LMFDB - Embedded newform 252.2.bi.c.139.24

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			139.24
Character	$\chi$	$=$	252.139
Dual form			252.2.bi.c.223.24

$q$-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} +(-2.63514 + 0.236713i) 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} +(-1.10242 - 3.57556i) 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} +(-3.22835 - 3.25235i) 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} +(4.62185 - 2.57653i) 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} +(3.54952 - 5.42226i) 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} +(6.88793 - 1.24754i) 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} +(4.92337 + 5.63564i) 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} +(0.768666 - 7.89995i) 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} +(0.400269 - 1.75268i) 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} +(5.77925 - 4.06671i) 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} +(8.54449 + 3.31538i) 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} +(3.75143 + 9.16116i) 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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

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

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	$-0.299068\pi$
$5$	0.416111	+	0.240242i	0.186091	+	0.107439i	−0.404061	+	0.914732i	$0.632402\pi$
$6$	−1.51957	+	1.92117i	−0.620363	+	0.784315i
$7$	−2.63514	+	0.236713i	−0.995990	+	0.0894690i
$7$	−2.63514	+	0.236713i	−0.995990	+	0.0894690i
$8$	−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	−0.806389	−	0.591385i	$-0.798581\pi$
$11$	−2.31311	+	1.33548i	−0.697429	+	0.402661i	0.108960	+	0.994046i	$0.465248\pi$
$12$	−3.10445	−	1.53701i	−0.896177	−	0.443697i
$13$	5.48694	+	3.16789i	1.52180	+	0.878614i	0.999668	+	0.0257515i	$0.00819785\pi$
$13$	5.48694	+	3.16789i	1.52180	+	0.878614i	0.522136	+	0.852862i	$0.325135\pi$
$14$	−1.10242	−	3.57556i	−0.294635	−	0.955610i
$15$	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	$-0.339899\pi$
$19$	4.20225			0.964062			0.482031	+	0.876154i	$0.339899\pi$
$20$	−0.955712	−	0.100361i	−0.213704	−	0.0224414i
$21$	−3.22835	−	3.25235i	−0.704484	−	0.709720i
$22$	−2.52763	−	2.80696i	−0.538893	−	0.598446i
$23$	4.15320	+	2.39785i	0.866001	+	0.499986i	0.866017	−	0.500014i	$-0.166672\pi$
$23$	4.15320	+	2.39785i	0.866001	+	0.499986i	−1.59909e−5		1.00000i	$0.500005\pi$
$24$	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
$28$	4.62185	−	2.57653i	0.873447	−	0.486919i
$29$	1.45060	+	2.51250i	0.269369	+	0.466560i	0.968699	−	0.248238i	$-0.0798516\pi$
$29$	1.45060	+	2.51250i	0.269369	+	0.466560i	−0.699330	+	0.714799i	$0.746518\pi$
$30$	−1.09386	+	0.434356i	−0.199710	+	0.0793022i
$31$	3.14399	−	5.44556i	0.564678	−	0.978051i	−0.432402	−	0.901681i	$-0.642334\pi$
$31$	3.14399	−	5.44556i	0.564678	−	0.978051i	0.997080	−	0.0763698i	$-0.0243330\pi$
$32$	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	−0.994573	−	0.104043i	$-0.966822\pi$
$41$	−10.1295	−	5.84827i	−1.58196	−	0.913347i	−0.587390	−	0.809304i	$-0.699845\pi$
$42$	3.54952	−	5.42226i	0.547703	−	0.836673i
$43$	1.16280	−	0.671344i	0.177326	−	0.102379i	−0.408710	−	0.912664i	$-0.634021\pi$
$43$	1.16280	−	0.671344i	0.177326	−	0.102379i	0.586036	+	0.810285i	$0.300688\pi$
$44$	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	0.998676	+	0.0514505i	$0.0163844\pi$
$47$	3.72876	+	6.45840i	0.543895	+	0.942054i	−0.454780	+	0.890604i	$0.650282\pi$
$48$	6.92245	+	0.282242i	0.999170	+	0.0407381i
$49$	6.88793	−	1.24754i	0.983991	−	0.178220i
$50$	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
$56$	4.92337	+	5.63564i	0.657913	+	0.753094i
$57$	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	$-0.839154\pi$
$59$	−0.140454	+	0.243273i	−0.0182855	+	0.0316715i	0.856738	+	0.515752i	$0.172487\pi$
$60$	−0.922541	−	1.38539i	−0.119099	−	0.178852i
$61$	9.52219	−	5.49764i	1.21919	−	0.703900i	0.254446	−	0.967087i	$-0.418107\pi$
$61$	9.52219	−	5.49764i	1.21919	−	0.703900i	0.964745	+	0.263186i	$0.0847735\pi$
$62$	8.45745	+	2.74757i	1.07410	+	0.348941i
$63$	0.768666	−	7.89995i	0.0968428	−	0.995300i
$64$	−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	0.611026	−	0.791611i	$-0.290757\pi$
$67$	1.89068	+	1.09159i	0.230984	+	0.133358i	−0.380042	+	0.924969i	$0.624091\pi$
$68$	1.92837	+	4.33012i	0.233849	+	0.525104i
$69$	1.39308	+	8.18874i	0.167707	+	0.985809i
$70$	0.400269	−	1.75268i	0.0478413	−	0.209485i
$71$			0.198757i			0.0235881i	0.999930	+	0.0117940i	$0.00375425\pi$
$71$			0.198757i			0.0235881i	−0.999930	+	0.0117940i	$0.996246\pi$
$72$	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
$77$	5.77925	−	4.06671i	0.658607	−	0.463444i
$78$	−14.4239	+	5.72753i	−1.63318	+	0.648515i
$79$	−3.42117	+	1.97521i	−0.384912	+	0.222229i	−0.679953	−	0.733256i	$-0.738000\pi$
$79$	−3.42117	+	1.97521i	−0.384912	+	0.222229i	0.295041	+	0.955484i	$0.404667\pi$
$80$	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	−0.997566	−	0.0697297i	$-0.977786\pi$
