LMFDB - Embedded newform 380.2.n.b.31.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(31,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.n (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.03431527681$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.4
Character	$\chi$	$=$	380.31
Dual form			380.2.n.b.331.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18980 - 0.764449i) q^{2} +(-1.38246 - 2.39450i) q^{3} +(0.831236 + 1.81908i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.185619 + 3.90579i) q^{6} -2.18272i q^{7} +(0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +O(q^{10})$	\(q+(-1.18980 - 0.764449i) q^{2} +(-1.38246 - 2.39450i) q^{3} +(0.831236 + 1.81908i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.185619 + 3.90579i) q^{6} -2.18272i q^{7} +(0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +(-0.0671334 + 1.41262i) q^{10} -2.17298i q^{11} +(3.20663 - 4.50520i) q^{12} +(-4.38226 - 2.53010i) q^{13} +(-1.66858 + 2.59700i) q^{14} +(-1.38246 + 2.39450i) q^{15} +(-2.61809 + 3.02417i) q^{16} +(1.50270 + 2.60275i) q^{17} +(5.83823 - 3.01064i) q^{18} +(-3.96739 - 1.80549i) q^{19} +(1.15975 - 1.62941i) q^{20} +(-5.22653 + 3.01754i) q^{21} +(-1.66113 + 2.58541i) q^{22} +(4.62252 + 2.66881i) q^{23} +(-7.25923 + 2.90898i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.27987 + 6.36032i) q^{26} +4.54783 q^{27} +(3.97055 - 1.81436i) q^{28} +(7.07391 + 4.08413i) q^{29} +(3.47532 - 1.79214i) q^{30} -1.63029 q^{31} +(5.42682 - 1.59675i) q^{32} +(-5.20320 + 3.00407i) q^{33} +(0.201763 - 4.24549i) q^{34} +(-1.89029 + 1.09136i) q^{35} +(-9.24779 - 0.880974i) q^{36} +1.65367i q^{37} +(3.34018 + 5.18104i) q^{38} +13.9911i q^{39} +(-2.62547 + 1.05210i) q^{40} +(3.52888 - 2.03740i) q^{41} +(8.52526 + 0.405155i) q^{42} +(-10.2968 + 5.94484i) q^{43} +(3.95282 - 1.80626i) q^{44} +4.64483 q^{45} +(-3.45969 - 6.70902i) q^{46} +(0.310910 + 0.179504i) q^{47} +(10.8608 + 2.08822i) q^{48} +2.23572 q^{49} +(1.25693 - 0.648170i) q^{50} +(4.15486 - 7.19643i) q^{51} +(0.959756 - 10.0748i) q^{52} +(-9.75968 - 5.63476i) q^{53} +(-5.41099 - 3.47658i) q^{54} +(-1.88186 + 1.08649i) q^{55} +(-6.11113 - 0.876560i) q^{56} +(1.16153 + 11.9959i) q^{57} +(-5.29442 - 10.2669i) q^{58} +(-2.15002 - 3.72394i) q^{59} +(-5.50493 - 0.524418i) q^{60} +(-4.18333 + 7.24574i) q^{61} +(1.93971 + 1.24627i) q^{62} +(8.78009 + 5.06919i) q^{63} +(-7.67745 - 2.24872i) q^{64} +5.06020i q^{65} +(8.48721 + 0.403346i) q^{66} +(4.10768 - 7.11471i) q^{67} +(-3.48552 + 4.89704i) q^{68} -14.7581i q^{69} +(3.08336 + 0.146534i) q^{70} +(-3.24775 - 5.62526i) q^{71} +(10.3295 + 8.11764i) q^{72} +(-2.49186 - 4.31602i) q^{73} +(1.26415 - 1.96754i) q^{74} +2.76493 q^{75} +(-0.0135042 - 8.71779i) q^{76} -4.74302 q^{77} +(10.6955 - 16.6466i) q^{78} +(-3.74126 - 6.48006i) q^{79} +(3.92805 + 0.755252i) q^{80} +(0.680033 + 1.17785i) q^{81} +(-5.75614 - 0.273555i) q^{82} -0.827326i q^{83} +(-9.83361 - 6.99918i) q^{84} +(1.50270 - 2.60275i) q^{85} +(16.7956 + 0.798194i) q^{86} -22.5846i q^{87} +(-6.08385 - 0.872647i) q^{88} +(-14.4063 - 8.31749i) q^{89} +(-5.52640 - 3.55073i) q^{90} +(-5.52251 + 9.56526i) q^{91} +(-1.01238 + 10.6271i) q^{92} +(2.25382 + 3.90372i) q^{93} +(-0.232698 - 0.451248i) q^{94} +(0.420092 + 4.33861i) q^{95} +(-11.3258 - 10.7871i) q^{96} +(12.9391 - 7.47039i) q^{97} +(-2.66005 - 1.70909i) q^{98} +(8.74090 + 5.04656i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	$ 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) $ 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/380\mathbb{Z}\right)^\times$.

$n$	$21$	$77$	$191$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.18980	−	0.764449i	−0.841314	−	0.540547i
$2$	−1.18980	−	0.764449i	−0.841314	−	0.540547i
$3$	−1.38246	−	2.39450i	−0.798166	−	1.38246i	−0.920809	−	0.390013i	$-0.872470\pi$
$3$	−1.38246	−	2.39450i	−0.798166	−	1.38246i	0.122643	−	0.992451i	$-0.460863\pi$
$4$	0.831236	+	1.81908i	0.415618	+	0.909539i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.185619	+	3.90579i	−0.0757786	+	1.59453i
$7$		−	2.18272i		−	0.824992i	−0.910959	−	0.412496i	$-0.864657\pi$
$7$		−	2.18272i		−	0.824992i	0.910959	−	0.412496i	$-0.135343\pi$
$8$	0.401590	−	2.79977i	0.141983	−	0.989869i
$9$	−2.32241	+	4.02254i	−0.774138	+	1.34085i
$10$	−0.0671334	+	1.41262i	−0.0212294	+	0.446709i
$11$		−	2.17298i		−	0.655178i	−0.944820	−	0.327589i	$-0.893764\pi$
$11$		−	2.17298i		−	0.655178i	0.944820	−	0.327589i	$-0.106236\pi$
$12$	3.20663	−	4.50520i	0.925673	−	1.30054i
$13$	−4.38226	−	2.53010i	−1.21542	−	0.701723i	−0.251485	−	0.967861i	$-0.580919\pi$
$13$	−4.38226	−	2.53010i	−1.21542	−	0.701723i	−0.963935	+	0.266138i	$0.914252\pi$
$14$	−1.66858	+	2.59700i	−0.445947	+	0.694077i
$15$	−1.38246	+	2.39450i	−0.356951	+	0.618257i
$16$	−2.61809	+	3.02417i	−0.654523	+	0.756042i
$17$	1.50270	+	2.60275i	0.364459	+	0.631261i	0.988689	−	0.149979i	$-0.0479207\pi$
$17$	1.50270	+	2.60275i	0.364459	+	0.631261i	−0.624231	+	0.781240i	$0.714587\pi$
$18$	5.83823	−	3.01064i	1.37608	−	0.709614i
$19$	−3.96739	−	1.80549i	−0.910182	−	0.414209i
$19$	−3.96739	−	1.80549i	−0.910182	−	0.414209i
$20$	1.15975	−	1.62941i	0.259328	−	0.364347i
$21$	−5.22653	+	3.01754i	−1.14052	+	0.658481i
$22$	−1.66113	+	2.58541i	−0.354155	+	0.551211i
$23$	4.62252	+	2.66881i	0.963862	+	0.556486i	0.897359	−	0.441301i	$-0.145483\pi$
$23$	4.62252	+	2.66881i	0.963862	+	0.556486i	0.0665022	+	0.997786i	$0.478816\pi$
$24$	−7.25923	+	2.90898i	−1.48178	+	0.593793i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	3.27987	+	6.36032i	0.643236	+	1.24736i
$27$	4.54783			0.875230
$28$	3.97055	−	1.81436i	0.750363	−	0.342882i
$29$	7.07391	+	4.08413i	1.31359	+	0.758403i	0.982689	−	0.185261i	$-0.0593132\pi$
$29$	7.07391	+	4.08413i	1.31359	+	0.758403i	0.330904	+	0.943665i	$0.392647\pi$
$30$	3.47532	−	1.79214i	0.634504	−	0.327199i
$31$	−1.63029			−0.292808			−0.146404	−	0.989225i	$-0.546770\pi$
$31$	−1.63029			−0.292808			−0.146404	+	0.989225i	$0.546770\pi$
$32$	5.42682	−	1.59675i	0.959336	−	0.282268i
$33$	−5.20320	+	3.00407i	−0.905760	+	0.522941i
$34$	0.201763	−	4.24549i	0.0346020	−	0.728095i
$35$	−1.89029	+	1.09136i	−0.319518	+	0.184474i
$36$	−9.24779	−	0.880974i	−1.54130	−	0.146829i
$37$			1.65367i			0.271862i	0.990718	+	0.135931i	$0.0434026\pi$
$37$			1.65367i			0.271862i	−0.990718	+	0.135931i	$0.956597\pi$
$38$	3.34018	+	5.18104i	0.541850	+	0.840476i
$39$			13.9911i			2.24037i
$40$	−2.62547	+	1.05210i	−0.415123	+	0.166351i
$41$	3.52888	−	2.03740i	0.551119	−	0.318189i	−0.198454	−	0.980110i	$-0.563592\pi$
$41$	3.52888	−	2.03740i	0.551119	−	0.318189i	0.749573	+	0.661922i	$0.230259\pi$
$42$	8.52526	+	0.405155i	1.31548	+	0.0625167i
$43$	−10.2968	+	5.94484i	−1.57024	+	0.906580i	−0.574104	+	0.818783i	$0.694649\pi$
$43$	−10.2968	+	5.94484i	−1.57024	+	0.906580i	−0.996138	+	0.0877972i	$0.972017\pi$
$44$	3.95282	−	1.80626i	0.595910	−	0.272304i
$45$	4.64483			0.692410
$46$	−3.45969	−	6.70902i	−0.510103	−	0.989192i
$47$	0.310910	+	0.179504i	0.0453509	+	0.0261833i	0.522504	−	0.852637i	$-0.324998\pi$
$47$	0.310910	+	0.179504i	0.0453509	+	0.0261833i	−0.477153	+	0.878820i	$0.658331\pi$
$48$	10.8608	+	2.08822i	1.56762	+	0.301408i
$49$	2.23572			0.319388
$50$	1.25693	−	0.648170i	0.177757	−	0.0916651i
$51$	4.15486	−	7.19643i	0.581797	−	1.00770i
$52$	0.959756	−	10.0748i	0.133094	−	1.39712i
$53$	−9.75968	−	5.63476i	−1.34060	−	0.773993i	−0.353701	−	0.935359i	$-0.615077\pi$
$53$	−9.75968	−	5.63476i	−1.34060	−	0.773993i	−0.986895	+	0.161365i	$0.948410\pi$
$54$	−5.41099	−	3.47658i	−0.736343	−	0.473103i
$55$	−1.88186	+	1.08649i	−0.253749	+	0.146502i
$56$	−6.11113	−	0.876560i	−0.816634	−	0.117135i
$57$	1.16153	+	11.9959i	0.153848	+	1.58890i
$58$	−5.29442	−	10.2669i	−0.695191	−	1.34811i
$59$	−2.15002	−	3.72394i	−0.279908	−	0.484816i	0.691453	−	0.722421i	$-0.256971\pi$
$59$	−2.15002	−	3.72394i	−0.279908	−	0.484816i	−0.971362	+	0.237606i	$0.923637\pi$
$60$	−5.50493	−	0.524418i	−0.710684	−	0.0677020i
$61$	−4.18333	+	7.24574i	−0.535621	+	0.927722i	0.463512	+	0.886091i	$0.346589\pi$
$61$	−4.18333	+	7.24574i	−0.535621	+	0.927722i	−0.999133	+	0.0416319i	$0.986744\pi$
$62$	1.93971	+	1.24627i	0.246344	+	0.158277i
$63$	8.78009	+	5.06919i	1.10619	+	0.638657i
$64$	−7.67745	−	2.24872i	−0.959681	−	0.281090i
$65$			5.06020i			0.627640i
$66$	8.48721	+	0.403346i	1.04470	+	0.0496485i
$67$	4.10768	−	7.11471i	0.501833	−	0.869200i	−0.498165	−	0.867082i	$-0.665993\pi$
$67$	4.10768	−	7.11471i	0.501833	−	0.869200i	0.999998	−	0.00211743i	$-0.000673998\pi$
$68$	−3.48552	+	4.89704i	−0.422681	+	0.593853i
$69$		−	14.7581i		−	1.77667i
$70$	3.08336	+	0.146534i	0.368532	+	0.0175141i
$71$	−3.24775	−	5.62526i	−0.385437	−	0.667596i	0.606393	−	0.795165i	$-0.292616\pi$
$71$	−3.24775	−	5.62526i	−0.385437	−	0.667596i	−0.991830	+	0.127569i	$0.959283\pi$
$72$	10.3295	+	8.11764i	1.21735	+	0.956673i
$73$	−2.49186	−	4.31602i	−0.291650	−	0.505152i	0.682550	−	0.730839i	$-0.260871\pi$
$73$	−2.49186	−	4.31602i	−0.291650	−	0.505152i	−0.974200	+	0.225686i	$0.927538\pi$
