LMFDB - Embedded newform 370.2.l.b.11.1

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			11.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	370.11
Dual form			370.2.l.b.101.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.866025 + 1.50000i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} -1.73205i q^{6} +(1.00000 - 1.73205i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(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} +5.46410 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} +(-4.73205 + 2.73205i) q^{22} +5.46410i 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} -0.535898i q^{29} +(0.866025 - 1.50000i) q^{30} +2.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.73205 + 8.19615i) 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} +7.92820i q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.73205 - 4.73205i) q^{46} +12.9282 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} +(4.73205 + 2.73205i) q^{55} +(1.73205 + 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(0.267949 + 0.464102i) q^{58} +(3.46410 - 2.00000i) q^{59} +1.73205i q^{60} +(-6.46410 - 3.73205i) q^{61} +(-1.13397 - 1.96410i) q^{62} -1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} -9.46410i q^{66} +(5.73205 - 9.92820i) q^{67} +(-8.19615 - 4.73205i) q^{69} +(-1.00000 + 1.73205i) q^{70} +(6.00000 - 10.3923i) q^{71} -9.46410 q^{73} +(5.00000 - 3.46410i) q^{74} -1.73205 q^{75} +(1.73205 - 1.00000i) q^{76} +(5.46410 - 9.46410i) 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} +(4.26795 + 7.39230i) q^{83} +3.46410 q^{84} +(-3.96410 - 6.86603i) q^{86} +(0.803848 + 0.464102i) q^{87} +5.46410i q^{88} +(6.92820 - 4.00000i) q^{89} +(-1.73205 + 1.00000i) q^{91} +(4.73205 + 2.73205i) q^{92} +(-3.40192 - 1.96410i) q^{93} +(-11.1962 + 6.46410i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-1.50000 + 0.866025i) q^{96} -4.92820i 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 $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

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	0.500000	+	0.866025i	$0.333333\pi$
$3$	−0.866025	+	1.50000i	−0.500000	+	0.866025i	−1.00000			$\pi$
$4$	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	−0.612801	−	0.790237i	$-0.709957\pi$
$7$	1.00000	−	1.73205i	0.377964	−	0.654654i	0.990766	+	0.135583i	$0.0432908\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000			−0.316228
$11$	5.46410			1.64749			0.823744	−	0.566961i	$-0.191881\pi$
$11$	5.46410			1.64749			0.823744	+	0.566961i	$0.191881\pi$
$12$	0.866025	+	1.50000i	0.250000	+	0.433013i
$13$	−0.866025	−	0.500000i	−0.240192	−	0.138675i	0.375073	−	0.926995i	$-0.377618\pi$
$13$	−0.866025	−	0.500000i	−0.240192	−	0.138675i	−0.615265	+	0.788320i	$0.710951\pi$
$14$			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	$-0.666667\pi$
$17$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$18$		0			0
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	0.685344	−	0.728219i	$-0.259652\pi$
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	−0.287984	+	0.957635i	$0.592985\pi$
$20$	0.866025	−	0.500000i	0.193649	−	0.111803i
$21$	1.73205	+	3.00000i	0.377964	+	0.654654i
$22$	−4.73205	+	2.73205i	−1.00888	+	0.582475i
$23$			5.46410i			1.13934i	0.821872	+	0.569672i	$0.192930\pi$
$23$			5.46410i			1.13934i	−0.821872	+	0.569672i	$0.807070\pi$
$24$	−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
$29$		−	0.535898i		−	0.0995138i	−0.998761	−	0.0497569i	$-0.984155\pi$
$29$		−	0.535898i		−	0.0995138i	0.998761	−	0.0497569i	$-0.0158447\pi$
$30$	0.866025	−	1.50000i	0.158114	−	0.273861i
$31$			2.26795i			0.407336i	0.979040	+	0.203668i	$0.0652863\pi$
$31$			2.26795i			0.407336i	−0.979040	+	0.203668i	$0.934714\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.73205	+	8.19615i	−0.823744	+	1.42677i
$34$		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	−0.902424	−	0.430848i	$-0.858214\pi$
$41$	−0.500000	+	0.866025i	−0.0780869	+	0.135250i	0.824338	+	0.566099i	$0.191548\pi$
$42$	−3.00000	−	1.73205i	−0.462910	−	0.267261i
$43$			7.92820i			1.20904i	0.796590	+	0.604520i	$0.206635\pi$
$43$			7.92820i			1.20904i	−0.796590	+	0.604520i	$0.793365\pi$
$44$	2.73205	−	4.73205i	0.411872	−	0.713384i
$45$		0			0
$46$	−2.73205	−	4.73205i	−0.402819	−	0.697703i
$47$	12.9282			1.88577			0.942886	−	0.333115i	$-0.108100\pi$
$47$	12.9282			1.88577			0.942886	+	0.333115i	$0.108100\pi$
$48$	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	$-0.282824\pi$
$53$	−2.59808	−	4.50000i	−0.356873	−	0.618123i	−0.987437	+	0.158015i	$0.949491\pi$
$54$	4.50000	−	2.59808i	0.612372	−	0.353553i
$55$	4.73205	+	2.73205i	0.638070	+	0.368390i
$56$	1.73205	+	1.00000i	0.231455	+	0.133631i
$57$	−3.00000	+	1.73205i	−0.397360	+	0.229416i
$58$	0.267949	+	0.464102i	0.0351835	+	0.0609395i
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	−0.257260	−	0.966342i	$-0.582820\pi$
$59$	3.46410	−	2.00000i	0.450988	−	0.260378i	0.708247	+	0.705965i	$0.249486\pi$
$60$			1.73205i			0.223607i
$61$	−6.46410	−	3.73205i	−0.827643	−	0.477840i	0.0254017	−	0.999677i	$-0.491914\pi$
$61$	−6.46410	−	3.73205i	−0.827643	−	0.477840i	−0.853045	+	0.521837i	$0.825247\pi$
$62$	−1.13397	−	1.96410i	−0.144015	−	0.249441i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−0.500000	−	0.866025i	−0.0620174	−	0.107417i
$66$		−	9.46410i		−	1.16495i
$67$	5.73205	−	9.92820i	0.700281	−	1.21292i	−0.268086	−	0.963395i	$-0.586391\pi$
$67$	5.73205	−	9.92820i	0.700281	−	1.21292i	0.968368	−	0.249528i	$-0.0802755\pi$
$68$		0			0
$69$	−8.19615	−	4.73205i	−0.986701	−	0.569672i
$70$	−1.00000	+	1.73205i	−0.119523	+	0.207020i
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	−0.252010	−	0.967725i	$-0.581092\pi$
$71$	6.00000	−	10.3923i	0.712069	−	1.23334i	0.964079	−	0.265615i	$-0.0855750\pi$
$72$		0			0
$73$	−9.46410			−1.10769			−0.553845	−	0.832620i	$-0.686840\pi$
$73$	−9.46410			−1.10769			−0.553845	+	0.832620i	$0.686840\pi$
$74$	5.00000	−	3.46410i	0.581238	−	0.402694i
$75$	−1.73205			−0.200000
$76$	1.73205	−	1.00000i	0.198680	−	0.114708i
$77$	5.46410	−	9.46410i	0.622692	−	1.07853i
$78$	−0.866025	+	1.50000i	−0.0980581	+	0.169842i
$79$	−3.00000	−	1.73205i	−0.337526	−	0.194871i	0.321651	−	0.946858i	$-0.395762\pi$
$79$	−3.00000	−	1.73205i	−0.337526	−	0.194871i	−0.659178	+	0.751987i	$0.729095\pi$
$80$		−	1.00000i		−	0.111803i
$81$	4.50000	−	7.79423i	0.500000	−	0.866025i
$82$		−	1.00000i		−	0.110432i
$83$	4.26795	+	7.39230i	0.468468	+	0.811411i	0.999351	−	0.0360347i	$-0.0114727\pi$
$83$	4.26795	+	7.39230i	0.468468	+	0.811411i	−0.530882	+	0.847446i	$0.678139\pi$
$84$	3.46410			0.377964
$85$		0			0
$86$	−3.96410	−	6.86603i	−0.427460	−	0.740383i
$87$	0.803848	+	0.464102i	0.0861815	+	0.0497569i
$88$			5.46410i			0.582475i
$89$	6.92820	−	4.00000i	0.734388	−	0.423999i	−0.0856373	−	0.996326i	$-0.527293\pi$
$89$	6.92820	−	4.00000i	0.734388	−	0.423999i	0.820025	+	0.572327i	$0.193959\pi$
$90$		0			0
$91$	−1.73205	+	1.00000i	−0.181568	+	0.104828i
$92$	4.73205	+	2.73205i	0.493350	+	0.284836i
$93$	−3.40192	−	1.96410i	−0.352763	−	0.203668i
$94$	−11.1962	+	6.46410i	−1.15479	+	0.666721i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$	−1.50000	+	0.866025i	−0.153093	+	0.0883883i
$97$		−	4.92820i		−	0.500383i	−0.968196	−	0.250192i	$-0.919506\pi$
$97$		−	4.92820i		−	0.500383i	0.968196	−	0.250192i	$-0.0804936\pi$
