LMFDB - Embedded newform 1134.2.f.j.379.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1134,2,Mod(379,1134)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [2,1,0,-1,-2,0,1,-2,0,-4,-4,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.j.757.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-3.00000 - 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -4.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(2.00000 + 3.46410i) q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{28} +(-1.00000 + 1.73205i) q^{29} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} -2.00000 q^{35} -10.0000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +8.00000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-3.00000 + 5.19615i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(1.00000 + 1.73205i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-1.00000 + 1.73205i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +2.00000 q^{80} -6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(2.00000 + 3.46410i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(2.00000 - 3.46410i) q^{88} +6.00000 q^{89} -6.00000 q^{91} +(4.00000 - 6.92820i) q^{92} +(4.00000 + 6.92820i) q^{95} +(7.00000 - 12.1244i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} - 4 q^{10} - 4 q^{11} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} - 8 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + q^{25} - 12 q^{26} - 2 q^{28} - 2 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8 - 4 * q^10 - 4 * q^11 - 6 * q^13 - q^14 - q^16 - 4 * q^17 - 8 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + q^25 - 12 * q^26 - 2 * q^28 - 2 * q^29 + q^32 - 2 * q^34 - 4 * q^35 - 20 * q^37 - 4 * q^38 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 8 * q^44 + 16 * q^46 - q^49 - q^50 - 6 * q^52 - 12 * q^53 + 16 * q^55 - q^56 + 2 * q^58 + 4 * q^59 - 6 * q^61 + 2 * q^64 - 12 * q^65 - 4 * q^67 + 2 * q^68 - 2 * q^70 - 16 * q^71 + 20 * q^73 - 10 * q^74 + 4 * q^76 + 4 * q^77 + 4 * q^80 - 12 * q^82 - 4 * q^83 + 4 * q^85 - 4 * q^86 + 4 * q^88 + 12 * q^89 - 12 * q^91 + 8 * q^92 + 8 * q^95 + 14 * q^97 - 2 * q^98

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	0.550990	−	0.834512i	$-0.314250\pi$
$5$	−1.00000	−	1.73205i	−0.447214	−	0.774597i	−0.998203	+	0.0599153i	$0.980917\pi$
$6$		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
$10$	−2.00000			−0.632456
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	0.389338	+	0.921095i	$0.372704\pi$
$11$	−2.00000	+	3.46410i	−0.603023	+	1.04447i	−0.992361	+	0.123371i	$0.960630\pi$
$12$		0			0
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	−0.896410	−	0.443227i	$-0.853834\pi$
$13$	−3.00000	−	5.19615i	−0.832050	−	1.44115i	0.0643593	−	0.997927i	$-0.479500\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.00000			−0.485071			−0.242536	−	0.970143i	$-0.577979\pi$
$17$	−2.00000			−0.485071			−0.242536	+	0.970143i	$0.577979\pi$
$18$		0			0
$19$	−4.00000			−0.917663			−0.458831	−	0.888523i	$-0.651732\pi$
$19$	−4.00000			−0.917663			−0.458831	+	0.888523i	$0.651732\pi$
$20$	−1.00000	+	1.73205i	−0.223607	+	0.387298i
$21$		0			0
$22$	2.00000	+	3.46410i	0.426401	+	0.738549i
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	0.894795	+	0.446476i	$0.147321\pi$
$23$	4.00000	+	6.92820i	0.834058	+	1.44463i	−0.0607377	+	0.998154i	$0.519345\pi$
$24$		0			0
$25$	0.500000	−	0.866025i	0.100000	−	0.173205i
$26$	−6.00000			−1.17670
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	−0.943811	−	0.330487i	$-0.892787\pi$
$29$	−1.00000	+	1.73205i	−0.185695	+	0.321634i	0.758115	+	0.652121i	$0.226120\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	−2.00000			−0.338062
$36$		0			0
$37$	−10.0000			−1.64399			−0.821995	−	0.569495i	$-0.807139\pi$
$37$	−10.0000			−1.64399			−0.821995	+	0.569495i	$0.807139\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$		0			0
$40$	1.00000	+	1.73205i	0.158114	+	0.273861i
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$		0			0
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	−0.672264	−	0.740312i	$-0.734678\pi$
$43$	2.00000	−	3.46410i	0.304997	−	0.528271i	0.977261	+	0.212041i	$0.0680112\pi$
$44$	4.00000			0.603023
$45$		0			0
$46$	8.00000			1.17954
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$		0			0
$52$	−3.00000	+	5.19615i	−0.416025	+	0.720577i
$53$	−6.00000			−0.824163			−0.412082	−	0.911147i	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		0			0
$55$	8.00000			1.07872
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	1.00000	+	1.73205i	0.131306	+	0.227429i
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	−0.991645	−	0.128994i	$-0.958825\pi$
$61$	−3.00000	+	5.19615i	−0.384111	+	0.665299i	0.607535	+	0.794293i	$0.292159\pi$
$62$		0			0
$63$		0			0
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$		0			0
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	0.717607	−	0.696449i	$-0.245238\pi$
$67$	−2.00000	−	3.46410i	−0.244339	−	0.423207i	−0.961946	+	0.273241i	$0.911904\pi$
$68$	1.00000	+	1.73205i	0.121268	+	0.210042i
$69$		0			0
$70$	−1.00000	+	1.73205i	−0.119523	+	0.207020i
$71$	−8.00000			−0.949425			−0.474713	−	0.880141i	$-0.657448\pi$
$71$	−8.00000			−0.949425			−0.474713	+	0.880141i	$0.657448\pi$
$72$		0			0
$73$	10.0000			1.17041			0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000			1.17041			0.585206	+	0.810885i	$0.301014\pi$
$74$	−5.00000	+	8.66025i	−0.581238	+	1.00673i
$75$		0			0
$76$	2.00000	+	3.46410i	0.229416	+	0.397360i
$77$	2.00000	+	3.46410i	0.227921	+	0.394771i
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	2.00000			0.223607
$81$		0			0
$82$	−6.00000			−0.662589
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	−0.954664	−	0.297686i	$-0.903785\pi$
$83$	−2.00000	+	3.46410i	−0.219529	+	0.380235i	0.735135	+	0.677920i	$0.237119\pi$
$84$		0			0
$85$	2.00000	+	3.46410i	0.216930	+	0.375735i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	2.00000	−	3.46410i	0.213201	−	0.369274i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	−6.00000			−0.628971
$92$	4.00000	−	6.92820i	0.417029	−	0.722315i
$93$		0			0
$94$		0			0
$95$	4.00000	+	6.92820i	0.410391	+	0.710819i
$96$		0			0
