LMFDB - Embedded newform 1134.2.f.a.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1134,2,Mod(379,1134)]

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([4, 0]))

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1134 = 2 \cdot 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1134.f (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:	no (minimal twist has level 378)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			757.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.757
Dual form			1134.2.f.a.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +4.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(-1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.00000 q^{17} +2.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-5.50000 - 9.52628i) q^{25} +3.00000 q^{26} -1.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(4.50000 - 7.79423i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.50000 + 6.06218i) q^{34} -4.00000 q^{35} +2.00000 q^{37} +(-1.00000 - 1.73205i) q^{38} +(-2.00000 + 3.46410i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} -4.00000 q^{44} -1.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(-1.50000 - 2.59808i) q^{52} -9.00000 q^{53} -16.0000 q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(2.50000 - 4.33013i) q^{59} +(3.00000 + 5.19615i) q^{61} -9.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(3.50000 - 6.06218i) q^{68} +(2.00000 + 3.46410i) q^{70} -7.00000 q^{71} -14.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(3.00000 + 5.19615i) q^{79} +4.00000 q^{80} +6.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(14.0000 - 24.2487i) q^{85} +(-5.50000 + 9.52628i) q^{86} +(2.00000 + 3.46410i) q^{88} -3.00000 q^{89} -3.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 - 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 - 4 * q^5 + q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} - 4 q^{5} + q^{7} + 2 q^{8} + 8 q^{10} + 4 q^{11} - 3 q^{13} + q^{14} - q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} + 4 q^{22} + q^{23} - 11 q^{25} + 6 q^{26} - 2 q^{28} - q^{29} + 9 q^{31} - q^{32} + 7 q^{34} - 8 q^{35} + 4 q^{37} - 2 q^{38} - 4 q^{40} - 6 q^{41} - 11 q^{43} - 8 q^{44} - 2 q^{46} + 6 q^{47} - q^{49} - 11 q^{50} - 3 q^{52} - 18 q^{53} - 32 q^{55} + q^{56} - q^{58} + 5 q^{59} + 6 q^{61} - 18 q^{62} + 2 q^{64} - 12 q^{65} - 7 q^{67} + 7 q^{68} + 4 q^{70} - 14 q^{71} - 28 q^{73} - 2 q^{74} - 2 q^{76} - 4 q^{77} + 6 q^{79} + 8 q^{80} + 12 q^{82} + 4 q^{83} + 28 q^{85} - 11 q^{86} + 4 q^{88} - 6 q^{89} - 6 q^{91} + q^{92} + 6 q^{94} - 8 q^{95} + 8 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 - 4 * q^5 + q^7 + 2 * q^8 + 8 * q^10 + 4 * q^11 - 3 * q^13 + q^14 - q^16 - 14 * q^17 + 4 * q^19 - 4 * q^20 + 4 * q^22 + q^23 - 11 * q^25 + 6 * q^26 - 2 * q^28 - q^29 + 9 * q^31 - q^32 + 7 * q^34 - 8 * q^35 + 4 * q^37 - 2 * q^38 - 4 * q^40 - 6 * q^41 - 11 * q^43 - 8 * q^44 - 2 * q^46 + 6 * q^47 - q^49 - 11 * q^50 - 3 * q^52 - 18 * q^53 - 32 * q^55 + q^56 - q^58 + 5 * q^59 + 6 * q^61 - 18 * q^62 + 2 * q^64 - 12 * q^65 - 7 * q^67 + 7 * q^68 + 4 * q^70 - 14 * q^71 - 28 * q^73 - 2 * q^74 - 2 * q^76 - 4 * q^77 + 6 * q^79 + 8 * q^80 + 12 * q^82 + 4 * q^83 + 28 * q^85 - 11 * q^86 + 4 * q^88 - 6 * q^89 - 6 * q^91 + q^92 + 6 * q^94 - 8 * q^95 + 8 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.0599153	+	0.998203i	$0.519083\pi$
$5$	−2.00000	+	3.46410i	−0.894427	+	1.54919i	−0.834512	+	0.550990i	$0.814250\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	4.00000			1.26491
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	0.992361	+	0.123371i	$0.0393705\pi$
$11$	2.00000	+	3.46410i	0.603023	+	1.04447i	−0.389338	+	0.921095i	$0.627296\pi$
$12$		0			0
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	−0.995535	−	0.0943882i	$-0.969911\pi$
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	0.579510	+	0.814965i	$0.303244\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−7.00000			−1.69775			−0.848875	−	0.528594i	$-0.822719\pi$
$17$	−7.00000			−1.69775			−0.848875	+	0.528594i	$0.822719\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$		0			0
$22$	2.00000	−	3.46410i	0.426401	−	0.738549i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$		0			0
$25$	−5.50000	−	9.52628i	−1.10000	−	1.90526i
$26$	3.00000			0.588348
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	0.815861	−	0.578249i	$-0.196264\pi$
$29$	−0.500000	−	0.866025i	−0.0928477	−	0.160817i	−0.908708	+	0.417432i	$0.862930\pi$
$30$		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
$34$	3.50000	+	6.06218i	0.600245	+	1.03965i
$35$	−4.00000			−0.676123
$36$		0			0
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	−1.00000	−	1.73205i	−0.162221	−	0.280976i
$39$		0			0
$40$	−2.00000	+	3.46410i	−0.316228	+	0.547723i
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	−0.999353	−	0.0359748i	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	−0.890947	−	0.454108i	$-0.849958\pi$
$43$	−5.50000	−	9.52628i	−0.838742	−	1.45274i	0.0522047	−	0.998636i	$-0.483375\pi$
$44$	−4.00000			−0.603023
$45$		0			0
$46$	−1.00000			−0.147442
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	−5.50000	+	9.52628i	−0.777817	+	1.34722i
$51$		0			0
$52$	−1.50000	−	2.59808i	−0.208013	−	0.360288i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$		0			0
$55$	−16.0000			−2.15744
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	−0.500000	+	0.866025i	−0.0656532	+	0.113715i
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	−0.656136	−	0.754643i	$-0.727810\pi$
$59$	2.50000	−	4.33013i	0.325472	−	0.563735i	0.981608	+	0.190909i	$0.0611434\pi$
$60$		0			0
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	0.991645	−	0.128994i	$-0.0411748\pi$
$61$	3.00000	+	5.19615i	0.384111	+	0.665299i	−0.607535	+	0.794293i	$0.707841\pi$
$62$	−9.00000			−1.14300
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	−	10.3923i	−0.744208	−	1.28901i
$66$		0			0
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	−0.996659	−	0.0816792i	$-0.973972\pi$
$67$	−3.50000	+	6.06218i	−0.427593	+	0.740613i	0.569066	+	0.822292i	$0.307305\pi$
$68$	3.50000	−	6.06218i	0.424437	−	0.735147i
$69$		0			0
$70$	2.00000	+	3.46410i	0.239046	+	0.414039i
$71$	−7.00000			−0.830747			−0.415374	−	0.909651i	$-0.636349\pi$
$71$	−7.00000			−0.830747			−0.415374	+	0.909651i	$0.636349\pi$
$72$		0			0
$73$	−14.0000			−1.63858			−0.819288	−	0.573382i	$-0.805631\pi$
$73$	−14.0000			−1.63858			−0.819288	+	0.573382i	$0.805631\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$		0			0
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−2.00000	+	3.46410i	−0.227921	+	0.394771i
