LMFDB - Embedded newform 585.2.bs.c.289.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [585,2,Mod(289,585)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(585, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("585.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 585 = 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	585.bs (of order $6$, 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:	$4.67124851824$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			289.9
Character	$\chi$	$=$	585.289
Dual form			585.2.bs.c.334.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160403 - 0.0926085i) q^{2} +(-0.982847 + 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(-1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +O(q^{10})$	\(q+(0.160403 - 0.0926085i) q^{2} +(-0.982847 + 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(-1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +(-0.0396663 + 0.412254i) q^{10} +(-1.95887 - 3.39287i) q^{11} +(2.82258 + 2.24344i) q^{13} -0.355576 q^{14} +(-1.89767 - 3.28687i) q^{16} +(-2.88464 - 1.66545i) q^{17} +(0.645658 - 1.11831i) q^{19} +(-1.82304 - 3.99954i) q^{20} +(-0.628417 - 0.362817i) q^{22} +(-5.24134 + 3.02609i) q^{23} +(-1.62851 - 4.72736i) q^{25} +(0.660511 + 0.0984590i) q^{26} +(3.26812 - 1.88685i) q^{28} +(-4.97112 - 8.61024i) q^{29} +4.08666 q^{31} +(-1.88100 - 1.08600i) q^{32} -0.616938 q^{34} +(3.90612 - 1.78045i) q^{35} +(-8.81645 + 5.09018i) q^{37} -0.239174i q^{38} +(-1.33719 - 0.953666i) q^{40} +(-2.79717 - 4.84485i) q^{41} +(7.62743 + 4.40370i) q^{43} +7.70110 q^{44} +(-0.560483 + 0.970786i) q^{46} +9.87842i q^{47} +(-1.65723 - 2.87040i) q^{49} +(-0.699010 - 0.607468i) q^{50} +(-6.59327 + 2.60004i) q^{52} -7.52756i q^{53} +(8.72008 + 0.839030i) q^{55} +(0.705052 - 1.22119i) q^{56} +(-1.59476 - 0.920737i) q^{58} +(-2.77451 + 4.80560i) q^{59} +(-4.38052 + 7.58728i) q^{61} +(0.655511 - 0.378459i) q^{62} +7.18840 q^{64} +(-7.74894 + 2.22573i) q^{65} +(-4.09765 + 2.36578i) q^{67} +(5.67032 - 3.27376i) q^{68} +(0.461666 - 0.647328i) q^{70} +(-5.63164 + 9.75428i) q^{71} -1.67510i q^{73} +(-0.942788 + 1.63296i) q^{74} +(1.26917 + 2.19826i) q^{76} +7.52121i q^{77} +0.965695 q^{79} +(8.44764 + 0.812815i) q^{80} +(-0.897348 - 0.518084i) q^{82} +11.4078i q^{83} +(6.77727 - 3.08916i) q^{85} +1.63128 q^{86} +(2.49211 - 1.43882i) q^{88} +(1.78109 + 3.08493i) q^{89} +(-2.53930 - 6.43926i) q^{91} -11.8967i q^{92} +(0.914825 + 1.58452i) q^{94} +(1.19760 + 2.62740i) q^{95} +(-8.05122 - 4.64838i) q^{97} +(-0.531647 - 0.306946i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 20 q^{4}+O(q^{10}) $ 32 * q + 20 * q^4	$ 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) $ 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.160403	−	0.0926085i	0.113422	−	0.0654841i	−0.442216	−	0.896909i	$-0.645808\pi$
$2$	0.160403	−	0.0926085i	0.113422	−	0.0654841i	0.555638	+	0.831425i	$0.312474\pi$
$3$		0			0
$3$		0			0
$4$	−0.982847	+	1.70234i	−0.491424	+	0.851171i
$5$	−1.29836	+	1.82051i	−0.580646	+	0.814156i
$5$	−1.29836	+	1.82051i	−0.580646	+	0.814156i
$6$		0			0
$7$	−1.66258	−	0.959889i	−0.628395	−	0.362804i	0.151735	−	0.988421i	$-0.451514\pi$
$7$	−1.66258	−	0.959889i	−0.628395	−	0.362804i	−0.780130	+	0.625617i	$0.784847\pi$
$8$			0.734514i			0.259690i
$9$		0			0
$10$	−0.0396663	+	0.412254i	−0.0125436	+	0.130366i
$11$	−1.95887	−	3.39287i	−0.590623	−	1.02299i	−0.994149	−	0.108021i	$-0.965549\pi$
$11$	−1.95887	−	3.39287i	−0.590623	−	1.02299i	0.403526	−	0.914968i	$-0.367785\pi$
$12$		0			0
$13$	2.82258	+	2.24344i	0.782843	+	0.622219i
$13$	2.82258	+	2.24344i	0.782843	+	0.622219i
$14$	−0.355576			−0.0950316
$15$		0			0
$16$	−1.89767	−	3.28687i	−0.474418	−	0.821716i
$17$	−2.88464	−	1.66545i	−0.699628	−	0.403930i	0.107581	−	0.994196i	$-0.465690\pi$
$17$	−2.88464	−	1.66545i	−0.699628	−	0.403930i	−0.807209	+	0.590266i	$0.799023\pi$
$18$		0			0
$19$	0.645658	−	1.11831i	0.148124	−	0.256559i	−0.782410	−	0.622764i	$-0.786010\pi$
$19$	0.645658	−	1.11831i	0.148124	−	0.256559i	0.930534	+	0.366205i	$0.119343\pi$
$20$	−1.82304	−	3.99954i	−0.407643	−	0.894324i
$21$		0			0
$22$	−0.628417	−	0.362817i	−0.133979	−	0.0773528i
$23$	−5.24134	+	3.02609i	−1.09290	+	0.630984i	−0.934346	−	0.356367i	$-0.884015\pi$
$23$	−5.24134	+	3.02609i	−1.09290	+	0.630984i	−0.158550	+	0.987351i	$0.550682\pi$
$24$		0			0
$25$	−1.62851	−	4.72736i	−0.325701	−	0.945473i
$26$	0.660511	+	0.0984590i	0.129537	+	0.0193094i
$27$		0			0
$28$	3.26812	−	1.88685i	0.617616	−	0.356581i
$29$	−4.97112	−	8.61024i	−0.923115	−	1.59888i	−0.794566	−	0.607178i	$-0.792301\pi$
$29$	−4.97112	−	8.61024i	−0.923115	−	1.59888i	−0.128549	−	0.991703i	$-0.541032\pi$
$30$		0			0
$31$	4.08666			0.733986			0.366993	−	0.930224i	$-0.380387\pi$
$31$	4.08666			0.733986			0.366993	+	0.930224i	$0.380387\pi$
$32$	−1.88100	−	1.08600i	−0.332517	−	0.191979i
$33$		0			0
$34$	−0.616938			−0.105804
$35$	3.90612	−	1.78045i	0.660254	−	0.300951i
$36$		0			0
$37$	−8.81645	+	5.09018i	−1.44942	+	0.836821i	−0.998446	−	0.0557190i	$-0.982255\pi$
$37$	−8.81645	+	5.09018i	−1.44942	+	0.836821i	−0.450969	+	0.892540i	$0.648922\pi$
$38$		−	0.239174i		−	0.0387991i
$39$		0			0
$40$	−1.33719	−	0.953666i	−0.211428	−	0.150788i
$41$	−2.79717	−	4.84485i	−0.436845	−	0.756638i	0.560599	−	0.828087i	$-0.310571\pi$
$41$	−2.79717	−	4.84485i	−0.436845	−	0.756638i	−0.997444	+	0.0714494i	$0.977238\pi$
$42$		0			0
$43$	7.62743	+	4.40370i	1.16317	+	0.671558i	0.952062	−	0.305904i	$-0.0989588\pi$
$43$	7.62743	+	4.40370i	1.16317	+	0.671558i	0.211110	+	0.977462i	$0.432292\pi$
$44$	7.70110			1.16098
$45$		0			0
$46$	−0.560483	+	0.970786i	−0.0826388	+	0.143135i
$47$			9.87842i			1.44092i	0.693499	+	0.720458i	$0.256068\pi$
$47$			9.87842i			1.44092i	−0.693499	+	0.720458i	$0.743932\pi$
$48$		0			0
$49$	−1.65723	−	2.87040i	−0.236747	−	0.410057i
$50$	−0.699010	−	0.607468i	−0.0988550	−	0.0859089i
$51$		0			0
$52$	−6.59327	+	2.60004i	−0.914322	+	0.360560i
$53$		−	7.52756i		−	1.03399i	−0.855988	−	0.516995i	$-0.827051\pi$
$53$		−	7.52756i		−	1.03399i	0.855988	−	0.516995i	$-0.172949\pi$
$54$		0			0
$55$	8.72008	+	0.839030i	1.17582	+	0.113135i
$56$	0.705052	−	1.22119i	0.0942165	−	0.163188i
$57$		0			0
$58$	−1.59476	−	0.920737i	−0.209403	−	0.120899i
$59$	−2.77451	+	4.80560i	−0.361211	+	0.625636i	−0.988160	−	0.153424i	$-0.950970\pi$
$59$	−2.77451	+	4.80560i	−0.361211	+	0.625636i	0.626949	+	0.779060i	$0.284303\pi$
$60$		0			0
$61$	−4.38052	+	7.58728i	−0.560868	+	0.971452i	0.436553	+	0.899679i	$0.356199\pi$
$61$	−4.38052	+	7.58728i	−0.560868	+	0.971452i	−0.997421	+	0.0717734i	$0.977134\pi$
$62$	0.655511	−	0.378459i	0.0832500	−	0.0480644i
$63$		0			0
$64$	7.18840			0.898550
$65$	−7.74894	+	2.22573i	−0.961138	+	0.276068i
$66$		0			0
$67$	−4.09765	+	2.36578i	−0.500608	+	0.289026i	−0.728965	−	0.684551i	$-0.759998\pi$
$67$	−4.09765	+	2.36578i	−0.500608	+	0.289026i	0.228357	+	0.973578i	$0.426665\pi$
$68$	5.67032	−	3.27376i	0.687627	−	0.397002i
$69$		0			0
$70$	0.461666	−	0.647328i	0.0551797	−	0.0773705i
$71$	−5.63164	+	9.75428i	−0.668352	+	1.15762i	0.310013	+	0.950732i	$0.399667\pi$
$71$	−5.63164	+	9.75428i	−0.668352	+	1.15762i	−0.978365	+	0.206888i	$0.933667\pi$
$72$		0			0
$73$		−	1.67510i		−	0.196056i	−0.995184	−	0.0980280i	$-0.968747\pi$
$73$		−	1.67510i		−	0.196056i	0.995184	−	0.0980280i	$-0.0312535\pi$
