LMFDB - Embedded newform 338.2.e.d.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,2,Mod(23,338)] 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("338.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(338, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.69894358832$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.2.e.d.147.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.73205 + 1.00000i) q^{11} +3.00000 q^{12} +1.00000 q^{14} +(-2.59808 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -6.00000i q^{18} +(5.19615 + 3.00000i) q^{19} +(0.866025 + 0.500000i) q^{20} -3.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-2.59808 + 1.50000i) q^{24} +4.00000 q^{25} -9.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(1.50000 - 2.59808i) q^{30} -4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} -3.00000i q^{34} +(0.500000 - 0.866025i) q^{35} +(3.00000 + 5.19615i) q^{36} +(2.59808 - 1.50000i) q^{37} -6.00000 q^{38} -1.00000 q^{40} +(1.50000 + 2.59808i) q^{42} +(-2.50000 + 4.33013i) q^{43} +2.00000i q^{44} +(-5.19615 - 3.00000i) q^{45} +(3.46410 + 2.00000i) q^{46} +13.0000i q^{47} +(1.50000 - 2.59808i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(-3.46410 + 2.00000i) q^{50} -9.00000 q^{51} +12.0000 q^{53} +(7.79423 - 4.50000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(0.500000 - 0.866025i) q^{56} +18.0000i q^{57} +(1.73205 + 1.00000i) q^{58} +(8.66025 + 5.00000i) q^{59} +3.00000i q^{60} +(4.00000 - 6.92820i) q^{61} +(2.00000 + 3.46410i) q^{62} +(5.19615 - 3.00000i) q^{63} -1.00000 q^{64} +6.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +1.00000i q^{70} +(-4.33013 - 2.50000i) q^{71} +(-5.19615 - 3.00000i) q^{72} -10.0000i q^{73} +(-1.50000 + 2.59808i) q^{74} +(6.00000 + 10.3923i) q^{75} +(5.19615 - 3.00000i) q^{76} +2.00000 q^{77} -4.00000 q^{79} +(0.866025 - 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.59808 - 1.50000i) q^{84} +(-2.59808 - 1.50000i) q^{85} -5.00000i q^{86} +(3.00000 - 5.19615i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(5.19615 - 3.00000i) q^{89} +6.00000 q^{90} -4.00000 q^{92} +(10.3923 - 6.00000i) q^{93} +(-6.50000 - 11.2583i) q^{94} +(-3.00000 + 5.19615i) q^{95} +3.00000i q^{96} +(12.1244 + 7.00000i) q^{97} +(5.19615 + 3.00000i) q^{98} -12.0000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{3} + 2 q^{4} - 12 q^{9} - 2 q^{10} + 12 q^{12} + 4 q^{14} - 2 q^{16} - 6 q^{17} + 4 q^{22} - 8 q^{23} + 16 q^{25} - 36 q^{27} - 4 q^{29} + 6 q^{30} + 2 q^{35} + 12 q^{36} - 24 q^{38} - 4 q^{40}+ \cdots - 12 q^{95}+O(q^{100}) $ 4 * q + 6 * q^3 + 2 * q^4 - 12 * q^9 - 2 * q^10 + 12 * q^12 + 4 * q^14 - 2 * q^16 - 6 * q^17 + 4 * q^22 - 8 * q^23 + 16 * q^25 - 36 * q^27 - 4 * q^29 + 6 * q^30 + 2 * q^35 + 12 * q^36 - 24 * q^38 - 4 * q^40 + 6 * q^42 - 10 * q^43 + 6 * q^48 - 12 * q^49 - 36 * q^51 + 48 * q^53 - 4 * q^55 + 2 * q^56 + 16 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 + 6 * q^68 + 24 * q^69 - 6 * q^74 + 24 * q^75 + 8 * q^77 - 16 * q^79 - 18 * q^81 + 12 * q^87 - 4 * q^88 + 24 * q^90 - 16 * q^92 - 26 * q^94 - 12 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	1.50000	+	2.59808i	0.866025	+	1.50000i			1.00000i	$0.5\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			1.00000i			0.447214i	0.974679	+	0.223607i	$0.0717831\pi$
$5$			1.00000i			0.447214i	−0.974679	+	0.223607i	$0.928217\pi$
$6$	−2.59808	−	1.50000i	−1.06066	−	0.612372i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	0.327327	−	0.944911i	$-0.393852\pi$
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i	−0.654654	+	0.755929i	$0.727186\pi$
$8$			1.00000i			0.353553i
$9$	−3.00000	+	5.19615i	−1.00000	+	1.73205i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	−0.737848	−	0.674967i	$-0.764158\pi$
$11$	−1.73205	+	1.00000i	−0.522233	+	0.301511i	0.215615	+	0.976478i	$0.430824\pi$
$12$	3.00000			0.866025
$13$		0			0
$13$		0			0
$14$	1.00000			0.267261
$15$	−2.59808	+	1.50000i	−0.670820	+	0.387298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		−	6.00000i		−	1.41421i
$19$	5.19615	+	3.00000i	1.19208	+	0.688247i	0.958778	−	0.284157i	$-0.0917138\pi$
$19$	5.19615	+	3.00000i	1.19208	+	0.688247i	0.233301	+	0.972404i	$0.425047\pi$
$20$	0.866025	+	0.500000i	0.193649	+	0.111803i
$21$		−	3.00000i		−	0.654654i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	−2.59808	+	1.50000i	−0.530330	+	0.306186i
$25$	4.00000			0.800000
$26$		0			0
$27$	−9.00000			−1.73205
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	0.758115	−	0.652121i	$-0.226120\pi$
$29$	−1.00000	−	1.73205i	−0.185695	−	0.321634i	−0.943811	+	0.330487i	$0.892787\pi$
$30$	1.50000	−	2.59808i	0.273861	−	0.474342i
$31$		−	4.00000i		−	0.718421i	−0.933257	−	0.359211i	$-0.883046\pi$
$31$		−	4.00000i		−	0.718421i	0.933257	−	0.359211i	$-0.116954\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$		−	3.00000i		−	0.514496i
$35$	0.500000	−	0.866025i	0.0845154	−	0.146385i
$36$	3.00000	+	5.19615i	0.500000	+	0.866025i
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	−0.270998	−	0.962580i	$-0.587354\pi$
$37$	2.59808	−	1.50000i	0.427121	−	0.246598i	0.698119	+	0.715981i	$0.254020\pi$
$38$	−6.00000			−0.973329
$39$		0			0
$40$	−1.00000			−0.158114
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	1.50000	+	2.59808i	0.231455	+	0.400892i
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$			2.00000i			0.301511i
$45$	−5.19615	−	3.00000i	−0.774597	−	0.447214i
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$			13.0000i			1.89624i	0.317905	+	0.948122i	$0.397021\pi$
$47$			13.0000i			1.89624i	−0.317905	+	0.948122i	$0.602979\pi$
$48$	1.50000	−	2.59808i	0.216506	−	0.375000i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$	−3.46410	+	2.00000i	−0.489898	+	0.282843i
$51$	−9.00000			−1.26025
$52$		0			0
$53$	12.0000			1.64833			0.824163	−	0.566352i	$-0.191646\pi$
$53$	12.0000			1.64833			0.824163	+	0.566352i	$0.191646\pi$
$54$	7.79423	−	4.50000i	1.06066	−	0.612372i
$55$	−1.00000	−	1.73205i	−0.134840	−	0.233550i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$			18.0000i			2.38416i
$58$	1.73205	+	1.00000i	0.227429	+	0.131306i
$59$	8.66025	+	5.00000i	1.12747	+	0.650945i	0.943297	−	0.331949i	$-0.107706\pi$
$59$	8.66025	+	5.00000i	1.12747	+	0.650945i	0.184172	+	0.982894i	$0.441040\pi$
$60$			3.00000i			0.387298i
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	−0.487753	−	0.872982i	$-0.662183\pi$
$61$	4.00000	−	6.92820i	0.512148	−	0.887066i	0.999901	−	0.0140840i	$-0.00448323\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	5.19615	−	3.00000i	0.654654	−	0.377964i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	6.00000			0.738549
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	−0.390453	−	0.920623i	$-0.627682\pi$
$67$	1.73205	−	1.00000i	0.211604	−	0.122169i	0.602056	+	0.798454i	$0.294348\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	6.00000	−	10.3923i	0.722315	−	1.25109i
$70$			1.00000i			0.119523i
$71$	−4.33013	−	2.50000i	−0.513892	−	0.296695i	0.220540	−	0.975378i	$-0.429218\pi$
$71$	−4.33013	−	2.50000i	−0.513892	−	0.296695i	−0.734432	+	0.678682i	$0.762551\pi$
$72$	−5.19615	−	3.00000i	−0.612372	−	0.353553i
$73$		−	10.0000i		−	1.17041i	−0.810885	−	0.585206i	$-0.801014\pi$
$73$		−	10.0000i		−	1.17041i	0.810885	−	0.585206i	$-0.198986\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$	6.00000	+	10.3923i	0.692820	+	1.20000i
$76$	5.19615	−	3.00000i	0.596040	−	0.344124i
$77$	2.00000			0.227921
$78$		0			0
$79$	−4.00000			−0.450035			−0.225018	−	0.974355i	$-0.572244\pi$
$79$	−4.00000			−0.450035			−0.225018	+	0.974355i	$0.572244\pi$
$80$	0.866025	−	0.500000i	0.0968246	−	0.0559017i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$		0			0		1.00000			$0$
$83$		0			0		−1.00000			$\pi$
$84$	−2.59808	−	1.50000i	−0.283473	−	0.163663i
$85$	−2.59808	−	1.50000i	−0.281801	−	0.162698i