$78$		0			0
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	4.00000			0.447214
$81$		0			0
$82$	6.00000			0.662589
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	0.954664	−	0.297686i	$-0.0962148\pi$
$83$	2.00000	+	3.46410i	0.219529	+	0.380235i	−0.735135	+	0.677920i	$0.762881\pi$
$84$		0			0
$85$	14.0000	−	24.2487i	1.51851	−	2.63014i
$86$	−5.50000	+	9.52628i	−0.593080	+	1.02725i
$87$		0			0
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	−3.00000			−0.314485
$92$	0.500000	+	0.866025i	0.0521286	+	0.0902894i
$93$		0			0
$94$	3.00000	−	5.19615i	0.309426	−	0.535942i
$95$	−4.00000	+	6.92820i	−0.410391	+	0.710819i
$96$		0			0
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	0.994453	−	0.105180i	$-0.0335417\pi$
$97$	4.00000	+	6.92820i	0.406138	+	0.703452i	−0.588315	+	0.808632i	$0.700208\pi$
$98$	1.00000			0.101015
$99$		0			0
$100$	11.0000			1.10000
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	0.502477	−	0.864590i	$-0.332422\pi$
$101$	−5.00000	−	8.66025i	−0.497519	−	0.861727i	−0.999996	+	0.00286291i	$0.999089\pi$
$102$		0			0
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	0.0544240	+	0.998518i	$0.482668\pi$
$103$	−8.50000	+	14.7224i	−0.837530	+	1.45064i	−0.891954	+	0.452126i	$0.850666\pi$
$104$	−1.50000	+	2.59808i	−0.147087	+	0.254762i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$		0			0
$109$	16.0000			1.53252			0.766261	−	0.642529i	$-0.222115\pi$
$109$	16.0000			1.53252			0.766261	+	0.642529i	$0.222115\pi$
$110$	8.00000	+	13.8564i	0.762770	+	1.32116i
$111$		0			0
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	−0.614231	−	0.789127i	$-0.710534\pi$
$113$	4.00000	−	6.92820i	0.376288	−	0.651751i	0.990519	+	0.137376i	$0.0438669\pi$
$114$		0			0
$115$	2.00000	+	3.46410i	0.186501	+	0.323029i
$116$	1.00000			0.0928477
$117$		0			0
$118$	−5.00000			−0.460287
$119$	−3.50000	−	6.06218i	−0.320844	−	0.555719i
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	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
$127$		0			0			−	1.00000i	$-0.5\pi$
$127$		0			0				1.00000i	$0.5\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	−6.00000	+	10.3923i	−0.526235	+	0.911465i
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	−0.887041	−	0.461690i	$-0.847243\pi$
$131$	−0.500000	+	0.866025i	−0.0436852	+	0.0756650i	0.843356	+	0.537355i	$0.180577\pi$
$132$		0			0
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$	7.00000			0.604708
$135$		0			0
$136$	−7.00000			−0.600245
$137$	−11.0000	−	19.0526i	−0.939793	−	1.62777i	−0.765855	−	0.643013i	$-0.777684\pi$
$137$	−11.0000	−	19.0526i	−0.939793	−	1.62777i	−0.173939	−	0.984757i	$-0.555649\pi$
$138$		0			0
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	−0.996335	−	0.0855324i	$-0.972741\pi$
$139$	−5.00000	+	8.66025i	−0.424094	+	0.734553i	0.572241	+	0.820086i	$0.306074\pi$
$140$	2.00000	−	3.46410i	0.169031	−	0.292770i
$141$		0			0
$142$	3.50000	+	6.06218i	0.293713	+	0.508727i
$143$	−12.0000			−1.00349
$144$		0			0
$145$	4.00000			0.332182
$146$	7.00000	+	12.1244i	0.579324	+	1.00342i
$147$		0			0
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	−0.798019	−	0.602632i	$-0.794119\pi$
$149$	1.50000	−	2.59808i	0.122885	−	0.212843i	0.920904	+	0.389789i	$0.127452\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	2.00000			0.162221
$153$		0			0
$154$	4.00000			0.322329
$155$	18.0000	+	31.1769i	1.44579	+	2.50419i
$156$		0			0
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	0.297097	+	0.954847i	$0.403982\pi$
$157$	−8.50000	+	14.7224i	−0.678374	+	1.17498i	−0.975470	+	0.220131i	$0.929352\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$	−2.00000	−	3.46410i	−0.158114	−	0.273861i
$161$	1.00000			0.0788110
$162$		0			0
$163$	−1.00000			−0.0783260			−0.0391630	−	0.999233i	$-0.512469\pi$
$163$	−1.00000			−0.0783260			−0.0391630	+	0.999233i	$0.512469\pi$
$164$	−3.00000	−	5.19615i	−0.234261	−	0.405751i
$165$		0			0
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	−0.668730	−	0.743505i	$-0.733162\pi$
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	0.978259	+	0.207385i	$0.0664952\pi$
$168$		0			0
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$	−28.0000			−2.14750
$171$		0			0
$172$	11.0000			0.838742
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	0.977064	−	0.212947i	$-0.0683062\pi$
$173$	4.00000	+	6.92820i	0.304114	+	0.526742i	−0.672949	+	0.739689i	$0.734973\pi$
$174$		0			0
$175$	5.50000	−	9.52628i	0.415761	−	0.720119i
$176$	2.00000	−	3.46410i	0.150756	−	0.261116i
$177$		0			0
$178$	1.50000	+	2.59808i	0.112430	+	0.194734i
$179$	−12.0000			−0.896922			−0.448461	−	0.893802i	$-0.648028\pi$
$179$	−12.0000			−0.896922			−0.448461	+	0.893802i	$0.648028\pi$
$180$		0			0
$181$	−9.00000			−0.668965			−0.334482	−	0.942402i	$-0.608561\pi$
$181$	−9.00000			−0.668965			−0.334482	+	0.942402i	$0.608561\pi$
$182$	1.50000	+	2.59808i	0.111187	+	0.192582i
$183$		0			0
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−4.00000	+	6.92820i	−0.294086	+	0.509372i
$186$		0			0
$187$	−14.0000	−	24.2487i	−1.02378	−	1.77324i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	8.00000			0.580381
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	0.563081	−	0.826402i	$-0.309616\pi$
$191$	−6.00000	−	10.3923i	−0.434145	−	0.751961i	−0.997225	+	0.0744412i	$0.976283\pi$
$192$		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	$0.224262\pi$
$194$	4.00000	−	6.92820i	0.287183	−	0.497416i
$195$		0			0
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	26.0000			1.85242			0.926212	−	0.377004i	$-0.123046\pi$
$197$	26.0000			1.85242			0.926212	+	0.377004i	$0.123046\pi$
$198$		0			0
$199$	−7.00000			−0.496217			−0.248108	−	0.968732i	$-0.579809\pi$
$199$	−7.00000			−0.496217			−0.248108	+	0.968732i	$0.579809\pi$
$200$	−5.50000	−	9.52628i	−0.388909	−	0.673610i
$201$		0			0
$202$	−5.00000	+	8.66025i	−0.351799	+	0.609333i
$203$	0.500000	−	0.866025i	0.0350931	−	0.0607831i
$204$		0			0
$205$	−12.0000	−	20.7846i	−0.838116	−	1.45166i
$206$	17.0000			1.18445
$207$		0			0
$208$	3.00000			0.208013
$209$	4.00000	+	6.92820i	0.276686	+	0.479234i
$210$		0			0
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	−0.848301	−	0.529514i	$-0.822374\pi$
$211$	0.500000	−	0.866025i	0.0344214	−	0.0596196i	0.882723	+	0.469894i	$0.155708\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	44.0000			3.00078
$216$		0			0
$217$	9.00000			0.610960
$218$	−8.00000	−	13.8564i	−0.541828	−	0.938474i
$219$		0			0
$220$	8.00000	−	13.8564i	0.539360	−	0.934199i
$221$	10.5000	−	18.1865i	0.706306	−	1.22336i
$222$		0			0
