LMFDB - Embedded newform 920.2.bb.a.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [920,2,Mod(11,920)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(920, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 0, 9]))

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

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

chi := DirichletCharacter("920.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 920 = 2^{3} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	920.bb (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.34623698596$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	920.11
Dual form			920.2.bb.a.251.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.844050 - 1.13472i) q^{2} +(0.217100 - 1.50996i) q^{3} +(-0.575160 + 1.91551i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.89662 + 1.02814i) q^{6} +(0.306327 + 0.353520i) q^{7} +(2.65903 - 0.964146i) q^{8} +(0.645619 + 0.189571i) q^{9} +(1.12955 + 0.850956i) q^{10} +(-2.09129 + 3.25412i) q^{11} +(2.76749 + 1.28433i) q^{12} +(-1.90925 - 1.65437i) q^{13} +(0.142590 - 0.645982i) q^{14} +(0.217100 + 1.50996i) q^{15} +(-3.33838 - 2.20345i) q^{16} +(4.27222 - 1.95106i) q^{17} +(-0.329826 - 0.892602i) q^{18} +(5.47716 + 2.50133i) q^{19} +(0.0121994 - 1.99996i) q^{20} +(0.600306 - 0.385793i) q^{21} +(5.45765 - 0.373612i) q^{22} +(-0.123410 - 4.79424i) q^{23} +(-0.878550 - 4.22435i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.265743 + 3.56283i) q^{26} +(2.32755 - 5.09661i) q^{27} +(-0.853359 + 0.383442i) q^{28} +(-1.80958 + 0.826407i) q^{29} +(1.53014 - 1.52083i) q^{30} +(7.13133 - 1.02533i) q^{31} +(0.317468 + 5.64794i) q^{32} +(4.45958 + 3.86425i) q^{33} +(-5.81986 - 3.20096i) q^{34} +(-0.393516 - 0.252898i) q^{35} +(-0.734460 + 1.12766i) q^{36} +(-5.33547 - 1.56664i) q^{37} +(-1.78469 - 8.32627i) q^{38} +(-2.91254 + 2.52373i) q^{39} +(-2.27969 + 1.67423i) q^{40} +(1.99867 - 0.586863i) q^{41} +(-0.944454 - 0.355548i) q^{42} +(10.6282 + 1.52810i) q^{43} +(-5.03047 - 5.87754i) q^{44} -0.672876 q^{45} +(-5.33594 + 4.18662i) q^{46} -10.1005i q^{47} +(-4.05190 + 4.56247i) q^{48} +(0.965064 - 6.71216i) q^{49} +(-1.32353 - 0.498256i) q^{50} +(-2.01853 - 6.87447i) q^{51} +(4.26710 - 2.70566i) q^{52} +(4.77172 + 5.50686i) q^{53} +(-7.74777 + 1.66069i) q^{54} +(1.08979 - 3.71149i) q^{55} +(1.15538 + 0.644675i) q^{56} +(4.96602 - 7.72727i) q^{57} +(2.46511 + 1.35583i) q^{58} +(-0.375623 + 0.433492i) q^{59} +(-3.01722 - 0.452613i) q^{60} +(1.08545 + 7.54950i) q^{61} +(-7.18265 - 7.22660i) q^{62} +(0.130753 + 0.286310i) q^{63} +(6.14085 - 5.12738i) q^{64} +(2.29800 + 1.04946i) q^{65} +(0.620715 - 8.32197i) q^{66} +(-6.46972 - 10.0671i) q^{67} +(1.28007 + 9.30565i) q^{68} +(-7.26593 - 0.854486i) q^{69} +(0.0451805 + 0.659987i) q^{70} +(-2.60712 - 4.05677i) q^{71} +(1.89949 - 0.118397i) q^{72} +(-3.37025 + 7.37983i) q^{73} +(2.72572 + 7.37656i) q^{74} +(-0.633712 - 1.38764i) q^{75} +(-7.94158 + 9.05290i) q^{76} +(-1.79101 + 0.257509i) q^{77} +(5.32205 + 1.17475i) q^{78} +(9.41665 - 10.8674i) q^{79} +(3.82394 + 1.17367i) q^{80} +(-5.49222 - 3.52963i) q^{81} +(-2.35290 - 1.77258i) q^{82} +(-1.24160 + 4.22849i) q^{83} +(0.393720 + 1.37179i) q^{84} +(-3.54948 + 3.07565i) q^{85} +(-7.23676 - 13.3498i) q^{86} +(0.854985 + 2.91181i) q^{87} +(-2.42336 + 10.6691i) q^{88} +(-16.3745 - 2.35430i) q^{89} +(0.567941 + 0.763523i) q^{90} -1.18174i q^{91} +(9.25442 + 2.52106i) q^{92} -10.9906i q^{93} +(-11.4612 + 8.52536i) q^{94} +(-5.96000 - 0.856919i) q^{95} +(8.59711 + 0.746802i) q^{96} +(3.37985 + 11.5107i) q^{97} +(-8.43096 + 4.57033i) q^{98} +(-1.96707 + 1.70447i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) $ 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/920\mathbb{Z}\right)^\times$.

$n$	$231$	$281$	$461$	$737$
$\chi(n)$	$-1$	$e\left(\frac{9}{22}\right)$	$-1$	$1$

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 $

$2$	−0.844050	−	1.13472i	−0.596833	−	0.802365i
$2$	−0.844050	−	1.13472i	−0.596833	−	0.802365i
$3$	0.217100	−	1.50996i	0.125343	−	0.871778i	−0.826006	−	0.563662i	$-0.809392\pi$
$3$	0.217100	−	1.50996i	0.125343	−	0.871778i	0.951349	−	0.308117i	$-0.0996987\pi$
$4$	−0.575160	+	1.91551i	−0.287580	+	0.957757i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$5$	−0.959493	+	0.281733i	−0.429098	+	0.125995i
$6$	−1.89662	+	1.02814i	−0.774293	+	0.419736i
$7$	0.306327	+	0.353520i	0.115781	+	0.133618i	0.810681	−	0.585488i	$-0.199097\pi$
$7$	0.306327	+	0.353520i	0.115781	+	0.133618i	−0.694900	+	0.719106i	$0.744552\pi$
$8$	2.65903	−	0.964146i	0.940108	−	0.340877i
$9$	0.645619	+	0.189571i	0.215206	+	0.0631903i
$10$	1.12955	+	0.850956i	0.357194	+	0.269096i
$11$	−2.09129	+	3.25412i	−0.630549	+	0.981153i	0.368131	+	0.929774i	$0.379998\pi$
$11$	−2.09129	+	3.25412i	−0.630549	+	0.981153i	−0.998679	+	0.0513787i	$0.983638\pi$
$12$	2.76749	+	1.28433i	0.798905	+	0.370754i
$13$	−1.90925	−	1.65437i	−0.529531	−	0.458841i	0.348593	−	0.937274i	$-0.386659\pi$
$13$	−1.90925	−	1.65437i	−0.529531	−	0.458841i	−0.878124	+	0.478433i	$0.841205\pi$
$14$	0.142590	−	0.645982i	0.0381087	−	0.172646i
$15$	0.217100	+	1.50996i	0.0560550	+	0.389871i
$16$	−3.33838	−	2.20345i	−0.834596	−	0.550863i
$17$	4.27222	−	1.95106i	1.03616	−	0.473200i	0.176629	−	0.984277i	$-0.443481\pi$
$17$	4.27222	−	1.95106i	1.03616	−	0.473200i	0.859535	+	0.511077i	$0.170753\pi$
$18$	−0.329826	−	0.892602i	−0.0777407	−	0.210388i
$19$	5.47716	+	2.50133i	1.25655	+	0.573845i	0.928681	−	0.370879i	$-0.120944\pi$
$19$	5.47716	+	2.50133i	1.25655	+	0.573845i	0.327865	+	0.944725i	$0.393671\pi$
$20$	0.0121994	−	1.99996i	0.00272787	−	0.447205i
$21$	0.600306	−	0.385793i	0.130997	−	0.0841870i
$22$	5.45765	−	0.373612i	1.16358	−	0.0796544i
$23$	−0.123410	−	4.79424i	−0.0257327	−	0.999669i
$23$	−0.123410	−	4.79424i	−0.0257327	−	0.999669i
$24$	−0.878550	−	4.22435i	−0.179333	−	0.862292i
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.265743	+	3.56283i	−0.0521165	+	0.698729i
$27$	2.32755	−	5.09661i	0.447936	−	0.980844i
$28$	−0.853359	+	0.383442i	−0.161270	+	0.0724638i
$29$	−1.80958	+	0.826407i	−0.336030	+	0.153460i	−0.576282	−	0.817251i	$-0.695497\pi$
$29$	−1.80958	+	0.826407i	−0.336030	+	0.153460i	0.240252	+	0.970711i	$0.422770\pi$
$30$	1.53014	−	1.52083i	0.279364	−	0.277665i
$31$	7.13133	−	1.02533i	1.28082	−	0.184155i	0.531898	−	0.846808i	$-0.321479\pi$
$31$	7.13133	−	1.02533i	1.28082	−	0.184155i	0.748926	+	0.662654i	$0.230570\pi$
$32$	0.317468	+	5.64794i	0.0561210	+	0.998424i
$33$	4.45958	+	3.86425i	0.776313	+	0.672679i
$34$	−5.81986	−	3.20096i	−0.998097	−	0.548961i
$35$	−0.393516	−	0.252898i	−0.0665164	−	0.0427475i
$36$	−0.734460	+	1.12766i	−0.122410	+	0.187943i
$37$	−5.33547	−	1.56664i	−0.877146	−	0.257553i	−0.187994	−	0.982170i	$-0.560199\pi$
$37$	−5.33547	−	1.56664i	−0.877146	−	0.257553i	−0.689152	+	0.724617i	$0.742017\pi$
$38$	−1.78469	−	8.32627i	−0.289515	−	1.35070i
$39$	−2.91254	+	2.52373i	−0.466380	+	0.404121i
$40$	−2.27969	+	1.67423i	−0.360450	+	0.264718i
$41$	1.99867	−	0.586863i	0.312140	−	0.0916526i	−0.121910	−	0.992541i	$-0.538902\pi$
$41$	1.99867	−	0.586863i	0.312140	−	0.0916526i	0.434051	+	0.900888i	$0.357084\pi$
$42$	−0.944454	−	0.355548i	−0.145732	−	0.0548622i
$43$	10.6282	+	1.52810i	1.62078	+	0.233033i	0.892107	−	0.451825i	$-0.149227\pi$
$43$	10.6282	+	1.52810i	1.62078	+	0.233033i	0.728676	+	0.684858i	$0.240136\pi$
$44$	−5.03047	−	5.87754i	−0.758372	−	0.886072i
$45$	−0.672876			−0.100306
$46$	−5.33594	+	4.18662i	−0.786741	+	0.617283i
$47$		−	10.1005i		−	1.47332i	−0.676266	−	0.736658i	$-0.736403\pi$
$47$		−	10.1005i		−	1.47332i	0.676266	−	0.736658i	$-0.263597\pi$
$48$	−4.05190	+	4.56247i	−0.584841	+	0.658536i
$49$	0.965064	−	6.71216i	0.137866	−	0.958881i
$50$	−1.32353	−	0.498256i	−0.187176	−	0.0704640i
$51$	−2.01853	−	6.87447i	−0.282650	−	0.962618i
$52$	4.26710	−	2.70566i	0.591740	−	0.375208i
$53$	4.77172	+	5.50686i	0.655446	+	0.756425i	0.982026	−	0.188745i	$-0.0604419\pi$
$53$	4.77172	+	5.50686i	0.655446	+	0.756425i	−0.326580	+	0.945169i	$0.605896\pi$
$54$	−7.74777	+	1.66069i	−1.05434	+	0.225992i
$55$	1.08979	−	3.71149i	0.146947	−	0.500457i
$56$	1.15538	+	0.644675i	0.154394	+	0.0861483i
$57$	4.96602	−	7.72727i	0.657765	−	1.02350i
$58$	2.46511	+	1.35583i	0.323685	+	0.178029i
$59$	−0.375623	+	0.433492i	−0.0489020	+	0.0564359i	−0.779674	−	0.626186i	$-0.784615\pi$
$59$	−0.375623	+	0.433492i	−0.0489020	+	0.0564359i	0.730772	+	0.682622i	$0.239160\pi$
$60$	−3.01722	−	0.452613i	−0.389522	−	0.0584321i
$61$	1.08545	+	7.54950i	0.138978	+	0.966614i	0.933295	+	0.359111i	$0.116920\pi$
$61$	1.08545	+	7.54950i	0.138978	+	0.966614i	−0.794317	+	0.607504i	$0.792171\pi$
$62$	−7.18265	−	7.22660i	−0.912198	−	0.917779i
$63$	0.130753	+	0.286310i	0.0164734	+	0.0360717i
$64$	6.14085	−	5.12738i	0.767606	−	0.640922i
$65$	2.29800	+	1.04946i	0.285032	+	0.130170i
$66$	0.620715	−	8.32197i	0.0764048	−	1.02436i
$67$	−6.46972	−	10.0671i	−0.790402	−	1.22989i	−0.969266	−	0.246016i	$-0.920878\pi$
$67$	−6.46972	−	10.0671i	−0.790402	−	1.22989i	0.178863	−	0.983874i	$-0.442758\pi$
$68$	1.28007	+	9.30565i	0.155231	+	1.12848i
$69$	−7.26593	−	0.854486i	−0.874715	−	0.102868i
$70$	0.0451805	+	0.659987i	0.00540010	+	0.0788836i
$71$	−2.60712	−	4.05677i	−0.309409	−	0.481449i	0.651372	−	0.758759i	$-0.274194\pi$
$71$	−2.60712	−	4.05677i	−0.309409	−	0.481449i	−0.960781	+	0.277309i	$0.910557\pi$
$72$	1.89949	−	0.118397i	0.223857	−	0.0139532i