$86$		−	5.00000i		−	0.539164i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	−0.198650	−	0.980071i	$-0.563656\pi$
$89$	5.19615	−	3.00000i	0.550791	−	0.317999i	0.749441	+	0.662071i	$0.230322\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$	−4.00000			−0.417029
$93$	10.3923	−	6.00000i	1.07763	−	0.622171i
$94$	−6.50000	−	11.2583i	−0.670424	−	1.16121i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$			3.00000i			0.306186i
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.967247	−	0.253837i	$-0.0816925\pi$
$97$	12.1244	+	7.00000i	1.23104	+	0.710742i	0.263795	+	0.964579i	$0.415026\pi$
$98$	5.19615	+	3.00000i	0.524891	+	0.303046i
$99$		−	12.0000i		−	1.20605i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	0.948207	−	0.317653i	$-0.102895\pi$
$101$	2.00000	+	3.46410i	0.199007	+	0.344691i	−0.749199	+	0.662344i	$0.769562\pi$
$102$	7.79423	−	4.50000i	0.771744	−	0.445566i
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$		0			0
$105$	3.00000			0.292770
$106$	−10.3923	+	6.00000i	−1.00939	+	0.582772i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	−4.50000	+	7.79423i	−0.433013	+	0.750000i
$109$		−	19.0000i		−	1.81987i	−0.414751	−	0.909935i	$-0.636131\pi$
$109$		−	19.0000i		−	1.81987i	0.414751	−	0.909935i	$-0.363869\pi$
$110$	1.73205	+	1.00000i	0.165145	+	0.0953463i
$111$	7.79423	+	4.50000i	0.739795	+	0.427121i
$112$			1.00000i			0.0944911i
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	−0.909221	−	0.416314i	$-0.863322\pi$
$113$	−1.00000	+	1.73205i	−0.0940721	+	0.162938i	0.815149	+	0.579252i	$0.196655\pi$
$114$	−9.00000	−	15.5885i	−0.842927	−	1.45999i
$115$	3.46410	−	2.00000i	0.323029	−	0.186501i
$116$	−2.00000			−0.185695
$117$		0			0
$118$	−10.0000			−0.920575
$119$	2.59808	−	1.50000i	0.238165	−	0.137505i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−3.50000	+	6.06218i	−0.318182	+	0.551107i
$122$			8.00000i			0.724286i
$123$		0			0
$124$	−3.46410	−	2.00000i	−0.311086	−	0.179605i
$125$			9.00000i			0.804984i
$126$	−3.00000	+	5.19615i	−0.267261	+	0.462910i
$127$	8.00000	+	13.8564i	0.709885	+	1.22956i	0.964899	+	0.262620i	$0.0845865\pi$
$127$	8.00000	+	13.8564i	0.709885	+	1.22956i	−0.255014	+	0.966937i	$0.582080\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−15.0000			−1.32068
$130$		0			0
$131$	−1.00000			−0.0873704			−0.0436852	−	0.999045i	$-0.513910\pi$
$131$	−1.00000			−0.0873704			−0.0436852	+	0.999045i	$0.513910\pi$
$132$	−5.19615	+	3.00000i	−0.452267	+	0.261116i
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	−1.00000	+	1.73205i	−0.0863868	+	0.149626i
$135$		−	9.00000i		−	0.774597i
$136$	−2.59808	−	1.50000i	−0.222783	−	0.128624i
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.0146279	−	0.999893i	$-0.504656\pi$
$137$	−10.3923	−	6.00000i	−0.887875	−	0.512615i	−0.873247	+	0.487278i	$0.837990\pi$
$138$			12.0000i			1.02151i
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−3.50000	+	6.06218i	−0.296866	+	0.514187i	0.678551	+	0.734553i	$0.262608\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$	−33.7750	+	19.5000i	−2.84437	+	1.64220i
$142$	5.00000			0.419591
$143$		0			0
$144$	6.00000			0.500000
$145$	1.73205	−	1.00000i	0.143839	−	0.0830455i
$146$	5.00000	+	8.66025i	0.413803	+	0.716728i
$147$	9.00000	−	15.5885i	0.742307	−	1.28571i
$148$		−	3.00000i		−	0.246598i
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.300750	−	0.953703i	$-0.597237\pi$
$149$	−15.5885	−	9.00000i	−1.27706	−	0.737309i	−0.976306	+	0.216394i	$0.930570\pi$
$150$	−10.3923	−	6.00000i	−0.848528	−	0.489898i
$151$		−	9.00000i		−	0.732410i	−0.930534	−	0.366205i	$-0.880657\pi$
$151$		−	9.00000i		−	0.732410i	0.930534	−	0.366205i	$-0.119343\pi$
$152$	−3.00000	+	5.19615i	−0.243332	+	0.421464i
$153$	−9.00000	−	15.5885i	−0.727607	−	1.26025i
$154$	−1.73205	+	1.00000i	−0.139573	+	0.0805823i
$155$	4.00000			0.321288
$156$		0			0
$157$	−10.0000			−0.798087			−0.399043	−	0.916932i	$-0.630658\pi$
$157$	−10.0000			−0.798087			−0.399043	+	0.916932i	$0.630658\pi$
$158$	3.46410	−	2.00000i	0.275589	−	0.159111i
$159$	18.0000	+	31.1769i	1.42749	+	2.47249i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$			4.00000i			0.315244i
$162$	7.79423	+	4.50000i	0.612372	+	0.353553i
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	0.629492	−	0.777007i	$-0.283263\pi$
$163$	3.46410	+	2.00000i	0.271329	+	0.156652i	−0.358162	+	0.933659i	$0.616597\pi$
$164$		0			0
$165$	3.00000	−	5.19615i	0.233550	−	0.404520i
$166$		0			0
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$	3.00000			0.231455
$169$		0			0
$170$	3.00000			0.230089
$171$	−31.1769	+	18.0000i	−2.38416	+	1.37649i
$172$	2.50000	+	4.33013i	0.190623	+	0.330169i
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	−0.182417	−	0.983221i	$-0.558392\pi$
$173$	10.0000	−	17.3205i	0.760286	−	1.31685i	0.942703	−	0.333633i	$-0.108275\pi$
$174$			6.00000i			0.454859i
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$	1.73205	+	1.00000i	0.130558	+	0.0753778i
$177$			30.0000i			2.25494i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	0.647397	−	0.762153i	$-0.275858\pi$
$179$	−4.50000	−	7.79423i	−0.336346	−	0.582568i	−0.983742	+	0.179585i	$0.942524\pi$
$180$	−5.19615	+	3.00000i	−0.387298	+	0.223607i
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$		0			0
$183$	24.0000			1.77413
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	1.50000	+	2.59808i	0.110282	+	0.191014i
$186$	−6.00000	+	10.3923i	−0.439941	+	0.762001i
$187$		−	6.00000i		−	0.438763i
$188$	11.2583	+	6.50000i	0.821098	+	0.474061i
$189$	7.79423	+	4.50000i	0.566947	+	0.327327i
$190$		−	6.00000i		−	0.435286i
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	−1.50000	−	2.59808i	−0.108253	−	0.187500i
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.907480	−	0.420096i	$-0.861996\pi$
$193$	−13.8564	+	8.00000i	−0.997406	+	0.575853i	−0.0899262	+	0.995948i	$0.528663\pi$
$194$	−14.0000			−1.00514
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−7.79423	+	4.50000i	−0.555316	+	0.320612i	−0.751263	−	0.660003i	$-0.770555\pi$
$197$	−7.79423	+	4.50000i	−0.555316	+	0.320612i	0.195947	+	0.980614i	$0.437222\pi$
$198$	6.00000	+	10.3923i	0.426401	+	0.738549i
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	−0.987022	−	0.160585i	$-0.948662\pi$
$199$	−5.00000	+	8.66025i	−0.354441	+	0.613909i	0.632581	+	0.774494i	$0.281995\pi$
$200$			4.00000i			0.282843i
$201$	5.19615	+	3.00000i	0.366508	+	0.211604i
$202$	−3.46410	−	2.00000i	−0.243733	−	0.140720i
$203$			2.00000i			0.140372i
$204$	−4.50000	+	7.79423i	−0.315063	+	0.545705i
$205$		0			0
$206$	−6.92820	+	4.00000i	−0.482711	+	0.278693i
$207$	24.0000			1.66812
$208$		0			0
$209$	−12.0000			−0.830057
$210$	−2.59808	+	1.50000i	−0.179284	+	0.103510i
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	−0.924918	−	0.380166i	$-0.875867\pi$
$211$	−11.5000	−	19.9186i	−0.791693	−	1.37125i	0.133226	−	0.991086i	$-0.457467\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		−	15.0000i		−	1.02778i
$214$	−3.46410	−	2.00000i	−0.236801	−	0.136717i
$215$	−4.33013	−	2.50000i	−0.295312	−	0.170499i
$216$		−	9.00000i		−	0.612372i
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	9.50000	+	16.4545i	0.643421	+	1.11444i
$219$	25.9808	−	15.0000i	1.75562	−	1.01361i
$220$	−2.00000			−0.134840
$221$		0			0
$222$	−9.00000			−0.604040
$223$	18.1865	−	10.5000i	1.21786	−	0.703132i	0.253401	−	0.967361i	$-0.418451\pi$
$223$	18.1865	−	10.5000i	1.21786	−	0.703132i	0.964460	+	0.264229i	$0.0851176\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−12.0000	+	20.7846i	−0.800000	+	1.38564i
$226$		−	2.00000i		−	0.133038i
$227$	−20.7846	−	12.0000i	−1.37952	−	0.796468i	−0.387421	−	0.921903i	$-0.626634\pi$
$227$	−20.7846	−	12.0000i	−1.37952	−	0.796468i	−0.992102	+	0.125435i	$0.959967\pi$
$228$	15.5885	+	9.00000i	1.03237	+	0.596040i
$229$		−	15.0000i		−	0.991228i	−0.868543	−	0.495614i	$-0.834943\pi$
