LMFDB - Embedded newform 733.2.e.a.426.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [733,2,Mod(308,733)] 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("733.308"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(733, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 733 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	733.e (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,0,-2] 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:	$5.85303446816$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			426.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	733.426
Dual form			733.2.e.a.308.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} -1.73205i q^{5} +(3.00000 + 1.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{10} +3.46410i q^{11} +(1.00000 - 1.73205i) q^{12} +(-3.00000 + 5.19615i) q^{14} +(3.00000 + 1.73205i) q^{15} -5.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.50000 + 0.866025i) q^{18} -2.00000 q^{19} +1.73205i q^{20} +(6.00000 - 3.46410i) q^{21} +6.00000 q^{22} +(-6.00000 - 3.46410i) q^{23} +(3.00000 + 1.73205i) q^{24} +2.00000 q^{25} -4.00000 q^{27} +(3.00000 + 1.73205i) q^{28} +(3.00000 - 5.19615i) q^{30} +(2.00000 + 3.46410i) q^{31} +5.19615i q^{32} +(-6.00000 - 3.46410i) q^{33} +(4.50000 + 2.59808i) q^{34} +(-3.00000 + 5.19615i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} +3.46410i q^{38} -3.00000 q^{40} +(-3.00000 + 5.19615i) q^{41} +(-6.00000 - 10.3923i) q^{42} +(-9.00000 + 5.19615i) q^{43} -3.46410i q^{44} +(-1.50000 + 0.866025i) q^{45} +(-6.00000 + 10.3923i) q^{46} -6.00000 q^{47} +(5.00000 - 8.66025i) q^{48} +(2.50000 + 4.33013i) q^{49} -3.46410i q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.50000 + 2.59808i) q^{53} +6.92820i q^{54} +6.00000 q^{55} +(-3.00000 + 5.19615i) q^{56} +(2.00000 - 3.46410i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(3.50000 + 6.06218i) q^{61} +(6.00000 - 3.46410i) q^{62} +3.46410i q^{63} -1.00000 q^{64} +(-6.00000 + 10.3923i) q^{66} +6.92820i q^{67} +(1.50000 - 2.59808i) q^{68} +(12.0000 - 6.92820i) q^{69} +(9.00000 + 5.19615i) q^{70} +(-3.00000 - 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-1.50000 - 0.866025i) q^{74} +(-2.00000 + 3.46410i) q^{75} +2.00000 q^{76} +(6.00000 - 10.3923i) q^{77} +(8.00000 - 13.8564i) q^{79} +8.66025i q^{80} +(5.50000 - 9.52628i) q^{81} +(9.00000 + 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(4.50000 + 2.59808i) q^{85} +(9.00000 + 15.5885i) q^{86} +6.00000 q^{88} +(-4.50000 - 7.79423i) q^{89} +(1.50000 + 2.59808i) q^{90} +(6.00000 + 3.46410i) q^{92} -8.00000 q^{93} +10.3923i q^{94} +3.46410i q^{95} +(-9.00000 - 5.19615i) q^{96} +(-6.50000 - 11.2583i) q^{97} +(7.50000 - 4.33013i) q^{98} +(3.00000 - 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} - q^{9} - 6 q^{10} + 2 q^{12} - 6 q^{14} + 6 q^{15} - 10 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 12 q^{21} + 12 q^{22} - 12 q^{23} + 6 q^{24} + 4 q^{25} - 8 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 - q^9 - 6 * q^10 + 2 * q^12 - 6 * q^14 + 6 * q^15 - 10 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 12 * q^21 + 12 * q^22 - 12 * q^23 + 6 * q^24 + 4 * q^25 - 8 * q^27 + 6 * q^28 + 6 * q^30 + 4 * q^31 - 12 * q^33 + 9 * q^34 - 6 * q^35 + q^36 + q^37 - 6 * q^40 - 6 * q^41 - 12 * q^42 - 18 * q^43 - 3 * q^45 - 12 * q^46 - 12 * q^47 + 10 * q^48 + 5 * q^49 - 6 * q^51 - 3 * q^53 + 12 * q^55 - 6 * q^56 + 4 * q^57 - 6 * q^59 - 6 * q^60 + 7 * q^61 + 12 * q^62 - 2 * q^64 - 12 * q^66 + 3 * q^68 + 24 * q^69 + 18 * q^70 - 6 * q^71 - 3 * q^72 - 14 * q^73 - 3 * q^74 - 4 * q^75 + 4 * q^76 + 12 * q^77 + 16 * q^79 + 11 * q^81 + 18 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^85 + 18 * q^86 + 12 * q^88 - 9 * q^89 + 3 * q^90 + 12 * q^92 - 16 * q^93 - 18 * q^96 - 13 * q^97 + 15 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/733\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.73205i		−	1.22474i	−0.790569	−	0.612372i	$-0.790215\pi$
$2$		−	1.73205i		−	1.22474i	0.790569	−	0.612372i	$-0.209785\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	0.418432	+	0.908248i	$0.362580\pi$
$3$	−1.00000	+	1.73205i	−0.577350	+	1.00000i	−0.995782	+	0.0917517i	$0.970753\pi$
$4$	−1.00000			−0.500000
$5$		−	1.73205i		−	0.774597i	−0.921954	−	0.387298i	$-0.873408\pi$
$5$		−	1.73205i		−	0.774597i	0.921954	−	0.387298i	$-0.126592\pi$
$6$	3.00000	+	1.73205i	1.22474	+	0.707107i
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−3.00000	−	1.73205i	−1.13389	−	0.654654i	−0.944911	+	0.327327i	$0.893852\pi$
$8$		−	1.73205i		−	0.612372i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.00000			−0.948683
$11$			3.46410i			1.04447i	0.852803	+	0.522233i	$0.174901\pi$
$11$			3.46410i			1.04447i	−0.852803	+	0.522233i	$0.825099\pi$
$12$	1.00000	−	1.73205i	0.288675	−	0.500000i
$13$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$13$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$14$	−3.00000	+	5.19615i	−0.801784	+	1.38873i
$15$	3.00000	+	1.73205i	0.774597	+	0.447214i
$16$	−5.00000			−1.25000
$17$	−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	$0.285189\pi$
$18$	−1.50000	+	0.866025i	−0.353553	+	0.204124i
$19$	−2.00000			−0.458831			−0.229416	−	0.973329i	$-0.573682\pi$
$19$	−2.00000			−0.458831			−0.229416	+	0.973329i	$0.573682\pi$
$20$			1.73205i			0.387298i
$21$	6.00000	−	3.46410i	1.30931	−	0.755929i
$22$	6.00000			1.27920
$23$	−6.00000	−	3.46410i	−1.25109	−	0.722315i	−0.279761	−	0.960070i	$-0.590255\pi$
$23$	−6.00000	−	3.46410i	−1.25109	−	0.722315i	−0.971325	+	0.237754i	$0.923589\pi$
$24$	3.00000	+	1.73205i	0.612372	+	0.353553i
$25$	2.00000			0.400000
$26$		0			0
$27$	−4.00000			−0.769800
$28$	3.00000	+	1.73205i	0.566947	+	0.327327i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$	3.00000	−	5.19615i	0.547723	−	0.948683i
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	0.987829	−	0.155543i	$-0.0497126\pi$
$31$	2.00000	+	3.46410i	0.359211	+	0.622171i	−0.628619	+	0.777714i	$0.716379\pi$
$32$			5.19615i			0.918559i
$33$	−6.00000	−	3.46410i	−1.04447	−	0.603023i
$34$	4.50000	+	2.59808i	0.771744	+	0.445566i
$35$	−3.00000	+	5.19615i	−0.507093	+	0.878310i
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$			3.46410i			0.561951i
$39$		0			0
$40$	−3.00000			−0.474342
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$	−6.00000	−	10.3923i	−0.925820	−	1.60357i
$43$	−9.00000	+	5.19615i	−1.37249	+	0.792406i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−9.00000	+	5.19615i	−1.37249	+	0.792406i	−0.381246	+	0.924473i	$0.624505\pi$
$44$		−	3.46410i		−	0.522233i
$45$	−1.50000	+	0.866025i	−0.223607	+	0.129099i
$46$	−6.00000	+	10.3923i	−0.884652	+	1.53226i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	5.00000	−	8.66025i	0.721688	−	1.25000i
$49$	2.50000	+	4.33013i	0.357143	+	0.618590i
$50$		−	3.46410i		−	0.489898i
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	−0.950464	−	0.310835i	$-0.899391\pi$
$53$	−1.50000	+	2.59808i	−0.206041	+	0.356873i	0.744423	+	0.667708i	$0.232725\pi$
$54$			6.92820i			0.942809i
$55$	6.00000			0.809040
$56$	−3.00000	+	5.19615i	−0.400892	+	0.694365i
$57$	2.00000	−	3.46410i	0.264906	−	0.458831i
$58$		0			0
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	−3.00000	−	1.73205i	−0.387298	−	0.223607i
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	0.998264	−	0.0588933i	$-0.0187572\pi$
$61$	3.50000	+	6.06218i	0.448129	+	0.776182i	−0.550135	+	0.835076i	$0.685424\pi$
$62$	6.00000	−	3.46410i	0.762001	−	0.439941i
$63$			3.46410i			0.436436i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000	+	10.3923i	−0.738549	+	1.27920i
