LMFDB - Embedded newform 1050.2.o.h.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1050,2,Mod(499,1050)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1050, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1050.499");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1050.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$8.38429221223$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1050.499
Dual form			1050.2.o.h.949.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.59808 - 1.50000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-2.00000 - 1.73205i) q^{21} -6.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(-3.46410 + 2.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} -3.00000 q^{41} +(-0.866025 - 2.50000i) q^{42} +8.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(7.79423 + 4.50000i) q^{47} +1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(3.46410 - 2.00000i) q^{52} +(10.3923 - 6.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} +4.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-1.00000 + 1.73205i) q^{61} -5.00000i q^{62} +(-2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} -3.00000 q^{69} -9.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-10.3923 + 12.0000i) q^{77} -4.00000i q^{78} +(-3.50000 + 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(0.500000 - 2.59808i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(5.19615 - 3.00000i) q^{87} +(5.19615 - 3.00000i) q^{88} +(1.50000 - 2.59808i) q^{89} +(-10.0000 + 3.46410i) q^{91} -3.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(4.50000 + 7.79423i) q^{94} +(-0.500000 + 0.866025i) q^{96} -17.0000i q^{97} +(-6.92820 + 1.00000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	$ 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{19} - 8 q^{21} + 2 q^{24} + 8 q^{26} + 24 q^{29} - 10 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 12 q^{41} + 12 q^{44} - 6 q^{46} - 22 q^{49} + 6 q^{51} + 2 q^{54} + 10 q^{56} + 12 q^{59} - 4 q^{61} - 4 q^{64} - 12 q^{66} - 12 q^{69} - 36 q^{71} + 16 q^{74} - 16 q^{76} - 14 q^{79} - 2 q^{81} + 2 q^{84} - 16 q^{86} + 6 q^{89} - 40 q^{91} + 18 q^{94} - 2 q^{96} - 24 q^{99}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^19 - 8 * q^21 + 2 * q^24 + 8 * q^26 + 24 * q^29 - 10 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 12 * q^41 + 12 * q^44 - 6 * q^46 - 22 * q^49 + 6 * q^51 + 2 * q^54 + 10 * q^56 + 12 * q^59 - 4 * q^61 - 4 * q^64 - 12 * q^66 - 12 * q^69 - 36 * q^71 + 16 * q^74 - 16 * q^76 - 14 * q^79 - 2 * q^81 + 2 * q^84 - 16 * q^86 + 6 * q^89 - 40 * q^91 + 18 * q^94 - 2 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times$.

$n$	$127$	$451$	$701$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0
$5$		0			0
$6$	1.00000			0.408248
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$7$	−0.866025	−	2.50000i	−0.327327	−	0.944911i
$8$			1.00000i			0.353553i
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	0.866025	+	0.500000i	0.250000	+	0.144338i
$13$		−	4.00000i		−	1.10940i	−0.832050	−	0.554700i	$-0.812833\pi$
$13$		−	4.00000i		−	1.10940i	0.832050	−	0.554700i	$-0.187167\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.59808	−	1.50000i	0.630126	−	0.363803i	−0.150675	−	0.988583i	$-0.548145\pi$
$17$	2.59808	−	1.50000i	0.630126	−	0.363803i	0.780801	+	0.624780i	$0.214811\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$		0			0
$21$	−2.00000	−	1.73205i	−0.436436	−	0.377964i
$22$		−	6.00000i		−	1.27920i
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	0.204046	−	0.978961i	$-0.434591\pi$
$23$	−2.59808	−	1.50000i	−0.541736	−	0.312772i	−0.745782	+	0.666190i	$0.767924\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$		0			0
$26$	2.00000	−	3.46410i	0.392232	−	0.679366i
$27$		−	1.00000i		−	0.192450i
$28$	1.73205	−	2.00000i	0.327327	−	0.377964i
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	0.549309	−	0.835619i	$-0.314891\pi$
$31$	−2.50000	−	4.33013i	−0.449013	−	0.777714i	−0.998322	+	0.0579057i	$0.981558\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$	3.00000			0.514496
$35$		0			0
$36$	1.00000			0.166667
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.946180	−	0.323640i	$-0.104907\pi$
$37$	6.92820	+	4.00000i	1.13899	+	0.657596i	0.192809	+	0.981236i	$0.438240\pi$
$38$	−3.46410	+	2.00000i	−0.561951	+	0.324443i
$39$	−2.00000	−	3.46410i	−0.320256	−	0.554700i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$	−0.866025	−	2.50000i	−0.133631	−	0.385758i
$43$			8.00000i			1.21999i	0.792406	+	0.609994i	$0.208828\pi$
$43$			8.00000i			1.21999i	−0.792406	+	0.609994i	$0.791172\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$		0			0
$46$	−1.50000	−	2.59808i	−0.221163	−	0.383065i
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.945662	−	0.325150i	$-0.105415\pi$
$47$	7.79423	+	4.50000i	1.13691	+	0.656392i	0.191243	+	0.981543i	$0.438748\pi$
$48$			1.00000i			0.144338i
$49$	−5.50000	+	4.33013i	−0.785714	+	0.618590i
$50$		0			0
$51$	1.50000	−	2.59808i	0.210042	−	0.363803i
$52$	3.46410	−	2.00000i	0.480384	−	0.277350i
$53$	10.3923	−	6.00000i	1.42749	−	0.824163i	0.430570	−	0.902557i	$-0.358312\pi$
$53$	10.3923	−	6.00000i	1.42749	−	0.824163i	0.996922	+	0.0783936i	$0.0249791\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	2.50000	−	0.866025i	0.334077	−	0.115728i
$57$			4.00000i			0.529813i
$58$	5.19615	+	3.00000i	0.682288	+	0.393919i
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		−	5.00000i		−	0.635001i
$63$	−2.59808	−	0.500000i	−0.327327	−	0.0629941i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−3.00000	−	5.19615i	−0.369274	−	0.639602i
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	−0.859440	−	0.511237i	$-0.829187\pi$
$67$	−6.92820	+	4.00000i	−0.846415	+	0.488678i	0.0130248	+	0.999915i	$0.495854\pi$
$68$	2.59808	+	1.50000i	0.315063	+	0.181902i
$69$	−3.00000			−0.361158
$70$		0			0
$71$	−9.00000			−1.06810			−0.534052	−	0.845452i	$-0.679331\pi$
$71$	−9.00000			−1.06810			−0.534052	+	0.845452i	$0.679331\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.422833	−	0.906208i	$-0.361036\pi$
$73$	12.1244	−	7.00000i	1.41905	−	0.819288i	0.996215	+	0.0869195i	$0.0277023\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$		0			0
$76$	−4.00000			−0.458831
$77$	−10.3923	+	12.0000i	−1.18431	+	1.36753i
$78$		−	4.00000i		−	0.452911i
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	−0.992945	−	0.118578i	$-0.962166\pi$
$79$	−3.50000	+	6.06218i	−0.393781	+	0.682048i	0.599164	+	0.800626i	$0.295500\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.59808	−	1.50000i	−0.286910	−	0.165647i
$83$		−	6.00000i		−	0.658586i	−0.944228	−	0.329293i	$-0.893190\pi$
$83$		−	6.00000i		−	0.658586i	0.944228	−	0.329293i	$-0.106810\pi$
$84$	0.500000	−	2.59808i	0.0545545	−	0.283473i
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$	5.19615	−	3.00000i	0.553912	−	0.319801i
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	−10.0000	+	3.46410i	−1.04828	+	0.363137i
$92$		−	3.00000i		−	0.312772i
$93$	−4.33013	−	2.50000i	−0.449013	−	0.259238i
$94$	4.50000	+	7.79423i	0.464140	+	0.803913i
