LMFDB - Embedded newform 171.2.u.d.28.1

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			28.1
Root			$1.58445 - 0.914781i$ of defining polynomial
Character	$\chi$	$=$	171.28
Dual form			171.2.u.d.55.1

$q$-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 $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{4}{9}\right)$

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	−0.691381	−	0.722491i	$-0.742997\pi$
$2$	−0.408427	−	2.31631i	−0.288802	−	1.63788i	0.402579	−	0.915385i	$-0.368114\pi$
$3$		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	$-0.687140\pi$
$5$	−3.38621	−	1.23248i	−1.51436	−	0.551182i	−0.959732	+	0.280916i	$0.909362\pi$
$6$		0			0
$7$	−0.0923963	+	0.160035i	−0.0349225	+	0.0604876i	−0.882958	−	0.469451i	$-0.844452\pi$
$7$	−0.0923963	+	0.160035i	−0.0349225	+	0.0604876i	0.848036	+	0.529939i	$0.177785\pi$
$8$	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	$-0.00812685\pi$
$11$	1.58445	+	2.74434i	0.477729	+	0.827450i	−0.521945	+	0.852979i	$0.674794\pi$
$12$		0			0
$13$	−4.64543	−	3.89798i	−1.28841	−	1.08110i	−0.992026	−	0.126036i	$-0.959775\pi$
$13$	−4.64543	−	3.89798i	−1.28841	−	1.08110i	−0.296385	−	0.955069i	$-0.595781\pi$
$14$	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	−0.971383	−	0.237520i	$-0.923666\pi$
$17$	−0.576485	−	3.26941i	−0.139818	−	0.792948i	0.831565	−	0.555428i	$-0.187446\pi$
$18$		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	$-0.763569\pi$
$23$	−4.15381	+	1.51186i	−0.866128	+	0.315245i	−0.129530	+	0.991575i	$0.541347\pi$
$24$		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	−0.576417	−	0.817155i	$-0.695550\pi$
$29$	1.31786	−	7.47398i	0.244721	−	1.38788i	0.821139	−	0.570729i	$-0.193339\pi$
$30$		0			0
$31$	3.70574	−	6.41852i	0.665570	−	1.15280i	−0.313560	−	0.949568i	$-0.601522\pi$
$31$	3.70574	−	6.41852i	0.665570	−	1.15280i	0.979130	−	0.203233i	$-0.0651448\pi$
$32$	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	$-0.777665\pi$
$41$	−1.70008	+	1.42654i	−0.265508	+	0.222788i	0.500308	+	0.865848i	$0.333220\pi$
$42$		0			0
$43$	−6.35117	−	2.31164i	−0.968544	−	0.352521i	−0.191168	−	0.981557i	$-0.561227\pi$
$43$	−6.35117	−	2.31164i	−0.968544	−	0.352521i	−0.777376	+	0.629036i	$0.783450\pi$
$44$	−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	−0.861597	−	0.507592i	$-0.830536\pi$
$47$	0.833963	−	4.72964i	0.121646	−	0.689889i	0.983244	−	0.182297i	$-0.0583532\pi$
$48$		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	$-0.614411\pi$
$53$	−0.141845	+	0.0516275i	−0.0194840	+	0.00709158i	0.332260	+	0.943188i	$0.392189\pi$
$54$		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	0.952357	+	0.304986i	$0.0986518\pi$
$59$	1.24239	+	7.04595i	0.161745	+	0.917304i	−0.790611	+	0.612318i	$0.790237\pi$
$60$		0			0
$61$	5.56418	−	2.02520i	0.712420	−	0.259300i	0.0397156	−	0.999211i	$-0.487355\pi$
$61$	5.56418	−	2.02520i	0.712420	−	0.259300i	0.672704	+	0.739911i	$0.265133\pi$
$62$	−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	−0.966520	−	0.256591i	$-0.917401\pi$
$67$	0.241230	−	1.36808i	0.0294709	−	0.167138i	0.995991	+	0.0894530i	$0.0285119\pi$
$68$	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	$-0.208978\pi$
$71$	8.48161	+	3.08705i	1.00658	+	0.366366i	0.214463	+	0.976732i	$0.431200\pi$
$72$		0			0
$73$	−6.66637	+	5.59375i	−0.780240	+	0.654699i	−0.943309	−	0.331915i	$-0.892305\pi$
$73$	−6.66637	+	5.59375i	−0.780240	+	0.654699i	0.163069	+	0.986615i	$0.447861\pi$
$74$	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	−0.758094	−	0.652145i	$-0.773869\pi$
$79$	−2.19981	+	1.84586i	−0.247498	+	0.207675i	0.510596	+	0.859821i	$0.329425\pi$
