LMFDB - Embedded newform 220.2.l.c.23.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,2,Mod(23,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("220.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	220.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.75670884447$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			23.5
Character	$\chi$	$=$	220.23
Dual form			220.2.l.c.67.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.892874 + 1.09671i) q^{2} +(1.63523 - 1.63523i) q^{3} +(-0.405551 - 1.95845i) q^{4} +(2.22762 + 0.194242i) q^{5} +(0.333320 + 3.25343i) q^{6} +(-2.27323 - 2.27323i) q^{7} +(2.50996 + 1.30388i) q^{8} -2.34794i q^{9} +(-2.20201 + 2.26962i) q^{10} -1.00000i q^{11} +(-3.86568 - 2.53934i) q^{12} +(-0.723993 - 0.723993i) q^{13} +(4.52278 - 0.463369i) q^{14} +(3.96029 - 3.32503i) q^{15} +(-3.67106 + 1.58850i) q^{16} +(-0.922419 + 0.922419i) q^{17} +(2.57501 + 2.09641i) q^{18} +1.41633 q^{19} +(-0.522999 - 4.44145i) q^{20} -7.43450 q^{21} +(1.09671 + 0.892874i) q^{22} +(3.57116 - 3.57116i) q^{23} +(6.23649 - 1.97222i) q^{24} +(4.92454 + 0.865394i) q^{25} +(1.44045 - 0.147577i) q^{26} +(1.06627 + 1.06627i) q^{27} +(-3.53010 + 5.37392i) q^{28} +9.64395i q^{29} +(0.110556 + 7.31213i) q^{30} +7.64876i q^{31} +(1.53566 - 5.44442i) q^{32} +(-1.63523 - 1.63523i) q^{33} +(-0.188023 - 1.83523i) q^{34} +(-4.62232 - 5.50544i) q^{35} +(-4.59832 + 0.952210i) q^{36} +(-1.95305 + 1.95305i) q^{37} +(-1.26460 + 1.55330i) q^{38} -2.36779 q^{39} +(5.33796 + 3.39208i) q^{40} +8.11796 q^{41} +(6.63807 - 8.15350i) q^{42} +(-3.57789 + 3.57789i) q^{43} +(-1.95845 + 0.405551i) q^{44} +(0.456069 - 5.23031i) q^{45} +(0.727934 + 7.10512i) q^{46} +(-8.61919 - 8.61919i) q^{47} +(-3.40545 + 8.60058i) q^{48} +3.33515i q^{49} +(-5.34608 + 4.62811i) q^{50} +3.01673i q^{51} +(-1.12429 + 1.71152i) q^{52} +(-7.92764 - 7.92764i) q^{53} +(-2.12143 + 0.217345i) q^{54} +(0.194242 - 2.22762i) q^{55} +(-2.74171 - 8.66973i) q^{56} +(2.31601 - 2.31601i) q^{57} +(-10.5766 - 8.61084i) q^{58} -2.51199 q^{59} +(-8.11800 - 6.40756i) q^{60} -3.54775 q^{61} +(-8.38848 - 6.82938i) q^{62} +(-5.33741 + 5.33741i) q^{63} +(4.59981 + 6.54536i) q^{64} +(-1.47215 - 1.75341i) q^{65} +(3.25343 - 0.333320i) q^{66} +(7.01754 + 7.01754i) q^{67} +(2.18060 + 1.43242i) q^{68} -11.6793i q^{69} +(10.1650 - 0.153691i) q^{70} +14.9871i q^{71} +(3.06143 - 5.89324i) q^{72} +(1.98983 + 1.98983i) q^{73} +(-0.398104 - 3.88576i) q^{74} +(9.46786 - 6.63763i) q^{75} +(-0.574393 - 2.77380i) q^{76} +(-2.27323 + 2.27323i) q^{77} +(2.11414 - 2.59678i) q^{78} -14.1444 q^{79} +(-8.48626 + 2.82550i) q^{80} +10.5310 q^{81} +(-7.24831 + 8.90305i) q^{82} +(3.37507 - 3.37507i) q^{83} +(3.01507 + 14.5601i) q^{84} +(-2.23397 + 1.87562i) q^{85} +(-0.729306 - 7.11851i) q^{86} +(15.7701 + 15.7701i) q^{87} +(1.30388 - 2.50996i) q^{88} +4.70719i q^{89} +(5.32892 + 5.17018i) q^{90} +3.29161i q^{91} +(-8.44222 - 5.54565i) q^{92} +(12.5075 + 12.5075i) q^{93} +(17.1486 - 1.75691i) q^{94} +(3.15503 + 0.275110i) q^{95} +(-6.39172 - 11.4140i) q^{96} +(0.309689 - 0.309689i) q^{97} +(-3.65769 - 2.97787i) q^{98} -2.34794 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) $ 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.892874	+	1.09671i	−0.631357	+	0.775492i
$2$	−0.892874	+	1.09671i	−0.631357	+	0.775492i
$3$	1.63523	−	1.63523i	0.944099	−	0.944099i	−0.0544190	−	0.998518i	$-0.517331\pi$
$3$	1.63523	−	1.63523i	0.944099	−	0.944099i	0.998518	+	0.0544190i	$0.0173307\pi$
$4$	−0.405551	−	1.95845i	−0.202776	−	0.979225i
$5$	2.22762	+	0.194242i	0.996220	+	0.0868678i
$5$	2.22762	+	0.194242i	0.996220	+	0.0868678i
$6$	0.333320	+	3.25343i	0.136077	+	1.32821i
$7$	−2.27323	−	2.27323i	−0.859200	−	0.859200i	0.132044	−	0.991244i	$-0.457846\pi$
$7$	−2.27323	−	2.27323i	−0.859200	−	0.859200i	−0.991244	+	0.132044i	$0.957846\pi$
$8$	2.50996	+	1.30388i	0.887405	+	0.460990i
$9$		−	2.34794i		−	0.782647i
$10$	−2.20201	+	2.26962i	−0.696336	+	0.717716i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−3.86568	−	2.53934i	−1.11593	−	0.733045i
$13$	−0.723993	−	0.723993i	−0.200800	−	0.200800i	0.599543	−	0.800343i	$-0.295349\pi$
$13$	−0.723993	−	0.723993i	−0.200800	−	0.200800i	−0.800343	+	0.599543i	$0.795349\pi$
$14$	4.52278	−	0.463369i	1.20877	−	0.123840i
$15$	3.96029	−	3.32503i	1.02254	−	0.858519i
$16$	−3.67106	+	1.58850i	−0.917764	+	0.397126i
$17$	−0.922419	+	0.922419i	−0.223720	+	0.223720i	−0.810063	−	0.586343i	$-0.800567\pi$
$17$	−0.922419	+	0.922419i	−0.223720	+	0.223720i	0.586343	+	0.810063i	$0.300567\pi$
$18$	2.57501	+	2.09641i	0.606936	+	0.494130i
$19$	1.41633			0.324927			0.162464	−	0.986715i	$-0.448056\pi$
$19$	1.41633			0.324927			0.162464	+	0.986715i	$0.448056\pi$
$20$	−0.522999	−	4.44145i	−0.116946	−	0.993138i
$21$	−7.43450			−1.62234
$22$	1.09671	+	0.892874i	0.233820	+	0.190361i
$23$	3.57116	−	3.57116i	0.744638	−	0.744638i	−0.228829	−	0.973467i	$-0.573490\pi$
$23$	3.57116	−	3.57116i	0.744638	−	0.744638i	0.973467	+	0.228829i	$0.0734896\pi$
$24$	6.23649	−	1.97222i	1.27302	−	0.402578i
$25$	4.92454	+	0.865394i	0.984908	+	0.173079i
$26$	1.44045	−	0.147577i	0.282495	−	0.0289422i
$27$	1.06627	+	1.06627i	0.205203	+	0.205203i
$28$	−3.53010	+	5.37392i	−0.667126	+	1.01558i
$29$			9.64395i			1.79084i	0.445225	+	0.895419i	$0.353124\pi$
$29$			9.64395i			1.79084i	−0.445225	+	0.895419i	$0.646876\pi$
$30$	0.110556	+	7.31213i	0.0201847	+	1.33501i
$31$			7.64876i			1.37376i	0.726772	+	0.686879i	$0.241020\pi$
$31$			7.64876i			1.37376i	−0.726772	+	0.686879i	$0.758980\pi$
$32$	1.53566	−	5.44442i	0.271469	−	0.962447i
$33$	−1.63523	−	1.63523i	−0.284657	−	0.284657i
$34$	−0.188023	−	1.83523i	−0.0322457	−	0.314740i
$35$	−4.62232	−	5.50544i	−0.781315	−	0.930589i
$36$	−4.59832	+	0.952210i	−0.766387	+	0.158702i
$37$	−1.95305	+	1.95305i	−0.321080	+	0.321080i	−0.849181	−	0.528102i	$-0.822904\pi$
$37$	−1.95305	+	1.95305i	−0.321080	+	0.321080i	0.528102	+	0.849181i	$0.322904\pi$
$38$	−1.26460	+	1.55330i	−0.205145	+	0.251979i
$39$	−2.36779			−0.379149
$40$	5.33796	+	3.39208i	0.844006	+	0.536335i
$41$	8.11796			1.26781			0.633906	−	0.773410i	$-0.281451\pi$
$41$	8.11796			1.26781			0.633906	+	0.773410i	$0.281451\pi$
$42$	6.63807	−	8.15350i	1.02428	−	1.25811i
$43$	−3.57789	+	3.57789i	−0.545623	+	0.545623i	−0.925172	−	0.379549i	$-0.876079\pi$
$43$	−3.57789	+	3.57789i	−0.545623	+	0.545623i	0.379549	+	0.925172i	$0.376079\pi$
$44$	−1.95845	+	0.405551i	−0.295248	+	0.0611392i
$45$	0.456069	−	5.23031i	0.0679868	−	0.779688i
$46$	0.727934	+	7.10512i	0.107328	+	1.04759i
$47$	−8.61919	−	8.61919i	−1.25724	−	1.25724i	−0.952406	−	0.304833i	$-0.901399\pi$
$47$	−8.61919	−	8.61919i	−1.25724	−	1.25724i	−0.304833	−	0.952406i	$-0.598601\pi$
$48$	−3.40545	+	8.60058i	−0.491534	+	1.24139i
$49$			3.33515i			0.476450i
$50$	−5.34608	+	4.62811i	−0.756050	+	0.654514i
$51$			3.01673i			0.422427i
$52$	−1.12429	+	1.71152i	−0.155911	+	0.237345i
$53$	−7.92764	−	7.92764i	−1.08894	−	1.08894i	−0.995637	−	0.0933073i	$-0.970256\pi$
$53$	−7.92764	−	7.92764i	−1.08894	−	1.08894i	−0.0933073	−	0.995637i	$-0.529744\pi$
$54$	−2.12143	+	0.217345i	−0.288690	+	0.0295769i
$55$	0.194242	−	2.22762i	0.0261916	−	0.300372i
$56$	−2.74171	−	8.66973i	−0.366376	−	1.15854i
$57$	2.31601	−	2.31601i	0.306764	−	0.306764i
$58$	−10.5766	−	8.61084i	−1.38878	−	1.13066i
$59$	−2.51199			−0.327034			−0.163517	−	0.986541i	$-0.552284\pi$
$59$	−2.51199			−0.327034			−0.163517	+	0.986541i	$0.552284\pi$
$60$	−8.11800	−	6.40756i	−1.04803	−	0.827212i
$61$	−3.54775			−0.454243			−0.227122	−	0.973866i	$-0.572931\pi$
$61$	−3.54775			−0.454243			−0.227122	+	0.973866i	$0.572931\pi$
$62$	−8.38848	−	6.82938i	−1.06534	−	0.867332i
$63$	−5.33741	+	5.33741i	−0.672450	+	0.672450i
$64$	4.59981	+	6.54536i	0.574976	+	0.818170i
$65$	−1.47215	−	1.75341i	−0.182598	−	0.217484i
$66$	3.25343	−	0.333320i	0.400469	−	0.0410289i
$67$	7.01754	+	7.01754i	0.857329	+	0.857329i	0.991023	−	0.133693i	$-0.0426837\pi$
$67$	7.01754	+	7.01754i	0.857329	+	0.857329i	−0.133693	+	0.991023i	$0.542684\pi$
$68$	2.18060	+	1.43242i	0.264437	+	0.173707i
$69$		−	11.6793i		−	1.40602i
$70$	10.1650	−	0.153691i	1.21495	−	0.0183696i
$71$			14.9871i			1.77864i	0.457284	+	0.889321i	$0.348822\pi$
$71$			14.9871i			1.77864i	−0.457284	+	0.889321i	$0.651178\pi$
$72$	3.06143	−	5.89324i	0.360792	−	0.694525i
$73$	1.98983	+	1.98983i	0.232891	+	0.232891i	0.813899	−	0.581007i	$-0.197341\pi$
$73$	1.98983	+	1.98983i	0.232891	+	0.232891i	−0.581007	+	0.813899i	$0.697341\pi$
$74$	−0.398104	−	3.88576i	−0.0462787	−	0.451711i
$75$	9.46786	−	6.63763i	1.09325	−	0.766447i
$76$	−0.574393	−	2.77380i	−0.0658873	−	0.318177i
$77$	−2.27323	+	2.27323i	−0.259059	+	0.259059i
$78$	2.11414	−	2.59678i	0.239379	−	0.294027i
$79$	−14.1444			−1.59136			−0.795682	−	0.605714i	$-0.792888\pi$
