LMFDB - Embedded newform 1134.2.g.c.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(163,1134)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1134.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.g (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:	$9.05503558921$
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:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.163
Dual form			1134.2.g.c.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.50000 - 6.06218i) q^{19} -3.00000 q^{20} +3.00000 q^{22} +(-4.50000 + 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.50000 + 6.06218i) q^{38} +(1.50000 - 2.59808i) q^{40} -3.00000 q^{41} -1.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{46} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(1.50000 - 2.59808i) q^{58} +(-1.00000 + 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 - 5.19615i) q^{70} -12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(0.500000 + 0.866025i) q^{74} -7.00000 q^{76} +(-6.00000 + 5.19615i) q^{77} +(8.00000 - 13.8564i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +9.00000 q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(0.500000 + 2.59808i) q^{91} +9.00000 q^{92} +(-10.5000 - 18.1865i) q^{95} -1.00000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} - 3 q^{11} - 2 q^{13} + 5 q^{14} - q^{16} + 3 q^{17} + 7 q^{19} - 6 q^{20} + 6 q^{22} - 9 q^{23} - 4 q^{25} + q^{26} - 4 q^{28} - 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 15 q^{35} + q^{37} + 7 q^{38} + 3 q^{40} - 6 q^{41} - 2 q^{43} - 3 q^{44} - 9 q^{46} - 13 q^{49} + 8 q^{50} + q^{52} + 3 q^{53} - 18 q^{55} - q^{56} + 3 q^{58} - 2 q^{61} + 16 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} + 3 q^{68} + 12 q^{70} - 24 q^{71} - 11 q^{73} + q^{74} - 14 q^{76} - 12 q^{77} + 16 q^{79} + 3 q^{80} + 3 q^{82} + 18 q^{83} + 18 q^{85} + q^{86} - 3 q^{88} + 3 q^{89} + q^{91} + 18 q^{92} - 21 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8 + 3 * q^10 - 3 * q^11 - 2 * q^13 + 5 * q^14 - q^16 + 3 * q^17 + 7 * q^19 - 6 * q^20 + 6 * q^22 - 9 * q^23 - 4 * q^25 + q^26 - 4 * q^28 - 6 * q^29 - 8 * q^31 - q^32 - 6 * q^34 - 15 * q^35 + q^37 + 7 * q^38 + 3 * q^40 - 6 * q^41 - 2 * q^43 - 3 * q^44 - 9 * q^46 - 13 * q^49 + 8 * q^50 + q^52 + 3 * q^53 - 18 * q^55 - q^56 + 3 * q^58 - 2 * q^61 + 16 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 24 * q^71 - 11 * q^73 + q^74 - 14 * q^76 - 12 * q^77 + 16 * q^79 + 3 * q^80 + 3 * q^82 + 18 * q^83 + 18 * q^85 + q^86 - 3 * q^88 + 3 * q^89 + q^91 + 18 * q^92 - 21 * q^95 - 2 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	−0.306851	−	0.951757i	$-0.599275\pi$
$5$	1.50000	−	2.59808i	0.670820	−	1.16190i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$7$	−0.500000	−	2.59808i	−0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$		0			0
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		0			0
$13$	−1.00000			−0.277350			−0.138675	−	0.990338i	$-0.544284\pi$
$13$	−1.00000			−0.277350			−0.138675	+	0.990338i	$0.544284\pi$
$14$	2.50000	+	0.866025i	0.668153	+	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$		0			0
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	−0.114708	−	0.993399i	$-0.536593\pi$
$19$	3.50000	−	6.06218i	0.802955	−	1.39076i	0.917663	−	0.397360i	$-0.130073\pi$
$20$	−3.00000			−0.670820
$21$		0			0
$22$	3.00000			0.639602
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.169701	+	0.985496i	$0.554280\pi$
$23$	−4.50000	+	7.79423i	−0.938315	+	1.62521i	−0.768613	+	0.639713i	$0.779053\pi$
$24$		0			0
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$		0			0
$28$	−2.00000	+	1.73205i	−0.377964	+	0.327327i
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	−0.961625	−	0.274367i	$-0.911532\pi$
$31$	−4.00000	−	6.92820i	−0.718421	−	1.24434i	0.243204	−	0.969975i	$-0.421802\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−3.00000			−0.514496
$35$	−7.50000	−	2.59808i	−1.26773	−	0.439155i
$36$		0			0
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	−0.821995	−	0.569495i	$-0.807139\pi$
$37$	0.500000	−	0.866025i	0.0821995	−	0.142374i	0.904194	+	0.427121i	$0.140472\pi$
$38$	3.50000	+	6.06218i	0.567775	+	0.983415i
$39$		0			0
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	−1.00000			−0.152499			−0.0762493	−	0.997089i	$-0.524294\pi$
$43$	−1.00000			−0.152499			−0.0762493	+	0.997089i	$0.524294\pi$
$44$	−1.50000	+	2.59808i	−0.226134	+	0.391675i
$45$		0			0
$46$	−4.50000	−	7.79423i	−0.663489	−	1.14920i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−6.50000	+	2.59808i	−0.928571	+	0.371154i
$50$	4.00000			0.565685
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	0.950464	−	0.310835i	$-0.100609\pi$
$53$	1.50000	+	2.59808i	0.206041	+	0.356873i	−0.744423	+	0.667708i	$0.767275\pi$
$54$		0			0
$55$	−9.00000			−1.21356
$56$	−0.500000	−	2.59808i	−0.0668153	−	0.347183i
$57$		0			0
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$	8.00000			1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−1.50000	+	2.59808i	−0.186052	+	0.322252i
$66$		0			0
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	0.961946	−	0.273241i	$-0.0880957\pi$
$67$	2.00000	+	3.46410i	0.244339	+	0.423207i	−0.717607	+	0.696449i	$0.754762\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	6.00000	−	5.19615i	0.717137	−	0.621059i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	0.500000	+	0.866025i	0.0581238	+	0.100673i
$75$		0			0
$76$	−7.00000			−0.802955
$77$	−6.00000	+	5.19615i	−0.683763	+	0.592157i
$78$		0			0
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.0726692	−	0.997356i	$-0.476848\pi$
$79$	8.00000	−	13.8564i	0.900070	−	1.55897i	0.827401	−	0.561611i	$-0.189818\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$		0			0
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	9.00000			0.987878			0.493939	−	0.869496i	$-0.335557\pi$
$83$	9.00000			0.987878			0.493939	+	0.869496i	$0.335557\pi$
$84$		0			0
$85$	9.00000			0.976187
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	−0.775509	−	0.631337i	$-0.782506\pi$
$89$	1.50000	−	2.59808i	0.159000	−	0.275396i	0.934508	+	0.355942i	$0.115840\pi$
$90$		0			0
$91$	0.500000	+	2.59808i	0.0524142	+	0.272352i
$92$	9.00000			0.938315
$93$		0			0
$94$		0			0
$95$	−10.5000	−	18.1865i	−1.07728	−	1.86590i
$96$		0			0
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$		0			0
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	0.930953	−	0.365140i	$-0.118979\pi$
$101$	1.50000	+	2.59808i	0.149256	+	0.258518i	−0.781697	+	0.623658i	$0.785646\pi$