$74$	−0.942788	+	1.63296i	−0.109597	+	0.189827i
$75$		0			0
$76$	1.26917	+	2.19826i	0.145583	+	0.252158i
$77$			7.52121i			0.857121i
$78$		0			0
$79$	0.965695			0.108649			0.0543246	−	0.998523i	$-0.482699\pi$
$79$	0.965695			0.108649			0.0543246	+	0.998523i	$0.482699\pi$
$80$	8.44764	+	0.812815i	0.944474	+	0.0908755i
$81$		0			0
$82$	−0.897348	−	0.518084i	−0.0990955	−	0.0572128i
$83$			11.4078i			1.25216i	0.779757	+	0.626082i	$0.215342\pi$
$83$			11.4078i			1.25216i	−0.779757	+	0.626082i	$0.784658\pi$
$84$		0			0
$85$	6.77727	−	3.08916i	0.735098	−	0.335066i
$86$	1.63128			0.175905
$87$		0			0
$88$	2.49211	−	1.43882i	0.265660	−	0.153379i
$89$	1.78109	+	3.08493i	0.188795	+	0.327002i	0.944849	−	0.327507i	$-0.106209\pi$
$89$	1.78109	+	3.08493i	0.188795	+	0.327002i	−0.756054	+	0.654509i	$0.772875\pi$
$90$		0			0
$91$	−2.53930	−	6.43926i	−0.266191	−	0.675018i
$92$		−	11.8967i		−	1.24032i
$93$		0			0
$94$	0.914825	+	1.58452i	0.0943570	+	0.163431i
$95$	1.19760	+	2.62740i	0.122871	+	0.269566i
$96$		0			0
$97$	−8.05122	−	4.64838i	−0.817478	−	0.471971i	0.0320681	−	0.999486i	$-0.489791\pi$
$97$	−8.05122	−	4.64838i	−0.817478	−	0.471971i	−0.849546	+	0.527515i	$0.823124\pi$
$98$	−0.531647	−	0.306946i	−0.0537044	−	0.0310063i
$99$		0			0
$100$	9.64816	+	1.87400i	0.964816	+	0.187400i
$101$	3.19004	+	5.52531i	0.317421	+	0.549789i	0.979949	−	0.199248i	$-0.0638500\pi$
$101$	3.19004	+	5.52531i	0.317421	+	0.549789i	−0.662528	+	0.749037i	$0.730517\pi$
$102$		0			0
$103$		−	4.96784i		−	0.489496i	−0.969587	−	0.244748i	$-0.921295\pi$
$103$		−	4.96784i		−	0.489496i	0.969587	−	0.244748i	$-0.0787052\pi$
$104$	−1.64784	+	2.07323i	−0.161584	+	0.203296i
$105$		0			0
$106$	−0.697116	−	1.20744i	−0.0677099	−	0.117277i
$107$	16.1336	−	9.31474i	1.55969	−	0.900490i	0.562409	−	0.826859i	$-0.309875\pi$
$107$	16.1336	−	9.31474i	1.55969	−	0.900490i	0.997286	−	0.0736305i	$-0.0234585\pi$
$108$		0			0
$109$	−10.6581			−1.02086			−0.510432	−	0.859918i	$-0.670514\pi$
$109$	−10.6581			−1.02086			−0.510432	+	0.859918i	$0.670514\pi$
$110$	1.47642	−	0.672971i	0.140772	−	0.0641653i
$111$		0			0
$112$			7.28622i			0.688483i
$113$	2.83241	+	1.63529i	0.266451	+	0.153835i	0.627274	−	0.778799i	$-0.284171\pi$
$113$	2.83241	+	1.63529i	0.266451	+	0.153835i	−0.360823	+	0.932634i	$0.617504\pi$
$114$		0			0
$115$	1.29614	−	13.4709i	0.120866	−	1.25617i
$116$	19.5434			1.81456
$117$		0			0
$118$			1.02777i			0.0946143i
$119$	3.19729	+	5.53787i	0.293095	+	0.507656i
$120$		0			0
$121$	−2.17438	+	3.76613i	−0.197671	+	0.342376i
$122$			1.62269i			0.146912i
$123$		0			0
$124$	−4.01656	+	6.95689i	−0.360698	+	0.624747i
$125$	10.7206	+	3.17313i	0.958880	+	0.283813i
$126$		0			0
$127$	−14.2207	+	8.21033i	−1.26188	+	0.728549i	−0.973439	−	0.228948i	$-0.926471\pi$
$127$	−14.2207	+	8.21033i	−1.26188	+	0.728549i	−0.288445	+	0.957497i	$0.593138\pi$
$128$	4.91504	−	2.83770i	0.434432	−	0.250819i
$129$		0			0
$130$	−1.03683	+	1.07463i	−0.0909359	+	0.0942514i
$131$	−15.1810			−1.32637			−0.663186	−	0.748455i	$-0.730796\pi$
$131$	−15.1810			−1.32637			−0.663186	+	0.748455i	$0.730796\pi$
$132$		0			0
$133$	−2.14691	+	1.23952i	−0.186161	+	0.107480i
$134$	−0.438183	+	0.758955i	−0.0378532	+	0.0655637i
$135$		0			0
$136$	1.22329	−	2.11881i	0.104897	−	0.181686i
$137$	−9.30474	−	5.37210i	−0.794958	−	0.458969i	0.0467472	−	0.998907i	$-0.485114\pi$
$137$	−9.30474	−	5.37210i	−0.794958	−	0.458969i	−0.841705	+	0.539938i	$0.818448\pi$
$138$		0			0
$139$	6.65468	−	11.5263i	0.564443	−	0.977644i	−0.432658	−	0.901558i	$-0.642424\pi$
$139$	6.65468	−	11.5263i	0.564443	−	0.977644i	0.997101	−	0.0760858i	$-0.0242423\pi$
$140$	−0.808179	+	8.39945i	−0.0683036	+	0.709883i
$141$		0			0
$142$			2.08615i			0.175066i
$143$	2.08263	−	13.9713i	0.174158	−	1.16834i
$144$		0			0
$145$	22.1293	+	2.12924i	1.83774	+	0.176824i
$146$	−0.155129	−	0.268691i	−0.0128385	−	0.0222370i
$147$		0			0
$148$		−	20.0115i		−	1.64493i
$149$	0.660511	−	1.14404i	0.0541112	−	0.0937233i	−0.837701	−	0.546129i	$-0.816101\pi$
$149$	0.660511	−	1.14404i	0.0541112	−	0.0937233i	0.891812	+	0.452406i	$0.149434\pi$
$150$		0			0
$151$	5.51911			0.449138			0.224569	−	0.974458i	$-0.427903\pi$
$151$	5.51911			0.449138			0.224569	+	0.974458i	$0.427903\pi$
$152$	0.821416	+	0.474245i	0.0666257	+	0.0384663i
$153$		0			0
$154$	0.696528	+	1.20642i	0.0561278	+	0.0972162i
$155$	−5.30597	+	7.43980i	−0.426186	+	0.597579i
$156$		0			0
$157$		−	0.0783052i		−	0.00624943i	−0.999995	−	0.00312472i	$-0.999005\pi$
$157$		−	0.0783052i		−	0.00624943i	0.999995	−	0.00312472i	$-0.000994630\pi$
$158$	0.154900	−	0.0894315i	0.0123232	−	0.00711479i
$159$		0			0
$160$	4.41928	−	2.01436i	0.349375	−	0.159249i
$161$	11.6188			0.915693
$162$		0			0
$163$	−2.49562	−	1.44085i	−0.195472	−	0.112856i	0.399070	−	0.916921i	$-0.369333\pi$
$163$	−2.49562	−	1.44085i	−0.195472	−	0.112856i	−0.594542	+	0.804065i	$0.702666\pi$
$164$	10.9968			0.858704
$165$		0			0
$166$	1.05645	+	1.82983i	0.0819968	+	0.142023i
$167$	8.22025	−	4.74597i	0.636102	−	0.367254i	−0.147009	−	0.989135i	$-0.546965\pi$
$167$	8.22025	−	4.74597i	0.636102	−	0.367254i	0.783112	+	0.621881i	$0.213631\pi$
$168$		0			0
$169$	2.93393	+	12.6646i	0.225687	+	0.974200i
$170$	0.801010	−	1.12314i	0.0614347	−	0.0861410i
$171$		0			0
$172$	−14.9932	+	8.65633i	−1.14322	+	0.660039i
$173$	10.2617	+	5.92457i	0.780179	+	0.450437i	0.836494	−	0.547976i	$-0.184602\pi$
$173$	10.2617	+	5.92457i	0.780179	+	0.450437i	−0.0563146	+	0.998413i	$0.517935\pi$
$174$		0			0
$175$	−1.83023	+	9.42279i	−0.138352	+	0.712296i
$176$	−7.43460	+	12.8771i	−0.560404	+	0.970649i
$177$		0			0
$178$	0.571382	+	0.329887i	0.0428269	+	0.0247261i
$179$	4.37781	+	7.58260i	0.327213	+	0.566750i	0.981958	−	0.189100i	$-0.0605572\pi$
$179$	4.37781	+	7.58260i	0.327213	+	0.566750i	−0.654745	+	0.755850i	$0.727224\pi$
$180$		0			0
$181$	−7.01805			−0.521648			−0.260824	−	0.965386i	$-0.583994\pi$
$181$	−7.01805			−0.521648			−0.260824	+	0.965386i	$0.583994\pi$
$182$	−1.00364	−	0.797713i	−0.0743948	−	0.0591304i
$183$		0			0
$184$	−2.22271	−	3.84984i	−0.163860	−	0.283814i
$185$	2.18024	−	22.6593i	0.160294	−	1.66595i
$186$		0			0
$187$			13.0496i			0.954282i
$188$	−16.8164	−	9.70898i	−1.22646	−	0.708100i
$189$		0			0
$190$	0.435418	+	0.310534i	0.0315885	+	0.0225285i
$191$	−6.05441	+	10.4865i	−0.438082	+	0.758780i	−0.997542	−	0.0700776i	$-0.977675\pi$
$191$	−6.05441	+	10.4865i	−0.438082	+	0.758780i	0.559460	+	0.828858i	$0.311009\pi$
$192$		0			0
$193$	−2.07910	+	1.20037i	−0.149657	+	0.0864044i	−0.572958	−	0.819584i	$-0.694204\pi$
$193$	−2.07910	+	1.20037i	−0.149657	+	0.0864044i	0.423302	+	0.905989i	$0.360871\pi$
$194$	−1.72192			−0.123626
$195$		0			0
$196$	6.51520			0.465371
$197$	−7.37151	+	4.25594i	−0.525199	+	0.303224i	−0.739059	−	0.673641i	$-0.764730\pi$
$197$	−7.37151	+	4.25594i	−0.525199	+	0.303224i	0.213860	+	0.976864i	$0.431396\pi$
$198$		0			0
$199$	−0.802884	+	1.39064i	−0.0569149	+	0.0985795i	−0.893079	−	0.449900i	$-0.851460\pi$
$199$	−0.802884	+	1.39064i	−0.0569149	+	0.0985795i	0.836164	+	0.548479i	$0.184793\pi$
$200$	3.47231	−	1.19616i	0.245530	−	0.0845813i
$201$		0			0
$202$	1.02338	+	0.590849i	0.0720048	+	0.0415720i
$203$			19.0869i			1.33964i
$204$		0			0
$205$	12.4518	+	1.19809i	0.869674	+	0.0836783i
$206$	−0.460064	−	0.796855i	−0.0320542	−	0.0555195i
$207$		0			0