$80$	−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	$-0.702015\pi$
$83$	3.65280	−	6.32683i	0.400946	−	0.694460i	0.993840	+	0.110821i	$0.0353480\pi$
$84$		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	$-0.150595\pi$
$89$	5.62262	+	4.71794i	0.595996	+	0.500100i	−0.294160	+	0.955756i	$0.595040\pi$
$90$		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	0.976534	−	0.215363i	$-0.0690934\pi$
$97$	−0.145430	−	0.824773i	−0.0147661	−	0.0837430i	−0.991300	+	0.131620i	$0.957982\pi$
$98$	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	$-0.346760\pi$
$101$	−3.31074	−	2.77804i	−0.329431	−	0.276425i	−0.792468	+	0.609914i	$0.791204\pi$
$102$		0			0
$103$	3.42855	+	5.93842i	0.337825	+	0.585130i	0.984023	−	0.178040i	$-0.0569755\pi$
$103$	3.42855	+	5.93842i	0.337825	+	0.585130i	−0.646198	+	0.763169i	$0.723642\pi$
$104$	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	−0.420213	−	0.907425i	$-0.638045\pi$
$107$	5.95557	−	10.3154i	0.575747	−	0.997223i	0.995960	−	0.0897975i	$-0.0286220\pi$
$108$		0			0
$109$	−6.21688	−	2.26276i	−0.595469	−	0.216733i	0.0266640	−	0.999644i	$-0.491512\pi$
$109$	−6.21688	−	2.26276i	−0.595469	−	0.216733i	−0.622133	+	0.782911i	$0.713734\pi$
$110$	−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	$-0.415569\pi$
$113$	5.57336			0.524297			0.262149	+	0.965027i	$0.415569\pi$
$114$		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	0.791680	−	0.610936i	$-0.209207\pi$
$127$	3.69072	+	3.09688i	0.327499	+	0.274804i	−0.464181	+	0.885740i	$0.653651\pi$
$128$	−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	−0.838620	−	0.544717i	$-0.816637\pi$
$131$	−2.71120	−	15.3760i	−0.236879	−	1.34341i	0.601741	−	0.798691i	$-0.294474\pi$
$132$		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	$-0.685040\pi$
$137$	−5.06324	+	1.84287i	−0.432582	+	0.157447i	0.116546	+	0.993185i	$0.462818\pi$
$138$		0			0
$139$	−17.6027	−	14.7704i	−1.49304	−	1.25281i	−0.890720	−	0.454552i	$-0.849799\pi$
$139$	−17.6027	−	14.7704i	−1.49304	−	1.25281i	−0.602318	−	0.798256i	$-0.705756\pi$
$140$	−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	$-0.933290\pi$
$149$	−11.5118	+	9.65956i	−0.943085	+	0.791342i	0.0350344	+	0.999386i	$0.488846\pi$
$150$		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	0.650078	−	0.759868i	$-0.274736\pi$
$157$	8.26517	+	3.00827i	0.659632	+	0.240086i	0.00955462	+	0.999954i	$0.496959\pi$
$158$	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	0.847688	−	0.530496i	$-0.177994\pi$
$163$	−0.454241	−	0.786768i	−0.0355789	−	0.0616244i	−0.883267	+	0.468871i	$0.844661\pi$
$164$	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	$-0.422795\pi$
$167$	13.5449	−	4.92992i	1.04813	−	0.381489i	0.807958	+	0.589241i	$0.200573\pi$
$168$		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	$-0.107670\pi$
$173$	−0.744542	−	4.22251i	−0.0566065	−	0.321031i	−0.999942	+	0.0108104i	$0.996559\pi$
$174$		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	$-0.166118\pi$
$179$	0.0230504	+	0.0399245i	0.00172287	+	0.00298410i	−0.865163	+	0.501491i	$0.832785\pi$
$180$		0			0
$181$	−0.540707	+	3.06650i	−0.0401904	+	0.227931i	−0.998286	−	0.0585159i	$-0.981363\pi$
$181$	−0.540707	+	3.06650i	−0.0401904	+	0.227931i	0.958096	+	0.286447i	$0.0924743\pi$
$182$	−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	$-0.833739\pi$
$191$	−23.9550			−1.73333			−0.866663	+	0.498895i	$0.833739\pi$
$192$		0			0
$193$	4.36618	−	3.66366i	0.314285	−	0.263716i	−0.471976	−	0.881612i	$-0.656459\pi$
$193$	4.36618	−	3.66366i	0.314285	−	0.263716i	0.786260	+	0.617895i	$0.212015\pi$
