LMFDB - Embedded newform 882.2.l.c.227.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(227,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("882.227");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.l (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:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			227.20
Character	$\chi$	$=$	882.227
Dual form			882.2.l.c.509.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(0.848829 - 1.50980i) q^{3} -1.00000 q^{4} +(-1.96067 + 3.39598i) q^{5} +(1.50980 + 0.848829i) q^{6} -1.00000i q^{8} +(-1.55898 - 2.56312i) q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(0.848829 - 1.50980i) q^{3} -1.00000 q^{4} +(-1.96067 + 3.39598i) q^{5} +(1.50980 + 0.848829i) q^{6} -1.00000i q^{8} +(-1.55898 - 2.56312i) q^{9} +(-3.39598 - 1.96067i) q^{10} +(-3.02739 + 1.74787i) q^{11} +(-0.848829 + 1.50980i) q^{12} +(2.18922 - 1.26395i) q^{13} +(3.46297 + 5.84282i) q^{15} +1.00000 q^{16} +(-1.62026 + 2.80636i) q^{17} +(2.56312 - 1.55898i) q^{18} +(1.85515 - 1.07107i) q^{19} +(1.96067 - 3.39598i) q^{20} +(-1.74787 - 3.02739i) q^{22} +(-8.15025 - 4.70555i) q^{23} +(-1.50980 - 0.848829i) q^{24} +(-5.18846 - 8.98667i) q^{25} +(1.26395 + 2.18922i) q^{26} +(-5.19310 + 0.178091i) q^{27} +(-7.38647 - 4.26458i) q^{29} +(-5.84282 + 3.46297i) q^{30} +3.29659i q^{31} +1.00000i q^{32} +(0.0691851 + 6.05439i) q^{33} +(-2.80636 - 1.62026i) q^{34} +(1.55898 + 2.56312i) q^{36} +(-1.31130 - 2.27123i) q^{37} +(1.07107 + 1.85515i) q^{38} +(-0.0500304 - 4.37816i) q^{39} +(3.39598 + 1.96067i) q^{40} +(0.541126 + 0.937258i) q^{41} +(-3.98981 + 6.91055i) q^{43} +(3.02739 - 1.74787i) q^{44} +(11.7610 - 0.268826i) q^{45} +(4.70555 - 8.15025i) q^{46} -8.47645 q^{47} +(0.848829 - 1.50980i) q^{48} +(8.98667 - 5.18846i) q^{50} +(2.86172 + 4.82838i) q^{51} +(-2.18922 + 1.26395i) q^{52} +(9.31359 + 5.37720i) q^{53} +(-0.178091 - 5.19310i) q^{54} -13.7080i q^{55} +(-0.0423959 - 3.71006i) q^{57} +(4.26458 - 7.38647i) q^{58} -2.34116 q^{59} +(-3.46297 - 5.84282i) q^{60} +4.15474i q^{61} -3.29659 q^{62} -1.00000 q^{64} +9.91274i q^{65} +(-6.05439 + 0.0691851i) q^{66} +0.712278 q^{67} +(1.62026 - 2.80636i) q^{68} +(-14.0226 + 8.31102i) q^{69} -4.96411i q^{71} +(-2.56312 + 1.55898i) q^{72} +(5.69382 + 3.28733i) q^{73} +(2.27123 - 1.31130i) q^{74} +(-17.9722 + 0.205373i) q^{75} +(-1.85515 + 1.07107i) q^{76} +(4.37816 - 0.0500304i) q^{78} -8.67280 q^{79} +(-1.96067 + 3.39598i) q^{80} +(-4.13917 + 7.99170i) q^{81} +(-0.937258 + 0.541126i) q^{82} +(-0.694462 + 1.20284i) q^{83} +(-6.35357 - 11.0047i) q^{85} +(-6.91055 - 3.98981i) q^{86} +(-12.7085 + 7.53217i) q^{87} +(1.74787 + 3.02739i) q^{88} +(7.96740 + 13.7999i) q^{89} +(0.268826 + 11.7610i) q^{90} +(8.15025 + 4.70555i) q^{92} +(4.97718 + 2.79824i) q^{93} -8.47645i q^{94} +8.40009i q^{95} +(1.50980 + 0.848829i) q^{96} +(3.18669 + 1.83984i) q^{97} +(9.19963 + 5.03469i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) $ 48 * q - 48 * q^4 + 16 * q^9	$ 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) $ 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	0.848829	−	1.50980i	0.490072	−	0.871682i
$3$	0.848829	−	1.50980i	0.490072	−	0.871682i
$4$	−1.00000			−0.500000
$5$	−1.96067	+	3.39598i	−0.876838	+	1.51873i	−0.0220471	+	0.999757i	$0.507018\pi$
$5$	−1.96067	+	3.39598i	−0.876838	+	1.51873i	−0.854791	+	0.518972i	$0.826315\pi$
$6$	1.50980	+	0.848829i	0.616372	+	0.346533i
$7$		0			0
$7$		0			0
$8$		−	1.00000i		−	0.353553i
$9$	−1.55898	−	2.56312i	−0.519659	−	0.854373i
$10$	−3.39598	−	1.96067i	−1.07390	−	0.620018i
$11$	−3.02739	+	1.74787i	−0.912793	+	0.527001i	−0.881329	−	0.472504i	$-0.843350\pi$
$11$	−3.02739	+	1.74787i	−0.912793	+	0.527001i	−0.0314643	+	0.999505i	$0.510017\pi$
$12$	−0.848829	+	1.50980i	−0.245036	+	0.435841i
$13$	2.18922	−	1.26395i	0.607181	−	0.350556i	−0.164681	−	0.986347i	$-0.552659\pi$
$13$	2.18922	−	1.26395i	0.607181	−	0.350556i	0.771861	+	0.635791i	$0.219326\pi$
$14$		0			0
$15$	3.46297	+	5.84282i	0.894135	+	1.50861i
$16$	1.00000			0.250000
$17$	−1.62026	+	2.80636i	−0.392970	+	0.680643i	−0.992840	−	0.119454i	$-0.961886\pi$
$17$	−1.62026	+	2.80636i	−0.392970	+	0.680643i	0.599870	+	0.800097i	$0.295219\pi$
$18$	2.56312	−	1.55898i	0.604133	−	0.367455i
$19$	1.85515	−	1.07107i	0.425601	−	0.245721i	−0.271870	−	0.962334i	$-0.587642\pi$
$19$	1.85515	−	1.07107i	0.425601	−	0.245721i	0.697471	+	0.716613i	$0.254309\pi$
$20$	1.96067	−	3.39598i	0.438419	−	0.759364i
$21$		0			0
$22$	−1.74787	−	3.02739i	−0.372646	−	0.645442i
$23$	−8.15025	−	4.70555i	−1.69945	−	0.981175i	−0.946283	−	0.323341i	$-0.895194\pi$
$23$	−8.15025	−	4.70555i	−1.69945	−	0.981175i	−0.753163	−	0.657834i	$-0.771473\pi$
$24$	−1.50980	−	0.848829i	−0.308186	−	0.173267i
$25$	−5.18846	−	8.98667i	−1.03769	−	1.79733i
$26$	1.26395	+	2.18922i	0.247880	+	0.429342i
$27$	−5.19310	+	0.178091i	−0.999412	+	0.0342736i
$28$		0			0
$29$	−7.38647	−	4.26458i	−1.37163	−	0.791912i	−0.380499	−	0.924781i	$-0.624248\pi$
$29$	−7.38647	−	4.26458i	−1.37163	−	0.791912i	−0.991134	+	0.132869i	$0.957581\pi$
$30$	−5.84282	+	3.46297i	−1.06675	+	0.632249i
$31$			3.29659i			0.592085i	0.955175	+	0.296042i	$0.0956670\pi$
$31$			3.29659i			0.592085i	−0.955175	+	0.296042i	$0.904333\pi$
$32$			1.00000i			0.176777i
$33$	0.0691851	+	6.05439i	0.0120436	+	1.05393i
$34$	−2.80636	−	1.62026i	−0.481288	−	0.277871i
$35$		0			0
$36$	1.55898	+	2.56312i	0.259830	+	0.427187i
$37$	−1.31130	−	2.27123i	−0.215576	−	0.373388i	0.737875	−	0.674938i	$-0.235829\pi$
$37$	−1.31130	−	2.27123i	−0.215576	−	0.373388i	−0.953450	+	0.301550i	$0.902496\pi$
$38$	1.07107	+	1.85515i	0.173751	+	0.300946i
$39$	−0.0500304	−	4.37816i	−0.00801127	−	0.701066i
$40$	3.39598	+	1.96067i	0.536952	+	0.310009i
$41$	0.541126	+	0.937258i	0.0845097	+	0.146375i	0.905182	−	0.425024i	$-0.139734\pi$
$41$	0.541126	+	0.937258i	0.0845097	+	0.146375i	−0.820672	+	0.571399i	$0.806401\pi$
$42$		0			0
$43$	−3.98981	+	6.91055i	−0.608440	+	1.05385i	0.383057	+	0.923725i	$0.374871\pi$
$43$	−3.98981	+	6.91055i	−0.608440	+	1.05385i	−0.991498	+	0.130125i	$0.958462\pi$
$44$	3.02739	−	1.74787i	0.456397	−	0.263501i
$45$	11.7610	−	0.268826i	1.75322	−	0.0400742i
$46$	4.70555	−	8.15025i	0.693796	−	1.20169i
$47$	−8.47645			−1.23642			−0.618209	−	0.786014i	$-0.712141\pi$
$47$	−8.47645			−1.23642			−0.618209	+	0.786014i	$0.712141\pi$
$48$	0.848829	−	1.50980i	0.122518	−	0.217921i
$49$		0			0
$50$	8.98667	−	5.18846i	1.27091	−	0.733759i
$51$	2.86172	+	4.82838i	0.400721	+	0.676109i
$52$	−2.18922	+	1.26395i	−0.303590	+	0.175278i
$53$	9.31359	+	5.37720i	1.27932	+	0.738616i	0.976723	−	0.214503i	$-0.0688132\pi$
$53$	9.31359	+	5.37720i	1.27932	+	0.738616i	0.302597	+	0.953119i	$0.402147\pi$
$54$	−0.178091	−	5.19310i	−0.0242351	−	0.706691i
$55$		−	13.7080i		−	1.84838i
$56$		0			0
$57$	−0.0423959	−	3.71006i	−0.00561548	−	0.491410i
$58$	4.26458	−	7.38647i	0.559967	−	0.969891i
$59$	−2.34116			−0.304793			−0.152396	−	0.988319i	$-0.548699\pi$
$59$	−2.34116			−0.304793			−0.152396	+	0.988319i	$0.548699\pi$
$60$	−3.46297	−	5.84282i	−0.447067	−	0.754305i
$61$			4.15474i			0.531960i	0.963979	+	0.265980i	$0.0856954\pi$
$61$			4.15474i			0.531960i	−0.963979	+	0.265980i	$0.914305\pi$
$62$	−3.29659			−0.418667
$63$		0			0
$64$	−1.00000			−0.125000
$65$			9.91274i			1.22952i
$66$	−6.05439	+	0.0691851i	−0.745244	+	0.00851610i
$67$	0.712278			0.0870186			0.0435093	−	0.999053i	$-0.486146\pi$
$67$	0.712278			0.0870186			0.0435093	+	0.999053i	$0.486146\pi$
$68$	1.62026	−	2.80636i	0.196485	−	0.340322i
$69$	−14.0226	+	8.31102i	−1.68812	+	1.00053i
$70$		0			0
$71$		−	4.96411i		−	0.589131i	−0.955631	−	0.294565i	$-0.904825\pi$
$71$		−	4.96411i		−	0.589131i	0.955631	−	0.294565i	$-0.0951749\pi$
$72$	−2.56312	+	1.55898i	−0.302067	+	0.183727i
$73$	5.69382	+	3.28733i	0.666411	+	0.384753i	0.794715	−	0.606982i	$-0.207620\pi$
$73$	5.69382	+	3.28733i	0.666411	+	0.384753i	−0.128304	+	0.991735i	$0.540953\pi$
$74$	2.27123	−	1.31130i	0.264025	−	0.152435i
$75$	−17.9722	+	0.205373i	−2.07525	+	0.0237144i
$76$	−1.85515	+	1.07107i	−0.212801	+	0.122861i
$77$		0			0
$78$	4.37816	−	0.0500304i	0.495729	−	0.00566482i
$79$	−8.67280			−0.975766			−0.487883	−	0.872909i	$-0.662231\pi$
$79$	−8.67280			−0.975766			−0.487883	+	0.872909i	$0.662231\pi$
$80$	−1.96067	+	3.39598i	−0.219210	+	0.379682i