$83$	−5.09429	−	8.82356i	−0.559171	−	0.968512i	0.438395	−	0.898782i	$-0.355547\pi$
$84$	8.54449	+	3.31538i	0.932280	+	0.361737i
$85$	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	$-0.631604\pi$
$97$	1.87526	−	1.08268i	0.190403	−	0.109929i	0.592171	+	0.805812i	$0.298271\pi$
$98$	3.75143	+	9.16116i	0.378951	+	0.925417i
$99$	−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	$-0.583368\pi$
$101$	4.50341	−	2.60004i	0.448106	−	0.258714i	0.707030	+	0.707184i	$0.250035\pi$
$102$	4.55327	+	3.60146i	0.450841	+	0.356597i
$103$	1.13040	−	1.95791i	0.111382	−	0.192919i	−0.804946	−	0.593348i	$-0.797806\pi$
$103$	1.13040	−	1.95791i	0.111382	−	0.192919i	0.916328	+	0.400429i	$0.131139\pi$
$104$	−1.87562	−	17.8219i	−0.183920	−	1.74758i
$105$	−0.562002	−	2.12892i	−0.0548458	−	0.207762i
$106$	−2.64594	−	12.4454i	−0.256996	−	1.20880i
$107$		−	14.8308i		−	1.43375i	−0.697204	−	0.716873i	$-0.745573\pi$
$107$		−	14.8308i		−	1.43375i	0.697204	−	0.716873i	$-0.254427\pi$
$108$	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
$112$	−6.34782	+	8.46789i	−0.599813	+	0.800140i
$113$	−4.72782	+	8.18882i	−0.444756	+	0.770339i	−0.998035	−	0.0626563i	$-0.980043\pi$
$113$	−4.72782	+	8.18882i	−0.444756	+	0.770339i	0.553280	+	0.832996i	$0.313376\pi$
$114$	−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
$119$	0.561020	+	6.24541i	0.0514286	+	0.572516i
$120$	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
$126$	11.1540	−	1.26004i	0.993680	−	0.112253i
$127$		−	1.45847i		−	0.129419i	−0.997904	−	0.0647093i	$-0.979388\pi$
$127$		−	1.45847i		−	0.129419i	0.997904	−	0.0647093i	$-0.0206120\pi$
$128$	−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	0.457641	+	0.889137i	$0.348695\pi$
$131$	−6.19426	+	10.7288i	−0.541195	+	0.937377i	−0.998836	+	0.0482400i	$0.984639\pi$
$132$	9.23357	−	0.590636i	0.803680	−	0.0514083i
$133$	−11.0735	+	0.994726i	−0.960196	+	0.0862537i
$134$	−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	0.610257	−	0.792203i	$-0.291066\pi$
$137$	−4.45878	−	7.72284i	−0.380939	−	0.659806i	−0.991197	+	0.132397i	$0.957733\pi$
$138$	−10.9178	+	4.33530i	−0.929382	+	0.369045i
$139$	−1.37546	+	2.38237i	−0.116665	+	0.202070i	−0.918444	−	0.395551i	$-0.870554\pi$
$139$	−1.37546	+	2.38237i	−0.116665	+	0.202070i	0.801779	+	0.597621i	$0.203887\pi$
$140$	2.54219	+	0.0382367i	0.214855	+	0.00323159i
$141$	−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
$147$	9.27703	+	7.80620i	0.765156	+	0.643845i
$148$	−8.57724	+	3.81977i	−0.705045	+	0.313983i
$149$	−0.0762596	+	0.132086i	−0.00624743	+	0.0108209i	−0.869132	−	0.494580i	$-0.835322\pi$
$149$	−0.0762596	+	0.132086i	−0.00624743	+	0.0108209i	0.862885	+	0.505401i	$0.168655\pi$
$150$	11.5583	+	1.69496i	0.943734	+	0.138393i
$151$	−10.8876	+	6.28594i	−0.886017	+	0.511542i	−0.872638	−	0.488368i	$-0.837592\pi$
$151$	−10.8876	+	6.28594i	−0.886017	+	0.511542i	−0.0133797	+	0.999910i	$0.504259\pi$
$152$	−6.98759	−	9.61482i	−0.566768	−	0.779865i
$153$	6.98674	+	1.31895i	0.564844	+	0.106631i
$154$	7.32511	+	6.79842i	0.590274	+	0.547832i
$155$	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	$-0.485122\pi$
$157$	−9.96123	−	5.75112i	−0.794993	−	0.458989i	−0.841717	+	0.539919i	$0.818455\pi$
$158$	−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	$-0.714135\pi$
$163$		−	19.9710i		−	1.56425i	0.623121	−	0.782126i	$-0.285865\pi$
$164$	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	−0.0326095	−	0.999468i	$-0.510382\pi$
$167$	10.9749	−	19.0090i	0.849260	−	1.47096i	0.881870	−	0.471493i	$-0.156285\pi$
$168$	−2.07326	+	12.7946i	−0.159956	+	0.987124i
$169$	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	$-0.469155\pi$
$173$	13.2462	−	7.64770i	1.00709	−	0.581444i	0.910339	+	0.413864i	$0.135821\pi$
$174$	−7.03124	−	1.03109i	−0.533037	−	0.0781666i
$175$	7.26134	+	10.3192i	0.548906	+	0.780057i
$176$	−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	$0.130905\pi$
$179$			10.6967i			0.799512i	−0.916622	+	0.399756i	$0.869095\pi$
$180$	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	$-0.0866498\pi$
$182$	5.27805	−	23.1113i	0.391235	−	1.71312i
$183$	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
$189$	11.3843	−	7.70699i	0.828086	−	0.560601i
$190$	−0.882260	+	2.71574i	−0.0640059	+	0.197020i
$191$	−17.2598	+	9.96493i	−1.24887	+	0.721037i	−0.970885	−	0.239547i	$-0.923001\pi$
$191$	−17.2598	+	9.96493i	−1.24887	+	0.721037i	−0.277988	+	0.960584i	$0.589668\pi$
$192$	−12.8771	+	5.11672i	−0.929323	+	0.369268i
$193$	7.12877	−	12.3474i	0.513140	−	0.888784i	−0.486744	−	0.873545i	$-0.661816\pi$
$193$	7.12877	−	12.3474i	0.513140	−	0.888784i	0.999884	−	0.0152396i	$-0.00485112\pi$
$194$	2.04917	+	2.27562i	0.147122	+	0.163380i
$195$	−1.83322	+	4.94383i	−0.131279	+	0.354035i
$196$	−11.5693	+	7.88358i	−0.826380	+	0.563113i
$197$	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	$-0.216210\pi$
$199$	21.9514			1.55610			0.778048	+	0.628205i	$0.216210\pi$
$200$	−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
$203$	−4.41726	−	6.27743i	−0.310031	−	0.440589i
$204$	−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
