LMFDB - Embedded newform 252.2.bi.c.223.23

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [252,2,Mod(139,252)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(252, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("252.139"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.bi (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [80,-6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			223.23
Character	$\chi$	$=$	252.223
Dual form			252.2.bi.c.139.23

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.294095 - 1.38330i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(-1.82702 - 0.813640i) q^{4} +(-0.416111 + 0.240242i) q^{5} +(1.51957 + 1.92117i) q^{6} +(-1.52257 - 2.16374i) q^{7} +(-1.66282 + 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +(0.209950 + 0.646259i) q^{10} +(-2.31311 - 1.33548i) q^{11} +(3.10445 - 1.53701i) q^{12} +(-5.48694 + 3.16789i) q^{13} +(-3.44088 + 1.46982i) q^{14} +(0.139573 - 0.820435i) q^{15} +(2.67598 + 2.97307i) q^{16} -2.37005i q^{17} +(-4.24153 - 0.0971545i) q^{18} -4.20225 q^{19} +(0.955712 - 0.100361i) q^{20} +(4.56831 + 0.361276i) q^{21} +(-2.52763 + 2.80696i) q^{22} +(4.15320 - 2.39785i) q^{23} +(-1.21314 - 4.74640i) q^{24} +(-2.38457 + 4.13019i) q^{25} +(2.76845 + 8.52173i) q^{26} +(4.54623 + 2.51631i) q^{27} +(1.02125 + 5.19202i) q^{28} +(1.45060 - 2.51250i) q^{29} +(-1.09386 - 0.434356i) q^{30} +(-3.14399 - 5.44556i) q^{31} +(4.89962 - 2.82731i) q^{32} +(4.33762 - 1.60843i) q^{33} +(-3.27848 - 0.697018i) q^{34} +(1.15338 + 0.534572i) q^{35} +(-1.38180 + 5.83872i) q^{36} +4.69467 q^{37} +(-1.23586 + 5.81295i) q^{38} +(1.84044 - 10.8185i) q^{39} +(0.142241 - 1.35155i) q^{40} +(10.1295 - 5.84827i) q^{41} +(1.84327 - 6.21308i) q^{42} +(1.16280 + 0.671344i) q^{43} +(3.13950 + 4.32198i) q^{44} +(0.939786 + 1.09297i) q^{45} +(-2.09550 - 6.45030i) q^{46} +(-3.72876 + 6.45840i) q^{47} +(-6.92245 + 0.282242i) q^{48} +(-2.36356 + 6.58890i) q^{49} +(5.01199 + 4.51323i) q^{50} +(3.16049 + 2.61967i) q^{51} +(12.6023 - 1.32339i) q^{52} -8.99689 q^{53} +(4.81783 - 5.54874i) q^{54} +1.28335 q^{55} +(7.48244 + 0.114250i) q^{56} +(4.64485 - 5.60375i) q^{57} +(-3.04893 - 2.74552i) q^{58} +(0.140454 + 0.243273i) q^{59} +(-0.922541 + 1.38539i) q^{60} +(-9.52219 - 5.49764i) q^{61} +(-8.45745 + 2.74757i) q^{62} +(-5.53124 + 5.69257i) q^{63} +(-2.47005 - 7.60913i) q^{64} +(1.52212 - 2.63639i) q^{65} +(-0.949260 - 6.47324i) q^{66} +(1.89068 - 1.09159i) q^{67} +(-1.92837 + 4.33012i) q^{68} +(-1.39308 + 8.18874i) q^{69} +(1.07867 - 1.43825i) q^{70} -0.198757i q^{71} +(7.67029 + 3.62858i) q^{72} +4.84941i q^{73} +(1.38068 - 6.49412i) q^{74} +(-2.87194 - 7.74506i) q^{75} +(7.67758 + 3.41912i) q^{76} +(0.632248 + 7.03833i) q^{77} +(-14.4239 - 5.72753i) q^{78} +(-3.42117 - 1.97521i) q^{79} +(-1.82776 - 0.594244i) q^{80} +(-8.38060 + 3.28110i) q^{81} +(-5.11086 - 15.7321i) q^{82} +(5.09429 - 8.82356i) q^{83} +(-8.05243 - 4.37702i) q^{84} +(0.569384 + 0.986203i) q^{85} +(1.27064 - 1.41106i) q^{86} +(1.74707 + 4.71152i) q^{87} +(6.90188 - 3.07178i) q^{88} -2.67188i q^{89} +(1.78829 - 0.978565i) q^{90} +(15.2087 + 7.04900i) q^{91} +(-9.53895 + 1.00170i) q^{92} +(10.7369 + 1.82656i) q^{93} +(7.83727 + 7.05736i) q^{94} +(1.74860 - 1.00956i) q^{95} +(-1.64543 + 9.65881i) q^{96} +(-1.87526 - 1.08268i) q^{97} +(8.41929 + 5.20727i) q^{98} +(-2.64962 + 7.56210i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) $ 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$-1$

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 $

$2$	0.294095	−	1.38330i	0.207956	−	0.978138i
$2$	0.294095	−	1.38330i	0.207956	−	0.978138i
$3$	−1.10533	+	1.33351i	−0.638160	+	0.769904i
$3$	−1.10533	+	1.33351i	−0.638160	+	0.769904i
$4$	−1.82702	−	0.813640i	−0.913508	−	0.406820i
$5$	−0.416111	+	0.240242i	−0.186091	+	0.107439i	−0.590151	−	0.807293i	$-0.700932\pi$
$5$	−0.416111	+	0.240242i	−0.186091	+	0.107439i	0.404061	+	0.914732i	$0.367598\pi$
$6$	1.51957	+	1.92117i	0.620363	+	0.784315i
$7$	−1.52257	−	2.16374i	−0.575477	−	0.817818i
$7$	−1.52257	−	2.16374i	−0.575477	−	0.817818i
$8$	−1.66282	+	2.28802i	−0.587896	+	0.808937i
$9$	−0.556509	−	2.94793i	−0.185503	−	0.982644i
$10$	0.209950	+	0.646259i	0.0663919	+	0.204365i
$11$	−2.31311	−	1.33548i	−0.697429	−	0.402661i	0.108960	−	0.994046i	$-0.465248\pi$
$11$	−2.31311	−	1.33548i	−0.697429	−	0.402661i	−0.806389	+	0.591385i	$0.798581\pi$
$12$	3.10445	−	1.53701i	0.896177	−	0.443697i
$13$	−5.48694	+	3.16789i	−1.52180	+	0.878614i	−0.522136	+	0.852862i	$0.674865\pi$
$13$	−5.48694	+	3.16789i	−1.52180	+	0.878614i	−0.999668	+	0.0257515i	$0.991802\pi$
$14$	−3.44088	+	1.46982i	−0.919613	+	0.392826i
$15$	0.139573	−	0.820435i	0.0360376	−	0.211835i
$16$	2.67598	+	2.97307i	0.668995	+	0.743267i
$17$		−	2.37005i		−	0.574821i	−0.957808	−	0.287410i	$-0.907206\pi$
$17$		−	2.37005i		−	0.574821i	0.957808	−	0.287410i	$-0.0927944\pi$
$18$	−4.24153	−	0.0971545i	−0.999738	−	0.0228995i
$19$	−4.20225			−0.964062			−0.482031	−	0.876154i	$-0.660101\pi$
$19$	−4.20225			−0.964062			−0.482031	+	0.876154i	$0.660101\pi$
$20$	0.955712	−	0.100361i	0.213704	−	0.0224414i
$21$	4.56831	+	0.361276i	0.996888	+	0.0788369i
$22$	−2.52763	+	2.80696i	−0.538893	+	0.598446i
$23$	4.15320	−	2.39785i	0.866001	−	0.499986i	−1.59909e−5	−	1.00000i	$-0.500005\pi$
$23$	4.15320	−	2.39785i	0.866001	−	0.499986i	0.866017	+	0.500014i	$0.166672\pi$
$24$	−1.21314	−	4.74640i	−0.247631	−	0.968854i
$25$	−2.38457	+	4.13019i	−0.476914	+	0.826038i
$26$	2.76845	+	8.52173i	0.542937	+	1.67125i
$27$	4.54623	+	2.51631i	0.874921	+	0.484265i
$28$	1.02125	+	5.19202i	0.192999	+	0.981199i
$29$	1.45060	−	2.51250i	0.269369	−	0.466560i	−0.699330	−	0.714799i	$-0.746518\pi$
$29$	1.45060	−	2.51250i	0.269369	−	0.466560i	0.968699	+	0.248238i	$0.0798516\pi$
$30$	−1.09386	−	0.434356i	−0.199710	−	0.0793022i
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	−0.997080	−	0.0763698i	$-0.975667\pi$
$31$	−3.14399	−	5.44556i	−0.564678	−	0.978051i	0.432402	−	0.901681i	$-0.357666\pi$
$32$	4.89962	−	2.82731i	0.866139	−	0.499802i
$33$	4.33762	−	1.60843i	0.755082	−	0.279991i
$34$	−3.27848	−	0.697018i	−0.562254	−	0.119538i
$35$	1.15338	+	0.534572i	0.194957	+	0.0903592i
$36$	−1.38180	+	5.83872i	−0.230301	+	0.973120i
$37$	4.69467			0.771799			0.385900	−	0.922541i	$-0.373891\pi$
$37$	4.69467			0.771799			0.385900	+	0.922541i	$0.373891\pi$
$38$	−1.23586	+	5.81295i	−0.200483	+	0.942986i
$39$	1.84044	−	10.8185i	0.294707	−	1.73234i
$40$	0.142241	−	1.35155i	0.0224902	−	0.213699i
$41$	10.1295	−	5.84827i	1.58196	−	0.913347i	0.587390	−	0.809304i	$-0.300155\pi$
$41$	10.1295	−	5.84827i	1.58196	−	0.913347i	0.994573	−	0.104043i	$-0.0331779\pi$
$42$	1.84327	−	6.21308i	0.284422	−	0.958699i
$43$	1.16280	+	0.671344i	0.177326	+	0.102379i	0.586036	−	0.810285i	$-0.300688\pi$
$43$	1.16280	+	0.671344i	0.177326	+	0.102379i	−0.408710	+	0.912664i	$0.634021\pi$
$44$	3.13950	+	4.32198i	0.473297	+	0.651562i
$45$	0.939786	+	1.09297i	0.140095	+	0.162930i
$46$	−2.09550	−	6.45030i	−0.308965	−	0.951044i
$47$	−3.72876	+	6.45840i	−0.543895	+	0.942054i	0.454780	+	0.890604i	$0.349718\pi$
$47$	−3.72876	+	6.45840i	−0.543895	+	0.942054i	−0.998676	+	0.0514505i	$0.983616\pi$
$48$	−6.92245	+	0.282242i	−0.999170	+	0.0407381i
$49$	−2.36356	+	6.58890i	−0.337652	+	0.941271i
$50$	5.01199	+	4.51323i	0.708803	+	0.638267i
$51$	3.16049	+	2.61967i	0.442557	+	0.366828i
$52$	12.6023	−	1.32339i	1.74762	−	0.183521i
$53$	−8.99689			−1.23582			−0.617909	−	0.786250i	$-0.712020\pi$
$53$	−8.99689			−1.23582			−0.617909	+	0.786250i	$0.712020\pi$
$54$	4.81783	−	5.54874i	0.655623	−	0.755088i
$55$	1.28335			0.173047
$56$	7.48244	+	0.114250i	0.999883	+	0.0152673i
$57$	4.64485	−	5.60375i	0.615226	−	0.742235i
$58$	−3.04893	−	2.74552i	−0.400344	−	0.360504i
$59$	0.140454	+	0.243273i	0.0182855	+	0.0316715i	0.875023	−	0.484081i	$-0.160846\pi$
$59$	0.140454	+	0.243273i	0.0182855	+	0.0316715i	−0.856738	+	0.515752i	$0.827513\pi$
$60$	−0.922541	+	1.38539i	−0.119099	+	0.178852i
$61$	−9.52219	−	5.49764i	−1.21919	−	0.703900i	−0.254446	−	0.967087i	$-0.581893\pi$
$61$	−9.52219	−	5.49764i	−1.21919	−	0.703900i	−0.964745	+	0.263186i	$0.915227\pi$
$62$	−8.45745	+	2.74757i	−1.07410	+	0.348941i
$63$	−5.53124	+	5.69257i	−0.696871	+	0.717197i
$64$	−2.47005	−	7.60913i	−0.308757	−	0.951141i
$65$	1.52212	−	2.63639i	0.188796	−	0.327003i
$66$	−0.949260	−	6.47324i	−0.116846	−	0.796800i
$67$	1.89068	−	1.09159i	0.230984	−	0.133358i	−0.380042	−	0.924969i	$-0.624091\pi$
$67$	1.89068	−	1.09159i	0.230984	−	0.133358i	0.611026	+	0.791611i	$0.290757\pi$
$68$	−1.92837	+	4.33012i	−0.233849	+	0.525104i
$69$	−1.39308	+	8.18874i	−0.167707	+	0.985809i
$70$	1.07867	−	1.43825i	0.128926	−	0.171904i
$71$		−	0.198757i		−	0.0235881i	−0.999930	−	0.0117940i	$-0.996246\pi$
$71$		−	0.198757i		−	0.0235881i	0.999930	−	0.0117940i	$-0.00375425\pi$
$72$	7.67029	+	3.62858i	0.903953	+	0.427632i
$73$			4.84941i			0.567580i	0.958886	+	0.283790i	$0.0915919\pi$
$73$			4.84941i			0.567580i	−0.958886	+	0.283790i	$0.908408\pi$
$74$	1.38068	−	6.49412i	0.160501	−	0.754926i
$75$	−2.87194	−	7.74506i	−0.331623	−	0.894322i
$76$	7.67758	+	3.41912i	0.880679	+	0.392200i
$77$	0.632248	+	7.03833i	0.0720514	+	0.802092i
$78$	−14.4239	−	5.72753i	−1.63318	−	0.648515i
