LMFDB - Embedded newform 740.2.ce.b.363.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [740,2,Mod(3,740)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(740, base_ring=CyclotomicField(36)) chi = DirichletCharacter(H, H._module([18, 27, 26])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("740.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 740 = 2^{2} \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	740.ce (of order $36$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$5.90892974957$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\Q(\zeta_{36})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{U}(1)[D_{36}]$

Embedding invariants

Embedding label			363.1
Root			$0.342020 + 0.939693i$ of defining polynomial
Character	$\chi$	$=$	740.363
Dual form			740.2.ce.b.687.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.28171 + 0.597672i) q^{2} +(1.28558 + 1.53209i) q^{4} +(0.637511 + 2.14326i) q^{5} +(0.732051 + 2.73205i) q^{8} +(-1.92836 + 2.29813i) q^{9} +(-0.463863 + 3.12807i) q^{10} +(0.472089 - 5.39601i) q^{13} +(-0.694593 + 3.93923i) q^{16} +(0.542711 + 6.20322i) q^{17} +(-3.84514 + 1.79302i) q^{18} +(-2.46410 + 3.73205i) q^{20} +(-4.18716 + 2.73271i) q^{25} +(3.83013 - 6.63397i) q^{26} +(5.11580 - 8.86082i) q^{29} +(-3.24464 + 4.63382i) q^{32} +(-3.01189 + 8.27511i) q^{34} -6.00000 q^{36} +(-5.23905 + 3.09068i) q^{37} +(-5.38881 + 3.31069i) q^{40} +(6.47989 - 5.43727i) q^{41} +(-6.15486 - 2.66790i) q^{45} +(2.39414 + 6.57785i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(8.87407 - 6.21369i) q^{52} +(11.9254 - 8.35026i) q^{53} +(11.8529 - 8.29946i) q^{58} +(9.88215 + 11.7771i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(11.8660 - 2.42820i) q^{65} +(-8.80619 + 8.80619i) q^{68} +(-7.69028 - 3.58603i) q^{72} +(-7.02628 - 7.02628i) q^{73} +(-8.56218 + 0.830127i) q^{74} +(-8.88562 + 1.02261i) q^{80} +(-1.56283 - 8.86327i) q^{81} +(11.5551 - 3.09617i) q^{82} +(-12.9492 + 5.11780i) q^{85} +(-3.03770 + 17.2276i) q^{89} +(-6.29423 - 7.09808i) q^{90} +(4.82148 - 17.9940i) q^{97} +(-0.862798 + 9.86182i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) $ 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/740\mathbb{Z}\right)^\times$.

$n$	$261$	$297$	$371$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.28171	+	0.597672i	0.906308	+	0.422618i
$2$	1.28171	+	0.597672i	0.906308	+	0.422618i
$3$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$3$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$4$	1.28558	+	1.53209i	0.642788	+	0.766044i
$5$	0.637511	+	2.14326i	0.285104	+	0.958497i
$5$	0.637511	+	2.14326i	0.285104	+	0.958497i
$6$		0			0
$7$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$7$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$8$	0.732051	+	2.73205i	0.258819	+	0.965926i
$9$	−1.92836	+	2.29813i	−0.642788	+	0.766044i
$10$	−0.463863	+	3.12807i	−0.146686	+	0.989183i
$11$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$11$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$12$		0			0
$13$	0.472089	−	5.39601i	0.130934	−	1.49658i	−0.592153	−	0.805826i	$-0.701722\pi$
$13$	0.472089	−	5.39601i	0.130934	−	1.49658i	0.723087	−	0.690757i	$-0.242723\pi$
$14$		0			0
$15$		0			0
$16$	−0.694593	+	3.93923i	−0.173648	+	0.984808i
$17$	0.542711	+	6.20322i	0.131627	+	1.50450i	0.718900	+	0.695113i	$0.244646\pi$
$17$	0.542711	+	6.20322i	0.131627	+	1.50450i	−0.587273	+	0.809389i	$0.699799\pi$
$18$	−3.84514	+	1.79302i	−0.906308	+	0.422618i
$19$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$19$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$20$	−2.46410	+	3.73205i	−0.550990	+	0.834512i
$21$		0			0
$22$		0			0
$23$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$23$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$24$		0			0
$25$	−4.18716	+	2.73271i	−0.837432	+	0.546542i
$26$	3.83013	−	6.63397i	0.751150	−	1.30103i
$27$		0			0
$28$		0			0
$29$	5.11580	−	8.86082i	0.949980	−	1.64541i	0.204520	−	0.978862i	$-0.434437\pi$
$29$	5.11580	−	8.86082i	0.949980	−	1.64541i	0.745460	−	0.666551i	$-0.232230\pi$
$30$		0			0
$31$		0			0			−	1.00000i	$-0.5\pi$
$31$		0			0				1.00000i	$0.5\pi$
$32$	−3.24464	+	4.63382i	−0.573576	+	0.819152i
$33$		0			0
$34$	−3.01189	+	8.27511i	−0.516536	+	1.41917i
$35$		0			0
$36$	−6.00000			−1.00000
$37$	−5.23905	+	3.09068i	−0.861295	+	0.508105i
$37$	−5.23905	+	3.09068i	−0.861295	+	0.508105i
$38$		0			0
$39$		0			0
$40$	−5.38881	+	3.31069i	−0.852046	+	0.523466i
$41$	6.47989	−	5.43727i	1.01199	−	0.849159i	0.0233886	−	0.999726i	$-0.492554\pi$
$41$	6.47989	−	5.43727i	1.01199	−	0.849159i	0.988600	+	0.150567i	$0.0481100\pi$
$42$		0			0
$43$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$43$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$44$		0			0
$45$	−6.15486	−	2.66790i	−0.917512	−	0.397708i
$46$		0			0
$47$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$47$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$48$		0			0
$49$	2.39414	+	6.57785i	0.342020	+	0.939693i
$50$	−7.00000	+	1.00000i	−0.989949	+	0.141421i
$51$		0			0
$52$	8.87407	−	6.21369i	1.23061	−	0.861684i
$53$	11.9254	−	8.35026i	1.63808	−	1.14700i	0.809577	−	0.587014i	$-0.199697\pi$
$53$	11.9254	−	8.35026i	1.63808	−	1.14700i	0.828504	−	0.559983i	$-0.189192\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$		0			0
$58$	11.8529	−	8.29946i	1.55636	−	1.08977i
$59$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$59$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$60$		0			0
$61$	9.88215	+	11.7771i	1.26528	+	1.50790i	0.768221	+	0.640184i	$0.221142\pi$
$61$	9.88215	+	11.7771i	1.26528	+	1.50790i	0.497058	+	0.867717i	$0.334413\pi$
$62$		0			0
$63$		0			0
$64$	−6.92820	+	4.00000i	−0.866025	+	0.500000i