$98$	−2.59808	−	1.50000i	−0.262445	−	0.151523i
$99$		0			0
$100$	1.00000			0.100000
$101$	−18.9282			−1.88343			−0.941713	−	0.336416i	$-0.890785\pi$
$101$	−18.9282			−1.88343			−0.941713	+	0.336416i	$0.890785\pi$
$102$		0			0
$103$			6.92820i			0.682656i	0.939944	+	0.341328i	$0.110877\pi$
$103$			6.92820i			0.682656i	−0.939944	+	0.341328i	$0.889123\pi$
$104$	0.500000	−	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	$-0.695851\pi$
$107$	4.33013	−	7.50000i	0.418609	−	0.725052i	0.995800	+	0.0915571i	$0.0291844\pi$
$108$	−2.59808	+	4.50000i	−0.250000	+	0.433013i
$109$	0.464102	−	0.267949i	0.0444529	−	0.0256649i	−0.477609	−	0.878573i	$-0.658496\pi$
$109$	0.464102	−	0.267949i	0.0444529	−	0.0256649i	0.522062	+	0.852908i	$0.325163\pi$
$110$	−5.46410			−0.520982
$111$	4.50000	−	9.52628i	0.427121	−	0.904194i
$112$	−2.00000			−0.188982
$113$	4.39230	−	2.53590i	0.413193	−	0.238557i	−0.278968	−	0.960301i	$-0.589992\pi$
$113$	4.39230	−	2.53590i	0.413193	−	0.238557i	0.692161	+	0.721743i	$0.256659\pi$
$114$	1.73205	−	3.00000i	0.162221	−	0.280976i
$115$	−2.73205	+	4.73205i	−0.254765	+	0.441266i
$116$	−0.464102	−	0.267949i	−0.0430908	−	0.0248785i
$117$		0			0
$118$	−2.00000	+	3.46410i	−0.184115	+	0.318896i
$119$		0			0
$120$	−0.866025	−	1.50000i	−0.0790569	−	0.136931i
$121$	18.8564			1.71422
$122$	7.46410			0.675768
$123$	−0.866025	−	1.50000i	−0.0780869	−	0.135250i
$124$	1.96410	+	1.13397i	0.176382	+	0.101834i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$	−10.1962	−	17.6603i	−0.904762	−	1.56709i	−0.821236	−	0.570589i	$-0.806715\pi$
$127$	−10.1962	−	17.6603i	−0.904762	−	1.56709i	−0.0835261	−	0.996506i	$-0.526618\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−11.8923	−	6.86603i	−1.04706	−	0.604520i
$130$	0.866025	+	0.500000i	0.0759555	+	0.0438529i
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	−0.786872	−	0.617117i	$-0.788301\pi$
$131$	−7.39230	+	4.26795i	−0.645869	+	0.372892i	0.141003	+	0.990009i	$0.454967\pi$
$132$	4.73205	+	8.19615i	0.411872	+	0.713384i
$133$	3.46410	−	2.00000i	0.300376	−	0.173422i
$134$			11.4641i			0.990348i
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$		0			0
$137$	8.39230			0.717003			0.358501	−	0.933529i	$-0.383288\pi$
$137$	8.39230			0.717003			0.358501	+	0.933529i	$0.383288\pi$
$138$	9.46410			0.805638
$139$	−1.26795	−	2.19615i	−0.107546	−	0.186275i	0.807230	−	0.590238i	$-0.200966\pi$
$139$	−1.26795	−	2.19615i	−0.107546	−	0.186275i	−0.914776	+	0.403962i	$0.867633\pi$
$140$		−	2.00000i		−	0.169031i
$141$	−11.1962	+	19.3923i	−0.942886	+	1.63313i
$142$			12.0000i			1.00702i
$143$	−4.73205	−	2.73205i	−0.395714	−	0.228466i
$144$		0			0
$145$	0.267949	−	0.464102i	0.0222520	−	0.0385415i
$146$	8.19615	−	4.73205i	0.678318	−	0.391627i
$147$	−5.19615			−0.428571
$148$	−2.59808	+	5.50000i	−0.213561	+	0.452097i
$149$	−9.46410			−0.775329			−0.387665	−	0.921800i	$-0.626718\pi$
$149$	−9.46410			−0.775329			−0.387665	+	0.921800i	$0.626718\pi$
$150$	1.50000	−	0.866025i	0.122474	−	0.0707107i
$151$	−6.42820	+	11.1340i	−0.523120	+	0.906070i	0.476518	+	0.879165i	$0.341899\pi$
$151$	−6.42820	+	11.1340i	−0.523120	+	0.906070i	−0.999638	+	0.0269054i	$0.991435\pi$
$152$	−1.00000	+	1.73205i	−0.0811107	+	0.140488i
$153$		0			0
$154$			10.9282i			0.880620i
$155$	−1.13397	+	1.96410i	−0.0910830	+	0.157760i
$156$		−	1.73205i		−	0.138675i
$157$	2.86603	+	4.96410i	0.228734	+	0.396178i	0.957433	−	0.288655i	$-0.0932082\pi$
$157$	2.86603	+	4.96410i	0.228734	+	0.396178i	−0.728699	+	0.684834i	$0.759875\pi$
$158$	3.46410			0.275589
$159$	9.00000			0.713746
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	9.46410	+	5.46410i	0.745876	+	0.430632i
$162$			9.00000i			0.707107i
$163$	6.06218	−	3.50000i	0.474826	−	0.274141i	−0.243432	−	0.969918i	$-0.578273\pi$
$163$	6.06218	−	3.50000i	0.474826	−	0.274141i	0.718258	+	0.695777i	$0.244940\pi$
$164$	0.500000	+	0.866025i	0.0390434	+	0.0676252i
$165$	−8.19615	+	4.73205i	−0.638070	+	0.368390i
$166$	−7.39230	−	4.26795i	−0.573754	−	0.331257i
$167$	3.92820	+	2.26795i	0.303973	+	0.175499i	0.644227	−	0.764835i	$-0.277179\pi$
$167$	3.92820	+	2.26795i	0.303973	+	0.175499i	−0.340253	+	0.940334i	$0.610513\pi$
$168$	−3.00000	+	1.73205i	−0.231455	+	0.133631i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$		0			0
$172$	6.86603	+	3.96410i	0.523530	+	0.302260i
$173$	−2.53590	−	4.39230i	−0.192801	−	0.333941i	0.753377	−	0.657589i	$-0.228424\pi$
$173$	−2.53590	−	4.39230i	−0.192801	−	0.333941i	−0.946177	+	0.323649i	$0.895090\pi$
$174$	−0.928203			−0.0703669
$175$	2.00000			0.151186
$176$	−2.73205	−	4.73205i	−0.205936	−	0.356692i
$177$			6.92820i			0.520756i
$178$	−4.00000	+	6.92820i	−0.299813	+	0.519291i
$179$			25.8564i			1.93260i	0.257421	+	0.966299i	$0.417127\pi$
$179$			25.8564i			1.93260i	−0.257421	+	0.966299i	$0.582873\pi$
$180$		0			0
$181$	−4.46410	+	7.73205i	−0.331814	+	0.574719i	−0.982868	−	0.184313i	$-0.940994\pi$
$181$	−4.46410	+	7.73205i	−0.331814	+	0.574719i	0.651054	+	0.759032i	$0.274327\pi$
$182$	1.00000	−	1.73205i	0.0741249	−	0.128388i
$183$	11.1962	−	6.46410i	0.827643	−	0.477840i
$184$	−5.46410			−0.402819
$185$	−5.50000	−	2.59808i	−0.404368	−	0.191014i
$186$	3.92820			0.288030
$187$		0			0
$188$	6.46410	−	11.1962i	0.471443	−	0.816563i
$189$	−5.19615	+	9.00000i	−0.377964	+	0.654654i
$190$	−1.73205	−	1.00000i	−0.125656	−	0.0725476i
$191$		−	12.6603i		−	0.916064i	−0.888936	−	0.458032i	$-0.848555\pi$
$191$		−	12.6603i		−	0.916064i	0.888936	−	0.458032i	$-0.151445\pi$
$192$	0.866025	−	1.50000i	0.0625000	−	0.108253i
$193$		−	14.9282i		−	1.07456i	−0.843405	−	0.537278i	$-0.819453\pi$
$193$		−	14.9282i		−	1.07456i	0.843405	−	0.537278i	$-0.180547\pi$
$194$	2.46410	+	4.26795i	0.176912	+	0.306421i
$195$	1.73205			0.124035
$196$	3.00000			0.214286
$197$	1.13397	+	1.96410i	0.0807923	+	0.139936i	0.903591	−	0.428397i	$-0.140922\pi$
$197$	1.13397	+	1.96410i	0.0807923	+	0.139936i	−0.822798	+	0.568334i	$0.807588\pi$
$198$		0			0
$199$		−	1.19615i		−	0.0847930i	−0.999101	−	0.0423965i	$-0.986501\pi$
$199$		−	1.19615i		−	0.0847930i	0.999101	−	0.0423965i	$-0.0134993\pi$
$200$	−0.866025	+	0.500000i	−0.0612372	+	0.0353553i
$201$	9.92820	+	17.1962i	0.700281	+	1.21292i
$202$	16.3923	−	9.46410i	1.15336	−	0.665892i
$203$	−0.928203	−	0.535898i	−0.0651471	−	0.0376127i
$204$		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
$209$	9.46410	+	5.46410i	0.654646	+	0.377960i
$210$	−1.73205	−	3.00000i	−0.119523	−	0.207020i
$211$	4.92820			0.339272			0.169636	−	0.985507i	$-0.445741\pi$
$211$	4.92820			0.339272			0.169636	+	0.985507i	$0.445741\pi$
$212$	−5.19615			−0.356873
$213$	10.3923	+	18.0000i	0.712069	+	1.23334i
$214$			8.66025i			0.592003i
$215$	−3.96410	+	6.86603i	−0.270349	+	0.468259i
$216$		−	5.19615i		−	0.353553i
$217$	3.92820	+	2.26795i	0.266664	+	0.153958i
$218$	−0.267949	+	0.464102i	−0.0181478	+	0.0314329i
$219$	8.19615	−	14.1962i	0.553845	−	0.959287i
$220$	4.73205	−	2.73205i	0.319035	−	0.184195i
$221$		0			0
$222$	0.866025	+	10.5000i	0.0581238	+	0.704714i
$223$	−19.3205			−1.29380			−0.646898	−	0.762576i	$-0.723934\pi$
$223$	−19.3205			−1.29380			−0.646898	+	0.762576i	$0.723934\pi$
$224$	1.73205	−	1.00000i	0.115728	−	0.0668153i
$225$		0			0
$226$	−2.53590	+	4.39230i	−0.168685	+	0.292172i
$227$	−20.5981	−	11.8923i	−1.36714	−	0.789320i	−0.376580	−	0.926384i	$-0.622900\pi$
