LMFDB - Embedded newform 360.2.x.a.53.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(53,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))

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

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

chi := DirichletCharacter("360.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.x (of order $4$, degree $2$, 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:	$2.87461447277$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.17
Character	$\chi$	$=$	360.53
Dual form			360.2.x.a.197.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.760261 - 1.19248i) q^{2} +(-0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-2.80385 - 0.372039i) q^{8} +O(q^{10})$	\(q+(0.760261 - 1.19248i) q^{2} +(-0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-2.80385 - 0.372039i) q^{8} +(1.68648 - 2.67503i) q^{10} -0.335652 q^{11} +(3.50404 - 3.50404i) q^{13} +(-0.203990 - 0.921620i) q^{14} +(-2.57531 + 3.06068i) q^{16} +(-2.53299 - 2.53299i) q^{17} +4.07474 q^{19} +(-1.90775 - 4.04481i) q^{20} +(-0.255183 + 0.400257i) q^{22} +(-6.20627 + 6.20627i) q^{23} +(4.99974 - 0.0506050i) q^{25} +(-1.51450 - 6.84248i) q^{26} +(-1.25410 - 0.457418i) q^{28} +2.42367i q^{29} -6.41004 q^{31} +(1.69189 + 5.39792i) q^{32} +(-4.94626 + 1.09480i) q^{34} +(1.04999 - 1.06067i) q^{35} +(2.24893 + 2.24893i) q^{37} +(3.09787 - 4.85903i) q^{38} +(-6.27373 - 0.800167i) q^{40} -5.80736i q^{41} +(4.87603 - 4.87603i) q^{43} +(0.283292 + 0.608600i) q^{44} +(2.68245 + 12.1192i) q^{46} +(1.68276 + 1.68276i) q^{47} +6.55450i q^{49} +(3.74077 - 6.00056i) q^{50} +(-9.31092 - 3.39606i) q^{52} +(3.05444 + 3.05444i) q^{53} +(-0.750530 + 0.00379815i) q^{55} +(-1.49890 + 1.14772i) q^{56} +(2.89018 + 1.84263i) q^{58} +12.2950i q^{59} +7.49787i q^{61} +(-4.87331 + 7.64383i) q^{62} +(7.72317 + 2.08629i) q^{64} +(7.79553 - 7.87483i) q^{65} +(-5.55519 - 5.55519i) q^{67} +(-2.45493 + 6.73064i) q^{68} +(-0.466558 - 2.05847i) q^{70} +13.4793i q^{71} +(5.05035 + 5.05035i) q^{73} +(4.39157 - 0.972023i) q^{74} +(-3.43910 - 7.38827i) q^{76} +(-0.158415 + 0.158415i) q^{77} +8.85503i q^{79} +(-5.72386 + 6.87295i) q^{80} +(-6.92515 - 4.41511i) q^{82} +(-4.78510 - 4.78510i) q^{83} +(-5.69252 - 5.63520i) q^{85} +(-2.10750 - 9.52162i) q^{86} +(0.941117 + 0.124876i) q^{88} +8.33405 q^{89} -3.30755i q^{91} +(16.4913 + 6.01502i) q^{92} +(3.28598 - 0.727315i) q^{94} +(9.11128 - 0.0461088i) q^{95} +(10.1367 - 10.1367i) q^{97} +(7.81610 + 4.98313i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q+O(q^{10}) $ 48 * q	$ 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) $ 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	0.760261	−	1.19248i	0.537586	−	0.843209i
$2$	0.760261	−	1.19248i	0.537586	−	0.843209i
$3$		0			0
$3$		0			0
$4$	−0.844006	−	1.81319i	−0.422003	−	0.906594i
$5$	2.23604	−	0.0113158i	0.999987	−	0.00506057i
$5$	2.23604	−	0.0113158i	0.999987	−	0.00506057i
$6$		0			0
$7$	0.471963	−	0.471963i	0.178385	−	0.178385i	−0.612266	−	0.790652i	$-0.709742\pi$
$7$	0.471963	−	0.471963i	0.178385	−	0.178385i	0.790652	+	0.612266i	$0.209742\pi$
$8$	−2.80385	−	0.372039i	−0.991311	−	0.131536i
$9$		0			0
$10$	1.68648	−	2.67503i	0.533312	−	0.845919i
$11$	−0.335652			−0.101203			−0.0506014	−	0.998719i	$-0.516114\pi$
$11$	−0.335652			−0.101203			−0.0506014	+	0.998719i	$0.516114\pi$
$12$		0			0
$13$	3.50404	−	3.50404i	0.971846	−	0.971846i	−0.0277680	−	0.999614i	$-0.508840\pi$
$13$	3.50404	−	3.50404i	0.971846	−	0.971846i	0.999614	+	0.0277680i	$0.00883995\pi$
$14$	−0.203990	−	0.921620i	−0.0545186	−	0.246313i
$15$		0			0
$16$	−2.57531	+	3.06068i	−0.643827	+	0.765171i
$17$	−2.53299	−	2.53299i	−0.614340	−	0.614340i	0.329734	−	0.944074i	$-0.393041\pi$
$17$	−2.53299	−	2.53299i	−0.614340	−	0.614340i	−0.944074	+	0.329734i	$0.893041\pi$
$18$		0			0
$19$	4.07474			0.934809			0.467405	−	0.884044i	$-0.345189\pi$
$19$	4.07474			0.934809			0.467405	+	0.884044i	$0.345189\pi$
$20$	−1.90775	−	4.04481i	−0.426585	−	0.904447i
$21$		0			0
$22$	−0.255183	+	0.400257i	−0.0544052	+	0.0853351i
$23$	−6.20627	+	6.20627i	−1.29410	+	1.29410i	−0.361868	+	0.932229i	$0.617861\pi$
$23$	−6.20627	+	6.20627i	−1.29410	+	1.29410i	−0.932229	+	0.361868i	$0.882139\pi$
$24$		0			0
$25$	4.99974	−	0.0506050i	0.999949	−	0.0101210i
$26$	−1.51450	−	6.84248i	−0.297019	−	1.34192i
$27$		0			0
$28$	−1.25410	−	0.457418i	−0.237002	−	0.0864439i
$29$			2.42367i			0.450065i	0.974351	+	0.225032i	$0.0722488\pi$
$29$			2.42367i			0.450065i	−0.974351	+	0.225032i	$0.927751\pi$
$30$		0			0
$31$	−6.41004			−1.15128			−0.575639	−	0.817704i	$-0.695247\pi$
$31$	−6.41004			−1.15128			−0.575639	+	0.817704i	$0.695247\pi$
$32$	1.69189	+	5.39792i	0.299087	+	0.954226i
$33$		0			0
$34$	−4.94626	+	1.09480i	−0.848277	+	0.187756i
$35$	1.04999	−	1.06067i	0.177480	−	0.179286i
$36$		0			0
$37$	2.24893	+	2.24893i	0.369721	+	0.369721i	0.867375	−	0.497654i	$-0.165805\pi$
$37$	2.24893	+	2.24893i	0.369721	+	0.369721i	−0.497654	+	0.867375i	$0.665805\pi$
$38$	3.09787	−	4.85903i	0.502540	−	0.788239i
$39$		0			0
$40$	−6.27373	−	0.800167i	−0.991964	−	0.126517i
$41$		−	5.80736i		−	0.906957i	−0.891267	−	0.453479i	$-0.850183\pi$
$41$		−	5.80736i		−	0.906957i	0.891267	−	0.453479i	$-0.149817\pi$
$42$		0			0
$43$	4.87603	−	4.87603i	0.743588	−	0.743588i	−0.229678	−	0.973267i	$-0.573767\pi$
$43$	4.87603	−	4.87603i	0.743588	−	0.743588i	0.973267	+	0.229678i	$0.0737675\pi$
$44$	0.283292	+	0.608600i	0.0427078	+	0.0917498i
$45$		0			0
$46$	2.68245	+	12.1192i	0.395506	+	1.78688i
$47$	1.68276	+	1.68276i	0.245455	+	0.245455i	0.819102	−	0.573647i	$-0.194472\pi$
$47$	1.68276	+	1.68276i	0.245455	+	0.245455i	−0.573647	+	0.819102i	$0.694472\pi$
$48$		0			0
$49$			6.55450i			0.936358i
$50$	3.74077	−	6.00056i	0.529024	−	0.848607i
$51$		0			0
$52$	−9.31092	−	3.39606i	−1.29119	−	0.470949i
$53$	3.05444	+	3.05444i	0.419560	+	0.419560i	0.885052	−	0.465492i	$-0.154123\pi$
$53$	3.05444	+	3.05444i	0.419560	+	0.419560i	−0.465492	+	0.885052i	$0.654123\pi$
$54$		0			0
$55$	−0.750530	+	0.00379815i	−0.101201	+	0.000512143i
$56$	−1.49890	+	1.14772i	−0.200299	+	0.153371i
$57$		0			0
$58$	2.89018	+	1.84263i	0.379499	+	0.241949i
$59$			12.2950i			1.60067i	0.599553	+	0.800335i	$0.295345\pi$
$59$			12.2950i			1.60067i	−0.599553	+	0.800335i	$0.704655\pi$
$60$		0			0
$61$			7.49787i			0.960004i	0.877267	+	0.480002i	$0.159364\pi$
$61$			7.49787i			0.960004i	−0.877267	+	0.480002i	$0.840636\pi$
$62$	−4.87331	+	7.64383i	−0.618910	+	0.970767i
$63$		0			0
$64$	7.72317	+	2.08629i	0.965397	+	0.260786i
$65$	7.79553	−	7.87483i	0.966916	−	0.976752i
$66$		0			0
$67$	−5.55519	−	5.55519i	−0.678674	−	0.678674i	0.281026	−	0.959700i	$-0.409325\pi$
$67$	−5.55519	−	5.55519i	−0.678674	−	0.678674i	−0.959700	+	0.281026i	$0.909325\pi$
$68$	−2.45493	+	6.73064i	−0.297704	+	0.816210i
$69$		0			0
$70$	−0.466558	−	2.05847i	−0.0557644	−	0.246034i
$71$			13.4793i			1.59970i	0.600199	+	0.799851i	$0.295088\pi$
$71$			13.4793i			1.59970i	−0.600199	+	0.799851i	$0.704912\pi$
$72$		0			0
$73$	5.05035	+	5.05035i	0.591099	+	0.591099i	0.937928	−	0.346830i	$-0.112742\pi$
$73$	5.05035	+	5.05035i	0.591099	+	0.591099i	−0.346830	+	0.937928i	$0.612742\pi$
$74$	4.39157	−	0.972023i	0.510509	−	0.112995i
$75$		0			0
$76$	−3.43910	−	7.38827i	−0.394492	−	0.847493i
$77$	−0.158415	+	0.158415i	−0.0180531	+	0.0180531i
