LMFDB - Embedded newform 37.2.c.a.10.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(10,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("37.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.c (of order $3$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			10.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	37.10
Dual form			37.2.c.a.26.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} -2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(3.00000 + 5.19615i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +(1.00000 - 1.73205i) q^{28} +9.00000 q^{29} -10.0000 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-1.00000 + 1.73205i) q^{35} +3.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} -6.00000 q^{38} +(1.50000 + 2.59808i) q^{40} +(4.50000 + 7.79423i) q^{41} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -3.00000 q^{45} +(2.00000 - 3.46410i) q^{46} +6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.00000 + 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(5.00000 - 8.66025i) q^{62} -6.00000 q^{63} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(5.00000 + 8.66025i) q^{67} -3.00000 q^{68} +(-1.00000 - 1.73205i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-4.50000 + 7.79423i) q^{72} -10.0000 q^{73} +(5.00000 - 3.46410i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(2.00000 + 3.46410i) q^{77} +(-5.00000 - 8.66025i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +3.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +6.00000 q^{88} +(-3.50000 + 6.06218i) q^{89} +(1.50000 - 2.59808i) q^{90} +(2.00000 - 3.46410i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +7.00000 q^{97} +(1.50000 + 2.59808i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9	$ 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + 3 q^{18} + 6 q^{19} + q^{20} + 2 q^{22} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 2 q^{28} + 18 q^{29} - 20 q^{31} - 5 q^{32} - 3 q^{34} - 2 q^{35} + 6 q^{36} - 11 q^{37} - 12 q^{38} + 3 q^{40} + 9 q^{41} + 4 q^{43} - 2 q^{44} - 6 q^{45} + 4 q^{46} + 12 q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{52} + 2 q^{53} + 2 q^{55} + 6 q^{56} - 9 q^{58} + 4 q^{59} - q^{61} + 10 q^{62} - 12 q^{63} + 14 q^{64} + 2 q^{65} + 10 q^{67} - 6 q^{68} - 2 q^{70} - 6 q^{71} - 9 q^{72} - 20 q^{73} + 10 q^{74} - 6 q^{76} + 4 q^{77} - 10 q^{79} - 2 q^{80} - 9 q^{81} - 18 q^{82} + 12 q^{83} + 6 q^{85} - 2 q^{86} + 12 q^{88} - 7 q^{89} + 3 q^{90} + 4 q^{91} - 4 q^{92} - 6 q^{94} + 6 q^{95} + 14 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^13 + 4 * q^14 + q^16 - 3 * q^17 + 3 * q^18 + 6 * q^19 + q^20 + 2 * q^22 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 2 * q^28 + 18 * q^29 - 20 * q^31 - 5 * q^32 - 3 * q^34 - 2 * q^35 + 6 * q^36 - 11 * q^37 - 12 * q^38 + 3 * q^40 + 9 * q^41 + 4 * q^43 - 2 * q^44 - 6 * q^45 + 4 * q^46 + 12 * q^47 + 3 * q^49 + 4 * q^50 - 2 * q^52 + 2 * q^53 + 2 * q^55 + 6 * q^56 - 9 * q^58 + 4 * q^59 - q^61 + 10 * q^62 - 12 * q^63 + 14 * q^64 + 2 * q^65 + 10 * q^67 - 6 * q^68 - 2 * q^70 - 6 * q^71 - 9 * q^72 - 20 * q^73 + 10 * q^74 - 6 * q^76 + 4 * q^77 - 10 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 + 6 * q^85 - 2 * q^86 + 12 * q^88 - 7 * q^89 + 3 * q^90 + 4 * q^91 - 4 * q^92 - 6 * q^94 + 6 * q^95 + 14 * q^97 + 3 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$		0			0
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	0.612801	−	0.790237i	$-0.290043\pi$
$7$	−1.00000	−	1.73205i	−0.377964	−	0.654654i	−0.990766	+	0.135583i	$0.956709\pi$
$8$	−3.00000			−1.06066
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.00000			0.316228
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	0.970725	−	0.240192i	$-0.0772105\pi$
$13$	1.00000	+	1.73205i	0.277350	+	0.480384i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	2.00000			0.534522
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	0.972404	+	0.233301i	$0.0749529\pi$
$19$	3.00000	+	5.19615i	0.688247	+	1.19208i	−0.284157	+	0.958778i	$0.591714\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−2.00000			−0.392232
$27$		0			0
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	9.00000			1.67126			0.835629	−	0.549294i	$-0.185103\pi$
$29$	9.00000			1.67126			0.835629	+	0.549294i	$0.185103\pi$
$30$		0			0
$31$	−10.0000			−1.79605			−0.898027	−	0.439941i	$-0.854999\pi$
$31$	−10.0000			−1.79605			−0.898027	+	0.439941i	$0.854999\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	−1.00000	+	1.73205i	−0.169031	+	0.292770i
$36$	3.00000			0.500000
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$37$	−5.50000	−	2.59808i	−0.904194	−	0.427121i
$38$	−6.00000			−0.973329
$39$		0			0
$40$	1.50000	+	2.59808i	0.237171	+	0.410792i
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	0.967486	+	0.252924i	$0.0813924\pi$
$41$	4.50000	+	7.79423i	0.702782	+	1.21725i	−0.264704	+	0.964330i	$0.585274\pi$
$42$		0			0
$43$	2.00000			0.304997			0.152499	−	0.988304i	$-0.451268\pi$
$43$	2.00000			0.304997			0.152499	+	0.988304i	$0.451268\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$	−3.00000			−0.447214
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$	2.00000	+	3.46410i	0.282843	+	0.489898i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	−0.789136	−	0.614218i	$-0.789471\pi$
$53$	1.00000	−	1.73205i	0.137361	−	0.237915i	0.926497	+	0.376303i	$0.122805\pi$
$54$		0			0
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	3.00000	+	5.19615i	0.400892	+	0.694365i
$57$		0			0
$58$	−4.50000	+	7.79423i	−0.590879	+	1.02343i
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	−0.705965	−	0.708247i	$-0.749486\pi$
$59$	2.00000	−	3.46410i	0.260378	−	0.450988i	0.966342	+	0.257260i	$0.0828195\pi$
$60$		0			0
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	0.832240	−	0.554416i	$-0.187058\pi$
$61$	−0.500000	−	0.866025i	−0.0640184	−	0.110883i	−0.896258	+	0.443533i	$0.853725\pi$
$62$	5.00000	−	8.66025i	0.635001	−	1.09985i
$63$	−6.00000			−0.755929
$64$	7.00000			0.875000
$65$	1.00000	−	1.73205i	0.124035	−	0.214834i
$66$		0			0
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	−3.00000			−0.363803
$69$		0			0
$70$	−1.00000	−	1.73205i	−0.119523	−	0.207020i
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	−4.50000	+	7.79423i	−0.530330	+	0.918559i
$73$	−10.0000			−1.17041			−0.585206	−	0.810885i	$-0.698986\pi$
$73$	−10.0000			−1.17041			−0.585206	+	0.810885i	$0.698986\pi$
$74$	5.00000	−	3.46410i	0.581238	−	0.402694i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	−0.997274	−	0.0737937i	$-0.976489\pi$
$79$	−5.00000	−	8.66025i	−0.562544	−	0.974355i	0.434730	−	0.900561i	$-0.356844\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−9.00000			−0.993884
