LMFDB - Embedded newform 1386.2.k.h.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.h.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(1.50000 + 2.59808i) q^{19} -2.00000 q^{20} +1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.50000 + 0.866025i) q^{28} -1.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +1.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +(2.50000 + 4.33013i) q^{37} +(1.50000 - 2.59808i) q^{38} +(1.00000 + 1.73205i) q^{40} -10.0000 q^{41} +1.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} -2.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(0.500000 + 0.866025i) q^{58} +(1.50000 - 2.59808i) q^{59} +(7.00000 + 12.1244i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(5.00000 - 1.73205i) q^{70} +5.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(2.50000 - 4.33013i) q^{74} -3.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} +(1.00000 - 1.73205i) q^{80} +(5.00000 + 8.66025i) q^{82} -6.00000 q^{83} -2.00000 q^{85} +(-0.500000 - 0.866025i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(4.00000 + 3.46410i) q^{91} -1.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} + 2 q^{10} - q^{11} + 4 q^{13} + q^{14} - q^{16} - q^{17} + 3 q^{19} - 4 q^{20} + 2 q^{22} + q^{23} + q^{25} - 2 q^{26} - 5 q^{28} - 2 q^{29} + 2 q^{31} - q^{32} + 2 q^{34} - 2 q^{35} + 5 q^{37} + 3 q^{38} + 2 q^{40} - 20 q^{41} + 2 q^{43} - q^{44} + q^{46} - 7 q^{47} + 2 q^{49} - 2 q^{50} - 2 q^{52} - 12 q^{53} - 4 q^{55} + 4 q^{56} + q^{58} + 3 q^{59} + 14 q^{61} - 4 q^{62} + 2 q^{64} + 4 q^{65} - 12 q^{67} - q^{68} + 10 q^{70} + 10 q^{71} + 8 q^{73} + 5 q^{74} - 6 q^{76} - 5 q^{77} + 2 q^{80} + 10 q^{82} - 12 q^{83} - 4 q^{85} - q^{86} - q^{88} + 6 q^{89} + 8 q^{91} - 2 q^{92} - 7 q^{94} - 6 q^{95} + 14 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 + 2 * q^10 - q^11 + 4 * q^13 + q^14 - q^16 - q^17 + 3 * q^19 - 4 * q^20 + 2 * q^22 + q^23 + q^25 - 2 * q^26 - 5 * q^28 - 2 * q^29 + 2 * q^31 - q^32 + 2 * q^34 - 2 * q^35 + 5 * q^37 + 3 * q^38 + 2 * q^40 - 20 * q^41 + 2 * q^43 - q^44 + q^46 - 7 * q^47 + 2 * q^49 - 2 * q^50 - 2 * q^52 - 12 * q^53 - 4 * q^55 + 4 * q^56 + q^58 + 3 * q^59 + 14 * q^61 - 4 * q^62 + 2 * q^64 + 4 * q^65 - 12 * q^67 - q^68 + 10 * q^70 + 10 * q^71 + 8 * q^73 + 5 * q^74 - 6 * q^76 - 5 * q^77 + 2 * q^80 + 10 * q^82 - 12 * q^83 - 4 * q^85 - q^86 - q^88 + 6 * q^89 + 8 * q^91 - 2 * q^92 - 7 * q^94 - 6 * q^95 + 14 * q^97 + 11 * 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
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	0.998203	−	0.0599153i	$-0.0190830\pi$
$5$	1.00000	+	1.73205i	0.447214	+	0.774597i	−0.550990	+	0.834512i	$0.685750\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	−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
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	−0.920268	−	0.391289i	$-0.872029\pi$
$17$	−0.500000	+	0.866025i	−0.121268	+	0.210042i	0.799000	+	0.601331i	$0.205363\pi$
$18$		0			0
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	0.985194	−	0.171442i	$-0.0548427\pi$
$19$	1.50000	+	2.59808i	0.344124	+	0.596040i	−0.641071	+	0.767482i	$0.721509\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$	1.00000			0.213201
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−1.00000	−	1.73205i	−0.196116	−	0.339683i
$27$		0			0
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	−0.762140	−	0.647412i	$-0.775851\pi$
$31$	1.00000	−	1.73205i	0.179605	−	0.311086i	0.941745	+	0.336327i	$0.109185\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	1.00000			0.171499
$35$	−1.00000	+	5.19615i	−0.169031	+	0.878310i
$36$		0			0
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	0.994999	−	0.0998840i	$-0.0318472\pi$
$37$	2.50000	+	4.33013i	0.410997	+	0.711868i	−0.584002	+	0.811752i	$0.698514\pi$
$38$	1.50000	−	2.59808i	0.243332	−	0.421464i
$39$		0			0
$40$	1.00000	+	1.73205i	0.158114	+	0.273861i
$41$	−10.0000			−1.56174			−0.780869	−	0.624695i	$-0.785223\pi$
$41$	−10.0000			−1.56174			−0.780869	+	0.624695i	$0.785223\pi$
$42$		0			0
$43$	1.00000			0.152499			0.0762493	−	0.997089i	$-0.475706\pi$
$43$	1.00000			0.152499			0.0762493	+	0.997089i	$0.475706\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−1.00000			−0.141421
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	0.500000	+	0.866025i	0.0656532	+	0.113715i
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$		0			0
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.832240	+	0.554416i	$0.187058\pi$
$61$	7.00000	+	12.1244i	0.896258	+	1.55236i	0.0640184	+	0.997949i	$0.479608\pi$
$62$	−2.00000			−0.254000
$63$		0			0
$64$	1.00000			0.125000
$65$	2.00000	+	3.46410i	0.248069	+	0.429669i
$66$		0			0
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	0.222571	+	0.974916i	$0.428555\pi$
$67$	−6.00000	+	10.3923i	−0.733017	+	1.26962i	−0.955588	+	0.294706i	$0.904778\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$		0			0
$70$	5.00000	−	1.73205i	0.597614	−	0.207020i
$71$	5.00000			0.593391			0.296695	−	0.954972i	$-0.404115\pi$
$71$	5.00000			0.593391			0.296695	+	0.954972i	$0.404115\pi$
$72$		0			0
$73$	4.00000	−	6.92820i	0.468165	−	0.810885i	−0.531174	−	0.847263i	$-0.678249\pi$
$73$	4.00000	−	6.92820i	0.468165	−	0.810885i	0.999338	+	0.0363782i	$0.0115821\pi$
$74$	2.50000	−	4.33013i	0.290619	−	0.503367i
$75$		0			0
$76$	−3.00000			−0.344124
$77$	−2.50000	+	0.866025i	−0.284901	+	0.0986928i
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$		0			0
$82$	5.00000	+	8.66025i	0.552158	+	0.956365i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	−0.500000	−	0.866025i	−0.0539164	−	0.0933859i
$87$		0			0
$88$	−0.500000	+	0.866025i	−0.0533002	+	0.0923186i
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	4.00000	+	3.46410i	0.419314	+	0.363137i
$92$	−1.00000			−0.104257
$93$		0			0
$94$	−3.50000	+	6.06218i	−0.360997	+	0.625266i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	−0.550474	−	0.834853i	$-0.685553\pi$
$101$	4.50000	−	7.79423i	0.447767	−	0.775555i	0.998240	+	0.0592978i	$0.0188862\pi$
$102$		0			0
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	0.975124	−	0.221660i	$-0.0711475\pi$
$103$	3.00000	+	5.19615i	0.295599	+	0.511992i	−0.679525	+	0.733652i	$0.737814\pi$
$104$	2.00000			0.196116
$105$		0			0
$106$	12.0000			1.16554
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	0.910306	−	0.413936i	$-0.135846\pi$
