LMFDB - Embedded newform 336.2.bc.e.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [336,2,Mod(17,336)] 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("336.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(336, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.bc (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.68297350792$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			17.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	336.17
Dual form			336.2.bc.e.257.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 1.50000i) q^{3} +(-0.866025 - 1.50000i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +3.46410i q^{13} -3.00000 q^{15} +(1.73205 - 3.00000i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(0.866025 - 4.50000i) q^{21} +(5.19615 - 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} -5.19615 q^{27} +3.00000i q^{29} +(1.50000 + 0.866025i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-3.46410 - 3.00000i) q^{35} +(1.00000 + 1.73205i) q^{37} +(5.19615 + 3.00000i) q^{39} -6.92820 q^{41} +8.00000 q^{43} +(-2.59808 + 4.50000i) q^{45} +(3.46410 + 6.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(7.79423 + 4.50000i) q^{53} +5.19615i q^{55} +6.00000i q^{57} +(-0.866025 + 1.50000i) q^{59} +(-6.00000 - 5.19615i) q^{63} +(5.19615 - 3.00000i) q^{65} +(1.00000 - 1.73205i) q^{67} -10.3923i q^{69} +12.0000i q^{71} +(6.00000 + 3.46410i) q^{73} +(-1.73205 - 3.00000i) q^{75} +(-7.79423 - 1.50000i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} -8.66025 q^{83} -6.00000 q^{85} +(4.50000 + 2.59808i) q^{87} +(5.19615 + 9.00000i) q^{89} +(3.00000 + 8.66025i) q^{91} +(2.59808 - 1.50000i) q^{93} +(5.19615 + 3.00000i) q^{95} +5.19615i q^{97} +9.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{7} - 6 q^{9} - 12 q^{15} - 12 q^{19} + 4 q^{25} + 6 q^{31} - 18 q^{33} + 4 q^{37} + 32 q^{43} + 22 q^{49} - 12 q^{51} - 24 q^{63} + 4 q^{67} + 24 q^{73} - 2 q^{79} - 18 q^{81} - 24 q^{85} + 18 q^{87}+ \cdots + 12 q^{91}+O(q^{100}) $ 4 * q + 10 * q^7 - 6 * q^9 - 12 * q^15 - 12 * q^19 + 4 * q^25 + 6 * q^31 - 18 * q^33 + 4 * q^37 + 32 * q^43 + 22 * q^49 - 12 * q^51 - 24 * q^63 + 4 * q^67 + 24 * q^73 - 2 * q^79 - 18 * q^81 - 24 * q^85 + 18 * q^87 + 12 * q^91

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$3$	0.866025	−	1.50000i	0.500000	−	0.866025i
$4$		0			0
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	0.604787	−	0.796387i	$-0.293258\pi$
$5$	−0.866025	−	1.50000i	−0.387298	−	0.670820i	−0.992085	+	0.125567i	$0.959925\pi$
$6$		0			0
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$		0			0
$9$	−1.50000	−	2.59808i	−0.500000	−	0.866025i
$10$		0			0
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	0.0542666	−	0.998526i	$-0.482718\pi$
$11$	−2.59808	−	1.50000i	−0.783349	−	0.452267i	−0.837616	+	0.546259i	$0.816051\pi$
$12$		0			0
$13$			3.46410i			0.960769i	0.877058	+	0.480384i	$0.159503\pi$
$13$			3.46410i			0.960769i	−0.877058	+	0.480384i	$0.840497\pi$
$14$		0			0
$15$	−3.00000			−0.774597
$16$		0			0
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	−0.575863	−	0.817546i	$-0.695334\pi$
$17$	1.73205	−	3.00000i	0.420084	−	0.727607i	0.995947	+	0.0899392i	$0.0286673\pi$
$18$		0			0
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−3.00000	+	1.73205i	−0.688247	+	0.397360i	0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	0.866025	−	4.50000i	0.188982	−	0.981981i
$22$		0			0
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.151642	−	0.988436i	$-0.451544\pi$
$23$	5.19615	−	3.00000i	1.08347	−	0.625543i	0.931831	+	0.362892i	$0.118211\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$		0			0
$27$	−5.19615			−1.00000
$28$		0			0
$29$			3.00000i			0.557086i	0.960424	+	0.278543i	$0.0898515\pi$
$29$			3.00000i			0.557086i	−0.960424	+	0.278543i	$0.910149\pi$
$30$		0			0
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	1.50000	+	0.866025i	0.269408	+	0.155543i	−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	−4.50000	+	2.59808i	−0.783349	+	0.452267i
$34$		0			0
$35$	−3.46410	−	3.00000i	−0.585540	−	0.507093i
$36$		0			0
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	0.936442	−	0.350823i	$-0.114098\pi$
$37$	1.00000	+	1.73205i	0.164399	+	0.284747i	−0.772043	+	0.635571i	$0.780765\pi$
$38$		0			0
$39$	5.19615	+	3.00000i	0.832050	+	0.480384i
$40$		0			0
$41$	−6.92820			−1.08200			−0.541002	−	0.841021i	$-0.681955\pi$
$41$	−6.92820			−1.08200			−0.541002	+	0.841021i	$0.681955\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$	−2.59808	+	4.50000i	−0.387298	+	0.670820i
$46$		0			0
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	0.999981	+	0.00612051i	$0.00194823\pi$
$47$	3.46410	+	6.00000i	0.505291	+	0.875190i	−0.494690	+	0.869069i	$0.664718\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$	−3.00000	−	5.19615i	−0.420084	−	0.727607i
$52$		0			0
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.928351	−	0.371706i	$-0.121227\pi$
$53$	7.79423	+	4.50000i	1.07062	+	0.618123i	0.142269	+	0.989828i	$0.454560\pi$
$54$		0			0
$55$			5.19615i			0.700649i
$56$		0			0
$57$			6.00000i			0.794719i
$58$		0			0
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	−0.916877	−	0.399170i	$-0.869298\pi$
$59$	−0.866025	+	1.50000i	−0.112747	+	0.195283i	0.804130	+	0.594454i	$0.202632\pi$
$60$		0			0
$61$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$61$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$62$		0			0
$63$	−6.00000	−	5.19615i	−0.755929	−	0.654654i
$64$		0			0
$65$	5.19615	−	3.00000i	0.644503	−	0.372104i
$66$		0			0
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	−0.798454	−	0.602056i	$-0.794348\pi$
$67$	1.00000	−	1.73205i	0.122169	−	0.211604i	0.920623	+	0.390453i	$0.127682\pi$
$68$		0			0
$69$		−	10.3923i		−	1.25109i
$70$		0			0
$71$			12.0000i			1.42414i	0.702109	+	0.712069i	$0.252242\pi$
$71$			12.0000i			1.42414i	−0.702109	+	0.712069i	$0.747758\pi$
$72$		0			0
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	0.808184	−	0.588930i	$-0.200451\pi$
$73$	6.00000	+	3.46410i	0.702247	+	0.405442i	−0.105937	+	0.994373i	$0.533784\pi$
$74$		0			0
$75$	−1.73205	−	3.00000i	−0.200000	−	0.346410i
$76$		0			0
$77$	−7.79423	−	1.50000i	−0.888235	−	0.170941i
$78$		0			0
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$		0			0
$83$	−8.66025			−0.950586			−0.475293	−	0.879827i	$-0.657658\pi$