$81$	−4.13917	+	7.99170i	−0.459908	+	0.887967i
$82$	−0.937258	+	0.541126i	−0.103503	+	0.0597574i
$83$	−0.694462	+	1.20284i	−0.0762271	+	0.132029i	−0.901619	−	0.432531i	$-0.857621\pi$
$83$	−0.694462	+	1.20284i	−0.0762271	+	0.132029i	0.825392	+	0.564560i	$0.190954\pi$
$84$		0			0
$85$	−6.35357	−	11.0047i	−0.689142	−	1.19363i
$86$	−6.91055	−	3.98981i	−0.745184	−	0.430232i
$87$	−12.7085	+	7.53217i	−1.36249	+	0.807534i
$88$	1.74787	+	3.02739i	0.186323	+	0.322721i
$89$	7.96740	+	13.7999i	0.844543	+	1.46279i	0.886017	+	0.463652i	$0.153461\pi$
$89$	7.96740	+	13.7999i	0.844543	+	1.46279i	−0.0414744	+	0.999140i	$0.513205\pi$
$90$	0.268826	+	11.7610i	0.0283368	+	1.23971i
$91$		0			0
$92$	8.15025	+	4.70555i	0.849723	+	0.490588i
$93$	4.97718	+	2.79824i	0.516110	+	0.290164i
$94$		−	8.47645i		−	0.874279i
$95$			8.40009i			0.861831i
$96$	1.50980	+	0.848829i	0.154093	+	0.0866333i
$97$	3.18669	+	1.83984i	0.323559	+	0.186807i	0.652978	−	0.757377i	$-0.273519\pi$
$97$	3.18669	+	1.83984i	0.323559	+	0.186807i	−0.329419	+	0.944184i	$0.606853\pi$
$98$		0			0
$99$	9.19963	+	5.03469i	0.924597	+	0.506005i
$100$	5.18846	+	8.98667i	0.518846	+	0.898667i
$101$	−8.90448	−	15.4230i	−0.886029	−	1.53465i	−0.844530	−	0.535509i	$-0.820120\pi$
$101$	−8.90448	−	15.4230i	−0.886029	−	1.53465i	−0.0414993	−	0.999139i	$-0.513213\pi$
$102$	−4.82838	+	2.86172i	−0.478081	+	0.283353i
$103$	−3.29833	−	1.90429i	−0.324994	−	0.187635i	0.328622	−	0.944461i	$-0.393416\pi$
$103$	−3.29833	−	1.90429i	−0.324994	−	0.187635i	−0.653616	+	0.756826i	$0.726749\pi$
$104$	−1.26395	−	2.18922i	−0.123940	−	0.214671i
$105$		0			0
$106$	−5.37720	+	9.31359i	−0.522280	+	0.904616i
$107$	7.64701	−	4.41500i	0.739264	−	0.426814i	−0.0825377	−	0.996588i	$-0.526302\pi$
$107$	7.64701	−	4.41500i	0.739264	−	0.426814i	0.821802	+	0.569774i	$0.192969\pi$
$108$	5.19310	−	0.178091i	0.499706	−	0.0171368i
$109$	−0.361552	+	0.626226i	−0.0346304	+	0.0599816i	−0.882821	−	0.469709i	$-0.844359\pi$
$109$	−0.361552	+	0.626226i	−0.0346304	+	0.0599816i	0.848191	+	0.529691i	$0.177692\pi$
$110$	13.7080			1.30700
$111$	−4.54216	+	0.0519045i	−0.431123	+	0.00492656i
$112$		0			0
$113$	14.4754	−	8.35737i	1.36173	−	0.786195i	0.371876	−	0.928282i	$-0.378715\pi$
$113$	14.4754	−	8.35737i	1.36173	−	0.786195i	0.989854	+	0.142087i	$0.0453813\pi$
$114$	3.71006	−	0.0423959i	0.347479	−	0.00397074i
$115$	31.9599	−	18.4521i	2.98028	−	1.72066i
$116$	7.38647	+	4.26458i	0.685816	+	0.395956i
$117$	−6.65260	−	3.64077i	−0.615033	−	0.336589i
$118$		−	2.34116i		−	0.215521i
$119$		0			0
$120$	5.84282	−	3.46297i	0.533374	−	0.316124i
$121$	0.610068	−	1.05667i	0.0554608	−	0.0960609i
$122$	−4.15474			−0.376152
$123$	1.87439	−	0.0214192i	0.169008	−	0.00193130i
$124$		−	3.29659i		−	0.296042i
$125$	21.0847			1.88587
$126$		0			0
$127$	−16.6620			−1.47851			−0.739256	−	0.673424i	$-0.764823\pi$
$127$	−16.6620			−1.47851			−0.739256	+	0.673424i	$0.764823\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	7.04687	+	11.8897i	0.620442	+	1.04683i
$130$	−9.91274			−0.869404
$131$	−3.94325	+	6.82992i	−0.344524	+	0.596733i	−0.985267	−	0.171022i	$-0.945293\pi$
$131$	−3.94325	+	6.82992i	−0.344524	+	0.596733i	0.640743	+	0.767755i	$0.278626\pi$
$132$	−0.0691851	−	6.05439i	−0.00602179	−	0.526967i
$133$		0			0
$134$			0.712278i			0.0615315i
$135$	9.57716	−	17.9848i	0.824271	−	1.54789i
$136$	2.80636	+	1.62026i	0.240644	+	0.138936i
$137$	1.24395	−	0.718193i	0.106278	−	0.0613594i	−0.445919	−	0.895073i	$-0.647123\pi$
$137$	1.24395	−	0.718193i	0.106278	−	0.0613594i	0.552197	+	0.833714i	$0.313790\pi$
$138$	−8.31102	−	14.0226i	−0.707481	−	1.19368i
$139$	0.676208	−	0.390409i	0.0573552	−	0.0331140i	−0.471048	−	0.882107i	$-0.656124\pi$
$139$	0.676208	−	0.390409i	0.0573552	−	0.0331140i	0.528403	+	0.848993i	$0.322791\pi$
$140$		0			0
$141$	−7.19506	+	12.7977i	−0.605933	+	1.07776i
$142$	4.96411			0.416578
$143$	−4.41842	+	7.65293i	−0.369487	+	0.639970i
$144$	−1.55898	−	2.56312i	−0.129915	−	0.213593i
$145$	28.9649	−	16.7229i	2.40540	−	1.38876i
$146$	−3.28733	+	5.69382i	−0.272061	+	0.471224i
$147$		0			0
$148$	1.31130	+	2.27123i	0.107788	+	0.186694i
$149$	11.2358	+	6.48697i	0.920469	+	0.531433i	0.883785	−	0.467894i	$-0.154987\pi$
$149$	11.2358	+	6.48697i	0.920469	+	0.531433i	0.0366847	+	0.999327i	$0.488320\pi$
$150$	−0.205373	−	17.9722i	−0.0167686	−	1.46742i
$151$	8.96690	+	15.5311i	0.729716	+	1.26391i	0.957003	+	0.290077i	$0.0936810\pi$
$151$	8.96690	+	15.5311i	0.729716	+	1.26391i	−0.227287	+	0.973828i	$0.572986\pi$
$152$	−1.07107	−	1.85515i	−0.0868755	−	0.150473i
$153$	9.71899	−	0.222152i	0.785734	−	0.0179599i
$154$		0			0
$155$	−11.1952	−	6.46353i	−0.899217	−	0.519163i
$156$	0.0500304	+	4.37816i	0.00400564	+	0.350533i
$157$			13.4739i			1.07533i	0.843158	+	0.537666i	$0.180694\pi$
$157$			13.4739i			1.07533i	−0.843158	+	0.537666i	$0.819306\pi$
$158$		−	8.67280i		−	0.689971i
$159$	16.0241	−	9.49731i	1.27080	−	0.753186i
$160$	−3.39598	−	1.96067i	−0.268476	−	0.155005i
$161$		0			0
$162$	−7.99170	−	4.13917i	−0.627887	−	0.325204i
$163$	−6.07661	−	10.5250i	−0.475957	−	0.824381i	0.523664	−	0.851925i	$-0.324565\pi$
$163$	−6.07661	−	10.5250i	−0.475957	−	0.824381i	−0.999621	+	0.0275438i	$0.991231\pi$
$164$	−0.541126	−	0.937258i	−0.0422549	−	0.0731876i
$165$	−20.6962	−	11.6357i	−1.61120	−	0.905839i
$166$	−1.20284	−	0.694462i	−0.0933588	−	0.0539007i
$167$	−2.58248	−	4.47299i	−0.199839	−	0.346130i	0.748637	−	0.662980i	$-0.230708\pi$
$167$	−2.58248	−	4.47299i	−0.199839	−	0.346130i	−0.948476	+	0.316849i	$0.897375\pi$
$168$		0			0
$169$	−3.30487	+	5.72421i	−0.254221	+	0.440324i
$170$	11.0047	−	6.35357i	0.844023	−	0.487297i
$171$	−5.63743	−	3.08520i	−0.431105	−	0.235931i
$172$	3.98981	−	6.91055i	0.304220	−	0.526925i
$173$	19.8227			1.50710			0.753548	−	0.657393i	$-0.228341\pi$
$173$	19.8227			1.50710			0.753548	+	0.657393i	$0.228341\pi$
$174$	−7.53217	−	12.7085i	−0.571013	−	0.963429i
$175$		0			0
$176$	−3.02739	+	1.74787i	−0.228198	+	0.131750i
$177$	−1.98724	+	3.53468i	−0.149370	+	0.265682i
$178$	−13.7999	+	7.96740i	−1.03435	+	0.597182i
$179$	7.07019	+	4.08197i	0.528451	+	0.305101i	0.740385	−	0.672183i	$-0.234643\pi$
$179$	7.07019	+	4.08197i	0.528451	+	0.305101i	−0.211935	+	0.977284i	$0.567976\pi$
$180$	−11.7610	+	0.268826i	−0.876609	+	0.0200371i
$181$			3.09557i			0.230092i	0.993360	+	0.115046i	$0.0367015\pi$
$181$			3.09557i			0.230092i	−0.993360	+	0.115046i	$0.963298\pi$
$182$		0			0
$183$	6.27281	+	3.52666i	0.463700	+	0.260698i
$184$	−4.70555	+	8.15025i	−0.346898	+	0.600845i
$185$	10.2841			0.756100
$186$	−2.79824	+	4.97718i	−0.205177	+	0.364945i
$187$		−	11.3280i		−	0.828382i
$188$	8.47645			0.618209
$189$		0			0
$190$	−8.40009			−0.609406
$191$			4.52911i			0.327715i	0.986484	+	0.163857i	$0.0523937\pi$
$191$			4.52911i			0.327715i	−0.986484	+	0.163857i	$0.947606\pi$
$192$	−0.848829	+	1.50980i	−0.0612590	+	0.108960i
$193$	−6.04602			−0.435202			−0.217601	−	0.976038i	$-0.569823\pi$
$193$	−6.04602			−0.435202			−0.217601	+	0.976038i	$0.569823\pi$
$194$	−1.83984	+	3.18669i	−0.132092	+	0.228791i
$195$	14.9662	+	8.41422i	1.07175	+	0.602555i
$196$		0			0
$197$		−	4.48816i		−	0.319768i	−0.987136	−	0.159884i	$-0.948888\pi$
$197$		−	4.48816i		−	0.319768i	0.987136	−	0.159884i	$-0.0511120\pi$
$198$	−5.03469	+	9.19963i	−0.357800	+	0.653789i
$199$	−14.4866	−	8.36386i	−1.02693	−	0.592899i	−0.110827	−	0.993840i	$-0.535350\pi$
$199$	−14.4866	−	8.36386i	−1.02693	−	0.592899i	−0.916104	+	0.400941i	$0.868683\pi$
$200$	−8.98667	+	5.18846i	−0.635454	+	0.366879i
$201$	0.604603	−	1.07540i	0.0426454	−	0.0758526i
$202$	15.4230	−	8.90448i	1.08516	−	0.626517i
$203$		0			0
$204$	−2.86172	−	4.82838i	−0.200361	−	0.338054i
$205$	−4.24388			−0.296406
$206$	1.90429	−	3.29833i	0.132678	−	0.229806i
$207$	0.645175	+	28.2259i	0.0448428	+	1.96184i
$208$	2.18922	−	1.26395i	0.151795	−	0.0876390i
$209$	−3.74418	+	6.48512i	−0.258991	+	0.448585i
$210$		0			0
$211$	−3.14133	−	5.44095i	−0.216258	−	0.374570i	0.737403	−	0.675453i	$-0.236052\pi$
$211$	−3.14133	−	5.44095i	−0.216258	−	0.374570i	−0.953661	+	0.300883i	$0.902719\pi$
$212$	−9.31359	−	5.37720i	−0.639660	−	0.369308i
$213$	−7.49479	−	4.21368i	−0.513535	−	0.288716i
$214$	4.41500	+	7.64701i	0.301803	+	0.522739i
$215$	−15.6454	−	27.0986i	−1.06701	−	1.84811i
$216$	0.178091	+	5.19310i	0.0121175	+	0.353346i
$217$		0			0
$218$	−0.626226	−	0.361552i	−0.0424134	−	0.0244874i