$73$	−3.37025	+	7.37983i	−0.394458	+	0.863743i	0.603344	+	0.797481i	$0.293835\pi$
$73$	−3.37025	+	7.37983i	−0.394458	+	0.863743i	−0.997802	+	0.0662623i	$0.978893\pi$
$74$	2.72572	+	7.37656i	0.316858	+	0.857508i
$75$	−0.633712	−	1.38764i	−0.0731748	−	0.160230i
$76$	−7.94158	+	9.05290i	−0.910962	+	1.03844i
$77$	−1.79101	+	0.257509i	−0.204105	+	0.0293459i
$78$	5.32205	+	1.17475i	0.602604	+	0.133015i
$79$	9.41665	−	10.8674i	1.05946	−	1.22268i	0.0854047	−	0.996346i	$-0.472782\pi$
$79$	9.41665	−	10.8674i	1.05946	−	1.22268i	0.974051	−	0.226330i	$-0.0726729\pi$
$80$	3.82394	+	1.17367i	0.427529	+	0.131220i
$81$	−5.49222	−	3.52963i	−0.610246	−	0.392182i
$82$	−2.35290	−	1.77258i	−0.259835	−	0.195749i
$83$	−1.24160	+	4.22849i	−0.136283	+	0.464137i	−0.999147	−	0.0412991i	$-0.986850\pi$
$83$	−1.24160	+	4.22849i	−0.136283	+	0.464137i	0.862864	+	0.505437i	$0.168669\pi$
$84$	0.393720	+	1.37179i	0.0429584	+	0.149674i
$85$	−3.54948	+	3.07565i	−0.384996	+	0.333601i
$86$	−7.23676	−	13.3498i	−0.780359	−	1.43954i
$87$	0.854985	+	2.91181i	0.0916640	+	0.312179i
$88$	−2.42336	+	10.6691i	−0.258331	+	1.13733i
$89$	−16.3745	−	2.35430i	−1.73569	−	0.249555i	−0.799406	−	0.600791i	$-0.794852\pi$
$89$	−16.3745	−	2.35430i	−1.73569	−	0.249555i	−0.936287	+	0.351236i	$0.885762\pi$
$90$	0.567941	+	0.763523i	0.0598662	+	0.0804823i
$91$		−	1.18174i		−	0.123880i
$92$	9.25442	+	2.52106i	0.964840	+	0.262839i
$93$		−	10.9906i		−	1.13968i
$94$	−11.4612	+	8.52536i	−1.18214	+	0.879324i
$95$	−5.96000	−	0.856919i	−0.611483	−	0.0879180i
$96$	8.59711	+	0.746802i	0.877439	+	0.0762202i
$97$	3.37985	+	11.5107i	0.343172	+	1.16874i	0.932599	+	0.360914i	$0.117535\pi$
$97$	3.37985	+	11.5107i	0.343172	+	1.16874i	−0.589427	+	0.807821i	$0.700647\pi$
$98$	−8.43096	+	4.57033i	−0.851656	+	0.461673i
$99$	−1.96707	+	1.70447i	−0.197697	+	0.171306i
$100$	0.551749	+	1.92239i	0.0551749	+	0.192239i
$101$	−0.212248	+	0.722852i	−0.0211195	+	0.0719264i	−0.969379	−	0.245571i	$-0.921024\pi$
$101$	−0.212248	+	0.722852i	−0.0211195	+	0.0719264i	0.948259	+	0.317498i	$0.102843\pi$
$102$	−6.09683	+	8.09284i	−0.603676	+	0.801311i
$103$	15.2576	+	9.80543i	1.50337	+	0.966158i	0.994435	+	0.105354i	$0.0335976\pi$
$103$	15.2576	+	9.80543i	1.50337	+	0.966158i	0.508937	+	0.860804i	$0.330039\pi$
$104$	−6.67181	−	2.55823i	−0.654224	−	0.250855i
$105$	−0.467299	+	0.539292i	−0.0456037	+	0.0526295i
$106$	2.22115	−	10.0626i	0.215737	−	0.977366i
$107$	7.75217	−	1.11459i	0.749431	−	0.107752i	0.242993	−	0.970028i	$-0.421871\pi$
$107$	7.75217	−	1.11459i	0.749431	−	0.107752i	0.506438	+	0.862276i	$0.330962\pi$
$108$	8.42392	+	7.38981i	0.810592	+	0.711085i
$109$	0.584421	+	1.27970i	0.0559774	+	0.122573i	0.935554	−	0.353184i	$-0.114901\pi$
$109$	0.584421	+	1.27970i	0.0559774	+	0.122573i	−0.879576	+	0.475758i	$0.842174\pi$
$110$	−5.13132	+	1.89608i	−0.489252	+	0.180784i
$111$	−3.52389	+	7.71625i	−0.334473	+	0.732394i
$112$	−0.243671	−	1.85516i	−0.0230248	−	0.175296i
$113$	−3.66713	−	5.70616i	−0.344974	−	0.536790i	0.624803	−	0.780782i	$-0.285179\pi$
$113$	−3.66713	−	5.70616i	−0.344974	−	0.536790i	−0.969777	+	0.243992i	$0.921543\pi$
$114$	−12.9598	+	0.887186i	−1.21380	+	0.0830925i
$115$	1.46911	+	4.56527i	0.136995	+	0.425714i
$116$	−0.542196	−	3.94159i	−0.0503416	−	0.365967i
$117$	−0.919028	−	1.43003i	−0.0849641	−	0.132207i
$118$	0.808935	+	0.0603365i	0.0744685	+	0.00555443i
$119$	1.99843	+	0.912653i	0.183196	+	0.0836627i
$120$	2.03310	+	3.80572i	0.185596	+	0.347413i
$121$	−1.64620	−	3.60467i	−0.149654	−	0.327697i
$122$	7.65036	−	7.60384i	0.692631	−	0.688419i
$123$	−0.452230	−	3.14533i	−0.0407762	−	0.283605i
$124$	−2.13762	+	14.2499i	−0.191964	+	1.27968i
$125$	−0.654861	+	0.755750i	−0.0585725	+	0.0675963i
$126$	0.214518	−	0.390028i	0.0191108	−	0.0347464i
$127$	−6.02594	+	9.37654i	−0.534715	+	0.832034i	−0.998547	−	0.0538900i	$-0.982838\pi$
$127$	−6.02594	+	9.37654i	−0.534715	+	0.832034i	0.463831	+	0.885923i	$0.346474\pi$
$128$	−11.0013	−	2.64035i	−0.972386	−	0.233376i
$129$	4.61476	−	15.7164i	0.406307	−	1.38375i
$130$	−0.748787	−	3.49338i	−0.0656730	−	0.306390i
$131$	−9.91002	−	11.4368i	−0.865842	−	0.999235i	−0.999966	−	0.00827051i	$-0.997367\pi$
$131$	−9.91002	−	11.4368i	−0.865842	−	0.999235i	0.134124	−	0.990965i	$-0.457178\pi$
$132$	−9.96699	+	6.31982i	−0.867515	+	0.550070i
$133$	0.793528	+	2.70251i	0.0688076	+	0.234337i
$134$	−5.96251	+	15.8384i	−0.515083	+	1.36823i
$135$	−0.797382	+	5.54591i	−0.0686277	+	0.477316i
$136$	9.47883	−	9.30695i	0.812803	−	0.798064i
$137$		−	15.8701i		−	1.35587i	−0.735121	−	0.677936i	$-0.762875\pi$
$137$		−	15.8701i		−	1.35587i	0.735121	−	0.677936i	$-0.237125\pi$
$138$	5.16321	+	8.96599i	0.439521	+	0.763236i
$139$	12.7571			1.08205			0.541023	−	0.841008i	$-0.318037\pi$
$139$	12.7571			1.08205			0.541023	+	0.841008i	$0.318037\pi$
$140$	0.710764	−	0.608329i	0.0600705	−	0.0514132i
$141$	−15.2515	−	2.19283i	−1.28440	−	0.184669i
$142$	−2.40273	+	6.38246i	−0.201633	+	0.535604i
$143$	9.37633	−	2.75314i	0.784088	−	0.230229i
$144$	−1.73761	−	2.05545i	−0.144801	−	0.171288i
$145$	1.50345	−	1.30275i	0.124855	−	0.108187i
$146$	11.2187	−	2.40466i	0.928464	−	0.199011i
$147$	−9.92561	−	2.91442i	−0.818651	−	0.240378i
$148$	6.06966	−	9.31910i	0.498923	−	0.766025i
$149$	−3.99715	−	2.56881i	−0.327459	−	0.210445i	0.366573	−	0.930389i	$-0.380531\pi$
$149$	−3.99715	−	2.56881i	−0.327459	−	0.210445i	−0.694032	+	0.719944i	$0.744167\pi$
$150$	−1.03969	+	1.89032i	−0.0848902	+	0.154344i
$151$	3.59097	+	3.11159i	0.292229	+	0.253218i	0.788620	−	0.614882i	$-0.210796\pi$
$151$	3.59097	+	3.11159i	0.292229	+	0.253218i	−0.496391	+	0.868099i	$0.665342\pi$
$152$	16.9756	+	1.37034i	1.37690	+	0.111149i
$153$	3.12809	−	0.449751i	0.252891	−	0.0363602i
$154$	1.80390	+	1.81494i	0.145363	+	0.146252i
$155$	−6.55359	+	2.99292i	−0.526397	+	0.240397i
$156$	−3.15907	−	7.03057i	−0.252928	−	0.562896i
$157$	4.47461	−	9.79804i	0.357113	−	0.781969i	−0.642760	−	0.766067i	$-0.722211\pi$
$157$	4.47461	−	9.79804i	0.357113	−	0.781969i	0.999874	−	0.0159015i	$-0.00506180\pi$
$158$	−20.2795	−	1.51260i	−1.61335	−	0.120336i
$159$	9.35109	−	6.00958i	0.741590	−	0.476591i
$160$	−1.89582	−	5.32972i	−0.149877	−	0.421351i
$161$	1.65706	−	1.51223i	0.130594	−	0.119181i
$162$	0.630574	+	9.21129i	0.0495426	+	0.723708i
$163$	−5.22432	+	3.35747i	−0.409200	+	0.262977i	−0.729008	−	0.684506i	$-0.760018\pi$
$163$	−5.22432	+	3.35747i	−0.409200	+	0.262977i	0.319807	+	0.947483i	$0.396382\pi$
$164$	−0.0254120	+	4.16602i	−0.00198434	+	0.325312i
$165$	−5.36762	−	2.45131i	−0.417869	−	0.190834i
$166$	5.84611	−	2.16020i	0.453746	−	0.167664i
$167$	23.1563	−	10.5751i	1.79189	−	0.818327i	0.824146	−	0.566378i	$-0.191656\pi$
$167$	23.1563	−	10.5751i	1.79189	−	0.818327i	0.967741	−	0.251949i	$-0.0810715\pi$
$168$	1.22427	−	1.60462i	0.0944544	−	0.123799i
$169$	−0.941812	−	6.55045i	−0.0724471	−	0.503881i
$170$	6.48593	+	1.43166i	0.497448	+	0.109803i
$171$	3.06198	+	2.65322i	0.234155	+	0.202897i
$172$	−9.04001	+	19.4795i	−0.689294	+	1.48530i
$173$	−5.57230	+	8.67067i	−0.423654	+	0.659219i	−0.985820	−	0.167806i	$-0.946332\pi$
$173$	−5.57230	+	8.67067i	−0.423654	+	0.659219i	0.562166	+	0.827024i	$0.309968\pi$
$174$	2.58243	−	3.42788i	0.195773	−	0.259867i
$175$	0.448826	+	0.131787i	0.0339280	+	0.00996217i
$176$	14.1518	−	6.25542i	1.06673	−	0.471520i
$177$	0.573010	+	0.661289i	0.0430701	+	0.0497055i
$178$	11.1494	+	20.5675i	0.835685	+	1.54160i
$179$	10.7453	−	3.15510i	0.803141	−	0.235824i	0.145700	−	0.989329i	$-0.453457\pi$
$179$	10.7453	−	3.15510i	0.803141	−	0.235824i	0.657442	+	0.753505i	$0.271639\pi$
$180$	0.387011	−	1.28890i	0.0288461	−	0.0960691i
$181$	−1.12160	+	7.80090i	−0.0833679	+	0.579836i	0.904727	+	0.425991i	$0.140075\pi$
$181$	−1.12160	+	7.80090i	−0.0833679	+	0.579836i	−0.988095	+	0.153845i	$0.950834\pi$
$182$	−1.34094	+	0.997445i	−0.0993968	+	0.0739355i
$183$	11.6351			0.860093
$184$	−4.95050	−	12.6290i	−0.364956	−	0.931025i
$185$	5.56072			0.408832
$186$	−12.4713	+	9.27665i	−0.914437	+	0.680197i
$187$	−2.58549	+	17.9825i	−0.189070	+	1.31501i
$188$	19.3477	+	5.80942i	1.41108	+	0.423696i
$189$	2.51474	−	0.738395i	0.182921	−	0.0537104i
$190$	4.05818	+	7.48619i	0.294411	+	0.543105i
$191$	13.1826	+	15.2135i	0.953856	+	1.10081i	0.994820	+	0.101648i	$0.0324116\pi$
$191$	13.1826	+	15.2135i	0.953856	+	1.10081i	−0.0409641	+	0.999161i	$0.513043\pi$
$192$	−6.40898	−	10.3856i	−0.462528	−	0.749517i
$193$	24.4447	+	7.17761i	1.75957	+	0.516656i	0.992212	−	0.124565i	$-0.0397534\pi$
$193$	24.4447	+	7.17761i	1.75957	+	0.516656i	0.767357	+	0.641220i	$0.221572\pi$
$194$	10.2086	−	13.5508i	0.732937	−	0.972890i
$195$	2.08355	−	3.24206i	0.149206	−	0.232169i
$196$	12.3022	+	5.70916i	0.878727	+	0.407797i
$197$	−0.191808	−	0.166202i	−0.0136657	−	0.0118414i	0.648001	−	0.761639i	$-0.275605\pi$
$197$	−0.191808	−	0.166202i	−0.0136657	−	0.0118414i	−0.661667	+	0.749798i	$0.730151\pi$
$198$	3.59439	+	0.793401i	0.255442	+	0.0563846i
$199$	2.81457	+	19.5758i	0.199519	+	1.38769i	0.805682	+	0.592348i	$0.201799\pi$
$199$	2.81457	+	19.5758i	0.199519	+	1.38769i	−0.606163	+	0.795341i	$0.707292\pi$
$200$	1.71566	−	2.24867i	0.121315	−	0.159005i
$201$	−16.6055	+	7.58348i	−1.17126	+	0.534898i
$202$	0.999379	−	0.369281i	0.0703161	−	0.0259825i
$203$	−0.846473	−	0.386571i	−0.0594108	−	0.0271320i
$204$	14.3291	+	0.0874048i	1.00324	+	0.00611956i
$205$	−1.75237	+	1.12618i	−0.122391	+	0.0786560i
$206$	−1.75175	−	25.5893i	−0.122050	−	1.78289i
$207$	0.829174	−	3.11865i	0.0576315	−	0.216761i
