 + 60 * q^70 - 42 * q^73 + 12 * q^76 + 48 * q^79 + 66 * q^82 - 78 * q^85 - 12 * q^91 - 12 * q^94 + 30 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.408427	−	2.31631i	0.288802	−	1.63788i	−0.402579	−	0.915385i	$-0.631886\pi$
$2$	0.408427	−	2.31631i	0.288802	−	1.63788i	0.691381	−	0.722491i	$-0.257003\pi$
$3$		0			0
$3$		0			0
$4$	−3.31908	−	1.20805i	−1.65954	−	0.604023i
$5$	3.38621	−	1.23248i	1.51436	−	0.551182i	0.554628	−	0.832098i	$-0.312860\pi$
$5$	3.38621	−	1.23248i	1.51436	−	0.551182i	0.959732	+	0.280916i	$0.0906382\pi$
$6$		0			0
$7$	−0.0923963	−	0.160035i	−0.0349225	−	0.0604876i	0.848036	−	0.529939i	$-0.177785\pi$
$7$	−0.0923963	−	0.160035i	−0.0349225	−	0.0604876i	−0.882958	+	0.469451i	$0.844452\pi$
$8$	−1.80177	+	3.12075i	−0.637021	+	1.10335i
$9$		0			0
$10$	−1.47178	−	8.34689i	−0.465418	−	2.63952i
$11$	−1.58445	+	2.74434i	−0.477729	+	0.827450i	−0.999674	−	0.0255285i	$-0.991873\pi$
$11$	−1.58445	+	2.74434i	−0.477729	+	0.827450i	0.521945	+	0.852979i	$0.325206\pi$
$12$		0			0
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.296385	+	0.955069i	$0.595781\pi$
$13$	−4.64543	+	3.89798i	−1.28841	+	1.08110i	−0.992026	+	0.126036i	$0.959775\pi$
$14$	−0.408427	+	0.148655i	−0.109157	+	0.0397298i
$15$		0			0
$16$	1.08125	+	0.907278i	0.270313	+	0.226820i
$17$	0.576485	−	3.26941i	0.139818	−	0.792948i	−0.831565	−	0.555428i	$-0.812554\pi$
$17$	0.576485	−	3.26941i	0.139818	−	0.792948i	0.971383	−	0.237520i	$-0.0763344\pi$
$18$		0			0
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$19$	2.77719	+	3.35965i	0.637131	+	0.770756i
$20$	−12.7280			−2.84607
$21$		0			0
$22$	5.70961	+	4.79093i	1.21729	+	1.02143i
$23$	4.15381	+	1.51186i	0.866128	+	0.315245i	0.736598	−	0.676331i	$-0.236431\pi$
$23$	4.15381	+	1.51186i	0.866128	+	0.315245i	0.129530	+	0.991575i	$0.458653\pi$
$24$		0			0
$25$	6.11721	−	5.13295i	1.22344	−	1.02659i
$26$	7.13159	+	12.3523i	1.39862	+	2.42248i
$27$		0			0
$28$	0.113341	+	0.642788i	0.0214194	+	0.121475i
$29$	−1.31786	−	7.47398i	−0.244721	−	1.38788i	−0.821139	−	0.570729i	$-0.806661\pi$
$29$	−1.31786	−	7.47398i	−0.244721	−	1.38788i	0.576417	−	0.817155i	$-0.304450\pi$
$30$		0			0
$31$	3.70574	+	6.41852i	0.665570	+	1.15280i	0.979130	+	0.203233i	$0.0651448\pi$
$31$	3.70574	+	6.41852i	0.665570	+	1.15280i	−0.313560	+	0.949568i	$0.601522\pi$
$32$	−2.97779	+	2.49866i	−0.526403	+	0.441705i
$33$		0			0
$34$	−7.33750	−	2.67063i	−1.25837	−	0.458009i
$35$	−0.510114	−	0.428036i	−0.0862249	−	0.0723513i
$36$		0			0
$37$	−1.77332			−0.291532			−0.145766	−	0.989319i	$-0.546565\pi$
$37$	−1.77332			−0.291532			−0.145766	+	0.989319i	$0.546565\pi$
$38$	8.91625	−	5.06065i	1.44641	−	0.820946i
$39$		0			0
$40$	−2.25490	+	12.7882i	−0.356531	+	2.02199i
$41$	1.70008	+	1.42654i	0.265508	+	0.222788i	0.765816	−	0.643060i	$-0.222335\pi$
$41$	1.70008	+	1.42654i	0.265508	+	0.222788i	−0.500308	+	0.865848i	$0.666780\pi$
$42$		0			0
$43$	−6.35117	+	2.31164i	−0.968544	+	0.352521i	−0.777376	−	0.629036i	$-0.783450\pi$
$43$	−6.35117	+	2.31164i	−0.968544	+	0.352521i	−0.191168	+	0.981557i	$0.561227\pi$
$44$	8.57419	−	7.19460i	1.29261	−	1.08463i
$45$		0			0
$46$	5.19846	−	9.00400i	0.766472	−	1.32757i
$47$	−0.833963	−	4.72964i	−0.121646	−	0.689889i	−0.983244	−	0.182297i	$-0.941647\pi$
$47$	−0.833963	−	4.72964i	−0.121646	−	0.689889i	0.861597	−	0.507592i	$-0.169464\pi$
$48$		0			0
$49$	3.48293	−	6.03260i	0.497561	−	0.861801i
$50$	−9.39105	−	16.2658i	−1.32809	−	2.30033i
$51$		0			0
$52$	20.1275	−	7.32580i	2.79118	−	1.01591i
$53$	0.141845	+	0.0516275i	0.0194840	+	0.00709158i	0.351744	−	0.936096i	$-0.385589\pi$
$53$	0.141845	+	0.0516275i	0.0194840	+	0.00709158i	−0.332260	+	0.943188i	$0.607811\pi$
$54$		0			0
$55$	−1.98293	+	11.2457i	−0.267378	+	1.51637i
$56$	0.665906			0.0889854
$57$		0			0
$58$	−17.8503			−2.34386
$59$	−1.24239	+	7.04595i	−0.161745	+	0.917304i	0.790611	+	0.612318i	$0.209763\pi$
$59$	−1.24239	+	7.04595i	−0.161745	+	0.917304i	−0.952357	+	0.304986i	$0.901348\pi$
$60$		0			0
$61$	5.56418	+	2.02520i	0.712420	+	0.259300i	0.672704	−	0.739911i	$-0.265133\pi$
$61$	5.56418	+	2.02520i	0.712420	+	0.259300i	0.0397156	+	0.999211i	$0.487355\pi$
$62$	16.3808	−	5.96212i	2.08036	−	0.757190i
$63$		0			0
$64$	5.98293	+	10.3627i	0.747866	+	1.29534i
$65$	−10.9262	+	18.9248i	−1.35523	+	2.34733i
$66$		0			0
$67$	0.241230	+	1.36808i	0.0294709	+	0.167138i	0.995991	−	0.0894530i	$-0.0285119\pi$
$67$	0.241230	+	1.36808i	0.0294709	+	0.167138i	−0.966520	+	0.256591i	$0.917401\pi$
$68$	−5.86299	+	10.1550i	−0.710992	+	1.23147i
$69$		0			0
$70$	−1.19981	+	1.00676i	−0.143404	+	0.120331i
$71$	−8.48161	+	3.08705i	−1.00658	+	0.366366i	−0.792119	−	0.610366i	$-0.791022\pi$
$71$	−8.48161	+	3.08705i	−1.00658	+	0.366366i	−0.214463	+	0.976732i	$0.568800\pi$
$72$		0			0
$73$	−6.66637	−	5.59375i	−0.780240	−	0.654699i	0.163069	−	0.986615i	$-0.447861\pi$
$73$	−6.66637	−	5.59375i	−0.780240	−	0.654699i	−0.943309	+	0.331915i	$0.892305\pi$
$74$	−0.724272	+	4.10755i	−0.0841949	+	0.477493i
$75$		0			0
$76$	−5.15910	−	14.5059i	−0.591789	−	1.66394i
$77$	0.585588			0.0667339
$78$		0			0
$79$	−2.19981	−	1.84586i	−0.247498	−	0.207675i	0.510596	−	0.859821i	$-0.329425\pi$
$79$	−2.19981	−	1.84586i	−0.247498	−	0.207675i	−0.758094	+	0.652145i	$0.773869\pi$
$80$	4.77955	+	1.73961i	0.534370	+	0.194495i
$81$		0			0
$82$	3.99866	−	3.35527i	0.441578	−	0.370528i
$83$	−3.65280	−	6.32683i	−0.400946	−	0.694460i	0.592894	−	0.805281i	$-0.297985\pi$
$83$	−3.65280	−	6.32683i	−0.400946	−	0.694460i	−0.993840	+	0.110821i	$0.964652\pi$
$84$		0			0
$85$	−2.07738	−	11.7814i	−0.225324	−	1.27787i
$86$	2.76047	+	15.6554i	0.297669	+	1.68816i
$87$		0			0
$88$	−5.70961	−	9.88933i	−0.608646	−	1.05421i
$89$	−5.62262	+	4.71794i	−0.595996	+	0.500100i	−0.890156	−	0.455656i	$-0.849405\pi$
$89$	−5.62262	+	4.71794i	−0.595996	+	0.500100i	0.294160	+	0.955756i	$0.404960\pi$
$90$		0			0
$91$	1.05303	+	0.383273i	0.110388	+	0.0401779i
$92$	−11.9604	−	10.0360i	−1.24696	−	1.04632i
$93$		0			0
$94$	−11.2959			−1.16508
$95$	13.5449	+	7.95365i	1.38967	+	0.816027i
$96$		0			0
$97$	−0.145430	+	0.824773i	−0.0147661	+	0.0837430i	−0.991300	−	0.131620i	$-0.957982\pi$
$97$	−0.145430	+	0.824773i	−0.0147661	+	0.0837430i	0.976534	+	0.215363i	$0.0690934\pi$
$98$	−12.5508	−	10.5314i	−1.26783	−	1.06383i
$99$		0			0
$100$	−26.5043	+	9.64679i	−2.65043	+	0.964679i
$101$	3.31074	−	2.77804i	0.329431	−	0.276425i	−0.463037	−	0.886339i	$-0.653240\pi$
$101$	3.31074	−	2.77804i	0.329431	−	0.276425i	0.792468	+	0.609914i	$0.208796\pi$
$102$		0			0
$103$	3.42855	−	5.93842i	0.337825	−	0.585130i	−0.646198	−	0.763169i	$-0.723642\pi$
$103$	3.42855	−	5.93842i	0.337825	−	0.585130i	0.984023	+	0.178040i	$0.0569755\pi$
$104$	−3.79464	−	21.5205i	−0.372095	−	2.11026i
$105$		0			0
$106$	0.177519	−	0.307471i	0.0172421	−	0.0298642i
$107$	−5.95557	−	10.3154i	−0.575747	−	0.997223i	−0.995960	−	0.0897975i	$-0.971378\pi$
$107$	−5.95557	−	10.3154i	−0.575747	−	0.997223i	0.420213	−	0.907425i	$-0.361955\pi$
$108$		0			0
$109$	−6.21688	+	2.26276i	−0.595469	+	0.216733i	−0.622133	−	0.782911i	$-0.713734\pi$
$109$	−6.21688	+	2.26276i	−0.595469	+	0.216733i	0.0266640	+	0.999644i	$0.491512\pi$
$110$	25.2387	+	9.18613i	2.40641	+	0.875863i
$111$		0			0
$112$	0.0452926	−	0.256867i	0.00427975	−	0.0242717i