$102$		0			0
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	−0.344865	−	0.938652i	$-0.612075\pi$
$103$	6.50000	−	11.2583i	0.640464	−	1.10932i	0.985329	−	0.170664i	$-0.0545913\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−3.00000			−0.291386
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	−0.562267	−	0.826956i	$-0.690071\pi$
$107$	4.50000	−	7.79423i	0.435031	−	0.753497i	0.997298	+	0.0734594i	$0.0234039\pi$
$108$		0			0
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	0.989002	+	0.147901i	$0.0472517\pi$
$109$	6.50000	+	11.2583i	0.622587	+	1.07835i	−0.366415	+	0.930451i	$0.619415\pi$
$110$	4.50000	−	7.79423i	0.429058	−	0.743151i
$111$		0			0
$112$	2.50000	+	0.866025i	0.236228	+	0.0818317i
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$		0			0
$115$	13.5000	+	23.3827i	1.25888	+	2.18045i
$116$	1.50000	+	2.59808i	0.139272	+	0.241225i
$117$		0			0
$118$		0			0
$119$	6.00000	−	5.19615i	0.550019	−	0.476331i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−1.00000	−	1.73205i	−0.0905357	−	0.156813i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	3.00000			0.268328
$126$		0			0
$127$	−4.00000			−0.354943			−0.177471	−	0.984126i	$-0.556792\pi$
$127$	−4.00000			−0.354943			−0.177471	+	0.984126i	$0.556792\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	−0.326546	−	0.945181i	$-0.605885\pi$
$131$	7.50000	−	12.9904i	0.655278	−	1.13497i	0.981824	−	0.189794i	$-0.0607819\pi$
$132$		0			0
$133$	−17.5000	−	6.06218i	−1.51744	−	0.525657i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$		0			0
$139$	−7.00000			−0.593732			−0.296866	−	0.954919i	$-0.595942\pi$
$139$	−7.00000			−0.593732			−0.296866	+	0.954919i	$0.595942\pi$
$140$	1.50000	+	7.79423i	0.126773	+	0.658733i
$141$		0			0
$142$	6.00000	−	10.3923i	0.503509	−	0.872103i
$143$	1.50000	+	2.59808i	0.125436	+	0.217262i
$144$		0			0
$145$	−4.50000	+	7.79423i	−0.373705	+	0.647275i
$146$	11.0000			0.910366
$147$		0			0
$148$	−1.00000			−0.0821995
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	−0.989355	−	0.145519i	$-0.953515\pi$
$149$	−4.50000	+	7.79423i	−0.368654	+	0.638528i	0.620701	+	0.784047i	$0.286848\pi$
$150$		0			0
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	0.972567	−	0.232623i	$-0.0747309\pi$
$151$	3.50000	+	6.06218i	0.284826	+	0.493333i	−0.687741	+	0.725956i	$0.741398\pi$
$152$	3.50000	−	6.06218i	0.283887	−	0.491708i
$153$		0			0
$154$	−1.50000	−	7.79423i	−0.120873	−	0.628077i
$155$	−24.0000			−1.92773
$156$		0			0
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.853646	+	0.520854i	$0.174386\pi$
$157$	11.0000	+	19.0526i	0.877896	+	1.52056i	0.0242497	+	0.999706i	$0.492280\pi$
$158$	8.00000	+	13.8564i	0.636446	+	1.10236i
$159$		0			0
$160$	−3.00000			−0.237171
$161$	22.5000	+	7.79423i	1.77325	+	0.614271i
$162$		0			0
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	−0.206518	−	0.978443i	$-0.566213\pi$
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	0.950615	−	0.310372i	$-0.100454\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	−4.50000	+	7.79423i	−0.349268	+	0.604949i
$167$	15.0000			1.16073			0.580367	−	0.814355i	$-0.302909\pi$
$167$	15.0000			1.16073			0.580367	+	0.814355i	$0.302909\pi$
$168$		0			0
$169$	−12.0000			−0.923077
$170$	−4.50000	+	7.79423i	−0.345134	+	0.597790i
$171$		0			0
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	−0.957241	−	0.289292i	$-0.906580\pi$
$173$	−3.00000	+	5.19615i	−0.228086	+	0.395056i	0.729155	+	0.684349i	$0.239913\pi$
$174$		0			0
$175$	−8.00000	+	6.92820i	−0.604743	+	0.523723i
$176$	3.00000			0.226134
$177$		0			0
$178$	1.50000	+	2.59808i	0.112430	+	0.194734i
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	−0.929114	−	0.369792i	$-0.879429\pi$
$179$	−10.5000	−	18.1865i	−0.784807	−	1.35933i	0.144308	−	0.989533i	$-0.453905\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−2.50000	−	0.866025i	−0.185312	−	0.0641941i
$183$		0			0
$184$	−4.50000	+	7.79423i	−0.331744	+	0.574598i
$185$	−1.50000	−	2.59808i	−0.110282	−	0.191014i
$186$		0			0
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$		0			0
$189$		0			0
$190$	21.0000			1.52350
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	−0.999990	−	0.00447566i	$-0.998575\pi$
$193$	−7.00000	−	12.1244i	−0.503871	−	0.872730i	0.496119	−	0.868255i	$-0.334758\pi$
$194$	0.500000	−	0.866025i	0.0358979	−	0.0621770i
$195$		0			0
$196$	5.50000	+	4.33013i	0.392857	+	0.309295i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$		0			0
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.844446	+	0.535641i	$0.179930\pi$
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.0416556	+	0.999132i	$0.486737\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$		0			0
$202$	−3.00000			−0.211079
$203$	1.50000	+	7.79423i	0.105279	+	0.547048i
$204$		0			0
$205$	−4.50000	+	7.79423i	−0.314294	+	0.544373i
$206$	6.50000	+	11.2583i	0.452876	+	0.784405i
$207$		0			0
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	−21.0000			−1.45260
$210$		0			0
$211$	5.00000			0.344214			0.172107	−	0.985078i	$-0.444942\pi$
$211$	5.00000			0.344214			0.172107	+	0.985078i	$0.444942\pi$
$212$	1.50000	−	2.59808i	0.103020	−	0.178437i
$213$		0			0
$214$	4.50000	+	7.79423i	0.307614	+	0.532803i
$215$	−1.50000	+	2.59808i	−0.102299	+	0.177187i
$216$		0			0
$217$	−16.0000	+	13.8564i	−1.08615	+	0.940634i
$218$	−13.0000			−0.880471
$219$		0			0
$220$	4.50000	+	7.79423i	0.303390	+	0.525487i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$		0			0
$223$	−1.00000			−0.0669650			−0.0334825	−	0.999439i	$-0.510660\pi$
$223$	−1.00000			−0.0669650			−0.0334825	+	0.999439i	$0.510660\pi$
$224$	−2.00000	+	1.73205i	−0.133631	+	0.115728i
$225$		0			0
$226$	−4.50000	+	7.79423i	−0.299336	+	0.518464i
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$		0			0
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$	−27.0000			−1.78033
$231$		0			0
$232$	−3.00000			−0.196960
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	−0.812700	−	0.582683i	$-0.802003\pi$
$233$	1.50000	−	2.59808i	0.0982683	−	0.170206i	0.910968	+	0.412477i	$0.135336\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$	1.50000	+	7.79423i	0.0972306	+	0.505225i
$239$	3.00000			0.194054			0.0970269	−	0.995282i	$-0.469067\pi$
$239$	3.00000			0.194054			0.0970269	+	0.995282i	$0.469067\pi$
$240$		0			0
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	0.995809	−	0.0914555i	$-0.0291519\pi$
$241$	6.50000	+	11.2583i	0.418702	+	0.725213i	−0.577107	+	0.816668i	$0.695819\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$		0			0