$227$	−20.5981	−	11.8923i	−1.36714	−	0.789320i	−0.990562	+	0.137064i	$0.956233\pi$
$228$			3.46410i			0.229416i
$229$	1.53590	−	2.66025i	0.101495	−	0.175795i	−0.810806	−	0.585315i	$-0.800971\pi$
$229$	1.53590	−	2.66025i	0.101495	−	0.175795i	0.912301	+	0.409521i	$0.134304\pi$
$230$		−	5.46410i		−	0.360292i
$231$	9.46410	+	16.3923i	0.622692	+	1.07853i
$232$	0.535898			0.0351835
$233$	8.92820			0.584906			0.292453	−	0.956280i	$-0.405528\pi$
$233$	8.92820			0.584906			0.292453	+	0.956280i	$0.405528\pi$
$234$		0			0
$235$	11.1962	+	6.46410i	0.730356	+	0.421671i
$236$		−	4.00000i		−	0.260378i
$237$	5.19615	−	3.00000i	0.337526	−	0.194871i
$238$		0			0
$239$	25.3923	−	14.6603i	1.64249	−	0.948293i	0.662548	−	0.749020i	$-0.269475\pi$
$239$	25.3923	−	14.6603i	1.64249	−	0.948293i	0.979944	−	0.199273i	$-0.0638581\pi$
$240$	1.50000	+	0.866025i	0.0968246	+	0.0559017i
$241$	−8.53590	−	4.92820i	−0.549846	−	0.317453i	0.199214	−	0.979956i	$-0.436161\pi$
$241$	−8.53590	−	4.92820i	−0.549846	−	0.317453i	−0.749060	+	0.662503i	$0.769494\pi$
$242$	−16.3301	+	9.42820i	−1.04974	+	0.606068i
$243$		0			0
$244$	−6.46410	+	3.73205i	−0.413822	+	0.238920i
$245$			3.00000i			0.191663i
$246$	1.50000	+	0.866025i	0.0956365	+	0.0552158i
$247$	−1.00000	−	1.73205i	−0.0636285	−	0.110208i
$248$	−2.26795			−0.144015
$249$	−14.7846			−0.936937
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$		−	11.0718i		−	0.698846i	−0.936965	−	0.349423i	$-0.886378\pi$
$251$		−	11.0718i		−	0.698846i	0.936965	−	0.349423i	$-0.113622\pi$
$252$		0			0
$253$			29.8564i			1.87706i
$254$	17.6603	+	10.1962i	1.10810	+	0.639764i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−19.7321	+	11.3923i	−1.23085	+	0.710632i	−0.967207	−	0.253988i	$-0.918258\pi$
$257$	−19.7321	+	11.3923i	−1.23085	+	0.710632i	−0.263644	+	0.964620i	$0.584924\pi$
$258$	13.7321			0.854920
$259$	−5.19615	+	11.0000i	−0.322873	+	0.683507i
$260$	−1.00000			−0.0620174
$261$		0			0
$262$	4.26795	−	7.39230i	0.263675	−	0.456698i
$263$	−1.19615	+	2.07180i	−0.0737579	+	0.127752i	−0.900545	−	0.434762i	$-0.856833\pi$
$263$	−1.19615	+	2.07180i	−0.0737579	+	0.127752i	0.826788	+	0.562514i	$0.190166\pi$
$264$	−8.19615	−	4.73205i	−0.504438	−	0.291238i
$265$		−	5.19615i		−	0.319197i
$266$	−2.00000	+	3.46410i	−0.122628	+	0.212398i
$267$			13.8564i			0.847998i
$268$	−5.73205	−	9.92820i	−0.350141	−	0.606462i
$269$	−6.92820			−0.422420			−0.211210	−	0.977441i	$-0.567740\pi$
$269$	−6.92820			−0.422420			−0.211210	+	0.977441i	$0.567740\pi$
$270$	5.19615			0.316228
$271$	−13.9641	−	24.1865i	−0.848259	−	1.46923i	−0.882761	−	0.469823i	$-0.844318\pi$
$271$	−13.9641	−	24.1865i	−0.848259	−	1.46923i	0.0345021	−	0.999405i	$-0.489015\pi$
$272$		0			0
$273$		−	3.46410i		−	0.209657i
$274$	−7.26795	+	4.19615i	−0.439073	+	0.253499i
$275$	2.73205	+	4.73205i	0.164749	+	0.285353i
$276$	−8.19615	+	4.73205i	−0.493350	+	0.284836i
$277$	−13.9186	−	8.03590i	−0.836287	−	0.482830i	0.0197136	−	0.999806i	$-0.493725\pi$
$277$	−13.9186	−	8.03590i	−0.836287	−	0.482830i	−0.856000	+	0.516975i	$0.827058\pi$
$278$	2.19615	+	1.26795i	0.131716	+	0.0760465i
$279$		0			0
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	12.8205	−	7.40192i	0.764807	−	0.441562i	−0.0662117	−	0.997806i	$-0.521091\pi$
$281$	12.8205	−	7.40192i	0.764807	−	0.441562i	0.831019	+	0.556244i	$0.187758\pi$
$282$		−	22.3923i		−	1.33344i
$283$	−26.7224	−	15.4282i	−1.58848	−	0.917111i	−0.993557	−	0.113331i	$-0.963848\pi$
$283$	−26.7224	−	15.4282i	−1.58848	−	0.917111i	−0.594926	−	0.803780i	$-0.702819\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$	−3.46410			−0.205196
$286$	5.46410			0.323099
$287$	1.00000	+	1.73205i	0.0590281	+	0.102240i
$288$		0			0
$289$	−8.50000	+	14.7224i	−0.500000	+	0.866025i
$290$			0.535898i			0.0314690i
$291$	7.39230	+	4.26795i	0.433345	+	0.250192i
$292$	−4.73205	+	8.19615i	−0.276922	+	0.479644i
$293$	12.0622	−	20.8923i	0.704680	−	1.22054i	−0.262127	−	0.965033i	$-0.584424\pi$
$293$	12.0622	−	20.8923i	0.704680	−	1.22054i	0.966807	−	0.255508i	$-0.0822427\pi$
$294$	4.50000	−	2.59808i	0.262445	−	0.151523i
$295$	4.00000			0.232889
$296$	−0.500000	−	6.06218i	−0.0290619	−	0.352357i
$297$	−28.3923			−1.64749
$298$	8.19615	−	4.73205i	0.474790	−	0.274120i
$299$	2.73205	−	4.73205i	0.157999	−	0.273662i
$300$	−0.866025	+	1.50000i	−0.0500000	+	0.0866025i
$301$	13.7321	+	7.92820i	0.791502	+	0.456974i
$302$		−	12.8564i		−	0.739803i
$303$	16.3923	−	28.3923i	0.941713	−	1.63110i
$304$		−	2.00000i		−	0.114708i
$305$	−3.73205	−	6.46410i	−0.213697	−	0.370133i
$306$		0			0
$307$	7.87564			0.449487			0.224743	−	0.974418i	$-0.427846\pi$
$307$	7.87564			0.449487			0.224743	+	0.974418i	$0.427846\pi$
$308$	−5.46410	−	9.46410i	−0.311346	−	0.539267i
$309$	−10.3923	−	6.00000i	−0.591198	−	0.341328i
$310$		−	2.26795i		−	0.128811i
$311$	−19.9641	+	11.5263i	−1.13206	+	0.653595i	−0.944452	−	0.328649i	$-0.893407\pi$
$311$	−19.9641	+	11.5263i	−1.13206	+	0.653595i	−0.187608	+	0.982244i	$0.560073\pi$
$312$	0.866025	+	1.50000i	0.0490290	+	0.0849208i
$313$	19.7321	−	11.3923i	1.11532	−	0.643931i	0.175119	−	0.984547i	$-0.443969\pi$
$313$	19.7321	−	11.3923i	1.11532	−	0.643931i	0.940202	+	0.340616i	$0.110636\pi$
$314$	−4.96410	−	2.86603i	−0.280140	−	0.161739i
$315$		0			0
$316$	−3.00000	+	1.73205i	−0.168763	+	0.0974355i
$317$	0.866025	+	1.50000i	0.0486408	+	0.0842484i	0.889321	−	0.457284i	$-0.151178\pi$
$317$	0.866025	+	1.50000i	0.0486408	+	0.0842484i	−0.840680	+	0.541532i	$0.817844\pi$
$318$	−7.79423	+	4.50000i	−0.437079	+	0.252347i
$319$		−	2.92820i		−	0.163948i
$320$	−0.866025	−	0.500000i	−0.0484123	−	0.0279508i
$321$	7.50000	+	12.9904i	0.418609	+	0.725052i
$322$	−10.9282			−0.609005
$323$		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
$327$			0.928203i			0.0513298i
$328$	−0.866025	−	0.500000i	−0.0478183	−	0.0276079i
$329$	12.9282	−	22.3923i	0.712755	−	1.23453i
$330$	4.73205	−	8.19615i	0.260491	−	0.451183i
$331$	7.39230	−	4.26795i	0.406318	−	0.234588i	−0.282889	−	0.959153i	$-0.591293\pi$
$331$	7.39230	−	4.26795i	0.406318	−	0.234588i	0.689206	+	0.724565i	$0.257959\pi$
$332$	8.53590			0.468468
$333$		0			0
$334$	−4.53590			−0.248193
$335$	9.92820	−	5.73205i	0.542436	−	0.313175i
$336$	1.73205	−	3.00000i	0.0944911	−	0.163663i
$337$	−1.53590	+	2.66025i	−0.0836657	+	0.144913i	−0.904822	−	0.425790i	$-0.859996\pi$
$337$	−1.53590	+	2.66025i	−0.0836657	+	0.144913i	0.821156	+	0.570704i	$0.193329\pi$
$338$	10.3923	+	6.00000i	0.565267	+	0.326357i
$339$			8.78461i			0.477115i
$340$		0			0
$341$			12.3923i			0.671081i
$342$		0			0
$343$	20.0000			1.07990
$344$	−7.92820			−0.427460
$345$	−4.73205	−	8.19615i	−0.254765	−	0.441266i
$346$	4.39230	+	2.53590i	0.236132	+	0.136331i
$347$			31.7128i			1.70243i	0.524815	+	0.851216i	$0.324135\pi$
$347$			31.7128i			1.70243i	−0.524815	+	0.851216i	$0.675865\pi$
$348$	0.803848	−	0.464102i	0.0430908	−	0.0248785i
$349$	2.80385	+	4.85641i	0.150087	+	0.259957i	0.931259	−	0.364358i	$-0.118711\pi$
$349$	2.80385	+	4.85641i	0.150087	+	0.259957i	−0.781173	+	0.624315i	$0.785378\pi$
$350$	−1.73205	+	1.00000i	−0.0925820	+	0.0534522i
$351$	4.50000	+	2.59808i	0.240192	+	0.138675i
$352$	4.73205	+	2.73205i	0.252219	+	0.145619i
$353$	11.5359	−	6.66025i	0.613994	−	0.354490i	−0.160533	−	0.987030i	$-0.551321\pi$
$353$	11.5359	−	6.66025i	0.613994	−	0.354490i	0.774527	+	0.632541i	$0.217988\pi$
