LMFDB - Embedded newform 585.2.bs.c.334.7

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			334.7
Character	$\chi$	$=$	585.334
Dual form			585.2.bs.c.289.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.160403 - 0.0926085i) q^{2} +(-0.982847 - 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +O(q^{10})$	\(q+(-0.160403 - 0.0926085i) q^{2} +(-0.982847 - 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +(0.376855 - 0.171775i) q^{10} +(-1.95887 + 3.39287i) q^{11} +(-2.82258 + 2.24344i) q^{13} -0.355576 q^{14} +(-1.89767 + 3.28687i) q^{16} +(2.88464 - 1.66545i) q^{17} +(0.645658 + 1.11831i) q^{19} +(4.37522 + 0.420975i) q^{20} +(0.628417 - 0.362817i) q^{22} +(5.24134 + 3.02609i) q^{23} +(-1.62851 - 4.72736i) q^{25} +(0.660511 - 0.0984590i) q^{26} +(-3.26812 - 1.88685i) q^{28} +(-4.97112 + 8.61024i) q^{29} +4.08666 q^{31} +(1.88100 - 1.08600i) q^{32} -0.616938 q^{34} +(-0.411142 + 4.27302i) q^{35} +(8.81645 + 5.09018i) q^{37} -0.239174i q^{38} +(-1.33719 - 0.953666i) q^{40} +(-2.79717 + 4.84485i) q^{41} +(-7.62743 + 4.40370i) q^{43} +7.70110 q^{44} +(-0.560483 - 0.970786i) q^{46} +9.87842i q^{47} +(-1.65723 + 2.87040i) q^{49} +(-0.176577 + 0.909095i) q^{50} +(6.59327 + 2.60004i) q^{52} -7.52756i q^{53} +(-3.63342 - 7.97133i) q^{55} +(0.705052 + 1.22119i) q^{56} +(1.59476 - 0.920737i) q^{58} +(-2.77451 - 4.80560i) q^{59} +(-4.38052 - 7.58728i) q^{61} +(-0.655511 - 0.378459i) q^{62} +7.18840 q^{64} +(-0.419471 - 8.05134i) q^{65} +(4.09765 + 2.36578i) q^{67} +(-5.67032 - 3.27376i) q^{68} +(0.461666 - 0.647328i) q^{70} +(-5.63164 - 9.75428i) q^{71} -1.67510i q^{73} +(-0.942788 - 1.63296i) q^{74} +(1.26917 - 2.19826i) q^{76} +7.52121i q^{77} +0.965695 q^{79} +(-3.51990 - 7.72227i) q^{80} +(0.897348 - 0.518084i) q^{82} +11.4078i q^{83} +(-0.713348 + 7.41387i) q^{85} +1.63128 q^{86} +(-2.49211 - 1.43882i) q^{88} +(1.78109 - 3.08493i) q^{89} +(-2.53930 + 6.43926i) q^{91} -11.8967i q^{92} +(0.914825 - 1.58452i) q^{94} +(-2.87420 - 0.276550i) q^{95} +(8.05122 - 4.64838i) q^{97} +(0.531647 - 0.306946i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/585\mathbb{Z}\right)^\times$.

$n$	$326$	$352$	$496$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

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	$-0.354192\pi$
$2$	−0.160403	−	0.0926085i	−0.113422	−	0.0654841i	−0.555638	+	0.831425i	$0.687526\pi$
$3$		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	$-0.548486\pi$
$7$	1.66258	−	0.959889i	0.628395	−	0.362804i	0.780130	+	0.625617i	$0.215153\pi$
$8$			0.734514i			0.259690i
$9$		0			0
$10$	0.376855	−	0.171775i	0.119172	−	0.0543200i
$11$	−1.95887	+	3.39287i	−0.590623	+	1.02299i	0.403526	+	0.914968i	$0.367785\pi$
$11$	−1.95887	+	3.39287i	−0.590623	+	1.02299i	−0.994149	+	0.108021i	$0.965549\pi$
$12$		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	$-0.534310\pi$
$17$	2.88464	−	1.66545i	0.699628	−	0.403930i	0.807209	+	0.590266i	$0.200977\pi$
$18$		0			0
$19$	0.645658	+	1.11831i	0.148124	+	0.256559i	0.930534	−	0.366205i	$-0.119343\pi$
$19$	0.645658	+	1.11831i	0.148124	+	0.256559i	−0.782410	+	0.622764i	$0.786010\pi$
$20$	4.37522	+	0.420975i	0.978329	+	0.0941330i
$21$		0			0
$22$	0.628417	−	0.362817i	0.133979	−	0.0773528i
$23$	5.24134	+	3.02609i	1.09290	+	0.630984i	0.934346	−	0.356367i	$-0.115985\pi$
$23$	5.24134	+	3.02609i	1.09290	+	0.630984i	0.158550	+	0.987351i	$0.449318\pi$
$24$		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	−0.128549	+	0.991703i	$0.541032\pi$
$29$	−4.97112	+	8.61024i	−0.923115	+	1.59888i	−0.794566	+	0.607178i	$0.792301\pi$
$30$		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
$35$	−0.411142	+	4.27302i	−0.0694957	+	0.722272i
$36$		0			0
$37$	8.81645	+	5.09018i	1.44942	+	0.836821i	0.998446	−	0.0557190i	$-0.0177451\pi$
$37$	8.81645	+	5.09018i	1.44942	+	0.836821i	0.450969	+	0.892540i	$0.351078\pi$
$38$		−	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	−0.997444	−	0.0714494i	$-0.977238\pi$
$41$	−2.79717	+	4.84485i	−0.436845	+	0.756638i	0.560599	+	0.828087i	$0.310571\pi$
$42$		0			0
$43$	−7.62743	+	4.40370i	−1.16317	+	0.671558i	−0.952062	−	0.305904i	$-0.901041\pi$
$43$	−7.62743	+	4.40370i	−1.16317	+	0.671558i	−0.211110	+	0.977462i	$0.567708\pi$
$44$	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
$50$	−0.176577	+	0.909095i	−0.0249718	+	0.128565i
$51$		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
$55$	−3.63342	−	7.97133i	−0.489930	−	1.07485i
