LMFDB - Embedded newform 460.2.m.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(41,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("460.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.m (of order $11$, degree $10$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	460.81
Dual form			460.2.m.a.301.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.241946 - 1.68277i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(2.58157 + 2.97929i) q^{7} +(0.105306 + 0.0309206i) q^{9} +O(q^{10})$	\(q+(0.241946 - 1.68277i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(2.58157 + 2.97929i) q^{7} +(0.105306 + 0.0309206i) q^{9} +(1.84361 + 1.18481i) q^{11} +(2.08288 - 2.40377i) q^{13} +(0.241946 + 1.68277i) q^{15} +(0.820281 + 1.79617i) q^{17} +(0.904027 - 1.97954i) q^{19} +(5.63805 - 3.62336i) q^{21} +(-3.74040 - 3.00157i) q^{23} +(0.841254 - 0.540641i) q^{25} +(2.19622 - 4.80905i) q^{27} +(0.693399 + 1.51833i) q^{29} +(0.122568 + 0.852481i) q^{31} +(2.43982 - 2.81570i) q^{33} +(-3.31636 - 2.13129i) q^{35} +(1.64535 + 0.483119i) q^{37} +(-3.54104 - 4.08658i) q^{39} +(-1.93728 + 0.568838i) q^{41} +(1.39884 - 9.72914i) q^{43} -0.109752 q^{45} -6.47457 q^{47} +(-1.21546 + 8.45371i) q^{49} +(3.22099 - 0.945769i) q^{51} +(6.84462 + 7.89911i) q^{53} +(-2.10273 - 0.617417i) q^{55} +(-3.11239 - 2.00021i) q^{57} +(-8.37319 + 9.66318i) q^{59} +(1.26755 + 8.81598i) q^{61} +(0.179733 + 0.393561i) q^{63} +(-1.32129 + 2.89321i) q^{65} +(11.5834 - 7.44419i) q^{67} +(-5.95592 + 5.56801i) q^{69} +(2.28434 - 1.46806i) q^{71} +(0.192036 - 0.420501i) q^{73} +(-0.706236 - 1.54644i) q^{75} +(1.22949 + 8.55131i) q^{77} +(-6.61761 + 7.63713i) q^{79} +(-7.28416 - 4.68125i) q^{81} +(-7.69481 - 2.25940i) q^{83} +(-1.29309 - 1.49231i) q^{85} +(2.72277 - 0.799477i) q^{87} +(-0.0222007 + 0.154409i) q^{89} +12.5386 q^{91} +1.46418 q^{93} +(-0.309706 + 2.15405i) q^{95} +(-11.4900 + 3.37375i) q^{97} +(0.157508 + 0.181774i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9	$ 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) $ 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$1$	$1$	$e\left(\frac{10}{11}\right)$

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			0
$2$		0			0
$3$	0.241946	−	1.68277i	0.139687	−	0.971547i	−0.792578	−	0.609771i	$-0.791261\pi$
$3$	0.241946	−	1.68277i	0.139687	−	0.971547i	0.932265	−	0.361776i	$-0.117829\pi$
$4$		0			0
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$		0			0
$7$	2.58157	+	2.97929i	0.975741	+	1.12606i	0.992005	+	0.126197i	$0.0402772\pi$
$7$	2.58157	+	2.97929i	0.975741	+	1.12606i	−0.0162644	+	0.999868i	$0.505177\pi$
$8$		0			0
$9$	0.105306	+	0.0309206i	0.0351020	+	0.0103069i
$10$		0			0
$11$	1.84361	+	1.18481i	0.555868	+	0.357235i	0.788217	−	0.615398i	$-0.211005\pi$
$11$	1.84361	+	1.18481i	0.555868	+	0.357235i	−0.232348	+	0.972633i	$0.574641\pi$
$12$		0			0
$13$	2.08288	−	2.40377i	0.577686	−	0.666685i	−0.389420	−	0.921060i	$-0.627324\pi$
$13$	2.08288	−	2.40377i	0.577686	−	0.666685i	0.967106	+	0.254376i	$0.0818699\pi$
$14$		0			0
$15$	0.241946	+	1.68277i	0.0624701	+	0.434489i
$16$		0			0
$17$	0.820281	+	1.79617i	0.198947	+	0.435634i	0.982642	−	0.185512i	$-0.0593945\pi$
$17$	0.820281	+	1.79617i	0.198947	+	0.435634i	−0.783695	+	0.621146i	$0.786667\pi$
$18$		0			0
$19$	0.904027	−	1.97954i	0.207398	−	0.454138i	−0.777136	−	0.629333i	$-0.783328\pi$
$19$	0.904027	−	1.97954i	0.207398	−	0.454138i	0.984534	+	0.175195i	$0.0560555\pi$
$20$		0			0
$21$	5.63805	−	3.62336i	1.23032	−	0.790681i
$22$		0			0
$23$	−3.74040	−	3.00157i	−0.779927	−	0.625871i
$23$	−3.74040	−	3.00157i	−0.779927	−	0.625871i
$24$		0			0
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$		0			0
$27$	2.19622	−	4.80905i	0.422662	−	0.925502i
$28$		0			0
$29$	0.693399	+	1.51833i	0.128761	+	0.281947i	0.963022	−	0.269422i	$-0.0868327\pi$
$29$	0.693399	+	1.51833i	0.128761	+	0.281947i	−0.834261	+	0.551370i	$0.814105\pi$
$30$		0			0
$31$	0.122568	+	0.852481i	0.0220139	+	0.153110i	0.997863	−	0.0653335i	$-0.0208111\pi$
$31$	0.122568	+	0.852481i	0.0220139	+	0.153110i	−0.975850	+	0.218444i	$0.929902\pi$
$32$		0			0
$33$	2.43982	−	2.81570i	0.424718	−	0.490151i
$34$		0			0
$35$	−3.31636	−	2.13129i	−0.560567	−	0.360254i
$36$		0			0
$37$	1.64535	+	0.483119i	0.270494	+	0.0794243i	0.414167	−	0.910201i	$-0.364073\pi$
$37$	1.64535	+	0.483119i	0.270494	+	0.0794243i	−0.143673	+	0.989625i	$0.545891\pi$
$38$		0			0
$39$	−3.54104	−	4.08658i	−0.567020	−	0.654376i
$40$		0			0
$41$	−1.93728	+	0.568838i	−0.302553	+	0.0888376i	−0.429485	−	0.903074i	$-0.641305\pi$
$41$	−1.93728	+	0.568838i	−0.302553	+	0.0888376i	0.126932	+	0.991911i	$0.459487\pi$
$42$		0			0
$43$	1.39884	−	9.72914i	0.213321	−	1.48368i	−0.548640	−	0.836058i	$-0.684854\pi$
$43$	1.39884	−	9.72914i	0.213321	−	1.48368i	0.761962	−	0.647622i	$-0.224236\pi$
$44$		0			0
$45$	−0.109752			−0.0163608
$46$		0			0
$47$	−6.47457			−0.944413			−0.472206	−	0.881488i	$-0.656542\pi$
$47$	−6.47457			−0.944413			−0.472206	+	0.881488i	$0.656542\pi$
$48$		0			0
$49$	−1.21546	+	8.45371i	−0.173637	+	1.20767i
$50$		0			0
$51$	3.22099	−	0.945769i	0.451029	−	0.132434i
$52$		0			0
$53$	6.84462	+	7.89911i	0.940181	+	1.08503i	0.996243	+	0.0865993i	$0.0276000\pi$
$53$	6.84462	+	7.89911i	0.940181	+	1.08503i	−0.0560624	+	0.998427i	$0.517855\pi$
$54$		0			0
$55$	−2.10273	−	0.617417i	−0.283532	−	0.0832525i
$56$		0			0
$57$	−3.11239	−	2.00021i	−0.412246	−	0.264934i
$58$		0			0
$59$	−8.37319	+	9.66318i	−1.09010	+	1.25804i	−0.126130	+	0.992014i	$0.540256\pi$
$59$	−8.37319	+	9.66318i	−1.09010	+	1.25804i	−0.963966	+	0.266025i	$0.914290\pi$
$60$		0			0
$61$	1.26755	+	8.81598i	0.162293	+	1.12877i	0.894298	+	0.447472i	$0.147675\pi$
$61$	1.26755	+	8.81598i	0.162293	+	1.12877i	−0.732005	+	0.681299i	$0.761415\pi$
$62$		0			0
$63$	0.179733	+	0.393561i	0.0226442	+	0.0495840i
$64$		0			0
$65$	−1.32129	+	2.89321i	−0.163885	+	0.358859i
$66$		0			0
$67$	11.5834	−	7.44419i	1.41514	−	0.909453i	0.415137	−	0.909759i	$-0.363734\pi$
$67$	11.5834	−	7.44419i	1.41514	−	0.909453i	1.00000		0.000305859i	$9.73578e-5\pi$
$68$		0			0
$69$	−5.95592	+	5.56801i	−0.717009	+	0.670309i
$70$		0			0
$71$	2.28434	−	1.46806i	0.271101	−	0.174226i	−0.398026	−	0.917374i	$-0.630305\pi$
$71$	2.28434	−	1.46806i	0.271101	−	0.174226i	0.669127	+	0.743148i	$0.266668\pi$
$72$		0			0
$73$	0.192036	−	0.420501i	0.0224761	−	0.0492159i	−0.898061	−	0.439871i	$-0.855024\pi$
$73$	0.192036	−	0.420501i	0.0224761	−	0.0492159i	0.920537	+	0.390655i	$0.127751\pi$
$74$		0			0
$75$	−0.706236	−	1.54644i	−0.0815491	−	0.178568i
$76$		0			0
$77$	1.22949	+	8.55131i	0.140114	+	0.974513i
$78$		0			0
$79$	−6.61761	+	7.63713i	−0.744540	+	0.859245i	−0.994027	−	0.109133i	$-0.965192\pi$
$79$	−6.61761	+	7.63713i	−0.744540	+	0.859245i	0.249487	+	0.968378i	$0.419738\pi$
$80$		0			0
$81$	−7.28416	−	4.68125i	−0.809351	−	0.520138i
