LMFDB - Embedded newform 1386.2.k.m.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1386,2,Mod(793,1386)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1386, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1386.793");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1386.k (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:	$11.0672657201$
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			991.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.m.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(3.00000 + 5.19615i) q^{19} +1.00000 q^{20} -1.00000 q^{22} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} +(2.00000 - 1.73205i) q^{28} +8.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.00000 q^{34} +(0.500000 + 2.59808i) q^{35} +(4.00000 + 6.92820i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} -7.00000 q^{41} +4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.50000 + 6.06218i) q^{46} +(-0.500000 - 0.866025i) q^{47} +(5.50000 + 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +1.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(4.00000 + 6.92820i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(2.50000 + 4.33013i) q^{68} +(-2.00000 + 1.73205i) q^{70} +8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-4.00000 + 6.92820i) q^{74} -6.00000 q^{76} +(2.00000 - 1.73205i) q^{77} +(4.50000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.50000 - 6.06218i) q^{82} +15.0000 q^{83} -5.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-5.00000 - 1.73205i) q^{91} -7.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(3.00000 - 5.19615i) q^{95} +13.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 - 5 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - q^{5} - 5 q^{7} - 2 q^{8} + q^{10} - q^{11} + 4 q^{13} - q^{14} - q^{16} + 5 q^{17} + 6 q^{19} + 2 q^{20} - 2 q^{22} + 7 q^{23} + 4 q^{25} + 2 q^{26} + 4 q^{28} + 16 q^{29} - 10 q^{31} + q^{32} + 10 q^{34} + q^{35} + 8 q^{37} - 6 q^{38} + q^{40} - 14 q^{41} + 8 q^{43} - q^{44} - 7 q^{46} - q^{47} + 11 q^{49} + 8 q^{50} - 2 q^{52} + 6 q^{53} + 2 q^{55} + 5 q^{56} + 8 q^{58} + 6 q^{59} - q^{61} - 20 q^{62} + 2 q^{64} - 2 q^{65} - 3 q^{67} + 5 q^{68} - 4 q^{70} + 16 q^{71} - 10 q^{73} - 8 q^{74} - 12 q^{76} + 4 q^{77} + 9 q^{79} - q^{80} - 7 q^{82} + 30 q^{83} - 10 q^{85} + 4 q^{86} + q^{88} - 12 q^{89} - 10 q^{91} - 14 q^{92} + q^{94} + 6 q^{95} + 26 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 - 5 * q^7 - 2 * q^8 + q^10 - q^11 + 4 * q^13 - q^14 - q^16 + 5 * q^17 + 6 * q^19 + 2 * q^20 - 2 * q^22 + 7 * q^23 + 4 * q^25 + 2 * q^26 + 4 * q^28 + 16 * q^29 - 10 * q^31 + q^32 + 10 * q^34 + q^35 + 8 * q^37 - 6 * q^38 + q^40 - 14 * q^41 + 8 * q^43 - q^44 - 7 * q^46 - q^47 + 11 * q^49 + 8 * q^50 - 2 * q^52 + 6 * q^53 + 2 * q^55 + 5 * q^56 + 8 * q^58 + 6 * q^59 - q^61 - 20 * q^62 + 2 * q^64 - 2 * q^65 - 3 * q^67 + 5 * q^68 - 4 * q^70 + 16 * q^71 - 10 * q^73 - 8 * q^74 - 12 * q^76 + 4 * q^77 + 9 * q^79 - q^80 - 7 * q^82 + 30 * q^83 - 10 * q^85 + 4 * q^86 + q^88 - 12 * q^89 - 10 * q^91 - 14 * q^92 + q^94 + 6 * q^95 + 26 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1386\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$1135$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	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
$5$	−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
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	−1.00000			−0.353553
$9$		0			0
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$	−0.500000	−	2.59808i	−0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	−0.385499	−	0.922708i	$-0.625971\pi$
$17$	2.50000	−	4.33013i	0.606339	−	1.05021i	0.991838	−	0.127502i	$-0.0406959\pi$
$18$		0			0
$19$	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	$0.591714\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	−1.00000			−0.213201
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	0.956967	+	0.290196i	$0.0937204\pi$
$23$	3.50000	+	6.06218i	0.729800	+	1.26405i	−0.227167	+	0.973856i	$0.572946\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$		0			0
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.0680129	+	0.997684i	$0.521666\pi$
$31$	−5.00000	+	8.66025i	−0.898027	+	1.55543i	−0.830014	+	0.557743i	$0.811667\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	5.00000			0.857493
$35$	0.500000	+	2.59808i	0.0845154	+	0.439155i
$36$		0			0
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	0.981236	+	0.192809i	$0.0617599\pi$
$37$	4.00000	+	6.92820i	0.657596	+	1.13899i	−0.323640	+	0.946180i	$0.604907\pi$
$38$	−3.00000	+	5.19615i	−0.486664	+	0.842927i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	−3.50000	+	6.06218i	−0.516047	+	0.893819i
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	0.827253	−	0.561830i	$-0.189902\pi$
$47$	−0.500000	−	0.866025i	−0.0729325	−	0.126323i	−0.900185	+	0.435507i	$0.856569\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	4.00000			0.565685
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$		0			0
$55$	1.00000			0.134840
$56$	2.50000	+	0.866025i	0.334077	+	0.115728i
$57$		0			0
$58$	4.00000	+	6.92820i	0.525226	+	0.909718i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		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	$0.853725\pi$
$62$	−10.0000			−1.27000
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.00000	−	1.73205i	−0.124035	−	0.214834i
$66$		0			0
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$	2.50000	+	4.33013i	0.303170	+	0.525105i
$69$		0			0
$70$	−2.00000	+	1.73205i	−0.239046	+	0.207020i
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	0.409644	+	0.912245i	$0.365653\pi$
$73$	−5.00000	+	8.66025i	−0.585206	+	1.01361i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	−4.00000	+	6.92820i	−0.464991	+	0.805387i
$75$		0			0
$76$	−6.00000			−0.688247
$77$	2.00000	−	1.73205i	0.227921	−	0.197386i
$78$		0			0
$79$	4.50000	+	7.79423i	0.506290	+	0.876919i	0.999974	+	0.00727784i	$0.00231663\pi$
$79$	4.50000	+	7.79423i	0.506290	+	0.876919i	−0.493684	+	0.869641i	$0.664350\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$		0			0
$82$	−3.50000	−	6.06218i	−0.386510	−	0.669456i
$83$	15.0000			1.64646			0.823232	−	0.567705i	$-0.192169\pi$
$83$	15.0000			1.64646			0.823232	+	0.567705i	$0.192169\pi$
$84$		0			0
$85$	−5.00000			−0.542326
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$	−5.00000	−	1.73205i	−0.524142	−	0.181568i
$92$	−7.00000			−0.729800
$93$		0			0
$94$	0.500000	−	0.866025i	0.0515711	−	0.0893237i