$74$	1.26415	−	1.96754i	0.146954	−	0.228721i
$75$	2.76493			0.319266
$76$	−0.0135042	−	8.71779i	−0.00154903	−	0.999999i
$77$	−4.74302			−0.540517
$78$	10.6955	−	16.6466i	1.21102	−	1.88485i
$79$	−3.74126	−	6.48006i	−0.420925	−	0.729063i	0.575105	−	0.818079i	$-0.304961\pi$
$79$	−3.74126	−	6.48006i	−0.420925	−	0.729063i	−0.996030	+	0.0890162i	$0.971628\pi$
$80$	3.92805	+	0.755252i	0.439170	+	0.0844397i
$81$	0.680033	+	1.17785i	0.0755592	+	0.130872i
$82$	−5.75614	−	0.273555i	−0.635660	−	0.0302091i
$83$		−	0.827326i		−	0.0908108i	−0.998969	−	0.0454054i	$-0.985542\pi$
$83$		−	0.827326i		−	0.0908108i	0.998969	−	0.0454054i	$-0.0144580\pi$
$84$	−9.83361	−	6.99918i	−1.07294	−	0.763673i
$85$	1.50270	−	2.60275i	0.162991	−	0.282308i
$86$	16.7956	+	0.798194i	1.81112	+	0.0860715i
$87$		−	22.5846i		−	2.42133i
$88$	−6.08385	−	0.872647i	−0.648541	−	0.0930245i
$89$	−14.4063	−	8.31749i	−1.52707	−	0.881652i	−0.999483	−	0.0321483i	$-0.989765\pi$
$89$	−14.4063	−	8.31749i	−1.52707	−	0.881652i	−0.527583	−	0.849504i	$-0.676902\pi$
$90$	−5.52640	−	3.55073i	−0.582534	−	0.374280i
$91$	−5.52251	+	9.56526i	−0.578916	+	1.00271i
$92$	−1.01238	+	10.6271i	−0.105547	+	1.10796i
$93$	2.25382	+	3.90372i	0.233710	+	0.404797i
$94$	−0.232698	−	0.451248i	−0.0240010	−	0.0465427i
$95$	0.420092	+	4.33861i	0.0431006	+	0.445132i
$96$	−11.3258	−	10.7871i	−1.15593	−	1.10095i
$97$	12.9391	−	7.47039i	1.31377	−	0.758503i	0.331048	−	0.943614i	$-0.392598\pi$
$97$	12.9391	−	7.47039i	1.31377	−	0.758503i	0.982718	+	0.185111i	$0.0592643\pi$
$98$	−2.66005	−	1.70909i	−0.268706	−	0.172644i
$99$	8.74090	+	5.04656i	0.878493	+	0.507198i
$100$	−1.99099	−	0.189668i	−0.199099	−	0.0189668i
$101$	2.26854	−	3.92923i	0.225728	−	0.390973i	−0.730809	−	0.682581i	$-0.760857\pi$
$101$	2.26854	−	3.92923i	0.225728	−	0.390973i	0.956538	+	0.291609i	$0.0941906\pi$
$102$	−10.4447	+	5.38612i	−1.03418	+	0.533305i
$103$	−17.9724			−1.77088			−0.885438	−	0.464757i	$-0.846142\pi$
$103$	−17.9724			−1.77088			−0.885438	+	0.464757i	$0.846142\pi$
$104$	−8.84357	+	11.2533i	−0.867184	+	1.10347i
$105$	5.22653	+	3.01754i	0.510057	+	0.294481i
$106$	7.30456	+	14.1650i	0.709482	+	1.37583i
$107$	13.8396			1.33792			0.668961	−	0.743297i	$-0.266739\pi$
$107$	13.8396			1.33792			0.668961	+	0.743297i	$0.266739\pi$
$108$	3.78032	+	8.27285i	0.363761	+	0.796056i
$109$	6.20653	−	3.58334i	0.594478	−	0.343222i	−0.172388	−	0.985029i	$-0.555148\pi$
$109$	6.20653	−	3.58334i	0.594478	−	0.343222i	0.766866	+	0.641807i	$0.221815\pi$
$110$	3.06959	+	0.145880i	0.292674	+	0.0139091i
$111$	3.95971	−	2.28614i	0.375840	−	0.216991i
$112$	6.60092	+	5.71457i	0.623728	+	0.539977i
$113$		−	3.59380i		−	0.338076i	−0.985610	−	0.169038i	$-0.945934\pi$
$113$		−	3.59380i		−	0.338076i	0.985610	−	0.169038i	$-0.0540661\pi$
$114$	7.78830	−	15.1607i	0.729441	−	1.41993i
$115$		−	5.33762i		−	0.497736i
$116$	−1.54925	+	16.2629i	−0.143845	+	1.50997i
$117$	20.3548	−	11.7519i	1.88181	−	1.08646i
$118$	−0.288676	+	6.07431i	−0.0265748	+	0.559186i
$119$	5.68109	−	3.27998i	0.520785	−	0.300675i
$120$	6.14887	+	4.83219i	0.561312	+	0.441117i
$121$	6.27815			0.570741
$122$	10.5163	−	5.42302i	0.952103	−	0.490978i
$123$	−9.75710	−	5.63327i	−0.879769	−	0.507935i
$124$	−1.35515	−	2.96562i	−0.121696	−	0.266321i
$125$	1.00000			0.0894427
$126$	−6.57139	−	12.7432i	−0.585426	−	1.13526i
$127$	−7.38413	+	12.7897i	−0.655236	+	1.13490i	0.326599	+	0.945163i	$0.394097\pi$
$127$	−7.38413	+	12.7897i	−0.655236	+	1.13490i	−0.981835	+	0.189739i	$0.939236\pi$
$128$	7.41558	+	8.54454i	0.655451	+	0.755238i
$129$	28.4698	+	16.4371i	2.50663	+	1.44720i
$130$	3.86826	−	6.02061i	0.339269	−	0.528042i
$131$	3.92080	−	2.26367i	0.342561	−	0.197778i	−0.318843	−	0.947808i	$-0.603294\pi$
$131$	3.92080	−	2.26367i	0.342561	−	0.197778i	0.661404	+	0.750030i	$0.269961\pi$
$132$	−9.78972	−	6.96794i	−0.852086	−	0.606481i
$133$	−3.94089	+	8.65972i	−0.341719	+	0.750893i
$134$	−10.3261	+	5.32495i	−0.892042	+	0.460006i
$135$	−2.27391	−	3.93853i	−0.195707	−	0.338975i
$136$	7.89059	−	3.16198i	0.676613	−	0.271138i
$137$	−2.88771	+	5.00166i	−0.246714	+	0.427320i	−0.962612	−	0.270884i	$-0.912684\pi$
$137$	−2.88771	+	5.00166i	−0.246714	+	0.427320i	0.715898	+	0.698204i	$0.246017\pi$
$138$	−11.2818	+	17.5592i	−0.960375	+	1.49474i
$139$	7.50843	+	4.33499i	0.636857	+	0.367689i	0.783403	−	0.621514i	$-0.213482\pi$
$139$	7.50843	+	4.33499i	0.636857	+	0.367689i	−0.146546	+	0.989204i	$0.546816\pi$
$140$	−3.55655	−	2.53141i	−0.300584	−	0.213944i
$141$		−	0.992631i		−	0.0835946i
$142$	−0.436064	+	9.17566i	−0.0365937	+	0.770004i
$143$	−5.49786	+	9.52257i	−0.459754	+	0.796317i
$144$	−6.08453	−	17.5547i	−0.507044	−	1.46290i
$145$		−	8.16825i		−	0.678336i
$146$	−0.334574	+	7.04009i	−0.0276895	+	0.582642i
$147$	−3.09080	−	5.35342i	−0.254925	−	0.441543i
$148$	−3.00816	+	1.37459i	−0.247269	+	0.112991i
$149$	−10.3988	−	18.0113i	−0.851907	−	1.47555i	−0.879485	−	0.475926i	$-0.842113\pi$
$149$	−10.3988	−	18.0113i	−0.851907	−	1.47555i	0.0275781	−	0.999620i	$-0.491221\pi$
$150$	−3.28970	−	2.11365i	−0.268603	−	0.172578i
$151$	−13.8156			−1.12430			−0.562151	−	0.827035i	$-0.690026\pi$
$151$	−13.8156			−1.12430			−0.562151	+	0.827035i	$0.690026\pi$
$152$	−6.64824	+	10.3827i	−0.539243	+	0.842150i
$153$	−13.9596			−1.12856
$154$	5.64323	+	3.62579i	0.454744	+	0.292175i
$155$	0.815144	+	1.41187i	0.0654740	+	0.113404i
$156$	−25.4509	+	11.6299i	−2.03770	+	0.931137i
$157$	−10.7080	−	18.5468i	−0.854589	−	1.48019i	−0.877026	−	0.480444i	$-0.840476\pi$
$157$	−10.7080	−	18.5468i	−0.854589	−	1.48019i	0.0224363	−	0.999748i	$-0.492858\pi$
$158$	−0.502327	+	10.5700i	−0.0399630	+	0.840901i
$159$			31.1594i			2.47110i
$160$	−4.09624	−	3.90139i	−0.323836	−	0.308432i
$161$	5.82528	−	10.0897i	0.459096	−	0.795178i
$162$	0.0913058	−	1.92126i	0.00717366	−	0.150948i
$163$		−	13.9029i		−	1.08896i	−0.838773	−	0.544481i	$-0.816727\pi$
$163$		−	13.9029i		−	1.08896i	0.838773	−	0.544481i	$-0.183273\pi$
$164$	6.63953	+	4.72575i	0.518460	+	0.369019i
$165$	5.20320	+	3.00407i	0.405068	+	0.233866i
$166$	−0.632448	+	0.984350i	−0.0490875	+	0.0764004i
$167$	−3.32755	+	5.76348i	−0.257494	+	0.445992i	−0.965570	−	0.260144i	$-0.916230\pi$
$167$	−3.32755	+	5.76348i	−0.257494	+	0.445992i	0.708076	+	0.706136i	$0.249563\pi$
$168$	6.34950	+	15.8449i	0.489874	+	1.22246i
$169$	6.30280	+	10.9168i	0.484831	+	0.839752i
$170$	−3.77758	+	1.94801i	−0.289727	+	0.149406i
$171$	16.4766	−	11.7659i	1.26000	−	0.899759i
$172$	−19.3732	−	13.7891i	−1.47719	−	1.05141i
$173$	−10.7277	+	6.19363i	−0.815611	+	0.470893i	−0.848901	−	0.528553i	$-0.822735\pi$
$173$	−10.7277	+	6.19363i	−0.815611	+	0.470893i	0.0332896	+	0.999446i	$0.489402\pi$
$174$	−17.2648	+	26.8711i	−1.30884	+	2.03710i
$175$	1.89029	+	1.09136i	0.142893	+	0.0824992i
$176$	6.57146	+	5.68907i	0.495342	+	0.428830i
$177$	−5.94464	+	10.2964i	−0.446827	+	0.773926i
$178$	10.7823	+	20.9090i	0.808167	+	1.56720i
$179$	8.20196			0.613043			0.306522	−	0.951864i	$-0.400835\pi$
$179$	8.20196			0.613043			0.306522	+	0.951864i	$0.400835\pi$
$180$	3.86095	+	8.44930i	0.287778	+	0.629774i
$181$	−4.15238	−	2.39738i	−0.308644	−	0.178196i	0.337676	−	0.941263i	$-0.390359\pi$
$181$	−4.15238	−	2.39738i	−0.308644	−	0.178196i	−0.646320	+	0.763067i	$0.723693\pi$
$182$	13.8828	−	7.15905i	1.02906	−	0.530664i
$183$	23.1332			1.71006
$184$	9.32842	−	11.8702i	0.687700	−	0.875085i
$185$	1.43212	−	0.826836i	0.105292	−	0.0607902i
$186$	0.302612	−	6.36757i	0.0221886	−	0.466893i
$187$	5.65574	−	3.26534i	0.413588	−	0.238785i
$188$	−0.0680922	+	0.714780i	−0.00496614	+	0.0521307i
$189$		−	9.92665i		−	0.722057i
$190$	2.81682	−	5.48320i	0.204354	−	0.397793i
$191$			2.08371i			0.150772i	0.997154	+	0.0753861i	$0.0240189\pi$
$191$			2.08371i			0.150772i	−0.997154	+	0.0753861i	$0.975981\pi$
$192$	5.22924	+	21.4924i	0.377388	+	1.55108i
$193$	14.5234	−	8.38512i	1.04542	−	0.603574i	0.124057	−	0.992275i	$-0.460410\pi$
$193$	14.5234	−	8.38512i	1.04542	−	0.603574i	0.921364	+	0.388701i	$0.127076\pi$
$194$	−21.1056	−	1.00302i	−1.51530	−	0.0720130i
$195$	12.1166	−	6.99554i	0.867690	−	0.500961i
$196$	1.85841	+	4.06695i	0.132743	+	0.290496i
$197$	2.20542			0.157130			0.0785648	−	0.996909i	$-0.474966\pi$
$197$	2.20542			0.157130			0.0785648	+	0.996909i	$0.474966\pi$
$198$	−6.54206	−	12.6864i	−0.464924	−	0.901580i
$199$	−20.3102	−	11.7261i	−1.43975	−	0.831243i	−0.441923	−	0.897053i	$-0.645703\pi$
$199$	−20.3102	−	11.7261i	−1.43975	−	0.831243i	−0.997832	+	0.0658103i	$0.979037\pi$
$200$	2.22388	+	1.74767i	0.157252	+	0.123579i
$201$	−22.7149			−1.60218
$202$	−5.70280	+	2.94080i	−0.401247	+	0.206914i
$203$	8.91452	−	15.4404i	0.625677	−	1.08370i
$204$	16.5445	+	1.57609i	1.15835	+	0.110348i
$205$	−3.52888	−	2.03740i	−0.246468	−	0.142298i
$206$	21.3836	+	13.7390i	1.48986	+	0.957242i
$207$	−21.4708	+	12.3962i	−1.49232	+	0.861593i
$208$	19.1246	−	6.62865i	1.32605	−	0.459614i
$209$	−3.92330	+	8.62106i	−0.271381	+	0.596332i
$210$	−3.91176	−	7.58567i	−0.269937	−	0.523461i
$211$	13.5923	+	23.5425i	0.935730	+	1.62073i	0.773326	+	0.634008i	$0.218591\pi$