$244$	2.00000			0.128037
$245$	−3.00000	+	20.7846i	−0.191663	+	1.32788i
$246$		0			0
$247$	−3.50000	+	6.06218i	−0.222700	+	0.385727i
$248$	−4.00000	−	6.92820i	−0.254000	−	0.439941i
$249$		0			0
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	−12.0000			−0.757433			−0.378717	−	0.925513i	$-0.623635\pi$
$251$	−12.0000			−0.757433			−0.378717	+	0.925513i	$0.623635\pi$
$252$		0			0
$253$	27.0000			1.69748
$254$	2.00000	−	3.46410i	0.125491	−	0.217357i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	0.326929	+	0.945049i	$0.393986\pi$
$257$	−10.5000	+	18.1865i	−0.654972	+	1.13444i	−0.981901	+	0.189396i	$0.939347\pi$
$258$		0			0
$259$	−2.50000	−	0.866025i	−0.155342	−	0.0538122i
$260$	3.00000			0.186052
$261$		0			0
$262$	7.50000	+	12.9904i	0.463352	+	0.802548i
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$		0			0
$265$	9.00000			0.552866
$266$	14.0000	−	12.1244i	0.858395	−	0.743392i
$267$		0			0
$268$	2.00000	−	3.46410i	0.122169	−	0.211604i
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	0.998816	−	0.0486418i	$-0.0154893\pi$
$269$	7.50000	+	12.9904i	0.457283	+	0.792038i	−0.541533	+	0.840679i	$0.682156\pi$
$270$		0			0
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	−0.931913	−	0.362682i	$-0.881861\pi$
$271$	−2.50000	+	4.33013i	−0.151864	+	0.263036i	0.780049	+	0.625719i	$0.215194\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$	9.00000			0.543710
$275$	−6.00000	+	10.3923i	−0.361814	+	0.626680i
$276$		0			0
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	0.880656	−	0.473757i	$-0.157103\pi$
$277$	0.500000	+	0.866025i	0.0300421	+	0.0520344i	−0.850613	+	0.525792i	$0.823769\pi$
$278$	3.50000	−	6.06218i	0.209916	−	0.363585i
$279$		0			0
$280$	−7.50000	−	2.59808i	−0.448211	−	0.155265i
$281$	21.0000			1.25275			0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000			1.25275			0.626377	+	0.779520i	$0.284537\pi$
$282$		0			0
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	−3.00000			−0.177394
$287$	1.50000	+	7.79423i	0.0885422	+	0.460079i
$288$		0			0
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−4.50000	−	7.79423i	−0.264249	−	0.457693i
$291$		0			0
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	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
$295$		0			0
$296$	0.500000	−	0.866025i	0.0290619	−	0.0503367i
$297$		0			0
$298$	−4.50000	−	7.79423i	−0.260678	−	0.451508i
$299$	4.50000	−	7.79423i	0.260242	−	0.450752i
$300$		0			0
$301$	0.500000	+	2.59808i	0.0288195	+	0.149751i
$302$	−7.00000			−0.402805
$303$		0			0
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	3.00000	+	5.19615i	0.171780	+	0.297531i
$306$		0			0
$307$	−28.0000			−1.59804			−0.799022	−	0.601302i	$-0.794649\pi$
$307$	−28.0000			−1.59804			−0.799022	+	0.601302i	$0.794649\pi$
$308$	7.50000	+	2.59808i	0.427352	+	0.148039i
$309$		0			0
$310$	12.0000	−	20.7846i	0.681554	−	1.18049i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	−0.689412	−	0.724370i	$-0.742131\pi$
$313$	5.00000	−	8.66025i	0.282617	−	0.489506i	0.972028	+	0.234863i	$0.0754642\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$	−16.0000			−0.900070
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	4.50000	+	7.79423i	0.251952	+	0.436393i
$320$	1.50000	−	2.59808i	0.0838525	−	0.145237i
$321$		0			0
$322$	−18.0000	+	15.5885i	−1.00310	+	0.868711i
$323$	21.0000			1.16847
$324$		0			0
$325$	2.00000	+	3.46410i	0.110940	+	0.192154i
$326$	9.50000	+	16.4545i	0.526156	+	0.911330i
$327$		0			0
$328$	−3.00000			−0.165647
$329$		0			0
$330$		0			0
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	−0.954765	−	0.297361i	$-0.903893\pi$
$331$	−4.00000	+	6.92820i	−0.219860	+	0.380808i	0.734905	+	0.678170i	$0.237227\pi$
$332$	−4.50000	−	7.79423i	−0.246970	−	0.427764i
$333$		0			0
$334$	−7.50000	+	12.9904i	−0.410382	+	0.710802i
$335$	12.0000			0.655630
$336$		0			0
$337$	−13.0000			−0.708155			−0.354078	−	0.935216i	$-0.615205\pi$
$337$	−13.0000			−0.708155			−0.354078	+	0.935216i	$0.615205\pi$
$338$	6.00000	−	10.3923i	0.326357	−	0.565267i
$339$		0			0
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	−12.0000	+	20.7846i	−0.649836	+	1.12555i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$	−1.00000			−0.0539164
$345$		0			0
$346$	−3.00000	−	5.19615i	−0.161281	−	0.279347i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	23.0000			1.23116			0.615581	−	0.788074i	$-0.288921\pi$
$349$	23.0000			1.23116			0.615581	+	0.788074i	$0.288921\pi$
$350$	−2.00000	−	10.3923i	−0.106904	−	0.555492i
$351$		0			0
$352$	−1.50000	+	2.59808i	−0.0799503	+	0.138478i
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	−18.0000	+	31.1769i	−0.955341	+	1.65470i
$356$	−3.00000			−0.159000
$357$		0			0
$358$	21.0000			1.10988
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	−0.722496	−	0.691375i	$-0.757005\pi$
$359$	4.50000	−	7.79423i	0.237501	−	0.411364i	0.959997	+	0.280012i	$0.0903384\pi$
$360$		0			0
$361$	−15.0000	−	25.9808i	−0.789474	−	1.36741i
$362$	−1.00000	+	1.73205i	−0.0525588	+	0.0910346i
$363$		0			0
$364$	2.00000	−	1.73205i	0.104828	−	0.0907841i
$365$	−33.0000			−1.72730
$366$		0			0
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	−4.50000	−	7.79423i	−0.234579	−	0.406302i
$369$		0			0
$370$	3.00000			0.155963
$371$	6.00000	−	5.19615i	0.311504	−	0.269771i
$372$		0			0
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	−0.647225	−	0.762299i	$-0.724071\pi$
$373$	6.50000	−	11.2583i	0.336557	−	0.582934i	0.983783	+	0.179364i	$0.0574041\pi$
$374$	4.50000	+	7.79423i	0.232689	+	0.403030i
$375$		0			0
$376$		0			0
$377$	3.00000			0.154508
$378$		0			0
$379$	−28.0000			−1.43826			−0.719132	−	0.694874i	$-0.755460\pi$
$379$	−28.0000			−1.43826			−0.719132	+	0.694874i	$0.755460\pi$
$380$	−10.5000	+	18.1865i	−0.538639	+	0.932949i
$381$		0			0
$382$		0			0
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	−0.608290	−	0.793715i	$-0.708144\pi$
$383$	7.50000	−	12.9904i	0.383232	−	0.663777i	0.991522	+	0.129937i	$0.0414776\pi$
$384$		0			0
$385$	4.50000	+	23.3827i	0.229341	+	1.19169i
$386$	14.0000			0.712581
$387$		0			0
$388$	0.500000	+	0.866025i	0.0253837	+	0.0439658i
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	0.973601	+	0.228257i	$0.0733028\pi$
$389$	13.5000	+	23.3827i	0.684477	+	1.18555i	−0.289124	+	0.957292i	$0.593364\pi$
$390$		0			0
$391$	−27.0000			−1.36545
$392$	−6.50000	+	2.59808i	−0.328300	+	0.131223i
$393$		0			0
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	−24.0000	−	41.5692i	−1.20757	−	2.09157i
$396$		0			0
