LMFDB - Embedded newform 220.2.u.a.17.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(13,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 15, 2]))

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

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

chi := DirichletCharacter("220.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.u (of order $20$, degree $8$, 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:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$6$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.4
Character	$\chi$	$=$	220.17
Dual form			220.2.u.a.13.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.194131 - 0.0307474i) q^{3} +(1.80035 + 1.32618i) q^{5} +(-0.509098 + 3.21432i) q^{7} +(-2.81643 + 0.915113i) q^{9} +(2.95000 + 1.51575i) q^{11} +(2.41910 - 4.74775i) q^{13} +(0.390280 + 0.202097i) q^{15} +(-1.82128 - 3.57446i) q^{17} +(4.43615 + 3.22305i) q^{19} +0.639653i q^{21} +(-2.60297 + 2.60297i) q^{23} +(1.48249 + 4.77517i) q^{25} +(-1.04400 + 0.531947i) q^{27} +(3.79815 - 2.75952i) q^{29} +(-2.52450 - 7.76962i) q^{31} +(0.619293 + 0.203550i) q^{33} +(-5.17932 + 5.11173i) q^{35} +(-11.1573 - 1.76715i) q^{37} +(0.323642 - 0.996068i) q^{39} +(5.80437 - 7.98904i) q^{41} +(-5.17742 - 5.17742i) q^{43} +(-6.28415 - 2.08757i) q^{45} +(-0.104856 - 0.662035i) q^{47} +(-3.41527 - 1.10969i) q^{49} +(-0.463472 - 0.637915i) q^{51} +(5.66778 + 2.88788i) q^{53} +(3.30087 + 6.64111i) q^{55} +(0.960296 + 0.489295i) q^{57} +(4.44597 + 6.11936i) q^{59} +(-7.85138 - 2.55107i) q^{61} +(-1.50763 - 9.51878i) q^{63} +(10.6516 - 5.33943i) q^{65} +(-7.99503 - 7.99503i) q^{67} +(-0.425284 + 0.585353i) q^{69} +(-3.11574 + 9.58925i) q^{71} +(-1.12278 - 0.177831i) q^{73} +(0.434622 + 0.881427i) q^{75} +(-6.37394 + 8.71058i) q^{77} +(1.14340 + 3.51903i) q^{79} +(7.00107 - 5.08658i) q^{81} +(-1.67047 + 0.851148i) q^{83} +(1.46145 - 8.85060i) q^{85} +(0.652493 - 0.652493i) q^{87} +1.02792i q^{89} +(14.0292 + 10.1928i) q^{91} +(-0.728981 - 1.43071i) q^{93} +(3.71226 + 11.6857i) q^{95} +(1.52904 - 3.00091i) q^{97} +(-9.69555 - 1.56941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) $ 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.194131	−	0.0307474i	0.112082	−	0.0177520i	−0.100142	−	0.994973i	$-0.531930\pi$
$3$	0.194131	−	0.0307474i	0.112082	−	0.0177520i	0.212223	+	0.977221i	$0.431930\pi$
$4$		0			0
$5$	1.80035	+	1.32618i	0.805139	+	0.593086i
$5$	1.80035	+	1.32618i	0.805139	+	0.593086i
$6$		0			0
$7$	−0.509098	+	3.21432i	−0.192421	+	1.21490i	0.682592	+	0.730799i	$0.260852\pi$
$7$	−0.509098	+	3.21432i	−0.192421	+	1.21490i	−0.875013	+	0.484099i	$0.839148\pi$
$8$		0			0
$9$	−2.81643	+	0.915113i	−0.938809	+	0.305038i
$10$		0			0
$11$	2.95000	+	1.51575i	0.889459	+	0.457015i
$11$	2.95000	+	1.51575i	0.889459	+	0.457015i
$12$		0			0
$13$	2.41910	−	4.74775i	0.670938	−	1.31679i	−0.264872	−	0.964284i	$-0.585330\pi$
$13$	2.41910	−	4.74775i	0.670938	−	1.31679i	0.935810	−	0.352506i	$-0.114670\pi$
$14$		0			0
$15$	0.390280	+	0.202097i	0.100770	+	0.0521813i
$16$		0			0
$17$	−1.82128	−	3.57446i	−0.441724	−	0.866933i	−0.999322	−	0.0368214i	$-0.988277\pi$
$17$	−1.82128	−	3.57446i	−0.441724	−	0.866933i	0.557597	−	0.830111i	$-0.311723\pi$
$18$		0			0
$19$	4.43615	+	3.22305i	1.01772	+	0.739418i	0.965815	−	0.259233i	$-0.0834699\pi$
$19$	4.43615	+	3.22305i	1.01772	+	0.739418i	0.0519075	+	0.998652i	$0.483470\pi$
$20$		0			0
$21$			0.639653i			0.139584i
$22$		0			0
$23$	−2.60297	+	2.60297i	−0.542757	+	0.542757i	−0.924336	−	0.381579i	$-0.875380\pi$
$23$	−2.60297	+	2.60297i	−0.542757	+	0.542757i	0.381579	+	0.924336i	$0.375380\pi$
$24$		0			0
$25$	1.48249	+	4.77517i	0.296498	+	0.955033i
$26$		0			0
$27$	−1.04400	+	0.531947i	−0.200919	+	0.102373i
$28$		0			0
$29$	3.79815	−	2.75952i	0.705299	−	0.512430i	−0.176354	−	0.984327i	$-0.556430\pi$
$29$	3.79815	−	2.75952i	0.705299	−	0.512430i	0.881654	+	0.471897i	$0.156430\pi$
$30$		0			0
$31$	−2.52450	−	7.76962i	−0.453414	−	1.39547i	−0.872987	−	0.487744i	$-0.837820\pi$
$31$	−2.52450	−	7.76962i	−0.453414	−	1.39547i	0.419573	−	0.907722i	$-0.362180\pi$
$32$		0			0
$33$	0.619293	+	0.203550i	0.107805	+	0.0354334i
$34$		0			0
$35$	−5.17932	+	5.11173i	−0.875465	+	0.864040i
$36$		0			0
$37$	−11.1573	−	1.76715i	−1.83426	−	0.290518i	−0.859063	−	0.511870i	$-0.828953\pi$
$37$	−11.1573	−	1.76715i	−1.83426	−	0.290518i	−0.975194	+	0.221353i	$0.928953\pi$
$38$		0			0
$39$	0.323642	−	0.996068i	0.0518242	−	0.159499i
$40$		0			0
$41$	5.80437	−	7.98904i	0.906491	−	1.24768i	−0.0618598	−	0.998085i	$-0.519703\pi$
$41$	5.80437	−	7.98904i	0.906491	−	1.24768i	0.968351	−	0.249593i	$-0.0802968\pi$
$42$		0			0
$43$	−5.17742	−	5.17742i	−0.789549	−	0.789549i	0.191871	−	0.981420i	$-0.438544\pi$
$43$	−5.17742	−	5.17742i	−0.789549	−	0.789549i	−0.981420	+	0.191871i	$0.938544\pi$
$44$		0			0
$45$	−6.28415	−	2.08757i	−0.936786	−	0.311197i
$46$		0			0
$47$	−0.104856	−	0.662035i	−0.0152948	−	0.0965678i	0.978860	−	0.204531i	$-0.0655670\pi$
$47$	−0.104856	−	0.662035i	−0.0152948	−	0.0965678i	−0.994155	+	0.107964i	$0.965567\pi$
$48$		0			0
$49$	−3.41527	−	1.10969i	−0.487895	−	0.158527i
$50$		0			0
$51$	−0.463472	−	0.637915i	−0.0648991	−	0.0893259i
$52$		0			0
$53$	5.66778	+	2.88788i	0.778530	+	0.396681i	0.797638	−	0.603137i	$-0.206083\pi$
$53$	5.66778	+	2.88788i	0.778530	+	0.396681i	−0.0191079	+	0.999817i	$0.506083\pi$
$54$		0			0
$55$	3.30087	+	6.64111i	0.445089	+	0.895486i
$56$		0			0
$57$	0.960296	+	0.489295i	0.127194	+	0.0648087i
$58$		0			0
$59$	4.44597	+	6.11936i	0.578817	+	0.796673i	0.993565	−	0.113263i	$-0.0361304\pi$
$59$	4.44597	+	6.11936i	0.578817	+	0.796673i	−0.414748	+	0.909936i	$0.636130\pi$
$60$		0			0
$61$	−7.85138	−	2.55107i	−1.00527	−	0.326631i	−0.240298	−	0.970699i	$-0.577245\pi$
$61$	−7.85138	−	2.55107i	−1.00527	−	0.326631i	−0.764968	+	0.644068i	$0.777245\pi$
$62$		0			0
$63$	−1.50763	−	9.51878i	−0.189943	−	1.19925i
$64$		0			0
$65$	10.6516	−	5.33943i	1.32117	−	0.662275i
$66$		0			0
$67$	−7.99503	−	7.99503i	−0.976748	−	0.976748i	0.0229875	−	0.999736i	$-0.492682\pi$
$67$	−7.99503	−	7.99503i	−0.976748	−	0.976748i	−0.999736	+	0.0229875i	$0.992682\pi$
$68$		0			0
$69$	−0.425284	+	0.585353i	−0.0511982	+	0.0704682i
$70$		0			0
$71$	−3.11574	+	9.58925i	−0.369770	+	1.13803i	0.577170	+	0.816624i	$0.304157\pi$
$71$	−3.11574	+	9.58925i	−0.369770	+	1.13803i	−0.946940	+	0.321410i	$0.895843\pi$
$72$		0			0
$73$	−1.12278	−	0.177831i	−0.131412	−	0.0208136i	0.0903820	−	0.995907i	$-0.471191\pi$
$73$	−1.12278	−	0.177831i	−0.131412	−	0.0208136i	−0.221794	+	0.975094i	$0.571191\pi$
$74$		0			0
$75$	0.434622	+	0.881427i	0.0501858	+	0.101778i
$76$		0			0
$77$	−6.37394	+	8.71058i	−0.726378	+	0.992662i
$78$		0			0
$79$	1.14340	+	3.51903i	0.128643	+	0.395922i	0.994547	−	0.104288i	$-0.0332563\pi$
$79$	1.14340	+	3.51903i	0.128643	+	0.395922i	−0.865904	+	0.500210i	$0.833256\pi$