$79$	−3.42117	−	1.97521i	−0.384912	−	0.222229i	0.295041	−	0.955484i	$-0.404667\pi$
$79$	−3.42117	−	1.97521i	−0.384912	−	0.222229i	−0.679953	+	0.733256i	$0.738000\pi$
$80$	−1.82776	−	0.594244i	−0.204350	−	0.0664385i
$81$	−8.38060	+	3.28110i	−0.931177	+	0.364567i
$82$	−5.11086	−	15.7321i	−0.564400	−	1.73731i
$83$	5.09429	−	8.82356i	0.559171	−	0.968512i	−0.438395	−	0.898782i	$-0.644453\pi$
$83$	5.09429	−	8.82356i	0.559171	−	0.968512i	0.997566	−	0.0697297i	$-0.0222137\pi$
$84$	−8.05243	−	4.37702i	−0.878593	−	0.477572i
$85$	0.569384	+	0.986203i	0.0617584	+	0.106969i
$86$	1.27064	−	1.41106i	0.137017	−	0.152159i
$87$	1.74707	+	4.71152i	0.187306	+	0.505128i
$88$	6.90188	−	3.07178i	0.735743	−	0.327453i
$89$		−	2.67188i		−	0.283219i	−0.989923	−	0.141609i	$-0.954772\pi$
$89$		−	2.67188i		−	0.283219i	0.989923	−	0.141609i	$-0.0452277\pi$
$90$	1.78829	−	0.978565i	0.188502	−	0.103150i
$91$	15.2087	+	7.04900i	1.59431	+	0.738936i
$92$	−9.53895	+	1.00170i	−0.994504	+	0.104435i
$93$	10.7369	+	1.82656i	1.11336	+	0.189406i
$94$	7.83727	+	7.05736i	0.808353	+	0.727911i
$95$	1.74860	−	1.00956i	0.179403	−	0.103578i
$96$	−1.64543	+	9.65881i	−0.167936	+	0.985798i
$97$	−1.87526	−	1.08268i	−0.190403	−	0.109929i	0.401768	−	0.915741i	$-0.368396\pi$
$97$	−1.87526	−	1.08268i	−0.190403	−	0.109929i	−0.592171	+	0.805812i	$0.701729\pi$
$98$	8.41929	+	5.20727i	0.850476	+	0.526013i
$99$	−2.64962	+	7.56210i	−0.266297	+	0.760019i
$100$	7.71713	−	5.60575i	0.771713	−	0.560575i
$101$	−4.50341	−	2.60004i	−0.448106	−	0.258714i	0.258924	−	0.965898i	$-0.416632\pi$
$101$	−4.50341	−	2.60004i	−0.448106	−	0.258714i	−0.707030	+	0.707184i	$0.749965\pi$
$102$	4.55327	−	3.60146i	0.450841	−	0.356597i
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	0.804946	−	0.593348i	$-0.202194\pi$
$103$	−1.13040	−	1.95791i	−0.111382	−	0.192919i	−0.916328	+	0.400429i	$0.868861\pi$
$104$	1.87562	−	17.8219i	0.183920	−	1.74758i
$105$	−1.98772	+	0.947169i	−0.193981	+	0.0924342i
$106$	−2.64594	+	12.4454i	−0.256996	+	1.20880i
$107$			14.8308i			1.43375i	0.697204	+	0.716873i	$0.254427\pi$
$107$			14.8308i			1.43375i	−0.697204	+	0.716873i	$0.745573\pi$
$108$	−6.25866	−	8.29634i	−0.602239	−	0.798316i
$109$	−10.9535			−1.04916			−0.524578	−	0.851363i	$-0.675777\pi$
$109$	−10.9535			−1.04916			−0.524578	+	0.851363i	$0.675777\pi$
$110$	0.377426	−	1.77525i	0.0359861	−	0.169264i
$111$	−5.18914	+	6.26040i	−0.492532	+	0.594211i
$112$	2.35859	−	10.3168i	0.222866	−	0.974849i
$113$	−4.72782	−	8.18882i	−0.444756	−	0.770339i	0.553280	−	0.832996i	$-0.313376\pi$
$113$	−4.72782	−	8.18882i	−0.444756	−	0.770339i	−0.998035	+	0.0626563i	$0.980043\pi$
$114$	−6.38562	−	8.07324i	−0.598068	−	0.756128i
$115$	−1.15213	+	1.99554i	−0.107436	+	0.186085i
$116$	−4.69454	+	3.41013i	−0.435877	+	0.316622i
$117$	12.3922	+	14.4122i	1.14566	+	1.33241i
$118$	0.377825	−	0.122744i	0.0347816	−	0.0112995i
$119$	−5.12817	+	3.60856i	−0.470099	+	0.330796i
$120$	1.64508	+	1.68358i	0.150175	+	0.153689i
$121$	−1.93301	−	3.34807i	−0.175728	−	0.304370i
$122$	−10.4053	+	11.5552i	−0.942050	+	1.04616i
$123$	−3.39766	+	19.9721i	−0.306357	+	1.80082i
$124$	1.31341	+	12.5072i	0.117947	+	1.12318i
$125$		−	4.69391i		−	0.419836i
$126$	6.24780	+	9.32550i	0.556599	+	0.830782i
$127$			1.45847i			0.129419i	0.997904	+	0.0647093i	$0.0206120\pi$
$127$			1.45847i			0.129419i	−0.997904	+	0.0647093i	$0.979388\pi$
$128$	−11.2521	+	1.17901i	−0.994555	+	0.104211i
$129$	−2.18052	+	0.808556i	−0.191984	+	0.0711894i
$130$	−3.19926	−	2.88089i	−0.280593	−	0.252671i
$131$	6.19426	+	10.7288i	0.541195	+	0.937377i	0.998836	+	0.0482400i	$0.0153612\pi$
$131$	6.19426	+	10.7288i	0.541195	+	0.937377i	−0.457641	+	0.889137i	$0.651305\pi$
$132$	−9.23357	−	0.590636i	−0.803680	−	0.0514083i
$133$	6.39822	+	9.09258i	0.554796	+	0.788427i
$134$	−0.953947	−	2.93640i	−0.0824085	−	0.253667i
$135$	−2.49626	+	0.0451274i	−0.214844	+	0.00388394i
$136$	5.42271	+	3.94096i	0.464994	+	0.337935i
$137$	−4.45878	+	7.72284i	−0.380939	+	0.659806i	−0.991197	−	0.132397i	$-0.957733\pi$
$137$	−4.45878	+	7.72284i	−0.380939	+	0.659806i	0.610257	+	0.792203i	$0.291066\pi$
$138$	10.9178	+	4.33530i	0.929382	+	0.369045i
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	0.918444	−	0.395551i	$-0.129446\pi$
$139$	1.37546	+	2.38237i	0.116665	+	0.202070i	−0.801779	+	0.597621i	$0.796113\pi$
$140$	−1.67229	−	1.91511i	−0.141335	−	0.161856i
$141$	−4.49086	−	12.1110i	−0.378198	−	1.01993i
$142$	−0.274939	−	0.0584533i	−0.0230724	−	0.00490529i
$143$	16.9225			1.41513
$144$	7.27519	−	9.54314i	0.606266	−	0.795262i
$145$			1.39397i			0.115763i
$146$	6.70817	+	1.42618i	0.555172	+	0.118032i
$147$	−6.17387	−	10.4347i	−0.509212	−	0.860641i
$148$	−8.57724	−	3.81977i	−0.705045	−	0.313983i
$149$	−0.0762596	−	0.132086i	−0.00624743	−	0.0108209i	0.862885	−	0.505401i	$-0.168655\pi$
$149$	−0.0762596	−	0.132086i	−0.00624743	−	0.0108209i	−0.869132	+	0.494580i	$0.835322\pi$
$150$	−11.5583	+	1.69496i	−0.943734	+	0.138393i
$151$	−10.8876	−	6.28594i	−0.886017	−	0.511542i	−0.0133797	−	0.999910i	$-0.504259\pi$
$151$	−10.8876	−	6.28594i	−0.886017	−	0.511542i	−0.872638	+	0.488368i	$0.837592\pi$
$152$	6.98759	−	9.61482i	0.566768	−	0.779865i
$153$	−6.98674	+	1.31895i	−0.564844	+	0.106631i
$154$	9.92204	+	1.19535i	0.799541	+	0.0963240i
$155$	2.61650	+	1.51064i	0.210162	+	0.121337i
$156$	−12.1648	+	18.2680i	−0.973967	+	1.46261i
$157$	9.96123	−	5.75112i	0.794993	−	0.458989i	−0.0467246	−	0.998908i	$-0.514878\pi$
$157$	9.96123	−	5.75112i	0.794993	−	0.458989i	0.841717	+	0.539919i	$0.181545\pi$
$158$	−3.73845	+	4.15159i	−0.297415	+	0.330283i
$159$	9.94450	−	11.9975i	0.788650	−	0.951461i
$160$	−1.35955	+	2.35357i	−0.107482	+	0.186066i
$161$	−11.5119	−	5.33556i	−0.907262	−	0.420501i
$162$	2.07404	+	12.5578i	0.162952	+	0.986634i
$163$			19.9710i			1.56425i	0.623121	+	0.782126i	$0.285865\pi$
$163$			19.9710i			1.56425i	−0.623121	+	0.782126i	$0.714135\pi$
$164$	−23.2652	+	2.44312i	−1.81670	+	0.190776i
$165$	−1.41852	+	1.71136i	−0.110431	+	0.133229i
$166$	−10.7074	−	9.64187i	−0.831055	−	0.748354i
$167$	−10.9749	−	19.0090i	−0.849260	−	1.47096i	−0.881870	−	0.471493i	$-0.843715\pi$
$167$	−10.9749	−	19.0090i	−0.849260	−	1.47096i	0.0326095	−	0.999468i	$-0.489618\pi$
$168$	−8.42289	+	9.85164i	−0.649840	+	0.760071i
$169$	13.5710	−	23.5057i	1.04392	−	1.80813i
$170$	1.53166	−	0.497590i	0.117473	−	0.0381634i
$171$	2.33859	+	12.3879i	0.178836	+	0.947329i
$172$	−1.57823	−	2.17266i	−0.120339	−	0.165664i
$173$	−13.2462	−	7.64770i	−1.00709	−	0.581444i	−0.0967521	−	0.995309i	$-0.530845\pi$
$173$	−13.2462	−	7.64770i	−1.00709	−	0.581444i	−0.910339	+	0.413864i	$0.864179\pi$
$174$	7.03124	−	1.03109i	0.533037	−	0.0781666i
$175$	12.5673	−	1.12891i	0.950002	−	0.0853379i
$176$	−2.21938	−	10.4507i	−0.167292	−	0.787754i
$177$	−0.479655	−	0.0815993i	−0.0360531	−	0.00613338i
$178$	−3.69600	−	0.785786i	−0.277027	−	0.0588971i
$179$		−	10.6967i		−	0.799512i	−0.916622	−	0.399756i	$-0.869095\pi$
$179$		−	10.6967i		−	0.799512i	0.916622	−	0.399756i	$-0.130905\pi$
$180$	−0.827720	−	2.76152i	−0.0616946	−	0.205832i
$181$		−	7.23452i		−	0.537738i	−0.963177	−	0.268869i	$-0.913350\pi$
$181$		−	7.23452i		−	0.537738i	0.963177	−	0.268869i	$-0.0866498\pi$
$182$	14.2237	−	18.9651i	1.05433	−	1.40579i
$183$	17.8563	−	6.62127i	1.31997	−	0.489458i
$184$	−1.41970	+	13.4898i	−0.104662	+	0.994480i
$185$	−1.95350	+	1.12786i	−0.143624	+	0.0829216i
$186$	5.68433	−	14.3151i	0.416795	−	1.04963i
$187$	−3.16514	+	5.48218i	−0.231458	+	0.400897i
$188$	12.0673	−	8.76573i	0.880099	−	0.639307i
$189$	−1.47729	−	13.6681i	−0.107457	−	0.994210i
$190$	−0.882260	−	2.71574i	−0.0640059	−	0.197020i
$191$	−17.2598	−	9.96493i	−1.24887	−	0.721037i	−0.277988	−	0.960584i	$-0.589668\pi$
$191$	−17.2598	−	9.96493i	−1.24887	−	0.721037i	−0.970885	+	0.239547i	$0.923001\pi$
$192$	12.8771	+	5.11672i	0.929323	+	0.369268i
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	0.999884	+	0.0152396i	$0.00485112\pi$
$193$	7.12877	+	12.3474i	0.513140	+	0.888784i	−0.486744	+	0.873545i	$0.661816\pi$
$194$	−2.04917	+	2.27562i	−0.147122	+	0.163380i
$195$	1.83322	+	4.94383i	0.131279	+	0.354035i
$196$	9.67926	−	10.1149i	0.691376	−	0.722495i
$197$	11.9516			0.851517			0.425759	−	0.904837i	$-0.360007\pi$
$197$	11.9516			0.851517			0.425759	+	0.904837i	$0.360007\pi$
$198$	9.68138	+	5.88919i	0.688026	+	0.418526i
$199$	−21.9514			−1.55610			−0.778048	−	0.628205i	$-0.783790\pi$
$199$	−21.9514			−1.55610			−0.778048	+	0.628205i	$0.783790\pi$
$200$	−5.48485	−	12.3237i	−0.387837	−	0.871418i
$201$	−0.634177	+	3.72781i	−0.0447314	+	0.262939i
$202$	−4.92106	+	5.46489i	−0.346244	+	0.384508i
$203$	−7.64505	+	0.686749i	−0.536577	+	0.0482003i
$204$	−3.64279	−	7.35769i	−0.255046	−	0.515141i
$205$	−2.81000	+	4.86706i	−0.196259	+	0.339930i
$206$	−3.04082	+	0.987869i	−0.211864	+	0.0688281i
$207$	−9.37998	−	10.9089i	−0.651954	−	0.758222i
$208$	−24.1013	−	7.83585i	−1.67112	−	0.543318i
$209$	9.72027	+	5.61200i	0.672365	+	0.388190i
$210$	0.725637	+	3.02816i	0.0500737	+	0.208963i
$211$	8.92341	−	5.15194i	0.614313	−	0.354674i	−0.160338	−	0.987062i	$-0.551259\pi$
$211$	8.92341	−	5.15194i	0.614313	−	0.354674i	0.774652	+	0.632388i	$0.217925\pi$
$212$	16.4375	+	7.32023i	1.12893	+	0.502756i