$229$		−	15.0000i		−	0.991228i	0.868543	−	0.495614i	$-0.165057\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$	3.00000	+	5.19615i	0.197386	+	0.341882i
$232$	1.73205	−	1.00000i	0.113715	−	0.0656532i
$233$	11.0000			0.720634			0.360317	−	0.932830i	$-0.382669\pi$
$233$	11.0000			0.720634			0.360317	+	0.932830i	$0.382669\pi$
$234$		0			0
$235$	−13.0000			−0.848026
$236$	8.66025	−	5.00000i	0.563735	−	0.325472i
$237$	−6.00000	−	10.3923i	−0.389742	−	0.675053i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$		−	9.00000i		−	0.582162i	−0.956698	−	0.291081i	$-0.905985\pi$
$239$		−	9.00000i		−	0.582162i	0.956698	−	0.291081i	$-0.0940149\pi$
$240$	2.59808	+	1.50000i	0.167705	+	0.0968246i
$241$	−15.5885	−	9.00000i	−1.00414	−	0.579741i	−0.0946700	−	0.995509i	$-0.530180\pi$
$241$	−15.5885	−	9.00000i	−1.00414	−	0.579741i	−0.909471	+	0.415768i	$0.863513\pi$
$242$		−	7.00000i		−	0.449977i
$243$		0			0
$244$	−4.00000	−	6.92820i	−0.256074	−	0.443533i
$245$	5.19615	−	3.00000i	0.331970	−	0.191663i
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$251$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$252$		−	6.00000i		−	0.377964i
$253$	6.92820	+	4.00000i	0.435572	+	0.251478i
$254$	−13.8564	−	8.00000i	−0.869428	−	0.501965i
$255$		−	9.00000i		−	0.563602i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	12.9904	−	7.50000i	0.808746	−	0.466930i
$259$	−3.00000			−0.186411
$260$		0			0
$261$	12.0000			0.742781
$262$	0.866025	−	0.500000i	0.0535032	−	0.0308901i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$			12.0000i			0.737154i
$266$	5.19615	+	3.00000i	0.318597	+	0.183942i
$267$	15.5885	+	9.00000i	0.953998	+	0.550791i
$268$		−	2.00000i		−	0.122169i
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	−0.224523	−	0.974469i	$-0.572083\pi$
$269$	12.0000	−	20.7846i	0.731653	−	1.26726i	0.956176	−	0.292791i	$-0.0945841\pi$
$270$	4.50000	+	7.79423i	0.273861	+	0.474342i
$271$	11.2583	−	6.50000i	0.683895	−	0.394847i	−0.117426	−	0.993082i	$-0.537464\pi$
$271$	11.2583	−	6.50000i	0.683895	−	0.394847i	0.801321	+	0.598235i	$0.204131\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	12.0000			0.724947
$275$	−6.92820	+	4.00000i	−0.417786	+	0.241209i
$276$	−6.00000	−	10.3923i	−0.361158	−	0.625543i
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	−0.627539	−	0.778585i	$-0.715938\pi$
$277$	6.00000	−	10.3923i	0.360505	−	0.624413i	0.988044	+	0.154172i	$0.0492710\pi$
$278$		−	7.00000i		−	0.419832i
$279$	20.7846	+	12.0000i	1.24434	+	0.718421i
$280$	0.866025	+	0.500000i	0.0517549	+	0.0298807i
$281$		−	26.0000i		−	1.55103i	−0.631329	−	0.775515i	$-0.717490\pi$
$281$		−	26.0000i		−	1.55103i	0.631329	−	0.775515i	$-0.282510\pi$
$282$	19.5000	−	33.7750i	1.16121	−	2.01127i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−4.33013	+	2.50000i	−0.256946	+	0.148348i
$285$	−18.0000			−1.06623
$286$		0			0
$287$		0			0
$288$	−5.19615	+	3.00000i	−0.306186	+	0.176777i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$			42.0000i			2.46208i
$292$	−8.66025	−	5.00000i	−0.506803	−	0.292603i
$293$	−6.06218	−	3.50000i	−0.354156	−	0.204472i	0.312358	−	0.949964i	$-0.398881\pi$
$293$	−6.06218	−	3.50000i	−0.354156	−	0.204472i	−0.666514	+	0.745492i	$0.732214\pi$
$294$			18.0000i			1.04978i
$295$	−5.00000	+	8.66025i	−0.291111	+	0.504219i
$296$	1.50000	+	2.59808i	0.0871857	+	0.151010i
$297$	15.5885	−	9.00000i	0.904534	−	0.522233i
$298$	18.0000			1.04271
$299$		0			0
$300$	12.0000			0.692820
$301$	4.33013	−	2.50000i	0.249584	−	0.144098i
$302$	4.50000	+	7.79423i	0.258946	+	0.448507i
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$		−	6.00000i		−	0.344124i
$305$	6.92820	+	4.00000i	0.396708	+	0.229039i
$306$	15.5885	+	9.00000i	0.891133	+	0.514496i
$307$			14.0000i			0.799022i	0.916728	+	0.399511i	$0.130820\pi$
$307$			14.0000i			0.799022i	−0.916728	+	0.399511i	$0.869180\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$	12.0000	+	20.7846i	0.682656	+	1.18240i
$310$	−3.46410	+	2.00000i	−0.196748	+	0.113592i
$311$	−18.0000			−1.02069			−0.510343	−	0.859971i	$-0.670482\pi$
$311$	−18.0000			−1.02069			−0.510343	+	0.859971i	$0.670482\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	8.66025	−	5.00000i	0.488726	−	0.282166i
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	−2.00000	+	3.46410i	−0.112509	+	0.194871i
$317$			18.0000i			1.01098i	0.862832	+	0.505490i	$0.168688\pi$
$317$			18.0000i			1.01098i	−0.862832	+	0.505490i	$0.831312\pi$
$318$	−31.1769	−	18.0000i	−1.74831	−	1.00939i
$319$	3.46410	+	2.00000i	0.193952	+	0.111979i
$320$		−	1.00000i		−	0.0559017i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$	−2.00000	−	3.46410i	−0.111456	−	0.193047i
$323$	−15.5885	+	9.00000i	−0.867365	+	0.500773i
$324$	−9.00000			−0.500000
$325$		0			0
$326$	−4.00000			−0.221540
$327$	49.3634	−	28.5000i	2.72980	−	1.57605i
$328$		0			0
$329$	6.50000	−	11.2583i	0.358357	−	0.620692i
$330$			6.00000i			0.330289i
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	0.401768	−	0.915742i	$-0.368396\pi$
$331$	−3.46410	−	2.00000i	−0.190404	−	0.109930i	−0.592172	+	0.805812i	$0.701729\pi$
$332$		0			0
$333$			18.0000i			0.986394i
$334$		0			0
$335$	1.00000	+	1.73205i	0.0546358	+	0.0946320i
$336$	−2.59808	+	1.50000i	−0.141737	+	0.0818317i
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$	−2.59808	+	1.50000i	−0.140900	+	0.0813489i
$341$	4.00000	+	6.92820i	0.216612	+	0.375183i
$342$	18.0000	−	31.1769i	0.973329	−	1.68585i
$343$			13.0000i			0.701934i
$344$	−4.33013	−	2.50000i	−0.233465	−	0.134791i
$345$	10.3923	+	6.00000i	0.559503	+	0.323029i
$346$			20.0000i			1.07521i
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	−0.719590	−	0.694399i	$-0.755670\pi$
$347$	4.50000	−	7.79423i	0.241573	−	0.418416i	0.961162	+	0.275983i	$0.0890035\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	6.06218	−	3.50000i	0.324501	−	0.187351i	−0.328896	−	0.944366i	$-0.606677\pi$
$349$	6.06218	−	3.50000i	0.324501	−	0.187351i	0.653397	+	0.757015i	$0.273343\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−2.00000			−0.106600
$353$	−3.46410	+	2.00000i	−0.184376	+	0.106449i	−0.589347	−	0.807880i	$-0.700615\pi$
$353$	−3.46410	+	2.00000i	−0.184376	+	0.106449i	0.404971	+	0.914329i	$0.367282\pi$
$354$	−15.0000	−	25.9808i	−0.797241	−	1.38086i
$355$	2.50000	−	4.33013i	0.132686	−	0.229819i
$356$		−	6.00000i		−	0.317999i
$357$	7.79423	+	4.50000i	0.412514	+	0.238165i
$358$	7.79423	+	4.50000i	0.411938	+	0.237832i
$359$			24.0000i			1.26667i	0.773877	+	0.633336i	$0.218315\pi$
$359$			24.0000i			1.26667i	−0.773877	+	0.633336i	$0.781685\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	8.50000	+	14.7224i	0.447368	+	0.774865i
$362$		0			0
$363$	−21.0000			−1.10221
$364$		0			0
$365$	10.0000			0.523424
$366$	−20.7846	+	12.0000i	−1.08643	+	0.627250i
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$		0			0
$370$	−2.59808	−	1.50000i	−0.135068	−	0.0779813i
$371$	−10.3923	−	6.00000i	−0.539542	−	0.311504i
$372$		−	12.0000i		−	0.622171i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$	−23.3827	+	13.5000i	−1.20748	+	0.697137i
$376$	−13.0000			−0.670424
$377$		0			0
$378$	−9.00000			−0.462910
$379$	−13.8564	+	8.00000i	−0.711756	+	0.410932i	−0.811711	−	0.584060i	$-0.801463\pi$
$379$	−13.8564	+	8.00000i	−0.711756	+	0.410932i	0.0999550	+	0.994992i	$0.468130\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	−24.0000	+	41.5692i	−1.22956	+	2.12966i
$382$		−	10.0000i		−	0.511645i
$383$	23.3827	+	13.5000i	1.19480	+	0.689818i	0.959391	−	0.282079i	$-0.0910240\pi$
$383$	23.3827	+	13.5000i	1.19480	+	0.689818i	0.235408	+	0.971897i	$0.424357\pi$
$384$	2.59808	+	1.50000i	0.132583	+	0.0765466i
$385$			2.00000i			0.101929i
$386$	8.00000	−	13.8564i	0.407189	−	0.705273i
$387$	−15.0000	−	25.9808i	−0.762493	−	1.32068i
$388$	12.1244	−	7.00000i	0.615521	−	0.355371i
$389$	30.0000			1.52106			0.760530	−	0.649303i	$-0.224939\pi$