$65$	11.8660	−	2.42820i	1.47180	−	0.301182i
$66$		0			0
$67$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$67$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$68$	−8.80619	+	8.80619i	−1.06791	+	1.06791i
$69$		0			0
$70$		0			0
$71$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$71$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$72$	−7.69028	−	3.58603i	−0.906308	−	0.422618i
$73$	−7.02628	−	7.02628i	−0.822364	−	0.822364i	0.164083	−	0.986447i	$-0.447534\pi$
$73$	−7.02628	−	7.02628i	−0.822364	−	0.822364i	−0.986447	+	0.164083i	$0.947534\pi$
$74$	−8.56218	+	0.830127i	−0.995333	+	0.0965003i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$79$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$80$	−8.88562	+	1.02261i	−0.993443	+	0.114331i
$81$	−1.56283	−	8.86327i	−0.173648	−	0.984808i
$82$	11.5551	−	3.09617i	1.27604	−	0.341915i
$83$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$83$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$84$		0			0
$85$	−12.9492	+	5.11780i	−1.40453	+	0.555103i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−3.03770	+	17.2276i	−0.321995	+	1.82613i	0.208004	+	0.978128i	$0.433303\pi$
$89$	−3.03770	+	17.2276i	−0.321995	+	1.82613i	−0.529999	+	0.847998i	$0.677808\pi$
$90$	−6.29423	−	7.09808i	−0.663470	−	0.748203i
$91$		0			0
$92$		0			0
$93$		0			0
$94$		0			0
$95$		0			0
$96$		0			0
$97$	4.82148	−	17.9940i	0.489547	−	1.82701i	−0.0691034	−	0.997610i	$-0.522014\pi$
$97$	4.82148	−	17.9940i	0.489547	−	1.82701i	0.558650	−	0.829403i	$-0.311320\pi$
$98$	−0.862798	+	9.86182i	−0.0871557	+	0.996195i
$99$		0			0
$100$	−9.56966	−	2.90199i	−0.956966	−	0.290199i
$101$	−5.66183	−	9.80658i	−0.563373	−	0.975791i	−0.997199	−	0.0747944i	$-0.976170\pi$
$101$	−5.66183	−	9.80658i	−0.563373	−	0.975791i	0.433826	−	0.900997i	$-0.357163\pi$
$102$		0			0
$103$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$103$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$104$	15.0878	−	2.66038i	1.47948	−	0.260872i
$105$		0			0
$106$	20.2757	−	3.57515i	1.96935	−	0.347249i
$107$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$107$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$108$		0			0
$109$	8.81602	−	3.20877i	0.844421	−	0.307344i	0.116658	−	0.993172i	$-0.462782\pi$
$109$	8.81602	−	3.20877i	0.844421	−	0.307344i	0.727764	+	0.685828i	$0.240560\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	8.06283	−	17.2908i	0.758487	−	1.62658i	−0.0206968	−	0.999786i	$-0.506588\pi$
$113$	8.06283	−	17.2908i	0.758487	−	1.62658i	0.779184	−	0.626795i	$-0.215634\pi$
$114$		0			0
$115$		0			0
$116$	20.1523	−	3.55340i	1.87109	−	0.329924i
$117$	11.4904	+	11.4904i	1.06229	+	1.06229i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	−5.50000	−	9.52628i	−0.500000	−	0.866025i
$122$	5.62724	+	21.0011i	0.509466	+	1.90135i
$123$		0			0
$124$		0			0
$125$	−8.52628	−	7.23205i	−0.762614	−	0.646854i
$126$		0			0
$127$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$127$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$128$	−11.2707	+	0.986055i	−0.996195	+	0.0871557i
$129$		0			0
$130$	16.6601	+	3.97974i	1.46119	+	0.349046i
$131$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$131$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$		0			0
$136$	−16.5502	+	6.02379i	−1.41917	+	0.516536i
$137$	−6.03559	−	22.5251i	−0.515655	−	1.92445i	−0.342297	−	0.939592i	$-0.611205\pi$
$137$	−6.03559	−	22.5251i	−0.515655	−	1.92445i	−0.173358	−	0.984859i	$-0.555462\pi$
$138$		0			0
$139$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$139$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		0			0
$144$	−7.71345	−	9.19253i	−0.642788	−	0.766044i
$145$	22.2525	+	5.31563i	1.84797	+	0.441439i
$146$	−4.80626	−	13.2051i	−0.397769	−	1.09286i
$147$		0			0
$148$	−11.4704	−	4.05339i	−0.942861	−	0.333187i
$149$			19.9961i			1.63814i	0.573691	+	0.819072i	$0.305511\pi$
$149$			19.9961i			1.63814i	−0.573691	+	0.819072i	$0.694489\pi$
$150$		0			0
$151$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$151$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$152$		0			0
$153$	−15.3024	−	10.7148i	−1.23712	−	0.866243i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	22.3631	−	1.95652i	1.78477	−	0.156147i	0.853646	−	0.520854i	$-0.174386\pi$
$157$	22.3631	−	1.95652i	1.78477	−	0.156147i	0.931122	+	0.364707i	$0.118831\pi$
$158$		0			0
$159$		0			0
$160$	−12.0000	−	4.00000i	−0.948683	−	0.316228i
$161$		0			0
$162$	3.29423	−	12.2942i	0.258819	−	0.965926i
$163$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$163$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$164$	16.6608	+	2.93774i	1.30099	+	0.229399i
$165$		0			0
$166$		0			0
$167$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$167$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$168$		0			0
$169$	−16.0915	−	2.83737i	−1.23781	−	0.218259i
$170$	−19.6559	−	1.17981i	−1.50754	−	0.0904870i
$171$		0			0
$172$		0			0
$173$	−13.2442	−	6.17585i	−1.00693	−	0.469541i	−0.152057	−	0.988372i	$-0.548590\pi$
$173$	−13.2442	−	6.17585i	−1.00693	−	0.469541i	−0.854877	+	0.518831i	$0.826368\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$		0			0
$178$	−14.1899	+	20.2653i	−1.06358	+	1.51895i
$179$		0			0		1.00000			$0$
$179$		0			0		−1.00000			$\pi$
$180$	−3.82507	−	12.8596i	−0.285104	−	0.958497i
$181$	−7.71718	+	6.47548i	−0.573614	+	0.481319i	−0.882843	−	0.469669i	$-0.844373\pi$
$181$	−7.71718	+	6.47548i	−0.573614	+	0.481319i	0.309229	+	0.950988i	$0.399929\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−9.96410	−	9.25833i	−0.732575	−	0.680686i
$186$		0			0
$187$		0			0
$188$		0			0
$189$		0			0
$190$		0			0
$191$		0			0			−	1.00000i	$-0.5\pi$
$191$		0			0				1.00000i	$0.5\pi$
$192$		0			0
$193$	4.15106	+	15.4920i	0.298800	+	1.11514i	0.938152	+	0.346222i	$0.112536\pi$