$95$	3.00000	−	5.19615i	0.307794	−	0.533114i
$96$		0			0
$97$	13.0000			1.31995			0.659975	−	0.751288i	$-0.270567\pi$
$97$	13.0000			1.31995			0.659975	+	0.751288i	$0.270567\pi$
$98$	−1.00000	+	6.92820i	−0.101015	+	0.699854i
$99$		0			0
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$		0			0
$103$	−6.00000	−	10.3923i	−0.591198	−	1.02398i	−0.994071	−	0.108729i	$-0.965322\pi$
$103$	−6.00000	−	10.3923i	−0.591198	−	1.02398i	0.402874	−	0.915255i	$-0.368011\pi$
$104$	−2.00000			−0.196116
$105$		0			0
$106$	6.00000			0.582772
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	−0.987877	−	0.155238i	$-0.950386\pi$
$107$	−6.50000	−	11.2583i	−0.628379	−	1.08838i	0.359498	−	0.933146i	$-0.382948\pi$
$108$		0			0
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.0957826	+	0.995402i	$0.530535\pi$
$109$	−9.50000	+	16.4545i	−0.909935	+	1.57605i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$		0			0
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	−14.0000			−1.31701			−0.658505	−	0.752577i	$-0.728811\pi$
$113$	−14.0000			−1.31701			−0.658505	+	0.752577i	$0.728811\pi$
$114$		0			0
$115$	3.50000	−	6.06218i	0.326377	−	0.565301i
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$		0			0
$118$	6.00000			0.552345
$119$	−10.0000	+	8.66025i	−0.916698	+	0.793884i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.500000	−	0.866025i	0.0452679	−	0.0784063i
$123$		0			0
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$	−9.00000			−0.804984
$126$		0			0
$127$	17.0000			1.50851			0.754253	−	0.656584i	$-0.227999\pi$
$127$	17.0000			1.50851			0.754253	+	0.656584i	$0.227999\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	1.00000	−	1.73205i	0.0877058	−	0.151911i
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	0.999602	+	0.0281993i	$0.00897729\pi$
$131$	6.00000	+	10.3923i	0.524222	+	0.907980i	−0.475380	+	0.879781i	$0.657689\pi$
$132$		0			0
$133$	−3.00000	−	15.5885i	−0.260133	−	1.35169i
$134$	−3.00000			−0.259161
$135$		0			0
$136$	−2.50000	+	4.33013i	−0.214373	+	0.371305i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$	−2.50000	−	0.866025i	−0.211289	−	0.0731925i
$141$		0			0
$142$	4.00000	+	6.92820i	0.335673	+	0.581402i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$		0			0
$145$	−4.00000	−	6.92820i	−0.332182	−	0.575356i
$146$	−10.0000			−0.827606
$147$		0			0
$148$	−8.00000			−0.657596
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	0.772399	−	0.635138i	$-0.219057\pi$
$149$	−2.00000	−	3.46410i	−0.163846	−	0.283790i	−0.936245	+	0.351348i	$0.885723\pi$
$150$		0			0
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	−0.988969	−	0.148124i	$-0.952676\pi$
$151$	−4.50000	+	7.79423i	−0.366205	+	0.634285i	0.622764	+	0.782410i	$0.286010\pi$
$152$	−3.00000	−	5.19615i	−0.243332	−	0.421464i
$153$		0			0
$154$	2.50000	+	0.866025i	0.201456	+	0.0697863i
$155$	10.0000			0.803219
$156$		0			0
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	−0.934731	−	0.355357i	$-0.884359\pi$
$157$	−2.00000	+	3.46410i	−0.159617	+	0.276465i	0.775113	+	0.631822i	$0.217693\pi$
$158$	−4.50000	+	7.79423i	−0.358001	+	0.620076i
$159$		0			0
$160$	−1.00000			−0.0790569
$161$	−3.50000	−	18.1865i	−0.275839	−	1.43330i
$162$		0			0
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	−0.999944	−	0.0105623i	$-0.996638\pi$
$163$	−6.50000	−	11.2583i	−0.509119	−	0.881820i	0.490825	−	0.871258i	$-0.336695\pi$
$164$	3.50000	−	6.06218i	0.273304	−	0.473377i
$165$		0			0
$166$	7.50000	+	12.9904i	0.582113	+	1.00825i
$167$	8.00000			0.619059			0.309529	−	0.950890i	$-0.399829\pi$
$167$	8.00000			0.619059			0.309529	+	0.950890i	$0.399829\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	−2.50000	−	4.33013i	−0.191741	−	0.332106i
$171$		0			0
$172$	−2.00000	+	3.46410i	−0.152499	+	0.264135i
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	−0.999293	−	0.0375896i	$-0.988032\pi$
$173$	−7.00000	−	12.1244i	−0.532200	−	0.921798i	0.467093	−	0.884208i	$-0.345301\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	1.00000			0.0753778
$177$		0			0
$178$	6.00000	−	10.3923i	0.449719	−	0.778936i
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	−0.900975	−	0.433872i	$-0.857147\pi$
$179$	−1.00000	+	1.73205i	−0.0747435	+	0.129460i	0.826231	+	0.563331i	$0.190480\pi$
$180$		0			0
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−1.00000	−	5.19615i	−0.0741249	−	0.385164i
$183$		0			0
$184$	−3.50000	−	6.06218i	−0.258023	−	0.446910i
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$		0			0
$187$	2.50000	+	4.33013i	0.182818	+	0.316650i
$188$	1.00000			0.0729325
$189$		0			0
$190$	6.00000			0.435286
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	0.959558	+	0.281511i	$0.0908356\pi$
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	−0.235983	+	0.971757i	$0.575831\pi$
$192$		0			0
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	−0.973315	−	0.229475i	$-0.926299\pi$
$193$	−4.00000	+	6.92820i	−0.287926	+	0.498703i	0.685388	+	0.728178i	$0.259632\pi$
$194$	6.50000	+	11.2583i	0.466673	+	0.808301i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	24.0000			1.70993			0.854965	−	0.518686i	$-0.173579\pi$
$197$	24.0000			1.70993			0.854965	+	0.518686i	$0.173579\pi$
$198$		0			0
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.124521	−	0.992217i	$-0.460261\pi$
$199$	13.0000	−	22.5167i	0.921546	−	1.59616i	0.797025	−	0.603947i	$-0.206406\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	12.0000			0.844317
$203$	−20.0000	−	6.92820i	−1.40372	−	0.486265i
$204$		0			0
$205$	3.50000	+	6.06218i	0.244451	+	0.423401i
$206$	6.00000	−	10.3923i	0.418040	−	0.724066i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	6.50000	−	11.2583i	0.444331	−	0.769604i
$215$	−2.00000	−	3.46410i	−0.136399	−	0.236250i
$216$		0			0
$217$	20.0000	−	17.3205i	1.35769	−	1.17579i
$218$	−19.0000			−1.28684
$219$		0			0
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$	5.00000	−	8.66025i	0.336336	−	0.582552i
$222$		0			0
$223$	10.0000			0.669650			0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000			0.669650			0.334825	+	0.942280i	$0.391323\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	0.432962	+	0.901412i	$0.357468\pi$
$227$	−8.50000	+	14.7224i	−0.564165	+	0.977162i	−0.997127	+	0.0757500i	$0.975865\pi$
$228$		0			0
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	7.00000			0.461566
$231$		0			0
$232$	−8.00000			−0.525226
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	0.972523	+	0.232806i	$0.0747909\pi$
$233$	10.5000	+	18.1865i	0.687878	+	1.19144i	−0.284645	+	0.958633i	$0.591876\pi$
