LMFDB - Embedded newform 1078.2.i.b.1011.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1078,2,Mod(901,1078)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1078, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("1078.901");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1078 = 2 \cdot 7^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1078.i (of order $6$, 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:	$8.60787333789$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	16.0.162447943996702457856.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{12} - 15x^{8} - 16x^{4} + 256 $ x^16 - x^12 - 15x^8 - 16x^4 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	no (minimal twist has level 154)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1011.2
Root			$1.40721 - 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1078.1011
Dual form			1078.2.i.b.901.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.559525 - 0.323042i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 - 2.23658i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.559525 - 0.323042i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 - 2.23658i) q^{9} +(-1.54779 + 2.68085i) q^{10} +(3.31297 - 0.155657i) q^{11} +(-0.559525 + 0.323042i) q^{12} +0.646084 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87083 - 3.24037i) q^{17} +(2.23658 + 1.29129i) q^{18} +(0.901703 + 1.56180i) q^{19} -3.09557i q^{20} +(-2.79129 + 1.79129i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.323042 - 0.559525i) q^{24} +(2.29129 - 3.96863i) q^{25} +(-0.559525 + 0.323042i) q^{26} +3.60681i q^{27} +1.58258i q^{29} +(1.73205 - 1.00000i) q^{30} +(7.48301 + 4.32032i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.90397 - 0.983134i) q^{33} +3.74166i q^{34} -2.58258 q^{36} +(-1.79129 - 3.10260i) q^{37} +(-1.56180 - 0.901703i) q^{38} +(-0.361500 - 0.208712i) q^{39} +(1.54779 + 2.68085i) q^{40} -9.93280 q^{41} -7.16515i q^{43} +(1.52168 - 2.94694i) q^{44} +(-6.92349 - 3.99728i) q^{45} +(3.46410 + 2.00000i) q^{46} +(-8.60206 + 4.96640i) q^{47} +0.646084i q^{48} +4.58258i q^{50} +(-2.09355 + 1.20871i) q^{51} +(0.323042 - 0.559525i) q^{52} +(5.79129 - 10.0308i) q^{53} +(-1.80341 - 3.12359i) q^{54} +(8.64064 - 5.54506i) q^{55} -1.16515i q^{57} +(-0.791288 - 1.37055i) q^{58} +(0.559525 + 0.323042i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-0.969126 - 1.67858i) q^{61} -8.64064 q^{62} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{65} +(2.14046 - 0.100567i) q^{66} +(3.79129 - 6.56670i) q^{67} +(-1.87083 - 3.24037i) q^{68} +2.58434i q^{69} +2.00000 q^{71} +(2.23658 - 1.29129i) q^{72} +(-8.06198 + 13.9638i) q^{73} +(3.10260 + 1.79129i) q^{74} +(-2.56407 + 1.48036i) q^{75} +1.80341 q^{76} +0.417424 q^{78} +(-3.46410 + 2.00000i) q^{79} +(-2.68085 - 1.54779i) q^{80} +(-2.70871 + 4.69163i) q^{81} +(8.60206 - 4.96640i) q^{82} +12.8935 q^{83} -11.5826i q^{85} +(3.58258 + 6.20520i) q^{86} +(0.511238 - 0.885491i) q^{87} +(0.155657 + 3.31297i) q^{88} +(8.48528 - 4.89898i) q^{89} +7.99455 q^{90} -4.00000 q^{92} +(-2.79129 - 4.83465i) q^{93} +(4.96640 - 8.60206i) q^{94} +(4.83465 + 2.79129i) q^{95} +(-0.323042 - 0.559525i) q^{96} -8.50579i q^{97} +(-4.62614 - 7.20871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{4} + 16 q^{9}+O(q^{10}) $ 16 * q + 8 * q^4 + 16 * q^9	$ 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99}+O(q^{100}) $ 16 * q + 8 * q^4 + 16 * q^9 - 4 * q^11 - 32 * q^15 - 8 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 8 * q^37 + 4 * q^44 + 56 * q^53 + 24 * q^58 - 16 * q^60 - 16 * q^64 + 24 * q^67 + 32 * q^71 + 80 * q^78 - 80 * q^81 - 16 * q^86 - 4 * q^88 - 64 * q^92 - 8 * q^93 - 184 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.559525	−	0.323042i	−0.323042	−	0.186508i	0.329706	−	0.944084i	$-0.393050\pi$
$3$	−0.559525	−	0.323042i	−0.323042	−	0.186508i	−0.652748	+	0.757575i	$0.726384\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.68085	−	1.54779i	1.19891	−	0.692191i	0.238598	−	0.971118i	$-0.423312\pi$
$5$	2.68085	−	1.54779i	1.19891	−	0.692191i	0.960312	+	0.278927i	$0.0899788\pi$
$6$	0.646084			0.263763
$7$		0			0
$7$		0			0
$8$			1.00000i			0.353553i
$9$	−1.29129	−	2.23658i	−0.430429	−	0.745525i
$10$	−1.54779	+	2.68085i	−0.489453	+	0.847758i
$11$	3.31297	−	0.155657i	0.998898	−	0.0469323i
$11$	3.31297	−	0.155657i	0.998898	−	0.0469323i
$12$	−0.559525	+	0.323042i	−0.161521	+	0.0932542i
$13$	0.646084			0.179191			0.0895957	−	0.995978i	$-0.471443\pi$
$13$	0.646084			0.179191			0.0895957	+	0.995978i	$0.471443\pi$
$14$		0			0
$15$	−2.00000			−0.516398
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.87083	−	3.24037i	0.453743	−	0.785905i	−0.544872	−	0.838519i	$-0.683422\pi$
$17$	1.87083	−	3.24037i	0.453743	−	0.785905i	0.998615	+	0.0526138i	$0.0167552\pi$
$18$	2.23658	+	1.29129i	0.527166	+	0.304359i
$19$	0.901703	+	1.56180i	0.206865	+	0.358300i	0.950725	−	0.310035i	$-0.100341\pi$
$19$	0.901703	+	1.56180i	0.206865	+	0.358300i	−0.743860	+	0.668335i	$0.767007\pi$
$20$		−	3.09557i		−	0.692191i
$21$		0			0
$22$	−2.79129	+	1.79129i	−0.595105	+	0.381904i
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	0.578610	−	0.815604i	$-0.303595\pi$
$23$	−2.00000	−	3.46410i	−0.417029	−	0.722315i	−0.995639	+	0.0932891i	$0.970262\pi$
$24$	0.323042	−	0.559525i	0.0659407	−	0.114213i
$25$	2.29129	−	3.96863i	0.458258	−	0.793725i
$26$	−0.559525	+	0.323042i	−0.109732	+	0.0633537i
$27$			3.60681i			0.694131i
$28$		0			0
$29$			1.58258i			0.293877i	0.989146	+	0.146938i	$0.0469419\pi$
$29$			1.58258i			0.293877i	−0.989146	+	0.146938i	$0.953058\pi$
$30$	1.73205	−	1.00000i	0.316228	−	0.182574i
$31$	7.48301	+	4.32032i	1.34399	+	0.775952i	0.987390	−	0.158306i	$-0.0506032\pi$
$31$	7.48301	+	4.32032i	1.34399	+	0.775952i	0.356598	+	0.934258i	$0.383936\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.90397	−	0.983134i	−0.331439	−	0.171142i
$34$			3.74166i			0.641689i
$35$		0			0
$36$	−2.58258			−0.430429
$37$	−1.79129	−	3.10260i	−0.294486	−	0.510065i	0.680379	−	0.732860i	$-0.261815\pi$
$37$	−1.79129	−	3.10260i	−0.294486	−	0.510065i	−0.974865	+	0.222796i	$0.928482\pi$
$38$	−1.56180	−	0.901703i	−0.253357	−	0.146276i
$39$	−0.361500	−	0.208712i	−0.0578863	−	0.0334207i
$40$	1.54779	+	2.68085i	0.244727	+	0.423879i
$41$	−9.93280			−1.55124			−0.775622	−	0.631198i	$-0.782564\pi$
$41$	−9.93280			−1.55124			−0.775622	+	0.631198i	$0.782564\pi$
$42$		0			0
$43$		−	7.16515i		−	1.09268i	−0.837565	−	0.546338i	$-0.816022\pi$
$43$		−	7.16515i		−	1.09268i	0.837565	−	0.546338i	$-0.183978\pi$
$44$	1.52168	−	2.94694i	0.229402	−	0.444269i
$45$	−6.92349	−	3.99728i	−1.03209	−	0.595879i
$46$	3.46410	+	2.00000i	0.510754	+	0.294884i
$47$	−8.60206	+	4.96640i	−1.25474	+	0.724424i	−0.972047	−	0.234786i	$-0.924561\pi$
$47$	−8.60206	+	4.96640i	−1.25474	+	0.724424i	−0.282693	+	0.959211i	$0.591228\pi$
$48$			0.646084i			0.0932542i
$49$		0			0
$50$			4.58258i			0.648074i
$51$	−2.09355	+	1.20871i	−0.293156	+	0.169254i
$52$	0.323042	−	0.559525i	0.0447979	−	0.0775922i
$53$	5.79129	−	10.0308i	0.795495	−	1.37784i	−0.127030	−	0.991899i	$-0.540544\pi$
$53$	5.79129	−	10.0308i	0.795495	−	1.37784i	0.922525	−	0.385938i	$-0.126122\pi$
$54$	−1.80341	−	3.12359i	−0.245412	−	0.425067i
$55$	8.64064	−	5.54506i	1.16510	−	0.747696i
$56$		0			0
$57$		−	1.16515i		−	0.154328i
$58$	−0.791288	−	1.37055i	−0.103901	−	0.179962i
$59$	0.559525	+	0.323042i	0.0728440	+	0.0420565i	0.535980	−	0.844231i	$-0.319942\pi$
$59$	0.559525	+	0.323042i	0.0728440	+	0.0420565i	−0.463136	+	0.886287i	$0.653276\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	−0.969126	−	1.67858i	−0.124084	−	0.214920i	0.797291	−	0.603596i	$-0.206266\pi$
$61$	−0.969126	−	1.67858i	−0.124084	−	0.214920i	−0.921374	+	0.388676i	$0.872933\pi$
$62$	−8.64064			−1.09736
$63$		0			0
$64$	−1.00000			−0.125000
$65$	1.73205	−	1.00000i	0.214834	−	0.124035i
$66$	2.14046	−	0.100567i	0.263472	−	0.0123790i
$67$	3.79129	−	6.56670i	0.463180	−	0.802250i	−0.535938	−	0.844257i	$-0.680042\pi$
$67$	3.79129	−	6.56670i	0.463180	−	0.802250i	0.999117	+	0.0420070i	$0.0133752\pi$
$68$	−1.87083	−	3.24037i	−0.226871	−	0.392953i
