LMFDB - Embedded newform 1134.2.h.h.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(109,1134)]

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([2, 4]))

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

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

chi := DirichletCharacter("1134.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.05503558921$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.541
Dual form			1134.2.h.h.109.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(2.00000 - 3.46410i) q^{19} +(-2.00000 + 3.46410i) q^{20} +(-1.00000 - 1.73205i) q^{22} -1.00000 q^{23} +11.0000 q^{25} +(-3.00000 + 5.19615i) q^{26} +(-2.50000 + 0.866025i) q^{28} +(-2.00000 + 3.46410i) q^{29} +(4.50000 - 7.79423i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(8.00000 + 6.92820i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{38} +4.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} +(4.50000 + 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-5.50000 - 9.52628i) q^{50} +6.00000 q^{52} +(6.00000 + 10.3923i) q^{53} +8.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +4.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} -9.00000 q^{62} +1.00000 q^{64} +(-12.0000 - 20.7846i) q^{65} +(7.00000 - 12.1244i) q^{67} +2.00000 q^{68} +(2.00000 - 10.3923i) q^{70} -1.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(4.00000 + 3.46410i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(-7.00000 + 12.1244i) q^{83} +(-4.00000 - 6.92820i) q^{85} +2.00000 q^{86} +2.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +(3.00000 - 15.5885i) q^{91} +(0.500000 - 0.866025i) q^{92} +(4.50000 - 7.79423i) q^{94} +(8.00000 - 13.8564i) q^{95} +(-5.00000 + 8.66025i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 8 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 8 * q^5 + 4 * q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 8 q^{5} + 4 q^{7} + 2 q^{8} - 4 q^{10} + 4 q^{11} - 6 q^{13} + q^{14} - q^{16} - 2 q^{17} + 4 q^{19} - 4 q^{20} - 2 q^{22} - 2 q^{23} + 22 q^{25} - 6 q^{26} - 5 q^{28} - 4 q^{29} + 9 q^{31} - q^{32} - 2 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{38} + 8 q^{40} - 3 q^{41} - 2 q^{43} - 2 q^{44} + q^{46} + 9 q^{47} + 2 q^{49} - 11 q^{50} + 12 q^{52} + 12 q^{53} + 16 q^{55} + 4 q^{56} + 8 q^{58} - 4 q^{59} - 6 q^{61} - 18 q^{62} + 2 q^{64} - 24 q^{65} + 14 q^{67} + 4 q^{68} + 4 q^{70} - 2 q^{71} - 7 q^{73} + 16 q^{74} + 4 q^{76} + 8 q^{77} + 3 q^{79} - 4 q^{80} - 3 q^{82} - 14 q^{83} - 8 q^{85} + 4 q^{86} + 4 q^{88} + 3 q^{89} + 6 q^{91} + q^{92} + 9 q^{94} + 16 q^{95} - 10 q^{97} + 11 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 8 * q^5 + 4 * q^7 + 2 * q^8 - 4 * q^10 + 4 * q^11 - 6 * q^13 + q^14 - q^16 - 2 * q^17 + 4 * q^19 - 4 * q^20 - 2 * q^22 - 2 * q^23 + 22 * q^25 - 6 * q^26 - 5 * q^28 - 4 * q^29 + 9 * q^31 - q^32 - 2 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^38 + 8 * q^40 - 3 * q^41 - 2 * q^43 - 2 * q^44 + q^46 + 9 * q^47 + 2 * q^49 - 11 * q^50 + 12 * q^52 + 12 * q^53 + 16 * q^55 + 4 * q^56 + 8 * q^58 - 4 * q^59 - 6 * q^61 - 18 * q^62 + 2 * q^64 - 24 * q^65 + 14 * q^67 + 4 * q^68 + 4 * q^70 - 2 * q^71 - 7 * q^73 + 16 * q^74 + 4 * q^76 + 8 * q^77 + 3 * q^79 - 4 * q^80 - 3 * q^82 - 14 * q^83 - 8 * q^85 + 4 * q^86 + 4 * q^88 + 3 * q^89 + 6 * q^91 + q^92 + 9 * q^94 + 16 * q^95 - 10 * q^97 + 11 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$325$	$407$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	4.00000			1.78885			0.894427	−	0.447214i	$-0.147584\pi$
$5$	4.00000			1.78885			0.894427	+	0.447214i	$0.147584\pi$
$6$		0			0
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$7$	2.00000	+	1.73205i	0.755929	+	0.654654i
$8$	1.00000			0.353553
$9$		0			0
$10$	−2.00000	−	3.46410i	−0.632456	−	1.09545i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	0.500000	−	2.59808i	0.133631	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	0.718900	−	0.695113i	$-0.244646\pi$
$17$	−1.00000	−	1.73205i	−0.242536	−	0.420084i	−0.961436	+	0.275029i	$0.911312\pi$
$18$		0			0
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	−0.540068	−	0.841621i	$-0.681602\pi$
$19$	2.00000	−	3.46410i	0.458831	−	0.794719i	0.998899	+	0.0469020i	$0.0149348\pi$
$20$	−2.00000	+	3.46410i	−0.447214	+	0.774597i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$		0			0
$25$	11.0000			2.20000
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$		0			0
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	−0.989780	−	0.142605i	$-0.954452\pi$
$29$	−2.00000	+	3.46410i	−0.371391	+	0.643268i	0.618389	+	0.785872i	$0.287786\pi$
$30$		0			0
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	−0.105869	−	0.994380i	$-0.533762\pi$
$31$	4.50000	−	7.79423i	0.808224	−	1.39988i	0.914093	−	0.405505i	$-0.132904\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	8.00000	+	6.92820i	1.35225	+	1.17108i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$	−4.00000			−0.648886
$39$		0			0
$40$	4.00000			0.632456
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	0.724797	−	0.688963i	$-0.241934\pi$
$41$	−1.50000	−	2.59808i	−0.234261	−	0.405751i	−0.959058	+	0.283211i	$0.908600\pi$
$42$		0			0
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	−0.932145	−	0.362084i	$-0.882065\pi$
$43$	−1.00000	+	1.73205i	−0.152499	+	0.264135i	0.779647	+	0.626219i	$0.215399\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$		0			0
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−5.50000	−	9.52628i	−0.777817	−	1.34722i
$51$		0			0
$52$	6.00000			0.832050
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$	2.00000	+	1.73205i	0.267261	+	0.231455i
$57$		0			0
$58$	4.00000			0.525226
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	0.607535	−	0.794293i	$-0.292159\pi$
$61$	−3.00000	−	5.19615i	−0.384111	−	0.665299i	−0.991645	+	0.128994i	$0.958825\pi$
$62$	−9.00000			−1.14300
$63$		0			0
$64$	1.00000			0.125000
$65$	−12.0000	−	20.7846i	−1.48842	−	2.57801i
$66$		0			0
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	−0.0212861	−	0.999773i	$-0.506776\pi$
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	0.876472	−	0.481452i	$-0.159891\pi$
$68$	2.00000			0.242536
$69$		0			0
$70$	2.00000	−	10.3923i	0.239046	−	1.24212i
$71$	−1.00000			−0.118678			−0.0593391	−	0.998238i	$-0.518899\pi$
$71$	−1.00000			−0.118678			−0.0593391	+	0.998238i	$0.518899\pi$
$72$		0			0
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	0.585206	−	0.810885i	$-0.301014\pi$
$73$	−3.50000	−	6.06218i	−0.409644	−	0.709524i	−0.994850	+	0.101361i	$0.967680\pi$
$74$	8.00000			0.929981
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	4.00000	+	3.46410i	0.455842	+	0.394771i
$78$		0			0
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	0.937985	−	0.346675i	$-0.112689\pi$