$234$		0			0
$235$	−0.500000	+	0.866025i	−0.0326164	+	0.0564933i
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$		0			0
$238$	−12.5000	−	4.33013i	−0.810255	−	0.280680i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$		0			0
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	−0.991975	−	0.126432i	$-0.959647\pi$
$241$	−6.00000	+	10.3923i	−0.386494	+	0.669427i	0.605481	+	0.795860i	$0.292981\pi$
$242$	0.500000	−	0.866025i	0.0321412	−	0.0556702i
$243$		0			0
$244$	1.00000			0.0640184
$245$	1.00000	−	6.92820i	0.0638877	−	0.442627i
$246$		0			0
$247$	6.00000	+	10.3923i	0.381771	+	0.661247i
$248$	5.00000	−	8.66025i	0.317500	−	0.549927i
$249$		0			0
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	−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
$253$	−7.00000			−0.440086
$254$	8.50000	+	14.7224i	0.533337	+	0.923768i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$257$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$258$		0			0
$259$	−4.00000	−	20.7846i	−0.248548	−	1.29149i
$260$	2.00000			0.124035
$261$		0			0
$262$	−6.00000	+	10.3923i	−0.370681	+	0.642039i
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	−0.442943	−	0.896550i	$-0.646065\pi$
$263$	9.00000	−	15.5885i	0.554964	−	0.961225i	0.997906	−	0.0646755i	$-0.0206012\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	12.0000	−	10.3923i	0.735767	−	0.637193i
$267$		0			0
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	−0.816668	−	0.577108i	$-0.804181\pi$
$269$	1.50000	−	2.59808i	0.0914566	−	0.158408i	0.908124	+	0.418701i	$0.137514\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	−5.00000			−0.303170
$273$		0			0
$274$	−18.0000			−1.08742
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	9.00000	−	15.5885i	0.540758	−	0.936620i	−0.458103	−	0.888899i	$-0.651471\pi$
$277$	9.00000	−	15.5885i	0.540758	−	0.936620i	0.998861	−	0.0477206i	$-0.0151957\pi$
$278$	1.00000	+	1.73205i	0.0599760	+	0.103882i
$279$		0			0
$280$	−0.500000	−	2.59808i	−0.0298807	−	0.155265i
$281$	19.0000			1.13344			0.566722	−	0.823909i	$-0.308211\pi$
$281$	19.0000			1.13344			0.566722	+	0.823909i	$0.308211\pi$
$282$		0			0
$283$	−12.0000	+	20.7846i	−0.713326	+	1.23552i	0.250276	+	0.968175i	$0.419479\pi$
$283$	−12.0000	+	20.7846i	−0.713326	+	1.23552i	−0.963602	+	0.267342i	$0.913855\pi$
$284$	−4.00000	+	6.92820i	−0.237356	+	0.411113i
$285$		0			0
$286$	−2.00000			−0.118262
$287$	17.5000	+	6.06218i	1.03299	+	0.357839i
$288$		0			0
$289$	−4.00000	−	6.92820i	−0.235294	−	0.407541i
$290$	4.00000	−	6.92820i	0.234888	−	0.406838i
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	−6.00000			−0.350524			−0.175262	−	0.984522i	$-0.556077\pi$
$293$	−6.00000			−0.350524			−0.175262	+	0.984522i	$0.556077\pi$
$294$		0			0
$295$	−6.00000			−0.349334
$296$	−4.00000	−	6.92820i	−0.232495	−	0.402694i
$297$		0			0
$298$	2.00000	−	3.46410i	0.115857	−	0.200670i
$299$	7.00000	+	12.1244i	0.404820	+	0.701170i
$300$		0			0
$301$	−10.0000	−	3.46410i	−0.576390	−	0.199667i
$302$	−9.00000			−0.517892
$303$		0			0
$304$	3.00000	−	5.19615i	0.172062	−	0.298020i
$305$	−0.500000	+	0.866025i	−0.0286299	+	0.0495885i
$306$		0			0
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$	0.500000	+	2.59808i	0.0284901	+	0.148039i
$309$		0			0
$310$	5.00000	+	8.66025i	0.283981	+	0.491869i
$311$	8.50000	−	14.7224i	0.481991	−	0.834833i	−0.517796	−	0.855504i	$-0.673247\pi$
$311$	8.50000	−	14.7224i	0.481991	−	0.834833i	0.999786	+	0.0206719i	$0.00658053\pi$
$312$		0			0
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	−4.00000			−0.225733
$315$		0			0
$316$	−9.00000			−0.506290
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	0.820822	−	0.571184i	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$		0			0
$322$	14.0000	−	12.1244i	0.780189	−	0.675664i
$323$	30.0000			1.66924
$324$		0			0
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$	6.50000	−	11.2583i	0.360002	−	0.623541i
$327$		0			0
$328$	7.00000			0.386510
$329$	0.500000	+	2.59808i	0.0275659	+	0.143237i
$330$		0			0
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	0.630232	−	0.776407i	$-0.282960\pi$
$331$	−6.50000	−	11.2583i	−0.357272	−	0.618814i	−0.987504	+	0.157593i	$0.949627\pi$
$332$	−7.50000	+	12.9904i	−0.411616	+	0.712940i
$333$		0			0
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	3.00000			0.163908
$336$		0			0
$337$	18.0000			0.980522			0.490261	−	0.871576i	$-0.336901\pi$
$337$	18.0000			0.980522			0.490261	+	0.871576i	$0.336901\pi$
$338$	−4.50000	−	7.79423i	−0.244768	−	0.423950i
$339$		0			0
$340$	2.50000	−	4.33013i	0.135582	−	0.234834i
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$		0			0
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	−4.00000			−0.215666
$345$		0			0
$346$	7.00000	−	12.1244i	0.376322	−	0.651809i
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	−0.986061	−	0.166383i	$-0.946791\pi$
$347$	−6.50000	+	11.2583i	−0.348938	+	0.604379i	0.637123	+	0.770762i	$0.280124\pi$
$348$		0			0
$349$	−13.0000			−0.695874			−0.347937	−	0.937518i	$-0.613118\pi$
$349$	−13.0000			−0.695874			−0.347937	+	0.937518i	$0.613118\pi$
$350$	−10.0000	−	3.46410i	−0.534522	−	0.185164i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	−0.934751	−	0.355303i	$-0.884378\pi$
$353$	−3.00000	+	5.19615i	−0.159674	+	0.276563i	0.775077	+	0.631867i	$0.217711\pi$
$354$		0			0
$355$	−4.00000	−	6.92820i	−0.212298	−	0.367711i
$356$	12.0000			0.635999
$357$		0			0
$358$	−2.00000			−0.105703
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$		0			0
$364$	4.00000	−	3.46410i	0.209657	−	0.181568i
$365$	10.0000			0.523424
$366$		0			0
$367$	1.00000	−	1.73205i	0.0521996	−	0.0904123i	−0.838745	−	0.544524i	$-0.816710\pi$
$367$	1.00000	−	1.73205i	0.0521996	−	0.0904123i	0.890945	+	0.454112i	$0.150043\pi$
$368$	3.50000	−	6.06218i	0.182450	−	0.316013i
$369$		0			0
$370$	8.00000			0.415900
$371$	−12.0000	+	10.3923i	−0.623009	+	0.539542i
$372$		0			0
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	0.983783	−	0.179364i	$-0.0574041\pi$
$373$	6.50000	+	11.2583i	0.336557	+	0.582934i	−0.647225	+	0.762299i	$0.724071\pi$
$374$	−2.50000	+	4.33013i	−0.129272	+	0.223906i
$375$		0			0
$376$	0.500000	+	0.866025i	0.0257855	+	0.0446619i
$377$	16.0000			0.824042
$378$		0			0
$379$	−17.0000			−0.873231			−0.436616	−	0.899648i	$-0.643823\pi$
$379$	−17.0000			−0.873231			−0.436616	+	0.899648i	$0.643823\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$		0			0
$382$	−10.0000	+	17.3205i	−0.511645	+	0.886194i
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$		0			0
