LMFDB - Embedded newform 1386.2.k.r.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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{7})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 7x^{2} + 49 $ x^4 + 7*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 462)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$-1.32288 - 2.29129i$ of defining polynomial
Character	$\chi$	$=$	1386.991
Dual form			1386.2.k.r.793.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(-1.32288 + 2.29129i) q^{10} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +(1.32288 - 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(2.64575 + 4.58258i) q^{19} +2.64575 q^{20} -1.00000 q^{22} +(1.32288 + 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(2.00000 + 3.46410i) q^{26} -2.64575 q^{28} -2.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(3.50000 - 6.06218i) q^{35} +(4.64575 + 8.04668i) q^{37} +(2.64575 - 4.58258i) q^{38} +(-1.32288 - 2.29129i) q^{40} -9.00000 q^{41} -1.29150 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.32288 - 2.29129i) q^{46} +(5.96863 + 10.3380i) q^{47} +(-3.50000 + 6.06218i) q^{49} +2.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} -2.64575 q^{55} +(1.32288 + 2.29129i) q^{56} +(1.00000 + 1.73205i) q^{58} +(-7.29150 + 12.6293i) q^{59} +(1.96863 + 3.40976i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(5.29150 + 9.16515i) q^{65} +(6.79150 - 11.7632i) q^{67} +(-1.50000 - 2.59808i) q^{68} -7.00000 q^{70} +13.2915 q^{71} +(2.35425 - 4.07768i) q^{73} +(4.64575 - 8.04668i) q^{74} -5.29150 q^{76} +2.64575 q^{77} +(-2.67712 - 4.63692i) q^{79} +(-1.32288 + 2.29129i) q^{80} +(4.50000 + 7.79423i) q^{82} +5.58301 q^{83} +7.93725 q^{85} +(0.645751 + 1.11847i) q^{86} +(0.500000 - 0.866025i) q^{88} +(6.64575 + 11.5108i) q^{89} +(-5.29150 - 9.16515i) q^{91} -2.64575 q^{92} +(5.96863 - 10.3380i) q^{94} +(7.00000 - 12.1244i) q^{95} +9.58301 q^{97} +7.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	$ 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{11} - 16 q^{13} - 2 q^{16} - 6 q^{17} - 4 q^{22} - 4 q^{25} + 8 q^{26} - 8 q^{29} + 8 q^{31} - 2 q^{32} + 12 q^{34} + 14 q^{35} + 8 q^{37} - 36 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{47} - 14 q^{49} + 8 q^{50} + 8 q^{52} + 8 q^{53} + 4 q^{58} - 8 q^{59} - 8 q^{61} - 16 q^{62} + 4 q^{64} + 6 q^{67} - 6 q^{68} - 28 q^{70} + 32 q^{71} + 20 q^{73} + 8 q^{74} - 16 q^{79} + 18 q^{82} - 20 q^{83} - 8 q^{86} + 2 q^{88} + 16 q^{89} + 8 q^{94} + 28 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) $ 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^11 - 16 * q^13 - 2 * q^16 - 6 * q^17 - 4 * q^22 - 4 * q^25 + 8 * q^26 - 8 * q^29 + 8 * q^31 - 2 * q^32 + 12 * q^34 + 14 * q^35 + 8 * q^37 - 36 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^47 - 14 * q^49 + 8 * q^50 + 8 * q^52 + 8 * q^53 + 4 * q^58 - 8 * q^59 - 8 * q^61 - 16 * q^62 + 4 * q^64 + 6 * q^67 - 6 * q^68 - 28 * q^70 + 32 * q^71 + 20 * q^73 + 8 * q^74 - 16 * q^79 + 18 * q^82 - 20 * q^83 - 8 * q^86 + 2 * q^88 + 16 * q^89 + 8 * q^94 + 28 * q^95 - 4 * q^97 + 28 * 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
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	−0.994016	−	0.109235i	$-0.965160\pi$
$5$	−1.32288	−	2.29129i	−0.591608	−	1.02470i	0.402408	−	0.915460i	$-0.368173\pi$
$6$		0			0
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$7$	1.32288	+	2.29129i	0.500000	+	0.866025i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.32288	+	2.29129i	−0.418330	+	0.724569i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$		0			0
$13$	−4.00000			−1.10940			−0.554700	−	0.832050i	$-0.687167\pi$
$13$	−4.00000			−1.10940			−0.554700	+	0.832050i	$0.687167\pi$
$14$	1.32288	−	2.29129i	0.353553	−	0.612372i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	2.64575	+	4.58258i	0.606977	+	1.05131i	0.991736	+	0.128298i	$0.0409513\pi$
$19$	2.64575	+	4.58258i	0.606977	+	1.05131i	−0.384759	+	0.923017i	$0.625715\pi$
$20$	2.64575			0.591608
$21$		0			0
$22$	−1.00000			−0.213201
$23$	1.32288	+	2.29129i	0.275839	+	0.477767i	0.970346	−	0.241719i	$-0.0777111\pi$
$23$	1.32288	+	2.29129i	0.275839	+	0.477767i	−0.694508	+	0.719485i	$0.744378\pi$
$24$		0			0
$25$	−1.00000	+	1.73205i	−0.200000	+	0.346410i
$26$	2.00000	+	3.46410i	0.392232	+	0.679366i
$27$		0			0
$28$	−2.64575			−0.500000
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$		0			0
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	−0.628619	−	0.777714i	$-0.716379\pi$
$31$	2.00000	−	3.46410i	0.359211	−	0.622171i	0.987829	+	0.155543i	$0.0497126\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	3.00000			0.514496
$35$	3.50000	−	6.06218i	0.591608	−	1.02470i
$36$		0			0
$37$	4.64575	+	8.04668i	0.763757	+	1.32287i	0.940901	+	0.338681i	$0.109981\pi$
$37$	4.64575	+	8.04668i	0.763757	+	1.32287i	−0.177145	+	0.984185i	$0.556686\pi$
$38$	2.64575	−	4.58258i	0.429198	−	0.743392i
$39$		0			0
$40$	−1.32288	−	2.29129i	−0.209165	−	0.362284i
$41$	−9.00000			−1.40556			−0.702782	−	0.711405i	$-0.748059\pi$
$41$	−9.00000			−1.40556			−0.702782	+	0.711405i	$0.748059\pi$
$42$		0			0
$43$	−1.29150			−0.196952			−0.0984762	−	0.995139i	$-0.531397\pi$
$43$	−1.29150			−0.196952			−0.0984762	+	0.995139i	$0.531397\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$		0			0
$46$	1.32288	−	2.29129i	0.195047	−	0.337832i
$47$	5.96863	+	10.3380i	0.870614	+	1.50795i	0.861363	+	0.507990i	$0.169611\pi$
$47$	5.96863	+	10.3380i	0.870614	+	1.50795i	0.00925075	+	0.999957i	$0.497055\pi$
$48$		0			0
$49$	−3.50000	+	6.06218i	−0.500000	+	0.866025i
$50$	2.00000			0.282843
$51$		0			0
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$		0			0
$55$	−2.64575			−0.356753
$56$	1.32288	+	2.29129i	0.176777	+	0.306186i
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	−7.29150	+	12.6293i	−0.949273	+	1.64419i	−0.202311	+	0.979321i	$0.564845\pi$
$59$	−7.29150	+	12.6293i	−0.949273	+	1.64419i	−0.746961	+	0.664867i	$0.768488\pi$
$60$		0			0
$61$	1.96863	+	3.40976i	0.252057	+	0.436575i	0.964092	−	0.265569i	$-0.0855597\pi$
$61$	1.96863	+	3.40976i	0.252057	+	0.436575i	−0.712035	+	0.702144i	$0.752226\pi$
$62$	−4.00000			−0.508001
$63$		0			0
$64$	1.00000			0.125000
$65$	5.29150	+	9.16515i	0.656330	+	1.13680i
$66$		0			0
$67$	6.79150	−	11.7632i	0.829714	−	1.43711i	−0.0685485	−	0.997648i	$-0.521837\pi$
$67$	6.79150	−	11.7632i	0.829714	−	1.43711i	0.898263	−	0.439459i	$-0.144830\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$		0			0
$70$	−7.00000			−0.836660
$71$	13.2915			1.57741			0.788706	−	0.614771i	$-0.210752\pi$
$71$	13.2915			1.57741			0.788706	+	0.614771i	$0.210752\pi$
$72$		0			0
$73$	2.35425	−	4.07768i	0.275544	−	0.477256i	−0.694728	−	0.719272i	$-0.744475\pi$
$73$	2.35425	−	4.07768i	0.275544	−	0.477256i	0.970272	+	0.242016i	$0.0778087\pi$
$74$	4.64575	−	8.04668i	0.540058	−	0.935407i
$75$		0			0
$76$	−5.29150			−0.606977
$77$	2.64575			0.301511
$78$		0			0