$210$	2.77965	−	1.40352i	0.191814	−	0.0968520i
$211$	8.92341	+	5.15194i	0.614313	+	0.354674i	0.774652	−	0.632388i	$-0.217925\pi$
$211$	8.92341	+	5.15194i	0.614313	+	0.354674i	−0.160338	+	0.987062i	$0.551259\pi$
$212$	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	$-0.00571235\pi$
$223$	7.23332	+	12.5285i	0.484379	+	0.838969i	−0.515460	+	0.856914i	$0.672379\pi$
$224$	−13.5805	−	6.29055i	−0.907383	−	0.420305i
$225$	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	−0.984932	−	0.172945i	$-0.944672\pi$
$227$	−9.67633	−	16.7599i	−0.642240	−	1.11239i	0.342691	−	0.939448i	$-0.388662\pi$
$228$	−13.0457	−	6.45890i	−0.863970	−	0.427751i
$229$	−17.0595	−	9.84933i	−1.12733	−	0.650862i	−0.184065	−	0.982914i	$-0.558926\pi$
$229$	−17.0595	−	9.84933i	−1.12733	−	0.650862i	−0.943261	+	0.332052i	$0.892259\pi$
$230$	−2.42159	+	2.18061i	−0.159675	+	0.143785i
$231$	11.8110	+	3.21166i	0.777104	+	0.211312i
$232$	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
$238$	−8.47426	+	2.61280i	−0.549304	+	0.169363i
$239$	8.34611	+	4.81863i	0.539865	+	0.311691i	0.745024	−	0.667037i	$-0.232438\pi$
$239$	8.34611	+	4.81863i	0.539865	+	0.311691i	−0.205159	+	0.978729i	$0.565771\pi$
$240$	2.81270	+	1.78051i	0.181559	+	0.114931i
$241$	3.56210	−	2.05658i	0.229455	−	0.132476i	−0.380865	−	0.924630i	$-0.624374\pi$
$241$	3.56210	−	2.05658i	0.229455	−	0.132476i	0.610321	+	0.792154i	$0.291041\pi$
$242$	−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
$245$	3.16586	+	1.13565i	0.202259	+	0.0725542i
$246$	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	$-0.466605\pi$
$251$	3.31816			0.209441			0.104720	+	0.994502i	$0.466605\pi$
$252$	5.02335	+	15.0588i	0.316441	+	0.948612i
$253$	−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	$-0.152362\pi$
$257$	14.9497	+	8.63121i	0.932537	+	0.538400i	0.0449237	+	0.998990i	$0.485696\pi$
$258$	−0.477193	+	3.25410i	−0.0297088	+	0.202591i
$259$	−12.3711	+	1.11129i	−0.768704	+	0.0690521i
$260$	−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	−0.103729	−	0.994606i	$-0.533078\pi$
$263$	11.4455	−	6.60806i	0.705760	−	0.407471i	0.809489	+	0.587135i	$0.199744\pi$
$264$	3.53257	+	12.5991i	0.217415	+	0.775419i
$265$	−3.74371	−	2.16143i	−0.229974	−	0.132776i
$266$	−4.63266	−	15.0254i	−0.284047	−	0.921267i
$267$	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	$-0.723277\pi$
$271$	−21.2467			−1.29065			−0.645323	+	0.763910i	$0.723277\pi$
$272$	−7.04631	−	6.34220i	−0.427245	−	0.384552i
$273$	−7.41069	−	28.0725i	−0.448516	−	1.69902i
$274$	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	0.997397	−	0.0721016i	$-0.0229706\pi$
$277$	7.26076	+	12.5760i	0.436257	+	0.755619i	−0.561140	+	0.827721i	$0.689637\pi$
$278$	−3.70004	−	1.20203i	−0.221914	−	0.0720930i
$279$	14.3035	+	12.2988i	0.856326	+	0.736309i
$280$	0.694753	+	3.52785i	0.0415194	+	0.210829i
$281$	6.35647	+	11.0097i	0.379195	+	0.656785i	0.990945	−	0.134266i	$-0.0428676\pi$
$281$	6.35647	+	11.0097i	0.379195	+	0.656785i	−0.611750	+	0.791051i	$0.709534\pi$
$282$	−18.0738	−	2.65041i	−1.07628	−	0.157830i
$283$	10.4272	−	18.0605i	0.619834	−	1.07358i	−0.369682	−	0.929158i	$-0.620533\pi$
$283$	10.4272	−	18.0605i	0.619834	−	1.07358i	0.989516	−	0.144425i	$-0.0461332\pi$
$284$	−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	$-0.270570\pi$
$293$	5.80807	+	3.35329i	0.339311	+	0.195901i	−0.320656	+	0.947196i	$0.603903\pi$
$294$	−8.06997	+	15.1286i	−0.470650	+	0.882320i
$295$	−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
$301$	−2.90523	+	2.04434i	−0.167455	+	0.117834i
$302$	−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	$-0.612019\pi$
$307$	−12.0792			−0.689397			−0.344699	+	0.938713i	$0.612019\pi$
$308$	−7.24995	+	12.1322i	−0.413104	+	0.691295i
$309$	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	$-0.815060\pi$
$311$	1.01185	−	1.75258i	0.0573769	−	0.0993797i	0.893287	+	0.449486i	$0.148393\pi$
$312$	21.6925	−	22.2001i	1.22810	−	1.25683i
$313$	−16.8337	+	9.71892i	−0.951495	+	0.549346i	−0.893545	−	0.448974i	$-0.851790\pi$
$313$	−16.8337	+	9.71892i	−0.951495	+	0.549346i	−0.0579500	+	0.998319i	$0.518456\pi$
$314$	5.02596	−	15.4707i	0.283631	−	0.873062i
$315$	2.21775	−	3.10259i	0.124956	−	0.174811i
$316$	4.64342	−	6.39235i	0.261213	−	0.359598i
$317$	−5.21828	−	9.03832i	−0.293088	−	0.507643i	0.681451	−	0.731864i	$-0.261349\pi$
$317$	−5.21828	−	9.03832i	−0.293088	−	0.507643i	−0.974538	+	0.224222i	$0.928016\pi$
$318$	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
$322$	3.99508	−	17.4935i	0.222637	−	0.974873i
$323$		−	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
$329$	−11.3546	−	16.1361i	−0.625999	−	0.889614i
$330$	1.95014	−	2.46553i	0.107352	−	0.135723i
$331$	−31.2751	+	18.0567i	−1.71903	+	0.992484i	−0.798328	+	0.602223i	$0.794282\pi$
$331$	−31.2751	+	18.0567i	−1.71903	+	0.992484i	−0.920704	+	0.390261i	$0.872385\pi$
$332$	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
$336$	−18.3084	+	0.894885i	−0.998808	+	0.0488200i
$337$	3.70539	−	6.41792i	0.201845	−	0.349606i	−0.747278	−	0.664512i	$-0.768639\pi$
$337$	3.70539	−	6.41792i	0.201845	−	0.349606i	0.949123	+	0.314905i	$0.101973\pi$