$354$	−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
$358$	−12.9282	−	22.3923i	−0.683277	−	1.18347i
$359$	32.7128			1.72652			0.863258	−	0.504763i	$-0.168420\pi$
$359$	32.7128			1.72652			0.863258	+	0.504763i	$0.168420\pi$
$360$		0			0
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$		−	8.92820i		−	0.469256i
$363$	−16.3301	+	28.2846i	−0.857109	+	1.48456i
$364$			2.00000i			0.104828i
$365$	−8.19615	−	4.73205i	−0.429006	−	0.247687i
$366$	−6.46410	+	11.1962i	−0.337884	+	0.585232i
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	−0.130723	−	0.991419i	$-0.541730\pi$
$367$	15.1962	−	26.3205i	0.793233	−	1.37392i	0.923955	−	0.382500i	$-0.124937\pi$
$368$	4.73205	−	2.73205i	0.246675	−	0.142418i
$369$		0			0
$370$	6.06218	−	0.500000i	0.315158	−	0.0259938i
$371$	−10.3923			−0.539542
$372$	−3.40192	+	1.96410i	−0.176382	+	0.101834i
$373$	15.7942	−	27.3564i	0.817794	−	1.41646i	−0.0895099	−	0.995986i	$-0.528530\pi$
$373$	15.7942	−	27.3564i	0.817794	−	1.41646i	0.907304	−	0.420475i	$-0.138137\pi$
$374$		0			0
$375$	−1.50000	−	0.866025i	−0.0774597	−	0.0447214i
$376$			12.9282i			0.666721i
$377$	−0.267949	+	0.464102i	−0.0138001	+	0.0239024i
$378$		−	10.3923i		−	0.534522i
$379$	−7.66025	−	13.2679i	−0.393481	−	0.681529i	0.599425	−	0.800431i	$-0.295396\pi$
$379$	−7.66025	−	13.2679i	−0.393481	−	0.681529i	−0.992906	+	0.118902i	$0.962063\pi$
$380$	2.00000			0.102598
$381$	35.3205			1.80952
$382$	6.33013	+	10.9641i	0.323877	+	0.560972i
$383$	−17.7846	−	10.2679i	−0.908751	−	0.524668i	−0.0287220	−	0.999587i	$-0.509144\pi$
$383$	−17.7846	−	10.2679i	−0.908751	−	0.524668i	−0.880029	+	0.474920i	$0.842477\pi$
$384$			1.73205i			0.0883883i
$385$	9.46410	−	5.46410i	0.482335	−	0.278476i
$386$	7.46410	+	12.9282i	0.379913	+	0.658028i
$387$		0			0
$388$	−4.26795	−	2.46410i	−0.216672	−	0.125096i
$389$	−26.1962	−	15.1244i	−1.32820	−	0.766835i	−0.343177	−	0.939271i	$-0.611503\pi$
$389$	−26.1962	−	15.1244i	−1.32820	−	0.766835i	−0.985021	+	0.172436i	$0.944836\pi$
$390$	−1.50000	+	0.866025i	−0.0759555	+	0.0438529i
$391$		0			0
$392$	−2.59808	+	1.50000i	−0.131223	+	0.0757614i
$393$		−	14.7846i		−	0.745785i
$394$	−1.96410	−	1.13397i	−0.0989500	−	0.0571288i
$395$	−1.73205	−	3.00000i	−0.0871489	−	0.150946i
$396$		0			0
$397$	22.8038			1.14449			0.572246	−	0.820082i	$-0.306072\pi$
$397$	22.8038			1.14449			0.572246	+	0.820082i	$0.306072\pi$
$398$	0.598076	+	1.03590i	0.0299789	+	0.0519249i
$399$			6.92820i			0.346844i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$			27.7128i			1.38391i	0.721940	+	0.691956i	$0.243251\pi$
$401$			27.7128i			1.38391i	−0.721940	+	0.691956i	$0.756749\pi$
$402$	−17.1962	−	9.92820i	−0.857666	−	0.495174i
$403$	1.13397	−	1.96410i	0.0564873	−	0.0978389i
$404$	−9.46410	+	16.3923i	−0.470857	+	0.815548i
$405$	7.79423	−	4.50000i	0.387298	−	0.223607i
$406$	1.07180			0.0531924
$407$	−33.1244	+	2.73205i	−1.64191	+	0.135423i
$408$		0			0
$409$	−26.4282	+	15.2583i	−1.30679	+	0.754476i	−0.981559	−	0.191159i	$-0.938776\pi$
$409$	−26.4282	+	15.2583i	−1.30679	+	0.754476i	−0.325231	+	0.945634i	$0.605442\pi$
$410$	0.500000	−	0.866025i	0.0246932	−	0.0427699i
$411$	−7.26795	+	12.5885i	−0.358501	+	0.620943i
$412$	6.00000	+	3.46410i	0.295599	+	0.170664i
$413$		−	8.00000i		−	0.393654i
$414$		0			0
$415$			8.53590i			0.419011i
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$	4.39230			0.215092
$418$	−10.9282			−0.534516
$419$	4.92820	+	8.53590i	0.240758	+	0.417006i	0.960931	−	0.276790i	$-0.0892705\pi$
$419$	4.92820	+	8.53590i	0.240758	+	0.417006i	−0.720172	+	0.693795i	$0.755937\pi$
$420$	3.00000	+	1.73205i	0.146385	+	0.0845154i
$421$		−	1.60770i		−	0.0783543i	−0.999232	−	0.0391771i	$-0.987526\pi$
$421$		−	1.60770i		−	0.0783543i	0.999232	−	0.0391771i	$-0.0124737\pi$
$422$	−4.26795	+	2.46410i	−0.207761	+	0.119951i
$423$		0			0
$424$	4.50000	−	2.59808i	0.218539	−	0.126174i
$425$		0			0
$426$	−18.0000	−	10.3923i	−0.872103	−	0.503509i
$427$	−12.9282	+	7.46410i	−0.625640	+	0.361213i
$428$	−4.33013	−	7.50000i	−0.209305	−	0.362526i
$429$	8.19615	−	4.73205i	0.395714	−	0.228466i
$430$		−	7.92820i		−	0.382332i
$431$	−3.82051	−	2.20577i	−0.184027	−	0.106248i	0.405156	−	0.914248i	$-0.367217\pi$
$431$	−3.82051	−	2.20577i	−0.184027	−	0.106248i	−0.589184	+	0.807999i	$0.700550\pi$
$432$	2.59808	+	4.50000i	0.125000	+	0.216506i
$433$	13.4641			0.647043			0.323522	−	0.946221i	$-0.395133\pi$
$433$	13.4641			0.647043			0.323522	+	0.946221i	$0.395133\pi$
$434$	−4.53590			−0.217730
$435$	0.464102	+	0.803848i	0.0222520	+	0.0385415i
$436$		−	0.535898i		−	0.0256649i
$437$	−5.46410	+	9.46410i	−0.261383	+	0.452729i
$438$			16.3923i			0.783255i
$439$	−6.57180	−	3.79423i	−0.313655	−	0.181089i	0.334906	−	0.942252i	$-0.391295\pi$
$439$	−6.57180	−	3.79423i	−0.313655	−	0.181089i	−0.648561	+	0.761163i	$0.724629\pi$
$440$	−2.73205	+	4.73205i	−0.130245	+	0.225592i
$441$		0			0
$442$		0			0
$443$	−17.1962			−0.817014			−0.408507	−	0.912755i	$-0.633950\pi$
$443$	−17.1962			−0.817014			−0.408507	+	0.912755i	$0.633950\pi$
$444$	−6.00000	−	8.66025i	−0.284747	−	0.410997i
$445$	8.00000			0.379236
$446$	16.7321	−	9.66025i	0.792286	−	0.457426i
$447$	8.19615	−	14.1962i	0.387665	−	0.671455i
$448$	−1.00000	+	1.73205i	−0.0472456	+	0.0818317i
$449$	31.9641	+	18.4545i	1.50848	+	0.870921i	0.999951	+	0.00987542i	$0.00314350\pi$
$449$	31.9641	+	18.4545i	1.50848	+	0.870921i	0.508528	+	0.861045i	$0.330190\pi$
$450$		0			0
$451$	−2.73205	+	4.73205i	−0.128647	+	0.222824i
$452$		−	5.07180i		−	0.238557i
$453$	−11.1340	−	19.2846i	−0.523120	−	0.906070i
$454$	23.7846			1.11627
$455$	−2.00000			−0.0937614
$456$	−1.73205	−	3.00000i	−0.0811107	−	0.140488i
$457$	30.0000	+	17.3205i	1.40334	+	0.810219i	0.994734	−	0.102491i	$-0.0326814\pi$
$457$	30.0000	+	17.3205i	1.40334	+	0.810219i	0.408607	+	0.912710i	$0.366015\pi$
$458$			3.07180i			0.143536i
$459$		0			0
$460$	2.73205	+	4.73205i	0.127383	+	0.220633i
$461$	−33.2487	+	19.1962i	−1.54855	+	0.894054i	−0.550294	+	0.834971i	$0.685484\pi$
$461$	−33.2487	+	19.1962i	−1.54855	+	0.894054i	−0.998253	+	0.0590828i	$0.981182\pi$
$462$	−16.3923	−	9.46410i	−0.762639	−	0.440310i
$463$	10.0526	+	5.80385i	0.467182	+	0.269728i	0.715059	−	0.699064i	$-0.246400\pi$
$463$	10.0526	+	5.80385i	0.467182	+	0.269728i	−0.247877	+	0.968791i	$0.579733\pi$
$464$	−0.464102	+	0.267949i	−0.0215454	+	0.0124392i
$465$	−1.96410	−	3.40192i	−0.0910830	−	0.157760i
$466$	−7.73205	+	4.46410i	−0.358180	+	0.206796i
$467$			33.9282i			1.57001i	0.619489	+	0.785005i	$0.287340\pi$
$467$			33.9282i			1.57001i	−0.619489	+	0.785005i	$0.712660\pi$
$468$		0			0
$469$	−11.4641	−	19.8564i	−0.529363	−	0.916884i
$470$	−12.9282			−0.596334
$471$	−9.92820			−0.457467
$472$	2.00000	+	3.46410i	0.0920575	+	0.159448i
$473$			43.3205i			1.99188i
$474$	−3.00000	+	5.19615i	−0.137795	+	0.238667i
$475$			2.00000i			0.0917663i
$476$		0			0
$477$		0			0
$478$	−14.6603	+	25.3923i	−0.670544	+	1.16142i
$479$	−7.03590	+	4.06218i	−0.321478	+	0.185606i	−0.652051	−	0.758175i	$-0.726091\pi$
$479$	−7.03590	+	4.06218i	−0.321478	+	0.185606i	0.330573	+	0.943780i	$0.392758\pi$
$480$	−1.73205			−0.0790569
$481$	5.50000	+	2.59808i	0.250778	+	0.118462i
$482$	9.85641			0.448947
$483$	−16.3923	+	9.46410i	−0.745876	+	0.430632i
$484$	9.42820	−	16.3301i	0.428555	−	0.742279i
$485$	2.46410	−	4.26795i	0.111889	−	0.193798i
$486$		0			0