$107$	1.00000	+	1.73205i	0.0966736	+	0.167444i	−0.813632	+	0.581380i	$0.802513\pi$
$108$		0			0
$109$	10.0000	−	17.3205i	0.957826	−	1.65900i	0.230063	−	0.973176i	$-0.426107\pi$
$109$	10.0000	−	17.3205i	0.957826	−	1.65900i	0.727764	−	0.685828i	$-0.240560\pi$
$110$	1.00000	+	1.73205i	0.0953463	+	0.165145i
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	10.0000			0.940721			0.470360	−	0.882474i	$-0.344124\pi$
$113$	10.0000			0.940721			0.470360	+	0.882474i	$0.344124\pi$
$114$		0			0
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$	0.500000	−	0.866025i	0.0464238	−	0.0804084i
$117$		0			0
$118$	−3.00000			−0.276172
$119$	−2.50000	+	0.866025i	−0.229175	+	0.0793884i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	7.00000	−	12.1244i	0.633750	−	1.09769i
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	12.0000			1.07331
$126$		0			0
$127$	−1.00000			−0.0887357			−0.0443678	−	0.999015i	$-0.514127\pi$
$127$	−1.00000			−0.0887357			−0.0443678	+	0.999015i	$0.514127\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$		0			0
$133$	−1.50000	+	7.79423i	−0.130066	+	0.675845i
$134$	12.0000			1.03664
$135$		0			0
$136$	−0.500000	+	0.866025i	−0.0428746	+	0.0742611i
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	−0.965250	−	0.261329i	$-0.915839\pi$
$137$	−3.00000	+	5.19615i	−0.256307	+	0.443937i	0.708942	+	0.705266i	$0.249173\pi$
$138$		0			0
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$	−4.00000	−	3.46410i	−0.338062	−	0.292770i
$141$		0			0
$142$	−2.50000	−	4.33013i	−0.209795	−	0.363376i
$143$	−1.00000	+	1.73205i	−0.0836242	+	0.144841i
$144$		0			0
$145$	−1.00000	−	1.73205i	−0.0830455	−	0.143839i
$146$	−8.00000			−0.662085
$147$		0			0
$148$	−5.00000			−0.410997
$149$	5.50000	+	9.52628i	0.450578	+	0.780423i	0.998422	−	0.0561570i	$-0.0178847\pi$
$149$	5.50000	+	9.52628i	0.450578	+	0.780423i	−0.547844	+	0.836580i	$0.684551\pi$
$150$		0			0
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	−0.380841	−	0.924640i	$-0.624366\pi$
$151$	7.50000	−	12.9904i	0.610341	−	1.05714i	0.991183	−	0.132502i	$-0.0423010\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$		0			0
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$	4.00000			0.321288
$156$		0			0
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	−0.885288	−	0.465044i	$-0.846039\pi$
$157$	−0.500000	+	0.866025i	−0.0399043	+	0.0691164i	0.845383	+	0.534160i	$0.179372\pi$
$158$		0			0
$159$		0			0
$160$	−2.00000			−0.158114
$161$	−0.500000	+	2.59808i	−0.0394055	+	0.204757i
$162$		0			0
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	0.601035	−	0.799223i	$-0.294755\pi$
$163$	−5.00000	−	8.66025i	−0.391630	−	0.678323i	−0.992665	+	0.120900i	$0.961422\pi$
$164$	5.00000	−	8.66025i	0.390434	−	0.676252i
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$	2.00000			0.154765			0.0773823	−	0.997001i	$-0.475344\pi$
$167$	2.00000			0.154765			0.0773823	+	0.997001i	$0.475344\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$	1.00000	+	1.73205i	0.0766965	+	0.132842i
$171$		0			0
$172$	−0.500000	+	0.866025i	−0.0381246	+	0.0660338i
$173$	−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
$175$	2.50000	−	0.866025i	0.188982	−	0.0654654i
$176$	1.00000			0.0753778
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	−0.705066	−	0.709142i	$-0.749082\pi$
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	0.966668	+	0.256034i	$0.0824158\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	1.00000	−	5.19615i	0.0741249	−	0.385164i
$183$		0			0
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	−5.00000	+	8.66025i	−0.367607	+	0.636715i
$186$		0			0
$187$	−0.500000	−	0.866025i	−0.0365636	−	0.0633300i
$188$	7.00000			0.510527
$189$		0			0
$190$	6.00000			0.435286
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$		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	$0.259632\pi$
$194$	−3.50000	−	6.06218i	−0.251285	−	0.435239i
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	27.0000			1.92367			0.961835	−	0.273629i	$-0.0882242\pi$
$197$	27.0000			1.92367			0.961835	+	0.273629i	$0.0882242\pi$
$198$		0			0
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$		0			0
$202$	−9.00000			−0.633238
$203$	−2.00000	−	1.73205i	−0.140372	−	0.121566i
$204$		0			0
$205$	−10.0000	−	17.3205i	−0.698430	−	1.20972i
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$		0			0
$208$	−1.00000	−	1.73205i	−0.0693375	−	0.120096i
$209$	−3.00000			−0.207514
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−6.00000	−	10.3923i	−0.412082	−	0.713746i
$213$		0			0
$214$	1.00000	−	1.73205i	0.0683586	−	0.118401i
$215$	1.00000	+	1.73205i	0.0681994	+	0.118125i
$216$		0			0
$217$	5.00000	−	1.73205i	0.339422	−	0.117579i
$218$	−20.0000			−1.35457
$219$		0			0
$220$	1.00000	−	1.73205i	0.0674200	−	0.116775i
$221$	−1.00000	+	1.73205i	−0.0672673	+	0.116510i
$222$		0			0
$223$	−26.0000			−1.74109			−0.870544	−	0.492090i	$-0.836233\pi$
$223$	−26.0000			−1.74109			−0.870544	+	0.492090i	$0.836233\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	−5.00000	−	8.66025i	−0.332595	−	0.576072i
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	−0.651015	−	0.759065i	$-0.725657\pi$
$227$	5.00000	−	8.66025i	0.331862	−	0.574801i	0.982877	+	0.184263i	$0.0589899\pi$
$228$		0			0
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	2.00000			0.131876
$231$		0			0
$232$	−1.00000			−0.0656532
$233$	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
$235$	7.00000	−	12.1244i	0.456630	−	0.790906i
$236$	1.50000	+	2.59808i	0.0976417	+	0.169120i
$237$		0			0
$238$	2.00000	+	1.73205i	0.129641	+	0.112272i
$239$	−22.0000			−1.42306			−0.711531	−	0.702655i	$-0.751998\pi$
$239$	−22.0000			−1.42306			−0.711531	+	0.702655i	$0.751998\pi$
$240$		0			0
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	−0.605481	−	0.795860i	$-0.707019\pi$
$241$	6.00000	−	10.3923i	0.386494	−	0.669427i	0.991975	+	0.126432i	$0.0403527\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	−14.0000			−0.896258
$245$	−11.0000	+	8.66025i	−0.702764	+	0.553283i
$246$		0			0
$247$	3.00000	+	5.19615i	0.190885	+	0.330623i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$		0			0
$250$	−6.00000	−	10.3923i	−0.379473	−	0.657267i
$251$	−21.0000			−1.32551			−0.662754	−	0.748837i	$-0.730613\pi$