$213$	0.265044	+	0.219691i	0.0181605	+	0.0150530i
$214$	20.5154	+	4.36165i	1.40240	+	0.298156i
$215$	−0.645139			−0.0439981
$216$	−13.3169	+	6.21767i	−0.906102	+	0.423059i
$217$	−6.99583	+	15.0940i	−0.474908	+	1.02465i
$218$	−3.22137	+	15.1519i	−0.218179	+	1.02622i
$219$	−6.46674	−	5.36017i	−0.436982	−	0.362207i
$220$	−2.34470	−	1.04418i	−0.158080	−	0.0703988i
$221$	7.50804	+	13.0043i	0.505046	+	0.874765i
$222$	7.13389	+	9.01927i	0.478795	+	0.605334i
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	−0.999839	−	0.0179449i	$-0.994288\pi$
$223$	−7.23332	+	12.5285i	−0.484379	+	0.838969i	0.515460	+	0.856914i	$0.327621\pi$
$224$	−13.5776	−	6.29675i	−0.907191	−	0.420719i
$225$	13.5026	+	4.73105i	0.900170	+	0.315404i
$226$	−12.7180	+	4.13168i	−0.845988	+	0.274835i
$227$	9.67633	−	16.7599i	0.642240	−	1.11239i	−0.342691	−	0.939448i	$-0.611338\pi$
$227$	9.67633	−	16.7599i	0.642240	−	1.11239i	0.984932	−	0.172945i	$-0.0553282\pi$
$228$	−13.0457	+	6.45890i	−0.863970	+	0.427751i
$229$	17.0595	−	9.84933i	1.12733	−	0.650862i	0.184065	−	0.982914i	$-0.441074\pi$
$229$	17.0595	−	9.84933i	1.12733	−	0.650862i	0.943261	+	0.332052i	$0.107741\pi$
$230$	2.42159	+	2.18061i	0.159675	+	0.143785i
$231$	−10.0845	−	6.93654i	−0.663514	−	0.456391i
$232$	3.33658	+	7.49683i	0.219057	+	0.492191i
$233$	7.34808			0.481389			0.240694	−	0.970601i	$-0.422625\pi$
$233$	7.34808			0.481389			0.240694	+	0.970601i	$0.422625\pi$
$234$	23.5808	−	12.9036i	1.54152	−	0.843535i
$235$		−	3.58321i		−	0.233743i
$236$	−0.0586747	−	0.558743i	−0.00381940	−	0.0363711i
$237$	6.41548	−	2.37892i	0.416730	−	0.154527i
$238$	3.48354	+	8.15504i	0.225804	+	0.528613i
$239$	8.34611	−	4.81863i	0.539865	−	0.311691i	−0.205159	−	0.978729i	$-0.565771\pi$
$239$	8.34611	−	4.81863i	0.539865	−	0.311691i	0.745024	+	0.667037i	$0.232438\pi$
$240$	2.81270	−	1.78051i	0.181559	−	0.114931i
$241$	−3.56210	−	2.05658i	−0.229455	−	0.132476i	0.380865	−	0.924630i	$-0.375626\pi$
$241$	−3.56210	−	2.05658i	−0.229455	−	0.132476i	−0.610321	+	0.792154i	$0.708959\pi$
$242$	−5.19986	+	1.68928i	−0.334260	+	0.108591i
$243$	4.88791	−	14.8023i	0.313559	−	0.949569i
$244$	12.9241	+	17.7919i	0.827381	+	1.13901i
$245$	−0.599424	−	3.30954i	−0.0382958	−	0.211439i
$246$	26.6280	+	10.5737i	1.69774	+	0.674152i
$247$	23.0575	−	13.3123i	1.46711	−	0.847038i
$248$	17.6874	+	1.86147i	1.12315	+	0.118204i
$249$	6.13548	+	16.5462i	0.388820	+	1.04857i
$250$	−6.49307	−	1.38045i	−0.410658	−	0.0873076i
$251$	−3.31816			−0.209441			−0.104720	−	0.994502i	$-0.533395\pi$
$251$	−3.31816			−0.209441			−0.104720	+	0.994502i	$0.533395\pi$
$252$	14.7374	−	5.89998i	0.928367	−	0.371664i
$253$	−12.8091			−0.805300
$254$	2.01750	+	0.428929i	0.126589	+	0.0269134i
$255$	−1.94447	−	0.330795i	−0.121767	−	0.0207152i
$256$	−1.67826	+	15.9117i	−0.104892	+	0.994484i
$257$	−14.9497	+	8.63121i	−0.932537	+	0.538400i	−0.887613	−	0.460590i	$-0.847638\pi$
$257$	−14.9497	+	8.63121i	−0.932537	+	0.538400i	−0.0449237	+	0.998990i	$0.514304\pi$
$258$	0.477193	+	3.25410i	0.0297088	+	0.202591i
$259$	−7.14796	−	10.1581i	−0.444153	−	0.631191i
$260$	−4.92600	+	3.57826i	−0.305498	+	0.221915i
$261$	−8.21396	−	2.87802i	−0.508431	−	0.178145i
$262$	16.6628	−	5.41322i	1.02943	−	0.334430i
$263$	11.4455	+	6.60806i	0.705760	+	0.407471i	0.809489	−	0.587135i	$-0.199744\pi$
$263$	11.4455	+	6.60806i	0.705760	+	0.407471i	−0.103729	+	0.994606i	$0.533078\pi$
$264$	−3.53257	+	12.5991i	−0.217415	+	0.775419i
$265$	3.74371	−	2.16143i	0.229974	−	0.132776i
$266$	14.4594	−	6.17655i	0.886564	−	0.378708i
$267$	3.56298	+	2.95330i	0.218051	+	0.180739i
$268$	−4.34247	+	0.456011i	−0.265258	+	0.0278553i
$269$			27.5600i			1.68036i	0.542304	+	0.840182i	$0.317552\pi$
$269$			27.5600i			1.68036i	−0.542304	+	0.840182i	$0.682448\pi$
$270$	−0.671712	+	3.46634i	−0.0408791	+	0.210955i
$271$	21.2467			1.29065			0.645323	−	0.763910i	$-0.276723\pi$
$271$	21.2467			1.29065			0.645323	+	0.763910i	$0.276723\pi$
$272$	7.04631	−	6.34220i	0.427245	−	0.384552i
$273$	−26.2105	+	12.4896i	−1.58633	+	0.755905i
$274$	9.37167	+	8.43906i	0.566163	+	0.509822i
$275$	11.0315	−	6.36906i	0.665227	−	0.384069i
$276$	9.20786	−	13.8275i	0.554248	−	0.832318i
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	−0.561140	−	0.827721i	$-0.689637\pi$
$277$	7.26076	−	12.5760i	0.436257	−	0.755619i	0.997397	+	0.0721016i	$0.0229706\pi$
$278$	3.70004	−	1.20203i	0.221914	−	0.0720930i
$279$	−14.3035	+	12.2988i	−0.856326	+	0.736309i
$280$	−3.14097	+	1.75005i	−0.187709	+	0.104586i
$281$	6.35647	−	11.0097i	0.379195	−	0.656785i	−0.611750	−	0.791051i	$-0.709534\pi$
$281$	6.35647	−	11.0097i	0.379195	−	0.656785i	0.990945	+	0.134266i	$0.0428676\pi$
$282$	−18.0738	+	2.65041i	−1.07628	+	0.157830i
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	−0.989516	−	0.144425i	$-0.953867\pi$
$283$	−10.4272	−	18.0605i	−0.619834	−	1.07358i	0.369682	−	0.929158i	$-0.379467\pi$
$284$	−0.161716	+	0.363132i	−0.00959610	+	0.0215479i
$285$	−0.586520	+	3.44767i	−0.0347425	+	0.204222i
$286$	4.97683	−	23.4089i	0.294286	−	1.38420i
$287$	−28.0770	−	13.0132i	−1.65733	−	0.768147i
$288$	−11.0614	−	12.8703i	−0.651799	−	0.758392i
$289$	11.3829			0.669581
$290$	1.92828	+	0.409960i	0.113232	+	0.0240737i
$291$	3.51653	−	1.30396i	0.206143	−	0.0764396i
$292$	3.94567	−	8.85995i	0.230903	−	0.518489i
$293$	−5.80807	+	3.35329i	−0.339311	+	0.195901i	−0.659967	−	0.751294i	$-0.729430\pi$
$293$	−5.80807	+	3.35329i	−0.339311	+	0.195901i	0.320656	+	0.947196i	$0.396097\pi$
$294$	−16.2500	+	5.47149i	−0.947720	+	0.319104i
$295$	−0.116889	−	0.0674857i	−0.00680552	−	0.00392917i
$296$	−7.80640	+	10.7415i	−0.453738	+	0.624336i
$297$	−7.15545	−	11.8919i	−0.415201	−	0.690037i
$298$	−0.205141	+	0.0666440i	−0.0118835	+	0.00386058i
$299$	−15.1922	+	26.3137i	−0.878590	+	1.52176i
$300$	−1.05461	+	16.4871i	−0.0608882	+	0.951882i
$301$	−0.317831	−	3.53817i	−0.0183195	−	0.203937i
$302$	−11.8973	+	13.2121i	−0.684612	+	0.760269i
$303$	8.44492	−	3.13145i	0.485148	−	0.179897i
$304$	−11.2451	−	12.4936i	−0.644953	−	0.716555i
$305$	5.28305			0.302507
$306$	−0.230261	+	10.0526i	−0.0131631	+	0.574670i
$307$	12.0792			0.689397			0.344699	−	0.938713i	$-0.387981\pi$
$307$	12.0792			0.689397			0.344699	+	0.938713i	$0.387981\pi$
$308$	4.57154	−	13.3736i	0.260488	−	0.762030i
$309$	3.86037	+	0.656729i	0.219609	+	0.0373600i
$310$	2.85916	−	3.17513i	0.162389	−	0.180335i
$311$	−1.01185	−	1.75258i	−0.0573769	−	0.0993797i	0.835910	−	0.548866i	$-0.184940\pi$
$311$	−1.01185	−	1.75258i	−0.0573769	−	0.0993797i	−0.893287	+	0.449486i	$0.851607\pi$
$312$	21.6925	+	22.2001i	1.22810	+	1.25683i
$313$	16.8337	+	9.71892i	0.951495	+	0.549346i	0.893545	−	0.448974i	$-0.148210\pi$
$313$	16.8337	+	9.71892i	0.951495	+	0.549346i	0.0579500	+	0.998319i	$0.481544\pi$
$314$	−5.02596	−	15.4707i	−0.283631	−	0.873062i
$315$	0.934016	−	3.69758i	0.0526259	−	0.208335i
$316$	4.64342	+	6.39235i	0.261213	+	0.359598i
$317$	−5.21828	+	9.03832i	−0.293088	+	0.507643i	−0.974538	−	0.224222i	$-0.928016\pi$
$317$	−5.21828	+	9.03832i	−0.293088	+	0.507643i	0.681451	+	0.731864i	$0.261349\pi$
$318$	−13.6714	−	17.2846i	−0.766655	−	0.969271i
$319$	−6.71078	+	3.87447i	−0.375731	+	0.216929i
$320$	2.85585	+	2.57283i	0.159647	+	0.143826i
$321$	−19.7770	−	16.3928i	−1.10385	−	0.914959i
$322$	−10.7662	+	14.3552i	−0.599979	+	0.799981i
$323$			9.95953i			0.554163i
$324$	17.9811	+	0.824167i	0.998951	+	0.0457871i
$325$		−	30.2162i		−	1.67609i
$326$	27.6258	+	5.87337i	1.53005	+	0.325296i
$327$	12.1072	−	14.6066i	0.669529	−	0.807748i
$328$	−3.46260	+	32.9011i	−0.191190	+	1.81666i
$329$	19.6516	−	1.76529i	1.08343	−	0.0973235i
$330$	1.95014	+	2.46553i	0.107352	+	0.135723i
$331$	−31.2751	−	18.0567i	−1.71903	−	0.992484i	−0.920704	−	0.390261i	$-0.872385\pi$
$331$	−31.2751	−	18.0567i	−1.71903	−	0.992484i	−0.798328	−	0.602223i	$-0.794282\pi$
$332$	−16.4866	+	11.9759i	−0.904817	+	0.657262i
$333$	−2.61262	−	13.8396i	−0.143171	−	0.758404i
$334$	−29.5227	+	9.59103i	−1.61541	+	0.524798i
$335$	−0.524489	+	0.908442i	−0.0286559	+	0.0496335i
$336$	11.1506	+	14.5487i	0.608316	+	0.793695i
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	0.949123	−	0.314905i	$-0.101973\pi$
$337$	3.70539	+	6.41792i	0.201845	+	0.349606i	−0.747278	+	0.664512i	$0.768639\pi$
$338$	−28.5242	−	25.6856i	−1.55151	−	1.39712i
$339$	16.1457	+	2.74671i	0.876912	+	0.149181i
$340$	−0.237861	−	2.26508i	−0.0128998	−	0.122841i
$341$			16.7949i			0.909495i
$342$	17.8240	+	0.408267i	0.963809	+	0.0220766i
$343$	17.8554	−	4.91791i	0.964099	−	0.265542i
$344$	−3.46958	+	1.54419i	−0.187067	+	0.0832570i
$345$	−1.38760	−	3.74210i	−0.0747061	−	0.201468i
$346$	−14.4747	+	16.0743i	−0.778163	+	0.864159i
$347$	−24.8678	+	14.3574i	−1.33497	+	0.770747i	−0.986057	−	0.166408i	$-0.946783\pi$
$347$	−24.8678	+	14.3574i	−1.33497	+	0.770747i	−0.348915	+	0.937154i	$0.613450\pi$
$348$	0.641550	−	10.0295i	0.0343907	−	0.537639i
$349$	−0.744758	−	0.429986i	−0.0398660	−	0.0230166i	0.479935	−	0.877304i	$-0.340660\pi$
$349$	−0.744758	−	0.429986i	−0.0398660	−	0.0230166i	−0.519801	+	0.854288i	$0.673994\pi$
$350$	2.13436	−	17.7164i	0.114087	−	0.946980i
$351$	−32.9163	+	0.595060i	−1.75694	+	0.0317620i
$352$	−15.1092	−	0.00344740i	−0.805322	−	0.000183747i
$353$	27.7159	+	16.0018i	1.47517	+	0.851690i	0.999608	−	0.0279920i	$-0.00891130\pi$
