LMFDB - Embedded newform 384.2.v.a.109.28

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [384,2,Mod(13,384)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(384, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 15, 0]))

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 384 = 2^{7} \cdot 3 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	384.v (of order $32$, degree $16$, 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:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			109.28
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.28

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26090 + 0.640414i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.17974 + 1.61500i) q^{4} +(-0.276206 + 0.336558i) q^{5} +(-0.810126 - 1.15918i) q^{6} +(0.338802 + 0.226380i) q^{7} +(0.453269 + 2.79187i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(1.26090 + 0.640414i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.17974 + 1.61500i) q^{4} +(-0.276206 + 0.336558i) q^{5} +(-0.810126 - 1.15918i) q^{6} +(0.338802 + 0.226380i) q^{7} +(0.453269 + 2.79187i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.563804 + 0.247480i) q^{10} +(5.34125 + 1.62025i) q^{11} +(-0.279134 - 1.98043i) q^{12} +(-0.687095 + 0.563884i) q^{13} +(0.282218 + 0.502416i) q^{14} +(0.402244 - 0.166615i) q^{15} +(-1.21643 + 3.81055i) q^{16} +(-2.42587 - 1.00483i) q^{17} +(0.168034 + 1.40420i) q^{18} +(-0.274116 + 2.78314i) q^{19} +(-0.869391 - 0.0490207i) q^{20} +(-0.192082 - 0.359359i) q^{21} +(5.69715 + 5.46359i) q^{22} +(2.38024 + 0.473459i) q^{23} +(0.916332 - 2.67588i) q^{24} +(0.938470 + 4.71801i) q^{25} +(-1.22748 + 0.270977i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(0.0340950 + 0.814233i) q^{28} +(-2.19967 - 7.25133i) q^{29} +(0.613892 + 0.0475178i) q^{30} +(6.54326 - 6.54326i) q^{31} +(-3.97412 + 4.02571i) q^{32} +(-3.94678 - 3.94678i) q^{33} +(-2.41527 - 2.82054i) q^{34} +(-0.169769 + 0.0514989i) q^{35} +(-0.687392 + 1.87816i) q^{36} +(-8.61002 + 0.848013i) q^{37} +(-2.12800 + 3.33372i) q^{38} +(0.871777 - 0.173407i) q^{39} +(-1.06482 - 0.618580i) q^{40} +(1.68923 - 8.49234i) q^{41} +(-0.0120570 - 0.576128i) q^{42} +(-3.39302 + 1.81361i) q^{43} +(3.68459 + 10.5376i) q^{44} +(-0.433289 - 0.0426753i) q^{45} +(2.69803 + 2.12132i) q^{46} +(2.17271 - 5.24538i) q^{47} +(2.86907 - 2.78719i) q^{48} +(-2.61525 - 6.31376i) q^{49} +(-1.83816 + 6.54995i) q^{50} +(1.66575 + 2.02972i) q^{51} +(-1.72126 - 0.444419i) q^{52} +(0.0205226 - 0.0676539i) q^{53} +(0.513740 - 1.31760i) q^{54} +(-2.02059 + 1.35012i) q^{55} +(-0.478456 + 1.04850i) q^{56} +(1.55371 - 2.32530i) q^{57} +(1.87029 - 10.5519i) q^{58} +(-2.24028 - 1.83855i) q^{59} +(0.743626 + 0.453060i) q^{60} +(-2.98198 + 5.57890i) q^{61} +(12.4408 - 4.06000i) q^{62} +0.407473i q^{63} +(-7.58910 + 2.53094i) q^{64} -0.386995i q^{65} +(-2.44893 - 7.50407i) q^{66} +(-3.71158 + 6.94388i) q^{67} +(-1.23910 - 5.10320i) q^{68} +(-1.87600 - 