$69$			2.58434i			0.311117i
$70$		0			0
$71$	2.00000			0.237356			0.118678	−	0.992933i	$-0.462134\pi$
$71$	2.00000			0.237356			0.118678	+	0.992933i	$0.462134\pi$
$72$	2.23658	−	1.29129i	0.263583	−	0.152180i
$73$	−8.06198	+	13.9638i	−0.943583	+	1.63433i	−0.185019	+	0.982735i	$0.559235\pi$
$73$	−8.06198	+	13.9638i	−0.943583	+	1.63433i	−0.758564	+	0.651599i	$0.774099\pi$
$74$	3.10260	+	1.79129i	0.360670	+	0.208233i
$75$	−2.56407	+	1.48036i	−0.296073	+	0.170938i
$76$	1.80341			0.206865
$77$		0			0
$78$	0.417424			0.0472640
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	−0.682048	−	0.731307i	$-0.738911\pi$
$79$	−3.46410	+	2.00000i	−0.389742	+	0.225018i	0.292306	+	0.956325i	$0.405577\pi$
$80$	−2.68085	−	1.54779i	−0.299728	−	0.173048i
$81$	−2.70871	+	4.69163i	−0.300968	+	0.521292i
$82$	8.60206	−	4.96640i	0.949939	−	0.548447i
$83$	12.8935			1.41525			0.707625	−	0.706589i	$-0.249767\pi$
$83$	12.8935			1.41525			0.707625	+	0.706589i	$0.249767\pi$
$84$		0			0
$85$		−	11.5826i		−	1.25631i
$86$	3.58258	+	6.20520i	0.386319	+	0.669124i
$87$	0.511238	−	0.885491i	0.0548105	−	0.0949346i
$88$	0.155657	+	3.31297i	0.0165931	+	0.353164i
$89$	8.48528	−	4.89898i	0.899438	−	0.519291i	0.0224202	−	0.999749i	$-0.492863\pi$
$89$	8.48528	−	4.89898i	0.899438	−	0.519291i	0.877018	+	0.480458i	$0.159529\pi$
$90$	7.99455			0.842700
$91$		0			0
$92$	−4.00000			−0.417029
$93$	−2.79129	−	4.83465i	−0.289443	−	0.501330i
$94$	4.96640	−	8.60206i	0.512245	−	0.887235i
$95$	4.83465	+	2.79129i	0.496025	+	0.286380i
$96$	−0.323042	−	0.559525i	−0.0329703	−	0.0571063i
$97$		−	8.50579i		−	0.863632i	−0.901962	−	0.431816i	$-0.857873\pi$
$97$		−	8.50579i		−	0.863632i	0.901962	−	0.431816i	$-0.142127\pi$
$98$		0			0
$99$	−4.62614	−	7.20871i	−0.464944	−	0.724503i
$100$	−2.29129	−	3.96863i	−0.229129	−	0.396863i
$101$	5.86811	−	10.1639i	0.583898	−	1.01134i	−0.411114	−	0.911584i	$-0.634860\pi$
$101$	5.86811	−	10.1639i	0.583898	−	1.01134i	0.995012	−	0.0997573i	$-0.0318067\pi$
$102$	1.20871	−	2.09355i	0.119680	−	0.207292i
$103$	5.24491	−	3.02815i	0.516796	−	0.298373i	−0.218827	−	0.975764i	$-0.570223\pi$
$103$	5.24491	−	3.02815i	0.516796	−	0.298373i	0.735623	+	0.677391i	$0.236890\pi$
$104$			0.646084i			0.0633537i
$105$		0			0
$106$			11.5826i			1.12500i
$107$	15.2270	−	8.79129i	1.47205	−	0.849886i	0.472539	−	0.881310i	$-0.343337\pi$
$107$	15.2270	−	8.79129i	1.47205	−	0.849886i	0.999506	+	0.0314237i	$0.0100041\pi$
$108$	3.12359	+	1.80341i	0.300568	+	0.173533i
$109$	−14.8655	−	8.58258i	−1.42385	−	0.822062i	−0.427227	−	0.904144i	$-0.640509\pi$
$109$	−14.8655	−	8.58258i	−1.42385	−	0.822062i	−0.996626	+	0.0820827i	$0.973843\pi$
$110$	−4.71048	+	9.12248i	−0.449127	+	0.869795i
$111$			2.31464i			0.219696i
$112$		0			0
$113$	10.7477			1.01106			0.505531	−	0.862809i	$-0.331297\pi$
$113$	10.7477			1.01106			0.505531	+	0.862809i	$0.331297\pi$
$114$	0.582576	+	1.00905i	0.0545632	+	0.0945063i
$115$	−10.7234	−	6.19115i	−0.999960	−	0.577327i
$116$	1.37055	+	0.791288i	0.127252	+	0.0734692i
$117$	−0.834280	−	1.44502i	−0.0771292	−	0.133592i
$118$	−0.646084			−0.0594768
$119$		0			0
$120$		−	2.00000i		−	0.182574i
$121$	10.9515	−	1.03137i	0.995595	−	0.0937612i
$122$	1.67858	+	0.969126i	0.151971	+	0.0877405i
$123$	5.55765	+	3.20871i	0.501117	+	0.289320i
$124$	7.48301	−	4.32032i	0.671994	−	0.387976i
$125$			1.29217i			0.115575i
$126$		0			0
$127$		−	3.58258i		−	0.317902i	−0.987286	−	0.158951i	$-0.949189\pi$
$127$		−	3.58258i		−	0.317902i	0.987286	−	0.158951i	$-0.0508112\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.31464	+	4.00908i	−0.203793	+	0.352980i
$130$	−1.00000	+	1.73205i	−0.0877058	+	0.151911i
$131$	8.38502	+	14.5233i	0.732602	+	1.26890i	0.955767	+	0.294124i	$0.0950278\pi$
$131$	8.38502	+	14.5233i	0.732602	+	1.26890i	−0.223165	+	0.974781i	$0.571639\pi$
$132$	−1.80341	+	1.15732i	−0.156966	+	0.100732i
$133$		0			0
$134$			7.58258i			0.655035i
$135$	5.58258	+	9.66930i	0.480472	+	0.832201i
$136$	3.24037	+	1.87083i	0.277859	+	0.160422i
$137$	1.58258	−	2.74110i	0.135209	−	0.234188i	−0.790469	−	0.612503i	$-0.790163\pi$
$137$	1.58258	−	2.74110i	0.135209	−	0.234188i	0.925677	+	0.378315i	$0.123496\pi$
$138$	−1.29217	−	2.23810i	−0.109997	−	0.190520i
$139$	−15.4779			−1.31282			−0.656408	−	0.754406i	$-0.727925\pi$
$139$	−15.4779			−1.31282			−0.656408	+	0.754406i	$0.727925\pi$
$140$		0			0
$141$	6.41742			0.540445
$142$	−1.73205	+	1.00000i	−0.145350	+	0.0839181i
$143$	2.14046	−	0.100567i	0.178994	−	0.00840987i
$144$	−1.29129	+	2.23658i	−0.107607	+	0.186381i
$145$	2.44949	+	4.24264i	0.203419	+	0.352332i
$146$		−	16.1240i		−	1.33443i
$147$		0			0
$148$	−3.58258			−0.294486
$149$	−12.1244	+	7.00000i	−0.993266	+	0.573462i	−0.906249	−	0.422744i	$-0.861067\pi$
$149$	−12.1244	+	7.00000i	−0.993266	+	0.573462i	−0.0870170	+	0.996207i	$0.527733\pi$
$150$	1.48036	−	2.56407i	0.120871	−	0.209355i
$151$	−4.83465	−	2.79129i	−0.393438	−	0.227152i	0.290210	−	0.956963i	$-0.406275\pi$
$151$	−4.83465	−	2.79129i	−0.393438	−	0.227152i	−0.683649	+	0.729811i	$0.739608\pi$
$152$	−1.56180	+	0.901703i	−0.126678	+	0.0731378i
$153$	−9.66311			−0.781216
$154$		0			0
$155$	26.7477			2.14843
$156$	−0.361500	+	0.208712i	−0.0289432	+	0.0167103i
$157$	11.3997	+	6.58161i	0.909794	+	0.525270i	0.880365	−	0.474297i	$-0.157298\pi$
$157$	11.3997	+	6.58161i	0.909794	+	0.525270i	0.0294291	+	0.999567i	$0.490631\pi$
$158$	2.00000	−	3.46410i	0.159111	−	0.275589i
$159$	−6.48074	+	3.74166i	−0.513956	+	0.296733i
$160$	3.09557			0.244727
$161$		0			0
$162$		−	5.41742i		−	0.425633i
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	0.777007	−	0.629492i	$-0.216737\pi$
$163$	−2.00000	−	3.46410i	−0.156652	−	0.271329i	−0.933659	+	0.358162i	$0.883403\pi$
$164$	−4.96640	+	8.60206i	−0.387811	+	0.671708i
$165$	−6.62594	+	0.311314i	−0.515829	+	0.0242357i
$166$	−11.1661	+	6.44677i	−0.866660	+	0.500366i
$167$	1.29217			0.0999909			0.0499955	−	0.998749i	$-0.484079\pi$
$167$	1.29217			0.0999909			0.0499955	+	0.998749i	$0.484079\pi$
$168$		0			0
$169$	−12.5826			−0.967890
$170$	5.79129	+	10.0308i	0.444172	+	0.769328i
$171$	2.32872	−	4.03345i	0.178081	−	0.308446i
$172$	−6.20520	−	3.58258i	−0.473142	−	0.273169i
$173$	−5.35687	−	9.27837i	−0.407275	−	0.705421i	0.587308	−	0.809363i	$-0.300188\pi$
$173$	−5.35687	−	9.27837i	−0.407275	−	0.705421i	−0.994583	+	0.103942i	$0.966854\pi$
$174$			1.02248i			0.0775137i
$175$		0			0
$176$	−1.79129	−	2.79129i	−0.135023	−	0.210401i
$177$	−0.208712	−	0.361500i	−0.0156878	−	0.0271720i
$178$	−4.89898	+	8.48528i	−0.367194	+	0.635999i
$179$	−5.58258	+	9.66930i	−0.417261	+	0.722718i	−0.995663	−	0.0930344i	$-0.970343\pi$
$179$	−5.58258	+	9.66930i	−0.417261	+	0.722718i	0.578402	+	0.815752i	$0.303677\pi$
$180$	−6.92349	+	3.99728i	−0.516046	+	0.297939i
$181$			5.41022i			0.402138i	0.979577	+	0.201069i	$0.0644416\pi$
$181$			5.41022i			0.402138i	−0.979577	+	0.201069i	$0.935558\pi$
$182$		0			0
$183$			1.25227i			0.0925707i
$184$	3.46410	−	2.00000i	0.255377	−	0.147442i
$185$	−9.60433	−	5.54506i	−0.706124	−	0.407681i
$186$	4.83465	+	2.79129i	0.354494	+	0.204667i
$187$	5.69361	−	11.0265i	0.416358	−	0.806334i
$188$			9.93280i			0.724424i
$189$		0			0
$190$	−5.58258			−0.405003
$191$	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	$0.607592\pi$
$192$	0.559525	+	0.323042i	0.0403802	+	0.0233135i
$193$	−14.1425	−	8.16515i	−1.01800	−	0.587740i	−0.104473	−	0.994528i	$-0.533316\pi$
$193$	−14.1425	−	8.16515i	−1.01800	−	0.587740i	−0.913523	+	0.406787i	$0.866649\pi$
$194$	4.25290	+	7.36623i	0.305340	+	0.528865i
$195$	−1.29217			−0.0925340
$196$		0			0
$197$			8.74773i			0.623250i	0.950205	+	0.311625i	$0.100873\pi$
$197$			8.74773i			0.623250i	−0.950205	+	0.311625i	$0.899127\pi$
$198$	7.61071	+	3.92986i	0.540869	+	0.279283i
$199$	8.36850	+	4.83156i	0.593227	+	0.342500i	0.766373	−	0.642396i	$-0.222060\pi$
$199$	8.36850	+	4.83156i	0.593227	+	0.342500i	−0.173145	+	0.984896i	$0.555393\pi$
$200$	3.96863	+	2.29129i	0.280624	+	0.162019i
$201$	−4.24264	+	2.44949i	−0.299253	+	0.172774i
$202$			11.7362i			0.825757i
$203$		0			0
$204$			2.41742i			0.169254i
$205$	−26.6283	+	15.3739i	−1.85980	+	1.07376i