$211$	13.5923	+	23.5425i	0.935730	+	1.62073i	0.162404	+	0.986724i	$0.448075\pi$
$212$	2.13746	−	22.4374i	0.146802	−	1.54101i
$213$	−8.97979	+	15.5534i	−0.615285	+	1.06570i
$214$	−16.4663	−	10.5796i	−1.12561	−	0.723210i
$215$	10.2968	+	5.94484i	0.702234	+	0.405435i
$216$	1.82636	−	12.7329i	0.124268	−	0.866363i
$217$			3.55847i			0.241565i
$218$	−10.1238	−	0.481124i	−0.685670	−	0.0325858i
$219$	−6.88981	+	11.9335i	−0.465570	+	0.806391i
$220$	−3.54068	−	2.52011i	−0.238712	−	0.169906i
$221$		−	15.2079i		−	1.02300i
$222$	−6.45890	−	0.306953i	−0.433493	−	0.0206013i
$223$	5.83141	+	10.1003i	0.390500	+	0.676365i	0.992515	−	0.122119i	$-0.0389689\pi$
$223$	5.83141	+	10.1003i	0.390500	+	0.676365i	−0.602016	+	0.798484i	$0.705636\pi$
$224$	−3.48526	−	11.8453i	−0.232869	−	0.791444i
$225$	−2.32241	−	4.02254i	−0.154828	−	0.268169i
$226$	−2.74727	+	4.27589i	−0.182746	+	0.284428i
$227$	−18.2541			−1.21157			−0.605784	−	0.795629i	$-0.707141\pi$
$227$	−18.2541			−1.21157			−0.605784	+	0.795629i	$0.707141\pi$
$228$	−20.8561	+	12.0844i	−1.38123	+	0.800306i
$229$	12.6355			0.834974			0.417487	−	0.908683i	$-0.362911\pi$
$229$	12.6355			0.834974			0.417487	+	0.908683i	$0.362911\pi$
$230$	−4.08034	+	6.35069i	−0.269050	+	0.418752i
$231$	6.55705	+	11.3571i	0.431422	+	0.747245i
$232$	14.2754	−	18.1652i	0.937228	−	1.19260i
$233$	−5.05480	−	8.75517i	−0.331151	−	0.573571i	0.651587	−	0.758574i	$-0.274104\pi$
$233$	−5.05480	−	8.75517i	−0.331151	−	0.573571i	−0.982738	+	0.185004i	$0.940770\pi$
$234$	−33.2018	−	1.57789i	−2.17047	−	0.103150i
$235$		−	0.359008i		−	0.0234191i
$236$	4.98697	−	7.00652i	0.324624	−	0.456086i
$237$	−10.3443	+	17.9169i	−0.671936	+	1.16383i
$238$	−9.26673	−	0.440392i	−0.600673	−	0.0285464i
$239$			16.7508i			1.08352i	0.840533	+	0.541760i	$0.182242\pi$
$239$			16.7508i			1.08352i	−0.840533	+	0.541760i	$0.817758\pi$
$240$	−3.62194	−	10.4498i	−0.233795	−	0.674533i
$241$	−11.4567	−	6.61455i	−0.737993	−	0.426081i	0.0833459	−	0.996521i	$-0.473439\pi$
$241$	−11.4567	−	6.61455i	−0.737993	−	0.426081i	−0.821339	+	0.570440i	$0.806773\pi$
$242$	−7.46973	−	4.79933i	−0.480173	−	0.308512i
$243$	8.70198	−	15.0723i	0.558232	−	0.966887i
$244$	−16.6579	−	1.58689i	−1.06641	−	0.101590i
$245$	−1.11786	−	1.93619i	−0.0714174	−	0.123699i
$246$	7.30263	+	14.1613i	0.465599	+	0.902889i
$247$	12.8181	+	17.9500i	0.815594	+	1.14213i
$248$	−0.654708	+	4.56444i	−0.0415740	+	0.289842i
$249$	−1.98103	+	1.14375i	−0.125543	+	0.0724821i
$250$	−1.18980	−	0.764449i	−0.0752494	−	0.0483480i
$251$	1.63502	+	0.943979i	0.103201	+	0.0595834i	0.550712	−	0.834695i	$-0.314356\pi$
$251$	1.63502	+	0.943979i	0.103201	+	0.0595834i	−0.447511	+	0.894278i	$0.647689\pi$
$252$	−1.92292	+	20.1854i	−0.121133	+	1.27156i
$253$	5.79928	−	10.0446i	0.364597	−	0.631501i
$254$	18.5627	−	9.57236i	1.16473	−	0.600623i
$255$	−8.30972			−0.520375
$256$	−2.29117	−	15.8351i	−0.143198	−	0.989694i
$257$	9.93205	+	5.73427i	0.619544	+	0.357694i	0.776691	−	0.629881i	$-0.216896\pi$
$257$	9.93205	+	5.73427i	0.619544	+	0.357694i	−0.157147	+	0.987575i	$0.550230\pi$
$258$	−21.3080	−	41.3205i	−1.32658	−	2.57250i
$259$	3.60951			0.224284
$260$	−9.20490	+	4.20622i	−0.570864	+	0.260859i
$261$	−32.8571	+	18.9701i	−2.03380	+	1.17422i
$262$	−6.39541	−	0.303936i	−0.395110	−	0.0187772i
$263$	11.5681	−	6.67887i	0.713322	−	0.411837i	−0.0989677	−	0.995091i	$-0.531554\pi$
$263$	11.5681	−	6.67887i	0.713322	−	0.411837i	0.812290	+	0.583254i	$0.198221\pi$
$264$	6.32115	+	15.7742i	0.389040	+	0.970833i
$265$			11.2695i			0.692281i
$266$	11.3088	−	7.29070i	0.693386	−	0.447022i
$267$			45.9945i			2.81482i
$268$	16.3567	+	1.55819i	0.999142	+	0.0951815i
$269$	20.0598	−	11.5815i	1.22307	−	0.706138i	0.257496	−	0.966279i	$-0.417103\pi$
$269$	20.0598	−	11.5815i	1.22307	−	0.706138i	0.965570	+	0.260142i	$0.0837693\pi$
$270$	−0.305311	+	6.42435i	−0.0185806	+	0.390973i
$271$	18.2451	−	10.5338i	1.10831	−	0.639885i	0.169922	−	0.985458i	$-0.445649\pi$
$271$	18.2451	−	10.5338i	1.10831	−	0.639885i	0.938392	+	0.345572i	$0.112315\pi$
$272$	−11.8054	−	2.26984i	−0.715806	−	0.137629i
$273$	30.5387			1.84828
$274$	7.25930	−	3.74345i	0.438550	−	0.226150i
$275$	1.88186	+	1.08649i	0.113480	+	0.0655178i
$276$	26.8462	−	12.2675i	1.61595	−	0.738417i
$277$	−24.5511			−1.47513			−0.737566	−	0.675275i	$-0.764025\pi$
$277$	−24.5511			−1.47513			−0.737566	+	0.675275i	$0.764025\pi$
$278$	−5.61963	−	10.8976i	−0.337043	−	0.653593i
$279$	3.78620	−	6.55790i	0.226674	−	0.392611i
$280$	2.29644	+	5.73067i	0.137239	+	0.342473i
$281$	5.01344	+	2.89451i	0.299077	+	0.172672i	0.642028	−	0.766681i	$-0.278093\pi$
$281$	5.01344	+	2.89451i	0.299077	+	0.172672i	−0.342951	+	0.939353i	$0.611427\pi$
$282$	−0.758816	+	1.18103i	−0.0451868	+	0.0703293i
$283$	14.1273	−	8.15640i	0.839781	−	0.484848i	−0.0174087	−	0.999848i	$-0.505542\pi$
$283$	14.1273	−	8.15640i	0.839781	−	0.484848i	0.857190	+	0.515001i	$0.172208\pi$
$284$	7.53315	−	10.5838i	0.447010	−	0.628035i
$285$	9.80803	−	7.00388i	0.580977	−	0.414874i
$286$	13.8209	−	7.12710i	0.817244	−	0.421434i
$287$	−4.44708	−	7.70257i	−0.262503	−	0.454669i
$288$	−6.18034	+	25.5379i	−0.364180	+	1.50484i
$289$	3.98378	−	6.90011i	0.234340	−	0.405889i
$290$	−6.24421	+	9.71857i	−0.366673	+	0.570694i
$291$	−35.7757	−	20.6551i	−2.09721	−	1.21082i
$292$	5.77986	−	8.12052i	0.338241	−	0.475217i
$293$			9.21300i			0.538229i	0.963108	+	0.269115i	$0.0867311\pi$
$293$			9.21300i			0.538229i	−0.963108	+	0.269115i	$0.913269\pi$
$294$	−0.414991	+	8.73224i	−0.0242028	+	0.509275i
$295$	−2.15002	+	3.72394i	−0.125179	+	0.216816i
$296$	4.62991	+	0.664098i	0.269108	+	0.0385999i
$297$		−	9.88234i		−	0.573432i
$298$	−1.39622	+	29.3792i	−0.0808808	+	1.70189i
$299$	−13.5047	−	23.3909i	−0.780998	−	1.35273i
$300$	2.29831	+	5.02962i	0.132693	+	0.290385i
$301$	12.9759	+	22.4750i	0.747921	+	1.29544i
$302$	16.4378	+	10.5614i	0.945890	+	0.607738i
$303$	−12.5447			−0.720674
$304$	15.8471	−	7.27110i	0.908894	−	0.417026i
$305$	8.36666			0.479074
$306$	16.6091	+	10.6714i	0.949477	+	0.610042i
$307$	0.206707	+	0.358027i	0.0117974	+	0.0204337i	0.871864	−	0.489748i	$-0.162911\pi$
$307$	0.206707	+	0.358027i	0.0117974	+	0.0204337i	−0.860066	+	0.510182i	$0.829578\pi$
$308$	−3.94257	−	8.62792i	−0.224649	−	0.491621i
$309$	24.8462	+	43.0349i	1.41345	+	2.44817i
$310$	0.109447	−	2.30298i	0.00621616	−	0.130800i
$311$			4.30800i			0.244284i	0.992513	+	0.122142i	$0.0389764\pi$
$311$			4.30800i			0.244284i	−0.992513	+	0.122142i	$0.961024\pi$
$312$	39.1718	+	5.61868i	2.21767	+	0.318095i
$313$	11.4791	−	19.8824i	0.648838	−	1.12382i	−0.334563	−	0.942374i	$-0.608589\pi$
$313$	11.4791	−	19.8824i	0.648838	−	1.12382i	0.983401	−	0.181447i	$-0.0580781\pi$
$314$	−1.43772	+	30.2526i	−0.0811355	+	1.70725i
$315$		−	10.1384i		−	0.571233i
$316$	8.67786	−	12.1921i	0.488168	−	0.685859i
$317$	12.5590	+	7.25094i	0.705383	+	0.407253i	0.809349	−	0.587328i	$-0.199820\pi$
$317$	12.5590	+	7.25094i	0.705383	+	0.407253i	−0.103966	+	0.994581i	$0.533153\pi$
$318$	23.8198	−	37.0734i	1.33575	−	2.07897i
$319$	8.87473	−	15.3715i	0.496889	−	0.860638i
$320$	1.89128	+	7.77323i	0.105726	+	0.434537i
$321$	−19.1327	−	33.1388i	−1.06788	−	1.84963i
$322$	−14.6439	+	7.55155i	−0.816075	+	0.420831i
$323$	−1.26255	−	13.0393i	−0.0702500	−	0.725524i
$324$	−1.57734	+	2.21611i	−0.0876298	+	0.123117i
$325$	4.38226	−	2.53010i	0.243084	−	0.140345i
$326$	−10.6281	+	16.5417i	−0.588635	+	0.916159i
$327$	−17.1606	−	9.90769i	−0.948984	−	0.547896i
$328$	−4.28710	−	10.6983i	−0.236715	−	0.590713i
$329$	0.391808	−	0.678631i	0.0216011	−	0.0374141i
$330$	−3.89430	−	7.55181i	−0.214374	−	0.415713i
$331$	−11.0317			−0.606359			−0.303179	−	0.952934i	$-0.598048\pi$
$331$	−11.0317			−0.606359			−0.303179	+	0.952934i	$0.598048\pi$
$332$	1.50497	−	0.687703i	0.0825960	−	0.0377426i
$333$	−6.65196	−	3.84051i	−0.364525	−	0.210459i
$334$	8.36500	−	4.31364i	0.457712	−	0.236032i
$335$	−8.21535			−0.448853
$336$	4.55800	−	23.7061i	0.248659	−	1.29327i
$337$	−17.1575	+	9.90587i	−0.934627	+	0.539607i	−0.888272	−	0.459318i	$-0.848094\pi$
$337$	−17.1575	+	9.90587i	−0.934627	+	0.539607i	−0.0463550	+	0.998925i	$0.514761\pi$
$338$	0.846257	−	17.8069i	0.0460303	−	0.968569i
$339$	−8.60534	+	4.96830i	−0.467378	+	0.269841i
$340$	5.98372	+	0.570028i	0.324513	+	0.0309141i
$341$			3.54259i			0.191842i
$342$	−28.5982	+	1.40351i	−1.54641	+	0.0758929i
$343$		−	20.1590i		−	1.08848i
$344$	12.5091	+	31.2160i	0.674447	+	1.68305i
$345$	−12.7809	+	7.37907i	−0.688102	+	0.397276i
$346$	17.4985	+	0.831599i	0.940725	+	0.0447070i
$347$	17.6766	−	10.2056i	0.948932	−	0.547866i	0.0561829	−	0.998420i	$-0.482107\pi$
$347$	17.6766	−	10.2056i	0.948932	−	0.547866i	0.892749	+	0.450554i	$0.148774\pi$
$348$	41.0832	−	18.7732i	2.20229	−	1.00635i
$349$	−3.44772			−0.184552			−0.0922762	−	0.995733i	$-0.529414\pi$
$349$	−3.44772			−0.184552			−0.0922762	+	0.995733i	$0.529414\pi$
$350$	−1.41478	−	2.74353i	−0.0756230	−	0.146648i
$351$	−19.9298	−	11.5065i	−1.06377	−	0.614169i
$352$	−3.46970	−	11.7924i	−0.184936	−	0.628536i
$353$	−31.8847			−1.69705			−0.848526	−	0.529154i	$-0.822509\pi$