$385$	−2.50000	−	0.866025i	−0.127412	−	0.0441367i
$386$	−8.00000			−0.407189
$387$		0			0
$388$	−6.50000	+	11.2583i	−0.329988	+	0.571555i
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	−0.610835	−	0.791758i	$-0.709166\pi$
$389$	7.50000	−	12.9904i	0.380265	−	0.658638i	0.991100	+	0.133120i	$0.0424994\pi$
$390$		0			0
$391$	35.0000			1.77003
$392$	−5.50000	−	4.33013i	−0.277792	−	0.218704i
$393$		0			0
$394$	12.0000	+	20.7846i	0.604551	+	1.04711i
$395$	4.50000	−	7.79423i	0.226420	−	0.392170i
$396$		0			0
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	−0.976392	+	0.216004i	$0.930698\pi$
$398$	26.0000			1.30326
$399$		0			0
$400$	−4.00000			−0.200000
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	0.676425	−	0.736512i	$-0.263528\pi$
$401$	−6.00000	−	10.3923i	−0.299626	−	0.518967i	−0.976050	+	0.217545i	$0.930195\pi$
$402$		0			0
$403$	−10.0000	+	17.3205i	−0.498135	+	0.862796i
$404$	6.00000	+	10.3923i	0.298511	+	0.517036i
$405$		0			0
$406$	−4.00000	−	20.7846i	−0.198517	−	1.03152i
$407$	−8.00000			−0.396545
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	−3.50000	+	6.06218i	−0.172853	+	0.299390i
$411$		0			0
$412$	12.0000			0.591198
$413$	−12.0000	+	10.3923i	−0.590481	+	0.511372i
$414$		0			0
$415$	−7.50000	−	12.9904i	−0.368161	−	0.637673i
$416$	1.00000	−	1.73205i	0.0490290	−	0.0849208i
$417$		0			0
$418$	−3.00000	−	5.19615i	−0.146735	−	0.254152i
$419$	−10.0000			−0.488532			−0.244266	−	0.969708i	$-0.578547\pi$
$419$	−10.0000			−0.488532			−0.244266	+	0.969708i	$0.578547\pi$
$420$		0			0
$421$	16.0000			0.779792			0.389896	−	0.920859i	$-0.372511\pi$
$421$	16.0000			0.779792			0.389896	+	0.920859i	$0.372511\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$		0			0
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	−10.0000	−	17.3205i	−0.485071	−	0.840168i
$426$		0			0
$427$	0.500000	+	2.59808i	0.0241967	+	0.125730i
$428$	13.0000			0.628379
$429$		0			0
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	−0.720113	−	0.693857i	$-0.755910\pi$
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	0.960954	+	0.276707i	$0.0892433\pi$
$432$		0			0
$433$	−13.0000			−0.624740			−0.312370	−	0.949960i	$-0.601123\pi$
$433$	−13.0000			−0.624740			−0.312370	+	0.949960i	$0.601123\pi$
$434$	25.0000	+	8.66025i	1.20004	+	0.415705i
$435$		0			0
$436$	−9.50000	−	16.4545i	−0.454967	−	0.788027i
$437$	−21.0000	+	36.3731i	−1.00457	+	1.73996i
$438$		0			0
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	0.770334	−	0.637641i	$-0.220089\pi$
$439$	−3.50000	−	6.06218i	−0.167046	−	0.289332i	−0.937380	+	0.348309i	$0.886756\pi$
$440$	−1.00000			−0.0476731
$441$		0			0
$442$	10.0000			0.475651
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	0.996551	+	0.0829786i	$0.0264433\pi$
$443$	12.0000	+	20.7846i	0.570137	+	0.987507i	−0.426414	+	0.904528i	$0.640223\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	5.00000	+	8.66025i	0.236757	+	0.410075i
$447$		0			0
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−36.0000			−1.69895			−0.849473	−	0.527633i	$-0.823080\pi$
$449$	−36.0000			−1.69895			−0.849473	+	0.527633i	$0.823080\pi$
$450$		0			0
$451$	3.50000	−	6.06218i	0.164809	−	0.285457i
$452$	7.00000	−	12.1244i	0.329252	−	0.570282i
$453$		0			0
$454$	−17.0000			−0.797850
$455$	1.00000	+	5.19615i	0.0468807	+	0.243599i
$456$		0			0
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	0.757174	−	0.653213i	$-0.226579\pi$
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	−0.944286	+	0.329125i	$0.893246\pi$
$458$	10.0000	−	17.3205i	0.467269	−	0.809334i
$459$		0			0
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	30.0000			1.39724			0.698620	−	0.715493i	$-0.253798\pi$
$461$	30.0000			1.39724			0.698620	+	0.715493i	$0.253798\pi$
$462$		0			0
$463$	4.00000			0.185896			0.0929479	−	0.995671i	$-0.470371\pi$
$463$	4.00000			0.185896			0.0929479	+	0.995671i	$0.470371\pi$
$464$	−4.00000	−	6.92820i	−0.185695	−	0.321634i
$465$		0			0
$466$	−10.5000	+	18.1865i	−0.486403	+	0.842475i
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	0.927052	−	0.374934i	$-0.122335\pi$
$467$	3.00000	+	5.19615i	0.138823	+	0.240449i	−0.788228	+	0.615383i	$0.789001\pi$
$468$		0			0
$469$	6.00000	−	5.19615i	0.277054	−	0.239936i
$470$	−1.00000			−0.0461266
$471$		0			0
$472$	−3.00000	+	5.19615i	−0.138086	+	0.239172i
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	24.0000			1.10120
$476$	−2.50000	−	12.9904i	−0.114587	−	0.595413i
$477$		0			0
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	−0.908093	−	0.418769i	$-0.862462\pi$
$479$	−2.00000	+	3.46410i	−0.0913823	+	0.158279i	0.816711	+	0.577047i	$0.195795\pi$
$480$		0			0
$481$	8.00000	+	13.8564i	0.364769	+	0.631798i
$482$	−12.0000			−0.546585
$483$		0			0
$484$	1.00000			0.0454545
$485$	−6.50000	−	11.2583i	−0.295150	−	0.511214i
$486$		0			0
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	−0.730218	−	0.683214i	$-0.760582\pi$
$487$	5.00000	−	8.66025i	0.226572	−	0.392434i	0.956790	+	0.290780i	$0.0939149\pi$
$488$	0.500000	+	0.866025i	0.0226339	+	0.0392031i
$489$		0			0
$490$	6.50000	−	2.59808i	0.293640	−	0.117369i
$491$	−9.00000			−0.406164			−0.203082	−	0.979162i	$-0.565096\pi$
$491$	−9.00000			−0.406164			−0.203082	+	0.979162i	$0.565096\pi$
$492$		0			0
$493$	20.0000	−	34.6410i	0.900755	−	1.56015i
$494$	−6.00000	+	10.3923i	−0.269953	+	0.467572i
$495$		0			0
$496$	10.0000			0.449013
$497$	−20.0000	−	6.92820i	−0.897123	−	0.310772i
$498$		0			0
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	0.988204	+	0.153141i	$0.0489388\pi$
$499$	14.0000	+	24.2487i	0.626726	+	1.08552i	−0.361478	+	0.932381i	$0.617728\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$		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
$505$	−12.0000			−0.533993
$506$	−3.50000	−	6.06218i	−0.155594	−	0.269497i
$507$		0			0
$508$	−8.50000	+	14.7224i	−0.377127	+	0.653202i
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	0.512331	−	0.858788i	$-0.328782\pi$
$509$	−11.0000	−	19.0526i	−0.487566	−	0.844490i	−0.999898	+	0.0142980i	$0.995449\pi$
$510$		0			0
$511$	20.0000	−	17.3205i	0.884748	−	0.766214i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		0			0
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$		0			0
$517$	1.00000			0.0439799
$518$	16.0000	−	13.8564i	0.703000	−	0.608816i
$519$		0			0
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	−0.735465	−	0.677563i	$-0.763036\pi$
$521$	5.00000	−	8.66025i	0.219054	−	0.379413i	0.954519	+	0.298150i	$0.0963696\pi$
$522$		0			0
