LMFDB - Embedded newform 370.2.l.b.101.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(11,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("370.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.l (of order $6$, degree $2$, 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:	$2.95446487479$
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			101.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.101
Dual form			370.2.l.b.11.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000i q^{8} -1.00000 q^{10} -1.46410 q^{11} +(-0.866025 + 1.50000i) q^{12} +(0.866025 - 0.500000i) q^{13} +2.00000i q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.73205 + 3.00000i) q^{21} +(-1.26795 - 0.732051i) q^{22} -1.46410i q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +5.19615 q^{27} +(-1.00000 + 1.73205i) q^{28} -7.46410i q^{29} +(-0.866025 - 1.50000i) q^{30} +5.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.26795 - 2.19615i) q^{33} +(-1.73205 - 1.00000i) q^{35} +(6.06218 + 0.500000i) q^{37} -2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(-3.00000 + 1.73205i) q^{42} -5.92820i q^{43} +(-0.732051 - 1.26795i) q^{44} +(0.732051 - 1.26795i) q^{46} -0.928203 q^{47} -1.73205 q^{48} +(1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.866025 + 0.500000i) q^{52} +(2.59808 - 4.50000i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.26795 - 0.732051i) q^{55} +(-1.73205 + 1.00000i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(3.73205 - 6.46410i) q^{58} +(-3.46410 - 2.00000i) q^{59} -1.73205i q^{60} +(0.464102 - 0.267949i) q^{61} +(-2.86603 + 4.96410i) q^{62} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -2.53590i q^{66} +(2.26795 + 3.92820i) q^{67} +(2.19615 - 1.26795i) q^{69} +(-1.00000 - 1.73205i) q^{70} +(6.00000 + 10.3923i) q^{71} -2.53590 q^{73} +(5.00000 + 3.46410i) q^{74} +1.73205 q^{75} +(-1.73205 - 1.00000i) q^{76} +(-1.46410 - 2.53590i) q^{77} +(0.866025 + 1.50000i) q^{78} +(-3.00000 + 1.73205i) q^{79} -1.00000i q^{80} +(4.50000 + 7.79423i) q^{81} -1.00000i q^{82} +(7.73205 - 13.3923i) q^{83} -3.46410 q^{84} +(2.96410 - 5.13397i) q^{86} +(11.1962 - 6.46410i) q^{87} -1.46410i q^{88} +(-6.92820 - 4.00000i) q^{89} +(1.73205 + 1.00000i) q^{91} +(1.26795 - 0.732051i) q^{92} +(-8.59808 + 4.96410i) q^{93} +(-0.803848 - 0.464102i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-1.50000 - 0.866025i) q^{96} +8.92820i q^{97} +(2.59808 - 1.50000i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} + 4 q^{7}+O(q^{10}) $ 4 * q + 2 * q^4 + 4 * q^7	$ 4 q + 2 q^{4} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 6 q^{15} - 2 q^{16} - 12 q^{22} - 6 q^{24} + 2 q^{25} + 4 q^{26} - 4 q^{28} - 12 q^{33} - 8 q^{38} + 6 q^{39} - 2 q^{40} - 2 q^{41} - 12 q^{42} + 4 q^{44} - 4 q^{46} + 24 q^{47} + 6 q^{49} + 18 q^{54} + 12 q^{55} - 12 q^{57} + 8 q^{58} - 12 q^{61} - 8 q^{62} - 4 q^{64} - 2 q^{65} + 16 q^{67} - 12 q^{69} - 4 q^{70} + 24 q^{71} - 24 q^{73} + 20 q^{74} + 8 q^{77} - 12 q^{79} + 18 q^{81} + 24 q^{83} - 2 q^{86} + 24 q^{87} + 12 q^{92} - 24 q^{93} - 24 q^{94} + 4 q^{95} - 6 q^{96}+O(q^{100}) $ 4 * q + 2 * q^4 + 4 * q^7 - 4 * q^10 + 8 * q^11 - 6 * q^15 - 2 * q^16 - 12 * q^22 - 6 * q^24 + 2 * q^25 + 4 * q^26 - 4 * q^28 - 12 * q^33 - 8 * q^38 + 6 * q^39 - 2 * q^40 - 2 * q^41 - 12 * q^42 + 4 * q^44 - 4 * q^46 + 24 * q^47 + 6 * q^49 + 18 * q^54 + 12 * q^55 - 12 * q^57 + 8 * q^58 - 12 * q^61 - 8 * q^62 - 4 * q^64 - 2 * q^65 + 16 * q^67 - 12 * q^69 - 4 * q^70 + 24 * q^71 - 24 * q^73 + 20 * q^74 + 8 * q^77 - 12 * q^79 + 18 * q^81 + 24 * q^83 - 2 * q^86 + 24 * q^87 + 12 * q^92 - 24 * q^93 - 24 * q^94 + 4 * q^95 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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	+	1.50000i	0.500000	+	0.866025i	1.00000			$0$
$3$	0.866025	+	1.50000i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$5$	−0.866025	+	0.500000i	−0.387298	+	0.223607i
$6$			1.73205i			0.707107i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	−1.46410			−0.441443			−0.220722	−	0.975337i	$-0.570841\pi$
$11$	−1.46410			−0.441443			−0.220722	+	0.975337i	$0.570841\pi$
$12$	−0.866025	+	1.50000i	−0.250000	+	0.433013i
$13$	0.866025	−	0.500000i	0.240192	−	0.138675i	−0.375073	−	0.926995i	$-0.622382\pi$
$13$	0.866025	−	0.500000i	0.240192	−	0.138675i	0.615265	+	0.788320i	$0.289049\pi$
$14$			2.00000i			0.534522i
$15$	−1.50000	−	0.866025i	−0.387298	−	0.223607i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$17$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$18$		0			0
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	−0.685344	−	0.728219i	$-0.740348\pi$
$19$	−1.73205	+	1.00000i	−0.397360	+	0.229416i	0.287984	+	0.957635i	$0.407015\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$	−1.73205	+	3.00000i	−0.377964	+	0.654654i
$22$	−1.26795	−	0.732051i	−0.270328	−	0.156074i
$23$		−	1.46410i		−	0.305286i	−0.988281	−	0.152643i	$-0.951221\pi$
$23$		−	1.46410i		−	0.305286i	0.988281	−	0.152643i	$-0.0487785\pi$
$24$	−1.50000	+	0.866025i	−0.306186	+	0.176777i
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	1.00000			0.196116
$27$	5.19615			1.00000
$28$	−1.00000	+	1.73205i	−0.188982	+	0.327327i
$29$		−	7.46410i		−	1.38605i	−0.720914	−	0.693024i	$-0.756278\pi$
$29$		−	7.46410i		−	1.38605i	0.720914	−	0.693024i	$-0.243722\pi$
$30$	−0.866025	−	1.50000i	−0.158114	−	0.273861i
$31$			5.73205i			1.02951i	0.857338	+	0.514753i	$0.172117\pi$
$31$			5.73205i			1.02951i	−0.857338	+	0.514753i	$0.827883\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−1.26795	−	2.19615i	−0.220722	−	0.382301i
$34$		0			0
$35$	−1.73205	−	1.00000i	−0.292770	−	0.169031i
$36$		0			0
$37$	6.06218	+	0.500000i	0.996616	+	0.0821995i
$37$	6.06218	+	0.500000i	0.996616	+	0.0821995i
$38$	−2.00000			−0.324443
$39$	1.50000	+	0.866025i	0.240192	+	0.138675i
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	0.824338	−	0.566099i	$-0.191548\pi$
$41$	−0.500000	−	0.866025i	−0.0780869	−	0.135250i	−0.902424	+	0.430848i	$0.858214\pi$
$42$	−3.00000	+	1.73205i	−0.462910	+	0.267261i
$43$		−	5.92820i		−	0.904043i	−0.892007	−	0.452021i	$-0.850703\pi$
$43$		−	5.92820i		−	0.904043i	0.892007	−	0.452021i	$-0.149297\pi$
$44$	−0.732051	−	1.26795i	−0.110361	−	0.191151i
$45$		0			0
$46$	0.732051	−	1.26795i	0.107935	−	0.186949i
$47$	−0.928203			−0.135392			−0.0676962	−	0.997706i	$-0.521565\pi$
$47$	−0.928203			−0.135392			−0.0676962	+	0.997706i	$0.521565\pi$
$48$	−1.73205			−0.250000
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	0.866025	−	0.500000i	0.122474	−	0.0707107i
$51$		0			0
$52$	0.866025	+	0.500000i	0.120096	+	0.0693375i
$53$	2.59808	−	4.50000i	0.356873	−	0.618123i	−0.630563	−	0.776138i	$-0.717176\pi$
$53$	2.59808	−	4.50000i	0.356873	−	0.618123i	0.987437	+	0.158015i	$0.0505095\pi$
$54$	4.50000	+	2.59808i	0.612372	+	0.353553i
$55$	1.26795	−	0.732051i	0.170970	−	0.0987097i
$56$	−1.73205	+	1.00000i	−0.231455	+	0.133631i
$57$	−3.00000	−	1.73205i	−0.397360	−	0.229416i
$58$	3.73205	−	6.46410i	0.490042	−	0.848778i
$59$	−3.46410	−	2.00000i	−0.450988	−	0.260378i	0.257260	−	0.966342i	$-0.417180\pi$
$59$	−3.46410	−	2.00000i	−0.450988	−	0.260378i	−0.708247	+	0.705965i	$0.750514\pi$
$60$		−	1.73205i		−	0.223607i
$61$	0.464102	−	0.267949i	0.0594221	−	0.0343074i	−0.469995	−	0.882669i	$-0.655744\pi$
$61$	0.464102	−	0.267949i	0.0594221	−	0.0343074i	0.529417	+	0.848362i	$0.322411\pi$
$62$	−2.86603	+	4.96410i	−0.363986	+	0.630442i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		−	2.53590i		−	0.312148i
$67$	2.26795	+	3.92820i	0.277074	+	0.479906i	0.970656	−	0.240471i	$-0.0773019\pi$
$67$	2.26795	+	3.92820i	0.277074	+	0.479906i	−0.693582	+	0.720377i	$0.743969\pi$
$68$		0			0
$69$	2.19615	−	1.26795i	0.264386	−	0.152643i
$70$	−1.00000	−	1.73205i	−0.119523	−	0.207020i
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	0.964079	+	0.265615i	$0.0855750\pi$
$71$	6.00000	+	10.3923i	0.712069	+	1.23334i	−0.252010	+	0.967725i	$0.581092\pi$
$72$		0			0
