LMFDB - Embedded newform 1134.2.f.s.379.2

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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			379.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	1134.379
Dual form			1134.2.f.s.757.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.133975 - 0.232051i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.133975 - 0.232051i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -0.267949 q^{10} +(-3.09808 + 5.36603i) q^{11} +(3.23205 + 5.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +0.732051 q^{19} +(-0.133975 + 0.232051i) q^{20} +(3.09808 + 5.36603i) q^{22} +(2.09808 + 3.63397i) q^{23} +(2.46410 - 4.26795i) q^{25} +6.46410 q^{26} -1.00000 q^{28} +(-0.767949 + 1.33013i) q^{29} +(-4.09808 - 7.09808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.50000 - 6.06218i) q^{34} -0.267949 q^{35} +10.6603 q^{37} +(0.366025 - 0.633975i) q^{38} +(0.133975 + 0.232051i) q^{40} +(-1.26795 - 2.19615i) q^{41} +(0.732051 - 1.26795i) q^{43} +6.19615 q^{44} +4.19615 q^{46} +(-2.36603 + 4.09808i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.46410 - 4.26795i) q^{50} +(3.23205 - 5.59808i) q^{52} -9.46410 q^{53} +1.66025 q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.767949 + 1.33013i) q^{58} +(-2.09808 - 3.63397i) q^{59} +(-1.96410 + 3.40192i) q^{61} -8.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(3.36603 + 5.83013i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(-0.133975 + 0.232051i) q^{70} +6.53590 q^{71} +8.26795 q^{73} +(5.33013 - 9.23205i) q^{74} +(-0.366025 - 0.633975i) q^{76} +(3.09808 + 5.36603i) q^{77} +(4.56218 - 7.90192i) q^{79} +0.267949 q^{80} -2.53590 q^{82} +(-8.29423 + 14.3660i) q^{83} +(-0.937822 - 1.62436i) q^{85} +(-0.732051 - 1.26795i) q^{86} +(3.09808 - 5.36603i) q^{88} +9.92820 q^{89} +6.46410 q^{91} +(2.09808 - 3.63397i) q^{92} +(2.36603 + 4.09808i) q^{94} +(-0.0980762 - 0.169873i) q^{95} +(-5.46410 + 9.46410i) q^{97} -1.00000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8	$ 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8} - 8 q^{10} - 2 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 28 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} - 2 q^{23} - 4 q^{25} + 12 q^{26} - 4 q^{28} - 10 q^{29} - 6 q^{31} + 2 q^{32} + 14 q^{34} - 8 q^{35} + 8 q^{37} - 2 q^{38} + 4 q^{40} - 12 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 6 q^{47} - 2 q^{49} + 4 q^{50} + 6 q^{52} - 24 q^{53} - 28 q^{55} - 2 q^{56} + 10 q^{58} + 2 q^{59} + 6 q^{61} - 12 q^{62} + 4 q^{64} + 10 q^{67} - 14 q^{68} - 4 q^{70} + 40 q^{71} + 40 q^{73} + 4 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 24 q^{82} - 2 q^{83} - 28 q^{85} + 4 q^{86} + 2 q^{88} + 12 q^{89} + 12 q^{91} - 2 q^{92} + 6 q^{94} + 10 q^{95} - 8 q^{97} - 4 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8 - 8 * q^10 - 2 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 28 * q^17 - 4 * q^19 - 4 * q^20 + 2 * q^22 - 2 * q^23 - 4 * q^25 + 12 * q^26 - 4 * q^28 - 10 * q^29 - 6 * q^31 + 2 * q^32 + 14 * q^34 - 8 * q^35 + 8 * q^37 - 2 * q^38 + 4 * q^40 - 12 * q^41 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 6 * q^47 - 2 * q^49 + 4 * q^50 + 6 * q^52 - 24 * q^53 - 28 * q^55 - 2 * q^56 + 10 * q^58 + 2 * q^59 + 6 * q^61 - 12 * q^62 + 4 * q^64 + 10 * q^67 - 14 * q^68 - 4 * q^70 + 40 * q^71 + 40 * q^73 + 4 * q^74 + 2 * q^76 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 24 * q^82 - 2 * q^83 - 28 * q^85 + 4 * q^86 + 2 * q^88 + 12 * q^89 + 12 * q^91 - 2 * q^92 + 6 * q^94 + 10 * q^95 - 8 * q^97 - 4 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.133975	−	0.232051i	−0.0599153	−	0.103776i	0.834512	−	0.550990i	$-0.185750\pi$
$5$	−0.133975	−	0.232051i	−0.0599153	−	0.103776i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		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
$10$	−0.267949			−0.0847330
$11$	−3.09808	+	5.36603i	−0.934105	+	1.61792i	−0.157883	+	0.987458i	$0.550467\pi$
$11$	−3.09808	+	5.36603i	−0.934105	+	1.61792i	−0.776222	+	0.630460i	$0.782866\pi$
$12$		0			0
$13$	3.23205	+	5.59808i	0.896410	+	1.55263i	0.832050	+	0.554700i	$0.187167\pi$
$13$	3.23205	+	5.59808i	0.896410	+	1.55263i	0.0643593	+	0.997927i	$0.479500\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	7.00000			1.69775			0.848875	−	0.528594i	$-0.177281\pi$
$17$	7.00000			1.69775			0.848875	+	0.528594i	$0.177281\pi$
$18$		0			0
$19$	0.732051			0.167944			0.0839720	−	0.996468i	$-0.473239\pi$
$19$	0.732051			0.167944			0.0839720	+	0.996468i	$0.473239\pi$
$20$	−0.133975	+	0.232051i	−0.0299576	+	0.0518881i
$21$		0			0
$22$	3.09808	+	5.36603i	0.660512	+	1.14404i
$23$	2.09808	+	3.63397i	0.437479	+	0.757736i	0.997494	−	0.0707462i	$-0.0225381\pi$
$23$	2.09808	+	3.63397i	0.437479	+	0.757736i	−0.560015	+	0.828482i	$0.689205\pi$
$24$		0			0
$25$	2.46410	−	4.26795i	0.492820	−	0.853590i
$26$	6.46410			1.26771
$27$		0			0
$28$	−1.00000			−0.188982
$29$	−0.767949	+	1.33013i	−0.142605	+	0.246998i	−0.928477	−	0.371391i	$-0.878881\pi$
$29$	−0.767949	+	1.33013i	−0.142605	+	0.246998i	0.785872	+	0.618389i	$0.212214\pi$
$30$		0			0
$31$	−4.09808	−	7.09808i	−0.736036	−	1.27485i	−0.954267	−	0.298955i	$-0.903362\pi$
$31$	−4.09808	−	7.09808i	−0.736036	−	1.27485i	0.218231	−	0.975897i	$-0.429971\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$		0			0
$34$	3.50000	−	6.06218i	0.600245	−	1.03965i
$35$	−0.267949			−0.0452917
$36$		0			0
$37$	10.6603			1.75253			0.876267	−	0.481825i	$-0.160026\pi$
$37$	10.6603			1.75253			0.876267	+	0.481825i	$0.160026\pi$
$38$	0.366025	−	0.633975i	0.0593772	−	0.102844i
$39$		0			0
$40$	0.133975	+	0.232051i	0.0211832	+	0.0366905i
$41$	−1.26795	−	2.19615i	−0.198020	−	0.342981i	0.749866	−	0.661590i	$-0.230118\pi$
$41$	−1.26795	−	2.19615i	−0.198020	−	0.342981i	−0.947886	+	0.318608i	$0.896785\pi$
$42$		0			0
$43$	0.732051	−	1.26795i	0.111637	−	0.193360i	−0.804794	−	0.593555i	$-0.797724\pi$
$43$	0.732051	−	1.26795i	0.111637	−	0.193360i	0.916430	+	0.400194i	$0.131057\pi$
$44$	6.19615			0.934105
$45$		0			0
$46$	4.19615			0.618689
$47$	−2.36603	+	4.09808i	−0.345120	+	0.597766i	−0.985376	−	0.170396i	$-0.945495\pi$
$47$	−2.36603	+	4.09808i	−0.345120	+	0.597766i	0.640255	+	0.768162i	$0.278829\pi$
$48$		0			0
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−2.46410	−	4.26795i	−0.348477	−	0.603579i
$51$		0			0
$52$	3.23205	−	5.59808i	0.448205	−	0.776313i
$53$	−9.46410			−1.29999			−0.649997	−	0.759937i	$-0.725230\pi$
$53$	−9.46410			−1.29999			−0.649997	+	0.759937i	$0.725230\pi$
$54$		0			0
$55$	1.66025			0.223869
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$		0			0
$58$	0.767949	+	1.33013i	0.100837	+	0.174654i
$59$	−2.09808	−	3.63397i	−0.273146	−	0.473103i	0.696520	−	0.717538i	$-0.254731\pi$
$59$	−2.09808	−	3.63397i	−0.273146	−	0.473103i	−0.969666	+	0.244435i	$0.921398\pi$
$60$		0			0
$61$	−1.96410	+	3.40192i	−0.251477	+	0.435572i	−0.963933	−	0.266146i	$-0.914250\pi$
$61$	−1.96410	+	3.40192i	−0.251477	+	0.435572i	0.712455	+	0.701717i	$0.247583\pi$
$62$	−8.19615			−1.04091
$63$		0			0
$64$	1.00000			0.125000
$65$	0.866025	−	1.50000i	0.107417	−	0.186052i
$66$		0			0
$67$	3.36603	+	5.83013i	0.411225	+	0.712263i	0.995024	−	0.0996351i	$-0.0317676\pi$