$251$	−21.0000			−1.32551			−0.662754	+	0.748837i	$0.730613\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$	0.500000	+	0.866025i	0.0313728	+	0.0543393i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	0.944294	−	0.329104i	$-0.106747\pi$
$257$	3.00000	+	5.19615i	0.187135	+	0.324127i	−0.757159	+	0.653231i	$0.773413\pi$
$258$		0			0
$259$	−2.50000	+	12.9904i	−0.155342	+	0.807183i
$260$	−4.00000			−0.248069
$261$		0			0
$262$		0			0
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	−0.758585	−	0.651575i	$-0.774109\pi$
$263$	3.00000	−	5.19615i	0.184988	−	0.320408i	0.943572	+	0.331166i	$0.107442\pi$
$264$		0			0
$265$	−24.0000			−1.47431
$266$	7.50000	−	2.59808i	0.459855	−	0.159298i
$267$		0			0
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	−0.988908	−	0.148527i	$-0.952547\pi$
$269$	−6.00000	+	10.3923i	−0.365826	+	0.633630i	0.623082	+	0.782157i	$0.285880\pi$
$270$		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	$0.994865\pi$
$272$	1.00000			0.0606339
$273$		0			0
$274$	6.00000			0.362473
$275$	0.500000	+	0.866025i	0.0301511	+	0.0522233i
$276$		0			0
$277$	12.0000	−	20.7846i	0.721010	−	1.24883i	−0.239585	−	0.970875i	$-0.577011\pi$
$277$	12.0000	−	20.7846i	0.721010	−	1.24883i	0.960595	−	0.277951i	$-0.0896552\pi$
$278$	6.50000	+	11.2583i	0.389844	+	0.675230i
$279$		0			0
$280$	−1.00000	+	5.19615i	−0.0597614	+	0.310530i
$281$	7.00000			0.417585			0.208792	−	0.977960i	$-0.433047\pi$
$281$	7.00000			0.417585			0.208792	+	0.977960i	$0.433047\pi$
$282$		0			0
$283$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$283$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$284$	−2.50000	+	4.33013i	−0.148348	+	0.256946i
$285$		0			0
$286$	2.00000			0.118262
$287$	−20.0000	−	17.3205i	−1.18056	−	1.02240i
$288$		0			0
$289$	8.00000	+	13.8564i	0.470588	+	0.815083i
$290$	−1.00000	+	1.73205i	−0.0587220	+	0.101710i
$291$		0			0
$292$	4.00000	+	6.92820i	0.234082	+	0.405442i
$293$	9.00000			0.525786			0.262893	−	0.964825i	$-0.415323\pi$
$293$	9.00000			0.525786			0.262893	+	0.964825i	$0.415323\pi$
$294$		0			0
$295$	6.00000			0.349334
$296$	2.50000	+	4.33013i	0.145310	+	0.251684i
$297$		0			0
$298$	5.50000	−	9.52628i	0.318606	−	0.551843i
$299$	1.00000	+	1.73205i	0.0578315	+	0.100167i
$300$		0			0
$301$	2.00000	+	1.73205i	0.115278	+	0.0998337i
$302$	−15.0000			−0.863153
$303$		0			0
$304$	1.50000	−	2.59808i	0.0860309	−	0.149010i
$305$	−14.0000	+	24.2487i	−0.801638	+	1.38848i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$	0.500000	−	2.59808i	0.0284901	−	0.148039i
$309$		0			0
$310$	−2.00000	−	3.46410i	−0.113592	−	0.196748i
$311$	−6.50000	+	11.2583i	−0.368581	+	0.638401i	−0.989344	−	0.145597i	$-0.953490\pi$
$311$	−6.50000	+	11.2583i	−0.368581	+	0.638401i	0.620763	+	0.783998i	$0.286823\pi$
$312$		0			0
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	0.749993	−	0.661445i	$-0.230057\pi$
$313$	−3.50000	−	6.06218i	−0.197832	−	0.342655i	−0.947825	+	0.318791i	$0.896723\pi$
$314$	1.00000			0.0564333
$315$		0			0
$316$		0			0
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	0.769395	−	0.638774i	$-0.220558\pi$
$317$	−3.00000	−	5.19615i	−0.168497	−	0.291845i	−0.937892	+	0.346929i	$0.887225\pi$
$318$		0			0
$319$	0.500000	−	0.866025i	0.0279946	−	0.0484881i
$320$	1.00000	+	1.73205i	0.0559017	+	0.0968246i
$321$		0			0
$322$	2.50000	−	0.866025i	0.139320	−	0.0482617i
$323$	−3.00000			−0.166924
$324$		0			0
$325$	1.00000	−	1.73205i	0.0554700	−	0.0960769i
$326$	−5.00000	+	8.66025i	−0.276924	+	0.479647i
$327$		0			0
$328$	−10.0000			−0.552158
$329$	3.50000	−	18.1865i	0.192961	−	1.00266i
$330$		0			0
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	0.892199	−	0.451643i	$-0.149162\pi$
$331$	1.00000	+	1.73205i	0.0549650	+	0.0952021i	−0.837234	+	0.546845i	$0.815829\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$		0			0
$334$	−1.00000	−	1.73205i	−0.0547176	−	0.0947736i
$335$	−24.0000			−1.31126
$336$		0			0
$337$		0			0			−	1.00000i	$-0.5\pi$
$337$		0			0				1.00000i	$0.5\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	1.00000	−	1.73205i	0.0542326	−	0.0939336i
$341$	1.00000	+	1.73205i	0.0541530	+	0.0937958i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	1.00000			0.0539164
$345$		0			0
$346$	−7.00000	+	12.1244i	−0.376322	+	0.651809i
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	−0.0140303	−	0.999902i	$-0.504466\pi$
$347$	16.0000	−	27.7128i	0.858925	−	1.48770i	0.872955	−	0.487800i	$-0.162201\pi$
$348$		0			0
$349$	−16.0000			−0.856460			−0.428230	−	0.903670i	$-0.640863\pi$
$349$	−16.0000			−0.856460			−0.428230	+	0.903670i	$0.640863\pi$
$350$	−2.00000	−	1.73205i	−0.106904	−	0.0925820i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	−0.775077	−	0.631867i	$-0.782289\pi$
$353$	3.00000	−	5.19615i	0.159674	−	0.276563i	0.934751	+	0.355303i	$0.115622\pi$
$354$		0			0
$355$	5.00000	+	8.66025i	0.265372	+	0.459639i
$356$	−6.00000			−0.317999
$357$		0			0
$358$	−7.00000			−0.369961
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	0.703382	−	0.710812i	$-0.251672\pi$
$359$	−5.00000	−	8.66025i	−0.263890	−	0.457071i	−0.967272	+	0.253741i	$0.918339\pi$
$360$		0			0
$361$	5.00000	−	8.66025i	0.263158	−	0.455803i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$		0			0
$364$	−5.00000	+	1.73205i	−0.262071	+	0.0907841i
$365$	16.0000			0.837478
$366$		0			0
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	−0.0586798	−	0.998277i	$-0.518689\pi$
$367$	16.0000	−	27.7128i	0.835193	−	1.44660i	0.893873	−	0.448320i	$-0.147978\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$		0			0
$370$	10.0000			0.519875
$371$	−30.0000	+	10.3923i	−1.55752	+	0.539542i
$372$		0			0
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	−0.977016	−	0.213165i	$-0.931623\pi$
$373$	−13.0000	−	22.5167i	−0.673114	−	1.16587i	0.303902	−	0.952703i	$-0.401711\pi$
$374$	−0.500000	+	0.866025i	−0.0258544	+	0.0447811i
$375$		0			0
$376$	−3.50000	−	6.06218i	−0.180499	−	0.312633i
$377$	−2.00000			−0.103005
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	−3.00000	−	5.19615i	−0.153897	−	0.266557i
$381$		0			0
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	−12.5000	−	21.6506i	−0.638720	−	1.10630i	−0.985714	−	0.168428i	$-0.946131\pi$
$383$	−12.5000	−	21.6506i	−0.638720	−	1.10630i	0.346994	−	0.937867i	$-0.387203\pi$
$384$		0			0
$385$	−4.00000	−	3.46410i	−0.203859	−	0.176547i