$208$	2.72847	+	9.72988i	0.189185	+	0.674646i
$209$	−19.5940	+	12.5923i	−1.35534	+	0.871026i
$210$	1.00637	+	0.0750624i	0.0694459	+	0.00517980i
$211$	7.54838	−	16.5286i	0.519652	−	1.13788i	−0.449919	−	0.893069i	$-0.648547\pi$
$211$	7.54838	−	16.5286i	0.519652	−	1.13788i	0.969571	−	0.244810i	$-0.0787255\pi$
$212$	−13.2930	+	5.97297i	−0.912964	+	0.410225i
$213$	−6.69158	+	3.05594i	−0.458499	+	0.209390i
$214$	−7.80797	−	7.85574i	−0.533742	−	0.537007i
$215$	−10.6282	+	1.52810i	−0.724836	+	0.104216i
$216$	1.27513	−	15.7961i	0.0867615	−	1.07479i
$217$	2.54699	+	2.20698i	0.172901	+	0.149820i
$218$	0.958819	−	1.74328i	0.0649394	−	0.118070i
$219$	10.4116	+	6.69112i	0.703550	+	0.452144i
$220$	6.48260	+	4.22221i	0.437057	+	0.284661i
$221$	−11.3845	−	3.34279i	−0.765805	−	0.224861i
$222$	11.7301	−	2.51428i	0.787272	−	0.168748i
$223$	−16.0107	+	13.8733i	−1.07215	+	0.929027i	−0.997672	−	0.0681952i	$-0.978276\pi$
$223$	−16.0107	+	13.8733i	−1.07215	+	0.929027i	−0.0744824	+	0.997222i	$0.523730\pi$
$224$	−1.89941	+	1.84235i	−0.126910	+	0.123097i
$225$	0.645619	−	0.189571i	0.0430413	−	0.0126381i
$226$	−3.37963	+	8.97743i	−0.224810	+	0.597170i
$227$	−18.4068	−	2.64649i	−1.22170	−	0.175654i	−0.498868	−	0.866678i	$-0.666251\pi$
$227$	−18.4068	−	2.64649i	−1.22170	−	0.175654i	−0.722832	+	0.691024i	$0.757160\pi$
$228$	11.9454	+	13.9569i	0.791106	+	0.924318i
$229$	14.6206			0.966156			0.483078	−	0.875577i	$-0.339519\pi$
$229$	14.6206			0.966156			0.483078	+	0.875577i	$0.339519\pi$
$230$	3.94029	−	5.52034i	0.259815	−	0.364000i
$231$			2.76027i			0.181613i
$232$	−4.01494	+	3.94213i	−0.263594	+	0.258814i
$233$	−3.09702	+	21.5403i	−0.202893	+	1.41115i	0.592751	+	0.805386i	$0.298042\pi$
$233$	−3.09702	+	21.5403i	−0.202893	+	1.41115i	−0.795644	+	0.605765i	$0.792867\pi$
$234$	−0.846978	+	2.24986i	−0.0553687	+	0.147078i
$235$	2.84565	+	9.69140i	0.185630	+	0.632197i
$236$	−0.614317	−	0.968839i	−0.0399886	−	0.0630660i
$237$	−14.3650	−	16.5781i	−0.933108	−	1.07686i
$238$	−0.651173	−	3.03797i	−0.0422093	−	0.196923i
$239$	−1.65270	+	5.62857i	−0.106904	+	0.364082i	−0.995518	−	0.0945745i	$-0.969851\pi$
$239$	−1.65270	+	5.62857i	−0.106904	+	0.364082i	0.888614	+	0.458656i	$0.151669\pi$
$240$	2.60237	−	5.51921i	0.167982	−	0.356263i
$241$	−4.80197	+	7.47201i	−0.309322	+	0.481315i	−0.960758	−	0.277389i	$-0.910531\pi$
$241$	−4.80197	+	7.47201i	−0.309322	+	0.481315i	0.651435	+	0.758704i	$0.274167\pi$
$242$	−2.70080	+	4.91049i	−0.173614	+	0.315658i
$243$	4.48546	−	5.17649i	0.287742	−	0.332072i
$244$	−15.0855	−	2.26297i	−0.965749	−	0.144872i
$245$	0.965064	+	6.71216i	0.0616557	+	0.428824i
$246$	−3.18735	+	3.16797i	−0.203218	+	0.201982i
$247$	−6.31912	−	13.8369i	−0.402076	−	0.880424i
$248$	17.9738	−	9.60202i	1.14134	−	0.609729i
$249$	6.11532	+	2.79277i	0.387543	+	0.176985i
$250$	1.41030	+	0.105191i	0.0891950	+	0.00665283i
$251$	4.77269	+	7.42645i	0.301249	+	0.468753i	0.958570	−	0.284858i	$-0.0919465\pi$
$251$	4.77269	+	7.42645i	0.301249	+	0.468753i	−0.657320	+	0.753611i	$0.728310\pi$
$252$	−0.623634	+	0.0857858i	−0.0392853	+	0.00540400i
$253$	15.8591	+	9.62458i	0.997054	+	0.605092i
$254$	15.7259	−	1.07654i	0.986731	−	0.0675482i
$255$	3.87352	+	6.02732i	0.242569	+	0.377445i
$256$	6.28959	+	14.7119i	0.393100	+	0.919496i
$257$	−2.37493	+	5.20038i	−0.148144	+	0.324391i	−0.969127	−	0.246562i	$-0.920699\pi$
$257$	−2.37493	+	5.20038i	−0.148144	+	0.324391i	0.820983	+	0.570953i	$0.193426\pi$
$258$	−21.7288	+	8.02901i	−1.35277	+	0.499864i
$259$	−1.08056	−	2.36610i	−0.0671427	−	0.147022i
$260$	−3.33198	+	3.79825i	−0.206641	+	0.235557i
$261$	−1.32496	+	0.190501i	−0.0820130	+	0.0117917i
$262$	−4.61293	+	20.8983i	−0.284988	+	1.29110i
$263$	−2.31794	+	2.67504i	−0.142930	+	0.164950i	−0.822701	−	0.568474i	$-0.807534\pi$
$263$	−2.31794	+	2.67504i	−0.142930	+	0.164950i	0.679771	+	0.733425i	$0.262079\pi$
$264$	15.5838	+	5.97545i	0.959119	+	0.367764i
$265$	−6.12989	−	3.93944i	−0.376556	−	0.241998i
$266$	2.39680	−	3.18148i	0.146957	−	0.195069i
$267$	−7.10981	+	24.2138i	−0.435113	+	1.48186i
$268$	23.0048	−	6.60266i	1.40524	−	0.403321i
$269$	−8.34347	+	7.22966i	−0.508710	+	0.440800i	−0.871013	−	0.491261i	$-0.836536\pi$
$269$	−8.34347	+	7.22966i	−0.508710	+	0.440800i	0.362302	+	0.932061i	$0.381991\pi$
$270$	6.96606	−	3.77622i	0.423941	−	0.229814i
$271$	4.05322	+	13.8040i	0.246216	+	0.838533i	0.986150	+	0.165854i	$0.0530382\pi$
$271$	4.05322	+	13.8040i	0.246216	+	0.838533i	−0.739935	+	0.672679i	$0.765144\pi$
$272$	−18.5613	−	2.90026i	−1.12545	−	0.175854i
$273$	−1.78438	−	0.256555i	−0.107996	−	0.0155274i
$274$	−18.0080	+	13.3951i	−1.08790	+	0.809229i
$275$			3.86817i			0.233260i
$276$	5.81585	−	13.4265i	0.350073	−	0.808181i
$277$			2.27504i			0.136694i	0.997662	+	0.0683470i	$0.0217725\pi$
$277$			2.27504i			0.136694i	−0.997662	+	0.0683470i	$0.978228\pi$
$278$	−10.7676	−	14.4757i	−0.645801	−	0.868196i
$279$	4.79850	+	0.689920i	0.287278	+	0.0413044i
$280$	−1.29020	−	0.293054i	−0.0771042	−	0.0175134i
$281$	−4.05884	−	13.8232i	−0.242130	−	0.824620i	−0.987453	−	0.157916i	$-0.949523\pi$
$281$	−4.05884	−	13.8232i	−0.242130	−	0.824620i	0.745322	−	0.666704i	$-0.232296\pi$
$282$	10.3847	+	19.1569i	0.618403	+	1.14078i
$283$	−4.15165	+	3.59742i	−0.246790	+	0.213845i	−0.769468	−	0.638686i	$-0.779478\pi$
$283$	−4.15165	+	3.59742i	−0.246790	+	0.213845i	0.522678	+	0.852530i	$0.324933\pi$
$284$	9.27030	−	2.66069i	0.550091	−	0.157883i
$285$	−2.58783	+	8.81335i	−0.153290	+	0.522058i
$286$	−11.0381	−	8.31568i	−0.652698	−	0.491717i
$287$	0.819714	+	0.526798i	0.0483862	+	0.0310959i
$288$	−0.865722	+	3.70660i	−0.0510131	+	0.218414i
$289$	3.31257	−	3.82291i	0.194857	−	0.224877i
$290$	−2.74724	−	0.606406i	−0.161323	−	0.0356094i
$291$	18.1145	−	2.60448i	1.06189	−	0.152677i
$292$	−12.1977	−	10.7003i	−0.713818	−	0.626190i
$293$	−11.8890	−	26.0333i	−0.694563	−	1.52088i	−0.846442	−	0.532482i	$-0.821260\pi$
$293$	−11.8890	−	26.0333i	−0.694563	−	1.52088i	0.151879	−	0.988399i	$-0.451468\pi$
$294$	5.07067	+	13.7227i	0.295727	+	0.800322i
$295$	0.238279	−	0.521758i	0.0138731	−	0.0303779i
$296$	−15.6976	+	0.978445i	−0.912406	+	0.0568709i
$297$	11.7174	+	18.2326i	0.679912	+	1.05796i
$298$	0.458922	+	6.70384i	0.0265846	+	0.388343i
$299$	−7.69585	+	9.35758i	−0.445063	+	0.541163i
$300$	3.02252	−	0.415771i	0.174505	−	0.0240046i
$301$	2.71548	+	4.22537i	0.156518	+	0.243546i
$302$	0.499816	−	6.70107i	0.0287612	−	0.385603i
$303$	1.04540	+	0.477419i	0.0600567	+	0.0274270i
$304$	−12.7733	−	20.4191i	−0.732598	−	1.17111i
$305$	−3.16843	−	6.93788i	−0.181424	−	0.397262i
$306$	−3.15060	−	3.16988i	−0.180108	−	0.181210i
$307$	−3.34143	−	23.2402i	−0.190706	−	1.32639i	−0.830146	−	0.557546i	$-0.811743\pi$
$307$	−3.34143	−	23.2402i	−0.190706	−	1.32639i	0.639441	−	0.768840i	$-0.279166\pi$
$308$	0.536857	−	3.57882i	0.0305903	−	0.203922i
$309$	18.1183	−	20.9096i	1.03071	−	1.18951i
$310$	8.92767	+	4.91028i	0.507058	+	0.278885i
$311$	−1.87192	+	2.91276i	−0.106147	+	0.165168i	−0.890264	−	0.455446i	$-0.849480\pi$
$311$	−1.87192	+	2.91276i	−0.106147	+	0.165168i	0.784117	+	0.620613i	$0.213116\pi$
$312$	−5.31129	+	9.51880i	−0.300692	+	0.538896i
$313$	3.32112	−	11.3107i	0.187721	−	0.639318i	−0.810819	−	0.585297i	$-0.800978\pi$
$313$	3.32112	−	11.3107i	0.187721	−	0.639318i	0.998540	−	0.0540211i	$-0.0172038\pi$
$314$	−14.8948	+	3.19262i	−0.840562	+	0.180170i
$315$	−0.206120	−	0.237875i	−0.0116135	−	0.0134027i
$316$	15.4005	+	24.2882i	0.866349	+	1.36632i
$317$	−2.95441	−	10.0618i	−0.165936	−	0.565126i	−0.999911	−	0.0133242i	$-0.995759\pi$
$317$	−2.95441	−	10.0618i	−0.165936	−	0.565126i	0.833975	−	0.551802i	$-0.186060\pi$
$318$	−14.7120	−	5.53845i	−0.825006	−	0.310581i
$319$	1.09514	−	7.61683i	0.0613158	−	0.426461i
$320$	−4.44755	+	6.64976i	−0.248626	+	0.371733i
$321$		−	11.9475i		−	0.666843i
$322$	−3.11459	−	0.603889i	−0.173569	−	0.0336534i
$323$	28.2798			1.57353
$324$	9.91996	−	8.49031i	0.551109	−	0.471684i
$325$	−2.50059	−	0.359530i	−0.138708	−	0.0199431i
$326$	8.21936	+	3.09425i	0.455228	+	0.171375i
$327$	2.05918	−	0.604631i	0.113873	−	0.0334362i
$328$	4.74870	−	3.48750i	0.262203	−	0.192565i
$329$	3.57074	−	3.09406i	0.196861	−	0.170581i
$330$	1.74900	+	8.15975i	0.0962792	+	0.449179i
$331$	−15.9163	−	4.67346i	−0.874841	−	0.256877i	−0.186668	−	0.982423i	$-0.559769\pi$
$331$	−15.9163	−	4.67346i	−0.874841	−	0.256877i	−0.688173	+	0.725546i	$0.741587\pi$
$332$	−7.38562	−	4.81036i	−0.405338	−	0.264003i
$333$	−3.14769	−	2.02290i	−0.172493	−	0.110854i
$334$	−31.5448	−	17.3499i	−1.72605	−	0.949342i
$335$	9.04388	+	7.83657i	0.494120	+	0.428157i
$336$	−2.85413	−	0.0348206i	−0.155705	−	0.00189962i
$337$	13.2017	−	1.89811i	0.719140	−	0.103397i	0.226977	−	0.973900i	$-0.427116\pi$
$337$	13.2017	−	1.89811i	0.719140	−	0.103397i	0.492162	+	0.870503i	$0.336207\pi$
$338$	−6.63796	+	6.59759i	−0.361057	+	0.358862i
$339$	−9.41223	+	4.29842i	−0.511202	+	0.233458i
$340$	−3.84992	−	8.56807i	−0.208791	−	0.464669i
$341$	−11.5772	+	25.3504i	−0.626938	+	1.37280i
$342$	0.426188	−	5.71393i	0.0230456	−	0.308974i
$343$	5.42312	−	3.48523i	0.292821	−	0.188185i
$344$	29.7339	−	6.18385i	1.60315	−	0.333411i
$345$	7.21234	−	1.22718i	0.388300	−	0.0660689i
$346$	14.5420	−	0.995499i	0.781785	−	0.0535184i
$347$	−13.4560	+	8.64765i	−0.722356	+	0.464230i	−0.849456	−	0.527660i	$-0.823070\pi$
$347$	−13.4560	+	8.64765i	−0.722356	+	0.464230i	0.127100	+	0.991890i	$0.459433\pi$
$348$	−6.06937	−	0.0370220i	−0.325352	−	0.00198459i