$79$	−2.67712	−	4.63692i	−0.301200	−	0.521694i	0.675208	−	0.737627i	$-0.264054\pi$
$79$	−2.67712	−	4.63692i	−0.301200	−	0.521694i	−0.976408	+	0.215934i	$0.930721\pi$
$80$	−1.32288	+	2.29129i	−0.147902	+	0.256174i
$81$		0			0
$82$	4.50000	+	7.79423i	0.496942	+	0.860729i
$83$	5.58301			0.612814			0.306407	−	0.951901i	$-0.400873\pi$
$83$	5.58301			0.612814			0.306407	+	0.951901i	$0.400873\pi$
$84$		0			0
$85$	7.93725			0.860916
$86$	0.645751	+	1.11847i	0.0696332	+	0.120608i
$87$		0			0
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	6.64575	+	11.5108i	0.704448	+	1.22014i	0.966890	+	0.255192i	$0.0821388\pi$
$89$	6.64575	+	11.5108i	0.704448	+	1.22014i	−0.262442	+	0.964948i	$0.584528\pi$
$90$		0			0
$91$	−5.29150	−	9.16515i	−0.554700	−	0.960769i
$92$	−2.64575			−0.275839
$93$		0			0
$94$	5.96863	−	10.3380i	0.615617	−	1.06628i
$95$	7.00000	−	12.1244i	0.718185	−	1.24393i
$96$		0			0
$97$	9.58301			0.973007			0.486503	−	0.873679i	$-0.338272\pi$
$97$	9.58301			0.973007			0.486503	+	0.873679i	$0.338272\pi$
$98$	7.00000			0.707107
$99$		0			0
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	−1.64575	+	2.85052i	−0.163758	+	0.283638i	−0.936214	−	0.351431i	$-0.885695\pi$
$101$	−1.64575	+	2.85052i	−0.163758	+	0.283638i	0.772455	+	0.635069i	$0.219028\pi$
$102$		0			0
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	0.999964	−	0.00844953i	$-0.00268960\pi$
$103$	5.00000	+	8.66025i	0.492665	+	0.853320i	−0.507300	+	0.861770i	$0.669356\pi$
$104$	−4.00000			−0.392232
$105$		0			0
$106$	−4.00000			−0.388514
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	0.997298	−	0.0734594i	$-0.0234039\pi$
$107$	4.50000	+	7.79423i	0.435031	+	0.753497i	−0.562267	+	0.826956i	$0.690071\pi$
$108$		0			0
$109$	−5.96863	+	10.3380i	−0.571691	+	0.990197i	0.424702	+	0.905333i	$0.360379\pi$
$109$	−5.96863	+	10.3380i	−0.571691	+	0.990197i	−0.996393	+	0.0848642i	$0.972954\pi$
$110$	1.32288	+	2.29129i	0.126131	+	0.218466i
$111$		0			0
$112$	1.32288	−	2.29129i	0.125000	−	0.216506i
$113$	8.58301			0.807421			0.403711	−	0.914887i	$-0.367720\pi$
$113$	8.58301			0.807421			0.403711	+	0.914887i	$0.367720\pi$
$114$		0			0
$115$	3.50000	−	6.06218i	0.326377	−	0.565301i
$116$	1.00000	−	1.73205i	0.0928477	−	0.160817i
$117$		0			0
$118$	14.5830			1.34247
$119$	−7.93725			−0.727607
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.96863	−	3.40976i	0.178231	−	0.308705i
$123$		0			0
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	−7.93725			−0.709930
$126$		0			0
$127$	−2.64575			−0.234772			−0.117386	−	0.993086i	$-0.537452\pi$
$127$	−2.64575			−0.234772			−0.117386	+	0.993086i	$0.537452\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	5.29150	−	9.16515i	0.464095	−	0.803837i
$131$	1.29150	+	2.23695i	0.112839	+	0.195443i	0.916914	−	0.399085i	$-0.130672\pi$
$131$	1.29150	+	2.23695i	0.112839	+	0.195443i	−0.804075	+	0.594528i	$0.797339\pi$
$132$		0			0
$133$	−7.00000	+	12.1244i	−0.606977	+	1.05131i
$134$	−13.5830			−1.17339
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−1.35425	+	2.34563i	−0.115701	+	0.200400i	−0.918060	−	0.396442i	$-0.870245\pi$
$137$	−1.35425	+	2.34563i	−0.115701	+	0.200400i	0.802359	+	0.596842i	$0.203578\pi$
$138$		0			0
$139$	8.58301			0.728001			0.364001	−	0.931399i	$-0.381411\pi$
$139$	8.58301			0.728001			0.364001	+	0.931399i	$0.381411\pi$
$140$	3.50000	+	6.06218i	0.295804	+	0.512348i
$141$		0			0
$142$	−6.64575	−	11.5108i	−0.557699	−	0.965963i
$143$	−2.00000	+	3.46410i	−0.167248	+	0.289683i
$144$		0			0
$145$	2.64575	+	4.58258i	0.219718	+	0.380562i
$146$	−4.70850			−0.389678
$147$		0			0
$148$	−9.29150			−0.763757
$149$	−5.93725	−	10.2836i	−0.486399	−	0.842467i	0.513479	−	0.858102i	$-0.328356\pi$
$149$	−5.93725	−	10.2836i	−0.486399	−	0.842467i	−0.999878	+	0.0156348i	$0.995023\pi$
$150$		0			0
$151$	−8.67712	+	15.0292i	−0.706134	+	1.22306i	0.260146	+	0.965569i	$0.416229\pi$
$151$	−8.67712	+	15.0292i	−0.706134	+	1.22306i	−0.966281	+	0.257491i	$0.917104\pi$
$152$	2.64575	+	4.58258i	0.214599	+	0.371696i
$153$		0			0
$154$	−1.32288	−	2.29129i	−0.106600	−	0.184637i
$155$	−10.5830			−0.850047
$156$		0			0
$157$	5.64575	−	9.77873i	0.450580	−	0.780427i	−0.547842	−	0.836582i	$-0.684551\pi$
$157$	5.64575	−	9.77873i	0.450580	−	0.780427i	0.998422	+	0.0561543i	$0.0178839\pi$
$158$	−2.67712	+	4.63692i	−0.212981	+	0.368893i
$159$		0			0
$160$	2.64575			0.209165
$161$	−3.50000	+	6.06218i	−0.275839	+	0.477767i
$162$		0			0
$163$	−7.79150	−	13.4953i	−0.610278	−	1.05703i	−0.991193	−	0.132422i	$-0.957725\pi$
$163$	−7.79150	−	13.4953i	−0.610278	−	1.05703i	0.380916	−	0.924610i	$-0.375609\pi$
$164$	4.50000	−	7.79423i	0.351391	−	0.608627i
$165$		0			0
$166$	−2.79150	−	4.83502i	−0.216663	−	0.375271i
$167$	−19.2915			−1.49282			−0.746411	−	0.665486i	$-0.768224\pi$
$167$	−19.2915			−1.49282			−0.746411	+	0.665486i	$0.768224\pi$
$168$		0			0
$169$	3.00000			0.230769
$170$	−3.96863	−	6.87386i	−0.304380	−	0.527201i
$171$		0			0
$172$	0.645751	−	1.11847i	0.0492381	−	0.0852828i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$		0			0
$175$	−5.29150			−0.400000
$176$	−1.00000			−0.0753778
$177$		0			0
$178$	6.64575	−	11.5108i	0.498120	−	0.862769i
$179$	7.64575	−	13.2428i	0.571470	−	0.989816i	−0.424945	−	0.905219i	$-0.639707\pi$
$179$	7.64575	−	13.2428i	0.571470	−	0.989816i	0.996415	−	0.0845964i	$-0.0269601\pi$
$180$		0			0
$181$	5.29150			0.393314			0.196657	−	0.980472i	$-0.436991\pi$
$181$	5.29150			0.393314			0.196657	+	0.980472i	$0.436991\pi$
$182$	−5.29150	+	9.16515i	−0.392232	+	0.679366i
$183$		0			0
$184$	1.32288	+	2.29129i	0.0975237	+	0.168916i
$185$	12.2915	−	21.2895i	0.903689	−	1.56524i
$186$		0			0
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	−11.9373			−0.870614
$189$		0			0
$190$	−14.0000			−1.01567
$191$	8.64575	+	14.9749i	0.625585	+	1.08354i	0.988428	+	0.151694i	$0.0484728\pi$
$191$	8.64575	+	14.9749i	0.625585	+	1.08354i	−0.362843	+	0.931850i	$0.618194\pi$
$192$		0			0
$193$	−7.93725	+	13.7477i	−0.571336	+	0.989583i	0.425093	+	0.905150i	$0.360241\pi$
$193$	−7.93725	+	13.7477i	−0.571336	+	0.989583i	−0.996429	+	0.0844334i	$0.973092\pi$
$194$	−4.79150	−	8.29913i	−0.344010	−	0.595843i
$195$		0			0
$196$	−3.50000	−	6.06218i	−0.250000	−	0.433013i
$197$	9.87451			0.703530			0.351765	−	0.936088i	$-0.385582\pi$
$197$	9.87451			0.703530			0.351765	+	0.936088i	$0.385582\pi$
$198$		0			0
$199$	−11.5830	+	20.0624i	−0.821097	+	1.42218i	0.0837682	+	0.996485i	$0.473304\pi$
$199$	−11.5830	+	20.0624i	−0.821097	+	1.42218i	−0.904866	+	0.425697i	$0.860029\pi$
$200$	−1.00000	+	1.73205i	−0.0707107	+	0.122474i
$201$		0			0
$202$	3.29150			0.231589
$203$	−2.64575	−	4.58258i	−0.185695	−	0.321634i
$204$		0			0
$205$	11.9059	+	20.6216i	0.831543	+	1.44027i
$206$	5.00000	−	8.66025i	0.348367	−	0.603388i
$207$		0			0
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	5.29150			0.366021
$210$		0			0
$211$	10.7085			0.737203			0.368602	−	0.929587i	$-0.379837\pi$
$211$	10.7085			0.737203			0.368602	+	0.929587i	$0.379837\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$		0			0
