LMFDB - Embedded newform 162.2.c.d.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [162,2,Mod(55,162)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(162, 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("162.55");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 162 = 2 \cdot 3^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	162.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.29357651274$
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			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	162.109
Dual form			162.2.c.d.55.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +3.00000 q^{10} +(0.500000 - 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} -4.00000 q^{19} +(1.50000 + 2.59808i) q^{20} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{26} -4.00000 q^{28} +(-4.50000 - 7.79423i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} +12.0000 q^{35} -1.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(6.00000 + 10.3923i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} +(0.500000 + 0.866025i) q^{52} -6.00000 q^{53} +(-2.00000 - 3.46410i) q^{56} +(4.50000 - 7.79423i) q^{58} +(0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{70} -12.0000 q^{71} +11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(8.00000 + 13.8564i) q^{79} -3.00000 q^{80} -6.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(4.00000 - 6.92820i) q^{86} -3.00000 q^{89} +4.00000 q^{91} +(-6.00000 + 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{97} -9.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + 3 q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 + 3 * q^5 + 4 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} + 3 q^{5} + 4 q^{7} - 2 q^{8} + 6 q^{10} + q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 8 q^{19} + 3 q^{20} - 4 q^{25} + 2 q^{26} - 8 q^{28} - 9 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} + 24 q^{35} - 2 q^{37} - 4 q^{38} - 3 q^{40} - 6 q^{41} - 8 q^{43} + 12 q^{47} - 9 q^{49} + 4 q^{50} + q^{52} - 12 q^{53} - 4 q^{56} + 9 q^{58} + q^{61} + 8 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} + 3 q^{68} + 12 q^{70} - 24 q^{71} + 22 q^{73} - q^{74} + 4 q^{76} + 16 q^{79} - 6 q^{80} - 12 q^{82} + 12 q^{83} - 9 q^{85} + 8 q^{86} - 6 q^{89} + 8 q^{91} - 12 q^{94} - 12 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + 3 * q^5 + 4 * q^7 - 2 * q^8 + 6 * q^10 + q^13 - 4 * q^14 - q^16 - 6 * q^17 - 8 * q^19 + 3 * q^20 - 4 * q^25 + 2 * q^26 - 8 * q^28 - 9 * q^29 + 4 * q^31 + q^32 - 3 * q^34 + 24 * q^35 - 2 * q^37 - 4 * q^38 - 3 * q^40 - 6 * q^41 - 8 * q^43 + 12 * q^47 - 9 * q^49 + 4 * q^50 + q^52 - 12 * q^53 - 4 * q^56 + 9 * q^58 + q^61 + 8 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 24 * q^71 + 22 * q^73 - q^74 + 4 * q^76 + 16 * q^79 - 6 * q^80 - 12 * q^82 + 12 * q^83 - 9 * q^85 + 8 * q^86 - 6 * q^89 + 8 * q^91 - 12 * q^94 - 12 * q^95 - 2 * q^97 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/162\mathbb{Z}\right)^\times$.

$n$	$83$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	3.00000			0.948683
$11$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$11$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$12$		0			0
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	−0.788320	−	0.615265i	$-0.789049\pi$
$13$	0.500000	−	0.866025i	0.138675	−	0.240192i	0.926995	+	0.375073i	$0.122382\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	1.50000	+	2.59808i	0.335410	+	0.580948i
$21$		0			0
$22$		0			0
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	1.00000			0.196116
$27$		0			0
$28$	−4.00000			−0.755929
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−1.50000	−	2.59808i	−0.257248	−	0.445566i
$35$	12.0000			2.02837
$36$		0			0
$37$	−1.00000			−0.164399			−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	−1.00000			−0.164399			−0.0821995	+	0.996616i	$0.526194\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$		0			0
$40$	−1.50000	+	2.59808i	−0.237171	+	0.410792i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−4.00000	−	6.92820i	−0.609994	−	1.05654i	0.381246	−	0.924473i	$-0.375495\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.856560	+	0.516047i	$0.172597\pi$
$47$	6.00000	+	10.3923i	0.875190	+	1.51587i	0.0186297	+	0.999826i	$0.494070\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	2.00000	−	3.46410i	0.282843	−	0.489898i
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$		0			0
$56$	−2.00000	−	3.46410i	−0.267261	−	0.462910i
$57$		0			0
$58$	4.50000	−	7.79423i	0.590879	−	1.02343i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$		0			0
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	0.500000	+	0.866025i	0.0640184	+	0.110883i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	4.00000			0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.50000	−	2.59808i	−0.186052	−	0.322252i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	6.00000	+	10.3923i	0.717137	+	1.24212i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	−0.500000	−	0.866025i	−0.0581238	−	0.100673i
$75$		0			0
$76$	2.00000	−	3.46410i	0.229416	−	0.397360i
$77$		0			0
$78$		0			0
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.827401	+	0.561611i	$0.189818\pi$
$79$	8.00000	+	13.8564i	0.900070	+	1.55897i	0.0726692	+	0.997356i	$0.476848\pi$
$80$	−3.00000			−0.335410
$81$		0			0
$82$	−6.00000			−0.662589
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$		0			0