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	−0.253837	−	0.967247i	$-0.581693\pi$
$97$	7.00000	−	12.1244i	0.710742	−	1.23104i	0.964579	−	0.263795i	$-0.0849741\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	−0.911479	−	0.411346i	$-0.865059\pi$
$101$	−1.00000	+	1.73205i	−0.0995037	+	0.172345i	0.811976	+	0.583691i	$0.198392\pi$
$102$		0			0
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	0.598858	−	0.800855i	$-0.295621\pi$
$103$	−4.00000	−	6.92820i	−0.394132	−	0.682656i	−0.992990	+	0.118199i	$0.962288\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.291386	+	0.504695i
$107$	−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
$109$	−2.00000			−0.191565			−0.0957826	−	0.995402i	$-0.530535\pi$
$109$	−2.00000			−0.191565			−0.0957826	+	0.995402i	$0.530535\pi$
$110$	4.00000	−	6.92820i	0.381385	−	0.660578i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	−0.981003	−	0.193993i	$-0.937856\pi$
$113$	−7.00000	−	12.1244i	−0.658505	−	1.14056i	0.322498	−	0.946570i	$-0.395477\pi$
$114$		0			0
$115$	8.00000	−	13.8564i	0.746004	−	1.29212i
$116$	2.00000			0.185695
$117$		0			0
$118$	4.00000			0.368230
$119$	−1.00000	+	1.73205i	−0.0916698	+	0.158777i
$120$		0			0
$121$	−2.50000	−	4.33013i	−0.227273	−	0.393648i
$122$	3.00000	+	5.19615i	0.271607	+	0.470438i
$123$		0			0
$124$		0			0
$125$	−12.0000			−1.07331
$126$		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
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.858137	−	0.513421i	$-0.828378\pi$
$131$	−10.0000	−	17.3205i	−0.873704	−	1.51330i	−0.0155672	−	0.999879i	$-0.504955\pi$
$132$		0			0
$133$	−2.00000	+	3.46410i	−0.173422	+	0.300376i
$134$	−4.00000			−0.345547
$135$		0			0
$136$	2.00000			0.171499
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	−0.569442	−	0.822031i	$-0.692841\pi$
$137$	5.00000	−	8.66025i	0.427179	−	0.739895i	0.996621	+	0.0821359i	$0.0261741\pi$
$138$		0			0
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	0.768655	−	0.639664i	$-0.220926\pi$
$139$	−2.00000	−	3.46410i	−0.169638	−	0.293821i	−0.938293	+	0.345843i	$0.887593\pi$
$140$	1.00000	+	1.73205i	0.0845154	+	0.146385i
$141$		0			0
$142$	−4.00000	+	6.92820i	−0.335673	+	0.581402i
$143$	24.0000			2.00698
$144$		0			0
$145$	4.00000			0.332182
$146$	5.00000	−	8.66025i	0.413803	−	0.716728i
$147$		0			0
$148$	5.00000	+	8.66025i	0.410997	+	0.711868i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$	4.00000			0.324443
$153$		0			0
$154$	4.00000			0.322329
$155$		0			0
$156$		0			0
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$		0			0
$159$		0			0
$160$	1.00000	−	1.73205i	0.0790569	−	0.136931i
$161$	8.00000			0.630488
$162$		0			0
$163$	20.0000			1.56652			0.783260	−	0.621694i	$-0.213555\pi$
$163$	20.0000			1.56652			0.783260	+	0.621694i	$0.213555\pi$
$164$	−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	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	−11.5000	+	19.9186i	−0.884615	+	1.53220i
$170$	4.00000			0.306786
$171$		0			0
$172$	−4.00000			−0.304997
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	−0.0566411	−	0.998395i	$-0.518039\pi$
$173$	11.0000	−	19.0526i	0.836315	−	1.44854i	0.892956	−	0.450145i	$-0.148628\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	−2.00000	−	3.46410i	−0.150756	−	0.261116i
$177$		0			0
$178$	3.00000	−	5.19615i	0.224860	−	0.389468i
$179$	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
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$	−3.00000	+	5.19615i	−0.222375	+	0.385164i
$183$		0			0
$184$	−4.00000	−	6.92820i	−0.294884	−	0.510754i
$185$	10.0000	+	17.3205i	0.735215	+	1.27343i
$186$		0			0
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$		0			0
$189$		0			0
$190$	8.00000			0.580381
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	−7.00000	−	12.1244i	−0.502571	−	0.870478i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	1.00000	+	1.73205i	0.0703598	+	0.121867i
$203$	1.00000	+	1.73205i	0.0701862	+	0.121566i
$204$		0			0
$205$	−6.00000	+	10.3923i	−0.419058	+	0.725830i
$206$	−8.00000			−0.557386
$207$		0			0
$208$	6.00000			0.416025
$209$	8.00000	−	13.8564i	0.553372	−	0.958468i
$210$		0			0
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	−0.972346	−	0.233544i	$-0.924968\pi$
$211$	−10.0000	−	17.3205i	−0.688428	−	1.19239i	0.283918	−	0.958849i	$-0.408366\pi$
$212$	3.00000	+	5.19615i	0.206041	+	0.356873i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−8.00000			−0.545595
$216$		0			0
$217$		0			0
$218$	−1.00000	+	1.73205i	−0.0677285	+	0.117309i
$219$		0			0
$220$	−4.00000	−	6.92820i	−0.269680	−	0.467099i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	−14.0000			−0.931266
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	−0.595274	−	0.803523i	$-0.702957\pi$
$227$	6.00000	−	10.3923i	0.398234	−	0.689761i	0.993508	+	0.113761i	$0.0362899\pi$
$228$		0			0
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	0.897173	−	0.441679i	$-0.145617\pi$
$229$	1.00000	+	1.73205i	0.0660819	+	0.114457i	−0.831092	+	0.556136i	$0.812283\pi$
$230$	−8.00000	−	13.8564i	−0.527504	−	0.913664i
$231$		0			0
$232$	1.00000	−	1.73205i	0.0656532	−	0.113715i
$233$	22.0000			1.44127			0.720634	−	0.693316i	$-0.243851\pi$
$233$	22.0000			1.44127			0.720634	+	0.693316i	$0.243851\pi$
$234$		0			0
$235$		0			0
$236$	2.00000	−	3.46410i	0.130189	−	0.225494i
$237$		0			0
$238$	1.00000	+	1.73205i	0.0648204	+	0.112272i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$		0			0
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	−0.896435	−	0.443176i	$-0.853852\pi$
$241$	−1.00000	+	1.73205i	−0.0644157	+	0.111571i	0.832019	+	0.554747i	$0.187185\pi$
$242$	−5.00000			−0.321412
$243$		0			0
$244$	6.00000			0.384111
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	12.0000	+	20.7846i	0.763542	+	1.32249i
$248$		0			0
$249$		0			0
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$		0			0
$253$	−32.0000			−2.01182
$254$		0			0
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.773427	−	0.633885i	$-0.781459\pi$
$257$	−15.0000	−	25.9808i	−0.935674	−	1.62064i	−0.162247	−	0.986750i	$-0.551874\pi$
$258$		0			0
$259$	−5.00000	+	8.66025i	−0.310685	+	0.538122i
$260$	12.0000			0.744208
$261$		0			0
$262$	−20.0000			−1.23560