$206$	−3.02815	+	5.24491i	−0.210981	+	0.365430i
$207$	−5.16515	+	8.94630i	−0.359003	+	0.621811i
$208$	−0.323042	−	0.559525i	−0.0223989	−	0.0387961i
$209$	3.23042	+	5.03383i	0.223453	+	0.348197i
$210$		0			0
$211$			16.7477i			1.15296i	0.817111	+	0.576481i	$0.195574\pi$
$211$			16.7477i			1.15296i	−0.817111	+	0.576481i	$0.804426\pi$
$212$	−5.79129	−	10.0308i	−0.397747	−	0.688919i
$213$	−1.11905	−	0.646084i	−0.0766760	−	0.0442689i
$214$	−8.79129	+	15.2270i	−0.600960	+	1.04089i
$215$	−11.0901	−	19.2087i	−0.756340	−	1.31002i
$216$	−3.60681			−0.245412
$217$		0			0
$218$	17.1652			1.16257
$219$	9.02175	−	5.20871i	0.609634	−	0.351972i
$220$	−0.481847	−	10.2555i	−0.0324861	−	0.691429i
$221$	1.20871	−	2.09355i	0.0813068	−	0.140827i
$222$	−1.15732	−	2.00454i	−0.0776744	−	0.134536i
$223$			16.1240i			1.07974i	0.841749	+	0.539870i	$0.181527\pi$
$223$			16.1240i			1.07974i	−0.841749	+	0.539870i	$0.818473\pi$
$224$		0			0
$225$	−11.8348			−0.788990
$226$	−9.30780	+	5.37386i	−0.619146	+	0.357464i
$227$	0.255619	−	0.442745i	0.0169660	−	0.0293860i	−0.857418	−	0.514621i	$-0.827933\pi$
$227$	0.255619	−	0.442745i	0.0169660	−	0.0293860i	0.874384	+	0.485235i	$0.161266\pi$
$228$	−1.00905	−	0.582576i	−0.0668260	−	0.0385820i
$229$	−4.91895	+	2.83995i	−0.325053	+	0.187669i	−0.653643	−	0.756803i	$-0.726760\pi$
$229$	−4.91895	+	2.83995i	−0.325053	+	0.187669i	0.328590	+	0.944473i	$0.393427\pi$
$230$	12.3823			0.816464
$231$		0			0
$232$	−1.58258			−0.103901
$233$	−23.5257	+	13.5826i	−1.54122	+	0.889824i	−0.542458	+	0.840083i	$0.682506\pi$
$233$	−23.5257	+	13.5826i	−1.54122	+	0.889824i	−0.998762	+	0.0497415i	$0.984160\pi$
$234$	1.44502	+	0.834280i	0.0944636	+	0.0545386i
$235$	−15.3739	+	26.6283i	−1.00288	+	1.73704i
$236$	0.559525	−	0.323042i	0.0364220	−	0.0210282i
$237$	2.58434			0.167871
$238$		0			0
$239$		−	8.41742i		−	0.544478i	−0.962230	−	0.272239i	$-0.912236\pi$
$239$		−	8.41742i		−	0.544478i	0.962230	−	0.272239i	$-0.0877641\pi$
$240$	1.00000	+	1.73205i	0.0645497	+	0.111803i
$241$	1.73598	−	3.00681i	0.111825	−	0.193686i	−0.804681	−	0.593707i	$-0.797664\pi$
$241$	1.73598	−	3.00681i	0.111825	−	0.193686i	0.916506	+	0.400021i	$0.130997\pi$
$242$	−8.96863	+	6.36897i	−0.576525	+	0.409413i
$243$	12.4020	−	7.16027i	0.795586	−	0.459332i
$244$	−1.93825			−0.124084
$245$		0			0
$246$	−6.41742			−0.409160
$247$	0.582576	+	1.00905i	0.0370684	+	0.0642044i
$248$	−4.32032	+	7.48301i	−0.274340	+	0.475172i
$249$	−7.21425	−	4.16515i	−0.457185	−	0.263956i
$250$	−0.646084	−	1.11905i	−0.0408619	−	0.0707749i
$251$			24.1185i			1.52235i	0.648549	+	0.761173i	$0.275376\pi$
$251$			24.1185i			1.52235i	−0.648549	+	0.761173i	$0.724624\pi$
$252$		0			0
$253$	−7.16515	−	11.1652i	−0.450469	−	0.701947i
$254$	1.79129	+	3.10260i	0.112395	+	0.194675i
$255$	−3.74166	+	6.48074i	−0.234312	+	0.405840i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−4.24264	+	2.44949i	−0.264649	+	0.152795i	−0.626453	−	0.779459i	$-0.715494\pi$
$257$	−4.24264	+	2.44949i	−0.264649	+	0.152795i	0.361805	+	0.932254i	$0.382161\pi$
$258$		−	4.62929i		−	0.288207i
$259$		0			0
$260$		−	2.00000i		−	0.124035i
$261$	3.53955	−	2.04356i	0.219093	−	0.126493i
$262$	−14.5233	−	8.38502i	−0.897251	−	0.518028i
$263$	7.21425	+	4.16515i	0.444850	+	0.256834i	0.705653	−	0.708558i	$-0.250654\pi$
$263$	7.21425	+	4.16515i	0.444850	+	0.256834i	−0.260803	+	0.965392i	$0.583987\pi$
$264$	0.983134	−	1.90397i	0.0605077	−	0.117181i
$265$		−	35.8547i		−	2.20254i
$266$		0			0
$267$	−6.33030			−0.387408
$268$	−3.79129	−	6.56670i	−0.231590	−	0.401125i
$269$	14.2897	+	8.25017i	0.871259	+	0.503022i	0.867767	−	0.496972i	$-0.165555\pi$
$269$	14.2897	+	8.25017i	0.871259	+	0.503022i	0.00349288	+	0.999994i	$0.498888\pi$
$270$	−9.66930	−	5.58258i	−0.588455	−	0.339745i
$271$	2.44949	+	4.24264i	0.148796	+	0.257722i	0.930783	−	0.365573i	$-0.119127\pi$
$271$	2.44949	+	4.24264i	0.148796	+	0.257722i	−0.781987	+	0.623295i	$0.785794\pi$
$272$	−3.74166			−0.226871
$273$		0			0
$274$			3.16515i			0.191214i
$275$	6.97322	−	13.5046i	0.420501	−	0.814358i
$276$	2.23810	+	1.29217i	0.134718	+	0.0777794i
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	0.447062	−	0.894503i	$-0.352470\pi$
$277$	−1.73205	−	1.00000i	−0.104069	−	0.0600842i	−0.551131	+	0.834419i	$0.685804\pi$
$278$	13.4042	−	7.73893i	0.803932	−	0.464150i
$279$		−	22.3151i		−	1.33597i
$280$		0			0
$281$			11.1652i			0.666057i	0.942917	+	0.333029i	$0.108071\pi$
$281$			11.1652i			0.666057i	−0.942917	+	0.333029i	$0.891929\pi$
$282$	−5.55765	+	3.20871i	−0.330953	+	0.191076i
$283$	9.03110	−	15.6423i	0.536843	−	0.929840i	−0.462228	−	0.886761i	$-0.652950\pi$
$283$	9.03110	−	15.6423i	0.536843	−	0.929840i	0.999072	−	0.0430789i	$-0.0137167\pi$
$284$	1.00000	−	1.73205i	0.0593391	−	0.102778i
$285$	−1.80341	−	3.12359i	−0.106825	−	0.185026i
$286$	−1.80341	+	1.15732i	−0.106638	+	0.0684339i
$287$		0			0
$288$		−	2.58258i		−	0.152180i
$289$	1.50000	+	2.59808i	0.0882353	+	0.152828i
$290$	−4.24264	−	2.44949i	−0.249136	−	0.143839i
$291$	−2.74773	+	4.75920i	−0.161075	+	0.278989i
$292$	8.06198	+	13.9638i	0.471791	+	0.817167i
$293$	25.1410			1.46875			0.734376	−	0.678743i	$-0.237475\pi$
$293$	25.1410			1.46875			0.734376	+	0.678743i	$0.237475\pi$
$294$		0			0
$295$	2.00000			0.116445
$296$	3.10260	−	1.79129i	0.180335	−	0.104116i
$297$	0.561425	+	11.9493i	0.0325772	+	0.693366i
$298$	7.00000	−	12.1244i	0.405499	−	0.702345i
$299$	−1.29217	−	2.23810i	−0.0747280	−	0.129433i
$300$			2.96073i			0.170938i
$301$		0			0
$302$	5.58258			0.321241
$303$	−6.56670	+	3.79129i	−0.377247	+	0.217804i
$304$	0.901703	−	1.56180i	0.0517162	−	0.0895751i
$305$	−5.19615	−	3.00000i	−0.297531	−	0.171780i
$306$	8.36850	−	4.83156i	0.478395	−	0.276202i
$307$	−10.5789			−0.603769			−0.301885	−	0.953344i	$-0.597616\pi$
$307$	−10.5789			−0.603769			−0.301885	+	0.953344i	$0.597616\pi$
$308$		0			0
$309$	−3.91288			−0.222596
$310$	−23.1642	+	13.3739i	−1.31564	+	0.759584i
$311$	−4.35942	−	2.51691i	−0.247200	−	0.142721i	0.371281	−	0.928520i	$-0.378919\pi$
$311$	−4.35942	−	2.51691i	−0.247200	−	0.142721i	−0.618482	+	0.785799i	$0.712252\pi$
$312$	0.208712	−	0.361500i	0.0118160	−	0.0204659i
$313$	−20.3277	+	11.7362i	−1.14899	+	0.663370i	−0.948641	−	0.316355i	$-0.897541\pi$
$313$	−20.3277	+	11.7362i	−1.14899	+	0.663370i	−0.200349	+	0.979725i	$0.564208\pi$
$314$	−13.1632			−0.742844
$315$		0			0
$316$			4.00000i			0.225018i
$317$	−4.58258	−	7.93725i	−0.257383	−	0.445801i	0.708157	−	0.706055i	$-0.249527\pi$
$317$	−4.58258	−	7.93725i	−0.257383	−	0.445801i	−0.965540	+	0.260254i	$0.916194\pi$
$318$	3.74166	−	6.48074i	0.209822	−	0.363422i
$319$	0.246339	+	5.24303i	0.0137923	+	0.293553i
$320$	−2.68085	+	1.54779i	−0.149864	+	0.0865239i
$321$	−11.3598			−0.634043
$322$		0			0
$323$	6.74773			0.375454
$324$	2.70871	+	4.69163i	0.150484	+	0.260646i
$325$	1.48036	−	2.56407i	0.0821158	−	0.142229i
$326$	3.46410	+	2.00000i	0.191859	+	0.110770i
$327$	5.54506	+	9.60433i	0.306643	+	0.531121i
$328$		−	9.93280i		−	0.548447i
$329$		0			0
$330$	5.58258	−	3.58258i	0.307311	−	0.197214i
$331$	11.7913	+	20.4231i	0.648108	+	1.12256i	0.983574	+	0.180504i	$0.0577727\pi$
$331$	11.7913	+	20.4231i	0.648108	+	1.12256i	−0.335467	+	0.942052i	$0.608894\pi$
$332$	6.44677	−	11.1661i	0.353812	−	0.612821i
$333$	−4.62614	+	8.01270i	−0.253511	+	0.439093i
$334$	−1.11905	+	0.646084i	−0.0612317	+	0.0353521i
$335$		−	23.4724i		−	1.28244i
$336$		0			0
$337$			10.8348i			0.590212i	0.955465	+	0.295106i	$0.0953549\pi$
$337$			10.8348i			0.590212i	−0.955465	+	0.295106i	$0.904645\pi$
$338$	10.8968	−	6.29129i	0.592709	−	0.342201i
$339$	−6.01362	−	3.47197i	−0.326615	−	0.188571i
$340$	−10.0308	−	5.79129i	−0.543997	−	0.314077i
$341$	25.4635	+	13.1483i	1.37892	+	0.712021i
$342$			4.65743i			0.251845i
$343$		0			0
$344$	7.16515			0.386319
$345$	4.00000	+	6.92820i	0.215353	+	0.373002i
$346$	9.27837	+	5.35687i	0.498808	+	0.287987i
$347$	16.5975	+	9.58258i	0.891001	+	0.514420i	0.874270	−	0.485440i	$-0.161341\pi$
$347$	16.5975	+	9.58258i	0.891001	+	0.514420i	0.0167312	+	0.999860i	$0.494674\pi$
$348$	−0.511238	−	0.885491i	−0.0274052	−	0.0474673i
$349$	24.1185			1.29103			0.645517	−	0.763746i	$-0.276642\pi$