1.53959i) q^{69} +(-0.247042 - 0.0437875i) q^{70} +(5.59391 - 8.37188i) q^{71} +(-2.06953 + 1.92796i) q^{72} +(8.63592 - 5.77034i) q^{73} +(-11.3995 - 4.44472i) q^{74} +(1.39640 - 4.60330i) q^{75} +(-4.81815 + 2.84069i) q^{76} +(1.44283 + 1.75810i) q^{77} +(1.21028 + 0.339649i) q^{78} +(-1.25986 - 3.04156i) q^{79} +(-0.946487 - 1.46189i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(7.56857 - 9.62619i) q^{82} +(-0.917680 - 0.0903836i) q^{83} +(0.353758 - 0.734162i) q^{84} +(1.00822 - 0.538905i) q^{85} +(-5.43972 + 0.113841i) q^{86} +(-1.47832 + 7.43202i) q^{87} +(-2.10251 + 15.6465i) q^{88} +(-6.22319 + 1.23787i) q^{89} +(-0.519005 - 0.331294i) q^{90} +(-0.360441 + 0.0355003i) q^{91} +(2.04343 + 4.40263i) q^{92} +(-8.85511 + 2.68617i) q^{93} +(6.09878 - 5.22247i) q^{94} +(-0.860977 - 0.860977i) q^{95} +(5.40257 - 1.67697i) q^{96} +(-9.59489 + 9.59489i) q^{97} +(0.745856 - 9.63586i) q^{98} +(1.62025 + 5.34125i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{23}{32}\right)$	$1$

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 $

$2$	1.26090	+	0.640414i	0.891591	+	0.452841i
$2$	1.26090	+	0.640414i	0.891591	+	0.452841i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$4$	1.17974	+	1.61500i	0.589870	+	0.807498i
$5$	−0.276206	+	0.336558i	−0.123523	+	0.150513i	−0.831100	−	0.556123i	$-0.812288\pi$
$5$	−0.276206	+	0.336558i	−0.123523	+	0.150513i	0.707577	+	0.706636i	$0.249788\pi$
$6$	−0.810126	−	1.15918i	−0.330733	−	0.473233i
$7$	0.338802	+	0.226380i	0.128055	+	0.0855636i	0.617948	−	0.786219i	$-0.287964\pi$
$7$	0.338802	+	0.226380i	0.128055	+	0.0855636i	−0.489893	+	0.871783i	$0.662964\pi$
$8$	0.453269	+	2.79187i	0.160255	+	0.987076i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	−0.563804	+	0.247480i	−0.178291	+	0.0782600i
$11$	5.34125	+	1.62025i	1.61045	+	0.488524i	0.962072	−	0.272796i	$-0.0879485\pi$
$11$	5.34125	+	1.62025i	1.61045	+	0.488524i	0.648376	+	0.761320i	$0.275449\pi$
$12$	−0.279134	−	1.98043i	−0.0805790	−	0.571700i
$13$	−0.687095	+	0.563884i	−0.190566	+	0.156393i	−0.724838	−	0.688919i	$-0.758086\pi$
$13$	−0.687095	+	0.563884i	−0.190566	+	0.156393i	0.534273	+	0.845312i	$0.320586\pi$
$14$	0.282218	+	0.502416i	0.0754260	+	0.134276i
$15$	0.402244	−	0.166615i	0.103859	−	0.0430198i
$16$	−1.21643	+	3.81055i	−0.304107	+	0.952638i
$17$	−2.42587	−	1.00483i	−0.588359	−	0.243706i	0.0685856	−	0.997645i	$-0.478151\pi$
$17$	−2.42587	−	1.00483i	−0.588359	−	0.243706i	−0.656944	+	0.753939i	$0.728151\pi$
$18$	0.168034	+	1.40420i	0.0396060	+	0.330972i
$19$	−0.274116	+	2.78314i	−0.0628865	+	0.638497i	0.911145	+	0.412085i	$0.135199\pi$
$19$	−0.274116	+	2.78314i	−0.0628865	+	0.638497i	−0.974032	+	0.226412i	$0.927301\pi$
$20$	−0.869391	−	0.0490207i	−0.194402	−	0.0109614i
$21$	−0.192082	−	0.359359i	−0.0419157	−	0.0784187i
$22$	5.69715	+	5.46359i	1.21464	+	1.16484i
$23$	2.38024	+	0.473459i	0.496314	+	0.0987230i	0.436899	−	0.899510i	$-0.356077\pi$
$23$	2.38024	+	0.473459i	0.496314	+	0.0987230i	0.0594146	+	0.998233i	$0.481077\pi$