$56$	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	0.626949	−	0.779060i	$-0.284303\pi$
$59$	−2.77451	−	4.80560i	−0.361211	−	0.625636i	−0.988160	+	0.153424i	$0.950970\pi$
$60$		0			0
$61$	−4.38052	−	7.58728i	−0.560868	−	0.971452i	−0.997421	−	0.0717734i	$-0.977134\pi$
$61$	−4.38052	−	7.58728i	−0.560868	−	0.971452i	0.436553	−	0.899679i	$-0.356199\pi$
$62$	−0.655511	−	0.378459i	−0.0832500	−	0.0480644i
$63$		0			0
$64$	7.18840			0.898550
$65$	−0.419471	−	8.05134i	−0.0520290	−	0.998646i
$66$		0			0
$67$	4.09765	+	2.36578i	0.500608	+	0.289026i	0.728965	−	0.684551i	$-0.240002\pi$
$67$	4.09765	+	2.36578i	0.500608	+	0.289026i	−0.228357	+	0.973578i	$0.573335\pi$
$68$	−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	−0.978365	−	0.206888i	$-0.933667\pi$
$71$	−5.63164	−	9.75428i	−0.668352	−	1.15762i	0.310013	−	0.950732i	$-0.399667\pi$
$72$		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	$0.482699\pi$
$80$	−3.51990	−	7.72227i	−0.393537	−	0.863377i
$81$		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
$85$	−0.713348	+	7.41387i	−0.0773735	+	0.804147i
$86$	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	−0.756054	−	0.654509i	$-0.772875\pi$
$89$	1.78109	−	3.08493i	0.188795	−	0.327002i	0.944849	+	0.327507i	$0.106209\pi$
$90$		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
$95$	−2.87420	−	0.276550i	−0.294886	−	0.0283734i
$96$		0			0
$97$	8.05122	−	4.64838i	0.817478	−	0.471971i	−0.0320681	−	0.999486i	$-0.510209\pi$
$97$	8.05122	−	4.64838i	0.817478	−	0.471971i	0.849546	+	0.527515i	$0.176876\pi$
$98$	0.531647	−	0.306946i	0.0537044	−	0.0310063i
$99$		0			0
$100$	−6.44702	+	7.41855i	−0.644702	+	0.741855i
$101$	3.19004	−	5.52531i	0.317421	−	0.549789i	−0.662528	−	0.749037i	$-0.730517\pi$
$101$	3.19004	−	5.52531i	0.317421	−	0.549789i	0.979949	+	0.199248i	$0.0638500\pi$
$102$		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	−0.997286	−	0.0736305i	$-0.976541\pi$
$107$	−16.1336	−	9.31474i	−1.55969	−	0.900490i	−0.562409	−	0.826859i	$-0.690125\pi$
$108$		0			0
$109$	−10.6581			−1.02086			−0.510432	−	0.859918i	$-0.670514\pi$
$109$	−10.6581			−1.02086			−0.510432	+	0.859918i	$0.670514\pi$
$110$	−0.155402	+	1.61511i	−0.0148170	+	0.153994i
$111$		0			0
$112$			7.28622i			0.688483i
$113$	−2.83241	+	1.63529i	−0.266451	+	0.153835i	−0.627274	−	0.778799i	$-0.715829\pi$
$113$	−2.83241	+	1.63529i	−0.266451	+	0.153835i	0.360823	+	0.932634i	$0.382496\pi$
$114$		0			0
$115$	−12.3142	+	5.61295i	−1.14830	+	0.523410i
$116$	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	$-0.0735285\pi$
$127$	14.2207	+	8.21033i	1.26188	+	0.728549i	0.288445	+	0.957497i	$0.406862\pi$
$128$	−4.91504	−	2.83770i	−0.434432	−	0.250819i
$129$		0			0
$130$	−0.678338	+	1.33030i	−0.0594942	+	0.116675i
$131$	−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	$-0.514886\pi$
$137$	9.30474	−	5.37210i	0.794958	−	0.458969i	0.841705	+	0.539938i	$0.181552\pi$
$138$		0			0
$139$	6.65468	+	11.5263i	0.564443	+	0.977644i	0.997101	+	0.0760858i	$0.0242423\pi$
$139$	6.65468	+	11.5263i	0.564443	+	0.977644i	−0.432658	+	0.901558i	$0.642424\pi$
$140$	7.67823	−	3.49982i	0.648929	−	0.295789i
$141$		0			0
$142$			2.08615i			0.175066i
$143$	−2.08263	−	13.9713i	−0.174158	−	1.16834i
$144$		0			0
$145$	−9.22069	−	20.2292i	−0.765737	−	1.67994i
$146$	−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	0.891812	−	0.452406i	$-0.149434\pi$
$149$	0.660511	+	1.14404i	0.0541112	+	0.0937233i	−0.837701	+	0.546129i	$0.816101\pi$
$150$		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
$160$	−0.465156	+	4.83439i	−0.0367738	+	0.382192i
$161$	11.6188			0.915693
$162$		0			0
$163$	2.49562	−	1.44085i	0.195472	−	0.112856i	−0.399070	−	0.916921i	$-0.630667\pi$
$163$	2.49562	−	1.44085i	0.195472	−	0.112856i	0.594542	+	0.804065i	$0.297334\pi$
$164$	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	$-0.453035\pi$
$167$	−8.22025	−	4.74597i	−0.636102	−	0.367254i	−0.783112	+	0.621881i	$0.786369\pi$
$168$		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	$-0.815398\pi$
$173$	−10.2617	+	5.92457i	−0.780179	+	0.450437i	0.0563146	+	0.998413i	$0.482065\pi$
$174$		0			0
$175$	−7.24526	−	6.29642i	−0.547690	−	0.475965i
$176$	−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	−0.654745	−	0.755850i	$-0.727224\pi$
$179$	4.37781	−	7.58260i	0.327213	−	0.566750i	0.981958	+	0.189100i	$0.0605572\pi$
$180$		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