$80$		0			0
$81$	7.00107	−	5.08658i	0.777897	−	0.565175i
$82$		0			0
$83$	−1.67047	+	0.851148i	−0.183358	+	0.0934256i	−0.543260	−	0.839565i	$-0.682810\pi$
$83$	−1.67047	+	0.851148i	−0.183358	+	0.0934256i	0.359902	+	0.932990i	$0.382810\pi$
$84$		0			0
$85$	1.46145	−	8.85060i	0.158516	−	0.959982i
$86$		0			0
$87$	0.652493	−	0.652493i	0.0699546	−	0.0699546i
$88$		0			0
$89$			1.02792i			0.108959i	0.998515	+	0.0544795i	$0.0173500\pi$
$89$			1.02792i			0.108959i	−0.998515	+	0.0544795i	$0.982650\pi$
$90$		0			0
$91$	14.0292	+	10.1928i	1.47066	+	1.06850i
$92$		0			0
$93$	−0.728981	−	1.43071i	−0.0755918	−	0.148357i
$94$		0			0
$95$	3.71226	+	11.6857i	0.380869	+	1.19893i
$96$		0			0
$97$	1.52904	−	3.00091i	0.155250	−	0.304696i	−0.800260	−	0.599653i	$-0.795305\pi$
$97$	1.52904	−	3.00091i	0.155250	−	0.304696i	0.955511	+	0.294957i	$0.0953053\pi$
$98$		0			0
$99$	−9.69555	−	1.56941i	−0.974439	−	0.157732i
$100$		0			0
$101$	0.104950	−	0.0341002i	0.0104429	−	0.00339310i	−0.303791	−	0.952739i	$-0.598252\pi$
$101$	0.104950	−	0.0341002i	0.0104429	−	0.00339310i	0.314234	+	0.949346i	$0.398252\pi$
$102$		0			0
$103$	0.0161183	−	0.101767i	0.00158818	−	0.0100274i	−0.986882	−	0.161446i	$-0.948384\pi$
$103$	0.0161183	−	0.101767i	0.00158818	−	0.0100274i	0.988470	+	0.151419i	$0.0483842\pi$
$104$		0			0
$105$	−0.848296	+	1.15160i	−0.0827852	+	0.112384i
$106$		0			0
$107$	15.7562	−	2.49553i	1.52321	−	0.241252i	0.661999	−	0.749505i	$-0.269708\pi$
$107$	15.7562	−	2.49553i	1.52321	−	0.241252i	0.861208	+	0.508252i	$0.169708\pi$
$108$		0			0
$109$	−0.774585			−0.0741918			−0.0370959	−	0.999312i	$-0.511811\pi$
$109$	−0.774585			−0.0741918			−0.0370959	+	0.999312i	$0.511811\pi$
$110$		0			0
$111$	−2.22033			−0.210744
$112$		0			0
$113$	8.69124	−	1.37656i	0.817603	−	0.129496i	0.266395	−	0.963864i	$-0.414167\pi$
$113$	8.69124	−	1.37656i	0.817603	−	0.129496i	0.551207	+	0.834368i	$0.314167\pi$
$114$		0			0
$115$	−8.13826	+	1.23424i	−0.758897	+	0.115093i
$116$		0			0
$117$	−2.46849	+	15.5855i	−0.228212	+	1.44088i
$118$		0			0
$119$	12.4166	−	4.03441i	1.13823	−	0.369834i
$120$		0			0
$121$	6.40501	+	8.94292i	0.582274	+	0.812993i
$122$		0			0
$123$	0.881169	−	1.72939i	0.0794523	−	0.155934i
$124$		0			0
$125$	−3.66373	+	10.5630i	−0.327694	+	0.944784i
$126$		0			0
$127$	1.86542	+	3.66110i	0.165529	+	0.324870i	0.958840	−	0.283948i	$-0.0916442\pi$
$127$	1.86542	+	3.66110i	0.165529	+	0.324870i	−0.793310	+	0.608817i	$0.791644\pi$
$128$		0			0
$129$	−1.16429	−	0.845907i	−0.102510	−	0.0744780i
$130$		0			0
$131$		−	8.42076i		−	0.735725i	−0.929880	−	0.367863i	$-0.880090\pi$
$131$		−	8.42076i		−	0.735725i	0.929880	−	0.367863i	$-0.119910\pi$
$132$		0			0
$133$	−12.6183	+	12.6183i	−1.09415	+	1.09415i
$134$		0			0
$135$	−2.58503	−	0.426850i	−0.222484	−	0.0367374i
$136$		0			0
$137$	3.28044	−	1.67147i	0.280267	−	0.142803i	−0.308207	−	0.951319i	$-0.599729\pi$
$137$	3.28044	−	1.67147i	0.280267	−	0.142803i	0.588474	+	0.808516i	$0.299729\pi$
$138$		0			0
$139$	2.79197	−	2.02848i	0.236811	−	0.172054i	−0.463050	−	0.886332i	$-0.653245\pi$
$139$	2.79197	−	2.02848i	0.236811	−	0.172054i	0.699862	+	0.714279i	$0.253245\pi$
$140$		0			0
$141$	−0.0407117	−	0.125298i	−0.00342854	−	0.0105520i
$142$		0			0
$143$	14.3327	−	10.3391i	1.19856	−	0.864601i
$144$		0			0
$145$	10.4976	+	0.0689452i	0.871779	+	0.00572559i
$146$		0			0
$147$	−0.697130	−	0.110415i	−0.0574983	−	0.00910684i
$148$		0			0
$149$	−1.65385	+	5.09001i	−0.135488	+	0.416990i	−0.995666	−	0.0930049i	$-0.970353\pi$
$149$	−1.65385	+	5.09001i	−0.135488	+	0.416990i	0.860177	+	0.509995i	$0.170353\pi$
$150$		0			0
$151$	2.65450	−	3.65361i	0.216020	−	0.297326i	−0.687231	−	0.726439i	$-0.741174\pi$
$151$	2.65450	−	3.65361i	0.216020	−	0.297326i	0.903251	+	0.429113i	$0.141174\pi$
$152$		0			0
$153$	8.40052	+	8.40052i	0.679142	+	0.679142i
$154$		0			0
$155$	5.75894	−	17.3360i	0.462569	−	1.39246i
$156$		0			0
$157$	0.910804	+	5.75059i	0.0726901	+	0.458947i	0.997006	+	0.0773197i	$0.0246362\pi$
$157$	0.910804	+	5.75059i	0.0726901	+	0.458947i	−0.924316	+	0.381627i	$0.875364\pi$
$158$		0			0
$159$	1.18909	+	0.386359i	0.0943009	+	0.0306402i
$160$		0			0
$161$	−7.04161	−	9.69195i	−0.554957	−	0.763832i
$162$		0			0
$163$	−11.0851	−	5.64816i	−0.868255	−	0.442398i	−0.0376700	−	0.999290i	$-0.511994\pi$
$163$	−11.0851	−	5.64816i	−0.868255	−	0.442398i	−0.830585	+	0.556892i	$0.811994\pi$
$164$		0			0
$165$	0.844998	+	1.18775i	0.0657830	+	0.0924665i
$166$		0			0
$167$	−5.59615	−	2.85138i	−0.433043	−	0.220646i	0.223861	−	0.974621i	$-0.428134\pi$
$167$	−5.59615	−	2.85138i	−0.433043	−	0.220646i	−0.656903	+	0.753975i	$0.728134\pi$
$168$		0			0
$169$	−9.04789	−	12.4534i	−0.695992	−	0.957950i
$170$		0			0
$171$	−15.4435	−	5.01791i	−1.18100	−	0.383729i
$172$		0			0
$173$	2.37792	+	15.0136i	0.180790	+	1.14146i	0.896493	+	0.443058i	$0.146106\pi$
$173$	2.37792	+	15.0136i	0.180790	+	1.14146i	−0.715703	+	0.698405i	$0.753894\pi$
$174$		0			0
$175$	−16.1036	+	2.33417i	−1.21732	+	0.176447i
$176$		0			0
$177$	1.05126	+	1.05126i	0.0790173	+	0.0790173i
$178$		0			0
$179$	−4.23571	+	5.82995i	−0.316592	+	0.435751i	−0.937423	−	0.348193i	$-0.886795\pi$
$179$	−4.23571	+	5.82995i	−0.316592	+	0.435751i	0.620831	+	0.783944i	$0.286795\pi$
$180$		0			0
$181$	−3.59279	+	11.0575i	−0.267050	+	0.821896i	0.724164	+	0.689628i	$0.242226\pi$
$181$	−3.59279	+	11.0575i	−0.267050	+	0.821896i	−0.991214	+	0.132268i	$0.957774\pi$
$182$		0			0
$183$	−1.60264	−	0.253833i	−0.118470	−	0.0187639i
$184$		0			0
$185$	−17.7435	−	17.9781i	−1.30453	−	1.32178i
$186$		0			0
$187$	0.0452105	−	13.3052i	0.00330612	−	0.972976i
$188$		0			0
$189$	−1.17835	−	3.62658i	−0.0857121	−	0.263795i
$190$		0			0
$191$	−13.0699	+	9.49582i	−0.945703	+	0.687094i	−0.949787	−	0.312898i	$-0.898700\pi$
$191$	−13.0699	+	9.49582i	−0.945703	+	0.687094i	0.00408349	+	0.999992i	$0.498700\pi$
$192$		0			0
$193$	−7.18138	+	3.65910i	−0.516927	+	0.263388i	−0.692934	−	0.721001i	$-0.743682\pi$
$193$	−7.18138	+	3.65910i	−0.516927	+	0.263388i	0.176006	+	0.984389i	$0.443682\pi$
$194$		0			0
$195$	1.90363	−	1.36406i	0.136322	−	0.0976824i
$196$		0			0
$197$	7.99806	−	7.99806i	0.569838	−	0.569838i	−0.362245	−	0.932083i	$-0.617990\pi$
$197$	7.99806	−	7.99806i	0.569838	−	0.569838i	0.932083	+	0.362245i	$0.117990\pi$
$198$		0			0
$199$		−	7.97776i		−	0.565529i	−0.959189	−	0.282764i	$-0.908749\pi$
$199$		−	7.97776i		−	0.565529i	0.959189	−	0.282764i	$-0.0912514\pi$
$200$		0			0
$201$	−1.79791	−	1.30626i	−0.126815	−	0.0921365i
$202$		0			0
$203$	6.93634	+	13.6133i	0.486836	+	0.955469i
$204$		0			0
$205$	21.0448	−	6.68538i	1.46983	−	0.466927i
$206$		0			0
$207$	4.94907	−	9.71309i	0.343984	−	0.675107i
$208$		0			0
$209$	8.20131	+	16.2321i	0.567296	+	1.12280i
$210$		0			0
$211$	4.86478	−	1.58066i	0.334905	−	0.108817i	−0.136737	−	0.990607i	$-0.543661\pi$