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	−8.00000			−0.532152
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	0.975833	−	0.218517i	$-0.0701218\pi$
$227$	4.50000	+	7.79423i	0.298675	+	0.517321i	−0.677158	+	0.735838i	$0.736789\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	2.00000	−	3.46410i	0.131876	−	0.228416i
$231$		0			0
$232$	−0.500000	−	0.866025i	−0.0328266	−	0.0568574i
$233$	−4.00000			−0.262049			−0.131024	−	0.991379i	$-0.541827\pi$
$233$	−4.00000			−0.262049			−0.131024	+	0.991379i	$0.541827\pi$
$234$		0			0
$235$	−24.0000			−1.56559
$236$	2.50000	+	4.33013i	0.162736	+	0.281867i
$237$		0			0
$238$	−3.50000	+	6.06218i	−0.226871	+	0.392953i
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	−0.992195	−	0.124696i	$-0.960204\pi$
$239$	−6.00000	+	10.3923i	−0.388108	+	0.672222i	0.604087	+	0.796918i	$0.293538\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	5.00000			0.321412
$243$		0			0
$244$	−6.00000			−0.384111
$245$	−2.00000	−	3.46410i	−0.127775	−	0.221313i
$246$		0			0
$247$	−3.00000	+	5.19615i	−0.190885	+	0.330623i
$248$	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
$253$	4.00000			0.251478
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.162247	+	0.986750i	$0.551874\pi$
$257$	−15.0000	+	25.9808i	−0.935674	+	1.62064i	−0.773427	+	0.633885i	$0.781459\pi$
$258$		0			0
$259$	1.00000	+	1.73205i	0.0621370	+	0.107624i
$260$	12.0000			0.744208
$261$		0			0
$262$	1.00000			0.0617802
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	0.693276	−	0.720672i	$-0.256167\pi$
$263$	−4.50000	−	7.79423i	−0.277482	−	0.480613i	−0.970758	+	0.240059i	$0.922833\pi$
$264$		0			0
$265$	18.0000	−	31.1769i	1.10573	−	1.91518i
$266$	1.00000	−	1.73205i	0.0613139	−	0.106199i
$267$		0			0
$268$	−3.50000	−	6.06218i	−0.213797	−	0.370306i
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$		0			0
$271$	3.00000			0.182237			0.0911185	−	0.995840i	$-0.470956\pi$
$271$	3.00000			0.182237			0.0911185	+	0.995840i	$0.470956\pi$
$272$	3.50000	+	6.06218i	0.212219	+	0.367574i
$273$		0			0
$274$	−11.0000	+	19.0526i	−0.664534	+	1.15101i
$275$	22.0000	−	38.1051i	1.32665	−	2.29783i
$276$		0			0
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	0.720473	−	0.693482i	$-0.243925\pi$
$277$	−4.00000	−	6.92820i	−0.240337	−	0.416275i	−0.960810	+	0.277207i	$0.910591\pi$
$278$	10.0000			0.599760
$279$		0			0
$280$	−4.00000			−0.239046
$281$	5.00000	+	8.66025i	0.298275	+	0.516627i	0.975741	−	0.218926i	$-0.0702554\pi$
$281$	5.00000	+	8.66025i	0.298275	+	0.516627i	−0.677466	+	0.735554i	$0.736922\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	3.50000	−	6.06218i	0.207687	−	0.359724i
$285$		0			0
$286$	6.00000	+	10.3923i	0.354787	+	0.614510i
$287$	−6.00000			−0.354169
$288$		0			0
$289$	32.0000			1.88235
$290$	−2.00000	−	3.46410i	−0.117444	−	0.203419i
$291$		0			0
$292$	7.00000	−	12.1244i	0.409644	−	0.709524i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$		0			0
$295$	10.0000	+	17.3205i	0.582223	+	1.00844i
$296$	2.00000			0.116248
$297$		0			0
$298$	−3.00000			−0.173785
$299$	1.50000	+	2.59808i	0.0867472	+	0.150251i
$300$		0			0
$301$	5.50000	−	9.52628i	0.317015	−	0.549086i
$302$	−5.00000	+	8.66025i	−0.287718	+	0.498342i
$303$		0			0
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	−24.0000			−1.37424
$306$		0			0
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	−2.00000	−	3.46410i	−0.113961	−	0.197386i
$309$		0			0
$310$	18.0000	−	31.1769i	1.02233	−	1.77073i
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	−0.730044	−	0.683400i	$-0.760501\pi$
$311$	4.00000	−	6.92820i	0.226819	−	0.392862i	0.956864	+	0.290537i	$0.0938340\pi$
$312$		0			0
$313$	13.0000	+	22.5167i	0.734803	+	1.27272i	0.954810	+	0.297218i	$0.0960589\pi$
$313$	13.0000	+	22.5167i	0.734803	+	1.27272i	−0.220006	+	0.975499i	$0.570608\pi$
$314$	17.0000			0.959366
$315$		0			0
$316$	−6.00000			−0.337526
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	2.00000	−	3.46410i	0.111979	−	0.193952i
$320$	−2.00000	+	3.46410i	−0.111803	+	0.193649i
$321$		0			0
$322$	−0.500000	−	0.866025i	−0.0278639	−	0.0482617i
$323$	−14.0000			−0.778981
$324$		0			0
$325$	33.0000			1.83051
$326$	0.500000	+	0.866025i	0.0276924	+	0.0479647i
$327$		0			0
$328$	−3.00000	+	5.19615i	−0.165647	+	0.286910i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	15.5000	+	26.8468i	0.851957	+	1.47563i	0.879440	+	0.476011i	$0.157918\pi$
$331$	15.5000	+	26.8468i	0.851957	+	1.47563i	−0.0274825	+	0.999622i	$0.508749\pi$
$332$	−4.00000			−0.219529
$333$		0			0
$334$	−8.00000			−0.437741
$335$	−14.0000	−	24.2487i	−0.764902	−	1.32485i
$336$		0			0
$337$	−13.5000	+	23.3827i	−0.735392	+	1.27374i	0.219159	+	0.975689i	$0.429669\pi$
$337$	−13.5000	+	23.3827i	−0.735392	+	1.27374i	−0.954551	+	0.298047i	$0.903665\pi$
$338$	2.00000	−	3.46410i	0.108786	−	0.188422i
$339$		0			0
$340$	14.0000	+	24.2487i	0.759257	+	1.31507i
$341$	36.0000			1.94951
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−5.50000	−	9.52628i	−0.296540	−	0.513623i
$345$		0			0
$346$	4.00000	−	6.92820i	0.215041	−	0.372463i
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	−0.999813	−	0.0193540i	$-0.993839\pi$
$347$	−9.00000	+	15.5885i	−0.483145	+	0.836832i	0.516667	+	0.856186i	$0.327172\pi$
$348$		0			0
$349$	−12.5000	−	21.6506i	−0.669110	−	1.15893i	−0.978153	−	0.207884i	$-0.933342\pi$
$349$	−12.5000	−	21.6506i	−0.669110	−	1.15893i	0.309044	−	0.951048i	$-0.399991\pi$
$350$	−11.0000			−0.587975
$351$		0			0
$352$	−4.00000			−0.213201
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	0.594441	−	0.804139i	$-0.297373\pi$
$353$	−7.50000	−	12.9904i	−0.399185	−	0.691408i	−0.993626	+	0.112731i	$0.964040\pi$
$354$		0			0
$355$	14.0000	−	24.2487i	0.743043	−	1.28699i
$356$	1.50000	−	2.59808i	0.0794998	−	0.137698i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−11.0000			−0.580558			−0.290279	−	0.956942i	$-0.593748\pi$
$359$	−11.0000			−0.580558			−0.290279	+	0.956942i	$0.593748\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	4.50000	+	7.79423i	0.236515	+	0.409656i
$363$		0			0
$364$	1.50000	−	2.59808i	0.0786214	−	0.136176i
$365$	28.0000	−	48.4974i	1.46559	−	2.53847i
$366$		0			0
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	0.982516	+	0.186180i	$0.0596109\pi$
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	−0.330021	+	0.943974i	$0.607056\pi$
$368$	−1.00000			−0.0521286
$369$		0			0
$370$	8.00000			0.415900
$371$	−4.50000	−	7.79423i	−0.233628	−	0.404656i
$372$		0			0
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.336557	−	0.941663i	$-0.390737\pi$
$373$	19.0000	−	32.9090i	0.983783	−	1.70396i	0.647225	−	0.762299i	$-0.275929\pi$