$185$	−20.7137	+	9.44153i	−1.52290	+	0.694155i
$186$		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	0.559460	−	0.828858i	$-0.311009\pi$
$191$	−6.05441	−	10.4865i	−0.438082	−	0.758780i	−0.997542	+	0.0700776i	$0.977675\pi$
$192$		0			0
$193$	2.07910	+	1.20037i	0.149657	+	0.0864044i	0.572958	−	0.819584i	$-0.305796\pi$
$193$	2.07910	+	1.20037i	0.149657	+	0.0864044i	−0.423302	+	0.905989i	$0.639129\pi$
$194$	−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	$-0.235270\pi$
$197$	7.37151	+	4.25594i	0.525199	+	0.303224i	−0.213860	+	0.976864i	$0.568604\pi$
$198$		0			0
$199$	−0.802884	−	1.39064i	−0.0569149	−	0.0985795i	0.836164	−	0.548479i	$-0.184793\pi$
$199$	−0.802884	−	1.39064i	−0.0569149	−	0.0985795i	−0.893079	+	0.449900i	$0.851460\pi$
$200$	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
$205$	−5.18834	−	11.3826i	−0.362369	−	0.794999i
$206$	−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	−0.914318	−	0.404996i	$-0.867273\pi$
$211$	−1.54587	+	2.67753i	−0.106422	+	0.184329i	0.807896	+	0.589325i	$0.200606\pi$
$212$	−12.8145	+	7.39845i	−0.880102	+	0.508127i
$213$		0			0
$214$	1.72525	+	2.98822i	0.117936	+	0.204270i
$215$	1.88620	−	19.6034i	0.128638	−	1.33694i
$216$		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	$-0.116196\pi$
$223$	16.3071	+	9.41489i	1.09200	+	0.630468i	0.157893	+	0.987456i	$0.449530\pi$
$224$	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	$-0.654755\pi$
$227$	0.976316	−	0.563676i	0.0648004	−	0.0374125i	0.532050	+	0.846713i	$0.321422\pi$
$228$		0			0
$229$	−0.238960			−0.0157909			−0.00789547	−	0.999969i	$-0.502513\pi$
$229$	−0.238960			−0.0157909			−0.00789547	+	0.999969i	$0.502513\pi$
$230$	2.49503	+	0.240067i	0.164518	+	0.0158296i
$231$		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	0.866277	+	0.499563i	$0.166506\pi$
$241$	13.4404	+	23.2795i	0.865773	+	1.49956i	−0.000504148		1.00000i	$0.500160\pi$
$242$			0.805463i			0.0517772i
$243$		0			0
$244$	−8.61076	+	14.9143i	−0.551248	+	0.954789i
$245$	−3.07391	−	6.74381i	−0.196385	−	0.430847i
$246$		0			0
$247$	−4.33129	−	1.70803i	−0.275594	−	0.108679i
$248$			3.00171i			0.190609i
$249$		0			0
$250$	−1.42575	−	1.50180i	−0.0901726	−	0.0949819i
$251$	12.2567	+	21.2292i	0.773636	+	1.33998i	0.935558	+	0.353173i	$0.114897\pi$
$251$	12.2567	+	21.2292i	0.773636	+	1.33998i	−0.161922	+	0.986804i	$0.551769\pi$
$252$		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	$-0.00988684\pi$
$257$	23.6041	+	13.6278i	1.47238	+	0.850080i	0.472864	+	0.881135i	$0.343220\pi$
$258$		0			0
$259$	19.5440			1.21441
$260$	−13.2939	+	8.62732i	−0.824450	+	0.535044i
$261$		0			0
$262$	2.43508	+	1.40589i	0.150439	+	0.0868562i
$263$	−17.1987	−	9.92967i	−1.06052	−	0.612290i	−0.134941	−	0.990854i	$-0.543085\pi$
$263$	−17.1987	−	9.92967i	−1.06052	−	0.612290i	−0.925575	+	0.378564i	$0.876418\pi$
$264$		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	0.952240	+	0.305351i	$0.0987737\pi$
$269$	12.1461	+	21.0377i	0.740561	+	1.28269i	−0.211678	+	0.977339i	$0.567893\pi$
$270$		0			0
$271$	4.45413	−	7.71477i	0.270569	−	0.468639i	−0.698439	−	0.715670i	$-0.746122\pi$
$271$	4.45413	−	7.71477i	0.270569	−	0.468639i	0.969008	+	0.247031i	$0.0794549\pi$
$272$			12.6419i			0.766527i
$273$		0			0
$274$	−1.99001			−0.120221
$275$	19.2294	+	3.73500i	1.15957	+	0.225229i
$276$		0			0
$277$	16.5880	−	9.57707i	0.996674	−	0.575430i	0.0894116	−	0.995995i	$-0.471501\pi$
$277$	16.5880	−	9.57707i	0.996674	−	0.575430i	0.907263	+	0.420565i	$0.138168\pi$
$278$		−	2.46512i		−	0.147848i
$279$		0			0
$280$	−3.13859	−	0.301989i	−0.187567	−	0.0180473i
$281$	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	$-0.445571\pi$
$283$	−10.0625	−	5.80959i	−0.598154	−	0.345344i	−0.768315	+	0.640072i	$0.778905\pi$
$284$	−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
$290$	−0.394372	+	4.09873i	−0.0231583	+	0.240686i
$291$		0			0
$292$	−2.85160	+	1.64637i	−0.166877	+	0.0963465i
$293$	26.8933	−	15.5268i	1.57112	−	0.907087i	0.575089	−	0.818091i	$-0.304967\pi$
$293$	26.8933	−	15.5268i	1.57112	−	0.907087i	0.996032	−	0.0889965i	$-0.0283660\pi$
$294$		0			0
$295$	12.3510	+	1.18839i	0.719101	+	0.0691905i
$296$	−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
$305$	19.5002	+	1.87627i	1.11658	+	0.107435i
$306$		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
$310$	1.54008	−	0.701986i	0.0874707	−	0.0398701i
$311$	−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