$386$	8.00000			0.407189
$387$		0			0
$388$	−3.50000	+	6.06218i	−0.177686	+	0.307760i
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	−1.00000			−0.0505722
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	−13.5000	−	23.3827i	−0.680120	−	1.17800i
$395$		0			0
$396$		0			0
$397$	13.5000	+	23.3827i	0.677546	+	1.17354i	0.975718	+	0.219031i	$0.0702897\pi$
$397$	13.5000	+	23.3827i	0.677546	+	1.17354i	−0.298172	+	0.954512i	$0.596377\pi$
$398$	−2.00000			−0.100251
$399$		0			0
$400$	−1.00000			−0.0500000
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	0.992932	+	0.118686i	$0.0378683\pi$
$401$	12.0000	+	20.7846i	0.599251	+	1.03793i	−0.393680	+	0.919247i	$0.628798\pi$
$402$		0			0
$403$	2.00000	−	3.46410i	0.0996271	−	0.172559i
$404$	4.50000	+	7.79423i	0.223883	+	0.387777i
$405$		0			0
$406$	−0.500000	+	2.59808i	−0.0248146	+	0.128940i
$407$	−5.00000			−0.247841
$408$		0			0
$409$	−8.00000	+	13.8564i	−0.395575	+	0.685155i	−0.993174	−	0.116639i	$-0.962788\pi$
$409$	−8.00000	+	13.8564i	−0.395575	+	0.685155i	0.597600	+	0.801795i	$0.296121\pi$
$410$	−10.0000	+	17.3205i	−0.493865	+	0.855399i
$411$		0			0
$412$	−6.00000			−0.295599
$413$	7.50000	−	2.59808i	0.369051	−	0.127843i
$414$		0			0
$415$	−6.00000	−	10.3923i	−0.294528	−	0.510138i
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$	1.50000	+	2.59808i	0.0733674	+	0.127076i
$419$	29.0000			1.41674			0.708371	−	0.705840i	$-0.249430\pi$
$419$	29.0000			1.41674			0.708371	+	0.705840i	$0.249430\pi$
$420$		0			0
$421$	−17.0000			−0.828529			−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000			−0.828529			−0.414265	+	0.910156i	$0.635961\pi$
$422$	−2.00000	−	3.46410i	−0.0973585	−	0.168630i
$423$		0			0
$424$	−6.00000	+	10.3923i	−0.291386	+	0.504695i
$425$	0.500000	+	0.866025i	0.0242536	+	0.0420084i
$426$		0			0
$427$	−7.00000	+	36.3731i	−0.338754	+	1.76022i
$428$	−2.00000			−0.0966736
$429$		0			0
$430$	1.00000	−	1.73205i	0.0482243	−	0.0835269i
$431$	8.00000	−	13.8564i	0.385346	−	0.667440i	−0.606471	−	0.795106i	$-0.707415\pi$
$431$	8.00000	−	13.8564i	0.385346	−	0.667440i	0.991817	+	0.127666i	$0.0407486\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	−4.00000	−	3.46410i	−0.192006	−	0.166282i
$435$		0			0
$436$	10.0000	+	17.3205i	0.478913	+	0.829502i
$437$	−1.50000	+	2.59808i	−0.0717547	+	0.124283i
$438$		0			0
$439$	−15.5000	−	26.8468i	−0.739775	−	1.28133i	−0.952597	−	0.304236i	$-0.901599\pi$
$439$	−15.5000	−	26.8468i	−0.739775	−	1.28133i	0.212822	−	0.977091i	$-0.431735\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$	2.00000			0.0951303
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$		0			0
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$	13.0000	+	22.5167i	0.615568	+	1.06619i
$447$		0			0
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$		0			0
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	−5.00000	+	8.66025i	−0.235180	+	0.407344i
$453$		0			0
$454$	−10.0000			−0.469323
$455$	−2.00000	+	10.3923i	−0.0937614	+	0.487199i
$456$		0			0
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$		0			0
$460$	−1.00000	−	1.73205i	−0.0466252	−	0.0807573i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$	16.0000			0.743583			0.371792	−	0.928316i	$-0.378744\pi$
$463$	16.0000			0.743583			0.371792	+	0.928316i	$0.378744\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$		0			0
$466$	10.5000	−	18.1865i	0.486403	−	0.842475i
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	−0.988598	−	0.150581i	$-0.951886\pi$
$467$	−13.5000	−	23.3827i	−0.624705	−	1.08202i	0.363892	−	0.931441i	$-0.381448\pi$
$468$		0			0
$469$	−30.0000	+	10.3923i	−1.38527	+	0.479872i
$470$	−14.0000			−0.645772
$471$		0			0
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	−0.500000	+	0.866025i	−0.0229900	+	0.0398199i
$474$		0			0
$475$	3.00000			0.137649
$476$	0.500000	−	2.59808i	0.0229175	−	0.119083i
$477$		0			0
$478$	11.0000	+	19.0526i	0.503128	+	0.871444i
$479$	13.0000	−	22.5167i	0.593985	−	1.02881i	−0.399704	−	0.916644i	$-0.630887\pi$
$479$	13.0000	−	22.5167i	0.593985	−	1.02881i	0.993689	−	0.112168i	$-0.0357796\pi$
$480$		0			0
$481$	5.00000	+	8.66025i	0.227980	+	0.394874i
$482$	−12.0000			−0.546585
$483$		0			0
$484$	1.00000			0.0454545
$485$	7.00000	+	12.1244i	0.317854	+	0.550539i
$486$		0			0
$487$	17.0000	−	29.4449i	0.770344	−	1.33427i	−0.167031	−	0.985952i	$-0.553418\pi$
$487$	17.0000	−	29.4449i	0.770344	−	1.33427i	0.937375	−	0.348323i	$-0.113249\pi$
$488$	7.00000	+	12.1244i	0.316875	+	0.548844i
$489$		0			0
$490$	13.0000	+	5.19615i	0.587280	+	0.234738i
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	0.500000	−	0.866025i	0.0225189	−	0.0390038i
$494$	3.00000	−	5.19615i	0.134976	−	0.233786i
$495$		0			0
$496$	−2.00000			−0.0898027
$497$	10.0000	+	8.66025i	0.448561	+	0.388465i
$498$		0			0
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	0.762496	−	0.646993i	$-0.223974\pi$
$499$	−4.00000	−	6.92820i	−0.179065	−	0.310149i	−0.941560	+	0.336844i	$0.890640\pi$
$500$	−6.00000	+	10.3923i	−0.268328	+	0.464758i
$501$		0			0
$502$	10.5000	+	18.1865i	0.468638	+	0.811705i
$503$	−42.0000			−1.87269			−0.936344	−	0.351085i	$-0.885813\pi$
$503$	−42.0000			−1.87269			−0.936344	+	0.351085i	$0.885813\pi$
$504$		0			0
$505$	18.0000			0.800989
$506$	0.500000	+	0.866025i	0.0222277	+	0.0384995i
$507$		0			0
$508$	0.500000	−	0.866025i	0.0221839	−	0.0384237i
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	0.997928	−	0.0643419i	$-0.0204948\pi$
$509$	10.0000	+	17.3205i	0.443242	+	0.767718i	−0.554686	+	0.832060i	$0.687161\pi$
$510$		0			0
$511$	20.0000	−	6.92820i	0.884748	−	0.306486i
$512$	1.00000			0.0441942
$513$		0			0
$514$	3.00000	−	5.19615i	0.132324	−	0.229192i
$515$	−6.00000	+	10.3923i	−0.264392	+	0.457940i
$516$		0			0
$517$	7.00000			0.307860
$518$	12.5000	−	4.33013i	0.549218	−	0.190255i
$519$		0			0
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	−0.977633	−	0.210318i	$-0.932550\pi$
$521$	−7.00000	+	12.1244i	−0.306676	+	0.531178i	0.670957	+	0.741496i	$0.265883\pi$
$522$		0			0
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	0.906434	−	0.422347i	$-0.138794\pi$
$523$	2.00000	+	3.46410i	0.0874539	+	0.151475i	−0.818980	+	0.573822i	$0.805460\pi$
$524$		0			0
$525$		0			0
$526$	−6.00000			−0.261612
$527$	1.00000	+	1.73205i	0.0435607	+	0.0754493i
$528$		0			0