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	4.00000			0.419314
$92$		0			0
$93$		0			0
$94$	−6.00000	+	10.3923i	−0.618853	+	1.07188i
$95$	−6.00000	+	10.3923i	−0.615587	+	1.06623i
$96$		0			0
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	−9.00000			−0.909137
$99$		0			0
$100$	4.00000			0.400000
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	0.975796	−	0.218685i	$-0.0701767\pi$
$101$	3.00000	+	5.19615i	0.298511	+	0.517036i	−0.677284	+	0.735721i	$0.736843\pi$
$102$		0			0
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−0.500000	+	0.866025i	−0.0490290	+	0.0849208i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	11.0000			1.05361			0.526804	−	0.849987i	$-0.323390\pi$
$109$	11.0000			1.05361			0.526804	+	0.849987i	$0.323390\pi$
$110$		0			0
$111$		0			0
$112$	2.00000	−	3.46410i	0.188982	−	0.327327i
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	−0.260955	−	0.965351i	$-0.584038\pi$
$113$	7.50000	−	12.9904i	0.705541	−	1.22203i	0.966496	−	0.256681i	$-0.0826291\pi$
$114$		0			0
$115$		0			0
$116$	9.00000			0.835629
$117$		0			0
$118$		0			0
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	5.50000	−	9.52628i	0.500000	−	0.866025i
$122$	−0.500000	+	0.866025i	−0.0452679	+	0.0784063i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	3.00000			0.268328
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.50000	−	2.59808i	0.131559	−	0.227866i
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−8.00000	−	13.8564i	−0.693688	−	1.20150i
$134$	4.00000			0.345547
$135$		0			0
$136$	3.00000			0.257248
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	−6.00000	+	10.3923i	−0.507093	+	0.878310i
$141$		0			0
$142$	−6.00000	−	10.3923i	−0.503509	−	0.872103i
$143$		0			0
$144$		0			0
$145$	−27.0000			−2.24223
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$		0			0
$148$	0.500000	−	0.866025i	0.0410997	−	0.0711868i
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$		0			0
$155$	−6.00000	−	10.3923i	−0.481932	−	0.834730i
$156$		0			0
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$	−8.00000	+	13.8564i	−0.636446	+	1.10236i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$		0			0
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	−0.999169	−	0.0407502i	$-0.987025\pi$
$167$	−6.00000	+	10.3923i	−0.464294	+	0.804181i	0.534875	+	0.844931i	$0.320359\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$	−9.00000			−0.690268
$171$		0			0
$172$	8.00000			0.609994
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$		0			0
$175$	8.00000	−	13.8564i	0.604743	−	1.04745i
$176$		0			0
$177$		0			0
$178$	−1.50000	−	2.59808i	−0.112430	−	0.194734i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	2.00000	+	3.46410i	0.148250	+	0.256776i
$183$		0			0
$184$		0			0
$185$	−1.50000	+	2.59808i	−0.110282	+	0.191014i
$186$		0			0
$187$		0			0
$188$	−12.0000			−0.875190
$189$		0			0
$190$	−12.0000			−0.870572
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		0			0
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	−0.531446	−	0.847092i	$-0.678351\pi$
$193$	6.50000	−	11.2583i	0.467880	−	0.810392i	0.999326	+	0.0366998i	$0.0116845\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$		0			0
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	18.0000	−	31.1769i	1.26335	−	2.18819i
$204$		0			0
$205$	9.00000	+	15.5885i	0.628587	+	1.08875i
$206$	4.00000			0.278693
$207$		0			0
$208$	−1.00000			−0.0693375
$209$		0			0
$210$		0			0
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	−0.970229	−	0.242190i	$-0.922134\pi$
$211$	−4.00000	+	6.92820i	−0.275371	+	0.476957i	0.694857	+	0.719148i	$0.255467\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	−24.0000			−1.63679
$216$		0			0
$217$	16.0000			1.08615
$218$	5.50000	+	9.52628i	0.372507	+	0.645201i
$219$		0			0
$220$		0			0
$221$	−1.50000	+	2.59808i	−0.100901	+	0.174766i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	4.00000			0.267261
$225$		0			0
$226$	15.0000			0.997785
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	0.993508	−	0.113761i	$-0.0362899\pi$
$227$	6.00000	+	10.3923i	0.398234	+	0.689761i	−0.595274	+	0.803523i	$0.702957\pi$
$228$		0			0
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	0.182939	+	0.983124i	$0.441439\pi$
$229$	−11.5000	+	19.9186i	−0.759941	+	1.31626i	−0.942880	+	0.333133i	$0.891894\pi$
$230$		0			0
$231$		0			0
$232$	4.50000	+	7.79423i	0.295439	+	0.511716i
$233$	21.0000			1.37576			0.687878	−	0.725826i	$-0.258542\pi$
$233$	21.0000			1.37576			0.687878	+	0.725826i	$0.258542\pi$
$234$		0			0
$235$	36.0000			2.34838
$236$		0			0
$237$		0			0
$238$	6.00000	−	10.3923i	0.388922	−	0.673633i
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	11.0000			0.707107
$243$		0			0
$244$	−1.00000			−0.0640184
$245$	13.5000	+	23.3827i	0.862483	+	1.49387i
$246$		0			0
$247$	−2.00000	+	3.46410i	−0.127257	+	0.220416i
$248$	−2.00000	+	3.46410i	−0.127000	+	0.219971i
$249$		0			0
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	−24.0000			−1.51487			−0.757433	−	0.652913i	$-0.773547\pi$
$251$	−24.0000			−1.51487			−0.757433	+	0.652913i	$0.773547\pi$
$252$		0			0
$253$		0			0
$254$	−8.00000	−	13.8564i	−0.501965	−	0.869428i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		0			0
$259$	−2.00000	−	3.46410i	−0.124274	−	0.215249i
$260$	3.00000			0.186052
$261$		0			0
$262$	12.0000			0.741362
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−9.00000	+	15.5885i	−0.552866	+	0.957591i