$487$			14.0000i			0.634401i	0.948359	+	0.317200i	$0.102743\pi$
$487$			14.0000i			0.634401i	−0.948359	+	0.317200i	$0.897257\pi$
$488$	3.73205	−	6.46410i	0.168942	−	0.292616i
$489$			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
$496$	1.96410	−	1.13397i	0.0881908	−	0.0509170i
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$	12.8038	−	7.39230i	0.573754	−	0.331257i
$499$	30.2487	+	17.4641i	1.35412	+	0.781801i	0.988823	−	0.149091i	$-0.0476348\pi$
$499$	30.2487	+	17.4641i	1.35412	+	0.781801i	0.365295	+	0.930892i	$0.380968\pi$
$500$	0.866025	+	0.500000i	0.0387298	+	0.0223607i
$501$	−6.80385	+	3.92820i	−0.303973	+	0.175499i
$502$	5.53590	+	9.58846i	0.247079	+	0.427954i
$503$	−3.58846	+	2.07180i	−0.160001	+	0.0923769i	−0.577863	−	0.816134i	$-0.696113\pi$
$503$	−3.58846	+	2.07180i	−0.160001	+	0.0923769i	0.417861	+	0.908511i	$0.362780\pi$
$504$		0			0
$505$	−16.3923	−	9.46410i	−0.729448	−	0.421147i
$506$	−14.9282	−	25.8564i	−0.663640	−	1.14946i
$507$	20.7846			0.923077
$508$	−20.3923			−0.904762
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	0.710573	−	0.703623i	$-0.248436\pi$
$509$	−5.73205	−	9.92820i	−0.254069	−	0.440060i	−0.964642	+	0.263563i	$0.915102\pi$
$510$		0			0
$511$	−9.46410	+	16.3923i	−0.418667	+	0.725153i
$512$		−	1.00000i		−	0.0441942i
$513$	−9.00000	−	5.19615i	−0.397360	−	0.229416i
$514$	11.3923	−	19.7321i	0.502493	−	0.870343i
$515$	−3.46410	+	6.00000i	−0.152647	+	0.264392i
$516$	−11.8923	+	6.86603i	−0.523530	+	0.302260i
$517$	70.6410			3.10679
$518$	−1.00000	−	12.1244i	−0.0439375	−	0.532714i
$519$	8.78461			0.385602
$520$	0.866025	−	0.500000i	0.0379777	−	0.0219265i
$521$	−13.8205	+	23.9378i	−0.605487	+	1.04874i	0.386487	+	0.922295i	$0.373688\pi$
$521$	−13.8205	+	23.9378i	−0.605487	+	1.04874i	−0.991974	+	0.126440i	$0.959645\pi$
$522$		0			0
$523$	0.866025	+	0.500000i	0.0378686	+	0.0218635i	0.518815	−	0.854887i	$-0.326373\pi$
$523$	0.866025	+	0.500000i	0.0378686	+	0.0218635i	−0.480946	+	0.876750i	$0.659707\pi$
$524$			8.53590i			0.372892i
$525$	−1.73205	+	3.00000i	−0.0755929	+	0.130931i
$526$		−	2.39230i		−	0.104309i
$527$		0			0
$528$	9.46410			0.411872
$529$	−6.85641			−0.298105
$530$	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
$536$	9.92820	+	5.73205i	0.428833	+	0.247587i
$537$	−38.7846	−	22.3923i	−1.67368	−	0.966299i
$538$	6.00000	−	3.46410i	0.258678	−	0.149348i
$539$	8.19615	+	14.1962i	0.353033	+	0.611472i
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$		−	18.3923i		−	0.790747i	−0.918520	−	0.395373i	$-0.870615\pi$
$541$		−	18.3923i		−	0.790747i	0.918520	−	0.395373i	$-0.129385\pi$
$542$	24.1865	+	13.9641i	1.03890	+	0.599810i
$543$	−7.73205	−	13.3923i	−0.331814	−	0.574719i
$544$		0			0
$545$	0.535898			0.0229554
$546$	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	$0.866857\pi$
$548$	4.19615	−	7.26795i	0.179251	−	0.310471i
$549$		0			0
$550$	−4.73205	−	2.73205i	−0.201775	−	0.116495i
$551$	0.535898	−	0.928203i	0.0228300	−	0.0395428i
$552$	4.73205	−	8.19615i	0.201409	−	0.348851i
$553$	−6.00000	+	3.46410i	−0.255146	+	0.147309i
$554$	16.0718			0.682825
$555$	8.66025	−	6.00000i	0.367607	−	0.254686i
$556$	−2.53590			−0.107546
$557$	12.0622	−	6.96410i	0.511091	−	0.295078i	−0.222191	−	0.975003i	$-0.571321\pi$
$557$	12.0622	−	6.96410i	0.511091	−	0.295078i	0.733282	+	0.679925i	$0.237988\pi$
$558$		0			0
$559$	3.96410	−	6.86603i	0.167664	−	0.290402i
$560$	−1.73205	−	1.00000i	−0.0731925	−	0.0422577i
$561$		0			0
$562$	−7.40192	+	12.8205i	−0.312231	+	0.540800i
$563$			30.9282i			1.30347i	0.758447	+	0.651734i	$0.225958\pi$
$563$			30.9282i			1.30347i	−0.758447	+	0.651734i	$0.774042\pi$
$564$	11.1962	+	19.3923i	0.471443	+	0.816563i
$565$	5.07180			0.213372
$566$	30.8564			1.29699
$567$	−9.00000	−	15.5885i	−0.377964	−	0.654654i
$568$	10.3923	+	6.00000i	0.436051	+	0.251754i
$569$			6.80385i			0.285232i	0.989778	+	0.142616i	$0.0455514\pi$
$569$			6.80385i			0.285232i	−0.989778	+	0.142616i	$0.954449\pi$
$570$	3.00000	−	1.73205i	0.125656	−	0.0725476i
$571$	13.6603	+	23.6603i	0.571664	+	0.990151i	0.996395	+	0.0848314i	$0.0270352\pi$
$571$	13.6603	+	23.6603i	0.571664	+	0.990151i	−0.424731	+	0.905319i	$0.639631\pi$
$572$	−4.73205	+	2.73205i	−0.197857	+	0.114233i
$573$	18.9904	+	10.9641i	0.793335	+	0.458032i
$574$	−1.73205	−	1.00000i	−0.0722944	−	0.0417392i
$575$	−4.73205	+	2.73205i	−0.197340	+	0.113934i
$576$		0			0
$577$	−14.3205	+	8.26795i	−0.596171	+	0.344199i	−0.767534	−	0.641009i	$-0.778516\pi$
$577$	−14.3205	+	8.26795i	−0.596171	+	0.344199i	0.171363	+	0.985208i	$0.445183\pi$
$578$		−	17.0000i		−	0.707107i
$579$	22.3923	+	12.9282i	0.930592	+	0.537278i
$580$	−0.267949	−	0.464102i	−0.0111260	−	0.0192708i
$581$	17.0718			0.708257
$582$	−8.53590			−0.353824
$583$	−14.1962	−	24.5885i	−0.587945	−	1.01835i
$584$		−	9.46410i		−	0.391627i
$585$		0			0
$586$			24.1244i			0.996568i
$587$	−17.9378	−	10.3564i	−0.740373	−	0.427455i	0.0818318	−	0.996646i	$-0.473923\pi$
$587$	−17.9378	−	10.3564i	−0.740373	−	0.427455i	−0.822205	+	0.569192i	$0.807256\pi$
$588$	−2.59808	+	4.50000i	−0.107143	+	0.185577i
$589$	−2.26795	+	3.92820i	−0.0934492	+	0.161859i
$590$	−3.46410	+	2.00000i	−0.142615	+	0.0823387i
$591$	−3.92820			−0.161585
$592$	3.46410	+	5.00000i	0.142374	+	0.205499i
$593$	5.07180			0.208274			0.104137	−	0.994563i	$-0.466792\pi$
$593$	5.07180			0.208274			0.104137	+	0.994563i	$0.466792\pi$
$594$	24.5885	−	14.1962i	1.00888	−	0.582475i
$595$		0			0
$596$	−4.73205	+	8.19615i	−0.193832	+	0.335727i
$597$	1.79423	+	1.03590i	0.0734329	+	0.0423965i
$598$			5.46410i			0.223444i
$599$	15.0359	−	26.0429i	0.614350	−	1.06409i	−0.376148	−	0.926560i	$-0.622752\pi$
$599$	15.0359	−	26.0429i	0.614350	−	1.06409i	0.990498	−	0.137526i	$-0.0439151\pi$
$600$		−	1.73205i		−	0.0707107i
$601$	−13.3564	−	23.1340i	−0.544819	−	0.943655i	−0.998618	−	0.0525505i	$-0.983265\pi$
$601$	−13.3564	−	23.1340i	−0.544819	−	0.943655i	0.453799	−	0.891104i	$-0.350068\pi$
$602$	−15.8564			−0.646259
$603$		0			0
$604$	6.42820	+	11.1340i	0.261560	+	0.453035i
$605$	16.3301	+	9.42820i	0.663914	+	0.383311i
$606$			32.7846i			1.33178i
$607$	21.5885	−	12.4641i	0.876248	−	0.505902i	0.00682883	−	0.999977i	$-0.497826\pi$
$607$	21.5885	−	12.4641i	0.876248	−	0.505902i	0.869420	+	0.494074i	$0.164493\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$	1.60770	−	0.928203i	0.0651471	−	0.0376127i
$610$	6.46410	+	3.73205i	0.261724	+	0.151106i
$611$	−11.1962	−	6.46410i	−0.452948	−	0.261510i
$612$		0			0
$613$	13.8564	+	24.0000i	0.559655	+	0.969351i	0.997525	+	0.0703126i	$0.0223997\pi$
$613$	13.8564	+	24.0000i	0.559655	+	0.969351i	−0.437870	+	0.899038i	$0.644267\pi$
$614$	−6.82051	+	3.93782i	−0.275253	+	0.158918i
$615$		−	1.73205i		−	0.0698430i
$616$	9.46410	+	5.46410i	0.381320	+	0.220155i
$617$	3.92820	+	6.80385i	0.158144	+	0.273913i	0.934199	−	0.356752i	$-0.116116\pi$
$617$	3.92820	+	6.80385i	0.158144	+	0.273913i	−0.776056	+	0.630664i	$0.782782\pi$
$618$	12.0000			0.482711
$619$	−47.8564			−1.92351			−0.961756	−	0.273909i	$-0.911683\pi$
$619$	−47.8564			−1.92351			−0.961756	+	0.273909i	$0.911683\pi$
$620$	1.13397	+	1.96410i	0.0455415	+	0.0788802i
$621$		−	28.3923i		−	1.13934i
$622$	11.5263	−	19.9641i	0.462162	−	0.800488i
$623$		−	16.0000i		−	0.641026i
$624$	−1.50000	−	0.866025i	−0.0600481	−	0.0346688i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−11.3923	+	19.7321i	−0.455328	+	0.788651i