$374$	−14.0000	+	24.2487i	−0.723923	+	1.25387i
$375$		0			0
$376$	3.00000	+	5.19615i	0.154713	+	0.267971i
$377$	3.00000			0.154508
$378$		0			0
$379$	−8.00000			−0.410932			−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−8.00000			−0.410932			−0.205466	+	0.978664i	$0.565871\pi$
$380$	−4.00000	−	6.92820i	−0.205196	−	0.355409i
$381$		0			0
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	−0.810394	−	0.585886i	$-0.800747\pi$
$383$	2.00000	−	3.46410i	0.102195	−	0.177007i	0.912589	+	0.408879i	$0.134080\pi$
$384$		0			0
$385$	−8.00000	−	13.8564i	−0.407718	−	0.706188i
$386$	5.00000			0.254493
$387$		0			0
$388$	−8.00000			−0.406138
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	0.987103	−	0.160085i	$-0.0511768\pi$
$389$	7.00000	+	12.1244i	0.354914	+	0.614729i	−0.632189	+	0.774814i	$0.717843\pi$
$390$		0			0
$391$	−3.50000	+	6.06218i	−0.177003	+	0.306578i
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$		0			0
$394$	−13.0000	−	22.5167i	−0.654931	−	1.13437i
$395$	−24.0000			−1.20757
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	3.50000	+	6.06218i	0.175439	+	0.303870i
$399$		0			0
$400$	−5.50000	+	9.52628i	−0.275000	+	0.476314i
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	0.199207	+	0.979957i	$0.436163\pi$
$401$	−15.0000	+	25.9808i	−0.749064	+	1.29742i	−0.948272	+	0.317460i	$0.897170\pi$
$402$		0			0
$403$	13.5000	+	23.3827i	0.672483	+	1.16477i
$404$	10.0000			0.497519
$405$		0			0
$406$	−1.00000			−0.0496292
$407$	4.00000	+	6.92820i	0.198273	+	0.343418i
$408$		0			0
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	−0.889689	−	0.456566i	$-0.849079\pi$
$409$	−1.00000	+	1.73205i	−0.0494468	+	0.0856444i	0.840243	+	0.542211i	$0.182412\pi$
$410$	−12.0000	+	20.7846i	−0.592638	+	1.02648i
$411$		0			0
$412$	−8.50000	−	14.7224i	−0.418765	−	0.725322i
$413$	5.00000			0.246034
$414$		0			0
$415$	−16.0000			−0.785409
$416$	−1.50000	−	2.59808i	−0.0735436	−	0.127381i
$417$		0			0
$418$	4.00000	−	6.92820i	0.195646	−	0.338869i
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	−0.109483	−	0.993989i	$-0.534920\pi$
$419$	16.5000	−	28.5788i	0.806078	−	1.39617i	0.915561	−	0.402179i	$-0.131747\pi$
$420$		0			0
$421$	3.00000	+	5.19615i	0.146211	+	0.253245i	0.929824	−	0.368004i	$-0.119959\pi$
$421$	3.00000	+	5.19615i	0.146211	+	0.253245i	−0.783613	+	0.621249i	$0.786625\pi$
$422$	−1.00000			−0.0486792
$423$		0			0
$424$	−9.00000			−0.437079
$425$	38.5000	+	66.6840i	1.86752	+	3.23465i
$426$		0			0
$427$	−3.00000	+	5.19615i	−0.145180	+	0.251459i
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	−22.0000	−	38.1051i	−1.06093	−	1.83759i
$431$	24.0000			1.15604			0.578020	−	0.816023i	$-0.303826\pi$
$431$	24.0000			1.15604			0.578020	+	0.816023i	$0.303826\pi$
$432$		0			0
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$	−4.50000	−	7.79423i	−0.216007	−	0.374135i
$435$		0			0
$436$	−8.00000	+	13.8564i	−0.383131	+	0.663602i
$437$	1.00000	−	1.73205i	0.0478365	−	0.0828552i
$438$		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	$0.902235\pi$
$440$	−16.0000			−0.762770
$441$		0			0
$442$	−21.0000			−0.998868
$443$	−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
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	4.00000			0.188772			0.0943858	−	0.995536i	$-0.469911\pi$
$449$	4.00000			0.188772			0.0943858	+	0.995536i	$0.469911\pi$
$450$		0			0
$451$	−24.0000			−1.13012
$452$	4.00000	+	6.92820i	0.188144	+	0.325875i
$453$		0			0
$454$	4.50000	−	7.79423i	0.211195	−	0.365801i
$455$	6.00000	−	10.3923i	0.281284	−	0.487199i
$456$		0			0
$457$	14.5000	+	25.1147i	0.678281	+	1.17482i	0.975498	+	0.220008i	$0.0706083\pi$
$457$	14.5000	+	25.1147i	0.678281	+	1.17482i	−0.297217	+	0.954810i	$0.596058\pi$
$458$	−14.0000			−0.654177
$459$		0			0
$460$	−4.00000			−0.186501
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	0.981719	−	0.190337i	$-0.0609581\pi$
$461$	7.00000	+	12.1244i	0.326023	+	0.564688i	−0.655696	+	0.755025i	$0.727625\pi$
$462$		0			0
$463$	−11.0000	+	19.0526i	−0.511213	+	0.885448i	0.488702	+	0.872451i	$0.337470\pi$
$463$	−11.0000	+	19.0526i	−0.511213	+	0.885448i	−0.999916	+	0.0129968i	$0.995863\pi$
$464$	−0.500000	+	0.866025i	−0.0232119	+	0.0402042i
$465$		0			0
$466$	2.00000	+	3.46410i	0.0926482	+	0.160471i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$		0			0
$469$	−7.00000			−0.323230
$470$	12.0000	+	20.7846i	0.553519	+	0.958723i
$471$		0			0
$472$	2.50000	−	4.33013i	0.115072	−	0.199310i
$473$	22.0000	−	38.1051i	1.01156	−	1.75208i
$474$		0			0
$475$	−11.0000	−	19.0526i	−0.504715	−	0.874191i
$476$	7.00000			0.320844
$477$		0			0
$478$	12.0000			0.548867
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	0.760056	−	0.649857i	$-0.225171\pi$
$479$	−4.00000	−	6.92820i	−0.182765	−	0.316558i	−0.942821	+	0.333300i	$0.891838\pi$
$480$		0			0
$481$	−3.00000	+	5.19615i	−0.136788	+	0.236924i
$482$	5.00000	−	8.66025i	0.227744	−	0.394464i
$483$		0			0
$484$	−2.50000	−	4.33013i	−0.113636	−	0.196824i
$485$	−32.0000			−1.45305
$486$		0			0
$487$	26.0000			1.17817			0.589086	−	0.808070i	$-0.299488\pi$
$487$	26.0000			1.17817			0.589086	+	0.808070i	$0.299488\pi$
$488$	3.00000	+	5.19615i	0.135804	+	0.235219i
$489$		0			0
$490$	−2.00000	+	3.46410i	−0.0903508	+	0.156492i
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	0.457263	+	0.889332i	$0.348830\pi$
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	−0.998815	+	0.0486647i	$0.984503\pi$
$492$		0			0
$493$	3.50000	+	6.06218i	0.157632	+	0.273027i
$494$	6.00000			0.269953
$495$		0			0
$496$	−9.00000			−0.404112
$497$	−3.50000	−	6.06218i	−0.156996	−	0.271926i
$498$		0			0
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	0.361478	+	0.932381i	$0.382272\pi$
$499$	−14.0000	+	24.2487i	−0.626726	+	1.08552i	−0.988204	+	0.153141i	$0.951061\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$		0			0
$502$		0			0
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$		0			0
$505$	40.0000			1.77998
$506$	−2.00000	−	3.46410i	−0.0889108	−	0.153998i
$507$		0			0
$508$		0			0
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	−7.00000	−	12.1244i	−0.309662	−	0.536350i
$512$	1.00000			0.0441942
$513$		0			0
$514$	30.0000			1.32324
$515$	−34.0000	−	58.8897i	−1.49822	−	2.59499i
$516$		0			0
$517$	−12.0000	+	20.7846i	−0.527759	+	0.914106i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	−15.0000			−0.657162			−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000			−0.657162			−0.328581	+	0.944476i	$0.606570\pi$
$522$		0			0
$523$	−16.0000			−0.699631			−0.349816	−	0.936819i	$-0.613756\pi$
$523$	−16.0000			−0.699631			−0.349816	+	0.936819i	$0.613756\pi$