$83$	−8.66025			−0.950586			−0.475293	+	0.879827i	$0.657658\pi$
$84$		0			0
$85$	−6.00000			−0.650791
$86$		0			0
$87$	4.50000	+	2.59808i	0.482451	+	0.278543i
$88$		0			0
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	0.998218	+	0.0596775i	$0.0190072\pi$
$89$	5.19615	+	9.00000i	0.550791	+	0.953998i	−0.447427	+	0.894321i	$0.647659\pi$
$90$		0			0
$91$	3.00000	+	8.66025i	0.314485	+	0.907841i
$92$		0			0
$93$	2.59808	−	1.50000i	0.269408	−	0.155543i
$94$		0			0
$95$	5.19615	+	3.00000i	0.533114	+	0.307794i
$96$		0			0
$97$			5.19615i			0.527589i	0.964579	+	0.263795i	$0.0849741\pi$
$97$			5.19615i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$98$		0			0
$99$			9.00000i			0.904534i
$100$		0			0
$101$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$101$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$102$		0			0
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	3.00000	−	1.73205i	0.295599	−	0.170664i	0.640464	+	0.767988i	$0.278742\pi$
$104$		0			0
$105$	−7.50000	+	2.59808i	−0.731925	+	0.253546i
$106$		0			0
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	−0.369132	−	0.929377i	$-0.620345\pi$
$107$	2.59808	−	1.50000i	0.251166	−	0.145010i	0.620298	+	0.784366i	$0.287012\pi$
$108$		0			0
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	3.46410			0.328798
$112$		0			0
$113$			12.0000i			1.12887i	0.825479	+	0.564433i	$0.190905\pi$
$113$			12.0000i			1.12887i	−0.825479	+	0.564433i	$0.809095\pi$
$114$		0			0
$115$	−9.00000	−	5.19615i	−0.839254	−	0.484544i
$116$		0			0
$117$	9.00000	−	5.19615i	0.832050	−	0.480384i
$118$		0			0
$119$	1.73205	−	9.00000i	0.158777	−	0.825029i
$120$		0			0
$121$	−1.00000	−	1.73205i	−0.0909091	−	0.157459i
$122$		0			0
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$		0			0
$125$	−12.1244			−1.08444
$126$		0			0
$127$	−11.0000			−0.976092			−0.488046	−	0.872818i	$-0.662290\pi$
$127$	−11.0000			−0.976092			−0.488046	+	0.872818i	$0.662290\pi$
$128$		0			0
$129$	6.92820	−	12.0000i	0.609994	−	1.05654i
$130$		0			0
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	0.729921	−	0.683531i	$-0.239557\pi$
$131$	−2.59808	−	4.50000i	−0.226995	−	0.393167i	−0.956916	+	0.290365i	$0.906223\pi$
$132$		0			0
$133$	−6.00000	+	6.92820i	−0.520266	+	0.600751i
$134$		0			0
$135$	4.50000	+	7.79423i	0.387298	+	0.670820i
$136$		0			0
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.346235	−	0.938148i	$-0.612540\pi$
$137$	−15.5885	−	9.00000i	−1.33181	−	0.768922i	−0.985577	+	0.169226i	$0.945873\pi$
$138$		0			0
$139$		−	17.3205i		−	1.46911i	−0.678551	−	0.734553i	$-0.737392\pi$
$139$		−	17.3205i		−	1.46911i	0.678551	−	0.734553i	$-0.262608\pi$
$140$		0			0
$141$	12.0000			1.01058
$142$		0			0
$143$	5.19615	−	9.00000i	0.434524	−	0.752618i
$144$		0			0
$145$	4.50000	−	2.59808i	0.373705	−	0.215758i
$146$		0			0
$147$	−1.73205	−	12.0000i	−0.142857	−	0.989743i
$148$		0			0
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.300750	−	0.953703i	$-0.402763\pi$
$149$	15.5885	−	9.00000i	1.27706	−	0.737309i	0.976306	+	0.216394i	$0.0694297\pi$
$150$		0			0
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	−0.687741	−	0.725956i	$-0.741398\pi$
$151$	3.50000	−	6.06218i	0.284826	−	0.493333i	0.972567	+	0.232623i	$0.0747309\pi$
$152$		0			0
$153$	−10.3923			−0.840168
$154$		0			0
$155$		−	3.00000i		−	0.240966i
$156$		0			0
$157$	−18.0000	−	10.3923i	−1.43656	−	0.829396i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	−18.0000	−	10.3923i	−1.43656	−	0.829396i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$		0			0
$159$	13.5000	−	7.79423i	1.07062	−	0.618123i
$160$		0			0
$161$	10.3923	−	12.0000i	0.819028	−	0.945732i
$162$		0			0
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	0.998392	+	0.0566798i	$0.0180514\pi$
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	−0.450110	+	0.892973i	$0.648615\pi$
$164$		0			0
$165$	7.79423	+	4.50000i	0.606780	+	0.350325i
$166$		0			0
$167$	−17.3205			−1.34030			−0.670151	−	0.742225i	$-0.733770\pi$
$167$	−17.3205			−1.34030			−0.670151	+	0.742225i	$0.733770\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	9.00000	+	5.19615i	0.688247	+	0.397360i
$172$		0			0
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$		0			0
$175$	1.00000	−	5.19615i	0.0755929	−	0.392792i
$176$		0			0
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$		0			0
$179$	10.3923	+	6.00000i	0.776757	+	0.448461i	0.835280	−	0.549825i	$-0.185306\pi$
$179$	10.3923	+	6.00000i	0.776757	+	0.448461i	−0.0585225	+	0.998286i	$0.518639\pi$
$180$		0			0
$181$			6.92820i			0.514969i	0.966282	+	0.257485i	$0.0828937\pi$
$181$			6.92820i			0.514969i	−0.966282	+	0.257485i	$0.917106\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	1.73205	−	3.00000i	0.127343	−	0.220564i
$186$		0			0
$187$	−9.00000	+	5.19615i	−0.658145	+	0.379980i
$188$		0			0
$189$	−12.9904	+	4.50000i	−0.944911	+	0.327327i
$190$		0			0
$191$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$191$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$192$		0			0
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	11.5000	−	19.9186i	0.827788	−	1.43377i	0.899770	−	0.436365i	$-0.143734\pi$
$194$		0			0
$195$		−	10.3923i		−	0.744208i
$196$		0			0
$197$		−	18.0000i		−	1.28245i	−0.767354	−	0.641223i	$-0.778427\pi$
$197$		−	18.0000i		−	1.28245i	0.767354	−	0.641223i	$-0.221573\pi$
$198$		0			0
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	0.145848	−	0.989307i	$-0.453409\pi$
$199$	−9.00000	−	5.19615i	−0.637993	−	0.368345i	−0.783841	+	0.620962i	$0.786742\pi$
$200$		0			0
$201$	−1.73205	−	3.00000i	−0.122169	−	0.211604i
$202$		0			0
$203$	2.59808	+	7.50000i	0.182349	+	0.526397i
$204$		0			0
$205$	6.00000	+	10.3923i	0.419058	+	0.725830i
$206$		0			0
$207$	−15.5885	−	9.00000i	−1.08347	−	0.625543i
$208$		0			0
$209$	10.3923			0.718851
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$	18.0000	+	10.3923i	1.23334	+	0.712069i
$214$		0			0
$215$	−6.92820	−	12.0000i	−0.472500	−	0.818393i
$216$		0			0
$217$	4.50000	+	0.866025i	0.305480	+	0.0587896i
$218$		0			0
$219$	10.3923	−	6.00000i	0.702247	−	0.405442i
$220$		0			0
$221$	10.3923	+	6.00000i	0.699062	+	0.403604i
$222$		0			0
$223$			25.9808i			1.73980i	0.493228	+	0.869900i	$0.335817\pi$
$223$			25.9808i			1.73980i	−0.493228	+	0.869900i	$0.664183\pi$
$224$		0			0
$225$	−6.00000			−0.400000
$226$		0			0