$79$	1.50000	+	2.59808i	0.168763	+	0.292306i	−0.769222	+	0.638982i	$0.779356\pi$
$80$	−2.00000	−	3.46410i	−0.223607	−	0.387298i
$81$		0			0
$82$	−1.50000	+	2.59808i	−0.165647	+	0.286910i
$83$	−7.00000	+	12.1244i	−0.768350	+	1.33082i	0.170107	+	0.985426i	$0.445589\pi$
$83$	−7.00000	+	12.1244i	−0.768350	+	1.33082i	−0.938457	+	0.345395i	$0.887745\pi$
$84$		0			0
$85$	−4.00000	−	6.92820i	−0.433861	−	0.751469i
$86$	2.00000			0.215666
$87$		0			0
$88$	2.00000			0.213201
$89$	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
$91$	3.00000	−	15.5885i	0.314485	−	1.63411i
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$		0			0
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	8.00000	−	13.8564i	0.820783	−	1.42164i
$96$		0			0
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	0.492287	+	0.870433i	$0.336161\pi$
$97$	−5.00000	+	8.66025i	−0.507673	+	0.879316i	−0.999961	+	0.00888289i	$0.997172\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$		0			0
$100$	−5.50000	+	9.52628i	−0.550000	+	0.952628i
$101$	−8.00000			−0.796030			−0.398015	−	0.917379i	$-0.630301\pi$
$101$	−8.00000			−0.796030			−0.398015	+	0.917379i	$0.630301\pi$
$102$		0			0
$103$	−7.00000			−0.689730			−0.344865	−	0.938652i	$-0.612075\pi$
$103$	−7.00000			−0.689730			−0.344865	+	0.938652i	$0.612075\pi$
$104$	−3.00000	−	5.19615i	−0.294174	−	0.509525i
$105$		0			0
$106$	6.00000	−	10.3923i	0.582772	−	1.00939i
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.00813215	−	0.999967i	$-0.497411\pi$
$107$	9.00000	−	15.5885i	0.870063	−	1.50699i	0.861931	−	0.507026i	$-0.169255\pi$
$108$		0			0
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$	−4.00000	−	6.92820i	−0.381385	−	0.660578i
$111$		0			0
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	0.981003	+	0.193993i	$0.0621440\pi$
$113$	7.00000	+	12.1244i	0.658505	+	1.14056i	−0.322498	+	0.946570i	$0.604523\pi$
$114$		0			0
$115$	−4.00000			−0.373002
$116$	−2.00000	−	3.46410i	−0.185695	−	0.321634i
$117$		0			0
$118$	4.00000			0.368230
$119$	1.00000	−	5.19615i	0.0916698	−	0.476331i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−3.00000	+	5.19615i	−0.271607	+	0.470438i
$123$		0			0
$124$	4.50000	+	7.79423i	0.404112	+	0.699942i
$125$	24.0000			2.14663
$126$		0			0
$127$	3.00000			0.266207			0.133103	−	0.991102i	$-0.457506\pi$
$127$	3.00000			0.266207			0.133103	+	0.991102i	$0.457506\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−12.0000	+	20.7846i	−1.05247	+	1.82293i
$131$	10.0000			0.873704			0.436852	−	0.899533i	$-0.356093\pi$
$131$	10.0000			0.873704			0.436852	+	0.899533i	$0.356093\pi$
$132$		0			0
$133$	10.0000	−	3.46410i	0.867110	−	0.300376i
$134$	−14.0000			−1.20942
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−5.00000			−0.427179			−0.213589	−	0.976924i	$-0.568515\pi$
$137$	−5.00000			−0.427179			−0.213589	+	0.976924i	$0.568515\pi$
$138$		0			0
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	0.905314	−	0.424743i	$-0.139635\pi$
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	−0.820495	+	0.571654i	$0.806302\pi$
$140$	−10.0000	+	3.46410i	−0.845154	+	0.292770i
$141$		0			0
$142$	0.500000	+	0.866025i	0.0419591	+	0.0726752i
$143$	−6.00000	−	10.3923i	−0.501745	−	0.869048i
$144$		0			0
$145$	−8.00000	+	13.8564i	−0.664364	+	1.15071i
$146$	−3.50000	+	6.06218i	−0.289662	+	0.501709i
$147$		0			0
$148$	−4.00000	−	6.92820i	−0.328798	−	0.569495i
$149$		0			0			−	1.00000i	$-0.5\pi$
$149$		0			0				1.00000i	$0.5\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$	2.00000	−	3.46410i	0.162221	−	0.280976i
$153$		0			0
$154$	1.00000	−	5.19615i	0.0805823	−	0.418718i
$155$	18.0000	−	31.1769i	1.44579	−	2.50419i
$156$		0			0
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	−0.903167	−	0.429289i	$-0.858764\pi$
$157$	−1.00000	+	1.73205i	−0.0798087	+	0.138233i	0.823359	+	0.567521i	$0.192098\pi$
$158$	1.50000	−	2.59808i	0.119334	−	0.206692i
$159$		0			0
$160$	−2.00000	+	3.46410i	−0.158114	+	0.273861i
$161$	−2.00000	−	1.73205i	−0.157622	−	0.136505i
$162$		0			0
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	0.450110	+	0.892973i	$0.351385\pi$
$163$	−7.00000	+	12.1244i	−0.548282	+	0.949653i	−0.998392	+	0.0566798i	$0.981949\pi$
$164$	3.00000			0.234261
$165$		0			0
$166$	14.0000			1.08661
$167$	−3.50000	−	6.06218i	−0.270838	−	0.469105i	0.698239	−	0.715865i	$-0.253967\pi$
$167$	−3.50000	−	6.06218i	−0.270838	−	0.469105i	−0.969077	+	0.246760i	$0.920634\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	−4.00000	+	6.92820i	−0.306786	+	0.531369i
$171$		0			0
$172$	−1.00000	−	1.73205i	−0.0762493	−	0.132068i
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	0.999293	+	0.0375896i	$0.0119679\pi$
$173$	7.00000	+	12.1244i	0.532200	+	0.921798i	−0.467093	+	0.884208i	$0.654699\pi$
$174$		0			0
$175$	22.0000	+	19.0526i	1.66304	+	1.44024i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$		0			0
$178$	−3.00000			−0.224860
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$		0			0			−	1.00000i	$-0.5\pi$
$181$		0			0				1.00000i	$0.5\pi$
$182$	−15.0000	+	5.19615i	−1.11187	+	0.385164i
$183$		0			0
$184$	−1.00000			−0.0737210
$185$	−16.0000	+	27.7128i	−1.17634	+	2.03749i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	−9.00000			−0.656392
$189$		0			0
$190$	−16.0000			−1.16076
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	−0.941865	−	0.335993i	$-0.890928\pi$
$193$	−2.50000	+	4.33013i	−0.179954	+	0.311689i	0.761911	+	0.647682i	$0.224262\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$	−16.0000			−1.13995			−0.569976	−	0.821661i	$-0.693048\pi$
$197$	−16.0000			−1.13995			−0.569976	+	0.821661i	$0.693048\pi$
$198$		0			0
$199$	−2.50000	−	4.33013i	−0.177220	−	0.306955i	0.763707	−	0.645563i	$-0.223377\pi$
$199$	−2.50000	−	4.33013i	−0.177220	−	0.306955i	−0.940927	+	0.338608i	$0.890044\pi$
$200$	11.0000			0.777817
$201$		0			0
$202$	4.00000	+	6.92820i	0.281439	+	0.487467i
$203$	−10.0000	+	3.46410i	−0.701862	+	0.243132i
$204$		0			0
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$	3.50000	+	6.06218i	0.243857	+	0.422372i
$207$		0			0
$208$	−3.00000	+	5.19615i	−0.208013	+	0.360288i
$209$	4.00000	−	6.92820i	0.276686	−	0.479234i
$210$		0			0
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	0.517884	−	0.855451i	$-0.326720\pi$
$211$	−7.00000	−	12.1244i	−0.481900	−	0.834675i	−0.999784	+	0.0207756i	$0.993386\pi$
$212$	−12.0000			−0.824163
$213$		0			0
$214$	−18.0000			−1.23045
$215$	−4.00000	+	6.92820i	−0.272798	+	0.472500i
$216$		0			0
$217$	22.5000	−	7.79423i	1.52740	−	0.529107i
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$		0			0
$220$	−4.00000	+	6.92820i	−0.269680	+	0.467099i
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$		0			0
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	−0.0552786	−	0.998471i	$-0.517605\pi$