$67$	3.36603	+	5.83013i	0.411225	+	0.712263i	−0.583799	+	0.811899i	$0.698434\pi$
$68$	−3.50000	−	6.06218i	−0.424437	−	0.735147i
$69$		0			0
$70$	−0.133975	+	0.232051i	−0.0160130	+	0.0277354i
$71$	6.53590			0.775668			0.387834	−	0.921729i	$-0.373223\pi$
$71$	6.53590			0.775668			0.387834	+	0.921729i	$0.373223\pi$
$72$		0			0
$73$	8.26795			0.967690			0.483845	−	0.875154i	$-0.339240\pi$
$73$	8.26795			0.967690			0.483845	+	0.875154i	$0.339240\pi$
$74$	5.33013	−	9.23205i	0.619615	−	1.07320i
$75$		0			0
$76$	−0.366025	−	0.633975i	−0.0419860	−	0.0727219i
$77$	3.09808	+	5.36603i	0.353059	+	0.611515i
$78$		0			0
$79$	4.56218	−	7.90192i	0.513285	−	0.889036i	−0.486596	−	0.873627i	$-0.661762\pi$
$79$	4.56218	−	7.90192i	0.513285	−	0.889036i	0.999881	−	0.0154089i	$-0.00490499\pi$
$80$	0.267949			0.0299576
$81$		0			0
$82$	−2.53590			−0.280043
$83$	−8.29423	+	14.3660i	−0.910410	+	1.57688i	−0.0969238	+	0.995292i	$0.530900\pi$
$83$	−8.29423	+	14.3660i	−0.910410	+	1.57688i	−0.813486	+	0.581584i	$0.802433\pi$
$84$		0			0
$85$	−0.937822	−	1.62436i	−0.101721	−	0.176186i
$86$	−0.732051	−	1.26795i	−0.0789391	−	0.136726i
$87$		0			0
$88$	3.09808	−	5.36603i	0.330256	−	0.572020i
$89$	9.92820			1.05239			0.526194	−	0.850365i	$-0.323619\pi$
$89$	9.92820			1.05239			0.526194	+	0.850365i	$0.323619\pi$
$90$		0			0
$91$	6.46410			0.677622
$92$	2.09808	−	3.63397i	0.218740	−	0.378868i
$93$		0			0
$94$	2.36603	+	4.09808i	0.244037	+	0.422684i
$95$	−0.0980762	−	0.169873i	−0.0100624	−	0.0174286i
$96$		0			0
$97$	−5.46410	+	9.46410i	−0.554795	+	0.960934i	0.443124	+	0.896460i	$0.353870\pi$
$97$	−5.46410	+	9.46410i	−0.554795	+	0.960934i	−0.997919	+	0.0644736i	$0.979463\pi$
$98$	−1.00000			−0.101015
$99$		0			0
$100$	−4.92820			−0.492820
$101$	−4.46410	+	7.73205i	−0.444195	+	0.769368i	−0.997996	−	0.0632812i	$-0.979843\pi$
$101$	−4.46410	+	7.73205i	−0.444195	+	0.769368i	0.553801	+	0.832649i	$0.313177\pi$
$102$		0			0
$103$	4.19615	+	7.26795i	0.413459	+	0.716132i	0.995265	−	0.0971952i	$-0.0309871\pi$
$103$	4.19615	+	7.26795i	0.413459	+	0.716132i	−0.581806	+	0.813327i	$0.697654\pi$
$104$	−3.23205	−	5.59808i	−0.316929	−	0.548937i
$105$		0			0
$106$	−4.73205	+	8.19615i	−0.459617	+	0.796081i
$107$		0			0			−	1.00000i	$-0.5\pi$
$107$		0			0				1.00000i	$0.5\pi$
$108$		0			0
$109$	3.19615			0.306136			0.153068	−	0.988216i	$-0.451085\pi$
$109$	3.19615			0.306136			0.153068	+	0.988216i	$0.451085\pi$
$110$	0.830127	−	1.43782i	0.0791495	−	0.137091i
$111$		0			0
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	2.86603	+	4.96410i	0.269613	+	0.466983i	0.968762	−	0.247993i	$-0.0797709\pi$
$113$	2.86603	+	4.96410i	0.269613	+	0.466983i	−0.699149	+	0.714976i	$0.746438\pi$
$114$		0			0
$115$	0.562178	−	0.973721i	0.0524234	−	0.0907999i
$116$	1.53590			0.142605
$117$		0			0
$118$	−4.19615			−0.386287
$119$	3.50000	−	6.06218i	0.320844	−	0.555719i
$120$		0			0
$121$	−13.6962	−	23.7224i	−1.24510	−	2.15658i
$122$	1.96410	+	3.40192i	0.177821	+	0.307996i
$123$		0			0
$124$	−4.09808	+	7.09808i	−0.368018	+	0.637426i
$125$	−2.66025			−0.237940
$126$		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
$130$	−0.866025	−	1.50000i	−0.0759555	−	0.131559i
$131$	−5.26795	−	9.12436i	−0.460263	−	0.797199i	0.538711	−	0.842491i	$-0.318912\pi$
$131$	−5.26795	−	9.12436i	−0.460263	−	0.797199i	−0.998974	+	0.0452920i	$0.985578\pi$
$132$		0			0
$133$	0.366025	−	0.633975i	0.0317384	−	0.0549726i
$134$	6.73205			0.581561
$135$		0			0
$136$	−7.00000			−0.600245
$137$	4.13397	−	7.16025i	0.353189	−	0.611742i	−0.633617	−	0.773647i	$-0.718430\pi$
$137$	4.13397	−	7.16025i	0.353189	−	0.611742i	0.986806	+	0.161905i	$0.0517638\pi$
$138$		0			0
$139$	1.63397	+	2.83013i	0.138592	+	0.240048i	0.926964	−	0.375151i	$-0.122409\pi$
$139$	1.63397	+	2.83013i	0.138592	+	0.240048i	−0.788372	+	0.615199i	$0.789076\pi$
$140$	0.133975	+	0.232051i	0.0113229	+	0.0196119i
$141$		0			0
$142$	3.26795	−	5.66025i	0.274240	−	0.474998i
$143$	−40.0526			−3.34936
$144$		0			0
$145$	0.411543			0.0341768
$146$	4.13397	−	7.16025i	0.342130	−	0.592587i
$147$		0			0
$148$	−5.33013	−	9.23205i	−0.438134	−	0.758870i
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	0.620701	−	0.784047i	$-0.286848\pi$
$149$	−4.50000	−	7.79423i	−0.368654	−	0.638528i	−0.989355	+	0.145519i	$0.953515\pi$
$150$		0			0
$151$	2.90192	−	5.02628i	0.236155	−	0.409033i	−0.723453	−	0.690374i	$-0.757446\pi$
$151$	2.90192	−	5.02628i	0.236155	−	0.409033i	0.959608	+	0.281341i	$0.0907793\pi$
$152$	−0.732051			−0.0593772
$153$		0			0
$154$	6.19615			0.499300
$155$	−1.09808	+	1.90192i	−0.0881996	+	0.152766i
$156$		0			0
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	0.885288	−	0.465044i	$-0.153961\pi$
$157$	0.500000	+	0.866025i	0.0399043	+	0.0691164i	−0.845383	+	0.534160i	$0.820628\pi$
$158$	−4.56218	−	7.90192i	−0.362947	−	0.628643i
$159$		0			0
$160$	0.133975	−	0.232051i	0.0105916	−	0.0183452i
$161$	4.19615			0.330703
$162$		0			0
$163$	−13.4641			−1.05459			−0.527295	−	0.849682i	$-0.676794\pi$
$163$	−13.4641			−1.05459			−0.527295	+	0.849682i	$0.676794\pi$
$164$	−1.26795	+	2.19615i	−0.0990102	+	0.171491i
$165$		0			0
$166$	8.29423	+	14.3660i	0.643757	+	1.11502i
$167$	0.901924	+	1.56218i	0.0697930	+	0.120885i	0.898810	−	0.438338i	$-0.144433\pi$
$167$	0.901924	+	1.56218i	0.0697930	+	0.120885i	−0.829017	+	0.559223i	$0.811099\pi$
$168$		0			0
$169$	−14.3923	+	24.9282i	−1.10710	+	1.91755i
$170$	−1.87564			−0.143855
$171$		0			0
$172$	−1.46410			−0.111637
$173$	−3.13397	+	5.42820i	−0.238272	+	0.412699i	−0.960218	−	0.279250i	$-0.909914\pi$
$173$	−3.13397	+	5.42820i	−0.238272	+	0.412699i	0.721947	+	0.691949i	$0.243248\pi$
$174$		0			0
$175$	−2.46410	−	4.26795i	−0.186269	−	0.322627i
$176$	−3.09808	−	5.36603i	−0.233526	−	0.404479i
$177$		0			0
$178$	4.96410	−	8.59808i	0.372075	−	0.644453i
$179$	−2.19615			−0.164148			−0.0820741	−	0.996626i	$-0.526154\pi$
$179$	−2.19615			−0.164148			−0.0820741	+	0.996626i	$0.526154\pi$
$180$		0			0
$181$	−16.3923			−1.21843			−0.609215	−	0.793005i	$-0.708515\pi$
$181$	−16.3923			−1.21843			−0.609215	+	0.793005i	$0.708515\pi$
$182$	3.23205	−	5.59808i	0.239576	−	0.414957i
$183$		0			0
$184$	−2.09808	−	3.63397i	−0.154672	−	0.267900i
$185$	−1.42820	−	2.47372i	−0.105004	−	0.181872i
$186$		0			0
$187$	−21.6865	+	37.5622i	−1.58588	+	2.74682i
$188$	4.73205			0.345120
$189$		0			0
$190$	−0.196152			−0.0142304
$191$	2.83013	−	4.90192i	0.204781	−	0.354691i	−0.745282	−	0.666749i	$-0.767685\pi$
$191$	2.83013	−	4.90192i	0.204781	−	0.354691i	0.950063	+	0.312059i	$0.101019\pi$
$192$		0			0
$193$	−9.42820	−	16.3301i	−0.678657	−	1.17547i	−0.975386	−	0.220506i	$-0.929229\pi$
$193$	−9.42820	−	16.3301i	−0.678657	−	1.17547i	0.296729	−	0.954962i	$-0.404104\pi$
$194$	5.46410	+	9.46410i	0.392300	+	0.679483i
$195$		0			0
$196$	−0.500000	+	0.866025i	−0.0357143	+	0.0618590i
$197$	15.7846			1.12461			0.562303	−	0.826931i	$-0.309915\pi$
$197$	15.7846			1.12461			0.562303	+	0.826931i	$0.309915\pi$
$198$		0			0
$199$	−19.1244			−1.35569			−0.677845	−	0.735205i	$-0.737086\pi$
$199$	−19.1244			−1.35569			−0.677845	+	0.735205i	$0.737086\pi$
$200$	−2.46410	+	4.26795i	−0.174238	+	0.301790i
$201$		0			0
$202$	4.46410	+	7.73205i	0.314093	+	0.544025i