$389$	30.0000			1.52106			0.760530	+	0.649303i	$0.224939\pi$
$390$		0			0
$391$	12.0000			0.606866
$392$	5.19615	−	3.00000i	0.262445	−	0.151523i
$393$	−1.50000	−	2.59808i	−0.0756650	−	0.131056i
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$		−	4.00000i		−	0.201262i
$396$	−10.3923	−	6.00000i	−0.522233	−	0.301511i
$397$	19.0526	+	11.0000i	0.956221	+	0.552074i	0.895008	−	0.446051i	$-0.147170\pi$
$397$	19.0526	+	11.0000i	0.956221	+	0.552074i	0.0612128	+	0.998125i	$0.480503\pi$
$398$		−	10.0000i		−	0.501255i
$399$	9.00000	−	15.5885i	0.450564	−	0.780399i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	20.7846	−	12.0000i	1.03793	−	0.599251i	0.118686	−	0.992932i	$-0.462132\pi$
$401$	20.7846	−	12.0000i	1.03793	−	0.599251i	0.919247	+	0.393680i	$0.128798\pi$
$402$	−6.00000			−0.299253
$403$		0			0
$404$	4.00000			0.199007
$405$	7.79423	−	4.50000i	0.387298	−	0.223607i
$406$	−1.00000	−	1.73205i	−0.0496292	−	0.0859602i
$407$	−3.00000	+	5.19615i	−0.148704	+	0.257564i
$408$		−	9.00000i		−	0.445566i
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	0.583193	−	0.812333i	$-0.301803\pi$
$409$	3.46410	+	2.00000i	0.171289	+	0.0988936i	−0.411905	+	0.911227i	$0.635136\pi$
$410$		0			0
$411$		−	36.0000i		−	1.77575i
$412$	4.00000	−	6.92820i	0.197066	−	0.341328i
$413$	−5.00000	−	8.66025i	−0.246034	−	0.426143i
$414$	−20.7846	+	12.0000i	−1.02151	+	0.589768i
$415$		0			0
$416$		0			0
$417$	−21.0000			−1.02837
$418$	10.3923	−	6.00000i	0.508304	−	0.293470i
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	−0.999887	−	0.0150285i	$-0.995216\pi$
$419$	−10.5000	−	18.1865i	−0.512959	−	0.888470i	0.486928	−	0.873442i	$-0.338117\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$			5.00000i			0.243685i	0.992549	+	0.121843i	$0.0388803\pi$
$421$			5.00000i			0.243685i	−0.992549	+	0.121843i	$0.961120\pi$
$422$	19.9186	+	11.5000i	0.969622	+	0.559811i
$423$	−67.5500	−	39.0000i	−3.28439	−	1.89624i
$424$			12.0000i			0.582772i
$425$	−6.00000	+	10.3923i	−0.291043	+	0.504101i
$426$	7.50000	+	12.9904i	0.363376	+	0.629386i
$427$	−6.92820	+	4.00000i	−0.335279	+	0.193574i
$428$	4.00000			0.193347
$429$		0			0
$430$	5.00000			0.241121
$431$	−28.5788	+	16.5000i	−1.37659	+	0.794777i	−0.991748	−	0.128204i	$-0.959079\pi$
$431$	−28.5788	+	16.5000i	−1.37659	+	0.794777i	−0.384846	+	0.922981i	$0.625746\pi$
$432$	4.50000	+	7.79423i	0.216506	+	0.375000i
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	−0.769588	−	0.638541i	$-0.779538\pi$
$433$	3.50000	−	6.06218i	0.168199	−	0.291330i	0.937787	+	0.347212i	$0.112871\pi$
$434$		−	4.00000i		−	0.192006i
$435$	5.19615	+	3.00000i	0.249136	+	0.143839i
$436$	−16.4545	−	9.50000i	−0.788027	−	0.454967i
$437$		−	24.0000i		−	1.14808i
$438$	−15.0000	+	25.9808i	−0.716728	+	1.24141i
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	−0.999576	−	0.0291138i	$-0.990731\pi$
$439$	−11.0000	−	19.0526i	−0.525001	−	0.909329i	0.474575	−	0.880215i	$-0.342602\pi$
$440$	1.73205	−	1.00000i	0.0825723	−	0.0476731i
$441$	36.0000			1.71429
$442$		0			0
$443$	−39.0000			−1.85295			−0.926473	−	0.376361i	$-0.877175\pi$
$443$	−39.0000			−1.85295			−0.926473	+	0.376361i	$0.877175\pi$
$444$	7.79423	−	4.50000i	0.369898	−	0.213561i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−10.5000	+	18.1865i	−0.497189	+	0.861157i
$447$		−	54.0000i		−	2.55411i
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	22.5167	+	13.0000i	1.06263	+	0.613508i	0.926158	−	0.377136i	$-0.123091\pi$
$449$	22.5167	+	13.0000i	1.06263	+	0.613508i	0.136469	+	0.990644i	$0.456425\pi$
$450$		−	24.0000i		−	1.13137i
$451$		0			0
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$	23.3827	−	13.5000i	1.09861	−	0.634285i
$454$	24.0000			1.12638
$455$		0			0
$456$	−18.0000			−0.842927
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	−0.688686	−	0.725059i	$-0.741812\pi$
$457$	−8.66025	+	5.00000i	−0.405110	+	0.233890i	0.283577	+	0.958950i	$0.408479\pi$
$458$	7.50000	+	12.9904i	0.350452	+	0.607001i
$459$	13.5000	−	23.3827i	0.630126	−	1.09141i
$460$		−	4.00000i		−	0.186501i
$461$	−18.1865	−	10.5000i	−0.847031	−	0.489034i	0.0126168	−	0.999920i	$-0.495984\pi$
$461$	−18.1865	−	10.5000i	−0.847031	−	0.489034i	−0.859648	+	0.510887i	$0.829317\pi$
$462$	−5.19615	−	3.00000i	−0.241747	−	0.139573i
$463$			16.0000i			0.743583i	0.928316	+	0.371792i	$0.121256\pi$
$463$			16.0000i			0.743583i	−0.928316	+	0.371792i	$0.878744\pi$
$464$	−1.00000	+	1.73205i	−0.0464238	+	0.0804084i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	−9.52628	+	5.50000i	−0.441296	+	0.254783i
$467$	−20.0000			−0.925490			−0.462745	−	0.886492i	$-0.653135\pi$
$467$	−20.0000			−0.925490			−0.462745	+	0.886492i	$0.653135\pi$
$468$		0			0
$469$	−2.00000			−0.0923514
$470$	11.2583	−	6.50000i	0.519308	−	0.299823i
$471$	−15.0000	−	25.9808i	−0.691164	−	1.19713i
$472$	−5.00000	+	8.66025i	−0.230144	+	0.398621i
$473$		−	10.0000i		−	0.459800i
$474$	10.3923	+	6.00000i	0.477334	+	0.275589i
$475$	20.7846	+	12.0000i	0.953663	+	0.550598i
$476$		−	3.00000i		−	0.137505i
$477$	−36.0000	+	62.3538i	−1.64833	+	2.85499i
$478$	4.50000	+	7.79423i	0.205825	+	0.356500i
$479$	−2.59808	+	1.50000i	−0.118709	+	0.0685367i	−0.558179	−	0.829721i	$-0.688500\pi$
$479$	−2.59808	+	1.50000i	−0.118709	+	0.0685367i	0.439470	+	0.898257i	$0.355166\pi$
$480$	−3.00000			−0.136931
$481$		0			0
$482$	18.0000			0.819878
$483$	−10.3923	+	6.00000i	−0.472866	+	0.273009i
$484$	3.50000	+	6.06218i	0.159091	+	0.275554i
$485$	−7.00000	+	12.1244i	−0.317854	+	0.550539i
$486$		0			0
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	6.92820	+	4.00000i	0.313625	+	0.181071i
$489$			12.0000i			0.542659i
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	0.804084	−	0.594515i	$-0.202656\pi$
$491$	−2.50000	−	4.33013i	−0.112823	−	0.195416i	−0.916908	+	0.399100i	$0.869323\pi$
$492$		0			0
$493$	6.00000			0.270226
$494$		0			0
$495$	12.0000			0.539360
$496$	−3.46410	+	2.00000i	−0.155543	+	0.0898027i
$497$	2.50000	+	4.33013i	0.112140	+	0.194233i
$498$		0			0
$499$			32.0000i			1.43252i	0.697835	+	0.716258i	$0.254147\pi$
$499$			32.0000i			1.43252i	−0.697835	+	0.716258i	$0.745853\pi$
$500$	7.79423	+	4.50000i	0.348569	+	0.201246i
$501$		0			0
$502$		0			0
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	−0.666705	−	0.745321i	$-0.732296\pi$
$503$	7.00000	−	12.1244i	0.312115	−	0.540598i	0.978820	+	0.204723i	$0.0656294\pi$
$504$	3.00000	+	5.19615i	0.133631	+	0.231455i
$505$	−3.46410	+	2.00000i	−0.154150	+	0.0889988i
$506$	−8.00000			−0.355643
$507$		0			0
$508$	16.0000			0.709885
$509$	−29.4449	+	17.0000i	−1.30512	+	0.753512i	−0.981278	−	0.192599i	$-0.938308\pi$
$509$	−29.4449	+	17.0000i	−1.30512	+	0.753512i	−0.323843	+	0.946111i	$0.604975\pi$
$510$	4.50000	+	7.79423i	0.199263	+	0.345134i
$511$	−5.00000	+	8.66025i	−0.221187	+	0.383107i
$512$		−	1.00000i		−	0.0441942i
$513$	−46.7654	−	27.0000i	−2.06474	−	1.19208i
$514$	12.9904	+	7.50000i	0.572981	+	0.330811i
$515$			8.00000i			0.352522i
$516$	−7.50000	+	12.9904i	−0.330169	+	0.571870i
$517$	−13.0000	−	22.5167i	−0.571739	−	0.990282i
$518$	2.59808	−	1.50000i	0.114153	−	0.0659062i
$519$	60.0000			2.63371
$520$		0			0
$521$	39.0000			1.70862			0.854311	−	0.519763i	$-0.173980\pi$
$521$	39.0000			1.70862			0.854311	+	0.519763i	$0.173980\pi$
$522$	−10.3923	+	6.00000i	−0.454859	+	0.262613i
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	0.927746	+	0.373213i	$0.121744\pi$
$523$	18.0000	+	31.1769i	0.787085	+	1.36327i	−0.140660	+	0.990058i	$0.544923\pi$
$524$	−0.500000	+	0.866025i	−0.0218426	+	0.0378325i
$525$		−	12.0000i		−	0.523723i
$526$	10.3923	+	6.00000i	0.453126	+	0.261612i
$527$	10.3923	+	6.00000i	0.452696	+	0.261364i
$528$			6.00000i			0.261116i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	−51.9615	+	30.0000i	−2.25494	+	1.30189i
$532$	−6.00000			−0.260133
$533$		0			0
$534$	−18.0000			−0.778936