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	−0.655534	−	0.755166i	$-0.727556\pi$
$397$	6.50000	−	11.2583i	0.326226	−	0.565039i	0.981760	+	0.190126i	$0.0608897\pi$
$398$	−25.0000			−1.25314
$399$		0			0
$400$	4.00000			0.200000
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	−0.302556	−	0.953131i	$-0.597840\pi$
$401$	13.5000	−	23.3827i	0.674158	−	1.16768i	0.976714	−	0.214544i	$-0.0688266\pi$
$402$		0			0
$403$	4.00000	+	6.92820i	0.199254	+	0.345118i
$404$	1.50000	−	2.59808i	0.0746278	−	0.129259i
$405$		0			0
$406$	−7.50000	−	2.59808i	−0.372219	−	0.128940i
$407$	−3.00000			−0.148704
$408$		0			0
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	0.889392	+	0.457146i	$0.151128\pi$
$409$	17.0000	+	29.4449i	0.840596	+	1.45595i	−0.0487958	+	0.998809i	$0.515538\pi$
$410$	−4.50000	−	7.79423i	−0.222239	−	0.384930i
$411$		0			0
$412$	−13.0000			−0.640464
$413$		0			0
$414$		0			0
$415$	13.5000	−	23.3827i	0.662689	−	1.14781i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$		0			0
$418$	10.5000	−	18.1865i	0.513572	−	0.889532i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$		0			0
$421$	35.0000			1.70580			0.852898	−	0.522078i	$-0.174843\pi$
$421$	35.0000			1.70580			0.852898	+	0.522078i	$0.174843\pi$
$422$	−2.50000	+	4.33013i	−0.121698	+	0.210787i
$423$		0			0
$424$	1.50000	+	2.59808i	0.0728464	+	0.126174i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	5.00000	+	1.73205i	0.241967	+	0.0838198i
$428$	−9.00000			−0.435031
$429$		0			0
$430$	−1.50000	−	2.59808i	−0.0723364	−	0.125290i
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	0.983057	+	0.183301i	$0.0586785\pi$
$431$	13.5000	+	23.3827i	0.650272	+	1.12630i	−0.332785	+	0.943003i	$0.607988\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$	−4.00000	−	20.7846i	−0.192006	−	0.997693i
$435$		0			0
$436$	6.50000	−	11.2583i	0.311294	−	0.539176i
$437$	31.5000	+	54.5596i	1.50685	+	2.60994i
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	−9.00000			−0.429058
$441$		0			0
$442$	3.00000			0.142695
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	−0.0212481	−	0.999774i	$-0.506764\pi$
$443$	18.0000	−	31.1769i	0.855206	−	1.48126i	0.876454	−	0.481486i	$-0.159903\pi$
$444$		0			0
$445$	−4.50000	−	7.79423i	−0.213320	−	0.369482i
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$		0			0
$448$	−0.500000	−	2.59808i	−0.0236228	−	0.122748i
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$		0			0
$451$	4.50000	+	7.79423i	0.211897	+	0.367016i
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$		0			0
$454$	3.00000			0.140797
$455$	7.50000	+	2.59808i	0.351605	+	0.121800i
$456$		0			0
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	−0.725059	−	0.688686i	$-0.758188\pi$
$457$	5.00000	−	8.66025i	0.233890	−	0.405110i	0.958950	+	0.283577i	$0.0915211\pi$
$458$	6.50000	+	11.2583i	0.303725	+	0.526067i
$459$		0			0
$460$	13.5000	−	23.3827i	0.629441	−	1.09022i
$461$	9.00000			0.419172			0.209586	−	0.977790i	$-0.432788\pi$
$461$	9.00000			0.419172			0.209586	+	0.977790i	$0.432788\pi$
$462$		0			0
$463$	41.0000			1.90543			0.952716	−	0.303863i	$-0.0982765\pi$
$463$	41.0000			1.90543			0.952716	+	0.303863i	$0.0982765\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	1.50000	+	2.59808i	0.0694862	+	0.120354i
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	−0.898642	−	0.438682i	$-0.855446\pi$
$467$	−1.50000	+	2.59808i	−0.0694117	+	0.120225i	0.829231	+	0.558906i	$0.188779\pi$
$468$		0			0
$469$	8.00000	−	6.92820i	0.369406	−	0.319915i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	1.50000	+	2.59808i	0.0689701	+	0.119460i
$474$		0			0
$475$	−28.0000			−1.28473
$476$	−7.50000	−	2.59808i	−0.343762	−	0.119083i
$477$		0			0
$478$	−1.50000	+	2.59808i	−0.0686084	+	0.118833i
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	0.829721	−	0.558179i	$-0.188500\pi$
$479$	−1.50000	−	2.59808i	−0.0685367	−	0.118709i	−0.898257	+	0.439470i	$0.855166\pi$
$480$		0			0
$481$	−0.500000	+	0.866025i	−0.0227980	+	0.0394874i
$482$	−13.0000			−0.592134
$483$		0			0
$484$	−2.00000			−0.0909091
$485$	−1.50000	+	2.59808i	−0.0681115	+	0.117973i
$486$		0			0
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	0.996915	+	0.0784867i	$0.0250088\pi$
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	−0.430486	+	0.902597i	$0.641658\pi$
$488$	−1.00000	+	1.73205i	−0.0452679	+	0.0784063i
$489$		0			0
$490$	−16.5000	−	12.9904i	−0.745394	−	0.586846i
$491$	−21.0000			−0.947717			−0.473858	−	0.880601i	$-0.657139\pi$
$491$	−21.0000			−0.947717			−0.473858	+	0.880601i	$0.657139\pi$
$492$		0			0
$493$	−4.50000	−	7.79423i	−0.202670	−	0.351034i
$494$	−3.50000	−	6.06218i	−0.157472	−	0.272750i
$495$		0			0
$496$	8.00000			0.359211
$497$	6.00000	+	31.1769i	0.269137	+	1.39848i
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	−1.50000	−	2.59808i	−0.0670820	−	0.116190i
$501$		0			0
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	9.00000			0.400495
$506$	−13.5000	+	23.3827i	−0.600148	+	1.03949i
$507$		0			0
$508$	2.00000	+	3.46410i	0.0887357	+	0.153695i
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	−0.948353	−	0.317217i	$-0.897252\pi$
$509$	−4.50000	+	7.79423i	−0.199459	+	0.345473i	0.748894	+	0.662690i	$0.230585\pi$
$510$		0			0
$511$	−22.0000	+	19.0526i	−0.973223	+	0.842836i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$	−19.5000	−	33.7750i	−0.859273	−	1.48830i
$516$		0			0
$517$		0			0
$518$	2.00000	−	1.73205i	0.0878750	−	0.0761019i
$519$		0			0
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	0.897011	−	0.442007i	$-0.145733\pi$
$521$	1.50000	+	2.59808i	0.0657162	+	0.113824i	−0.831295	+	0.555831i	$0.812400\pi$
$522$		0			0
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	−0.779301	−	0.626650i	$-0.784426\pi$
$523$	3.50000	−	6.06218i	0.153044	−	0.265081i	0.932345	+	0.361569i	$0.117759\pi$
$524$	−15.0000			−0.655278
$525$		0			0
$526$	−9.00000			−0.392419
$527$	12.0000	−	20.7846i	0.522728	−	0.905392i
$528$		0			0
$529$	−29.0000	−	50.2295i	−1.26087	−	2.18389i
$530$	−4.50000	+	7.79423i	−0.195468	+	0.338560i
$531$		0			0
$532$	3.50000	+	18.1865i	0.151744	+	0.788486i
$533$	3.00000			0.129944
$534$		0			0
$535$	−13.5000	−	23.3827i	−0.583656	−	1.01092i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−15.0000			−0.646696
$539$	16.5000	+	12.9904i	0.710705	+	0.559535i
$540$		0			0
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	−0.959697	−	0.281037i	$-0.909322\pi$
$541$	−5.50000	+	9.52628i	−0.236463	+	0.409567i	0.723234	+	0.690604i	$0.242655\pi$