$227$	2.59808	−	4.50000i	0.172440	−	0.298675i	−0.766832	−	0.641848i	$-0.778168\pi$
$227$	2.59808	−	4.50000i	0.172440	−	0.298675i	0.939272	+	0.343172i	$0.111501\pi$
$228$		0			0
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	−0.841011	−	0.541017i	$-0.818039\pi$
$229$	−12.0000	+	6.92820i	−0.792982	+	0.457829i	0.0480291	+	0.998846i	$0.484706\pi$
$230$		0			0
$231$	−9.00000	+	10.3923i	−0.592157	+	0.683763i
$232$		0			0
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.914461	−	0.404674i	$-0.867385\pi$
$233$	−15.5885	+	9.00000i	−1.02123	+	0.589610i	−0.106773	+	0.994283i	$0.534052\pi$
$234$		0			0
$235$	6.00000	−	10.3923i	0.391397	−	0.677919i
$236$		0			0
$237$	−1.73205			−0.112509
$238$		0			0
$239$		−	6.00000i		−	0.388108i	−0.980991	−	0.194054i	$-0.937836\pi$
$239$		−	6.00000i		−	0.388108i	0.980991	−	0.194054i	$-0.0621637\pi$
$240$		0			0
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	−22.5000	−	12.9904i	−1.44935	−	0.836784i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.500000	+	0.866025i
$244$		0			0
$245$	−11.2583	−	4.50000i	−0.719268	−	0.287494i
$246$		0			0
$247$	−6.00000	−	10.3923i	−0.381771	−	0.661247i
$248$		0			0
$249$	−7.50000	+	12.9904i	−0.475293	+	0.823232i
$250$		0			0
$251$	19.0526			1.20259			0.601293	−	0.799028i	$-0.294652\pi$
$251$	19.0526			1.20259			0.601293	+	0.799028i	$0.294652\pi$
$252$		0			0
$253$	−18.0000			−1.13165
$254$		0			0
$255$	−5.19615	+	9.00000i	−0.325396	+	0.563602i
$256$		0			0
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	0.657208	−	0.753709i	$-0.271737\pi$
$257$	−5.19615	−	9.00000i	−0.324127	−	0.561405i	−0.981335	+	0.192304i	$0.938404\pi$
$258$		0			0
$259$	4.00000	+	3.46410i	0.248548	+	0.215249i
$260$		0			0
$261$	7.79423	−	4.50000i	0.482451	−	0.278543i
$262$		0			0
$263$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$263$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$264$		0			0
$265$		−	15.5885i		−	0.957591i
$266$		0			0
$267$	18.0000			1.10158
$268$		0			0
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.0671428	+	0.997743i	$0.521388\pi$
$269$	−14.7224	+	25.5000i	−0.897643	+	1.55476i	−0.830500	+	0.557019i	$0.811945\pi$
$270$		0			0
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	−0.630412	−	0.776261i	$-0.717114\pi$
$271$	−4.50000	+	2.59808i	−0.273356	+	0.157822i	0.357056	+	0.934083i	$0.383781\pi$
$272$		0			0
$273$	15.5885	+	3.00000i	0.943456	+	0.181568i
$274$		0			0
$275$	−5.19615	+	3.00000i	−0.313340	+	0.180907i
$276$		0			0
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$		0			0
$279$		−	5.19615i		−	0.311086i
$280$		0			0
$281$			30.0000i			1.78965i	0.446417	+	0.894825i	$0.352700\pi$
$281$			30.0000i			1.78965i	−0.446417	+	0.894825i	$0.647300\pi$
$282$		0			0
$283$	−24.0000	−	13.8564i	−1.42665	−	0.823678i	−0.429797	−	0.902926i	$-0.641415\pi$
$283$	−24.0000	−	13.8564i	−1.42665	−	0.823678i	−0.996855	+	0.0792477i	$0.974748\pi$
$284$		0			0
$285$	9.00000	−	5.19615i	0.533114	−	0.307794i
$286$		0			0
$287$	−17.3205	+	6.00000i	−1.02240	+	0.354169i
$288$		0			0
$289$	2.50000	+	4.33013i	0.147059	+	0.254713i
$290$		0			0
$291$	7.79423	+	4.50000i	0.456906	+	0.263795i
$292$		0			0
$293$	19.0526			1.11306			0.556531	−	0.830827i	$-0.312132\pi$
$293$	19.0526			1.11306			0.556531	+	0.830827i	$0.312132\pi$
$294$		0			0
$295$	3.00000			0.174667
$296$		0			0
$297$	13.5000	+	7.79423i	0.783349	+	0.452267i
$298$		0			0
$299$	10.3923	+	18.0000i	0.601003	+	1.04097i
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$		0			0
$303$		0			0
$304$		0			0
$305$		0			0
$306$		0			0
$307$			24.2487i			1.38395i	0.721923	+	0.691974i	$0.243259\pi$
$307$			24.2487i			1.38395i	−0.721923	+	0.691974i	$0.756741\pi$
$308$		0			0
$309$		−	6.00000i		−	0.341328i
$310$		0			0
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	−0.992826	−	0.119570i	$-0.961848\pi$
$311$	−6.92820	+	12.0000i	−0.392862	+	0.680458i	0.599963	+	0.800027i	$0.295182\pi$
$312$		0			0
$313$	1.50000	−	0.866025i	0.0847850	−	0.0489506i	−0.457008	−	0.889463i	$-0.651079\pi$
$313$	1.50000	−	0.866025i	0.0847850	−	0.0489506i	0.541793	+	0.840512i	$0.317746\pi$
$314$		0			0
$315$	−2.59808	+	13.5000i	−0.146385	+	0.760639i
$316$		0			0
$317$	−12.9904	+	7.50000i	−0.729612	+	0.421242i	−0.818280	−	0.574819i	$-0.805072\pi$
$317$	−12.9904	+	7.50000i	−0.729612	+	0.421242i	0.0886679	+	0.996061i	$0.471739\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$		−	5.19615i		−	0.290021i
$322$		0			0
$323$			12.0000i			0.667698i
$324$		0			0
$325$	6.00000	+	3.46410i	0.332820	+	0.192154i
$326$		0			0
$327$	−1.73205	−	3.00000i	−0.0957826	−	0.165900i
$328$		0			0
$329$	13.8564	+	12.0000i	0.763928	+	0.661581i
$330$		0			0
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	0.734905	−	0.678170i	$-0.237227\pi$
$331$	−4.00000	−	6.92820i	−0.219860	−	0.380808i	−0.954765	+	0.297361i	$0.903893\pi$
$332$		0			0
$333$	3.00000	−	5.19615i	0.164399	−	0.284747i
$334$		0			0
$335$	−3.46410			−0.189264
$336$		0			0
$337$	13.0000			0.708155			0.354078	−	0.935216i	$-0.384795\pi$
$337$	13.0000			0.708155			0.354078	+	0.935216i	$0.384795\pi$
$338$		0			0
$339$	18.0000	+	10.3923i	0.977626	+	0.564433i
$340$		0			0
$341$	−2.59808	−	4.50000i	−0.140694	−	0.243689i
$342$		0			0
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$		0			0
$345$	−15.5885	+	9.00000i	−0.839254	+	0.484544i
$346$		0			0
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	0.194409	−	0.980921i	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$			10.3923i			0.556287i	0.960539	+	0.278144i	$0.0897191\pi$
$349$			10.3923i			0.556287i	−0.960539	+	0.278144i	$0.910281\pi$
$350$		0			0
$351$		−	18.0000i		−	0.960769i
$352$		0			0
$353$	17.3205	−	30.0000i	0.921878	−	1.59674i	0.125370	−	0.992110i	$-0.459988\pi$
$353$	17.3205	−	30.0000i	0.921878	−	1.59674i	0.796507	−	0.604629i	$-0.206679\pi$
$354$		0			0
$355$	18.0000	−	10.3923i	0.955341	−	0.551566i
$356$		0			0
$357$	−12.0000	−	10.3923i	−0.635107	−	0.550019i
$358$		0			0
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	−0.630814	−	0.775934i	$-0.717279\pi$
$359$	−5.19615	+	3.00000i	−0.274242	+	0.158334i	0.356572	+	0.934268i	$0.383946\pi$
$360$		0			0
$361$	−3.50000	+	6.06218i	−0.184211	+	0.319062i
$362$		0			0
$363$	−3.46410			−0.181818
$364$		0			0
$365$		−	12.0000i		−	0.628109i
$366$		0			0
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.913493	−	0.406855i	$-0.133375\pi$