$24$	0.916332	−	2.67588i	0.187045	−	0.546212i
$25$	0.938470	+	4.71801i	0.187694	+	0.943602i
$26$	−1.22748	+	0.270977i	−0.240728	+	0.0531429i
$27$	−0.0980171	−	0.995185i	−0.0188634	−	0.191523i
$28$	0.0340950	+	0.814233i	0.00644334	+	0.153876i
$29$	−2.19967	−	7.25133i	−0.408468	−	1.34654i	−0.884266	−	0.466984i	$-0.845341\pi$
$29$	−2.19967	−	7.25133i	−0.408468	−	1.34654i	0.475798	−	0.879555i	$-0.342159\pi$
$30$	0.613892	+	0.0475178i	0.112081	+	0.00867553i
$31$	6.54326	−	6.54326i	1.17520	−	1.17520i	0.194252	−	0.980952i	$-0.437772\pi$
$31$	6.54326	−	6.54326i	1.17520	−	1.17520i	0.980952	−	0.194252i	$-0.0622278\pi$
$32$	−3.97412	+	4.02571i	−0.702532	+	0.711652i
$33$	−3.94678	−	3.94678i	−0.687047	−	0.687047i
$34$	−2.41527	−	2.82054i	−0.414215	−	0.483719i
$35$	−0.169769	+	0.0514989i	−0.0286962	+	0.00870490i
$36$	−0.687392	+	1.87816i	−0.114565	+	0.313027i
$37$	−8.61002	+	0.848013i	−1.41548	+	0.139413i	−0.776648	−	0.629935i	$-0.783082\pi$
$37$	−8.61002	+	0.848013i	−1.41548	+	0.139413i	−0.638831	+	0.769347i	$0.720582\pi$
$38$	−2.12800	+	3.33372i	−0.345207	+	0.540801i
$39$	0.871777	−	0.173407i	0.139596	−	0.0277674i
$40$	−1.06482	−	0.618580i	−0.168363	−	0.0978061i
$41$	1.68923	−	8.49234i	0.263814	−	1.32628i	−0.590717	−	0.806879i	$-0.701155\pi$
$41$	1.68923	−	8.49234i	0.263814	−	1.32628i	0.854530	−	0.519402i	$-0.173845\pi$
$42$	−0.0120570	−	0.576128i	−0.00186044	−	0.0888985i
$43$	−3.39302	+	1.81361i	−0.517431	+	0.276573i	−0.709373	−	0.704834i	$-0.751022\pi$
$43$	−3.39302	+	1.81361i	−0.517431	+	0.276573i	0.191942	+	0.981406i	$0.438522\pi$
$44$	3.68459	+	10.5376i	0.555473	+	1.58860i
$45$	−0.433289	−	0.0426753i	−0.0645910	−	0.00636165i
$46$	2.69803	+	2.12132i	0.397803	+	0.312772i
$47$	2.17271	−	5.24538i	0.316922	−	0.765117i	−0.682492	−	0.730893i	$-0.739104\pi$
$47$	2.17271	−	5.24538i	0.316922	−	0.765117i	0.999414	−	0.0342243i	$-0.0108960\pi$
$48$	2.86907	−	2.78719i	0.414115	−	0.402296i
$49$	−2.61525	−	6.31376i	−0.373606	−	0.901966i
$50$	−1.83816	+	6.54995i	−0.259955	+	0.926302i
$51$	1.66575	+	2.02972i	0.233252	+	0.284218i
$52$	−1.72126	−	0.444419i	−0.238696	−	0.0616298i
$53$	0.0205226	−	0.0676539i	0.00281899	−	0.00929298i	−0.955520	−	0.294928i	$-0.904704\pi$
$53$	0.0205226	−	0.0676539i	0.00281899	−	0.00929298i	0.958339	+	0.285635i	$0.0922044\pi$
$54$	0.513740	−	1.31760i	0.0699112	−	0.179303i
$55$	−2.02059	+	1.35012i	−0.272457	+	0.182050i
$56$	−0.478456	+	1.04850i	−0.0639364	+	0.140112i
$57$	1.55371	−	2.32530i	0.205794	−	0.307993i
$58$	1.87029	−	10.5519i	0.245581	−	1.38553i
$59$	−2.24028	−	1.83855i	−0.291660	−	0.239359i	0.477172	−	0.878810i	$-0.341662\pi$
$59$	−2.24028	−	1.83855i	−0.291660	−	0.239359i	−0.768832	+	0.639451i	$0.779162\pi$
$60$	0.743626	+	0.453060i	0.0960017	+	0.0584898i
$61$	−2.98198	+	5.57890i	−0.381804	+	0.714304i	−0.997269	−	0.0738598i	$-0.976468\pi$
$61$	−2.98198	+	5.57890i	−0.381804	+	0.714304i	0.615465	+	0.788164i	$0.288968\pi$
$62$	12.4408	−	4.06000i	1.57998	−	0.515621i