$208$	2.01756	−	13.5348i	0.139892	−	0.938467i
$209$	−5.05905			−0.349942
$210$		0			0
$211$	−1.54587	−	2.67753i	−0.106422	−	0.184329i	0.807896	−	0.589325i	$-0.200606\pi$
$211$	−1.54587	−	2.67753i	−0.106422	−	0.184329i	−0.914318	+	0.404996i	$0.867273\pi$
$212$	12.8145	+	7.39845i	0.880102	+	0.508127i
$213$		0			0
$214$	1.72525	−	2.98822i	0.117936	−	0.204270i
$215$	−17.9202	+	8.16821i	−1.22214	+	0.557067i
$216$		0			0
$217$	−6.79439	−	3.92274i	−0.461233	−	0.266293i
$218$	−1.70959	+	0.987033i	−0.115788	+	0.0668503i
$219$		0			0
$220$	−9.99882	+	14.0199i	−0.674121	+	0.945223i
$221$	−4.40579	−	11.1724i	−0.296366	−	0.751536i
$222$		0			0
$223$	−16.3071	+	9.41489i	−1.09200	+	0.630468i	−0.934109	−	0.356988i	$-0.883804\pi$
$223$	−16.3071	+	9.41489i	−1.09200	+	0.630468i	−0.157893	+	0.987456i	$0.550470\pi$
$224$	2.08487	+	3.61110i	0.139301	+	0.241277i
$225$		0			0
$226$	0.605768			0.0402951
$227$	−0.976316	−	0.563676i	−0.0648004	−	0.0374125i	0.467250	−	0.884125i	$-0.345245\pi$
$227$	−0.976316	−	0.563676i	−0.0648004	−	0.0374125i	−0.532050	+	0.846713i	$0.678578\pi$
$228$		0			0
$229$	−0.238960			−0.0157909			−0.00789547	−	0.999969i	$-0.502513\pi$
$229$	−0.238960			−0.0157909			−0.00789547	+	0.999969i	$0.502513\pi$
$230$	−1.03961	−	2.28080i	−0.0685500	−	0.150391i
$231$		0			0
$232$	6.32434	−	3.65136i	0.415213	−	0.239724i
$233$			6.95586i			0.455694i	0.973697	+	0.227847i	$0.0731685\pi$
$233$			6.95586i			0.455694i	−0.973697	+	0.227847i	$0.926831\pi$
$234$		0			0
$235$	−17.9837	−	12.8258i	−1.17313	−	0.836661i
$236$	−5.45385	−	9.44634i	−0.355015	−	0.614904i
$237$		0			0
$238$	1.02571	+	0.592192i	0.0664867	+	0.0383861i
$239$	−18.6088			−1.20370			−0.601851	−	0.798608i	$-0.705570\pi$
$239$	−18.6088			−1.20370			−0.601851	+	0.798608i	$0.705570\pi$
$240$		0			0
$241$	13.4404	−	23.2795i	0.865773	−	1.49956i	−0.000504148	−	1.00000i	$-0.500160\pi$
$241$	13.4404	−	23.2795i	0.865773	−	1.49956i	0.866277	−	0.499563i	$-0.166506\pi$
$242$			0.805463i			0.0517772i
$243$		0			0
$244$	−8.61076	−	14.9143i	−0.551248	−	0.954789i
$245$	7.37727	+	0.709827i	0.471316	+	0.0453492i
$246$		0			0
$247$	4.33129	−	1.70803i	0.275594	−	0.108679i
$248$			3.00171i			0.190609i
$249$		0			0
$250$	2.01347	−	0.483841i	0.127343	−	0.0306008i
$251$	12.2567	−	21.2292i	0.773636	−	1.33998i	−0.161922	−	0.986804i	$-0.551769\pi$
$251$	12.2567	−	21.2292i	0.773636	−	1.33998i	0.935558	−	0.353173i	$-0.114897\pi$
$252$		0			0
$253$	20.5343	+	11.8555i	1.29098	+	0.745347i
$254$	−1.52069	+	2.63392i	−0.0954167	+	0.165267i
$255$		0			0
$256$	−6.66281	+	11.5403i	−0.416426	+	0.721270i
$257$	−23.6041	+	13.6278i	−1.47238	+	0.850080i	−0.999518	−	0.0310554i	$-0.990113\pi$
$257$	−23.6041	+	13.6278i	−1.47238	+	0.850080i	−0.472864	+	0.881135i	$0.656780\pi$
$258$		0			0
$259$	19.5440			1.21441
$260$	3.82707	−	15.3789i	0.237345	−	0.953759i
$261$		0			0
$262$	−2.43508	+	1.40589i	−0.150439	+	0.0868562i
$263$	17.1987	−	9.92967i	1.06052	−	0.612290i	0.134941	−	0.990854i	$-0.456915\pi$
$263$	17.1987	−	9.92967i	1.06052	−	0.612290i	0.925575	+	0.378564i	$0.123582\pi$
$264$		0			0
$265$	13.7040	+	9.77351i	0.841830	+	0.600382i
$266$	−0.229580	+	0.397645i	−0.0140765	+	0.0243812i
$267$		0			0
$268$		−	9.30080i		−	0.568137i
$269$	12.1461	−	21.0377i	0.740561	−	1.28269i	−0.211678	−	0.977339i	$-0.567893\pi$
$269$	12.1461	−	21.0377i	0.740561	−	1.28269i	0.952240	−	0.305351i	$-0.0987737\pi$
$270$		0			0
$271$	4.45413	+	7.71477i	0.270569	+	0.468639i	0.969008	−	0.247031i	$-0.0794549\pi$
$271$	4.45413	+	7.71477i	0.270569	+	0.468639i	−0.698439	+	0.715670i	$0.746122\pi$
$272$			12.6419i			0.766527i
$273$		0			0
$274$	−1.99001			−0.120221
$275$	−12.8493	+	14.7856i	−0.774842	+	0.891606i
$276$		0			0
$277$	−16.5880	−	9.57707i	−0.996674	−	0.575430i	−0.0894116	−	0.995995i	$-0.528499\pi$
$277$	−16.5880	−	9.57707i	−0.996674	−	0.575430i	−0.907263	+	0.420565i	$0.861832\pi$
$278$		−	2.46512i		−	0.147848i
$279$		0			0
$280$	1.30777	+	2.86910i	0.0781540	+	0.171461i
$281$	14.4246			0.860497			0.430248	−	0.902711i	$-0.358426\pi$
$281$	14.4246			0.860497			0.430248	+	0.902711i	$0.358426\pi$
$282$		0			0
$283$	10.0625	−	5.80959i	0.598154	−	0.345344i	−0.170161	−	0.985416i	$-0.554429\pi$
$283$	10.0625	−	5.80959i	0.598154	−	0.345344i	0.768315	+	0.640072i	$0.221095\pi$
$284$	−11.0701	−	19.1739i	−0.656888	−	1.13776i
$285$		0			0
$286$	−0.959800	−	2.43390i	−0.0567542	−	0.143919i
$287$			10.7399i			0.633957i
$288$		0			0
$289$	−2.95257	−	5.11400i	−0.173681	−	0.300824i
$290$	3.74679	−	1.70783i	0.220019	−	0.100287i
$291$		0			0
$292$	2.85160	+	1.64637i	0.166877	+	0.0963465i
$293$	−26.8933	−	15.5268i	−1.57112	−	0.907087i	−0.996032	−	0.0889965i	$-0.971634\pi$
$293$	−26.8933	−	15.5268i	−1.57112	−	0.907087i	−0.575089	−	0.818091i	$-0.695033\pi$
$294$		0			0
$295$	−5.14631	−	11.2904i	−0.299630	−	0.657355i
$296$	−3.73881	−	6.47581i	−0.217314	−	0.376399i
$297$		0			0
$298$		−	0.244676i		−	0.0141737i
$299$	−21.5830	−	3.21726i	−1.24818	−	0.186059i
$300$		0			0
$301$	−8.45413	−	14.6430i	−0.487288	−	0.844007i
$302$	0.885279	−	0.511116i	0.0509421	−	0.0294114i
$303$		0			0
$304$	−4.90099			−0.281091
$305$	−8.12521	−	17.8258i	−0.465248	−	1.02070i
$306$		0			0
$307$		−	9.37642i		−	0.535141i	−0.963538	−	0.267570i	$-0.913779\pi$
$307$		−	9.37642i		−	0.535141i	0.963538	−	0.267570i	$-0.0862208\pi$
$308$	−12.8037	−	7.39220i	−0.729557	−	0.421210i
$309$		0			0
$310$	−0.162103	+	1.68474i	−0.00920681	+	0.0956869i
$311$	−0.920129			−0.0521757			−0.0260879	−	0.999660i	$-0.508305\pi$
$311$	−0.920129			−0.0521757			−0.0260879	+	0.999660i	$0.508305\pi$
$312$		0			0
$313$			26.6753i			1.50778i	0.657003	+	0.753888i	$0.271824\pi$
$313$			26.6753i			1.50778i	−0.657003	+	0.753888i	$0.728176\pi$
$314$	−0.00725172	−	0.0125604i	−0.000409238	−	0.000708822i
$315$		0			0
$316$	−0.949130	+	1.64394i	−0.0533928	+	0.0924790i
$317$		−	6.83096i		−	0.383665i	−0.981428	−	0.191832i	$-0.938557\pi$
$317$		−	6.83096i		−	0.383665i	0.981428	−	0.191832i	$-0.0614430\pi$
$318$		0			0
$319$	−19.4756	+	33.7328i	−1.09043	+	1.88867i
$320$	−9.33316	+	13.0865i	−0.521739	+	0.731560i
$321$		0			0
$322$	1.86369	−	1.07600i	0.103860	−	0.0599633i
$323$	−3.72498	+	2.15062i	−0.207264	+	0.119664i
$324$		0			0
$325$	6.00898	−	16.9968i	0.333318	−	0.942814i
$326$	−0.533739			−0.0295610
$327$		0			0
$328$	3.55861	−	2.05456i	0.196491	−	0.113444i
$329$	9.48218	−	16.4236i	0.522770	−	0.905464i
$330$		0			0
$331$	−9.29476	+	16.0990i	−0.510886	+	0.884881i	0.489034	+	0.872265i	$0.337349\pi$
$331$	−9.29476	+	16.0990i	−0.510886	+	0.884881i	−0.999920	+	0.0126160i	$0.995984\pi$
$332$	−19.4199	−	11.2121i	−1.06581	−	0.615343i
$333$		0			0
$334$	0.879033	−	1.52253i	0.0480986	−	0.0833092i
$335$	1.01332	−	10.5315i	0.0553634	−	0.575395i
$336$		0			0
$337$			6.87517i			0.374515i	0.982311	+	0.187257i	$0.0599598\pi$
$337$			6.87517i			0.374515i	−0.982311	+	0.187257i	$0.940040\pi$
$338$	1.64346	+	1.75973i	0.0893924	+	0.0957166i
$339$		0			0
$340$	−1.40222	+	14.5734i	−0.0760463	+	0.790354i
$341$	−8.00526	−	13.8655i	−0.433509	−	0.750860i
$342$		0			0
$343$			19.8015i			1.06918i
$344$	−3.23458	+	5.60245i	−0.174397	+	0.302064i
$345$		0			0
$346$	2.19466			0.117986
$347$	−10.4073	−	6.00868i	−0.558695	−	0.322563i	0.193926	−	0.981016i	$-0.437878\pi$
$347$	−10.4073	−	6.00868i	−0.558695	−	0.322563i	−0.752622	+	0.658453i	$0.771211\pi$
$348$		0			0