$113$	−5.57336			−0.524297			−0.262149	−	0.965027i	$-0.584431\pi$
$113$	−5.57336			−0.524297			−0.262149	+	0.965027i	$0.584431\pi$
$114$		0			0
$115$	15.9290			1.48539
$116$	−4.65482	+	26.3988i	−0.432189	+	2.45106i
$117$		0			0
$118$	15.8131	+	5.75552i	1.45572	+	0.529838i
$119$	−0.576485	+	0.209823i	−0.0528463	+	0.0192345i
$120$		0			0
$121$	0.479055	+	0.829748i	0.0435505	+	0.0754317i
$122$	6.96353	−	12.0612i	0.630449	−	1.09197i
$123$		0			0
$124$	−4.54576	−	25.7803i	−0.408221	−	2.31514i
$125$	5.37909	−	9.31685i	0.481120	−	0.833325i
$126$		0			0
$127$	3.69072	−	3.09688i	0.327499	−	0.274804i	−0.464181	−	0.885740i	$-0.653651\pi$
$127$	3.69072	−	3.09688i	0.327499	−	0.274804i	0.791680	+	0.610936i	$0.209207\pi$
$128$	19.1413	−	6.96685i	1.69186	−	0.615788i
$129$		0			0
$130$	39.3730	+	33.0379i	3.45324	+	2.89762i
$131$	2.71120	−	15.3760i	0.236879	−	1.34341i	−0.601741	−	0.798691i	$-0.705526\pi$
$131$	2.71120	−	15.3760i	0.236879	−	1.34341i	0.838620	−	0.544717i	$-0.183363\pi$
$132$		0			0
$133$	0.281059	−	0.754866i	0.0243709	−	0.0654552i
$134$	3.26742			0.282262
$135$		0			0
$136$	9.16431	+	7.68977i	0.785834	+	0.659393i
$137$	5.06324	+	1.84287i	0.432582	+	0.157447i	0.549128	−	0.835738i	$-0.314960\pi$
$137$	5.06324	+	1.84287i	0.432582	+	0.157447i	−0.116546	+	0.993185i	$0.537182\pi$
$138$		0			0
$139$	−17.6027	+	14.7704i	−1.49304	+	1.25281i	−0.602318	+	0.798256i	$0.705756\pi$
$139$	−17.6027	+	14.7704i	−1.49304	+	1.25281i	−0.890720	+	0.454552i	$0.849799\pi$
$140$	1.17602	+	2.03693i	0.0993918	+	0.172152i
$141$		0			0
$142$	3.68644	+	20.9068i	0.309359	+	1.75446i
$143$	−3.33695	−	18.9248i	−0.279050	−	1.58257i
$144$		0			0
$145$	−13.6741	−	23.6843i	−1.13557	−	1.96687i
$146$	−15.6796	+	13.1567i	−1.29765	+	1.08886i
$147$		0			0
$148$	5.88578	+	2.14225i	0.483808	+	0.176092i
$149$	11.5118	+	9.65956i	0.943085	+	0.791342i	0.978120	−	0.208044i	$-0.0667096\pi$
$149$	11.5118	+	9.65956i	0.943085	+	0.791342i	−0.0350344	+	0.999386i	$0.511154\pi$
$150$		0			0
$151$	−14.7219			−1.19805			−0.599027	−	0.800729i	$-0.704446\pi$
$151$	−14.7219			−1.19805			−0.599027	+	0.800729i	$0.704446\pi$
$152$	−15.4885	+	2.61362i	−1.25628	+	0.211992i
$153$		0			0
$154$	0.239170	−	1.35640i	0.0192729	−	0.109302i
$155$	20.4591	+	17.1672i	1.64332	+	1.37891i
$156$		0			0
$157$	8.26517	−	3.00827i	0.659632	−	0.240086i	0.00955462	−	0.999954i	$-0.496959\pi$
$157$	8.26517	−	3.00827i	0.659632	−	0.240086i	0.650078	+	0.759868i	$0.274736\pi$
$158$	−5.17403	+	4.34153i	−0.411624	+	0.345394i
$159$		0			0
$160$	−7.00387	+	12.1311i	−0.553705	+	0.959044i
$161$	−0.141845	−	0.804445i	−0.0111790	−	0.0633991i
$162$		0			0
$163$	−0.454241	+	0.786768i	−0.0355789	+	0.0616244i	−0.883267	−	0.468871i	$-0.844661\pi$
$163$	−0.454241	+	0.786768i	−0.0355789	+	0.0616244i	0.847688	+	0.530496i	$0.177994\pi$
$164$	−3.91938	−	6.78856i	−0.306052	−	0.530098i
$165$		0			0
$166$	−16.1468	+	5.87695i	−1.25323	+	0.456139i
$167$	−13.5449	−	4.92992i	−1.04813	−	0.381489i	−0.240175	−	0.970730i	$-0.577205\pi$
$167$	−13.5449	−	4.92992i	−1.04813	−	0.381489i	−0.807958	+	0.589241i	$0.799427\pi$
$168$		0			0
$169$	4.12836	−	23.4131i	0.317566	−	1.80101i
$170$	−28.1378			−2.15807
$171$		0			0
$172$	23.8726			1.82027
$173$	0.744542	−	4.22251i	0.0566065	−	0.321031i	−0.943335	−	0.331842i	$-0.892330\pi$
$173$	0.744542	−	4.22251i	0.0566065	−	0.321031i	0.999942	+	0.0108104i	$0.00344113\pi$
$174$		0			0
$175$	−1.38666	−	0.504703i	−0.104822	−	0.0381519i
$176$	−4.20307	+	1.52979i	−0.316818	+	0.115312i
$177$		0			0
$178$	8.63176	+	14.9506i	0.646978	+	1.12060i
$179$	−0.0230504	+	0.0399245i	−0.00172287	+	0.00298410i	−0.866886	−	0.498507i	$-0.833882\pi$
$179$	−0.0230504	+	0.0399245i	−0.00172287	+	0.00298410i	0.865163	+	0.501491i	$0.167215\pi$
$180$		0			0
$181$	−0.540707	−	3.06650i	−0.0401904	−	0.227931i	0.958096	−	0.286447i	$-0.0924743\pi$
$181$	−0.540707	−	3.06650i	−0.0401904	−	0.227931i	−0.998286	+	0.0585159i	$0.981363\pi$
$182$	1.31786	−	2.28261i	0.0976867	−	0.169198i
$183$		0			0
$184$	−12.2023	+	10.2390i	−0.899568	+	0.754827i
$185$	−6.00483	+	2.18558i	−0.441484	+	0.160687i
$186$		0			0
$187$	8.05896	+	6.76227i	0.589330	+	0.494506i
$188$	−2.94563	+	16.7055i	−0.214832	+	1.21837i
$189$		0			0
$190$	23.9552	−	28.1255i	1.73789	−	2.04044i
$191$	23.9550			1.73333			0.866663	−	0.498895i	$-0.166261\pi$
$191$	23.9550			1.73333			0.866663	+	0.498895i	$0.166261\pi$
$192$		0			0
$193$	4.36618	+	3.66366i	0.314285	+	0.263716i	0.786260	−	0.617895i	$-0.212015\pi$
$193$	4.36618	+	3.66366i	0.314285	+	0.263716i	−0.471976	+	0.881612i	$0.656459\pi$
$194$	1.85103	+	0.673719i	0.132896	+	0.0483702i
$195$		0			0
$196$	−18.8478	+	15.8152i	−1.34627	+	1.12965i
$197$	−1.29165	−	2.23721i	−0.0920265	−	0.159395i	0.816337	−	0.577576i	$-0.196001\pi$
$197$	−1.29165	−	2.23721i	−0.0920265	−	0.159395i	−0.908364	+	0.418181i	$0.862668\pi$
$198$		0			0
$199$	2.99747	+	16.9995i	0.212485	+	1.20506i	0.885217	+	0.465178i	$0.154010\pi$
$199$	2.99747	+	16.9995i	0.212485	+	1.20506i	−0.672732	+	0.739886i	$0.734879\pi$
$200$	4.99687	+	28.3387i	0.353332	+	2.00385i
$201$		0			0
$202$	−5.08260	−	8.80331i	−0.357610	−	0.619399i
$203$	−1.07433	+	0.901473i	−0.0754034	+	0.0632710i
$204$		0			0
$205$	7.51501	+	2.73524i	0.524871	+	0.191038i
$206$	−12.3549	−	10.3670i	−0.860806	−	0.722302i
$207$		0			0
$208$	−8.55943			−0.593490
$209$	−13.6203	+	2.29838i	−0.942138	+	0.158982i
$210$		0			0
$211$	−0.800660	+	4.54077i	−0.0551197	+	0.312599i	−0.999885	−	0.0151476i	$-0.995178\pi$
$211$	−0.800660	+	4.54077i	−0.0551197	+	0.312599i	0.944766	+	0.327747i	$0.106289\pi$
$212$	−0.408427	−	0.342711i	−0.0280509	−	0.0235375i
$213$		0			0
$214$	−26.3259	+	9.58186i	−1.79960	+	0.655002i
$215$	−18.6574	+	15.6554i	−1.27242	+	1.06769i
$216$		0			0
$217$	0.684793	−	1.18610i	0.0464867	−	0.0805174i
$218$	2.70210	+	15.3244i	0.183009	+	1.03790i
$219$		0			0
$220$	20.1668	−	34.9300i	1.35965	−	2.35498i
$221$	10.0661	+	17.4349i	0.677116	+	1.17280i
$222$		0			0
$223$	16.8405	−	6.12944i	1.12772	−	0.410457i	0.290258	−	0.956949i	$-0.406259\pi$
$223$	16.8405	−	6.12944i	1.12772	−	0.410457i	0.837465	+	0.546491i	$0.184037\pi$
$224$	0.675009	+	0.245683i	0.0451010	+	0.0164154i
$225$		0			0
$226$	−2.27631	+	12.9096i	−0.151418	+	0.858734i
$227$	26.5223			1.76035			0.880174	−	0.474650i	$-0.157426\pi$
$227$	26.5223			1.76035			0.880174	+	0.474650i	$0.157426\pi$
$228$		0			0
$229$	−3.36959			−0.222668			−0.111334	−	0.993783i	$-0.535512\pi$
$229$	−3.36959			−0.222668			−0.111334	+	0.993783i	$0.535512\pi$
$230$	6.50585	−	36.8965i	0.428983	−	2.43288i
$231$		0			0
$232$	25.6989	+	9.35365i	1.68722	+	0.614097i
$233$	17.2410	−	6.27520i	1.12949	−	0.411102i	0.291385	−	0.956606i	$-0.405884\pi$
$233$	17.2410	−	6.27520i	1.12949	−	0.411102i	0.838108	+	0.545504i	$0.183662\pi$
$234$		0			0
$235$	−8.65317	−	14.9877i	−0.564471	−	0.977692i
$236$	12.6354	−	21.8852i	0.822496	−	1.42460i
$237$		0			0
$238$	0.250563	+	1.42101i	0.0162416	+	0.0921106i
$239$	−4.79666	+	8.30806i	−0.310270	+	0.537404i	−0.978421	−	0.206622i	$-0.933753\pi$
$239$	−4.79666	+	8.30806i	−0.310270	+	0.537404i	0.668151	+	0.744026i	$0.267086\pi$
$240$		0			0
$241$	4.69459	−	3.93923i	0.302405	−	0.253748i	−0.478939	−	0.877848i	$-0.658979\pi$
$241$	4.69459	−	3.93923i	0.302405	−	0.253748i	0.781345	+	0.624100i	$0.214534\pi$