$194$	−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	$-0.803999\pi$
$197$	1.29165	−	2.23721i	0.0920265	−	0.159395i	0.908364	+	0.418181i	$0.137332\pi$
$198$		0			0
$199$	2.99747	−	16.9995i	0.212485	−	1.20506i	−0.672732	−	0.739886i	$-0.734879\pi$
$199$	2.99747	−	16.9995i	0.212485	−	1.20506i	0.885217	−	0.465178i	$-0.154010\pi$
$200$	−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	0.944766	−	0.327747i	$-0.106289\pi$
$211$	−0.800660	−	4.54077i	−0.0551197	−	0.312599i	−0.999885	+	0.0151476i	$0.995178\pi$
$212$	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	0.837465	−	0.546491i	$-0.184037\pi$
$223$	16.8405	+	6.12944i	1.12772	+	0.410457i	0.290258	+	0.956949i	$0.406259\pi$
$224$	−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	$-0.842574\pi$
$227$	−26.5223			−1.76035			−0.880174	+	0.474650i	$0.842574\pi$
$228$		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	$-0.594116\pi$
$233$	−17.2410	−	6.27520i	−1.12949	−	0.411102i	−0.838108	+	0.545504i	$0.816338\pi$
$234$		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	$-0.0662471\pi$
$239$	4.79666	+	8.30806i	0.310270	+	0.537404i	−0.668151	+	0.744026i	$0.732914\pi$
$240$		0			0
$241$	4.69459	+	3.93923i	0.302405	+	0.253748i	0.781345	−	0.624100i	$-0.214534\pi$
$241$	4.69459	+	3.93923i	0.302405	+	0.253748i	−0.478939	+	0.877848i	$0.658979\pi$
$242$	−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	$-0.365393\pi$
$251$	20.7690	−	7.55931i	1.31093	−	0.477139i	0.900541	+	0.434771i	$0.143171\pi$
$252$		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	−0.744946	−	0.667124i	$-0.767525\pi$
$257$	2.93763	−	16.6601i	0.183244	−	1.03923i	0.928191	−	0.372105i	$-0.121364\pi$
$258$		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	$-0.642119\pi$
$263$	6.18684	−	5.19137i	0.381497	−	0.320114i	0.813290	+	0.581859i	$0.197674\pi$
$264$		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	$-0.612939\pi$
$269$	8.45856	−	7.09758i	0.515728	−	0.432747i	0.863139	+	0.504966i	$0.168495\pi$
$270$		0			0
$271$	1.90033	+	0.691663i	0.115437	+	0.0420156i	0.399093	−	0.916911i	$-0.369325\pi$
$271$	1.90033	+	0.691663i	0.115437	+	0.0420156i	−0.283656	+	0.958926i	$0.591547\pi$
$272$	−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	−0.988532	−	0.151013i	$-0.951746\pi$
$277$	−10.4029	−	18.0183i	−0.625047	−	1.08261i	0.363485	−	0.931600i	$-0.381587\pi$
$278$	−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	$-0.531227\pi$
$281$	7.82371	−	2.84760i	0.466723	−	0.169873i	0.564668	+	0.825318i	$0.309004\pi$
$282$		0			0
$283$	1.93835	+	10.9929i	0.115223	+	0.653461i	0.986640	+	0.162918i	$0.0520906\pi$
$283$	1.93835	+	10.9929i	0.115223	+	0.653461i	−0.871417	+	0.490543i	$0.836798\pi$
$284$	−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	$-0.202888\pi$
$293$	−1.94361	−	3.36643i	−0.113547	−	0.196669i	−0.917198	+	0.398432i	$0.869555\pi$
$294$		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	−0.186093	−	0.982532i	$-0.559582\pi$
$307$	13.1270	−	11.0149i	0.749198	−	0.628652i	0.935291	+	0.353880i	$0.115138\pi$
$308$	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	$-0.772737\pi$
$311$	3.33695	−	5.77977i	0.189221	−	0.327741i	0.944991	+	0.327097i	$0.106070\pi$
$312$		0			0
$313$	−3.72921	+	21.1494i	−0.210787	+	1.19543i	0.677282	+	0.735724i	$0.263158\pi$
$313$	−3.72921	+	21.1494i	−0.210787	+	1.19543i	−0.888069	+	0.459710i	$0.847953\pi$
$314$	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	0.937854	+	0.347030i	$0.112810\pi$
$317$	25.6824	+	21.5501i	1.44247	+	1.21037i	0.504615	+	0.863345i	$0.331635\pi$