$367$	19.5000	+	11.2583i	1.01789	+	0.587680i	0.104399	+	0.994535i	$0.466708\pi$
$368$		0			0
$369$	10.3923	+	18.0000i	0.541002	+	0.937043i
$370$		0			0
$371$	23.3827	+	4.50000i	1.21397	+	0.233628i
$372$		0			0
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	−0.899255	−	0.437425i	$-0.855891\pi$
$373$	−16.0000	−	27.7128i	−0.828449	−	1.43492i	0.0708063	−	0.997490i	$-0.477443\pi$
$374$		0			0
$375$	−10.5000	+	18.1865i	−0.542218	+	0.939149i
$376$		0			0
$377$	−10.3923			−0.535231
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	−9.52628	+	16.5000i	−0.488046	+	0.845321i
$382$		0			0
$383$	1.73205	+	3.00000i	0.0885037	+	0.153293i	0.906879	−	0.421392i	$-0.138458\pi$
$383$	1.73205	+	3.00000i	0.0885037	+	0.153293i	−0.818375	+	0.574684i	$0.805125\pi$
$384$		0			0
$385$	4.50000	+	12.9904i	0.229341	+	0.662051i
$386$		0			0
$387$	−12.0000	−	20.7846i	−0.609994	−	1.05654i
$388$		0			0
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	0.840091	−	0.542445i	$-0.182501\pi$
$389$	15.5885	+	9.00000i	0.790366	+	0.456318i	−0.0497253	+	0.998763i	$0.515835\pi$
$390$		0			0
$391$		−	20.7846i		−	1.05112i
$392$		0			0
$393$	−9.00000			−0.453990
$394$		0			0
$395$	−0.866025	+	1.50000i	−0.0435745	+	0.0754732i
$396$		0			0
$397$	−24.0000	+	13.8564i	−1.20453	+	0.695433i	−0.961558	−	0.274601i	$-0.911454\pi$
$397$	−24.0000	+	13.8564i	−1.20453	+	0.695433i	−0.242967	+	0.970034i	$0.578121\pi$
$398$		0			0
$399$	5.19615	+	15.0000i	0.260133	+	0.750939i
$400$		0			0
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	−0.736512	−	0.676425i	$-0.763528\pi$
$401$	−10.3923	+	6.00000i	−0.518967	+	0.299626i	0.217545	+	0.976050i	$0.430195\pi$
$402$		0			0
$403$	−3.00000	+	5.19615i	−0.149441	+	0.258839i
$404$		0			0
$405$	15.5885			0.774597
$406$		0			0
$407$		−	6.00000i		−	0.297409i
$408$		0			0
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	0.673830	−	0.738886i	$-0.264648\pi$
$409$	7.50000	+	4.33013i	0.370851	+	0.214111i	−0.302979	+	0.952997i	$0.597981\pi$
$410$		0			0
$411$	−27.0000	+	15.5885i	−1.33181	+	0.768922i
$412$		0			0
$413$	−0.866025	+	4.50000i	−0.0426143	+	0.221431i
$414$		0			0
$415$	7.50000	+	12.9904i	0.368161	+	0.637673i
$416$		0			0
$417$	−25.9808	−	15.0000i	−1.27228	−	0.734553i
$418$		0			0
$419$	24.2487			1.18463			0.592314	−	0.805708i	$-0.298215\pi$
$419$	24.2487			1.18463			0.592314	+	0.805708i	$0.298215\pi$
$420$		0			0
$421$	32.0000			1.55958			0.779792	−	0.626038i	$-0.215325\pi$
$421$	32.0000			1.55958			0.779792	+	0.626038i	$0.215325\pi$
$422$		0			0
$423$	10.3923	−	18.0000i	0.505291	−	0.875190i
$424$		0			0
$425$	−3.46410	−	6.00000i	−0.168034	−	0.291043i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−9.00000	−	15.5885i	−0.434524	−	0.752618i
$430$		0			0
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.0925683	−	0.995706i	$-0.529508\pi$
$431$	−20.7846	−	12.0000i	−1.00116	−	0.578020i	−0.908591	+	0.417687i	$0.862841\pi$
$432$		0			0
$433$			34.6410i			1.66474i	0.554220	+	0.832370i	$0.313017\pi$
$433$			34.6410i			1.66474i	−0.554220	+	0.832370i	$0.686983\pi$
$434$		0			0
$435$		−	9.00000i		−	0.431517i
$436$		0			0
$437$	−10.3923	+	18.0000i	−0.497131	+	0.861057i
$438$		0			0
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.503421	+	0.864041i	$0.667925\pi$
$439$	−31.5000	+	18.1865i	−1.50341	+	0.867996i	−0.999992	+	0.00395451i	$0.998741\pi$
$440$		0			0
$441$	−19.5000	−	7.79423i	−0.928571	−	0.371154i
$442$		0			0
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	−0.673596	−	0.739100i	$-0.735251\pi$
$443$	−7.79423	+	4.50000i	−0.370315	+	0.213801i	0.303281	+	0.952901i	$0.401918\pi$
$444$		0			0
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$		0			0
$447$		−	31.1769i		−	1.47462i
$448$		0			0
$449$		−	30.0000i		−	1.41579i	−0.706319	−	0.707894i	$-0.749646\pi$
$449$		−	30.0000i		−	1.41579i	0.706319	−	0.707894i	$-0.250354\pi$
$450$		0			0
$451$	18.0000	+	10.3923i	0.847587	+	0.489355i
$452$		0			0
$453$	−6.06218	−	10.5000i	−0.284826	−	0.493333i
$454$		0			0
$455$	10.3923	−	12.0000i	0.487199	−	0.562569i
$456$		0			0
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	0.918556	−	0.395292i	$-0.129357\pi$
$457$	2.50000	+	4.33013i	0.116945	+	0.202555i	−0.801611	+	0.597847i	$0.796023\pi$
$458$		0			0
$459$	−9.00000	+	15.5885i	−0.420084	+	0.727607i
$460$		0			0
$461$	13.8564			0.645357			0.322679	−	0.946509i	$-0.395417\pi$
$461$	13.8564			0.645357			0.322679	+	0.946509i	$0.395417\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$		0			0
$465$	−4.50000	−	2.59808i	−0.208683	−	0.120483i
$466$		0			0
$467$	−15.5885	−	27.0000i	−0.721348	−	1.24941i	−0.960460	−	0.278419i	$-0.910190\pi$
$467$	−15.5885	−	27.0000i	−0.721348	−	1.24941i	0.239112	−	0.970992i	$-0.423144\pi$
$468$		0			0
$469$	1.00000	−	5.19615i	0.0461757	−	0.239936i
$470$		0			0
$471$	−31.1769	+	18.0000i	−1.43656	+	0.829396i
$472$		0			0
$473$	−20.7846	−	12.0000i	−0.955677	−	0.551761i
$474$		0			0
$475$			6.92820i			0.317888i
$476$		0			0
$477$		−	27.0000i		−	1.23625i
$478$		0			0
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	−0.934248	−	0.356624i	$-0.883928\pi$
$479$	−3.46410	+	6.00000i	−0.158279	+	0.274147i	0.775969	+	0.630771i	$0.217261\pi$
$480$		0			0
$481$	−6.00000	+	3.46410i	−0.273576	+	0.157949i
$482$		0			0
$483$	−9.00000	−	25.9808i	−0.409514	−	1.18217i
$484$		0			0
$485$	7.79423	−	4.50000i	0.353918	−	0.204334i
$486$		0			0
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	−0.854475	−	0.519493i	$-0.826121\pi$
$487$	0.500000	−	0.866025i	0.0226572	−	0.0392434i	0.877132	+	0.480250i	$0.159454\pi$
$488$		0			0
$489$	24.2487			1.09656
$490$		0			0
$491$		−	33.0000i		−	1.48927i	−0.667472	−	0.744635i	$-0.732624\pi$
$491$		−	33.0000i		−	1.48927i	0.667472	−	0.744635i	$-0.267376\pi$
$492$		0			0
$493$	9.00000	+	5.19615i	0.405340	+	0.234023i
$494$		0			0
$495$	13.5000	−	7.79423i	0.606780	−	0.350325i
$496$		0			0
$497$	10.3923	+	30.0000i	0.466159	+	1.34568i
$498$		0			0
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	0.999962	−	0.00872186i	$-0.00277629\pi$
$499$	11.0000	+	19.0526i	0.492428	+	0.852910i	−0.507534	+	0.861632i	$0.669443\pi$
$500$		0			0
$501$	−15.0000	+	25.9808i	−0.670151	+	1.16073i
$502$		0			0
$503$	38.1051			1.69902			0.849512	−	0.527570i	$-0.176897\pi$
$503$	38.1051			1.69902			0.849512	+	0.527570i	$0.176897\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	0.866025	−	1.50000i	0.0384615	−	0.0666173i