$349$	−15.5077	−	7.08215i	−0.830110	−	0.379099i	−0.0454058	−	0.998969i	$-0.514458\pi$
$349$	−15.5077	−	7.08215i	−0.830110	−	0.379099i	−0.784705	+	0.619870i	$0.787185\pi$
$350$	−0.229290	−	0.620524i	−0.0122561	−	0.0331684i
$351$	−12.8756	+	5.88008i	−0.687247	+	0.313855i
$352$	−19.0430	−	10.7784i	−1.01499	−	0.574492i
$353$	4.65702	+	32.3903i	0.247868	+	1.72396i	0.610490	+	0.792024i	$0.290973\pi$
$353$	4.65702	+	32.3903i	0.247868	+	1.72396i	−0.362622	+	0.931936i	$0.618118\pi$
$354$	0.266726	−	1.20836i	0.0141763	−	0.0642238i
$355$	3.64444	+	3.15793i	0.193427	+	0.167605i
$356$	13.9276	−	30.0115i	0.738164	−	1.59060i
$357$	1.81193	−	2.81942i	0.0958976	−	0.149220i
$358$	−12.6497	−	9.52980i	−0.668558	−	0.503665i
$359$	−12.2185	−	3.58769i	−0.644870	−	0.189351i	−0.0570863	−	0.998369i	$-0.518181\pi$
$359$	−12.2185	−	3.58769i	−0.644870	−	0.189351i	−0.587783	+	0.809018i	$0.699999\pi$
$360$	−1.78919	+	0.648750i	−0.0942988	+	0.0341921i
$361$	11.3002	+	13.0412i	0.594749	+	0.686377i
$362$	9.79849	−	5.31165i	0.514997	−	0.279174i
$363$	−5.80031	+	1.70312i	−0.304437	+	0.0893909i
$364$	2.26363	+	0.679688i	0.118647	+	0.0356253i
$365$	1.15460	−	8.03040i	0.0604344	−	0.420330i
$366$	−9.82063	−	13.2026i	−0.513332	−	0.690109i
$367$	−6.21044			−0.324182			−0.162091	−	0.986776i	$-0.551824\pi$
$367$	−6.21044			−0.324182			−0.162091	+	0.986776i	$0.551824\pi$
$368$	−10.1519	+	16.2769i	−0.529204	+	0.848494i
$369$	1.40163			0.0729661
$370$	−4.69352	−	6.30983i	−0.244005	−	0.328033i
$371$	−0.485078	+	3.37379i	−0.0251840	+	0.175159i
$372$	21.0527	+	6.32138i	1.09153	+	0.327748i
$373$	−29.2191	+	8.57951i	−1.51291	+	0.444230i	−0.929769	−	0.368142i	$-0.879994\pi$
$373$	−29.2191	+	8.57951i	−1.51291	+	0.444230i	−0.583139	+	0.812372i	$0.698176\pi$
$374$	22.5873	−	12.2443i	1.16796	−	0.633139i
$375$	0.998985	+	1.15289i	0.0515873	+	0.0595350i
$376$	−9.73839	−	26.8576i	−0.502219	−	1.38508i
$377$	4.82212	+	1.41590i	0.248352	+	0.0729227i
$378$	−2.96044	−	2.23028i	−0.152268	−	0.114713i
$379$	−4.19474	+	6.52714i	−0.215469	+	0.335277i	−0.932116	−	0.362159i	$-0.882040\pi$
$379$	−4.19474	+	6.52714i	−0.215469	+	0.335277i	0.716647	+	0.697436i	$0.245676\pi$
$380$	5.06939	−	10.9236i	0.260054	−	0.560369i
$381$	12.8500	+	11.1346i	0.658326	+	0.570443i
$382$	6.13624	−	27.7994i	0.313958	−	1.42234i
$383$	−3.41705	−	23.7661i	−0.174603	−	1.21439i	−0.869004	−	0.494804i	$-0.835240\pi$
$383$	−3.41705	−	23.7661i	−0.174603	−	1.21439i	0.694401	−	0.719588i	$-0.255669\pi$
$384$	−6.37522	+	16.0383i	−0.325334	+	0.818453i
$385$	1.64592	−	0.751665i	0.0838837	−	0.0383084i
$386$	−12.4880	−	33.7961i	−0.635622	−	1.72017i
$387$	6.57208	+	3.00137i	0.334078	+	0.152568i
$388$	−23.9929	−	0.146352i	−1.21805	−	0.00742990i
$389$	19.4476	−	12.4982i	0.986033	−	0.633685i	0.0549484	−	0.998489i	$-0.482501\pi$
$389$	19.4476	−	12.4982i	0.986033	−	0.633685i	0.931084	+	0.364805i	$0.118864\pi$
$390$	−5.43744	+	0.372229i	−0.275335	+	0.0188485i
$391$	−9.88107	−	20.2413i	−0.499707	−	1.02364i
$392$	−3.90537	−	18.7783i	−0.197251	−	0.948447i
$393$	−19.4206	+	12.4808i	−0.979639	+	0.629575i
$394$	−0.0266971	+	0.357930i	−0.00134498	+	0.0180323i
$395$	−5.97351	+	13.0802i	−0.300560	+	0.658134i
$396$	−2.13356	−	4.74828i	−0.107215	−	0.238610i
$397$	−10.2214	+	4.66794i	−0.512995	+	0.234277i	−0.655055	−	0.755581i	$-0.727355\pi$
$397$	−10.2214	+	4.66794i	−0.512995	+	0.234277i	0.142060	+	0.989858i	$0.454627\pi$
$398$	19.8373	−	19.7166i	0.994353	−	0.988306i
$399$	4.25297	−	0.611484i	0.212915	−	0.0306125i
$400$	−3.99970	−	0.0487967i	−0.199985	−	0.00243983i
$401$	−2.86041	−	2.47856i	−0.142842	−	0.123774i	0.580509	−	0.814254i	$-0.302854\pi$
$401$	−2.86041	−	2.47856i	−0.142842	−	0.123774i	−0.723351	+	0.690480i	$0.757399\pi$
$402$	22.6210	+	12.4417i	1.12823	+	0.620536i
$403$	−15.3118	−	9.84028i	−0.762734	−	0.490179i
$404$	−1.26255	−	0.822320i	−0.0628145	−	0.0409119i
$405$	6.26416	+	1.83932i	0.311268	+	0.0913967i
$406$	0.275817	+	1.28679i	0.0136886	+	0.0638624i
$407$	16.2560	−	14.0859i	0.805782	−	0.698214i
$408$	−11.9953	−	16.3332i	−0.593856	−	0.808616i
$409$	−34.9008	+	10.2478i	−1.72573	+	0.506721i	−0.986081	−	0.166266i	$-0.946829\pi$
$409$	−34.9008	+	10.2478i	−1.72573	+	0.506721i	−0.739654	+	0.672988i	$0.765011\pi$
$410$	2.75699	+	1.03789i	0.136158	+	0.0512578i
$411$	−23.9632	−	3.44539i	−1.18202	−	0.169949i
$412$	−27.5580	+	23.5864i	−1.35768	+	1.16202i
$413$	−0.268312			−0.0132027
$414$	−4.23865	+	1.69142i	−0.208318	+	0.0831288i
$415$		−	4.40701i		−	0.216332i
$416$	8.73768	−	11.3085i	0.428400	−	0.554447i
$417$	2.76957	−	19.2628i	0.135627	−	0.943304i
$418$	30.8270	+	11.6051i	1.50780	+	0.567623i
$419$	5.12184	+	17.4434i	0.250218	+	0.852165i	0.984807	+	0.173652i	$0.0555569\pi$
$419$	5.12184	+	17.4434i	0.250218	+	0.852165i	−0.734589	+	0.678513i	$0.762625\pi$
$420$	−0.764249	−	1.20530i	−0.0372915	−	0.0588124i
$421$	22.1093	+	25.5154i	1.07754	+	1.24355i	0.968369	+	0.249524i	$0.0802741\pi$
$421$	22.1093	+	25.5154i	1.07754	+	1.24355i	0.109171	+	0.994023i	$0.465180\pi$
$422$	−25.1265	+	5.38573i	−1.22314	+	0.262173i
$423$	1.91477	−	6.52110i	0.0930992	−	0.317067i
$424$	17.9975	+	10.0422i	0.874038	+	0.487695i
$425$	2.53920	−	3.95107i	0.123169	−	0.191655i
$426$	9.11565	+	5.01367i	0.441655	+	0.242913i
$427$	−2.33639	+	2.69634i	−0.113066	+	0.130485i
$428$	−2.32372	+	15.4905i	−0.112321	+	0.748760i
$429$	−2.12154	−	14.7556i	−0.102429	−	0.712408i
$430$	10.7047	+	10.7702i	0.516225	+	0.519384i
$431$	12.8691	+	28.1794i	0.619882	+	1.35735i	0.915605	+	0.402079i	$0.131712\pi$
$431$	12.8691	+	28.1794i	0.619882	+	1.35735i	−0.295723	+	0.955274i	$0.595560\pi$
$432$	−19.0004	+	11.8858i	−0.914156	+	0.571856i
$433$	−15.9013	−	7.26188i	−0.764168	−	0.348984i	−0.00509298	−	0.999987i	$-0.501621\pi$
$433$	−15.9013	−	7.26188i	−0.764168	−	0.348984i	−0.759075	+	0.651003i	$0.774348\pi$
$434$	0.354508	−	4.75291i	0.0170169	−	0.228147i
$435$	−1.64070	−	2.55299i	−0.0786657	−	0.122406i
$436$	−2.78742	+	0.383432i	−0.133493	+	0.0183631i
$437$	11.3161	−	26.5675i	0.541321	−	1.27090i
$438$	−1.19538	−	17.4618i	−0.0571174	−	0.834359i
$439$	−0.559741	−	0.870973i	−0.0267150	−	0.0415693i	0.827639	−	0.561260i	$-0.189683\pi$
$439$	−0.559741	−	0.870973i	−0.0267150	−	0.0415693i	−0.854354	+	0.519691i	$0.826047\pi$
$440$	−0.680631	−	10.9197i	−0.0324478	−	0.520574i
$441$	1.89550	−	4.15056i	0.0902617	−	0.197646i
$442$	5.81597	+	15.7397i	0.276637	+	0.748659i
$443$	−0.133268	−	0.291817i	−0.00633176	−	0.0138646i	0.906440	−	0.422335i	$-0.138790\pi$
$443$	−0.133268	−	0.291817i	−0.00633176	−	0.0138646i	−0.912771	+	0.408471i	$0.866062\pi$
$444$	−12.7538	−	11.1881i	−0.605268	−	0.530966i
$445$	16.3745	−	2.35430i	0.776226	−	0.111604i
$446$	29.2561	+	6.45779i	1.38532	+	0.305785i
$447$	−4.74660	+	5.47787i	−0.224506	+	0.259094i
$448$	3.69373	+	0.600258i	0.174513	+	0.0283595i
$449$	11.1854	+	7.18840i	0.527870	+	0.339242i	0.777278	−	0.629157i	$-0.216600\pi$
$449$	11.1854	+	7.18840i	0.527870	+	0.339242i	−0.249408	+	0.968398i	$0.580236\pi$
$450$	−0.760044	−	0.572587i	−0.0358288	−	0.0269920i
$451$	−2.27009	+	7.73121i	−0.106894	+	0.364049i
$452$	13.0394	−	3.74248i	0.613322	−	0.176031i
$453$	5.47799	−	4.74671i	0.257379	−	0.223020i
$454$	12.5332	+	23.1202i	0.588213	+	1.08509i
$455$	0.332934	+	1.13387i	0.0156082	+	0.0531566i
$456$	5.75456	−	25.3350i	0.269482	−	1.18642i
$457$	−18.0559	−	2.59605i	−0.844620	−	0.121438i	−0.293598	−	0.955929i	$-0.594853\pi$
$457$	−18.0559	−	2.59605i	−0.844620	−	0.121438i	−0.551022	+	0.834491i	$0.685762\pi$
$458$	−12.3405	−	16.5902i	−0.576634	−	0.775210i
$459$		−	26.3150i		−	1.22828i
$460$	−9.58981	+	0.188328i	−0.447127	+	0.00878085i
$461$		−	19.7442i		−	0.919581i	−0.888027	−	0.459790i	$-0.847925\pi$
$461$		−	19.7442i		−	0.919581i	0.888027	−	0.459790i	$-0.152075\pi$
$462$	3.13212	−	2.32981i	0.145720	−	0.108392i
$463$	−27.7288	−	3.98681i	−1.28867	−	0.185283i	−0.536301	−	0.844026i	$-0.680179\pi$
$463$	−27.7288	−	3.98681i	−1.28867	−	0.185283i	−0.752367	+	0.658744i	$0.771088\pi$
$464$	7.86201	+	1.22846i	0.364985	+	0.0570298i
$465$	3.09642	+	10.5455i	0.143593	+	0.489034i
$466$	27.0561	−	14.6668i	1.25335	−	0.679427i
$467$	−25.0533	+	21.7088i	−1.15933	+	1.00456i	−0.159478	+	0.987201i	$0.550981\pi$
$467$	−25.0533	+	21.7088i	−1.15933	+	1.00456i	−0.999849	+	0.0173616i	$0.994473\pi$
$468$	3.26784	−	0.937911i	0.151056	−	0.0433549i
$469$	1.57707	−	5.37099i	0.0728221	−	0.248009i
$470$	8.59511	−	11.4090i	0.396463	−	0.526259i
$471$	−13.8233	−	8.88366i	−0.636942	−	0.409338i
$472$	−0.580842	+	1.51482i	−0.0267354	+	0.0697254i
$473$	−27.1993	+	31.3896i	−1.25062	+	1.44330i
$474$	−6.68666	+	30.2930i	−0.307128	+	1.39140i
$475$	5.96000	−	0.856919i	0.273464	−	0.0393181i
$476$	−2.89761	+	3.30310i	−0.132812	+	0.151397i
$477$	2.03677	+	4.45991i	0.0932574	+	0.204205i
$478$	7.78179	−	2.87545i	0.355931	−	0.131520i
$479$	8.80309	−	19.2761i	0.402223	−	0.880747i	−0.594817	−	0.803862i	$-0.702775\pi$
$479$	8.80309	−	19.2761i	0.402223	−	0.880747i	0.997040	−	0.0768850i	$-0.0244974\pi$
$480$	−8.45926	+	1.70553i	−0.386111	+	0.0778466i
$481$	7.59494	+	11.8180i	0.346300	+	0.538853i
$482$	12.5317	−	0.857878i	0.570804	−	0.0390753i
$483$	−1.92367	−	2.83040i	−0.0875300	−	0.128788i
$484$	7.85162	−	1.08005i	0.356892	−	0.0490932i
$485$	−6.48588	−	10.0922i	−0.294509	−	0.458265i
$486$	−9.65979	−	0.720500i	−0.438177	−	0.0326826i
$487$	−20.4715	−	9.34902i	−0.927652	−	0.423644i	−0.106473	−	0.994316i	$-0.533956\pi$
$487$	−20.4715	−	9.34902i	−0.927652	−	0.423644i	−0.821179	+	0.570671i	$0.806683\pi$