$318$		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	0.980669	+	0.195673i	$0.0626891\pi$
$331$	12.0039	+	20.7913i	0.659792	+	1.14279i	−0.320877	+	0.947121i	$0.603978\pi$
$332$	−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	0.941941	−	0.335778i	$-0.108999\pi$
$337$	26.5758	+	9.67280i	1.44768	+	0.526911i	0.505734	+	0.862689i	$0.331222\pi$
$338$	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	$-0.181166\pi$
$347$	21.2589	+	7.73760i	1.14124	+	0.415376i	0.298876	+	0.954292i	$0.403388\pi$
$348$		0			0
$349$	−8.81521	+	15.2684i	−0.471867	+	0.817298i	−0.999482	−	0.0321858i	$-0.989753\pi$
$349$	−8.81521	+	15.2684i	−0.471867	+	0.817298i	0.527615	+	0.849484i	$0.323087\pi$
$350$	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	−0.974387	−	0.224880i	$-0.927801\pi$
$353$	−12.8126	−	22.1920i	−0.681945	−	1.18116i	0.292442	−	0.956283i	$-0.405532\pi$
$354$		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	0.666985	+	0.745071i	$0.267585\pi$
$359$	5.59047	+	31.7051i	0.295054	+	1.67333i	−0.371931	+	0.928260i	$0.621304\pi$
$360$		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	0.941115	−	0.338085i	$-0.109779\pi$
$367$	14.7815	+	12.4032i	0.771589	+	0.647440i	−0.169526	+	0.985526i	$0.554224\pi$
$368$	−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	−0.597675	−	0.801739i	$-0.703909\pi$
$373$	7.63816	−	13.2297i	0.395489	−	0.685007i	0.993163	+	0.116732i	$0.0372419\pi$
$374$	−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	$-0.681829\pi$
$383$	3.79464	−	3.18408i	0.193897	−	0.162699i	0.734568	+	0.678535i	$0.237385\pi$
$384$		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	0.397275	+	0.917700i	$0.369956\pi$
$389$	−5.71798	+	32.4283i	−0.289913	+	1.64418i	−0.687188	+	0.726480i	$0.741155\pi$
$390$		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	−0.759698	−	0.650276i	$-0.774653\pi$
$397$	−5.34430	−	30.3091i	−0.268223	−	1.52117i	0.491475	−	0.870892i	$-0.336458\pi$
$398$	−40.6003			−2.03511
$399$		0			0
$400$	11.2713			0.563563
$401$	−2.65284	−	15.0450i	−0.132476	−	0.751311i	−0.976584	−	0.215137i	$-0.930980\pi$
$401$	−2.65284	−	15.0450i	−0.132476	−	0.751311i	0.844107	−	0.536174i	$-0.180131\pi$
$402$		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	0.881158	+	0.472821i	$0.156764\pi$
$409$	−2.19577	+	12.4529i	−0.108574	+	0.615754i	−0.989732	+	0.142933i	$0.954347\pi$
$410$	−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	$-0.692561\pi$
$419$	−23.2828			−1.13744			−0.568720	+	0.822531i	$0.692561\pi$
$420$		0			0
$421$	17.5424	−	14.7198i	0.854962	−	0.717398i	−0.105914	−	0.994375i	$-0.533777\pi$
$421$	17.5424	−	14.7198i	0.854962	−	0.717398i	0.960877	+	0.276977i	$0.0893325\pi$
$422$	−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	$-0.535409\pi$
$431$	−23.0236	−	19.3191i	−1.10901	−	0.930570i	−0.997998	+	0.0632493i	$0.979854\pi$
$432$		0			0
$433$	−5.19119	+	1.88944i	−0.249473	+	0.0908006i	−0.463730	−	0.885977i	$-0.653489\pi$
$433$	−5.19119	+	1.88944i	−0.249473	+	0.0908006i	0.214257	+	0.976777i	$0.431267\pi$
$434$	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	−0.966313	−	0.257370i	$-0.917144\pi$
$439$	−3.06536	−	17.3845i	−0.146302	−	0.829718i	0.820011	−	0.572347i	$-0.193967\pi$
$440$	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	$-0.341821\pi$
$443$	−6.44432	−	5.40742i	−0.306179	−	0.256915i	−0.782911	+	0.622134i	$0.786266\pi$
$444$		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	$-0.948071\pi$
$449$	−7.47365	+	12.9447i	−0.352703	+	0.610900i	0.634019	+	0.773318i	$0.281404\pi$
$450$		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	$-0.398763\pi$