$542$	−2.50000	−	4.33013i	−0.107384	−	0.185995i
$543$		0			0
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	39.0000			1.67058
$546$		0			0
$547$	11.0000			0.470326			0.235163	−	0.971956i	$-0.424438\pi$
$547$	11.0000			0.470326			0.235163	+	0.971956i	$0.424438\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$		0			0
$550$	−6.00000	−	10.3923i	−0.255841	−	0.443129i
$551$	−10.5000	+	18.1865i	−0.447315	+	0.774772i
$552$		0			0
$553$	−40.0000	−	13.8564i	−1.70097	−	0.589234i
$554$	−1.00000			−0.0424859
$555$		0			0
$556$	3.50000	+	6.06218i	0.148433	+	0.257094i
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	0.754802	−	0.655953i	$-0.227733\pi$
$557$	−4.50000	−	7.79423i	−0.190671	−	0.330252i	−0.945473	+	0.325701i	$0.894400\pi$
$558$		0			0
$559$	1.00000			0.0422955
$560$	6.00000	−	5.19615i	0.253546	−	0.219578i
$561$		0			0
$562$	−10.5000	+	18.1865i	−0.442916	+	0.767153i
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	13.5000	−	23.3827i	0.567949	−	0.983717i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	−12.0000			−0.503509
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	−0.978022	−	0.208502i	$-0.933141\pi$
$571$	−16.0000	−	27.7128i	−0.669579	−	1.15975i	0.308443	−	0.951243i	$-0.400192\pi$
$572$	1.50000	−	2.59808i	0.0627182	−	0.108631i
$573$		0			0
$574$	−7.50000	−	2.59808i	−0.313044	−	0.108442i
$575$	36.0000			1.50130
$576$		0			0
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	0.999719	+	0.0236970i	$0.00754370\pi$
$577$	12.5000	+	21.6506i	0.520382	+	0.901328i	−0.479337	+	0.877631i	$0.659123\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	9.00000			0.373705
$581$	−4.50000	−	23.3827i	−0.186691	−	0.970077i
$582$		0			0
$583$	4.50000	−	7.79423i	0.186371	−	0.322804i
$584$	−5.50000	−	9.52628i	−0.227592	−	0.394200i
$585$		0			0
$586$	−4.50000	+	7.79423i	−0.185893	+	0.321977i
$587$	−3.00000			−0.123823			−0.0619116	−	0.998082i	$-0.519720\pi$
$587$	−3.00000			−0.123823			−0.0619116	+	0.998082i	$0.519720\pi$
$588$		0			0
$589$	−56.0000			−2.30744
$590$		0			0
$591$		0			0
$592$	0.500000	+	0.866025i	0.0205499	+	0.0355934i
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	−0.118342	−	0.992973i	$-0.537758\pi$
$593$	19.5000	−	33.7750i	0.800769	−	1.38697i	0.919111	−	0.394000i	$-0.128909\pi$
$594$		0			0
$595$	−4.50000	−	23.3827i	−0.184482	−	0.958597i
$596$	9.00000			0.368654
$597$		0			0
$598$	4.50000	+	7.79423i	0.184019	+	0.318730i
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	0.509631	−	0.860393i	$-0.329782\pi$
$599$	−12.0000	−	20.7846i	−0.490307	−	0.849236i	−0.999938	+	0.0111569i	$0.996449\pi$
$600$		0			0
$601$	−25.0000			−1.01977			−0.509886	−	0.860242i	$-0.670312\pi$
$601$	−25.0000			−1.01977			−0.509886	+	0.860242i	$0.670312\pi$
$602$	−2.50000	−	0.866025i	−0.101892	−	0.0352966i
$603$		0			0
$604$	3.50000	−	6.06218i	0.142413	−	0.246667i
$605$	−3.00000	−	5.19615i	−0.121967	−	0.211254i
$606$		0			0
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	−0.703429	−	0.710766i	$-0.748349\pi$
$607$	6.50000	−	11.2583i	0.263827	−	0.456962i	0.967256	+	0.253804i	$0.0816819\pi$
$608$	−7.00000			−0.283887
$609$		0			0
$610$	−6.00000			−0.242933
$611$		0			0
$612$		0			0
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	0.534697	−	0.845044i	$-0.320426\pi$
$613$	−11.5000	−	19.9186i	−0.464481	−	0.804504i	−0.999178	+	0.0405396i	$0.987092\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$	−6.00000	+	5.19615i	−0.241747	+	0.209359i
$617$	45.0000			1.81163			0.905816	−	0.423672i	$-0.139259\pi$
$617$	45.0000			1.81163			0.905816	+	0.423672i	$0.139259\pi$
$618$		0			0
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	0.643094	−	0.765787i	$-0.277650\pi$
$619$	−8.50000	−	14.7224i	−0.341644	−	0.591744i	−0.984738	+	0.174042i	$0.944317\pi$
$620$	12.0000	+	20.7846i	0.481932	+	0.834730i
$621$		0			0
$622$	24.0000			0.962312
$623$	−7.50000	−	2.59808i	−0.300481	−	0.104090i
$624$		0			0
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$		0			0
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	3.00000			0.119618
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$	8.00000	−	13.8564i	0.318223	−	0.551178i
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$	−6.00000	+	10.3923i	−0.238103	+	0.412406i
$636$		0			0
$637$	6.50000	−	2.59808i	0.257539	−	0.102940i
$638$	−9.00000			−0.356313
$639$		0			0
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	−0.982708	−	0.185164i	$-0.940718\pi$
$641$	−16.5000	−	28.5788i	−0.651711	−	1.12880i	0.330997	−	0.943632i	$-0.392615\pi$
$642$		0			0
$643$	29.0000			1.14365			0.571824	−	0.820376i	$-0.306236\pi$
$643$	29.0000			1.14365			0.571824	+	0.820376i	$0.306236\pi$
$644$	−4.50000	−	23.3827i	−0.177325	−	0.921407i
$645$		0			0
$646$	−10.5000	+	18.1865i	−0.413117	+	0.715540i
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	0.582397	−	0.812905i	$-0.302115\pi$
$647$	−10.5000	−	18.1865i	−0.412798	−	0.714986i	−0.995194	+	0.0979182i	$0.968782\pi$
$648$		0			0
$649$		0			0
$650$	−4.00000			−0.156893
$651$		0			0
$652$	−19.0000			−0.744097
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	−0.681137	−	0.732156i	$-0.738514\pi$
$653$	7.50000	−	12.9904i	0.293498	−	0.508353i	0.974634	+	0.223803i	$0.0718474\pi$
$654$		0			0
$655$	−22.5000	−	38.9711i	−0.879148	−	1.52273i
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$		0			0
$658$		0			0
$659$	−3.00000			−0.116863			−0.0584317	−	0.998291i	$-0.518610\pi$
$659$	−3.00000			−0.116863			−0.0584317	+	0.998291i	$0.518610\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−4.00000	−	6.92820i	−0.155464	−	0.269272i
$663$		0			0
$664$	9.00000			0.349268
$665$	−42.0000	+	36.3731i	−1.62869	+	1.41049i
$666$		0			0
$667$	13.5000	−	23.3827i	0.522722	−	0.905381i
$668$	−7.50000	−	12.9904i	−0.290184	−	0.502613i
$669$		0			0
$670$	−6.00000	+	10.3923i	−0.231800	+	0.401490i
$671$	6.00000			0.231627
$672$		0			0
$673$	35.0000			1.34915			0.674575	−	0.738206i	$-0.264327\pi$
$673$	35.0000			1.34915			0.674575	+	0.738206i	$0.264327\pi$
$674$	6.50000	−	11.2583i	0.250371	−	0.433655i
$675$		0			0
$676$	6.00000	+	10.3923i	0.230769	+	0.399704i
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$677$	−15.0000	+	25.9808i	−0.576497	+	0.998522i	−0.995877	+	0.0907112i	$0.971086\pi$
$678$		0			0
$679$	0.500000	+	2.59808i	0.0191882	+	0.0997050i
$680$	9.00000			0.345134
$681$		0			0
$682$	−12.0000	−	20.7846i	−0.459504	−	0.795884i
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	0.766997	−	0.641651i	$-0.221750\pi$
$683$	−4.50000	−	7.79423i	−0.172188	−	0.298238i	−0.939184	+	0.343413i	$0.888417\pi$