$349$	5.24389	+	9.08268i	0.280699	+	0.486185i	0.971557	−	0.236806i	$-0.0761005\pi$
$349$	5.24389	+	9.08268i	0.280699	+	0.486185i	−0.690858	+	0.722990i	$0.742767\pi$
$350$	0.579057	+	1.68093i	0.0309519	+	0.0898497i
$351$		0			0
$352$			8.50931i			0.453548i
$353$	−27.5593	+	15.9114i	−1.46683	+	0.846877i	−0.999311	−	0.0371046i	$-0.988187\pi$
$353$	−27.5593	+	15.9114i	−1.46683	+	0.846877i	−0.467522	+	0.883981i	$0.654853\pi$
$354$		0			0
$355$	−10.4458	−	22.9170i	−0.554408	−	1.21631i
$356$	−7.00215			−0.371113
$357$		0			0
$358$	1.40443	+	0.810845i	0.0742262	+	0.0428545i
$359$	15.8015			0.833973			0.416987	−	0.908913i	$-0.363086\pi$
$359$	15.8015			0.833973			0.416987	+	0.908913i	$0.363086\pi$
$360$		0			0
$361$	8.66625	+	15.0104i	0.456118	+	0.790020i
$362$	−1.12571	+	0.649931i	−0.0591662	+	0.0341596i
$363$		0			0
$364$	13.4576	+	2.00605i	0.705368	+	0.105146i
$365$	3.04954	+	2.17489i	0.159620	+	0.113839i
$366$		0			0
$367$	22.4730	−	12.9748i	1.17308	−	0.677280i	0.218679	−	0.975797i	$-0.429825\pi$
$367$	22.4730	−	12.9748i	1.17308	−	0.677280i	0.954404	+	0.298517i	$0.0964919\pi$
$368$	19.8927	+	11.4851i	1.03698	+	0.598700i
$369$		0			0
$370$	−1.74873	−	3.83652i	−0.0909122	−	0.199451i
$371$	−7.22563	+	12.5152i	−0.375136	+	0.649754i
$372$		0			0
$373$	−11.7359	−	6.77570i	−0.607660	−	0.350833i	0.164389	−	0.986396i	$-0.447435\pi$
$373$	−11.7359	−	6.77570i	−0.607660	−	0.350833i	−0.772049	+	0.635563i	$0.780768\pi$
$374$	1.20850	+	2.09319i	0.0624903	+	0.108236i
$375$		0			0
$376$	−7.25583			−0.374191
$377$	5.28518	−	35.4555i	0.272200	−	1.82605i
$378$		0			0
$379$	−2.73986	−	4.74557i	−0.140737	−	0.243764i	0.787037	−	0.616905i	$-0.211614\pi$
$379$	−2.73986	−	4.74557i	−0.140737	−	0.243764i	−0.927774	+	0.373142i	$0.878281\pi$
$380$	−5.64979	−	0.543612i	−0.289828	−	0.0278867i
$381$		0			0
$382$			2.24276i			0.114750i
$383$	17.3693	+	10.0282i	0.887529	+	0.512415i	0.873133	−	0.487481i	$-0.162084\pi$
$383$	17.3693	+	10.0282i	0.887529	+	0.512415i	0.0143954	+	0.999896i	$0.495418\pi$
$384$		0			0
$385$	−13.6924	−	9.76526i	−0.697831	−	0.497684i
$386$	−0.222329	+	0.385084i	−0.0113162	+	0.0196003i
$387$		0			0
$388$	15.8262	−	9.13729i	0.803456	−	0.463875i
$389$	22.8966			1.16090			0.580452	−	0.814294i	$-0.302876\pi$
$389$	22.8966			1.16090			0.580452	+	0.814294i	$0.302876\pi$
$390$		0			0
$391$	20.1592			1.01949
$392$	2.10835	−	1.21726i	0.106488	−	0.0614807i
$393$		0			0
$394$	−0.788273	+	1.36533i	−0.0397126	+	0.0687843i
$395$	−1.25382	+	1.75806i	−0.0630867	+	0.0884574i
$396$		0			0
$397$	−15.6036	−	9.00873i	−0.783121	−	0.452135i	0.0544144	−	0.998518i	$-0.482671\pi$
$397$	−15.6036	−	9.00873i	−0.783121	−	0.452135i	−0.837535	+	0.546383i	$0.816004\pi$
$398$			0.297415i			0.0149081i
$399$		0			0
$400$	−12.4478	+	14.3237i	−0.622392	+	0.716183i
$401$	−1.65394	−	2.86471i	−0.0825938	−	0.143057i	0.821770	−	0.569820i	$-0.192987\pi$
$401$	−1.65394	−	2.86471i	−0.0825938	−	0.143057i	−0.904363	+	0.426763i	$0.859654\pi$
$402$		0			0
$403$	11.5349	+	9.16819i	0.574596	+	0.456700i
$404$	−12.5413			−0.623952
$405$		0			0
$406$	1.76761	+	3.06159i	0.0877250	+	0.151944i
$407$	34.5406	+	19.9420i	1.71212	+	0.988491i
$408$		0			0
$409$	10.7585	−	18.6343i	0.531973	−	0.921405i	−0.467330	−	0.884083i	$-0.654784\pi$
$409$	10.7585	−	18.6343i	0.531973	−	0.921405i	0.999303	−	0.0373220i	$-0.0118827\pi$
$410$	2.10826	−	0.960968i	0.104120	−	0.0474588i
$411$		0			0
$412$	8.45697	+	4.88263i	0.416645	+	0.240550i
$413$	9.22569	−	5.32645i	0.453966	−	0.262098i
$414$		0			0
$415$	−20.7679	−	14.8114i	−1.01946	−	0.727064i
$416$	−2.87290	−	7.28522i	−0.140856	−	0.357187i
$417$		0			0
$418$	−0.811485	+	0.468511i	−0.0396910	+	0.0229156i
$419$	−9.85964	−	17.0774i	−0.481675	−	0.834286i	0.518104	−	0.855318i	$-0.326638\pi$
$419$	−9.85964	−	17.0774i	−0.481675	−	0.834286i	−0.999779	+	0.0210321i	$0.993305\pi$
$420$		0			0
$421$	−23.2308			−1.13220			−0.566099	−	0.824337i	$-0.691548\pi$
$421$	−23.2308			−1.13220			−0.566099	+	0.824337i	$0.691548\pi$
$422$	−0.495924	−	0.286322i	−0.0241412	−	0.0139379i
$423$		0			0
$424$	5.52910			0.268517
$425$	−3.17552	+	16.3489i	−0.154036	+	0.793040i
$426$		0			0
$427$	14.5659	−	8.40963i	0.704893	−	0.406970i
$428$			36.6199i			1.77009i
$429$		0			0
$430$	−2.11799	+	2.96976i	−0.102139	+	0.143215i
$431$	18.4156	+	31.8968i	0.887048	+	1.53641i	0.843348	+	0.537368i	$0.180581\pi$
$431$	18.4156	+	31.8968i	0.887048	+	1.53641i	0.0437002	+	0.999045i	$0.486085\pi$
$432$		0			0
$433$	5.69241	+	3.28652i	0.273560	+	0.157940i	0.630504	−	0.776186i	$-0.282848\pi$
$433$	5.69241	+	3.28652i	0.273560	+	0.157940i	−0.356944	+	0.934126i	$0.616181\pi$
$434$	−1.45312			−0.0697518
$435$		0			0
$436$	10.4753	−	18.1438i	0.501676	−	0.868929i
$437$			7.81528i			0.373856i
$438$		0			0
$439$	−13.3758	−	23.1676i	−0.638394	−	1.10573i	−0.985785	−	0.168010i	$-0.946266\pi$
$439$	−13.3758	−	23.1676i	−0.638394	−	1.10573i	0.347392	−	0.937720i	$-0.387067\pi$
$440$	−0.616279	+	6.40502i	−0.0293799	+	0.305347i
$441$		0			0
$442$	−1.74136	−	1.38407i	−0.0828280	−	0.0658333i
$443$		−	19.0569i		−	0.905420i	−0.891658	−	0.452710i	$-0.850457\pi$
$443$		−	19.0569i		−	0.905420i	0.891658	−	0.452710i	$-0.149543\pi$
$444$		0			0
$445$	−7.92865	−	0.762879i	−0.375854	−	0.0361639i
$446$	−1.74380	+	3.02035i	−0.0825712	+	0.143018i
$447$		0			0
$448$	−11.9513	−	6.90007i	−0.564644	−	0.325998i
$449$	−9.51947	+	16.4882i	−0.449252	+	0.778127i	−0.998337	−	0.0576392i	$-0.981643\pi$
$449$	−9.51947	+	16.4882i	−0.449252	+	0.778127i	0.549086	+	0.835766i	$0.314976\pi$
$450$		0			0
$451$	−10.9586	+	18.9809i	−0.516021	+	0.893775i
$452$	−5.56765	+	3.21448i	−0.261880	+	0.151197i
$453$		0			0
$454$	−0.208805			−0.00979970
$455$	15.0197	+	3.73768i	0.704133	+	0.175225i
$456$		0			0
$457$	18.7529	−	10.8270i	0.877225	−	0.506466i	0.00748246	−	0.999972i	$-0.497618\pi$
$457$	18.7529	−	10.8270i	0.877225	−	0.506466i	0.869742	+	0.493506i	$0.164285\pi$
$458$	−0.0383299	+	0.0221298i	−0.00179104	+	0.00103406i
$459$		0			0
$460$	21.6581	+	15.4463i	1.00982	+	0.720187i
$461$	3.79060	−	6.56551i	0.176546	−	0.305786i	−0.764149	−	0.645039i	$-0.776841\pi$
$461$	3.79060	−	6.56551i	0.176546	−	0.305786i	0.940695	+	0.339253i	$0.110174\pi$
$462$		0			0
$463$			1.36457i			0.0634169i	0.999497	+	0.0317084i	$0.0100948\pi$
$463$			1.36457i			0.0634169i	−0.999497	+	0.0317084i	$0.989905\pi$
$464$	−18.8671	+	32.6788i	−0.875885	+	1.51708i
$465$		0			0
$466$	0.644172	+	1.11574i	0.0298407	+	0.0516856i
$467$		−	8.20177i		−	0.379532i	−0.981829	−	0.189766i	$-0.939227\pi$
$467$		−	8.20177i		−	0.379532i	0.981829	−	0.189766i	$-0.0607730\pi$
$468$		0			0
$469$	9.08355			0.419439
$470$	−4.07241	−	0.391840i	−0.187846	−	0.0180742i
$471$		0			0
$472$	−3.52978	−	2.03792i	−0.162471	−	0.0938028i
$473$		−	34.5052i		−	1.58655i
$474$		0			0
$475$	−6.33813	−	1.23108i	−0.290813	−	0.0564859i
$476$	−12.5698			−0.576135
$477$		0			0
$478$	−2.98490	+	1.72333i	−0.136526	+	0.0788234i
$479$	9.07391	+	15.7165i	0.414598	+	0.718104i	0.995386	−	0.0959503i	$-0.0305890\pi$
$479$	9.07391	+	15.7165i	0.414598	+	0.718104i	−0.580788	+	0.814055i	$0.697256\pi$
$480$		0			0
$481$	−36.3047	−	5.41175i	−1.65535	−	0.246755i
$482$		−	4.97879i		−	0.226777i
$483$		0			0
$484$	−4.27416	−	7.40307i	−0.194280	−	0.336503i
$485$	18.9158	−	8.62204i	0.858923	−	0.391507i
$486$		0			0
$487$	23.1050	+	13.3397i	1.04699	+	0.604478i	0.921804	−	0.387656i	$-0.126715\pi$