$508$		0			0
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	0.573914	−	0.818916i	$-0.305424\pi$
$509$	−9.52628	−	16.5000i	−0.422245	−	0.731350i	−0.996159	+	0.0875661i	$0.972091\pi$
$510$		0			0
$511$	18.0000	+	3.46410i	0.796273	+	0.153243i
$512$		0			0
$513$	15.5885	−	9.00000i	0.688247	−	0.397360i
$514$		0			0
$515$	−5.19615	−	3.00000i	−0.228970	−	0.132196i
$516$		0			0
$517$		−	20.7846i		−	0.914106i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	−0.384662	−	0.923057i	$-0.625682\pi$
$521$	13.8564	−	24.0000i	0.607060	−	1.05146i	0.991722	−	0.128402i	$-0.0409847\pi$
$522$		0			0
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.444941	−	0.895560i	$-0.353225\pi$
$523$	33.0000	−	19.0526i	1.44299	−	0.833110i	0.998048	+	0.0624496i	$0.0198913\pi$
$524$		0			0
$525$	−6.92820	−	6.00000i	−0.302372	−	0.261861i
$526$		0			0
$527$	5.19615	−	3.00000i	0.226348	−	0.130682i
$528$		0			0
$529$	6.50000	−	11.2583i	0.282609	−	0.489493i
$530$		0			0
$531$	5.19615			0.225494
$532$		0			0
$533$		−	24.0000i		−	1.03956i
$534$		0			0
$535$	−4.50000	−	2.59808i	−0.194552	−	0.112325i
$536$		0			0
$537$	18.0000	−	10.3923i	0.776757	−	0.448461i
$538$		0			0
$539$	−20.7846	+	3.00000i	−0.895257	+	0.129219i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$		0			0
$543$	10.3923	+	6.00000i	0.445976	+	0.257485i
$544$		0			0
$545$	−3.46410			−0.148386
$546$		0			0
$547$	−2.00000			−0.0855138			−0.0427569	−	0.999086i	$-0.513614\pi$
$547$	−2.00000			−0.0855138			−0.0427569	+	0.999086i	$0.513614\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−5.19615	−	9.00000i	−0.221364	−	0.383413i
$552$		0			0
$553$	−2.00000	−	1.73205i	−0.0850487	−	0.0736543i
$554$		0			0
$555$	−3.00000	−	5.19615i	−0.127343	−	0.220564i
$556$		0			0
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	0.554031	−	0.832496i	$-0.313089\pi$
$557$	2.59808	+	1.50000i	0.110084	+	0.0635570i	−0.443947	+	0.896053i	$0.646422\pi$
$558$		0			0
$559$			27.7128i			1.17213i
$560$		0			0
$561$			18.0000i			0.759961i
$562$		0			0
$563$	−12.9904	+	22.5000i	−0.547479	+	0.948262i	0.450967	+	0.892541i	$0.351079\pi$
$563$	−12.9904	+	22.5000i	−0.547479	+	0.948262i	−0.998446	+	0.0557214i	$0.982254\pi$
$564$		0			0
$565$	18.0000	−	10.3923i	0.757266	−	0.437208i
$566$		0			0
$567$	−4.50000	+	23.3827i	−0.188982	+	0.981981i
$568$		0			0
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	−0.604947	−	0.796266i	$-0.706806\pi$
$569$	−5.19615	+	3.00000i	−0.217834	+	0.125767i	0.387113	+	0.922032i	$0.373472\pi$
$570$		0			0
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$		−	12.0000i		−	0.500435i
$576$		0			0
$577$	−1.50000	−	0.866025i	−0.0624458	−	0.0360531i	0.468452	−	0.883489i	$-0.344812\pi$
$577$	−1.50000	−	0.866025i	−0.0624458	−	0.0360531i	−0.530898	+	0.847436i	$0.678145\pi$
$578$		0			0
$579$	−19.9186	−	34.5000i	−0.827788	−	1.43377i
$580$		0			0
$581$	−21.6506	+	7.50000i	−0.898220	+	0.311152i
$582$		0			0
$583$	−13.5000	−	23.3827i	−0.559113	−	0.968412i
$584$		0			0
$585$	−15.5885	−	9.00000i	−0.644503	−	0.372104i
$586$		0			0
$587$	−15.5885			−0.643404			−0.321702	−	0.946841i	$-0.604255\pi$
$587$	−15.5885			−0.643404			−0.321702	+	0.946841i	$0.604255\pi$
$588$		0			0
$589$	−6.00000			−0.247226
$590$		0			0
$591$	−27.0000	−	15.5885i	−1.11063	−	0.641223i
$592$		0			0
$593$	19.0526	+	33.0000i	0.782395	+	1.35515i	0.930543	+	0.366182i	$0.119335\pi$
$593$	19.0526	+	33.0000i	0.782395	+	1.35515i	−0.148148	+	0.988965i	$0.547331\pi$
$594$		0			0
$595$	−15.0000	+	5.19615i	−0.614940	+	0.213021i
$596$		0			0
$597$	−15.5885	+	9.00000i	−0.637993	+	0.368345i
$598$		0			0
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.925859	−	0.377869i	$-0.123343\pi$
$599$	25.9808	+	15.0000i	1.06155	+	0.612883i	0.135686	+	0.990752i	$0.456676\pi$
$600$		0			0
$601$		−	29.4449i		−	1.20108i	−0.799594	−	0.600541i	$-0.794952\pi$
$601$		−	29.4449i		−	1.20108i	0.799594	−	0.600541i	$-0.205048\pi$
$602$		0			0
$603$	−6.00000			−0.244339
$604$		0			0
$605$	−1.73205	+	3.00000i	−0.0704179	+	0.121967i
$606$		0			0
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	−0.840484	−	0.541837i	$-0.817729\pi$
$607$	−19.5000	+	11.2583i	−0.791481	+	0.456962i	0.0490029	+	0.998799i	$0.484396\pi$
$608$		0			0
$609$	13.5000	+	2.59808i	0.547048	+	0.105279i
$610$		0			0
$611$	−20.7846	+	12.0000i	−0.840855	+	0.485468i
$612$		0			0
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$	20.7846			0.838116
$616$		0			0
$617$		−	12.0000i		−	0.483102i	−0.970388	−	0.241551i	$-0.922344\pi$
$617$		−	12.0000i		−	0.483102i	0.970388	−	0.241551i	$-0.0776561\pi$
$618$		0			0
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	0.374550	−	0.927207i	$-0.377797\pi$
$619$	−6.00000	−	3.46410i	−0.241160	−	0.139234i	−0.615710	+	0.787973i	$0.711131\pi$
$620$		0			0
$621$	−27.0000	+	15.5885i	−1.08347	+	0.625543i
$622$		0			0
$623$	20.7846	+	18.0000i	0.832718	+	0.721155i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	9.00000	−	15.5885i	0.359425	−	0.622543i
$628$		0			0
$629$	6.92820			0.276246
$630$		0			0
$631$	31.0000			1.23409			0.617045	−	0.786928i	$-0.288330\pi$
$631$	31.0000			1.23409			0.617045	+	0.786928i	$0.288330\pi$
$632$		0			0
$633$	−3.46410	+	6.00000i	−0.137686	+	0.238479i
$634$		0			0
$635$	9.52628	+	16.5000i	0.378039	+	0.654783i
$636$		0			0
$637$	15.0000	+	19.0526i	0.594322	+	0.754890i
$638$		0			0
$639$	31.1769	−	18.0000i	1.23334	−	0.712069i
$640$		0			0
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	0.0297987	−	0.999556i	$-0.490513\pi$
$641$	−20.7846	−	12.0000i	−0.820943	−	0.473972i	−0.850741	+	0.525584i	$0.823847\pi$
$642$		0			0
$643$			17.3205i			0.683054i	0.939872	+	0.341527i	$0.110944\pi$
$643$			17.3205i			0.683054i	−0.939872	+	0.341527i	$0.889056\pi$
$644$		0			0
$645$	−24.0000			−0.944999
$646$		0			0
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$		0			0
$649$	4.50000	−	2.59808i	0.176640	−	0.101983i
$650$		0			0
$651$	5.19615	−	6.00000i	0.203653	−	0.235159i
$652$		0			0
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	−0.549973	−	0.835182i	$-0.685362\pi$
$653$	−2.59808	+	1.50000i	−0.101671	+	0.0586995i	0.448303	+	0.893882i	$0.352029\pi$
$654$		0			0
$655$	−4.50000	+	7.79423i	−0.175830	+	0.304546i
$656$		0			0
$657$		−	20.7846i		−	0.810885i
$658$		0			0
$659$		−	12.0000i		−	0.467454i	−0.972302	−	0.233727i	$-0.924908\pi$