$214$	4.50000	−	7.79423i	0.307614	−	0.532803i
$215$	1.70850	+	2.95920i	0.116519	+	0.201816i
$216$		0			0
$217$	10.5830			0.718421
$218$	11.9373			0.808493
$219$		0			0
$220$	1.32288	−	2.29129i	0.0891883	−	0.154479i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	−24.4575			−1.63780			−0.818898	−	0.573939i	$-0.805415\pi$
$223$	−24.4575			−1.63780			−0.818898	+	0.573939i	$0.805415\pi$
$224$	−2.64575			−0.176777
$225$		0			0
$226$	−4.29150	−	7.43310i	−0.285467	−	0.494442i
$227$	11.7915	−	20.4235i	0.782630	−	1.35555i	−0.147775	−	0.989021i	$-0.547211\pi$
$227$	11.7915	−	20.4235i	0.782630	−	1.35555i	0.930405	−	0.366533i	$-0.119455\pi$
$228$		0			0
$229$	−8.64575	−	14.9749i	−0.571327	−	0.989568i	−0.996430	−	0.0844228i	$-0.973095\pi$
$229$	−8.64575	−	14.9749i	−0.571327	−	0.989568i	0.425103	−	0.905145i	$-0.360238\pi$
$230$	−7.00000			−0.461566
$231$		0			0
$232$	−2.00000			−0.131306
$233$	−11.0830	−	19.1963i	−0.726072	−	1.25759i	−0.958531	−	0.284987i	$-0.908011\pi$
$233$	−11.0830	−	19.1963i	−0.726072	−	1.25759i	0.232460	−	0.972606i	$-0.425323\pi$
$234$		0			0
$235$	15.7915	−	27.3517i	1.03012	−	1.78423i
$236$	−7.29150	−	12.6293i	−0.474636	−	0.822094i
$237$		0			0
$238$	3.96863	+	6.87386i	0.257248	+	0.445566i
$239$	−13.2915			−0.859756			−0.429878	−	0.902887i	$-0.641443\pi$
$239$	−13.2915			−0.859756			−0.429878	+	0.902887i	$0.641443\pi$
$240$		0			0
$241$	−7.58301	+	13.1342i	−0.488464	+	0.846045i	−0.999912	−	0.0132694i	$-0.995776\pi$
$241$	−7.58301	+	13.1342i	−0.488464	+	0.846045i	0.511448	+	0.859314i	$0.329109\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$		0			0
$244$	−3.93725			−0.252057
$245$	18.5203			1.18322
$246$		0			0
$247$	−10.5830	−	18.3303i	−0.673380	−	1.16633i
$248$	2.00000	−	3.46410i	0.127000	−	0.219971i
$249$		0			0
$250$	3.96863	+	6.87386i	0.250998	+	0.434741i
$251$	−12.7085			−0.802153			−0.401077	−	0.916045i	$-0.631364\pi$
$251$	−12.7085			−0.802153			−0.401077	+	0.916045i	$0.631364\pi$
$252$		0			0
$253$	2.64575			0.166337
$254$	1.32288	+	2.29129i	0.0830046	+	0.143768i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.645751	−	1.11847i	−0.0402809	−	0.0697685i	0.845182	−	0.534478i	$-0.179492\pi$
$257$	−0.645751	−	1.11847i	−0.0402809	−	0.0697685i	−0.885463	+	0.464710i	$0.846159\pi$
$258$		0			0
$259$	−12.2915	+	21.2895i	−0.763757	+	1.32287i
$260$	−10.5830			−0.656330
$261$		0			0
$262$	1.29150	−	2.23695i	0.0797893	−	0.138199i
$263$	−4.93725	+	8.55157i	−0.304444	+	0.527313i	−0.977137	−	0.212609i	$-0.931804\pi$
$263$	−4.93725	+	8.55157i	−0.304444	+	0.527313i	0.672693	+	0.739921i	$0.265137\pi$
$264$		0			0
$265$	−10.5830			−0.650109
$266$	14.0000			0.858395
$267$		0			0
$268$	6.79150	+	11.7632i	0.414857	+	0.718553i
$269$	−2.67712	+	4.63692i	−0.163227	+	0.282718i	−0.936024	−	0.351935i	$-0.885524\pi$
$269$	−2.67712	+	4.63692i	−0.163227	+	0.282718i	0.772797	+	0.634653i	$0.218857\pi$
$270$		0			0
$271$	0.645751	+	1.11847i	0.0392266	+	0.0679425i	0.884972	−	0.465644i	$-0.154177\pi$
$271$	0.645751	+	1.11847i	0.0392266	+	0.0679425i	−0.845746	+	0.533586i	$0.820844\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$	2.70850			0.163626
$275$	1.00000	+	1.73205i	0.0603023	+	0.104447i
$276$		0			0
$277$	−12.5830	+	21.7944i	−0.756040	+	1.30950i	0.188816	+	0.982012i	$0.439535\pi$
$277$	−12.5830	+	21.7944i	−0.756040	+	1.30950i	−0.944856	+	0.327486i	$0.893798\pi$
$278$	−4.29150	−	7.43310i	−0.257387	−	0.445808i
$279$		0			0
$280$	3.50000	−	6.06218i	0.209165	−	0.362284i
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	11.2288	−	19.4488i	0.667480	−	1.15611i	−0.311126	−	0.950369i	$-0.600706\pi$
$283$	11.2288	−	19.4488i	0.667480	−	1.15611i	0.978606	−	0.205741i	$-0.0659605\pi$
$284$	−6.64575	+	11.5108i	−0.394353	+	0.683039i
$285$		0			0
$286$	4.00000			0.236525
$287$	−11.9059	−	20.6216i	−0.702782	−	1.21725i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	2.64575	−	4.58258i	0.155364	−	0.269098i
$291$		0			0
$292$	2.35425	+	4.07768i	0.137772	+	0.238628i
$293$	−6.58301			−0.384583			−0.192292	−	0.981338i	$-0.561592\pi$
$293$	−6.58301			−0.384583			−0.192292	+	0.981338i	$0.561592\pi$
$294$		0			0
$295$	38.5830			2.24639
$296$	4.64575	+	8.04668i	0.270029	+	0.467704i
$297$		0			0
$298$	−5.93725	+	10.2836i	−0.343936	+	0.595714i
$299$	−5.29150	−	9.16515i	−0.306015	−	0.530034i
$300$		0			0
$301$	−1.70850	−	2.95920i	−0.0984762	−	0.170566i
$302$	17.3542			0.998625
$303$		0			0
$304$	2.64575	−	4.58258i	0.151744	−	0.262829i
$305$	5.20850	−	9.02138i	0.298238	−	0.516563i
$306$		0			0
$307$	−32.5830			−1.85961			−0.929805	−	0.368052i	$-0.880025\pi$
$307$	−32.5830			−1.85961			−0.929805	+	0.368052i	$0.880025\pi$
$308$	−1.32288	+	2.29129i	−0.0753778	+	0.130558i
$309$		0			0
$310$	5.29150	+	9.16515i	0.300537	+	0.520546i
$311$	−7.26013	+	12.5749i	−0.411684	+	0.713058i	−0.995074	−	0.0991343i	$-0.968393\pi$
$311$	−7.26013	+	12.5749i	−0.411684	+	0.713058i	0.583390	+	0.812192i	$0.301726\pi$
$312$		0			0
$313$	−0.291503	−	0.504897i	−0.0164767	−	0.0285385i	0.857669	−	0.514201i	$-0.171912\pi$
$313$	−0.291503	−	0.504897i	−0.0164767	−	0.0285385i	−0.874146	+	0.485663i	$0.838578\pi$
$314$	−11.2915			−0.637216
$315$		0			0
$316$	5.35425			0.301200
$317$	−8.61438	−	14.9205i	−0.483832	−	0.838021i	0.515996	−	0.856591i	$-0.327422\pi$
$317$	−8.61438	−	14.9205i	−0.483832	−	0.838021i	−0.999828	+	0.0185700i	$0.994089\pi$
$318$		0			0
$319$	−1.00000	+	1.73205i	−0.0559893	+	0.0969762i
$320$	−1.32288	−	2.29129i	−0.0739510	−	0.128087i
$321$		0			0
$322$	7.00000			0.390095
$323$	−15.8745			−0.883281
$324$		0			0
$325$	4.00000	−	6.92820i	0.221880	−	0.384308i
$326$	−7.79150	+	13.4953i	−0.431531	+	0.747434i
$327$		0			0
$328$	−9.00000			−0.496942
$329$	−15.7915	+	27.3517i	−0.870614	+	1.50795i
$330$		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	$0.949627\pi$
$332$	−2.79150	+	4.83502i	−0.153204	+	0.265356i
$333$		0			0
$334$	9.64575	+	16.7069i	0.527792	+	0.914163i
$335$	−35.9373			−1.96346
$336$		0			0
$337$	17.2915			0.941928			0.470964	−	0.882152i	$-0.343906\pi$
$337$	17.2915			0.941928			0.470964	+	0.882152i	$0.343906\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$		0			0
$340$	−3.96863	+	6.87386i	−0.215229	+	0.372788i
$341$	−2.00000	−	3.46410i	−0.108306	−	0.187592i
$342$		0			0
$343$	−18.5203			−1.00000
$344$	−1.29150			−0.0696332
$345$		0			0
$346$	2.00000	−	3.46410i	0.107521	−	0.186231i
$347$	4.20850	−	7.28933i	0.225924	−	0.391312i	−0.730672	−	0.682728i	$-0.760793\pi$
$347$	4.20850	−	7.28933i	0.225924	−	0.391312i	0.956596	+	0.291417i	$0.0941266\pi$
$348$		0			0
$349$	13.2288			0.708119			0.354060	−	0.935223i	$-0.384801\pi$
$349$	13.2288			0.708119			0.354060	+	0.935223i	$0.384801\pi$
$350$	2.64575	+	4.58258i	0.141421	+	0.244949i
$351$		0			0
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	−6.35425	+	11.0059i	−0.338203	+	0.585784i	−0.984095	−	0.177645i	$-0.943152\pi$
$353$	−6.35425	+	11.0059i	−0.338203	+	0.585784i	0.645892	+	0.763429i	$0.276486\pi$