$524$	−0.500000	−	0.866025i	−0.0218426	−	0.0378325i
$525$		0			0
$526$	−4.50000	+	7.79423i	−0.196209	+	0.339845i
$527$	−31.5000	+	54.5596i	−1.37216	+	2.37665i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−36.0000			−1.56374
$531$		0			0
$532$	−2.00000			−0.0867110
$533$	−9.00000	−	15.5885i	−0.389833	−	0.675211i
$534$		0			0
$535$	−24.0000	+	41.5692i	−1.03761	+	1.79719i
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$		0			0
$538$	−2.00000	−	3.46410i	−0.0862261	−	0.149348i
$539$	−4.00000			−0.172292
$540$		0			0
$541$	−36.0000			−1.54776			−0.773880	−	0.633332i	$-0.781687\pi$
$541$	−36.0000			−1.54776			−0.773880	+	0.633332i	$0.781687\pi$
$542$	−1.50000	−	2.59808i	−0.0644305	−	0.111597i
$543$		0			0
$544$	3.50000	−	6.06218i	0.150061	−	0.259914i
$545$	−32.0000	+	55.4256i	−1.37073	+	2.37417i
$546$		0			0
$547$	−18.0000	−	31.1769i	−0.769624	−	1.33303i	−0.937767	−	0.347266i	$-0.887110\pi$
$547$	−18.0000	−	31.1769i	−0.769624	−	1.33303i	0.168142	−	0.985763i	$-0.446223\pi$
$548$	22.0000			0.939793
$549$		0			0
$550$	−44.0000			−1.87617
$551$	−1.00000	−	1.73205i	−0.0426014	−	0.0737878i
$552$		0			0
$553$	−3.00000	+	5.19615i	−0.127573	+	0.220963i
$554$	−4.00000	+	6.92820i	−0.169944	+	0.294351i
$555$		0			0
$556$	−5.00000	−	8.66025i	−0.212047	−	0.367277i
$557$	1.00000			0.0423714			0.0211857	−	0.999776i	$-0.493256\pi$
$557$	1.00000			0.0423714			0.0211857	+	0.999776i	$0.493256\pi$
$558$		0			0
$559$	33.0000			1.39575
$560$	2.00000	+	3.46410i	0.0845154	+	0.146385i
$561$		0			0
$562$	5.00000	−	8.66025i	0.210912	−	0.365311i
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	−0.958337	−	0.285640i	$-0.907794\pi$
$563$	−5.50000	+	9.52628i	−0.231797	+	0.401485i	0.726540	+	0.687124i	$0.241127\pi$
$564$		0			0
$565$	16.0000	+	27.7128i	0.673125	+	1.16589i
$566$	28.0000			1.17693
$567$		0			0
$568$	−7.00000			−0.293713
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	0.712415	−	0.701758i	$-0.247601\pi$
$569$	−6.00000	−	10.3923i	−0.251533	−	0.435668i	−0.963948	+	0.266090i	$0.914268\pi$
$570$		0			0
$571$	19.5000	−	33.7750i	0.816050	−	1.41344i	−0.0925222	−	0.995711i	$-0.529493\pi$
$571$	19.5000	−	33.7750i	0.816050	−	1.41344i	0.908572	−	0.417729i	$-0.137174\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$		0			0
$574$	3.00000	+	5.19615i	0.125218	+	0.216883i
$575$	−11.0000			−0.458732
$576$		0			0
$577$	10.0000			0.416305			0.208153	−	0.978096i	$-0.433255\pi$
$577$	10.0000			0.416305			0.208153	+	0.978096i	$0.433255\pi$
$578$	−16.0000	−	27.7128i	−0.665512	−	1.15270i
$579$		0			0
$580$	−2.00000	+	3.46410i	−0.0830455	+	0.143839i
$581$	−2.00000	+	3.46410i	−0.0829740	+	0.143715i
$582$		0			0
$583$	−18.0000	−	31.1769i	−0.745484	−	1.29122i
$584$	−14.0000			−0.579324
$585$		0			0
$586$	6.00000			0.247858
$587$	12.5000	+	21.6506i	0.515930	+	0.893617i	0.999829	+	0.0184934i	$0.00588696\pi$
$587$	12.5000	+	21.6506i	0.515930	+	0.893617i	−0.483899	+	0.875124i	$0.660780\pi$
$588$		0			0
$589$	9.00000	−	15.5885i	0.370839	−	0.642311i
$590$	10.0000	−	17.3205i	0.411693	−	0.713074i
$591$		0			0
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$		0			0
$595$	28.0000			1.14789
$596$	1.50000	+	2.59808i	0.0614424	+	0.106421i
$597$		0			0
$598$	1.50000	−	2.59808i	0.0613396	−	0.106243i
$599$	−10.5000	+	18.1865i	−0.429018	+	0.743082i	−0.996786	−	0.0801071i	$-0.974474\pi$
$599$	−10.5000	+	18.1865i	−0.429018	+	0.743082i	0.567768	+	0.823189i	$0.307807\pi$
$600$		0			0
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	0.996456	+	0.0841128i	$0.0268056\pi$
$601$	14.0000	+	24.2487i	0.571072	+	0.989126i	−0.425384	+	0.905013i	$0.639861\pi$
$602$	−11.0000			−0.448327
$603$		0			0
$604$	10.0000			0.406894
$605$	−10.0000	−	17.3205i	−0.406558	−	0.704179i
$606$		0			0
$607$	−19.5000	+	33.7750i	−0.791481	+	1.37088i	0.133570	+	0.991039i	$0.457356\pi$
$607$	−19.5000	+	33.7750i	−0.791481	+	1.37088i	−0.925050	+	0.379845i	$0.875977\pi$
$608$	−1.00000	+	1.73205i	−0.0405554	+	0.0702439i
$609$		0			0
$610$	12.0000	+	20.7846i	0.485866	+	0.841544i
$611$	−18.0000			−0.728202
$612$		0			0
$613$	−6.00000			−0.242338			−0.121169	−	0.992632i	$-0.538664\pi$
$613$	−6.00000			−0.242338			−0.121169	+	0.992632i	$0.538664\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$	−2.00000	+	3.46410i	−0.0805823	+	0.139573i
$617$	−7.00000	+	12.1244i	−0.281809	+	0.488108i	−0.971830	−	0.235681i	$-0.924268\pi$
$617$	−7.00000	+	12.1244i	−0.281809	+	0.488108i	0.690021	+	0.723789i	$0.257601\pi$
$618$		0			0
$619$	7.00000	+	12.1244i	0.281354	+	0.487319i	0.971718	−	0.236143i	$-0.0758832\pi$
$619$	7.00000	+	12.1244i	0.281354	+	0.487319i	−0.690365	+	0.723462i	$0.742550\pi$
$620$	−36.0000			−1.44579
$621$		0			0
$622$	−8.00000			−0.320771
$623$	−1.50000	−	2.59808i	−0.0600962	−	0.104090i
$624$		0			0
$625$	−20.5000	+	35.5070i	−0.820000	+	1.42028i
$626$	13.0000	−	22.5167i	0.519584	−	0.899947i
$627$		0			0
$628$	−8.50000	−	14.7224i	−0.339187	−	0.587489i
$629$	−14.0000			−0.558217
$630$		0			0
$631$	−4.00000			−0.159237			−0.0796187	−	0.996825i	$-0.525370\pi$
$631$	−4.00000			−0.159237			−0.0796187	+	0.996825i	$0.525370\pi$
$632$	3.00000	+	5.19615i	0.119334	+	0.206692i
$633$		0			0
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$		0			0
$636$		0			0
$637$	−1.50000	−	2.59808i	−0.0594322	−	0.102940i
$638$	−4.00000			−0.158362
$639$		0			0
$640$	4.00000			0.158114
$641$	14.0000	+	24.2487i	0.552967	+	0.957767i	0.998059	+	0.0622816i	$0.0198377\pi$
$641$	14.0000	+	24.2487i	0.552967	+	0.957767i	−0.445092	+	0.895485i	$0.646829\pi$
$642$		0			0
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	−0.823891	−	0.566748i	$-0.808201\pi$
$643$	2.00000	−	3.46410i	0.0788723	−	0.136611i	0.902764	+	0.430137i	$0.141535\pi$
$644$	−0.500000	+	0.866025i	−0.0197028	+	0.0341262i
$645$		0			0
$646$	7.00000	+	12.1244i	0.275411	+	0.477026i
$647$	42.0000			1.65119			0.825595	−	0.564263i	$-0.190840\pi$
$647$	42.0000			1.65119			0.825595	+	0.564263i	$0.190840\pi$
$648$		0			0
$649$	20.0000			0.785069
$650$	−16.5000	−	28.5788i	−0.647183	−	1.12095i
$651$		0			0
$652$	0.500000	−	0.866025i	0.0195815	−	0.0339162i
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	−0.893882	−	0.448303i	$-0.852029\pi$
$653$	−1.50000	+	2.59808i	−0.0586995	+	0.101671i	0.835182	+	0.549973i	$0.185362\pi$
$654$		0			0
$655$	−2.00000	−	3.46410i	−0.0781465	−	0.135354i
$656$	6.00000			0.234261
$657$		0			0
$658$	6.00000			0.233904
$659$	14.0000	+	24.2487i	0.545363	+	0.944596i	0.998584	+	0.0531977i	$0.0169414\pi$
$659$	14.0000	+	24.2487i	0.545363	+	0.944596i	−0.453221	+	0.891398i	$0.649725\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	15.5000	−	26.8468i	0.602425	−	1.04343i
