LMFDB - Embedded newform 416.2.bf.a.157.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(53,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5, 0]))

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

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

chi := DirichletCharacter("416.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bf (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$48$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			157.1
Character	$\chi$	$=$	416.157
Dual form			416.2.bf.a.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.41213 + 0.0766792i) q^{2} +(2.98623 + 1.23694i) q^{3} +(1.98824 - 0.216563i) q^{4} +(-1.24588 - 3.00782i) q^{5} +(-4.31180 - 1.51774i) q^{6} +(2.81433 - 2.81433i) q^{7} +(-2.79105 + 0.458272i) q^{8} +(5.26623 + 5.26623i) q^{9} +(1.98999 + 4.15191i) q^{10} +(-2.28952 + 0.948348i) q^{11} +(6.20521 + 1.81262i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(-3.75841 + 4.19002i) q^{14} -10.5231i q^{15} +(3.90620 - 0.861157i) q^{16} -5.03098i q^{17} +(-7.84043 - 7.03281i) q^{18} +(-0.451597 + 1.09025i) q^{19} +(-3.12849 - 5.71046i) q^{20} +(11.8854 - 4.92309i) q^{21} +(3.16038 - 1.51475i) q^{22} +(-3.29411 - 3.29411i) q^{23} +(-8.90158 - 2.08385i) q^{24} +(-3.95924 + 3.95924i) q^{25} +(0.469558 - 1.33398i) q^{26} +(5.50136 + 13.2815i) q^{27} +(4.98609 - 6.20505i) q^{28} +(6.38189 + 2.64347i) q^{29} +(0.806905 + 14.8600i) q^{30} -2.68063 q^{31} +(-5.45004 + 1.51559i) q^{32} -8.01006 q^{33} +(0.385771 + 7.10441i) q^{34} +(-11.9713 - 4.95869i) q^{35} +(11.6110 + 9.33006i) q^{36} +(2.87519 + 6.94132i) q^{37} +(0.554115 - 1.57421i) q^{38} +(-2.28556 + 2.28556i) q^{39} +(4.85572 + 7.82404i) q^{40} +(5.68170 + 5.68170i) q^{41} +(-16.4063 + 7.86343i) q^{42} +(-2.51795 + 1.04297i) q^{43} +(-4.34673 + 2.38137i) q^{44} +(9.27879 - 22.4010i) q^{45} +(4.90431 + 4.39913i) q^{46} +2.66003i q^{47} +(12.7300 + 2.26011i) q^{48} -8.84095i q^{49} +(5.28738 - 5.89457i) q^{50} +(6.22300 - 15.0236i) q^{51} +(-0.560789 + 1.91977i) q^{52} +(-4.80489 + 1.99025i) q^{53} +(-8.78707 - 18.3334i) q^{54} +(5.70493 + 5.70493i) q^{55} +(-6.56523 + 9.14469i) q^{56} +(-2.69714 + 2.69714i) q^{57} +(-9.21478 - 3.24357i) q^{58} +(4.29152 + 10.3607i) q^{59} +(-2.27891 - 20.9225i) q^{60} +(-7.28600 - 3.01796i) q^{61} +(3.78540 - 0.205548i) q^{62} +29.6419 q^{63} +(7.57997 - 2.55812i) q^{64} +3.25564 q^{65} +(11.3113 - 0.614206i) q^{66} +(7.16645 + 2.96844i) q^{67} +(-1.08952 - 10.0028i) q^{68} +(-5.76236 - 13.9116i) q^{69} +(17.2854 + 6.08438i) q^{70} +(-4.87700 + 4.87700i) q^{71} +(-17.1117 - 12.2850i) q^{72} +(-4.84461 - 4.84461i) q^{73} +(-4.59241 - 9.58161i) q^{74} +(-16.7205 + 6.92587i) q^{75} +(-0.661775 + 2.26548i) q^{76} +(-3.77449 + 9.11243i) q^{77} +(3.05226 - 3.40277i) q^{78} -1.23125i q^{79} +(-7.45687 - 10.6763i) q^{80} +24.1236i q^{81} +(-8.45898 - 7.58765i) q^{82} +(-0.0450971 + 0.108874i) q^{83} +(22.5649 - 12.3622i) q^{84} +(-15.1323 + 6.26799i) q^{85} +(3.47571 - 1.66589i) q^{86} +(15.7880 + 15.7880i) q^{87} +(5.95556 - 3.69611i) q^{88} +(-2.37318 + 2.37318i) q^{89} +(-11.3852 + 32.3446i) q^{90} +(1.52311 + 3.67710i) q^{91} +(-7.26287 - 5.83610i) q^{92} +(-8.00496 - 3.31576i) q^{93} +(-0.203969 - 3.75632i) q^{94} +3.84192 q^{95} +(-18.1498 - 2.21545i) q^{96} -5.42571 q^{97} +(0.677918 + 12.4846i) q^{98} +(-17.0513 - 7.06289i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) $ 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$	$1$

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 $

$2$	−1.41213	+	0.0766792i	−0.998529	+	0.0542204i
$2$	−1.41213	+	0.0766792i	−0.998529	+	0.0542204i
$3$	2.98623	+	1.23694i	1.72410	+	0.714146i	0.999693	+	0.0247726i	$0.00788619\pi$
$3$	2.98623	+	1.23694i	1.72410	+	0.714146i	0.724407	+	0.689373i	$0.242114\pi$
$4$	1.98824	−	0.216563i	0.994120	−	0.108281i
$5$	−1.24588	−	3.00782i	−0.557175	−	1.34514i	−0.911994	−	0.410204i	$-0.865458\pi$
$5$	−1.24588	−	3.00782i	−0.557175	−	1.34514i	0.354819	−	0.934935i	$-0.384542\pi$
$6$	−4.31180	−	1.51774i	−1.76028	−	0.619614i
$7$	2.81433	−	2.81433i	1.06372	−	1.06372i	0.0658916	−	0.997827i	$-0.479011\pi$
$7$	2.81433	−	2.81433i	1.06372	−	1.06372i	0.997827	−	0.0658916i	$-0.0209891\pi$
$8$	−2.79105	+	0.458272i	−0.986787	+	0.162024i
$9$	5.26623	+	5.26623i	1.75541	+	1.75541i
$10$	1.98999	+	4.15191i	0.629289	+	1.31295i
$11$	−2.28952	+	0.948348i	−0.690315	+	0.285938i	−0.700131	−	0.714014i	$-0.746875\pi$
$11$	−2.28952	+	0.948348i	−0.690315	+	0.285938i	0.00981654	+	0.999952i	$0.496875\pi$
$12$	6.20521	+	1.81262i	1.79129	+	0.523259i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$13$	−0.382683	+	0.923880i	−0.106137	+	0.256238i
$14$	−3.75841	+	4.19002i	−1.00448	+	1.11983i
$15$		−	10.5231i		−	2.71706i
$16$	3.90620	−	0.861157i	0.976550	−	0.215289i
$17$		−	5.03098i		−	1.22019i	−0.792328	−	0.610095i	$-0.791131\pi$
$17$		−	5.03098i		−	1.22019i	0.792328	−	0.610095i	$-0.208869\pi$
$18$	−7.84043	−	7.03281i	−1.84801	−	1.65765i
$19$	−0.451597	+	1.09025i	−0.103603	+	0.250121i	−0.967178	−	0.254101i	$-0.918220\pi$
$19$	−0.451597	+	1.09025i	−0.103603	+	0.250121i	0.863574	+	0.504222i	$0.168220\pi$
$20$	−3.12849	−	5.71046i	−0.699552	−	1.27690i
$21$	11.8854	−	4.92309i	2.59361	−	1.07431i
$22$	3.16038	−	1.51475i	0.673796	−	0.322946i
$23$	−3.29411	−	3.29411i	−0.686870	−	0.686870i	0.274669	−	0.961539i	$-0.411432\pi$
$23$	−3.29411	−	3.29411i	−0.686870	−	0.686870i	−0.961539	+	0.274669i	$0.911432\pi$
$24$	−8.90158	−	2.08385i	−1.81703	−	0.425364i
$25$	−3.95924	+	3.95924i	−0.791848	+	0.791848i
$26$	0.469558	−	1.33398i	0.0920878	−	0.261616i
$27$	5.50136	+	13.2815i	1.05874	+	2.55602i
$28$	4.98609	−	6.20505i	0.942283	−	1.17264i
$29$	6.38189	+	2.64347i	1.18509	+	0.490879i	0.886152	−	0.463394i	$-0.153368\pi$
$29$	6.38189	+	2.64347i	1.18509	+	0.490879i	0.298935	+	0.954273i	$0.403368\pi$
$30$	0.806905	+	14.8600i	0.147320	+	2.71306i
$31$	−2.68063			−0.481455			−0.240727	−	0.970593i	$-0.577386\pi$
$31$	−2.68063			−0.481455			−0.240727	+	0.970593i	$0.577386\pi$
$32$	−5.45004	+	1.51559i	−0.963441	+	0.267922i
$33$	−8.01006			−1.39437
$34$	0.385771	+	7.10441i	0.0661592	+	1.21840i
$35$	−11.9713	−	4.95869i	−2.02353	−	0.838172i
$36$	11.6110	+	9.33006i	1.93517	+	1.55501i
$37$	2.87519	+	6.94132i	0.472678	+	1.14115i	0.962975	+	0.269591i	$0.0868885\pi$
$37$	2.87519	+	6.94132i	0.472678	+	1.14115i	−0.490296	+	0.871556i	$0.663112\pi$
$38$	0.554115	−	1.57421i	0.0898893	−	0.255370i
$39$	−2.28556	+	2.28556i	−0.365983	+	0.365983i
$40$	4.85572	+	7.82404i	0.767757	+	1.23709i
$41$	5.68170	+	5.68170i	0.887332	+	0.887332i	0.994266	−	0.106934i	$-0.0341033\pi$
$41$	5.68170	+	5.68170i	0.887332	+	0.887332i	−0.106934	+	0.994266i	$0.534103\pi$
$42$	−16.4063	+	7.86343i	−2.53154	+	1.21335i
$43$	−2.51795	+	1.04297i	−0.383984	+	0.159051i	−0.566321	−	0.824185i	$-0.691634\pi$
$43$	−2.51795	+	1.04297i	−0.383984	+	0.159051i	0.182337	+	0.983236i	$0.441634\pi$
$44$	−4.34673	+	2.38137i	−0.655294	+	0.359005i
$45$	9.27879	−	22.4010i	1.38320	−	3.33934i
$46$	4.90431	+	4.39913i	0.723102	+	0.648617i
$47$			2.66003i			0.388006i	0.981001	+	0.194003i	$0.0621471\pi$
$47$			2.66003i			0.388006i	−0.981001	+	0.194003i	$0.937853\pi$
$48$	12.7300	+	2.26011i	1.83742	+	0.326219i
$49$		−	8.84095i		−	1.26299i
$50$	5.28738	−	5.89457i	0.747749	−	0.833618i
$51$	6.22300	−	15.0236i	0.871394	−	2.10373i
$52$	−0.560789	+	1.91977i	−0.0777674	+	0.266224i
$53$	−4.80489	+	1.99025i	−0.660002	+	0.273382i	−0.687439	−	0.726242i	$-0.741265\pi$
$53$	−4.80489	+	1.99025i	−0.660002	+	0.273382i	0.0274375	+	0.999624i	$0.491265\pi$
$54$	−8.78707	−	18.3334i	−1.19577	−	2.49485i
$55$	5.70493	+	5.70493i	0.769252	+	0.769252i
$56$	−6.56523	+	9.14469i	−0.877316	+	1.22201i
$57$	−2.69714	+	2.69714i	−0.357245	+	0.357245i
$58$	−9.21478	−	3.24357i	−1.20996	−	0.425901i
$59$	4.29152	+	10.3607i	0.558709	+	1.34884i	0.910789	+	0.412873i	$0.135475\pi$
$59$	4.29152	+	10.3607i	0.558709	+	1.34884i	−0.352080	+	0.935970i	$0.614525\pi$
$60$	−2.27891	−	20.9225i	−0.294207	−	2.70108i
$61$	−7.28600	−	3.01796i	−0.932877	−	0.386410i	−0.136108	−	0.990694i	$-0.543459\pi$
$61$	−7.28600	−	3.01796i	−0.932877	−	0.386410i	−0.796769	+	0.604284i	$0.793459\pi$
$62$	3.78540	−	0.205548i	0.480746	−	0.0261047i
$63$	29.6419			3.73452
$64$	7.57997	−	2.55812i	0.947497	−	0.319766i
$65$	3.25564			0.403813
$66$	11.3113	−	0.614206i	1.39232	−	0.0756035i
$67$	7.16645	+	2.96844i	0.875521	+	0.362653i	0.774758	−	0.632258i	$-0.217872\pi$
$67$	7.16645	+	2.96844i	0.875521	+	0.362653i	0.100763	+	0.994910i	$0.467872\pi$
$68$	−1.08952	−	10.0028i	−0.132124	−	1.21302i
$69$	−5.76236	−	13.9116i	−0.693707	−	1.67476i
$70$	17.2854	+	6.08438i	2.06600	+	0.727223i
$71$	−4.87700	+	4.87700i	−0.578794	+	0.578794i	−0.934571	−	0.355777i	$-0.884216\pi$
$71$	−4.87700	+	4.87700i	−0.578794	+	0.578794i	0.355777	+	0.934571i	$0.384216\pi$
$72$	−17.1117	−	12.2850i	−2.01663	−	1.44780i
$73$	−4.84461	−	4.84461i	−0.567018	−	0.567018i	0.364274	−	0.931292i	$-0.381317\pi$