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$	12.0000	+	20.7846i	0.521247	+	0.902826i
$531$		0			0
$532$	−6.00000	−	5.19615i	−0.260133	−	0.225282i
$533$	−20.0000			−0.866296
$534$		0			0
$535$	−2.00000	+	3.46410i	−0.0864675	+	0.149766i
$536$	−6.00000	+	10.3923i	−0.259161	+	0.448879i
$537$		0			0
$538$	12.0000			0.517357
$539$	−6.50000	−	2.59808i	−0.279975	−	0.111907i
$540$		0			0
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	0.985162	−	0.171628i	$-0.0549027\pi$
$541$	8.00000	+	13.8564i	0.343947	+	0.595733i	−0.641215	+	0.767361i	$0.721569\pi$
$542$	−8.00000	+	13.8564i	−0.343629	+	0.595184i
$543$		0			0
$544$	−0.500000	−	0.866025i	−0.0214373	−	0.0371305i
$545$	40.0000			1.71341
$546$		0			0
$547$	39.0000			1.66752			0.833760	−	0.552127i	$-0.186184\pi$
$547$	39.0000			1.66752			0.833760	+	0.552127i	$0.186184\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$		0			0
$550$	0.500000	−	0.866025i	0.0213201	−	0.0369274i
$551$	−1.50000	−	2.59808i	−0.0639021	−	0.110682i
$552$		0			0
$553$		0			0
$554$	−24.0000			−1.01966
$555$		0			0
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	17.5000	−	30.3109i	0.741499	−	1.28431i	−0.210314	−	0.977634i	$-0.567449\pi$
$557$	17.5000	−	30.3109i	0.741499	−	1.28431i	0.951813	−	0.306680i	$-0.0992180\pi$
$558$		0			0
$559$	2.00000			0.0845910
$560$	5.00000	−	1.73205i	0.211289	−	0.0731925i
$561$		0			0
$562$	−3.50000	−	6.06218i	−0.147639	−	0.255718i
$563$	19.0000	−	32.9090i	0.800755	−	1.38695i	−0.118366	−	0.992970i	$-0.537765\pi$
$563$	19.0000	−	32.9090i	0.800755	−	1.38695i	0.919120	−	0.393977i	$-0.128901\pi$
$564$		0			0
$565$	10.0000	+	17.3205i	0.420703	+	0.728679i
$566$		0			0
$567$		0			0
$568$	5.00000			0.209795
$569$	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
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	−0.929921	−	0.367760i	$-0.880125\pi$
$571$	−3.50000	+	6.06218i	−0.146470	+	0.253694i	0.783450	+	0.621455i	$0.213458\pi$
$572$	−1.00000	−	1.73205i	−0.0418121	−	0.0724207i
$573$		0			0
$574$	−5.00000	+	25.9808i	−0.208696	+	1.08442i
$575$	1.00000			0.0417029
$576$		0			0
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	−0.974144	−	0.225927i	$-0.927459\pi$
$577$	−7.00000	+	12.1244i	−0.291414	+	0.504744i	0.682730	+	0.730670i	$0.260792\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$		0			0
$580$	2.00000			0.0830455
$581$	−12.0000	−	10.3923i	−0.497844	−	0.431145i
$582$		0			0
$583$	−6.00000	−	10.3923i	−0.248495	−	0.430405i
$584$	4.00000	−	6.92820i	0.165521	−	0.286691i
$585$		0			0
$586$	−4.50000	−	7.79423i	−0.185893	−	0.321977i
$587$	12.0000			0.495293			0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000			0.495293			0.247647	+	0.968850i	$0.420343\pi$
$588$		0			0
$589$	6.00000			0.247226
$590$	−3.00000	−	5.19615i	−0.123508	−	0.213922i
$591$		0			0
$592$	2.50000	−	4.33013i	0.102749	−	0.177967i
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$		0			0
$595$	−4.00000	−	3.46410i	−0.163984	−	0.142014i
$596$	−11.0000			−0.450578
$597$		0			0
$598$	1.00000	−	1.73205i	0.0408930	−	0.0708288i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	8.00000			0.326327			0.163163	−	0.986599i	$-0.447830\pi$
$601$	8.00000			0.326327			0.163163	+	0.986599i	$0.447830\pi$
$602$	0.500000	−	2.59808i	0.0203785	−	0.105890i
$603$		0			0
$604$	7.50000	+	12.9904i	0.305171	+	0.528571i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	0.996740	+	0.0806818i	$0.0257098\pi$
$607$	14.0000	+	24.2487i	0.568242	+	0.984225i	−0.428497	+	0.903543i	$0.640957\pi$
$608$	−3.00000			−0.121666
$609$		0			0
$610$	28.0000			1.13369
$611$	−7.00000	−	12.1244i	−0.283190	−	0.490499i
$612$		0			0
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	−0.689328	−	0.724449i	$-0.742094\pi$
$613$	7.00000	−	12.1244i	0.282727	−	0.489698i	0.972056	+	0.234751i	$0.0754275\pi$
$614$	2.00000	+	3.46410i	0.0807134	+	0.139800i
$615$		0			0
$616$	−2.50000	+	0.866025i	−0.100728	+	0.0348932i
$617$	36.0000			1.44931			0.724653	−	0.689114i	$-0.242000\pi$
$617$	36.0000			1.44931			0.724653	+	0.689114i	$0.242000\pi$
$618$		0			0
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	0.477143	+	0.878826i	$0.341672\pi$
$619$	−13.0000	+	22.5167i	−0.522514	+	0.905021i	−0.999657	+	0.0261952i	$0.991661\pi$
$620$	−2.00000	+	3.46410i	−0.0803219	+	0.139122i
$621$		0			0
$622$	13.0000			0.521253
$623$	−3.00000	+	15.5885i	−0.120192	+	0.624538i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	−3.50000	+	6.06218i	−0.139888	+	0.242293i
$627$		0			0
$628$	−0.500000	−	0.866025i	−0.0199522	−	0.0345582i
$629$	−5.00000			−0.199363
$630$		0			0
$631$	18.0000			0.716569			0.358284	−	0.933613i	$-0.383362\pi$
$631$	18.0000			0.716569			0.358284	+	0.933613i	$0.383362\pi$
$632$		0			0
$633$		0			0
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−1.00000	−	1.73205i	−0.0396838	−	0.0687343i
$636$		0			0
$637$	2.00000	+	13.8564i	0.0792429	+	0.549011i
$638$	−1.00000			−0.0395904
$639$		0			0
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	−0.722862	−	0.690992i	$-0.757174\pi$
$641$	6.00000	−	10.3923i	0.236986	−	0.410471i	0.959848	+	0.280521i	$0.0905072\pi$
$642$		0			0
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$	−2.00000	−	1.73205i	−0.0788110	−	0.0682524i
$645$		0			0
$646$	1.50000	+	2.59808i	0.0590167	+	0.102220i
$647$	−24.0000	+	41.5692i	−0.943537	+	1.63425i	−0.184884	+	0.982760i	$0.559191\pi$
$647$	−24.0000	+	41.5692i	−0.943537	+	1.63425i	−0.758654	+	0.651494i	$0.774142\pi$
$648$		0			0
$649$	1.50000	+	2.59808i	0.0588802	+	0.101983i
$650$	−2.00000			−0.0784465
$651$		0			0
$652$	10.0000			0.391630
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	0.695934	−	0.718106i	$-0.254991\pi$
$653$	−7.00000	−	12.1244i	−0.273931	−	0.474463i	−0.969865	+	0.243643i	$0.921657\pi$
$654$		0			0
$655$		0			0
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$		0			0
$658$	−17.5000	+	6.06218i	−0.682221	+	0.236328i
$659$	44.0000			1.71400			0.856998	−	0.515319i	$-0.172327\pi$
$659$	44.0000			1.71400			0.856998	+	0.515319i	$0.172327\pi$
$660$		0			0
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	−0.910541	−	0.413419i	$-0.864334\pi$
$661$	−2.50000	+	4.33013i	−0.0972387	+	0.168422i	0.813302	+	0.581842i	$0.197668\pi$
$662$	1.00000	−	1.73205i	0.0388661	−	0.0673181i
$663$		0			0
$664$	−6.00000			−0.232845
$665$	−15.0000	+	5.19615i	−0.581675	+	0.201498i
