LMFDB - Embedded newform 1078.2.i.b.901.2

Newspace parameters

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

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
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			901.2
Root			$1.40721 + 0.140577i$ of defining polynomial
Character	$\chi$	$=$	1078.901
Dual form			1078.2.i.b.1011.2

$q$-expansion

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.559525 + 0.323042i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.68085 + 1.54779i) q^{5} +0.646084 q^{6} -1.00000i q^{8} +(-1.29129 + 2.23658i) q^{9} +O(q^{10})$	\(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 $\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times$.

$n$	$199$	$981$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$

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	−0.652748	−	0.757575i	$-0.726384\pi$
$3$	−0.559525	+	0.323042i	−0.323042	+	0.186508i	0.329706	+	0.944084i	$0.393050\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.68085	+	1.54779i	1.19891	+	0.692191i	0.960312	−	0.278927i	$-0.0899788\pi$
$5$	2.68085	+	1.54779i	1.19891	+	0.692191i	0.238598	+	0.971118i	$0.423312\pi$
$6$	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	0.998615	−	0.0526138i	$-0.0167552\pi$
$17$	1.87083	+	3.24037i	0.453743	+	0.785905i	−0.544872	+	0.838519i	$0.683422\pi$
$18$	2.23658	−	1.29129i	0.527166	−	0.304359i
$19$	0.901703	−	1.56180i	0.206865	−	0.358300i	−0.743860	−	0.668335i	$-0.767007\pi$
$19$	0.901703	−	1.56180i	0.206865	−	0.358300i	0.950725	+	0.310035i	$0.100341\pi$
$20$			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	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$	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	$-0.953058\pi$
$29$		−	1.58258i		−	0.293877i	0.989146	−	0.146938i	$-0.0469419\pi$
$30$	1.73205	+	1.00000i	0.316228	+	0.182574i
$31$	7.48301	−	4.32032i	1.34399	−	0.775952i	0.356598	−	0.934258i	$-0.383936\pi$
$31$	7.48301	−	4.32032i	1.34399	−	0.775952i	0.987390	+	0.158306i	$0.0506032\pi$
$32$	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	−0.974865	−	0.222796i	$-0.928482\pi$
$37$	−1.79129	+	3.10260i	−0.294486	+	0.510065i	0.680379	+	0.732860i	$0.261815\pi$
$38$	−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	$0.183978\pi$
$43$			7.16515i			1.09268i	−0.837565	+	0.546338i	$0.816022\pi$
$44$	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	−0.282693	−	0.959211i	$-0.591228\pi$
$47$	−8.60206	−	4.96640i	−1.25474	−	0.724424i	−0.972047	+	0.234786i	$0.924561\pi$
$48$		−	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	0.922525	+	0.385938i	$0.126122\pi$
$53$	5.79129	+	10.0308i	0.795495	+	1.37784i	−0.127030	+	0.991899i	$0.540544\pi$
$54$	−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	−0.463136	−	0.886287i	$-0.653276\pi$
$59$	0.559525	−	0.323042i	0.0728440	−	0.0420565i	0.535980	+	0.844231i	$0.319942\pi$
$60$	−1.00000	−	1.73205i	−0.129099	−	0.223607i
$61$	−0.969126	+	1.67858i	−0.124084	+	0.214920i	−0.921374	−	0.388676i	$-0.872933\pi$
$61$	−0.969126	+	1.67858i	−0.124084	+	0.214920i	0.797291	+	0.603596i	$0.206266\pi$
$62$	−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	0.999117	−	0.0420070i	$-0.0133752\pi$
$67$	3.79129	+	6.56670i	0.463180	+	0.802250i	−0.535938	+	0.844257i	$0.680042\pi$
$68$	−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	−0.758564	−	0.651599i	$-0.774099\pi$
$73$	−8.06198	−	13.9638i	−0.943583	−	1.63433i	−0.185019	−	0.982735i	$-0.559235\pi$
$74$	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	0.292306	−	0.956325i	$-0.405577\pi$