$353$	27.7159	+	16.0018i	1.47517	+	0.851690i	0.475562	+	0.879682i	$0.342245\pi$
$354$	−0.253940	+	0.639507i	−0.0134968	+	0.0339894i
$355$	0.0477497	+	0.0827049i	0.00253429	+	0.00438952i
$356$	−2.17395	+	4.88157i	−0.115219	+	0.258723i
$357$	0.856241	−	10.8271i	0.0453171	−	0.573032i
$358$	−14.7968	−	3.14586i	−0.782033	−	0.166264i
$359$		−	5.52163i		−	0.291421i	−0.989327	−	0.145710i	$-0.953453\pi$
$359$		−	5.52163i		−	0.291421i	0.989327	−	0.145710i	$-0.0465468\pi$
$360$	−4.06343	+	0.332833i	−0.214162	+	0.0175418i
$361$	−1.34111			−0.0705845
$362$	−10.0075	−	2.12763i	−0.525982	−	0.111826i
$363$	6.60130	+	1.12302i	0.346478	+	0.0589432i
$364$	−22.0513	−	25.2531i	−1.15580	−	1.32362i
$365$	−1.16503	−	2.01789i	−0.0609805	−	0.105621i
$366$	−3.90774	−	26.6478i	−0.204261	−	1.39290i
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	0.393886	+	0.919159i	$0.371131\pi$
$367$	−11.4766	+	19.8780i	−0.599072	+	1.03762i	−0.992958	+	0.118465i	$0.962203\pi$
$368$	18.2428	+	5.93114i	0.950974	+	0.309182i
$369$	−22.8775	−	26.6065i	−1.19095	−	1.38508i
$370$	0.985644	+	3.03397i	0.0512412	+	0.157729i
$371$	13.6984	+	19.4670i	0.711185	+	1.01067i
$372$	−18.1302	−	12.0731i	−0.940010	−	0.625961i
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	−0.953032	−	0.302871i	$-0.902055\pi$
$373$	−14.2688	−	24.7143i	−0.738810	−	1.27966i	0.214222	−	0.976785i	$-0.431278\pi$
$374$	6.65263	+	5.99061i	0.343999	+	0.309767i
$375$	6.25938	+	5.18830i	0.323233	+	0.267923i
$376$	−8.57667	−	19.2706i	−0.442308	−	0.993807i
$377$			18.3813i			0.946685i
$378$	−19.3415	−	1.97619i	−0.994821	−	0.101644i
$379$			13.3942i			0.688014i	0.938967	+	0.344007i	$0.111784\pi$
$379$			13.3942i			0.688014i	−0.938967	+	0.344007i	$0.888216\pi$
$380$	−4.01614	+	0.421743i	−0.206024	+	0.0216349i
$381$	−1.94489	−	1.61209i	−0.0996398	−	0.0825898i
$382$	−18.8605	+	20.9447i	−0.964985	+	1.07163i
$383$	11.1930	+	19.3869i	0.571937	+	0.990625i	0.996367	+	0.0851637i	$0.0271413\pi$
$383$	11.1930	+	19.3869i	0.571937	+	0.990625i	−0.424430	+	0.905461i	$0.639525\pi$
$384$	10.8650	−	16.3080i	0.554453	−	0.832215i
$385$	−1.95399	−	2.77684i	−0.0995844	−	0.141521i
$386$	19.1766	−	6.22990i	0.976064	−	0.317093i
$387$	1.33197	−	3.80147i	0.0677076	−	0.193239i
$388$	2.54521	+	3.50386i	0.129214	+	0.177881i
$389$	13.5306	−	23.4357i	0.686029	−	1.18824i	−0.287083	−	0.957906i	$-0.592686\pi$
$389$	13.5306	−	23.4357i	0.686029	−	1.18824i	0.973112	−	0.230332i	$-0.0739811\pi$
$390$	7.37792	−	1.08193i	0.373595	−	0.0547855i
$391$	−5.68302	−	9.84327i	−0.287402	−	0.497796i
$392$	−11.1453	−	16.3640i	−0.562924	−	0.826508i
$393$	−21.1536	−	3.59867i	−1.06706	−	0.181529i
$394$	3.51491	−	16.5326i	0.177078	−	0.832901i
$395$	1.89812			0.0955046
$396$	10.9937	−	11.6602i	0.552456	−	0.585949i
$397$		−	11.6658i		−	0.585487i	−0.956191	−	0.292744i	$-0.905432\pi$
$397$		−	11.6658i		−	0.585487i	0.956191	−	0.292744i	$-0.0945683\pi$
$398$	−6.45580	+	30.3653i	−0.323600	+	1.52208i
$399$	−19.1972	−	1.51817i	−0.961061	−	0.0760037i
$400$	−18.6604	+	3.96283i	−0.933020	+	0.198142i
$401$	−8.33464	−	14.4360i	−0.416212	−	0.720901i	0.579343	−	0.815084i	$-0.303309\pi$
$401$	−8.33464	−	14.4360i	−0.416212	−	0.720901i	−0.995555	+	0.0941835i	$0.969976\pi$
$402$	4.97015	+	1.97358i	0.247889	+	0.0984334i
$403$	34.5018	+	19.9196i	1.71866	+	0.992268i
$404$	6.11230	+	8.41447i	0.304098	+	0.418636i
$405$	2.69900	−	3.37867i	0.134114	−	0.167888i
$406$	−1.29839	+	10.7773i	−0.0644380	+	0.534870i
$407$	−10.8593	−	6.26962i	−0.538275	−	0.310773i
$408$	−11.2492	+	2.87520i	−0.556918	+	0.142344i
$409$	0.589282	−	0.340222i	0.0291381	−	0.0168229i	−0.485360	−	0.874314i	$-0.661312\pi$
$409$	0.589282	−	0.340222i	0.0291381	−	0.0168229i	0.514498	+	0.857491i	$0.327978\pi$
$410$	5.90618	+	5.31844i	0.291686	+	0.262659i
$411$	−5.37009	−	14.4821i	−0.264887	−	0.714349i
$412$	0.472227	+	4.49688i	0.0232649	+	0.221546i
$413$	0.312530	−	0.674306i	0.0153786	−	0.0331804i
$414$	−17.8489	+	9.76704i	−0.877224	+	0.480024i
$415$			4.89544i			0.240308i
$416$	−17.9274	+	31.0347i	−0.878961	+	1.52160i
$417$	−4.69726	−	0.799101i	−0.230026	−	0.0391322i
$418$	10.6217	−	11.7956i	0.519526	−	0.576939i
$419$	5.19926	+	9.00538i	0.254000	+	0.439941i	0.964624	−	0.263631i	$-0.0849202\pi$
$419$	5.19926	+	9.00538i	0.254000	+	0.439941i	−0.710623	+	0.703573i	$0.751587\pi$
$420$	4.40225	−	0.113205i	0.214808	−	0.00552386i
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	−0.937384	−	0.348298i	$-0.886760\pi$
$421$	−3.42772	+	5.93699i	−0.167057	+	0.289351i	0.770327	+	0.637649i	$0.220093\pi$
$422$	−4.50232	−	13.8589i	−0.219170	−	0.674640i
$423$	21.1140	+	7.39797i	1.02660	+	0.359701i
$424$	14.9602	−	20.5850i	0.726532	−	0.999698i
$425$	9.78875	+	5.65154i	0.474824	+	0.274140i
$426$	0.381846	−	0.302025i	0.0185005	−	0.0146332i
$427$	2.60272	+	28.9741i	0.125955	+	1.40215i
$428$	12.0669	−	27.0961i	0.583276	−	1.30974i
$429$	−18.7049	+	22.5664i	−0.903083	+	1.08952i
$430$	−0.189732	+	0.892419i	−0.00914969	+	0.0430363i
$431$			15.2572i			0.734914i	0.930040	+	0.367457i	$0.119772\pi$
$431$			15.2572i			0.734914i	−0.930040	+	0.367457i	$0.880228\pi$
$432$	4.68443	+	20.2498i	0.225380	+	0.974271i
$433$			34.6459i			1.66498i	0.554042	+	0.832489i	$0.313085\pi$
$433$			34.6459i			1.66498i	−0.554042	+	0.832489i	$0.686915\pi$
$434$	18.8221	+	14.1164i	0.903489	+	0.677608i
$435$	−1.85888	−	1.54080i	−0.0891266	−	0.0738755i
$436$	20.0122	+	8.91221i	0.958412	+	0.426817i
$437$	−17.4528	+	10.0764i	−0.834879	+	0.482018i
$438$	−9.31654	+	7.36902i	−0.445162	+	0.352105i
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	−0.682149	−	0.731213i	$-0.738955\pi$
$439$	6.12174	−	10.6032i	0.292175	−	0.506061i	0.974324	+	0.225152i	$0.0722878\pi$
$440$	−2.13398	+	2.93632i	−0.101733	+	0.139984i
$441$	20.7390	+	3.30084i	0.987569	+	0.157183i
$442$	20.1969	−	6.56135i	0.960668	−	0.312091i
$443$	24.2468	+	13.9989i	1.15200	+	0.665108i	0.949374	−	0.314148i	$-0.101719\pi$
$443$	24.2468	+	13.9989i	1.15200	+	0.665108i	0.202627	+	0.979256i	$0.435052\pi$
$444$	14.5744	−	7.21576i	0.691669	−	0.342445i
$445$	0.641897	+	1.11180i	0.0304288	+	0.0527043i
$446$	15.2033	+	13.6904i	0.719898	+	0.648258i
$447$	0.260429	+	0.0443045i	0.0123179	+	0.00209553i
$448$	−12.7034	+	16.9300i	−0.600178	+	0.799867i
$449$	23.8270			1.12446			0.562232	−	0.826979i	$-0.309943\pi$
$449$	23.8270			1.12446			0.562232	+	0.826979i	$0.309943\pi$
$450$	10.5155	−	17.2867i	0.495704	−	0.814901i
$451$	−31.2409			−1.47108
$452$	1.97505	+	18.8079i	0.0928985	+	0.884647i
$453$	20.4167	−	7.57069i	0.959260	−	0.355702i
$454$	−20.3381	−	18.3142i	−0.954516	−	0.859529i
$455$	−8.02199	+	0.720609i	−0.376077	+	0.0337827i
$456$	5.09792	+	19.9455i	0.238732	+	0.934036i
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	0.440607	+	0.897700i	$0.354763\pi$
$457$	−11.9100	+	20.6288i	−0.557128	+	0.964974i	−0.997735	+	0.0672735i	$0.978570\pi$
$458$	−8.60742	−	26.4950i	−0.402198	−	1.23803i
$459$	5.96378	−	10.7748i	0.278366	−	0.502923i
$460$	3.72861	−	2.70847i	0.173847	−	0.126283i
$461$	0.317557	+	0.183341i	0.0147901	+	0.00853906i	0.507377	−	0.861724i	$-0.330615\pi$
$461$	0.317557	+	0.183341i	0.0147901	+	0.00853906i	−0.492587	+	0.870263i	$0.663949\pi$
$462$	−12.5611	+	11.9099i	−0.584395	+	0.554099i
$463$	−14.3509	+	8.28549i	−0.666943	+	0.385060i	−0.794917	−	0.606718i	$-0.792486\pi$
$463$	−14.3509	+	8.28549i	−0.666943	+	0.385060i	0.127974	+	0.991777i	$0.459152\pi$
$464$	11.3516	−	2.41069i	0.526985	−	0.111914i
$465$	−4.90654	+	1.81939i	−0.227535	+	0.0843721i
$466$	2.16103	−	10.1646i	0.100108	−	0.470865i
$467$	−26.1463			−1.20991			−0.604953	−	0.796261i	$-0.706808\pi$
$467$	−26.1463			−1.20991			−0.604953	+	0.796261i	$0.706808\pi$
$468$	−10.9145	−	36.4141i	−0.504524	−	1.68324i
$469$	−5.24061	−	2.42893i	−0.241989	−	0.112158i
$470$	−4.95665	−	1.05380i	−0.228633	−	0.0486084i
$471$	−3.34122	+	19.6403i	−0.153955	+	0.904976i
$472$	−0.790163	−	0.0831588i	−0.0363702	−	0.00382769i
$473$	−1.79313	−	3.10579i	−0.0824480	−	0.142804i
$474$	−1.40399	−	9.57414i	−0.0644873	−	0.439755i
$475$	10.0205	−	17.3561i	0.459774	−	0.796352i
$476$	12.3053	−	2.42042i	0.564014	−	0.110940i
$477$	5.00685	+	26.5222i	0.229248	+	1.21437i
$478$	−4.21104	−	12.9623i	−0.192609	−	0.592880i
$479$	19.0772	−	33.0427i	0.871661	−	1.50976i	0.0113840	−	0.999935i	$-0.496376\pi$
$479$	19.0772	−	33.0427i	0.871661	−	1.50976i	0.860277	−	0.509826i	$-0.170290\pi$
$480$	−1.63577	−	4.41444i	−0.0746622	−	0.201491i
$481$	−25.7594	+	14.8722i	−1.17453	+	0.678113i
$482$	−3.89246	+	4.32261i	−0.177297	+	0.196890i
$483$	19.8394	−	9.45367i	0.902723	−	0.430157i
$484$	0.807517	+	7.68976i	0.0367053	+	0.349534i
$485$	1.04042			0.0472430
$486$	−19.0385	−	11.1147i	−0.863603	−	0.504173i
$487$			8.93817i			0.405027i	0.979279	+	0.202514i	$0.0649110\pi$
$487$			8.93817i			0.405027i	−0.979279	+	0.202514i	$0.935089\pi$
$488$	28.4124	−	12.6454i	1.28617	−	0.572428i
$489$	−26.6316	−	22.0745i	−1.20432	−	0.998243i
$490$	−4.75436	−	0.144137i	−0.214780	−	0.00651146i
$491$	−8.03087	+	4.63662i	−0.362428	+	0.209248i	−0.670145	−	0.742230i	$-0.733768\pi$
$491$	−8.03087	+	4.63662i	−0.362428	+	0.209248i	0.307717	+	0.951478i	$0.400435\pi$
$492$	22.4577	−	33.7248i	1.01247	−	1.52043i
$493$	−5.95475	−	3.43798i	−0.268189	−	0.154839i