$223$	12.5000	−	21.6506i	0.837062	−	1.44983i	0.892341	−	0.451363i	$-0.149062\pi$
$224$	−2.50000	+	0.866025i	−0.167038	+	0.0578638i
$225$		0			0
$226$	7.00000	−	12.1244i	0.465633	−	0.806500i
$227$	30.0000			1.99117			0.995585	−	0.0938647i	$-0.0299221\pi$
$227$	30.0000			1.99117			0.995585	+	0.0938647i	$0.0299221\pi$
$228$		0			0
$229$	−20.0000			−1.32164			−0.660819	−	0.750546i	$-0.729791\pi$
$229$	−20.0000			−1.32164			−0.660819	+	0.750546i	$0.729791\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	0.0280525	+	0.999606i	$0.491069\pi$
$233$	−13.0000	+	22.5167i	−0.851658	+	1.47512i	−0.879711	+	0.475509i	$0.842264\pi$
$234$		0			0
$235$	18.0000	+	31.1769i	1.17419	+	2.03376i
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$		0			0
$238$	−5.00000	+	1.73205i	−0.324102	+	0.112272i
$239$	−4.50000	−	7.79423i	−0.291081	−	0.504167i	0.682985	−	0.730433i	$-0.260682\pi$
$239$	−4.50000	−	7.79423i	−0.291081	−	0.504167i	−0.974066	+	0.226266i	$0.927348\pi$
$240$		0			0
$241$	−7.00000			−0.450910			−0.225455	−	0.974254i	$-0.572387\pi$
$241$	−7.00000			−0.450910			−0.225455	+	0.974254i	$0.572387\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$		0			0
$244$	6.00000			0.384111
$245$	4.00000	+	27.7128i	0.255551	+	1.77051i
$246$		0			0
$247$	−24.0000			−1.52708
$248$	4.50000	−	7.79423i	0.285750	−	0.494934i
$249$		0			0
$250$	−12.0000	−	20.7846i	−0.758947	−	1.31453i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	−1.50000	−	2.59808i	−0.0941184	−	0.163018i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−3.00000			−0.187135			−0.0935674	−	0.995613i	$-0.529827\pi$
$257$	−3.00000			−0.187135			−0.0935674	+	0.995613i	$0.529827\pi$
$258$		0			0
$259$	−20.0000	+	6.92820i	−1.24274	+	0.430498i
$260$	24.0000			1.48842
$261$		0			0
$262$	−5.00000	−	8.66025i	−0.308901	−	0.535032i
$263$	−24.0000			−1.47990			−0.739952	−	0.672660i	$-0.765152\pi$
$263$	−24.0000			−1.47990			−0.739952	+	0.672660i	$0.765152\pi$
$264$		0			0
$265$	24.0000	+	41.5692i	1.47431	+	2.55358i
$266$	−8.00000	−	6.92820i	−0.490511	−	0.424795i
$267$		0			0
$268$	7.00000	+	12.1244i	0.427593	+	0.740613i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$		0			0
$274$	2.50000	+	4.33013i	0.151031	+	0.261593i
$275$	22.0000			1.32665
$276$		0			0
$277$	26.0000			1.56219			0.781094	−	0.624413i	$-0.214662\pi$
$277$	26.0000			1.56219			0.781094	+	0.624413i	$0.214662\pi$
$278$	1.00000	−	1.73205i	0.0599760	−	0.103882i
$279$		0			0
$280$	8.00000	+	6.92820i	0.478091	+	0.414039i
$281$	−2.50000	+	4.33013i	−0.149137	+	0.258314i	−0.930909	−	0.365251i	$-0.880983\pi$
$281$	−2.50000	+	4.33013i	−0.149137	+	0.258314i	0.781771	+	0.623565i	$0.214316\pi$
$282$		0			0
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	−0.919327	−	0.393494i	$-0.871266\pi$
$283$	−2.00000	+	3.46410i	−0.118888	+	0.205919i	0.800439	+	0.599414i	$0.204600\pi$
$284$	0.500000	−	0.866025i	0.0296695	−	0.0513892i
$285$		0			0
$286$	−6.00000	+	10.3923i	−0.354787	+	0.614510i
$287$	1.50000	−	7.79423i	0.0885422	−	0.460079i
$288$		0			0
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	16.0000			0.939552
$291$		0			0
$292$	7.00000			0.409644
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	0.764990	−	0.644042i	$-0.222744\pi$
$293$	−3.00000	−	5.19615i	−0.175262	−	0.303562i	−0.940252	+	0.340480i	$0.889411\pi$
$294$		0			0
$295$	−8.00000	+	13.8564i	−0.465778	+	0.806751i
$296$	−4.00000	+	6.92820i	−0.232495	+	0.402694i
$297$		0			0
$298$		0			0
$299$	3.00000	+	5.19615i	0.173494	+	0.300501i
$300$		0			0
$301$	−5.00000	+	1.73205i	−0.288195	+	0.0998337i
$302$	8.50000	+	14.7224i	0.489120	+	0.847181i
$303$		0			0
$304$	−4.00000			−0.229416
$305$	−12.0000	−	20.7846i	−0.687118	−	1.19012i
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	−5.00000	+	1.73205i	−0.284901	+	0.0986928i
$309$		0			0
$310$	−36.0000			−2.04466
$311$	−8.00000	+	13.8564i	−0.453638	+	0.785725i	−0.998609	−	0.0527306i	$-0.983208\pi$
$311$	−8.00000	+	13.8564i	−0.453638	+	0.785725i	0.544970	+	0.838455i	$0.316541\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	2.00000			0.112867
$315$		0			0
$316$	−3.00000			−0.168763
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	4.00000			0.223607
$321$		0			0
$322$	−0.500000	+	2.59808i	−0.0278639	+	0.144785i
$323$	−8.00000			−0.445132
$324$		0			0
$325$	−33.0000	−	57.1577i	−1.83051	−	3.17054i
$326$	14.0000			0.775388
$327$		0			0
$328$	−1.50000	−	2.59808i	−0.0828236	−	0.143455i
$329$	−4.50000	+	23.3827i	−0.248093	+	1.28913i
$330$		0			0
$331$	17.0000	+	29.4449i	0.934405	+	1.61844i	0.775692	+	0.631111i	$0.217401\pi$
$331$	17.0000	+	29.4449i	0.934405	+	1.61844i	0.158712	+	0.987325i	$0.449266\pi$
$332$	−7.00000	−	12.1244i	−0.384175	−	0.665410i
$333$		0			0
$334$	−3.50000	+	6.06218i	−0.191511	+	0.331708i
$335$	28.0000	−	48.4974i	1.52980	−	2.64970i
$336$		0			0
$337$	9.00000	+	15.5885i	0.490261	+	0.849157i	0.999937	−	0.0112091i	$-0.00356804\pi$
$337$	9.00000	+	15.5885i	0.490261	+	0.849157i	−0.509676	+	0.860366i	$0.670235\pi$
$338$	23.0000			1.25104
$339$		0			0
$340$	8.00000			0.433861
$341$	9.00000	−	15.5885i	0.487377	−	0.844162i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$	−1.00000	+	1.73205i	−0.0539164	+	0.0933859i
$345$		0			0
$346$	7.00000	−	12.1244i	0.376322	−	0.651809i
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	−0.658824	−	0.752297i	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	−0.738883	−	0.673833i	$-0.764647\pi$
$349$	4.00000	−	6.92820i	0.214115	−	0.370858i	0.952998	+	0.302975i	$0.0979799\pi$
$350$	5.50000	−	28.5788i	0.293987	−	1.52760i
$351$		0			0
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	−3.00000			−0.159674			−0.0798369	−	0.996808i	$-0.525440\pi$
$353$	−3.00000			−0.159674			−0.0798369	+	0.996808i	$0.525440\pi$
$354$		0			0
$355$	−4.00000			−0.212298
$356$	1.50000	+	2.59808i	0.0794998	+	0.137698i
$357$		0			0
$358$	−3.00000	+	5.19615i	−0.158555	+	0.274625i
$359$	−12.5000	+	21.6506i	−0.659725	+	1.14268i	0.320962	+	0.947092i	$0.395994\pi$
$359$	−12.5000	+	21.6506i	−0.659725	+	1.14268i	−0.980687	+	0.195585i	$0.937340\pi$
$360$		0			0
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$		0			0
$363$		0			0
$364$	12.0000	+	10.3923i	0.628971	+	0.544705i
$365$	−14.0000	−	24.2487i	−0.732793	−	1.26924i
$366$		0			0
$367$	−7.00000			−0.365397			−0.182699	−	0.983169i	$-0.558483\pi$
$367$	−7.00000			−0.365397			−0.182699	+	0.983169i	$0.558483\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$		0			0
$370$	32.0000			1.66360
$371$	−6.00000	+	31.1769i	−0.311504	+	1.61862i
$372$		0			0
$373$	−26.0000			−1.34623			−0.673114	−	0.739538i	$-0.735044\pi$
$373$	−26.0000			−1.34623			−0.673114	+	0.739538i	$0.735044\pi$
$374$	−2.00000	+	3.46410i	−0.103418	+	0.179124i
$375$		0			0
$376$	4.50000	+	7.79423i	0.232070	+	0.401957i
$377$	24.0000			1.23606