$82$		0			0
$83$	−7.69481	−	2.25940i	−0.844616	−	0.248001i	−0.169331	−	0.985559i	$-0.554161\pi$
$83$	−7.69481	−	2.25940i	−0.844616	−	0.248001i	−0.675284	+	0.737558i	$0.735979\pi$
$84$		0			0
$85$	−1.29309	−	1.49231i	−0.140256	−	0.161864i
$86$		0			0
$87$	2.72277	−	0.799477i	0.291911	−	0.0857129i
$88$		0			0
$89$	−0.0222007	+	0.154409i	−0.00235327	+	0.0163673i	−0.990964	−	0.134126i	$-0.957177\pi$
$89$	−0.0222007	+	0.154409i	−0.00235327	+	0.0163673i	0.988611	+	0.150494i	$0.0480863\pi$
$90$		0			0
$91$	12.5386			1.31440
$92$		0			0
$93$	1.46418			0.151829
$94$		0			0
$95$	−0.309706	+	2.15405i	−0.0317751	+	0.221001i
$96$		0			0
$97$	−11.4900	+	3.37375i	−1.16663	+	0.342553i	−0.807005	−	0.590545i	$-0.798913\pi$
$97$	−11.4900	+	3.37375i	−1.16663	+	0.342553i	−0.359623	+	0.933098i	$0.617095\pi$
$98$		0			0
$99$	0.157508	+	0.181774i	0.0158301	+	0.0182689i
$100$		0			0
$101$	−7.01280	−	2.05914i	−0.697800	−	0.204893i	−0.0864538	−	0.996256i	$-0.527554\pi$
$101$	−7.01280	−	2.05914i	−0.697800	−	0.204893i	−0.611346	+	0.791363i	$0.709372\pi$
$102$		0			0
$103$	0.320351	+	0.205877i	0.0315652	+	0.0202857i	0.556328	−	0.830963i	$-0.312210\pi$
$103$	0.320351	+	0.205877i	0.0315652	+	0.0202857i	−0.524763	+	0.851248i	$0.675846\pi$
$104$		0			0
$105$	−4.38885	+	5.06501i	−0.428308	+	0.494294i
$106$		0			0
$107$	−1.71641	−	11.9379i	−0.165932	−	1.15408i	−0.887187	−	0.461410i	$-0.847344\pi$
$107$	−1.71641	−	11.9379i	−0.165932	−	1.15408i	0.721255	−	0.692669i	$-0.243565\pi$
$108$		0			0
$109$	5.14715	+	11.2707i	0.493008	+	1.07954i	0.978679	+	0.205395i	$0.0658478\pi$
$109$	5.14715	+	11.2707i	0.493008	+	1.07954i	−0.485672	+	0.874141i	$0.661425\pi$
$110$		0			0
$111$	1.21106	−	2.65186i	0.114949	−	0.251703i
$112$		0			0
$113$	4.84902	−	3.11628i	0.456158	−	0.293155i	−0.292313	−	0.956323i	$-0.594425\pi$
$113$	4.84902	−	3.11628i	0.456158	−	0.293155i	0.748471	+	0.663168i	$0.230789\pi$
$114$		0			0
$115$	4.43453	+	1.82619i	0.413522	+	0.170293i
$116$		0			0
$117$	0.293665	−	0.188727i	0.0271494	−	0.0174478i
$118$		0			0
$119$	−3.23368	+	7.08077i	−0.296431	+	0.649094i
$120$		0			0
$121$	−2.57446	−	5.63729i	−0.234042	−	0.512481i
$122$		0			0
$123$	0.488505	+	3.39763i	0.0440470	+	0.306354i
$124$		0			0
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$		0			0
$127$	−8.09131	−	5.19997i	−0.717988	−	0.461423i	0.129949	−	0.991521i	$-0.458519\pi$
$127$	−8.09131	−	5.19997i	−0.717988	−	0.461423i	−0.847936	+	0.530098i	$0.822155\pi$
$128$		0			0
$129$	−16.0335	−	4.70785i	−1.41167	−	0.414503i
$130$		0			0
$131$	−7.25086	−	8.36794i	−0.633511	−	0.731110i	0.344703	−	0.938712i	$-0.387980\pi$
$131$	−7.25086	−	8.36794i	−0.633511	−	0.731110i	−0.978213	+	0.207602i	$0.933434\pi$
$132$		0			0
$133$	8.23143	−	2.41697i	0.713756	−	0.209578i
$134$		0			0
$135$	−0.752391	+	5.23299i	−0.0647555	+	0.450384i
$136$		0			0
$137$	−14.4697			−1.23623			−0.618114	−	0.786088i	$-0.712103\pi$
$137$	−14.4697			−1.23623			−0.618114	+	0.786088i	$0.712103\pi$
$138$		0			0
$139$	−17.1539			−1.45498			−0.727489	−	0.686119i	$-0.759313\pi$
$139$	−17.1539			−1.45498			−0.727489	+	0.686119i	$0.759313\pi$
$140$		0			0
$141$	−1.56649	+	10.8952i	−0.131923	+	0.917542i
$142$		0			0
$143$	6.68802	−	1.96378i	0.559280	−	0.164220i
$144$		0			0
$145$	−1.09308	−	1.26148i	−0.0907750	−	0.104760i
$146$		0			0
$147$	13.9316	+	4.09068i	1.14906	+	0.337393i
$148$		0			0
$149$	−8.68795	−	5.58341i	−0.711745	−	0.457411i	0.134012	−	0.990980i	$-0.457214\pi$
$149$	−8.68795	−	5.58341i	−0.711745	−	0.457411i	−0.845756	+	0.533569i	$0.820850\pi$
$150$		0			0
$151$	−10.0556	+	11.6047i	−0.818310	+	0.944380i	−0.999235	−	0.0391173i	$-0.987545\pi$
$151$	−10.0556	+	11.6047i	−0.818310	+	0.944380i	0.180925	+	0.983497i	$0.442091\pi$
$152$		0			0
$153$	0.0308420	+	0.214511i	0.00249343	+	0.0173422i
$154$		0			0
$155$	−0.357775	−	0.783419i	−0.0287372	−	0.0629257i
$156$		0			0
$157$	−7.26939	+	15.9177i	−0.580160	+	1.27037i	0.361048	+	0.932547i	$0.382419\pi$
$157$	−7.26939	+	15.9177i	−0.580160	+	1.27037i	−0.941208	+	0.337827i	$0.890308\pi$
$158$		0			0
$159$	14.9484	−	9.60676i	1.18549	−	0.761865i
$160$		0			0
$161$	−0.713551	−	18.8925i	−0.0562357	−	1.48894i
$162$		0			0
$163$	16.6127	−	10.6764i	1.30121	−	0.836237i	0.307867	−	0.951429i	$-0.400385\pi$
$163$	16.6127	−	10.6764i	1.30121	−	0.836237i	0.993343	+	0.115193i	$0.0367485\pi$
$164$		0			0
$165$	−1.54772	+	3.38903i	−0.120490	+	0.263835i
$166$		0			0
$167$	−1.97673	−	4.32843i	−0.152964	−	0.334944i	0.817600	−	0.575786i	$-0.195304\pi$
$167$	−1.97673	−	4.32843i	−0.152964	−	0.334944i	−0.970564	+	0.240842i	$0.922577\pi$
$168$		0			0
$169$	0.410370	+	2.85419i	0.0315669	+	0.219553i
$170$		0			0
$171$	0.156408	−	0.180505i	0.0119608	−	0.0138035i
$172$		0			0
$173$	−0.520223	−	0.334327i	−0.0395518	−	0.0254184i	0.520716	−	0.853730i	$-0.325665\pi$
$173$	−0.520223	−	0.334327i	−0.0395518	−	0.0254184i	−0.560267	+	0.828312i	$0.689302\pi$
$174$		0			0
$175$	3.78248	+	1.11064i	0.285928	+	0.0839562i
$176$		0			0
$177$	14.2350	+	16.4281i	1.06997	+	1.23481i
$178$		0			0
$179$	−16.2201	+	4.76264i	−1.21234	+	0.355976i	−0.824560	−	0.565774i	$-0.808577\pi$
$179$	−16.2201	+	4.76264i	−1.21234	+	0.355976i	−0.387784	+	0.921750i	$0.626759\pi$
$180$		0			0
$181$	2.95827	−	20.5752i	0.219886	−	1.52934i	−0.518566	−	0.855038i	$-0.673534\pi$
$181$	2.95827	−	20.5752i	0.219886	−	1.52934i	0.738452	−	0.674306i	$-0.235557\pi$
$182$		0			0
$183$	15.1419			1.11932
$184$		0			0
$185$	−1.71481			−0.126076
$186$		0			0
$187$	−0.615846	+	4.28330i	−0.0450351	+	0.313226i
$188$		0			0
$189$	19.9972	−	5.87171i	1.45458	−	0.427104i
$190$		0			0
$191$	8.29242	+	9.56996i	0.600019	+	0.692458i	0.971785	−	0.235868i	$-0.0757933\pi$
$191$	8.29242	+	9.56996i	0.600019	+	0.692458i	−0.371767	+	0.928326i	$0.621248\pi$
$192$		0			0
$193$	9.03665	+	2.65340i	0.650472	+	0.190996i	0.590290	−	0.807191i	$-0.299013\pi$
$193$	9.03665	+	2.65340i	0.650472	+	0.190996i	0.0601827	+	0.998187i	$0.480832\pi$
$194$		0			0
$195$	4.54893	+	2.92342i	0.325755	+	0.209350i
$196$		0			0
$197$	9.60682	−	11.0869i	0.684458	−	0.789906i	−0.302107	−	0.953274i	$-0.597690\pi$
$197$	9.60682	−	11.0869i	0.684458	−	0.789906i	0.986565	+	0.163367i	$0.0522356\pi$
$198$		0			0
$199$	−3.39975	−	23.6458i	−0.241002	−	1.67621i	−0.647122	−	0.762386i	$-0.724028\pi$
$199$	−3.39975	−	23.6458i	−0.241002	−	1.67621i	0.406120	−	0.913820i	$-0.366881\pi$
$200$		0			0
$201$	−9.72431	−	21.2933i	−0.685900	−	1.50191i
$202$		0			0
$203$	−2.73349	+	5.98551i	−0.191854	+	0.420101i
$204$		0			0
$205$	1.69855	−	1.09159i	0.118632	−	0.0762401i
$206$		0			0
$207$	−0.301076	−	0.431739i	−0.0209262	−	0.0300079i
$208$		0			0
$209$	4.01206	−	2.57840i	0.277520	−	0.178351i
$210$		0			0
$211$	−2.26444	+	4.95842i	−0.155890	+	0.341352i	−0.971421	−	0.237361i	$-0.923718\pi$
$211$	−2.26444	+	4.95842i	−0.155890	+	0.341352i	0.815531	+	0.578713i	$0.196445\pi$