$193$	4.15106	+	15.4920i	0.298800	+	1.11514i	−0.639353	+	0.768914i	$0.720798\pi$
$194$	16.9343	−	20.1815i	1.21581	−	1.44894i
$195$		0			0
$196$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$197$	−6.09493	+	13.0706i	−0.434246	+	0.931243i	0.560431	+	0.828201i	$0.310635\pi$
$197$	−6.09493	+	13.0706i	−0.434246	+	0.931243i	−0.994677	+	0.103042i	$0.967142\pi$
$198$		0			0
$199$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$199$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$200$	−10.5311	−	9.43905i	−0.744662	−	0.667441i
$201$		0			0
$202$	−1.39572	−	15.9531i	−0.0982024	−	1.12246i
$203$		0			0
$204$		0			0
$205$	15.7845	+	10.4218i	1.10244	+	0.727889i
$206$		0			0
$207$		0			0
$208$	20.9282	+	5.60770i	1.45111	+	0.388824i
$209$		0			0
$210$		0			0
$211$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$211$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$212$	28.1244	+	7.53590i	1.93159	+	0.517568i
$213$		0			0
$214$		0			0
$215$		0			0
$216$		0			0
$217$		0			0
$218$	13.2174	+	1.15637i	0.895195	+	0.0783194i
$219$		0			0
$220$		0			0
$221$	33.7288			2.26885
$222$		0			0
$223$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$223$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$224$		0			0
$225$	1.79423	−	14.8923i	0.119615	−	0.992820i
$226$	20.6685	−	17.3429i	1.37485	−	1.15363i
$227$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$227$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$228$		0			0
$229$	−22.0083	+	3.88066i	−1.45435	+	0.256441i	−0.844278	−	0.535906i	$-0.819970\pi$
$229$	−22.0083	+	3.88066i	−1.45435	+	0.256441i	−0.610071	+	0.792347i	$0.708859\pi$
$230$		0			0
$231$		0			0
$232$	27.9532	+	7.49005i	1.83522	+	0.491746i
$233$	16.2296	−	4.34871i	1.06324	−	0.284893i	0.315525	−	0.948917i	$-0.397819\pi$
$233$	16.2296	−	4.34871i	1.06324	−	0.284893i	0.747711	+	0.664024i	$0.231153\pi$
$234$	7.85988	+	21.5949i	0.513817	+	1.41170i
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$239$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$240$		0			0
$241$	−7.49989	+	20.6058i	−0.483110	+	1.32733i	0.423703	+	0.905801i	$0.360730\pi$
$241$	−7.49989	+	20.6058i	−0.483110	+	1.32733i	−0.906813	+	0.421533i	$0.861492\pi$
$242$	−1.35583	−	15.4972i	−0.0871557	−	0.996195i
$243$		0			0
$244$	−5.33930	+	30.2807i	−0.341814	+	1.93852i
$245$	−12.5718	+	9.32473i	−0.803181	+	0.595735i
$246$		0			0
$247$		0			0
$248$		0			0
$249$		0			0
$250$	−6.60584	−	14.3653i	−0.417790	−	0.908544i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		0			0
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−15.0351	−	5.47232i	−0.939693	−	0.342020i
$257$	−29.0495	−	13.5460i	−1.81206	−	0.844976i	−0.916528	−	0.399971i	$-0.869020\pi$
$257$	−29.0495	−	13.5460i	−1.81206	−	0.844976i	−0.895528	−	0.445005i	$-0.853202\pi$
$258$		0			0
$259$		0			0
$260$	18.9749	+	15.0582i	1.17677	+	0.933868i
$261$	10.4982	+	28.8437i	0.649824	+	1.78538i
$262$		0			0
$263$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$263$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$264$		0			0
$265$	25.4994	+	20.2359i	1.56642	+	1.24308i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−26.2583	+	15.1603i	−1.60100	+	0.924337i	−0.609711	+	0.792624i	$0.708714\pi$
$269$	−26.2583	+	15.1603i	−1.60100	+	0.924337i	−0.991288	+	0.131713i	$0.957952\pi$
$270$		0			0
$271$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$271$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$272$	−24.8129	−	2.17085i	−1.50450	−	0.131627i
$273$		0			0
$274$	5.72675	−	32.4780i	0.345966	−	1.96207i
$275$		0			0
$276$		0			0
$277$	−11.8954	−	25.5097i	−0.714724	−	1.53273i	−0.841178	−	0.540758i	$-0.818138\pi$
$277$	−11.8954	−	25.5097i	−0.714724	−	1.53273i	0.126455	−	0.991972i	$-0.459640\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	1.52421	+	0.268758i	0.0909265	+	0.0160328i	0.218926	−	0.975741i	$-0.429745\pi$
$281$	1.52421	+	0.268758i	0.0909265	+	0.0160328i	−0.128000	+	0.991774i	$0.540856\pi$
$282$		0			0
$283$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$283$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		0			0
$288$	−4.39230	−	16.3923i	−0.258819	−	0.965926i
$289$	−21.4437	+	3.78110i	−1.26139	+	0.222418i
$290$	25.3443	+	20.1128i	1.48827	+	1.18106i
$291$		0			0
$292$	1.73207	−	19.7977i	0.101362	−	1.15857i
$293$	−0.431698	−	0.925778i	−0.0252200	−	0.0540846i	0.893294	−	0.449472i	$-0.148388\pi$
$293$	−0.431698	−	0.925778i	−0.0252200	−	0.0540846i	−0.918514	+	0.395388i	$0.870610\pi$
$294$		0			0
$295$		0			0
$296$	−12.2792	−	12.0508i	−0.713711	−	0.700440i
$297$		0			0
$298$	−11.9511	+	25.6293i	−0.692310	+	1.48466i
$299$		0			0
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−18.9414	+	28.6881i	−1.08458	+	1.64267i
$306$	−13.2093	−	22.8791i	−0.755124	−	1.30791i
$307$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$307$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$311$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$312$		0			0
$313$	−10.7224	+	0.938084i	−0.606063	+	0.0530237i	−0.386057	−	0.922475i	$-0.626163\pi$
$313$	−10.7224	+	0.938084i	−0.606063	+	0.0530237i	−0.220006	+	0.975499i	$0.570608\pi$
$314$	29.8324	+	10.8581i	1.68354	+	0.612758i
$315$		0			0
$316$		0			0
$317$	5.91792	+	8.45166i	0.332383	+	0.474693i	0.950205	−	0.311626i	$-0.100873\pi$
$317$	5.91792	+	8.45166i	0.332383	+	0.474693i	−0.617822	+	0.786318i	$0.711985\pi$
$318$		0			0
$319$		0			0
$320$	−12.9899	−	12.2989i	−0.726155	−	0.687531i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	11.5702	−	13.7888i	0.642788	−	0.766044i
$325$	12.7690	+	23.8840i	0.708297	+	1.32485i
$326$		0			0
$327$		0			0
$328$	19.5985	+	13.7230i	1.08215	+	0.757727i
$329$		0			0
$330$		0			0