$73$	−4.84461	−	4.84461i	−0.567018	−	0.567018i	−0.931292	+	0.364274i	$0.881317\pi$
$74$	−4.59241	−	9.58161i	−0.533857	−	1.11384i
$75$	−16.7205	+	6.92587i	−1.93072	+	0.799731i
$76$	−0.661775	+	2.26548i	−0.0759108	+	0.259868i
$77$	−3.77449	+	9.11243i	−0.430143	+	1.03846i
$78$	3.05226	−	3.40277i	0.345600	−	0.385288i
$79$		−	1.23125i		−	0.138526i	−0.997598	−	0.0692630i	$-0.977935\pi$
$79$		−	1.23125i		−	0.138526i	0.997598	−	0.0692630i	$-0.0220648\pi$
$80$	−7.45687	−	10.6763i	−0.833703	−	1.19364i
$81$			24.1236i			2.68040i
$82$	−8.45898	−	7.58765i	−0.934138	−	0.837915i
$83$	−0.0450971	+	0.108874i	−0.00495005	+	0.0119505i	−0.926335	−	0.376700i	$-0.877059\pi$
$83$	−0.0450971	+	0.108874i	−0.00495005	+	0.0119505i	0.921385	+	0.388651i	$0.127059\pi$
$84$	22.5649	−	12.3622i	2.46203	−	1.34883i
$85$	−15.1323	+	6.26799i	−1.64133	+	0.679860i
$86$	3.47571	−	1.66589i	0.374795	−	0.179637i
$87$	15.7880	+	15.7880i	1.69265	+	1.69265i
$88$	5.95556	−	3.69611i	0.634865	−	0.394007i
$89$	−2.37318	+	2.37318i	−0.251556	+	0.251556i	−0.821609	−	0.570052i	$-0.806923\pi$
$89$	−2.37318	+	2.37318i	−0.251556	+	0.251556i	0.570052	+	0.821609i	$0.306923\pi$
$90$	−11.3852	+	32.3446i	−1.20010	+	3.40943i
$91$	1.52311	+	3.67710i	0.159665	+	0.385465i
$92$	−7.26287	−	5.83610i	−0.757206	−	0.608456i
$93$	−8.00496	−	3.31576i	−0.830076	−	0.343829i
$94$	−0.203969	−	3.75632i	−0.0210378	−	0.387435i
$95$	3.84192			0.394172
$96$	−18.1498	−	2.21545i	−1.85240	−	0.226113i
$97$	−5.42571			−0.550898			−0.275449	−	0.961316i	$-0.588826\pi$
$97$	−5.42571			−0.550898			−0.275449	+	0.961316i	$0.588826\pi$
$98$	0.677918	+	12.4846i	0.0684800	+	1.26114i
$99$	−17.0513	−	7.06289i	−1.71372	−	0.709847i
$100$	−7.01450	+	8.72935i	−0.701450	+	0.872935i
$101$	1.71982	+	4.15201i	0.171128	+	0.413140i	0.986054	−	0.166425i	$-0.0532224\pi$
$101$	1.71982	+	4.15201i	0.171128	+	0.413140i	−0.814926	+	0.579565i	$0.803222\pi$
$102$	−7.63570	+	21.6926i	−0.756047	+	2.14788i
$103$	−5.04947	+	5.04947i	−0.497539	+	0.497539i	−0.910671	−	0.413132i	$-0.864435\pi$
$103$	−5.04947	+	5.04947i	−0.497539	+	0.497539i	0.413132	+	0.910671i	$0.364435\pi$
$104$	0.644702	−	2.75397i	0.0632183	−	0.270049i
$105$	−29.6156	−	29.6156i	−2.89018	−	2.89018i
$106$	6.63253	−	3.17893i	0.644208	−	0.308765i
$107$	1.05578	−	0.437319i	0.102066	−	0.0422772i	−0.331066	−	0.943608i	$-0.607408\pi$
$107$	1.05578	−	0.437319i	0.102066	−	0.0422772i	0.433132	+	0.901330i	$0.357408\pi$
$108$	13.8143	+	25.2154i	1.32928	+	2.42635i
$109$	4.72303	−	11.4024i	0.452384	−	1.09215i	−0.519029	−	0.854757i	$-0.673706\pi$
$109$	4.72303	−	11.4024i	0.452384	−	1.09215i	0.971413	−	0.237396i	$-0.0762937\pi$
$110$	−8.49356	−	7.61867i	−0.809830	−	0.726411i
$111$			24.2848i			2.30501i
$112$	8.56977	−	13.4169i	0.809767	−	1.26778i
$113$		−	15.2252i		−	1.43227i	−0.697964	−	0.716133i	$-0.745911\pi$
$113$		−	15.2252i		−	1.43227i	0.697964	−	0.716133i	$-0.254089\pi$
$114$	3.60191	−	4.01554i	0.337350	−	0.376090i
$115$	−5.80403	+	14.0122i	−0.541229	+	1.30664i
$116$	13.2612	+	3.87377i	1.23127	+	0.359670i
$117$	−6.88066	+	2.85006i	−0.636117	+	0.263488i
$118$	−6.85465	−	14.3016i	−0.631022	−	1.31656i
$119$	−14.1588	−	14.1588i	−1.29794	−	1.29794i
$120$	4.82245	+	29.3706i	0.440228	+	2.68116i
$121$	−3.43566	+	3.43566i	−0.312333	+	0.312333i
$122$	10.5202	+	3.70308i	0.952456	+	0.335261i
$123$	9.93895	+	23.9947i	0.896165	+	2.16353i
$124$	−5.32973	+	0.580523i	−0.478624	+	0.0521325i
$125$	1.80233	+	0.746548i	0.161205	+	0.0667733i
$126$	−41.8582	+	2.27292i	−3.72903	+	0.202487i
$127$	−4.37941			−0.388609			−0.194305	−	0.980941i	$-0.562245\pi$
$127$	−4.37941			−0.388609			−0.194305	+	0.980941i	$0.562245\pi$
$128$	−10.5078	+	4.19364i	−0.928765	+	0.370669i
$129$	−8.80926			−0.775612
$130$	−4.59740	+	0.249640i	−0.403219	+	0.0218949i
$131$	−13.8357	−	5.73093i	−1.20883	−	0.500714i	−0.314988	−	0.949096i	$-0.602001\pi$
$131$	−13.8357	−	5.73093i	−1.20883	−	0.500714i	−0.893842	+	0.448381i	$0.852001\pi$
$132$	−15.9259	+	1.73468i	−1.38617	+	0.150985i
$133$	1.79739	+	4.33927i	0.155853	+	0.376263i
$134$	−10.3476	−	3.64231i	−0.893896	−	0.314648i
$135$	33.0942	−	33.0942i	2.84830	−	2.84830i
$136$	2.30556	+	14.0417i	0.197700	+	1.20407i
$137$	6.40347	+	6.40347i	0.547085	+	0.547085i	0.925597	−	0.378512i	$-0.123564\pi$
$137$	6.40347	+	6.40347i	0.547085	+	0.547085i	−0.378512	+	0.925597i	$0.623564\pi$
$138$	9.20395	+	19.2031i	0.783492	+	1.63468i
$139$	11.2427	−	4.65688i	0.953594	−	0.394992i	0.149013	−	0.988835i	$-0.452390\pi$
$139$	11.2427	−	4.65688i	0.953594	−	0.394992i	0.804580	+	0.593844i	$0.202390\pi$
$140$	−24.8758	−	7.26653i	−2.10239	−	0.614134i
$141$	−3.29029	+	7.94346i	−0.277092	+	0.668960i
$142$	6.51301	−	7.26094i	0.546560	−	0.609325i
$143$		−	2.47815i		−	0.207234i
$144$	25.1060	+	16.0359i	2.09217	+	1.33632i
$145$		−	22.4890i		−	1.86761i
$146$	7.21271	+	6.46975i	0.596928	+	0.535440i
$147$	10.9357	−	26.4011i	0.901961	−	2.17753i
$148$	7.21980	+	13.1784i	0.593464	+	1.08325i
$149$	2.69314	−	1.11554i	0.220631	−	0.0913883i	−0.269630	−	0.962964i	$-0.586901\pi$
$149$	2.69314	−	1.11554i	0.220631	−	0.0913883i	0.490261	+	0.871576i	$0.336901\pi$
$150$	23.0805	−	11.0624i	1.88452	−	0.903239i
$151$	−4.19802	−	4.19802i	−0.341630	−	0.341630i	0.515350	−	0.856980i	$-0.327662\pi$
$151$	−4.19802	−	4.19802i	−0.341630	−	0.341630i	−0.856980	+	0.515350i	$0.827662\pi$
$152$	0.760800	−	3.24990i	0.0617090	−	0.263602i
$153$	26.4943	−	26.4943i	2.14193	−	2.14193i
$154$	4.63135	−	13.1574i	0.373205	−	1.06025i
$155$	3.33974	+	8.06285i	0.268254	+	0.647623i
$156$	−4.04928	+	5.03921i	−0.324202	+	0.403460i
$157$	14.2653	+	5.90890i	1.13850	+	0.471582i	0.870662	−	0.491883i	$-0.163691\pi$
$157$	14.2653	+	5.90890i	1.13850	+	0.471582i	0.267837	+	0.963464i	$0.413691\pi$
$158$	0.0944110	+	1.73868i	0.00751093	+	0.138322i
$159$	−16.8103			−1.33314
$160$	11.3487	+	14.5045i	0.897197	+	1.14668i
$161$	−18.5415			−1.46127
$162$	−1.84978	−	34.0658i	−0.145332	−	2.67646i
$163$	−6.27570	−	2.59948i	−0.491551	−	0.203607i	0.123119	−	0.992392i	$-0.460710\pi$
$163$	−6.27570	−	2.59948i	−0.491551	−	0.203607i	−0.614669	+	0.788785i	$0.710710\pi$
$164$	12.5270	+	10.0661i	0.978196	+	0.786033i
$165$	9.97958	+	24.0928i	0.776909	+	1.87563i
$166$	0.0553348	−	0.157203i	0.00429481	−	0.0122013i
$167$	16.5953	−	16.5953i	1.28418	−	1.28418i	0.345913	−	0.938267i	$-0.387569\pi$
$167$	16.5953	−	16.5953i	1.28418	−	1.28418i	0.938267	−	0.345913i	$-0.112431\pi$
$168$	−30.9167	+	19.1874i	−2.38527	+	1.48034i
$169$	−0.707107	−	0.707107i	−0.0543928	−	0.0543928i
$170$	20.8882	−	10.0116i	1.60205	−	0.767853i
$171$	−8.11972	+	3.36330i	−0.620931	+	0.257198i
$172$	−4.78042	+	2.61897i	−0.364504	+	0.199694i
$173$	2.99935	−	7.24108i	0.228036	−	0.550529i	−0.767902	−	0.640568i	$-0.778699\pi$
$173$	2.99935	−	7.24108i	0.228036	−	0.550529i	0.995938	+	0.0900388i	$0.0286991\pi$
$174$	−23.5054	−	21.0841i	−1.78194	−	1.59838i
$175$			22.2853i			1.68461i
$176$	−8.12663	+	5.67607i	−0.612568	+	0.427850i
$177$			36.2476i			2.72454i
$178$	3.16927	−	3.53322i	0.237547	−	0.264826i
$179$	−6.59756	+	15.9279i	−0.493124	+	1.19051i	0.459997	+	0.887920i	$0.347850\pi$
$179$	−6.59756	+	15.9279i	−0.493124	+	1.19051i	−0.953122	+	0.302587i	$0.902150\pi$
$180$	13.5972	−	46.5480i	1.01348	−	3.46948i
$181$	−2.64475	+	1.09549i	−0.196582	+	0.0814271i	−0.478803	−	0.877923i	$-0.658929\pi$
$181$	−2.64475	+	1.09549i	−0.196582	+	0.0814271i	0.282220	+	0.959350i	$0.408929\pi$
$182$	−2.43279	−	5.07577i	−0.180330	−	0.376241i
$183$	−18.0246	−	18.0246i	−1.33242	−	1.33242i
$184$	10.7036	+	7.68444i	0.789083	+	0.566505i
$185$	17.2961	−	17.2961i	1.27164	−	1.27164i
$186$	11.5583	+	4.06849i	0.847497	+	0.298316i
$187$	4.77112	+	11.5185i	0.348899	+	0.842316i
$188$	0.576064	+	5.28878i	0.0420138	+	0.385724i
$189$	52.8612	+	21.8958i	3.84508	+	1.59269i
$190$	−5.42530	+	0.294595i	−0.393593	+	0.0213722i
$191$	−16.3917			−1.18606			−0.593032	−	0.805179i	$-0.702069\pi$
$191$	−16.3917			−1.18606			−0.593032	+	0.805179i	$0.702069\pi$
$192$	25.7998	+	1.73680i	1.86194	+	0.125343i
$193$	−7.28239			−0.524198			−0.262099	−	0.965041i	$-0.584415\pi$
$193$	−7.28239			−0.524198			−0.262099	+	0.965041i	$0.584415\pi$
$194$	7.66183	−	0.416039i	0.550087	−	0.0298699i
$195$	9.72209	+	4.02702i	0.696214	+	0.288381i
$196$	−1.91462	−	17.5779i	−0.136759	−	1.25557i
$197$	−7.07961	−	17.0917i	−0.504401	−	1.21773i	−0.947064	−	0.321044i	$-0.895966\pi$
$197$	−7.07961	−	17.0917i	−0.504401	−	1.21773i	0.442663	−	0.896688i	$-0.354034\pi$
$198$	24.6203	+	8.66626i	1.74969	+	0.615884i
$199$	−11.5241	+	11.5241i	−0.816920	+	0.816920i	−0.985661	−	0.168740i	$-0.946030\pi$
$199$	−11.5241	+	11.5241i	−0.816920	+	0.816920i	0.168740	+	0.985661i	$0.446030\pi$
$200$	9.23605	−	12.8649i	0.653087	−	0.909684i
$201$	17.7289	+	17.7289i	1.25050	+	1.25050i
$202$	−2.74698	−	5.73131i	−0.193277	−	0.403254i
$203$	25.4004	−	10.5212i	1.78276	−	0.738442i
$204$	9.11925	−	31.2183i	0.638475	−	2.18572i
$205$	10.0108	−	24.1683i	0.699186	−	1.68798i
$206$	6.74334	−	7.51772i	0.469831	−	0.523784i
$207$		−	34.6951i		−	2.41147i