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	0.950958	+	0.309320i	$0.100101\pi$
$523$	17.0000	+	29.4449i	0.743358	+	1.28753i	−0.207600	+	0.978214i	$0.566565\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$	18.0000			0.784837
$527$	25.0000	+	43.3013i	1.08902	+	1.88623i
$528$		0			0
$529$	−13.0000	+	22.5167i	−0.565217	+	0.978985i
$530$	−3.00000	−	5.19615i	−0.130312	−	0.225706i
$531$		0			0
$532$	15.0000	+	5.19615i	0.650332	+	0.225282i
$533$	−14.0000			−0.606407
$534$		0			0
$535$	−6.50000	+	11.2583i	−0.281020	+	0.486740i
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$		0			0
$538$	3.00000			0.129339
$539$	−6.50000	+	2.59808i	−0.279975	+	0.111907i
$540$		0			0
$541$	0.500000	+	0.866025i	0.0214967	+	0.0372333i	0.876574	−	0.481268i	$-0.159824\pi$
$541$	0.500000	+	0.866025i	0.0214967	+	0.0372333i	−0.855077	+	0.518501i	$0.826490\pi$
$542$	8.00000	−	13.8564i	0.343629	−	0.595184i
$543$		0			0
$544$	−2.50000	−	4.33013i	−0.107187	−	0.185653i
$545$	19.0000			0.813871
$546$		0			0
$547$	6.00000			0.256541			0.128271	−	0.991739i	$-0.459057\pi$
$547$	6.00000			0.256541			0.128271	+	0.991739i	$0.459057\pi$
$548$	−9.00000	−	15.5885i	−0.384461	−	0.665906i
$549$		0			0
$550$	−2.00000	+	3.46410i	−0.0852803	+	0.147710i
$551$	24.0000	+	41.5692i	1.02243	+	1.77091i
$552$		0			0
$553$	−4.50000	−	23.3827i	−0.191359	−	0.994333i
$554$	18.0000			0.764747
$555$		0			0
$556$	−1.00000	+	1.73205i	−0.0424094	+	0.0734553i
$557$	−8.00000	+	13.8564i	−0.338971	+	0.587115i	−0.984239	−	0.176841i	$-0.943412\pi$
$557$	−8.00000	+	13.8564i	−0.338971	+	0.587115i	0.645269	+	0.763956i	$0.276745\pi$
$558$		0			0
$559$	8.00000			0.338364
$560$	2.00000	−	1.73205i	0.0845154	−	0.0731925i
$561$		0			0
$562$	9.50000	+	16.4545i	0.400733	+	0.694090i
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	0.404198	+	0.914671i	$0.367551\pi$
$563$	−14.0000	+	24.2487i	−0.590030	+	1.02196i	−0.994228	+	0.107290i	$0.965783\pi$
$564$		0			0
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	−24.0000			−1.00880
$567$		0			0
$568$	−8.00000			−0.335673
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.850935	−	0.525271i	$-0.823964\pi$
$569$	−21.0000	−	36.3731i	−0.880366	−	1.52484i	−0.0294311	−	0.999567i	$-0.509370\pi$
$570$		0			0
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	0.648655	+	0.761083i	$0.275332\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$	3.50000	+	18.1865i	0.146087	+	0.759091i
$575$	28.0000			1.16768
$576$		0			0
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	−0.783930	−	0.620850i	$-0.786788\pi$
$577$	3.50000	−	6.06218i	0.145707	−	0.252372i	0.929636	+	0.368478i	$0.120121\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	8.00000			0.332182
$581$	−37.5000	−	12.9904i	−1.55576	−	0.538932i
$582$		0			0
$583$	3.00000	+	5.19615i	0.124247	+	0.215203i
$584$	5.00000	−	8.66025i	0.206901	−	0.358364i
$585$		0			0
$586$	−3.00000	−	5.19615i	−0.123929	−	0.214651i
$587$	−42.0000			−1.73353			−0.866763	−	0.498721i	$-0.833803\pi$
$587$	−42.0000			−1.73353			−0.866763	+	0.498721i	$0.833803\pi$
$588$		0			0
$589$	−60.0000			−2.47226
$590$	−3.00000	−	5.19615i	−0.123508	−	0.213922i
$591$		0			0
$592$	4.00000	−	6.92820i	0.164399	−	0.284747i
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	0.797831	−	0.602881i	$-0.205981\pi$
$593$	−3.00000	−	5.19615i	−0.123195	−	0.213380i	−0.921026	+	0.389501i	$0.872647\pi$
$594$		0			0
$595$	12.5000	+	4.33013i	0.512450	+	0.177518i
$596$	4.00000			0.163846
$597$		0			0
$598$	−7.00000	+	12.1244i	−0.286251	+	0.495802i
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	−0.833753	−	0.552137i	$-0.813812\pi$
$599$	1.50000	−	2.59808i	0.0612883	−	0.106155i	0.895042	+	0.445983i	$0.147146\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$	−2.00000	−	10.3923i	−0.0815139	−	0.423559i
$603$		0			0
$604$	−4.50000	−	7.79423i	−0.183102	−	0.317143i
$605$	−0.500000	+	0.866025i	−0.0203279	+	0.0352089i
$606$		0			0
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−14.5000	−	25.1147i	−0.588537	−	1.01938i	0.405887	−	0.913923i	$-0.366962\pi$
$608$	6.00000			0.243332
$609$		0			0
$610$	−1.00000			−0.0404888
$611$	−1.00000	−	1.73205i	−0.0404557	−	0.0700713i
$612$		0			0
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	−0.733316	−	0.679888i	$-0.762028\pi$
$613$	5.50000	−	9.52628i	0.222143	−	0.384763i	0.955458	+	0.295126i	$0.0953615\pi$
$614$	4.00000	+	6.92820i	0.161427	+	0.279600i
$615$		0			0
$616$	−2.00000	+	1.73205i	−0.0805823	+	0.0697863i
$617$	24.0000			0.966204			0.483102	−	0.875564i	$-0.339510\pi$
$617$	24.0000			0.966204			0.483102	+	0.875564i	$0.339510\pi$
$618$		0			0
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	−0.787075	−	0.616858i	$-0.788405\pi$
$619$	3.50000	−	6.06218i	0.140677	−	0.243659i	0.927752	+	0.373198i	$0.121739\pi$
$620$	−5.00000	+	8.66025i	−0.200805	+	0.347804i
$621$		0			0
$622$	17.0000			0.681638
$623$	6.00000	+	31.1769i	0.240385	+	1.24908i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	11.0000	−	19.0526i	0.439648	−	0.761493i
$627$		0			0
$628$	−2.00000	−	3.46410i	−0.0798087	−	0.138233i
$629$	40.0000			1.59490
$630$		0			0
$631$	−42.0000			−1.67199			−0.835997	−	0.548734i	$-0.815110\pi$
$631$	−42.0000			−1.67199			−0.835997	+	0.548734i	$0.815110\pi$
$632$	−4.50000	−	7.79423i	−0.179000	−	0.310038i
$633$		0			0
$634$	1.50000	−	2.59808i	0.0595726	−	0.103183i
$635$	−8.50000	−	14.7224i	−0.337312	−	0.584242i
$636$		0			0
$637$	11.0000	+	8.66025i	0.435836	+	0.343132i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	−0.959848	−	0.280521i	$-0.909493\pi$
$641$	−6.00000	+	10.3923i	−0.236986	+	0.410471i	0.722862	+	0.690992i	$0.242826\pi$
$642$		0			0
$643$	4.00000			0.157745			0.0788723	−	0.996885i	$-0.474868\pi$
$643$	4.00000			0.157745			0.0788723	+	0.996885i	$0.474868\pi$
$644$	17.5000	+	6.06218i	0.689597	+	0.238883i
$645$		0			0
$646$	15.0000	+	25.9808i	0.590167	+	1.02220i
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.0383563	+	0.999264i	$0.512212\pi$
$647$	−22.5000	+	38.9711i	−0.884566	+	1.53211i	−0.846210	+	0.532850i	$0.821121\pi$
$648$		0			0
$649$	3.00000	+	5.19615i	0.117760	+	0.203967i
$650$	8.00000			0.313786
$651$		0			0
$652$	13.0000			0.509119
$653$	6.50000	+	11.2583i	0.254365	+	0.440573i	0.964723	−	0.263268i	$-0.0848003\pi$
$653$	6.50000	+	11.2583i	0.254365	+	0.440573i	−0.710358	+	0.703840i	$0.751467\pi$
$654$		0			0
$655$	6.00000	−	10.3923i	0.234439	−	0.406061i
$656$	3.50000	+	6.06218i	0.136652	+	0.236688i
$657$		0			0
$658$	−2.00000	+	1.73205i	−0.0779681	+	0.0675224i
$659$	−19.0000			−0.740135			−0.370067	−	0.929005i	$-0.620665\pi$