$535$	−3.46410	+	2.00000i	−0.149766	+	0.0864675i
$536$	1.00000	+	1.73205i	0.0431934	+	0.0748132i
$537$	13.5000	−	23.3827i	0.582568	−	1.00904i
$538$			24.0000i			1.03471i
$539$	10.3923	+	6.00000i	0.447628	+	0.258438i
$540$	−7.79423	−	4.50000i	−0.335410	−	0.193649i
$541$			17.0000i			0.730887i	0.930834	+	0.365444i	$0.119083\pi$
$541$			17.0000i			0.730887i	−0.930834	+	0.365444i	$0.880917\pi$
$542$	−6.50000	+	11.2583i	−0.279199	+	0.483587i
$543$		0			0
$544$	−2.59808	+	1.50000i	−0.111392	+	0.0643120i
$545$	19.0000			0.813871
$546$		0			0
$547$	37.0000			1.58201			0.791003	−	0.611812i	$-0.209559\pi$
$547$	37.0000			1.58201			0.791003	+	0.611812i	$0.209559\pi$
$548$	−10.3923	+	6.00000i	−0.443937	+	0.256307i
$549$	24.0000	+	41.5692i	1.02430	+	1.77413i
$550$	4.00000	−	6.92820i	0.170561	−	0.295420i
$551$		−	12.0000i		−	0.511217i
$552$	10.3923	+	6.00000i	0.442326	+	0.255377i
$553$	3.46410	+	2.00000i	0.147309	+	0.0850487i
$554$			12.0000i			0.509831i
$555$	−4.50000	+	7.79423i	−0.191014	+	0.330847i
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.247964	−	0.968769i	$-0.420239\pi$
$557$	28.5788	−	16.5000i	1.21092	−	0.699127i	0.962961	+	0.269642i	$0.0869053\pi$
$558$	−24.0000			−1.01600
$559$		0			0
$560$	−1.00000			−0.0422577
$561$	15.5885	−	9.00000i	0.658145	−	0.379980i
$562$	13.0000	+	22.5167i	0.548372	+	0.949808i
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	−0.726540	−	0.687124i	$-0.758873\pi$
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	0.958337	+	0.285640i	$0.0922060\pi$
$564$			39.0000i			1.64220i
$565$	−1.73205	−	1.00000i	−0.0728679	−	0.0420703i
$566$	−3.46410	−	2.00000i	−0.145607	−	0.0840663i
$567$			9.00000i			0.377964i
$568$	2.50000	−	4.33013i	0.104898	−	0.181688i
$569$	15.5000	+	26.8468i	0.649794	+	1.12548i	0.983172	+	0.182683i	$0.0584781\pi$
$569$	15.5000	+	26.8468i	0.649794	+	1.12548i	−0.333378	+	0.942793i	$0.608189\pi$
$570$	15.5885	−	9.00000i	0.652929	−	0.376969i
$571$	−33.0000			−1.38101			−0.690504	−	0.723329i	$-0.742611\pi$
$571$	−33.0000			−1.38101			−0.690504	+	0.723329i	$0.742611\pi$
$572$		0			0
$573$	−30.0000			−1.25327
$574$		0			0
$575$	−8.00000	−	13.8564i	−0.333623	−	0.577852i
$576$	3.00000	−	5.19615i	0.125000	−	0.216506i
$577$		−	18.0000i		−	0.749350i	−0.927156	−	0.374675i	$-0.877754\pi$
$577$		−	18.0000i		−	0.749350i	0.927156	−	0.374675i	$-0.122246\pi$
$578$	−6.92820	−	4.00000i	−0.288175	−	0.166378i
$579$	−41.5692	−	24.0000i	−1.72756	−	0.997406i
$580$		−	2.00000i		−	0.0830455i
$581$		0			0
$582$	−21.0000	−	36.3731i	−0.870478	−	1.50771i
$583$	−20.7846	+	12.0000i	−0.860811	+	0.496989i
$584$	10.0000			0.413803
$585$		0			0
$586$	7.00000			0.289167
$587$	24.2487	−	14.0000i	1.00085	−	0.577842i	0.0923513	−	0.995726i	$-0.470562\pi$
$587$	24.2487	−	14.0000i	1.00085	−	0.577842i	0.908500	+	0.417885i	$0.137228\pi$
$588$	−9.00000	−	15.5885i	−0.371154	−	0.642857i
$589$	12.0000	−	20.7846i	0.494451	−	0.856415i
$590$		−	10.0000i		−	0.411693i
$591$	−23.3827	−	13.5000i	−0.961835	−	0.555316i
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$		−	22.0000i		−	0.903432i	−0.892162	−	0.451716i	$-0.850812\pi$
$593$		−	22.0000i		−	0.903432i	0.892162	−	0.451716i	$-0.149188\pi$
$594$	−9.00000	+	15.5885i	−0.369274	+	0.639602i
$595$	1.50000	+	2.59808i	0.0614940	+	0.106511i
$596$	−15.5885	+	9.00000i	−0.638528	+	0.368654i
$597$	−30.0000			−1.22782
$598$		0			0
$599$	−2.00000			−0.0817178			−0.0408589	−	0.999165i	$-0.513009\pi$
$599$	−2.00000			−0.0817178			−0.0408589	+	0.999165i	$0.513009\pi$
$600$	−10.3923	+	6.00000i	−0.424264	+	0.244949i
$601$	17.5000	+	30.3109i	0.713840	+	1.23641i	0.963405	+	0.268049i	$0.0863789\pi$
$601$	17.5000	+	30.3109i	0.713840	+	1.23641i	−0.249565	+	0.968358i	$0.580288\pi$
$602$	−2.50000	+	4.33013i	−0.101892	+	0.176483i
$603$			12.0000i			0.488678i
$604$	−7.79423	−	4.50000i	−0.317143	−	0.183102i
$605$	−6.06218	−	3.50000i	−0.246463	−	0.142295i
$606$		−	12.0000i		−	0.487467i
$607$	−3.00000	+	5.19615i	−0.121766	+	0.210905i	−0.920464	−	0.390827i	$-0.872189\pi$
$607$	−3.00000	+	5.19615i	−0.121766	+	0.210905i	0.798698	+	0.601732i	$0.205522\pi$
$608$	3.00000	+	5.19615i	0.121666	+	0.210732i
$609$	−5.19615	+	3.00000i	−0.210559	+	0.121566i
$610$	−8.00000			−0.323911
$611$		0			0
$612$	−18.0000			−0.727607
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.880251	−	0.474509i	$-0.842626\pi$
$613$	−22.5167	+	13.0000i	−0.909439	+	0.525065i	−0.0291886	+	0.999574i	$0.509292\pi$
$614$	−7.00000	−	12.1244i	−0.282497	−	0.489299i
$615$		0			0
$616$			2.00000i			0.0805823i
$617$	13.8564	+	8.00000i	0.557838	+	0.322068i	0.752277	−	0.658847i	$-0.228955\pi$
$617$	13.8564	+	8.00000i	0.557838	+	0.322068i	−0.194439	+	0.980915i	$0.562289\pi$
$618$	−20.7846	−	12.0000i	−0.836080	−	0.482711i
$619$			4.00000i			0.160774i	0.996764	+	0.0803868i	$0.0256155\pi$
$619$			4.00000i			0.160774i	−0.996764	+	0.0803868i	$0.974384\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	18.0000	+	31.1769i	0.722315	+	1.25109i
$622$	15.5885	−	9.00000i	0.625040	−	0.360867i
$623$	−6.00000			−0.240385
$624$		0			0
$625$	11.0000			0.440000
$626$	0.866025	−	0.500000i	0.0346133	−	0.0199840i
$627$	−18.0000	−	31.1769i	−0.718851	−	1.24509i
$628$	−5.00000	+	8.66025i	−0.199522	+	0.345582i
$629$			9.00000i			0.358854i
$630$	−5.19615	−	3.00000i	−0.207020	−	0.119523i
$631$	4.33013	+	2.50000i	0.172380	+	0.0995234i	0.583707	−	0.811964i	$-0.301602\pi$
$631$	4.33013	+	2.50000i	0.172380	+	0.0995234i	−0.411328	+	0.911487i	$0.634935\pi$
$632$		−	4.00000i		−	0.159111i
$633$	34.5000	−	59.7558i	1.37125	−	2.37508i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$	−13.8564	+	8.00000i	−0.549875	+	0.317470i
$636$	36.0000			1.42749
$637$		0			0
$638$	−4.00000			−0.158362
$639$	25.9808	−	15.0000i	1.02778	−	0.593391i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	−0.885098	−	0.465404i	$-0.845909\pi$
$641$	−1.00000	+	1.73205i	−0.0394976	+	0.0684119i	0.845601	+	0.533816i	$0.179242\pi$
$642$		−	12.0000i		−	0.473602i
$643$	12.1244	+	7.00000i	0.478138	+	0.276053i	0.719640	−	0.694347i	$-0.244307\pi$
$643$	12.1244	+	7.00000i	0.478138	+	0.276053i	−0.241502	+	0.970400i	$0.577640\pi$
$644$	3.46410	+	2.00000i	0.136505	+	0.0788110i
$645$		−	15.0000i		−	0.590624i
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	−0.949270	−	0.314462i	$-0.898176\pi$
$647$	−19.0000	−	32.9090i	−0.746967	−	1.29378i	0.202303	−	0.979323i	$-0.435157\pi$
$648$	7.79423	−	4.50000i	0.306186	−	0.176777i
$649$	−20.0000			−0.785069
$650$		0			0
$651$	−12.0000			−0.470317
$652$	3.46410	−	2.00000i	0.135665	−	0.0783260i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	−28.5000	+	49.3634i	−1.11444	+	1.93026i
$655$		−	1.00000i		−	0.0390732i
$656$		0			0
$657$	51.9615	+	30.0000i	2.02721	+	1.17041i
$658$			13.0000i			0.506793i
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	−0.725175	−	0.688565i	$-0.758241\pi$
$659$	6.00000	−	10.3923i	0.233727	−	0.404827i	0.958902	+	0.283738i	$0.0915745\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−8.66025	+	5.00000i	−0.336845	+	0.194477i	−0.658876	−	0.752252i	$-0.728968\pi$
$661$	−8.66025	+	5.00000i	−0.336845	+	0.194477i	0.322031	+	0.946729i	$0.395634\pi$
$662$	4.00000			0.155464
$663$		0			0
$664$		0			0
$665$	5.19615	−	3.00000i	0.201498	−	0.116335i
$666$	−9.00000	−	15.5885i	−0.348743	−	0.604040i
$667$	−4.00000	+	6.92820i	−0.154881	+	0.268261i
$668$		0			0
$669$	54.5596	+	31.5000i	2.10940	+	1.21786i
$670$	−1.73205	−	1.00000i	−0.0669150	−	0.0386334i
$671$			16.0000i			0.617673i
$672$	1.50000	−	2.59808i	0.0578638	−	0.100223i
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	0.963679	+	0.267063i	$0.0860531\pi$
$673$	18.5000	+	32.0429i	0.713123	+	1.23516i	−0.250557	+	0.968102i	$0.580614\pi$
$674$	19.9186	−	11.5000i	0.767235	−	0.442963i
$675$	−36.0000			−1.38564
$676$		0			0
$677$	−36.0000			−1.38359			−0.691796	−	0.722093i	$-0.743180\pi$
