LMFDB - Embedded newform 1134.2.f.m.379.1

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:	yes
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.m.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{17} +2.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(1.00000 + 1.73205i) q^{23} +(2.00000 - 3.46410i) q^{25} -3.00000 q^{26} -1.00000 q^{28} +(3.50000 - 6.06218i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{34} +1.00000 q^{35} -7.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.50000 + 2.59808i) q^{52} +6.00000 q^{53} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.50000 - 6.06218i) q^{58} +(5.00000 + 8.66025i) q^{59} +(4.50000 - 7.79423i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(0.500000 - 0.866025i) q^{70} +4.00000 q^{71} -11.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +6.00000 q^{82} +(-5.00000 + 8.66025i) q^{83} +(0.500000 + 0.866025i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{88} -15.0000 q^{89} -3.00000 q^{91} +(1.00000 - 1.73205i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 2 q^{11} - 3 q^{13} - q^{14} - q^{16} + 2 q^{17} + 4 q^{19} + q^{20} - 2 q^{22} + 2 q^{23} + 4 q^{25} - 6 q^{26} - 2 q^{28} + 7 q^{29} - 6 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 + 2 * q^10 + 2 * q^11 - 3 * q^13 - q^14 - q^16 + 2 * q^17 + 4 * q^19 + q^20 - 2 * q^22 + 2 * q^23 + 4 * q^25 - 6 * q^26 - 2 * q^28 + 7 * q^29 - 6 * q^31 + q^32 + q^34 + 2 * q^35 - 14 * q^37 + 2 * q^38 - q^40 + 6 * q^41 + 4 * q^43 - 4 * q^44 + 4 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 3 * q^52 + 12 * q^53 + 4 * q^55 - q^56 - 7 * q^58 + 10 * q^59 + 9 * q^61 - 12 * q^62 + 2 * q^64 + 3 * q^65 - 10 * q^67 - q^68 + q^70 + 8 * q^71 - 22 * q^73 - 7 * q^74 - 2 * q^76 - 2 * q^77 + 6 * q^79 - 2 * q^80 + 12 * q^82 - 10 * q^83 + q^85 - 4 * q^86 - 2 * q^88 - 30 * q^89 - 6 * q^91 + 2 * q^92 - 6 * q^94 + 2 * q^95 + 2 * 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
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	0.955901	−	0.293691i	$-0.0948835\pi$
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i	−0.732294	+	0.680989i	$0.761550\pi$
$6$		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
$10$	1.00000			0.316228
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	0.579510	−	0.814965i	$-0.303244\pi$
$13$	−1.50000	−	2.59808i	−0.416025	−	0.720577i	−0.995535	+	0.0943882i	$0.969911\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000			0.242536			0.121268	−	0.992620i	$-0.461304\pi$
$17$	1.00000			0.242536			0.121268	+	0.992620i	$0.461304\pi$
$18$		0			0
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	0.951247	−	0.308431i	$-0.0998038\pi$
$23$	1.00000	+	1.73205i	0.208514	+	0.361158i	−0.742732	+	0.669588i	$0.766471\pi$
$24$		0			0
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−3.00000			−0.588348
$27$		0			0
$28$	−1.00000			−0.188982
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$		0			0
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	−0.998968	−	0.0454165i	$-0.985539\pi$
$31$	−3.00000	−	5.19615i	−0.538816	−	0.933257i	0.460152	−	0.887840i	$-0.347795\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	0.500000	−	0.866025i	0.0857493	−	0.148522i
$35$	1.00000			0.169031
$36$		0			0
$37$	−7.00000			−1.15079			−0.575396	−	0.817875i	$-0.695152\pi$
$37$	−7.00000			−1.15079			−0.575396	+	0.817875i	$0.695152\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	0.999353	−	0.0359748i	$-0.0114536\pi$
$41$	3.00000	+	5.19615i	0.468521	+	0.811503i	−0.530831	+	0.847477i	$0.678120\pi$
$42$		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	$0.0680112\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	2.00000			0.294884
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$		0			0
$52$	−1.50000	+	2.59808i	−0.208013	+	0.360288i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$		0			0
$55$	2.00000			0.269680
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	−3.50000	−	6.06218i	−0.459573	−	0.796003i
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	0.982894	+	0.184172i	$0.0589603\pi$
$59$	5.00000	+	8.66025i	0.650945	+	1.12747i	−0.331949	+	0.943297i	$0.607706\pi$
$60$		0			0
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	−0.419748	−	0.907641i	$-0.637882\pi$
$61$	4.50000	−	7.79423i	0.576166	−	0.997949i	0.995914	−	0.0903080i	$-0.0287851\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	1.50000	−	2.59808i	0.186052	−	0.322252i
$66$		0			0
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	−0.991098	−	0.133135i	$-0.957496\pi$
$67$	−5.00000	−	8.66025i	−0.610847	−	1.05802i	0.380251	−	0.924883i	$-0.375838\pi$
$68$	−0.500000	−	0.866025i	−0.0606339	−	0.105021i
$69$		0			0
$70$	0.500000	−	0.866025i	0.0597614	−	0.103510i
$71$	4.00000			0.474713			0.237356	−	0.971423i	$-0.423719\pi$
$71$	4.00000			0.474713			0.237356	+	0.971423i	$0.423719\pi$
$72$		0			0
$73$	−11.0000			−1.28745			−0.643726	−	0.765256i	$-0.722612\pi$
$73$	−11.0000			−1.28745			−0.643726	+	0.765256i	$0.722612\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$		0			0
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	−1.00000	−	1.73205i	−0.113961	−	0.197386i
$78$		0			0
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	−1.00000			−0.111803
$81$		0			0
$82$	6.00000			0.662589
$83$	−5.00000	+	8.66025i	−0.548821	+	0.950586i	0.449534	+	0.893263i	$0.351590\pi$
$83$	−5.00000	+	8.66025i	−0.548821	+	0.950586i	−0.998356	+	0.0573233i	$0.981743\pi$
$84$		0			0
$85$	0.500000	+	0.866025i	0.0542326	+	0.0939336i
$86$	−2.00000	−	3.46410i	−0.215666	−	0.373544i
$87$		0			0
$88$	−1.00000	+	1.73205i	−0.106600	+	0.184637i
$89$	−15.0000			−1.59000			−0.794998	−	0.606612i	$-0.792528\pi$
$89$	−15.0000			−1.59000			−0.794998	+	0.606612i	$0.792528\pi$
$90$		0			0
$91$	−3.00000			−0.314485
$92$	1.00000	−	1.73205i	0.104257	−	0.180579i
$93$		0			0
$94$	−3.00000	−	5.19615i	−0.309426	−	0.535942i
$95$	1.00000	+	1.73205i	0.102598	+	0.177705i
$96$		0			0
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	−0.810782	−	0.585348i	$-0.800958\pi$
$97$	1.00000	−	1.73205i	0.101535	−	0.175863i	0.912317	+	0.409484i	$0.134291\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−4.00000			−0.400000