$659$		−	12.0000i		−	0.467454i	0.972302	−	0.233727i	$-0.0750921\pi$
$660$		0			0
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	0.378754	−	0.925497i	$-0.376353\pi$
$661$	−6.00000	−	3.46410i	−0.233373	−	0.134738i	−0.612127	+	0.790759i	$0.709686\pi$
$662$		0			0
$663$	18.0000	−	10.3923i	0.699062	−	0.403604i
$664$		0			0
$665$	15.5885	+	3.00000i	0.604494	+	0.116335i
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$		0			0
$669$	38.9711	+	22.5000i	1.50671	+	0.869900i
$670$		0			0
$671$		0			0
$672$		0			0
$673$	−41.0000			−1.58043			−0.790217	−	0.612827i	$-0.790032\pi$
$673$	−41.0000			−1.58043			−0.790217	+	0.612827i	$0.790032\pi$
$674$		0			0
$675$	−5.19615	+	9.00000i	−0.200000	+	0.346410i
$676$		0			0
$677$	2.59808	+	4.50000i	0.0998522	+	0.172949i	0.911623	−	0.411027i	$-0.134830\pi$
$677$	2.59808	+	4.50000i	0.0998522	+	0.172949i	−0.811771	+	0.583976i	$0.801496\pi$
$678$		0			0
$679$	4.50000	+	12.9904i	0.172694	+	0.498525i
$680$		0			0
$681$	−4.50000	−	7.79423i	−0.172440	−	0.298675i
$682$		0			0
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	0.109926	−	0.993940i	$-0.464939\pi$
$683$	−18.1865	−	10.5000i	−0.695888	−	0.401771i	−0.805814	+	0.592168i	$0.798272\pi$
$684$		0			0
$685$			31.1769i			1.19121i
$686$		0			0
$687$			24.0000i			0.915657i
$688$		0			0
$689$	−15.5885	+	27.0000i	−0.593873	+	1.02862i
$690$		0			0
$691$	6.00000	−	3.46410i	0.228251	−	0.131781i	−0.381514	−	0.924363i	$-0.624597\pi$
$691$	6.00000	−	3.46410i	0.228251	−	0.131781i	0.609765	+	0.792582i	$0.291264\pi$
$692$		0			0
$693$	7.79423	+	22.5000i	0.296078	+	0.854704i
$694$		0			0
$695$	−25.9808	+	15.0000i	−0.985506	+	0.568982i
$696$		0			0
$697$	−12.0000	+	20.7846i	−0.454532	+	0.787273i
$698$		0			0
$699$			31.1769i			1.17922i
$700$		0			0
$701$		−	3.00000i		−	0.113308i	−0.998394	−	0.0566542i	$-0.981957\pi$
$701$		−	3.00000i		−	0.113308i	0.998394	−	0.0566542i	$-0.0180433\pi$
$702$		0			0
$703$	−6.00000	−	3.46410i	−0.226294	−	0.130651i
$704$		0			0
$705$	−10.3923	−	18.0000i	−0.391397	−	0.677919i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	0.963512	+	0.267664i	$0.0862517\pi$
$709$	19.0000	+	32.9090i	0.713560	+	1.23592i	−0.249952	+	0.968258i	$0.580415\pi$
$710$		0			0
$711$	−1.50000	+	2.59808i	−0.0562544	+	0.0974355i
$712$		0			0
$713$	10.3923			0.389195
$714$		0			0
$715$	−18.0000			−0.673162
$716$		0			0
$717$	−9.00000	−	5.19615i	−0.336111	−	0.194054i
$718$		0			0
$719$	22.5167	+	39.0000i	0.839730	+	1.45445i	0.890121	+	0.455725i	$0.150620\pi$
$719$	22.5167	+	39.0000i	0.839730	+	1.45445i	−0.0503909	+	0.998730i	$0.516047\pi$
$720$		0			0
$721$	6.00000	−	6.92820i	0.223452	−	0.258020i
$722$		0			0
$723$	−38.9711	+	22.5000i	−1.44935	+	0.836784i
$724$		0			0
$725$	5.19615	+	3.00000i	0.192980	+	0.111417i
$726$		0			0
$727$		−	29.4449i		−	1.09205i	−0.837769	−	0.546025i	$-0.816140\pi$
$727$		−	29.4449i		−	1.09205i	0.837769	−	0.546025i	$-0.183860\pi$
$728$		0			0
$729$	27.0000			1.00000
$730$		0			0
$731$	13.8564	−	24.0000i	0.512498	−	0.887672i
$732$		0			0
$733$	30.0000	−	17.3205i	1.10808	−	0.639748i	0.169745	−	0.985488i	$-0.445706\pi$
$733$	30.0000	−	17.3205i	1.10808	−	0.639748i	0.938330	+	0.345740i	$0.112372\pi$
$734$		0			0
$735$	−16.5000	+	12.9904i	−0.608612	+	0.479157i
$736$		0			0
$737$	−5.19615	+	3.00000i	−0.191403	+	0.110506i
$738$		0			0
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	−0.943215	−	0.332184i	$-0.892215\pi$
$739$	−5.00000	+	8.66025i	−0.183928	+	0.318573i	0.759287	+	0.650756i	$0.225548\pi$
$740$		0			0
$741$	−20.7846			−0.763542
$742$		0			0
$743$			18.0000i			0.660356i	0.943919	+	0.330178i	$0.107109\pi$
$743$			18.0000i			0.660356i	−0.943919	+	0.330178i	$0.892891\pi$
$744$		0			0
$745$	−27.0000	−	15.5885i	−0.989203	−	0.571117i
$746$		0			0
$747$	12.9904	+	22.5000i	0.475293	+	0.823232i
$748$		0			0
$749$	5.19615	−	6.00000i	0.189863	−	0.219235i
$750$		0			0
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	0.748056	−	0.663636i	$-0.230988\pi$
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	−0.948753	+	0.316017i	$0.897654\pi$
$752$		0			0
$753$	16.5000	−	28.5788i	0.601293	−	1.04147i
$754$		0			0
$755$	−12.1244			−0.441250
$756$		0			0
$757$	4.00000			0.145382			0.0726912	−	0.997354i	$-0.476841\pi$
$757$	4.00000			0.145382			0.0726912	+	0.997354i	$0.476841\pi$
$758$		0			0
$759$	−15.5885	+	27.0000i	−0.565825	+	0.980038i
$760$		0			0
$761$	8.66025	+	15.0000i	0.313934	+	0.543750i	0.979210	−	0.202848i	$-0.0650196\pi$
$761$	8.66025	+	15.0000i	0.313934	+	0.543750i	−0.665276	+	0.746597i	$0.731686\pi$
$762$		0			0
$763$	1.00000	−	5.19615i	0.0362024	−	0.188113i
$764$		0			0
$765$	9.00000	+	15.5885i	0.325396	+	0.563602i
$766$		0			0
$767$	−5.19615	−	3.00000i	−0.187622	−	0.108324i
$768$		0			0
$769$			19.0526i			0.687053i	0.939143	+	0.343526i	$0.111621\pi$
$769$			19.0526i			0.687053i	−0.939143	+	0.343526i	$0.888379\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$		0			0
$773$	−13.8564	+	24.0000i	−0.498380	+	0.863220i	−0.999998	−	0.00186926i	$-0.999405\pi$
$773$	−13.8564	+	24.0000i	−0.498380	+	0.863220i	0.501618	+	0.865089i	$0.332738\pi$
$774$		0			0
$775$	3.00000	−	1.73205i	0.107763	−	0.0622171i
$776$		0			0
$777$	8.66025	−	3.00000i	0.310685	−	0.107624i
$778$		0			0
$779$	20.7846	−	12.0000i	0.744686	−	0.429945i
$780$		0			0
$781$	18.0000	−	31.1769i	0.644091	−	1.11560i
$782$		0			0
$783$		−	15.5885i		−	0.557086i
$784$		0			0
$785$			36.0000i			1.28490i
$786$		0			0
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.305818	−	0.952090i	$-0.598930\pi$
$787$	−36.0000	−	20.7846i	−1.28326	−	0.740891i	−0.977443	+	0.211199i	$0.932263\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	10.3923	+	30.0000i	0.369508	+	1.06668i
$792$		0			0
$793$		0			0
$794$		0			0
$795$	−23.3827	−	13.5000i	−0.829298	−	0.478796i
$796$		0			0
$797$	25.9808			0.920286			0.460143	−	0.887845i	$-0.347798\pi$
$797$	25.9808			0.920286			0.460143	+	0.887845i	$0.347798\pi$
$798$		0			0
$799$	24.0000			0.849059
$800$		0			0
$801$	15.5885	−	27.0000i	0.550791	−	0.953998i
$802$		0			0
$803$	−10.3923	−	18.0000i	−0.366736	−	0.635206i
$804$		0			0
$805$	−27.0000	−	5.19615i	−0.951625	−	0.183140i
$806$		0			0
$807$	25.5000	+	44.1673i	0.897643	+	1.55476i
$808$		0			0
$809$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$809$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$810$		0			0
$811$		−	31.1769i		−	1.09477i	−0.836881	−	0.547385i	$-0.815623\pi$