$95$		0			0
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$		−	17.0000i		−	1.72609i	−0.505128	−	0.863044i	$-0.668555\pi$
$97$		−	17.0000i		−	1.72609i	0.505128	−	0.863044i	$-0.331445\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$	−6.00000			−0.603023
$100$		0			0
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	2.59808	−	1.50000i	0.257248	−	0.148522i
$103$	11.2583	+	6.50000i	1.10932	+	0.640464i	0.938652	−	0.344865i	$-0.112075\pi$
$103$	11.2583	+	6.50000i	1.10932	+	0.640464i	0.170664	+	0.985329i	$0.445409\pi$
$104$	4.00000			0.392232
$105$		0			0
$106$	12.0000			1.16554
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	0.729676	−	0.683793i	$-0.239671\pi$
$107$	5.19615	+	3.00000i	0.502331	+	0.290021i	−0.227345	+	0.973814i	$0.573004\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	0.754204	−	0.656640i	$-0.228023\pi$
$109$	−2.00000	−	3.46410i	−0.191565	−	0.331801i	−0.945769	+	0.324840i	$0.894690\pi$
$110$		0			0
$111$	8.00000			0.759326
$112$	2.59808	+	0.500000i	0.245495	+	0.0472456i
$113$			3.00000i			0.282216i	0.989994	+	0.141108i	$0.0450665\pi$
$113$			3.00000i			0.282216i	−0.989994	+	0.141108i	$0.954933\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$		0			0
$116$	3.00000	+	5.19615i	0.278543	+	0.482451i
$117$	−3.46410	−	2.00000i	−0.320256	−	0.184900i
$118$			6.00000i			0.552345i
$119$	−6.00000	−	5.19615i	−0.550019	−	0.476331i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−1.73205	+	1.00000i	−0.156813	+	0.0905357i
$123$	−2.59808	+	1.50000i	−0.234261	+	0.135250i
$124$	2.50000	−	4.33013i	0.224507	−	0.388857i
$125$		0			0
$126$	−2.00000	−	1.73205i	−0.178174	−	0.154303i
$127$			16.0000i			1.41977i	0.704317	+	0.709885i	$0.251253\pi$
$127$			16.0000i			1.41977i	−0.704317	+	0.709885i	$0.748747\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		−	6.00000i		−	0.522233i
$133$	10.3923	+	2.00000i	0.901127	+	0.173422i
$134$	−8.00000			−0.691095
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.171054	−	0.985262i	$-0.445283\pi$
$137$	12.9904	−	7.50000i	1.10984	−	0.640768i	0.938789	+	0.344493i	$0.111949\pi$
$138$	−2.59808	−	1.50000i	−0.221163	−	0.127688i
$139$	−2.00000			−0.169638			−0.0848189	−	0.996396i	$-0.527031\pi$
$139$	−2.00000			−0.169638			−0.0848189	+	0.996396i	$0.527031\pi$
$140$		0			0
$141$	9.00000			0.757937
$142$	−7.79423	−	4.50000i	−0.654077	−	0.377632i
$143$	−20.7846	+	12.0000i	−1.73810	+	1.00349i
$144$	0.500000	+	0.866025i	0.0416667	+	0.0721688i
$145$		0			0
$146$	14.0000			1.15865
$147$	−2.59808	+	6.50000i	−0.214286	+	0.536111i
$148$			8.00000i			0.657596i
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	0.982873	+	0.184284i	$0.0589965\pi$
$151$	8.00000	+	13.8564i	0.651031	+	1.12762i	−0.331842	+	0.943335i	$0.607670\pi$
$152$	−3.46410	−	2.00000i	−0.280976	−	0.162221i
$153$		−	3.00000i		−	0.242536i
$154$	−15.0000	+	5.19615i	−1.20873	+	0.418718i
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−12.1244	+	7.00000i	−0.967629	+	0.558661i	−0.898513	−	0.438948i	$-0.855351\pi$
$157$	−12.1244	+	7.00000i	−0.967629	+	0.558661i	−0.0691164	+	0.997609i	$0.522018\pi$
$158$	−6.06218	+	3.50000i	−0.482281	+	0.278445i
$159$	6.00000	−	10.3923i	0.475831	−	0.824163i
$160$		0			0
$161$	−1.50000	+	7.79423i	−0.118217	+	0.614271i
$162$		−	1.00000i		−	0.0785674i
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	0.203497	−	0.979076i	$-0.434769\pi$
$163$	−6.92820	−	4.00000i	−0.542659	−	0.313304i	−0.746156	+	0.665771i	$0.768103\pi$
$164$	−1.50000	−	2.59808i	−0.117130	−	0.202876i
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$		0			0		1.00000			$0$
$167$		0			0		−1.00000			$\pi$
$168$	1.73205	−	2.00000i	0.133631	−	0.154303i
$169$	−3.00000			−0.230769
$170$		0			0
$171$	2.00000	+	3.46410i	0.152944	+	0.264906i
$172$	−6.92820	+	4.00000i	−0.528271	+	0.304997i
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	0.684349	−	0.729155i	$-0.260087\pi$
$173$	5.19615	+	3.00000i	0.395056	+	0.228086i	−0.289292	+	0.957241i	$0.593420\pi$
$174$	6.00000			0.454859
$175$		0			0
$176$	6.00000			0.452267
$177$	5.19615	+	3.00000i	0.390567	+	0.225494i
$178$	2.59808	−	1.50000i	0.194734	−	0.112430i
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	−0.977138	−	0.212607i	$-0.931805\pi$
$179$	−9.00000	−	15.5885i	−0.672692	−	1.16514i	0.304446	−	0.952529i	$-0.401529\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−10.3923	−	2.00000i	−0.770329	−	0.148250i
$183$			2.00000i			0.147844i
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$	−15.5885	−	9.00000i	−1.13994	−	0.658145i
$188$			9.00000i			0.656392i
$189$	−2.50000	+	0.866025i	−0.181848	+	0.0629941i
$190$		0			0
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	0.456068	+	0.889945i	$0.349257\pi$
$191$	−7.50000	+	12.9904i	−0.542681	+	0.939951i	−0.998749	+	0.0500060i	$0.984076\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	4.33013	−	2.50000i	0.311689	−	0.179954i	−0.335993	−	0.941865i	$-0.609072\pi$
$193$	4.33013	−	2.50000i	0.311689	−	0.179954i	0.647682	+	0.761911i	$0.275738\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$		0			0		1.00000			$0$
$197$		0			0		−1.00000			$\pi$
$198$	−5.19615	−	3.00000i	−0.369274	−	0.213201i
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	0.940927	−	0.338608i	$-0.109956\pi$
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	−0.763707	+	0.645563i	$0.776623\pi$
$200$		0			0
$201$	−4.00000	+	6.92820i	−0.282138	+	0.488678i
$202$		−	12.0000i		−	0.844317i
$203$	−5.19615	−	15.0000i	−0.364698	−	1.05279i
$204$	3.00000			0.210042
$205$		0			0
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$	−2.59808	+	1.50000i	−0.180579	+	0.104257i
$208$	3.46410	+	2.00000i	0.240192	+	0.138675i
$209$	24.0000			1.66011
$210$		0			0
$211$	8.00000			0.550743			0.275371	−	0.961338i	$-0.411199\pi$
$211$	8.00000			0.550743			0.275371	+	0.961338i	$0.411199\pi$
$212$	10.3923	+	6.00000i	0.713746	+	0.412082i
$213$	−7.79423	+	4.50000i	−0.534052	+	0.308335i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	1.00000			0.0680414
$217$	−8.66025	+	10.0000i	−0.587896	+	0.678844i
$218$		−	4.00000i		−	0.270914i
$219$	7.00000	−	12.1244i	0.473016	−	0.819288i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	6.92820	+	4.00000i	0.464991	+	0.268462i
$223$			11.0000i			0.736614i	0.929704	+	0.368307i	$0.120063\pi$
$223$			11.0000i			0.736614i	−0.929704	+	0.368307i	$0.879937\pi$
$224$	2.00000	+	1.73205i	0.133631	+	0.115728i
$225$		0			0
$226$	−1.50000	+	2.59808i	−0.0997785	+	0.172821i
$227$	15.5885	−	9.00000i	1.03464	−	0.597351i	0.116331	−	0.993210i	$-0.462887\pi$
$227$	15.5885	−	9.00000i	1.03464	−	0.597351i	0.918311	+	0.395860i	$0.129553\pi$
$228$	−3.46410	+	2.00000i	−0.229416	+	0.132453i
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$		0			0
$231$	−3.00000	+	15.5885i	−0.197386	+	1.02565i
$232$			6.00000i			0.393919i
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	0.320043	−	0.947403i	$-0.396303\pi$
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	−0.660454	+	0.750867i	$0.729636\pi$
$234$	−2.00000	−	3.46410i	−0.130744	−	0.226455i
$235$		0			0
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$			7.00000i			0.454699i