$73$	−2.53590			−0.296804			−0.148402	−	0.988927i	$-0.547413\pi$
$73$	−2.53590			−0.296804			−0.148402	+	0.988927i	$0.547413\pi$
$74$	5.00000	+	3.46410i	0.581238	+	0.402694i
$75$	1.73205			0.200000
$76$	−1.73205	−	1.00000i	−0.198680	−	0.114708i
$77$	−1.46410	−	2.53590i	−0.166850	−	0.288992i
$78$	0.866025	+	1.50000i	0.0980581	+	0.169842i
$79$	−3.00000	+	1.73205i	−0.337526	+	0.194871i	−0.659178	−	0.751987i	$-0.729095\pi$
$79$	−3.00000	+	1.73205i	−0.337526	+	0.194871i	0.321651	+	0.946858i	$0.395762\pi$
$80$		−	1.00000i		−	0.111803i
$81$	4.50000	+	7.79423i	0.500000	+	0.866025i
$82$		−	1.00000i		−	0.110432i
$83$	7.73205	−	13.3923i	0.848703	−	1.47000i	−0.0336635	−	0.999433i	$-0.510717\pi$
$83$	7.73205	−	13.3923i	0.848703	−	1.47000i	0.882366	−	0.470563i	$-0.155949\pi$
$84$	−3.46410			−0.377964
$85$		0			0
$86$	2.96410	−	5.13397i	0.319627	−	0.553611i
$87$	11.1962	−	6.46410i	1.20035	−	0.693024i
$88$		−	1.46410i		−	0.156074i
$89$	−6.92820	−	4.00000i	−0.734388	−	0.423999i	0.0856373	−	0.996326i	$-0.472707\pi$
$89$	−6.92820	−	4.00000i	−0.734388	−	0.423999i	−0.820025	+	0.572327i	$0.806041\pi$
$90$		0			0
$91$	1.73205	+	1.00000i	0.181568	+	0.104828i
$92$	1.26795	−	0.732051i	0.132193	−	0.0763216i
$93$	−8.59808	+	4.96410i	−0.891579	+	0.514753i
$94$	−0.803848	−	0.464102i	−0.0829105	−	0.0478684i
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$			8.92820i			0.906522i	0.891378	+	0.453261i	$0.149739\pi$
$97$			8.92820i			0.906522i	−0.891378	+	0.453261i	$0.850261\pi$
$98$	2.59808	−	1.50000i	0.262445	−	0.151523i
$99$		0			0
$100$	1.00000			0.100000
$101$	−5.07180			−0.504663			−0.252331	−	0.967641i	$-0.581197\pi$
$101$	−5.07180			−0.504663			−0.252331	+	0.967641i	$0.581197\pi$
$102$		0			0
$103$		−	6.92820i		−	0.682656i	−0.939944	−	0.341328i	$-0.889123\pi$
$103$		−	6.92820i		−	0.682656i	0.939944	−	0.341328i	$-0.110877\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$		−	3.46410i		−	0.338062i
$106$	4.50000	−	2.59808i	0.437079	−	0.252347i
$107$	−4.33013	−	7.50000i	−0.418609	−	0.725052i	0.577191	−	0.816609i	$-0.304149\pi$
$107$	−4.33013	−	7.50000i	−0.418609	−	0.725052i	−0.995800	+	0.0915571i	$0.970816\pi$
$108$	2.59808	+	4.50000i	0.250000	+	0.433013i
$109$	−6.46410	−	3.73205i	−0.619149	−	0.357466i	0.157389	−	0.987537i	$-0.449692\pi$
$109$	−6.46410	−	3.73205i	−0.619149	−	0.357466i	−0.776537	+	0.630071i	$0.783026\pi$
$110$	1.46410			0.139597
$111$	4.50000	+	9.52628i	0.427121	+	0.904194i
$112$	−2.00000			−0.188982
$113$	−16.3923	−	9.46410i	−1.54206	−	0.890308i	−0.998709	−	0.0508012i	$-0.983823\pi$
$113$	−16.3923	−	9.46410i	−1.54206	−	0.890308i	−0.543350	−	0.839507i	$-0.682844\pi$
$114$	−1.73205	−	3.00000i	−0.162221	−	0.280976i
$115$	0.732051	+	1.26795i	0.0682641	+	0.118237i
$116$	6.46410	−	3.73205i	0.600177	−	0.346512i
$117$		0			0
$118$	−2.00000	−	3.46410i	−0.184115	−	0.318896i
$119$		0			0
$120$	0.866025	−	1.50000i	0.0790569	−	0.136931i
$121$	−8.85641			−0.805128
$122$	0.535898			0.0485180
$123$	0.866025	−	1.50000i	0.0780869	−	0.135250i
$124$	−4.96410	+	2.86603i	−0.445789	+	0.257377i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	0.196152	−	0.339746i	0.0174057	−	0.0301476i	−0.857191	−	0.514998i	$-0.827793\pi$
$127$	0.196152	−	0.339746i	0.0174057	−	0.0301476i	0.874597	+	0.484850i	$0.161126\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	8.89230	−	5.13397i	0.782924	−	0.452021i
$130$	−0.866025	+	0.500000i	−0.0759555	+	0.0438529i
$131$	13.3923	+	7.73205i	1.17009	+	0.675552i	0.953702	−	0.300755i	$-0.0972385\pi$
$131$	13.3923	+	7.73205i	1.17009	+	0.675552i	0.216390	+	0.976307i	$0.430572\pi$
$132$	1.26795	−	2.19615i	0.110361	−	0.191151i
$133$	−3.46410	−	2.00000i	−0.300376	−	0.173422i
$134$			4.53590i			0.391842i
$135$	−4.50000	+	2.59808i	−0.387298	+	0.223607i
$136$		0			0
$137$	−12.3923			−1.05875			−0.529373	−	0.848389i	$-0.677573\pi$
$137$	−12.3923			−1.05875			−0.529373	+	0.848389i	$0.677573\pi$
$138$	2.53590			0.215870
$139$	−4.73205	+	8.19615i	−0.401367	+	0.695189i	−0.993891	−	0.110364i	$-0.964798\pi$
$139$	−4.73205	+	8.19615i	−0.401367	+	0.695189i	0.592524	+	0.805553i	$0.298132\pi$
$140$		−	2.00000i		−	0.169031i
$141$	−0.803848	−	1.39230i	−0.0676962	−	0.117253i
$142$			12.0000i			1.00702i
$143$	−1.26795	+	0.732051i	−0.106031	+	0.0612172i
$144$		0			0
$145$	3.73205	+	6.46410i	0.309930	+	0.536814i
$146$	−2.19615	−	1.26795i	−0.181755	−	0.104936i
$147$	5.19615			0.428571
$148$	2.59808	+	5.50000i	0.213561	+	0.452097i
$149$	−2.53590			−0.207749			−0.103874	−	0.994590i	$-0.533124\pi$
$149$	−2.53590			−0.207749			−0.103874	+	0.994590i	$0.533124\pi$
$150$	1.50000	+	0.866025i	0.122474	+	0.0707107i
$151$	7.42820	+	12.8660i	0.604499	+	1.04702i	0.992131	+	0.125208i	$0.0399598\pi$
$151$	7.42820	+	12.8660i	0.604499	+	1.04702i	−0.387632	+	0.921814i	$0.626707\pi$
$152$	−1.00000	−	1.73205i	−0.0811107	−	0.140488i
$153$		0			0
$154$		−	2.92820i		−	0.235961i
$155$	−2.86603	−	4.96410i	−0.230205	−	0.398726i
$156$			1.73205i			0.138675i
$157$	1.13397	−	1.96410i	0.0905010	−	0.156752i	−0.817221	−	0.576324i	$-0.804486\pi$
$157$	1.13397	−	1.96410i	0.0905010	−	0.156752i	0.907722	+	0.419572i	$0.137820\pi$
$158$	−3.46410			−0.275589
$159$	9.00000			0.713746
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	2.53590	−	1.46410i	0.199857	−	0.115387i
$162$			9.00000i			0.707107i
$163$	−6.06218	−	3.50000i	−0.474826	−	0.274141i	0.243432	−	0.969918i	$-0.421727\pi$
$163$	−6.06218	−	3.50000i	−0.474826	−	0.274141i	−0.718258	+	0.695777i	$0.755060\pi$
$164$	0.500000	−	0.866025i	0.0390434	−	0.0676252i
$165$	2.19615	+	1.26795i	0.170970	+	0.0987097i
$166$	13.3923	−	7.73205i	1.03944	−	0.600124i
$167$	−9.92820	+	5.73205i	−0.768267	+	0.443559i	−0.832256	−	0.554391i	$-0.812951\pi$
$167$	−9.92820	+	5.73205i	−0.768267	+	0.443559i	0.0639888	+	0.997951i	$0.479618\pi$
$168$	−3.00000	−	1.73205i	−0.231455	−	0.133631i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$		0			0
$172$	5.13397	−	2.96410i	0.391462	−	0.226011i
$173$	−9.46410	+	16.3923i	−0.719542	+	1.24628i	0.241639	+	0.970366i	$0.422315\pi$
$173$	−9.46410	+	16.3923i	−0.719542	+	1.24628i	−0.961181	+	0.275918i	$0.911018\pi$
$174$	12.9282			0.980085
$175$	2.00000			0.151186
$176$	0.732051	−	1.26795i	0.0551804	−	0.0955753i
$177$		−	6.92820i		−	0.520756i
$178$	−4.00000	−	6.92820i	−0.299813	−	0.519291i
$179$		−	1.85641i		−	0.138754i	−0.997591	−	0.0693772i	$-0.977899\pi$
$179$		−	1.85641i		−	0.138754i	0.997591	−	0.0693772i	$-0.0221012\pi$
$180$		0			0
$181$	2.46410	+	4.26795i	0.183155	+	0.317234i	0.942953	−	0.332925i	$-0.108036\pi$
$181$	2.46410	+	4.26795i	0.183155	+	0.317234i	−0.759798	+	0.650159i	$0.774702\pi$
$182$	1.00000	+	1.73205i	0.0741249	+	0.128388i
$183$	0.803848	+	0.464102i	0.0594221	+	0.0343074i
$184$	1.46410			0.107935
$185$	−5.50000	+	2.59808i	−0.404368	+	0.191014i
$186$	−9.92820			−0.727971
$187$		0			0
$188$	−0.464102	−	0.803848i	−0.0338481	−	0.0586266i
$189$	5.19615	+	9.00000i	0.377964	+	0.654654i
$190$	1.73205	−	1.00000i	0.125656	−	0.0725476i
$191$			4.66025i			0.337204i	0.985684	+	0.168602i	$0.0539253\pi$
$191$			4.66025i			0.337204i	−0.985684	+	0.168602i	$0.946075\pi$
$192$	−0.866025	−	1.50000i	−0.0625000	−	0.108253i
$193$		−	1.07180i		−	0.0771496i	−0.999256	−	0.0385748i	$-0.987718\pi$
$193$		−	1.07180i		−	0.0771496i	0.999256	−	0.0385748i	$-0.0122818\pi$
$194$	−4.46410	+	7.73205i	−0.320504	+	0.555129i
$195$	−1.73205			−0.124035
$196$	3.00000			0.214286
$197$	2.86603	−	4.96410i	0.204196	−	0.353678i	−0.745680	−	0.666304i	$-0.767875\pi$
$197$	2.86603	−	4.96410i	0.204196	−	0.353678i	0.949876	+	0.312626i	$0.101209\pi$
$198$		0			0
$199$			9.19615i			0.651898i	0.945387	+	0.325949i	$0.105684\pi$
$199$			9.19615i			0.651898i	−0.945387	+	0.325949i	$0.894316\pi$
$200$	0.866025	+	0.500000i	0.0612372	+	0.0353553i
$201$	−3.92820	+	6.80385i	−0.277074	+	0.479906i
$202$	−4.39230	−	2.53590i	−0.309041	−	0.178425i
$203$	12.9282	−	7.46410i	0.907382	−	0.523877i
$204$		0			0
$205$	0.866025	+	0.500000i	0.0604858	+	0.0349215i
$206$	3.46410	−	6.00000i	0.241355	−	0.418040i
$207$		0			0
$208$			1.00000i			0.0693375i