$663$		0			0
$664$	2.00000	+	3.46410i	0.0776151	+	0.134433i
$665$	−8.00000			−0.310227
$666$		0			0
$667$	−1.00000			−0.0387202
$668$	4.00000	+	6.92820i	0.154765	+	0.268060i
$669$		0			0
$670$	−14.0000	+	24.2487i	−0.540867	+	0.936809i
$671$	−12.0000	+	20.7846i	−0.463255	+	0.802381i
$672$		0			0
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	0.554639	−	0.832091i	$-0.312856\pi$
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	−0.997932	+	0.0642860i	$0.979523\pi$
$674$	27.0000			1.04000
$675$		0			0
$676$	−4.00000			−0.153846
$677$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$677$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$678$		0			0
$679$	−4.00000	+	6.92820i	−0.153506	+	0.265880i
$680$	14.0000	−	24.2487i	0.536875	−	0.929896i
$681$		0			0
$682$	−18.0000	−	31.1769i	−0.689256	−	1.19383i
$683$	−48.0000			−1.83667			−0.918334	−	0.395805i	$-0.870466\pi$
$683$	−48.0000			−1.83667			−0.918334	+	0.395805i	$0.870466\pi$
$684$		0			0
$685$	88.0000			3.36231
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		0			0
$688$	−5.50000	+	9.52628i	−0.209686	+	0.363186i
$689$	13.5000	−	23.3827i	0.514309	−	0.890809i
$690$		0			0
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	0.942420	+	0.334431i	$0.108544\pi$
$691$	20.0000	+	34.6410i	0.760836	+	1.31781i	−0.181584	+	0.983375i	$0.558123\pi$
$692$	−8.00000			−0.304114
$693$		0			0
$694$	18.0000			0.683271
$695$	−20.0000	−	34.6410i	−0.758643	−	1.31401i
$696$		0			0
$697$	21.0000	−	36.3731i	0.795432	−	1.37773i
$698$	−12.5000	+	21.6506i	−0.473132	+	0.819489i
$699$		0			0
$700$	5.50000	+	9.52628i	0.207880	+	0.360060i
$701$	−2.00000			−0.0755390			−0.0377695	−	0.999286i	$-0.512025\pi$
$701$	−2.00000			−0.0755390			−0.0377695	+	0.999286i	$0.512025\pi$
$702$		0			0
$703$	4.00000			0.150863
$704$	2.00000	+	3.46410i	0.0753778	+	0.130558i
$705$		0			0
$706$	−7.50000	+	12.9904i	−0.282266	+	0.488899i
$707$	5.00000	−	8.66025i	0.188044	−	0.325702i
$708$		0			0
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	0.947282	+	0.320400i	$0.103817\pi$
$709$	20.0000	+	34.6410i	0.751116	+	1.30097i	−0.196167	+	0.980571i	$0.562849\pi$
$710$	−28.0000			−1.05082
$711$		0			0
$712$	−3.00000			−0.112430
$713$	−4.50000	−	7.79423i	−0.168526	−	0.291896i
$714$		0			0
$715$	24.0000	−	41.5692i	0.897549	−	1.55460i
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	5.50000	+	9.52628i	0.205258	+	0.355518i
$719$	48.0000			1.79010			0.895049	−	0.445968i	$-0.147140\pi$
$719$	48.0000			1.79010			0.895049	+	0.445968i	$0.147140\pi$
$720$		0			0
$721$	−17.0000			−0.633113
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$		0			0
$724$	4.50000	−	7.79423i	0.167241	−	0.289670i
$725$	−5.50000	+	9.52628i	−0.204265	+	0.353797i
$726$		0			0
$727$	14.5000	+	25.1147i	0.537775	+	0.931454i	0.999023	+	0.0441829i	$0.0140684\pi$
$727$	14.5000	+	25.1147i	0.537775	+	0.931454i	−0.461248	+	0.887271i	$0.652598\pi$
$728$	−3.00000			−0.111187
$729$		0			0
$730$	−56.0000			−2.07265
$731$	38.5000	+	66.6840i	1.42397	+	2.46640i
$732$		0			0
$733$	7.50000	−	12.9904i	0.277019	−	0.479811i	−0.693624	−	0.720338i	$-0.743987\pi$
$733$	7.50000	−	12.9904i	0.277019	−	0.479811i	0.970642	+	0.240527i	$0.0773202\pi$
$734$	12.5000	−	21.6506i	0.461383	−	0.799140i
$735$		0			0
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	−28.0000			−1.03139
$738$		0			0
$739$	12.0000			0.441427			0.220714	−	0.975339i	$-0.429161\pi$
$739$	12.0000			0.441427			0.220714	+	0.975339i	$0.429161\pi$
$740$	−4.00000	−	6.92820i	−0.147043	−	0.254686i
$741$		0			0
$742$	−4.50000	+	7.79423i	−0.165200	+	0.286135i
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.161772	+	0.986828i	$0.551721\pi$
$743$	−25.5000	+	44.1673i	−0.935504	+	1.62034i	−0.773732	+	0.633513i	$0.781612\pi$
$744$		0			0
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	−38.0000			−1.39128
$747$		0			0
$748$	28.0000			1.02378
$749$	6.00000	+	10.3923i	0.219235	+	0.379727i
$750$		0			0
$751$	−3.00000	+	5.19615i	−0.109472	+	0.189610i	−0.915556	−	0.402190i	$-0.868249\pi$
$751$	−3.00000	+	5.19615i	−0.109472	+	0.189610i	0.806085	+	0.591800i	$0.201583\pi$
$752$	3.00000	−	5.19615i	0.109399	−	0.189484i
$753$		0			0
$754$	−1.50000	−	2.59808i	−0.0546268	−	0.0946164i
$755$	40.0000			1.45575
$756$		0			0
$757$	−12.0000			−0.436147			−0.218074	−	0.975932i	$-0.569977\pi$
$757$	−12.0000			−0.436147			−0.218074	+	0.975932i	$0.569977\pi$
$758$	4.00000	+	6.92820i	0.145287	+	0.251644i
$759$		0			0
$760$	−4.00000	+	6.92820i	−0.145095	+	0.251312i
$761$	6.50000	−	11.2583i	0.235625	−	0.408114i	−0.723829	−	0.689979i	$-0.757620\pi$
$761$	6.50000	−	11.2583i	0.235625	−	0.408114i	0.959454	+	0.281865i	$0.0909530\pi$
$762$		0			0
$763$	8.00000	+	13.8564i	0.289619	+	0.501636i
$764$	12.0000			0.434145
$765$		0			0
$766$	−4.00000			−0.144526
$767$	7.50000	+	12.9904i	0.270809	+	0.469055i
$768$		0			0
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	−0.899831	−	0.436239i	$-0.856310\pi$
$769$	−2.00000	+	3.46410i	−0.0721218	+	0.124919i	0.827709	+	0.561157i	$0.189644\pi$
$770$	−8.00000	+	13.8564i	−0.288300	+	0.499350i
$771$		0			0
$772$	−2.50000	−	4.33013i	−0.0899770	−	0.155845i
$773$	4.00000			0.143870			0.0719350	−	0.997409i	$-0.477083\pi$
$773$	4.00000			0.143870			0.0719350	+	0.997409i	$0.477083\pi$
$774$		0			0
$775$	−99.0000			−3.55618
$776$	4.00000	+	6.92820i	0.143592	+	0.248708i
$777$		0			0
$778$	7.00000	−	12.1244i	0.250962	−	0.434679i
$779$	−6.00000	+	10.3923i	−0.214972	+	0.372343i
$780$		0			0
$781$	−14.0000	−	24.2487i	−0.500959	−	0.867687i
$782$	7.00000			0.250319
$783$		0			0
$784$	1.00000			0.0357143
$785$	−34.0000	−	58.8897i	−1.21351	−	2.10186i
$786$		0			0
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	−0.980656	−	0.195737i	$-0.937290\pi$
$787$	−9.00000	+	15.5885i	−0.320815	+	0.555668i	0.659841	+	0.751405i	$0.270624\pi$
$788$	−13.0000	+	22.5167i	−0.463106	+	0.802123i
$789$		0			0
$790$	12.0000	+	20.7846i	0.426941	+	0.739483i
$791$	8.00000			0.284447
$792$		0			0
$793$	−18.0000			−0.639199
$794$	−3.00000	−	5.19615i	−0.106466	−	0.184405i
$795$		0			0
$796$	3.50000	−	6.06218i	0.124054	−	0.214868i
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	−0.661441	−	0.749997i	$-0.730055\pi$
$797$	9.00000	−	15.5885i	0.318796	−	0.552171i	0.980237	+	0.197826i	$0.0633881\pi$
$798$		0			0
$799$	−21.0000	−	36.3731i	−0.742927	−	1.28679i
$800$	11.0000			0.388909
$801$		0			0
$802$	30.0000			1.05934
$803$	−28.0000	−	48.4974i	−0.988099	−	1.71144i
$804$		0			0
$805$	−2.00000	+	3.46410i	−0.0704907	+	0.122094i
$806$	13.5000	−	23.3827i	0.475517	−	0.823620i
$807$		0			0