$338$	−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	−0.348915	−	0.937154i	$-0.613450\pi$
$347$	−24.8678	−	14.3574i	−1.33497	−	0.770747i	−0.986057	+	0.166408i	$0.946783\pi$
$348$	−0.641550	−	10.0295i	−0.0343907	−	0.537639i
$349$	0.744758	−	0.429986i	0.0398660	−	0.0230166i	−0.479935	−	0.877304i	$-0.659340\pi$
$349$	0.744758	−	0.429986i	0.0398660	−	0.0230166i	0.519801	+	0.854288i	$0.326006\pi$
$350$	−12.1390	+	13.0794i	−0.648855	+	0.699123i
$351$	−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	$-0.991089\pi$
$353$	−27.7159	+	16.0018i	−1.47517	+	0.851690i	−0.475562	+	0.879682i	$0.657755\pi$
$354$	−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
$357$	−7.70822	+	7.65134i	−0.407962	+	0.404952i
$358$	−14.7968	+	3.14586i	−0.782033	+	0.166264i
$359$			5.52163i			0.291421i	0.989327	+	0.145710i	$0.0465468\pi$
$359$			5.52163i			0.291421i	−0.989327	+	0.145710i	$0.953453\pi$
$360$	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
$364$	33.5220	+	0.504199i	1.75703	+	0.0264272i
$365$	−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	0.992958	+	0.118465i	$0.0377972\pi$
$367$	11.4766	+	19.8780i	0.599072	+	1.03762i	−0.393886	+	0.919159i	$0.628869\pi$
$368$	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
$371$	23.7081	−	2.12968i	1.23086	−	0.110567i
$372$	−18.1302	+	12.0731i	−0.940010	+	0.625961i
$373$	−14.2688	+	24.7143i	−0.738810	+	1.27966i	0.214222	+	0.976785i	$0.431278\pi$
$373$	−14.2688	+	24.7143i	−0.738810	+	1.27966i	−0.953032	+	0.302871i	$0.902055\pi$
$374$	−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
$378$	14.0091	+	13.4813i	0.720551	+	0.693402i
$379$		−	13.3942i		−	0.688014i	−0.938967	−	0.344007i	$-0.888216\pi$
$379$		−	13.3942i		−	0.688014i	0.938967	−	0.344007i	$-0.111784\pi$
$380$	−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	0.424430	+	0.905461i	$0.360475\pi$
$383$	−11.1930	+	19.3869i	−0.571937	+	0.990625i	−0.996367	+	0.0851637i	$0.972859\pi$
$384$	−10.8650	−	16.3080i	−0.554453	−	0.832215i
$385$	3.38180	−	0.303785i	0.172353	−	0.0154823i
$386$	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	0.973112	+	0.230332i	$0.0739811\pi$
$389$	13.5306	+	23.4357i	0.686029	+	1.18824i	−0.287083	+	0.957906i	$0.592686\pi$
$390$	−7.37792	−	1.08193i	−0.373595	−	0.0547855i
$391$	5.68302	−	9.84327i	0.287402	−	0.497796i
$392$	−14.3078	−	13.6853i	−0.722653	−	0.691211i
$393$	−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
$399$	−13.5663	−	13.6672i	−0.679166	−	0.684214i
$400$	−18.6604	−	3.96283i	−0.933020	−	0.198142i
$401$	−8.33464	+	14.4360i	−0.416212	+	0.720901i	−0.995555	−	0.0941835i	$-0.969976\pi$
$401$	−8.33464	+	14.4360i	−0.416212	+	0.720901i	0.579343	+	0.815084i	$0.303309\pi$
$402$	−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
$406$	7.38445	−	7.95654i	0.366484	−	0.394877i
$407$	−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	$-0.338688\pi$
$409$	−0.589282	−	0.340222i	−0.0291381	−	0.0168229i	−0.514498	+	0.857491i	$0.672022\pi$
$410$	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	$-0.915080\pi$
$419$	−5.19926	+	9.00538i	−0.254000	+	0.439941i	0.710623	+	0.703573i	$0.248413\pi$
$420$	2.75896	+	3.43231i	0.134624	+	0.167480i
$421$	−3.42772	−	5.93699i	−0.167057	−	0.289351i	0.770327	−	0.637649i	$-0.220093\pi$
$421$	−3.42772	−	5.93699i	−0.167057	−	0.289351i	−0.937384	+	0.348298i	$0.886760\pi$
$422$	−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
$427$	−23.7909	+	16.7411i	−1.15132	+	0.810157i
$428$	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	$-0.880228\pi$
$431$		−	15.2572i		−	0.734914i	0.930040	−	0.367457i	$-0.119772\pi$
$432$	−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	$0.686915\pi$
$434$	−22.9370	−	5.23824i	−1.10101	−	0.251443i
$435$	−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	$-0.261045\pi$
$439$	−6.12174	−	10.6032i	−0.292175	−	0.506061i	−0.974324	+	0.225152i	$0.927712\pi$
$440$	2.13398	+	2.93632i	0.101733	+	0.139984i
$441$	−0.155525	+	20.9994i	−0.00740597	+	0.999973i
$442$	20.1969	+	6.56135i	0.960668	+	0.312091i
$443$	24.2468	−	13.9989i	1.15200	−	0.665108i	0.202627	−	0.979256i	$-0.435052\pi$
$443$	24.2468	−	13.9989i	1.15200	−	0.665108i	0.949374	+	0.314148i	$0.101719\pi$
$444$	−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
$448$	4.70776	−	20.6358i	0.222421	−	0.974951i
$449$	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
$455$	−4.63506	−	6.58694i	−0.217295	−	0.308801i
$456$	5.09792	−	19.9455i	0.238732	−	0.934036i
$457$	−11.9100	−	20.6288i	−0.557128	−	0.964974i	−0.997735	−	0.0672735i	$-0.978570\pi$
$457$	−11.9100	−	20.6288i	−0.557128	−	0.964974i	0.440607	−	0.897700i	$-0.354763\pi$
$458$	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	$-0.669385\pi$
$461$	−0.317557	+	0.183341i	−0.0147901	+	0.00853906i	0.492587	+	0.870263i	$0.336051\pi$
$462$	−0.969137	+	17.2826i	−0.0450883	+	0.804059i
$463$	−14.3509	−	8.28549i	−0.666943	−	0.385060i	0.127974	−	0.991777i	$-0.459152\pi$
$463$	−14.3509	−	8.28549i	−0.666943	−	0.385060i	−0.794917	+	0.606718i	$0.792486\pi$
$464$	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	$-0.293192\pi$