$203$	0.767949	+	1.33013i	0.0538995	+	0.0933566i
$204$		0			0
$205$	−0.339746	+	0.588457i	−0.0237289	+	0.0410996i
$206$	8.39230			0.584720
$207$		0			0
$208$	−6.46410			−0.448205
$209$	−2.26795	+	3.92820i	−0.156877	+	0.271719i
$210$		0			0
$211$	8.63397	+	14.9545i	0.594387	+	1.02951i	0.993633	+	0.112665i	$0.0359387\pi$
$211$	8.63397	+	14.9545i	0.594387	+	1.02951i	−0.399246	+	0.916844i	$0.630728\pi$
$212$	4.73205	+	8.19615i	0.324999	+	0.562914i
$213$		0			0
$214$		0			0
$215$	−0.392305			−0.0267550
$216$		0			0
$217$	−8.19615			−0.556391
$218$	1.59808	−	2.76795i	0.108235	−	0.187469i
$219$		0			0
$220$	−0.830127	−	1.43782i	−0.0559672	−	0.0969380i
$221$	22.6244	+	39.1865i	1.52188	+	2.63597i
$222$		0			0
$223$	12.7321	−	22.0526i	0.852601	−	1.47675i	−0.0262515	−	0.999655i	$-0.508357\pi$
$223$	12.7321	−	22.0526i	0.852601	−	1.47675i	0.878853	−	0.477093i	$-0.158310\pi$
$224$	1.00000			0.0668153
$225$		0			0
$226$	5.73205			0.381290
$227$	9.46410	−	16.3923i	0.628154	−	1.08800i	−0.359767	−	0.933042i	$-0.617144\pi$
$227$	9.46410	−	16.3923i	0.628154	−	1.08800i	0.987922	−	0.154953i	$-0.0495227\pi$
$228$		0			0
$229$	1.23205	+	2.13397i	0.0814162	+	0.141017i	0.903858	−	0.427832i	$-0.140722\pi$
$229$	1.23205	+	2.13397i	0.0814162	+	0.141017i	−0.822442	+	0.568849i	$0.807389\pi$
$230$	−0.562178	−	0.973721i	−0.0370689	−	0.0642052i
$231$		0			0
$232$	0.767949	−	1.33013i	0.0504183	−	0.0873271i
$233$	−2.80385			−0.183686			−0.0918431	−	0.995773i	$-0.529276\pi$
$233$	−2.80385			−0.183686			−0.0918431	+	0.995773i	$0.529276\pi$
$234$		0			0
$235$	1.26795			0.0827119
$236$	−2.09808	+	3.63397i	−0.136573	+	0.236552i
$237$		0			0
$238$	−3.50000	−	6.06218i	−0.226871	−	0.392953i
$239$	5.02628	+	8.70577i	0.325123	+	0.563130i	0.981537	−	0.191271i	$-0.0612610\pi$
$239$	5.02628	+	8.70577i	0.325123	+	0.563130i	−0.656414	+	0.754401i	$0.727928\pi$
$240$		0			0
$241$	7.13397	−	12.3564i	0.459540	−	0.795946i	−0.539397	−	0.842052i	$-0.681348\pi$
$241$	7.13397	−	12.3564i	0.459540	−	0.795946i	0.998937	+	0.0461056i	$0.0146811\pi$
$242$	−27.3923			−1.76084
$243$		0			0
$244$	3.92820			0.251477
$245$	−0.133975	+	0.232051i	−0.00855932	+	0.0148252i
$246$		0			0
$247$	2.36603	+	4.09808i	0.150547	+	0.260754i
$248$	4.09808	+	7.09808i	0.260228	+	0.450728i
$249$		0			0
$250$	−1.33013	+	2.30385i	−0.0841246	+	0.145708i
$251$	−22.0526			−1.39195			−0.695973	−	0.718068i	$-0.745027\pi$
$251$	−22.0526			−1.39195			−0.695973	+	0.718068i	$0.745027\pi$
$252$		0			0
$253$	−26.0000			−1.63461
$254$	6.00000	−	10.3923i	0.376473	−	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.23205	−	5.59808i	−0.201610	−	0.349198i	0.747437	−	0.664332i	$-0.231284\pi$
$257$	−3.23205	−	5.59808i	−0.201610	−	0.349198i	−0.949047	+	0.315134i	$0.897951\pi$
$258$		0			0
$259$	5.33013	−	9.23205i	0.331198	−	0.573652i
$260$	−1.73205			−0.107417
$261$		0			0
$262$	−10.5359			−0.650910
$263$	3.16987	−	5.49038i	0.195463	−	0.338551i	−0.751589	−	0.659631i	$-0.770712\pi$
$263$	3.16987	−	5.49038i	0.195463	−	0.338551i	0.947052	+	0.321080i	$0.104046\pi$
$264$		0			0
$265$	1.26795	+	2.19615i	0.0778895	+	0.134909i
$266$	−0.366025	−	0.633975i	−0.0224425	−	0.0388715i
$267$		0			0
$268$	3.36603	−	5.83013i	0.205613	−	0.356132i
$269$	5.58846			0.340734			0.170367	−	0.985381i	$-0.445505\pi$
$269$	5.58846			0.340734			0.170367	+	0.985381i	$0.445505\pi$
$270$		0			0
$271$	−19.5167			−1.18555			−0.592776	−	0.805367i	$-0.701968\pi$
$271$	−19.5167			−1.18555			−0.592776	+	0.805367i	$0.701968\pi$
$272$	−3.50000	+	6.06218i	−0.212219	+	0.367574i
$273$		0			0
$274$	−4.13397	−	7.16025i	−0.249743	−	0.432567i
$275$	15.2679	+	26.4449i	0.920692	+	1.59469i
$276$		0			0
$277$	9.39230	−	16.2679i	0.564329	−	0.977446i	−0.432783	−	0.901498i	$-0.642468\pi$
$277$	9.39230	−	16.2679i	0.564329	−	0.977446i	0.997112	−	0.0759481i	$-0.0241983\pi$
$278$	3.26795			0.195999
$279$		0			0
$280$	0.267949			0.0160130
$281$	6.59808	−	11.4282i	0.393608	−	0.681749i	−0.599314	−	0.800514i	$-0.704560\pi$
$281$	6.59808	−	11.4282i	0.393608	−	0.681749i	0.992922	+	0.118764i	$0.0378933\pi$
$282$		0			0
$283$	−7.66025	−	13.2679i	−0.455355	−	0.788698i	0.543354	−	0.839504i	$-0.317154\pi$
$283$	−7.66025	−	13.2679i	−0.455355	−	0.788698i	−0.998709	+	0.0508062i	$0.983821\pi$
$284$	−3.26795	−	5.66025i	−0.193917	−	0.335874i
$285$		0			0
$286$	−20.0263	+	34.6865i	−1.18418	+	2.05106i
$287$	−2.53590			−0.149689
$288$		0			0
$289$	32.0000			1.88235
$290$	0.205771	−	0.356406i	0.0120833	−	0.0209289i
$291$		0			0
$292$	−4.13397	−	7.16025i	−0.241923	−	0.419022i
$293$	−1.66987	−	2.89230i	−0.0975550	−	0.168970i	0.813117	−	0.582100i	$-0.197769\pi$
$293$	−1.66987	−	2.89230i	−0.0975550	−	0.168970i	−0.910672	+	0.413130i	$0.864436\pi$
$294$		0			0
$295$	−0.562178	+	0.973721i	−0.0327313	+	0.0566922i
$296$	−10.6603			−0.619615
$297$		0			0
$298$	−9.00000			−0.521356
$299$	−13.5622	+	23.4904i	−0.784321	+	1.35848i
$300$		0			0
$301$	−0.732051	−	1.26795i	−0.0421947	−	0.0730834i
$302$	−2.90192	−	5.02628i	−0.166987	−	0.289230i
$303$		0			0
$304$	−0.366025	+	0.633975i	−0.0209930	+	0.0363609i
$305$	1.05256			0.0602693
$306$		0			0
$307$	−21.8564			−1.24741			−0.623706	−	0.781659i	$-0.714374\pi$
$307$	−21.8564			−1.24741			−0.623706	+	0.781659i	$0.714374\pi$
$308$	3.09808	−	5.36603i	0.176529	−	0.305758i
$309$		0			0
$310$	1.09808	+	1.90192i	0.0623665	+	0.108022i
$311$	−5.09808	−	8.83013i	−0.289085	−	0.500711i	0.684506	−	0.729007i	$-0.260018\pi$
$311$	−5.09808	−	8.83013i	−0.289085	−	0.500711i	−0.973592	+	0.228296i	$0.926684\pi$
$312$		0			0
$313$	−12.7942	+	22.1603i	−0.723173	+	1.25257i	0.236549	+	0.971620i	$0.423984\pi$
$313$	−12.7942	+	22.1603i	−0.723173	+	1.25257i	−0.959722	+	0.280952i	$0.909350\pi$
$314$	1.00000			0.0564333
$315$		0			0
$316$	−9.12436			−0.513285
$317$	15.6962	−	27.1865i	0.881584	−	1.52695i	0.0320039	−	0.999488i	$-0.489811\pi$
$317$	15.6962	−	27.1865i	0.881584	−	1.52695i	0.849580	−	0.527460i	$-0.176856\pi$
$318$		0			0
$319$	−4.75833	−	8.24167i	−0.266415	−	0.461445i
$320$	−0.133975	−	0.232051i	−0.00748941	−	0.0129720i
$321$		0			0
$322$	2.09808	−	3.63397i	0.116921	−	0.202513i
$323$	5.12436			0.285127
$324$		0			0
$325$	31.8564			1.76708
$326$	−6.73205	+	11.6603i	−0.372854	+	0.645802i
$327$		0			0
$328$	1.26795	+	2.19615i	0.0700108	+	0.121262i
$329$	2.36603	+	4.09808i	0.130443	+	0.225934i
$330$		0			0
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	−0.984539	−	0.175166i	$-0.943954\pi$
$331$	−6.19615	+	10.7321i	−0.340571	+	0.589887i	0.643968	+	0.765053i	$0.277287\pi$
$332$	16.5885			0.910410
$333$		0			0
$334$	1.80385			0.0987021
$335$	0.901924	−	1.56218i	0.0492774	−	0.0853509i
$336$		0			0
$337$	8.19615	+	14.1962i	0.446473	+	0.773314i	0.998154	−	0.0607417i	$-0.0193466\pi$
$337$	8.19615	+	14.1962i	0.446473	+	0.773314i	−0.551681	+	0.834055i	$0.686013\pi$
$338$	14.3923	+	24.9282i	0.782838	+	1.35592i
$339$		0			0
$340$	−0.937822	+	1.62436i	−0.0508605	+	0.0880931i
$341$	50.7846			2.75014
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−0.732051	+	1.26795i	−0.0394695	+	0.0683632i
$345$		0			0
$346$	3.13397	+	5.42820i	0.168484	+	0.291822i
$347$	−10.7321	−	18.5885i	−0.576127	−	0.997881i	−0.995918	−	0.0902601i	$-0.971230\pi$