$211$	4.86478	−	1.58066i	0.334905	−	0.108817i	0.471642	+	0.881790i	$0.343661\pi$
$212$		0			0
$213$	−0.310018	+	1.95737i	−0.0212421	+	0.134117i
$214$		0			0
$215$	−2.45495	−	16.1873i	−0.167427	−	1.10397i
$216$		0			0
$217$	26.2593	−	4.15906i	1.78259	−	0.282335i
$218$		0			0
$219$	−0.223435			−0.0150984
$220$		0			0
$221$	−21.3765			−1.43794
$222$		0			0
$223$	−9.55172	+	1.51284i	−0.639631	+	0.101308i	−0.467822	−	0.883823i	$-0.654961\pi$
$223$	−9.55172	+	1.51284i	−0.639631	+	0.101308i	−0.171809	+	0.985130i	$0.554961\pi$
$224$		0			0
$225$	−8.54515	−	12.0923i	−0.569677	−	0.806151i
$226$		0			0
$227$	−1.91526	+	12.0925i	−0.127120	+	0.802607i	0.838927	+	0.544243i	$0.183183\pi$
$227$	−1.91526	+	12.0925i	−0.127120	+	0.802607i	−0.966048	+	0.258363i	$0.916817\pi$
$228$		0			0
$229$	−9.71729	+	3.15734i	−0.642137	+	0.208643i	−0.611944	−	0.790901i	$-0.709612\pi$
$229$	−9.71729	+	3.15734i	−0.642137	+	0.208643i	−0.0301930	+	0.999544i	$0.509612\pi$
$230$		0			0
$231$	−0.969554	+	1.88698i	−0.0637920	+	0.124154i
$232$		0			0
$233$	−0.650378	+	1.27644i	−0.0426077	+	0.0836222i	−0.911329	−	0.411679i	$-0.864942\pi$
$233$	−0.650378	+	1.27644i	−0.0426077	+	0.0836222i	0.868721	+	0.495301i	$0.164942\pi$
$234$		0			0
$235$	0.689201	−	1.33095i	0.0449585	−	0.0868217i
$236$		0			0
$237$	0.330171	+	0.647998i	0.0214469	+	0.0420920i
$238$		0			0
$239$	−22.4095	−	16.2815i	−1.44955	−	1.05316i	−0.985936	−	0.167125i	$-0.946552\pi$
$239$	−22.4095	−	16.2815i	−1.44955	−	1.05316i	−0.463617	−	0.886036i	$-0.653448\pi$
$240$		0			0
$241$			6.65481i			0.428674i	0.976760	+	0.214337i	$0.0687591\pi$
$241$			6.65481i			0.428674i	−0.976760	+	0.214337i	$0.931241\pi$
$242$		0			0
$243$	3.68831	−	3.68831i	0.236605	−	0.236605i
$244$		0			0
$245$	−4.67701	−	6.52708i	−0.298804	−	0.417000i
$246$		0			0
$247$	26.0337	−	13.2648i	1.65649	−	0.844022i
$248$		0			0
$249$	−0.298120	+	0.216597i	−0.0188926	+	0.0137263i
$250$		0			0
$251$	7.36460	+	22.6659i	0.464849	+	1.43066i	0.859172	+	0.511687i	$0.170979\pi$
$251$	7.36460	+	22.6659i	0.464849	+	1.43066i	−0.394323	+	0.918972i	$0.629021\pi$
$252$		0			0
$253$	−11.6242	+	3.73332i	−0.730808	+	0.234712i
$254$		0			0
$255$	0.0115796	−	1.76311i	0.000725143	−	0.110411i
$256$		0			0
$257$	4.32895	+	0.685639i	0.270033	+	0.0427690i	0.289982	−	0.957032i	$-0.406351\pi$
$257$	4.32895	+	0.685639i	0.270033	+	0.0427690i	−0.0199496	+	0.999801i	$0.506351\pi$
$258$		0			0
$259$	11.3604	−	34.9636i	0.705899	−	2.17253i
$260$		0			0
$261$	−8.17195	+	11.2477i	−0.505831	+	0.696217i
$262$		0			0
$263$	−12.6404	−	12.6404i	−0.779442	−	0.779442i	0.200294	−	0.979736i	$-0.435810\pi$
$263$	−12.6404	−	12.6404i	−0.779442	−	0.779442i	−0.979736	+	0.200294i	$0.935810\pi$
$264$		0			0
$265$	6.37412	+	12.7157i	0.391559	+	0.781119i
$266$		0			0
$267$	0.0316058	+	0.199551i	0.00193424	+	0.0122123i
$268$		0			0
$269$	−19.6421	−	6.38211i	−1.19760	−	0.389124i	−0.358723	−	0.933444i	$-0.616788\pi$
$269$	−19.6421	−	6.38211i	−1.19760	−	0.389124i	−0.838878	+	0.544320i	$0.816788\pi$
$270$		0			0
$271$	−3.67960	−	5.06454i	−0.223520	−	0.307649i	0.682499	−	0.730887i	$-0.260893\pi$
$271$	−3.67960	−	5.06454i	−0.223520	−	0.307649i	−0.906018	+	0.423238i	$0.860893\pi$
$272$		0			0
$273$	3.03692	+	1.54739i	0.183802	+	0.0936520i
$274$		0			0
$275$	−2.86460	+	16.3338i	−0.172742	+	0.984967i
$276$		0			0
$277$	−20.8758	−	10.6368i	−1.25431	−	0.639102i	−0.304672	−	0.952457i	$-0.598547\pi$
$277$	−20.8758	−	10.6368i	−1.25431	−	0.639102i	−0.949636	+	0.313356i	$0.898547\pi$
$278$		0			0
$279$	14.2202	+	19.5724i	0.851339	+	1.17177i
$280$		0			0
$281$	9.65989	+	3.13869i	0.576261	+	0.187238i	0.582625	−	0.812741i	$-0.302026\pi$
$281$	9.65989	+	3.13869i	0.576261	+	0.187238i	−0.00636405	+	0.999980i	$0.502026\pi$
$282$		0			0
$283$	2.06021	+	13.0076i	0.122467	+	0.773225i	0.970111	+	0.242660i	$0.0780200\pi$
$283$	2.06021	+	13.0076i	0.122467	+	0.773225i	−0.847645	+	0.530564i	$0.821980\pi$
$284$		0			0
$285$	1.07997	+	2.15443i	0.0639720	+	0.127617i
$286$		0			0
$287$	22.7243	+	22.7243i	1.34137	+	1.34137i
$288$		0			0
$289$	0.532661	−	0.733145i	0.0313330	−	0.0431262i
$290$		0			0
$291$	0.204564	−	0.629584i	0.0119918	−	0.0369069i
$292$		0			0
$293$	−7.75437	−	1.22817i	−0.453015	−	0.0717506i	−0.0742424	−	0.997240i	$-0.523654\pi$
$293$	−7.75437	−	1.22817i	−0.453015	−	0.0717506i	−0.378773	+	0.925490i	$0.623654\pi$
$294$		0			0
$295$	−0.111080	+	16.9131i	−0.00646735	+	0.984720i
$296$		0			0
$297$	−3.88611	−	0.0132048i	−0.225495	−	0.000766221i
$298$		0			0
$299$	6.06141	+	18.6551i	0.350541	+	1.07885i
$300$		0			0
$301$	19.2777	−	14.0061i	1.11115	−	0.807296i
$302$		0			0
$303$	0.0193255	−	0.00984686i	0.00111022	−	0.000565687i
$304$		0			0
$305$	−10.7520	−	15.0052i	−0.615659	−	0.859193i
$306$		0			0
$307$	−6.65300	+	6.65300i	−0.379707	+	0.379707i	−0.870996	−	0.491289i	$-0.836526\pi$
$307$	−6.65300	+	6.65300i	−0.379707	+	0.379707i	0.491289	+	0.870996i	$0.336526\pi$
$308$		0			0
$309$		−	0.0202518i		−	0.00115208i
$310$		0			0
$311$	6.20361	+	4.50719i	0.351774	+	0.255579i	0.749613	−	0.661876i	$-0.230240\pi$
$311$	6.20361	+	4.50719i	0.351774	+	0.255579i	−0.397839	+	0.917455i	$0.630240\pi$
$312$		0			0
$313$	14.3750	+	28.2126i	0.812526	+	1.59467i	0.803941	+	0.594709i	$0.202733\pi$
$313$	14.3750	+	28.2126i	0.812526	+	1.59467i	0.00858451	+	0.999963i	$0.497267\pi$
$314$		0			0
$315$	9.90937	−	19.1365i	0.558330	−	1.07822i
$316$		0			0
$317$	−3.88557	+	7.62587i	−0.218236	+	0.428311i	−0.974005	−	0.226526i	$-0.927263\pi$
$317$	−3.88557	+	7.62587i	−0.218236	+	0.428311i	0.755769	+	0.654838i	$0.227263\pi$
$318$		0			0
$319$	15.3873	−	2.38354i	0.861523	−	0.133453i
$320$		0			0
$321$	2.98204	−	0.968923i	0.166441	−	0.0540800i
$322$		0			0
$323$	3.44120	−	21.7269i	0.191473	−	1.20892i
$324$		0			0
$325$	26.2576	+	4.51310i	1.45651	+	0.250342i
$326$		0			0
$327$	−0.150371	+	0.0238165i	−0.00831555	+	0.00131705i
$328$		0			0
$329$	2.18137			0.120263
$330$		0			0
$331$	−16.9166			−0.929820			−0.464910	−	0.885358i	$-0.653913\pi$
$331$	−16.9166			−0.929820			−0.464910	+	0.885358i	$0.653913\pi$
$332$		0			0
$333$	33.0410	−	5.23318i	1.81064	−	0.286777i
$334$		0			0
$335$	−3.79097	−	24.9967i	−0.207123	−	1.36571i
$336$		0			0
$337$	−2.68338	+	16.9422i	−0.146173	+	0.922901i	0.800178	+	0.599762i	$0.204738\pi$
$337$	−2.68338	+	16.9422i	−0.146173	+	0.922901i	−0.946352	+	0.323139i	$0.895262\pi$
$338$		0			0
$339$	1.64492	−	0.534466i	0.0893396	−	0.0290282i
$340$		0			0
$341$	4.32951	−	26.7469i	0.234456	−	1.44843i
$342$		0			0
$343$	−5.03663	+	9.88494i	−0.271952	+	0.533736i
$344$		0			0
$345$	−1.54194	+	0.489835i	−0.0830153	+	0.0263718i
$346$		0			0
$347$	11.4038	+	22.3812i	0.612187	+	1.20149i	0.964122	+	0.265461i	$0.0855240\pi$
$347$	11.4038	+	22.3812i	0.612187	+	1.20149i	−0.351934	+	0.936025i	$0.614476\pi$
$348$		0			0
$349$	4.91014	+	3.56743i	0.262834	+	0.190960i	0.711395	−	0.702792i	$-0.248064\pi$