$488$	10.1651	+	19.0278i	0.460151	+	0.861347i
$489$	3.93545	+	8.61744i	0.177967	+	0.389694i
$490$	6.80184	−	6.76047i	0.307276	−	0.305407i
$491$	−0.364964	−	2.53838i	−0.0164706	−	0.114556i	0.979928	−	0.199354i	$-0.0638844\pi$
$491$	−0.364964	−	2.53838i	−0.0164706	−	0.114556i	−0.996398	+	0.0847985i	$0.972975\pi$
$492$	6.28503	+	0.942815i	0.283351	+	0.0425054i
$493$	−6.11854	+	7.06117i	−0.275565	+	0.318019i
$494$	−10.3673	+	18.8495i	−0.466449	+	0.848078i
$495$	1.40718	−	2.18962i	0.0632480	−	0.0984159i
$496$	−26.0664	−	12.2906i	−1.17041	−	0.551864i
$497$	0.635515	−	2.16437i	0.0285068	−	0.0970851i
$498$	−1.99263	−	9.29639i	−0.0892920	−	0.416581i
$499$	12.4414	+	14.3581i	0.556951	+	0.642756i	0.962489	−	0.271322i	$-0.0874609\pi$
$499$	12.4414	+	14.3581i	0.556951	+	0.642756i	−0.405537	+	0.914079i	$0.632915\pi$
$500$	−1.07100	−	1.68907i	−0.0478965	−	0.0755376i
$501$	−10.9408	−	37.2610i	−0.488800	−	1.66470i
$502$	4.39852	−	11.6839i	0.196316	−	0.521480i
$503$	1.56696	−	10.8985i	0.0698674	−	0.485938i	−0.924604	−	0.380930i	$-0.875604\pi$
$503$	1.56696	−	10.8985i	0.0698674	−	0.485938i	0.994471	−	0.105008i	$-0.0334869\pi$
$504$	0.623721	+	0.635240i	0.0277827	+	0.0282959i
$505$		−	0.753368i		−	0.0335244i
$506$	−2.46472	−	26.1192i	−0.109570	−	1.16114i
$507$	−10.0954			−0.448353
$508$	−14.4950	−	16.9358i	−0.643112	−	0.751403i
$509$	−32.1680	−	4.62506i	−1.42582	−	0.205002i	−0.614184	−	0.789163i	$-0.710515\pi$
$509$	−32.1680	−	4.62506i	−1.42582	−	0.205002i	−0.811638	+	0.584160i	$0.801424\pi$
$510$	3.56985	−	9.48270i	0.158075	−	0.419901i
$511$	−3.64131	+	1.06919i	−0.161082	+	0.0472980i
$512$	11.3851	−	19.5545i	0.503157	−	0.864195i
$513$	25.4967	−	22.0930i	1.12571	−	0.975429i
$514$	7.90552	−	1.69450i	0.348697	−	0.0747414i
$515$	−17.4020	−	5.10970i	−0.766825	−	0.225160i
$516$	27.4508	+	17.8791i	1.20845	+	0.787083i
$517$	32.8683	+	21.1232i	1.44555	+	0.928997i
$518$	−1.77280	+	3.22323i	−0.0778924	+	0.141621i
$519$	11.8827	+	10.2964i	0.521591	+	0.451961i
$520$	7.12229	+	0.574940i	0.312333	+	0.0252128i
$521$	−16.0502	+	2.30767i	−0.703173	+	0.101101i	−0.484621	−	0.874724i	$-0.661042\pi$
$521$	−16.0502	+	2.30767i	−0.703173	+	0.101101i	−0.218552	+	0.975825i	$0.570133\pi$
$522$	1.33450	+	1.34266i	0.0584094	+	0.0587667i
$523$	27.3375	−	12.4846i	1.19539	−	0.545915i	0.284542	−	0.958664i	$-0.408158\pi$
$523$	27.3375	−	12.4846i	1.19539	−	0.545915i	0.910845	+	0.412748i	$0.135431\pi$
$524$	27.6071	−	12.4048i	1.20602	−	0.541906i
$525$	0.296434	−	0.649100i	0.0129374	−	0.0283290i
$526$	4.99187	+	0.372331i	0.217656	+	0.0162344i
$527$	28.4661	−	18.2940i	1.24000	−	0.796901i
$528$	−6.37309	−	22.7268i	−0.277353	−	0.989057i
$529$	−22.9695	+	1.18331i	−0.998676	+	0.0514484i
$530$	0.703786	+	10.2808i	0.0305705	+	0.446568i
$531$	−0.324687	+	0.208664i	−0.0140902	+	0.00905524i
$532$	−5.63310	−	0.0343608i	−0.244226	−	0.00148973i
$533$	−4.78686	−	2.18608i	−0.207342	−	0.0946898i
$534$	33.4768	−	12.3700i	1.44868	−	0.535304i
$535$	−7.12414	+	3.25348i	−0.308003	+	0.140660i
$536$	−26.9093	−	20.5309i	−1.16230	−	0.886799i
$537$	−2.43129	−	16.9100i	−0.104918	−	0.729720i
$538$	15.2459	+	3.36527i	0.657298	+	0.145087i
$539$	19.8239	+	17.1775i	0.853877	+	0.739889i
$540$	−10.1646	−	4.71718i	−0.437417	−	0.202995i
$541$	−17.6848	+	27.5180i	−0.760327	+	1.18309i	0.217984	+	0.975952i	$0.430052\pi$
$541$	−17.6848	+	27.5180i	−0.760327	+	1.18309i	−0.978311	+	0.207140i	$0.933584\pi$
$542$	12.2425	−	16.2505i	0.525860	−	0.698019i
$543$	11.5356	+	3.38715i	0.495039	+	0.145357i
$544$	12.3757	+	23.5098i	0.530605	+	1.00797i
$545$	−0.921282	−	1.06322i	−0.0394634	−	0.0455432i
$546$	1.21499	+	2.24131i	0.0519967	+	0.0959192i
$547$	11.8887	−	3.49083i	0.508323	−	0.149257i	−0.0175070	−	0.999847i	$-0.505573\pi$
$547$	11.8887	−	3.49083i	0.508323	−	0.149257i	0.525830	+	0.850590i	$0.323755\pi$
$548$	30.3993	+	9.12782i	1.29859	+	0.389921i
$549$	−0.730376	+	5.07987i	−0.0311717	+	0.216804i
$550$	4.38928	−	3.26493i	0.187159	−	0.139217i
$551$	−11.9785			−0.510300
$552$	−20.1441	+	4.73331i	−0.857392	+	0.201463i
$553$	6.72641			0.286036
$554$	2.58152	−	1.92025i	0.109678	−	0.0815835i
$555$	1.20723	−	8.39648i	0.0512442	−	0.356411i
$556$	−7.33739	+	24.4364i	−0.311175	+	1.03634i
$557$	8.33297	−	2.44678i	0.353079	−	0.103673i	−0.100383	−	0.994949i	$-0.532007\pi$
$557$	8.33297	−	2.44678i	0.353079	−	0.103673i	0.453462	+	0.891275i	$0.350189\pi$
$558$	−3.26731	−	6.02726i	−0.138316	−	0.255154i
$559$	−17.7638	−	20.5005i	−0.751329	−	0.867080i
$560$	0.756460	+	1.71136i	0.0319663	+	0.0723183i
$561$	26.5916	+	7.80801i	1.12270	+	0.329654i
$562$	−12.2595	+	16.2731i	−0.517135	+	0.686438i
$563$	−1.25584	+	1.95413i	−0.0529275	+	0.0823568i	−0.866709	−	0.498814i	$-0.833769\pi$
$563$	−1.25584	+	1.95413i	−0.0529275	+	0.0823568i	0.813781	+	0.581171i	$0.197405\pi$
$564$	12.9724	−	27.9531i	0.546237	−	1.17704i
$565$	5.12619	+	4.44187i	0.215661	+	0.186871i
$566$	7.58625	+	1.67454i	0.318874	+	0.0703860i
$567$	−0.434617	−	3.02283i	−0.0182522	−	0.126947i
$568$	−10.8437	−	8.27340i	−0.454993	−	0.347144i
$569$	−39.7879	+	18.1705i	−1.66800	+	0.761748i	−0.668153	+	0.744024i	$0.732915\pi$
$569$	−39.7879	+	18.1705i	−1.66800	+	0.761748i	−0.999843	+	0.0177243i	$0.994358\pi$
$570$	12.1849	−	4.50245i	0.510370	−	0.188587i
$571$	−22.4410	−	10.2485i	−0.939127	−	0.428885i	−0.113777	−	0.993506i	$-0.536295\pi$
$571$	−22.4410	−	10.2485i	−0.939127	−	0.428885i	−0.825350	+	0.564621i	$0.809022\pi$
$572$	−0.119215	+	19.5440i	−0.00498461	+	0.817175i
$573$	25.8337	−	16.6023i	1.07922	−	0.693573i
$574$	−0.0941133	−	1.37479i	−0.00392821	−	0.0573825i
$575$	−2.69578	−	3.96645i	−0.112422	−	0.165413i
$576$	4.93665	−	2.14621i	0.205694	−	0.0894254i
$577$	23.6442	−	15.1952i	0.984319	−	0.632584i	0.0536942	−	0.998557i	$-0.482900\pi$
$577$	23.6442	−	15.1952i	0.984319	−	0.632584i	0.930625	+	0.365974i	$0.119264\pi$
$578$	−7.13390	−	0.532100i	−0.296731	−	0.0221324i
$579$	16.1449	−	35.3524i	0.670959	−	1.46919i
$580$	1.63071	+	3.62917i	0.0677114	+	0.150693i
$581$	−1.87519	+	0.856371i	−0.0777960	+	0.0355283i
$582$	−18.2449	−	18.3565i	−0.756276	−	0.760903i
$583$	−27.8990	+	4.01127i	−1.15546	+	0.166130i
$584$	−1.84637	+	22.8726i	−0.0764032	+	0.946474i
$585$	1.28469	+	1.11319i	0.0531153	+	0.0460247i
$586$	−19.5055	+	35.4640i	−0.805764	+	1.46501i
$587$	−28.5973	−	18.3784i	−1.18034	−	0.758557i	−0.204889	−	0.978785i	$-0.565683\pi$
$587$	−28.5973	−	18.3784i	−1.18034	−	0.758557i	−0.975448	+	0.220228i	$0.929320\pi$
$588$	11.2914	−	17.3364i	0.465651	−	0.714940i
$589$	41.6241	+	12.2219i	1.71509	+	0.503596i
$590$	−0.793166	+	0.170011i	−0.0326541	+	0.00699924i
$591$	−0.292601	+	0.253540i	−0.0120360	+	0.0104292i
$592$	14.3598	+	16.9865i	0.590185	+	0.698140i
$593$	−26.4795	+	7.77508i	−1.08738	+	0.319284i	−0.775828	−	0.630944i	$-0.782668\pi$
$593$	−26.4795	+	7.77508i	−1.08738	+	0.319284i	−0.311554	+	0.950228i	$0.600850\pi$
$594$	10.7988	−	28.6851i	0.443079	−	1.17697i
$595$	−2.17460	−	0.312661i	−0.0891501	−	0.0128178i
$596$	7.21960	−	6.17912i	0.295726	−	0.253107i
$597$	30.1697			1.23476
$598$	17.1139	+	0.834347i	0.699838	+	0.0341190i
$599$		−	1.74992i		−	0.0714996i	−0.999361	−	0.0357498i	$-0.988618\pi$
$599$		−	1.74992i		−	0.0714996i	0.999361	−	0.0357498i	$-0.0113819\pi$
$600$	−3.02294	−	3.07877i	−0.123411	−	0.125690i
$601$	3.76836	−	26.2095i	0.153715	−	1.06911i	−0.756208	−	0.654331i	$-0.772950\pi$
$601$	3.76836	−	26.2095i	0.153715	−	1.06911i	0.909923	−	0.414778i	$-0.136141\pi$
$602$	2.50259	−	6.64773i	0.101998	−	0.270941i
$603$	−2.26855	−	7.72598i	−0.0923826	−	0.314626i
$604$	−8.02568	+	5.08888i	−0.326560	+	0.207064i
$605$	2.59507	+	2.99487i	0.105504	+	0.121759i
$606$	−0.340636	−	1.58920i	−0.0138374	−	0.0645567i
$607$	−0.707810	+	2.41058i	−0.0287291	+	0.0978424i	−0.972610	−	0.232445i	$-0.925327\pi$
$607$	−0.707810	+	2.41058i	−0.0287291	+	0.0978424i	0.943880	+	0.330287i	$0.107146\pi$
$608$	−12.3886	+	31.7288i	−0.502422	+	1.28677i
$609$	−0.767478	+	1.19422i	−0.0310998	+	0.0483922i
$610$	−5.19822	+	9.45118i	−0.210470	+	0.382667i
$611$	−16.7101	+	19.2845i	−0.676017	+	0.780166i
$612$	−0.937646	+	6.25057i	−0.0379021	+	0.252664i
$613$	−0.707669	−	4.92195i	−0.0285825	−	0.198796i	0.970527	−	0.240993i	$-0.0774732\pi$
$613$	−0.707669	−	4.92195i	−0.0285825	−	0.198796i	−0.999109	+	0.0421977i	$0.986564\pi$
$614$	−23.5506	+	23.4074i	−0.950427	+	0.944647i
$615$	1.32005	+	2.89052i	0.0532297	+	0.116557i
$616$	−4.51408	+	2.41152i	−0.181877	+	0.0971629i
$617$	20.7994	+	9.49876i	0.837351	+	0.382406i	0.787473	−	0.616350i	$-0.211389\pi$
$617$	20.7994	+	9.49876i	0.837351	+	0.382406i	0.0498788	+	0.998755i	$0.484116\pi$
$618$	−39.0192	−	2.91035i	−1.56958	−	0.117071i
$619$	5.16682	+	8.03973i	0.207672	+	0.323144i	0.929428	−	0.369004i	$-0.120301\pi$
$619$	5.16682	+	8.03973i	0.207672	+	0.323144i	−0.721756	+	0.692148i	$0.756665\pi$
$620$	−1.96362	−	14.2749i	−0.0788610	−	0.573294i
$621$	−24.7217	−	10.5298i	−0.992046	−	0.422548i
$622$	4.88515	−	0.334421i	0.195877	−	0.0134090i
$623$	−4.18365	−	6.50989i	−0.167615	−	0.260813i
$624$	15.2841	−	2.00754i	0.611854	−	0.0803657i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	−15.6376	+	5.77826i	−0.625004	+	0.230946i
$627$	14.7600	+	32.3200i	0.589459	+	1.29074i
$628$	16.1947	+	14.2066i	0.646237	+	0.566906i
$629$	−25.8509	+	3.71679i	−1.03074	+	0.148198i
$630$	−0.0959450	+	0.434666i	−0.00382254	+	0.0173175i
$631$	−24.9651	+	28.8112i	−0.993843	+	1.14696i	−0.00470179	+	0.999989i	$0.501497\pi$
$631$	−24.9651	+	28.8112i	−0.993843	+	1.14696i	−0.989141	+	0.146967i	$0.953049\pi$