$79$	−3.46410	−	2.00000i	−0.389742	−	0.225018i	−0.682048	+	0.731307i	$0.738911\pi$
$80$	−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	0.877018	−	0.480458i	$-0.159529\pi$
$89$	8.48528	+	4.89898i	0.899438	+	0.519291i	0.0224202	+	0.999749i	$0.492863\pi$
$90$	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	$0.142127\pi$
$97$			8.50579i			0.863632i	−0.901962	+	0.431816i	$0.857873\pi$
$98$		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	0.995012	+	0.0997573i	$0.0318067\pi$
$101$	5.86811	+	10.1639i	0.583898	+	1.01134i	−0.411114	+	0.911584i	$0.634860\pi$
$102$	1.20871	+	2.09355i	0.119680	+	0.207292i
$103$	5.24491	+	3.02815i	0.516796	+	0.298373i	0.735623	−	0.677391i	$-0.236890\pi$
$103$	5.24491	+	3.02815i	0.516796	+	0.298373i	−0.218827	+	0.975764i	$0.570223\pi$
$104$		−	0.646084i		−	0.0633537i
$105$		0			0
$106$		−	11.5826i		−	1.12500i
$107$	15.2270	+	8.79129i	1.47205	+	0.849886i	0.999506	−	0.0314237i	$-0.0100041\pi$
$107$	15.2270	+	8.79129i	1.47205	+	0.849886i	0.472539	+	0.881310i	$0.343337\pi$
$108$	3.12359	−	1.80341i	0.300568	−	0.173533i
$109$	−14.8655	+	8.58258i	−1.42385	+	0.822062i	−0.996626	−	0.0820827i	$-0.973843\pi$
$109$	−14.8655	+	8.58258i	−1.42385	+	0.822062i	−0.427227	+	0.904144i	$0.640509\pi$
$110$	−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	$0.0508112\pi$
$127$			3.58258i			0.317902i	−0.987286	+	0.158951i	$0.949189\pi$
$128$	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	−0.223165	−	0.974781i	$-0.571639\pi$
$131$	8.38502	−	14.5233i	0.732602	−	1.26890i	0.955767	−	0.294124i	$-0.0950278\pi$
$132$	−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	0.925677	−	0.378315i	$-0.123496\pi$
$137$	1.58258	+	2.74110i	0.135209	+	0.234188i	−0.790469	+	0.612503i	$0.790163\pi$
$138$	−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	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	−12.1244	−	7.00000i	−0.993266	−	0.573462i	−0.906249	+	0.422744i	$0.861067\pi$
$150$	1.48036	+	2.56407i	0.120871	+	0.209355i
$151$	−4.83465	+	2.79129i	−0.393438	+	0.227152i	−0.683649	−	0.729811i	$-0.739608\pi$
$151$	−4.83465	+	2.79129i	−0.393438	+	0.227152i	0.290210	+	0.956963i	$0.406275\pi$
$152$	−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	0.0294291	−	0.999567i	$-0.490631\pi$
$157$	11.3997	−	6.58161i	0.909794	−	0.525270i	0.880365	+	0.474297i	$0.157298\pi$
$158$	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	−0.933659	−	0.358162i	$-0.883403\pi$
$163$	−2.00000	+	3.46410i	−0.156652	+	0.271329i	0.777007	+	0.629492i	$0.216737\pi$
$164$	−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	−0.994583	−	0.103942i	$-0.966854\pi$
$173$	−5.35687	+	9.27837i	−0.407275	+	0.705421i	0.587308	+	0.809363i	$0.300188\pi$
$174$		−	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	0.578402	−	0.815752i	$-0.303677\pi$
$179$	−5.58258	−	9.66930i	−0.417261	−	0.722718i	−0.995663	+	0.0930344i	$0.970343\pi$
$180$	−6.92349	−	3.99728i	−0.516046	−	0.297939i
$181$		−	5.41022i		−	0.402138i	−0.979577	−	0.201069i	$-0.935558\pi$
$181$		−	5.41022i		−	0.402138i	0.979577	−	0.201069i	$-0.0644416\pi$
$182$		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	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.559525	−	0.323042i	0.0403802	−	0.0233135i
$193$	−14.1425	+	8.16515i	−1.01800	+	0.587740i	−0.913523	−	0.406787i	$-0.866649\pi$
$193$	−14.1425	+	8.16515i	−1.01800	+	0.587740i	−0.104473	+	0.994528i	$0.533316\pi$
$194$	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	$-0.899127\pi$
$197$		−	8.74773i		−	0.623250i	0.950205	−	0.311625i	$-0.100873\pi$