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	8.00000	+	13.8564i	0.410391	+	0.710819i
$381$		0			0
$382$	6.00000	−	10.3923i	0.306987	−	0.531717i
$383$	23.0000			1.17525			0.587623	−	0.809135i	$-0.300064\pi$
$383$	23.0000			1.17525			0.587623	+	0.809135i	$0.300064\pi$
$384$		0			0
$385$	16.0000	+	13.8564i	0.815436	+	0.706188i
$386$	5.00000			0.254493
$387$		0			0
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−14.0000			−0.709828			−0.354914	−	0.934899i	$-0.615490\pi$
$389$	−14.0000			−0.709828			−0.354914	+	0.934899i	$0.615490\pi$
$390$		0			0
$391$	1.00000	+	1.73205i	0.0505722	+	0.0875936i
$392$	1.00000	+	6.92820i	0.0505076	+	0.349927i
$393$		0			0
$394$	8.00000	+	13.8564i	0.403034	+	0.698076i
$395$	6.00000	+	10.3923i	0.301893	+	0.522894i
$396$		0			0
$397$	6.00000	−	10.3923i	0.301131	−	0.521575i	−0.675261	−	0.737579i	$-0.735969\pi$
$397$	6.00000	−	10.3923i	0.301131	−	0.521575i	0.976392	+	0.216004i	$0.0693024\pi$
$398$	−2.50000	+	4.33013i	−0.125314	+	0.217050i
$399$		0			0
$400$	−5.50000	−	9.52628i	−0.275000	−	0.476314i
$401$	3.00000			0.149813			0.0749064	−	0.997191i	$-0.476134\pi$
$401$	3.00000			0.149813			0.0749064	+	0.997191i	$0.476134\pi$
$402$		0			0
$403$	−54.0000			−2.68993
$404$	4.00000	−	6.92820i	0.199007	−	0.344691i
$405$		0			0
$406$	8.00000	+	6.92820i	0.397033	+	0.343841i
$407$	−8.00000	+	13.8564i	−0.396545	+	0.686837i
$408$		0			0
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	−0.529657	−	0.848212i	$-0.677679\pi$
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	0.999402	+	0.0345902i	$0.0110126\pi$
$410$	−6.00000	+	10.3923i	−0.296319	+	0.513239i
$411$		0			0
$412$	3.50000	−	6.06218i	0.172433	−	0.298662i
$413$	−10.0000	+	3.46410i	−0.492068	+	0.170457i
$414$		0			0
$415$	−28.0000	+	48.4974i	−1.37447	+	2.38064i
$416$	6.00000			0.294174
$417$		0			0
$418$	−8.00000			−0.391293
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	−0.955683	−	0.294398i	$-0.904881\pi$
$419$	−15.0000	−	25.9808i	−0.732798	−	1.26924i	0.222885	−	0.974845i	$-0.428453\pi$
$420$		0			0
$421$	15.0000	−	25.9808i	0.731055	−	1.26622i	−0.225377	−	0.974272i	$-0.572361\pi$
$421$	15.0000	−	25.9808i	0.731055	−	1.26622i	0.956433	−	0.291953i	$-0.0943052\pi$
$422$	−7.00000	+	12.1244i	−0.340755	+	0.590204i
$423$		0			0
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$	−11.0000	−	19.0526i	−0.533578	−	0.924185i
$426$		0			0
$427$	3.00000	−	15.5885i	0.145180	−	0.754378i
$428$	9.00000	+	15.5885i	0.435031	+	0.753497i
$429$		0			0
$430$	8.00000			0.385794
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	0.626907	−	0.779094i	$-0.284321\pi$
$431$	−7.50000	−	12.9904i	−0.361262	−	0.625725i	−0.988169	+	0.153370i	$0.950987\pi$
$432$		0			0
$433$	−19.0000			−0.913082			−0.456541	−	0.889702i	$-0.650912\pi$
$433$	−19.0000			−0.913082			−0.456541	+	0.889702i	$0.650912\pi$
$434$	−18.0000	−	15.5885i	−0.864028	−	0.748270i
$435$		0			0
$436$	−2.00000			−0.0957826
$437$	−2.00000	+	3.46410i	−0.0956730	+	0.165710i
$438$		0			0
$439$	−4.50000	−	7.79423i	−0.214773	−	0.371998i	0.738429	−	0.674331i	$-0.235568\pi$
$439$	−4.50000	−	7.79423i	−0.214773	−	0.371998i	−0.953202	+	0.302333i	$0.902235\pi$
$440$	8.00000			0.381385
$441$		0			0
$442$	12.0000			0.570782
$443$	−13.0000	−	22.5167i	−0.617649	−	1.06980i	−0.989914	−	0.141672i	$-0.954752\pi$
$443$	−13.0000	−	22.5167i	−0.617649	−	1.06980i	0.372265	−	0.928126i	$-0.378581\pi$
$444$		0			0
$445$	6.00000	−	10.3923i	0.284427	−	0.492642i
$446$	−25.0000			−1.18378
$447$		0			0
$448$	2.00000	+	1.73205i	0.0944911	+	0.0818317i
$449$	−2.00000			−0.0943858			−0.0471929	−	0.998886i	$-0.515028\pi$
$449$	−2.00000			−0.0943858			−0.0471929	+	0.998886i	$0.515028\pi$
$450$		0			0
$451$	−3.00000	−	5.19615i	−0.141264	−	0.244677i
$452$	−14.0000			−0.658505
$453$		0			0
$454$	−15.0000	−	25.9808i	−0.703985	−	1.21934i
$455$	12.0000	−	62.3538i	0.562569	−	2.92319i
$456$		0			0
$457$	−17.0000	−	29.4449i	−0.795226	−	1.37737i	−0.922695	−	0.385530i	$-0.874019\pi$
$457$	−17.0000	−	29.4449i	−0.795226	−	1.37737i	0.127469	−	0.991843i	$-0.459315\pi$
$458$	10.0000	+	17.3205i	0.467269	+	0.809334i
$459$		0			0
$460$	2.00000	−	3.46410i	0.0932505	−	0.161515i
$461$	−11.0000	+	19.0526i	−0.512321	+	0.887366i	0.487577	+	0.873080i	$0.337881\pi$
$461$	−11.0000	+	19.0526i	−0.512321	+	0.887366i	−0.999898	+	0.0142861i	$0.995452\pi$
$462$		0			0
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	0.854173	−	0.519989i	$-0.174064\pi$
$463$	−0.500000	−	0.866025i	−0.0232370	−	0.0402476i	−0.877410	+	0.479741i	$0.840731\pi$
$464$	4.00000			0.185695
$465$		0			0
$466$	26.0000			1.20443
$467$	−20.0000	+	34.6410i	−0.925490	+	1.60300i	−0.134718	+	0.990884i	$0.543013\pi$
$467$	−20.0000	+	34.6410i	−0.925490	+	1.60300i	−0.790772	+	0.612111i	$0.790321\pi$
$468$		0			0
$469$	35.0000	−	12.1244i	1.61615	−	0.559851i
$470$	18.0000	−	31.1769i	0.830278	−	1.43808i
$471$		0			0
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−2.00000	+	3.46410i	−0.0919601	+	0.159280i
$474$		0			0
$475$	22.0000	−	38.1051i	1.00943	−	1.74838i
$476$	4.00000	+	3.46410i	0.183340	+	0.158777i
$477$		0			0
$478$	−4.50000	+	7.79423i	−0.205825	+	0.356500i
$479$	23.0000			1.05090			0.525448	−	0.850825i	$-0.323898\pi$
$479$	23.0000			1.05090			0.525448	+	0.850825i	$0.323898\pi$
$480$		0			0
$481$	48.0000			2.18861
$482$	3.50000	+	6.06218i	0.159421	+	0.276125i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−20.0000	+	34.6410i	−0.908153	+	1.57297i
$486$		0			0
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	−0.999698	−	0.0245553i	$-0.992183\pi$
$487$	−11.5000	−	19.9186i	−0.521115	−	0.902597i	0.478584	−	0.878042i	$-0.341150\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$		0			0
$490$	22.0000	−	17.3205i	0.993859	−	0.782461i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$	8.00000			0.360302
$494$	12.0000	+	20.7846i	0.539906	+	0.935144i
$495$		0			0
$496$	−9.00000			−0.404112
$497$	−2.00000	−	1.73205i	−0.0897123	−	0.0776931i
$498$		0			0
$499$	4.00000			0.179065			0.0895323	−	0.995984i	$-0.471463\pi$
$499$	4.00000			0.179065			0.0895323	+	0.995984i	$0.471463\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$		0			0
$502$		0			0
$503$	15.0000			0.668817			0.334408	−	0.942428i	$-0.391463\pi$
$503$	15.0000			0.668817			0.334408	+	0.942428i	$0.391463\pi$
$504$		0			0
$505$	−32.0000			−1.42398
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$		0			0
$508$	−1.50000	+	2.59808i	−0.0665517	+	0.115271i
$509$	−36.0000			−1.59567			−0.797836	−	0.602875i	$-0.794022\pi$
$509$	−36.0000			−1.59567			−0.797836	+	0.602875i	$0.794022\pi$
$510$		0			0
$511$	3.50000	−	18.1865i	0.154831	−	0.804525i
$512$	1.00000			0.0441942
$513$		0			0
$514$	1.50000	+	2.59808i	0.0661622	+	0.114596i
$515$	−28.0000			−1.23383
$516$		0			0
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	16.0000	+	13.8564i	0.703000	+	0.608816i