$467$	26.1463			1.20991			0.604953	+	0.796261i	$0.293192\pi$
$468$	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
$476$	−6.10651	−	10.9540i	−0.279891	−	0.502076i
$477$	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	−0.860277	−	0.509826i	$-0.829710\pi$
$479$	−19.0772	−	33.0427i	−0.871661	−	1.50976i	−0.0113840	−	0.999935i	$-0.503624\pi$
$480$	−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
$483$	−5.60933	−	21.2487i	−0.255233	−	0.966851i
$484$	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	$-0.935089\pi$
$487$		−	8.93817i		−	0.405027i	0.979279	−	0.202514i	$-0.0649110\pi$
$488$	−28.4124	−	12.6454i	−1.28617	−	0.572428i
$489$	26.6316	−	22.0745i	1.20432	−	0.998243i
$490$	−0.639884	+	4.71331i	−0.0289070	+	0.212926i
$491$	−8.03087	−	4.63662i	−0.362428	−	0.209248i	0.307717	−	0.951478i	$-0.400435\pi$
$491$	−8.03087	−	4.63662i	−0.362428	−	0.209248i	−0.670145	+	0.742230i	$0.733768\pi$
$492$	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
$497$	−0.0470482	−	0.523752i	−0.00211040	−	0.0234935i
$498$	24.6927	+	3.62104i	1.10651	+	0.162262i
$499$	15.0365	+	8.68131i	0.673125	+	0.388629i	0.797260	−	0.603636i	$-0.206282\pi$
$499$	15.0365	+	8.68131i	0.673125	+	0.388629i	−0.124135	+	0.992265i	$0.539615\pi$
$500$	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	$-0.544382\pi$
$503$	−6.23388			−0.277955			−0.138978	+	0.990296i	$0.544382\pi$
$504$	−19.3534	+	11.3775i	−0.862068	+	0.506793i
$505$	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	$-0.304550\pi$
$509$	3.52873	+	2.03731i	0.156408	+	0.0903023i	−0.419753	+	0.907638i	$0.637883\pi$
$510$	1.02944	+	2.59249i	0.0455846	+	0.114797i
$511$	−1.14792	−	12.7789i	−0.0507808	−	0.565304i
$512$	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
$518$	−5.17552	−	16.7861i	−0.227399	−	0.737539i
$519$	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	$-0.475982\pi$
$523$	3.44794			0.150768			0.0753838	+	0.997155i	$0.475982\pi$
$524$	2.58766	−	24.6415i	0.113042	−	1.07647i
$525$	−5.73460	+	21.0891i	−0.250279	+	0.920406i
$526$	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
$532$	19.4222	−	10.8272i	0.842057	−	0.469420i
$533$	−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
$546$	36.6531	−	18.5072i	1.56861	−	0.792033i
$547$	−5.72221	+	3.30372i	−0.244664	+	0.141257i	−0.617319	−	0.786713i	$-0.711781\pi$
$547$	−5.72221	+	3.30372i	−0.244664	+	0.141257i	0.372654	+	0.927970i	$0.378448\pi$
$548$	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
$553$	8.54771	−	6.01480i	0.363485	−	0.255775i
$554$	−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
$560$	−4.67574	+	1.99857i	−0.197586	+	0.0844550i
$561$	−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	−0.443480	−	0.896284i	$-0.646256\pi$
$563$	13.1561	−	22.7871i	0.554465	−	0.960361i	0.997945	−	0.0640767i	$-0.0204102\pi$
$564$	−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
$567$	22.8607	+	6.66236i	0.960060	+	0.279793i
$568$	0.454759	−	0.330497i	0.0190813	−	0.0138673i
$569$	−0.683478	−	1.18382i	−0.0286529	−	0.0496283i	0.851343	−	0.524609i	$-0.175788\pi$
$569$	−0.683478	−	1.18382i	−0.0286529	−	0.0496283i	−0.879996	+	0.474981i	$0.842455\pi$
$570$	−4.59666	+	1.82527i	−0.192533	+	0.0764523i
$571$	−14.6500	−	8.45818i	−0.613083	−	0.353964i	0.161088	−	0.986940i	$-0.448500\pi$
$571$	−14.6500	−	8.45818i	−0.613083	−	0.353964i	−0.774171	+	0.632976i	$0.781833\pi$
$572$	30.9178	−	13.7689i	1.29274	−	0.575705i
$573$	−32.3660	−	12.0016i	−1.35211	−	0.501375i
$574$	−9.74386	+	42.6660i	−0.406701	+	1.78084i
$575$		−	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
$581$	15.5128	+	22.0455i	0.643580	+	0.914599i
$582$	−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	−0.997015	−	0.0772082i	$-0.975399\pi$
$587$	−13.6979	−	23.7254i	−0.565372	−	0.979253i	0.431643	−	0.902044i	$-0.357934\pi$
$588$	−23.3007	−	6.71390i	−0.960905	−	0.276877i
$589$	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	0.787869	−	0.615843i	$-0.211185\pi$
$599$	15.8709	+	9.16306i	0.648467	+	0.374392i	−0.139402	+	0.990236i	$0.544518\pi$
$600$	−22.4964	+	6.30760i	−0.918410	+	0.257507i
$601$	−19.1583	+	11.0611i	−0.781485	+	0.451190i	−0.836956	−	0.547270i	$-0.815667\pi$
$601$	−19.1583	+	11.0611i	−0.781485	+	0.451190i	0.0554716	+	0.998460i	$0.482334\pi$
$602$	−3.68233	−	3.41757i	−0.150081	−	0.139290i
$603$	−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	$-0.937577\pi$
$607$	−7.92507	+	13.7266i	−0.321669	+	0.557146i	0.659164	+	0.751999i	$0.270910\pi$
$608$	20.5894	+	11.8811i	0.835012	+	0.481840i
$609$	3.48851	−	12.8291i	0.141362	−	0.519861i
$610$	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
$616$	−18.9146	−	6.46082i	−0.762089	−	0.260314i
$617$	−15.9608	+	27.6449i	−0.642557	+	1.11294i	0.342303	+	0.939590i	$0.388793\pi$
$617$	−15.9608	+	27.6449i	−0.642557	+	1.11294i	−0.984860	+	0.173352i	$0.944540\pi$
$618$	2.04376	+	5.14689i	0.0822122	+	0.207038i
$619$	0.227459	+	0.393971i	0.00914236	+	0.0158350i	0.870560	−	0.492062i	$-0.163757\pi$
$619$	0.227459	+	0.393971i	0.00914236	+	0.0158350i	−0.861418	+	0.507897i	$0.830423\pi$