$331$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$331$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$332$		0			0
$333$	3.00000	−	18.0000i	0.164399	−	0.986394i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−1.80591	+	20.6416i	−0.0983742	+	1.12442i	0.773201	+	0.634161i	$0.218654\pi$
$337$	−1.80591	+	20.6416i	−0.0983742	+	1.12442i	−0.871576	+	0.490261i	$0.836901\pi$
$338$	−18.9289	−	13.2541i	−1.02960	−	0.720930i
$339$		0			0
$340$	−24.4880	−	13.2599i	−1.32805	−	0.719121i
$341$		0			0
$342$		0			0
$343$		0			0
$344$		0			0
$345$		0			0
$346$	−13.2841	−	15.8313i	−0.714156	−	0.851098i
$347$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$347$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$348$		0			0
$349$	33.4889	+	5.90499i	1.79262	+	0.316087i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	33.4889	+	5.90499i	1.79262	+	0.316087i	0.824364	+	0.566059i	$0.191533\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−12.9264	+	1.13092i	−0.688005	+	0.0601927i	−0.425797	−	0.904819i	$-0.640006\pi$
$353$	−12.9264	+	1.13092i	−0.688005	+	0.0601927i	−0.262208	+	0.965011i	$0.584451\pi$
$354$		0			0
$355$		0			0
$356$	−30.2995	+	17.4934i	−1.60587	+	0.927149i
$357$		0			0
$358$		0			0
$359$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$359$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$360$	2.78318	−	18.7684i	0.146686	−	0.989183i
$361$	14.5548	+	12.2130i	0.766044	+	0.642788i
$362$	−13.7614	+	3.68736i	−0.723285	+	0.193804i
$363$		0			0
$364$		0			0
$365$	10.5798	−	19.5385i	0.553774	−	1.02269i
$366$		0			0
$367$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$367$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$368$		0			0
$369$			25.3767i			1.32106i
$370$	−7.23767	−	17.8218i	−0.376268	−	0.926511i
$371$		0			0
$372$		0			0
$373$	3.87990	+	8.32047i	0.200894	+	0.430818i	0.980784	−	0.195099i	$-0.0625028\pi$
$373$	3.87990	+	8.32047i	0.200894	+	0.430818i	−0.779890	+	0.625917i	$0.784725\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−45.3979	−	31.7880i	−2.33811	−	1.63716i
$378$		0			0
$379$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$379$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$		0			0		0.0871557	−	0.996195i	$-0.472222\pi$
$383$		0			0		−0.0871557	+	0.996195i	$0.527778\pi$
$384$		0			0
$385$		0			0
$386$	−3.93866	+	22.3372i	−0.200472	+	1.13693i
$387$		0			0
$388$	33.7668	−	15.7457i	1.71425	−	0.799367i
$389$	28.5878	+	10.4051i	1.44946	+	0.527561i	0.942441	−	0.334374i	$-0.108525\pi$
$389$	28.5878	+	10.4051i	1.44946	+	0.527561i	0.507020	+	0.861934i	$0.330747\pi$
$390$		0			0
$391$		0			0
$392$	−16.2184	+	11.3562i	−0.819152	+	0.573576i
$393$		0			0
$394$	−15.6239	+	13.1100i	−0.787121	+	0.660473i
$395$		0			0
$396$		0			0
$397$	−26.0174	−	6.97134i	−1.30578	−	0.349881i	−0.462144	−	0.886805i	$-0.652920\pi$
$397$	−26.0174	−	6.97134i	−1.30578	−	0.349881i	−0.843631	+	0.536923i	$0.819586\pi$
$398$		0			0
$399$		0			0
$400$	−7.85641	−	18.3923i	−0.392820	−	0.919615i
$401$		−	18.2679i		−	0.912258i	−0.889914	−	0.456129i	$-0.849236\pi$
$401$		−	18.2679i		−	0.912258i	0.889914	−	0.456129i	$-0.150764\pi$
$402$		0			0
$403$		0			0
$404$	7.74584	−	21.2815i	0.385370	−	1.05880i
$405$	18.0000	−	9.00000i	0.894427	−	0.447214i
$406$		0			0
$407$		0			0
$408$		0			0
$409$	−33.3925	+	12.1539i	−1.65115	+	0.600971i	−0.988936	−	0.148340i	$-0.952607\pi$
$409$	−33.3925	+	12.1539i	−1.65115	+	0.600971i	−0.662218	+	0.749311i	$0.730385\pi$
$410$	14.0024	+	22.7917i	0.691529	+	1.12560i
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$		0			0
$416$	23.4724	+	19.6957i	1.15083	+	0.965659i
$417$		0			0
$418$		0			0
$419$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$419$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$420$		0			0
$421$	19.3688	−	11.1826i	0.943978	−	0.545006i	0.0527728	−	0.998607i	$-0.483194\pi$
$421$	19.3688	−	11.1826i	0.943978	−	0.545006i	0.891205	+	0.453601i	$0.149861\pi$
$422$		0			0
$423$		0			0
$424$	31.5433	+	26.4680i	1.53188	+	1.28540i
$425$	−19.2240	−	24.4908i	−0.932502	−	1.18798i
$426$		0			0
$427$		0			0
$428$		0			0
$429$		0			0
$430$		0			0
$431$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$431$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$432$		0			0
$433$	−37.8269	+	10.1357i	−1.81784	+	0.487090i	−0.996519	−	0.0833719i	$-0.973431\pi$
$433$	−37.8269	+	10.1357i	−1.81784	+	0.487090i	−0.821324	+	0.570461i	$0.806764\pi$
$434$		0			0
$435$		0			0
$436$	16.2498	+	9.38181i	0.778223	+	0.449307i
$437$		0			0
$438$		0			0
$439$		0			0		−0.173648	−	0.984808i	$-0.555556\pi$
$439$		0			0		0.173648	+	0.984808i	$0.444444\pi$
$440$		0			0
$441$	−19.7335	−	7.18242i	−0.939693	−	0.342020i
$442$	43.2307	+	20.1588i	2.05627	+	0.958856i
$443$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$443$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$444$		0			0
$445$	−38.8599	+	4.47223i	−1.84214	+	0.212004i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.36759	−	7.75600i	−0.0645406	−	0.366028i	−0.999923	−	0.0123907i	$-0.996056\pi$
$449$	−1.36759	−	7.75600i	−0.0645406	−	0.366028i	0.935383	−	0.353637i	$-0.115055\pi$
$450$	11.2004	−	18.0153i	0.527992	−	0.849249i
$451$		0			0
$452$	36.8564	−	9.87564i	1.73358	−	0.464511i
$453$		0			0
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−38.8446	−	3.39846i	−1.81707	−	0.158973i	−0.872788	−	0.488099i	$-0.837691\pi$
$457$	−38.8446	−	3.39846i	−1.81707	−	0.158973i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	−30.5277	−	8.17986i	−1.42646	−	0.382220i
$459$		0			0
$460$		0			0
$461$	−14.7256	+	17.5493i	−0.685840	+	0.817352i	−0.990846	−	0.134999i	$-0.956897\pi$
$461$	−14.7256	+	17.5493i	−0.685840	+	0.817352i	0.305006	+	0.952350i	$0.401341\pi$
$462$		0			0
$463$		0			0		0.906308	−	0.422618i	$-0.138889\pi$