$242$	2.11761	−	0.770747i	0.136125	−	0.0495455i
$243$		0			0
$244$	−16.0214	−	13.4436i	−1.02567	−	0.860636i
$245$	4.35886	−	24.7203i	0.278477	−	1.57932i
$246$		0			0
$247$	−25.9971	−	4.78158i	−1.65415	−	0.304245i
$248$	−26.7075			−1.69593
$249$		0			0
$250$	−19.3837	−	16.2649i	−1.22593	−	1.02868i
$251$	−20.7690	−	7.55931i	−1.31093	−	0.477139i	−0.410389	−	0.911911i	$-0.634607\pi$
$251$	−20.7690	−	7.55931i	−1.31093	−	0.477139i	−0.900541	+	0.434771i	$0.856829\pi$
$252$		0			0
$253$	−10.7306	+	9.00400i	−0.674624	+	0.566077i
$254$	−5.66594	−	9.81370i	−0.355513	−	0.615766i
$255$		0			0
$256$	−4.16385	−	23.6144i	−0.260240	−	1.47590i
$257$	−2.93763	−	16.6601i	−0.183244	−	1.03923i	−0.928191	−	0.372105i	$-0.878636\pi$
$257$	−2.93763	−	16.6601i	−0.183244	−	1.03923i	0.744946	−	0.667124i	$-0.232475\pi$
$258$		0			0
$259$	0.163848	+	0.283793i	0.0101810	+	0.0176340i
$260$	59.1270	−	49.6135i	3.66690	−	3.07690i
$261$		0			0
$262$	−34.5082	−	12.5600i	−2.13192	−	0.775957i
$263$	−6.18684	−	5.19137i	−0.381497	−	0.320114i	0.431793	−	0.901973i	$-0.357881\pi$
$263$	−6.18684	−	5.19137i	−0.381497	−	0.320114i	−0.813290	+	0.581859i	$0.802326\pi$
$264$		0			0
$265$	0.543948			0.0334145
$266$	−1.63371	−	0.959327i	−0.100169	−	0.0588201i
$267$		0			0
$268$	0.852044	−	4.83218i	0.0520469	−	0.295173i
$269$	−8.45856	−	7.09758i	−0.515728	−	0.432747i	0.347412	−	0.937713i	$-0.387061\pi$
$269$	−8.45856	−	7.09758i	−0.515728	−	0.432747i	−0.863139	+	0.504966i	$0.831505\pi$
$270$		0			0
$271$	1.90033	−	0.691663i	0.115437	−	0.0420156i	−0.283656	−	0.958926i	$-0.591547\pi$
$271$	1.90033	−	0.691663i	0.115437	−	0.0420156i	0.399093	+	0.916911i	$0.369325\pi$
$272$	3.58959	−	3.01202i	0.217651	−	0.182631i
$273$		0			0
$274$	6.33662	−	10.9753i	0.382809	−	0.663045i
$275$	4.39418	+	24.9206i	0.264979	+	1.50277i
$276$		0			0
$277$	−10.4029	+	18.0183i	−0.625047	+	1.08261i	0.363485	+	0.931600i	$0.381587\pi$
$277$	−10.4029	+	18.0183i	−0.625047	+	1.08261i	−0.988532	+	0.151013i	$0.951746\pi$
$278$	27.0233	+	46.8058i	1.62075	+	2.80723i
$279$		0			0
$280$	2.25490	−	0.820717i	0.134756	−	0.0490472i
$281$	−7.82371	−	2.84760i	−0.466723	−	0.169873i	0.0979441	−	0.995192i	$-0.468773\pi$
$281$	−7.82371	−	2.84760i	−0.466723	−	0.169873i	−0.564668	+	0.825318i	$0.690996\pi$
$282$		0			0
$283$	1.93835	−	10.9929i	0.115223	−	0.653461i	−0.871417	−	0.490543i	$-0.836798\pi$
$283$	1.93835	−	10.9929i	0.115223	−	0.653461i	0.986640	−	0.162918i	$-0.0520906\pi$
$284$	31.8804			1.89176
$285$		0			0
$286$	−45.1985			−2.67264
$287$	0.0712148	−	0.403879i	0.00420368	−	0.0238402i
$288$		0			0
$289$	5.61809	+	2.04482i	0.330476	+	0.120283i
$290$	−60.4449	+	22.0001i	−3.54945	+	1.29189i
$291$		0			0
$292$	15.3687	+	26.6194i	0.899386	+	1.55778i
$293$	1.94361	−	3.36643i	0.113547	−	0.196669i	−0.803651	−	0.595101i	$-0.797112\pi$
$293$	1.94361	−	3.36643i	0.113547	−	0.196669i	0.917198	+	0.398432i	$0.130445\pi$
$294$		0			0
$295$	4.47700	+	25.3903i	0.260661	+	1.47828i
$296$	3.19511	−	5.53409i	0.185712	−	0.321662i
$297$		0			0
$298$	27.0763	−	22.7197i	1.56849	−	1.31612i
$299$	−25.1894	+	9.16820i	−1.45674	+	0.530211i
$300$		0			0
$301$	0.956767	+	0.802823i	0.0551471	+	0.0462739i
$302$	−6.01284	+	34.1005i	−0.346000	+	1.96226i
$303$		0			0
$304$	−0.0452926	+	6.15231i	−0.00259771	+	0.352859i
$305$	21.3375			1.22178
$306$		0			0
$307$	13.1270	+	11.0149i	0.749198	+	0.628652i	0.935291	−	0.353880i	$-0.115138\pi$
$307$	13.1270	+	11.0149i	0.749198	+	0.628652i	−0.186093	+	0.982532i	$0.559582\pi$
$308$	−1.94361	−	0.707417i	−0.110748	−	0.0403088i
$309$		0			0
$310$	48.1207	−	40.3780i	2.73307	−	2.29332i
$311$	−3.33695	−	5.77977i	−0.189221	−	0.327741i	0.755770	−	0.654838i	$-0.227263\pi$
$311$	−3.33695	−	5.77977i	−0.189221	−	0.327741i	−0.944991	+	0.327097i	$0.893930\pi$
$312$		0			0
$313$	−3.72921	−	21.1494i	−0.210787	−	1.19543i	−0.888069	−	0.459710i	$-0.847953\pi$
$313$	−3.72921	−	21.1494i	−0.210787	−	1.19543i	0.677282	−	0.735724i	$-0.263158\pi$
$314$	−3.59237	−	20.3733i	−0.202729	−	1.14973i
$315$		0			0
$316$	5.07145	+	8.78401i	0.285291	+	0.494139i
$317$	−25.6824	+	21.5501i	−1.44247	+	1.21037i	−0.504615	+	0.863345i	$0.668365\pi$
$317$	−25.6824	+	21.5501i	−1.44247	+	1.21037i	−0.937854	+	0.347030i	$0.887190\pi$
$318$		0			0
$319$	22.5993	+	8.22546i	1.26532	+	0.460537i
$320$	33.0313	+	27.7166i	1.84651	+	1.54940i
$321$		0			0
$322$	−1.92127			−0.107068
$323$	12.5851	−	7.14298i	0.700251	−	0.397446i
$324$		0			0
$325$	−8.40895	+	47.6895i	−0.466445	+	2.64534i
$326$	1.63687	+	1.37350i	0.0906579	+	0.0760710i
$327$		0			0
$328$	−7.51501	+	2.73524i	−0.414947	+	0.151028i
$329$	−0.679853	+	0.570465i	−0.0374815	+	0.0314507i
$330$		0			0
$331$	12.0039	−	20.7913i	0.659792	−	1.14279i	−0.320877	−	0.947121i	$-0.603978\pi$
$331$	12.0039	−	20.7913i	0.659792	−	1.14279i	0.980669	−	0.195673i	$-0.0626891\pi$
$332$	4.48082	+	25.4120i	0.245917	+	1.39466i
$333$		0			0
$334$	−16.9513	+	29.3605i	−0.927534	+	1.60654i
$335$	2.50299	+	4.33530i	0.136753	+	0.236863i
$336$		0			0
$337$	26.5758	−	9.67280i	1.44768	−	0.526911i	0.505734	−	0.862689i	$-0.331222\pi$
$337$	26.5758	−	9.67280i	1.44768	−	0.526911i	0.941941	+	0.335778i	$0.108999\pi$
$338$	−52.5457	−	19.1251i	−2.85811	−	1.04027i
$339$		0			0
$340$	−7.33750	+	41.6130i	−0.397932	+	2.25678i
$341$	−23.4862			−1.27185
$342$		0			0
$343$	−2.58079			−0.139349
$344$	4.22928	−	23.9854i	0.228028	−	1.29321i
$345$		0			0
$346$	−9.47653	−	3.44917i	−0.509461	−	0.185429i
$347$	−21.2589	+	7.73760i	−1.14124	+	0.415376i	−0.842360	−	0.538916i	$-0.818834\pi$
$347$	−21.2589	+	7.73760i	−1.14124	+	0.415376i	−0.298876	+	0.954292i	$0.596612\pi$
$348$		0			0
$349$	−8.81521	−	15.2684i	−0.471867	−	0.817298i	0.527615	−	0.849484i	$-0.323087\pi$
$349$	−8.81521	−	15.2684i	−0.471867	−	0.817298i	−0.999482	+	0.0321858i	$0.989753\pi$
$350$	−1.73540	+	3.00579i	−0.0927608	+	0.160666i
$351$		0			0
$352$	−2.13903	−	12.1311i	−0.114011	−	0.646588i
$353$	12.8126	−	22.1920i	0.681945	−	1.18116i	−0.292442	−	0.956283i	$-0.594468\pi$
$353$	12.8126	−	22.1920i	0.681945	−	1.18116i	0.974387	−	0.224880i	$-0.0721989\pi$
$354$		0			0
$355$	−24.9158	+	20.9068i	−1.32239	+	1.10962i
$356$	24.3614	−	8.86682i	1.29115	−	0.469941i
$357$		0			0
$358$	0.0830629	+	0.0696981i	0.00439001	+	0.00368366i
$359$	−5.59047	+	31.7051i	−0.295054	+	1.67333i	0.371931	+	0.928260i	$0.378696\pi$
$359$	−5.59047	+	31.7051i	−0.295054	+	1.67333i	−0.666985	+	0.745071i	$0.732415\pi$
$360$		0			0
$361$	−3.57444	+	18.6607i	−0.188129	+	0.982144i
$362$	−7.32380			−0.384930
$363$		0			0
$364$	−3.03209	−	2.54422i	−0.158925	−	0.133354i
$365$	−29.4680	−	10.7255i	−1.54242	−	0.561396i
$366$		0			0
$367$	14.7815	−	12.4032i	0.771589	−	0.647440i	−0.169526	−	0.985526i	$-0.554224\pi$
$367$	14.7815	−	12.4032i	0.771589	−	0.647440i	0.941115	+	0.338085i	$0.109779\pi$
$368$	3.11963	+	5.40336i	0.162622	+	0.281670i
$369$		0			0
$370$	2.60994	+	14.8017i	0.135684	+	0.769503i
$371$	−0.00484377	−	0.0274704i	−0.000251476	−	0.00142619i
$372$		0			0
$373$	7.63816	+	13.2297i	0.395489	+	0.685007i	0.993163	−	0.116732i	$-0.0372419\pi$
$373$	7.63816	+	13.2297i	0.395489	+	0.685007i	−0.597675	+	0.801739i	$0.703909\pi$
$374$	18.9550	−	15.9051i	0.980140	−	0.822435i
$375$		0			0
$376$	16.2626	+	5.91912i	0.838682	+	0.305255i
