LMFDB - Embedded newform 380.2.k.d.267.6

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			267.6
Character	$\chi$	$=$	380.267
Dual form			380.2.k.d.343.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.14458 - 0.830627i) q^{2} +(1.85040 + 1.85040i) q^{3} +(0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 - 3.65493i) q^{6} +(-1.96775 + 1.96775i) q^{7} +(0.869611 - 2.69143i) q^{8} +3.84798i q^{9} +O(q^{10})$	\(q+(-1.14458 - 0.830627i) 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} +(0.869611 - 2.69143i) q^{8} +3.84798i q^{9} +(0.298148 - 3.14819i) q^{10} +1.03788i q^{11} +(-2.37095 + 4.66589i) 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} +(3.19624 - 4.40432i) q^{18} -1.00000 q^{19} +(-2.95623 + 3.35570i) q^{20} -7.28228 q^{21} +(0.862088 - 1.18793i) 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} +(-4.96179 - 2.52132i) q^{28} -2.61679i q^{29} +(6.37712 - 5.27373i) q^{30} +6.46970i q^{31} +(5.65683 - 0.0154926i) 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} +(1.14458 + 0.830627i) q^{38} +11.2073 q^{39} +(6.17097 - 1.38534i) q^{40} +9.51266 q^{41} +(8.33513 + 6.04886i) 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} +(-10.3422 - 1.61482i) q^{48} -0.744112i q^{49} +(6.40079 - 3.00497i) q^{50} -5.56388i q^{51} +(7.63613 + 3.88027i) 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} +(-2.17358 + 2.99512i) q^{58} +12.7281 q^{59} +(-11.6796 + 0.739189i) q^{60} -0.547956 q^{61} +(5.37391 - 7.40508i) 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} +(1.92636 - 3.79096i) q^{68} -7.64387i q^{69} +(5.60818 + 6.78155i) q^{70} +0.212626i q^{71} +(10.3566 + 3.34625i) 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} +(-12.8276 - 9.30910i) q^{78} -2.35125 q^{79} +(-8.21385 - 3.54014i) q^{80} +5.73698 q^{81} +(-10.8880 - 7.90148i) 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} +(2.79337 + 0.902548i) q^{88} +12.3109i q^{89} +(12.1142 + 1.14727i) q^{90} +11.9181i q^{91} +(2.64651 - 5.20817i) 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} +(-0.618080 + 0.851695i) 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} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 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 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * 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 $

$2$	−1.14458	−	0.830627i	−0.809339	−	0.587342i
$2$	−1.14458	−	0.830627i	−0.809339	−	0.587342i
$3$	1.85040	+	1.85040i	1.06833	+	1.06833i	0.997487	+	0.0708431i	$0.0225690\pi$
$3$	1.85040	+	1.85040i	1.06833	+	1.06833i	0.0708431	+	0.997487i	$0.477431\pi$
$4$	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	−0.973296	−	0.229555i	$-0.926273\pi$
$7$	−1.96775	+	1.96775i	−0.743741	+	0.743741i	0.229555	+	0.973296i	$0.426273\pi$
$8$	0.869611	−	2.69143i	0.307454	−	0.951563i
$9$			3.84798i			1.28266i
$10$	0.298148	−	3.14819i	0.0942826	−	0.995545i
$11$			1.03788i			0.312931i	0.987683	+	0.156466i	$0.0500101\pi$
$11$			1.03788i			0.312931i	−0.987683	+	0.156466i	$0.949990\pi$
$12$	−2.37095	+	4.66589i	−0.684435	+	1.34693i
$13$	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	$0.833009\pi$
$18$	3.19624	−	4.40432i	0.753360	−	1.03811i
$19$	−1.00000			−0.229416
$19$	−1.00000			−0.229416
$20$	−2.95623	+	3.35570i	−0.661032	+	0.750357i
$21$	−7.28228			−1.58912
$22$	0.862088	−	1.18793i	0.183798	−	0.253268i
$23$	−2.06546	−	2.06546i	−0.430678	−	0.430678i	0.458181	−	0.888859i	$-0.348501\pi$
$23$	−2.06546	−	2.06546i	−0.430678	−	0.430678i	−0.888859	+	0.458181i	$0.848501\pi$
$24$	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
$28$	−4.96179	−	2.52132i	−0.937691	−	0.476484i
$29$		−	2.61679i		−	0.485926i	−0.970036	−	0.242963i	$-0.921881\pi$
$29$		−	2.61679i		−	0.485926i	0.970036	−	0.242963i	$-0.0781193\pi$
$30$	6.37712	−	5.27373i	1.16430	−	0.962847i
$31$			6.46970i			1.16199i	0.813906	+	0.580997i	$0.197337\pi$
$31$			6.46970i			1.16199i	−0.813906	+	0.580997i	$0.802663\pi$
$32$	5.65683	−	0.0154926i	0.999996	−	0.00273874i
$33$	−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	$0.980083\pi$
$38$	1.14458	+	0.830627i	0.185675	+	0.134746i
$39$	11.2073			1.79461
$40$	6.17097	−	1.38534i	0.975716	−	0.219041i
$41$	9.51266			1.48563			0.742814	−	0.669498i	$-0.233491\pi$
$41$	9.51266			1.48563			0.742814	+	0.669498i	$0.233491\pi$
$42$	8.33513	+	6.04886i	1.28614	+	0.933359i
$43$	7.42165	+	7.42165i	1.13179	+	1.13179i	0.989879	+	0.141911i	$0.0453247\pi$
$43$	7.42165	+	7.42165i	1.13179	+	1.13179i	0.141911	+	0.989879i	$0.454675\pi$
$44$	−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	−0.570180	−	0.821520i	$-0.693126\pi$
$47$	1.72310	−	1.72310i	0.251340	−	0.251340i	0.821520	+	0.570180i	$0.193126\pi$
$48$	−10.3422	−	1.61482i	−1.49276	−	0.233079i
$49$		−	0.744112i		−	0.106302i
