LMFDB - Embedded newform 1134.2.f.d.757.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1134, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("1134.379");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$9.05503558921$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{10} +(-1.00000 - 1.73205i) q^{11} +(-1.50000 + 2.59808i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.00000 q^{17} +2.00000 q^{19} +(-0.500000 - 0.866025i) q^{20} +(-1.00000 + 1.73205i) q^{22} +(-1.00000 + 1.73205i) q^{23} +(2.00000 + 3.46410i) q^{25} +3.00000 q^{26} -1.00000 q^{28} +(-3.50000 - 6.06218i) q^{29} +(-3.00000 + 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(0.500000 + 0.866025i) q^{34} -1.00000 q^{35} -7.00000 q^{37} +(-1.00000 - 1.73205i) q^{38} +(-0.500000 + 0.866025i) q^{40} +(-3.00000 + 5.19615i) q^{41} +(2.00000 + 3.46410i) q^{43} +2.00000 q^{44} +2.00000 q^{46} +(-3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{49} +(2.00000 - 3.46410i) q^{50} +(-1.50000 - 2.59808i) q^{52} -6.00000 q^{53} +2.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +(-3.50000 + 6.06218i) q^{58} +(-5.00000 + 8.66025i) q^{59} +(4.50000 + 7.79423i) q^{61} +6.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{65} +(-5.00000 + 8.66025i) q^{67} +(0.500000 - 0.866025i) q^{68} +(0.500000 + 0.866025i) q^{70} -4.00000 q^{71} -11.0000 q^{73} +(3.50000 + 6.06218i) q^{74} +(-1.00000 + 1.73205i) q^{76} +(1.00000 - 1.73205i) q^{77} +(3.00000 + 5.19615i) q^{79} +1.00000 q^{80} +6.00000 q^{82} +(5.00000 + 8.66025i) q^{83} +(0.500000 - 0.866025i) q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.00000 - 1.73205i) q^{88} +15.0000 q^{89} -3.00000 q^{91} +(-1.00000 - 1.73205i) q^{92} +(-3.00000 + 5.19615i) q^{94} +(-1.00000 + 1.73205i) q^{95} +(1.00000 + 1.73205i) q^{97} +1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/1134\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$		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	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$		0			0
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	−0.995535	−	0.0943882i	$-0.969911\pi$
$13$	−1.50000	+	2.59808i	−0.416025	+	0.720577i	0.579510	+	0.814965i	$0.303244\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.00000			−0.242536			−0.121268	−	0.992620i	$-0.538696\pi$
$17$	−1.00000			−0.242536			−0.121268	+	0.992620i	$0.538696\pi$
$18$		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	$-0.900196\pi$
$23$	−1.00000	+	1.73205i	−0.208514	+	0.361158i	0.742732	+	0.669588i	$0.233529\pi$
$24$		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	−0.983138	−	0.182864i	$-0.941463\pi$
$29$	−3.50000	−	6.06218i	−0.649934	−	1.12572i	0.333205	−	0.942855i	$-0.391870\pi$
$30$		0			0
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	0.460152	+	0.887840i	$0.347795\pi$
$31$	−3.00000	+	5.19615i	−0.538816	+	0.933257i	−0.998968	+	0.0454165i	$0.985539\pi$
$32$	−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	$-0.988546\pi$
$41$	−3.00000	+	5.19615i	−0.468521	+	0.811503i	0.530831	+	0.847477i	$0.321880\pi$
$42$		0			0
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	0.977261	−	0.212041i	$-0.0680112\pi$
$43$	2.00000	+	3.46410i	0.304997	+	0.528271i	−0.672264	+	0.740312i	$0.734678\pi$
$44$	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	$-0.310836\pi$
$47$	−3.00000	−	5.19615i	−0.437595	−	0.757937i	−0.997503	+	0.0706177i	$0.977503\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	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	$-0.635198\pi$
$53$	−6.00000			−0.824163			−0.412082	+	0.911147i	$0.635198\pi$
$54$		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	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	0.995914	+	0.0903080i	$0.0287851\pi$
$61$	4.50000	+	7.79423i	0.576166	+	0.997949i	−0.419748	+	0.907641i	$0.637882\pi$
$62$	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	0.380251	+	0.924883i	$0.375838\pi$
$67$	−5.00000	+	8.66025i	−0.610847	+	1.05802i	−0.991098	+	0.133135i	$0.957496\pi$
$68$	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	$-0.576281\pi$