$347$	−10.7321	−	18.5885i	−0.576127	−	0.997881i	0.419792	−	0.907621i	$-0.362103\pi$
$348$		0			0
$349$	−0.732051	+	1.26795i	−0.0391858	+	0.0678718i	−0.884953	−	0.465680i	$-0.845810\pi$
$349$	−0.732051	+	1.26795i	−0.0391858	+	0.0678718i	0.845767	+	0.533552i	$0.179143\pi$
$350$	−4.92820			−0.263424
$351$		0			0
$352$	−6.19615			−0.330256
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	−0.520689	−	0.853746i	$-0.674325\pi$
$353$	9.00000	−	15.5885i	0.479022	−	0.829690i	0.999711	+	0.0240566i	$0.00765819\pi$
$354$		0			0
$355$	−0.875644	−	1.51666i	−0.0464744	−	0.0804960i
$356$	−4.96410	−	8.59808i	−0.263097	−	0.455697i
$357$		0			0
$358$	−1.09808	+	1.90192i	−0.0580351	+	0.100520i
$359$	−10.9282			−0.576769			−0.288384	−	0.957515i	$-0.593118\pi$
$359$	−10.9282			−0.576769			−0.288384	+	0.957515i	$0.593118\pi$
$360$		0			0
$361$	−18.4641			−0.971795
$362$	−8.19615	+	14.1962i	−0.430780	+	0.746133i
$363$		0			0
$364$	−3.23205	−	5.59808i	−0.169405	−	0.293419i
$365$	−1.10770	−	1.91858i	−0.0579794	−	0.100423i
$366$		0			0
$367$	−5.56218	+	9.63397i	−0.290343	+	0.502889i	−0.973891	−	0.227017i	$-0.927103\pi$
$367$	−5.56218	+	9.63397i	−0.290343	+	0.502889i	0.683548	+	0.729906i	$0.260436\pi$
$368$	−4.19615			−0.218740
$369$		0			0
$370$	−2.85641			−0.148498
$371$	−4.73205	+	8.19615i	−0.245676	+	0.425523i
$372$		0			0
$373$	3.07180	+	5.32051i	0.159052	+	0.275485i	0.934527	−	0.355892i	$-0.115823\pi$
$373$	3.07180	+	5.32051i	0.159052	+	0.275485i	−0.775475	+	0.631378i	$0.782490\pi$
$374$	21.6865	+	37.5622i	1.12138	+	1.94229i
$375$		0			0
$376$	2.36603	−	4.09808i	0.122018	−	0.211342i
$377$	−9.92820			−0.511328
$378$		0			0
$379$	−27.5167			−1.41344			−0.706718	−	0.707495i	$-0.749825\pi$
$379$	−27.5167			−1.41344			−0.706718	+	0.707495i	$0.749825\pi$
$380$	−0.0980762	+	0.169873i	−0.00503120	+	0.00871430i
$381$		0			0
$382$	−2.83013	−	4.90192i	−0.144802	−	0.250804i
$383$	−9.85641	−	17.0718i	−0.503639	−	0.872328i	−0.999991	−	0.00420688i	$-0.998661\pi$
$383$	−9.85641	−	17.0718i	−0.503639	−	0.872328i	0.496352	−	0.868121i	$-0.334672\pi$
$384$		0			0
$385$	0.830127	−	1.43782i	0.0423072	−	0.0732782i
$386$	−18.8564			−0.959766
$387$		0			0
$388$	10.9282			0.554795
$389$	6.73205	−	11.6603i	0.341329	−	0.591198i	−0.643351	−	0.765571i	$-0.722456\pi$
$389$	6.73205	−	11.6603i	0.341329	−	0.591198i	0.984680	+	0.174373i	$0.0557898\pi$
$390$		0			0
$391$	14.6865	+	25.4378i	0.742730	+	1.28645i
$392$	0.500000	+	0.866025i	0.0252538	+	0.0437409i
$393$		0			0
$394$	7.89230	−	13.6699i	0.397609	−	0.688678i
$395$	−2.44486			−0.123014
$396$		0			0
$397$	−21.0000			−1.05396			−0.526980	−	0.849878i	$-0.676676\pi$
$397$	−21.0000			−1.05396			−0.526980	+	0.849878i	$0.676676\pi$
$398$	−9.56218	+	16.5622i	−0.479309	+	0.830187i
$399$		0			0
$400$	2.46410	+	4.26795i	0.123205	+	0.213397i
$401$	−5.25833	−	9.10770i	−0.262588	−	0.454817i	0.704341	−	0.709862i	$-0.251243\pi$
$401$	−5.25833	−	9.10770i	−0.262588	−	0.454817i	−0.966929	+	0.255046i	$0.917909\pi$
$402$		0			0
$403$	26.4904	−	45.8827i	1.31958	−	2.28558i
$404$	8.92820			0.444195
$405$		0			0
$406$	1.53590			0.0762254
$407$	−33.0263	+	57.2032i	−1.63705	+	2.83546i
$408$		0			0
$409$	−8.66987	−	15.0167i	−0.428698	−	0.742526i	0.568060	−	0.822987i	$-0.307694\pi$
$409$	−8.66987	−	15.0167i	−0.428698	−	0.742526i	−0.996758	+	0.0804610i	$0.974361\pi$
$410$	0.339746	+	0.588457i	0.0167789	+	0.0290618i
$411$		0			0
$412$	4.19615	−	7.26795i	0.206730	−	0.358066i
$413$	−4.19615			−0.206479
$414$		0			0
$415$	4.44486			0.218190
$416$	−3.23205	+	5.59808i	−0.158464	+	0.274468i
$417$		0			0
$418$	2.26795	+	3.92820i	0.110929	+	0.192135i
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	0.958154	−	0.286252i	$-0.0924094\pi$
$419$	4.73205	+	8.19615i	0.231176	+	0.400408i	−0.726979	+	0.686660i	$0.759076\pi$
$420$		0			0
$421$	−0.0621778	+	0.107695i	−0.00303036	+	0.00524874i	−0.867537	−	0.497373i	$-0.834298\pi$
$421$	−0.0621778	+	0.107695i	−0.00303036	+	0.00524874i	0.864506	+	0.502622i	$0.167631\pi$
$422$	17.2679			0.840591
$423$		0			0
$424$	9.46410			0.459617
$425$	17.2487	−	29.8756i	0.836685	−	1.44918i
$426$		0			0
$427$	1.96410	+	3.40192i	0.0950495	+	0.164631i
$428$		0			0
$429$		0			0
$430$	−0.196152	+	0.339746i	−0.00945931	+	0.0163840i
$431$	−14.5359			−0.700170			−0.350085	−	0.936718i	$-0.613847\pi$
$431$	−14.5359			−0.700170			−0.350085	+	0.936718i	$0.613847\pi$
$432$		0			0
$433$	15.7321			0.756034			0.378017	−	0.925799i	$-0.376606\pi$
$433$	15.7321			0.756034			0.378017	+	0.925799i	$0.376606\pi$
$434$	−4.09808	+	7.09808i	−0.196714	+	0.340719i
$435$		0			0
$436$	−1.59808	−	2.76795i	−0.0765340	−	0.132561i
$437$	1.53590	+	2.66025i	0.0734720	+	0.127257i
$438$		0			0
$439$	−11.6603	+	20.1962i	−0.556514	+	0.963910i	0.441270	+	0.897374i	$0.354528\pi$
$439$	−11.6603	+	20.1962i	−0.556514	+	0.963910i	−0.997784	+	0.0665356i	$0.978805\pi$
$440$	−1.66025			−0.0791495
$441$		0			0
$442$	45.2487			2.15226
$443$	7.63397	−	13.2224i	0.362701	−	0.628217i	−0.625703	−	0.780061i	$-0.715188\pi$
$443$	7.63397	−	13.2224i	0.362701	−	0.628217i	0.988404	+	0.151844i	$0.0485213\pi$
$444$		0			0
$445$	−1.33013	−	2.30385i	−0.0630541	−	0.109213i
$446$	−12.7321	−	22.0526i	−0.602880	−	1.04422i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	15.8564			0.748310			0.374155	−	0.927366i	$-0.377933\pi$
$449$	15.8564			0.748310			0.374155	+	0.927366i	$0.377933\pi$
$450$		0			0
$451$	15.7128			0.739887
$452$	2.86603	−	4.96410i	0.134806	−	0.233492i
$453$		0			0
$454$	−9.46410	−	16.3923i	−0.444172	−	0.769329i
$455$	−0.866025	−	1.50000i	−0.0405999	−	0.0703211i
$456$		0			0
$457$	3.42820	−	5.93782i	0.160365	−	0.277760i	−0.774635	−	0.632409i	$-0.782066\pi$
$457$	3.42820	−	5.93782i	0.160365	−	0.277760i	0.934999	+	0.354649i	$0.115400\pi$
$458$	2.46410			0.115140
$459$		0			0
$460$	−1.12436			−0.0524234
$461$	3.39230	−	5.87564i	0.157995	−	0.273656i	−0.776150	−	0.630548i	$-0.782830\pi$
$461$	3.39230	−	5.87564i	0.157995	−	0.273656i	0.934146	+	0.356892i	$0.116164\pi$
$462$		0			0
$463$	0.705771	+	1.22243i	0.0328000	+	0.0568112i	0.881959	−	0.471325i	$-0.156224\pi$
$463$	0.705771	+	1.22243i	0.0328000	+	0.0568112i	−0.849159	+	0.528137i	$0.822891\pi$
$464$	−0.767949	−	1.33013i	−0.0356511	−	0.0617496i
$465$		0			0
$466$	−1.40192	+	2.42820i	−0.0649429	+	0.112484i
$467$	−16.5885			−0.767622			−0.383811	−	0.923412i	$-0.625389\pi$
$467$	−16.5885			−0.767622			−0.383811	+	0.923412i	$0.625389\pi$
$468$		0			0
$469$	6.73205			0.310857
$470$	0.633975	−	1.09808i	0.0292431	−	0.0506505i
$471$		0			0
$472$	2.09808	+	3.63397i	0.0965718	+	0.167267i
$473$	4.53590	+	7.85641i	0.208561	+	0.361238i
$474$		0			0
$475$	1.80385	−	3.12436i	0.0827662	−	0.143355i
$476$	−7.00000			−0.320844
$477$		0			0
$478$	10.0526			0.459793
$479$	10.7583	−	18.6340i	0.491561	−	0.851408i	−0.508392	−	0.861126i	$-0.669760\pi$
$479$	10.7583	−	18.6340i	0.491561	−	0.851408i	0.999953	+	0.00971765i	$0.00309327\pi$
$480$		0			0
$481$	34.4545	+	59.6769i	1.57099	+	2.72103i
$482$	−7.13397	−	12.3564i	−0.324944	−	0.562819i
$483$		0			0
$484$	−13.6962	+	23.7224i	−0.622552	+	1.07829i
$485$	2.92820			0.132963
$486$		0			0
$487$	2.58846			0.117294			0.0586471	−	0.998279i	$-0.481321\pi$
$487$	2.58846			0.117294			0.0586471	+	0.998279i	$0.481321\pi$