$101$	−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
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	0.927030	+	0.374987i	$0.122353\pi$
$103$	8.00000	+	13.8564i	0.788263	+	1.36531i	−0.138767	+	0.990325i	$0.544314\pi$
$104$	1.50000	+	2.59808i	0.147087	+	0.254762i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	−11.0000			−1.05361			−0.526804	−	0.849987i	$-0.676610\pi$
$109$	−11.0000			−1.05361			−0.526804	+	0.849987i	$0.676610\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	0.888585	−	0.458712i	$-0.151689\pi$
$113$	0.500000	+	0.866025i	0.0470360	+	0.0814688i	−0.841549	+	0.540181i	$0.818356\pi$
$114$		0			0
$115$	−1.00000	+	1.73205i	−0.0932505	+	0.161515i
$116$	−7.00000			−0.649934
$117$		0			0
$118$	10.0000			0.920575
$119$	0.500000	−	0.866025i	0.0458349	−	0.0793884i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−4.50000	−	7.79423i	−0.407411	−	0.705656i
$123$		0			0
$124$	−3.00000	+	5.19615i	−0.269408	+	0.466628i
$125$	9.00000			0.804984
$126$		0			0
$127$	12.0000			1.06483			0.532414	−	0.846484i	$-0.321285\pi$
$127$	12.0000			1.06483			0.532414	+	0.846484i	$0.321285\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	0.968826	+	0.247741i	$0.0796882\pi$
$131$	8.00000	+	13.8564i	0.698963	+	1.21064i	−0.269863	+	0.962899i	$0.586978\pi$
$132$		0			0
$133$	1.00000	−	1.73205i	0.0867110	−	0.150188i
$134$	−10.0000			−0.863868
$135$		0			0
$136$	−1.00000			−0.0857493
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	−0.999408	−	0.0344182i	$-0.989042\pi$
$137$	−5.50000	+	9.52628i	−0.469897	+	0.813885i	0.529511	+	0.848303i	$0.322376\pi$
$138$		0			0
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	0.905314	−	0.424743i	$-0.139635\pi$
$139$	1.00000	+	1.73205i	0.0848189	+	0.146911i	−0.820495	+	0.571654i	$0.806302\pi$
$140$	−0.500000	−	0.866025i	−0.0422577	−	0.0731925i
$141$		0			0
$142$	2.00000	−	3.46410i	0.167836	−	0.290701i
$143$	−6.00000			−0.501745
$144$		0			0
$145$	7.00000			0.581318
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$		0			0
$148$	3.50000	+	6.06218i	0.287698	+	0.498308i
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	−0.871742	−	0.489966i	$-0.837009\pi$
$149$	−10.5000	−	18.1865i	−0.860194	−	1.48990i	0.0115483	−	0.999933i	$-0.496324\pi$
$150$		0			0
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	−0.994540	−	0.104357i	$-0.966722\pi$
$151$	−5.00000	+	8.66025i	−0.406894	+	0.704761i	0.587646	+	0.809118i	$0.300055\pi$
$152$	−2.00000			−0.162221
$153$		0			0
$154$	−2.00000			−0.161165
$155$	3.00000	−	5.19615i	0.240966	−	0.417365i
$156$		0			0
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	−3.00000	−	5.19615i	−0.238667	−	0.413384i
$159$		0			0
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	2.00000			0.157622
$162$		0			0
$163$	−16.0000			−1.25322			−0.626608	−	0.779334i	$-0.715557\pi$
$163$	−16.0000			−1.25322			−0.626608	+	0.779334i	$0.715557\pi$
$164$	3.00000	−	5.19615i	0.234261	−	0.405751i
$165$		0			0
$166$	5.00000	+	8.66025i	0.388075	+	0.672166i
$167$	11.0000	+	19.0526i	0.851206	+	1.47433i	0.880121	+	0.474749i	$0.157461\pi$
$167$	11.0000	+	19.0526i	0.851206	+	1.47433i	−0.0289155	+	0.999582i	$0.509205\pi$
$168$		0			0
$169$	2.00000	−	3.46410i	0.153846	−	0.266469i
$170$	1.00000			0.0766965
$171$		0			0
$172$	−4.00000			−0.304997
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	−0.505792	−	0.862656i	$-0.668800\pi$
$173$	6.50000	−	11.2583i	0.494186	−	0.855955i	0.999978	+	0.00670064i	$0.00213290\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	−7.50000	+	12.9904i	−0.562149	+	0.973670i
$179$	18.0000			1.34538			0.672692	−	0.739923i	$-0.265138\pi$
$179$	18.0000			1.34538			0.672692	+	0.739923i	$0.265138\pi$
$180$		0			0
$181$	18.0000			1.33793			0.668965	−	0.743294i	$-0.266738\pi$
$181$	18.0000			1.33793			0.668965	+	0.743294i	$0.266738\pi$
$182$	−1.50000	+	2.59808i	−0.111187	+	0.192582i
$183$		0			0
$184$	−1.00000	−	1.73205i	−0.0737210	−	0.127688i
$185$	−3.50000	−	6.06218i	−0.257325	−	0.445700i
$186$		0			0
$187$	1.00000	−	1.73205i	0.0731272	−	0.126660i
$188$	−6.00000			−0.437595
$189$		0			0
$190$	2.00000			0.145095
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	0.597317	−	0.802005i	$-0.296234\pi$
$193$	−5.50000	−	9.52628i	−0.395899	−	0.685717i	−0.993215	+	0.116289i	$0.962900\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	1.00000			0.0712470			0.0356235	−	0.999365i	$-0.488658\pi$
$197$	1.00000			0.0712470			0.0356235	+	0.999365i	$0.488658\pi$
$198$		0			0
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$		0			0
$202$	1.00000	+	1.73205i	0.0703598	+	0.121867i
$203$	−3.50000	−	6.06218i	−0.245652	−	0.425481i
$204$		0			0
$205$	−3.00000	+	5.19615i	−0.209529	+	0.362915i
$206$	16.0000			1.11477
$207$		0			0
$208$	3.00000			0.208013
$209$	2.00000	−	3.46410i	0.138343	−	0.239617i
$210$		0			0
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	0.944237	+	0.329266i	$0.106801\pi$
$211$	11.0000	+	19.0526i	0.757271	+	1.31163i	−0.186966	+	0.982366i	$0.559865\pi$
$212$	−3.00000	−	5.19615i	−0.206041	−	0.356873i
$213$		0			0
$214$		0			0
$215$	4.00000			0.272798
$216$		0			0
$217$	−6.00000			−0.407307
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$		0			0
$220$	−1.00000	−	1.73205i	−0.0674200	−	0.116775i
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$		0			0
$223$	−10.0000	+	17.3205i	−0.669650	+	1.15987i	0.308353	+	0.951272i	$0.400222\pi$
$223$	−10.0000	+	17.3205i	−0.669650	+	1.15987i	−0.978002	+	0.208595i	$0.933111\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	1.00000			0.0665190
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	0.125435	+	0.992102i	$0.459967\pi$
$227$	−12.0000	+	20.7846i	−0.796468	+	1.37952i	−0.921903	+	0.387421i	$0.873366\pi$
$228$		0			0
$229$	14.5000	+	25.1147i	0.958187	+	1.65963i	0.726900	+	0.686743i	$0.240960\pi$
$229$	14.5000	+	25.1147i	0.958187	+	1.65963i	0.231287	+	0.972886i	$0.425707\pi$
$230$	1.00000	+	1.73205i	0.0659380	+	0.114208i
$231$		0			0
$232$	−3.50000	+	6.06218i	−0.229786	+	0.398001i
$233$	19.0000			1.24473			0.622366	−	0.782727i	$-0.286172\pi$
$233$	19.0000			1.24473			0.622366	+	0.782727i	$0.286172\pi$
$234$		0			0
$235$	6.00000			0.391397
$236$	5.00000	−	8.66025i	0.325472	−	0.563735i