$666$		0			0
$667$	−0.500000	−	0.866025i	−0.0193601	−	0.0335326i
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$		0			0
$670$	12.0000	+	20.7846i	0.463600	+	0.802980i
$671$	−14.0000			−0.540464
$672$		0			0
$673$	22.0000			0.848038			0.424019	−	0.905653i	$-0.360619\pi$
$673$	22.0000			0.848038			0.424019	+	0.905653i	$0.360619\pi$
$674$		0			0
$675$		0			0
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	0.790897	−	0.611950i	$-0.209615\pi$
$677$	−3.50000	−	6.06218i	−0.134516	−	0.232988i	−0.925412	+	0.378962i	$0.876281\pi$
$678$		0			0
$679$	14.0000	+	12.1244i	0.537271	+	0.465290i
$680$	−2.00000			−0.0766965
$681$		0			0
$682$	1.00000	−	1.73205i	0.0382920	−	0.0663237i
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	−0.203510	−	0.979073i	$-0.565235\pi$
$683$	19.5000	−	33.7750i	0.746147	−	1.29236i	0.949657	−	0.313291i	$-0.101432\pi$
$684$		0			0
$685$	−12.0000			−0.458496
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	−12.0000	+	20.7846i	−0.457164	+	0.791831i
$690$		0			0
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	0.984873	−	0.173275i	$-0.0554350\pi$
$691$	9.00000	+	15.5885i	0.342376	+	0.593013i	−0.642497	+	0.766288i	$0.722102\pi$
$692$	14.0000			0.532200
$693$		0			0
$694$	−32.0000			−1.21470
$695$	−13.0000	−	22.5167i	−0.493118	−	0.854106i
$696$		0			0
$697$	5.00000	−	8.66025i	0.189389	−	0.328031i
$698$	8.00000	+	13.8564i	0.302804	+	0.524473i
$699$		0			0
$700$	−0.500000	+	2.59808i	−0.0188982	+	0.0981981i
$701$	9.00000			0.339925			0.169963	−	0.985451i	$-0.445635\pi$
$701$	9.00000			0.339925			0.169963	+	0.985451i	$0.445635\pi$
$702$		0			0
$703$	−7.50000	+	12.9904i	−0.282868	+	0.489942i
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	−6.00000			−0.225813
$707$	22.5000	−	7.79423i	0.846200	−	0.293132i
$708$		0			0
$709$	−4.50000	−	7.79423i	−0.169001	−	0.292718i	0.769068	−	0.639167i	$-0.220721\pi$
$709$	−4.50000	−	7.79423i	−0.169001	−	0.292718i	−0.938069	+	0.346449i	$0.887387\pi$
$710$	5.00000	−	8.66025i	0.187647	−	0.325014i
$711$		0			0
$712$	3.00000	+	5.19615i	0.112430	+	0.194734i
$713$	2.00000			0.0749006
$714$		0			0
$715$	−4.00000			−0.149592
$716$	3.50000	+	6.06218i	0.130801	+	0.226554i
$717$		0			0
$718$	−5.00000	+	8.66025i	−0.186598	+	0.323198i
$719$	−11.5000	−	19.9186i	−0.428878	−	0.742838i	0.567896	−	0.823100i	$-0.307758\pi$
$719$	−11.5000	−	19.9186i	−0.428878	−	0.742838i	−0.996774	+	0.0802624i	$0.974424\pi$
$720$		0			0
$721$	−3.00000	+	15.5885i	−0.111726	+	0.580544i
$722$	−10.0000			−0.372161
$723$		0			0
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	−0.500000	+	0.866025i	−0.0185695	+	0.0321634i
$726$		0			0
$727$	14.0000			0.519231			0.259616	−	0.965712i	$-0.416404\pi$
$727$	14.0000			0.519231			0.259616	+	0.965712i	$0.416404\pi$
$728$	4.00000	+	3.46410i	0.148250	+	0.128388i
$729$		0			0
$730$	−8.00000	−	13.8564i	−0.296093	−	0.512849i
$731$	−0.500000	+	0.866025i	−0.0184932	+	0.0320311i
$732$		0			0
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	0.943468	−	0.331463i	$-0.107542\pi$
$733$	5.00000	+	8.66025i	0.184679	+	0.319874i	−0.758789	+	0.651336i	$0.774209\pi$
$734$	−32.0000			−1.18114
$735$		0			0
$736$	−1.00000			−0.0368605
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	−18.0000	+	31.1769i	−0.662141	+	1.14686i	0.317911	+	0.948120i	$0.397019\pi$
$739$	−18.0000	+	31.1769i	−0.662141	+	1.14686i	−0.980052	+	0.198741i	$0.936315\pi$
$740$	−5.00000	−	8.66025i	−0.183804	−	0.318357i
$741$		0			0
$742$	24.0000	+	20.7846i	0.881068	+	0.763027i
$743$	36.0000			1.32071			0.660356	−	0.750953i	$-0.270405\pi$
$743$	36.0000			1.32071			0.660356	+	0.750953i	$0.270405\pi$
$744$		0			0
$745$	−11.0000	+	19.0526i	−0.403009	+	0.698032i
$746$	−13.0000	+	22.5167i	−0.475964	+	0.824394i
$747$		0			0
$748$	1.00000			0.0365636
$749$	−1.00000	+	5.19615i	−0.0365392	+	0.189863i
$750$		0			0
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	0.995018	+	0.0996961i	$0.0317870\pi$
$751$	16.0000	+	27.7128i	0.583848	+	1.01125i	−0.411170	+	0.911559i	$0.634880\pi$
$752$	−3.50000	+	6.06218i	−0.127632	+	0.221065i
$753$		0			0
$754$	1.00000	+	1.73205i	0.0364179	+	0.0630776i
$755$	30.0000			1.09181
$756$		0			0
$757$	47.0000			1.70824			0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000			1.70824			0.854122	+	0.520073i	$0.174095\pi$
$758$	4.00000	+	6.92820i	0.145287	+	0.251644i
$759$		0			0
$760$	−3.00000	+	5.19615i	−0.108821	+	0.188484i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$	50.0000	−	17.3205i	1.81012	−	0.627044i
$764$	−8.00000			−0.289430
$765$		0			0
$766$	−12.5000	+	21.6506i	−0.451643	+	0.782269i
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		0			0
$769$	−20.0000			−0.721218			−0.360609	−	0.932717i	$-0.617431\pi$
$769$	−20.0000			−0.721218			−0.360609	+	0.932717i	$0.617431\pi$
$770$	−1.00000	+	5.19615i	−0.0360375	+	0.187256i
$771$		0			0
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	0.336323	+	0.941747i	$0.390817\pi$
$773$	−18.0000	+	31.1769i	−0.647415	+	1.12136i	−0.983738	+	0.179609i	$0.942517\pi$
$774$		0			0
$775$	−1.00000	−	1.73205i	−0.0359211	−	0.0622171i
$776$	7.00000			0.251285
$777$		0			0
$778$	−30.0000			−1.07555
$779$	−15.0000	−	25.9808i	−0.537431	−	0.930857i
$780$		0			0
$781$	−2.50000	+	4.33013i	−0.0894570	+	0.154944i
$782$	0.500000	+	0.866025i	0.0178800	+	0.0309690i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−2.00000			−0.0713831
$786$		0			0
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	−0.445577	−	0.895244i	$-0.647001\pi$
$787$	15.5000	−	26.8468i	0.552515	−	0.956985i	0.998092	−	0.0617409i	$-0.0196653\pi$
$788$	−13.5000	+	23.3827i	−0.480918	+	0.832974i
$789$		0			0
$790$		0			0
$791$	20.0000	+	17.3205i	0.711118	+	0.615846i
$792$		0			0
$793$	14.0000	+	24.2487i	0.497155	+	0.861097i
$794$	13.5000	−	23.3827i	0.479097	−	0.829820i
$795$		0			0
$796$	1.00000	+	1.73205i	0.0354441	+	0.0613909i
$797$	22.0000			0.779280			0.389640	−	0.920967i	$-0.372599\pi$
$797$	22.0000			0.779280			0.389640	+	0.920967i	$0.372599\pi$
$798$		0			0
$799$	7.00000			0.247642
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	12.0000	−	20.7846i	0.423735	−	0.733930i
$803$	4.00000	+	6.92820i	0.141157	+	0.244491i
$804$		0			0
$805$	−5.00000	+	1.73205i	−0.176227	+	0.0610468i
$806$	−4.00000			−0.140894
$807$		0			0
$808$	4.50000	−	7.79423i	0.158309	−	0.274200i