$349$	4.91014	+	3.56743i	0.262834	+	0.190960i	−0.448562	+	0.893752i	$0.648064\pi$
$350$		0			0
$351$			6.24351i			0.333254i
$352$		0			0
$353$	17.8379	−	17.8379i	0.949413	−	0.949413i	−0.0493677	−	0.998781i	$-0.515721\pi$
$353$	17.8379	−	17.8379i	0.949413	−	0.949413i	0.998781	+	0.0493677i	$0.0157206\pi$
$354$		0			0
$355$	−18.3265	+	13.1319i	−0.972668	+	0.696971i
$356$		0			0
$357$	2.28641	−	1.16499i	0.121010	−	0.0616576i
$358$		0			0
$359$	−7.65250	+	5.55987i	−0.403883	+	0.293439i	−0.771121	−	0.636689i	$-0.780304\pi$
$359$	−7.65250	+	5.55987i	−0.403883	+	0.293439i	0.367237	+	0.930127i	$0.380304\pi$
$360$		0			0
$361$	3.42003	+	10.5258i	0.180002	+	0.553989i
$362$		0			0
$363$	1.51838	+	1.53916i	0.0796945	+	0.0807852i
$364$		0			0
$365$	−1.78556	−	1.80917i	−0.0934605	−	0.0946963i
$366$		0			0
$367$	−17.3544	−	2.74867i	−0.905895	−	0.143480i	−0.313932	−	0.949445i	$-0.601647\pi$
$367$	−17.3544	−	2.74867i	−0.905895	−	0.143480i	−0.591962	+	0.805966i	$0.701647\pi$
$368$		0			0
$369$	−9.03673	+	27.8122i	−0.470434	+	1.44785i
$370$		0			0
$371$	−12.1680	+	16.7478i	−0.631732	+	0.869505i
$372$		0			0
$373$	10.6232	+	10.6232i	0.550050	+	0.550050i	0.926455	−	0.376405i	$-0.122840\pi$
$373$	10.6232	+	10.6232i	0.550050	+	0.550050i	−0.376405	+	0.926455i	$0.622840\pi$
$374$		0			0
$375$	−0.386461	+	2.16326i	−0.0199568	+	0.111710i
$376$		0			0
$377$	−3.91340	−	24.7082i	−0.201550	−	1.27254i
$378$		0			0
$379$	−0.421294	−	0.136887i	−0.0216404	−	0.00703139i	0.298177	−	0.954511i	$-0.403621\pi$
$379$	−0.421294	−	0.136887i	−0.0216404	−	0.00703139i	−0.319817	+	0.947479i	$0.603621\pi$
$380$		0			0
$381$	0.474706	+	0.653377i	0.0243199	+	0.0334735i
$382$		0			0
$383$	12.2989	+	6.26658i	0.628442	+	0.320207i	0.739044	−	0.673658i	$-0.235278\pi$
$383$	12.2989	+	6.26658i	0.628442	+	0.320207i	−0.110602	+	0.993865i	$0.535278\pi$
$384$		0			0
$385$	−23.0271	+	7.22906i	−1.17357	+	0.368427i
$386$		0			0
$387$	19.3197	+	9.84390i	0.982078	+	0.500394i
$388$		0			0
$389$	−10.4451	−	14.3765i	−0.529588	−	0.728915i	0.457480	−	0.889220i	$-0.348752\pi$
$389$	−10.4451	−	14.3765i	−0.529588	−	0.728915i	−0.987068	+	0.160305i	$0.948752\pi$
$390$		0			0
$391$	14.0449	+	4.56348i	0.710283	+	0.230785i
$392$		0			0
$393$	−0.258916	−	1.63473i	−0.0130606	−	0.0824614i
$394$		0			0
$395$	−2.60835	+	7.85183i	−0.131240	+	0.395069i
$396$		0			0
$397$	21.6616	+	21.6616i	1.08717	+	1.08717i	0.995819	+	0.0913478i	$0.0291175\pi$
$397$	21.6616	+	21.6616i	1.08717	+	1.08717i	0.0913478	+	0.995819i	$0.470883\pi$
$398$		0			0
$399$	−2.06164	+	2.83760i	−0.103211	+	0.142058i
$400$		0			0
$401$	1.10249	−	3.39310i	0.0550555	−	0.169444i	−0.919748	−	0.392510i	$-0.871607\pi$
$401$	1.10249	−	3.39310i	0.0550555	−	0.169444i	0.974803	+	0.223067i	$0.0716068\pi$
$402$		0			0
$403$	−42.9953	−	6.80978i	−2.14175	−	0.339219i
$404$		0			0
$405$	19.3501	+	0.127085i	0.961513	+	0.00631493i
$406$		0			0
$407$	−30.2356	−	22.1248i	−1.49872	−	1.09669i
$408$		0			0
$409$	−7.83663	−	24.1187i	−0.387497	−	1.19259i	−0.934653	−	0.355561i	$-0.884290\pi$
$409$	−7.83663	−	24.1187i	−0.387497	−	1.19259i	0.547156	−	0.837030i	$-0.315710\pi$
$410$		0			0
$411$	0.585443	−	0.425349i	0.0288778	−	0.0209809i
$412$		0			0
$413$	−21.9330	+	11.1754i	−1.07925	+	0.549907i
$414$		0			0
$415$	−4.13620	−	0.682986i	−0.203038	−	0.0335265i
$416$		0			0
$417$	0.479638	−	0.479638i	0.0234880	−	0.0234880i
$418$		0			0
$419$		−	18.4358i		−	0.900648i	−0.892865	−	0.450324i	$-0.851308\pi$
$419$		−	18.4358i		−	0.900648i	0.892865	−	0.450324i	$-0.148692\pi$
$420$		0			0
$421$	−21.0494	−	15.2933i	−1.02589	−	0.745351i	−0.0584058	−	0.998293i	$-0.518602\pi$
$421$	−21.0494	−	15.2933i	−1.02589	−	0.745351i	−0.967481	+	0.252942i	$0.918602\pi$
$422$		0			0
$423$	0.901157	+	1.76862i	0.0438157	+	0.0859932i
$424$		0			0
$425$	14.3686	−	13.9960i	0.696979	−	0.678906i
$426$		0			0
$427$	12.1971	−	23.9381i	0.590258	−	1.15845i
$428$		0			0
$429$	2.46453	−	2.44784i	0.118989	−	0.118183i
$430$		0			0
$431$	8.15236	−	2.64886i	0.392685	−	0.127591i	−0.106018	−	0.994364i	$-0.533810\pi$
$431$	8.15236	−	2.64886i	0.392685	−	0.127591i	0.498703	+	0.866773i	$0.333810\pi$
$432$		0			0
$433$	3.37639	−	21.3177i	0.162259	−	1.02446i	−0.763351	−	0.645983i	$-0.776447\pi$
$433$	3.37639	−	21.3177i	0.162259	−	1.02446i	0.925610	−	0.378478i	$-0.123553\pi$
$434$		0			0
$435$	2.04004	−	0.309390i	0.0978122	−	0.0148341i
$436$		0			0
$437$	−19.9367	+	3.15766i	−0.953700	+	0.151051i
$438$		0			0
$439$	12.2003			0.582288			0.291144	−	0.956679i	$-0.405964\pi$
$439$	12.2003			0.582288			0.291144	+	0.956679i	$0.405964\pi$
$440$		0			0
$441$	10.6343			0.506397
$442$		0			0
$443$	−10.9493	+	1.73420i	−0.520218	+	0.0823944i	−0.411021	−	0.911626i	$-0.634828\pi$
$443$	−10.9493	+	1.73420i	−0.520218	+	0.0823944i	−0.109197	+	0.994020i	$0.534828\pi$
$444$		0			0
$445$	−1.36320	+	1.85061i	−0.0646221	+	0.0877272i
$446$		0			0
$447$	−0.164559	+	1.03898i	−0.00778336	+	0.0491422i
$448$		0			0
$449$	−8.90862	+	2.89459i	−0.420424	+	0.136604i	−0.511586	−	0.859232i	$-0.670942\pi$
$449$	−8.90862	+	2.89459i	−0.420424	+	0.136604i	0.0911622	+	0.995836i	$0.470942\pi$
$450$		0			0
$451$	29.2323	−	14.7697i	1.37649	−	0.695478i
$452$		0			0
$453$	0.402983	−	0.790899i	0.0189338	−	0.0371597i
$454$		0			0
$455$	11.7399	+	36.9559i	0.550377	+	1.73252i
$456$		0			0
$457$	−5.96901	−	11.7148i	−0.279218	−	0.547997i	0.708222	−	0.705990i	$-0.249498\pi$
$457$	−5.96901	−	11.7148i	−0.279218	−	0.547997i	−0.987440	+	0.157993i	$0.949498\pi$
$458$		0			0
$459$	3.80284	+	2.76293i	0.177502	+	0.128962i
$460$		0			0
$461$		−	12.4764i		−	0.581084i	−0.956862	−	0.290542i	$-0.906164\pi$
$461$		−	12.4764i		−	0.581084i	0.956862	−	0.290542i	$-0.0938355\pi$
$462$		0			0
$463$	0.334220	−	0.334220i	0.0155325	−	0.0155325i	−0.699298	−	0.714830i	$-0.746504\pi$
$463$	0.334220	−	0.334220i	0.0155325	−	0.0155325i	0.714830	+	0.699298i	$0.246504\pi$
$464$		0			0
$465$	0.584956	−	3.54253i	0.0271267	−	0.164281i
$466$		0			0
$467$	−0.919938	+	0.468732i	−0.0425697	+	0.0216903i	−0.475146	−	0.879907i	$-0.657605\pi$
$467$	−0.919938	+	0.468732i	−0.0425697	+	0.0216903i	0.432576	+	0.901597i	$0.357605\pi$
$468$		0			0
$469$	29.7688	−	21.6283i	1.37460	−	0.998703i
$470$		0			0
$471$	0.353631	+	1.08836i	0.0162945	+	0.0501492i
$472$		0			0
$473$	−7.42572	−	23.1211i	−0.341435	−	1.06311i
$474$		0			0
$475$	−8.81405	+	25.9615i	−0.404416	+	1.19120i
$476$		0			0
$477$	−18.6056	−	2.94684i	−0.851894	−	0.134927i
$478$		0			0
$479$	−12.2212	+	37.6130i	−0.558401	+	1.71858i	0.128388	+	0.991724i	$0.459020\pi$
$479$	−12.2212	+	37.6130i	−0.558401	+	1.71858i	−0.686789	+	0.726857i	$0.740980\pi$
$480$		0			0
$481$	−35.3807	+	48.6974i	−1.61322	+	2.22041i
$482$		0			0
$483$	−1.66500	−	1.66500i	−0.0757601	−	0.0757601i
$484$		0			0
$485$	6.73254	−	3.37489i	0.305709	−	0.153246i
$486$		0			0