$354$		0			0
$355$	−17.5830	−	30.4547i	−0.933209	−	1.61637i
$356$	−13.2915			−0.704448
$357$		0			0
$358$	−15.2915			−0.808181
$359$	−0.291503	−	0.504897i	−0.0153849	−	0.0266475i	0.858230	−	0.513265i	$-0.171564\pi$
$359$	−0.291503	−	0.504897i	−0.0153849	−	0.0266475i	−0.873615	+	0.486617i	$0.838231\pi$
$360$		0			0
$361$	−4.50000	+	7.79423i	−0.236842	+	0.410223i
$362$	−2.64575	−	4.58258i	−0.139058	−	0.240855i
$363$		0			0
$364$	10.5830			0.554700
$365$	−12.4575			−0.652056
$366$		0			0
$367$	−10.6458	+	18.4390i	−0.555704	+	0.962507i	0.442145	+	0.896944i	$0.354218\pi$
$367$	−10.6458	+	18.4390i	−0.555704	+	0.962507i	−0.997848	+	0.0655633i	$0.979116\pi$
$368$	1.32288	−	2.29129i	0.0689597	−	0.119442i
$369$		0			0
$370$	−24.5830			−1.27801
$371$	10.5830			0.549442
$372$		0			0
$373$	−15.9059	−	27.5498i	−0.823575	−	1.42647i	−0.903003	−	0.429634i	$-0.858643\pi$
$373$	−15.9059	−	27.5498i	−0.823575	−	1.42647i	0.0794280	−	0.996841i	$-0.474691\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$		0			0
$376$	5.96863	+	10.3380i	0.307808	+	0.533140i
$377$	8.00000			0.412021
$378$		0			0
$379$	−6.41699			−0.329619			−0.164809	−	0.986325i	$-0.552701\pi$
$379$	−6.41699			−0.329619			−0.164809	+	0.986325i	$0.552701\pi$
$380$	7.00000	+	12.1244i	0.359092	+	0.621966i
$381$		0			0
$382$	8.64575	−	14.9749i	0.442355	−	0.766182i
$383$	14.6458	+	25.3672i	0.748363	+	1.29620i	0.948607	+	0.316457i	$0.102493\pi$
$383$	14.6458	+	25.3672i	0.748363	+	1.29620i	−0.200244	+	0.979746i	$0.564174\pi$
$384$		0			0
$385$	−3.50000	−	6.06218i	−0.178377	−	0.308957i
$386$	15.8745			0.807991
$387$		0			0
$388$	−4.79150	+	8.29913i	−0.243252	+	0.421324i
$389$	8.03137	−	13.9107i	0.407207	−	0.705303i	−0.587369	−	0.809319i	$-0.699836\pi$
$389$	8.03137	−	13.9107i	0.407207	−	0.705303i	0.994576	+	0.104017i	$0.0331695\pi$
$390$		0			0
$391$	−7.93725			−0.401404
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$		0			0
$394$	−4.93725	−	8.55157i	−0.248735	−	0.430822i
$395$	−7.08301	+	12.2681i	−0.356385	+	0.617276i
$396$		0			0
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	0.780870	−	0.624694i	$-0.214776\pi$
$397$	−3.00000	−	5.19615i	−0.150566	−	0.260787i	−0.931436	+	0.363906i	$0.881443\pi$
$398$	23.1660			1.16121
$399$		0			0
$400$	2.00000			0.100000
$401$	−2.06275	−	3.57278i	−0.103009	−	0.178416i	0.809914	−	0.586548i	$-0.199514\pi$
$401$	−2.06275	−	3.57278i	−0.103009	−	0.178416i	−0.912923	+	0.408132i	$0.866180\pi$
$402$		0			0
$403$	−8.00000	+	13.8564i	−0.398508	+	0.690237i
$404$	−1.64575	−	2.85052i	−0.0818792	−	0.141819i
$405$		0			0
$406$	−2.64575	+	4.58258i	−0.131306	+	0.227429i
$407$	9.29150			0.460563
$408$		0			0
$409$	−2.06275	+	3.57278i	−0.101996	+	0.176663i	−0.912507	−	0.409061i	$-0.865856\pi$
$409$	−2.06275	+	3.57278i	−0.101996	+	0.176663i	0.810511	+	0.585724i	$0.199190\pi$
$410$	11.9059	−	20.6216i	0.587990	−	1.01843i
$411$		0			0
$412$	−10.0000			−0.492665
$413$	−38.5830			−1.89855
$414$		0			0
$415$	−7.38562	−	12.7923i	−0.362546	−	0.627948i
$416$	2.00000	−	3.46410i	0.0980581	−	0.169842i
$417$		0			0
$418$	−2.64575	−	4.58258i	−0.129408	−	0.224141i
$419$	−21.8745			−1.06864			−0.534320	−	0.845282i	$-0.679432\pi$
$419$	−21.8745			−1.06864			−0.534320	+	0.845282i	$0.679432\pi$
$420$		0			0
$421$	37.8745			1.84589			0.922945	−	0.384931i	$-0.125775\pi$
$421$	37.8745			1.84589			0.922945	+	0.384931i	$0.125775\pi$
$422$	−5.35425	−	9.27383i	−0.260641	−	0.451443i
$423$		0			0
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$	−3.00000	−	5.19615i	−0.145521	−	0.252050i
$426$		0			0
$427$	−5.20850	+	9.02138i	−0.252057	+	0.436575i
$428$	−9.00000			−0.435031
$429$		0			0
$430$	1.70850	−	2.95920i	0.0823911	−	0.142706i
$431$	−3.35425	+	5.80973i	−0.161568	+	0.279845i	−0.935431	−	0.353508i	$-0.884989\pi$
$431$	−3.35425	+	5.80973i	−0.161568	+	0.279845i	0.773863	+	0.633353i	$0.218322\pi$
$432$		0			0
$433$	−19.5830			−0.941099			−0.470550	−	0.882374i	$-0.655944\pi$
$433$	−19.5830			−0.941099			−0.470550	+	0.882374i	$0.655944\pi$
$434$	−5.29150	−	9.16515i	−0.254000	−	0.439941i
$435$		0			0
$436$	−5.96863	−	10.3380i	−0.285845	−	0.495099i
$437$	−7.00000	+	12.1244i	−0.334855	+	0.579987i
$438$		0			0
$439$	7.32288	+	12.6836i	0.349502	+	0.605355i	0.986161	−	0.165790i	$-0.0530175\pi$
$439$	7.32288	+	12.6836i	0.349502	+	0.605355i	−0.636659	+	0.771145i	$0.719684\pi$
$440$	−2.64575			−0.126131
$441$		0			0
$442$	−12.0000			−0.570782
$443$	5.58301	+	9.67005i	0.265257	+	0.459438i	0.967631	−	0.252370i	$-0.0812100\pi$
$443$	5.58301	+	9.67005i	0.265257	+	0.459438i	−0.702374	+	0.711808i	$0.747877\pi$
$444$		0			0
$445$	17.5830	−	30.4547i	0.833514	−	1.44369i
$446$	12.2288	+	21.1808i	0.579048	+	1.00294i
$447$		0			0
$448$	1.32288	+	2.29129i	0.0625000	+	0.108253i
$449$	22.4575			1.05984			0.529918	−	0.848049i	$-0.322223\pi$
$449$	22.4575			1.05984			0.529918	+	0.848049i	$0.322223\pi$
$450$		0			0
$451$	−4.50000	+	7.79423i	−0.211897	+	0.367016i
$452$	−4.29150	+	7.43310i	−0.201855	+	0.349624i
$453$		0			0
$454$	−23.5830			−1.10681
$455$	−14.0000	+	24.2487i	−0.656330	+	1.13680i
$456$		0			0
$457$	9.70850	+	16.8156i	0.454144	+	0.786601i	0.998639	−	0.0521635i	$-0.0166117\pi$
$457$	9.70850	+	16.8156i	0.454144	+	0.786601i	−0.544494	+	0.838765i	$0.683278\pi$
$458$	−8.64575	+	14.9749i	−0.403989	+	0.699730i
$459$		0			0
$460$	3.50000	+	6.06218i	0.163188	+	0.282650i
$461$	3.41699			0.159145			0.0795727	−	0.996829i	$-0.474644\pi$
$461$	3.41699			0.159145			0.0795727	+	0.996829i	$0.474644\pi$
$462$		0			0
$463$	−35.0405			−1.62847			−0.814235	−	0.580535i	$-0.802844\pi$
$463$	−35.0405			−1.62847			−0.814235	+	0.580535i	$0.802844\pi$
$464$	1.00000	+	1.73205i	0.0464238	+	0.0804084i
$465$		0			0
$466$	−11.0830	+	19.1963i	−0.513410	+	0.889253i
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	0.943610	−	0.331061i	$-0.107406\pi$
$467$	4.00000	+	6.92820i	0.185098	+	0.320599i	−0.758512	+	0.651660i	$0.774073\pi$
$468$		0			0
$469$	35.9373			1.65943
$470$	−31.5830			−1.45682
$471$		0			0
$472$	−7.29150	+	12.6293i	−0.335619	+	0.581308i
$473$	−0.645751	+	1.11847i	−0.0296917	+	0.0514275i
$474$		0			0
$475$	−10.5830			−0.485582
$476$	3.96863	−	6.87386i	0.181902	−	0.315063i
$477$		0			0
$478$	6.64575	+	11.5108i	0.303970	+	0.526491i
$479$	−1.06275	+	1.84073i	−0.0485581	+	0.0841051i	−0.889283	−	0.457358i	$-0.848796\pi$
$479$	−1.06275	+	1.84073i	−0.0485581	+	0.0841051i	0.840725	+	0.541463i	$0.182129\pi$
$480$		0			0
$481$	−18.5830	−	32.1867i	−0.847312	−	1.46759i
$482$	15.1660			0.690793
$483$		0			0
$484$	1.00000			0.0454545
$485$	−12.6771	−	21.9574i	−0.575639	−	0.997035i
$486$		0			0
$487$	4.93725	−	8.55157i	0.223728	−	0.387509i	−0.732209	−	0.681080i	$-0.761510\pi$
$487$	4.93725	−	8.55157i	0.223728	−	0.387509i	0.955937	+	0.293571i	$0.0948438\pi$
$488$	1.96863	+	3.40976i	0.0891156	+	0.154353i
$489$		0			0
$490$	−9.26013	−	16.0390i	−0.418330	−	0.724569i
$491$	1.00000			0.0451294			0.0225647	−	0.999745i	$-0.492817\pi$