$50$	6.40079	−	3.00497i	0.905209	−	0.424967i
$51$		−	5.56388i		−	0.779099i
$52$	7.63613	+	3.88027i	1.05894	+	0.538097i
$53$	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
$58$	−2.17358	+	2.99512i	−0.285405	+	0.393279i
$59$	12.7281			1.65706			0.828531	−	0.559943i	$-0.189177\pi$
$59$	12.7281			1.65706			0.828531	+	0.559943i	$0.189177\pi$
$60$	−11.6796	+	0.739189i	−1.50783	+	0.0954289i
$61$	−0.547956			−0.0701585			−0.0350793	−	0.999385i	$-0.511168\pi$
$61$	−0.547956			−0.0701585			−0.0350793	+	0.999385i	$0.511168\pi$
$62$	5.37391	−	7.40508i	0.682487	−	0.940446i
$63$	−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	$0.548250\pi$
$67$	−9.32750	+	9.32750i	−1.13954	+	1.13954i	−0.988533	+	0.151002i	$0.951750\pi$
$68$	1.92636	−	3.79096i	0.233606	−	0.459721i
$69$		−	7.64387i		−	0.920214i
$70$	5.60818	+	6.78155i	0.670306	+	0.810550i
$71$			0.212626i			0.0252340i	0.999920	+	0.0126170i	$0.00401623\pi$
$71$			0.212626i			0.0252340i	−0.999920	+	0.0126170i	$0.995984\pi$
$72$	10.3566	+	3.34625i	1.22053	+	0.394359i
$73$	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
$78$	−12.8276	−	9.30910i	−1.45244	−	1.05405i
$79$	−2.35125			−0.264536			−0.132268	−	0.991214i	$-0.542226\pi$
$79$	−2.35125			−0.264536			−0.132268	+	0.991214i	$0.542226\pi$
$80$	−8.21385	−	3.54014i	−0.918337	−	0.395800i
$81$	5.73698			0.637442
$82$	−10.8880	−	7.90148i	−1.20238	−	0.872572i
$83$	−8.09918	−	8.09918i	−0.889000	−	0.889000i	0.105427	−	0.994427i	$-0.466379\pi$
$83$	−8.09918	−	8.09918i	−0.889000	−	0.889000i	−0.994427	+	0.105427i	$0.966379\pi$
$84$	−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
$88$	2.79337	+	0.902548i	0.297774	+	0.0962120i
$89$			12.3109i			1.30495i	0.757809	+	0.652477i	$0.226270\pi$
$89$			12.3109i			1.30495i	−0.757809	+	0.652477i	$0.773730\pi$
$90$	12.1142	+	1.14727i	1.27695	+	0.120933i
$91$			11.9181i			1.24935i
$92$	2.64651	−	5.20817i	0.275918	−	0.542989i
$93$	−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	$0.982167\pi$
$98$	−0.618080	+	0.851695i	−0.0624355	+	0.0860342i
$99$	−3.99373			−0.401385
$100$	−9.82222	−	1.87725i	−0.982222	−	0.187725i
$101$	−5.10423			−0.507889			−0.253945	−	0.967219i	$-0.581728\pi$
$101$	−5.10423			−0.507889			−0.253945	+	0.967219i	$0.581728\pi$
$102$	−4.62151	+	6.36829i	−0.457597	+	0.630555i
$103$	−12.3348	−	12.3348i	−1.21539	−	1.21539i	−0.969230	−	0.246156i	$-0.920832\pi$
$103$	−12.3348	−	12.3348i	−1.21539	−	1.21539i	−0.246156	−	0.969230i	$-0.579168\pi$
$104$	−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	−0.0392276	−	0.999230i	$-0.512490\pi$
$107$	9.93034	−	9.93034i	0.960003	−	0.960003i	0.999230	+	0.0392276i	$0.0124898\pi$
$108$	−3.95659	−	2.01053i	−0.380723	−	0.193463i
$109$			11.4759i			1.09919i	0.835430	+	0.549597i	$0.185219\pi$
$109$			11.4759i			1.09919i	−0.835430	+	0.549597i	$0.814781\pi$
$110$	3.26743	+	0.309440i	0.311538	+	0.0295040i
$111$		−	21.0594i		−	1.99887i
$112$	1.71723	−	10.9980i	0.162263	−	1.03922i
$113$	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
$118$	−14.5683	−	10.5723i	−1.34113	−	0.973262i
$119$	5.91673			0.542386
$120$	13.9822	+	8.85534i	1.27640	+	0.808378i
$121$	9.92281			0.902074
$122$	0.627178	+	0.455147i	0.0567820	+	0.0412071i
$123$	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	−0.614362	−	0.789024i	$-0.710587\pi$
$127$	1.96834	−	1.96834i	0.174662	−	0.174662i	0.789024	+	0.614362i	$0.210587\pi$
$128$	3.53736	+	10.7465i	0.312661	+	0.949865i
$129$			27.4661i			2.41825i
$130$	−8.63091	−	10.4367i	−0.756981	−	0.915359i
$131$		−	12.7341i		−	1.11258i	−0.830987	−	0.556292i	$-0.812224\pi$
$131$		−	12.7341i		−	1.11258i	0.830987	−	0.556292i	$-0.187776\pi$
$132$	−4.84261	−	2.46076i	−0.421495	−	0.214181i
$133$	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	$0.560221\pi$
$138$	−6.34921	+	8.74901i	−0.540480	+	0.744765i
$139$	−1.49578			−0.126871			−0.0634353	−	0.997986i	$-0.520206\pi$
$139$	−1.49578			−0.126871			−0.0634353	+	0.997986i	$0.520206\pi$
$140$	−0.786068	−	12.4203i	−0.0664348	−	1.04971i
$141$	6.37687			0.537029
$142$	0.176613	−	0.243367i	0.0148210	−	0.0204229i
$143$	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
$148$	7.29134	−	14.3489i	0.599344	−	1.17947i
$149$		−	11.6245i		−	0.952314i	−0.879360	−	0.476157i	$-0.842029\pi$
$149$		−	11.6245i		−	0.952314i	0.879360	−	0.476157i	$-0.157971\pi$
$150$	17.4045	+	6.28365i	1.42107	+	0.513058i
$151$		−	7.58726i		−	0.617442i	−0.951153	−	0.308721i	$-0.900099\pi$
$151$		−	7.58726i		−	0.617442i	0.951153	−	0.308721i	$-0.0999010\pi$
$152$	−0.869611	+	2.69143i	−0.0705347	+	0.218304i
$153$	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	$0.880246\pi$
$158$	2.69119	+	1.95301i	0.214099	+	0.155373i
$159$	23.3646			1.85293
$160$	6.46086	+	10.8746i	0.510776	+	0.859714i
$161$	8.12864			0.640627