$519$		0			0
$520$	−12.0000	−	20.7846i	−0.526235	−	0.911465i
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	−0.877283	−	0.479973i	$-0.840646\pi$
$521$	−19.5000	−	33.7750i	−0.854311	−	1.47971i	0.0229727	−	0.999736i	$-0.492687\pi$
$522$		0			0
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	0.0665832	+	0.997781i	$0.478790\pi$
$523$	−19.0000	+	32.9090i	−0.830812	+	1.43901i	−0.897395	+	0.441228i	$0.854543\pi$
$524$	−5.00000	+	8.66025i	−0.218426	+	0.378325i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$	−18.0000			−0.784092
$528$		0			0
$529$	−22.0000			−0.956522
$530$	24.0000	−	41.5692i	1.04249	−	1.80565i
$531$		0			0
$532$	−2.00000	+	10.3923i	−0.0867110	+	0.450564i
$533$	−9.00000	+	15.5885i	−0.389833	+	0.675211i
$534$		0			0
$535$	36.0000	−	62.3538i	1.55642	−	2.69579i
$536$	7.00000	−	12.1244i	0.302354	−	0.523692i
$537$		0			0
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	2.00000	+	13.8564i	0.0861461	+	0.596838i
$540$		0			0
$541$	3.00000	−	5.19615i	0.128980	−	0.223400i	−0.794302	−	0.607524i	$-0.792163\pi$
$541$	3.00000	−	5.19615i	0.128980	−	0.223400i	0.923282	+	0.384124i	$0.125496\pi$
$542$		0			0
$543$		0			0
$544$	2.00000			0.0857493
$545$	4.00000	+	6.92820i	0.171341	+	0.296772i
$546$		0			0
$547$	3.00000	−	5.19615i	0.128271	−	0.222171i	−0.794736	−	0.606955i	$-0.792391\pi$
$547$	3.00000	−	5.19615i	0.128271	−	0.222171i	0.923007	+	0.384784i	$0.125724\pi$
$548$	2.50000	−	4.33013i	0.106795	−	0.184974i
$549$		0			0
$550$	−11.0000	−	19.0526i	−0.469042	−	0.812404i
$551$	8.00000	+	13.8564i	0.340811	+	0.590303i
$552$		0			0
$553$	−1.50000	+	7.79423i	−0.0637865	+	0.331444i
$554$	−13.0000	−	22.5167i	−0.552317	−	0.956641i
$555$		0			0
$556$	−2.00000			−0.0848189
$557$	10.0000	+	17.3205i	0.423714	+	0.733893i	0.996299	−	0.0859514i	$-0.0273930\pi$
$557$	10.0000	+	17.3205i	0.423714	+	0.733893i	−0.572586	+	0.819845i	$0.694060\pi$
$558$		0			0
$559$	12.0000			0.507546
$560$	2.00000	−	10.3923i	0.0845154	−	0.439155i
$561$		0			0
$562$	5.00000			0.210912
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	−0.404198	−	0.914671i	$-0.632449\pi$
$563$	14.0000	−	24.2487i	0.590030	−	1.02196i	0.994228	−	0.107290i	$-0.0342173\pi$
$564$		0			0
$565$	28.0000	+	48.4974i	1.17797	+	2.04030i
$566$	4.00000			0.168133
$567$		0			0
$568$	−1.00000			−0.0419591
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	−0.907532	−	0.419984i	$-0.862036\pi$
$569$	−19.5000	−	33.7750i	−0.817483	−	1.41592i	0.0900490	−	0.995937i	$-0.471298\pi$
$570$		0			0
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	−0.963827	−	0.266529i	$-0.914123\pi$
$571$	−6.00000	+	10.3923i	−0.251092	+	0.434904i	0.712735	+	0.701434i	$0.247456\pi$
$572$	12.0000			0.501745
$573$		0			0
$574$	−7.50000	+	2.59808i	−0.313044	+	0.108442i
$575$	−11.0000			−0.458732
$576$		0			0
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	−13.0000			−0.540729
$579$		0			0
$580$	−8.00000	−	13.8564i	−0.332182	−	0.575356i
$581$	−35.0000	+	12.1244i	−1.45204	+	0.503003i
$582$		0			0
$583$	12.0000	+	20.7846i	0.496989	+	0.860811i
$584$	−3.50000	−	6.06218i	−0.144831	−	0.250855i
$585$		0			0
$586$	−3.00000	+	5.19615i	−0.123929	+	0.214651i
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	−0.652355	−	0.757914i	$-0.726219\pi$
$587$	8.00000	−	13.8564i	0.330195	−	0.571915i	0.982550	+	0.185999i	$0.0595520\pi$
$588$		0			0
$589$	−18.0000	−	31.1769i	−0.741677	−	1.28462i
$590$	16.0000			0.658710
$591$		0			0
$592$	8.00000			0.328798
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	4.00000	−	20.7846i	0.163984	−	0.852086i
$596$		0			0
$597$		0			0
$598$	3.00000	−	5.19615i	0.122679	−	0.212486i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$		0			0
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	−0.855648	−	0.517559i	$-0.826841\pi$
$601$	0.500000	−	0.866025i	0.0203954	−	0.0353259i	0.876043	+	0.482233i	$0.160174\pi$
$602$	4.00000	+	3.46410i	0.163028	+	0.141186i
$603$		0			0
$604$	8.50000	−	14.7224i	0.345860	−	0.599047i
$605$	−28.0000			−1.13836
$606$		0			0
$607$		0			0			−	1.00000i	$-0.5\pi$
$607$		0			0				1.00000i	$0.5\pi$
$608$	2.00000	+	3.46410i	0.0811107	+	0.140488i
$609$		0			0
$610$	−12.0000	+	20.7846i	−0.485866	+	0.841544i
$611$	27.0000	−	46.7654i	1.09230	−	1.89192i
$612$		0			0
$613$	18.0000	+	31.1769i	0.727013	+	1.25922i	0.958140	+	0.286300i	$0.0924254\pi$
$613$	18.0000	+	31.1769i	0.727013	+	1.25922i	−0.231127	+	0.972924i	$0.574241\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$		0			0
$616$	4.00000	+	3.46410i	0.161165	+	0.139573i
$617$	9.50000	+	16.4545i	0.382456	+	0.662433i	0.991413	−	0.130771i	$-0.0417452\pi$
$617$	9.50000	+	16.4545i	0.382456	+	0.662433i	−0.608957	+	0.793203i	$0.708412\pi$
$618$		0			0
$619$	34.0000			1.36658			0.683288	−	0.730149i	$-0.260549\pi$
$619$	34.0000			1.36658			0.683288	+	0.730149i	$0.260549\pi$
$620$	18.0000	+	31.1769i	0.722897	+	1.25210i
$621$		0			0
$622$	16.0000			0.641542
$623$	7.50000	−	2.59808i	0.300481	−	0.104090i
$624$		0			0
$625$	41.0000			1.64000
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$		0			0
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	16.0000			0.637962
$630$		0			0
$631$	20.0000			0.796187			0.398094	−	0.917345i	$-0.369672\pi$
$631$	20.0000			0.796187			0.398094	+	0.917345i	$0.369672\pi$
$632$	1.50000	+	2.59808i	0.0596668	+	0.103346i
$633$		0			0
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$	12.0000			0.476205
$636$		0			0
$637$	33.0000	−	25.9808i	1.30751	−	1.02940i
$638$	8.00000			0.316723
$639$		0			0
$640$	−2.00000	−	3.46410i	−0.0790569	−	0.136931i
$641$	−13.0000			−0.513469			−0.256735	−	0.966482i	$-0.582647\pi$
$641$	−13.0000			−0.513469			−0.256735	+	0.966482i	$0.582647\pi$
$642$		0			0
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	0.998122	+	0.0612510i	$0.0195090\pi$
$643$	14.0000	+	24.2487i	0.552106	+	0.956276i	−0.446016	+	0.895025i	$0.647158\pi$
$644$	2.50000	−	0.866025i	0.0985138	−	0.0341262i
$645$		0			0
$646$	4.00000	+	6.92820i	0.157378	+	0.272587i
$647$	−13.5000	−	23.3827i	−0.530740	−	0.919268i	−0.999357	−	0.0358667i	$-0.988581\pi$
$647$	−13.5000	−	23.3827i	−0.530740	−	0.919268i	0.468617	−	0.883402i	$-0.344753\pi$
$648$		0			0
$649$	−4.00000	+	6.92820i	−0.157014	+	0.271956i
$650$	−33.0000	+	57.1577i	−1.29437	+	2.24191i
$651$		0			0
$652$	−7.00000	−	12.1244i	−0.274141	−	0.474826i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$		0			0
$655$	40.0000			1.56293
$656$	−1.50000	+	2.59808i	−0.0585652	+	0.101438i
$657$		0			0
$658$	22.5000	−	7.79423i	0.877141	−	0.303851i
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	−0.777689	−	0.628649i	$-0.783608\pi$
$661$	4.00000	−	6.92820i	0.155582	−	0.269476i	0.933271	+	0.359174i	$0.116941\pi$
$662$	17.0000	−	29.4449i	0.660724	−	1.14441i
$663$		0			0
$664$	−7.00000	+	12.1244i	−0.271653	+	0.470516i