$208$	−0.699233	+	3.93841i	−0.0484831	+	0.273080i
$209$		−	2.92442i		−	0.202286i
$210$	44.0920	+	39.5502i	3.04264	+	2.72923i
$211$	−3.16194	+	7.63359i	−0.217677	+	0.525518i	−0.994565	−	0.104121i	$-0.966797\pi$
$211$	−3.16194	+	7.63359i	−0.217677	+	0.525518i	0.776888	+	0.629639i	$0.216797\pi$
$212$	−9.12225	+	4.99765i	−0.626519	+	0.343240i
$213$	−20.5964	+	8.53130i	−1.41124	+	0.584555i
$214$	−1.45737	+	0.698509i	−0.0996238	+	0.0477491i
$215$	6.27413	+	6.27413i	0.427892	+	0.427892i
$216$	−21.4411	−	34.5482i	−1.45888	−	2.35071i
$217$	−7.54418	+	7.54418i	−0.512132	+	0.512132i
$218$	−5.79522	+	16.4639i	−0.392502	+	1.11507i
$219$	−8.47463	−	20.4596i	−0.572662	−	1.38253i
$220$	12.5782	+	10.1073i	0.848025	+	0.681433i
$221$	4.64801	+	1.92527i	0.312659	+	0.129508i
$222$	−1.86214	−	34.2934i	−0.124979	−	2.30162i
$223$	−7.05196			−0.472234			−0.236117	−	0.971725i	$-0.575875\pi$
$223$	−7.05196			−0.472234			−0.236117	+	0.971725i	$0.575875\pi$
$224$	−11.0729	+	19.6036i	−0.739836	+	1.30982i
$225$	−41.7005			−2.78004
$226$	1.16746	+	21.5000i	0.0776580	+	1.43016i
$227$	3.19053	+	1.32156i	0.211763	+	0.0877151i	0.486043	−	0.873935i	$-0.338440\pi$
$227$	3.19053	+	1.32156i	0.211763	+	0.0877151i	−0.274281	+	0.961650i	$0.588440\pi$
$228$	−4.77847	+	5.94667i	−0.316462	+	0.393828i
$229$	−6.59378	−	15.9188i	−0.435729	−	1.05194i	−0.977409	−	0.211358i	$-0.932211\pi$
$229$	−6.59378	−	15.9188i	−0.435729	−	1.05194i	0.541680	−	0.840585i	$-0.317789\pi$
$230$	7.12162	−	20.2321i	0.469586	−	1.33406i
$231$	−22.5430	+	22.5430i	−1.48322	+	1.48322i
$232$	−19.0236	−	4.45342i	−1.24896	−	0.292381i
$233$	−12.1049	−	12.1049i	−0.793018	−	0.793018i	0.188965	−	0.981984i	$-0.439487\pi$
$233$	−12.1049	−	12.1049i	−0.793018	−	0.793018i	−0.981984	+	0.188965i	$0.939487\pi$
$234$	9.49787	−	4.55227i	0.620895	−	0.297591i
$235$	8.00090	−	3.31408i	0.521921	−	0.216187i
$236$	10.7763	+	19.6701i	0.701478	+	1.28041i
$237$	1.52297	−	3.67678i	0.0989277	−	0.238833i
$238$	21.0799	+	18.9085i	1.36640	+	1.22566i
$239$			4.78738i			0.309670i	0.987940	+	0.154835i	$0.0494846\pi$
$239$			4.78738i			0.309670i	−0.987940	+	0.154835i	$0.950515\pi$
$240$	−9.06206	−	41.1054i	−0.584953	−	2.65334i
$241$		−	19.6957i		−	1.26871i	−0.773041	−	0.634355i	$-0.781266\pi$
$241$		−	19.6957i		−	1.26871i	0.773041	−	0.634355i	$-0.218734\pi$
$242$	4.58816	−	5.11505i	0.294938	−	0.328808i
$243$	−13.3353	+	32.1942i	−0.855459	+	2.06526i
$244$	−15.1399	−	4.42256i	−0.969233	−	0.283125i
$245$	−26.5920	+	11.0148i	−1.69890	+	0.703708i
$246$	−15.8750	−	33.1217i	−1.01215	−	2.11176i
$247$	−0.834442	−	0.834442i	−0.0530943	−	0.0530943i
$248$	7.48178	−	1.22846i	0.475093	−	0.0780070i
$249$	−0.269341	+	0.269341i	−0.0170688	+	0.0170688i
$250$	−2.60237	−	0.916024i	−0.164588	−	0.0579344i
$251$	3.39654	+	8.19996i	0.214387	+	0.517577i	0.994088	−	0.108575i	$-0.0346288\pi$
$251$	3.39654	+	8.19996i	0.214387	+	0.517577i	−0.779701	+	0.626152i	$0.784629\pi$
$252$	58.9351	−	6.41932i	3.71256	−	0.404379i
$253$	10.6659	+	4.41795i	0.670558	+	0.277754i
$254$	6.18430	−	0.335810i	0.388038	−	0.0210706i
$255$	−52.9416			−3.31533
$256$	14.5168	−	6.72771i	0.907301	−	0.420482i
$257$	24.4356			1.52425			0.762125	−	0.647430i	$-0.224156\pi$
$257$	24.4356			1.52425			0.762125	+	0.647430i	$0.224156\pi$
$258$	12.4399	−	0.675487i	0.774471	−	0.0420540i
$259$	27.6270	+	11.4435i	1.71666	+	0.711062i
$260$	6.47300	−	0.705051i	0.401439	−	0.0437254i
$261$	19.6874	+	47.5296i	1.21862	+	2.94201i
$262$	19.9773	+	7.03193i	1.23420	+	0.434434i
$263$	−14.0555	+	14.0555i	−0.866699	+	0.866699i	−0.992105	−	0.125407i	$-0.959976\pi$
$263$	−14.0555	+	14.0555i	−0.866699	+	0.866699i	0.125407	+	0.992105i	$0.459976\pi$
$264$	22.3565	−	3.67079i	1.37595	−	0.225921i
$265$	11.9726	+	11.9726i	0.735473	+	0.735473i
$266$	−2.87088	−	5.98981i	−0.176025	−	0.367259i
$267$	−10.0223	+	4.15138i	−0.613356	+	0.254061i
$268$	14.8915	+	4.34999i	0.909641	+	0.265718i
$269$	−8.73781	+	21.0949i	−0.532754	+	1.28618i	0.396939	+	0.917845i	$0.370073\pi$
$269$	−8.73781	+	21.0949i	−0.532754	+	1.28618i	−0.929693	+	0.368336i	$0.879927\pi$
$270$	−44.1958	+	49.2711i	−2.68967	+	2.99855i
$271$		−	13.8283i		−	0.840008i	−0.907522	−	0.420004i	$-0.862029\pi$
$271$		−	13.8283i		−	0.840008i	0.907522	−	0.420004i	$-0.137971\pi$
$272$	−4.33246	−	19.6520i	−0.262694	−	1.19158i
$273$			12.8647i			0.778605i
$274$	−9.53356	−	8.55153i	−0.575943	−	0.516617i
$275$	5.31000	−	12.8195i	0.320205	−	0.773044i
$276$	−14.4697	−	26.4116i	−0.870973	−	1.58979i
$277$	7.98404	−	3.30710i	0.479714	−	0.198704i	−0.129704	−	0.991553i	$-0.541403\pi$
$277$	7.98404	−	3.30710i	0.479714	−	0.198704i	0.609419	+	0.792849i	$0.291403\pi$
$278$	−15.5191	+	7.43822i	−0.930775	+	0.446115i
$279$	−14.1168	−	14.1168i	−0.845150	−	0.845150i
$280$	35.6851	+	8.35385i	2.13259	+	0.499238i
$281$	20.4757	−	20.4757i	1.22148	−	1.22148i	0.254371	−	0.967107i	$-0.418132\pi$
$281$	20.4757	−	20.4757i	1.22148	−	1.22148i	0.967107	−	0.254371i	$-0.0818685\pi$
$282$	4.03723	−	11.4695i	0.240414	−	0.683000i
$283$	7.02096	+	16.9501i	0.417353	+	1.00758i	0.983112	+	0.183007i	$0.0585832\pi$
$283$	7.02096	+	16.9501i	0.417353	+	1.00758i	−0.565759	+	0.824571i	$0.691417\pi$
$284$	−8.64048	+	10.7528i	−0.512718	+	0.638063i
$285$	11.4728	+	4.75221i	0.679592	+	0.281496i
$286$	0.190023	+	3.49948i	0.0112363	+	0.206929i
$287$	31.9804			1.88774
$288$	−36.6826	−	20.7197i	−2.16155	−	1.22092i
$289$	−8.31071			−0.488865
$290$	1.72444	+	31.7575i	0.101263	+	1.86487i
$291$	−16.2024	−	6.71126i	−0.949802	−	0.393421i
$292$	−10.6814	−	8.58308i	−0.625082	−	0.502287i
$293$	7.62665	+	18.4124i	0.445554	+	1.07566i	0.973970	+	0.226676i	$0.0727859\pi$
$293$	7.62665	+	18.4124i	0.445554	+	1.07566i	−0.528417	+	0.848985i	$0.677214\pi$
$294$	−13.4182	+	38.1204i	−0.782568	+	2.22323i
$295$	25.8163	−	25.8163i	1.50308	−	1.50308i
$296$	−11.2058	−	18.0560i	−0.651326	−	1.04948i
$297$	−25.1909	−	25.1909i	−1.46172	−	1.46172i
$298$	−3.71754	+	1.78179i	−0.215351	+	0.103217i
$299$	4.30396	−	1.78276i	0.248905	−	0.103100i
$300$	−31.7445	+	17.3913i	−1.83277	+	1.00409i
$301$	−4.15109	+	10.0216i	−0.239265	+	0.577636i
$302$	6.25007	+	5.60627i	0.359651	+	0.322604i
$303$			14.5261i			0.834505i
$304$	−0.825150	+	4.64764i	−0.0473256	+	0.266560i
$305$			25.6750i			1.47015i
$306$	−35.3819	+	39.4450i	−2.02265	+	2.25492i
$307$	−3.91358	+	9.44823i	−0.223360	+	0.539239i	−0.995342	−	0.0964054i	$-0.969265\pi$
$307$	−3.91358	+	9.44823i	−0.223360	+	0.539239i	0.771982	+	0.635644i	$0.219265\pi$
$308$	−5.53119	+	18.9351i	−0.315169	+	1.07893i
$309$	−21.3247	+	8.83300i	−1.21312	+	0.502492i
$310$	−5.33441	−	11.1297i	−0.302974	−	0.632126i
$311$	11.1550	+	11.1550i	0.632544	+	0.632544i	0.948705	−	0.316161i	$-0.102394\pi$
$311$	11.1550	+	11.1550i	0.632544	+	0.632544i	−0.316161	+	0.948705i	$0.602394\pi$
$312$	5.33172	−	7.42653i	0.301849	−	0.420445i
$313$	−0.338915	+	0.338915i	−0.0191566	+	0.0191566i	−0.716620	−	0.697464i	$-0.754312\pi$
$313$	−0.338915	+	0.338915i	−0.0191566	+	0.0191566i	0.697464	+	0.716620i	$0.254312\pi$
$314$	−20.5977	−	7.25030i	−1.16239	−	0.409158i
$315$	−36.9302	−	89.1574i	−2.08078	−	5.02345i
$316$	−0.266642	−	2.44801i	−0.0149998	−	0.137711i
$317$	−25.8141	−	10.6926i	−1.44987	−	0.600554i	−0.487699	−	0.873012i	$-0.662164\pi$
$317$	−25.8141	−	10.6926i	−1.44987	−	0.600554i	−0.962168	+	0.272458i	$0.912164\pi$
$318$	23.7384	−	1.28900i	1.33118	−	0.0722836i
$319$	−17.1184			−0.958445
$320$	−17.1381	−	19.6121i	−0.958050	−	1.09635i
$321$	3.69374			0.206164
$322$	26.1830	−	1.42174i	1.45912	−	0.0792307i
$323$	5.48503	+	2.27197i	0.305195	+	0.126416i
$324$	5.22427	+	47.9635i	0.290237	+	2.66464i
$325$	−2.14273	−	5.17300i	−0.118857	−	0.286946i
$326$	9.06145	+	3.18960i	0.501867	+	0.176655i
$327$	28.2081	−	28.2081i	1.55991	−	1.55991i
$328$	−18.4617	−	13.2542i	−1.01938	−	0.731839i
$329$	7.48622	+	7.48622i	0.412729	+	0.412729i
$330$	−15.9399	−	33.2571i	−0.877464	−	1.83074i
$331$	−5.33866	+	2.21135i	−0.293439	+	0.121547i	−0.524547	−	0.851382i	$-0.675765\pi$
$331$	−5.33866	+	2.21135i	−0.293439	+	0.121547i	0.231107	+	0.972928i	$0.425765\pi$
$332$	−0.0660859	+	0.226234i	−0.00362694	+	0.0124162i
$333$	−21.4132	+	51.6960i	−1.17344	+	2.83292i
$334$	−22.1622	+	24.7072i	−1.21266	+	1.35192i
$335$		−	25.2537i		−	1.37976i
$336$	42.1872	−	29.4658i	2.30150	−	1.60749i
$337$		−	15.0228i		−	0.818345i	−0.912457	−	0.409172i	$-0.865817\pi$
$337$		−	15.0228i		−	0.818345i	0.912457	−	0.409172i	$-0.134183\pi$
$338$	1.05275	+	0.944309i	0.0572620	+	0.0513636i
$339$	18.8326	−	45.4659i	1.02285	−	2.46937i
$340$	−28.7292	+	15.7394i	−1.55806	+	0.853587i
$341$	6.13733	−	2.54217i	0.332355	−	0.137666i
$342$	11.2082	−	5.37204i	0.606072	−	0.290487i
$343$	−5.18106	−	5.18106i	−0.279751	−	0.279751i
$344$	6.54977	−	4.06489i	0.353140	−	0.219164i
$345$	−34.6643	+	34.6643i	−1.86626	+	1.86626i
$346$	−3.68024	+	10.4554i	−0.197851	+	0.562083i
$347$	5.43101	+	13.1116i	0.291552	+	0.703869i	0.999998	−	0.00189580i	$-0.000603454\pi$
$347$	5.43101	+	13.1116i	0.291552	+	0.703869i	−0.708446	+	0.705765i	$0.750603\pi$