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	−0.322396	−	0.946605i	$-0.604488\pi$
$83$	6.00000	−	10.3923i	0.658586	−	1.14070i	0.980982	−	0.194099i	$-0.0621783\pi$
$84$		0			0
$85$	3.00000			0.325396
$86$	−1.00000	+	1.73205i	−0.107833	+	0.186772i
$87$		0			0
$88$	6.00000			0.639602
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	−0.989720	−	0.143022i	$-0.954318\pi$
$89$	−3.50000	+	6.06218i	−0.370999	+	0.642590i	0.618720	+	0.785611i	$0.287651\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	2.00000	−	3.46410i	0.209657	−	0.363137i
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$		0			0
$94$	−3.00000	+	5.19615i	−0.309426	+	0.535942i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	1.50000	+	2.59808i	0.151523	+	0.262445i
$99$	−3.00000	+	5.19615i	−0.301511	+	0.522233i
$100$	4.00000			0.400000
$101$	−3.00000			−0.298511			−0.149256	−	0.988799i	$-0.547688\pi$
$101$	−3.00000			−0.298511			−0.149256	+	0.988799i	$0.547688\pi$
$102$		0			0
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	1.00000	+	1.73205i	0.0971286	+	0.168232i
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$	−2.00000			−0.190693
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	4.50000	+	7.79423i	0.417815	+	0.723676i
$117$	6.00000			0.554700
$118$	2.00000	+	3.46410i	0.184115	+	0.318896i
$119$	6.00000			0.550019
$120$		0			0
$121$	−7.00000			−0.636364
$122$	1.00000			0.0905357
$123$		0			0
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$	−9.00000			−0.804984
$126$	3.00000	−	5.19615i	0.267261	−	0.462910i
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$		0			0
$130$	1.00000	+	1.73205i	0.0877058	+	0.151911i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		0			0
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$	−10.0000			−0.863868
$135$		0			0
$136$	4.50000	−	7.79423i	0.385872	−	0.668350i
$137$	−9.00000			−0.768922			−0.384461	−	0.923141i	$-0.625613\pi$
$137$	−9.00000			−0.768922			−0.384461	+	0.923141i	$0.625613\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	−2.00000			−0.169031
$141$		0			0
$142$	6.00000			0.503509
$143$	−2.00000	−	3.46410i	−0.167248	−	0.289683i
$144$	−1.50000	−	2.59808i	−0.125000	−	0.216506i
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$	5.00000	−	8.66025i	0.413803	−	0.716728i
$147$		0			0
$148$	−0.500000	−	6.06218i	−0.0410997	−	0.498308i
$149$	−11.0000			−0.901155			−0.450578	−	0.892737i	$-0.648782\pi$
$149$	−11.0000			−0.901155			−0.450578	+	0.892737i	$0.648782\pi$
$150$		0			0
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−9.00000	−	15.5885i	−0.729996	−	1.26439i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	−4.00000			−0.322329
$155$	5.00000	+	8.66025i	0.401610	+	0.695608i
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$	10.0000			0.795557
$159$		0			0
$160$	−2.50000	+	4.33013i	−0.197642	+	0.342327i
$161$	4.00000	+	6.92820i	0.315244	+	0.546019i
$162$	9.00000			0.707107
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	−0.724288	−	0.689497i	$-0.757831\pi$
$163$	3.00000	−	5.19615i	0.234978	−	0.406994i	0.959266	+	0.282503i	$0.0911648\pi$
$164$	−4.50000	+	7.79423i	−0.351391	+	0.608627i
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	0.534875	−	0.844931i	$-0.320359\pi$
$167$	−6.00000	−	10.3923i	−0.464294	−	0.804181i	−0.999169	+	0.0407502i	$0.987025\pi$
$168$		0			0
$169$	4.50000	−	7.79423i	0.346154	−	0.599556i
$170$	−1.50000	+	2.59808i	−0.115045	+	0.199263i
$171$	18.0000			1.37649
$172$	1.00000	+	1.73205i	0.0762493	+	0.132068i
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	0.122422	+	0.992478i	$0.460934\pi$
$173$	−10.5000	+	18.1865i	−0.798300	+	1.38270i	−0.920722	+	0.390218i	$0.872399\pi$
$174$		0			0
$175$	−8.00000			−0.604743
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$		0			0
$178$	−3.50000	−	6.06218i	−0.262336	−	0.454379i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	0.758030	−	0.652219i	$-0.226162\pi$
$181$	−2.50000	−	4.33013i	−0.185824	−	0.321856i	−0.943854	+	0.330364i	$0.892829\pi$
$182$	2.00000	+	3.46410i	0.148250	+	0.256776i
$183$		0			0
$184$	12.0000			0.884652
$185$	0.500000	+	6.06218i	0.0367607	+	0.445700i
$186$		0			0
$187$	3.00000	−	5.19615i	0.219382	−	0.379980i
$188$	3.00000	+	5.19615i	0.218797	+	0.378968i
$189$		0			0
$190$	3.00000	+	5.19615i	0.217643	+	0.376969i
$191$	−4.00000			−0.289430			−0.144715	−	0.989473i	$-0.546227\pi$
$191$	−4.00000			−0.289430			−0.144715	+	0.989473i	$0.546227\pi$
$192$		0			0
$193$	19.0000			1.36765			0.683825	−	0.729646i	$-0.260315\pi$
$193$	19.0000			1.36765			0.683825	+	0.729646i	$0.260315\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$		0			0
$196$	3.00000			0.214286
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	−0.464841	−	0.885394i	$-0.653889\pi$
$197$	7.50000	−	12.9904i	0.534353	−	0.925526i	0.999194	−	0.0401324i	$-0.0127780\pi$
$198$	−3.00000	−	5.19615i	−0.213201	−	0.369274i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	−6.00000	+	10.3923i	−0.424264	+	0.734847i
$201$		0			0
$202$	1.50000	−	2.59808i	0.105540	−	0.182800i
$203$	−9.00000	−	15.5885i	−0.631676	−	1.09410i
$204$		0			0
$205$	4.50000	−	7.79423i	0.314294	−	0.544373i
$206$	−3.00000	+	5.19615i	−0.209020	+	0.362033i
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$	2.00000			0.138675
$209$	−6.00000	−	10.3923i	−0.415029	−	0.718851i
$210$		0			0
$211$	2.00000			0.137686			0.0688428	−	0.997628i	$-0.478069\pi$
$211$	2.00000			0.137686			0.0688428	+	0.997628i	$0.478069\pi$
$212$	2.00000			0.137361
$213$		0			0
$214$	−18.0000			−1.23045
$215$	−1.00000	−	1.73205i	−0.0681994	−	0.118125i
$216$		0			0
$217$	10.0000	+	17.3205i	0.678844	+	1.17579i
$218$	−2.50000	−	4.33013i	−0.169321	−	0.293273i
$219$		0			0
$220$	−1.00000	+	1.73205i	−0.0674200	+	0.116775i
$221$	−6.00000			−0.403604
$222$		0			0
$223$	28.0000			1.87502			0.937509	−	0.347960i	$-0.113126\pi$
$223$	28.0000			1.87502			0.937509	+	0.347960i	$0.113126\pi$
$224$	−5.00000	+	8.66025i	−0.334077	+	0.578638i
$225$	−6.00000	−	10.3923i	−0.400000	−	0.692820i
$226$	−3.00000	−	5.19615i	−0.199557	−	0.345643i
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	0.534577	−	0.845120i	$-0.320471\pi$
$227$	−7.00000	−	12.1244i	−0.464606	−	0.804722i	−0.999184	+	0.0403978i	$0.987137\pi$
$228$		0			0
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	0.849032	−	0.528341i	$-0.177186\pi$
$229$	−0.500000	−	0.866025i	−0.0330409	−	0.0572286i	−0.882073	+	0.471113i	$0.843853\pi$
$230$	−4.00000			−0.263752
$231$		0			0
$232$	−27.0000			−1.77264
$233$	3.00000			0.196537			0.0982683	−	0.995160i	$-0.468670\pi$
$233$	3.00000			0.196537			0.0982683	+	0.995160i	$0.468670\pi$
$234$	−3.00000	+	5.19615i	−0.196116	+	0.339683i
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	4.00000			0.260378
$237$		0			0