$198$	7.61071	−	3.92986i	0.540869	−	0.279283i
$199$	8.36850	−	4.83156i	0.593227	−	0.342500i	−0.173145	−	0.984896i	$-0.555393\pi$
$199$	8.36850	−	4.83156i	0.593227	−	0.342500i	0.766373	+	0.642396i	$0.222060\pi$
$200$	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	$-0.804426\pi$
$211$		−	16.7477i		−	1.15296i	0.817111	−	0.576481i	$-0.195574\pi$
$212$	−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	$-0.818473\pi$
$223$		−	16.1240i		−	1.07974i	0.841749	−	0.539870i	$-0.181527\pi$
$224$		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	0.874384	−	0.485235i	$-0.161266\pi$
$227$	0.255619	+	0.442745i	0.0169660	+	0.0293860i	−0.857418	+	0.514621i	$0.827933\pi$
$228$	−1.00905	+	0.582576i	−0.0668260	+	0.0385820i
$229$	−4.91895	−	2.83995i	−0.325053	−	0.187669i	0.328590	−	0.944473i	$-0.393427\pi$
$229$	−4.91895	−	2.83995i	−0.325053	−	0.187669i	−0.653643	+	0.756803i	$0.726760\pi$
$230$	12.3823			0.816464
$231$		0			0
$232$	−1.58258			−0.103901
$233$	−23.5257	−	13.5826i	−1.54122	−	0.889824i	−0.998762	−	0.0497415i	$-0.984160\pi$
$233$	−23.5257	−	13.5826i	−1.54122	−	0.889824i	−0.542458	−	0.840083i	$-0.682506\pi$
$234$	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	$0.0877641\pi$
$239$			8.41742i			0.544478i	−0.962230	+	0.272239i	$0.912236\pi$
$240$	1.00000	−	1.73205i	0.0645497	−	0.111803i
$241$	1.73598	+	3.00681i	0.111825	+	0.193686i	0.916506	−	0.400021i	$-0.130997\pi$
$241$	1.73598	+	3.00681i	0.111825	+	0.193686i	−0.804681	+	0.593707i	$0.797664\pi$
$242$	−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	$-0.724624\pi$
$251$		−	24.1185i		−	1.52235i	0.648549	−	0.761173i	$-0.275376\pi$
$252$		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	0.361805	−	0.932254i	$-0.382161\pi$
$257$	−4.24264	−	2.44949i	−0.264649	−	0.152795i	−0.626453	+	0.779459i	$0.715494\pi$
$258$			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	−0.260803	−	0.965392i	$-0.583987\pi$
$263$	7.21425	−	4.16515i	0.444850	−	0.256834i	0.705653	+	0.708558i	$0.250654\pi$
$264$	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	0.00349288	−	0.999994i	$-0.498888\pi$
$269$	14.2897	−	8.25017i	0.871259	−	0.503022i	0.867767	+	0.496972i	$0.165555\pi$
$270$	−9.66930	+	5.58258i	−0.588455	+	0.339745i
$271$	2.44949	−	4.24264i	0.148796	−	0.257722i	−0.781987	−	0.623295i	$-0.785794\pi$
$271$	2.44949	−	4.24264i	0.148796	−	0.257722i	0.930783	+	0.365573i	$0.119127\pi$
$272$	−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	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$	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	$-0.891929\pi$
$281$		−	11.1652i		−	0.666057i	0.942917	−	0.333029i	$-0.108071\pi$
$282$	−5.55765	−	3.20871i	−0.330953	−	0.191076i
$283$	9.03110	+	15.6423i	0.536843	+	0.929840i	0.999072	+	0.0430789i	$0.0137167\pi$
$283$	9.03110	+	15.6423i	0.536843	+	0.929840i	−0.462228	+	0.886761i	$0.652950\pi$
$284$	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	−0.618482	−	0.785799i	$-0.712252\pi$
$311$	−4.35942	+	2.51691i	−0.247200	+	0.142721i	0.371281	+	0.928520i	$0.378919\pi$
$312$	0.208712	+	0.361500i	0.0118160	+	0.0204659i
$313$	−20.3277	−	11.7362i	−1.14899	−	0.663370i	−0.200349	−	0.979725i	$-0.564208\pi$
$313$	−20.3277	−	11.7362i	−1.14899	−	0.663370i	−0.948641	+	0.316355i	$0.897541\pi$
$314$	−13.1632			−0.742844
$315$		0			0
$316$		−	4.00000i		−	0.225018i
$317$	−4.58258	+	7.93725i	−0.257383	+	0.445801i	−0.965540	−	0.260254i	$-0.916194\pi$
$317$	−4.58258	+	7.93725i	−0.257383	+	0.445801i	0.708157	+	0.706055i	$0.249527\pi$