$811$		−	31.1769i		−	1.09477i	0.836881	−	0.547385i	$-0.184377\pi$
$812$		0			0
$813$			9.00000i			0.315644i
$814$		0			0
$815$	12.1244	−	21.0000i	0.424698	−	0.735598i
$816$		0			0
$817$	−24.0000	+	13.8564i	−0.839654	+	0.484774i
$818$		0			0
$819$	18.0000	−	20.7846i	0.628971	−	0.726273i
$820$		0			0
$821$	2.59808	−	1.50000i	0.0906735	−	0.0523504i	−0.453978	−	0.891013i	$-0.649995\pi$
$821$	2.59808	−	1.50000i	0.0906735	−	0.0523504i	0.544651	+	0.838663i	$0.316662\pi$
$822$		0			0
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	−0.787850	−	0.615867i	$-0.788806\pi$
$823$	4.00000	−	6.92820i	0.139431	−	0.241502i	0.927281	+	0.374365i	$0.122139\pi$
$824$		0			0
$825$			10.3923i			0.361814i
$826$		0			0
$827$			9.00000i			0.312961i	0.987681	+	0.156480i	$0.0500148\pi$
$827$			9.00000i			0.312961i	−0.987681	+	0.156480i	$0.949985\pi$
$828$		0			0
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	0.216361	−	0.976314i	$-0.430581\pi$
$829$	−15.0000	−	8.66025i	−0.520972	−	0.300783i	−0.737332	+	0.675530i	$0.763915\pi$
$830$		0			0
$831$	6.92820	+	12.0000i	0.240337	+	0.416275i
$832$		0			0
$833$	−3.46410	−	24.0000i	−0.120024	−	0.831551i
$834$		0			0
$835$	15.0000	+	25.9808i	0.519096	+	0.899101i
$836$		0			0
$837$	−7.79423	−	4.50000i	−0.269408	−	0.155543i
$838$		0			0
$839$	3.46410			0.119594			0.0597970	−	0.998211i	$-0.480955\pi$
$839$	3.46410			0.119594			0.0597970	+	0.998211i	$0.480955\pi$
$840$		0			0
$841$	20.0000			0.689655
$842$		0			0
$843$	45.0000	+	25.9808i	1.54988	+	0.894825i
$844$		0			0
$845$	−0.866025	−	1.50000i	−0.0297922	−	0.0516016i
$846$		0			0
$847$	−4.00000	−	3.46410i	−0.137442	−	0.119028i
$848$		0			0
$849$	−41.5692	+	24.0000i	−1.42665	+	0.823678i
$850$		0			0
$851$	10.3923	+	6.00000i	0.356244	+	0.205677i
$852$		0			0
$853$		−	24.2487i		−	0.830260i	−0.909762	−	0.415130i	$-0.863736\pi$
$853$		−	24.2487i		−	0.830260i	0.909762	−	0.415130i	$-0.136264\pi$
$854$		0			0
$855$		−	18.0000i		−	0.615587i
$856$		0			0
$857$	6.92820	−	12.0000i	0.236663	−	0.409912i	−0.723092	−	0.690752i	$-0.757280\pi$
$857$	6.92820	−	12.0000i	0.236663	−	0.409912i	0.959755	+	0.280840i	$0.0906130\pi$
$858$		0			0
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	−0.160437	−	0.987046i	$-0.551290\pi$
$859$	18.0000	−	10.3923i	0.614152	−	0.354581i	0.774589	+	0.632465i	$0.217957\pi$
$860$		0			0
$861$	−6.00000	+	31.1769i	−0.204479	+	1.06251i
$862$		0			0
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.598933	−	0.800799i	$-0.295592\pi$
$863$	46.7654	−	27.0000i	1.59191	−	0.919091i	0.992979	−	0.118291i	$-0.0377417\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	8.66025			0.294118
$868$		0			0
$869$			3.00000i			0.101768i
$870$		0			0
$871$	6.00000	+	3.46410i	0.203302	+	0.117377i
$872$		0			0
$873$	13.5000	−	7.79423i	0.456906	−	0.263795i
$874$		0			0
$875$	−30.3109	+	10.5000i	−1.02470	+	0.354965i
$876$		0			0
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	−0.951175	−	0.308651i	$-0.900123\pi$
$877$	−22.0000	−	38.1051i	−0.742887	−	1.28672i	0.208288	−	0.978068i	$-0.433211\pi$
$878$		0			0
$879$	16.5000	−	28.5788i	0.556531	−	0.963940i
$880$		0			0
$881$	−10.3923			−0.350126			−0.175063	−	0.984557i	$-0.556013\pi$
$881$	−10.3923			−0.350126			−0.175063	+	0.984557i	$0.556013\pi$
$882$		0			0
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$		0			0
$885$	2.59808	−	4.50000i	0.0873334	−	0.151266i
$886$		0			0
$887$	−12.1244	−	21.0000i	−0.407096	−	0.705111i	0.587467	−	0.809248i	$-0.300125\pi$
$887$	−12.1244	−	21.0000i	−0.407096	−	0.705111i	−0.994563	+	0.104137i	$0.966792\pi$
$888$		0			0
$889$	−27.5000	+	9.52628i	−0.922320	+	0.319501i
$890$		0			0
$891$	23.3827	−	13.5000i	0.783349	−	0.452267i
$892$		0			0
$893$	−20.7846	−	12.0000i	−0.695530	−	0.401565i
$894$		0			0
$895$		−	20.7846i		−	0.694753i
$896$		0			0
$897$	36.0000			1.20201
$898$		0			0
$899$	−2.59808	+	4.50000i	−0.0866507	+	0.150083i
$900$		0			0
$901$	27.0000	−	15.5885i	0.899500	−	0.519327i
$902$		0			0
$903$	6.92820	−	36.0000i	0.230556	−	1.19800i
$904$		0			0
$905$	10.3923	−	6.00000i	0.345452	−	0.199447i
$906$		0			0
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	−0.997016	−	0.0771920i	$-0.975405\pi$
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	0.565358	+	0.824845i	$0.308738\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$		0			0		1.00000			$0$
$911$		0			0		−1.00000			$\pi$
$912$		0			0
$913$	22.5000	+	12.9904i	0.744641	+	0.429919i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−10.3923	−	9.00000i	−0.343184	−	0.297206i
$918$		0			0
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	0.652616	−	0.757689i	$-0.273671\pi$
$919$	−10.0000	−	17.3205i	−0.329870	−	0.571351i	−0.982486	+	0.186338i	$0.940338\pi$
$920$		0			0
$921$	36.3731	+	21.0000i	1.19853	+	0.691974i
$922$		0			0
$923$	−41.5692			−1.36827
$924$		0			0
$925$	4.00000			0.131519
$926$		0			0
$927$	−9.00000	−	5.19615i	−0.295599	−	0.170664i
$928$		0			0
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	−0.922474	−	0.386060i	$-0.873836\pi$
$929$	−24.2487	−	42.0000i	−0.795574	−	1.37798i	0.126899	−	0.991916i	$-0.459497\pi$
$930$		0			0
$931$	−9.00000	+	22.5167i	−0.294963	+	0.737954i
$932$		0			0
$933$	12.0000	+	20.7846i	0.392862	+	0.680458i
$934$		0			0
$935$	15.5885	+	9.00000i	0.509797	+	0.294331i
$936$		0			0
$937$			22.5167i			0.735587i	0.929907	+	0.367794i	$0.119887\pi$
$937$			22.5167i			0.735587i	−0.929907	+	0.367794i	$0.880113\pi$
$938$		0			0
$939$		−	3.00000i		−	0.0979013i
$940$		0			0
$941$	16.4545	−	28.5000i	0.536401	−	0.929073i	−0.462693	−	0.886518i	$-0.653117\pi$
$941$	16.4545	−	28.5000i	0.536401	−	0.929073i	0.999094	−	0.0425550i	$-0.0135498\pi$
$942$		0			0
$943$	−36.0000	+	20.7846i	−1.17232	+	0.676840i
$944$		0			0
$945$	18.0000	+	15.5885i	0.585540	+	0.507093i
$946$		0			0
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	−0.321552	−	0.946892i	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		0			0
$949$	−12.0000	+	20.7846i	−0.389536	+	0.674697i
$950$		0			0
$951$			25.9808i			0.842484i
$952$		0			0
$953$			24.0000i			0.777436i	0.921357	+	0.388718i	$0.127082\pi$
$953$			24.0000i			0.777436i	−0.921357	+	0.388718i	$0.872918\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	−7.79423	−	13.5000i	−0.251952	−	0.436393i
$958$		0			0
$959$	−46.7654	−	9.00000i	−1.51013	−	0.290625i
$960$		0			0