$238$	−2.59808	−	7.50000i	−0.168408	−	0.486153i
$239$	−3.00000			−0.194054			−0.0970269	−	0.995282i	$-0.530933\pi$
$239$	−3.00000			−0.194054			−0.0970269	+	0.995282i	$0.530933\pi$
$240$		0			0
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	0.965387	+	0.260822i	$0.0839937\pi$
$241$	11.0000	+	19.0526i	0.708572	+	1.22728i	−0.256814	+	0.966461i	$0.582673\pi$
$242$	−21.6506	+	12.5000i	−1.39176	+	0.803530i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−2.00000			−0.128037
$245$		0			0
$246$	−3.00000			−0.191273
$247$	13.8564	+	8.00000i	0.881662	+	0.509028i
$248$	4.33013	−	2.50000i	0.274963	−	0.158750i
$249$	−3.00000	−	5.19615i	−0.190117	−	0.329293i
$250$		0			0
$251$	24.0000			1.51487			0.757433	−	0.652913i	$-0.226453\pi$
$251$	24.0000			1.51487			0.757433	+	0.652913i	$0.226453\pi$
$252$	−0.866025	−	2.50000i	−0.0545545	−	0.157485i
$253$			18.0000i			1.13165i
$254$	−8.00000	+	13.8564i	−0.501965	+	0.869428i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.0724199	−	0.997374i	$-0.523072\pi$
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.899961	+	0.435970i	$0.856405\pi$
$258$			8.00000i			0.498058i
$259$	4.00000	−	20.7846i	0.248548	−	1.29149i
$260$		0			0
$261$	3.00000	−	5.19615i	0.185695	−	0.321634i
$262$	15.5885	−	9.00000i	0.963058	−	0.556022i
$263$	−2.59808	+	1.50000i	−0.160204	+	0.0924940i	−0.577959	−	0.816066i	$-0.696151\pi$
$263$	−2.59808	+	1.50000i	−0.160204	+	0.0924940i	0.417755	+	0.908560i	$0.362817\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	8.00000	+	6.92820i	0.490511	+	0.424795i
$267$		−	3.00000i		−	0.183597i
$268$	−6.92820	−	4.00000i	−0.423207	−	0.244339i
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	−0.183876	−	0.982949i	$-0.558865\pi$
$271$	12.5000	−	21.6506i	0.759321	−	1.31518i	0.943197	−	0.332233i	$-0.107802\pi$
$272$			3.00000i			0.181902i
$273$	−6.92820	+	8.00000i	−0.419314	+	0.484182i
$274$	15.0000			0.906183
$275$		0			0
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.988654	−	0.150210i	$-0.952005\pi$
$277$	−22.5167	+	13.0000i	−1.35290	+	0.781094i	−0.364241	+	0.931305i	$0.618672\pi$
$278$	−1.73205	−	1.00000i	−0.103882	−	0.0599760i
$279$	−5.00000			−0.299342
$280$		0			0
$281$	27.0000			1.61068			0.805342	−	0.592810i	$-0.201981\pi$
$281$	27.0000			1.61068			0.805342	+	0.592810i	$0.201981\pi$
$282$	7.79423	+	4.50000i	0.464140	+	0.267971i
$283$	−19.0526	+	11.0000i	−1.13256	+	0.653882i	−0.944577	−	0.328291i	$-0.893527\pi$
$283$	−19.0526	+	11.0000i	−1.13256	+	0.653882i	−0.187980	+	0.982173i	$0.560194\pi$
$284$	−4.50000	−	7.79423i	−0.267026	−	0.462502i
$285$		0			0
$286$	−24.0000			−1.41915
$287$	2.59808	+	7.50000i	0.153360	+	0.442711i
$288$			1.00000i			0.0589256i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$	12.1244	+	7.00000i	0.709524	+	0.409644i
$293$		−	18.0000i		−	1.05157i	−0.850617	−	0.525786i	$-0.823771\pi$
$293$		−	18.0000i		−	1.05157i	0.850617	−	0.525786i	$-0.176229\pi$
$294$	−5.50000	+	4.33013i	−0.320767	+	0.252538i
$295$		0			0
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$	−5.19615	+	3.00000i	−0.301511	+	0.174078i
$298$	−5.19615	+	3.00000i	−0.301005	+	0.173785i
$299$	−6.00000	+	10.3923i	−0.346989	+	0.601003i
$300$		0			0
$301$	20.0000	−	6.92820i	1.15278	−	0.399335i
$302$			16.0000i			0.920697i
$303$	−10.3923	−	6.00000i	−0.597022	−	0.344691i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$		0			0
$306$	1.50000	−	2.59808i	0.0857493	−	0.148522i
$307$		−	20.0000i		−	1.14146i	−0.821138	−	0.570730i	$-0.806660\pi$
$307$		−	20.0000i		−	1.14146i	0.821138	−	0.570730i	$-0.193340\pi$
$308$	−15.5885	−	3.00000i	−0.888235	−	0.170941i
$309$	13.0000			0.739544
$310$		0			0
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	−0.993490	−	0.113917i	$-0.963660\pi$
$311$	−10.5000	−	18.1865i	−0.595400	−	1.03126i	0.398090	−	0.917346i	$-0.369673\pi$
$312$	3.46410	−	2.00000i	0.196116	−	0.113228i
$313$	−14.7224	−	8.50000i	−0.832161	−	0.480448i	0.0224310	−	0.999748i	$-0.492859\pi$
$313$	−14.7224	−	8.50000i	−0.832161	−	0.480448i	−0.854592	+	0.519300i	$0.826193\pi$
$314$	−14.0000			−0.790066
$315$		0			0
$316$	−7.00000			−0.393781
$317$	10.3923	+	6.00000i	0.583690	+	0.336994i	0.762598	−	0.646872i	$-0.223923\pi$
$317$	10.3923	+	6.00000i	0.583690	+	0.336994i	−0.178908	+	0.983866i	$0.557257\pi$
$318$	10.3923	−	6.00000i	0.582772	−	0.336463i
$319$	−18.0000	−	31.1769i	−1.00781	−	1.74557i
$320$		0			0
$321$	6.00000			0.334887
$322$	−5.19615	+	6.00000i	−0.289570	+	0.334367i
$323$			12.0000i			0.667698i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$		0			0
$326$	−4.00000	−	6.92820i	−0.221540	−	0.383718i
$327$	−3.46410	−	2.00000i	−0.191565	−	0.110600i
$328$		−	3.00000i		−	0.165647i
$329$	4.50000	−	23.3827i	0.248093	−	1.28913i
$330$		0			0
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	0.248590	+	0.968609i	$0.420033\pi$
$331$	−13.0000	+	22.5167i	−0.714545	+	1.23763i	−0.963135	+	0.269019i	$0.913301\pi$
$332$	5.19615	−	3.00000i	0.285176	−	0.164646i
$333$	6.92820	−	4.00000i	0.379663	−	0.219199i
$334$		0			0
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$			13.0000i			0.708155i	0.935216	+	0.354078i	$0.115205\pi$
$337$			13.0000i			0.708155i	−0.935216	+	0.354078i	$0.884795\pi$
$338$	−2.59808	−	1.50000i	−0.141317	−	0.0815892i
$339$	1.50000	+	2.59808i	0.0814688	+	0.141108i
$340$		0			0
$341$	−15.0000	+	25.9808i	−0.812296	+	1.40694i
$342$			4.00000i			0.216295i
$343$	15.5885	+	10.0000i	0.841698	+	0.539949i
$344$	−8.00000			−0.431331
$345$		0			0
$346$	3.00000	+	5.19615i	0.161281	+	0.279347i
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	−0.856186	−	0.516667i	$-0.827172\pi$
$347$	−15.5885	+	9.00000i	−0.836832	+	0.483145i	0.0193540	+	0.999813i	$0.493839\pi$
$348$	5.19615	+	3.00000i	0.278543	+	0.160817i
$349$	28.0000			1.49881			0.749403	−	0.662114i	$-0.230341\pi$
$349$	28.0000			1.49881			0.749403	+	0.662114i	$0.230341\pi$
$350$		0			0
$351$	−4.00000			−0.213504
$352$	5.19615	+	3.00000i	0.276956	+	0.159901i
$353$	12.9904	−	7.50000i	0.691408	−	0.399185i	−0.112731	−	0.993626i	$-0.535960\pi$
$353$	12.9904	−	7.50000i	0.691408	−	0.399185i	0.804139	+	0.594441i	$0.202627\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	3.00000			0.159000
$357$	−7.79423	−	1.50000i	−0.412514	−	0.0793884i
$358$		−	18.0000i		−	0.951330i
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.204595	+	0.978847i	$0.565588\pi$
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.745409	+	0.666608i	$0.767746\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	1.73205	+	1.00000i	0.0910346	+	0.0525588i
$363$			25.0000i			1.31216i
$364$	−8.00000	−	6.92820i	−0.419314	−	0.363137i
$365$		0			0
$366$	−1.00000	+	1.73205i	−0.0522708	+	0.0905357i
$367$	24.2487	−	14.0000i	1.26577	−	0.730794i	0.291587	−	0.956544i	$-0.405817\pi$
$367$	24.2487	−	14.0000i	1.26577	−	0.730794i	0.974185	+	0.225750i	$0.0724833\pi$
$368$	2.59808	−	1.50000i	0.135434	−	0.0781929i
$369$	−1.50000	+	2.59808i	−0.0780869	+	0.135250i
$370$		0			0
$371$	−24.0000	−	20.7846i	−1.24602	−	1.07908i
$372$		−	5.00000i		−	0.259238i