$665$	40.0000	−	13.8564i	1.55113	−	0.537328i
$666$		0			0
$667$	2.00000	−	3.46410i	0.0774403	−	0.134131i
$668$	7.00000			0.270838
$669$		0			0
$670$	−56.0000			−2.16347
$671$	−6.00000	−	10.3923i	−0.231627	−	0.401190i
$672$		0			0
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	−0.0702442	−	0.997530i	$-0.522378\pi$
$673$	21.5000	−	37.2391i	0.828764	−	1.43546i	0.899008	−	0.437932i	$-0.144289\pi$
$674$	9.00000	−	15.5885i	0.346667	−	0.600445i
$675$		0			0
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	0.917899	−	0.396813i	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		0			0
$679$	−25.0000	+	8.66025i	−0.959412	+	0.332350i
$680$	−4.00000	−	6.92820i	−0.153393	−	0.265684i
$681$		0			0
$682$	−18.0000			−0.689256
$683$	3.00000	+	5.19615i	0.114792	+	0.198825i	0.917697	−	0.397282i	$-0.130047\pi$
$683$	3.00000	+	5.19615i	0.114792	+	0.198825i	−0.802905	+	0.596107i	$0.796713\pi$
$684$		0			0
$685$	−20.0000			−0.764161
$686$	18.5000	+	0.866025i	0.706333	+	0.0330650i
$687$		0			0
$688$	2.00000			0.0762493
$689$	36.0000	−	62.3538i	1.37149	−	2.37549i
$690$		0			0
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	0.999276	+	0.0380440i	$0.0121127\pi$
$691$	14.0000	+	24.2487i	0.532585	+	0.922464i	−0.466691	+	0.884420i	$0.654554\pi$
$692$	−14.0000			−0.532200
$693$		0			0
$694$	−12.0000			−0.455514
$695$	4.00000	+	6.92820i	0.151729	+	0.262802i
$696$		0			0
$697$	−3.00000	+	5.19615i	−0.113633	+	0.196818i
$698$	−8.00000			−0.302804
$699$		0			0
$700$	−27.5000	+	9.52628i	−1.03940	+	0.360060i
$701$	10.0000			0.377695			0.188847	−	0.982006i	$-0.439525\pi$
$701$	10.0000			0.377695			0.188847	+	0.982006i	$0.439525\pi$
$702$		0			0
$703$	16.0000	+	27.7128i	0.603451	+	1.04521i
$704$	2.00000			0.0753778
$705$		0			0
$706$	1.50000	+	2.59808i	0.0564532	+	0.0977799i
$707$	−16.0000	−	13.8564i	−0.601742	−	0.521124i
$708$		0			0
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	0.781086	−	0.624423i	$-0.214666\pi$
$709$	−4.00000	−	6.92820i	−0.150223	−	0.260194i	−0.931309	+	0.364229i	$0.881333\pi$
$710$	2.00000	+	3.46410i	0.0750587	+	0.130005i
$711$		0			0
$712$	1.50000	−	2.59808i	0.0562149	−	0.0973670i
$713$	−4.50000	+	7.79423i	−0.168526	+	0.291896i
$714$		0			0
$715$	−24.0000	−	41.5692i	−0.897549	−	1.55460i
$716$	6.00000			0.224231
$717$		0			0
$718$	25.0000			0.932992
$719$	1.50000	−	2.59808i	0.0559406	−	0.0968919i	−0.836699	−	0.547663i	$-0.815518\pi$
$719$	1.50000	−	2.59808i	0.0559406	−	0.0968919i	0.892640	+	0.450771i	$0.148851\pi$
$720$		0			0
$721$	−14.0000	−	12.1244i	−0.521387	−	0.451535i
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$		0			0
$724$		0			0
$725$	−22.0000	+	38.1051i	−0.817059	+	1.41519i
$726$		0			0
$727$	−12.5000	+	21.6506i	−0.463599	+	0.802978i	−0.999137	−	0.0415337i	$-0.986776\pi$
$727$	−12.5000	+	21.6506i	−0.463599	+	0.802978i	0.535538	+	0.844511i	$0.320109\pi$
$728$	3.00000	−	15.5885i	0.111187	−	0.577747i
$729$		0			0
$730$	−14.0000	+	24.2487i	−0.518163	+	0.897485i
$731$	4.00000			0.147945
$732$		0			0
$733$	−42.0000			−1.55131			−0.775653	−	0.631160i	$-0.782579\pi$
$733$	−42.0000			−1.55131			−0.775653	+	0.631160i	$0.782579\pi$
$734$	3.50000	+	6.06218i	0.129187	+	0.223759i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	14.0000	−	24.2487i	0.515697	−	0.893213i
$738$		0			0
$739$	−15.0000	−	25.9808i	−0.551784	−	0.955718i	−0.998146	−	0.0608653i	$-0.980614\pi$
$739$	−15.0000	−	25.9808i	−0.551784	−	0.955718i	0.446362	−	0.894852i	$-0.352719\pi$
$740$	−16.0000	−	27.7128i	−0.588172	−	1.01874i
$741$		0			0
$742$	30.0000	−	10.3923i	1.10133	−	0.381514i
$743$	16.5000	+	28.5788i	0.605326	+	1.04846i	0.992000	+	0.126239i	$0.0402907\pi$
$743$	16.5000	+	28.5788i	0.605326	+	1.04846i	−0.386674	+	0.922217i	$0.626376\pi$
$744$		0			0
$745$		0			0
$746$	13.0000	+	22.5167i	0.475964	+	0.824394i
$747$		0			0
$748$	4.00000			0.146254
$749$	45.0000	−	15.5885i	1.64426	−	0.569590i
$750$		0			0
$751$	27.0000			0.985244			0.492622	−	0.870243i	$-0.336039\pi$
$751$	27.0000			0.985244			0.492622	+	0.870243i	$0.336039\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$		0			0
$754$	−12.0000	−	20.7846i	−0.437014	−	0.756931i
$755$	−68.0000			−2.47477
$756$		0			0
$757$	−36.0000			−1.30844			−0.654221	−	0.756303i	$-0.727003\pi$
$757$	−36.0000			−1.30844			−0.654221	+	0.756303i	$0.727003\pi$
$758$	4.00000	+	6.92820i	0.145287	+	0.251644i
$759$		0			0
$760$	8.00000	−	13.8564i	0.290191	−	0.502625i
$761$	−13.0000			−0.471250			−0.235625	−	0.971844i	$-0.575714\pi$
$761$	−13.0000			−0.471250			−0.235625	+	0.971844i	$0.575714\pi$
$762$		0			0
$763$	−1.00000	+	5.19615i	−0.0362024	+	0.188113i
$764$	−12.0000			−0.434145
$765$		0			0
$766$	−11.5000	−	19.9186i	−0.415512	−	0.719688i
$767$	24.0000			0.866590
$768$		0			0
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	0.761680	−	0.647954i	$-0.224375\pi$
$769$	−5.00000	−	8.66025i	−0.180305	−	0.312297i	−0.941984	+	0.335657i	$0.891042\pi$
$770$	4.00000	−	20.7846i	0.144150	−	0.749025i
$771$		0			0
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	16.0000	+	27.7128i	0.575480	+	0.996761i	0.995989	+	0.0894724i	$0.0285181\pi$
$773$	16.0000	+	27.7128i	0.575480	+	0.996761i	−0.420509	+	0.907288i	$0.638149\pi$
$774$		0			0
$775$	49.5000	−	85.7365i	1.77809	−	3.07975i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$		0			0
$778$	7.00000	+	12.1244i	0.250962	+	0.434679i
$779$	−12.0000			−0.429945
$780$		0			0
$781$	−2.00000			−0.0715656
$782$	1.00000	−	1.73205i	0.0357599	−	0.0619380i
$783$		0			0
$784$	5.50000	−	4.33013i	0.196429	−	0.154647i
$785$	−4.00000	+	6.92820i	−0.142766	+	0.247278i
$786$		0			0
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	−0.952925	−	0.303207i	$-0.901942\pi$
$787$	−6.00000	+	10.3923i	−0.213877	+	0.370446i	0.739048	+	0.673653i	$0.235276\pi$
$788$	8.00000	−	13.8564i	0.284988	−	0.493614i
$789$		0			0
$790$	6.00000	−	10.3923i	0.213470	−	0.369742i
$791$	−7.00000	+	36.3731i	−0.248891	+	1.29328i
$792$		0			0
$793$	−18.0000	+	31.1769i	−0.639199	+	1.10712i
$794$	−12.0000			−0.425864
$795$		0			0
$796$	5.00000			0.177220
$797$	12.0000	+	20.7846i	0.425062	+	0.736229i	0.996426	−	0.0844678i	$-0.0269190\pi$
$797$	12.0000	+	20.7846i	0.425062	+	0.736229i	−0.571364	+	0.820696i	$0.693586\pi$
$798$		0			0
$799$	9.00000	−	15.5885i	0.318397	−	0.551480i
$800$	−5.50000	+	9.52628i	−0.194454	+	0.336805i
$801$		0			0
$802$	−1.50000	−	2.59808i	−0.0529668	−	0.0917413i
$803$	−7.00000	−	12.1244i	−0.247025	−	0.427859i
$804$		0			0
$805$	−8.00000	−	6.92820i	−0.281963	−	0.244187i
$806$	27.0000	+	46.7654i	0.951034	+	1.64724i
$807$		0			0
$808$	−8.00000			−0.281439
$809$	−15.5000	−	26.8468i	−0.544951	−	0.943883i	−0.998610	−	0.0527074i	$-0.983215\pi$
$809$	−15.5000	−	26.8468i	−0.544951	−	0.943883i	0.453659	−	0.891175i	$-0.350118\pi$
$810$		0			0
$811$	46.0000			1.61528			0.807639	−	0.589677i	$-0.200745\pi$