$79$	−14.1444			−1.59136			−0.795682	+	0.605714i	$0.792888\pi$
$80$	−8.48626	+	2.82550i	−0.948792	+	0.315901i
$81$	10.5310			1.17011
$82$	−7.24831	+	8.90305i	−0.800442	+	0.983178i
$83$	3.37507	−	3.37507i	0.370462	−	0.370462i	−0.497183	−	0.867645i	$-0.665632\pi$
$83$	3.37507	−	3.37507i	0.370462	−	0.370462i	0.867645	+	0.497183i	$0.165632\pi$
$84$	3.01507	+	14.5601i	0.328971	+	1.58864i
$85$	−2.23397	+	1.87562i	−0.242308	+	0.203440i
$86$	−0.729306	−	7.11851i	−0.0786431	−	0.767609i
$87$	15.7701	+	15.7701i	1.69073	+	1.69073i
$88$	1.30388	−	2.50996i	0.138994	−	0.267563i
$89$			4.70719i			0.498961i	0.968380	+	0.249481i	$0.0802599\pi$
$89$			4.70719i			0.498961i	−0.968380	+	0.249481i	$0.919740\pi$
$90$	5.32892	+	5.17018i	0.561718	+	0.544985i
$91$			3.29161i			0.345054i
$92$	−8.44222	−	5.54565i	−0.880162	−	0.578174i
$93$	12.5075	+	12.5075i	1.29696	+	1.29696i
$94$	17.1486	−	1.75691i	1.76875	−	0.181212i
$95$	3.15503	+	0.275110i	0.323699	+	0.0282257i
$96$	−6.39172	−	11.4140i	−0.652352	−	1.16494i
$97$	0.309689	−	0.309689i	0.0314442	−	0.0314442i	−0.691210	−	0.722654i	$-0.742922\pi$
$97$	0.309689	−	0.309689i	0.0314442	−	0.0314442i	0.722654	+	0.691210i	$0.242922\pi$
$98$	−3.65769	−	2.97787i	−0.369483	−	0.300810i
$99$	−2.34794			−0.235977
$100$	−0.302323	−	9.99543i	−0.0302323	−	0.999543i
$101$	8.34044			0.829905			0.414952	−	0.909843i	$-0.363798\pi$
$101$	8.34044			0.829905			0.414952	+	0.909843i	$0.363798\pi$
$102$	−3.30848	−	2.69356i	−0.327589	−	0.266702i
$103$	−9.04433	+	9.04433i	−0.891164	+	0.891164i	−0.994633	−	0.103469i	$-0.967006\pi$
$103$	−9.04433	+	9.04433i	−0.891164	+	0.891164i	0.103469	+	0.994633i	$0.467006\pi$
$104$	−0.873196	−	2.76119i	−0.0856240	−	0.270757i
$105$	−16.5612	−	1.44409i	−1.61621	−	0.140929i
$106$	15.7727	−	1.61595i	1.53198	−	0.156955i
$107$	−0.464738	−	0.464738i	−0.0449280	−	0.0449280i	0.684286	−	0.729214i	$-0.260114\pi$
$107$	−0.464738	−	0.464738i	−0.0449280	−	0.0449280i	−0.729214	+	0.684286i	$0.760114\pi$
$108$	1.65580	−	2.52066i	0.159330	−	0.242550i
$109$		−	6.78445i		−	0.649832i	−0.945743	−	0.324916i	$-0.894664\pi$
$109$		−	6.78445i		−	0.649832i	0.945743	−	0.324916i	$-0.105336\pi$
$110$	2.26962	+	2.20201i	0.216399	+	0.209953i
$111$			6.38737i			0.606262i
$112$	11.9562	+	4.73412i	1.12975	+	0.447332i
$113$	−3.36794	−	3.36794i	−0.316829	−	0.316829i	0.530719	−	0.847548i	$-0.321922\pi$
$113$	−3.36794	−	3.36794i	−0.316829	−	0.316829i	−0.847548	+	0.530719i	$0.821922\pi$
$114$	0.472090	+	4.60791i	0.0442152	+	0.431570i
$115$	8.64883	−	7.26149i	0.806508	−	0.677138i
$116$	18.8872	−	3.91112i	1.75363	−	0.363138i
$117$	−1.69989	+	1.69989i	−0.157155	+	0.157155i
$118$	2.24290	−	2.75493i	0.206475	−	0.253612i
$119$	4.19374			0.384440
$120$	14.2756	−	3.18196i	1.30318	−	0.290472i
$121$	−1.00000			−0.0909091
$122$	3.16770	−	3.89086i	0.286790	−	0.352262i
$123$	13.2747	−	13.2747i	1.19694	−	1.19694i
$124$	14.9797	−	3.10197i	1.34522	−	0.278565i
$125$	10.8019	+	2.88432i	0.966150	+	0.257981i
$126$	−1.08796	−	10.6192i	−0.0969233	−	0.946036i
$127$	−5.74732	−	5.74732i	−0.509992	−	0.509992i	0.404532	−	0.914524i	$-0.367434\pi$
$127$	−5.74732	−	5.74732i	−0.509992	−	0.509992i	−0.914524	+	0.404532i	$0.867434\pi$
$128$	−11.2854	−	0.799523i	−0.997500	−	0.0706685i
$129$			11.7013i			1.03024i
$130$	3.23743	−	0.0489485i	0.283941	−	0.00429307i
$131$		−	18.0937i		−	1.58085i	−0.612556	−	0.790427i	$-0.709859\pi$
$131$		−	18.0937i		−	1.58085i	0.612556	−	0.790427i	$-0.290141\pi$
$132$	−2.53934	+	3.86568i	−0.221022	+	0.336464i
$133$	−3.21963	−	3.21963i	−0.279178	−	0.279178i
$134$	−13.9620	+	1.43044i	−1.20613	+	0.123571i
$135$	2.16812	+	2.58235i	0.186602	+	0.222253i
$136$	−3.51796	+	1.11252i	−0.301662	+	0.0953974i
$137$	6.35346	−	6.35346i	0.542812	−	0.542812i	−0.381540	−	0.924352i	$-0.624606\pi$
$137$	6.35346	−	6.35346i	0.542812	−	0.542812i	0.924352	+	0.381540i	$0.124606\pi$
$138$	12.8088	+	10.4282i	1.09036	+	0.887704i
$139$	−0.935850			−0.0793778			−0.0396889	−	0.999212i	$-0.512637\pi$
$139$	−0.935850			−0.0793778			−0.0396889	+	0.999212i	$0.512637\pi$
$140$	−8.90754	+	11.2853i	−0.752824	+	0.953785i
$141$	−28.1887			−2.37392
$142$	−16.4365	−	13.3816i	−1.37932	−	1.12296i
$143$	−0.723993	+	0.723993i	−0.0605433	+	0.0605433i
$144$	3.72971	+	8.61942i	0.310809	+	0.718285i
$145$	−1.87326	+	21.4830i	−0.155566	+	1.78407i
$146$	−3.95893	+	0.405600i	−0.327643	+	0.0335677i
$147$	5.45373	+	5.45373i	0.449816	+	0.449816i
$148$	4.61702	+	3.03289i	0.379516	+	0.249302i
$149$		−	12.5283i		−	1.02636i	−0.858281	−	0.513180i	$-0.828467\pi$
$149$		−	12.5283i		−	1.02636i	0.858281	−	0.513180i	$-0.171533\pi$
$150$	−1.17405	+	16.3101i	−0.0958605	+	1.33171i
$151$		−	11.6081i		−	0.944655i	−0.881423	−	0.472328i	$-0.843414\pi$
$151$		−	11.6081i		−	0.944655i	0.881423	−	0.472328i	$-0.156586\pi$
$152$	3.55492	+	1.84671i	0.288342	+	0.149788i
$153$	2.16579	+	2.16579i	0.175093	+	0.175093i
$154$	−0.463369	−	4.52278i	−0.0373393	−	0.364456i
$155$	−1.48571	+	17.0385i	−0.119335	+	1.36857i
$156$	0.960259	+	4.63719i	0.0768823	+	0.371273i
$157$	2.67425	−	2.67425i	0.213428	−	0.213428i	−0.592294	−	0.805722i	$-0.701778\pi$
$157$	2.67425	−	2.67425i	0.213428	−	0.213428i	0.805722	+	0.592294i	$0.201778\pi$
$158$	12.6291	−	15.5123i	1.00472	−	1.23409i
$159$	−25.9270			−2.05614
$160$	4.47840	−	11.8298i	0.354049	−	0.935227i
$161$	−16.2361			−1.27959
$162$	−9.40286	+	11.5495i	−0.738758	+	0.907412i
$163$	−5.14228	+	5.14228i	−0.402775	+	0.402775i	−0.879210	−	0.476435i	$-0.841929\pi$
$163$	−5.14228	+	5.14228i	−0.402775	+	0.402775i	0.476435	+	0.879210i	$0.341929\pi$
$164$	−3.29225	−	15.8986i	−0.257081	−	1.24147i
$165$	−3.32503	−	3.96029i	−0.258853	−	0.308308i
$166$	0.687964	+	6.71499i	0.0533964	+	0.521184i
$167$	10.2219	+	10.2219i	0.790991	+	0.790991i	0.981655	−	0.190665i	$-0.0610643\pi$
$167$	10.2219	+	10.2219i	0.790991	+	0.790991i	−0.190665	+	0.981655i	$0.561064\pi$
$168$	−18.6603	−	9.69367i	−1.43967	−	0.747883i
$169$		−	11.9517i		−	0.919359i
$170$	−0.0623640	−	4.12471i	−0.00478310	−	0.316351i
$171$		−	3.32545i		−	0.254303i
$172$	8.45813	+	5.55610i	0.644927	+	0.423649i
$173$	13.4480	+	13.4480i	1.02244	+	1.02244i	0.999742	+	0.0226936i	$0.00722423\pi$
$173$	13.4480	+	13.4480i	1.02244	+	1.02244i	0.0226936	+	0.999742i	$0.492776\pi$
$174$	−31.3759	+	3.21452i	−2.37860	+	0.243692i
$175$	−9.22737	−	13.1618i	−0.697524	−	0.994942i
$176$	1.58850	+	3.67106i	0.119738	+	0.276716i
$177$	−4.10768	+	4.10768i	−0.308752	+	0.308752i
$178$	−5.16243	−	4.20293i	−0.386941	−	0.315023i
$179$	5.08038			0.379725			0.189863	−	0.981811i	$-0.439196\pi$
$179$	5.08038			0.379725			0.189863	+	0.981811i	$0.439196\pi$
$180$	−10.4283	+	1.22797i	−0.777276	+	0.0915274i
$181$	−9.69715			−0.720783			−0.360392	−	0.932801i	$-0.617357\pi$
$181$	−9.69715			−0.720783			−0.360392	+	0.932801i	$0.617357\pi$
$182$	−3.60994	−	2.93899i	−0.267587	−	0.217852i
$183$	−5.80138	+	5.80138i	−0.428851	+	0.428851i
$184$	13.6198	−	4.30711i	1.00407	−	0.317525i
$185$	−4.73001	+	3.97128i	−0.347757	+	0.291974i
$186$	−24.8847	+	2.54949i	−1.82463	+	0.186937i
$187$	0.922419	+	0.922419i	0.0674540	+	0.0674540i
$188$	−13.3847	+	20.3758i	−0.976183	+	1.48606i
$189$		−	4.84774i		−	0.352621i
$190$	−3.11876	+	3.21452i	−0.226259	+	0.233206i
$191$			6.59943i			0.477518i	0.971079	+	0.238759i	$0.0767405\pi$
$191$			6.59943i			0.477518i	−0.971079	+	0.238759i	$0.923259\pi$
$192$	18.2249	+	3.18142i	1.31527	+	0.229599i
$193$	−7.19452	−	7.19452i	−0.517873	−	0.517873i	0.399054	−	0.916927i	$-0.369338\pi$
$193$	−7.19452	−	7.19452i	−0.517873	−	0.517873i	−0.916927	+	0.399054i	$0.869338\pi$
$194$	0.0631262	+	0.616153i	0.00453219	+	0.0442372i
$195$	−5.27452	−	0.459924i	−0.377716	−	0.0329359i
$196$	6.53172	−	1.35257i	0.466551	−	0.0966124i
$197$	14.8919	−	14.8919i	1.06100	−	1.06100i	0.0629865	−	0.998014i	$-0.479937\pi$
$197$	14.8919	−	14.8919i	1.06100	−	1.06100i	0.998014	−	0.0629865i	$-0.0200625\pi$
$198$	2.09641	−	2.57501i	0.148986	−	0.182998i
$199$	−20.8386			−1.47721			−0.738605	−	0.674139i	$-0.764515\pi$
$199$	−20.8386			−1.47721			−0.738605	+	0.674139i	$0.764515\pi$
$200$	11.2320	+	8.59310i	0.794225	+	0.607624i
$201$	22.9506			1.61881
$202$	−7.44696	+	9.14705i	−0.523966	+	0.643584i
$203$	21.9229	−	21.9229i	1.53869	−	1.53869i
$204$	5.90812	−	1.22344i	0.413651	−	0.0856579i
$205$	18.0837	+	1.57685i	1.26302	+	0.110132i
$206$	−1.84357	−	17.9945i	−0.128448	−	1.25373i
$207$	−8.38486	−	8.38486i	−0.582788	−	0.582788i
$208$	3.80789	+	1.50775i	0.264029	+	0.104544i
$209$		−	1.41633i		−	0.0979693i
$210$	16.3708	−	16.8735i	1.12969	−	1.16438i
$211$			1.74833i			0.120360i	0.998188	+	0.0601799i	$0.0191674\pi$
$211$			1.74833i			0.120360i	−0.998188	+	0.0601799i	$0.980833\pi$
$212$	−12.3108	+	18.7409i	−0.845511	+	1.28713i
$213$	24.5073	+	24.5073i	1.67921	+	1.67921i
$214$	0.924637	−	0.0947309i	0.0632069	−	0.00647567i