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	0.309794	−	0.950804i	$-0.399740\pi$
$373$	−6.92820	−	4.00000i	−0.358729	−	0.207112i	−0.668523	+	0.743691i	$0.733073\pi$
$374$	−9.00000	−	15.5885i	−0.465379	−	0.806060i
$375$		0			0
$376$	−4.50000	+	7.79423i	−0.232070	+	0.401957i
$377$		−	24.0000i		−	1.23606i
$378$	−2.59808	−	0.500000i	−0.133631	−	0.0257172i
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$		0			0
$381$	8.00000	+	13.8564i	0.409852	+	0.709885i
$382$	−12.9904	+	7.50000i	−0.664646	+	0.383733i
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.0427020	−	0.999088i	$-0.513597\pi$
$383$	−18.1865	−	10.5000i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	5.00000			0.254493
$387$	6.92820	+	4.00000i	0.352180	+	0.203331i
$388$	14.7224	−	8.50000i	0.747418	−	0.431522i
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$		0			0
$391$	−9.00000			−0.455150
$392$	−4.33013	−	5.50000i	−0.218704	−	0.277792i
$393$		−	18.0000i		−	0.907980i
$394$		0			0
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	0.542834	−	0.839840i	$-0.317351\pi$
$397$	1.73205	+	1.00000i	0.0869291	+	0.0501886i	−0.455905	+	0.890028i	$0.650684\pi$
$398$			5.00000i			0.250627i
$399$	10.0000	−	3.46410i	0.500626	−	0.173422i
$400$		0			0
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	−6.92820	+	4.00000i	−0.345547	+	0.199502i
$403$	−17.3205	+	10.0000i	−0.862796	+	0.498135i
$404$	6.00000	−	10.3923i	0.298511	−	0.517036i
$405$		0			0
$406$	3.00000	−	15.5885i	0.148888	−	0.773642i
$407$		−	48.0000i		−	2.37927i
$408$	2.59808	+	1.50000i	0.128624	+	0.0742611i
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	0.962191	+	0.272374i	$0.0878089\pi$
$409$	14.5000	+	25.1147i	0.716979	+	1.24184i	−0.245212	+	0.969469i	$0.578858\pi$
$410$		0			0
$411$	7.50000	−	12.9904i	0.369948	−	0.640768i
$412$			13.0000i			0.640464i
$413$	10.3923	−	12.0000i	0.511372	−	0.590481i
$414$	−3.00000			−0.147442
$415$		0			0
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	−1.73205	+	1.00000i	−0.0848189	+	0.0489702i
$418$	20.7846	+	12.0000i	1.01661	+	0.586939i
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−4.00000			−0.194948			−0.0974740	−	0.995238i	$-0.531076\pi$
$421$	−4.00000			−0.194948			−0.0974740	+	0.995238i	$0.531076\pi$
$422$	6.92820	+	4.00000i	0.337260	+	0.194717i
$423$	7.79423	−	4.50000i	0.378968	−	0.218797i
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$		0			0
$426$	−9.00000			−0.436051
$427$	5.19615	+	1.00000i	0.251459	+	0.0483934i
$428$			6.00000i			0.290021i
$429$	−12.0000	+	20.7846i	−0.579365	+	1.00349i
$430$		0			0
$431$	−10.5000	−	18.1865i	−0.505767	−	0.876014i	−0.999978	−	0.00667224i	$-0.997876\pi$
$431$	−10.5000	−	18.1865i	−0.505767	−	0.876014i	0.494211	−	0.869342i	$-0.335457\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$		−	7.00000i		−	0.336399i	−0.985753	−	0.168199i	$-0.946205\pi$
$433$		−	7.00000i		−	0.336399i	0.985753	−	0.168199i	$-0.0537952\pi$
$434$	−12.5000	+	4.33013i	−0.600019	+	0.207853i
$435$		0			0
$436$	2.00000	−	3.46410i	0.0957826	−	0.165900i
$437$	10.3923	−	6.00000i	0.497131	−	0.287019i
$438$	12.1244	−	7.00000i	0.579324	−	0.334473i
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	−0.978412	−	0.206666i	$-0.933739\pi$
$439$	−6.50000	+	11.2583i	−0.310228	+	0.537331i	0.668184	+	0.743996i	$0.267072\pi$
$440$		0			0
$441$	1.00000	+	6.92820i	0.0476190	+	0.329914i
$442$		−	12.0000i		−	0.570782i
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.904528	−	0.426414i	$-0.140223\pi$
$443$	20.7846	+	12.0000i	0.987507	+	0.570137i	0.0829786	+	0.996551i	$0.473557\pi$
$444$	4.00000	+	6.92820i	0.189832	+	0.328798i
$445$		0			0
$446$	−5.50000	+	9.52628i	−0.260433	+	0.451082i
$447$			6.00000i			0.283790i
$448$	0.866025	+	2.50000i	0.0409159	+	0.118114i
$449$	3.00000			0.141579			0.0707894	−	0.997491i	$-0.477448\pi$
$449$	3.00000			0.141579			0.0707894	+	0.997491i	$0.477448\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−2.59808	+	1.50000i	−0.122203	+	0.0705541i
$453$	13.8564	+	8.00000i	0.651031	+	0.375873i
$454$	18.0000			0.844782
$455$		0			0
$456$	−4.00000			−0.187317
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	0.539964	−	0.841688i	$-0.318438\pi$
$457$	1.73205	+	1.00000i	0.0810219	+	0.0467780i	−0.458942	+	0.888466i	$0.651771\pi$
$458$	−19.0526	+	11.0000i	−0.890268	+	0.513996i
$459$	−1.50000	−	2.59808i	−0.0700140	−	0.121268i
$460$		0			0
$461$	36.0000			1.67669			0.838344	−	0.545142i	$-0.183524\pi$
$461$	36.0000			1.67669			0.838344	+	0.545142i	$0.183524\pi$
$462$	−10.3923	+	12.0000i	−0.483494	+	0.558291i
$463$		−	13.0000i		−	0.604161i	−0.953282	−	0.302081i	$-0.902319\pi$
$463$		−	13.0000i		−	0.604161i	0.953282	−	0.302081i	$-0.0976812\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	−3.00000	−	5.19615i	−0.138972	−	0.240707i
$467$	−25.9808	−	15.0000i	−1.20225	−	0.694117i	−0.241192	−	0.970477i	$-0.577538\pi$
$467$	−25.9808	−	15.0000i	−1.20225	−	0.694117i	−0.961054	+	0.276360i	$0.910872\pi$
$468$		−	4.00000i		−	0.184900i
$469$	16.0000	+	13.8564i	0.738811	+	0.639829i
$470$		0			0
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	−5.19615	+	3.00000i	−0.239172	+	0.138086i
$473$	41.5692	−	24.0000i	1.91135	−	1.10352i
$474$	−3.50000	+	6.06218i	−0.160760	+	0.278445i
$475$		0			0
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$		−	12.0000i		−	0.549442i
$478$	−2.59808	−	1.50000i	−0.118833	−	0.0686084i
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	0.999730	−	0.0232187i	$-0.00739140\pi$
$479$	10.5000	+	18.1865i	0.479757	+	0.830964i	−0.519973	+	0.854183i	$0.674058\pi$
$480$		0			0
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$			22.0000i			1.00207i
$483$	2.59808	+	7.50000i	0.118217	+	0.341262i
$484$	−25.0000			−1.13636
$485$		0			0
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	21.6506	−	12.5000i	0.981084	−	0.566429i	0.0784867	−	0.996915i	$-0.474991\pi$
$487$	21.6506	−	12.5000i	0.981084	−	0.566429i	0.902597	+	0.430486i	$0.141658\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$	−8.00000			−0.361773
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−2.59808	−	1.50000i	−0.117130	−	0.0676252i
$493$	15.5885	−	9.00000i	0.702069	−	0.405340i
$494$	8.00000	+	13.8564i	0.359937	+	0.623429i
$495$		0			0
$496$	5.00000			0.224507
$497$	7.79423	+	22.5000i	0.349619	+	1.00926i
$498$		−	6.00000i		−	0.268866i
$499$	19.0000	−	32.9090i	0.850557	−	1.47321i	−0.0301498	−	0.999545i	$-0.509598\pi$
$499$	19.0000	−	32.9090i	0.850557	−	1.47321i	0.880707	−	0.473662i	$-0.157068\pi$
$500$		0			0
$501$		0			0
$502$	20.7846	+	12.0000i	0.927663	+	0.535586i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$	0.500000	−	2.59808i	0.0222718	−	0.115728i
$505$		0			0
$506$	−9.00000	+	15.5885i	−0.400099	+	0.692991i
$507$	−2.59808	+	1.50000i	−0.115385	+	0.0666173i
$508$	−13.8564	+	8.00000i	−0.614779	+	0.354943i
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−28.0000	−	24.2487i	−1.23865	−	1.07270i
$512$		−	1.00000i		−	0.0441942i
$513$	3.46410	+	2.00000i	0.152944	+	0.0883022i
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$		−	54.0000i		−	2.37492i
$518$	13.8564	−	16.0000i	0.608816	−	0.703000i
$519$	6.00000			0.263371