$487$	−5.73768	−	36.2263i	−0.259999	−	1.64157i	−0.679399	−	0.733769i	$-0.737759\pi$
$487$	−5.73768	−	36.2263i	−0.259999	−	1.64157i	0.419400	−	0.907802i	$-0.362241\pi$
$488$		0			0
$489$	−2.32564	−	0.755646i	−0.105169	−	0.0341715i
$490$		0			0
$491$	−24.5974	−	33.8554i	−1.11006	−	1.52787i	−0.821322	−	0.570465i	$-0.806763\pi$
$491$	−24.5974	−	33.8554i	−1.11006	−	1.52787i	−0.288742	−	0.957407i	$-0.593237\pi$
$492$		0			0
$493$	−16.7813	−	8.55048i	−0.755790	−	0.385094i
$494$		0			0
$495$	−15.3740	−	15.6835i	−0.691011	−	0.704922i
$496$		0			0
$497$	−29.2367	−	14.8968i	−1.31144	−	0.668214i
$498$		0			0
$499$	25.8822	+	35.6238i	1.15865	+	1.59474i	0.716109	+	0.697989i	$0.245921\pi$
$499$	25.8822	+	35.6238i	1.15865	+	1.59474i	0.442537	+	0.896750i	$0.354079\pi$
$500$		0			0
$501$	−1.17406	−	0.381475i	−0.0524531	−	0.0170431i
$502$		0			0
$503$	3.05893	+	19.3133i	0.136391	+	0.861137i	0.957093	+	0.289781i	$0.0935825\pi$
$503$	3.05893	+	19.3133i	0.136391	+	0.861137i	−0.820702	+	0.571356i	$0.806417\pi$
$504$		0			0
$505$	0.234169	+	0.0777901i	0.0104204	+	0.00346161i
$506$		0			0
$507$	−2.13939	−	2.13939i	−0.0950135	−	0.0950135i
$508$		0			0
$509$	2.50898	−	3.45331i	0.111208	−	0.153065i	−0.749785	−	0.661682i	$-0.769843\pi$
$509$	2.50898	−	3.45331i	0.111208	−	0.153065i	0.860993	+	0.508617i	$0.169843\pi$
$510$		0			0
$511$	1.14321	−	3.51845i	0.0505728	−	0.155647i
$512$		0			0
$513$	−6.34585	−	1.00508i	−0.280176	−	0.0443756i
$514$		0			0
$515$	0.163980	−	0.161840i	0.00722582	−	0.00713152i
$516$		0			0
$517$	0.694154	−	2.11194i	0.0305288	−	0.0928830i
$518$		0			0
$519$	0.923258	+	2.84149i	0.0405265	+	0.124728i
$520$		0			0
$521$	7.92382	−	5.75699i	0.347149	−	0.252218i	−0.400523	−	0.916287i	$-0.631172\pi$
$521$	7.92382	−	5.75699i	0.347149	−	0.252218i	0.747672	+	0.664068i	$0.231172\pi$
$522$		0			0
$523$	26.5041	−	13.5045i	1.15894	−	0.590511i	0.234607	−	0.972090i	$-0.424620\pi$
$523$	26.5041	−	13.5045i	1.15894	−	0.590511i	0.924336	+	0.381580i	$0.124620\pi$
$524$		0			0
$525$	−3.05445	+	0.948281i	−0.133307	+	0.0413864i
$526$		0			0
$527$	−23.1744	+	23.1744i	−1.00949	+	1.00949i
$528$		0			0
$529$			9.44908i			0.410830i
$530$		0			0
$531$	−18.1217	−	13.1662i	−0.786414	−	0.571363i
$532$		0			0
$533$	−23.8886	−	46.8840i	−1.03473	−	2.03077i
$534$		0			0
$535$	31.6761	+	16.4027i	1.36948	+	0.709151i
$536$		0			0
$537$	−0.643028	+	1.26201i	−0.0277487	+	0.0544599i
$538$		0			0
$539$	−8.39303	−	8.45026i	−0.361513	−	0.363979i
$540$		0			0
$541$	37.2531	−	12.1043i	1.60164	−	0.520404i	0.634126	−	0.773230i	$-0.281360\pi$
$541$	37.2531	−	12.1043i	1.60164	−	0.520404i	0.967512	+	0.252826i	$0.0813601\pi$
$542$		0			0
$543$	−0.357485	+	2.25707i	−0.0153412	+	0.0968602i
$544$		0			0
$545$	−1.39452	−	1.02724i	−0.0597347	−	0.0440021i
$546$		0			0
$547$	−38.7467	+	6.13688i	−1.65669	+	0.262394i	−0.913545	−	0.406737i	$-0.866667\pi$
$547$	−38.7467	+	6.13688i	−1.65669	+	0.262394i	−0.743144	+	0.669131i	$0.766667\pi$
$548$		0			0
$549$	24.4474			1.04339
$550$		0			0
$551$	25.7432			1.09670
$552$		0			0
$553$	−11.8934	+	1.88373i	−0.505759	+	0.0801043i
$554$		0			0
$555$	−3.99736	−	2.94455i	−0.169678	−	0.124989i
$556$		0			0
$557$	−3.12546	+	19.7334i	−0.132430	+	0.836131i	0.828631	+	0.559795i	$0.189120\pi$
$557$	−3.12546	+	19.7334i	−0.132430	+	0.836131i	−0.961061	+	0.276336i	$0.910880\pi$
$558$		0			0
$559$	−37.1058	+	12.0564i	−1.56941	+	0.509931i
$560$		0			0
$561$	−0.400325	−	2.58436i	−0.0169017	−	0.109112i
$562$		0			0
$563$	13.3788	−	26.2573i	0.563848	−	1.10661i	−0.416462	−	0.909153i	$-0.636730\pi$
$563$	13.3788	−	26.2573i	0.563848	−	1.10661i	0.980311	−	0.197462i	$-0.0632699\pi$
$564$		0			0
$565$	17.4728	+	9.04787i	0.735086	+	0.380647i
$566$		0			0
$567$	12.7856	+	25.0932i	0.536947	+	1.05382i
$568$		0			0
$569$	−12.5719	−	9.13401i	−0.527041	−	0.382918i	0.292209	−	0.956355i	$-0.405610\pi$
$569$	−12.5719	−	9.13401i	−0.527041	−	0.382918i	−0.819250	+	0.573437i	$0.805610\pi$
$570$		0			0
$571$		−	0.662428i		−	0.0277217i	−0.999904	−	0.0138609i	$-0.995588\pi$
$571$		−	0.662428i		−	0.0277217i	0.999904	−	0.0138609i	$-0.00441219\pi$
$572$		0			0
$573$	−2.24530	+	2.24530i	−0.0937988	+	0.0937988i
$574$		0			0
$575$	−16.2885	−	8.57074i	−0.679278	−	0.357425i
$576$		0			0
$577$	34.6459	−	17.6530i	1.44233	−	0.734903i	0.454543	−	0.890725i	$-0.349803\pi$
$577$	34.6459	−	17.6530i	1.44233	−	0.734903i	0.987785	+	0.155822i	$0.0498026\pi$
$578$		0			0
$579$	−1.28162	+	0.931154i	−0.0532625	+	0.0386974i
$580$		0			0
$581$	−1.88543	−	5.80275i	−0.0782207	−	0.240739i
$582$		0			0
$583$	12.3427	+	17.1102i	0.511181	+	0.708632i
$584$		0			0
$585$	−25.1133	+	24.7855i	−1.03831	+	1.02476i
$586$		0			0
$587$	−2.37146	−	0.375602i	−0.0978805	−	0.0155027i	0.107302	−	0.994226i	$-0.465779\pi$
$587$	−2.37146	−	0.375602i	−0.0978805	−	0.0155027i	−0.205183	+	0.978724i	$0.565779\pi$
$588$		0			0
$589$	13.8428	−	42.6038i	0.570383	−	1.75546i
$590$		0			0
$591$	1.30675	−	1.79859i	0.0537527	−	0.0739842i
$592$		0			0
$593$	31.9523	+	31.9523i	1.31213	+	1.31213i	0.919846	+	0.392280i	$0.128313\pi$
$593$	31.9523	+	31.9523i	1.31213	+	1.31213i	0.392280	+	0.919846i	$0.371687\pi$
$594$		0			0
$595$	27.7046	+	9.20337i	1.13578	+	0.377301i
$596$		0			0
$597$	−0.245295	−	1.54873i	−0.0100393	−	0.0633855i
$598$		0			0
$599$	15.0927	+	4.90391i	0.616670	+	0.200368i	0.600661	−	0.799504i	$-0.294904\pi$
$599$	15.0927	+	4.90391i	0.616670	+	0.200368i	0.0160087	+	0.999872i	$0.494904\pi$
$600$		0			0
$601$	−4.48148	−	6.16823i	−0.182803	−	0.251607i	0.707774	−	0.706439i	$-0.249699\pi$
$601$	−4.48148	−	6.16823i	−0.182803	−	0.251607i	−0.890578	+	0.454831i	$0.849699\pi$
$602$		0			0
$603$	29.8338	+	15.2011i	1.21493	+	0.619035i
$604$		0			0
$605$	−0.328688	+	24.5946i	−0.0133631	+	0.999911i
$606$		0			0
$607$	−15.8982	−	8.10055i	−0.645289	−	0.328791i	0.100536	−	0.994933i	$-0.467944\pi$
$607$	−15.8982	−	8.10055i	−0.645289	−	0.328791i	−0.745825	+	0.666142i	$0.767944\pi$
$608$		0			0
$609$	1.76514	+	2.42950i	0.0715269	+	0.0984484i
$610$		0			0
$611$	−3.39684	−	1.10370i	−0.137421	−	0.0446509i
$612$		0			0
$613$	−0.210333	−	1.32799i	−0.00849527	−	0.0536370i	0.983077	−	0.183195i	$-0.0586441\pi$
$613$	−0.210333	−	1.32799i	−0.00849527	−	0.0536370i	−0.991572	+	0.129558i	$0.958644\pi$
$614$		0			0
$615$	3.87989	−	1.94491i	0.156452	−	0.0784265i
$616$		0			0
$617$	2.91978	+	2.91978i	0.117546	+	0.117546i	0.763433	−	0.645887i	$-0.223512\pi$
$617$	2.91978	+	2.91978i	0.117546	+	0.117546i	−0.645887	+	0.763433i	$0.723512\pi$
$618$		0			0
$619$	−3.15329	+	4.34013i	−0.126741	+	0.174445i	−0.867672	−	0.497137i	$-0.834385\pi$
$619$	−3.15329	+	4.34013i	−0.126741	+	0.174445i	0.740931	+	0.671582i	$0.234385\pi$
$620$		0			0
$621$	1.33287	−	4.10216i	0.0534863	−	0.164614i
$622$		0			0
$623$	−3.30405	−	0.523311i	−0.132374	−	0.0209660i
$624$		0			0
$625$	−20.6044	+	14.1583i	−0.824177	+	0.566332i
$626$		0			0
$627$	2.09123	+	2.89899i	0.0835155	+	0.115774i