$237$		0			0
$238$	−0.500000	−	0.866025i	−0.0324102	−	0.0561361i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	7.00000			0.449977
$243$		0			0
$244$	−9.00000			−0.576166
$245$	0.500000	−	0.866025i	0.0319438	−	0.0553283i
$246$		0			0
$247$	−3.00000	−	5.19615i	−0.190885	−	0.330623i
$248$	3.00000	+	5.19615i	0.190500	+	0.329956i
$249$		0			0
$250$	4.50000	−	7.79423i	0.284605	−	0.492950i
$251$	6.00000			0.378717			0.189358	−	0.981908i	$-0.439359\pi$
$251$	6.00000			0.378717			0.189358	+	0.981908i	$0.439359\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	0.690856	−	0.722993i	$-0.257234\pi$
$257$	−4.50000	−	7.79423i	−0.280702	−	0.486191i	−0.971558	+	0.236802i	$0.923901\pi$
$258$		0			0
$259$	−3.50000	+	6.06218i	−0.217479	+	0.376685i
$260$	−3.00000			−0.186052
$261$		0			0
$262$	16.0000			0.988483
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	0.442943	+	0.896550i	$0.353935\pi$
$263$	−9.00000	+	15.5885i	−0.554964	+	0.961225i	−0.997906	+	0.0646755i	$0.979399\pi$
$264$		0			0
$265$	3.00000	+	5.19615i	0.184289	+	0.319197i
$266$	−1.00000	−	1.73205i	−0.0613139	−	0.106199i
$267$		0			0
$268$	−5.00000	+	8.66025i	−0.305424	+	0.529009i
$269$	−1.00000			−0.0609711			−0.0304855	−	0.999535i	$-0.509705\pi$
$269$	−1.00000			−0.0609711			−0.0304855	+	0.999535i	$0.509705\pi$
$270$		0			0
$271$	30.0000			1.82237			0.911185	−	0.411997i	$-0.135169\pi$
$271$	30.0000			1.82237			0.911185	+	0.411997i	$0.135169\pi$
$272$	−0.500000	+	0.866025i	−0.0303170	+	0.0525105i
$273$		0			0
$274$	5.50000	+	9.52628i	0.332267	+	0.575504i
$275$	−4.00000	−	6.92820i	−0.241209	−	0.417786i
$276$		0			0
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	−0.995997	−	0.0893846i	$-0.971510\pi$
$277$	−7.00000	+	12.1244i	−0.420589	+	0.728482i	0.575408	+	0.817867i	$0.304843\pi$
$278$	2.00000			0.119952
$279$		0			0
$280$	−1.00000			−0.0597614
$281$	14.5000	−	25.1147i	0.864997	−	1.49822i	−0.00205220	−	0.999998i	$-0.500653\pi$
$281$	14.5000	−	25.1147i	0.864997	−	1.49822i	0.867050	−	0.498222i	$-0.166013\pi$
$282$		0			0
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	0.524057	−	0.851683i	$-0.324418\pi$
$283$	−8.00000	−	13.8564i	−0.475551	−	0.823678i	−0.999608	+	0.0280052i	$0.991084\pi$
$284$	−2.00000	−	3.46410i	−0.118678	−	0.205557i
$285$		0			0
$286$	−3.00000	+	5.19615i	−0.177394	+	0.307255i
$287$	6.00000			0.354169
$288$		0			0
$289$	−16.0000			−0.941176
$290$	3.50000	−	6.06218i	0.205527	−	0.355983i
$291$		0			0
$292$	5.50000	+	9.52628i	0.321863	+	0.557483i
$293$	−7.50000	−	12.9904i	−0.438155	−	0.758906i	0.559393	−	0.828903i	$-0.311034\pi$
$293$	−7.50000	−	12.9904i	−0.438155	−	0.758906i	−0.997547	+	0.0699967i	$0.977701\pi$
$294$		0			0
$295$	−5.00000	+	8.66025i	−0.291111	+	0.504219i
$296$	7.00000			0.406867
$297$		0			0
$298$	−21.0000			−1.21650
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	−2.00000	−	3.46410i	−0.115278	−	0.199667i
$302$	5.00000	+	8.66025i	0.287718	+	0.498342i
$303$		0			0
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	9.00000			0.515339
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$		0			0
$310$	−3.00000	−	5.19615i	−0.170389	−	0.295122i
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	0.596412	−	0.802678i	$-0.296592\pi$
$311$	−7.00000	−	12.1244i	−0.396934	−	0.687509i	−0.993346	+	0.115169i	$0.963259\pi$
$312$		0			0
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	13.0000			0.733632
$315$		0			0
$316$	−6.00000			−0.337526
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$		0			0
$319$	−7.00000	−	12.1244i	−0.391925	−	0.678834i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	1.00000	−	1.73205i	0.0557278	−	0.0965234i
$323$	2.00000			0.111283
$324$		0			0
$325$	−12.0000			−0.665640
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$		0			0
$328$	−3.00000	−	5.19615i	−0.165647	−	0.286910i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	0.448649	+	0.893708i	$0.351905\pi$
$331$	−10.0000	+	17.3205i	−0.549650	+	0.952021i	−0.998298	+	0.0583130i	$0.981428\pi$
$332$	10.0000			0.548821
$333$		0			0
$334$	22.0000			1.20379
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$		0			0
$337$	9.00000	+	15.5885i	0.490261	+	0.849157i	0.999937	−	0.0112091i	$-0.00356804\pi$
$337$	9.00000	+	15.5885i	0.490261	+	0.849157i	−0.509676	+	0.860366i	$0.670235\pi$
$338$	−2.00000	−	3.46410i	−0.108786	−	0.188422i
$339$		0			0
$340$	0.500000	−	0.866025i	0.0271163	−	0.0469668i
$341$	−12.0000			−0.649836
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	−6.50000	−	11.2583i	−0.349442	−	0.605252i
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	0.658824	−	0.752297i	$-0.271054\pi$
$347$	−6.00000	−	10.3923i	−0.322097	−	0.557888i	−0.980921	+	0.194409i	$0.937721\pi$
$348$		0			0
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	−0.968253	−	0.249973i	$-0.919578\pi$
$349$	−5.00000	+	8.66025i	−0.267644	+	0.463573i	0.700609	+	0.713545i	$0.252912\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	2.00000			0.106600
$353$	−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
$355$	2.00000	+	3.46410i	0.106149	+	0.183855i
$356$	7.50000	+	12.9904i	0.397499	+	0.688489i
$357$		0			0
$358$	9.00000	−	15.5885i	0.475665	−	0.823876i
$359$	−16.0000			−0.844448			−0.422224	−	0.906492i	$-0.638750\pi$
$359$	−16.0000			−0.844448			−0.422224	+	0.906492i	$0.638750\pi$
$360$		0			0
$361$	−15.0000			−0.789474
$362$	9.00000	−	15.5885i	0.473029	−	0.819311i
$363$		0			0
$364$	1.50000	+	2.59808i	0.0786214	+	0.136176i
$365$	−5.50000	−	9.52628i	−0.287883	−	0.498628i
$366$		0			0
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	−2.00000			−0.104257
$369$		0			0
$370$	−7.00000			−0.363913
$371$	3.00000	−	5.19615i	0.155752	−	0.269771i
$372$		0			0
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	0.707055	−	0.707159i	$-0.250023\pi$
$373$	−5.00000	−	8.66025i	−0.258890	−	0.448411i	−0.965945	+	0.258748i	$0.916690\pi$
$374$	−1.00000	−	1.73205i	−0.0517088	−	0.0895622i
$375$		0			0
$376$	−3.00000	+	5.19615i	−0.154713	+	0.267971i
$377$	−21.0000			−1.08156
$378$		0			0
$379$	10.0000			0.513665			0.256833	−	0.966456i	$-0.417321\pi$
$379$	10.0000			0.513665			0.256833	+	0.966456i	$0.417321\pi$
$380$	1.00000	−	1.73205i	0.0512989	−	0.0888523i