$463$		0			0		−0.906308	+	0.422618i	$0.861111\pi$
$464$	31.3514	+	26.3070i	1.45545	+	1.22127i
$465$		0			0
$466$	23.4008	+	4.12619i	1.08402	+	0.191142i
$467$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$467$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$468$	−2.83254	+	32.3760i	−0.130934	+	1.49658i
$469$		0			0
$470$		0			0
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$		0			0
$476$		0			0
$477$	−3.80650	+	43.5085i	−0.174288	+	1.99212i
$478$		0			0
$479$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$479$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$480$		0			0
$481$	14.2040	+	29.7290i	0.647648	+	1.35553i
$482$	−21.9282	+	21.9282i	−0.998802	+	0.998802i
$483$		0			0
$484$	7.52444	−	20.6732i	0.342020	−	0.939693i
$485$	41.6396	−	1.13768i	1.89076	−	0.0516594i
$486$		0			0
$487$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$487$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$488$	−24.9414	+	35.6200i	−1.12904	+	1.61244i
$489$		0			0
$490$	−21.6865	+	4.43782i	−0.979698	+	0.200480i
$491$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$491$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$492$		0			0
$493$	57.7420	+	26.9255i	2.60057	+	1.21267i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$499$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$500$	0.118971	−	22.3604i	0.00532055	−	0.999986i
$501$		0			0
$502$		0			0
$503$		0			0		−0.573576	−	0.819152i	$-0.694444\pi$
$503$		0			0		0.573576	+	0.819152i	$0.305556\pi$
$504$		0			0
$505$	17.4086	−	18.3866i	0.774673	−	0.818193i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	28.7755	−	34.2933i	1.27545	−	1.52002i	0.541771	−	0.840526i	$-0.317754\pi$
$509$	28.7755	−	34.2933i	1.27545	−	1.52002i	0.733679	−	0.679496i	$-0.237801\pi$
$510$		0			0
$511$		0			0
$512$	−16.0000	−	16.0000i	−0.707107	−	0.707107i
$513$		0			0
$514$	−29.1370	−	34.7241i	−1.28518	−	1.53162i
$515$		0			0
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$	15.3205	+	30.6410i	0.671849	+	1.34370i
$521$	22.2153	+	8.08570i	0.973269	+	0.354241i	0.779220	−	0.626751i	$-0.215616\pi$
$521$	22.2153	+	8.08570i	0.973269	+	0.354241i	0.194050	+	0.980992i	$0.437838\pi$
$522$	−3.78334	+	43.2438i	−0.165592	+	1.89273i
$523$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$523$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$		0			0
$528$		0			0
$529$	19.9186	+	11.5000i	0.866025	+	0.500000i
$530$	20.5885	+	41.1769i	0.894305	+	1.78861i
$531$		0			0
$532$		0			0
$533$	−26.2805	−	37.5324i	−1.13833	−	1.62571i
$534$		0			0
$535$		0			0
$536$		0			0
$537$		0			0
$538$	−42.7165	+	3.73721i	−1.84164	+	0.161123i
$539$		0			0
$540$		0			0
$541$	−32.8128	+	18.9445i	−1.41073	+	0.814487i	−0.995457	−	0.0952089i	$-0.969648\pi$
$541$	−32.8128	+	18.9445i	−1.41073	+	0.814487i	−0.415275	+	0.909696i	$0.636315\pi$
$542$		0			0
$543$		0			0
$544$	−30.5055	−	17.6124i	−1.30791	−	0.755124i
$545$	12.4975	+	16.8494i	0.535336	+	0.721750i
$546$		0			0
$547$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$547$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$548$	26.7513	−	38.2048i	1.14276	−	1.63203i
$549$	−46.1217			−1.96843
$550$		0			0
$551$		0			0
$552$		0			0
$553$		0			0
$554$		−	39.8057i		−	1.69118i
$555$		0			0
$556$		0			0
$557$	13.6559	+	6.36786i	0.578620	+	0.269815i	0.689817	−	0.723983i	$-0.257691\pi$
$557$	13.6559	+	6.36786i	0.578620	+	0.269815i	−0.111198	+	0.993798i	$0.535469\pi$
$558$		0			0
$559$		0			0
$560$		0			0
$561$		0			0
$562$	1.79296	+	1.25545i	0.0756316	+	0.0529578i
$563$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$563$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$564$		0			0
$565$	42.1989	+	6.25769i	1.77532	+	0.263263i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−6.96465	−	12.0631i	−0.291973	−	0.505713i	0.682303	−	0.731070i	$-0.260979\pi$
$569$	−6.96465	−	12.0631i	−0.291973	−	0.505713i	−0.974276	+	0.225357i	$0.927645\pi$
$570$		0			0
$571$		0			0		0.173648	−	0.984808i	$-0.444444\pi$
$571$		0			0		−0.173648	+	0.984808i	$0.555556\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		0			0
$576$	4.16756	−	23.6354i	0.173648	−	0.984808i
$577$	−11.7591	+	8.23378i	−0.489536	+	0.342777i	−0.792140	−	0.610340i	$-0.791033\pi$
$577$	−11.7591	+	8.23378i	−0.489536	+	0.342777i	0.302604	+	0.953116i	$0.402144\pi$
$578$	−29.7445	−	7.97001i	−1.23721	−	0.331509i
$579$		0			0
$580$	20.4632	+	40.9264i	0.849688	+	1.69938i
$581$		0			0
$582$		0			0
$583$		0			0
$584$	14.0526	−	24.3397i	0.581499	−	1.00719i
$585$	−17.3017	+	31.9522i	−0.715336	+	1.32106i
$586$		−	1.44460i		−	0.0596757i
$587$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$587$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$588$		0			0
$589$		0			0
$590$		0			0
$591$		0			0
$592$	−8.53590	−	22.7846i	−0.350823	−	0.936442i
$593$	8.43575	+	8.43575i	0.346415	+	0.346415i	0.858772	−	0.512358i	$-0.171228\pi$
$593$	8.43575	+	8.43575i	0.346415	+	0.346415i	−0.512358	+	0.858772i	$0.671228\pi$
$594$		0			0
$595$		0			0
$596$	−30.6358	+	25.7065i	−1.25489	+	1.05298i
$597$		0			0
$598$		0			0
$599$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$599$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$600$		0			0
$601$	23.2435	+	19.5036i	0.948123	+	0.795570i	0.978980	−	0.203954i	$-0.0653794\pi$
$601$	23.2435	+	19.5036i	0.948123	+	0.795570i	−0.0308576	+	0.999524i	$0.509824\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	16.9110	−	17.8611i	0.687531	−	0.726155i
$606$		0			0
$607$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$607$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$608$		0			0
$609$		0			0
$610$	−41.4235	+	25.4491i	−1.67719	+	1.03040i
$611$		0			0
$612$	−3.25627	−	37.2193i	−0.131627	−	1.50450i