$488$	1.96410	−	3.40192i	0.0889107	−	0.153998i
$489$		0			0
$490$	0.133975	+	0.232051i	0.00605236	+	0.0104830i
$491$	−13.2679	−	22.9808i	−0.598774	−	1.03711i	−0.993002	−	0.118095i	$-0.962321\pi$
$491$	−13.2679	−	22.9808i	−0.598774	−	1.03711i	0.394228	−	0.919013i	$-0.371012\pi$
$492$		0			0
$493$	−5.37564	+	9.31089i	−0.242107	+	0.419341i
$494$	4.73205			0.212905
$495$		0			0
$496$	8.19615			0.368018
$497$	3.26795	−	5.66025i	0.146588	−	0.253897i
$498$		0			0
$499$	−9.90192	−	17.1506i	−0.443271	−	0.767768i	0.554659	−	0.832078i	$-0.312849\pi$
$499$	−9.90192	−	17.1506i	−0.443271	−	0.767768i	−0.997930	+	0.0643099i	$0.979515\pi$
$500$	1.33013	+	2.30385i	0.0594851	+	0.103031i
$501$		0			0
$502$	−11.0263	+	19.0981i	−0.492127	+	0.852389i
$503$	40.0526			1.78586			0.892928	−	0.450200i	$-0.148647\pi$
$503$	40.0526			1.78586			0.892928	+	0.450200i	$0.148647\pi$
$504$		0			0
$505$	2.39230			0.106456
$506$	−13.0000	+	22.5167i	−0.577920	+	1.00099i
$507$		0			0
$508$	−6.00000	−	10.3923i	−0.266207	−	0.461084i
$509$	−15.9282	−	27.5885i	−0.706005	−	1.22284i	−0.966328	−	0.257315i	$-0.917162\pi$
$509$	−15.9282	−	27.5885i	−0.706005	−	1.22284i	0.260322	−	0.965522i	$-0.416171\pi$
$510$		0			0
$511$	4.13397	−	7.16025i	0.182876	−	0.316751i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−6.46410			−0.285119
$515$	1.12436	−	1.94744i	0.0495450	−	0.0858145i
$516$		0			0
$517$	−14.6603	−	25.3923i	−0.644757	−	1.11675i
$518$	−5.33013	−	9.23205i	−0.234192	−	0.405633i
$519$		0			0
$520$	−0.866025	+	1.50000i	−0.0379777	+	0.0657794i
$521$	−30.0000			−1.31432			−0.657162	−	0.753749i	$-0.728243\pi$
$521$	−30.0000			−1.31432			−0.657162	+	0.753749i	$0.728243\pi$
$522$		0			0
$523$	33.1769			1.45073			0.725363	−	0.688367i	$-0.241672\pi$
$523$	33.1769			1.45073			0.725363	+	0.688367i	$0.241672\pi$
$524$	−5.26795	+	9.12436i	−0.230131	+	0.398599i
$525$		0			0
$526$	−3.16987	−	5.49038i	−0.138213	−	0.239392i
$527$	−28.6865	−	49.6865i	−1.24961	−	2.16438i
$528$		0			0
$529$	2.69615	−	4.66987i	0.117224	−	0.203038i
$530$	2.53590			0.110152
$531$		0			0
$532$	−0.732051			−0.0317384
$533$	8.19615	−	14.1962i	0.355015	−	0.614904i
$534$		0			0
$535$		0			0
$536$	−3.36603	−	5.83013i	−0.145390	−	0.251823i
$537$		0			0
$538$	2.79423	−	4.83975i	0.120468	−	0.208656i
$539$	6.19615			0.266887
$540$		0			0
$541$	3.33975			0.143587			0.0717934	−	0.997420i	$-0.477128\pi$
$541$	3.33975			0.143587			0.0717934	+	0.997420i	$0.477128\pi$
$542$	−9.75833	+	16.9019i	−0.419156	+	0.726000i
$543$		0			0
$544$	3.50000	+	6.06218i	0.150061	+	0.259914i
$545$	−0.428203	−	0.741670i	−0.0183422	−	0.0317696i
$546$		0			0
$547$	11.3660	−	19.6865i	0.485976	−	0.841735i	−0.513894	−	0.857854i	$-0.671798\pi$
$547$	11.3660	−	19.6865i	0.485976	−	0.841735i	0.999870	+	0.0161183i	$0.00513085\pi$
$548$	−8.26795			−0.353189
$549$		0			0
$550$	30.5359			1.30206
$551$	−0.562178	+	0.973721i	−0.0239496	+	0.0414819i
$552$		0			0
$553$	−4.56218	−	7.90192i	−0.194004	−	0.336024i
$554$	−9.39230	−	16.2679i	−0.399041	−	0.691159i
$555$		0			0
$556$	1.63397	−	2.83013i	0.0692960	−	0.120024i
$557$	23.9282			1.01387			0.506935	−	0.861984i	$-0.330778\pi$
$557$	23.9282			1.01387			0.506935	+	0.861984i	$0.330778\pi$
$558$		0			0
$559$	9.46410			0.400289
$560$	0.133975	−	0.232051i	0.00566146	−	0.00980594i
$561$		0			0
$562$	−6.59808	−	11.4282i	−0.278323	−	0.482070i
$563$	−9.85641	−	17.0718i	−0.415398	−	0.719490i	0.580072	−	0.814565i	$-0.303024\pi$
$563$	−9.85641	−	17.0718i	−0.415398	−	0.719490i	−0.995470	+	0.0950747i	$0.969691\pi$
$564$		0			0
$565$	0.767949	−	1.33013i	0.0323079	−	0.0559589i
$566$	−15.3205			−0.643969
$567$		0			0
$568$	−6.53590			−0.274240
$569$	−11.5981	+	20.0885i	−0.486217	+	0.842152i	−0.999874	−	0.0158432i	$-0.994957\pi$
$569$	−11.5981	+	20.0885i	−0.486217	+	0.842152i	0.513658	+	0.857995i	$0.328290\pi$
$570$		0			0
$571$	11.3660	+	19.6865i	0.475653	+	0.823856i	0.999611	−	0.0278885i	$-0.00887834\pi$
$571$	11.3660	+	19.6865i	0.475653	+	0.823856i	−0.523958	+	0.851744i	$0.675545\pi$
$572$	20.0263	+	34.6865i	0.837341	+	1.45032i
$573$		0			0
$574$	−1.26795	+	2.19615i	−0.0529232	+	0.0916656i
$575$	20.6795			0.862394
$576$		0			0
$577$	24.6603			1.02662			0.513310	−	0.858203i	$-0.328419\pi$
$577$	24.6603			1.02662			0.513310	+	0.858203i	$0.328419\pi$
$578$	16.0000	−	27.7128i	0.665512	−	1.15270i
$579$		0			0
$580$	−0.205771	−	0.356406i	−0.00854419	−	0.0147990i
$581$	8.29423	+	14.3660i	0.344103	+	0.596003i
$582$		0			0
$583$	29.3205	−	50.7846i	1.21433	−	2.10328i
$584$	−8.26795			−0.342130
$585$		0			0
$586$	−3.33975			−0.137964
$587$	−7.36603	+	12.7583i	−0.304028	+	0.526593i	−0.977045	−	0.213035i	$-0.931665\pi$
$587$	−7.36603	+	12.7583i	−0.304028	+	0.526593i	0.673016	+	0.739628i	$0.264998\pi$
$588$		0			0
$589$	−3.00000	−	5.19615i	−0.123613	−	0.214104i
$590$	0.562178	+	0.973721i	0.0231445	+	0.0400874i
$591$		0			0
$592$	−5.33013	+	9.23205i	−0.219067	+	0.379435i
$593$	−22.1769			−0.910697			−0.455348	−	0.890313i	$-0.650485\pi$
$593$	−22.1769			−0.910697			−0.455348	+	0.890313i	$0.650485\pi$
$594$		0			0
$595$	−1.87564			−0.0768939
$596$	−4.50000	+	7.79423i	−0.184327	+	0.319264i
$597$		0			0
$598$	13.5622	+	23.4904i	0.554599	+	0.960593i
$599$	7.56218	+	13.0981i	0.308982	+	0.535173i	0.978140	−	0.207947i	$-0.0666783\pi$
$599$	7.56218	+	13.0981i	0.308982	+	0.535173i	−0.669158	+	0.743120i	$0.733345\pi$
$600$		0			0
$601$	−9.59808	+	16.6244i	−0.391514	+	0.678122i	−0.992649	−	0.121025i	$-0.961382\pi$
$601$	−9.59808	+	16.6244i	−0.391514	+	0.678122i	0.601136	+	0.799147i	$0.294715\pi$
$602$	−1.46410			−0.0596723
$603$		0			0
$604$	−5.80385			−0.236155
$605$	−3.66987	+	6.35641i	−0.149202	+	0.258425i
$606$		0			0
$607$	12.2942	+	21.2942i	0.499007	+	0.864306i	0.999999	−	0.00114584i	$-0.000364732\pi$
$607$	12.2942	+	21.2942i	0.499007	+	0.864306i	−0.500992	+	0.865452i	$0.667031\pi$
$608$	0.366025	+	0.633975i	0.0148443	+	0.0257111i
$609$		0			0
$610$	0.526279	−	0.911543i	0.0213084	−	0.0369073i
$611$	−30.5885			−1.23748
$612$		0			0
$613$	26.7846			1.08182			0.540910	−	0.841080i	$-0.318080\pi$
$613$	26.7846			1.08182			0.540910	+	0.841080i	$0.318080\pi$
$614$	−10.9282	+	18.9282i	−0.441026	+	0.763880i
$615$		0			0
$616$	−3.09808	−	5.36603i	−0.124825	−	0.216203i
$617$	−5.99038	−	10.3756i	−0.241164	−	0.417708i	0.719882	−	0.694096i	$-0.244196\pi$
$617$	−5.99038	−	10.3756i	−0.241164	−	0.417708i	−0.961046	+	0.276388i	$0.910862\pi$
$618$		0			0
$619$	11.8564	−	20.5359i	0.476549	−	0.825407i	−0.523090	−	0.852278i	$-0.675221\pi$
$619$	11.8564	−	20.5359i	0.476549	−	0.825407i	0.999639	+	0.0268702i	$0.00855407\pi$
$620$	2.19615			0.0881996
$621$		0			0
$622$	−10.1962			−0.408828
$623$	4.96410	−	8.59808i	0.198883	−	0.344475i
$624$		0			0
$625$	−11.9641	−	20.7224i	−0.478564	−	0.828897i
$626$	12.7942	+	22.1603i	0.511360	+	0.885702i
$627$		0			0
$628$	0.500000	−	0.866025i	0.0199522	−	0.0345582i
$629$	74.6218			2.97537
$630$		0			0
$631$	−3.66025			−0.145712			−0.0728562	−	0.997342i	$-0.523211\pi$
$631$	−3.66025			−0.145712			−0.0728562	+	0.997342i	$0.523211\pi$
$632$	−4.56218	+	7.90192i	−0.181474	+	0.314322i
$633$		0			0
$634$	−15.6962	−	27.1865i	−0.623374	−	1.07972i
$635$	−1.60770	−	2.78461i	−0.0637994	−	0.110504i