$212$		0			0
$213$	−1.91771	−	4.19920i	−0.131400	−	0.287725i
$214$		0			0
$215$	1.39884	+	9.72914i	0.0954001	+	0.663522i
$216$		0			0
$217$	−2.22337	+	2.56590i	−0.150932	+	0.174185i
$218$		0			0
$219$	−0.661143	−	0.424891i	−0.0446759	−	0.0287115i
$220$		0			0
$221$	6.02610	+	1.76942i	0.405360	+	0.119024i
$222$		0			0
$223$	3.60267	+	4.15771i	0.241253	+	0.278421i	0.863444	−	0.504445i	$-0.168303\pi$
$223$	3.60267	+	4.15771i	0.241253	+	0.278421i	−0.622191	+	0.782865i	$0.713757\pi$
$224$		0			0
$225$	0.105306	−	0.0309206i	0.00702040	−	0.00206138i
$226$		0			0
$227$	3.29987	−	22.9511i	0.219020	−	1.52332i	−0.522646	−	0.852550i	$-0.675055\pi$
$227$	3.29987	−	22.9511i	0.219020	−	1.52332i	0.741666	−	0.670769i	$-0.234036\pi$
$228$		0			0
$229$	14.2193			0.939635			0.469818	−	0.882764i	$-0.344320\pi$
$229$	14.2193			0.939635			0.469818	+	0.882764i	$0.344320\pi$
$230$		0			0
$231$	14.6874			0.966357
$232$		0			0
$233$	−3.59061	+	24.9732i	−0.235229	+	1.63605i	0.439683	+	0.898153i	$0.355091\pi$
$233$	−3.59061	+	24.9732i	−0.235229	+	1.63605i	−0.674912	+	0.737898i	$0.735818\pi$
$234$		0			0
$235$	6.21230	−	1.82410i	0.405246	−	0.118991i
$236$		0			0
$237$	11.2504	+	12.9837i	0.730794	+	0.843381i
$238$		0			0
$239$	12.5795	+	3.69366i	0.813697	+	0.238923i	0.662000	−	0.749504i	$-0.269708\pi$
$239$	12.5795	+	3.69366i	0.813697	+	0.238923i	0.151697	+	0.988427i	$0.451526\pi$
$240$		0			0
$241$	21.6963	+	13.9434i	1.39758	+	0.898171i	0.999813	−	0.0193156i	$-0.00614872\pi$
$241$	21.6963	+	13.9434i	1.39758	+	0.898171i	0.397767	+	0.917486i	$0.369785\pi$
$242$		0			0
$243$	0.746537	−	0.861550i	0.0478904	−	0.0552685i
$244$		0			0
$245$	−1.21546	−	8.45371i	−0.0776529	−	0.540088i
$246$		0			0
$247$	−2.87538	−	6.29621i	−0.182956	−	0.400618i
$248$		0			0
$249$	−5.66378	+	12.4019i	−0.358927	+	0.785941i
$250$		0			0
$251$	−19.1427	+	12.3023i	−1.20828	+	0.776512i	−0.980369	−	0.197171i	$-0.936825\pi$
$251$	−19.1427	+	12.3023i	−1.20828	+	0.776512i	−0.227907	+	0.973683i	$0.573188\pi$
$252$		0			0
$253$	−3.33952	−	9.96539i	−0.209954	−	0.626519i
$254$		0			0
$255$	−2.82407	+	1.81492i	−0.176850	+	0.113655i
$256$		0			0
$257$	−0.309807	+	0.678382i	−0.0193252	+	0.0423163i	−0.919048	−	0.394144i	$-0.871041\pi$
$257$	−0.309807	+	0.678382i	−0.0193252	+	0.0423163i	0.899723	+	0.436461i	$0.143768\pi$
$258$		0			0
$259$	2.80824	+	6.14918i	0.174495	+	0.382092i
$260$		0			0
$261$	0.0260713	+	0.181330i	0.00161377	+	0.0112240i
$262$		0			0
$263$	−11.3480	+	13.0963i	−0.699750	+	0.807554i	−0.988719	−	0.149784i	$-0.952142\pi$
$263$	−11.3480	+	13.0963i	−0.699750	+	0.807554i	0.288969	+	0.957338i	$0.406688\pi$
$264$		0			0
$265$	−8.79280	−	5.65079i	−0.540138	−	0.347125i
$266$		0			0
$267$	0.254464	+	0.0747173i	0.0155729	+	0.00457262i
$268$		0			0
$269$	16.9178	+	19.5242i	1.03150	+	1.19041i	0.981460	+	0.191665i	$0.0613886\pi$
$269$	16.9178	+	19.5242i	1.03150	+	1.19041i	0.0500373	+	0.998747i	$0.484066\pi$
$270$		0			0
$271$	4.83679	−	1.42021i	0.293814	−	0.0862717i	−0.131504	−	0.991316i	$-0.541980\pi$
$271$	4.83679	−	1.42021i	0.293814	−	0.0862717i	0.425318	+	0.905044i	$0.360162\pi$
$272$		0			0
$273$	3.03366	−	21.0996i	0.183605	−	1.27700i
$274$		0			0
$275$	2.19150			0.132152
$276$		0			0
$277$	−13.2268			−0.794720			−0.397360	−	0.917663i	$-0.630074\pi$
$277$	−13.2268			−0.794720			−0.397360	+	0.917663i	$0.630074\pi$
$278$		0			0
$279$	−0.0134521	+	0.0935613i	−0.000805355	+	0.00560137i
$280$		0			0
$281$	−2.06162	+	0.605346i	−0.122986	+	0.0361119i	−0.342646	−	0.939464i	$-0.611323\pi$
$281$	−2.06162	+	0.605346i	−0.122986	+	0.0361119i	0.219660	+	0.975576i	$0.429505\pi$
$282$		0			0
$283$	−4.09886	−	4.73034i	−0.243652	−	0.281189i	0.620731	−	0.784024i	$-0.286836\pi$
$283$	−4.09886	−	4.73034i	−0.243652	−	0.281189i	−0.864383	+	0.502834i	$0.832291\pi$
$284$		0			0
$285$	3.54984	+	1.04233i	0.210274	+	0.0617421i
$286$		0			0
$287$	−6.69596	−	4.30323i	−0.395250	−	0.254012i
$288$		0			0
$289$	8.57928	−	9.90102i	0.504664	−	0.582413i
$290$		0			0
$291$	2.89731	+	20.1512i	0.169843	+	1.18128i
$292$		0			0
$293$	−5.19288	−	11.3708i	−0.303371	−	0.664290i	0.695138	−	0.718876i	$-0.255343\pi$
$293$	−5.19288	−	11.3708i	−0.303371	−	0.664290i	−0.998509	+	0.0545862i	$0.982616\pi$
$294$		0			0
$295$	5.31159	−	11.6307i	0.309252	−	0.677168i
$296$		0			0
$297$	9.74679	−	6.26388i	0.565566	−	0.363467i
$298$		0			0
$299$	−15.0059	+	2.73915i	−0.867811	+	0.158409i
$300$		0			0
$301$	32.5971	−	20.9489i	1.87887	−	1.20747i
$302$		0			0
$303$	−5.16178	+	11.3027i	−0.296537	+	0.649325i
$304$		0			0
$305$	−3.69995	−	8.10176i	−0.211859	−	0.463905i
$306$		0			0
$307$	−1.86343	−	12.9604i	−0.106352	−	0.739691i	−0.971305	−	0.237839i	$-0.923561\pi$
$307$	−1.86343	−	12.9604i	−0.106352	−	0.739691i	0.864953	−	0.501853i	$-0.167348\pi$
$308$		0			0
$309$	0.423951	−	0.489266i	0.0241178	−	0.0278334i
$310$		0			0
$311$	−23.6964	−	15.2287i	−1.34370	−	0.863543i	−0.346479	−	0.938058i	$-0.612623\pi$
$311$	−23.6964	−	15.2287i	−1.34370	−	0.863543i	−0.997220	+	0.0745144i	$0.976259\pi$
$312$		0			0
$313$	0.0686569	+	0.0201595i	0.00388072	+	0.00113948i	0.283672	−	0.958921i	$-0.408447\pi$
$313$	0.0686569	+	0.0201595i	0.00388072	+	0.00113948i	−0.279792	+	0.960061i	$0.590265\pi$
$314$		0			0
$315$	−0.283332	−	0.326982i	−0.0159639	−	0.0184233i
$316$		0			0
$317$	14.5984	−	4.28647i	0.819926	−	0.240752i	0.155242	−	0.987877i	$-0.450384\pi$
$317$	14.5984	−	4.28647i	0.819926	−	0.240752i	0.664684	+	0.747125i	$0.268566\pi$
$318$		0			0
$319$	−0.520586	+	3.62076i	−0.0291472	+	0.202724i
$320$		0			0
$321$	−20.5040			−1.14442
$322$		0			0
$323$	4.29714			0.239099
$324$		0			0
$325$	0.452652	−	3.14826i	0.0251086	−	0.174634i
$326$		0			0
$327$	20.2113	−	5.93457i	1.11769	−	0.328182i
$328$		0			0
$329$	−16.7145	−	19.2896i	−0.921502	−	1.06347i
$330$		0			0
$331$	14.1847	+	4.16499i	0.779659	+	0.228929i	0.647261	−	0.762268i	$-0.275914\pi$
$331$	14.1847	+	4.16499i	0.779659	+	0.228929i	0.132398	+	0.991197i	$0.457732\pi$
$332$		0			0
$333$	0.158327	+	0.101751i	0.00867628	+	0.00557590i
$334$		0			0
$335$	−9.01691	+	10.4061i	−0.492647	+	0.568544i
$336$		0			0
$337$	−3.72179	−	25.8856i	−0.202739	−	1.41008i	−0.796110	−	0.605152i	$-0.793112\pi$
$337$	−3.72179	−	25.8856i	−0.202739	−	1.41008i	0.593371	−	0.804929i	$-0.297797\pi$
$338$		0			0
$339$	−4.07077	−	8.91375i	−0.221094	−	0.484129i
$340$		0			0
$341$	−0.784064	+	1.71686i	−0.0424595	+	0.0929733i
$342$		0			0
$343$	−5.10933	+	3.28357i	−0.275878	+	0.177296i
$344$		0			0
$345$	4.14597	−	7.02044i	0.223212	−	0.377968i
$346$		0			0
$347$	−26.1914	+	16.8322i	−1.40603	+	0.903600i	−0.999948	−	0.0102365i	$-0.996742\pi$
$347$	−26.1914	+	16.8322i	−1.40603	+	0.903600i	−0.406082	+	0.913837i	$0.633105\pi$
$348$		0			0
$349$	−6.90520	+	15.1203i	−0.369627	+	0.809370i	0.629840	+	0.776725i	$0.283120\pi$
$349$	−6.90520	+	15.1203i	−0.369627	+	0.809370i	−0.999467	+	0.0326449i	$0.989607\pi$