$632$	14.5614	−	37.9757i	0.579220	−	1.51059i
$633$	−23.3189	−	14.9862i	−0.926844	−	0.595646i
$634$	−8.92360	+	11.8451i	−0.354401	+	0.470427i
$635$	3.14017	−	10.6944i	0.124614	−	0.424395i
$636$	6.13306	+	21.3686i	0.243192	+	0.847321i
$637$	−12.9470	+	11.2186i	−0.512978	+	0.444498i
$638$	−9.56729	+	5.18632i	−0.378773	+	0.205328i
$639$	−0.914165	−	3.11336i	−0.0361638	−	0.123163i
$640$	11.2995	−	0.566023i	0.446654	−	0.0223740i
$641$	7.70514	+	1.10783i	0.304335	+	0.0437567i	0.292790	−	0.956177i	$-0.405416\pi$
$641$	7.70514	+	1.10783i	0.304335	+	0.0437567i	0.0115443	+	0.999933i	$0.496325\pi$
$642$	−13.5570	+	10.0843i	−0.535052	+	0.397994i
$643$		−	18.9247i		−	0.746319i	−0.927767	−	0.373160i	$-0.878274\pi$
$643$		−	18.9247i		−	0.746319i	0.927767	−	0.373160i	$-0.121726\pi$
$644$	1.94363	+	4.04389i	0.0765897	+	0.159352i
$645$			16.3799i			0.644959i
$646$	−23.8696	−	32.0896i	−0.939137	−	1.26255i
$647$	−23.3778	−	3.36122i	−0.919077	−	0.132143i	−0.333491	−	0.942753i	$-0.608227\pi$
$647$	−23.3778	−	3.36122i	−0.919077	−	0.132143i	−0.585586	+	0.810610i	$0.699136\pi$
$648$	−18.0070	−	4.09009i	−0.707383	−	0.160674i
$649$	−0.625096	−	2.12888i	−0.0245372	−	0.0835659i
$650$	1.70265	+	3.14092i	0.0667836	+	0.123197i
$651$	3.88541	−	3.36673i	0.152281	−	0.131953i
$652$	−3.42645	−	11.9383i	−0.134190	−	0.467541i
$653$	0.298288	−	1.01588i	0.0116729	−	0.0397543i	−0.953451	−	0.301549i	$-0.902496\pi$
$653$	0.298288	−	1.01588i	0.0116729	−	0.0397543i	0.965124	+	0.261795i	$0.0843144\pi$
$654$	−2.42414	−	1.82625i	−0.0947913	−	0.0714120i
$655$	12.7307	+	8.18152i	0.497430	+	0.319679i
$656$	−7.96546	−	2.44481i	−0.310999	−	0.0954537i
$657$	−3.57490	+	4.12566i	−0.139470	+	0.160957i
$658$	−6.52477	−	1.44023i	−0.254362	−	0.0561461i
$659$	15.5006	−	2.22865i	0.603817	−	0.0868158i	0.166375	−	0.986063i	$-0.446794\pi$
$659$	15.5006	−	2.22865i	0.603817	−	0.0868158i	0.437442	+	0.899247i	$0.355885\pi$
$660$	7.78275	−	8.87185i	0.302943	−	0.345336i
$661$	6.42641	+	14.0719i	0.249959	+	0.547333i	0.992468	−	0.122502i	$-0.0390919\pi$
$661$	6.42641	+	14.0719i	0.249959	+	0.547333i	−0.742510	+	0.669835i	$0.766365\pi$
$662$	8.13114	+	22.0052i	0.316026	+	0.855255i
$663$	−7.51907	+	16.4645i	−0.292017	+	0.639427i
$664$	0.775442	+	12.4408i	0.0300930	+	0.482795i
$665$	−1.52277	−	2.36948i	−0.0590505	−	0.0918843i
$666$	0.361394	+	5.27917i	0.0140037	+	0.204564i
$667$	4.18531	+	8.57357i	0.162056	+	0.331970i
$668$	6.93821	+	50.4385i	0.268448	+	1.95153i
$669$	17.4723	+	27.1875i	0.675519	+	1.05113i
$670$	1.25879	−	16.8767i	0.0486313	−	0.652003i
$671$	−26.8370	−	12.2560i	−1.03603	−	0.473139i
$672$	2.36951	+	3.26801i	0.0914060	+	0.126066i
$673$	3.02254	+	6.61844i	0.116510	+	0.255122i	0.958899	−	0.283749i	$-0.0915783\pi$
$673$	3.02254	+	6.61844i	0.116510	+	0.255122i	−0.842388	+	0.538871i	$0.818851\pi$
$674$	−13.2967	−	13.3780i	−0.512168	−	0.515302i
$675$	−0.797382	−	5.54591i	−0.0306912	−	0.213462i
$676$	13.0892	+	1.96350i	0.503429	+	0.0755193i
$677$	−10.6122	+	12.2471i	−0.407859	+	0.470694i	−0.922100	−	0.386951i	$-0.873528\pi$
$677$	−10.6122	+	12.2471i	−0.407859	+	0.470694i	0.514241	+	0.857646i	$0.328074\pi$
$678$	12.8219	+	7.05213i	0.492421	+	0.270835i
$679$	−3.03393	+	4.72088i	−0.116431	+	0.181171i
$680$	−6.47280	+	11.6004i	−0.248221	+	0.444857i
$681$	−7.99222	+	27.2190i	−0.306263	+	1.04303i
$682$	38.5372	−	8.26025i	1.47567	−	0.316301i
$683$	10.3458	+	11.9397i	0.395872	+	0.456861i	0.918337	−	0.395800i	$-0.129533\pi$
$683$	10.3458	+	11.9397i	0.395872	+	0.456861i	−0.522464	+	0.852661i	$0.674987\pi$
$684$	−6.84341	+	4.33924i	−0.261664	+	0.165915i
$685$	4.47111	+	15.2272i	0.170832	+	0.581802i
$686$	−8.53213	−	3.21200i	−0.325758	−	0.122635i
$687$	3.17413	−	22.0766i	0.121101	−	0.842274i
$688$	−32.1138	−	28.5201i	−1.22433	−	1.08732i
$689$		−	18.4082i		−	0.701296i
$690$	−7.48007	−	7.14816i	−0.284761	−	0.272126i
$691$	−9.68716			−0.368517			−0.184258	−	0.982878i	$-0.558988\pi$
$691$	−9.68716			−0.368517			−0.184258	+	0.982878i	$0.558988\pi$
$692$	−13.4038	−	15.6608i	−0.509537	−	0.595336i
$693$	−1.20513	−	0.173271i	−0.0457791	−	0.00658204i
$694$	21.1702	+	7.96969i	0.803608	+	0.302525i
$695$	−12.2404	+	3.59410i	−0.464304	+	0.136332i
$696$	5.08084	+	6.91825i	0.192589	+	0.262236i
$697$	7.39376	−	6.40673i	0.280058	−	0.242672i
$698$	5.05308	+	23.5746i	0.191262	+	0.892310i
$699$	31.8527	+	9.35279i	1.20478	+	0.353755i
$700$	−0.510586	+	0.783933i	−0.0192984	+	0.0296299i
$701$	22.9116	+	14.7244i	0.865358	+	0.556132i	0.896330	−	0.443388i	$-0.146224\pi$
$701$	22.9116	+	14.7244i	0.865358	+	0.556132i	−0.0309714	+	0.999520i	$0.509860\pi$
$702$	17.5398	+	9.64704i	0.661999	+	0.364104i
$703$	−25.3045	−	21.9265i	−0.954378	−	0.826974i
$704$	3.84277	+	30.7059i	0.144830	+	1.15727i
$705$	15.2515	−	2.19283i	0.574403	−	0.0825867i
$706$	32.8230	−	32.6234i	1.23531	−	1.22780i
$707$	−0.320560	+	0.146395i	−0.0120559	+	0.00550574i
$708$	−1.59628	+	0.717261i	−0.0599919	+	0.0269563i
$709$	−4.74148	+	10.3824i	−0.178070	+	0.389919i	−0.977529	−	0.210802i	$-0.932392\pi$
$709$	−4.74148	+	10.3824i	−0.178070	+	0.389919i	0.799459	+	0.600721i	$0.205120\pi$
$710$	0.507259	−	6.80085i	0.0190371	−	0.255231i
$711$	8.13971	−	5.23107i	0.305263	−	0.196181i
$712$	−45.8101	+	9.52726i	−1.71681	+	0.357049i
$713$	−5.79576	−	34.0628i	−0.217053	−	1.27566i
$714$	−4.72860	+	0.323704i	−0.176964	+	0.0121143i
$715$	−8.22087	+	5.28323i	−0.307443	+	0.197582i
$716$	−0.136620	+	22.3975i	−0.00510574	+	0.837032i
$717$	8.14014	+	3.71748i	0.303999	+	0.138832i
$718$	6.24205	+	16.8927i	0.232951	+	0.630432i
$719$	−26.7794	+	12.2298i	−0.998705	+	0.456093i	−0.846576	−	0.532268i	$-0.821340\pi$
$719$	−26.7794	+	12.2298i	−0.998705	+	0.456093i	−0.152129	+	0.988361i	$0.548613\pi$
$720$	2.24632	+	1.48265i	0.0837153	+	0.0552551i
$721$	1.20738	+	8.39751i	0.0449652	+	0.312740i
$722$	5.26006	−	23.8300i	0.195759	−	0.886859i
$723$	10.2400	+	8.87298i	0.380828	+	0.329990i
$724$	−14.2976	−	6.63520i	−0.531367	−	0.246595i
$725$	−1.07552	+	1.67355i	−0.0399440	+	0.0621541i
$726$	6.82831	+	5.14418i	0.253422	+	0.190918i
$727$	9.94361	+	2.91971i	0.368788	+	0.108286i	0.460875	−	0.887465i	$-0.347536\pi$
$727$	9.94361	+	2.91971i	0.368788	+	0.108286i	−0.0920869	+	0.995751i	$0.529354\pi$
$728$	−1.13937	−	3.14227i	−0.0422277	−	0.116460i
$729$	−19.6685	−	22.6987i	−0.728464	−	0.840692i
$730$	−10.0868	+	5.46792i	−0.373328	+	0.202377i
$731$	48.3873	−	14.2078i	1.78967	−	0.525494i
$732$	−6.69206	+	22.2872i	−0.247346	+	0.823760i
$733$	−4.61206	+	32.0776i	−0.170350	+	1.18481i	0.707795	+	0.706418i	$0.249690\pi$
$733$	−4.61206	+	32.0776i	−0.170350	+	1.18481i	−0.878145	+	0.478394i	$0.841219\pi$
$734$	5.24192	+	7.04708i	0.193483	+	0.260113i
$735$	10.3446			0.381568
$736$	27.0384	−	2.21903i	0.996649	−	0.0817946i
$737$	46.2895			1.70510
$738$	−1.18305	−	1.59046i	−0.0435486	−	0.0585455i
$739$	−0.721050	+	5.01501i	−0.0265243	+	0.184480i	−0.998776	−	0.0494554i	$-0.984251\pi$
$739$	−0.721050	+	5.01501i	−0.0265243	+	0.184480i	0.972252	+	0.233936i	$0.0751605\pi$
$740$	−3.19830	+	10.6516i	−0.117572	+	0.391562i
$741$	−22.2652	+	6.53765i	−0.817932	+	0.240166i
$742$	4.23773	−	2.29722i	0.155572	−	0.0843337i
$743$	21.0543	+	24.2979i	0.772406	+	0.891404i	0.996537	−	0.0831550i	$-0.0264997\pi$
$743$	21.0543	+	24.2979i	0.772406	+	0.891404i	−0.224131	+	0.974559i	$0.571954\pi$
$744$	−10.5966	−	29.2244i	−0.388490	−	1.07142i
$745$	4.55896	+	1.33863i	0.167027	+	0.0490436i
$746$	34.3977	+	25.9139i	1.25939	+	0.948774i
$747$	−1.60320	+	2.49463i	−0.0586580	+	0.0912736i
$748$	−32.9587	−	15.2954i	−1.20509	−	0.559254i
$749$	2.76873	+	2.39912i	0.101167	+	0.0876618i
$750$	0.465009	−	2.10666i	0.0169797	−	0.0769243i
$751$	−2.01575	−	14.0199i	−0.0735558	−	0.511592i	−0.992976	−	0.118315i	$-0.962251\pi$
$751$	−2.01575	−	14.0199i	−0.0735558	−	0.511592i	0.919420	−	0.393277i	$-0.128658\pi$
$752$	−22.2561	+	33.7195i	−0.811595	+	1.22962i
$753$	12.2498	−	5.59431i	0.446408	−	0.203868i
$754$	−2.46346	−	6.66683i	−0.0897141	−	0.242792i
$755$	−4.32215	−	1.97386i	−0.157299	−	0.0718360i
$756$	−0.0319735	+	5.24172i	−0.00116286	+	0.190640i
$757$	37.0149	−	23.7880i	1.34533	−	0.864590i	0.347990	−	0.937498i	$-0.386864\pi$
$757$	37.0149	−	23.7880i	1.34533	−	0.864590i	0.997339	+	0.0729081i	$0.0232280\pi$
$758$	10.9470	−	0.749396i	0.397614	−	0.0272193i
$759$	17.9758	−	21.8572i	0.652480	−	0.793366i
$760$	−16.6740	+	3.46774i	−0.604830	+	0.125788i
$761$	−12.9342	+	8.31233i	−0.468866	+	0.301322i	−0.753657	−	0.657268i	$-0.771712\pi$
$761$	−12.9342	+	8.31233i	−0.468866	+	0.301322i	0.284791	+	0.958590i	$0.408076\pi$
$762$	1.78855	−	23.9793i	0.0647925	−	0.868677i
$763$	−0.273377	+	0.598612i	−0.00989690	+	0.0216712i
$764$	−36.7237	+	16.5012i	−1.32862	+	0.596992i
$765$	−2.87467	+	1.31282i	−0.103934	+	0.0474650i
$766$	−24.0836	+	23.9372i	−0.870177	+	0.864885i
$767$	1.43432	−	0.206224i	0.0517902	−	0.00744631i
$768$	23.5800	−	6.30310i	0.850869	−	0.227443i
$769$	−11.8471	−	10.2656i	−0.427218	−	0.370186i	0.414550	−	0.910027i	$-0.363939\pi$
$769$	−11.8471	−	10.2656i	−0.427218	−	0.370186i	−0.841767	+	0.539840i	$0.818485\pi$
$770$	−2.24216	−	1.23320i	−0.0808019	−	0.0444416i
$771$	7.33679	+	4.71507i	0.264228	+	0.169809i
$772$	−27.8084	+	42.6959i	−1.00085	+	1.53666i
$773$	11.1069	+	3.26128i	0.399487	+	0.117300i	0.475304	−	0.879822i	$-0.342338\pi$
$773$	11.1069	+	3.26128i	0.399487	+	0.117300i	−0.0758168	+	0.997122i	$0.524156\pi$
$774$	−2.14146	−	9.99074i	−0.0769733	−	0.359110i