$487$	23.1050	+	13.3397i	1.04699	+	0.604478i	0.125182	+	0.992134i	$0.460049\pi$
$488$	−5.57296	−	3.21755i	−0.252276	−	0.145652i
$489$		0			0
$490$	1.24907	−	0.569340i	0.0564272	−	0.0257201i
$491$	10.8984	+	18.8766i	0.491837	+	0.851887i	0.999956	−	0.00939990i	$-0.00299213\pi$
$491$	10.8984	+	18.8766i	0.491837	+	0.851887i	−0.508118	+	0.861287i	$0.669659\pi$
$492$		0			0
$493$			33.1166i			1.49150i
$494$	0.536572	−	0.675087i	0.0241415	−	0.0303736i
$495$		0			0
$496$	−7.75514	−	13.4323i	−0.348216	−	0.603128i
$497$	18.7261	−	10.8115i	0.839978	−	0.484962i
$498$		0			0
$499$	−10.7891			−0.482986			−0.241493	−	0.970403i	$-0.577637\pi$
$499$	−10.7891			−0.482986			−0.241493	+	0.970403i	$0.577637\pi$
$500$	−15.9385	+	15.1314i	−0.712790	+	0.676698i
$501$		0			0
$502$		−	4.54030i		−	0.202643i
$503$	6.97584	+	4.02750i	0.311037	+	0.179577i	0.647391	−	0.762158i	$-0.275860\pi$
$503$	6.97584	+	4.02750i	0.311037	+	0.179577i	−0.336353	+	0.941736i	$0.609194\pi$
$504$		0			0
$505$	−14.2007	−	1.36636i	−0.631923	−	0.0608024i
$506$	4.39167			0.195233
$507$		0			0
$508$		−	32.2780i		−	1.43210i
$509$	12.8439	+	22.2463i	0.569296	+	0.986050i	0.996636	+	0.0819589i	$0.0261176\pi$
$509$	12.8439	+	22.2463i	0.569296	+	0.986050i	−0.427339	+	0.904091i	$0.640549\pi$
$510$		0			0
$511$	−1.60791	+	2.78499i	−0.0711299	+	0.123201i
$512$			13.8189i			0.610716i
$513$		0			0
$514$	−2.52410	+	4.37187i	−0.111333	+	0.192835i
$515$	9.04400	+	6.45006i	0.398526	+	0.284224i
$516$		0			0
$517$	33.5162	−	19.3506i	1.47404	−	0.851037i
$518$	3.13491	−	1.80994i	0.137740	−	0.0795244i
$519$		0			0
$520$	−1.63483	−	5.69171i	−0.0716921	−	0.249598i
$521$	32.0386			1.40364			0.701819	−	0.712355i	$-0.252371\pi$
$521$	32.0386			1.40364			0.701819	+	0.712355i	$0.252371\pi$
$522$		0			0
$523$	−28.8652	+	16.6653i	−1.26219	+	0.728724i	−0.973497	−	0.228699i	$-0.926553\pi$
$523$	−28.8652	+	16.6653i	−1.26219	+	0.728724i	−0.288690	+	0.957423i	$0.593220\pi$
$524$	14.9206	−	25.8433i	0.651811	−	1.12897i
$525$		0			0
$526$	1.83914	−	3.18549i	0.0801904	−	0.138894i
$527$	−11.7885	−	6.80612i	−0.513517	−	0.296479i
$528$		0			0
$529$	6.81445	−	11.8030i	0.296280	−	0.513173i
$530$	3.10327	+	0.298590i	0.134797	+	0.0129699i
$531$		0			0
$532$		−	4.87304i		−	0.211273i
$533$	2.97388	−	19.9503i	0.128813	−	0.864142i
$534$		0			0
$535$	−3.98971	+	41.4653i	−0.172490	+	1.79270i
$536$	−1.73770	−	3.00978i	−0.0750571	−	0.130003i
$537$		0			0
$538$		−	4.49933i		−	0.193980i
$539$	−6.49259	+	11.2455i	−0.279656	+	0.484378i
$540$		0			0
$541$	44.5119			1.91372			0.956858	−	0.290555i	$-0.0938400\pi$
$541$	44.5119			1.91372			0.956858	+	0.290555i	$0.0938400\pi$
$542$	1.42891	+	0.824980i	0.0613768	+	0.0354359i
$543$		0			0
$544$	3.61733	+	6.26541i	0.155092	+	0.268627i
$545$	13.8381	−	19.4032i	0.592760	−	0.831142i
$546$		0			0
$547$		−	24.8392i		−	1.06205i	−0.847357	−	0.531024i	$-0.821807\pi$
$547$		−	24.8392i		−	1.06205i	0.847357	−	0.531024i	$-0.178193\pi$
$548$	18.2903	−	10.5599i	0.781322	−	0.451097i
$549$		0			0
$550$	−0.691786	+	3.56161i	−0.0294979	+	0.151867i
$551$	−12.8386			−0.546942
$552$		0			0
$553$	−1.60554	−	0.926960i	−0.0682746	−	0.0394183i
$554$	−3.54767			−0.150726
$555$		0			0
$556$	13.0811	+	22.6571i	0.554761	+	0.960875i
$557$	−1.17326	+	0.677380i	−0.0497125	+	0.0287015i	−0.524650	−	0.851318i	$-0.675804\pi$
$557$	−1.17326	+	0.677380i	−0.0497125	+	0.0287015i	0.474938	+	0.880019i	$0.342471\pi$
$558$		0			0
$559$	11.6496	+	29.5415i	0.492726	+	1.24947i
$560$	−13.2646	−	9.46016i	−0.560533	−	0.399765i
$561$		0			0
$562$	2.31374	−	1.33584i	0.0975990	−	0.0563488i
$563$	1.83848	+	1.06145i	0.0774827	+	0.0447347i	0.538241	−	0.842791i	$-0.319089\pi$
$563$	1.83848	+	1.06145i	0.0774827	+	0.0447347i	−0.460758	+	0.887526i	$0.652422\pi$
$564$		0			0
$565$	−6.65456	+	3.03322i	−0.279959	+	0.127609i
$566$	1.07603	−	1.86375i	0.0452291	−	0.0783391i
$567$		0			0
$568$	−7.16465	−	4.13651i	−0.300622	−	0.173564i
$569$	2.62664	+	4.54947i	0.110114	+	0.190724i	0.915816	−	0.401598i	$-0.131545\pi$
$569$	2.62664	+	4.54947i	0.110114	+	0.190724i	−0.805702	+	0.592321i	$0.798212\pi$
$570$		0			0
$571$	19.3960			0.811699			0.405849	−	0.913940i	$-0.366976\pi$
$571$	19.3960			0.811699			0.405849	+	0.913940i	$0.366976\pi$
$572$	21.7370	+	17.2770i	0.908869	+	0.722386i
$573$		0			0
$574$	0.994606	+	1.72271i	0.0415141	+	0.0719045i
$575$	22.8410	+	19.8497i	0.952535	+	0.827791i
$576$		0			0
$577$		−	28.5208i		−	1.18734i	−0.804710	−	0.593668i	$-0.797679\pi$
$577$		−	28.5208i		−	1.18734i	0.804710	−	0.593668i	$-0.202321\pi$
$578$	−0.947200	−	0.546866i	−0.0393983	−	0.0227466i
$579$		0			0
$580$	−25.3745	+	35.5790i	−1.05362	+	1.47734i
$581$	10.9502	−	18.9663i	0.454290	−	0.786853i
$582$		0			0
$583$	−25.5400	+	14.7456i	−1.05776	+	0.610698i
$584$	1.23039			0.0509137
$585$		0			0
$586$	−5.75167			−0.237599
$587$	−15.0887	+	8.71149i	−0.622779	+	0.359562i	−0.777950	−	0.628326i	$-0.783740\pi$
$587$	−15.0887	+	8.71149i	−0.622779	+	0.359562i	0.155171	+	0.987888i	$0.450407\pi$
$588$		0			0
$589$	2.63859	−	4.57017i	0.108721	−	0.188310i
$590$	−1.87107	−	1.33442i	−0.0770308	−	0.0549374i
$591$		0			0
$592$	33.4615	+	19.3190i	1.37526	+	0.794006i
$593$			18.0632i			0.741766i	0.928680	+	0.370883i	$0.120945\pi$
$593$			18.0632i			0.741766i	−0.928680	+	0.370883i	$0.879055\pi$
$594$		0			0
$595$	−14.2330	−	1.36947i	−0.583495	−	0.0561428i
$596$	1.29836	+	2.24883i	0.0531830	+	0.0921157i
$597$		0			0
$598$	−3.75991	+	1.48271i	−0.153754	+	0.0606325i
$599$	27.5548			1.12586			0.562929	−	0.826505i	$-0.309674\pi$
$599$	27.5548			1.12586			0.562929	+	0.826505i	$0.309674\pi$
$600$		0			0
$601$	1.42944	+	2.47586i	0.0583079	+	0.100992i	0.893706	−	0.448653i	$-0.148096\pi$
$601$	1.42944	+	2.47586i	0.0583079	+	0.100992i	−0.835398	+	0.549645i	$0.814763\pi$
$602$	−2.71213	−	1.56585i	−0.110538	−	0.0638192i
$603$		0			0
$604$	−5.42444	+	9.39540i	−0.220717	+	0.382294i
$605$	−4.03315	−	8.84828i	−0.163971	−	0.359734i
$606$		0			0
$607$	21.5745	+	12.4560i	0.875682	+	0.505575i	0.869232	−	0.494404i	$-0.164614\pi$
$607$	21.5745	+	12.4560i	0.875682	+	0.505575i	0.00645001	+	0.999979i	$0.497947\pi$
$608$	−2.42896	+	1.40236i	−0.0985075	+	0.0568733i
$609$		0			0
$610$	−2.95413	−	2.10685i	−0.119609	−	0.0853037i
$611$	−22.1617	+	27.8826i	−0.896565	+	1.12801i
$612$		0			0
$613$	7.90832	−	4.56587i	0.319414	−	0.184414i	−0.331717	−	0.943379i	$-0.607628\pi$
$613$	7.90832	−	4.56587i	0.319414	−	0.184414i	0.651131	+	0.758965i	$0.274295\pi$
$614$	−0.868336	−	1.50400i	−0.0350432	−	0.0606966i
$615$		0			0
$616$	−5.52443			−0.222586
$617$	8.08476	+	4.66774i	0.325480	+	0.187916i	0.653833	−	0.756639i	$-0.273160\pi$
$617$	8.08476	+	4.66774i	0.325480	+	0.187916i	−0.328353	+	0.944555i	$0.606493\pi$
$618$		0			0
$619$	−28.7730			−1.15648			−0.578242	−	0.815865i	$-0.696261\pi$
$619$	−28.7730			−1.15648			−0.578242	+	0.815865i	$0.696261\pi$
$620$	−7.45013	−	16.3448i	−0.299204	−	0.656422i
$621$		0			0
$622$	−0.147591	+	0.0852117i	−0.00591786	+	0.00341668i
$623$		−	6.83858i		−	0.273982i
$624$		0			0
$625$	−19.6959	+	15.3971i	−0.787838	+	0.615883i
$626$	2.47036	+	4.27878i	0.0987353	+	0.171015i
$627$		0			0
$628$	0.133302	+	0.0769620i	0.00531933	+	0.00307112i
$629$	33.9097			1.35207
$630$		0			0
$631$	19.4374	−	33.6665i	0.773790	−	1.34024i	−0.161683	−	0.986843i	$-0.551692\pi$