$215$	−8.66514	+	7.27518i	−0.590957	+	0.496163i
$216$	1.28601	+	4.06657i	0.0875017	+	0.276695i
$217$	17.3874	−	17.3874i	1.18033	−	1.18033i
$218$	7.44058	+	6.05766i	0.503940	+	0.410276i
$219$	6.50764			0.439745
$220$	−4.44145	+	0.522999i	−0.299442	+	0.0352606i
$221$	1.33565			0.0898456
$222$	−7.00510	−	5.70312i	−0.470151	−	0.382768i
$223$	4.01382	−	4.01382i	0.268785	−	0.268785i	−0.559825	−	0.828611i	$-0.689132\pi$
$223$	4.01382	−	4.01382i	0.268785	−	0.268785i	0.828611	+	0.559825i	$0.189132\pi$
$224$	−15.8673	+	8.88551i	−1.06018	+	0.593688i
$225$	2.03189	−	11.5625i	0.135460	−	0.770835i
$226$	6.70080	−	0.686511i	0.445731	−	0.0456660i
$227$	7.34061	+	7.34061i	0.487213	+	0.487213i	0.907426	−	0.420213i	$-0.138044\pi$
$227$	7.34061	+	7.34061i	0.487213	+	0.487213i	−0.420213	+	0.907426i	$0.638044\pi$
$228$	−5.47506	−	3.59654i	−0.362595	−	0.238186i
$229$		−	1.92059i		−	0.126916i	−0.997985	−	0.0634581i	$-0.979787\pi$
$229$		−	1.92059i		−	0.126916i	0.997985	−	0.0634581i	$-0.0202129\pi$
$230$	0.241443	+	15.9689i	0.0159203	+	1.05296i
$231$			7.43450i			0.489154i
$232$	−12.5745	+	24.2059i	−0.825558	+	1.58920i
$233$	−15.6936	−	15.6936i	−1.02812	−	1.02812i	−0.999593	−	0.0285271i	$-0.990918\pi$
$233$	−15.6936	−	15.6936i	−1.02812	−	1.02812i	−0.0285271	−	0.999593i	$-0.509082\pi$
$234$	−0.346501	−	3.38208i	−0.0226515	−	0.221094i
$235$	−17.5260	−	20.8745i	−1.14327	−	1.36170i
$236$	1.01874	+	4.91962i	0.0663145	+	0.320240i
$237$	−23.1293	+	23.1293i	−1.50241	+	1.50241i
$238$	−3.74448	+	4.59932i	−0.242719	+	0.298130i
$239$	24.5204			1.58609			0.793047	−	0.609161i	$-0.208494\pi$
$239$	24.5204			1.58609			0.793047	+	0.609161i	$0.208494\pi$
$240$	−9.25662	+	18.4973i	−0.597512	+	1.19400i
$241$	5.52210			0.355710			0.177855	−	0.984057i	$-0.443084\pi$
$241$	5.52210			0.355710			0.177855	+	0.984057i	$0.443084\pi$
$242$	0.892874	−	1.09671i	0.0573961	−	0.0704993i
$243$	14.0218	−	14.0218i	0.899498	−	0.899498i
$244$	1.43880	+	6.94810i	0.0921095	+	0.444806i
$245$	−0.647826	+	7.42942i	−0.0413881	+	0.474649i
$246$	2.70588	+	26.4112i	0.172520	+	1.68391i
$247$	−1.02541	−	1.02541i	−0.0652453	−	0.0652453i
$248$	−9.97305	+	19.1981i	−0.633289	+	1.21908i
$249$		−	11.0380i		−	0.699506i
$250$	−12.8080	+	9.27122i	−0.810048	+	0.586363i
$251$		−	13.1078i		−	0.827357i	−0.910423	−	0.413678i	$-0.864244\pi$
$251$		−	13.1078i		−	0.827357i	0.910423	−	0.413678i	$-0.135756\pi$
$252$	12.6176	+	8.28845i	0.794837	+	0.522124i
$253$	−3.57116	−	3.57116i	−0.224517	−	0.224517i
$254$	11.4348	−	1.17152i	0.717482	−	0.0735075i
$255$	−0.585977	+	6.72012i	−0.0366953	+	0.420830i
$256$	10.9533	−	11.6630i	0.684582	−	0.728936i
$257$	−20.6594	+	20.6594i	−1.28870	+	1.28870i	−0.353121	+	0.935578i	$0.614880\pi$
$257$	−20.6594	+	20.6594i	−1.28870	+	1.28870i	−0.935578	+	0.353121i	$0.885120\pi$
$258$	−12.8330	−	10.4478i	−0.798946	−	0.650452i
$259$	8.87947			0.551743
$260$	−2.83693	+	3.59423i	−0.175939	+	0.222904i
$261$	22.6434			1.40159
$262$	19.8436	+	16.1554i	1.22594	+	0.998084i
$263$	−5.86258	+	5.86258i	−0.361502	+	0.361502i	−0.864366	−	0.502864i	$-0.832280\pi$
$263$	−5.86258	+	5.86258i	−0.361502	+	0.361502i	0.502864	+	0.864366i	$0.332280\pi$
$264$	−1.97222	−	6.23649i	−0.121382	−	0.383830i
$265$	−16.1198	−	19.1996i	−0.990234	−	1.17942i
$266$	6.40574	−	0.656281i	0.392761	−	0.0402391i
$267$	7.69733	+	7.69733i	0.471069	+	0.471069i
$268$	10.8975	−	16.5895i	0.665673	−	1.01336i
$269$		−	12.8329i		−	0.782437i	−0.920298	−	0.391219i	$-0.872054\pi$
$269$		−	12.8329i		−	0.782437i	0.920298	−	0.391219i	$-0.127946\pi$
$270$	−4.76795	+	0.0720893i	−0.290168	+	0.00438722i
$271$		−	18.6929i		−	1.13551i	−0.823196	−	0.567757i	$-0.807811\pi$
$271$		−	18.6929i		−	1.13551i	0.823196	−	0.567757i	$-0.192189\pi$
$272$	1.92099	−	4.85152i	0.116477	−	0.294167i
$273$	5.38252	+	5.38252i	0.325765	+	0.325765i
$274$	1.29507	+	12.6407i	0.0782380	+	0.763655i
$275$	0.865394	−	4.92454i	0.0521852	−	0.296961i
$276$	−22.8734	+	4.73656i	−1.37681	+	0.285107i
$277$	−6.37661	+	6.37661i	−0.383133	+	0.383133i	−0.872230	−	0.489097i	$-0.837327\pi$
$277$	−6.37661	+	6.37661i	−0.383133	+	0.383133i	0.489097	+	0.872230i	$0.337327\pi$
$278$	0.835597	−	1.02636i	0.0501158	−	0.0615568i
$279$	17.9588			1.07517
$280$	−4.42344	−	19.8454i	−0.264351	−	1.18599i
$281$	−16.5985			−0.990183			−0.495092	−	0.868841i	$-0.664866\pi$
$281$	−16.5985			−0.990183			−0.495092	+	0.868841i	$0.664866\pi$
$282$	25.1690	−	30.9149i	1.49879	−	1.84095i
$283$	−10.6084	+	10.6084i	−0.630606	+	0.630606i	−0.948220	−	0.317614i	$-0.897118\pi$
$283$	−10.6084	+	10.6084i	−0.630606	+	0.630606i	0.317614	+	0.948220i	$0.397118\pi$
$284$	29.3515	−	6.07804i	1.74169	−	0.360665i
$285$	5.60906	−	4.70932i	0.332252	−	0.278956i
$286$	−0.147577	−	1.44045i	−0.00872639	−	0.0851754i
$287$	−18.4540	−	18.4540i	−1.08930	−	1.08930i
$288$	−12.7832	−	3.60564i	−0.753256	−	0.212464i
$289$			15.2983i			0.899899i
$290$	−21.8881	−	21.2361i	−1.28531	−	1.24702i
$291$		−	1.01283i		−	0.0593729i
$292$	3.09000	−	4.70395i	0.180828	−	0.275278i
$293$	−15.3588	−	15.3588i	−0.897270	−	0.897270i	0.0979236	−	0.995194i	$-0.468780\pi$
$293$	−15.3588	−	15.3588i	−0.897270	−	0.897270i	−0.995194	+	0.0979236i	$0.968780\pi$
$294$	−10.8507	+	1.11167i	−0.632823	+	0.0648340i
$295$	−5.59576	−	0.487935i	−0.325798	−	0.0284087i
$296$	−7.44862	+	2.35554i	−0.432942	+	0.136913i
$297$	1.06627	−	1.06627i	0.0618711	−	0.0618711i
$298$	13.7399	+	11.1862i	0.795933	+	0.647999i
$299$	−5.17099			−0.299046
$300$	−16.8392	−	15.8504i	−0.972210	−	0.915125i
$301$	16.2667			0.937598
$302$	12.7308	+	10.3646i	0.732573	+	0.596415i
$303$	13.6385	−	13.6385i	0.783512	−	0.783512i
$304$	−5.19941	+	2.24984i	−0.298207	+	0.129037i
$305$	−7.90303	−	0.689123i	−0.452526	−	0.0394591i
$306$	−4.30902	+	0.441467i	−0.246330	+	0.0252370i
$307$	0.975912	+	0.975912i	0.0556982	+	0.0556982i	0.734407	−	0.678709i	$-0.237460\pi$
$307$	0.975912	+	0.975912i	0.0556982	+	0.0556982i	−0.678709	+	0.734407i	$0.737460\pi$
$308$	5.37392	+	3.53010i	0.306207	+	0.201146i
$309$			29.5791i			1.68269i
$310$	−17.3598	−	16.8426i	−0.985968	−	0.956597i
$311$			5.31250i			0.301244i	0.988591	+	0.150622i	$0.0481277\pi$
$311$			5.31250i			0.301244i	−0.988591	+	0.150622i	$0.951872\pi$
$312$	−5.94305	−	3.08730i	−0.336459	−	0.174784i
$313$	4.06321	+	4.06321i	0.229666	+	0.229666i	0.812553	−	0.582887i	$-0.198077\pi$
$313$	4.06321	+	4.06321i	0.229666	+	0.229666i	−0.582887	+	0.812553i	$0.698077\pi$
$314$	0.545110	+	5.32064i	0.0307624	+	0.300261i
$315$	−12.9264	+	10.8529i	−0.728322	+	0.611494i
$316$	5.73626	+	27.7010i	0.322690	+	1.55830i
$317$	−7.01485	+	7.01485i	−0.393993	+	0.393993i	−0.876108	−	0.482115i	$-0.839869\pi$
$317$	−7.01485	+	7.01485i	−0.393993	+	0.393993i	0.482115	+	0.876108i	$0.339869\pi$
$318$	23.1495	−	28.4344i	1.29816	−	1.59452i
$319$	9.64395			0.539958
$320$	8.97522	+	15.4740i	0.501730	+	0.865024i
$321$	−1.51991			−0.0848329
$322$	14.4968	−	17.8063i	0.807876	−	0.992308i
$323$	−1.30645	+	1.30645i	−0.0726926	+	0.0726926i
$324$	−4.27086	−	20.6244i	−0.237270	−	1.14580i
$325$	−2.93879	−	4.19187i	−0.163015	−	0.232523i
$326$	−1.04819	−	10.2310i	−0.0580537	−	0.566643i
$327$	−11.0941	−	11.0941i	−0.613506	−	0.613506i
$328$	20.3758	+	10.5848i	1.12506	+	0.584449i
$329$			39.1868i			2.16044i
$330$	7.31213	−	0.110556i	0.402519	−	0.00608592i
$331$		−	25.0017i		−	1.37422i	−0.726556	−	0.687108i	$-0.758880\pi$
$331$		−	25.0017i		−	1.37422i	0.726556	−	0.687108i	$-0.241120\pi$
$332$	−7.97867	−	5.24114i	−0.437886	−	0.287645i
$333$	4.58565	+	4.58565i	0.251292	+	0.251292i
$334$	−20.3372	+	2.08359i	−1.11280	+	0.114009i
$335$	14.2693	+	16.9955i	0.779614	+	0.928563i
$336$	27.2925	−	11.8097i	1.48893	−	0.644274i
$337$	2.87545	−	2.87545i	0.156636	−	0.156636i	−0.624438	−	0.781074i	$-0.714672\pi$
$337$	2.87545	−	2.87545i	0.156636	−	0.156636i	0.781074	+	0.624438i	$0.214672\pi$
$338$	13.1075	+	10.6713i	0.712956	+	0.580444i
$339$	−11.0147			−0.598236
$340$	4.57930	+	3.61446i	0.248348	+	0.196021i
$341$	7.64876			0.414204
$342$	3.64706	+	2.96921i	0.197210	+	0.160556i
$343$	−8.33105	+	8.33105i	−0.449835	+	0.449835i
$344$	−13.6455	+	4.31523i	−0.735715	+	0.232662i
$345$	2.26862	−	26.0170i	0.122138	−	1.40071i
$346$	−26.7560	+	2.74121i	−1.43841	+	0.147368i
$347$	0.444682	+	0.444682i	0.0238718	+	0.0238718i	0.718942	−	0.695070i	$-0.244627\pi$
$347$	0.444682	+	0.444682i	0.0238718	+	0.0238718i	−0.695070	+	0.718942i	$0.744627\pi$
$348$	24.4893	−	37.2805i	1.31277	−	1.99844i
$349$			11.1765i			0.598262i	0.954212	+	0.299131i	$0.0966968\pi$
$349$			11.1765i			0.598262i	−0.954212	+	0.299131i	$0.903303\pi$
$350$	22.6736	+	1.63211i	1.21196	+	0.0872401i
$351$		−	1.54394i		−	0.0824094i
$352$	−5.44442	−	1.53566i	−0.290189	−	0.0818510i
$353$	9.52218	+	9.52218i	0.506814	+	0.506814i	0.913547	−	0.406733i	$-0.133332\pi$