$219$	9.79628	−	5.80614i	0.661971	−	0.392342i
$220$			13.7080i			0.924190i
$221$			8.19167i			0.551031i
$222$	−0.0519045	−	4.54216i	−0.00348360	−	0.304850i
$223$	11.8166	+	6.82229i	0.791295	+	0.456854i	0.840418	−	0.541938i	$-0.182309\pi$
$223$	11.8166	+	6.82229i	0.791295	+	0.456854i	−0.0491233	+	0.998793i	$0.515643\pi$
$224$		0			0
$225$	−14.9452	+	27.3087i	−0.996348	+	1.82058i
$226$	8.35737	+	14.4754i	0.555924	+	0.962889i
$227$	10.3042	+	17.8475i	0.683916	+	1.18458i	0.973776	+	0.227509i	$0.0730581\pi$
$227$	10.3042	+	17.8475i	0.683916	+	1.18458i	−0.289860	+	0.957069i	$0.593609\pi$
$228$	0.0423959	+	3.71006i	0.00280774	+	0.245705i
$229$	−21.1564	−	12.2146i	−1.39805	−	0.807166i	−0.403863	−	0.914819i	$-0.632333\pi$
$229$	−21.1564	−	12.2146i	−1.39805	−	0.807166i	−0.994188	+	0.107654i	$0.965666\pi$
$230$	18.4521	+	31.9599i	1.21669	+	2.10737i
$231$		0			0
$232$	−4.26458	+	7.38647i	−0.279983	+	0.484945i
$233$	−11.9080	+	6.87509i	−0.780120	+	0.450402i	−0.836473	−	0.548009i	$-0.815386\pi$
$233$	−11.9080	+	6.87509i	−0.780120	+	0.450402i	0.0563529	+	0.998411i	$0.482053\pi$
$234$	3.64077	−	6.65260i	0.238005	−	0.434894i
$235$	16.6195	−	28.7859i	1.08414	−	1.87778i
$236$	2.34116			0.152396
$237$	−7.36173	+	13.0942i	−0.478196	+	0.850558i
$238$		0			0
$239$	0.638992	−	0.368922i	0.0413330	−	0.0238636i	−0.479191	−	0.877711i	$-0.659070\pi$
$239$	0.638992	−	0.368922i	0.0413330	−	0.0238636i	0.520524	+	0.853847i	$0.325737\pi$
$240$	3.46297	+	5.84282i	0.223534	+	0.377153i
$241$	−7.39301	+	4.26836i	−0.476226	+	0.274949i	−0.718842	−	0.695173i	$-0.755328\pi$
$241$	−7.39301	+	4.26836i	−0.476226	+	0.274949i	0.242617	+	0.970122i	$0.421994\pi$
$242$	1.05667	+	0.610068i	0.0679253	+	0.0392167i
$243$	8.55240	+	13.0329i	0.548637	+	0.836061i
$244$		−	4.15474i		−	0.265980i
$245$		0			0
$246$	0.0214192	+	1.87439i	0.00136564	+	0.119507i
$247$	2.70756	−	4.68963i	0.172278	−	0.298394i
$248$	3.29659			0.209334
$249$	1.22657	+	2.06951i	0.0777308	+	0.131150i
$250$			21.0847i			1.33351i
$251$	18.0198			1.13740			0.568700	−	0.822545i	$-0.307446\pi$
$251$	18.0198			1.13740			0.568700	+	0.822545i	$0.307446\pi$
$252$		0			0
$253$	32.8987			2.06832
$254$		−	16.6620i		−	1.04547i
$255$	−22.0080	+	0.251491i	−1.37819	+	0.0157490i
$256$	1.00000			0.0625000
$257$	−9.58490	+	16.6015i	−0.597889	+	1.03557i	0.395243	+	0.918577i	$0.370660\pi$
$257$	−9.58490	+	16.6015i	−0.597889	+	1.03557i	−0.993132	+	0.116998i	$0.962673\pi$
$258$	−11.8897	+	7.04687i	−0.740219	+	0.438719i
$259$		0			0
$260$		−	9.91274i		−	0.614762i
$261$	0.584714	+	25.5808i	0.0361929	+	1.58341i
$262$	−6.82992	−	3.94325i	−0.421954	−	0.243615i
$263$	−7.23178	+	4.17527i	−0.445931	+	0.257458i	−0.706110	−	0.708102i	$-0.749552\pi$
$263$	−7.23178	+	4.17527i	−0.445931	+	0.257458i	0.260179	+	0.965560i	$0.416218\pi$
$264$	6.05439	−	0.0691851i	0.372622	−	0.00425805i
$265$	−36.5218	+	21.0858i	−2.24351	+	1.29529i
$266$		0			0
$267$	27.5981	−	0.315371i	1.68898	−	0.0193004i
$268$	−0.712278			−0.0435093
$269$	5.04657	−	8.74091i	0.307695	−	0.532943i	−0.670163	−	0.742214i	$-0.733776\pi$
$269$	5.04657	−	8.74091i	0.307695	−	0.532943i	0.977858	+	0.209271i	$0.0671092\pi$
$270$	17.9848	+	9.57716i	1.09452	+	0.582848i
$271$	9.18278	−	5.30168i	0.557814	−	0.322054i	−0.194454	−	0.980912i	$-0.562293\pi$
$271$	9.18278	−	5.30168i	0.557814	−	0.322054i	0.752268	+	0.658858i	$0.228960\pi$
$272$	−1.62026	+	2.80636i	−0.0982424	+	0.170161i
$273$		0			0
$274$	0.718193	+	1.24395i	0.0433876	+	0.0751496i
$275$	31.4150	+	18.1374i	1.89439	+	1.09373i
$276$	14.0226	−	8.31102i	0.844061	−	0.500265i
$277$	−5.10161	−	8.83625i	−0.306526	−	0.530919i	0.671074	−	0.741391i	$-0.265833\pi$
$277$	−5.10161	−	8.83625i	−0.306526	−	0.530919i	−0.977600	+	0.210472i	$0.932500\pi$
$278$	0.390409	+	0.676208i	0.0234152	+	0.0405563i
$279$	8.44956	−	5.13931i	0.505862	−	0.307683i
$280$		0			0
$281$	0.427812	+	0.246997i	0.0255211	+	0.0147346i	0.512706	−	0.858564i	$-0.328643\pi$
$281$	0.427812	+	0.246997i	0.0255211	+	0.0147346i	−0.487185	+	0.873299i	$0.661976\pi$
$282$	−12.7977	−	7.19506i	−0.762093	−	0.428459i
$283$			19.8625i			1.18071i	0.807145	+	0.590353i	$0.201011\pi$
$283$			19.8625i			1.18071i	−0.807145	+	0.590353i	$0.798989\pi$
$284$			4.96411i			0.294565i
$285$	12.6824	+	7.13024i	0.751242	+	0.422359i
$286$	−7.65293	−	4.41842i	−0.452527	−	0.261267i
$287$		0			0
$288$	2.56312	−	1.55898i	0.151033	−	0.0918637i
$289$	3.24955	+	5.62838i	0.191150	+	0.331081i
$290$	16.7229	+	28.9649i	0.982000	+	1.70087i
$291$	5.48273	−	3.24955i	0.321404	−	0.190492i
$292$	−5.69382	−	3.28733i	−0.333206	−	0.192376i
$293$	−4.12998	−	7.15333i	−0.241276	−	0.417902i	0.719802	−	0.694179i	$-0.244233\pi$
$293$	−4.12998	−	7.15333i	−0.241276	−	0.417902i	−0.961078	+	0.276277i	$0.910899\pi$
$294$		0			0
$295$	4.59024	−	7.95053i	0.267254	−	0.462898i
$296$	−2.27123	+	1.31130i	−0.132013	+	0.0762175i
$297$	15.4103	−	9.61599i	0.894195	−	0.557976i
$298$	−6.48697	+	11.2358i	−0.375780	+	0.650870i
$299$	−23.7903			−1.37583
$300$	17.9722	−	0.205373i	1.03762	−	0.0118572i
$301$		0			0
$302$	−15.5311	+	8.96690i	−0.893716	+	0.515987i
$303$	−30.8440	+	0.352463i	−1.77194	+	0.0202485i
$304$	1.85515	−	1.07107i	0.106400	−	0.0614303i
$305$	−14.1094	−	8.14607i	−0.807902	−	0.466443i
$306$	0.222152	+	9.71899i	0.0126996	+	0.555598i
$307$		−	4.49595i		−	0.256597i	−0.991736	−	0.128299i	$-0.959048\pi$
$307$		−	4.49595i		−	0.256597i	0.991736	−	0.128299i	$-0.0409516\pi$
$308$		0			0
$309$	−5.67481	+	3.36339i	−0.322829	+	0.191337i
$310$	6.46353	−	11.1952i	0.367104	−	0.635842i
$311$	−11.4625			−0.649982			−0.324991	−	0.945717i	$-0.605361\pi$
$311$	−11.4625			−0.649982			−0.324991	+	0.945717i	$0.605361\pi$
$312$	−4.37816	+	0.0500304i	−0.247864	+	0.00283241i
$313$		−	12.7442i		−	0.720345i	−0.932886	−	0.360173i	$-0.882718\pi$
$313$		−	12.7442i		−	0.720345i	0.932886	−	0.360173i	$-0.117282\pi$
$314$	−13.4739			−0.760374
$315$		0			0
$316$	8.67280			0.487883
$317$			14.8180i			0.832264i	0.909304	+	0.416132i	$0.136615\pi$
$317$			14.8180i			0.832264i	−0.909304	+	0.416132i	$0.863385\pi$
$318$	9.49731	+	16.0241i	0.532583	+	0.898589i
$319$	29.8156			1.66936
$320$	1.96067	−	3.39598i	0.109605	−	0.189841i
$321$	−0.174757	−	15.2930i	−0.00975401	−	0.853573i
$322$		0			0
$323$			6.94165i			0.386244i
$324$	4.13917	−	7.99170i	0.229954	−	0.443983i
$325$	−22.7174	−	13.1159i	−1.26013	−	0.727538i
$326$	10.5250	−	6.07661i	0.582926	−	0.336552i
$327$	0.638579	+	1.07743i	0.0353135	+	0.0595819i
$328$	0.937258	−	0.541126i	0.0517514	−	0.0298787i
$329$		0			0
$330$	11.6357	−	20.6962i	0.640525	−	1.13929i
$331$	−5.03387			−0.276687			−0.138343	−	0.990384i	$-0.544178\pi$
$331$	−5.03387			−0.276687			−0.138343	+	0.990384i	$0.544178\pi$
$332$	0.694462	−	1.20284i	0.0381136	−	0.0660146i
$333$	−3.77716	+	6.90181i	−0.206987	+	0.378217i
$334$	4.47299	−	2.58248i	0.244751	−	0.141307i
$335$	−1.39654	+	2.41888i	−0.0763013	+	0.132158i
$336$		0			0
$337$	−8.15768	−	14.1295i	−0.444377	−	0.769683i	0.553632	−	0.832762i	$-0.313242\pi$
$337$	−8.15768	−	14.1295i	−0.444377	−	0.769683i	−0.998009	+	0.0630783i	$0.979908\pi$
$338$	−5.72421	−	3.30487i	−0.311356	−	0.179761i
$339$	−0.330807	−	28.9489i	−0.0179670	−	1.57229i
$340$	6.35357	+	11.0047i	0.344571	+	0.596814i
$341$	−5.76200	−	9.98007i	−0.312030	−	0.540451i
$342$	3.08520	−	5.63743i	0.166829	−	0.304837i
$343$		0			0
$344$	6.91055	+	3.98981i	0.372592	+	0.215116i
$345$	−0.730382	−	63.9157i	−0.0393224	−	3.44110i
$346$			19.8227i			1.06568i
$347$		−	27.3946i		−	1.47062i	−0.677731	−	0.735310i	$-0.737037\pi$
$347$		−	27.3946i		−	1.47062i	0.677731	−	0.735310i	$-0.262963\pi$
$348$	12.7085	−	7.53217i	0.681247	−	0.403767i
$349$	−14.5762	−	8.41557i	−0.780246	−	0.450475i	0.0562717	−	0.998415i	$-0.482079\pi$
$349$	−14.5762	−	8.41557i	−0.780246	−	0.450475i	−0.836517	+	0.547940i	$0.815412\pi$
$350$		0			0
$351$	−11.1437	+	6.95368i	−0.594809	+	0.371160i
$352$	−1.74787	−	3.02739i	−0.0931616	−	0.161361i
$353$	−7.36690	−	12.7598i	−0.392101	−	0.679138i	0.600626	−	0.799530i	$-0.294918\pi$
$353$	−7.36690	−	12.7598i	−0.392101	−	0.679138i	−0.992726	+	0.120392i	$0.961585\pi$
$354$	−3.53468	−	1.98724i	−0.187866	−	0.105621i
$355$	16.8580	+	9.73297i	0.894730	+	0.516573i
$356$	−7.96740	−	13.7999i	−0.422272	−	0.731396i
$357$		0			0
$358$	−4.08197	+	7.07019i	−0.215739	+	0.373671i