$78$		0			0
$79$			8.85503i			0.996268i	0.867100	+	0.498134i	$0.165981\pi$
$79$			8.85503i			0.996268i	−0.867100	+	0.498134i	$0.834019\pi$
$80$	−5.72386	+	6.87295i	−0.639947	+	0.768419i
$81$		0			0
$82$	−6.92515	−	4.41511i	−0.764755	−	0.487567i
$83$	−4.78510	−	4.78510i	−0.525233	−	0.525233i	0.393914	−	0.919147i	$-0.371121\pi$
$83$	−4.78510	−	4.78510i	−0.525233	−	0.525233i	−0.919147	+	0.393914i	$0.871121\pi$
$84$		0			0
$85$	−5.69252	−	5.63520i	−0.617441	−	0.611223i
$86$	−2.10750	−	9.52162i	−0.227258	−	1.02674i
$87$		0			0
$88$	0.941117	+	0.124876i	0.100323	+	0.0133118i
$89$	8.33405			0.883408			0.441704	−	0.897161i	$-0.354374\pi$
$89$	8.33405			0.883408			0.441704	+	0.897161i	$0.354374\pi$
$90$		0			0
$91$		−	3.30755i		−	0.346726i
$92$	16.4913	+	6.01502i	1.71933	+	0.627109i
$93$		0			0
$94$	3.28598	−	0.727315i	0.338923	−	0.0750168i
$95$	9.11128	−	0.0461088i	0.934797	−	0.00473066i
$96$		0			0
$97$	10.1367	−	10.1367i	1.02922	−	1.02922i	0.0296647	−	0.999560i	$-0.490556\pi$
$97$	10.1367	−	10.1367i	1.02922	−	1.02922i	0.999560	−	0.0296647i	$-0.00944397\pi$
$98$	7.81610	+	4.98313i	0.789545	+	0.503373i
$99$		0			0
$100$	−4.31157	−	9.02277i	−0.431157	−	0.902277i
$101$	−9.88830			−0.983922			−0.491961	−	0.870617i	$-0.663720\pi$
$101$	−9.88830			−0.983922			−0.491961	+	0.870617i	$0.663720\pi$
$102$		0			0
$103$	−10.0033	−	10.0033i	−0.985653	−	0.985653i	0.0142455	−	0.999899i	$-0.495465\pi$
$103$	−10.0033	−	10.0033i	−0.985653	−	0.985653i	−0.999899	+	0.0142455i	$0.995465\pi$
$104$	−11.1285	+	8.52117i	−1.09124	+	0.835570i
$105$		0			0
$106$	5.96453	−	1.32018i	0.579326	−	0.128227i
$107$	10.2013	−	10.2013i	0.986198	−	0.986198i	−0.0137076	−	0.999906i	$-0.504363\pi$
$107$	10.2013	−	10.2013i	0.986198	−	0.986198i	0.999906	+	0.0137076i	$0.00436339\pi$
$108$		0			0
$109$	−11.0144			−1.05498			−0.527492	−	0.849560i	$-0.676867\pi$
$109$	−11.0144			−1.05498			−0.527492	+	0.849560i	$0.676867\pi$
$110$	−0.566070	+	0.897878i	−0.0539726	+	0.0856093i
$111$		0			0
$112$	0.229079	+	2.65998i	0.0216459	+	0.251344i
$113$	−2.45369	+	2.45369i	−0.230823	+	0.230823i	−0.813036	−	0.582213i	$-0.802187\pi$
$113$	−2.45369	+	2.45369i	−0.230823	+	0.230823i	0.582213	+	0.813036i	$0.302187\pi$
$114$		0			0
$115$	−13.8072	+	13.9477i	−1.28753	+	1.30063i
$116$	4.39458	−	2.04559i	0.408026	−	0.189929i
$117$		0			0
$118$	14.6615	+	9.34740i	1.34970	+	0.860498i
$119$	−2.39095			−0.219178
$120$		0			0
$121$	−10.8873			−0.989758
$122$	8.94105	+	5.70034i	0.809484	+	0.516085i
$123$		0			0
$124$	5.41011	+	11.6226i	0.485842	+	1.04374i
$125$	11.1791	−	0.169731i	0.999885	−	0.0151812i
$126$		0			0
$127$	6.00329	−	6.00329i	0.532705	−	0.532705i	−0.388671	−	0.921377i	$-0.627066\pi$
$127$	6.00329	−	6.00329i	0.532705	−	0.532705i	0.921377	+	0.388671i	$0.127066\pi$
$128$	8.35948	−	7.62359i	0.738881	−	0.673836i
$129$		0			0
$130$	−3.46392	−	15.2829i	−0.303806	−	1.34040i
$131$	−11.3345			−0.990301			−0.495151	−	0.868807i	$-0.664887\pi$
$131$	−11.3345			−0.990301			−0.495151	+	0.868807i	$0.664887\pi$
$132$		0			0
$133$	1.92312	−	1.92312i	0.166756	−	0.166756i
$134$	−10.8478	+	2.40104i	−0.937109	+	0.207418i
$135$		0			0
$136$	6.15975	+	8.04449i	0.528194	+	0.689809i
$137$	−10.8670	−	10.8670i	−0.928434	−	0.928434i	0.0691711	−	0.997605i	$-0.477965\pi$
$137$	−10.8670	−	10.8670i	−0.928434	−	0.928434i	−0.997605	+	0.0691711i	$0.977965\pi$
$138$		0			0
$139$	13.3432			1.13176			0.565878	−	0.824489i	$-0.308537\pi$
$139$	13.3432			1.13176			0.565878	+	0.824489i	$0.308537\pi$
$140$	−2.80938	−	1.00861i	−0.237436	−	0.0852434i
$141$		0			0
$142$	16.0738	+	10.2478i	1.34888	+	0.859977i
$143$	−1.17614	+	1.17614i	−0.0983535	+	0.0983535i
$144$		0			0
$145$	0.0274257	+	5.41943i	0.00227758	+	0.450059i
$146$	9.86201	−	2.18284i	0.816186	−	0.180653i
$147$		0			0
$148$	2.17962	−	5.97583i	0.179164	−	0.491211i
$149$		−	13.5961i		−	1.11384i	−0.830566	−	0.556919i	$-0.811983\pi$
$149$		−	13.5961i		−	1.11384i	0.830566	−	0.556919i	$-0.188017\pi$
$150$		0			0
$151$	−9.64289			−0.784727			−0.392364	−	0.919810i	$-0.628343\pi$
$151$	−9.64289			−0.784727			−0.392364	+	0.919810i	$0.628343\pi$
$152$	−11.4250	−	1.51596i	−0.926687	−	0.122961i
$153$		0			0
$154$	0.0684695	+	0.309343i	0.00551743	+	0.0249276i
$155$	−14.3331	+	0.0725345i	−1.15126	+	0.00582611i
$156$		0			0
$157$	7.62403	+	7.62403i	0.608464	+	0.608464i	0.942545	−	0.334080i	$-0.108426\pi$
$157$	7.62403	+	7.62403i	0.608464	+	0.608464i	−0.334080	+	0.942545i	$0.608426\pi$
$158$	10.5594	+	6.73213i	0.840062	+	0.535580i
$159$		0			0
$160$	3.84421	+	12.0508i	0.303912	+	0.952700i
$161$			5.85826i			0.461695i
$162$		0			0
$163$	−16.2490	+	16.2490i	−1.27272	+	1.27272i	−0.328065	+	0.944655i	$0.606397\pi$
$163$	−16.2490	+	16.2490i	−1.27272	+	1.27272i	−0.944655	+	0.328065i	$0.893603\pi$
$164$	−10.5298	+	4.90145i	−0.822242	+	0.382739i
$165$		0			0
$166$	−9.34405	+	2.06820i	−0.725239	+	0.160523i
$167$	−13.7067	−	13.7067i	−1.06066	−	1.06066i	−0.998037	−	0.0626204i	$-0.980054\pi$
$167$	−13.7067	−	13.7067i	−1.06066	−	1.06066i	−0.0626204	−	0.998037i	$-0.519946\pi$
$168$		0			0
$169$		−	11.5566i		−	0.888971i
$170$	−11.0476	+	2.50398i	−0.847316	+	0.192047i
$171$		0			0
$172$	−12.9566	−	4.72577i	−0.987929	−	0.360337i
$173$	−3.35678	−	3.35678i	−0.255211	−	0.255211i	0.567892	−	0.823103i	$-0.307759\pi$
$173$	−3.35678	−	3.35678i	−0.255211	−	0.255211i	−0.823103	+	0.567892i	$0.807759\pi$
$174$		0			0
$175$	2.33581	−	2.38358i	0.176571	−	0.180181i
$176$	0.864406	−	1.02732i	0.0651571	−	0.0774374i
$177$		0			0
$178$	6.33606	−	9.93817i	0.474907	−	0.744897i
$179$		−	10.7537i		−	0.803772i	−0.915690	−	0.401886i	$-0.868355\pi$
$179$		−	10.7537i		−	0.803772i	0.915690	−	0.401886i	$-0.131645\pi$
$180$		0			0
$181$			10.1290i			0.752883i	0.926440	+	0.376441i	$0.122852\pi$
$181$			10.1290i			0.752883i	−0.926440	+	0.376441i	$0.877148\pi$
$182$	−3.94418	−	2.51460i	−0.292362	−	0.186395i
$183$		0			0
$184$	19.7104	−	15.0925i	1.45307	−	1.11263i
$185$	5.05414	+	5.00324i	0.371587	+	0.367845i
$186$		0			0
$187$	0.850201	+	0.850201i	0.0621728	+	0.0621728i
$188$	1.63090	−	4.47141i	0.118946	−	0.326111i
$189$		0			0
$190$	6.87197	−	10.9000i	0.498545	−	0.790773i
$191$		−	4.32194i		−	0.312725i	−0.987700	−	0.156362i	$-0.950023\pi$
$191$		−	4.32194i		−	0.312725i	0.987700	−	0.156362i	$-0.0499768\pi$
$192$		0			0
$193$	−7.97419	−	7.97419i	−0.573995	−	0.573995i	0.359248	−	0.933242i	$-0.383033\pi$
$193$	−7.97419	−	7.97419i	−0.573995	−	0.573995i	−0.933242	+	0.359248i	$0.883033\pi$
$194$	−4.38124	−	19.7943i	−0.314555	−	1.42115i
$195$		0			0
$196$	11.8846	−	5.53204i	0.848897	−	0.395146i
$197$	4.30206	−	4.30206i	0.306509	−	0.306509i	−0.537045	−	0.843554i	$-0.680459\pi$
$197$	4.30206	−	4.30206i	0.306509	−	0.306509i	0.843554	+	0.537045i	$0.180459\pi$
$198$		0			0
$199$		−	3.02113i		−	0.214162i	−0.994250	−	0.107081i	$-0.965850\pi$
$199$		−	3.02113i		−	0.214162i	0.994250	−	0.107081i	$-0.0341505\pi$
$200$	−14.0374	−	1.71821i	−0.992592	−	0.121496i
$201$		0			0
$202$	−7.51769	+	11.7916i	−0.528943	+	0.829652i
$203$	1.14388	+	1.14388i	0.0802849	+	0.0802849i
$204$		0			0
$205$	−0.0657147	−	12.9855i	−0.00458972	−	0.906946i
$206$	−19.5338	+	4.32358i	−1.36098	+	0.301238i
$207$		0			0
$208$	1.70078	+	19.7488i	0.117928	+	1.36933i
$209$	−1.36769			−0.0946052
$210$		0			0
$211$		−	8.87754i		−	0.611155i	−0.952167	−	0.305577i	$-0.901151\pi$