$620$	−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
$623$	0.632468	+	7.04078i	0.0253393	+	0.282083i
$624$	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
$630$	4.94403	+	2.15535i	0.196975	+	0.0858711i
$631$			28.8331i			1.14783i	0.818916	+	0.573913i	$0.194575\pi$
$631$			28.8331i			1.14783i	−0.818916	+	0.573913i	$0.805425\pi$
$632$	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
$637$	41.7458	+	14.9750i	1.65403	+	0.593331i
$638$	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	0.932748	−	0.360530i	$-0.117404\pi$
$641$	3.90266	+	6.75961i	0.154146	+	0.266989i	−0.778602	+	0.627518i	$0.784071\pi$
$642$	28.4925	+	22.5364i	1.12451	+	0.889442i
$643$	−2.26137	+	3.91681i	−0.0891797	+	0.154464i	−0.907165	−	0.420776i	$-0.861758\pi$
$643$	−2.26137	+	3.91681i	−0.0891797	+	0.154464i	0.817985	+	0.575240i	$0.195091\pi$
$644$	25.3736	+	0.381640i	0.999859	+	0.0150387i
$645$	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	$-0.720535\pi$
$647$	−32.4931			−1.27744			−0.638718	+	0.769441i	$0.720535\pi$
$648$	6.42822	+	24.6308i	0.252524	+	0.967591i
$649$		−	0.750290i		−	0.0294515i
$650$	41.7979	−	8.88641i	1.63945	−	0.348554i
$651$	−27.8608	+	7.35480i	−1.09195	+	0.288257i
$652$	16.2492	+	36.4874i	0.636369	+	1.42896i
$653$	3.99865	−	6.92587i	0.156479	−	0.271030i	−0.777117	−	0.629356i	$-0.783319\pi$
$653$	3.99865	−	6.92587i	0.156479	−	0.271030i	0.933597	+	0.358325i	$0.116652\pi$
$654$	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
$658$	18.9817	−	20.4523i	0.739985	−	0.797314i
$659$	−6.89888	+	3.98307i	−0.268742	+	0.155158i	−0.628316	−	0.777958i	$-0.716255\pi$
$659$	−6.89888	+	3.98307i	−0.268742	+	0.155158i	0.359574	+	0.933117i	$0.382922\pi$
$660$	3.98409	+	1.97252i	0.155080	+	0.0767803i
$661$	−0.220771	−	0.127462i	−0.00858700	−	0.00495771i	0.495700	−	0.868494i	$-0.334911\pi$
$661$	−0.220771	−	0.127462i	−0.00858700	−	0.00495771i	−0.504287	+	0.863536i	$0.668245\pi$
$662$	−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
$672$	−6.62231	−	25.0628i	−0.255461	−	0.966819i
$673$	−0.198313	−	0.343488i	−0.00764441	−	0.0132405i	0.862178	−	0.506606i	$-0.169100\pi$
$673$	−0.198313	−	0.343488i	−0.00764441	−	0.0132405i	−0.869822	+	0.493365i	$0.835767\pi$
$674$	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	0.684720	−	0.728806i	$-0.259924\pi$
$677$	43.1462	−	24.9105i	1.65824	−	0.957388i	0.973525	−	0.228582i	$-0.0734090\pi$
$678$	−8.54787	−	21.5264i	−0.328279	−	0.826718i
$679$	−4.68528	+	3.29691i	−0.179804	+	0.126524i
$680$	−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	$0.183212\pi$
$683$			28.4508i			1.08864i	−0.838878	+	0.544320i	$0.816788\pi$
$684$	−5.80668	−	24.5357i	−0.222024	−	0.938148i
$685$		−	4.28474i		−	0.163712i
$686$	−12.0541	−	23.2529i	−0.460228	−	0.887801i
$687$	−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	$-0.0923284\pi$
$691$	6.08340	+	10.5368i	0.231423	+	0.400837i	−0.726804	+	0.686845i	$0.758995\pi$
$692$	−17.9786	+	24.7501i	−0.683443	+	0.940859i
$693$	8.77218	+	19.3000i	0.333227	+	0.733146i
$694$	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
$700$	−21.6627	−	12.9452i	−0.818773	−	0.489283i
$701$	−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
$707$	−11.2516	+	7.91749i	−0.423162	+	0.297768i
$708$	0.809945	−	0.539350i	0.0304396	−	0.0202700i
$709$	−22.5400	−	39.0404i	−0.846507	−	1.46619i	−0.884306	−	0.466907i	$-0.845368\pi$
$709$	−22.5400	−	39.0404i	−0.846507	−	1.46619i	0.0377999	−	0.999285i	$-0.487965\pi$
$710$	−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
$714$	−12.8510	−	8.41253i	−0.480937	−	0.314831i
$715$	−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	$-0.427186\pi$
$719$	12.1609			0.453526			0.226763	+	0.973950i	$0.427186\pi$
$720$	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	$-0.267460\pi$
$727$	−8.39590	−	14.5421i	−0.311387	−	0.539337i	−0.978663	+	0.205473i	$0.934127\pi$
$728$	9.16118	+	46.5191i	0.339536	+	1.72411i
$729$	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	$-0.204371\pi$
$733$	18.4832	+	10.6713i	0.682693	+	0.394153i	−0.118176	+	0.992993i	$0.537705\pi$
$734$	−24.1220	+	21.7215i	−0.890359	+	0.801756i
$735$	1.98490	+	5.47698i	0.0732140	+	0.202021i
$736$	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	$0.380074\pi$
$739$			50.5558i			1.85973i	−0.367907	+	0.929863i	$0.619926\pi$
$740$	−4.48675	−	0.471163i	−0.164936	−	0.0173203i
$741$	7.73400	+	45.4618i	0.284116	+	1.67008i
$742$	9.91839	+	32.1690i	0.364116	+	1.18096i
$743$	32.1395	+	18.5558i	1.17909	+	0.680745i	0.955803	−	0.294009i	$-0.0949895\pi$
$743$	32.1395	+	18.5558i	1.17909	+	0.680745i	0.223282	+	0.974754i	$0.428323\pi$
$744$	−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
$749$	3.51063	+	39.0812i	0.128276	+	1.42800i
$750$	9.01781	+	7.13273i	0.329284	+	0.260451i
$751$	−37.8228	−	21.8370i	−1.38017	−	0.796843i	−0.387993	−	0.921662i	$-0.626832\pi$
$751$	−37.8228	−	21.8370i	−1.38017	−	0.796843i	−0.992180	+	0.124819i	$0.960165\pi$
$752$	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
$756$	−14.5286	+	23.3435i	−0.528400	+	0.848996i