$238$	−3.00000	+	5.19615i	−0.194461	+	0.336817i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$		0			0
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	0.547533	−	0.836784i	$-0.315567\pi$
$241$	−7.00000	−	12.1244i	−0.450910	−	0.780998i	−0.998443	+	0.0557856i	$0.982234\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$		0			0
$244$	0.500000	−	0.866025i	0.0320092	−	0.0554416i
$245$	−3.00000			−0.191663
$246$		0			0
$247$	−6.00000	+	10.3923i	−0.381771	+	0.661247i
$248$	30.0000			1.90500
$249$		0			0
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	−14.0000			−0.883672			−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000			−0.883672			−0.441836	+	0.897096i	$0.645673\pi$
$252$	−3.00000	−	5.19615i	−0.188982	−	0.327327i
$253$	8.00000			0.502956
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$		0			0
$259$	1.00000	+	12.1244i	0.0621370	+	0.753371i
$260$	2.00000			0.124035
$261$	13.5000	−	23.3827i	0.835629	−	1.44735i
$262$		0			0
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	0.797752	−	0.602986i	$-0.206023\pi$
$263$	−2.00000	−	3.46410i	−0.123325	−	0.213606i	−0.921077	+	0.389380i	$0.872689\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$	6.00000	+	10.3923i	0.367884	+	0.637193i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		0			0
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	−0.996441	−	0.0842940i	$-0.973137\pi$
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	0.571221	+	0.820796i	$0.306470\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	−4.00000	+	6.92820i	−0.241209	+	0.417786i
$276$		0			0
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	0.907564	−	0.419914i	$-0.137940\pi$
$277$	1.50000	+	2.59808i	0.0901263	+	0.156103i	−0.817438	+	0.576017i	$0.804606\pi$
$278$	−8.00000	−	13.8564i	−0.479808	−	0.831052i
$279$	−15.0000	+	25.9808i	−0.898027	+	1.55543i
$280$	3.00000	−	5.19615i	0.179284	−	0.310530i
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	0.110717	+	0.993852i	$0.464685\pi$
$281$	−13.5000	+	23.3827i	−0.805342	+	1.39489i	−0.916060	+	0.401042i	$0.868648\pi$
$282$		0			0
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$		0			0
$286$	4.00000			0.236525
$287$	9.00000	−	15.5885i	0.531253	−	0.920158i
$288$	−15.0000			−0.883883
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000			0.528498
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	11.5000	+	19.9186i	0.671837	+	1.16366i	0.977383	+	0.211479i	$0.0678279\pi$
$293$	11.5000	+	19.9186i	0.671837	+	1.16366i	−0.305545	+	0.952177i	$0.598839\pi$
$294$		0			0
$295$	−4.00000			−0.232889
$296$	16.5000	+	7.79423i	0.959043	+	0.453030i
$297$		0			0
$298$	5.50000	−	9.52628i	0.318606	−	0.551843i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	4.00000			0.230174
$303$		0			0
$304$	6.00000			0.344124
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$	−9.00000			−0.514496
$307$	−14.0000			−0.799022			−0.399511	−	0.916728i	$-0.630820\pi$
$307$	−14.0000			−0.799022			−0.399511	+	0.916728i	$0.630820\pi$
$308$	−2.00000	+	3.46410i	−0.113961	+	0.197386i
$309$		0			0
$310$	−10.0000			−0.567962
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	−0.947825	−	0.318791i	$-0.896723\pi$
$313$	−3.50000	+	6.06218i	−0.197832	+	0.342655i	0.749993	+	0.661445i	$0.230057\pi$
$314$	−8.50000	−	14.7224i	−0.479683	−	0.830835i
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	5.00000	−	8.66025i	0.281272	−	0.487177i
$317$	−0.500000	+	0.866025i	−0.0280828	+	0.0486408i	−0.879725	−	0.475482i	$-0.842274\pi$
$317$	−0.500000	+	0.866025i	−0.0280828	+	0.0486408i	0.851642	+	0.524123i	$0.175607\pi$
$318$		0			0
$319$	−18.0000			−1.00781
$320$	−3.50000	−	6.06218i	−0.195656	−	0.338886i
$321$		0			0
$322$	−8.00000			−0.445823
$323$	−18.0000			−1.00155
$324$	4.50000	−	7.79423i	0.250000	−	0.433013i
$325$	8.00000			0.443760
$326$	3.00000	+	5.19615i	0.166155	+	0.287788i
$327$		0			0
$328$	−13.5000	−	23.3827i	−0.745413	−	1.29109i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	−0.448649	−	0.893708i	$-0.648095\pi$
$331$	10.0000	−	17.3205i	0.549650	−	0.952021i	0.998298	−	0.0583130i	$-0.0185721\pi$
$332$	12.0000			0.658586
$333$	−15.0000	+	10.3923i	−0.821995	+	0.569495i
$334$	12.0000			0.656611
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$		0			0
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	0.879322	−	0.476227i	$-0.157996\pi$
$337$	0.500000	+	0.866025i	0.0272367	+	0.0471754i	−0.852086	+	0.523402i	$0.824663\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$	20.0000			1.08306
$342$	−9.00000	+	15.5885i	−0.486664	+	0.842927i
$343$	−20.0000			−1.07990
$344$	−6.00000			−0.323498
$345$		0			0
$346$	−10.5000	−	18.1865i	−0.564483	−	0.977714i
$347$	−16.0000			−0.858925			−0.429463	−	0.903085i	$-0.641297\pi$
$347$	−16.0000			−0.858925			−0.429463	+	0.903085i	$0.641297\pi$
$348$		0			0
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	−0.960965	−	0.276670i	$-0.910769\pi$
$349$	−4.50000	+	7.79423i	−0.240879	+	0.417215i	0.720086	+	0.693885i	$0.244103\pi$
$350$	4.00000	−	6.92820i	0.213809	−	0.370328i
$351$		0			0
$352$	5.00000	+	8.66025i	0.266501	+	0.461593i
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	−0.313894	−	0.949458i	$-0.601634\pi$
$353$	12.5000	−	21.6506i	0.665308	−	1.15235i	0.979202	−	0.202889i	$-0.0650330\pi$
$354$		0			0
$355$	−3.00000	+	5.19615i	−0.159223	+	0.275783i
$356$	−7.00000			−0.370999
$357$		0			0
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	9.00000			0.474342
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	5.00000			0.262794
$363$		0			0
$364$	4.00000			0.209657
$365$	5.00000	+	8.66025i	0.261712	+	0.453298i
$366$		0			0
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	27.0000			1.40556
$370$	−5.50000	−	2.59808i	−0.285931	−	0.135068i
$371$	−4.00000			−0.207670
$372$		0			0
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	0.557584	−	0.830120i	$-0.311728\pi$
$373$	−8.50000	−	14.7224i	−0.440113	−	0.762299i	−0.997697	+	0.0678218i	$0.978395\pi$
$374$	3.00000	+	5.19615i	0.155126	+	0.268687i
$375$		0			0
$376$	−18.0000			−0.928279
$377$	9.00000	+	15.5885i	0.463524	+	0.802846i
$378$		0			0
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	−0.932731	−	0.360573i	$-0.882581\pi$
$379$	−3.00000	+	5.19615i	−0.154100	+	0.266908i	0.778631	+	0.627482i	$0.215914\pi$
$380$	6.00000			0.307794
$381$		0			0
$382$	2.00000	−	3.46410i	0.102329	−	0.177239i
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.863367	+	0.504576i	$0.168351\pi$
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.00529229	+	0.999986i	$0.498315\pi$
$384$		0			0
$385$	2.00000	−	3.46410i	0.101929	−	0.176547i
$386$	−9.50000	+	16.4545i	−0.483537	+	0.837511i
$387$	3.00000	−	5.19615i	0.152499	−	0.264135i
$388$	3.50000	+	6.06218i	0.177686	+	0.307760i
$389$	−12.5000	−	21.6506i	−0.633775	−	1.09773i	−0.986773	−	0.162107i	$-0.948171\pi$