$628$		0			0
$629$	14.0040	+	43.0999i	0.558376	+	1.71851i
$630$		0			0
$631$	28.0962	−	20.4131i	1.11849	−	0.812631i	0.134511	−	0.990912i	$-0.457054\pi$
$631$	28.0962	−	20.4131i	1.11849	−	0.812631i	0.983980	+	0.178281i	$0.0570535\pi$
$632$		0			0
$633$	0.895805	−	0.456435i	0.0356050	−	0.0181417i
$634$		0			0
$635$	−1.49687	+	9.06513i	−0.0594014	+	0.359739i
$636$		0			0
$637$	−13.5304	+	13.5304i	−0.536093	+	0.536093i
$638$		0			0
$639$		−	29.8587i		−	1.18119i
$640$		0			0
$641$	37.5802	+	27.3036i	1.48433	+	1.07843i	0.976130	+	0.217189i	$0.0696888\pi$
$641$	37.5802	+	27.3036i	1.48433	+	1.07843i	0.508200	+	0.861239i	$0.330311\pi$
$642$		0			0
$643$	12.1697	+	23.8844i	0.479927	+	0.941911i	0.996332	+	0.0855661i	$0.0272699\pi$
$643$	12.1697	+	23.8844i	0.479927	+	0.941911i	−0.516405	+	0.856344i	$0.672730\pi$
$644$		0			0
$645$	−0.974302	−	3.06699i	−0.0383631	−	0.120762i
$646$		0			0
$647$	−3.58002	+	7.02618i	−0.140745	+	0.276228i	−0.950610	−	0.310389i	$-0.899541\pi$
$647$	−3.58002	+	7.02618i	−0.140745	+	0.276228i	0.809865	+	0.586617i	$0.199541\pi$
$648$		0			0
$649$	3.84022	+	24.7911i	0.150742	+	0.973136i
$650$		0			0
$651$	4.96987	−	1.61481i	0.194784	−	0.0632893i
$652$		0			0
$653$	2.98154	−	18.8247i	0.116677	−	0.736668i	−0.858099	−	0.513483i	$-0.828355\pi$
$653$	2.98154	−	18.8247i	0.116677	−	0.736668i	0.974776	−	0.223185i	$-0.0716452\pi$
$654$		0			0
$655$	11.1674	−	15.1603i	0.436348	−	0.592361i
$656$		0			0
$657$	3.32497	−	0.526624i	0.129720	−	0.0205456i
$658$		0			0
$659$	−42.2869			−1.64726			−0.823632	−	0.567125i	$-0.808056\pi$
$659$	−42.2869			−1.64726			−0.823632	+	0.567125i	$0.808056\pi$
$660$		0			0
$661$	25.4299			0.989109			0.494555	−	0.869147i	$-0.335331\pi$
$661$	25.4299			0.989109			0.494555	+	0.869147i	$0.335331\pi$
$662$		0			0
$663$	−4.14984	+	0.657271i	−0.161167	+	0.0255263i
$664$		0			0
$665$	−39.4516	+	5.98319i	−1.52987	+	0.232018i
$666$		0			0
$667$	−2.70353	+	17.0694i	−0.104681	+	0.660931i
$668$		0			0
$669$	−1.80777	+	0.587381i	−0.0698925	+	0.0227095i
$670$		0			0
$671$	−19.2948	−	19.4264i	−0.744868	−	0.749947i
$672$		0			0
$673$	9.74788	−	19.1313i	0.375753	−	0.737457i	−0.623253	−	0.782020i	$-0.714189\pi$
$673$	9.74788	−	19.1313i	0.375753	−	0.737457i	0.999007	+	0.0445627i	$0.0141894\pi$
$674$		0			0
$675$	−4.08786	−	4.19669i	−0.157342	−	0.161531i
$676$		0			0
$677$	19.4189	+	38.1118i	0.746330	+	1.46475i	0.880625	+	0.473813i	$0.157123\pi$
$677$	19.4189	+	38.1118i	0.746330	+	1.46475i	−0.134296	+	0.990941i	$0.542877\pi$
$678$		0			0
$679$	8.86744	+	6.44257i	0.340301	+	0.247243i
$680$		0			0
$681$			2.40642i			0.0922142i
$682$		0			0
$683$	−7.18559	+	7.18559i	−0.274949	+	0.274949i	−0.831089	−	0.556140i	$-0.812282\pi$
$683$	−7.18559	+	7.18559i	−0.274949	+	0.274949i	0.556140	+	0.831089i	$0.312282\pi$
$684$		0			0
$685$	8.12260	+	1.34123i	0.310348	+	0.0512459i
$686$		0			0
$687$	−1.78935	+	0.911720i	−0.0682680	+	0.0347843i
$688$		0			0
$689$	27.4219	−	19.9232i	1.04469	−	0.759012i
$690$		0			0
$691$	5.61862	+	17.2923i	0.213742	+	0.657831i	0.999240	+	0.0389674i	$0.0124068\pi$
$691$	5.61862	+	17.2923i	0.213742	+	0.657831i	−0.785498	+	0.618864i	$0.787593\pi$
$692$		0			0
$693$	9.98058	−	30.3656i	0.379131	−	1.15349i
$694$		0			0
$695$	7.71664	+	0.0506806i	0.292709	+	0.00192242i
$696$		0			0
$697$	−39.1278	−	6.19724i	−1.48207	−	0.234737i
$698$		0			0
$699$	−0.0870116	+	0.267794i	−0.00329108	+	0.0101289i
$700$		0			0
$701$	6.05920	−	8.33978i	0.228853	−	0.314989i	−0.679112	−	0.734034i	$-0.737635\pi$
$701$	6.05920	−	8.33978i	0.228853	−	0.314989i	0.907965	+	0.419045i	$0.137635\pi$
$702$		0			0
$703$	−43.8000	−	43.8000i	−1.65195	−	1.65195i
$704$		0			0
$705$	0.0928723	−	0.279570i	0.00349777	−	0.0105292i
$706$		0			0
$707$	0.0561793	+	0.354702i	0.00211284	+	0.0133400i
$708$		0			0
$709$	31.6001	+	10.2675i	1.18677	+	0.385604i	0.834877	−	0.550437i	$-0.185539\pi$
$709$	31.6001	+	10.2675i	1.18677	+	0.385604i	0.351891	+	0.936041i	$0.385539\pi$
$710$		0			0
$711$	−6.44062	−	8.86476i	−0.241542	−	0.332454i
$712$		0			0
$713$	26.7953	+	13.6529i	1.00349	+	0.511305i
$714$		0			0
$715$	39.5154	+	0.393806i	1.47779	+	0.0147275i
$716$		0			0
$717$	−4.85101	−	2.47171i	−0.181164	−	0.0923077i
$718$		0			0
$719$	−14.2160	−	19.5667i	−0.530169	−	0.729715i	0.456987	−	0.889473i	$-0.348928\pi$
$719$	−14.2160	−	19.5667i	−0.530169	−	0.729715i	−0.987156	+	0.159758i	$0.948928\pi$
$720$		0			0
$721$	0.318906	+	0.103619i	0.0118767	+	0.00385896i
$722$		0			0
$723$	0.204618	+	1.29191i	0.00760983	+	0.0480466i
$724$		0			0
$725$	18.8079	+	14.0459i	0.698508	+	0.521650i
$726$		0			0
$727$	−0.348445	−	0.348445i	−0.0129231	−	0.0129231i	0.700616	−	0.713539i	$-0.252909\pi$
$727$	−0.348445	−	0.348445i	−0.0129231	−	0.0129231i	−0.713539	+	0.700616i	$0.752909\pi$
$728$		0			0
$729$	−14.6571	+	20.1738i	−0.542856	+	0.747178i
$730$		0			0
$731$	−9.07694	+	27.9360i	−0.335723	+	1.03325i
$732$		0			0
$733$	−40.2060	−	6.36801i	−1.48504	−	0.235208i	−0.639366	−	0.768902i	$-0.720803\pi$
$733$	−40.2060	−	6.36801i	−1.48504	−	0.235208i	−0.845677	+	0.533694i	$0.820803\pi$
$734$		0			0
$735$	−1.10865	−	1.12330i	−0.0408930	−	0.0414337i
$736$		0			0
$737$	−11.4669	−	35.7038i	−0.422388	−	1.31517i
$738$		0			0
$739$	−3.05832	−	9.41255i	−0.112502	−	0.346246i	0.878916	−	0.476977i	$-0.158268\pi$
$739$	−3.05832	−	9.41255i	−0.112502	−	0.346246i	−0.991418	+	0.130731i	$0.958268\pi$
$740$		0			0
$741$	4.64610	−	3.37559i	0.170679	−	0.124005i
$742$		0			0
$743$	24.1015	−	12.2803i	0.884198	−	0.450521i	0.0479352	−	0.998850i	$-0.484736\pi$
$743$	24.1015	−	12.2803i	0.884198	−	0.450521i	0.836263	+	0.548329i	$0.184736\pi$
$744$		0			0
$745$	−9.72777	+	6.97049i	−0.356398	+	0.255379i
$746$		0			0
$747$	3.92587	−	3.92587i	0.143640	−	0.143640i
$748$		0			0
$749$			51.9159i			1.89696i
$750$		0			0
$751$	4.69796	+	3.41327i	0.171431	+	0.124552i	0.670192	−	0.742187i	$-0.266212\pi$
$751$	4.69796	+	3.41327i	0.171431	+	0.124552i	−0.498761	+	0.866739i	$0.666212\pi$
$752$		0			0
$753$	2.12662	+	4.17372i	0.0774982	+	0.152099i
$754$		0			0
$755$	9.62437	−	3.05741i	0.350267	−	0.111271i
$756$		0			0
$757$	−16.2935	+	31.9778i	−0.592197	+	1.16225i	0.379316	+	0.925267i	$0.376159\pi$
$757$	−16.2935	+	31.9778i	−0.592197	+	1.16225i	−0.971513	+	0.236985i	$0.923841\pi$
$758$		0			0
$759$	−2.14184	+	1.08217i	−0.0777437	+	0.0392802i
$760$		0			0
$761$	−18.4521	+	5.99545i	−0.668888	+	0.217335i	−0.623724	−	0.781645i	$-0.714381\pi$
$761$	−18.4521	+	5.99545i	−0.668888	+	0.217335i	−0.0451642	+	0.998980i	$0.514381\pi$
$762$		0			0
$763$	0.394340	−	2.48976i	0.0142761	−	0.0901354i
$764$		0			0
$765$	3.98324	+	26.2645i	0.144014	+	0.949594i
$766$		0			0
$767$	39.8085	−	6.30504i	1.43740	−	0.227662i
$768$		0			0
$769$	−23.1799			−0.835887			−0.417944	−	0.908473i	$-0.637249\pi$
$769$	−23.1799			−0.835887			−0.417944	+	0.908473i	$0.637249\pi$
$770$		0			0