$353$	9.52218	+	9.52218i	0.506814	+	0.506814i	−0.406733	+	0.913547i	$0.633332\pi$
$354$	−0.837298	−	8.17259i	−0.0445019	−	0.434368i
$355$	−2.91113	+	33.3855i	−0.154507	+	1.77192i
$356$	9.21880	−	1.90901i	0.488596	−	0.101177i
$357$	6.85772	−	6.85772i	0.362949	−	0.362949i
$358$	−4.53614	+	5.57171i	−0.239742	+	0.294474i
$359$	23.9996			1.26665			0.633326	−	0.773885i	$-0.281689\pi$
$359$	23.9996			1.26665			0.633326	+	0.773885i	$0.281689\pi$
$360$	7.96439	−	12.5332i	0.419760	−	0.660558i
$361$	−16.9940			−0.894422
$362$	8.65833	−	10.6350i	0.455072	−	0.558962i
$363$	−1.63523	+	1.63523i	−0.0858272	+	0.0858272i
$364$	6.44645	−	1.33491i	0.337886	−	0.0699686i
$365$	4.04606	+	4.81907i	0.211780	+	0.252242i
$366$	−1.18254	−	11.5424i	−0.0618122	−	0.603328i
$367$	10.7096	+	10.7096i	0.559038	+	0.559038i	0.929033	−	0.369996i	$-0.120641\pi$
$367$	10.7096	+	10.7096i	0.559038	+	0.559038i	−0.369996	+	0.929033i	$0.620641\pi$
$368$	−7.43712	+	18.7827i	−0.387687	+	0.979117i
$369$		−	19.0605i		−	0.992249i
$370$	−0.132044	−	8.73331i	−0.00686464	−	0.454023i
$371$			36.0427i			1.87124i
$372$	19.4228	−	29.5677i	1.00703	−	1.53301i
$373$	−12.7491	−	12.7491i	−0.660125	−	0.660125i	0.295284	−	0.955409i	$-0.404586\pi$
$373$	−12.7491	−	12.7491i	−0.660125	−	0.660125i	−0.955409	+	0.295284i	$0.904586\pi$
$374$	−1.83523	+	0.188023i	−0.0948976	+	0.00972245i
$375$	22.3801	−	12.9470i	1.15570	−	0.668581i
$376$	−10.3955	−	32.8722i	−0.536105	−	1.69526i
$377$	6.98216	−	6.98216i	0.359599	−	0.359599i
$378$	5.31657	+	4.32842i	0.273455	+	0.222630i
$379$	−11.9690			−0.614804			−0.307402	−	0.951580i	$-0.599460\pi$
$379$	−11.9690			−0.614804			−0.307402	+	0.951580i	$0.599460\pi$
$380$	−0.740736	−	6.29054i	−0.0379990	−	0.322698i
$381$	−18.7963			−0.962966
$382$	−7.23766	−	5.89246i	−0.370311	−	0.301484i
$383$	−0.0817471	+	0.0817471i	−0.00417708	+	0.00417708i	−0.709192	−	0.705015i	$-0.750940\pi$
$383$	−0.0817471	+	0.0817471i	−0.00417708	+	0.00417708i	0.705015	+	0.709192i	$0.250940\pi$
$384$	−19.7616	+	17.1468i	−1.00846	+	0.875021i
$385$	−5.50544	+	4.62232i	−0.280583	+	0.235575i
$386$	14.3141	−	1.46651i	0.728569	−	0.0746434i
$387$	8.40067	+	8.40067i	0.427030	+	0.427030i
$388$	−0.732106	−	0.480916i	−0.0371671	−	0.0244148i
$389$		−	13.0833i		−	0.663347i	−0.943394	−	0.331674i	$-0.892387\pi$
$389$		−	13.0833i		−	0.663347i	0.943394	−	0.331674i	$-0.107613\pi$
$390$	5.21389	−	5.37397i	0.264015	−	0.272122i
$391$			6.58821i			0.333180i
$392$	−4.34862	+	8.37109i	−0.219639	+	0.422804i
$393$	−29.5873	−	29.5873i	−1.49248	−	1.49248i
$394$	3.03551	+	29.6286i	0.152927	+	1.49267i
$395$	−31.5082	−	2.74743i	−1.58535	−	0.138238i
$396$	0.952210	+	4.59832i	0.0478504	+	0.231074i
$397$	13.8205	−	13.8205i	0.693631	−	0.693631i	−0.269398	−	0.963029i	$-0.586825\pi$
$397$	13.8205	−	13.8205i	0.693631	−	0.693631i	0.963029	+	0.269398i	$0.0868248\pi$
$398$	18.6063	−	22.8539i	0.932647	−	1.14556i
$399$	−10.5297			−0.527143
$400$	−19.4529	+	4.64574i	−0.972647	+	0.232287i
$401$	29.9011			1.49319			0.746595	−	0.665279i	$-0.231687\pi$
$401$	29.9011			1.49319			0.746595	+	0.665279i	$0.231687\pi$
$402$	−20.4920	+	25.1701i	−1.02205	+	1.25537i
$403$	5.53765	−	5.53765i	0.275850	−	0.275850i
$404$	−3.38248	−	16.3343i	−0.168284	−	0.812664i
$405$	23.4590	+	2.04556i	1.16569	+	0.101645i
$406$	4.46870	+	43.6175i	0.221778	+	2.16470i
$407$	1.95305	+	1.95305i	0.0968091	+	0.0968091i
$408$	−3.93345	+	7.57188i	−0.194735	+	0.374864i
$409$			25.5845i			1.26507i	0.774531	+	0.632536i	$0.217986\pi$
$409$			25.5845i			1.26507i	−0.774531	+	0.632536i	$0.782014\pi$
$410$	−17.8758	+	18.4247i	−0.882823	+	0.909929i
$411$		−	20.7787i		−	1.02494i
$412$	21.3808	+	14.0449i	1.05336	+	0.691944i
$413$	5.71034	+	5.71034i	0.280988	+	0.280988i
$414$	16.6824	−	1.70915i	0.819895	−	0.0839999i
$415$	8.17394	−	6.86277i	0.401243	−	0.336880i
$416$	−5.05353	+	2.82992i	−0.247770	+	0.138748i
$417$	−1.53033	+	1.53033i	−0.0749405	+	0.0749405i
$418$	1.55330	+	1.26460i	0.0759744	+	0.0618536i
$419$	−5.31123			−0.259470			−0.129735	−	0.991549i	$-0.541413\pi$
$419$	−5.31123			−0.259470			−0.129735	+	0.991549i	$0.541413\pi$
$420$	3.88823	+	33.0199i	0.189726	+	1.61121i
$421$	14.3707			0.700385			0.350192	−	0.936678i	$-0.386116\pi$
$421$	14.3707			0.700385			0.350192	+	0.936678i	$0.386116\pi$
$422$	−1.91741	−	1.56104i	−0.0933381	−	0.0759900i
$423$	−20.2374	+	20.2374i	−0.983974	+	0.983974i
$424$	−9.56139	−	30.2347i	−0.464342	−	1.46833i
$425$	−5.34075	+	3.74424i	−0.259064	+	0.181622i
$426$	−48.7594	+	4.99550i	−2.36240	+	0.242033i
$427$	8.06486	+	8.06486i	0.390286	+	0.390286i
$428$	−0.721692	+	1.09864i	−0.0348843	+	0.0531049i
$429$			2.36779i			0.114318i
$430$	−0.241898	−	15.9990i	−0.0116653	−	0.771539i
$431$			38.3768i			1.84854i	0.381734	+	0.924272i	$0.375327\pi$
$431$			38.3768i			1.84854i	−0.381734	+	0.924272i	$0.624673\pi$
$432$	−5.60809	−	2.22056i	−0.269820	−	0.106837i
$433$	−6.38327	−	6.38327i	−0.306760	−	0.306760i	0.536891	−	0.843651i	$-0.319599\pi$
$433$	−6.38327	−	6.38327i	−0.306760	−	0.306760i	−0.843651	+	0.536891i	$0.819599\pi$
$434$	3.54420	+	34.5937i	0.170127	+	1.66055i
$435$	32.0664	+	38.1928i	1.53747	+	1.83121i
$436$	−13.2870	+	2.75144i	−0.636332	+	0.131770i
$437$	5.05792	−	5.05792i	0.241953	−	0.241953i
$438$	−5.81050	+	7.13700i	−0.277636	+	0.341019i
$439$	16.3392			0.779827			0.389913	−	0.920852i	$-0.372505\pi$
$439$	16.3392			0.779827			0.389913	+	0.920852i	$0.372505\pi$
$440$	3.39208	−	5.33796i	0.161711	−	0.254477i
$441$	7.83073			0.372892
$442$	−1.19257	+	1.46482i	−0.0567247	+	0.0696745i
$443$	6.87247	−	6.87247i	0.326521	−	0.326521i	−0.524741	−	0.851262i	$-0.675838\pi$
$443$	6.87247	−	6.87247i	0.326521	−	0.326521i	0.851262	+	0.524741i	$0.175838\pi$
$444$	12.5093	−	2.59040i	0.593667	−	0.122935i
$445$	−0.914335	+	10.4858i	−0.0433437	+	0.497075i
$446$	0.818166	+	7.98584i	0.0387413	+	0.378141i
$447$	−20.4866	−	20.4866i	−0.968985	−	0.968985i
$448$	4.42269	−	25.3355i	0.208952	−	1.19699i
$449$			4.44137i			0.209601i	0.994493	+	0.104801i	$0.0334204\pi$
$449$			4.44137i			0.209601i	−0.994493	+	0.104801i	$0.966580\pi$
$450$	10.8665	+	12.5523i	0.512253	+	0.591720i
$451$		−	8.11796i		−	0.382260i
$452$	−5.23007	+	7.96181i	−0.246002	+	0.374492i
$453$	−18.9819	−	18.9819i	−0.891848	−	0.891848i
$454$	−14.6048	+	1.49629i	−0.685436	+	0.0702243i
$455$	−0.639369	+	7.33243i	−0.0299741	+	0.343750i
$456$	8.83291	−	2.79331i	0.413639	−	0.130809i
$457$	−11.8533	+	11.8533i	−0.554476	+	0.554476i	−0.927729	−	0.373254i	$-0.878242\pi$
$457$	−11.8533	+	11.8533i	−0.554476	+	0.554476i	0.373254	+	0.927729i	$0.378242\pi$
$458$	2.10633	+	1.71485i	0.0984225	+	0.0801295i
$459$	−1.96709			−0.0918159
$460$	−17.7288	−	13.9934i	−0.826611	−	0.652446i
$461$	−25.5894			−1.19182			−0.595909	−	0.803052i	$-0.703208\pi$
$461$	−25.5894			−1.19182			−0.595909	+	0.803052i	$0.703208\pi$
$462$	−8.15350	−	6.63807i	−0.379335	−	0.308831i
$463$	−16.4285	+	16.4285i	−0.763499	+	0.763499i	−0.976953	−	0.213454i	$-0.931529\pi$
$463$	−16.4285	+	16.4285i	−0.763499	+	0.763499i	0.213454	+	0.976953i	$0.431529\pi$
$464$	−15.3195	−	35.4035i	−0.711188	−	1.64357i
$465$	25.4324	+	30.2913i	1.17940	+	1.40473i
$466$	31.2237	−	3.19893i	1.44641	−	0.148188i
$467$	−19.5335	−	19.5335i	−0.903901	−	0.903901i	0.0918697	−	0.995771i	$-0.470716\pi$
$467$	−19.5335	−	19.5335i	−0.903901	−	0.903901i	−0.995771	+	0.0918697i	$0.970716\pi$
$468$	4.01855	+	2.63976i	0.185757	+	0.122023i
$469$		−	31.9050i		−	1.47323i
$470$	38.5418	−	0.582736i	1.77780	−	0.0268796i
$471$		−	8.74600i		−	0.402995i
$472$	−6.30501	−	3.27533i	−0.290212	−	0.150759i
$473$	3.57789	+	3.57789i	0.164511	+	0.164511i
$474$	−4.71460	−	46.0176i	−0.216549	−	2.11366i
$475$	6.97475	+	1.22568i	0.320024	+	0.0562380i
$476$	−1.70078	−	8.21324i	−0.0779550	−	0.376453i
$477$	−18.6136	+	18.6136i	−0.852259	+	0.852259i
$478$	−21.8936	+	26.8918i	−1.00139	+	1.23000i
$479$	−1.19428			−0.0545681			−0.0272840	−	0.999628i	$-0.508686\pi$
$479$	−1.19428			−0.0545681			−0.0272840	+	0.999628i	$0.508686\pi$
$480$	−12.0212	−	26.6676i	−0.548690	−	1.21720i
$481$	2.82799			0.128945
$482$	−4.93054	+	6.05615i	−0.224580	+	0.275850i
$483$	−26.5498	+	26.5498i	−1.20806	+	1.20806i
$484$	0.405551	+	1.95845i	0.0184341	+	0.0890205i
$485$	0.750023	−	0.629714i	0.0340568	−	0.0285938i
$486$	2.85816	+	27.8975i	0.129649	+	1.26546i
$487$	−3.24221	−	3.24221i	−0.146919	−	0.146919i	0.629821	−	0.776740i	$-0.283128\pi$
$487$	−3.24221	−	3.24221i	−0.146919	−	0.146919i	−0.776740	+	0.629821i	$0.783128\pi$
$488$	−8.90472	−	4.62583i	−0.403098	−	0.209402i
$489$			16.8176i			0.760518i
$490$	−7.56951	−	7.34402i	−0.341955	−	0.331769i
$491$		−	11.6132i		−	0.524095i	−0.965055	−	0.262047i	$-0.915602\pi$
$491$		−	11.6132i		−	0.524095i	0.965055	−	0.262047i	$-0.0843977\pi$
$492$	−31.3814	−	20.6143i	−1.41478	−	0.929364i
$493$	−8.89577	−	8.89577i	−0.400645	−	0.400645i