$266$	8.00000	−	13.8564i	0.490511	−	0.849591i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	21.0000			1.28039			0.640196	−	0.768211i	$-0.278853\pi$
$269$	21.0000			1.28039			0.640196	+	0.768211i	$0.278853\pi$
$270$		0			0
$271$	−16.0000			−0.971931			−0.485965	−	0.873978i	$-0.661532\pi$
$271$	−16.0000			−0.971931			−0.485965	+	0.873978i	$0.661532\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$		0			0
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$		0			0
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	−20.0000			−1.19952
$279$		0			0
$280$	−12.0000			−0.717137
$281$	13.5000	+	23.3827i	0.805342	+	1.39489i	0.916060	+	0.401042i	$0.131352\pi$
$281$	13.5000	+	23.3827i	0.805342	+	1.39489i	−0.110717	+	0.993852i	$0.535315\pi$
$282$		0			0
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	6.00000	−	10.3923i	0.356034	−	0.616670i
$285$		0			0
$286$		0			0
$287$	−24.0000			−1.41668
$288$		0			0
$289$	−8.00000			−0.470588
$290$	−13.5000	−	23.3827i	−0.792747	−	1.37308i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	−0.967009	−	0.254741i	$-0.918010\pi$
$293$	−4.50000	+	7.79423i	−0.262893	+	0.455344i	0.704117	+	0.710084i	$0.251343\pi$
$294$		0			0
$295$		0			0
$296$	1.00000			0.0581238
$297$		0			0
$298$	−9.00000			−0.521356
$299$		0			0
$300$		0			0
$301$	16.0000	−	27.7128i	0.922225	−	1.59734i
$302$	4.00000	−	6.92820i	0.230174	−	0.398673i
$303$		0			0
$304$	2.00000	+	3.46410i	0.114708	+	0.198680i
$305$	3.00000			0.171780
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$		0			0
$309$		0			0
$310$	6.00000	−	10.3923i	0.340777	−	0.590243i
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	0.294384	+	0.955687i	$0.404886\pi$
$311$	−12.0000	+	20.7846i	−0.680458	+	1.17859i	−0.974841	+	0.222900i	$0.928448\pi$
$312$		0			0
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	−0.983118	−	0.182973i	$-0.941428\pi$
$313$	−11.5000	−	19.9186i	−0.650018	−	1.12586i	0.333099	−	0.942892i	$-0.391906\pi$
$314$	13.0000			0.733632
$315$		0			0
$316$	−16.0000			−0.900070
$317$	−10.5000	−	18.1865i	−0.589739	−	1.02146i	−0.994266	−	0.106932i	$-0.965897\pi$
$317$	−10.5000	−	18.1865i	−0.589739	−	1.02146i	0.404528	−	0.914526i	$-0.367436\pi$
$318$		0			0
$319$		0			0
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$		0			0
$322$		0			0
$323$	12.0000			0.667698
$324$		0			0
$325$	−4.00000			−0.221880
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$		0			0
$328$	3.00000	−	5.19615i	0.165647	−	0.286910i
$329$	−24.0000	+	41.5692i	−1.32316	+	2.29179i
$330$		0			0
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−12.0000			−0.658586
$333$		0			0
$334$	−12.0000			−0.656611
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	−0.891976	−	0.452082i	$-0.850681\pi$
$337$	−1.00000	+	1.73205i	−0.0544735	+	0.0943508i	0.837503	+	0.546433i	$0.184015\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$		0			0
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$		0			0
$342$		0			0
$343$	−8.00000			−0.431959
$344$	4.00000	+	6.92820i	0.215666	+	0.373544i
$345$		0			0
$346$	−1.50000	+	2.59808i	−0.0806405	+	0.139673i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	16.0000			0.855236
$351$		0			0
$352$		0			0
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−5.00000	−	8.66025i	−0.262794	−	0.455173i
$363$		0			0
$364$	−2.00000	+	3.46410i	−0.104828	+	0.181568i
$365$	16.5000	−	28.5788i	0.863649	−	1.49588i
$366$		0			0
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	0.742538	−	0.669804i	$-0.233622\pi$
$367$	−4.00000	−	6.92820i	−0.208798	−	0.361649i	−0.951336	+	0.308155i	$0.900289\pi$
$368$		0			0
$369$		0			0
$370$	−3.00000			−0.155963
$371$	−12.0000	−	20.7846i	−0.623009	−	1.07908i
$372$		0			0
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	−0.707055	−	0.707159i	$-0.749977\pi$
$373$	5.00000	−	8.66025i	0.258890	−	0.448411i	0.965945	+	0.258748i	$0.0833099\pi$
$374$		0			0
$375$		0			0
$376$	−6.00000	−	10.3923i	−0.309426	−	0.535942i
$377$	−9.00000			−0.463524
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−6.00000	−	10.3923i	−0.307794	−	0.533114i
$381$		0			0
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$		0			0
$385$		0			0
$386$	13.0000			0.661683
$387$		0			0
$388$	2.00000			0.101535
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$		0			0
$392$	4.50000	−	7.79423i	0.227284	−	0.393668i
$393$		0			0
$394$	−1.50000	−	2.59808i	−0.0755689	−	0.130889i
$395$	48.0000			2.41514
$396$		0			0
$397$	−25.0000			−1.25471			−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000			−1.25471			−0.627357	+	0.778732i	$0.715863\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−6.00000			−0.298511
$405$		0			0
$406$	36.0000			1.78665
$407$		0			0
$408$		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	$-0.0454247\pi$
$410$	−9.00000	+	15.5885i	−0.444478	+	0.769859i
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$		0			0
$414$		0			0
$415$	36.0000			1.76717
$416$	−0.500000	−	0.866025i	−0.0245145	−	0.0424604i
$417$		0			0
$418$		0			0
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	−0.408481	−	0.912767i	$-0.633942\pi$
$419$	12.0000	−	20.7846i	0.586238	−	1.01539i	0.994720	−	0.102628i	$-0.0327251\pi$
$420$		0			0
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	0.979817	−	0.199899i	$-0.0640614\pi$
$421$	6.50000	+	11.2583i	0.316791	+	0.548697i	−0.663026	+	0.748596i	$0.730728\pi$
$422$	−8.00000			−0.389434
$423$		0			0