$491$	1.00000			0.0451294			0.0225647	+	0.999745i	$0.492817\pi$
$492$		0			0
$493$	3.00000	−	5.19615i	0.135113	−	0.234023i
$494$	−10.5830	+	18.3303i	−0.476152	+	0.824719i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	17.5830	+	30.4547i	0.788706	+	1.36608i
$498$		0			0
$499$	−1.29150	−	2.23695i	−0.0578156	−	0.100140i	0.835669	−	0.549233i	$-0.185080\pi$
$499$	−1.29150	−	2.23695i	−0.0578156	−	0.100140i	−0.893485	+	0.449094i	$0.851747\pi$
$500$	3.96863	−	6.87386i	0.177482	−	0.307409i
$501$		0			0
$502$	6.35425	+	11.0059i	0.283604	+	0.491217i
$503$	−9.29150			−0.414288			−0.207144	−	0.978311i	$-0.566417\pi$
$503$	−9.29150			−0.414288			−0.207144	+	0.978311i	$0.566417\pi$
$504$		0			0
$505$	8.70850			0.387523
$506$	−1.32288	−	2.29129i	−0.0588090	−	0.101860i
$507$		0			0
$508$	1.32288	−	2.29129i	0.0586931	−	0.101659i
$509$	−8.58301	−	14.8662i	−0.380435	−	0.658933i	0.610689	−	0.791870i	$-0.290892\pi$
$509$	−8.58301	−	14.8662i	−0.380435	−	0.658933i	−0.991124	+	0.132937i	$0.957559\pi$
$510$		0			0
$511$	12.4575			0.551088
$512$	1.00000			0.0441942
$513$		0			0
$514$	−0.645751	+	1.11847i	−0.0284829	+	0.0493338i
$515$	13.2288	−	22.9129i	0.582929	−	1.00966i
$516$		0			0
$517$	11.9373			0.525000
$518$	24.5830			1.08012
$519$		0			0
$520$	5.29150	+	9.16515i	0.232048	+	0.401918i
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.120656	−	0.992694i	$-0.461500\pi$
$521$	21.0000	−	36.3731i	0.920027	−	1.59353i	0.799370	−	0.600839i	$-0.205167\pi$
$522$		0			0
$523$	−6.64575	−	11.5108i	−0.290598	−	0.503331i	0.683353	−	0.730088i	$-0.260521\pi$
$523$	−6.64575	−	11.5108i	−0.290598	−	0.503331i	−0.973951	+	0.226757i	$0.927188\pi$
$524$	−2.58301			−0.112839
$525$		0			0
$526$	9.87451			0.430549
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$		0			0
$529$	8.00000	−	13.8564i	0.347826	−	0.602452i
$530$	5.29150	+	9.16515i	0.229848	+	0.398109i
$531$		0			0
$532$	−7.00000	−	12.1244i	−0.303488	−	0.525657i
$533$	36.0000			1.55933
$534$		0			0
$535$	11.9059	−	20.6216i	0.514736	−	0.891549i
$536$	6.79150	−	11.7632i	0.293348	−	0.508094i
$537$		0			0
$538$	5.35425			0.230838
$539$	3.50000	+	6.06218i	0.150756	+	0.261116i
$540$		0			0
$541$	21.9059	+	37.9421i	0.941807	+	1.63126i	0.762021	+	0.647553i	$0.224207\pi$
$541$	21.9059	+	37.9421i	0.941807	+	1.63126i	0.179787	+	0.983706i	$0.442459\pi$
$542$	0.645751	−	1.11847i	0.0277374	−	0.0480426i
$543$		0			0
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$	31.5830			1.35287
$546$		0			0
$547$	25.2915			1.08139			0.540693	−	0.841220i	$-0.318162\pi$
$547$	25.2915			1.08139			0.540693	+	0.841220i	$0.318162\pi$
$548$	−1.35425	−	2.34563i	−0.0578506	−	0.100200i
$549$		0			0
$550$	1.00000	−	1.73205i	0.0426401	−	0.0738549i
$551$	−5.29150	−	9.16515i	−0.225426	−	0.390449i
$552$		0			0
$553$	7.08301	−	12.2681i	0.301200	−	0.521694i
$554$	25.1660			1.06920
$555$		0			0
$556$	−4.29150	+	7.43310i	−0.182000	+	0.315234i
$557$	−4.35425	+	7.54178i	−0.184495	+	0.319555i	−0.943406	−	0.331639i	$-0.892398\pi$
$557$	−4.35425	+	7.54178i	−0.184495	+	0.319555i	0.758911	+	0.651194i	$0.225732\pi$
$558$		0			0
$559$	5.16601			0.218499
$560$	−7.00000			−0.295804
$561$		0			0
$562$	−1.50000	−	2.59808i	−0.0632737	−	0.109593i
$563$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$563$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$564$		0			0
$565$	−11.3542	−	19.6661i	−0.477677	−	0.827361i
$566$	−22.4575			−0.943960
$567$		0			0
$568$	13.2915			0.557699
$569$	13.5830	+	23.5265i	0.569429	+	0.986280i	0.996622	+	0.0821200i	$0.0261691\pi$
$569$	13.5830	+	23.5265i	0.569429	+	0.986280i	−0.427193	+	0.904160i	$0.640498\pi$
$570$		0			0
$571$	−16.8745	+	29.2275i	−0.706176	+	1.22313i	0.260089	+	0.965585i	$0.416248\pi$
$571$	−16.8745	+	29.2275i	−0.706176	+	1.22313i	−0.966265	+	0.257548i	$0.917085\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$		0			0
$574$	−11.9059	+	20.6216i	−0.496942	+	0.860729i
$575$	−5.29150			−0.220671
$576$		0			0
$577$	20.3745	−	35.2897i	0.848202	−	1.46913i	−0.0346094	−	0.999401i	$-0.511019\pi$
$577$	20.3745	−	35.2897i	0.848202	−	1.46913i	0.882811	−	0.469728i	$-0.155648\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$		0			0
$580$	−5.29150			−0.219718
$581$	7.38562	+	12.7923i	0.306407	+	0.530713i
$582$		0			0
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	2.35425	−	4.07768i	0.0974195	−	0.168736i
$585$		0			0
$586$	3.29150	+	5.70105i	0.135971	+	0.235508i
$587$	21.8745			0.902858			0.451429	−	0.892307i	$-0.350914\pi$
$587$	21.8745			0.902858			0.451429	+	0.892307i	$0.350914\pi$
$588$		0			0
$589$	21.1660			0.872130
$590$	−19.2915	−	33.4139i	−0.794219	−	1.37563i
$591$		0			0
$592$	4.64575	−	8.04668i	0.190939	−	0.330716i
$593$	18.8745	+	32.6916i	0.775083	+	1.34248i	0.934748	+	0.355312i	$0.115625\pi$
$593$	18.8745	+	32.6916i	0.775083	+	1.34248i	−0.159665	+	0.987171i	$0.551041\pi$
$594$		0			0
$595$	10.5000	+	18.1865i	0.430458	+	0.745575i
$596$	11.8745			0.486399
$597$		0			0
$598$	−5.29150	+	9.16515i	−0.216386	+	0.374791i
$599$	17.3229	−	30.0041i	0.707794	−	1.22593i	−0.257880	−	0.966177i	$-0.583024\pi$
$599$	17.3229	−	30.0041i	0.707794	−	1.22593i	0.965674	−	0.259757i	$-0.0836426\pi$
$600$		0			0
$601$	−17.4170			−0.710454			−0.355227	−	0.934780i	$-0.615596\pi$
$601$	−17.4170			−0.710454			−0.355227	+	0.934780i	$0.615596\pi$
$602$	−1.70850	+	2.95920i	−0.0696332	+	0.120608i
$603$		0			0
$604$	−8.67712	−	15.0292i	−0.353067	−	0.611530i
$605$	−1.32288	+	2.29129i	−0.0537825	+	0.0931541i
$606$		0			0
$607$	−22.5516	−	39.0606i	−0.915343	−	1.58542i	−0.806399	−	0.591372i	$-0.798587\pi$
$607$	−22.5516	−	39.0606i	−0.915343	−	1.58542i	−0.108943	−	0.994048i	$-0.534747\pi$
$608$	−5.29150			−0.214599
$609$		0			0
$610$	−10.4170			−0.421772
$611$	−23.8745	−	41.3519i	−0.965859	−	1.67292i
$612$		0			0
$613$	19.9059	−	34.4780i	0.803991	−	1.39255i	−0.112979	−	0.993597i	$-0.536039\pi$
$613$	19.9059	−	34.4780i	0.803991	−	1.39255i	0.916970	−	0.398956i	$-0.130627\pi$
$614$	16.2915	+	28.2177i	0.657472	+	1.13877i
$615$		0			0
$616$	2.64575			0.106600
$617$	25.2915			1.01820			0.509099	−	0.860708i	$-0.329979\pi$
$617$	25.2915			1.01820			0.509099	+	0.860708i	$0.329979\pi$
$618$		0			0
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	−0.0787435	−	0.996895i	$-0.525091\pi$
$619$	20.5000	−	35.5070i	0.823965	−	1.42715i	0.902708	−	0.430254i	$-0.141576\pi$
$620$	5.29150	−	9.16515i	0.212512	−	0.368081i
$621$		0			0
$622$	14.5203			0.582209
$623$	−17.5830	+	30.4547i	−0.704448	+	1.22014i
$624$		0			0
$625$	15.5000	+	26.8468i	0.620000	+	1.07387i
$626$	−0.291503	+	0.504897i	−0.0116508	+	0.0201798i
$627$		0			0
$628$	5.64575	+	9.77873i	0.225290	+	0.390214i
$629$	−27.8745			−1.11143
$630$		0			0
$631$	10.1255			0.403089			0.201545	−	0.979479i	$-0.435404\pi$
$631$	10.1255			0.403089			0.201545	+	0.979479i	$0.435404\pi$
$632$	−2.67712	−	4.63692i	−0.106490	−	0.184447i
$633$		0			0
$634$	−8.61438	+	14.9205i	−0.342121	+	0.592570i
$635$	3.50000	+	6.06218i	0.138893	+	0.240570i
$636$		0			0