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	6.00000	+	10.3923i	0.368577	+	0.638394i
$266$	2.00000	+	3.46410i	0.122628	+	0.212398i
$267$		0			0
$268$	−2.00000	+	3.46410i	−0.122169	+	0.211604i
$269$	−22.0000			−1.34136			−0.670682	−	0.741745i	$-0.733998\pi$
$269$	−22.0000			−1.34136			−0.670682	+	0.741745i	$0.733998\pi$
$270$		0			0
$271$		0			0			−	1.00000i	$-0.5\pi$
$271$		0			0				1.00000i	$0.5\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	−5.00000	−	8.66025i	−0.302061	−	0.523185i
$275$	2.00000	+	3.46410i	0.120605	+	0.208893i
$276$		0			0
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$	−4.00000			−0.239904
$279$		0			0
$280$	2.00000			0.119523
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	−0.158990	−	0.987280i	$-0.550824\pi$
$281$	13.0000	−	22.5167i	0.775515	−	1.34323i	0.934505	−	0.355951i	$-0.115843\pi$
$282$		0			0
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	4.00000	+	6.92820i	0.237356	+	0.411113i
$285$		0			0
$286$	12.0000	−	20.7846i	0.709575	−	1.22902i
$287$	−6.00000			−0.354169
$288$		0			0
$289$	−13.0000			−0.764706
$290$	2.00000	−	3.46410i	0.117444	−	0.203419i
$291$		0			0
$292$	−5.00000	−	8.66025i	−0.292603	−	0.506803i
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.855361	+	0.518032i	$0.173335\pi$
$293$	15.0000	+	25.9808i	0.876309	+	1.51781i	0.0209480	+	0.999781i	$0.493332\pi$
$294$		0			0
$295$	4.00000	−	6.92820i	0.232889	−	0.403376i
$296$	10.0000			0.581238
$297$		0			0
$298$	6.00000			0.347571
$299$	24.0000	−	41.5692i	1.38796	−	2.40401i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	−4.00000	−	6.92820i	−0.230174	−	0.398673i
$303$		0			0
$304$	2.00000	−	3.46410i	0.114708	−	0.198680i
$305$	12.0000			0.687118
$306$		0			0
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	2.00000	−	3.46410i	0.113961	−	0.197386i
$309$		0			0
$310$		0			0
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	0.730044	−	0.683400i	$-0.239499\pi$
$311$	−4.00000	−	6.92820i	−0.226819	−	0.392862i	−0.956864	+	0.290537i	$0.906166\pi$
$312$		0			0
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	−0.972028	−	0.234863i	$-0.924536\pi$
$313$	−5.00000	+	8.66025i	−0.282617	+	0.489506i	0.689412	+	0.724370i	$0.257869\pi$
$314$	10.0000			0.564333
$315$		0			0
$316$		0			0
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	0.494489	+	0.869184i	$0.335355\pi$
$317$	−9.00000	+	15.5885i	−0.505490	+	0.875535i	−0.999980	+	0.00635137i	$0.997978\pi$
$318$		0			0
$319$	−4.00000	−	6.92820i	−0.223957	−	0.387905i
$320$	−1.00000	−	1.73205i	−0.0559017	−	0.0968246i
$321$		0			0
$322$	4.00000	−	6.92820i	0.222911	−	0.386094i
$323$	8.00000			0.445132
$324$		0			0
$325$	−6.00000			−0.332820
$326$	10.0000	−	17.3205i	0.553849	−	0.959294i
$327$		0			0
$328$	3.00000	+	5.19615i	0.165647	+	0.286910i
$329$		0			0
$330$		0			0
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	−0.805812	−	0.592172i	$-0.798271\pi$
$331$	2.00000	−	3.46410i	0.109930	−	0.190404i	0.915742	+	0.401768i	$0.131604\pi$
$332$	4.00000			0.219529
$333$		0			0
$334$	−8.00000			−0.437741
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	0.509676	−	0.860366i	$-0.329765\pi$
$337$	−9.00000	−	15.5885i	−0.490261	−	0.849157i	−0.999937	+	0.0112091i	$0.996432\pi$
$338$	11.5000	+	19.9186i	0.625518	+	1.08343i
$339$		0			0
$340$	2.00000	−	3.46410i	0.108465	−	0.187867i
$341$		0			0
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	−11.0000	−	19.0526i	−0.591364	−	1.02427i
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	0.980921	−	0.194409i	$-0.0622790\pi$
$347$	6.00000	+	10.3923i	0.322097	+	0.557888i	−0.658824	+	0.752297i	$0.728946\pi$
$348$		0			0
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	0.405571	+	0.914063i	$0.367073\pi$
$349$	−11.0000	+	19.0526i	−0.588817	+	1.01986i	−0.994388	+	0.105797i	$0.966261\pi$
$350$	−1.00000			−0.0534522
$351$		0			0
$352$	−4.00000			−0.213201
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	0.122308	+	0.992492i	$0.460970\pi$
$353$	−15.0000	+	25.9808i	−0.798369	+	1.38282i	−0.920677	+	0.390324i	$0.872363\pi$
$354$		0			0
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$		0			0
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	8.00000			0.422224			0.211112	−	0.977462i	$-0.432292\pi$
$359$	8.00000			0.422224			0.211112	+	0.977462i	$0.432292\pi$
$360$		0			0
$361$	−3.00000			−0.157895
$362$	−9.00000	+	15.5885i	−0.473029	+	0.819311i
$363$		0			0
$364$	3.00000	+	5.19615i	0.157243	+	0.272352i
$365$	−10.0000	−	17.3205i	−0.523424	−	0.906597i
$366$		0			0
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	0.0586798	+	0.998277i	$0.481311\pi$
$367$	−16.0000	+	27.7128i	−0.835193	+	1.44660i	−0.893873	+	0.448320i	$0.852022\pi$
$368$	−8.00000			−0.417029
$369$		0			0
$370$	20.0000			1.03975
$371$	−3.00000	+	5.19615i	−0.155752	+	0.269771i
$372$		0			0
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	−0.996610	−	0.0822766i	$-0.973781\pi$
$373$	−11.0000	−	19.0526i	−0.569558	−	0.986504i	0.427051	−	0.904227i	$-0.359552\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$		0			0
$376$		0			0
$377$	12.0000			0.618031
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$	4.00000	−	6.92820i	0.205196	−	0.355409i
$381$		0			0
$382$		0			0
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	0.585973	−	0.810331i	$-0.300713\pi$
$383$	−8.00000	−	13.8564i	−0.408781	−	0.708029i	−0.994753	+	0.102302i	$0.967379\pi$
$384$		0			0
$385$	4.00000	−	6.92820i	0.203859	−	0.353094i
$386$	−2.00000			−0.101797
$387$		0			0
$388$	−14.0000			−0.710742
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	0.321716	+	0.946836i	$0.395740\pi$
$389$	−13.0000	+	22.5167i	−0.659126	+	1.14164i	−0.980842	+	0.194804i	$0.937593\pi$
$390$		0			0
$391$	−8.00000	−	13.8564i	−0.404577	−	0.700749i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	5.00000	−	8.66025i	0.251896	−	0.436297i
$395$		0			0
$396$		0			0
$397$	6.00000			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$397$	6.00000			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$398$	4.00000	−	6.92820i	0.200502	−	0.347279i
$399$		0			0
$400$	0.500000	+	0.866025i	0.0250000	+	0.0433013i
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	0.998350	−	0.0574304i	$-0.0182907\pi$