$162$	−6.56642	−	4.76529i	−0.515907	−	0.374397i
$163$	8.64721	+	8.64721i	0.677302	+	0.677302i	0.959389	−	0.282087i	$-0.0910266\pi$
$163$	8.64721	+	8.64721i	0.677302	+	0.677302i	−0.282087	+	0.959389i	$0.591027\pi$
$164$	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	−0.854408	−	0.519602i	$-0.826080\pi$
$167$	−4.32665	+	4.32665i	−0.334806	+	0.334806i	0.519602	+	0.854408i	$0.326080\pi$
$168$	−6.33274	+	19.5997i	−0.488582	+	1.51215i
$169$		−	5.34174i		−	0.410903i
$170$	−5.18130	+	4.28482i	−0.397388	+	0.328631i
$171$		−	3.84798i		−	0.294263i
$172$	−9.50949	+	18.7141i	−0.725091	+	1.42693i
$173$	−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
$178$	10.2258	−	14.0908i	0.766454	−	1.05615i
$179$	−21.2426			−1.58775			−0.793875	−	0.608081i	$-0.791939\pi$
$179$	−21.2426			−1.58775			−0.793875	+	0.608081i	$0.791939\pi$
$180$	−12.9127	−	11.3755i	−0.962454	−	0.847880i
$181$	7.04939			0.523977			0.261988	−	0.965071i	$-0.415622\pi$
$181$	7.04939			0.523977			0.261988	+	0.965071i	$0.415622\pi$
$182$	9.89947	−	13.6412i	0.733798	−	1.01115i
$183$	−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
$188$	4.34489	+	2.20784i	0.316884	+	0.161023i
$189$		−	6.17524i		−	0.449182i
$190$	−0.298148	+	3.14819i	−0.0216299	+	0.228394i
$191$		−	19.1334i		−	1.38445i	−0.721684	−	0.692223i	$-0.756632\pi$
$191$		−	19.1334i		−	1.38445i	0.721684	−	0.692223i	$-0.243368\pi$
$192$	−3.34288	−	20.6663i	−0.241252	−	1.49146i
$193$	−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	$0.703296\pi$
$198$	4.57113	+	3.31730i	0.324856	+	0.235750i
$199$	−10.8066			−0.766058			−0.383029	−	0.923736i	$-0.625119\pi$
$199$	−10.8066			−0.766058			−0.383029	+	0.923736i	$0.625119\pi$
$200$	9.68300	+	10.3073i	0.684691	+	0.728833i
$201$	−34.5193			−2.43480
$202$	5.84218	+	4.23971i	0.411055	+	0.298305i
$203$	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
$208$	−2.64279	+	16.9258i	−0.183244	+	1.17359i
$209$		−	1.03788i		−	0.0717914i
$210$	−2.17119	+	22.9260i	−0.149827	+	1.58204i
$211$			12.5073i			0.861037i	0.902582	+	0.430519i	$0.141669\pi$
$211$			12.5073i			0.861037i	−0.902582	+	0.430519i	$0.858331\pi$
$212$	15.9195	+	8.08945i	1.09336	+	0.555586i
$213$	−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
$218$	9.53221	−	13.1351i	0.645603	−	0.889620i
$219$	26.5974			1.79729
$220$	−3.48280	−	3.06820i	−0.234810	−	0.206858i
$221$	−9.10576			−0.612520
$222$	−17.4925	+	24.1042i	−1.17402	+	1.61777i
$223$	10.6640	+	10.6640i	0.714115	+	0.714115i	0.967393	−	0.253278i	$-0.0815089\pi$
$223$	10.6640	+	10.6640i	0.714115	+	0.714115i	−0.253278	+	0.967393i	$0.581509\pi$
$224$	−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	$-0.360388\pi$
$227$	20.0388	−	20.0388i	1.33002	−	1.33002i	0.905345	−	0.424676i	$-0.139612\pi$
$228$	2.37095	−	4.66589i	0.157020	−	0.309006i
$229$			4.26484i			0.281828i	0.990022	+	0.140914i	$0.0450042\pi$
$229$			4.26484i			0.281828i	−0.990022	+	0.140914i	$0.954996\pi$
$230$	−7.11828	+	5.88666i	−0.469366	+	0.388155i
$231$		−	7.55810i		−	0.497287i
$232$	−7.04290	−	2.27559i	−0.462389	−	0.149400i
$233$	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
$238$	−6.77216	−	4.91460i	−0.438974	−	0.318566i
$239$	−12.9188			−0.835649			−0.417825	−	0.908528i	$-0.637207\pi$
$239$	−12.9188			−0.835649			−0.417825	+	0.908528i	$0.637207\pi$
$240$	−8.64825	−	21.7496i	−0.558242	−	1.40393i
$241$	11.4927			0.740311			0.370155	−	0.928970i	$-0.379304\pi$
$241$	11.4927			0.740311			0.370155	+	0.928970i	$0.379304\pi$
$242$	−11.3574	−	8.24216i	−0.730083	−	0.529826i
$243$	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
$248$	17.4127	+	5.62612i	1.10571	+	0.357259i
$249$		−	29.9735i		−	1.89949i
$250$	13.0629	+	8.90850i	0.826169	+	0.563423i
$251$			0.449035i			0.0283428i	0.999900	+	0.0141714i	$0.00451105\pi$
$251$			0.449035i			0.0283428i	−0.999900	+	0.0141714i	$0.995489\pi$
$252$	9.70198	−	19.0929i	0.611168	−	1.20274i
$253$	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	$0.964363\pi$
$258$	22.8141	−	31.4371i	1.42034	−	1.95719i
$259$	22.3950			1.39156
$260$	1.20975	+	19.1147i	0.0750253	+	1.18544i
$261$	10.0694			0.623278
$262$	−10.5773	+	14.5752i	−0.653467	+	0.900457i
$263$	−13.5610	−	13.5610i	−0.836207	−	0.836207i	0.152150	−	0.988357i	$-0.451380\pi$
$263$	−13.5610	−	13.5610i	−0.836207	−	0.836207i	−0.988357	+	0.152150i	$0.951380\pi$
$264$	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
$268$	−23.5198	−	11.9515i	−1.43670	−	0.730054i
$269$		−	18.6745i		−	1.13861i	−0.822128	−	0.569303i	$-0.807213\pi$
$269$		−	18.6745i		−	1.13861i	0.822128	−	0.569303i	$-0.192787\pi$
$270$	4.47203	+	5.40768i	0.272159	+	0.329101i
$271$		−	17.2153i		−	1.04575i	−0.852408	−	0.522877i	$-0.824859\pi$
$271$		−	17.2153i		−	1.04575i	0.852408	−	0.522877i	$-0.175141\pi$
$272$	8.40283	+	1.31201i	0.509497	+	0.0795524i