$494$	−11.6337	−	35.8104i	−0.523425	−	1.61119i
$495$	−0.714194	−	3.78322i	−0.0321007	−	0.170043i
$496$	7.77675	−	23.9195i	0.349186	−	1.07402i
$497$	−0.430058	+	0.302621i	−0.0192908	+	0.0135744i
$498$	24.6927	−	3.62104i	1.10651	−	0.162262i
$499$	15.0365	−	8.68131i	0.673125	−	0.388629i	−0.124135	−	0.992265i	$-0.539615\pi$
$499$	15.0365	−	8.68131i	0.673125	−	0.388629i	0.797260	+	0.603636i	$0.206282\pi$
$500$	−3.81915	+	8.57585i	−0.170798	+	0.383524i
$501$	37.4795	+	6.37605i	1.67446	+	0.284861i
$502$	−0.975855	+	4.59000i	−0.0435545	+	0.204862i
$503$	6.23388			0.277955			0.138978	−	0.990296i	$-0.455618\pi$
$503$	6.23388			0.277955			0.138978	+	0.990296i	$0.455618\pi$
$504$	−3.82724	−	22.1213i	−0.170479	−	0.985361i
$505$	2.49856			0.111184
$506$	−3.76708	+	17.7187i	−0.167467	+	0.787694i
$507$	16.3447	+	44.0786i	0.725895	+	1.95760i
$508$	1.18667	−	2.66465i	0.0526500	−	0.118225i
$509$	−3.52873	+	2.03731i	−0.156408	+	0.0903023i	−0.576161	−	0.817336i	$-0.695450\pi$
$509$	−3.52873	+	2.03731i	−0.156408	+	0.0903023i	0.419753	+	0.907638i	$0.362117\pi$
$510$	−1.02944	+	2.59249i	−0.0455846	+	0.114797i
$511$	10.4929	−	7.38356i	0.464177	−	0.326629i
$512$	21.5171	+	7.00109i	0.950930	+	0.309408i
$513$	−19.1044	−	10.5742i	−0.843478	−	0.466861i
$514$	7.54290	+	23.2183i	0.332703	+	1.02411i
$515$	0.940746	+	0.543140i	0.0414542	+	0.0239336i
$516$	4.64172	+	0.296913i	0.204340	+	0.0130709i
$517$	17.2501	−	9.95933i	0.758657	−	0.438011i
$518$	−16.1538	+	6.90032i	−0.709756	+	0.303183i
$519$	24.8397	−	9.21077i	1.09034	−	0.404308i
$520$	3.50109	+	7.86647i	0.153533	+	0.344968i
$521$		−	27.2193i		−	1.19250i	−0.802798	−	0.596251i	$-0.796656\pi$
$521$		−	27.2193i		−	1.19250i	0.802798	−	0.596251i	$-0.203344\pi$
$522$	−6.39684	+	10.5159i	−0.279982	+	0.460270i
$523$	−3.44794			−0.150768			−0.0753838	−	0.997155i	$-0.524018\pi$
$523$	−3.44794			−0.150768			−0.0753838	+	0.997155i	$0.524018\pi$
$524$	−2.58766	−	24.6415i	−0.113042	−	1.07647i
$525$	−12.3856	+	18.0065i	−0.540551	+	0.785869i
$526$	12.5070	−	13.8891i	0.545330	−	0.605595i
$527$	−12.9062	+	7.45141i	−0.562204	+	0.324589i
$528$	16.3893	+	8.59191i	0.713254	+	0.373915i
$529$	−0.000637027		0.00110336i	−2.76968e−5		4.79723e-5i
$530$	−1.88889	−	5.81432i	−0.0820483	−	0.252558i
$531$	0.638988	−	0.549432i	0.0277297	−	0.0238433i
$532$	−4.29156	−	21.8181i	−0.186063	−	0.945937i
$533$	−37.0533	+	64.1783i	−1.60496	+	2.77987i
$534$	5.13314	−	4.06011i	0.222133	−	0.175698i
$535$	−3.56297	−	6.17125i	−0.154041	−	0.266806i
$536$	−0.646298	+	6.14103i	−0.0279158	+	0.265252i
$537$	14.2642	+	11.8234i	0.615547	+	0.510217i
$538$	38.1237	+	8.10525i	1.64363	+	0.349442i
$539$	14.2665	−	12.0844i	0.614502	−	0.520511i
$540$	4.59742	+	1.94861i	0.197842	+	0.0838547i
$541$	5.99277			0.257649			0.128825	−	0.991667i	$-0.458880\pi$
$541$	5.99277			0.257649			0.128825	+	0.991667i	$0.458880\pi$
$542$	6.24854	−	29.3905i	0.268398	−	1.26243i
$543$	9.64732	+	7.99651i	0.414006	+	0.343163i
$544$	−6.70086	−	11.6123i	−0.287297	−	0.497875i
$545$	4.55787	−	2.63149i	0.195238	−	0.112721i
$546$	9.56843	+	39.9301i	0.409491	+	1.70885i
$547$	−5.72221	−	3.30372i	−0.244664	−	0.141257i	0.372654	−	0.927970i	$-0.378448\pi$
$547$	−5.72221	−	3.30372i	−0.244664	−	0.141257i	−0.617319	+	0.786713i	$0.711781\pi$
$548$	14.4299	−	10.4819i	0.616414	−	0.447765i
$549$	−10.9075	+	31.1302i	−0.465520	+	1.32861i
$550$	−5.56598	−	17.1330i	−0.237334	−	0.730553i
$551$	−6.09576	+	10.5582i	−0.259688	+	0.449793i
$552$	−16.4196	−	16.8038i	−0.698863	−	0.715217i
$553$	0.935116	+	10.4099i	0.0397652	+	0.442675i
$554$	−15.2610	−	13.7423i	−0.648377	−	0.583855i
$555$	0.655249	−	3.85167i	0.0278138	−	0.163494i
$556$	−0.574601	−	5.47176i	−0.0243685	−	0.232055i
$557$	6.08351			0.257767			0.128883	−	0.991660i	$-0.458861\pi$
$557$	6.08351			0.257767			0.128883	+	0.991660i	$0.458861\pi$
$558$	12.8063	+	23.4029i	0.542133	+	0.990725i
$559$	−8.50697			−0.359806
$560$	1.49710	+	4.85958i	0.0632640	+	0.205355i
$561$	−3.81205	−	10.2804i	−0.160945	−	0.434037i
$562$	−13.3603	−	12.0308i	−0.563571	−	0.507488i
$563$	−13.1561	−	22.7871i	−0.554465	−	0.960361i	−0.997945	−	0.0640767i	$-0.979590\pi$
$563$	−13.1561	−	22.7871i	−0.554465	−	0.960361i	0.443480	−	0.896284i	$-0.353744\pi$
$564$	−1.64910	+	25.7809i	−0.0694398	+	1.08557i
$565$	3.93459	+	2.27164i	0.165530	+	0.0955686i
$566$	−28.0496	+	9.11244i	−1.17901	+	0.383024i
$567$	19.8595	+	13.1378i	0.834020	+	0.551734i
$568$	0.454759	+	0.330497i	0.0190813	+	0.0138673i
$569$	−0.683478	+	1.18382i	−0.0286529	+	0.0496283i	−0.879996	−	0.474981i	$-0.842455\pi$
$569$	−0.683478	+	1.18382i	−0.0286529	+	0.0496283i	0.851343	+	0.524609i	$0.175788\pi$
$570$	4.59666	+	1.82527i	0.192533	+	0.0764523i
$571$	−14.6500	+	8.45818i	−0.613083	+	0.353964i	−0.774171	−	0.632976i	$-0.781833\pi$
$571$	−14.6500	+	8.45818i	−0.613083	+	0.353964i	0.161088	+	0.986940i	$0.448500\pi$
$572$	−30.9178	−	13.7689i	−1.29274	−	0.575705i
$573$	32.3660	−	12.0016i	1.35211	−	0.501375i
$574$	−26.2585	+	35.0117i	−1.09601	+	1.46136i
$575$			22.8713i			0.953801i
$576$	−21.0566	+	11.5161i	−0.877358	+	0.479837i
$577$		−	0.277722i		−	0.0115617i	−0.999983	−	0.00578087i	$-0.998160\pi$
$577$		−	0.277722i		−	0.0115617i	0.999983	−	0.00578087i	$-0.00184012\pi$
$578$	3.34764	−	15.7459i	0.139244	−	0.654943i
$579$	−24.3450	−	4.14159i	−1.01174	−	0.172119i
$580$	1.13419	−	2.54681i	0.0470948	−	0.105751i
$581$	−26.8483	+	2.41176i	−1.11386	+	0.100057i
$582$	−0.769572	−	5.24790i	−0.0318998	−	0.217532i
$583$	20.8108	+	12.0151i	0.861896	+	0.497616i
$584$	−11.0955	−	8.06369i	−0.459136	−	0.333678i
$585$	−8.61896	−	3.01993i	−0.356350	−	0.124859i
$586$	2.93047	+	9.02046i	0.121057	+	0.372632i
$587$	13.6979	−	23.7254i	0.565372	−	0.979253i	−0.431643	−	0.902044i	$-0.642066\pi$
$587$	13.6979	−	23.7254i	0.565372	−	0.979253i	0.997015	−	0.0772082i	$-0.0246006\pi$
$588$	2.78965	+	24.0877i	0.115043	+	0.993360i
$589$	13.2118	+	22.8836i	0.544385	+	0.942902i
$590$	−0.127729	+	0.141845i	−0.00525852	+	0.00583965i
$591$	−13.2104	+	15.9376i	−0.543404	+	0.655586i
$592$	12.5628	+	13.9576i	0.516330	+	0.573653i
$593$		−	32.0154i		−	1.31471i	−0.753579	−	0.657357i	$-0.771674\pi$
$593$		−	32.0154i		−	1.31471i	0.753579	−	0.657357i	$-0.228326\pi$
$594$	−18.5544	+	6.40077i	−0.761296	+	0.262627i
$595$	1.26696	−	2.73356i	0.0519403	−	0.112065i
$596$	0.0318575	+	0.303370i	0.00130494	+	0.0124265i
$597$	24.2635	−	29.2725i	0.993038	−	1.19804i
$598$	31.9317	+	28.7541i	1.30578	+	1.17584i
$599$	15.8709	−	9.16306i	0.648467	−	0.374392i	−0.139402	−	0.990236i	$-0.544518\pi$
$599$	15.8709	−	9.16306i	0.648467	−	0.374392i	0.787869	+	0.615843i	$0.211185\pi$
$600$	22.4964	+	6.30760i	0.918410	+	0.257507i
$601$	19.1583	+	11.0611i	0.781485	+	0.451190i	0.836956	−	0.547270i	$-0.184333\pi$
$601$	19.1583	+	11.0611i	0.781485	+	0.451190i	−0.0554716	+	0.998460i	$0.517666\pi$
$602$	−4.98781	−	0.600902i	−0.203288	−	0.0244910i
$603$	−4.27010	−	4.96612i	−0.173892	−	0.202236i
$604$	14.7773	+	20.3431i	0.601279	+	0.827748i
$605$	1.60869	+	0.928780i	0.0654027	+	0.0377603i
$606$	−1.84812	−	12.6028i	−0.0750747	−	0.511953i
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	0.980832	−	0.194853i	$-0.0624230\pi$
$607$	7.92507	+	13.7266i	0.321669	+	0.557146i	−0.659164	+	0.751999i	$0.729090\pi$
$608$	−20.5894	+	11.8811i	−0.835012	+	0.481840i
$609$	7.53448	−	10.9538i	0.305313	−	0.443872i
$610$	1.55372	−	7.30802i	0.0629082	−	0.295893i
$611$		−	47.2491i		−	1.91150i
$612$	13.8380	+	3.27494i	0.559369	+	0.132382i
$613$	24.5067			0.989818			0.494909	−	0.868945i	$-0.335201\pi$
$613$	24.5067			0.989818			0.494909	+	0.868945i	$0.335201\pi$
$614$	3.55243	−	16.7091i	0.143365	−	0.674326i
$615$	−3.38432	−	9.12686i	−0.136469	−	0.368030i
$616$	−17.1551	−	10.2569i	−0.691201	−	0.413262i
$617$	−15.9608	−	27.6449i	−0.642557	−	1.11294i	−0.984860	−	0.173352i	$-0.944540\pi$
$617$	−15.9608	−	27.6449i	−0.642557	−	1.11294i	0.342303	−	0.939590i	$-0.388793\pi$
$618$	2.04376	−	5.14689i	0.0822122	−	0.207038i
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	−0.870560	−	0.492062i	$-0.836243\pi$
$619$	−0.227459	+	0.393971i	−0.00914236	+	0.0158350i	0.861418	+	0.507897i	$0.169577\pi$
$620$	−3.55128	−	4.88885i	−0.142623	−	0.196341i
$621$	24.9151	−	0.450415i	0.999809	−	0.0180745i
$622$	−2.72192	+	0.884267i	−0.109139	+	0.0354559i
$623$	−5.78126	+	4.06812i	−0.231621	+	0.162986i
$624$	37.0890	−	23.4782i	1.48475	−	0.939880i
$625$	−10.7952	−	18.6978i	−0.431807	−	0.747911i
$626$	18.3948	−	20.4277i	0.735206	−	0.816454i
$627$	−18.2277	+	6.75901i	−0.727946	+	0.269929i
$628$	−22.8787	+	2.40253i	−0.912958	+	0.0958716i
$629$		−	11.1266i		−	0.443646i
$630$	−4.84016	−	2.37946i	−0.192836	−	0.0947999i
$631$		−	28.8331i		−	1.14783i	−0.818916	−	0.573913i	$-0.805425\pi$
$631$		−	28.8331i		−	1.14783i	0.818916	−	0.573913i	$-0.194575\pi$
$632$	10.2081	−	4.54327i	0.406057	−	0.180722i
$633$	−2.99311	+	17.5940i	−0.118966	+	0.699301i
$634$	10.9680	+	9.87654i	0.435595	+	0.392248i
$635$	−0.350386	−	0.606887i	−0.0139046	−	0.0240836i
$636$	−27.9304	+	13.8283i	−1.10751	+	0.548329i
$637$	−7.90415	−	43.6404i	−0.313174	−	1.72910i
$638$	3.38593	+	10.4225i	0.134050	+	0.412629i
$639$	−0.585921	+	0.110610i	−0.0231787	+	0.00437566i
$640$	4.39888	−	3.19383i	0.173881	−	0.126247i
$641$	3.90266	−	6.75961i	0.154146	−	0.266989i	−0.778602	−	0.627518i	$-0.784071\pi$