$67$			6.92820i			0.846415i	0.906033	+	0.423207i	$0.139096\pi$
$67$			6.92820i			0.846415i	−0.906033	+	0.423207i	$0.860904\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	12.0000	−	6.92820i	1.44463	−	0.834058i
$70$	9.00000	+	5.19615i	1.07571	+	0.621059i
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	0.311305	−	0.950310i	$-0.399234\pi$
$71$	−3.00000	−	1.73205i	−0.356034	−	0.205557i	−0.667340	+	0.744753i	$0.732567\pi$
$72$	−1.50000	+	0.866025i	−0.176777	+	0.102062i
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	0.0869195	+	0.996215i	$0.472298\pi$
$73$	−7.00000	+	12.1244i	−0.819288	+	1.41905i	−0.906208	+	0.422833i	$0.861036\pi$
$74$	−1.50000	−	0.866025i	−0.174371	−	0.100673i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	2.00000			0.229416
$77$	6.00000	−	10.3923i	0.683763	−	1.18431i
$78$		0			0
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$			8.66025i			0.968246i
$81$	5.50000	−	9.52628i	0.611111	−	1.05848i
$82$	9.00000	+	5.19615i	0.993884	+	0.573819i
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$	−6.00000	+	3.46410i	−0.654654	+	0.377964i
$85$	4.50000	+	2.59808i	0.488094	+	0.281801i
$86$	9.00000	+	15.5885i	0.970495	+	1.68095i
$87$		0			0
$88$	6.00000			0.639602
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	0.522654	−	0.852545i	$-0.324942\pi$
$89$	−4.50000	−	7.79423i	−0.476999	−	0.826187i	−0.999653	+	0.0263586i	$0.991609\pi$
$90$	1.50000	+	2.59808i	0.158114	+	0.273861i
$91$		0			0
$92$	6.00000	+	3.46410i	0.625543	+	0.361158i
$93$	−8.00000			−0.829561
$94$			10.3923i			1.07188i
$95$			3.46410i			0.355409i
$96$	−9.00000	−	5.19615i	−0.918559	−	0.530330i
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	−0.980622	−	0.195911i	$-0.937234\pi$
$97$	−6.50000	−	11.2583i	−0.659975	−	1.14311i	0.320647	−	0.947199i	$-0.396100\pi$
$98$	7.50000	−	4.33013i	0.757614	−	0.437409i
$99$	3.00000	−	1.73205i	0.301511	−	0.174078i
$100$	−2.00000			−0.200000
$101$	10.5000	+	6.06218i	1.04479	+	0.603209i	0.921186	−	0.389123i	$-0.127222\pi$
$101$	10.5000	+	6.06218i	1.04479	+	0.603209i	0.123603	+	0.992332i	$0.460555\pi$
$102$	−9.00000	+	5.19615i	−0.891133	+	0.514496i
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$		0			0
$105$	−6.00000	−	10.3923i	−0.585540	−	1.01419i
$106$	4.50000	+	2.59808i	0.437079	+	0.252347i
$107$	12.0000	−	6.92820i	1.16008	−	0.669775i	0.208760	−	0.977967i	$-0.433057\pi$
$107$	12.0000	−	6.92820i	1.16008	−	0.669775i	0.951324	+	0.308192i	$0.0997240\pi$
$108$	4.00000			0.384900
$109$		−	8.66025i		−	0.829502i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$		−	8.66025i		−	0.829502i	0.909935	−	0.414751i	$-0.136131\pi$
$110$		−	10.3923i		−	0.990867i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$	15.0000	+	8.66025i	1.41737	+	0.818317i
$113$	12.0000	−	6.92820i	1.12887	−	0.651751i	0.185216	−	0.982698i	$-0.440702\pi$
$113$	12.0000	−	6.92820i	1.12887	−	0.651751i	0.943649	+	0.330947i	$0.107368\pi$
$114$	−6.00000	−	3.46410i	−0.561951	−	0.324443i
$115$	−6.00000	+	10.3923i	−0.559503	+	0.969087i
$116$		0			0
$117$		0			0
$118$	−9.00000	+	5.19615i	−0.828517	+	0.478345i
$119$	9.00000	−	5.19615i	0.825029	−	0.476331i
$120$	3.00000	−	5.19615i	0.273861	−	0.474342i
$121$	−1.00000			−0.0909091
$122$	10.5000	−	6.06218i	0.950625	−	0.548844i
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$		−	12.1244i		−	1.08444i
$126$	6.00000			0.534522
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−10.0000	−	17.3205i	−0.887357	−	1.53695i	−0.0443678	−	0.999015i	$-0.514127\pi$
$128$			12.1244i			1.07165i
$129$		−	20.7846i		−	1.82998i
$130$		0			0
$131$		−	13.8564i		−	1.21064i	−0.795982	−	0.605320i	$-0.793045\pi$
$131$		−	13.8564i		−	1.21064i	0.795982	−	0.605320i	$-0.206955\pi$
$132$	6.00000	+	3.46410i	0.522233	+	0.301511i
$133$	6.00000	+	3.46410i	0.520266	+	0.300376i
$134$	12.0000			1.03664
$135$			6.92820i			0.596285i
$136$	4.50000	+	2.59808i	0.385872	+	0.222783i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$	−12.0000	−	20.7846i	−1.02151	−	1.76930i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$	3.00000	−	5.19615i	0.253546	−	0.439155i
$141$	6.00000	−	10.3923i	0.505291	−	0.875190i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$		0			0
$144$	2.50000	+	4.33013i	0.208333	+	0.360844i
$145$		0			0
$146$	21.0000	+	12.1244i	1.73797	+	1.00342i
$147$	−10.0000			−0.824786
$148$	−0.500000	+	0.866025i	−0.0410997	+	0.0711868i
$149$	−4.50000	−	2.59808i	−0.368654	−	0.212843i	0.304216	−	0.952603i	$-0.401606\pi$
$149$	−4.50000	−	2.59808i	−0.368654	−	0.212843i	−0.672870	+	0.739760i	$0.734939\pi$
$150$	6.00000	+	3.46410i	0.489898	+	0.282843i
$151$			13.8564i			1.12762i	0.825905	+	0.563809i	$0.190665\pi$
$151$			13.8564i			1.12762i	−0.825905	+	0.563809i	$0.809335\pi$
$152$			3.46410i			0.280976i
$153$	3.00000			0.242536
$154$	−18.0000	−	10.3923i	−1.45048	−	0.837436i
$155$	6.00000	−	3.46410i	0.481932	−	0.278243i
$156$		0			0
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	0.997609	+	0.0691164i	$0.0220180\pi$
$157$	7.00000	+	12.1244i	0.558661	+	0.967629i	−0.438948	+	0.898513i	$0.644649\pi$
$158$	−24.0000	−	13.8564i	−1.90934	−	1.10236i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$	9.00000			0.711512
$161$	12.0000	+	20.7846i	0.945732	+	1.63806i
$162$	−16.5000	−	9.52628i	−1.29636	−	0.748455i
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	−0.902528	−	0.430632i	$-0.858291\pi$
$163$	−1.00000	+	1.73205i	−0.0783260	+	0.135665i	0.824202	+	0.566296i	$0.191624\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$	−6.00000	+	10.3923i	−0.467099	+	0.809040i
$166$	−18.0000	+	10.3923i	−1.39707	+	0.806599i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	−6.00000	−	10.3923i	−0.462910	−	0.801784i
$169$	−6.50000	+	11.2583i	−0.500000	+	0.866025i
$170$	4.50000	−	7.79423i	0.345134	−	0.597790i
$171$	1.00000	+	1.73205i	0.0764719	+	0.132453i
$172$	9.00000	−	5.19615i	0.686244	−	0.396203i
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	−0.426329	−	0.904568i	$-0.640193\pi$
$173$	7.50000	−	12.9904i	0.570214	−	0.987640i	0.996544	−	0.0830722i	$-0.0264732\pi$
$174$		0			0
$175$	−6.00000	−	3.46410i	−0.453557	−	0.261861i
$176$		−	17.3205i		−	1.30558i
$177$	12.0000			0.901975
$178$	−13.5000	+	7.79423i	−1.01187	+	0.584202i
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	1.50000	−	0.866025i	0.111803	−	0.0645497i
$181$	3.50000	+	6.06218i	0.260153	+	0.450598i	0.966282	−	0.257485i	$-0.0828937\pi$
$181$	3.50000	+	6.06218i	0.260153	+	0.450598i	−0.706129	+	0.708083i	$0.749560\pi$
$182$		0			0
$183$	−14.0000			−1.03491
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$	−1.50000	−	0.866025i	−0.110282	−	0.0636715i
$186$			13.8564i			1.01600i
$187$	−9.00000	−	5.19615i	−0.658145	−	0.379980i
$188$	6.00000			0.437595
$189$	12.0000	+	6.92820i	0.872872	+	0.503953i
$190$	6.00000			0.435286
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	1.00000	−	1.73205i	0.0721688	−	0.125000i
$193$		−	15.5885i		−	1.12208i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$		−	15.5885i		−	1.12208i	0.827788	−	0.561041i	$-0.189599\pi$
$194$	−19.5000	+	11.2583i	−1.40002	+	0.808301i
$195$		0			0
$196$	−2.50000	−	4.33013i	−0.178571	−	0.309295i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$		−	3.46410i		−	0.244949i
$201$	−12.0000	−	6.92820i	−0.846415	−	0.488678i
$202$	10.5000	−	18.1865i	0.738777	−	1.27960i
$203$		0			0
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$	9.00000	+	5.19615i	0.628587	+	0.362915i
$206$	12.0000			0.836080
$207$			6.92820i			0.481543i
$208$		0			0
$209$		−	6.92820i		−	0.479234i
$210$	−18.0000	+	10.3923i	−1.24212	+	0.717137i