$359$	−12.3103	+	7.10734i	−0.649712	+	0.375111i	−0.788346	−	0.615232i	$-0.789062\pi$
$359$	−12.3103	+	7.10734i	−0.649712	+	0.375111i	0.138634	+	0.990344i	$0.455729\pi$
$360$	−0.268826	−	11.7610i	−0.0141684	−	0.619857i
$361$	−7.20560	+	12.4805i	−0.379242	+	0.656867i
$362$	−3.09557			−0.162699
$363$	−1.07751	−	1.81801i	−0.0565548	−	0.0954209i
$364$		0			0
$365$	−22.3274	+	12.8907i	−1.16867	+	0.674732i
$366$	−3.52666	+	6.27281i	−0.184342	+	0.327885i
$367$	7.27668	−	4.20119i	0.379840	−	0.219301i	−0.297909	−	0.954594i	$-0.596289\pi$
$367$	7.27668	−	4.20119i	0.379840	−	0.219301i	0.677749	+	0.735294i	$0.262956\pi$
$368$	−8.15025	−	4.70555i	−0.424861	−	0.245294i
$369$	1.55870	−	2.84814i	0.0811428	−	0.148268i
$370$			10.2841i			0.534643i
$371$		0			0
$372$	−4.97718	−	2.79824i	−0.258055	−	0.145082i
$373$	−16.3887	+	28.3860i	−0.848572	+	1.46977i	0.0339102	+	0.999425i	$0.489204\pi$
$373$	−16.3887	+	28.3860i	−0.848572	+	1.46977i	−0.882482	+	0.470345i	$0.844129\pi$
$374$	11.3280			0.585755
$375$	17.8973	−	31.8336i	0.924213	−	1.64388i
$376$			8.47645i			0.437139i
$377$	−21.5608			−1.11044
$378$		0			0
$379$	7.58954			0.389848			0.194924	−	0.980818i	$-0.437554\pi$
$379$	7.58954			0.389848			0.194924	+	0.980818i	$0.437554\pi$
$380$		−	8.40009i		−	0.430915i
$381$	−14.1432	+	25.1562i	−0.724577	+	1.28879i
$382$	−4.52911			−0.231729
$383$	−5.40174	+	9.35608i	−0.276016	+	0.478073i	−0.970391	−	0.241540i	$-0.922348\pi$
$383$	−5.40174	+	9.35608i	−0.276016	+	0.478073i	0.694375	+	0.719613i	$0.255681\pi$
$384$	−1.50980	−	0.848829i	−0.0770465	−	0.0433166i
$385$		0			0
$386$		−	6.04602i		−	0.307735i
$387$	23.9326	−	0.547040i	1.21656	−	0.0278076i
$388$	−3.18669	−	1.83984i	−0.161780	−	0.0934035i
$389$	11.0290	−	6.36757i	0.559190	−	0.322849i	−0.193630	−	0.981075i	$-0.562026\pi$
$389$	11.0290	−	6.36757i	0.559190	−	0.322849i	0.752820	+	0.658226i	$0.228693\pi$
$390$	−8.41422	+	14.9662i	−0.426071	+	0.757844i
$391$	26.4110	−	15.2484i	1.33566	−	0.771144i
$392$		0			0
$393$	6.96464	+	11.7509i	0.351320	+	0.592757i
$394$	4.48816			0.226110
$395$	17.0045	−	29.4527i	0.855590	−	1.48192i
$396$	−9.19963	−	5.03469i	−0.462299	−	0.253002i
$397$	−19.1183	+	11.0380i	−0.959521	+	0.553980i	−0.896026	−	0.444002i	$-0.853558\pi$
$397$	−19.1183	+	11.0380i	−0.959521	+	0.553980i	−0.0634954	+	0.997982i	$0.520225\pi$
$398$	8.36386	−	14.4866i	0.419243	−	0.726150i
$399$		0			0
$400$	−5.18846	−	8.98667i	−0.259423	−	0.449334i
$401$	0.237776	+	0.137280i	0.0118740	+	0.00685544i	0.505925	−	0.862577i	$-0.331151\pi$
$401$	0.237776	+	0.137280i	0.0118740	+	0.00685544i	−0.494051	+	0.869433i	$0.664484\pi$
$402$	1.07540	+	0.604603i	0.0536359	+	0.0301548i
$403$	4.16672	+	7.21696i	0.207559	+	0.359503i
$404$	8.90448	+	15.4230i	0.443015	+	0.767324i
$405$	−19.0241	−	29.7256i	−0.945315	−	1.47708i
$406$		0			0
$407$	7.93961	+	4.58394i	0.393552	+	0.227217i
$408$	4.82838	−	2.86172i	0.239040	−	0.141676i
$409$		−	11.7571i		−	0.581353i	−0.956821	−	0.290676i	$-0.906120\pi$
$409$		−	11.7571i		−	0.581353i	0.956821	−	0.290676i	$-0.0938803\pi$
$410$		−	4.24388i		−	0.209590i
$411$	−0.0284280	−	2.48773i	−0.00140225	−	0.122711i
$412$	3.29833	+	1.90429i	0.162497	+	0.0938177i
$413$		0			0
$414$	−28.2259	+	0.645175i	−1.38723	+	0.0317086i
$415$	−2.72322	−	4.71676i	−0.133678	−	0.231537i
$416$	1.26395	+	2.18922i	0.0619701	+	0.107335i
$417$	−0.0154534	−	1.35233i	−0.000756757	−	0.0662238i
$418$	−6.48512	−	3.74418i	−0.317197	−	0.183134i
$419$	−15.2331	−	26.3845i	−0.744186	−	1.28897i	−0.950574	−	0.310498i	$-0.899504\pi$
$419$	−15.2331	−	26.3845i	−0.744186	−	1.28897i	0.206388	−	0.978470i	$-0.433829\pi$
$420$		0			0
$421$	−0.945989	+	1.63850i	−0.0461047	+	0.0798557i	−0.888157	−	0.459540i	$-0.848014\pi$
$421$	−0.945989	+	1.63850i	−0.0461047	+	0.0798557i	0.842052	+	0.539396i	$0.181347\pi$
$422$	5.44095	−	3.14133i	0.264861	−	0.152918i
$423$	13.2146	+	21.7262i	0.642516	+	1.05636i
$424$	5.37720	−	9.31359i	0.261140	−	0.452308i
$425$	33.6265			1.63112
$426$	4.21368	−	7.49479i	0.204153	−	0.363124i
$427$		0			0
$428$	−7.64701	+	4.41500i	−0.369632	+	0.213407i
$429$	7.80389	+	13.1669i	0.376775	+	0.635706i
$430$	27.0986	−	15.6454i	1.30681	−	0.754488i
$431$	−28.0189	−	16.1767i	−1.34962	−	0.779206i	−0.361428	−	0.932400i	$-0.617711\pi$
$431$	−28.0189	−	16.1767i	−1.34962	−	0.779206i	−0.988196	+	0.153194i	$0.951044\pi$
$432$	−5.19310	+	0.178091i	−0.249853	+	0.00856840i
$433$			24.2391i			1.16485i	0.812883	+	0.582427i	$0.197897\pi$
$433$			24.2391i			1.16485i	−0.812883	+	0.582427i	$0.802103\pi$
$434$		0			0
$435$	−0.661935	−	57.9259i	−0.0317374	−	2.77734i
$436$	0.361552	−	0.626226i	0.0173152	−	0.0299908i
$437$	−20.1600			−0.964381
$438$	5.80614	+	9.79628i	0.277428	+	0.468084i
$439$			25.7773i			1.23028i	0.788417	+	0.615141i	$0.210901\pi$
$439$			25.7773i			1.23028i	−0.788417	+	0.615141i	$0.789099\pi$
$440$	−13.7080			−0.653501
$441$		0			0
$442$	−8.19167			−0.389638
$443$		−	24.6563i		−	1.17146i	−0.810507	−	0.585729i	$-0.800808\pi$
$443$		−	24.6563i		−	1.17146i	0.810507	−	0.585729i	$-0.199192\pi$
$444$	4.54216	−	0.0519045i	0.215562	−	0.00246328i
$445$	−62.4858			−2.96211
$446$	−6.82229	+	11.8166i	−0.323045	+	0.559530i
$447$	19.3313	−	11.4574i	0.914337	−	0.541916i
$448$		0			0
$449$		−	21.8330i		−	1.03036i	−0.857081	−	0.515182i	$-0.827724\pi$
$449$		−	21.8330i		−	1.03036i	0.857081	−	0.515182i	$-0.172276\pi$
$450$	−27.3087	−	14.9452i	−1.28734	−	0.704525i
$451$	−3.27640	−	1.89163i	−0.154280	−	0.0890735i
$452$	−14.4754	+	8.35737i	−0.680865	+	0.393098i
$453$	31.0602	−	0.354934i	1.45934	−	0.0166762i
$454$	−17.8475	+	10.3042i	−0.837623	+	0.483602i
$455$		0			0
$456$	−3.71006	+	0.0423959i	−0.173740	+	0.00198537i
$457$	−3.16073			−0.147853			−0.0739265	−	0.997264i	$-0.523553\pi$
$457$	−3.16073			−0.147853			−0.0739265	+	0.997264i	$0.523553\pi$
$458$	12.2146	−	21.1564i	0.570752	−	0.988572i
$459$	7.91436	−	14.8623i	0.369411	−	0.693712i
$460$	−31.9599	+	18.4521i	−1.49014	+	0.860332i
$461$	−5.18303	+	8.97728i	−0.241398	+	0.418113i	−0.961113	−	0.276156i	$-0.910939\pi$
$461$	−5.18303	+	8.97728i	−0.241398	+	0.418113i	0.719715	+	0.694270i	$0.244273\pi$
$462$		0			0
$463$	11.4460	+	19.8250i	0.531939	+	0.921346i	0.999305	+	0.0372815i	$0.0118698\pi$
$463$	11.4460	+	19.8250i	0.531939	+	0.921346i	−0.467366	+	0.884064i	$0.654797\pi$
$464$	−7.38647	−	4.26458i	−0.342908	−	0.197978i
$465$	−19.2614	+	11.4160i	−0.893226	+	0.529404i
$466$	−6.87509	−	11.9080i	−0.318483	−	0.551628i
$467$	−2.27634	−	3.94274i	−0.105337	−	0.182448i	0.808539	−	0.588443i	$-0.200259\pi$
$467$	−2.27634	−	3.94274i	−0.105337	−	0.182448i	−0.913876	+	0.405994i	$0.866925\pi$
$468$	6.65260	+	3.64077i	0.307516	+	0.168295i
$469$		0			0
$470$	28.7859	+	16.6195i	1.32779	+	0.766601i
$471$	20.3428	+	11.4370i	0.937347	+	0.526990i
$472$			2.34116i			0.107761i
$473$		−	27.8946i		−	1.28260i
$474$	−13.0942	−	7.36173i	−0.601435	−	0.338135i
$475$	−19.2508	−	11.1144i	−0.883286	−	0.509965i
$476$		0			0
$477$	−0.737265	−	32.2548i	−0.0337570	−	1.47685i
$478$	0.368922	+	0.638992i	0.0168741	+	0.0292268i
$479$	−17.4420	−	30.2104i	−0.796945	−	1.38035i	−0.921597	−	0.388148i	$-0.873115\pi$
$479$	−17.4420	−	30.2104i	−0.796945	−	1.38035i	0.124652	−	0.992200i	$-0.460218\pi$
$480$	−5.84282	+	3.46297i	−0.266687	+	0.158062i
$481$	−5.74143	−	3.31482i	−0.261787	−	0.151143i
$482$	−4.26836	−	7.39301i	−0.194418	−	0.336742i
$483$		0			0
$484$	−0.610068	+	1.05667i	−0.0277304	+	0.0480304i
$485$	−12.4961	+	7.21462i	−0.567418	+	0.327599i
$486$	−13.0329	+	8.55240i	−0.591184	+	0.387945i
$487$	−0.567874	+	0.983587i	−0.0257328	+	0.0445706i	−0.878605	−	0.477549i	$-0.841525\pi$
$487$	−0.567874	+	0.983587i	−0.0257328	+	0.0445706i	0.852872	+	0.522120i	$0.174859\pi$
$488$	4.15474			0.188076
$489$	−21.0486	+	0.240528i	−0.951851	+	0.0108771i
$490$		0			0
$491$	10.6183	−	6.13045i	0.479195	−	0.276663i	−0.240886	−	0.970553i	$-0.577438\pi$
$491$	10.6183	−	6.13045i	0.479195	−	0.276663i	0.720081	+	0.693890i	$0.244105\pi$
$492$	−1.87439	+	0.0214192i	−0.0845042	+	0.000965652i
$493$	23.9359	−	13.8194i	1.07802	−	0.622395i
$494$	4.68963	+	2.70756i	0.210996	+	0.121819i
$495$	−35.1351	+	21.3704i	−1.57921	+	0.960528i
$496$			3.29659i			0.148021i
$497$		0			0
$498$	−2.06951	+	1.22657i	−0.0927368	+	0.0549640i
$499$	20.4415	−	35.4057i	0.915086	−	1.58498i	0.108312	−	0.994117i	$-0.465456\pi$
$499$	20.4415	−	35.4057i	0.915086	−	1.58498i	0.806775	−	0.590859i	$-0.201211\pi$