$349$	24.1185			1.29103			0.645517	+	0.763746i	$0.276642\pi$
$350$		0			0
$351$			2.33030i			0.124382i
$352$	2.94694	+	1.52168i	0.157073	+	0.0811059i
$353$	−6.48074	−	3.74166i	−0.344935	−	0.199148i	0.317517	−	0.948253i	$-0.397151\pi$
$353$	−6.48074	−	3.74166i	−0.344935	−	0.199148i	−0.662452	+	0.749104i	$0.730484\pi$
$354$	0.361500	+	0.208712i	0.0192135	+	0.0110929i
$355$	5.36169	−	3.09557i	0.284569	−	0.164296i
$356$		−	9.79796i		−	0.519291i
$357$		0			0
$358$		−	11.1652i		−	0.590097i
$359$	−8.29875	+	4.79129i	−0.437991	+	0.252875i	−0.702745	−	0.711442i	$-0.748043\pi$
$359$	−8.29875	+	4.79129i	−0.437991	+	0.252875i	0.264754	+	0.964316i	$0.414709\pi$
$360$	3.99728	−	6.92349i	0.210675	−	0.364900i
$361$	7.87386	−	13.6379i	0.414414	−	0.717786i
$362$	−2.70511	−	4.68539i	−0.142177	−	0.246258i
$363$	−6.46084	−	2.96073i	−0.339106	−	0.155398i
$364$		0			0
$365$			49.9129i			2.61256i
$366$	−0.626136	−	1.08450i	−0.0327287	−	0.0566877i
$367$	−18.2064	−	10.5115i	−0.950366	−	0.548694i	−0.0571714	−	0.998364i	$-0.518208\pi$
$367$	−18.2064	−	10.5115i	−0.950366	−	0.548694i	−0.893195	+	0.449670i	$0.851541\pi$
$368$	−2.00000	+	3.46410i	−0.104257	+	0.180579i
$369$	12.8261	+	22.2155i	0.667701	+	1.15649i
$370$	11.0901			0.576548
$371$		0			0
$372$	−5.58258			−0.289443
$373$	8.29875	−	4.79129i	0.429693	−	0.248083i	−0.269523	−	0.962994i	$-0.586866\pi$
$373$	8.29875	−	4.79129i	0.429693	−	0.248083i	0.699216	+	0.714911i	$0.253533\pi$
$374$	0.582415	+	12.3960i	0.0301159	+	0.640982i
$375$	0.417424	−	0.723000i	0.0215557	−	0.0373356i
$376$	−4.96640	−	8.60206i	−0.256123	−	0.443617i
$377$			1.02248i			0.0526602i
$378$		0			0
$379$	−22.3303			−1.14703			−0.573515	−	0.819195i	$-0.694421\pi$
$379$	−22.3303			−1.14703			−0.573515	+	0.819195i	$0.694421\pi$
$380$	4.83465	−	2.79129i	0.248012	−	0.143190i
$381$	−1.15732	+	2.00454i	−0.0592914	+	0.102696i
$382$	−15.5885	−	9.00000i	−0.797575	−	0.460480i
$383$	17.0873	−	9.86538i	0.873122	−	0.504097i	0.00473782	−	0.999989i	$-0.498492\pi$
$383$	17.0873	−	9.86538i	0.873122	−	0.504097i	0.868385	+	0.495891i	$0.165159\pi$
$384$	−0.646084			−0.0329703
$385$		0			0
$386$	16.3303			0.831191
$387$	−16.0254	+	9.25227i	−0.814617	+	0.470319i
$388$	−7.36623	−	4.25290i	−0.373964	−	0.215908i
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	−0.964490	−	0.264120i	$-0.914918\pi$
$389$	−5.00000	+	8.66025i	−0.253510	+	0.439092i	0.710980	+	0.703213i	$0.248252\pi$
$390$	1.11905	−	0.646084i	0.0566653	−	0.0327157i
$391$	−14.9666			−0.756895
$392$		0			0
$393$		−	10.8348i		−	0.546546i
$394$	−4.37386	−	7.57575i	−0.220352	−	0.381661i
$395$	−6.19115	+	10.7234i	−0.311510	+	0.539552i
$396$	−8.55600	+	0.401996i	−0.429955	+	0.0202010i
$397$	−23.8940	+	13.7952i	−1.19921	+	0.692363i	−0.960379	−	0.278699i	$-0.910097\pi$
$397$	−23.8940	+	13.7952i	−1.19921	+	0.692363i	−0.238829	+	0.971062i	$0.576764\pi$
$398$	−9.66311			−0.484368
$399$		0			0
$400$	−4.58258			−0.229129
$401$	−3.79129	−	6.56670i	−0.189328	−	0.327926i	0.755698	−	0.654920i	$-0.227298\pi$
$401$	−3.79129	−	6.56670i	−0.189328	−	0.327926i	−0.945026	+	0.326994i	$0.893964\pi$
$402$	2.44949	−	4.24264i	0.122169	−	0.211604i
$403$	4.83465	+	2.79129i	0.240831	+	0.139044i
$404$	−5.86811	−	10.1639i	−0.291949	−	0.505671i
$405$			16.7700i			0.833310i
$406$		0			0
$407$	−6.41742	−	10.0000i	−0.318100	−	0.495682i
$408$	−1.20871	−	2.09355i	−0.0598402	−	0.103646i
$409$	2.51691	−	4.35942i	0.124453	−	0.215559i	−0.797066	−	0.603892i	$-0.793616\pi$
$409$	2.51691	−	4.35942i	0.124453	−	0.215559i	0.921519	+	0.388333i	$0.126949\pi$
$410$	15.3739	−	26.6283i	0.759261	−	1.31508i
$411$	−1.77098	+	1.02248i	−0.0873561	+	0.0504350i
$412$		−	6.05630i		−	0.298373i
$413$		0			0
$414$		−	10.3303i		−	0.507707i
$415$	34.5656	−	19.9564i	1.69676	−	0.979623i
$416$	0.559525	+	0.323042i	0.0274330	+	0.0158384i
$417$	8.66025	+	5.00000i	0.424094	+	0.244851i
$418$	−5.31454	−	2.74421i	−0.259943	−	0.134224i
$419$			13.0284i			0.636478i	0.948011	+	0.318239i	$0.103091\pi$
$419$			13.0284i			0.636478i	−0.948011	+	0.318239i	$0.896909\pi$
$420$		0			0
$421$	7.58258			0.369552			0.184776	−	0.982781i	$-0.440844\pi$
$421$	7.58258			0.369552			0.184776	+	0.982781i	$0.440844\pi$
$422$	−8.37386	−	14.5040i	−0.407633	−	0.706042i
$423$	22.2155	+	12.8261i	1.08015	+	0.623627i
$424$	10.0308	+	5.79129i	0.487139	+	0.281250i
$425$	−8.57321	−	14.8492i	−0.415862	−	0.720294i
$426$	1.29217			0.0626057
$427$		0			0
$428$		−	17.5826i		−	0.849886i
$429$	−1.23013	−	0.635187i	−0.0593911	−	0.0306671i
$430$	19.2087	+	11.0901i	0.926324	+	0.534813i
$431$	24.1733	+	13.9564i	1.16439	+	0.672258i	0.952351	−	0.305004i	$-0.0986579\pi$
$431$	24.1733	+	13.9564i	1.16439	+	0.672258i	0.212034	+	0.977262i	$0.431991\pi$
$432$	3.12359	−	1.80341i	0.150284	−	0.0867664i
$433$			35.5850i			1.71011i	0.518540	+	0.855054i	$0.326476\pi$
$433$			35.5850i			1.71011i	−0.518540	+	0.855054i	$0.673524\pi$
$434$		0			0
$435$		−	3.16515i		−	0.151757i
$436$	−14.8655	+	8.58258i	−0.711926	+	0.411031i
$437$	3.60681	−	6.24718i	0.172537	−	0.298843i
$438$	−5.20871	+	9.02175i	−0.248882	+	0.431076i
$439$	−8.64064	−	14.9660i	−0.412395	−	0.714289i	0.582756	−	0.812647i	$-0.301974\pi$
$439$	−8.64064	−	14.9660i	−0.412395	−	0.714289i	−0.995151	+	0.0983579i	$0.968641\pi$
$440$	5.54506	+	8.64064i	0.264351	+	0.411926i
$441$		0			0
$442$			2.41742i			0.114985i
$443$	−7.58258	−	13.1334i	−0.360259	−	0.623987i	0.627744	−	0.778420i	$-0.283978\pi$
$443$	−7.58258	−	13.1334i	−0.360259	−	0.623987i	−0.988003	+	0.154433i	$0.950645\pi$
$444$	2.00454	+	1.15732i	0.0951313	+	0.0549241i
$445$	15.1652	−	26.2668i	0.718897	−	1.24517i
$446$	−8.06198	−	13.9638i	−0.381746	−	0.661203i
$447$	9.04517			0.427822
$448$		0			0
$449$	31.1652			1.47077			0.735387	−	0.677647i	$-0.237000\pi$
$449$	31.1652			1.47077			0.735387	+	0.677647i	$0.237000\pi$
$450$	10.2493	−	5.91742i	0.483156	−	0.278950i
$451$	−32.9071	+	1.54611i	−1.54953	+	0.0728034i
$452$	5.37386	−	9.30780i	0.252765	−	0.437802i
$453$	1.80341	+	3.12359i	0.0847314	+	0.146759i
$454$			0.511238i			0.0239936i
$455$		0			0
$456$	1.16515			0.0545632
$457$	28.7219	−	16.5826i	1.34355	−	0.775700i	0.356225	−	0.934400i	$-0.384064\pi$
$457$	28.7219	−	16.5826i	1.34355	−	0.775700i	0.987327	+	0.158700i	$0.0507302\pi$
$458$	2.83995	−	4.91895i	0.132702	−	0.229847i
$459$	11.6874	+	6.74773i	0.545521	+	0.314957i
$460$	−10.7234	+	6.19115i	−0.499980	+	0.288664i
$461$	30.0400			1.39910			0.699550	−	0.714583i	$-0.253384\pi$
$461$	30.0400			1.39910			0.699550	+	0.714583i	$0.253384\pi$
$462$		0			0
$463$	5.16515			0.240045			0.120022	−	0.992771i	$-0.461703\pi$
$463$	5.16515			0.240045			0.120022	+	0.992771i	$0.461703\pi$
$464$	1.37055	−	0.791288i	0.0636262	−	0.0367346i
$465$	−14.9660	−	8.64064i	−0.694033	−	0.400700i
$466$	13.5826	−	23.5257i	0.629201	−	1.08981i
$467$	−10.1639	+	5.86811i	−0.470327	+	0.271544i	−0.716377	−	0.697714i	$-0.754201\pi$
$467$	−10.1639	+	5.86811i	−0.470327	+	0.271544i	0.246049	+	0.969257i	$0.420867\pi$
$468$	−1.66856			−0.0771292
$469$		0			0
$470$		−	30.7477i		−	1.41829i
$471$	−4.25227	−	7.36515i	−0.195934	−	0.339368i
$472$	−0.323042	+	0.559525i	−0.0148692	+	0.0257542i
$473$	−1.11530	−	23.7379i	−0.0512818	−	1.09147i
$474$	−2.23810	+	1.29217i	−0.102799	+	0.0593512i
$475$	8.26424			0.379190
$476$		0			0
$477$	−29.9129			−1.36962
$478$	4.20871	+	7.28970i	0.192502	+	0.333423i
$479$	−15.4779	+	26.8085i	−0.707202	+	1.22491i	0.258689	+	0.965961i	$0.416709\pi$
$479$	−15.4779	+	26.8085i	−0.707202	+	1.22491i	−0.965891	+	0.258949i	$0.916624\pi$
$480$	−1.73205	−	1.00000i	−0.0790569	−	0.0456435i
$481$	−1.15732	−	2.00454i	−0.0527693	−	0.0913992i
$482$			3.47197i			0.158144i
$483$		0			0
$484$	4.58258	−	10.0000i	0.208299	−	0.454545i
$485$	−13.1652	−	22.8027i	−0.597799	−	1.03542i
$486$	−7.16027	+	12.4020i	−0.324797	+	0.562564i
$487$	−10.7477	+	18.6156i	−0.487026	+	0.843554i	−0.999889	−	0.0149168i	$-0.995252\pi$
$487$	−10.7477	+	18.6156i	−0.487026	+	0.843554i	0.512863	+	0.858471i	$0.328585\pi$
$488$	1.67858	−	0.969126i	0.0759855	−	0.0438703i
$489$			2.58434i			0.116868i
$490$		0			0
$491$			33.4955i			1.51163i	0.654786	+	0.755814i	$0.272759\pi$