$494$	2.04014	−	0.209017i	0.0917903	−	0.00940410i
$495$	−5.23031	−	0.456069i	−0.235085	−	0.0204988i
$496$	−12.1501	−	28.0790i	−0.545555	−	1.26079i
$497$	34.0691	−	34.0691i	1.52821	−	1.52821i
$498$	12.1055	+	9.85556i	0.542461	+	0.441638i
$499$	16.5509			0.740919			0.370459	−	0.928849i	$-0.379200\pi$
$499$	16.5509			0.740919			0.370459	+	0.928849i	$0.379200\pi$
$500$	1.26808	−	22.3247i	0.0567101	−	0.998391i
$501$	33.4301			1.49355
$502$	14.3755	+	11.7036i	0.641608	+	0.522358i
$503$	−2.09623	+	2.09623i	−0.0934662	+	0.0934662i	−0.752294	−	0.658828i	$-0.771053\pi$
$503$	−2.09623	+	2.09623i	−0.0934662	+	0.0934662i	0.658828	+	0.752294i	$0.271053\pi$
$504$	−20.3560	+	6.43736i	−0.906729	+	0.286743i
$505$	18.5793	+	1.62007i	0.826767	+	0.0720920i
$506$	7.10512	−	0.727934i	0.315861	−	0.0323606i
$507$	−19.5437	−	19.5437i	−0.867966	−	0.867966i
$508$	−8.92500	+	13.5867i	−0.395983	+	0.602811i
$509$		−	34.7631i		−	1.54085i	−0.637533	−	0.770423i	$-0.720045\pi$
$509$		−	34.7631i		−	1.54085i	0.637533	−	0.770423i	$-0.279955\pi$
$510$	−6.84683	−	6.64287i	−0.303183	−	0.294151i
$511$		−	9.04666i		−	0.400201i
$512$	3.01099	+	22.4262i	0.133068	+	0.991107i
$513$	1.51018	+	1.51018i	0.0666761	+	0.0666761i
$514$	−4.21115	−	41.1037i	−0.185746	−	1.81301i
$515$	−21.9041	+	18.3905i	−0.965209	+	0.810382i
$516$	22.9165	−	4.74549i	1.00884	−	0.208908i
$517$	−8.61919	+	8.61919i	−0.379072	+	0.379072i
$518$	−7.92825	+	9.73821i	−0.348347	+	0.427872i
$519$	43.9812			1.93056
$520$	−1.40881	−	6.32049i	−0.0617802	−	0.277172i
$521$	−28.2376			−1.23711			−0.618555	−	0.785741i	$-0.712282\pi$
$521$	−28.2376			−1.23711			−0.618555	+	0.785741i	$0.712282\pi$
$522$	−20.2177	+	24.8333i	−0.884906	+	1.08692i
$523$	−23.3918	+	23.3918i	−1.02285	+	1.02285i	−0.0231215	+	0.999733i	$0.507360\pi$
$523$	−23.3918	+	23.3918i	−1.02285	+	1.02285i	−0.999733	+	0.0231215i	$0.992640\pi$
$524$	−35.4356	+	7.33793i	−1.54801	+	0.320559i
$525$	−36.6115	−	6.43377i	−1.59786	−	0.280793i
$526$	−1.19501	−	11.6641i	−0.0521049	−	0.508579i
$527$	−7.05537	−	7.05537i	−0.307337	−	0.307337i
$528$	8.60058	+	3.40545i	0.374292	+	0.148203i
$529$		−	2.50633i		−	0.108971i
$530$	35.4494	−	0.535980i	1.53982	−	0.0232815i
$531$			5.89801i			0.255952i
$532$	−4.99977	+	7.61122i	−0.216767	+	0.329988i
$533$	−5.87734	−	5.87734i	−0.254576	−	0.254576i
$534$	−15.3145	+	1.56900i	−0.662723	+	0.0678973i
$535$	−0.944987	−	1.12553i	−0.0408553	−	0.0486609i
$536$	8.46374	+	26.7638i	0.365578	+	1.15602i
$537$	8.30757	−	8.30757i	0.358498	−	0.358498i
$538$	14.0740	+	11.4582i	0.606774	+	0.493997i
$539$	3.33515			0.143655
$540$	4.17811	−	5.29343i	0.179797	−	0.227793i
$541$	−21.3400			−0.917478			−0.458739	−	0.888571i	$-0.651699\pi$
$541$	−21.3400			−0.917478			−0.458739	+	0.888571i	$0.651699\pi$
$542$	20.5008	+	16.6904i	0.880583	+	0.716916i
$543$	−15.8570	+	15.8570i	−0.680491	+	0.680491i
$544$	3.60552	+	6.43857i	0.154585	+	0.276051i
$545$	1.31783	−	15.1131i	0.0564495	−	0.647376i
$546$	−10.7090	+	1.09716i	−0.458303	+	0.0469540i
$547$	17.5485	+	17.5485i	0.750320	+	0.750320i	0.974539	−	0.224219i	$-0.0719830\pi$
$547$	17.5485	+	17.5485i	0.750320	+	0.750320i	−0.224219	+	0.974539i	$0.571983\pi$
$548$	−15.0196	−	9.86628i	−0.641605	−	0.421466i
$549$			8.32991i			0.355512i
$550$	4.62811	+	5.34608i	0.197343	+	0.227958i
$551$			13.6590i			0.581892i
$552$	15.2284	−	29.3146i	0.648163	−	1.24771i
$553$	32.1534	+	32.1534i	1.36730	+	1.36730i
$554$	−1.29979	−	12.6868i	−0.0552227	−	0.539011i
$555$	−1.24070	+	14.2286i	−0.0526646	+	0.603970i
$556$	0.379535	+	1.83282i	0.0160959	+	0.0777287i
$557$	−5.97438	+	5.97438i	−0.253143	+	0.253143i	−0.822258	−	0.569115i	$-0.807286\pi$
$557$	−5.97438	+	5.97438i	−0.253143	+	0.253143i	0.569115	+	0.822258i	$0.307286\pi$
$558$	−16.0350	+	19.6957i	−0.678815	+	0.833784i
$559$	5.18073			0.219122
$560$	25.7142	+	12.8682i	1.08662	+	0.543780i
$561$	3.01673			0.127367
$562$	14.8204	−	18.2038i	0.625160	−	0.767879i
$563$	5.46575	−	5.46575i	0.230354	−	0.230354i	−0.582486	−	0.812840i	$-0.697920\pi$
$563$	5.46575	−	5.46575i	0.230354	−	0.230354i	0.812840	+	0.582486i	$0.197920\pi$
$564$	11.4320	+	55.2062i	0.481372	+	2.32460i
$565$	−6.84828	−	8.15667i	−0.288109	−	0.343154i
$566$	−2.16239	−	21.1064i	−0.0908921	−	0.887168i
$567$	−23.9394	−	23.9394i	−1.00536	−	1.00536i
$568$	−19.5413	+	37.6170i	−0.819936	+	1.57838i
$569$			35.6456i			1.49434i	0.664632	+	0.747171i	$0.268588\pi$
$569$			35.6456i			1.49434i	−0.664632	+	0.747171i	$0.731412\pi$
$570$	0.156584	+	10.3563i	0.00655857	+	0.433780i
$571$			0.929679i			0.0389059i	0.999811	+	0.0194529i	$0.00619245\pi$
$571$			0.929679i			0.0389059i	−0.999811	+	0.0194529i	$0.993808\pi$
$572$	1.71152	+	1.12429i	0.0715623	+	0.0470089i
$573$	10.7916	+	10.7916i	0.450824	+	0.450824i
$574$	36.7158	−	3.76161i	1.53249	−	0.157006i
$575$	20.6768	−	14.4958i	0.862281	−	0.604519i
$576$	15.3681	−	10.8001i	0.640338	−	0.450003i
$577$	−21.1801	+	21.1801i	−0.881740	+	0.881740i	−0.993711	−	0.111972i	$-0.964283\pi$
$577$	−21.1801	+	21.1801i	−0.881740	+	0.881740i	0.111972	+	0.993711i	$0.464283\pi$
$578$	−16.7778	−	13.6594i	−0.697865	−	0.568158i
$579$	−23.5294			−0.977847
$580$	42.8331	−	5.04377i	1.77855	−	0.209431i
$581$	−15.3446			−0.636602
$582$	1.11078	+	0.904325i	0.0460432	+	0.0374855i
$583$	−7.92764	+	7.92764i	−0.328329	+	0.328329i
$584$	2.39990	+	7.58887i	0.0993084	+	0.314030i
$585$	−4.11690	+	3.45652i	−0.170213	+	0.142909i
$586$	30.5576	−	3.13069i	1.26232	−	0.129328i
$587$	−9.39519	−	9.39519i	−0.387781	−	0.387781i	0.486114	−	0.873895i	$-0.338414\pi$
$587$	−9.39519	−	9.39519i	−0.387781	−	0.387781i	−0.873895	+	0.486114i	$0.838414\pi$
$588$	8.46909	−	12.8926i	0.349259	−	0.531683i
$589$			10.8331i			0.446372i
$590$	5.53143	−	5.70127i	0.227725	−	0.234717i
$591$		−	48.7032i		−	2.00338i
$592$	4.06733	−	10.2722i	0.167166	−	0.422184i
$593$	22.6726	+	22.6726i	0.931054	+	0.931054i	0.997772	−	0.0667183i	$-0.0212529\pi$
$593$	22.6726	+	22.6726i	0.931054	+	0.931054i	−0.0667183	+	0.997772i	$0.521253\pi$
$594$	0.217345	+	2.12143i	0.00891776	+	0.0870433i
$595$	9.34205	+	0.814602i	0.382987	+	0.0333954i
$596$	−24.5361	+	5.08087i	−1.00504	+	0.208121i
$597$	−34.0759	+	34.0759i	−1.39463	+	1.39463i
$598$	4.61704	−	5.67108i	0.188805	−	0.231908i
$599$	17.6219			0.720011			0.360006	−	0.932950i	$-0.382775\pi$
$599$	17.6219			0.720011			0.360006	+	0.932950i	$0.382775\pi$
$600$	32.4186	−	4.31526i	1.32348	−	0.176170i
$601$	−9.95444			−0.406050			−0.203025	−	0.979174i	$-0.565077\pi$
$601$	−9.95444			−0.406050			−0.203025	+	0.979174i	$0.565077\pi$
$602$	−14.5241	+	17.8399i	−0.591960	+	0.727100i
$603$	16.4768	−	16.4768i	0.670986	−	0.670986i
$604$	−22.7339	+	4.70769i	−0.925030	+	0.191553i
$605$	−2.22762	−	0.194242i	−0.0905654	−	0.00789707i
$606$	2.78004	+	27.1350i	0.112931	+	1.10228i
$607$	−30.5524	−	30.5524i	−1.24008	−	1.24008i	−0.959966	−	0.280116i	$-0.909627\pi$
$607$	−30.5524	−	30.5524i	−1.24008	−	1.24008i	−0.280116	−	0.959966i	$-0.590373\pi$
$608$	2.17500	−	7.71107i	0.0882077	−	0.312725i
$609$		−	71.6979i		−	2.90535i
$610$	7.81218	−	8.05204i	0.316306	−	0.326018i
$611$			12.4805i			0.504906i
$612$	3.36325	−	5.11992i	0.135951	−	0.206961i
$613$	−15.5026	−	15.5026i	−0.626145	−	0.626145i	0.320951	−	0.947096i	$-0.395998\pi$
$613$	−15.5026	−	15.5026i	−0.626145	−	0.626145i	−0.947096	+	0.320951i	$0.895998\pi$
$614$	−1.94166	+	0.198927i	−0.0783590	+	0.00802804i
$615$	32.1495	−	26.9924i	1.29639	−	1.08844i
$616$	−8.66973	+	2.74171i	−0.349313	+	0.110466i
$617$	25.9842	−	25.9842i	1.04608	−	1.04608i	0.0471977	−	0.998886i	$-0.484971\pi$
$617$	25.9842	−	25.9842i	1.04608	−	1.04608i	0.998886	−	0.0471977i	$-0.0150291\pi$
$618$	−32.4397	−	26.4104i	−1.30492	−	1.06238i
$619$	8.25617			0.331843			0.165922	−	0.986139i	$-0.446940\pi$
$619$	8.25617			0.331843			0.165922	+	0.986139i	$0.446940\pi$
$620$	33.9716	−	4.00029i	1.36433	−	0.160656i
$621$	7.61561			0.305604
$622$	−5.82628	−	4.74339i	−0.233613	−	0.190193i
$623$	10.7005	−	10.7005i	0.428708	−	0.428708i
$624$	8.69228	−	3.76124i	0.347970	−	0.150570i
$625$	23.5022	+	8.52333i	0.940087	+	0.340933i
$626$	−8.08410	+	0.828233i	−0.323106	+	0.0331028i
$627$	−2.31601	−	2.31601i	−0.0924927	−	0.0924927i
$628$	−6.32192	−	4.15283i	−0.252272	−	0.165716i
$629$		−	3.60306i		−	0.143664i
$630$	−0.360857	−	23.8669i	−0.0143769	−	0.950879i
$631$		−	10.1166i		−	0.402735i	−0.979516	−	0.201367i	$-0.935462\pi$
$631$		−	10.1166i		−	0.402735i	0.979516	−	0.201367i	$-0.0645385\pi$
$632$	−35.5018	−	18.4425i	−1.41219	−	0.733604i
$633$	2.85891	+	2.85891i	0.113632	+	0.113632i
$634$	−1.42989	−	13.9566i	−0.0567880	−	0.554289i
$635$	−11.6864	−	13.9192i	−0.463762	−	0.552366i
$636$	10.5147	+	50.7767i	0.416936	+	2.01343i
$637$	2.41462	−	2.41462i	0.0956709	−	0.0956709i
$638$	−8.61084	+	10.5766i	−0.340906	+	0.418733i