$424$	6.00000			0.291386
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$		0			0
$427$	−2.00000	+	3.46410i	−0.0967868	+	0.167640i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	−12.0000	−	20.7846i	−0.578691	−	1.00232i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$	8.00000	+	13.8564i	0.384012	+	0.665129i
$435$		0			0
$436$	−5.50000	+	9.52628i	−0.263402	+	0.456226i
$437$		0			0
$438$		0			0
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	0.978412	+	0.206666i	$0.0662612\pi$
$439$	14.0000	+	24.2487i	0.668184	+	1.15733i	−0.310228	+	0.950662i	$0.600405\pi$
$440$		0			0
$441$		0			0
$442$	−3.00000			−0.142695
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	0.972626	−	0.232377i	$-0.0746503\pi$
$443$	6.00000	+	10.3923i	0.285069	+	0.493753i	−0.687557	+	0.726130i	$0.741317\pi$
$444$		0			0
$445$	−4.50000	+	7.79423i	−0.213320	+	0.369482i
$446$	4.00000	−	6.92820i	0.189405	−	0.328060i
$447$		0			0
$448$	2.00000	+	3.46410i	0.0944911	+	0.163663i
$449$	−18.0000			−0.849473			−0.424736	−	0.905317i	$-0.639633\pi$
$449$	−18.0000			−0.849473			−0.424736	+	0.905317i	$0.639633\pi$
$450$		0			0
$451$		0			0
$452$	7.50000	+	12.9904i	0.352770	+	0.611016i
$453$		0			0
$454$	−6.00000	+	10.3923i	−0.281594	+	0.487735i
$455$	6.00000	−	10.3923i	0.281284	−	0.487199i
$456$		0			0
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	0.877483	−	0.479608i	$-0.159221\pi$
$457$	0.500000	+	0.866025i	0.0233890	+	0.0405110i	−0.854094	+	0.520119i	$0.825888\pi$
$458$	−23.0000			−1.07472
$459$		0			0
$460$		0			0
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	0.576685	−	0.816967i	$-0.304346\pi$
$461$	−9.00000	−	15.5885i	−0.419172	−	0.726027i	−0.995856	+	0.0909401i	$0.971013\pi$
$462$		0			0
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	−0.943878	−	0.330294i	$-0.892852\pi$
$463$	−4.00000	+	6.92820i	−0.185896	+	0.321981i	0.757982	+	0.652275i	$0.226185\pi$
$464$	−4.50000	+	7.79423i	−0.208907	+	0.361838i
$465$		0			0
$466$	10.5000	+	18.1865i	0.486403	+	0.842475i
$467$	−24.0000			−1.11059			−0.555294	−	0.831654i	$-0.687394\pi$
$467$	−24.0000			−1.11059			−0.555294	+	0.831654i	$0.687394\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	18.0000	+	31.1769i	0.830278	+	1.43808i
$471$		0			0
$472$		0			0
$473$		0			0
$474$		0			0
$475$	8.00000	+	13.8564i	0.367065	+	0.635776i
$476$	12.0000			0.550019
$477$		0			0
$478$	−12.0000			−0.548867
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	0.969920	−	0.243426i	$-0.0782712\pi$
$479$	6.00000	+	10.3923i	0.274147	+	0.474837i	−0.695773	+	0.718262i	$0.744938\pi$
$480$		0			0
$481$	−0.500000	+	0.866025i	−0.0227980	+	0.0394874i
$482$	−6.50000	+	11.2583i	−0.296067	+	0.512803i
$483$		0			0
$484$	5.50000	+	9.52628i	0.250000	+	0.433013i
$485$	−6.00000			−0.272446
$486$		0			0
$487$	−4.00000			−0.181257			−0.0906287	−	0.995885i	$-0.528888\pi$
$487$	−4.00000			−0.181257			−0.0906287	+	0.995885i	$0.528888\pi$
$488$	−0.500000	−	0.866025i	−0.0226339	−	0.0392031i
$489$		0			0
$490$	−13.5000	+	23.3827i	−0.609868	+	1.05632i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$		0			0
$493$	13.5000	+	23.3827i	0.608009	+	1.05310i
$494$	−4.00000			−0.179969
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−24.0000	−	41.5692i	−1.07655	−	1.86463i
$498$		0			0
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.0619186	−	0.998081i	$-0.480278\pi$
$499$	20.0000	−	34.6410i	0.895323	−	1.55074i	0.833404	−	0.552664i	$-0.186389\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$		0			0
$502$	−12.0000	−	20.7846i	−0.535586	−	0.927663i
$503$		0			0			−	1.00000i	$-0.5\pi$
$503$		0			0				1.00000i	$0.5\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$		0			0
$507$		0			0
$508$	8.00000	−	13.8564i	0.354943	−	0.614779i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$		0			0
$511$	22.0000	+	38.1051i	0.973223	+	1.68567i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	15.0000			0.661622
$515$	−6.00000	−	10.3923i	−0.264392	−	0.457940i
$516$		0			0
$517$		0			0
$518$	2.00000	−	3.46410i	0.0878750	−	0.152204i
$519$		0			0
$520$	1.50000	+	2.59808i	0.0657794	+	0.113933i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	6.00000	−	10.3923i	0.261612	−	0.453126i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	−18.0000			−0.781870
$531$		0			0
$532$	16.0000			0.693688
$533$	3.00000	+	5.19615i	0.129944	+	0.225070i
$534$		0			0
$535$	18.0000	−	31.1769i	0.778208	−	1.34790i
$536$	−2.00000	+	3.46410i	−0.0863868	+	0.149626i
$537$		0			0
$538$	10.5000	+	18.1865i	0.452687	+	0.784077i
$539$		0			0
$540$		0			0
$541$	−1.00000			−0.0429934			−0.0214967	−	0.999769i	$-0.506843\pi$
$541$	−1.00000			−0.0429934			−0.0214967	+	0.999769i	$0.506843\pi$
$542$	−8.00000	−	13.8564i	−0.343629	−	0.595184i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	16.5000	−	28.5788i	0.706782	−	1.22418i
$546$		0			0
$547$	−22.0000	−	38.1051i	−0.940652	−	1.62926i	−0.764231	−	0.644942i	$-0.776881\pi$
$547$	−22.0000	−	38.1051i	−0.940652	−	1.62926i	−0.176421	−	0.984315i	$-0.556452\pi$
$548$	9.00000			0.384461
$549$		0			0
$550$		0			0
$551$	18.0000	+	31.1769i	0.766826	+	1.32818i
$552$		0			0
$553$	−32.0000	+	55.4256i	−1.36078	+	2.35694i
$554$	−5.00000	+	8.66025i	−0.212430	+	0.367939i
$555$		0			0
$556$	−10.0000	−	17.3205i	−0.424094	−	0.734553i
$557$	−3.00000			−0.127114			−0.0635570	−	0.997978i	$-0.520244\pi$
$557$	−3.00000			−0.127114			−0.0635570	+	0.997978i	$0.520244\pi$