$808$	−5.00000	−	8.66025i	−0.175899	−	0.304667i
$809$	−32.0000			−1.12506			−0.562530	−	0.826777i	$-0.690172\pi$
$809$	−32.0000			−1.12506			−0.562530	+	0.826777i	$0.690172\pi$
$810$		0			0
$811$	−26.0000			−0.912983			−0.456492	−	0.889728i	$-0.650894\pi$
$811$	−26.0000			−0.912983			−0.456492	+	0.889728i	$0.650894\pi$
$812$	0.500000	+	0.866025i	0.0175466	+	0.0303915i
$813$		0			0
$814$	4.00000	−	6.92820i	0.140200	−	0.242833i
$815$	2.00000	−	3.46410i	0.0700569	−	0.121342i
$816$		0			0
$817$	−11.0000	−	19.0526i	−0.384841	−	0.666565i
$818$	2.00000			0.0699284
$819$		0			0
$820$	24.0000			0.838116
$821$	6.50000	+	11.2583i	0.226852	+	0.392918i	0.956873	−	0.290505i	$-0.0938234\pi$
$821$	6.50000	+	11.2583i	0.226852	+	0.392918i	−0.730022	+	0.683424i	$0.760490\pi$
$822$		0			0
$823$	19.0000	−	32.9090i	0.662298	−	1.14713i	−0.317712	−	0.948187i	$-0.602914\pi$
$823$	19.0000	−	32.9090i	0.662298	−	1.14713i	0.980010	−	0.198947i	$-0.0637522\pi$
$824$	−8.50000	+	14.7224i	−0.296112	+	0.512880i
$825$		0			0
$826$	−2.50000	−	4.33013i	−0.0869861	−	0.150664i
$827$	42.0000			1.46048			0.730242	−	0.683189i	$-0.239408\pi$
$827$	42.0000			1.46048			0.730242	+	0.683189i	$0.239408\pi$
$828$		0			0
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$	8.00000	+	13.8564i	0.277684	+	0.480963i
$831$		0			0
$832$	−1.50000	+	2.59808i	−0.0520031	+	0.0900721i
$833$	3.50000	−	6.06218i	0.121268	−	0.210042i
$834$		0			0
$835$	16.0000	+	27.7128i	0.553703	+	0.959041i
$836$	−8.00000			−0.276686
$837$		0			0
$838$	−33.0000			−1.13997
$839$	5.00000	+	8.66025i	0.172619	+	0.298985i	0.939335	−	0.343002i	$-0.111444\pi$
$839$	5.00000	+	8.66025i	0.172619	+	0.298985i	−0.766716	+	0.641987i	$0.778110\pi$
$840$		0			0
$841$	14.0000	−	24.2487i	0.482759	−	0.836162i
$842$	3.00000	−	5.19615i	0.103387	−	0.179071i
$843$		0			0
$844$	0.500000	+	0.866025i	0.0172107	+	0.0298098i
$845$	−16.0000			−0.550417
$846$		0			0
$847$	−5.00000			−0.171802
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$		0			0
$850$	38.5000	−	66.6840i	1.32054	−	2.28724i
$851$	1.00000	−	1.73205i	0.0342796	−	0.0593739i
$852$		0			0
$853$	−26.5000	−	45.8993i	−0.907343	−	1.57156i	−0.817741	−	0.575586i	$-0.804774\pi$
$853$	−26.5000	−	45.8993i	−0.907343	−	1.57156i	−0.0896015	−	0.995978i	$-0.528559\pi$
$854$	6.00000			0.205316
$855$		0			0
$856$	12.0000			0.410152
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	0.537867	−	0.843029i	$-0.319230\pi$
$857$	−13.5000	−	23.3827i	−0.461151	−	0.798737i	−0.999019	+	0.0442921i	$0.985897\pi$
$858$		0			0
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	−0.882581	−	0.470160i	$-0.844196\pi$
$859$	−1.00000	+	1.73205i	−0.0341196	+	0.0590968i	0.848461	+	0.529257i	$0.177529\pi$
$860$	−22.0000	+	38.1051i	−0.750194	+	1.29937i
$861$		0			0
$862$	−12.0000	−	20.7846i	−0.408722	−	0.707927i
$863$	1.00000			0.0340404			0.0170202	−	0.999855i	$-0.494582\pi$
$863$	1.00000			0.0340404			0.0170202	+	0.999855i	$0.494582\pi$
$864$		0			0
$865$	−32.0000			−1.08803
$866$	−4.00000	−	6.92820i	−0.135926	−	0.235430i
$867$		0			0
$868$	−4.50000	+	7.79423i	−0.152740	+	0.264553i
$869$	−12.0000	+	20.7846i	−0.407072	+	0.705070i
$870$		0			0
$871$	−10.5000	−	18.1865i	−0.355779	−	0.616227i
$872$	16.0000			0.541828
$873$		0			0
$874$	−2.00000			−0.0676510
$875$	12.0000	+	20.7846i	0.405674	+	0.702648i
$876$		0			0
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	−0.790554	−	0.612392i	$-0.790207\pi$
$877$	4.00000	−	6.92820i	0.135070	−	0.233949i	0.925624	+	0.378444i	$0.123541\pi$
$878$	−4.50000	+	7.79423i	−0.151868	+	0.263042i
$879$		0			0
$880$	8.00000	+	13.8564i	0.269680	+	0.467099i
$881$	15.0000			0.505363			0.252681	−	0.967550i	$-0.418688\pi$
$881$	15.0000			0.505363			0.252681	+	0.967550i	$0.418688\pi$
$882$		0			0
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	10.5000	+	18.1865i	0.353153	+	0.611679i
$885$		0			0
$886$	−13.0000	+	22.5167i	−0.436744	+	0.756462i
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	−0.747539	−	0.664218i	$-0.768765\pi$
$887$	6.00000	−	10.3923i	0.201460	−	0.348939i	0.948999	+	0.315279i	$0.102098\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$		0			0
$892$	8.00000			0.267860
$893$	6.00000	+	10.3923i	0.200782	+	0.347765i
$894$		0			0
$895$	24.0000	−	41.5692i	0.802232	−	1.38951i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$		0			0
$898$	−2.00000	−	3.46410i	−0.0667409	−	0.115599i
$899$	−9.00000			−0.300167
$900$		0			0
$901$	63.0000			2.09883
$902$	12.0000	+	20.7846i	0.399556	+	0.692052i
$903$		0			0
$904$	4.00000	−	6.92820i	0.133038	−	0.230429i
$905$	18.0000	−	31.1769i	0.598340	−	1.03636i
$906$		0			0
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	0.749051	−	0.662512i	$-0.230510\pi$
$907$	−6.00000	−	10.3923i	−0.199227	−	0.345071i	−0.948278	+	0.317441i	$0.897176\pi$
$908$	−9.00000			−0.298675
$909$		0			0
$910$	−12.0000			−0.397796
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	0.922740	+	0.385422i	$0.125944\pi$
$911$	24.0000	+	41.5692i	0.795155	+	1.37725i	−0.127585	+	0.991828i	$0.540723\pi$
$912$		0			0
$913$	−8.00000	+	13.8564i	−0.264761	+	0.458580i
$914$	14.5000	−	25.1147i	0.479617	−	0.830722i
$915$		0			0
$916$	7.00000	+	12.1244i	0.231287	+	0.400600i
$917$	−1.00000			−0.0330229
$918$		0			0
$919$	22.0000			0.725713			0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000			0.725713			0.362857	+	0.931845i	$0.381802\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$		0			0
$922$	7.00000	−	12.1244i	0.230533	−	0.399294i
$923$	10.5000	−	18.1865i	0.345612	−	0.598617i
$924$		0			0
$925$	−11.0000	−	19.0526i	−0.361678	−	0.626444i
$926$	22.0000			0.722965
$927$		0			0
$928$	1.00000			0.0328266
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	0.999959	−	0.00905914i	$-0.00288365\pi$
$929$	15.0000	+	25.9808i	0.492134	+	0.852401i	−0.507825	+	0.861460i	$0.669550\pi$
$930$		0			0
$931$	−1.00000	+	1.73205i	−0.0327737	+	0.0567657i
$932$	2.00000	−	3.46410i	0.0655122	−	0.113470i
$933$		0			0
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$	112.000			3.66279
$936$		0			0
$937$	−52.0000			−1.69877			−0.849383	−	0.527777i	$-0.823026\pi$
$937$	−52.0000			−1.69877			−0.849383	+	0.527777i	$0.823026\pi$
$938$	3.50000	+	6.06218i	0.114279	+	0.197937i
$939$		0			0
$940$	12.0000	−	20.7846i	0.391397	−	0.677919i
$941$	1.00000	−	1.73205i	0.0325991	−	0.0564632i	−0.849266	−	0.527966i	$-0.822955\pi$
$941$	1.00000	−	1.73205i	0.0325991	−	0.0564632i	0.881865	+	0.471503i	$0.156288\pi$
$942$		0			0
$943$	3.00000	+	5.19615i	0.0976934	+	0.169210i
$944$	−5.00000			−0.162736
$945$		0			0
$946$	−44.0000			−1.43056
$947$	1.00000	+	1.73205i	0.0324956	+	0.0562841i	0.881816	−	0.471594i	$-0.156321\pi$