$389$	−12.5000	−	21.6506i	−0.633775	−	1.09773i	0.352998	−	0.935624i	$-0.385162\pi$
$390$		0			0
$391$	6.00000	−	10.3923i	0.303433	−	0.525561i
$392$	−4.50000	+	7.79423i	−0.227284	+	0.393668i
$393$		0			0
$394$	7.50000	+	12.9904i	0.377845	+	0.654446i
$395$	−5.00000	+	8.66025i	−0.251577	+	0.435745i
$396$	−6.00000			−0.301511
$397$	13.0000			0.652451			0.326226	−	0.945292i	$-0.394223\pi$
$397$	13.0000			0.652451			0.326226	+	0.945292i	$0.394223\pi$
$398$	5.00000	−	8.66025i	0.250627	−	0.434099i
$399$		0			0
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−18.0000			−0.898877			−0.449439	−	0.893311i	$-0.648376\pi$
$401$	−18.0000			−0.898877			−0.449439	+	0.893311i	$0.648376\pi$
$402$		0			0
$403$	−10.0000	−	17.3205i	−0.498135	−	0.862796i
$404$	−1.50000	−	2.59808i	−0.0746278	−	0.129259i
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$	18.0000			0.893325
$407$	11.0000	+	5.19615i	0.545250	+	0.257564i
$408$		0			0
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	−0.371750	−	0.928333i	$-0.621242\pi$
$409$	12.5000	−	21.6506i	0.618085	−	1.07056i	0.989835	−	0.142222i	$-0.0454247\pi$
$410$	4.50000	+	7.79423i	0.222239	+	0.384930i
$411$		0			0
$412$	3.00000	+	5.19615i	0.147799	+	0.255996i
$413$	−8.00000			−0.393654
$414$	−6.00000	−	10.3923i	−0.294884	−	0.510754i
$415$	−12.0000			−0.589057
$416$	5.00000	−	8.66025i	0.245145	−	0.424604i
$417$		0			0
$418$	12.0000			0.586939
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	−0.351404	−	0.936224i	$-0.614296\pi$
$419$	13.0000	−	22.5167i	0.635092	−	1.10001i	0.986496	−	0.163787i	$-0.0523710\pi$
$420$		0			0
$421$	9.00000			0.438633			0.219317	−	0.975654i	$-0.429617\pi$
$421$	9.00000			0.438633			0.219317	+	0.975654i	$0.429617\pi$
$422$	−1.00000	+	1.73205i	−0.0486792	+	0.0843149i
$423$	9.00000	−	15.5885i	0.437595	−	0.757937i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	−1.00000	+	1.73205i	−0.0483934	+	0.0838198i
$428$	−9.00000	+	15.5885i	−0.435031	+	0.753497i
$429$		0			0
$430$	2.00000			0.0964486
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	0.563658	−	0.826008i	$-0.309393\pi$
$431$	−9.00000	−	15.5885i	−0.433515	−	0.750870i	−0.997173	+	0.0751385i	$0.976060\pi$
$432$		0			0
$433$	−21.0000			−1.00920			−0.504598	−	0.863355i	$-0.668359\pi$
$433$	−21.0000			−1.00920			−0.504598	+	0.863355i	$0.668359\pi$
$434$	−20.0000			−0.960031
$435$		0			0
$436$	−5.00000			−0.239457
$437$	−12.0000	−	20.7846i	−0.574038	−	0.994263i
$438$		0			0
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$	−3.00000	−	5.19615i	−0.143019	−	0.247717i
$441$	−4.50000	−	7.79423i	−0.214286	−	0.371154i
$442$	3.00000	−	5.19615i	0.142695	−	0.247156i
$443$	−32.0000			−1.52037			−0.760183	−	0.649709i	$-0.774891\pi$
$443$	−32.0000			−1.52037			−0.760183	+	0.649709i	$0.774891\pi$
$444$		0			0
$445$	7.00000			0.331832
$446$	−14.0000	+	24.2487i	−0.662919	+	1.14821i
$447$		0			0
$448$	−7.00000	−	12.1244i	−0.330719	−	0.572822i
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	0.786513	−	0.617574i	$-0.211885\pi$
$449$	−3.00000	−	5.19615i	−0.141579	−	0.245222i	−0.928091	+	0.372353i	$0.878551\pi$
$450$	12.0000			0.565685
$451$	−9.00000	−	15.5885i	−0.423793	−	0.734032i
$452$	−6.00000			−0.282216
$453$		0			0
$454$	14.0000			0.657053
$455$	−4.00000			−0.187523
$456$		0			0
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	0.828807	−	0.559534i	$-0.189020\pi$
$457$	−1.50000	−	2.59808i	−0.0701670	−	0.121533i	−0.898974	+	0.438001i	$0.855687\pi$
$458$	1.00000			0.0467269
$459$		0			0
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$		0			0
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	0.999916	+	0.0129968i	$0.00413714\pi$
$463$	11.0000	+	19.0526i	0.511213	+	0.885448i	−0.488702	+	0.872451i	$0.662530\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$	10.0000	−	17.3205i	0.461757	−	0.799787i
$470$	6.00000			0.276759
$471$		0			0
$472$	−6.00000	+	10.3923i	−0.276172	+	0.478345i
$473$	−4.00000			−0.183920
$474$		0			0
$475$	24.0000			1.10120
$476$	3.00000	+	5.19615i	0.137505	+	0.238165i
$477$	−3.00000	−	5.19615i	−0.137361	−	0.237915i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		0			0
$481$	−1.00000	−	12.1244i	−0.0455961	−	0.552823i
$482$	14.0000			0.637683
$483$		0			0
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$	−3.50000	−	6.06218i	−0.158927	−	0.275269i
$486$		0			0
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$	1.50000	+	2.59808i	0.0679018	+	0.117609i
$489$		0			0
$490$	1.50000	−	2.59808i	0.0677631	−	0.117369i
$491$	2.00000			0.0902587			0.0451294	−	0.998981i	$-0.485630\pi$
$491$	2.00000			0.0902587			0.0451294	+	0.998981i	$0.485630\pi$
$492$		0			0
$493$	−13.5000	+	23.3827i	−0.608009	+	1.05310i
$494$	−6.00000	−	10.3923i	−0.269953	−	0.467572i
$495$	6.00000			0.269680
$496$	−5.00000	+	8.66025i	−0.224507	+	0.388857i
$497$	−6.00000	+	10.3923i	−0.269137	+	0.466159i
$498$		0			0
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	0.994074	−	0.108705i	$-0.0346705\pi$
$499$	9.00000	+	15.5885i	0.402895	+	0.697835i	−0.591179	+	0.806541i	$0.701337\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	7.00000	−	12.1244i	0.312425	−	0.541136i
$503$	13.0000	−	22.5167i	0.579641	−	1.00397i	−0.415879	−	0.909420i	$-0.636526\pi$
$503$	13.0000	−	22.5167i	0.579641	−	1.00397i	0.995520	−	0.0945483i	$-0.0301407\pi$
$504$	18.0000			0.801784
$505$	1.50000	+	2.59808i	0.0667491	+	0.115613i
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$		0			0
$508$	8.00000			0.354943
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	−0.777973	−	0.628297i	$-0.783752\pi$
$509$	3.50000	−	6.06218i	0.155135	−	0.268701i	0.933108	+	0.359596i	$0.117085\pi$
$510$		0			0
$511$	10.0000	+	17.3205i	0.442374	+	0.766214i
$512$	−11.0000			−0.486136
$513$		0			0
$514$	10.5000	+	18.1865i	0.463135	+	0.802174i
$515$	−3.00000	−	5.19615i	−0.132196	−	0.228970i
$516$		0			0
$517$	−12.0000			−0.527759
$518$	−11.0000	−	5.19615i	−0.483312	−	0.228306i
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.799370	+	0.600839i	$0.205167\pi$
$521$	21.0000	+	36.3731i	0.920027	+	1.59353i	0.120656	+	0.992694i	$0.461500\pi$
$522$	13.5000	+	23.3827i	0.590879	+	1.02343i
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	−4.00000	−	6.92820i	−0.174908	−	0.302949i	−0.940129	+	0.340818i	$0.889296\pi$
$524$		0			0
$525$		0			0
$526$	4.00000			0.174408
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		0			0
$529$	−7.00000			−0.304348
$530$	1.00000	−	1.73205i	0.0434372	−	0.0752355i
$531$	−6.00000	−	10.3923i	−0.260378	−	0.450988i
$532$	12.0000			0.520266
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	9.00000	−	15.5885i	0.389104	−	0.673948i
$536$	−15.0000	−	25.9808i	−0.647901	−	1.12220i
$537$		0			0
$538$	−9.00000	+	15.5885i	−0.388018	+	0.672066i