$71$	−4.00000			−0.474713			−0.237356	+	0.971423i	$0.576281\pi$
$72$		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	0.983967	−	0.178352i	$-0.0570765\pi$
$79$	3.00000	+	5.19615i	0.337526	+	0.584613i	−0.646440	+	0.762964i	$0.723743\pi$
$80$	1.00000			0.111803
$81$		0			0
$82$	6.00000			0.662589
$83$	5.00000	+	8.66025i	0.548821	+	0.950586i	0.998356	+	0.0573233i	$0.0182566\pi$
$83$	5.00000	+	8.66025i	0.548821	+	0.950586i	−0.449534	+	0.893263i	$0.648410\pi$
$84$		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	$-0.207472\pi$
$89$	15.0000			1.59000			0.794998	+	0.606612i	$0.207472\pi$
$90$		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	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	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	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	−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	$-0.848311\pi$
$113$	−0.500000	+	0.866025i	−0.0470360	+	0.0814688i	0.841549	+	0.540181i	$0.181644\pi$
$114$		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	0.269863	+	0.962899i	$0.413022\pi$
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	−0.968826	+	0.247741i	$0.920312\pi$
$132$		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	$-0.0109578\pi$
$137$	5.50000	+	9.52628i	0.469897	+	0.813885i	−0.529511	+	0.848303i	$0.677624\pi$
$138$		0			0
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	−0.820495	−	0.571654i	$-0.806302\pi$
$139$	1.00000	−	1.73205i	0.0848189	−	0.146911i	0.905314	+	0.424743i	$0.139635\pi$
$140$	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	−0.0115483	−	0.999933i	$-0.503676\pi$
$149$	10.5000	−	18.1865i	0.860194	−	1.48990i	0.871742	−	0.489966i	$-0.162991\pi$
$150$		0			0
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	0.587646	−	0.809118i	$-0.300055\pi$
$151$	−5.00000	−	8.66025i	−0.406894	−	0.704761i	−0.994540	+	0.104357i	$0.966722\pi$
$152$	2.00000			0.162221
$153$		0			0
$154$	−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	−0.481006	−	0.876717i	$-0.659728\pi$
$157$	6.50000	−	11.2583i	0.518756	−	0.898513i	0.999762	−	0.0217953i	$-0.00693820\pi$
$158$	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	0.0289155	+	0.999582i	$0.490795\pi$
$167$	−11.0000	+	19.0526i	−0.851206	+	1.47433i	−0.880121	+	0.474749i	$0.842539\pi$
$168$		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	$-0.331200\pi$
$173$	−6.50000	−	11.2583i	−0.494186	−	0.855955i	−0.999978	+	0.00670064i	$0.997867\pi$
$174$		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	$-0.734862\pi$
$179$	−18.0000			−1.34538			−0.672692	+	0.739923i	$0.734862\pi$
$180$		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	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	−0.993215	−	0.116289i	$-0.962900\pi$
$193$	−5.50000	+	9.52628i	−0.395899	+	0.685717i	0.597317	+	0.802005i	$0.296234\pi$
$194$	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	$-0.511342\pi$
$197$	−1.00000			−0.0712470			−0.0356235	+	0.999365i	$0.511342\pi$
$198$		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	−0.186966	−	0.982366i	$-0.559865\pi$
$211$	11.0000	−	19.0526i	0.757271	−	1.31163i	0.944237	−	0.329266i	$-0.106801\pi$
$212$	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	−0.978002	−	0.208595i	$-0.933111\pi$
$223$	−10.0000	−	17.3205i	−0.669650	−	1.15987i	0.308353	−	0.951272i	$-0.400222\pi$
$224$	−1.00000			−0.0668153
$225$		0			0
$226$	1.00000			0.0665190
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	0.921903	+	0.387421i	$0.126634\pi$
$227$	12.0000	+	20.7846i	0.796468	+	1.37952i	−0.125435	+	0.992102i	$0.540033\pi$
$228$		0			0
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.231287	−	0.972886i	$-0.425707\pi$
$229$	14.5000	−	25.1147i	0.958187	−	1.65963i	0.726900	−	0.686743i	$-0.240960\pi$
$230$	−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	$-0.713828\pi$
$233$	−19.0000			−1.24473			−0.622366	+	0.782727i	$0.713828\pi$
$234$		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	$-0.771170\pi$
$239$	3.00000	−	5.19615i	0.194054	−	0.336111i	0.946590	+	0.322440i	$0.104503\pi$
$240$		0			0