$273$	−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	$0.566868\pi$
$278$	1.71204	+	1.24244i	0.102681	+	0.0745164i
$279$	−24.8953			−1.49044
$280$	−9.41694	+	14.8690i	−0.562770	+	0.888590i
$281$	−17.6380			−1.05219			−0.526096	−	0.850425i	$-0.676345\pi$
$281$	−17.6380			−1.05219			−0.526096	+	0.850425i	$0.676345\pi$
$282$	−7.29882	−	5.29680i	−0.434638	−	0.315420i
$283$	−11.1509	−	11.1509i	−0.662854	−	0.662854i	0.293198	−	0.956052i	$-0.405281\pi$
$283$	−11.1509	−	11.1509i	−0.662854	−	0.662854i	−0.956052	+	0.293198i	$0.905281\pi$
$284$	−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
$288$	0.0596154	+	21.7674i	0.00351287	+	1.28266i
$289$		−	12.4794i		−	0.734085i
$290$	−8.23816	−	0.780190i	−0.483761	−	0.0458143i
$291$		−	34.3506i		−	2.01367i
$292$	18.1222	+	9.20873i	1.06052	+	0.538900i
$293$	−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
$298$	−9.65560	+	13.3051i	−0.559334	+	0.770745i
$299$	−12.5099			−0.723464
$300$	−14.7014	−	21.6487i	−0.848785	−	1.24989i
$301$	−29.2080			−1.68352
$302$	−6.30218	+	8.68421i	−0.362650	+	0.499720i
$303$	−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	−0.814899	−	0.579603i	$-0.803208\pi$
$307$	−4.12272	+	4.12272i	−0.235296	+	0.235296i	0.579603	+	0.814899i	$0.303208\pi$
$308$	2.61682	−	5.14973i	0.149107	−	0.293433i
$309$		−	45.6488i		−	2.59687i
$310$	20.3679	+	1.92893i	1.15682	+	0.109556i
$311$		−	1.78593i		−	0.101271i	−0.998717	−	0.0506355i	$-0.983875\pi$
$311$		−	1.78593i		−	0.101271i	0.998717	−	0.0506355i	$-0.0161247\pi$
$312$	9.74600	−	30.1637i	0.551759	−	1.70768i
$313$	−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	$0.479927\pi$
$318$	−26.7426	−	19.4073i	−1.49965	−	1.08831i
$319$	2.71591			0.152061
$320$	1.63780	−	17.8134i	0.0915557	−	0.995800i
$321$	36.7503			2.05120
$322$	−9.30386	−	6.75187i	−0.518484	−	0.376267i
$323$	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
$328$	8.27231	−	25.6026i	0.456762	−	1.41367i
$329$			6.78128i			0.373864i
$330$	5.47348	+	6.61866i	0.301305	+	0.364345i
$331$		−	10.4089i		−	0.572123i	−0.958211	−	0.286062i	$-0.907654\pi$
$331$		−	10.4089i		−	0.572123i	0.958211	−	0.286062i	$-0.0923462\pi$
$332$	10.3776	−	20.4225i	0.569546	−	1.12083i
$333$	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	$0.739997\pi$
$338$	−4.43699	+	6.11404i	−0.241341	+	0.332560i
$339$	11.6874			0.634774
$340$	9.48950	−	0.600579i	0.514640	−	0.0325710i
$341$	−6.71475			−0.363624
$342$	−3.19624	+	4.40432i	−0.172833	+	0.238158i
$343$	−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	−0.738921	−	0.673792i	$-0.764664\pi$
$347$	−1.21322	+	1.21322i	−0.0651292	+	0.0651292i	0.673792	+	0.738921i	$0.264664\pi$
$348$	12.2097	+	6.20429i	0.654506	+	0.332585i
$349$			17.7577i			0.950546i	0.879838	+	0.475273i	$0.157651\pi$
$349$			17.7577i			0.950546i	−0.879838	+	0.475273i	$0.842349\pi$
$350$	−6.68215	+	18.5082i	−0.357176	+	0.989306i
$351$			9.50360i			0.507265i
$352$	0.0160795	+	5.87109i	0.000857038	+	0.312930i
$353$	−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
$358$	24.3139	+	17.6447i	1.28503	+	0.932552i
$359$	−18.0679			−0.953588			−0.476794	−	0.879015i	$-0.658201\pi$
$359$	−18.0679			−0.953588			−0.476794	+	0.879015i	$0.658201\pi$
$360$	5.33076	+	23.7458i	0.280956	+	1.25151i
$361$	1.00000			0.0526316
$362$	−8.06858	−	5.85541i	−0.424075	−	0.307754i
$363$	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	−0.521585	−	0.853199i	$-0.674659\pi$
$367$	6.35282	−	6.35282i	0.331615	−	0.331615i	0.853199	+	0.521585i	$0.174659\pi$
$368$	11.5441	+	1.80249i	0.601780	+	0.0939615i
$369$			36.6046i			1.90556i
$370$	−19.6114	+	16.2182i	−1.01955	+	0.843143i
$371$			24.8464i			1.28996i
$372$	−30.1869	−	15.3394i	−1.56512	−	0.795309i
$373$	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
$378$	−5.12932	+	7.06804i	−0.263824	+	0.363541i
$379$	13.5325			0.695117			0.347558	−	0.937658i	$-0.387011\pi$
$379$	13.5325			0.695117			0.347558	+	0.937658i	$0.387011\pi$
$380$	2.95623	−	3.35570i	0.151651	−	0.172144i
$381$	7.28444			0.373193
$382$	−15.8927	+	21.8997i	−0.813143	+	1.12049i
$383$	19.1908	+	19.1908i	0.980603	+	0.980603i	0.999815	−	0.0192125i	$-0.00611592\pi$
$383$	19.1908	+	19.1908i	0.980603	+	0.980603i	−0.0192125	+	0.999815i	$0.506116\pi$
$384$	−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
$388$	11.8931	−	23.4049i	0.603781	−	1.18820i
$389$			9.02156i			0.457411i	0.973496	+	0.228706i	$0.0734493\pi$
$389$			9.02156i			0.457411i	−0.973496	+	0.228706i	$0.926551\pi$
$390$	3.34144	−	35.2828i	0.169200	−	1.78661i
$391$			6.21052i			0.314080i
$392$	−2.00272	−	0.647088i	−0.101153	−	0.0326829i
$393$	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	$0.701873\pi$
$398$	12.3690	+	8.97624i	0.620001	+	0.449938i
$399$	7.28228			0.364570
$400$	−2.52145	−	19.8404i	−0.126073	−	0.992021i