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	−0.979739	−	0.200279i	$-0.935815\pi$
$809$	−9.00000	+	15.5885i	−0.316423	+	0.548061i	0.663316	+	0.748340i	$0.269149\pi$
$810$		0			0
$811$	−28.0000			−0.983213			−0.491606	−	0.870817i	$-0.663590\pi$
$811$	−28.0000			−0.983213			−0.491606	+	0.870817i	$0.663590\pi$
$812$	2.50000	−	0.866025i	0.0877328	−	0.0303915i
$813$		0			0
$814$	2.50000	+	4.33013i	0.0876250	+	0.151771i
$815$	10.0000	−	17.3205i	0.350285	−	0.606711i
$816$		0			0
$817$	1.50000	+	2.59808i	0.0524784	+	0.0908952i
$818$	16.0000			0.559427
$819$		0			0
$820$	20.0000			0.698430
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	0.999626	+	0.0273557i	$0.00870868\pi$
$821$	15.0000	+	25.9808i	0.523504	+	0.906735i	−0.476122	+	0.879379i	$0.657958\pi$
$822$		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	$0.888479\pi$
$824$	3.00000	+	5.19615i	0.104510	+	0.181017i
$825$		0			0
$826$	−6.00000	−	5.19615i	−0.208767	−	0.180797i
$827$	34.0000			1.18230			0.591148	−	0.806563i	$-0.298675\pi$
$827$	34.0000			1.18230			0.591148	+	0.806563i	$0.298675\pi$
$828$		0			0
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−3.50000	+	6.06218i	−0.121560	+	0.210548i	0.798823	+	0.601566i	$0.205456\pi$
$830$	−6.00000	+	10.3923i	−0.208263	+	0.360722i
$831$		0			0
$832$	2.00000			0.0693375
$833$	−6.50000	−	2.59808i	−0.225212	−	0.0900180i
$834$		0			0
$835$	2.00000	+	3.46410i	0.0692129	+	0.119880i
$836$	1.50000	−	2.59808i	0.0518786	−	0.0898563i
$837$		0			0
$838$	−14.5000	−	25.1147i	−0.500894	−	0.867574i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	8.50000	+	14.7224i	0.292929	+	0.507369i
$843$		0			0
$844$	−2.00000	+	3.46410i	−0.0688428	+	0.119239i
$845$	−9.00000	−	15.5885i	−0.309609	−	0.536259i
$846$		0			0
$847$	0.500000	−	2.59808i	0.0171802	−	0.0892710i
$848$	12.0000			0.412082
$849$		0			0
$850$	0.500000	−	0.866025i	0.0171499	−	0.0297044i
$851$	−2.50000	+	4.33013i	−0.0856989	+	0.148435i
$852$		0			0
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	35.0000	−	12.1244i	1.19768	−	0.414887i
$855$		0			0
$856$	1.00000	+	1.73205i	0.0341793	+	0.0592003i
$857$	23.5000	−	40.7032i	0.802745	−	1.39039i	−0.115058	−	0.993359i	$-0.536706\pi$
$857$	23.5000	−	40.7032i	0.802745	−	1.39039i	0.917803	−	0.397036i	$-0.129961\pi$
$858$		0			0
$859$	13.0000	+	22.5167i	0.443554	+	0.768259i	0.997950	−	0.0639945i	$-0.0203840\pi$
$859$	13.0000	+	22.5167i	0.443554	+	0.768259i	−0.554396	+	0.832253i	$0.687051\pi$
$860$	−2.00000			−0.0681994
$861$		0			0
$862$	−16.0000			−0.544962
$863$	−22.0000	−	38.1051i	−0.748889	−	1.29711i	−0.948356	−	0.317209i	$-0.897254\pi$
$863$	−22.0000	−	38.1051i	−0.748889	−	1.29711i	0.199467	−	0.979905i	$-0.436079\pi$
$864$		0			0
$865$	14.0000	−	24.2487i	0.476014	−	0.824481i
$866$	9.50000	+	16.4545i	0.322823	+	0.559146i
$867$		0			0
$868$	−1.00000	+	5.19615i	−0.0339422	+	0.176369i
$869$		0			0
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	10.0000	−	17.3205i	0.338643	−	0.586546i
$873$		0			0
$874$	3.00000			0.101477
$875$	24.0000	+	20.7846i	0.811348	+	0.702648i
$876$		0			0
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	0.959671	−	0.281126i	$-0.0907079\pi$
$877$	7.00000	+	12.1244i	0.236373	+	0.409410i	−0.723298	+	0.690536i	$0.757375\pi$
$878$	−15.5000	+	26.8468i	−0.523100	+	0.906035i
$879$		0			0
$880$	1.00000	+	1.73205i	0.0337100	+	0.0583874i
$881$	12.0000			0.404290			0.202145	−	0.979356i	$-0.435209\pi$
$881$	12.0000			0.404290			0.202145	+	0.979356i	$0.435209\pi$
$882$		0			0
$883$	40.0000			1.34611			0.673054	−	0.739594i	$-0.264982\pi$
$883$	40.0000			1.34611			0.673054	+	0.739594i	$0.264982\pi$
$884$	−1.00000	−	1.73205i	−0.0336336	−	0.0582552i
$885$		0			0
$886$	−7.50000	+	12.9904i	−0.251967	+	0.436420i
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	−0.953086	−	0.302698i	$-0.902113\pi$
$887$	−22.0000	−	38.1051i	−0.738688	−	1.27944i	0.214399	−	0.976746i	$-0.431221\pi$
$888$		0			0
$889$	−2.00000	−	1.73205i	−0.0670778	−	0.0580911i
$890$	12.0000			0.402241
$891$		0			0
$892$	13.0000	−	22.5167i	0.435272	−	0.753914i
$893$	10.5000	−	18.1865i	0.351369	−	0.608589i
$894$		0			0
$895$	14.0000			0.467968
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	6.00000	+	10.3923i	0.200223	+	0.346796i
$899$	−1.00000	+	1.73205i	−0.0333519	+	0.0577671i
$900$		0			0
$901$	−6.00000	−	10.3923i	−0.199889	−	0.346218i
$902$	−10.0000			−0.332964
$903$		0			0
$904$	10.0000			0.332595
$905$	−10.0000	−	17.3205i	−0.332411	−	0.575753i
$906$		0			0
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	−0.315442	−	0.948945i	$-0.602153\pi$
$907$	20.0000	−	34.6410i	0.664089	−	1.15024i	0.979531	−	0.201291i	$-0.0645138\pi$
$908$	5.00000	+	8.66025i	0.165931	+	0.287401i
$909$		0			0
$910$	10.0000	−	3.46410i	0.331497	−	0.114834i
$911$	−45.0000			−1.49092			−0.745458	−	0.666552i	$-0.767769\pi$
$911$	−45.0000			−1.49092			−0.745458	+	0.666552i	$0.767769\pi$
$912$		0			0
$913$	3.00000	−	5.19615i	0.0992855	−	0.171968i
$914$	−16.0000	+	27.7128i	−0.529233	+	0.916658i
$915$		0			0
$916$	−10.0000			−0.330409
$917$		0			0
$918$		0			0
$919$	−28.5000	−	49.3634i	−0.940128	−	1.62835i	−0.765224	−	0.643765i	$-0.777372\pi$
$919$	−28.5000	−	49.3634i	−0.940128	−	1.62835i	−0.174905	−	0.984585i	$-0.555962\pi$
$920$	−1.00000	+	1.73205i	−0.0329690	+	0.0571040i
$921$		0			0
$922$	−16.5000	−	28.5788i	−0.543399	−	0.941194i
$923$	10.0000			0.329154
$924$		0			0
$925$	5.00000			0.164399
$926$	−8.00000	−	13.8564i	−0.262896	−	0.455350i
$927$		0			0
$928$	0.500000	−	0.866025i	0.0164133	−	0.0284287i
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	−0.994157	−	0.107944i	$-0.965573\pi$
$929$	−18.0000	−	31.1769i	−0.590561	−	1.02288i	0.403596	−	0.914937i	$-0.367760\pi$
$930$		0			0
$931$	−16.5000	+	12.9904i	−0.540766	+	0.425743i
$932$	−21.0000			−0.687878
$933$		0			0
$934$	−13.5000	+	23.3827i	−0.441733	+	0.765105i
$935$	1.00000	−	1.73205i	0.0327035	−	0.0566441i
$936$		0			0
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$	24.0000	+	20.7846i	0.783628	+	0.678642i
$939$		0			0
$940$	7.00000	+	12.1244i	0.228315	+	0.395453i
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	0.426033	+	0.904708i	$0.359911\pi$
$941$	−17.5000	+	30.3109i	−0.570484	+	0.988107i	−0.996516	+	0.0833989i	$0.973422\pi$
$942$		0			0
$943$	−5.00000	−	8.66025i	−0.162822	−	0.282017i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	1.00000			0.0325128