$350$		0			0
$351$	−6.98538	−	15.2958i	−0.372852	−	0.816432i
$352$		0			0
$353$	−2.82843	−	19.6722i	−0.150542	−	1.04704i	−0.915313	−	0.402742i	$-0.868057\pi$
$353$	−2.82843	−	19.6722i	−0.150542	−	1.04704i	0.764771	−	0.644302i	$-0.222852\pi$
$354$		0			0
$355$	−1.77821	+	2.05216i	−0.0943775	+	0.108917i
$356$		0			0
$357$	11.1329	+	7.15470i	0.589217	+	0.378667i
$358$		0			0
$359$	17.5829	+	5.16279i	0.927987	+	0.272482i	0.710594	−	0.703602i	$-0.248426\pi$
$359$	17.5829	+	5.16279i	0.927987	+	0.272482i	0.217394	+	0.976084i	$0.430245\pi$
$360$		0			0
$361$	9.34103	+	10.7801i	0.491633	+	0.567375i
$362$		0			0
$363$	−10.1091	+	2.96831i	−0.530592	+	0.155796i
$364$		0			0
$365$	−0.0657887	+	0.457570i	−0.00344354	+	0.0239503i
$366$		0			0
$367$	−16.9068			−0.882525			−0.441263	−	0.897378i	$-0.645469\pi$
$367$	−16.9068			−0.882525			−0.441263	+	0.897378i	$0.645469\pi$
$368$		0			0
$369$	−0.221597			−0.0115359
$370$		0			0
$371$	−5.86388	+	40.7842i	−0.304437	+	2.11741i
$372$		0			0
$373$	−22.2975	+	6.54715i	−1.15452	+	0.338999i	−0.802302	−	0.596918i	$-0.796392\pi$
$373$	−22.2975	+	6.54715i	−1.15452	+	0.338999i	−0.352221	+	0.935917i	$0.614573\pi$
$374$		0			0
$375$	1.11331	+	1.28483i	0.0574911	+	0.0663483i
$376$		0			0
$377$	5.09398	+	1.49573i	0.262353	+	0.0770339i
$378$		0			0
$379$	12.6620	+	8.13739i	0.650405	+	0.417990i	0.823814	−	0.566860i	$-0.191842\pi$
$379$	12.6620	+	8.13739i	0.650405	+	0.417990i	−0.173409	+	0.984850i	$0.555478\pi$
$380$		0			0
$381$	−10.7080	+	12.3577i	−0.548588	+	0.633104i
$382$		0			0
$383$	2.13807	+	14.8706i	0.109250	+	0.759851i	0.968629	+	0.248511i	$0.0799413\pi$
$383$	2.13807	+	14.8706i	0.109250	+	0.759851i	−0.859379	+	0.511339i	$0.829150\pi$
$384$		0			0
$385$	−3.58887	−	7.85854i	−0.182906	−	0.400508i
$386$		0			0
$387$	0.448138	−	0.981285i	0.0227801	−	0.0498815i
$388$		0			0
$389$	21.3885	−	13.7455i	1.08444	−	0.696927i	0.128860	−	0.991663i	$-0.458868\pi$
$389$	21.3885	−	13.7455i	1.08444	−	0.696927i	0.955579	+	0.294736i	$0.0952318\pi$
$390$		0			0
$391$	2.32314	−	9.18050i	0.117486	−	0.464278i
$392$		0			0
$393$	−15.8356	+	10.1769i	−0.798801	+	0.513359i
$394$		0			0
$395$	4.19792	−	9.19217i	0.211221	−	0.462508i
$396$		0			0
$397$	4.50490	+	9.86435i	0.226094	+	0.495078i	0.988350	−	0.152199i	$-0.0486353\pi$
$397$	4.50490	+	9.86435i	0.226094	+	0.495078i	−0.762256	+	0.647276i	$0.775908\pi$
$398$		0			0
$399$	−2.07564	−	14.4364i	−0.103912	−	0.722723i
$400$		0			0
$401$	−5.98123	+	6.90270i	−0.298688	+	0.344705i	−0.885178	−	0.465252i	$-0.845964\pi$
$401$	−5.98123	+	6.90270i	−0.298688	+	0.344705i	0.586490	+	0.809956i	$0.300509\pi$
$402$		0			0
$403$	2.30446	+	1.48099i	0.114793	+	0.0737732i
$404$		0			0
$405$	8.30796	+	2.43944i	0.412826	+	0.121217i
$406$		0			0
$407$	2.46098	+	2.84012i	0.121986	+	0.140779i
$408$		0			0
$409$	−9.78041	+	2.87179i	−0.483610	+	0.142001i	−0.514444	−	0.857524i	$-0.672002\pi$
$409$	−9.78041	+	2.87179i	−0.483610	+	0.142001i	0.0308343	+	0.999525i	$0.490184\pi$
$410$		0			0
$411$	−3.50088	+	24.3491i	−0.172686	+	1.20105i
$412$		0			0
$413$	−50.4053			−2.48028
$414$		0			0
$415$	8.01967			0.393670
$416$		0			0
$417$	−4.15032	+	28.8661i	−0.203242	+	1.41358i
$418$		0			0
$419$	31.7234	−	9.31484i	1.54979	−	0.455060i	0.608752	−	0.793360i	$-0.291670\pi$
$419$	31.7234	−	9.31484i	1.54979	−	0.455060i	0.941038	+	0.338301i	$0.109852\pi$
$420$		0			0
$421$	−21.4295	−	24.7310i	−1.04441	−	1.20531i	−0.978234	−	0.207506i	$-0.933465\pi$
$421$	−21.4295	−	24.7310i	−1.04441	−	1.20531i	−0.0661771	−	0.997808i	$-0.521080\pi$
$422$		0			0
$423$	−0.681811	−	0.200198i	−0.0331508	−	0.00973395i
$424$		0			0
$425$	1.66114	+	1.06755i	0.0805773	+	0.0517839i
$426$		0			0
$427$	−22.9931	+	26.5354i	−1.11271	+	1.28414i
$428$		0			0
$429$	−1.68645	−	11.7295i	−0.0814226	−	0.566307i
$430$		0			0
$431$	4.62218	+	10.1212i	0.222643	+	0.487519i	0.987684	−	0.156462i	$-0.0500088\pi$
$431$	4.62218	+	10.1212i	0.222643	+	0.487519i	−0.765041	+	0.643981i	$0.777282\pi$
$432$		0			0
$433$	−12.5951	+	27.5793i	−0.605280	+	1.32538i	0.320476	+	0.947256i	$0.396157\pi$
$433$	−12.5951	+	27.5793i	−0.605280	+	1.32538i	−0.925756	+	0.378121i	$0.876570\pi$
$434$		0			0
$435$	−2.38724	+	1.53418i	−0.114459	+	0.0735585i
$436$		0			0
$437$	−9.32316	+	4.69078i	−0.445987	+	0.224390i
$438$		0			0
$439$	1.95931	−	1.25917i	0.0935128	−	0.0600970i	−0.493049	−	0.870002i	$-0.664118\pi$
$439$	1.95931	−	1.25917i	0.0935128	−	0.0600970i	0.586562	+	0.809905i	$0.300481\pi$
$440$		0			0
$441$	−0.389390	+	0.852644i	−0.0185424	+	0.0406021i
$442$		0			0
$443$	−8.86811	−	19.4184i	−0.421337	−	0.922598i	−0.994654	−	0.103265i	$-0.967071\pi$
$443$	−8.86811	−	19.4184i	−0.421337	−	0.922598i	0.573317	−	0.819333i	$-0.305656\pi$
$444$		0			0
$445$	−0.0222007	−	0.154409i	−0.00105241	−	0.00731970i
$446$		0			0
$447$	−11.4976	+	13.2689i	−0.543818	+	0.627599i
$448$		0			0
$449$	−32.2929	−	20.7534i	−1.52400	−	0.979413i	−0.991083	−	0.133243i	$-0.957461\pi$
$449$	−32.2929	−	20.7534i	−1.52400	−	0.979413i	−0.532913	−	0.846170i	$-0.678903\pi$
$450$		0			0
$451$	−4.24556	−	1.24661i	−0.199916	−	0.0587005i
$452$		0			0
$453$	17.0952	+	19.7289i	0.803202	+	0.926944i
$454$		0			0
$455$	−12.0307	+	3.53253i	−0.564008	+	0.165608i
$456$		0			0
$457$	3.89954	−	27.1219i	0.182413	−	1.26871i	−0.668623	−	0.743601i	$-0.733116\pi$
$457$	3.89954	−	27.1219i	0.182413	−	1.26871i	0.851036	−	0.525107i	$-0.175975\pi$
$458$		0			0
$459$	10.4394			0.487268
$460$		0			0
$461$	−17.0131			−0.792381			−0.396190	−	0.918168i	$-0.629668\pi$
$461$	−17.0131			−0.792381			−0.396190	+	0.918168i	$0.629668\pi$
$462$		0			0
$463$	−2.64651	+	18.4069i	−0.122994	+	0.855441i	0.831141	+	0.556062i	$0.187688\pi$
$463$	−2.64651	+	18.4069i	−0.122994	+	0.855441i	−0.954134	+	0.299378i	$0.903221\pi$
$464$		0			0
$465$	−1.40487	+	0.412508i	−0.0651495	+	0.0191296i
$466$		0			0
$467$	11.9296	+	13.7675i	0.552038	+	0.637086i	0.961357	−	0.275306i	$-0.0887791\pi$
$467$	11.9296	+	13.7675i	0.552038	+	0.637086i	−0.409319	+	0.912391i	$0.634234\pi$
$468$		0			0
$469$	52.0817	+	15.2926i	2.40491	+	0.706145i
$470$		0			0
$471$	25.0271	+	16.0839i	1.15319	+	0.741108i
$472$		0			0
$473$	14.1061	−	16.2794i	0.648601	−	0.748526i
$474$		0			0
$475$	−0.309706	−	2.15405i	−0.0142103	−	0.0988347i
$476$		0			0
$477$	0.476534	+	1.04346i	0.0218190	+	0.0477769i
$478$		0			0
$479$	6.76936	−	14.8228i	0.309300	−	0.677273i	−0.689599	−	0.724192i	$-0.742213\pi$
$479$	6.76936	−	14.8228i	0.309300	−	0.677273i	0.998899	+	0.0469191i	$0.0149403\pi$
$480$		0			0
$481$	4.58837	−	2.94877i	0.209212	−	0.134452i
$482$		0			0
$483$	−31.9643	−	3.37021i	−1.45443	−	0.153350i
$484$		0			0
$485$	10.0740	−	6.47419i	0.457438	−	0.293978i
$486$		0			0
$487$	−12.3960	+	27.1434i	−0.561715	+	1.22998i	0.389377	+	0.921078i	$0.372690\pi$
$487$	−12.3960	+	27.1434i	−0.561715	+	1.22998i	−0.951092	+	0.308906i	$0.900037\pi$