$500$	−21.0847			−0.942937
$501$	−8.94540	+	0.102221i	−0.399651	+	0.00456692i
$502$			18.0198i			0.804264i
$503$	6.36278			0.283702			0.141851	−	0.989888i	$-0.454695\pi$
$503$	6.36278			0.283702			0.141851	+	0.989888i	$0.454695\pi$
$504$		0			0
$505$	69.8350			3.10762
$506$			32.8987i			1.46252i
$507$	5.83713	+	9.84857i	0.259236	+	0.437390i
$508$	16.6620			0.739256
$509$	11.5004	−	19.9192i	0.509744	−	0.882903i	−0.490192	−	0.871614i	$-0.663073\pi$
$509$	11.5004	−	19.9192i	0.509744	−	0.882903i	0.999936	−	0.0112884i	$-0.00359327\pi$
$510$	−0.251491	−	22.0080i	−0.0111362	−	0.974530i
$511$		0			0
$512$			1.00000i			0.0441942i
$513$	−9.44325	+	5.89258i	−0.416930	+	0.260164i
$514$	−16.6015	−	9.58490i	−0.732262	−	0.422772i
$515$	12.9339	−	7.46738i	0.569935	−	0.329052i
$516$	−7.04687	−	11.8897i	−0.310221	−	0.523414i
$517$	25.6615	−	14.8157i	1.12859	−	0.651593i
$518$		0			0
$519$	16.8261	−	29.9283i	0.738585	−	1.31371i
$520$	9.91274			0.434702
$521$	−14.9993	+	25.9795i	−0.657131	+	1.13818i	0.324224	+	0.945980i	$0.394897\pi$
$521$	−14.9993	+	25.9795i	−0.657131	+	1.13818i	−0.981355	+	0.192203i	$0.938437\pi$
$522$	−25.5808	+	0.584714i	−1.11964	+	0.0255922i
$523$	−18.6402	+	10.7619i	−0.815079	+	0.470586i	−0.848716	−	0.528848i	$-0.822624\pi$
$523$	−18.6402	+	10.7619i	−0.815079	+	0.470586i	0.0336377	+	0.999434i	$0.489291\pi$
$524$	3.94325	−	6.82992i	0.172262	−	0.298366i
$525$		0			0
$526$	−4.17527	−	7.23178i	−0.182050	−	0.315321i
$527$	−9.25143	−	5.34132i	−0.402999	−	0.232671i
$528$	0.0691851	+	6.05439i	0.00301090	+	0.263483i
$529$	32.7844	+	56.7843i	1.42541	+	2.46888i
$530$	−21.0858	−	36.5218i	−0.915911	−	1.58640i
$531$	3.64981	+	6.00067i	0.158388	+	0.260407i
$532$		0			0
$533$	2.36929	+	1.36791i	0.102625	+	0.0592508i
$534$	0.315371	+	27.5981i	0.0136474	+	1.19429i
$535$			34.6254i			1.49699i
$536$		−	0.712278i		−	0.0307657i
$537$	12.1643	−	7.20965i	0.524930	−	0.311120i
$538$	8.74091	+	5.04657i	0.376847	+	0.217573i
$539$		0			0
$540$	−9.57716	+	17.9848i	−0.412135	+	0.773944i
$541$	−13.8405	−	23.9725i	−0.595051	−	1.03066i	−0.993540	−	0.113486i	$-0.963798\pi$
$541$	−13.8405	−	23.9725i	−0.595051	−	1.03066i	0.398488	−	0.917173i	$-0.369535\pi$
$542$	5.30168	+	9.18278i	0.227727	+	0.394434i
$543$	4.67368	+	2.62761i	0.200567	+	0.112761i
$544$	−2.80636	−	1.62026i	−0.120322	−	0.0694679i
$545$	−1.41777	−	2.45565i	−0.0607305	−	0.105188i
$546$		0			0
$547$	4.28757	−	7.42630i	0.183323	−	0.317526i	−0.759687	−	0.650289i	$-0.774648\pi$
$547$	4.28757	−	7.42630i	0.183323	−	0.317526i	0.943010	+	0.332764i	$0.107981\pi$
$548$	−1.24395	+	0.718193i	−0.0531388	+	0.0306797i
$549$	10.6491	−	6.47715i	0.454492	−	0.276438i
$550$	−18.1374	+	31.4150i	−0.773383	+	1.33954i
$551$	−18.2707			−0.778358
$552$	8.31102	+	14.0226i	0.353741	+	0.596842i
$553$		0			0
$554$	8.83625	−	5.10161i	0.375416	−	0.216747i
$555$	8.72942	−	15.5269i	0.370543	−	0.659079i
$556$	−0.676208	+	0.390409i	−0.0286776	+	0.0165570i
$557$	24.3375	+	14.0512i	1.03121	+	0.595370i	0.917331	−	0.398125i	$-0.130339\pi$
$557$	24.3375	+	14.0512i	1.03121	+	0.595370i	0.113880	+	0.993495i	$0.463672\pi$
$558$	5.13931	+	8.44956i	0.217564	+	0.357698i
$559$			20.1716i			0.853169i
$560$		0			0
$561$	−17.1029	−	9.61550i	−0.722086	−	0.405967i
$562$	−0.246997	+	0.427812i	−0.0104190	+	0.0180462i
$563$	5.13035			0.216218			0.108109	−	0.994139i	$-0.465520\pi$
$563$	5.13035			0.216218			0.108109	+	0.994139i	$0.465520\pi$
$564$	7.19506	−	12.7977i	0.302967	−	0.538881i
$565$			65.5442i			2.75746i
$566$	−19.8625			−0.834885
$567$		0			0
$568$	−4.96411			−0.208289
$569$		−	40.8553i		−	1.71275i	−0.516359	−	0.856373i	$-0.672713\pi$
$569$		−	40.8553i		−	1.71275i	0.516359	−	0.856373i	$-0.327287\pi$
$570$	−7.13024	+	12.6824i	−0.298653	+	0.531209i
$571$	−18.5903			−0.777980			−0.388990	−	0.921242i	$-0.627176\pi$
$571$	−18.5903			−0.777980			−0.388990	+	0.921242i	$0.627176\pi$
$572$	4.41842	−	7.65293i	0.184743	−	0.319985i
$573$	6.83803	+	3.84444i	0.285663	+	0.160604i
$574$		0			0
$575$			97.6582i			4.07263i
$576$	1.55898	+	2.56312i	0.0649574	+	0.106797i
$577$	6.62819	+	3.82678i	0.275935	+	0.159311i	0.631582	−	0.775309i	$-0.282406\pi$
$577$	6.62819	+	3.82678i	0.275935	+	0.159311i	−0.355647	+	0.934620i	$0.615739\pi$
$578$	−5.62838	+	3.24955i	−0.234110	+	0.135163i
$579$	−5.13204	+	9.12827i	−0.213280	+	0.379358i
$580$	−28.9649	+	16.7229i	−1.20270	+	0.694379i
$581$		0			0
$582$	3.24955	+	5.48273i	0.134698	+	0.227267i
$583$	−37.5945			−1.55701
$584$	3.28733	−	5.69382i	0.136031	−	0.235612i
$585$	25.4075	−	15.4537i	1.05047	−	0.638934i
$586$	7.15333	−	4.12998i	0.295501	−	0.170608i
$587$	−14.9114	+	25.8274i	−0.615461	+	1.06601i	0.374843	+	0.927088i	$0.377697\pi$
$587$	−14.9114	+	25.8274i	−0.615461	+	1.06601i	−0.990303	+	0.138921i	$0.955637\pi$
$588$		0			0
$589$	3.53089	+	6.11568i	0.145488	+	0.251992i
$590$	7.95053	+	4.59024i	0.327318	+	0.188977i
$591$	−6.77621	−	3.80968i	−0.278736	−	0.156709i
$592$	−1.31130	−	2.27123i	−0.0538939	−	0.0933470i
$593$	13.7732	+	23.8559i	0.565598	+	0.979644i	0.996994	+	0.0774814i	$0.0246878\pi$
$593$	13.7732	+	23.8559i	0.565598	+	0.979644i	−0.431396	+	0.902163i	$0.641979\pi$
$594$	9.61599	+	15.4103i	0.394549	+	0.632291i
$595$		0			0
$596$	−11.2358	−	6.48697i	−0.460235	−	0.265717i
$597$	−24.9244	+	14.7724i	−1.02009	+	0.604594i
$598$		−	23.7903i		−	0.972857i
$599$		−	9.20217i		−	0.375991i	−0.982170	−	0.187995i	$-0.939801\pi$
$599$		−	9.20217i		−	0.375991i	0.982170	−	0.187995i	$-0.0601990\pi$
$600$	0.205373	+	17.9722i	0.00838431	+	0.733711i
$601$	30.6394	+	17.6896i	1.24981	+	0.721576i	0.971071	−	0.238792i	$-0.0767516\pi$
$601$	30.6394	+	17.6896i	1.24981	+	0.721576i	0.278735	+	0.960368i	$0.410085\pi$
$602$		0			0
$603$	−1.11043	−	1.82566i	−0.0452201	−	0.0743464i
$604$	−8.96690	−	15.5311i	−0.364858	−	0.631953i
$605$	2.39229	+	4.14356i	0.0972603	+	0.168460i
$606$	−0.352463	−	30.8440i	−0.0143178	−	1.25295i
$607$	−18.4638	−	10.6601i	−0.749423	−	0.432680i	0.0760623	−	0.997103i	$-0.475765\pi$
$607$	−18.4638	−	10.6601i	−0.749423	−	0.432680i	−0.825485	+	0.564423i	$0.809099\pi$
$608$	1.07107	+	1.85515i	0.0434378	+	0.0752364i
$609$		0			0
$610$	8.14607	−	14.1094i	0.329825	−	0.571273i
$611$	−18.5568	+	10.7138i	−0.750728	+	0.433433i
$612$	−9.71899	+	0.222152i	−0.392867	+	0.00897997i
$613$	17.5594	−	30.4139i	0.709219	−	1.22840i	−0.255928	−	0.966696i	$-0.582381\pi$
$613$	17.5594	−	30.4139i	0.709219	−	1.22840i	0.965147	−	0.261708i	$-0.0842857\pi$
$614$	4.49595			0.181442
$615$	−3.60233	+	6.40740i	−0.145260	+	0.258371i
$616$		0			0
$617$	−2.01203	+	1.16165i	−0.0810014	+	0.0467662i	−0.539954	−	0.841695i	$-0.681558\pi$
$617$	−2.01203	+	1.16165i	−0.0810014	+	0.0467662i	0.458952	+	0.888461i	$0.348225\pi$
$618$	−3.36339	−	5.67481i	−0.135296	−	0.228274i
$619$	−2.35448	+	1.35936i	−0.0946344	+	0.0546372i	−0.546570	−	0.837413i	$-0.684067\pi$
$619$	−2.35448	+	1.35936i	−0.0946344	+	0.0546372i	0.451936	+	0.892050i	$0.350734\pi$
$620$	11.1952	+	6.46353i	0.449608	+	0.259581i
$621$	43.1631	+	22.9849i	1.73208	+	0.922353i
$622$		−	11.4625i		−	0.459606i
$623$		0			0
$624$	−0.0500304	−	4.37816i	−0.00200282	−	0.175267i
$625$	−15.3979	+	26.6699i	−0.615915	+	1.06680i
$626$	12.7442			0.509361
$627$	6.61304	+	11.1577i	0.264099	+	0.445596i
$628$		−	13.4739i		−	0.537666i
$629$	8.49853			0.338859
$630$		0			0
$631$	−11.8136			−0.470291			−0.235146	−	0.971960i	$-0.575557\pi$
$631$	−11.8136			−0.470291			−0.235146	+	0.971960i	$0.575557\pi$
$632$			8.67280i			0.344986i
$633$	−10.8812	+	0.124342i	−0.432488	+	0.00494216i
$634$	−14.8180			−0.588499
$635$	32.6687	−	56.5838i	1.29642	−	2.24546i
$636$	−16.0241	+	9.49731i	−0.635398	+	0.376593i
$637$		0			0
$638$			29.8156i			1.18041i
$639$	−12.7236	+	7.73893i	−0.503338	+	0.306147i
$640$	3.39598	+	1.96067i	0.134238	+	0.0775023i
$641$	−0.646292	+	0.373137i	−0.0255270	+	0.0147380i	−0.512709	−	0.858562i	$-0.671358\pi$
$641$	−0.646292	+	0.373137i	−0.0255270	+	0.0147380i	0.487182	+	0.873300i	$0.338025\pi$
$642$	15.2930	−	0.174757i	0.603567	−	0.00689712i
$643$	12.0878	−	6.97891i	0.476697	−	0.275221i	−0.242342	−	0.970191i	$-0.577916\pi$
$643$	12.0878	−	6.97891i	0.476697	−	0.275221i	0.719039	+	0.694970i	$0.244582\pi$
$644$		0			0
$645$	−54.1937	+	0.619286i	−2.13388	+	0.0243844i
$646$	−6.94165			−0.273115
$647$	−10.5619	+	18.2938i	−0.415232	+	0.719203i	−0.995453	−	0.0952562i	$-0.969633\pi$