$947$	26.5000	+	45.8993i	0.861134	+	1.49153i	0.870835	+	0.491575i	$0.163579\pi$
$947$	26.5000	+	45.8993i	0.861134	+	1.49153i	−0.00970072	+	0.999953i	$0.503088\pi$
$948$		0			0
$949$	8.00000	−	13.8564i	0.259691	−	0.449798i
$950$	−1.50000	−	2.59808i	−0.0486664	−	0.0842927i
$951$		0			0
$952$	−2.50000	+	0.866025i	−0.0810255	+	0.0280680i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$	−8.00000	+	13.8564i	−0.258874	+	0.448383i
$956$	11.0000	−	19.0526i	0.355765	−	0.616204i
$957$		0			0
$958$	−26.0000			−0.840022
$959$	−15.0000	+	5.19615i	−0.484375	+	0.167793i
$960$		0			0
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	5.00000	−	8.66025i	0.161206	−	0.279218i
$963$		0			0
$964$	6.00000	+	10.3923i	0.193247	+	0.334714i
$965$	−16.0000			−0.515058
$966$		0			0
$967$	−1.00000			−0.0321578			−0.0160789	−	0.999871i	$-0.505118\pi$
$967$	−1.00000			−0.0321578			−0.0160789	+	0.999871i	$0.505118\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	7.00000	−	12.1244i	0.224756	−	0.389290i
$971$	−2.00000	−	3.46410i	−0.0641831	−	0.111168i	0.832148	−	0.554553i	$-0.187111\pi$
$971$	−2.00000	−	3.46410i	−0.0641831	−	0.111168i	−0.896331	+	0.443385i	$0.853777\pi$
$972$		0			0
$973$	−26.0000	−	22.5167i	−0.833522	−	0.721851i
$974$	−34.0000			−1.08943
$975$		0			0
$976$	7.00000	−	12.1244i	0.224065	−	0.388091i
$977$	−14.0000	+	24.2487i	−0.447900	+	0.775785i	−0.998249	−	0.0591494i	$-0.981161\pi$
$977$	−14.0000	+	24.2487i	−0.447900	+	0.775785i	0.550349	+	0.834934i	$0.314494\pi$
$978$		0			0
$979$	−6.00000			−0.191761
$980$	−2.00000	−	13.8564i	−0.0638877	−	0.442627i
$981$		0			0
$982$	3.00000	+	5.19615i	0.0957338	+	0.165816i
$983$	−19.5000	+	33.7750i	−0.621953	+	1.07725i	0.367168	+	0.930155i	$0.380327\pi$
$983$	−19.5000	+	33.7750i	−0.621953	+	1.07725i	−0.989122	+	0.147100i	$0.953006\pi$
$984$		0			0
$985$	27.0000	+	46.7654i	0.860292	+	1.49007i
$986$	−1.00000			−0.0318465
$987$		0			0
$988$	−6.00000			−0.190885
$989$	0.500000	+	0.866025i	0.0158991	+	0.0275380i
$990$		0			0
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	−0.964658	−	0.263504i	$-0.915122\pi$
$991$	−8.00000	+	13.8564i	−0.254128	+	0.440163i	0.710530	+	0.703667i	$0.248455\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$	2.50000	−	12.9904i	0.0792952	−	0.412030i
$995$	4.00000			0.126809
$996$		0			0
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	−0.314188	−	0.949361i	$-0.601732\pi$
$997$	21.0000	−	36.3731i	0.665077	−	1.15195i	0.979265	−	0.202586i	$-0.0649345\pi$
$998$	−4.00000	+	6.92820i	−0.126618	+	0.219308i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.h.991.1	yes	2
3.2	odd	2		1386.2.k.l.991.1	yes	2
7.2	even	3	inner	1386.2.k.h.793.1	✓	2
7.3	odd	6		9702.2.a.ca.1.1		1
7.4	even	3		9702.2.a.bi.1.1		1
21.2	odd	6		1386.2.k.l.793.1	yes	2
21.11	odd	6		9702.2.a.s.1.1		1
21.17	even	6		9702.2.a.f.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1386.2.k.h.793.1	✓	2	7.2	even	3	inner
1386.2.k.h.991.1	yes	2	1.1	even	1	trivial
1386.2.k.l.793.1	yes	2	21.2	odd	6
1386.2.k.l.991.1	yes	2	3.2	odd	2
9702.2.a.f.1.1		1	21.17	even	6
9702.2.a.s.1.1		1	21.11	odd	6
9702.2.a.bi.1.1		1	7.4	even	3
9702.2.a.ca.1.1		1	7.3	odd	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(1.00000 + 1.73205i) q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{10} +(-0.500000 + 0.866025i) q^{11} +2.00000 q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.500000 + 0.866025i) q^{17} +(1.50000 + 2.59808i) q^{19} -2.00000 q^{20} +1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 - 0.866025i) q^{25} +(-1.00000 - 1.73205i) q^{26} +(-2.50000 + 0.866025i) q^{28} -1.00000 q^{29} +(1.00000 - 1.73205i) q^{31} +(-0.500000 + 0.866025i) q^{32} +1.00000 q^{34} +(-1.00000 + 5.19615i) q^{35} +(2.50000 + 4.33013i) q^{37} +(1.50000 - 2.59808i) q^{38} +(1.00000 + 1.73205i) q^{40} -10.0000 q^{41} +1.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} +(-3.50000 - 6.06218i) q^{47} +(1.00000 + 6.92820i) q^{49} -1.00000 q^{50} +(-1.00000 + 1.73205i) q^{52} +(-6.00000 + 10.3923i) q^{53} -2.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +(0.500000 + 0.866025i) q^{58} +(1.50000 - 2.59808i) q^{59} +(7.00000 + 12.1244i) q^{61} -2.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{65} +(-6.00000 + 10.3923i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(5.00000 - 1.73205i) q^{70} +5.00000 q^{71} +(4.00000 - 6.92820i) q^{73} +(2.50000 - 4.33013i) q^{74} -3.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} +(1.00000 - 1.73205i) q^{80} +(5.00000 + 8.66025i) q^{82} -6.00000 q^{83} -2.00000 q^{85} +(-0.500000 - 0.866025i) q^{86} +(-0.500000 + 0.866025i) q^{88} +(3.00000 + 5.19615i) q^{89} +(4.00000 + 3.46410i) q^{91} -1.00000 q^{92} +(-3.50000 + 6.06218i) q^{94} +(-3.00000 + 5.19615i) q^{95} +7.00000 q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 2 q^{5} + 4 q^{7} + 2 q^{8} + 2 q^{10} - q^{11} + 4 q^{13} + q^{14} - q^{16} - q^{17} + 3 q^{19} - 4 q^{20} + 2 q^{22} + q^{23} + q^{25} - 2 q^{26} - 5 q^{28} - 2 q^{29} + 2 q^{31} - q^{32} + 2 q^{34} - 2 q^{35} + 5 q^{37} + 3 q^{38} + 2 q^{40} - 20 q^{41} + 2 q^{43} - q^{44} + q^{46} - 7 q^{47} + 2 q^{49} - 2 q^{50} - 2 q^{52} - 12 q^{53} - 4 q^{55} + 4 q^{56} + q^{58} + 3 q^{59} + 14 q^{61} - 4 q^{62} + 2 q^{64} + 4 q^{65} - 12 q^{67} - q^{68} + 10 q^{70} + 10 q^{71} + 8 q^{73} + 5 q^{74} - 6 q^{76} - 5 q^{77} + 2 q^{80} + 10 q^{82} - 12 q^{83} - 4 q^{85} - q^{86} - q^{88} + 6 q^{89} + 8 q^{91} - 2 q^{92} - 7 q^{94} - 6 q^{95} + 14 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 2 * q^5 + 4 * q^7 + 2 * q^8 + 2 * q^10 - q^11 + 4 * q^13 + q^14 - q^16 - q^17 + 3 * q^19 - 4 * q^20 + 2 * q^22 + q^23 + q^25 - 2 * q^26 - 5 * q^28 - 2 * q^29 + 2 * q^31 - q^32 + 2 * q^34 - 2 * q^35 + 5 * q^37 + 3 * q^38 + 2 * q^40 - 20 * q^41 + 2 * q^43 - q^44 + q^46 - 7 * q^47 + 2 * q^49 - 2 * q^50 - 2 * q^52 - 12 * q^53 - 4 * q^55 + 4 * q^56 + q^58 + 3 * q^59 + 14 * q^61 - 4 * q^62 + 2 * q^64 + 4 * q^65 - 12 * q^67 - q^68 + 10 * q^70 + 10 * q^71 + 8 * q^73 + 5 * q^74 - 6 * q^76 - 5 * q^77 + 2 * q^80 + 10 * q^82 - 12 * q^83 - 4 * q^85 - q^86 - q^88 + 6 * q^89 + 8 * q^91 - 2 * q^92 - 7 * q^94 - 6 * q^95 + 14 * q^97 + 11 * q^98

Introduction

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Database

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