$209$	2.53590	−	1.46410i	0.175412	−	0.101274i
$210$	1.73205	−	3.00000i	0.119523	−	0.207020i
$211$	−8.92820			−0.614643			−0.307321	−	0.951606i	$-0.599433\pi$
$211$	−8.92820			−0.614643			−0.307321	+	0.951606i	$0.599433\pi$
$212$	5.19615			0.356873
$213$	−10.3923	+	18.0000i	−0.712069	+	1.23334i
$214$		−	8.66025i		−	0.592003i
$215$	2.96410	+	5.13397i	0.202150	+	0.350134i
$216$			5.19615i			0.353553i
$217$	−9.92820	+	5.73205i	−0.673970	+	0.389117i
$218$	−3.73205	−	6.46410i	−0.252766	−	0.437804i
$219$	−2.19615	−	3.80385i	−0.148402	−	0.257040i
$220$	1.26795	+	0.732051i	0.0854851	+	0.0493549i
$221$		0			0
$222$	−0.866025	+	10.5000i	−0.0581238	+	0.704714i
$223$	15.3205			1.02594			0.512969	−	0.858407i	$-0.328546\pi$
$223$	15.3205			1.02594			0.512969	+	0.858407i	$0.328546\pi$
$224$	−1.73205	−	1.00000i	−0.115728	−	0.0668153i
$225$		0			0
$226$	−9.46410	−	16.3923i	−0.629543	−	1.09040i
$227$	−15.4019	+	8.89230i	−1.02226	+	0.590203i	−0.914758	−	0.404002i	$-0.867619\pi$
$227$	−15.4019	+	8.89230i	−1.02226	+	0.590203i	−0.107503	+	0.994205i	$0.534286\pi$
$228$		−	3.46410i		−	0.229416i
$229$	8.46410	+	14.6603i	0.559324	+	0.968777i	0.997553	+	0.0699137i	$0.0222724\pi$
$229$	8.46410	+	14.6603i	0.559324	+	0.968777i	−0.438229	+	0.898863i	$0.644394\pi$
$230$			1.46410i			0.0965400i
$231$	2.53590	−	4.39230i	0.166850	−	0.288992i
$232$	7.46410			0.490042
$233$	−4.92820			−0.322857			−0.161429	−	0.986884i	$-0.551610\pi$
$233$	−4.92820			−0.322857			−0.161429	+	0.986884i	$0.551610\pi$
$234$		0			0
$235$	0.803848	−	0.464102i	0.0524372	−	0.0302747i
$236$		−	4.00000i		−	0.260378i
$237$	−5.19615	−	3.00000i	−0.337526	−	0.194871i
$238$		0			0
$239$	4.60770	+	2.66025i	0.298047	+	0.172078i	0.641565	−	0.767068i	$-0.278285\pi$
$239$	4.60770	+	2.66025i	0.298047	+	0.172078i	−0.343518	+	0.939146i	$0.611619\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	−15.4641	+	8.92820i	−0.996130	+	0.575116i	−0.907101	−	0.420913i	$-0.861710\pi$
$241$	−15.4641	+	8.92820i	−0.996130	+	0.575116i	−0.0890293	+	0.996029i	$0.528376\pi$
$242$	−7.66987	−	4.42820i	−0.493038	−	0.284656i
$243$		0			0
$244$	0.464102	+	0.267949i	0.0297111	+	0.0171537i
$245$			3.00000i			0.191663i
$246$	1.50000	−	0.866025i	0.0956365	−	0.0552158i
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$	−5.73205			−0.363986
$249$	26.7846			1.69741
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		−	24.9282i		−	1.57345i	−0.617301	−	0.786727i	$-0.711774\pi$
$251$		−	24.9282i		−	1.57345i	0.617301	−	0.786727i	$-0.288226\pi$
$252$		0			0
$253$			2.14359i			0.134767i
$254$	0.339746	−	0.196152i	0.0213176	−	0.0123077i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−16.2679	−	9.39230i	−1.01477	−	0.585876i	−0.102183	−	0.994766i	$-0.532583\pi$
$257$	−16.2679	−	9.39230i	−1.01477	−	0.585876i	−0.912584	+	0.408890i	$0.865916\pi$
$258$	10.2679			0.639255
$259$	5.19615	+	11.0000i	0.322873	+	0.683507i
$260$	−1.00000			−0.0620174
$261$		0			0
$262$	7.73205	+	13.3923i	0.477688	+	0.827379i
$263$	9.19615	+	15.9282i	0.567059	+	0.982175i	0.996855	+	0.0792490i	$0.0252522\pi$
$263$	9.19615	+	15.9282i	0.567059	+	0.982175i	−0.429796	+	0.902926i	$0.641414\pi$
$264$	2.19615	−	1.26795i	0.135164	−	0.0780369i
$265$			5.19615i			0.319197i
$266$	−2.00000	−	3.46410i	−0.122628	−	0.212398i
$267$		−	13.8564i		−	0.847998i
$268$	−2.26795	+	3.92820i	−0.138537	+	0.239953i
$269$	6.92820			0.422420			0.211210	−	0.977441i	$-0.432260\pi$
$269$	6.92820			0.422420			0.211210	+	0.977441i	$0.432260\pi$
$270$	−5.19615			−0.316228
$271$	−7.03590	+	12.1865i	−0.427400	+	0.740279i	−0.996641	−	0.0818916i	$-0.973904\pi$
$271$	−7.03590	+	12.1865i	−0.427400	+	0.740279i	0.569241	+	0.822171i	$0.307237\pi$
$272$		0			0
$273$			3.46410i			0.209657i
$274$	−10.7321	−	6.19615i	−0.648347	−	0.374323i
$275$	−0.732051	+	1.26795i	−0.0441443	+	0.0764602i
$276$	2.19615	+	1.26795i	0.132193	+	0.0763216i
$277$	25.9186	−	14.9641i	1.55730	−	0.899106i	0.559783	−	0.828639i	$-0.310885\pi$
$277$	25.9186	−	14.9641i	1.55730	−	0.899106i	0.997514	−	0.0704662i	$-0.0224487\pi$
$278$	−8.19615	+	4.73205i	−0.491573	+	0.283810i
$279$		0			0
$280$	1.00000	−	1.73205i	0.0597614	−	0.103510i
$281$	−21.8205	−	12.5981i	−1.30170	−	0.751538i	−0.321006	−	0.947077i	$-0.604021\pi$
$281$	−21.8205	−	12.5981i	−1.30170	−	0.751538i	−0.980696	+	0.195539i	$0.937354\pi$
$282$		−	1.60770i		−	0.0957369i
$283$	2.72243	−	1.57180i	0.161832	−	0.0934336i	−0.416897	−	0.908954i	$-0.636882\pi$
$283$	2.72243	−	1.57180i	0.161832	−	0.0934336i	0.578729	+	0.815520i	$0.303549\pi$
$284$	−6.00000	+	10.3923i	−0.356034	+	0.616670i
$285$	3.46410			0.205196
$286$	−1.46410			−0.0865741
$287$	1.00000	−	1.73205i	0.0590281	−	0.102240i
$288$		0			0
$289$	−8.50000	−	14.7224i	−0.500000	−	0.866025i
$290$			7.46410i			0.438307i
$291$	−13.3923	+	7.73205i	−0.785071	+	0.453261i
$292$	−1.26795	−	2.19615i	−0.0742011	−	0.128520i
$293$	−0.0621778	−	0.107695i	−0.00363247	−	0.00629162i	0.864203	−	0.503143i	$-0.167823\pi$
$293$	−0.0621778	−	0.107695i	−0.00363247	−	0.00629162i	−0.867836	+	0.496851i	$0.834490\pi$
$294$	4.50000	+	2.59808i	0.262445	+	0.151523i
$295$	4.00000			0.232889
$296$	−0.500000	+	6.06218i	−0.0290619	+	0.352357i
$297$	−7.60770			−0.441443
$298$	−2.19615	−	1.26795i	−0.127220	−	0.0734503i
$299$	−0.732051	−	1.26795i	−0.0423356	−	0.0733274i
$300$	0.866025	+	1.50000i	0.0500000	+	0.0866025i
$301$	10.2679	−	5.92820i	0.591835	−	0.341696i
$302$			14.8564i			0.854890i
$303$	−4.39230	−	7.60770i	−0.252331	−	0.437051i
$304$		−	2.00000i		−	0.114708i
$305$	−0.267949	+	0.464102i	−0.0153427	+	0.0265744i
$306$		0			0
$307$	32.1244			1.83343			0.916717	−	0.399537i	$-0.130829\pi$
$307$	32.1244			1.83343			0.916717	+	0.399537i	$0.130829\pi$
$308$	1.46410	−	2.53590i	0.0834249	−	0.144496i
$309$	10.3923	−	6.00000i	0.591198	−	0.341328i
$310$		−	5.73205i		−	0.325559i
$311$	−13.0359	−	7.52628i	−0.739198	−	0.426776i	0.0825797	−	0.996584i	$-0.473684\pi$
$311$	−13.0359	−	7.52628i	−0.739198	−	0.426776i	−0.821778	+	0.569808i	$0.807017\pi$
$312$	−0.866025	+	1.50000i	−0.0490290	+	0.0849208i
$313$	16.2679	+	9.39230i	0.919519	+	0.530884i	0.883482	−	0.468466i	$-0.155193\pi$
$313$	16.2679	+	9.39230i	0.919519	+	0.530884i	0.0360373	+	0.999350i	$0.488526\pi$
$314$	1.96410	−	1.13397i	0.110841	−	0.0639939i
$315$		0			0
$316$	−3.00000	−	1.73205i	−0.168763	−	0.0974355i
$317$	−0.866025	+	1.50000i	−0.0486408	+	0.0842484i	−0.889321	−	0.457284i	$-0.848822\pi$
$317$	−0.866025	+	1.50000i	−0.0486408	+	0.0842484i	0.840680	+	0.541532i	$0.182156\pi$
$318$	7.79423	+	4.50000i	0.437079	+	0.252347i
$319$			10.9282i			0.611862i
$320$	0.866025	−	0.500000i	0.0484123	−	0.0279508i
$321$	7.50000	−	12.9904i	0.418609	−	0.725052i
$322$	2.92820			0.163182
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$		−	1.00000i		−	0.0554700i
$326$	−3.50000	−	6.06218i	−0.193847	−	0.335753i
$327$		−	12.9282i		−	0.714931i
$328$	0.866025	−	0.500000i	0.0478183	−	0.0276079i
$329$	−0.928203	−	1.60770i	−0.0511735	−	0.0886351i
$330$	1.26795	+	2.19615i	0.0697983	+	0.120894i
$331$	−13.3923	−	7.73205i	−0.736108	−	0.424992i	0.0845447	−	0.996420i	$-0.473056\pi$
$331$	−13.3923	−	7.73205i	−0.736108	−	0.424992i	−0.820652	+	0.571428i	$0.806390\pi$
$332$	15.4641			0.848703
$333$		0			0
$334$	−11.4641			−0.627288
$335$	−3.92820	−	2.26795i	−0.214621	−	0.123911i
$336$	−1.73205	−	3.00000i	−0.0944911	−	0.163663i
$337$	−8.46410	−	14.6603i	−0.461069	−	0.798595i	0.537946	−	0.842980i	$-0.319201\pi$
$337$	−8.46410	−	14.6603i	−0.461069	−	0.798595i	−0.999015	+	0.0443847i	$0.985867\pi$
$338$	−10.3923	+	6.00000i	−0.565267	+	0.326357i
$339$		−	32.7846i		−	1.78062i
$340$		0			0
$341$		−	8.39230i		−	0.454469i
$342$		0			0
$343$	20.0000			1.07990
$344$	5.92820			0.319627
$345$	−1.26795	+	2.19615i	−0.0682641	+	0.118237i
$346$	−16.3923	+	9.46410i	−0.881256	+	0.508793i
$347$		−	23.7128i		−	1.27297i	−0.771289	−	0.636485i	$-0.780388\pi$
$347$		−	23.7128i		−	1.27297i	0.771289	−	0.636485i	$-0.219612\pi$
$348$	11.1962	+	6.46410i	0.600177	+	0.346512i