$401$	9.00000	+	15.5885i	0.449439	+	0.778450i	−0.548911	+	0.835881i	$0.684957\pi$
$402$		0			0
$403$		0			0
$404$	2.00000			0.0995037
$405$		0			0
$406$	2.00000			0.0992583
$407$	20.0000	−	34.6410i	0.991363	−	1.71709i
$408$		0			0
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	0.998674	+	0.0514740i	$0.0163919\pi$
$409$	11.0000	+	19.0526i	0.543915	+	0.942088i	−0.454759	+	0.890614i	$0.650275\pi$
$410$	6.00000	+	10.3923i	0.296319	+	0.513239i
$411$		0			0
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	4.00000			0.196827
$414$		0			0
$415$	8.00000			0.392705
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$		0			0
$418$	−8.00000	−	13.8564i	−0.391293	−	0.677739i
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.852047	−	0.523465i	$-0.824639\pi$
$419$	−18.0000	−	31.1769i	−0.879358	−	1.52309i	−0.0273103	−	0.999627i	$-0.508694\pi$
$420$		0			0
$421$	−3.00000	+	5.19615i	−0.146211	+	0.253245i	−0.929824	−	0.368004i	$-0.880041\pi$
$421$	−3.00000	+	5.19615i	−0.146211	+	0.253245i	0.783613	+	0.621249i	$0.213375\pi$
$422$	−20.0000			−0.973585
$423$		0			0
$424$	6.00000			0.291386
$425$	−1.00000	+	1.73205i	−0.0485071	+	0.0840168i
$426$		0			0
$427$	3.00000	+	5.19615i	0.145180	+	0.251459i
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$		0			0
$430$	−4.00000	+	6.92820i	−0.192897	+	0.334108i
$431$		0			0			−	1.00000i	$-0.5\pi$
$431$		0			0				1.00000i	$0.5\pi$
$432$		0			0
$433$	2.00000			0.0961139			0.0480569	−	0.998845i	$-0.484697\pi$
$433$	2.00000			0.0961139			0.0480569	+	0.998845i	$0.484697\pi$
$434$		0			0
$435$		0			0
$436$	1.00000	+	1.73205i	0.0478913	+	0.0829502i
$437$	−16.0000	−	27.7128i	−0.765384	−	1.32568i
$438$		0			0
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	−0.423556	−	0.905870i	$-0.639218\pi$
$439$	12.0000	−	20.7846i	0.572729	−	0.991995i	0.996284	−	0.0861252i	$-0.0274485\pi$
$440$	−8.00000			−0.381385
$441$		0			0
$442$	12.0000			0.570782
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	−0.909618	−	0.415445i	$-0.863626\pi$
$443$	−2.00000	+	3.46410i	−0.0950229	+	0.164584i	0.814595	+	0.580030i	$0.196959\pi$
$444$		0			0
$445$	−6.00000	−	10.3923i	−0.284427	−	0.492642i
$446$	−8.00000	−	13.8564i	−0.378811	−	0.656120i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−34.0000			−1.60456			−0.802280	−	0.596948i	$-0.796380\pi$
$449$	−34.0000			−1.60456			−0.802280	+	0.596948i	$0.796380\pi$
$450$		0			0
$451$	24.0000			1.13012
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	−6.00000	−	10.3923i	−0.281594	−	0.487735i
$455$	6.00000	+	10.3923i	0.281284	+	0.487199i
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	2.00000			0.0934539
$459$		0			0
$460$	−16.0000			−0.746004
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	−0.487577	−	0.873080i	$-0.662119\pi$
$461$	11.0000	−	19.0526i	0.512321	−	0.887366i	0.999898	−	0.0142861i	$-0.00454755\pi$
$462$		0			0
$463$	16.0000	+	27.7128i	0.743583	+	1.28792i	0.950854	+	0.309640i	$0.100209\pi$
$463$	16.0000	+	27.7128i	0.743583	+	1.28792i	−0.207271	+	0.978284i	$0.566458\pi$
$464$	−1.00000	−	1.73205i	−0.0464238	−	0.0804084i
$465$		0			0
$466$	11.0000	−	19.0526i	0.509565	−	0.882593i
$467$	−28.0000			−1.29569			−0.647843	−	0.761774i	$-0.724329\pi$
$467$	−28.0000			−1.29569			−0.647843	+	0.761774i	$0.724329\pi$
$468$		0			0
$469$	−4.00000			−0.184703
$470$		0			0
$471$		0			0
$472$	−2.00000	−	3.46410i	−0.0920575	−	0.159448i
$473$	8.00000	+	13.8564i	0.367840	+	0.637118i
$474$		0			0
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$	2.00000			0.0916698
$477$		0			0
$478$		0			0
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	−0.988861	−	0.148842i	$-0.952445\pi$
$479$	−8.00000	+	13.8564i	−0.365529	+	0.633115i	0.623332	+	0.781958i	$0.285779\pi$
$480$		0			0
$481$	30.0000	+	51.9615i	1.36788	+	2.36924i
$482$	1.00000	+	1.73205i	0.0455488	+	0.0788928i
$483$		0			0
$484$	−2.50000	+	4.33013i	−0.113636	+	0.196824i
$485$	−28.0000			−1.27141
$486$		0			0
$487$	8.00000			0.362515			0.181257	−	0.983436i	$-0.441983\pi$
$487$	8.00000			0.362515			0.181257	+	0.983436i	$0.441983\pi$
$488$	3.00000	−	5.19615i	0.135804	−	0.235219i
$489$		0			0
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	0.969061	−	0.246822i	$-0.0793863\pi$
$491$	6.00000	+	10.3923i	0.270776	+	0.468998i	−0.698285	+	0.715820i	$0.746053\pi$
$492$		0			0
$493$	2.00000	−	3.46410i	0.0900755	−	0.156015i
$494$	24.0000			1.07981
$495$		0			0
$496$		0			0
$497$	−4.00000	+	6.92820i	−0.179425	+	0.310772i
$498$		0			0
$499$	22.0000	+	38.1051i	0.984855	+	1.70582i	0.642578	+	0.766220i	$0.277865\pi$
$499$	22.0000	+	38.1051i	0.984855	+	1.70582i	0.342277	+	0.939599i	$0.388802\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	6.00000	−	10.3923i	0.267793	−	0.463831i
$503$	−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
$505$	4.00000			0.177998
$506$	−16.0000	+	27.7128i	−0.711287	+	1.23198i
$507$		0			0
$508$		0			0
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	5.00000	−	8.66025i	0.221187	−	0.383107i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−30.0000			−1.32324
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$		0			0
$518$	5.00000	+	8.66025i	0.219687	+	0.380510i
$519$		0			0
$520$	6.00000	−	10.3923i	0.263117	−	0.455733i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$		0			0
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	−10.0000	+	17.3205i	−0.436852	+	0.756650i
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$		0			0
$528$		0			0
$529$	−20.5000	+	35.5070i	−0.891304	+	1.54378i
$530$	12.0000			0.521247
$531$		0			0
$532$	4.00000			0.173422
$533$	−18.0000	+	31.1769i	−0.779667	+	1.35042i
$534$		0			0
$535$	12.0000	+	20.7846i	0.518805	+	0.898597i
$536$	2.00000	+	3.46410i	0.0863868	+	0.149626i
$537$		0			0
$538$	−11.0000	+	19.0526i	−0.474244	+	0.821414i
$539$	4.00000			0.172292
$540$		0			0
$541$	30.0000			1.28980			0.644900	−	0.764267i	$-0.276899\pi$
$541$	30.0000			1.28980			0.644900	+	0.764267i	$0.276899\pi$
$542$		0			0
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	2.00000	+	3.46410i	0.0856706	+	0.148386i
$546$		0			0
$547$	6.00000	−	10.3923i	0.256541	−	0.444343i	−0.708772	−	0.705438i	$-0.750750\pi$