$771$	0.861467			0.0310250
$772$		0			0
$773$	−23.3930	+	3.70509i	−0.841389	+	0.133263i	−0.562229	−	0.826982i	$-0.690056\pi$
$773$	−23.3930	+	3.70509i	−0.841389	+	0.133263i	−0.279160	+	0.960245i	$0.590056\pi$
$774$		0			0
$775$	33.3587	−	23.5733i	1.19828	−	0.846779i
$776$		0			0
$777$	1.13036	−	7.13683i	0.0405516	−	0.256033i
$778$		0			0
$779$	51.4981	−	16.7328i	1.84511	−	0.599513i
$780$		0			0
$781$	−23.7263	+	23.5656i	−0.848994	+	0.843244i
$782$		0			0
$783$	−2.49737	+	4.90137i	−0.0892488	+	0.175161i
$784$		0			0
$785$	−5.98656	+	11.5609i	−0.213669	+	0.412628i
$786$		0			0
$787$	−18.3836	−	36.0798i	−0.655304	−	1.28611i	−0.944398	−	0.328806i	$-0.893354\pi$
$787$	−18.3836	−	36.0798i	−0.655304	−	1.28611i	0.289094	−	0.957301i	$-0.406646\pi$
$788$		0			0
$789$	−2.84256	−	2.06524i	−0.101198	−	0.0735246i
$790$		0			0
$791$			28.6372i			1.01822i
$792$		0			0
$793$	−31.1051	+	31.1051i	−1.10458	+	1.10458i
$794$		0			0
$795$	1.62839	+	2.27253i	0.0577531	+	0.0805982i
$796$		0			0
$797$	43.3942	−	22.1104i	1.53710	−	0.783192i	0.538855	−	0.842399i	$-0.318857\pi$
$797$	43.3942	−	22.1104i	1.53710	−	0.783192i	0.998246	+	0.0592071i	$0.0188572\pi$
$798$		0			0
$799$	−2.17544	+	1.58055i	−0.0769617	+	0.0559159i
$800$		0			0
$801$	−0.940661	−	2.89506i	−0.0332366	−	0.102292i
$802$		0			0
$803$	−3.04266	−	2.22646i	−0.107373	−	0.0785700i
$804$		0			0
$805$	0.175931	−	26.7873i	0.00620075	−	0.944128i
$806$		0			0
$807$	−4.00938	−	0.635024i	−0.141137	−	0.0223539i
$808$		0			0
$809$	8.36499	−	25.7448i	0.294097	−	0.905138i	−0.689426	−	0.724356i	$-0.742137\pi$
$809$	8.36499	−	25.7448i	0.294097	−	0.905138i	0.983523	−	0.180782i	$-0.0578628\pi$
$810$		0			0
$811$	−5.42770	+	7.47059i	−0.190592	+	0.262328i	−0.893610	−	0.448845i	$-0.851836\pi$
$811$	−5.42770	+	7.47059i	−0.190592	+	0.262328i	0.703017	+	0.711173i	$0.251836\pi$
$812$		0			0
$813$	−0.870047	−	0.870047i	−0.0305139	−	0.0305139i
$814$		0			0
$815$	−12.4666	−	24.8695i	−0.436686	−	0.871141i
$816$		0			0
$817$	−6.28072	−	39.6549i	−0.219734	−	1.38735i
$818$		0			0
$819$	−48.8399	−	15.8690i	−1.70660	−	0.554509i
$820$		0			0
$821$	−18.4645	−	25.4142i	−0.644416	−	0.886962i	0.354426	−	0.935084i	$-0.384676\pi$
$821$	−18.4645	−	25.4142i	−0.644416	−	0.886962i	−0.998841	+	0.0481218i	$0.984676\pi$
$822$		0			0
$823$	−19.0482	−	9.70553i	−0.663977	−	0.338313i	0.0893109	−	0.996004i	$-0.471534\pi$
$823$	−19.0482	−	9.70553i	−0.663977	−	0.338313i	−0.753288	+	0.657690i	$0.771534\pi$
$824$		0			0
$825$	−0.0538862	+	3.25899i	−0.00187608	+	0.113463i
$826$		0			0
$827$	3.45645	+	1.76115i	0.120193	+	0.0612412i	0.513053	−	0.858357i	$-0.328514\pi$
$827$	3.45645	+	1.76115i	0.120193	+	0.0612412i	−0.392860	+	0.919598i	$0.628514\pi$
$828$		0			0
$829$	−3.49646	−	4.81246i	−0.121437	−	0.167144i	0.743970	−	0.668213i	$-0.232940\pi$
$829$	−3.49646	−	4.81246i	−0.121437	−	0.167144i	−0.865407	+	0.501069i	$0.832940\pi$
$830$		0			0
$831$	−4.37971	−	1.42305i	−0.151930	−	0.0493652i
$832$		0			0
$833$	2.25361	+	14.2288i	0.0780831	+	0.492997i
$834$		0			0
$835$	−6.29356	−	12.5550i	−0.217797	−	0.434482i
$836$		0			0
$837$	6.76862	+	6.76862i	0.233958	+	0.233958i
$838$		0			0
$839$	19.8076	−	27.2628i	0.683834	−	0.941217i	−0.316138	−	0.948713i	$-0.602386\pi$
$839$	19.8076	−	27.2628i	0.683834	−	0.941217i	0.999972	+	0.00749608i	$0.00238610\pi$
$840$		0			0
$841$	−2.15047	+	6.61847i	−0.0741542	+	0.228223i
$842$		0			0
$843$	1.97179	+	0.312301i	0.0679122	+	0.0107562i
$844$		0			0
$845$	0.226057	−	34.4195i	0.00777659	−	1.18407i
$846$		0			0
$847$	−32.0062	+	16.0349i	−1.09975	+	0.550966i
$848$		0			0
$849$	0.799902	+	2.46185i	0.0274526	+	0.0844904i
$850$		0			0
$851$	33.6421	−	24.4424i	1.15324	−	0.837875i
$852$		0			0
$853$	−19.0672	+	9.71522i	−0.652848	+	0.332643i	−0.748851	−	0.662738i	$-0.769394\pi$
$853$	−19.0672	+	9.71522i	−0.652848	+	0.332643i	0.0960029	+	0.995381i	$0.469394\pi$
$854$		0			0
$855$	−21.1491	−	29.5149i	−0.723283	−	1.00939i
$856$		0			0
$857$	18.6774	−	18.6774i	0.638008	−	0.638008i	−0.312056	−	0.950064i	$-0.601018\pi$
$857$	18.6774	−	18.6774i	0.638008	−	0.638008i	0.950064	+	0.312056i	$0.101018\pi$
$858$		0			0
$859$			6.24532i			0.213088i	0.994308	+	0.106544i	$0.0339784\pi$
$859$			6.24532i			0.213088i	−0.994308	+	0.106544i	$0.966022\pi$
$860$		0			0
$861$	5.11021	+	3.71279i	0.174156	+	0.126531i
$862$		0			0
$863$	7.97514	+	15.6521i	0.271477	+	0.532804i	0.985987	−	0.166822i	$-0.0533504\pi$
$863$	7.97514	+	15.6521i	0.271477	+	0.532804i	−0.714510	+	0.699625i	$0.753350\pi$
$864$		0			0
$865$	−15.6297	+	30.1832i	−0.531424	+	1.02626i
$866$		0			0
$867$	0.0808639	−	0.158704i	0.00274628	−	0.00538989i
$868$		0			0
$869$	−1.96093	+	12.1143i	−0.0665200	+	0.410948i
$870$		0			0
$871$	−57.2992	+	18.6176i	−1.94151	+	0.630835i
$872$		0			0
$873$	−1.56026	+	9.85108i	−0.0528068	+	0.333409i
$874$		0			0
$875$	−32.0877	−	17.1540i	−1.08476	−	0.579911i
$876$		0			0
$877$	49.6327	−	7.86105i	1.67598	−	0.265449i	0.755188	−	0.655509i	$-0.227546\pi$
$877$	49.6327	−	7.86105i	1.67598	−	0.265449i	0.920789	+	0.390060i	$0.127546\pi$
$878$		0			0
$879$	−1.54313			−0.0520485
$880$		0			0
$881$	−48.4041			−1.63077			−0.815387	−	0.578916i	$-0.803476\pi$
$881$	−48.4041			−1.63077			−0.815387	+	0.578916i	$0.803476\pi$
$882$		0			0
$883$	37.8161	−	5.98949i	1.27261	−	0.201562i	0.516662	−	0.856189i	$-0.327174\pi$
$883$	37.8161	−	5.98949i	1.27261	−	0.201562i	0.755952	+	0.654627i	$0.227174\pi$
$884$		0			0
$885$	0.498470	+	3.28678i	0.0167559	+	0.110484i
$886$		0			0
$887$	−6.88389	+	43.4632i	−0.231138	+	1.45935i	0.550090	+	0.835105i	$0.314593\pi$
$887$	−6.88389	+	43.4632i	−0.231138	+	1.45935i	−0.781228	+	0.624245i	$0.785407\pi$
$888$		0			0
$889$	−12.7176	+	4.13220i	−0.426535	+	0.138590i
$890$		0			0
$891$	28.3631	−	4.39354i	0.950201	−	0.147189i
$892$		0			0
$893$	1.66862	−	3.27484i	0.0558381	−	0.109588i
$894$		0			0
$895$	−15.3573	+	4.87862i	−0.513338	+	0.163074i
$896$		0			0
$897$	1.75031	+	3.43517i	0.0584410	+	0.114697i
$898$		0			0
$899$	−31.0289	−	22.5438i	−1.03487	−	0.751878i
$900$		0			0
$901$		−	25.5189i		−	0.850157i
$902$		0			0
$903$	3.31175	−	3.31175i	0.110208	−	0.110208i
$904$		0			0
$905$	−21.1325	+	15.1426i	−0.702467	+	0.503357i
$906$		0			0
$907$	−9.58372	+	4.88315i	−0.318222	+	0.162142i	−0.605804	−	0.795614i	$-0.707149\pi$
$907$	−9.58372	+	4.88315i	−0.318222	+	0.162142i	0.287582	+	0.957756i	$0.407149\pi$
$908$		0			0
$909$	−0.264378	+	0.192082i	−0.00876886	+	0.00637095i
$910$		0			0
$911$	−5.83452	−	17.9568i	−0.193306	−	0.594936i	−0.999992	−	0.00395526i	$-0.998741\pi$
$911$	−5.83452	−	17.9568i	−0.193306	−	0.594936i	0.806686	−	0.590981i	$-0.201259\pi$
$912$		0			0
$913$	−6.21802	−	0.0211285i	−0.205786	−	0.000699252i
$914$		0			0
$915$	−2.54867	−	2.58237i	−0.0842566	−	0.0853707i
$916$		0			0
$917$	27.0670	+	4.28699i	0.893831	+	0.141569i
$918$		0			0