$539$	−3.00000	+	5.19615i	−0.129219	+	0.223814i
$540$		0			0
$541$	17.0000			0.730887			0.365444	−	0.930834i	$-0.380917\pi$
$541$	17.0000			0.730887			0.365444	+	0.930834i	$0.380917\pi$
$542$	−7.00000	−	12.1244i	−0.300676	−	0.520786i
$543$		0			0
$544$	15.0000			0.643120
$545$	5.00000			0.214176
$546$		0			0
$547$	2.00000			0.0855138			0.0427569	−	0.999086i	$-0.486386\pi$
$547$	2.00000			0.0855138			0.0427569	+	0.999086i	$0.486386\pi$
$548$	−4.50000	−	7.79423i	−0.192230	−	0.332953i
$549$	−3.00000			−0.128037
$550$	−4.00000	−	6.92820i	−0.170561	−	0.295420i
$551$	27.0000	+	46.7654i	1.15024	+	1.99227i
$552$		0			0
$553$	−10.0000	+	17.3205i	−0.425243	+	0.736543i
$554$	−3.00000			−0.127458
$555$		0			0
$556$	−16.0000			−0.678551
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	0.269642	+	0.962961i	$0.413095\pi$
$557$	−16.5000	+	28.5788i	−0.699127	+	1.21092i	−0.968769	+	0.247964i	$0.920239\pi$
$558$	−15.0000	−	25.9808i	−0.635001	−	1.09985i
$559$	2.00000	+	3.46410i	0.0845910	+	0.146516i
$560$	1.00000	+	1.73205i	0.0422577	+	0.0731925i
$561$		0			0
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		0			0
$565$	6.00000			0.252422
$566$	−14.0000			−0.588464
$567$	−9.00000	+	15.5885i	−0.377964	+	0.654654i
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	3.00000			0.125767			0.0628833	−	0.998021i	$-0.479970\pi$
$569$	3.00000			0.125767			0.0628833	+	0.998021i	$0.479970\pi$
$570$		0			0
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.122292	−	0.992494i	$-0.460975\pi$
$571$	22.0000	−	38.1051i	0.920671	−	1.59465i	0.798379	−	0.602155i	$-0.205691\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$		0			0
$574$	9.00000	+	15.5885i	0.375653	+	0.650650i
$575$	−8.00000	+	13.8564i	−0.333623	+	0.577852i
$576$	10.5000	−	18.1865i	0.437500	−	0.757772i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	−8.00000			−0.332756
$579$		0			0
$580$	4.50000	−	7.79423i	0.186852	−	0.323638i
$581$	−24.0000			−0.995688
$582$		0			0
$583$	−2.00000	+	3.46410i	−0.0828315	+	0.143468i
$584$	30.0000			1.24141
$585$	−3.00000	−	5.19615i	−0.124035	−	0.214834i
$586$	−23.0000			−0.950121
$587$	−20.0000	−	34.6410i	−0.825488	−	1.42979i	−0.901546	−	0.432684i	$-0.857566\pi$
$587$	−20.0000	−	34.6410i	−0.825488	−	1.42979i	0.0760572	−	0.997103i	$-0.475767\pi$
$588$		0			0
$589$	−30.0000	−	51.9615i	−1.23613	−	2.14104i
$590$	2.00000	−	3.46410i	0.0823387	−	0.142615i
$591$		0			0
$592$	−5.00000	+	3.46410i	−0.205499	+	0.142374i
$593$	−29.0000			−1.19089			−0.595444	−	0.803397i	$-0.703024\pi$
$593$	−29.0000			−1.19089			−0.595444	+	0.803397i	$0.703024\pi$
$594$		0			0
$595$	−3.00000	−	5.19615i	−0.122988	−	0.213021i
$596$	−5.50000	−	9.52628i	−0.225289	−	0.390212i
$597$		0			0
$598$	8.00000			0.327144
$599$	19.0000	+	32.9090i	0.776319	+	1.34462i	0.934050	+	0.357142i	$0.116249\pi$
$599$	19.0000	+	32.9090i	0.776319	+	1.34462i	−0.157731	+	0.987482i	$0.550418\pi$
$600$		0			0
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−11.5000	+	19.9186i	−0.469095	+	0.812496i	0.530281	+	0.847822i	$0.322086\pi$
$602$	4.00000			0.163028
$603$	30.0000			1.22169
$604$	2.00000	−	3.46410i	0.0813788	−	0.140952i
$605$	3.50000	+	6.06218i	0.142295	+	0.246463i
$606$		0			0
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	−0.688274	−	0.725450i	$-0.741632\pi$
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	0.972396	+	0.233338i	$0.0749648\pi$
$608$	15.0000	−	25.9808i	0.608330	−	1.05366i
$609$		0			0
$610$	−0.500000	−	0.866025i	−0.0202444	−	0.0350643i
$611$	6.00000	+	10.3923i	0.242734	+	0.420428i
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	−16.5000	+	28.5788i	−0.666429	+	1.15429i	0.312467	+	0.949929i	$0.398845\pi$
$613$	−16.5000	+	28.5788i	−0.666429	+	1.15429i	−0.978896	+	0.204360i	$0.934489\pi$
$614$	7.00000	−	12.1244i	0.282497	−	0.489299i
$615$		0			0
$616$	−6.00000	−	10.3923i	−0.241747	−	0.418718i
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	−0.555056	−	0.831813i	$-0.687303\pi$
$617$	11.0000	−	19.0526i	0.442843	−	0.767027i	0.997899	+	0.0647859i	$0.0206365\pi$
$618$		0			0
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$	−5.00000	+	8.66025i	−0.200805	+	0.347804i
$621$		0			0
$622$	9.00000	+	15.5885i	0.360867	+	0.625040i
$623$	14.0000			0.560898
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	−3.50000	−	6.06218i	−0.139888	−	0.242293i
$627$		0			0
$628$	−17.0000			−0.678374
$629$	15.0000	−	10.3923i	0.598089	−	0.414368i
$630$	−6.00000			−0.239046
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	−0.993491	−	0.113913i	$-0.963661\pi$
$631$	−10.0000	+	17.3205i	−0.398094	+	0.689519i	0.595397	+	0.803432i	$0.296995\pi$
$632$	15.0000	+	25.9808i	0.596668	+	1.03346i
$633$		0			0
$634$	−0.500000	−	0.866025i	−0.0198575	−	0.0343943i
$635$	−8.00000			−0.317470
$636$		0			0
$637$	6.00000			0.237729
$638$	9.00000	−	15.5885i	0.356313	−	0.617153i
$639$	−18.0000			−0.712069
$640$	−3.00000			−0.118585
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	−0.225876	−	0.974156i	$-0.572524\pi$
$641$	18.5000	−	32.0429i	0.730706	−	1.26562i	0.956582	−	0.291464i	$-0.0941423\pi$
$642$		0			0
$643$	14.0000			0.552106			0.276053	−	0.961142i	$-0.410973\pi$
$643$	14.0000			0.552106			0.276053	+	0.961142i	$0.410973\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$		0			0
$646$	9.00000	−	15.5885i	0.354100	−	0.613320i
$647$	7.00000	+	12.1244i	0.275198	+	0.476658i	0.970185	−	0.242365i	$-0.0779231\pi$
$647$	7.00000	+	12.1244i	0.275198	+	0.476658i	−0.694987	+	0.719023i	$0.744590\pi$
$648$	13.5000	+	23.3827i	0.530330	+	0.918559i
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	−4.00000	+	6.92820i	−0.156893	+	0.271746i
$651$		0			0
$652$	6.00000			0.234978
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	0.941248	+	0.337715i	$0.109654\pi$
$653$	19.5000	+	33.7750i	0.763094	+	1.32172i	−0.178154	+	0.984003i	$0.557013\pi$
$654$		0			0
$655$		0			0
$656$	9.00000			0.351391
$657$	−15.0000	+	25.9808i	−0.585206	+	1.01361i
$658$	12.0000			0.467809
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	0.926030	−	0.377450i	$-0.123199\pi$
$661$	3.50000	+	6.06218i	0.136134	+	0.235791i	−0.789896	+	0.613241i	$0.789865\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	−18.0000	+	31.1769i	−0.698535	+	1.20990i
$665$	−12.0000			−0.465340
$666$	−1.50000	−	18.1865i	−0.0581238	−	0.704714i
$667$	−36.0000			−1.39393
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$		0			0
$670$	5.00000	+	8.66025i	0.193167	+	0.334575i
$671$	1.00000	+	1.73205i	0.0386046	+	0.0668651i
$672$		0			0
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	0.802395	−	0.596794i	$-0.203559\pi$
$673$	−3.00000	−	5.19615i	−0.115642	−	0.200297i	−0.918036	+	0.396497i	$0.870226\pi$
$674$	−1.00000			−0.0385186
$675$		0			0
$676$	9.00000			0.346154