$637$	14.0000	−	24.2487i	0.554700	−	0.960769i
$638$	2.00000			0.0791808
$639$		0			0
$640$	−1.32288	+	2.29129i	−0.0522913	+	0.0905711i
$641$	−2.70850	+	4.69126i	−0.106979	+	0.185293i	−0.914545	−	0.404484i	$-0.867451\pi$
$641$	−2.70850	+	4.69126i	−0.106979	+	0.185293i	0.807566	+	0.589777i	$0.200784\pi$
$642$		0			0
$643$	41.1660			1.62343			0.811714	−	0.584054i	$-0.198535\pi$
$643$	41.1660			1.62343			0.811714	+	0.584054i	$0.198535\pi$
$644$	−3.50000	−	6.06218i	−0.137919	−	0.238883i
$645$		0			0
$646$	7.93725	+	13.7477i	0.312287	+	0.540897i
$647$	21.1974	−	36.7149i	0.833355	−	1.44341i	−0.0620075	−	0.998076i	$-0.519750\pi$
$647$	21.1974	−	36.7149i	0.833355	−	1.44341i	0.895363	−	0.445338i	$-0.146916\pi$
$648$		0			0
$649$	7.29150	+	12.6293i	0.286217	+	0.495742i
$650$	−8.00000			−0.313786
$651$		0			0
$652$	15.5830			0.610278
$653$	6.55163	+	11.3478i	0.256385	+	0.444072i	0.965271	−	0.261251i	$-0.0841351\pi$
$653$	6.55163	+	11.3478i	0.256385	+	0.444072i	−0.708886	+	0.705323i	$0.750802\pi$
$654$		0			0
$655$	3.41699	−	5.91841i	0.133513	−	0.231251i
$656$	4.50000	+	7.79423i	0.175695	+	0.304314i
$657$		0			0
$658$	31.5830			1.23123
$659$	−18.1660			−0.707647			−0.353824	−	0.935312i	$-0.615119\pi$
$659$	−18.1660			−0.707647			−0.353824	+	0.935312i	$0.615119\pi$
$660$		0			0
$661$	−15.6458	+	27.0992i	−0.608549	+	1.05404i	0.382931	+	0.923777i	$0.374915\pi$
$661$	−15.6458	+	27.0992i	−0.608549	+	1.05404i	−0.991480	+	0.130261i	$0.958418\pi$
$662$	−6.50000	+	11.2583i	−0.252630	+	0.437567i
$663$		0			0
$664$	5.58301			0.216663
$665$	37.0405			1.43637
$666$		0			0
$667$	−2.64575	−	4.58258i	−0.102444	−	0.177438i
$668$	9.64575	−	16.7069i	0.373205	−	0.646411i
$669$		0			0
$670$	17.9686	+	31.1226i	0.694189	+	1.20237i
$671$	3.93725			0.151996
$672$		0			0
$673$	−40.5830			−1.56436			−0.782180	−	0.623053i	$-0.785892\pi$
$673$	−40.5830			−1.56436			−0.782180	+	0.623053i	$0.785892\pi$
$674$	−8.64575	−	14.9749i	−0.333022	−	0.576811i
$675$		0			0
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	−19.9373	−	34.5323i	−0.766251	−	1.32719i	−0.939583	−	0.342322i	$-0.888787\pi$
$677$	−19.9373	−	34.5323i	−0.766251	−	1.32719i	0.173332	−	0.984863i	$-0.444547\pi$
$678$		0			0
$679$	12.6771	+	21.9574i	0.486503	+	0.842649i
$680$	7.93725			0.304380
$681$		0			0
$682$	−2.00000	+	3.46410i	−0.0765840	+	0.132647i
$683$	12.5830	−	21.7944i	0.481475	−	0.833940i	−0.518299	−	0.855200i	$-0.673434\pi$
$683$	12.5830	−	21.7944i	0.481475	−	0.833940i	0.999774	+	0.0212600i	$0.00676777\pi$
$684$		0			0
$685$	7.16601			0.273799
$686$	9.26013	+	16.0390i	0.353553	+	0.612372i
$687$		0			0
$688$	0.645751	+	1.11847i	0.0246190	+	0.0426414i
$689$	−8.00000	+	13.8564i	−0.304776	+	0.527887i
$690$		0			0
$691$	14.0830	+	24.3925i	0.535743	+	0.927934i	0.999127	+	0.0417762i	$0.0133017\pi$
$691$	14.0830	+	24.3925i	0.535743	+	0.927934i	−0.463384	+	0.886157i	$0.653365\pi$
$692$	−4.00000			−0.152057
$693$		0			0
$694$	−8.41699			−0.319505
$695$	−11.3542	−	19.6661i	−0.430691	−	0.745979i
$696$		0			0
$697$	13.5000	−	23.3827i	0.511349	−	0.885682i
$698$	−6.61438	−	11.4564i	−0.250358	−	0.433633i
$699$		0			0
$700$	2.64575	−	4.58258i	0.100000	−	0.173205i
$701$	10.4575			0.394975			0.197487	−	0.980305i	$-0.436722\pi$
$701$	10.4575			0.394975			0.197487	+	0.980305i	$0.436722\pi$
$702$		0			0
$703$	−24.5830	+	42.5790i	−0.927166	+	1.60590i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$		0			0
$706$	12.7085			0.478291
$707$	−8.70850			−0.327517
$708$		0			0
$709$	23.8745	+	41.3519i	0.896626	+	1.55300i	0.831779	+	0.555106i	$0.187322\pi$
$709$	23.8745	+	41.3519i	0.896626	+	1.55300i	0.0648467	+	0.997895i	$0.479344\pi$
$710$	−17.5830	+	30.4547i	−0.659878	+	1.14294i
$711$		0			0
$712$	6.64575	+	11.5108i	0.249060	+	0.431385i
$713$	10.5830			0.396337
$714$		0			0
$715$	10.5830			0.395782
$716$	7.64575	+	13.2428i	0.285735	+	0.494908i
$717$		0			0
$718$	−0.291503	+	0.504897i	−0.0108788	+	0.0188426i
$719$	−21.9686	−	38.0508i	−0.819292	−	1.41905i	−0.906205	−	0.422839i	$-0.861034\pi$
$719$	−21.9686	−	38.0508i	−0.819292	−	1.41905i	0.0869134	−	0.996216i	$-0.472300\pi$
$720$		0			0
$721$	−13.2288	+	22.9129i	−0.492665	+	0.853320i
$722$	9.00000			0.334945
$723$		0			0
$724$	−2.64575	+	4.58258i	−0.0983286	+	0.170310i
$725$	2.00000	−	3.46410i	0.0742781	−	0.128654i
$726$		0			0
$727$	−2.00000			−0.0741759			−0.0370879	−	0.999312i	$-0.511808\pi$
$727$	−2.00000			−0.0741759			−0.0370879	+	0.999312i	$0.511808\pi$
$728$	−5.29150	−	9.16515i	−0.196116	−	0.339683i
$729$		0			0
$730$	6.22876	+	10.7885i	0.230537	+	0.399301i
$731$	1.93725	−	3.35542i	0.0716519	−	0.124105i
$732$		0			0
$733$	1.96863	+	3.40976i	0.0727129	+	0.125942i	0.900089	−	0.435705i	$-0.143501\pi$
$733$	1.96863	+	3.40976i	0.0727129	+	0.125942i	−0.827377	+	0.561648i	$0.810168\pi$
$734$	21.2915			0.785884
$735$		0			0
$736$	−2.64575			−0.0975237
$737$	−6.79150	−	11.7632i	−0.250168	−	0.433304i
$738$		0			0
$739$	1.70850	−	2.95920i	0.0628481	−	0.108856i	−0.832889	−	0.553440i	$-0.813315\pi$
$739$	1.70850	−	2.95920i	0.0628481	−	0.108856i	0.895737	+	0.444584i	$0.146648\pi$
$740$	12.2915	+	21.2895i	0.451845	+	0.782618i
$741$		0			0
$742$	−5.29150	−	9.16515i	−0.194257	−	0.336463i
$743$	29.2915			1.07460			0.537301	−	0.843391i	$-0.319444\pi$
$743$	29.2915			1.07460			0.537301	+	0.843391i	$0.319444\pi$
$744$		0			0
$745$	−15.7085	+	27.2079i	−0.575515	+	0.996821i
$746$	−15.9059	+	27.5498i	−0.582356	+	1.00867i
$747$		0			0
$748$	−3.00000			−0.109691
$749$	−11.9059	+	20.6216i	−0.435031	+	0.753497i
$750$		0			0
$751$	9.35425	+	16.2020i	0.341341	+	0.591221i	0.984682	−	0.174359i	$-0.0557854\pi$
$751$	9.35425	+	16.2020i	0.341341	+	0.591221i	−0.643341	+	0.765580i	$0.722452\pi$
$752$	5.96863	−	10.3380i	0.217653	−	0.376987i
$753$		0			0
$754$	−4.00000	−	6.92820i	−0.145671	−	0.252310i
$755$	45.9150			1.67102
$756$		0			0
$757$	−11.4170			−0.414958			−0.207479	−	0.978240i	$-0.566526\pi$
$757$	−11.4170			−0.414958			−0.207479	+	0.978240i	$0.566526\pi$
$758$	3.20850	+	5.55728i	0.116538	+	0.201850i
$759$		0			0
$760$	7.00000	−	12.1244i	0.253917	−	0.439797i
$761$	13.2085	+	22.8778i	0.478808	+	0.829319i	0.999705	−	0.0243003i	$-0.00773579\pi$
$761$	13.2085	+	22.8778i	0.478808	+	0.829319i	−0.520897	+	0.853620i	$0.674402\pi$
$762$		0			0
$763$	−31.5830			−1.14338
$764$	−17.2915			−0.625585
$765$		0			0
$766$	14.6458	−	25.3672i	0.529173	−	0.916554i
$767$	29.1660	−	50.5170i	1.05312	−	1.82406i
$768$		0			0
$769$	−41.2915			−1.48901			−0.744505	−	0.667617i	$-0.767314\pi$
$769$	−41.2915			−1.48901			−0.744505	+	0.667617i	$0.767314\pi$
$770$	−3.50000	+	6.06218i	−0.126131	+	0.218466i
$771$		0			0
$772$	−7.93725	−	13.7477i	−0.285668	−	0.494792i
$773$	−11.9686	+	20.7303i	−0.430482	+	0.745616i	−0.996915	−	0.0784917i	$-0.974990\pi$
$773$	−11.9686	+	20.7303i	−0.430482	+	0.745616i	0.566433	+	0.824108i	$0.308323\pi$
$774$		0			0
$775$	4.00000	+	6.92820i	0.143684	+	0.248868i
$776$	9.58301			0.344010
$777$		0			0
$778$	−16.0627			−0.575877