$491$			33.4955i			1.51163i	−0.654786	+	0.755814i	$0.727241\pi$
$492$	5.55765	−	3.20871i	0.250558	−	0.144660i
$493$	5.12813	+	2.96073i	0.230959	+	0.133344i
$494$	−1.00905	−	0.582576i	−0.0453993	−	0.0262113i
$495$	−23.5595	−	12.1652i	−1.05892	−	0.546784i
$496$		−	8.64064i		−	0.387976i
$497$		0			0
$498$	8.33030			0.373290
$499$	8.95644	+	15.5130i	0.400945	+	0.694458i	0.993840	−	0.110822i	$-0.0353484\pi$
$499$	8.95644	+	15.5130i	0.400945	+	0.694458i	−0.592895	+	0.805280i	$0.702015\pi$
$500$	1.11905	+	0.646084i	0.0500454	+	0.0288937i
$501$	−0.723000	−	0.417424i	−0.0323013	−	0.0186491i
$502$	−12.0593	−	20.8872i	−0.538231	−	0.932243i
$503$	−17.0116			−0.758509			−0.379254	−	0.925292i	$-0.623820\pi$
$503$	−17.0116			−0.758509			−0.379254	+	0.925292i	$0.623820\pi$
$504$		0			0
$505$		−	36.3303i		−	1.61668i
$506$	11.7878	+	6.08673i	0.524031	+	0.270588i
$507$	7.04027	+	4.06470i	0.312669	+	0.180520i
$508$	−3.10260	−	1.79129i	−0.137656	−	0.0794755i
$509$	0.676305	−	0.390465i	0.0299767	−	0.0173070i	−0.484937	−	0.874549i	$-0.661157\pi$
$509$	0.676305	−	0.390465i	0.0299767	−	0.0173070i	0.514913	+	0.857242i	$0.327824\pi$
$510$		−	7.48331i		−	0.331367i
$511$		0			0
$512$		−	1.00000i		−	0.0441942i
$513$	−5.63310	+	3.25227i	−0.248708	+	0.143591i
$514$	2.44949	−	4.24264i	0.108042	−	0.187135i
$515$	9.37386	−	16.2360i	0.413062	−	0.715444i
$516$	2.31464	+	4.00908i	0.101897	+	0.176490i
$517$	−27.7253	+	17.7925i	−1.21936	+	0.782514i
$518$		0			0
$519$			6.92197i			0.303841i
$520$	1.00000	+	1.73205i	0.0438529	+	0.0759555i
$521$	24.3368	+	14.0509i	1.06621	+	0.615579i	0.927145	−	0.374703i	$-0.122255\pi$
$521$	24.3368	+	14.0509i	1.06621	+	0.615579i	0.139070	+	0.990283i	$0.455589\pi$
$522$	−2.04356	+	3.53955i	−0.0894442	+	0.154922i
$523$	7.22770	+	12.5187i	0.316045	+	0.547406i	0.979659	−	0.200669i	$-0.0643116\pi$
$523$	7.22770	+	12.5187i	0.316045	+	0.547406i	−0.663614	+	0.748075i	$0.730978\pi$
$524$	16.7700			0.732602
$525$		0			0
$526$	−8.33030			−0.363218
$527$	27.9989	−	16.1652i	1.21965	−	0.704165i
$528$	0.100567	+	2.14046i	0.00437663	+	0.0931514i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	17.9274	+	31.0511i	0.778715	+	1.34877i
$531$		−	1.66856i		−	0.0724094i
$532$		0			0
$533$	−6.41742			−0.277970
$534$	5.48220	−	3.16515i	0.237238	−	0.136969i
$535$	27.2141	−	47.1362i	1.17657	−	2.03787i
$536$	6.56670	+	3.79129i	0.283638	+	0.163759i
$537$	6.24718	−	3.60681i	0.269586	−	0.155645i
$538$	−16.5003			−0.711380
$539$		0			0
$540$	11.1652			0.480472
$541$	−31.8245	+	18.3739i	−1.36824	+	0.789954i	−0.990703	−	0.136040i	$-0.956562\pi$
$541$	−31.8245	+	18.3739i	−1.36824	+	0.789954i	−0.377537	+	0.925994i	$0.623229\pi$
$542$	−4.24264	−	2.44949i	−0.182237	−	0.105215i
$543$	1.74773	−	3.02715i	0.0750021	−	0.129908i
$544$	3.24037	−	1.87083i	0.138930	−	0.0802111i
$545$	−53.1360			−2.27610
$546$		0			0
$547$		−	24.7477i		−	1.05814i	−0.848579	−	0.529068i	$-0.822542\pi$
$547$		−	24.7477i		−	1.05814i	0.848579	−	0.529068i	$-0.177458\pi$
$548$	−1.58258	−	2.74110i	−0.0676043	−	0.117094i
$549$	−2.50284	+	4.33505i	−0.106819	+	0.185015i
$550$	0.713309	+	15.1819i	0.0304156	+	0.647360i
$551$	−2.47166	+	1.42701i	−0.105296	+	0.0607928i
$552$	−2.58434			−0.109997
$553$		0			0
$554$	2.00000			0.0849719
$555$	3.58258	+	6.20520i	0.152072	+	0.263396i
$556$	−7.73893	+	13.4042i	−0.328204	+	0.568466i
$557$	31.1015	+	17.9564i	1.31781	+	0.760839i	0.983376	−	0.181580i	$-0.0581211\pi$
$557$	31.1015	+	17.9564i	1.31781	+	0.760839i	0.334435	+	0.942419i	$0.391454\pi$
$558$	11.1575	+	19.3254i	0.472337	+	0.818111i
$559$		−	4.62929i		−	0.195798i
$560$		0			0
$561$	−6.74773	+	4.33030i	−0.284889	+	0.182826i
$562$	−5.58258	−	9.66930i	−0.235487	−	0.407875i
$563$	−11.8570	+	20.5369i	−0.499712	+	0.865527i	−1.00000		0.000332178i	$-0.999894\pi$
$563$	−11.8570	+	20.5369i	−0.499712	+	0.865527i	0.500288	+	0.865859i	$0.333228\pi$
$564$	3.20871	−	5.55765i	0.135111	−	0.234019i
$565$	28.8130	−	16.6352i	1.21217	−	0.699848i
$566$			18.0622i			0.759211i
$567$		0			0
$568$			2.00000i			0.0839181i
$569$	34.2041	−	19.7477i	1.43391	−	0.827868i	0.436493	−	0.899708i	$-0.356220\pi$
$569$	34.2041	−	19.7477i	1.43391	−	0.827868i	0.997416	+	0.0718399i	$0.0228871\pi$
$570$	3.12359	+	1.80341i	0.130833	+	0.0755364i
$571$	4.83465	+	2.79129i	0.202324	+	0.116812i	0.597739	−	0.801691i	$-0.296066\pi$
$571$	4.83465	+	2.79129i	0.202324	+	0.116812i	−0.395415	+	0.918503i	$0.629399\pi$
$572$	0.983134	−	1.90397i	0.0411069	−	0.0796091i
$573$		−	11.6295i		−	0.485830i
$574$		0			0
$575$	−18.3303			−0.764426
$576$	1.29129	+	2.23658i	0.0538037	+	0.0931907i
$577$	−25.6894	−	14.8318i	−1.06946	−	0.617455i	−0.141429	−	0.989948i	$-0.545170\pi$
$577$	−25.6894	−	14.8318i	−1.06946	−	0.617455i	−0.928035	+	0.372493i	$0.878503\pi$
$578$	−2.59808	−	1.50000i	−0.108066	−	0.0623918i
$579$	5.27537	+	9.13721i	0.219237	+	0.379730i
$580$	4.89898			0.203419
$581$		0			0
$582$		−	5.49545i		−	0.227794i
$583$	17.6250	−	34.1332i	0.729953	−	1.41365i
$584$	−13.9638	−	8.06198i	−0.577824	−	0.333607i
$585$	−4.47315	−	2.58258i	−0.184942	−	0.106776i
$586$	−21.7727	+	12.5705i	−0.899423	+	0.519282i
$587$		−	39.0851i		−	1.61322i	−0.591087	−	0.806608i	$-0.701301\pi$
$587$		−	39.0851i		−	1.61322i	0.591087	−	0.806608i	$-0.298699\pi$
$588$		0			0
$589$			15.5826i			0.642069i
$590$	−1.73205	+	1.00000i	−0.0713074	+	0.0411693i
$591$	2.82588	−	4.89457i	0.116241	−	0.201336i
$592$	−1.79129	+	3.10260i	−0.0736215	+	0.127516i
$593$	7.41589	+	12.8447i	0.304534	+	0.527469i	0.977158	−	0.212516i	$-0.0681659\pi$
$593$	7.41589	+	12.8447i	0.304534	+	0.527469i	−0.672623	+	0.739985i	$0.734833\pi$
$594$	−6.46084	−	10.0677i	−0.265091	−	0.413081i
$595$		0			0
$596$			14.0000i			0.573462i
$597$	−3.12159	−	5.40675i	−0.127758	−	0.221284i
$598$	2.23810	+	1.29217i	0.0915227	+	0.0528407i
$599$	10.5826	−	18.3296i	0.432392	−	0.748925i	−0.564686	−	0.825306i	$-0.691003\pi$
$599$	10.5826	−	18.3296i	0.432392	−	0.748925i	0.997079	+	0.0763801i	$0.0243362\pi$
$600$	−1.48036	−	2.56407i	−0.0604356	−	0.104678i
$601$	21.0229			0.857543			0.428772	−	0.903413i	$-0.358947\pi$
$601$	21.0229			0.857543			0.428772	+	0.903413i	$0.358947\pi$
$602$		0			0
$603$	−19.5826			−0.797464
$604$	−4.83465	+	2.79129i	−0.196719	+	0.113576i
$605$	27.7630	−	19.7156i	1.12873	−	0.801553i
$606$	3.79129	−	6.56670i	0.154011	−	0.266754i
$607$	−1.02248	−	1.77098i	−0.0415010	−	0.0718819i	0.844529	−	0.535510i	$-0.179881\pi$
$607$	−1.02248	−	1.77098i	−0.0415010	−	0.0718819i	−0.886030	+	0.463628i	$0.846547\pi$
$608$			1.80341i			0.0731378i
$609$		0			0
$610$	6.00000			0.242933
$611$	−5.55765	+	3.20871i	−0.224839	+	0.129811i
$612$	−4.83156	+	8.36850i	−0.195304	+	0.338277i
$613$	−27.6374	−	15.9564i	−1.11626	−	0.644475i	−0.175818	−	0.984423i	$-0.556257\pi$
$613$	−27.6374	−	15.9564i	−1.11626	−	0.644475i	−0.940444	+	0.339948i	$0.889590\pi$
$614$	9.16159	−	5.28944i	0.369732	−	0.213465i
$615$	19.8656			0.801059
$616$		0			0
$617$	−19.9129			−0.801662			−0.400831	−	0.916152i	$-0.631279\pi$
$617$	−19.9129			−0.801662			−0.400831	+	0.916152i	$0.631279\pi$
$618$	3.38865	−	1.95644i	0.136312	−	0.0786995i
$619$	15.5255	+	8.96368i	0.624024	+	0.360281i	0.778434	−	0.627726i	$-0.216014\pi$
$619$	15.5255	+	8.96368i	0.624024	+	0.360281i	−0.154410	+	0.988007i	$0.549348\pi$
$620$	13.3739	−	23.1642i	0.537107	−	0.930297i
$621$	12.4944	−	7.21362i	0.501382	−	0.289473i
$622$	5.03383			0.201838
$623$		0			0
$624$			0.417424i			0.0167103i
$625$	13.4564	+	23.3072i	0.538258	+	0.932289i
$626$	11.7362	−	20.3277i	0.469073	−	0.812459i
$627$	−0.181364	−	3.86011i	−0.00724297	−	0.154158i
$628$	11.3997	−	6.58161i	0.454897	−	0.262635i
$629$	−13.4048			−0.534483
$630$		0			0
$631$	13.1652			0.524096			0.262048	−	0.965055i	$-0.415602\pi$
$631$	13.1652			0.524096			0.262048	+	0.965055i	$0.415602\pi$
$632$	−2.00000	−	3.46410i	−0.0795557	−	0.137795i
$633$	5.41022	−	9.37077i	0.215037	−	0.372455i
$634$	7.93725	+	4.58258i	0.315229	+	0.181997i
$635$	−5.54506	−	9.60433i	−0.220049	−	0.381136i
$636$			7.48331i			0.296733i
$637$		0			0
$638$	−2.83485	−	4.41742i	−0.112233	−	0.174888i
$639$	−2.58258	−	4.47315i	−0.102165	−	0.176955i
$640$	1.54779	−	2.68085i	0.0611816	−	0.105970i