$677$	13.0000			0.499631			0.249815	−	0.968294i	$-0.419630\pi$
$677$	13.0000			0.499631			0.249815	+	0.968294i	$0.419630\pi$
$678$		0			0
$679$	−7.00000	−	12.1244i	−0.268635	−	0.465290i
$680$	−9.00000			−0.345134
$681$		0			0
$682$	−10.0000	+	17.3205i	−0.382920	+	0.663237i
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	−0.422195	−	0.906505i	$-0.638740\pi$
$683$	15.0000	−	25.9808i	0.573959	−	0.994126i	0.996154	−	0.0876211i	$-0.0279265\pi$
$684$	9.00000	+	15.5885i	0.344124	+	0.596040i
$685$	4.50000	+	7.79423i	0.171936	+	0.297802i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$		0			0
$688$	1.00000	−	1.73205i	0.0381246	−	0.0660338i
$689$	4.00000			0.152388
$690$		0			0
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	−0.701609	−	0.712562i	$-0.747535\pi$
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	0.967901	+	0.251330i	$0.0808679\pi$
$692$	−21.0000			−0.798300
$693$	12.0000			0.455842
$694$	8.00000	−	13.8564i	0.303676	−	0.525982i
$695$	16.0000			0.606915
$696$		0			0
$697$	−27.0000			−1.02270
$698$	−4.50000	−	7.79423i	−0.170328	−	0.295016i
$699$		0			0
$700$	−4.00000	−	6.92820i	−0.151186	−	0.261861i
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	−0.917102	−	0.398652i	$-0.869478\pi$
$701$	−3.00000	+	5.19615i	−0.113308	+	0.196256i	0.803794	+	0.594908i	$0.202811\pi$
$702$		0			0
$703$	−3.00000	−	36.3731i	−0.113147	−	1.37184i
$704$	−14.0000			−0.527645
$705$		0			0
$706$	12.5000	+	21.6506i	0.470444	+	0.814832i
$707$	3.00000	+	5.19615i	0.112827	+	0.195421i
$708$		0			0
$709$	10.0000			0.375558			0.187779	−	0.982211i	$-0.439871\pi$
$709$	10.0000			0.375558			0.187779	+	0.982211i	$0.439871\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$	−30.0000			−1.12509
$712$	10.5000	−	18.1865i	0.393504	−	0.681569i
$713$	40.0000			1.49801
$714$		0			0
$715$	−2.00000	+	3.46410i	−0.0747958	+	0.129550i
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$		0			0
$718$	−12.0000	+	20.7846i	−0.447836	+	0.775675i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	−6.00000	−	10.3923i	−0.223452	−	0.387030i
$722$	−8.50000	−	14.7224i	−0.316337	−	0.547912i
$723$		0			0
$724$	2.50000	−	4.33013i	0.0929118	−	0.160928i
$725$	18.0000	−	31.1769i	0.668503	−	1.15788i
$726$		0			0
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	−0.951694	−	0.307049i	$-0.900659\pi$
$727$	−20.0000	−	34.6410i	−0.741759	−	1.28476i	0.209935	−	0.977715i	$-0.432675\pi$
$728$	−6.00000	+	10.3923i	−0.222375	+	0.385164i
$729$	−27.0000			−1.00000
$730$	−10.0000			−0.370117
$731$	−3.00000	+	5.19615i	−0.110959	+	0.192187i
$732$		0			0
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	0.588177	−	0.808732i	$-0.299846\pi$
$733$	−11.0000	−	19.0526i	−0.406294	−	0.703722i	−0.994471	+	0.105010i	$0.966513\pi$
$734$	−28.0000			−1.03350
$735$		0			0
$736$	10.0000	+	17.3205i	0.368605	+	0.638442i
$737$	−10.0000	−	17.3205i	−0.368355	−	0.638009i
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	12.0000			0.441427			0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000			0.441427			0.220714	+	0.975339i	$0.429161\pi$
$740$	−5.00000	+	3.46410i	−0.183804	+	0.127343i
$741$		0			0
$742$	2.00000	−	3.46410i	0.0734223	−	0.127171i
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$		0			0
$745$	5.50000	+	9.52628i	0.201504	+	0.349016i
$746$	17.0000			0.622414
$747$	−18.0000	−	31.1769i	−0.658586	−	1.14070i
$748$	6.00000			0.219382
$749$	18.0000	−	31.1769i	0.657706	−	1.13918i
$750$		0			0
$751$	10.0000			0.364905			0.182453	−	0.983215i	$-0.441596\pi$
$751$	10.0000			0.364905			0.182453	+	0.983215i	$0.441596\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	−18.0000			−0.655521
$755$	−2.00000	+	3.46410i	−0.0727875	+	0.126072i
$756$		0			0
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$		0			0
$760$	−9.00000	+	15.5885i	−0.326464	+	0.565453i
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	−0.922464	−	0.386082i	$-0.873828\pi$
$761$	−3.50000	+	6.06218i	−0.126875	+	0.219754i	0.795589	+	0.605836i	$0.207161\pi$
$762$		0			0
$763$	10.0000			0.362024
$764$	−2.00000	−	3.46410i	−0.0723575	−	0.125327i
$765$	4.50000	−	7.79423i	0.162698	−	0.281801i
$766$	−34.0000			−1.22847
$767$	8.00000			0.288863
$768$		0			0
$769$	14.0000			0.504853			0.252426	−	0.967616i	$-0.418771\pi$
$769$	14.0000			0.504853			0.252426	+	0.967616i	$0.418771\pi$
$770$	2.00000	+	3.46410i	0.0720750	+	0.124838i
$771$		0			0
$772$	9.50000	+	16.4545i	0.341912	+	0.592210i
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	0.613062	−	0.790034i	$-0.289937\pi$
$773$	−10.5000	−	18.1865i	−0.377659	−	0.654124i	−0.990721	+	0.135910i	$0.956604\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	−20.0000	+	34.6410i	−0.718421	+	1.24434i
$776$	−21.0000			−0.753856
$777$		0			0
$778$	25.0000			0.896293
$779$	−27.0000	+	46.7654i	−0.967375	+	1.67554i
$780$		0			0
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	6.00000	+	10.3923i	0.214560	+	0.371628i
$783$		0			0
$784$	−1.50000	−	2.59808i	−0.0535714	−	0.0927884i
$785$	17.0000			0.606756
$786$		0			0
$787$	4.00000			0.142585			0.0712923	−	0.997455i	$-0.477288\pi$
$787$	4.00000			0.142585			0.0712923	+	0.997455i	$0.477288\pi$
$788$	15.0000			0.534353
$789$		0			0
$790$	−5.00000	−	8.66025i	−0.177892	−	0.308118i
$791$	12.0000			0.426671
$792$	9.00000	−	15.5885i	0.319801	−	0.553912i
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	−6.50000	+	11.2583i	−0.230676	+	0.399543i
$795$		0			0
$796$	−5.00000	−	8.66025i	−0.177220	−	0.306955i
$797$	13.0000	−	22.5167i	0.460484	−	0.797581i	−0.538501	−	0.842625i	$-0.681009\pi$
$797$	13.0000	−	22.5167i	0.460484	−	0.797581i	0.998985	+	0.0450436i	$0.0143427\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	−20.0000			−0.707107
$801$	10.5000	+	18.1865i	0.370999	+	0.642590i
$802$	9.00000	−	15.5885i	0.317801	−	0.550448i
$803$	20.0000			0.705785
$804$		0			0
$805$	4.00000	−	6.92820i	0.140981	−	0.244187i
$806$	20.0000			0.704470
$807$		0			0
$808$	9.00000			0.316619
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	0.940435	−	0.339975i	$-0.110418\pi$
$809$	5.00000	+	8.66025i	0.175791	+	0.304478i	−0.764644	+	0.644453i	$0.777085\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	8.00000	+	13.8564i	0.280918	+	0.486564i	0.971611	−	0.236584i	$-0.0760278\pi$
$811$	8.00000	+	13.8564i	0.280918	+	0.486564i	−0.690693	+	0.723148i	$0.742694\pi$
$812$	9.00000	−	15.5885i	0.315838	−	0.547048i
$813$		0			0
$814$	−10.0000	+	6.92820i	−0.350500	+	0.242833i
$815$	−6.00000			−0.210171
$816$		0			0
$817$	6.00000	+	10.3923i	0.209913	+	0.363581i
$818$	12.5000	+	21.6506i	0.437052	+	0.756997i
$819$	−6.00000	−	10.3923i	−0.209657	−	0.363137i
$820$	9.00000			0.314294
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	0.765487	−	0.643451i	$-0.222498\pi$