$381$		0			0
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	16.0000	+	27.7128i	0.817562	+	1.41606i	0.907474	+	0.420109i	$0.138008\pi$
$383$	16.0000	+	27.7128i	0.817562	+	1.41606i	−0.0899119	+	0.995950i	$0.528659\pi$
$384$		0			0
$385$	1.00000	−	1.73205i	0.0509647	−	0.0882735i
$386$	−11.0000			−0.559885
$387$		0			0
$388$	−2.00000			−0.101535
$389$	17.0000	−	29.4449i	0.861934	−	1.49291i	−0.00812520	−	0.999967i	$-0.502586\pi$
$389$	17.0000	−	29.4449i	0.861934	−	1.49291i	0.870059	−	0.492947i	$-0.164080\pi$
$390$		0			0
$391$	1.00000	+	1.73205i	0.0505722	+	0.0875936i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	0.500000	−	0.866025i	0.0251896	−	0.0436297i
$395$	6.00000			0.301893
$396$		0			0
$397$	39.0000			1.95735			0.978677	−	0.205406i	$-0.0658513\pi$
$397$	39.0000			1.95735			0.978677	+	0.205406i	$0.0658513\pi$
$398$	−5.00000	+	8.66025i	−0.250627	+	0.434099i
$399$		0			0
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	0.826139	−	0.563466i	$-0.190532\pi$
$401$	−1.50000	−	2.59808i	−0.0749064	−	0.129742i	−0.901046	+	0.433724i	$0.857199\pi$
$402$		0			0
$403$	−9.00000	+	15.5885i	−0.448322	+	0.776516i
$404$	2.00000			0.0995037
$405$		0			0
$406$	−7.00000			−0.347404
$407$	−7.00000	+	12.1244i	−0.346977	+	0.600982i
$408$		0			0
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	0.939490	−	0.342578i	$-0.111300\pi$
$409$	3.50000	+	6.06218i	0.173064	+	0.299755i	−0.766426	+	0.642333i	$0.777967\pi$
$410$	3.00000	+	5.19615i	0.148159	+	0.256620i
$411$		0			0
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	10.0000			0.492068
$414$		0			0
$415$	−10.0000			−0.490881
$416$	1.50000	−	2.59808i	0.0735436	−	0.127381i
$417$		0			0
$418$	−2.00000	−	3.46410i	−0.0978232	−	0.169435i
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	0.974546	−	0.224189i	$-0.0719734\pi$
$419$	6.00000	+	10.3923i	0.293119	+	0.507697i	−0.681426	+	0.731887i	$0.738640\pi$
$420$		0			0
$421$	−4.50000	+	7.79423i	−0.219317	+	0.379867i	−0.954599	−	0.297893i	$-0.903716\pi$
$421$	−4.50000	+	7.79423i	−0.219317	+	0.379867i	0.735283	+	0.677761i	$0.237049\pi$
$422$	22.0000			1.07094
$423$		0			0
$424$	−6.00000			−0.291386
$425$	2.00000	−	3.46410i	0.0970143	−	0.168034i
$426$		0			0
$427$	−4.50000	−	7.79423i	−0.217770	−	0.377189i
$428$		0			0
$429$		0			0
$430$	2.00000	−	3.46410i	0.0964486	−	0.167054i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	5.00000			0.240285			0.120142	−	0.992757i	$-0.461665\pi$
$433$	5.00000			0.240285			0.120142	+	0.992757i	$0.461665\pi$
$434$	−3.00000	+	5.19615i	−0.144005	+	0.249423i
$435$		0			0
$436$	5.50000	+	9.52628i	0.263402	+	0.456226i
$437$	2.00000	+	3.46410i	0.0956730	+	0.165710i
$438$		0			0
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	−0.686575	−	0.727059i	$-0.740887\pi$
$439$	6.00000	−	10.3923i	0.286364	−	0.495998i	0.972939	+	0.231062i	$0.0742199\pi$
$440$	−2.00000			−0.0953463
$441$		0			0
$442$	−3.00000			−0.142695
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	0.477028	+	0.878888i	$0.341714\pi$
$443$	−11.0000	+	19.0526i	−0.522626	+	0.905214i	−0.999653	+	0.0263261i	$0.991619\pi$
$444$		0			0
$445$	−7.50000	−	12.9904i	−0.355534	−	0.615803i
$446$	10.0000	+	17.3205i	0.473514	+	0.820150i
$447$		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
$451$	12.0000			0.565058
$452$	0.500000	−	0.866025i	0.0235180	−	0.0407344i
$453$		0			0
$454$	12.0000	+	20.7846i	0.563188	+	0.975470i
$455$	−1.50000	−	2.59808i	−0.0703211	−	0.121800i
$456$		0			0
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.233890	−	0.972263i	$-0.424854\pi$
$457$	20.5000	−	35.5070i	0.958950	−	1.66095i	0.725059	−	0.688686i	$-0.241812\pi$
$458$	29.0000			1.35508
$459$		0			0
$460$	2.00000			0.0932505
$461$	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
$463$	−17.0000	−	29.4449i	−0.790057	−	1.36842i	−0.925931	−	0.377693i	$-0.876718\pi$
$463$	−17.0000	−	29.4449i	−0.790057	−	1.36842i	0.135874	−	0.990726i	$-0.456616\pi$
$464$	3.50000	+	6.06218i	0.162483	+	0.281430i
$465$		0			0
$466$	9.50000	−	16.4545i	0.440079	−	0.762239i
$467$	−34.0000			−1.57333			−0.786666	−	0.617379i	$-0.788195\pi$
$467$	−34.0000			−1.57333			−0.786666	+	0.617379i	$0.788195\pi$
$468$		0			0
$469$	−10.0000			−0.461757
$470$	3.00000	−	5.19615i	0.138380	−	0.239681i
$471$		0			0
$472$	−5.00000	−	8.66025i	−0.230144	−	0.398621i
$473$	−4.00000	−	6.92820i	−0.183920	−	0.318559i
$474$		0			0
$475$	4.00000	−	6.92820i	0.183533	−	0.317888i
$476$	−1.00000			−0.0458349
$477$		0			0
$478$	−6.00000			−0.274434
$479$	−11.0000	+	19.0526i	−0.502603	+	0.870534i	0.497393	+	0.867526i	$0.334291\pi$
$479$	−11.0000	+	19.0526i	−0.502603	+	0.870534i	−0.999995	+	0.00300810i	$0.999042\pi$
$480$		0			0
$481$	10.5000	+	18.1865i	0.478759	+	0.829235i
$482$	−3.50000	−	6.06218i	−0.159421	−	0.276125i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	2.00000			0.0908153
$486$		0			0
$487$	−10.0000			−0.453143			−0.226572	−	0.973995i	$-0.572752\pi$
$487$	−10.0000			−0.453143			−0.226572	+	0.973995i	$0.572752\pi$
$488$	−4.50000	+	7.79423i	−0.203705	+	0.352828i
$489$		0			0
$490$	−0.500000	−	0.866025i	−0.0225877	−	0.0391230i
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	0.911230	+	0.411897i	$0.135134\pi$
$491$	18.0000	+	31.1769i	0.812329	+	1.40699i	−0.0989017	+	0.995097i	$0.531533\pi$
$492$		0			0
$493$	3.50000	−	6.06218i	0.157632	−	0.273027i
$494$	−6.00000			−0.269953
$495$		0			0
$496$	6.00000			0.269408
$497$	2.00000	−	3.46410i	0.0897123	−	0.155386i
$498$		0			0
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	0.507534	−	0.861632i	$-0.330557\pi$
$499$	−11.0000	−	19.0526i	−0.492428	−	0.852910i	−0.999962	+	0.00872186i	$0.997224\pi$
$500$	−4.50000	−	7.79423i	−0.201246	−	0.348569i
$501$		0			0
$502$	3.00000	−	5.19615i	0.133897	−	0.231916i
$503$	6.00000			0.267527			0.133763	−	0.991013i	$-0.457294\pi$
$503$	6.00000			0.267527			0.133763	+	0.991013i	$0.457294\pi$
$504$		0			0
$505$	−2.00000			−0.0889988
$506$	2.00000	−	3.46410i	0.0889108	−	0.153998i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	0.594675	−	0.803966i	$-0.297281\pi$
$509$	−9.00000	−	15.5885i	−0.398918	−	0.690946i	−0.993593	+	0.113020i	$0.963948\pi$
$510$		0			0