$627$	−16.3923	+	9.46410i	−0.654646	+	0.377960i
$628$	5.73205			0.228734
$629$		0			0
$630$		0			0
$631$	−26.2128	+	15.1340i	−1.04352	+	0.602474i	−0.920827	−	0.389971i	$-0.872485\pi$
$631$	−26.2128	+	15.1340i	−1.04352	+	0.602474i	−0.122689	+	0.992445i	$0.539152\pi$
$632$	1.73205	−	3.00000i	0.0688973	−	0.119334i
$633$	−4.26795	+	7.39230i	−0.169636	+	0.293818i
$634$	−1.50000	−	0.866025i	−0.0595726	−	0.0343943i
$635$		−	20.3923i		−	0.809244i
$636$	4.50000	−	7.79423i	0.178437	−	0.309061i
$637$		−	3.00000i		−	0.118864i
$638$	1.46410	+	2.53590i	0.0579643	+	0.100397i
$639$		0			0
$640$	1.00000			0.0395285
$641$	−7.03590	−	12.1865i	−0.277901	−	0.481339i	0.692962	−	0.720974i	$-0.256305\pi$
$641$	−7.03590	−	12.1865i	−0.277901	−	0.481339i	−0.970863	+	0.239635i	$0.922972\pi$
$642$	−12.9904	−	7.50000i	−0.512689	−	0.296001i
$643$		−	27.9282i		−	1.10138i	−0.834710	−	0.550690i	$-0.814364\pi$
$643$		−	27.9282i		−	1.10138i	0.834710	−	0.550690i	$-0.185636\pi$
$644$	9.46410	−	5.46410i	0.372938	−	0.215316i
$645$	−6.86603	−	11.8923i	−0.270349	−	0.468259i
$646$		0			0
$647$	39.1244	+	22.5885i	1.53814	+	0.888044i	0.998948	+	0.0458592i	$0.0146026\pi$
$647$	39.1244	+	22.5885i	1.53814	+	0.888044i	0.539189	+	0.842185i	$0.318731\pi$
$648$	7.79423	+	4.50000i	0.306186	+	0.176777i
$649$	18.9282	−	10.9282i	0.742997	−	0.428969i
$650$	0.500000	+	0.866025i	0.0196116	+	0.0339683i
$651$	−6.80385	+	3.92820i	−0.266664	+	0.153958i
$652$		−	7.00000i		−	0.274141i
$653$	4.33013	+	2.50000i	0.169451	+	0.0978326i	0.582327	−	0.812955i	$-0.302142\pi$
$653$	4.33013	+	2.50000i	0.169451	+	0.0978326i	−0.412876	+	0.910787i	$0.635476\pi$
$654$	−0.464102	−	0.803848i	−0.0181478	−	0.0314329i
$655$	−8.53590			−0.333525
$656$	1.00000			0.0390434
$657$		0			0
$658$			25.8564i			1.00799i
$659$	−9.07180	+	15.7128i	−0.353387	+	0.612084i	−0.986841	−	0.161696i	$-0.948303\pi$
$659$	−9.07180	+	15.7128i	−0.353387	+	0.612084i	0.633454	+	0.773781i	$0.281637\pi$
$660$			9.46410i			0.368390i
$661$	−23.5359	−	13.5885i	−0.915440	−	0.528530i	−0.0332628	−	0.999447i	$-0.510590\pi$
$661$	−23.5359	−	13.5885i	−0.915440	−	0.528530i	−0.882178	+	0.470917i	$0.843923\pi$
$662$	−4.26795	+	7.39230i	−0.165879	+	0.287310i
$663$		0			0
$664$	−7.39230	+	4.26795i	−0.286877	+	0.165629i
$665$	4.00000			0.155113
$666$		0			0
$667$	2.92820			0.113380
$668$	3.92820	−	2.26795i	0.151987	−	0.0877496i
$669$	16.7321	−	28.9808i	0.646898	−	1.12046i
$670$	−5.73205	+	9.92820i	−0.221448	+	0.383560i
$671$	−35.3205	−	20.3923i	−1.36353	−	0.787236i
$672$			3.46410i			0.133631i
$673$	1.19615	−	2.07180i	0.0461083	−	0.0798619i	−0.842050	−	0.539399i	$-0.818651\pi$
$673$	1.19615	−	2.07180i	0.0461083	−	0.0798619i	0.888158	+	0.459537i	$0.151985\pi$
$674$		−	3.07180i		−	0.118321i
$675$	−2.59808	−	4.50000i	−0.100000	−	0.173205i
$676$	−12.0000			−0.461538
$677$	−0.784610			−0.0301550			−0.0150775	−	0.999886i	$-0.504799\pi$
$677$	−0.784610			−0.0301550			−0.0150775	+	0.999886i	$0.504799\pi$
$678$	−4.39230	−	7.60770i	−0.168685	−	0.292172i
$679$	−8.53590	−	4.92820i	−0.327578	−	0.189127i
$680$		0			0
$681$	35.6769	−	20.5981i	1.36714	−	0.789320i
$682$	−6.19615	−	10.7321i	−0.237263	−	0.410951i
$683$	28.2058	−	16.2846i	1.07926	−	0.623113i	0.148566	−	0.988902i	$-0.452534\pi$
$683$	28.2058	−	16.2846i	1.07926	−	0.623113i	0.930698	+	0.365789i	$0.119201\pi$
$684$		0			0
$685$	7.26795	+	4.19615i	0.277694	+	0.160327i
$686$	−17.3205	+	10.0000i	−0.661300	+	0.381802i
$687$	2.66025	+	4.60770i	0.101495	+	0.175795i
$688$	6.86603	−	3.96410i	0.261765	−	0.151130i
$689$			5.19615i			0.197958i
$690$	8.19615	+	4.73205i	0.312022	+	0.180146i
$691$	−9.92820	−	17.1962i	−0.377687	−	0.654172i	0.613039	−	0.790053i	$-0.289947\pi$
$691$	−9.92820	−	17.1962i	−0.377687	−	0.654172i	−0.990725	+	0.135881i	$0.956614\pi$
$692$	−5.07180			−0.192801
$693$		0			0
$694$	−15.8564	−	27.4641i	−0.601901	−	1.04252i
$695$		−	2.53590i		−	0.0961921i
$696$	−0.464102	+	0.803848i	−0.0175917	+	0.0304698i
$697$		0			0
$698$	−4.85641	−	2.80385i	−0.183818	−	0.106127i
$699$	−7.73205	+	13.3923i	−0.292453	+	0.506543i
$700$	1.00000	−	1.73205i	0.0377964	−	0.0654654i
$701$	−17.1962	+	9.92820i	−0.649490	+	0.374983i	−0.788261	−	0.615341i	$-0.789018\pi$
$701$	−17.1962	+	9.92820i	−0.649490	+	0.374983i	0.138771	+	0.990325i	$0.455685\pi$
$702$	−5.19615			−0.196116
$703$	−11.0000	−	5.19615i	−0.414873	−	0.195977i
$704$	−5.46410			−0.205936
$705$	−19.3923	+	11.1962i	−0.730356	+	0.421671i
$706$	−6.66025	+	11.5359i	−0.250662	+	0.434159i
$707$	−18.9282	+	32.7846i	−0.711868	+	1.23299i
$708$	6.00000	+	3.46410i	0.225494	+	0.130189i
$709$			19.3205i			0.725597i	0.931868	+	0.362798i	$0.118179\pi$
$709$			19.3205i			0.725597i	−0.931868	+	0.362798i	$0.881821\pi$
$710$	−6.00000	+	10.3923i	−0.225176	+	0.390016i
$711$		0			0
$712$	4.00000	+	6.92820i	0.149906	+	0.259645i
$713$	−12.3923			−0.464095
$714$		0			0
$715$	−2.73205	−	4.73205i	−0.102173	−	0.176969i
$716$	22.3923	+	12.9282i	0.836840	+	0.483150i
$717$			50.7846i			1.89659i
$718$	−28.3301	+	16.3564i	−1.05727	+	0.610416i
$719$	17.8923	+	30.9904i	0.667270	+	1.15575i	0.978664	+	0.205465i	$0.0658708\pi$
$719$	17.8923	+	30.9904i	0.667270	+	1.15575i	−0.311394	+	0.950281i	$0.600796\pi$
$720$		0			0
$721$	12.0000	+	6.92820i	0.446903	+	0.258020i
$722$	12.9904	+	7.50000i	0.483452	+	0.279121i
$723$	14.7846	−	8.53590i	0.549846	−	0.317453i
$724$	4.46410	+	7.73205i	0.165907	+	0.287359i
$725$	0.464102	−	0.267949i	0.0172363	−	0.00995138i
$726$		−	32.6603i		−	1.21214i
$727$	−35.3205	−	20.3923i	−1.30997	−	0.756309i	−0.327875	−	0.944721i	$-0.606333\pi$
$727$	−35.3205	−	20.3923i	−1.30997	−	0.756309i	−0.982090	+	0.188412i	$0.939666\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	27.0000			1.00000
$730$	9.46410			0.350282
$731$		0			0
$732$		−	12.9282i		−	0.477840i
$733$	−5.07180	+	8.78461i	−0.187331	+	0.324467i	−0.944360	−	0.328915i	$-0.893317\pi$
$733$	−5.07180	+	8.78461i	−0.187331	+	0.324467i	0.757028	+	0.653382i	$0.226650\pi$
$734$			30.3923i			1.12180i
$735$	−4.50000	−	2.59808i	−0.165985	−	0.0958315i
$736$	−2.73205	+	4.73205i	−0.100705	+	0.174426i
$737$	31.3205	−	54.2487i	1.15371	−	1.99828i
$738$		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
$743$	−13.4641	+	23.3205i	−0.493950	+	0.855546i	−0.999976	−	0.00697193i	$-0.997781\pi$
$743$	−13.4641	+	23.3205i	−0.493950	+	0.855546i	0.506026	+	0.862518i	$0.331114\pi$
$744$	1.96410	−	3.40192i	0.0720075	−	0.124721i
$745$	−8.19615	−	4.73205i	−0.300284	−	0.173369i
$746$			31.5885i			1.15654i
$747$		0			0
$748$		0			0
$749$	−8.66025	−	15.0000i	−0.316439	−	0.548088i
$750$	1.73205			0.0632456
$751$	50.5692			1.84530			0.922649	−	0.385642i	$-0.126020\pi$
$751$	50.5692			1.84530			0.922649	+	0.385642i	$0.126020\pi$
$752$	−6.46410	−	11.1962i	−0.235722	−	0.408282i
$753$	16.6077	+	9.58846i	0.605218	+	0.349423i
$754$		−	0.535898i		−	0.0195163i
$755$	−11.1340	+	6.42820i	−0.405207	+	0.233946i
$756$	5.19615	+	9.00000i	0.188982	+	0.327327i
$757$	1.91858	−	1.10770i	0.0697321	−	0.0402599i	−0.464729	−	0.885453i	$-0.653848\pi$
$757$	1.91858	−	1.10770i	0.0697321	−	0.0402599i	0.534461	+	0.845193i	$0.320515\pi$
$758$	13.2679	+	7.66025i	0.481914	+	0.278233i
$759$	−44.7846	−	25.8564i	−1.62558	−	0.938528i
$760$	−1.73205	+	1.00000i	−0.0628281	+	0.0362738i
$761$	−17.3923	−	30.1244i	−0.630471	−	1.09201i	−0.987456	−	0.157897i	$-0.949529\pi$
