LMFDB - Embedded newform 380.2.k.c.267.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [380,2,Mod(267,380)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(380, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0]))

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

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

chi := DirichletCharacter("380.267");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 380 = 2^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	380.k (of order $4$, 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:	$52$
Relative dimension:	$26$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			267.8
Character	$\chi$	$=$	380.267
Dual form			380.2.k.c.343.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.830627 - 1.14458i) q^{2} +(-1.85040 - 1.85040i) q^{3} +(-0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 + 3.65493i) q^{6} +(1.96775 - 1.96775i) q^{7} +(2.69143 - 0.869611i) q^{8} +3.84798i q^{9} +O(q^{10})$	\(q+(-0.830627 - 1.14458i) q^{2} +(-1.85040 - 1.85040i) q^{3} +(-0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 + 3.65493i) q^{6} +(1.96775 - 1.96775i) q^{7} +(2.69143 - 0.869611i) q^{8} +3.84798i q^{9} +(1.25958 - 2.90060i) q^{10} -1.03788i q^{11} +(4.66589 - 2.37095i) q^{12} +(3.02834 - 3.02834i) q^{13} +(-3.88672 - 0.617778i) q^{14} +(1.45930 - 5.66660i) q^{15} +(-3.23091 - 2.35823i) q^{16} +(-1.50342 - 1.50342i) q^{17} +(4.40432 - 3.19624i) q^{18} +1.00000 q^{19} +(-4.36620 + 0.967629i) q^{20} -7.28228 q^{21} +(-1.18793 + 0.862088i) q^{22} +(2.06546 + 2.06546i) q^{23} +(-6.58935 - 3.37109i) q^{24} +(-2.41510 + 4.37805i) q^{25} +(-5.98160 - 0.950751i) q^{26} +(1.56911 - 1.56911i) q^{27} +(2.52132 + 4.96179i) q^{28} -2.61679i q^{29} +(-7.69800 + 3.03655i) q^{30} -6.46970i q^{31} +(-0.0154926 + 5.65683i) q^{32} +(-1.92049 + 1.92049i) q^{33} +(-0.472001 + 2.96957i) q^{34} +(6.02597 + 1.55185i) q^{35} +(-7.31669 - 2.38620i) q^{36} +(-5.69050 - 5.69050i) q^{37} +(-0.830627 - 1.14458i) q^{38} -11.2073 q^{39} +(4.73421 + 4.19372i) q^{40} +9.51266 q^{41} +(6.04886 + 8.33513i) q^{42} +(-7.42165 - 7.42165i) q^{43} +(1.97345 + 0.643605i) q^{44} +(-7.40929 + 4.37462i) q^{45} +(0.648453 - 4.07971i) q^{46} +(-1.72310 + 1.72310i) q^{47} +(1.61482 + 10.3422i) q^{48} -0.744112i q^{49} +(7.01706 - 0.872254i) q^{50} +5.56388i q^{51} +(3.88027 + 7.63613i) q^{52} +(6.31339 - 6.31339i) q^{53} +(-3.09931 - 0.492623i) q^{54} +(1.99843 - 1.17992i) q^{55} +(3.58489 - 7.00725i) q^{56} +(-1.85040 - 1.85040i) q^{57} +(-2.99512 + 2.17358i) q^{58} -12.7281 q^{59} +(9.86973 + 6.28872i) q^{60} -0.547956 q^{61} +(-7.40508 + 5.37391i) q^{62} +(7.57188 + 7.57188i) q^{63} +(6.48755 - 4.68099i) q^{64} +(9.27388 + 2.38827i) q^{65} +(3.79336 + 0.602939i) q^{66} +(9.32750 - 9.32750i) q^{67} +(3.79096 - 1.92636i) q^{68} -7.64387i q^{69} +(-3.22912 - 8.18620i) q^{70} -0.212626i q^{71} +(3.34625 + 10.3566i) q^{72} +(7.18693 - 7.18693i) q^{73} +(-1.78654 + 11.2399i) q^{74} +(12.5701 - 3.63224i) q^{75} +(-0.620117 + 1.90143i) q^{76} +(-2.04229 - 2.04229i) q^{77} +(9.30910 + 12.8276i) q^{78} +2.35125 q^{79} +(0.867673 - 8.90209i) q^{80} +5.73698 q^{81} +(-7.90148 - 10.8880i) q^{82} +(8.09918 + 8.09918i) q^{83} +(4.51587 - 13.8468i) q^{84} +(1.18566 - 4.60402i) q^{85} +(-2.33003 + 14.6593i) q^{86} +(-4.84212 + 4.84212i) q^{87} +(-0.902548 - 2.79337i) q^{88} +12.3109i q^{89} +(11.1614 + 4.84683i) q^{90} -11.9181i q^{91} +(-5.20817 + 2.64651i) q^{92} +(-11.9716 + 11.9716i) q^{93} +(3.40348 + 0.540969i) q^{94} +(1.13686 + 1.92550i) q^{95} +(10.4961 - 10.4388i) q^{96} +(-9.28193 - 9.28193i) q^{97} +(-0.851695 + 0.618080i) q^{98} +3.99373 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	$ 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) $ 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$21$	$77$	$191$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	−0.830627	−	1.14458i	−0.587342	−	0.809339i
$2$	−0.830627	−	1.14458i	−0.587342	−	0.809339i
$3$	−1.85040	−	1.85040i	−1.06833	−	1.06833i	−0.997487	−	0.0708431i	$-0.977431\pi$
$3$	−1.85040	−	1.85040i	−1.06833	−	1.06833i	−0.0708431	−	0.997487i	$-0.522569\pi$
$4$	−0.620117	+	1.90143i	−0.310059	+	0.950717i
$5$	1.13686	+	1.92550i	0.508419	+	0.861110i
$5$	1.13686	+	1.92550i	0.508419	+	0.861110i
$6$	−0.580936	+	3.65493i	−0.237166	+	1.49212i
$7$	1.96775	−	1.96775i	0.743741	−	0.743741i	−0.229555	−	0.973296i	$-0.573727\pi$
$7$	1.96775	−	1.96775i	0.743741	−	0.743741i	0.973296	+	0.229555i	$0.0737270\pi$
$8$	2.69143	−	0.869611i	0.951563	−	0.307454i
$9$			3.84798i			1.28266i
$10$	1.25958	−	2.90060i	0.398314	−	0.917249i
$11$		−	1.03788i		−	0.312931i	−0.987683	−	0.156466i	$-0.949990\pi$
$11$		−	1.03788i		−	0.312931i	0.987683	−	0.156466i	$-0.0500101\pi$
$12$	4.66589	−	2.37095i	1.34693	−	0.684435i
$13$	3.02834	−	3.02834i	0.839912	−	0.839912i	−0.148935	−	0.988847i	$-0.547585\pi$
$13$	3.02834	−	3.02834i	0.839912	−	0.839912i	0.988847	+	0.148935i	$0.0475846\pi$
$14$	−3.88672	−	0.617778i	−1.03877	−	0.165108i
$15$	1.45930	−	5.66660i	0.376790	−	1.46311i
$16$	−3.23091	−	2.35823i	−0.807727	−	0.589556i
$17$	−1.50342	−	1.50342i	−0.364634	−	0.364634i	0.500882	−	0.865516i	$-0.333009\pi$
$17$	−1.50342	−	1.50342i	−0.364634	−	0.364634i	−0.865516	+	0.500882i	$0.833009\pi$
$18$	4.40432	−	3.19624i	1.03811	−	0.753360i
$19$	1.00000			0.229416
$19$	1.00000			0.229416
$20$	−4.36620	+	0.967629i	−0.976312	+	0.216368i
$21$	−7.28228			−1.58912
$22$	−1.18793	+	0.862088i	−0.253268	+	0.183798i
$23$	2.06546	+	2.06546i	0.430678	+	0.430678i	0.888859	−	0.458181i	$-0.151499\pi$
$23$	2.06546	+	2.06546i	0.430678	+	0.430678i	−0.458181	+	0.888859i	$0.651499\pi$
$24$	−6.58935	−	3.37109i	−1.34505	−	0.688122i
$25$	−2.41510	+	4.37805i	−0.483020	+	0.875609i
$26$	−5.98160	−	0.950751i	−1.17309	−	0.186458i
$27$	1.56911	−	1.56911i	0.301975	−	0.301975i
$28$	2.52132	+	4.96179i	0.476484	+	0.937691i
$29$		−	2.61679i		−	0.485926i	−0.970036	−	0.242963i	$-0.921881\pi$
$29$		−	2.61679i		−	0.485926i	0.970036	−	0.242963i	$-0.0781193\pi$
$30$	−7.69800	+	3.03655i	−1.40546	+	0.554395i
$31$		−	6.46970i		−	1.16199i	−0.813906	−	0.580997i	$-0.802663\pi$
$31$		−	6.46970i		−	1.16199i	0.813906	−	0.580997i	$-0.197337\pi$
$32$	−0.0154926	+	5.65683i	−0.00273874	+	0.999996i
$33$	−1.92049	+	1.92049i	−0.334314	+	0.334314i
$34$	−0.472001	+	2.96957i	−0.0809475	+	0.509277i
$35$	6.02597	+	1.55185i	1.01857	+	0.262311i
$36$	−7.31669	−	2.38620i	−1.21945	−	0.397700i
$37$	−5.69050	−	5.69050i	−0.935512	−	0.935512i	0.0625306	−	0.998043i	$-0.480083\pi$
$37$	−5.69050	−	5.69050i	−0.935512	−	0.935512i	−0.998043	+	0.0625306i	$0.980083\pi$
$38$	−0.830627	−	1.14458i	−0.134746	−	0.185675i
$39$	−11.2073			−1.79461
$40$	4.73421	+	4.19372i	0.748544	+	0.663085i
$41$	9.51266			1.48563			0.742814	−	0.669498i	$-0.233491\pi$
$41$	9.51266			1.48563			0.742814	+	0.669498i	$0.233491\pi$
$42$	6.04886	+	8.33513i	0.933359	+	1.28614i
$43$	−7.42165	−	7.42165i	−1.13179	−	1.13179i	−0.989879	−	0.141911i	$-0.954675\pi$
$43$	−7.42165	−	7.42165i	−1.13179	−	1.13179i	−0.141911	−	0.989879i	$-0.545325\pi$
$44$	1.97345	+	0.643605i	0.297509	+	0.0970271i
$45$	−7.40929	+	4.37462i	−1.10451	+	0.652129i
$46$	0.648453	−	4.07971i	0.0956092	−	0.601520i
$47$	−1.72310	+	1.72310i	−0.251340	+	0.251340i	−0.821520	−	0.570180i	$-0.806874\pi$
$47$	−1.72310	+	1.72310i	−0.251340	+	0.251340i	0.570180	+	0.821520i	$0.306874\pi$
$48$	1.61482	+	10.3422i	0.233079	+	1.49276i
$49$		−	0.744112i		−	0.106302i
$50$	7.01706	−	0.872254i	0.992363	−	0.123355i
$51$			5.56388i			0.779099i
$52$	3.88027	+	7.63613i	0.538097	+	1.05894i
$53$	6.31339	−	6.31339i	0.867210	−	0.867210i	−0.124952	−	0.992163i	$-0.539878\pi$
$53$	6.31339	−	6.31339i	0.867210	−	0.867210i	0.992163	+	0.124952i	$0.0398778\pi$
$54$	−3.09931	−	0.492623i	−0.421763	−	0.0670375i
$55$	1.99843	−	1.17992i	0.269468	−	0.159100i
$56$	3.58489	−	7.00725i	0.479051	−	0.936383i
$57$	−1.85040	−	1.85040i	−0.245092	−	0.245092i
$58$	−2.99512	+	2.17358i	−0.393279	+	0.285405i
$59$	−12.7281			−1.65706			−0.828531	−	0.559943i	$-0.810823\pi$
$59$	−12.7281			−1.65706			−0.828531	+	0.559943i	$0.810823\pi$
$60$	9.86973	+	6.28872i	1.27418	+	0.811871i
$61$	−0.547956			−0.0701585			−0.0350793	−	0.999385i	$-0.511168\pi$
$61$	−0.547956			−0.0701585			−0.0350793	+	0.999385i	$0.511168\pi$
$62$	−7.40508	+	5.37391i	−0.940446	+	0.682487i
$63$	7.57188	+	7.57188i	0.953967	+	0.953967i
$64$	6.48755	−	4.68099i	0.810944	−	0.585123i
$65$	9.27388	+	2.38827i	1.15028	+	0.296229i
$66$	3.79336	+	0.602939i	0.466930	+	0.0742167i
$67$	9.32750	−	9.32750i	1.13954	−	1.13954i	0.151002	−	0.988533i	$-0.451750\pi$
$67$	9.32750	−	9.32750i	1.13954	−	1.13954i	0.988533	−	0.151002i	$-0.0482501\pi$
$68$	3.79096	−	1.92636i	0.459721	−	0.233606i
$69$		−	7.64387i		−	0.920214i
$70$	−3.22912	−	8.18620i	−0.385954	−	0.978438i
$71$		−	0.212626i		−	0.0252340i	−0.999920	−	0.0126170i	$-0.995984\pi$
$71$		−	0.212626i		−	0.0252340i	0.999920	−	0.0126170i	$-0.00401623\pi$