$488$		0			0
$489$	−13.9465	−	30.5385i	−0.630681	−	1.38100i
$490$		0			0
$491$	3.29656	+	22.9281i	0.148772	+	1.03473i	0.918234	+	0.396038i	$0.129615\pi$
$491$	3.29656	+	22.9281i	0.148772	+	1.03473i	−0.769463	+	0.638692i	$0.779476\pi$
$492$		0			0
$493$	−2.15839	+	2.49092i	−0.0972092	+	0.112185i
$494$		0			0
$495$	−0.202339	−	0.130035i	−0.00909447	−	0.00584466i
$496$		0			0
$497$	10.2709	+	3.01582i	0.460714	+	0.135278i
$498$		0			0
$499$	−11.0505	−	12.7529i	−0.494688	−	0.570900i	0.452425	−	0.891803i	$-0.350559\pi$
$499$	−11.0505	−	12.7529i	−0.494688	−	0.570900i	−0.947112	+	0.320903i	$0.896014\pi$
$500$		0			0
$501$	−7.76202	+	2.27913i	−0.346781	+	0.101824i
$502$		0			0
$503$	1.00237	−	6.97162i	0.0446933	−	0.310849i	−0.955196	−	0.295974i	$-0.904356\pi$
$503$	1.00237	−	6.97162i	0.0446933	−	0.310849i	0.999889	−	0.0148751i	$-0.00473507\pi$
$504$		0			0
$505$	7.30886			0.325240
$506$		0			0
$507$	4.90223			0.217715
$508$		0			0
$509$	3.72507	−	25.9085i	0.165111	−	1.14837i	−0.723705	−	0.690109i	$-0.757563\pi$
$509$	3.72507	−	25.9085i	0.165111	−	1.14837i	0.888816	−	0.458263i	$-0.151528\pi$
$510$		0			0
$511$	1.74855	−	0.513420i	0.0773511	−	0.0227123i
$512$		0			0
$513$	−7.53427	−	8.69502i	−0.332646	−	0.383894i
$514$		0			0
$515$	−0.365377	−	0.107284i	−0.0161004	−	0.00472752i
$516$		0			0
$517$	−11.9366	−	7.67116i	−0.524969	−	0.337377i
$518$		0			0
$519$	−0.688461	+	0.794526i	−0.0302201	+	0.0348758i
$520$		0			0
$521$	0.217375	+	1.51188i	0.00952337	+	0.0662365i	0.994029	−	0.109117i	$-0.0348023\pi$
$521$	0.217375	+	1.51188i	0.00952337	+	0.0662365i	−0.984506	+	0.175353i	$0.943893\pi$
$522$		0			0
$523$	−4.46561	−	9.77833i	−0.195268	−	0.427577i	0.786518	−	0.617567i	$-0.211882\pi$
$523$	−4.46561	−	9.77833i	−0.195268	−	0.427577i	−0.981786	+	0.189990i	$0.939154\pi$
$524$		0			0
$525$	2.78410	−	6.09632i	0.121508	−	0.266065i
$526$		0			0
$527$	−1.43066	+	0.919427i	−0.0623204	+	0.0400509i
$528$		0			0
$529$	4.98116	+	22.4541i	0.216572	+	0.976267i
$530$		0			0
$531$	−1.18054	+	0.758686i	−0.0512310	+	0.0329242i
$532$		0			0
$533$	−2.66777	+	5.84160i	−0.115554	+	0.253028i
$534$		0			0
$535$	5.01017	+	10.9708i	0.216609	+	0.474307i
$536$		0			0
$537$	4.09005	+	28.4469i	0.176499	+	1.22757i
$538$		0			0
$539$	−12.2569	+	14.1452i	−0.527943	+	0.609278i
$540$		0			0
$541$	12.5230	+	8.04805i	0.538406	+	0.346013i	0.781415	−	0.624011i	$-0.214498\pi$
$541$	12.5230	+	8.04805i	0.538406	+	0.346013i	−0.243009	+	0.970024i	$0.578134\pi$
$542$		0			0
$543$	−33.9076	−	9.95617i	−1.45511	−	0.427260i
$544$		0			0
$545$	−8.11397	−	9.36402i	−0.347564	−	0.401111i
$546$		0			0
$547$	31.4688	−	9.24007i	1.34551	−	0.395077i	0.471877	−	0.881665i	$-0.343577\pi$
$547$	31.4688	−	9.24007i	1.34551	−	0.395077i	0.873632	+	0.486588i	$0.161759\pi$
$548$		0			0
$549$	−0.139115	+	0.967569i	−0.00593730	+	0.0412948i
$550$		0			0
$551$	3.63246			0.154748
$552$		0			0
$553$	−39.8370			−1.69404
$554$		0			0
$555$	−0.414892	+	2.88564i	−0.0176112	+	0.122488i
$556$		0			0
$557$	35.0586	−	10.2941i	1.48548	−	0.436177i	0.564386	−	0.825511i	$-0.309113\pi$
$557$	35.0586	−	10.2941i	1.48548	−	0.436177i	0.921097	+	0.389334i	$0.127295\pi$
$558$		0			0
$559$	−20.4730	−	23.6271i	−0.865915	−	0.999319i
$560$		0			0
$561$	7.05881	+	2.07265i	0.298023	+	0.0875075i
$562$		0			0
$563$	30.3853	+	19.5275i	1.28059	+	0.822985i	0.990960	−	0.134154i	$-0.0428318\pi$
$563$	30.3853	+	19.5275i	1.28059	+	0.822985i	0.289629	+	0.957139i	$0.406468\pi$
$564$		0			0
$565$	−3.77465	+	4.35617i	−0.158801	+	0.183266i
$566$		0			0
$567$	−4.85777	−	33.7866i	−0.204007	−	1.41890i
$568$		0			0
$569$	3.65977	+	8.01378i	0.153426	+	0.335955i	0.970700	−	0.240293i	$-0.0772435\pi$
$569$	3.65977	+	8.01378i	0.153426	+	0.335955i	−0.817275	+	0.576248i	$0.804516\pi$
$570$		0			0
$571$	−0.710988	+	1.55685i	−0.0297539	+	0.0651520i	−0.923925	−	0.382573i	$-0.875038\pi$
$571$	−0.710988	+	1.55685i	−0.0297539	+	0.0651520i	0.894172	+	0.447725i	$0.147765\pi$
$572$		0			0
$573$	18.1104	−	11.6388i	0.756571	−	0.486219i
$574$		0			0
$575$	−4.76939	−	0.502869i	−0.198897	−	0.0209711i
$576$		0			0
$577$	−33.1398	+	21.2977i	−1.37963	+	0.886634i	−0.999270	−	0.0382050i	$-0.987836\pi$
$577$	−33.1398	+	21.2977i	−1.37963	+	0.886634i	−0.380359	+	0.924839i	$0.624200\pi$
$578$		0			0
$579$	6.65144	−	14.5646i	0.276424	−	0.605285i
$580$		0			0
$581$	−13.1333	−	28.7579i	−0.544860	−	1.19308i
$582$		0			0
$583$	3.25981	+	22.6725i	0.135007	+	0.938998i
$584$		0			0
$585$	−0.228599	+	0.263818i	−0.00945141	+	0.0109075i
$586$		0			0
$587$	11.4489	+	7.35776i	0.472546	+	0.303687i	0.755153	−	0.655549i	$-0.227563\pi$
$587$	11.4489	+	7.35776i	0.472546	+	0.303687i	−0.282606	+	0.959236i	$0.591199\pi$
$588$		0			0
$589$	1.79833	+	0.528037i	0.0740988	+	0.0217574i
$590$		0			0
$591$	−16.3323	−	18.8485i	−0.671821	−	0.775323i
$592$		0			0
$593$	38.6668	−	11.3536i	1.58785	−	0.466236i	0.635720	−	0.771919i	$-0.280703\pi$
$593$	38.6668	−	11.3536i	1.58785	−	0.466236i	0.952133	+	0.305684i	$0.0988850\pi$
$594$		0			0
$595$	1.10781	−	7.70499i	0.0454158	−	0.315874i
$596$		0			0
$597$	−40.6130			−1.66218
$598$		0			0
$599$	48.4251			1.97859			0.989297	−	0.145914i	$-0.0466124\pi$
$599$	48.4251			1.97859			0.989297	+	0.145914i	$0.0466124\pi$
$600$		0			0
$601$	5.48857	−	38.1739i	0.223883	−	1.55714i	−0.499264	−	0.866450i	$-0.666396\pi$
$601$	5.48857	−	38.1739i	0.223883	−	1.55714i	0.723147	−	0.690694i	$-0.242695\pi$
$602$		0			0
$603$	1.44998	−	0.425753i	0.0590478	−	0.0173380i
$604$		0			0
$605$	4.05839	+	4.68363i	0.164997	+	0.190417i
$606$		0			0
$607$	−19.3731	−	5.68846i	−0.786330	−	0.230887i	−0.136171	−	0.990685i	$-0.543480\pi$
$607$	−19.3731	−	5.68846i	−0.786330	−	0.230887i	−0.650159	+	0.759798i	$0.725298\pi$
$608$		0			0
$609$	9.41088	+	6.04800i	0.381348	+	0.245078i
$610$		0			0
$611$	−13.4857	+	15.5634i	−0.545574	+	0.629626i
$612$		0			0
$613$	6.73249	+	46.8255i	0.271923	+	1.89126i	0.428411	+	0.903584i	$0.359073\pi$
$613$	6.73249	+	46.8255i	0.271923	+	1.89126i	−0.156489	+	0.987680i	$0.550017\pi$
$614$		0			0
$615$	−1.42594	−	3.12237i	−0.0574994	−	0.125906i
$616$		0			0
$617$	13.3727	−	29.2822i	0.538366	−	1.17886i	−0.423641	−	0.905830i	$-0.639248\pi$
$617$	13.3727	−	29.2822i	0.538366	−	1.17886i	0.962007	−	0.273026i	$-0.0880245\pi$
$618$		0			0
$619$	36.3012	−	23.3294i	1.45907	−	0.937687i	0.460316	−	0.887755i	$-0.347736\pi$
$619$	36.3012	−	23.3294i	1.45907	−	0.937687i	0.998753	−	0.0499315i	$-0.0159003\pi$
$620$		0			0
$621$	−22.6494	+	11.3956i	−0.908890	+	0.457292i
$622$		0			0
$623$	−0.517342	+	0.332476i	−0.0207269	+	0.0133203i
$624$		0			0
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$		0			0
$627$	−3.36814	−	7.37520i	−0.134511	−	0.294537i
$628$		0			0
$629$	0.481890	+	3.35162i	0.0192142	+	0.133638i
$630$		0			0
$631$	8.02835	−	9.26521i	0.319603	−	0.368842i	−0.573101	−	0.819485i	$-0.694260\pi$