$211$		−	8.87754i		−	0.611155i	0.952167	−	0.305577i	$-0.0988495\pi$
$212$	2.96031	−	8.11625i	0.203315	−	0.557426i
$213$		0			0
$214$	−4.40918	−	19.9205i	−0.301405	−	1.36174i
$215$	10.8478	−	10.9582i	0.739816	−	0.747342i
$216$		0			0
$217$	−3.02530	+	3.02530i	−0.205371	+	0.205371i
$218$	−8.37379	+	13.1344i	−0.567144	+	0.889572i
$219$		0			0
$220$	0.640338	+	1.35765i	0.0431716	+	0.0915325i
$221$	−17.7514			−1.19409
$222$		0			0
$223$	9.93808	+	9.93808i	0.665503	+	0.665503i	0.956672	−	0.291169i	$-0.0940441\pi$
$223$	9.93808	+	9.93808i	0.665503	+	0.665503i	−0.291169	+	0.956672i	$0.594044\pi$
$224$	3.34612	+	1.74911i	0.223572	+	0.116867i
$225$		0			0
$226$	1.06052	+	4.79141i	0.0705449	+	0.318720i
$227$	7.21442	−	7.21442i	0.478838	−	0.478838i	−0.425922	−	0.904760i	$-0.640050\pi$
$227$	7.21442	−	7.21442i	0.478838	−	0.478838i	0.904760	+	0.425922i	$0.140050\pi$
$228$		0			0
$229$	−21.8687			−1.44512			−0.722562	−	0.691306i	$-0.757035\pi$
$229$	−21.8687			−1.44512			−0.722562	+	0.691306i	$0.757035\pi$
$230$	6.13521	+	27.0687i	0.404544	+	1.78486i
$231$		0			0
$232$	0.901702	−	6.79562i	0.0591996	−	0.446154i
$233$	−6.78300	+	6.78300i	−0.444369	+	0.444369i	−0.893477	−	0.449108i	$-0.851742\pi$
$233$	−6.78300	+	6.78300i	−0.444369	+	0.444369i	0.449108	+	0.893477i	$0.351742\pi$
$234$		0			0
$235$	3.78175	+	3.74367i	0.246694	+	0.244210i
$236$	22.2931	−	10.3770i	1.45116	−	0.675488i
$237$		0			0
$238$	−1.81775	+	2.85115i	−0.117827	+	0.184813i
$239$	4.63287			0.299676			0.149838	−	0.988711i	$-0.452125\pi$
$239$	4.63287			0.299676			0.149838	+	0.988711i	$0.452125\pi$
$240$		0			0
$241$	−9.72150			−0.626217			−0.313109	−	0.949717i	$-0.601370\pi$
$241$	−9.72150			−0.626217			−0.313109	+	0.949717i	$0.601370\pi$
$242$	−8.27722	+	12.9829i	−0.532080	+	0.834573i
$243$		0			0
$244$	13.5951	−	6.32825i	0.870335	−	0.405125i
$245$	0.0741692	+	14.6561i	0.00473850	+	0.936346i
$246$		0			0
$247$	14.2781	−	14.2781i	0.908491	−	0.908491i
$248$	17.9728	+	2.38479i	1.14127	+	0.151434i
$249$		0			0
$250$	8.29660	−	13.4598i	0.524723	−	0.851273i
$251$	30.6190			1.93265			0.966327	−	0.257316i	$-0.0828382\pi$
$251$	30.6190			1.93265			0.966327	+	0.257316i	$0.0828382\pi$
$252$		0			0
$253$	2.08314	−	2.08314i	0.130966	−	0.130966i
$254$	−2.59472	−	11.7228i	−0.162807	−	0.735557i
$255$		0			0
$256$	−2.73557	−	15.7644i	−0.170973	−	0.985276i
$257$	−1.63773	−	1.63773i	−0.102158	−	0.102158i	0.654180	−	0.756339i	$-0.273014\pi$
$257$	−1.63773	−	1.63773i	−0.102158	−	0.102158i	−0.756339	+	0.654180i	$0.773014\pi$
$258$		0			0
$259$	2.12282			0.131905
$260$	−20.8580	−	7.48836i	−1.29356	−	0.464408i
$261$		0			0
$262$	−8.61719	+	13.5162i	−0.532372	+	0.835031i
$263$	7.77099	−	7.77099i	0.479180	−	0.479180i	−0.425689	−	0.904869i	$-0.639968\pi$
$263$	7.77099	−	7.77099i	0.479180	−	0.479180i	0.904869	+	0.425689i	$0.139968\pi$
$264$		0			0
$265$	6.86441	+	6.79529i	0.421678	+	0.417431i
$266$	−0.831206	−	3.75536i	−0.0509645	−	0.230256i
$267$		0			0
$268$	−5.38399	+	14.7612i	−0.328880	+	0.901684i
$269$		−	16.1341i		−	0.983714i	−0.870676	−	0.491857i	$-0.836318\pi$
$269$		−	16.1341i		−	0.983714i	0.870676	−	0.491857i	$-0.163682\pi$
$270$		0			0
$271$	16.8474			1.02341			0.511704	−	0.859162i	$-0.329014\pi$
$271$	16.8474			1.02341			0.511704	+	0.859162i	$0.329014\pi$
$272$	14.2759	−	1.22945i	0.865603	−	0.0745463i
$273$		0			0
$274$	−21.2205	+	4.69691i	−1.28198	+	0.283751i
$275$	−1.67817	+	0.0169856i	−0.101198	+	0.00102427i
$276$		0			0
$277$	16.3206	+	16.3206i	0.980611	+	0.980611i	0.999816	−	0.0192042i	$-0.00611328\pi$
$277$	16.3206	+	16.3206i	0.980611	+	0.980611i	−0.0192042	+	0.999816i	$0.506113\pi$
$278$	10.1443	−	15.9115i	0.608416	−	0.954307i
$279$		0			0
$280$	−3.33862	+	2.58332i	−0.199520	+	0.154383i
$281$			31.2898i			1.86659i	0.359106	+	0.933297i	$0.383082\pi$
$281$			31.2898i			1.86659i	−0.359106	+	0.933297i	$0.616918\pi$
$282$		0			0
$283$	9.97554	−	9.97554i	0.592984	−	0.592984i	−0.345452	−	0.938436i	$-0.612274\pi$
$283$	9.97554	−	9.97554i	0.592984	−	0.592984i	0.938436	+	0.345452i	$0.112274\pi$
$284$	24.4406	−	11.3766i	1.45028	−	0.675079i
$285$		0			0
$286$	0.508346	+	2.29669i	0.0300591	+	0.135806i
$287$	−2.74086	−	2.74086i	−0.161788	−	0.161788i
$288$		0			0
$289$		−	4.16795i		−	0.245174i
$290$	6.48340	+	4.08748i	0.380718	+	0.240025i
$291$		0			0
$292$	4.89471	−	13.4198i	0.286441	−	0.785332i
$293$	5.26253	+	5.26253i	0.307440	+	0.307440i	0.843916	−	0.536476i	$-0.180245\pi$
$293$	5.26253	+	5.26253i	0.307440	+	0.307440i	−0.536476	+	0.843916i	$0.680245\pi$
$294$		0			0
$295$	0.139127	+	27.4921i	0.00810030	+	1.60065i
$296$	−5.46897	−	7.14235i	−0.317877	−	0.415140i
$297$		0			0
$298$	−16.2131	−	10.3366i	−0.939199	−	0.598784i
$299$			43.4941i			2.51533i
$300$		0			0
$301$		−	4.60261i		−	0.265290i
$302$	−7.33112	+	11.4989i	−0.421858	+	0.661689i
$303$		0			0
$304$	−10.4937	+	12.4715i	−0.601855	+	0.715289i
$305$	0.0848442	+	16.7655i	0.00485816	+	0.959992i
$306$		0			0
$307$	−9.54586	−	9.54586i	−0.544811	−	0.544811i	0.380124	−	0.924935i	$-0.375881\pi$
$307$	−9.54586	−	9.54586i	−0.544811	−	0.544811i	−0.924935	+	0.380124i	$0.875881\pi$
$308$	0.420939	+	0.153533i	0.0239852	+	0.00874836i
$309$		0			0
$310$	−10.8104	+	17.1471i	−0.613990	+	0.973887i
$311$		−	4.08587i		−	0.231688i	−0.993267	−	0.115844i	$-0.963043\pi$
$311$		−	4.08587i		−	0.231688i	0.993267	−	0.115844i	$-0.0369573\pi$
$312$		0			0
$313$	−14.4004	−	14.4004i	−0.813958	−	0.813958i	0.171266	−	0.985225i	$-0.445214\pi$
$313$	−14.4004	−	14.4004i	−0.813958	−	0.813958i	−0.985225	+	0.171266i	$0.945214\pi$
$314$	14.8877	−	3.29523i	0.840164	−	0.185961i
$315$		0			0
$316$	16.0558	−	7.47369i	0.903211	−	0.420428i
$317$	−12.0841	+	12.0841i	−0.678710	+	0.678710i	−0.959708	−	0.280998i	$-0.909334\pi$
$317$	−12.0841	+	12.0841i	−0.678710	+	0.678710i	0.280998	+	0.959708i	$0.409334\pi$
$318$		0			0
$319$		−	0.813510i		−	0.0455478i
$320$	17.2929	+	4.57763i	0.966704	+	0.255897i
$321$		0			0
$322$	6.98584	+	4.45381i	0.389306	+	0.248201i
$323$	−10.3213	−	10.3213i	−0.574290	−	0.574290i
$324$		0			0
$325$	17.3420	−	17.6966i	0.961961	−	0.981633i
$326$	7.02309	+	31.7301i	0.388973	+	1.75737i
$327$		0			0
$328$	−2.16057	+	16.2830i	−0.119297	+	0.899077i
$329$	1.58840			0.0875711
$330$		0			0
$331$		−	33.6119i		−	1.84747i	−0.383027	−	0.923737i	$-0.625118\pi$
$331$		−	33.6119i		−	1.84747i	0.383027	−	0.923737i	$-0.374882\pi$
$332$	−4.63764	+	12.7149i	−0.254523	+	0.697823i
$333$		0			0
$334$	−26.7656	+	5.92427i	−1.46455	+	0.324162i
$335$	−12.4845	−	12.3588i	−0.682100	−	0.675231i
$336$		0			0
$337$	−20.2142	+	20.2142i	−1.10114	+	1.10114i	−0.106864	+	0.994274i	$0.534081\pi$
$337$	−20.2142	+	20.2142i	−1.10114	+	1.10114i	−0.994274	+	0.106864i	$0.965919\pi$
$338$	−13.7810	−	8.78605i	−0.749588	−	0.477898i
$339$		0			0
$340$	−5.41315	+	15.0778i	−0.293570	+	0.817706i
$341$	2.15154			0.116512
$342$		0			0
$343$	6.39722	+	6.39722i	0.345417	+	0.345417i
$344$	−15.4858	+	11.8576i	−0.834936	+	0.639319i
$345$		0			0
$346$	−6.55492	+	1.45086i	−0.352394	+	0.0779985i
$347$	−0.443163	+	0.443163i	−0.0237903	+	0.0237903i	−0.718902	−	0.695112i	$-0.755355\pi$
$347$	−0.443163	+	0.443163i	−0.0237903	+	0.0237903i	0.695112	+	0.718902i	$0.255355\pi$
$348$		0			0
$349$	−10.8766			−0.582212			−0.291106	−	0.956691i	$-0.594023\pi$
$349$	−10.8766			−0.582212			−0.291106	+	0.956691i	$0.594023\pi$