$647$	−10.5619	+	18.2938i	−0.415232	+	0.719203i	0.580221	+	0.814459i	$0.302966\pi$
$648$	7.99170	+	4.13917i	0.313944	+	0.162602i
$649$	7.08760	−	4.09203i	0.278213	−	0.160626i
$650$	13.1159	−	22.7174i	0.514447	−	0.891048i
$651$		0			0
$652$	6.07661	+	10.5250i	0.237978	+	0.412191i
$653$	−9.78350	−	5.64851i	−0.382858	−	0.221043i	0.296203	−	0.955125i	$-0.404280\pi$
$653$	−9.78350	−	5.64851i	−0.382858	−	0.221043i	−0.679061	+	0.734082i	$0.737613\pi$
$654$	−1.07743	+	0.638579i	−0.0421308	+	0.0249704i
$655$	−15.4628	−	26.7824i	−0.604183	−	1.04648i
$656$	0.541126	+	0.937258i	0.0211274	+	0.0365938i
$657$	−0.450723	−	19.7188i	−0.0175844	−	0.769304i
$658$		0			0
$659$	−10.3938	−	6.00088i	−0.404886	−	0.233761i	0.283704	−	0.958912i	$-0.408437\pi$
$659$	−10.3938	−	6.00088i	−0.404886	−	0.233761i	−0.688590	+	0.725151i	$0.741770\pi$
$660$	20.6962	+	11.6357i	0.805600	+	0.452919i
$661$		−	23.9216i		−	0.930443i	−0.885194	−	0.465221i	$-0.845975\pi$
$661$		−	23.9216i		−	0.930443i	0.885194	−	0.465221i	$-0.154025\pi$
$662$		−	5.03387i		−	0.195647i
$663$	12.3678	+	6.95333i	0.480324	+	0.270045i
$664$	1.20284	+	0.694462i	0.0466794	+	0.0269504i
$665$		0			0
$666$	−6.90181	−	3.77716i	−0.267440	−	0.146362i
$667$	40.1344	+	69.5148i	1.55401	+	2.69162i
$668$	2.58248	+	4.47299i	0.0999193	+	0.173065i
$669$	20.3305	−	12.0496i	0.786023	−	0.465866i
$670$	−2.41888	−	1.39654i	−0.0934496	−	0.0539532i
$671$	−7.26192	−	12.5780i	−0.280343	−	0.485569i
$672$		0			0
$673$	−3.45087	+	5.97708i	−0.133021	+	0.230399i	−0.924840	−	0.380357i	$-0.875801\pi$
$673$	−3.45087	+	5.97708i	−0.133021	+	0.230399i	0.791819	+	0.610756i	$0.209135\pi$
$674$	14.1295	−	8.15768i	0.544248	−	0.314222i
$675$	28.5446	+	45.7447i	1.09868	+	1.76071i
$676$	3.30487	−	5.72421i	0.127111	−	0.220162i
$677$	−40.7204			−1.56501			−0.782505	−	0.622644i	$-0.786059\pi$
$677$	−40.7204			−1.56501			−0.782505	+	0.622644i	$0.786059\pi$
$678$	28.9489	−	0.330807i	1.11178	−	0.0127046i
$679$		0			0
$680$	−11.0047	+	6.35357i	−0.422011	+	0.243648i
$681$	35.6926	−	0.407869i	1.36774	−	0.0156296i
$682$	9.98007	−	5.76200i	0.382157	−	0.220638i
$683$	−22.0942	−	12.7561i	−0.845413	−	0.488099i	0.0136877	−	0.999906i	$-0.495643\pi$
$683$	−22.0942	−	12.7561i	−0.845413	−	0.488099i	−0.859100	+	0.511807i	$0.828976\pi$
$684$	5.63743	+	3.08520i	0.215553	+	0.117966i
$685$			5.63256i			0.215209i
$686$		0			0
$687$	−36.3998	+	21.5737i	−1.38874	+	0.823088i
$688$	−3.98981	+	6.91055i	−0.152110	+	0.263462i
$689$	27.1860			1.03570
$690$	63.9157	−	0.730382i	2.43323	−	0.0278052i
$691$		−	46.8100i		−	1.78074i	−0.455242	−	0.890368i	$-0.650447\pi$
$691$		−	46.8100i		−	1.78074i	0.455242	−	0.890368i	$-0.349553\pi$
$692$	−19.8227			−0.753548
$693$		0			0
$694$	27.3946			1.03989
$695$			3.06185i			0.116143i
$696$	7.53217	+	12.7085i	0.285506	+	0.481714i
$697$	−3.50705			−0.132839
$698$	8.41557	−	14.5762i	0.318534	−	0.551717i
$699$	0.272134	+	23.8145i	0.0102931	+	0.900746i
$700$		0			0
$701$		−	14.0123i		−	0.529239i	−0.964353	−	0.264619i	$-0.914754\pi$
$701$		−	14.0123i		−	0.529239i	0.964353	−	0.264619i	$-0.0852463\pi$
$702$	−6.95368	−	11.1437i	−0.262450	−	0.420594i
$703$	−4.86531	−	2.80899i	−0.183499	−	0.105943i
$704$	3.02739	−	1.74787i	0.114099	−	0.0658752i
$705$	−29.3537	−	49.5264i	−1.10552	−	1.86527i
$706$	12.7598	−	7.36690i	0.480223	−	0.277257i
$707$		0			0
$708$	1.98724	−	3.53468i	0.0746852	−	0.132841i
$709$	31.2006			1.17176			0.585882	−	0.810397i	$-0.300748\pi$
$709$	31.2006			1.17176			0.585882	+	0.810397i	$0.300748\pi$
$710$	−9.73297	+	16.8580i	−0.365272	+	0.632670i
$711$	13.5207	+	22.2294i	0.507066	+	0.833669i
$712$	13.7999	−	7.96740i	0.517175	−	0.298591i
$713$	15.5123	−	26.8680i	0.580939	−	1.00622i
$714$		0			0
$715$	−17.3261	−	30.0097i	−0.647961	−	1.12230i
$716$	−7.07019	−	4.08197i	−0.264225	−	0.152551i
$717$	−0.0146029	−	1.27790i	−0.000545356	−	0.0477241i
$718$	−7.10734	−	12.3103i	−0.265244	−	0.459416i
$719$	4.89336	+	8.47555i	0.182491	+	0.316085i	0.942728	−	0.333561i	$-0.108250\pi$
$719$	4.89336	+	8.47555i	0.182491	+	0.316085i	−0.760237	+	0.649646i	$0.774917\pi$
$720$	11.7610	−	0.268826i	0.438305	−	0.0100186i
$721$		0			0
$722$	−12.4805	−	7.20560i	−0.464475	−	0.268165i
$723$	0.168953	+	14.7851i	0.00628342	+	0.549862i
$724$		−	3.09557i		−	0.115046i
$725$			88.5063i			3.28704i
$726$	1.81801	−	1.07751i	0.0674727	−	0.0399903i
$727$	33.8434	+	19.5395i	1.25518	+	0.724680i	0.972134	−	0.234425i	$-0.0753209\pi$
$727$	33.8434	+	19.5395i	1.25518	+	0.724680i	0.283049	+	0.959106i	$0.408654\pi$
$728$		0			0
$729$	26.9366	−	1.84969i	0.997651	−	0.0685069i
$730$	−12.8907	−	22.3274i	−0.477107	−	0.826374i
$731$	−12.9290	−	22.3937i	−0.478197	−	0.828262i
$732$	−6.27281	−	3.52666i	−0.231850	−	0.130349i
$733$	−16.2421	−	9.37737i	−0.599915	−	0.346361i	0.169093	−	0.985600i	$-0.445916\pi$
$733$	−16.2421	−	9.37737i	−0.599915	−	0.346361i	−0.769008	+	0.639239i	$0.779249\pi$
$734$	4.20119	+	7.27668i	0.155069	+	0.268587i
$735$		0			0
$736$	4.70555	−	8.15025i	0.173449	−	0.300422i
$737$	−2.15635	+	1.24497i	−0.0794300	+	0.0458589i
$738$	2.84814	+	1.55870i	0.104841	+	0.0573766i
$739$	−4.43154	+	7.67565i	−0.163017	+	0.282353i	−0.935949	−	0.352135i	$-0.885456\pi$
$739$	−4.43154	+	7.67565i	−0.163017	+	0.282353i	0.772932	+	0.634488i	$0.218789\pi$
$740$	−10.2841			−0.378050
$741$	−4.78214	−	8.06856i	−0.175676	−	0.296406i
$742$		0			0
$743$	−39.0618	+	22.5523i	−1.43304	+	0.827365i	−0.997351	−	0.0727333i	$-0.976828\pi$
$743$	−39.0618	+	22.5523i	−1.43304	+	0.827365i	−0.435687	+	0.900098i	$0.643494\pi$
$744$	2.79824	−	4.97718i	0.102589	−	0.182472i
$745$	−44.0593	+	25.4376i	−1.61421	+	0.931962i
$746$	−28.3860	−	16.3887i	−1.03928	−	0.600031i
$747$	4.16568	−	0.0952173i	0.152414	−	0.00348382i
$748$			11.3280i			0.414191i
$749$		0			0
$750$	31.8336	+	17.8973i	1.16240	+	0.653518i
$751$	15.9780	−	27.6746i	0.583044	−	1.00986i	−0.412072	−	0.911151i	$-0.635195\pi$
$751$	15.9780	−	27.6746i	0.583044	−	1.00986i	0.995116	−	0.0987103i	$-0.0314717\pi$
$752$	−8.47645			−0.309104
$753$	15.2957	−	27.2063i	0.557408	−	0.991452i
$754$		−	21.5608i		−	0.785198i
$755$	−70.3245			−2.55937
$756$		0			0
$757$	−8.17899			−0.297270			−0.148635	−	0.988892i	$-0.547488\pi$
$757$	−8.17899			−0.297270			−0.148635	+	0.988892i	$0.547488\pi$
$758$			7.58954i			0.275664i
$759$	27.9254	−	49.6704i	1.01363	−	1.80292i
$760$	8.40009			0.304703
$761$	−0.290457	+	0.503087i	−0.0105291	+	0.0182369i	−0.871242	−	0.490854i	$-0.836685\pi$
$761$	−0.290457	+	0.503087i	−0.0105291	+	0.0182369i	0.860713	+	0.509091i	$0.170018\pi$
$762$	−25.1562	−	14.1432i	−0.911314	−	0.512354i
$763$		0			0
$764$		−	4.52911i		−	0.163857i
$765$	−18.3013	+	33.4411i	−0.661685	+	1.20906i
$766$	−9.35608	−	5.40174i	−0.338049	−	0.195173i
$767$	−5.12531	+	2.95910i	−0.185064	+	0.106847i
$768$	0.848829	−	1.50980i	0.0306295	−	0.0544801i
$769$	−11.1955	+	6.46370i	−0.403719	+	0.233087i	−0.688087	−	0.725628i	$-0.741549\pi$
$769$	−11.1955	+	6.46370i	−0.403719	+	0.233087i	0.284369	+	0.958715i	$0.408216\pi$
$770$		0			0
$771$	16.9290	+	28.5631i	0.609683	+	1.02868i
$772$	6.04602			0.217601
$773$	−27.2020	+	47.1153i	−0.978388	+	1.69462i	−0.310121	+	0.950697i	$0.600370\pi$
$773$	−27.2020	+	47.1153i	−0.978388	+	1.69462i	−0.668267	+	0.743921i	$0.732964\pi$
$774$	0.547040	+	23.9326i	0.0196630	+	0.860240i
$775$	29.6254	−	17.1042i	1.06417	−	0.614401i
$776$	1.83984	−	3.18669i	0.0660462	−	0.114395i
$777$		0			0
$778$	6.36757	+	11.0290i	0.228288	+	0.395407i
$779$	2.00774	+	1.15917i	0.0719349	+	0.0415316i
$780$	−14.9662	−	8.41422i	−0.535877	−	0.301277i
$781$	8.67659	+	15.0283i	0.310473	+	0.537755i
$782$	15.2484	+	26.4110i	0.545281	+	0.944455i
$783$	39.1181	+	20.8309i	1.39797	+	0.744436i
$784$		0			0
$785$	−45.7570	−	26.4178i	−1.63314	−	0.942892i
$786$	−11.7509	+	6.96464i	−0.419142	+	0.248421i
$787$		−	29.0755i		−	1.03643i	−0.855251	−	0.518214i	$-0.826597\pi$
$787$		−	29.0755i		−	1.03643i	0.855251	−	0.518214i	$-0.173403\pi$
$788$			4.48816i			0.159884i
$789$	0.165268	+	14.4626i	0.00588371	+	0.514883i
$790$	29.4527	+	17.0045i	1.04788	+	0.604993i
$791$		0			0
$792$	5.03469	−	9.19963i	0.178900	−	0.326895i
$793$	5.25137	+	9.09564i	0.186482	+	0.322996i
$794$	−11.0380	−	19.1183i	−0.391723	−	0.678484i
$795$	0.834634	+	73.0387i	0.0296014	+	2.59042i
$796$	14.4866	+	8.36386i	0.513465	+	0.296449i