$761$	−17.3923	−	30.1244i	−0.630471	−	1.09201i	0.356985	−	0.934110i	$-0.383805\pi$
$762$	−30.5885	+	17.6603i	−1.10810	+	0.639764i
$763$		−	1.07180i		−	0.0388016i
$764$	−10.9641	−	6.33013i	−0.396667	−	0.229016i
$765$		0			0
$766$	20.5359			0.741992
$767$	−4.00000			−0.144432
$768$	−0.866025	−	1.50000i	−0.0312500	−	0.0541266i
$769$			47.7128i			1.72057i	0.509815	+	0.860284i	$0.329714\pi$
$769$			47.7128i			1.72057i	−0.509815	+	0.860284i	$0.670286\pi$
$770$	−5.46410	+	9.46410i	−0.196913	+	0.341063i
$771$		−	39.4641i		−	1.42126i
$772$	−12.9282	−	7.46410i	−0.465296	−	0.268639i
$773$	−18.3301	+	31.7487i	−0.659289	+	1.14192i	0.321511	+	0.946906i	$0.395809\pi$
$773$	−18.3301	+	31.7487i	−0.659289	+	1.14192i	−0.980800	+	0.195016i	$0.937524\pi$
$774$		0			0
$775$	−1.96410	+	1.13397i	−0.0705526	+	0.0407336i
$776$	4.92820			0.176912
$777$	−12.0000	−	17.3205i	−0.430498	−	0.621370i
$778$	30.2487			1.08447
$779$	−1.73205	+	1.00000i	−0.0620572	+	0.0358287i
$780$	0.866025	−	1.50000i	0.0310087	−	0.0537086i
$781$	32.7846	−	56.7846i	1.17313	−	2.03191i
$782$		0			0
$783$			2.78461i			0.0995138i
$784$	1.50000	−	2.59808i	0.0535714	−	0.0927884i
$785$			5.73205i			0.204586i
$786$	7.39230	+	12.8038i	0.263675	+	0.456698i
$787$	4.41154			0.157255			0.0786273	−	0.996904i	$-0.474946\pi$
$787$	4.41154			0.157255			0.0786273	+	0.996904i	$0.474946\pi$
$788$	2.26795			0.0807923
$789$	−2.07180	−	3.58846i	−0.0737579	−	0.127752i
$790$	3.00000	+	1.73205i	0.106735	+	0.0616236i
$791$		−	10.1436i		−	0.360665i
$792$		0			0
$793$	3.73205	+	6.46410i	0.132529	+	0.229547i
$794$	−19.7487	+	11.4019i	−0.700856	+	0.404639i
$795$	7.79423	+	4.50000i	0.276433	+	0.159599i
$796$	−1.03590	−	0.598076i	−0.0367164	−	0.0211982i
$797$	−11.0096	+	6.35641i	−0.389981	+	0.225155i	−0.682152	−	0.731211i	$-0.738956\pi$
$797$	−11.0096	+	6.35641i	−0.389981	+	0.225155i	0.292171	+	0.956366i	$0.405622\pi$
$798$	−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
$803$	−51.7128			−1.82491
$804$	19.8564			0.700281
$805$	5.46410	+	9.46410i	0.192584	+	0.333566i
$806$			2.26795i			0.0798851i
$807$	6.00000	−	10.3923i	0.211210	−	0.365826i
$808$		−	18.9282i		−	0.665892i
$809$	−27.6051	−	15.9378i	−0.970544	−	0.560344i	−0.0711421	−	0.997466i	$-0.522664\pi$
$809$	−27.6051	−	15.9378i	−0.970544	−	0.560344i	−0.899402	+	0.437122i	$0.855998\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	5.12436	−	8.87564i	0.179940	−	0.311666i	−0.761919	−	0.647672i	$-0.775743\pi$
$811$	5.12436	−	8.87564i	0.179940	−	0.311666i	0.941860	+	0.336006i	$0.109076\pi$
$812$	−0.928203	+	0.535898i	−0.0325735	+	0.0188063i
$813$	48.3731			1.69652
$814$	27.3205	−	18.9282i	0.957583	−	0.663433i
$815$	7.00000			0.245199
$816$		0			0
$817$	−7.92820	+	13.7321i	−0.277373	+	0.480424i
$818$	15.2583	−	26.4282i	0.533495	−	0.924040i
$819$		0			0
$820$			1.00000i			0.0349215i
$821$	19.7321	−	34.1769i	0.688653	−	1.19278i	−0.283620	−	0.958937i	$-0.591536\pi$
$821$	19.7321	−	34.1769i	0.688653	−	1.19278i	0.972274	−	0.233846i	$-0.0751311\pi$
$822$		−	14.5359i		−	0.506998i
$823$	−18.6603	−	32.3205i	−0.650456	−	1.12662i	−0.983012	−	0.183539i	$-0.941245\pi$
$823$	−18.6603	−	32.3205i	−0.650456	−	1.12662i	0.332557	−	0.943083i	$-0.392089\pi$
$824$	−6.92820			−0.241355
$825$	−9.46410			−0.329498
$826$	4.00000	+	6.92820i	0.139178	+	0.241063i
$827$	−5.32051	−	3.07180i	−0.185012	−	0.106817i	0.404633	−	0.914479i	$-0.367399\pi$
$827$	−5.32051	−	3.07180i	−0.185012	−	0.106817i	−0.589645	+	0.807662i	$0.700733\pi$
$828$		0			0
$829$	−22.8564	+	13.1962i	−0.793836	+	0.458321i	−0.841311	−	0.540551i	$-0.818216\pi$
$829$	−22.8564	+	13.1962i	−0.793836	+	0.458321i	0.0474754	+	0.998872i	$0.484882\pi$
$830$	−4.26795	−	7.39230i	−0.148143	−	0.256591i
$831$	24.1077	−	13.9186i	0.836287	−	0.482830i
$832$	0.866025	+	0.500000i	0.0300240	+	0.0173344i
$833$		0			0
$834$	−3.80385	+	2.19615i	−0.131716	+	0.0760465i
$835$	2.26795	+	3.92820i	0.0784856	+	0.135941i
$836$	9.46410	−	5.46410i	0.327323	−	0.188980i
$837$		−	11.7846i		−	0.407336i
$838$	−8.53590	−	4.92820i	−0.294868	−	0.170242i
$839$	−7.03590	−	12.1865i	−0.242906	−	0.420726i	0.718635	−	0.695388i	$-0.244767\pi$
$839$	−7.03590	−	12.1865i	−0.242906	−	0.420726i	−0.961541	+	0.274662i	$0.911434\pi$
$840$	−3.46410			−0.119523
$841$	28.7128			0.990097
$842$	0.803848	+	1.39230i	0.0277024	+	0.0479820i
$843$			25.6410i			0.883124i
$844$	2.46410	−	4.26795i	0.0848179	−	0.146909i
$845$		−	12.0000i		−	0.412813i
$846$		0			0
$847$	18.8564	−	32.6603i	0.647914	−	1.12222i
$848$	−2.59808	+	4.50000i	−0.0892183	+	0.154531i
$849$	46.2846	−	26.7224i	1.58848	−	0.917111i
$850$		0			0
$851$	−2.73205	−	33.1244i	−0.0936535	−	1.13549i
$852$	20.7846			0.712069
$853$	−30.0622	+	17.3564i	−1.02931	+	0.594272i	−0.916787	−	0.399377i	$-0.869226\pi$
$853$	−30.0622	+	17.3564i	−1.02931	+	0.594272i	−0.112523	+	0.993649i	$0.535893\pi$
$854$	7.46410	−	12.9282i	0.255416	−	0.442394i
$855$		0			0
$856$	7.50000	+	4.33013i	0.256345	+	0.148001i
$857$		−	37.5692i		−	1.28334i	−0.766981	−	0.641670i	$-0.778242\pi$
$857$		−	37.5692i		−	1.28334i	0.766981	−	0.641670i	$-0.221758\pi$
$858$	−4.73205	+	8.19615i	−0.161550	+	0.279812i
$859$			12.6795i			0.432619i	0.976325	+	0.216309i	$0.0694020\pi$
$859$			12.6795i			0.432619i	−0.976325	+	0.216309i	$0.930598\pi$
$860$	3.96410	+	6.86603i	0.135175	+	0.234130i
$861$	−3.46410			−0.118056
$862$	4.41154			0.150258
$863$	−0.339746	−	0.588457i	−0.0115651	−	0.0200313i	0.860185	−	0.509982i	$-0.170348\pi$
$863$	−0.339746	−	0.588457i	−0.0115651	−	0.0200313i	−0.871750	+	0.489951i	$0.837015\pi$
$864$	−4.50000	−	2.59808i	−0.153093	−	0.0883883i
$865$		−	5.07180i		−	0.172446i
$866$	−11.6603	+	6.73205i	−0.396232	+	0.228764i
$867$	−14.7224	−	25.5000i	−0.500000	−	0.866025i
$868$	3.92820	−	2.26795i	0.133332	−	0.0769792i
$869$	−16.3923	−	9.46410i	−0.556071	−	0.321048i
$870$	−0.803848	−	0.464102i	−0.0272530	−	0.0157345i
$871$	−9.92820	+	5.73205i	−0.336404	+	0.194223i
$872$	0.267949	+	0.464102i	0.00907390	+	0.0157165i
$873$		0			0
$874$		−	10.9282i		−	0.369652i
$875$	1.73205	+	1.00000i	0.0585540	+	0.0338062i
$876$	−8.19615	−	14.1962i	−0.276922	−	0.479644i
$877$	27.8756			0.941294			0.470647	−	0.882322i	$-0.344021\pi$
$877$	27.8756			0.941294			0.470647	+	0.882322i	$0.344021\pi$
$878$	7.58846			0.256098
$879$	20.8923	+	36.1865i	0.704680	+	1.22054i
$880$		−	5.46410i		−	0.184195i
$881$	9.53590	−	16.5167i	0.321273	−	0.556460i	−0.659478	−	0.751724i	$-0.729223\pi$
$881$	9.53590	−	16.5167i	0.321273	−	0.556460i	0.980751	+	0.195263i	$0.0625561\pi$
$882$		0			0
$883$	−11.1340	−	6.42820i	−0.374688	−	0.216326i	0.300817	−	0.953682i	$-0.402741\pi$
$883$	−11.1340	−	6.42820i	−0.374688	−	0.216326i	−0.675505	+	0.737356i	$0.736074\pi$
$884$		0			0
$885$	−3.46410	+	6.00000i	−0.116445	+	0.201688i
$886$	14.8923	−	8.59808i	0.500317	−	0.288858i
$887$	32.9282			1.10562			0.552810	−	0.833307i	$-0.313555\pi$
$887$	32.9282			1.10562			0.552810	+	0.833307i	$0.313555\pi$
$888$	9.52628	+	4.50000i	0.319681	+	0.151010i
$889$	−40.7846			−1.36787
$890$	−6.92820	+	4.00000i	−0.232234	+	0.134080i
$891$	24.5885	−	42.5885i	0.823744	−	1.42677i
$892$	−9.66025	+	16.7321i	−0.323449	+	0.560230i
$893$	22.3923	+	12.9282i	0.749330	+	0.432626i
$894$			16.3923i			0.548241i
$895$	−12.9282	+	22.3923i	−0.432142	+	0.748492i
$896$		−	2.00000i		−	0.0668153i
$897$	4.73205	+	8.19615i	0.157999	+	0.273662i
$898$	−36.9090			−1.23167