$350$	−1.06654	−	4.59754i	−0.0570088	−	0.245749i
$351$		0			0
$352$	−0.567885	−	1.81182i	−0.0302684	−	0.0965703i
$353$	−10.0437	+	10.0437i	−0.534572	+	0.534572i	−0.921930	−	0.387357i	$-0.873388\pi$
$353$	−10.0437	+	10.0437i	−0.534572	+	0.534572i	0.387357	+	0.921930i	$0.373388\pi$
$354$		0			0
$355$	0.152529	+	30.1403i	0.00809540	+	1.59968i
$356$	−7.03399	−	15.1112i	−0.372801	−	0.800893i
$357$		0			0
$358$	−12.8236	−	8.17565i	−0.677748	−	0.432097i
$359$	19.6724			1.03827			0.519136	−	0.854692i	$-0.326254\pi$
$359$	19.6724			1.03827			0.519136	+	0.854692i	$0.326254\pi$
$360$		0			0
$361$	−2.39651			−0.126132
$362$	12.0786	+	7.70069i	0.634837	+	0.404739i
$363$		0			0
$364$	−5.99722	+	2.79159i	−0.314340	+	0.146319i
$365$	11.3499	+	11.2356i	0.594082	+	0.588100i
$366$		0			0
$367$	−9.86005	+	9.86005i	−0.514690	+	0.514690i	−0.915960	−	0.401270i	$-0.868569\pi$
$367$	−9.86005	+	9.86005i	−0.514690	+	0.514690i	0.401270	+	0.915960i	$0.368569\pi$
$368$	−3.01237	−	34.9785i	−0.157031	−	1.82338i
$369$		0			0
$370$	9.80871	−	2.22317i	0.509931	−	0.115577i
$371$	2.88316			0.149686
$372$		0			0
$373$	12.6526	−	12.6526i	0.655127	−	0.655127i	−0.299096	−	0.954223i	$-0.596685\pi$
$373$	12.6526	−	12.6526i	0.655127	−	0.655127i	0.954223	+	0.299096i	$0.0966852\pi$
$374$	1.66022	−	0.367471i	0.0858480	−	0.0190015i
$375$		0			0
$376$	−4.09215	−	5.34425i	−0.211036	−	0.275609i
$377$	8.49265	+	8.49265i	0.437394	+	0.437394i
$378$		0			0
$379$	37.9577			1.94975			0.974877	−	0.222743i	$-0.0715010\pi$
$379$	37.9577			1.94975			0.974877	+	0.222743i	$0.0715010\pi$
$380$	−7.77357	−	16.4815i	−0.398776	−	0.845486i
$381$		0			0
$382$	−5.15382	−	3.28581i	−0.263692	−	0.168116i
$383$	9.18320	−	9.18320i	0.469240	−	0.469240i	−0.432428	−	0.901668i	$-0.642343\pi$
$383$	9.18320	−	9.18320i	0.469240	−	0.469240i	0.901668	+	0.432428i	$0.142343\pi$
$384$		0			0
$385$	−0.352429	+	0.356015i	−0.0179615	+	0.0181442i
$386$	−15.5715	+	3.44657i	−0.792569	+	0.175426i
$387$		0			0
$388$	−26.9352	−	9.82431i	−1.36743	−	0.498754i
$389$			4.22258i			0.214093i	0.994254	+	0.107047i	$0.0341394\pi$
$389$			4.22258i			0.214093i	−0.994254	+	0.107047i	$0.965861\pi$
$390$		0			0
$391$	31.4408			1.59003
$392$	2.43853	−	18.3779i	0.123165	−	0.928222i
$393$		0			0
$394$	−1.85942	−	8.40081i	−0.0936764	−	0.423227i
$395$	0.100201	+	19.8002i	0.00504168	+	0.996256i
$396$		0			0
$397$	−1.27679	−	1.27679i	−0.0640801	−	0.0640801i	0.674340	−	0.738421i	$-0.264428\pi$
$397$	−1.27679	−	1.27679i	−0.0640801	−	0.0640801i	−0.738421	+	0.674340i	$0.764428\pi$
$398$	−3.60263	−	2.29685i	−0.180584	−	0.115131i
$399$		0			0
$400$	−12.7210	+	15.4330i	−0.636050	+	0.771648i
$401$			0.899990i			0.0449434i	0.999747	+	0.0224717i	$0.00715356\pi$
$401$			0.899990i			0.0449434i	−0.999747	+	0.0224717i	$0.992846\pi$
$402$		0			0
$403$	−22.4611	+	22.4611i	−1.11886	+	1.11886i
$404$	8.34578	+	17.9294i	0.415218	+	0.892019i
$405$		0			0
$406$	2.23371	−	0.494405i	0.110857	−	0.0245369i
$407$	−0.754855	−	0.754855i	−0.0374168	−	0.0374168i
$408$		0			0
$409$			24.1722i			1.19524i	0.801781	+	0.597618i	$0.203886\pi$
$409$			24.1722i			1.19524i	−0.801781	+	0.597618i	$0.796114\pi$
$410$	−15.5349	−	9.79400i	−0.767212	−	0.483691i
$411$		0			0
$412$	−9.69502	+	26.5807i	−0.477639	+	1.30954i
$413$	5.80277	+	5.80277i	0.285536	+	0.285536i
$414$		0			0
$415$	−10.7538	−	10.6455i	−0.527884	−	0.522568i
$416$	24.8430	+	12.9861i	1.21803	+	0.636695i
$417$		0			0
$418$	−1.03980	+	1.63094i	−0.0508584	+	0.0797720i
$419$		−	8.45513i		−	0.413060i	−0.978440	−	0.206530i	$-0.933783\pi$
$419$		−	8.45513i		−	0.413060i	0.978440	−	0.206530i	$-0.0662171\pi$
$420$		0			0
$421$		−	13.8561i		−	0.675307i	−0.941270	−	0.337654i	$-0.890367\pi$
$421$		−	13.8561i		−	0.675307i	0.941270	−	0.337654i	$-0.109633\pi$
$422$	−10.5863	−	6.74925i	−0.515331	−	0.328548i
$423$		0			0
$424$	−7.42783	−	9.70057i	−0.360727	−	0.471102i
$425$	−12.7925	−	12.5361i	−0.620526	−	0.608090i
$426$		0			0
$427$	3.53872	+	3.53872i	0.171250	+	0.171250i
$428$	−27.1069	−	9.88694i	−1.31026	−	0.477904i
$429$		0			0
$430$	−4.82020	−	21.2669i	−0.232451	−	1.02558i
$431$		−	5.84351i		−	0.281472i	−0.990047	−	0.140736i	$-0.955053\pi$
$431$		−	5.84351i		−	0.281472i	0.990047	−	0.140736i	$-0.0449469\pi$
$432$		0			0
$433$	10.0632	+	10.0632i	0.483605	+	0.483605i	0.906281	−	0.422676i	$-0.138909\pi$
$433$	10.0632	+	10.0632i	0.483605	+	0.483605i	−0.422676	+	0.906281i	$0.638909\pi$
$434$	1.30758	+	5.90762i	0.0627660	+	0.283575i
$435$		0			0
$436$	9.29618	+	19.9711i	0.445206	+	0.956442i
$437$	−25.2889	+	25.2889i	−1.20973	+	1.20973i
$438$		0			0
$439$			34.0222i			1.62379i	0.583802	+	0.811896i	$0.301564\pi$
$439$			34.0222i			1.62379i	−0.583802	+	0.811896i	$0.698436\pi$
$440$	2.10579	+	0.268577i	0.100390	+	0.0128039i
$441$		0			0
$442$	−13.4957	+	21.1681i	−0.641925	+	1.00687i
$443$	6.45259	+	6.45259i	0.306572	+	0.306572i	0.843578	−	0.537006i	$-0.180445\pi$
$443$	6.45259	+	6.45259i	0.306572	+	0.306572i	−0.537006	+	0.843578i	$0.680445\pi$
$444$		0			0
$445$	18.6353	−	0.0943062i	0.883396	−	0.00447054i
$446$	19.4065	−	4.29540i	0.918923	−	0.203393i
$447$		0			0
$448$	4.62970	−	2.66040i	0.218733	−	0.125692i
$449$	5.72541			0.270199			0.135099	−	0.990832i	$-0.456865\pi$
$449$	5.72541			0.270199			0.135099	+	0.990832i	$0.456865\pi$
$450$		0			0
$451$			1.94925i			0.0917866i
$452$	6.51992	+	2.37807i	0.306671	+	0.111855i
$453$		0			0
$454$	−3.11819	−	14.0879i	−0.146344	−	0.661177i
$455$	−0.0374275	−	7.39582i	−0.00175463	−	0.346721i
$456$		0			0
$457$	14.9718	−	14.9718i	0.700352	−	0.700352i	−0.264134	−	0.964486i	$-0.585086\pi$
$457$	14.9718	−	14.9718i	0.700352	−	0.700352i	0.964486	+	0.264134i	$0.0850862\pi$
$458$	−16.6259	+	26.0779i	−0.776878	+	1.21854i
$459$		0			0
$460$	36.9432	+	13.2632i	1.72249	+	0.618400i
$461$	25.8187			1.20250			0.601249	−	0.799062i	$-0.294670\pi$
$461$	25.8187			1.20250			0.601249	+	0.799062i	$0.294670\pi$
$462$		0			0
$463$	−20.5140	−	20.5140i	−0.953368	−	0.953368i	0.0455925	−	0.998960i	$-0.485482\pi$
$463$	−20.5140	−	20.5140i	−0.953368	−	0.953368i	−0.998960	+	0.0455925i	$0.985482\pi$
$464$	−7.41810	−	6.24171i	−0.344377	−	0.289764i
$465$		0			0
$466$	2.93172	+	13.2454i	0.135810	+	0.613583i
$467$	3.07112	−	3.07112i	0.142114	−	0.142114i	−0.632470	−	0.774585i	$-0.717959\pi$
$467$	3.07112	−	3.07112i	0.142114	−	0.142114i	0.774585	+	0.632470i	$0.217959\pi$
$468$		0			0
$469$	−5.24368			−0.242131
$470$	7.33936	−	1.66349i	0.338539	−	0.0767310i
$471$		0			0
$472$	4.57422	−	34.4733i	0.210545	−	1.58676i
$473$	−1.63665	+	1.63665i	−0.0752532	+	0.0752532i
$474$		0			0
$475$	20.3726	−	0.206202i	0.934761	−	0.00946120i
$476$	2.01798	+	4.33524i	0.0924938	+	0.198706i
$477$		0			0
$478$	3.52219	−	5.52460i	0.161101	−	0.252689i
$479$	−33.2621			−1.51979			−0.759893	−	0.650049i	$-0.774748\pi$
$479$	−33.2621			−1.51979			−0.759893	+	0.650049i	$0.774748\pi$
$480$		0			0
$481$	15.7607			0.718624
$482$	−7.39088	+	11.5927i	−0.336645	+	0.528032i
$483$		0			0
$484$	9.18898	+	19.7408i	0.417681	+	0.897309i
$485$	22.5513	−	22.7807i	1.02400	−	1.03442i
$486$		0			0
$487$	1.39322	−	1.39322i	0.0631329	−	0.0631329i	−0.674835	−	0.737968i	$-0.735785\pi$
$487$	1.39322	−	1.39322i	0.0631329	−	0.0631329i	0.737968	+	0.674835i	$0.235785\pi$
$488$	2.78950	−	21.0229i	0.126275	−	0.951663i
$489$		0			0
$490$	17.5335	+	11.0540i	0.792082	+	0.499371i