$547$	6.00000	−	10.3923i	0.256541	−	0.444343i	0.965313	+	0.261095i	$0.0840836\pi$
$548$	−10.0000			−0.427179
$549$		0			0
$550$	4.00000			0.170561
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$		0			0
$554$	−5.00000	−	8.66025i	−0.212430	−	0.367939i
$555$		0			0
$556$	−2.00000	+	3.46410i	−0.0848189	+	0.146911i
$557$	2.00000			0.0847427			0.0423714	−	0.999102i	$-0.486509\pi$
$557$	2.00000			0.0847427			0.0423714	+	0.999102i	$0.486509\pi$
$558$		0			0
$559$	−24.0000			−1.01509
$560$	1.00000	−	1.73205i	0.0422577	−	0.0731925i
$561$		0			0
$562$	−13.0000	−	22.5167i	−0.548372	−	0.949808i
$563$	22.0000	+	38.1051i	0.927189	+	1.60594i	0.788002	+	0.615673i	$0.211116\pi$
$563$	22.0000	+	38.1051i	0.927189	+	1.60594i	0.139188	+	0.990266i	$0.455551\pi$
$564$		0			0
$565$	−14.0000	+	24.2487i	−0.588984	+	1.02015i
$566$	−4.00000			−0.168133
$567$		0			0
$568$	8.00000			0.335673
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	−0.922032	−	0.387113i	$-0.873472\pi$
$569$	−3.00000	+	5.19615i	−0.125767	+	0.217834i	0.796266	+	0.604947i	$0.206806\pi$
$570$		0			0
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	0.712735	−	0.701434i	$-0.247456\pi$
$571$	−6.00000	−	10.3923i	−0.251092	−	0.434904i	−0.963827	+	0.266529i	$0.914123\pi$
$572$	−12.0000	−	20.7846i	−0.501745	−	0.869048i
$573$		0			0
$574$	−3.00000	+	5.19615i	−0.125218	+	0.216883i
$575$	8.00000			0.333623
$576$		0			0
$577$	34.0000			1.41544			0.707719	−	0.706494i	$-0.249724\pi$
$577$	34.0000			1.41544			0.707719	+	0.706494i	$0.249724\pi$
$578$	−6.50000	+	11.2583i	−0.270364	+	0.468285i
$579$		0			0
$580$	−2.00000	−	3.46410i	−0.0830455	−	0.143839i
$581$	2.00000	+	3.46410i	0.0829740	+	0.143715i
$582$		0			0
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	−10.0000			−0.413803
$585$		0			0
$586$	30.0000			1.23929
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	0.417885	+	0.908500i	$0.362772\pi$
$587$	−14.0000	+	24.2487i	−0.577842	+	1.00085i	−0.995726	+	0.0923513i	$0.970562\pi$
$588$		0			0
$589$		0			0
$590$	−4.00000	−	6.92820i	−0.164677	−	0.285230i
$591$		0			0
$592$	5.00000	−	8.66025i	0.205499	−	0.355934i
$593$	−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
$595$	4.00000			0.163984
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$		0			0
$598$	−24.0000	−	41.5692i	−0.981433	−	1.69989i
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	0.469095	+	0.883148i	$0.344580\pi$
$601$	−13.0000	+	22.5167i	−0.530281	+	0.918474i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$	−4.00000			−0.163028
$603$		0			0
$604$	−8.00000			−0.325515
$605$	−5.00000	+	8.66025i	−0.203279	+	0.352089i
$606$		0			0
$607$	−24.0000	−	41.5692i	−0.974130	−	1.68724i	−0.682777	−	0.730627i	$-0.739228\pi$
$607$	−24.0000	−	41.5692i	−0.974130	−	1.68724i	−0.291353	−	0.956616i	$-0.594105\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$		0			0
$610$	6.00000	−	10.3923i	0.242933	−	0.420772i
$611$		0			0
$612$		0			0
$613$	−42.0000			−1.69636			−0.848182	−	0.529705i	$-0.822303\pi$
$613$	−42.0000			−1.69636			−0.848182	+	0.529705i	$0.822303\pi$
$614$	14.0000	−	24.2487i	0.564994	−	0.978598i
$615$		0			0
$616$	−2.00000	−	3.46410i	−0.0805823	−	0.139573i
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	0.555056	−	0.831813i	$-0.312697\pi$
$617$	−11.0000	−	19.0526i	−0.442843	−	0.767027i	−0.997899	+	0.0647859i	$0.979364\pi$
$618$		0			0
$619$	22.0000	−	38.1051i	0.884255	−	1.53157i	0.0376891	−	0.999290i	$-0.488000\pi$
$619$	22.0000	−	38.1051i	0.884255	−	1.53157i	0.846566	−	0.532284i	$-0.178666\pi$
$620$		0			0
$621$		0			0
$622$	−8.00000			−0.320771
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$		0			0
$625$	9.50000	+	16.4545i	0.380000	+	0.658179i
$626$	5.00000	+	8.66025i	0.199840	+	0.346133i
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	20.0000			0.797452
$630$		0			0
$631$	8.00000			0.318475			0.159237	−	0.987240i	$-0.449096\pi$
$631$	8.00000			0.318475			0.159237	+	0.987240i	$0.449096\pi$
$632$		0			0
$633$		0			0
$634$	9.00000	+	15.5885i	0.357436	+	0.619097i
$635$		0			0
$636$		0			0
$637$	−3.00000	+	5.19615i	−0.118864	+	0.205879i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	−2.00000			−0.0790569
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$		0			0
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	0.902764	−	0.430137i	$-0.141535\pi$
$643$	2.00000	+	3.46410i	0.0788723	+	0.136611i	−0.823891	+	0.566748i	$0.808201\pi$
$644$	−4.00000	−	6.92820i	−0.157622	−	0.273009i
$645$		0			0
$646$	4.00000	−	6.92820i	0.157378	−	0.272587i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$		0			0
$649$	−16.0000			−0.628055
$650$	−3.00000	+	5.19615i	−0.117670	+	0.203810i
$651$		0			0
$652$	−10.0000	−	17.3205i	−0.391630	−	0.678323i
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	0.634437	−	0.772975i	$-0.281232\pi$
$653$	−9.00000	−	15.5885i	−0.352197	−	0.610023i	−0.986634	+	0.162951i	$0.947899\pi$
$654$		0			0
$655$	−20.0000	+	34.6410i	−0.781465	+	1.35354i
$656$	6.00000			0.234261
$657$		0			0
$658$		0			0
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	0.453221	+	0.891398i	$0.350275\pi$
$659$	−14.0000	+	24.2487i	−0.545363	+	0.944596i	−0.998584	+	0.0531977i	$0.983059\pi$
$660$		0			0
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	0.884818	−	0.465937i	$-0.154283\pi$
$661$	1.00000	+	1.73205i	0.0388955	+	0.0673690i	−0.845922	+	0.533306i	$0.820949\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$	8.00000			0.310227
$666$		0			0
$667$	−16.0000			−0.619522
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$		0			0
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$	−12.0000	−	20.7846i	−0.463255	−	0.802381i
$672$		0			0
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	−0.884655	−	0.466246i	$-0.845606\pi$
$673$	−1.00000	+	1.73205i	−0.0385472	+	0.0667657i	0.846108	+	0.533011i	$0.178940\pi$
$674$	−18.0000			−0.693334
$675$		0			0
$676$	23.0000			0.884615
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	−7.00000	−	12.1244i	−0.268635	−	0.465290i
$680$	−2.00000	−	3.46410i	−0.0766965	−	0.132842i
$681$		0			0
$682$		0			0
$683$	−12.0000			−0.459167			−0.229584	−	0.973289i	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		0			0
$685$	−20.0000			−0.764161