$821$	−5.00000	−	8.66025i	−0.174501	−	0.302245i	−0.939989	+	0.341206i	$0.889165\pi$
$822$		0			0
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−18.0000			−0.627060
$825$		0			0
$826$	4.00000	−	6.92820i	0.139178	−	0.241063i
$827$	4.00000	+	6.92820i	0.139094	+	0.240917i	0.927154	−	0.374681i	$-0.122248\pi$
$827$	4.00000	+	6.92820i	0.139094	+	0.240917i	−0.788060	+	0.615598i	$0.788914\pi$
$828$	−12.0000			−0.417029
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	7.00000	+	12.1244i	0.242681	+	0.420336i
$833$	4.50000	+	7.79423i	0.155916	+	0.270054i
$834$		0			0
$835$	−6.00000	+	10.3923i	−0.207639	+	0.359641i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$		0			0
$838$	13.0000	+	22.5167i	0.449078	+	0.777825i
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	−0.281205	−	0.959648i	$-0.590734\pi$
$839$	20.0000	−	34.6410i	0.690477	−	1.19594i	0.971682	−	0.236293i	$-0.0759325\pi$
$840$		0			0
$841$	52.0000			1.79310
$842$	−4.50000	+	7.79423i	−0.155080	+	0.268607i
$843$		0			0
$844$	1.00000	+	1.73205i	0.0344214	+	0.0596196i
$845$	−9.00000			−0.309609
$846$	9.00000	+	15.5885i	0.309426	+	0.535942i
$847$	7.00000	+	12.1244i	0.240523	+	0.416598i
$848$	−1.00000	−	1.73205i	−0.0343401	−	0.0594789i
$849$		0			0
$850$	−12.0000			−0.411597
$851$	22.0000	+	10.3923i	0.754150	+	0.356244i
$852$		0			0
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	−0.656294	−	0.754505i	$-0.727877\pi$
$853$	9.50000	−	16.4545i	0.325274	−	0.563391i	0.981568	+	0.191115i	$0.0612102\pi$
$854$	−1.00000	−	1.73205i	−0.0342193	−	0.0592696i
$855$	−9.00000	−	15.5885i	−0.307794	−	0.533114i
$856$	−27.0000	−	46.7654i	−0.922841	−	1.59841i
$857$	−45.0000			−1.53717			−0.768585	−	0.639747i	$-0.779039\pi$
$857$	−45.0000			−1.53717			−0.768585	+	0.639747i	$0.779039\pi$
$858$		0			0
$859$	−50.0000			−1.70598			−0.852989	−	0.521929i	$-0.825213\pi$
$859$	−50.0000			−1.70598			−0.852989	+	0.521929i	$0.825213\pi$
$860$	1.00000	−	1.73205i	0.0340997	−	0.0590624i
$861$		0			0
$862$	18.0000			0.613082
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	0.378052	+	0.925785i	$0.376594\pi$
$863$	−18.0000	+	31.1769i	−0.612727	+	1.06127i	−0.990779	+	0.135490i	$0.956739\pi$
$864$		0			0
$865$	21.0000			0.714021
$866$	10.5000	−	18.1865i	0.356805	−	0.618004i
$867$		0			0
$868$	−10.0000	+	17.3205i	−0.339422	+	0.587896i
$869$	10.0000	+	17.3205i	0.339227	+	0.587558i
$870$		0			0
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$	7.50000	−	12.9904i	0.253982	−	0.439910i
$873$	10.5000	−	18.1865i	0.355371	−	0.615521i
$874$	24.0000			0.811812
$875$	9.00000	+	15.5885i	0.304256	+	0.526986i
$876$		0			0
$877$	17.0000			0.574049			0.287025	−	0.957923i	$-0.407334\pi$
$877$	17.0000			0.574049			0.287025	+	0.957923i	$0.407334\pi$
$878$	−20.0000			−0.674967
$879$		0			0
$880$	2.00000			0.0674200
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	0.660438	−	0.750881i	$-0.270371\pi$
$881$	−9.50000	−	16.4545i	−0.320063	−	0.554366i	−0.980501	+	0.196515i	$0.937037\pi$
$882$	9.00000			0.303046
$883$	−24.0000	−	41.5692i	−0.807664	−	1.39892i	−0.914478	−	0.404637i	$-0.867398\pi$
$883$	−24.0000	−	41.5692i	−0.807664	−	1.39892i	0.106813	−	0.994279i	$-0.465935\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$		0			0
$886$	16.0000	−	27.7128i	0.537531	−	0.931030i
$887$	−8.00000			−0.268614			−0.134307	−	0.990940i	$-0.542881\pi$
$887$	−8.00000			−0.268614			−0.134307	+	0.990940i	$0.542881\pi$
$888$		0			0
$889$	−16.0000			−0.536623
$890$	−3.50000	+	6.06218i	−0.117320	+	0.203205i
$891$	9.00000	+	15.5885i	0.301511	+	0.522233i
$892$	14.0000	+	24.2487i	0.468755	+	0.811907i
$893$	18.0000	+	31.1769i	0.602347	+	1.04330i
$894$		0			0
$895$	−6.00000	−	10.3923i	−0.200558	−	0.347376i
$896$	−6.00000			−0.200446
$897$		0			0
$898$	6.00000			0.200223
$899$	−90.0000			−3.00167
$900$	6.00000	−	10.3923i	0.200000	−	0.346410i
$901$	3.00000	+	5.19615i	0.0999445	+	0.173109i
$902$	18.0000			0.599334
$903$		0			0
$904$	9.00000	−	15.5885i	0.299336	−	0.518464i
$905$	−2.50000	+	4.33013i	−0.0831028	+	0.143938i
$906$		0			0
$907$	19.0000	+	32.9090i	0.630885	+	1.09272i	0.987371	+	0.158424i	$0.0506412\pi$
$907$	19.0000	+	32.9090i	0.630885	+	1.09272i	−0.356487	+	0.934300i	$0.616025\pi$
$908$	7.00000	−	12.1244i	0.232303	−	0.402361i
$909$	−4.50000	+	7.79423i	−0.149256	+	0.258518i
$910$	2.00000	−	3.46410i	0.0662994	−	0.114834i
$911$	−40.0000			−1.32526			−0.662630	−	0.748947i	$-0.730560\pi$
$911$	−40.0000			−1.32526			−0.662630	+	0.748947i	$0.730560\pi$
$912$		0			0
$913$	−12.0000	+	20.7846i	−0.397142	+	0.687870i
$914$	3.00000			0.0992312
$915$		0			0
$916$	0.500000	−	0.866025i	0.0165205	−	0.0286143i
$917$		0			0
$918$		0			0
$919$	−4.00000			−0.131948			−0.0659739	−	0.997821i	$-0.521015\pi$
$919$	−4.00000			−0.131948			−0.0659739	+	0.997821i	$0.521015\pi$
$920$	−6.00000	−	10.3923i	−0.197814	−	0.342624i
$921$		0			0
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	6.00000	−	10.3923i	0.197492	−	0.342067i
$924$		0			0
$925$	−20.0000	+	13.8564i	−0.657596	+	0.455596i
$926$	−22.0000			−0.722965
$927$	9.00000	−	15.5885i	0.295599	−	0.511992i
$928$	−22.5000	−	38.9711i	−0.738599	−	1.27929i
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	0.716364	−	0.697727i	$-0.245805\pi$
$929$	−7.50000	−	12.9904i	−0.246067	−	0.426201i	−0.962431	+	0.271526i	$0.912472\pi$
$930$		0			0
$931$	18.0000			0.589926
$932$	1.50000	+	2.59808i	0.0491341	+	0.0851028i
$933$		0			0
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	−6.00000			−0.196221
$936$	−18.0000			−0.588348
$937$	2.50000	−	4.33013i	0.0816714	−	0.141459i	−0.822297	−	0.569059i	$-0.807308\pi$
$937$	2.50000	−	4.33013i	0.0816714	−	0.141459i	0.903968	+	0.427600i	$0.140641\pi$
$938$	10.0000	+	17.3205i	0.326512	+	0.565535i
$939$		0			0
$940$	3.00000	−	5.19615i	0.0978492	−	0.169480i
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	−0.970661	−	0.240453i	$-0.922704\pi$
$941$	−8.50000	+	14.7224i	−0.277092	+	0.479938i	0.693569	+	0.720390i	$0.256037\pi$
$942$		0			0
$943$	−18.0000	−	31.1769i	−0.586161	−	1.01526i
$944$	−2.00000	−	3.46410i	−0.0650945	−	0.112747i
$945$		0			0
$946$	2.00000	−	3.46410i	0.0650256	−	0.112628i
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	0.409964	+	0.912102i	$0.365541\pi$
$947$	−18.0000	+	31.1769i	−0.584921	+	1.01311i	−0.994885	+	0.101012i	$0.967792\pi$
$948$		0			0
$949$	−10.0000	−	17.3205i	−0.324614	−	0.562247i
$950$	−12.0000	+	20.7846i	−0.389331	+	0.674342i
$951$		0			0
$952$	−18.0000			−0.583383
$953$	25.0000	−	43.3013i	0.809829	−	1.40267i	−0.103152	−	0.994666i	$-0.532893\pi$
$953$	25.0000	−	43.3013i	0.809829	−	1.40267i	0.912982	−	0.408000i	$-0.133774\pi$
$954$	6.00000			0.194257
$955$	2.00000	+	3.46410i	0.0647185	+	0.112096i
$956$	−6.00000			−0.194054
$957$		0			0
$958$	2.00000	+	3.46410i	0.0646171	+	0.111920i