$558$		0			0
$559$	−8.00000			−0.338364
$560$	−6.00000	−	10.3923i	−0.253546	−	0.439155i
$561$		0			0
$562$	−13.5000	+	23.3827i	−0.569463	+	0.986339i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$		0			0
$565$	−22.5000	−	38.9711i	−0.946582	−	1.63953i
$566$	4.00000			0.168133
$567$		0			0
$568$	12.0000			0.503509
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$		0			0
$573$		0			0
$574$	−12.0000	−	20.7846i	−0.500870	−	0.867533i
$575$		0			0
$576$		0			0
$577$	−25.0000			−1.04076			−0.520382	−	0.853934i	$-0.674210\pi$
$577$	−25.0000			−1.04076			−0.520382	+	0.853934i	$0.674210\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$		0			0
$580$	13.5000	−	23.3827i	0.560557	−	0.970913i
$581$	−24.0000	+	41.5692i	−0.995688	+	1.72458i
$582$		0			0
$583$		0			0
$584$	−11.0000			−0.455183
$585$		0			0
$586$	−9.00000			−0.371787
$587$	12.0000	+	20.7846i	0.495293	+	0.857873i	0.999985	−	0.00542667i	$-0.00172737\pi$
$587$	12.0000	+	20.7846i	0.495293	+	0.857873i	−0.504692	+	0.863299i	$0.668394\pi$
$588$		0			0
$589$	−8.00000	+	13.8564i	−0.329634	+	0.570943i
$590$		0			0
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	33.0000			1.35515			0.677574	−	0.735455i	$-0.263031\pi$
$593$	33.0000			1.35515			0.677574	+	0.735455i	$0.263031\pi$
$594$		0			0
$595$	−36.0000			−1.47586
$596$	−4.50000	−	7.79423i	−0.184327	−	0.319264i
$597$		0			0
$598$		0			0
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	−0.219061	−	0.975711i	$-0.570299\pi$
$599$	18.0000	−	31.1769i	0.735460	−	1.27385i	0.954521	−	0.298143i	$-0.0963673\pi$
$600$		0			0
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$	32.0000			1.30422
$603$		0			0
$604$	8.00000			0.325515
$605$	−16.5000	−	28.5788i	−0.670820	−	1.16190i
$606$		0			0
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	0.588537	+	0.808470i	$0.299704\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$		0			0
$610$	1.50000	+	2.59808i	0.0607332	+	0.105193i
$611$	12.0000			0.485468
$612$		0			0
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$	10.0000	+	17.3205i	0.403567	+	0.698999i
$615$		0			0
$616$		0			0
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	−0.834251	−	0.551385i	$-0.814100\pi$
$617$	1.50000	−	2.59808i	0.0603877	−	0.104595i	0.894639	+	0.446790i	$0.147433\pi$
$618$		0			0
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	0.774373	−	0.632730i	$-0.218066\pi$
$619$	−4.00000	−	6.92820i	−0.160774	−	0.278468i	−0.935146	+	0.354262i	$0.884732\pi$
$620$	12.0000			0.481932
$621$		0			0
$622$	−24.0000			−0.962312
$623$	−6.00000	−	10.3923i	−0.240385	−	0.416359i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	11.5000	−	19.9186i	0.459632	−	0.796107i
$627$		0			0
$628$	6.50000	+	11.2583i	0.259378	+	0.449256i
$629$	3.00000			0.119618
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	−8.00000	−	13.8564i	−0.318223	−	0.551178i
$633$		0			0
$634$	10.5000	−	18.1865i	0.417008	−	0.722280i
$635$	−24.0000	+	41.5692i	−0.952411	+	1.64962i
$636$		0			0
$637$	4.50000	+	7.79423i	0.178296	+	0.308819i
$638$		0			0
$639$		0			0
$640$	3.00000			0.118585
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.841417	−	0.540386i	$-0.818278\pi$
$641$	−22.5000	−	38.9711i	−0.888697	−	1.53927i	−0.0472793	−	0.998882i	$-0.515055\pi$
$642$		0			0
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$644$		0			0
$645$		0			0
$646$	6.00000	+	10.3923i	0.236067	+	0.408880i
$647$	36.0000			1.41531			0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000			1.41531			0.707653	+	0.706560i	$0.249754\pi$
$648$		0			0
$649$		0			0
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$		0			0
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		0			0
$655$	−18.0000	−	31.1769i	−0.703318	−	1.21818i
$656$	6.00000			0.234261
$657$		0			0
$658$	−48.0000			−1.87123
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$	10.0000	−	17.3205i	0.388661	−	0.673181i
$663$		0			0
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	−48.0000			−1.86136
$666$		0			0
$667$		0			0
$668$	−6.00000	−	10.3923i	−0.232147	−	0.402090i
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$		0			0
$672$		0			0
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	0.740334	−	0.672239i	$-0.234667\pi$
$673$	−5.50000	−	9.52628i	−0.212009	−	0.367211i	−0.952343	+	0.305028i	$0.901334\pi$
$674$	−2.00000			−0.0770371
$675$		0			0
$676$	−12.0000			−0.461538
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	4.00000	−	6.92820i	0.153506	−	0.265880i
$680$	4.50000	−	7.79423i	0.172567	−	0.298895i
$681$		0			0
$682$		0			0
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$	−27.0000			−1.03162
$686$	−4.00000	−	6.92820i	−0.152721	−	0.264520i
$687$		0			0
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−3.00000	+	5.19615i	−0.114291	+	0.197958i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−3.00000			−0.114043
$693$		0			0
$694$	−12.0000			−0.455514
$695$	30.0000	+	51.9615i	1.13796	+	1.97101i
$696$		0			0
$697$	9.00000	−	15.5885i	0.340899	−	0.590455i
$698$	7.00000	−	12.1244i	0.264954	−	0.458914i
$699$		0			0
$700$	8.00000	+	13.8564i	0.302372	+	0.523723i
$701$	−51.0000			−1.92624			−0.963122	−	0.269066i	$-0.913285\pi$
$701$	−51.0000			−1.92624			−0.963122	+	0.269066i	$0.913285\pi$
$702$		0			0
$703$	4.00000			0.150863
$704$		0			0
$705$		0			0
$706$	−9.00000	+	15.5885i	−0.338719	+	0.586679i
$707$	−12.0000	+	20.7846i	−0.451306	+	0.781686i
$708$		0			0
$709$	−23.5000	−	40.7032i	−0.882561	−	1.52864i	−0.848484	−	0.529221i	$-0.822484\pi$