$401$	−5.54417			−0.276863			−0.138431	−	0.990372i	$-0.544206\pi$
$401$	−5.54417			−0.276863			−0.138431	+	0.990372i	$0.544206\pi$
$402$	39.5100	+	28.6726i	1.97058	+	1.43006i
$403$	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
$408$	−14.9748	−	4.83841i	−0.741361	−	0.239537i
$409$			9.73164i			0.481199i	0.970625	+	0.240599i	$0.0773440\pi$
$409$			9.73164i			0.481199i	−0.970625	+	0.240599i	$0.922656\pi$
$410$	2.83618	−	29.9477i	0.140069	−	1.47901i
$411$			34.3976i			1.69671i
$412$	15.8048	−	31.1029i	0.778648	−	1.53233i
$413$	−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
$418$	−0.862088	+	1.18793i	−0.0421661	+	0.0581036i
$419$	−14.5558			−0.711095			−0.355548	−	0.934658i	$-0.615706\pi$
$419$	−14.5558			−0.711095			−0.355548	+	0.934658i	$0.615706\pi$
$420$	21.5281	−	24.4371i	1.05046	−	1.19241i
$421$	−16.2488			−0.791917			−0.395958	−	0.918268i	$-0.629588\pi$
$421$	−16.2488			−0.791917			−0.395958	+	0.918268i	$0.629588\pi$
$422$	10.3889	−	14.3156i	0.505723	−	0.696871i
$423$	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
$428$	25.0399	+	12.7239i	1.21035	+	0.615034i
$429$			11.6318i			0.561589i
$430$	25.5775	−	21.1520i	1.23346	−	1.02004i
$431$			6.61387i			0.318579i	0.987232	+	0.159289i	$0.0509203\pi$
$431$			6.61387i			0.318579i	−0.987232	+	0.159289i	$0.949080\pi$
$432$	1.36933	−	8.76996i	0.0658821	−	0.421945i
$433$	−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
$438$	−30.4428	−	22.0925i	−1.45461	−	1.05562i
$439$	27.5314			1.31400			0.657001	−	0.753889i	$-0.271825\pi$
$439$	27.5314			1.31400			0.657001	+	0.753889i	$0.271825\pi$
$440$	1.43781	+	6.40470i	0.0685450	+	0.305332i
$441$	2.86333			0.136349
$442$	10.4223	+	7.56349i	0.495736	+	0.359759i
$443$	21.2911	+	21.2911i	1.01157	+	1.01157i	0.999932	+	0.0116391i	$0.00370493\pi$
$443$	21.2911	+	21.2911i	1.01157	+	1.01157i	0.0116391	+	0.999932i	$0.496295\pi$
$444$	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
$448$	21.9769	−	3.55488i	1.03831	−	0.167952i
$449$			4.80815i			0.226910i	0.993543	+	0.113455i	$0.0361919\pi$
$449$			4.80815i			0.226910i	−0.993543	+	0.113455i	$0.963808\pi$
$450$	11.5631	+	24.6301i	0.545088	+	1.16108i
$451$			9.87297i			0.464900i
$452$	7.96326	+	4.04650i	0.374560	+	0.190331i
$453$	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	$0.924281\pi$
$458$	3.54249	−	4.88144i	0.165530	−	0.228095i
$459$	4.71807			0.220220
$460$	13.0370	−	0.825099i	0.607855	−	0.0384705i
$461$	−21.0202			−0.979008			−0.489504	−	0.872001i	$-0.662822\pi$
$461$	−21.0202			−0.979008			−0.489504	+	0.872001i	$0.662822\pi$
$462$	−6.27796	+	8.65084i	−0.292077	+	0.402473i
$463$	−25.9750	−	25.9750i	−1.20716	−	1.20716i	−0.971942	−	0.235221i	$-0.924419\pi$
$463$	−25.9750	−	25.9750i	−1.20716	−	1.20716i	−0.235221	−	0.971942i	$-0.575581\pi$
$464$	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	−0.954126	−	0.299406i	$-0.903211\pi$
$467$	−14.1486	+	14.1486i	−0.654720	+	0.654720i	0.299406	+	0.954126i	$0.403211\pi$
$468$	−14.9312	+	29.3837i	−0.690195	+	1.35826i
$469$		−	36.7085i		−	1.69504i
$470$	−4.91092	−	5.93839i	−0.226524	−	0.273918i
$471$		−	26.0909i		−	1.20220i
$472$	11.0685	−	34.2569i	0.509470	−	1.57680i
$473$	−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
$478$	14.7866	+	10.7307i	0.676323	+	0.490812i
$479$	−19.7192			−0.900995			−0.450497	−	0.892778i	$-0.648753\pi$
$479$	−19.7192			−0.900995			−0.450497	+	0.892778i	$0.648753\pi$
$480$	−8.16724	+	32.0776i	−0.372782	+	1.46414i
$481$	−34.4656			−1.57150
$482$	−13.1543	−	9.54616i	−0.599162	−	0.434816i
$483$	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	−0.649584	−	0.760290i	$-0.725057\pi$
$487$	2.44306	−	2.44306i	0.110705	−	0.110705i	0.760290	+	0.649584i	$0.225057\pi$
$488$	−0.476508	+	1.47478i	−0.0215705	+	0.0667603i
$489$			32.0017i			1.44716i
$490$	−2.34261	−	0.221855i	−0.105828	−	0.0100224i
$491$			10.1967i			0.460172i	0.973170	+	0.230086i	$0.0739008\pi$
$491$			10.1967i			0.460172i	−0.973170	+	0.230086i	$0.926099\pi$
$492$	−22.5541	+	44.3850i	−1.01682	+	2.00103i
$493$	−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
$498$	−24.8968	+	34.3070i	−1.11565	+	1.53733i
$499$	−41.0266			−1.83660			−0.918302	−	0.395880i	$-0.870439\pi$
$499$	−41.0266			−1.83660			−0.918302	+	0.395880i	$0.870439\pi$
$500$	−7.55183	−	21.0468i	−0.337728	−	0.941244i
$501$	−16.0121			−0.715368
$502$	0.372981	−	0.513955i	0.0166469	−	0.0229390i
$503$	18.8172	+	18.8172i	0.839018	+	0.839018i	0.988730	−	0.149711i	$-0.0478344\pi$
$503$	18.8172	+	18.8172i	0.839018	+	0.839018i	−0.149711	+	0.988730i	$0.547834\pi$
$504$	−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
$508$	4.96327	+	2.52207i	0.220210	+	0.111899i
$509$			23.1012i			1.02394i	0.859003	+	0.511971i	$0.171084\pi$
$509$			23.1012i			1.02394i	−0.859003	+	0.511971i	$0.828916\pi$