$377$	35.2555	+	29.5829i	1.81575	+	1.52359i
$378$		0			0
$379$	20.9718			1.07725			0.538625	−	0.842545i	$-0.318944\pi$
$379$	20.9718			1.07725			0.538625	+	0.842545i	$0.318944\pi$
$380$	−35.3481	−	42.7616i	−1.81332	−	2.19362i
$381$		0			0
$382$	9.78389	−	55.4872i	0.500587	−	2.83897i
$383$	−3.79464	−	3.18408i	−0.193897	−	0.162699i	0.540671	−	0.841234i	$-0.318171\pi$
$383$	−3.79464	−	3.18408i	−0.193897	−	0.162699i	−0.734568	+	0.678535i	$0.762615\pi$
$384$		0			0
$385$	1.98293	−	0.721726i	0.101059	−	0.0367826i
$386$	10.2694	−	8.61708i	0.522700	−	0.438598i
$387$		0			0
$388$	1.47906	−	2.56180i	0.0750877	−	0.130056i
$389$	5.71798	+	32.4283i	0.289913	+	1.64418i	0.687188	+	0.726480i	$0.258845\pi$
$389$	5.71798	+	32.4283i	0.289913	+	1.64418i	−0.397275	+	0.917700i	$0.630044\pi$
$390$		0			0
$391$	7.33750	−	12.7089i	0.371073	−	0.642718i
$392$	12.5508	+	21.7387i	0.633913	+	1.09797i
$393$		0			0
$394$	−5.70961	+	2.07813i	−0.287646	+	0.104695i
$395$	−9.72400	−	3.53925i	−0.489268	−	0.178079i
$396$		0			0
$397$	−5.34430	+	30.3091i	−0.268223	+	1.52117i	0.491475	+	0.870892i	$0.336458\pi$
$397$	−5.34430	+	30.3091i	−0.268223	+	1.52117i	−0.759698	+	0.650276i	$0.774653\pi$
$398$	40.6003			2.03511
$399$		0			0
$400$	11.2713			0.563563
$401$	2.65284	−	15.0450i	0.132476	−	0.751311i	−0.844107	−	0.536174i	$-0.819869\pi$
$401$	2.65284	−	15.0450i	0.132476	−	0.751311i	0.976584	−	0.215137i	$-0.0690198\pi$
$402$		0			0
$403$	−42.2340	−	15.3719i	−2.10383	−	0.765730i
$404$	−14.3446	+	5.22101i	−0.713671	+	0.259755i
$405$		0			0
$406$	1.64930	+	2.85667i	0.0818534	+	0.141774i
$407$	2.80973	−	4.86659i	0.139273	−	0.241228i
$408$		0			0
$409$	−2.19577	−	12.4529i	−0.108574	−	0.615754i	−0.989732	−	0.142933i	$-0.954347\pi$
$409$	−2.19577	−	12.4529i	−0.108574	−	0.615754i	0.881158	−	0.472821i	$-0.156764\pi$
$410$	9.40500	−	16.2899i	0.464480	−	0.804502i
$411$		0			0
$412$	−18.5535	+	15.5682i	−0.914065	+	0.766992i
$413$	1.24239	−	0.452193i	0.0611340	−	0.0222510i
$414$		0			0
$415$	−20.1668	−	16.9220i	−0.989951	−	0.830668i
$416$	4.09338	−	23.2147i	0.200694	−	1.13819i
$417$		0			0
$418$	−0.239170	+	32.4876i	−0.0116982	+	1.58902i
$419$	23.2828			1.13744			0.568720	−	0.822531i	$-0.307439\pi$
$419$	23.2828			1.13744			0.568720	+	0.822531i	$0.307439\pi$
$420$		0			0
$421$	17.5424	+	14.7198i	0.854962	+	0.717398i	0.960877	−	0.276977i	$-0.0893325\pi$
$421$	17.5424	+	14.7198i	0.854962	+	0.717398i	−0.105914	+	0.994375i	$0.533777\pi$
$422$	10.1908	+	3.70915i	0.496080	+	0.180558i
$423$		0			0
$424$	−0.416689	+	0.349643i	−0.0202362	+	0.0169802i
$425$	−13.2552	−	22.9587i	−0.642973	−	1.11366i
$426$		0			0
$427$	−0.190007	−	1.07758i	−0.00919509	−	0.0521479i
$428$	7.30559	+	41.4321i	0.353129	+	2.00269i
$429$		0			0
$430$	28.6425	+	49.6103i	1.38126	+	2.39242i
$431$	23.0236	−	19.3191i	1.10901	−	0.930570i	0.111012	−	0.993819i	$-0.464591\pi$
$431$	23.0236	−	19.3191i	1.10901	−	0.930570i	0.997998	+	0.0632493i	$0.0201463\pi$
$432$		0			0
$433$	−5.19119	−	1.88944i	−0.249473	−	0.0908006i	0.214257	−	0.976777i	$-0.431267\pi$
$433$	−5.19119	−	1.88944i	−0.249473	−	0.0908006i	−0.463730	+	0.885977i	$0.653489\pi$
$434$	−2.46767	−	2.07062i	−0.118452	−	0.0993931i
$435$		0			0
$436$	23.3678			1.11912
$437$	6.45658	+	18.1540i	0.308860	+	0.868426i
$438$		0			0
$439$	−3.06536	+	17.3845i	−0.146302	+	0.829718i	0.820011	+	0.572347i	$0.193967\pi$
$439$	−3.06536	+	17.3845i	−0.146302	+	0.829718i	−0.966313	+	0.257370i	$0.917144\pi$
$440$	−31.5224	−	26.4504i	−1.50277	−	1.26097i
$441$		0			0
$442$	44.4959	−	16.1952i	2.11645	−	0.770326i
$443$	6.44432	−	5.40742i	0.306179	−	0.256915i	−0.476732	−	0.879049i	$-0.658179\pi$
$443$	6.44432	−	5.40742i	0.306179	−	0.256915i	0.782911	+	0.622134i	$0.213734\pi$
$444$		0			0
$445$	−13.2246	+	22.9057i	−0.626907	+	1.08584i
$446$	−7.31954	−	41.5112i	−0.346590	−	1.96561i
$447$		0			0
$448$	1.10560	−	1.91496i	0.0522347	−	0.0904731i
$449$	7.47365	+	12.9447i	0.352703	+	0.610900i	0.986722	−	0.162418i	$-0.0519292\pi$
$449$	7.47365	+	12.9447i	0.352703	+	0.610900i	−0.634019	+	0.773318i	$0.718596\pi$
$450$		0			0
$451$	−6.60859	+	2.40533i	−0.311186	+	0.113263i
$452$	18.4984	+	6.73287i	0.870092	+	0.316688i
$453$		0			0
$454$	10.8324	−	61.4338i	0.508392	−	2.88323i
$455$	4.03817			0.189312
$456$		0			0
$457$	31.2267			1.46072			0.730361	−	0.683061i	$-0.239352\pi$
$457$	31.2267			1.46072			0.730361	+	0.683061i	$0.239352\pi$
$458$	−1.37623	+	7.80499i	−0.0643070	+	0.364703i
$459$		0			0
$460$	−52.8696	−	19.2430i	−2.46506	−	0.897208i
$461$	1.25149	−	0.455507i	0.0582879	−	0.0212151i	−0.312712	−	0.949848i	$-0.601237\pi$
$461$	1.25149	−	0.455507i	0.0582879	−	0.0212151i	0.371000	+	0.928633i	$0.379015\pi$
$462$		0			0
$463$	2.60859	+	4.51822i	0.121232	+	0.209979i	0.920254	−	0.391322i	$-0.127982\pi$
$463$	2.60859	+	4.51822i	0.121232	+	0.209979i	−0.799022	+	0.601302i	$0.794649\pi$
$464$	5.35604	−	9.27693i	0.248648	−	0.430671i
$465$		0			0
$466$	−7.49360	−	42.4983i	−0.347134	−	1.96870i
$467$	10.2834	−	17.8113i	0.475858	−	0.824210i	−0.523760	−	0.851866i	$-0.675471\pi$
$467$	10.2834	−	17.8113i	0.475858	−	0.824210i	0.999618	+	0.0276560i	$0.00880430\pi$
$468$		0			0
$469$	0.196652	−	0.165011i	0.00908055	−	0.00761949i
$470$	−38.2504	+	13.9220i	−1.76436	+	0.642174i
$471$		0			0
$472$	−19.7502	−	16.5723i	−0.909074	−	0.762804i
$473$	3.71917	−	21.0924i	0.171007	−	0.969832i
$474$		0			0
$475$	34.2335	+	6.29649i	1.57074	+	0.288903i
$476$	2.16687			0.0993185
$477$		0			0
$478$	17.2849	+	14.5038i	0.790594	+	0.663387i
$479$	−14.6604	−	5.33597i	−0.669853	−	0.243806i	−0.0153683	−	0.999882i	$-0.504892\pi$
$479$	−14.6604	−	5.33597i	−0.669853	−	0.243806i	−0.654485	+	0.756075i	$0.727114\pi$
$480$		0			0
$481$	8.23783	−	6.91236i	0.375613	−	0.315176i
$482$	−7.20707	−	12.4830i	−0.328273	−	0.568585i
$483$		0			0
$484$	−0.587649	−	3.33272i	−0.0267113	−	0.151487i
$485$	0.524061	+	2.97210i	0.0237964	+	0.134956i
$486$		0			0
$487$	−11.1163	−	19.2541i	−0.503729	−	0.872485i	−0.999991	−	0.00431144i	$-0.998628\pi$
$487$	−11.1163	−	19.2541i	−0.503729	−	0.872485i	0.496262	−	0.868173i	$-0.334706\pi$
$488$	−16.3455	+	13.7155i	−0.739925	+	0.620871i
$489$		0			0
$490$	−55.4796	−	20.1929i	−2.50631	−	0.912223i
$491$	−24.7639	−	20.7794i	−1.11758	−	0.937760i	−0.119099	−	0.992882i	$-0.538001\pi$
$491$	−24.7639	−	20.7794i	−1.11758	−	0.937760i	−0.998480	+	0.0551228i	$0.982445\pi$
$492$		0			0
$493$	−25.1952			−1.13474
$494$	−21.6935	+	58.2642i	−0.976037	+	2.62143i
$495$		0			0
$496$	−1.81655	+	10.3022i	−0.0815656	+	0.462581i
$497$	1.27771	+	1.07212i	0.0573129	+	0.0480913i
$498$		0			0
$499$	3.94609	−	1.43626i	0.176651	−	0.0642958i	−0.252180	−	0.967680i	$-0.581148\pi$
$499$	3.94609	−	1.43626i	0.176651	−	0.0642958i	0.428832	+	0.903384i	$0.358925\pi$
$500$	−29.1088	+	24.4252i	−1.30178	+	1.09233i
$501$		0			0
$502$	−25.9923	+	45.0200i	−1.16009	+	2.00934i
$503$	2.71437	+	15.3939i	0.121028	+	0.686382i	0.983588	+	0.180428i	$0.0577482\pi$
$503$	2.71437	+	15.3939i	0.121028	+	0.686382i	−0.862561	+	0.505954i	$0.831141\pi$
$504$		0			0
$505$	7.78699	−	13.4875i	0.346516	−	0.600184i
$506$	16.4734	+	28.5327i	0.732331	+	1.26843i
$507$		0			0
$508$	−15.9910	+	5.82024i	−0.709485	+	0.258231i
$509$	40.9445	+	14.9026i	1.81483	+	0.660545i	0.996286	+	0.0861027i	$0.0274413\pi$