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	−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	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$		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	$-0.742766\pi$
$257$	4.50000	−	7.79423i	0.280702	−	0.486191i	0.971558	+	0.236802i	$0.0760993\pi$
$258$		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	0.997906	+	0.0646755i	$0.0206012\pi$
$263$	9.00000	+	15.5885i	0.554964	+	0.961225i	−0.442943	+	0.896550i	$0.646065\pi$
$264$		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	$-0.490295\pi$
$269$	1.00000			0.0609711			0.0304855	+	0.999535i	$0.490295\pi$
$270$		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	0.575408	−	0.817867i	$-0.304843\pi$
$277$	−7.00000	−	12.1244i	−0.420589	−	0.728482i	−0.995997	+	0.0893846i	$0.971510\pi$
$278$	−2.00000			−0.119952
$279$		0			0
$280$	−1.00000			−0.0597614
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	−0.867050	−	0.498222i	$-0.833987\pi$
$281$	−14.5000	−	25.1147i	−0.864997	−	1.49822i	0.00205220	−	0.999998i	$-0.499347\pi$
$282$		0			0
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	−0.999608	−	0.0280052i	$-0.991084\pi$
$283$	−8.00000	+	13.8564i	−0.475551	+	0.823678i	0.524057	+	0.851683i	$0.324418\pi$
$284$	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	$-0.688966\pi$
$293$	7.50000	−	12.9904i	0.438155	−	0.758906i	0.997547	+	0.0699967i	$0.0222989\pi$
$294$		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	$-0.703408\pi$
$311$	7.00000	−	12.1244i	0.396934	−	0.687509i	0.993346	+	0.115169i	$0.0367410\pi$
$312$		0			0
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	0.851549	−	0.524276i	$-0.175664\pi$
$313$	−0.500000	−	0.866025i	−0.0282617	−	0.0489506i	−0.879810	+	0.475325i	$0.842331\pi$
$314$	−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	$-0.193516\pi$
$317$	−1.50000	−	2.59808i	−0.0842484	−	0.145922i	−0.905071	+	0.425261i	$0.860182\pi$
$318$		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	−0.998298	−	0.0583130i	$-0.981428\pi$
$331$	−10.0000	−	17.3205i	−0.549650	−	0.952021i	0.448649	−	0.893708i	$-0.351905\pi$
$332$	−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	−0.509676	−	0.860366i	$-0.670235\pi$
$337$	9.00000	−	15.5885i	0.490261	−	0.849157i	0.999937	+	0.0112091i	$0.00356804\pi$
$338$	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	$-0.728946\pi$
$347$	6.00000	−	10.3923i	0.322097	−	0.557888i	0.980921	+	0.194409i	$0.0622790\pi$
$348$		0			0
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	0.700609	−	0.713545i	$-0.252912\pi$
$349$	−5.00000	−	8.66025i	−0.267644	−	0.463573i	−0.968253	+	0.249973i	$0.919578\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	2.00000			0.106600
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	0.920677	+	0.390324i	$0.127637\pi$
$353$	15.0000	+	25.9808i	0.798369	+	1.38282i	−0.122308	+	0.992492i	$0.539030\pi$
$354$		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	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$		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	0.966507	−	0.256639i	$-0.0826151\pi$
$367$	5.00000	+	8.66025i	0.260998	+	0.452062i	−0.705509	+	0.708700i	$0.749282\pi$
$368$	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	−0.965945	−	0.258748i	$-0.916690\pi$
$373$	−5.00000	+	8.66025i	−0.258890	+	0.448411i	0.707055	+	0.707159i	$0.250023\pi$
$374$	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	0.0899119	+	0.995950i	$0.471341\pi$
$383$	−16.0000	+	27.7128i	−0.817562	+	1.41606i	−0.907474	+	0.420109i	$0.861992\pi$
$384$		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	−0.870059	−	0.492947i	$-0.835920\pi$
$389$	−17.0000	−	29.4449i	−0.861934	−	1.49291i	0.00812520	−	0.999967i	$-0.497414\pi$
$390$		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	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		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	−0.766426	−	0.642333i	$-0.777967\pi$
$409$	3.50000	−	6.06218i	0.173064	−	0.299755i	0.939490	+	0.342578i	$0.111300\pi$
$410$	−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	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$	−4.50000	−	7.79423i	−0.219317	−	0.379867i	0.735283	−	0.677761i	$-0.237049\pi$