$709$	−23.5000	−	40.7032i	−0.882561	−	1.52864i	−0.0340772	−	0.999419i	$-0.510849\pi$
$710$	−36.0000			−1.35106
$711$		0			0
$712$	3.00000			0.112430
$713$		0			0
$714$		0			0
$715$		0			0
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$		0			0
$718$		0			0
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	−1.50000	−	2.59808i	−0.0558242	−	0.0966904i
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−18.0000	+	31.1769i	−0.668503	+	1.15788i
$726$		0			0
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	0.999750	+	0.0223506i	$0.00711500\pi$
$727$	14.0000	+	24.2487i	0.519231	+	0.899335i	−0.480519	+	0.876984i	$0.659552\pi$
$728$	−4.00000			−0.148250
$729$		0			0
$730$	33.0000			1.22138
$731$	12.0000	+	20.7846i	0.443836	+	0.768747i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	4.00000	−	6.92820i	0.147643	−	0.255725i
$735$		0			0
$736$		0			0
$737$		0			0
$738$		0			0
$739$	20.0000			0.735712			0.367856	−	0.929883i	$-0.380092\pi$
$739$	20.0000			0.735712			0.367856	+	0.929883i	$0.380092\pi$
$740$	−1.50000	−	2.59808i	−0.0551411	−	0.0955072i
$741$		0			0
$742$	12.0000	−	20.7846i	0.440534	−	0.763027i
$743$	−6.00000	+	10.3923i	−0.220119	+	0.381257i	−0.954844	−	0.297108i	$-0.903978\pi$
$743$	−6.00000	+	10.3923i	−0.220119	+	0.381257i	0.734725	+	0.678365i	$0.237311\pi$
$744$		0			0
$745$	13.5000	+	23.3827i	0.494602	+	0.856675i
$746$	10.0000			0.366126
$747$		0			0
$748$		0			0
$749$	24.0000	+	41.5692i	0.876941	+	1.51891i
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$	6.00000	−	10.3923i	0.218797	−	0.378968i
$753$		0			0
$754$	−4.50000	−	7.79423i	−0.163880	−	0.283849i
$755$	−24.0000			−0.873449
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	−14.0000	−	24.2487i	−0.508503	−	0.880753i
$759$		0			0
$760$	6.00000	−	10.3923i	0.217643	−	0.376969i
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	−0.697467	−	0.716617i	$-0.745690\pi$
$761$	7.50000	−	12.9904i	0.271875	−	0.470901i	0.969342	+	0.245716i	$0.0790230\pi$
$762$		0			0
$763$	22.0000	+	38.1051i	0.796453	+	1.37950i
$764$	12.0000			0.434145
$765$		0			0
$766$	12.0000			0.433578
$767$		0			0
$768$		0			0
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	−0.311577	−	0.950221i	$-0.600857\pi$
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	0.978704	−	0.205277i	$-0.0658095\pi$
$770$		0			0
$771$		0			0
$772$	6.50000	+	11.2583i	0.233940	+	0.405196i
$773$	−27.0000			−0.971123			−0.485561	−	0.874203i	$-0.661385\pi$
$773$	−27.0000			−0.971123			−0.485561	+	0.874203i	$0.661385\pi$
$774$		0			0
$775$	−16.0000			−0.574737
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	−3.00000	+	5.19615i	−0.107555	+	0.186291i
$779$	12.0000	−	20.7846i	0.429945	−	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$	9.00000			0.321429
$785$	−19.5000	−	33.7750i	−0.695985	−	1.20548i
$786$		0			0
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	0.426193	+	0.904632i	$0.359855\pi$
$787$	−16.0000	+	27.7128i	−0.570338	+	0.987855i	−0.996531	+	0.0832226i	$0.973479\pi$
$788$	1.50000	−	2.59808i	0.0534353	−	0.0925526i
$789$		0			0
$790$	24.0000	+	41.5692i	0.853882	+	1.47897i
$791$	60.0000			2.13335
$792$		0			0
$793$	1.00000			0.0355110
$794$	−12.5000	−	21.6506i	−0.443608	−	0.768352i
$795$		0			0
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	25.5000	−	44.1673i	0.903256	−	1.56449i	0.0800155	−	0.996794i	$-0.474503\pi$
$797$	25.5000	−	44.1673i	0.903256	−	1.56449i	0.823241	−	0.567692i	$-0.192164\pi$
$798$		0			0
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$	−4.00000			−0.141421
$801$		0			0
$802$	3.00000			0.105934
$803$		0			0
$804$		0			0
$805$		0			0
$806$	2.00000	−	3.46410i	0.0704470	−	0.122018i
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	−39.0000			−1.37117			−0.685583	−	0.727994i	$-0.740453\pi$
$809$	−39.0000			−1.37117			−0.685583	+	0.727994i	$0.740453\pi$
$810$		0			0
$811$	−16.0000			−0.561836			−0.280918	−	0.959732i	$-0.590639\pi$
$811$	−16.0000			−0.561836			−0.280918	+	0.959732i	$0.590639\pi$
$812$	18.0000	+	31.1769i	0.631676	+	1.09410i
$813$		0			0
$814$		0			0
$815$	12.0000	−	20.7846i	0.420342	−	0.728053i
$816$		0			0
$817$	16.0000	+	27.7128i	0.559769	+	0.969549i
$818$	25.0000			0.874105
$819$		0			0
$820$	−18.0000			−0.628587
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	0.966708	−	0.255884i	$-0.0823665\pi$
$821$	7.50000	+	12.9904i	0.261752	+	0.453367i	−0.704956	+	0.709251i	$0.749033\pi$
$822$		0			0
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		0			0
$826$		0			0
$827$	−48.0000			−1.66912			−0.834562	−	0.550914i	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$		0			0
$829$	14.0000			0.486240			0.243120	−	0.969996i	$-0.421829\pi$
$829$	14.0000			0.486240			0.243120	+	0.969996i	$0.421829\pi$
$830$	18.0000	+	31.1769i	0.624789	+	1.08217i
$831$		0			0
$832$	0.500000	−	0.866025i	0.0173344	−	0.0300240i
$833$	13.5000	−	23.3827i	0.467747	−	0.810162i
$834$		0			0
$835$	18.0000	+	31.1769i	0.622916	+	1.07892i
$836$		0			0
$837$		0			0
$838$	24.0000			0.829066
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$	−6.50000	+	11.2583i	−0.224005	+	0.387988i
$843$		0			0
$844$	−4.00000	−	6.92820i	−0.137686	−	0.238479i
$845$	36.0000			1.23844
$846$		0			0
$847$	44.0000			1.51186
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$		0			0
$850$	−6.00000	+	10.3923i	−0.205798	+	0.356453i
$851$		0			0
$852$		0			0