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	0.972346	+	0.233544i	$0.0750324\pi$
$211$	10.0000	+	17.3205i	0.688428	+	1.19239i	−0.283918	+	0.958849i	$0.591634\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$	6.00000	−	3.46410i	0.411113	−	0.237356i
$214$	−12.0000	−	20.7846i	−0.820303	−	1.42081i
$215$	9.00000	+	15.5885i	0.613795	+	1.06312i
$216$			6.92820i			0.471405i
$217$		−	13.8564i		−	0.940634i
$218$	−15.0000			−1.01593
$219$	−14.0000	−	24.2487i	−0.946032	−	1.63858i
$220$	−6.00000			−0.404520
$221$		0			0
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	0.897564	−	0.440884i	$-0.145335\pi$
$223$	1.00000	+	1.73205i	0.0669650	+	0.115987i	−0.830599	+	0.556871i	$0.812002\pi$
$224$	9.00000	−	15.5885i	0.601338	−	1.04155i
$225$	−1.00000	−	1.73205i	−0.0666667	−	0.115470i
$226$	−12.0000	−	20.7846i	−0.798228	−	1.38257i
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	0.685722	−	0.727864i	$-0.259487\pi$
$227$	6.00000	+	3.46410i	0.398234	+	0.229920i	−0.287488	+	0.957784i	$0.592820\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	−7.00000			−0.462573			−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000			−0.462573			−0.231287	+	0.972886i	$0.574293\pi$
$230$	18.0000	+	10.3923i	1.18688	+	0.685248i
$231$	12.0000	+	20.7846i	0.789542	+	1.36753i
$232$		0			0
$233$		−	13.8564i		−	0.907763i	−0.891062	−	0.453882i	$-0.850039\pi$
$233$		−	13.8564i		−	0.907763i	0.891062	−	0.453882i	$-0.149961\pi$
$234$		0			0
$235$			10.3923i			0.677919i
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	16.0000	+	27.7128i	1.03931	+	1.80014i
$238$	−9.00000	−	15.5885i	−0.583383	−	1.01045i
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	−0.995223	−	0.0976302i	$-0.968874\pi$
$239$	−9.00000	−	15.5885i	−0.582162	−	1.00833i	0.413061	−	0.910703i	$-0.364460\pi$
$240$	−15.0000	−	8.66025i	−0.968246	−	0.559017i
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	−0.998443	−	0.0557856i	$-0.982234\pi$
$241$	−8.50000	−	14.7224i	−0.547533	−	0.948355i	0.450910	−	0.892570i	$-0.351100\pi$
$242$			1.73205i			0.111340i
$243$	5.00000	+	8.66025i	0.320750	+	0.555556i
$244$	−3.50000	−	6.06218i	−0.224065	−	0.388091i
$245$	7.50000	−	4.33013i	0.479157	−	0.276642i
$246$	−18.0000	+	10.3923i	−1.14764	+	0.662589i
$247$		0			0
$248$	6.00000	−	3.46410i	0.381000	−	0.219971i
$249$	24.0000			1.52094
$250$	−21.0000			−1.32816
$251$	−18.0000	+	10.3923i	−1.13615	+	0.655956i	−0.945474	−	0.325697i	$-0.894401\pi$
$251$	−18.0000	+	10.3923i	−1.13615	+	0.655956i	−0.190676	+	0.981653i	$0.561068\pi$
$252$		−	3.46410i		−	0.218218i
$253$	12.0000	−	20.7846i	0.754434	−	1.30672i
$254$	−30.0000	+	17.3205i	−1.88237	+	1.08679i
$255$	−9.00000	+	5.19615i	−0.563602	+	0.325396i
$256$	19.0000			1.18750
$257$	−7.50000	+	4.33013i	−0.467837	+	0.270106i	−0.715334	−	0.698783i	$-0.753725\pi$
$257$	−7.50000	+	4.33013i	−0.467837	+	0.270106i	0.247497	+	0.968889i	$0.420392\pi$
$258$	−36.0000			−2.24126
$259$	−3.00000	+	1.73205i	−0.186411	+	0.107624i
$260$		0			0
$261$		0			0
$262$	−24.0000			−1.48272
$263$	12.0000			0.739952			0.369976	−	0.929041i	$-0.379366\pi$
$263$	12.0000			0.739952			0.369976	+	0.929041i	$0.379366\pi$
$264$	−6.00000	+	10.3923i	−0.369274	+	0.639602i
$265$	4.50000	+	2.59808i	0.276433	+	0.159599i
$266$	6.00000	−	10.3923i	0.367884	−	0.637193i
$267$	18.0000			1.10158
$268$		−	6.92820i		−	0.423207i
$269$			1.73205i			0.105605i	0.998605	+	0.0528025i	$0.0168154\pi$
$269$			1.73205i			0.105605i	−0.998605	+	0.0528025i	$0.983185\pi$
$270$	12.0000			0.730297
$271$	−9.00000	+	5.19615i	−0.546711	+	0.315644i	−0.747794	−	0.663930i	$-0.768887\pi$
$271$	−9.00000	+	5.19615i	−0.546711	+	0.315644i	0.201083	+	0.979574i	$0.435554\pi$
$272$	7.50000	−	12.9904i	0.454754	−	0.787658i
$273$		0			0
$274$		0			0
$275$			6.92820i			0.417786i
$276$	−12.0000	+	6.92820i	−0.722315	+	0.417029i
$277$	12.0000	+	6.92820i	0.721010	+	0.416275i	0.815124	−	0.579286i	$-0.196669\pi$
$277$	12.0000	+	6.92820i	0.721010	+	0.416275i	−0.0941142	+	0.995561i	$0.530002\pi$
$278$			3.46410i			0.207763i
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$	9.00000	+	5.19615i	0.537853	+	0.310530i
$281$	−7.50000	+	4.33013i	−0.447412	+	0.258314i	−0.706737	−	0.707477i	$-0.749833\pi$
$281$	−7.50000	+	4.33013i	−0.447412	+	0.258314i	0.259324	+	0.965790i	$0.416500\pi$
$282$	−18.0000	−	10.3923i	−1.07188	−	0.618853i
$283$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$283$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$284$	3.00000	+	1.73205i	0.178017	+	0.102778i
$285$	−6.00000	−	3.46410i	−0.355409	−	0.205196i
$286$		0			0
$287$	18.0000	−	10.3923i	1.06251	−	0.613438i
$288$	4.50000	−	2.59808i	0.265165	−	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	26.0000			1.52415
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$		0			0		1.00000			$0$
$293$		0			0		−1.00000			$\pi$
$294$			17.3205i			1.01015i
$295$	−9.00000	+	5.19615i	−0.524000	+	0.302532i
$296$	−1.50000	−	0.866025i	−0.0871857	−	0.0503367i
$297$		−	13.8564i		−	0.804030i
$298$	−4.50000	+	7.79423i	−0.260678	+	0.451508i
$299$		0			0
$300$	2.00000	−	3.46410i	0.115470	−	0.200000i
$301$	36.0000			2.07501
$302$	24.0000			1.38104
$303$	−21.0000	+	12.1244i	−1.20642	+	0.696526i
$304$	10.0000			0.573539
$305$	10.5000	−	6.06218i	0.601228	−	0.347119i
$306$		−	5.19615i		−	0.297044i
$307$	1.00000	+	1.73205i	0.0570730	+	0.0988534i	0.893150	−	0.449758i	$-0.148490\pi$
$307$	1.00000	+	1.73205i	0.0570730	+	0.0988534i	−0.836077	+	0.548612i	$0.815157\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	−12.0000	−	6.92820i	−0.682656	−	0.394132i
$310$	−6.00000	−	10.3923i	−0.340777	−	0.590243i
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	−0.582640	−	0.812731i	$-0.697980\pi$
$311$	−3.00000	+	1.73205i	−0.170114	+	0.0982156i	0.412525	+	0.910946i	$0.364647\pi$
$312$		0			0
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	21.0000	−	12.1244i	1.18510	−	0.684217i
$315$	6.00000			0.338062
$316$	−8.00000	+	13.8564i	−0.450035	+	0.779484i
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	−0.943750	−	0.330661i	$-0.892728\pi$
$317$	−13.5000	−	23.3827i	−0.758236	−	1.31330i	0.185514	−	0.982642i	$-0.440605\pi$
$318$	−9.00000	+	5.19615i	−0.504695	+	0.291386i
$319$		0			0
$320$			1.73205i			0.0968246i
$321$			27.7128i			1.54678i
$322$	36.0000	−	20.7846i	2.00620	−	1.15828i
$323$	3.00000	−	5.19615i	0.166924	−	0.289122i
$324$	−5.50000	+	9.52628i	−0.305556	+	0.529238i
$325$		0			0
$326$	3.00000	+	1.73205i	0.166155	+	0.0959294i
$327$	15.0000	+	8.66025i	0.829502	+	0.478913i
$328$	9.00000	+	5.19615i	0.496942	+	0.286910i
$329$	18.0000	+	10.3923i	0.992372	+	0.572946i
$330$	18.0000	+	10.3923i	0.990867	+	0.572078i
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−1.00000			−0.0547997
$334$		0			0
$335$	12.0000			0.655630
$336$	−30.0000	+	17.3205i	−1.63663	+	0.944911i
$337$	4.50000	−	2.59808i	0.245131	−	0.141526i	−0.372402	−	0.928072i	$-0.621466\pi$
$337$	4.50000	−	2.59808i	0.245131	−	0.141526i	0.617533	+	0.786545i	$0.288132\pi$
$338$	19.5000	+	11.2583i	1.06066	+	0.612372i
$339$			27.7128i			1.50515i
$340$	−4.50000	−	2.59808i	−0.244047	−	0.140900i
$341$	−12.0000	+	6.92820i	−0.649836	+	0.375183i
$342$	3.00000	−	1.73205i	0.162221	−	0.0936586i
$343$			6.92820i			0.374088i
$344$	9.00000	+	15.5885i	0.485247	+	0.840473i
$345$	−12.0000	−	20.7846i	−0.646058	−	1.11901i
$346$	−22.5000	−	12.9904i	−1.20961	−	0.698367i
$347$	18.0000			0.966291			0.483145	−	0.875540i	$-0.339494\pi$
$347$	18.0000			0.966291			0.483145	+	0.875540i	$0.339494\pi$
$348$		0			0
$349$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$349$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$350$	−6.00000	+	10.3923i	−0.320713	+	0.555492i