$613$	37.7045	−	26.4010i	1.52287	−	1.06633i	0.549948	−	0.835199i	$-0.314648\pi$
$613$	37.7045	−	26.4010i	1.52287	−	1.06633i	0.972924	−	0.231127i	$-0.0742412\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	8.90647	−	19.1000i	0.358561	−	0.768936i	−0.641437	−	0.767175i	$-0.721662\pi$
$617$	8.90647	−	19.1000i	0.358561	−	0.768936i	0.999998	−	0.00176117i	$-0.000560597\pi$
$618$		0			0
$619$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$619$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$		0			0
$624$		0			0
$625$	10.0646	−	22.8846i	0.402584	−	0.915383i
$626$	−14.3036	−	5.20610i	−0.571689	−	0.208078i
$627$		0			0
$628$	31.7470	+	31.7470i	1.26684	+	1.26684i
$629$	−22.0155	−	30.8217i	−0.877814	−	1.22894i
$630$		0			0
$631$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$631$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$632$		0			0
$633$		0			0
$634$	2.53374	+	14.3696i	0.100628	+	0.570689i
$635$		0			0
$636$		0			0
$637$	36.6244	−	9.81347i	1.45111	−	0.388824i
$638$		0			0
$639$		0			0
$640$	−9.29855	−	23.5274i	−0.367557	−	0.930001i
$641$	−9.00551	+	3.27774i	−0.355696	+	0.129463i	−0.513687	−	0.857978i	$-0.671721\pi$
$641$	−9.00551	+	3.27774i	−0.355696	+	0.129463i	0.157991	+	0.987441i	$0.449498\pi$
$642$		0			0
$643$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$643$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$647$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$648$	23.0708	−	10.7581i	0.906308	−	0.422618i
$649$		0			0
$650$	2.09138	+	38.2441i	0.0820307	+	1.50006i
$651$		0			0
$652$		0			0
$653$	4.44108	−	50.7618i	0.173793	−	1.98646i	0.0101092	−	0.999949i	$-0.496782\pi$
$653$	4.44108	−	50.7618i	0.173793	−	1.98646i	0.163684	−	0.986513i	$-0.447662\pi$
$654$		0			0
$655$		0			0
$656$	16.9178	+	29.3025i	0.660529	+	1.14407i
$657$	29.6965	−	2.59811i	1.15857	−	0.101362i
$658$		0			0
$659$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$659$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$660$		0			0
$661$	−42.2289	+	7.44610i	−1.64252	+	0.289620i	−0.917090	−	0.398681i	$-0.869468\pi$
$661$	−42.2289	+	7.44610i	−1.64252	+	0.289620i	−0.725426	+	0.688301i	$0.758357\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$		0			0
$666$	14.6032	−	21.2778i	0.565864	−	0.824498i
$667$		0			0
$668$		0			0
$669$		0			0
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−6.46796	+	9.23720i	−0.249322	+	0.356068i	−0.924232	−	0.381832i	$-0.875293\pi$
$673$	−6.46796	+	9.23720i	−0.249322	+	0.356068i	0.674910	+	0.737900i	$0.264182\pi$
$674$	−14.6516	+	25.3773i	−0.564358	+	0.977498i
$675$		0			0
$676$	−16.3397	−	28.3013i	−0.628452	−	1.08851i
$677$	0.657325	+	2.45317i	0.0252631	+	0.0942830i	0.977406	−	0.211369i	$-0.0677922\pi$
$677$	0.657325	+	2.45317i	0.0252631	+	0.0942830i	−0.952143	+	0.305652i	$0.901126\pi$
$678$		0			0
$679$		0			0
$680$	−23.4615	−	31.6313i	−0.899708	−	1.21300i
$681$		0			0
$682$		0			0
$683$		0			0		0.996195	−	0.0871557i	$-0.0277778\pi$
$683$		0			0		−0.996195	+	0.0871557i	$0.972222\pi$
$684$		0			0
$685$	44.4295	−	27.2959i	1.69756	−	1.04292i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−39.4282	−	68.2917i	−1.50209	−	2.60170i
$690$		0			0
$691$		0			0		0.939693	−	0.342020i	$-0.111111\pi$
$691$		0			0		−0.939693	+	0.342020i	$0.888889\pi$
$692$	−7.56440	−	28.2307i	−0.287555	−	1.07317i
$693$		0			0
$694$		0			0
$695$		0			0
$696$		0			0
$697$	37.2453	+	37.2453i	1.41077	+	1.41077i
$698$	39.3938	+	27.5839i	1.49108	+	1.04406i
$699$		0			0
$700$		0			0
$701$	−17.1124	−	47.0159i	−0.646327	−	1.77577i	−0.630872	−	0.775887i	$-0.717303\pi$
$701$	−17.1124	−	47.0159i	−0.646327	−	1.77577i	−0.0154547	−	0.999881i	$-0.504920\pi$
$702$		0			0
$703$		0			0
$704$		0			0
$705$		0			0
$706$	−17.2439	−	6.27627i	−0.648983	−	0.236210i
$707$		0			0
$708$		0			0
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$		0			0
$711$		0			0
$712$	−49.2905	+	4.31236i	−1.84724	+	0.161613i
$713$		0			0
$714$		0			0
$715$		0			0
$716$		0			0
$717$		0			0
$718$		0			0
$719$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$719$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$720$	14.7846	−	22.3923i	0.550990	−	0.834512i
$721$		0			0
$722$	11.3558	+	24.3525i	0.422618	+	0.906308i
$723$		0			0
$724$	−19.8420	−	3.49869i	−0.737423	−	0.130028i
$725$	2.79340	+	51.0817i	0.103744	+	1.89712i
$726$		0			0
$727$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$727$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$728$		0			0
$729$	23.3827	+	13.5000i	0.866025	+	0.500000i
$730$	25.2379	−	18.7195i	0.934098	−	0.692839i
$731$		0			0
$732$		0			0
$733$	10.2326	−	14.6136i	0.377948	−	0.539766i	−0.584442	−	0.811435i	$-0.698687\pi$
$733$	10.2326	−	14.6136i	0.377948	−	0.539766i	0.962391	+	0.271669i	$0.0875756\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		0			0
$738$	−15.1669	+	32.5256i	−0.558303	+	1.19728i
$739$		0			0			−	1.00000i	$-0.5\pi$
$739$		0			0				1.00000i	$0.5\pi$
$740$	1.37498	−	27.1682i	0.0505454	−	0.998722i
$741$		0			0
$742$		0			0
$743$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$743$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$744$		0			0
$745$	−42.8569	+	12.7477i	−1.57016	+	0.467041i
$746$			12.9834i			0.475355i
$747$		0			0
$748$		0			0
$749$		0			0
$750$		0			0
$751$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$751$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$752$		0			0
$753$		0			0
$754$	−39.1883	−	67.8761i	−1.42715	−	2.47190i
$755$		0			0
$756$		0			0
$757$	−4.37812	−	50.0422i	−0.159126	−	1.81881i	−0.486236	−	0.873827i	$-0.661631\pi$
$757$	−4.37812	−	50.0422i	−0.159126	−	1.81881i	0.327111	−	0.944986i	$-0.393925\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.57633	−	48.6388i	0.310892	−	1.76315i	−0.283493	−	0.958974i	$-0.591493\pi$