$757$	−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	$-0.468582\pi$
$761$	−19.6964	−	11.3717i	−0.713994	−	0.412225i	−0.812538	+	0.582908i	$0.801915\pi$
$762$	2.80198	+	2.21625i	0.101505	+	0.0802864i
$763$	28.8640	−	2.59283i	1.04495	−	0.0938669i
$764$	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	$-0.267491\pi$
$769$	9.86460	+	5.69533i	0.355726	+	0.205379i	−0.311478	+	0.950253i	$0.600824\pi$
$770$	1.41479	+	4.58869i	0.0509857	+	0.165365i
$771$	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
$777$	−15.1560	−	15.2687i	−0.543720	−	0.547762i
$778$	−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
$784$	14.7229	−	23.8167i	0.525819	−	0.850596i
$785$	−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	$-0.720262\pi$
$787$	9.75700	−	16.8996i	0.347799	−	0.602406i	0.985858	+	0.167581i	$0.0535957\pi$
$788$	−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	$-0.155162\pi$
$797$	25.9632	+	14.9898i	0.919663	+	0.530968i	0.0361355	+	0.999347i	$0.488495\pi$
$798$	14.9160	−	22.7857i	0.528019	−	0.806605i
$799$	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
$805$	−3.50839	−	4.98581i	−0.123654	−	0.175727i
$806$	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	$-0.400527\pi$
$811$	17.5107			0.614883			0.307442	+	0.951567i	$0.400527\pi$
$812$	13.1780	+	7.87490i	0.462457	+	0.276355i
$813$	−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
$819$	29.2438	−	40.9115i	1.02186	−	1.42956i
$820$	9.09395	+	6.60587i	0.317575	+	0.230687i
$821$	−9.47071	−	16.4037i	−0.330530	−	0.572495i	0.652086	−	0.758145i	$-0.273894\pi$
$821$	−9.47071	−	16.4037i	−0.330530	−	0.572495i	−0.982616	+	0.185650i	$0.940561\pi$
$822$	21.6123	+	3.16932i	0.753817	+	0.110543i
$823$	8.43975	+	4.87269i	0.294191	+	0.169851i	0.639831	−	0.768516i	$-0.279005\pi$
$823$	8.43975	+	4.87269i	0.294191	+	0.169851i	−0.345639	+	0.938367i	$0.612338\pi$
$824$	−6.35940	+	0.669280i	−0.221540	+	0.0233155i
$825$	3.70023	+	21.7506i	0.128825	+	0.757258i
$826$	1.02468	+	0.234011i	0.0356531	+	0.00814229i
$827$			38.9872i			1.35572i	0.735193	+	0.677858i	$0.237092\pi$
$827$			38.9872i			1.35572i	−0.735193	+	0.677858i	$0.762908\pi$
$828$	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
$833$	−2.95673	−	16.3247i	−0.102445	−	0.565618i
$834$	−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	$-0.0112681\pi$
$839$	13.5859	+	23.5314i	0.469036	+	0.812394i	−0.530337	+	0.847787i	$0.677935\pi$
$840$	−3.93650	+	4.82589i	−0.135822	+	0.166509i
$841$	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	$-0.534276\pi$
$853$	20.4384	−	11.8001i	0.699797	−	0.404028i	0.807272	+	0.590180i	$0.200943\pi$
$854$	−30.1547	−	27.9865i	−1.03187	−	0.957677i
$855$	−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	$-0.580009\pi$
$857$	13.6342	−	7.87173i	0.465737	−	0.268893i	0.714453	+	0.699683i	$0.246675\pi$
$858$	25.7150	−	32.5111i	0.877896	−	1.10991i
$859$	−13.3695	+	23.1566i	−0.456160	+	0.790093i	−0.998754	−	0.0499024i	$-0.984109\pi$
$859$	−13.3695	+	23.1566i	−0.456160	+	0.790093i	0.542594	+	0.839995i	$0.317442\pi$
$860$	−1.17868	+	0.524911i	−0.0401927	+	0.0178993i
$861$	13.6810	+	51.8249i	0.466246	+	1.76619i
$862$	21.1052	−	4.48706i	0.718847	−	0.152830i
$863$		−	50.8477i		−	1.73088i	−0.501015	−	0.865438i	$-0.667040\pi$
$863$		−	50.8477i		−	1.73088i	0.501015	−	0.865438i	$-0.332960\pi$
$864$	−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
$868$	0.500396	−	33.2691i	0.0169845	−	1.12923i
$869$	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
$875$	1.11111	+	12.3691i	0.0375623	+	0.418152i
$876$	7.45359	−	15.0547i	0.251834	−	0.508652i
$877$	6.79088	−	11.7621i	0.229312	−	0.397179i	−0.728293	−	0.685266i	$-0.759686\pi$
$877$	6.79088	−	11.7621i	0.229312	−	0.397179i	0.957604	+	0.288087i	$0.0930192\pi$
$878$	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	$-0.0274828\pi$
$882$	−29.0942	+	5.96068i	−0.979651	+	0.200707i
$883$			36.5196i			1.22898i	0.788924	+	0.614491i	$0.210639\pi$
$883$			36.5196i			1.22898i	−0.788924	+	0.614491i	$0.789361\pi$
$884$	−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	−0.457417	−	0.889252i	$-0.651225\pi$
$887$	16.1245	−	27.9284i	0.541407	−	0.937744i	0.998824	−	0.0484917i	$-0.0154415\pi$
$888$	5.69529	−	22.2828i	0.191122	−	0.747761i
$889$	0.345239	+	3.84328i	0.0115789	+	0.128899i
$890$	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
$896$	29.9300	+	0.443341i	0.999890	+	0.0148110i
$897$	−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
$903$	−5.93737	−	1.61450i	−0.197583	−	0.0537273i
$904$	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	−0.846813	−	0.531891i	$-0.821482\pi$
$907$	−24.3819	+	14.0769i	−0.809588	+	0.467416i	0.0372246	+	0.999307i	$0.488148\pi$
$908$	31.3153	+	22.7475i	1.03924	+	0.754904i
$909$	5.15856	+	14.7227i	0.171099	+	0.488320i
$910$	7.74855	−	8.34885i	0.256862	−	0.276762i
$911$	−33.2831	+	19.2160i	−1.10272	+	0.636655i	−0.936934	−	0.349507i	$-0.886349\pi$
$911$	−33.2831	+	19.2160i	−1.10272	+	0.636655i	−0.165785	+	0.986162i	$0.553016\pi$
$912$	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	$-0.907676\pi$