$631$	19.4374	−	33.6665i	0.773790	−	1.34024i	0.935472	−	0.353400i	$-0.114975\pi$
$632$			0.709316i			0.0282151i
$633$		0			0
$634$	−0.632604	−	1.09570i	−0.0251239	−	0.0435159i
$635$	3.51667	−	36.5489i	0.139555	−	1.45040i
$636$		0			0
$637$	1.76192	−	11.8198i	0.0698098	−	0.468319i
$638$			7.21443i			0.285622i
$639$		0			0
$640$	−1.21545	+	12.6322i	−0.0480448	+	0.499333i
$641$	−3.79991	+	6.58164i	−0.150087	+	0.259959i	−0.931259	−	0.364357i	$-0.881289\pi$
$641$	−3.79991	+	6.58164i	−0.150087	+	0.259959i	0.781172	+	0.624316i	$0.214622\pi$
$642$		0			0
$643$	−29.7637	−	17.1841i	−1.17377	−	0.677675i	−0.219203	−	0.975679i	$-0.570346\pi$
$643$	−29.7637	−	17.1841i	−1.17377	−	0.677675i	−0.954564	+	0.298005i	$0.903679\pi$
$644$	−11.4196	+	19.7792i	−0.449993	+	0.779411i
$645$		0			0
$646$	−0.398331	+	0.689930i	−0.0156721	+	0.0271449i
$647$	14.9026	−	8.60403i	0.585882	−	0.338259i	−0.177585	−	0.984105i	$-0.556829\pi$
$647$	14.9026	−	8.60403i	0.585882	−	0.338259i	0.763468	+	0.645846i	$0.223495\pi$
$648$		0			0
$649$	21.7397			0.853358
$650$	−0.610194	−	3.28282i	−0.0239338	−	0.128763i
$651$		0			0
$652$	4.90563	−	2.83227i	0.192119	−	0.110920i
$653$	20.3301	−	11.7376i	0.795578	−	0.459327i	−0.0463449	−	0.998925i	$-0.514757\pi$
$653$	20.3301	−	11.7376i	0.795578	−	0.459327i	0.841922	+	0.539599i	$0.181424\pi$
$654$		0			0
$655$	19.7105	−	27.6372i	0.770152	−	1.07987i
$656$	−10.6162	+	18.3879i	−0.414494	+	0.717925i
$657$		0			0
$658$		−	3.51252i		−	0.136932i
$659$	−5.05905	+	8.76254i	−0.197073	+	0.341340i	−0.947578	−	0.319524i	$-0.896477\pi$
$659$	−5.05905	+	8.76254i	−0.197073	+	0.341340i	0.750505	+	0.660864i	$0.229810\pi$
$660$		0			0
$661$	−2.75291	−	4.76818i	−0.107076	−	0.185461i	0.807509	−	0.589856i	$-0.200815\pi$
$661$	−2.75291	−	4.76818i	−0.107076	−	0.185461i	−0.914584	+	0.404395i	$0.867482\pi$
$662$			3.44309i			0.133820i
$663$		0			0
$664$	−8.37915			−0.325174
$665$	0.530914	−	5.51782i	0.0205880	−	0.213972i
$666$		0			0
$667$	52.1107	+	30.0861i	2.01774	+	1.16494i
$668$			18.6582i			0.721909i
$669$		0			0
$670$	−0.812763	−	1.78311i	−0.0313998	−	0.0688877i
$671$	34.3236			1.32505
$672$		0			0
$673$	−29.2998	+	16.9162i	−1.12942	+	0.652073i	−0.943790	−	0.330546i	$-0.892767\pi$
$673$	−29.2998	+	16.9162i	−1.12942	+	0.652073i	−0.185633	+	0.982619i	$0.559434\pi$
$674$	0.636699	+	1.10280i	0.0245247	+	0.0424781i
$675$		0			0
$676$	−24.4431	−	7.45281i	−0.940118	−	0.286647i
$677$		−	13.1587i		−	0.505730i	−0.967502	−	0.252865i	$-0.918627\pi$
$677$		−	13.1587i		−	0.505730i	0.967502	−	0.252865i	$-0.0813728\pi$
$678$		0			0
$679$	8.92385	+	15.4566i	0.342466	+	0.593168i
$680$	2.26903	+	4.97800i	0.0870133	+	0.190898i
$681$		0			0
$682$	−2.56813	−	1.48271i	−0.0983387	−	0.0567759i
$683$	−6.69626	−	3.86609i	−0.256225	−	0.147932i	0.366386	−	0.930463i	$-0.380595\pi$
$683$	−6.69626	−	3.86609i	−0.256225	−	0.147932i	−0.622611	+	0.782531i	$0.713928\pi$
$684$		0			0
$685$	21.8609	−	9.96443i	0.835261	−	0.380721i
$686$	1.83378	+	3.17621i	0.0700142	+	0.121268i
$687$		0			0
$688$		−	33.4271i		−	1.27440i
$689$	16.8877	−	21.2472i	0.643368	−	0.809452i
$690$		0			0
$691$	−20.2247	−	35.0301i	−0.769382	−	1.33261i	−0.937898	−	0.346910i	$-0.887231\pi$
$691$	−20.2247	−	35.0301i	−0.769382	−	1.33261i	0.168516	−	0.985699i	$-0.446103\pi$
$692$	−20.1713	+	11.6459i	−0.766797	+	0.442710i
$693$		0			0
$694$	−2.22582			−0.0844909
$695$	12.3434	+	27.0802i	0.468214	+	1.02721i
$696$		0			0
$697$			18.6342i			0.705820i
$698$	1.68227	+	0.971257i	0.0636747	+	0.0367626i
$699$		0			0
$700$	−14.2420	−	12.3768i	−0.538296	−	0.467801i
$701$	−32.0531			−1.21063			−0.605315	−	0.795986i	$-0.706953\pi$
$701$	−32.0531			−1.21063			−0.605315	+	0.795986i	$0.706953\pi$
$702$		0			0
$703$			13.1461i			0.495813i
$704$	−14.0812	−	24.3893i	−0.530704	−	0.919207i
$705$		0			0
$706$	−2.94706	+	5.10445i	−0.110914	+	0.192109i
$707$		−	12.2483i		−	0.460646i
$708$		0			0
$709$	−17.6894	+	30.6389i	−0.664339	+	1.15067i	0.315125	+	0.949050i	$0.397953\pi$
$709$	−17.6894	+	30.6389i	−0.664339	+	1.15067i	−0.979464	+	0.201619i	$0.935380\pi$
$710$	−3.79785	−	2.70858i	−0.142531	−	0.101651i
$711$		0			0
$712$	−2.26593	+	1.30823i	−0.0849192	+	0.0490281i
$713$	−21.4196	+	12.3666i	−0.802170	+	0.463133i
$714$		0			0
$715$	22.7308	+	21.9312i	0.850085	+	0.820181i
$716$	−17.2109			−0.643201
$717$		0			0
$718$	2.53461	−	1.46336i	0.0945907	−	0.0546120i
$719$	−20.0549	+	34.7361i	−0.747922	+	1.29544i	0.200895	+	0.979613i	$0.435615\pi$
$719$	−20.0549	+	34.7361i	−0.747922	+	1.29544i	−0.948817	+	0.315826i	$0.897718\pi$
$720$		0			0
$721$	−4.76858	+	8.25942i	−0.177591	+	0.307597i
$722$	2.78018	+	1.60514i	0.103468	+	0.0597370i
$723$		0			0
$724$	6.89767	−	11.9471i	0.256350	−	0.444011i
$725$	−32.6082	+	37.5221i	−1.21104	+	1.39354i
$726$		0			0
$727$		−	29.2478i		−	1.08474i	−0.840140	−	0.542370i	$-0.817527\pi$
$727$		−	29.2478i		−	1.08474i	0.840140	−	0.542370i	$-0.182473\pi$
$728$	4.72973	−	1.86515i	0.175295	−	0.0691272i
$729$		0			0
$730$	0.690567	+	0.0664451i	0.0255590	+	0.00245924i
$731$	−14.6683	−	25.4062i	−0.542525	−	0.939681i
$732$		0			0
$733$		−	24.3583i		−	0.899693i	−0.893106	−	0.449846i	$-0.851479\pi$
$733$		−	24.3583i		−	0.899693i	0.893106	−	0.449846i	$-0.148521\pi$
$734$	2.40316	−	4.16239i	0.0887021	−	0.153637i
$735$		0			0
$736$	13.1453			0.484541
$737$	16.0536	+	9.26853i	0.591341	+	0.341411i
$738$		0			0
$739$	−11.1663	−	19.3405i	−0.410757	−	0.711452i	0.584216	−	0.811599i	$-0.301402\pi$
$739$	−11.1663	−	19.3405i	−0.410757	−	0.711452i	−0.994973	+	0.100146i	$0.968069\pi$
$740$	36.4311	+	25.9822i	1.33923	+	0.955124i
$741$		0			0
$742$			2.67662i			0.0982617i
$743$	5.99031	−	3.45851i	0.219763	−	0.126880i	−0.386077	−	0.922466i	$-0.626170\pi$
$743$	5.99031	−	3.45851i	0.219763	−	0.126880i	0.605841	+	0.795586i	$0.292837\pi$
$744$		0			0
$745$	1.22515	+	2.68784i	0.0448860	+	0.0984750i
$746$	−2.50995			−0.0918958
$747$		0			0
$748$	−22.2149	−	12.8258i	−0.812257	−	0.468957i
$749$	−35.7645			−1.30681
$750$		0			0
$751$	7.22928	+	12.5215i	0.263800	+	0.456915i	0.967249	−	0.253831i	$-0.0816908\pi$
$751$	7.22928	+	12.5215i	0.263800	+	0.456915i	−0.703449	+	0.710746i	$0.748357\pi$
$752$	32.4690	−	18.7460i	1.18402	−	0.683596i
$753$		0			0
$754$	−2.43573	−	6.17661i	−0.0887040	−	0.224939i
$755$	−7.16580	+	10.0476i	−0.260790	+	0.365669i
$756$		0			0
$757$	23.6428	−	13.6502i	0.859313	−	0.496125i	−0.00446897	−	0.999990i	$-0.501423\pi$
$757$	23.6428	−	13.6502i	0.859313	−	0.496125i	0.863782	+	0.503865i	$0.168089\pi$
$758$	−0.878961	−	0.507468i	−0.0319253	−	0.0184321i
$759$		0			0
$760$	−1.92986	+	0.879654i	−0.0700035	+	0.0319084i
$761$	0.207699	−	0.359744i	0.00752907	−	0.0130407i	−0.862236	−	0.506506i	$-0.830937\pi$
$761$	0.207699	−	0.359744i	0.00752907	−	0.0130407i	0.869765	+	0.493465i	$0.164270\pi$
$762$		0			0
$763$	17.7199	+	10.2306i	0.641505	+	0.370373i
$764$	−11.9011	−	20.6134i	−0.430568	−	0.745765i
$765$		0			0
$766$	3.71477			0.134220
$767$	−18.6124	+	7.33973i	−0.672054	+	0.265022i
$768$		0			0
$769$	−4.61941	−	8.00105i	−0.166580	−	0.288525i	0.770635	−	0.637277i	$-0.219939\pi$
$769$	−4.61941	−	8.00105i	−0.166580	−	0.288525i	−0.937215	+	0.348751i	$0.886606\pi$
$770$	−3.10065	−	0.298338i	−0.111740	−	0.0107514i
$771$		0			0
$772$		−	4.71911i		−	0.169845i
$773$	−14.7907	−	8.53943i	−0.531986	−	0.307142i	0.209839	−	0.977736i	$-0.432706\pi$