$509$	40.9445	+	14.9026i	1.81483	+	0.660545i	0.818545	+	0.574442i	$0.194781\pi$
$510$		0			0
$511$	−0.279248	+	1.58370i	−0.0123532	+	0.0700586i
$512$	−15.6593			−0.692050
$513$		0			0
$514$	−39.7897			−1.75505
$515$	4.29081	−	24.3344i	0.189076	−	1.07230i
$516$		0			0
$517$	14.3011	+	5.20518i	0.628963	+	0.228924i
$518$	0.724272	−	0.263613i	0.0318227	−	0.0115825i
$519$		0			0
$520$	−39.3730	−	68.1961i	−1.72662	−	2.99060i
$521$	3.98891	−	6.90900i	0.174757	−	0.302689i	−0.765320	−	0.643650i	$-0.777419\pi$
$521$	3.98891	−	6.90900i	0.174757	−	0.302689i	0.940077	+	0.340961i	$0.110753\pi$
$522$		0			0
$523$	−2.04529	−	11.5994i	−0.0894344	−	0.507208i	−0.996311	−	0.0858121i	$-0.972652\pi$
$523$	−2.04529	−	11.5994i	−0.0894344	−	0.507208i	0.906877	−	0.421396i	$-0.138460\pi$
$524$	−27.5736	+	47.7589i	−1.20456	+	2.08636i
$525$		0			0
$526$	−14.5517	+	12.2103i	−0.634484	+	0.532395i
$527$	23.1211	−	8.41538i	1.00717	−	0.366580i
$528$		0			0
$529$	−2.65064	−	2.22415i	−0.115245	−	0.0967024i
$530$	0.222163	−	1.25995i	0.00965016	−	0.0547288i
$531$		0			0
$532$	−1.84477	+	2.16593i	−0.0799809	+	0.0939049i
$533$	−13.4582			−0.582940
$534$		0			0
$535$	−32.8803	−	27.5899i	−1.42154	−	1.19281i
$536$	−4.70408	−	1.71214i	−0.203185	−	0.0739534i
$537$		0			0
$538$	−19.8949	+	16.6938i	−0.857729	+	0.719720i
$539$	11.0370	+	19.1167i	0.475398	+	0.823414i
$540$		0			0
$541$	−0.535082	−	3.03460i	−0.0230050	−	0.130468i	0.971142	−	0.238501i	$-0.0766559\pi$
$541$	−0.535082	−	3.03460i	−0.0230050	−	0.130468i	−0.994147	+	0.108033i	$0.965545\pi$
$542$	−0.825958	−	4.68424i	−0.0354779	−	0.201205i
$543$		0			0
$544$	6.45249	+	11.1760i	0.276648	+	0.479168i
$545$	−18.2629	+	15.3244i	−0.782296	+	0.656424i
$546$		0			0
$547$	−11.3503	−	4.13117i	−0.485303	−	0.176636i	0.0877688	−	0.996141i	$-0.472026\pi$
$547$	−11.3503	−	4.13117i	−0.485303	−	0.176636i	−0.573072	+	0.819505i	$0.694249\pi$
$548$	−14.5790	−	12.2333i	−0.622785	−	0.522579i
$549$		0			0
$550$	59.5185			2.53788
$551$	21.4500	−	25.1842i	0.913800	−	1.07288i
$552$		0			0
$553$	−0.0921479	+	0.522597i	−0.00391853	+	0.0222231i
$554$	37.4870	+	31.4554i	1.59267	+	1.33641i
$555$		0			0
$556$	76.2679	−	27.7592i	3.23448	−	1.17725i
$557$	−27.7277	+	23.2663i	−1.17486	+	0.985826i	−0.174862	+	0.984593i	$0.555948\pi$
$557$	−27.7277	+	23.2663i	−1.17486	+	0.985826i	−0.999999	+	0.00123268i	$0.999608\pi$
$558$		0			0
$559$	20.4932	−	35.4953i	0.866770	−	1.50129i
$560$	−0.163214	−	0.925630i	−0.00689703	−	0.0391150i
$561$		0			0
$562$	−9.79133	+	16.9591i	−0.413022	+	0.715375i
$563$	−14.1476	−	24.5043i	−0.596248	−	1.03273i	−0.993369	−	0.114966i	$-0.963324\pi$
$563$	−14.1476	−	24.5043i	−0.596248	−	1.03273i	0.397121	−	0.917766i	$-0.370009\pi$
$564$		0			0
$565$	−18.8726	+	6.86906i	−0.793975	+	0.288983i
$566$	−24.6713	−	8.97962i	−1.03701	−	0.377442i
$567$		0			0
$568$	5.64796	−	32.0311i	0.236983	−	1.34400i
$569$	−25.3757			−1.06380			−0.531902	−	0.846806i	$-0.678523\pi$
$569$	−25.3757			−1.06380			−0.531902	+	0.846806i	$0.678523\pi$
$570$		0			0
$571$	41.8025			1.74938			0.874691	−	0.484682i	$-0.161065\pi$
$571$	41.8025			1.74938			0.874691	+	0.484682i	$0.161065\pi$
$572$	−11.7864	+	66.8440i	−0.492814	+	2.79489i
$573$		0			0
$574$	−0.906422	−	0.329911i	−0.0378333	−	0.0137702i
$575$	33.1700	−	12.0729i	1.38329	−	0.503475i
$576$		0			0
$577$	−17.6373	−	30.5487i	−0.734250	−	1.27176i	−0.955052	−	0.296439i	$-0.904201\pi$
$577$	−17.6373	−	30.5487i	−0.734250	−	1.27176i	0.220802	−	0.975319i	$-0.429132\pi$
$578$	7.03100	−	12.1781i	0.292451	−	0.506540i
$579$		0			0
$580$	16.7738	+	95.1289i	0.696494	+	3.95001i
$581$	−0.675009	+	1.16915i	−0.0280041	+	0.0485045i
$582$		0			0
$583$	−0.366430	+	0.307471i	−0.0151760	+	0.0127342i
$584$	29.4680	−	10.7255i	1.21939	−	0.443823i
$585$		0			0
$586$	−7.00387	−	5.87695i	−0.289327	−	0.242774i
$587$	−4.06716	+	23.0660i	−0.167870	+	0.952037i	0.778186	+	0.628034i	$0.216140\pi$
$587$	−4.06716	+	23.0660i	−0.167870	+	0.952037i	−0.946056	+	0.324003i	$0.894971\pi$
$588$		0			0
$589$	−11.2724	+	30.2754i	−0.464473	+	1.24748i
$590$	60.6403			2.49652
$591$		0			0
$592$	−1.91740	−	1.60889i	−0.0788048	−	0.0661251i
$593$	−5.05730	−	1.84071i	−0.207678	−	0.0755888i	0.236086	−	0.971732i	$-0.424135\pi$
$593$	−5.05730	−	1.84071i	−0.207678	−	0.0755888i	−0.443765	+	0.896143i	$0.646357\pi$
$594$		0			0
$595$	−1.69350	+	1.42101i	−0.0694266	+	0.0582558i
$596$	−26.5394	−	45.9677i	−1.08710	−	1.88291i
$597$		0			0
$598$	10.9483	+	62.0910i	0.447710	+	2.53909i
$599$	−6.78153	−	38.4600i	−0.277086	−	1.57143i	−0.732257	−	0.681028i	$-0.761533\pi$
$599$	−6.78153	−	38.4600i	−0.277086	−	1.57143i	0.455172	−	0.890404i	$-0.349578\pi$
$600$		0			0
$601$	14.3983	+	24.9385i	0.587318	+	1.01726i	0.994582	+	0.103954i	$0.0331494\pi$
$601$	14.3983	+	24.9385i	0.587318	+	1.01726i	−0.407264	+	0.913310i	$0.633517\pi$
$602$	2.25035	−	1.88827i	0.0917175	−	0.0769602i
$603$		0			0
$604$	48.8632	+	17.7848i	1.98822	+	0.723652i
$605$	2.64483	+	2.21928i	0.107528	+	0.0902265i
$606$		0			0
$607$	−32.4766			−1.31818			−0.659092	−	0.752062i	$-0.729059\pi$
$607$	−32.4766			−1.31818			−0.659092	+	0.752062i	$0.729059\pi$
$608$	−16.6645	−	3.06506i	−0.675834	−	0.124305i
$609$		0			0
$610$	8.71482	−	49.4242i	0.352853	−	2.00113i
$611$	22.3102	+	18.7204i	0.902572	+	0.757348i
$612$		0			0
$613$	−32.0685	+	11.6720i	−1.29524	+	0.471427i	−0.895442	−	0.445178i	$-0.853140\pi$
$613$	−32.0685	+	11.6720i	−1.29524	+	0.471427i	−0.399793	+	0.916605i	$0.630918\pi$
$614$	30.8752	−	25.9074i	1.24602	−	1.04554i
$615$		0			0
$616$	−1.05509	+	1.82747i	−0.0425109	+	0.0736310i
$617$	−3.10568	−	17.6132i	−0.125030	−	0.709081i	−0.981290	−	0.192536i	$-0.938329\pi$
$617$	−3.10568	−	17.6132i	−0.125030	−	0.709081i	0.856260	−	0.516545i	$-0.172782\pi$
$618$		0			0
$619$	5.33140	−	9.23426i	0.214287	−	0.371156i	−0.738765	−	0.673964i	$-0.764590\pi$
$619$	5.33140	−	9.23426i	0.214287	−	0.371156i	0.953052	+	0.302807i	$0.0979238\pi$
$620$	−47.1666	−	81.6950i	−1.89426	−	3.28095i
$621$		0			0
$622$	−14.7506	+	5.36879i	−0.591446	+	0.215269i
$623$	1.27454	+	0.463896i	0.0510635	+	0.0185856i
$624$		0			0
$625$	−0.201400	+	1.14220i	−0.00805599	+	0.0456878i
$626$	−50.5116			−2.01885
$627$		0			0
$628$	−31.0669			−1.23970
$629$	−1.02229	+	5.79770i	−0.0407614	+	0.231169i
$630$		0			0
$631$	28.9996	+	10.5550i	1.15446	+	0.420187i	0.847114	−	0.531412i	$-0.178338\pi$
$631$	28.9996	+	10.5550i	1.15446	+	0.420187i	0.307342	+	0.951599i	$0.400561\pi$
$632$	9.72400	−	3.53925i	0.386800	−	0.140784i
$633$		0			0
$634$	39.4273	+	68.2900i	1.56586	+	2.71214i
$635$	8.68072	−	15.0355i	0.344484	−	0.596664i
$636$		0			0
$637$	7.33527	+	41.6004i	0.290634	+	1.64827i
$638$	28.2828	−	48.9873i	1.11973	−	1.93943i
$639$		0			0
$640$	56.2299	−	47.1825i	2.22268	−	1.86505i
$641$	40.1769	−	14.6232i	1.58689	−	0.577581i	0.610203	−	0.792245i	$-0.291088\pi$
$641$	40.1769	−	14.6232i	1.58689	−	0.577581i	0.976688	+	0.214664i	$0.0688656\pi$
$642$		0			0
$643$	−19.3464	−	16.2336i	−0.762948	−	0.640190i	0.175944	−	0.984400i	$-0.443702\pi$
$643$	−19.3464	−	16.2336i	−0.762948	−	0.640190i	−0.938892	+	0.344211i	$0.888147\pi$
$644$	−0.501010	+	2.84137i	−0.0197426	+	0.111966i
$645$		0			0
$646$	−11.4052	−	32.0682i	−0.448733	−	1.26171i
$647$	−6.93939			−0.272815			−0.136408	−	0.990653i	$-0.543556\pi$