$349$	13.1962	−	22.8564i	0.706374	−	1.22348i	−0.259820	−	0.965657i	$-0.583663\pi$
$349$	13.1962	−	22.8564i	0.706374	−	1.22348i	0.966193	−	0.257818i	$-0.0830036\pi$
$350$	1.73205	+	1.00000i	0.0925820	+	0.0534522i
$351$	4.50000	−	2.59808i	0.240192	−	0.138675i
$352$	1.26795	−	0.732051i	0.0675819	−	0.0390184i
$353$	18.4641	+	10.6603i	0.982745	+	0.567388i	0.903098	−	0.429435i	$-0.141287\pi$
$353$	18.4641	+	10.6603i	0.982745	+	0.567388i	0.0796472	+	0.996823i	$0.474621\pi$
$354$	3.46410	−	6.00000i	0.184115	−	0.318896i
$355$	−10.3923	−	6.00000i	−0.551566	−	0.318447i
$356$		−	8.00000i		−	0.423999i
$357$		0			0
$358$	0.928203	−	1.60770i	0.0490571	−	0.0849693i
$359$	−22.7128			−1.19874			−0.599368	−	0.800473i	$-0.704581\pi$
$359$	−22.7128			−1.19874			−0.599368	+	0.800473i	$0.704581\pi$
$360$		0			0
$361$	−7.50000	+	12.9904i	−0.394737	+	0.683704i
$362$			4.92820i			0.259021i
$363$	−7.66987	−	13.2846i	−0.402564	−	0.697261i
$364$			2.00000i			0.104828i
$365$	2.19615	−	1.26795i	0.114952	−	0.0663675i
$366$	0.464102	+	0.803848i	0.0242590	+	0.0420178i
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	0.963735	−	0.266861i	$-0.0859866\pi$
$367$	4.80385	+	8.32051i	0.250759	+	0.434327i	−0.712976	+	0.701188i	$0.752653\pi$
$368$	1.26795	+	0.732051i	0.0660964	+	0.0381608i
$369$		0			0
$370$	−6.06218	−	0.500000i	−0.315158	−	0.0259938i
$371$	10.3923			0.539542
$372$	−8.59808	−	4.96410i	−0.445789	−	0.257377i
$373$	0.205771	+	0.356406i	0.0106544	+	0.0184540i	0.871303	−	0.490745i	$-0.163275\pi$
$373$	0.205771	+	0.356406i	0.0106544	+	0.0184540i	−0.860649	+	0.509199i	$0.829942\pi$
$374$		0			0
$375$	−1.50000	+	0.866025i	−0.0774597	+	0.0447214i
$376$		−	0.928203i		−	0.0478684i
$377$	−3.73205	−	6.46410i	−0.192210	−	0.332918i
$378$			10.3923i			0.534522i
$379$	9.66025	−	16.7321i	0.496214	−	0.859468i	−0.503777	−	0.863834i	$-0.668057\pi$
$379$	9.66025	−	16.7321i	0.496214	−	0.859468i	0.999990	+	0.00436629i	$0.00138984\pi$
$380$	2.00000			0.102598
$381$	0.679492			0.0348114
$382$	−2.33013	+	4.03590i	−0.119220	+	0.206495i
$383$	23.7846	−	13.7321i	1.21534	−	0.701675i	0.251420	−	0.967878i	$-0.419103\pi$
$383$	23.7846	−	13.7321i	1.21534	−	0.701675i	0.963917	+	0.266203i	$0.0857692\pi$
$384$		−	1.73205i		−	0.0883883i
$385$	2.53590	+	1.46410i	0.129241	+	0.0746175i
$386$	0.535898	−	0.928203i	0.0272765	−	0.0472443i
$387$		0			0
$388$	−7.73205	+	4.46410i	−0.392535	+	0.226630i
$389$	−15.8038	+	9.12436i	−0.801287	+	0.462623i	−0.843921	−	0.536468i	$-0.819758\pi$
$389$	−15.8038	+	9.12436i	−0.801287	+	0.462623i	0.0426341	+	0.999091i	$0.486425\pi$
$390$	−1.50000	−	0.866025i	−0.0759555	−	0.0438529i
$391$		0			0
$392$	2.59808	+	1.50000i	0.131223	+	0.0757614i
$393$			26.7846i			1.35110i
$394$	4.96410	−	2.86603i	0.250088	−	0.144388i
$395$	1.73205	−	3.00000i	0.0871489	−	0.150946i
$396$		0			0
$397$	33.1962			1.66607			0.833034	−	0.553222i	$-0.186602\pi$
$397$	33.1962			1.66607			0.833034	+	0.553222i	$0.186602\pi$
$398$	−4.59808	+	7.96410i	−0.230481	+	0.399204i
$399$		−	6.92820i		−	0.346844i
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$		−	27.7128i		−	1.38391i	−0.721940	−	0.691956i	$-0.756749\pi$
$401$		−	27.7128i		−	1.38391i	0.721940	−	0.691956i	$-0.243251\pi$
$402$	−6.80385	+	3.92820i	−0.339345	+	0.195921i
$403$	2.86603	+	4.96410i	0.142767	+	0.247280i
$404$	−2.53590	−	4.39230i	−0.126166	−	0.218525i
$405$	−7.79423	−	4.50000i	−0.387298	−	0.223607i
$406$	14.9282			0.740874
$407$	−8.87564	−	0.732051i	−0.439949	−	0.0362864i
$408$		0			0
$409$	−12.5718	−	7.25833i	−0.621635	−	0.358901i	0.155870	−	0.987778i	$-0.450182\pi$
$409$	−12.5718	−	7.25833i	−0.621635	−	0.358901i	−0.777505	+	0.628876i	$0.783515\pi$
$410$	0.500000	+	0.866025i	0.0246932	+	0.0427699i
$411$	−10.7321	−	18.5885i	−0.529373	−	0.916901i
$412$	6.00000	−	3.46410i	0.295599	−	0.170664i
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$			15.4641i			0.759103i
$416$	−0.500000	+	0.866025i	−0.0245145	+	0.0424604i
$417$	−16.3923			−0.802735
$418$	2.92820			0.143223
$419$	−8.92820	+	15.4641i	−0.436171	+	0.755471i	−0.997390	−	0.0721964i	$-0.976999\pi$
$419$	−8.92820	+	15.4641i	−0.436171	+	0.755471i	0.561219	+	0.827667i	$0.310332\pi$
$420$	3.00000	−	1.73205i	0.146385	−	0.0845154i
$421$		−	22.3923i		−	1.09133i	−0.838002	−	0.545667i	$-0.816276\pi$
$421$		−	22.3923i		−	1.09133i	0.838002	−	0.545667i	$-0.183724\pi$
$422$	−7.73205	−	4.46410i	−0.376390	−	0.217309i
$423$		0			0
$424$	4.50000	+	2.59808i	0.218539	+	0.126174i
$425$		0			0
$426$	−18.0000	+	10.3923i	−0.872103	+	0.503509i
$427$	0.928203	+	0.535898i	0.0449189	+	0.0259339i
$428$	4.33013	−	7.50000i	0.209305	−	0.362526i
$429$	−2.19615	−	1.26795i	−0.106031	−	0.0612172i
$430$			5.92820i			0.285883i
$431$	30.8205	−	17.7942i	1.48457	−	0.857118i	0.484726	−	0.874666i	$-0.338919\pi$
$431$	30.8205	−	17.7942i	1.48457	−	0.857118i	0.999846	+	0.0175484i	$0.00558613\pi$
$432$	−2.59808	+	4.50000i	−0.125000	+	0.216506i
$433$	6.53590			0.314095			0.157048	−	0.987591i	$-0.449802\pi$
$433$	6.53590			0.314095			0.157048	+	0.987591i	$0.449802\pi$
$434$	−11.4641			−0.550294
$435$	−6.46410	+	11.1962i	−0.309930	+	0.536814i
$436$		−	7.46410i		−	0.357466i
$437$	1.46410	+	2.53590i	0.0700375	+	0.121308i
$438$		−	4.39230i		−	0.209872i
$439$	−20.4282	+	11.7942i	−0.974985	+	0.562908i	−0.900752	−	0.434333i	$-0.856984\pi$
$439$	−20.4282	+	11.7942i	−0.974985	+	0.562908i	−0.0742326	+	0.997241i	$0.523651\pi$
$440$	0.732051	+	1.26795i	0.0348992	+	0.0604471i
$441$		0			0
$442$		0			0
$443$	−6.80385			−0.323261			−0.161630	−	0.986851i	$-0.551675\pi$
$443$	−6.80385			−0.323261			−0.161630	+	0.986851i	$0.551675\pi$
$444$	−6.00000	+	8.66025i	−0.284747	+	0.410997i
$445$	8.00000			0.379236
$446$	13.2679	+	7.66025i	0.628256	+	0.362724i
$447$	−2.19615	−	3.80385i	−0.103874	−	0.179916i
$448$	−1.00000	−	1.73205i	−0.0472456	−	0.0818317i
$449$	25.0359	−	14.4545i	1.18152	−	0.682149i	0.225152	−	0.974324i	$-0.427712\pi$
$449$	25.0359	−	14.4545i	1.18152	−	0.682149i	0.956365	+	0.292174i	$0.0943788\pi$
$450$		0			0
$451$	0.732051	+	1.26795i	0.0344709	+	0.0597054i
$452$		−	18.9282i		−	0.890308i
$453$	−12.8660	+	22.2846i	−0.604499	+	1.04702i
$454$	−17.7846			−0.834673
$455$	−2.00000			−0.0937614
$456$	1.73205	−	3.00000i	0.0811107	−	0.140488i
$457$	30.0000	−	17.3205i	1.40334	−	0.810219i	0.408607	−	0.912710i	$-0.366015\pi$
$457$	30.0000	−	17.3205i	1.40334	−	0.810219i	0.994734	+	0.102491i	$0.0326814\pi$
$458$			16.9282i			0.791003i
$459$		0			0
$460$	−0.732051	+	1.26795i	−0.0341320	+	0.0591184i
$461$	15.2487	+	8.80385i	0.710203	+	0.410036i	0.811136	−	0.584857i	$-0.198849\pi$
$461$	15.2487	+	8.80385i	0.710203	+	0.410036i	−0.100933	+	0.994893i	$0.532183\pi$
$462$	4.39230	−	2.53590i	0.204349	−	0.117981i
$463$	−28.0526	+	16.1962i	−1.30371	+	0.752699i	−0.981039	−	0.193811i	$-0.937915\pi$
$463$	−28.0526	+	16.1962i	−1.30371	+	0.752699i	−0.322674	+	0.946510i	$0.604582\pi$
$464$	6.46410	+	3.73205i	0.300088	+	0.173256i
$465$	4.96410	−	8.59808i	0.230205	−	0.398726i
$466$	−4.26795	−	2.46410i	−0.197709	−	0.114147i
$467$			20.0718i			0.928812i	0.885622	+	0.464406i	$0.153732\pi$
$467$			20.0718i			0.928812i	−0.885622	+	0.464406i	$0.846268\pi$
$468$		0			0
$469$	−4.53590	+	7.85641i	−0.209448	+	0.362775i
$470$	0.928203			0.0428148
$471$	3.92820			0.181002
$472$	2.00000	−	3.46410i	0.0920575	−	0.159448i
$473$			8.67949i			0.399083i
$474$	−3.00000	−	5.19615i	−0.137795	−	0.238667i
$475$			2.00000i			0.0917663i
$476$		0			0
$477$		0			0
$478$	2.66025	+	4.60770i	0.121677	+	0.210751i
$479$	−13.9641	−	8.06218i	−0.638036	−	0.368370i	0.145822	−	0.989311i	$-0.453417\pi$
$479$	−13.9641	−	8.06218i	−0.638036	−	0.368370i	−0.783858	+	0.620941i	$0.786751\pi$
$480$	1.73205			0.0790569
$481$	5.50000	−	2.59808i	0.250778	−	0.118462i
$482$	−17.8564			−0.813337
$483$	4.39230	+	2.53590i	0.199857	+	0.115387i
$484$	−4.42820	−	7.66987i	−0.201282	−	0.348631i
$485$	−4.46410	−	7.73205i	−0.202704	−	0.351094i
$486$		0			0
$487$			14.0000i			0.634401i	0.948359	+	0.317200i	$0.102743\pi$
$487$			14.0000i			0.634401i	−0.948359	+	0.317200i	$0.897257\pi$