$491$	14.4709			0.653061			0.326530	−	0.945187i	$-0.394120\pi$
$491$	14.4709			0.653061			0.326530	+	0.945187i	$0.394120\pi$
$492$		0			0
$493$	6.13913	−	6.13913i	0.276493	−	0.276493i
$494$	−6.17121	−	27.8813i	−0.277656	−	1.25444i
$495$		0			0
$496$	16.5078	−	19.6191i	0.741224	−	0.880924i
$497$	6.36174	+	6.36174i	0.285363	+	0.285363i
$498$		0			0
$499$	−20.4107			−0.913710			−0.456855	−	0.889541i	$-0.651024\pi$
$499$	−20.4107			−0.913710			−0.456855	+	0.889541i	$0.651024\pi$
$500$	−9.74294	−	20.1265i	−0.435717	−	0.900084i
$501$		0			0
$502$	23.2784	−	36.5125i	1.03897	−	1.62963i
$503$	−2.54697	+	2.54697i	−0.113564	+	0.113564i	−0.761605	−	0.648041i	$-0.775588\pi$
$503$	−2.54697	+	2.54697i	−0.113564	+	0.113564i	0.648041	+	0.761605i	$0.275588\pi$
$504$		0			0
$505$	−22.1106	+	0.111894i	−0.983910	+	0.00497920i
$506$	−0.900369	−	4.06784i	−0.0400263	−	0.180837i
$507$		0			0
$508$	−15.9519	−	5.81828i	−0.707751	−	0.258145i
$509$		−	13.5045i		−	0.598575i	−0.954163	−	0.299288i	$-0.903251\pi$
$509$		−	13.5045i		−	0.598575i	0.954163	−	0.299288i	$-0.0967490\pi$
$510$		0			0
$511$	4.76715			0.210886
$512$	−20.8785	−	8.72296i	−0.922706	−	0.385504i
$513$		0			0
$514$	−3.19805	+	0.707852i	−0.141060	+	0.0312220i
$515$	−22.4809	−	22.2545i	−0.990628	−	0.980652i
$516$		0			0
$517$	−0.564820	−	0.564820i	−0.0248407	−	0.0248407i
$518$	1.61390	−	2.53141i	0.0709105	−	0.111224i
$519$		0			0
$520$	−24.7872	+	19.1796i	−1.08699	+	0.841081i
$521$		−	13.5151i		−	0.592108i	−0.955171	−	0.296054i	$-0.904329\pi$
$521$		−	13.5151i		−	0.592108i	0.955171	−	0.296054i	$-0.0956708\pi$
$522$		0			0
$523$	12.6641	−	12.6641i	0.553760	−	0.553760i	−0.373764	−	0.927524i	$-0.621933\pi$
$523$	12.6641	−	12.6641i	0.553760	−	0.553760i	0.927524	+	0.373764i	$0.121933\pi$
$524$	9.56640	+	20.5516i	0.417910	+	0.897802i
$525$		0			0
$526$	−3.35875	−	15.1747i	−0.146448	−	0.661649i
$527$	16.2365	+	16.2365i	0.707275	+	0.707275i
$528$		0			0
$529$		−	54.0356i		−	2.34938i
$530$	13.3220	−	3.01947i	0.578670	−	0.131157i
$531$		0			0
$532$	−5.11011	−	1.86386i	−0.221552	−	0.0808086i
$533$	−20.3492	−	20.3492i	−0.881423	−	0.881423i
$534$		0			0
$535$	22.6951	−	22.9260i	0.981195	−	0.991177i
$536$	13.5092	+	17.6427i	0.583507	+	0.762047i
$537$		0			0
$538$	−19.2396	−	12.2661i	−0.829476	−	0.528831i
$539$		−	2.20003i		−	0.0947619i
$540$		0			0
$541$			17.1804i			0.738644i	0.929301	+	0.369322i	$0.120410\pi$
$541$			17.1804i			0.738644i	−0.929301	+	0.369322i	$0.879590\pi$
$542$	12.8084	−	20.0902i	0.550170	−	0.862947i
$543$		0			0
$544$	9.38732	−	17.9584i	0.402478	−	0.769960i
$545$	−24.6285	+	0.124636i	−1.05497	+	0.00533881i
$546$		0			0
$547$	−17.4105	−	17.4105i	−0.744417	−	0.744417i	0.229007	−	0.973425i	$-0.426452\pi$
$547$	−17.4105	−	17.4105i	−0.744417	−	0.744417i	−0.973425	+	0.229007i	$0.926452\pi$
$548$	−10.5322	+	28.8758i	−0.449911	+	1.23351i
$549$		0			0
$550$	−1.25559	+	2.01410i	−0.0535387	+	0.0858813i
$551$			9.87584i			0.420725i
$552$		0			0
$553$	4.17924	+	4.17924i	0.177719	+	0.177719i
$554$	31.8699	−	7.05404i	1.35402	−	0.299698i
$555$		0			0
$556$	−11.2617	−	24.1938i	−0.477604	−	1.02604i
$557$	9.22732	−	9.22732i	0.390974	−	0.390974i	−0.484060	−	0.875035i	$-0.660838\pi$
$557$	9.22732	−	9.22732i	0.390974	−	0.390974i	0.875035	+	0.484060i	$0.160838\pi$
$558$		0			0
$559$		−	34.1717i		−	1.44531i
$560$	0.542329	+	5.94522i	0.0229176	+	0.251231i
$561$		0			0
$562$	37.3124	+	23.7884i	1.57393	+	1.00345i
$563$	−19.8727	−	19.8727i	−0.837535	−	0.837535i	0.150999	−	0.988534i	$-0.451751\pi$
$563$	−19.8727	−	19.8727i	−0.837535	−	0.837535i	−0.988534	+	0.150999i	$0.951751\pi$
$564$		0			0
$565$	−5.45877	+	5.51430i	−0.229652	+	0.231988i
$566$	−4.31159	−	19.4796i	−0.181230	−	0.818790i
$567$		0			0
$568$	5.01484	−	37.7940i	0.210418	−	1.58580i
$569$	−4.73031			−0.198305			−0.0991524	−	0.995072i	$-0.531613\pi$
$569$	−4.73031			−0.198305			−0.0991524	+	0.995072i	$0.531613\pi$
$570$		0			0
$571$		−	5.54039i		−	0.231858i	−0.993257	−	0.115929i	$-0.963015\pi$
$571$		−	5.54039i		−	0.231858i	0.993257	−	0.115929i	$-0.0369845\pi$
$572$	3.12523	+	1.13989i	0.130672	+	0.0476613i
$573$		0			0
$574$	−5.35218	+	1.18464i	−0.223396	+	0.0494460i
$575$	−30.7157	+	31.3438i	−1.28093	+	1.30713i
$576$		0			0
$577$	−12.9105	+	12.9105i	−0.537472	+	0.537472i	−0.922786	−	0.385314i	$-0.874093\pi$
$577$	−12.9105	+	12.9105i	−0.537472	+	0.537472i	0.385314	+	0.922786i	$0.374093\pi$
$578$	−4.97019	−	3.16873i	−0.206733	−	0.131802i
$579$		0			0
$580$	9.80330	−	4.62376i	0.407060	−	0.191991i
$581$	−4.51677			−0.187387
$582$		0			0
$583$	−1.02523	−	1.02523i	−0.0424606	−	0.0424606i
$584$	−12.2815	−	16.0394i	−0.508212	−	0.663713i
$585$		0			0
$586$	10.2763	−	2.27455i	0.424512	−	0.0939609i
$587$	−1.90309	+	1.90309i	−0.0785487	+	0.0785487i	−0.745290	−	0.666741i	$-0.767689\pi$
$587$	−1.90309	+	1.90309i	−0.0785487	+	0.0785487i	0.666741	+	0.745290i	$0.267689\pi$
$588$		0			0
$589$	−26.1192			−1.07622
$590$	32.8894	+	20.7352i	1.35404	+	0.853657i
$591$		0			0
$592$	−12.6749	+	1.09157i	−0.520936	+	0.0448634i
$593$	11.7312	−	11.7312i	0.481745	−	0.481745i	−0.423944	−	0.905688i	$-0.639355\pi$
$593$	11.7312	−	11.7312i	0.481745	−	0.481745i	0.905688	+	0.423944i	$0.139355\pi$
$594$		0			0
$595$	−5.34626	+	0.0270554i	−0.219175	+	0.00110916i
$596$	−24.6524	+	11.4752i	−1.00980	+	0.470043i
$597$		0			0
$598$	51.8657	+	33.0669i	2.12095	+	1.35220i
$599$	2.61594			0.106884			0.0534422	−	0.998571i	$-0.482981\pi$
$599$	2.61594			0.106884			0.0534422	+	0.998571i	$0.482981\pi$
$600$		0			0
$601$	20.1722			0.822840			0.411420	−	0.911446i	$-0.365033\pi$
$601$	20.1722			0.822840			0.411420	+	0.911446i	$0.365033\pi$
$602$	−5.48851	−	3.49919i	−0.223695	−	0.142616i
$603$		0			0
$604$	8.13865	+	17.4844i	0.331157	+	0.711429i
$605$	−24.3445	+	0.123199i	−0.989745	+	0.00500873i
$606$		0			0
$607$	−17.3218	+	17.3218i	−0.703069	+	0.703069i	−0.965068	−	0.261999i	$-0.915618\pi$
$607$	−17.3218	+	17.3218i	−0.703069	+	0.703069i	0.261999	+	0.965068i	$0.415618\pi$
$608$	6.89401	+	21.9951i	0.279589	+	0.892019i
$609$		0			0
$610$	20.0570	+	12.6450i	0.812086	+	0.511982i
$611$	11.7929			0.477090
$612$		0			0
$613$	−16.8299	+	16.8299i	−0.679754	+	0.679754i	−0.959944	−	0.280191i	$-0.909602\pi$
$613$	−16.8299	+	16.8299i	−0.679754	+	0.679754i	0.280191	+	0.959944i	$0.409602\pi$
$614$	−18.6406	+	4.12588i	−0.752273	+	0.166507i
$615$		0			0
$616$	0.503109	−	0.385236i	0.0202708	−	0.0155216i
$617$	−2.56139	−	2.56139i	−0.103118	−	0.103118i	0.653666	−	0.756783i	$-0.273230\pi$
$617$	−2.56139	−	2.56139i	−0.103118	−	0.103118i	−0.756783	+	0.653666i	$0.773230\pi$
$618$		0			0
$619$	16.9662			0.681931			0.340965	−	0.940076i	$-0.389246\pi$
$619$	16.9662			0.681931			0.340965	+	0.940076i	$0.389246\pi$
$620$	12.2287	+	25.9274i	0.491118	+	1.04127i
$621$		0			0
$622$	−4.87231	−	3.10633i	−0.195362	−	0.124552i
$623$	3.93336	−	3.93336i	0.157587	−	0.157587i
$624$		0			0
$625$	24.9949	−	0.506024i	0.999795	−	0.0202410i
$626$	−28.1202	+	6.22409i	−1.12391	+	0.248765i
$627$		0			0
$628$	7.38909	−	20.2585i	0.294857	−	0.808404i
$629$		−	11.3930i		−	0.454269i
$630$		0			0
$631$	−39.5630			−1.57498			−0.787488	−	0.616330i	$-0.788619\pi$
$631$	−39.5630			−1.57498			−0.787488	+	0.616330i	$0.788619\pi$
$632$	3.29442	−	24.8282i	0.131045	−	0.987612i
$633$		0			0
$634$	5.22294	+	23.5971i	0.207429	+	0.937159i
$635$	13.3557	−	13.4915i	0.530003	−	0.535394i