$811$	46.0000			1.61528			0.807639	+	0.589677i	$0.200745\pi$
$812$	2.00000	−	10.3923i	0.0701862	−	0.364698i
$813$		0			0
$814$	16.0000			0.560800
$815$	−28.0000	+	48.4974i	−0.980797	+	1.69879i
$816$		0			0
$817$	4.00000	+	6.92820i	0.139942	+	0.242387i
$818$	−19.0000			−0.664319
$819$		0			0
$820$	12.0000			0.419058
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	−0.979795	−	0.200002i	$-0.935905\pi$
$821$	−19.0000	−	32.9090i	−0.663105	−	1.14853i	0.316691	−	0.948529i	$-0.397428\pi$
$822$		0			0
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	−0.956791	−	0.290776i	$-0.906086\pi$
$823$	−6.50000	+	11.2583i	−0.226576	+	0.392441i	0.730215	+	0.683217i	$0.239420\pi$
$824$	−7.00000			−0.243857
$825$		0			0
$826$	8.00000	+	6.92820i	0.278356	+	0.241063i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$		0			0
$829$	4.00000	+	6.92820i	0.138926	+	0.240626i	0.927090	−	0.374838i	$-0.122302\pi$
$829$	4.00000	+	6.92820i	0.138926	+	0.240626i	−0.788165	+	0.615465i	$0.788968\pi$
$830$	56.0000			1.94379
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	11.0000	−	8.66025i	0.381127	−	0.300060i
$834$		0			0
$835$	−14.0000	−	24.2487i	−0.484490	−	0.839161i
$836$	4.00000	+	6.92820i	0.138343	+	0.239617i
$837$		0			0
$838$	−15.0000	+	25.9808i	−0.518166	+	0.897491i
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	−0.985397	−	0.170272i	$-0.945535\pi$
$839$	−10.0000	+	17.3205i	−0.345238	+	0.597970i	0.640159	+	0.768243i	$0.278869\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	−30.0000			−1.03387
$843$		0			0
$844$	14.0000			0.481900
$845$	−46.0000	+	79.6743i	−1.58245	+	2.74088i
$846$		0			0
$847$	−14.0000	−	12.1244i	−0.481046	−	0.416598i
$848$	6.00000	−	10.3923i	0.206041	−	0.356873i
$849$		0			0
$850$	−11.0000	+	19.0526i	−0.377297	+	0.653497i
$851$	4.00000	−	6.92820i	0.137118	−	0.237496i
$852$		0			0
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	−0.998060	−	0.0622597i	$-0.980169\pi$
$853$	−13.0000	+	22.5167i	−0.445112	+	0.770956i	0.552948	+	0.833215i	$0.313503\pi$
$854$	−15.0000	+	5.19615i	−0.513289	+	0.177809i
$855$		0			0
$856$	9.00000	−	15.5885i	0.307614	−	0.532803i
$857$	−21.0000			−0.717346			−0.358673	−	0.933463i	$-0.616771\pi$
$857$	−21.0000			−0.717346			−0.358673	+	0.933463i	$0.616771\pi$
$858$		0			0
$859$	20.0000			0.682391			0.341196	−	0.939992i	$-0.389168\pi$
$859$	20.0000			0.682391			0.341196	+	0.939992i	$0.389168\pi$
$860$	−4.00000	−	6.92820i	−0.136399	−	0.236250i
$861$		0			0
$862$	−7.50000	+	12.9904i	−0.255451	+	0.442454i
$863$	−0.500000	+	0.866025i	−0.0170202	+	0.0294798i	−0.874410	−	0.485188i	$-0.838751\pi$
$863$	−0.500000	+	0.866025i	−0.0170202	+	0.0294798i	0.857390	+	0.514667i	$0.172085\pi$
$864$		0			0
$865$	28.0000	+	48.4974i	0.952029	+	1.64896i
$866$	9.50000	+	16.4545i	0.322823	+	0.559146i
$867$		0			0
$868$	−4.50000	+	23.3827i	−0.152740	+	0.793660i
$869$	3.00000	+	5.19615i	0.101768	+	0.176267i
$870$		0			0
$871$	−84.0000			−2.84623
$872$	1.00000	+	1.73205i	0.0338643	+	0.0586546i
$873$		0			0
$874$	4.00000			0.135302
$875$	48.0000	+	41.5692i	1.62270	+	1.40530i
$876$		0			0
$877$	−8.00000			−0.270141			−0.135070	−	0.990836i	$-0.543126\pi$
$877$	−8.00000			−0.270141			−0.135070	+	0.990836i	$0.543126\pi$
$878$	−4.50000	+	7.79423i	−0.151868	+	0.263042i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	21.0000			0.707508			0.353754	−	0.935339i	$-0.384905\pi$
$881$	21.0000			0.707508			0.353754	+	0.935339i	$0.384905\pi$
$882$		0			0
$883$	−34.0000			−1.14419			−0.572096	−	0.820187i	$-0.693869\pi$
$883$	−34.0000			−1.14419			−0.572096	+	0.820187i	$0.693869\pi$
$884$	−6.00000	−	10.3923i	−0.201802	−	0.349531i
$885$		0			0
$886$	−13.0000	+	22.5167i	−0.436744	+	0.756462i
$887$	3.00000			0.100730			0.0503651	−	0.998731i	$-0.483962\pi$
$887$	3.00000			0.100730			0.0503651	+	0.998731i	$0.483962\pi$
$888$		0			0
$889$	6.00000	+	5.19615i	0.201234	+	0.174273i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	12.5000	+	21.6506i	0.418531	+	0.724917i
$893$	36.0000			1.20469
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$	0.500000	−	2.59808i	0.0167038	−	0.0867956i
$897$		0			0
$898$	1.00000	+	1.73205i	0.0333704	+	0.0577993i
$899$	18.0000	+	31.1769i	0.600334	+	1.03981i
$900$		0			0
$901$	12.0000	−	20.7846i	0.399778	−	0.692436i
$902$	−3.00000	+	5.19615i	−0.0998891	+	0.173013i
$903$		0			0
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$		0			0
$906$		0			0
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$	−15.0000	+	25.9808i	−0.497792	+	0.862202i
$909$		0			0
$910$	−60.0000	+	20.7846i	−1.98898	+	0.689003i
$911$	−16.5000	+	28.5788i	−0.546669	+	0.946859i	0.451830	+	0.892104i	$0.350771\pi$
$911$	−16.5000	+	28.5788i	−0.546669	+	0.946859i	−0.998500	+	0.0547553i	$0.982562\pi$
$912$		0			0
$913$	−14.0000	+	24.2487i	−0.463332	+	0.802515i
$914$	−17.0000	+	29.4449i	−0.562310	+	0.973950i
$915$		0			0
$916$	10.0000	−	17.3205i	0.330409	−	0.572286i
$917$	20.0000	+	17.3205i	0.660458	+	0.571974i
$918$		0			0
$919$	−14.0000	+	24.2487i	−0.461817	+	0.799891i	−0.999052	−	0.0435419i	$-0.986136\pi$
$919$	−14.0000	+	24.2487i	−0.461817	+	0.799891i	0.537234	+	0.843433i	$0.319469\pi$
$920$	−4.00000			−0.131876
$921$		0			0
$922$	22.0000			0.724531
$923$	3.00000	+	5.19615i	0.0987462	+	0.171033i
$924$		0			0
$925$	−44.0000	+	76.2102i	−1.44671	+	2.50578i
$926$	−0.500000	+	0.866025i	−0.0164310	+	0.0284594i
$927$		0			0
$928$	−2.00000	−	3.46410i	−0.0656532	−	0.113715i
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	0.985262	−	0.171054i	$-0.0547172\pi$
$929$	10.5000	+	18.1865i	0.344494	+	0.596681i	−0.640768	+	0.767735i	$0.721384\pi$
$930$		0			0
$931$	26.0000	+	10.3923i	0.852116	+	0.340594i
$932$	−13.0000	−	22.5167i	−0.425829	−	0.737558i
$933$		0			0
$934$	40.0000			1.30884
$935$	−8.00000	−	13.8564i	−0.261628	−	0.453153i
$936$		0			0
$937$	−13.0000			−0.424691			−0.212346	−	0.977195i	$-0.568110\pi$
$937$	−13.0000			−0.424691			−0.212346	+	0.977195i	$0.568110\pi$
$938$	−28.0000	−	24.2487i	−0.914232	−	0.791748i
$939$		0			0
$940$	−36.0000			−1.17419
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	−0.729079	−	0.684429i	$-0.760051\pi$
$941$	7.00000	−	12.1244i	0.228193	−	0.395243i	0.957273	+	0.289187i	$0.0933848\pi$
$942$		0			0
$943$	1.50000	+	2.59808i	0.0488467	+	0.0846050i
$944$	4.00000			0.130189
$945$		0			0
$946$	4.00000			0.130051
$947$	7.00000	+	12.1244i	0.227469	+	0.393989i	0.957057	−	0.289898i	$-0.0936215\pi$
$947$	7.00000	+	12.1244i	0.227469	+	0.393989i	−0.729588	+	0.683887i	$0.760288\pi$
$948$		0			0
$949$	−21.0000	+	36.3731i	−0.681689	+	1.18072i
$950$	−44.0000			−1.42755
$951$		0			0
$952$	1.00000	−	5.19615i	0.0324102	−	0.168408i
$953$	−25.0000			−0.809829			−0.404915	−	0.914354i	$-0.632699\pi$
$953$	−25.0000			−0.809829			−0.404915	+	0.914354i	$0.632699\pi$