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	−4.00000			−0.136877
$855$		0			0
$856$	−12.0000			−0.410152
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	0.978984	+	0.203938i	$0.0653741\pi$
$857$	19.5000	+	33.7750i	0.666107	+	1.15373i	−0.312877	+	0.949794i	$0.601293\pi$
$858$		0			0
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.0438309	−	0.999039i	$-0.486044\pi$
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.843278	−	0.537478i	$-0.180623\pi$
$860$	12.0000	−	20.7846i	0.409197	−	0.708749i
$861$		0			0
$862$	−6.00000	−	10.3923i	−0.204361	−	0.353963i
$863$	24.0000			0.816970			0.408485	−	0.912765i	$-0.366057\pi$
$863$	24.0000			0.816970			0.408485	+	0.912765i	$0.366057\pi$
$864$		0			0
$865$	9.00000			0.306009
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$		0			0
$868$	−8.00000	+	13.8564i	−0.271538	+	0.470317i
$869$		0			0
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	−11.0000			−0.372507
$873$		0			0
$874$		0			0
$875$	6.00000	+	10.3923i	0.202837	+	0.351324i
$876$		0			0
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	−0.574049	−	0.818821i	$-0.694628\pi$
$877$	12.5000	−	21.6506i	0.422095	−	0.731090i	0.996144	+	0.0877308i	$0.0279615\pi$
$878$	−14.0000	+	24.2487i	−0.472477	+	0.818354i
$879$		0			0
$880$		0			0
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$		0			0
$883$	−4.00000			−0.134611			−0.0673054	−	0.997732i	$-0.521440\pi$
$883$	−4.00000			−0.134611			−0.0673054	+	0.997732i	$0.521440\pi$
$884$	−1.50000	−	2.59808i	−0.0504505	−	0.0873828i
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$		0			0
$889$	−32.0000	−	55.4256i	−1.07325	−	1.85892i
$890$	−9.00000			−0.301681
$891$		0			0
$892$	8.00000			0.267860
$893$	−24.0000	−	41.5692i	−0.803129	−	1.39106i
$894$		0			0
$895$	18.0000	−	31.1769i	0.601674	−	1.04213i
$896$	−2.00000	+	3.46410i	−0.0668153	+	0.115728i
$897$		0			0
$898$	−9.00000	−	15.5885i	−0.300334	−	0.520194i
$899$	−36.0000			−1.20067
$900$		0			0
$901$	18.0000			0.599667
$902$		0			0
$903$		0			0
$904$	−7.50000	+	12.9904i	−0.249446	+	0.432054i
$905$	−15.0000	+	25.9808i	−0.498617	+	0.863630i
$906$		0			0
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	0.967730	−	0.251990i	$-0.0810849\pi$
$907$	8.00000	+	13.8564i	0.265636	+	0.460094i	−0.702094	+	0.712084i	$0.747752\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	12.0000			0.397796
$911$	−12.0000	−	20.7846i	−0.397578	−	0.688625i	0.595849	−	0.803097i	$-0.296816\pi$
$911$	−12.0000	−	20.7846i	−0.397578	−	0.688625i	−0.993426	+	0.114472i	$0.963482\pi$
$912$		0			0
$913$		0			0
$914$	−0.500000	+	0.866025i	−0.0165385	+	0.0286456i
$915$		0			0
$916$	−11.5000	−	19.9186i	−0.379971	−	0.658129i
$917$	48.0000			1.58510
$918$		0			0
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$		0			0
$921$		0			0
$922$	9.00000	−	15.5885i	0.296399	−	0.513378i
$923$	−6.00000	+	10.3923i	−0.197492	+	0.342067i
$924$		0			0
$925$	2.00000	+	3.46410i	0.0657596	+	0.113899i
$926$	−8.00000			−0.262896
$927$		0			0
$928$	−9.00000			−0.295439
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	0.889583	−	0.456774i	$-0.150995\pi$
$929$	1.50000	+	2.59808i	0.0492134	+	0.0852401i	−0.840369	+	0.542014i	$0.817662\pi$
$930$		0			0
$931$	18.0000	−	31.1769i	0.589926	−	1.02178i
$932$	−10.5000	+	18.1865i	−0.343939	+	0.595720i
$933$		0			0
$934$	−12.0000	−	20.7846i	−0.392652	−	0.680093i
$935$		0			0
$936$		0			0
$937$	−37.0000			−1.20874			−0.604369	−	0.796705i	$-0.706575\pi$
$937$	−37.0000			−1.20874			−0.604369	+	0.796705i	$0.706575\pi$
$938$	8.00000	+	13.8564i	0.261209	+	0.452428i
$939$		0			0
$940$	−18.0000	+	31.1769i	−0.587095	+	1.01688i
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	−0.557608	−	0.830104i	$-0.688281\pi$
$941$	13.5000	−	23.3827i	0.440087	−	0.762254i	0.997695	+	0.0678506i	$0.0216141\pi$
$942$		0			0
$943$		0			0
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	5.50000	−	9.52628i	0.178538	−	0.309236i
$950$	−8.00000	+	13.8564i	−0.259554	+	0.449561i
$951$		0			0
$952$	6.00000	+	10.3923i	0.194461	+	0.336817i
$953$	9.00000			0.291539			0.145769	−	0.989319i	$-0.453434\pi$
$953$	9.00000			0.291539			0.145769	+	0.989319i	$0.453434\pi$
$954$		0			0
$955$	−36.0000			−1.16493
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$	−6.00000	+	10.3923i	−0.193851	+	0.335760i
$959$	18.0000	−	31.1769i	0.581250	−	1.00676i
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−1.00000			−0.0322413
$963$		0			0
$964$	−13.0000			−0.418702
$965$	−19.5000	−	33.7750i	−0.627727	−	1.08726i
$966$		0			0
$967$	2.00000	−	3.46410i	0.0643157	−	0.111398i	−0.832075	−	0.554664i	$-0.812847\pi$
$967$	2.00000	−	3.46410i	0.0643157	−	0.111398i	0.896390	+	0.443266i	$0.146180\pi$
$968$	−5.50000	+	9.52628i	−0.176777	+	0.306186i
$969$		0			0
$970$	−3.00000	−	5.19615i	−0.0963242	−	0.166838i
$971$	−36.0000			−1.15529			−0.577647	−	0.816286i	$-0.696029\pi$
$971$	−36.0000			−1.15529			−0.577647	+	0.816286i	$0.696029\pi$
$972$		0			0
$973$	−80.0000			−2.56468
$974$	−2.00000	−	3.46410i	−0.0640841	−	0.110997i
$975$		0			0
$976$	0.500000	−	0.866025i	0.0160046	−	0.0277208i
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	−0.685381	−	0.728184i	$-0.740364\pi$
$977$	9.00000	−	15.5885i	0.287936	−	0.498719i	0.973317	+	0.229465i	$0.0736978\pi$
$978$		0			0
$979$		0			0
$980$	−27.0000			−0.862483
$981$		0			0
$982$		0			0
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	−0.939992	−	0.341197i	$-0.889168\pi$