$325$	15.2022	+	9.68991i	0.843264	+	0.537500i
$326$	−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	−0.999920	−	0.0126160i	$-0.995984\pi$
$331$	−9.29476	−	16.0990i	−0.510886	−	0.884881i	0.489034	−	0.872265i	$-0.337349\pi$
$332$	19.4199	−	11.2121i	1.06581	−	0.615343i
$333$		0			0
$334$	0.879033	+	1.52253i	0.0480986	+	0.0833092i
$335$	−9.62717	+	4.38817i	−0.525988	+	0.239751i
$336$		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
$340$	13.3220	−	6.07234i	0.722489	−	0.329319i
$341$	−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	$-0.562122\pi$
$347$	10.4073	−	6.00868i	0.558695	−	0.322563i	0.752622	+	0.658453i	$0.228789\pi$
$348$		0			0
$349$	5.24389	−	9.08268i	0.280699	−	0.486185i	−0.690858	−	0.722990i	$-0.742767\pi$
$349$	5.24389	−	9.08268i	0.280699	−	0.486185i	0.971557	+	0.236806i	$0.0761005\pi$
$350$	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	$-0.0118135\pi$
$353$	27.5593	+	15.9114i	1.46683	+	0.846877i	0.467522	+	0.883981i	$0.345147\pi$
$354$		0			0
$355$	25.0697	+	2.41215i	1.33056	+	0.128024i
$356$	−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	$-0.570175\pi$
$367$	−22.4730	−	12.9748i	−1.17308	−	0.677280i	−0.954404	+	0.298517i	$0.903508\pi$
$368$	−19.8927	+	11.4851i	−1.03698	+	0.598700i
$369$		0			0
$370$	4.19689	+	0.403817i	0.218186	+	0.0209934i
$371$	−7.22563	−	12.5152i	−0.375136	−	0.649754i
$372$		0			0
$373$	11.7359	−	6.77570i	0.607660	−	0.350833i	−0.164389	−	0.986396i	$-0.552565\pi$
$373$	11.7359	−	6.77570i	0.607660	−	0.350833i	0.772049	+	0.635563i	$0.219232\pi$
$374$	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	−0.927774	−	0.373142i	$-0.878281\pi$
$379$	−2.73986	+	4.74557i	−0.140737	+	0.243764i	0.787037	+	0.616905i	$0.211614\pi$
$380$	2.35412	+	5.16467i	0.120764	+	0.264942i
$381$		0			0
$382$			2.24276i			0.114750i
$383$	−17.3693	+	10.0282i	−0.887529	+	0.512415i	−0.873133	−	0.487481i	$-0.837916\pi$
$383$	−17.3693	+	10.0282i	−0.887529	+	0.512415i	−0.0143954	+	0.999896i	$0.504582\pi$
$384$		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	$-0.517329\pi$
$397$	15.6036	−	9.00873i	0.783121	−	0.452135i	0.837535	+	0.546383i	$0.183996\pi$
$398$			0.297415i			0.0149081i
$399$		0			0
$400$	18.6286	+	3.61831i	0.931429	+	0.180916i
$401$	−1.65394	+	2.86471i	−0.0825938	+	0.143057i	−0.904363	−	0.426763i	$-0.859654\pi$
$401$	−1.65394	+	2.86471i	−0.0825938	+	0.143057i	0.821770	+	0.569820i	$0.192987\pi$
$402$		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	0.999303	+	0.0373220i	$0.0118827\pi$
$409$	10.7585	+	18.6343i	0.531973	+	0.921405i	−0.467330	+	0.884083i	$0.654784\pi$
$410$	−0.221907	+	2.30629i	−0.0109592	+	0.113900i
$411$		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	−0.999779	−	0.0210321i	$-0.993305\pi$
$419$	−9.85964	+	17.0774i	−0.481675	+	0.834286i	0.518104	+	0.855318i	$0.326638\pi$
$420$		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
$425$	−12.5708	−	10.9245i	−0.609775	−	0.529919i
$426$		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	0.0437002	−	0.999045i	$-0.486085\pi$
$431$	18.4156	−	31.8968i	0.887048	−	1.53641i	0.843348	−	0.537368i	$-0.180581\pi$
$432$		0			0
$433$	−5.69241	+	3.28652i	−0.273560	+	0.157940i	−0.630504	−	0.776186i	$-0.717152\pi$
$433$	−5.69241	+	3.28652i	−0.273560	+	0.157940i	0.356944	+	0.934126i	$0.383819\pi$
$434$	−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	0.347392	+	0.937720i	$0.387067\pi$
$439$	−13.3758	+	23.1676i	−0.638394	+	1.10573i	−0.985785	+	0.168010i	$0.946266\pi$
$440$	5.85505	−	2.66880i	0.279129	−	0.127230i
$441$		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
$445$	3.30365	+	7.24785i	0.156608	+	0.343581i
$446$	−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	0.549086	−	0.835766i	$-0.314976\pi$
$449$	−9.51947	−	16.4882i	−0.449252	−	0.778127i	−0.998337	+	0.0576392i	$0.981643\pi$
$450$		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
$455$	−8.42580	−	12.9833i	−0.395007	−	0.608668i
$456$		0			0
$457$	−18.7529	−	10.8270i	−0.877225	−	0.506466i	−0.00748246	−	0.999972i	$-0.502382\pi$
$457$	−18.7529	−	10.8270i	−0.877225	−	0.506466i	−0.869742	+	0.493506i	$0.835715\pi$
$458$	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	0.940695	−	0.339253i	$-0.110174\pi$
$461$	3.79060	+	6.56551i	0.176546	+	0.305786i	−0.764149	+	0.645039i	$0.776841\pi$
$462$		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
$470$	1.69686	+	3.72273i	0.0782705	+	0.171717i