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	18.0000	+	31.1769i	0.685745	+	1.18775i
$690$		0			0
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	−0.825473	−	0.564441i	$-0.809092\pi$
$691$	2.00000	−	3.46410i	0.0760836	−	0.131781i	0.901557	+	0.432660i	$0.142425\pi$
$692$	−22.0000			−0.836315
$693$		0			0
$694$	12.0000			0.455514
$695$	−4.00000	+	6.92820i	−0.151729	+	0.262802i
$696$		0			0
$697$	6.00000	+	10.3923i	0.227266	+	0.393637i
$698$	11.0000	+	19.0526i	0.416356	+	0.721150i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	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
$703$	40.0000			1.50863
$704$	−2.00000	+	3.46410i	−0.0753778	+	0.130558i
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	1.00000	+	1.73205i	0.0376089	+	0.0651405i
$708$		0			0
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	−0.756730	−	0.653727i	$-0.773204\pi$
$709$	5.00000	−	8.66025i	0.187779	−	0.325243i	0.944509	+	0.328484i	$0.106538\pi$
$710$	16.0000			0.600469
$711$		0			0
$712$	−6.00000			−0.224860
$713$		0			0
$714$		0			0
$715$	−24.0000	−	41.5692i	−0.897549	−	1.55460i
$716$	−6.00000	−	10.3923i	−0.224231	−	0.388379i
$717$		0			0
$718$	4.00000	−	6.92820i	0.149279	−	0.258558i
$719$		0			0			−	1.00000i	$-0.5\pi$
$719$		0			0				1.00000i	$0.5\pi$
$720$		0			0
$721$	−8.00000			−0.297936
$722$	−1.50000	+	2.59808i	−0.0558242	+	0.0966904i
$723$		0			0
$724$	9.00000	+	15.5885i	0.334482	+	0.579340i
$725$	1.00000	+	1.73205i	0.0371391	+	0.0643268i
$726$		0			0
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	−0.782267	−	0.622944i	$-0.785937\pi$
$727$	4.00000	−	6.92820i	0.148352	−	0.256953i	0.930618	+	0.365991i	$0.119270\pi$
$728$	6.00000			0.222375
$729$		0			0
$730$	−20.0000			−0.740233
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	0.805289	−	0.592883i	$-0.202010\pi$
$733$	−3.00000	−	5.19615i	−0.110808	−	0.191924i	−0.916096	+	0.400959i	$0.868677\pi$
$734$	16.0000	+	27.7128i	0.590571	+	1.02290i
$735$		0			0
$736$	−4.00000	+	6.92820i	−0.147442	+	0.255377i
$737$	16.0000			0.589368
$738$		0			0
$739$	−12.0000			−0.441427			−0.220714	−	0.975339i	$-0.570839\pi$
$739$	−12.0000			−0.441427			−0.220714	+	0.975339i	$0.570839\pi$
$740$	10.0000	−	17.3205i	0.367607	−	0.636715i
$741$		0			0
$742$	3.00000	+	5.19615i	0.110133	+	0.190757i
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$		0			0
$745$	6.00000	−	10.3923i	0.219823	−	0.380745i
$746$	−22.0000			−0.805477
$747$		0			0
$748$	−8.00000			−0.292509
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.855938	−	0.517079i	$-0.827019\pi$
$751$	−24.0000	−	41.5692i	−0.875772	−	1.51688i	−0.0198348	−	0.999803i	$-0.506314\pi$
$752$		0			0
$753$		0			0
$754$	6.00000	−	10.3923i	0.218507	−	0.378465i
$755$	−16.0000			−0.582300
$756$		0			0
$757$	6.00000			0.218074			0.109037	−	0.994038i	$-0.465223\pi$
$757$	6.00000			0.218074			0.109037	+	0.994038i	$0.465223\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$		0			0
$760$	−4.00000	−	6.92820i	−0.145095	−	0.251312i
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	0.594822	−	0.803857i	$-0.297222\pi$
$761$	−11.0000	−	19.0526i	−0.398750	−	0.690655i	−0.993572	+	0.113203i	$0.963889\pi$
$762$		0			0
$763$	−1.00000	+	1.73205i	−0.0362024	+	0.0627044i
$764$		0			0
$765$		0			0
$766$	−16.0000			−0.578103
$767$	12.0000	−	20.7846i	0.433295	−	0.750489i
$768$		0			0
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	0.964193	−	0.265200i	$-0.0854381\pi$
$769$	7.00000	+	12.1244i	0.252426	+	0.437215i	−0.711767	+	0.702416i	$0.752105\pi$
$770$	−4.00000	−	6.92820i	−0.144150	−	0.249675i
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	2.00000			0.0719350			0.0359675	−	0.999353i	$-0.488549\pi$
$773$	2.00000			0.0719350			0.0359675	+	0.999353i	$0.488549\pi$
$774$		0			0
$775$		0			0
$776$	−7.00000	+	12.1244i	−0.251285	+	0.435239i
$777$		0			0
$778$	13.0000	+	22.5167i	0.466073	+	0.807261i
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$		0			0
$781$	16.0000	−	27.7128i	0.572525	−	0.991642i
$782$	−16.0000			−0.572159
$783$		0			0
$784$	1.00000			0.0357143
$785$	10.0000	−	17.3205i	0.356915	−	0.618195i
$786$		0			0
$787$	18.0000	+	31.1769i	0.641631	+	1.11134i	0.985069	+	0.172162i	$0.0550751\pi$
$787$	18.0000	+	31.1769i	0.641631	+	1.11134i	−0.343438	+	0.939175i	$0.611592\pi$
$788$	−5.00000	−	8.66025i	−0.178118	−	0.308509i
$789$		0			0
$790$		0			0
$791$	−14.0000			−0.497783
$792$		0			0
$793$	36.0000			1.27840
$794$	3.00000	−	5.19615i	0.106466	−	0.184405i
$795$		0			0
$796$	−4.00000	−	6.92820i	−0.141776	−	0.245564i
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	0.914255	−	0.405140i	$-0.132777\pi$
$797$	3.00000	+	5.19615i	0.106265	+	0.184057i	−0.807989	+	0.589197i	$0.799444\pi$
$798$		0			0
$799$		0			0
$800$	1.00000			0.0353553
$801$		0			0
$802$	18.0000			0.635602
$803$	−20.0000	+	34.6410i	−0.705785	+	1.22245i
$804$		0			0
$805$	−8.00000	−	13.8564i	−0.281963	−	0.488374i
$806$		0			0
$807$		0			0
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	−10.0000			−0.351581			−0.175791	−	0.984428i	$-0.556248\pi$
$809$	−10.0000			−0.351581			−0.175791	+	0.984428i	$0.556248\pi$
$810$		0			0
$811$	−44.0000			−1.54505			−0.772524	−	0.634985i	$-0.781006\pi$
$811$	−44.0000			−1.54505			−0.772524	+	0.634985i	$0.781006\pi$
$812$	1.00000	−	1.73205i	0.0350931	−	0.0607831i
$813$		0			0
$814$	−20.0000	−	34.6410i	−0.701000	−	1.21417i
$815$	−20.0000	−	34.6410i	−0.700569	−	1.21342i
$816$		0			0
$817$	−8.00000	+	13.8564i	−0.279885	+	0.484774i
$818$	22.0000			0.769212
$819$		0			0
$820$	12.0000			0.419058
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	−0.316691	−	0.948529i	$-0.602572\pi$
$821$	19.0000	−	32.9090i	0.663105	−	1.14853i	0.979795	−	0.200002i	$-0.0640949\pi$
$822$		0			0
$823$	28.0000	+	48.4974i	0.976019	+	1.69051i	0.676532	+	0.736413i	$0.263482\pi$
$823$	28.0000	+	48.4974i	0.976019	+	1.69051i	0.299487	+	0.954100i	$0.403185\pi$
$824$	4.00000	+	6.92820i	0.139347	+	0.241355i
$825$		0			0
$826$	2.00000	−	3.46410i	0.0695889	−	0.120532i
$827$	36.0000			1.25184			0.625921	−	0.779886i	$-0.284723\pi$
$827$	36.0000			1.25184			0.625921	+	0.779886i	$0.284723\pi$
$828$		0			0
$829$	−26.0000			−0.903017			−0.451509	−	0.892267i	$-0.649114\pi$