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$		0			0
$961$	69.0000			2.22581
$962$	11.0000	+	5.19615i	0.354654	+	0.167531i
$963$	54.0000			1.74013
$964$	7.00000	−	12.1244i	0.225455	−	0.390499i
$965$	−9.50000	−	16.4545i	−0.305816	−	0.529689i
$966$		0			0
$967$	4.00000	+	6.92820i	0.128631	+	0.222796i	0.923147	−	0.384448i	$-0.125608\pi$
$967$	4.00000	+	6.92820i	0.128631	+	0.222796i	−0.794515	+	0.607244i	$0.792275\pi$
$968$	21.0000			0.674966
$969$		0			0
$970$	7.00000			0.224756
$971$	−14.0000	+	24.2487i	−0.449281	+	0.778178i	−0.998339	−	0.0576061i	$-0.981653\pi$
$971$	−14.0000	+	24.2487i	−0.449281	+	0.778178i	0.549058	+	0.835784i	$0.314987\pi$
$972$		0			0
$973$	32.0000			1.02587
$974$	−6.00000	+	10.3923i	−0.192252	+	0.332991i
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	−0.849586	−	0.527451i	$-0.823148\pi$
$977$	1.00000	−	1.73205i	0.0319928	−	0.0554132i	0.881579	+	0.472037i	$0.156481\pi$
$978$		0			0
$979$	7.00000	−	12.1244i	0.223721	−	0.387496i
$980$	−1.50000	−	2.59808i	−0.0479157	−	0.0829925i
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$	−1.00000	+	1.73205i	−0.0319113	+	0.0552720i
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	−0.686050	−	0.727554i	$-0.740657\pi$
$983$	9.00000	−	15.5885i	0.287055	−	0.497195i	0.973106	+	0.230360i	$0.0739903\pi$
$984$		0			0
$985$	−15.0000			−0.477940
$986$	−13.5000	−	23.3827i	−0.429928	−	0.744656i
$987$		0			0
$988$	−12.0000			−0.381771
$989$	−8.00000			−0.254385
$990$	−3.00000	+	5.19615i	−0.0953463	+	0.165145i
$991$	−30.0000			−0.952981			−0.476491	−	0.879180i	$-0.658091\pi$
$991$	−30.0000			−0.952981			−0.476491	+	0.879180i	$0.658091\pi$
$992$	25.0000	+	43.3013i	0.793751	+	1.37482i
$993$		0			0
$994$	−6.00000	−	10.3923i	−0.190308	−	0.329624i
$995$	5.00000	+	8.66025i	0.158511	+	0.274549i
$996$		0			0
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	−0.687584	−	0.726105i	$-0.741329\pi$
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	0.972617	+	0.232413i	$0.0746622\pi$
$998$	−18.0000			−0.569780
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.c.a.10.1	✓	2
3.2	odd	2		333.2.f.a.10.1		2
4.3	odd	2		592.2.i.c.417.1		2
5.2	odd	4		925.2.o.a.824.1		4
5.3	odd	4		925.2.o.a.824.2		4
5.4	even	2		925.2.e.a.676.1		2
37.10	even	3		1369.2.a.d.1.1		1
37.14	odd	12		1369.2.b.b.1368.2		2
37.23	odd	12		1369.2.b.b.1368.1		2
37.26	even	3	inner	37.2.c.a.26.1	yes	2
37.27	even	6		1369.2.a.b.1.1		1
111.26	odd	6		333.2.f.a.100.1		2
148.63	odd	6		592.2.i.c.433.1		2
185.63	odd	12		925.2.o.a.174.1		4
185.137	odd	12		925.2.o.a.174.2		4
185.174	even	6		925.2.e.a.26.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.c.a.10.1	✓	2	1.1	even	1	trivial
37.2.c.a.26.1	yes	2	37.26	even	3	inner
333.2.f.a.10.1		2	3.2	odd	2
333.2.f.a.100.1		2	111.26	odd	6
592.2.i.c.417.1		2	4.3	odd	2
592.2.i.c.433.1		2	148.63	odd	6
925.2.e.a.26.1		2	185.174	even	6
925.2.e.a.676.1		2	5.4	even	2
925.2.o.a.174.1		4	185.63	odd	12
925.2.o.a.174.2		4	185.137	odd	12
925.2.o.a.824.1		4	5.2	odd	4
925.2.o.a.824.2		4	5.3	odd	4
1369.2.a.b.1.1		1	37.27	even	6
1369.2.a.d.1.1		1	37.10	even	3
1369.2.b.b.1368.1		2	37.23	odd	12
1369.2.b.b.1368.2		2	37.14	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-1.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} -2.00000 q^{11} +(1.00000 + 1.73205i) q^{13} +2.00000 q^{14} +(0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 + 2.59808i) q^{18} +(3.00000 + 5.19615i) q^{19} +(0.500000 - 0.866025i) q^{20} +(1.00000 - 1.73205i) q^{22} -4.00000 q^{23} +(2.00000 - 3.46410i) q^{25} -2.00000 q^{26} +(1.00000 - 1.73205i) q^{28} +9.00000 q^{29} -10.0000 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.50000 - 2.59808i) q^{34} +(-1.00000 + 1.73205i) q^{35} +3.00000 q^{36} +(-5.50000 - 2.59808i) q^{37} -6.00000 q^{38} +(1.50000 + 2.59808i) q^{40} +(4.50000 + 7.79423i) q^{41} +2.00000 q^{43} +(-1.00000 - 1.73205i) q^{44} -3.00000 q^{45} +(2.00000 - 3.46410i) q^{46} +6.00000 q^{47} +(1.50000 - 2.59808i) q^{49} +(2.00000 + 3.46410i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(1.00000 - 1.73205i) q^{53} +(1.00000 + 1.73205i) q^{55} +(3.00000 + 5.19615i) q^{56} +(-4.50000 + 7.79423i) q^{58} +(2.00000 - 3.46410i) q^{59} +(-0.500000 - 0.866025i) q^{61} +(5.00000 - 8.66025i) q^{62} -6.00000 q^{63} +7.00000 q^{64} +(1.00000 - 1.73205i) q^{65} +(5.00000 + 8.66025i) q^{67} -3.00000 q^{68} +(-1.00000 - 1.73205i) q^{70} +(-3.00000 - 5.19615i) q^{71} +(-4.50000 + 7.79423i) q^{72} -10.0000 q^{73} +(5.00000 - 3.46410i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(2.00000 + 3.46410i) q^{77} +(-5.00000 - 8.66025i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 - 10.3923i) q^{83} +3.00000 q^{85} +(-1.00000 + 1.73205i) q^{86} +6.00000 q^{88} +(-3.50000 + 6.06218i) q^{89} +(1.50000 - 2.59808i) q^{90} +(2.00000 - 3.46410i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(3.00000 - 5.19615i) q^{95} +7.00000 q^{97} +(1.50000 + 2.59808i) q^{98} +(-3.00000 + 5.19615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9	\( 2 q - q^{2} + q^{4} - q^{5} - 2 q^{7} - 6 q^{8} + 3 q^{9} + 2 q^{10} - 4 q^{11} + 2 q^{13} + 4 q^{14} + q^{16} - 3 q^{17} + 3 q^{18} + 6 q^{19} + q^{20} + 2 q^{22} - 8 q^{23} + 4 q^{25} - 4 q^{26} + 2 q^{28} + 18 q^{29} - 20 q^{31} - 5 q^{32} - 3 q^{34} - 2 q^{35} + 6 q^{36} - 11 q^{37} - 12 q^{38} + 3 q^{40} + 9 q^{41} + 4 q^{43} - 2 q^{44} - 6 q^{45} + 4 q^{46} + 12 q^{47} + 3 q^{49} + 4 q^{50} - 2 q^{52} + 2 q^{53} + 2 q^{55} + 6 q^{56} - 9 q^{58} + 4 q^{59} - q^{61} + 10 q^{62} - 12 q^{63} + 14 q^{64} + 2 q^{65} + 10 q^{67} - 6 q^{68} - 2 q^{70} - 6 q^{71} - 9 q^{72} - 20 q^{73} + 10 q^{74} - 6 q^{76} + 4 q^{77} - 10 q^{79} - 2 q^{80} - 9 q^{81} - 18 q^{82} + 12 q^{83} + 6 q^{85} - 2 q^{86} + 12 q^{88} - 7 q^{89} + 3 q^{90} + 4 q^{91} - 4 q^{92} - 6 q^{94} + 6 q^{95} + 14 q^{97} + 3 q^{98} - 6 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^4 - q^5 - 2 * q^7 - 6 * q^8 + 3 * q^9 + 2 * q^10 - 4 * q^11 + 2 * q^13 + 4 * q^14 + q^16 - 3 * q^17 + 3 * q^18 + 6 * q^19 + q^20 + 2 * q^22 - 8 * q^23 + 4 * q^25 - 4 * q^26 + 2 * q^28 + 18 * q^29 - 20 * q^31 - 5 * q^32 - 3 * q^34 - 2 * q^35 + 6 * q^36 - 11 * q^37 - 12 * q^38 + 3 * q^40 + 9 * q^41 + 4 * q^43 - 2 * q^44 - 6 * q^45 + 4 * q^46 + 12 * q^47 + 3 * q^49 + 4 * q^50 - 2 * q^52 + 2 * q^53 + 2 * q^55 + 6 * q^56 - 9 * q^58 + 4 * q^59 - q^61 + 10 * q^62 - 12 * q^63 + 14 * q^64 + 2 * q^65 + 10 * q^67 - 6 * q^68 - 2 * q^70 - 6 * q^71 - 9 * q^72 - 20 * q^73 + 10 * q^74 - 6 * q^76 + 4 * q^77 - 10 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 + 6 * q^85 - 2 * q^86 + 12 * q^88 - 7 * q^89 + 3 * q^90 + 4 * q^91 - 4 * q^92 - 6 * q^94 + 6 * q^95 + 14 * q^97 + 3 * q^98 - 6 * q^99

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