$797$	6.31652	+	10.9405i	0.223743	+	0.387534i	0.955941	−	0.293557i	$-0.0948391\pi$
$797$	6.31652	+	10.9405i	0.223743	+	0.387534i	−0.732199	+	0.681091i	$0.761506\pi$
$798$		0			0
$799$	13.7340	−	23.7880i	0.485874	−	0.841559i
$800$	8.98667	−	5.18846i	0.317727	−	0.183440i
$801$	22.9499	−	41.9352i	0.810895	−	1.48171i
$802$	−0.137280	+	0.237776i	−0.00484752	+	0.00839616i
$803$	−22.9832			−0.811061
$804$	−0.604603	+	1.07540i	−0.0213227	+	0.0379263i
$805$		0			0
$806$	−7.21696	+	4.16672i	−0.254207	+	0.146766i
$807$	−8.91333	−	15.0388i	−0.313764	−	0.529392i
$808$	−15.4230	+	8.90448i	−0.542580	+	0.313259i
$809$	−38.4162	−	22.1796i	−1.35064	−	0.779794i	−0.362303	−	0.932060i	$-0.618009\pi$
$809$	−38.4162	−	22.1796i	−1.35064	−	0.779794i	−0.988339	+	0.152266i	$0.951343\pi$
$810$	29.7256	−	19.0241i	1.04445	−	0.668439i
$811$		−	13.4875i		−	0.473611i	−0.971557	−	0.236805i	$-0.923900\pi$
$811$		−	13.4875i		−	0.473611i	0.971557	−	0.236805i	$-0.0761004\pi$
$812$		0			0
$813$	−0.209855	−	18.3644i	−0.00735992	−	0.644066i
$814$	−4.58394	+	7.93961i	−0.160667	+	0.278283i
$815$	47.6569			1.66935
$816$	2.86172	+	4.82838i	0.100180	+	0.169027i
$817$			17.0935i			0.598026i
$818$	11.7571			0.411079
$819$		0			0
$820$	4.24388			0.148203
$821$			8.98879i			0.313711i	0.987622	+	0.156855i	$0.0501357\pi$
$821$			8.98879i			0.313711i	−0.987622	+	0.156855i	$0.949864\pi$
$822$	2.48773	−	0.0284280i	0.0867696	−	0.000991539i
$823$	−43.3743			−1.51193			−0.755967	−	0.654610i	$-0.772833\pi$
$823$	−43.3743			−1.51193			−0.755967	+	0.654610i	$0.772833\pi$
$824$	−1.90429	+	3.29833i	−0.0663391	+	0.114903i
$825$	54.0498	−	32.0347i	1.88177	−	1.11530i
$826$		0			0
$827$			37.1736i			1.29265i	0.763060	+	0.646327i	$0.223696\pi$
$827$			37.1736i			1.29265i	−0.763060	+	0.646327i	$0.776304\pi$
$828$	−0.645175	−	28.2259i	−0.0224214	−	0.980919i
$829$	−4.08117	−	2.35626i	−0.141745	−	0.0818364i	0.427450	−	0.904039i	$-0.359412\pi$
$829$	−4.08117	−	2.35626i	−0.141745	−	0.0818364i	−0.569195	+	0.822202i	$0.692745\pi$
$830$	4.71676	−	2.72322i	0.163721	−	0.0945244i
$831$	−17.6713	+	0.201935i	−0.613012	+	0.00700506i
$832$	−2.18922	+	1.26395i	−0.0758976	+	0.0438195i
$833$		0			0
$834$	1.35233	−	0.0154534i	0.0468273	−	0.000535108i
$835$	20.2536			0.700904
$836$	3.74418	−	6.48512i	0.129495	−	0.224292i
$837$	−0.587093	−	17.1195i	−0.0202929	−	0.591737i
$838$	26.3845	−	15.2331i	0.911438	−	0.526219i
$839$	−21.6818	+	37.5540i	−0.748540	+	1.29651i	0.199983	+	0.979799i	$0.435911\pi$
$839$	−21.6818	+	37.5540i	−0.748540	+	1.29651i	−0.948523	+	0.316710i	$0.897422\pi$
$840$		0			0
$841$	21.8733	+	37.8856i	0.754250	+	1.30640i
$842$	−1.63850	−	0.945989i	−0.0564665	−	0.0326009i
$843$	0.736056	−	0.436251i	0.0253511	−	0.0150253i
$844$	3.14133	+	5.44095i	0.108129	+	0.187285i
$845$	−12.9595	−	22.4466i	−0.445822	−	0.772186i
$846$	−21.7262	+	13.2146i	−0.746961	+	0.454327i
$847$		0			0
$848$	9.31359	+	5.37720i	0.319830	+	0.184654i
$849$	29.9884	+	16.8599i	1.02920	+	0.578630i
$850$			33.6265i			1.15338i
$851$			24.6815i			0.846070i
$852$	7.49479	+	4.21368i	0.256767	+	0.144358i
$853$	−10.3059	−	5.95011i	−0.352867	−	0.203728i	0.313080	−	0.949727i	$-0.398639\pi$
$853$	−10.3059	−	5.95011i	−0.352867	−	0.203728i	−0.665947	+	0.745999i	$0.731972\pi$
$854$		0			0
$855$	21.5304	−	13.0956i	0.736325	−	0.447858i
$856$	−4.41500	−	7.64701i	−0.150902	−	0.261369i
$857$	23.9689	+	41.5154i	0.818762	+	1.41814i	0.906594	+	0.422003i	$0.138673\pi$
$857$	23.9689	+	41.5154i	0.818762	+	1.41814i	−0.0878320	+	0.996135i	$0.527994\pi$
$858$	−13.1669	+	7.80389i	−0.449512	+	0.266420i
$859$	0.894714	+	0.516564i	0.0305273	+	0.0176249i	0.515186	−	0.857078i	$-0.327723\pi$
$859$	0.894714	+	0.516564i	0.0305273	+	0.0176249i	−0.484659	+	0.874703i	$0.661056\pi$
$860$	15.6454	+	27.0986i	0.533504	+	0.924056i
$861$		0			0
$862$	16.1767	−	28.0189i	0.550982	−	0.954328i
$863$	19.2330	−	11.1042i	0.654698	−	0.377990i	−0.135556	−	0.990770i	$-0.543282\pi$
$863$	19.2330	−	11.1042i	0.654698	−	0.377990i	0.790254	+	0.612780i	$0.209949\pi$
$864$	−0.178091	−	5.19310i	−0.00605877	−	0.176673i
$865$	−38.8659	+	67.3177i	−1.32148	+	2.28887i
$866$	−24.2391			−0.823677
$867$	11.2560	−	0.128626i	0.382275	−	0.00436836i
$868$		0			0
$869$	26.2560	−	15.1589i	0.890673	−	0.514230i
$870$	57.9259	−	0.661935i	1.96387	−	0.0224417i
$871$	1.55933	−	0.900282i	0.0528360	−	0.0305049i
$872$	0.626226	+	0.361552i	0.0212067	+	0.0122437i
$873$	−0.252259	−	11.0361i	−0.00853766	−	0.373516i
$874$		−	20.1600i		−	0.681921i
$875$		0			0
$876$	−9.79628	+	5.80614i	−0.330986	+	0.196171i
$877$	27.3523	−	47.3756i	0.923621	−	1.59976i	0.129858	−	0.991533i	$-0.458548\pi$
$877$	27.3523	−	47.3756i	0.923621	−	1.59976i	0.793763	−	0.608227i	$-0.208119\pi$
$878$	−25.7773			−0.869941
$879$	−14.3057	+	0.163475i	−0.482520	+	0.00551389i
$880$		−	13.7080i		−	0.462095i
$881$	48.4985			1.63396			0.816978	−	0.576669i	$-0.195648\pi$
$881$	48.4985			1.63396			0.816978	+	0.576669i	$0.195648\pi$
$882$		0			0
$883$	−13.6777			−0.460291			−0.230146	−	0.973156i	$-0.573920\pi$
$883$	−13.6777			−0.460291			−0.230146	+	0.973156i	$0.573920\pi$
$884$		−	8.19167i		−	0.275516i
$885$	−8.10736	−	13.6790i	−0.272526	−	0.459814i
$886$	24.6563			0.828346
$887$	12.3191	−	21.3374i	0.413636	−	0.716438i	−0.581648	−	0.813440i	$-0.697592\pi$
$887$	12.3191	−	21.3374i	0.413636	−	0.716438i	0.995284	+	0.0970021i	$0.0309253\pi$
$888$	0.0519045	+	4.54216i	0.00174180	+	0.152425i
$889$		0			0
$890$		−	62.4858i		−	2.09453i
$891$	−1.43752	−	31.4287i	−0.0481586	−	1.05290i
$892$	−11.8166	−	6.82229i	−0.395647	−	0.228427i
$893$	−15.7251	+	9.07890i	−0.526221	+	0.303814i
$894$	11.4574	+	19.3313i	0.383193	+	0.646534i
$895$	−27.7246	+	16.0068i	−0.926732	+	0.535049i
$896$		0			0
$897$	−20.1939	+	35.9185i	−0.674254	+	1.19928i
$898$	21.8330			0.728577
$899$	14.0586	−	24.3502i	0.468879	−	0.812123i
$900$	14.9452	−	27.3087i	0.498174	−	0.910289i
$901$	−30.1808	+	17.4249i	−1.00547	+	0.580507i
$902$	1.89163	−	3.27640i	0.0629845	−	0.109092i
$903$		0			0
$904$	−8.35737	−	14.4754i	−0.277962	−	0.481444i
$905$	−10.5125	−	6.06939i	−0.349447	−	0.201753i
$906$	0.354934	+	31.0602i	0.0117919	+	1.03191i
$907$	−7.55544	−	13.0864i	−0.250874	−	0.434527i	0.712893	−	0.701273i	$-0.247385\pi$
$907$	−7.55544	−	13.0864i	−0.250874	−	0.434527i	−0.963767	+	0.266746i	$0.914051\pi$
$908$	−10.3042	−	17.8475i	−0.341958	−	0.592289i
$909$	−25.6491	+	46.8674i	−0.850729	+	1.55449i
$910$		0			0
$911$	32.9330	+	19.0139i	1.09112	+	0.629958i	0.933874	−	0.357601i	$-0.116405\pi$
$911$	32.9330	+	19.0139i	1.09112	+	0.629958i	0.157246	+	0.987560i	$0.449739\pi$
$912$	−0.0423959	−	3.71006i	−0.00140387	−	0.122852i
$913$		−	4.85531i		−	0.160687i
$914$		−	3.16073i		−	0.104548i
$915$	−24.2754	+	14.3877i	−0.802520	+	0.475644i
$916$	21.1564	+	12.2146i	0.699026	+	0.403583i
$917$		0			0
$918$	14.8623	+	7.91436i	0.490528	+	0.261213i
$919$	8.39703	+	14.5441i	0.276993	+	0.479765i	0.970636	−	0.240553i	$-0.0773289\pi$
$919$	8.39703	+	14.5441i	0.276993	+	0.479765i	−0.693643	+	0.720319i	$0.743996\pi$
$920$	−18.4521	−	31.9599i	−0.608347	−	1.05369i
$921$	−6.78797	−	3.81629i	−0.223671	−	0.125751i
$922$	−8.97728	−	5.18303i	−0.295651	−	0.170694i
$923$	−6.27437	−	10.8675i	−0.206523	−	0.357709i
$924$		0			0
$925$	−13.6072	+	23.5684i	−0.447402	+	0.774923i
$926$	−19.8250	+	11.4460i	−0.651490	+	0.376138i
$927$	0.261096	+	11.4228i	0.00857552	+	0.375173i
$928$	4.26458	−	7.38647i	0.139992	−	0.242473i
$929$	15.0980			0.495351			0.247675	−	0.968843i	$-0.420333\pi$
$929$	15.0980			0.495351			0.247675	+	0.968843i	$0.420333\pi$
$930$	−11.4160	−	19.2614i	−0.374345	−	0.631606i
$931$		0			0
$932$	11.9080	−	6.87509i	0.390060	−	0.225201i
$933$	−9.72975	+	17.3061i	−0.318538	+	0.566577i
$934$	3.94274	−	2.27634i	0.129011	−	0.0744843i
$935$	38.4695	+	22.2104i	1.25809	+	0.726357i
$936$	−3.64077	+	6.65260i	−0.119002	+	0.217447i
$937$			50.3200i			1.64388i	0.569571	+	0.821942i	$0.307109\pi$
$937$			50.3200i			1.64388i	−0.569571	+	0.821942i	$0.692891\pi$
$938$		0			0
$939$	−19.2412	−	10.8177i	−0.627912	−	0.353021i
$940$	−16.6195	+	28.7859i	−0.542069	+	0.938891i
$941$	54.3268			1.77100			0.885501	−	0.464638i	$-0.153815\pi$
$941$	54.3268			1.77100			0.885501	+	0.464638i	$0.153815\pi$
$942$	−11.4370	+	20.3428i	−0.372638	+	0.662805i
$943$		−	10.1852i		−	0.331675i
$944$	−2.34116			−0.0761982
$945$		0			0
$946$	27.8946			0.906932