$353$	−31.8847			−1.69705			−0.848526	+	0.529154i	$0.822509\pi$
$354$	14.9440	−	7.70628i	0.794265	−	0.409584i
$355$	−3.24775	+	5.62526i	−0.172373	+	0.298558i
$356$	3.15512	−	33.1200i	0.167221	−	1.75536i
$357$	−15.7078	−	9.06891i	−0.831346	−	0.479978i
$358$	−9.75867	−	6.26998i	−0.515762	−	0.331379i
$359$	−14.6161	+	8.43860i	−0.771408	+	0.445372i	−0.833377	−	0.552706i	$-0.813595\pi$
$359$	−14.6161	+	8.43860i	−0.771408	+	0.445372i	0.0619688	+	0.998078i	$0.480262\pi$
$360$	1.86532	−	13.0045i	0.0983108	−	0.685395i
$361$	12.4804	+	14.3262i	0.656862	+	0.754010i
$362$	3.10782	+	6.02668i	0.163343	+	0.316755i
$363$	−8.67932	−	15.0330i	−0.455546	−	0.789029i
$364$	−21.9905	−	2.09488i	−1.15261	−	0.109802i
$365$	−2.49186	+	4.31602i	−0.130430	+	0.225911i
$366$	−27.5239	−	17.6842i	−1.43869	−	0.924366i
$367$	2.53795	+	1.46528i	0.132480	+	0.0764873i	0.564775	−	0.825245i	$-0.308963\pi$
$367$	2.53795	+	1.46528i	0.132480	+	0.0764873i	−0.432295	+	0.901732i	$0.642296\pi$
$368$	−20.1731	+	6.99207i	−1.05160	+	0.364487i
$369$			18.9267i			0.985287i
$370$	−2.33601	−	0.111017i	−0.121443	−	0.00577148i
$371$	−12.2991	+	21.3027i	−0.638538	+	1.10598i
$372$	−5.22773	+	7.34478i	−0.271045	+	0.380809i
$373$			4.27609i			0.221408i	0.993853	+	0.110704i	$0.0353105\pi$
$373$			4.27609i			0.221408i	−0.993853	+	0.110704i	$0.964689\pi$
$374$	−9.22537	−	0.438427i	−0.477032	−	0.0226705i
$375$	−1.38246	−	2.39450i	−0.0713901	−	0.123651i
$376$	0.627429	−	0.798390i	0.0323572	−	0.0411738i
$377$	−20.6665	−	35.7954i	−1.06438	−	1.84356i
$378$	−7.58842	+	11.8107i	−0.390306	+	0.607477i
$379$	−18.2739			−0.938667			−0.469334	−	0.883021i	$-0.655506\pi$
$379$	−18.2739			−0.938667			−0.469334	+	0.883021i	$0.655506\pi$
$380$	−7.54307	+	4.37059i	−0.386951	+	0.224206i
$381$	40.8332			2.09195
$382$	1.59289	−	2.47920i	0.0814994	−	0.126847i
$383$	−11.3931	−	19.7334i	−0.582160	−	1.00833i	−0.995223	−	0.0976278i	$-0.968875\pi$
$383$	−11.3931	−	19.7334i	−0.582160	−	1.00833i	0.413063	−	0.910702i	$-0.364459\pi$
$384$	10.2081	−	29.5691i	0.520931	−	1.50894i
$385$	2.37151	+	4.10757i	0.120863	+	0.209341i
$386$	−23.6900	−	1.12584i	−1.20579	−	0.0573039i
$387$		−	55.2255i		−	2.80727i
$388$	24.3447	+	17.3276i	1.23591	+	0.879674i
$389$	5.83415	−	10.1050i	0.295803	−	0.512346i	−0.679368	−	0.733797i	$-0.737746\pi$
$389$	5.83415	−	10.1050i	0.295803	−	0.512346i	0.975171	+	0.221452i	$0.0710795\pi$
$390$	−19.7641	−	0.939268i	−1.00079	−	0.0475617i
$391$			16.0417i			0.811264i
$392$	0.897842	−	6.25950i	0.0453478	−	0.316152i
$393$	−10.8407	−	6.25889i	−0.546842	−	0.315719i
$394$	−2.62400	−	1.68593i	−0.132195	−	0.0849360i
$395$	−3.74126	+	6.48006i	−0.188243	+	0.326047i
$396$	−1.91434	+	20.0953i	−0.0961992	+	1.00982i
$397$	10.7828	+	18.6764i	0.541174	+	0.937341i	0.998837	+	0.0482151i	$0.0153533\pi$
$397$	10.7828	+	18.6764i	0.541174	+	0.937341i	−0.457663	+	0.889126i	$0.651313\pi$
$398$	15.2011	+	29.4779i	0.761960	+	1.47759i
$399$	26.1838	−	2.53529i	1.31083	−	0.126923i
$400$	−1.30996	−	3.77942i	−0.0654979	−	0.188971i
$401$	11.1929	−	6.46224i	0.558948	−	0.322709i	−0.193775	−	0.981046i	$-0.562073\pi$
$401$	11.1929	−	6.46224i	0.558948	−	0.322709i	0.752723	+	0.658337i	$0.228740\pi$
$402$	27.0261	+	17.3643i	1.34794	+	0.866055i
$403$	7.14435	+	4.12479i	0.355885	+	0.205471i
$404$	9.03326	+	0.860538i	0.449422	+	0.0428134i
$405$	0.680033	−	1.17785i	0.0337911	−	0.0585279i
$406$	−22.4099	+	11.5563i	−1.11218	+	0.573527i
$407$	3.59340			0.178118
$408$	−18.4798	−	14.5227i	−0.914887	−	0.718980i
$409$	−16.0872	−	9.28793i	−0.795459	−	0.459259i	0.0464217	−	0.998922i	$-0.485218\pi$
$409$	−16.0872	−	9.28793i	−0.795459	−	0.459259i	−0.841881	+	0.539663i	$0.818552\pi$
$410$	2.64117	+	5.12174i	0.130438	+	0.252945i
$411$	15.9686			0.787673
$412$	−14.9393	−	32.6933i	−0.736008	−	1.61068i
$413$	−8.12833	+	4.69289i	−0.399969	+	0.230922i
$414$	35.0221	+	1.66439i	1.72124	+	0.0818005i
$415$	−0.716485	+	0.413663i	−0.0351709	+	0.0203059i
$416$	−27.8217	−	6.73303i	−1.36407	−	0.330114i
$417$		−	23.9719i		−	1.17391i
$418$	11.2583	−	7.25816i	0.550661	−	0.355008i
$419$		−	15.9107i		−	0.777289i	−0.921388	−	0.388644i	$-0.872944\pi$
$419$		−	15.9107i		−	0.777289i	0.921388	−	0.388644i	$-0.127056\pi$
$420$	−1.14466	+	12.0157i	−0.0558536	+	0.586308i
$421$	−14.6473	+	8.45663i	−0.713867	+	0.412151i	−0.812491	−	0.582974i	$-0.801889\pi$
$421$	−14.6473	+	8.45663i	−0.713867	+	0.412151i	0.0986244	+	0.995125i	$0.468556\pi$
$422$	1.82499	−	38.4014i	0.0888391	−	1.86935i
$423$	−1.44412	+	0.833765i	−0.0702157	+	0.0405390i
$424$	−19.6954	+	25.0620i	−0.956494	+	1.21712i
$425$	−3.00540			−0.145783
$426$	22.5739	−	11.6409i	1.09371	−	0.564002i
$427$	15.8155	+	9.13106i	0.765364	+	0.441883i
$428$	11.5040	+	25.1753i	0.556065	+	1.21689i
$429$	30.4024			1.46784
$430$	−7.70654	−	14.9445i	−0.371642	−	0.720688i
$431$	9.69484	−	16.7920i	0.466984	−	0.808840i	−0.532304	−	0.846553i	$-0.678674\pi$
$431$	9.69484	−	16.7920i	0.466984	−	0.808840i	0.999289	+	0.0377126i	$0.0120072\pi$
$432$	−11.9066	+	13.7534i	−0.572858	+	0.661710i
$433$	31.2255	+	18.0280i	1.50060	+	0.866372i	1.00000		0.000692918i	$0.000220563\pi$
$433$	31.2255	+	18.0280i	1.50060	+	0.866372i	0.500600	+	0.865679i	$0.333113\pi$
$434$	2.72027	−	4.23386i	0.130577	−	0.203232i
$435$	−19.5589	+	11.2923i	−0.937776	+	0.541425i
$436$	11.6775	+	8.31157i	0.559250	+	0.398052i
$437$	−13.5208	−	18.9341i	−0.646788	−	0.905743i
$438$	17.3200	−	8.93154i	0.827582	−	0.426765i
$439$	−10.3371	−	17.9044i	−0.493364	−	0.854531i	0.506607	−	0.862177i	$-0.330900\pi$
$439$	−10.3371	−	17.9044i	−0.493364	−	0.854531i	−0.999971	+	0.00764596i	$0.997566\pi$
$440$	2.28619	+	5.70509i	0.108990	+	0.271980i
$441$	−5.19226	+	8.99326i	−0.247250	+	0.428250i
$442$	−11.6257	+	18.0944i	−0.552977	+	0.860661i
$443$	31.9909	+	18.4699i	1.51993	+	0.877534i	0.999724	+	0.0234946i	$0.00747926\pi$
$443$	31.9909	+	18.4699i	1.51993	+	0.877534i	0.520209	+	0.854039i	$0.325854\pi$
$444$	7.45013	+	5.30271i	0.353568	+	0.251655i
$445$			16.6350i			0.788573i
$446$	0.782964	−	16.4751i	0.0370744	−	0.780119i
$447$	−28.7521	+	49.8000i	−1.35993	+	2.35546i
$448$	−4.90834	+	16.7578i	−0.231897	+	0.791729i
$449$			23.3017i			1.09967i	0.835272	+	0.549837i	$0.185310\pi$
$449$			23.3017i			1.09967i	−0.835272	+	0.549837i	$0.814690\pi$
$450$	−0.311823	+	6.56137i	−0.0146995	+	0.309306i
$451$	−4.42723	−	7.66819i	−0.208470	−	0.361081i
$452$	6.53740	−	2.98729i	0.307493	−	0.140510i
$453$	19.0996	+	33.0815i	0.897379	+	1.55431i
$454$	21.7187	+	13.9543i	1.01931	+	0.654910i
$455$	11.0450			0.517798
$456$	34.0524	+	1.56544i	1.59465	+	0.0733085i
$457$	−20.3308			−0.951034			−0.475517	−	0.879706i	$-0.657739\pi$
$457$	−20.3308			−0.951034			−0.475517	+	0.879706i	$0.657739\pi$
$458$	−15.0336	−	9.65916i	−0.702476	−	0.451343i
$459$	6.83403	+	11.8369i	0.318985	+	0.552498i
$460$	9.70956	−	4.43683i	0.452710	−	0.206868i
$461$	4.86101	+	8.41951i	0.226400	+	0.392136i	0.956738	−	0.290949i	$-0.0939711\pi$
$461$	4.86101	+	8.41951i	0.226400	+	0.392136i	−0.730339	+	0.683085i	$0.760638\pi$
$462$	0.880394	−	18.5252i	0.0409596	−	0.861872i
$463$		−	0.171279i		−	0.00796003i	−0.999992	−	0.00398001i	$-0.998733\pi$
$463$		−	0.171279i		−	0.00796003i	0.999992	−	0.00398001i	$-0.00126688\pi$
$464$	−30.8712	+	10.7001i	−1.43316	+	0.496738i
$465$	2.25382	−	3.90372i	0.104518	−	0.181031i
$466$	−0.678692	+	14.2810i	−0.0314398	+	0.661556i
$467$			4.88083i			0.225858i	0.993603	+	0.112929i	$0.0360233\pi$
$467$			4.88083i			0.225858i	−0.993603	+	0.112929i	$0.963977\pi$
$468$	38.2972	+	27.2585i	1.77029	+	1.26002i
$469$	−15.5294	−	8.96592i	−0.717083	−	0.414008i
$470$	−0.274443	+	0.427147i	−0.0126591	+	0.0197028i
$471$	−29.6068	+	51.2804i	−1.36421	+	2.36288i
$472$	−11.2896	+	4.52406i	−0.519646	+	0.208237i
$473$	12.9180	+	22.3747i	0.593971	+	1.02879i
$474$	26.0042	−	13.4098i	1.19441	−	0.615931i
$475$	3.54730	−	2.53311i	0.162761	−	0.116227i
$476$	10.6889	+	7.60792i	0.489924	+	0.348708i
$477$	45.3320	−	26.1725i	2.07561	−	1.19835i
$478$	12.8051	−	19.9301i	0.585694	−	0.911581i
$479$	9.28818	+	5.36254i	0.424388	+	0.245020i	0.696953	−	0.717117i	$-0.254539\pi$
$479$	9.28818	+	5.36254i	0.424388	+	0.245020i	−0.272565	+	0.962137i	$0.587872\pi$
$480$	−3.67898	+	15.2020i	−0.167922	+	0.693871i
$481$	4.18395	−	7.24682i	0.190772	−	0.330427i
$482$	8.57471	+	16.6281i	0.390567	+	0.757388i
$483$	−32.2130			−1.46574
$484$	5.21863	+	11.4205i	0.237210	+	0.519112i
$485$	−12.9391	−	7.47039i	−0.587534	−	0.339213i
$486$	−21.8756	+	11.2807i	−0.992296	+	0.511705i
$487$	−4.63382			−0.209978			−0.104989	−	0.994473i	$-0.533481\pi$
$487$	−4.63382			−0.209978			−0.104989	+	0.994473i	$0.533481\pi$
$488$	18.6064	+	14.6222i	0.842274	+	0.661916i
$489$	−33.2905	+	19.2203i	−1.50545	+	0.869172i
$490$	−0.150091	+	3.15822i	−0.00678043	+	0.142674i
$491$	18.3657	−	10.6034i	0.828833	−	0.478527i	−0.0246202	−	0.999697i	$-0.507838\pi$
$491$	18.3657	−	10.6034i	0.828833	−	0.478527i	0.853453	+	0.521170i	$0.174504\pi$
$492$	2.13690	−	22.4315i	0.0963388	−	1.01129i
$493$			24.5489i			1.10563i
$494$	−1.52902	−	31.1557i	−0.0687937	−	1.40176i
$495$		−	10.0931i		−	0.453652i