$636$		0			0
$637$	3.23205	−	5.59808i	0.128059	−	0.221804i
$638$	−9.51666			−0.376768
$639$		0			0
$640$	−0.267949			−0.0105916
$641$	−19.7224	+	34.1603i	−0.778989	+	1.34925i	0.153536	+	0.988143i	$0.450934\pi$
$641$	−19.7224	+	34.1603i	−0.778989	+	1.34925i	−0.932525	+	0.361106i	$0.882399\pi$
$642$		0			0
$643$	4.70577	+	8.15064i	0.185578	+	0.321430i	0.943771	−	0.330600i	$-0.107251\pi$
$643$	4.70577	+	8.15064i	0.185578	+	0.321430i	−0.758193	+	0.652030i	$0.773918\pi$
$644$	−2.09808	−	3.63397i	−0.0826758	−	0.143199i
$645$		0			0
$646$	2.56218	−	4.43782i	0.100808	−	0.174604i
$647$	−4.39230			−0.172679			−0.0863397	−	0.996266i	$-0.527517\pi$
$647$	−4.39230			−0.172679			−0.0863397	+	0.996266i	$0.527517\pi$
$648$		0			0
$649$	26.0000			1.02059
$650$	15.9282	−	27.5885i	0.624756	−	1.08211i
$651$		0			0
$652$	6.73205	+	11.6603i	0.263647	+	0.456651i
$653$	15.1244	+	26.1962i	0.591862	+	1.02513i	0.993982	+	0.109548i	$0.0349402\pi$
$653$	15.1244	+	26.1962i	0.591862	+	1.02513i	−0.402120	+	0.915587i	$0.631726\pi$
$654$		0			0
$655$	−1.41154	+	2.44486i	−0.0551535	+	0.0955287i
$656$	2.53590			0.0990102
$657$		0			0
$658$	4.73205			0.184475
$659$	18.1962	−	31.5167i	0.708821	−	1.22771i	−0.256473	−	0.966551i	$-0.582561\pi$
$659$	18.1962	−	31.5167i	0.708821	−	1.22771i	0.965295	−	0.261163i	$-0.0841061\pi$
$660$		0			0
$661$	6.42820	+	11.1340i	0.250028	+	0.433061i	0.963533	−	0.267589i	$-0.0862268\pi$
$661$	6.42820	+	11.1340i	0.250028	+	0.433061i	−0.713505	+	0.700650i	$0.752893\pi$
$662$	6.19615	+	10.7321i	0.240820	+	0.417113i
$663$		0			0
$664$	8.29423	−	14.3660i	0.321878	−	0.557510i
$665$	−0.196152			−0.00760646
$666$		0			0
$667$	−6.44486			−0.249546
$668$	0.901924	−	1.56218i	0.0348965	−	0.0604425i
$669$		0			0
$670$	−0.901924	−	1.56218i	−0.0348444	−	0.0603522i
$671$	−12.1699	−	21.0788i	−0.469813	−	0.813740i
$672$		0			0
$673$	9.16025	−	15.8660i	0.353102	−	0.611590i	−0.633689	−	0.773588i	$-0.718460\pi$
$673$	9.16025	−	15.8660i	0.353102	−	0.611590i	0.986791	+	0.161997i	$0.0517936\pi$
$674$	16.3923			0.631408
$675$		0			0
$676$	28.7846			1.10710
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	0.279453	+	0.960159i	$0.409847\pi$
$677$	−18.0000	+	31.1769i	−0.691796	+	1.19823i	−0.971249	+	0.238067i	$0.923486\pi$
$678$		0			0
$679$	5.46410	+	9.46410i	0.209693	+	0.363199i
$680$	0.937822	+	1.62436i	0.0359638	+	0.0622912i
$681$		0			0
$682$	25.3923	−	43.9808i	0.972322	−	1.68411i
$683$	−1.85641			−0.0710334			−0.0355167	−	0.999369i	$-0.511308\pi$
$683$	−1.85641			−0.0710334			−0.0355167	+	0.999369i	$0.511308\pi$
$684$		0			0
$685$	−2.21539			−0.0846457
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$		0			0
$688$	0.732051	+	1.26795i	0.0279092	+	0.0483401i
$689$	−30.5885	−	52.9808i	−1.16533	−	2.01841i
$690$		0			0
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	−0.466691	−	0.884420i	$-0.654554\pi$
$691$	14.0000	−	24.2487i	0.532585	−	0.922464i	0.999276	−	0.0380440i	$-0.0121127\pi$
$692$	6.26795			0.238272
$693$		0			0
$694$	−21.4641			−0.814766
$695$	0.437822	−	0.758330i	0.0166075	−	0.0287651i
$696$		0			0
$697$	−8.87564	−	15.3731i	−0.336189	−	0.582296i
$698$	0.732051	+	1.26795i	0.0277085	+	0.0479926i
$699$		0			0
$700$	−2.46410	+	4.26795i	−0.0931343	+	0.161313i
$701$	27.3923			1.03459			0.517297	−	0.855806i	$-0.326938\pi$
$701$	27.3923			1.03459			0.517297	+	0.855806i	$0.326938\pi$
$702$		0			0
$703$	7.80385			0.294328
$704$	−3.09808	+	5.36603i	−0.116763	+	0.202240i
$705$		0			0
$706$	−9.00000	−	15.5885i	−0.338719	−	0.586679i
$707$	4.46410	+	7.73205i	0.167890	+	0.290794i
$708$		0			0
$709$	1.93782	−	3.35641i	0.0727764	−	0.126052i	−0.827341	−	0.561700i	$-0.810147\pi$
$709$	1.93782	−	3.35641i	0.0727764	−	0.126052i	0.900117	+	0.435648i	$0.143481\pi$
$710$	−1.75129			−0.0657247
$711$		0			0
$712$	−9.92820			−0.372075
$713$	17.1962	−	29.7846i	0.644001	−	1.11544i
$714$		0			0
$715$	5.36603	+	9.29423i	0.200678	+	0.347584i
$716$	1.09808	+	1.90192i	0.0410370	+	0.0710782i
$717$		0			0
$718$	−5.46410	+	9.46410i	−0.203918	+	0.353197i
$719$	−9.46410			−0.352951			−0.176476	−	0.984305i	$-0.556470\pi$
$719$	−9.46410			−0.352951			−0.176476	+	0.984305i	$0.556470\pi$
$720$		0			0
$721$	8.39230			0.312546
$722$	−9.23205	+	15.9904i	−0.343581	+	0.595100i
$723$		0			0
$724$	8.19615	+	14.1962i	0.304608	+	0.527596i
$725$	3.78461	+	6.55514i	0.140557	+	0.243452i
$726$		0			0
$727$	−25.6603	+	44.4449i	−0.951686	+	1.64837i	−0.209911	+	0.977721i	$0.567317\pi$
$727$	−25.6603	+	44.4449i	−0.951686	+	1.64837i	−0.741776	+	0.670648i	$0.766016\pi$
$728$	−6.46410			−0.239576
$729$		0			0
$730$	−2.21539			−0.0819953
$731$	5.12436	−	8.87564i	0.189531	−	0.328278i
$732$		0			0
$733$	−23.6603	−	40.9808i	−0.873911	−	1.51366i	−0.857918	−	0.513787i	$-0.828242\pi$
$733$	−23.6603	−	40.9808i	−0.873911	−	1.51366i	−0.0159936	−	0.999872i	$-0.505091\pi$
$734$	5.56218	+	9.63397i	0.205304	+	0.355596i
$735$		0			0
$736$	−2.09808	+	3.63397i	−0.0773361	+	0.133950i
$737$	−41.7128			−1.53651
$738$		0			0
$739$	−13.2679			−0.488069			−0.244035	−	0.969767i	$-0.578471\pi$
$739$	−13.2679			−0.488069			−0.244035	+	0.969767i	$0.578471\pi$
$740$	−1.42820	+	2.47372i	−0.0525018	+	0.0909358i
$741$		0			0
$742$	4.73205	+	8.19615i	0.173719	+	0.300890i
$743$	20.1962	+	34.9808i	0.740925	+	1.28332i	0.952075	+	0.305866i	$0.0989459\pi$
$743$	20.1962	+	34.9808i	0.740925	+	1.28332i	−0.211150	+	0.977454i	$0.567721\pi$
$744$		0			0
$745$	−1.20577	+	2.08846i	−0.0441760	+	0.0765152i
$746$	6.14359			0.224933
$747$		0			0
$748$	43.3731			1.58588
$749$		0			0
$750$		0			0
$751$	11.0718	+	19.1769i	0.404016	+	0.699776i	0.994206	−	0.107488i	$-0.0342808\pi$
$751$	11.0718	+	19.1769i	0.404016	+	0.699776i	−0.590191	+	0.807264i	$0.700947\pi$
$752$	−2.36603	−	4.09808i	−0.0862801	−	0.149441i
$753$		0			0
$754$	−4.96410	+	8.59808i	−0.180782	+	0.313123i
$755$	−1.55514			−0.0565972
$756$		0			0
$757$	20.7846			0.755429			0.377715	−	0.925922i	$-0.376710\pi$
$757$	20.7846			0.755429			0.377715	+	0.925922i	$0.376710\pi$
$758$	−13.7583	+	23.8301i	−0.499725	+	0.865549i
$759$		0			0
$760$	0.0980762	+	0.169873i	0.00355760	+	0.00616194i
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	−0.977727	−	0.209879i	$-0.932693\pi$
$761$	−18.5000	−	32.0429i	−0.670624	−	1.16156i	0.307103	−	0.951676i	$-0.400640\pi$
$762$		0			0
$763$	1.59808	−	2.76795i	0.0578542	−	0.100206i
$764$	−5.66025			−0.204781
$765$		0			0
$766$	−19.7128			−0.712253
$767$	13.5622	−	23.4904i	0.489702	−	0.848189i
$768$		0			0
$769$	2.20577	+	3.82051i	0.0795421	+	0.137771i	0.903052	−	0.429530i	$-0.141321\pi$
$769$	2.20577	+	3.82051i	0.0795421	+	0.137771i	−0.823510	+	0.567301i	$0.807988\pi$
$770$	−0.830127	−	1.43782i	−0.0299157	−	0.0518155i
$771$		0			0
$772$	−9.42820	+	16.3301i	−0.339328	+	0.587734i
$773$	−4.12436			−0.148343			−0.0741714	−	0.997246i	$-0.523631\pi$
$773$	−4.12436			−0.148343			−0.0741714	+	0.997246i	$0.523631\pi$
$774$		0			0
$775$	−40.3923			−1.45093
$776$	5.46410	−	9.46410i	0.196150	−	0.339741i
$777$		0			0
$778$	−6.73205	−	11.6603i	−0.241356	−	0.418040i
$779$	−0.928203	−	1.60770i	−0.0332563	−	0.0576017i
$780$		0			0
$781$	−20.2487	+	35.0718i	−0.724556	+	1.25497i
$782$	29.3731			1.05038
$783$		0			0
$784$	1.00000			0.0357143