$636$		0			0
$637$	22.9673	+	22.9673i	0.909996	+	0.909996i
$638$	−0.970092	−	0.618480i	−0.0384063	−	0.0244859i
$639$		0			0
$640$	18.6059	−	17.1412i	0.735461	−	0.677567i
$641$		−	47.3441i		−	1.86998i	−0.354676	−	0.934989i	$-0.615409\pi$
$641$		−	47.3441i		−	1.86998i	0.354676	−	0.934989i	$-0.384591\pi$
$642$		0			0
$643$	−14.8250	+	14.8250i	−0.584639	+	0.584639i	−0.936175	−	0.351535i	$-0.885660\pi$
$643$	−14.8250	+	14.8250i	−0.584639	+	0.584639i	0.351535	+	0.936175i	$0.385660\pi$
$644$	10.6221	−	4.94440i	0.418570	−	0.194837i
$645$		0			0
$646$	−20.1547	+	4.46102i	−0.792977	+	0.175516i
$647$	4.86574	+	4.86574i	0.191292	+	0.191292i	0.796254	−	0.604962i	$-0.206812\pi$
$647$	4.86574	+	4.86574i	0.191292	+	0.191292i	−0.604962	+	0.796254i	$0.706812\pi$
$648$		0			0
$649$		−	4.12683i		−	0.161992i
$650$	−7.91840	−	34.1340i	−0.310585	−	1.33885i
$651$		0			0
$652$	43.1768	+	15.7483i	1.69093	+	0.616750i
$653$	11.8214	+	11.8214i	0.462609	+	0.462609i	0.899510	−	0.436901i	$-0.143924\pi$
$653$	11.8214	+	11.8214i	0.462609	+	0.462609i	−0.436901	+	0.899510i	$0.643924\pi$
$654$		0			0
$655$	−25.3444	+	0.128259i	−0.990289	+	0.00501149i
$656$	17.7745	+	14.9557i	0.693977	+	0.583924i
$657$		0			0
$658$	1.20760	−	1.89413i	0.0470770	−	0.0738408i
$659$			6.02230i			0.234595i	0.993097	+	0.117298i	$0.0374232\pi$
$659$			6.02230i			0.234595i	−0.993097	+	0.117298i	$0.962577\pi$
$660$		0			0
$661$			37.9790i			1.47721i	0.674137	+	0.738606i	$0.264516\pi$
$661$			37.9790i			1.47721i	−0.674137	+	0.738606i	$0.735484\pi$
$662$	−40.0814	−	25.5538i	−1.55781	−	0.993176i
$663$		0			0
$664$	11.6365	+	15.1970i	0.451582	+	0.589756i
$665$	4.27842	−	4.32194i	0.165910	−	0.167598i
$666$		0			0
$667$	−15.0420	−	15.0420i	−0.582428	−	0.582428i
$668$	−13.2843	+	36.4214i	−0.513986	+	1.40919i
$669$		0			0
$670$	−24.2290	+	5.49158i	−0.936048	+	0.212158i
$671$		−	2.51667i		−	0.0971551i
$672$		0			0
$673$	7.99686	+	7.99686i	0.308256	+	0.308256i	0.844233	−	0.535977i	$-0.180057\pi$
$673$	7.99686	+	7.99686i	0.308256	+	0.308256i	−0.535977	+	0.844233i	$0.680057\pi$
$674$	8.73691	+	39.4731i	0.336533	+	1.52045i
$675$		0			0
$676$	−20.9543	+	9.75386i	−0.805936	+	0.375148i
$677$	7.11103	−	7.11103i	0.273299	−	0.273299i	−0.557128	−	0.830427i	$-0.688097\pi$
$677$	7.11103	−	7.11103i	0.273299	−	0.273299i	0.830427	+	0.557128i	$0.188097\pi$
$678$		0			0
$679$		−	9.56827i		−	0.367197i
$680$	13.8645	+	17.9181i	0.531678	+	0.687128i
$681$		0			0
$682$	1.63573	−	2.56566i	0.0626354	−	0.0982443i
$683$	7.99061	+	7.99061i	0.305752	+	0.305752i	0.843259	−	0.537507i	$-0.180634\pi$
$683$	7.99061	+	7.99061i	0.305752	+	0.305752i	−0.537507	+	0.843259i	$0.680634\pi$
$684$		0			0
$685$	−24.4221	−	24.1762i	−0.933120	−	0.923723i
$686$	12.4921	−	2.76498i	0.476950	−	0.105568i
$687$		0			0
$688$	2.36671	+	27.4813i	0.0902298	+	1.04771i
$689$	21.4058			0.815495
$690$		0			0
$691$			32.5931i			1.23990i	0.784641	+	0.619951i	$0.212848\pi$
$691$			32.5931i			1.23990i	−0.784641	+	0.619951i	$0.787152\pi$
$692$	−3.25334	+	8.91962i	−0.123673	+	0.339073i
$693$		0			0
$694$	0.191542	+	0.865382i	0.00727085	+	0.0328495i
$695$	29.8359	−	0.150989i	1.13174	−	0.00572732i
$696$		0			0
$697$	−14.7100	+	14.7100i	−0.557180	+	0.557180i
$698$	−8.26907	+	12.9701i	−0.312989	+	0.490927i
$699$		0			0
$700$	−6.29331	−	2.22351i	−0.237865	−	0.0840408i
$701$	−42.9064			−1.62055			−0.810277	−	0.586047i	$-0.800683\pi$
$701$	−42.9064			−1.62055			−0.810277	+	0.586047i	$0.800683\pi$
$702$		0			0
$703$	9.16379	+	9.16379i	0.345619	+	0.345619i
$704$	−2.59229	−	0.700265i	−0.0977008	−	0.0263922i
$705$		0			0
$706$	4.34105	+	19.6127i	0.163378	+	0.738135i
$707$	−4.66691	+	4.66691i	−0.175517	+	0.175517i
$708$		0			0
$709$	−10.3299			−0.387949			−0.193975	−	0.981007i	$-0.562138\pi$
$709$	−10.3299			−0.387949			−0.193975	+	0.981007i	$0.562138\pi$
$710$	36.0576	+	22.7326i	1.35322	+	0.853140i
$711$		0			0
$712$	−23.3674	−	3.10059i	−0.875732	−	0.116200i
$713$	39.7825	−	39.7825i	1.48986	−	1.48986i
$714$		0			0
$715$	−2.61658	+	2.64320i	−0.0978545	+	0.0988500i
$716$	−19.4986	+	9.07622i	−0.728696	+	0.339194i
$717$		0			0
$718$	14.9562	−	23.4589i	0.558160	−	0.875480i
$719$	−6.49219			−0.242118			−0.121059	−	0.992645i	$-0.538629\pi$
$719$	−6.49219			−0.242118			−0.121059	+	0.992645i	$0.538629\pi$
$720$		0			0
$721$	−9.44235			−0.351652
$722$	−1.82197	+	2.85778i	−0.0678067	+	0.106356i
$723$		0			0
$724$	18.3658	−	8.54893i	0.682559	−	0.317719i
$725$	0.122650	+	12.1177i	0.00455511	+	0.450042i
$726$		0			0
$727$	−11.0479	+	11.0479i	−0.409744	+	0.409744i	−0.881649	−	0.471905i	$-0.843566\pi$
$727$	−11.0479	+	11.0479i	−0.409744	+	0.409744i	0.471905	+	0.881649i	$0.343566\pi$
$728$	−1.23054	+	9.27389i	−0.0456068	+	0.343713i
$729$		0			0
$730$	22.0271	−	4.99252i	0.815261	−	0.184781i
$731$	−24.7019			−0.913631
$732$		0			0
$733$	−19.5376	+	19.5376i	−0.721636	+	0.721636i	−0.968938	−	0.247302i	$-0.920456\pi$
$733$	−19.5376	+	19.5376i	−0.721636	+	0.721636i	0.247302	+	0.968938i	$0.420456\pi$
$734$	4.26167	+	19.2541i	0.157301	+	0.710682i
$735$		0			0
$736$	−44.0013	−	23.0006i	−1.62191	−	0.847814i
$737$	1.86461	+	1.86461i	0.0686837	+	0.0686837i
$738$		0			0
$739$	−24.8980			−0.915890			−0.457945	−	0.888981i	$-0.651414\pi$
$739$	−24.8980			−0.915890			−0.457945	+	0.888981i	$0.651414\pi$
$740$	4.80610	−	13.3869i	0.176676	−	0.492111i
$741$		0			0
$742$	2.19196	−	3.43811i	0.0804693	−	0.126217i
$743$	−15.8961	+	15.8961i	−0.583171	+	0.583171i	−0.935773	−	0.352602i	$-0.885297\pi$
$743$	−15.8961	+	15.8961i	−0.583171	+	0.583171i	0.352602	+	0.935773i	$0.385297\pi$
$744$		0			0
$745$	−0.153851	−	30.4015i	−0.00563665	−	1.11382i
$746$	−5.46866	−	24.7072i	−0.200222	−	0.904595i
$747$		0			0
$748$	0.824000	−	2.25915i	0.0301284	−	0.0826027i
$749$		−	9.62928i		−	0.351846i
$750$		0			0
$751$	11.5535			0.421594			0.210797	−	0.977530i	$-0.432394\pi$
$751$	11.5535			0.421594			0.210797	+	0.977530i	$0.432394\pi$
$752$	−9.48400	+	0.816768i	−0.345846	+	0.0297845i
$753$		0			0
$754$	16.5839	−	3.67066i	0.603951	−	0.133678i
$755$	−21.5619	+	0.109117i	−0.784717	+	0.00397116i
$756$		0			0
$757$	−18.8612	−	18.8612i	−0.685524	−	0.685524i	0.275716	−	0.961239i	$-0.411085\pi$
$757$	−18.8612	−	18.8612i	−0.685524	−	0.685524i	−0.961239	+	0.275716i	$0.911085\pi$
$758$	28.8577	−	45.2637i	1.04816	−	1.64405i
$759$		0			0
$760$	−25.5638	−	3.26047i	−0.927297	−	0.118270i
$761$		−	33.0567i		−	1.19830i	−0.800636	−	0.599151i	$-0.795505\pi$
$761$		−	33.0567i		−	1.19830i	0.800636	−	0.599151i	$-0.204495\pi$
$762$		0			0
$763$	−5.19836	+	5.19836i	−0.188193	+	0.188193i
$764$	−7.83650	+	3.64774i	−0.283515	+	0.131971i
$765$		0			0
$766$	−3.96913	−	17.9324i	−0.143411	−	0.647924i
$767$	43.0821	+	43.0821i	1.55561	+	1.55561i
$768$		0			0
$769$			44.9240i			1.62000i	0.586429	+	0.810001i	$0.300533\pi$
$769$			44.9240i			1.62000i	−0.586429	+	0.810001i	$0.699467\pi$
$770$	0.156601	+	0.690928i	0.00564351	+	0.0248993i
$771$		0			0
$772$	−7.72845	+	21.1890i	−0.278153	+	0.762608i
$773$	28.3672	+	28.3672i	1.02030	+	1.02030i	0.999790	+	0.0205060i	$0.00652772\pi$
$773$	28.3672	+	28.3672i	1.02030	+	1.02030i	0.0205060	+	0.999790i	$0.493472\pi$
$774$		0			0
$775$	−32.0486	+	0.324380i	−1.15122	+	0.0116521i
$776$	−32.1930	+	24.6505i	−1.15566	+	0.884902i
$777$		0			0
$778$	5.03533	+	3.21026i	0.180525	+	0.115093i
$779$		−	23.6635i		−	0.847832i