$947$	1.00000	+	1.73205i	0.0324956	+	0.0562841i	−0.849320	+	0.527878i	$0.822988\pi$
$948$		0			0
$949$	21.0000	−	36.3731i	0.681689	−	1.18072i
$950$	−11.0000	+	19.0526i	−0.356887	+	0.618147i
$951$		0			0
$952$	−3.50000	−	6.06218i	−0.113436	−	0.196476i
$953$	8.00000			0.259145			0.129573	−	0.991570i	$-0.458639\pi$
$953$	8.00000			0.259145			0.129573	+	0.991570i	$0.458639\pi$
$954$		0			0
$955$	48.0000			1.55324
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$		0			0
$958$	−4.00000	+	6.92820i	−0.129234	+	0.223840i
$959$	11.0000	−	19.0526i	0.355209	−	0.615239i
$960$		0			0
$961$	−25.0000	−	43.3013i	−0.806452	−	1.39682i
$962$	6.00000			0.193448
$963$		0			0
$964$	−10.0000			−0.322078
$965$	−10.0000	−	17.3205i	−0.321911	−	0.557567i
$966$		0			0
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	−0.341567	−	0.939857i	$-0.610958\pi$
$967$	20.0000	−	34.6410i	0.643157	−	1.11398i	0.984724	−	0.174123i	$-0.0557089\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$		0			0
$970$	16.0000	+	27.7128i	0.513729	+	0.889805i
$971$	−15.0000			−0.481373			−0.240686	−	0.970603i	$-0.577373\pi$
$971$	−15.0000			−0.481373			−0.240686	+	0.970603i	$0.577373\pi$
$972$		0			0
$973$	−10.0000			−0.320585
$974$	−13.0000	−	22.5167i	−0.416547	−	0.721480i
$975$		0			0
$976$	3.00000	−	5.19615i	0.0960277	−	0.166325i
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	−0.305530	−	0.952183i	$-0.598833\pi$
$977$	21.0000	−	36.3731i	0.671850	−	1.16368i	0.977379	−	0.211495i	$-0.0678332\pi$
$978$		0			0
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$	4.00000			0.127775
$981$		0			0
$982$	24.0000			0.765871
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	−0.996138	−	0.0878058i	$-0.972015\pi$
$983$	−18.0000	−	31.1769i	−0.574111	−	0.994389i	0.422027	−	0.906583i	$-0.361319\pi$
$984$		0			0
$985$	−52.0000	+	90.0666i	−1.65686	+	2.86976i
$986$	3.50000	−	6.06218i	0.111463	−	0.193059i
$987$		0			0
$988$	−3.00000	−	5.19615i	−0.0954427	−	0.165312i
$989$	−11.0000			−0.349780
$990$		0			0
$991$	26.0000			0.825917			0.412959	−	0.910750i	$-0.364495\pi$
$991$	26.0000			0.825917			0.412959	+	0.910750i	$0.364495\pi$
$992$	4.50000	+	7.79423i	0.142875	+	0.247467i
$993$		0			0
$994$	−3.50000	+	6.06218i	−0.111013	+	0.192281i
$995$	14.0000	−	24.2487i	0.443830	−	0.768736i
$996$		0			0
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	−0.997963	−	0.0637961i	$-0.979679\pi$
$997$	−17.5000	−	30.3109i	−0.554231	−	0.959955i	0.443732	−	0.896159i	$-0.353654\pi$
$998$	28.0000			0.886325
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.a.757.1		2
3.2	odd	2		1134.2.f.p.757.1		2
9.2	odd	6		1134.2.f.p.379.1		2
9.4	even	3		378.2.a.h.1.1	yes	1
9.5	odd	6		378.2.a.a.1.1	✓	1
9.7	even	3	inner	1134.2.f.a.379.1		2
36.23	even	6		3024.2.a.a.1.1		1
36.31	odd	6		3024.2.a.bd.1.1		1
45.4	even	6		9450.2.a.bc.1.1		1
45.14	odd	6		9450.2.a.dv.1.1		1
63.13	odd	6		2646.2.a.p.1.1		1
63.41	even	6		2646.2.a.o.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
378.2.a.a.1.1	✓	1	9.5	odd	6
378.2.a.h.1.1	yes	1	9.4	even	3
1134.2.f.a.379.1		2	9.7	even	3	inner
1134.2.f.a.757.1		2	1.1	even	1	trivial
1134.2.f.p.379.1		2	9.2	odd	6
1134.2.f.p.757.1		2	3.2	odd	2
2646.2.a.o.1.1		1	63.41	even	6
2646.2.a.p.1.1		1	63.13	odd	6
3024.2.a.a.1.1		1	36.23	even	6
3024.2.a.bd.1.1		1	36.31	odd	6
9450.2.a.bc.1.1		1	45.4	even	6
9450.2.a.dv.1.1		1	45.14	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.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 + 3.46410i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +4.00000 q^{10} +(2.00000 + 3.46410i) q^{11} +(-1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -7.00000 q^{17} +2.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(2.00000 - 3.46410i) q^{22} +(0.500000 - 0.866025i) q^{23} +(-5.50000 - 9.52628i) q^{25} +3.00000 q^{26} -1.00000 q^{28} +(-0.500000 - 0.866025i) q^{29} +(4.50000 - 7.79423i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.50000 + 6.06218i) q^{34} -4.00000 q^{35} +2.00000 q^{37} +(-1.00000 - 1.73205i) q^{38} +(-2.00000 + 3.46410i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(-5.50000 - 9.52628i) q^{43} -4.00000 q^{44} -1.00000 q^{46} +(3.00000 + 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(-5.50000 + 9.52628i) q^{50} +(-1.50000 - 2.59808i) q^{52} -9.00000 q^{53} -16.0000 q^{55} +(0.500000 + 0.866025i) q^{56} +(-0.500000 + 0.866025i) q^{58} +(2.50000 - 4.33013i) q^{59} +(3.00000 + 5.19615i) q^{61} -9.00000 q^{62} +1.00000 q^{64} +(-6.00000 - 10.3923i) q^{65} +(-3.50000 + 6.06218i) q^{67} +(3.50000 - 6.06218i) q^{68} +(2.00000 + 3.46410i) q^{70} -7.00000 q^{71} -14.0000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(-2.00000 + 3.46410i) q^{77} +(3.00000 + 5.19615i) q^{79} +4.00000 q^{80} +6.00000 q^{82} +(2.00000 + 3.46410i) q^{83} +(14.0000 - 24.2487i) q^{85} +(-5.50000 + 9.52628i) q^{86} +(2.00000 + 3.46410i) q^{88} -3.00000 q^{89} -3.00000 q^{91} +(0.500000 + 0.866025i) q^{92} +(3.00000 - 5.19615i) q^{94} +(-4.00000 + 6.92820i) q^{95} +(4.00000 + 6.92820i) q^{97} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 - 4 * q^5 + q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} - 4 q^{5} + q^{7} + 2 q^{8} + 8 q^{10} + 4 q^{11} - 3 q^{13} + q^{14} - q^{16} - 14 q^{17} + 4 q^{19} - 4 q^{20} + 4 q^{22} + q^{23} - 11 q^{25} + 6 q^{26} - 2 q^{28} - q^{29} + 9 q^{31} - q^{32} + 7 q^{34} - 8 q^{35} + 4 q^{37} - 2 q^{38} - 4 q^{40} - 6 q^{41} - 11 q^{43} - 8 q^{44} - 2 q^{46} + 6 q^{47} - q^{49} - 11 q^{50} - 3 q^{52} - 18 q^{53} - 32 q^{55} + q^{56} - q^{58} + 5 q^{59} + 6 q^{61} - 18 q^{62} + 2 q^{64} - 12 q^{65} - 7 q^{67} + 7 q^{68} + 4 q^{70} - 14 q^{71} - 28 q^{73} - 2 q^{74} - 2 q^{76} - 4 q^{77} + 6 q^{79} + 8 q^{80} + 12 q^{82} + 4 q^{83} + 28 q^{85} - 11 q^{86} + 4 q^{88} - 6 q^{89} - 6 q^{91} + q^{92} + 6 q^{94} - 8 q^{95} + 8 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 - 4 * q^5 + q^7 + 2 * q^8 + 8 * q^10 + 4 * q^11 - 3 * q^13 + q^14 - q^16 - 14 * q^17 + 4 * q^19 - 4 * q^20 + 4 * q^22 + q^23 - 11 * q^25 + 6 * q^26 - 2 * q^28 - q^29 + 9 * q^31 - q^32 + 7 * q^34 - 8 * q^35 + 4 * q^37 - 2 * q^38 - 4 * q^40 - 6 * q^41 - 11 * q^43 - 8 * q^44 - 2 * q^46 + 6 * q^47 - q^49 - 11 * q^50 - 3 * q^52 - 18 * q^53 - 32 * q^55 + q^56 - q^58 + 5 * q^59 + 6 * q^61 - 18 * q^62 + 2 * q^64 - 12 * q^65 - 7 * q^67 + 7 * q^68 + 4 * q^70 - 14 * q^71 - 28 * q^73 - 2 * q^74 - 2 * q^76 - 4 * q^77 + 6 * q^79 + 8 * q^80 + 12 * q^82 + 4 * q^83 + 28 * q^85 - 11 * q^86 + 4 * q^88 - 6 * q^89 - 6 * q^91 + q^92 + 6 * q^94 - 8 * q^95 + 8 * q^97 + 2 * q^98

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