$641$	7.95644	−	13.7810i	0.314260	−	0.544315i	−0.665020	−	0.746826i	$-0.731577\pi$
$641$	7.95644	−	13.7810i	0.314260	−	0.544315i	0.979280	+	0.202511i	$0.0649101\pi$
$642$	9.83789	−	5.67991i	0.388271	−	0.224168i
$643$		−	9.42157i		−	0.371550i	−0.982592	−	0.185775i	$-0.940520\pi$
$643$		−	9.42157i		−	0.371550i	0.982592	−	0.185775i	$-0.0594796\pi$
$644$		0			0
$645$			14.3303i			0.564255i
$646$	−5.84370	+	3.37386i	−0.229917	+	0.132743i
$647$	26.0397	+	15.0341i	1.02373	+	0.591050i	0.915182	−	0.403042i	$-0.132047\pi$
$647$	26.0397	+	15.0341i	1.02373	+	0.591050i	0.108546	+	0.994091i	$0.465380\pi$
$648$	−4.69163	−	2.70871i	−0.184305	−	0.106408i
$649$	1.90397	+	0.983134i	0.0747375	+	0.0385914i
$650$			2.96073i			0.116129i
$651$		0			0
$652$	−4.00000			−0.156652
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$	−9.60433	−	5.54506i	−0.375559	−	0.216829i
$655$	44.9579	+	25.9564i	1.75665	+	1.01420i
$656$	4.96640	+	8.60206i	0.193905	+	0.335854i
$657$	41.6413			1.62458
$658$		0			0
$659$		−	6.33030i		−	0.246594i	−0.992370	−	0.123297i	$-0.960653\pi$
$659$		−	6.33030i		−	0.246594i	0.992370	−	0.123297i	$-0.0393467\pi$
$660$	−3.04336	+	5.89389i	−0.118463	+	0.229419i
$661$	−7.15705	−	4.13212i	−0.278377	−	0.160721i	0.354312	−	0.935127i	$-0.384715\pi$
$661$	−7.15705	−	4.13212i	−0.278377	−	0.160721i	−0.632688	+	0.774407i	$0.718049\pi$
$662$	−20.4231	−	11.7913i	−0.793767	−	0.458281i
$663$	−1.35261	+	0.780929i	−0.0525310	+	0.0303288i
$664$			12.8935i			0.500366i
$665$		0			0
$666$		−	9.25227i		−	0.358518i
$667$	5.48220	−	3.16515i	0.212272	−	0.122555i
$668$	0.646084	−	1.11905i	0.0249977	−	0.0432973i
$669$	5.20871	−	9.02175i	0.201380	−	0.348801i
$670$	11.7362	+	20.3277i	0.453409	+	0.785328i
$671$	−3.47197	−	5.41022i	−0.134034	−	0.208859i
$672$		0			0
$673$		−	18.3303i		−	0.706581i	−0.935514	−	0.353291i	$-0.885063\pi$
$673$		−	18.3303i		−	0.706581i	0.935514	−	0.353291i	$-0.114937\pi$
$674$	−5.41742	−	9.38325i	−0.208671	−	0.361429i
$675$	14.3141	+	8.26424i	0.550950	+	0.318091i
$676$	−6.29129	+	10.8968i	−0.241973	+	0.419109i
$677$	−2.63769	−	4.56861i	−0.101375	−	0.175586i	0.810877	−	0.585217i	$-0.198991\pi$
$677$	−2.63769	−	4.56861i	−0.101375	−	0.175586i	−0.912251	+	0.409631i	$0.865657\pi$
$678$	6.94393			0.266680
$679$		0			0
$680$	11.5826			0.444172
$681$	−0.286051	+	0.165151i	−0.0109615	+	0.00632862i
$682$	−28.6262	+	1.34497i	−1.09615	+	0.0515017i
$683$	4.74773	−	8.22330i	0.181667	−	0.314656i	−0.760782	−	0.649008i	$-0.775184\pi$
$683$	4.74773	−	8.22330i	0.181667	−	0.314656i	0.942448	+	0.334352i	$0.108517\pi$
$684$	−2.32872	−	4.03345i	−0.0890407	−	0.154223i
$685$		−	9.79796i		−	0.374361i
$686$		0			0
$687$	3.66970			0.140008
$688$	−6.20520	+	3.58258i	−0.236571	+	0.136584i
$689$	3.74166	−	6.48074i	0.142546	−	0.246897i
$690$	−6.92820	−	4.00000i	−0.263752	−	0.152277i
$691$	−3.44956	+	1.99160i	−0.131227	+	0.0757641i	−0.564177	−	0.825654i	$-0.690806\pi$
$691$	−3.44956	+	1.99160i	−0.131227	+	0.0757641i	0.432949	+	0.901418i	$0.357473\pi$
$692$	−10.7137			−0.407275
$693$		0			0
$694$	−19.1652			−0.727499
$695$	−41.4938	+	23.9564i	−1.57395	+	0.908720i
$696$	0.885491	+	0.511238i	0.0335644	+	0.0193784i
$697$	−18.5826	+	32.1860i	−0.703865	+	1.21913i
$698$	−20.8872	+	12.0593i	−0.790594	+	0.456449i
$699$	17.5510			0.663838
$700$		0			0
$701$			12.3303i			0.465709i	0.972512	+	0.232855i	$0.0748066\pi$
$701$			12.3303i			0.465709i	−0.972512	+	0.232855i	$0.925193\pi$
$702$	−1.16515	−	2.01810i	−0.0439758	−	0.0761683i
$703$	3.23042	−	5.59525i	0.121838	−	0.211029i
$704$	−3.31297	+	0.155657i	−0.124862	+	0.00586654i
$705$	17.2041	−	9.93280i	0.647945	−	0.374091i
$706$	7.48331			0.281638
$707$		0			0
$708$	−0.417424			−0.0156878
$709$	−26.1652	−	45.3194i	−0.982653	−	1.70200i	−0.651935	−	0.758275i	$-0.726042\pi$
$709$	−26.1652	−	45.3194i	−0.982653	−	1.70200i	−0.330718	−	0.943730i	$-0.607291\pi$
$710$	−3.09557	+	5.36169i	−0.116175	+	0.201221i
$711$	8.94630	+	5.16515i	0.335513	+	0.193708i
$712$	4.89898	+	8.48528i	0.183597	+	0.317999i
$713$		−	34.5625i		−	1.29438i
$714$		0			0
$715$	5.58258	−	3.58258i	0.208776	−	0.133981i
$716$	5.58258	+	9.66930i	0.208631	+	0.361359i
$717$	−2.71918	+	4.70976i	−0.101550	+	0.175889i
$718$	4.79129	−	8.29875i	0.178809	−	0.309707i
$719$	−20.2109	+	11.6688i	−0.753741	+	0.435172i	−0.827044	−	0.562137i	$-0.809979\pi$
$719$	−20.2109	+	11.6688i	−0.753741	+	0.435172i	0.0733033	+	0.997310i	$0.476646\pi$
$720$			7.99455i			0.297939i
$721$		0			0
$722$			15.7477i			0.586070i
$723$	−1.94265	+	1.12159i	−0.0722480	+	0.0417124i
$724$	4.68539	+	2.70511i	0.174131	+	0.100535i
$725$	6.28065	+	3.62614i	0.233258	+	0.134671i
$726$	7.07561	−	0.666353i	0.262601	−	0.0247307i
$727$			37.5514i			1.39271i	0.717700	+	0.696353i	$0.245195\pi$
$727$			37.5514i			1.39271i	−0.717700	+	0.696353i	$0.754805\pi$
$728$		0			0
$729$	7.00000			0.259259
$730$	−24.9564	−	43.2258i	−0.923679	−	1.59986i
$731$	−23.2177	−	13.4048i	−0.858739	−	0.495793i
$732$	1.08450	+	0.626136i	0.0400843	+	0.0231427i
$733$	−5.35687	−	9.27837i	−0.197860	−	0.342704i	0.749974	−	0.661467i	$-0.230066\pi$
$733$	−5.35687	−	9.27837i	−0.197860	−	0.342704i	−0.947834	+	0.318763i	$0.896733\pi$
$734$	21.0229			0.775971
$735$		0			0
$736$		−	4.00000i		−	0.147442i
$737$	11.5383	−	22.3454i	0.425018	−	0.823105i
$738$	−22.2155	−	12.8261i	−0.817763	−	0.472136i
$739$	−1.37055	−	0.791288i	−0.0504165	−	0.0291080i	0.474580	−	0.880212i	$-0.342600\pi$
$739$	−1.37055	−	0.791288i	−0.0504165	−	0.0291080i	−0.524996	+	0.851104i	$0.675933\pi$
$740$	−9.60433	+	5.54506i	−0.353062	+	0.203841i
$741$		−	0.752785i		−	0.0276543i
$742$		0			0
$743$			1.91288i			0.0701767i	0.999384	+	0.0350884i	$0.0111713\pi$
$743$			1.91288i			0.0701767i	−0.999384	+	0.0350884i	$0.988829\pi$
$744$	4.83465	−	2.79129i	0.177247	−	0.102334i
$745$	−21.6690	+	37.5318i	−0.793891	+	1.37506i
$746$	−4.79129	+	8.29875i	−0.175422	+	0.303839i
$747$	−16.6493	−	28.8374i	−0.609165	−	1.05510i
$748$	−6.70239	−	10.4440i	−0.245063	−	0.381872i
$749$		0			0
$750$			0.834849i			0.0304844i
$751$	20.7477	+	35.9361i	0.757095	+	1.31133i	0.944326	+	0.329012i	$0.106716\pi$
$751$	20.7477	+	35.9361i	0.757095	+	1.31133i	−0.187231	+	0.982316i	$0.559951\pi$
$752$	8.60206	+	4.96640i	0.313685	+	0.181106i
$753$	7.79129	−	13.4949i	0.283930	−	0.491782i
$754$	−0.511238	−	0.885491i	−0.0186182	−	0.0322477i
$755$	−17.2813			−0.628930
$756$		0			0
$757$	−30.8348			−1.12071			−0.560356	−	0.828252i	$-0.689336\pi$
$757$	−30.8348			−1.12071			−0.560356	+	0.828252i	$0.689336\pi$
$758$	19.3386	−	11.1652i	0.702410	−	0.405537i
$759$	0.402270	+	8.56183i	0.0146015	+	0.310775i
$760$	−2.79129	+	4.83465i	−0.101251	+	0.175371i
$761$	−14.1183	−	24.4536i	−0.511787	−	0.886441i	−0.999907	−	0.0136645i	$-0.995650\pi$
$761$	−14.1183	−	24.4536i	−0.511787	−	0.886441i	0.488119	−	0.872777i	$-0.337683\pi$
$762$		−	2.31464i		−	0.0838507i
$763$		0			0
$764$	18.0000			0.651217
$765$	−25.9053	+	14.9564i	−0.936609	+	0.540751i
$766$	−9.86538	+	17.0873i	−0.356451	+	0.617391i
$767$	0.361500	+	0.208712i	0.0130530	+	0.00753616i
$768$	0.559525	−	0.323042i	0.0201901	−	0.0116568i
$769$	−15.1015			−0.544573			−0.272287	−	0.962216i	$-0.587780\pi$
$769$	−15.1015			−0.544573			−0.272287	+	0.962216i	$0.587780\pi$
$770$		0			0
$771$	3.16515			0.113990
$772$	−14.1425	+	8.16515i	−0.508998	+	0.293870i
$773$	−8.69447	−	5.01975i	−0.312718	−	0.180548i	0.335424	−	0.942067i	$-0.391120\pi$
$773$	−8.69447	−	5.01975i	−0.312718	−	0.180548i	−0.648142	+	0.761519i	$0.724454\pi$
$774$	9.25227	−	16.0254i	0.332566	−	0.576021i
$775$	34.2915	−	19.7982i	1.23179	−	0.711172i
$776$	8.50579			0.305340
$777$		0			0
$778$		−	10.0000i		−	0.358517i
$779$	−8.95644	−	15.5130i	−0.320898	−	0.555811i
$780$	−0.646084	+	1.11905i	−0.0231335	+	0.0400684i
$781$	6.62594	−	0.311314i	0.237095	−	0.0111397i
$782$	12.9615	−	7.48331i	0.463502	−	0.267603i
$783$	−5.70805			−0.203989
$784$		0			0
$785$	40.7477			1.45435
$786$	5.41742	+	9.38325i	0.193233	+	0.334690i
$787$	−11.6154	+	20.1185i	−0.414046	+	0.717148i	−0.995328	−	0.0965541i	$-0.969218\pi$
$787$	−11.6154	+	20.1185i	−0.414046	+	0.717148i	0.581282	+	0.813702i	$0.302551\pi$
$788$	7.57575	+	4.37386i	0.269875	+	0.155812i