$684$		0			0
$685$	−27.0000			−1.03162
$686$	−18.5000	+	0.866025i	−0.706333	+	0.0330650i
$687$		0			0
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−1.50000	−	2.59808i	−0.0571454	−	0.0989788i
$690$		0			0
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	0.0555386	+	0.998457i	$0.482312\pi$
$691$	−22.0000	+	38.1051i	−0.836919	+	1.44959i	−0.892458	+	0.451130i	$0.851021\pi$
$692$	6.00000			0.228086
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−10.5000	+	18.1865i	−0.398288	+	0.689855i
$696$		0			0
$697$	−4.50000	−	7.79423i	−0.170450	−	0.295227i
$698$	−11.5000	+	19.9186i	−0.435281	+	0.753930i
$699$		0			0
$700$	10.0000	+	3.46410i	0.377964	+	0.130931i
$701$	18.0000			0.679851			0.339925	−	0.940452i	$-0.389598\pi$
$701$	18.0000			0.679851			0.339925	+	0.940452i	$0.389598\pi$
$702$		0			0
$703$	−3.50000	−	6.06218i	−0.132005	−	0.228639i
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	−3.00000			−0.112906
$707$	6.00000	−	5.19615i	0.225653	−	0.195421i
$708$		0			0
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$	−18.0000	−	31.1769i	−0.675528	−	1.17005i
$711$		0			0
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$	72.0000			2.69642
$714$		0			0
$715$	9.00000			0.336581
$716$	−10.5000	+	18.1865i	−0.392403	+	0.679663i
$717$		0			0
$718$	4.50000	+	7.79423i	0.167939	+	0.290878i
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$719$	−7.50000	+	12.9904i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$720$		0			0
$721$	−32.5000	−	11.2583i	−1.21036	−	0.419282i
$722$	30.0000			1.11648
$723$		0			0
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$		0			0
$727$	−13.0000			−0.482143			−0.241072	−	0.970507i	$-0.577499\pi$
$727$	−13.0000			−0.482143			−0.241072	+	0.970507i	$0.577499\pi$
$728$	0.500000	+	2.59808i	0.0185312	+	0.0962911i
$729$		0			0
$730$	16.5000	−	28.5788i	0.610692	−	1.05775i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$		0			0
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	−0.856644	−	0.515908i	$-0.827454\pi$
$733$	0.500000	−	0.866025i	0.0184679	−	0.0319874i	0.875112	+	0.483921i	$0.160788\pi$
$734$	17.0000			0.627481
$735$		0			0
$736$	9.00000			0.331744
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$		0			0
$739$	−11.5000	−	19.9186i	−0.423034	−	0.732717i	0.573200	−	0.819415i	$-0.305702\pi$
$739$	−11.5000	−	19.9186i	−0.423034	−	0.732717i	−0.996235	+	0.0866983i	$0.972368\pi$
$740$	−1.50000	+	2.59808i	−0.0551411	+	0.0955072i
$741$		0			0
$742$	1.50000	+	7.79423i	0.0550667	+	0.286135i
$743$	−21.0000			−0.770415			−0.385208	−	0.922830i	$-0.625870\pi$
$743$	−21.0000			−0.770415			−0.385208	+	0.922830i	$0.625870\pi$
$744$		0			0
$745$	13.5000	+	23.3827i	0.494602	+	0.856675i
$746$	6.50000	+	11.2583i	0.237982	+	0.412197i
$747$		0			0
$748$	−9.00000			−0.329073
$749$	−22.5000	−	7.79423i	−0.822132	−	0.284795i
$750$		0			0
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	−0.722718	−	0.691143i	$-0.757107\pi$
$751$	6.50000	−	11.2583i	0.237188	−	0.410822i	0.959906	+	0.280321i	$0.0904408\pi$
$752$		0			0
$753$		0			0
$754$	−1.50000	+	2.59808i	−0.0546268	+	0.0946164i
$755$	21.0000			0.764268
$756$		0			0
$757$	−22.0000			−0.799604			−0.399802	−	0.916602i	$-0.630921\pi$
$757$	−22.0000			−0.799604			−0.399802	+	0.916602i	$0.630921\pi$
$758$	14.0000	−	24.2487i	0.508503	−	0.880753i
$759$		0			0
$760$	−10.5000	−	18.1865i	−0.380875	−	0.659695i
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	0.0932544	+	0.995642i	$0.470273\pi$
$761$	−22.5000	+	38.9711i	−0.815624	+	1.41270i	−0.908879	+	0.417061i	$0.863060\pi$
$762$		0			0
$763$	26.0000	−	22.5167i	0.941263	−	0.815158i
$764$		0			0
$765$		0			0
$766$	7.50000	+	12.9904i	0.270986	+	0.469362i
$767$		0			0
$768$		0			0
$769$	23.0000			0.829401			0.414701	−	0.909958i	$-0.363886\pi$
$769$	23.0000			0.829401			0.414701	+	0.909958i	$0.363886\pi$
$770$	−22.5000	−	7.79423i	−0.810844	−	0.280885i
$771$		0			0
$772$	−7.00000	+	12.1244i	−0.251936	+	0.436365i
$773$	13.5000	+	23.3827i	0.485561	+	0.841017i	0.999862	−	0.0165929i	$-0.00528194\pi$
$773$	13.5000	+	23.3827i	0.485561	+	0.841017i	−0.514301	+	0.857610i	$0.671949\pi$
$774$		0			0
$775$	−16.0000	+	27.7128i	−0.574737	+	0.995474i
$776$	−1.00000			−0.0358979
$777$		0			0
$778$	−27.0000			−0.967997
$779$	−10.5000	+	18.1865i	−0.376202	+	0.651600i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	13.5000	−	23.3827i	0.482759	−	0.836163i
$783$		0			0
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$	66.0000			2.35564
$786$		0			0
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	0.999999	−	0.00110111i	$-0.000350496\pi$
$787$	14.0000	+	24.2487i	0.499046	+	0.864373i	−0.500953	+	0.865474i	$0.667017\pi$
$788$	9.00000	+	15.5885i	0.320612	+	0.555316i
$789$		0			0
$790$	48.0000			1.70776
$791$	−4.50000	−	23.3827i	−0.160002	−	0.831393i
$792$		0			0
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$	6.50000	+	11.2583i	0.230676	+	0.399543i
$795$		0			0
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	21.0000			0.743858			0.371929	−	0.928261i	$-0.378696\pi$
$797$	21.0000			0.743858			0.371929	+	0.928261i	$0.378696\pi$
$798$		0			0
$799$		0			0
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$		0			0
$802$	13.5000	+	23.3827i	0.476702	+	0.825671i
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$		0			0
$805$	54.0000	−	46.7654i	1.90325	−	1.64826i
$806$	−8.00000			−0.281788
$807$		0			0
$808$	1.50000	+	2.59808i	0.0527698	+	0.0914000i
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	−0.995466	−	0.0951198i	$-0.969677\pi$
$809$	−16.5000	−	28.5788i	−0.580109	−	1.00478i	0.415357	−	0.909659i	$-0.363657\pi$
$810$		0			0
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	6.00000	−	5.19615i	0.210559	−	0.182349i
$813$		0			0
$814$	1.50000	−	2.59808i	0.0525750	−	0.0910625i
$815$	−28.5000	−	49.3634i	−0.998311	−	1.72913i
$816$		0			0
$817$	−3.50000	+	6.06218i	−0.122449	+	0.212089i
$818$	−34.0000			−1.18878
$819$		0			0
$820$	9.00000			0.314294
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$	6.50000	−	11.2583i	0.226438	−	0.392203i
$825$		0			0
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$		0			0
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	0.754567	−	0.656223i	$-0.227847\pi$
$829$	−5.50000	−	9.52628i	−0.191023	−	0.330861i	−0.945589	+	0.325362i	$0.894514\pi$
$830$	13.5000	+	23.3827i	0.468592	+	0.811625i
$831$		0			0
$832$	−1.00000			−0.0346688
$833$	−16.5000	−	12.9904i	−0.571691	−	0.450090i
$834$		0			0
$835$	22.5000	−	38.9711i	0.778645	−	1.34865i