$641$	3.90266	−	6.75961i	0.154146	−	0.266989i	0.932748	+	0.360530i	$0.117404\pi$
$642$	−28.4925	+	22.5364i	−1.12451	+	0.889442i
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	0.907165	−	0.420776i	$-0.138242\pi$
$643$	2.26137	+	3.91681i	0.0891797	+	0.154464i	−0.817985	+	0.575240i	$0.804909\pi$
$644$	16.6911	+	19.1147i	0.657723	+	0.753223i
$645$	0.713089	−	0.860301i	0.0280779	−	0.0338743i
$646$	13.7770	+	2.92904i	0.542048	+	0.115242i
$647$	32.4931			1.27744			0.638718	−	0.769441i	$-0.279465\pi$
$647$	32.4931			1.27744			0.638718	+	0.769441i	$0.279465\pi$
$648$	6.42822	−	24.6308i	0.252524	−	0.967591i
$649$		−	0.750290i		−	0.0294515i
$650$	−41.7979	−	8.88641i	−1.63945	−	0.348554i
$651$	−12.3954	−	26.0129i	−0.485814	−	1.01952i
$652$	16.2492	−	36.4874i	0.636369	−	1.42896i
$653$	3.99865	+	6.92587i	0.156479	+	0.271030i	0.933597	−	0.358325i	$-0.116652\pi$
$653$	3.99865	+	6.92587i	0.156479	+	0.271030i	−0.777117	+	0.629356i	$0.783319\pi$
$654$	−16.6446	−	21.0436i	−0.650857	−	0.822869i
$655$	−5.15500	−	2.97624i	−0.201422	−	0.116291i
$656$	44.4937	+	14.4658i	1.73719	+	0.564796i
$657$	14.2957	−	2.69874i	0.557729	−	0.105288i
$658$	3.33751	−	27.7031i	0.130110	−	1.07998i
$659$	−6.89888	−	3.98307i	−0.268742	−	0.155158i	0.359574	−	0.933117i	$-0.382922\pi$
$659$	−6.89888	−	3.98307i	−0.268742	−	0.155158i	−0.628316	+	0.777958i	$0.716255\pi$
$660$	3.98409	−	1.97252i	0.155080	−	0.0767803i
$661$	0.220771	−	0.127462i	0.00858700	−	0.00495771i	−0.495700	−	0.868494i	$-0.665089\pi$
$661$	0.220771	−	0.127462i	0.00858700	−	0.00495771i	0.504287	+	0.863536i	$0.331755\pi$
$662$	−34.1755	+	37.9523i	−1.32827	+	1.47506i
$663$	−25.6402	−	4.36194i	−0.995784	−	0.169404i
$664$	11.7176	+	26.3278i	0.454731	+	1.02172i
$665$	−4.84679	−	2.24641i	−0.187950	−	0.0871119i
$666$	−19.9126	−	0.456108i	−0.771597	−	0.0176738i
$667$		−	13.9132i		−	0.538723i
$668$	4.58476	+	43.6594i	0.177390	+	1.68923i
$669$	−8.71170	−	23.4938i	−0.336814	−	0.908321i
$670$	1.10239	+	0.992692i	0.0425892	+	0.0383510i
$671$	14.6839	+	25.4333i	0.566867	+	0.981842i
$672$	23.4045	−	11.1459i	0.902847	−	0.429963i
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	−0.869822	−	0.493365i	$-0.835767\pi$
$673$	−0.198313	+	0.343488i	−0.00764441	+	0.0132405i	0.862178	+	0.506606i	$0.169100\pi$
$674$	9.96762	−	3.23817i	0.383938	−	0.124730i
$675$	−21.2336	+	12.7765i	−0.817283	+	0.491766i
$676$	−43.9197	+	31.9034i	−1.68922	+	1.22705i
$677$	−43.1462	−	24.9105i	−1.65824	−	0.957388i	−0.973525	−	0.228582i	$-0.926591\pi$
$677$	−43.1462	−	24.9105i	−1.65824	−	0.957388i	−0.684720	−	0.728806i	$-0.740076\pi$
$678$	8.54787	−	21.5264i	0.328279	−	0.826718i
$679$	0.512568	+	5.70602i	0.0196706	+	0.218977i
$680$	−3.20323	−	0.337117i	−0.122838	−	0.0129278i
$681$	11.6540	+	31.4286i	0.446583	+	1.20435i
$682$	23.2323	+	4.93929i	0.889612	+	0.189135i
$683$		−	28.4508i		−	1.08864i	−0.838878	−	0.544320i	$-0.816788\pi$
$683$		−	28.4508i		−	1.08864i	0.838878	−	0.544320i	$-0.183212\pi$
$684$	5.80668	−	24.5357i	0.222024	−	0.938148i
$685$		−	4.28474i		−	0.163712i
$686$	−1.55176	−	26.1456i	−0.0592465	−	0.998243i
$687$	−5.72215	+	33.6358i	−0.218314	+	1.28329i
$688$	1.11568	+	5.25359i	0.0425350	+	0.200291i
$689$	49.3654	−	28.5011i	1.88067	−	1.08581i
$690$	−5.58452	+	0.818936i	−0.212599	+	0.0311764i
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	−0.958227	−	0.286008i	$-0.907672\pi$
$691$	−6.08340	+	10.5368i	−0.231423	+	0.400837i	0.726804	+	0.686845i	$0.241005\pi$
$692$	17.9786	+	24.7501i	0.683443	+	0.940859i
$693$	20.3967	−	5.78072i	0.774805	−	0.219591i
$694$	12.5471	+	38.6219i	0.476281	+	1.46607i
$695$	−1.14469	−	0.660887i	−0.0434206	−	0.0250689i
$696$	−13.6851	−	3.83708i	−0.518733	−	0.145444i
$697$	−13.8607	−	24.0074i	−0.525011	−	0.909345i
$698$	−0.813827	+	0.903764i	−0.0308038	+	0.0342080i
$699$	−8.12202	+	9.79875i	−0.307203	+	0.370623i
$700$	−23.8793	−	8.16275i	−0.902552	−	0.308523i
$701$	−9.67651			−0.365477			−0.182738	−	0.983162i	$-0.558496\pi$
$701$	−9.67651			−0.365477			−0.182738	+	0.983162i	$0.558496\pi$
$702$	−8.85736	+	45.7080i	−0.334299	+	1.72514i
$703$	−19.7282			−0.744062
$704$	−4.44830	+	20.8995i	−0.167652	+	0.787678i
$705$	4.77826	+	3.96062i	0.179960	+	0.149166i
$706$	30.2863	−	33.6333i	1.13984	−	1.26581i
$707$	1.23093	+	13.7030i	0.0462938	+	0.515353i
$708$	0.809945	+	0.539350i	0.0304396	+	0.0202700i
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	0.0377999	+	0.999285i	$0.487965\pi$
$709$	−22.5400	+	39.0404i	−0.846507	+	1.46619i	−0.884306	+	0.466907i	$0.845368\pi$
$710$	0.128448	−	0.0417289i	0.00482058	−	0.00156606i
$711$	−3.91888	+	11.1846i	−0.146970	+	0.419455i
$712$	6.11331	+	4.44286i	0.229106	+	0.166503i
$713$	−26.1153	−	15.0776i	−0.978024	−	0.564662i
$714$	−14.7253	−	4.36863i	−0.551080	−	0.163492i
$715$	−7.04166	+	4.06550i	−0.263343	+	0.152041i
$716$	−8.70330	+	19.5431i	−0.325258	+	0.730361i
$717$	−2.79947	+	16.4558i	−0.104548	+	0.614553i
$718$	−7.63805	−	1.62388i	−0.285050	−	0.0606028i
$719$	−12.1609			−0.453526			−0.226763	−	0.973950i	$-0.572814\pi$
$719$	−12.1609			−0.453526			−0.226763	+	0.973950i	$0.572814\pi$
$720$	−0.734626	+	5.71881i	−0.0273779	+	0.213128i
$721$	−2.51531	+	5.42696i	−0.0936749	+	0.202111i
$722$	−0.394412	+	1.85515i	−0.0146785	+	0.0690414i
$723$	6.67976	−	2.47691i	0.248423	−	0.0921174i
$724$	−5.88630	+	13.2176i	−0.218762	+	0.491228i
$725$	6.91809	+	11.9825i	0.256931	+	0.445018i
$726$	3.49487	−	8.80128i	0.129707	−	0.326646i
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	−0.667276	−	0.744810i	$-0.732540\pi$
$727$	8.39590	−	14.5421i	0.311387	−	0.539337i	0.978663	+	0.205473i	$0.0658733\pi$
$728$	−41.4177	+	23.0767i	−1.53504	+	0.855278i
$729$	14.3363	+	22.8795i	0.530975	+	0.847387i
$730$	−3.13397	+	1.01813i	−0.115993	+	0.0376827i
$731$	1.59112	−	2.75589i	0.0588496	−	0.101930i
$732$	−38.0111	−	2.43142i	−1.40493	−	0.0898679i
$733$	−18.4832	+	10.6713i	−0.682693	+	0.394153i	−0.800869	−	0.598840i	$-0.795629\pi$
$733$	−18.4832	+	10.6713i	−0.682693	+	0.394153i	0.118176	+	0.992993i	$0.462295\pi$
$734$	24.1220	+	21.7215i	0.890359	+	0.801756i
$735$	5.07587	+	2.85878i	0.187226	+	0.105448i
$736$	13.5696	−	23.4909i	0.500184	−	0.865887i
$737$	−5.83114			−0.214793
$738$	−43.5328	+	23.8215i	−1.60246	+	0.876881i
$739$		−	50.5558i		−	1.85973i	−0.367907	−	0.929863i	$-0.619926\pi$
$739$		−	50.5558i		−	1.85973i	0.367907	−	0.929863i	$-0.380074\pi$
$740$	4.48675	−	0.471163i	0.164936	−	0.0173203i
$741$	−7.73400	+	45.4618i	−0.284116	+	1.67008i
$742$	30.9572	−	13.2238i	1.13647	−	0.485461i
$743$	32.1395	−	18.5558i	1.17909	−	0.680745i	0.223282	−	0.974754i	$-0.428323\pi$
$743$	32.1395	−	18.5558i	1.17909	−	0.680745i	0.955803	+	0.294009i	$0.0949895\pi$
$744$	−22.0327	+	21.5289i	−0.807757	+	0.789287i
$745$	0.0634650	+	0.0366415i	0.00232518	+	0.00134244i
$746$	−38.3835	+	12.4696i	−1.40532	+	0.456545i
$747$	−28.8463	−	10.1072i	−1.05543	−	0.369804i
$748$	10.2433	−	7.44075i	0.374532	−	0.272061i
$749$	32.0900	−	22.5809i	1.17254	−	0.825088i
$750$	9.01781	−	7.13273i	0.329284	−	0.260451i
$751$	−37.8228	+	21.8370i	−1.38017	+	0.796843i	−0.992180	−	0.124819i	$-0.960165\pi$
$751$	−37.8228	+	21.8370i	−1.38017	+	0.796843i	−0.387993	+	0.921662i	$0.626832\pi$
$752$	−29.1793	+	6.19669i	−1.06406	+	0.225970i
$753$	3.66765	−	4.42481i	0.133657	−	0.161249i
$754$	25.4268	+	5.40584i	0.925988	+	0.196869i
$755$	6.04058			0.219839
$756$	−8.42190	+	26.1739i	−0.306302	+	0.951935i
$757$	−53.5207			−1.94524			−0.972622	−	0.232392i	$-0.925345\pi$
$757$	−53.5207			−1.94524			−0.972622	+	0.232392i	$0.925345\pi$
$758$	18.5281	+	3.93916i	0.672972	+	0.143077i
$759$	14.1582	−	17.0811i	0.513910	−	0.620003i
$760$	−0.597730	+	5.67954i	−0.0216820	+	0.206019i
$761$	19.6964	−	11.3717i	0.713994	−	0.412225i	−0.0985439	−	0.995133i	$-0.531418\pi$
$761$	19.6964	−	11.3717i	0.713994	−	0.412225i	0.812538	+	0.582908i	$0.198085\pi$
$762$	−2.80198	+	2.21625i	−0.101505	+	0.0802864i
$763$	16.6775	+	23.7006i	0.603765	+	0.858018i
$764$	23.4260	+	32.2493i	0.847524	+	1.16674i
$765$	2.59039	−	2.22734i	0.0936558	−	0.0805295i
$766$	30.1096	−	9.78170i	1.08791	−	0.353427i
$767$	−1.54132	−	0.889883i	−0.0556540	−	0.0321318i
$768$	−19.3635	−	19.8256i	−0.698719	−	0.715396i
$769$	−9.86460	+	5.69533i	−0.355726	+	0.205379i	−0.667204	−	0.744875i	$-0.732509\pi$
$769$	−9.86460	+	5.69533i	−0.355726	+	0.205379i	0.311478	+	0.950253i	$0.399176\pi$
$770$	−4.41584	+	1.88629i	−0.159136	+	0.0679772i
$771$	5.01447	−	29.4759i	0.180592	−	1.06155i
$772$	−2.97805	−	28.3591i	−0.107182	−	1.02067i
$773$		−	30.6663i		−	1.10299i	−0.834178	−	0.551495i	$-0.814058\pi$
$773$		−	30.6663i		−	1.10299i	0.834178	−	0.551495i	$-0.185942\pi$
$774$	−4.86683	−	2.96050i	−0.174935	−	0.106413i
$775$	29.9883			1.07721
$776$	5.59540	−	2.49032i	0.200863	−	0.0893972i
$777$	21.4467	+	1.69607i	0.769397	+	0.0608462i
$778$	−28.4392	−	25.6092i	−1.01960	−	0.918133i
$779$	−42.5667	+	24.5759i	−1.52511	+	0.880523i
$780$	0.673182	−	10.5240i	0.0241038	−	0.376821i
$781$	−0.265435	+	0.459746i	−0.00949800	+	0.0164510i
$782$	−15.2875	+	4.96644i	−0.546680	+	0.177600i
$783$	12.9170	−	7.77226i	0.461615	−	0.277758i
$784$	−25.9141	+	10.6047i	−0.925503	+	0.378740i
$785$	−2.76332	+	4.78621i	−0.0986271	+	0.170827i
$786$	−11.1992	+	28.2034i	−0.399462	+	1.00598i