$348$	34.8094	+	27.9712i	1.86598	+	1.49942i
$349$	21.4996	+	8.90544i	1.15085	+	0.476697i	0.874818	−	0.484452i	$-0.160981\pi$
$349$	21.4996	+	8.90544i	1.15085	+	0.476697i	0.276031	+	0.961149i	$0.410981\pi$
$350$	−1.70882	−	31.4698i	−0.0913401	−	1.68213i
$351$	−14.3758			−0.767321
$352$	11.0406	−	8.63851i	0.588469	−	0.460434i
$353$	34.0510			1.81235			0.906176	−	0.422900i	$-0.138988\pi$
$353$	34.0510			1.81235			0.906176	+	0.422900i	$0.138988\pi$
$354$	−2.77944	−	51.1865i	−0.147726	−	2.72053i
$355$	20.7453	+	8.59299i	1.10105	+	0.456069i
$356$	−4.20451	+	5.23239i	−0.222839	+	0.277316i
$357$	−24.7680	−	59.7951i	−1.31086	−	3.16469i
$358$	8.09529	−	22.9982i	0.427849	−	1.21549i
$359$	10.3817	−	10.3817i	0.547927	−	0.547927i	−0.377914	−	0.925841i	$-0.623359\pi$
$359$	10.3817	−	10.3817i	0.547927	−	0.547927i	0.925841	+	0.377914i	$0.123359\pi$
$360$	−15.6319	+	66.7745i	−0.823871	+	3.51933i
$361$	12.4503	+	12.4503i	0.655280	+	0.655280i
$362$	3.65073	−	1.74977i	0.191878	−	0.0919661i
$363$	−14.5094	+	6.00997i	−0.761544	+	0.315442i
$364$	3.82463	+	6.98112i	0.200465	+	0.365910i
$365$	−8.53591	+	20.6075i	−0.446790	+	1.07865i
$366$	26.8353	+	24.0711i	1.40270	+	1.25822i
$367$		−	34.1426i		−	1.78223i	−0.453780	−	0.891114i	$-0.649925\pi$
$367$		−	34.1426i		−	1.78223i	0.453780	−	0.891114i	$-0.350075\pi$
$368$	−15.7042	−	10.0307i	−0.818638	−	0.522887i
$369$			59.8422i			3.11526i
$370$	−23.0982	+	25.7507i	−1.20082	+	1.33871i
$371$	−7.92133	+	19.1238i	−0.411255	+	0.992857i
$372$	−16.6339	−	4.85896i	−0.862426	−	0.251925i
$373$	3.74850	−	1.55268i	0.194090	−	0.0803946i	−0.283522	−	0.958966i	$-0.591503\pi$
$373$	3.74850	−	1.55268i	0.194090	−	0.0803946i	0.477611	+	0.878571i	$0.341503\pi$
$374$	−7.62068	−	15.8998i	−0.394056	−	0.822159i
$375$	4.45872	+	4.45872i	0.230248	+	0.230248i
$376$	−1.21902	−	7.42430i	−0.0628661	−	0.382879i
$377$	−4.88449	+	4.88449i	−0.251564	+	0.251564i
$378$	−76.3260	−	26.8664i	−3.92578	−	1.38186i
$379$	6.21125	+	14.9953i	0.319050	+	0.770256i	0.999305	+	0.0372799i	$0.0118693\pi$
$379$	6.21125	+	14.9953i	0.319050	+	0.770256i	−0.680254	+	0.732976i	$0.738131\pi$
$380$	7.63865	−	0.832016i	0.391855	−	0.0426815i
$381$	−13.0779	−	5.41705i	−0.670001	−	0.277524i
$382$	23.1473	−	1.25691i	1.18432	−	0.0643089i
$383$	28.7391			1.46850			0.734249	−	0.678880i	$-0.237534\pi$
$383$	28.7391			1.46850			0.734249	+	0.678880i	$0.237534\pi$
$384$	−36.5659	−	0.474285i	−1.86600	−	0.0242032i
$385$	32.1111			1.63654
$386$	10.2837	−	0.558408i	0.523427	−	0.0284222i
$387$	−18.7526	−	7.76759i	−0.953249	−	0.394849i
$388$	−10.7876	+	1.17501i	−0.547658	+	0.0596519i
$389$	−6.72659	−	16.2394i	−0.341052	−	0.823372i	−0.997610	−	0.0690965i	$-0.977988\pi$
$389$	−6.72659	−	16.2394i	−0.341052	−	0.823372i	0.656558	−	0.754275i	$-0.272012\pi$
$390$	−14.0377	−	4.94121i	−0.710826	−	0.250208i
$391$	−16.5726	+	16.5726i	−0.838112	+	0.838112i
$392$	4.05156	+	24.6756i	0.204635	+	1.24631i
$393$	−34.2278	−	34.2278i	−1.72656	−	1.72656i
$394$	11.3079	+	23.5929i	0.569685	+	1.18859i
$395$	−3.70337	+	1.53398i	−0.186337	+	0.0771832i
$396$	−35.4317	−	10.3500i	−1.78051	−	0.520109i
$397$	7.41312	−	17.8969i	0.372054	−	0.898218i	−0.621348	−	0.783535i	$-0.713415\pi$
$397$	7.41312	−	17.8969i	0.372054	−	0.898218i	0.993402	−	0.114683i	$-0.0365853\pi$
$398$	15.3899	−	17.1572i	0.771425	−	0.860012i
$399$			15.1813i			0.760017i
$400$	−12.0561	+	18.8751i	−0.602803	+	0.943756i
$401$			14.3453i			0.716370i	0.933651	+	0.358185i	$0.116604\pi$
$401$			14.3453i			0.716370i	−0.933651	+	0.358185i	$0.883396\pi$
$402$	−26.3950	−	23.6761i	−1.31646	−	1.18086i
$403$	1.02583	−	2.47658i	0.0511003	−	0.123367i
$404$	4.31858	+	7.88274i	0.214857	+	0.392181i
$405$	72.5595	−	30.0551i	3.60551	−	1.49345i
$406$	−35.0620	+	16.8050i	−1.74010	+	0.834018i
$407$	−13.1656	−	13.1656i	−0.652594	−	0.652594i
$408$	−10.4838	+	44.7836i	−0.519026	+	2.21712i
$409$	2.93002	−	2.93002i	0.144880	−	0.144880i	−0.630946	−	0.775826i	$-0.717333\pi$
$409$	2.93002	−	2.93002i	0.144880	−	0.144880i	0.775826	+	0.630946i	$0.217333\pi$
$410$	−12.2834	+	34.8964i	−0.606634	+	1.72341i
$411$	11.2015	+	27.0429i	0.552531	+	1.33393i
$412$	−8.94604	+	11.1331i	−0.440740	+	0.548488i
$413$	41.2361	+	17.0806i	2.02910	+	0.840480i
$414$	2.66039	+	48.9941i	0.130751	+	2.40793i
$415$	0.383660			0.0188331
$416$	0.685416	−	5.61518i	0.0336053	−	0.275307i
$417$	39.3336			1.92617
$418$	0.224242	+	4.12967i	0.0109680	+	0.201989i
$419$	22.5931	+	9.35836i	1.10374	+	0.457186i	0.858779	−	0.512346i	$-0.171223\pi$
$419$	22.5931	+	9.35836i	1.10374	+	0.457186i	0.244965	+	0.969532i	$0.421223\pi$
$420$	−65.2965	−	52.4693i	−3.18614	−	2.56024i
$421$	−5.67597	−	13.7030i	−0.276630	−	0.667844i	0.723108	−	0.690735i	$-0.242713\pi$
$421$	−5.67597	−	13.7030i	−0.276630	−	0.667844i	−0.999738	+	0.0228913i	$0.992713\pi$
$422$	3.87974	−	11.0221i	0.188863	−	0.536548i
$423$	−14.0083	+	14.0083i	−0.681109	+	0.681109i
$424$	12.4986	−	7.75684i	0.606987	−	0.376705i
$425$	19.9188	+	19.9188i	0.966206	+	0.966206i
$426$	28.4307	−	13.6266i	1.37747	−	0.660213i
$427$	−28.9988	+	12.0117i	−1.40335	+	0.581286i
$428$	2.00444	−	1.09814i	0.0968882	−	0.0530805i
$429$	3.06532	−	7.40033i	0.147995	−	0.357291i
$430$	−9.34100	−	8.37881i	−0.450463	−	0.404062i
$431$			12.3254i			0.593695i	0.954925	+	0.296848i	$0.0959354\pi$
$431$			12.3254i			0.593695i	−0.954925	+	0.296848i	$0.904065\pi$
$432$	32.9269	+	47.1425i	1.58419	+	2.26815i
$433$		−	27.8891i		−	1.34026i	−0.742243	−	0.670131i	$-0.766238\pi$
$433$		−	27.8891i		−	1.34026i	0.742243	−	0.670131i	$-0.233762\pi$
$434$	10.0749	−	11.2319i	0.483611	−	0.539147i
$435$	27.8175	−	67.1574i	1.33375	−	3.21995i
$436$	6.92119	−	23.6936i	0.331465	−	1.13472i
$437$	5.07902	−	2.10380i	0.242962	−	0.100638i
$438$	13.5361	+	28.2418i	0.646781	+	1.34945i
$439$	−16.3895	−	16.3895i	−0.782230	−	0.782230i	0.197977	−	0.980207i	$-0.436563\pi$
$439$	−16.3895	−	16.3895i	−0.782230	−	0.782230i	−0.980207	+	0.197977i	$0.936563\pi$
$440$	−18.5372	−	13.3084i	−0.883725	−	0.634451i
$441$	46.5585	−	46.5585i	2.21707	−	2.21707i
$442$	−6.71124	−	2.36233i	−0.319221	−	0.112365i
$443$	−15.2525	−	36.8227i	−0.724667	−	1.74950i	−0.659597	−	0.751619i	$-0.729273\pi$
$443$	−15.2525	−	36.8227i	−0.724667	−	1.74950i	−0.0650697	−	0.997881i	$-0.520727\pi$
$444$	5.25918	+	48.2840i	0.249590	+	2.29146i
$445$	10.0948	+	4.18140i	0.478539	+	0.198217i
$446$	9.95830	−	0.540739i	0.471539	−	0.0256047i
$447$	9.42218			0.445654
$448$	14.1332	−	28.5320i	0.667729	−	1.34801i
$449$	−31.4242			−1.48300			−0.741501	−	0.670952i	$-0.765886\pi$
$449$	−31.4242			−1.48300			−0.741501	+	0.670952i	$0.765886\pi$
$450$	58.8867	−	3.19757i	2.77595	−	0.150735i
$451$	−18.3966	−	7.62011i	−0.866260	−	0.358817i
$452$	−3.29721	−	30.2713i	−0.155088	−	1.42384i
$453$	−7.34357	−	17.7289i	−0.345031	−	0.832978i
$454$	−4.60679	−	1.62157i	−0.216207	−	0.0761042i
$455$	9.16247	−	9.16247i	0.429543	−	0.429543i
$456$	6.29185	−	8.76390i	0.294643	−	0.410407i
$457$	−4.52894	−	4.52894i	−0.211855	−	0.211855i	0.593200	−	0.805055i	$-0.297864\pi$
$457$	−4.52894	−	4.52894i	−0.211855	−	0.211855i	−0.805055	+	0.593200i	$0.797864\pi$
$458$	10.5319	+	21.9738i	0.492125	+	1.02677i
$459$	66.8187	−	27.6772i	3.11883	−	1.29186i
$460$	−8.50530	+	29.1165i	−0.396561	+	1.35756i
$461$	−6.62676	+	15.9984i	−0.308639	+	0.745120i	0.691111	+	0.722749i	$0.257122\pi$
$461$	−6.62676	+	15.9984i	−0.308639	+	0.745120i	−0.999750	+	0.0223714i	$0.992878\pi$
$462$	30.1051	−	33.5623i	1.40062	−	1.56146i
$463$			6.20003i			0.288140i	0.989568	+	0.144070i	$0.0460190\pi$
$463$			6.20003i			0.288140i	−0.989568	+	0.144070i	$0.953981\pi$
$464$	27.2054	+	4.83010i	1.26298	+	0.224232i
$465$			28.2086i			1.30814i
$466$	18.0219	+	16.1655i	0.834850	+	0.748854i
$467$	3.69171	−	8.91258i	0.170832	−	0.412425i	−0.815156	−	0.579242i	$-0.803349\pi$
$467$	3.69171	−	8.91258i	0.170832	−	0.412425i	0.985988	+	0.166817i	$0.0533488\pi$
$468$	−13.0632	+	7.15670i	−0.603846	+	0.330819i
$469$	28.5230	−	11.8146i	1.31707	−	0.545547i
$470$	−11.0442	+	5.29343i	−0.509432	+	0.244168i
$471$	35.2907	+	35.2907i	1.62611	+	1.62611i
$472$	−16.7259	−	26.9505i	−0.769871	−	1.24050i
$473$	4.77579	−	4.77579i	0.219591	−	0.219591i
$474$	−1.86871	+	5.30888i	−0.0858325	+	0.243845i
$475$	−2.52859	−	6.10455i	−0.116019	−	0.280096i
$476$	−31.2175	−	25.0849i	−1.43085	−	1.14977i
$477$	−35.7847	−	14.8225i	−1.63847	−	0.678677i
$478$	−0.367093	−	6.76042i	−0.0167904	−	0.309214i
$479$	7.58274			0.346464			0.173232	−	0.984881i	$-0.444579\pi$
$479$	7.58274			0.346464			0.173232	+	0.984881i	$0.444579\pi$
$480$	15.9488	+	57.3515i	0.727958	+	2.61772i
$481$	−7.51324			−0.342574
$482$	1.51025	+	27.8129i	0.0687900	+	1.26684i
$483$	−55.3690	−	22.9346i	−2.51938	−	1.04356i
$484$	−6.08688	+	7.57495i	−0.276676	+	0.344316i
$485$	6.75979	+	16.3196i	0.306946	+	0.741034i
$486$	16.3626	−	46.4851i	0.742221	−	2.10861i
$487$	−21.0479	+	21.0479i	−0.953772	+	0.953772i	−0.998978	−	0.0452060i	$-0.985606\pi$
$487$	−21.0479	+	21.0479i	−0.953772	+	0.953772i	0.0452060	+	0.998978i	$0.485606\pi$