$496$	4.26825	−	4.93027i	0.191650	−	0.221375i
$497$	−12.2784	+	7.08893i	−0.550761	+	0.317982i
$498$	3.23136	+	0.153567i	0.144801	+	0.00688152i
$499$	−0.173776	+	0.100330i	−0.00777929	+	0.00449138i	−0.503885	−	0.863771i	$-0.668096\pi$
$499$	−0.173776	+	0.100330i	−0.00777929	+	0.00449138i	0.496105	+	0.868262i	$0.334763\pi$
$500$	0.831236	+	1.81908i	0.0371740	+	0.0813517i
$501$	18.4009			0.822090
$502$	−1.22372	−	2.37303i	−0.0546172	−	0.105914i
$503$	9.70051	+	5.60059i	0.432525	+	0.249718i	0.700422	−	0.713729i	$-0.252995\pi$
$503$	9.70051	+	5.60059i	0.432525	+	0.249718i	−0.267897	+	0.963448i	$0.586329\pi$
$504$	17.7186	−	22.5465i	0.789248	−	1.00430i
$505$	−4.53708			−0.201897
$506$	−14.5786	+	7.51784i	−0.648097	+	0.334209i
$507$	17.4268	−	30.1841i	0.773951	−	1.34052i
$508$	−29.4034	−	2.80106i	−1.30457	−	0.124277i
$509$	−4.70571	−	2.71684i	−0.208577	−	0.120422i	0.392073	−	0.919934i	$-0.371758\pi$
$509$	−4.70571	−	2.71684i	−0.208577	−	0.120422i	−0.600650	+	0.799512i	$0.705091\pi$
$510$	9.88689	+	6.35236i	0.437799	+	0.281287i
$511$	−9.42069	+	5.43904i	−0.416747	+	0.240609i
$512$	−9.37909	+	20.5921i	−0.414501	+	0.910049i
$513$	−18.0430	−	8.21107i	−0.796618	−	0.362528i
$514$	−7.43357	−	14.4152i	−0.327881	−	0.635825i
$515$	8.98621	+	15.5646i	0.395980	+	0.685857i
$516$	−6.23516	+	65.4519i	−0.274488	+	2.88136i
$517$	0.390059	−	0.675601i	0.0171548	−	0.0297129i
$518$	−4.29459	−	2.75929i	−0.188693	−	0.121236i
$519$	29.6613	+	17.1249i	1.30199	+	0.751702i
$520$	14.1674	+	2.03212i	0.621282	+	0.0891146i
$521$		−	28.5989i		−	1.25294i	−0.779445	−	0.626470i	$-0.784499\pi$
$521$		−	28.5989i		−	1.25294i	0.779445	−	0.626470i	$-0.215501\pi$
$522$	53.5949	+	2.54705i	2.34579	+	0.111481i
$523$	−22.3991	+	38.7963i	−0.979443	+	1.69645i	−0.315028	+	0.949082i	$0.602014\pi$
$523$	−22.3991	+	38.7963i	−0.979443	+	1.69645i	−0.664416	+	0.747363i	$0.731319\pi$
$524$	7.37690	+	5.25059i	0.322262	+	0.229373i
$525$		−	6.03507i		−	0.263392i
$526$	−18.8694	−	0.896750i	−0.822745	−	0.0391002i
$527$	−2.44984	−	4.24324i	−0.106717	−	0.184839i
$528$	4.53766	−	23.6003i	0.197476	−	1.02707i
$529$	2.74511	+	4.75468i	0.119353	+	0.206725i
$530$	8.61496	−	13.4084i	0.374210	−	0.582425i
$531$	19.9729			0.866751
$532$	−19.0285	+	0.0294759i	−0.824991	+	0.00127794i
$533$	−20.6193			−0.893121
$534$	35.1604	−	54.7241i	1.52154	−	2.36815i
$535$	−6.91979	−	11.9854i	−0.299169	−	0.518175i
$536$	−18.2700	−	14.3578i	−0.789142	−	0.620161i
$537$	−11.3389	−	19.6396i	−0.489310	−	0.847510i
$538$	−32.7205	−	1.55501i	−1.41068	−	0.0670413i
$539$		−	4.85817i		−	0.209256i
$540$	5.27434	−	7.41028i	0.226972	−	0.318888i
$541$	−21.4447	+	37.1434i	−0.921981	+	1.59692i	−0.125636	+	0.992076i	$0.540097\pi$
$541$	−21.4447	+	37.1434i	−0.921981	+	1.59692i	−0.796345	+	0.604842i	$0.793236\pi$
$542$	−29.7606	−	1.41434i	−1.27833	−	0.0607513i
$543$			13.2572i			0.568919i
$544$	12.3108	+	11.7253i	0.527823	+	0.502716i
$545$	−6.20653	−	3.58334i	−0.265859	−	0.153494i
$546$	−36.3348	−	23.3452i	−1.55499	−	0.999084i
$547$	−4.41258	+	7.64282i	−0.188668	+	0.326783i	−0.944807	−	0.327629i	$-0.893750\pi$
$547$	−4.41258	+	7.64282i	−0.188668	+	0.326783i	0.756138	+	0.654412i	$0.227084\pi$
$548$	−11.4988	−	1.09541i	−0.491203	−	0.0467936i
$549$	−19.4309	−	33.6552i	−0.829289	−	1.43637i
$550$	−1.40846	−	2.73129i	−0.0600570	−	0.116462i
$551$	−20.6911	−	28.9752i	−0.881471	−	1.23439i
$552$	−41.3194	−	5.92672i	−1.75867	−	0.252258i
$553$	−14.1442	+	8.16614i	−0.601471	+	0.347260i
$554$	29.2108	+	18.7681i	1.24105	+	0.797378i
$555$	−3.95971	−	2.28614i	−0.168081	−	0.0970413i
$556$	−1.64442	+	17.2618i	−0.0697388	+	0.732065i
$557$	−20.0537	+	34.7340i	−0.849702	+	1.47173i	0.0317722	+	0.999495i	$0.489885\pi$
$557$	−20.0537	+	34.7340i	−0.849702	+	1.47173i	−0.881474	+	0.472232i	$0.843448\pi$
$558$	−9.51799	+	4.90821i	−0.402929	+	0.207781i
$559$	60.1641			2.54467
$560$	1.64851	−	8.57385i	0.0696621	−	0.362311i
$561$	−15.6377	−	9.02843i	−0.660224	−	0.381181i
$562$	−3.75227	−	7.27640i	−0.158280	−	0.306936i
$563$	6.87673			0.289819			0.144910	−	0.989445i	$-0.453711\pi$
$563$	6.87673			0.289819			0.144910	+	0.989445i	$0.453711\pi$
$564$	1.80567	−	0.825111i	0.0760326	−	0.0347434i
$565$	−3.11232	+	1.79690i	−0.130936	+	0.0755961i
$566$	−23.0438	−	1.09513i	−0.968602	−	0.0460319i
$567$	2.57093	−	1.48432i	0.107969	−	0.0623358i
$568$	−17.0537	+	6.83390i	−0.715558	+	0.286744i
$569$		−	12.3097i		−	0.516050i	−0.966138	−	0.258025i	$-0.916928\pi$
$569$		−	12.3097i		−	0.516050i	0.966138	−	0.258025i	$-0.0830718\pi$
$570$	−17.0237	+	0.835465i	−0.713043	+	0.0349938i
$571$		−	7.15670i		−	0.299499i	−0.988724	−	0.149749i	$-0.952153\pi$
$571$		−	7.15670i		−	0.299499i	0.988724	−	0.149749i	$-0.0478467\pi$
$572$	−21.8923	−	2.08553i	−0.915364	−	0.0872005i
$573$	4.98945	−	2.88066i	0.208437	−	0.120341i
$574$	−0.597095	+	12.5641i	−0.0249223	+	0.524414i
$575$	−4.62252	+	2.66881i	−0.192772	+	0.111297i
$576$	26.8758	−	25.6604i	1.11982	−	1.06918i
$577$	35.3209			1.47043			0.735215	−	0.677834i	$-0.237081\pi$
$577$	35.3209			1.47043			0.735215	+	0.677834i	$0.237081\pi$
$578$	−10.0147	+	5.16433i	−0.416555	+	0.214808i
$579$	−40.1563	−	23.1842i	−1.66884	−	0.963504i
$580$	14.8587	−	6.78975i	0.616974	−	0.281929i
$581$	−1.80582			−0.0749182
$582$	26.7760	+	51.9240i	1.10990	+	2.15232i
$583$	−12.2442	+	21.2076i	−0.507104	+	0.878329i
$584$	−13.0846	+	5.24336i	−0.541444	+	0.216972i
$585$	−20.3548	−	11.7519i	−0.841569	−	0.485880i
$586$	7.04287	−	10.9616i	0.290938	−	0.452820i
$587$	21.0448	−	12.1502i	0.868613	−	0.501494i	0.00172609	−	0.999999i	$-0.499451\pi$
$587$	21.0448	−	12.1502i	0.868613	−	0.501494i	0.866887	+	0.498504i	$0.166117\pi$
$588$	7.16911	−	10.0724i	0.295649	−	0.415377i
$589$	6.46799	+	2.94348i	0.266509	+	0.121284i
$590$	5.40485	−	2.78715i	0.222514	−	0.114745i
$591$	−3.04891	−	5.28087i	−0.125416	−	0.217226i
$592$	−5.00098	−	4.32947i	−0.205539	−	0.177940i
$593$	13.7573	−	23.8284i	0.564946	−	0.978515i	−0.432109	−	0.901821i	$-0.642230\pi$
$593$	13.7573	−	23.8284i	0.564946	−	0.978515i	0.997055	−	0.0766934i	$-0.0244363\pi$
$594$	−7.55454	+	11.7580i	−0.309967	+	0.482436i
$595$	−5.68109	−	3.27998i	−0.232902	−	0.134466i
$596$	24.1201	−	33.8880i	0.987999	−	1.38811i
$597$			64.8438i			2.65388i
$598$	−1.81323	+	38.1540i	−0.0741487	+	1.56023i
$599$	13.3675	−	23.1532i	0.546182	−	0.946016i	−0.452349	−	0.891841i	$-0.649414\pi$
$599$	13.3675	−	23.1532i	0.546182	−	0.946016i	0.998531	−	0.0541747i	$-0.0172528\pi$
$600$	1.11037	−	7.74117i	0.0453306	−	0.316032i
$601$			6.93661i			0.282950i	0.989942	+	0.141475i	$0.0451845\pi$
$601$			6.93661i			0.282950i	−0.989942	+	0.141475i	$0.954815\pi$
$602$	1.74224	−	36.6601i	0.0710083	−	1.49416i
$603$	19.0794	+	33.0466i	0.776975	+	1.34576i
$604$	−11.4841	−	25.1317i	−0.467280	−	1.02260i
$605$	−3.13908	−	5.43704i	−0.127622	−	0.221047i
$606$	14.9257	+	9.58978i	0.606313	+	0.389558i
$607$	−3.37786			−0.137103			−0.0685516	−	0.997648i	$-0.521838\pi$
$607$	−3.37786			−0.137103			−0.0685516	+	0.997648i	$0.521838\pi$
$608$	−24.4132	−	3.46317i	−0.990088	−	0.140450i
$609$	−49.2960			−1.99757
$610$	−9.95464	−	6.39589i	−0.403051	−	0.258962i
$611$	−0.908326	−	1.57327i	−0.0367469	−	0.0636475i
$612$	−11.6037	−	25.3936i	−0.469052	−	1.02647i
$613$	7.47134	+	12.9407i	0.301765	+	0.522672i	0.976536	−	0.215355i	$-0.0690910\pi$
$613$	7.47134	+	12.9407i	0.301765	+	0.522672i	−0.674771	+	0.738027i	$0.735758\pi$
$614$	0.0277538	−	0.583996i	0.00112005	−	0.0235682i
$615$			11.2665i			0.454311i
$616$	−1.90475	+	13.2794i	−0.0767445	+	0.535041i
$617$	−0.978279	+	1.69443i	−0.0393840	+	0.0682152i	−0.885046	−	0.465504i	$-0.845873\pi$
$617$	−0.978279	+	1.69443i	−0.0393840	+	0.0682152i	0.845661	+	0.533720i	$0.179206\pi$
$618$	3.33602	−	70.1965i	0.134195	−	2.82372i
$619$		−	4.32563i		−	0.173862i	−0.996214	−	0.0869309i	$-0.972294\pi$
$619$		−	4.32563i		−	0.173862i	0.996214	−	0.0869309i	$-0.0277059\pi$
$620$	−1.89073	+	2.65641i	−0.0759334	+	0.106684i
$621$	21.0224	+	12.1373i	0.843600	+	0.487053i
$622$	3.29324	−	5.12564i	0.132047	−	0.205520i
$623$	−18.1548	+	31.4450i	−0.727356	+	1.25982i
$624$	−42.3114	−	36.6300i	−1.69381	−	1.46637i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−28.8569	+	14.8809i	−1.15335	+	0.594758i
$627$	26.0669	−	2.52397i	1.04101	−	0.100798i
$628$	24.8371	−	34.8954i	0.991110	−	1.39248i
$629$	−4.30410	+	2.48498i	−0.171616	+	0.0990825i
$630$	−7.75027	+	12.0626i	−0.308778	+	0.480586i
$631$	27.3094	+	15.7671i	1.08717	+	0.627679i	0.932822	−	0.360337i	$-0.117338\pi$
$631$	27.3094	+	15.7671i	1.08717	+	0.627679i	0.154350	+	0.988016i	$0.450672\pi$
$632$	−19.6451	+	7.87236i	−0.781441	+	0.313146i
$633$	37.5816	−	65.0933i	1.49374	−	2.58723i
$634$	−9.39969	−	18.2279i	−0.373309	−	0.723921i
$635$	14.7683			0.586061
$636$	−56.6814	+	25.9008i	−2.24756	+	1.02703i
$637$	−9.79749	−	5.65659i	−0.388191	−	0.224122i
$638$	−22.3098	+	11.5047i	−0.883255	+	0.455474i
$639$	30.1704			1.19352
$640$	3.69200	−	10.6944i	0.145939	−	0.422731i
$641$	23.2718	−	13.4360i	0.919181	−	0.530689i	0.0358072	−	0.999359i	$-0.488600\pi$