$961$	−14.0000	−	24.2487i	−0.451613	−	0.782216i
$962$		0			0
$963$	−7.79423	−	4.50000i	−0.251166	−	0.145010i
$964$		0			0
$965$	−39.8372			−1.28240
$966$		0			0
$967$	7.00000			0.225105			0.112552	−	0.993646i	$-0.464097\pi$
$967$	7.00000			0.225105			0.112552	+	0.993646i	$0.464097\pi$
$968$		0			0
$969$	18.0000	+	10.3923i	0.578243	+	0.333849i
$970$		0			0
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	0.927103	−	0.374806i	$-0.122291\pi$
$971$	4.33013	+	7.50000i	0.138960	+	0.240686i	−0.788143	+	0.615492i	$0.788957\pi$
$972$		0			0
$973$	−15.0000	−	43.3013i	−0.480878	−	1.38817i
$974$		0			0
$975$	10.3923	−	6.00000i	0.332820	−	0.192154i
$976$		0			0
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	0.794164	−	0.607704i	$-0.207909\pi$
$977$	20.7846	+	12.0000i	0.664959	+	0.383914i	−0.129205	+	0.991618i	$0.541243\pi$
$978$		0			0
$979$		−	31.1769i		−	0.996419i
$980$		0			0
$981$	−6.00000			−0.191565
$982$		0			0
$983$	6.92820	−	12.0000i	0.220975	−	0.382741i	−0.734129	−	0.679010i	$-0.762409\pi$
$983$	6.92820	−	12.0000i	0.220975	−	0.382741i	0.955104	+	0.296269i	$0.0957426\pi$
$984$		0			0
$985$	−27.0000	+	15.5885i	−0.860292	+	0.496690i
$986$		0			0
$987$	30.0000	−	10.3923i	0.954911	−	0.330791i
$988$		0			0
$989$	41.5692	−	24.0000i	1.32182	−	0.763156i
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$		0			0
$993$	−13.8564			−0.439720
$994$		0			0
$995$			18.0000i			0.570638i
$996$		0			0
$997$	15.0000	+	8.66025i	0.475055	+	0.274273i	0.718353	−	0.695678i	$-0.244896\pi$
$997$	15.0000	+	8.66025i	0.475055	+	0.274273i	−0.243299	+	0.969951i	$0.578229\pi$
$998$		0			0
$999$	−5.19615	−	9.00000i	−0.164399	−	0.284747i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.bc.e.17.2		4
3.2	odd	2	inner	336.2.bc.e.17.1		4
4.3	odd	2		42.2.f.a.17.2	yes	4
7.3	odd	6		2352.2.k.e.881.4		4
7.4	even	3		2352.2.k.e.881.2		4
7.5	odd	6	inner	336.2.bc.e.257.1		4
12.11	even	2		42.2.f.a.17.1	yes	4
20.3	even	4		1050.2.u.a.899.2		4
20.7	even	4		1050.2.u.d.899.1		4
20.19	odd	2		1050.2.s.b.101.1		4
21.5	even	6	inner	336.2.bc.e.257.2		4
21.11	odd	6		2352.2.k.e.881.3		4
21.17	even	6		2352.2.k.e.881.1		4
28.3	even	6		294.2.d.a.293.3		4
28.11	odd	6		294.2.d.a.293.4		4
28.19	even	6		42.2.f.a.5.1	✓	4
28.23	odd	6		294.2.f.a.215.1		4
28.27	even	2		294.2.f.a.227.2		4
36.7	odd	6		1134.2.t.d.1025.1		4
36.11	even	6		1134.2.t.d.1025.2		4
36.23	even	6		1134.2.l.c.269.1		4
36.31	odd	6		1134.2.l.c.269.2		4
60.23	odd	4		1050.2.u.d.899.2		4
60.47	odd	4		1050.2.u.a.899.1		4
60.59	even	2		1050.2.s.b.101.2		4
84.11	even	6		294.2.d.a.293.1		4
84.23	even	6		294.2.f.a.215.2		4
84.47	odd	6		42.2.f.a.5.2	yes	4
84.59	odd	6		294.2.d.a.293.2		4
84.83	odd	2		294.2.f.a.227.1		4
140.19	even	6		1050.2.s.b.551.2		4
140.47	odd	12		1050.2.u.d.299.2		4
140.103	odd	12		1050.2.u.a.299.1		4
252.47	odd	6		1134.2.l.c.215.1		4
252.103	even	6		1134.2.t.d.593.2		4
252.131	odd	6		1134.2.t.d.593.1		4
252.187	even	6		1134.2.l.c.215.2		4
420.47	even	12		1050.2.u.a.299.2		4
420.299	odd	6		1050.2.s.b.551.1		4
420.383	even	12		1050.2.u.d.299.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.f.a.5.1	✓	4	28.19	even	6
42.2.f.a.5.2	yes	4	84.47	odd	6
42.2.f.a.17.1	yes	4	12.11	even	2
42.2.f.a.17.2	yes	4	4.3	odd	2
294.2.d.a.293.1		4	84.11	even	6
294.2.d.a.293.2		4	84.59	odd	6
294.2.d.a.293.3		4	28.3	even	6
294.2.d.a.293.4		4	28.11	odd	6
294.2.f.a.215.1		4	28.23	odd	6
294.2.f.a.215.2		4	84.23	even	6
294.2.f.a.227.1		4	84.83	odd	2
294.2.f.a.227.2		4	28.27	even	2
336.2.bc.e.17.1		4	3.2	odd	2	inner
336.2.bc.e.17.2		4	1.1	even	1	trivial
336.2.bc.e.257.1		4	7.5	odd	6	inner
336.2.bc.e.257.2		4	21.5	even	6	inner
1050.2.s.b.101.1		4	20.19	odd	2
1050.2.s.b.101.2		4	60.59	even	2
1050.2.s.b.551.1		4	420.299	odd	6
1050.2.s.b.551.2		4	140.19	even	6
1050.2.u.a.299.1		4	140.103	odd	12
1050.2.u.a.299.2		4	420.47	even	12
1050.2.u.a.899.1		4	60.47	odd	4
1050.2.u.a.899.2		4	20.3	even	4
1050.2.u.d.299.1		4	420.383	even	12
1050.2.u.d.299.2		4	140.47	odd	12
1050.2.u.d.899.1		4	20.7	even	4
1050.2.u.d.899.2		4	60.23	odd	4
1134.2.l.c.215.1		4	252.47	odd	6
1134.2.l.c.215.2		4	252.187	even	6
1134.2.l.c.269.1		4	36.23	even	6
1134.2.l.c.269.2		4	36.31	odd	6
1134.2.t.d.593.1		4	252.131	odd	6
1134.2.t.d.593.2		4	252.103	even	6
1134.2.t.d.1025.1		4	36.7	odd	6
1134.2.t.d.1025.2		4	36.11	even	6
2352.2.k.e.881.1		4	21.17	even	6
2352.2.k.e.881.2		4	7.4	even	3
2352.2.k.e.881.3		4	21.11	odd	6
2352.2.k.e.881.4		4	7.3	odd	6

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bc (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 1.50000i) q^{3} +(-0.866025 - 1.50000i) q^{5} +(2.50000 - 0.866025i) q^{7} +(-1.50000 - 2.59808i) q^{9} +(-2.59808 - 1.50000i) q^{11} +3.46410i q^{13} -3.00000 q^{15} +(1.73205 - 3.00000i) q^{17} +(-3.00000 + 1.73205i) q^{19} +(0.866025 - 4.50000i) q^{21} +(5.19615 - 3.00000i) q^{23} +(1.00000 - 1.73205i) q^{25} -5.19615 q^{27} +3.00000i q^{29} +(1.50000 + 0.866025i) q^{31} +(-4.50000 + 2.59808i) q^{33} +(-3.46410 - 3.00000i) q^{35} +(1.00000 + 1.73205i) q^{37} +(5.19615 + 3.00000i) q^{39} -6.92820 q^{41} +8.00000 q^{43} +(-2.59808 + 4.50000i) q^{45} +(3.46410 + 6.00000i) q^{47} +(5.50000 - 4.33013i) q^{49} +(-3.00000 - 5.19615i) q^{51} +(7.79423 + 4.50000i) q^{53} +5.19615i q^{55} +6.00000i q^{57} +(-0.866025 + 1.50000i) q^{59} +(-6.00000 - 5.19615i) q^{63} +(5.19615 - 3.00000i) q^{65} +(1.00000 - 1.73205i) q^{67} -10.3923i q^{69} +12.0000i q^{71} +(6.00000 + 3.46410i) q^{73} +(-1.73205 - 3.00000i) q^{75} +(-7.79423 - 1.50000i) q^{77} +(-0.500000 - 0.866025i) q^{79} +(-4.50000 + 7.79423i) q^{81} -8.66025 q^{83} -6.00000 q^{85} +(4.50000 + 2.59808i) q^{87} +(5.19615 + 9.00000i) q^{89} +(3.00000 + 8.66025i) q^{91} +(2.59808 - 1.50000i) q^{93} +(5.19615 + 3.00000i) q^{95} +5.19615i q^{97} +9.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{7} - 6 q^{9} - 12 q^{15} - 12 q^{19} + 4 q^{25} + 6 q^{31} - 18 q^{33} + 4 q^{37} + 32 q^{43} + 22 q^{49} - 12 q^{51} - 24 q^{63} + 4 q^{67} + 24 q^{73} - 2 q^{79} - 18 q^{81} - 24 q^{85} + 18 q^{87}+ \cdots + 12 q^{91}+O(q^{100}) \) 4 * q + 10 * q^7 - 6 * q^9 - 12 * q^15 - 12 * q^19 + 4 * q^25 + 6 * q^31 - 18 * q^33 + 4 * q^37 + 32 * q^43 + 22 * q^49 - 12 * q^51 - 24 * q^63 + 4 * q^67 + 24 * q^73 - 2 * q^79 - 18 * q^81 - 24 * q^85 + 18 * q^87 + 12 * q^91

Introduction

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