$780$		0			0
$781$		−	4.52436i		−	0.161894i
$782$	23.9032	−	37.4925i	0.854778	−	1.34073i
$783$		0			0
$784$	−20.0613	−	16.8799i	−0.716474	−	0.602852i
$785$	17.1339	+	16.9614i	0.611536	+	0.605377i
$786$		0			0
$787$	4.79302	+	4.79302i	0.170853	+	0.170853i	0.787354	−	0.616501i	$-0.211450\pi$
$787$	4.79302	+	4.79302i	0.170853	+	0.170853i	−0.616501	+	0.787354i	$0.711450\pi$
$788$	−11.4314	−	4.16949i	−0.407228	−	0.148532i
$789$		0			0
$790$	23.6875	+	14.9338i	0.842762	+	0.531322i
$791$			2.31610i			0.0823509i
$792$		0			0
$793$	26.2729	+	26.2729i	0.932977	+	0.932977i
$794$	−2.49323	+	0.551849i	−0.0884815	+	0.0195844i
$795$		0			0
$796$	−5.47788	+	2.54985i	−0.194158	+	0.0903771i
$797$	−7.30136	+	7.30136i	−0.258627	+	0.258627i	−0.824496	−	0.565868i	$-0.808541\pi$
$797$	−7.30136	+	7.30136i	−0.258627	+	0.258627i	0.565868	+	0.824496i	$0.308541\pi$
$798$		0			0
$799$		−	8.52480i		−	0.301586i
$800$	8.73218	+	26.9026i	0.308729	+	0.951150i
$801$		0			0
$802$	1.07322	+	0.684228i	0.0378966	+	0.0241609i
$803$	−1.69516	−	1.69516i	−0.0598208	−	0.0598208i
$804$		0			0
$805$	0.0662907	+	13.0993i	0.00233644	+	0.461689i
$806$	9.70804	+	43.8606i	0.341951	+	1.54492i
$807$		0			0
$808$	27.7253	+	3.67884i	0.975373	+	0.129421i
$809$	−26.9078			−0.946026			−0.473013	−	0.881055i	$-0.656834\pi$
$809$	−26.9078			−0.946026			−0.473013	+	0.881055i	$0.656834\pi$
$810$		0			0
$811$		−	4.38227i		−	0.153882i	−0.997036	−	0.0769412i	$-0.975485\pi$
$811$		−	4.38227i		−	0.153882i	0.997036	−	0.0769412i	$-0.0245154\pi$
$812$	1.10863	−	3.03952i	0.0389054	−	0.106666i
$813$		0			0
$814$	−1.47404	+	0.326261i	−0.0516649	+	0.0114354i
$815$	−36.1495	+	36.5173i	−1.26626	+	1.27914i
$816$		0			0
$817$	19.8686	−	19.8686i	0.695113	−	0.695113i
$818$	28.8248	+	18.3772i	1.00783	+	0.642542i
$819$		0			0
$820$	−23.4897	+	11.0790i	−0.820295	+	0.386895i
$821$	34.5890			1.20716			0.603582	−	0.797301i	$-0.293739\pi$
$821$	34.5890			1.20716			0.603582	+	0.797301i	$0.293739\pi$
$822$		0			0
$823$	−5.63496	−	5.63496i	−0.196422	−	0.196422i	0.602042	−	0.798464i	$-0.294354\pi$
$823$	−5.63496	−	5.63496i	−0.196422	−	0.196422i	−0.798464	+	0.602042i	$0.794354\pi$
$824$	24.3261	+	31.7694i	0.847441	+	1.10674i
$825$		0			0
$826$	11.3313	−	2.50805i	0.394266	−	0.0872663i
$827$	−29.8906	+	29.8906i	−1.03940	+	1.03940i	−0.0402073	+	0.999191i	$0.512802\pi$
$827$	−29.8906	+	29.8906i	−1.03940	+	1.03940i	−0.999191	+	0.0402073i	$0.987198\pi$
$828$		0			0
$829$	45.0207			1.56363			0.781817	−	0.623508i	$-0.214293\pi$
$829$	45.0207			1.56363			0.781817	+	0.623508i	$0.214293\pi$
$830$	−20.8703	+	4.73031i	−0.724417	+	0.164191i
$831$		0			0
$832$	34.3728	−	19.7519i	1.19166	−	0.684774i
$833$	16.6025	−	16.6025i	0.575241	−	0.575241i
$834$		0			0
$835$	−30.8039	−	30.4937i	−1.06601	−	1.05528i
$836$	1.15434	+	2.47988i	0.0399237	+	0.0857686i
$837$		0			0
$838$	−10.0826	−	6.42811i	−0.348296	−	0.222055i
$839$	−6.14853			−0.212271			−0.106135	−	0.994352i	$-0.533848\pi$
$839$	−6.14853			−0.212271			−0.106135	+	0.994352i	$0.533848\pi$
$840$		0			0
$841$	23.1258			0.797442
$842$	−16.5231	−	10.5343i	−0.569425	−	0.363036i
$843$		0			0
$844$	−16.0966	+	7.49269i	−0.554070	+	0.257909i
$845$	−0.130772	−	25.8411i	−0.00449870	−	0.888960i
$846$		0			0
$847$	−5.13842	+	5.13842i	−0.176558	+	0.176558i
$848$	−17.2148	+	1.48255i	−0.591159	+	0.0509110i
$849$		0			0
$850$	−24.6746	+	5.72402i	−0.846333	+	0.196332i
$851$	−27.9149			−0.956910
$852$		0			0
$853$	11.5962	−	11.5962i	0.397046	−	0.397046i	−0.480144	−	0.877190i	$-0.659415\pi$
$853$	11.5962	−	11.5962i	0.397046	−	0.397046i	0.877190	+	0.480144i	$0.159415\pi$
$854$	6.91019	−	1.52949i	0.236462	−	0.0523381i
$855$		0			0
$856$	−32.3983	+	24.8077i	−1.10735	+	0.847909i
$857$	23.8521	+	23.8521i	0.814772	+	0.814772i	0.985345	−	0.170573i	$-0.0545619\pi$
$857$	23.8521	+	23.8521i	0.814772	+	0.814772i	−0.170573	+	0.985345i	$0.554562\pi$
$858$		0			0
$859$	31.3817			1.07073			0.535365	−	0.844621i	$-0.320174\pi$
$859$	31.3817			1.07073			0.535365	+	0.844621i	$0.320174\pi$
$860$	−29.0249	−	10.4204i	−0.989740	−	0.355332i
$861$		0			0
$862$	−6.96825	−	4.44259i	−0.237340	−	0.151315i
$863$	12.4212	−	12.4212i	0.422823	−	0.422823i	−0.463351	−	0.886175i	$-0.653353\pi$
$863$	12.4212	−	12.4212i	0.422823	−	0.422823i	0.886175	+	0.463351i	$0.153353\pi$
$864$		0			0
$865$	−7.54388	−	7.46791i	−0.256500	−	0.253917i
$866$	19.6507	−	4.34946i	0.667759	−	0.147801i
$867$		0			0
$868$	8.03881	+	2.93207i	0.272855	+	0.0995209i
$869$		−	2.97220i		−	0.100825i
$870$		0			0
$871$	−38.9312			−1.31913
$872$	30.8826	+	4.09777i	1.04582	+	0.138768i
$873$		0			0
$874$	10.9303	+	49.3827i	0.369723	+	1.67039i
$875$	5.19599	−	5.35620i	0.175656	−	0.181073i
$876$		0			0
$877$	−38.0074	−	38.0074i	−1.28342	−	1.28342i	−0.938710	−	0.344708i	$-0.887978\pi$
$877$	−38.0074	−	38.0074i	−1.28342	−	1.28342i	−0.344708	−	0.938710i	$-0.612022\pi$
$878$	40.5707	+	25.8658i	1.36920	+	0.872928i
$879$		0			0
$880$	1.92122	−	2.30692i	0.0647644	−	0.0777661i
$881$		−	10.9118i		−	0.367626i	−0.982961	−	0.183813i	$-0.941156\pi$
$881$		−	10.9118i		−	0.367626i	0.982961	−	0.183813i	$-0.0588442\pi$
$882$		0			0
$883$	−1.85770	+	1.85770i	−0.0625165	+	0.0625165i	−0.737674	−	0.675157i	$-0.764076\pi$
$883$	−1.85770	+	1.85770i	−0.0625165	+	0.0625165i	0.675157	+	0.737674i	$0.264076\pi$
$884$	14.9823	+	32.1866i	0.503908	+	1.08255i
$885$		0			0
$886$	12.6002	−	2.78891i	0.423313	−	0.0936954i
$887$	−3.17163	−	3.17163i	−0.106493	−	0.106493i	0.651853	−	0.758346i	$-0.273992\pi$
$887$	−3.17163	−	3.17163i	−0.106493	−	0.106493i	−0.758346	+	0.651853i	$0.773992\pi$
$888$		0			0
$889$		−	5.66665i		−	0.190053i
$890$	14.0552	−	22.2938i	0.471132	−	0.747291i
$891$		0			0
$892$	9.63182	−	26.4074i	0.322497	−	0.884185i
$893$	6.85679	+	6.85679i	0.229454	+	0.229454i
$894$		0			0
$895$	−0.121687	−	24.0458i	−0.00406754	−	0.803762i
$896$	0.347313	−	7.54341i	0.0116029	−	0.252008i
$897$		0			0
$898$	4.35281	−	6.82743i	0.145255	−	0.227834i
$899$		−	15.5358i		−	0.518150i
$900$		0			0
$901$		−	15.4737i		−	0.515504i
$902$	2.32444	+	1.48194i	0.0773953	+	0.0493432i
$903$		0			0
$904$	7.79264	−	5.96690i	0.259179	−	0.198456i
$905$	0.114617	+	22.6488i	0.00381001	+	0.752873i
$906$		0			0
$907$	5.88501	+	5.88501i	0.195408	+	0.195408i	0.798028	−	0.602620i	$-0.205876\pi$
$907$	5.88501	+	5.88501i	0.195408	+	0.195408i	−0.602620	+	0.798028i	$0.705876\pi$
$908$	−19.1701	−	6.99209i	−0.636183	−	0.232041i
$909$		0			0
$910$	−8.84780	−	5.57812i	−0.293302	−	0.184913i
$911$		−	10.3886i		−	0.344188i	−0.985080	−	0.172094i	$-0.944947\pi$
$911$		−	10.3886i		−	0.344188i	0.985080	−	0.172094i	$-0.0550534\pi$
$912$		0			0
$913$	1.60613	+	1.60613i	0.0531550	+	0.0531550i
$914$	−6.47106	−	29.2360i	−0.214044	−	0.967042i
$915$		0			0
$916$	18.4573	+	39.6521i	0.609846	+	1.31014i
$917$	−5.34947	+	5.34947i	−0.176655	+	0.176655i
$918$		0			0
$919$		−	14.5186i		−	0.478924i	−0.970906	−	0.239462i	$-0.923029\pi$
$919$		−	14.5186i		−	0.478924i	0.970906	−	0.239462i	$-0.0769710\pi$
$920$	43.9026	−	33.9704i	1.44742	−	1.11997i
$921$		0			0
$922$	19.6290	−	30.7883i	0.646446	−	1.01396i
$923$	47.2321	+	47.2321i	1.55466	+	1.55466i
$924$		0			0
$925$	11.3579	+	11.1302i	0.373444	+	0.365960i
$926$	−40.0585	+	8.86650i	−1.31641	+	0.291371i
$927$		0			0
$928$	−13.0828	+	4.10059i	−0.429464	+	0.134608i
$929$	−44.3689			−1.45570			−0.727848	−	0.685738i	$-0.759480\pi$