$520$		0			0
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	0.538948	−	0.842339i	$-0.318822\pi$
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	−0.998961	+	0.0455727i	$0.985489\pi$
$522$	5.19615	−	3.00000i	0.227429	−	0.131306i
$523$	29.4449	+	17.0000i	1.28753	+	0.743358i	0.978214	−	0.207600i	$-0.0665652\pi$
$523$	29.4449	+	17.0000i	1.28753	+	0.743358i	0.309320	+	0.950958i	$0.399899\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$	−3.00000			−0.130806
$527$	−12.9904	−	7.50000i	−0.565870	−	0.326705i
$528$	5.19615	−	3.00000i	0.226134	−	0.130558i
$529$	−7.00000	−	12.1244i	−0.304348	−	0.527146i
$530$		0			0
$531$	6.00000			0.260378
$532$	3.46410	+	10.0000i	0.150188	+	0.433555i
$533$			12.0000i			0.519778i
$534$	1.50000	−	2.59808i	0.0649113	−	0.112430i
$535$		0			0
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	−15.5885	−	9.00000i	−0.672692	−	0.388379i
$538$		0			0
$539$	39.0000	+	15.5885i	1.67985	+	0.671442i
$540$		0			0
$541$	14.0000	−	24.2487i	0.601907	−	1.04253i	−0.390625	−	0.920550i	$-0.627741\pi$
$541$	14.0000	−	24.2487i	0.601907	−	1.04253i	0.992532	−	0.121984i	$-0.0389256\pi$
$542$	21.6506	−	12.5000i	0.929974	−	0.536921i
$543$	1.73205	−	1.00000i	0.0743294	−	0.0429141i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$		0			0
$546$	−10.0000	+	3.46410i	−0.427960	+	0.148250i
$547$		−	8.00000i		−	0.342055i	−0.985266	−	0.171028i	$-0.945291\pi$
$547$		−	8.00000i		−	0.342055i	0.985266	−	0.171028i	$-0.0547087\pi$
$548$	12.9904	+	7.50000i	0.554922	+	0.320384i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$		0			0
$551$	−12.0000	+	20.7846i	−0.511217	+	0.885454i
$552$		−	3.00000i		−	0.127688i
$553$	18.1865	+	3.50000i	0.773370	+	0.148835i
$554$	−26.0000			−1.10463
$555$		0			0
$556$	−1.00000	−	1.73205i	−0.0424094	−	0.0734553i
$557$	25.9808	−	15.0000i	1.10084	−	0.635570i	0.164399	−	0.986394i	$-0.447432\pi$
$557$	25.9808	−	15.0000i	1.10084	−	0.635570i	0.936442	+	0.350824i	$0.114098\pi$
$558$	−4.33013	−	2.50000i	−0.183309	−	0.105833i
$559$	32.0000			1.35346
$560$		0			0
$561$	−18.0000			−0.759961
$562$	23.3827	+	13.5000i	0.986339	+	0.569463i
$563$	10.3923	−	6.00000i	0.437983	−	0.252870i	−0.264758	−	0.964315i	$-0.585292\pi$
$563$	10.3923	−	6.00000i	0.437983	−	0.252870i	0.702742	+	0.711445i	$0.251959\pi$
$564$	4.50000	+	7.79423i	0.189484	+	0.328196i
$565$		0			0
$566$	−22.0000			−0.924729
$567$	−1.73205	+	2.00000i	−0.0727393	+	0.0839921i
$568$		−	9.00000i		−	0.377632i
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−20.7846	−	12.0000i	−0.869048	−	0.501745i
$573$			15.0000i			0.626634i
$574$	−1.50000	+	7.79423i	−0.0626088	+	0.325325i
$575$		0			0
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−1.73205	+	1.00000i	−0.0721062	+	0.0416305i	−0.535620	−	0.844459i	$-0.679922\pi$
$577$	−1.73205	+	1.00000i	−0.0721062	+	0.0416305i	0.463513	+	0.886090i	$0.346589\pi$
$578$	−6.92820	+	4.00000i	−0.288175	+	0.166378i
$579$	2.50000	−	4.33013i	0.103896	−	0.179954i
$580$		0			0
$581$	−15.0000	+	5.19615i	−0.622305	+	0.215573i
$582$		−	17.0000i		−	0.704673i
$583$	−62.3538	−	36.0000i	−2.58243	−	1.49097i
$584$	7.00000	+	12.1244i	0.289662	+	0.501709i
$585$		0			0
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$		−	18.0000i		−	0.742940i	−0.928445	−	0.371470i	$-0.878854\pi$
$587$		−	18.0000i		−	0.742940i	0.928445	−	0.371470i	$-0.121146\pi$
$588$	−6.92820	+	1.00000i	−0.285714	+	0.0412393i
$589$	20.0000			0.824086
$590$		0			0
$591$		0			0
$592$	−6.92820	+	4.00000i	−0.284747	+	0.164399i
$593$	28.5788	+	16.5000i	1.17359	+	0.677574i	0.954524	−	0.298136i	$-0.0963648\pi$
$593$	28.5788	+	16.5000i	1.17359	+	0.677574i	0.219069	+	0.975709i	$0.429698\pi$
$594$	−6.00000			−0.246183
$595$		0			0
$596$	−6.00000			−0.245770
$597$	4.33013	+	2.50000i	0.177220	+	0.102318i
$598$	−10.3923	+	6.00000i	−0.424973	+	0.245358i
$599$	4.50000	+	7.79423i	0.183865	+	0.318464i	0.943193	−	0.332244i	$-0.107806\pi$
$599$	4.50000	+	7.79423i	0.183865	+	0.318464i	−0.759328	+	0.650708i	$0.774472\pi$
$600$		0			0
$601$	−34.0000			−1.38689			−0.693444	−	0.720510i	$-0.743908\pi$
$601$	−34.0000			−1.38689			−0.693444	+	0.720510i	$0.743908\pi$
$602$	20.7846	+	4.00000i	0.847117	+	0.163028i
$603$			8.00000i			0.325785i
$604$	−8.00000	+	13.8564i	−0.325515	+	0.563809i
$605$		0			0
$606$	−6.00000	−	10.3923i	−0.243733	−	0.422159i
$607$	9.52628	+	5.50000i	0.386660	+	0.223238i	0.680712	−	0.732551i	$-0.261671\pi$
$607$	9.52628	+	5.50000i	0.386660	+	0.223238i	−0.294052	+	0.955789i	$0.595004\pi$
$608$		−	4.00000i		−	0.162221i
$609$	−12.0000	−	10.3923i	−0.486265	−	0.421117i
$610$		0			0
$611$	18.0000	−	31.1769i	0.728202	−	1.26128i
$612$	2.59808	−	1.50000i	0.105021	−	0.0606339i
$613$	−29.4449	+	17.0000i	−1.18927	+	0.686624i	−0.958140	−	0.286300i	$-0.907575\pi$
$613$	−29.4449	+	17.0000i	−1.18927	+	0.686624i	−0.231127	+	0.972924i	$0.574241\pi$
$614$	10.0000	−	17.3205i	0.403567	−	0.698999i
$615$		0			0
$616$	−12.0000	−	10.3923i	−0.483494	−	0.418718i
$617$			21.0000i			0.845428i	0.906263	+	0.422714i	$0.138923\pi$
$617$			21.0000i			0.845428i	−0.906263	+	0.422714i	$0.861077\pi$
$618$	11.2583	+	6.50000i	0.452876	+	0.261468i
$619$	−23.0000	−	39.8372i	−0.924448	−	1.60119i	−0.792446	−	0.609941i	$-0.791193\pi$
$619$	−23.0000	−	39.8372i	−0.924448	−	1.60119i	−0.132002	−	0.991250i	$-0.542140\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$		−	21.0000i		−	0.842023i
$623$	−7.79423	−	1.50000i	−0.312269	−	0.0600962i
$624$	4.00000			0.160128
$625$		0			0
$626$	−8.50000	−	14.7224i	−0.339728	−	0.588427i
$627$	20.7846	−	12.0000i	0.830057	−	0.479234i
$628$	−12.1244	−	7.00000i	−0.483814	−	0.279330i
$629$	24.0000			0.956943
$630$		0			0
$631$	17.0000			0.676759			0.338380	−	0.941010i	$-0.390121\pi$
$631$	17.0000			0.676759			0.338380	+	0.941010i	$0.390121\pi$
$632$	−6.06218	−	3.50000i	−0.241140	−	0.139223i
$633$	6.92820	−	4.00000i	0.275371	−	0.158986i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$		0			0
$636$	12.0000			0.475831
$637$	17.3205	+	22.0000i	0.686264	+	0.871672i
$638$		−	36.0000i		−	1.42525i
$639$	−4.50000	+	7.79423i	−0.178017	+	0.308335i
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$	5.19615	+	3.00000i	0.205076	+	0.118401i
$643$		−	34.0000i		−	1.34083i	−0.741987	−	0.670415i	$-0.766116\pi$
$643$		−	34.0000i		−	1.34083i	0.741987	−	0.670415i	$-0.233884\pi$
$644$	−7.50000	+	2.59808i	−0.295541	+	0.102379i
$645$		0			0
$646$	−6.00000	+	10.3923i	−0.236067	+	0.408880i
$647$	−10.3923	+	6.00000i	−0.408564	+	0.235884i	−0.690172	−	0.723645i	$-0.742465\pi$
$647$	−10.3923	+	6.00000i	−0.408564	+	0.235884i	0.281609	+	0.959529i	$0.409132\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	18.0000	−	31.1769i	0.706562	−	1.22380i
$650$		0			0
$651$	−2.50000	+	12.9904i	−0.0979827	+	0.509133i
$652$		−	8.00000i		−	0.313304i
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.964928	−	0.262515i	$-0.0845520\pi$
$653$	31.1769	+	18.0000i	1.22005	+	0.704394i	0.255119	+	0.966910i	$0.417885\pi$
$654$	−2.00000	−	3.46410i	−0.0782062	−	0.135457i
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$		−	14.0000i		−	0.546192i
$658$	15.5885	−	18.0000i	0.607701	−	0.701713i