$829$	−26.0000			−0.903017			−0.451509	+	0.892267i	$0.649114\pi$
$830$	4.00000	−	6.92820i	0.138842	−	0.240481i
$831$		0			0
$832$	−3.00000	−	5.19615i	−0.104006	−	0.180144i
$833$	1.00000	+	1.73205i	0.0346479	+	0.0600120i
$834$		0			0
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	−16.0000			−0.553372
$837$		0			0
$838$	−36.0000			−1.24360
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.261600	−	0.965176i	$-0.415750\pi$
$839$	28.0000	−	48.4974i	0.966667	−	1.67432i	0.705067	−	0.709141i	$-0.250917\pi$
$840$		0			0
$841$	12.5000	+	21.6506i	0.431034	+	0.746574i
$842$	3.00000	+	5.19615i	0.103387	+	0.179071i
$843$		0			0
$844$	−10.0000	+	17.3205i	−0.344214	+	0.596196i
$845$	46.0000			1.58245
$846$		0			0
$847$	−5.00000			−0.171802
$848$	3.00000	−	5.19615i	0.103020	−	0.178437i
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	−40.0000	−	69.2820i	−1.37118	−	2.37496i
$852$		0			0
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	−0.960621	−	0.277862i	$-0.910374\pi$
$853$	−7.00000	+	12.1244i	−0.239675	+	0.415130i	0.720946	+	0.692992i	$0.243708\pi$
$854$	6.00000			0.205316
$855$		0			0
$856$	12.0000			0.410152
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	−0.244701	−	0.969599i	$-0.578690\pi$
$857$	21.0000	−	36.3731i	0.717346	−	1.24248i	0.962048	−	0.272882i	$-0.0879768\pi$
$858$		0			0
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	0.643459	−	0.765480i	$-0.277499\pi$
$859$	−10.0000	−	17.3205i	−0.341196	−	0.590968i	−0.984655	+	0.174512i	$0.944165\pi$
$860$	4.00000	+	6.92820i	0.136399	+	0.236250i
$861$		0			0
$862$		0			0
$863$	32.0000			1.08929			0.544646	−	0.838666i	$-0.316664\pi$
$863$	32.0000			1.08929			0.544646	+	0.838666i	$0.316664\pi$
$864$		0			0
$865$	−44.0000			−1.49604
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$		0			0
$868$		0			0
$869$		0			0
$870$		0			0
$871$	−12.0000	+	20.7846i	−0.406604	+	0.704260i
$872$	2.00000			0.0677285
$873$		0			0
$874$	−32.0000			−1.08242
$875$	−6.00000	+	10.3923i	−0.202837	+	0.351324i
$876$		0			0
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	0.882415	−	0.470471i	$-0.155916\pi$
$877$	1.00000	+	1.73205i	0.0337676	+	0.0584872i	−0.848648	+	0.528958i	$0.822583\pi$
$878$	−12.0000	−	20.7846i	−0.404980	−	0.701447i
$879$		0			0
$880$	−4.00000	+	6.92820i	−0.134840	+	0.233550i
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	2.00000	+	3.46410i	0.0671913	+	0.116379i
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$		0			0
$890$	−12.0000			−0.402241
$891$		0			0
$892$	−16.0000			−0.535720
$893$		0			0
$894$		0			0
$895$	−12.0000	−	20.7846i	−0.401116	−	0.694753i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−17.0000	+	29.4449i	−0.567297	+	0.982588i
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$	12.0000	−	20.7846i	0.399556	−	0.692052i
$903$		0			0
$904$	7.00000	+	12.1244i	0.232817	+	0.403250i
$905$	18.0000	+	31.1769i	0.598340	+	1.03636i
$906$		0			0
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	−0.948278	−	0.317441i	$-0.897176\pi$
$907$	−6.00000	+	10.3923i	−0.199227	+	0.345071i	0.749051	+	0.662512i	$0.230510\pi$
$908$	−12.0000			−0.398234
$909$		0			0
$910$	12.0000			0.397796
$911$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$911$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$912$		0			0
$913$	−8.00000	−	13.8564i	−0.264761	−	0.458580i
$914$	5.00000	+	8.66025i	0.165385	+	0.286456i
$915$		0			0
$916$	1.00000	−	1.73205i	0.0330409	−	0.0572286i
$917$	−20.0000			−0.660458
$918$		0			0
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$	−8.00000	+	13.8564i	−0.263752	+	0.456832i
$921$		0			0
$922$	−11.0000	−	19.0526i	−0.362266	−	0.627463i
$923$	24.0000	+	41.5692i	0.789970	+	1.36827i
$924$		0			0
$925$	−5.00000	+	8.66025i	−0.164399	+	0.284747i
$926$	32.0000			1.05159
$927$		0			0
$928$	−2.00000			−0.0656532
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	2.00000	+	3.46410i	0.0655474	+	0.113531i
$932$	−11.0000	−	19.0526i	−0.360317	−	0.624087i
$933$		0			0
$934$	−14.0000	+	24.2487i	−0.458094	+	0.793442i
$935$	−16.0000			−0.523256
$936$		0			0
$937$	−22.0000			−0.718709			−0.359354	−	0.933201i	$-0.617003\pi$
$937$	−22.0000			−0.718709			−0.359354	+	0.933201i	$0.617003\pi$
$938$	−2.00000	+	3.46410i	−0.0653023	+	0.113107i
$939$		0			0
$940$		0			0
$941$	−13.0000	−	22.5167i	−0.423788	−	0.734022i	0.572518	−	0.819892i	$-0.305966\pi$
$941$	−13.0000	−	22.5167i	−0.423788	−	0.734022i	−0.996306	+	0.0858697i	$0.972633\pi$
$942$		0			0
$943$	24.0000	−	41.5692i	0.781548	−	1.35368i
$944$	−4.00000			−0.130189
$945$		0			0
$946$	16.0000			0.520205
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	−0.831699	−	0.555227i	$-0.812631\pi$
$947$	2.00000	−	3.46410i	0.0649913	−	0.112568i	0.896690	+	0.442659i	$0.145965\pi$
$948$		0			0
$949$	−30.0000	−	51.9615i	−0.973841	−	1.68674i
$950$	2.00000	+	3.46410i	0.0648886	+	0.112390i
$951$		0			0
$952$	1.00000	−	1.73205i	0.0324102	−	0.0561361i
$953$	−26.0000			−0.842223			−0.421111	−	0.907009i	$-0.638360\pi$
$953$	−26.0000			−0.842223			−0.421111	+	0.907009i	$0.638360\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$		0			0
$958$	8.00000	+	13.8564i	0.258468	+	0.447680i
$959$	−5.00000	−	8.66025i	−0.161458	−	0.279654i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	60.0000			1.93448
$963$		0			0
$964$	2.00000			0.0644157
$965$	−2.00000	+	3.46410i	−0.0643823	+	0.111513i
$966$		0			0
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	0.794515	−	0.607244i	$-0.207725\pi$
$967$	−4.00000	−	6.92820i	−0.128631	−	0.222796i	−0.923147	+	0.384448i	$0.874392\pi$
$968$	2.50000	+	4.33013i	0.0803530	+	0.139176i
$969$		0			0
$970$	−14.0000	+	24.2487i	−0.449513	+	0.778579i
$971$	12.0000			0.385098			0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000			0.385098			0.192549	+	0.981287i	$0.438325\pi$
$972$		0			0
$973$	−4.00000			−0.128234
$974$	4.00000	−	6.92820i	0.128168	−	0.221994i
$975$		0			0
$976$	−3.00000	−	5.19615i	−0.0960277	−	0.166325i
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	0.973317	−	0.229465i	$-0.0736978\pi$
$977$	9.00000	+	15.5885i	0.287936	+	0.498719i	−0.685381	+	0.728184i	$0.740364\pi$
$978$		0			0
$979$	−12.0000	+	20.7846i	−0.383522	+	0.664279i
$980$	2.00000			0.0638877
$981$		0			0