$488$	21.7187	+	5.08432i	0.983158	+	0.230156i
$489$	−15.5253	−	15.5253i	−0.702077	−	0.702077i
$490$	36.7069	−	17.5934i	1.65825	−	0.794788i
$491$	−27.2676	+	11.2946i	−1.23057	+	0.509719i	−0.900755	−	0.434327i	$-0.856986\pi$
$491$	−27.2676	+	11.2946i	−1.23057	+	0.509719i	−0.329814	+	0.944046i	$0.606986\pi$
$492$	24.9574	+	45.5549i	1.12517	+	2.05377i
$493$	13.2992	−	32.1071i	0.598967	−	1.44603i
$494$	1.24233	+	1.11436i	0.0558950	+	0.0501374i
$495$			60.0869i			2.70070i
$496$	−10.4711	+	2.30844i	−0.470165	+	0.103652i
$497$			27.4510i			1.23135i
$498$	0.359692	−	0.400998i	0.0161182	−	0.0179691i
$499$	1.62725	−	3.92854i	0.0728459	−	0.175866i	−0.883262	−	0.468879i	$-0.844658\pi$
$499$	1.62725	−	3.92854i	0.0728459	−	0.175866i	0.956108	+	0.293013i	$0.0946581\pi$
$500$	3.74513	+	1.09400i	0.167487	+	0.0489252i
$501$	70.0845	−	29.0300i	3.13114	−	1.29696i
$502$	−5.42513	−	11.3190i	−0.242135	−	0.505192i
$503$	5.43931	+	5.43931i	0.242527	+	0.242527i	0.817895	−	0.575368i	$-0.195141\pi$
$503$	5.43931	+	5.43931i	0.242527	+	0.242527i	−0.575368	+	0.817895i	$0.695141\pi$
$504$	−82.7320	+	13.5840i	−3.68518	+	0.605081i
$505$	10.3458	−	10.3458i	0.460382	−	0.460382i
$506$	−15.4004	−	5.42089i	−0.684632	−	0.240988i
$507$	−1.23694	−	2.98623i	−0.0549343	−	0.132623i
$508$	−8.70731	+	0.948416i	−0.386325	+	0.0420791i
$509$	−13.0802	−	5.41799i	−0.579769	−	0.240148i	0.0734731	−	0.997297i	$-0.476592\pi$
$509$	−13.0802	−	5.41799i	−0.579769	−	0.240148i	−0.653242	+	0.757149i	$0.726592\pi$
$510$	74.7605	−	4.05952i	3.31045	−	0.179758i
$511$	−27.2687			−1.20630
$512$	−19.9838	+	10.6136i	−0.883168	+	0.469057i
$513$	−16.9645			−0.749002
$514$	−34.5063	+	1.87370i	−1.52201	+	0.0826455i
$515$	21.4789	+	8.89687i	0.946476	+	0.392043i
$516$	−17.5149	+	1.90776i	−0.771052	+	0.0839843i
$517$	−2.52264	−	6.09018i	−0.110945	−	0.267846i
$518$	−39.8904	−	14.0413i	−1.75268	−	0.616938i
$519$	17.9135	−	17.9135i	0.786315	−	0.786315i
$520$	−9.08668	+	1.49197i	−0.398477	+	0.0654272i
$521$	−4.78754	−	4.78754i	−0.209746	−	0.209746i	0.594413	−	0.804160i	$-0.297384\pi$
$521$	−4.78754	−	4.78754i	−0.209746	−	0.209746i	−0.804160	+	0.594413i	$0.797384\pi$
$522$	−31.4458	−	65.6085i	−1.37634	−	2.87161i
$523$	15.8038	−	6.54613i	0.691050	−	0.286242i	−0.00938762	−	0.999956i	$-0.502988\pi$
$523$	15.8038	−	6.54613i	0.691050	−	0.286242i	0.700438	+	0.713714i	$0.252988\pi$
$524$	−28.7498	−	8.39818i	−1.25594	−	0.366876i
$525$	−27.5654	+	66.5489i	−1.20305	+	2.90443i
$526$	18.7705	−	20.9260i	0.818431	−	0.912416i
$527$			13.4862i			0.587467i
$528$	−31.2889	+	6.89792i	−1.36168	+	0.300194i
$529$		−	1.29767i		−	0.0564204i
$530$	−17.8250	−	15.9889i	−0.774268	−	0.694513i
$531$	−31.9614	+	77.1617i	−1.38701	+	3.34853i
$532$	4.51336	+	8.23828i	0.195679	+	0.357175i
$533$	−7.42350	+	3.07491i	−0.321547	+	0.133189i
$534$	13.8345	−	6.63081i	0.598679	−	0.286943i
$535$	−2.63075	−	2.63075i	−0.113737	−	0.113737i
$536$	−21.3623	−	5.00089i	−0.922711	−	0.216006i
$537$	−39.4036	+	39.4036i	−1.70039	+	1.70039i
$538$	10.7214	−	30.4589i	0.462233	−	1.31318i
$539$	8.38430	+	20.2415i	0.361138	+	0.871863i
$540$	58.6323	−	72.9663i	2.52313	−	3.13997i
$541$	−30.0551	−	12.4492i	−1.29217	−	0.535234i	−0.372539	−	0.928017i	$-0.621513\pi$
$541$	−30.0551	−	12.4492i	−1.29217	−	0.535234i	−0.919632	+	0.392782i	$0.871513\pi$
$542$	1.06034	+	19.5274i	0.0455456	+	0.838773i
$543$	−9.25287			−0.397079
$544$	7.62491	+	27.4190i	0.326915	+	1.17558i
$545$	−40.1807			−1.72115
$546$	−0.986453	−	18.1666i	−0.0422163	−	0.777459i
$547$	25.3753	+	10.5108i	1.08497	+	0.449409i	0.852250	−	0.523135i	$-0.175238\pi$
$547$	25.3753	+	10.5108i	1.08497	+	0.449409i	0.232720	+	0.972544i	$0.425238\pi$
$548$	14.1184	+	11.3449i	0.603107	+	0.484629i
$549$	−22.4765	−	54.2630i	−0.959273	−	2.31589i
$550$	−6.51544	+	18.5100i	−0.277819	+	0.789268i
$551$	−5.76408	+	5.76408i	−0.245558	+	0.245558i
$552$	22.4584	+	36.1872i	0.955891	+	1.54023i
$553$	−3.46514	−	3.46514i	−0.147353	−	0.147353i
$554$	−11.0209	+	5.28227i	−0.468235	+	0.224422i
$555$	73.0444	−	30.2560i	3.10056	−	1.28429i
$556$	21.3447	−	11.6938i	0.905217	−	0.495925i
$557$	−1.93473	+	4.67085i	−0.0819771	+	0.197910i	−0.959553	−	0.281527i	$-0.909159\pi$
$557$	−1.93473	+	4.67085i	−0.0819771	+	0.197910i	0.877576	+	0.479437i	$0.159159\pi$
$558$	21.0173	+	18.8523i	0.889731	+	0.798083i
$559$		−	2.72541i		−	0.115273i
$560$	−51.0327	−	9.06044i	−2.15652	−	0.382874i
$561$			40.2984i			1.70140i
$562$	−27.3444	+	30.4845i	−1.15345	+	1.28591i
$563$	−4.40787	+	10.6416i	−0.185770	+	0.448488i	−0.989137	−	0.146996i	$-0.953040\pi$
$563$	−4.40787	+	10.6416i	−0.185770	+	0.448488i	0.803367	+	0.595484i	$0.203040\pi$
$564$	−4.82163	+	16.5061i	−0.203027	+	0.695031i
$565$	−45.7947	+	18.9688i	−1.92660	+	0.798022i
$566$	−11.2142	−	23.3974i	−0.471370	−	0.983467i
$567$	67.8919	+	67.8919i	2.85119	+	2.85119i
$568$	11.3770	−	15.8470i	0.477368	−	0.664924i
$569$	−2.52239	+	2.52239i	−0.105744	+	0.105744i	−0.757999	−	0.652255i	$-0.773823\pi$
$569$	−2.52239	+	2.52239i	−0.105744	+	0.105744i	0.652255	+	0.757999i	$0.273823\pi$
$570$	−16.5656	−	5.83102i	−0.693856	−	0.244235i
$571$	−8.71735	−	21.0455i	−0.364810	−	0.880729i	−0.994583	−	0.103949i	$-0.966852\pi$
$571$	−8.71735	−	21.0455i	−0.364810	−	0.880729i	0.629773	−	0.776779i	$-0.283148\pi$
$572$	−0.536675	−	4.92717i	−0.0224395	−	0.206015i
$573$	−48.9495	−	20.2755i	−2.04489	−	0.847023i
$574$	−45.1606	+	2.45223i	−1.88497	+	0.102354i
$575$	26.0844			1.08779
$576$	53.3895	+	26.4462i	2.22456	+	1.10193i
$577$	22.8350			0.950633			0.475316	−	0.879815i	$-0.342334\pi$
$577$	22.8350			0.950633			0.475316	+	0.879815i	$0.342334\pi$
$578$	11.7358	−	0.637259i	0.488146	−	0.0265065i
$579$	−21.7469	−	9.00785i	−0.903770	−	0.374354i
$580$	−4.87029	−	44.7136i	−0.202228	−	1.85663i
$581$	0.179490	+	0.433327i	0.00744649	+	0.0179774i
$582$	23.3946	+	8.23480i	0.969737	+	0.341344i
$583$	9.11341	−	9.11341i	0.377439	−	0.377439i
$584$	15.7417	+	11.3014i	0.651396	+	0.467656i
$585$	17.1450	+	17.1450i	0.708857	+	0.708857i
$586$	−12.1817	−	25.4159i	−0.503221	−	1.04992i
$587$	−39.1161	+	16.2024i	−1.61449	+	0.668746i	−0.993369	−	0.114966i	$-0.963324\pi$
$587$	−39.1161	+	16.2024i	−1.61449	+	0.668746i	−0.621125	+	0.783711i	$0.713324\pi$
$588$	16.0253	−	54.8600i	0.660872	−	2.26239i
$589$	1.21056	−	2.92256i	0.0498803	−	0.120422i
$590$	−34.4765	+	38.4356i	−1.41937	+	1.58237i
$591$		−	59.7967i		−	2.45971i
$592$	17.2086	+	24.6382i	0.707271	+	1.01262i
$593$		−	36.7908i		−	1.51082i	−0.655254	−	0.755408i	$-0.727438\pi$
$593$		−	36.7908i		−	1.51082i	0.655254	−	0.755408i	$-0.272562\pi$
$594$	37.5045	+	33.6413i	1.53883	+	1.38032i
$595$	−24.9471	+	60.2275i	−1.02273	+	2.46909i
$596$	5.11303	−	2.80119i	0.209438	−	0.114741i
$597$	−48.6681	+	20.1590i	−1.99185	+	0.825052i
$598$	−5.94107	+	2.84752i	−0.242948	+	0.116444i
$599$	20.7087	+	20.7087i	0.846135	+	0.846135i	0.989648	−	0.143513i	$-0.0458400\pi$
$599$	20.7087	+	20.7087i	0.846135	+	0.846135i	−0.143513	+	0.989648i	$0.545840\pi$
$600$	43.4940	−	26.9930i	1.77563	−	1.10199i
$601$	−28.0329	+	28.0329i	−1.14349	+	1.14349i	−0.155680	+	0.987808i	$0.549757\pi$
$601$	−28.0329	+	28.0329i	−1.14349	+	1.14349i	−0.987808	+	0.155680i	$0.950243\pi$
$602$	5.09344	−	14.4702i	0.207593	−	0.589760i
$603$	22.1077	+	53.3726i	0.900294	+	2.17350i
$604$	−9.25582	−	7.43755i	−0.376614	−	0.302629i
$605$	14.6143	+	6.05343i	0.594155	+	0.246107i
$606$	−1.11385	−	20.5128i	−0.0452472	−	0.833277i
$607$	−2.89763			−0.117611			−0.0588056	−	0.998269i	$-0.518729\pi$
$607$	−2.89763			−0.117611			−0.0588056	+	0.998269i	$0.518729\pi$
$608$	0.808845	−	6.62635i	0.0328030	−	0.268734i
$609$	88.8654			3.60101
$610$	−1.96874	−	36.2565i	−0.0797120	−	1.46798i
$611$	−2.45755	−	1.01795i	−0.0994218	−	0.0411819i
$612$	46.9393	−	58.4146i	1.89741	−	2.36127i
$613$	−2.68520	−	6.48264i	−0.108454	−	0.261832i	0.860330	−	0.509738i	$-0.170258\pi$
$613$	−2.68520	−	6.48264i	−0.108454	−	0.261832i	−0.968784	+	0.247906i	$0.920258\pi$
$614$	4.80202	−	13.6422i	0.193794	−	0.550556i
$615$	59.7892	−	59.7892i	2.41093	−	2.41093i
$616$	6.35884	−	27.1630i	0.256205	−	1.09443i
$617$	−14.2576	−	14.2576i	−0.573990	−	0.573990i	0.359251	−	0.933241i	$-0.383032\pi$
$617$	−14.2576	−	14.2576i	−0.573990	−	0.573990i	−0.933241	+	0.359251i	$0.883032\pi$
$618$	29.4361	−	14.1085i	1.18409	−	0.567529i
$619$	−37.4055	+	15.4939i	−1.50345	+	0.622751i	−0.974195	−	0.225709i	$-0.927530\pi$
$619$	−37.4055	+	15.4939i	−1.50345	+	0.622751i	−0.529259	+	0.848460i	$0.677530\pi$
$620$	8.38632	+	15.3076i	0.336803	+	0.614769i
$621$	25.6285	−	61.8727i	1.02844	−	2.48287i
$622$	−16.6078	−	14.8970i	−0.665911	−	0.597317i
$623$			13.3578i			0.535170i
$624$	−6.95963	+	10.8961i	−0.278608	+	0.436193i
$625$			21.6449i			0.865795i
$626$	0.452606	−	0.504581i	0.0180898	−	0.0201671i
$627$	3.61732	−	8.73298i	0.144462	−	0.348762i
$628$	29.6426	+	8.65898i	1.18287	+	0.345531i
$629$	34.9216	−	14.4650i	1.39242	−	0.576758i
$630$	58.9869	+	123.070i	2.35009	+	4.90324i