$511$	−5.50000	+	9.52628i	−0.243306	+	0.421418i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−9.00000			−0.396973
$515$	−8.00000	+	13.8564i	−0.352522	+	0.610586i
$516$		0			0
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	3.50000	+	6.06218i	0.153781	+	0.266357i
$519$		0			0
$520$	−1.50000	+	2.59808i	−0.0657794	+	0.113933i
$521$	−42.0000			−1.84005			−0.920027	−	0.391856i	$-0.871833\pi$
$521$	−42.0000			−1.84005			−0.920027	+	0.391856i	$0.871833\pi$
$522$		0			0
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	8.00000	−	13.8564i	0.349482	−	0.605320i
$525$		0			0
$526$	9.00000	+	15.5885i	0.392419	+	0.679689i
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$		0			0
$529$	9.50000	−	16.4545i	0.413043	−	0.715412i
$530$	6.00000			0.260623
$531$		0			0
$532$	−2.00000			−0.0867110
$533$	9.00000	−	15.5885i	0.389833	−	0.675211i
$534$		0			0
$535$		0			0
$536$	5.00000	+	8.66025i	0.215967	+	0.374066i
$537$		0			0
$538$	−0.500000	+	0.866025i	−0.0215565	+	0.0373370i
$539$	−2.00000			−0.0861461
$540$		0			0
$541$	−3.00000			−0.128980			−0.0644900	−	0.997918i	$-0.520542\pi$
$541$	−3.00000			−0.128980			−0.0644900	+	0.997918i	$0.520542\pi$
$542$	15.0000	−	25.9808i	0.644305	−	1.11597i
$543$		0			0
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	−5.50000	−	9.52628i	−0.235594	−	0.408061i
$546$		0			0
$547$	3.00000	−	5.19615i	0.128271	−	0.222171i	−0.794736	−	0.606955i	$-0.792391\pi$
$547$	3.00000	−	5.19615i	0.128271	−	0.222171i	0.923007	+	0.384784i	$0.125724\pi$
$548$	11.0000			0.469897
$549$		0			0
$550$	−8.00000			−0.341121
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$		0			0
$553$	−3.00000	−	5.19615i	−0.127573	−	0.220963i
$554$	7.00000	+	12.1244i	0.297402	+	0.515115i
$555$		0			0
$556$	1.00000	−	1.73205i	0.0424094	−	0.0734553i
$557$	17.0000			0.720313			0.360157	−	0.932892i	$-0.382723\pi$
$557$	17.0000			0.720313			0.360157	+	0.932892i	$0.382723\pi$
$558$		0			0
$559$	−12.0000			−0.507546
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$		0			0
$562$	−14.5000	−	25.1147i	−0.611646	−	1.05940i
$563$	4.00000	+	6.92820i	0.168580	+	0.291989i	0.937921	−	0.346850i	$-0.112749\pi$
$563$	4.00000	+	6.92820i	0.168580	+	0.291989i	−0.769341	+	0.638838i	$0.779415\pi$
$564$		0			0
$565$	−0.500000	+	0.866025i	−0.0210352	+	0.0364340i
$566$	−16.0000			−0.672530
$567$		0			0
$568$	−4.00000			−0.167836
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	0.431011	+	0.902347i	$0.358157\pi$
$569$	−13.5000	+	23.3827i	−0.565949	+	0.980253i	−0.996961	+	0.0779066i	$0.975176\pi$
$570$		0			0
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	0.613933	−	0.789359i	$-0.289587\pi$
$571$	−9.00000	−	15.5885i	−0.376638	−	0.652357i	−0.990571	+	0.137002i	$0.956253\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$		0			0
$574$	3.00000	−	5.19615i	0.125218	−	0.216883i
$575$	8.00000			0.333623
$576$		0			0
$577$	−35.0000			−1.45707			−0.728535	−	0.685009i	$-0.759798\pi$
$577$	−35.0000			−1.45707			−0.728535	+	0.685009i	$0.759798\pi$
$578$	−8.00000	+	13.8564i	−0.332756	+	0.576351i
$579$		0			0
$580$	−3.50000	−	6.06218i	−0.145330	−	0.251718i
$581$	5.00000	+	8.66025i	0.207435	+	0.359288i
$582$		0			0
$583$	6.00000	−	10.3923i	0.248495	−	0.430405i
$584$	11.0000			0.455183
$585$		0			0
$586$	−15.0000			−0.619644
$587$	1.00000	−	1.73205i	0.0412744	−	0.0714894i	−0.844650	−	0.535319i	$-0.820192\pi$
$587$	1.00000	−	1.73205i	0.0412744	−	0.0714894i	0.885925	+	0.463829i	$0.153525\pi$
$588$		0			0
$589$	−6.00000	−	10.3923i	−0.247226	−	0.428207i
$590$	5.00000	+	8.66025i	0.205847	+	0.356537i
$591$		0			0
$592$	3.50000	−	6.06218i	0.143849	−	0.249154i
$593$	−39.0000			−1.60154			−0.800769	−	0.598973i	$-0.795576\pi$
$593$	−39.0000			−1.60154			−0.800769	+	0.598973i	$0.795576\pi$
$594$		0			0
$595$	1.00000			0.0409960
$596$	−10.5000	+	18.1865i	−0.430097	+	0.744949i
$597$		0			0
$598$	−3.00000	−	5.19615i	−0.122679	−	0.212486i
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	0.798206	−	0.602384i	$-0.205782\pi$
$599$	−3.00000	−	5.19615i	−0.122577	−	0.212309i	−0.920783	+	0.390075i	$0.872449\pi$
$600$		0			0
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$	−4.00000			−0.163028
$603$		0			0
$604$	10.0000			0.406894
$605$	−3.50000	+	6.06218i	−0.142295	+	0.246463i
$606$		0			0
$607$	3.00000	+	5.19615i	0.121766	+	0.210905i	0.920464	−	0.390827i	$-0.127811\pi$
$607$	3.00000	+	5.19615i	0.121766	+	0.210905i	−0.798698	+	0.601732i	$0.794478\pi$
$608$	1.00000	+	1.73205i	0.0405554	+	0.0702439i
$609$		0			0
$610$	4.50000	−	7.79423i	0.182200	−	0.315579i
$611$	−18.0000			−0.728202
$612$		0			0
$613$	−18.0000			−0.727013			−0.363507	−	0.931592i	$-0.618421\pi$
$613$	−18.0000			−0.727013			−0.363507	+	0.931592i	$0.618421\pi$
$614$	8.00000	−	13.8564i	0.322854	−	0.559199i
$615$		0			0
$616$	1.00000	+	1.73205i	0.0402911	+	0.0697863i
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	0.786933	−	0.617039i	$-0.211668\pi$
$617$	−3.50000	−	6.06218i	−0.140905	−	0.244054i	−0.927838	+	0.372985i	$0.878334\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	−6.00000			−0.240966
$621$		0			0
$622$	−14.0000			−0.561349
$623$	−7.50000	+	12.9904i	−0.300481	+	0.520449i
$624$		0			0
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$		0			0
$628$	6.50000	−	11.2583i	0.259378	−	0.449256i
$629$	−7.00000			−0.279108
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$	−3.00000	+	5.19615i	−0.119334	+	0.206692i
$633$		0			0
$634$	−1.50000	−	2.59808i	−0.0595726	−	0.103183i
$635$	6.00000	+	10.3923i	0.238103	+	0.412406i
$636$		0			0
$637$	−1.50000	+	2.59808i	−0.0594322	+	0.102940i
$638$	−14.0000			−0.554265
$639$		0			0
$640$	1.00000			0.0395285
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	−0.647895	−	0.761730i	$-0.724350\pi$
$641$	8.50000	−	14.7224i	0.335730	−	0.581501i	0.983625	+	0.180229i	$0.0576838\pi$
$642$		0			0
$643$	−13.0000	−	22.5167i	−0.512670	−	0.887970i	−0.999892	−	0.0146923i	$-0.995323\pi$
$643$	−13.0000	−	22.5167i	−0.512670	−	0.887970i	0.487222	−	0.873278i	$-0.338010\pi$
$644$	−1.00000	−	1.73205i	−0.0394055	−	0.0682524i
$645$		0			0
$646$	1.00000	−	1.73205i	0.0393445	−	0.0681466i
$647$	−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
$649$	20.0000			0.785069
$650$	−6.00000	+	10.3923i	−0.235339	+	0.407620i