$72$	3.34625	+	10.3566i	0.394359	+	1.22053i
$73$	7.18693	−	7.18693i	0.841166	−	0.841166i	−0.147845	−	0.989011i	$-0.547234\pi$
$73$	7.18693	−	7.18693i	0.841166	−	0.841166i	0.989011	+	0.147845i	$0.0472335\pi$
$74$	−1.78654	+	11.2399i	−0.207681	+	1.30661i
$75$	12.5701	−	3.63224i	1.45147	−	0.419415i
$76$	−0.620117	+	1.90143i	−0.0711323	+	0.218110i
$77$	−2.04229	−	2.04229i	−0.232740	−	0.232740i
$78$	9.30910	+	12.8276i	1.05405	+	1.45244i
$79$	2.35125			0.264536			0.132268	−	0.991214i	$-0.457774\pi$
$79$	2.35125			0.264536			0.132268	+	0.991214i	$0.457774\pi$
$80$	0.867673	−	8.90209i	0.0970088	−	0.995284i
$81$	5.73698			0.637442
$82$	−7.90148	−	10.8880i	−0.872572	−	1.20238i
$83$	8.09918	+	8.09918i	0.889000	+	0.889000i	0.994427	−	0.105427i	$-0.0336209\pi$
$83$	8.09918	+	8.09918i	0.889000	+	0.889000i	−0.105427	+	0.994427i	$0.533621\pi$
$84$	4.51587	−	13.8468i	0.492721	−	1.51081i
$85$	1.18566	−	4.60402i	0.128603	−	0.499376i
$86$	−2.33003	+	14.6593i	−0.251254	+	1.58075i
$87$	−4.84212	+	4.84212i	−0.519129	+	0.519129i
$88$	−0.902548	−	2.79337i	−0.0962120	−	0.297774i
$89$			12.3109i			1.30495i	0.757809	+	0.652477i	$0.226270\pi$
$89$			12.3109i			1.30495i	−0.757809	+	0.652477i	$0.773730\pi$
$90$	11.1614	+	4.84683i	1.17652	+	0.510901i
$91$		−	11.9181i		−	1.24935i
$92$	−5.20817	+	2.64651i	−0.542989	+	0.275918i
$93$	−11.9716	+	11.9716i	−1.24139	+	1.24139i
$94$	3.40348	+	0.540969i	0.351042	+	0.0557967i
$95$	1.13686	+	1.92550i	0.116639	+	0.197552i
$96$	10.4961	−	10.4388i	1.07125	−	1.06540i
$97$	−9.28193	−	9.28193i	−0.942438	−	0.942438i	0.0559936	−	0.998431i	$-0.482167\pi$
$97$	−9.28193	−	9.28193i	−0.942438	−	0.942438i	−0.998431	+	0.0559936i	$0.982167\pi$
$98$	−0.851695	+	0.618080i	−0.0860342	+	0.0624355i
$99$	3.99373			0.401385
$100$	−6.82693	−	7.30706i	−0.682693	−	0.730706i
$101$	−5.10423			−0.507889			−0.253945	−	0.967219i	$-0.581728\pi$
$101$	−5.10423			−0.507889			−0.253945	+	0.967219i	$0.581728\pi$
$102$	6.36829	−	4.62151i	0.630555	−	0.457597i
$103$	12.3348	+	12.3348i	1.21539	+	1.21539i	0.969230	+	0.246156i	$0.0791677\pi$
$103$	12.3348	+	12.3348i	1.21539	+	1.21539i	0.246156	+	0.969230i	$0.420832\pi$
$104$	5.51709	−	10.7840i	0.540995	−	1.05746i
$105$	−8.27893	−	14.0220i	−0.807940	−	1.36841i
$106$	−12.4702	−	1.98209i	−1.21122	−	0.192518i
$107$	−9.93034	+	9.93034i	−0.960003	+	0.960003i	−0.999230	−	0.0392276i	$-0.987510\pi$
$107$	−9.93034	+	9.93034i	−0.960003	+	0.960003i	0.0392276	+	0.999230i	$0.487510\pi$
$108$	2.01053	+	3.95659i	0.193463	+	0.380723i
$109$			11.4759i			1.09919i	0.835430	+	0.549597i	$0.185219\pi$
$109$			11.4759i			1.09919i	−0.835430	+	0.549597i	$0.814781\pi$
$110$	−3.01046	−	1.30729i	−0.287036	−	0.124645i
$111$			21.0594i			1.99887i
$112$	−10.9980	+	1.71723i	−1.03922	+	0.162263i
$113$	3.15808	−	3.15808i	0.297087	−	0.297087i	−0.542785	−	0.839872i	$-0.682630\pi$
$113$	3.15808	−	3.15808i	0.297087	−	0.297087i	0.839872	+	0.542785i	$0.182630\pi$
$114$	−0.580936	+	3.65493i	−0.0544096	+	0.342315i
$115$	−1.62891	+	6.32519i	−0.151896	+	0.589827i
$116$	4.97566	+	1.62272i	0.461978	+	0.150666i
$117$	11.6530	+	11.6530i	1.07732	+	1.07732i
$118$	10.5723	+	14.5683i	0.973262	+	1.34113i
$119$	−5.91673			−0.542386
$120$	−1.00013	−	16.5203i	−0.0912990	−	1.50809i
$121$	9.92281			0.902074
$122$	0.455147	+	0.627178i	0.0412071	+	0.0567820i
$123$	−17.6023	−	17.6023i	−1.58714	−	1.58714i
$124$	12.3017	+	4.01198i	1.10473	+	0.360286i
$125$	−11.1756	+	0.326951i	−0.999572	+	0.0292434i
$126$	2.37720	−	14.9560i	0.211778	−	1.33239i
$127$	−1.96834	+	1.96834i	−0.174662	+	0.174662i	−0.789024	−	0.614362i	$-0.789413\pi$
$127$	−1.96834	+	1.96834i	−0.174662	+	0.174662i	0.614362	+	0.789024i	$0.289413\pi$
$128$	−10.7465	−	3.53736i	−0.949865	−	0.312661i
$129$			27.4661i			2.41825i
$130$	−4.96957	−	12.5984i	−0.435860	−	1.10496i
$131$			12.7341i			1.11258i	0.830987	+	0.556292i	$0.187776\pi$
$131$			12.7341i			1.11258i	−0.830987	+	0.556292i	$0.812224\pi$
$132$	−2.46076	−	4.84261i	−0.214181	−	0.421495i
$133$	1.96775	−	1.96775i	0.170626	−	0.170626i
$134$	−18.4237	−	2.92838i	−1.59157	−	0.252973i
$135$	4.80517	+	1.23746i	0.413563	+	0.106504i
$136$	−5.35374	−	2.73896i	−0.459080	−	0.234864i
$137$	9.29462	+	9.29462i	0.794093	+	0.794093i	0.982157	−	0.188064i	$-0.0602212\pi$
$137$	9.29462	+	9.29462i	0.794093	+	0.794093i	−0.188064	+	0.982157i	$0.560221\pi$
$138$	−8.74901	+	6.34921i	−0.744765	+	0.540480i
$139$	1.49578			0.126871			0.0634353	−	0.997986i	$-0.479794\pi$
$139$	1.49578			0.126871			0.0634353	+	0.997986i	$0.479794\pi$
$140$	−6.68755	+	10.4957i	−0.565201	+	0.887045i
$141$	6.37687			0.537029
$142$	−0.243367	+	0.176613i	−0.0204229	+	0.0148210i
$143$	−3.14305	−	3.14305i	−0.262835	−	0.262835i
$144$	9.07441	−	12.4325i	0.756201	−	1.03604i
$145$	5.03863	−	2.97492i	0.418435	−	0.247054i
$146$	−14.1957	−	2.25634i	−1.17484	−	0.186736i
$147$	−1.37691	+	1.37691i	−0.113565	+	0.113565i
$148$	14.3489	−	7.29134i	1.17947	−	0.599344i
$149$		−	11.6245i		−	0.952314i	−0.879360	−	0.476157i	$-0.842029\pi$
$149$		−	11.6245i		−	0.952314i	0.879360	−	0.476157i	$-0.157971\pi$
$150$	−14.5984	−	11.3704i	−1.19196	−	0.928387i
$151$			7.58726i			0.617442i	0.951153	+	0.308721i	$0.0999010\pi$
$151$			7.58726i			0.617442i	−0.951153	+	0.308721i	$0.900099\pi$
$152$	2.69143	−	0.869611i	0.218304	−	0.0705347i
$153$	5.78514	−	5.78514i	0.467701	−	0.467701i
$154$	−0.641177	+	4.03393i	−0.0516675	+	0.325064i
$155$	12.4574	−	7.35515i	1.00060	−	0.590779i
$156$	6.94985	−	21.3100i	0.556433	−	1.70616i
$157$	−7.05006	−	7.05006i	−0.562656	−	0.562656i	0.367405	−	0.930061i	$-0.380246\pi$
$157$	−7.05006	−	7.05006i	−0.562656	−	0.562656i	−0.930061	+	0.367405i	$0.880246\pi$
$158$	−1.95301	−	2.69119i	−0.155373	−	0.214099i
$159$	−23.3646			−1.85293
$160$	−10.9098	+	6.40119i	−0.862499	+	0.506059i
$161$	8.12864			0.640627
$162$	−4.76529	−	6.56642i	−0.374397	−	0.515907i
$163$	−8.64721	−	8.64721i	−0.677302	−	0.677302i	0.282087	−	0.959389i	$-0.408973\pi$
$163$	−8.64721	−	8.64721i	−0.677302	−	0.677302i	−0.959389	+	0.282087i	$0.908973\pi$
$164$	−5.89897	+	18.0877i	−0.460632	+	1.41241i
$165$	−5.88123	−	1.51458i	−0.457853	−	0.117910i
$166$	2.54274	−	15.9975i	0.197355	−	1.24165i
$167$	4.32665	−	4.32665i	0.334806	−	0.334806i	−0.519602	−	0.854408i	$-0.673920\pi$
$167$	4.32665	−	4.32665i	0.334806	−	0.334806i	0.854408	+	0.519602i	$0.173920\pi$
$168$	−19.5997	+	6.33274i	−1.51215	+	0.488582i
$169$		−	5.34174i		−	0.410903i
$170$	−6.25450	+	2.46715i	−0.479698	+	0.189221i
$171$			3.84798i			0.294263i
$172$	18.7141	−	9.50949i	1.42693	−	0.725091i
$173$	−6.78296	+	6.78296i	−0.515699	+	0.515699i	−0.916267	−	0.400568i	$-0.868813\pi$
$173$	−6.78296	+	6.78296i	−0.515699	+	0.515699i	0.400568	+	0.916267i	$0.368813\pi$
$174$	9.56417	+	1.52019i	0.725058	+	0.115245i
$175$	3.86260	+	13.3672i	0.291985	+	1.01047i
$176$	−2.44755	+	3.35328i	−0.184491	+	0.252763i
$177$	23.5522	+	23.5522i	1.77029	+	1.77029i
$178$	14.0908	−	10.2258i	1.05615	−	0.766454i
$179$	21.2426			1.58775			0.793875	−	0.608081i	$-0.208061\pi$
$179$	21.2426			1.58775			0.793875	+	0.608081i	$0.208061\pi$
$180$	−3.72342	−	16.8011i	−0.277527	−	1.25228i
$181$	7.04939			0.523977			0.261988	−	0.965071i	$-0.415622\pi$
$181$	7.04939			0.523977			0.261988	+	0.965071i	$0.415622\pi$
$182$	−13.6412	+	9.89947i	−1.01115	+	0.733798i
$183$	1.01394	+	1.01394i	0.0749525	+	0.0749525i
$184$	7.35519	+	3.76289i	0.542231	+	0.277404i
$185$	4.48776	−	17.4264i	0.329946	−	1.28121i
$186$	23.6463	+	3.75848i	1.73383	+	0.275585i
$187$	−1.56037	+	1.56037i	−0.114105	+	0.114105i
$188$	−2.20784	−	4.34489i	−0.161023	−	0.316884i
$189$		−	6.17524i		−	0.449182i
$190$	1.25958	−	2.90060i	0.0913794	−	0.210431i
$191$			19.1334i			1.38445i	0.721684	+	0.692223i	$0.243368\pi$
$191$			19.1334i			1.38445i	−0.721684	+	0.692223i	$0.756632\pi$
$192$	−20.6663	−	3.34288i	−1.49146	−	0.241252i
$193$	−11.6404	+	11.6404i	−0.837896	+	0.837896i	−0.988582	−	0.150686i	$-0.951852\pi$
$193$	−11.6404	+	11.6404i	−0.837896	+	0.837896i	0.150686	+	0.988582i	$0.451852\pi$
$194$	−2.91407	+	18.3337i	−0.209218	+	1.31628i
$195$	−12.7411	−	21.5797i	−0.912412	−	1.54535i
$196$	1.41488	+	0.461437i	0.101063	+	0.0329598i
$197$	2.90195	+	2.90195i	0.206755	+	0.206755i	0.802887	−	0.596132i	$-0.203296\pi$
$197$	2.90195	+	2.90195i	0.206755	+	0.206755i	−0.596132	+	0.802887i	$0.703296\pi$
$198$	−3.31730	−	4.57113i	−0.235750	−	0.324856i
$199$	10.8066			0.766058			0.383029	−	0.923736i	$-0.374881\pi$
$199$	10.8066			0.766058			0.383029	+	0.923736i	$0.374881\pi$
$200$	−2.69287	+	13.8834i	−0.190415	+	0.981704i
$201$	−34.5193			−2.43480
$202$	4.23971	+	5.84218i	0.298305	+	0.411055i
$203$	−5.14920	−	5.14920i	−0.361403	−	0.361403i
$204$	−10.5793	−	3.45026i	−0.740703	−	0.241566i
$205$	10.8146	+	18.3166i	0.755322	+	1.27929i
$206$	3.87253	−	24.3638i	0.269812	−	1.69751i
$207$	−7.94786	+	7.94786i	−0.552414	+	0.552414i
$208$	−16.9258	+	2.64279i	−1.17359	+	0.183244i
$209$		−	1.03788i		−	0.0717914i
$210$	−9.17260	+	21.1229i	−0.632969	+	1.45762i