$659$	30.0000			1.16863			0.584317	−	0.811525i	$-0.301362\pi$
$659$	30.0000			1.16863			0.584317	+	0.811525i	$0.301362\pi$
$660$		0			0
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	0.946729	−	0.322031i	$-0.104366\pi$
$661$	5.00000	+	8.66025i	0.194477	+	0.336845i	−0.752252	+	0.658876i	$0.771032\pi$
$662$	−22.5167	+	13.0000i	−0.875135	+	0.505259i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$	6.00000			0.232845
$665$		0			0
$666$	8.00000			0.309994
$667$	−15.5885	−	9.00000i	−0.603587	−	0.348481i
$668$		0			0
$669$	5.50000	+	9.52628i	0.212642	+	0.368307i
$670$		0			0
$671$	12.0000			0.463255
$672$	2.59808	+	0.500000i	0.100223	+	0.0192879i
$673$		−	19.0000i		−	0.732396i	−0.930537	−	0.366198i	$-0.880659\pi$
$673$		−	19.0000i		−	0.732396i	0.930537	−	0.366198i	$-0.119341\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$		0			0
$676$	−1.50000	−	2.59808i	−0.0576923	−	0.0999260i
$677$	15.5885	+	9.00000i	0.599113	+	0.345898i	0.768693	−	0.639618i	$-0.220908\pi$
$677$	15.5885	+	9.00000i	0.599113	+	0.345898i	−0.169580	+	0.985517i	$0.554241\pi$
$678$			3.00000i			0.115214i
$679$	−42.5000	+	14.7224i	−1.63100	+	0.564995i
$680$		0			0
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$	−25.9808	+	15.0000i	−0.994855	+	0.574380i
$683$	15.5885	−	9.00000i	0.596476	−	0.344375i	−0.171178	−	0.985240i	$-0.554757\pi$
$683$	15.5885	−	9.00000i	0.596476	−	0.344375i	0.767654	+	0.640865i	$0.221424\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$		0			0
$686$	8.50000	+	16.4545i	0.324532	+	0.628235i
$687$			22.0000i			0.839352i
$688$	−6.92820	−	4.00000i	−0.264135	−	0.152499i
$689$	−24.0000	−	41.5692i	−0.914327	−	1.58366i
$690$		0			0
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	−0.337193	−	0.941435i	$-0.609478\pi$
$691$	17.0000	−	29.4449i	0.646710	−	1.12014i	0.983904	−	0.178700i	$-0.0571891\pi$
$692$			6.00000i			0.228086i
$693$	5.19615	+	15.0000i	0.197386	+	0.569803i
$694$	−18.0000			−0.683271
$695$		0			0
$696$	3.00000	+	5.19615i	0.113715	+	0.196960i
$697$	−7.79423	+	4.50000i	−0.295227	+	0.170450i
$698$	24.2487	+	14.0000i	0.917827	+	0.529908i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−48.0000			−1.81293			−0.906467	−	0.422276i	$-0.861231\pi$
$701$	−48.0000			−1.81293			−0.906467	+	0.422276i	$0.861231\pi$
$702$	−3.46410	−	2.00000i	−0.130744	−	0.0754851i
$703$	−27.7128	+	16.0000i	−1.04521	+	0.603451i
$704$	3.00000	+	5.19615i	0.113067	+	0.195837i
$705$		0			0
$706$	15.0000			0.564532
$707$	−20.7846	+	24.0000i	−0.781686	+	0.902613i
$708$			6.00000i			0.225494i
$709$	−23.0000	+	39.8372i	−0.863783	+	1.49612i	0.00446726	+	0.999990i	$0.498578\pi$
$709$	−23.0000	+	39.8372i	−0.863783	+	1.49612i	−0.868250	+	0.496126i	$0.834755\pi$
$710$		0			0
$711$	3.50000	+	6.06218i	0.131260	+	0.227349i
$712$	2.59808	+	1.50000i	0.0973670	+	0.0562149i
$713$			15.0000i			0.561754i
$714$	−6.00000	−	5.19615i	−0.224544	−	0.194461i
$715$		0			0
$716$	9.00000	−	15.5885i	0.336346	−	0.582568i
$717$	−2.59808	+	1.50000i	−0.0970269	+	0.0560185i
$718$	−31.1769	+	18.0000i	−1.16351	+	0.671754i
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	0.496527	+	0.868021i	$0.334608\pi$
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	−0.999992	+	0.00400572i	$0.998725\pi$
$720$		0			0
$721$	6.50000	−	33.7750i	0.242073	−	1.25785i
$722$			3.00000i			0.111648i
$723$	19.0526	+	11.0000i	0.708572	+	0.409094i
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$	−12.5000	+	21.6506i	−0.463919	+	0.803530i
$727$			31.0000i			1.14973i	0.818250	+	0.574863i	$0.194945\pi$
$727$			31.0000i			1.14973i	−0.818250	+	0.574863i	$0.805055\pi$
$728$	−3.46410	−	10.0000i	−0.128388	−	0.370625i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$	−1.73205	+	1.00000i	−0.0640184	+	0.0369611i
$733$	−43.3013	−	25.0000i	−1.59937	−	0.923396i	−0.991609	−	0.129275i	$-0.958735\pi$
$733$	−43.3013	−	25.0000i	−1.59937	−	0.923396i	−0.607760	−	0.794121i	$-0.707932\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	3.00000			0.110581
$737$	41.5692	+	24.0000i	1.53122	+	0.884051i
$738$	−2.59808	+	1.50000i	−0.0956365	+	0.0552158i
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	0.680534	−	0.732717i	$-0.261748\pi$
$739$	−8.00000	−	13.8564i	−0.294285	−	0.509716i	−0.974818	+	0.223001i	$0.928415\pi$
$740$		0			0
$741$	16.0000			0.587775
$742$	−10.3923	−	30.0000i	−0.381514	−	1.10133i
$743$			9.00000i			0.330178i	0.986279	+	0.165089i	$0.0527911\pi$
$743$			9.00000i			0.330178i	−0.986279	+	0.165089i	$0.947209\pi$
$744$	2.50000	−	4.33013i	0.0916544	−	0.158750i
$745$		0			0
$746$	−4.00000	−	6.92820i	−0.146450	−	0.253660i
$747$	−5.19615	−	3.00000i	−0.190117	−	0.109764i
$748$		−	18.0000i		−	0.658145i
$749$	3.00000	−	15.5885i	0.109618	−	0.569590i
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	−7.79423	+	4.50000i	−0.284226	+	0.164098i
$753$	20.7846	−	12.0000i	0.757433	−	0.437304i
$754$	12.0000	−	20.7846i	0.437014	−	0.756931i
$755$		0			0
$756$	−2.00000	−	1.73205i	−0.0727393	−	0.0629941i
$757$			4.00000i			0.145382i	0.997354	+	0.0726912i	$0.0231588\pi$
$757$			4.00000i			0.145382i	−0.997354	+	0.0726912i	$0.976841\pi$
$758$	8.66025	+	5.00000i	0.314555	+	0.181608i
$759$	9.00000	+	15.5885i	0.326679	+	0.565825i
$760$		0			0
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	−0.935988	−	0.352032i	$-0.885491\pi$
$761$	−4.50000	+	7.79423i	−0.163125	+	0.282541i	0.772863	+	0.634573i	$0.218824\pi$
$762$			16.0000i			0.579619i
$763$	−6.92820	+	8.00000i	−0.250818	+	0.289619i
$764$	−15.0000			−0.542681
$765$		0			0
$766$	−10.5000	−	18.1865i	−0.379380	−	0.657106i
$767$	20.7846	−	12.0000i	0.750489	−	0.433295i
$768$	−0.866025	−	0.500000i	−0.0312500	−	0.0180422i
$769$	−50.0000			−1.80305			−0.901523	−	0.432731i	$-0.857550\pi$
$769$	−50.0000			−1.80305			−0.901523	+	0.432731i	$0.857550\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	4.33013	+	2.50000i	0.155845	+	0.0899770i
$773$	−10.3923	+	6.00000i	−0.373785	+	0.215805i	−0.675111	−	0.737716i	$-0.735904\pi$
$773$	−10.3923	+	6.00000i	−0.373785	+	0.215805i	0.301326	+	0.953521i	$0.402571\pi$
$774$	4.00000	+	6.92820i	0.143777	+	0.249029i
$775$		0			0
$776$	17.0000			0.610264
$777$	−6.92820	−	20.0000i	−0.248548	−	0.717496i
$778$		0			0
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	27.0000	+	46.7654i	0.966136	+	1.67340i
$782$	−7.79423	−	4.50000i	−0.278721	−	0.160920i
$783$		−	6.00000i		−	0.214423i
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$		0			0
$786$	9.00000	−	15.5885i	0.321019	−	0.556022i
$787$	−6.92820	+	4.00000i	−0.246964	+	0.142585i	−0.618373	−	0.785885i	$-0.712208\pi$
$787$	−6.92820	+	4.00000i	−0.246964	+	0.142585i	0.371409	+	0.928469i	$0.378875\pi$
$788$		0			0
$789$	−1.50000	+	2.59808i	−0.0534014	+	0.0924940i
$790$		0			0
$791$	7.50000	−	2.59808i	0.266669	−	0.0923770i
$792$		−	6.00000i		−	0.213201i
$793$	6.92820	+	4.00000i	0.246028	+	0.142044i
$794$	1.00000	+	1.73205i	0.0354887	+	0.0614682i
$795$		0			0
$796$	−2.50000	+	4.33013i	−0.0886102	+	0.153477i
$797$			18.0000i			0.637593i	0.947823	+	0.318796i	$0.103279\pi$
$797$			18.0000i			0.637593i	−0.947823	+	0.318796i	$0.896721\pi$
