LMFDB - Embedded newform 1134.2.f.p.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.p.379.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

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	$-0.480917\pi$
$5$	2.00000	−	3.46410i	0.894427	−	1.54919i	0.834512	−	0.550990i	$-0.185750\pi$
$6$		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	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		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	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$		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	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		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	0.908708	−	0.417432i	$-0.137070\pi$
$29$	0.500000	+	0.866025i	0.0928477	+	0.160817i	−0.815861	+	0.578249i	$0.803736\pi$
$30$		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	−0.530831	−	0.847477i	$-0.678120\pi$
$41$	3.00000	−	5.19615i	0.468521	−	0.811503i	0.999353	+	0.0359748i	$0.0114536\pi$
$42$		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	0.559908	−	0.828554i	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		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	$-0.287894\pi$
$53$	9.00000			1.23625			0.618123	+	0.786082i	$0.287894\pi$
$54$		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	−0.981608	−	0.190909i	$-0.938857\pi$
$59$	−2.50000	+	4.33013i	−0.325472	+	0.563735i	0.656136	+	0.754643i	$0.272190\pi$
$60$		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	$-0.363651\pi$
$71$	7.00000			0.830747			0.415374	+	0.909651i	$0.363651\pi$
$72$		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	0.735135	−	0.677920i	$-0.237119\pi$
$83$	−2.00000	−	3.46410i	−0.219529	−	0.380235i	−0.954664	+	0.297686i	$0.903785\pi$
$84$		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	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		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	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$		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	$-0.696964\pi$
$107$	−12.0000			−1.16008			−0.580042	+	0.814587i	$0.696964\pi$
$108$		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	−0.990519	−	0.137376i	$-0.956133\pi$
$113$	−4.00000	+	6.92820i	−0.376288	+	0.651751i	0.614231	+	0.789127i	$0.289466\pi$
$114$		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	−0.843356	−	0.537355i	$-0.819423\pi$
$131$	0.500000	−	0.866025i	0.0436852	−	0.0756650i	0.887041	+	0.461690i	$0.152757\pi$
$132$		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	$0.222316\pi$
$137$	11.0000	+	19.0526i	0.939793	+	1.62777i	0.173939	+	0.984757i	$0.444351\pi$
$138$		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	−0.920904	−	0.389789i	$-0.872548\pi$
$149$	−1.50000	+	2.59808i	−0.122885	+	0.212843i	0.798019	+	0.602632i	$0.205881\pi$
$150$		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	−0.978259	−	0.207385i	$-0.933505\pi$
$167$	−4.00000	+	6.92820i	−0.309529	+	0.536120i	0.668730	+	0.743505i	$0.266838\pi$
$168$		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	0.672949	−	0.739689i	$-0.265027\pi$
$173$	−4.00000	−	6.92820i	−0.304114	−	0.526742i	−0.977064	+	0.212947i	$0.931694\pi$
$174$		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	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		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	0.997225	−	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	$0.224262\pi$
$194$	−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	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$		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	0.677158	−	0.735838i	$-0.263211\pi$
$227$	−4.50000	−	7.79423i	−0.298675	−	0.517321i	−0.975833	+	0.218517i	$0.929878\pi$
$228$		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	$-0.458173\pi$
$233$	4.00000			0.262049			0.131024	+	0.991379i	$0.458173\pi$
$234$		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	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$		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	$-0.448126\pi$
$257$	15.0000	−	25.9808i	0.935674	−	1.62064i	0.773427	−	0.633885i	$-0.218541\pi$
$258$		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	0.970758	−	0.240059i	$-0.0771668\pi$
$263$	4.50000	+	7.79423i	0.277482	+	0.480613i	−0.693276	+	0.720672i	$0.743833\pi$
$264$		0			0
$265$	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	$-0.538912\pi$
$269$	−4.00000			−0.243884			−0.121942	+	0.992537i	$0.538912\pi$
$270$		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	0.677466	−	0.735554i	$-0.263078\pi$