$211$		−	12.5073i		−	0.861037i	−0.902582	−	0.430519i	$-0.858331\pi$
$211$		−	12.5073i		−	0.861037i	0.902582	−	0.430519i	$-0.141669\pi$
$212$	8.08945	+	15.9195i	0.555586	+	1.09336i
$213$	−0.393443	+	0.393443i	−0.0269583	+	0.0269583i
$214$	19.6145	+	3.11764i	1.34082	+	0.213118i
$215$	5.85301	−	22.7278i	0.399172	−	1.55002i
$216$	2.85863	−	5.58765i	0.194505	−	0.380192i
$217$	−12.7308	−	12.7308i	−0.864222	−	0.864222i
$218$	13.1351	−	9.53221i	0.889620	−	0.645603i
$219$	−26.5974			−1.79729
$220$	1.00428	+	4.53157i	0.0677085	+	0.305519i
$221$	−9.10576			−0.612520
$222$	24.1042	−	17.4925i	1.61777	−	1.17402i
$223$	−10.6640	−	10.6640i	−0.714115	−	0.714115i	0.253278	−	0.967393i	$-0.418491\pi$
$223$	−10.6640	−	10.6640i	−0.714115	−	0.714115i	−0.967393	+	0.253278i	$0.918491\pi$
$224$	11.1008	+	11.1617i	0.741701	+	0.745775i
$225$	−16.8466	−	9.29326i	−1.12311	−	0.619551i
$226$	−6.23785	−	0.991482i	−0.414936	−	0.0659524i
$227$	−20.0388	+	20.0388i	−1.33002	+	1.33002i	−0.424676	+	0.905345i	$0.639612\pi$
$227$	−20.0388	+	20.0388i	−1.33002	+	1.33002i	−0.905345	+	0.424676i	$0.860388\pi$
$228$	4.66589	−	2.37095i	0.309006	−	0.157020i
$229$			4.26484i			0.281828i	0.990022	+	0.140914i	$0.0450042\pi$
$229$			4.26484i			0.281828i	−0.990022	+	0.140914i	$0.954996\pi$
$230$	8.59268	−	3.38946i	0.566585	−	0.223494i
$231$			7.55810i			0.497287i
$232$	−2.27559	−	7.04290i	−0.149400	−	0.462389i
$233$	5.66793	−	5.66793i	0.371318	−	0.371318i	−0.496639	−	0.867957i	$-0.665433\pi$
$233$	5.66793	−	5.66793i	0.371318	−	0.371318i	0.867957	+	0.496639i	$0.165433\pi$
$234$	3.65847	−	23.0171i	0.239162	−	1.50467i
$235$	−5.27676	−	1.35891i	−0.344218	−	0.0886454i
$236$	7.89294	−	24.2017i	0.513787	−	1.57540i
$237$	−4.35076	−	4.35076i	−0.282612	−	0.282612i
$238$	4.91460	+	6.77216i	0.318566	+	0.438974i
$239$	12.9188			0.835649			0.417825	−	0.908528i	$-0.362793\pi$
$239$	12.9188			0.835649			0.417825	+	0.908528i	$0.362793\pi$
$240$	−18.0780	+	14.8669i	−1.16693	+	0.959654i
$241$	11.4927			0.740311			0.370155	−	0.928970i	$-0.379304\pi$
$241$	11.4927			0.740311			0.370155	+	0.928970i	$0.379304\pi$
$242$	−8.24216	−	11.3574i	−0.529826	−	0.730083i
$243$	−15.3231	−	15.3231i	−0.982974	−	0.982974i
$244$	0.339797	−	1.04190i	0.0217533	−	0.0667009i
$245$	1.43279	−	0.845951i	0.0915375	−	0.0540459i
$246$	−5.52625	+	34.7681i	−0.352341	+	2.21673i
$247$	3.02834	−	3.02834i	0.192689	−	0.192689i
$248$	−5.62612	−	17.4127i	−0.357259	−	1.10571i
$249$		−	29.9735i		−	1.89949i
$250$	9.65694	+	12.5197i	0.610759	+	0.791817i
$251$		−	0.449035i		−	0.0283428i	−0.999900	−	0.0141714i	$-0.995489\pi$
$251$		−	0.449035i		−	0.0283428i	0.999900	−	0.0141714i	$-0.00451105\pi$
$252$	−19.0929	+	9.70198i	−1.20274	+	0.611168i
$253$	2.14369	−	2.14369i	0.134773	−	0.134773i
$254$	3.88787	+	0.617962i	0.243947	+	0.0387744i
$255$	−10.7132	+	6.32535i	−0.670889	+	0.396109i
$256$	4.87754	+	15.2384i	0.304847	+	0.952401i
$257$	−14.1398	−	14.1398i	−0.882018	−	0.882018i	0.111722	−	0.993740i	$-0.464363\pi$
$257$	−14.1398	−	14.1398i	−0.882018	−	0.882018i	−0.993740	+	0.111722i	$0.964363\pi$
$258$	31.4371	−	22.8141i	1.95719	−	1.42034i
$259$	−22.3950			−1.39156
$260$	−10.2920	+	16.1527i	−0.638285	+	1.00175i
$261$	10.0694			0.623278
$262$	14.5752	−	10.5773i	0.900457	−	0.653467i
$263$	13.5610	+	13.5610i	0.836207	+	0.836207i	0.988357	−	0.152150i	$-0.0486198\pi$
$263$	13.5610	+	13.5610i	0.836207	+	0.836207i	−0.152150	+	0.988357i	$0.548620\pi$
$264$	−3.49878	+	6.83893i	−0.215335	+	0.420907i
$265$	19.3339	+	4.97899i	1.18767	+	0.305857i
$266$	−3.88672	−	0.617778i	−0.238310	−	0.0378784i
$267$	22.7801	−	22.7801i	1.39412	−	1.39412i
$268$	11.9515	+	23.5198i	0.730054	+	1.43670i
$269$		−	18.6745i		−	1.13861i	−0.822128	−	0.569303i	$-0.807213\pi$
$269$		−	18.6745i		−	1.13861i	0.822128	−	0.569303i	$-0.192787\pi$
$270$	−2.57494	−	6.52776i	−0.156706	−	0.397267i
$271$			17.2153i			1.04575i	0.852408	+	0.522877i	$0.175141\pi$
$271$			17.2153i			1.04575i	−0.852408	+	0.522877i	$0.824859\pi$
$272$	1.31201	+	8.40283i	0.0795524	+	0.509497i
$273$	−22.0532	+	22.0532i	−1.33472	+	1.33472i
$274$	2.91805	−	18.3588i	0.176286	−	1.10909i
$275$	4.54387	+	2.50657i	0.274006	+	0.151152i
$276$	14.5343	+	4.74010i	0.874864	+	0.285320i
$277$	12.8068	+	12.8068i	0.769487	+	0.769487i	0.978016	−	0.208529i	$-0.0668675\pi$
$277$	12.8068	+	12.8068i	0.769487	+	0.769487i	−0.208529	+	0.978016i	$0.566868\pi$
$278$	−1.24244	−	1.71204i	−0.0745164	−	0.102681i
$279$	24.8953			1.49044
$280$	17.5680	−	1.06356i	1.04989	−	0.0635597i
$281$	−17.6380			−1.05219			−0.526096	−	0.850425i	$-0.676345\pi$
$281$	−17.6380			−1.05219			−0.526096	+	0.850425i	$0.676345\pi$
$282$	−5.29680	−	7.29882i	−0.315420	−	0.434638i
$283$	11.1509	+	11.1509i	0.662854	+	0.662854i	0.956052	−	0.293198i	$-0.0947195\pi$
$283$	11.1509	+	11.1509i	0.662854	+	0.662854i	−0.293198	+	0.956052i	$0.594719\pi$
$284$	0.404294	+	0.131853i	0.0239904	+	0.00782403i
$285$	1.45930	−	5.66660i	0.0864416	−	0.335660i
$286$	−0.986762	+	6.20816i	−0.0583485	+	0.367096i
$287$	18.7186	−	18.7186i	1.10492	−	1.10492i
$288$	−21.7674	−	0.0596154i	−1.28266	−	0.00351287i
$289$		−	12.4794i		−	0.734085i
$290$	−7.59025	−	3.29605i	−0.445715	−	0.193551i
$291$			34.3506i			2.01367i
$292$	9.20873	+	18.1222i	0.538900	+	1.06052i
$293$	−9.77537	+	9.77537i	−0.571083	+	0.571083i	−0.932431	−	0.361348i	$-0.882317\pi$
$293$	−9.77537	+	9.77537i	−0.571083	+	0.571083i	0.361348	+	0.932431i	$0.382317\pi$
$294$	2.71968	+	0.432281i	0.158615	+	0.0252112i
$295$	−14.4701	−	24.5080i	−0.842482	−	1.42691i
$296$	−20.2641	−	10.3670i	−1.17783	−	0.602572i
$297$	−1.62854	−	1.62854i	−0.0944975	−	0.0944975i
$298$	−13.3051	+	9.65560i	−0.770745	+	0.559334i
$299$	12.5099			0.723464
$300$	−0.888439	+	26.1536i	−0.0512940	+	1.50998i
$301$	−29.2080			−1.68352
$302$	8.68421	−	6.30218i	0.499720	−	0.362650i
$303$	9.44488	+	9.44488i	0.542594	+	0.542594i
$304$	−3.23091	−	2.35823i	−0.185305	−	0.135254i
$305$	−0.622949	−	1.05509i	−0.0356699	−	0.0604142i
$306$	−11.4268	−	1.81625i	−0.653229	−	0.103828i
$307$	4.12272	−	4.12272i	0.235296	−	0.235296i	−0.579603	−	0.814899i	$-0.696792\pi$
$307$	4.12272	−	4.12272i	0.235296	−	0.235296i	0.814899	+	0.579603i	$0.196792\pi$
$308$	5.14973	−	2.61682i	0.293433	−	0.149107i
$309$		−	45.6488i		−	2.59687i
$310$	−18.7660	−	8.14910i	−1.06584	−	0.462838i
$311$			1.78593i			0.101271i	0.998717	+	0.0506355i	$0.0161247\pi$
$311$			1.78593i			0.101271i	−0.998717	+	0.0506355i	$0.983875\pi$
$312$	−30.1637	+	9.74600i	−1.70768	+	0.551759i
$313$	−17.3651	+	17.3651i	−0.981531	+	0.981531i	−0.999833	−	0.0183017i	$-0.994174\pi$
$313$	−17.3651	+	17.3651i	−0.981531	+	0.981531i	0.0183017	+	0.999833i	$0.494174\pi$
$314$	−2.21337	+	13.9253i	−0.124908	+	0.785850i
$315$	−5.97149	+	23.1878i	−0.336455	+	1.30649i
$316$	−1.45805	+	4.47075i	−0.0820217	+	0.251499i
$317$	18.8911	+	18.8911i	1.06103	+	1.06103i	0.998012	+	0.0630180i	$0.0200725\pi$
$317$	18.8911	+	18.8911i	1.06103	+	1.06103i	0.0630180	+	0.998012i	$0.479927\pi$
$318$	19.4073	+	26.7426i	1.08831	+	1.49965i
$319$	−2.71591			−0.152061
$320$	16.3887	+	7.17016i	0.916155	+	0.400824i
$321$	36.7503			2.05120
$322$	−6.75187	−	9.30386i	−0.376267	−	0.518484i
$323$	−1.50342	−	1.50342i	−0.0836527	−	0.0836527i
$324$	−3.55760	+	10.9085i	−0.197645	+	0.606028i
$325$	5.94448	+	20.5720i	0.329740	+	1.14113i
$326$	−2.71480	+	17.0800i	−0.150359	+	0.945975i
$327$	21.2351	−	21.2351i	1.17430	−	1.17430i
$328$	25.6026	−	8.27231i	1.41367	−	0.456762i
$329$			6.78128i			0.373864i
$330$	3.15156	+	7.98957i	0.173488	+	0.439811i
$331$			10.4089i			0.572123i	0.958211	+	0.286062i	$0.0923462\pi$
$331$			10.4089i			0.572123i	−0.958211	+	0.286062i	$0.907654\pi$
$332$	−20.4225	+	10.3776i	−1.12083	+	0.569546i
$333$	21.8969	−	21.8969i	1.19995	−	1.19995i
$334$	−8.54602	−	1.35836i	−0.467618	−	0.0743259i
$335$	28.5642	+	7.35604i	1.56063	+	0.401904i
$336$	23.5284	+	17.1732i	1.28358	+	0.936878i
$337$	0.815754	+	0.815754i	0.0444370	+	0.0444370i	0.728976	−	0.684539i	$-0.239997\pi$
$337$	0.815754	+	0.815754i	0.0444370	+	0.0444370i	−0.684539	+	0.728976i	$0.739997\pi$
$338$	−6.11404	+	4.43699i	−0.332560	+	0.241341i
$339$	−11.6874			−0.634774
$340$	8.01900	+	5.10949i	0.434891	+	0.277101i
$341$	−6.71475			−0.363624
$342$	4.40432	−	3.19624i	0.238158	−	0.172833i
$343$	12.3100	+	12.3100i	0.664680	+	0.664680i
$344$	−26.4288	−	13.5209i	−1.42494	−	0.728997i
$345$	14.7183	−	8.69001i	0.792405	−	0.467854i
$346$	13.3977	+	2.12952i	0.720267	+	0.114484i
$347$	1.21322	−	1.21322i	0.0651292	−	0.0651292i	−0.673792	−	0.738921i	$-0.735336\pi$
$347$	1.21322	−	1.21322i	0.0651292	−	0.0651292i	0.738921	+	0.673792i	$0.235336\pi$
$348$	−6.20429	−	12.2097i	−0.332585	−	0.654506i
$349$			17.7577i			0.950546i	0.879838	+	0.475273i	$0.157651\pi$
$349$			17.7577i			0.950546i	−0.879838	+	0.475273i	$0.842349\pi$
$350$	12.0915	−	15.5242i	0.646316	−	0.829805i
$351$		−	9.50360i		−	0.507265i
$352$	5.87109	+	0.0160795i	0.312930	+	0.000857038i