$471$		0			0
$472$	3.52978	−	2.03792i	0.162471	−	0.0938028i
$473$		−	34.5052i		−	1.58655i
$474$		0			0
$475$	4.23521	−	4.87344i	0.194325	−	0.223609i
$476$	−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	−0.580788	−	0.814055i	$-0.697256\pi$
$479$	9.07391	−	15.7165i	0.414598	−	0.718104i	0.995386	+	0.0959503i	$0.0305890\pi$
$480$		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
$485$	−1.99100	+	20.6926i	−0.0904068	+	0.939603i
$486$		0			0
$487$	−23.1050	+	13.3397i	−1.04699	+	0.604478i	−0.921804	−	0.387656i	$-0.873285\pi$
$487$	−23.1050	+	13.3397i	−1.04699	+	0.604478i	−0.125182	+	0.992134i	$0.539951\pi$
$488$	5.57296	−	3.21755i	0.252276	−	0.145652i
$489$		0			0
$490$	−0.131472	+	1.36640i	−0.00593930	+	0.0617274i
$491$	10.8984	−	18.8766i	0.491837	−	0.851887i	−0.508118	−	0.861287i	$-0.669659\pi$
$491$	10.8984	−	18.8766i	0.491837	−	0.851887i	0.999956	+	0.00939990i	$0.00299213\pi$
$492$		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	$0.577637\pi$
$500$	−5.13497	−	21.3688i	−0.229643	−	0.955643i
$501$		0			0
$502$		−	4.54030i		−	0.202643i
$503$	−6.97584	+	4.02750i	−0.311037	+	0.179577i	−0.647391	−	0.762158i	$-0.724140\pi$
$503$	−6.97584	+	4.02750i	−0.311037	+	0.179577i	0.336353	+	0.941736i	$0.390806\pi$
$504$		0			0
$505$	5.91704	+	12.9813i	0.263305	+	0.577662i
$506$	4.39167			0.195233
$507$		0			0
$508$		−	32.2780i		−	1.43210i
$509$	12.8439	−	22.2463i	0.569296	−	0.986050i	−0.427339	−	0.904091i	$-0.640549\pi$
$509$	12.8439	−	22.2463i	0.569296	−	0.986050i	0.996636	−	0.0819589i	$-0.0261176\pi$
$510$		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
$520$	5.91382	−	0.308107i	0.259338	−	0.0135114i
$521$	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	$-0.0734471\pi$
$523$	28.8652	+	16.6653i	1.26219	+	0.728724i	0.288690	+	0.957423i	$0.406780\pi$
$524$	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
$530$	−1.29305	−	2.83680i	−0.0561663	−	0.123223i
$531$		0			0
$532$		−	4.87304i		−	0.211273i
$533$	−2.97388	−	19.9503i	−0.128813	−	0.864142i
$534$		0			0
$535$	37.9048	−	17.2775i	1.63877	−	0.746969i
$536$	−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
$550$	−2.73855	−	2.37991i	−0.116772	−	0.101480i
$551$	−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	$-0.324196\pi$
$557$	1.17326	+	0.677380i	0.0497125	+	0.0287015i	−0.474938	+	0.880019i	$0.657529\pi$
$558$		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	$-0.680911\pi$
$563$	−1.83848	+	1.06145i	−0.0774827	+	0.0447347i	0.460758	+	0.887526i	$0.347578\pi$
$564$		0			0
$565$	0.700432	−	7.27963i	0.0294674	−	0.306256i
$566$	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	−0.805702	−	0.592321i	$-0.798212\pi$
$569$	2.62664	−	4.54947i	0.110114	−	0.190724i	0.915816	+	0.401598i	$0.131545\pi$
$570$		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
$575$	5.76988	−	29.7057i	0.240620	−	1.23882i
$576$		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	$-0.216260\pi$
$587$	15.0887	+	8.71149i	0.622779	+	0.359562i	−0.155171	+	0.987888i	$0.549593\pi$
$588$		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
$595$	5.93049	+	13.0109i	0.243127	+	0.533393i
$596$	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	−0.835398	−	0.549645i	$-0.814763\pi$
$601$	1.42944	−	2.47586i	0.0583079	−	0.100992i	0.893706	+	0.448653i	$0.148096\pi$
$602$	2.71213	−	1.56585i	0.110538	−	0.0638192i
$603$		0			0
$604$	−5.42444	−	9.39540i	−0.220717	−	0.382294i
$605$	9.67941	+	0.931335i	0.393524	+	0.0378641i
$606$		0			0
$607$	−21.5745	+	12.4560i	−0.875682	+	0.505575i	−0.869232	−	0.494404i	$-0.835386\pi$
$607$	−21.5745	+	12.4560i	−0.875682	+	0.505575i	−0.00645001	+	0.999979i	$0.502053\pi$
$608$	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	$-0.392372\pi$
$613$	−7.90832	−	4.56587i	−0.319414	−	0.184414i	−0.651131	+	0.758965i	$0.725705\pi$
$614$	−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	$-0.726840\pi$
$617$	−8.08476	+	4.66774i	−0.325480	+	0.187916i	0.328353	+	0.944555i	$0.393507\pi$
$618$		0			0
$619$	−28.7730			−1.15648			−0.578242	−	0.815865i	$-0.696261\pi$
$619$	−28.7730			−1.15648			−0.578242	+	0.815865i	$0.696261\pi$
$620$	17.8800	+	1.72038i	0.718080	+	0.0690923i
$621$		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	0.935472	+	0.353400i	$0.114975\pi$
$631$	19.4374	+	33.6665i	0.773790	+	1.34024i	−0.161683	+	0.986843i	$0.551692\pi$
$632$			0.709316i			0.0282151i
$633$		0			0
$634$	−0.632604	+	1.09570i	−0.0251239	+	0.0435159i