$954$		0			0
$955$	24.0000	+	41.5692i	0.776622	+	1.34515i
$956$	9.00000			0.291081
$957$		0			0
$958$	−11.5000	−	19.9186i	−0.371548	−	0.643540i
$959$	−10.0000	−	8.66025i	−0.322917	−	0.279654i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$	−24.0000	−	41.5692i	−0.773791	−	1.34025i
$963$		0			0
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$	−10.0000	+	17.3205i	−0.321911	+	0.557567i
$966$		0			0
$967$	18.5000	+	32.0429i	0.594920	+	1.03043i	0.993558	+	0.113323i	$0.0361496\pi$
$967$	18.5000	+	32.0429i	0.594920	+	1.03043i	−0.398638	+	0.917108i	$0.630517\pi$
$968$	−7.00000			−0.224989
$969$		0			0
$970$	40.0000			1.28432
$971$	21.0000	−	36.3731i	0.673922	−	1.16727i	−0.302861	−	0.953035i	$-0.597942\pi$
$971$	21.0000	−	36.3731i	0.673922	−	1.16727i	0.976783	−	0.214232i	$-0.0687250\pi$
$972$		0			0
$973$	−1.00000	+	5.19615i	−0.0320585	+	0.166581i
$974$	−11.5000	+	19.9186i	−0.368484	+	0.638233i
$975$		0			0
$976$	−3.00000	+	5.19615i	−0.0960277	+	0.166325i
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	0.0929223	+	0.995673i	$0.470379\pi$
$977$	−25.5000	+	44.1673i	−0.815817	+	1.41304i	−0.908740	+	0.417364i	$0.862954\pi$
$978$		0			0
$979$	3.00000	−	5.19615i	0.0958804	−	0.166070i
$980$	−26.0000	−	10.3923i	−0.830540	−	0.331970i
$981$		0			0
$982$	6.00000	−	10.3923i	0.191468	−	0.331632i
$983$	12.0000			0.382741			0.191370	−	0.981518i	$-0.438707\pi$
$983$	12.0000			0.382741			0.191370	+	0.981518i	$0.438707\pi$
$984$		0			0
$985$	−64.0000			−2.03921
$986$	−4.00000	−	6.92820i	−0.127386	−	0.220639i
$987$		0			0
$988$	12.0000	−	20.7846i	0.381771	−	0.661247i
$989$	1.00000	−	1.73205i	0.0317982	−	0.0550760i
$990$		0			0
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	−0.997832	−	0.0658059i	$-0.979038\pi$
$991$	−17.5000	−	30.3109i	−0.555906	−	0.962857i	0.441927	−	0.897051i	$-0.354295\pi$
$992$	4.50000	+	7.79423i	0.142875	+	0.247467i
$993$		0			0
$994$	−0.500000	+	2.59808i	−0.0158590	+	0.0824060i
$995$	−10.0000	−	17.3205i	−0.317021	−	0.549097i
$996$		0			0
$997$	2.00000			0.0633406			0.0316703	−	0.999498i	$-0.489917\pi$
$997$	2.00000			0.0633406			0.0316703	+	0.999498i	$0.489917\pi$
$998$	−2.00000	−	3.46410i	−0.0633089	−	0.109654i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.h.h.541.1		2
3.2	odd	2		1134.2.h.i.541.1		2
7.4	even	3		1134.2.e.i.865.1		2
9.2	odd	6		1134.2.g.h.163.1	yes	2
9.4	even	3		1134.2.e.i.919.1		2
9.5	odd	6		1134.2.e.h.919.1		2
9.7	even	3		1134.2.g.a.163.1	✓	2
21.11	odd	6		1134.2.e.h.865.1		2
63.2	odd	6		7938.2.a.a.1.1		1
63.4	even	3	inner	1134.2.h.h.109.1		2
63.11	odd	6		1134.2.g.h.487.1	yes	2
63.16	even	3		7938.2.a.bf.1.1		1
63.25	even	3		1134.2.g.a.487.1	yes	2
63.32	odd	6		1134.2.h.i.109.1		2
63.47	even	6		7938.2.a.p.1.1		1
63.61	odd	6		7938.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.e.h.865.1		2	21.11	odd	6
1134.2.e.h.919.1		2	9.5	odd	6
1134.2.e.i.865.1		2	7.4	even	3
1134.2.e.i.919.1		2	9.4	even	3
1134.2.g.a.163.1	✓	2	9.7	even	3
1134.2.g.a.487.1	yes	2	63.25	even	3
1134.2.g.h.163.1	yes	2	9.2	odd	6
1134.2.g.h.487.1	yes	2	63.11	odd	6
1134.2.h.h.109.1		2	63.4	even	3	inner
1134.2.h.h.541.1		2	1.1	even	1	trivial
1134.2.h.i.109.1		2	63.32	odd	6
1134.2.h.i.541.1		2	3.2	odd	2
7938.2.a.a.1.1		1	63.2	odd	6
7938.2.a.p.1.1		1	63.47	even	6
7938.2.a.q.1.1		1	63.61	odd	6
7938.2.a.bf.1.1		1	63.16	even	3

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.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +4.00000 q^{5} +(2.00000 + 1.73205i) q^{7} +1.00000 q^{8} +(-2.00000 - 3.46410i) q^{10} +2.00000 q^{11} +(-3.00000 - 5.19615i) q^{13} +(0.500000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.00000 - 1.73205i) q^{17} +(2.00000 - 3.46410i) q^{19} +(-2.00000 + 3.46410i) q^{20} +(-1.00000 - 1.73205i) q^{22} -1.00000 q^{23} +11.0000 q^{25} +(-3.00000 + 5.19615i) q^{26} +(-2.50000 + 0.866025i) q^{28} +(-2.00000 + 3.46410i) q^{29} +(4.50000 - 7.79423i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(8.00000 + 6.92820i) q^{35} +(-4.00000 + 6.92820i) q^{37} -4.00000 q^{38} +4.00000 q^{40} +(-1.50000 - 2.59808i) q^{41} +(-1.00000 + 1.73205i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(0.500000 + 0.866025i) q^{46} +(4.50000 + 7.79423i) q^{47} +(1.00000 + 6.92820i) q^{49} +(-5.50000 - 9.52628i) q^{50} +6.00000 q^{52} +(6.00000 + 10.3923i) q^{53} +8.00000 q^{55} +(2.00000 + 1.73205i) q^{56} +4.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +(-3.00000 - 5.19615i) q^{61} -9.00000 q^{62} +1.00000 q^{64} +(-12.0000 - 20.7846i) q^{65} +(7.00000 - 12.1244i) q^{67} +2.00000 q^{68} +(2.00000 - 10.3923i) q^{70} -1.00000 q^{71} +(-3.50000 - 6.06218i) q^{73} +8.00000 q^{74} +(2.00000 + 3.46410i) q^{76} +(4.00000 + 3.46410i) q^{77} +(1.50000 + 2.59808i) q^{79} +(-2.00000 - 3.46410i) q^{80} +(-1.50000 + 2.59808i) q^{82} +(-7.00000 + 12.1244i) q^{83} +(-4.00000 - 6.92820i) q^{85} +2.00000 q^{86} +2.00000 q^{88} +(1.50000 - 2.59808i) q^{89} +(3.00000 - 15.5885i) q^{91} +(0.500000 - 0.866025i) q^{92} +(4.50000 - 7.79423i) q^{94} +(8.00000 - 13.8564i) q^{95} +(-5.00000 + 8.66025i) q^{97} +(5.50000 - 4.33013i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 8 q^{5} + 4 q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 8 * q^5 + 4 * q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 8 q^{5} + 4 q^{7} + 2 q^{8} - 4 q^{10} + 4 q^{11} - 6 q^{13} + q^{14} - q^{16} - 2 q^{17} + 4 q^{19} - 4 q^{20} - 2 q^{22} - 2 q^{23} + 22 q^{25} - 6 q^{26} - 5 q^{28} - 4 q^{29} + 9 q^{31} - q^{32} - 2 q^{34} + 16 q^{35} - 8 q^{37} - 8 q^{38} + 8 q^{40} - 3 q^{41} - 2 q^{43} - 2 q^{44} + q^{46} + 9 q^{47} + 2 q^{49} - 11 q^{50} + 12 q^{52} + 12 q^{53} + 16 q^{55} + 4 q^{56} + 8 q^{58} - 4 q^{59} - 6 q^{61} - 18 q^{62} + 2 q^{64} - 24 q^{65} + 14 q^{67} + 4 q^{68} + 4 q^{70} - 2 q^{71} - 7 q^{73} + 16 q^{74} + 4 q^{76} + 8 q^{77} + 3 q^{79} - 4 q^{80} - 3 q^{82} - 14 q^{83} - 8 q^{85} + 4 q^{86} + 4 q^{88} + 3 q^{89} + 6 q^{91} + q^{92} + 9 q^{94} + 16 q^{95} - 10 q^{97} + 11 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 8 * q^5 + 4 * q^7 + 2 * q^8 - 4 * q^10 + 4 * q^11 - 6 * q^13 + q^14 - q^16 - 2 * q^17 + 4 * q^19 - 4 * q^20 - 2 * q^22 - 2 * q^23 + 22 * q^25 - 6 * q^26 - 5 * q^28 - 4 * q^29 + 9 * q^31 - q^32 - 2 * q^34 + 16 * q^35 - 8 * q^37 - 8 * q^38 + 8 * q^40 - 3 * q^41 - 2 * q^43 - 2 * q^44 + q^46 + 9 * q^47 + 2 * q^49 - 11 * q^50 + 12 * q^52 + 12 * q^53 + 16 * q^55 + 4 * q^56 + 8 * q^58 - 4 * q^59 - 6 * q^61 - 18 * q^62 + 2 * q^64 - 24 * q^65 + 14 * q^67 + 4 * q^68 + 4 * q^70 - 2 * q^71 - 7 * q^73 + 16 * q^74 + 4 * q^76 + 8 * q^77 + 3 * q^79 - 4 * q^80 - 3 * q^82 - 14 * q^83 - 8 * q^85 + 4 * q^86 + 4 * q^88 + 3 * q^89 + 6 * q^91 + q^92 + 9 * q^94 + 16 * q^95 - 10 * q^97 + 11 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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