$353$	−11.7628	+	11.7628i	−0.626071	+	0.626071i	−0.947077	−	0.321006i	$-0.895979\pi$
$353$	−11.7628	+	11.7628i	−0.626071	+	0.626071i	0.321006	+	0.947077i	$0.395979\pi$
$354$	7.39423	−	46.5204i	0.392999	−	2.47253i
$355$	0.409411	−	0.241726i	0.0217293	−	0.0128295i
$356$	−23.4084	−	7.63421i	−1.24064	−	0.404612i
$357$	10.9483	+	10.9483i	0.579448	+	0.579448i
$358$	−17.6447	−	24.3139i	−0.932552	−	1.28503i
$359$	18.0679			0.953588			0.476794	−	0.879015i	$-0.341799\pi$
$359$	18.0679			0.953588			0.476794	+	0.879015i	$0.341799\pi$
$360$	−16.1373	+	18.2172i	−0.850513	+	0.960128i
$361$	1.00000			0.0526316
$362$	−5.85541	−	8.06858i	−0.307754	−	0.424075i
$363$	−18.3612	−	18.3612i	−0.963713	−	0.963713i
$364$	22.6614	+	7.39060i	1.18778	+	0.387373i
$365$	22.0090	+	5.66790i	1.15200	+	0.296671i
$366$	0.318327	−	2.00274i	0.0166392	−	0.104685i
$367$	−6.35282	+	6.35282i	−0.331615	+	0.331615i	−0.853199	−	0.521585i	$-0.825341\pi$
$367$	−6.35282	+	6.35282i	−0.331615	+	0.331615i	0.521585	+	0.853199i	$0.325341\pi$
$368$	−1.80249	−	11.5441i	−0.0939615	−	0.601780i
$369$			36.6046i			1.90556i
$370$	−23.6735	+	9.33822i	−1.23073	+	0.485471i
$371$		−	24.8464i		−	1.28996i
$372$	−15.3394	−	30.1869i	−0.795309	−	1.56512i
$373$	16.2918	−	16.2918i	0.843559	−	0.843559i	−0.145760	−	0.989320i	$-0.546563\pi$
$373$	16.2918	−	16.2918i	0.843559	−	0.843559i	0.989320	+	0.145760i	$0.0465629\pi$
$374$	3.08204	+	0.489879i	0.159369	+	0.0253310i
$375$	21.2843	+	20.0743i	1.09912	+	1.03663i
$376$	−3.13918	+	6.13603i	−0.161891	+	0.316442i
$377$	−7.92454	−	7.92454i	−0.408135	−	0.408135i
$378$	−7.06804	+	5.12932i	−0.363541	+	0.263824i
$379$	−13.5325			−0.695117			−0.347558	−	0.937658i	$-0.612989\pi$
$379$	−13.5325			−0.695117			−0.347558	+	0.937658i	$0.612989\pi$
$380$	−4.36620	+	0.967629i	−0.223981	+	0.0496383i
$381$	7.28444			0.373193
$382$	21.8997	−	15.8927i	1.12049	−	0.813143i
$383$	−19.1908	−	19.1908i	−0.980603	−	0.980603i	0.0192125	−	0.999815i	$-0.493884\pi$
$383$	−19.1908	−	19.1908i	−0.980603	−	0.980603i	−0.999815	+	0.0192125i	$0.993884\pi$
$384$	13.3398	+	26.4309i	0.680744	+	1.34880i
$385$	1.61063	−	6.25421i	0.0820852	−	0.318744i
$386$	22.9922	+	3.65452i	1.17027	+	0.186010i
$387$	28.5584	−	28.5584i	1.45170	−	1.45170i
$388$	23.4049	−	11.8931i	1.18820	−	0.603781i
$389$			9.02156i			0.457411i	0.973496	+	0.228706i	$0.0734493\pi$
$389$			9.02156i			0.457411i	−0.973496	+	0.228706i	$0.926551\pi$
$390$	−14.1165	+	32.5079i	−0.714816	+	1.64610i
$391$		−	6.21052i		−	0.314080i
$392$	−0.647088	−	2.00272i	−0.0326829	−	0.101153i
$393$	23.5632	−	23.5632i	1.18861	−	1.18861i
$394$	0.911069	−	5.73194i	0.0458990	−	0.288771i
$395$	2.67304	+	4.52733i	0.134495	+	0.227795i
$396$	−2.47658	+	7.59382i	−0.124453	+	0.381604i
$397$	4.24421	+	4.24421i	0.213011	+	0.213011i	0.805545	−	0.592534i	$-0.201873\pi$
$397$	4.24421	+	4.24421i	0.213011	+	0.213011i	−0.592534	+	0.805545i	$0.701873\pi$
$398$	−8.97624	−	12.3690i	−0.449938	−	0.620001i
$399$	−7.28228			−0.364570
$400$	18.1274	−	8.44972i	0.906369	−	0.422486i
$401$	−5.54417			−0.276863			−0.138431	−	0.990372i	$-0.544206\pi$
$401$	−5.54417			−0.276863			−0.138431	+	0.990372i	$0.544206\pi$
$402$	28.6726	+	39.5100i	1.43006	+	1.97058i
$403$	−19.5925	−	19.5925i	−0.975971	−	0.975971i
$404$	3.16522	−	9.70535i	0.157476	−	0.482859i
$405$	6.52214	+	11.0466i	0.324088	+	0.548908i
$406$	−1.61660	+	10.1707i	−0.0802303	+	0.504765i
$407$	−5.90604	+	5.90604i	−0.292751	+	0.292751i
$408$	4.83841	+	14.9748i	0.239537	+	0.741361i
$409$			9.73164i			0.481199i	0.970625	+	0.240599i	$0.0773440\pi$
$409$			9.73164i			0.481199i	−0.970625	+	0.240599i	$0.922656\pi$
$410$	11.9819	−	27.5924i	0.591746	−	1.36269i
$411$		−	34.3976i		−	1.69671i
$412$	−31.1029	+	15.8048i	−1.53233	+	0.778648i
$413$	−25.0458	+	25.0458i	−1.23243	+	1.23243i
$414$	15.6986	+	2.49524i	0.771547	+	0.122634i
$415$	−6.38734	+	24.8026i	−0.313542	+	1.21751i
$416$	17.0839	+	17.1778i	0.837608	+	0.842209i
$417$	−2.76780	−	2.76780i	−0.135540	−	0.135540i
$418$	−1.18793	+	0.862088i	−0.0581036	+	0.0421661i
$419$	14.5558			0.711095			0.355548	−	0.934658i	$-0.384294\pi$
$419$	14.5558			0.711095			0.355548	+	0.934658i	$0.384294\pi$
$420$	31.7959	−	7.04654i	1.55148	−	0.343836i
$421$	−16.2488			−0.791917			−0.395958	−	0.918268i	$-0.629588\pi$
$421$	−16.2488			−0.791917			−0.395958	+	0.918268i	$0.629588\pi$
$422$	−14.3156	+	10.3889i	−0.696871	+	0.505723i
$423$	−6.63047	−	6.63047i	−0.322384	−	0.322384i
$424$	11.5018	−	22.4822i	0.558578	−	1.09183i
$425$	10.2130	−	2.95114i	0.495402	−	0.143151i
$426$	0.777131	+	0.123522i	0.0376521	+	0.00598466i
$427$	−1.07824	+	1.07824i	−0.0521798	+	0.0521798i
$428$	−12.7239	−	25.0399i	−0.615034	−	1.21035i
$429$			11.6318i			0.561589i
$430$	−30.8754	+	12.1791i	−1.48894	+	0.587326i
$431$		−	6.61387i		−	0.318579i	−0.987232	−	0.159289i	$-0.949080\pi$
$431$		−	6.61387i		−	0.318579i	0.987232	−	0.159289i	$-0.0509203\pi$
$432$	−8.76996	+	1.36933i	−0.421945	+	0.0658821i
$433$	−7.49867	+	7.49867i	−0.360363	+	0.360363i	−0.863947	−	0.503584i	$-0.832015\pi$
$433$	−7.49867	+	7.49867i	−0.360363	+	0.360363i	0.503584	+	0.863947i	$0.332015\pi$
$434$	−3.99684	+	25.1459i	−0.191855	+	1.20704i
$435$	−14.8283	−	3.81869i	−0.710963	−	0.183092i
$436$	−21.8207	−	7.11642i	−1.04502	−	0.340814i
$437$	2.06546	+	2.06546i	0.0988044	+	0.0988044i
$438$	22.0925	+	30.4428i	1.05562	+	1.45461i
$439$	−27.5314			−1.31400			−0.657001	−	0.753889i	$-0.728175\pi$
$439$	−27.5314			−1.31400			−0.657001	+	0.753889i	$0.728175\pi$
$440$	4.35256	−	4.91352i	0.207500	−	0.234243i
$441$	2.86333			0.136349
$442$	7.56349	+	10.4223i	0.359759	+	0.495736i
$443$	−21.2911	−	21.2911i	−1.01157	−	1.01157i	−0.999932	−	0.0116391i	$-0.996295\pi$
$443$	−21.2911	−	21.2911i	−1.01157	−	1.01157i	−0.0116391	−	0.999932i	$-0.503705\pi$
$444$	−40.0431	−	13.0593i	−1.90036	−	0.619768i
$445$	−23.7047	+	13.9958i	−1.12371	+	0.663464i
$446$	−3.34798	+	21.0636i	−0.158531	+	0.997391i
$447$	−21.5100	+	21.5100i	−1.01739	+	1.01739i
$448$	3.55488	−	21.9769i	0.167952	−	1.03831i
$449$			4.80815i			0.226910i	0.993543	+	0.113455i	$0.0361919\pi$
$449$			4.80815i			0.226910i	−0.993543	+	0.113455i	$0.963808\pi$
$450$	3.35642	+	27.0015i	0.158223	+	1.27286i
$451$		−	9.87297i		−	0.464900i
$452$	4.04650	+	7.96326i	0.190331	+	0.374560i
$453$	14.0395	−	14.0395i	0.659632	−	0.659632i
$454$	39.5807	+	6.29120i	1.85762	+	0.295261i
$455$	22.9483	−	13.5492i	1.07583	−	0.635195i
$456$	−6.58935	−	3.37109i	−0.308575	−	0.157866i
$457$	−15.7382	−	15.7382i	−0.736201	−	0.736201i	0.235640	−	0.971840i	$-0.424281\pi$
$457$	−15.7382	−	15.7382i	−0.736201	−	0.736201i	−0.971840	+	0.235640i	$0.924281\pi$
$458$	4.88144	−	3.54249i	0.228095	−	0.165530i
$459$	−4.71807			−0.220220
$460$	−11.0168	−	7.01962i	−0.513662	−	0.327291i
$461$	−21.0202			−0.979008			−0.489504	−	0.872001i	$-0.662822\pi$
$461$	−21.0202			−0.979008			−0.489504	+	0.872001i	$0.662822\pi$
$462$	8.65084	−	6.27796i	0.402473	−	0.292077i
$463$	25.9750	+	25.9750i	1.20716	+	1.20716i	0.971942	+	0.235221i	$0.0755813\pi$
$463$	25.9750	+	25.9750i	1.20716	+	1.20716i	0.235221	+	0.971942i	$0.424419\pi$
$464$	−6.17098	+	8.45461i	−0.286481	+	0.392496i
$465$	−36.6612	−	9.44125i	−1.70012	−	0.437828i
$466$	−11.1953	−	1.77945i	−0.518613	−	0.0824315i
$467$	14.1486	−	14.1486i	0.654720	−	0.654720i	−0.299406	−	0.954126i	$-0.596789\pi$
$467$	14.1486	−	14.1486i	0.654720	−	0.654720i	0.954126	+	0.299406i	$0.0967885\pi$
$468$	−29.3837	+	14.9312i	−1.35826	+	0.690195i
$469$		−	36.7085i		−	1.69504i
$470$	2.82764	+	7.16841i	0.130429	+	0.330654i
$471$			26.0909i			1.20220i
$472$	−34.2569	+	11.0685i	−1.57680	+	0.509470i
$473$	−7.70275	+	7.70275i	−0.354173	+	0.354173i
$474$	−1.36592	+	8.59364i	−0.0627390	+	0.394719i
$475$	−2.41510	+	4.37805i	−0.110812	+	0.200879i
$476$	3.66907	−	11.2503i	0.168172	−	0.515656i
$477$	24.2938	+	24.2938i	1.11234	+	1.11234i
$478$	−10.7307	−	14.7866i	−0.490812	−	0.676323i
$479$	19.7192			0.900995			0.450497	−	0.892778i	$-0.351247\pi$
$479$	19.7192			0.900995			0.450497	+	0.892778i	$0.351247\pi$
$480$	32.0324	+	8.34282i	1.46207	+	0.380796i
$481$	−34.4656			−1.57150
$482$	−9.54616	−	13.1543i	−0.434816	−	0.599162i
$483$	−15.0413	−	15.0413i	−0.684401	−	0.684401i
$484$	−6.15331	+	18.8676i	−0.279696	+	0.857617i
$485$	7.32011	−	28.4246i	0.332389	−	1.29070i
$486$	−4.81069	+	30.2662i	−0.218217	+	1.37290i
$487$	−2.44306	+	2.44306i	−0.110705	+	0.110705i	−0.760290	−	0.649584i	$-0.774943\pi$
$487$	−2.44306	+	2.44306i	−0.110705	+	0.110705i	0.649584	+	0.760290i	$0.274943\pi$
$488$	−1.47478	+	0.476508i	−0.0667603	+	0.0215705i
$489$			32.0017i			1.44716i
$490$	−2.15837	−	0.937268i	−0.0975052	−	0.0423414i
$491$		−	10.1967i		−	0.460172i	−0.973170	−	0.230086i	$-0.926099\pi$
$491$		−	10.1967i		−	0.460172i	0.973170	−	0.230086i	$-0.0739008\pi$
$492$	44.3850	−	22.5541i	2.00103	−	1.01682i
$493$	−3.93414	+	3.93414i	−0.177185	+	0.177185i
$494$	−5.98160	−	0.950751i	−0.269125	−	0.0427763i
$495$	4.54031	+	7.68993i	0.204072	+	0.345636i