$785$	0.133975	−	0.232051i	0.00478176	−	0.00828225i
$786$		0			0
$787$	14.1962	+	24.5885i	0.506038	+	0.876484i	0.999976	+	0.00698638i	$0.00222385\pi$
$787$	14.1962	+	24.5885i	0.506038	+	0.876484i	−0.493937	+	0.869497i	$0.664443\pi$
$788$	−7.89230	−	13.6699i	−0.281152	−	0.486969i
$789$		0			0
$790$	−1.22243	+	2.11731i	−0.0434922	+	0.0753307i
$791$	5.73205			0.203808
$792$		0			0
$793$	−25.3923			−0.901707
$794$	−10.5000	+	18.1865i	−0.372631	+	0.645416i
$795$		0			0
$796$	9.56218	+	16.5622i	0.338922	+	0.587031i
$797$	14.7224	+	25.5000i	0.521495	+	0.903256i	0.999687	+	0.0250011i	$0.00795892\pi$
$797$	14.7224	+	25.5000i	0.521495	+	0.903256i	−0.478192	+	0.878255i	$0.658708\pi$
$798$		0			0
$799$	−16.5622	+	28.6865i	−0.585928	+	1.01486i
$800$	4.92820			0.174238
$801$		0			0
$802$	−10.5167			−0.371356
$803$	−25.6147	+	44.3660i	−0.903924	+	1.56564i
$804$		0			0
$805$	−0.562178	−	0.973721i	−0.0198142	−	0.0343191i
$806$	−26.4904	−	45.8827i	−0.933084	−	1.61615i
$807$		0			0
$808$	4.46410	−	7.73205i	0.157047	−	0.272013i
$809$	32.1244			1.12943			0.564716	−	0.825285i	$-0.308986\pi$
$809$	32.1244			1.12943			0.564716	+	0.825285i	$0.308986\pi$
$810$		0			0
$811$	18.1962			0.638953			0.319477	−	0.947594i	$-0.396493\pi$
$811$	18.1962			0.638953			0.319477	+	0.947594i	$0.396493\pi$
$812$	0.767949	−	1.33013i	0.0269497	−	0.0466783i
$813$		0			0
$814$	33.0263	+	57.2032i	1.15757	+	2.00497i
$815$	1.80385	+	3.12436i	0.0631860	+	0.109441i
$816$		0			0
$817$	0.535898	−	0.928203i	0.0187487	−	0.0324737i
$818$	−17.3397			−0.606270
$819$		0			0
$820$	0.679492			0.0237289
$821$	−12.9641	+	22.4545i	−0.452450	+	0.783667i	−0.998538	−	0.0540614i	$-0.982783\pi$
$821$	−12.9641	+	22.4545i	−0.452450	+	0.783667i	0.546087	+	0.837728i	$0.316117\pi$
$822$		0			0
$823$	−0.392305	−	0.679492i	−0.0136749	−	0.0236856i	0.859107	−	0.511796i	$-0.171020\pi$
$823$	−0.392305	−	0.679492i	−0.0136749	−	0.0236856i	−0.872782	+	0.488110i	$0.837686\pi$
$824$	−4.19615	−	7.26795i	−0.146180	−	0.253191i
$825$		0			0
$826$	−2.09808	+	3.63397i	−0.0730014	+	0.126442i
$827$	−23.3205			−0.810934			−0.405467	−	0.914110i	$-0.632891\pi$
$827$	−23.3205			−0.810934			−0.405467	+	0.914110i	$0.632891\pi$
$828$		0			0
$829$	−14.0000			−0.486240			−0.243120	−	0.969996i	$-0.578171\pi$
$829$	−14.0000			−0.486240			−0.243120	+	0.969996i	$0.578171\pi$
$830$	2.22243	−	3.84936i	0.0771417	−	0.133613i
$831$		0			0
$832$	3.23205	+	5.59808i	0.112051	+	0.194078i
$833$	−3.50000	−	6.06218i	−0.121268	−	0.210042i
$834$		0			0
$835$	0.241670	−	0.418584i	0.00836333	−	0.0144857i
$836$	4.53590			0.156877
$837$		0			0
$838$	9.46410			0.326932
$839$	−0.732051	+	1.26795i	−0.0252732	+	0.0437745i	−0.878385	−	0.477953i	$-0.841379\pi$
$839$	−0.732051	+	1.26795i	−0.0252732	+	0.0437745i	0.853112	+	0.521728i	$0.174712\pi$
$840$		0			0
$841$	13.3205	+	23.0718i	0.459328	+	0.795579i
$842$	0.0621778	+	0.107695i	0.00214279	+	0.00371142i
$843$		0			0
$844$	8.63397	−	14.9545i	0.297194	−	0.514755i
$845$	7.71281			0.265329
$846$		0			0
$847$	−27.3923			−0.941211
$848$	4.73205	−	8.19615i	0.162499	−	0.281457i
$849$		0			0
$850$	−17.2487	−	29.8756i	−0.591626	−	1.02473i
$851$	22.3660	+	38.7391i	0.766697	+	1.32796i
$852$		0			0
$853$	24.8564	−	43.0526i	0.851067	−	1.47409i	−0.0291790	−	0.999574i	$-0.509289\pi$
$853$	24.8564	−	43.0526i	0.851067	−	1.47409i	0.880246	−	0.474517i	$-0.157377\pi$
$854$	3.92820			0.134420
$855$		0			0
$856$		0			0
$857$	8.42820	−	14.5981i	0.287902	−	0.498661i	−0.685407	−	0.728160i	$-0.740376\pi$
$857$	8.42820	−	14.5981i	0.287902	−	0.498661i	0.973309	+	0.229500i	$0.0737089\pi$
$858$		0			0
$859$	−12.1962	−	21.1244i	−0.416127	−	0.720754i	0.579419	−	0.815030i	$-0.303280\pi$
$859$	−12.1962	−	21.1244i	−0.416127	−	0.720754i	−0.995546	+	0.0942763i	$0.969946\pi$
$860$	0.196152	+	0.339746i	0.00668874	+	0.0115852i
$861$		0			0
$862$	−7.26795	+	12.5885i	−0.247547	+	0.428765i
$863$	−7.12436			−0.242516			−0.121258	−	0.992621i	$-0.538693\pi$
$863$	−7.12436			−0.242516			−0.121258	+	0.992621i	$0.538693\pi$
$864$		0			0
$865$	1.67949			0.0571044
$866$	7.86603	−	13.6244i	0.267298	−	0.462974i
$867$		0			0
$868$	4.09808	+	7.09808i	0.139098	+	0.240924i
$869$	28.2679	+	48.9615i	0.958924	+	1.66091i
$870$		0			0
$871$	−21.7583	+	37.6865i	−0.737253	+	1.27696i
$872$	−3.19615			−0.108235
$873$		0			0
$874$	3.07180			0.103905
$875$	−1.33013	+	2.30385i	−0.0449665	+	0.0778843i
$876$		0			0
$877$	18.2583	+	31.6244i	0.616540	+	1.06788i	0.990112	+	0.140278i	$0.0447995\pi$
$877$	18.2583	+	31.6244i	0.616540	+	1.06788i	−0.373572	+	0.927601i	$0.621867\pi$
$878$	11.6603	+	20.1962i	0.393515	+	0.681587i
$879$		0			0
$880$	−0.830127	+	1.43782i	−0.0279836	+	0.0484690i
$881$	30.2487			1.01910			0.509552	−	0.860440i	$-0.329811\pi$
$881$	30.2487			1.01910			0.509552	+	0.860440i	$0.329811\pi$
$882$		0			0
$883$	−9.66025			−0.325093			−0.162547	−	0.986701i	$-0.551971\pi$
$883$	−9.66025			−0.325093			−0.162547	+	0.986701i	$0.551971\pi$
$884$	22.6244	−	39.1865i	0.760939	−	1.31799i
$885$		0			0
$886$	−7.63397	−	13.2224i	−0.256468	−	0.444216i
$887$	28.2224	+	48.8827i	0.947617	+	1.64132i	0.750426	+	0.660955i	$0.229849\pi$
$887$	28.2224	+	48.8827i	0.947617	+	1.64132i	0.197191	+	0.980365i	$0.436818\pi$
$888$		0			0
$889$	6.00000	−	10.3923i	0.201234	−	0.348547i
$890$	−2.66025			−0.0891719
$891$		0			0
$892$	−25.4641			−0.852601
$893$	−1.73205	+	3.00000i	−0.0579609	+	0.100391i
$894$		0			0
$895$	0.294229	+	0.509619i	0.00983498	+	0.0170347i
$896$	−0.500000	−	0.866025i	−0.0167038	−	0.0289319i
$897$		0			0
$898$	7.92820	−	13.7321i	0.264568	−	0.458244i
$899$	12.5885			0.419849
$900$		0			0
$901$	−66.2487			−2.20706
$902$	7.85641	−	13.6077i	0.261590	−	0.453087i
$903$		0			0
$904$	−2.86603	−	4.96410i	−0.0953226	−	0.165104i
$905$	2.19615	+	3.80385i	0.0730026	+	0.126444i
$906$		0			0
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	−0.395482	−	0.918474i	$-0.629423\pi$
$907$	18.0000	−	31.1769i	0.597680	−	1.03521i	0.993163	−	0.116739i	$-0.0372441\pi$
$908$	−18.9282			−0.628154
$909$		0			0
$910$	−1.73205			−0.0574169
$911$	−21.1244	+	36.5885i	−0.699881	+	1.21223i	0.268626	+	0.963245i	$0.413430\pi$
$911$	−21.1244	+	36.5885i	−0.699881	+	1.21223i	−0.968507	+	0.248985i	$0.919903\pi$
$912$		0			0
$913$	−51.3923	−	89.0141i	−1.70084	−	2.94594i
$914$	−3.42820	−	5.93782i	−0.113395	−	0.196406i
$915$		0			0
$916$	1.23205	−	2.13397i	0.0407081	−	0.0705085i
$917$	−10.5359			−0.347926
$918$		0			0
$919$	26.9808			0.890013			0.445007	−	0.895527i	$-0.353201\pi$
$919$	26.9808			0.890013			0.445007	+	0.895527i	$0.353201\pi$
$920$	−0.562178	+	0.973721i	−0.0185345	+	0.0321026i
$921$		0			0
$922$	−3.39230	−	5.87564i	−0.111720	−	0.193504i
$923$	21.1244	+	36.5885i	0.695317	+	1.20432i
$924$		0			0
$925$	26.2679	−	45.4974i	0.863685	−	1.49595i
$926$	1.41154			0.0463862
$927$		0			0
$928$	−1.53590			−0.0504183
$929$	25.7487	−	44.5981i	0.844788	−	1.46322i	−0.0410175	−	0.999158i	$-0.513060\pi$
$929$	25.7487	−	44.5981i	0.844788	−	1.46322i	0.885805	−	0.464057i	$-0.153607\pi$
$930$		0			0
$931$	−0.366025	−	0.633975i	−0.0119960	−	0.0207777i
$932$	1.40192	+	2.42820i	0.0459215	+	0.0795384i
$933$		0			0
$934$	−8.29423	+	14.3660i	−0.271395	+	0.470071i
$935$	11.6218			0.380073
$936$		0			0