$641$	23.2718	−	13.4360i	0.919181	−	0.530689i	0.883374	+	0.468669i	$0.155266\pi$
$642$	−2.56889	+	54.0545i	−0.101386	+	2.13336i
$643$	7.20688	−	4.16089i	0.284212	−	0.164090i	−0.351117	−	0.936332i	$-0.614198\pi$
$643$	7.20688	−	4.16089i	0.284212	−	0.164090i	0.635329	+	0.772242i	$0.280865\pi$
$644$	23.1961	+	2.20974i	0.914054	+	0.0870758i
$645$		−	32.8741i		−	1.29442i
$646$	−8.46568	+	16.4792i	−0.333078	+	0.648367i
$647$		−	4.26130i		−	0.167529i	−0.996486	−	0.0837645i	$-0.973306\pi$
$647$		−	4.26130i		−	0.167529i	0.996486	−	0.0837645i	$-0.0266943\pi$
$648$	3.57081	−	1.43092i	0.140275	−	0.0562120i
$649$	−8.09205	+	4.67195i	−0.317641	+	0.183390i
$650$	−7.14813	−	0.339708i	−0.280373	−	0.0133244i
$651$	8.52075	−	4.91946i	0.333954	−	0.192809i
$652$	25.2905	−	11.5566i	0.990453	−	0.452592i
$653$	8.36559			0.327371			0.163685	−	0.986513i	$-0.447662\pi$
$653$	8.36559			0.327371			0.163685	+	0.986513i	$0.447662\pi$
$654$	12.8437	+	24.9066i	0.502230	+	0.973924i
$655$	−3.92080	−	2.26367i	−0.153198	−	0.0884490i
$656$	−3.07750	+	16.0060i	−0.120156	+	0.624931i
$657$	23.1485			0.903109
$658$	−0.984950	+	0.507916i	−0.0383974	+	0.0198006i
$659$	1.32499	−	2.29495i	0.0516142	−	0.0893985i	−0.839064	−	0.544033i	$-0.816897\pi$
$659$	1.32499	−	2.29495i	0.0516142	−	0.0893985i	0.890678	+	0.454634i	$0.150230\pi$
$660$	−1.13955	+	11.9621i	−0.0443569	+	0.465625i
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634815i	−0.163434	−	0.986554i	$-0.552257\pi$
$661$	−28.2689	−	16.3211i	−1.09953	−	0.634815i	−0.936098	+	0.351739i	$0.885591\pi$
$662$	13.1255	+	8.43319i	0.510138	+	0.327765i
$663$	−36.4154	+	21.0244i	−1.41426	+	0.816521i
$664$	−2.31632	−	0.332246i	−0.0898908	−	0.0128936i
$665$	9.46998	−	0.916946i	0.367230	−	0.0355576i
$666$	4.97861	+	9.65451i	0.192917	+	0.374105i
$667$	21.7995	+	37.7579i	0.844081	+	1.46199i
$668$	−13.2502	−	1.26226i	−0.512666	−	0.0488382i
$669$	16.1234	−	27.9266i	0.623367	−	1.07970i
$670$	9.77461	+	6.28022i	0.377626	+	0.242626i
$671$	15.7449	+	9.09030i	0.607824	+	0.350927i
$672$	−23.5452	+	24.7211i	−0.908275	+	0.953636i
$673$		−	35.9561i		−	1.38601i	−0.720935	−	0.693003i	$-0.756287\pi$
$673$		−	35.9561i		−	1.38601i	0.720935	−	0.693003i	$-0.243713\pi$
$674$	27.9864	+	1.33003i	1.07800	+	0.0512308i
$675$	−2.27391	+	3.93853i	−0.0875230	+	0.151594i
$676$	−14.6194	+	20.5397i	−0.562283	+	0.789989i
$677$			43.5015i			1.67190i	0.548805	+	0.835950i	$0.315083\pi$
$677$			43.5015i			1.67190i	−0.548805	+	0.835950i	$0.684917\pi$
$678$	14.0366	+	0.667077i	0.539073	+	0.0256189i
$679$	−16.3058	−	28.2425i	−0.625759	−	1.08385i
$680$	−6.68365	−	5.25246i	−0.256306	−	0.201423i
$681$	25.2357	+	43.7095i	0.967033	+	1.67495i
$682$	2.70813	−	4.21496i	0.103699	−	0.161399i
$683$	−26.1006			−0.998711			−0.499356	−	0.866397i	$-0.666430\pi$
$683$	−26.1006			−0.998711			−0.499356	+	0.866397i	$0.666430\pi$
$684$	35.0990	+	20.1920i	1.34204	+	0.772060i
$685$	5.77542			0.220667
$686$	−15.4105	+	23.9851i	−0.588377	+	0.915757i
$687$	−17.4681	−	30.2556i	−0.666448	−	1.15432i
$688$	8.97970	−	46.7033i	0.342348	−	1.78055i
$689$	28.5130	+	49.3859i	1.08626	+	1.88145i
$690$	20.8476	+	0.990764i	0.793656	+	0.0377177i
$691$		−	35.7207i		−	1.35888i	−0.733732	−	0.679439i	$-0.762223\pi$
$691$		−	35.7207i		−	1.35888i	0.733732	−	0.679439i	$-0.237777\pi$
$692$	−20.1839	−	14.3661i	−0.767278	−	0.546119i
$693$	11.0152	−	19.0790i	0.418435	−	0.724750i
$694$	−28.8333	−	1.37027i	−1.09450	−	0.0520149i
$695$		−	8.66999i		−	0.328871i
$696$	−63.2318	−	9.06976i	−2.39680	−	0.343788i
$697$	10.6057	+	6.12321i	0.401720	+	0.231933i
$698$	4.10209	+	2.63561i	0.155267	+	0.0997593i
$699$	−13.9762	+	24.2074i	−0.528627	+	0.915609i
$700$	−0.413992	+	4.34577i	−0.0156474	+	0.164255i
$701$	−17.1309	−	29.6716i	−0.647026	−	1.12068i	−0.983830	−	0.179107i	$-0.942679\pi$
$701$	−17.1309	−	29.6716i	−0.647026	−	1.12068i	0.336804	−	0.941575i	$-0.390654\pi$
$702$	14.9163	+	28.9256i	0.562979	+	1.09173i
$703$	2.98569	−	6.56077i	0.112608	−	0.247444i
$704$	−4.88643	+	16.6830i	−0.184164	+	0.628762i
$705$	−0.859644	+	0.496316i	−0.0323761	+	0.0186923i
$706$	37.9363	+	24.3742i	1.42775	+	0.917336i
$707$	−8.57642	−	4.95160i	−0.322549	−	0.186224i
$708$	−23.6714	−	2.25501i	−0.889626	−	0.0847486i
$709$	0.650040	−	1.12590i	0.0244128	−	0.0422842i	−0.853561	−	0.520993i	$-0.825562\pi$
$709$	0.650040	−	1.12590i	0.0244128	−	0.0422842i	0.877974	+	0.478709i	$0.158895\pi$
$710$	8.16439	−	4.21019i	0.306404	−	0.158006i
$711$	34.7550			1.30342
$712$	−29.0725	+	36.9942i	−1.08954	+	1.38642i
$713$	−7.53604	−	4.35093i	−0.282227	−	0.162944i
$714$	11.7564	+	22.7980i	0.439972	+	0.853193i
$715$	10.9957			0.411216
$716$	6.81776	+	14.9200i	0.254792	+	0.557587i
$717$	40.1098	−	23.1574i	1.49793	−	0.864829i
$718$	23.8411	+	1.13302i	0.889741	+	0.0422841i
$719$	−15.9031	+	9.18168i	−0.593087	+	0.342419i	−0.766317	−	0.642463i	$-0.777913\pi$
$719$	−15.9031	+	9.18168i	−0.593087	+	0.342419i	0.173230	+	0.984881i	$0.444579\pi$
$720$	−12.1606	+	14.0467i	−0.453198	+	0.523491i
$721$			39.2288i			1.46096i
$722$	−3.89749	−	26.5859i	−0.145049	−	0.989424i
$723$			36.5775i			1.36033i
$724$	0.909411	−	9.54629i	0.0337980	−	0.354785i
$725$	−7.07391	+	4.08413i	−0.262719	+	0.151681i
$726$	−1.16534	+	24.5212i	−0.0432500	+	0.910065i
$727$	−7.98924	+	4.61259i	−0.296305	+	0.171072i	−0.640782	−	0.767723i	$-0.721390\pi$
$727$	−7.98924	+	4.61259i	−0.296305	+	0.171072i	0.344477	+	0.938795i	$0.388056\pi$
$728$	24.5628	+	19.3031i	0.910357	+	0.715420i
$729$	−44.0405			−1.63113
$730$	6.26418	−	3.23030i	0.231848	−	0.119559i
$731$	−30.9459	−	17.8666i	−1.14458	−	0.660822i
$732$	19.2292	+	42.0812i	0.710731	+	1.55536i
$733$	9.19832			0.339748			0.169874	−	0.985466i	$-0.445664\pi$
$733$	9.19832			0.339748			0.169874	+	0.985466i	$0.445664\pi$
$734$	−1.89951	−	3.68352i	−0.0701121	−	0.135961i
$735$	−3.09080	+	5.35342i	−0.114006	+	0.197464i
$736$	29.3470	+	7.10217i	1.08174	+	0.261789i
$737$	−15.4601	−	8.92590i	−0.569481	−	0.328790i
$738$	14.4685	−	22.5190i	0.532594	−	0.828936i
$739$	25.4237	−	14.6784i	0.935227	−	0.539954i	0.0467663	−	0.998906i	$-0.485108\pi$
$739$	25.4237	−	14.6784i	0.935227	−	0.539954i	0.888461	+	0.458952i	$0.151775\pi$
$740$	2.69451	+	1.91785i	0.0990522	+	0.0705015i
$741$	25.2608	−	55.5081i	0.927979	−	2.03914i
$742$	30.9183	−	15.9438i	1.13505	−	0.585317i
$743$	−9.29972	−	16.1076i	−0.341174	−	0.590930i	0.643477	−	0.765465i	$-0.277491\pi$
$743$	−9.29972	−	16.1076i	−0.341174	−	0.590930i	−0.984651	+	0.174535i	$0.944158\pi$
$744$	11.8346	−	4.74247i	0.433879	−	0.173868i
$745$	−10.3988	+	18.0113i	−0.380984	+	0.659884i
$746$	3.26885	−	5.08769i	0.119681	−	0.186273i
$747$	3.32795	+	1.92139i	0.121763	+	0.0703001i
$748$	10.6412	+	7.57396i	0.389079	+	0.276931i
$749$		−	30.2080i		−	1.10378i
$750$	−0.185619	+	3.90579i	−0.00677784	+	0.142619i
$751$	12.8124	−	22.1917i	0.467530	−	0.809786i	−0.531782	−	0.846881i	$-0.678477\pi$
$751$	12.8124	−	22.1917i	0.467530	−	0.809786i	0.999312	+	0.0370957i	$0.0118106\pi$
$752$	−1.35684	+	0.470286i	−0.0494789	+	0.0171496i
$753$		−	5.22007i		−	0.190230i
$754$	−2.77482	+	58.3878i	−0.101053	+	2.12636i
$755$	6.90782	+	11.9647i	0.251401	+	0.435440i
$756$	18.0574	−	8.25139i	0.656740	−	0.300100i
$757$	−3.08640	−	5.34580i	−0.112177	−	0.194296i	0.804471	−	0.593992i	$-0.202449\pi$
$757$	−3.08640	−	5.34580i	−0.112177	−	0.194296i	−0.916648	+	0.399696i	$0.869116\pi$
$758$	21.7422	+	13.9695i	0.789714	+	0.507394i
$759$	−32.0692			−1.16404
$760$	12.3158	+	0.566178i	0.446742	+	0.0205374i
$761$	33.0112			1.19666			0.598328	−	0.801251i	$-0.295832\pi$
$761$	33.0112			1.19666			0.598328	+	0.801251i	$0.295832\pi$
$762$	−48.5832	−	31.2149i	−1.75999	−	1.13080i
$763$	−7.82145	−	13.5471i	−0.283156	−	0.490440i
$764$	−3.79044	+	1.73206i	−0.137133	+	0.0626636i
$765$	6.97979	+	12.0893i	0.252355	+	0.437091i
$766$	−1.52971	+	32.1882i	−0.0552708	+	1.16301i
$767$			21.7590i			0.785673i
$768$	−34.7497	+	27.3777i	−1.25392	+	0.987907i
$769$	21.2189	−	36.7522i	0.765174	−	1.32532i	−0.174981	−	0.984572i	$-0.555986\pi$
$769$	21.2189	−	36.7522i	0.765174	−	1.32532i	0.940155	−	0.340748i	$-0.110680\pi$
$770$	0.318415	−	6.70008i	0.0114749	−	0.241454i
$771$		−	31.7097i		−	1.14200i
$772$	27.3256	+	19.4493i	0.983470	+	0.699995i
$773$	24.1948	+	13.9689i	0.870226	+	0.502425i	0.867423	−	0.497571i	$-0.165775\pi$
$773$	24.1948	+	13.9689i	0.870226	+	0.502425i	0.00280270	+	0.999996i	$0.499108\pi$
$774$	−42.2171	+	65.7072i	−1.51746	+	2.36180i
$775$	0.815144	−	1.41187i	0.0292808	−	0.0507159i
$776$	−15.7192	−	39.2266i	−0.564286	−	1.40815i
$777$	−4.99002	−	8.64296i	−0.179016	−	0.310065i
$778$	−14.6662	+	7.56304i	−0.525810	+	0.271148i
$779$	−17.6790	+	1.71179i	−0.633415	+	0.0613314i
$780$	22.7972	+	16.2262i	0.816271	+	0.580990i
$781$	−12.2236	+	7.05729i	−0.437394	+	0.252530i
$782$	12.2631	−	19.0864i	0.438526	−	0.682528i
$783$	32.1709	+	18.5739i	1.14970	+	0.663777i
$784$	−5.85332	+	6.76118i	−0.209047	+	0.241471i
$785$	−10.7080	+	18.5468i	−0.382184	+	0.661962i
$786$	8.11366	+	15.7340i	0.289405	+	0.561213i
$787$	20.9075			0.745271			0.372635	−	0.927978i	$-0.378454\pi$