$496$	−15.2570	+	20.9030i	−0.685060	+	0.938573i
$497$	−0.418395	−	0.418395i	−0.0187676	−	0.0187676i
$498$	−34.3070	+	24.8968i	−1.53733	+	1.11565i
$499$	41.0266			1.83660			0.918302	−	0.395880i	$-0.129561\pi$
$499$	41.0266			1.83660			0.918302	+	0.395880i	$0.129561\pi$
$500$	6.30848	−	21.4523i	0.282124	−	0.959378i
$501$	−16.0121			−0.715368
$502$	−0.513955	+	0.372981i	−0.0229390	+	0.0166469i
$503$	−18.8172	−	18.8172i	−0.839018	−	0.839018i	0.149711	−	0.988730i	$-0.452166\pi$
$503$	−18.8172	−	18.8172i	−0.839018	−	0.839018i	−0.988730	+	0.149711i	$0.952166\pi$
$504$	26.9638	+	13.7946i	1.20106	+	0.614459i
$505$	−5.80279	−	9.82819i	−0.258221	−	0.437349i
$506$	−4.23423	−	0.673015i	−0.188235	−	0.0299191i
$507$	−9.88437	+	9.88437i	−0.438980	+	0.438980i
$508$	−2.52207	−	4.96327i	−0.111899	−	0.220210i
$509$			23.1012i			1.02394i	0.859003	+	0.511971i	$0.171084\pi$
$509$			23.1012i			1.02394i	−0.859003	+	0.511971i	$0.828916\pi$
$510$	16.1386	+	7.00814i	0.714628	+	0.310326i
$511$		−	28.2842i		−	1.25122i
$512$	13.3901	−	18.2402i	0.591766	−	0.806110i
$513$	1.56911	−	1.56911i	0.0692778	−	0.0692778i
$514$	−4.43921	+	27.9290i	−0.195805	+	1.23190i
$515$	−9.72774	+	37.7737i	−0.428655	+	1.66451i
$516$	−52.2249	−	17.0322i	−2.29908	−	0.749800i
$517$	1.78837	+	1.78837i	0.0786523	+	0.0786523i
$518$	18.6019	+	25.6328i	0.817321	+	1.12624i
$519$	25.1024			1.10187
$520$	27.0368	−	1.63680i	1.18564	−	0.0717784i
$521$	17.4818			0.765892			0.382946	−	0.923771i	$-0.374910\pi$
$521$	17.4818			0.765892			0.382946	+	0.923771i	$0.374910\pi$
$522$	−8.36389	−	11.5252i	−0.366077	−	0.504443i
$523$	22.9784	+	22.9784i	1.00478	+	1.00478i	0.999989	+	0.00478820i	$0.00152414\pi$
$523$	22.9784	+	22.9784i	1.00478	+	1.00478i	0.00478820	+	0.999989i	$0.498476\pi$
$524$	−24.2131	−	7.89664i	−1.05775	−	0.344966i
$525$	17.5874	−	31.8821i	0.767578	−	1.39145i
$526$	4.25749	−	26.7857i	0.185635	−	1.16791i
$527$	−9.72670	+	9.72670i	−0.423702	+	0.423702i
$528$	10.7339	−	1.67598i	0.467132	−	0.0729376i
$529$		−	14.4677i		−	0.629032i
$530$	−10.3604	−	26.2648i	−0.450026	−	1.14087i
$531$		−	48.9776i		−	2.12545i
$532$	2.52132	+	4.96179i	0.109313	+	0.215121i
$533$	28.8076	−	28.8076i	1.24780	−	1.24780i
$534$	−44.9955	−	7.15185i	−1.94714	−	0.309491i
$535$	−30.4103	−	7.83147i	−1.31475	−	0.338584i
$536$	16.9930	−	33.2156i	0.733986	−	1.43469i
$537$	−39.3074	−	39.3074i	−1.69624	−	1.69624i
$538$	−21.3745	+	15.5116i	−0.921519	+	0.668751i
$539$	−0.772297			−0.0332652
$540$	−5.33272	+	8.36935i	−0.229484	+	0.360160i
$541$	35.7902			1.53874			0.769371	−	0.638802i	$-0.220570\pi$
$541$	35.7902			1.53874			0.769371	+	0.638802i	$0.220570\pi$
$542$	19.7042	−	14.2995i	0.846369	−	0.614215i
$543$	−13.0442	−	13.0442i	−0.559781	−	0.559781i
$544$	8.52790	−	8.48132i	0.365631	−	0.363634i
$545$	−22.0969	+	13.0465i	−0.946526	+	0.558851i
$546$	43.5597	+	6.92363i	1.86418	+	0.296304i
$547$	19.9722	−	19.9722i	0.853950	−	0.853950i	−0.136667	−	0.990617i	$-0.543639\pi$
$547$	19.9722	−	19.9722i	0.853950	−	0.853950i	0.990617	+	0.136667i	$0.0436390\pi$
$548$	−23.4369	+	11.9094i	−1.00117	+	0.508742i
$549$		−	2.10852i		−	0.0899896i
$550$	−0.905292	−	7.28284i	−0.0386018	−	0.310541i
$551$		−	2.61679i		−	0.111479i
$552$	−6.64719	−	20.5729i	−0.282923	−	0.875642i
$553$	4.62668	−	4.62668i	0.196746	−	0.196746i
$554$	4.02071	−	25.2961i	0.170824	−	1.07473i
$555$	−40.5499	+	23.9416i	−1.72125	+	1.01627i
$556$	−0.927560	+	2.84413i	−0.0393373	+	0.120618i
$557$	−18.9695	−	18.9695i	−0.803765	−	0.803765i	0.179917	−	0.983682i	$-0.442417\pi$
$557$	−18.9695	−	18.9695i	−0.803765	−	0.803765i	−0.983682	+	0.179917i	$0.942417\pi$
$558$	−20.6787	−	28.4946i	−0.875400	−	1.20627i
$559$	−44.9506			−1.90121
$560$	−15.8098	−	19.2245i	−0.668084	−	0.812383i
$561$	5.77462			0.243804
$562$	14.6506	+	20.1880i	0.617997	+	0.851581i
$563$	33.3205	+	33.3205i	1.40429	+	1.40429i	0.785757	+	0.618535i	$0.212274\pi$
$563$	33.3205	+	33.3205i	1.40429	+	1.40429i	0.618535	+	0.785757i	$0.287726\pi$
$564$	−3.95441	+	12.1252i	−0.166511	+	0.510563i
$565$	9.67117	+	2.49059i	0.406869	+	0.104780i
$566$	3.50084	−	22.0254i	0.147151	−	0.925795i
$567$	11.2890	−	11.2890i	0.474092	−	0.474092i
$568$	−0.184902	−	0.572267i	−0.00775830	−	0.0240118i
$569$		−	44.6559i		−	1.87207i	−0.351905	−	0.936036i	$-0.614466\pi$
$569$		−	44.6559i		−	1.87207i	0.351905	−	0.936036i	$-0.385534\pi$
$570$	−7.69800	+	3.03655i	−0.322434	+	0.127187i
$571$			2.61268i			0.109337i	0.998505	+	0.0546686i	$0.0174102\pi$
$571$			2.61268i			0.109337i	−0.998505	+	0.0546686i	$0.982590\pi$
$572$	7.92536	−	4.02724i	0.331376	−	0.168387i
$573$	35.4045	−	35.4045i	1.47905	−	1.47905i
$574$	−36.9730	−	5.87672i	−1.54322	−	0.245289i
$575$	−14.0310	+	4.05439i	−0.585132	+	0.169080i
$576$	18.0123	+	24.9640i	0.750515	+	1.04017i
$577$	9.78791	+	9.78791i	0.407476	+	0.407476i	0.880857	−	0.473382i	$-0.156967\pi$
$577$	9.78791	+	9.78791i	0.407476	+	0.407476i	−0.473382	+	0.880857i	$0.656967\pi$
$578$	−14.2837	+	10.3658i	−0.594123	+	0.431159i
$579$	43.0789			1.79030
$580$	2.53208	+	11.4254i	0.105139	+	0.474415i
$581$	31.8744			1.32237
$582$	39.3170	−	28.5326i	1.62974	−	1.18271i
$583$	−6.55251	−	6.55251i	−0.271377	−	0.271377i
$584$	13.0933	−	25.5929i	0.541803	−	1.05904i
$585$	−9.19003	+	35.6857i	−0.379961	+	1.47542i
$586$	19.3084	+	3.06898i	0.797621	+	0.126779i
$587$	4.41302	−	4.41302i	0.182145	−	0.182145i	−0.610145	−	0.792290i	$-0.708889\pi$
$587$	4.41302	−	4.41302i	0.182145	−	0.182145i	0.792290	+	0.610145i	$0.208889\pi$
$588$	−1.76426	−	3.47194i	−0.0727567	−	0.143181i
$589$		−	6.46970i		−	0.266579i
$590$	−16.0321	+	36.9192i	−0.660031	+	1.51994i
$591$		−	10.7395i		−	0.441766i
$592$	4.96600	+	31.8050i	0.204102	+	1.30718i
$593$	−14.5035	+	14.5035i	−0.595586	+	0.595586i	−0.939135	−	0.343549i	$-0.888371\pi$
$593$	−14.5035	+	14.5035i	−0.595586	+	0.595586i	0.343549	+	0.939135i	$0.388371\pi$
$594$	−0.511282	+	3.21670i	−0.0209781	+	0.131983i
$595$	−6.72650	−	11.3927i	−0.275759	−	0.467054i
$596$	22.1032	+	7.20854i	0.905382	+	0.295273i
$597$	−19.9965	−	19.9965i	−0.818404	−	0.818404i
$598$	−10.3910	−	14.3185i	−0.424921	−	0.585527i
$599$	−16.3544			−0.668223			−0.334112	−	0.942534i	$-0.608436\pi$
$599$	−16.3544			−0.668223			−0.334112	+	0.942534i	$0.608436\pi$
$600$	30.6728	−	20.7070i	1.25221	−	0.845359i
$601$	−26.4268			−1.07797			−0.538986	−	0.842315i	$-0.681193\pi$
$601$	−26.4268			−1.07797			−0.538986	+	0.842315i	$0.681193\pi$
$602$	24.2609	+	33.4308i	0.988801	+	1.36254i
$603$	35.8921	+	35.8921i	1.46164	+	1.46164i
$604$	−14.4267	−	4.70499i	−0.587013	−	0.191443i
$605$	11.2808	+	19.1064i	0.458632	+	0.776785i
$606$	2.96523	−	18.6556i	0.120454	−	0.757831i
$607$	−29.7918	+	29.7918i	−1.20921	+	1.20921i	−0.237928	+	0.971283i	$0.576468\pi$
$607$	−29.7918	+	29.7918i	−1.20921	+	1.20921i	−0.971283	+	0.237928i	$0.923532\pi$
$608$	−0.0154926	+	5.65683i	−0.000628310	+	0.229415i
$609$			19.0562i			0.772196i
$610$	−0.690193	+	1.58940i	−0.0279451	+	0.0643529i
$611$			10.4363i			0.422207i
$612$	7.41261	+	14.5875i	0.299637	+	0.589666i
$613$	7.62941	−	7.62941i	0.308149	−	0.308149i	−0.536042	−	0.844191i	$-0.680081\pi$
$613$	7.62941	−	7.62941i	0.308149	−	0.308149i	0.844191	+	0.536042i	$0.180081\pi$
$614$	−8.14322	−	1.29433i	−0.328634	−	0.0522350i
$615$	13.8818	−	53.9045i	0.559770	−	2.17364i
$616$	−7.27265	−	3.72067i	−0.293024	−	0.149910i
$617$	−15.2565	−	15.2565i	−0.614202	−	0.614202i	0.329836	−	0.944038i	$-0.393006\pi$
$617$	−15.2565	−	15.2565i	−0.614202	−	0.614202i	−0.944038	+	0.329836i	$0.893006\pi$
$618$	−52.2486	+	37.9171i	−2.10175	+	1.52525i
$619$	3.44832			0.138600			0.0692998	−	0.997596i	$-0.477923\pi$
$619$	3.44832			0.138600			0.0692998	+	0.997596i	$0.477923\pi$
$620$	6.26027	+	28.2480i	0.251419	+	1.13447i
$621$	6.48186			0.260108
$622$	2.04414	−	1.48344i	0.0819626	−	0.0594807i
$623$	24.2248	+	24.2248i	0.970548	+	0.970548i
$624$	36.2098	+	26.4294i	1.44955	+	1.05802i
$625$	−13.3346	−	21.1468i	−0.533383	−	0.845874i
$626$	34.2995	+	5.45177i	1.37089	+	0.217897i
$627$	−1.92049	+	1.92049i	−0.0766970	+	0.0766970i
$628$	17.7771	−	9.03336i	0.709383	−	0.360470i
$629$			17.1105i			0.682239i
$630$	31.5004	−	12.4256i	1.25500	−	0.495048i
$631$			0.748834i			0.0298106i	0.999889	+	0.0149053i	$0.00474468\pi$
$631$			0.748834i			0.0298106i	−0.999889	+	0.0149053i	$0.995255\pi$
$632$	6.32821	−	2.04467i	0.251723	−	0.0813326i
$633$	−23.1435	+	23.1435i	−0.919873	+	0.919873i
$634$	5.93088	−	37.3138i	0.235545	−	1.48192i
$635$	−6.02776	−	1.55231i	−0.239205	−	0.0616016i
$636$	14.4888	−	44.4263i	0.574518	−	1.76162i
$637$	−2.25343	−	2.25343i	−0.0892841	−	0.0892841i
$638$	2.25590	+	3.10857i	0.0893121	+	0.123069i
$639$	0.818180			0.0323667
$640$	−5.40607	−	24.7139i	−0.213694	−	0.976901i
$641$	31.9208			1.26080			0.630399	−	0.776272i	$-0.282891\pi$
$641$	31.9208			1.26080			0.630399	+	0.776272i	$0.282891\pi$
$642$	−30.5258	−	42.0636i	−1.20476	−	1.66012i
$643$	−17.2796	−	17.2796i	−0.681442	−	0.681442i	0.278883	−	0.960325i	$-0.410036\pi$