$789$	−2.69104	−	4.66101i	−0.0958035	−	0.165936i
$790$		−	12.3823i		−	0.440542i
$791$		0			0
$792$	7.20871	−	4.62614i	0.256150	−	0.164383i
$793$	−0.626136	−	1.08450i	−0.0222348	−	0.0385117i
$794$	13.7952	−	23.8940i	0.489575	−	0.847968i
$795$	−11.5826	+	20.0616i	−0.410792	+	0.711512i
$796$	8.36850	−	4.83156i	0.296614	−	0.171250i
$797$			25.0061i			0.885763i	0.896580	+	0.442881i	$0.146044\pi$
$797$			25.0061i			0.885763i	−0.896580	+	0.442881i	$0.853956\pi$
$798$		0			0
$799$			37.1652i			1.31481i
$800$	3.96863	−	2.29129i	0.140312	−	0.0810093i
$801$	−21.9139	−	12.6520i	−0.774289	−	0.447036i
$802$	6.56670	+	3.79129i	0.231878	+	0.133875i
$803$	−24.5355	+	47.5164i	−0.865840	+	1.67682i
$804$			4.89898i			0.172774i
$805$		0			0
$806$	−5.58258			−0.196638
$807$	−5.33030	−	9.23236i	−0.187636	−	0.324994i
$808$	10.1639	+	5.86811i	0.357563	+	0.206439i
$809$	−12.8474	−	7.41742i	−0.451689	−	0.260783i	0.256854	−	0.966450i	$-0.417314\pi$
$809$	−12.8474	−	7.41742i	−0.451689	−	0.260783i	−0.708543	+	0.705667i	$0.750647\pi$
$810$	−8.38502	−	14.5233i	−0.294619	−	0.510296i
$811$	3.36526			0.118170			0.0590852	−	0.998253i	$-0.481182\pi$
$811$	3.36526			0.118170			0.0590852	+	0.998253i	$0.481182\pi$
$812$		0			0
$813$		−	3.16515i		−	0.111007i
$814$	10.5577	+	5.45154i	0.370046	+	0.191076i
$815$	−10.7234	−	6.19115i	−0.375624	−	0.216866i
$816$	2.09355	+	1.20871i	0.0732889	+	0.0423134i
$817$	11.1905	−	6.46084i	0.391506	−	0.226036i
$818$			5.03383i			0.176004i
$819$		0			0
$820$			30.7477i			1.07376i
$821$	−37.6682	+	21.7477i	−1.31463	+	0.759001i	−0.982859	−	0.184360i	$-0.940979\pi$
$821$	−37.6682	+	21.7477i	−1.31463	+	0.759001i	−0.331769	+	0.943361i	$0.607646\pi$
$822$	1.02248	−	1.77098i	0.0356630	−	0.0617701i
$823$	1.83485	−	3.17805i	0.0639588	−	0.110780i	−0.832273	−	0.554366i	$-0.812961\pi$
$823$	1.83485	−	3.17805i	0.0639588	−	0.110780i	0.896232	+	0.443586i	$0.146294\pi$
$824$	3.02815	+	5.24491i	0.105491	+	0.182715i
$825$	−8.26424	+	5.30352i	−0.287724	+	0.184645i
$826$		0			0
$827$			3.16515i			0.110063i	0.998485	+	0.0550315i	$0.0175259\pi$
$827$			3.16515i			0.110063i	−0.998485	+	0.0550315i	$0.982474\pi$
$828$	5.16515	+	8.94630i	0.179501	+	0.310906i
$829$	−6.92349	−	3.99728i	−0.240463	−	0.138831i	0.374927	−	0.927054i	$-0.377668\pi$
$829$	−6.92349	−	3.99728i	−0.240463	−	0.138831i	−0.615389	+	0.788223i	$0.711001\pi$
$830$	−19.9564	+	34.5656i	−0.692698	+	1.19979i
$831$	0.646084	+	1.11905i	0.0224124	+	0.0388194i
$832$	−0.646084			−0.0223989
$833$		0			0
$834$	−10.0000			−0.346272
$835$	3.46410	−	2.00000i	0.119880	−	0.0692129i
$836$	5.97463	−	0.280712i	0.206637	−	0.00970864i
$837$	−15.5826	+	26.9898i	−0.538613	+	0.932904i
$838$	−6.51419	−	11.2829i	−0.225029	−	0.389762i
$839$		−	9.66311i		−	0.333608i	−0.985990	−	0.166804i	$-0.946655\pi$
$839$		−	9.66311i		−	0.333608i	0.985990	−	0.166804i	$-0.0533447\pi$
$840$		0			0
$841$	26.4955			0.913636
$842$	−6.56670	+	3.79129i	−0.226304	+	0.130656i
$843$	3.60681	−	6.24718i	0.124225	−	0.215164i
$844$	14.5040	+	8.37386i	0.499247	+	0.288240i
$845$	−33.7319	+	19.4751i	−1.16041	+	0.669965i
$846$	−25.6522			−0.881941
$847$		0			0
$848$	−11.5826			−0.397747
$849$	−10.1063	+	5.83485i	−0.346846	+	0.200251i
$850$	14.8492	+	8.57321i	0.509325	+	0.294059i
$851$	−7.16515	+	12.4104i	−0.245618	+	0.425423i
$852$	−1.11905	+	0.646084i	−0.0383380	+	0.0221345i
$853$	11.4665			0.392606			0.196303	−	0.980543i	$-0.437106\pi$
$853$	11.4665			0.392606			0.196303	+	0.980543i	$0.437106\pi$
$854$		0			0
$855$		−	14.4174i		−	0.493066i
$856$	8.79129	+	15.2270i	0.300480	+	0.520447i
$857$	15.5453	−	26.9252i	0.531017	−	0.919748i	−0.468328	−	0.883555i	$-0.655143\pi$
$857$	15.5453	−	26.9252i	0.531017	−	0.919748i	0.999345	−	0.0361936i	$-0.0115233\pi$
$858$	1.38291	−	0.0649750i	0.0472119	−	0.00221821i
$859$	−21.1208	+	12.1941i	−0.720632	+	0.416057i	−0.814985	−	0.579482i	$-0.803255\pi$
$859$	−21.1208	+	12.1941i	−0.720632	+	0.416057i	0.0943531	+	0.995539i	$0.469922\pi$
$860$	−22.1803			−0.756340
$861$		0			0
$862$	−27.9129			−0.950716
$863$	7.41742	+	12.8474i	0.252492	+	0.437329i	0.964211	−	0.265135i	$-0.0854165\pi$
$863$	7.41742	+	12.8474i	0.252492	+	0.437329i	−0.711719	+	0.702464i	$0.752083\pi$
$864$	−1.80341	+	3.12359i	−0.0613531	+	0.106267i
$865$	−28.7219	−	16.5826i	−0.976573	−	0.563824i
$866$	−17.7925	−	30.8175i	−0.604614	−	1.04722i
$867$		−	1.93825i		−	0.0658265i
$868$		0			0
$869$	−11.1652	+	7.16515i	−0.378752	+	0.243061i
$870$	1.58258	+	2.74110i	0.0536543	+	0.0929320i
$871$	2.44949	−	4.24264i	0.0829978	−	0.143756i
$872$	8.58258	−	14.8655i	0.290643	−	0.503408i
$873$	−19.0239	+	10.9834i	−0.643860	+	0.371733i
$874$			7.21362i			0.244004i
$875$		0			0
$876$		−	10.4174i		−	0.351972i
$877$	−5.91915	+	3.41742i	−0.199876	+	0.115398i	−0.596597	−	0.802541i	$-0.703481\pi$
$877$	−5.91915	+	3.41742i	−0.199876	+	0.115398i	0.396722	+	0.917939i	$0.370148\pi$
$878$	14.9660	+	8.64064i	0.505079	+	0.291607i
$879$	−14.0670	−	8.12159i	−0.474468	−	0.273934i
$880$	−9.12248	−	4.71048i	−0.307519	−	0.158790i
$881$			7.21362i			0.243033i	0.992589	+	0.121517i	$0.0387758\pi$
$881$			7.21362i			0.243033i	−0.992589	+	0.121517i	$0.961224\pi$
$882$		0			0
$883$	12.8348			0.431927			0.215964	−	0.976401i	$-0.430711\pi$
$883$	12.8348			0.431927			0.215964	+	0.976401i	$0.430711\pi$
$884$	−1.20871	−	2.09355i	−0.0406534	−	0.0704137i
$885$	−1.11905	−	0.646084i	−0.0376165	−	0.0217179i
$886$	13.1334	+	7.58258i	0.441225	+	0.254742i
$887$	26.7028	+	46.2507i	0.896594	+	1.55295i	0.831820	+	0.555046i	$0.187299\pi$
$887$	26.7028	+	46.2507i	0.896594	+	1.55295i	0.0647738	+	0.997900i	$0.479367\pi$
$888$	−2.31464			−0.0776744
$889$		0			0
$890$			30.3303i			1.01667i
$891$	−8.24360	+	15.9648i	−0.276171	+	0.534843i
$892$	13.9638	+	8.06198i	0.467541	+	0.269935i
$893$	−15.5130	−	8.95644i	−0.519123	−	0.299716i
$894$	−7.83335	+	4.52259i	−0.261986	+	0.151258i
$895$			34.5625i			1.15530i
$896$		0			0
$897$			1.66970i			0.0557496i
$898$	−26.9898	+	15.5826i	−0.900662	+	0.519997i
$899$	−6.83723	+	11.8424i	−0.228034	+	0.394967i
$900$	−5.91742	+	10.2493i	−0.197247	+	0.341643i
$901$	−21.6690	−	37.5318i	−0.721900	−	1.25037i
$902$	27.7253	−	17.7925i	0.923152	−	0.592426i
$903$		0			0
$904$			10.7477i			0.357464i
$905$	8.37386	+	14.5040i	0.278357	+	0.482128i
$906$	−3.12359	−	1.80341i	−0.103774	−	0.0599141i
$907$	−2.95644	+	5.12070i	−0.0981670	+	0.170030i	−0.910926	−	0.412570i	$-0.864631\pi$
$907$	−2.95644	+	5.12070i	−0.0981670	+	0.170030i	0.812759	+	0.582600i	$0.197965\pi$
$908$	−0.255619	−	0.442745i	−0.00848302	−	0.0146930i
$909$	−30.3097			−1.00531
$910$		0			0
$911$	3.16515			0.104866			0.0524331	−	0.998624i	$-0.483302\pi$
$911$	3.16515			0.104866			0.0524331	+	0.998624i	$0.483302\pi$
$912$	−1.00905	+	0.582576i	−0.0334130	+	0.0192910i
$913$	42.7159	−	2.00697i	1.41369	−	0.0664209i
$914$	−16.5826	+	28.7219i	−0.548503	+	0.950035i
$915$	1.93825	+	3.35715i	0.0640766	+	0.110984i
$916$			5.67991i			0.187669i
$917$		0			0
$918$	−13.4955			−0.445416
$919$	16.8836	−	9.74773i	0.556937	−	0.321548i	−0.194978	−	0.980808i	$-0.562464\pi$
$919$	16.8836	−	9.74773i	0.556937	−	0.321548i	0.751915	+	0.659260i	$0.229130\pi$
$920$	6.19115	−	10.7234i	0.204116	−	0.353539i
$921$	5.91915	+	3.41742i	0.195043	+	0.112608i
$922$	−26.0154	+	15.0200i	−0.856771	+	0.494657i
$923$	1.29217			0.0425322
$924$		0			0
$925$	−16.4174			−0.539802
$926$	−4.47315	+	2.58258i	−0.146997	+	0.0848687i
$927$	−13.5454	−	7.82043i	−0.444889	−	0.256857i
$928$	−0.791288	+	1.37055i	−0.0259753	+	0.0449905i
$929$	37.7654	−	21.8039i	1.23904	−	0.715361i	0.270144	−	0.962820i	$-0.412929\pi$
$929$	37.7654	−	21.8039i	1.23904	−	0.715361i	0.968898	+	0.247459i	$0.0795954\pi$
$930$	17.2813			0.566675
$931$		0			0
$932$			27.1652i			0.889824i
$933$	1.62614	+	2.81655i	0.0532373	+	0.0922097i
$934$	5.86811	−	10.1639i	0.192010	−	0.332572i
$935$	−1.80291	−	38.3727i	−0.0589614	−	1.25492i
$936$	1.44502	−	0.834280i	0.0472318	−	0.0272693i
$937$	30.0681			0.982282			0.491141	−	0.871080i	$-0.336580\pi$
$937$	30.0681			0.982282			0.491141	+	0.871080i	$0.336580\pi$
$938$		0			0
$939$	15.1652			0.494896
$940$	15.3739	+	26.6283i	0.501440	+	0.868520i