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	0.638059	−	0.769988i	$-0.279738\pi$
$787$	−9.75700	−	16.8996i	−0.347799	−	0.602406i	−0.985858	+	0.167581i	$0.946404\pi$
$788$	−21.8358	−	9.72431i	−0.777868	−	0.346414i
$789$	−21.4629	+	7.95865i	−0.764101	+	0.283335i
$790$	0.558226	−	2.62566i	0.0198608	−	0.0934166i
$791$	−10.5201	+	22.6978i	−0.374050	+	0.807042i
$792$	−12.8964	−	18.6368i	−0.458252	−	0.662230i
$793$	69.6636			2.47383
$794$	−16.1372	−	3.43084i	−0.572688	−	0.121756i
$795$	−1.25572	+	7.38136i	−0.0445359	+	0.261790i
$796$	40.1056	+	17.8606i	1.42151	+	0.633051i
$797$	−25.9632	+	14.9898i	−0.919663	+	0.530968i	−0.883528	−	0.468379i	$-0.844838\pi$
$797$	−25.9632	+	14.9898i	−0.919663	+	0.530968i	−0.0361355	+	0.999347i	$0.511505\pi$
$798$	−7.74587	+	26.1089i	−0.274201	+	0.924245i
$799$	15.3067	+	8.83733i	0.541512	+	0.312642i
$800$	−0.00615553	+	26.9783i	−0.000217631	+	0.953827i
$801$	−7.87652	+	1.48692i	−0.278303	+	0.0525379i
$802$	−22.4205	+	7.28372i	−0.791694	+	0.257197i
$803$	6.47626	−	11.2172i	0.228542	−	0.395847i
$804$	4.19174	−	6.29477i	0.147831	−	0.221999i
$805$	6.07204	−	0.545446i	0.214011	−	0.0192245i
$806$	37.7016	−	41.8680i	1.32798	−	1.47474i
$807$	−36.7516	−	30.4628i	−1.29372	−	1.07234i
$808$	13.4373	−	5.98047i	0.472723	−	0.210392i
$809$	−54.5869			−1.91917			−0.959586	−	0.281415i	$-0.909196\pi$
$809$	−54.5869			−1.91917			−0.959586	+	0.281415i	$0.909196\pi$
$810$	−3.87994	−	4.72717i	−0.136327	−	0.166096i
$811$	−17.5107			−0.614883			−0.307442	−	0.951567i	$-0.599473\pi$
$811$	−17.5107			−0.614883			−0.307442	+	0.951567i	$0.599473\pi$
$812$	14.5264	+	4.96561i	0.509776	+	0.174259i
$813$	−23.4845	+	28.3327i	−0.823639	+	0.993672i
$814$	−11.8664	+	13.1778i	−0.415917	+	0.461880i
$815$	−4.79788	−	8.31016i	−0.168062	−	0.291092i
$816$	0.668927	+	16.4065i	0.0234171	+	0.574344i
$817$	−4.88638	−	2.82115i	−0.170953	−	0.0986997i
$818$	−0.297323	−	0.915209i	−0.0103957	−	0.0319995i
$819$	12.3162	−	48.7572i	0.430362	−	1.70371i
$820$	9.09395	−	6.60587i	0.317575	−	0.230687i
$821$	−9.47071	+	16.4037i	−0.330530	+	0.572495i	−0.982616	−	0.185650i	$-0.940561\pi$
$821$	−9.47071	+	16.4037i	−0.330530	+	0.572495i	0.652086	+	0.758145i	$0.273894\pi$
$822$	−21.6123	+	3.16932i	−0.753817	+	0.110543i
$823$	8.43975	−	4.87269i	0.294191	−	0.169851i	−0.345639	−	0.938367i	$-0.612338\pi$
$823$	8.43975	−	4.87269i	0.294191	−	0.169851i	0.639831	+	0.768516i	$0.279005\pi$
$824$	6.35940	+	0.669280i	0.221540	+	0.0233155i
$825$	−3.70023	+	21.7506i	−0.128825	+	0.757258i
$826$	−0.840852	−	0.630631i	−0.0292570	−	0.0219425i
$827$		−	38.9872i		−	1.35572i	−0.735193	−	0.677858i	$-0.762908\pi$
$827$		−	38.9872i		−	1.35572i	0.735193	−	0.677858i	$-0.237092\pi$
$828$	8.26146	+	27.5627i	0.287106	+	0.957870i
$829$		−	8.11853i		−	0.281968i	−0.990012	−	0.140984i	$-0.954973\pi$
$829$		−	8.11853i		−	0.281968i	0.990012	−	0.140984i	$-0.0450266\pi$
$830$	6.77185	+	1.43972i	0.235054	+	0.0499735i
$831$	8.74475	+	23.5829i	0.303352	+	0.818082i
$832$	37.6579	+	33.9260i	1.30555	+	1.17617i
$833$	15.6160	+	5.60176i	0.541062	+	0.194089i
$834$	−2.48683	+	6.26269i	−0.0861119	+	0.216859i
$835$	9.13352	+	5.27324i	0.316078	+	0.182488i
$836$	−13.1929	−	18.1620i	−0.456288	−	0.628147i
$837$	−0.590572	−	32.6680i	−0.0204132	−	1.12917i
$838$	13.9862	−	4.54368i	0.483144	−	0.156959i
$839$	−13.5859	+	23.5314i	−0.469036	+	0.812394i	−0.999373	−	0.0353923i	$-0.988732\pi$
$839$	−13.5859	+	23.5314i	−0.469036	+	0.812394i	0.530337	+	0.847787i	$0.322065\pi$
$840$	1.13808	−	6.12291i	0.0392675	−	0.211260i
$841$	10.2915	+	17.8255i	0.354881	+	0.614672i
$842$	7.20454	+	6.48759i	0.248285	+	0.223577i
$843$	7.65563	+	20.6458i	0.263674	+	0.711078i
$844$	−20.4950	+	2.15223i	−0.705469	+	0.0740826i
$845$			13.0413i			0.448635i
$846$	16.4431	−	27.0312i	0.565325	−	0.929352i
$847$	−4.30122	+	9.28021i	−0.147792	+	0.318872i
$848$	−24.0755	−	26.7484i	−0.826756	−	0.918543i
$849$	35.6093	+	6.05789i	1.22211	+	0.207906i
$850$	10.6966	−	11.8787i	0.366889	−	0.407434i
$851$	19.4979	−	11.2571i	0.668379	−	0.385889i
$852$	−0.305491	−	0.617030i	−0.0104660	−	0.0211391i
$853$	−20.4384	−	11.8001i	−0.699797	−	0.404028i	0.107475	−	0.994208i	$-0.465724\pi$
$853$	−20.4384	−	11.8001i	−0.699797	−	0.404028i	−0.807272	+	0.590180i	$0.799057\pi$
$854$	40.8452	+	4.92079i	1.39769	+	0.168386i
$855$	−3.94921	−	4.59293i	−0.135060	−	0.157075i
$856$	−33.9331	−	24.6609i	−1.15981	−	0.842893i
$857$	−13.6342	−	7.87173i	−0.465737	−	0.268893i	0.248717	−	0.968576i	$-0.419991\pi$
$857$	−13.6342	−	7.87173i	−0.465737	−	0.268893i	−0.714453	+	0.699683i	$0.753325\pi$
$858$	25.7150	+	32.5111i	0.877896	+	1.10991i
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	0.998754	−	0.0499024i	$-0.0158910\pi$
$859$	13.3695	+	23.1566i	0.456160	+	0.790093i	−0.542594	+	0.839995i	$0.682558\pi$
$860$	1.17868	+	0.524911i	0.0401927	+	0.0178993i
$861$	48.3876	−	23.0572i	1.64904	−	0.785787i
$862$	21.1052	+	4.48706i	0.718847	+	0.152830i
$863$			50.8477i			1.73088i	0.501015	+	0.865438i	$0.332960\pi$
$863$			50.8477i			1.73088i	−0.501015	+	0.865438i	$0.667040\pi$
$864$	29.3892	−	0.524590i	0.999841	−	0.0178469i
$865$	7.34919			0.249880
$866$	47.9256	+	10.1892i	1.62858	+	0.346243i
$867$	−12.5818	+	15.1792i	−0.427300	+	0.515513i
$868$	25.0626	−	21.8850i	0.850681	−	0.742824i
$869$	5.27570	+	9.13778i	0.178966	+	0.309978i
$870$	−2.67806	+	2.11824i	−0.0907949	+	0.0718152i
$871$	−6.91604	+	11.9789i	−0.234341	+	0.405891i
$872$	18.2137	−	25.0618i	0.616794	−	0.848700i
$873$	−2.14807	+	6.13064i	−0.0727011	+	0.207491i
$874$	8.80582	+	27.1057i	0.297861	+	0.916866i
$875$	−10.1564	+	7.14680i	−0.343349	+	0.241606i
$876$	7.45359	+	15.0547i	0.251834	+	0.508652i
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	0.957604	−	0.288087i	$-0.0930192\pi$
$877$	6.79088	+	11.7621i	0.229312	+	0.397179i	−0.728293	+	0.685266i	$0.759686\pi$
$878$	−12.8669	−	11.5865i	−0.434238	−	0.391026i
$879$	1.94816	−	11.4516i	0.0657097	−	0.386253i
$880$	3.43421	+	3.81548i	0.115767	+	0.128620i
$881$		−	5.11905i		−	0.172465i	−0.996275	−	0.0862325i	$-0.972517\pi$
$881$		−	5.11905i		−	0.172465i	0.996275	−	0.0862325i	$-0.0274828\pi$
$882$	10.6653	−	27.7174i	0.359118	−	0.933292i
$883$		−	36.5196i		−	1.22898i	−0.788924	−	0.614491i	$-0.789361\pi$
$883$		−	36.5196i		−	1.22898i	0.788924	−	0.614491i	$-0.210639\pi$
$884$	−3.13649	−	29.8679i	−0.105492	−	1.00457i
$885$	0.219193	−	0.0812788i	0.00736810	−	0.00273216i
$886$	26.4955	−	29.4235i	0.890133	−	0.988502i
$887$	−16.1245	−	27.9284i	−0.541407	−	0.937744i	−0.998824	−	0.0484917i	$-0.984559\pi$
$887$	−16.1245	−	27.9284i	−0.541407	−	0.937744i	0.457417	−	0.889252i	$-0.348775\pi$
$888$	−5.69529	−	22.2828i	−0.191122	−	0.747761i
$889$	3.15576	−	2.22063i	0.105841	−	0.0744774i
$890$	1.72673	−	0.560960i	0.0578800	−	0.0188034i
$891$	23.7671	+	3.60253i	0.796227	+	0.120689i
$892$	23.4091	−	17.0044i	0.783793	−	0.569350i
$893$	15.6692	−	27.1398i	0.524349	−	0.908199i
$894$	0.137877	−	0.347221i	0.00461130	−	0.0116128i
$895$	2.56981	+	4.45103i	0.0858991	+	0.148782i
$896$	19.6832	+	22.5515i	0.657569	+	0.753394i
$897$	−18.2973	−	49.3443i	−0.610929	−	1.64756i
$898$	7.00739	−	32.9598i	0.233840	−	1.09988i
$899$	−18.2427			−0.608426
$900$	−20.8200	−	19.6299i	−0.694001	−	0.654331i
$901$			21.3231i			0.710374i
$902$	−9.18778	+	43.2154i	−0.305920	+	1.43892i
$903$	5.06950	+	3.48700i	0.168702	+	0.116040i
$904$	26.5977	+	2.79921i	0.884626	+	0.0931003i
$905$	1.73803	+	3.01036i	0.0577742	+	0.100068i
$906$	−4.46807	−	30.4688i	−0.148442	−	1.01226i
$907$	−24.3819	−	14.0769i	−0.809588	−	0.467416i	0.0372246	−	0.999307i	$-0.488148\pi$
$907$	−24.3819	−	14.0769i	−0.809588	−	0.467416i	−0.846813	+	0.531891i	$0.821482\pi$
$908$	−31.3153	+	22.7475i	−1.03924	+	0.754904i
$909$	−5.15856	+	14.7227i	−0.171099	+	0.488320i
$910$	−1.36241	+	11.3087i	−0.0451634	+	0.374880i
$911$	−33.2831	−	19.2160i	−1.10272	−	0.636655i	−0.165785	−	0.986162i	$-0.553016\pi$
$911$	−33.2831	−	19.2160i	−1.10272	−	0.636655i	−0.936934	+	0.349507i	$0.886349\pi$
$912$	29.0899	−	1.18605i	0.963262	−	0.0392741i
$913$	−23.5673	+	13.6066i	−0.779964	+	0.450312i
$914$	25.0330	+	22.5419i	0.828019	+	0.745620i
$915$	−5.83949	+	7.04501i	−0.193048	+	0.232901i
$916$	−39.1819	+	4.11456i	−1.29461	+	0.135949i
$917$	13.7831	−	29.7381i	0.455158	−	0.982038i
$918$	−13.1508	−	11.4185i	−0.434040	−	0.376866i
$919$			17.3398i			0.571988i	0.958231	+	0.285994i	$0.0923238\pi$
$919$			17.3398i			0.571988i	−0.958231	+	0.285994i	$0.907676\pi$
$920$	−2.65006	−	5.95432i	−0.0873698	−	0.196308i
$921$	−13.3515	+	16.1078i	−0.439946	+	0.530769i
$922$	0.347007	−	0.385355i	0.0114281	−	0.0126910i
$923$	0.629639	+	1.09057i	0.0207248	+	0.0358964i
$924$	12.7808	+	20.8784i	0.420457	+	0.686848i
$925$	−11.1948	+	19.3899i	−0.368081	+	0.637536i
$926$	7.24077	+	22.2883i	0.237946	+	0.732438i
$927$	−5.14272	+	4.42195i	−0.168909	+	0.145236i
$928$	0.00374457	−	16.4116i	0.000122922	−	0.538738i
$929$	48.7835	+	28.1651i	1.60053	+	0.924068i	0.991380	+	0.131016i	$0.0418238\pi$
$929$	48.7835	+	28.1651i	1.60053	+	0.924068i	0.609153	+	0.793053i	$0.291510\pi$
$930$	1.07377	+	7.32227i	0.0352102	+	0.240107i
$931$	9.93228	−	27.6882i	0.325517	−	0.907444i
$932$	−13.4251	−	5.97869i	−0.439753	−	0.195839i
$933$	3.45551	+	0.587855i	0.113128	+	0.0192455i