$488$	0.267949	+	0.464102i	0.0121295	+	0.0210089i
$489$		−	12.1244i		−	0.548282i
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−8.00000			−0.361035			−0.180517	−	0.983572i	$-0.557777\pi$
$491$	−8.00000			−0.361035			−0.180517	+	0.983572i	$0.557777\pi$
$492$	1.73205			0.0780869
$493$		0			0
$494$	−1.73205	+	1.00000i	−0.0779287	+	0.0449921i
$495$		0			0
$496$	−4.96410	−	2.86603i	−0.222895	−	0.128688i
$497$	−12.0000	+	20.7846i	−0.538274	+	0.932317i
$498$	23.1962	+	13.3923i	1.03944	+	0.600124i
$499$	−18.2487	+	10.5359i	−0.816925	+	0.471652i	−0.849355	−	0.527822i	$-0.823009\pi$
$499$	−18.2487	+	10.5359i	−0.816925	+	0.471652i	0.0324302	+	0.999474i	$0.489675\pi$
$500$	−0.866025	+	0.500000i	−0.0387298	+	0.0223607i
$501$	−17.1962	−	9.92820i	−0.768267	−	0.443559i
$502$	12.4641	−	21.5885i	0.556300	−	0.963540i
$503$	27.5885	+	15.9282i	1.23011	+	0.710203i	0.967052	−	0.254577i	$-0.0819363\pi$
$503$	27.5885	+	15.9282i	1.23011	+	0.710203i	0.263056	+	0.964781i	$0.415270\pi$
$504$		0			0
$505$	4.39230	−	2.53590i	0.195455	−	0.112846i
$506$	−1.07180	+	1.85641i	−0.0476472	+	0.0825273i
$507$	−20.7846			−0.923077
$508$	0.392305			0.0174057
$509$	−2.26795	+	3.92820i	−0.100525	+	0.174115i	−0.911901	−	0.410410i	$-0.865386\pi$
$509$	−2.26795	+	3.92820i	−0.100525	+	0.174115i	0.811376	+	0.584525i	$0.198719\pi$
$510$		0			0
$511$	−2.53590	−	4.39230i	−0.112182	−	0.194304i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.00000	+	5.19615i	−0.397360	+	0.229416i
$514$	−9.39230	−	16.2679i	−0.414277	−	0.717548i
$515$	3.46410	+	6.00000i	0.152647	+	0.264392i
$516$	8.89230	+	5.13397i	0.391462	+	0.226011i
$517$	1.35898			0.0597680
$518$	−1.00000	+	12.1244i	−0.0439375	+	0.532714i
$519$	−32.7846			−1.43908
$520$	−0.866025	−	0.500000i	−0.0379777	−	0.0219265i
$521$	20.8205	+	36.0622i	0.912163	+	1.57991i	0.811003	+	0.585043i	$0.198922\pi$
$521$	20.8205	+	36.0622i	0.912163	+	1.57991i	0.101160	+	0.994870i	$0.467744\pi$
$522$		0			0
$523$	−0.866025	+	0.500000i	−0.0378686	+	0.0218635i	−0.518815	−	0.854887i	$-0.673627\pi$
$523$	−0.866025	+	0.500000i	−0.0378686	+	0.0218635i	0.480946	+	0.876750i	$0.340293\pi$
$524$			15.4641i			0.675552i
$525$	1.73205	+	3.00000i	0.0755929	+	0.130931i
$526$			18.3923i			0.801943i
$527$		0			0
$528$	2.53590			0.110361
$529$	20.8564			0.906800
$530$	−2.59808	+	4.50000i	−0.112853	+	0.195468i
$531$		0			0
$532$		−	4.00000i		−	0.173422i
$533$	−0.866025	−	0.500000i	−0.0375117	−	0.0216574i
$534$	6.92820	−	12.0000i	0.299813	−	0.519291i
$535$	7.50000	+	4.33013i	0.324253	+	0.187208i
$536$	−3.92820	+	2.26795i	−0.169673	+	0.0979605i
$537$	2.78461	−	1.60770i	0.120165	−	0.0693772i
$538$	6.00000	+	3.46410i	0.258678	+	0.149348i
$539$	−2.19615	+	3.80385i	−0.0945950	+	0.163843i
$540$	−4.50000	−	2.59808i	−0.193649	−	0.111803i
$541$			2.39230i			0.102853i	0.998677	+	0.0514266i	$0.0163768\pi$
$541$			2.39230i			0.102853i	−0.998677	+	0.0514266i	$0.983623\pi$
$542$	−12.1865	+	7.03590i	−0.523456	+	0.302218i
$543$	−4.26795	+	7.39230i	−0.183155	+	0.317234i
$544$		0			0
$545$	7.46410			0.319727
$546$	−1.73205	+	3.00000i	−0.0741249	+	0.128388i
$547$			19.0000i			0.812381i	0.913788	+	0.406191i	$0.133143\pi$
$547$			19.0000i			0.812381i	−0.913788	+	0.406191i	$0.866857\pi$
$548$	−6.19615	−	10.7321i	−0.264687	−	0.458450i
$549$		0			0
$550$	−1.26795	+	0.732051i	−0.0540655	+	0.0312148i
$551$	7.46410	+	12.9282i	0.317981	+	0.550760i
$552$	1.26795	+	2.19615i	0.0539675	+	0.0934745i
$553$	−6.00000	−	3.46410i	−0.255146	−	0.147309i
$554$	29.9282			1.27153
$555$	−8.66025	−	6.00000i	−0.367607	−	0.254686i
$556$	−9.46410			−0.401367
$557$	−0.0621778	−	0.0358984i	−0.00263456	−	0.00152106i	0.498682	−	0.866785i	$-0.333818\pi$
$557$	−0.0621778	−	0.0358984i	−0.00263456	−	0.00152106i	−0.501317	+	0.865264i	$0.667151\pi$
$558$		0			0
$559$	−2.96410	−	5.13397i	−0.125368	−	0.217144i
$560$	1.73205	−	1.00000i	0.0731925	−	0.0422577i
$561$		0			0
$562$	−12.5981	−	21.8205i	−0.531418	−	0.920443i
$563$			17.0718i			0.719490i	0.933051	+	0.359745i	$0.117136\pi$
$563$			17.0718i			0.719490i	−0.933051	+	0.359745i	$0.882864\pi$
$564$	0.803848	−	1.39230i	0.0338481	−	0.0586266i
$565$	18.9282			0.796315
$566$	3.14359			0.132135
$567$	−9.00000	+	15.5885i	−0.377964	+	0.654654i
$568$	−10.3923	+	6.00000i	−0.436051	+	0.251754i
$569$			17.1962i			0.720900i	0.932778	+	0.360450i	$0.117377\pi$
$569$			17.1962i			0.720900i	−0.932778	+	0.360450i	$0.882623\pi$
$570$	3.00000	+	1.73205i	0.125656	+	0.0725476i
$571$	−3.66025	+	6.33975i	−0.153177	+	0.265310i	−0.932394	−	0.361444i	$-0.882284\pi$
$571$	−3.66025	+	6.33975i	−0.153177	+	0.265310i	0.779217	+	0.626754i	$0.215617\pi$
$572$	−1.26795	−	0.732051i	−0.0530156	−	0.0306086i
$573$	−6.99038	+	4.03590i	−0.292027	+	0.168602i
$574$	1.73205	−	1.00000i	0.0722944	−	0.0417392i
$575$	−1.26795	−	0.732051i	−0.0528771	−	0.0305286i
$576$		0			0
$577$	20.3205	+	11.7321i	0.845954	+	0.488412i	0.859284	−	0.511499i	$-0.170910\pi$
$577$	20.3205	+	11.7321i	0.845954	+	0.488412i	−0.0133298	+	0.999911i	$0.504243\pi$
$578$		−	17.0000i		−	0.707107i
$579$	1.60770	−	0.928203i	0.0668135	−	0.0385748i
$580$	−3.73205	+	6.46410i	−0.154965	+	0.268407i
$581$	30.9282			1.28312
$582$	−15.4641			−0.641008
$583$	−3.80385	+	6.58846i	−0.157539	+	0.272866i
$584$		−	2.53590i		−	0.104936i
$585$		0			0
$586$		−	0.124356i		−	0.00513708i
$587$	−30.0622	+	17.3564i	−1.24080	+	0.716376i	−0.969257	−	0.246051i	$-0.920867\pi$
$587$	−30.0622	+	17.3564i	−1.24080	+	0.716376i	−0.271542	+	0.962427i	$0.587534\pi$
$588$	2.59808	+	4.50000i	0.107143	+	0.185577i
$589$	−5.73205	−	9.92820i	−0.236185	−	0.409084i
$590$	3.46410	+	2.00000i	0.142615	+	0.0823387i
$591$	9.92820			0.408392
$592$	−3.46410	+	5.00000i	−0.142374	+	0.205499i
$593$	18.9282			0.777288			0.388644	−	0.921388i	$-0.372944\pi$
$593$	18.9282			0.777288			0.388644	+	0.921388i	$0.372944\pi$
$594$	−6.58846	−	3.80385i	−0.270328	−	0.156074i
$595$		0			0
$596$	−1.26795	−	2.19615i	−0.0519372	−	0.0899579i
$597$	−13.7942	+	7.96410i	−0.564560	+	0.325949i
$598$		−	1.46410i		−	0.0598716i
$599$	21.9641	+	38.0429i	0.897429	+	1.55439i	0.830770	+	0.556617i	$0.187901\pi$
$599$	21.9641	+	38.0429i	0.897429	+	1.55439i	0.0666594	+	0.997776i	$0.478766\pi$
$600$			1.73205i			0.0707107i
$601$	14.3564	−	24.8660i	0.585610	−	1.01431i	−0.409189	−	0.912450i	$-0.634188\pi$
$601$	14.3564	−	24.8660i	0.585610	−	1.01431i	0.994799	−	0.101857i	$-0.0324783\pi$
$602$	11.8564			0.483231
$603$		0			0
$604$	−7.42820	+	12.8660i	−0.302249	+	0.523511i
$605$	7.66987	−	4.42820i	0.311825	−	0.180032i
$606$		−	8.78461i		−	0.356850i
$607$	−9.58846	−	5.53590i	−0.389183	−	0.224695i	0.292623	−	0.956228i	$-0.405472\pi$
$607$	−9.58846	−	5.53590i	−0.389183	−	0.224695i	−0.681806	+	0.731533i	$0.738805\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	22.3923	+	12.9282i	0.907382	+	0.523877i
$610$	−0.464102	+	0.267949i	−0.0187909	+	0.0108489i
$611$	−0.803848	+	0.464102i	−0.0325202	+	0.0187755i
$612$		0			0
$613$	−13.8564	+	24.0000i	−0.559655	+	0.969351i	0.437870	+	0.899038i	$0.355733\pi$
$613$	−13.8564	+	24.0000i	−0.559655	+	0.969351i	−0.997525	+	0.0703126i	$0.977600\pi$
$614$	27.8205	+	16.0622i	1.12274	+	0.648217i
$615$			1.73205i			0.0698430i
$616$	2.53590	−	1.46410i	0.102174	−	0.0589903i
$617$	−9.92820	+	17.1962i	−0.399694	+	0.692291i	−0.993688	−	0.112179i	$-0.964217\pi$
$617$	−9.92820	+	17.1962i	−0.399694	+	0.692291i	0.593994	+	0.804470i	$0.297550\pi$
$618$	12.0000			0.482711
$619$	−20.1436			−0.809639			−0.404820	−	0.914397i	$-0.632666\pi$
$619$	−20.1436			−0.809639			−0.404820	+	0.914397i	$0.632666\pi$
$620$	2.86603	−	4.96410i	0.115102	−	0.199363i
$621$		−	7.60770i		−	0.305286i
$622$	−7.52628	−	13.0359i	−0.301776	−	0.522692i
$623$		−	16.0000i		−	0.641026i
$624$	−1.50000	+	0.866025i	−0.0600481	+	0.0346688i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	9.39230	+	16.2679i	0.375392	+	0.650198i
$627$	4.39230	+	2.53590i	0.175412	+	0.101274i
$628$	2.26795			0.0905010
$629$		0			0
$630$		0			0
$631$	29.2128	+	16.8660i	1.16294	+	0.671426i	0.952008	−	0.306074i	$-0.0990155\pi$