$761$	8.57633	−	48.6388i	0.310892	−	1.76315i	0.594385	−	0.804181i	$-0.297396\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	13.2093	−	39.6278i	0.477583	−	1.43275i
$766$		0			0
$767$		0			0
$768$		0			0
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.0760054	−	0.997107i	$-0.475783\pi$
$769$	25.0000	−	43.3013i	0.901523	−	1.56148i	0.825518	−	0.564376i	$-0.190883\pi$
$770$		0			0
$771$		0			0
$772$	−18.3986	+	26.2759i	−0.662179	+	0.945690i
$773$	−40.7138	−	3.56199i	−1.46437	−	0.128116i	−0.673087	−	0.739563i	$-0.735032\pi$
$773$	−40.7138	−	3.56199i	−1.46437	−	0.128116i	−0.791285	+	0.611448i	$0.790588\pi$
$774$		0			0
$775$		0			0
$776$	52.6901			1.89146
$777$		0			0
$778$	30.4225	+	30.4225i	1.09070	+	1.09070i
$779$		0			0
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	−27.5746	+	4.86215i	−0.984808	+	0.173648i
$785$	18.4501	+	46.6827i	0.658511	+	1.66618i
$786$		0			0
$787$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$787$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$788$	−27.8608	+	7.46529i	−0.992502	+	0.265940i
$789$		0			0
$790$		0			0
$791$		0			0
$792$		0			0
$793$	68.2145	−	47.7643i	2.42237	−	1.69616i
$794$	−29.1802	−	24.4851i	−1.03557	−	0.868945i
$795$		0			0
$796$		0			0
$797$	4.56050	+	52.1268i	0.161541	+	1.84643i	0.455046	+	0.890468i	$0.349623\pi$
$797$	4.56050	+	52.1268i	0.161541	+	1.84643i	−0.293505	+	0.955958i	$0.594822\pi$
$798$		0			0
$799$		0			0
$800$	0.922918	−	28.2692i	0.0326301	−	0.999467i
$801$	−33.7336	−	40.2022i	−1.19192	−	1.42047i
$802$	10.9183	−	23.4143i	0.385537	−	0.826786i
$803$		0			0
$804$		0			0
$805$		0			0
$806$		0			0
$807$		0			0
$808$	22.6473	−	22.6473i	0.796730	−	0.796730i
$809$	−7.55325	−	42.8366i	−0.265558	−	1.50605i	−0.767441	−	0.641119i	$-0.778470\pi$
$809$	−7.55325	−	42.8366i	−0.265558	−	1.50605i	0.501883	−	0.864935i	$-0.332641\pi$
$810$	28.4499	−	0.777310i	0.999627	−	0.0273119i
$811$		0			0		−0.939693	−	0.342020i	$-0.888889\pi$
$811$		0			0		0.939693	+	0.342020i	$0.111111\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$		0			0
$816$		0			0
$817$		0			0
$818$	−50.0637	−	4.38000i	−1.75044	−	0.153143i
$819$		0			0
$820$	4.32507	+	37.5813i	0.151038	+	1.31239i
$821$	9.95026	+	56.4307i	0.347267	+	1.96945i	0.186544	+	0.982447i	$0.440271\pi$
$821$	9.95026	+	56.4307i	0.347267	+	1.96945i	0.160722	+	0.987000i	$0.448618\pi$
$822$		0			0
$823$		0			0		−0.0871557	−	0.996195i	$-0.527778\pi$
$823$		0			0		0.0871557	+	0.996195i	$0.472222\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		0			0		−0.996195	−	0.0871557i	$-0.972222\pi$
$827$		0			0		0.996195	+	0.0871557i	$0.0277778\pi$
$828$		0			0
$829$	−3.47296	+	19.6962i	−0.120621	+	0.684076i	0.863192	+	0.504876i	$0.168462\pi$
$829$	−3.47296	+	19.6962i	−0.120621	+	0.684076i	−0.983813	+	0.179200i	$0.942649\pi$
$830$		0			0
$831$		0			0
$832$	18.3133	+	39.2730i	0.634899	+	1.36155i
$833$	−39.5045	+	18.4213i	−1.36875	+	0.638259i
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$		0			0
$839$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$839$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$840$		0			0
$841$	−37.8428	−	65.5456i	−1.30492	−	2.26019i
$842$	31.5088	−	2.75666i	1.08586	−	0.0950008i
$843$		0			0
$844$		0			0
$845$	−4.17729	−	36.2972i	−0.143703	−	1.24866i
$846$		0			0
$847$		0			0
$848$	24.6103	+	52.7770i	0.845121	+	1.81237i
$849$		0			0
$850$	−10.0022	−	42.8798i	−0.343073	−	1.47077i
$851$		0			0
$852$		0			0
$853$	1.31221	−	2.81405i	0.0449293	−	0.0963511i	−0.882562	−	0.470196i	$-0.844183\pi$
$853$	1.31221	−	2.81405i	0.0449293	−	0.0963511i	0.927491	+	0.373845i	$0.121961\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−39.5604	−	39.5604i	−1.35136	−	1.35136i	−0.884147	−	0.467210i	$-0.845259\pi$
$857$	−39.5604	−	39.5604i	−1.35136	−	1.35136i	−0.467210	−	0.884147i	$-0.654741\pi$
$858$		0			0
$859$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$859$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$		0			0		−0.906308	−	0.422618i	$-0.861111\pi$
$863$		0			0		0.906308	+	0.422618i	$0.138889\pi$
$864$		0			0
$865$	4.79318	−	32.3229i	0.162973	−	1.09901i
$866$	−54.5410	−	9.61705i	−1.85338	−	0.326801i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$		0			0
$872$	15.2203	+	21.7368i	0.515424	+	0.736102i
$873$	32.0550	+	45.7793i	1.08490	+	1.54940i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	4.40235	+	16.4298i	0.148657	+	0.554795i	0.999565	+	0.0294808i	$0.00938538\pi$
$877$	4.40235	+	16.4298i	0.148657	+	0.554795i	−0.850909	+	0.525314i	$0.823948\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.83766	−	55.7921i	−0.331439	−	1.87968i	−0.459902	−	0.887970i	$-0.652115\pi$
$881$	−9.83766	−	55.7921i	−0.331439	−	1.87968i	0.128463	−	0.991714i	$-0.458996\pi$
$882$	−21.0000	−	21.0000i	−0.707107	−	0.707107i
$883$		0			0		−0.819152	−	0.573576i	$-0.805556\pi$
$883$		0			0		0.819152	+	0.573576i	$0.194444\pi$
$884$	43.3609	+	51.6756i	1.45839	+	1.73804i
$885$		0			0
$886$		0			0
$887$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$887$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$888$		0			0
$889$		0			0
$890$	−52.4802	−	17.4934i	−1.75914	−	0.586380i
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$	2.88269	−	10.7583i	0.0961965	−	0.359010i
$899$		0			0
$900$	25.1230	−	16.3963i	0.837432	−	0.546542i
$901$	58.2706	+	69.4442i	1.94127	+	2.31352i
$902$		0			0
$903$		0			0
$904$	53.1417	+	9.37032i	1.76747	+	0.311652i
$905$	−18.7985	−	12.4118i	−0.624882	−	0.412581i
$906$		0			0
$907$		0			0		−0.422618	−	0.906308i	$-0.638889\pi$
$907$		0			0		0.422618	+	0.906308i	$0.361111\pi$
$908$		0			0
$909$	33.4549	+	5.89900i	1.10963	+	0.195657i
$910$		0			0
$911$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$911$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$912$		0			0