$779$	−23.8118	−	41.2432i	−0.853145	−	1.47769i
$780$		0			0
$781$	6.64575	−	11.5108i	0.237804	−	0.411888i
$782$	3.96863	+	6.87386i	0.141918	+	0.245809i
$783$		0			0
$784$	7.00000			0.250000
$785$	−29.8745			−1.06627
$786$		0			0
$787$	0.645751	−	1.11847i	0.0230185	−	0.0398693i	−0.854287	−	0.519802i	$-0.826006\pi$
$787$	0.645751	−	1.11847i	0.0230185	−	0.0398693i	0.877305	+	0.479933i	$0.159339\pi$
$788$	−4.93725	+	8.55157i	−0.175882	+	0.304637i
$789$		0			0
$790$	14.1660			0.504004
$791$	11.3542	+	19.6661i	0.403711	+	0.699247i
$792$		0			0
$793$	−7.87451	−	13.6390i	−0.279632	−	0.484337i
$794$	−3.00000	+	5.19615i	−0.106466	+	0.184405i
$795$		0			0
$796$	−11.5830	−	20.0624i	−0.410549	−	0.711091i
$797$	13.1033			0.464141			0.232071	−	0.972699i	$-0.425450\pi$
$797$	13.1033			0.464141			0.232071	+	0.972699i	$0.425450\pi$
$798$		0			0
$799$	−35.8118			−1.26693
$800$	−1.00000	−	1.73205i	−0.0353553	−	0.0612372i
$801$		0			0
$802$	−2.06275	+	3.57278i	−0.0728381	+	0.126159i
$803$	−2.35425	−	4.07768i	−0.0830796	−	0.143898i
$804$		0			0
$805$	18.5203			0.652753
$806$	16.0000			0.563576
$807$		0			0
$808$	−1.64575	+	2.85052i	−0.0578973	+	0.100281i
$809$	−19.6660	+	34.0625i	−0.691420	+	1.19757i	0.279953	+	0.960014i	$0.409681\pi$
$809$	−19.6660	+	34.0625i	−0.691420	+	1.19757i	−0.971373	+	0.237561i	$0.923652\pi$
$810$		0			0
$811$	−4.58301			−0.160931			−0.0804655	−	0.996757i	$-0.525641\pi$
$811$	−4.58301			−0.160931			−0.0804655	+	0.996757i	$0.525641\pi$
$812$	5.29150			0.185695
$813$		0			0
$814$	−4.64575	−	8.04668i	−0.162833	−	0.282036i
$815$	−20.6144	+	35.7052i	−0.722090	+	1.25070i
$816$		0			0
$817$	−3.41699	−	5.91841i	−0.119546	−	0.207059i
$818$	4.12549			0.144244
$819$		0			0
$820$	−23.8118			−0.831543
$821$	27.1660	+	47.0529i	0.948100	+	1.64216i	0.749421	+	0.662093i	$0.230332\pi$
$821$	27.1660	+	47.0529i	0.948100	+	1.64216i	0.198679	+	0.980065i	$0.436335\pi$
$822$		0			0
$823$	21.9373	−	37.9964i	0.764685	−	1.32447i	−0.175729	−	0.984439i	$-0.556228\pi$
$823$	21.9373	−	37.9964i	0.764685	−	1.32447i	0.940413	−	0.340034i	$-0.110439\pi$
$824$	5.00000	+	8.66025i	0.174183	+	0.301694i
$825$		0			0
$826$	19.2915	+	33.4139i	0.671237	+	1.16262i
$827$	49.3320			1.71544			0.857721	−	0.514115i	$-0.171880\pi$
$827$	49.3320			1.71544			0.857721	+	0.514115i	$0.171880\pi$
$828$		0			0
$829$	5.93725	−	10.2836i	0.206209	−	0.357165i	−0.744308	−	0.667836i	$-0.767221\pi$
$829$	5.93725	−	10.2836i	0.206209	−	0.357165i	0.950517	+	0.310671i	$0.100554\pi$
$830$	−7.38562	+	12.7923i	−0.256359	+	0.444026i
$831$		0			0
$832$	−4.00000			−0.138675
$833$	−10.5000	−	18.1865i	−0.363803	−	0.630126i
$834$		0			0
$835$	25.5203	+	44.2024i	0.883165	+	1.52969i
$836$	−2.64575	+	4.58258i	−0.0915052	+	0.158492i
$837$		0			0
$838$	10.9373	+	18.9439i	0.377821	+	0.654405i
$839$	−21.1033			−0.728566			−0.364283	−	0.931288i	$-0.618686\pi$
$839$	−21.1033			−0.728566			−0.364283	+	0.931288i	$0.618686\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	−18.9373	−	32.8003i	−0.652621	−	1.13037i
$843$		0			0
$844$	−5.35425	+	9.27383i	−0.184301	+	0.319218i
$845$	−3.96863	−	6.87386i	−0.136525	−	0.236468i
$846$		0			0
$847$	1.32288	−	2.29129i	0.0454545	−	0.0787296i
$848$	−4.00000			−0.137361
$849$		0			0
$850$	−3.00000	+	5.19615i	−0.102899	+	0.178227i
$851$	−12.2915	+	21.2895i	−0.421347	+	0.729795i
$852$		0			0
$853$	−22.5203			−0.771079			−0.385539	−	0.922691i	$-0.625985\pi$
$853$	−22.5203			−0.771079			−0.385539	+	0.922691i	$0.625985\pi$
$854$	10.4170			0.356462
$855$		0			0
$856$	4.50000	+	7.79423i	0.153807	+	0.266401i
$857$	26.0830	−	45.1771i	0.890978	−	1.54322i	0.0522743	−	0.998633i	$-0.483353\pi$
$857$	26.0830	−	45.1771i	0.890978	−	1.54322i	0.838704	−	0.544587i	$-0.183314\pi$
$858$		0			0
$859$	7.37451	+	12.7730i	0.251615	+	0.435810i	0.963971	−	0.266009i	$-0.0857050\pi$
$859$	7.37451	+	12.7730i	0.251615	+	0.435810i	−0.712356	+	0.701819i	$0.752372\pi$
$860$	−3.41699			−0.116519
$861$		0			0
$862$	6.70850			0.228492
$863$	12.5516	+	21.7401i	0.427263	+	0.740040i	0.996629	−	0.0820436i	$-0.0261447\pi$
$863$	12.5516	+	21.7401i	0.427263	+	0.740040i	−0.569366	+	0.822084i	$0.692811\pi$
$864$		0			0
$865$	5.29150	−	9.16515i	0.179916	−	0.311624i
$866$	9.79150	+	16.9594i	0.332729	+	0.576303i
$867$		0			0
$868$	−5.29150	+	9.16515i	−0.179605	+	0.311086i
$869$	−5.35425			−0.181630
$870$		0			0
$871$	−27.1660	+	47.0529i	−0.920485	+	1.59433i
$872$	−5.96863	+	10.3380i	−0.202123	+	0.350088i
$873$		0			0
$874$	14.0000			0.473557
$875$	−10.5000	−	18.1865i	−0.354965	−	0.614817i
$876$		0			0
$877$	−18.6144	−	32.2410i	−0.628563	−	1.08870i	−0.987840	−	0.155472i	$-0.950310\pi$
$877$	−18.6144	−	32.2410i	−0.628563	−	1.08870i	0.359277	−	0.933231i	$-0.383023\pi$
$878$	7.32288	−	12.6836i	0.247135	−	0.428051i
$879$		0			0
$880$	1.32288	+	2.29129i	0.0445941	+	0.0772393i
$881$	19.1660			0.645719			0.322860	−	0.946447i	$-0.395356\pi$
$881$	19.1660			0.645719			0.322860	+	0.946447i	$0.395356\pi$
$882$		0			0
$883$	−55.5830			−1.87052			−0.935259	−	0.353965i	$-0.884833\pi$
$883$	−55.5830			−1.87052			−0.935259	+	0.353965i	$0.884833\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	5.58301	−	9.67005i	0.187565	−	0.324872i
$887$	21.5203	+	37.2742i	0.722580	+	1.25154i	0.959963	+	0.280128i	$0.0903770\pi$
$887$	21.5203	+	37.2742i	0.722580	+	1.25154i	−0.237383	+	0.971416i	$0.576290\pi$
$888$		0			0
$889$	−3.50000	−	6.06218i	−0.117386	−	0.203319i
$890$	−35.1660			−1.17877
$891$		0			0
$892$	12.2288	−	21.1808i	0.409449	−	0.709187i
$893$	−31.5830	+	54.7034i	−1.05688	+	1.83058i
$894$		0			0
$895$	−40.4575			−1.35235
$896$	1.32288	−	2.29129i	0.0441942	−	0.0765466i
$897$		0			0
$898$	−11.2288	−	19.4488i	−0.374708	−	0.649014i
$899$	−4.00000	+	6.92820i	−0.133407	+	0.231069i
$900$		0			0
$901$	6.00000	+	10.3923i	0.199889	+	0.346218i
$902$	9.00000			0.299667
$903$		0			0
$904$	8.58301			0.285467
$905$	−7.00000	−	12.1244i	−0.232688	−	0.403027i
$906$		0			0
$907$	29.0830	−	50.3732i	0.965685	−	1.67262i	0.257923	−	0.966165i	$-0.416962\pi$
$907$	29.0830	−	50.3732i	0.965685	−	1.67262i	0.707762	−	0.706451i	$-0.249705\pi$
$908$	11.7915	+	20.4235i	0.391315	+	0.677777i
$909$		0			0
$910$	28.0000			0.928191
$911$	−50.3948			−1.66965			−0.834827	−	0.550513i	$-0.814432\pi$
$911$	−50.3948			−1.66965			−0.834827	+	0.550513i	$0.814432\pi$
$912$		0			0
$913$	2.79150	−	4.83502i	0.0923853	−	0.160016i
$914$	9.70850	−	16.8156i	0.321129	−	0.556211i
$915$		0			0
$916$	17.2915			0.571327
$917$	−3.41699	+	5.91841i	−0.112839	+	0.195443i
$918$		0			0
$919$	−7.32288	−	12.6836i	−0.241559	−	0.418393i	0.719599	−	0.694390i	$-0.244326\pi$
$919$	−7.32288	−	12.6836i	−0.241559	−	0.418393i	−0.961159	+	0.275996i	$0.910992\pi$
$920$	3.50000	−	6.06218i	0.115392	−	0.199864i
$921$		0			0
$922$	−1.70850	−	2.95920i	−0.0562664	−	0.0974562i
$923$	−53.1660			−1.74998
$924$		0			0
$925$	−18.5830			−0.611005
$926$	17.5203	+	30.3460i	0.575751	+	0.997231i
$927$		0			0
$928$	1.00000	−	1.73205i	0.0328266	−	0.0568574i