$461$	−1.25149	−	0.455507i	−0.0582879	−	0.0212151i	−0.371000	+	0.928633i	$0.620985\pi$
$462$		0			0
$463$	2.60859	−	4.51822i	0.121232	−	0.209979i	−0.799022	−	0.601302i	$-0.794649\pi$
$463$	2.60859	−	4.51822i	0.121232	−	0.209979i	0.920254	+	0.391322i	$0.127982\pi$
$464$	−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	$-0.324529\pi$
$467$	−10.2834	−	17.8113i	−0.475858	−	0.824210i	−0.999618	+	0.0276560i	$0.991196\pi$
$468$		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	$-0.495108\pi$
$479$	14.6604	−	5.33597i	0.669853	−	0.243806i	0.654485	+	0.756075i	$0.272886\pi$
$480$		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	0.496262	+	0.868173i	$0.334706\pi$
$487$	−11.1163	+	19.2541i	−0.503729	+	0.872485i	−0.999991	+	0.00431144i	$0.998628\pi$
$488$	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	$-0.461999\pi$
$491$	24.7639	−	20.7794i	1.11758	−	0.937760i	0.998480	+	0.0551228i	$0.0175550\pi$
$492$		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	0.428832	−	0.903384i	$-0.358925\pi$
$499$	3.94609	+	1.43626i	0.176651	+	0.0642958i	−0.252180	+	0.967680i	$0.581148\pi$
$500$	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	0.862561	+	0.505954i	$0.168859\pi$
$503$	−2.71437	+	15.3939i	−0.121028	+	0.686382i	−0.983588	+	0.180428i	$0.942252\pi$
$504$		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	−0.818545	+	0.574442i	$0.805219\pi$
$509$	−40.9445	+	14.9026i	−1.81483	+	0.660545i	−0.996286	+	0.0861027i	$0.972559\pi$
$510$		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	$-0.222581\pi$
$521$	−3.98891	−	6.90900i	−0.174757	−	0.302689i	−0.940077	+	0.340961i	$0.889247\pi$
$522$		0			0
$523$	−2.04529	+	11.5994i	−0.0894344	+	0.507208i	0.906877	+	0.421396i	$0.138460\pi$
$523$	−2.04529	+	11.5994i	−0.0894344	+	0.507208i	−0.996311	+	0.0858121i	$0.972652\pi$
$524$	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	−0.994147	−	0.108033i	$-0.965545\pi$
$541$	−0.535082	+	3.03460i	−0.0230050	+	0.130468i	0.971142	+	0.238501i	$0.0766559\pi$
$542$	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	−0.573072	−	0.819505i	$-0.694249\pi$
$547$	−11.3503	+	4.13117i	−0.485303	+	0.176636i	0.0877688	+	0.996141i	$0.472026\pi$
$548$	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	0.999999	+	0.00123268i	$0.000392375\pi$
$557$	27.7277	+	23.2663i	1.17486	+	0.985826i	0.174862	+	0.984593i	$0.444052\pi$
$558$		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	−0.397121	−	0.917766i	$-0.629991\pi$
$563$	14.1476	−	24.5043i	0.596248	−	1.03273i	0.993369	−	0.114966i	$-0.0366759\pi$
$564$		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	$-0.321477\pi$
$569$	25.3757			1.06380			0.531902	+	0.846806i	$0.321477\pi$
$570$		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	0.220802	+	0.975319i	$0.429132\pi$
$577$	−17.6373	+	30.5487i	−0.734250	+	1.27176i	−0.955052	+	0.296439i	$0.904201\pi$
$578$	−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	0.946056	+	0.324003i	$0.105029\pi$
$587$	4.06716	+	23.0660i	0.167870	+	0.952037i	−0.778186	+	0.628034i	$0.783860\pi$
$588$		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	$-0.575865\pi$
$593$	5.05730	−	1.84071i	0.207678	−	0.0755888i	0.443765	+	0.896143i	$0.353643\pi$
$594$		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	−0.455172	−	0.890404i	$-0.650422\pi$
$599$	6.78153	−	38.4600i	0.277086	−	1.57143i	0.732257	−	0.681028i	$-0.238467\pi$
$600$		0			0
$601$	14.3983	−	24.9385i	0.587318	−	1.01726i	−0.407264	−	0.913310i	$-0.633517\pi$
$601$	14.3983	−	24.9385i	0.587318	−	1.01726i	0.994582	−	0.103954i	$-0.0331494\pi$