$659$	−19.0000			−0.740135			−0.370067	+	0.929005i	$0.620665\pi$
$660$		0			0
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	6.50000	−	11.2583i	0.252630	−	0.437567i
$663$		0			0
$664$	−15.0000			−0.582113
$665$	−12.0000	+	10.3923i	−0.465340	+	0.402996i
$666$		0			0
$667$	28.0000	+	48.4974i	1.08416	+	1.87783i
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$		0			0
$670$	1.50000	+	2.59808i	0.0579501	+	0.100372i
$671$	1.00000			0.0386046
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$	9.00000	+	15.5885i	0.346667	+	0.600445i
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	0.884602	−	0.466347i	$-0.154430\pi$
$677$	1.00000	+	1.73205i	0.0384331	+	0.0665681i	−0.846169	+	0.532915i	$0.821097\pi$
$678$		0			0
$679$	−32.5000	−	11.2583i	−1.24724	−	0.432055i
$680$	5.00000			0.191741
$681$		0			0
$682$	5.00000	−	8.66025i	0.191460	−	0.331618i
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$		0			0
$685$	18.0000			0.687745
$686$	8.50000	−	16.4545i	0.324532	−	0.628235i
$687$		0			0
$688$	−2.00000	−	3.46410i	−0.0762493	−	0.132068i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	0.687372	−	0.726306i	$-0.258764\pi$
$691$	−7.50000	−	12.9904i	−0.285313	−	0.494177i	−0.972685	+	0.232128i	$0.925431\pi$
$692$	14.0000			0.532200
$693$		0			0
$694$	−13.0000			−0.493473
$695$	−1.00000	−	1.73205i	−0.0379322	−	0.0657004i
$696$		0			0
$697$	−17.5000	+	30.3109i	−0.662860	+	1.14811i
$698$	−6.50000	−	11.2583i	−0.246029	−	0.426134i
$699$		0			0
$700$	−2.00000	−	10.3923i	−0.0755929	−	0.392792i
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−24.0000	+	41.5692i	−0.905177	+	1.56781i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−6.00000			−0.225813
$707$	−24.0000	+	20.7846i	−0.902613	+	0.781686i
$708$		0			0
$709$	21.0000	+	36.3731i	0.788672	+	1.36602i	0.926781	+	0.375602i	$0.122564\pi$
$709$	21.0000	+	36.3731i	0.788672	+	1.36602i	−0.138109	+	0.990417i	$0.544103\pi$
$710$	4.00000	−	6.92820i	0.150117	−	0.260011i
$711$		0			0
$712$	6.00000	+	10.3923i	0.224860	+	0.389468i
$713$	−70.0000			−2.62152
$714$		0			0
$715$	2.00000			0.0747958
$716$	−1.00000	−	1.73205i	−0.0373718	−	0.0647298i
$717$		0			0
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	0.815636	−	0.578565i	$-0.196387\pi$
$719$	−2.50000	−	4.33013i	−0.0932343	−	0.161486i	−0.908870	+	0.417079i	$0.863054\pi$
$720$		0			0
$721$	6.00000	+	31.1769i	0.223452	+	1.16109i
$722$	−17.0000			−0.632674
$723$		0			0
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	16.0000	−	27.7128i	0.594225	−	1.02923i
$726$		0			0
$727$	20.0000			0.741759			0.370879	−	0.928681i	$-0.379056\pi$
$727$	20.0000			0.741759			0.370879	+	0.928681i	$0.379056\pi$
$728$	5.00000	+	1.73205i	0.185312	+	0.0641941i
$729$		0			0
$730$	5.00000	+	8.66025i	0.185058	+	0.320530i
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$		0			0
$733$	18.5000	+	32.0429i	0.683313	+	1.18353i	0.973964	+	0.226704i	$0.0727949\pi$
$733$	18.5000	+	32.0429i	0.683313	+	1.18353i	−0.290651	+	0.956829i	$0.593872\pi$
$734$	2.00000			0.0738213
$735$		0			0
$736$	7.00000			0.258023
$737$	−1.50000	−	2.59808i	−0.0552532	−	0.0957014i
$738$		0			0
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	−0.915914	−	0.401374i	$-0.868533\pi$
$739$	−3.00000	+	5.19615i	−0.110357	+	0.191144i	0.805557	+	0.592518i	$0.201866\pi$
$740$	4.00000	+	6.92820i	0.147043	+	0.254686i
$741$		0			0
$742$	−15.0000	−	5.19615i	−0.550667	−	0.190757i
$743$	12.0000			0.440237			0.220119	−	0.975473i	$-0.429356\pi$
$743$	12.0000			0.440237			0.220119	+	0.975473i	$0.429356\pi$
$744$		0			0
$745$	−2.00000	+	3.46410i	−0.0732743	+	0.126915i
$746$	−6.50000	+	11.2583i	−0.237982	+	0.412197i
$747$		0			0
$748$	−5.00000			−0.182818
$749$	6.50000	+	33.7750i	0.237505	+	1.23411i
$750$		0			0
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	0.970744	+	0.240118i	$0.0771860\pi$
$751$	19.0000	+	32.9090i	0.693320	+	1.20087i	−0.277424	+	0.960748i	$0.589481\pi$
$752$	−0.500000	+	0.866025i	−0.0182331	+	0.0315807i
$753$		0			0
$754$	8.00000	+	13.8564i	0.291343	+	0.504621i
$755$	9.00000			0.327544
$756$		0			0
$757$	−10.0000			−0.363456			−0.181728	−	0.983349i	$-0.558169\pi$
$757$	−10.0000			−0.363456			−0.181728	+	0.983349i	$0.558169\pi$
$758$	−8.50000	−	14.7224i	−0.308734	−	0.534743i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−19.5000	−	33.7750i	−0.706874	−	1.22434i	−0.966011	−	0.258502i	$-0.916771\pi$
$761$	−19.5000	−	33.7750i	−0.706874	−	1.22434i	0.259136	−	0.965841i	$-0.416562\pi$
$762$		0			0
$763$	38.0000	−	32.9090i	1.37569	−	1.19138i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	8.00000	−	13.8564i	0.289052	−	0.500652i
$767$	6.00000	−	10.3923i	0.216647	−	0.375244i
$768$		0			0
$769$	34.0000			1.22607			0.613036	−	0.790055i	$-0.289948\pi$
$769$	34.0000			1.22607			0.613036	+	0.790055i	$0.289948\pi$
$770$	−0.500000	−	2.59808i	−0.0180187	−	0.0936282i
$771$		0			0
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	−16.5000	+	28.5788i	−0.593464	+	1.02791i	0.400298	+	0.916385i	$0.368907\pi$
$773$	−16.5000	+	28.5788i	−0.593464	+	1.02791i	−0.993762	+	0.111524i	$0.964427\pi$
$774$		0			0
$775$	20.0000	+	34.6410i	0.718421	+	1.24434i
$776$	−13.0000			−0.466673
$777$		0			0
$778$	15.0000			0.537776
$779$	−21.0000	−	36.3731i	−0.752403	−	1.30320i
$780$		0			0
$781$	−4.00000	+	6.92820i	−0.143131	+	0.247911i
$782$	17.5000	+	30.3109i	0.625799	+	1.08392i
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	4.00000			0.142766
$786$		0			0
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	−0.963394	−	0.268091i	$-0.913607\pi$
$787$	−7.00000	+	12.1244i	−0.249523	+	0.432187i	0.713871	+	0.700278i	$0.246941\pi$
$788$	−12.0000	+	20.7846i	−0.427482	+	0.740421i
$789$		0			0
$790$	9.00000			0.320206
$791$	35.0000	+	12.1244i	1.24446	+	0.431092i
$792$		0			0
$793$	−1.00000	−	1.73205i	−0.0355110	−	0.0615069i
$794$	6.00000	−	10.3923i	0.212932	−	0.368809i
$795$		0			0
$796$	13.0000	+	22.5167i	0.460773	+	0.798082i
$797$	−23.0000			−0.814702			−0.407351	−	0.913272i	$-0.633547\pi$
$797$	−23.0000			−0.814702			−0.407351	+	0.913272i	$0.633547\pi$
$798$		0			0
$799$	−5.00000			−0.176887
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$		0			0
$802$	6.00000	−	10.3923i	0.211867	−	0.366965i
$803$	−5.00000	−	8.66025i	−0.176446	−	0.305614i
$804$		0			0
$805$	−14.0000	+	12.1244i	−0.493435	+	0.427327i
$806$	−20.0000			−0.704470
$807$		0			0
$808$	−6.00000	+	10.3923i	−0.211079	+	0.365600i
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	−0.776012	−	0.630718i	$-0.782761\pi$