$677$	−36.0000			−1.38359			−0.691796	+	0.722093i	$0.743180\pi$
$678$	5.19615	−	3.00000i	0.199557	−	0.115214i
$679$	−7.00000	−	12.1244i	−0.268635	−	0.465290i
$680$	1.50000	−	2.59808i	0.0575224	−	0.0996317i
$681$		−	72.0000i		−	2.75905i
$682$	−6.92820	−	4.00000i	−0.265295	−	0.153168i
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.998916	−	0.0465592i	$-0.0148256\pi$
$683$	38.1051	+	22.0000i	1.45805	+	0.841807i	0.459136	+	0.888366i	$0.348159\pi$
$684$			36.0000i			1.37649i
$685$	6.00000	−	10.3923i	0.229248	−	0.397070i
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	38.9711	−	22.5000i	1.48684	−	0.858429i
$688$	5.00000			0.190623
$689$		0			0
$690$	−12.0000			−0.456832
$691$	6.92820	−	4.00000i	0.263561	−	0.152167i	−0.362397	−	0.932024i	$-0.618041\pi$
$691$	6.92820	−	4.00000i	0.263561	−	0.152167i	0.625958	+	0.779857i	$0.284708\pi$
$692$	−10.0000	−	17.3205i	−0.380143	−	0.658427i
$693$	−6.00000	+	10.3923i	−0.227921	+	0.394771i
$694$			9.00000i			0.341635i
$695$	−6.06218	−	3.50000i	−0.229952	−	0.132763i
$696$	5.19615	+	3.00000i	0.196960	+	0.113715i
$697$		0			0
$698$	−3.50000	+	6.06218i	−0.132477	+	0.229457i
$699$	16.5000	+	28.5788i	0.624087	+	1.08095i
$700$	−3.46410	+	2.00000i	−0.130931	+	0.0755929i
$701$	12.0000			0.453234			0.226617	−	0.973984i	$-0.427233\pi$
$701$	12.0000			0.453234			0.226617	+	0.973984i	$0.427233\pi$
$702$		0			0
$703$	18.0000			0.678883
$704$	1.73205	−	1.00000i	0.0652791	−	0.0376889i
$705$	−19.5000	−	33.7750i	−0.734412	−	1.27204i
$706$	2.00000	−	3.46410i	0.0752710	−	0.130373i
$707$		−	4.00000i		−	0.150435i
$708$	25.9808	+	15.0000i	0.976417	+	0.563735i
$709$	−32.9090	−	19.0000i	−1.23592	−	0.713560i	−0.267664	−	0.963512i	$-0.586252\pi$
$709$	−32.9090	−	19.0000i	−1.23592	−	0.713560i	−0.968258	+	0.249952i	$0.919585\pi$
$710$			5.00000i			0.187647i
$711$	12.0000	−	20.7846i	0.450035	−	0.779484i
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	−13.8564	+	8.00000i	−0.518927	+	0.299602i
$714$	−9.00000			−0.336817
$715$		0			0
$716$	−9.00000			−0.336346
$717$	23.3827	−	13.5000i	0.873242	−	0.504167i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	−0.994915	−	0.100721i	$-0.967885\pi$
$719$	−11.0000	+	19.0526i	−0.410231	+	0.710541i	0.584684	+	0.811261i	$0.301219\pi$
$720$			6.00000i			0.223607i
$721$	−6.92820	−	4.00000i	−0.258020	−	0.148968i
$722$	−14.7224	−	8.50000i	−0.547912	−	0.316337i
$723$		−	54.0000i		−	2.00828i
$724$		0			0
$725$	−4.00000	−	6.92820i	−0.148556	−	0.257307i
$726$	18.1865	−	10.5000i	0.674966	−	0.389692i
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	−8.66025	+	5.00000i	−0.320530	+	0.185058i
$731$	−7.50000	−	12.9904i	−0.277398	−	0.480467i
$732$	12.0000	−	20.7846i	0.443533	−	0.768221i
$733$			43.0000i			1.58824i	0.607760	+	0.794121i	$0.292068\pi$
$733$			43.0000i			1.58824i	−0.607760	+	0.794121i	$0.707932\pi$
$734$	−8.66025	−	5.00000i	−0.319656	−	0.184553i
$735$	15.5885	+	9.00000i	0.574989	+	0.331970i
$736$		−	4.00000i		−	0.147442i
$737$	−2.00000	+	3.46410i	−0.0736709	+	0.127602i
$738$		0			0
$739$	10.3923	−	6.00000i	0.382287	−	0.220714i	−0.296526	−	0.955025i	$-0.595828\pi$
$739$	10.3923	−	6.00000i	0.382287	−	0.220714i	0.678813	+	0.734311i	$0.262495\pi$
$740$	3.00000			0.110282
$741$		0			0
$742$	12.0000			0.440534
$743$	40.7032	−	23.5000i	1.49326	−	0.862131i	0.493285	−	0.869868i	$-0.335796\pi$
$743$	40.7032	−	23.5000i	1.49326	−	0.862131i	0.999970	+	0.00773621i	$0.00246254\pi$
$744$	6.00000	+	10.3923i	0.219971	+	0.381000i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$			4.00000i			0.146450i
$747$		0			0
$748$	−5.19615	−	3.00000i	−0.189990	−	0.109691i
$749$		−	4.00000i		−	0.146157i
$750$	13.5000	−	23.3827i	0.492950	−	0.853815i
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	0.997526	−	0.0702946i	$-0.0223939\pi$
$751$	12.0000	+	20.7846i	0.437886	+	0.758441i	−0.559640	+	0.828736i	$0.689061\pi$
$752$	11.2583	−	6.50000i	0.410549	−	0.237031i
$753$		0			0
$754$		0			0
$755$	9.00000			0.327544
$756$	7.79423	−	4.50000i	0.283473	−	0.163663i
$757$	6.00000	+	10.3923i	0.218074	+	0.377715i	0.954219	−	0.299109i	$-0.0966893\pi$
$757$	6.00000	+	10.3923i	0.218074	+	0.377715i	−0.736145	+	0.676824i	$0.763356\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$			24.0000i			0.871145i
$760$	−5.19615	−	3.00000i	−0.188484	−	0.108821i
$761$	−5.19615	−	3.00000i	−0.188360	−	0.108750i	0.402854	−	0.915264i	$-0.368018\pi$
$761$	−5.19615	−	3.00000i	−0.188360	−	0.108750i	−0.591215	+	0.806514i	$0.701351\pi$
$762$		−	48.0000i		−	1.73886i
$763$	−9.50000	+	16.4545i	−0.343923	+	0.595692i
$764$	5.00000	+	8.66025i	0.180894	+	0.313317i
$765$	15.5885	−	9.00000i	0.563602	−	0.325396i
$766$	−27.0000			−0.975550
$767$		0			0
$768$	−3.00000			−0.108253
$769$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$769$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$	22.5000	−	38.9711i	0.810318	−	1.40351i
$772$			16.0000i			0.575853i
$773$	9.52628	+	5.50000i	0.342636	+	0.197821i	0.661437	−	0.750000i	$-0.269947\pi$
$773$	9.52628	+	5.50000i	0.342636	+	0.197821i	−0.318801	+	0.947822i	$0.603280\pi$
$774$	25.9808	+	15.0000i	0.933859	+	0.539164i
$775$		−	16.0000i		−	0.574737i
$776$	−7.00000	+	12.1244i	−0.251285	+	0.435239i
$777$	−4.50000	−	7.79423i	−0.161437	−	0.279616i
$778$	−25.9808	+	15.0000i	−0.931455	+	0.537776i
$779$		0			0
$780$		0			0
$781$	10.0000			0.357828
$782$	−10.3923	+	6.00000i	−0.371628	+	0.214560i
$783$	9.00000	+	15.5885i	0.321634	+	0.557086i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$		−	10.0000i		−	0.356915i
$786$	2.59808	+	1.50000i	0.0926703	+	0.0535032i
$787$	−27.7128	−	16.0000i	−0.987855	−	0.570338i	−0.0832226	−	0.996531i	$-0.526521\pi$
$787$	−27.7128	−	16.0000i	−0.987855	−	0.570338i	−0.904632	+	0.426193i	$0.859855\pi$
$788$			9.00000i			0.320612i
$789$	18.0000	−	31.1769i	0.640817	−	1.10993i
$790$	2.00000	+	3.46410i	0.0711568	+	0.123247i
$791$	1.73205	−	1.00000i	0.0615846	−	0.0355559i
$792$	12.0000			0.426401
$793$		0			0
$794$	−22.0000			−0.780751
$795$	−31.1769	+	18.0000i	−1.10573	+	0.638394i
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	0.206868	+	0.978369i	$0.433673\pi$
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	−0.950726	+	0.310031i	$0.899660\pi$
$798$			18.0000i			0.637193i
$799$	−33.7750	−	19.5000i	−1.19487	−	0.689860i
$800$	3.46410	+	2.00000i	0.122474	+	0.0707107i
$801$			36.0000i			1.27200i
$802$	−12.0000	+	20.7846i	−0.423735	+	0.733930i
$803$	10.0000	+	17.3205i	0.352892	+	0.611227i
$804$	5.19615	−	3.00000i	0.183254	−	0.105802i
$805$	−4.00000			−0.140981
$806$		0			0
$807$	72.0000			2.53452
$808$	−3.46410	+	2.00000i	−0.121867	+	0.0703598i
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	0.934224	−	0.356687i	$-0.116094\pi$
$809$	4.50000	+	7.79423i	0.158212	+	0.274030i	−0.776012	+	0.630718i	$0.782761\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$			28.0000i			0.983213i	0.870817	+	0.491606i	$0.163590\pi$
$811$			28.0000i			0.983213i	−0.870817	+	0.491606i	$0.836410\pi$
$812$	1.73205	+	1.00000i	0.0607831	+	0.0350931i
$813$	33.7750	+	19.5000i	1.18454	+	0.683895i
$814$		−	6.00000i		−	0.210300i
$815$	−2.00000	+	3.46410i	−0.0700569	+	0.121342i
$816$	4.50000	+	7.79423i	0.157532	+	0.272853i
$817$	−25.9808	+	15.0000i	−0.908952	+	0.524784i
$818$	−4.00000			−0.139857
$819$		0			0
$820$		0			0
$821$	21.6506	−	12.5000i	0.755612	−	0.436253i	−0.0721058	−	0.997397i	$-0.522972\pi$
$821$	21.6506	−	12.5000i	0.755612	−	0.436253i	0.827718	+	0.561144i	$0.189639\pi$
$822$	18.0000	+	31.1769i	0.627822	+	1.08742i
$823$	27.0000	−	46.7654i	0.941161	−	1.63014i	0.177899	−	0.984049i	$-0.443070\pi$
$823$	27.0000	−	46.7654i	0.941161	−	1.63014i	0.763261	−	0.646090i	$-0.223597\pi$
$824$			8.00000i			0.278693i
$825$	−20.7846	−	12.0000i	−0.723627	−	0.417786i
$826$	8.66025	+	5.00000i	0.301329	+	0.173972i
$827$			30.0000i			1.04320i	0.853189	+	0.521601i	$0.174665\pi$
$827$			30.0000i			1.04320i	−0.853189	+	0.521601i	$0.825335\pi$