$602$	−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	−0.399793	−	0.916605i	$-0.630918\pi$
$613$	−32.0685	−	11.6720i	−1.29524	−	0.471427i	−0.895442	+	0.445178i	$0.853140\pi$
$614$	−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	−0.856260	−	0.516545i	$-0.827218\pi$
$617$	3.10568	−	17.6132i	0.125030	−	0.709081i	0.981290	−	0.192536i	$-0.0616712\pi$
$618$		0			0
$619$	5.33140	+	9.23426i	0.214287	+	0.371156i	0.953052	−	0.302807i	$-0.0979238\pi$
$619$	5.33140	+	9.23426i	0.214287	+	0.371156i	−0.738765	+	0.673964i	$0.764590\pi$
$620$	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	0.307342	−	0.951599i	$-0.400561\pi$
$631$	28.9996	−	10.5550i	1.15446	−	0.420187i	0.847114	+	0.531412i	$0.178338\pi$
$632$	−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	$-0.708912\pi$
$641$	−40.1769	−	14.6232i	−1.58689	−	0.577581i	−0.976688	+	0.214664i	$0.931134\pi$
$642$		0			0
$643$	−19.3464	+	16.2336i	−0.762948	+	0.640190i	−0.938892	−	0.344211i	$-0.888147\pi$
$643$	−19.3464	+	16.2336i	−0.762948	+	0.640190i	0.175944	+	0.984400i	$0.443702\pi$
$644$	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	$-0.456444\pi$
$647$	6.93939			0.272815			0.136408	+	0.990653i	$0.456444\pi$
$648$		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	0.276120	+	0.961123i	$0.410951\pi$
$653$	−17.7420	+	30.7300i	−0.694297	+	1.20256i	−0.970417	+	0.241435i	$0.922382\pi$
$654$		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	$-0.0743576\pi$
$659$	23.4583	+	19.6838i	0.913805	+	0.766773i	−0.0590341	+	0.998256i	$0.518802\pi$
$660$		0			0
$661$	6.27466	−	2.28379i	0.244056	−	0.0888292i	−0.217096	−	0.976150i	$-0.569658\pi$
$661$	6.27466	−	2.28379i	0.244056	−	0.0888292i	0.461152	+	0.887321i	$0.347436\pi$
$662$	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	0.899374	−	0.437181i	$-0.144023\pi$
$673$	1.84389	+	3.19372i	0.0710768	+	0.123109i	−0.828297	+	0.560290i	$0.810690\pi$
$674$	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	$-0.772187\pi$
$677$	4.96750	−	8.60396i	0.190916	−	0.330677i	0.945554	+	0.325465i	$0.105521\pi$
$678$		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	$-0.439698\pi$
$683$	9.84280			0.376624			0.188312	+	0.982109i	$0.439698\pi$
$684$		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	−0.725331	−	0.688400i	$-0.758313\pi$
$691$	6.13816	−	10.6316i	0.233506	−	0.404445i	0.958838	+	0.283955i	$0.0916467\pi$
$692$	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	−0.999996	−	0.00289416i	$-0.999079\pi$
$701$	−1.62292	−	9.20406i	−0.0612970	−	0.347632i	0.938699	−	0.344738i	$-0.112032\pi$
$702$		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	0.0836048	−	0.996499i	$-0.473357\pi$
$709$	−23.5180	−	19.7340i	−0.883237	−	0.741124i	−0.966842	+	0.255375i	$0.917801\pi$
$710$	−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	$-0.753045\pi$
$719$	−3.97180	+	3.33274i	−0.148123	+	0.124290i	0.565715	+	0.824601i	$0.308600\pi$
$720$		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	0.600293	−	0.799780i	$-0.295050\pi$
$727$	14.7233	+	5.35883i	0.546056	+	0.198748i	−0.0542372	+	0.998528i	$0.517273\pi$
$728$	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	0.999850	−	0.0173215i	$-0.00551388\pi$
$733$	13.1288	+	22.7398i	0.484924	+	0.839913i	−0.514926	+	0.857235i	$0.672181\pi$
$734$	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	−0.999892	−	0.0146736i	$-0.995329\pi$
$739$	−1.77568	−	10.0704i	−0.0653195	−	0.370445i	0.934573	−	0.355772i	$-0.115782\pi$
$740$	−22.5708			−0.829719
$741$		0			0
$742$	−0.0656082			−0.00240855
$743$	6.31158	+	35.7947i	0.231549	+	1.31318i	0.849760	+	0.527169i	$0.176747\pi$