$631$	29.2128	+	16.8660i	1.16294	+	0.671426i	0.210936	+	0.977500i	$0.432349\pi$
$632$	−1.73205	−	3.00000i	−0.0688973	−	0.119334i
$633$	−7.73205	−	13.3923i	−0.307321	−	0.532296i
$634$	−1.50000	+	0.866025i	−0.0595726	+	0.0343943i
$635$			0.392305i			0.0155681i
$636$	4.50000	+	7.79423i	0.178437	+	0.309061i
$637$		−	3.00000i		−	0.118864i
$638$	−5.46410	+	9.46410i	−0.216326	+	0.374687i
$639$		0			0
$640$	1.00000			0.0395285
$641$	−13.9641	+	24.1865i	−0.551549	+	0.955311i	0.446614	+	0.894727i	$0.352630\pi$
$641$	−13.9641	+	24.1865i	−0.551549	+	0.955311i	−0.998163	+	0.0605840i	$0.980704\pi$
$642$	12.9904	−	7.50000i	0.512689	−	0.296001i
$643$		−	14.0718i		−	0.554937i	−0.960735	−	0.277469i	$-0.910505\pi$
$643$		−	14.0718i		−	0.554937i	0.960735	−	0.277469i	$-0.0894955\pi$
$644$	2.53590	+	1.46410i	0.0999284	+	0.0576937i
$645$	−5.13397	+	8.89230i	−0.202150	+	0.350134i
$646$		0			0
$647$	14.8756	−	8.58846i	0.584822	−	0.337647i	−0.178225	−	0.983990i	$-0.557036\pi$
$647$	14.8756	−	8.58846i	0.584822	−	0.337647i	0.763047	+	0.646343i	$0.223702\pi$
$648$	−7.79423	+	4.50000i	−0.306186	+	0.176777i
$649$	5.07180	+	2.92820i	0.199085	+	0.114942i
$650$	0.500000	−	0.866025i	0.0196116	−	0.0339683i
$651$	−17.1962	−	9.92820i	−0.673970	−	0.389117i
$652$		−	7.00000i		−	0.274141i
$653$	−4.33013	+	2.50000i	−0.169451	+	0.0978326i	−0.582327	−	0.812955i	$-0.697858\pi$
$653$	−4.33013	+	2.50000i	−0.169451	+	0.0978326i	0.412876	+	0.910787i	$0.364524\pi$
$654$	6.46410	−	11.1962i	0.252766	−	0.437804i
$655$	−15.4641			−0.604232
$656$	1.00000			0.0390434
$657$		0			0
$658$		−	1.85641i		−	0.0723703i
$659$	−22.9282	−	39.7128i	−0.893156	−	1.54699i	−0.836070	−	0.548622i	$-0.815153\pi$
$659$	−22.9282	−	39.7128i	−0.893156	−	1.54699i	−0.0570857	−	0.998369i	$-0.518181\pi$
$660$			2.53590i			0.0987097i
$661$	−30.4641	+	17.5885i	−1.18492	+	0.684112i	−0.957147	−	0.289603i	$-0.906477\pi$
$661$	−30.4641	+	17.5885i	−1.18492	+	0.684112i	−0.227769	+	0.973715i	$0.573143\pi$
$662$	−7.73205	−	13.3923i	−0.300515	−	0.520507i
$663$		0			0
$664$	13.3923	+	7.73205i	0.519722	+	0.300062i
$665$	4.00000			0.155113
$666$		0			0
$667$	−10.9282			−0.423142
$668$	−9.92820	−	5.73205i	−0.384134	−	0.221780i
$669$	13.2679	+	22.9808i	0.512969	+	0.888488i
$670$	−2.26795	−	3.92820i	−0.0876185	−	0.151760i
$671$	−0.679492	+	0.392305i	−0.0262315	+	0.0151448i
$672$		−	3.46410i		−	0.133631i
$673$	−9.19615	−	15.9282i	−0.354486	−	0.613987i	0.632544	−	0.774524i	$-0.282011\pi$
$673$	−9.19615	−	15.9282i	−0.354486	−	0.613987i	−0.987030	+	0.160537i	$0.948677\pi$
$674$		−	16.9282i		−	0.652050i
$675$	2.59808	−	4.50000i	0.100000	−	0.173205i
$676$	−12.0000			−0.461538
$677$	40.7846			1.56748			0.783740	−	0.621089i	$-0.213310\pi$
$677$	40.7846			1.56748			0.783740	+	0.621089i	$0.213310\pi$
$678$	16.3923	−	28.3923i	0.629543	−	1.09040i
$679$	−15.4641	+	8.92820i	−0.593458	+	0.342633i
$680$		0			0
$681$	−26.6769	−	15.4019i	−1.02226	−	0.590203i
$682$	4.19615	−	7.26795i	0.160679	−	0.278304i
$683$	43.7942	+	25.2846i	1.67574	+	0.967489i	0.964327	+	0.264714i	$0.0852776\pi$
$683$	43.7942	+	25.2846i	1.67574	+	0.967489i	0.711413	+	0.702775i	$0.248056\pi$
$684$		0			0
$685$	10.7321	−	6.19615i	0.410051	−	0.236743i
$686$	17.3205	+	10.0000i	0.661300	+	0.381802i
$687$	−14.6603	+	25.3923i	−0.559324	+	0.968777i
$688$	5.13397	+	2.96410i	0.195731	+	0.113005i
$689$		−	5.19615i		−	0.197958i
$690$	−2.19615	+	1.26795i	−0.0836061	+	0.0482700i
$691$	3.92820	−	6.80385i	0.149436	−	0.258831i	−0.781583	−	0.623801i	$-0.785588\pi$
$691$	3.92820	−	6.80385i	0.149436	−	0.258831i	0.931019	+	0.364970i	$0.118921\pi$
$692$	−18.9282			−0.719542
$693$		0			0
$694$	11.8564	−	20.5359i	0.450063	−	0.779532i
$695$		−	9.46410i		−	0.358994i
$696$	6.46410	+	11.1962i	0.245021	+	0.424389i
$697$		0			0
$698$	22.8564	−	13.1962i	0.865128	−	0.499482i
$699$	−4.26795	−	7.39230i	−0.161429	−	0.279603i
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	−6.80385	−	3.92820i	−0.256978	−	0.148366i	0.365977	−	0.930624i	$-0.380735\pi$
$701$	−6.80385	−	3.92820i	−0.256978	−	0.148366i	−0.622955	+	0.782258i	$0.714068\pi$
$702$	5.19615			0.196116
$703$	−11.0000	+	5.19615i	−0.414873	+	0.195977i
$704$	1.46410			0.0551804
$705$	1.39230	+	0.803848i	0.0524372	+	0.0302747i
$706$	10.6603	+	18.4641i	0.401204	+	0.694906i
$707$	−5.07180	−	8.78461i	−0.190745	−	0.330379i
$708$	6.00000	−	3.46410i	0.225494	−	0.130189i
$709$		−	15.3205i		−	0.575374i	−0.957725	−	0.287687i	$-0.907114\pi$
$709$		−	15.3205i		−	0.575374i	0.957725	−	0.287687i	$-0.0928862\pi$
$710$	−6.00000	−	10.3923i	−0.225176	−	0.390016i
$711$		0			0
$712$	4.00000	−	6.92820i	0.149906	−	0.259645i
$713$	8.39230			0.314294
$714$		0			0
$715$	0.732051	−	1.26795i	0.0273771	−	0.0474186i
$716$	1.60770	−	0.928203i	0.0600824	−	0.0346886i
$717$			9.21539i			0.344155i
$718$	−19.6699	−	11.3564i	−0.734073	−	0.423817i
$719$	−2.89230	+	5.00962i	−0.107865	+	0.186827i	−0.914905	−	0.403669i	$-0.867735\pi$
$719$	−2.89230	+	5.00962i	−0.107865	+	0.186827i	0.807040	+	0.590496i	$0.201068\pi$
$720$		0			0
$721$	12.0000	−	6.92820i	0.446903	−	0.258020i
$722$	−12.9904	+	7.50000i	−0.483452	+	0.279121i
$723$	−26.7846	−	15.4641i	−0.996130	−	0.575116i
$724$	−2.46410	+	4.26795i	−0.0915776	+	0.158617i
$725$	−6.46410	−	3.73205i	−0.240071	−	0.138605i
$726$		−	15.3397i		−	0.569311i
$727$	−0.679492	+	0.392305i	−0.0252010	+	0.0145498i	−0.512548	−	0.858659i	$-0.671298\pi$
$727$	−0.679492	+	0.392305i	−0.0252010	+	0.0145498i	0.487347	+	0.873209i	$0.337965\pi$
$728$	−1.00000	+	1.73205i	−0.0370625	+	0.0641941i
$729$	27.0000			1.00000
$730$	2.53590			0.0938578
$731$		0			0
$732$			0.928203i			0.0343074i
$733$	−18.9282	−	32.7846i	−0.699129	−	1.21093i	−0.968769	−	0.247966i	$-0.920238\pi$
$733$	−18.9282	−	32.7846i	−0.699129	−	1.21093i	0.269640	−	0.962961i	$-0.413095\pi$
$734$			9.60770i			0.354626i
$735$	−4.50000	+	2.59808i	−0.165985	+	0.0958315i
$736$	0.732051	+	1.26795i	0.0269838	+	0.0467372i
$737$	−3.32051	−	5.75129i	−0.122312	−	0.211851i
$738$		0			0
$739$	−48.0000			−1.76571			−0.882854	−	0.469647i	$-0.844381\pi$
$739$	−48.0000			−1.76571			−0.882854	+	0.469647i	$0.844381\pi$
$740$	−5.00000	−	3.46410i	−0.183804	−	0.127343i
$741$	−3.46410			−0.127257
$742$	9.00000	+	5.19615i	0.330400	+	0.190757i
$743$	−6.53590	−	11.3205i	−0.239779	−	0.415309i	0.720872	−	0.693068i	$-0.243742\pi$
$743$	−6.53590	−	11.3205i	−0.239779	−	0.415309i	−0.960651	+	0.277759i	$0.910408\pi$
$744$	−4.96410	−	8.59808i	−0.181993	−	0.315221i
$745$	2.19615	−	1.26795i	0.0804608	−	0.0464541i
$746$			0.411543i			0.0150676i
$747$		0			0
$748$		0			0
$749$	8.66025	−	15.0000i	0.316439	−	0.548088i
$750$	−1.73205			−0.0632456
$751$	−32.5692			−1.18847			−0.594234	−	0.804292i	$-0.702545\pi$
$751$	−32.5692			−1.18847			−0.594234	+	0.804292i	$0.702545\pi$
$752$	0.464102	−	0.803848i	0.0169240	−	0.0293133i
$753$	37.3923	−	21.5885i	1.36265	−	0.786727i
$754$		−	7.46410i		−	0.271827i
$755$	−12.8660	−	7.42820i	−0.468243	−	0.270340i
$756$	−5.19615	+	9.00000i	−0.188982	+	0.327327i
$757$	−37.9186	−	21.8923i	−1.37817	−	0.795689i	−0.386235	−	0.922401i	$-0.626225\pi$
$757$	−37.9186	−	21.8923i	−1.37817	−	0.795689i	−0.991940	+	0.126711i	$0.959558\pi$
$758$	16.7321	−	9.66025i	0.607735	−	0.350876i
$759$	−3.21539	+	1.85641i	−0.116711	+	0.0673833i
$760$	1.73205	+	1.00000i	0.0628281	+	0.0362738i
$761$	3.39230	−	5.87564i	0.122971	−	0.212992i	−0.797967	−	0.602701i	$-0.794091\pi$
$761$	3.39230	−	5.87564i	0.122971	−	0.212992i	0.920938	+	0.389709i	$0.127424\pi$
$762$	0.588457	+	0.339746i	0.0213176	+	0.0123077i
$763$		−	14.9282i		−	0.540437i
$764$	−4.03590	+	2.33013i	−0.146014	+	0.0843010i
$765$		0			0
$766$	27.4641			0.992318
$767$	−4.00000			−0.144432
$768$	0.866025	−	1.50000i	0.0312500	−	0.0541266i
$769$		−	7.71281i		−	0.278131i	−0.990283	−	0.139066i	$-0.955590\pi$
$769$		−	7.71281i		−	0.278131i	0.990283	−	0.139066i	$-0.0444099\pi$
$770$	1.46410	+	2.53590i	0.0527626	+	0.0913874i
$771$		−	32.5359i		−	1.17175i
$772$	0.928203	−	0.535898i	0.0334068	−	0.0192874i