$929$	9.22876	+	15.9847i	0.302786	+	0.524440i	0.976766	−	0.214309i	$-0.0687500\pi$
$929$	9.22876	+	15.9847i	0.302786	+	0.524440i	−0.673980	+	0.738749i	$0.735417\pi$
$930$		0			0
$931$	−37.0405			−1.21395
$932$	22.1660			0.726072
$933$		0			0
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$	3.96863	−	6.87386i	0.129788	−	0.224799i
$936$		0			0
$937$	50.0000			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$937$	50.0000			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$938$	−17.9686	−	31.1226i	−0.586696	−	1.01619i
$939$		0			0
$940$	15.7915	+	27.3517i	0.515062	+	0.892114i
$941$	12.2915	−	21.2895i	0.400692	−	0.694018i	−0.593118	−	0.805116i	$-0.702103\pi$
$941$	12.2915	−	21.2895i	0.400692	−	0.694018i	0.993810	+	0.111097i	$0.0354366\pi$
$942$		0			0
$943$	−11.9059	−	20.6216i	−0.387709	−	0.671531i
$944$	14.5830			0.474636
$945$		0			0
$946$	1.29150			0.0419904
$947$	−18.2915	−	31.6818i	−0.594394	−	1.02952i	−0.993632	−	0.112673i	$-0.964059\pi$
$947$	−18.2915	−	31.6818i	−0.594394	−	1.02952i	0.399238	−	0.916847i	$-0.369275\pi$
$948$		0			0
$949$	−9.41699	+	16.3107i	−0.305689	+	0.529468i
$950$	5.29150	+	9.16515i	0.171679	+	0.297357i
$951$		0			0
$952$	−7.93725			−0.257248
$953$	36.7490			1.19042			0.595209	−	0.803571i	$-0.297069\pi$
$953$	36.7490			1.19042			0.595209	+	0.803571i	$0.297069\pi$
$954$		0			0
$955$	22.8745	−	39.6198i	0.740202	−	1.28207i
$956$	6.64575	−	11.5108i	0.214939	−	0.372285i
$957$		0			0
$958$	2.12549			0.0686715
$959$	−7.16601			−0.231403
$960$		0			0
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$	−18.5830	+	32.1867i	−0.599140	+	1.03774i
$963$		0			0
$964$	−7.58301	−	13.1342i	−0.244232	−	0.423022i
$965$	42.0000			1.35203
$966$		0			0
$967$	55.9373			1.79882			0.899410	−	0.437105i	$-0.143996\pi$
$967$	55.9373			1.79882			0.899410	+	0.437105i	$0.143996\pi$
$968$	−0.500000	−	0.866025i	−0.0160706	−	0.0278351i
$969$		0			0
$970$	−12.6771	+	21.9574i	−0.407038	+	0.705010i
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	0.910140	−	0.414301i	$-0.135974\pi$
$971$	3.00000	+	5.19615i	0.0962746	+	0.166752i	−0.813865	+	0.581054i	$0.802641\pi$
$972$		0			0
$973$	11.3542	+	19.6661i	0.364001	+	0.630467i
$974$	−9.87451			−0.316400
$975$		0			0
$976$	1.96863	−	3.40976i	0.0630142	−	0.109144i
$977$	−14.5830	+	25.2585i	−0.466552	+	0.808091i	−0.999270	−	0.0382014i	$-0.987837\pi$
$977$	−14.5830	+	25.2585i	−0.466552	+	0.808091i	0.532718	+	0.846293i	$0.321170\pi$
$978$		0			0
$979$	13.2915			0.424798
$980$	−9.26013	+	16.0390i	−0.295804	+	0.512348i
$981$		0			0
$982$	−0.500000	−	0.866025i	−0.0159556	−	0.0276360i
$983$	2.73987	−	4.74559i	0.0873883	−	0.151361i	−0.819018	−	0.573768i	$-0.805481\pi$
$983$	2.73987	−	4.74559i	0.0873883	−	0.151361i	0.906406	+	0.422407i	$0.138815\pi$
$984$		0			0
$985$	−13.0627	−	22.6253i	−0.416214	−	0.720903i
$986$	−6.00000			−0.191079
$987$		0			0
$988$	21.1660			0.673380
$989$	−1.70850	−	2.95920i	−0.0543271	−	0.0940972i
$990$		0			0
$991$	6.06275	−	10.5010i	0.192589	−	0.333575i	−0.753518	−	0.657427i	$-0.771645\pi$
$991$	6.06275	−	10.5010i	0.192589	−	0.333575i	0.946108	+	0.323852i	$0.104978\pi$
$992$	2.00000	+	3.46410i	0.0635001	+	0.109985i
$993$		0			0
$994$	17.5830	−	30.4547i	0.557699	−	0.965963i
$995$	61.2915			1.94307
$996$		0			0
$997$	−24.5830	+	42.5790i	−0.778552	+	1.34849i	0.154225	+	0.988036i	$0.450712\pi$
$997$	−24.5830	+	42.5790i	−0.778552	+	1.34849i	−0.932777	+	0.360455i	$0.882621\pi$
$998$	−1.29150	+	2.23695i	−0.0408818	+	0.0708094i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1386.2.k.r.991.1		4
3.2	odd	2		462.2.i.e.67.2	✓	4
7.2	even	3	inner	1386.2.k.r.793.1		4
7.3	odd	6		9702.2.a.dm.1.1		2
7.4	even	3		9702.2.a.db.1.2		2
21.2	odd	6		462.2.i.e.331.2	yes	4
21.11	odd	6		3234.2.a.w.1.1		2
21.17	even	6		3234.2.a.ba.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.i.e.67.2	✓	4	3.2	odd	2
462.2.i.e.331.2	yes	4	21.2	odd	6
1386.2.k.r.793.1		4	7.2	even	3	inner
1386.2.k.r.991.1		4	1.1	even	1	trivial
3234.2.a.w.1.1		2	21.11	odd	6
3234.2.a.ba.1.2		2	21.17	even	6
9702.2.a.db.1.2		2	7.4	even	3
9702.2.a.dm.1.1		2	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)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-1.32288 - 2.29129i) q^{5} +(1.32288 + 2.29129i) q^{7} +1.00000 q^{8} +(-1.32288 + 2.29129i) q^{10} +(0.500000 - 0.866025i) q^{11} -4.00000 q^{13} +(1.32288 - 2.29129i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(2.64575 + 4.58258i) q^{19} +2.64575 q^{20} -1.00000 q^{22} +(1.32288 + 2.29129i) q^{23} +(-1.00000 + 1.73205i) q^{25} +(2.00000 + 3.46410i) q^{26} -2.64575 q^{28} -2.00000 q^{29} +(2.00000 - 3.46410i) q^{31} +(-0.500000 + 0.866025i) q^{32} +3.00000 q^{34} +(3.50000 - 6.06218i) q^{35} +(4.64575 + 8.04668i) q^{37} +(2.64575 - 4.58258i) q^{38} +(-1.32288 - 2.29129i) q^{40} -9.00000 q^{41} -1.29150 q^{43} +(0.500000 + 0.866025i) q^{44} +(1.32288 - 2.29129i) q^{46} +(5.96863 + 10.3380i) q^{47} +(-3.50000 + 6.06218i) q^{49} +2.00000 q^{50} +(2.00000 - 3.46410i) q^{52} +(2.00000 - 3.46410i) q^{53} -2.64575 q^{55} +(1.32288 + 2.29129i) q^{56} +(1.00000 + 1.73205i) q^{58} +(-7.29150 + 12.6293i) q^{59} +(1.96863 + 3.40976i) q^{61} -4.00000 q^{62} +1.00000 q^{64} +(5.29150 + 9.16515i) q^{65} +(6.79150 - 11.7632i) q^{67} +(-1.50000 - 2.59808i) q^{68} -7.00000 q^{70} +13.2915 q^{71} +(2.35425 - 4.07768i) q^{73} +(4.64575 - 8.04668i) q^{74} -5.29150 q^{76} +2.64575 q^{77} +(-2.67712 - 4.63692i) q^{79} +(-1.32288 + 2.29129i) q^{80} +(4.50000 + 7.79423i) q^{82} +5.58301 q^{83} +7.93725 q^{85} +(0.645751 + 1.11847i) q^{86} +(0.500000 - 0.866025i) q^{88} +(6.64575 + 11.5108i) q^{89} +(-5.29150 - 9.16515i) q^{91} -2.64575 q^{92} +(5.96863 - 10.3380i) q^{94} +(7.00000 - 12.1244i) q^{95} +9.58301 q^{97} +7.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8}+O(q^{10}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8	\( 4 q - 2 q^{2} - 2 q^{4} + 4 q^{8} + 2 q^{11} - 16 q^{13} - 2 q^{16} - 6 q^{17} - 4 q^{22} - 4 q^{25} + 8 q^{26} - 8 q^{29} + 8 q^{31} - 2 q^{32} + 12 q^{34} + 14 q^{35} + 8 q^{37} - 36 q^{41} + 16 q^{43} + 2 q^{44} + 8 q^{47} - 14 q^{49} + 8 q^{50} + 8 q^{52} + 8 q^{53} + 4 q^{58} - 8 q^{59} - 8 q^{61} - 16 q^{62} + 4 q^{64} + 6 q^{67} - 6 q^{68} - 28 q^{70} + 32 q^{71} + 20 q^{73} + 8 q^{74} - 16 q^{79} + 18 q^{82} - 20 q^{83} - 8 q^{86} + 2 q^{88} + 16 q^{89} + 8 q^{94} + 28 q^{95} - 4 q^{97} + 28 q^{98}+O(q^{100}) \) 4 * q - 2 * q^2 - 2 * q^4 + 4 * q^8 + 2 * q^11 - 16 * q^13 - 2 * q^16 - 6 * q^17 - 4 * q^22 - 4 * q^25 + 8 * q^26 - 8 * q^29 + 8 * q^31 - 2 * q^32 + 12 * q^34 + 14 * q^35 + 8 * q^37 - 36 * q^41 + 16 * q^43 + 2 * q^44 + 8 * q^47 - 14 * q^49 + 8 * q^50 + 8 * q^52 + 8 * q^53 + 4 * q^58 - 8 * q^59 - 8 * q^61 - 16 * q^62 + 4 * q^64 + 6 * q^67 - 6 * q^68 - 28 * q^70 + 32 * q^71 + 20 * q^73 + 8 * q^74 - 16 * q^79 + 18 * q^82 - 20 * q^83 - 8 * q^86 + 2 * q^88 + 16 * q^89 + 8 * q^94 + 28 * q^95 - 4 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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