$743$	6.31158	+	35.7947i	0.231549	+	1.31318i	−0.618211	+	0.786012i	$0.712142\pi$
$744$		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	−0.655247	−	0.755415i	$-0.727435\pi$
$751$	5.99747	−	34.0134i	0.218851	−	1.24117i	0.874098	−	0.485750i	$-0.161454\pi$
$752$	−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	−0.523236	−	0.852188i	$-0.675275\pi$
$757$	6.19459	−	5.19788i	0.225146	−	0.188920i	0.748382	+	0.663268i	$0.230831\pi$
$758$	−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	$-0.368587\pi$
$761$	22.1362			0.802435			0.401218	+	0.915983i	$0.368587\pi$
$762$		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	−0.999578	−	0.0290600i	$-0.990749\pi$
$769$	−1.39605	+	7.91739i	−0.0503428	+	0.285508i	0.949235	+	0.314568i	$0.101860\pi$
$770$	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	$-0.214522\pi$
$773$	8.40930	+	7.05624i	0.302461	+	0.253795i	−0.478906	+	0.877866i	$0.658967\pi$
$774$		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	0.795616	−	0.605802i	$-0.207148\pi$
$787$	−3.55809	−	6.16279i	−0.126832	−	0.219680i	−0.922448	+	0.386122i	$0.873814\pi$
$788$	−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	$-0.780842\pi$
$797$	−43.6001			−1.54439			−0.772197	+	0.635383i	$0.780842\pi$
$798$		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	$-0.0935652\pi$
$809$	6.47479	+	11.2147i	0.227641	+	0.394287i	−0.729467	+	0.684016i	$0.760232\pi$
$810$		0			0
$811$	−23.4800	−	19.7021i	−0.824494	−	0.691833i	0.129526	−	0.991576i	$-0.458654\pi$
$811$	−23.4800	−	19.7021i	−0.824494	−	0.691833i	−0.954020	+	0.299743i	$0.903099\pi$
$812$	−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	$-0.716986\pi$
$821$	−17.5830	+	6.39970i	−0.613652	+	0.223351i	0.0164485	+	0.999865i	$0.494764\pi$
$822$		0			0
$823$	−14.3387	−	12.0316i	−0.499815	−	0.419395i	0.357713	−	0.933831i	$-0.383557\pi$
$823$	−14.3387	−	12.0316i	−0.499815	−	0.419395i	−0.857528	+	0.514437i	$0.828001\pi$
$824$	−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	0.606924	+	0.794760i	$0.292403\pi$
$827$	−6.76442	+	38.3629i	−0.235222	+	1.33401i	−0.842146	+	0.539250i	$0.818708\pi$
$828$		0			0
$829$	11.3430	−	19.6467i	0.393959	−	0.682357i	−0.599009	−	0.800743i	$-0.704438\pi$
$829$	11.3430	−	19.6467i	0.393959	−	0.682357i	0.992968	+	0.118385i	$0.0377718\pi$
$830$	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	$-0.584422\pi$
$839$	18.6172	−	15.6217i	0.642737	−	0.539321i	0.904857	+	0.425715i	$0.139977\pi$
$840$		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	0.654375	+	0.756171i	$0.272932\pi$
$853$	8.70604	+	49.3744i	0.298089	+	1.69055i	−0.356285	+	0.934377i	$0.615957\pi$
$854$	2.57362			0.0880674
$855$		0			0
$856$	42.9222			1.46705
$857$	−3.47989	−	19.7355i	−0.118871	−	0.674151i	−0.984761	−	0.173916i	$-0.944358\pi$
$857$	−3.47989	−	19.7355i	−0.118871	−	0.674151i	0.865890	−	0.500235i	$-0.166753\pi$
$858$		0			0
$859$	−14.0103	+	5.09932i	−0.478024	+	0.173987i	−0.569784	−	0.821795i	$-0.692973\pi$
$859$	−14.0103	+	5.09932i	−0.478024	+	0.173987i	0.0917597	+	0.995781i	$0.470751\pi$
$860$	−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	$-0.0492021\pi$
$863$	10.5964	+	18.3536i	0.360707	+	0.624763i	−0.627370	+	0.778721i	$0.715869\pi$
$864$		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	0.318220	−	0.948017i	$-0.396915\pi$
$877$	38.7085	−	32.4803i	1.30709	−	1.09678i	0.988873	−	0.148764i	$-0.0475294\pi$
$878$	−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	$-0.958452\pi$
$881$	−11.3689	+	19.6915i	−0.383027	+	0.663423i	0.608466	+	0.793580i	$0.291785\pi$
$882$		0			0