$773$	−9.66987	−	16.7487i	−0.347801	−	0.602409i	0.638057	−	0.769989i	$-0.279738\pi$
$773$	−9.66987	−	16.7487i	−0.347801	−	0.602409i	−0.985859	+	0.167580i	$0.946405\pi$
$774$		0			0
$775$	4.96410	+	2.86603i	0.178316	+	0.102951i
$776$	−8.92820			−0.320504
$777$	−12.0000	+	17.3205i	−0.430498	+	0.621370i
$778$	−18.2487			−0.654248
$779$	1.73205	+	1.00000i	0.0620572	+	0.0358287i
$780$	−0.866025	−	1.50000i	−0.0310087	−	0.0537086i
$781$	−8.78461	−	15.2154i	−0.314338	−	0.544449i
$782$		0			0
$783$		−	38.7846i		−	1.38605i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$			2.26795i			0.0809466i
$786$	−13.3923	+	23.1962i	−0.477688	+	0.827379i
$787$	35.5885			1.26859			0.634296	−	0.773090i	$-0.281290\pi$
$787$	35.5885			1.26859			0.634296	+	0.773090i	$0.281290\pi$
$788$	5.73205			0.204196
$789$	−15.9282	+	27.5885i	−0.567059	+	0.982175i
$790$	3.00000	−	1.73205i	0.106735	−	0.0616236i
$791$		−	37.8564i		−	1.34602i
$792$		0			0
$793$	0.267949	−	0.464102i	0.00951515	−	0.0164807i
$794$	28.7487	+	16.5981i	1.02025	+	0.589044i
$795$	−7.79423	+	4.50000i	−0.276433	+	0.159599i
$796$	−7.96410	+	4.59808i	−0.282280	+	0.162974i
$797$	−36.9904	−	21.3564i	−1.31027	−	0.756483i	−0.328126	−	0.944634i	$-0.606417\pi$
$797$	−36.9904	−	21.3564i	−1.31027	−	0.756483i	−0.982140	+	0.188151i	$0.939751\pi$
$798$	3.46410	−	6.00000i	0.122628	−	0.212398i
$799$		0			0
$800$			1.00000i			0.0353553i
$801$		0			0
$802$	13.8564	−	24.0000i	0.489287	−	0.847469i
$803$	3.71281			0.131022
$804$	−7.85641			−0.277074
$805$	−1.46410	+	2.53590i	−0.0516028	+	0.0893787i
$806$			5.73205i			0.201903i
$807$	6.00000	+	10.3923i	0.211210	+	0.365826i
$808$		−	5.07180i		−	0.178425i
$809$	48.6051	−	28.0622i	1.70886	−	0.986614i	0.772895	−	0.634534i	$-0.218808\pi$
$809$	48.6051	−	28.0622i	1.70886	−	0.986614i	0.935970	−	0.352079i	$-0.114525\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	−19.1244	−	33.1244i	−0.671547	−	1.16315i	−0.977465	−	0.211096i	$-0.932297\pi$
$811$	−19.1244	−	33.1244i	−0.671547	−	1.16315i	0.305918	−	0.952058i	$-0.401037\pi$
$812$	12.9282	+	7.46410i	0.453691	+	0.261939i
$813$	−24.3731			−0.854801
$814$	−7.32051	−	5.07180i	−0.256584	−	0.177766i
$815$	7.00000			0.245199
$816$		0			0
$817$	5.92820	+	10.2679i	0.207402	+	0.359230i
$818$	−7.25833	−	12.5718i	−0.253782	−	0.439563i
$819$		0			0
$820$			1.00000i			0.0349215i
$821$	16.2679	+	28.1769i	0.567755	+	0.983381i	0.996787	+	0.0800919i	$0.0255214\pi$
$821$	16.2679	+	28.1769i	0.567755	+	0.983381i	−0.429032	+	0.903289i	$0.641145\pi$
$822$		−	21.4641i		−	0.748647i
$823$	−1.33975	+	2.32051i	−0.0467006	+	0.0808878i	−0.888431	−	0.459011i	$-0.848204\pi$
$823$	−1.33975	+	2.32051i	−0.0467006	+	0.0808878i	0.841730	+	0.539898i	$0.181537\pi$
$824$	6.92820			0.241355
$825$	−2.53590			−0.0882886
$826$	4.00000	−	6.92820i	0.139178	−	0.241063i
$827$	29.3205	−	16.9282i	1.01957	−	0.588651i	0.105593	−	0.994409i	$-0.466326\pi$
$827$	29.3205	−	16.9282i	1.01957	−	0.588651i	0.913981	+	0.405758i	$0.132992\pi$
$828$		0			0
$829$	4.85641	+	2.80385i	0.168670	+	0.0973817i	0.581959	−	0.813218i	$-0.302287\pi$
$829$	4.85641	+	2.80385i	0.168670	+	0.0973817i	−0.413289	+	0.910600i	$0.635620\pi$
$830$	−7.73205	+	13.3923i	−0.268383	+	0.464854i
$831$	44.8923	+	25.9186i	1.55730	+	0.899106i
$832$	−0.866025	+	0.500000i	−0.0300240	+	0.0173344i
$833$		0			0
$834$	−14.1962	−	8.19615i	−0.491573	−	0.283810i
$835$	5.73205	−	9.92820i	0.198366	−	0.343580i
$836$	2.53590	+	1.46410i	0.0877059	+	0.0506370i
$837$			29.7846i			1.02951i
$838$	−15.4641	+	8.92820i	−0.534199	+	0.308420i
$839$	−13.9641	+	24.1865i	−0.482094	+	0.835012i	−0.999789	−	0.0205537i	$-0.993457\pi$
$839$	−13.9641	+	24.1865i	−0.482094	+	0.835012i	0.517694	+	0.855566i	$0.326790\pi$
$840$	3.46410			0.119523
$841$	−26.7128			−0.921131
$842$	11.1962	−	19.3923i	0.385845	−	0.668303i
$843$		−	43.6410i		−	1.50308i
$844$	−4.46410	−	7.73205i	−0.153661	−	0.266148i
$845$		−	12.0000i		−	0.412813i
$846$		0			0
$847$	−8.85641	−	15.3397i	−0.304310	−	0.527080i
$848$	2.59808	+	4.50000i	0.0892183	+	0.154531i
$849$	4.71539	+	2.72243i	0.161832	+	0.0934336i
$850$		0			0
$851$	0.732051	−	8.87564i	0.0250944	−	0.304253i
$852$	−20.7846			−0.712069
$853$	−17.9378	−	10.3564i	−0.614179	−	0.354597i	0.160420	−	0.987049i	$-0.448715\pi$
$853$	−17.9378	−	10.3564i	−0.614179	−	0.354597i	−0.774599	+	0.632452i	$0.782048\pi$
$854$	0.535898	+	0.928203i	0.0183381	+	0.0317625i
$855$		0			0
$856$	7.50000	−	4.33013i	0.256345	−	0.148001i
$857$			45.5692i			1.55661i	0.627883	+	0.778307i	$0.283921\pi$
$857$			45.5692i			1.55661i	−0.627883	+	0.778307i	$0.716079\pi$
$858$	−1.26795	−	2.19615i	−0.0432871	−	0.0749754i
$859$			47.3205i			1.61455i	0.590172	+	0.807277i	$0.299060\pi$
$859$			47.3205i			1.61455i	−0.590172	+	0.807277i	$0.700940\pi$
$860$	−2.96410	+	5.13397i	−0.101075	+	0.175067i
$861$	3.46410			0.118056
$862$	35.5885			1.21215
$863$	−17.6603	+	30.5885i	−0.601162	+	1.04124i	0.391483	+	0.920185i	$0.371962\pi$
$863$	−17.6603	+	30.5885i	−0.601162	+	1.04124i	−0.992645	+	0.121058i	$0.961371\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		−	18.9282i		−	0.643578i
$866$	5.66025	+	3.26795i	0.192343	+	0.111049i
$867$	14.7224	−	25.5000i	0.500000	−	0.866025i
$868$	−9.92820	−	5.73205i	−0.336985	−	0.194558i
$869$	4.39230	−	2.53590i	0.148999	−	0.0860245i
$870$	−11.1962	+	6.46410i	−0.379585	+	0.219154i
$871$	3.92820	+	2.26795i	0.133102	+	0.0768465i
$872$	3.73205	−	6.46410i	0.126383	−	0.218902i
$873$		0			0
$874$			2.92820i			0.0990480i
$875$	−1.73205	+	1.00000i	−0.0585540	+	0.0338062i
$876$	2.19615	−	3.80385i	0.0742011	−	0.128520i
$877$	52.1244			1.76011			0.880057	−	0.474868i	$-0.157504\pi$
$877$	52.1244			1.76011			0.880057	+	0.474868i	$0.157504\pi$
$878$	−23.5885			−0.796072
$879$	0.107695	−	0.186533i	0.00363247	−	0.00629162i
$880$			1.46410i			0.0493549i
$881$	16.4641	+	28.5167i	0.554690	+	0.960751i	0.997928	+	0.0643467i	$0.0204964\pi$
$881$	16.4641	+	28.5167i	0.554690	+	0.960751i	−0.443238	+	0.896404i	$0.646170\pi$
$882$		0			0
$883$	−12.8660	+	7.42820i	−0.432976	+	0.249979i	−0.700614	−	0.713541i	$-0.747090\pi$
$883$	−12.8660	+	7.42820i	−0.432976	+	0.249979i	0.267638	+	0.963520i	$0.413757\pi$
$884$		0			0
$885$	3.46410	+	6.00000i	0.116445	+	0.201688i
$886$	−5.89230	−	3.40192i	−0.197956	−	0.114290i
$887$	19.0718			0.640368			0.320184	−	0.947355i	$-0.396255\pi$
$887$	19.0718			0.640368			0.320184	+	0.947355i	$0.396255\pi$
$888$	−9.52628	+	4.50000i	−0.319681	+	0.151010i
$889$	0.784610			0.0263150
$890$	6.92820	+	4.00000i	0.232234	+	0.134080i
$891$	−6.58846	−	11.4115i	−0.220722	−	0.382301i
$892$	7.66025	+	13.2679i	0.256484	+	0.444244i
$893$	1.60770	−	0.928203i	0.0537995	−	0.0310611i
$894$		−	4.39230i		−	0.146901i
$895$	0.928203	+	1.60770i	0.0310264	+	0.0537393i
$896$		−	2.00000i		−	0.0668153i
$897$	1.26795	−	2.19615i	0.0423356	−	0.0733274i
$898$	28.9090			0.964705
$899$	42.7846			1.42695
$900$		0			0
$901$		0			0
$902$			1.46410i			0.0487493i
$903$	17.7846	+	10.2679i	0.591835	+	0.341696i
$904$	9.46410	−	16.3923i	0.314771	−	0.545200i
$905$	−4.26795	−	2.46410i	−0.141871	−	0.0819095i
$906$	−22.2846	+	12.8660i	−0.740357	+	0.427445i
$907$	14.7846	−	8.53590i	0.490915	−	0.283430i	−0.234039	−	0.972227i	$-0.575194\pi$
$907$	14.7846	−	8.53590i	0.490915	−	0.283430i	0.724954	+	0.688797i	$0.241861\pi$
$908$	−15.4019	−	8.89230i	−0.511131	−	0.295102i
$909$		0			0
$910$	−1.73205	−	1.00000i	−0.0574169	−	0.0331497i
$911$		−	6.80385i		−	0.225422i	−0.993628	−	0.112711i	$-0.964047\pi$
$911$		−	6.80385i		−	0.225422i	0.993628	−	0.112711i	$-0.0359533\pi$
$912$	3.00000	−	1.73205i	0.0993399	−	0.0573539i
$913$	−11.3205	+	19.6077i	−0.374654	+	0.648920i
$914$	34.6410			1.14582
$915$	−0.928203			−0.0306855
$916$	−8.46410	+	14.6603i	−0.279662	+	0.484388i
$917$			30.9282i			1.02134i
$918$		0			0
$919$		−	28.5359i		−	0.941312i	−0.882317	−	0.470656i	$-0.844017\pi$
$919$		−	28.5359i		−	0.941312i	0.882317	−	0.470656i	$-0.155983\pi$
$920$	−1.26795	+	0.732051i	−0.0418030	+	0.0241350i
$921$	27.8205	+	48.1865i	0.916717	+	1.58780i
$922$	8.80385	+	15.2487i	0.289939	+	0.502190i