$631$	8.02835	−	9.26521i	0.319603	−	0.368842i	0.892704	+	0.450643i	$0.148805\pi$
$632$		0			0
$633$	7.79601	+	5.01019i	0.309863	+	0.199137i
$634$		0			0
$635$	9.22856	+	2.70975i	0.366224	+	0.107533i
$636$		0			0
$637$	17.7891	+	20.5297i	0.704830	+	0.813417i
$638$		0			0
$639$	0.285948	−	0.0839619i	0.0113119	−	0.00332148i
$640$		0			0
$641$	1.69343	−	11.7781i	0.0668864	−	0.465205i	−0.928660	−	0.370932i	$-0.879038\pi$
$641$	1.69343	−	11.7781i	0.0668864	−	0.465205i	0.995546	−	0.0942731i	$-0.0300527\pi$
$642$		0			0
$643$	−12.1095			−0.477552			−0.238776	−	0.971075i	$-0.576746\pi$
$643$	−12.1095			−0.477552			−0.238776	+	0.971075i	$0.576746\pi$
$644$		0			0
$645$	16.7103			0.657969
$646$		0			0
$647$	5.94441	−	41.3443i	0.233699	−	1.62541i	−0.448178	−	0.893944i	$-0.647927\pi$
$647$	5.94441	−	41.3443i	0.233699	−	1.62541i	0.681877	−	0.731467i	$-0.261164\pi$
$648$		0			0
$649$	−26.8859	+	7.89443i	−1.05537	+	0.309883i
$650$		0			0
$651$	3.77989	+	4.36223i	0.148146	+	0.170969i
$652$		0			0
$653$	19.1230	+	5.61501i	0.748340	+	0.219732i	0.633597	−	0.773663i	$-0.281578\pi$
$653$	19.1230	+	5.61501i	0.748340	+	0.219732i	0.114742	+	0.993395i	$0.463396\pi$
$654$		0			0
$655$	9.31467	+	5.98618i	0.363954	+	0.233899i
$656$		0			0
$657$	0.0332247	−	0.0383434i	0.00129622	−	0.00149592i
$658$		0			0
$659$	1.99431	+	13.8708i	0.0776875	+	0.540328i	0.991082	+	0.133253i	$0.0425423\pi$
$659$	1.99431	+	13.8708i	0.0776875	+	0.540328i	−0.913395	+	0.407075i	$0.866549\pi$
$660$		0			0
$661$	−9.79773	−	21.4540i	−0.381087	−	0.834465i	−0.998843	−	0.0480947i	$-0.984685\pi$
$661$	−9.79773	−	21.4540i	−0.381087	−	0.834465i	0.617755	−	0.786370i	$-0.288042\pi$
$662$		0			0
$663$	4.43552	−	9.71244i	0.172261	−	0.377200i
$664$		0			0
$665$	−7.21707	+	4.63813i	−0.279866	+	0.179859i
$666$		0			0
$667$	1.96379	−	7.76045i	0.0760383	−	0.300486i
$668$		0			0
$669$	7.86811	−	5.05653i	0.304199	−	0.195497i
$670$		0			0
$671$	−8.10844	+	17.7550i	−0.313023	+	0.685424i
$672$		0			0
$673$	4.83473	+	10.5866i	0.186365	+	0.408083i	0.979635	−	0.200788i	$-0.0643501\pi$
$673$	4.83473	+	10.5866i	0.186365	+	0.408083i	−0.793270	+	0.608871i	$0.791623\pi$
$674$		0			0
$675$	−0.752391	−	5.23299i	−0.0289595	−	0.201418i
$676$		0			0
$677$	−8.06822	+	9.31122i	−0.310087	+	0.357859i	−0.889306	−	0.457313i	$-0.848812\pi$
$677$	−8.06822	+	9.31122i	−0.310087	+	0.357859i	0.579219	+	0.815172i	$0.303358\pi$
$678$		0			0
$679$	−39.7135	−	25.5223i	−1.52406	−	0.979456i
$680$		0			0
$681$	−37.8230	−	11.1058i	−1.44938	−	0.425577i
$682$		0			0
$683$	−2.40269	−	2.77285i	−0.0919364	−	0.106100i	0.707917	−	0.706295i	$-0.249635\pi$
$683$	−2.40269	−	2.77285i	−0.0919364	−	0.106100i	−0.799854	+	0.600195i	$0.795090\pi$
$684$		0			0
$685$	13.8836	−	4.07658i	0.530464	−	0.155758i
$686$		0			0
$687$	3.44029	−	23.9277i	0.131255	−	0.912900i
$688$		0			0
$689$	33.2441			1.26650
$690$		0			0
$691$	40.9110			1.55633			0.778164	−	0.628061i	$-0.216151\pi$
$691$	40.9110			1.55633			0.778164	+	0.628061i	$0.216151\pi$
$692$		0			0
$693$	−0.134939	+	0.938522i	−0.00512591	+	0.0356515i
$694$		0			0
$695$	16.4591	−	4.83282i	0.624329	−	0.183319i
$696$		0			0
$697$	−2.61084	−	3.01307i	−0.0988928	−	0.114128i
$698$		0			0
$699$	41.1555	+	12.0843i	1.55664	+	0.457071i
$700$		0			0
$701$	3.73723	+	2.40177i	0.141153	+	0.0907136i	0.609311	−	0.792931i	$-0.291446\pi$
$701$	3.73723	+	2.40177i	0.141153	+	0.0907136i	−0.468158	+	0.883645i	$0.655082\pi$
$702$		0			0
$703$	2.44380	−	2.82029i	0.0921696	−	0.106369i
$704$		0			0
$705$	−1.56649	−	10.8952i	−0.0589976	−	0.410337i
$706$		0			0
$707$	−11.9692	−	26.2090i	−0.450150	−	0.985690i
$708$		0			0
$709$	−14.9124	+	32.6537i	−0.560048	+	1.22633i	0.391881	+	0.920016i	$0.371825\pi$
$709$	−14.9124	+	32.6537i	−0.560048	+	1.22633i	−0.951929	+	0.306319i	$0.900903\pi$
$710$		0			0
$711$	−0.933020	+	0.599615i	−0.0349910	+	0.0224873i
$712$		0			0
$713$	2.10033	−	3.55652i	0.0786579	−	0.133193i
$714$		0			0
$715$	−5.86385	+	3.76847i	−0.219295	+	0.140933i
$716$		0			0
$717$	9.25912	−	20.2746i	0.345788	−	0.757170i
$718$		0			0
$719$	15.5751	+	34.1048i	0.580854	+	1.27189i	0.940813	+	0.338925i	$0.110063\pi$
$719$	15.5751	+	34.1048i	0.580854	+	1.27189i	−0.359959	+	0.932968i	$0.617209\pi$
$720$		0			0
$721$	0.213641	+	1.48590i	0.00795640	+	0.0553380i
$722$		0			0
$723$	28.7128	−	33.1363i	1.06784	−	1.23235i
$724$		0			0
$725$	1.40420	+	0.902423i	0.0521506	+	0.0335151i
$726$		0			0
$727$	2.38744	+	0.701015i	0.0885452	+	0.0259992i	0.325705	−	0.945471i	$-0.394398\pi$
$727$	2.38744	+	0.701015i	0.0885452	+	0.0259992i	−0.237160	+	0.971471i	$0.576217\pi$
$728$		0			0
$729$	−18.2799	−	21.0961i	−0.677033	−	0.781338i
$730$		0			0
$731$	18.6226	−	5.46809i	0.688781	−	0.202244i
$732$		0			0
$733$	0.0854324	−	0.594196i	0.00315552	−	0.0219471i	−0.988183	−	0.153280i	$-0.951016\pi$
$733$	0.0854324	−	0.594196i	0.00315552	−	0.0219471i	0.991338	+	0.131333i	$0.0419256\pi$
$734$		0			0
$735$	−14.5197			−0.535568
$736$		0			0
$737$	30.1752			1.11152
$738$		0			0
$739$	2.68046	−	18.6430i	0.0986025	−	0.685795i	−0.879229	−	0.476400i	$-0.841941\pi$
$739$	2.68046	−	18.6430i	0.0986025	−	0.685795i	0.977831	−	0.209395i	$-0.0671495\pi$
$740$		0			0
$741$	−11.2908	+	3.31526i	−0.414776	+	0.121789i
$742$		0			0
$743$	10.2057	+	11.7780i	0.374411	+	0.432093i	0.911416	−	0.411485i	$-0.134990\pi$
$743$	10.2057	+	11.7780i	0.374411	+	0.432093i	−0.537005	+	0.843579i	$0.680444\pi$
$744$		0			0
$745$	9.90906	+	2.90956i	0.363040	+	0.106598i
$746$		0			0
$747$	−0.740448	−	0.475857i	−0.0270916	−	0.0174107i
$748$		0			0
$749$	31.1354	−	35.9321i	1.13766	−	1.31293i
$750$		0			0
$751$	2.95266	+	20.5362i	0.107744	+	0.749377i	0.970035	+	0.242964i	$0.0781198\pi$
$751$	2.95266	+	20.5362i	0.107744	+	0.749377i	−0.862291	+	0.506413i	$0.830971\pi$
$752$		0			0
$753$	16.0704	+	35.1892i	0.585637	+	1.28237i
$754$		0			0
$755$	6.37881	−	13.9676i	0.232148	−	0.508334i
$756$		0			0
$757$	3.53742	−	2.27336i	0.128570	−	0.0826268i	−0.474775	−	0.880107i	$-0.657471\pi$
$757$	3.53742	−	2.27336i	0.128570	−	0.0826268i	0.603345	+	0.797480i	$0.293834\pi$
$758$		0			0
$759$	−17.5774	+	3.20856i	−0.638020	+	0.116463i
$760$		0			0
$761$	−16.1522	+	10.3804i	−0.585516	+	0.376288i	−0.799605	−	0.600526i	$-0.794958\pi$
$761$	−16.1522	+	10.3804i	−0.585516	+	0.376288i	0.214090	+	0.976814i	$0.431322\pi$
$762$		0			0
$763$	−20.2909	+	44.4309i	−0.734580	+	1.60851i
$764$		0			0
$765$	−0.0900273	−	0.197132i	−0.00325494	−	0.00712733i
$766$		0			0
$767$	5.78771	+	40.2544i	0.208982	+	1.45350i
$768$		0			0
$769$	−23.8002	+	27.4669i	−0.858257	+	0.990481i	0.141743	+	0.989904i	$0.454729\pi$
$769$	−23.8002	+	27.4669i	−0.858257	+	0.990481i	−1.00000		0.000577919i	$0.999816\pi$
$770$		0			0
$771$	1.06660	+	0.685464i	0.0384128	+	0.0246864i
$772$		0			0
$773$	6.18512	+	1.81612i	0.222463	+	0.0653211i	0.391065	−	0.920363i	$-0.372107\pi$