$883$	6.56346	−	37.2232i	0.220878	−	1.25266i	−0.649532	−	0.760334i	$-0.725035\pi$
$883$	6.56346	−	37.2232i	0.220878	−	1.25266i	0.870410	−	0.492328i	$-0.163854\pi$
$884$	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	$-0.426051\pi$
$887$	−20.4944	−	17.1969i	−0.688136	−	0.577415i	−0.918371	+	0.395720i	$0.870495\pi$
$888$		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	0.590674	−	0.806910i	$-0.298862\pi$
$907$	15.7956	+	5.74913i	0.524485	+	0.190897i	−0.0661894	+	0.997807i	$0.521084\pi$
$908$	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	$-0.322670\pi$
$911$	31.9168			1.05745			0.528726	+	0.848793i	$0.322670\pi$
$912$		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	−0.716105	−	0.697993i	$-0.754077\pi$
$919$	7.47044	−	12.9392i	0.246427	−	0.426824i	0.962532	+	0.271169i	$0.0874101\pi$
$920$	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	0.928810	+	0.370557i	$0.120833\pi$
$929$	5.57020	+	31.5901i	0.182752	+	1.03644i	−0.746057	+	0.665882i	$0.768056\pi$
$930$		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	0.336817	−	0.941570i	$-0.390650\pi$
$937$	−16.2836	−	13.6636i	−0.531962	−	0.446369i	−0.868778	+	0.495202i	$0.835094\pi$
$938$	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	$-0.964448\pi$
$941$	−0.669068	+	3.79447i	−0.0218110	+	0.123696i	0.971958	+	0.235154i	$0.0755593\pi$
$942$		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	$-0.659093\pi$
$947$	9.28936	−	7.79470i	0.301864	−	0.253294i	0.781120	+	0.624382i	$0.214649\pi$
$948$		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	$-0.844015\pi$
$953$	−17.6585	+	14.8172i	−0.572015	+	0.479978i	0.310299	+	0.950639i	$0.399571\pi$
$954$		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	−0.978624	−	0.205659i	$-0.934066\pi$
$967$	−4.02259	−	22.8133i	−0.129358	−	0.733625i	0.849266	−	0.527966i	$-0.177045\pi$
$968$	3.45258			0.110970
$969$		0			0
$970$	7.09833			0.227914
$971$	5.48077	+	31.0830i	0.175886	+	0.997501i	0.937116	+	0.349019i	$0.113485\pi$
$971$	5.48077	+	31.0830i	0.175886	+	0.997501i	−0.761229	+	0.648483i	$0.775404\pi$
$972$		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	0.994755	+	0.102284i	$0.0326152\pi$
$977$	18.3153	+	31.7230i	0.585958	+	1.01491i	−0.408797	+	0.912625i	$0.634051\pi$
$978$		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	$-0.588084\pi$
$983$	−34.5141	−	12.5621i	−1.10083	−	0.400669i	−0.827622	+	0.561286i	$0.810307\pi$
$984$		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	−0.805543	−	0.592537i	$-0.798126\pi$
$991$	−11.3923	+	9.55931i	−0.361890	+	0.303661i	0.443654	+	0.896198i	$0.353682\pi$
$992$	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	−0.896733	−	0.442571i	$-0.854066\pi$
$997$	3.07192	−	17.4217i	0.0972886	−	0.551751i	0.994022	−	0.109180i	$-0.0348225\pi$
$998$	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.28.1	✓	12
3.2	odd	2	inner	171.2.u.d.28.2	yes	12
19.6	even	9		3249.2.a.bi.1.1		6
19.13	odd	18		3249.2.a.bj.1.6		6
19.17	even	9	inner	171.2.u.d.55.1	yes	12
57.17	odd	18	inner	171.2.u.d.55.2	yes	12
57.32	even	18		3249.2.a.bj.1.1		6
57.44	odd	18		3249.2.a.bi.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
171.2.u.d.28.1	✓	12	1.1	even	1	trivial
171.2.u.d.28.2	yes	12	3.2	odd	2	inner
171.2.u.d.55.1	yes	12	19.17	even	9	inner
171.2.u.d.55.2	yes	12	57.17	odd	18	inner
3249.2.a.bi.1.1		6	19.6	even	9
3249.2.a.bi.1.6		6	57.44	odd	18
3249.2.a.bj.1.1		6	57.32	even	18
3249.2.a.bj.1.6		6	19.13	odd	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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Database

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