$828$	12.0000	−	20.7846i	0.417029	−	0.722315i
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	−0.980642	−	0.195810i	$-0.937266\pi$
$829$	−19.0000	−	32.9090i	−0.659897	−	1.14298i	0.320745	−	0.947166i	$-0.396067\pi$
$830$		0			0
$831$	36.0000			1.24883
$832$		0			0
$833$	18.0000			0.623663
$834$	18.1865	−	10.5000i	0.629748	−	0.363585i
$835$		0			0
$836$	−6.00000	+	10.3923i	−0.207514	+	0.359425i
$837$			36.0000i			1.24434i
$838$	18.1865	+	10.5000i	0.628243	+	0.362716i
$839$	−48.4974	−	28.0000i	−1.67432	−	0.966667i	−0.965176	−	0.261600i	$-0.915750\pi$
$839$	−48.4974	−	28.0000i	−1.67432	−	0.966667i	−0.709141	−	0.705067i	$-0.750917\pi$
$840$			3.00000i			0.103510i
$841$	12.5000	−	21.6506i	0.431034	−	0.746574i
$842$	−2.50000	−	4.33013i	−0.0861557	−	0.149226i
$843$	67.5500	−	39.0000i	2.32654	−	1.34323i
$844$	−23.0000			−0.791693
$845$		0			0
$846$	78.0000			2.68170
$847$	6.06218	−	3.50000i	0.208299	−	0.120261i
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$	−6.00000	+	10.3923i	−0.205919	+	0.356663i
$850$		−	12.0000i		−	0.411597i
$851$	−10.3923	−	6.00000i	−0.356244	−	0.205677i
$852$	−12.9904	−	7.50000i	−0.445043	−	0.256946i
$853$			49.0000i			1.67773i	0.544341	+	0.838864i	$0.316780\pi$
$853$			49.0000i			1.67773i	−0.544341	+	0.838864i	$0.683220\pi$
$854$	4.00000	−	6.92820i	0.136877	−	0.237078i
$855$	−18.0000	−	31.1769i	−0.615587	−	1.06623i
$856$	−3.46410	+	2.00000i	−0.118401	+	0.0683586i
$857$	−46.0000			−1.57133			−0.785665	−	0.618652i	$-0.787679\pi$
$857$	−46.0000			−1.57133			−0.785665	+	0.618652i	$0.787679\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−4.33013	+	2.50000i	−0.147656	+	0.0852493i
$861$		0			0
$862$	16.5000	−	28.5788i	0.561992	−	0.973399i
$863$			11.0000i			0.374444i	0.982318	+	0.187222i	$0.0599484\pi$
$863$			11.0000i			0.374444i	−0.982318	+	0.187222i	$0.940052\pi$
$864$	−7.79423	−	4.50000i	−0.265165	−	0.153093i
$865$	17.3205	+	10.0000i	0.588915	+	0.340010i
$866$			7.00000i			0.237870i
$867$	−12.0000	+	20.7846i	−0.407541	+	0.705882i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	6.92820	−	4.00000i	0.235023	−	0.135691i
$870$	−6.00000			−0.203419
$871$		0			0
$872$	19.0000			0.643421
$873$	−72.7461	+	42.0000i	−2.46208	+	1.42148i
$874$	12.0000	+	20.7846i	0.405906	+	0.703050i
$875$	4.50000	−	7.79423i	0.152128	−	0.263493i
$876$		−	30.0000i		−	1.01361i
$877$	−33.7750	−	19.5000i	−1.14050	−	0.658468i	−0.193946	−	0.981012i	$-0.562129\pi$
$877$	−33.7750	−	19.5000i	−1.14050	−	0.658468i	−0.946554	+	0.322544i	$0.895462\pi$
$878$	19.0526	+	11.0000i	0.642993	+	0.371232i
$879$		−	21.0000i		−	0.708312i
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	10.5000	+	18.1865i	0.353754	+	0.612720i	0.986904	−	0.161309i	$-0.0515717\pi$
$881$	10.5000	+	18.1865i	0.353754	+	0.612720i	−0.633150	+	0.774029i	$0.718238\pi$
$882$	−31.1769	+	18.0000i	−1.04978	+	0.606092i
$883$	47.0000			1.58168			0.790838	−	0.612026i	$-0.209645\pi$
$883$	47.0000			1.58168			0.790838	+	0.612026i	$0.209645\pi$
$884$		0			0
$885$	−30.0000			−1.00844
$886$	33.7750	−	19.5000i	1.13469	−	0.655115i
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	0.925332	−	0.379157i	$-0.123786\pi$
$887$	4.00000	+	6.92820i	0.134307	+	0.232626i	−0.791026	+	0.611783i	$0.790453\pi$
$888$	−4.50000	+	7.79423i	−0.151010	+	0.261557i
$889$		−	16.0000i		−	0.536623i
$890$	−5.19615	−	3.00000i	−0.174175	−	0.100560i
$891$	15.5885	+	9.00000i	0.522233	+	0.301511i
$892$		−	21.0000i		−	0.703132i
$893$	−39.0000	+	67.5500i	−1.30509	+	2.26047i
$894$	27.0000	+	46.7654i	0.903015	+	1.56407i
$895$	7.79423	−	4.50000i	0.260532	−	0.150418i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−26.0000			−0.867631
$899$	−6.92820	+	4.00000i	−0.231069	+	0.133407i
$900$	12.0000	+	20.7846i	0.400000	+	0.692820i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$		0			0
$903$	12.9904	+	7.50000i	0.432293	+	0.249584i
$904$	−1.73205	−	1.00000i	−0.0576072	−	0.0332595i
$905$		0			0
$906$	−13.5000	+	23.3827i	−0.448507	+	0.776838i
$907$	−4.50000	−	7.79423i	−0.149420	−	0.258803i	0.781593	−	0.623788i	$-0.214407\pi$
$907$	−4.50000	−	7.79423i	−0.149420	−	0.258803i	−0.931013	+	0.364985i	$0.881074\pi$
$908$	−20.7846	+	12.0000i	−0.689761	+	0.398234i
$909$	−24.0000			−0.796030
$910$		0			0
$911$	−54.0000			−1.78910			−0.894550	−	0.446968i	$-0.852504\pi$
$911$	−54.0000			−1.78910			−0.894550	+	0.446968i	$0.852504\pi$
$912$	15.5885	−	9.00000i	0.516185	−	0.298020i
$913$		0			0
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$			24.0000i			0.793416i
$916$	−12.9904	−	7.50000i	−0.429214	−	0.247807i
$917$	0.866025	+	0.500000i	0.0285987	+	0.0165115i
$918$			27.0000i			0.891133i
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	−0.993208	−	0.116348i	$-0.962881\pi$
$919$	−12.0000	+	20.7846i	−0.395843	+	0.685621i	0.597365	+	0.801970i	$0.296214\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$	−36.3731	+	21.0000i	−1.19853	+	0.691974i
$922$	21.0000			0.691598
$923$		0			0
$924$	6.00000			0.197386
$925$	10.3923	−	6.00000i	0.341697	−	0.197279i
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$	−24.0000	+	41.5692i	−0.788263	+	1.36531i
$928$		−	2.00000i		−	0.0656532i
$929$	−31.1769	−	18.0000i	−1.02288	−	0.590561i	−0.107944	−	0.994157i	$-0.534427\pi$
$929$	−31.1769	−	18.0000i	−1.02288	−	0.590561i	−0.914937	+	0.403596i	$0.867760\pi$
$930$	−10.3923	−	6.00000i	−0.340777	−	0.196748i
$931$		−	36.0000i		−	1.17985i
$932$	5.50000	−	9.52628i	0.180158	−	0.312044i
$933$	−27.0000	−	46.7654i	−0.883940	−	1.53103i
$934$	17.3205	−	10.0000i	0.566744	−	0.327210i
$935$	6.00000			0.196221
$936$		0			0
$937$	−42.0000			−1.37208			−0.686040	−	0.727564i	$-0.740653\pi$
$937$	−42.0000			−1.37208			−0.686040	+	0.727564i	$0.740653\pi$
$938$	1.73205	−	1.00000i	0.0565535	−	0.0326512i
$939$	−1.50000	−	2.59808i	−0.0489506	−	0.0847850i
$940$	−6.50000	+	11.2583i	−0.212007	+	0.367206i
$941$		−	25.0000i		−	0.814977i	−0.913210	−	0.407488i	$-0.866405\pi$
$941$		−	25.0000i		−	0.814977i	0.913210	−	0.407488i	$-0.133595\pi$
$942$	25.9808	+	15.0000i	0.846499	+	0.488726i
$943$		0			0
$944$		−	10.0000i		−	0.325472i
$945$	−4.50000	+	7.79423i	−0.146385	+	0.253546i
$946$	5.00000	+	8.66025i	0.162564	+	0.281569i
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	−0.731417	−	0.681930i	$-0.761141\pi$
$947$	−15.5885	+	9.00000i	−0.506557	+	0.292461i	0.224860	+	0.974391i	$0.427807\pi$
$948$	−12.0000			−0.389742
$949$		0			0
$950$	−24.0000			−0.778663
$951$	−46.7654	+	27.0000i	−1.51647	+	0.875535i
$952$	1.50000	+	2.59808i	0.0486153	+	0.0842041i
$953$	11.5000	−	19.9186i	0.372522	−	0.645226i	−0.617431	−	0.786625i	$-0.711827\pi$
$953$	11.5000	−	19.9186i	0.372522	−	0.645226i	0.989953	+	0.141399i	$0.0451599\pi$
$954$		−	72.0000i		−	2.33109i
$955$	−8.66025	−	5.00000i	−0.280239	−	0.161796i
$956$	−7.79423	−	4.50000i	−0.252083	−	0.145540i
$957$			12.0000i			0.387905i
$958$	1.50000	−	2.59808i	0.0484628	−	0.0839400i
$959$	6.00000	+	10.3923i	0.193750	+	0.335585i
$960$	2.59808	−	1.50000i	0.0838525	−	0.0484123i
$961$	15.0000			0.483871
$962$		0			0
$963$	−24.0000			−0.773389
$964$	−15.5885	+	9.00000i	−0.502070	+	0.289870i
$965$	−8.00000	−	13.8564i	−0.257529	−	0.446054i
$966$	6.00000	−	10.3923i	0.193047	−	0.334367i
$967$		−	23.0000i		−	0.739630i	−0.929105	−	0.369815i	$-0.879421\pi$
$967$		−	23.0000i		−	0.739630i	0.929105	−	0.369815i	$-0.120579\pi$
$968$	−6.06218	−	3.50000i	−0.194846	−	0.112494i
$969$	−46.7654	−	27.0000i	−1.50232	−	0.867365i
$970$		−	14.0000i		−	0.449513i
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	−0.720224	−	0.693742i	$-0.755961\pi$
$971$	7.50000	−	12.9904i	0.240686	−	0.416881i	0.960910	+	0.276861i	$0.0892941\pi$
$972$		0			0
$973$	6.06218	−	3.50000i	0.194344	−	0.112205i
$974$	16.0000			0.512673
$975$		0			0
$976$	−8.00000			−0.256074
$977$	25.9808	−	15.0000i	0.831198	−	0.479893i	−0.0230645	−	0.999734i	$-0.507342\pi$