$775$	5.44492	−	4.71805i	0.195587	−	0.169477i
$776$	20.0851	+	27.3486i	0.721014	+	0.981758i
$777$	−3.80731	+	1.11793i	−0.136586	+	0.0401054i
$778$	−30.5967	−	11.5184i	−1.09694	−	0.412954i
$779$	12.4150	+	1.78501i	0.444813	+	0.0639545i
$780$	5.01184	+	5.85577i	0.179453	+	0.209670i
$781$	18.6534			0.667473
$782$	−14.6280	+	28.2968i	−0.523095	+	1.01189i
$783$			11.1462i			0.398333i
$784$	−18.0117	+	20.2813i	−0.643275	+	0.724332i
$785$	−1.53293	+	10.6618i	−0.0547128	+	0.380536i
$786$	30.5541	+	11.5024i	1.08983	+	0.410276i
$787$	−11.7414	−	39.9874i	−0.418534	−	1.42540i	−0.851675	−	0.524071i	$-0.824413\pi$
$787$	−11.7414	−	39.9874i	−0.418534	−	1.42540i	0.433140	−	0.901327i	$-0.357405\pi$
$788$	0.428683	−	0.271817i	0.0152712	−	0.00968309i
$789$	3.53600	+	4.08076i	0.125885	+	0.145279i
$790$	19.8842	−	4.26207i	0.707448	−	0.151638i
$791$	0.893902	−	3.04435i	0.0317835	−	0.108245i
$792$	−3.58712	+	6.42877i	−0.127463	+	0.228437i
$793$	10.4173	−	16.2096i	0.369929	−	0.575621i
$794$	13.9241	+	7.65837i	0.494149	+	0.271785i
$795$	−7.27921	+	8.40066i	−0.258167	+	0.297941i
$796$	−39.1164	−	5.86784i	−1.38645	−	0.207980i
$797$	3.81387	+	26.5261i	0.135094	+	0.939602i	0.938773	+	0.344538i	$0.111964\pi$
$797$	3.81387	+	26.5261i	0.135094	+	0.939602i	−0.803678	+	0.595064i	$0.797127\pi$
$798$	−4.28358	−	4.30979i	−0.151637	−	0.152565i
$799$	−19.7067	−	43.1517i	−0.697173	−	1.52660i
$800$	3.32058	+	4.57971i	0.117400	+	0.161917i
$801$	−10.1254	−	4.62411i	−0.357763	−	0.163385i
$802$	−0.398133	+	5.33779i	−0.0140586	+	0.188484i
$803$	−16.9666	−	26.4006i	−0.598739	−	0.931656i
$804$	−4.97544	−	36.1698i	−0.175470	−	1.27561i
$805$	−1.16389	+	1.91782i	−0.0410217	+	0.0675944i
$806$	1.75798	+	25.6802i	0.0619221	+	0.904546i
$807$	9.10515	+	14.1679i	0.320517	+	0.498734i
$808$	0.132560	+	2.12672i	0.00466345	+	0.0748177i
$809$	−7.09146	+	15.5281i	−0.249323	+	0.545940i	−0.992370	−	0.123299i	$-0.960653\pi$
$809$	−7.09146	+	15.5281i	−0.249323	+	0.545940i	0.743047	+	0.669239i	$0.233380\pi$
$810$	−3.20015	−	8.66052i	−0.112442	−	0.304300i
$811$	12.0343	+	26.3515i	0.422583	+	0.925328i	0.994473	+	0.104997i	$0.0334834\pi$
$811$	12.0343	+	26.3515i	0.422583	+	0.925328i	−0.571889	+	0.820331i	$0.693789\pi$
$812$	1.22734	−	1.39909i	0.0430712	−	0.0490984i
$813$	21.7235	−	3.12337i	0.761876	−	0.109541i
$814$	−29.7044	−	6.55675i	−1.04114	−	0.229814i
$815$	4.06679	−	4.69333i	0.142453	−	0.164400i
$816$	−8.40895	+	27.3973i	−0.294372	+	0.959098i
$817$	54.3900	+	34.9543i	1.90286	+	1.22290i
$818$	41.0864	+	30.9529i	1.43655	+	1.08224i
$819$	0.224023	−	0.762952i	0.00782800	−	0.0266597i
$820$	−1.14932	−	4.00443i	−0.0401361	−	0.139841i
$821$	−5.37382	+	4.65644i	−0.187548	+	0.162511i	−0.743574	−	0.668654i	$-0.766871\pi$
$821$	−5.37382	+	4.65644i	−0.187548	+	0.162511i	0.556026	+	0.831165i	$0.312325\pi$
$822$	16.3166	+	30.0995i	0.569107	+	1.04984i
$823$	−4.65663	−	15.8590i	−0.162320	−	0.552811i	−0.999978	−	0.00661633i	$-0.997894\pi$
$823$	−4.65663	−	15.8590i	−0.162320	−	0.552811i	0.837658	−	0.546195i	$-0.183924\pi$
$824$	50.0241	+	11.3624i	1.74267	+	0.395828i
$825$	5.84081	+	0.839781i	0.203351	+	0.0292374i
$826$	0.226468	+	0.304457i	0.00787984	+	0.0105934i
$827$		−	41.0091i		−	1.42603i	−0.701150	−	0.713013i	$-0.747330\pi$
$827$		−	41.0091i		−	1.42603i	0.701150	−	0.713013i	$-0.252670\pi$
$828$	5.49691	+	3.38202i	0.191031	+	0.117533i
$829$		−	32.8614i		−	1.14132i	−0.821185	−	0.570662i	$-0.806687\pi$
$829$		−	32.8614i		−	1.14132i	0.821185	−	0.570662i	$-0.193313\pi$
$830$	−5.00070	+	3.71973i	−0.173577	+	0.129114i
$831$	3.43523	+	0.493912i	0.119167	+	0.0171336i
$832$	−20.2070	−	0.369814i	−0.700552	−	0.0128210i
$833$	−8.97285	−	30.5587i	−0.310891	−	1.05880i
$834$	−24.1955	+	13.1161i	−0.837820	+	0.454173i
$835$	−19.2389	+	16.6706i	−0.665790	+	0.576911i
$836$	−12.8510	−	44.7751i	−0.444462	−	1.54858i
$837$	11.3728	−	38.7321i	0.393101	−	1.33878i
$838$	15.4702	−	20.5349i	0.534409	−	0.709367i
$839$	15.5070	+	9.96571i	0.535359	+	0.344055i	0.780222	−	0.625503i	$-0.215106\pi$
$839$	15.5070	+	9.96571i	0.535359	+	0.344055i	−0.244862	+	0.969558i	$0.578743\pi$
$840$	−0.722604	+	1.88453i	−0.0249322	+	0.0650226i
$841$	−16.3993	+	18.9258i	−0.565494	+	0.652615i
$842$	10.2915	−	46.6240i	0.354667	−	1.60677i
$843$	−21.7536	+	3.12770i	−0.749235	+	0.107724i
$844$	27.3193	+	23.9656i	0.940370	+	0.824931i
$845$	2.74914	+	6.01977i	0.0945732	+	0.207086i
$846$	−9.01576	+	3.33142i	−0.309968	+	0.114537i
$847$	0.770048	−	1.68617i	0.0264592	−	0.0579375i
$848$	−3.79572	−	28.8982i	−0.130346	−	0.992370i
$849$	4.53066	+	7.04984i	0.155492	+	0.241950i
$850$	−6.62655	+	0.453631i	−0.227289	+	0.0155594i
$851$	−6.85238	+	25.7729i	−0.234897	+	0.883483i
$852$	−2.00497	−	14.5755i	−0.0686891	−	0.499347i
$853$	12.2626	+	19.0809i	0.419862	+	0.653319i	0.985174	−	0.171559i	$-0.0548804\pi$
$853$	12.2626	+	19.0809i	0.419862	+	0.653319i	−0.565311	+	0.824878i	$0.691244\pi$
$854$	5.03162	+	0.375296i	0.172178	+	0.0128424i
$855$	−3.68545	−	1.68309i	−0.126040	−	0.0575604i
$856$	19.5386	−	10.4380i	0.667816	−	0.356762i
$857$	6.52194	+	14.2811i	0.222785	+	0.487831i	0.987712	−	0.156286i	$-0.0499521\pi$
$857$	6.52194	+	14.2811i	0.222785	+	0.487831i	−0.764927	+	0.644117i	$0.777225\pi$
$858$	−14.9528	+	14.8618i	−0.510479	+	0.507374i
$859$	−3.39410	−	23.6065i	−0.115805	−	0.805442i	−0.962094	−	0.272718i	$-0.912077\pi$
$859$	−3.39410	−	23.6065i	−0.115805	−	0.805442i	0.846289	−	0.532724i	$-0.178832\pi$
$860$	3.18580	−	21.2373i	0.108635	−	0.724187i
$861$	0.973407	−	1.12337i	0.0331736	−	0.0382844i
$862$	21.1134	−	38.3876i	0.719126	−	1.30749i
$863$	−26.6105	+	41.4067i	−0.905831	+	1.40950i	0.00647015	+	0.999979i	$0.497940\pi$
$863$	−26.6105	+	41.4067i	−0.905831	+	1.40950i	−0.912301	+	0.409521i	$0.865696\pi$
$864$	29.5243	+	11.5278i	1.00444	+	0.392184i
$865$	2.90377	−	9.88934i	0.0987313	−	0.336248i
$866$	5.18132	+	24.1729i	0.176068	+	0.821427i
$867$	−5.05330	−	5.83182i	−0.171619	−	0.198059i
$868$	−5.69243	+	3.60943i	−0.193214	+	0.122512i
$869$	15.6708	+	53.3697i	0.531595	+	1.81044i
$870$	−1.51208	+	4.01658i	−0.0512642	+	0.136175i
$871$	−4.30241	+	29.9239i	−0.145782	+	1.01393i
$872$	2.78781	+	2.83930i	0.0944072	+	0.0961508i
$873$			8.07226i			0.273205i
$874$	−39.6979	+	9.58379i	−1.34280	+	0.324176i
$875$	−0.467774			−0.0158136
$876$	−18.8053	+	16.0951i	−0.635371	+	0.543802i
$877$	32.8337	+	4.72077i	1.10871	+	0.159409i	0.672258	−	0.740317i	$-0.265324\pi$
$877$	32.8337	+	4.72077i	1.10871	+	0.159409i	0.436456	+	0.899726i	$0.356233\pi$
$878$	−0.515858	+	1.37029i	−0.0174094	+	0.0462451i
$879$	−41.8904	+	12.3001i	−1.41293	+	0.414873i
$880$	−11.8162	+	9.98906i	−0.398325	+	0.336731i
$881$	16.2418	−	14.0736i	0.547201	−	0.474152i	−0.336840	−	0.941562i	$-0.609358\pi$
$881$	16.2418	−	14.0736i	0.547201	−	0.474152i	0.884041	+	0.467410i	$0.154813\pi$
$882$	−6.30959	+	1.35243i	−0.212455	+	0.0455386i
$883$	36.3860	+	10.6839i	1.22449	+	0.359541i	0.829166	−	0.559002i	$-0.188816\pi$
$883$	36.3860	+	10.6839i	1.22449	+	0.359541i	0.395319	+	0.918544i	$0.370634\pi$
$884$	12.9511	−	19.8845i	0.435592	−	0.668789i
$885$	−0.736106	−	0.473066i	−0.0247439	−	0.0159020i
$886$	−0.218644	+	0.397529i	−0.00734548	+	0.0133553i
$887$	21.1747	+	18.3480i	0.710978	+	0.616066i	0.933380	−	0.358889i	$-0.116844\pi$
$887$	21.1747	+	18.3480i	0.710978	+	0.616066i	−0.222403	+	0.974955i	$0.571390\pi$
$888$	−1.93054	+	23.9153i	−0.0647846	+	0.802544i
$889$	−5.16070	+	0.741996i	−0.173084	+	0.0248858i
$890$	−16.4923	−	16.5933i	−0.552825	−	0.556207i
$891$	22.9717	−	10.4908i	0.769580	−	0.351455i
$892$	−17.3659	−	38.6481i	−0.581452	−	1.29403i
$893$	25.2648	−	55.3223i	0.845455	−	1.85129i
$894$	10.2222	+	0.762448i	0.341881	+	0.0255001i
$895$	−9.42114	+	6.05460i	−0.314914	+	0.202383i
$896$	−2.43657	−	4.69799i	−0.0814002	−	0.156949i
$897$	12.4588	+	13.6520i	0.415988	+	0.455827i
$898$	−1.28422	−	18.7596i	−0.0428549	−	0.626016i
$899$	−12.0574	+	7.74879i	−0.402135	+	0.258437i
$900$	−0.00820867	+	1.34573i	−0.000273622	+	0.0448575i
$901$	31.1300	+	14.2166i	1.03709	+	0.473623i
$902$	10.6888	−	3.94962i	0.355898	−	0.131508i
$903$	6.96969	−	3.18295i	0.231937	−	0.105922i
$904$	−15.2526	−	11.6372i	−0.507293	−	0.387047i
$905$	−1.12160	−	7.80090i	−0.0372832	−	0.259311i
$906$	−10.0099	−	2.20951i	−0.332555	−	0.0734059i
$907$	15.9081	+	13.7845i	0.528221	+	0.457706i	0.877681	−	0.479245i	$-0.159089\pi$
$907$	15.9081	+	13.7845i	0.528221	+	0.457706i	−0.349460	+	0.936951i	$0.613635\pi$
$908$	15.6562	−	33.7362i	0.519570	−	1.11958i
$909$	−0.274063	+	0.426451i	−0.00909011	+	0.0141445i
$910$	1.00561	−	1.33483i	0.0333355	−	0.0442491i
$911$	−19.8627	−	5.83221i	−0.658081	−	0.193230i	−0.0643918	−	0.997925i	$-0.520511\pi$
$911$	−19.8627	−	5.83221i	−0.658081	−	0.193230i	−0.593689	+	0.804695i	$0.702329\pi$
$912$	−33.6051	+	14.8542i	−1.11278	+	0.491872i
$913$	−11.1635	−	12.8833i	−0.369457	−	0.426376i
$914$	12.2943	+	22.6795i	0.406660	+	0.750172i
$915$	−11.1638	+	3.27799i	−0.369065	+	0.108367i
$916$	−8.40918	+	28.0059i	−0.277847	+	0.925342i
$917$	1.00742	−	7.00677i	0.0332680	−	0.231384i
$918$	−29.8600	+	22.2112i	−0.985528	+	0.733078i
$919$	−1.20286			−0.0396786			−0.0198393	−	0.999803i	$-0.506315\pi$
$919$	−1.20286			−0.0396786			−0.0198393	+	0.999803i	$0.506315\pi$
$920$	8.30798	+	10.7228i	0.273906	+	0.353519i
$921$	−35.8172			−1.18022
$922$	−22.4041	+	16.6651i	−0.737840	+	0.548836i
$923$	−1.73376	+	12.0585i	−0.0570673	+	0.396912i
$924$	−5.28734	−	1.58760i	−0.173941	−	0.0522281i
$925$	−5.33547	+	1.56664i	−0.175429	+	0.0515106i