$643$	−17.2796	−	17.2796i	−0.681442	−	0.681442i	−0.960325	+	0.278883i	$0.910036\pi$
$644$	−5.04071	+	15.4561i	−0.198632	+	0.609055i
$645$	−52.8859	+	31.2251i	−2.08238	+	1.22949i
$646$	−0.472001	+	2.96957i	−0.0185706	+	0.116836i
$647$	−5.83342	+	5.83342i	−0.229335	+	0.229335i	−0.812415	−	0.583080i	$-0.801848\pi$
$647$	−5.83342	+	5.83342i	−0.229335	+	0.229335i	0.583080	+	0.812415i	$0.301848\pi$
$648$	15.4407	−	4.98894i	0.606567	−	0.195984i
$649$			13.2102i			0.518547i
$650$	18.6086	−	23.8916i	0.729889	−	0.937104i
$651$			47.1142i			1.84655i
$652$	21.8044	−	11.0798i	0.853926	−	0.433919i
$653$	−12.2450	+	12.2450i	−0.479186	+	0.479186i	−0.904871	−	0.425685i	$-0.860033\pi$
$653$	−12.2450	+	12.2450i	−0.479186	+	0.479186i	0.425685	+	0.904871i	$0.360033\pi$
$654$	−41.9436	−	6.66677i	−1.64013	−	0.260691i
$655$	−24.5195	+	14.4769i	−0.958056	+	0.565659i
$656$	−30.7346	−	22.4330i	−1.19998	−	0.875862i
$657$	27.6552	+	27.6552i	1.07893	+	1.07893i
$658$	7.76171	−	5.63272i	0.302583	−	0.219586i
$659$	33.1519			1.29141			0.645707	−	0.763586i	$-0.276563\pi$
$659$	33.1519			1.29141			0.645707	+	0.763586i	$0.276563\pi$
$660$	6.52692	−	10.2436i	0.254060	−	0.398730i
$661$	13.0904			0.509157			0.254578	−	0.967052i	$-0.418063\pi$
$661$	13.0904			0.509157			0.254578	+	0.967052i	$0.418063\pi$
$662$	11.9138	−	8.64589i	0.463042	−	0.336032i
$663$	16.8493	+	16.8493i	0.654374	+	0.654374i
$664$	28.8415	+	14.7552i	1.11927	+	0.572613i
$665$	6.02597	+	1.55185i	0.233677	+	0.0601782i
$666$	−43.2509	−	6.87456i	−1.67594	−	0.266384i
$667$	5.40488	−	5.40488i	0.209278	−	0.209278i
$668$	5.54381	+	10.9099i	0.214497	+	0.422116i
$669$			39.4654i			1.52582i
$670$	−15.3066	−	38.8040i	−0.591346	−	1.49913i
$671$			0.568710i			0.0219548i
$672$	0.112822	−	41.1946i	0.00435219	−	1.58912i
$673$	−17.0954	+	17.0954i	−0.658979	+	0.658979i	−0.955138	−	0.296160i	$-0.904294\pi$
$673$	−17.0954	+	17.0954i	−0.658979	+	0.658979i	0.296160	+	0.955138i	$0.404294\pi$
$674$	0.256107	−	1.61128i	0.00986486	−	0.0620642i
$675$	3.08008	+	10.6592i	0.118552	+	0.410272i
$676$	10.1570	+	3.31251i	0.390653	+	0.127404i
$677$	−19.8258	−	19.8258i	−0.761966	−	0.761966i	0.214712	−	0.976678i	$-0.431119\pi$
$677$	−19.8258	−	19.8258i	−0.761966	−	0.761966i	−0.976678	+	0.214712i	$0.931119\pi$
$678$	9.70790	+	13.3772i	0.372830	+	0.513748i
$679$	−36.5291			−1.40186
$680$	−0.812590	−	13.4224i	−0.0311614	−	0.514727i
$681$	74.1597			2.84181
$682$	5.57745	+	7.68556i	0.213572	+	0.294295i
$683$	−9.54011	−	9.54011i	−0.365042	−	0.365042i	0.500623	−	0.865665i	$-0.333104\pi$
$683$	−9.54011	−	9.54011i	−0.365042	−	0.365042i	−0.865665	+	0.500623i	$0.833104\pi$
$684$	−7.31669	−	2.38620i	−0.279761	−	0.0912387i
$685$	−7.33011	+	28.4635i	−0.280069	+	1.08753i
$686$	3.86475	−	24.3149i	0.147557	−	0.928346i
$687$	7.89167	−	7.89167i	0.301086	−	0.301086i
$688$	6.47675	+	41.4806i	0.246924	+	1.58143i
$689$		−	38.2382i		−	1.45676i
$690$	−22.1718	−	9.62805i	−0.844066	−	0.366534i
$691$		−	6.36671i		−	0.242201i	−0.992640	−	0.121101i	$-0.961358\pi$
$691$		−	6.36671i		−	0.242201i	0.992640	−	0.121101i	$-0.0386423\pi$
$692$	−8.69113	−	17.1036i	−0.330387	−	0.650181i
$693$	7.85868	−	7.85868i	0.298526	−	0.298526i
$694$	−2.39636	−	0.380892i	−0.0909647	−	0.0144585i
$695$	1.70049	+	2.88013i	0.0645034	+	0.109249i
$696$	−8.82145	+	17.2430i	−0.334376	+	0.653593i
$697$	−14.3016	−	14.3016i	−0.541710	−	0.541710i
$698$	20.3250	−	14.7500i	0.769314	−	0.558296i
$699$	−20.9759			−0.793382
$700$	−27.8122	−	0.944783i	−1.05120	−	0.0357094i
$701$	−6.31090			−0.238359			−0.119180	−	0.992873i	$-0.538026\pi$
$701$	−6.31090			−0.238359			−0.119180	+	0.992873i	$0.538026\pi$
$702$	−10.8776	+	7.89395i	−0.410549	+	0.297938i
$703$	−5.69050	−	5.69050i	−0.214621	−	0.214621i
$704$	−4.85828	−	6.73328i	−0.183103	−	0.253770i
$705$	7.24960	+	12.2787i	0.273036	+	0.462441i
$706$	23.2340	+	3.69294i	0.874421	+	0.138986i
$707$	−10.0439	+	10.0439i	−0.377738	+	0.377738i
$708$	−59.3881	+	30.1778i	−2.23194	+	1.13415i
$709$			8.83115i			0.331661i	0.986154	+	0.165830i	$0.0530305\pi$
$709$			8.83115i			0.331661i	−0.986154	+	0.165830i	$0.946970\pi$
$710$	−0.616742	−	0.267819i	−0.0231459	−	0.0100511i
$711$			9.04756i			0.339310i
$712$	10.7057	+	33.1339i	0.401213	+	1.24175i
$713$	13.3629	−	13.3629i	0.500445	−	0.500445i
$714$	3.43724	−	21.6252i	0.128636	−	0.809303i
$715$	2.47873	−	9.62514i	0.0926994	−	0.359960i
$716$	−13.1729	+	40.3915i	−0.492295	+	1.50950i
$717$	−23.9050	−	23.9050i	−0.892749	−	0.892749i
$718$	−15.0077	−	20.6801i	−0.560082	−	0.771776i
$719$	−6.07284			−0.226479			−0.113239	−	0.993568i	$-0.536123\pi$
$719$	−6.07284			−0.226479			−0.113239	+	0.993568i	$0.536123\pi$
$720$	34.2551	+	3.33879i	1.27661	+	0.124429i
$721$	48.5438			1.80787
$722$	−0.830627	−	1.14458i	−0.0309127	−	0.0425968i
$723$	−21.2661	−	21.2661i	−0.790897	−	0.790897i
$724$	−4.37145	+	13.4040i	−0.162464	+	0.498154i
$725$	11.4564	+	6.31981i	0.425481	+	0.234712i
$726$	−5.76452	+	36.2671i	−0.213941	+	1.34600i
$727$	−7.04427	+	7.04427i	−0.261257	+	0.261257i	−0.825565	−	0.564307i	$-0.809143\pi$
$727$	−7.04427	+	7.04427i	−0.261257	+	0.261257i	0.564307	+	0.825565i	$0.309143\pi$
$728$	−10.3641	−	32.0766i	−0.384118	−	1.18884i
$729$			39.4967i			1.46284i
$730$	−11.7939	−	29.8989i	−0.436511	−	1.10661i
$731$			22.3157i			0.825378i
$732$	−2.55670	+	1.29918i	−0.0944983	+	0.0480190i
$733$	−5.60729	+	5.60729i	−0.207110	+	0.207110i	−0.803038	−	0.595928i	$-0.796784\pi$
$733$	−5.60729	+	5.60729i	−0.207110	+	0.207110i	0.595928	+	0.803038i	$0.296784\pi$
$734$	12.5481	+	1.99447i	0.463160	+	0.0736174i
$735$	−4.21659	−	1.08588i	−0.155531	−	0.0400535i
$736$	−11.7160	+	11.6520i	−0.431856	+	0.429497i
$737$	−9.68079	−	9.68079i	−0.356597	−	0.356597i
$738$	41.8968	−	30.4047i	1.54224	−	1.11921i
$739$	1.95220			0.0718127			0.0359063	−	0.999355i	$-0.488568\pi$
$739$	1.95220			0.0718127			0.0359063	+	0.999355i	$0.488568\pi$
$740$	30.3521	+	19.3396i	1.11577	+	0.710937i
$741$	−11.2073			−0.411711
$742$	−28.4386	+	20.6381i	−1.04401	+	0.757648i
$743$	15.3093	+	15.3093i	0.561643	+	0.561643i	0.929774	−	0.368131i	$-0.120002\pi$
$743$	15.3093	+	15.3093i	0.561643	+	0.561643i	−0.368131	+	0.929774i	$0.620002\pi$
$744$	−21.8100	+	42.6312i	−0.799593	+	1.56293i
$745$	22.3829	−	13.2154i	0.820047	−	0.484175i
$746$	−32.1797	−	5.11484i	−1.17818	−	0.187267i
$747$	−31.1655	+	31.1655i	−1.14029	+	1.14029i
$748$	−1.99933	−	3.93455i	−0.0731026	−	0.143861i
$749$			39.0810i			1.42799i
$750$	5.29730	−	41.0358i	0.193430	−	1.49841i
$751$		−	24.6066i		−	0.897906i	−0.893555	−	0.448953i	$-0.851797\pi$
$751$		−	24.6066i		−	0.897906i	0.893555	−	0.448953i	$-0.148203\pi$
$752$	9.63065	−	1.50372i	0.351194	−	0.0548351i
$753$	−0.830896	+	0.830896i	−0.0302795	+	0.0302795i
$754$	−2.48792	+	15.6526i	−0.0906046	+	0.570034i
$755$	−14.6093	+	8.62565i	−0.531685	+	0.313919i
$756$	11.7418	+	3.82937i	0.427046	+	0.139273i
$757$	11.5888	+	11.5888i	0.421202	+	0.421202i	0.885617	−	0.464415i	$-0.153736\pi$
$757$	11.5888	+	11.5888i	0.421202	+	0.421202i	−0.464415	+	0.885617i	$0.653736\pi$
$758$	11.2404	+	15.4890i	0.408271	+	0.562585i
$759$	−7.93339			−0.287964
$760$	4.73421	+	4.19372i	0.171728	+	0.152122i
$761$	7.77947			0.282006			0.141003	−	0.990009i	$-0.454967\pi$
$761$	7.77947			0.282006			0.141003	+	0.990009i	$0.454967\pi$
$762$	−6.05065	−	8.33761i	−0.219192	−	0.302040i
$763$	22.5818	+	22.5818i	0.817515	+	0.817515i
$764$	−36.3809	−	11.8650i	−1.31622	−	0.429259i
$765$	17.7162	+	4.56240i	0.640530	+	0.164954i
$766$	−6.02496	+	37.9057i	−0.217691	+	1.36959i
$767$	−38.5452	+	38.5452i	−1.39179	+	1.39179i
$768$	19.1718	−	37.2226i	0.691803	−	1.34316i
$769$		−	8.36208i		−	0.301544i	−0.988569	−	0.150772i	$-0.951824\pi$
$769$		−	8.36208i		−	0.301544i	0.988569	−	0.150772i	$-0.0481760\pi$
$770$	−8.49627	+	3.35143i	−0.306184	+	0.120777i
$771$			52.3287i			1.88457i
$772$	−14.9151	−	29.3519i	−0.536805	−	1.05640i
$773$	−33.8339	+	33.8339i	−1.21692	+	1.21692i	−0.248217	+	0.968705i	$0.579845\pi$
$773$	−33.8339	+	33.8339i	−1.21692	+	1.21692i	−0.968705	+	0.248217i	$0.920155\pi$
$774$	−56.4086	−	8.96592i	−2.02757	−	0.322273i
$775$	28.3247	+	15.6250i	1.01745	+	0.561266i
$776$	−33.0533	−	16.9100i	−1.18654	−	0.607033i
$777$	41.4398	+	41.4398i	1.48664	+	1.48664i
$778$	10.3259	−	7.49355i	0.370201	−	0.268657i
$779$	9.51266			0.340827
$780$	48.9334	−	10.8445i	1.75210	−	0.388296i
$781$	−0.220679			−0.00789653
$782$	−7.10843	+	5.15863i	−0.254197	+	0.184472i
$783$	−4.10603	−	4.10603i	−0.146737	−	0.146737i
$784$	−1.75478	+	2.40416i	−0.0626709	+	0.0858628i
$785$	5.55996	−	21.5898i	0.198443	−	0.770573i
$786$	−46.5422	−	7.39769i	−1.66010	−	0.263867i
$787$	10.0934	−	10.0934i	0.359789	−	0.359789i	−0.503946	−	0.863735i	$-0.668119\pi$
$787$	10.0934	−	10.0934i	0.359789	−	0.359789i	0.863735	+	0.503946i	$0.168119\pi$
$788$	−7.31741	+	3.71832i	−0.260672	+	0.132460i
$789$		−	50.1866i		−	1.78669i
$790$	2.96158	−	6.82002i	0.105368	−	0.242646i
$791$		−	12.4286i		−	0.441912i
$792$	10.7488	−	3.47299i	0.381943	−	0.123407i