$351$		0			0
$352$	−18.0000			−0.959403
$353$			20.7846i			1.10625i	0.833097	+	0.553127i	$0.186565\pi$
$353$			20.7846i			1.10625i	−0.833097	+	0.553127i	$0.813435\pi$
$354$		−	20.7846i		−	1.10469i
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	4.50000	+	7.79423i	0.238500	+	0.413093i
$357$			20.7846i			1.10004i
$358$	18.0000	+	10.3923i	0.951330	+	0.549250i
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	−0.663123	−	0.748511i	$-0.730769\pi$
$359$	6.00000	−	10.3923i	0.316668	−	0.548485i	0.979791	+	0.200026i	$0.0641026\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	−15.0000			−0.789474
$362$	10.5000	−	6.06218i	0.551868	−	0.318621i
$363$	1.00000	−	1.73205i	0.0524864	−	0.0909091i
$364$		0			0
$365$	21.0000	+	12.1244i	1.09919	+	0.634618i
$366$			24.2487i			1.26750i
$367$			20.7846i			1.08495i	0.840073	+	0.542474i	$0.182512\pi$
$367$			20.7846i			1.08495i	−0.840073	+	0.542474i	$0.817488\pi$
$368$	30.0000	+	17.3205i	1.56386	+	0.902894i
$369$	6.00000			0.312348
$370$	−1.50000	+	2.59808i	−0.0779813	+	0.135068i
$371$	9.00000	−	5.19615i	0.467257	−	0.269771i
$372$	8.00000			0.414781
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	21.0000	+	12.1244i	1.08444	+	0.626099i
$376$			10.3923i			0.535942i
$377$		0			0
$378$	12.0000	−	20.7846i	0.617213	−	1.06904i
$379$		−	10.3923i		−	0.533817i	−0.963722	−	0.266908i	$-0.913998\pi$
$379$		−	10.3923i		−	0.533817i	0.963722	−	0.266908i	$-0.0860021\pi$
$380$		−	3.46410i		−	0.177705i
$381$	40.0000			2.04926
$382$	9.00000	−	5.19615i	0.460480	−	0.265858i
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	−0.779143	−	0.626846i	$-0.784346\pi$
$383$	3.00000	−	5.19615i	0.153293	−	0.265511i	0.932436	+	0.361335i	$0.117679\pi$
$384$	−21.0000	−	12.1244i	−1.07165	−	0.618718i
$385$	−18.0000	−	10.3923i	−0.917365	−	0.529641i
$386$	−27.0000			−1.37426
$387$	9.00000	+	5.19615i	0.457496	+	0.264135i
$388$	6.50000	+	11.2583i	0.329988	+	0.571555i
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$		0			0
$391$	18.0000	−	10.3923i	0.910299	−	0.525561i
$392$	7.50000	−	4.33013i	0.378807	−	0.218704i
$393$	24.0000	+	13.8564i	1.21064	+	0.698963i
$394$			31.1769i			1.57067i
$395$	−24.0000	−	13.8564i	−1.20757	−	0.697191i
$396$	−3.00000	+	1.73205i	−0.150756	+	0.0870388i
$397$	−1.50000	+	0.866025i	−0.0752828	+	0.0434646i	−0.537169	−	0.843475i	$-0.680506\pi$
$397$	−1.50000	+	0.866025i	−0.0752828	+	0.0434646i	0.461886	+	0.886939i	$0.347173\pi$
$398$		0			0
$399$	−12.0000	+	6.92820i	−0.600751	+	0.346844i
$400$	−10.0000			−0.500000
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	−0.999598	−	0.0283431i	$-0.990977\pi$
$401$	−10.5000	−	18.1865i	−0.524345	−	0.908192i	0.475253	−	0.879849i	$-0.342356\pi$
$402$	−12.0000	+	20.7846i	−0.598506	+	1.03664i
$403$		0			0
$404$	−10.5000	−	6.06218i	−0.522395	−	0.301605i
$405$	−16.5000	−	9.52628i	−0.819892	−	0.473365i
$406$		0			0
$407$	3.00000	+	1.73205i	0.148704	+	0.0858546i
$408$	−9.00000	+	5.19615i	−0.445566	+	0.257248i
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	9.00000	−	15.5885i	0.444478	−	0.769859i
$411$		0			0
$412$		−	6.92820i		−	0.341328i
$413$			20.7846i			1.02274i
$414$	12.0000			0.589768
$415$	−18.0000	+	10.3923i	−0.883585	+	0.510138i
$416$		0			0
$417$	2.00000	−	3.46410i	0.0979404	−	0.169638i
$418$	−12.0000			−0.586939
$419$	−15.0000	+	8.66025i	−0.732798	+	0.423081i	−0.819445	−	0.573158i	$-0.805718\pi$
$419$	−15.0000	+	8.66025i	−0.732798	+	0.423081i	0.0866469	+	0.996239i	$0.472385\pi$
$420$	6.00000	+	10.3923i	0.292770	+	0.507093i
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	30.0000	−	17.3205i	1.46038	−	0.843149i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	4.50000	+	2.59808i	0.218539	+	0.126174i
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$	−6.00000	−	10.3923i	−0.290701	−	0.503509i
$427$		−	24.2487i		−	1.17348i
$428$	−12.0000	+	6.92820i	−0.580042	+	0.334887i
$429$		0			0
$430$	27.0000	−	15.5885i	1.30206	−	0.751742i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$	20.0000			0.962250
$433$	−11.5000	+	19.9186i	−0.552655	+	0.957226i	0.445427	+	0.895318i	$0.353052\pi$
$433$	−11.5000	+	19.9186i	−0.552655	+	0.957226i	−0.998082	+	0.0619079i	$0.980282\pi$
$434$	−24.0000			−1.15204
$435$		0			0
$436$			8.66025i			0.414751i
$437$	12.0000	+	6.92820i	0.574038	+	0.331421i
$438$	−42.0000	+	24.2487i	−2.00684	+	1.15865i
$439$			41.5692i			1.98399i	0.126275	+	0.991995i	$0.459698\pi$
$439$			41.5692i			1.98399i	−0.126275	+	0.991995i	$0.540302\pi$
$440$		−	10.3923i		−	0.495434i
$441$	2.50000	−	4.33013i	0.119048	−	0.206197i
$442$		0			0
$443$		−	34.6410i		−	1.64584i	−0.568154	−	0.822922i	$-0.692342\pi$
$443$		−	34.6410i		−	1.64584i	0.568154	−	0.822922i	$-0.307658\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	−13.5000	+	7.79423i	−0.639961	+	0.369482i
$446$	3.00000	−	1.73205i	0.142054	−	0.0820150i
$447$	9.00000	−	5.19615i	0.425685	−	0.245770i
$448$	3.00000	+	1.73205i	0.141737	+	0.0818317i
$449$	−34.5000	−	19.9186i	−1.62816	−	0.940016i	−0.984643	−	0.174581i	$-0.944143\pi$
$449$	−34.5000	−	19.9186i	−1.62816	−	0.940016i	−0.643513	−	0.765435i	$-0.722524\pi$
$450$	−3.00000	+	1.73205i	−0.141421	+	0.0816497i
$451$	−18.0000	−	10.3923i	−0.847587	−	0.489355i
$452$	−12.0000	+	6.92820i	−0.564433	+	0.325875i
$453$	−24.0000	−	13.8564i	−1.12762	−	0.651031i
$454$	6.00000	−	10.3923i	0.281594	−	0.487735i
$455$		0			0
$456$	−6.00000	−	3.46410i	−0.280976	−	0.162221i
$457$	6.00000	−	3.46410i	0.280668	−	0.162044i	−0.353058	−	0.935602i	$-0.614858\pi$
$457$	6.00000	−	3.46410i	0.280668	−	0.162044i	0.633726	+	0.773558i	$0.281525\pi$
$458$			12.1244i			0.566534i
$459$	6.00000	−	10.3923i	0.280056	−	0.485071i
$460$	6.00000	−	10.3923i	0.279751	−	0.484544i
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	−0.986127	−	0.165992i	$-0.946917\pi$
$461$	−7.50000	+	12.9904i	−0.349310	+	0.605022i	0.636817	+	0.771015i	$0.280251\pi$
$462$	36.0000	−	20.7846i	1.67487	−	0.966988i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$		0			0
$465$			13.8564i			0.642575i
$466$	−24.0000			−1.11178
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	−0.995582	−	0.0939008i	$-0.970066\pi$
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	0.579111	+	0.815249i	$0.303400\pi$
$468$		0			0
$469$	12.0000	−	20.7846i	0.554109	−	0.959744i
$470$	18.0000			0.830278
$471$	−28.0000			−1.29017
$472$	−9.00000	+	5.19615i	−0.414259	+	0.239172i
$473$	−18.0000	−	31.1769i	−0.827641	−	1.43352i
$474$	48.0000	−	27.7128i	2.20471	−	1.27289i
$475$	−4.00000			−0.183533
$476$	−9.00000	+	5.19615i	−0.412514	+	0.238165i
$477$	3.00000			0.137361
$478$	−27.0000	+	15.5885i	−1.23495	+	0.712999i
$479$	9.00000	−	5.19615i	0.411220	−	0.237418i	−0.280094	−	0.959973i	$-0.590365\pi$
$479$	9.00000	−	5.19615i	0.411220	−	0.237418i	0.691314	+	0.722554i	$0.257032\pi$
$480$	−9.00000	+	15.5885i	−0.410792	+	0.711512i
$481$		0			0
$482$	−25.5000	+	14.7224i	−1.16149	+	0.670588i
$483$	−48.0000			−2.18408
$484$	1.00000			0.0454545
$485$	−19.5000	+	11.2583i	−0.885449	+	0.511214i
$486$	15.0000	−	8.66025i	0.680414	−	0.392837i
$487$	−33.0000	+	19.0526i	−1.49537	+	0.863354i	−0.999986	−	0.00531860i	$-0.998307\pi$
$487$	−33.0000	+	19.0526i	−1.49537	+	0.863354i	−0.495387	+	0.868672i	$0.664974\pi$
$488$	10.5000	−	6.06218i	0.475313	−	0.274422i
$489$	−2.00000	−	3.46410i	−0.0904431	−	0.156652i
$490$	−7.50000	−	12.9904i	−0.338815	−	0.586846i
$491$		−	10.3923i		−	0.468998i	−0.972116	−	0.234499i	$-0.924655\pi$
$491$		−	10.3923i		−	0.468998i	0.972116	−	0.234499i	$-0.0753450\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$		0			0