$281$	−5.00000	−	8.66025i	−0.298275	−	0.516627i	−0.975741	+	0.218926i	$0.929745\pi$
$282$		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	−0.764990	−	0.644042i	$-0.777256\pi$
$293$	3.00000	−	5.19615i	0.175262	−	0.303562i	0.940252	+	0.340480i	$0.110589\pi$
$294$		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	−0.956864	−	0.290537i	$-0.906166\pi$
$311$	−4.00000	+	6.92820i	−0.226819	+	0.392862i	0.730044	+	0.683400i	$0.239499\pi$
$312$		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	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$		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	−0.516667	−	0.856186i	$-0.672828\pi$
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	0.999813	+	0.0193540i	$0.00616095\pi$
$348$		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	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$		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	$-0.406252\pi$
$359$	11.0000			0.580558			0.290279	+	0.956942i	$0.406252\pi$
$360$		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	−0.912589	−	0.408879i	$-0.865920\pi$
$383$	−2.00000	+	3.46410i	−0.102195	+	0.177007i	0.810394	+	0.585886i	$0.199253\pi$
$384$		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	0.632189	−	0.774814i	$-0.282157\pi$
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	−0.987103	+	0.160085i	$0.948823\pi$
$390$		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	$-0.563837\pi$
$401$	15.0000	−	25.9808i	0.749064	−	1.29742i	0.948272	−	0.317460i	$-0.102830\pi$
$402$		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	$0.465080\pi$
$419$	−16.5000	+	28.5788i	−0.806078	+	1.39617i	−0.915561	+	0.402179i	$0.868253\pi$
$420$		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	$-0.696174\pi$
$431$	−24.0000			−1.15604			−0.578020	+	0.816023i	$0.696174\pi$
$432$		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	$0.0452479\pi$
$443$	13.0000	+	22.5167i	0.617649	+	1.06980i	−0.372265	+	0.928126i	$0.621419\pi$
$444$		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	$-0.530089\pi$
$449$	−4.00000			−0.188772			−0.0943858	+	0.995536i	$0.530089\pi$
$450$		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	0.655696	−	0.755025i	$-0.272375\pi$
$461$	−7.00000	−	12.1244i	−0.326023	−	0.564688i	−0.981719	+	0.190337i	$0.939042\pi$
$462$		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	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		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	0.942821	−	0.333300i	$-0.108162\pi$
$479$	4.00000	+	6.92820i	0.182765	+	0.316558i	−0.760056	+	0.649857i	$0.774829\pi$
$480$		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	$-0.651170\pi$
$491$	12.0000	−	20.7846i	0.541552	−	0.937996i	0.998815	−	0.0486647i	$-0.0154966\pi$
$492$		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	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		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	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		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	$-0.393430\pi$
$521$	15.0000			0.657162			0.328581	+	0.944476i	$0.393430\pi$
$522$		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	$-0.506744\pi$
$557$	−1.00000			−0.0423714			−0.0211857	+	0.999776i	$0.506744\pi$
$558$		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	−0.726540	−	0.687124i	$-0.758873\pi$
$563$	5.50000	−	9.52628i	0.231797	−	0.401485i	0.958337	+	0.285640i	$0.0922060\pi$
$564$		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	0.963948	−	0.266090i	$-0.0857319\pi$
$569$	6.00000	+	10.3923i	0.251533	+	0.435668i	−0.712415	+	0.701758i	$0.752399\pi$
$570$		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	$-0.994113\pi$
$587$	−12.5000	−	21.6506i	−0.515930	−	0.893617i	0.483899	−	0.875124i	$-0.339220\pi$
$588$		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	$-0.379500\pi$
$593$	18.0000			0.739171			0.369586	+	0.929197i	$0.379500\pi$
$594$		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	−0.567768	−	0.823189i	$-0.692193\pi$
$599$	10.5000	−	18.1865i	0.429018	−	0.743082i	0.996786	+	0.0801071i	$0.0255262\pi$
$600$		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	−0.690021	−	0.723789i	$-0.742399\pi$
$617$	7.00000	−	12.1244i	0.281809	−	0.488108i	0.971830	+	0.235681i	$0.0757321\pi$
$618$		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	$-0.980162\pi$
$641$	−14.0000	−	24.2487i	−0.552967	−	0.957767i	0.445092	−	0.895485i	$-0.353171\pi$
$642$		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	$-0.809160\pi$
$647$	−42.0000			−1.65119			−0.825595	+	0.564263i	$0.809160\pi$