$773$	6.18512	+	1.81612i	0.222463	+	0.0653211i	−0.168601	+	0.985684i	$0.553925\pi$
$774$		0			0
$775$	0.563997	+	0.650888i	0.0202594	+	0.0233806i
$776$		0			0
$777$	11.0271	−	3.23785i	0.395595	−	0.116157i
$778$		0			0
$779$	−0.625318	+	4.34918i	−0.0224043	+	0.155826i
$780$		0			0
$781$	5.95080			0.212936
$782$		0			0
$783$	8.82459			0.315365
$784$		0			0
$785$	2.49038	−	17.3210i	0.0888855	−	0.618212i
$786$		0			0
$787$	−40.6562	+	11.9377i	−1.44924	+	0.425535i	−0.909290	−	0.416163i	$-0.863374\pi$
$787$	−40.6562	+	11.9377i	−1.44924	+	0.425535i	−0.539948	+	0.841698i	$0.681556\pi$
$788$		0			0
$789$	19.2925	+	22.2647i	0.686830	+	0.792645i
$790$		0			0
$791$	21.8024	+	6.40175i	0.775203	+	0.227620i
$792$		0			0
$793$	23.8317	+	15.3157i	0.846288	+	0.543876i
$794$		0			0
$795$	−11.6364	+	13.4291i	−0.412699	+	0.476280i
$796$		0			0
$797$	3.24659	+	22.5805i	0.115000	+	0.799843i	0.962933	+	0.269740i	$0.0869377\pi$
$797$	3.24659	+	22.5805i	0.115000	+	0.799843i	−0.847933	+	0.530103i	$0.822153\pi$
$798$		0			0
$799$	−5.31097	−	11.6294i	−0.187889	−	0.411418i
$800$		0			0
$801$	−0.00711230	+	0.0155738i	−0.000251301	+	0.000550272i
$802$		0			0
$803$	0.852254	−	0.547711i	0.0300754	−	0.0193283i
$804$		0			0
$805$	6.00727	+	17.9262i	0.211729	+	0.631814i
$806$		0			0
$807$	36.9479	−	23.7450i	1.30063	−	0.835863i
$808$		0			0
$809$	−13.0483	+	28.5719i	−0.458755	+	1.00453i	0.529015	+	0.848613i	$0.322562\pi$
$809$	−13.0483	+	28.5719i	−0.458755	+	1.00453i	−0.987770	+	0.155921i	$0.950166\pi$
$810$		0			0
$811$	−12.9852	−	28.4337i	−0.455973	−	0.998442i	−0.988387	−	0.151958i	$-0.951442\pi$
$811$	−12.9852	−	28.4337i	−0.455973	−	0.998442i	0.532414	−	0.846484i	$-0.321285\pi$
$812$		0			0
$813$	−1.21965	−	8.48282i	−0.0427748	−	0.297505i
$814$		0			0
$815$	−12.9319	+	14.9242i	−0.452986	+	0.522773i
$816$		0			0
$817$	−17.9947	−	11.5645i	−0.629554	−	0.404590i
$818$		0			0
$819$	1.32039	+	0.387701i	0.0461381	+	0.0135474i
$820$		0			0
$821$	1.50719	+	1.73939i	0.0526014	+	0.0607052i	0.781441	−	0.623980i	$-0.214485\pi$
$821$	1.50719	+	1.73939i	0.0526014	+	0.0607052i	−0.728839	+	0.684685i	$0.759940\pi$
$822$		0			0
$823$	30.7835	−	9.03884i	1.07304	−	0.315074i	0.302951	−	0.953006i	$-0.402028\pi$
$823$	30.7835	−	9.03884i	1.07304	−	0.315074i	0.770093	+	0.637932i	$0.220210\pi$
$824$		0			0
$825$	0.530224	−	3.68779i	0.0184600	−	0.128392i
$826$		0			0
$827$	−16.9699			−0.590101			−0.295051	−	0.955482i	$-0.595337\pi$
$827$	−16.9699			−0.590101			−0.295051	+	0.955482i	$0.595337\pi$
$828$		0			0
$829$	−22.0617			−0.766236			−0.383118	−	0.923699i	$-0.625150\pi$
$829$	−22.0617			−0.766236			−0.383118	+	0.923699i	$0.625150\pi$
$830$		0			0
$831$	−3.20016	+	22.2576i	−0.111012	+	0.772108i
$832$		0			0
$833$	−16.1813	+	4.75125i	−0.560648	+	0.164621i
$834$		0			0
$835$	3.11612	+	3.59619i	0.107838	+	0.124451i
$836$		0			0
$837$	4.36881	+	1.28280i	0.151008	+	0.0443400i
$838$		0			0
$839$	4.84240	+	3.11202i	0.167178	+	0.107439i	0.621555	−	0.783371i	$-0.286501\pi$
$839$	4.84240	+	3.11202i	0.167178	+	0.107439i	−0.454376	+	0.890810i	$0.650138\pi$
$840$		0			0
$841$	17.1664	−	19.8111i	0.591946	−	0.683142i
$842$		0			0
$843$	0.519858	+	3.61569i	0.0179049	+	0.124531i
$844$		0			0
$845$	−1.19786	−	2.62296i	−0.0412078	−	0.0902325i
$846$		0			0
$847$	10.1490	−	22.2231i	0.348722	−	0.763595i
$848$		0			0
$849$	−8.95176	+	5.75295i	−0.307224	+	0.197441i
$850$		0			0
$851$	−4.70416	−	6.74570i	−0.161256	−	0.231240i
$852$		0			0
$853$	13.8543	−	8.90360i	0.474361	−	0.304854i	−0.281528	−	0.959553i	$-0.590841\pi$
$853$	13.8543	−	8.90360i	0.474361	−	0.304854i	0.755889	+	0.654699i	$0.227205\pi$
$854$		0			0
$855$	−0.0992185	+	0.217258i	−0.00339320	+	0.00743008i
$856$		0			0
$857$	2.68383	+	5.87678i	0.0916780	+	0.200747i	0.949916	−	0.312505i	$-0.101168\pi$
$857$	2.68383	+	5.87678i	0.0916780	+	0.200747i	−0.858238	+	0.513252i	$0.828441\pi$
$858$		0			0
$859$	−2.66917	−	18.5645i	−0.0910709	−	0.633412i	−0.983322	−	0.181873i	$-0.941784\pi$
$859$	−2.66917	−	18.5645i	−0.0910709	−	0.633412i	0.892251	−	0.451540i	$-0.149125\pi$
$860$		0			0
$861$	−8.86140	+	10.2266i	−0.301996	+	0.348522i
$862$		0			0
$863$	15.6403	+	10.0514i	0.532402	+	0.342154i	0.779061	−	0.626948i	$-0.215696\pi$
$863$	15.6403	+	10.0514i	0.532402	+	0.342154i	−0.246659	+	0.969102i	$0.579333\pi$
$864$		0			0
$865$	0.593341	+	0.174221i	0.0201742	+	0.00592368i
$866$		0			0
$867$	−14.5854	−	16.8325i	−0.495346	−	0.571660i
$868$		0			0
$869$	−21.2489	+	6.23923i	−0.720818	+	0.211651i
$870$		0			0
$871$	6.23266	−	43.3491i	0.211186	−	1.46883i
$872$		0			0
$873$	−1.31428			−0.0444816
$874$		0			0
$875$	−3.94216			−0.133269
$876$		0			0
$877$	2.78319	−	19.3575i	0.0939816	−	0.653656i	−0.887316	−	0.461161i	$-0.847433\pi$
$877$	2.78319	−	19.3575i	0.0939816	−	0.653656i	0.981298	−	0.192495i	$-0.0616580\pi$
$878$		0			0
$879$	−20.3909	+	5.98729i	−0.687766	+	0.201946i
$880$		0			0
$881$	16.4365	+	18.9687i	0.553758	+	0.639071i	0.961755	−	0.273912i	$-0.0883178\pi$
$881$	16.4365	+	18.9687i	0.553758	+	0.639071i	−0.407996	+	0.912984i	$0.633772\pi$
$882$		0			0
$883$	−32.4232	−	9.52030i	−1.09113	−	0.320383i	−0.313805	−	0.949488i	$-0.601604\pi$
$883$	−32.4232	−	9.52030i	−1.09113	−	0.320383i	−0.777321	+	0.629104i	$0.783422\pi$
$884$		0			0
$885$	−18.2867	−	11.7522i	−0.614702	−	0.395045i
$886$		0			0
$887$	−25.4116	+	29.3266i	−0.853240	+	0.984691i	−0.999990	−	0.00448260i	$-0.998573\pi$
$887$	−25.4116	+	29.3266i	−0.853240	+	0.984691i	0.146750	+	0.989174i	$0.453119\pi$
$888$		0			0
$889$	−5.39606	−	37.5304i	−0.180978	−	1.25873i
$890$		0			0
$891$	−7.88272	−	17.2608i	−0.264081	−	0.578257i
$892$		0			0
$893$	−5.85319	+	12.8167i	−0.195869	+	0.428894i
$894$		0			0
$895$	14.2212	−	9.13944i	0.475364	−	0.305498i
$896$		0			0
$897$	0.978751	+	25.9141i	0.0326796	+	0.865247i
$898$		0			0
$899$	−1.20936	+	0.777210i	−0.0403345	+	0.0259214i
$900$		0			0
$901$	−8.57360	+	18.7736i	−0.285628	+	0.625438i
$902$		0			0
$903$	−27.3654	−	59.9219i	−0.910664	−	1.99408i
$904$		0			0
$905$	2.95827	+	20.5752i	0.0983362	+	0.683943i
$906$		0			0
$907$	−20.2992	+	23.4265i	−0.674024	+	0.777865i	−0.985000	−	0.172553i	$-0.944798\pi$
$907$	−20.2992	+	23.4265i	−0.674024	+	0.777865i	0.310977	+	0.950418i	$0.399344\pi$
$908$		0			0
$909$	−0.674820	−	0.433681i	−0.0223824	−	0.0143843i
$910$		0			0
$911$	−23.3365	−	6.85221i	−0.773173	−	0.227024i	−0.128733	−	0.991679i	$-0.541091\pi$
$911$	−23.3365	−	6.85221i	−0.773173	−	0.227024i	−0.644439	+	0.764655i	$0.722909\pi$
$912$		0			0
$913$	−11.5092	−	13.2824i	−0.380900	−	0.439582i
$914$		0			0
$915$	−14.5286	+	4.26597i	−0.480300	+	0.141029i
$916$		0			0
$917$	6.21191	−	43.2048i	0.205135	−	1.42675i
$918$		0			0
$919$	15.4524			0.509728			0.254864	−	0.966977i	$-0.417969\pi$
$919$	15.4524			0.509728			0.254864	+	0.966977i	$0.417969\pi$
$920$		0			0
$921$	−22.2603			−0.733501
$922$		0			0