$631$	2.35802	+	2.35802i	0.0938714	+	0.0938714i	0.752483	−	0.658612i	$-0.228856\pi$
$631$	2.35802	+	2.35802i	0.0938714	+	0.0938714i	−0.658612	+	0.752483i	$0.728856\pi$
$632$	0.564245	+	3.43647i	0.0224445	+	0.136696i
$633$	−18.8845	+	18.8845i	−0.750593	+	0.750593i
$634$	37.2729	+	13.1199i	1.48030	+	0.521059i
$635$	5.45622	+	13.1725i	0.216523	+	0.522734i
$636$	−33.4229	+	3.64048i	−1.32530	+	0.144354i
$637$	8.16798	+	3.38329i	0.323627	+	0.134051i
$638$	24.1734	−	1.31262i	0.957035	−	0.0519673i
$639$	−51.3668			−2.03204
$640$	25.7052	+	26.3808i	1.01609	+	1.04279i
$641$	33.0315			1.30467			0.652333	−	0.757932i	$-0.273790\pi$
$641$	33.0315			1.30467			0.652333	+	0.757932i	$0.273790\pi$
$642$	−5.21605	+	0.283233i	−0.205861	+	0.0111783i
$643$	−32.9748	−	13.6586i	−1.30040	−	0.538643i	−0.378331	−	0.925671i	$-0.623502\pi$
$643$	−32.9748	−	13.6586i	−1.30040	−	0.538643i	−0.922068	+	0.387028i	$0.873502\pi$
$644$	−36.8649	+	4.01539i	−1.45268	+	0.158228i
$645$	10.9753	+	26.4967i	0.432152	+	1.04331i
$646$	−7.91980	−	2.78774i	−0.311600	−	0.109682i
$647$	22.1855	−	22.1855i	0.872201	−	0.872201i	−0.120511	−	0.992712i	$-0.538453\pi$
$647$	22.1855	−	22.1855i	0.872201	−	0.872201i	0.992712	+	0.120511i	$0.0384534\pi$
$648$	−11.0552	−	67.3303i	−0.434288	−	2.64498i
$649$	−19.6510	−	19.6510i	−0.771370	−	0.771370i
$650$	3.42248	+	7.14066i	0.134241	+	0.280080i
$651$	−31.8603	+	13.1970i	−1.24870	+	0.517230i
$652$	−13.0405	−	3.80931i	−0.510707	−	0.149184i
$653$	−1.15931	+	2.79883i	−0.0453675	+	0.109527i	−0.944939	−	0.327247i	$-0.893879\pi$
$653$	−1.15931	+	2.79883i	−0.0453675	+	0.109527i	0.899571	+	0.436774i	$0.143879\pi$
$654$	−37.6706	+	41.9966i	−1.47304	+	1.64220i
$655$			48.7554i			1.90503i
$656$	27.0867	+	17.3010i	1.05756	+	0.675491i
$657$		−	51.0256i		−	1.99070i
$658$	−11.1456	−	9.99750i	−0.434500	−	0.389743i
$659$	10.1074	−	24.4013i	0.393727	−	0.950541i	−0.595394	−	0.803434i	$-0.703004\pi$
$659$	10.1074	−	24.4013i	0.393727	−	0.950541i	0.989121	−	0.147107i	$-0.0469961\pi$
$660$	25.0594	+	45.7412i	0.975437	+	1.78047i
$661$	−38.7561	+	16.0533i	−1.50744	+	0.624400i	−0.975027	−	0.222087i	$-0.928713\pi$
$661$	−38.7561	+	16.0533i	−1.50744	+	0.624400i	−0.532409	+	0.846487i	$0.678713\pi$
$662$	7.36933	−	3.53208i	0.286417	−	0.137278i
$663$	11.4986	+	11.4986i	0.446569	+	0.446569i
$664$	0.0759746	−	0.324540i	0.00294839	−	0.0125946i
$665$	10.8124	−	10.8124i	0.419288	−	0.419288i
$666$	26.2743	−	74.6436i	1.01811	−	2.89238i
$667$	−12.3148	−	29.7305i	−0.476831	−	1.15117i
$668$	29.4015	−	36.5893i	1.13758	−	1.41568i
$669$	−21.0588	−	8.72282i	−0.814179	−	0.337244i
$670$	1.93644	+	35.6616i	0.0748110	+	1.37773i
$671$	19.5435			0.754468
$672$	−57.3145	+	44.8445i	−2.21096	+	1.72991i
$673$	27.6438			1.06559			0.532795	−	0.846244i	$-0.321142\pi$
$673$	27.6438			1.06559			0.532795	+	0.846244i	$0.321142\pi$
$674$	1.15194	+	21.2142i	0.0443710	+	0.817141i
$675$	−74.3658	−	30.8033i	−2.86234	−	1.18562i
$676$	−1.55903	−	1.25277i	−0.0599627	−	0.0481833i
$677$	−7.13997	−	17.2374i	−0.274411	−	0.662488i	0.725251	−	0.688485i	$-0.241724\pi$
$677$	−7.13997	−	17.2374i	−0.274411	−	0.662488i	−0.999662	+	0.0259972i	$0.991724\pi$
$678$	−23.1078	+	65.6480i	−0.887451	+	2.52119i
$679$	−15.2698	+	15.2698i	−0.586000	+	0.586000i
$680$	39.3626	−	24.4290i	1.50949	−	0.936810i
$681$	7.89297	+	7.89297i	0.302459	+	0.302459i
$682$	−8.47180	+	4.06049i	−0.324402	+	0.155484i
$683$	37.7391	−	15.6320i	1.44405	−	0.598144i	0.483271	−	0.875471i	$-0.339449\pi$
$683$	37.7391	−	15.6320i	1.44405	−	0.598144i	0.960776	+	0.277327i	$0.0894485\pi$
$684$	−15.4156	+	8.44548i	−0.589430	+	0.322921i
$685$	11.2825	−	27.2384i	0.431083	−	1.04073i
$686$	7.71363	+	6.91907i	0.294508	+	0.264171i
$687$		−	55.6932i		−	2.12483i
$688$	−8.93746	+	6.24240i	−0.340737	+	0.237989i
$689$		−	5.20077i		−	0.198134i
$690$	46.2926	−	51.6087i	1.76233	−	1.96471i
$691$	12.2904	−	29.6715i	0.467547	−	1.12876i	−0.497683	−	0.867359i	$-0.665816\pi$
$691$	12.2904	−	29.6715i	0.467547	−	1.12876i	0.965231	−	0.261400i	$-0.0841842\pi$
$692$	4.39529	−	15.0465i	0.167084	−	0.571984i
$693$	−67.8655	+	28.1108i	−2.57800	+	1.06784i
$694$	−8.67471	−	18.0989i	−0.329287	−	0.687026i
$695$	−28.0141	−	28.0141i	−1.06264	−	1.06264i
$696$	−51.3003	−	36.8300i	−1.94453	−	1.39604i
$697$	28.5845	−	28.5845i	1.08271	−	1.08271i
$698$	−31.0432	−	10.9271i	−1.17500	−	0.413596i
$699$	−21.1750	−	51.1210i	−0.800912	−	1.93357i
$700$	4.82615	+	44.3085i	0.182411	+	1.67470i
$701$	47.3958	+	19.6320i	1.79012	+	0.741490i	0.989898	+	0.141782i	$0.0452831\pi$
$701$	47.3958	+	19.6320i	1.79012	+	0.741490i	0.800218	+	0.599709i	$0.204717\pi$
$702$	20.3005	−	1.10232i	0.766192	−	0.0416045i
$703$	−8.86621			−0.334396
$704$	−14.9285	+	13.0453i	−0.562638	+	0.491664i
$705$	27.9918			1.05423
$706$	−48.0846	+	2.61101i	−1.80969	+	0.0982665i
$707$	16.5253	+	6.84499i	0.621497	+	0.257432i
$708$	7.84988	+	72.0690i	0.295017	+	2.70852i
$709$	4.83578	+	11.6746i	0.181612	+	0.438449i	0.988299	−	0.152529i	$-0.0487418\pi$
$709$	4.83578	+	11.6746i	0.181612	+	0.438449i	−0.806687	+	0.590978i	$0.798742\pi$
$710$	−29.9541	−	10.5437i	−1.12416	−	0.395699i
$711$	6.48402	−	6.48402i	0.243170	−	0.243170i
$712$	5.53611	−	7.71123i	0.207475	−	0.288991i
$713$	8.83028	+	8.83028i	0.330697	+	0.330697i
$714$	39.5607	+	82.5395i	1.48052	+	3.08896i
$715$	−7.45384	+	3.08748i	−0.278758	+	0.115465i
$716$	−9.66814	+	33.0973i	−0.361315	+	1.23690i
$717$	−5.92168	+	14.2962i	−0.221149	+	0.533902i
$718$	−13.8643	+	15.4564i	−0.517412	+	0.576829i
$719$		−	13.4962i		−	0.503325i	−0.967815	−	0.251662i	$-0.919023\pi$
$719$		−	13.4962i		−	0.503325i	0.967815	−	0.251662i	$-0.0809773\pi$
$720$	16.9540	−	95.4932i	0.631840	−	3.55882i
$721$			28.4218i			1.05848i
$722$	−18.5362	−	16.6268i	−0.689846	−	0.618787i
$723$	24.3623	−	58.8158i	0.906044	−	2.18738i
$724$	−5.02115	+	2.75085i	−0.186610	+	0.102235i
$725$	−35.7336	+	14.8013i	−1.32711	+	0.549708i
$726$	20.0283	−	9.59945i	0.743320	−	0.356269i
$727$	21.8851	+	21.8851i	0.811673	+	0.811673i	0.984885	−	0.173211i	$-0.0554144\pi$
$727$	21.8851	+	21.8851i	0.811673	+	0.811673i	−0.173211	+	0.984885i	$0.555414\pi$
$728$	−5.93619	−	9.56500i	−0.220010	−	0.354503i
$729$	−28.4705	+	28.4705i	−1.05446	+	1.05446i
$730$	10.4737	−	29.7551i	0.387648	−	1.10128i
$731$	5.24715	+	12.6677i	0.194073	+	0.468533i
$732$	−39.7408	−	31.9339i	−1.46886	−	1.18031i
$733$	0.332272	+	0.137632i	0.0122728	+	0.00508355i	0.388811	−	0.921317i	$-0.372886\pi$
$733$	0.332272	+	0.137632i	0.0122728	+	0.00508355i	−0.376539	+	0.926401i	$0.622886\pi$
$734$	2.61803	+	48.2138i	0.0966331	+	1.77961i
$735$	−93.0344			−3.43163
$736$	22.9456	+	12.9605i	0.845785	+	0.477731i
$737$	−19.2228			−0.708081
$738$	−4.58866	−	84.5052i	−0.168911	−	3.11068i
$739$	39.4456	+	16.3389i	1.45103	+	0.601037i	0.962445	−	0.271478i	$-0.0875126\pi$
$739$	39.4456	+	16.3389i	1.45103	+	0.601037i	0.488587	+	0.872515i	$0.337513\pi$
$740$	30.6432	−	38.1346i	1.12647	−	1.40185i
$741$	−1.45968	−	3.52399i	−0.0536228	−	0.129457i
$742$	9.71957	−	27.6127i	0.356817	−	1.01369i
$743$	3.84570	−	3.84570i	0.141085	−	0.141085i	−0.633037	−	0.774122i	$-0.718192\pi$
$743$	3.84570	−	3.84570i	0.141085	−	0.141085i	0.774122	+	0.633037i	$0.218192\pi$
$744$	23.8618	+	5.58603i	0.874816	+	0.204794i
$745$	−6.71067	−	6.71067i	−0.245860	−	0.245860i
$746$	−5.17432	+	2.48002i	−0.189445	+	0.0908000i
$747$	−0.810848	+	0.335864i	−0.0296674	+	0.0122886i
$748$	11.9806	+	21.8683i	0.438054	+	0.799584i
$749$	1.74056	−	4.20208i	0.0635987	−	0.153541i
$750$	−6.63820	−	5.95442i	−0.242393	−	0.217425i
$751$			28.6037i			1.04376i	0.853018	+	0.521882i	$0.174770\pi$
$751$			28.6037i			1.04376i	−0.853018	+	0.521882i	$0.825230\pi$
$752$	2.29071	+	10.3906i	0.0835335	+	0.378907i
$753$			28.6883i			1.04546i
$754$	6.52301	−	7.27209i	0.237554	−	0.264834i
$755$	−7.39667	+	17.8571i	−0.269192	+	0.649888i
$756$	109.843	+	32.0864i	3.99493	+	1.16697i
$757$	12.8251	−	5.31232i	0.466135	−	0.193079i	−0.137239	−	0.990538i	$-0.543823\pi$
$757$	12.8251	−	5.31232i	0.466135	−	0.193079i	0.603374	+	0.797459i	$0.293823\pi$
$758$	−9.92094	−	20.6991i	−0.360345	−	0.751824i
$759$	26.3860	+	26.3860i	0.957752	+	0.957752i
$760$	−10.7230	+	1.76064i	−0.388964	+	0.0638652i
$761$	28.3230	−	28.3230i	1.02671	−	1.02671i	0.0270756	−	0.999633i	$-0.491381\pi$
$761$	28.3230	−	28.3230i	1.02671	−	1.02671i	0.999633	−	0.0270756i	$-0.00861949\pi$
$762$	18.8831	+	6.64679i	0.684063	+	0.240788i
$763$	−18.7980	−	45.3824i	−0.680533	−	1.64295i
$764$	−32.5907	+	3.54984i	−1.17909	+	0.128429i
$765$	−112.699	−	46.6813i	−4.07463	−	1.68777i
$766$	−40.5834	+	2.20369i	−1.46634	+	0.0796226i
$767$	−11.2143			−0.404925
$768$	51.6723	−	2.13409i	1.86456	−	0.0770074i
$769$	45.4051			1.63735			0.818675	−	0.574257i	$-0.194709\pi$
$769$	45.4051			1.63735			0.818675	+	0.574257i	$0.194709\pi$
$770$	−45.3452	+	2.46226i	−1.63413	+	0.0887336i
$771$	72.9703	+	30.2253i	2.62796	+	1.08854i
$772$	−14.4791	+	1.57709i	−0.521116	+	0.0567608i
$773$	3.34759	+	8.08179i	0.120404	+	0.290682i	0.972578	−	0.232578i	$-0.0747160\pi$