$919$		−	17.3398i		−	0.571988i	0.958231	−	0.285994i	$-0.0923238\pi$
$920$	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
$924$	−24.1920	+	3.74211i	−0.795857	+	0.123106i
$925$	−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	−0.609153	+	0.793053i	$0.708490\pi$
$929$	−48.7835	+	28.1651i	−1.60053	+	0.924068i	−0.991380	+	0.131016i	$0.958176\pi$
$930$	−1.07377	+	7.32227i	−0.0352102	+	0.240107i
$931$	28.9448	−	5.24248i	0.948628	−	0.171815i
$932$	−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	$-0.200944\pi$
$938$	1.81870	−	7.96365i	0.0593827	−	0.260022i
$939$	−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	$-0.406450\pi$
$941$	−12.0974	−	6.98446i	−0.394365	−	0.227687i	−0.684050	+	0.729435i	$0.739783\pi$
$942$	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
$945$	6.58867	−	0.471979i	0.214330	−	0.0153535i
$946$	−4.82357	−	1.56703i	−0.156828	−	0.0509485i
$947$	−11.0539	+	6.38196i	−0.359203	+	0.207386i	−0.668731	−	0.743505i	$-0.733162\pi$
$947$	−11.0539	+	6.38196i	−0.359203	+	0.207386i	0.309528	+	0.950890i	$0.399829\pi$
$948$	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
$952$	13.3567	−	11.6686i	0.432894	−	0.378182i
$953$	−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
$959$	13.5776	+	19.2953i	0.438444	+	0.623078i
$960$	−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
$966$	27.7436	−	14.0085i	0.892636	−	0.450716i
$967$	−20.2799	−	11.7086i	−0.652158	−	0.376524i	0.137125	−	0.990554i	$-0.456214\pi$
$967$	−20.2799	−	11.7086i	−0.652158	−	0.376524i	−0.789283	+	0.614030i	$0.789547\pi$
$968$	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	$-0.632062\pi$
$971$	−25.1209			−0.806167			−0.403084	+	0.915163i	$0.632062\pi$
$972$	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	−0.884847	−	0.465882i	$-0.845737\pi$
$977$	−1.21770	+	2.10911i	−0.0389575	+	0.0674764i	0.845889	+	0.533359i	$0.179070\pi$
$978$	38.3678	+	30.3474i	1.22687	+	0.970403i
$979$	3.56823	+	6.18036i	0.114041	+	0.197525i
$980$	−6.70809	+	0.501010i	−0.214282	+	0.0160042i
$981$	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	$-0.265752\pi$
$983$	−9.60279	−	16.6325i	−0.306281	−	0.530495i	−0.977546	+	0.210723i	$0.932418\pi$
$984$	−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
$987$	8.96722	−	32.9772i	0.285430	−	1.04968i
$988$	−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	$-0.845067\pi$
$991$		−	29.4493i		−	0.935489i	0.883864	−	0.467745i	$-0.154933\pi$
$992$	30.8007	−	17.7921i	0.977922	−	0.564901i
$993$	−58.6479	−	21.7472i	−1.86113	−	0.690125i
$994$	0.710667	−	0.219114i	0.0225410	−	0.00694988i
$995$	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	$-0.745420\pi$
$997$	−13.3933	+	7.73264i	−0.424171	+	0.244895i	0.272689	+	0.962102i	$0.412087\pi$
$998$	−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.139.24	yes	80
3.2	odd	2		756.2.bi.c.307.17		80
4.3	odd	2	inner	252.2.bi.c.139.33	yes	80
7.6	odd	2	inner	252.2.bi.c.139.23	✓	80
9.2	odd	6		756.2.bi.c.559.8		80
9.7	even	3	inner	252.2.bi.c.223.34	yes	80
12.11	even	2		756.2.bi.c.307.7		80
21.20	even	2		756.2.bi.c.307.18		80
28.27	even	2	inner	252.2.bi.c.139.34	yes	80
36.7	odd	6	inner	252.2.bi.c.223.23	yes	80
36.11	even	6		756.2.bi.c.559.18		80
63.20	even	6		756.2.bi.c.559.7		80
63.34	odd	6	inner	252.2.bi.c.223.33	yes	80
84.83	odd	2		756.2.bi.c.307.8		80
252.83	odd	6		756.2.bi.c.559.17		80
252.223	even	6	inner	252.2.bi.c.223.24	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.23	✓	80	7.6	odd	2	inner
252.2.bi.c.139.24	yes	80	1.1	even	1	trivial
252.2.bi.c.139.33	yes	80	4.3	odd	2	inner
252.2.bi.c.139.34	yes	80	28.27	even	2	inner
252.2.bi.c.223.23	yes	80	36.7	odd	6	inner
252.2.bi.c.223.24	yes	80	252.223	even	6	inner
252.2.bi.c.223.33	yes	80	63.34	odd	6	inner
252.2.bi.c.223.34	yes	80	9.7	even	3	inner
756.2.bi.c.307.7		80	12.11	even	2
756.2.bi.c.307.8		80	84.83	odd	2
756.2.bi.c.307.17		80	3.2	odd	2
756.2.bi.c.307.18		80	21.20	even	2
756.2.bi.c.559.7		80	63.20	even	6
756.2.bi.c.559.8		80	9.2	odd	6
756.2.bi.c.559.17		80	252.83	odd	6
756.2.bi.c.559.18		80	36.11	even	6

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} +(-2.63514 + 0.236713i) 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} +(-1.10242 - 3.57556i) 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} +(-3.22835 - 3.25235i) 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} +(4.62185 - 2.57653i) 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} +(3.54952 - 5.42226i) 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} +(6.88793 - 1.24754i) 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} +(4.92337 + 5.63564i) 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} +(0.768666 - 7.89995i) 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} +(0.400269 - 1.75268i) 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} +(5.77925 - 4.06671i) 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} +(8.54449 + 3.31538i) 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} +(3.75143 + 9.16116i) 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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