$977$	25.9808	−	15.0000i	0.831198	−	0.479893i	0.854263	+	0.519841i	$0.174009\pi$
$978$	−6.00000	−	10.3923i	−0.191859	−	0.332309i
$979$	−6.00000	+	10.3923i	−0.191761	+	0.332140i
$980$		−	6.00000i		−	0.191663i
$981$	98.7269	+	57.0000i	3.15211	+	1.81987i
$982$	4.33013	+	2.50000i	0.138180	+	0.0797782i
$983$		−	31.0000i		−	0.988746i	−0.869250	−	0.494373i	$-0.835398\pi$
$983$		−	31.0000i		−	0.988746i	0.869250	−	0.494373i	$-0.164602\pi$
$984$		0			0
$985$	−4.50000	−	7.79423i	−0.143382	−	0.248345i
$986$	−5.19615	+	3.00000i	−0.165479	+	0.0955395i
$987$	39.0000			1.24138
$988$		0			0
$989$	20.0000			0.635963
$990$	−10.3923	+	6.00000i	−0.330289	+	0.190693i
$991$	15.0000	+	25.9808i	0.476491	+	0.825306i	0.999637	−	0.0269367i	$-0.00857526\pi$
$991$	15.0000	+	25.9808i	0.476491	+	0.825306i	−0.523146	+	0.852243i	$0.675242\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		−	12.0000i		−	0.380808i
$994$	−4.33013	−	2.50000i	−0.137343	−	0.0792952i
$995$	−8.66025	−	5.00000i	−0.274549	−	0.158511i
$996$		0			0
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	−0.775923	−	0.630828i	$-0.782715\pi$
$997$	5.00000	−	8.66025i	0.158352	−	0.274273i	0.934274	+	0.356555i	$0.116049\pi$
$998$	−16.0000	−	27.7128i	−0.506471	−	0.877234i
$999$	−23.3827	+	13.5000i	−0.739795	+	0.427121i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.e.d.23.1		4
13.2	odd	12		338.2.a.a.1.1		1
13.3	even	3		338.2.b.a.337.1		2
13.4	even	6	inner	338.2.e.d.147.1		4
13.5	odd	4		338.2.c.g.315.1		2
13.6	odd	12		338.2.c.g.191.1		2
13.7	odd	12		338.2.c.c.191.1		2
13.8	odd	4		338.2.c.c.315.1		2
13.9	even	3	inner	338.2.e.d.147.2		4
13.10	even	6		338.2.b.a.337.2		2
13.11	odd	12		26.2.a.b.1.1	✓	1
13.12	even	2	inner	338.2.e.d.23.2		4
39.2	even	12		3042.2.a.l.1.1		1
39.11	even	12		234.2.a.b.1.1		1
39.23	odd	6		3042.2.b.f.1351.1		2
39.29	odd	6		3042.2.b.f.1351.2		2
52.3	odd	6		2704.2.f.j.337.2		2
52.11	even	12		208.2.a.d.1.1		1
52.15	even	12		2704.2.a.n.1.1		1
52.23	odd	6		2704.2.f.j.337.1		2
65.24	odd	12		650.2.a.g.1.1		1
65.37	even	12		650.2.b.a.599.2		2
65.54	odd	12		8450.2.a.y.1.1		1
65.63	even	12		650.2.b.a.599.1		2
91.11	odd	12		1274.2.f.l.79.1		2
91.24	even	12		1274.2.f.a.79.1		2
91.37	odd	12		1274.2.f.l.1145.1		2
91.76	even	12		1274.2.a.o.1.1		1
91.89	even	12		1274.2.f.a.1145.1		2
104.11	even	12		832.2.a.a.1.1		1
104.37	odd	12		832.2.a.j.1.1		1
117.11	even	12		2106.2.e.t.1405.1		2
117.50	even	12		2106.2.e.t.703.1		2
117.76	odd	12		2106.2.e.h.703.1		2
117.115	odd	12		2106.2.e.h.1405.1		2
143.76	even	12		3146.2.a.a.1.1		1
156.11	odd	12		1872.2.a.m.1.1		1
195.89	even	12		5850.2.a.bn.1.1		1
195.128	odd	12		5850.2.e.v.5149.2		2
195.167	odd	12		5850.2.e.v.5149.1		2
208.11	even	12		3328.2.b.k.1665.1		2
208.37	odd	12		3328.2.b.g.1665.2		2
208.115	even	12		3328.2.b.k.1665.2		2
208.141	odd	12		3328.2.b.g.1665.1		2
221.50	odd	12		7514.2.a.i.1.1		1
247.37	even	12		9386.2.a.f.1.1		1
260.219	even	12		5200.2.a.c.1.1		1
312.11	odd	12		7488.2.a.v.1.1		1
312.245	even	12		7488.2.a.w.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.a.b.1.1	✓	1	13.11	odd	12
208.2.a.d.1.1		1	52.11	even	12
234.2.a.b.1.1		1	39.11	even	12
338.2.a.a.1.1		1	13.2	odd	12
338.2.b.a.337.1		2	13.3	even	3
338.2.b.a.337.2		2	13.10	even	6
338.2.c.c.191.1		2	13.7	odd	12
338.2.c.c.315.1		2	13.8	odd	4
338.2.c.g.191.1		2	13.6	odd	12
338.2.c.g.315.1		2	13.5	odd	4
338.2.e.d.23.1		4	1.1	even	1	trivial
338.2.e.d.23.2		4	13.12	even	2	inner
338.2.e.d.147.1		4	13.4	even	6	inner
338.2.e.d.147.2		4	13.9	even	3	inner
650.2.a.g.1.1		1	65.24	odd	12
650.2.b.a.599.1		2	65.63	even	12
650.2.b.a.599.2		2	65.37	even	12
832.2.a.a.1.1		1	104.11	even	12
832.2.a.j.1.1		1	104.37	odd	12
1274.2.a.o.1.1		1	91.76	even	12
1274.2.f.a.79.1		2	91.24	even	12
1274.2.f.a.1145.1		2	91.89	even	12
1274.2.f.l.79.1		2	91.11	odd	12
1274.2.f.l.1145.1		2	91.37	odd	12
1872.2.a.m.1.1		1	156.11	odd	12
2106.2.e.h.703.1		2	117.76	odd	12
2106.2.e.h.1405.1		2	117.115	odd	12
2106.2.e.t.703.1		2	117.50	even	12
2106.2.e.t.1405.1		2	117.11	even	12
2704.2.a.n.1.1		1	52.15	even	12
2704.2.f.j.337.1		2	52.23	odd	6
2704.2.f.j.337.2		2	52.3	odd	6
3042.2.a.l.1.1		1	39.2	even	12
3042.2.b.f.1351.1		2	39.23	odd	6
3042.2.b.f.1351.2		2	39.29	odd	6
3146.2.a.a.1.1		1	143.76	even	12
3328.2.b.g.1665.1		2	208.141	odd	12
3328.2.b.g.1665.2		2	208.37	odd	12
3328.2.b.k.1665.1		2	208.11	even	12
3328.2.b.k.1665.2		2	208.115	even	12
5200.2.a.c.1.1		1	260.219	even	12
5850.2.a.bn.1.1		1	195.89	even	12
5850.2.e.v.5149.1		2	195.167	odd	12
5850.2.e.v.5149.2		2	195.128	odd	12
7488.2.a.v.1.1		1	312.11	odd	12
7488.2.a.w.1.1		1	312.245	even	12
7514.2.a.i.1.1		1	221.50	odd	12
8450.2.a.y.1.1		1	65.54	odd	12
9386.2.a.f.1.1		1	247.37	even	12

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(1.50000 + 2.59808i) q^{3} +(0.500000 - 0.866025i) q^{4} +1.00000i q^{5} +(-2.59808 - 1.50000i) q^{6} +(-0.866025 - 0.500000i) q^{7} +1.00000i q^{8} +(-3.00000 + 5.19615i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-1.73205 + 1.00000i) q^{11} +3.00000 q^{12} +1.00000 q^{14} +(-2.59808 + 1.50000i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} -6.00000i q^{18} +(5.19615 + 3.00000i) q^{19} +(0.866025 + 0.500000i) q^{20} -3.00000i q^{21} +(1.00000 - 1.73205i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(-2.59808 + 1.50000i) q^{24} +4.00000 q^{25} -9.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(-1.00000 - 1.73205i) q^{29} +(1.50000 - 2.59808i) q^{30} -4.00000i q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} -3.00000i q^{34} +(0.500000 - 0.866025i) q^{35} +(3.00000 + 5.19615i) q^{36} +(2.59808 - 1.50000i) q^{37} -6.00000 q^{38} -1.00000 q^{40} +(1.50000 + 2.59808i) q^{42} +(-2.50000 + 4.33013i) q^{43} +2.00000i q^{44} +(-5.19615 - 3.00000i) q^{45} +(3.46410 + 2.00000i) q^{46} +13.0000i q^{47} +(1.50000 - 2.59808i) q^{48} +(-3.00000 - 5.19615i) q^{49} +(-3.46410 + 2.00000i) q^{50} -9.00000 q^{51} +12.0000 q^{53} +(7.79423 - 4.50000i) q^{54} +(-1.00000 - 1.73205i) q^{55} +(0.500000 - 0.866025i) q^{56} +18.0000i q^{57} +(1.73205 + 1.00000i) q^{58} +(8.66025 + 5.00000i) q^{59} +3.00000i q^{60} +(4.00000 - 6.92820i) q^{61} +(2.00000 + 3.46410i) q^{62} +(5.19615 - 3.00000i) q^{63} -1.00000 q^{64} +6.00000 q^{66} +(1.73205 - 1.00000i) q^{67} +(1.50000 + 2.59808i) q^{68} +(6.00000 - 10.3923i) q^{69} +1.00000i q^{70} +(-4.33013 - 2.50000i) q^{71} +(-5.19615 - 3.00000i) q^{72} -10.0000i q^{73} +(-1.50000 + 2.59808i) q^{74} +(6.00000 + 10.3923i) q^{75} +(5.19615 - 3.00000i) q^{76} +2.00000 q^{77} -4.00000 q^{79} +(0.866025 - 0.500000i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-2.59808 - 1.50000i) q^{84} +(-2.59808 - 1.50000i) q^{85} -5.00000i q^{86} +(3.00000 - 5.19615i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(5.19615 - 3.00000i) q^{89} +6.00000 q^{90} -4.00000 q^{92} +(10.3923 - 6.00000i) q^{93} +(-6.50000 - 11.2583i) q^{94} +(-3.00000 + 5.19615i) q^{95} +3.00000i q^{96} +(12.1244 + 7.00000i) q^{97} +(5.19615 + 3.00000i) q^{98} -12.0000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{3} + 2 q^{4} - 12 q^{9} - 2 q^{10} + 12 q^{12} + 4 q^{14} - 2 q^{16} - 6 q^{17} + 4 q^{22} - 8 q^{23} + 16 q^{25} - 36 q^{27} - 4 q^{29} + 6 q^{30} + 2 q^{35} + 12 q^{36} - 24 q^{38} - 4 q^{40}+ \cdots - 12 q^{95}+O(q^{100}) \) 4 * q + 6 * q^3 + 2 * q^4 - 12 * q^9 - 2 * q^10 + 12 * q^12 + 4 * q^14 - 2 * q^16 - 6 * q^17 + 4 * q^22 - 8 * q^23 + 16 * q^25 - 36 * q^27 - 4 * q^29 + 6 * q^30 + 2 * q^35 + 12 * q^36 - 24 * q^38 - 4 * q^40 + 6 * q^42 - 10 * q^43 + 6 * q^48 - 12 * q^49 - 36 * q^51 + 48 * q^53 - 4 * q^55 + 2 * q^56 + 16 * q^61 + 8 * q^62 - 4 * q^64 + 24 * q^66 + 6 * q^68 + 24 * q^69 - 6 * q^74 + 24 * q^75 + 8 * q^77 - 16 * q^79 - 18 * q^81 + 12 * q^87 - 4 * q^88 + 24 * q^90 - 16 * q^92 - 26 * q^94 - 12 * q^95

Introduction

L-functions

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