$635$	−33.4106	+	15.2289i	−1.32586	+	0.604342i
$636$		0			0
$637$	−1.76192	−	11.8198i	−0.0698098	−	0.468319i
$638$			7.21443i			0.285622i
$639$		0			0
$640$	11.5476	−	5.26350i	0.456457	−	0.208058i
$641$	−3.79991	−	6.58164i	−0.150087	−	0.259959i	0.781172	−	0.624316i	$-0.214622\pi$
$641$	−3.79991	−	6.58164i	−0.150087	−	0.259959i	−0.931259	+	0.364357i	$0.881289\pi$
$642$		0			0
$643$	29.7637	−	17.1841i	1.17377	−	0.677675i	0.219203	−	0.975679i	$-0.429654\pi$
$643$	29.7637	−	17.1841i	1.17377	−	0.677675i	0.954564	+	0.298005i	$0.0963211\pi$
$644$	−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	$-0.443171\pi$
$647$	−14.9026	−	8.60403i	−0.585882	−	0.338259i	−0.763468	+	0.645846i	$0.776505\pi$
$648$		0			0
$649$	21.7397			0.853358
$650$	−1.54110	−	2.96214i	−0.0604468	−	0.116185i
$651$		0			0
$652$	−4.90563	−	2.83227i	−0.192119	−	0.110920i
$653$	−20.3301	−	11.7376i	−0.795578	−	0.459327i	0.0463449	−	0.998925i	$-0.485243\pi$
$653$	−20.3301	−	11.7376i	−0.795578	−	0.459327i	−0.841922	+	0.539599i	$0.818576\pi$
$654$		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	0.750505	−	0.660864i	$-0.229810\pi$
$659$	−5.05905	−	8.76254i	−0.197073	−	0.341340i	−0.947578	+	0.319524i	$0.896477\pi$
$660$		0			0
$661$	−2.75291	+	4.76818i	−0.107076	+	0.185461i	−0.914584	−	0.404395i	$-0.867482\pi$
$661$	−2.75291	+	4.76818i	−0.107076	+	0.185461i	0.807509	+	0.589856i	$0.200815\pi$
$662$			3.44309i			0.133820i
$663$		0			0
$664$	−8.37915			−0.325174
$665$	−5.04403	+	2.29913i	−0.195599	+	0.0891563i
$666$		0			0
$667$	−52.1107	+	30.0861i	−2.01774	+	1.16494i
$668$			18.6582i			0.721909i
$669$		0			0
$670$	1.95060	+	0.187683i	0.0753584	+	0.00725084i
$671$	34.3236			1.32505
$672$		0			0
$673$	29.2998	+	16.9162i	1.12942	+	0.652073i	0.943790	−	0.330546i	$-0.107233\pi$
$673$	29.2998	+	16.9162i	1.12942	+	0.652073i	0.185633	+	0.982619i	$0.440566\pi$
$674$	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
$680$	−5.44559	−	0.523964i	−0.208829	−	0.0200931i
$681$		0			0
$682$	2.56813	−	1.48271i	0.0983387	−	0.0567759i
$683$	6.69626	−	3.86609i	0.256225	−	0.147932i	−0.366386	−	0.930463i	$-0.619405\pi$
$683$	6.69626	−	3.86609i	0.256225	−	0.147932i	0.622611	+	0.782531i	$0.286072\pi$
$684$		0			0
$685$	−2.30099	+	23.9143i	−0.0879162	+	0.913718i
$686$	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	0.168516	+	0.985699i	$0.446103\pi$
$691$	−20.2247	+	35.0301i	−0.769382	+	1.33261i	−0.937898	+	0.346910i	$0.887231\pi$
$692$	20.1713	+	11.6459i	0.766797	+	0.442710i
$693$		0			0
$694$	−2.22582			−0.0844909
$695$	−29.6238	−	2.85035i	−1.12370	−	0.108120i
$696$		0			0
$697$			18.6342i			0.705820i
$698$	−1.68227	+	0.971257i	−0.0636747	+	0.0367626i
$699$		0			0
$700$	−3.59767	+	18.5223i	−0.135979	+	0.700078i
$701$	−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	−0.979464	−	0.201619i	$-0.935380\pi$
$709$	−17.6894	−	30.6389i	−0.664339	−	1.15067i	0.315125	−	0.949050i	$-0.397953\pi$
$710$	−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
$715$	28.1388	+	14.3483i	1.05233	+	0.536598i
$716$	−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	−0.948817	−	0.315826i	$-0.897718\pi$
$719$	−20.0549	−	34.7361i	−0.747922	−	1.29544i	0.200895	−	0.979613i	$-0.435615\pi$
$720$		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
$725$	48.7992	+	9.47849i	1.81236	+	0.352022i
$726$		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
$730$	−0.287741	−	0.631271i	−0.0106498	−	0.0233644i
$731$	−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	−0.994973	−	0.100146i	$-0.968069\pi$
$739$	−11.1663	+	19.3405i	−0.410757	+	0.711452i	0.584216	+	0.811599i	$0.301402\pi$
$740$	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	$-0.373830\pi$
$743$	−5.99031	−	3.45851i	−0.219763	−	0.126880i	−0.605841	+	0.795586i	$0.707163\pi$
$744$		0			0
$745$	−2.94032	−	0.282912i	−0.107725	−	0.0103651i
$746$	−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	−0.703449	−	0.710746i	$-0.748357\pi$
$751$	7.22928	−	12.5215i	0.263800	−	0.456915i	0.967249	+	0.253831i	$0.0816908\pi$
$752$	−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	$-0.498577\pi$
$757$	−23.6428	−	13.6502i	−0.859313	−	0.496125i	−0.863782	+	0.503865i	$0.831911\pi$
$758$	0.878961	−	0.507468i	0.0319253	−	0.0184321i
$759$		0			0
$760$	0.203130	−	2.11114i	0.00736829	−	0.0765790i
$761$	0.207699	+	0.359744i	0.00752907	+	0.0130407i	0.869765	−	0.493465i	$-0.164270\pi$