$648$		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	−0.835182	−	0.549973i	$-0.814638\pi$
$653$	1.50000	−	2.59808i	0.0586995	−	0.101671i	0.893882	+	0.448303i	$0.147971\pi$
$654$		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	$-0.983059\pi$
$659$	−14.0000	−	24.2487i	−0.545363	−	0.944596i	0.453221	−	0.891398i	$-0.350275\pi$
$660$		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	$-0.129534\pi$
$683$	48.0000			1.83667			0.918334	+	0.395805i	$0.129534\pi$
$684$		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	$-0.487975\pi$
$701$	2.00000			0.0755390			0.0377695	+	0.999286i	$0.487975\pi$
$702$		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	$-0.852860\pi$
$719$	−48.0000			−1.79010			−0.895049	+	0.445968i	$0.852860\pi$
$720$		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	$-0.448279\pi$
$743$	25.5000	−	44.1673i	0.935504	−	1.62034i	0.773732	−	0.633513i	$-0.218388\pi$
$744$		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	−0.959454	−	0.281865i	$-0.909047\pi$
$761$	−6.50000	+	11.2583i	−0.235625	+	0.408114i	0.723829	+	0.689979i	$0.242380\pi$
$762$		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	$-0.522917\pi$
$773$	−4.00000			−0.143870			−0.0719350	+	0.997409i	$0.522917\pi$
$774$		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	−0.980237	−	0.197826i	$-0.936612\pi$
$797$	−9.00000	+	15.5885i	−0.318796	+	0.552171i	0.661441	+	0.749997i	$0.269945\pi$
$798$		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	$-0.309828\pi$
$809$	32.0000			1.12506			0.562530	+	0.826777i	$0.309828\pi$
$810$		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	0.730022	−	0.683424i	$-0.239510\pi$
$821$	−6.50000	−	11.2583i	−0.226852	−	0.392918i	−0.956873	+	0.290505i	$0.906177\pi$
$822$		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	$-0.760592\pi$
$827$	−42.0000			−1.46048			−0.730242	+	0.683189i	$0.760592\pi$
$828$		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	0.766716	−	0.641987i	$-0.221890\pi$
$839$	−5.00000	−	8.66025i	−0.172619	−	0.298985i	−0.939335	+	0.343002i	$0.888556\pi$
$840$		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	0.999019	−	0.0442921i	$-0.0141032\pi$
$857$	13.5000	+	23.3827i	0.461151	+	0.798737i	−0.537867	+	0.843029i	$0.680770\pi$
$858$		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	$-0.505418\pi$
$863$	−1.00000			−0.0340404			−0.0170202	+	0.999855i	$0.505418\pi$
$864$		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	$-0.581312\pi$
$881$	−15.0000			−0.505363			−0.252681	+	0.967550i	$0.581312\pi$
$882$		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	−0.948999	−	0.315279i	$-0.897902\pi$
$887$	−6.00000	+	10.3923i	−0.201460	+	0.348939i	0.747539	+	0.664218i	$0.231235\pi$
$888$		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	$-0.874056\pi$
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	0.127585	−	0.991828i	$-0.459277\pi$
$912$		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	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		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	−0.881865	−	0.471503i	$-0.843712\pi$
$941$	−1.00000	+	1.73205i	−0.0325991	+	0.0564632i	0.849266	+	0.527966i	$0.177045\pi$
$942$		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	0.849320	−	0.527878i	$-0.177012\pi$
$947$	−1.00000	−	1.73205i	−0.0324956	−	0.0562841i	−0.881816	+	0.471594i	$0.843679\pi$
$948$		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	$-0.541361\pi$
$953$	−8.00000			−0.259145			−0.129573	+	0.991570i	$0.541361\pi$
$954$		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	$-0.422627\pi$
$971$	15.0000			0.481373			0.240686	+	0.970603i	$0.422627\pi$
$972$		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	$0.401167\pi$
$977$	−21.0000	+	36.3731i	−0.671850	+	1.16368i	−0.977379	+	0.211495i	$0.932167\pi$
$978$		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	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$		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.p.757.1		2
3.2	odd	2		1134.2.f.a.757.1		2
9.2	odd	6		1134.2.f.a.379.1		2
9.4	even	3		378.2.a.a.1.1	✓	1
9.5	odd	6		378.2.a.h.1.1	yes	1
9.7	even	3	inner	1134.2.f.p.379.1		2
36.23	even	6		3024.2.a.bd.1.1		1
36.31	odd	6		3024.2.a.a.1.1		1
45.4	even	6		9450.2.a.dv.1.1		1
45.14	odd	6		9450.2.a.bc.1.1		1
63.13	odd	6		2646.2.a.o.1.1		1
63.41	even	6		2646.2.a.p.1.1		1

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

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

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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