$773$	−14.7907	−	8.53943i	−0.531986	−	0.307142i	−0.741825	+	0.670594i	$0.766039\pi$
$774$		0			0
$775$	−6.65515	−	19.3191i	−0.239060	−	0.693964i
$776$	3.41430	−	5.91373i	0.122566	−	0.212291i
$777$		0			0
$778$	3.67268	−	2.12042i	0.131672	−	0.0760208i
$779$	−7.22407			−0.258829
$780$		0			0
$781$	44.1267			1.57898
$782$	3.23358	−	1.86691i	0.115633	−	0.0667606i
$783$		0			0
$784$	−6.28974	+	10.8942i	−0.224634	+	0.389077i
$785$	0.142555	+	0.101669i	0.00508801	+	0.00362871i
$786$		0			0
$787$	16.4631	+	9.50498i	0.586847	+	0.338816i	0.763850	−	0.645394i	$-0.223307\pi$
$787$	16.4631	+	9.50498i	0.586847	+	0.338816i	−0.177003	+	0.984210i	$0.556640\pi$
$788$		−	16.7318i		−	0.596045i
$789$		0			0
$790$	−0.0383055	+	0.398111i	−0.00136285	+	0.0141642i
$791$	−3.13940	−	5.43760i	−0.111624	−	0.193339i
$792$		0			0
$793$	−29.3860	+	11.5883i	−1.04353	+	0.411512i
$794$	−3.33714			−0.118431
$795$		0			0
$796$	−1.57822	−	2.73356i	−0.0559387	−	0.0968886i
$797$	−44.4322	−	25.6529i	−1.57387	−	0.908673i	−0.995688	−	0.0927635i	$-0.970430\pi$
$797$	−44.4322	−	25.6529i	−1.57387	−	0.908673i	−0.578180	−	0.815910i	$-0.696237\pi$
$798$		0			0
$799$	16.4520	−	28.4957i	0.582029	−	1.00810i
$800$	−2.07068	+	10.6607i	−0.0732095	+	0.376913i
$801$		0			0
$802$	−0.530592	−	0.306338i	−0.0187359	−	0.0108172i
$803$	−5.68341	+	3.28132i	−0.200563	+	0.115795i
$804$		0			0
$805$	−15.0855	+	21.1522i	−0.531693	+	0.745518i
$806$	2.69929	+	0.402369i	0.0950783	+	0.0141728i
$807$		0			0
$808$	−4.05842	+	2.34313i	−0.142775	+	0.0824309i
$809$	−12.1534	−	21.0502i	−0.427289	−	0.740087i	0.569342	−	0.822101i	$-0.307198\pi$
$809$	−12.1534	−	21.0502i	−0.427289	−	0.740087i	−0.996631	+	0.0820139i	$0.973865\pi$
$810$		0			0
$811$	−15.4909			−0.543959			−0.271979	−	0.962303i	$-0.587678\pi$
$811$	−15.4909			−0.543959			−0.271979	+	0.962303i	$0.587678\pi$
$812$	−32.4924	−	18.7595i	−1.14026	−	0.658330i
$813$		0			0
$814$	7.38721			0.258922
$815$	5.86330	−	2.67256i	0.205382	−	0.0936156i
$816$		0			0
$817$	9.84943	−	5.68657i	0.344588	−	0.198948i
$818$		−	3.98531i		−	0.139343i
$819$		0			0
$820$	−14.2778	+	20.0197i	−0.498603	+	0.699119i
$821$	7.85738	+	13.6094i	0.274224	+	0.474971i	0.969939	−	0.243348i	$-0.0782456\pi$
$821$	7.85738	+	13.6094i	0.274224	+	0.474971i	−0.695715	+	0.718318i	$0.744912\pi$
$822$		0			0
$823$	−27.9486	−	16.1361i	−0.974228	−	0.562471i	−0.0737051	−	0.997280i	$-0.523482\pi$
$823$	−27.9486	−	16.1361i	−0.974228	−	0.562471i	−0.900522	+	0.434810i	$0.856816\pi$
$824$	3.64895			0.127117
$825$		0			0
$826$	0.986549	−	1.70875i	0.0343264	−	0.0594551i
$827$			35.1730i			1.22309i	0.791211	+	0.611543i	$0.209451\pi$
$827$			35.1730i			1.22309i	−0.791211	+	0.611543i	$0.790549\pi$
$828$		0			0
$829$	−0.174879	−	0.302900i	−0.00607382	−	0.0105202i	0.862973	−	0.505251i	$-0.168600\pi$
$829$	−0.174879	−	0.302900i	−0.00607382	−	0.0105202i	−0.869046	+	0.494731i	$0.835267\pi$
$830$	−4.70289	−	0.452503i	−0.163240	−	0.0157066i
$831$		0			0
$832$	20.2898	+	16.1268i	0.703424	+	0.559095i
$833$			11.0401i			0.382516i
$834$		0			0
$835$	−2.03280	+	21.1270i	−0.0703480	+	0.731131i
$836$	4.97228	−	8.61224i	0.171970	−	0.297860i
$837$		0			0
$838$	−3.16302	−	1.82617i	−0.109265	−	0.0630841i
$839$	18.7040	−	32.3962i	0.645733	−	1.11844i	−0.338399	−	0.941003i	$-0.609885\pi$
$839$	18.7040	−	32.3962i	0.645733	−	1.11844i	0.984132	−	0.177439i	$-0.0567814\pi$
$840$		0			0
$841$	−34.9242	+	60.4904i	−1.20428	+	2.08588i
$842$	−3.72627	+	2.15137i	−0.128416	+	0.0741410i
$843$		0			0
$844$	6.07743			0.209194
$845$	−26.8653	−	11.1020i	−0.924195	−	0.381920i
$846$		0			0
$847$	7.23014	−	4.17432i	0.248431	−	0.143431i
$848$	−24.7421	+	14.2848i	−0.849647	+	0.490544i
$849$		0			0
$850$	1.00469	+	2.91649i	0.0344605	+	0.100035i
$851$	30.8067	−	53.3588i	1.05604	−	1.82911i
$852$		0			0
$853$			48.7810i			1.67023i	0.550076	+	0.835115i	$0.314599\pi$
$853$			48.7810i			1.67023i	−0.550076	+	0.835115i	$0.685401\pi$
$854$	1.55761	−	2.69785i	0.0533002	−	0.0923186i
$855$		0			0
$856$	6.84181	+	11.8504i	0.233848	+	0.405037i
$857$		−	2.79710i		−	0.0955471i	−0.998858	−	0.0477735i	$-0.984787\pi$
$857$		−	2.79710i		−	0.0955471i	0.998858	−	0.0477735i	$-0.0152126\pi$
$858$		0			0
$859$	−14.6250			−0.498998			−0.249499	−	0.968375i	$-0.580266\pi$
$859$	−14.6250			−0.498998			−0.249499	+	0.968375i	$0.580266\pi$
$860$	3.70770	−	38.5343i	0.126431	−	1.31401i
$861$		0			0
$862$	5.90782	+	3.41088i	0.201221	+	0.116175i
$863$			46.1012i			1.56930i	0.619938	+	0.784651i	$0.287158\pi$
$863$			46.1012i			1.56930i	−0.619938	+	0.784651i	$0.712842\pi$
$864$		0			0
$865$	−24.1091	+	10.9892i	−0.819734	+	0.373644i
$866$	1.21744			0.0413702
$867$		0			0
$868$	13.3557	−	7.71091i	0.453322	−	0.261725i
$869$	−1.89167	−	3.27648i	−0.0641707	−	0.111147i
$870$		0			0
$871$	−16.8734	−	2.51524i	−0.571735	−	0.0852256i
$872$		−	7.82854i		−	0.265108i
$873$		0			0
$874$	0.723761	+	1.25359i	0.0244816	+	0.0424034i
$875$	−14.7780	−	15.5662i	−0.499587	−	0.526232i
$876$		0			0
$877$	−32.5853	−	18.8131i	−1.10033	−	0.635275i	−0.164021	−	0.986457i	$-0.552446\pi$
$877$	−32.5853	−	18.8131i	−1.10033	−	0.635275i	−0.936307	+	0.351182i	$0.885780\pi$
$878$	−4.29104	−	2.47743i	−0.144815	−	0.0836092i
$879$		0			0
$880$	−13.7901	−	30.2539i	−0.464864	−	1.01986i
$881$	−21.7182	−	37.6169i	−0.731703	−	1.26735i	−0.956155	−	0.292862i	$-0.905392\pi$
$881$	−21.7182	−	37.6169i	−0.731703	−	1.26735i	0.224452	−	0.974485i	$-0.427941\pi$
$882$		0			0
$883$		−	13.5736i		−	0.456788i	−0.973569	−	0.228394i	$-0.926652\pi$
$883$		−	13.5736i		−	0.456788i	0.973569	−	0.228394i	$-0.0733475\pi$
$884$	23.3494	+	3.48058i	0.785326	+	0.117065i
$885$		0			0
$886$	−1.76483	−	3.05677i	−0.0592906	−	0.102694i
$887$	20.6104	−	11.8994i	0.692031	−	0.399544i	−0.112341	−	0.993670i	$-0.535835\pi$
$887$	20.6104	−	11.8994i	0.692031	−	0.399544i	0.804372	+	0.594125i	$0.202502\pi$
$888$		0			0
$889$	31.5240			1.05728
$890$	−1.34242	+	0.611892i	−0.0449982	+	0.0205107i
$891$		0			0
$892$		−	37.0136i		−	1.23931i
$893$	11.0472	+	6.37808i	0.369679	+	0.213434i
$894$		0			0
$895$	−19.4882	−	1.87511i	−0.651418	−	0.0626782i
$896$	−10.8955			−0.363993
$897$		0			0
$898$			3.52634i			0.117675i
$899$	−20.3153	−	35.1871i	−0.677553	−	1.17356i
$900$		0			0
$901$	−12.5368	+	21.7143i	−0.417660	+	0.723408i
$902$			4.05945i			0.135165i
$903$		0			0
$904$	−1.20114	+	2.08044i	−0.0399495	+	0.0691945i
$905$	9.11198	−	12.7764i	0.302892	−	0.424703i
$906$		0			0
$907$	3.69191	−	2.13152i	0.122588	−	0.0707761i	−0.437452	−	0.899242i	$-0.644119\pi$
$907$	3.69191	−	2.13152i	0.122588	−	0.0707761i	0.560040	+	0.828466i	$0.310786\pi$
$908$	1.91914	−	1.10802i	0.0636889	−	0.0367708i
$909$		0			0
$910$	2.75533	−	0.791416i	0.0913384	−	0.0262352i
$911$	−19.9751			−0.661806			−0.330903	−	0.943665i	$-0.607353\pi$
$911$	−19.9751			−0.661806			−0.330903	+	0.943665i	$0.607353\pi$
$912$		0			0
$913$	38.7050	−	22.3464i	1.28095	−	0.739557i
$914$	2.00535	−	3.47336i	0.0663309	−	0.114889i
$915$		0			0
$916$	0.234862	−	0.406792i	0.00776005	−	0.0134408i
$917$	25.2396	+	14.5721i	0.833485	+	0.481213i
$918$		0			0
$919$	14.6678	−	25.4054i	0.483846	−	0.838046i	−0.515982	−	0.856600i	$-0.672573\pi$
$919$	14.6678	−	25.4054i	0.483846	−	0.838046i	0.999828	+	0.0185533i	$0.00590603\pi$
$920$	9.89455	+	0.952034i	0.326214	+	0.0313876i
$921$		0			0
$922$		−	1.40417i		−	0.0462438i