$836$	10.5000	+	18.1865i	0.363150	+	0.628994i
$837$		0			0
$838$	4.50000	−	7.79423i	0.155450	−	0.269247i
$839$	−15.0000			−0.517858			−0.258929	−	0.965896i	$-0.583369\pi$
$839$	−15.0000			−0.517858			−0.258929	+	0.965896i	$0.583369\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$	−17.5000	+	30.3109i	−0.603090	+	1.04458i
$843$		0			0
$844$	−2.50000	−	4.33013i	−0.0860535	−	0.149049i
$845$	−18.0000	+	31.1769i	−0.619219	+	1.07252i
$846$		0			0
$847$	−5.00000	−	1.73205i	−0.171802	−	0.0595140i
$848$	−3.00000			−0.103020
$849$		0			0
$850$	6.00000	+	10.3923i	0.205798	+	0.356453i
$851$	4.50000	+	7.79423i	0.154258	+	0.267183i
$852$		0			0
$853$	−1.00000			−0.0342393			−0.0171197	−	0.999853i	$-0.505450\pi$
$853$	−1.00000			−0.0342393			−0.0171197	+	0.999853i	$0.505450\pi$
$854$	−4.00000	+	3.46410i	−0.136877	+	0.118539i
$855$		0			0
$856$	4.50000	−	7.79423i	0.153807	−	0.266401i
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	0.890507	−	0.454969i	$-0.150350\pi$
$857$	1.50000	+	2.59808i	0.0512390	+	0.0887486i	−0.839268	+	0.543718i	$0.817016\pi$
$858$		0			0
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	−0.570064	−	0.821600i	$-0.693082\pi$
$859$	12.5000	−	21.6506i	0.426494	−	0.738710i	0.996559	+	0.0828900i	$0.0264150\pi$
$860$	3.00000			0.102299
$861$		0			0
$862$	−27.0000			−0.919624
$863$	−25.5000	+	44.1673i	−0.868030	+	1.50347i	−0.00402340	+	0.999992i	$0.501281\pi$
$863$	−25.5000	+	44.1673i	−0.868030	+	1.50347i	−0.864007	+	0.503480i	$0.832053\pi$
$864$		0			0
$865$	9.00000	+	15.5885i	0.306009	+	0.530023i
$866$	−1.00000	+	1.73205i	−0.0339814	+	0.0588575i
$867$		0			0
$868$	20.0000	+	6.92820i	0.678844	+	0.235159i
$869$	−48.0000			−1.62829
$870$		0			0
$871$	−2.00000	−	3.46410i	−0.0677674	−	0.117377i
$872$	6.50000	+	11.2583i	0.220118	+	0.381255i
$873$		0			0
$874$	−63.0000			−2.13101
$875$	−1.50000	−	7.79423i	−0.0507093	−	0.263493i
$876$		0			0
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	0.130224	+	0.991485i	$0.458430\pi$
$877$	−23.5000	+	40.7032i	−0.793539	+	1.37445i	−0.923763	+	0.382965i	$0.874903\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	4.50000	−	7.79423i	0.151695	−	0.262743i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	−16.5000	+	28.5788i	−0.554016	+	0.959583i	0.443964	+	0.896045i	$0.353572\pi$
$887$	−16.5000	+	28.5788i	−0.554016	+	0.959583i	−0.997979	+	0.0635387i	$0.979761\pi$
$888$		0			0
$889$	2.00000	+	10.3923i	0.0670778	+	0.348547i
$890$	9.00000			0.301681
$891$		0			0
$892$	0.500000	+	0.866025i	0.0167412	+	0.0289967i
$893$		0			0
$894$		0			0
$895$	−63.0000			−2.10586
$896$	2.50000	+	0.866025i	0.0835191	+	0.0289319i
$897$		0			0
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$	12.0000	+	20.7846i	0.400222	+	0.693206i
$900$		0			0
$901$	−4.50000	+	7.79423i	−0.149917	+	0.259663i
$902$	−9.00000			−0.299667
$903$		0			0
$904$	9.00000			0.299336
$905$	3.00000	−	5.19615i	0.0997234	−	0.172726i
$906$		0			0
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	0.963384	+	0.268126i	$0.0864043\pi$
$907$	21.5000	+	37.2391i	0.713896	+	1.23650i	−0.249488	+	0.968378i	$0.580262\pi$
$908$	−1.50000	+	2.59808i	−0.0497792	+	0.0862202i
$909$		0			0
$910$	−6.00000	+	5.19615i	−0.198898	+	0.172251i
$911$	−39.0000			−1.29213			−0.646064	−	0.763283i	$-0.723586\pi$
$911$	−39.0000			−1.29213			−0.646064	+	0.763283i	$0.723586\pi$
$912$		0			0
$913$	−13.5000	−	23.3827i	−0.446785	−	0.773854i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	−13.0000			−0.429532
$917$	−37.5000	−	12.9904i	−1.23836	−	0.428980i
$918$		0			0
$919$	−26.5000	+	45.8993i	−0.874154	+	1.51408i	−0.0164935	+	0.999864i	$0.505250\pi$
$919$	−26.5000	+	45.8993i	−0.874154	+	1.51408i	−0.857661	+	0.514216i	$0.828083\pi$
$920$	13.5000	+	23.3827i	0.445082	+	0.770904i
$921$		0			0
$922$	−4.50000	+	7.79423i	−0.148200	+	0.256689i
$923$	12.0000			0.394985
$924$		0			0
$925$	−4.00000			−0.131519
$926$	−20.5000	+	35.5070i	−0.673672	+	1.16683i
$927$		0			0
$928$	1.50000	+	2.59808i	0.0492399	+	0.0852860i
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	−7.00000	+	48.4974i	−0.229416	+	1.58944i
$932$	−3.00000			−0.0982683
$933$		0			0
$934$	−1.50000	−	2.59808i	−0.0490815	−	0.0850117i
$935$	−13.5000	−	23.3827i	−0.441497	−	0.764696i
$936$		0			0
$937$	26.0000			0.849383			0.424691	−	0.905338i	$-0.360383\pi$
$937$	26.0000			0.849383			0.424691	+	0.905338i	$0.360383\pi$
$938$	2.00000	+	10.3923i	0.0653023	+	0.339321i
$939$		0			0
$940$		0			0
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	0.812975	−	0.582298i	$-0.197846\pi$
$941$	−3.00000	−	5.19615i	−0.0977972	−	0.169390i	−0.910773	+	0.412908i	$0.864513\pi$
$942$		0			0
$943$	13.5000	−	23.3827i	0.439620	−	0.761445i
$944$		0			0
$945$		0			0
$946$	−3.00000			−0.0975384
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	−0.751918	−	0.659256i	$-0.770871\pi$
$947$	6.00000	−	10.3923i	0.194974	−	0.337705i	0.946892	+	0.321552i	$0.104204\pi$
$948$		0			0
$949$	5.50000	+	9.52628i	0.178538	+	0.309236i
$950$	14.0000	−	24.2487i	0.454220	−	0.786732i
$951$		0			0
$952$	6.00000	−	5.19615i	0.194461	−	0.168408i
$953$	−6.00000			−0.194359			−0.0971795	−	0.995267i	$-0.530982\pi$
$953$	−6.00000			−0.194359			−0.0971795	+	0.995267i	$0.530982\pi$
$954$		0			0
$955$		0			0
$956$	−1.50000	−	2.59808i	−0.0485135	−	0.0840278i
$957$		0			0
$958$	3.00000			0.0969256
$959$	−18.0000	+	15.5885i	−0.581250	+	0.503378i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	−0.500000	−	0.866025i	−0.0161206	−	0.0279218i
$963$		0			0
$964$	6.50000	−	11.2583i	0.209351	−	0.362606i
$965$	−42.0000			−1.35203
$966$		0			0
$967$	41.0000			1.31847			0.659236	−	0.751936i	$-0.270880\pi$
$967$	41.0000			1.31847			0.659236	+	0.751936i	$0.270880\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$	−1.50000	−	2.59808i	−0.0481621	−	0.0834192i
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$		0			0
$973$	3.50000	+	18.1865i	0.112205	+	0.583033i
$974$	−25.0000			−0.801052
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	0.519841	−	0.854263i	$-0.325991\pi$
$977$	−15.0000	−	25.9808i	−0.479893	−	0.831198i	−0.999734	+	0.0230645i	$0.992658\pi$
$978$		0			0
$979$	−9.00000			−0.287641
$980$	19.5000	−	7.79423i	0.622905	−	0.248978i
$981$		0			0
$982$	10.5000	−	18.1865i	0.335068	−	0.580356i
$983$	−7.50000	−	12.9904i	−0.239213	−	0.414329i	0.721276	−	0.692648i	$-0.243556\pi$
$983$	−7.50000	−	12.9904i	−0.239213	−	0.414329i	−0.960489	+	0.278319i	$0.910223\pi$
$984$		0			0
$985$	−27.0000	+	46.7654i	−0.860292	+	1.49007i
$986$	9.00000			0.286618