$63$			0.407473i			0.0513368i
$64$	−7.58910	+	2.53094i	−0.948637	+	0.316367i
$65$		−	0.386995i		−	0.0480008i
$66$	−2.44893	−	7.50407i	−0.301442	−	0.923688i
$67$	−3.71158	+	6.94388i	−0.453442	+	0.848330i	0.546499	+	0.837460i	$0.315960\pi$
$67$	−3.71158	+	6.94388i	−0.453442	+	0.848330i	−0.999941	+	0.0108705i	$0.996540\pi$
$68$	−1.23910	−	5.10320i	−0.150263	−	0.618854i
$69$	−1.87600	−	1.53959i	−0.225843	−	0.185345i
$70$	−0.247042	−	0.0437875i	−0.0295272	−	0.00523361i
$71$	5.59391	−	8.37188i	0.663875	−	0.993560i	−0.334809	−	0.942286i	$-0.608672\pi$
$71$	5.59391	−	8.37188i	0.663875	−	0.993560i	0.998685	−	0.0512737i	$-0.0163281\pi$
$72$	−2.06953	+	1.92796i	−0.243897	+	0.227212i
$73$	8.63592	−	5.77034i	1.01076	−	0.675367i	0.0642124	−	0.997936i	$-0.479546\pi$
$73$	8.63592	−	5.77034i	1.01076	−	0.675367i	0.946546	+	0.322569i	$0.104546\pi$
$74$	−11.3995	−	4.44472i	−1.32516	−	0.516688i
$75$	1.39640	−	4.60330i	0.161242	−	0.531544i
$76$	−4.81815	+	2.84069i	−0.552680	+	0.325850i
$77$	1.44283	+	1.75810i	0.164426	+	0.200354i
$78$	1.21028	+	0.339649i	0.137037	+	0.0384576i
$79$	−1.25986	−	3.04156i	−0.141745	−	0.342202i	0.837025	−	0.547165i	$-0.184293\pi$
$79$	−1.25986	−	3.04156i	−0.141745	−	0.342202i	−0.978770	+	0.204962i	$0.934293\pi$
$80$	−0.946487	−	1.46189i	−0.105820	−	0.163445i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	7.56857	−	9.62619i	0.835808	−	1.06303i
$83$	−0.917680	−	0.0903836i	−0.100728	−	0.00992089i	0.0475273	−	0.998870i	$-0.484866\pi$
$83$	−0.917680	−	0.0903836i	−0.100728	−	0.00992089i	−0.148256	+	0.988949i	$0.547366\pi$
$84$	0.353758	−	0.734162i	0.0385981	−	0.0801036i
$85$	1.00822	−	0.538905i	0.109357	−	0.0584525i
$86$	−5.43972	+	0.113841i	−0.586580	+	0.0122758i
$87$	−1.47832	+	7.43202i	−0.158493	+	0.796796i
$88$	−2.10251	+	15.6465i	−0.224128	+	1.66792i
$89$	−6.22319	+	1.23787i	−0.659657	+	0.131214i	−0.513556	−	0.858056i	$-0.671672\pi$
$89$	−6.22319	+	1.23787i	−0.659657	+	0.131214i	−0.146100	+	0.989270i	$0.546672\pi$
$90$	−0.519005	−	0.331294i	−0.0547079	−	0.0349214i
$91$	−0.360441	+	0.0355003i	−0.0377845	+	0.00372145i
$92$	2.04343	+	4.40263i	0.213042	+	0.459006i
$93$	−8.85511	+	2.68617i	−0.918232	+	0.278543i
$94$	6.09878	−	5.22247i	0.629041	−	0.538656i
$95$	−0.860977	−	0.860977i	−0.0883344	−	0.0883344i
$96$	5.40257	−	1.67697i	0.551398	−	0.171155i
$97$	−9.59489	+	9.59489i	−0.974213	+	0.974213i	−0.999676	−	0.0254628i	$-0.991894\pi$
$97$	−9.59489	+	9.59489i	−0.974213	+	0.974213i	0.0254628	+	0.999676i	$0.491894\pi$
$98$	0.745856	−	9.63586i	0.0753428	−	0.973369i
$99$	1.62025	+	5.34125i	0.162841	+	0.536816i
$100$	−6.51242	+	7.08165i	−0.651242	+	0.708165i
$101$	−1.89083	−	19.1979i	−0.188145	−	1.91027i	−0.373560	−	0.927606i	$-0.621863\pi$
$101$	−1.89083	−	19.1979i	−0.188145	−	1.91027i	0.185416	−	0.982660i	$-0.440637\pi$
$102$	0.800483	+	3.62605i	0.0792596	+	0.359032i
$103$	−0.289447	−	1.45515i	−0.0285201	−	0.143380i	0.963902	−	0.266259i	$-0.0857875\pi$
$103$	−0.289447	−	1.45515i	−0.0285201	−	0.143380i	−0.992422	+	0.122878i	$0.960787\pi$