$923$	−37.7789	+	14.8980i	−1.24351	+	0.490374i
$924$		0			0
$925$	38.4208	+	33.3892i	1.26327	+	1.09783i
$926$	0.126371	+	0.218880i	0.00415280	+	0.00719285i
$927$		0			0
$928$			21.5945i			0.708873i
$929$	9.20844	−	15.9495i	0.302119	−	0.523286i	−0.674497	−	0.738278i	$-0.735639\pi$
$929$	9.20844	−	15.9495i	0.302119	−	0.523286i	0.976616	+	0.214992i	$0.0689726\pi$
$930$		0			0
$931$	−4.28001			−0.140272
$932$	−11.8413	−	6.83655i	−0.387873	−	0.223939i
$933$		0			0
$934$	−0.759553	−	1.31558i	−0.0248533	−	0.0430472i
$935$	−23.7569	−	16.9431i	−0.776935	−	0.554100i
$936$		0			0
$937$		−	17.5267i		−	0.572573i	−0.958144	−	0.286287i	$-0.907579\pi$
$937$		−	17.5267i		−	0.572573i	0.958144	−	0.286287i	$-0.0924210\pi$
$938$	1.45702	−	0.841214i	0.0475735	−	0.0274666i
$939$		0			0
$940$	39.5091	−	18.0087i	1.28865	−	0.587379i
$941$	−1.68724			−0.0550025			−0.0275012	−	0.999622i	$-0.508755\pi$
$941$	−1.68724			−0.0550025			−0.0275012	+	0.999622i	$0.508755\pi$
$942$		0			0
$943$	29.3219	+	16.9290i	0.954852	+	0.551284i
$944$	21.0605			0.685460
$945$		0			0
$946$	−3.19547	−	5.53472i	−0.103894	−	0.179949i
$947$	−45.1580	+	26.0720i	−1.46744	+	0.847226i	−0.999336	−	0.0364483i	$-0.988396\pi$
$947$	−45.1580	+	26.0720i	−1.46744	+	0.847226i	−0.468103	+	0.883674i	$0.655062\pi$
$948$		0			0
$949$	3.75800	−	4.72811i	0.121990	−	0.153481i
$950$	−1.13066	+	0.389496i	−0.0366835	+	0.0126369i
$951$		0			0
$952$	−4.06764	+	2.34845i	−0.131833	+	0.0761138i
$953$	−13.2161	−	7.63034i	−0.428113	−	0.247171i	0.270430	−	0.962740i	$-0.412834\pi$
$953$	−13.2161	−	7.63034i	−0.428113	−	0.247171i	−0.698542	+	0.715569i	$0.746168\pi$
$954$		0			0
$955$	−11.2300	−	24.6375i	−0.363395	−	0.797249i
$956$	18.2896	−	31.6785i	0.591528	−	1.02456i
$957$		0			0
$958$	2.91096	+	1.68064i	0.0940488	+	0.0542991i
$959$	10.3132	+	17.8630i	0.333032	+	0.576828i
$960$		0			0
$961$	−14.2992			−0.461264
$962$	−6.32454	+	2.49406i	−0.203911	+	0.0804118i
$963$		0			0
$964$	26.4198	+	45.7604i	0.850923	+	1.47384i
$965$	0.514144	−	5.34353i	0.0165509	−	0.172014i
$966$		0			0
$967$			14.9106i			0.479491i	0.970836	+	0.239746i	$0.0770640\pi$
$967$			14.9106i			0.479491i	−0.970836	+	0.239746i	$0.922936\pi$
$968$	−2.76628	−	1.59711i	−0.0889115	−	0.0513331i
$969$		0			0
$970$	2.23567	−	3.13476i	0.0717831	−	0.100651i
$971$	6.21770	−	10.7694i	0.199535	−	0.345605i	−0.748843	−	0.662748i	$-0.769390\pi$
$971$	6.21770	−	10.7694i	0.199535	−	0.345605i	0.948378	+	0.317143i	$0.102723\pi$
$972$		0			0
$973$	−22.1278	+	12.7755i	−0.709386	+	0.409564i
$974$	4.94146			0.158335
$975$		0			0
$976$	33.2512			1.06434
$977$	−3.87017	+	2.23444i	−0.123818	+	0.0714862i	−0.560630	−	0.828067i	$-0.689441\pi$
$977$	−3.87017	+	2.23444i	−0.123818	+	0.0714862i	0.436812	+	0.899553i	$0.356108\pi$
$978$		0			0
$979$	6.97785	−	12.0860i	0.223013	−	0.386270i
$980$	−8.45910	+	11.8610i	−0.270216	+	0.378885i
$981$		0			0
$982$	3.49626	+	2.01857i	0.111570	+	0.0644150i
$983$		−	21.5857i		−	0.688475i	−0.938883	−	0.344238i	$-0.888137\pi$
$983$		−	21.5857i		−	0.688475i	0.938883	−	0.344238i	$-0.111863\pi$
$984$		0			0
$985$	1.82292	−	18.9457i	0.0580829	−	0.603659i
$986$	3.06688	+	5.31199i	0.0976692	+	0.169168i
$987$		0			0
$988$	−1.34935	+	9.05208i	−0.0429284	+	0.287985i
$989$	−53.3040			−1.69497
$990$		0			0
$991$	−24.4812	−	42.4027i	−0.777671	−	1.34697i	−0.933281	−	0.359147i	$-0.883068\pi$
$991$	−24.4812	−	42.4027i	−0.777671	−	1.34697i	0.155610	−	0.987819i	$-0.450266\pi$
$992$	−7.68700	−	4.43809i	−0.244063	−	0.140910i
$993$		0			0
$994$	2.00247	−	3.46838i	0.0635145	−	0.110010i
$995$	−1.48923	−	3.26721i	−0.0472118	−	0.103577i
$996$		0			0
$997$	−31.3681	−	18.1104i	−0.993437	−	0.573561i	−0.0871373	−	0.996196i	$-0.527772\pi$
$997$	−31.3681	−	18.1104i	−0.993437	−	0.573561i	−0.906300	+	0.422635i	$0.861105\pi$
$998$	−1.73060	+	0.999161i	−0.0547811	+	0.0316279i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	585.2.bs.c.289.9	yes	32
3.2	odd	2	inner	585.2.bs.c.289.8	yes	32
5.4	even	2	inner	585.2.bs.c.289.7	✓	32
13.9	even	3	inner	585.2.bs.c.334.7	yes	32
15.14	odd	2	inner	585.2.bs.c.289.10	yes	32
39.35	odd	6	inner	585.2.bs.c.334.10	yes	32
65.9	even	6	inner	585.2.bs.c.334.9	yes	32
195.74	odd	6	inner	585.2.bs.c.334.8	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bs.c.289.7	✓	32	5.4	even	2	inner
585.2.bs.c.289.8	yes	32	3.2	odd	2	inner
585.2.bs.c.289.9	yes	32	1.1	even	1	trivial
585.2.bs.c.289.10	yes	32	15.14	odd	2	inner
585.2.bs.c.334.7	yes	32	13.9	even	3	inner
585.2.bs.c.334.8	yes	32	195.74	odd	6	inner
585.2.bs.c.334.9	yes	32	65.9	even	6	inner
585.2.bs.c.334.10	yes	32	39.35	odd	6	inner

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:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.bs (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160403 - 0.0926085i) q^{2} +(-0.982847 + 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(-1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +O(q^{10})\)	\(q+(0.160403 - 0.0926085i) q^{2} +(-0.982847 + 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(-1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +(-0.0396663 + 0.412254i) q^{10} +(-1.95887 - 3.39287i) q^{11} +(2.82258 + 2.24344i) q^{13} -0.355576 q^{14} +(-1.89767 - 3.28687i) q^{16} +(-2.88464 - 1.66545i) q^{17} +(0.645658 - 1.11831i) q^{19} +(-1.82304 - 3.99954i) q^{20} +(-0.628417 - 0.362817i) q^{22} +(-5.24134 + 3.02609i) q^{23} +(-1.62851 - 4.72736i) q^{25} +(0.660511 + 0.0984590i) q^{26} +(3.26812 - 1.88685i) q^{28} +(-4.97112 - 8.61024i) q^{29} +4.08666 q^{31} +(-1.88100 - 1.08600i) q^{32} -0.616938 q^{34} +(3.90612 - 1.78045i) q^{35} +(-8.81645 + 5.09018i) q^{37} -0.239174i q^{38} +(-1.33719 - 0.953666i) q^{40} +(-2.79717 - 4.84485i) q^{41} +(7.62743 + 4.40370i) q^{43} +7.70110 q^{44} +(-0.560483 + 0.970786i) q^{46} +9.87842i q^{47} +(-1.65723 - 2.87040i) q^{49} +(-0.699010 - 0.607468i) q^{50} +(-6.59327 + 2.60004i) q^{52} -7.52756i q^{53} +(8.72008 + 0.839030i) q^{55} +(0.705052 - 1.22119i) q^{56} +(-1.59476 - 0.920737i) q^{58} +(-2.77451 + 4.80560i) q^{59} +(-4.38052 + 7.58728i) q^{61} +(0.655511 - 0.378459i) q^{62} +7.18840 q^{64} +(-7.74894 + 2.22573i) q^{65} +(-4.09765 + 2.36578i) q^{67} +(5.67032 - 3.27376i) q^{68} +(0.461666 - 0.647328i) q^{70} +(-5.63164 + 9.75428i) q^{71} -1.67510i q^{73} +(-0.942788 + 1.63296i) q^{74} +(1.26917 + 2.19826i) q^{76} +7.52121i q^{77} +0.965695 q^{79} +(8.44764 + 0.812815i) q^{80} +(-0.897348 - 0.518084i) q^{82} +11.4078i q^{83} +(6.77727 - 3.08916i) q^{85} +1.63128 q^{86} +(2.49211 - 1.43882i) q^{88} +(1.78109 + 3.08493i) q^{89} +(-2.53930 - 6.43926i) q^{91} -11.8967i q^{92} +(0.914825 + 1.58452i) q^{94} +(1.19760 + 2.62740i) q^{95} +(-8.05122 - 4.64838i) q^{97} +(-0.531647 - 0.306946i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 32 * q + 20 * q^4	\( 32 q + 20 q^{4} - 6 q^{10} - 28 q^{16} - 8 q^{19} + 28 q^{25} + 8 q^{31} - 8 q^{34} - 20 q^{40} - 8 q^{46} + 44 q^{49} + 20 q^{55} - 56 q^{61} - 136 q^{64} - 80 q^{70} + 88 q^{76} - 72 q^{79} - 50 q^{85} - 28 q^{91} + 48 q^{94}+O(q^{100}) \) 32 * q + 20 * q^4 - 6 * q^10 - 28 * q^16 - 8 * q^19 + 28 * q^25 + 8 * q^31 - 8 * q^34 - 20 * q^40 - 8 * q^46 + 44 * q^49 + 20 * q^55 - 56 * q^61 - 136 * q^64 - 80 * q^70 + 88 * q^76 - 72 * q^79 - 50 * q^85 - 28 * q^91 + 48 * q^94

Introduction

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