$919$	5.20310	−	16.0135i	0.171634	−	0.528236i	−0.827829	−	0.560980i	$-0.810424\pi$
$919$	5.20310	−	16.0135i	0.171634	−	0.528236i	0.999464	+	0.0327436i	$0.0104245\pi$
$920$		0			0
$921$	−1.08699	+	1.49612i	−0.0358177	+	0.0492988i
$922$		0			0
$923$	37.9901	+	37.9901i	1.25046	+	1.25046i
$924$		0			0
$925$	−8.10224	−	55.8980i	−0.266400	−	1.83791i
$926$		0			0
$927$	0.0477322	+	0.301370i	0.00156773	+	0.00989827i
$928$		0			0
$929$	−14.0294	−	4.55842i	−0.460289	−	0.149557i	0.0696882	−	0.997569i	$-0.477800\pi$
$929$	−14.0294	−	4.55842i	−0.460289	−	0.149557i	−0.529977	+	0.848012i	$0.677800\pi$
$930$		0			0
$931$	−11.5740	−	15.9303i	−0.379324	−	0.522095i
$932$		0			0
$933$	1.34290	+	0.684241i	0.0439646	+	0.0224011i
$934$		0			0
$935$	17.7265	−	23.8941i	0.579720	−	0.781420i
$936$		0			0
$937$	35.4761	+	18.0760i	1.15895	+	0.590517i	0.924339	−	0.381571i	$-0.124617\pi$
$937$	35.4761	+	18.0760i	1.15895	+	0.590517i	0.234615	+	0.972088i	$0.424617\pi$
$938$		0			0
$939$	3.65811	+	5.03496i	0.119378	+	0.164310i
$940$		0			0
$941$	−22.5807	−	7.33691i	−0.736110	−	0.239177i	−0.0831160	−	0.996540i	$-0.526487\pi$
$941$	−22.5807	−	7.33691i	−0.736110	−	0.239177i	−0.652994	+	0.757363i	$0.726487\pi$
$942$		0			0
$943$	5.68661	+	35.9039i	0.185182	+	1.16919i
$944$		0			0
$945$	2.68806	−	8.09179i	0.0874427	−	0.263226i
$946$		0			0
$947$	−22.9342	−	22.9342i	−0.745261	−	0.745261i	0.228324	−	0.973585i	$-0.426675\pi$
$947$	−22.9342	−	22.9342i	−0.745261	−	0.745261i	−0.973585	+	0.228324i	$0.926675\pi$
$948$		0			0
$949$	−3.56042	+	4.90050i	−0.115576	+	0.159077i
$950$		0			0
$951$	−0.519836	+	1.59989i	−0.0168568	+	0.0518800i
$952$		0			0
$953$	31.6499	+	5.01286i	1.02524	+	0.162382i	0.646336	−	0.763053i	$-0.276300\pi$
$953$	31.6499	+	5.01286i	1.02524	+	0.162382i	0.378906	+	0.925435i	$0.376300\pi$
$954$		0			0
$955$	−36.1235	−	0.237248i	−1.16893	−	0.00767717i
$956$		0			0
$957$	2.91387	−	0.935839i	0.0941920	−	0.0302514i
$958$		0			0
$959$	3.70256	+	11.3953i	0.119562	+	0.367974i
$960$		0			0
$961$	−28.9144	+	21.0075i	−0.932722	+	0.677662i
$962$		0			0
$963$	−42.0925	+	21.4472i	−1.35641	+	0.691126i
$964$		0			0
$965$	−17.7816	−	2.93617i	−0.572410	−	0.0945185i
$966$		0			0
$967$	20.9981	−	20.9981i	0.675253	−	0.675253i	−0.283669	−	0.958922i	$-0.591552\pi$
$967$	20.9981	−	20.9981i	0.675253	−	0.675253i	0.958922	+	0.283669i	$0.0915518\pi$
$968$		0			0
$969$		−	4.32368i		−	0.138897i
$970$		0			0
$971$	0.106113	+	0.0770954i	0.00340532	+	0.00247411i	0.589487	−	0.807778i	$-0.299330\pi$
$971$	0.106113	+	0.0770954i	0.00340532	+	0.00247411i	−0.586081	+	0.810252i	$0.699330\pi$
$972$		0			0
$973$	5.09880	+	10.0070i	0.163460	+	0.320808i
$974$		0			0
$975$	5.23619	+	0.0687824i	0.167692	+	0.00220280i
$976$		0			0
$977$	7.34581	−	14.4170i	0.235013	−	0.461240i	−0.743137	−	0.669140i	$-0.766663\pi$
$977$	7.34581	−	14.4170i	0.235013	−	0.461240i	0.978150	+	0.207900i	$0.0666628\pi$
$978$		0			0
$979$	−1.55807	+	3.03236i	−0.0497960	+	0.0969146i
$980$		0			0
$981$	2.18156	−	0.708833i	0.0696519	−	0.0226313i
$982$		0			0
$983$	−6.35207	+	40.1054i	−0.202600	+	1.27916i	0.651338	+	0.758788i	$0.274208\pi$
$983$	−6.35207	+	40.1054i	−0.202600	+	1.27916i	−0.853937	+	0.520376i	$0.825792\pi$
$984$		0			0
$985$	25.0061	−	3.79241i	0.796762	−	0.120836i
$986$		0			0
$987$	0.423473	−	0.0670716i	0.0134793	−	0.00213491i
$988$		0			0
$989$	26.9533			0.857066
$990$		0			0
$991$	23.5944			0.749502			0.374751	−	0.927126i	$-0.377728\pi$
$991$	23.5944			0.749502			0.374751	+	0.927126i	$0.377728\pi$
$992$		0			0
$993$	−3.28404	+	0.520141i	−0.104216	+	0.0165062i
$994$		0			0
$995$	10.5800	−	14.3627i	0.335407	−	0.455329i
$996$		0			0
$997$	−0.510741	+	3.22469i	−0.0161753	+	0.102127i	−0.994455	−	0.105162i	$-0.966464\pi$
$997$	−0.510741	+	3.22469i	−0.0161753	+	0.102127i	0.978280	+	0.207289i	$0.0664640\pi$
$998$		0			0
$999$	12.5884	−	4.09020i	0.398278	−	0.129408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.u.a.17.4	yes	48
4.3	odd	2		880.2.cm.b.17.3		48
5.3	odd	4	inner	220.2.u.a.193.4	yes	48
11.2	odd	10	inner	220.2.u.a.57.4	yes	48
20.3	even	4		880.2.cm.b.193.3		48
44.35	even	10		880.2.cm.b.497.3		48
55.13	even	20	inner	220.2.u.a.13.4	✓	48
220.123	odd	20		880.2.cm.b.673.3		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.u.a.13.4	✓	48	55.13	even	20	inner
220.2.u.a.17.4	yes	48	1.1	even	1	trivial
220.2.u.a.57.4	yes	48	11.2	odd	10	inner
220.2.u.a.193.4	yes	48	5.3	odd	4	inner
880.2.cm.b.17.3		48	4.3	odd	2
880.2.cm.b.193.3		48	20.3	even	4
880.2.cm.b.497.3		48	44.35	even	10
880.2.cm.b.673.3		48	220.123	odd	20

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	220.u (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.194131 - 0.0307474i) q^{3} +(1.80035 + 1.32618i) q^{5} +(-0.509098 + 3.21432i) q^{7} +(-2.81643 + 0.915113i) q^{9} +(2.95000 + 1.51575i) q^{11} +(2.41910 - 4.74775i) q^{13} +(0.390280 + 0.202097i) q^{15} +(-1.82128 - 3.57446i) q^{17} +(4.43615 + 3.22305i) q^{19} +0.639653i q^{21} +(-2.60297 + 2.60297i) q^{23} +(1.48249 + 4.77517i) q^{25} +(-1.04400 + 0.531947i) q^{27} +(3.79815 - 2.75952i) q^{29} +(-2.52450 - 7.76962i) q^{31} +(0.619293 + 0.203550i) q^{33} +(-5.17932 + 5.11173i) q^{35} +(-11.1573 - 1.76715i) q^{37} +(0.323642 - 0.996068i) q^{39} +(5.80437 - 7.98904i) q^{41} +(-5.17742 - 5.17742i) q^{43} +(-6.28415 - 2.08757i) q^{45} +(-0.104856 - 0.662035i) q^{47} +(-3.41527 - 1.10969i) q^{49} +(-0.463472 - 0.637915i) q^{51} +(5.66778 + 2.88788i) q^{53} +(3.30087 + 6.64111i) q^{55} +(0.960296 + 0.489295i) q^{57} +(4.44597 + 6.11936i) q^{59} +(-7.85138 - 2.55107i) q^{61} +(-1.50763 - 9.51878i) q^{63} +(10.6516 - 5.33943i) q^{65} +(-7.99503 - 7.99503i) q^{67} +(-0.425284 + 0.585353i) q^{69} +(-3.11574 + 9.58925i) q^{71} +(-1.12278 - 0.177831i) q^{73} +(0.434622 + 0.881427i) q^{75} +(-6.37394 + 8.71058i) q^{77} +(1.14340 + 3.51903i) q^{79} +(7.00107 - 5.08658i) q^{81} +(-1.67047 + 0.851148i) q^{83} +(1.46145 - 8.85060i) q^{85} +(0.652493 - 0.652493i) q^{87} +1.02792i q^{89} +(14.0292 + 10.1928i) q^{91} +(-0.728981 - 1.43071i) q^{93} +(3.71226 + 11.6857i) q^{95} +(1.52904 - 3.00091i) q^{97} +(-9.69555 - 1.56941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 2 q^{3} + 4 q^{5} + 10 q^{7} - 16 q^{15} + 10 q^{17} + 16 q^{23} - 26 q^{25} - 10 q^{27} + 16 q^{31} + 28 q^{33} - 34 q^{37} - 20 q^{41} - 56 q^{45} - 2 q^{47} - 80 q^{51} + 6 q^{53} - 18 q^{55}+ \cdots + 6 q^{97}+O(q^{100}) \) 48 * q + 2 * q^3 + 4 * q^5 + 10 * q^7 - 16 * q^15 + 10 * q^17 + 16 * q^23 - 26 * q^25 - 10 * q^27 + 16 * q^31 + 28 * q^33 - 34 * q^37 - 20 * q^41 - 56 * q^45 - 2 * q^47 - 80 * q^51 + 6 * q^53 - 18 * q^55 - 120 * q^57 - 40 * q^61 - 50 * q^63 - 72 * q^67 + 4 * q^71 - 20 * q^73 + 20 * q^75 - 36 * q^77 + 100 * q^81 + 40 * q^85 - 8 * q^91 - 14 * q^93 + 50 * q^95 + 6 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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