$947$		−	17.0355i		−	0.553580i	−0.960930	−	0.276790i	$-0.910729\pi$
$947$		−	17.0355i		−	0.553580i	0.960930	−	0.276790i	$-0.0892707\pi$
$948$	7.36173	−	13.0942i	0.239098	−	0.425279i
$949$	16.6200			0.539509
$950$	11.1144	−	19.2508i	0.360600	−	0.624577i
$951$	22.3722	+	12.5780i	0.725470	+	0.407869i
$952$		0			0
$953$		−	29.8903i		−	0.968240i	−0.875002	−	0.484120i	$-0.839140\pi$
$953$		−	29.8903i		−	0.968240i	0.875002	−	0.484120i	$-0.160860\pi$
$954$	32.2548	−	0.737265i	1.04429	−	0.0238698i
$955$	−15.3808	−	8.88008i	−0.497710	−	0.287353i
$956$	−0.638992	+	0.368922i	−0.0206665	+	0.0119318i
$957$	25.3084	−	45.0156i	0.818104	−	1.45515i
$958$	30.2104	−	17.4420i	0.976054	−	0.563525i
$959$		0			0
$960$	−3.46297	−	5.84282i	−0.111767	−	0.188576i
$961$	20.1325			0.649435
$962$	3.31482	−	5.74143i	0.106874	−	0.185111i
$963$	−23.2377	−	12.7173i	−0.748824	−	0.409809i
$964$	7.39301	−	4.26836i	0.238113	−	0.137474i
$965$	11.8543	−	20.5322i	0.381602	−	0.660954i
$966$		0			0
$967$	−9.14125	−	15.8331i	−0.293963	−	0.509159i	0.680780	−	0.732488i	$-0.261641\pi$
$967$	−9.14125	−	15.8331i	−0.293963	−	0.509159i	−0.974743	+	0.223329i	$0.928308\pi$
$968$	−1.05667	−	0.610068i	−0.0339626	−	0.0196083i
$969$	10.4805	+	5.89227i	0.336682	+	0.189287i
$970$	−7.21462	−	12.4961i	−0.231648	−	0.401225i
$971$	3.45351	+	5.98165i	0.110828	+	0.191960i	0.916105	−	0.400940i	$-0.131316\pi$
$971$	3.45351	+	5.98165i	0.110828	+	0.191960i	−0.805276	+	0.592900i	$0.797983\pi$
$972$	−8.55240	−	13.0329i	−0.274318	−	0.418030i
$973$		0			0
$974$	−0.983587	−	0.567874i	−0.0315162	−	0.0181959i
$975$	−39.0855	+	23.1655i	−1.25174	+	0.741889i
$976$			4.15474i			0.132990i
$977$		−	2.27126i		−	0.0726640i	−0.999340	−	0.0363320i	$-0.988433\pi$
$977$		−	2.27126i		−	0.0726640i	0.999340	−	0.0363320i	$-0.0115674\pi$
$978$	−0.240528	−	21.0486i	−0.00769124	−	0.673060i
$979$	−48.2409	−	27.8519i	−1.54179	−	0.890151i
$980$		0			0
$981$	2.16874	−	0.0495721i	0.0692427	−	0.00158272i
$982$	6.13045	+	10.6183i	0.195631	+	0.338842i
$983$	6.24292	+	10.8131i	0.199118	+	0.344883i	0.948243	−	0.317546i	$-0.102859\pi$
$983$	6.24292	+	10.8131i	0.199118	+	0.344883i	−0.749124	+	0.662429i	$0.769526\pi$
$984$	−0.0214192	−	1.87439i	−0.000682819	−	0.0597535i
$985$	15.2417	+	8.79980i	0.485641	+	0.280385i
$986$	13.8194	+	23.9359i	0.440100	+	0.762275i
$987$		0			0
$988$	−2.70756	+	4.68963i	−0.0861390	+	0.149197i
$989$	65.0359	−	37.5485i	2.06802	−	1.19397i
$990$	−21.3704	−	35.1351i	−0.679196	−	1.11667i
$991$	23.5838	−	40.8484i	0.749165	−	1.29759i	−0.199059	−	0.979988i	$-0.563789\pi$
$991$	23.5838	−	40.8484i	0.749165	−	1.29759i	0.948224	−	0.317604i	$-0.102878\pi$
$992$	−3.29659			−0.104667
$993$	−4.27290	+	7.60013i	−0.135596	+	0.241183i
$994$		0			0
$995$	56.8070	−	32.7976i	1.80090	−	1.03975i
$996$	−1.22657	−	2.06951i	−0.0388654	−	0.0655748i
$997$	21.2219	−	12.2525i	0.672106	−	0.388040i	−0.124768	−	0.992186i	$-0.539819\pi$
$997$	21.2219	−	12.2525i	0.672106	−	0.388040i	0.796874	+	0.604146i	$0.206485\pi$
$998$	35.4057	+	20.4415i	1.12075	+	0.647064i
$999$	7.21417	+	11.5612i	0.228246	+	0.365780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.l.c.227.20		48
3.2	odd	2		2646.2.l.c.521.24		48
7.2	even	3		882.2.t.c.803.20		48
7.3	odd	6		882.2.m.c.587.12	yes	48
7.4	even	3		882.2.m.c.587.1	yes	48
7.5	odd	6		882.2.t.c.803.17		48
7.6	odd	2	inner	882.2.l.c.227.17		48
9.4	even	3		2646.2.t.c.2285.12		48
9.5	odd	6		882.2.t.c.815.17		48
21.2	odd	6		2646.2.t.c.1979.11		48
21.5	even	6		2646.2.t.c.1979.12		48
21.11	odd	6		2646.2.m.c.1763.24		48
21.17	even	6		2646.2.m.c.1763.23		48
21.20	even	2		2646.2.l.c.521.23		48
63.4	even	3		2646.2.m.c.881.23		48
63.5	even	6	inner	882.2.l.c.509.8		48
63.13	odd	6		2646.2.t.c.2285.11		48
63.23	odd	6	inner	882.2.l.c.509.5		48
63.31	odd	6		2646.2.m.c.881.24		48
63.32	odd	6		882.2.m.c.293.12	yes	48
63.40	odd	6		2646.2.l.c.1097.24		48
63.41	even	6		882.2.t.c.815.20		48
63.58	even	3		2646.2.l.c.1097.23		48
63.59	even	6		882.2.m.c.293.1	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.2.l.c.227.17		48	7.6	odd	2	inner
882.2.l.c.227.20		48	1.1	even	1	trivial
882.2.l.c.509.5		48	63.23	odd	6	inner
882.2.l.c.509.8		48	63.5	even	6	inner
882.2.m.c.293.1	✓	48	63.59	even	6
882.2.m.c.293.12	yes	48	63.32	odd	6
882.2.m.c.587.1	yes	48	7.4	even	3
882.2.m.c.587.12	yes	48	7.3	odd	6
882.2.t.c.803.17		48	7.5	odd	6
882.2.t.c.803.20		48	7.2	even	3
882.2.t.c.815.17		48	9.5	odd	6
882.2.t.c.815.20		48	63.41	even	6
2646.2.l.c.521.23		48	21.20	even	2
2646.2.l.c.521.24		48	3.2	odd	2
2646.2.l.c.1097.23		48	63.58	even	3
2646.2.l.c.1097.24		48	63.40	odd	6
2646.2.m.c.881.23		48	63.4	even	3
2646.2.m.c.881.24		48	63.31	odd	6
2646.2.m.c.1763.23		48	21.17	even	6
2646.2.m.c.1763.24		48	21.11	odd	6
2646.2.t.c.1979.11		48	21.2	odd	6
2646.2.t.c.1979.12		48	21.5	even	6
2646.2.t.c.2285.11		48	63.13	odd	6
2646.2.t.c.2285.12		48	9.4	even	3

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.l (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(0.848829 - 1.50980i) q^{3} -1.00000 q^{4} +(-1.96067 + 3.39598i) q^{5} +(1.50980 + 0.848829i) q^{6} -1.00000i q^{8} +(-1.55898 - 2.56312i) q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(0.848829 - 1.50980i) q^{3} -1.00000 q^{4} +(-1.96067 + 3.39598i) q^{5} +(1.50980 + 0.848829i) q^{6} -1.00000i q^{8} +(-1.55898 - 2.56312i) q^{9} +(-3.39598 - 1.96067i) q^{10} +(-3.02739 + 1.74787i) q^{11} +(-0.848829 + 1.50980i) q^{12} +(2.18922 - 1.26395i) q^{13} +(3.46297 + 5.84282i) q^{15} +1.00000 q^{16} +(-1.62026 + 2.80636i) q^{17} +(2.56312 - 1.55898i) q^{18} +(1.85515 - 1.07107i) q^{19} +(1.96067 - 3.39598i) q^{20} +(-1.74787 - 3.02739i) q^{22} +(-8.15025 - 4.70555i) q^{23} +(-1.50980 - 0.848829i) q^{24} +(-5.18846 - 8.98667i) q^{25} +(1.26395 + 2.18922i) q^{26} +(-5.19310 + 0.178091i) q^{27} +(-7.38647 - 4.26458i) q^{29} +(-5.84282 + 3.46297i) q^{30} +3.29659i q^{31} +1.00000i q^{32} +(0.0691851 + 6.05439i) q^{33} +(-2.80636 - 1.62026i) q^{34} +(1.55898 + 2.56312i) q^{36} +(-1.31130 - 2.27123i) q^{37} +(1.07107 + 1.85515i) q^{38} +(-0.0500304 - 4.37816i) q^{39} +(3.39598 + 1.96067i) q^{40} +(0.541126 + 0.937258i) q^{41} +(-3.98981 + 6.91055i) q^{43} +(3.02739 - 1.74787i) q^{44} +(11.7610 - 0.268826i) q^{45} +(4.70555 - 8.15025i) q^{46} -8.47645 q^{47} +(0.848829 - 1.50980i) q^{48} +(8.98667 - 5.18846i) q^{50} +(2.86172 + 4.82838i) q^{51} +(-2.18922 + 1.26395i) q^{52} +(9.31359 + 5.37720i) q^{53} +(-0.178091 - 5.19310i) q^{54} -13.7080i q^{55} +(-0.0423959 - 3.71006i) q^{57} +(4.26458 - 7.38647i) q^{58} -2.34116 q^{59} +(-3.46297 - 5.84282i) q^{60} +4.15474i q^{61} -3.29659 q^{62} -1.00000 q^{64} +9.91274i q^{65} +(-6.05439 + 0.0691851i) q^{66} +0.712278 q^{67} +(1.62026 - 2.80636i) q^{68} +(-14.0226 + 8.31102i) q^{69} -4.96411i q^{71} +(-2.56312 + 1.55898i) q^{72} +(5.69382 + 3.28733i) q^{73} +(2.27123 - 1.31130i) q^{74} +(-17.9722 + 0.205373i) q^{75} +(-1.85515 + 1.07107i) q^{76} +(4.37816 - 0.0500304i) q^{78} -8.67280 q^{79} +(-1.96067 + 3.39598i) q^{80} +(-4.13917 + 7.99170i) q^{81} +(-0.937258 + 0.541126i) q^{82} +(-0.694462 + 1.20284i) q^{83} +(-6.35357 - 11.0047i) q^{85} +(-6.91055 - 3.98981i) q^{86} +(-12.7085 + 7.53217i) q^{87} +(1.74787 + 3.02739i) q^{88} +(7.96740 + 13.7999i) q^{89} +(0.268826 + 11.7610i) q^{90} +(8.15025 + 4.70555i) q^{92} +(4.97718 + 2.79824i) q^{93} -8.47645i q^{94} +8.40009i q^{95} +(1.50980 + 0.848829i) q^{96} +(3.18669 + 1.83984i) q^{97} +(9.19963 + 5.03469i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 48 q^{4} + 16 q^{9}+O(q^{10}) \) 48 * q - 48 * q^4 + 16 * q^9	\( 48 q - 48 q^{4} + 16 q^{9} - 48 q^{11} + 48 q^{15} + 48 q^{16} + 16 q^{18} - 48 q^{23} - 24 q^{25} - 16 q^{30} - 16 q^{36} + 32 q^{39} + 48 q^{44} - 48 q^{50} - 48 q^{51} + 96 q^{53} - 80 q^{57} - 48 q^{60} - 48 q^{64} - 16 q^{72} + 32 q^{78} - 96 q^{79} + 96 q^{81} + 48 q^{85} - 96 q^{86} + 48 q^{92} + 104 q^{99}+O(q^{100}) \) 48 * q - 48 * q^4 + 16 * q^9 - 48 * q^11 + 48 * q^15 + 48 * q^16 + 16 * q^18 - 48 * q^23 - 24 * q^25 - 16 * q^30 - 16 * q^36 + 32 * q^39 + 48 * q^44 - 48 * q^50 - 48 * q^51 + 96 * q^53 - 80 * q^57 - 48 * q^60 - 48 * q^64 - 16 * q^72 + 32 * q^78 - 96 * q^79 + 96 * q^81 + 48 * q^85 - 96 * q^86 + 48 * q^92 + 104 * q^99

Introduction

L-functions

Modular forms

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