$787$	20.9075			0.745271			0.372635	+	0.927978i	$0.378454\pi$
$788$	1.83322	+	4.01183i	0.0653059	+	0.142916i
$789$	−31.9851	−	18.4666i	−1.13870	−	0.657428i
$790$	9.40501	−	4.84995i	0.334615	−	0.172553i
$791$	−7.84427			−0.278910
$792$	17.6395	−	22.4459i	0.626791	−	0.797579i
$793$	36.6649	−	21.1685i	1.30201	−	0.751715i
$794$	1.44777	−	30.4640i	0.0513796	−	1.08113i
$795$	26.9848	−	15.5797i	0.957053	−	0.552555i
$796$	4.44814	−	46.6931i	0.157660	−	1.65499i
$797$		−	44.4387i		−	1.57410i	−0.616890	−	0.787049i	$-0.711608\pi$
$797$		−	44.4387i		−	1.57410i	0.616890	−	0.787049i	$-0.288392\pi$
$798$	−33.0915	−	16.9997i	−1.17143	−	0.601783i
$799$			1.07896i			0.0381710i
$800$	−1.33059	+	5.49814i	−0.0470433	+	0.194389i
$801$	66.9148	−	38.6333i	2.36432	−	1.36504i
$802$	−18.2574	−	0.867664i	−0.644690	−	0.0306383i
$803$	−9.37864	+	5.41476i	−0.330965	+	0.191083i
$804$	−18.8814	−	41.3201i	−0.665896	−	1.45725i
$805$	−11.6506			−0.410628
$806$	−5.34714	−	10.3692i	−0.188345	−	0.365238i
$807$	−55.4638	−	32.0221i	−1.95242	−	1.12723i
$808$	−10.0899	−	7.92933i	−0.354962	−	0.278953i
$809$	8.29205			0.291533			0.145767	−	0.989319i	$-0.453435\pi$
$809$	8.29205			0.291533			0.145767	+	0.989319i	$0.453435\pi$
$810$	−1.70951	+	0.881555i	−0.0600660	+	0.0309747i
$811$	−10.6956	+	18.5253i	−0.375573	+	0.650512i	−0.990413	−	0.138140i	$-0.955887\pi$
$811$	−10.6956	+	18.5253i	−0.375573	+	0.650512i	0.614839	+	0.788652i	$0.289221\pi$
$812$	35.4974	+	3.38159i	1.24571	+	0.118671i
$813$	−50.4465	−	29.1253i	−1.76924	−	1.02147i
$814$	−4.27542	−	2.74697i	−0.149853	−	0.0962812i
$815$	−12.0403	+	6.95147i	−0.421753	+	0.243499i
$816$	10.8854	+	31.4059i	0.381065	+	1.09943i
$817$	51.5847	−	4.99477i	1.80472	−	0.174745i
$818$	12.0403	+	23.3486i	0.420980	+	0.816364i
$819$	−25.6511	−	44.4290i	−0.896321	−	1.55247i
$820$	0.772859	−	8.11287i	0.0269894	−	0.283314i
$821$	8.56684	−	14.8382i	0.298985	−	0.517857i	−0.676919	−	0.736057i	$-0.736685\pi$
$821$	8.56684	−	14.8382i	0.298985	−	0.517857i	0.975904	+	0.218201i	$0.0700187\pi$
$822$	−18.9994	−	12.2072i	−0.662681	−	0.425774i
$823$	−4.75672	−	2.74630i	−0.165809	−	0.0957298i	0.414799	−	0.909913i	$-0.363852\pi$
$823$	−4.75672	−	2.74630i	−0.165809	−	0.0957298i	−0.580608	+	0.814183i	$0.697185\pi$
$824$	−7.21755	+	50.3187i	−0.251435	+	1.75294i
$825$		−	6.00814i		−	0.209176i
$826$	13.2585	+	0.630099i	0.461324	+	0.0219240i
$827$	−3.78281	+	6.55202i	−0.131541	+	0.227836i	−0.924271	−	0.381737i	$-0.875326\pi$
$827$	−3.78281	+	6.55202i	−0.131541	+	0.227836i	0.792730	+	0.609573i	$0.208659\pi$
$828$	−40.3969	−	28.7529i	−1.40389	−	0.999233i
$829$		−	20.9352i		−	0.727111i	−0.931573	−	0.363555i	$-0.881563\pi$
$829$		−	20.9352i		−	0.727111i	0.931573	−	0.363555i	$-0.118437\pi$
$830$	1.16870	+	0.0555412i	0.0405660	+	0.00192786i
$831$	33.9410	+	58.7876i	1.17740	+	2.03932i
$832$	27.9551	+	29.2792i	0.969169	+	1.01507i
$833$	3.35962	+	5.81902i	0.116404	+	0.201617i
$834$	−18.3253	+	28.5217i	−0.634553	+	0.987626i
$835$	6.65510			0.230309
$836$	−18.9436	+	0.0293443i	−0.655178	+	0.00101489i
$837$	−7.41427			−0.256275
$838$	−12.1629	+	18.9305i	−0.420161	+	0.653944i
$839$	7.78062	+	13.4764i	0.268617	+	0.465258i	0.968505	−	0.248995i	$-0.0801001\pi$
$839$	7.78062	+	13.4764i	0.268617	+	0.465258i	−0.699888	+	0.714253i	$0.746767\pi$
$840$	10.5473	−	13.4213i	0.363918	−	0.463078i
$841$	18.8602	+	32.6668i	0.650351	+	1.12644i
$842$	23.8920	+	1.13544i	0.823373	+	0.0391300i
$843$		−	16.0062i		−	0.551284i
$844$	−31.5273	+	44.2948i	−1.08521	+	1.52469i
$845$	6.30280	−	10.9168i	0.216823	−	0.375548i
$846$	2.35558	+	0.111947i	0.0809867	+	0.00384881i
$847$		−	13.7035i		−	0.470857i
$848$	42.5922	−	14.7626i	1.46262	−	0.506950i
$849$	−39.0610	−	22.5519i	−1.34057	−	0.773978i
$850$	3.57582	+	2.29748i	0.122650	+	0.0788028i
$851$	−4.41334	+	7.64413i	−0.151287	+	0.262037i
$852$	−35.7573	−	3.40635i	−1.22502	−	0.116700i
$853$	5.31920	+	9.21312i	0.182126	+	0.315451i	0.942604	−	0.333912i	$-0.108369\pi$
$853$	5.31920	+	9.21312i	0.182126	+	0.315451i	−0.760478	+	0.649363i	$0.775035\pi$
$854$	−11.8370	−	22.9542i	−0.405053	−	0.785477i
$855$	−18.4278	−	8.38620i	−0.630219	−	0.286802i
$856$	5.55784	−	38.7477i	0.189963	−	1.32437i
$857$	41.1589	−	23.7631i	1.40596	−	0.811732i	0.410966	−	0.911651i	$-0.365191\pi$
$857$	41.1589	−	23.7631i	1.40596	−	0.811732i	0.994996	+	0.0999183i	$0.0318581\pi$
$858$	−36.1726	−	23.2410i	−1.23491	−	0.793436i
$859$	19.8002	+	11.4317i	0.675574	+	0.390043i	0.798185	−	0.602412i	$-0.205793\pi$
$859$	19.8002	+	11.4317i	0.675574	+	0.390043i	−0.122611	+	0.992455i	$0.539127\pi$
$860$	−2.25509	+	23.6722i	−0.0768979	+	0.807215i
$861$	−12.2959	+	21.2971i	−0.419042	+	0.725802i
$862$	−24.3715	+	12.5678i	−0.830096	+	0.428062i
$863$	36.5702			1.24486			0.622431	−	0.782674i	$-0.286145\pi$
$863$	36.5702			1.24486			0.622431	+	0.782674i	$0.286145\pi$
$864$	24.6802	−	7.26173i	0.839639	−	0.247049i
$865$	10.7277	+	6.19363i	0.364752	+	0.210590i
$866$	−23.3705	−	45.3200i	−0.794161	−	1.54004i
$867$	−22.0297			−0.748168
$868$	−6.47314	+	2.95793i	−0.219713	+	0.100399i
$869$	−14.0810	+	8.12969i	−0.477666	+	0.275781i
$870$	31.9035	+	1.51618i	1.08163	+	0.0514034i
$871$	−36.0018	+	20.7857i	−1.21988	+	0.704295i
$872$	−7.54007	−	18.8159i	−0.255339	−	0.637187i
$873$			69.3973i			2.34874i
$874$	1.61284	+	32.8638i	0.0545553	+	1.11163i
$875$		−	2.18272i		−	0.0737895i
$876$	−27.4350	−	2.61355i	−0.926943	−	0.0883036i
$877$	19.3735	−	11.1853i	0.654197	−	0.377701i	−0.135865	−	0.990727i	$-0.543381\pi$
$877$	19.3735	−	11.1853i	0.654197	−	0.377701i	0.790062	+	0.613027i	$0.210048\pi$
$878$	−1.38793	+	29.2048i	−0.0468404	+	0.985615i
$879$	22.0605	−	12.7366i	0.744083	−	0.429596i
$880$	1.64115	−	8.53558i	0.0553231	−	0.287734i
$881$	−44.2302			−1.49015			−0.745077	−	0.666978i	$-0.767587\pi$
$881$	−44.2302			−1.49015			−0.745077	+	0.666978i	$0.767587\pi$
$882$	13.0526	−	6.73094i	0.439505	−	0.226642i
$883$	14.0382	+	8.10497i	0.472424	+	0.272754i	0.717254	−	0.696812i	$-0.245399\pi$
$883$	14.0382	+	8.10497i	0.472424	+	0.272754i	−0.244830	+	0.969566i	$0.578732\pi$
$884$	27.6644	−	12.6414i	0.930455	−	0.425176i
$885$	11.8893			0.399654
$886$	−23.9433	−	46.4309i	−0.804392	−	1.55988i
$887$	−22.2717	+	38.5757i	−0.747811	+	1.29525i	0.201059	+	0.979579i	$0.435562\pi$
$887$	−22.2717	+	38.5757i	−0.747811	+	1.29525i	−0.948870	+	0.315667i	$0.897772\pi$
$888$	−4.81050	−	12.0044i	−0.161430	−	0.402841i
$889$	27.9164	+	16.1175i	0.936285	+	0.540564i
$890$	12.7166	−	19.7923i	0.426261	−	0.663438i
$891$	2.55945	−	1.47770i	0.0857448	−	0.0495048i
$892$	−13.5259	+	19.0035i	−0.452882	+	0.636285i
$893$	−0.909408	−	1.27351i	−0.0304322	−	0.0426163i
$894$	72.2787	−	37.2725i	2.41736	−	1.24658i
$895$	−4.10098	−	7.10310i	−0.137081	−	0.237431i
$896$	18.6504	−	16.1862i	0.623065	−	0.540742i
$897$	−37.3396	+	64.6740i	−1.24673	+	2.15940i
$898$	17.8129	−	27.7243i	0.594425	−	0.925170i
$899$	−11.5325	−	6.65830i	−0.384631	−	0.222067i
$900$	5.38684	−	7.56833i	0.179561	−	0.252278i
$901$		−	33.8694i		−	1.12835i
$902$	−0.594430	+	12.5080i	−0.0197924	+	0.416471i
$903$	35.8776	−	62.1417i	1.19393	−	2.06795i
$904$	−10.0618	−	1.44323i	−0.334651	−	0.0480012i
$905$			4.79476i			0.159383i
$906$	2.56445	−	53.9610i	0.0851980	−	1.79274i
$907$	12.5852	+	21.7982i	0.417885	+	0.723799i	0.995727	−	0.0923507i	$-0.0294381\pi$
$907$	12.5852	+	21.7982i	0.417885	+	0.723799i	−0.577841	+	0.816149i	$0.696105\pi$
$908$	−15.1735	−	33.2057i	−0.503550	−	1.10197i
$909$	10.5370	+	18.2506i	0.349489	+	0.605333i
$910$	−13.1413	−	8.44335i	−0.435631	−	0.279894i
$911$	45.7359			1.51530			0.757649	−	0.652662i	$-0.226348\pi$
$911$	45.7359			1.51530			0.757649	+	0.652662i	$0.226348\pi$
$912$	−39.3187	−	27.8938i	−1.30197	−	0.923657i
$913$	−1.79776			−0.0594973
$914$	24.1895	+	15.5419i	0.800118	+	0.514079i
$915$	−11.5666	−	20.0340i	−0.382380	−	0.662302i
$916$	10.5030	+	22.9849i	0.347030	+	0.759442i
$917$	−4.94097	−	8.55801i	−0.163165	−	0.282610i
$918$	0.917582	−	19.3078i	0.0302847	−	0.637251i
$919$		−	31.8418i		−	1.05037i	−0.850990	−	0.525183i	$-0.823997\pi$
$919$		−	31.8418i		−	1.05037i	0.850990	−	0.525183i	$-0.176003\pi$
$920$	−14.9441	−	2.14354i	−0.492693	−	0.0706703i
$921$	0.571529	−	0.989918i	0.0188325	−	0.0326189i
$922$	0.652672	−	13.7335i	0.0214946	−	0.452289i
$923$			32.8685i			1.08188i
$924$	−15.2091	+	21.3683i	−0.500342	+	0.702964i
$925$	−1.43212	−	0.826836i	−0.0470879	−	0.0271862i
$926$	−0.130934	+	0.203788i	−0.00430277	+	0.00669688i
$927$	41.7394	−	72.2948i	1.37090	−	2.37447i
$928$	44.9102	+	10.8686i	1.47425	+	0.356778i
$929$	11.8751	+	20.5683i	0.389609	+	0.674823i	0.992397	−	0.123079i	$-0.0392768\pi$
$929$	11.8751	+	20.5683i	0.389609	+	0.674823i	−0.602788	+	0.797902i	$0.705943\pi$
$930$	−5.66578	+	2.92171i	−0.185788	+	0.0958067i
$931$	−8.86997	−	4.03657i	−0.290701	−	0.132293i
$932$	11.7246	−	16.4727i	0.384053	−	0.539581i
$933$	10.3155	−	5.95565i	0.337714	−	0.194979i
$934$	3.73115	−	5.80720i	0.122087	−	0.190017i
$935$	−5.65574	−	3.26534i	−0.184962	−	0.106788i
$936$	−24.7283	−	61.7083i	−0.808269	−	2.01700i
$937$	−0.291481	+	0.504861i	−0.00952228	+	0.0164931i	−0.870747	−	0.491731i	$-0.836364\pi$