$798$	10.3923	+	2.00000i	0.367884	+	0.0707992i
$799$	27.0000			0.955191
$800$		0			0
$801$	−1.50000	−	2.59808i	−0.0529999	−	0.0917985i
$802$	5.19615	−	3.00000i	0.183483	−	0.105934i
$803$	−72.7461	−	42.0000i	−2.56716	−	1.48215i
$804$	−8.00000			−0.282138
$805$		0			0
$806$	−20.0000			−0.704470
$807$		0			0
$808$	10.3923	−	6.00000i	0.365600	−	0.211079i
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	0.808458	−	0.588555i	$-0.200303\pi$
$809$	−3.00000	−	5.19615i	−0.105474	−	0.182687i	−0.913932	+	0.405868i	$0.866969\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	10.3923	−	12.0000i	0.364698	−	0.421117i
$813$		−	25.0000i		−	0.876788i
$814$	24.0000	−	41.5692i	0.841200	−	1.45700i
$815$		0			0
$816$	1.50000	+	2.59808i	0.0525105	+	0.0909509i
$817$	−27.7128	−	16.0000i	−0.969549	−	0.559769i
$818$			29.0000i			1.01396i
$819$	−2.00000	+	10.3923i	−0.0698857	+	0.363137i
$820$		0			0
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	0.359708	+	0.933065i	$0.382876\pi$
$821$	−18.0000	+	31.1769i	−0.628204	+	1.08808i	−0.987912	+	0.155017i	$0.950457\pi$
$822$	12.9904	−	7.50000i	0.453092	−	0.261593i
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.343230	−	0.939251i	$-0.388479\pi$
$823$	38.1051	−	22.0000i	1.32826	−	0.766872i	0.985031	+	0.172379i	$0.0551455\pi$
$824$	−6.50000	+	11.2583i	−0.226438	+	0.392203i
$825$		0			0
$826$	15.0000	−	5.19615i	0.521917	−	0.180797i
$827$		−	30.0000i		−	1.04320i	−0.853189	−	0.521601i	$-0.825335\pi$
$827$		−	30.0000i		−	1.04320i	0.853189	−	0.521601i	$-0.174665\pi$
$828$	−2.59808	−	1.50000i	−0.0902894	−	0.0521286i
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	0.882869	−	0.469620i	$-0.155609\pi$
$829$	1.00000	+	1.73205i	0.0347314	+	0.0601566i	−0.848137	+	0.529777i	$0.822276\pi$
$830$		0			0
$831$	−13.0000	+	22.5167i	−0.450965	+	0.781094i
$832$			4.00000i			0.138675i
$833$	−7.79423	+	19.5000i	−0.270054	+	0.675635i
$834$	−2.00000			−0.0692543
$835$		0			0
$836$	12.0000	+	20.7846i	0.415029	+	0.718851i
$837$	−4.33013	+	2.50000i	−0.149671	+	0.0864126i
$838$	−20.7846	−	12.0000i	−0.717992	−	0.414533i
$839$	−15.0000			−0.517858			−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000			−0.517858			−0.258929	+	0.965896i	$0.583369\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−3.46410	−	2.00000i	−0.119381	−	0.0689246i
$843$	23.3827	−	13.5000i	0.805342	−	0.464965i
$844$	4.00000	+	6.92820i	0.137686	+	0.238479i
$845$		0			0
$846$	9.00000			0.309426
$847$	64.9519	+	12.5000i	2.23177	+	0.429505i
$848$			12.0000i			0.412082i
$849$	−11.0000	+	19.0526i	−0.377519	+	0.653882i
$850$		0			0
$851$	−12.0000	−	20.7846i	−0.411355	−	0.712487i
$852$	−7.79423	−	4.50000i	−0.267026	−	0.154167i
$853$		−	28.0000i		−	0.958702i	−0.877623	−	0.479351i	$-0.840872\pi$
$853$		−	28.0000i		−	0.958702i	0.877623	−	0.479351i	$-0.159128\pi$
$854$	4.00000	+	3.46410i	0.136877	+	0.118539i
$855$		0			0
$856$	−3.00000	+	5.19615i	−0.102538	+	0.177601i
$857$	−5.19615	+	3.00000i	−0.177497	+	0.102478i	−0.586116	−	0.810227i	$-0.699344\pi$
$857$	−5.19615	+	3.00000i	−0.177497	+	0.102478i	0.408619	+	0.912705i	$0.366010\pi$
$858$	−20.7846	+	12.0000i	−0.709575	+	0.409673i
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	−0.721544	−	0.692369i	$-0.756567\pi$
$859$	7.00000	−	12.1244i	0.238837	−	0.413678i	0.960381	+	0.278691i	$0.0899005\pi$
$860$		0			0
$861$	6.00000	+	5.19615i	0.204479	+	0.177084i
$862$		−	21.0000i		−	0.715263i
$863$	−18.1865	−	10.5000i	−0.619077	−	0.357424i	0.157433	−	0.987530i	$-0.449678\pi$
$863$	−18.1865	−	10.5000i	−0.619077	−	0.357424i	−0.776509	+	0.630106i	$0.783012\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	3.50000	−	6.06218i	0.118935	−	0.206001i
$867$			8.00000i			0.271694i
$868$	−12.9904	−	2.50000i	−0.440922	−	0.0848555i
$869$	42.0000			1.42475
$870$		0			0
$871$	16.0000	+	27.7128i	0.542139	+	0.939013i
$872$	3.46410	−	2.00000i	0.117309	−	0.0677285i
$873$	−14.7224	−	8.50000i	−0.498279	−	0.287681i
$874$	12.0000			0.405906
$875$		0			0
$876$	14.0000			0.473016
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	0.528958	−	0.848648i	$-0.322583\pi$
$877$	1.73205	+	1.00000i	0.0584872	+	0.0337676i	−0.470471	+	0.882415i	$0.655916\pi$
$878$	−11.2583	+	6.50000i	−0.379950	+	0.219364i
$879$	−9.00000	−	15.5885i	−0.303562	−	0.525786i
$880$		0			0
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$	−2.59808	+	6.50000i	−0.0874818	+	0.218866i
$883$			14.0000i			0.471138i	0.971858	+	0.235569i	$0.0756953\pi$
$883$			14.0000i			0.471138i	−0.971858	+	0.235569i	$0.924305\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	12.0000	+	20.7846i	0.403148	+	0.698273i
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	0.806557	−	0.591156i	$-0.201328\pi$
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	−0.108678	+	0.994077i	$0.534662\pi$
$888$			8.00000i			0.268462i
$889$	40.0000	−	13.8564i	1.34156	−	0.464729i
$890$		0			0
$891$	−3.00000	+	5.19615i	−0.100504	+	0.174078i
$892$	−9.52628	+	5.50000i	−0.318963	+	0.184154i
$893$	−31.1769	+	18.0000i	−1.04330	+	0.602347i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$		0			0
$896$	−0.500000	+	2.59808i	−0.0167038	+	0.0867956i
$897$			12.0000i			0.400668i
$898$	2.59808	+	1.50000i	0.0866989	+	0.0500556i
$899$	−15.0000	−	25.9808i	−0.500278	−	0.866507i
$900$		0			0
$901$	18.0000	−	31.1769i	0.599667	−	1.03865i
$902$			18.0000i			0.599334i
$903$	13.8564	−	16.0000i	0.461112	−	0.532447i
$904$	−3.00000			−0.0997785
$905$		0			0
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	−32.9090	+	19.0000i	−1.09272	+	0.630885i	−0.934300	−	0.356487i	$-0.883975\pi$
$907$	−32.9090	+	19.0000i	−1.09272	+	0.630885i	−0.158424	+	0.987371i	$0.550641\pi$
$908$	15.5885	+	9.00000i	0.517321	+	0.298675i
$909$	−12.0000			−0.398015
$910$		0			0
$911$	−21.0000			−0.695761			−0.347881	−	0.937539i	$-0.613099\pi$
$911$	−21.0000			−0.695761			−0.347881	+	0.937539i	$0.613099\pi$
$912$	−3.46410	−	2.00000i	−0.114708	−	0.0662266i
$913$	−31.1769	+	18.0000i	−1.03181	+	0.595713i
$914$	1.00000	+	1.73205i	0.0330771	+	0.0572911i
$915$		0			0
$916$	−22.0000			−0.726900
$917$	−46.7654	−	9.00000i	−1.54433	−	0.297206i
$918$		−	3.00000i		−	0.0990148i
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$		0			0
$921$	−10.0000	−	17.3205i	−0.329511	−	0.570730i
$922$	31.1769	+	18.0000i	1.02676	+	0.592798i
$923$			36.0000i			1.18495i
$924$	−15.0000	+	5.19615i	−0.493464	+	0.170941i
$925$		0			0
$926$	6.50000	−	11.2583i	0.213603	−	0.369972i
$927$	11.2583	−	6.50000i	0.369772	−	0.213488i
$928$	−5.19615	+	3.00000i	−0.170572	+	0.0984798i
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$	−4.00000	−	27.7128i	−0.131095	−	0.908251i
$932$		−	6.00000i		−	0.196537i
$933$	−18.1865	−	10.5000i	−0.595400	−	0.343755i
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$		0			0
$936$	2.00000	−	3.46410i	0.0653720	−	0.113228i
$937$			34.0000i			1.11073i	0.831606	+	0.555366i	$0.187422\pi$
$937$			34.0000i			1.11073i	−0.831606	+	0.555366i	$0.812578\pi$
$938$	6.92820	+	20.0000i	0.226214	+	0.653023i
$939$	−17.0000			−0.554774
$940$		0			0
$941$	−6.00000	−	10.3923i	−0.195594	−	0.338779i	0.751501	−	0.659732i	$-0.229330\pi$