$647$	−6.93939			−0.272815			−0.136408	+	0.990653i	$0.543556\pi$
$648$		0			0
$649$	−17.3680	−	14.5735i	−0.681753	−	0.572059i
$650$	107.029	+	38.9554i	4.19803	+	1.52796i
$651$		0			0
$652$	2.45811	−	2.06260i	0.0962671	−	0.0807776i
$653$	17.7420	+	30.7300i	0.694297	+	1.20256i	0.970417	+	0.241435i	$0.0776181\pi$
$653$	17.7420	+	30.7300i	0.694297	+	1.20256i	−0.276120	+	0.961123i	$0.589049\pi$
$654$		0			0
$655$	−9.76991	−	55.4079i	−0.381742	−	2.16497i
$656$	0.543950	+	3.08489i	0.0212377	+	0.120445i
$657$		0			0
$658$	1.04370	+	1.80774i	0.0406877	+	0.0704731i
$659$	−23.4583	+	19.6838i	−0.913805	+	0.766773i	−0.972839	−	0.231483i	$-0.925642\pi$
$659$	−23.4583	+	19.6838i	−0.913805	+	0.766773i	0.0590341	+	0.998256i	$0.481198\pi$
$660$		0			0
$661$	6.27466	+	2.28379i	0.244056	+	0.0888292i	0.461152	−	0.887321i	$-0.347436\pi$
$661$	6.27466	+	2.28379i	0.244056	+	0.0888292i	−0.217096	+	0.976150i	$0.569658\pi$
$662$	−43.2563	−	36.2964i	−1.68121	−	1.41070i
$663$		0			0
$664$	26.3259			1.02164
$665$	0.0213682	−	2.90254i	0.000828623	−	0.112556i
$666$		0			0
$667$	5.82547	−	33.0379i	0.225563	−	1.27923i
$668$	39.0009	+	32.7256i	1.50899	+	1.26619i
$669$		0			0
$670$	11.0642	−	4.02703i	0.427446	−	0.155578i
$671$	−14.3740	+	12.0612i	−0.554901	+	0.465617i
$672$		0			0
$673$	1.84389	−	3.19372i	0.0710768	−	0.123109i	−0.828297	−	0.560290i	$-0.810690\pi$
$673$	1.84389	−	3.19372i	0.0710768	−	0.123109i	0.899374	+	0.437181i	$0.144023\pi$
$674$	−11.5509	−	65.5083i	−0.444923	−	2.52329i
$675$		0			0
$676$	−41.9864	+	72.7226i	−1.61486	+	2.79702i
$677$	−4.96750	−	8.60396i	−0.190916	−	0.330677i	0.754638	−	0.656142i	$-0.227813\pi$
$677$	−4.96750	−	8.60396i	−0.190916	−	0.330677i	−0.945554	+	0.325465i	$0.894479\pi$
$678$		0			0
$679$	0.145430	−	0.0529321i	0.00558108	−	0.00203135i
$680$	40.5098	+	14.7444i	1.55348	+	0.565421i
$681$		0			0
$682$	−9.59240	+	54.4012i	−0.367312	+	2.08313i
$683$	−9.84280			−0.376624			−0.188312	−	0.982109i	$-0.560302\pi$
$683$	−9.84280			−0.376624			−0.188312	+	0.982109i	$0.560302\pi$
$684$		0			0
$685$	19.4165			0.741867
$686$	−1.05406	+	5.97789i	−0.0402443	+	0.228237i
$687$		0			0
$688$	−8.96451	−	3.26281i	−0.341769	−	0.124394i
$689$	−0.860175	+	0.313078i	−0.0327701	+	0.0119273i
$690$		0			0
$691$	6.13816	+	10.6316i	0.233506	+	0.404445i	0.958838	−	0.283955i	$-0.0916467\pi$
$691$	6.13816	+	10.6316i	0.233506	+	0.404445i	−0.725331	+	0.688400i	$0.758313\pi$
$692$	−7.57217	+	13.1154i	−0.287851	+	0.498572i
$693$		0			0
$694$	9.23994	+	52.4023i	0.350743	+	1.98916i
$695$	−41.4022	+	71.7106i	−1.57047	+	2.72014i
$696$		0			0
$697$	5.64400	−	4.73588i	0.213782	−	0.179384i
$698$	−38.9666	+	14.1827i	−1.47491	+	0.536823i
$699$		0			0
$700$	3.99273	+	3.35029i	0.150911	+	0.126629i
$701$	1.62292	−	9.20406i	0.0612970	−	0.347632i	−0.938699	−	0.344738i	$-0.887968\pi$
$701$	1.62292	−	9.20406i	0.0612970	−	0.347632i	0.999996	−	0.00289416i	$-0.000921240\pi$
$702$		0			0
$703$	−4.92484	−	5.95772i	−0.185744	−	0.224700i
$704$	−37.9185			−1.42911
$705$		0			0
$706$	−46.1705	−	38.7417i	−1.73765	−	1.45806i
$707$	−0.750484	−	0.273154i	−0.0282248	−	0.0102730i
$708$		0			0
$709$	−23.5180	+	19.7340i	−0.883237	+	0.741124i	−0.966842	−	0.255375i	$-0.917801\pi$
$709$	−23.5180	+	19.7340i	−0.883237	+	0.741124i	0.0836048	+	0.996499i	$0.473357\pi$
$710$	38.2504	+	66.2516i	1.43551	+	2.48638i
$711$		0			0
$712$	−4.59286	−	26.0474i	−0.172125	−	0.976168i
$713$	5.68899	+	32.2639i	0.213054	+	1.20829i
$714$		0			0
$715$	−34.6241	−	59.9707i	−1.29487	−	2.24278i
$716$	0.124737	−	0.104667i	0.00466163	−	0.00391157i
$717$		0			0
$718$	71.1554	+	25.8985i	2.65550	+	0.966522i
$719$	3.97180	+	3.33274i	0.148123	+	0.124290i	0.713838	−	0.700311i	$-0.246955\pi$
$719$	3.97180	+	3.33274i	0.148123	+	0.124290i	−0.565715	+	0.824601i	$0.691400\pi$
$720$		0			0
$721$	−1.26714			−0.0471908
$722$	41.7641	+	15.9011i	1.55430	+	0.591776i
$723$		0			0
$724$	−1.90983	+	10.8312i	−0.0709781	+	0.402537i
$725$	−46.4252	−	38.9554i	−1.72419	−	1.44677i
$726$		0			0
$727$	14.7233	−	5.35883i	0.546056	−	0.198748i	−0.0542372	−	0.998528i	$-0.517273\pi$
$727$	14.7233	−	5.35883i	0.546056	−	0.198748i	0.600293	+	0.799780i	$0.295050\pi$
$728$	−3.09342	+	2.59569i	−0.114650	+	0.0962026i
$729$		0			0
$730$	−36.8790	+	63.8763i	−1.36495	+	2.36417i
$731$	3.89633	+	22.0972i	0.144111	+	0.817293i
$732$		0			0
$733$	13.1288	−	22.7398i	0.484924	−	0.839913i	−0.514926	−	0.857235i	$-0.672181\pi$
$733$	13.1288	−	22.7398i	0.484924	−	0.839913i	0.999850	+	0.0173215i	$0.00551388\pi$
$734$	−22.6924	−	39.3043i	−0.837591	−	1.45075i
$735$		0			0
$736$	−16.1468	+	5.87695i	−0.595178	+	0.216627i
$737$	−4.13670	−	1.50563i	−0.152377	−	0.0554608i
$738$		0			0
$739$	−1.77568	+	10.0704i	−0.0653195	+	0.370445i	0.934573	+	0.355772i	$0.115782\pi$
$739$	−1.77568	+	10.0704i	−0.0653195	+	0.370445i	−0.999892	+	0.0146736i	$0.995329\pi$
$740$	22.5708			0.829719
$741$		0			0
$742$	−0.0656082			−0.00240855
$743$	−6.31158	+	35.7947i	−0.231549	+	1.31318i	0.618211	+	0.786012i	$0.287858\pi$
$743$	−6.31158	+	35.7947i	−0.231549	+	1.31318i	−0.849760	+	0.527169i	$0.823253\pi$
$744$		0			0
$745$	50.8867	+	18.5212i	1.86435	+	0.678566i
$746$	33.7636	−	12.2889i	1.23617	−	0.449930i
$747$		0			0
$748$	−18.5792	−	32.1801i	−0.679323	−	1.17662i
$749$	−1.10055	+	1.90620i	−0.0402131	+	0.0696510i
$750$		0			0
$751$	5.99747	+	34.0134i	0.218851	+	1.24117i	0.874098	+	0.485750i	$0.161454\pi$
$751$	5.99747	+	34.0134i	0.218851	+	1.24117i	−0.655247	+	0.755415i	$0.727435\pi$
$752$	3.38938	−	5.87057i	0.123598	−	0.214078i
$753$		0			0
$754$	82.9223	−	69.5800i	3.01985	−	2.53396i
$755$	−49.8516	+	18.1445i	−1.81429	+	0.660346i
$756$		0			0
$757$	6.19459	+	5.19788i	0.225146	+	0.188920i	0.748382	−	0.663268i	$-0.230831\pi$
$757$	6.19459	+	5.19788i	0.225146	+	0.188920i	−0.523236	+	0.852188i	$0.675275\pi$
$758$	8.56547	−	48.5772i	0.311112	−	1.76440i
$759$		0			0
$760$	−49.2260	+	27.9395i	−1.78562	+	1.01347i
$761$	−22.1362			−0.802435			−0.401218	−	0.915983i	$-0.631413\pi$
$761$	−22.1362			−0.802435			−0.401218	+	0.915983i	$0.631413\pi$
$762$		0			0
$763$	0.936537	+	0.785848i	0.0339049	+	0.0284496i
$764$	−79.5086	−	28.9388i	−2.87652	−	1.04697i
$765$		0			0
$766$	−8.92514	+	7.48909i	−0.322479	+	0.270592i
$767$	−21.6935	−	37.5743i	−0.783307	−	1.35673i
$768$		0			0
$769$	−1.39605	−	7.91739i	−0.0503428	−	0.285508i	0.949235	−	0.314568i	$-0.101860\pi$
$769$	−1.39605	−	7.91739i	−0.0503428	−	0.285508i	−0.999578	+	0.0290600i	$0.990749\pi$
$770$	−0.861857	−	4.88784i	−0.0310592	−	0.176145i
$771$		0			0
$772$	−10.0658	−	17.4345i	−0.362277	−	0.627482i
$773$	−8.40930	+	7.05624i	−0.302461	+	0.253795i	−0.781368	−	0.624071i	$-0.785478\pi$
$773$	−8.40930	+	7.05624i	−0.302461	+	0.253795i	0.478906	+	0.877866i	$0.341033\pi$
$774$		0			0
$775$	55.6147	+	20.2421i	1.99774	+	0.727118i
$776$	−2.31188	−	1.93990i	−0.0829917	−	0.0696383i
$777$		0			0
$778$	77.4492			2.77669
$779$	−0.0712148	+	9.67343i	−0.00255153	+	0.346587i
$780$		0			0
$781$	4.96673	−	28.1677i	0.177724	−	1.00792i
$782$	−26.4409	−	22.1866i	−0.945525	−	0.793390i
$783$		0			0
$784$	9.23917	−	3.36278i	0.329970	−	0.120099i
$785$	24.2800	−	20.3733i	0.866590	−	0.727155i
$786$		0			0
$787$	−3.55809	+	6.16279i	−0.126832	+	0.219680i	−0.922448	−	0.386122i	$-0.873814\pi$