$761$	0.207699	+	0.359744i	0.00752907	+	0.0130407i	−0.862236	+	0.506506i	$0.830937\pi$
$762$		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	−0.937215	−	0.348751i	$-0.886606\pi$
$769$	−4.61941	+	8.00105i	−0.166580	+	0.288525i	0.770635	+	0.637277i	$0.219939\pi$
$770$	1.29196	+	2.83441i	0.0465588	+	0.102145i
$771$		0			0
$772$		−	4.71911i		−	0.169845i
$773$	14.7907	−	8.53943i	0.531986	−	0.307142i	−0.209839	−	0.977736i	$-0.567294\pi$
$773$	14.7907	−	8.53943i	0.531986	−	0.307142i	0.741825	+	0.670594i	$0.233961\pi$
$774$		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	$-0.776693\pi$
$787$	−16.4631	+	9.50498i	−0.586847	+	0.338816i	0.177003	+	0.984210i	$0.443360\pi$
$788$		−	16.7318i		−	0.596045i
$789$		0			0
$790$	0.363927	−	0.165882i	0.0129480	−	0.00590182i
$791$	−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	0.578180	−	0.815910i	$-0.303763\pi$
$797$	44.4322	−	25.6529i	1.57387	−	0.908673i	0.995688	−	0.0927635i	$-0.0295700\pi$
$798$		0			0
$799$	16.4520	+	28.4957i	0.582029	+	1.00810i
$800$	−8.19711	−	7.12362i	−0.289812	−	0.251858i
$801$		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	−0.996631	−	0.0820139i	$-0.973865\pi$
$809$	−12.1534	+	21.0502i	−0.427289	+	0.740087i	0.569342	+	0.822101i	$0.307198\pi$
$810$		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
$815$	−0.617147	+	6.41404i	−0.0216177	+	0.224674i
$816$		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	−0.695715	−	0.718318i	$-0.744912\pi$
$821$	7.85738	−	13.6094i	0.274224	−	0.474971i	0.969939	+	0.243348i	$0.0782456\pi$
$822$		0			0
$823$	27.9486	−	16.1361i	0.974228	−	0.562471i	0.0737051	−	0.997280i	$-0.476518\pi$
$823$	27.9486	−	16.1361i	0.974228	−	0.562471i	0.900522	+	0.434810i	$0.143184\pi$
$824$	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	−0.869046	−	0.494731i	$-0.835267\pi$
$829$	−0.174879	+	0.302900i	−0.00607382	+	0.0105202i	0.862973	+	0.505251i	$0.168600\pi$
$830$	1.95957	+	4.29907i	0.0680175	+	0.149223i
$831$		0			0
$832$	−20.2898	+	16.1268i	−0.703424	+	0.559095i
$833$			11.0401i			0.382516i
$834$		0			0
$835$	19.3129	−	8.80306i	0.668352	−	0.304642i
$836$	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	0.984132	+	0.177439i	$0.0567814\pi$
$839$	18.7040	+	32.3962i	0.645733	+	1.11844i	−0.338399	+	0.941003i	$0.609885\pi$
$840$		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
$845$	19.2467	+	21.7845i	0.662107	+	0.749409i
$846$		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	$0.580266\pi$
$860$	−35.2255	+	16.0562i	−1.20118	+	0.547512i
$861$		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
$865$	2.53762	−	26.3737i	0.0862818	−	0.896732i
$866$	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
$875$	20.8697	−	5.01502i	0.705524	−	0.169539i
$876$		0			0
$877$	32.5853	−	18.8131i	1.10033	−	0.635275i	0.164021	−	0.986457i	$-0.447554\pi$
$877$	32.5853	−	18.8131i	1.10033	−	0.635275i	0.936307	+	0.351182i	$0.114220\pi$
$878$	4.29104	−	2.47743i	0.144815	−	0.0836092i
$879$		0			0
$880$	33.0957	+	3.18441i	1.11566	+	0.107346i
$881$	−21.7182	+	37.6169i	−0.731703	+	1.26735i	0.224452	+	0.974485i	$0.427941\pi$
$881$	−21.7182	+	37.6169i	−0.731703	+	1.26735i	−0.956155	+	0.292862i	$0.905392\pi$
$882$		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	$-0.464165\pi$
$887$	−20.6104	−	11.8994i	−0.692031	−	0.399544i	−0.804372	+	0.594125i	$0.797498\pi$
$888$		0			0
$889$	31.5240			1.05728
$890$	0.141298	−	1.46852i	0.00473632	−	0.0492249i
$891$		0			0
$892$		−	37.0136i		−	1.23931i
$893$	−11.0472	+	6.37808i	−0.369679	+	0.213434i
$894$		0			0
$895$	8.12019	+	17.8148i	0.271428	+	0.595483i
$896$	−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	$-0.355881\pi$
$907$	−3.69191	−	2.13152i	−0.122588	−	0.0707761i	−0.560040	+	0.828466i	$0.689214\pi$
$908$	−1.91914	−	1.10802i	−0.0636889	−	0.0367708i
$909$		0			0
$910$	0.149154	+	2.86286i	0.00494440	+	0.0949028i
$911$	−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	0.999828	−	0.0185533i	$-0.00590603\pi$
$919$	14.6678	+	25.4054i	0.483846	+	0.838046i	−0.515982	+	0.856600i	$0.672573\pi$
$920$	−4.12279	−	9.04495i	−0.135924	−	0.298203i
$921$		0			0
$922$		−	1.40417i		−	0.0462438i
$923$	37.7789	+	14.8980i	1.24351	+	0.490374i
$924$		0			0
$925$	9.70550	−	49.9680i	0.319115	−	1.64294i
$926$	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	0.976616	−	0.214992i	$-0.0689726\pi$
$929$	9.20844	+	15.9495i	0.302119	+	0.523286i	−0.674497	+	0.738278i	$0.735639\pi$