$941$	−6.00000	−	10.3923i	−0.195594	−	0.338779i	−0.947095	+	0.320953i	$0.895997\pi$
$942$	−12.1244	+	7.00000i	−0.395033	+	0.228072i
$943$	7.79423	+	4.50000i	0.253815	+	0.146540i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	48.0000			1.56061
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.362454	−	0.932002i	$-0.618061\pi$
$947$	−41.5692	−	24.0000i	−1.35082	−	0.779895i	−0.988364	+	0.152106i	$0.951394\pi$
$948$	−6.06218	+	3.50000i	−0.196890	+	0.113675i
$949$	−28.0000	−	48.4974i	−0.908918	−	1.57429i
$950$		0			0
$951$	12.0000			0.389127
$952$	5.19615	−	6.00000i	0.168408	−	0.194461i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$		0			0
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$	−31.1769	−	18.0000i	−1.00781	−	0.581857i
$958$			21.0000i			0.678479i
$959$	−30.0000	−	25.9808i	−0.968751	−	0.838963i
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	27.7128	−	16.0000i	0.893497	−	0.515861i
$963$	5.19615	−	3.00000i	0.167444	−	0.0966736i
$964$	−11.0000	+	19.0526i	−0.354286	+	0.613642i
$965$		0			0
$966$	−1.50000	+	7.79423i	−0.0482617	+	0.250775i
$967$			31.0000i			0.996893i	0.866921	+	0.498446i	$0.166096\pi$
$967$			31.0000i			0.996893i	−0.866921	+	0.498446i	$0.833904\pi$
$968$	−21.6506	−	12.5000i	−0.695878	−	0.401765i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	−0.910140	−	0.414301i	$-0.864026\pi$
$971$	−3.00000	+	5.19615i	−0.0962746	+	0.166752i	0.813865	+	0.581054i	$0.197359\pi$
$972$		−	1.00000i		−	0.0320750i
$973$	1.73205	+	5.00000i	0.0555270	+	0.160293i
$974$	25.0000			0.801052
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	−49.3634	+	28.5000i	−1.57928	+	0.911796i	−0.584316	+	0.811526i	$0.698637\pi$
$977$	−49.3634	+	28.5000i	−1.57928	+	0.911796i	−0.994960	+	0.100270i	$0.968029\pi$
$978$	−6.92820	−	4.00000i	−0.221540	−	0.127906i
$979$	−18.0000			−0.575282
$980$		0			0
$981$	−4.00000			−0.127710
$982$	−10.3923	−	6.00000i	−0.331632	−	0.191468i
$983$	−41.5692	+	24.0000i	−1.32585	+	0.765481i	−0.984655	−	0.174511i	$-0.944166\pi$
$983$	−41.5692	+	24.0000i	−1.32585	+	0.765481i	−0.341197	+	0.939992i	$0.610832\pi$
$984$	−1.50000	−	2.59808i	−0.0478183	−	0.0828236i
$985$		0			0
$986$	18.0000			0.573237
$987$	−7.79423	−	22.5000i	−0.248093	−	0.716183i
$988$			16.0000i			0.509028i
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$		0			0
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	0.974070	+	0.226246i	$0.0726454\pi$
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	−0.291100	+	0.956693i	$0.594021\pi$
$992$	4.33013	+	2.50000i	0.137482	+	0.0793751i
$993$			26.0000i			0.825085i
$994$	−4.50000	+	23.3827i	−0.142731	+	0.741654i
$995$		0			0
$996$	3.00000	−	5.19615i	0.0950586	−	0.164646i
$997$	3.46410	−	2.00000i	0.109709	−	0.0633406i	−0.444141	−	0.895957i	$-0.646491\pi$
$997$	3.46410	−	2.00000i	0.109709	−	0.0633406i	0.553851	+	0.832616i	$0.313158\pi$
$998$	32.9090	−	19.0000i	1.04172	−	0.601434i
$999$	4.00000	−	6.92820i	0.126554	−	0.219199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1050.2.o.h.499.2		4
5.2	odd	4		1050.2.i.c.751.1	yes	2
5.3	odd	4		1050.2.i.q.751.1	yes	2
5.4	even	2	inner	1050.2.o.h.499.1		4
7.4	even	3	inner	1050.2.o.h.949.1		4
35.2	odd	12		7350.2.a.cy.1.1		1
35.4	even	6	inner	1050.2.o.h.949.2		4
35.12	even	12		7350.2.a.cg.1.1		1
35.18	odd	12		1050.2.i.q.151.1	yes	2
35.23	odd	12		7350.2.a.s.1.1		1
35.32	odd	12		1050.2.i.c.151.1	✓	2
35.33	even	12		7350.2.a.bm.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1050.2.i.c.151.1	✓	2	35.32	odd	12
1050.2.i.c.751.1	yes	2	5.2	odd	4
1050.2.i.q.151.1	yes	2	35.18	odd	12
1050.2.i.q.751.1	yes	2	5.3	odd	4
1050.2.o.h.499.1		4	5.4	even	2	inner
1050.2.o.h.499.2		4	1.1	even	1	trivial
1050.2.o.h.949.1		4	7.4	even	3	inner
1050.2.o.h.949.2		4	35.4	even	6	inner
7350.2.a.s.1.1		1	35.23	odd	12
7350.2.a.bm.1.1		1	35.33	even	12
7350.2.a.cg.1.1		1	35.12	even	12
7350.2.a.cy.1.1		1	35.2	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1050.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(0.500000 + 0.866025i) q^{4} +1.00000 q^{6} +(-0.866025 - 2.50000i) q^{7} +1.00000i q^{8} +(0.500000 - 0.866025i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(0.866025 + 0.500000i) q^{12} -4.00000i q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(2.59808 - 1.50000i) q^{17} +(0.866025 - 0.500000i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-2.00000 - 1.73205i) q^{21} -6.00000i q^{22} +(-2.59808 - 1.50000i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{26} -1.00000i q^{27} +(1.73205 - 2.00000i) q^{28} +6.00000 q^{29} +(-2.50000 - 4.33013i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-5.19615 - 3.00000i) q^{33} +3.00000 q^{34} +1.00000 q^{36} +(6.92820 + 4.00000i) q^{37} +(-3.46410 + 2.00000i) q^{38} +(-2.00000 - 3.46410i) q^{39} -3.00000 q^{41} +(-0.866025 - 2.50000i) q^{42} +8.00000i q^{43} +(3.00000 - 5.19615i) q^{44} +(-1.50000 - 2.59808i) q^{46} +(7.79423 + 4.50000i) q^{47} +1.00000i q^{48} +(-5.50000 + 4.33013i) q^{49} +(1.50000 - 2.59808i) q^{51} +(3.46410 - 2.00000i) q^{52} +(10.3923 - 6.00000i) q^{53} +(0.500000 - 0.866025i) q^{54} +(2.50000 - 0.866025i) q^{56} +4.00000i q^{57} +(5.19615 + 3.00000i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-1.00000 + 1.73205i) q^{61} -5.00000i q^{62} +(-2.59808 - 0.500000i) q^{63} -1.00000 q^{64} +(-3.00000 - 5.19615i) q^{66} +(-6.92820 + 4.00000i) q^{67} +(2.59808 + 1.50000i) q^{68} -3.00000 q^{69} -9.00000 q^{71} +(0.866025 + 0.500000i) q^{72} +(12.1244 - 7.00000i) q^{73} +(4.00000 + 6.92820i) q^{74} -4.00000 q^{76} +(-10.3923 + 12.0000i) q^{77} -4.00000i q^{78} +(-3.50000 + 6.06218i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(-2.59808 - 1.50000i) q^{82} -6.00000i q^{83} +(0.500000 - 2.59808i) q^{84} +(-4.00000 + 6.92820i) q^{86} +(5.19615 - 3.00000i) q^{87} +(5.19615 - 3.00000i) q^{88} +(1.50000 - 2.59808i) q^{89} +(-10.0000 + 3.46410i) q^{91} -3.00000i q^{92} +(-4.33013 - 2.50000i) q^{93} +(4.50000 + 7.79423i) q^{94} +(-0.500000 + 0.866025i) q^{96} -17.0000i q^{97} +(-6.92820 + 1.00000i) q^{98} -6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9	\( 4 q + 2 q^{4} + 4 q^{6} + 2 q^{9} - 12 q^{11} + 2 q^{14} - 2 q^{16} - 8 q^{19} - 8 q^{21} + 2 q^{24} + 8 q^{26} + 24 q^{29} - 10 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 12 q^{41} + 12 q^{44} - 6 q^{46} - 22 q^{49} + 6 q^{51} + 2 q^{54} + 10 q^{56} + 12 q^{59} - 4 q^{61} - 4 q^{64} - 12 q^{66} - 12 q^{69} - 36 q^{71} + 16 q^{74} - 16 q^{76} - 14 q^{79} - 2 q^{81} + 2 q^{84} - 16 q^{86} + 6 q^{89} - 40 q^{91} + 18 q^{94} - 2 q^{96} - 24 q^{99}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^6 + 2 * q^9 - 12 * q^11 + 2 * q^14 - 2 * q^16 - 8 * q^19 - 8 * q^21 + 2 * q^24 + 8 * q^26 + 24 * q^29 - 10 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 12 * q^41 + 12 * q^44 - 6 * q^46 - 22 * q^49 + 6 * q^51 + 2 * q^54 + 10 * q^56 + 12 * q^59 - 4 * q^61 - 4 * q^64 - 12 * q^66 - 12 * q^69 - 36 * q^71 + 16 * q^74 - 16 * q^76 - 14 * q^79 - 2 * q^81 + 2 * q^84 - 16 * q^86 + 6 * q^89 - 40 * q^91 + 18 * q^94 - 2 * q^96 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more