$510$	−17.5161	−	1.65886i	−0.775628	−	0.0734554i
$511$			28.2842i			1.25122i
$512$	−18.2402	+	13.3901i	−0.806110	+	0.591766i
$513$	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
$518$	−25.6328	−	18.6019i	−1.12624	−	0.817321i
$519$	−25.1024			−1.10187
$520$	14.4925	−	22.8831i	0.635539	−	1.00349i
$521$	17.4818			0.765892			0.382946	−	0.923771i	$-0.374910\pi$
$521$	17.4818			0.765892			0.382946	+	0.923771i	$0.374910\pi$
$522$	−11.5252	−	8.36389i	−0.504443	−	0.366077i
$523$	−22.9784	−	22.9784i	−1.00478	−	1.00478i	−0.999989	−	0.00478820i	$-0.998476\pi$
$523$	−22.9784	−	22.9784i	−1.00478	−	1.00478i	−0.00478820	−	0.999989i	$-0.501524\pi$
$524$	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
$528$	1.67598	−	10.7339i	0.0729376	−	0.467132i
$529$		−	14.4677i		−	0.629032i
$530$	−17.9934	−	21.7581i	−0.781584	−	0.945110i
$531$			48.9776i			2.12545i
$532$	4.96179	+	2.52132i	0.215121	+	0.109313i
$533$	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
$538$	−15.5116	+	21.3745i	−0.668751	+	0.921519i
$539$	0.772297			0.0332652
$540$	−0.626819	−	9.90410i	−0.0269740	−	0.426204i
$541$	35.7902			1.53874			0.769371	−	0.638802i	$-0.220570\pi$
$541$	35.7902			1.53874			0.769371	+	0.638802i	$0.220570\pi$
$542$	−14.2995	+	19.7042i	−0.614215	+	0.846369i
$543$	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	−0.990617	−	0.136667i	$-0.956361\pi$
$547$	−19.9722	+	19.9722i	−0.853950	+	0.853950i	0.136667	+	0.990617i	$0.456361\pi$
$548$	−11.9094	+	23.4369i	−0.508742	+	1.00117i
$549$		−	2.10852i		−	0.0899896i
$550$	3.11879	+	6.64323i	0.132985	+	0.283268i
$551$			2.61679i			0.111479i
$552$	−20.5729	−	6.64719i	−0.875642	−	0.282923i
$553$	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	$0.942417\pi$
$558$	28.4946	+	20.6787i	1.20627	+	0.875400i
$559$	44.9506			1.90121
$560$	23.1290	−	9.19671i	0.977378	−	0.388632i
$561$	5.77462			0.243804
$562$	20.1880	+	14.6506i	0.851581	+	0.617997i
$563$	−33.3205	−	33.3205i	−1.40429	−	1.40429i	−0.785757	−	0.618535i	$-0.787726\pi$
$563$	−33.3205	−	33.3205i	−1.40429	−	1.40429i	−0.618535	−	0.785757i	$-0.712274\pi$
$564$	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
$568$	0.572267	+	0.184902i	0.0240118	+	0.00775830i
$569$		−	44.6559i		−	1.87207i	−0.351905	−	0.936036i	$-0.614466\pi$
$569$		−	44.6559i		−	1.87207i	0.351905	−	0.936036i	$-0.385534\pi$
$570$	−6.37712	+	5.27373i	−0.267108	+	0.220892i
$571$		−	2.61268i		−	0.109337i	−0.998505	−	0.0546686i	$-0.982590\pi$
$571$		−	2.61268i		−	0.109337i	0.998505	−	0.0546686i	$-0.0174102\pi$
$572$	−4.02724	+	7.92536i	−0.168387	+	0.331376i
$573$	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	$0.656967\pi$
$578$	−10.3658	+	14.2837i	−0.431159	+	0.594123i
$579$	−43.0789			−1.79030
$580$	8.78117	+	7.73582i	0.364618	+	0.321213i
$581$	31.8744			1.32237
$582$	−28.5326	+	39.3170i	−1.18271	+	1.62974i
$583$	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	−0.792290	−	0.610145i	$-0.791111\pi$
$587$	−4.41302	+	4.41302i	−0.182145	+	0.182145i	0.610145	+	0.792290i	$0.291111\pi$
$588$	3.47194	+	1.76426i	0.143181	+	0.0727567i
$589$		−	6.46970i		−	0.266579i
$590$	3.79487	−	40.0706i	0.156232	−	1.64968i
$591$			10.7395i			0.441766i
$592$	31.8050	+	4.96600i	1.30718	+	0.204102i
$593$	−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
$598$	14.3185	+	10.3910i	0.585527	+	0.424921i
$599$	16.3544			0.668223			0.334112	−	0.942534i	$-0.391564\pi$
$599$	16.3544			0.668223			0.334112	+	0.942534i	$0.391564\pi$
$600$	−1.15514	+	36.9900i	−0.0471584	+	1.51011i
$601$	−26.4268			−1.07797			−0.538986	−	0.842315i	$-0.681193\pi$
$601$	−26.4268			−1.07797			−0.538986	+	0.842315i	$0.681193\pi$
$602$	33.4308	+	24.2609i	1.36254	+	0.988801i
$603$	−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	$-0.423532\pi$
$607$	29.7918	−	29.7918i	1.20921	−	1.20921i	0.971283	−	0.237928i	$-0.0764683\pi$
$608$	−5.65683	+	0.0154926i	−0.229415	+	0.000628310i
$609$			19.0562i			0.772196i
$610$	−0.163372	+	1.72507i	−0.00661473	+	0.0698460i
$611$		−	10.4363i		−	0.422207i
$612$	14.5875	+	7.41261i	0.589666	+	0.299637i
$613$	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	$0.893006\pi$
$618$	−37.9171	+	52.2486i	−1.52525	+	2.10175i
$619$	−3.44832			−0.138600			−0.0692998	−	0.997596i	$-0.522077\pi$
$619$	−3.44832			−0.138600			−0.0692998	+	0.997596i	$0.522077\pi$
$620$	−21.7104	−	19.1259i	−0.871910	−	0.768115i
$621$	6.48186			0.260108
$622$	−1.48344	+	2.04414i	−0.0594807	+	0.0819626i
$623$	−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
$628$	9.03336	−	17.7771i	0.360470	−	0.709383i
$629$			17.1105i			0.682239i
$630$	−26.0953	+	21.5802i	−1.03966	+	0.859775i
$631$		−	0.748834i		−	0.0298106i	−0.999889	−	0.0149053i	$-0.995255\pi$
$631$		−	0.748834i		−	0.0298106i	0.999889	−	0.0149053i	$-0.00474468\pi$
$632$	−2.04467	+	6.32821i	−0.0813326	+	0.251723i