$923$	1.22913	−	8.54880i	0.0404573	−	0.281387i
$924$		0			0
$925$	1.64535	−	0.483119i	0.0540989	−	0.0158849i
$926$		0			0
$927$	0.0273691	+	0.0315856i	0.000898918	+	0.00103741i
$928$		0			0
$929$	19.2124	+	5.64127i	0.630339	+	0.185084i	0.581269	−	0.813711i	$-0.302556\pi$
$929$	19.2124	+	5.64127i	0.630339	+	0.185084i	0.0490695	+	0.998795i	$0.484374\pi$
$930$		0			0
$931$	15.6357	+	10.0484i	0.512439	+	0.329324i
$932$		0			0
$933$	−31.3597	+	36.1910i	−1.02667	+	1.18484i
$934$		0			0
$935$	−0.615846	−	4.28330i	−0.0201403	−	0.140079i
$936$		0			0
$937$	10.6321	+	23.2810i	0.347335	+	0.760557i	0.999996	+	0.00290672i	$0.000925239\pi$
$937$	10.6321	+	23.2810i	0.347335	+	0.760557i	−0.652661	+	0.757650i	$0.726347\pi$
$938$		0			0
$939$	0.0505350	−	0.110656i	0.00164915	−	0.00361113i
$940$		0			0
$941$	18.3172	−	11.7717i	0.597123	−	0.383748i	−0.206886	−	0.978365i	$-0.566333\pi$
$941$	18.3172	−	11.7717i	0.597123	−	0.383748i	0.804009	+	0.594617i	$0.202696\pi$
$942$		0			0
$943$	8.95362	+	3.68721i	0.291570	+	0.120072i
$944$		0			0
$945$	−17.5329	+	11.2677i	−0.570347	+	0.366539i
$946$		0			0
$947$	−1.73599	+	3.80128i	−0.0564119	+	0.123525i	−0.935739	−	0.352694i	$-0.885266\pi$
$947$	−1.73599	+	3.80128i	−0.0564119	+	0.123525i	0.879327	+	0.476219i	$0.157993\pi$
$948$		0			0
$949$	−0.610798	−	1.33746i	−0.0198273	−	0.0434158i
$950$		0			0
$951$	−3.68112	−	25.6028i	−0.119369	−	0.830226i
$952$		0			0
$953$	22.1931	−	25.6122i	0.718904	−	0.829659i	−0.272271	−	0.962221i	$-0.587775\pi$
$953$	22.1931	−	25.6122i	0.718904	−	0.829659i	0.991175	+	0.132561i	$0.0423201\pi$
$954$		0			0
$955$	−10.6527	−	6.84607i	−0.344713	−	0.221534i
$956$		0			0
$957$	5.96695	+	1.75205i	0.192884	+	0.0566358i
$958$		0			0
$959$	−37.3545	−	43.1094i	−1.20624	−	1.39207i
$960$		0			0
$961$	29.0326	−	8.52473i	0.936535	−	0.274991i
$962$		0			0
$963$	0.188379	−	1.31020i	0.00607043	−	0.0422207i
$964$		0			0
$965$	−9.41815			−0.303181
$966$		0			0
$967$	−15.4240			−0.496003			−0.248001	−	0.968760i	$-0.579774\pi$
$967$	−15.4240			−0.496003			−0.248001	+	0.968760i	$0.579774\pi$
$968$		0			0
$969$	1.03967	−	7.23110i	0.0333992	−	0.232296i
$970$		0			0
$971$	−20.7349	+	6.08830i	−0.665413	+	0.195383i	−0.596960	−	0.802271i	$-0.703625\pi$
$971$	−20.7349	+	6.08830i	−0.665413	+	0.195383i	−0.0684537	+	0.997654i	$0.521807\pi$
$972$		0			0
$973$	−44.2840	−	51.1065i	−1.41968	−	1.63840i
$974$		0			0
$975$	−5.18828	−	1.52342i	−0.166158	−	0.0487884i
$976$		0			0
$977$	30.3593	+	19.5108i	0.971282	+	0.624205i	0.927098	−	0.374819i	$-0.122295\pi$
$977$	30.3593	+	19.5108i	0.971282	+	0.624205i	0.0441835	+	0.999023i	$0.485931\pi$
$978$		0			0
$979$	−0.223876	+	0.258366i	−0.00715509	+	0.00825742i
$980$		0			0
$981$	0.193529	+	1.34602i	0.00617891	+	0.0429753i
$982$		0			0
$983$	1.13501	+	2.48532i	0.0362011	+	0.0792694i	0.926869	−	0.375386i	$-0.122490\pi$
$983$	1.13501	+	2.48532i	0.0362011	+	0.0792694i	−0.890668	+	0.454655i	$0.849762\pi$
$984$		0			0
$985$	−6.09415	+	13.3443i	−0.194176	+	0.425186i
$986$		0			0
$987$	−36.5040	+	23.4597i	−1.16193	+	0.746729i
$988$		0			0
$989$	−34.4349	+	32.1922i	−1.09497	+	1.02365i
$990$		0			0
$991$	−6.34454	+	4.07739i	−0.201541	+	0.129523i	−0.637519	−	0.770435i	$-0.720039\pi$
$991$	−6.34454	+	4.07739i	−0.201541	+	0.129523i	0.435978	+	0.899958i	$0.356403\pi$
$992$		0			0
$993$	10.4406	−	22.8618i	0.331323	−	0.725497i
$994$		0			0
$995$	9.92383	+	21.7302i	0.314606	+	0.688892i
$996$		0			0
$997$	7.67961	+	53.4128i	0.243216	+	1.69160i	0.635775	+	0.771875i	$0.280681\pi$
$997$	7.67961	+	53.4128i	0.243216	+	1.69160i	−0.392559	+	0.919727i	$0.628410\pi$
$998$		0			0
$999$	5.93690	−	6.85154i	0.187835	−	0.216773i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.m.a.81.3	✓	30
23.2	even	11	inner	460.2.m.a.301.3	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.m.a.81.3	✓	30	1.1	even	1	trivial
460.2.m.a.301.3	yes	30	23.2	even	11	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.m (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.241946 - 1.68277i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(2.58157 + 2.97929i) q^{7} +(0.105306 + 0.0309206i) q^{9} +O(q^{10})\)	\(q+(0.241946 - 1.68277i) q^{3} +(-0.959493 + 0.281733i) q^{5} +(2.58157 + 2.97929i) q^{7} +(0.105306 + 0.0309206i) q^{9} +(1.84361 + 1.18481i) q^{11} +(2.08288 - 2.40377i) q^{13} +(0.241946 + 1.68277i) q^{15} +(0.820281 + 1.79617i) q^{17} +(0.904027 - 1.97954i) q^{19} +(5.63805 - 3.62336i) q^{21} +(-3.74040 - 3.00157i) q^{23} +(0.841254 - 0.540641i) q^{25} +(2.19622 - 4.80905i) q^{27} +(0.693399 + 1.51833i) q^{29} +(0.122568 + 0.852481i) q^{31} +(2.43982 - 2.81570i) q^{33} +(-3.31636 - 2.13129i) q^{35} +(1.64535 + 0.483119i) q^{37} +(-3.54104 - 4.08658i) q^{39} +(-1.93728 + 0.568838i) q^{41} +(1.39884 - 9.72914i) q^{43} -0.109752 q^{45} -6.47457 q^{47} +(-1.21546 + 8.45371i) q^{49} +(3.22099 - 0.945769i) q^{51} +(6.84462 + 7.89911i) q^{53} +(-2.10273 - 0.617417i) q^{55} +(-3.11239 - 2.00021i) q^{57} +(-8.37319 + 9.66318i) q^{59} +(1.26755 + 8.81598i) q^{61} +(0.179733 + 0.393561i) q^{63} +(-1.32129 + 2.89321i) q^{65} +(11.5834 - 7.44419i) q^{67} +(-5.95592 + 5.56801i) q^{69} +(2.28434 - 1.46806i) q^{71} +(0.192036 - 0.420501i) q^{73} +(-0.706236 - 1.54644i) q^{75} +(1.22949 + 8.55131i) q^{77} +(-6.61761 + 7.63713i) q^{79} +(-7.28416 - 4.68125i) q^{81} +(-7.69481 - 2.25940i) q^{83} +(-1.29309 - 1.49231i) q^{85} +(2.72277 - 0.799477i) q^{87} +(-0.0222007 + 0.154409i) q^{89} +12.5386 q^{91} +1.46418 q^{93} +(-0.309706 + 2.15405i) q^{95} +(-11.4900 + 3.37375i) q^{97} +(0.157508 + 0.181774i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9}+O(q^{10}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9	\( 30 q - 3 q^{5} + q^{7} + 21 q^{9} + 2 q^{13} + 10 q^{17} + 3 q^{19} + 39 q^{21} + 10 q^{23} - 3 q^{25} + 21 q^{27} + 14 q^{29} - 2 q^{31} - 50 q^{33} - 10 q^{35} + 9 q^{37} + 38 q^{39} - 3 q^{41} - 50 q^{43} + 10 q^{45} - 6 q^{47} - 36 q^{49} - 36 q^{51} - 5 q^{53} - 11 q^{55} + 23 q^{57} + 14 q^{59} - 16 q^{61} - 52 q^{63} + 2 q^{65} + 27 q^{67} + 42 q^{69} + 19 q^{71} + 24 q^{73} - 10 q^{77} - 22 q^{79} + 35 q^{81} + 36 q^{83} + 10 q^{85} - 3 q^{87} - 28 q^{89} - 98 q^{91} - 60 q^{93} - 19 q^{95} - 2 q^{97} - 14 q^{99}+O(q^{100}) \) 30 * q - 3 * q^5 + q^7 + 21 * q^9 + 2 * q^13 + 10 * q^17 + 3 * q^19 + 39 * q^21 + 10 * q^23 - 3 * q^25 + 21 * q^27 + 14 * q^29 - 2 * q^31 - 50 * q^33 - 10 * q^35 + 9 * q^37 + 38 * q^39 - 3 * q^41 - 50 * q^43 + 10 * q^45 - 6 * q^47 - 36 * q^49 - 36 * q^51 - 5 * q^53 - 11 * q^55 + 23 * q^57 + 14 * q^59 - 16 * q^61 - 52 * q^63 + 2 * q^65 + 27 * q^67 + 42 * q^69 + 19 * q^71 + 24 * q^73 - 10 * q^77 - 22 * q^79 + 35 * q^81 + 36 * q^83 + 10 * q^85 - 3 * q^87 - 28 * q^89 - 98 * q^91 - 60 * q^93 - 19 * q^95 - 2 * q^97 - 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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