$809$	4.50000	−	7.79423i	0.158212	−	0.274030i	0.934224	+	0.356687i	$0.116094\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$	16.0000	−	13.8564i	0.561490	−	0.486265i
$813$		0			0
$814$	−4.00000	−	6.92820i	−0.140200	−	0.242833i
$815$	−6.50000	+	11.2583i	−0.227685	+	0.394362i
$816$		0			0
$817$	12.0000	+	20.7846i	0.419827	+	0.727161i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	−7.00000			−0.244451
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	0.913616	−	0.406578i	$-0.133278\pi$
$821$	3.00000	+	5.19615i	0.104701	+	0.181347i	−0.808915	+	0.587925i	$0.799945\pi$
$822$		0			0
$823$	5.00000	−	8.66025i	0.174289	−	0.301877i	−0.765626	−	0.643286i	$-0.777571\pi$
$823$	5.00000	−	8.66025i	0.174289	−	0.301877i	0.939915	+	0.341409i	$0.110904\pi$
$824$	6.00000	+	10.3923i	0.209020	+	0.362033i
$825$		0			0
$826$	−15.0000	−	5.19615i	−0.521917	−	0.180797i
$827$	43.0000			1.49526			0.747628	−	0.664117i	$-0.231193\pi$
$827$	43.0000			1.49526			0.747628	+	0.664117i	$0.231193\pi$
$828$		0			0
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	−0.638457	−	0.769657i	$-0.720427\pi$
$829$	10.0000	−	17.3205i	0.347314	−	0.601566i	0.985771	+	0.168091i	$0.0537604\pi$
$830$	7.50000	−	12.9904i	0.260329	−	0.450903i
$831$		0			0
$832$	2.00000			0.0693375
$833$	32.5000	−	12.9904i	1.12606	−	0.450090i
$834$		0			0
$835$	−4.00000	−	6.92820i	−0.138426	−	0.239760i
$836$	3.00000	−	5.19615i	0.103757	−	0.179713i
$837$		0			0
$838$	−5.00000	−	8.66025i	−0.172722	−	0.299164i
$839$	−21.0000			−0.725001			−0.362500	−	0.931984i	$-0.618077\pi$
$839$	−21.0000			−0.725001			−0.362500	+	0.931984i	$0.618077\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	8.00000	+	13.8564i	0.275698	+	0.477523i
$843$		0			0
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$		0			0
$847$	0.500000	+	2.59808i	0.0171802	+	0.0892710i
$848$	−6.00000			−0.206041
$849$		0			0
$850$	10.0000	−	17.3205i	0.342997	−	0.594089i
$851$	−28.0000	+	48.4974i	−0.959828	+	1.66247i
$852$		0			0
$853$	−7.00000			−0.239675			−0.119838	−	0.992793i	$-0.538237\pi$
$853$	−7.00000			−0.239675			−0.119838	+	0.992793i	$0.538237\pi$
$854$	−2.00000	+	1.73205i	−0.0684386	+	0.0592696i
$855$		0			0
$856$	6.50000	+	11.2583i	0.222165	+	0.384802i
$857$	−3.50000	+	6.06218i	−0.119558	+	0.207080i	−0.919592	−	0.392874i	$-0.871481\pi$
$857$	−3.50000	+	6.06218i	−0.119558	+	0.207080i	0.800035	+	0.599954i	$0.204814\pi$
$858$		0			0
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	0.570064	−	0.821600i	$-0.306918\pi$
$859$	−12.5000	−	21.6506i	−0.426494	−	0.738710i	−0.996559	+	0.0828900i	$0.973585\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$	10.0000			0.340601
$863$	−2.50000	−	4.33013i	−0.0851010	−	0.147399i	0.820333	−	0.571886i	$-0.193788\pi$
$863$	−2.50000	−	4.33013i	−0.0851010	−	0.147399i	−0.905434	+	0.424487i	$0.860455\pi$
$864$		0			0
$865$	−7.00000	+	12.1244i	−0.238007	+	0.412240i
$866$	−6.50000	−	11.2583i	−0.220879	−	0.382574i
$867$		0			0
$868$	5.00000	+	25.9808i	0.169711	+	0.881845i
$869$	−9.00000			−0.305304
$870$		0			0
$871$	−3.00000	+	5.19615i	−0.101651	+	0.176065i
$872$	9.50000	−	16.4545i	0.321711	−	0.557219i
$873$		0			0
$874$	−42.0000			−1.42067
$875$	22.5000	+	7.79423i	0.760639	+	0.263493i
$876$		0			0
$877$	20.5000	+	35.5070i	0.692236	+	1.19899i	0.971104	+	0.238658i	$0.0767075\pi$
$877$	20.5000	+	35.5070i	0.692236	+	1.19899i	−0.278868	+	0.960329i	$0.589959\pi$
$878$	3.50000	−	6.06218i	0.118119	−	0.204589i
$879$		0			0
$880$	−0.500000	−	0.866025i	−0.0168550	−	0.0291937i
$881$	54.0000			1.81931			0.909653	−	0.415369i	$-0.136347\pi$
$881$	54.0000			1.81931			0.909653	+	0.415369i	$0.136347\pi$
$882$		0			0
$883$	−47.0000			−1.58168			−0.790838	−	0.612026i	$-0.790355\pi$
$883$	−47.0000			−1.58168			−0.790838	+	0.612026i	$0.790355\pi$
$884$	5.00000	+	8.66025i	0.168168	+	0.291276i
$885$		0			0
$886$	−12.0000	+	20.7846i	−0.403148	+	0.698273i
$887$	−1.00000	−	1.73205i	−0.0335767	−	0.0581566i	0.848749	−	0.528796i	$-0.177356\pi$
$887$	−1.00000	−	1.73205i	−0.0335767	−	0.0581566i	−0.882325	+	0.470640i	$0.844023\pi$
$888$		0			0
$889$	−42.5000	−	14.7224i	−1.42540	−	0.493775i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−5.00000	+	8.66025i	−0.167412	+	0.289967i
$893$	3.00000	−	5.19615i	0.100391	−	0.173883i
$894$		0			0
$895$	2.00000			0.0668526
$896$	−0.500000	−	2.59808i	−0.0167038	−	0.0867956i
$897$		0			0
$898$	−18.0000	−	31.1769i	−0.600668	−	1.04039i
$899$	−40.0000	+	69.2820i	−1.33407	+	2.31069i
$900$		0			0
$901$	−15.0000	−	25.9808i	−0.499722	−	0.865545i
$902$	7.00000			0.233075
$903$		0			0
$904$	14.0000			0.465633
$905$	−10.0000	−	17.3205i	−0.332411	−	0.575753i
$906$		0			0
$907$	−8.50000	+	14.7224i	−0.282238	+	0.488850i	−0.971936	−	0.235247i	$-0.924410\pi$
$907$	−8.50000	+	14.7224i	−0.282238	+	0.488850i	0.689698	+	0.724097i	$0.257743\pi$
$908$	−8.50000	−	14.7224i	−0.282082	−	0.488581i
$909$		0			0
$910$	−4.00000	+	3.46410i	−0.132599	+	0.114834i
$911$	39.0000			1.29213			0.646064	−	0.763283i	$-0.276414\pi$
$911$	39.0000			1.29213			0.646064	+	0.763283i	$0.276414\pi$
$912$		0			0
$913$	−7.50000	+	12.9904i	−0.248214	+	0.429919i
$914$	4.00000	−	6.92820i	0.132308	−	0.229165i
$915$		0			0
$916$	20.0000			0.660819
$917$	−6.00000	−	31.1769i	−0.198137	−	1.02955i
$918$		0			0
$919$	−19.5000	−	33.7750i	−0.643246	−	1.11413i	−0.984704	−	0.174237i	$-0.944254\pi$
$919$	−19.5000	−	33.7750i	−0.643246	−	1.11413i	0.341458	−	0.939897i	$-0.389079\pi$
$920$	−3.50000	+	6.06218i	−0.115392	+	0.199864i
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	16.0000			0.526646
$924$		0			0
$925$	32.0000			1.05215
$926$	2.00000	+	3.46410i	0.0657241	+	0.113837i
$927$		0			0
$928$	4.00000	−	6.92820i	0.131306	−	0.227429i
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$	−6.00000	+	41.5692i	−0.196642	+	1.36238i
$932$	−21.0000			−0.687878
$933$		0			0
$934$	−3.00000	+	5.19615i	−0.0981630	+	0.170023i
$935$	2.50000	−	4.33013i	0.0817587	−	0.141610i
$936$		0			0
$937$	42.0000			1.37208			0.686040	−	0.727564i	$-0.259347\pi$
$937$	42.0000			1.37208			0.686040	+	0.727564i	$0.259347\pi$
$938$	7.50000	+	2.59808i	0.244884	+	0.0848302i
$939$		0			0
$940$	−0.500000	−	0.866025i	−0.0163082	−	0.0282466i
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	−0.957273	−	0.289187i	$-0.906615\pi$
$941$	−7.00000	+	12.1244i	−0.228193	+	0.395243i	0.729079	+	0.684429i	$0.239949\pi$
$942$		0			0
$943$	−24.5000	−	42.4352i	−0.797830	−	1.38188i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−4.00000			−0.130051
$947$	−29.0000	−	50.2295i	−0.942373	−	1.63224i	−0.760927	−	0.648838i	$-0.775255\pi$