$421$	−4.50000	−	7.79423i	−0.219317	−	0.379867i	−0.954599	+	0.297893i	$0.903716\pi$
$422$	−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	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$		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	0.972939	−	0.231062i	$-0.0742199\pi$
$439$	6.00000	+	10.3923i	0.286364	+	0.495998i	−0.686575	+	0.727059i	$0.740887\pi$
$440$	2.00000			0.0953463
$441$		0			0
$442$	−3.00000			−0.142695
$443$	11.0000	+	19.0526i	0.522626	+	0.905214i	0.999653	+	0.0263261i	$0.00838082\pi$
$443$	11.0000	+	19.0526i	0.522626	+	0.905214i	−0.477028	+	0.878888i	$0.658286\pi$
$444$		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	$-0.203620\pi$
$449$	34.0000			1.60456			0.802280	+	0.596948i	$0.203620\pi$
$450$		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	0.725059	+	0.688686i	$0.241812\pi$
$457$	20.5000	+	35.5070i	0.958950	+	1.66095i	0.233890	+	0.972263i	$0.424854\pi$
$458$	−29.0000			−1.35508
$459$		0			0
$460$	2.00000			0.0932505
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	−0.999898	−	0.0142861i	$-0.995452\pi$
$461$	−11.0000	−	19.0526i	−0.512321	−	0.887366i	0.487577	−	0.873080i	$-0.337881\pi$
$462$		0			0
$463$	−17.0000	+	29.4449i	−0.790057	+	1.36842i	0.135874	+	0.990726i	$0.456616\pi$
$463$	−17.0000	+	29.4449i	−0.790057	+	1.36842i	−0.925931	+	0.377693i	$0.876718\pi$
$464$	−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	$-0.211805\pi$
$467$	34.0000			1.57333			0.786666	+	0.617379i	$0.211805\pi$
$468$		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	0.999995	+	0.00300810i	$0.000957509\pi$
$479$	11.0000	+	19.0526i	0.502603	+	0.870534i	−0.497393	+	0.867526i	$0.665709\pi$
$480$		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	0.0989017	+	0.995097i	$0.468467\pi$
$491$	−18.0000	+	31.1769i	−0.812329	+	1.40699i	−0.911230	+	0.411897i	$0.864866\pi$
$492$		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	−0.999962	−	0.00872186i	$-0.997224\pi$
$499$	−11.0000	+	19.0526i	−0.492428	+	0.852910i	0.507534	+	0.861632i	$0.330557\pi$
$500$	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	$-0.542706\pi$
$503$	−6.00000			−0.267527			−0.133763	+	0.991013i	$0.542706\pi$
$504$		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	$-0.702719\pi$
$509$	9.00000	−	15.5885i	0.398918	−	0.690946i	0.993593	+	0.113020i	$0.0360525\pi$
$510$		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	$-0.128167\pi$
$521$	42.0000			1.84005			0.920027	+	0.391856i	$0.128167\pi$
$522$		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	0.923007	−	0.384784i	$-0.125724\pi$
$547$	3.00000	+	5.19615i	0.128271	+	0.222171i	−0.794736	+	0.606955i	$0.792391\pi$
$548$	−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	$-0.617277\pi$
$557$	−17.0000			−0.720313			−0.360157	+	0.932892i	$0.617277\pi$
$558$		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	$-0.887251\pi$
$563$	−4.00000	+	6.92820i	−0.168580	+	0.291989i	0.769341	+	0.638838i	$0.220585\pi$
$564$		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	0.996961	+	0.0779066i	$0.0248236\pi$
$569$	13.5000	+	23.3827i	0.565949	+	0.980253i	−0.431011	+	0.902347i	$0.641843\pi$
$570$		0			0
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	−0.990571	−	0.137002i	$-0.956253\pi$
$571$	−9.00000	+	15.5885i	−0.376638	+	0.652357i	0.613933	+	0.789359i	$0.289587\pi$
$572$	−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	$-0.179808\pi$
$587$	−1.00000	−	1.73205i	−0.0412744	−	0.0714894i	−0.885925	+	0.463829i	$0.846475\pi$
$588$		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	$-0.204424\pi$
$593$	39.0000			1.60154			0.800769	+	0.598973i	$0.204424\pi$
$594$		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	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$		0			0
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	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	−0.798698	−	0.601732i	$-0.794478\pi$
$607$	3.00000	−	5.19615i	0.121766	−	0.210905i	0.920464	+	0.390827i	$0.127811\pi$