$926$	18.8806	+	34.8294i	0.620456	+	1.14457i
$927$	7.99175	+	9.22297i	0.262483	+	0.302922i
$928$	−5.24198	−	9.95803i	−0.172076	−	0.326888i
$929$	25.3661	+	7.44815i	0.832234	+	0.244366i	0.669976	−	0.742383i	$-0.266304\pi$
$929$	25.3661	+	7.44815i	0.832234	+	0.244366i	0.162258	+	0.986748i	$0.448122\pi$
$930$	9.35255	−	12.4144i	0.306682	−	0.407086i
$931$	22.0752	−	34.3496i	0.723485	−	1.12576i
$932$	−39.4794	−	18.3215i	−1.29319	−	0.600140i
$933$	3.99177	+	3.45889i	0.130685	+	0.113239i
$934$	45.7795	+	10.1051i	1.49795	+	0.330647i
$935$	−2.58549	−	17.9825i	−0.0845547	−	0.588091i
$936$	−3.82248	−	2.91642i	−0.124942	−	0.0953263i
$937$	30.3504	−	13.8606i	0.991505	−	0.452805i	0.147454	−	0.989069i	$-0.452892\pi$
$937$	30.3504	−	13.8606i	0.991505	−	0.452805i	0.844050	+	0.536264i	$0.180165\pi$
$938$	−7.42567	+	2.74386i	−0.242457	+	0.0895903i
$939$	−16.3577	−	7.47032i	−0.533814	−	0.243785i
$940$	−20.2007	−	0.123220i	−0.658874	−	0.00401901i
$941$	48.6033	−	31.2355i	1.58442	−	1.01825i	0.610318	−	0.792157i	$-0.291042\pi$
$941$	48.6033	−	31.2355i	1.58442	−	1.01825i	0.974106	−	0.226091i	$-0.0725945\pi$
$942$	1.58708	+	23.1837i	0.0517098	+	0.755366i
$943$	−3.06022	−	9.50970i	−0.0996545	−	0.309678i
$944$	2.20915	−	0.619495i	0.0719018	−	0.0201628i
$945$	−2.20485	+	1.41697i	−0.0717237	+	0.0460940i
$946$	58.5759	+	4.36903i	1.90447	+	0.142049i
$947$	−16.0840	+	35.2191i	−0.522661	+	1.14447i	0.445761	+	0.895152i	$0.352933\pi$
$947$	−16.0840	+	35.2191i	−0.522661	+	1.14447i	−0.968422	+	0.249316i	$0.919794\pi$
$948$	40.0178	−	17.9813i	1.29972	−	0.584006i
$949$	18.6437	−	8.51427i	0.605199	−	0.276385i
$950$	−6.00290	−	6.03963i	−0.194760	−	0.195951i
$951$	−15.8343	+	2.27663i	−0.513463	+	0.0738249i
$952$	6.19381	+	0.499990i	0.200743	+	0.0162048i
$953$	−23.3502	−	20.2331i	−0.756389	−	0.655414i	0.188772	−	0.982021i	$-0.439549\pi$
$953$	−23.3502	−	20.2331i	−0.756389	−	0.655414i	−0.945160	+	0.326607i	$0.894095\pi$
$954$	3.34159	−	6.07555i	0.108188	−	0.196703i
$955$	−16.9347	−	10.8833i	−0.547994	−	0.352174i
$956$	−9.83103	−	6.40309i	−0.317958	−	0.207091i
$957$	−11.2634	−	3.30723i	−0.364094	−	0.106908i
$958$	−29.3031	+	6.28096i	−0.946741	+	0.202929i
$959$	5.61038	−	4.86142i	0.181169	−	0.156984i
$960$	9.07534	+	8.15930i	0.292905	+	0.263340i
$961$	20.0602	−	5.89022i	0.647105	−	0.190007i
$962$	6.99952	−	18.5931i	0.225674	−	0.599464i
$963$	5.21625	+	0.749983i	0.168091	+	0.0241679i
$964$	−11.5508	−	13.4958i	−0.372027	−	0.434672i
$965$	−25.4767			−0.820124
$966$	−1.58803	+	4.57182i	−0.0510940	+	0.147096i
$967$		−	41.9460i		−	1.34889i	−0.738324	−	0.674446i	$-0.764382\pi$
$967$		−	41.9460i		−	1.34889i	0.738324	−	0.674446i	$-0.235618\pi$
$968$	−7.85271	−	7.99774i	−0.252396	−	0.257057i
$969$	6.13956	−	42.7016i	0.197231	−	1.37177i
$970$	−5.97741	+	15.8780i	−0.191923	+	0.509811i
$971$	5.44457	+	18.5425i	0.174725	+	0.595057i	0.999559	+	0.0296835i	$0.00944994\pi$
$971$	5.44457	+	18.5425i	0.174725	+	0.595057i	−0.824835	+	0.565374i	$0.808732\pi$
$972$	7.33578	+	11.5693i	0.235295	+	0.371084i
$973$	3.90785	+	4.50990i	0.125280	+	0.144581i
$974$	6.67048	+	31.1204i	0.213736	+	0.997160i
$975$	−1.08575	+	3.69774i	−0.0347720	+	0.118422i
$976$	13.0113	−	27.5949i	0.416482	−	0.883290i
$977$	14.6080	−	22.7305i	0.467351	−	0.727212i	−0.524940	−	0.851139i	$-0.675912\pi$
$977$	14.6080	−	22.7305i	0.467351	−	0.727212i	0.992291	+	0.123927i	$0.0395488\pi$
$978$	6.45663	−	11.7392i	0.206460	−	0.375377i
$979$	41.9050	−	48.3610i	1.33929	−	1.54562i
$980$	−13.4123	−	2.01198i	−0.428440	−	0.0642702i
$981$	0.134719	+	0.936990i	0.00430124	+	0.0299158i
$982$	−2.57230	+	2.55665i	−0.0820853	+	0.0815861i
$983$	−8.52552	−	18.6683i	−0.271922	−	0.595426i	0.723572	−	0.690248i	$-0.242499\pi$
$983$	−8.52552	−	18.6683i	−0.271922	−	0.595426i	−0.995494	+	0.0948229i	$0.969772\pi$
$984$	−4.23505	−	7.92751i	−0.135008	−	0.252720i
$985$	0.230863	+	0.105431i	0.00735590	+	0.00335932i
$986$	13.1768	+	0.982824i	0.419634	+	0.0312995i
$987$	−3.89672	−	6.06341i	−0.124034	−	0.193001i
$988$	30.1394	−	4.14591i	0.958861	−	0.131899i
$989$	6.01447	−	51.1427i	0.191249	−	1.62624i
$990$	−3.67232	+	0.251395i	−0.116714	+	0.00798985i
$991$	23.0987	+	35.9424i	0.733756	+	1.14175i	0.984787	+	0.173767i	$0.0555941\pi$
$991$	23.0987	+	35.9424i	0.733756	+	1.14175i	−0.251031	+	0.967979i	$0.580770\pi$
$992$	8.05497	+	39.9518i	0.255746	+	1.26847i
$993$	−10.5122	+	23.0185i	−0.333594	+	0.730470i
$994$	−2.99235	+	1.10570i	−0.0949115	+	0.0350708i
$995$	−8.21569	−	17.9898i	−0.260455	−	0.570316i
$996$	−8.86689	+	10.1077i	−0.280958	+	0.320274i
$997$	−47.3922	+	6.81397i	−1.50093	+	0.215800i	−0.843258	−	0.537509i	$-0.819366\pi$
$997$	−47.3922	+	6.81397i	−1.50093	+	0.215800i	−0.657667	+	0.753309i	$0.728456\pi$
$998$	5.79123	−	26.2363i	0.183318	−	0.830497i
$999$	−20.4031	+	23.5464i	−0.645525	+	0.744976i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	920.2.bb.a.11.15	✓	480
8.3	odd	2		920.2.bb.b.11.34	yes	480
23.21	odd	22		920.2.bb.b.251.34	yes	480
184.67	even	22	inner	920.2.bb.a.251.15	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
920.2.bb.a.11.15	✓	480	1.1	even	1	trivial
920.2.bb.a.251.15	yes	480	184.67	even	22	inner
920.2.bb.b.11.34	yes	480	8.3	odd	2
920.2.bb.b.251.34	yes	480	23.21	odd	22

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:	\( N \)	\(=\)	\( 920 = 2^{3} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	920.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.844050 - 1.13472i) q^{2} +(0.217100 - 1.50996i) q^{3} +(-0.575160 + 1.91551i) q^{4} +(-0.959493 + 0.281733i) q^{5} +(-1.89662 + 1.02814i) q^{6} +(0.306327 + 0.353520i) q^{7} +(2.65903 - 0.964146i) q^{8} +(0.645619 + 0.189571i) q^{9} +(1.12955 + 0.850956i) q^{10} +(-2.09129 + 3.25412i) q^{11} +(2.76749 + 1.28433i) q^{12} +(-1.90925 - 1.65437i) q^{13} +(0.142590 - 0.645982i) q^{14} +(0.217100 + 1.50996i) q^{15} +(-3.33838 - 2.20345i) q^{16} +(4.27222 - 1.95106i) q^{17} +(-0.329826 - 0.892602i) q^{18} +(5.47716 + 2.50133i) q^{19} +(0.0121994 - 1.99996i) q^{20} +(0.600306 - 0.385793i) q^{21} +(5.45765 - 0.373612i) q^{22} +(-0.123410 - 4.79424i) q^{23} +(-0.878550 - 4.22435i) q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.265743 + 3.56283i) q^{26} +(2.32755 - 5.09661i) q^{27} +(-0.853359 + 0.383442i) q^{28} +(-1.80958 + 0.826407i) q^{29} +(1.53014 - 1.52083i) q^{30} +(7.13133 - 1.02533i) q^{31} +(0.317468 + 5.64794i) q^{32} +(4.45958 + 3.86425i) q^{33} +(-5.81986 - 3.20096i) q^{34} +(-0.393516 - 0.252898i) q^{35} +(-0.734460 + 1.12766i) q^{36} +(-5.33547 - 1.56664i) q^{37} +(-1.78469 - 8.32627i) q^{38} +(-2.91254 + 2.52373i) q^{39} +(-2.27969 + 1.67423i) q^{40} +(1.99867 - 0.586863i) q^{41} +(-0.944454 - 0.355548i) q^{42} +(10.6282 + 1.52810i) q^{43} +(-5.03047 - 5.87754i) q^{44} -0.672876 q^{45} +(-5.33594 + 4.18662i) q^{46} -10.1005i q^{47} +(-4.05190 + 4.56247i) q^{48} +(0.965064 - 6.71216i) q^{49} +(-1.32353 - 0.498256i) q^{50} +(-2.01853 - 6.87447i) q^{51} +(4.26710 - 2.70566i) q^{52} +(4.77172 + 5.50686i) q^{53} +(-7.74777 + 1.66069i) q^{54} +(1.08979 - 3.71149i) q^{55} +(1.15538 + 0.644675i) q^{56} +(4.96602 - 7.72727i) q^{57} +(2.46511 + 1.35583i) q^{58} +(-0.375623 + 0.433492i) q^{59} +(-3.01722 - 0.452613i) q^{60} +(1.08545 + 7.54950i) q^{61} +(-7.18265 - 7.22660i) q^{62} +(0.130753 + 0.286310i) q^{63} +(6.14085 - 5.12738i) q^{64} +(2.29800 + 1.04946i) q^{65} +(0.620715 - 8.32197i) q^{66} +(-6.46972 - 10.0671i) q^{67} +(1.28007 + 9.30565i) q^{68} +(-7.26593 - 0.854486i) q^{69} +(0.0451805 + 0.659987i) q^{70} +(-2.60712 - 4.05677i) q^{71} +(1.89949 - 0.118397i) q^{72} +(-3.37025 + 7.37983i) q^{73} +(2.72572 + 7.37656i) q^{74} +(-0.633712 - 1.38764i) q^{75} +(-7.94158 + 9.05290i) q^{76} +(-1.79101 + 0.257509i) q^{77} +(5.32205 + 1.17475i) q^{78} +(9.41665 - 10.8674i) q^{79} +(3.82394 + 1.17367i) q^{80} +(-5.49222 - 3.52963i) q^{81} +(-2.35290 - 1.77258i) q^{82} +(-1.24160 + 4.22849i) q^{83} +(0.393720 + 1.37179i) q^{84} +(-3.54948 + 3.07565i) q^{85} +(-7.23676 - 13.3498i) q^{86} +(0.854985 + 2.91181i) q^{87} +(-2.42336 + 10.6691i) q^{88} +(-16.3745 - 2.35430i) q^{89} +(0.567941 + 0.763523i) q^{90} -1.18174i q^{91} +(9.25442 + 2.52106i) q^{92} -10.9906i q^{93} +(-11.4612 + 8.52536i) q^{94} +(-5.96000 - 0.856919i) q^{95} +(8.59711 + 0.746802i) q^{96} +(3.37985 + 11.5107i) q^{97} +(-8.43096 + 4.57033i) q^{98} +(-1.96707 + 1.70447i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 2 q^{2} - 4 q^{4} - 48 q^{5} + 5 q^{6} - q^{8} - 48 q^{9} + 2 q^{10} + 3 q^{12} + 32 q^{16} + 7 q^{18} - 4 q^{20} + 8 q^{21} + 4 q^{23} + 2 q^{24} - 48 q^{25} + 7 q^{26} + 12 q^{27} + 5 q^{30}+ \cdots - 98 q^{98}+O(q^{100}) \) 480 * q + 2 * q^2 - 4 * q^4 - 48 * q^5 + 5 * q^6 - q^8 - 48 * q^9 + 2 * q^10 + 3 * q^12 + 32 * q^16 + 7 * q^18 - 4 * q^20 + 8 * q^21 + 4 * q^23 + 2 * q^24 - 48 * q^25 + 7 * q^26 + 12 * q^27 + 5 * q^30 - 118 * q^32 - 23 * q^34 + 54 * q^36 + 8 * q^37 - 65 * q^38 + 43 * q^40 - 10 * q^42 - q^44 + 480 * q^45 - 184 * q^46 - 44 * q^48 - 48 * q^49 - 9 * q^50 - 7 * q^52 + 32 * q^53 - 27 * q^54 + 67 * q^56 - 40 * q^58 - 12 * q^59 + 14 * q^60 - 8 * q^61 - 128 * q^62 + 59 * q^64 + 88 * q^66 + 10 * q^68 - 20 * q^69 + 3 * q^72 - 11 * q^74 + 110 * q^76 + 118 * q^78 - 144 * q^79 - q^80 - 56 * q^81 - 59 * q^82 - 162 * q^84 - 18 * q^86 - 76 * q^88 + 7 * q^90 - 149 * q^92 + 168 * q^94 + 65 * q^96 - 98 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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