$913$		0			0
$914$	−47.7565	−	27.5722i	−1.57964	−	0.912008i
$915$		0			0
$916$	−34.2388	−	28.7298i	−1.13128	−	0.949259i
$917$		0			0
$918$		0			0
$919$		0			0		1.00000			$0$
$919$		0			0		−1.00000			$\pi$
$920$		0			0
$921$		0			0
$922$	−29.3627	+	13.6921i	−0.967009	+	0.450924i
$923$		0			0
$924$		0			0
$925$	13.4908	−	27.2580i	0.443575	−	0.896237i
$926$		0			0
$927$		0			0
$928$	24.4606	+	52.4559i	0.802958	+	1.72195i
$929$	18.9912	+	22.6328i	0.623081	+	0.742559i	0.981597	−	0.190965i	$-0.0611616\pi$
$929$	18.9912	+	22.6328i	0.623081	+	0.742559i	−0.358516	+	0.933524i	$0.616717\pi$
$930$		0			0
$931$		0			0
$932$	27.5270	+	19.2746i	0.901676	+	0.631360i
$933$		0			0
$934$		0			0
$935$		0			0
$936$	−22.9808	+	39.8038i	−0.751150	+	1.30103i
$937$	−18.8088	+	40.3356i	−0.614457	+	1.31771i	0.315111	+	0.949055i	$0.397958\pi$
$937$	−18.8088	+	40.3356i	−0.614457	+	1.31771i	−0.929567	+	0.368652i	$0.879819\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	5.16912	−	29.3155i	0.168508	−	0.955658i	−0.776865	−	0.629668i	$-0.783191\pi$
$941$	5.16912	−	29.3155i	0.168508	−	0.955658i	0.945373	−	0.325991i	$-0.105698\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$947$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$948$		0			0
$949$	−41.2309	+	34.5968i	−1.33841	+	1.12306i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−5.30091	−	60.5897i	−0.171713	−	1.96269i	−0.257213	−	0.966355i	$-0.582804\pi$
$953$	−5.30091	−	60.5897i	−0.171713	−	1.96269i	0.0854999	−	0.996338i	$-0.472751\pi$
$954$	−30.8827	+	53.4904i	−0.999864	+	1.73182i
$955$		0			0
$956$		0			0
$957$		0			0
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−31.0000			−1.00000
$962$	0.437257	+	46.5935i	0.0140977	+	1.50223i
$963$		0			0
$964$	−41.2115	+	14.9998i	−1.32733	+	0.483110i
$965$	−30.5570	+	18.7731i	−0.983665	+	0.604328i
$966$		0			0
$967$		0			0		0.573576	−	0.819152i	$-0.305556\pi$
$967$		0			0		−0.573576	+	0.819152i	$0.694444\pi$
$968$	22.0000	−	22.0000i	0.707107	−	0.707107i
$969$		0			0
$970$	54.0500	+	23.4287i	1.73544	+	0.752249i
$971$		0			0		−0.766044	−	0.642788i	$-0.777778\pi$
$971$		0			0		0.766044	+	0.642788i	$0.222222\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$		0			0
$976$	−53.2567	+	30.7478i	−1.70471	+	0.984213i
$977$	50.7530	−	35.5376i	1.62373	−	1.13695i	0.735534	−	0.677488i	$-0.236931\pi$
$977$	50.7530	−	35.5376i	1.62373	−	1.13695i	0.888198	−	0.459462i	$-0.151958\pi$
$978$		0			0
$979$		0			0
$980$	−30.4483	−	7.27343i	−0.972634	−	0.232341i
$981$	−9.62630	+	26.4481i	−0.307344	+	0.844421i
$982$		0			0
$983$		0			0		0.819152	−	0.573576i	$-0.194444\pi$
$983$		0			0		−0.819152	+	0.573576i	$0.805556\pi$
$984$		0			0
$985$	−31.8994	−	4.73037i	−1.01640	−	0.150722i
$986$	57.9160	+	69.0216i	1.84442	+	2.19810i
$987$		0			0
$988$		0			0
$989$		0			0
$990$		0			0
$991$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$991$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$		0			0
$996$		0			0
$997$	47.4234	+	22.1139i	1.50191	+	0.700354i	0.987563	−	0.157226i	$-0.0502552\pi$
$997$	47.4234	+	22.1139i	1.50191	+	0.700354i	0.514351	+	0.857580i	$0.328033\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	740.2.ce.b.363.1	yes	12
4.3	odd	2	CM	740.2.ce.b.363.1	yes	12
5.2	odd	4		740.2.ce.a.67.1	✓	12
20.7	even	4		740.2.ce.a.67.1	✓	12
37.21	even	18		740.2.ce.a.243.1	yes	12
148.95	odd	18		740.2.ce.a.243.1	yes	12
185.132	odd	36	inner	740.2.ce.b.687.1	yes	12
740.687	even	36	inner	740.2.ce.b.687.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
740.2.ce.a.67.1	✓	12	5.2	odd	4
740.2.ce.a.67.1	✓	12	20.7	even	4
740.2.ce.a.243.1	yes	12	37.21	even	18
740.2.ce.a.243.1	yes	12	148.95	odd	18
740.2.ce.b.363.1	yes	12	1.1	even	1	trivial
740.2.ce.b.363.1	yes	12	4.3	odd	2	CM
740.2.ce.b.687.1	yes	12	185.132	odd	36	inner
740.2.ce.b.687.1	yes	12	740.687	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 740 = 2^{2} \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	740.ce (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.28171 + 0.597672i) q^{2} +(1.28558 + 1.53209i) q^{4} +(0.637511 + 2.14326i) q^{5} +(0.732051 + 2.73205i) q^{8} +(-1.92836 + 2.29813i) q^{9} +(-0.463863 + 3.12807i) q^{10} +(0.472089 - 5.39601i) q^{13} +(-0.694593 + 3.93923i) q^{16} +(0.542711 + 6.20322i) q^{17} +(-3.84514 + 1.79302i) q^{18} +(-2.46410 + 3.73205i) q^{20} +(-4.18716 + 2.73271i) q^{25} +(3.83013 - 6.63397i) q^{26} +(5.11580 - 8.86082i) q^{29} +(-3.24464 + 4.63382i) q^{32} +(-3.01189 + 8.27511i) q^{34} -6.00000 q^{36} +(-5.23905 + 3.09068i) q^{37} +(-5.38881 + 3.31069i) q^{40} +(6.47989 - 5.43727i) q^{41} +(-6.15486 - 2.66790i) q^{45} +(2.39414 + 6.57785i) q^{49} +(-7.00000 + 1.00000i) q^{50} +(8.87407 - 6.21369i) q^{52} +(11.9254 - 8.35026i) q^{53} +(11.8529 - 8.29946i) q^{58} +(9.88215 + 11.7771i) q^{61} +(-6.92820 + 4.00000i) q^{64} +(11.8660 - 2.42820i) q^{65} +(-8.80619 + 8.80619i) q^{68} +(-7.69028 - 3.58603i) q^{72} +(-7.02628 - 7.02628i) q^{73} +(-8.56218 + 0.830127i) q^{74} +(-8.88562 + 1.02261i) q^{80} +(-1.56283 - 8.86327i) q^{81} +(11.5551 - 3.09617i) q^{82} +(-12.9492 + 5.11780i) q^{85} +(-3.03770 + 17.2276i) q^{89} +(-6.29423 - 7.09808i) q^{90} +(4.82148 - 17.9940i) q^{97} +(-0.862798 + 9.86182i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{8} - 6 q^{17} + 12 q^{20} - 6 q^{26} - 30 q^{34} - 72 q^{36} + 24 q^{41} - 84 q^{50} - 18 q^{58} + 72 q^{61} + 132 q^{65} + 30 q^{73} - 30 q^{74} - 42 q^{85} - 60 q^{89} + 18 q^{90}+O(q^{100}) \) 12 * q - 12 * q^8 - 6 * q^17 + 12 * q^20 - 6 * q^26 - 30 * q^34 - 72 * q^36 + 24 * q^41 - 84 * q^50 - 18 * q^58 + 72 * q^61 + 132 * q^65 + 30 * q^73 - 30 * q^74 - 42 * q^85 - 60 * q^89 + 18 * q^90

Introduction

L-functions

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