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	−10.0000	−	17.3205i	−0.449013	−	0.777714i
$497$	6.00000	+	10.3923i	0.269137	+	0.466159i
$498$		−	41.5692i		−	1.86276i
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$			12.1244i			0.542218i
$501$		0			0
$502$	18.0000	+	31.1769i	0.803379	+	1.39149i
$503$	−9.00000	−	5.19615i	−0.401290	−	0.231685i	0.285750	−	0.958304i	$-0.407757\pi$
$503$	−9.00000	−	5.19615i	−0.401290	−	0.231685i	−0.687041	+	0.726619i	$0.741091\pi$
$504$	6.00000			0.267261
$505$	10.5000	−	18.1865i	0.467244	−	0.809290i
$506$	−36.0000	−	20.7846i	−1.60040	−	0.923989i
$507$	−13.0000	−	22.5167i	−0.577350	−	1.00000i
$508$	10.0000	+	17.3205i	0.443678	+	0.768473i
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	−0.999220	−	0.0394971i	$-0.987424\pi$
$509$	−10.5000	+	18.1865i	−0.465404	+	0.806104i	0.533815	+	0.845601i	$0.320758\pi$
$510$	9.00000	+	15.5885i	0.398527	+	0.690268i
$511$	42.0000	−	24.2487i	1.85797	−	1.07270i
$512$		−	8.66025i		−	0.382733i
$513$	8.00000			0.353209
$514$	7.50000	+	12.9904i	0.330811	+	0.572981i
$515$	12.0000			0.528783
$516$			20.7846i			0.914991i
$517$		−	20.7846i		−	0.914106i
$518$	3.00000	+	5.19615i	0.131812	+	0.228306i
$519$	15.0000	+	25.9808i	0.658427	+	1.14043i
$520$		0			0
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	−0.924229	−	0.381839i	$-0.875291\pi$
$521$	−3.00000	+	5.19615i	−0.131432	+	0.227648i	0.792797	+	0.609486i	$0.208624\pi$
$522$		0			0
$523$	12.0000	−	6.92820i	0.524723	−	0.302949i	−0.214142	−	0.976803i	$-0.568695\pi$
$523$	12.0000	−	6.92820i	0.524723	−	0.302949i	0.738865	+	0.673853i	$0.235362\pi$
$524$			13.8564i			0.605320i
$525$	12.0000	−	6.92820i	0.523723	−	0.302372i
$526$		−	20.7846i		−	0.906252i
$527$	−12.0000			−0.522728
$528$	30.0000	+	17.3205i	1.30558	+	0.753778i
$529$	12.5000	+	21.6506i	0.543478	+	0.941332i
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$	−3.00000	+	5.19615i	−0.130189	+	0.225494i
$532$	−6.00000	−	3.46410i	−0.260133	−	0.150188i
$533$		0			0
$534$		−	31.1769i		−	1.34916i
$535$	−12.0000	−	20.7846i	−0.518805	−	0.898597i
$536$	12.0000			0.518321
$537$	−12.0000	−	20.7846i	−0.517838	−	0.896922i
$538$	3.00000			0.129339
$539$	−15.0000	+	8.66025i	−0.646096	+	0.373024i
$540$		−	6.92820i		−	0.298142i
$541$	14.5000	−	25.1147i	0.623404	−	1.07977i	−0.365444	−	0.930834i	$-0.619083\pi$
$541$	14.5000	−	25.1147i	0.623404	−	1.07977i	0.988847	−	0.148933i	$-0.0475840\pi$
$542$	9.00000	+	15.5885i	0.386583	+	0.669582i
$543$	−14.0000			−0.600798
$544$	−13.5000	−	7.79423i	−0.578808	−	0.334175i
$545$	−15.0000			−0.642529
$546$		0			0
$547$		−	3.46410i		−	0.148114i	−0.997254	−	0.0740571i	$-0.976405\pi$
$547$		−	3.46410i		−	0.148114i	0.997254	−	0.0740571i	$-0.0235947\pi$
$548$		0			0
$549$	3.50000	−	6.06218i	0.149376	−	0.258727i
$550$	12.0000			0.511682
$551$		0			0
$552$	−12.0000	−	20.7846i	−0.510754	−	0.884652i
$553$	−48.0000	+	27.7128i	−2.04117	+	1.17847i
$554$	12.0000	−	20.7846i	0.509831	−	0.883053i
$555$	3.00000	−	1.73205i	0.127343	−	0.0735215i
$556$	2.00000			0.0848189
$557$			43.3013i			1.83473i	0.398043	+	0.917367i	$0.369690\pi$
$557$			43.3013i			1.83473i	−0.398043	+	0.917367i	$0.630310\pi$
$558$	−6.00000	−	3.46410i	−0.254000	−	0.146647i
$559$		0			0
$560$	15.0000	−	25.9808i	0.633866	−	1.09789i
$561$	18.0000	−	10.3923i	0.759961	−	0.438763i
$562$	7.50000	+	12.9904i	0.316368	+	0.547966i
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	−0.611656	−	0.791123i	$-0.709497\pi$
$563$	9.00000	−	15.5885i	0.379305	−	0.656975i	0.990961	+	0.134148i	$0.0428299\pi$
$564$	−6.00000	+	10.3923i	−0.252646	+	0.437595i
$565$	−12.0000	−	20.7846i	−0.504844	−	0.874415i
$566$		0			0
$567$	−33.0000	+	19.0526i	−1.38587	+	0.800132i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$	−6.00000	+	10.3923i	−0.251312	+	0.435286i
$571$	−36.0000	−	20.7846i	−1.50655	−	0.869809i	−0.999971	−	0.00761713i	$-0.997575\pi$
$571$	−36.0000	−	20.7846i	−1.50655	−	0.869809i	−0.506582	−	0.862192i	$-0.669091\pi$
$572$		0			0
$573$	−12.0000			−0.501307
$574$	−18.0000	−	31.1769i	−0.751305	−	1.30130i
$575$	−12.0000	−	6.92820i	−0.500435	−	0.288926i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$		−	1.73205i		−	0.0721062i	−0.999350	−	0.0360531i	$-0.988521\pi$
$577$		−	1.73205i		−	0.0721062i	0.999350	−	0.0360531i	$-0.0114785\pi$
$578$	12.0000	−	6.92820i	0.499134	−	0.288175i
$579$	27.0000	+	15.5885i	1.12208	+	0.647834i
$580$		0			0
$581$			41.5692i			1.72458i
$582$		−	45.0333i		−	1.86669i
$583$	−9.00000	−	5.19615i	−0.372742	−	0.215203i
$584$	21.0000	+	12.1244i	0.868986	+	0.501709i
$585$		0			0
$586$		0			0
$587$	15.0000	+	8.66025i	0.619116	+	0.357447i	0.776525	−	0.630087i	$-0.216981\pi$
$587$	15.0000	+	8.66025i	0.619116	+	0.357447i	−0.157409	+	0.987534i	$0.550314\pi$
$588$	10.0000			0.412393
$589$	−4.00000	−	6.92820i	−0.164817	−	0.285472i
$590$	9.00000	+	15.5885i	0.370524	+	0.641767i
$591$	18.0000	−	31.1769i	0.740421	−	1.28245i
$592$	−2.50000	+	4.33013i	−0.102749	+	0.177967i
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$	−24.0000			−0.984732
$595$	−9.00000	−	15.5885i	−0.368964	−	0.639064i
$596$	4.50000	+	2.59808i	0.184327	+	0.106421i
$597$		0			0
$598$		0			0
$599$	12.0000			0.490307			0.245153	−	0.969484i	$-0.421162\pi$
$599$	12.0000			0.490307			0.245153	+	0.969484i	$0.421162\pi$
$600$	6.00000	+	3.46410i	0.244949	+	0.141421i
$601$	25.5000	+	14.7224i	1.04017	+	0.600541i	0.919881	−	0.392199i	$-0.128285\pi$
$601$	25.5000	+	14.7224i	1.04017	+	0.600541i	0.120286	+	0.992739i	$0.461619\pi$
$602$		−	62.3538i		−	2.54135i
$603$	6.00000	−	3.46410i	0.244339	−	0.141069i
$604$		−	13.8564i		−	0.563809i
$605$			1.73205i			0.0704179i
$606$	21.0000	+	36.3731i	0.853067	+	1.47755i
$607$	20.0000			0.811775			0.405887	−	0.913923i	$-0.366962\pi$
$607$	20.0000			0.811775			0.405887	+	0.913923i	$0.366962\pi$
$608$		−	10.3923i		−	0.421464i
$609$		0			0
$610$	−10.5000	−	18.1865i	−0.425133	−	0.736351i
$611$		0			0
$612$	−3.00000			−0.121268
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	−0.747208	−	0.664590i	$-0.768606\pi$
$613$	5.00000	−	8.66025i	0.201948	−	0.349784i	0.949156	+	0.314806i	$0.101939\pi$
$614$	3.00000	−	1.73205i	0.121070	−	0.0698999i
$615$	−18.0000	+	10.3923i	−0.725830	+	0.419058i
$616$	−18.0000	−	10.3923i	−0.725241	−	0.418718i
$617$			41.5692i			1.67351i	0.547575	+	0.836757i	$0.315551\pi$
$617$			41.5692i			1.67351i	−0.547575	+	0.836757i	$0.684449\pi$
$618$	−12.0000	+	20.7846i	−0.482711	+	0.836080i
$619$	36.0000	+	20.7846i	1.44696	+	0.835404i	0.998299	−	0.0582971i	$-0.0185671\pi$
$619$	36.0000	+	20.7846i	1.44696	+	0.835404i	0.448663	+	0.893701i	$0.351900\pi$
$620$	−6.00000	+	3.46410i	−0.240966	+	0.139122i
$621$	24.0000	+	13.8564i	0.963087	+	0.556038i
$622$	3.00000	+	5.19615i	0.120289	+	0.208347i
$623$			31.1769i			1.24908i
$624$		0			0
$625$	−11.0000			−0.440000
$626$	−33.0000	+	19.0526i	−1.31895	+	0.761493i
$627$	12.0000	+	6.92820i	0.479234	+	0.276686i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	1.50000	+	2.59808i	0.0598089	+	0.103592i
$630$		−	10.3923i		−	0.414039i
$631$	−42.0000	+	24.2487i	−1.67199	+	0.965326i	−0.705473	+	0.708737i	$0.749265\pi$
$631$	−42.0000	+	24.2487i	−1.67199	+	0.965326i	−0.966521	+	0.256589i	$0.917401\pi$
$632$	−24.0000	−	13.8564i	−0.954669	−	0.551178i
$633$	−40.0000			−1.58986
$634$	−40.5000	+	23.3827i	−1.60846	+	0.928645i
$635$	−30.0000	+	17.3205i	−1.19051	+	0.687343i
$636$	3.00000	+	5.19615i	0.118958	+	0.206041i
$637$		0			0
$638$		0			0
$639$			3.46410i			0.137038i
$640$	21.0000			0.830098
$641$	4.50000	+	2.59808i	0.177739	+	0.102618i	0.586230	−	0.810145i	$-0.300611\pi$