$934$	−7.68949	+	36.1681i	−0.251608	+	1.18346i
$935$		−	3.04160i		−	0.0994708i
$936$	−53.5814	+	4.38882i	−1.75136	+	0.143453i
$937$		−	36.1315i		−	1.18036i	−0.807270	−	0.590182i	$-0.799056\pi$
$937$		−	36.1315i		−	1.18036i	0.807270	−	0.590182i	$-0.200944\pi$
$938$	−4.90117	+	6.53497i	−0.160029	+	0.213374i
$939$	−31.5670	+	11.7053i	−1.03015	+	0.381989i
$940$	−2.91545	+	6.54659i	−0.0950914	+	0.213526i
$941$	12.0974	−	6.98446i	0.394365	−	0.227687i	−0.289684	−	0.957122i	$-0.593550\pi$
$941$	12.0974	−	6.98446i	0.394365	−	0.227687i	0.684050	+	0.729435i	$0.260217\pi$
$942$	26.1857	+	10.3980i	0.853176	+	0.338785i
$943$	28.0466	−	48.5781i	0.913321	−	1.58192i
$944$	−0.347416	+	1.06857i	−0.0113074	+	0.0347791i
$945$	3.89837	+	5.33255i	0.126814	+	0.173468i
$946$	−4.82357	+	1.56703i	−0.156828	+	0.0509485i
$947$	−11.0539	−	6.38196i	−0.359203	−	0.207386i	0.309528	−	0.950890i	$-0.399829\pi$
$947$	−11.0539	−	6.38196i	−0.359203	−	0.207386i	−0.668731	+	0.743505i	$0.733162\pi$
$948$	−13.6568	−	0.873571i	−0.443551	−	0.0283723i
$949$	−15.3624	−	26.6084i	−0.498684	−	0.863746i
$950$	−21.0616	−	18.9657i	−0.683330	−	0.615329i
$951$	−6.28481	−	16.9489i	−0.203799	−	0.549606i
$952$	0.270777	−	17.7337i	0.00877595	−	0.574754i
$953$	−3.91673			−0.126875			−0.0634377	−	0.997986i	$-0.520206\pi$
$953$	−3.91673			−0.126875			−0.0634377	+	0.997986i	$0.520206\pi$
$954$	38.1606	+	0.874088i	1.23549	+	0.0282997i
$955$	9.57597			0.309871
$956$	−19.1691	+	2.01299i	−0.619973	+	0.0651046i
$957$	2.25095	−	13.2315i	0.0727627	−	0.427712i
$958$	−40.0974	−	36.1072i	−1.29549	−	1.16657i
$959$	23.4990	−	2.11090i	0.758823	−	0.0681645i
$960$	−6.58754	+	0.964488i	−0.212612	+	0.0311287i
$961$	−4.26940	+	7.39481i	−0.137722	+	0.238542i
$962$	12.9969	+	40.0067i	0.419038	+	1.28987i
$963$	43.7201	−	8.25345i	1.40886	−	0.265964i
$964$	4.83470	+	6.65568i	0.155715	+	0.214365i
$965$	−5.93272	−	3.42526i	−0.190981	−	0.110263i
$966$	−7.24257	−	30.2240i	−0.233026	−	0.972442i
$967$	−20.2799	+	11.7086i	−0.652158	+	0.376524i	−0.789283	−	0.614030i	$-0.789547\pi$
$967$	−20.2799	+	11.7086i	−0.652158	+	0.376524i	0.137125	+	0.990554i	$0.456214\pi$
$968$	10.8747	+	1.14448i	0.349526	+	0.0367850i
$969$	−13.2811	−	11.0085i	−0.426652	−	0.353645i
$970$	0.305982	−	1.43921i	0.00982448	−	0.0462102i
$971$	25.1209			0.806167			0.403084	−	0.915163i	$-0.367938\pi$
$971$	25.1209			0.806167			0.403084	+	0.915163i	$0.367938\pi$
$972$	−20.9740	+	23.0671i	−0.672743	+	0.739877i
$973$	3.06060	−	6.60347i	0.0981184	−	0.211698i
$974$	12.3641	+	2.62867i	0.396173	+	0.0842280i
$975$	40.2936	+	33.3987i	1.29043	+	1.06962i
$976$	−9.13633	−	43.0217i	−0.292447	−	1.37709i
$977$	−1.21770	−	2.10911i	−0.0389575	−	0.0674764i	0.845889	−	0.533359i	$-0.179070\pi$
$977$	−1.21770	−	2.10911i	−0.0389575	−	0.0674764i	−0.884847	+	0.465882i	$0.845737\pi$
$978$	−38.3678	+	30.3474i	−1.22687	+	0.970403i
$979$	−3.56823	+	6.18036i	−0.114041	+	0.197525i
$980$	−1.59762	+	6.53430i	−0.0510340	+	0.208731i
$981$	6.09572	+	32.2902i	0.194621	+	1.03095i
$982$	4.05199	+	12.4727i	0.129304	+	0.398019i
$983$	9.60279	−	16.6325i	0.306281	−	0.530495i	−0.671264	−	0.741218i	$-0.734248\pi$
$983$	9.60279	−	16.6325i	0.306281	−	0.530495i	0.977546	+	0.210723i	$0.0675818\pi$
$984$	−40.0467	−	40.9839i	−1.27664	−	1.30652i
$985$	−4.97320	+	2.87128i	−0.158459	+	0.0914865i
$986$	−6.50700	+	7.22610i	−0.207225	+	0.230126i
$987$	−19.3674	+	28.1569i	−0.616471	+	0.896243i
$988$	−52.9578	+	5.56120i	−1.68481	+	0.176925i
$989$	6.43913			0.204752
$990$	−5.44336	−	0.124683i	−0.173001	−	0.00396269i
$991$			29.4493i			0.935489i	0.883864	+	0.467745i	$0.154933\pi$
$991$			29.4493i			0.935489i	−0.883864	+	0.467745i	$0.845067\pi$
$992$	−30.8007	−	17.7921i	−0.977922	−	0.564901i
$993$	58.6479	−	21.7472i	1.86113	−	0.690125i
$994$	0.292137	+	0.683897i	0.00926601	+	0.0216919i
$995$	9.13423	−	5.27365i	0.289575	−	0.167186i
$996$	2.25303	−	35.2223i	0.0713901	−	1.11606i
$997$	13.3933	+	7.73264i	0.424171	+	0.244895i	0.696860	−	0.717207i	$-0.254580\pi$
$997$	13.3933	+	7.73264i	0.424171	+	0.244895i	−0.272689	+	0.962102i	$0.587913\pi$
$998$	−7.58668	−	23.3530i	−0.240152	−	0.739227i
$999$	21.3430	+	11.8133i	0.675264	+	0.373755i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.bi.c.223.23	yes	80
3.2	odd	2		756.2.bi.c.559.18		80
4.3	odd	2	inner	252.2.bi.c.223.34	yes	80
7.6	odd	2	inner	252.2.bi.c.223.24	yes	80
9.4	even	3	inner	252.2.bi.c.139.33	yes	80
9.5	odd	6		756.2.bi.c.307.7		80
12.11	even	2		756.2.bi.c.559.8		80
21.20	even	2		756.2.bi.c.559.17		80
28.27	even	2	inner	252.2.bi.c.223.33	yes	80
36.23	even	6		756.2.bi.c.307.17		80
36.31	odd	6	inner	252.2.bi.c.139.24	yes	80
63.13	odd	6	inner	252.2.bi.c.139.34	yes	80
63.41	even	6		756.2.bi.c.307.8		80
84.83	odd	2		756.2.bi.c.559.7		80
252.139	even	6	inner	252.2.bi.c.139.23	✓	80
252.167	odd	6		756.2.bi.c.307.18		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.23	✓	80	252.139	even	6	inner
252.2.bi.c.139.24	yes	80	36.31	odd	6	inner
252.2.bi.c.139.33	yes	80	9.4	even	3	inner
252.2.bi.c.139.34	yes	80	63.13	odd	6	inner
252.2.bi.c.223.23	yes	80	1.1	even	1	trivial
252.2.bi.c.223.24	yes	80	7.6	odd	2	inner
252.2.bi.c.223.33	yes	80	28.27	even	2	inner
252.2.bi.c.223.34	yes	80	4.3	odd	2	inner
756.2.bi.c.307.7		80	9.5	odd	6
756.2.bi.c.307.8		80	63.41	even	6
756.2.bi.c.307.17		80	36.23	even	6
756.2.bi.c.307.18		80	252.167	odd	6
756.2.bi.c.559.7		80	84.83	odd	2
756.2.bi.c.559.8		80	12.11	even	2
756.2.bi.c.559.17		80	21.20	even	2
756.2.bi.c.559.18		80	3.2	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.294095 - 1.38330i) q^{2} +(-1.10533 + 1.33351i) q^{3} +(-1.82702 - 0.813640i) q^{4} +(-0.416111 + 0.240242i) q^{5} +(1.51957 + 1.92117i) q^{6} +(-1.52257 - 2.16374i) q^{7} +(-1.66282 + 2.28802i) q^{8} +(-0.556509 - 2.94793i) q^{9} +(0.209950 + 0.646259i) q^{10} +(-2.31311 - 1.33548i) q^{11} +(3.10445 - 1.53701i) q^{12} +(-5.48694 + 3.16789i) q^{13} +(-3.44088 + 1.46982i) q^{14} +(0.139573 - 0.820435i) q^{15} +(2.67598 + 2.97307i) q^{16} -2.37005i q^{17} +(-4.24153 - 0.0971545i) q^{18} -4.20225 q^{19} +(0.955712 - 0.100361i) q^{20} +(4.56831 + 0.361276i) q^{21} +(-2.52763 + 2.80696i) q^{22} +(4.15320 - 2.39785i) q^{23} +(-1.21314 - 4.74640i) q^{24} +(-2.38457 + 4.13019i) q^{25} +(2.76845 + 8.52173i) q^{26} +(4.54623 + 2.51631i) q^{27} +(1.02125 + 5.19202i) q^{28} +(1.45060 - 2.51250i) q^{29} +(-1.09386 - 0.434356i) q^{30} +(-3.14399 - 5.44556i) q^{31} +(4.89962 - 2.82731i) q^{32} +(4.33762 - 1.60843i) q^{33} +(-3.27848 - 0.697018i) q^{34} +(1.15338 + 0.534572i) q^{35} +(-1.38180 + 5.83872i) q^{36} +4.69467 q^{37} +(-1.23586 + 5.81295i) q^{38} +(1.84044 - 10.8185i) q^{39} +(0.142241 - 1.35155i) q^{40} +(10.1295 - 5.84827i) q^{41} +(1.84327 - 6.21308i) q^{42} +(1.16280 + 0.671344i) q^{43} +(3.13950 + 4.32198i) q^{44} +(0.939786 + 1.09297i) q^{45} +(-2.09550 - 6.45030i) q^{46} +(-3.72876 + 6.45840i) q^{47} +(-6.92245 + 0.282242i) q^{48} +(-2.36356 + 6.58890i) q^{49} +(5.01199 + 4.51323i) q^{50} +(3.16049 + 2.61967i) q^{51} +(12.6023 - 1.32339i) q^{52} -8.99689 q^{53} +(4.81783 - 5.54874i) q^{54} +1.28335 q^{55} +(7.48244 + 0.114250i) q^{56} +(4.64485 - 5.60375i) q^{57} +(-3.04893 - 2.74552i) q^{58} +(0.140454 + 0.243273i) q^{59} +(-0.922541 + 1.38539i) q^{60} +(-9.52219 - 5.49764i) q^{61} +(-8.45745 + 2.74757i) q^{62} +(-5.53124 + 5.69257i) q^{63} +(-2.47005 - 7.60913i) q^{64} +(1.52212 - 2.63639i) q^{65} +(-0.949260 - 6.47324i) q^{66} +(1.89068 - 1.09159i) q^{67} +(-1.92837 + 4.33012i) q^{68} +(-1.39308 + 8.18874i) q^{69} +(1.07867 - 1.43825i) q^{70} -0.198757i q^{71} +(7.67029 + 3.62858i) q^{72} +4.84941i q^{73} +(1.38068 - 6.49412i) q^{74} +(-2.87194 - 7.74506i) q^{75} +(7.67758 + 3.41912i) q^{76} +(0.632248 + 7.03833i) q^{77} +(-14.4239 - 5.72753i) q^{78} +(-3.42117 - 1.97521i) q^{79} +(-1.82776 - 0.594244i) q^{80} +(-8.38060 + 3.28110i) q^{81} +(-5.11086 - 15.7321i) q^{82} +(5.09429 - 8.82356i) q^{83} +(-8.05243 - 4.37702i) q^{84} +(0.569384 + 0.986203i) q^{85} +(1.27064 - 1.41106i) q^{86} +(1.74707 + 4.71152i) q^{87} +(6.90188 - 3.07178i) q^{88} -2.67188i q^{89} +(1.78829 - 0.978565i) q^{90} +(15.2087 + 7.04900i) q^{91} +(-9.53895 + 1.00170i) q^{92} +(10.7369 + 1.82656i) q^{93} +(7.83727 + 7.05736i) q^{94} +(1.74860 - 1.00956i) q^{95} +(-1.64543 + 9.65881i) q^{96} +(-1.87526 - 1.08268i) q^{97} +(8.41929 + 5.20727i) q^{98} +(-2.64962 + 7.56210i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 6 q^{2} - 2 q^{4} - 24 q^{8} - 32 q^{9} + 10 q^{14} - 18 q^{16} - 22 q^{18} + 4 q^{21} - 14 q^{22} + 32 q^{25} + 28 q^{28} + 8 q^{29} - 16 q^{30} - 16 q^{32} + 34 q^{36} - 16 q^{37} - 8 q^{42} - 84 q^{44}+ \cdots + 20 q^{98}+O(q^{100}) \) 80 * q - 6 * q^2 - 2 * q^4 - 24 * q^8 - 32 * q^9 + 10 * q^14 - 18 * q^16 - 22 * q^18 + 4 * q^21 - 14 * q^22 + 32 * q^25 + 28 * q^28 + 8 * q^29 - 16 * q^30 - 16 * q^32 + 34 * q^36 - 16 * q^37 - 8 * q^42 - 84 * q^44 + 24 * q^46 - 24 * q^49 - 12 * q^50 - 48 * q^53 + 32 * q^56 + 72 * q^57 - 14 * q^58 + 56 * q^60 - 8 * q^64 - 40 * q^65 - 22 * q^70 - 100 * q^72 + 64 * q^74 - 12 * q^77 - 24 * q^78 - 104 * q^81 + 62 * q^84 + 40 * q^85 - 52 * q^86 + 6 * q^88 + 30 * q^92 + 48 * q^93 + 20 * q^98

Introduction

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