$318$	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	−0.335467	−	0.942052i	$-0.608894\pi$
$331$	11.7913	−	20.4231i	0.648108	−	1.12256i	0.983574	−	0.180504i	$-0.0577727\pi$
$332$	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	$-0.904645\pi$
$337$		−	10.8348i		−	0.590212i	0.955465	−	0.295106i	$-0.0953549\pi$
$338$	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	0.0167312	−	0.999860i	$-0.494674\pi$
$347$	16.5975	−	9.58258i	0.891001	−	0.514420i	0.874270	+	0.485440i	$0.161341\pi$
$348$	−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	−0.662452	−	0.749104i	$-0.730484\pi$
$353$	−6.48074	+	3.74166i	−0.344935	+	0.199148i	0.317517	+	0.948253i	$0.397151\pi$
$354$	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	0.264754	−	0.964316i	$-0.414709\pi$
$359$	−8.29875	−	4.79129i	−0.437991	−	0.252875i	−0.702745	+	0.711442i	$0.748043\pi$
$360$	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	−0.893195	−	0.449670i	$-0.851541\pi$
$367$	−18.2064	+	10.5115i	−0.950366	+	0.548694i	−0.0571714	+	0.998364i	$0.518208\pi$
$368$	−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	0.699216	−	0.714911i	$-0.253533\pi$
$373$	8.29875	+	4.79129i	0.429693	+	0.248083i	−0.269523	+	0.962994i	$0.586866\pi$
$374$	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	0.868385	−	0.495891i	$-0.165159\pi$
$383$	17.0873	+	9.86538i	0.873122	+	0.504097i	0.00473782	+	0.999989i	$0.498492\pi$
$384$	−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	0.710980	−	0.703213i	$-0.248252\pi$
$389$	−5.00000	−	8.66025i	−0.253510	−	0.439092i	−0.964490	+	0.264120i	$0.914918\pi$
$390$	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	−0.238829	−	0.971062i	$-0.576764\pi$
$397$	−23.8940	−	13.7952i	−1.19921	−	0.692363i	−0.960379	+	0.278699i	$0.910097\pi$
$398$	−9.66311			−0.484368
$399$		0			0
$400$	−4.58258			−0.229129
$401$	−3.79129	+	6.56670i	−0.189328	+	0.327926i	−0.945026	−	0.326994i	$-0.893964\pi$
$401$	−3.79129	+	6.56670i	−0.189328	+	0.327926i	0.755698	+	0.654920i	$0.227298\pi$
$402$	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	0.921519	−	0.388333i	$-0.126949\pi$
$409$	2.51691	+	4.35942i	0.124453	+	0.215559i	−0.797066	+	0.603892i	$0.793616\pi$
$410$	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	$-0.896909\pi$
$419$		−	13.0284i		−	0.636478i	0.948011	−	0.318239i	$-0.103091\pi$
$420$		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	0.212034	−	0.977262i	$-0.431991\pi$
$431$	24.1733	−	13.9564i	1.16439	−	0.672258i	0.952351	+	0.305004i	$0.0986579\pi$
$432$	3.12359	+	1.80341i	0.150284	+	0.0867664i
$433$		−	35.5850i		−	1.71011i	−0.518540	−	0.855054i	$-0.673524\pi$
$433$		−	35.5850i		−	1.71011i	0.518540	−	0.855054i	$-0.326476\pi$
$434$		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	−0.995151	−	0.0983579i	$-0.968641\pi$
$439$	−8.64064	+	14.9660i	−0.412395	+	0.714289i	0.582756	+	0.812647i	$0.301974\pi$
$440$	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	−0.988003	−	0.154433i	$-0.950645\pi$
$443$	−7.58258	+	13.1334i	−0.360259	+	0.623987i	0.627744	+	0.778420i	$0.283978\pi$
$444$	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	0.987327	−	0.158700i	$-0.0507302\pi$
$457$	28.7219	+	16.5826i	1.34355	+	0.775700i	0.356225	+	0.934400i	$0.384064\pi$
$458$	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	0.246049	−	0.969257i	$-0.420867\pi$
$467$	−10.1639	−	5.86811i	−0.470327	−	0.271544i	−0.716377	+	0.697714i	$0.754201\pi$
$468$	−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	−0.965891	−	0.258949i	$-0.916624\pi$
$479$	−15.4779	−	26.8085i	−0.707202	−	1.22491i	0.258689	−	0.965961i	$-0.416709\pi$