$983$	−24.0000	−	41.5692i	−0.765481	−	1.32585i	0.174511	−	0.984655i	$-0.444166\pi$
$984$		0			0
$985$	−4.50000	+	7.79423i	−0.143382	+	0.248345i
$986$	−13.5000	+	23.3827i	−0.429928	+	0.744656i
$987$		0			0
$988$	−2.00000	−	3.46410i	−0.0636285	−	0.110208i
$989$		0			0
$990$		0			0
$991$	−52.0000			−1.65183			−0.825917	−	0.563791i	$-0.809342\pi$
$991$	−52.0000			−1.65183			−0.825917	+	0.563791i	$0.809342\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$		0			0
$994$	24.0000	−	41.5692i	0.761234	−	1.31850i
$995$	−6.00000	+	10.3923i	−0.190213	+	0.329458i
$996$		0			0
$997$	18.5000	+	32.0429i	0.585901	+	1.01481i	0.994762	+	0.102214i	$0.0325925\pi$
$997$	18.5000	+	32.0429i	0.585901	+	1.01481i	−0.408862	+	0.912596i	$0.634074\pi$
$998$	40.0000			1.26618
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	162.2.c.d.109.1		2
3.2	odd	2		162.2.c.a.109.1		2
4.3	odd	2		1296.2.i.n.433.1		2
9.2	odd	6		162.2.c.a.55.1		2
9.4	even	3		162.2.a.a.1.1	✓	1
9.5	odd	6		162.2.a.d.1.1	yes	1
9.7	even	3	inner	162.2.c.d.55.1		2
12.11	even	2		1296.2.i.b.433.1		2
36.7	odd	6		1296.2.i.n.865.1		2
36.11	even	6		1296.2.i.b.865.1		2
36.23	even	6		1296.2.a.l.1.1		1
36.31	odd	6		1296.2.a.c.1.1		1
45.4	even	6		4050.2.a.bh.1.1		1
45.13	odd	12		4050.2.c.g.649.2		2
45.14	odd	6		4050.2.a.r.1.1		1
45.22	odd	12		4050.2.c.g.649.1		2
45.23	even	12		4050.2.c.n.649.1		2
45.32	even	12		4050.2.c.n.649.2		2
63.13	odd	6		7938.2.a.n.1.1		1
63.41	even	6		7938.2.a.s.1.1		1
72.5	odd	6		5184.2.a.c.1.1		1
72.13	even	6		5184.2.a.y.1.1		1
72.59	even	6		5184.2.a.h.1.1		1
72.67	odd	6		5184.2.a.bd.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
162.2.a.a.1.1	✓	1	9.4	even	3
162.2.a.d.1.1	yes	1	9.5	odd	6
162.2.c.a.55.1		2	9.2	odd	6
162.2.c.a.109.1		2	3.2	odd	2
162.2.c.d.55.1		2	9.7	even	3	inner
162.2.c.d.109.1		2	1.1	even	1	trivial
1296.2.a.c.1.1		1	36.31	odd	6
1296.2.a.l.1.1		1	36.23	even	6
1296.2.i.b.433.1		2	12.11	even	2
1296.2.i.b.865.1		2	36.11	even	6
1296.2.i.n.433.1		2	4.3	odd	2
1296.2.i.n.865.1		2	36.7	odd	6
4050.2.a.r.1.1		1	45.14	odd	6
4050.2.a.bh.1.1		1	45.4	even	6
4050.2.c.g.649.1		2	45.22	odd	12
4050.2.c.g.649.2		2	45.13	odd	12
4050.2.c.n.649.1		2	45.23	even	12
4050.2.c.n.649.2		2	45.32	even	12
5184.2.a.c.1.1		1	72.5	odd	6
5184.2.a.h.1.1		1	72.59	even	6
5184.2.a.y.1.1		1	72.13	even	6
5184.2.a.bd.1.1		1	72.67	odd	6
7938.2.a.n.1.1		1	63.13	odd	6
7938.2.a.s.1.1		1	63.41	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 162 = 2 \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	162.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(2.00000 + 3.46410i) q^{7} -1.00000 q^{8} +3.00000 q^{10} +(0.500000 - 0.866025i) q^{13} +(-2.00000 + 3.46410i) q^{14} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} -4.00000 q^{19} +(1.50000 + 2.59808i) q^{20} +(-2.00000 - 3.46410i) q^{25} +1.00000 q^{26} -4.00000 q^{28} +(-4.50000 - 7.79423i) q^{29} +(2.00000 - 3.46410i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.50000 - 2.59808i) q^{34} +12.0000 q^{35} -1.00000 q^{37} +(-2.00000 - 3.46410i) q^{38} +(-1.50000 + 2.59808i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-4.00000 - 6.92820i) q^{43} +(6.00000 + 10.3923i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(2.00000 - 3.46410i) q^{50} +(0.500000 + 0.866025i) q^{52} -6.00000 q^{53} +(-2.00000 - 3.46410i) q^{56} +(4.50000 - 7.79423i) q^{58} +(0.500000 + 0.866025i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(2.00000 - 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 + 10.3923i) q^{70} -12.0000 q^{71} +11.0000 q^{73} +(-0.500000 - 0.866025i) q^{74} +(2.00000 - 3.46410i) q^{76} +(8.00000 + 13.8564i) q^{79} -3.00000 q^{80} -6.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-4.50000 + 7.79423i) q^{85} +(4.00000 - 6.92820i) q^{86} -3.00000 q^{89} +4.00000 q^{91} +(-6.00000 + 10.3923i) q^{94} +(-6.00000 + 10.3923i) q^{95} +(-1.00000 - 1.73205i) q^{97} -9.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + 3 q^{5} + 4 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 + 3 * q^5 + 4 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} + 3 q^{5} + 4 q^{7} - 2 q^{8} + 6 q^{10} + q^{13} - 4 q^{14} - q^{16} - 6 q^{17} - 8 q^{19} + 3 q^{20} - 4 q^{25} + 2 q^{26} - 8 q^{28} - 9 q^{29} + 4 q^{31} + q^{32} - 3 q^{34} + 24 q^{35} - 2 q^{37} - 4 q^{38} - 3 q^{40} - 6 q^{41} - 8 q^{43} + 12 q^{47} - 9 q^{49} + 4 q^{50} + q^{52} - 12 q^{53} - 4 q^{56} + 9 q^{58} + q^{61} + 8 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} + 3 q^{68} + 12 q^{70} - 24 q^{71} + 22 q^{73} - q^{74} + 4 q^{76} + 16 q^{79} - 6 q^{80} - 12 q^{82} + 12 q^{83} - 9 q^{85} + 8 q^{86} - 6 q^{89} + 8 q^{91} - 12 q^{94} - 12 q^{95} - 2 q^{97} - 18 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + 3 * q^5 + 4 * q^7 - 2 * q^8 + 6 * q^10 + q^13 - 4 * q^14 - q^16 - 6 * q^17 - 8 * q^19 + 3 * q^20 - 4 * q^25 + 2 * q^26 - 8 * q^28 - 9 * q^29 + 4 * q^31 + q^32 - 3 * q^34 + 24 * q^35 - 2 * q^37 - 4 * q^38 - 3 * q^40 - 6 * q^41 - 8 * q^43 + 12 * q^47 - 9 * q^49 + 4 * q^50 + q^52 - 12 * q^53 - 4 * q^56 + 9 * q^58 + q^61 + 8 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 24 * q^71 + 22 * q^73 - q^74 + 4 * q^76 + 16 * q^79 - 6 * q^80 - 12 * q^82 + 12 * q^83 - 9 * q^85 + 8 * q^86 - 6 * q^89 + 8 * q^91 - 12 * q^94 - 12 * q^95 - 2 * q^97 - 18 * q^98

Introduction

L-functions

Modular forms

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Database

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