$941$	2.63769	−	4.56861i	0.0859861	−	0.148932i	−0.819825	−	0.572614i	$-0.805929\pi$
$941$	2.63769	−	4.56861i	0.0859861	−	0.148932i	0.905811	+	0.423682i	$0.139263\pi$
$942$	7.36515	+	4.25227i	0.239970	+	0.138547i
$943$	19.8656	+	34.4082i	0.646913	+	1.12049i
$944$		−	0.646084i		−	0.0210282i
$945$		0			0
$946$	12.8348	+	20.0000i	0.417297	+	0.650256i
$947$	−1.79129	−	3.10260i	−0.0582090	−	0.100821i	0.835452	−	0.549563i	$-0.185206\pi$
$947$	−1.79129	−	3.10260i	−0.0582090	−	0.100821i	−0.893662	+	0.448742i	$0.851872\pi$
$948$	1.29217	−	2.23810i	0.0419677	−	0.0726901i
$949$	−5.20871	+	9.02175i	−0.169082	+	0.292859i
$950$	−7.15705	+	4.13212i	−0.232205	+	0.134064i
$951$			5.92146i			0.192016i
$952$		0			0
$953$		−	18.3303i		−	0.593777i	−0.954912	−	0.296888i	$-0.904051\pi$
$953$		−	18.3303i		−	0.593777i	0.954912	−	0.296888i	$-0.0959489\pi$
$954$	25.9053	−	14.9564i	0.838715	−	0.484233i
$955$	48.2552	+	27.8602i	1.56150	+	0.901534i
$956$	−7.28970	−	4.20871i	−0.235766	−	0.136119i
$957$	1.55588	−	3.01318i	0.0502946	−	0.0974023i
$958$		−	30.9557i		−	1.00013i
$959$		0			0
$960$	2.00000			0.0645497
$961$	21.8303	+	37.8112i	0.704203	+	1.21972i
$962$	2.00454	+	1.15732i	0.0646290	+	0.0373136i
$963$	−39.3248	−	22.7042i	−1.26722	−	0.731632i
$964$	−1.73598	−	3.00681i	−0.0559123	−	0.0968429i
$965$	−50.5517			−1.62732
$966$		0			0
$967$		−	22.4174i		−	0.720896i	−0.932779	−	0.360448i	$-0.882624\pi$
$967$		−	22.4174i		−	0.720896i	0.932779	−	0.360448i	$-0.117376\pi$
$968$	1.03137	+	10.9515i	0.0331496	+	0.351996i
$969$	−3.77552	−	2.17980i	−0.121287	−	0.0700252i
$970$	22.8027	+	13.1652i	0.732151	+	0.422708i
$971$	12.1684	−	7.02543i	0.390502	−	0.225457i	−0.291875	−	0.956456i	$-0.594279\pi$
$971$	12.1684	−	7.02543i	0.390502	−	0.225457i	0.682378	+	0.731000i	$0.260946\pi$
$972$		−	14.3205i		−	0.459332i
$973$		0			0
$974$		−	21.4955i		−	0.688759i
$975$	−1.65660	+	0.956439i	−0.0530537	+	0.0306306i
$976$	−0.969126	+	1.67858i	−0.0310210	+	0.0537299i
$977$	−4.58258	+	7.93725i	−0.146610	+	0.253935i	−0.929972	−	0.367630i	$-0.880169\pi$
$977$	−4.58258	+	7.93725i	−0.146610	+	0.253935i	0.783363	+	0.621565i	$0.213503\pi$
$978$	−1.29217	−	2.23810i	−0.0413190	−	0.0715665i
$979$	27.3489	−	17.5510i	0.874075	−	0.560931i
$980$		0			0
$981$			44.3303i			1.41536i
$982$	−16.7477	−	29.0079i	−0.534441	−	0.925680i
$983$	−43.8958	−	25.3432i	−1.40006	−	0.808324i	−0.405660	−	0.914024i	$-0.632958\pi$
$983$	−43.8958	−	25.3432i	−1.40006	−	0.808324i	−0.994398	+	0.105700i	$0.966292\pi$
$984$	−3.20871	+	5.55765i	−0.102290	+	0.177171i
$985$	13.5396	+	23.4513i	0.431408	+	0.747221i
$986$	−5.92146			−0.188578
$987$		0			0
$988$	1.16515			0.0370684
$989$	−24.8208	+	14.3303i	−0.789256	+	0.455677i
$990$	26.4857	−	1.24441i	0.841771	−	0.0395499i
$991$	−23.3303	+	40.4093i	−0.741111	+	1.28364i	0.210878	+	0.977512i	$0.432368\pi$
$991$	−23.3303	+	40.4093i	−0.741111	+	1.28364i	−0.951990	+	0.306130i	$0.900966\pi$
$992$	4.32032	+	7.48301i	0.137170	+	0.237586i
$993$		−	15.2363i		−	0.483510i
$994$		0			0
$995$	29.9129			0.948302
$996$	−7.21425	+	4.16515i	−0.228592	+	0.131978i
$997$	−11.2783	+	19.5346i	−0.357188	+	0.618668i	−0.987490	−	0.157682i	$-0.949598\pi$
$997$	−11.2783	+	19.5346i	−0.357188	+	0.618668i	0.630302	+	0.776350i	$0.282931\pi$
$998$	−15.5130	−	8.95644i	−0.491056	−	0.283511i
$999$	11.1905	−	6.46084i	0.354052	−	0.204412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1078.2.i.b.1011.2		16
7.2	even	3	inner	1078.2.i.b.901.7		16
7.3	odd	6		154.2.c.a.153.2	✓	8
7.4	even	3		154.2.c.a.153.3	yes	8
7.5	odd	6	inner	1078.2.i.b.901.6		16
7.6	odd	2	inner	1078.2.i.b.1011.3		16
11.10	odd	2	inner	1078.2.i.b.1011.6		16
21.11	odd	6		1386.2.e.b.307.5		8
21.17	even	6		1386.2.e.b.307.8		8
28.3	even	6		1232.2.e.e.769.6		8
28.11	odd	6		1232.2.e.e.769.3		8
77.10	even	6		154.2.c.a.153.6	yes	8
77.32	odd	6		154.2.c.a.153.7	yes	8
77.54	even	6	inner	1078.2.i.b.901.2		16
77.65	odd	6	inner	1078.2.i.b.901.3		16
77.76	even	2	inner	1078.2.i.b.1011.7		16
231.32	even	6		1386.2.e.b.307.1		8
231.164	odd	6		1386.2.e.b.307.4		8
308.87	odd	6		1232.2.e.e.769.5		8
308.263	even	6		1232.2.e.e.769.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
154.2.c.a.153.2	✓	8	7.3	odd	6
154.2.c.a.153.3	yes	8	7.4	even	3
154.2.c.a.153.6	yes	8	77.10	even	6
154.2.c.a.153.7	yes	8	77.32	odd	6
1078.2.i.b.901.2		16	77.54	even	6	inner
1078.2.i.b.901.3		16	77.65	odd	6	inner
1078.2.i.b.901.6		16	7.5	odd	6	inner
1078.2.i.b.901.7		16	7.2	even	3	inner
1078.2.i.b.1011.2		16	1.1	even	1	trivial
1078.2.i.b.1011.3		16	7.6	odd	2	inner
1078.2.i.b.1011.6		16	11.10	odd	2	inner
1078.2.i.b.1011.7		16	77.76	even	2	inner
1232.2.e.e.769.3		8	28.11	odd	6
1232.2.e.e.769.4		8	308.263	even	6
1232.2.e.e.769.5		8	308.87	odd	6
1232.2.e.e.769.6		8	28.3	even	6
1386.2.e.b.307.1		8	231.32	even	6
1386.2.e.b.307.4		8	231.164	odd	6
1386.2.e.b.307.5		8	21.11	odd	6
1386.2.e.b.307.8		8	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1078 = 2 \cdot 7^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1078.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.559525 - 0.323042i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 - 2.23658i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.559525 - 0.323042i) q^{3} +(0.500000 - 0.866025i) q^{4} +(2.68085 - 1.54779i) q^{5} +0.646084 q^{6} +1.00000i q^{8} +(-1.29129 - 2.23658i) q^{9} +(-1.54779 + 2.68085i) q^{10} +(3.31297 - 0.155657i) q^{11} +(-0.559525 + 0.323042i) q^{12} +0.646084 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.87083 - 3.24037i) q^{17} +(2.23658 + 1.29129i) q^{18} +(0.901703 + 1.56180i) q^{19} -3.09557i q^{20} +(-2.79129 + 1.79129i) q^{22} +(-2.00000 - 3.46410i) q^{23} +(0.323042 - 0.559525i) q^{24} +(2.29129 - 3.96863i) q^{25} +(-0.559525 + 0.323042i) q^{26} +3.60681i q^{27} +1.58258i q^{29} +(1.73205 - 1.00000i) q^{30} +(7.48301 + 4.32032i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.90397 - 0.983134i) q^{33} +3.74166i q^{34} -2.58258 q^{36} +(-1.79129 - 3.10260i) q^{37} +(-1.56180 - 0.901703i) q^{38} +(-0.361500 - 0.208712i) q^{39} +(1.54779 + 2.68085i) q^{40} -9.93280 q^{41} -7.16515i q^{43} +(1.52168 - 2.94694i) q^{44} +(-6.92349 - 3.99728i) q^{45} +(3.46410 + 2.00000i) q^{46} +(-8.60206 + 4.96640i) q^{47} +0.646084i q^{48} +4.58258i q^{50} +(-2.09355 + 1.20871i) q^{51} +(0.323042 - 0.559525i) q^{52} +(5.79129 - 10.0308i) q^{53} +(-1.80341 - 3.12359i) q^{54} +(8.64064 - 5.54506i) q^{55} -1.16515i q^{57} +(-0.791288 - 1.37055i) q^{58} +(0.559525 + 0.323042i) q^{59} +(-1.00000 + 1.73205i) q^{60} +(-0.969126 - 1.67858i) q^{61} -8.64064 q^{62} -1.00000 q^{64} +(1.73205 - 1.00000i) q^{65} +(2.14046 - 0.100567i) q^{66} +(3.79129 - 6.56670i) q^{67} +(-1.87083 - 3.24037i) q^{68} +2.58434i q^{69} +2.00000 q^{71} +(2.23658 - 1.29129i) q^{72} +(-8.06198 + 13.9638i) q^{73} +(3.10260 + 1.79129i) q^{74} +(-2.56407 + 1.48036i) q^{75} +1.80341 q^{76} +0.417424 q^{78} +(-3.46410 + 2.00000i) q^{79} +(-2.68085 - 1.54779i) q^{80} +(-2.70871 + 4.69163i) q^{81} +(8.60206 - 4.96640i) q^{82} +12.8935 q^{83} -11.5826i q^{85} +(3.58258 + 6.20520i) q^{86} +(0.511238 - 0.885491i) q^{87} +(0.155657 + 3.31297i) q^{88} +(8.48528 - 4.89898i) q^{89} +7.99455 q^{90} -4.00000 q^{92} +(-2.79129 - 4.83465i) q^{93} +(4.96640 - 8.60206i) q^{94} +(4.83465 + 2.79129i) q^{95} +(-0.323042 - 0.559525i) q^{96} -8.50579i q^{97} +(-4.62614 - 7.20871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{4} + 16 q^{9}+O(q^{10}) \) 16 * q + 8 * q^4 + 16 * q^9	\( 16 q + 8 q^{4} + 16 q^{9} - 4 q^{11} - 32 q^{15} - 8 q^{16} - 8 q^{22} - 32 q^{23} + 32 q^{36} + 8 q^{37} + 4 q^{44} + 56 q^{53} + 24 q^{58} - 16 q^{60} - 16 q^{64} + 24 q^{67} + 32 q^{71} + 80 q^{78} - 80 q^{81} - 16 q^{86} - 4 q^{88} - 64 q^{92} - 8 q^{93} - 184 q^{99}+O(q^{100}) \) 16 * q + 8 * q^4 + 16 * q^9 - 4 * q^11 - 32 * q^15 - 8 * q^16 - 8 * q^22 - 32 * q^23 + 32 * q^36 + 8 * q^37 + 4 * q^44 + 56 * q^53 + 24 * q^58 - 16 * q^60 - 16 * q^64 + 24 * q^67 + 32 * q^71 + 80 * q^78 - 80 * q^81 - 16 * q^86 - 4 * q^88 - 64 * q^92 - 8 * q^93 - 184 * q^99

Introduction

L-functions

Modular forms

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