$480$	−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	0.512863	−	0.858471i	$-0.328585\pi$
$487$	−10.7477	−	18.6156i	−0.487026	−	0.843554i	−0.999889	+	0.0149168i	$0.995252\pi$
$488$	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	$-0.727241\pi$
$491$		−	33.4955i		−	1.51163i	0.654786	−	0.755814i	$-0.272759\pi$
$492$	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	−0.592895	−	0.805280i	$-0.702015\pi$
$499$	8.95644	−	15.5130i	0.400945	−	0.694458i	0.993840	+	0.110822i	$0.0353484\pi$
$500$	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	0.514913	−	0.857242i	$-0.327824\pi$
$509$	0.676305	+	0.390465i	0.0299767	+	0.0173070i	−0.484937	+	0.874549i	$0.661157\pi$
$510$			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	0.139070	−	0.990283i	$-0.455589\pi$
$521$	24.3368	−	14.0509i	1.06621	−	0.615579i	0.927145	+	0.374703i	$0.122255\pi$
$522$	−2.04356	−	3.53955i	−0.0894442	−	0.154922i
$523$	7.22770	−	12.5187i	0.316045	−	0.547406i	−0.663614	−	0.748075i	$-0.730978\pi$
$523$	7.22770	−	12.5187i	0.316045	−	0.547406i	0.979659	+	0.200669i	$0.0643116\pi$
$524$	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	−0.377537	−	0.925994i	$-0.623229\pi$
$541$	−31.8245	−	18.3739i	−1.36824	−	0.789954i	−0.990703	+	0.136040i	$0.956562\pi$
$542$	−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	$0.177458\pi$
$547$			24.7477i			1.05814i	−0.848579	+	0.529068i	$0.822542\pi$
$548$	−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	0.334435	−	0.942419i	$-0.391454\pi$
$557$	31.1015	−	17.9564i	1.31781	−	0.760839i	0.983376	+	0.181580i	$0.0581211\pi$
$558$	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	0.500288	−	0.865859i	$-0.333228\pi$
$563$	−11.8570	−	20.5369i	−0.499712	−	0.865527i	−1.00000		0.000332178i	$0.999894\pi$
$564$	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	0.997416	−	0.0718399i	$-0.0228871\pi$
$569$	34.2041	+	19.7477i	1.43391	+	0.827868i	0.436493	+	0.899708i	$0.356220\pi$
$570$	3.12359	−	1.80341i	0.130833	−	0.0755364i
$571$	4.83465	−	2.79129i	0.202324	−	0.116812i	−0.395415	−	0.918503i	$-0.629399\pi$
$571$	4.83465	−	2.79129i	0.202324	−	0.116812i	0.597739	+	0.801691i	$0.296066\pi$
$572$	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	−0.928035	−	0.372493i	$-0.878503\pi$
$577$	−25.6894	+	14.8318i	−1.06946	+	0.617455i	−0.141429	+	0.989948i	$0.545170\pi$
$578$	−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	$0.298699\pi$
$587$			39.0851i			1.61322i	−0.591087	+	0.806608i	$0.701301\pi$
$588$		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	−0.672623	−	0.739985i	$-0.734833\pi$
$593$	7.41589	−	12.8447i	0.304534	−	0.527469i	0.977158	+	0.212516i	$0.0681659\pi$
$594$	−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	0.997079	−	0.0763801i	$-0.0243362\pi$
$599$	10.5826	+	18.3296i	0.432392	+	0.748925i	−0.564686	+	0.825306i	$0.691003\pi$
$600$	−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	−0.886030	−	0.463628i	$-0.846547\pi$
$607$	−1.02248	+	1.77098i	−0.0415010	+	0.0718819i	0.844529	+	0.535510i	$0.179881\pi$
$608$		−	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	−0.940444	−	0.339948i	$-0.889590\pi$
$613$	−27.6374	+	15.9564i	−1.11626	+	0.644475i	−0.175818	+	0.984423i	$0.556257\pi$
$614$	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	−0.154410	−	0.988007i	$-0.549348\pi$
$619$	15.5255	−	8.96368i	0.624024	−	0.360281i	0.778434	+	0.627726i	$0.216014\pi$
$620$	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	0.979280	−	0.202511i	$-0.0649101\pi$