$899$	1.21539			0.0405355
$900$		0			0
$901$		0			0
$902$		−	5.46410i		−	0.181935i
$903$	−23.7846	+	13.7321i	−0.791502	+	0.456974i
$904$	2.53590	+	4.39230i	0.0843427	+	0.146086i
$905$	−7.73205	+	4.46410i	−0.257022	+	0.148392i
$906$	19.2846	+	11.1340i	0.640688	+	0.369902i
$907$	−26.7846	−	15.4641i	−0.889368	−	0.513477i	−0.0156325	−	0.999878i	$-0.504976\pi$
$907$	−26.7846	−	15.4641i	−0.889368	−	0.513477i	−0.873736	+	0.486401i	$0.838310\pi$
$908$	−20.5981	+	11.8923i	−0.683571	+	0.394660i
$909$		0			0
$910$	1.73205	−	1.00000i	0.0574169	−	0.0331497i
$911$		−	17.1962i		−	0.569734i	−0.958567	−	0.284867i	$-0.908051\pi$
$911$		−	17.1962i		−	0.569734i	0.958567	−	0.284867i	$-0.0919494\pi$
$912$	3.00000	+	1.73205i	0.0993399	+	0.0573539i
$913$	23.3205	+	40.3923i	0.771796	+	1.33679i
$914$	−34.6410			−1.14582
$915$	12.9282			0.427393
$916$	−1.53590	−	2.66025i	−0.0507475	−	0.0878973i
$917$			17.0718i			0.563760i
$918$		0			0
$919$		−	35.4641i		−	1.16985i	−0.811086	−	0.584926i	$-0.801123\pi$
$919$		−	35.4641i		−	1.16985i	0.811086	−	0.584926i	$-0.198877\pi$
$920$	−4.73205	−	2.73205i	−0.156011	−	0.0900730i
$921$	−6.82051	+	11.8135i	−0.224743	+	0.389267i
$922$	19.1962	−	33.2487i	0.632192	−	1.09499i
$923$	−10.3923	+	6.00000i	−0.342067	+	0.197492i
$924$	18.9282			0.622692
$925$	−3.46410	−	5.00000i	−0.113899	−	0.164399i
$926$	−11.6077			−0.381453
$927$		0			0
$928$	0.267949	−	0.464102i	0.00879586	−	0.0152349i
$929$	6.57180	−	11.3827i	0.215614	−	0.373454i	−0.737849	−	0.674966i	$-0.764158\pi$
$929$	6.57180	−	11.3827i	0.215614	−	0.373454i	0.953462	+	0.301512i	$0.0974915\pi$
$930$	3.40192	+	1.96410i	0.111553	+	0.0644054i
$931$			6.00000i			0.196642i
$932$	4.46410	−	7.73205i	0.146227	−	0.253272i
$933$		−	39.9282i		−	1.30719i
$934$	−16.9641	−	29.3827i	−0.555082	−	0.961431i
$935$		0			0
$936$		0			0
$937$	11.3923	+	19.7321i	0.372170	+	0.644618i	0.989899	−	0.141773i	$-0.0452804\pi$
$937$	11.3923	+	19.7321i	0.372170	+	0.644618i	−0.617729	+	0.786391i	$0.711947\pi$
$938$	19.8564	+	11.4641i	0.648335	+	0.374316i
$939$			39.4641i			1.28786i
$940$	11.1962	−	6.46410i	0.365178	−	0.210836i
$941$	20.5885	+	35.6603i	0.671165	+	1.16249i	0.977574	+	0.210591i	$0.0675389\pi$
$941$	20.5885	+	35.6603i	0.671165	+	1.16249i	−0.306410	+	0.951900i	$0.599128\pi$
$942$	8.59808	−	4.96410i	0.280140	−	0.161739i
$943$	−4.73205	−	2.73205i	−0.154097	−	0.0889678i
$944$	−3.46410	−	2.00000i	−0.112747	−	0.0650945i
$945$	−9.00000	+	5.19615i	−0.292770	+	0.169031i
$946$	−21.6603	−	37.5167i	−0.704236	−	1.21977i
$947$	−48.3109	+	27.8923i	−1.56989	+	0.906378i	−0.573713	+	0.819057i	$0.694497\pi$
$947$	−48.3109	+	27.8923i	−1.56989	+	0.906378i	−0.996180	+	0.0873216i	$0.972169\pi$
$948$		−	6.00000i		−	0.194871i
$949$	8.19615	+	4.73205i	0.266058	+	0.153609i
$950$	−1.00000	−	1.73205i	−0.0324443	−	0.0561951i
$951$	−3.00000			−0.0972817
$952$		0			0
$953$	−0.339746	−	0.588457i	−0.0110055	−	0.0190620i	0.860470	−	0.509501i	$-0.170170\pi$
$953$	−0.339746	−	0.588457i	−0.0110055	−	0.0190620i	−0.871476	+	0.490439i	$0.836837\pi$
$954$		0			0
$955$	6.33013	−	10.9641i	0.204838	−	0.354790i
$956$		−	29.3205i		−	0.948293i
$957$	4.39230	+	2.53590i	0.141983	+	0.0819740i
$958$	4.06218	−	7.03590i	0.131243	−	0.227320i
$959$	8.39230	−	14.5359i	0.271002	−	0.469389i
$960$	1.50000	−	0.866025i	0.0484123	−	0.0279508i
$961$	25.8564			0.834078
$962$	−6.06218	+	0.500000i	−0.195452	+	0.0161206i
$963$		0			0
$964$	−8.53590	+	4.92820i	−0.274923	+	0.158727i
$965$	7.46410	−	12.9282i	0.240278	−	0.416174i
$966$	9.46410	−	16.3923i	0.304502	−	0.527414i
$967$	21.3731	+	12.3397i	0.687311	+	0.396819i	0.802604	−	0.596512i	$-0.203447\pi$
$967$	21.3731	+	12.3397i	0.687311	+	0.396819i	−0.115293	+	0.993332i	$0.536781\pi$
$968$			18.8564i			0.606068i
$969$		0			0
$970$			4.92820i			0.158235i
$971$	25.4641	+	44.1051i	0.817182	+	1.41540i	0.907751	+	0.419510i	$0.137798\pi$
$971$	25.4641	+	44.1051i	0.817182	+	1.41540i	−0.0905686	+	0.995890i	$0.528868\pi$
$972$		0			0
$973$	−5.07180			−0.162594
$974$	−7.00000	−	12.1244i	−0.224294	−	0.388489i
$975$	1.50000	+	0.866025i	0.0480384	+	0.0277350i
$976$			7.46410i			0.238920i
$977$	−49.6410	+	28.6603i	−1.58816	+	0.916923i	−0.594546	+	0.804062i	$0.702668\pi$
$977$	−49.6410	+	28.6603i	−1.58816	+	0.916923i	−0.993611	+	0.112861i	$0.963998\pi$
$978$	−6.06218	−	10.5000i	−0.193847	−	0.335753i
$979$	37.8564	−	21.8564i	1.20990	−	0.698534i
$980$	2.59808	+	1.50000i	0.0829925	+	0.0479157i
$981$		0			0
$982$	6.92820	−	4.00000i	0.221088	−	0.127645i
$983$	19.1962	+	33.2487i	0.612262	+	1.06047i	0.990858	+	0.134907i	$0.0430736\pi$
$983$	19.1962	+	33.2487i	0.612262	+	1.06047i	−0.378596	+	0.925562i	$0.623593\pi$
$984$	1.50000	−	0.866025i	0.0478183	−	0.0276079i
$985$			2.26795i			0.0722629i
$986$		0			0
$987$	22.3923	+	38.7846i	0.712755	+	1.23453i
$988$	−2.00000			−0.0636285
$989$	−43.3205			−1.37751
$990$		0			0
$991$		−	3.05256i		−	0.0969677i	−0.998824	−	0.0484839i	$-0.984561\pi$
$991$		−	3.05256i		−	0.0969677i	0.998824	−	0.0484839i	$-0.0154389\pi$
$992$	−1.13397	+	1.96410i	−0.0360037	+	0.0623603i
$993$			14.7846i			0.469175i
$994$	20.7846	+	12.0000i	0.659248	+	0.380617i
$995$	0.598076	−	1.03590i	0.0189603	−	0.0328402i
$996$	−7.39230	+	12.8038i	−0.234234	+	0.405705i
$997$	23.0096	−	13.2846i	0.728722	−	0.420728i	−0.0892325	−	0.996011i	$-0.528441\pi$
$997$	23.0096	−	13.2846i	0.728722	−	0.420728i	0.817954	+	0.575283i	$0.195108\pi$
$998$	−34.9282			−1.10563
$999$	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.11.1	✓	4
37.27	even	6	inner	370.2.l.b.101.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.l.b.11.1	✓	4	1.1	even	1	trivial
370.2.l.b.101.1	yes	4	37.27	even	6	inner

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} +5.46410 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} +(-4.73205 + 2.73205i) q^{22} +5.46410i 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} -0.535898i q^{29} +(0.866025 - 1.50000i) q^{30} +2.26795i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.73205 + 8.19615i) 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} +7.92820i q^{43} +(2.73205 - 4.73205i) q^{44} +(-2.73205 - 4.73205i) q^{46} +12.9282 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} +(4.73205 + 2.73205i) q^{55} +(1.73205 + 1.00000i) q^{56} +(-3.00000 + 1.73205i) q^{57} +(0.267949 + 0.464102i) q^{58} +(3.46410 - 2.00000i) q^{59} +1.73205i q^{60} +(-6.46410 - 3.73205i) q^{61} +(-1.13397 - 1.96410i) q^{62} -1.00000 q^{64} +(-0.500000 - 0.866025i) q^{65} -9.46410i q^{66} +(5.73205 - 9.92820i) q^{67} +(-8.19615 - 4.73205i) q^{69} +(-1.00000 + 1.73205i) q^{70} +(6.00000 - 10.3923i) q^{71} -9.46410 q^{73} +(5.00000 - 3.46410i) q^{74} -1.73205 q^{75} +(1.73205 - 1.00000i) q^{76} +(5.46410 - 9.46410i) 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} +(4.26795 + 7.39230i) q^{83} +3.46410 q^{84} +(-3.96410 - 6.86603i) q^{86} +(0.803848 + 0.464102i) q^{87} +5.46410i q^{88} +(6.92820 - 4.00000i) q^{89} +(-1.73205 + 1.00000i) q^{91} +(4.73205 + 2.73205i) q^{92} +(-3.40192 - 1.96410i) q^{93} +(-11.1962 + 6.46410i) q^{94} +(1.00000 + 1.73205i) q^{95} +(-1.50000 + 0.866025i) q^{96} -4.92820i 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

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Representations

Groups

Database

Properties

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