$929$	−44.3689			−1.45570			−0.727848	+	0.685738i	$0.759480\pi$
$930$		0			0
$931$			26.7079i			0.875316i
$932$	18.0238	+	6.57397i	0.590388	+	0.215338i
$933$		0			0
$934$	−1.32739	−	5.99709i	−0.0434335	−	0.196231i
$935$	1.91070	+	1.89146i	0.0624867	+	0.0618574i
$936$		0			0
$937$	−2.66665	+	2.66665i	−0.0871157	+	0.0871157i	−0.749322	−	0.662206i	$-0.769620\pi$
$937$	−2.66665	+	2.66665i	−0.0871157	+	0.0871157i	0.662206	+	0.749322i	$0.269620\pi$
$938$	−3.98657	+	6.25297i	−0.130166	+	0.204167i
$939$		0			0
$940$	3.59616	−	10.0167i	0.117294	−	0.326709i
$941$	41.4675			1.35180			0.675901	−	0.736992i	$-0.263755\pi$
$941$	41.4675			1.35180			0.675901	+	0.736992i	$0.263755\pi$
$942$		0			0
$943$	36.0421	+	36.0421i	1.17369	+	1.17369i
$944$	−37.6311	−	31.6634i	−1.22479	−	1.03056i
$945$		0			0
$946$	0.707386	+	3.19595i	0.0229991	+	0.103909i
$947$	34.3858	−	34.3858i	1.11739	−	1.11739i	0.125264	−	0.992123i	$-0.460022\pi$
$947$	34.3858	−	34.3858i	1.11739	−	1.11739i	0.992123	−	0.125264i	$-0.0399779\pi$
$948$		0			0
$949$	35.3933			1.14891
$950$	15.2426	−	24.4507i	0.494537	−	0.793285i
$951$		0			0
$952$	6.70387	+	0.889527i	0.217274	+	0.0288298i
$953$	−5.82947	+	5.82947i	−0.188835	+	0.188835i	−0.795192	−	0.606357i	$-0.792630\pi$
$953$	−5.82947	+	5.82947i	−0.188835	+	0.188835i	0.606357	+	0.795192i	$0.292630\pi$
$954$		0			0
$955$	−0.0489061	−	9.66403i	−0.00158256	−	0.312721i
$956$	−3.91017	−	8.40027i	−0.126464	−	0.271684i
$957$		0			0
$958$	−25.2879	+	39.6643i	−0.817015	+	1.28150i
$959$	−10.2577			−0.331237
$960$		0			0
$961$	10.0886			0.325439
$962$	11.9822	−	18.7942i	0.386322	−	0.605951i
$963$		0			0
$964$	8.20501	+	17.6269i	0.264265	+	0.567725i
$965$	−17.9208	−	17.7404i	−0.576892	−	0.571083i
$966$		0			0
$967$	18.1550	−	18.1550i	0.583826	−	0.583826i	−0.352126	−	0.935952i	$-0.614541\pi$
$967$	18.1550	−	18.1550i	0.583826	−	0.583826i	0.935952	+	0.352126i	$0.114541\pi$
$968$	30.5265	+	4.05052i	0.981158	+	0.130189i
$969$		0			0
$970$	−10.0206	−	44.2113i	−0.321743	−	1.41954i
$971$	−6.87264			−0.220554			−0.110277	−	0.993901i	$-0.535174\pi$
$971$	−6.87264			−0.220554			−0.110277	+	0.993901i	$0.535174\pi$
$972$		0			0
$973$	6.29749	−	6.29749i	0.201888	−	0.201888i
$974$	−0.602173	−	2.72060i	−0.0192949	−	0.0871735i
$975$		0			0
$976$	−22.9486	−	19.3093i	−0.734567	−	0.618077i
$977$	−14.8533	−	14.8533i	−0.475200	−	0.475200i	0.428393	−	0.903593i	$-0.359080\pi$
$977$	−14.8533	−	14.8533i	−0.475200	−	0.475200i	−0.903593	+	0.428393i	$0.859080\pi$
$978$		0			0
$979$	−2.79734			−0.0894033
$980$	26.5117	−	12.5043i	0.846886	−	0.399436i
$981$		0			0
$982$	11.0016	−	17.2562i	0.351076	−	0.550667i
$983$	−21.3770	+	21.3770i	−0.681822	+	0.681822i	−0.960410	−	0.278589i	$-0.910133\pi$
$983$	−21.3770	+	21.3770i	−0.681822	+	0.681822i	0.278589	+	0.960410i	$0.410133\pi$
$984$		0			0
$985$	9.57090	−	9.66827i	0.304954	−	0.308057i
$986$	−2.65343	−	11.9881i	−0.0845026	−	0.381780i
$987$		0			0
$988$	−37.9396	−	13.8381i	−1.20702	−	0.440247i
$989$			60.5240i			1.92455i
$990$		0			0
$991$	27.1515			0.862497			0.431249	−	0.902233i	$-0.358073\pi$
$991$	27.1515			0.862497			0.431249	+	0.902233i	$0.358073\pi$
$992$	−10.8451	−	34.6009i	−0.344332	−	1.09858i
$993$		0			0
$994$	12.4228	−	2.74965i	0.394028	−	0.0872135i
$995$	−0.0341864	−	6.75537i	−0.00108378	−	0.214160i
$996$		0			0
$997$	−16.8850	−	16.8850i	−0.534754	−	0.534754i	0.387230	−	0.921983i	$-0.373432\pi$
$997$	−16.8850	−	16.8850i	−0.534754	−	0.534754i	−0.921983	+	0.387230i	$0.873432\pi$
$998$	−15.5175	+	24.3393i	−0.491198	+	0.770448i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.x.a.53.17	yes	48
3.2	odd	2	inner	360.2.x.a.53.8	yes	48
4.3	odd	2		1440.2.bj.a.593.24		48
5.2	odd	4	inner	360.2.x.a.197.20	yes	48
8.3	odd	2		1440.2.bj.a.593.2		48
8.5	even	2	inner	360.2.x.a.53.5	✓	48
12.11	even	2		1440.2.bj.a.593.1		48
15.2	even	4	inner	360.2.x.a.197.5	yes	48
20.7	even	4		1440.2.bj.a.17.23		48
24.5	odd	2	inner	360.2.x.a.53.20	yes	48
24.11	even	2		1440.2.bj.a.593.23		48
40.27	even	4		1440.2.bj.a.17.1		48
40.37	odd	4	inner	360.2.x.a.197.8	yes	48
60.47	odd	4		1440.2.bj.a.17.2		48
120.77	even	4	inner	360.2.x.a.197.17	yes	48
120.107	odd	4		1440.2.bj.a.17.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.x.a.53.5	✓	48	8.5	even	2	inner
360.2.x.a.53.8	yes	48	3.2	odd	2	inner
360.2.x.a.53.17	yes	48	1.1	even	1	trivial
360.2.x.a.53.20	yes	48	24.5	odd	2	inner
360.2.x.a.197.5	yes	48	15.2	even	4	inner
360.2.x.a.197.8	yes	48	40.37	odd	4	inner
360.2.x.a.197.17	yes	48	120.77	even	4	inner
360.2.x.a.197.20	yes	48	5.2	odd	4	inner
1440.2.bj.a.17.1		48	40.27	even	4
1440.2.bj.a.17.2		48	60.47	odd	4
1440.2.bj.a.17.23		48	20.7	even	4
1440.2.bj.a.17.24		48	120.107	odd	4
1440.2.bj.a.593.1		48	12.11	even	2
1440.2.bj.a.593.2		48	8.3	odd	2
1440.2.bj.a.593.23		48	24.11	even	2
1440.2.bj.a.593.24		48	4.3	odd	2

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.760261 - 1.19248i) q^{2} +(-0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-2.80385 - 0.372039i) q^{8} +O(q^{10})\)	\(q+(0.760261 - 1.19248i) q^{2} +(-0.844006 - 1.81319i) q^{4} +(2.23604 - 0.0113158i) q^{5} +(0.471963 - 0.471963i) q^{7} +(-2.80385 - 0.372039i) q^{8} +(1.68648 - 2.67503i) q^{10} -0.335652 q^{11} +(3.50404 - 3.50404i) q^{13} +(-0.203990 - 0.921620i) q^{14} +(-2.57531 + 3.06068i) q^{16} +(-2.53299 - 2.53299i) q^{17} +4.07474 q^{19} +(-1.90775 - 4.04481i) q^{20} +(-0.255183 + 0.400257i) q^{22} +(-6.20627 + 6.20627i) q^{23} +(4.99974 - 0.0506050i) q^{25} +(-1.51450 - 6.84248i) q^{26} +(-1.25410 - 0.457418i) q^{28} +2.42367i q^{29} -6.41004 q^{31} +(1.69189 + 5.39792i) q^{32} +(-4.94626 + 1.09480i) q^{34} +(1.04999 - 1.06067i) q^{35} +(2.24893 + 2.24893i) q^{37} +(3.09787 - 4.85903i) q^{38} +(-6.27373 - 0.800167i) q^{40} -5.80736i q^{41} +(4.87603 - 4.87603i) q^{43} +(0.283292 + 0.608600i) q^{44} +(2.68245 + 12.1192i) q^{46} +(1.68276 + 1.68276i) q^{47} +6.55450i q^{49} +(3.74077 - 6.00056i) q^{50} +(-9.31092 - 3.39606i) q^{52} +(3.05444 + 3.05444i) q^{53} +(-0.750530 + 0.00379815i) q^{55} +(-1.49890 + 1.14772i) q^{56} +(2.89018 + 1.84263i) q^{58} +12.2950i q^{59} +7.49787i q^{61} +(-4.87331 + 7.64383i) q^{62} +(7.72317 + 2.08629i) q^{64} +(7.79553 - 7.87483i) q^{65} +(-5.55519 - 5.55519i) q^{67} +(-2.45493 + 6.73064i) q^{68} +(-0.466558 - 2.05847i) q^{70} +13.4793i q^{71} +(5.05035 + 5.05035i) q^{73} +(4.39157 - 0.972023i) q^{74} +(-3.43910 - 7.38827i) q^{76} +(-0.158415 + 0.158415i) q^{77} +8.85503i q^{79} +(-5.72386 + 6.87295i) q^{80} +(-6.92515 - 4.41511i) q^{82} +(-4.78510 - 4.78510i) q^{83} +(-5.69252 - 5.63520i) q^{85} +(-2.10750 - 9.52162i) q^{86} +(0.941117 + 0.124876i) q^{88} +8.33405 q^{89} -3.30755i q^{91} +(16.4913 + 6.01502i) q^{92} +(3.28598 - 0.727315i) q^{94} +(9.11128 - 0.0461088i) q^{95} +(10.1367 - 10.1367i) q^{97} +(7.81610 + 4.98313i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q+O(q^{10}) \) 48 * q	\( 48 q + 16 q^{10} - 8 q^{16} + 16 q^{22} - 32 q^{28} + 32 q^{31} - 56 q^{40} - 16 q^{46} - 56 q^{52} - 80 q^{58} - 64 q^{70} + 48 q^{76} - 48 q^{82} + 64 q^{88} - 32 q^{97}+O(q^{100}) \) 48 * q + 16 * q^10 - 8 * q^16 + 16 * q^22 - 32 * q^28 + 32 * q^31 - 56 * q^40 - 16 * q^46 - 56 * q^52 - 80 * q^58 - 64 * q^70 + 48 * q^76 - 48 * q^82 + 64 * q^88 - 32 * q^97

Introduction

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