$641$	4.50000	+	2.59808i	0.177739	+	0.102618i	−0.408491	+	0.912762i	$0.633945\pi$
$642$	48.0000			1.89441
$643$	22.0000	+	38.1051i	0.867595	+	1.50272i	0.864447	+	0.502724i	$0.167669\pi$
$643$	22.0000	+	38.1051i	0.867595	+	1.50272i	0.00314839	+	0.999995i	$0.498998\pi$
$644$	−12.0000	−	20.7846i	−0.472866	−	0.819028i
$645$	−36.0000			−1.41750
$646$	−9.00000	−	5.19615i	−0.354100	−	0.204440i
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	0.918952	−	0.394369i	$-0.129037\pi$
$647$	3.00000	+	5.19615i	0.117942	+	0.204282i	−0.801010	+	0.598651i	$0.795704\pi$
$648$	−16.5000	−	9.52628i	−0.648181	−	0.374228i
$649$	18.0000	−	10.3923i	0.706562	−	0.407934i
$650$		0			0
$651$	24.0000	+	13.8564i	0.940634	+	0.543075i
$652$	1.00000	−	1.73205i	0.0391630	−	0.0678323i
$653$		−	29.4449i		−	1.15227i	−0.817356	−	0.576133i	$-0.804561\pi$
$653$		−	29.4449i		−	1.15227i	0.817356	−	0.576133i	$-0.195439\pi$
$654$	15.0000	−	25.9808i	0.586546	−	1.01593i
$655$	−24.0000			−0.937758
$656$	15.0000	−	25.9808i	0.585652	−	1.01438i
$657$	14.0000			0.546192
$658$	18.0000	−	31.1769i	0.701713	−	1.21540i
$659$	9.00000	+	5.19615i	0.350590	+	0.202413i	0.664945	−	0.746892i	$-0.268455\pi$
$659$	9.00000	+	5.19615i	0.350590	+	0.202413i	−0.314355	+	0.949306i	$0.601788\pi$
$660$	6.00000	−	10.3923i	0.233550	−	0.404520i
$661$	18.0000	−	10.3923i	0.700119	−	0.404214i	−0.107273	−	0.994230i	$-0.534212\pi$
$661$	18.0000	−	10.3923i	0.700119	−	0.404214i	0.807392	+	0.590016i	$0.200879\pi$
$662$	12.0000	+	6.92820i	0.466393	+	0.269272i
$663$		0			0
$664$	−18.0000	+	10.3923i	−0.698535	+	0.403300i
$665$	6.00000	−	10.3923i	0.232670	−	0.402996i
$666$			1.73205i			0.0671156i
$667$		0			0
$668$		0			0
$669$	−4.00000			−0.154649
$670$		−	20.7846i		−	0.802980i
$671$	−21.0000	+	12.1244i	−0.810696	+	0.468056i
$672$	18.0000	+	31.1769i	0.694365	+	1.20268i
$673$	−16.5000	−	9.52628i	−0.636028	−	0.367211i	0.147055	−	0.989128i	$-0.453021\pi$
$673$	−16.5000	−	9.52628i	−0.636028	−	0.367211i	−0.783083	+	0.621917i	$0.786354\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$	−8.00000			−0.307920
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	−0.480913	−	0.876768i	$-0.659695\pi$
$677$	13.5000	−	23.3827i	0.518847	−	0.898670i	0.999760	−	0.0219013i	$-0.00697196\pi$
$678$	48.0000			1.84343
$679$			45.0333i			1.72822i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$	−12.0000	+	6.92820i	−0.459841	+	0.265489i
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$			20.7846i			0.795301i	0.917537	+	0.397650i	$0.130174\pi$
$683$			20.7846i			0.795301i	−0.917537	+	0.397650i	$0.869826\pi$
$684$	−1.00000	−	1.73205i	−0.0382360	−	0.0662266i
$685$		0			0
$686$	12.0000			0.458162
$687$	7.00000	−	12.1244i	0.267067	−	0.462573i
$688$	45.0000	−	25.9808i	1.71561	−	0.990507i
$689$		0			0
$690$	−36.0000	+	20.7846i	−1.37050	+	0.791257i
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.856804	+	0.515642i	$0.172447\pi$
$691$	23.0000	+	39.8372i	0.874961	+	1.51548i	0.0181572	+	0.999835i	$0.494220\pi$
$692$	−7.50000	+	12.9904i	−0.285107	+	0.493820i
$693$	−12.0000			−0.455842
$694$		−	31.1769i		−	1.18346i
$695$			3.46410i			0.131401i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$	24.0000	+	13.8564i	0.907763	+	0.524097i
$700$	6.00000	+	3.46410i	0.226779	+	0.130931i
$701$		−	22.5167i		−	0.850443i	−0.905089	−	0.425221i	$-0.860196\pi$
$701$		−	22.5167i		−	0.850443i	0.905089	−	0.425221i	$-0.139804\pi$
$702$		0			0
$703$	−1.00000	+	1.73205i	−0.0377157	+	0.0653255i
$704$		−	3.46410i		−	0.130558i
$705$	−18.0000	−	10.3923i	−0.677919	−	0.391397i
$706$	36.0000			1.35488
$707$	−21.0000	−	36.3731i	−0.789786	−	1.36795i
$708$	−12.0000			−0.450988
$709$	−1.50000	−	0.866025i	−0.0563337	−	0.0325243i	0.471569	−	0.881829i	$-0.343688\pi$
$709$	−1.50000	−	0.866025i	−0.0563337	−	0.0325243i	−0.527902	+	0.849305i	$0.677021\pi$
$710$	9.00000	+	5.19615i	0.337764	+	0.195008i
$711$	−16.0000			−0.600047
$712$	−13.5000	+	7.79423i	−0.505934	+	0.292101i
$713$		−	27.7128i		−	1.03785i
$714$	36.0000			1.34727
$715$		0			0
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	36.0000			1.34444
$718$	−18.0000	−	10.3923i	−0.671754	−	0.387837i
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	−0.983608	−	0.180319i	$-0.942287\pi$
$719$	−9.00000	+	15.5885i	−0.335643	+	0.581351i	0.647965	+	0.761670i	$0.275620\pi$
$720$	7.50000	−	4.33013i	0.279508	−	0.161374i
$721$	12.0000	−	20.7846i	0.446903	−	0.774059i
$722$			25.9808i			0.966904i
$723$	34.0000			1.26447
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$		0			0
$726$	−3.00000	−	1.73205i	−0.111340	−	0.0642824i
$727$	27.0000	+	15.5885i	1.00137	+	0.578144i	0.908655	−	0.417548i	$-0.137111\pi$
$727$	27.0000	+	15.5885i	1.00137	+	0.578144i	0.0927199	+	0.995692i	$0.470444\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	21.0000	−	36.3731i	0.777245	−	1.34623i
$731$		−	31.1769i		−	1.15312i
$732$	14.0000			0.517455
$733$	−25.0000	−	10.3923i	−0.923396	−	0.383849i
$733$	−25.0000	−	10.3923i	−0.923396	−	0.383849i
$734$	36.0000			1.32878
$735$			17.3205i			0.638877i
$736$	18.0000	−	31.1769i	0.663489	−	1.14920i
$737$	−24.0000			−0.884051
$738$		−	10.3923i		−	0.382546i
$739$	−3.00000	−	1.73205i	−0.110357	−	0.0637145i	0.443806	−	0.896123i	$-0.353628\pi$
$739$	−3.00000	−	1.73205i	−0.110357	−	0.0637145i	−0.554162	+	0.832409i	$0.686961\pi$
$740$	1.50000	+	0.866025i	0.0551411	+	0.0318357i
$741$		0			0
$742$	−9.00000	−	15.5885i	−0.330400	−	0.572270i
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$			13.8564i			0.508001i
$745$	−4.50000	+	7.79423i	−0.164867	+	0.285558i
$746$	34.5000	−	19.9186i	1.26313	−	0.729271i
$747$	−6.00000	+	10.3923i	−0.219529	+	0.380235i
$748$	9.00000	+	5.19615i	0.329073	+	0.189990i
$749$	−48.0000			−1.75388
$750$	21.0000	−	36.3731i	0.766812	−	1.32816i
$751$	33.0000	−	19.0526i	1.20419	−	0.695238i	0.242704	−	0.970100i	$-0.421966\pi$
$751$	33.0000	−	19.0526i	1.20419	−	0.695238i	0.961483	+	0.274863i	$0.0886324\pi$
$752$	30.0000			1.09399
$753$		−	41.5692i		−	1.51487i
$754$		0			0
$755$	24.0000			0.873449
$756$	−12.0000	−	6.92820i	−0.436436	−	0.251976i
$757$	18.0000	+	10.3923i	0.654221	+	0.377715i	0.790072	−	0.613015i	$-0.210043\pi$
$757$	18.0000	+	10.3923i	0.654221	+	0.377715i	−0.135850	+	0.990729i	$0.543377\pi$
$758$	−18.0000			−0.653789
$759$	24.0000	+	41.5692i	0.871145	+	1.50887i
$760$	6.00000			0.217643
$761$	18.0000	+	10.3923i	0.652499	+	0.376721i	0.789413	−	0.613862i	$-0.210385\pi$
$761$	18.0000	+	10.3923i	0.652499	+	0.376721i	−0.136914	+	0.990583i	$0.543718\pi$
$762$		−	69.2820i		−	2.50982i
$763$	−15.0000	+	25.9808i	−0.543036	+	0.940567i
$764$	−3.00000	−	5.19615i	−0.108536	−	0.187990i
$765$		−	5.19615i		−	0.187867i
$766$	−9.00000	−	5.19615i	−0.325183	−	0.187745i
$767$		0			0
$768$	−19.0000	+	32.9090i	−0.685603	+	1.18750i
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.825518	−	0.564376i	$-0.809117\pi$
$769$	−25.0000	−	43.3013i	−0.901523	−	1.56148i	−0.0760054	−	0.997107i	$-0.524217\pi$
$770$	−18.0000	+	31.1769i	−0.648675	+	1.12354i
$771$		−	17.3205i		−	0.623783i
$772$			15.5885i			0.561041i
$773$	−9.00000			−0.323708			−0.161854	−	0.986815i	$-0.551747\pi$
$773$	−9.00000			−0.323708			−0.161854	+	0.986815i	$0.551747\pi$
$774$	9.00000	−	15.5885i	0.323498	−	0.560316i
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$	−19.5000	+	11.2583i	−0.700009	+	0.404151i
$777$		−	6.92820i		−	0.248548i
$778$	−22.5000	+	12.9904i	−0.806664	+	0.465728i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−18.0000	−	31.1769i	−0.643679	−	1.11488i
$783$		0			0
$784$	−12.5000	−	21.6506i	−0.446429	−	0.773237i
$785$	21.0000	−	12.1244i	0.749522	−	0.432737i
$786$	24.0000	−	41.5692i	0.856052	−	1.48272i