$641$	7.95644	+	13.7810i	0.314260	+	0.544315i	−0.665020	+	0.746826i	$0.731577\pi$
$642$	9.83789	+	5.67991i	0.388271	+	0.224168i
$643$			9.42157i			0.371550i	0.982592	+	0.185775i	$0.0594796\pi$
$643$			9.42157i			0.371550i	−0.982592	+	0.185775i	$0.940520\pi$
$644$		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	0.108546	−	0.994091i	$-0.465380\pi$
$647$	26.0397	−	15.0341i	1.02373	−	0.591050i	0.915182	+	0.403042i	$0.132047\pi$
$648$	−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	−0.801337	−	0.598213i	$-0.795878\pi$
$653$	3.00000	−	5.19615i	0.117399	−	0.203341i	0.918736	+	0.394872i	$0.129211\pi$
$654$	−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	$0.0393467\pi$
$659$			6.33030i			0.246594i	−0.992370	+	0.123297i	$0.960653\pi$
$660$	−3.04336	−	5.89389i	−0.118463	−	0.229419i
$661$	−7.15705	+	4.13212i	−0.278377	+	0.160721i	−0.632688	−	0.774407i	$-0.718049\pi$
$661$	−7.15705	+	4.13212i	−0.278377	+	0.160721i	0.354312	+	0.935127i	$0.384715\pi$
$662$	−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	$0.114937\pi$
$673$			18.3303i			0.706581i	−0.935514	+	0.353291i	$0.885063\pi$
$674$	−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	−0.912251	−	0.409631i	$-0.865657\pi$
$677$	−2.63769	+	4.56861i	−0.101375	+	0.175586i	0.810877	+	0.585217i	$0.198991\pi$
$678$	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	0.942448	−	0.334352i	$-0.108517\pi$
$683$	4.74773	+	8.22330i	0.181667	+	0.314656i	−0.760782	+	0.649008i	$0.775184\pi$
$684$	−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	0.432949	−	0.901418i	$-0.357473\pi$
$691$	−3.44956	−	1.99160i	−0.131227	−	0.0757641i	−0.564177	+	0.825654i	$0.690806\pi$
$692$	−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	$-0.925193\pi$
$701$		−	12.3303i		−	0.465709i	0.972512	−	0.232855i	$-0.0748066\pi$
$702$	−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	−0.330718	+	0.943730i	$0.607291\pi$
$709$	−26.1652	+	45.3194i	−0.982653	+	1.70200i	−0.651935	+	0.758275i	$0.726042\pi$
$710$	−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	0.0733033	−	0.997310i	$-0.476646\pi$
$719$	−20.2109	−	11.6688i	−0.753741	−	0.435172i	−0.827044	+	0.562137i	$0.809979\pi$
$720$		−	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	$-0.754805\pi$
$727$		−	37.5514i		−	1.39271i	0.717700	−	0.696353i	$-0.245195\pi$
$728$		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	−0.947834	−	0.318763i	$-0.896733\pi$
$733$	−5.35687	+	9.27837i	−0.197860	+	0.342704i	0.749974	+	0.661467i	$0.230066\pi$
$734$	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	−0.524996	−	0.851104i	$-0.675933\pi$
$739$	−1.37055	+	0.791288i	−0.0504165	+	0.0291080i	0.474580	+	0.880212i	$0.342600\pi$
$740$	−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	$-0.988829\pi$
$743$		−	1.91288i		−	0.0701767i	0.999384	−	0.0350884i	$-0.0111713\pi$
$744$	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	−0.187231	−	0.982316i	$-0.559951\pi$
$751$	20.7477	−	35.9361i	0.757095	−	1.31133i	0.944326	−	0.329012i	$-0.106716\pi$
$752$	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	0.488119	+	0.872777i	$0.337683\pi$
$761$	−14.1183	+	24.4536i	−0.511787	+	0.886441i	−0.999907	+	0.0136645i	$0.995650\pi$
$762$			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	−0.648142	−	0.761519i	$-0.724454\pi$
$773$	−8.69447	+	5.01975i	−0.312718	+	0.180548i	0.335424	+	0.942067i	$0.391120\pi$
$774$	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
$781$

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

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