$773$	3.34759	+	8.08179i	0.120404	+	0.290682i	−0.852174	+	0.523259i	$0.824716\pi$
$774$	27.0768	+	9.53093i	0.973256	+	0.342582i
$775$	10.6132	−	10.6132i	0.381239	−	0.381239i
$776$	15.1435	−	2.48645i	0.543618	−	0.0892584i
$777$	68.3456	+	68.3456i	2.45188	+	2.45188i
$778$	10.7441	+	22.4165i	0.385194	+	0.803669i
$779$	−8.76031	+	3.62864i	−0.313871	+	0.130010i
$780$	20.2020	+	5.90125i	0.723346	+	0.211299i
$781$	6.54087	−	15.7911i	0.234051	−	0.565049i
$782$	22.1319	−	24.6735i	0.791436	−	0.882322i
$783$			99.3036i			3.54882i
$784$	−7.61345	−	34.5345i	−0.271909	−	1.23338i
$785$		−	50.2694i		−	1.79419i
$786$	50.9587	+	45.7096i	1.81764	+	1.63041i
$787$	12.6679	−	30.5829i	0.451560	−	1.09016i	−0.520168	−	0.854064i	$-0.674131\pi$
$787$	12.6679	−	30.5829i	0.451560	−	1.09016i	0.971729	−	0.236100i	$-0.0758691\pi$
$788$	−17.7774	−	32.4492i	−0.633293	−	1.15595i
$789$	−59.3587	+	24.5872i	−2.11322	+	0.875326i
$790$	5.11202	−	2.45016i	0.181878	−	0.0871729i
$791$	−42.8488	−	42.8488i	−1.52353	−	1.52353i
$792$	50.8279	+	11.8988i	1.80609	+	0.422804i
$793$	5.57646	−	5.57646i	0.198026	−	0.198026i
$794$	−9.09600	+	25.8412i	−0.322805	+	0.917069i
$795$	20.9436	+	50.5624i	0.742794	+	1.79326i
$796$	−20.4170	+	25.4083i	−0.723660	+	0.900574i
$797$	23.0453	+	9.54566i	0.816305	+	0.338125i	0.751467	−	0.659771i	$-0.229347\pi$
$797$	23.0453	+	9.54566i	0.816305	+	0.338125i	0.0648386	+	0.997896i	$0.479347\pi$
$798$	−1.16409	−	21.4380i	−0.0412084	−	0.758899i
$799$	13.3826			0.473441
$800$	15.5774	−	27.5786i	0.550746	−	0.975052i
$801$	−24.9954			−0.883169
$802$	−1.09999	−	20.2575i	−0.0388419	−	0.715316i
$803$	15.6862	+	6.49743i	0.553553	+	0.229289i
$804$	39.0887	+	31.4099i	1.37855	+	1.10774i
$805$	23.1004	+	55.7694i	0.814184	+	1.96561i
$806$	−1.25871	+	3.57592i	−0.0443361	+	0.125956i
$807$	−52.1862	+	52.1862i	−1.83704	+	1.83704i
$808$	−6.70285	−	10.8003i	−0.235805	−	0.379954i
$809$	−29.0966	−	29.0966i	−1.02298	−	1.02298i	−0.999730	−	0.0232519i	$-0.992598\pi$
$809$	−29.0966	−	29.0966i	−1.02298	−	1.02298i	−0.0232519	−	0.999730i	$-0.507402\pi$
$810$	−100.159	+	48.0057i	−3.51923	+	1.68675i
$811$	−19.7763	+	8.19161i	−0.694440	+	0.287646i	−0.701849	−	0.712326i	$-0.747642\pi$
$811$	−19.7763	+	8.19161i	−0.694440	+	0.287646i	0.00740882	+	0.999973i	$0.497642\pi$
$812$	48.2236	−	26.4194i	1.69232	−	0.927140i
$813$	17.1047	−	41.2944i	0.599888	−	1.44826i
$814$	19.6011	+	17.5820i	0.687018	+	0.616250i
$815$			22.1148i			0.774649i
$816$	11.3706	−	64.0443i	0.398049	−	2.24200i
$817$		−	3.21620i		−	0.112521i
$818$	−3.91290	+	4.36225i	−0.136811	+	0.152522i
$819$	−11.3434	+	27.3855i	−0.396372	+	0.956927i
$820$	14.6700	−	50.2203i	0.512298	−	1.75377i
$821$	21.4278	−	8.87568i	0.747835	−	0.309764i	0.0239773	−	0.999713i	$-0.492367\pi$
$821$	21.4278	−	8.87568i	0.747835	−	0.309764i	0.723858	+	0.689949i	$0.242367\pi$
$822$	−17.8917	−	37.3292i	−0.624044	−	1.30201i
$823$	−1.90459	−	1.90459i	−0.0663899	−	0.0663899i	0.673132	−	0.739522i	$-0.264948\pi$
$823$	−1.90459	−	1.90459i	−0.0663899	−	0.0663899i	−0.739522	+	0.673132i	$0.764948\pi$
$824$	11.7793	−	16.4074i	0.410352	−	0.571578i
$825$	31.7138	−	31.7138i	1.10413	−	1.10413i
$826$	−59.5406	−	20.9581i	−2.07168	−	0.729225i
$827$	−1.79244	−	4.32734i	−0.0623294	−	0.150476i	0.889646	−	0.456651i	$-0.150951\pi$
$827$	−1.79244	−	4.32734i	−0.0623294	−	0.150476i	−0.951976	+	0.306174i	$0.900951\pi$
$828$	−7.51366	−	68.9822i	−0.261118	−	2.39730i
$829$	−51.2974	−	21.2481i	−1.78163	−	0.737976i	−0.992278	−	0.124036i	$-0.960416\pi$
$829$	−51.2974	−	21.2481i	−1.78163	−	0.737976i	−0.789353	−	0.613940i	$-0.789584\pi$
$830$	−0.541779	+	0.0294187i	−0.0188054	+	0.00102114i
$831$	27.9328			0.968979
$832$	−0.537331	+	7.98193i	−0.0186286	+	0.276724i
$833$	−44.4786			−1.54109
$834$	−55.5442	+	3.01607i	−1.92334	+	0.104438i
$835$	−70.5913	−	29.2399i	−2.44291	−	1.01189i
$836$	−0.633319	−	5.81445i	−0.0219038	−	0.201097i
$837$	−14.7471	−	35.6026i	−0.509734	−	1.23061i
$838$	−32.6220	−	11.4828i	−1.12691	−	0.396668i
$839$	0.770390	−	0.770390i	0.0265968	−	0.0265968i	−0.693683	−	0.720280i	$-0.744013\pi$
$839$	0.770390	−	0.770390i	0.0265968	−	0.0265968i	0.720280	+	0.693683i	$0.244013\pi$
$840$	96.2307	+	69.0867i	3.32027	+	2.38372i
$841$	13.2345	+	13.2345i	0.456364	+	0.456364i
$842$	9.06596	+	18.9152i	0.312434	+	0.651862i
$843$	86.4723	−	35.8180i	2.97826	−	1.23364i
$844$	−4.63354	+	15.8622i	−0.159493	+	0.545999i
$845$	−1.24588	+	3.00782i	−0.0428596	+	0.103472i
$846$	18.7075	−	20.8558i	0.643177	−	0.717037i
$847$			19.3382i			0.664468i
$848$	−17.0549	+	11.9121i	−0.585669	+	0.409062i
$849$			59.3013i			2.03522i
$850$	−29.6554	−	26.6007i	−1.01717	−	0.912397i
$851$	13.3943	−	32.3367i	0.459150	−	1.10849i
$852$	−39.1030	+	21.4227i	−1.33965	+	0.733929i
$853$	−33.5712	+	13.9057i	−1.14946	+	0.476121i	−0.874351	−	0.485293i	$-0.838713\pi$
$853$	−33.5712	+	13.9057i	−1.14946	+	0.476121i	−0.275105	+	0.961414i	$0.588713\pi$
$854$	40.0291	−	19.1857i	1.36977	−	0.656522i
$855$	20.2324	+	20.2324i	0.691934	+	0.691934i
$856$	−2.74633	+	1.70442i	−0.0938677	+	0.0582557i
$857$	−3.94632	+	3.94632i	−0.134804	+	0.134804i	−0.771289	−	0.636485i	$-0.780388\pi$
$857$	−3.94632	+	3.94632i	−0.134804	+	0.134804i	0.636485	+	0.771289i	$0.280388\pi$
$858$	−3.76119	+	10.6853i	−0.128405	+	0.364790i
$859$	16.0975	+	38.8628i	0.549239	+	1.32598i	0.918046	+	0.396474i	$0.129766\pi$
$859$	16.0975	+	38.8628i	0.549239	+	1.32598i	−0.368807	+	0.929506i	$0.620234\pi$
$860$	13.8332	+	11.1157i	0.471709	+	0.379044i
$861$	95.5008	+	39.5577i	3.25466	+	1.34812i
$862$	−0.945105	−	17.4052i	−0.0321904	−	0.592822i
$863$	15.9544			0.543092			0.271546	−	0.962425i	$-0.412465\pi$
$863$	15.9544			0.543092			0.271546	+	0.962425i	$0.412465\pi$
$864$	−50.1120	−	64.0467i	−1.70484	−	2.17891i
$865$	−25.5167			−0.867594
$866$	2.13851	+	39.3831i	0.0726696	+	1.33829i
$867$	−24.8177	−	10.2798i	−0.842853	−	0.349121i
$868$	−13.3659	+	16.6334i	−0.453667	+	0.564575i
$869$	1.16765	+	2.81895i	0.0396098	+	0.0956265i
$870$	−34.1325	+	96.9683i	−1.15720	+	3.28753i
$871$	−5.48496	+	5.48496i	−0.185851	+	0.185851i
$872$	−7.95683	+	33.9892i	−0.269452	+	1.15102i
$873$	−28.5730	−	28.5730i	−0.967051	−	0.967051i
$874$	−7.01093	+	3.36030i	−0.237148	+	0.113664i
$875$	7.17338	−	2.97131i	0.242505	−	0.100449i
$876$	−21.2804	−	38.8433i	−0.718997	−	1.31239i
$877$	−18.1587	+	43.8389i	−0.613175	+	1.48034i	0.246319	+	0.969189i	$0.420779\pi$
$877$	−18.1587	+	43.8389i	−0.613175	+	1.48034i	−0.859494	+	0.511146i	$0.829221\pi$
$878$	24.4009	+	21.8875i	0.823492	+	0.738666i
$879$			64.4172i			2.17274i
$880$	27.1974	+	17.3718i	0.916825	+	0.585602i
$881$		−	31.0301i		−	1.04543i	−0.852507	−	0.522715i	$-0.824919\pi$
$881$		−	31.0301i		−	1.04543i	0.852507	−	0.522715i	$-0.175081\pi$
$882$	−62.1767	+	69.3169i	−2.09360	+	2.33402i
$883$	3.34496	−	8.07544i	0.112567	−	0.271760i	−0.857549	−	0.514402i	$-0.828014\pi$
$883$	3.34496	−	8.07544i	0.112567	−	0.271760i	0.970116	+	0.242642i	$0.0780139\pi$
$884$	9.65831	+	2.82132i	0.324844	+	0.0948911i
$885$	109.026	−	45.1602i	3.66488	−	1.51804i
$886$	24.3621	+	50.8290i	0.818459	+	1.70763i
$887$	−28.3586	−	28.3586i	−0.952187	−	0.952187i	0.0467206	−	0.998908i	$-0.485123\pi$
$887$	−28.3586	−	28.3586i	−0.952187	−	0.952187i	−0.998908	+	0.0467206i	$0.985123\pi$
$888$	−11.1290	−	67.7802i	−0.373466	−	2.27456i
$889$	−12.3251	+	12.3251i	−0.413371	+	0.413371i
$890$	−14.5758	−	5.13064i	−0.488583	−	0.171979i
$891$	−22.8776	−	55.2314i	−0.766428	−	1.85032i
$892$	−14.0210	+	1.52719i	−0.469457	+	0.0511341i
$893$	−2.90010	−	1.20126i	−0.0970482	−	0.0401987i
$894$	−13.3054	+	0.722486i	−0.444998	+	0.0241635i
$895$	56.1281			1.87615
$896$	−17.7701	+	41.3747i	−0.593657	+	1.38223i
$897$	15.0578			0.502765
$898$	44.3752	−	2.40959i	1.48082	−	0.0804089i
$899$	−17.1075	−	7.08615i	−0.570566	−	0.236336i
$900$	−82.9107	+	9.03078i	−2.76369	+	0.301026i
$901$	10.0129	+	24.1733i	0.333578	+	0.805328i
$902$	26.5627	+	9.34997i	0.884441	+	0.311320i
$903$	−24.7922	+	24.7922i	−0.825033	+	0.825033i
$904$	6.97728	+	42.4943i	0.232061	+	1.41334i
$905$	6.59008	+	6.59008i	0.219062	+	0.219062i
$906$	11.7295	+	24.4725i	0.389688	+	0.813045i
$907$	−12.7342	+	5.27469i	−0.422833	+	0.175143i	−0.583945	−	0.811793i	$-0.698492\pi$
$907$	−12.7342	+	5.27469i	−0.422833	+	0.175143i	0.161113	+	0.986936i	$0.448492\pi$
$908$	6.62974	+	1.93663i	0.220016	+	0.0642694i
$909$	−12.8085	+	30.9224i	−0.424830	+	1.02563i
$910$	−12.2361	+	13.6412i	−0.405621	+	0.452201i
$911$			4.51131i			0.149466i	0.997204	+	0.0747332i	$0.0238105\pi$
$911$			4.51131i			0.149466i	−0.997204	+	0.0747332i	$0.976189\pi$
$912$	−8.21292	+	12.8582i	−0.271957	+	0.425779i
$913$		−	0.292037i		−	0.00966501i
$914$	6.74274	+	6.04819i	0.223030	+	0.200056i
$915$	−31.7584	+	76.6714i	−1.04990	+	2.53468i
$916$	−16.5574	−	30.2224i	−0.547073	−	0.998577i
$917$	−55.0671	+	22.8095i	−1.81847	+	0.753237i
$918$	−92.2347	+	44.2075i	−3.04420	+	1.45907i
$919$	−24.8850	−	24.8850i	−0.820880	−	0.820880i	0.165355	−	0.986234i	$-0.447123\pi$
$919$	−24.8850	−	24.8850i	−0.820880	−	0.820880i	−0.986234	+	0.165355i	$0.947123\pi$