$651$		0			0
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	0.986634	−	0.162951i	$-0.0521013\pi$
$653$	9.00000	+	15.5885i	0.352197	+	0.610023i	−0.634437	+	0.772975i	$0.718768\pi$
$654$		0			0
$655$	−8.00000	+	13.8564i	−0.312586	+	0.541415i
$656$	−6.00000			−0.234261
$657$		0			0
$658$	−6.00000			−0.233904
$659$	16.0000	−	27.7128i	0.623272	−	1.07954i	−0.365601	−	0.930772i	$-0.619136\pi$
$659$	16.0000	−	27.7128i	0.623272	−	1.07954i	0.988872	−	0.148766i	$-0.0475302\pi$
$660$		0			0
$661$	−3.50000	−	6.06218i	−0.136134	−	0.235791i	0.789896	−	0.613241i	$-0.210135\pi$
$661$	−3.50000	−	6.06218i	−0.136134	−	0.235791i	−0.926030	+	0.377450i	$0.876801\pi$
$662$	10.0000	+	17.3205i	0.388661	+	0.673181i
$663$		0			0
$664$	5.00000	−	8.66025i	0.194038	−	0.336083i
$665$	2.00000			0.0775567
$666$		0			0
$667$	14.0000			0.542082
$668$	11.0000	−	19.0526i	0.425603	−	0.737166i
$669$		0			0
$670$	−5.00000	−	8.66025i	−0.193167	−	0.334575i
$671$	−9.00000	−	15.5885i	−0.347441	−	0.601786i
$672$		0			0
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	−0.997932	−	0.0642860i	$-0.979523\pi$
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	0.554639	+	0.832091i	$0.312856\pi$
$674$	18.0000			0.693334
$675$		0			0
$676$	−4.00000			−0.153846
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	−0.917899	−	0.396813i	$-0.870116\pi$
$677$	−3.00000	+	5.19615i	−0.115299	+	0.199704i	0.802600	+	0.596518i	$0.203449\pi$
$678$		0			0
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	−0.500000	−	0.866025i	−0.0191741	−	0.0332106i
$681$		0			0
$682$	−6.00000	+	10.3923i	−0.229752	+	0.397942i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$		0			0
$685$	−11.0000			−0.420288
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	2.00000	+	3.46410i	0.0762493	+	0.132068i
$689$	−9.00000	−	15.5885i	−0.342873	−	0.593873i
$690$		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	$0.142425\pi$
$692$	−13.0000			−0.494186
$693$		0			0
$694$	−12.0000			−0.455514
$695$	−1.00000	+	1.73205i	−0.0379322	+	0.0657004i
$696$		0			0
$697$	3.00000	+	5.19615i	0.113633	+	0.196818i
$698$	5.00000	+	8.66025i	0.189253	+	0.327795i
$699$		0			0
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$	5.00000			0.188847			0.0944237	−	0.995532i	$-0.469899\pi$
$701$	5.00000			0.188847			0.0944237	+	0.995532i	$0.469899\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	1.00000	−	1.73205i	0.0376889	−	0.0652791i
$705$		0			0
$706$	15.0000	+	25.9808i	0.564532	+	0.977799i
$707$	1.00000	+	1.73205i	0.0376089	+	0.0651405i
$708$		0			0
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$	4.00000			0.150117
$711$		0			0
$712$	15.0000			0.562149
$713$	6.00000	−	10.3923i	0.224702	−	0.389195i
$714$		0			0
$715$	−3.00000	−	5.19615i	−0.112194	−	0.194325i
$716$	−9.00000	−	15.5885i	−0.336346	−	0.582568i
$717$		0			0
$718$	−8.00000	+	13.8564i	−0.298557	+	0.517116i
$719$	24.0000			0.895049			0.447524	−	0.894272i	$-0.352306\pi$
$719$	24.0000			0.895049			0.447524	+	0.894272i	$0.352306\pi$
$720$		0			0
$721$	16.0000			0.595871
$722$	−7.50000	+	12.9904i	−0.279121	+	0.483452i
$723$		0			0
$724$	−9.00000	−	15.5885i	−0.334482	−	0.579340i
$725$	−14.0000	−	24.2487i	−0.519947	−	0.900575i
$726$		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	$0.119270\pi$
$728$	3.00000			0.111187
$729$		0			0
$730$	−11.0000			−0.407128
$731$	2.00000	−	3.46410i	0.0739727	−	0.128124i
$732$		0			0
$733$	−21.0000	−	36.3731i	−0.775653	−	1.34347i	−0.934427	−	0.356155i	$-0.884088\pi$
$733$	−21.0000	−	36.3731i	−0.775653	−	1.34347i	0.158774	−	0.987315i	$-0.449246\pi$
$734$	−5.00000	−	8.66025i	−0.184553	−	0.319656i
$735$		0			0
$736$	−1.00000	+	1.73205i	−0.0368605	+	0.0638442i
$737$	−20.0000			−0.736709
$738$		0			0
$739$	−6.00000			−0.220714			−0.110357	−	0.993892i	$-0.535199\pi$
$739$	−6.00000			−0.220714			−0.110357	+	0.993892i	$0.535199\pi$
$740$	−3.50000	+	6.06218i	−0.128663	+	0.222850i
$741$		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
$745$	10.5000	−	18.1865i	0.384690	−	0.666303i
$746$	−10.0000			−0.366126
$747$		0			0
$748$	−2.00000			−0.0731272
$749$		0			0
$750$		0			0
$751$	−6.00000	−	10.3923i	−0.218943	−	0.379221i	0.735542	−	0.677479i	$-0.236928\pi$
$751$	−6.00000	−	10.3923i	−0.218943	−	0.379221i	−0.954485	+	0.298259i	$0.903594\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$		0			0
$754$	−10.5000	+	18.1865i	−0.382387	+	0.662314i
$755$	−10.0000			−0.363937
$756$		0			0
$757$	42.0000			1.52652			0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000			1.52652			0.763258	+	0.646094i	$0.223599\pi$
$758$	5.00000	−	8.66025i	0.181608	−	0.314555i
$759$		0			0
$760$	−1.00000	−	1.73205i	−0.0362738	−	0.0628281i
$761$	5.50000	+	9.52628i	0.199375	+	0.345327i	0.948326	−	0.317298i	$-0.102776\pi$
$761$	5.50000	+	9.52628i	0.199375	+	0.345327i	−0.748951	+	0.662625i	$0.769442\pi$
$762$		0			0
$763$	−5.50000	+	9.52628i	−0.199113	+	0.344874i
$764$	18.0000			0.651217
$765$		0			0
$766$	32.0000			1.15621
$767$	15.0000	−	25.9808i	0.541619	−	0.938111i
$768$		0			0
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$	−1.00000	−	1.73205i	−0.0360375	−	0.0624188i
$771$		0			0
$772$	−5.50000	+	9.52628i	−0.197949	+	0.342858i
$773$	35.0000			1.25886			0.629431	−	0.777056i	$-0.283288\pi$
$773$	35.0000			1.25886			0.629431	+	0.777056i	$0.283288\pi$
$774$		0			0
$775$	−24.0000			−0.862105
$776$	−1.00000	+	1.73205i	−0.0358979	+	0.0621770i
$777$		0			0
$778$	−17.0000	−	29.4449i	−0.609480	−	1.05565i
$779$	6.00000	+	10.3923i	0.214972	+	0.372343i
$780$		0			0
$781$	4.00000	−	6.92820i	0.143131	−	0.247911i
$782$	2.00000			0.0715199
$783$		0			0
$784$	1.00000			0.0357143
$785$	−6.50000	+	11.2583i	−0.231995	+	0.401827i
$786$		0			0
$787$	12.0000	+	20.7846i	0.427754	+	0.740891i	0.996673	−	0.0815020i	$-0.0259717\pi$
$787$	12.0000	+	20.7846i	0.427754	+	0.740891i	−0.568919	+	0.822393i	$0.692638\pi$
$788$	−0.500000	−	0.866025i	−0.0178118	−	0.0308509i
$789$		0			0
$790$	3.00000	−	5.19615i	0.106735	−	0.184871i
$791$	1.00000			0.0355559
$792$		0			0
$793$	−27.0000			−0.958798
$794$	19.5000	−	33.7750i	0.692029	−	1.19863i
$795$		0			0
$796$	5.00000	+	8.66025i	0.177220	+	0.306955i
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$		0			0