$982$	12.0000			0.382935
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	−0.991453	−	0.130465i	$-0.958353\pi$
$983$	−12.0000	+	20.7846i	−0.382741	+	0.662926i	0.608712	+	0.793391i	$0.291686\pi$
$984$		0			0
$985$	−10.0000	−	17.3205i	−0.318626	−	0.551877i
$986$	−2.00000	−	3.46410i	−0.0636930	−	0.110319i
$987$		0			0
$988$	12.0000	−	20.7846i	0.381771	−	0.661247i
$989$	32.0000			1.01754
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$		0			0
$994$	4.00000	+	6.92820i	0.126872	+	0.219749i
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$		0			0
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	−0.955322	−	0.295567i	$-0.904491\pi$
$997$	−7.00000	+	12.1244i	−0.221692	+	0.383982i	0.733630	+	0.679549i	$0.237825\pi$
$998$	44.0000			1.39280
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.j.379.1		2
3.2	odd	2		1134.2.f.g.379.1		2
9.2	odd	6		42.2.a.a.1.1	✓	1
9.4	even	3	inner	1134.2.f.j.757.1		2
9.5	odd	6		1134.2.f.g.757.1		2
9.7	even	3		126.2.a.a.1.1		1
36.7	odd	6		1008.2.a.j.1.1		1
36.11	even	6		336.2.a.d.1.1		1
45.2	even	12		1050.2.g.a.799.2		2
45.7	odd	12		3150.2.g.r.2899.1		2
45.29	odd	6		1050.2.a.i.1.1		1
45.34	even	6		3150.2.a.bo.1.1		1
45.38	even	12		1050.2.g.a.799.1		2
45.43	odd	12		3150.2.g.r.2899.2		2
63.2	odd	6		294.2.e.c.67.1		2
63.11	odd	6		294.2.e.c.79.1		2
63.16	even	3		882.2.g.h.361.1		2
63.20	even	6		294.2.a.g.1.1		1
63.25	even	3		882.2.g.h.667.1		2
63.34	odd	6		882.2.a.b.1.1		1
63.38	even	6		294.2.e.a.79.1		2
63.47	even	6		294.2.e.a.67.1		2
63.52	odd	6		882.2.g.j.667.1		2
63.61	odd	6		882.2.g.j.361.1		2
72.11	even	6		1344.2.a.i.1.1		1
72.29	odd	6		1344.2.a.q.1.1		1
72.43	odd	6		4032.2.a.m.1.1		1
72.61	even	6		4032.2.a.e.1.1		1
99.65	even	6		5082.2.a.d.1.1		1
117.38	odd	6		7098.2.a.f.1.1		1
144.11	even	12		5376.2.c.e.2689.1		2
144.29	odd	12		5376.2.c.bc.2689.1		2
144.83	even	12		5376.2.c.e.2689.2		2
144.101	odd	12		5376.2.c.bc.2689.2		2
180.119	even	6		8400.2.a.k.1.1		1
252.11	even	6		2352.2.q.i.961.1		2
252.47	odd	6		2352.2.q.n.1537.1		2
252.83	odd	6		2352.2.a.l.1.1		1
252.191	even	6		2352.2.q.i.1537.1		2
252.223	even	6		7056.2.a.k.1.1		1
252.227	odd	6		2352.2.q.n.961.1		2
315.209	even	6		7350.2.a.f.1.1		1
504.83	odd	6		9408.2.a.bw.1.1		1
504.461	even	6		9408.2.a.n.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.2.a.a.1.1	✓	1	9.2	odd	6
126.2.a.a.1.1		1	9.7	even	3
294.2.a.g.1.1		1	63.20	even	6
294.2.e.a.67.1		2	63.47	even	6
294.2.e.a.79.1		2	63.38	even	6
294.2.e.c.67.1		2	63.2	odd	6
294.2.e.c.79.1		2	63.11	odd	6
336.2.a.d.1.1		1	36.11	even	6
882.2.a.b.1.1		1	63.34	odd	6
882.2.g.h.361.1		2	63.16	even	3
882.2.g.h.667.1		2	63.25	even	3
882.2.g.j.361.1		2	63.61	odd	6
882.2.g.j.667.1		2	63.52	odd	6
1008.2.a.j.1.1		1	36.7	odd	6
1050.2.a.i.1.1		1	45.29	odd	6
1050.2.g.a.799.1		2	45.38	even	12
1050.2.g.a.799.2		2	45.2	even	12
1134.2.f.g.379.1		2	3.2	odd	2
1134.2.f.g.757.1		2	9.5	odd	6
1134.2.f.j.379.1		2	1.1	even	1	trivial
1134.2.f.j.757.1		2	9.4	even	3	inner
1344.2.a.i.1.1		1	72.11	even	6
1344.2.a.q.1.1		1	72.29	odd	6
2352.2.a.l.1.1		1	252.83	odd	6
2352.2.q.i.961.1		2	252.11	even	6
2352.2.q.i.1537.1		2	252.191	even	6
2352.2.q.n.961.1		2	252.227	odd	6
2352.2.q.n.1537.1		2	252.47	odd	6
3150.2.a.bo.1.1		1	45.34	even	6
3150.2.g.r.2899.1		2	45.7	odd	12
3150.2.g.r.2899.2		2	45.43	odd	12
4032.2.a.e.1.1		1	72.61	even	6
4032.2.a.m.1.1		1	72.43	odd	6
5082.2.a.d.1.1		1	99.65	even	6
5376.2.c.e.2689.1		2	144.11	even	12
5376.2.c.e.2689.2		2	144.83	even	12
5376.2.c.bc.2689.1		2	144.29	odd	12
5376.2.c.bc.2689.2		2	144.101	odd	12
7056.2.a.k.1.1		1	252.223	even	6
7098.2.a.f.1.1		1	117.38	odd	6
7350.2.a.f.1.1		1	315.209	even	6
8400.2.a.k.1.1		1	180.119	even	6
9408.2.a.n.1.1		1	504.461	even	6
9408.2.a.bw.1.1		1	504.83	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-1.00000 - 1.73205i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -2.00000 q^{10} +(-2.00000 + 3.46410i) q^{11} +(-3.00000 - 5.19615i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} -2.00000 q^{17} -4.00000 q^{19} +(-1.00000 + 1.73205i) q^{20} +(2.00000 + 3.46410i) q^{22} +(4.00000 + 6.92820i) q^{23} +(0.500000 - 0.866025i) q^{25} -6.00000 q^{26} -1.00000 q^{28} +(-1.00000 + 1.73205i) q^{29} +(0.500000 + 0.866025i) q^{32} +(-1.00000 + 1.73205i) q^{34} -2.00000 q^{35} -10.0000 q^{37} +(-2.00000 + 3.46410i) q^{38} +(1.00000 + 1.73205i) q^{40} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} +4.00000 q^{44} +8.00000 q^{46} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-3.00000 + 5.19615i) q^{52} -6.00000 q^{53} +8.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(1.00000 + 1.73205i) q^{58} +(2.00000 + 3.46410i) q^{59} +(-3.00000 + 5.19615i) q^{61} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(-2.00000 - 3.46410i) q^{67} +(1.00000 + 1.73205i) q^{68} +(-1.00000 + 1.73205i) q^{70} -8.00000 q^{71} +10.0000 q^{73} +(-5.00000 + 8.66025i) q^{74} +(2.00000 + 3.46410i) q^{76} +(2.00000 + 3.46410i) q^{77} +2.00000 q^{80} -6.00000 q^{82} +(-2.00000 + 3.46410i) q^{83} +(2.00000 + 3.46410i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(2.00000 - 3.46410i) q^{88} +6.00000 q^{89} -6.00000 q^{91} +(4.00000 - 6.92820i) q^{92} +(4.00000 + 6.92820i) q^{95} +(7.00000 - 12.1244i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 2 q^{5} + q^{7} - 2 q^{8} - 4 q^{10} - 4 q^{11} - 6 q^{13} - q^{14} - q^{16} - 4 q^{17} - 8 q^{19} - 2 q^{20} + 4 q^{22} + 8 q^{23} + q^{25} - 12 q^{26} - 2 q^{28} - 2 q^{29}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 2 * q^5 + q^7 - 2 * q^8 - 4 * q^10 - 4 * q^11 - 6 * q^13 - q^14 - q^16 - 4 * q^17 - 8 * q^19 - 2 * q^20 + 4 * q^22 + 8 * q^23 + q^25 - 12 * q^26 - 2 * q^28 - 2 * q^29 + q^32 - 2 * q^34 - 4 * q^35 - 20 * q^37 - 4 * q^38 + 2 * q^40 - 6 * q^41 + 4 * q^43 + 8 * q^44 + 16 * q^46 - q^49 - q^50 - 6 * q^52 - 12 * q^53 + 16 * q^55 - q^56 + 2 * q^58 + 4 * q^59 - 6 * q^61 + 2 * q^64 - 12 * q^65 - 4 * q^67 + 2 * q^68 - 2 * q^70 - 16 * q^71 + 20 * q^73 - 10 * q^74 + 4 * q^76 + 4 * q^77 + 4 * q^80 - 12 * q^82 - 4 * q^83 + 4 * q^85 - 4 * q^86 + 4 * q^88 + 12 * q^89 - 12 * q^91 + 8 * q^92 + 8 * q^95 + 14 * q^97 - 2 * q^98

Introduction

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