$608$	−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	$-0.788332\pi$
$617$	3.50000	−	6.06218i	0.140905	−	0.244054i	0.927838	+	0.372985i	$0.121666\pi$
$618$		0			0
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	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	$-0.275650\pi$
$641$	−8.50000	−	14.7224i	−0.335730	−	0.581501i	−0.983625	+	0.180229i	$0.942316\pi$
$642$		0			0
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	0.487222	+	0.873278i	$0.338010\pi$
$643$	−13.0000	+	22.5167i	−0.512670	+	0.887970i	−0.999892	+	0.0146923i	$0.995323\pi$
$644$	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	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$		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	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$		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	−0.988872	−	0.148766i	$-0.952470\pi$
$659$	−16.0000	−	27.7128i	−0.623272	−	1.07954i	0.365601	−	0.930772i	$-0.380864\pi$
$660$		0			0
$661$	−3.50000	+	6.06218i	−0.136134	+	0.235791i	−0.926030	−	0.377450i	$-0.876801\pi$
$661$	−3.50000	+	6.06218i	−0.136134	+	0.235791i	0.789896	+	0.613241i	$0.210135\pi$
$662$	−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	0.554639	−	0.832091i	$-0.312856\pi$
$673$	−11.5000	−	19.9186i	−0.443292	−	0.767805i	−0.997932	+	0.0642860i	$0.979523\pi$
$674$	−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	$-0.129884\pi$
$677$	3.00000	+	5.19615i	0.115299	+	0.199704i	−0.802600	+	0.596518i	$0.796551\pi$
$678$		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	$-0.573736\pi$
$683$	−12.0000			−0.459167			−0.229584	+	0.973289i	$0.573736\pi$
$684$		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	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	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	$-0.530101\pi$
$701$	−5.00000			−0.188847			−0.0944237	+	0.995532i	$0.530101\pi$
$702$		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	0.815255	−	0.579102i	$-0.196597\pi$
$709$	−2.50000	−	4.33013i	−0.0938895	−	0.162621i	−0.909145	+	0.416481i	$0.863263\pi$
$710$	−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	$-0.647694\pi$
$719$	−24.0000			−0.895049			−0.447524	+	0.894272i	$0.647694\pi$
$720$		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	0.930618	−	0.365991i	$-0.119270\pi$
$727$	4.00000	+	6.92820i	0.148352	+	0.256953i	−0.782267	+	0.622944i	$0.785937\pi$
$728$	−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	0.158774	+	0.987315i	$0.449246\pi$
$733$	−21.0000	+	36.3731i	−0.775653	+	1.34347i	−0.934427	+	0.356155i	$0.884088\pi$
$734$	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	$-0.978439\pi$
$743$	−12.0000	+	20.7846i	−0.440237	+	0.762513i	0.557470	+	0.830197i	$0.311772\pi$
$744$		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	−0.954485	−	0.298259i	$-0.903594\pi$
$751$	−6.00000	+	10.3923i	−0.218943	+	0.379221i	0.735542	+	0.677479i	$0.236928\pi$
$752$	−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	$-0.897224\pi$
$761$	−5.50000	+	9.52628i	−0.199375	+	0.345327i	0.748951	+	0.662625i	$0.230558\pi$
$762$		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	−0.580696	−	0.814120i	$-0.697220\pi$
$769$	11.5000	−	19.9186i	0.414701	−	0.718283i	0.995397	+	0.0958377i	$0.0305530\pi$
$770$	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	$-0.716712\pi$
$773$	−35.0000			−1.25886			−0.629431	+	0.777056i	$0.716712\pi$
$774$		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	−0.568919	−	0.822393i	$-0.692638\pi$
$787$	12.0000	−	20.7846i	0.427754	−	0.740891i	0.996673	+	0.0815020i	$0.0259717\pi$
$788$	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	$-0.816413\pi$
$797$	1.50000	−	2.59808i	0.0531327	−	0.0920286i	0.891368	+	0.453279i	$0.149746\pi$
$798$		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	$-0.494404\pi$
$809$	1.00000			0.0351581			0.0175791	+	0.999845i	$0.494404\pi$
$810$		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	$-0.228148\pi$
$821$	−5.50000	−	9.52628i	−0.191951	−	0.332469i	−0.945897	+	0.324468i	$0.894815\pi$
$822$		0			0