$947$	−29.0000	−	50.2295i	−0.942373	−	1.63224i	−0.181447	−	0.983401i	$-0.558078\pi$
$948$		0			0
$949$	−10.0000	+	17.3205i	−0.324614	+	0.562247i
$950$	12.0000	+	20.7846i	0.389331	+	0.674342i
$951$		0			0
$952$	10.0000	−	8.66025i	0.324102	−	0.280680i
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$		0			0
$955$	10.0000	−	17.3205i	0.323592	−	0.560478i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$		0			0
$958$	−4.00000			−0.129234
$959$	36.0000	−	31.1769i	1.16250	−	1.00676i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	−8.00000	+	13.8564i	−0.257930	+	0.446748i
$963$		0			0
$964$	−6.00000	−	10.3923i	−0.193247	−	0.334714i
$965$	8.00000			0.257529
$966$		0			0
$967$	35.0000			1.12552			0.562762	−	0.826619i	$-0.309739\pi$
$967$	35.0000			1.12552			0.562762	+	0.826619i	$0.309739\pi$
$968$	0.500000	+	0.866025i	0.0160706	+	0.0278351i
$969$		0			0
$970$	6.50000	−	11.2583i	0.208702	−	0.361483i
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	0.633768	−	0.773523i	$-0.281507\pi$
$971$	−11.0000	−	19.0526i	−0.353007	−	0.611426i	−0.986775	+	0.162098i	$0.948174\pi$
$972$		0			0
$973$	−5.00000	−	1.73205i	−0.160293	−	0.0555270i
$974$	10.0000			0.320421
$975$		0			0
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	−0.934856	−	0.355028i	$-0.884471\pi$
$977$	−5.00000	+	8.66025i	−0.159964	+	0.277066i	0.774891	+	0.632094i	$0.217805\pi$
$978$		0			0
$979$	12.0000			0.383522
$980$	5.50000	+	4.33013i	0.175691	+	0.138321i
$981$		0			0
$982$	−4.50000	−	7.79423i	−0.143601	−	0.248724i
$983$	7.50000	−	12.9904i	0.239213	−	0.414329i	−0.721276	−	0.692648i	$-0.756444\pi$
$983$	7.50000	−	12.9904i	0.239213	−	0.414329i	0.960489	+	0.278319i	$0.0897773\pi$
$984$		0			0
$985$	−12.0000	−	20.7846i	−0.382352	−	0.662253i
$986$	40.0000			1.27386
$987$		0			0
$988$	−12.0000			−0.381771
$989$	14.0000	+	24.2487i	0.445174	+	0.771064i
$990$		0			0
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	−0.795474	−	0.605988i	$-0.792778\pi$
$991$	4.00000	−	6.92820i	0.127064	−	0.220082i	0.922538	+	0.385906i	$0.126111\pi$
$992$	5.00000	+	8.66025i	0.158750	+	0.274963i
$993$		0			0
$994$	−4.00000	−	20.7846i	−0.126872	−	0.659248i
$995$	−26.0000			−0.824255
$996$		0			0
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	−0.524537	−	0.851388i	$-0.675762\pi$
$997$	15.0000	−	25.9808i	0.475055	−	0.822819i	0.999592	+	0.0285686i	$0.00909491\pi$
$998$	−14.0000	+	24.2487i	−0.443162	+	0.767580i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.m.991.1	yes	2
3.2	odd	2		1386.2.k.g.991.1	yes	2
7.2	even	3	inner	1386.2.k.m.793.1	yes	2
7.3	odd	6		9702.2.a.k.1.1		1
7.4	even	3		9702.2.a.p.1.1		1
21.2	odd	6		1386.2.k.g.793.1	✓	2
21.11	odd	6		9702.2.a.bj.1.1		1
21.17	even	6		9702.2.a.bw.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.g.793.1	✓	2	21.2	odd	6
1386.2.k.g.991.1	yes	2	3.2	odd	2
1386.2.k.m.793.1	yes	2	7.2	even	3	inner
1386.2.k.m.991.1	yes	2	1.1	even	1	trivial
9702.2.a.k.1.1		1	7.3	odd	6
9702.2.a.p.1.1		1	7.4	even	3
9702.2.a.bj.1.1		1	21.11	odd	6
9702.2.a.bw.1.1		1	21.17	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:	\( N \)	\(=\)	\( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1386.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-2.50000 - 0.866025i) q^{7} -1.00000 q^{8} +(0.500000 - 0.866025i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(-0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(2.50000 - 4.33013i) q^{17} +(3.00000 + 5.19615i) q^{19} +1.00000 q^{20} -1.00000 q^{22} +(3.50000 + 6.06218i) q^{23} +(2.00000 - 3.46410i) q^{25} +(1.00000 + 1.73205i) q^{26} +(2.00000 - 1.73205i) q^{28} +8.00000 q^{29} +(-5.00000 + 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +5.00000 q^{34} +(0.500000 + 2.59808i) q^{35} +(4.00000 + 6.92820i) q^{37} +(-3.00000 + 5.19615i) q^{38} +(0.500000 + 0.866025i) q^{40} -7.00000 q^{41} +4.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(-3.50000 + 6.06218i) q^{46} +(-0.500000 - 0.866025i) q^{47} +(5.50000 + 4.33013i) q^{49} +4.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(3.00000 - 5.19615i) q^{53} +1.00000 q^{55} +(2.50000 + 0.866025i) q^{56} +(4.00000 + 6.92820i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-0.500000 - 0.866025i) q^{61} -10.0000 q^{62} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{65} +(-1.50000 + 2.59808i) q^{67} +(2.50000 + 4.33013i) q^{68} +(-2.00000 + 1.73205i) q^{70} +8.00000 q^{71} +(-5.00000 + 8.66025i) q^{73} +(-4.00000 + 6.92820i) q^{74} -6.00000 q^{76} +(2.00000 - 1.73205i) q^{77} +(4.50000 + 7.79423i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-3.50000 - 6.06218i) q^{82} +15.0000 q^{83} -5.00000 q^{85} +(2.00000 + 3.46410i) q^{86} +(0.500000 - 0.866025i) q^{88} +(-6.00000 - 10.3923i) q^{89} +(-5.00000 - 1.73205i) q^{91} -7.00000 q^{92} +(0.500000 - 0.866025i) q^{94} +(3.00000 - 5.19615i) q^{95} +13.0000 q^{97} +(-1.00000 + 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} - 5 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 - 5 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - q^{5} - 5 q^{7} - 2 q^{8} + q^{10} - q^{11} + 4 q^{13} - q^{14} - q^{16} + 5 q^{17} + 6 q^{19} + 2 q^{20} - 2 q^{22} + 7 q^{23} + 4 q^{25} + 2 q^{26} + 4 q^{28} + 16 q^{29} - 10 q^{31} + q^{32} + 10 q^{34} + q^{35} + 8 q^{37} - 6 q^{38} + q^{40} - 14 q^{41} + 8 q^{43} - q^{44} - 7 q^{46} - q^{47} + 11 q^{49} + 8 q^{50} - 2 q^{52} + 6 q^{53} + 2 q^{55} + 5 q^{56} + 8 q^{58} + 6 q^{59} - q^{61} - 20 q^{62} + 2 q^{64} - 2 q^{65} - 3 q^{67} + 5 q^{68} - 4 q^{70} + 16 q^{71} - 10 q^{73} - 8 q^{74} - 12 q^{76} + 4 q^{77} + 9 q^{79} - q^{80} - 7 q^{82} + 30 q^{83} - 10 q^{85} + 4 q^{86} + q^{88} - 12 q^{89} - 10 q^{91} - 14 q^{92} + q^{94} + 6 q^{95} + 26 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 - 5 * q^7 - 2 * q^8 + q^10 - q^11 + 4 * q^13 - q^14 - q^16 + 5 * q^17 + 6 * q^19 + 2 * q^20 - 2 * q^22 + 7 * q^23 + 4 * q^25 + 2 * q^26 + 4 * q^28 + 16 * q^29 - 10 * q^31 + q^32 + 10 * q^34 + q^35 + 8 * q^37 - 6 * q^38 + q^40 - 14 * q^41 + 8 * q^43 - q^44 - 7 * q^46 - q^47 + 11 * q^49 + 8 * q^50 - 2 * q^52 + 6 * q^53 + 2 * q^55 + 5 * q^56 + 8 * q^58 + 6 * q^59 - q^61 - 20 * q^62 + 2 * q^64 - 2 * q^65 - 3 * q^67 + 5 * q^68 - 4 * q^70 + 16 * q^71 - 10 * q^73 - 8 * q^74 - 12 * q^76 + 4 * q^77 + 9 * q^79 - q^80 - 7 * q^82 + 30 * q^83 - 10 * q^85 + 4 * q^86 + q^88 - 12 * q^89 - 10 * q^91 - 14 * q^92 + q^94 + 6 * q^95 + 26 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

Properties

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