$633$	−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
$638$	−3.10857	−	2.25590i	−0.123069	−	0.0893121i
$639$	−0.818180			−0.0323667
$640$	−16.6709	+	19.0284i	−0.658975	+	0.752165i
$641$	31.9208			1.26080			0.630399	−	0.776272i	$-0.282891\pi$
$641$	31.9208			1.26080			0.630399	+	0.776272i	$0.282891\pi$
$642$	−42.0636	−	30.5258i	−1.66012	−	1.20476i
$643$	17.2796	+	17.2796i	0.681442	+	0.681442i	0.960325	−	0.278883i	$-0.0899641\pi$
$643$	17.2796	+	17.2796i	0.681442	+	0.681442i	−0.278883	+	0.960325i	$0.589964\pi$
$644$	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	−0.583080	−	0.812415i	$-0.698152\pi$
$647$	5.83342	−	5.83342i	0.229335	−	0.229335i	0.812415	+	0.583080i	$0.198152\pi$
$648$	4.98894	−	15.4407i	0.195984	−	0.606567i
$649$			13.2102i			0.518547i
$650$	10.2837	−	28.4839i	0.403361	−	1.11723i
$651$		−	47.1142i		−	1.84655i
$652$	−11.0798	+	21.8044i	−0.433919	+	0.853926i
$653$	−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
$658$	5.63272	−	7.76171i	0.219586	−	0.302583i
$659$	−33.1519			−1.29141			−0.645707	−	0.763586i	$-0.723437\pi$
$659$	−33.1519			−1.29141			−0.645707	+	0.763586i	$0.723437\pi$
$660$	−0.767187	−	12.1220i	−0.0298627	−	0.471848i
$661$	13.0904			0.509157			0.254578	−	0.967052i	$-0.418063\pi$
$661$	13.0904			0.509157			0.254578	+	0.967052i	$0.418063\pi$
$662$	−8.64589	+	11.9138i	−0.336032	+	0.463042i
$663$	−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
$668$	−10.9099	−	5.54381i	−0.422116	−	0.214497i
$669$			39.4654i			1.52582i
$670$	26.5838	+	32.1457i	1.02702	+	1.24190i
$671$		−	0.568710i		−	0.0219548i
$672$	−41.1946	+	0.112822i	−1.58912	+	0.00435219i
$673$	−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	$0.931119\pi$
$678$	−13.3772	−	9.70790i	−0.513748	−	0.372830i
$679$	36.5291			1.40186
$680$	−11.3603	−	7.19482i	−0.435649	−	0.275909i
$681$	74.1597			2.84181
$682$	7.68556	+	5.57745i	0.294295	+	0.213572i
$683$	9.54011	+	9.54011i	0.365042	+	0.365042i	0.865665	−	0.500623i	$-0.166896\pi$
$683$	9.54011	+	9.54011i	0.365042	+	0.365042i	−0.500623	+	0.865665i	$0.666896\pi$
$684$	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
$688$	−41.4806	−	6.47675i	−1.58143	−	0.246924i
$689$		−	38.2382i		−	1.45676i
$690$	−24.0644	−	2.27900i	−0.916115	−	0.0867602i
$691$			6.36671i			0.242201i	0.992640	+	0.121101i	$0.0386423\pi$
$691$			6.36671i			0.242201i	−0.992640	+	0.121101i	$0.961358\pi$
$692$	−17.1036	−	8.69113i	−0.650181	−	0.330387i
$693$	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
$698$	14.7500	−	20.3250i	0.558296	−	0.769314i
$699$	20.9759			0.793382
$700$	23.0217	−	15.6337i	0.870138	−	0.590900i
$701$	−6.31090			−0.238359			−0.119180	−	0.992873i	$-0.538026\pi$
$701$	−6.31090			−0.238359			−0.119180	+	0.992873i	$0.538026\pi$
$702$	7.89395	−	10.8776i	0.297938	−	0.410549i
$703$	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
$708$	−30.1778	+	59.3881i	−1.13415	+	2.23194i
$709$			8.83115i			0.331661i	0.986154	+	0.165830i	$0.0530305\pi$
$709$			8.83115i			0.331661i	−0.986154	+	0.165830i	$0.946970\pi$
$710$	0.669387	+	0.0633939i	0.0251216	+	0.00237913i
$711$		−	9.04756i		−	0.339310i
$712$	33.1339	+	10.7057i	1.24175	+	0.401213i
$713$	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
$718$	20.6801	+	15.0077i	0.771776	+	0.560082i
$719$	6.07284			0.226479			0.113239	−	0.993568i	$-0.463877\pi$
$719$	6.07284			0.226479			0.113239	+	0.993568i	$0.463877\pi$
$720$	13.6224	−	31.6068i	0.507677	−	1.17791i
$721$	48.5438			1.80787
$722$	−1.14458	−	0.830627i	−0.0425968	−	0.0309127i
$723$	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	−0.564307	−	0.825565i	$-0.690857\pi$
$727$	7.04427	−	7.04427i	0.261257	−	0.261257i	0.825565	+	0.564307i	$0.190857\pi$
$728$	32.0766	+	10.3641i	1.18884	+	0.384118i
$729$			39.4967i			1.46284i
$730$	−20.4831	−	24.7686i	−0.758112	−	0.916726i
$731$		−	22.3157i		−	0.825378i
$732$	1.29918	−	2.55670i	0.0480190	−	0.0944983i
$733$	−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
$738$	30.4047	−	41.8968i	1.11921	−	1.54224i
$739$	−1.95220			−0.0718127			−0.0359063	−	0.999355i	$-0.511432\pi$
$739$	−1.95220			−0.0718127			−0.0359063	+	0.999355i	$0.511432\pi$
$740$	35.9180	−	2.27321i	1.32037	−	0.0835649i
$741$	−11.2073			−0.411711
$742$	20.6381	−	28.4386i	0.757648	−	1.04401i
$743$	−15.3093	−	15.3093i	−0.561643	−	0.561643i	0.368131	−	0.929774i	$-0.379998\pi$
$743$	−15.3093	−	15.3093i	−0.561643	−	0.561643i	−0.929774	+	0.368131i	$0.879998\pi$
$744$	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
$748$	3.93455	+	1.99933i	0.143861	+	0.0731026i
$749$			39.0810i			1.42799i
$750$	7.68726	+	40.6559i	0.280699	+	1.48454i
$751$			24.6066i			0.897906i	0.893555	+	0.448953i	$0.148203\pi$
$751$			24.6066i			0.897906i	−0.893555	+	0.448953i	$0.851797\pi$
$752$	−1.50372	+	9.63065i	−0.0548351	+	0.351194i