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$	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	$-0.814279\pi$
$827$	−48.0000			−1.66912			−0.834562	+	0.550914i	$0.814279\pi$
$828$		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	−0.998102	−	0.0615805i	$-0.980386\pi$
$839$	−16.0000	−	27.7128i	−0.552381	−	0.956753i	0.445721	−	0.895172i	$-0.352947\pi$
$840$		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	0.938839	−	0.344358i	$-0.111903\pi$
$853$	5.00000	+	8.66025i	0.171197	+	0.296521i	−0.767642	+	0.640879i	$0.778570\pi$
$854$	9.00000			0.307974
$855$		0			0
$856$		0			0
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	0.839268	−	0.543718i	$-0.182984\pi$
$857$	−1.50000	−	2.59808i	−0.0512390	−	0.0887486i	−0.890507	+	0.454969i	$0.849650\pi$
$858$		0			0
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.0438309	−	0.999039i	$-0.486044\pi$
$859$	26.0000	−	45.0333i	0.887109	−	1.53652i	0.843278	−	0.537478i	$-0.180623\pi$
$860$	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	$-0.576585\pi$
$863$	−14.0000			−0.476566			−0.238283	+	0.971196i	$0.576585\pi$
$864$		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	−0.603897	−	0.797062i	$-0.706386\pi$
$877$	11.5000	−	19.9186i	0.388327	−	0.672603i	0.992225	+	0.124459i	$0.0397196\pi$
$878$	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	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		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	0.261540	+	0.965193i	$0.415770\pi$
$887$	−21.0000	+	36.3731i	−0.705111	+	1.22129i	−0.966651	+	0.256096i	$0.917564\pi$
$888$		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	0.948278	−	0.317441i	$-0.102824\pi$
$907$	6.00000	+	10.3923i	0.199227	+	0.345071i	−0.749051	+	0.662512i	$0.769490\pi$
$908$	−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	$-0.230367\pi$
$911$	−6.00000	−	10.3923i	−0.198789	−	0.344312i	−0.948136	+	0.317865i	$0.897034\pi$
$912$		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	0.998827	+	0.0484211i	$0.0154190\pi$
$929$	16.5000	+	28.5788i	0.541347	+	0.937641i	−0.457480	+	0.889220i	$0.651248\pi$
$930$		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	$-0.966929\pi$
$941$	−12.5000	+	21.6506i	−0.407488	+	0.705791i	0.587119	+	0.809500i	$0.300262\pi$
$942$		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	$-0.187369\pi$
$947$	−2.00000	−	3.46410i	−0.0649913	−	0.112568i	−0.896690	+	0.442659i	$0.854035\pi$
$948$		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	$-0.599571\pi$
$953$	−19.0000			−0.615470			−0.307735	+	0.951472i	$0.599571\pi$
$954$		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	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$	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	$-0.735392\pi$
$971$	−42.0000			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$972$		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	$-0.926302\pi$
$977$	−9.00000	+	15.5885i	−0.287936	+	0.498719i	0.685381	+	0.728184i	$0.259636\pi$
$978$		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	0.730073	+	0.683369i	$0.239486\pi$
$983$	30.0000	+	51.9615i	0.956851	+	1.65732i	0.226778	+	0.973946i	$0.427181\pi$
$984$		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	0.624440	−	0.781073i	$-0.285327\pi$
$997$	−11.5000	−	19.9186i	−0.364209	−	0.630828i	−0.988649	+	0.150245i	$0.951994\pi$
$998$	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.d.757.1		2
3.2	odd	2		1134.2.f.m.757.1		2
9.2	odd	6		1134.2.f.m.379.1		2
9.4	even	3		1134.2.a.g.1.1	yes	1
9.5	odd	6		1134.2.a.b.1.1	✓	1
9.7	even	3	inner	1134.2.f.d.379.1		2
36.23	even	6		9072.2.a.k.1.1		1
36.31	odd	6		9072.2.a.p.1.1		1
63.13	odd	6		7938.2.a.w.1.1		1
63.41	even	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	9.5	odd	6
1134.2.a.g.1.1	yes	1	9.4	even	3
1134.2.f.d.379.1		2	9.7	even	3	inner
1134.2.f.d.757.1		2	1.1	even	1	trivial
1134.2.f.m.379.1		2	9.2	odd	6
1134.2.f.m.757.1		2	3.2	odd	2
7938.2.a.j.1.1		1	63.41	even	6
7938.2.a.w.1.1		1	63.13	odd	6
9072.2.a.k.1.1		1	36.23	even	6
9072.2.a.p.1.1		1	36.31	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

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