$923$	10.3923	+	6.00000i	0.342067	+	0.197492i
$924$	5.07180			0.166850
$925$	3.46410	−	5.00000i	0.113899	−	0.164399i
$926$	−32.3923			−1.06448
$927$		0			0
$928$	3.73205	+	6.46410i	0.122511	+	0.212195i
$929$	20.4282	+	35.3827i	0.670228	+	1.16087i	0.977839	+	0.209356i	$0.0671369\pi$
$929$	20.4282	+	35.3827i	0.670228	+	1.16087i	−0.307612	+	0.951512i	$0.599530\pi$
$930$	8.59808	−	4.96410i	0.281942	−	0.162779i
$931$			6.00000i			0.196642i
$932$	−2.46410	−	4.26795i	−0.0807143	−	0.139801i
$933$		−	26.0718i		−	0.853552i
$934$	−10.0359	+	17.3827i	−0.328385	+	0.568779i
$935$		0			0
$936$		0			0
$937$	−9.39230	+	16.2679i	−0.306833	+	0.531451i	−0.977668	−	0.210156i	$-0.932603\pi$
$937$	−9.39230	+	16.2679i	−0.306833	+	0.531451i	0.670835	+	0.741607i	$0.265936\pi$
$938$	−7.85641	+	4.53590i	−0.256521	+	0.148102i
$939$			32.5359i			1.06177i
$940$	0.803848	+	0.464102i	0.0262186	+	0.0151373i
$941$	−10.5885	+	18.3397i	−0.345174	+	0.597859i	−0.985385	−	0.170340i	$-0.945513\pi$
$941$	−10.5885	+	18.3397i	−0.345174	+	0.597859i	0.640211	+	0.768199i	$0.278847\pi$
$942$	3.40192	+	1.96410i	0.110841	+	0.0639939i
$943$	−1.26795	+	0.732051i	−0.0412901	+	0.0238389i
$944$	3.46410	−	2.00000i	0.112747	−	0.0650945i
$945$	−9.00000	−	5.19615i	−0.292770	−	0.169031i
$946$	−4.33975	+	7.51666i	−0.141097	+	0.244388i
$947$	12.3109	+	7.10770i	0.400050	+	0.230969i	0.686506	−	0.727124i	$-0.259144\pi$
$947$	12.3109	+	7.10770i	0.400050	+	0.230969i	−0.286455	+	0.958094i	$0.592477\pi$
$948$		−	6.00000i		−	0.194871i
$949$	−2.19615	+	1.26795i	−0.0712901	+	0.0411594i
$950$	−1.00000	+	1.73205i	−0.0324443	+	0.0561951i
$951$	−3.00000			−0.0972817
$952$		0			0
$953$	−17.6603	+	30.5885i	−0.572072	+	0.990857i	0.424281	+	0.905530i	$0.360527\pi$
$953$	−17.6603	+	30.5885i	−0.572072	+	0.990857i	−0.996353	+	0.0853269i	$0.972807\pi$
$954$		0			0
$955$	−2.33013	−	4.03590i	−0.0754011	−	0.130599i
$956$			5.32051i			0.172078i
$957$	−16.3923	+	9.46410i	−0.529888	+	0.305931i
$958$	−8.06218	−	13.9641i	−0.260477	−	0.451160i
$959$	−12.3923	−	21.4641i	−0.400168	−	0.693112i
$960$	1.50000	+	0.866025i	0.0484123	+	0.0279508i
$961$	−1.85641			−0.0598841
$962$	6.06218	+	0.500000i	0.195452	+	0.0161206i
$963$		0			0
$964$	−15.4641	−	8.92820i	−0.498065	−	0.287558i
$965$	0.535898	+	0.928203i	0.0172512	+	0.0298799i
$966$	2.53590	+	4.39230i	0.0815912	+	0.141320i
$967$	−51.3731	+	29.6603i	−1.65205	+	0.953809i	−0.675817	+	0.737069i	$0.736209\pi$
$967$	−51.3731	+	29.6603i	−1.65205	+	0.953809i	−0.976229	+	0.216740i	$0.930458\pi$
$968$		−	8.85641i		−	0.284656i
$969$		0			0
$970$		−	8.92820i		−	0.286667i
$971$	18.5359	−	32.1051i	0.594845	−	1.03030i	−0.398723	−	0.917071i	$-0.630547\pi$
$971$	18.5359	−	32.1051i	0.594845	−	1.03030i	0.993569	−	0.113231i	$-0.0361200\pi$
$972$		0			0
$973$	−18.9282			−0.606810
$974$	−7.00000	+	12.1244i	−0.224294	+	0.388489i
$975$	1.50000	−	0.866025i	0.0480384	−	0.0277350i
$976$			0.535898i			0.0171537i
$977$	19.6410	+	11.3397i	0.628372	+	0.362791i	0.780121	−	0.625628i	$-0.215157\pi$
$977$	19.6410	+	11.3397i	0.628372	+	0.362791i	−0.151749	+	0.988419i	$0.548491\pi$
$978$	6.06218	−	10.5000i	0.193847	−	0.335753i
$979$	10.1436	+	5.85641i	0.324191	+	0.187172i
$980$	−2.59808	+	1.50000i	−0.0829925	+	0.0479157i
$981$		0			0
$982$	−6.92820	−	4.00000i	−0.221088	−	0.127645i
$983$	8.80385	−	15.2487i	0.280799	−	0.486358i	−0.690783	−	0.723062i	$-0.742734\pi$
$983$	8.80385	−	15.2487i	0.280799	−	0.486358i	0.971582	+	0.236704i	$0.0760672\pi$
$984$	1.50000	+	0.866025i	0.0478183	+	0.0276079i
$985$			5.73205i			0.182638i
$986$		0			0
$987$	1.60770	−	2.78461i	0.0511735	−	0.0886351i
$988$	−2.00000			−0.0636285
$989$	−8.67949			−0.275992
$990$		0			0
$991$			35.0526i			1.11348i	0.830686	+	0.556741i	$0.187948\pi$
$991$			35.0526i			1.11348i	−0.830686	+	0.556741i	$0.812052\pi$
$992$	−2.86603	−	4.96410i	−0.0909964	−	0.157610i
$993$		−	26.7846i		−	0.849984i
$994$	−20.7846	+	12.0000i	−0.659248	+	0.380617i
$995$	−4.59808	−	7.96410i	−0.145769	−	0.252479i
$996$	13.3923	+	23.1962i	0.424351	+	0.734998i
$997$	48.9904	+	28.2846i	1.55154	+	0.895783i	0.998017	+	0.0629495i	$0.0200507\pi$
$997$	48.9904	+	28.2846i	1.55154	+	0.895783i	0.553524	+	0.832833i	$0.313283\pi$
$998$	−21.0718			−0.667016
$999$	31.5000	+	2.59808i	0.996616	+	0.0821995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.l.b.101.2	yes	4
37.11	even	6	inner	370.2.l.b.11.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.b.11.2	✓	4	37.11	even	6	inner
370.2.l.b.101.2	yes	4	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.866025 + 1.50000i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{5} +1.73205i q^{6} +(1.00000 + 1.73205i) q^{7} +1.00000i q^{8} -1.00000 q^{10} -1.46410 q^{11} +(-0.866025 + 1.50000i) q^{12} +(0.866025 - 0.500000i) q^{13} +2.00000i q^{14} +(-1.50000 - 0.866025i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.73205 + 1.00000i) q^{19} +(-0.866025 - 0.500000i) q^{20} +(-1.73205 + 3.00000i) q^{21} +(-1.26795 - 0.732051i) q^{22} -1.46410i q^{23} +(-1.50000 + 0.866025i) q^{24} +(0.500000 - 0.866025i) q^{25} +1.00000 q^{26} +5.19615 q^{27} +(-1.00000 + 1.73205i) q^{28} -7.46410i q^{29} +(-0.866025 - 1.50000i) q^{30} +5.73205i q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.26795 - 2.19615i) q^{33} +(-1.73205 - 1.00000i) q^{35} +(6.06218 + 0.500000i) q^{37} -2.00000 q^{38} +(1.50000 + 0.866025i) q^{39} +(-0.500000 - 0.866025i) q^{40} +(-0.500000 - 0.866025i) q^{41} +(-3.00000 + 1.73205i) q^{42} -5.92820i q^{43} +(-0.732051 - 1.26795i) q^{44} +(0.732051 - 1.26795i) q^{46} -0.928203 q^{47} -1.73205 q^{48} +(1.50000 - 2.59808i) q^{49} +(0.866025 - 0.500000i) q^{50} +(0.866025 + 0.500000i) q^{52} +(2.59808 - 4.50000i) q^{53} +(4.50000 + 2.59808i) q^{54} +(1.26795 - 0.732051i) q^{55} +(-1.73205 + 1.00000i) q^{56} +(-3.00000 - 1.73205i) q^{57} +(3.73205 - 6.46410i) q^{58} +(-3.46410 - 2.00000i) q^{59} -1.73205i q^{60} +(0.464102 - 0.267949i) q^{61} +(-2.86603 + 4.96410i) q^{62} -1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} -2.53590i q^{66} +(2.26795 + 3.92820i) q^{67} +(2.19615 - 1.26795i) q^{69} +(-1.00000 - 1.73205i) q^{70} +(6.00000 + 10.3923i) q^{71} -2.53590 q^{73} +(5.00000 + 3.46410i) q^{74} +1.73205 q^{75} +(-1.73205 - 1.00000i) q^{76} +(-1.46410 - 2.53590i) q^{77} +(0.866025 + 1.50000i) q^{78} +(-3.00000 + 1.73205i) q^{79} -1.00000i q^{80} +(4.50000 + 7.79423i) q^{81} -1.00000i q^{82} +(7.73205 - 13.3923i) q^{83} -3.46410 q^{84} +(2.96410 - 5.13397i) q^{86} +(11.1962 - 6.46410i) q^{87} -1.46410i q^{88} +(-6.92820 - 4.00000i) q^{89} +(1.73205 + 1.00000i) q^{91} +(1.26795 - 0.732051i) q^{92} +(-8.59808 + 4.96410i) q^{93} +(-0.803848 - 0.464102i) q^{94} +(1.00000 - 1.73205i) q^{95} +(-1.50000 - 0.866025i) q^{96} +8.92820i q^{97} +(2.59808 - 1.50000i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} + 4 q^{7}+O(q^{10}) \) 4 * q + 2 * q^4 + 4 * q^7	\( 4 q + 2 q^{4} + 4 q^{7} - 4 q^{10} + 8 q^{11} - 6 q^{15} - 2 q^{16} - 12 q^{22} - 6 q^{24} + 2 q^{25} + 4 q^{26} - 4 q^{28} - 12 q^{33} - 8 q^{38} + 6 q^{39} - 2 q^{40} - 2 q^{41} - 12 q^{42} + 4 q^{44} - 4 q^{46} + 24 q^{47} + 6 q^{49} + 18 q^{54} + 12 q^{55} - 12 q^{57} + 8 q^{58} - 12 q^{61} - 8 q^{62} - 4 q^{64} - 2 q^{65} + 16 q^{67} - 12 q^{69} - 4 q^{70} + 24 q^{71} - 24 q^{73} + 20 q^{74} + 8 q^{77} - 12 q^{79} + 18 q^{81} + 24 q^{83} - 2 q^{86} + 24 q^{87} + 12 q^{92} - 24 q^{93} - 24 q^{94} + 4 q^{95} - 6 q^{96}+O(q^{100}) \) 4 * q + 2 * q^4 + 4 * q^7 - 4 * q^10 + 8 * q^11 - 6 * q^15 - 2 * q^16 - 12 * q^22 - 6 * q^24 + 2 * q^25 + 4 * q^26 - 4 * q^28 - 12 * q^33 - 8 * q^38 + 6 * q^39 - 2 * q^40 - 2 * q^41 - 12 * q^42 + 4 * q^44 - 4 * q^46 + 24 * q^47 + 6 * q^49 + 18 * q^54 + 12 * q^55 - 12 * q^57 + 8 * q^58 - 12 * q^61 - 8 * q^62 - 4 * q^64 - 2 * q^65 + 16 * q^67 - 12 * q^69 - 4 * q^70 + 24 * q^71 - 24 * q^73 + 20 * q^74 + 8 * q^77 - 12 * q^79 + 18 * q^81 + 24 * q^83 - 2 * q^86 + 24 * q^87 + 12 * q^92 - 24 * q^93 - 24 * q^94 + 4 * q^95 - 6 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more