$799$	3.00000	−	5.19615i	0.106132	−	0.183827i
$800$	4.00000			0.141421
$801$		0			0
$802$	−3.00000			−0.105934
$803$	−11.0000	+	19.0526i	−0.388182	+	0.672350i
$804$		0			0
$805$	1.00000	+	1.73205i	0.0352454	+	0.0610468i
$806$	9.00000	+	15.5885i	0.317011	+	0.549080i
$807$		0			0
$808$	1.00000	−	1.73205i	0.0351799	−	0.0609333i
$809$	−1.00000			−0.0351581			−0.0175791	−	0.999845i	$-0.505596\pi$
$809$	−1.00000			−0.0351581			−0.0175791	+	0.999845i	$0.505596\pi$
$810$		0			0
$811$	34.0000			1.19390			0.596951	−	0.802278i	$-0.296379\pi$
$811$	34.0000			1.19390			0.596951	+	0.802278i	$0.296379\pi$
$812$	−3.50000	+	6.06218i	−0.122826	+	0.212741i
$813$		0			0
$814$	7.00000	+	12.1244i	0.245350	+	0.424958i
$815$	−8.00000	−	13.8564i	−0.280228	−	0.485369i
$816$		0			0
$817$	4.00000	−	6.92820i	0.139942	−	0.242387i
$818$	7.00000			0.244749
$819$		0			0
$820$	6.00000			0.209529
$821$	5.50000	−	9.52628i	0.191951	−	0.332469i	−0.753946	−	0.656937i	$-0.771852\pi$
$821$	5.50000	−	9.52628i	0.191951	−	0.332469i	0.945897	+	0.324468i	$0.105185\pi$
$822$		0			0
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	0.692240	−	0.721668i	$-0.256624\pi$
$823$	−8.00000	−	13.8564i	−0.278862	−	0.483004i	−0.971102	+	0.238664i	$0.923291\pi$
$824$	−8.00000	−	13.8564i	−0.278693	−	0.482711i
$825$		0			0
$826$	5.00000	−	8.66025i	0.173972	−	0.301329i
$827$	48.0000			1.66912			0.834562	−	0.550914i	$-0.185721\pi$
$827$	48.0000			1.66912			0.834562	+	0.550914i	$0.185721\pi$
$828$		0			0
$829$	−2.00000			−0.0694629			−0.0347314	−	0.999397i	$-0.511058\pi$
$829$	−2.00000			−0.0694629			−0.0347314	+	0.999397i	$0.511058\pi$
$830$	−5.00000	+	8.66025i	−0.173553	+	0.300602i
$831$		0			0
$832$	−1.50000	−	2.59808i	−0.0520031	−	0.0900721i
$833$	−0.500000	−	0.866025i	−0.0173240	−	0.0300060i
$834$		0			0
$835$	−11.0000	+	19.0526i	−0.380671	+	0.659341i
$836$	−4.00000			−0.138343
$837$		0			0
$838$	12.0000			0.414533
$839$	16.0000	−	27.7128i	0.552381	−	0.956753i	−0.445721	−	0.895172i	$-0.647053\pi$
$839$	16.0000	−	27.7128i	0.552381	−	0.956753i	0.998102	−	0.0615805i	$-0.0196141\pi$
$840$		0			0
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	4.50000	+	7.79423i	0.155080	+	0.268607i
$843$		0			0
$844$	11.0000	−	19.0526i	0.378636	−	0.655816i
$845$	4.00000			0.137604
$846$		0			0
$847$	7.00000			0.240523
$848$	−3.00000	+	5.19615i	−0.103020	+	0.178437i
$849$		0			0
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	−7.00000	−	12.1244i	−0.239957	−	0.415618i
$852$		0			0
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	−0.767642	−	0.640879i	$-0.778570\pi$
$853$	5.00000	−	8.66025i	0.171197	−	0.296521i	0.938839	+	0.344358i	$0.111903\pi$
$854$	−9.00000			−0.307974
$855$		0			0
$856$		0			0
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	−0.839268	−	0.543718i	$-0.817016\pi$
$857$	1.50000	−	2.59808i	0.0512390	−	0.0887486i	0.890507	+	0.454969i	$0.150350\pi$
$858$		0			0
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.843278	+	0.537478i	$0.180623\pi$
$859$	26.0000	+	45.0333i	0.887109	+	1.53652i	0.0438309	+	0.999039i	$0.486044\pi$
$860$	−2.00000	−	3.46410i	−0.0681994	−	0.118125i
$861$		0			0
$862$	−6.00000	+	10.3923i	−0.204361	+	0.353963i
$863$	14.0000			0.476566			0.238283	−	0.971196i	$-0.423415\pi$
$863$	14.0000			0.476566			0.238283	+	0.971196i	$0.423415\pi$
$864$		0			0
$865$	13.0000			0.442013
$866$	2.50000	−	4.33013i	0.0849535	−	0.147144i
$867$		0			0
$868$	3.00000	+	5.19615i	0.101827	+	0.176369i
$869$	−6.00000	−	10.3923i	−0.203536	−	0.352535i
$870$		0			0
$871$	−15.0000	+	25.9808i	−0.508256	+	0.880325i
$872$	11.0000			0.372507
$873$		0			0
$874$	4.00000			0.135302
$875$	4.50000	−	7.79423i	0.152128	−	0.263493i
$876$		0			0
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	0.992225	−	0.124459i	$-0.0397196\pi$
$877$	11.5000	+	19.9186i	0.388327	+	0.672603i	−0.603897	+	0.797062i	$0.706386\pi$
$878$	−6.00000	−	10.3923i	−0.202490	−	0.350723i
$879$		0			0
$880$	−1.00000	+	1.73205i	−0.0337100	+	0.0583874i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$	−10.0000			−0.336527			−0.168263	−	0.985742i	$-0.553816\pi$
$883$	−10.0000			−0.336527			−0.168263	+	0.985742i	$0.553816\pi$
$884$	−1.50000	+	2.59808i	−0.0504505	+	0.0873828i
$885$		0			0
$886$	11.0000	+	19.0526i	0.369552	+	0.640083i
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	0.966651	+	0.256096i	$0.0824362\pi$
$887$	21.0000	+	36.3731i	0.705111	+	1.22129i	−0.261540	+	0.965193i	$0.584230\pi$
$888$		0			0
$889$	6.00000	−	10.3923i	0.201234	−	0.348547i
$890$	−15.0000			−0.502801
$891$		0			0
$892$	20.0000			0.669650
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$		0			0
$895$	9.00000	+	15.5885i	0.300837	+	0.521065i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	−17.0000	+	29.4449i	−0.567297	+	0.982588i
$899$	−42.0000			−1.40078
$900$		0			0
$901$	6.00000			0.199889
$902$	6.00000	−	10.3923i	0.199778	−	0.346026i
$903$		0			0
$904$	−0.500000	−	0.866025i	−0.0166298	−	0.0288036i
$905$	9.00000	+	15.5885i	0.299170	+	0.518178i
$906$		0			0
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	−0.749051	−	0.662512i	$-0.769490\pi$
$907$	6.00000	−	10.3923i	0.199227	−	0.345071i	0.948278	+	0.317441i	$0.102824\pi$
$908$	24.0000			0.796468
$909$		0			0
$910$	−3.00000			−0.0994490
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	−0.749347	−	0.662177i	$-0.769633\pi$
$911$	6.00000	−	10.3923i	0.198789	−	0.344312i	0.948136	+	0.317865i	$0.102966\pi$
$912$		0			0
$913$	10.0000	+	17.3205i	0.330952	+	0.573225i
$914$	−20.5000	−	35.5070i	−0.678080	−	1.17447i
$915$		0			0
$916$	14.5000	−	25.1147i	0.479093	−	0.829814i
$917$	16.0000			0.528367
$918$		0			0
$919$	10.0000			0.329870			0.164935	−	0.986304i	$-0.447259\pi$
$919$	10.0000			0.329870			0.164935	+	0.986304i	$0.447259\pi$
$920$	1.00000	−	1.73205i	0.0329690	−	0.0571040i
$921$		0			0
$922$	−11.0000	−	19.0526i	−0.362266	−	0.627463i
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		0			0
$925$	−14.0000	+	24.2487i	−0.460317	+	0.797293i
$926$	−34.0000			−1.11731
$927$		0			0
$928$	7.00000			0.229786
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	0.457480	+	0.889220i	$0.348752\pi$
$929$	−16.5000	+	28.5788i	−0.541347	+	0.937641i	−0.998827	+	0.0484211i	$0.984581\pi$