$987$		0			0
$988$	7.00000			0.222700
$989$	4.50000	−	7.79423i	0.143092	−	0.247842i
$990$		0			0
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	0.993364	−	0.115015i	$-0.0366917\pi$
$991$	12.5000	+	21.6506i	0.397076	+	0.687755i	−0.596288	+	0.802771i	$0.703358\pi$
$992$	−4.00000	+	6.92820i	−0.127000	+	0.219971i
$993$		0			0
$994$	−30.0000	−	10.3923i	−0.951542	−	0.329624i
$995$	75.0000			2.37766
$996$		0			0
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	0.950405	−	0.311014i	$-0.100668\pi$
$997$	6.50000	+	11.2583i	0.205857	+	0.356555i	−0.744548	+	0.667568i	$0.767335\pi$
$998$	12.5000	+	21.6506i	0.395681	+	0.685339i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.g.c.163.1		2
3.2	odd	2		1134.2.g.e.163.1		2
7.2	even	3		7938.2.a.t.1.1		1
7.4	even	3	inner	1134.2.g.c.487.1		2
7.5	odd	6		7938.2.a.be.1.1		1
9.2	odd	6		126.2.e.a.121.1	yes	2
9.4	even	3		378.2.h.a.289.1		2
9.5	odd	6		126.2.h.b.79.1	yes	2
9.7	even	3		378.2.e.b.37.1		2
21.2	odd	6		7938.2.a.m.1.1		1
21.5	even	6		7938.2.a.b.1.1		1
21.11	odd	6		1134.2.g.e.487.1		2
36.7	odd	6		3024.2.q.f.2305.1		2
36.11	even	6		1008.2.q.a.625.1		2
36.23	even	6		1008.2.t.f.961.1		2
36.31	odd	6		3024.2.t.a.289.1		2
63.2	odd	6		882.2.f.i.589.1		2
63.4	even	3		378.2.e.b.235.1		2
63.5	even	6		882.2.f.g.295.1		2
63.11	odd	6		126.2.h.b.67.1	yes	2
63.13	odd	6		2646.2.h.d.667.1		2
63.16	even	3		2646.2.f.d.1765.1		2
63.20	even	6		882.2.e.c.373.1		2
63.23	odd	6		882.2.f.i.295.1		2
63.25	even	3		378.2.h.a.361.1		2
63.31	odd	6		2646.2.e.g.2125.1		2
63.32	odd	6		126.2.e.a.25.1	✓	2
63.34	odd	6		2646.2.e.g.1549.1		2
63.38	even	6		882.2.h.i.67.1		2
63.40	odd	6		2646.2.f.a.883.1		2
63.41	even	6		882.2.h.i.79.1		2
63.47	even	6		882.2.f.g.589.1		2
63.52	odd	6		2646.2.h.d.361.1		2
63.58	even	3		2646.2.f.d.883.1		2
63.59	even	6		882.2.e.c.655.1		2
63.61	odd	6		2646.2.f.a.1765.1		2
252.11	even	6		1008.2.t.f.193.1		2
252.67	odd	6		3024.2.q.f.2881.1		2
252.95	even	6		1008.2.q.a.529.1		2
252.151	odd	6		3024.2.t.a.1873.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.e.a.25.1	✓	2	63.32	odd	6
126.2.e.a.121.1	yes	2	9.2	odd	6
126.2.h.b.67.1	yes	2	63.11	odd	6
126.2.h.b.79.1	yes	2	9.5	odd	6
378.2.e.b.37.1		2	9.7	even	3
378.2.e.b.235.1		2	63.4	even	3
378.2.h.a.289.1		2	9.4	even	3
378.2.h.a.361.1		2	63.25	even	3
882.2.e.c.373.1		2	63.20	even	6
882.2.e.c.655.1		2	63.59	even	6
882.2.f.g.295.1		2	63.5	even	6
882.2.f.g.589.1		2	63.47	even	6
882.2.f.i.295.1		2	63.23	odd	6
882.2.f.i.589.1		2	63.2	odd	6
882.2.h.i.67.1		2	63.38	even	6
882.2.h.i.79.1		2	63.41	even	6
1008.2.q.a.529.1		2	252.95	even	6
1008.2.q.a.625.1		2	36.11	even	6
1008.2.t.f.193.1		2	252.11	even	6
1008.2.t.f.961.1		2	36.23	even	6
1134.2.g.c.163.1		2	1.1	even	1	trivial
1134.2.g.c.487.1		2	7.4	even	3	inner
1134.2.g.e.163.1		2	3.2	odd	2
1134.2.g.e.487.1		2	21.11	odd	6
2646.2.e.g.1549.1		2	63.34	odd	6
2646.2.e.g.2125.1		2	63.31	odd	6
2646.2.f.a.883.1		2	63.40	odd	6
2646.2.f.a.1765.1		2	63.61	odd	6
2646.2.f.d.883.1		2	63.58	even	3
2646.2.f.d.1765.1		2	63.16	even	3
2646.2.h.d.361.1		2	63.52	odd	6
2646.2.h.d.667.1		2	63.13	odd	6
3024.2.q.f.2305.1		2	36.7	odd	6
3024.2.q.f.2881.1		2	252.67	odd	6
3024.2.t.a.289.1		2	36.31	odd	6
3024.2.t.a.1873.1		2	252.151	odd	6
7938.2.a.b.1.1		1	21.5	even	6
7938.2.a.m.1.1		1	21.2	odd	6
7938.2.a.t.1.1		1	7.2	even	3
7938.2.a.be.1.1		1	7.5	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:	\( N \)	\(=\)	\( 1134 = 2 \cdot 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1134.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(1.50000 - 2.59808i) q^{5} +(-0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(1.50000 + 2.59808i) q^{10} +(-1.50000 - 2.59808i) q^{11} -1.00000 q^{13} +(2.50000 + 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} +(3.50000 - 6.06218i) q^{19} -3.00000 q^{20} +3.00000 q^{22} +(-4.50000 + 7.79423i) q^{23} +(-2.00000 - 3.46410i) q^{25} +(0.500000 - 0.866025i) q^{26} +(-2.00000 + 1.73205i) q^{28} -3.00000 q^{29} +(-4.00000 - 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -3.00000 q^{34} +(-7.50000 - 2.59808i) q^{35} +(0.500000 - 0.866025i) q^{37} +(3.50000 + 6.06218i) q^{38} +(1.50000 - 2.59808i) q^{40} -3.00000 q^{41} -1.00000 q^{43} +(-1.50000 + 2.59808i) q^{44} +(-4.50000 - 7.79423i) q^{46} +(-6.50000 + 2.59808i) q^{49} +4.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(1.50000 + 2.59808i) q^{53} -9.00000 q^{55} +(-0.500000 - 2.59808i) q^{56} +(1.50000 - 2.59808i) q^{58} +(-1.00000 + 1.73205i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(-1.50000 + 2.59808i) q^{65} +(2.00000 + 3.46410i) q^{67} +(1.50000 - 2.59808i) q^{68} +(6.00000 - 5.19615i) q^{70} -12.0000 q^{71} +(-5.50000 - 9.52628i) q^{73} +(0.500000 + 0.866025i) q^{74} -7.00000 q^{76} +(-6.00000 + 5.19615i) q^{77} +(8.00000 - 13.8564i) q^{79} +(1.50000 + 2.59808i) q^{80} +(1.50000 - 2.59808i) q^{82} +9.00000 q^{83} +9.00000 q^{85} +(0.500000 - 0.866025i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(1.50000 - 2.59808i) q^{89} +(0.500000 + 2.59808i) q^{91} +9.00000 q^{92} +(-10.5000 - 18.1865i) q^{95} -1.00000 q^{97} +(1.00000 - 6.92820i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 3 q^{5} - q^{7} + 2 q^{8} + 3 q^{10} - 3 q^{11} - 2 q^{13} + 5 q^{14} - q^{16} + 3 q^{17} + 7 q^{19} - 6 q^{20} + 6 q^{22} - 9 q^{23} - 4 q^{25} + q^{26} - 4 q^{28} - 6 q^{29} - 8 q^{31} - q^{32} - 6 q^{34} - 15 q^{35} + q^{37} + 7 q^{38} + 3 q^{40} - 6 q^{41} - 2 q^{43} - 3 q^{44} - 9 q^{46} - 13 q^{49} + 8 q^{50} + q^{52} + 3 q^{53} - 18 q^{55} - q^{56} + 3 q^{58} - 2 q^{61} + 16 q^{62} + 2 q^{64} - 3 q^{65} + 4 q^{67} + 3 q^{68} + 12 q^{70} - 24 q^{71} - 11 q^{73} + q^{74} - 14 q^{76} - 12 q^{77} + 16 q^{79} + 3 q^{80} + 3 q^{82} + 18 q^{83} + 18 q^{85} + q^{86} - 3 q^{88} + 3 q^{89} + q^{91} + 18 q^{92} - 21 q^{95} - 2 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 3 * q^5 - q^7 + 2 * q^8 + 3 * q^10 - 3 * q^11 - 2 * q^13 + 5 * q^14 - q^16 + 3 * q^17 + 7 * q^19 - 6 * q^20 + 6 * q^22 - 9 * q^23 - 4 * q^25 + q^26 - 4 * q^28 - 6 * q^29 - 8 * q^31 - q^32 - 6 * q^34 - 15 * q^35 + q^37 + 7 * q^38 + 3 * q^40 - 6 * q^41 - 2 * q^43 - 3 * q^44 - 9 * q^46 - 13 * q^49 + 8 * q^50 + q^52 + 3 * q^53 - 18 * q^55 - q^56 + 3 * q^58 - 2 * q^61 + 16 * q^62 + 2 * q^64 - 3 * q^65 + 4 * q^67 + 3 * q^68 + 12 * q^70 - 24 * q^71 - 11 * q^73 + q^74 - 14 * q^76 - 12 * q^77 + 16 * q^79 + 3 * q^80 + 3 * q^82 + 18 * q^83 + 18 * q^85 + q^86 - 3 * q^88 + 3 * q^89 + q^91 + 18 * q^92 - 21 * q^95 - 2 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more