$639$	35.1888			1.39205
$640$	−24.9843	−	3.97314i	−0.987590	−	0.157052i
$641$	−33.6135			−1.32765			−0.663827	−	0.747886i	$-0.731069\pi$
$641$	−33.6135			−1.32765			−0.663827	+	0.747886i	$0.731069\pi$
$642$	1.35709	−	1.66690i	0.0535599	−	0.0657872i
$643$	29.4474	−	29.4474i	1.16129	−	1.16129i	0.177097	−	0.984193i	$-0.443329\pi$
$643$	29.4474	−	29.4474i	1.16129	−	1.16129i	0.984193	−	0.177097i	$-0.0566706\pi$
$644$	6.58458	+	31.7976i	0.259469	+	1.25300i
$645$	−2.27289	+	26.0660i	−0.0894950	+	1.02635i
$646$	−0.266302	−	2.59929i	−0.0104775	−	0.102268i
$647$	5.15400	+	5.15400i	0.202625	+	0.202625i	0.801124	−	0.598499i	$-0.204236\pi$
$647$	5.15400	+	5.15400i	0.202625	+	0.202625i	−0.598499	+	0.801124i	$0.704236\pi$
$648$	26.4324	+	13.7311i	1.03836	+	0.539410i
$649$			2.51199i			0.0986044i
$650$	7.22125	+	0.519806i	0.283241	+	0.0203885i
$651$		−	56.8647i		−	2.22870i
$652$	12.1564	+	7.98545i	0.476080	+	0.312734i
$653$	16.9805	+	16.9805i	0.664498	+	0.664498i	0.956437	−	0.291939i	$-0.0943004\pi$
$653$	16.9805	+	16.9805i	0.664498	+	0.664498i	−0.291939	+	0.956437i	$0.594300\pi$
$654$	22.0727	−	2.26139i	0.863111	−	0.0884275i
$655$	3.51456	−	40.3058i	0.137325	−	1.57488i
$656$	−29.8015	+	12.8954i	−1.16355	+	0.503481i
$657$	4.67199	−	4.67199i	0.182272	−	0.182272i
$658$	−42.9766	−	34.9889i	−1.67540	−	1.36401i
$659$	38.6928			1.50726			0.753629	−	0.657300i	$-0.228301\pi$
$659$	38.6928			1.50726			0.753629	+	0.657300i	$0.228301\pi$
$660$	−6.40756	+	8.11800i	−0.249414	+	0.315993i
$661$	3.52220			0.136998			0.0684988	−	0.997651i	$-0.478179\pi$
$661$	3.52220			0.136998			0.0684988	+	0.997651i	$0.478179\pi$
$662$	27.4196	+	22.3233i	1.06569	+	0.867621i
$663$	2.18409	−	2.18409i	0.0848231	−	0.0848231i
$664$	12.8720	−	4.07062i	0.499529	−	0.157971i
$665$	−6.54672	−	7.79749i	−0.253871	−	0.302374i
$666$	−9.12354	+	0.934725i	−0.353530	+	0.0362198i
$667$	34.4401	+	34.4401i	1.33352	+	1.33352i
$668$	15.8735	−	24.1645i	0.614164	−	0.934952i
$669$		−	13.1270i		−	0.507520i
$670$	−31.3798	+	0.474450i	−1.21231	+	0.0183296i
$671$			3.54775i			0.136960i
$672$	−11.4169	+	40.4765i	−0.440415	+	1.56142i
$673$	−2.73473	−	2.73473i	−0.105416	−	0.105416i	0.652432	−	0.757848i	$-0.273749\pi$
$673$	−2.73473	−	2.73473i	−0.105416	−	0.105416i	−0.757848	+	0.652432i	$0.773749\pi$
$674$	0.586124	+	5.72096i	0.0225766	+	0.220363i
$675$	4.32813	+	6.17361i	0.166590	+	0.237623i
$676$	−23.4067	+	4.84701i	−0.900260	+	0.186424i
$677$	3.78865	−	3.78865i	0.145610	−	0.145610i	−0.630544	−	0.776154i	$-0.717168\pi$
$677$	3.78865	−	3.78865i	0.145610	−	0.145610i	0.776154	+	0.630544i	$0.217168\pi$
$678$	9.83474	−	12.0799i	0.377701	−	0.463927i
$679$	−1.40799			−0.0540337
$680$	−8.05276	+	1.79492i	−0.308809	+	0.0688320i
$681$	24.0071			0.919955
$682$	−6.82938	+	8.38848i	−0.261511	+	0.321212i
$683$	−13.7937	+	13.7937i	−0.527802	+	0.527802i	−0.919916	−	0.392115i	$-0.871744\pi$
$683$	−13.7937	+	13.7937i	−0.527802	+	0.527802i	0.392115	+	0.919916i	$0.371744\pi$
$684$	−6.51272	+	1.34864i	−0.249020	+	0.0515665i
$685$	15.3872	−	12.9189i	0.587913	−	0.493608i
$686$	−1.69818	−	16.5753i	−0.0648367	−	0.632849i
$687$	−3.14060	−	3.14060i	−0.119822	−	0.119822i
$688$	7.45114	−	18.8181i	0.284072	−	0.717434i
$689$			11.4791i			0.437319i
$690$	26.5076	+	25.7179i	1.00913	+	0.979065i
$691$		−	22.1562i		−	0.842861i	−0.906861	−	0.421431i	$-0.861528\pi$
$691$		−	22.1562i		−	0.842861i	0.906861	−	0.421431i	$-0.138472\pi$
$692$	20.8835	−	31.7912i	0.793870	−	1.20852i
$693$	5.33741	+	5.33741i	0.202751	+	0.202751i
$694$	−0.884733	+	0.0906427i	−0.0335840	+	0.00344075i
$695$	−2.08471	−	0.181782i	−0.0790777	−	0.00689537i
$696$	19.0200	+	60.1445i	0.720952	+	2.27977i
$697$	−7.48816	+	7.48816i	−0.283634	+	0.283634i
$698$	−12.2573	−	9.97917i	−0.463948	−	0.377717i
$699$	−51.3251			−1.94129
$700$	−22.0347	+	23.4092i	−0.832832	+	0.884783i
$701$	3.91585			0.147899			0.0739497	−	0.997262i	$-0.476440\pi$
$701$	3.91585			0.147899			0.0739497	+	0.997262i	$0.476440\pi$
$702$	1.69326	+	1.37854i	0.0639078	+	0.0520298i
$703$	−2.76616	+	2.76616i	−0.104328	+	0.104328i
$704$	6.54536	−	4.59981i	0.246688	−	0.173362i
$705$	−62.7936	−	5.47543i	−2.36494	−	0.206217i
$706$	−18.9452	+	1.94097i	−0.713011	+	0.0730495i
$707$	−18.9597	−	18.9597i	−0.713054	−	0.713054i
$708$	9.71057	+	6.37882i	0.364946	+	0.239731i
$709$			14.8137i			0.556341i	0.960532	+	0.278170i	$0.0897280\pi$
$709$			14.8137i			0.556341i	−0.960532	+	0.278170i	$0.910272\pi$
$710$	−34.0150	−	33.0017i	−1.27656	−	1.23853i
$711$			33.2101i			1.24548i
$712$	−6.13760	+	11.8149i	−0.230016	+	0.442781i
$713$	27.3149	+	27.3149i	1.02295	+	1.02295i
$714$	1.39786	+	13.6440i	0.0523135	+	0.510615i
$715$	−1.75341	+	1.47215i	−0.0655738	+	0.0550552i
$716$	−2.06035	−	9.94966i	−0.0769990	−	0.371836i
$717$	40.0965	−	40.0965i	1.49743	−	1.49743i
$718$	−21.4286	+	26.3206i	−0.799710	+	0.982278i
$719$	10.4233			0.388724			0.194362	−	0.980930i	$-0.437736\pi$
$719$	10.4233			0.388724			0.194362	+	0.980930i	$0.437736\pi$
$720$	6.63411	+	19.9252i	0.247239	+	0.742569i
$721$	41.1197			1.53138
$722$	15.1735	−	18.6375i	0.564700	−	0.693617i
$723$	9.02990	−	9.02990i	0.335825	−	0.335825i
$724$	3.93269	+	18.9914i	0.146157	+	0.705809i
$725$	−8.34582	+	47.4920i	−0.309956	+	1.76381i
$726$	−0.333320	−	3.25343i	−0.0123707	−	0.120746i
$727$	21.3788	+	21.3788i	0.792897	+	0.792897i	0.981964	−	0.189067i	$-0.0605465\pi$
$727$	21.3788	+	21.3788i	0.792897	+	0.792897i	−0.189067	+	0.981964i	$0.560546\pi$
$728$	−4.29185	+	8.26180i	−0.159067	+	0.306203i
$729$		−	14.2646i		−	0.528319i
$730$	−8.89775	+	0.134530i	−0.329321	+	0.00497919i
$731$		−	6.60063i		−	0.244133i
$732$	13.7145	+	9.00897i	0.506902	+	0.332981i
$733$	1.02633	+	1.02633i	0.0379083	+	0.0379083i	0.725807	−	0.687899i	$-0.241467\pi$
$733$	1.02633	+	1.02633i	0.0379083	+	0.0379083i	−0.687899	+	0.725807i	$0.741467\pi$
$734$	−21.3077	+	2.18302i	−0.786482	+	0.0805766i
$735$	11.0895	+	13.2081i	0.409041	+	0.487190i
$736$	−13.9588	−	24.9270i	−0.514528	−	0.918821i
$737$	7.01754	−	7.01754i	0.258495	−	0.258495i
$738$	20.9038	+	17.0186i	0.769481	+	0.626464i
$739$	−5.29534			−0.194792			−0.0973961	−	0.995246i	$-0.531051\pi$
$739$	−5.29534			−0.194792			−0.0973961	+	0.995246i	$0.531051\pi$
$740$	9.69582	+	7.65293i	0.356425	+	0.281327i
$741$	−3.35356			−0.123196
$742$	−39.5284	−	32.1816i	−1.45113	−	1.18142i
$743$	32.9662	−	32.9662i	1.20941	−	1.20941i	0.238196	−	0.971217i	$-0.423444\pi$
$743$	32.9662	−	32.9662i	1.20941	−	1.20941i	0.971217	−	0.238196i	$-0.0765560\pi$
$744$	15.0851	+	47.7015i	0.553045	+	1.74882i
$745$	2.43353	−	27.9083i	0.0891575	−	1.02248i
$746$	25.3655	−	2.59875i	0.928697	−	0.0951469i
$747$	−7.92446	−	7.92446i	−0.289941	−	0.289941i
$748$	1.43242	−	2.18060i	0.0523746	−	0.0797307i
$749$			2.11291i			0.0772042i
$750$	−5.78343	+	36.1045i	−0.211181	+	1.31835i
$751$		−	21.6289i		−	0.789249i	−0.918842	−	0.394625i	$-0.870875\pi$
$751$		−	21.6289i		−	0.789249i	0.918842	−	0.394625i	$-0.129125\pi$
$752$	45.3332	+	17.9499i	1.65313	+	0.654566i
$753$	−21.4342	−	21.4342i	−0.781107	−	0.781107i
$754$	1.42322	+	13.8916i	0.0518307	+	0.505902i
$755$	2.25479	−	25.8584i	0.0820601	−	0.941084i
$756$	−9.49406	+	1.96601i	−0.345295	+	0.0715030i
$757$	18.2612	−	18.2612i	0.663714	−	0.663714i	−0.292539	−	0.956254i	$-0.594500\pi$
$757$	18.2612	−	18.2612i	0.663714	−	0.663714i	0.956254	+	0.292539i	$0.0945002\pi$
$758$	10.6868	−	13.1265i	0.388161	−	0.476776i
$759$	−11.6793			−0.423932
$760$	7.56029	+	4.80429i	0.274240	+	0.174270i
$761$	10.6344			0.385497			0.192749	−	0.981248i	$-0.438260\pi$
$761$	10.6344			0.385497			0.192749	+	0.981248i	$0.438260\pi$
$762$	16.7828	−	20.6142i	0.607976	−	0.746772i
$763$	−15.4226	+	15.4226i	−0.558336	+	0.558336i
$764$	12.9246	−	2.67641i	0.467597	−	0.0968290i
$765$	4.40385	+	5.24522i	0.159222	+	0.189641i
$766$	−0.0166631	−	0.162643i	−0.000602062	−	0.00587653i
$767$	1.81867	+	1.81867i	0.0656683	+	0.0656683i
$768$	−1.16047	−	36.9828i	−0.0418748	−	1.33450i
$769$		−	23.9199i		−	0.862572i	−0.902215	−	0.431286i	$-0.858060\pi$
$769$		−	23.9199i		−	0.862572i	0.902215	−	0.431286i	$-0.141940\pi$
$770$	−0.153691	−	10.1650i	−0.00553864	−	0.366322i
$771$			67.5657i			2.43332i
$772$	−11.1724	+	17.0079i	−0.402102	+	0.612126i
$773$	0.715023	+	0.715023i	0.0257176	+	0.0257176i	0.719849	−	0.694131i	$-0.244211\pi$
$773$	0.715023	+	0.715023i	0.0257176	+	0.0257176i	−0.694131	+	0.719849i	$0.744211\pi$
$774$	−16.7138	+	1.71237i	−0.600767	+	0.0615498i
$775$	−6.61919	+	37.6666i	−0.237768	+	1.35303i
$776$	1.18110	−	0.373511i	0.0423992	−	0.0134083i
$777$	14.5200	−	14.5200i	0.520900	−	0.520900i
$778$	14.3486	+	11.6817i	0.514421	+	0.418809i
$779$	11.4977			0.411947
$780$	1.23835	+	10.5164i	0.0443400	+	0.376548i
$781$	14.9871			0.536280
$782$	−7.22536	−	5.88244i	−0.258378	−	0.210356i
$783$	−10.2830	+	10.2830i	−0.367485	+	0.367485i