$930$		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
$940$	−4.15857	+	43.2203i	−0.135638	+	1.40969i
$941$	−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	$-0.0116044\pi$
$947$	45.1580	+	26.0720i	1.46744	+	0.847226i	0.468103	+	0.883674i	$0.344938\pi$
$948$		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	$-0.587166\pi$
$953$	13.2161	−	7.63034i	0.428113	−	0.247171i	0.698542	+	0.715569i	$0.253832\pi$
$954$		0			0
$955$	26.9517	+	2.59324i	0.872136	+	0.0839152i
$956$	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
$965$	−4.88471	+	2.22650i	−0.157244	+	0.0716737i
$966$		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	0.948378	−	0.317143i	$-0.102723\pi$
$971$	6.21770	+	10.7694i	0.199535	+	0.345605i	−0.748843	+	0.662748i	$0.769390\pi$
$972$		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	$-0.310559\pi$
$977$	3.87017	+	2.23444i	0.123818	+	0.0714862i	−0.436812	+	0.899553i	$0.643892\pi$
$978$		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
$985$	−17.3189	+	7.89414i	−0.551826	+	0.251528i
$986$	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	0.155610	+	0.987819i	$0.450266\pi$
$991$	−24.4812	+	42.4027i	−0.777671	+	1.34697i	−0.933281	+	0.359147i	$0.883068\pi$
$992$	7.68700	−	4.43809i	0.244063	−	0.140910i
$993$		0			0
$994$	2.00247	+	3.46838i	0.0635145	+	0.110010i
$995$	3.57410	+	0.343893i	0.113307	+	0.0109021i
$996$		0			0
$997$	31.3681	−	18.1104i	0.993437	−	0.573561i	0.0871373	−	0.996196i	$-0.472228\pi$
$997$	31.3681	−	18.1104i	0.993437	−	0.573561i	0.906300	+	0.422635i	$0.138895\pi$
$998$	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.334.7	yes	32
3.2	odd	2	inner	585.2.bs.c.334.10	yes	32
5.4	even	2	inner	585.2.bs.c.334.9	yes	32
13.3	even	3	inner	585.2.bs.c.289.9	yes	32
15.14	odd	2	inner	585.2.bs.c.334.8	yes	32
39.29	odd	6	inner	585.2.bs.c.289.8	yes	32
65.29	even	6	inner	585.2.bs.c.289.7	✓	32
195.29	odd	6	inner	585.2.bs.c.289.10	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
585.2.bs.c.289.7	✓	32	65.29	even	6	inner
585.2.bs.c.289.8	yes	32	39.29	odd	6	inner
585.2.bs.c.289.9	yes	32	13.3	even	3	inner
585.2.bs.c.289.10	yes	32	195.29	odd	6	inner
585.2.bs.c.334.7	yes	32	1.1	even	1	trivial
585.2.bs.c.334.8	yes	32	15.14	odd	2	inner
585.2.bs.c.334.9	yes	32	5.4	even	2	inner
585.2.bs.c.334.10	yes	32	3.2	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-0.160403 - 0.0926085i) q^{2} +(-0.982847 - 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +O(q^{10})\)	\(q+(-0.160403 - 0.0926085i) q^{2} +(-0.982847 - 1.70234i) q^{4} +(-1.29836 + 1.82051i) q^{5} +(1.66258 - 0.959889i) q^{7} +0.734514i q^{8} +(0.376855 - 0.171775i) q^{10} +(-1.95887 + 3.39287i) q^{11} +(-2.82258 + 2.24344i) q^{13} -0.355576 q^{14} +(-1.89767 + 3.28687i) q^{16} +(2.88464 - 1.66545i) q^{17} +(0.645658 + 1.11831i) q^{19} +(4.37522 + 0.420975i) q^{20} +(0.628417 - 0.362817i) q^{22} +(5.24134 + 3.02609i) q^{23} +(-1.62851 - 4.72736i) q^{25} +(0.660511 - 0.0984590i) q^{26} +(-3.26812 - 1.88685i) q^{28} +(-4.97112 + 8.61024i) q^{29} +4.08666 q^{31} +(1.88100 - 1.08600i) q^{32} -0.616938 q^{34} +(-0.411142 + 4.27302i) q^{35} +(8.81645 + 5.09018i) q^{37} -0.239174i q^{38} +(-1.33719 - 0.953666i) q^{40} +(-2.79717 + 4.84485i) q^{41} +(-7.62743 + 4.40370i) q^{43} +7.70110 q^{44} +(-0.560483 - 0.970786i) q^{46} +9.87842i q^{47} +(-1.65723 + 2.87040i) q^{49} +(-0.176577 + 0.909095i) q^{50} +(6.59327 + 2.60004i) q^{52} -7.52756i q^{53} +(-3.63342 - 7.97133i) q^{55} +(0.705052 + 1.22119i) q^{56} +(1.59476 - 0.920737i) q^{58} +(-2.77451 - 4.80560i) q^{59} +(-4.38052 - 7.58728i) q^{61} +(-0.655511 - 0.378459i) q^{62} +7.18840 q^{64} +(-0.419471 - 8.05134i) q^{65} +(4.09765 + 2.36578i) q^{67} +(-5.67032 - 3.27376i) q^{68} +(0.461666 - 0.647328i) q^{70} +(-5.63164 - 9.75428i) q^{71} -1.67510i q^{73} +(-0.942788 - 1.63296i) q^{74} +(1.26917 - 2.19826i) q^{76} +7.52121i q^{77} +0.965695 q^{79} +(-3.51990 - 7.72227i) q^{80} +(0.897348 - 0.518084i) q^{82} +11.4078i q^{83} +(-0.713348 + 7.41387i) q^{85} +1.63128 q^{86} +(-2.49211 - 1.43882i) q^{88} +(1.78109 - 3.08493i) q^{89} +(-2.53930 + 6.43926i) q^{91} -11.8967i q^{92} +(0.914825 - 1.58452i) q^{94} +(-2.87420 - 0.276550i) q^{95} +(8.05122 - 4.64838i) q^{97} +(0.531647 - 0.306946i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 20 q^{4}+O(q^{10}) \) 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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more