$937$	−0.291481	+	0.504861i	−0.00952228	+	0.0164931i	0.861225	+	0.508224i	$0.169698\pi$
$938$	11.6229	+	22.5391i	0.379501	+	0.735927i
$939$	−63.4779			−2.07152
$940$	0.653064	−	0.298420i	0.0213006	−	0.00973340i
$941$	38.3502	+	22.1415i	1.25018	+	0.721792i	0.971145	−	0.238489i	$-0.0766520\pi$
$941$	38.3502	+	22.1415i	1.25018	+	0.721792i	0.279035	+	0.960281i	$0.409985\pi$
$942$	74.4273	−	38.3805i	2.42497	−	1.25050i
$943$	21.7498			0.708270
$944$	16.8908	+	3.24761i	0.549747	+	0.105701i
$945$	−8.59673	+	4.96332i	−0.279652	+	0.161457i
$946$	1.73446	−	36.4965i	0.0563922	−	1.18660i
$947$	12.5413	−	7.24073i	0.407538	−	0.235292i	−0.282193	−	0.959358i	$-0.591062\pi$
$947$	12.5413	−	7.24073i	0.407538	−	0.235292i	0.689731	+	0.724065i	$0.257729\pi$
$948$	−41.1908	−	3.92397i	−1.33781	−	0.127445i
$949$			25.2186i			0.818630i
$950$	−6.15700	+	0.302165i	−0.199760	+	0.00980354i
$951$		−	40.0966i		−	1.30022i
$952$	−6.90173	−	17.2230i	−0.223686	−	0.558200i
$953$	−18.3631	+	10.6019i	−0.594838	+	0.343430i	−0.767008	−	0.641637i	$-0.778256\pi$
$953$	−18.3631	+	10.6019i	−0.594838	+	0.343430i	0.172170	+	0.985067i	$0.444922\pi$
$954$	−73.9434	−	3.51409i	−2.39401	−	0.113773i
$955$	1.80455	−	1.04186i	0.0583938	−	0.0337137i
$956$	−30.4711	+	13.9239i	−0.985505	+	0.450331i
$957$	−49.0760			−1.58640
$958$	−6.95167	−	13.4807i	−0.224598	−	0.435541i
$959$	10.9172	+	6.30307i	0.352536	+	0.203537i
$960$	15.9984	−	15.2749i	0.516345	−	0.492994i
$961$	−28.3422			−0.914263
$962$	−10.5179	+	5.42383i	−0.339110	+	0.174871i
$963$	−32.1412	+	55.6702i	−1.03574	+	1.79395i
$964$	2.50913	−	26.3390i	0.0808138	−	0.848321i
$965$	−14.5234	−	8.38512i	−0.467526	−	0.269926i
$966$	38.3269	+	24.6252i	1.23315	+	0.792301i
$967$	19.4740	−	11.2433i	0.626242	−	0.361561i	−0.153053	−	0.988218i	$-0.548911\pi$
$967$	19.4740	−	11.2433i	0.626242	−	0.361561i	0.779295	+	0.626657i	$0.215577\pi$
$968$	2.52124	−	17.5774i	0.0810358	−	0.564959i
$969$	−29.4771	+	21.0495i	−0.946940	+	0.676207i
$970$	9.68417	+	18.7795i	0.310940	+	0.602974i
$971$	7.24627	+	12.5509i	0.232544	+	0.402778i	0.958556	−	0.284904i	$-0.0919617\pi$
$971$	7.24627	+	12.5509i	0.232544	+	0.402778i	−0.726012	+	0.687682i	$0.758628\pi$
$972$	34.6511	+	3.30097i	1.11143	+	0.105879i
$973$	9.46210	−	16.3888i	0.303341	−	0.525402i
$974$	5.51331	+	3.54232i	0.176658	+	0.113503i
$975$	−12.1166	−	6.99554i	−0.388043	−	0.224037i
$976$	−10.9600	−	31.6211i	−0.350821	−	1.01217i
$977$		−	28.3116i		−	0.905769i	−0.891569	−	0.452884i	$-0.850395\pi$
$977$		−	28.3116i		−	0.905769i	0.891569	−	0.452884i	$-0.149605\pi$
$978$	54.3019	+	2.58065i	1.73638	+	0.0825200i
$979$	−18.0737	+	31.3046i	−0.577639	+	1.00050i
$980$	2.59287	−	3.64290i	0.0828263	−	0.116368i
$981$			33.2880i			1.06280i
$982$	−29.9573	−	1.42369i	−0.955974	−	0.0454318i
$983$	−26.5194	−	45.9330i	−0.845839	−	1.46504i	−0.884891	−	0.465799i	$-0.845767\pi$
$983$	−26.5194	−	45.9330i	−0.845839	−	1.46504i	0.0390516	−	0.999237i	$-0.487566\pi$
$984$	−19.6902	+	25.0554i	−0.627701	+	0.798737i
$985$	−1.10271	−	1.90995i	−0.0351353	−	0.0608561i
$986$	18.7664	−	29.2082i	0.597643	−	0.930179i
$987$	−2.16664			−0.0689649
$988$	−21.9977	+	38.2378i	−0.699840	+	1.21651i
$989$	−63.4626			−2.01799
$990$	−7.71567	+	12.0088i	−0.245220	+	0.381664i
$991$	−12.4689	−	21.5969i	−0.396089	−	0.686047i	0.597150	−	0.802129i	$-0.296300\pi$
$991$	−12.4689	−	21.5969i	−0.396089	−	0.686047i	−0.993240	+	0.116083i	$0.962966\pi$
$992$	−8.84729	+	2.60316i	−0.280902	+	0.0826504i
$993$	15.2510	+	26.4154i	0.483975	+	0.838269i
$994$	20.0279	+	0.951808i	0.635247	+	0.0301895i
$995$			23.4522i			0.743486i
$996$	−3.72727	−	2.65292i	−0.118103	−	0.0840611i
$997$	6.61929	−	11.4649i	0.209635	−	0.363099i	−0.741965	−	0.670439i	$-0.766106\pi$
$997$	6.61929	−	11.4649i	0.209635	−	0.363099i	0.951600	+	0.307341i	$0.0994391\pi$
$998$	0.283455	+	0.0134709i	0.00897263	+	0.000426415i
$999$			7.52062i			0.237942i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.b.31.4	✓	40
4.3	odd	2	inner	380.2.n.b.31.11	yes	40
19.8	odd	6	inner	380.2.n.b.331.11	yes	40
76.27	even	6	inner	380.2.n.b.331.4	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.b.31.4	✓	40	1.1	even	1	trivial
380.2.n.b.31.11	yes	40	4.3	odd	2	inner
380.2.n.b.331.4	yes	40	76.27	even	6	inner
380.2.n.b.331.11	yes	40	19.8	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 380 = 2^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	380.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18980 - 0.764449i) q^{2} +(-1.38246 - 2.39450i) q^{3} +(0.831236 + 1.81908i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.185619 + 3.90579i) q^{6} -2.18272i q^{7} +(0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +O(q^{10})\)	\(q+(-1.18980 - 0.764449i) q^{2} +(-1.38246 - 2.39450i) q^{3} +(0.831236 + 1.81908i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.185619 + 3.90579i) q^{6} -2.18272i q^{7} +(0.401590 - 2.79977i) q^{8} +(-2.32241 + 4.02254i) q^{9} +(-0.0671334 + 1.41262i) q^{10} -2.17298i q^{11} +(3.20663 - 4.50520i) q^{12} +(-4.38226 - 2.53010i) q^{13} +(-1.66858 + 2.59700i) q^{14} +(-1.38246 + 2.39450i) q^{15} +(-2.61809 + 3.02417i) q^{16} +(1.50270 + 2.60275i) q^{17} +(5.83823 - 3.01064i) q^{18} +(-3.96739 - 1.80549i) q^{19} +(1.15975 - 1.62941i) q^{20} +(-5.22653 + 3.01754i) q^{21} +(-1.66113 + 2.58541i) q^{22} +(4.62252 + 2.66881i) q^{23} +(-7.25923 + 2.90898i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(3.27987 + 6.36032i) q^{26} +4.54783 q^{27} +(3.97055 - 1.81436i) q^{28} +(7.07391 + 4.08413i) q^{29} +(3.47532 - 1.79214i) q^{30} -1.63029 q^{31} +(5.42682 - 1.59675i) q^{32} +(-5.20320 + 3.00407i) q^{33} +(0.201763 - 4.24549i) q^{34} +(-1.89029 + 1.09136i) q^{35} +(-9.24779 - 0.880974i) q^{36} +1.65367i q^{37} +(3.34018 + 5.18104i) q^{38} +13.9911i q^{39} +(-2.62547 + 1.05210i) q^{40} +(3.52888 - 2.03740i) q^{41} +(8.52526 + 0.405155i) q^{42} +(-10.2968 + 5.94484i) q^{43} +(3.95282 - 1.80626i) q^{44} +4.64483 q^{45} +(-3.45969 - 6.70902i) q^{46} +(0.310910 + 0.179504i) q^{47} +(10.8608 + 2.08822i) q^{48} +2.23572 q^{49} +(1.25693 - 0.648170i) q^{50} +(4.15486 - 7.19643i) q^{51} +(0.959756 - 10.0748i) q^{52} +(-9.75968 - 5.63476i) q^{53} +(-5.41099 - 3.47658i) q^{54} +(-1.88186 + 1.08649i) q^{55} +(-6.11113 - 0.876560i) q^{56} +(1.16153 + 11.9959i) q^{57} +(-5.29442 - 10.2669i) q^{58} +(-2.15002 - 3.72394i) q^{59} +(-5.50493 - 0.524418i) q^{60} +(-4.18333 + 7.24574i) q^{61} +(1.93971 + 1.24627i) q^{62} +(8.78009 + 5.06919i) q^{63} +(-7.67745 - 2.24872i) q^{64} +5.06020i q^{65} +(8.48721 + 0.403346i) q^{66} +(4.10768 - 7.11471i) q^{67} +(-3.48552 + 4.89704i) q^{68} -14.7581i q^{69} +(3.08336 + 0.146534i) q^{70} +(-3.24775 - 5.62526i) q^{71} +(10.3295 + 8.11764i) q^{72} +(-2.49186 - 4.31602i) q^{73} +(1.26415 - 1.96754i) q^{74} +2.76493 q^{75} +(-0.0135042 - 8.71779i) q^{76} -4.74302 q^{77} +(10.6955 - 16.6466i) q^{78} +(-3.74126 - 6.48006i) q^{79} +(3.92805 + 0.755252i) q^{80} +(0.680033 + 1.17785i) q^{81} +(-5.75614 - 0.273555i) q^{82} -0.827326i q^{83} +(-9.83361 - 6.99918i) q^{84} +(1.50270 - 2.60275i) q^{85} +(16.7956 + 0.798194i) q^{86} -22.5846i q^{87} +(-6.08385 - 0.872647i) q^{88} +(-14.4063 - 8.31749i) q^{89} +(-5.52640 - 3.55073i) q^{90} +(-5.52251 + 9.56526i) q^{91} +(-1.01238 + 10.6271i) q^{92} +(2.25382 + 3.90372i) q^{93} +(-0.232698 - 0.451248i) q^{94} +(0.420092 + 4.33861i) q^{95} +(-11.3258 - 10.7871i) q^{96} +(12.9391 - 7.47039i) q^{97} +(-2.66005 - 1.70909i) q^{98} +(8.74090 + 5.04656i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9	\( 40 q + 3 q^{2} + q^{4} - 20 q^{5} - 5 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} - 18 q^{14} + 9 q^{16} - 12 q^{17} - 2 q^{20} + 12 q^{21} + 20 q^{24} - 20 q^{25} + 34 q^{26} + 12 q^{28} + 10 q^{30} - 12 q^{32} - 6 q^{33} - 27 q^{34} - 6 q^{36} + 12 q^{38} + 36 q^{41} - 21 q^{42} + 28 q^{44} + 44 q^{45} + 36 q^{48} - 60 q^{49} + 15 q^{52} - 66 q^{53} - 31 q^{54} + 28 q^{57} + 2 q^{58} + 3 q^{60} + 4 q^{61} - 57 q^{62} - 80 q^{64} + 18 q^{66} - 20 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} + 30 q^{76} + 12 q^{77} + 144 q^{78} + 9 q^{80} + 16 q^{81} - 41 q^{82} - 12 q^{85} + 18 q^{86} - 18 q^{89} + 39 q^{90} + 40 q^{92} - 8 q^{93} - 160 q^{96} - 18 q^{97} - 66 q^{98}+O(q^{100}) \) 40 * q + 3 * q^2 + q^4 - 20 * q^5 - 5 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 - 18 * q^14 + 9 * q^16 - 12 * q^17 - 2 * q^20 + 12 * q^21 + 20 * q^24 - 20 * q^25 + 34 * q^26 + 12 * q^28 + 10 * q^30 - 12 * q^32 - 6 * q^33 - 27 * q^34 - 6 * q^36 + 12 * q^38 + 36 * q^41 - 21 * q^42 + 28 * q^44 + 44 * q^45 + 36 * q^48 - 60 * q^49 + 15 * q^52 - 66 * q^53 - 31 * q^54 + 28 * q^57 + 2 * q^58 + 3 * q^60 + 4 * q^61 - 57 * q^62 - 80 * q^64 + 18 * q^66 - 20 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 + 30 * q^76 + 12 * q^77 + 144 * q^78 + 9 * q^80 + 16 * q^81 - 41 * q^82 - 12 * q^85 + 18 * q^86 - 18 * q^89 + 39 * q^90 + 40 * q^92 - 8 * q^93 - 160 * q^96 - 18 * q^97 - 66 * q^98

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