$787$			34.6410i			1.23482i	0.786642	+	0.617409i	$0.211818\pi$
$787$			34.6410i			1.23482i	−0.786642	+	0.617409i	$0.788182\pi$
$788$	18.0000			0.641223
$789$	−12.0000	+	20.7846i	−0.427211	+	0.739952i
$790$	−24.0000	+	41.5692i	−0.853882	+	1.47897i
$791$	−48.0000			−1.70668
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$		0			0
$794$	1.50000	+	2.59808i	0.0532330	+	0.0922023i
$795$	−9.00000	+	5.19615i	−0.319197	+	0.184289i
$796$		0			0
$797$	3.00000			0.106265			0.0531327	−	0.998587i	$-0.483079\pi$
$797$	3.00000			0.106265			0.0531327	+	0.998587i	$0.483079\pi$
$798$	12.0000	+	20.7846i	0.424795	+	0.735767i
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$			10.3923i			0.367423i
$801$	−4.50000	+	7.79423i	−0.159000	+	0.275396i
$802$	−31.5000	+	18.1865i	−1.11230	+	0.642189i
$803$	−42.0000	−	24.2487i	−1.48215	−	0.855718i
$804$	12.0000	+	6.92820i	0.423207	+	0.244339i
$805$	36.0000	−	20.7846i	1.26883	−	0.732561i
$806$		0			0
$807$	−3.00000	−	1.73205i	−0.105605	−	0.0609711i
$808$	10.5000	−	18.1865i	0.369389	−	0.639800i
$809$	15.0000			0.527372			0.263686	−	0.964609i	$-0.415062\pi$
$809$	15.0000			0.527372			0.263686	+	0.964609i	$0.415062\pi$
$810$	−16.5000	+	28.5788i	−0.579751	+	1.00416i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$		−	20.7846i		−	0.728948i
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	3.00000	+	1.73205i	0.105085	+	0.0606711i
$816$	15.0000	+	25.9808i	0.525105	+	0.909509i
$817$	18.0000	−	10.3923i	0.629740	−	0.363581i
$818$	46.5000	+	26.8468i	1.62583	+	0.938676i
$819$		0			0
$820$	−9.00000	−	5.19615i	−0.314294	−	0.181458i
$821$	33.0000			1.15171			0.575854	−	0.817553i	$-0.304670\pi$
$821$	33.0000			1.15171			0.575854	+	0.817553i	$0.304670\pi$
$822$		0			0
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$	12.0000			0.418040
$825$	−12.0000	−	6.92820i	−0.417786	−	0.241209i
$826$	36.0000			1.25260
$827$		0			0		1.00000			$0$
$827$		0			0		−1.00000			$\pi$
$828$		−	6.92820i		−	0.240772i
$829$	−31.5000	−	18.1865i	−1.09404	−	0.631644i	−0.159391	−	0.987216i	$-0.550953\pi$
$829$	−31.5000	−	18.1865i	−1.09404	−	0.631644i	−0.934649	+	0.355571i	$0.884286\pi$
$830$	18.0000	+	31.1769i	0.624789	+	1.08217i
$831$	−24.0000	+	13.8564i	−0.832551	+	0.480673i
$832$		0			0
$833$	−15.0000			−0.519719
$834$	−6.00000	−	3.46410i	−0.207763	−	0.119952i
$835$		0			0
$836$			6.92820i			0.239617i
$837$	−8.00000	−	13.8564i	−0.276520	−	0.478947i
$838$	15.0000	+	25.9808i	0.518166	+	0.897491i
$839$	15.0000	+	8.66025i	0.517858	+	0.298985i	0.736058	−	0.676919i	$-0.236685\pi$
$839$	15.0000	+	8.66025i	0.517858	+	0.298985i	−0.218200	+	0.975904i	$0.570019\pi$
$840$	−18.0000	+	10.3923i	−0.621059	+	0.358569i
$841$	29.0000			1.00000
$842$		−	1.73205i		−	0.0596904i
$843$		−	17.3205i		−	0.596550i
$844$	−10.0000	−	17.3205i	−0.344214	−	0.596196i
$845$	19.5000	+	11.2583i	0.670820	+	0.387298i
$846$	9.00000	−	5.19615i	0.309426	−	0.178647i
$847$	3.00000	+	1.73205i	0.103081	+	0.0595140i
$848$	7.50000	−	12.9904i	0.257551	−	0.446092i
$849$		0			0
$850$	9.00000	+	5.19615i	0.308697	+	0.178227i
$851$	−6.00000	+	3.46410i	−0.205677	+	0.118748i
$852$	−6.00000	+	3.46410i	−0.205557	+	0.118678i
$853$	23.5000	−	40.7032i	0.804625	−	1.39365i	−0.111919	−	0.993717i	$-0.535700\pi$
$853$	23.5000	−	40.7032i	0.804625	−	1.39365i	0.916544	−	0.399934i	$-0.130967\pi$
$854$	−42.0000			−1.43721
$855$	3.00000	−	1.73205i	0.102598	−	0.0592349i
$856$	−12.0000	−	20.7846i	−0.410152	−	0.710403i
$857$	−25.5000	−	44.1673i	−0.871063	−	1.50873i	−0.860898	−	0.508778i	$-0.830097\pi$
$857$	−25.5000	−	44.1673i	−0.871063	−	1.50873i	−0.0101655	−	0.999948i	$-0.503236\pi$
$858$		0			0
$859$	−46.0000			−1.56950			−0.784750	−	0.619813i	$-0.787209\pi$
$859$	−46.0000			−1.56950			−0.784750	+	0.619813i	$0.787209\pi$
$860$	−9.00000	−	15.5885i	−0.306897	−	0.531562i
$861$			41.5692i			1.41668i
$862$		0			0
$863$	18.0000	−	10.3923i	0.612727	−	0.353758i	−0.161305	−	0.986905i	$-0.551570\pi$
$863$	18.0000	−	10.3923i	0.612727	−	0.353758i	0.774032	+	0.633146i	$0.218237\pi$
$864$		−	20.7846i		−	0.707107i
$865$	−22.5000	−	12.9904i	−0.765023	−	0.441686i
$866$	34.5000	+	19.9186i	1.17236	+	0.676861i
$867$	−16.0000			−0.543388
$868$			13.8564i			0.470317i
$869$	48.0000	+	27.7128i	1.62829	+	0.940093i
$870$		0			0
$871$		0			0
$872$	−15.0000			−0.507964
$873$	−6.50000	+	11.2583i	−0.219992	+	0.381037i
$874$	12.0000	−	20.7846i	0.405906	−	0.703050i
$875$	−21.0000	+	36.3731i	−0.709930	+	1.22963i
$876$	14.0000	+	24.2487i	0.473016	+	0.819288i
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	0.603897	−	0.797062i	$-0.293614\pi$
$877$	−11.5000	−	19.9186i	−0.388327	−	0.672603i	−0.992225	+	0.124459i	$0.960280\pi$
$878$	72.0000			2.42988
$879$		0			0
$880$	−30.0000			−1.01130
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.0951067	+	0.995467i	$0.530319\pi$
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.814546	+	0.580098i	$0.803014\pi$
$882$	−7.50000	−	4.33013i	−0.252538	−	0.145803i
$883$	30.0000	+	17.3205i	1.00958	+	0.582882i	0.911069	−	0.412254i	$-0.135259\pi$
$883$	30.0000	+	17.3205i	1.00958	+	0.582882i	0.0985116	+	0.995136i	$0.468592\pi$
$884$		0			0
$885$		−	20.7846i		−	0.698667i
$886$	−60.0000			−2.01574
$887$	18.0000	+	10.3923i	0.604381	+	0.348939i	0.770763	−	0.637122i	$-0.219875\pi$
$887$	18.0000	+	10.3923i	0.604381	+	0.348939i	−0.166382	+	0.986061i	$0.553209\pi$
$888$	3.00000	−	1.73205i	0.100673	−	0.0581238i
$889$			69.2820i			2.32364i
$890$	13.5000	+	23.3827i	0.452521	+	0.783789i
$891$	33.0000	+	19.0526i	1.10554	+	0.638285i
$892$	−1.00000	−	1.73205i	−0.0334825	−	0.0579934i
$893$	12.0000			0.401565
$894$	−9.00000	−	15.5885i	−0.301005	−	0.521356i
$895$	18.0000	+	10.3923i	0.601674	+	0.347376i
$896$	21.0000	−	36.3731i	0.701561	−	1.21514i
$897$		0			0
$898$	−34.5000	+	59.7558i	−1.15128	+	1.99408i
$899$		0			0
$900$	1.00000	+	1.73205i	0.0333333	+	0.0577350i
$901$	−4.50000	−	7.79423i	−0.149917	−	0.259663i
$902$	−18.0000	+	31.1769i	−0.599334	+	1.03808i
$903$	−36.0000	+	62.3538i	−1.19800	+	2.07501i
$904$	−12.0000	−	20.7846i	−0.399114	−	0.691286i
$905$	10.5000	−	6.06218i	0.349032	−	0.201514i
$906$	−24.0000	+	41.5692i	−0.797347	+	1.38104i
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	−0.924762	−	0.380547i	$-0.875736\pi$
$907$	−4.00000	+	6.92820i	−0.132818	+	0.230047i	0.791944	+	0.610594i	$0.209069\pi$
$908$	−6.00000	−	3.46410i	−0.199117	−	0.114960i
$909$		−	12.1244i		−	0.402139i
$910$		0			0
$911$	18.0000	−	10.3923i	0.596367	−	0.344312i	−0.171244	−	0.985229i	$-0.554779\pi$
$911$	18.0000	−	10.3923i	0.596367	−	0.344312i	0.767611	+	0.640916i	$0.221445\pi$
$912$	−10.0000	+	17.3205i	−0.331133	+	0.573539i
$913$	36.0000	−	20.7846i	1.19143	−	0.687870i
$914$	−6.00000	−	10.3923i	−0.198462	−	0.343747i
$915$			24.2487i			0.801638i
$916$	7.00000			0.231287
$917$	−24.0000	+	41.5692i	−0.792550	+	1.37274i
$918$	−18.0000	−	10.3923i	−0.594089	−	0.342997i
$919$		−	38.1051i		−	1.25697i	−0.777821	−	0.628486i	$-0.783675\pi$
$919$		−	38.1051i		−	1.25697i	0.777821	−	0.628486i	$-0.216325\pi$
$920$	18.0000	+	10.3923i	0.593442	+	0.342624i
$921$	−4.00000			−0.131804
$922$	22.5000	+	12.9904i	0.740998	+	0.427815i
$923$		0			0
$924$	−12.0000	−	20.7846i	−0.394771	−	0.683763i
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$			45.0333i			1.47989i
$927$	6.00000	−	3.46410i	0.197066	−	0.113776i
$928$		0			0
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	0.962431	−	0.271526i	$-0.0875283\pi$
$929$	7.50000	+	12.9904i	0.246067	+	0.426201i	−0.716364	+	0.697727i	$0.754195\pi$
$930$	24.0000			0.786991
$931$	−5.00000	−	8.66025i	−0.163868	−	0.283828i