$920$	9.77798	−	41.7686i	0.322370	−	1.37707i
$921$	−23.3737	+	23.3737i	−0.770190	+	0.770190i
$922$	8.13112	−	23.1000i	0.267784	−	0.760759i
$923$	−2.63941	−	6.37211i	−0.0868774	−	0.209741i
$924$	−39.9389	+	49.7029i	−1.31389	+	1.63510i
$925$	−38.8660	−	16.0988i	−1.27790	−	0.529325i
$926$	−0.475414	−	8.75527i	−0.0156231	−	0.287716i
$927$	−53.1833			−1.74677
$928$	−38.7880	−	4.73465i	−1.27328	−	0.155423i
$929$	−38.4701			−1.26216			−0.631081	−	0.775717i	$-0.717388\pi$
$929$	−38.4701			−1.26216			−0.631081	+	0.775717i	$0.717388\pi$
$930$	−2.16301	−	39.8342i	−0.0709279	−	1.30622i
$931$	9.63886	+	3.99255i	0.315901	+	0.130850i
$932$	−26.6889	−	21.4460i	−0.874225	−	0.702487i
$933$	19.5134	+	47.1096i	0.638841	+	1.54230i
$934$	−4.52978	+	12.8688i	−0.148219	+	0.421081i
$935$	28.7013	−	28.7013i	0.938634	−	0.938634i
$936$	17.8982	−	11.1079i	0.585021	−	0.363073i
$937$	35.6278	+	35.6278i	1.16391	+	1.16391i	0.983612	+	0.180299i	$0.0577066\pi$
$937$	35.6278	+	35.6278i	1.16391	+	1.16391i	0.180299	+	0.983612i	$0.442293\pi$
$938$	−39.3723	+	18.8709i	−1.28555	+	0.616157i
$939$	−1.43129	+	0.592862i	−0.0467085	+	0.0193473i
$940$	15.1900	−	8.32189i	0.495444	−	0.271430i
$941$	−20.7403	+	50.0716i	−0.676116	+	1.63229i	0.0949118	+	0.995486i	$0.469743\pi$
$941$	−20.7403	+	50.0716i	−0.676116	+	1.63229i	−0.771027	+	0.636802i	$0.780257\pi$
$942$	−52.5412	−	47.1290i	−1.71188	−	1.53555i
$943$		−	37.4323i		−	1.21896i
$944$	25.6857	+	36.7751i	0.835999	+	1.19693i
$945$		−	186.277i		−	6.05958i
$946$	−6.37784	+	7.11025i	−0.207362	+	0.231174i
$947$	8.72985	−	21.0757i	0.283682	−	0.684869i	−0.716233	−	0.697861i	$-0.754135\pi$
$947$	8.72985	−	21.0757i	0.283682	−	0.684869i	0.999916	+	0.0129915i	$0.00413542\pi$
$948$	2.23178	−	7.64014i	0.0724849	−	0.248140i
$949$	6.32978	−	2.62188i	0.205473	−	0.0851099i
$950$	4.03879	+	8.42654i	0.131036	+	0.273393i
$951$	−63.8609	−	63.8609i	−2.07083	−	2.07083i
$952$	46.0067	+	33.0295i	1.49109	+	1.07049i
$953$	13.3752	−	13.3752i	0.433266	−	0.433266i	−0.456472	−	0.889738i	$-0.650887\pi$
$953$	13.3752	−	13.3752i	0.433266	−	0.433266i	0.889738	+	0.456472i	$0.150887\pi$
$954$	51.6694	+	18.1874i	1.67286	+	0.588840i
$955$	20.4222	+	49.3034i	0.660845	+	1.59542i
$956$	1.03677	+	9.51846i	0.0335315	+	0.307849i
$957$	−51.1194	−	21.1743i	−1.65245	−	0.684469i
$958$	−10.7078	+	0.581439i	−0.345955	+	0.0187854i
$959$	36.0430			1.16389
$960$	−26.9195	−	79.7650i	−0.868822	−	2.57440i
$961$	−23.8142			−0.768201
$962$	10.6097	−	0.576109i	0.342070	−	0.0185745i
$963$	7.86300	+	3.25696i	0.253382	+	0.104954i
$964$	−4.26535	−	39.1598i	−0.137378	−	1.26125i
$965$	9.07299	+	21.9041i	0.292070	+	0.705119i
$966$	79.9470	+	28.1411i	2.57225	+	0.905424i
$967$	−32.8939	+	32.8939i	−1.05780	+	1.05780i	−0.0595717	+	0.998224i	$0.518974\pi$
$967$	−32.8939	+	32.8939i	−1.05780	+	1.05780i	−0.998224	+	0.0595717i	$0.981026\pi$
$968$	8.01465	−	11.1636i	0.257600	−	0.358811i
$969$	13.5693	+	13.5693i	0.435907	+	0.435907i
$970$	−10.7971	−	22.5271i	−0.346674	−	0.723301i
$971$	−42.2994	+	17.5210i	−1.35745	+	0.562275i	−0.938357	−	0.345668i	$-0.887652\pi$
$971$	−42.2994	+	17.5210i	−1.35745	+	0.562275i	−0.419094	+	0.907943i	$0.637652\pi$
$972$	−19.5417	+	66.8978i	−0.626800	+	2.14575i
$973$	18.5347	−	44.7468i	0.594196	−	1.43452i
$974$	28.1085	−	31.3364i	0.900655	−	1.00408i
$975$		−	18.0982i		−	0.579605i
$976$	−31.0595	−	5.51437i	−0.994191	−	0.176511i
$977$			5.00732i			0.160198i	0.996787	+	0.0800991i	$0.0255237\pi$
$977$			5.00732i			0.160198i	−0.996787	+	0.0800991i	$0.974476\pi$
$978$	23.1142	+	20.7333i	0.739111	+	0.662978i
$979$	3.18283	−	7.68403i	0.101724	−	0.245583i
$980$	−50.4859	+	27.6589i	−1.61271	+	0.883530i
$981$	84.9202	−	35.1751i	2.71129	−	1.12305i
$982$	37.6394	−	18.0404i	1.20112	−	0.575691i
$983$	10.7378	+	10.7378i	0.342481	+	0.342481i	0.857299	−	0.514818i	$-0.172141\pi$
$983$	10.7378	+	10.7378i	0.342481	+	0.342481i	−0.514818	+	0.857299i	$0.672141\pi$
$984$	−38.7363	−	62.4159i	−1.23487	−	1.98975i
$985$	−42.5884	+	42.5884i	−1.35698	+	1.35698i
$986$	−16.3183	+	46.3593i	−0.519681	+	1.47638i
$987$	13.0956	+	31.6155i	0.416837	+	1.00633i
$988$	−1.83978	−	1.47836i	−0.0585312	−	0.0470330i
$989$	11.7301	+	4.85875i	0.372994	+	0.154499i
$990$	−4.60742	−	84.8507i	−0.146433	−	2.69673i
$991$	−28.1195			−0.893246			−0.446623	−	0.894722i	$-0.647373\pi$
$991$	−28.1195			−0.893246			−0.446623	+	0.894722i	$0.647373\pi$
$992$	14.6095	−	4.06274i	0.463853	−	0.128992i
$993$	−18.6778			−0.592721
$994$	−2.10492	−	38.7645i	−0.0667641	−	1.22954i
$995$	49.0200	+	20.3048i	1.55404	+	0.643704i
$996$	−0.477185	+	0.593843i	−0.0151202	+	0.0188166i
$997$	−12.9675	−	31.3063i	−0.410685	−	0.991481i	−0.984954	−	0.172814i	$-0.944714\pi$
$997$	−12.9675	−	31.3063i	−0.410685	−	0.991481i	0.574270	−	0.818666i	$-0.305286\pi$
$998$	−1.99666	+	5.67240i	−0.0632032	+	0.179557i
$999$	−76.3735	+	76.3735i	−2.41635	+	2.41635i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	416.2.bf.a.157.1	yes	192
32.21	even	8	inner	416.2.bf.a.53.1	✓	192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
416.2.bf.a.53.1	✓	192	32.21	even	8	inner
416.2.bf.a.157.1	yes	192	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bf (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41213 + 0.0766792i) q^{2} +(2.98623 + 1.23694i) q^{3} +(1.98824 - 0.216563i) q^{4} +(-1.24588 - 3.00782i) q^{5} +(-4.31180 - 1.51774i) q^{6} +(2.81433 - 2.81433i) q^{7} +(-2.79105 + 0.458272i) q^{8} +(5.26623 + 5.26623i) q^{9} +(1.98999 + 4.15191i) q^{10} +(-2.28952 + 0.948348i) q^{11} +(6.20521 + 1.81262i) q^{12} +(-0.382683 + 0.923880i) q^{13} +(-3.75841 + 4.19002i) q^{14} -10.5231i q^{15} +(3.90620 - 0.861157i) q^{16} -5.03098i q^{17} +(-7.84043 - 7.03281i) q^{18} +(-0.451597 + 1.09025i) q^{19} +(-3.12849 - 5.71046i) q^{20} +(11.8854 - 4.92309i) q^{21} +(3.16038 - 1.51475i) q^{22} +(-3.29411 - 3.29411i) q^{23} +(-8.90158 - 2.08385i) q^{24} +(-3.95924 + 3.95924i) q^{25} +(0.469558 - 1.33398i) q^{26} +(5.50136 + 13.2815i) q^{27} +(4.98609 - 6.20505i) q^{28} +(6.38189 + 2.64347i) q^{29} +(0.806905 + 14.8600i) q^{30} -2.68063 q^{31} +(-5.45004 + 1.51559i) q^{32} -8.01006 q^{33} +(0.385771 + 7.10441i) q^{34} +(-11.9713 - 4.95869i) q^{35} +(11.6110 + 9.33006i) q^{36} +(2.87519 + 6.94132i) q^{37} +(0.554115 - 1.57421i) q^{38} +(-2.28556 + 2.28556i) q^{39} +(4.85572 + 7.82404i) q^{40} +(5.68170 + 5.68170i) q^{41} +(-16.4063 + 7.86343i) q^{42} +(-2.51795 + 1.04297i) q^{43} +(-4.34673 + 2.38137i) q^{44} +(9.27879 - 22.4010i) q^{45} +(4.90431 + 4.39913i) q^{46} +2.66003i q^{47} +(12.7300 + 2.26011i) q^{48} -8.84095i q^{49} +(5.28738 - 5.89457i) q^{50} +(6.22300 - 15.0236i) q^{51} +(-0.560789 + 1.91977i) q^{52} +(-4.80489 + 1.99025i) q^{53} +(-8.78707 - 18.3334i) q^{54} +(5.70493 + 5.70493i) q^{55} +(-6.56523 + 9.14469i) q^{56} +(-2.69714 + 2.69714i) q^{57} +(-9.21478 - 3.24357i) q^{58} +(4.29152 + 10.3607i) q^{59} +(-2.27891 - 20.9225i) q^{60} +(-7.28600 - 3.01796i) q^{61} +(3.78540 - 0.205548i) q^{62} +29.6419 q^{63} +(7.57997 - 2.55812i) q^{64} +3.25564 q^{65} +(11.3113 - 0.614206i) q^{66} +(7.16645 + 2.96844i) q^{67} +(-1.08952 - 10.0028i) q^{68} +(-5.76236 - 13.9116i) q^{69} +(17.2854 + 6.08438i) q^{70} +(-4.87700 + 4.87700i) q^{71} +(-17.1117 - 12.2850i) q^{72} +(-4.84461 - 4.84461i) q^{73} +(-4.59241 - 9.58161i) q^{74} +(-16.7205 + 6.92587i) q^{75} +(-0.661775 + 2.26548i) q^{76} +(-3.77449 + 9.11243i) q^{77} +(3.05226 - 3.40277i) q^{78} -1.23125i q^{79} +(-7.45687 - 10.6763i) q^{80} +24.1236i q^{81} +(-8.45898 - 7.58765i) q^{82} +(-0.0450971 + 0.108874i) q^{83} +(22.5649 - 12.3622i) q^{84} +(-15.1323 + 6.26799i) q^{85} +(3.47571 - 1.66589i) q^{86} +(15.7880 + 15.7880i) q^{87} +(5.95556 - 3.69611i) q^{88} +(-2.37318 + 2.37318i) q^{89} +(-11.3852 + 32.3446i) q^{90} +(1.52311 + 3.67710i) q^{91} +(-7.26287 - 5.83610i) q^{92} +(-8.00496 - 3.31576i) q^{93} +(-0.203969 - 3.75632i) q^{94} +3.84192 q^{95} +(-18.1498 - 2.21545i) q^{96} -5.42571 q^{97} +(0.677918 + 12.4846i) q^{98} +(-17.0513 - 7.06289i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 16 q^{10} - 16 q^{12} - 40 q^{16} - 40 q^{18} - 8 q^{22} - 16 q^{23} + 24 q^{24} + 80 q^{30} - 48 q^{31} - 48 q^{35} + 80 q^{36} - 56 q^{38} - 64 q^{40} - 16 q^{43} - 80 q^{44} + 24 q^{50} + 32 q^{51}+ \cdots + 56 q^{98}+O(q^{100}) \) 192 * q - 16 * q^10 - 16 * q^12 - 40 * q^16 - 40 * q^18 - 8 * q^22 - 16 * q^23 + 24 * q^24 + 80 * q^30 - 48 * q^31 - 48 * q^35 + 80 * q^36 - 56 * q^38 - 64 * q^40 - 16 * q^43 - 80 * q^44 + 24 * q^50 + 32 * q^51 - 32 * q^53 - 24 * q^54 + 32 * q^55 + 16 * q^56 - 64 * q^58 - 56 * q^60 - 64 * q^61 + 24 * q^62 + 80 * q^63 + 72 * q^64 + 96 * q^66 + 80 * q^67 - 32 * q^68 - 64 * q^69 - 120 * q^72 - 32 * q^74 + 32 * q^75 + 64 * q^76 - 32 * q^77 - 56 * q^80 - 80 * q^82 - 80 * q^83 + 112 * q^84 - 112 * q^87 - 88 * q^88 - 120 * q^90 + 144 * q^92 + 40 * q^94 + 136 * q^96 + 56 * q^98

Introduction

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