$930$		0			0
$931$	−1.00000	−	1.73205i	−0.0327737	−	0.0567657i
$932$	−9.50000	−	16.4545i	−0.311183	−	0.538985i
$933$		0			0
$934$	−17.0000	+	29.4449i	−0.556257	+	0.963465i
$935$	2.00000			0.0654070
$936$		0			0
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$	−5.00000	+	8.66025i	−0.163256	+	0.282767i
$939$		0			0
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	12.5000	+	21.6506i	0.407488	+	0.705791i	0.994608	−	0.103710i	$-0.0330714\pi$
$941$	12.5000	+	21.6506i	0.407488	+	0.705791i	−0.587119	+	0.809500i	$0.699738\pi$
$942$		0			0
$943$	−6.00000	+	10.3923i	−0.195387	+	0.338420i
$944$	−10.0000			−0.325472
$945$		0			0
$946$	−8.00000			−0.260102
$947$	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
$949$	16.5000	+	28.5788i	0.535613	+	0.927708i
$950$	−4.00000	−	6.92820i	−0.129777	−	0.224781i
$951$		0			0
$952$	−0.500000	+	0.866025i	−0.0162051	+	0.0280680i
$953$	19.0000			0.615470			0.307735	−	0.951472i	$-0.400429\pi$
$953$	19.0000			0.615470			0.307735	+	0.951472i	$0.400429\pi$
$954$		0			0
$955$	−18.0000			−0.582466
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$		0			0
$958$	11.0000	+	19.0526i	0.355394	+	0.615560i
$959$	5.50000	+	9.52628i	0.177604	+	0.307620i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$	21.0000			0.677067
$963$		0			0
$964$	−7.00000			−0.225455
$965$	5.50000	−	9.52628i	0.177051	−	0.306662i
$966$		0			0
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	0.986901	−	0.161328i	$-0.0515777\pi$
$967$	11.0000	+	19.0526i	0.353736	+	0.612689i	−0.633165	+	0.774017i	$0.718244\pi$
$968$	−3.50000	−	6.06218i	−0.112494	−	0.194846i
$969$		0			0
$970$	1.00000	−	1.73205i	0.0321081	−	0.0556128i
$971$	42.0000			1.34784			0.673922	−	0.738802i	$-0.264608\pi$
$971$	42.0000			1.34784			0.673922	+	0.738802i	$0.264608\pi$
$972$		0			0
$973$	2.00000			0.0641171
$974$	−5.00000	+	8.66025i	−0.160210	+	0.277492i
$975$		0			0
$976$	4.50000	+	7.79423i	0.144041	+	0.249487i
$977$	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
$979$	−15.0000	+	25.9808i	−0.479402	+	0.830349i
$980$	−1.00000			−0.0319438
$981$		0			0
$982$	36.0000			1.14881
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.226778	+	0.973946i	$0.572819\pi$
$983$	−30.0000	+	51.9615i	−0.956851	+	1.65732i	−0.730073	+	0.683369i	$0.760514\pi$
$984$		0			0
$985$	0.500000	+	0.866025i	0.0159313	+	0.0275939i
$986$	−3.50000	−	6.06218i	−0.111463	−	0.193059i
$987$		0			0
$988$	−3.00000	+	5.19615i	−0.0954427	+	0.165312i
$989$	8.00000			0.254385
$990$		0			0
$991$	62.0000			1.96949			0.984747	−	0.173990i	$-0.0556660\pi$
$991$	62.0000			1.96949			0.984747	+	0.173990i	$0.0556660\pi$
$992$	3.00000	−	5.19615i	0.0952501	−	0.164978i
$993$		0			0
$994$	−2.00000	−	3.46410i	−0.0634361	−	0.109875i
$995$	−5.00000	−	8.66025i	−0.158511	−	0.274549i
$996$		0			0
$997$	−11.5000	+	19.9186i	−0.364209	+	0.630828i	−0.988649	−	0.150245i	$-0.951994\pi$
$997$	−11.5000	+	19.9186i	−0.364209	+	0.630828i	0.624440	+	0.781073i	$0.285327\pi$
$998$	−22.0000			−0.696398
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.m.379.1		2
3.2	odd	2		1134.2.f.d.379.1		2
9.2	odd	6		1134.2.a.g.1.1	yes	1
9.4	even	3	inner	1134.2.f.m.757.1		2
9.5	odd	6		1134.2.f.d.757.1		2
9.7	even	3		1134.2.a.b.1.1	✓	1
36.7	odd	6		9072.2.a.k.1.1		1
36.11	even	6		9072.2.a.p.1.1		1
63.20	even	6		7938.2.a.w.1.1		1
63.34	odd	6		7938.2.a.j.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.b.1.1	✓	1	9.7	even	3
1134.2.a.g.1.1	yes	1	9.2	odd	6
1134.2.f.d.379.1		2	3.2	odd	2
1134.2.f.d.757.1		2	9.5	odd	6
1134.2.f.m.379.1		2	1.1	even	1	trivial
1134.2.f.m.757.1		2	9.4	even	3	inner
7938.2.a.j.1.1		1	63.34	odd	6
7938.2.a.w.1.1		1	63.20	even	6
9072.2.a.k.1.1		1	36.7	odd	6
9072.2.a.p.1.1		1	36.11	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +1.00000 q^{10} +(1.00000 - 1.73205i) q^{11} +(-1.50000 - 2.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +1.00000 q^{17} +2.00000 q^{19} +(0.500000 - 0.866025i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(1.00000 + 1.73205i) q^{23} +(2.00000 - 3.46410i) q^{25} -3.00000 q^{26} -1.00000 q^{28} +(3.50000 - 6.06218i) q^{29} +(-3.00000 - 5.19615i) q^{31} +(0.500000 + 0.866025i) q^{32} +(0.500000 - 0.866025i) q^{34} +1.00000 q^{35} -7.00000 q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(3.00000 + 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(-1.50000 + 2.59808i) q^{52} +6.00000 q^{53} +2.00000 q^{55} +(-0.500000 + 0.866025i) q^{56} +(-3.50000 - 6.06218i) q^{58} +(5.00000 + 8.66025i) q^{59} +(4.50000 - 7.79423i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(1.50000 - 2.59808i) q^{65} +(-5.00000 - 8.66025i) q^{67} +(-0.500000 - 0.866025i) q^{68} +(0.500000 - 0.866025i) q^{70} +4.00000 q^{71} -11.0000 q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{76} +(-1.00000 - 1.73205i) q^{77} +(3.00000 - 5.19615i) q^{79} -1.00000 q^{80} +6.00000 q^{82} +(-5.00000 + 8.66025i) q^{83} +(0.500000 + 0.866025i) q^{85} +(-2.00000 - 3.46410i) q^{86} +(-1.00000 + 1.73205i) q^{88} -15.0000 q^{89} -3.00000 q^{91} +(1.00000 - 1.73205i) q^{92} +(-3.00000 - 5.19615i) q^{94} +(1.00000 + 1.73205i) q^{95} +(1.00000 - 1.73205i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} + q^{5} + q^{7} - 2 q^{8} + 2 q^{10} + 2 q^{11} - 3 q^{13} - q^{14} - q^{16} + 2 q^{17} + 4 q^{19} + q^{20} - 2 q^{22} + 2 q^{23} + 4 q^{25} - 6 q^{26} - 2 q^{28} + 7 q^{29} - 6 q^{31}+ \cdots - 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 + q^5 + q^7 - 2 * q^8 + 2 * q^10 + 2 * q^11 - 3 * q^13 - q^14 - q^16 + 2 * q^17 + 4 * q^19 + q^20 - 2 * q^22 + 2 * q^23 + 4 * q^25 - 6 * q^26 - 2 * q^28 + 7 * q^29 - 6 * q^31 + q^32 + q^34 + 2 * q^35 - 14 * q^37 + 2 * q^38 - q^40 + 6 * q^41 + 4 * q^43 - 4 * q^44 + 4 * q^46 + 6 * q^47 - q^49 - 4 * q^50 - 3 * q^52 + 12 * q^53 + 4 * q^55 - q^56 - 7 * q^58 + 10 * q^59 + 9 * q^61 - 12 * q^62 + 2 * q^64 + 3 * q^65 - 10 * q^67 - q^68 + q^70 + 8 * q^71 - 22 * q^73 - 7 * q^74 - 2 * q^76 - 2 * q^77 + 6 * q^79 - 2 * q^80 + 12 * q^82 - 10 * q^83 + q^85 - 4 * q^86 - 2 * q^88 - 30 * q^89 - 6 * q^91 + 2 * q^92 - 6 * q^94 + 2 * q^95 + 2 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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