$932$			13.8564i			0.453882i
$933$		−	6.92820i		−	0.226819i
$934$	27.0000	+	15.5885i	0.883467	+	0.510070i
$935$	−9.00000	+	15.5885i	−0.294331	+	0.509797i
$936$		0			0
$937$	9.50000	+	16.4545i	0.310351	+	0.537545i	0.978438	−	0.206539i	$-0.0662199\pi$
$937$	9.50000	+	16.4545i	0.310351	+	0.537545i	−0.668087	+	0.744083i	$0.732887\pi$
$938$	−36.0000	−	20.7846i	−1.17544	−	0.678642i
$939$	44.0000			1.43589
$940$		−	10.3923i		−	0.338960i
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	−0.763825	−	0.645424i	$-0.776681\pi$
$941$	−18.0000	+	10.3923i	−0.586783	+	0.338779i	0.177041	+	0.984203i	$0.443347\pi$
$942$			48.4974i			1.58013i
$943$	36.0000	−	20.7846i	1.17232	−	0.676840i
$944$	15.0000	+	25.9808i	0.488208	+	0.845602i
$945$	12.0000	−	20.7846i	0.390360	−	0.676123i
$946$	−54.0000	+	31.1769i	−1.75569	+	1.01365i
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	−0.932002	−	0.362454i	$-0.881939\pi$
$947$	−24.0000	−	41.5692i	−0.779895	−	1.35082i	0.152106	−	0.988364i	$-0.451394\pi$
$948$	−16.0000	−	27.7128i	−0.519656	−	0.900070i
$949$		0			0
$950$			6.92820i			0.224781i
$951$	54.0000			1.75107
$952$	−9.00000	−	15.5885i	−0.291692	−	0.505225i
$953$	−51.0000			−1.65205			−0.826026	−	0.563632i	$-0.809404\pi$
$953$	−51.0000			−1.65205			−0.826026	+	0.563632i	$0.809404\pi$
$954$		−	5.19615i		−	0.168232i
$955$	9.00000	−	5.19615i	0.291233	−	0.168144i
$956$	9.00000	+	15.5885i	0.291081	+	0.504167i
$957$		0			0
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$		0			0
$960$	−3.00000	−	1.73205i	−0.0968246	−	0.0559017i
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	−12.0000	−	6.92820i	−0.386695	−	0.223258i
$964$	8.50000	+	14.7224i	0.273767	+	0.474178i
$965$	−27.0000			−0.869161
$966$			83.1384i			2.67494i
$967$	−4.00000	+	6.92820i	−0.128631	+	0.222796i	−0.923147	−	0.384448i	$-0.874392\pi$
$967$	−4.00000	+	6.92820i	−0.128631	+	0.222796i	0.794515	+	0.607244i	$0.207725\pi$
$968$			1.73205i			0.0556702i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$	19.5000	+	33.7750i	0.626107	+	1.08445i
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.715553	−	0.698558i	$-0.753825\pi$
$971$	−30.0000	−	51.9615i	−0.962746	−	1.66752i	−0.247193	−	0.968966i	$-0.579508\pi$
$972$	−5.00000	−	8.66025i	−0.160375	−	0.277778i
$973$	6.00000	+	3.46410i	0.192351	+	0.111054i
$974$	33.0000	+	57.1577i	1.05739	+	1.83145i
$975$		0			0
$976$	−17.5000	−	30.3109i	−0.560161	−	0.970228i
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	−0.977379	−	0.211495i	$-0.932167\pi$
$977$	−21.0000	−	36.3731i	−0.671850	−	1.16368i	0.305530	−	0.952183i	$-0.401167\pi$
$978$	−6.00000	+	3.46410i	−0.191859	+	0.110770i
$979$	27.0000	−	15.5885i	0.862924	−	0.498209i
$980$	−7.50000	+	4.33013i	−0.239579	+	0.138321i
$981$	−7.50000	+	4.33013i	−0.239457	+	0.138250i
$982$	−18.0000			−0.574403
$983$	18.0000			0.574111			0.287055	−	0.957914i	$-0.407324\pi$
$983$	18.0000			0.574111			0.287055	+	0.957914i	$0.407324\pi$
$984$	−18.0000	+	10.3923i	−0.573819	+	0.331295i
$985$			31.1769i			0.993379i
$986$		0			0
$987$	−36.0000	+	20.7846i	−1.14589	+	0.661581i
$988$		0			0
$989$	72.0000			2.28947
$990$	−9.00000	+	5.19615i	−0.286039	+	0.165145i
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	−18.0000	+	10.3923i	−0.571501	+	0.329956i
$993$	−8.00000	−	13.8564i	−0.253872	−	0.439720i
$994$	18.0000	−	10.3923i	0.570925	−	0.329624i
$995$		0			0
$996$	−24.0000			−0.760469
$997$	20.5000	−	35.5070i	0.649242	−	1.12452i	−0.334063	−	0.942551i	$-0.608420\pi$
$997$	20.5000	−	35.5070i	0.649242	−	1.12452i	0.983304	−	0.181968i	$-0.0582469\pi$
$998$	−60.0000	−	34.6410i	−1.89927	−	1.09654i
$999$	−2.00000	+	3.46410i	−0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	733.2.e.a.426.1	yes	2
733.308	even	6	inner	733.2.e.a.308.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
733.2.e.a.308.1	✓	2	733.308	even	6	inner
733.2.e.a.426.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 733 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	733.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.73205i q^{2} +(-1.00000 + 1.73205i) q^{3} -1.00000 q^{4} -1.73205i q^{5} +(3.00000 + 1.73205i) q^{6} +(-3.00000 - 1.73205i) q^{7} -1.73205i q^{8} +(-0.500000 - 0.866025i) q^{9} -3.00000 q^{10} +3.46410i q^{11} +(1.00000 - 1.73205i) q^{12} +(-3.00000 + 5.19615i) q^{14} +(3.00000 + 1.73205i) q^{15} -5.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(-1.50000 + 0.866025i) q^{18} -2.00000 q^{19} +1.73205i q^{20} +(6.00000 - 3.46410i) q^{21} +6.00000 q^{22} +(-6.00000 - 3.46410i) q^{23} +(3.00000 + 1.73205i) q^{24} +2.00000 q^{25} -4.00000 q^{27} +(3.00000 + 1.73205i) q^{28} +(3.00000 - 5.19615i) q^{30} +(2.00000 + 3.46410i) q^{31} +5.19615i q^{32} +(-6.00000 - 3.46410i) q^{33} +(4.50000 + 2.59808i) q^{34} +(-3.00000 + 5.19615i) q^{35} +(0.500000 + 0.866025i) q^{36} +(0.500000 - 0.866025i) q^{37} +3.46410i q^{38} -3.00000 q^{40} +(-3.00000 + 5.19615i) q^{41} +(-6.00000 - 10.3923i) q^{42} +(-9.00000 + 5.19615i) q^{43} -3.46410i q^{44} +(-1.50000 + 0.866025i) q^{45} +(-6.00000 + 10.3923i) q^{46} -6.00000 q^{47} +(5.00000 - 8.66025i) q^{48} +(2.50000 + 4.33013i) q^{49} -3.46410i q^{50} +(-3.00000 - 5.19615i) q^{51} +(-1.50000 + 2.59808i) q^{53} +6.92820i q^{54} +6.00000 q^{55} +(-3.00000 + 5.19615i) q^{56} +(2.00000 - 3.46410i) q^{57} +(-3.00000 - 5.19615i) q^{59} +(-3.00000 - 1.73205i) q^{60} +(3.50000 + 6.06218i) q^{61} +(6.00000 - 3.46410i) q^{62} +3.46410i q^{63} -1.00000 q^{64} +(-6.00000 + 10.3923i) q^{66} +6.92820i q^{67} +(1.50000 - 2.59808i) q^{68} +(12.0000 - 6.92820i) q^{69} +(9.00000 + 5.19615i) q^{70} +(-3.00000 - 1.73205i) q^{71} +(-1.50000 + 0.866025i) q^{72} +(-7.00000 + 12.1244i) q^{73} +(-1.50000 - 0.866025i) q^{74} +(-2.00000 + 3.46410i) q^{75} +2.00000 q^{76} +(6.00000 - 10.3923i) q^{77} +(8.00000 - 13.8564i) q^{79} +8.66025i q^{80} +(5.50000 - 9.52628i) q^{81} +(9.00000 + 5.19615i) q^{82} +(-6.00000 - 10.3923i) q^{83} +(-6.00000 + 3.46410i) q^{84} +(4.50000 + 2.59808i) q^{85} +(9.00000 + 15.5885i) q^{86} +6.00000 q^{88} +(-4.50000 - 7.79423i) q^{89} +(1.50000 + 2.59808i) q^{90} +(6.00000 + 3.46410i) q^{92} -8.00000 q^{93} +10.3923i q^{94} +3.46410i q^{95} +(-9.00000 - 5.19615i) q^{96} +(-6.50000 - 11.2583i) q^{97} +(7.50000 - 4.33013i) q^{98} +(3.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} - 2 q^{4} + 6 q^{6} - 6 q^{7} - q^{9} - 6 q^{10} + 2 q^{12} - 6 q^{14} + 6 q^{15} - 10 q^{16} - 3 q^{17} - 3 q^{18} - 4 q^{19} + 12 q^{21} + 12 q^{22} - 12 q^{23} + 6 q^{24} + 4 q^{25} - 8 q^{27}+ \cdots + 6 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 - 2 * q^4 + 6 * q^6 - 6 * q^7 - q^9 - 6 * q^10 + 2 * q^12 - 6 * q^14 + 6 * q^15 - 10 * q^16 - 3 * q^17 - 3 * q^18 - 4 * q^19 + 12 * q^21 + 12 * q^22 - 12 * q^23 + 6 * q^24 + 4 * q^25 - 8 * q^27 + 6 * q^28 + 6 * q^30 + 4 * q^31 - 12 * q^33 + 9 * q^34 - 6 * q^35 + q^36 + q^37 - 6 * q^40 - 6 * q^41 - 12 * q^42 - 18 * q^43 - 3 * q^45 - 12 * q^46 - 12 * q^47 + 10 * q^48 + 5 * q^49 - 6 * q^51 - 3 * q^53 + 12 * q^55 - 6 * q^56 + 4 * q^57 - 6 * q^59 - 6 * q^60 + 7 * q^61 + 12 * q^62 - 2 * q^64 - 12 * q^66 + 3 * q^68 + 24 * q^69 + 18 * q^70 - 6 * q^71 - 3 * q^72 - 14 * q^73 - 3 * q^74 - 4 * q^75 + 4 * q^76 + 12 * q^77 + 16 * q^79 + 11 * q^81 + 18 * q^82 - 12 * q^83 - 12 * q^84 + 9 * q^85 + 18 * q^86 + 12 * q^88 - 9 * q^89 + 3 * q^90 + 12 * q^92 - 16 * q^93 - 18 * q^96 - 13 * q^97 + 15 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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Representations

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Database

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