$784$	−5.29790	−	12.2435i	−0.189211	−	0.437268i
$785$	6.47664	−	5.43774i	0.231161	−	0.194081i
$786$	58.8665	−	6.03100i	2.09970	−	0.215119i
$787$	6.63240	+	6.63240i	0.236420	+	0.236420i	0.815366	−	0.578946i	$-0.196536\pi$
$787$	6.63240	+	6.63240i	0.236420	+	0.236420i	−0.578946	+	0.815366i	$0.696536\pi$
$788$	−35.2044	−	23.1256i	−1.25410	−	0.823814i
$789$			19.1733i			0.682587i
$790$	31.1460	−	32.1023i	1.10812	−	1.14215i
$791$			15.3122i			0.544439i
$792$	−5.89324	−	3.06143i	−0.209407	−	0.108783i
$793$	2.56855	+	2.56855i	0.0912119	+	0.0912119i
$794$	2.81713	+	27.4971i	0.0999762	+	0.975834i
$795$	−57.7553	−	5.03611i	−2.04837	−	0.178613i
$796$	8.45112	+	40.8114i	0.299542	+	1.44652i
$797$	2.54383	−	2.54383i	0.0901071	−	0.0901071i	−0.660616	−	0.750724i	$-0.729705\pi$
$797$	2.54383	−	2.54383i	0.0901071	−	0.0901071i	0.750724	+	0.660616i	$0.229705\pi$
$798$	9.40167	−	11.5480i	0.332815	−	0.408795i
$799$	15.9010			0.562538
$800$	12.2740	−	25.4823i	0.433951	−	0.900936i
$801$	11.0522			0.390510
$802$	−26.6979	+	32.7929i	−0.942736	+	1.15796i
$803$	1.98983	−	1.98983i	0.0702194	−	0.0702194i
$804$	−9.30763	−	44.9475i	−0.328255	−	1.58518i
$805$	−36.1678	−	3.15374i	−1.27475	−	0.111155i
$806$	1.12878	+	11.0176i	0.0397595	+	0.388080i
$807$	−20.9848	−	20.9848i	−0.738698	−	0.738698i
$808$	20.9342	+	10.8749i	0.736462	+	0.382578i
$809$		−	6.12905i		−	0.215486i	−0.994179	−	0.107743i	$-0.965638\pi$
$809$		−	6.12905i		−	0.215486i	0.994179	−	0.107743i	$-0.0343624\pi$
$810$	−23.1893	+	23.9013i	−0.814790	+	0.839807i
$811$			16.4078i			0.576156i	0.957607	+	0.288078i	$0.0930163\pi$
$811$			16.4078i			0.576156i	−0.957607	+	0.288078i	$0.906984\pi$
$812$	−51.8258	−	34.0441i	−1.81873	−	1.19471i
$813$	−30.5672	−	30.5672i	−1.07204	−	1.07204i
$814$	−3.88576	+	0.398104i	−0.136196	+	0.0139535i
$815$	−12.4539	+	10.4562i	−0.436240	+	0.366264i
$816$	−4.79209	−	11.0746i	−0.167757	−	0.387688i
$817$	−5.06745	+	5.06745i	−0.177288	+	0.177288i
$818$	−28.0588	−	22.8437i	−0.981053	−	0.798712i
$819$	7.72849			0.270055
$820$	−4.24568	−	36.0555i	−0.148266	−	1.25911i
$821$	1.10741			0.0386488			0.0193244	−	0.999813i	$-0.493848\pi$
$821$	1.10741			0.0386488			0.0193244	+	0.999813i	$0.493848\pi$
$822$	22.7882	+	18.5528i	0.794831	+	0.647102i
$823$	2.63390	−	2.63390i	0.0918121	−	0.0918121i	−0.659709	−	0.751521i	$-0.729320\pi$
$823$	2.63390	−	2.63390i	0.0918121	−	0.0918121i	0.751521	+	0.659709i	$0.229320\pi$
$824$	−34.4936	+	10.9082i	−1.20164	+	0.380006i
$825$	−6.63763	−	9.46786i	−0.231093	−	0.329629i
$826$	−11.3612	+	1.16398i	−0.395307	+	0.0405000i
$827$	−23.9250	−	23.9250i	−0.831955	−	0.831955i	0.155829	−	0.987784i	$-0.450195\pi$
$827$	−23.9250	−	23.9250i	−0.831955	−	0.831955i	−0.987784	+	0.155829i	$0.950195\pi$
$828$	−13.0208	+	19.8218i	−0.452506	+	0.688856i
$829$			7.35056i			0.255296i	0.991820	+	0.127648i	$0.0407427\pi$
$829$			7.35056i			0.255296i	−0.991820	+	0.127648i	$0.959257\pi$
$830$	0.228185	+	15.0920i	0.00792043	+	0.523852i
$831$			20.8544i			0.723431i
$832$	1.40857	−	8.06903i	0.0488333	−	0.279743i
$833$	−3.07640	−	3.07640i	−0.106591	−	0.106591i
$834$	−0.311938	−	3.04472i	−0.0108015	−	0.105430i
$835$	20.7848	+	24.7559i	0.719289	+	0.856712i
$836$	−2.77380	+	0.574393i	−0.0959340	+	0.0198658i
$837$	−8.15562	+	8.15562i	−0.281900	+	0.281900i
$838$	4.74226	−	5.82488i	0.163819	−	0.201217i
$839$	−43.5458			−1.50337			−0.751684	−	0.659523i	$-0.770758\pi$
$839$	−43.5458			−1.50337			−0.751684	+	0.659523i	$0.770758\pi$
$840$	−39.6850	−	25.2184i	−1.36926	−	0.870117i
$841$	−64.0058			−2.20710
$842$	−12.8312	+	15.7605i	−0.442193	+	0.543143i
$843$	−27.1423	+	27.1423i	−0.934831	+	0.934831i
$844$	3.42401	−	0.709036i	0.117859	−	0.0244060i
$845$	2.32152	−	26.6237i	0.0798627	−	0.915884i
$846$	−4.12512	−	40.2639i	−0.141825	−	1.38430i
$847$	2.27323	+	2.27323i	0.0781091	+	0.0781091i
$848$	41.6959	+	16.5097i	1.43184	+	0.566946i
$849$			34.6944i			1.19071i
$850$	0.662271	−	9.20039i	0.0227157	−	0.315571i
$851$			13.9493i			0.478176i
$852$	38.0574	−	57.9353i	1.30382	−	1.98483i
$853$	37.1733	+	37.1733i	1.27279	+	1.27279i	0.944617	+	0.328174i	$0.106433\pi$
$853$	37.1733	+	37.1733i	1.27279	+	1.27279i	0.328174	+	0.944617i	$0.393567\pi$
$854$	−16.0457	+	1.64392i	−0.549073	+	0.0562537i
$855$	0.645942	−	7.40782i	0.0220908	−	0.253342i
$856$	−0.560513	−	1.77244i	−0.0191580	−	0.0605807i
$857$	−12.1732	+	12.1732i	−0.415830	+	0.415830i	−0.883763	−	0.467934i	$-0.844999\pi$
$857$	−12.1732	+	12.1732i	−0.415830	+	0.415830i	0.467934	+	0.883763i	$0.344999\pi$
$858$	−2.59678	−	2.11414i	−0.0886526	−	0.0721754i
$859$	−9.73794			−0.332254			−0.166127	−	0.986104i	$-0.553126\pi$
$859$	−9.73794			−0.332254			−0.166127	+	0.986104i	$0.553126\pi$
$860$	17.7622	+	14.0198i	0.605687	+	0.478070i
$861$	−60.3529			−2.05682
$862$	−42.0882	−	34.2656i	−1.43353	−	1.16709i
$863$	9.20125	−	9.20125i	0.313214	−	0.313214i	−0.532939	−	0.846154i	$-0.678913\pi$
$863$	9.20125	−	9.20125i	0.313214	−	0.313214i	0.846154	+	0.532939i	$0.178913\pi$
$864$	7.44263	−	4.16778i	0.253203	−	0.141791i
$865$	27.3449	+	32.5693i	0.929754	+	1.10739i
$866$	12.7001	−	1.30115i	0.431565	−	0.0442148i
$867$	25.0162	+	25.0162i	0.849594	+	0.849594i
$868$	−41.1038	−	27.0009i	−1.39515	−	0.916469i
$869$			14.1444i			0.479815i
$870$	−70.5178	+	1.06620i	−2.39078	+	0.0361476i
$871$		−	10.1613i		−	0.344303i
$872$	8.84609	−	17.0287i	0.299566	−	0.576665i
$873$	−0.727132	−	0.727132i	−0.0246097	−	0.0246097i
$874$	1.03099	+	10.0632i	0.0348738	+	0.340392i
$875$	−17.9984	−	31.1119i	−0.608459	−	1.05177i
$876$	−2.63918	−	12.7449i	−0.0891696	−	0.430610i
$877$	17.7574	−	17.7574i	0.599624	−	0.599624i	−0.340588	−	0.940213i	$-0.610626\pi$
$877$	17.7574	−	17.7574i	0.599624	−	0.599624i	0.940213	+	0.340588i	$0.110626\pi$
$878$	−14.5888	+	17.9194i	−0.492349	+	0.604749i
$879$	−50.2303			−1.69422
$880$	2.82550	+	8.48626i	0.0952477	+	0.286072i
$881$	27.2559			0.918274			0.459137	−	0.888365i	$-0.348159\pi$
$881$	27.2559			0.918274			0.459137	+	0.888365i	$0.348159\pi$
$882$	−6.99185	+	8.58804i	−0.235428	+	0.289175i
$883$	−8.06986	+	8.06986i	−0.271573	+	0.271573i	−0.829733	−	0.558160i	$-0.811507\pi$
$883$	−8.06986	+	8.06986i	−0.271573	+	0.271573i	0.558160	+	0.829733i	$0.311507\pi$
$884$	−0.541675	−	2.61581i	−0.0182185	−	0.0879791i
$885$	−9.94823	+	8.35245i	−0.334406	+	0.280765i
$886$	1.40086	+	13.6734i	0.0470629	+	0.459366i
$887$	0.528230	+	0.528230i	0.0177362	+	0.0177362i	0.715919	−	0.698183i	$-0.246008\pi$
$887$	0.528230	+	0.528230i	0.0177362	+	0.0177362i	−0.698183	+	0.715919i	$0.746008\pi$
$888$	−8.32834	+	16.0320i	−0.279481	+	0.538000i
$889$			26.1299i			0.876370i
$890$	−10.6835	−	10.3653i	−0.358112	−	0.347445i
$891$		−	10.5310i		−	0.352802i
$892$	−9.48868	−	6.23306i	−0.317705	−	0.208698i
$893$	−12.2076	−	12.2076i	−0.408511	−	0.408511i
$894$	40.7599	−	4.17594i	1.36322	−	0.139664i
$895$	11.3171	+	0.986823i	0.378290	+	0.0329859i
$896$	23.8369	+	27.4719i	0.796334	+	0.917770i
$897$	−8.45574	+	8.45574i	−0.282329	+	0.282329i
$898$	−4.87090	−	3.96558i	−0.162544	−	0.132333i
$899$	−73.7643			−2.46018
$900$	−23.4687	+	0.709835i	−0.782289	+	0.0236612i
$901$	14.6252			0.487236
$902$	8.90305	+	7.24831i	0.296439	+	0.241342i
$903$	26.5998	−	26.5998i	0.885186	−	0.885186i
$904$	−4.06202	−	12.8448i	−0.135101	−	0.427211i
$905$	−21.6015	−	1.88359i	−0.718058	−	0.0626128i
$906$	37.7661	−	3.86922i	1.25470	−	0.128546i
$907$	1.27942	+	1.27942i	0.0424825	+	0.0424825i	0.728029	−	0.685546i	$-0.240437\pi$
$907$	1.27942	+	1.27942i	0.0424825	+	0.0424825i	−0.685546	+	0.728029i	$0.740437\pi$
$908$	11.3992	−	17.3532i	0.378296	−	0.575886i
$909$		−	19.5828i		−	0.649522i
$910$	−7.47068	−	7.24814i	−0.247651	−	0.240274i
$911$			39.0054i			1.29231i	0.763208	+	0.646153i	$0.223623\pi$
$911$			39.0054i			1.29231i	−0.763208	+	0.646153i	$0.776377\pi$
$912$	−4.82322	+	12.1812i	−0.159713	+	0.403360i
$913$	−3.37507	−	3.37507i	−0.111698	−	0.111698i
$914$	−2.41615	−	23.5832i	−0.0799191	−	0.780064i
$915$	−14.0501	+	11.7964i	−0.464483	+	0.389976i
$916$	−3.76138	+	0.778898i	−0.124280	+	0.0257355i
$917$	−41.1312	+	41.1312i	−1.35827	+	1.35827i
$918$	1.75636	−	2.15733i	0.0579687	−	0.0712025i
$919$	44.5397			1.46923			0.734615	−	0.678484i	$-0.237363\pi$
$919$	44.5397			1.46923			0.734615	+	0.678484i	$0.237363\pi$
$920$	31.1763	−	6.94905i	1.02785	−	0.229103i
$921$	3.19168			0.105169
$922$	22.8481	−	28.0642i	0.752463	−	0.924245i
$923$	10.8506	−	10.8506i	0.357150	−	0.357150i
$924$	14.5601	−	3.01507i	0.478992	−	0.0991885i
$925$	−11.3080	+	7.92772i	−0.371806	+	0.260662i
$926$	−3.34875	−	32.6860i	−0.110047	−	1.07413i
$927$	21.2355	+	21.2355i	0.697467	+	0.697467i
$928$	52.5058	+	14.8098i	1.72359	+	0.486157i
$929$		−	38.4798i		−	1.26248i	−0.775587	−	0.631241i	$-0.782546\pi$
$929$		−	38.4798i		−	1.26248i	0.775587	−	0.631241i	$-0.217454\pi$