$787$	−3.55809	+	6.16279i	−0.126832	+	0.219680i	0.795616	+	0.605802i	$0.207148\pi$
$788$	1.58445	+	8.98585i	0.0564436	+	0.320107i
$789$		0			0
$790$	−12.1695	+	21.0782i	−0.432972	+	0.749930i
$791$	0.514957	+	0.891932i	0.0183098	+	0.0317135i
$792$		0			0
$793$	−33.7422	+	12.2811i	−1.19822	+	0.436116i
$794$	68.0223	+	24.7581i	2.41402	+	0.878632i
$795$		0			0
$796$	10.5873	−	60.0438i	0.375258	−	2.12820i
$797$	43.6001			1.54439			0.772197	−	0.635383i	$-0.219158\pi$
$797$	43.6001			1.54439			0.772197	+	0.635383i	$0.219158\pi$
$798$		0			0
$799$	−15.9439			−0.564054
$800$	−5.39025	+	30.5697i	−0.190574	+	1.08080i
$801$		0			0
$802$	−33.7653	−	12.2896i	−1.19230	−	0.433960i
$803$	25.9137	−	9.43181i	0.914474	−	0.332841i
$804$		0			0
$805$	−1.47178	−	2.54920i	−0.0518735	−	0.0898475i
$806$	−52.8556	+	91.5486i	−1.86176	+	3.22466i
$807$		0			0
$808$	2.70439	+	15.3374i	0.0951402	+	0.539567i
$809$	−6.47479	+	11.2147i	−0.227641	+	0.394287i	−0.957109	−	0.289729i	$-0.906435\pi$
$809$	−6.47479	+	11.2147i	−0.227641	+	0.394287i	0.729467	+	0.684016i	$0.239768\pi$
$810$		0			0
$811$	−23.4800	+	19.7021i	−0.824494	+	0.691833i	−0.954020	−	0.299743i	$-0.903099\pi$
$811$	−23.4800	+	19.7021i	−0.824494	+	0.691833i	0.129526	+	0.991576i	$0.458654\pi$
$812$	4.65482	−	1.69421i	0.163352	−	0.0594553i
$813$		0			0
$814$	−10.1250	−	8.49584i	−0.354879	−	0.297779i
$815$	−0.568479	+	3.22401i	−0.0199130	+	0.112932i
$816$		0			0
$817$	−25.4047	−	14.9178i	−0.888797	−	0.521909i
$818$	−29.7414			−1.03989
$819$		0			0
$820$	−21.6386	−	18.1570i	−0.755653	−	0.634069i
$821$	17.5830	+	6.39970i	0.613652	+	0.223351i	0.630100	−	0.776514i	$-0.283014\pi$
$821$	17.5830	+	6.39970i	0.613652	+	0.223351i	−0.0164485	+	0.999865i	$0.505236\pi$
$822$		0			0
$823$	−14.3387	+	12.0316i	−0.499815	+	0.419395i	−0.857528	−	0.514437i	$-0.828001\pi$
$823$	−14.3387	+	12.0316i	−0.499815	+	0.419395i	0.357713	+	0.933831i	$0.383557\pi$
$824$	12.3549	+	21.3993i	0.430403	+	0.745480i
$825$		0			0
$826$	−0.539992	−	3.06245i	−0.0187887	−	0.106556i
$827$	6.76442	+	38.3629i	0.235222	+	1.33401i	0.842146	+	0.539250i	$0.181292\pi$
$827$	6.76442	+	38.3629i	0.235222	+	1.33401i	−0.606924	+	0.794760i	$0.707597\pi$
$828$		0			0
$829$	11.3430	+	19.6467i	0.393959	+	0.682357i	0.992968	−	0.118385i	$-0.0377718\pi$
$829$	11.3430	+	19.6467i	0.393959	+	0.682357i	−0.599009	+	0.800743i	$0.704438\pi$
$830$	−47.4332	+	39.8012i	−1.64643	+	1.38152i
$831$		0			0
$832$	−68.1870	−	24.8180i	−2.36396	−	0.860410i
$833$	−17.7152	−	14.8648i	−0.613795	−	0.515035i
$834$		0			0
$835$	−51.9418			−1.79752
$836$	47.9835	+	8.82549i	1.65954	+	0.305236i
$837$		0			0
$838$	9.50933	−	53.9301i	0.328494	−	1.86298i
$839$	−18.6172	−	15.6217i	−0.642737	−	0.539321i	0.262120	−	0.965035i	$-0.415578\pi$
$839$	−18.6172	−	15.6217i	−0.642737	−	0.539321i	−0.904857	+	0.425715i	$0.860023\pi$
$840$		0			0
$841$	−26.8726	+	9.78082i	−0.926641	+	0.337270i
$842$	41.2603	−	34.6215i	1.42192	−	1.19314i
$843$		0			0
$844$	8.14290	−	14.1039i	0.280290	−	0.485477i
$845$	−14.8767	−	84.3698i	−0.511773	−	2.90241i
$846$		0			0
$847$	0.0885259	−	0.153331i	0.00304178	−	0.00526853i
$848$	0.106530	+	0.184515i	0.00365826	+	0.00633629i
$849$		0			0
$850$	−58.5932	+	21.3262i	−2.00973	+	0.731482i
$851$	−7.36602	−	2.68101i	−0.252504	−	0.0919039i
$852$		0			0
$853$	8.70604	−	49.3744i	0.298089	−	1.69055i	−0.356285	−	0.934377i	$-0.615957\pi$
$853$	8.70604	−	49.3744i	0.298089	−	1.69055i	0.654375	−	0.756171i	$-0.272932\pi$
$854$	−2.57362			−0.0880674
$855$		0			0
$856$	42.9222			1.46705
$857$	3.47989	−	19.7355i	0.118871	−	0.674151i	−0.865890	−	0.500235i	$-0.833247\pi$
$857$	3.47989	−	19.7355i	0.118871	−	0.674151i	0.984761	−	0.173916i	$-0.0556420\pi$
$858$		0			0
$859$	−14.0103	−	5.09932i	−0.478024	−	0.173987i	0.0917597	−	0.995781i	$-0.470751\pi$
$859$	−14.0103	−	5.09932i	−0.478024	−	0.173987i	−0.569784	+	0.821795i	$0.692973\pi$
$860$	80.8376	−	29.4225i	2.75654	−	1.00330i
$861$		0			0
$862$	−35.3455	−	61.2203i	−1.20387	−	2.08517i
$863$	−10.5964	+	18.3536i	−0.360707	+	0.624763i	−0.988077	−	0.153958i	$-0.950798\pi$
$863$	−10.5964	+	18.3536i	−0.360707	+	0.624763i	0.627370	+	0.778721i	$0.284131\pi$
$864$		0			0
$865$	−2.68298	−	15.2159i	−0.0912241	−	0.517358i
$866$	−6.49674	+	11.2527i	−0.220768	+	0.382382i
$867$		0			0
$868$	−3.70574	+	3.10948i	−0.125781	+	0.105543i
$869$	8.55114	−	3.11236i	0.290078	−	0.105580i
$870$		0			0
$871$	−6.45336	−	5.41501i	−0.218664	−	0.183481i
$872$	4.13986	−	23.4783i	0.140193	−	0.795076i
$873$		0			0
$874$	44.6874	−	7.54082i	1.51157	−	0.255072i
$875$	−1.98803			−0.0672077
$876$		0			0
$877$	38.7085	+	32.4803i	1.30709	+	1.09678i	0.988873	+	0.148764i	$0.0475294\pi$
$877$	38.7085	+	32.4803i	1.30709	+	1.09678i	0.318220	+	0.948017i	$0.396915\pi$
$878$	39.0159	+	14.2006i	1.31672	+	0.479248i
$879$		0			0
$880$	−12.3470	+	10.3604i	−0.416219	+	0.349249i
$881$	11.3689	+	19.6915i	0.383027	+	0.663423i	0.991493	−	0.130157i	$-0.0415482\pi$
$881$	11.3689	+	19.6915i	0.383027	+	0.663423i	−0.608466	+	0.793580i	$0.708215\pi$
$882$		0			0
$883$	6.56346	+	37.2232i	0.220878	+	1.25266i	0.870410	+	0.492328i	$0.163854\pi$
$883$	6.56346	+	37.2232i	0.220878	+	1.25266i	−0.649532	+	0.760334i	$0.725035\pi$
$884$	−12.3478	−	70.0281i	−0.415303	−	2.35530i
$885$		0			0
$886$	−9.89322	−	17.1356i	−0.332369	−	0.575680i
$887$	20.4944	−	17.1969i	0.688136	−	0.577415i	−0.230235	−	0.973135i	$-0.573949\pi$
$887$	20.4944	−	17.1969i	0.688136	−	0.577415i	0.918371	+	0.395720i	$0.129505\pi$
$888$		0			0
$889$	−0.836619	−	0.304504i	−0.0280593	−	0.0102127i
$890$	47.6554	+	39.9876i	1.59741	+	1.34039i
$891$		0			0
$892$	−63.2995			−2.11943
$893$	13.5738	−	15.9369i	0.454231	−	0.533309i
$894$		0			0
$895$	−0.0288474	+	0.163602i	−0.000964264	+	0.00546861i
$896$	−2.88352	−	2.41956i	−0.0963317	−	0.0808319i
$897$		0			0
$898$	33.0364	−	12.0243i	1.10244	−	0.401255i
$899$	43.0883	−	36.1554i	1.43707	−	1.20585i
$900$		0			0
$901$	0.250563	−	0.433988i	0.00834746	−	0.0144582i
$902$	2.87235	+	16.2899i	0.0956389	+	0.542395i
$903$		0			0
$904$	10.0419	−	17.3931i	0.333988	−	0.578485i
$905$	−5.61035	−	9.71742i	−0.186495	−	0.323018i
$906$		0			0
$907$	15.7956	−	5.74913i	0.524485	−	0.190897i	−0.0661894	−	0.997807i	$-0.521084\pi$
$907$	15.7956	−	5.74913i	0.524485	−	0.190897i	0.590674	+	0.806910i	$0.298862\pi$
$908$	−88.0297	−	32.0402i	−2.92137	−	1.06329i
$909$		0			0
$910$	1.64930	−	9.35365i	0.0546738	−	0.310070i
$911$	−31.9168			−1.05745			−0.528726	−	0.848793i	$-0.677330\pi$
$911$	−31.9168			−1.05745			−0.528726	+	0.848793i	$0.677330\pi$
$912$		0			0
$913$	23.1506			0.766174
$914$	12.7538	−	72.3306i	0.421859	−	2.39248i
$915$		0			0
$916$	11.1839	+	4.07061i	0.369527	+	0.134497i
$917$	−2.71120	+	0.986798i	−0.0895319	+	0.0325869i
$918$		0			0
$919$	7.47044	+	12.9392i	0.246427	+	0.426824i	0.962532	−	0.271169i	$-0.0874101\pi$
$919$	7.47044	+	12.9392i	0.246427	+	0.426824i	−0.716105	+	0.697993i	$0.754077\pi$
$920$	−28.7004	+	49.7105i	−0.946223	+	1.63891i
$921$		0			0
$922$	−0.543948	−	3.08489i	−0.0179140	−	0.101595i
$923$	27.3675	−	47.4018i	0.900811	−	1.56025i
$924$		0			0
$925$	−10.8478	+	9.10235i	−0.356672	+	0.299284i
$926$	11.5310	−	4.19694i	0.378932	−	0.137920i
$927$		0			0
$928$	22.5993	+	18.9630i	0.741857	+	0.622492i