$793$	−1.65940	+	1.65940i	−0.0589270	+	0.0589270i
$794$	1.33247	−	8.38318i	0.0472877	−	0.297508i
$795$	−26.5623	−	44.9886i	−0.942067	−	1.59558i
$796$	−6.70135	+	20.5480i	−0.237523	+	0.728305i
$797$	−2.30808	−	2.30808i	−0.0817564	−	0.0817564i	0.665046	−	0.746802i	$-0.268412\pi$
$797$	−2.30808	−	2.30808i	−0.0817564	−	0.0817564i	−0.746802	+	0.665046i	$0.768412\pi$
$798$	6.04886	+	8.33513i	0.214127	+	0.295060i
$799$	5.18110			0.183294
$800$	−24.7285	−	13.7296i	−0.874283	−	0.485416i
$801$	−47.3722			−1.67381
$802$	4.60514	+	6.34574i	0.162613	+	0.224076i
$803$	−7.45914	−	7.45914i	−0.263227	−	0.263227i
$804$	21.4060	−	65.6361i	0.754931	−	2.31481i
$805$	9.24112	+	15.6517i	0.325707	+	0.551650i
$806$	−6.15108	+	38.6992i	−0.216663	+	1.36312i
$807$	−34.5554	+	34.5554i	−1.21641	+	1.21641i
$808$	−13.7377	+	4.43869i	−0.483289	+	0.156153i
$809$			8.61393i			0.302850i	0.988469	+	0.151425i	$0.0483861\pi$
$809$			8.61393i			0.302850i	−0.988469	+	0.151425i	$0.951614\pi$
$810$	7.22618	−	16.6407i	0.253902	−	0.584694i
$811$			13.8063i			0.484804i	0.970176	+	0.242402i	$0.0779354\pi$
$811$			13.8063i			0.484804i	−0.970176	+	0.242402i	$0.922065\pi$
$812$	12.9840	−	6.59776i	0.455648	−	0.231536i
$813$	31.8552	−	31.8552i	1.11721	−	1.11721i
$814$	11.6656	+	1.85421i	0.408880	+	0.0649899i
$815$	6.81954	−	26.4809i	0.238878	−	0.927585i
$816$	13.1209	−	17.9764i	0.459323	−	0.629299i
$817$	−7.42165	−	7.42165i	−0.259651	−	0.259651i
$818$	11.1386	−	8.08336i	0.389453	−	0.282628i
$819$	45.8605			1.60250
$820$	−41.5342	+	9.20473i	−1.45044	+	0.321443i
$821$	−30.3110			−1.05786			−0.528931	−	0.848665i	$-0.677407\pi$
$821$	−30.3110			−1.05786			−0.528931	+	0.848665i	$0.677407\pi$
$822$	−39.3707	+	28.5716i	−1.37321	+	0.996547i
$823$	38.7135	+	38.7135i	1.34947	+	1.34947i	0.886239	+	0.463227i	$0.153309\pi$
$823$	38.7135	+	38.7135i	1.34947	+	1.34947i	0.463227	+	0.886239i	$0.346691\pi$
$824$	43.9248	+	22.4718i	1.53019	+	0.782842i
$825$	−3.76982	−	13.0462i	−0.131248	−	0.454209i
$826$	49.4707	+	7.86317i	1.72131	+	0.273595i
$827$	−13.6616	+	13.6616i	−0.475061	+	0.475061i	−0.903548	−	0.428487i	$-0.859047\pi$
$827$	−13.6616	+	13.6616i	−0.475061	+	0.475061i	0.428487	+	0.903548i	$0.359047\pi$
$828$	−10.1837	−	20.0409i	−0.353909	−	0.696471i
$829$			20.2833i			0.704469i	0.935912	+	0.352235i	$0.114578\pi$
$829$			20.2833i			0.704469i	−0.935912	+	0.352235i	$0.885422\pi$
$830$	33.6940	−	13.2909i	1.16954	−	0.461334i
$831$		−	47.3956i		−	1.64413i
$832$	5.47091	−	33.8222i	0.189670	−	1.17257i
$833$	−1.11872	+	1.11872i	−0.0387612	+	0.0387612i
$834$	−0.868953	+	5.46697i	−0.0300894	+	0.189306i
$835$	13.2498	+	3.41217i	0.458527	+	0.118083i
$836$	1.97345	+	0.643605i	0.0682533	+	0.0222595i
$837$	−10.1517	−	10.1517i	−0.350893	−	0.350893i
$838$	−12.0904	−	16.6602i	−0.417656	−	0.575517i
$839$	23.7940			0.821461			0.410731	−	0.911757i	$-0.365274\pi$
$839$	23.7940			0.821461			0.410731	+	0.911757i	$0.365274\pi$
$840$	−34.4758	−	30.5398i	−1.18953	−	1.05372i
$841$	22.1524			0.763876
$842$	13.4967	+	18.5980i	0.465126	+	0.640929i
$843$	32.6373	+	32.6373i	1.12409	+	1.12409i
$844$	23.7818	+	7.75599i	0.818603	+	0.266972i
$845$	10.2855	−	6.07281i	0.353833	−	0.208911i
$846$	−2.08164	+	13.0965i	−0.0715683	+	0.450268i
$847$	19.5257	−	19.5257i	0.670909	−	0.670909i
$848$	−35.2864	+	5.50959i	−1.21174	+	0.189200i
$849$		−	41.2674i		−	1.41629i
$850$	−11.8610	−	9.23825i	−0.406828	−	0.316869i
$851$		−	23.5070i		−	0.805810i
$852$	−0.504126	−	0.992088i	−0.0172711	−	0.0339884i
$853$	3.24892	−	3.24892i	0.111241	−	0.111241i	−0.649295	−	0.760536i	$-0.724936\pi$
$853$	3.24892	−	3.24892i	0.111241	−	0.111241i	0.760536	+	0.649295i	$0.224936\pi$
$854$	2.12975	+	0.338515i	0.0728785	+	0.0115837i
$855$	−7.40929	+	4.37462i	−0.253392	+	0.149609i
$856$	−18.0913	+	35.3623i	−0.618347	+	1.20866i
$857$	9.35466	+	9.35466i	0.319549	+	0.319549i	0.848594	−	0.529045i	$-0.177450\pi$
$857$	9.35466	+	9.35466i	0.319549	+	0.319549i	−0.529045	+	0.848594i	$0.677450\pi$
$858$	13.3135	−	9.66169i	0.454516	−	0.329845i
$859$	−16.0797			−0.548632			−0.274316	−	0.961640i	$-0.588451\pi$
$859$	−16.0797			−0.548632			−0.274316	+	0.961640i	$0.588451\pi$
$860$	39.5858	+	25.2230i	1.34986	+	0.860097i
$861$	−69.2738			−2.36085
$862$	−7.57009	+	5.49366i	−0.257838	+	0.187115i
$863$	−11.7878	−	11.7878i	−0.401262	−	0.401262i	0.477416	−	0.878677i	$-0.341574\pi$
$863$	−11.7878	−	11.7878i	−0.401262	−	0.401262i	−0.878677	+	0.477416i	$0.841574\pi$
$864$	8.85187	+	8.90049i	0.301147	+	0.302801i
$865$	−20.7719	−	5.34932i	−0.706265	−	0.181882i
$866$	14.8114	+	2.35421i	0.503312	+	0.0799994i
$867$	−23.0920	+	23.0920i	−0.784245	+	0.784245i
$868$	32.1013	−	16.3122i	1.08959	−	0.553671i
$869$		−	2.44030i		−	0.0827817i
$870$	7.94600	+	20.1441i	0.269395	+	0.682947i
$871$		−	56.4938i		−	1.91422i
$872$	9.97958	+	30.8866i	0.337951	+	1.04595i
$873$	35.7167	−	35.7167i	1.20883	−	1.20883i
$874$	0.648453	−	4.07971i	0.0219343	−	0.137998i
$875$	−21.3474	+	22.6341i	−0.721674	+	0.765173i
$876$	16.4935	−	50.5733i	0.557264	−	1.70871i
$877$	13.3204	+	13.3204i	0.449797	+	0.449797i	0.895287	−	0.445490i	$-0.146971\pi$
$877$	13.3204	+	13.3204i	0.449797	+	0.449797i	−0.445490	+	0.895287i	$0.646971\pi$
$878$	22.8683	+	31.5119i	0.771769	+	1.06347i
$879$	36.1767			1.22021
$880$	−9.23926	−	0.900537i	−0.311456	−	0.0303571i
$881$	19.3901			0.653269			0.326634	−	0.945151i	$-0.394085\pi$
$881$	19.3901			0.653269			0.326634	+	0.945151i	$0.394085\pi$
$882$	−2.37836	−	3.27731i	−0.0800836	−	0.110353i
$883$	15.6537	+	15.6537i	0.526789	+	0.526789i	0.919613	−	0.392824i	$-0.128502\pi$
$883$	15.6537	+	15.6537i	0.526789	+	0.526789i	−0.392824	+	0.919613i	$0.628502\pi$
$884$	5.64664	−	17.3140i	0.189917	−	0.582333i
$885$	−18.5742	+	72.1253i	−0.624365	+	2.42446i
$886$	−6.68436	+	42.0543i	−0.224566	+	1.41284i
$887$	−12.2289	+	12.2289i	−0.410606	+	0.410606i	−0.881950	−	0.471343i	$-0.843769\pi$
$887$	−12.2289	+	12.2289i	−0.410606	+	0.410606i	0.471343	+	0.881950i	$0.343769\pi$
$888$	18.3135	+	56.6799i	0.614561	+	1.90205i
$889$			7.74642i			0.259806i
$890$	35.7090	+	15.5066i	1.19697	+	0.519781i
$891$		−	5.95428i		−	0.199476i
$892$	26.8899	−	13.6640i	0.900339	−	0.457504i
$893$	−1.72310	+	1.72310i	−0.0576614	+	0.0576614i
$894$	42.4866	+	6.75307i	1.42096	+	0.225857i
$895$	24.1499	+	40.9027i	0.807242	+	1.36723i
$896$	−28.1071	+	14.1858i	−0.938993	+	0.473914i
$897$	−23.1483	−	23.1483i	−0.772898	−	0.772898i
$898$	5.50330	−	3.99378i	0.183647	−	0.133274i
$899$	−16.9299			−0.564642
$900$	28.1174	−	26.2699i	0.937248	−	0.875663i
$901$	−18.9834			−0.632428
$902$	−11.3004	+	8.20076i	−0.376262	+	0.273055i
$903$	54.0465	+	54.0465i	1.79855	+	1.79855i
$904$	5.75344	−	11.2460i	0.191357	−	0.374038i
$905$	8.01417	+	13.5736i	0.266400	+	0.451202i
$906$	−27.7309	−	4.40771i	−0.921296	−	0.146436i
$907$	28.7770	−	28.7770i	0.955525	−	0.955525i	−0.0435268	−	0.999052i	$-0.513859\pi$
$907$	28.7770	−	28.7770i	0.955525	−	0.955525i	0.999052	+	0.0435268i	$0.0138594\pi$
$908$	−25.6761	−	50.5289i	−0.852090	−	1.67686i
$909$		−	19.6410i		−	0.651450i
$910$	−34.5695	−	15.0117i	−1.14597	−	0.497635i
$911$		−	8.57094i		−	0.283968i	−0.989869	−	0.141984i	$-0.954652\pi$
$911$		−	8.57094i		−	0.283968i	0.989869	−	0.141984i	$-0.0453481\pi$
$912$	1.61482	+	10.3422i	0.0534719	+	0.342463i
$913$	8.40594	−	8.40594i	0.278196	−	0.278196i
$914$	−4.94101	+	31.0861i	−0.163434	+	1.02824i
$915$	−0.799633	+	3.10505i	−0.0264350	+	0.102650i
$916$	−8.10931	−	2.64470i	−0.267939	−	0.0873833i
$917$	25.0576	+	25.0576i	0.827474	+	0.827474i
$918$	3.91895	+	5.40019i	0.129345	+	0.178233i
$919$	−50.2624			−1.65800			−0.829001	−	0.559247i	$-0.811090\pi$
$919$	−50.2624			−1.65800			−0.829001	+	0.559247i	$0.811090\pi$
$920$	1.11637	+	18.4403i	0.0368056	+	0.607958i
$921$	−15.2574			−0.502748
$922$	17.4599	+	24.0593i	0.575013	+	0.792349i
$923$	−0.643904	−	0.643904i	−0.0211944	−	0.0211944i
$924$	−14.3712	−	4.68691i	−0.472779	−	0.154188i
$925$	38.6564	−	11.1702i	1.27101	−	0.367272i
$926$	8.15489	−	51.3060i	0.267986	−	1.68602i
$927$	−47.4642	+	47.4642i	−1.55893	+	1.55893i
$928$	14.8027	+	0.0405410i	0.485924	+	0.00133082i
$929$		−	19.0851i		−	0.626163i	−0.949726	−	0.313081i	$-0.898639\pi$
$929$		−	19.0851i		−	0.626163i	0.949726	−	0.313081i	$-0.101361\pi$
$930$	19.6455	+	49.8038i	0.644203	+	1.63313i
$931$		−	0.744112i		−	0.0243873i
$932$	7.26242	+	14.2920i	0.237888	+	0.468149i
$933$	3.30470	−	3.30470i	0.108191	−	0.108191i
$934$	−27.9464	−	4.44197i	−0.914435	−	0.145346i
$935$	−4.77841	−	1.23057i	−0.156271	−	0.0402439i
$936$	41.4968	+	21.2296i	1.35637	+	0.693913i
$937$	26.1897	+	26.1897i	0.855581	+	0.855581i	0.990814	−	0.135233i	$-0.0431782\pi$
$937$	26.1897	+	26.1897i	0.855581	+	0.855581i	−0.135233	+	0.990814i	$0.543178\pi$
$938$	−42.0157	+	30.4910i	−1.37186	+	0.995568i
$939$	64.2647			2.09720
$940$	5.85608	−	9.19073i	0.191004	−	0.299769i
$941$	27.0871			0.883013			0.441506	−	0.897258i	$-0.354444\pi$
$941$	27.0871			0.883013			0.441506	+	0.897258i	$0.354444\pi$