$753$	−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	$0.653736\pi$
$758$	−15.4890	−	11.2404i	−0.562585	−	0.408271i
$759$	7.93339			0.287964
$760$	−6.17097	+	1.38534i	−0.223845	+	0.0502515i
$761$	7.77947			0.282006			0.141003	−	0.990009i	$-0.454967\pi$
$761$	7.77947			0.282006			0.141003	+	0.990009i	$0.454967\pi$
$762$	−8.33761	−	6.05065i	−0.302040	−	0.219192i
$763$	−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
$768$	37.2226	−	19.1718i	1.34316	−	0.691803i
$769$		−	8.36208i		−	0.301544i	−0.988569	−	0.150772i	$-0.951824\pi$
$769$		−	8.36208i		−	0.301544i	0.988569	−	0.150772i	$-0.0481760\pi$
$770$	−7.03841	+	5.82060i	−0.253647	+	0.209760i
$771$		−	52.3287i		−	1.88457i

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)

\(f(q)\)	\(=\)	\(q+(-1.14458 - 0.830627i) q^{2} +(1.85040 + 1.85040i) q^{3} +(0.620117 + 1.90143i) q^{4} +(1.13686 + 1.92550i) q^{5} +(-0.580936 - 3.65493i) q^{6} +(-1.96775 + 1.96775i) q^{7} +(0.869611 - 2.69143i) q^{8} +3.84798i q^{9} +O(q^{10})\)	\(q+(-1.14458 - 0.830627i) 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} +(0.869611 - 2.69143i) q^{8} +3.84798i q^{9} +(0.298148 - 3.14819i) q^{10} +1.03788i q^{11} +(-2.37095 + 4.66589i) 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} +(3.19624 - 4.40432i) q^{18} -1.00000 q^{19} +(-2.95623 + 3.35570i) q^{20} -7.28228 q^{21} +(0.862088 - 1.18793i) 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} +(-4.96179 - 2.52132i) q^{28} -2.61679i q^{29} +(6.37712 - 5.27373i) q^{30} +6.46970i q^{31} +(5.65683 - 0.0154926i) 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} +(1.14458 + 0.830627i) q^{38} +11.2073 q^{39} +(6.17097 - 1.38534i) q^{40} +9.51266 q^{41} +(8.33513 + 6.04886i) 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} +(-10.3422 - 1.61482i) q^{48} -0.744112i q^{49} +(6.40079 - 3.00497i) q^{50} -5.56388i q^{51} +(7.63613 + 3.88027i) 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} +(-2.17358 + 2.99512i) q^{58} +12.7281 q^{59} +(-11.6796 + 0.739189i) q^{60} -0.547956 q^{61} +(5.37391 - 7.40508i) 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} +(1.92636 - 3.79096i) q^{68} -7.64387i q^{69} +(5.60818 + 6.78155i) q^{70} +0.212626i q^{71} +(10.3566 + 3.34625i) 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} +(-12.8276 - 9.30910i) q^{78} -2.35125 q^{79} +(-8.21385 - 3.54014i) q^{80} +5.73698 q^{81} +(-10.8880 - 7.90148i) 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} +(2.79337 + 0.902548i) q^{88} +12.3109i q^{89} +(12.1142 + 1.14727i) q^{90} +11.9181i q^{91} +(2.64651 - 5.20817i) 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} +(-0.618080 + 0.851695i) 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	\( 52 q + 2 q^{2} + 2 q^{3} + 4 q^{5} - 4 q^{6} + 4 q^{7} - 4 q^{8} + 2 q^{10} + 22 q^{12} - 2 q^{13} - 2 q^{15} + 16 q^{16} - 20 q^{17} - 2 q^{18} - 52 q^{19} - 12 q^{20} - 16 q^{21} - 36 q^{22} - 20 q^{23} - 16 q^{25} + 8 q^{27} - 24 q^{28} + 40 q^{30} + 2 q^{32} + 8 q^{33} + 20 q^{34} - 12 q^{35} - 4 q^{36} + 10 q^{37} - 2 q^{38} + 64 q^{39} - 36 q^{40} - 4 q^{41} - 60 q^{42} + 28 q^{43} - 8 q^{44} + 12 q^{45} - 8 q^{46} + 4 q^{47} - 2 q^{48} + 46 q^{50} + 74 q^{52} - 2 q^{53} + 24 q^{54} + 12 q^{56} - 2 q^{57} - 20 q^{58} - 28 q^{59} - 110 q^{60} - 4 q^{61} - 32 q^{62} - 44 q^{63} - 24 q^{64} + 10 q^{65} + 36 q^{66} - 6 q^{67} + 28 q^{68} + 124 q^{70} + 124 q^{72} + 8 q^{73} + 88 q^{74} - 2 q^{75} + 12 q^{77} - 40 q^{78} + 52 q^{79} - 120 q^{80} - 24 q^{81} - 80 q^{82} + 76 q^{83} - 40 q^{84} + 12 q^{85} - 8 q^{86} - 12 q^{87} + 20 q^{88} + 78 q^{90} + 8 q^{92} + 24 q^{93} + 32 q^{94} - 4 q^{95} - 4 q^{96} - 10 q^{97} - 122 q^{98} - 128 q^{99}+O(q^{100}) \) 52 * q + 2 * q^2 + 2 * q^3 + 4 * q^5 - 4 * q^6 + 4 * q^7 - 4 * q^8 + 2 * q^10 + 22 * q^12 - 2 * q^13 - 2 * q^15 + 16 * q^16 - 20 * q^17 - 2 * q^18 - 52 * q^19 - 12 * q^20 - 16 * q^21 - 36 * q^22 - 20 * q^23 - 16 * q^25 + 8 * q^27 - 24 * q^28 + 40 * q^30 + 2 * q^32 + 8 * q^33 + 20 * q^34 - 12 * q^35 - 4 * q^36 + 10 * q^37 - 2 * q^38 + 64 * q^39 - 36 * q^40 - 4 * q^41 - 60 * q^42 + 28 * q^43 - 8 * q^44 + 12 * q^45 - 8 * q^46 + 4 * q^47 - 2 * q^48 + 46 * q^50 + 74 * q^52 - 2 * q^53 + 24 * q^54 + 12 * q^56 - 2 * q^57 - 20 * q^58 - 28 * q^59 - 110 * q^60 - 4 * q^61 - 32 * q^62 - 44 * q^63 - 24 * q^64 + 10 * q^65 + 36 * q^66 - 6 * q^67 + 28 * q^68 + 124 * q^70 + 124 * q^72 + 8 * q^73 + 88 * q^74 - 2 * q^75 + 12 * q^77 - 40 * q^78 + 52 * q^79 - 120 * q^80 - 24 * q^81 - 80 * q^82 + 76 * q^83 - 40 * q^84 + 12 * q^85 - 8 * q^86 - 12 * q^87 + 20 * q^88 + 78 * q^90 + 8 * q^92 + 24 * q^93 + 32 * q^94 - 4 * q^95 - 4 * q^96 - 10 * q^97 - 122 * q^98 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

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