$930$	−55.9287	+	0.845619i	−1.83397	+	0.0277289i
$931$			4.72365i			0.154811i
$932$	−24.3705	+	37.0996i	−0.798283	+	1.21524i
$933$	8.68715	+	8.68715i	0.284404	+	0.284404i
$934$	38.8635	−	3.98165i	1.27165	−	0.130283i
$935$	1.87562	+	2.23397i	0.0613394	+	0.0730586i
$936$	−6.48311	+	2.05021i	−0.211907	+	0.0670133i
$937$	−12.6310	+	12.6310i	−0.412637	+	0.412637i	−0.882656	−	0.470019i	$-0.844247\pi$
$937$	−12.6310	+	12.6310i	−0.412637	+	0.412637i	0.470019	+	0.882656i	$0.344247\pi$
$938$	34.9905	+	28.4871i	1.14248	+	0.930138i
$939$	13.2885			0.433655
$940$	−33.7739	+	42.7895i	−1.10158	+	1.39564i
$941$	−0.184281			−0.00600739			−0.00300370	−	0.999995i	$-0.500956\pi$
$941$	−0.184281			−0.00600739			−0.00300370	+	0.999995i	$0.500956\pi$
$942$	9.59184	+	7.80908i	0.312519	+	0.254434i
$943$	28.9905	−	28.9905i	0.944060	−	0.944060i
$944$	9.22167	−	3.99031i	0.300140	−	0.129874i
$945$	0.941636	−	10.7989i	0.0306314	−	0.351288i
$946$	−7.11851	+	0.729306i	−0.231443	+	0.0237118i
$947$	29.9611	+	29.9611i	0.973605	+	0.973605i	0.999660	−	0.0260556i	$-0.00829470\pi$
$947$	29.9611	+	29.9611i	0.973605	+	0.973605i	−0.0260556	+	0.999660i	$0.508295\pi$
$948$	54.6776	+	35.9174i	1.77585	+	1.16654i
$949$		−	2.88124i		−	0.0935290i
$950$	−7.57179	+	6.55491i	−0.245661	+	0.212669i
$951$			22.9417i			0.743937i
$952$	10.5261	+	5.46813i	0.341154	+	0.177223i
$953$	25.4062	+	25.4062i	0.822988	+	0.822988i	0.986535	−	0.163548i	$-0.0522938\pi$
$953$	25.4062	+	25.4062i	0.822988	+	0.822988i	−0.163548	+	0.986535i	$0.552294\pi$
$954$	−3.79414	−	37.0334i	−0.122840	−	1.19900i
$955$	−1.28189	+	14.7010i	−0.0414809	+	0.475713i
$956$	−9.94429	−	48.0220i	−0.321621	−	1.55314i
$957$	15.7701	−	15.7701i	0.509774	−	0.509774i
$958$	1.06634	−	1.30978i	0.0344520	−	0.0423171i
$959$	−28.8857			−0.932769
$960$	39.9801	+	10.6270i	1.29035	+	0.342986i
$961$	−27.5036			−0.887212
$962$	−2.52504	+	3.10149i	−0.0814106	+	0.0999960i
$963$	−1.09118	+	1.09118i	−0.0351627	+	0.0351627i
$964$	−2.23950	−	10.8148i	−0.0721293	−	0.348320i
$965$	−14.6291	−	17.4241i	−0.470929	−	0.560902i
$966$	−5.41182	−	52.8230i	−0.174123	−	1.69955i
$967$	14.3306	+	14.3306i	0.460842	+	0.460842i	0.898931	−	0.438089i	$-0.144345\pi$
$967$	14.3306	+	14.3306i	0.460842	+	0.460842i	−0.438089	+	0.898931i	$0.644345\pi$
$968$	−2.50996	−	1.30388i	−0.0806732	−	0.0419082i
$969$			4.27267i			0.137258i
$970$	0.0209378	+	1.38481i	0.000672273	+	0.0444637i
$971$			27.6798i			0.888287i	0.895956	+	0.444143i	$0.146492\pi$
$971$			27.6798i			0.888287i	−0.895956	+	0.444143i	$0.853508\pi$
$972$	−33.1475	−	21.7744i	−1.06321	−	0.698415i
$973$	2.12740	+	2.12740i	0.0682014	+	0.0682014i
$974$	6.45065	−	0.660882i	0.206692	−	0.0211760i
$975$	−11.6603	−	2.04907i	−0.373427	−	0.0656227i
$976$	13.0240	−	5.63562i	0.416888	−	0.180392i
$977$	−10.8893	+	10.8893i	−0.348381	+	0.348381i	−0.859506	−	0.511125i	$-0.829229\pi$
$977$	−10.8893	+	10.8893i	−0.348381	+	0.348381i	0.511125	+	0.859506i	$0.329229\pi$
$978$	−18.4441	−	15.0160i	−0.589776	−	0.480159i
$979$	4.70719			0.150443
$980$	14.8129	−	1.74428i	0.473180	−	0.0557189i
$981$	−15.9295			−0.508589
$982$	12.7363	+	10.3691i	0.406431	+	0.330891i
$983$	−1.95471	+	1.95471i	−0.0623455	+	0.0623455i	−0.737592	−	0.675247i	$-0.764037\pi$
$983$	−1.95471	+	1.95471i	−0.0623455	+	0.0623455i	0.675247	+	0.737592i	$0.264037\pi$
$984$	50.6276	−	16.0104i	1.61395	−	0.510393i
$985$	36.0660	−	30.2807i	1.14916	−	0.964823i
$986$	17.6989	−	1.81329i	0.563648	−	0.0577468i
$987$	64.0794	+	64.0794i	2.03967	+	2.03967i
$988$	−1.59236	+	2.42407i	−0.0506597	+	0.0771200i
$989$			25.5544i			0.812583i
$990$	5.17018	−	5.32892i	0.164319	−	0.169364i
$991$		−	0.700492i		−	0.0222519i	−0.999938	−	0.0111259i	$-0.996458\pi$
$991$		−	0.700492i		−	0.0222519i	0.999938	−	0.0111259i	$-0.00354157\pi$
$992$	41.6431	+	11.7459i	1.32217	+	0.372933i
$993$	−40.8834	−	40.8834i	−1.29740	−	1.29740i
$994$	6.94455	+	67.7834i	0.220268	+	2.14996i
$995$	−46.4204	−	4.04774i	−1.47163	−	0.128322i
$996$	−21.6174	+	4.47648i	−0.684974	+	0.141843i
$997$	4.80082	−	4.80082i	0.152044	−	0.152044i	−0.626987	−	0.779030i	$-0.715712\pi$
$997$	4.80082	−	4.80082i	0.152044	−	0.152044i	0.779030	+	0.626987i	$0.215712\pi$
$998$	−14.7778	+	18.1515i	−0.467785	+	0.574577i
$999$	−4.16495			−0.131773

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.2.l.c.23.5	✓	28
4.3	odd	2		220.2.l.d.23.3	yes	28
5.2	odd	4		220.2.l.d.67.3	yes	28
20.7	even	4	inner	220.2.l.c.67.5	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.2.l.c.23.5	✓	28	1.1	even	1	trivial
220.2.l.c.67.5	yes	28	20.7	even	4	inner
220.2.l.d.23.3	yes	28	4.3	odd	2
220.2.l.d.67.3	yes	28	5.2	odd	4

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.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.892874 + 1.09671i) q^{2} +(1.63523 - 1.63523i) q^{3} +(-0.405551 - 1.95845i) q^{4} +(2.22762 + 0.194242i) q^{5} +(0.333320 + 3.25343i) q^{6} +(-2.27323 - 2.27323i) q^{7} +(2.50996 + 1.30388i) q^{8} -2.34794i q^{9} +(-2.20201 + 2.26962i) q^{10} -1.00000i q^{11} +(-3.86568 - 2.53934i) q^{12} +(-0.723993 - 0.723993i) q^{13} +(4.52278 - 0.463369i) q^{14} +(3.96029 - 3.32503i) q^{15} +(-3.67106 + 1.58850i) q^{16} +(-0.922419 + 0.922419i) q^{17} +(2.57501 + 2.09641i) q^{18} +1.41633 q^{19} +(-0.522999 - 4.44145i) q^{20} -7.43450 q^{21} +(1.09671 + 0.892874i) q^{22} +(3.57116 - 3.57116i) q^{23} +(6.23649 - 1.97222i) q^{24} +(4.92454 + 0.865394i) q^{25} +(1.44045 - 0.147577i) q^{26} +(1.06627 + 1.06627i) q^{27} +(-3.53010 + 5.37392i) q^{28} +9.64395i q^{29} +(0.110556 + 7.31213i) q^{30} +7.64876i q^{31} +(1.53566 - 5.44442i) q^{32} +(-1.63523 - 1.63523i) q^{33} +(-0.188023 - 1.83523i) q^{34} +(-4.62232 - 5.50544i) q^{35} +(-4.59832 + 0.952210i) q^{36} +(-1.95305 + 1.95305i) q^{37} +(-1.26460 + 1.55330i) q^{38} -2.36779 q^{39} +(5.33796 + 3.39208i) q^{40} +8.11796 q^{41} +(6.63807 - 8.15350i) q^{42} +(-3.57789 + 3.57789i) q^{43} +(-1.95845 + 0.405551i) q^{44} +(0.456069 - 5.23031i) q^{45} +(0.727934 + 7.10512i) q^{46} +(-8.61919 - 8.61919i) q^{47} +(-3.40545 + 8.60058i) q^{48} +3.33515i q^{49} +(-5.34608 + 4.62811i) q^{50} +3.01673i q^{51} +(-1.12429 + 1.71152i) q^{52} +(-7.92764 - 7.92764i) q^{53} +(-2.12143 + 0.217345i) q^{54} +(0.194242 - 2.22762i) q^{55} +(-2.74171 - 8.66973i) q^{56} +(2.31601 - 2.31601i) q^{57} +(-10.5766 - 8.61084i) q^{58} -2.51199 q^{59} +(-8.11800 - 6.40756i) q^{60} -3.54775 q^{61} +(-8.38848 - 6.82938i) q^{62} +(-5.33741 + 5.33741i) q^{63} +(4.59981 + 6.54536i) q^{64} +(-1.47215 - 1.75341i) q^{65} +(3.25343 - 0.333320i) q^{66} +(7.01754 + 7.01754i) q^{67} +(2.18060 + 1.43242i) q^{68} -11.6793i q^{69} +(10.1650 - 0.153691i) q^{70} +14.9871i q^{71} +(3.06143 - 5.89324i) q^{72} +(1.98983 + 1.98983i) q^{73} +(-0.398104 - 3.88576i) q^{74} +(9.46786 - 6.63763i) q^{75} +(-0.574393 - 2.77380i) q^{76} +(-2.27323 + 2.27323i) q^{77} +(2.11414 - 2.59678i) q^{78} -14.1444 q^{79} +(-8.48626 + 2.82550i) q^{80} +10.5310 q^{81} +(-7.24831 + 8.90305i) q^{82} +(3.37507 - 3.37507i) q^{83} +(3.01507 + 14.5601i) q^{84} +(-2.23397 + 1.87562i) q^{85} +(-0.729306 - 7.11851i) q^{86} +(15.7701 + 15.7701i) q^{87} +(1.30388 - 2.50996i) q^{88} +4.70719i q^{89} +(5.32892 + 5.17018i) q^{90} +3.29161i q^{91} +(-8.44222 - 5.54565i) q^{92} +(12.5075 + 12.5075i) q^{93} +(17.1486 - 1.75691i) q^{94} +(3.15503 + 0.275110i) q^{95} +(-6.39172 - 11.4140i) q^{96} +(0.309689 - 0.309689i) q^{97} +(-3.65769 - 2.97787i) q^{98} -2.34794 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 2 q^{2} - 4 q^{3} + 4 q^{4} + 2 q^{5} - 12 q^{6} - 2 q^{7} - 14 q^{8} + 6 q^{10} - 8 q^{12} + 6 q^{13} - 20 q^{14} + 8 q^{15} + 8 q^{16} - 14 q^{17} + 34 q^{18} + 4 q^{19} + 8 q^{20} - 16 q^{21}+ \cdots - 20 q^{99}+O(q^{100}) \) 28 * q - 2 * q^2 - 4 * q^3 + 4 * q^4 + 2 * q^5 - 12 * q^6 - 2 * q^7 - 14 * q^8 + 6 * q^10 - 8 * q^12 + 6 * q^13 - 20 * q^14 + 8 * q^15 + 8 * q^16 - 14 * q^17 + 34 * q^18 + 4 * q^19 + 8 * q^20 - 16 * q^21 - 2 * q^22 - 8 * q^23 + 28 * q^24 - 4 * q^25 + 4 * q^26 + 44 * q^27 - 28 * q^28 - 2 * q^32 + 4 * q^33 - 52 * q^34 - 10 * q^35 - 4 * q^36 + 20 * q^37 + 16 * q^38 + 32 * q^39 - 6 * q^40 + 12 * q^41 - 32 * q^42 + 2 * q^43 - 10 * q^45 + 4 * q^46 - 44 * q^47 - 36 * q^48 + 22 * q^50 + 24 * q^52 - 28 * q^53 - 40 * q^54 - 2 * q^55 + 4 * q^56 - 8 * q^57 + 28 * q^58 - 16 * q^59 - 48 * q^60 - 12 * q^61 - 24 * q^62 - 10 * q^63 + 28 * q^64 - 30 * q^65 + 16 * q^67 - 32 * q^68 + 72 * q^70 + 18 * q^72 + 22 * q^73 - 20 * q^74 - 56 * q^75 + 4 * q^76 - 2 * q^77 + 104 * q^78 - 20 * q^79 - 44 * q^80 + 12 * q^81 - 92 * q^82 + 2 * q^83 + 120 * q^84 - 14 * q^85 - 20 * q^86 - 48 * q^87 + 2 * q^88 + 70 * q^90 + 52 * q^92 - 20 * q^93 - 20 * q^94 + 92 * q^95 + 40 * q^96 + 16 * q^97 + 18 * q^98 - 20 * q^99

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