$942$	29.8631	−	21.6718i	0.972991	−	0.706105i
$943$	19.6480	+	19.6480i	0.639828	+	0.639828i
$944$	41.1235	+	30.0158i	1.33845	+	0.976932i
$945$	11.8904	−	7.02038i	0.386795	−	0.228373i
$946$	15.2145	+	2.41829i	0.494667	+	0.0786253i
$947$	14.4376	−	14.4376i	0.469158	−	0.469158i	−0.432483	−	0.901642i	$-0.642363\pi$
$947$	14.4376	−	14.4376i	0.469158	−	0.469158i	0.901642	+	0.432483i	$0.142363\pi$
$948$	10.9707	−	5.57470i	0.356310	−	0.181058i
$949$		−	43.5290i		−	1.41301i
$950$	7.01706	−	0.872254i	0.227664	−	0.0282997i
$951$		−	69.9123i		−	2.26706i
$952$	−15.9245	+	5.14525i	−0.516115	+	0.166759i
$953$	41.4078	−	41.4078i	1.34133	−	1.34133i	0.446593	−	0.894737i	$-0.352637\pi$
$953$	41.4078	−	41.4078i	1.34133	−	1.34133i	0.894737	−	0.446593i	$-0.147363\pi$
$954$	7.62706	−	47.9852i	0.246935	−	1.55358i
$955$	−36.8414	+	21.7520i	−1.19216	+	0.703879i
$956$	−8.01119	+	24.5643i	−0.259100	+	0.794466i
$957$	5.02552	+	5.02552i	0.162452	+	0.162452i
$958$	−16.3793	−	22.5702i	−0.529192	−	0.729210i
$959$	36.5790			1.18120
$960$	−17.0580	−	43.5933i	−0.550544	−	1.40697i
$961$	−10.8571			−0.350228
$962$	28.6281	+	39.4486i	0.923005	+	1.27187i
$963$	−38.2118	−	38.2118i	−1.23136	−	1.23136i
$964$	−7.12683	+	21.8526i	−0.229540	+	0.703826i
$965$	−35.6471	−	9.18010i	−1.14752	−	0.295518i
$966$	−4.72222	+	29.7096i	−0.151935	+	0.955890i
$967$	−3.88025	+	3.88025i	−0.124780	+	0.124780i	−0.766739	−	0.641959i	$-0.778122\pi$
$967$	−3.88025	+	3.88025i	−0.124780	+	0.124780i	0.641959	+	0.766739i	$0.278122\pi$
$968$	26.7065	−	8.62898i	0.858380	−	0.277346i
$969$			5.56388i			0.178737i
$970$	−38.6145	+	15.2318i	−1.23984	+	0.489064i
$971$			46.6461i			1.49694i	0.663166	+	0.748472i	$0.269212\pi$
$971$			46.6461i			1.49694i	−0.663166	+	0.748472i	$0.730788\pi$
$972$	38.6379	−	19.6337i	1.23931	−	0.629751i
$973$	2.94333	−	2.94333i	0.0943588	−	0.0943588i
$974$	4.82554	+	0.767000i	0.154620	+	0.0245763i
$975$	27.0668	−	49.0661i	0.866831	−	1.57137i
$976$	1.77039	+	1.29220i	0.0566690	+	0.0413624i
$977$	23.7620	+	23.7620i	0.760212	+	0.760212i	0.976361	−	0.216148i	$-0.0693495\pi$
$977$	23.7620	+	23.7620i	0.760212	+	0.760212i	−0.216148	+	0.976361i	$0.569349\pi$
$978$	36.6284	−	26.5814i	1.17125	−	0.849981i
$979$	12.7772			0.408361
$980$	0.720025	+	3.24894i	0.0230003	+	0.103784i
$981$	−44.1591			−1.40989
$982$	−11.6710	+	8.46968i	−0.372435	+	0.270278i
$983$	−22.8129	−	22.8129i	−0.727618	−	0.727618i	0.242527	−	0.970145i	$-0.422024\pi$
$983$	−22.8129	−	22.8129i	−0.727618	−	0.727618i	−0.970145	+	0.242527i	$0.922024\pi$
$984$	−62.6823	−	32.0681i	−1.99824	−	1.02229i
$985$	−2.28859	+	8.88681i	−0.0729206	+	0.283157i
$986$	7.77074	+	1.23513i	0.247471	+	0.0393345i
$987$	12.5481	−	12.5481i	0.399411	−	0.399411i
$988$	3.88027	+	7.63613i	0.123448	+	0.242938i
$989$		−	30.6583i		−	0.974876i
$990$	5.03041	−	11.5842i	0.159877	−	0.368170i
$991$			37.7672i			1.19971i	0.800107	+	0.599857i	$0.204776\pi$
$991$			37.7672i			1.19971i	−0.800107	+	0.599857i	$0.795224\pi$
$992$	36.5980	+	0.100233i	1.16199	+	0.00318240i
$993$	19.2606	−	19.2606i	0.611217	−	0.611217i
$994$	−0.131356	+	0.826417i	−0.00416635	+	0.0262123i
$995$	12.2856	+	20.8081i	0.389479	+	0.659660i
$996$	56.9926	+	18.5871i	1.80588	+	0.588954i
$997$	0.463266	+	0.463266i	0.0146718	+	0.0146718i	0.714405	−	0.699733i	$-0.246698\pi$
$997$	0.463266	+	0.463266i	0.0146718	+	0.0146718i	−0.699733	+	0.714405i	$0.746698\pi$
$998$	−34.0778	−	46.9582i	−1.07871	−	1.48644i
$999$	−17.8580			−0.565003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.k.c.267.8	✓	52
4.3	odd	2		380.2.k.d.267.6	yes	52
5.3	odd	4		380.2.k.d.343.6	yes	52
20.3	even	4	inner	380.2.k.c.343.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.k.c.267.8	✓	52	1.1	even	1	trivial
380.2.k.c.343.8	yes	52	20.3	even	4	inner
380.2.k.d.267.6	yes	52	4.3	odd	2
380.2.k.d.343.6	yes	52	5.3	odd	4

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.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.830627 - 1.14458i) q^{2} +(-1.85040 - 1.85040i) q^{3} +(-0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 + 3.65493i) q^{6} +(1.96775 - 1.96775i) q^{7} +(2.69143 - 0.869611i) q^{8} +3.84798i q^{9} +O(q^{10})\)	\(q+(-0.830627 - 1.14458i) q^{2} +(-1.85040 - 1.85040i) q^{3} +(-0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 + 3.65493i) q^{6} +(1.96775 - 1.96775i) q^{7} +(2.69143 - 0.869611i) q^{8} +3.84798i q^{9} +(1.25958 - 2.90060i) q^{10} -1.03788i q^{11} +(4.66589 - 2.37095i) q^{12} +(3.02834 - 3.02834i) q^{13} +(-3.88672 - 0.617778i) q^{14} +(1.45930 - 5.66660i) q^{15} +(-3.23091 - 2.35823i) q^{16} +(-1.50342 - 1.50342i) q^{17} +(4.40432 - 3.19624i) q^{18} +1.00000 q^{19} +(-4.36620 + 0.967629i) q^{20} -7.28228 q^{21} +(-1.18793 + 0.862088i) q^{22} +(2.06546 + 2.06546i) q^{23} +(-6.58935 - 3.37109i) q^{24} +(-2.41510 + 4.37805i) q^{25} +(-5.98160 - 0.950751i) q^{26} +(1.56911 - 1.56911i) q^{27} +(2.52132 + 4.96179i) q^{28} -2.61679i q^{29} +(-7.69800 + 3.03655i) q^{30} -6.46970i q^{31} +(-0.0154926 + 5.65683i) q^{32} +(-1.92049 + 1.92049i) q^{33} +(-0.472001 + 2.96957i) q^{34} +(6.02597 + 1.55185i) q^{35} +(-7.31669 - 2.38620i) q^{36} +(-5.69050 - 5.69050i) q^{37} +(-0.830627 - 1.14458i) q^{38} -11.2073 q^{39} +(4.73421 + 4.19372i) q^{40} +9.51266 q^{41} +(6.04886 + 8.33513i) q^{42} +(-7.42165 - 7.42165i) q^{43} +(1.97345 + 0.643605i) q^{44} +(-7.40929 + 4.37462i) q^{45} +(0.648453 - 4.07971i) q^{46} +(-1.72310 + 1.72310i) q^{47} +(1.61482 + 10.3422i) q^{48} -0.744112i q^{49} +(7.01706 - 0.872254i) q^{50} +5.56388i q^{51} +(3.88027 + 7.63613i) q^{52} +(6.31339 - 6.31339i) q^{53} +(-3.09931 - 0.492623i) q^{54} +(1.99843 - 1.17992i) q^{55} +(3.58489 - 7.00725i) q^{56} +(-1.85040 - 1.85040i) q^{57} +(-2.99512 + 2.17358i) q^{58} -12.7281 q^{59} +(9.86973 + 6.28872i) q^{60} -0.547956 q^{61} +(-7.40508 + 5.37391i) q^{62} +(7.57188 + 7.57188i) q^{63} +(6.48755 - 4.68099i) q^{64} +(9.27388 + 2.38827i) q^{65} +(3.79336 + 0.602939i) q^{66} +(9.32750 - 9.32750i) q^{67} +(3.79096 - 1.92636i) q^{68} -7.64387i q^{69} +(-3.22912 - 8.18620i) q^{70} -0.212626i q^{71} +(3.34625 + 10.3566i) q^{72} +(7.18693 - 7.18693i) q^{73} +(-1.78654 + 11.2399i) q^{74} +(12.5701 - 3.63224i) q^{75} +(-0.620117 + 1.90143i) q^{76} +(-2.04229 - 2.04229i) q^{77} +(9.30910 + 12.8276i) q^{78} +2.35125 q^{79} +(0.867673 - 8.90209i) q^{80} +5.73698 q^{81} +(-7.90148 - 10.8880i) q^{82} +(8.09918 + 8.09918i) q^{83} +(4.51587 - 13.8468i) q^{84} +(1.18566 - 4.60402i) q^{85} +(-2.33003 + 14.6593i) q^{86} +(-4.84212 + 4.84212i) q^{87} +(-0.902548 - 2.79337i) q^{88} +12.3109i q^{89} +(11.1614 + 4.84683i) q^{90} -11.9181i q^{91} +(-5.20817 + 2.64651i) q^{92} +(-11.9716 + 11.9716i) q^{93} +(3.40348 + 0.540969i) q^{94} +(1.13686 + 1.92550i) q^{95} +(10.4961 - 10.4388i) q^{96} +(-9.28193 - 9.28193i) q^{97} +(-0.851695 + 0.618080i) q^{98} +3.99373 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8	\( 52 q - 2 q^{2} - 2 q^{3} + 4 q^{5} - 4 q^{6} - 4 q^{7} + 4 q^{8} - 18 q^{10} - 38 q^{12} - 2 q^{13} + 2 q^{15} + 16 q^{16} - 20 q^{17} + 2 q^{18} + 52 q^{19} + 20 q^{20} - 16 q^{21} + 20 q^{22} + 20 q^{23} - 16 q^{25} - 8 q^{27} - 8 q^{28} - 48 q^{30} - 42 q^{32} + 8 q^{33} - 20 q^{34} + 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} - 64 q^{39} + 60 q^{40} - 4 q^{41} + 60 q^{42} - 28 q^{43} + 8 q^{44} + 12 q^{45} - 8 q^{46} - 4 q^{47} - 18 q^{48} - 42 q^{50} - 54 q^{52} - 2 q^{53} - 24 q^{54} + 12 q^{56} - 2 q^{57} - 12 q^{58} + 28 q^{59} + 90 q^{60} - 4 q^{61} + 56 q^{62} + 44 q^{63} + 24 q^{64} + 10 q^{65} + 36 q^{66} + 6 q^{67} - 60 q^{68} - 32 q^{70} - 24 q^{72} + 8 q^{73} - 88 q^{74} + 2 q^{75} + 12 q^{77} + 64 q^{78} - 52 q^{79} - 8 q^{80} - 24 q^{81} + 56 q^{82} - 76 q^{83} + 40 q^{84} + 12 q^{85} - 8 q^{86} + 12 q^{87} - 40 q^{88} - 94 q^{90} - 48 q^{92} + 24 q^{93} - 32 q^{94} + 4 q^{95} - 4 q^{96} - 10 q^{97} + 58 q^{98} + 128 q^{99}+O(q^{100}) \) 52 * q - 2 * q^2 - 2 * q^3 + 4 * q^5 - 4 * q^6 - 4 * q^7 + 4 * q^8 - 18 * q^10 - 38 * q^12 - 2 * q^13 + 2 * q^15 + 16 * q^16 - 20 * q^17 + 2 * q^18 + 52 * q^19 + 20 * q^20 - 16 * q^21 + 20 * q^22 + 20 * q^23 - 16 * q^25 - 8 * q^27 - 8 * q^28 - 48 * q^30 - 42 * q^32 + 8 * q^33 - 20 * q^34 + 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 - 64 * q^39 + 60 * q^40 - 4 * q^41 + 60 * q^42 - 28 * q^43 + 8 * q^44 + 12 * q^45 - 8 * q^46 - 4 * q^47 - 18 * q^48 - 42 * q^50 - 54 * q^52 - 2 * q^53 - 24 * q^54 + 12 * q^56 - 2 * q^57 - 12 * q^58 + 28 * q^59 + 90 * q^60 - 4 * q^61 + 56 * q^62 + 44 * q^63 + 24 * q^64 + 10 * q^65 + 36 * q^66 + 6 * q^67 - 60 * q^68 - 32 * q^70 - 24 * q^72 + 8 * q^73 - 88 * q^74 + 2 * q^75 + 12 * q^77 + 64 * q^78 - 52 * q^79 - 8 * q^80 - 24 * q^81 + 56 * q^82 - 76 * q^83 + 40 * q^84 + 12 * q^85 - 8 * q^86 + 12 * q^87 - 40 * q^88 - 94 * q^90 - 48 * q^92 + 24 * q^93 - 32 * q^94 + 4 * q^95 - 4 * q^96 - 10 * q^97 + 58 * q^98 + 128 * q^99

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