$929$	−5.57020	+	31.5901i	−0.182752	+	1.03644i	0.746057	+	0.665882i	$0.231944\pi$
$929$	−5.57020	+	31.5901i	−0.182752	+	1.03644i	−0.928810	+	0.370557i	$0.879167\pi$
$930$		0			0
$931$	29.9402	−	5.05228i	0.981249	−	0.165582i
$932$	−64.8049			−2.12275
$933$		0			0
$934$	−37.0565	−	31.0941i	−1.21253	−	1.01743i
$935$	35.6237	+	12.9660i	1.16502	+	0.424033i
$936$		0			0
$937$	−16.2836	+	13.6636i	−0.531962	+	0.446369i	−0.868778	−	0.495202i	$-0.835094\pi$
$937$	−16.2836	+	13.6636i	−0.531962	+	0.446369i	0.336817	+	0.941570i	$0.390650\pi$
$938$	−0.301897	−	0.522901i	−0.00985730	−	0.0170733i
$939$		0			0
$940$	10.6147	+	60.1989i	0.346213	+	1.96347i
$941$	0.669068	+	3.79447i	0.0218110	+	0.123696i	0.993769	−	0.111457i	$-0.0355518\pi$
$941$	0.669068	+	3.79447i	0.0218110	+	0.123696i	−0.971958	+	0.235154i	$0.924441\pi$
$942$		0			0
$943$	4.90508	+	8.49584i	0.159731	+	0.276663i
$944$	−7.73597	+	6.49125i	−0.251784	+	0.211272i
$945$		0			0
$946$	−47.3376	−	17.2295i	−1.53908	−	0.560178i
$947$	−9.28936	−	7.79470i	−0.301864	−	0.253294i	0.479256	−	0.877675i	$-0.340907\pi$
$947$	−9.28936	−	7.79470i	−0.301864	−	0.253294i	−0.781120	+	0.624382i	$0.785351\pi$
$948$		0			0
$949$	52.7725			1.71307
$950$	28.5665	−	76.7237i	0.926821	−	2.48925i
$951$		0			0
$952$	0.383885	−	2.17712i	0.0124418	−	0.0705608i
$953$	17.6585	+	14.8172i	0.572015	+	0.479978i	0.882314	−	0.470661i	$-0.155985\pi$
$953$	17.6585	+	14.8172i	0.572015	+	0.479978i	−0.310299	+	0.950639i	$0.600429\pi$
$954$		0			0
$955$	81.1169	−	29.5241i	2.62488	−	0.955378i
$956$	25.9570	−	21.7805i	0.839510	−	0.704432i
$957$		0			0
$958$	−18.3475	+	31.7787i	−0.592779	+	1.02672i
$959$	−0.172901	−	0.980571i	−0.00558327	−	0.0316643i
$960$		0			0
$961$	−11.9650	+	20.7239i	−0.385967	+	0.668514i
$962$	−12.6466	−	21.9045i	−0.407742	−	0.706230i
$963$		0			0
$964$	−20.3405	+	7.40333i	−0.655123	+	0.238445i
$965$	19.3002	+	7.02470i	0.621296	+	0.226133i
$966$		0			0
$967$	−4.02259	+	22.8133i	−0.129358	+	0.733625i	0.849266	+	0.527966i	$0.177045\pi$
$967$	−4.02259	+	22.8133i	−0.129358	+	0.733625i	−0.978624	+	0.205659i	$0.934066\pi$
$968$	−3.45258			−0.110970
$969$		0			0
$970$	7.09833			0.227914
$971$	−5.48077	+	31.0830i	−0.175886	+	0.997501i	0.761229	+	0.648483i	$0.224596\pi$
$971$	−5.48077	+	31.0830i	−0.175886	+	0.997501i	−0.937116	+	0.349019i	$0.886515\pi$
$972$		0			0
$973$	3.99020	+	1.45231i	0.127920	+	0.0465590i
$974$	−49.1385	+	17.8850i	−1.57450	+	0.573071i
$975$		0			0
$976$	4.17886	+	7.23800i	0.133762	+	0.231683i
$977$	−18.3153	+	31.7230i	−0.585958	+	1.01491i	0.408797	+	0.912625i	$0.365949\pi$
$977$	−18.3153	+	31.7230i	−0.585958	+	1.01491i	−0.994755	+	0.102284i	$0.967385\pi$
$978$		0			0
$979$	−4.03890	−	22.9057i	−0.129084	−	0.732070i
$980$	−44.3307	+	76.7830i	−1.41609	+	2.45274i
$981$		0			0
$982$	−58.2456	+	48.8739i	−1.85869	+	1.55963i
$983$	34.5141	−	12.5621i	1.10083	−	0.400669i	0.273207	−	0.961955i	$-0.411916\pi$
$983$	34.5141	−	12.5621i	1.10083	−	0.400669i	0.827622	+	0.561286i	$0.189693\pi$
$984$		0			0
$985$	−7.13113	−	5.98373i	−0.227217	−	0.190657i
$986$	−10.2904	+	58.3599i	−0.327714	+	1.85856i
$987$		0			0
$988$	80.5099	+	47.2761i	2.56136	+	1.50405i
$989$	−29.8764			−0.950014
$990$		0			0
$991$	−11.3923	−	9.55931i	−0.361890	−	0.303661i	0.443654	−	0.896198i	$-0.353682\pi$
$991$	−11.3923	−	9.55931i	−0.361890	−	0.303661i	−0.805543	+	0.592537i	$0.798126\pi$
$992$	−27.0726	−	9.85362i	−0.859556	−	0.312853i
$993$		0			0
$994$	3.00521	−	2.52167i	0.0953196	−	0.0799827i
$995$	31.1017	+	53.8697i	0.985989	+	1.70778i
$996$		0			0
$997$	3.07192	+	17.4217i	0.0972886	+	0.551751i	0.994022	+	0.109180i	$0.0348225\pi$
$997$	3.07192	+	17.4217i	0.0972886	+	0.551751i	−0.896733	+	0.442571i	$0.854066\pi$
$998$	−1.71513	−	9.72696i	−0.0542913	−	0.307902i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.2.u.d.55.2	yes	12
3.2	odd	2	inner	171.2.u.d.55.1	yes	12
19.3	odd	18		3249.2.a.bj.1.1		6
19.9	even	9	inner	171.2.u.d.28.2	yes	12
19.16	even	9		3249.2.a.bi.1.6		6
57.35	odd	18		3249.2.a.bi.1.1		6
57.41	even	18		3249.2.a.bj.1.6		6
57.47	odd	18	inner	171.2.u.d.28.1	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.u.d.28.1	✓	12	57.47	odd	18	inner
171.2.u.d.28.2	yes	12	19.9	even	9	inner
171.2.u.d.55.1	yes	12	3.2	odd	2	inner
171.2.u.d.55.2	yes	12	1.1	even	1	trivial
3249.2.a.bi.1.1		6	57.35	odd	18
3249.2.a.bi.1.6		6	19.16	even	9
3249.2.a.bj.1.1		6	19.3	odd	18
3249.2.a.bj.1.6		6	57.41	even	18

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	171.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.408427 - 2.31631i) q^{2} +(-3.31908 - 1.20805i) q^{4} +(3.38621 - 1.23248i) q^{5} +(-0.0923963 - 0.160035i) q^{7} +(-1.80177 + 3.12075i) q^{8} +(-1.47178 - 8.34689i) q^{10} +(-1.58445 + 2.74434i) q^{11} +(-4.64543 + 3.89798i) q^{13} +(-0.408427 + 0.148655i) q^{14} +(1.08125 + 0.907278i) q^{16} +(0.576485 - 3.26941i) q^{17} +(2.77719 + 3.35965i) q^{19} -12.7280 q^{20} +(5.70961 + 4.79093i) q^{22} +(4.15381 + 1.51186i) q^{23} +(6.11721 - 5.13295i) q^{25} +(7.13159 + 12.3523i) q^{26} +(0.113341 + 0.642788i) q^{28} +(-1.31786 - 7.47398i) q^{29} +(3.70574 + 6.41852i) q^{31} +(-2.97779 + 2.49866i) q^{32} +(-7.33750 - 2.67063i) q^{34} +(-0.510114 - 0.428036i) q^{35} -1.77332 q^{37} +(8.91625 - 5.06065i) q^{38} +(-2.25490 + 12.7882i) q^{40} +(1.70008 + 1.42654i) q^{41} +(-6.35117 + 2.31164i) q^{43} +(8.57419 - 7.19460i) q^{44} +(5.19846 - 9.00400i) q^{46} +(-0.833963 - 4.72964i) q^{47} +(3.48293 - 6.03260i) q^{49} +(-9.39105 - 16.2658i) q^{50} +(20.1275 - 7.32580i) q^{52} +(0.141845 + 0.0516275i) q^{53} +(-1.98293 + 11.2457i) q^{55} +0.665906 q^{56} -17.8503 q^{58} +(-1.24239 + 7.04595i) q^{59} +(5.56418 + 2.02520i) q^{61} +(16.3808 - 5.96212i) q^{62} +(5.98293 + 10.3627i) q^{64} +(-10.9262 + 18.9248i) q^{65} +(0.241230 + 1.36808i) q^{67} +(-5.86299 + 10.1550i) q^{68} +(-1.19981 + 1.00676i) q^{70} +(-8.48161 + 3.08705i) q^{71} +(-6.66637 - 5.59375i) q^{73} +(-0.724272 + 4.10755i) q^{74} +(-5.15910 - 14.5059i) q^{76} +0.585588 q^{77} +(-2.19981 - 1.84586i) q^{79} +(4.77955 + 1.73961i) q^{80} +(3.99866 - 3.35527i) q^{82} +(-3.65280 - 6.32683i) q^{83} +(-2.07738 - 11.7814i) q^{85} +(2.76047 + 15.6554i) q^{86} +(-5.70961 - 9.88933i) q^{88} +(-5.62262 + 4.71794i) q^{89} +(1.05303 + 0.383273i) q^{91} +(-11.9604 - 10.0360i) q^{92} -11.2959 q^{94} +(13.5449 + 7.95365i) q^{95} +(-0.145430 + 0.824773i) q^{97} +(-12.5508 - 10.5314i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{4} + 6 q^{7} + 12 q^{10} - 24 q^{13} + 18 q^{16} + 12 q^{19} + 12 q^{25} - 12 q^{28} + 24 q^{31} - 78 q^{34} - 48 q^{37} - 30 q^{40} - 24 q^{43} + 6 q^{46} + 54 q^{52} + 18 q^{55} - 48 q^{58}+ \cdots + 30 q^{97}+O(q^{100}) \) 12 * q - 6 * q^4 + 6 * q^7 + 12 * q^10 - 24 * q^13 + 18 * q^16 + 12 * q^19 + 12 * q^25 - 12 * q^28 + 24 * q^31 - 78 * q^34 - 48 * q^37 - 30 * q^40 - 24 * q^43 + 6 * q^46 + 54 * q^52 + 18 * q^55 - 48 * q^58 + 30 * q^61 + 30 * q^64 + 48 * q^67 + 60 * q^70 - 42 * q^73 + 12 * q^76 + 48 * q^79 + 66 * q^82 - 78 * q^85 - 12 * q^91 - 12 * q^94 + 30 * q^97

Introduction

L-functions

Modular forms

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Representations

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Database

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