$937$	−25.8372			−0.844064			−0.422032	−	0.906581i	$-0.638683\pi$
$937$	−25.8372			−0.844064			−0.422032	+	0.906581i	$0.638683\pi$
$938$	3.36603	−	5.83013i	0.109905	−	0.190360i
$939$		0			0
$940$	−0.633975	−	1.09808i	−0.0206780	−	0.0358153i
$941$	17.0622	+	29.5526i	0.556211	+	0.963386i	0.997808	+	0.0661724i	$0.0210787\pi$
$941$	17.0622	+	29.5526i	0.556211	+	0.963386i	−0.441597	+	0.897213i	$0.645588\pi$
$942$		0			0
$943$	5.32051	−	9.21539i	0.173260	−	0.300094i
$944$	4.19615			0.136573
$945$		0			0
$946$	9.07180			0.294950
$947$	23.1244	−	40.0526i	0.751441	−	1.30153i	−0.195684	−	0.980667i	$-0.562693\pi$
$947$	23.1244	−	40.0526i	0.751441	−	1.30153i	0.947125	−	0.320866i	$-0.103974\pi$
$948$		0			0
$949$	26.7224	+	46.2846i	0.867447	+	1.50246i
$950$	−1.80385	−	3.12436i	−0.0585245	−	0.101367i
$951$		0			0
$952$	−3.50000	+	6.06218i	−0.113436	+	0.196476i
$953$	−41.5885			−1.34718			−0.673591	−	0.739104i	$-0.735249\pi$
$953$	−41.5885			−1.34718			−0.673591	+	0.739104i	$0.735249\pi$
$954$		0			0
$955$	−1.51666			−0.0490780
$956$	5.02628	−	8.70577i	0.162561	−	0.281565i
$957$		0			0
$958$	−10.7583	−	18.6340i	−0.347586	−	0.602036i
$959$	−4.13397	−	7.16025i	−0.133493	−	0.231217i
$960$		0			0
$961$	−18.0885	+	31.3301i	−0.583499	+	1.01065i
$962$	68.9090			2.22171
$963$		0			0
$964$	−14.2679			−0.459540
$965$	−2.52628	+	4.37564i	−0.0813238	+	0.140857i
$966$		0			0
$967$	1.83013	+	3.16987i	0.0588529	+	0.101936i	0.893951	−	0.448165i	$-0.147922\pi$
$967$	1.83013	+	3.16987i	0.0588529	+	0.101936i	−0.835098	+	0.550101i	$0.814589\pi$
$968$	13.6962	+	23.7224i	0.440211	+	0.762468i
$969$		0			0
$970$	1.46410	−	2.53590i	0.0470095	−	0.0814228i
$971$	8.87564			0.284833			0.142416	−	0.989807i	$-0.454513\pi$
$971$	8.87564			0.284833			0.142416	+	0.989807i	$0.454513\pi$
$972$		0			0
$973$	3.26795			0.104766
$974$	1.29423	−	2.24167i	0.0414698	−	0.0718277i
$975$		0			0
$976$	−1.96410	−	3.40192i	−0.0628694	−	0.108893i
$977$	−28.8564	−	49.9808i	−0.923198	−	1.59903i	−0.794434	−	0.607351i	$-0.792232\pi$
$977$	−28.8564	−	49.9808i	−0.923198	−	1.59903i	−0.128765	−	0.991675i	$-0.541101\pi$
$978$		0			0
$979$	−30.7583	+	53.2750i	−0.983040	+	1.70268i
$980$	0.267949			0.00855932
$981$		0			0
$982$	−26.5359			−0.846795
$983$	−29.3205	+	50.7846i	−0.935179	+	1.61978i	−0.160864	+	0.986977i	$0.551428\pi$
$983$	−29.3205	+	50.7846i	−0.935179	+	1.61978i	−0.774314	+	0.632801i	$0.781905\pi$
$984$		0			0
$985$	−2.11474	−	3.66283i	−0.0673811	−	0.116708i
$986$	5.37564	+	9.31089i	0.171195	+	0.296519i
$987$		0			0
$988$	2.36603	−	4.09808i	0.0752733	−	0.130377i
$989$	6.14359			0.195355
$990$		0			0
$991$	−27.6603			−0.878657			−0.439328	−	0.898327i	$-0.644784\pi$
$991$	−27.6603			−0.878657			−0.439328	+	0.898327i	$0.644784\pi$
$992$	4.09808	−	7.09808i	0.130114	−	0.225364i
$993$		0			0
$994$	−3.26795	−	5.66025i	−0.103653	−	0.179532i
$995$	2.56218	+	4.43782i	0.0812265	+	0.140688i
$996$		0			0
$997$	−20.6244	+	35.7224i	−0.653180	+	1.13134i	0.329167	+	0.944272i	$0.393232\pi$
$997$	−20.6244	+	35.7224i	−0.653180	+	1.13134i	−0.982347	+	0.187069i	$0.940101\pi$
$998$	−19.8038			−0.626880
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1134.2.f.s.379.2		4
3.2	odd	2		1134.2.f.r.379.1		4
9.2	odd	6		1134.2.a.m.1.2	yes	2
9.4	even	3	inner	1134.2.f.s.757.2		4
9.5	odd	6		1134.2.f.r.757.1		4
9.7	even	3		1134.2.a.l.1.1	✓	2
36.7	odd	6		9072.2.a.bp.1.1		2
36.11	even	6		9072.2.a.y.1.2		2
63.20	even	6		7938.2.a.bt.1.1		2
63.34	odd	6		7938.2.a.bg.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1134.2.a.l.1.1	✓	2	9.7	even	3
1134.2.a.m.1.2	yes	2	9.2	odd	6
1134.2.f.r.379.1		4	3.2	odd	2
1134.2.f.r.757.1		4	9.5	odd	6
1134.2.f.s.379.2		4	1.1	even	1	trivial
1134.2.f.s.757.2		4	9.4	even	3	inner
7938.2.a.bg.1.2		2	63.34	odd	6
7938.2.a.bt.1.1		2	63.20	even	6
9072.2.a.y.1.2		2	36.11	even	6
9072.2.a.bp.1.1		2	36.7	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.133975 - 0.232051i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.133975 - 0.232051i) q^{5} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -0.267949 q^{10} +(-3.09808 + 5.36603i) q^{11} +(3.23205 + 5.59808i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(-0.500000 + 0.866025i) q^{16} +7.00000 q^{17} +0.732051 q^{19} +(-0.133975 + 0.232051i) q^{20} +(3.09808 + 5.36603i) q^{22} +(2.09808 + 3.63397i) q^{23} +(2.46410 - 4.26795i) q^{25} +6.46410 q^{26} -1.00000 q^{28} +(-0.767949 + 1.33013i) q^{29} +(-4.09808 - 7.09808i) q^{31} +(0.500000 + 0.866025i) q^{32} +(3.50000 - 6.06218i) q^{34} -0.267949 q^{35} +10.6603 q^{37} +(0.366025 - 0.633975i) q^{38} +(0.133975 + 0.232051i) q^{40} +(-1.26795 - 2.19615i) q^{41} +(0.732051 - 1.26795i) q^{43} +6.19615 q^{44} +4.19615 q^{46} +(-2.36603 + 4.09808i) q^{47} +(-0.500000 - 0.866025i) q^{49} +(-2.46410 - 4.26795i) q^{50} +(3.23205 - 5.59808i) q^{52} -9.46410 q^{53} +1.66025 q^{55} +(-0.500000 + 0.866025i) q^{56} +(0.767949 + 1.33013i) q^{58} +(-2.09808 - 3.63397i) q^{59} +(-1.96410 + 3.40192i) q^{61} -8.19615 q^{62} +1.00000 q^{64} +(0.866025 - 1.50000i) q^{65} +(3.36603 + 5.83013i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(-0.133975 + 0.232051i) q^{70} +6.53590 q^{71} +8.26795 q^{73} +(5.33013 - 9.23205i) q^{74} +(-0.366025 - 0.633975i) q^{76} +(3.09808 + 5.36603i) q^{77} +(4.56218 - 7.90192i) q^{79} +0.267949 q^{80} -2.53590 q^{82} +(-8.29423 + 14.3660i) q^{83} +(-0.937822 - 1.62436i) q^{85} +(-0.732051 - 1.26795i) q^{86} +(3.09808 - 5.36603i) q^{88} +9.92820 q^{89} +6.46410 q^{91} +(2.09808 - 3.63397i) q^{92} +(2.36603 + 4.09808i) q^{94} +(-0.0980762 - 0.169873i) q^{95} +(-5.46410 + 9.46410i) q^{97} -1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8	\( 4 q + 2 q^{2} - 2 q^{4} - 4 q^{5} + 2 q^{7} - 4 q^{8} - 8 q^{10} - 2 q^{11} + 6 q^{13} - 2 q^{14} - 2 q^{16} + 28 q^{17} - 4 q^{19} - 4 q^{20} + 2 q^{22} - 2 q^{23} - 4 q^{25} + 12 q^{26} - 4 q^{28} - 10 q^{29} - 6 q^{31} + 2 q^{32} + 14 q^{34} - 8 q^{35} + 8 q^{37} - 2 q^{38} + 4 q^{40} - 12 q^{41} - 4 q^{43} + 4 q^{44} - 4 q^{46} - 6 q^{47} - 2 q^{49} + 4 q^{50} + 6 q^{52} - 24 q^{53} - 28 q^{55} - 2 q^{56} + 10 q^{58} + 2 q^{59} + 6 q^{61} - 12 q^{62} + 4 q^{64} + 10 q^{67} - 14 q^{68} - 4 q^{70} + 40 q^{71} + 40 q^{73} + 4 q^{74} + 2 q^{76} + 2 q^{77} - 6 q^{79} + 8 q^{80} - 24 q^{82} - 2 q^{83} - 28 q^{85} + 4 q^{86} + 2 q^{88} + 12 q^{89} + 12 q^{91} - 2 q^{92} + 6 q^{94} + 10 q^{95} - 8 q^{97} - 4 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 2 * q^4 - 4 * q^5 + 2 * q^7 - 4 * q^8 - 8 * q^10 - 2 * q^11 + 6 * q^13 - 2 * q^14 - 2 * q^16 + 28 * q^17 - 4 * q^19 - 4 * q^20 + 2 * q^22 - 2 * q^23 - 4 * q^25 + 12 * q^26 - 4 * q^28 - 10 * q^29 - 6 * q^31 + 2 * q^32 + 14 * q^34 - 8 * q^35 + 8 * q^37 - 2 * q^38 + 4 * q^40 - 12 * q^41 - 4 * q^43 + 4 * q^44 - 4 * q^46 - 6 * q^47 - 2 * q^49 + 4 * q^50 + 6 * q^52 - 24 * q^53 - 28 * q^55 - 2 * q^56 + 10 * q^58 + 2 * q^59 + 6 * q^61 - 12 * q^62 + 4 * q^64 + 10 * q^67 - 14 * q^68 - 4 * q^70 + 40 * q^71 + 40 * q^73 + 4 * q^74 + 2 * q^76 + 2 * q^77 - 6 * q^79 + 8 * q^80 - 24 * q^82 - 2 * q^83 - 28 * q^85 + 4 * q^86 + 2 * q^88 + 12 * q^89 + 12 * q^91 - 2 * q^92 + 6 * q^94 + 10 * q^95 - 8 * q^97 - 4 * q^98

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