$104$	−1.88573	−	1.66269i	−0.184911	−	0.163040i
$105$	0.173999	+	0.0346106i	0.0169806	+	0.00337765i
$106$	0.0692034	−	0.0721619i	0.00672163	−	0.00700898i
$107$	1.76083	+	3.29427i	0.170225	+	0.318469i	0.952540	−	0.304415i	$-0.0984608\pi$
$107$	1.76083	+	3.29427i	0.170225	+	0.318469i	−0.782314	+	0.622884i	$0.785961\pi$
$108$	1.49159	−	1.33236i	0.143528	−	0.128206i
$109$	−0.123447	+	1.25337i	−0.0118240	+	0.120052i	−0.999285	−	0.0378129i	$-0.987961\pi$
$109$	−0.123447	+	1.25337i	−0.0118240	+	0.120052i	0.987461	+	0.157864i	$0.0504609\pi$
$110$	−3.41240	+	0.408347i	−0.325360	+	0.0389344i
$111$	7.99311	+	3.31086i	0.758673	+	0.314252i
$112$	−1.27476	+	1.01565i	−0.120454	+	0.0959696i
$113$	5.98053	−	2.47722i	0.562601	−	0.233037i	−0.0832129	−	0.996532i	$-0.526518\pi$
$113$	5.98053	−	2.47722i	0.562601	−	0.233037i	0.645814	+	0.763495i	$0.276518\pi$
$114$	3.44823	−	1.93695i	0.322956	−	0.181412i
$115$	−0.816782	+	0.670316i	−0.0761653	+	0.0625073i
$116$	9.11584	−	12.1071i	0.846384	−	1.12412i
$117$	−0.850582	−	0.258021i	−0.0786363	−	0.0238541i
$118$	−1.64734	−	3.75294i	−0.151650	−	0.345486i
$119$	−0.594415	−	0.889605i	−0.0544899	−	0.0815499i
$120$	0.647492	+	1.04749i	0.0591077	+	0.0956225i
$121$	16.7576	+	11.1971i	1.52342	+	1.01791i
$122$	−7.33279	+	5.12473i	−0.663879	+	0.463971i
$123$	−5.49303	+	6.69328i	−0.495290	+	0.603513i
$124$	18.2867	+	2.84799i	1.64219	+	0.255757i
$125$	−3.76697	−	2.01349i	−0.336928	−	0.180092i
$126$	−0.260952	+	0.513783i	−0.0232474	+	0.0457715i
$127$	6.52238			0.578768			0.289384	−	0.957213i	$-0.406550\pi$
$127$	6.52238			0.578768			0.289384	+	0.957213i	$0.406550\pi$
$128$	−11.1899	−	1.66890i	−0.989060	−	0.147512i
$129$	3.84731			0.338737
$130$	0.247837	−	0.487962i	0.0217368	−	0.0427971i
$131$	11.7410	+	6.27569i	1.02581	+	0.548310i	0.896384	−	0.443279i	$-0.146185\pi$
$131$	11.7410	+	6.27569i	1.02581	+	0.548310i	0.129431	+	0.991588i	$0.458685\pi$
$132$	1.71786	−	11.0302i	0.149521	−	0.960057i
$133$	−0.722920	+	0.880880i	−0.0626851	+	0.0763820i
$134$	−9.12690	+	6.37860i	−0.788444	+	0.551027i
$135$	0.362010	+	0.241887i	0.0311569	+	0.0208184i
$136$	1.70578	−	7.22816i	0.146269	−	0.619810i
$137$	4.97167	+	7.44063i	0.424758	+	0.635696i	0.980698	−	0.195527i	$-0.0626416\pi$
$137$	4.97167	+	7.44063i	0.424758	+	0.635696i	−0.555940	+	0.831222i	$0.687642\pi$
$138$	−1.37947	−	3.14268i	−0.117428	−	0.267523i
$139$	7.24945	+	2.19910i	0.614891	+	0.186525i	0.582340	−	0.812945i	$-0.302137\pi$
$139$	7.24945	+	2.19910i	0.614891	+	0.186525i	0.0325502	+	0.999470i	$0.489637\pi$
$140$	−0.283454	−	0.213421i	−0.0239562	−	0.0180374i
$141$	−4.38881	+	3.60180i	−0.369604	+	0.303327i
$142$	12.4148	−	6.97369i	1.04183	−	0.585219i
$143$	−4.58358	+	1.89858i	−0.383298	+	0.158767i
$144$	−3.84417	+	1.10561i	−0.320347	+	0.0921339i
$145$	3.04805	+	1.26254i	0.253127	+	0.104849i
$146$	14.5844	−	1.74526i	1.20702	−	0.144439i
$147$	−0.669846	+	6.80106i	−0.0552479	+	0.560942i
$148$	−11.5271	−	12.9047i	−0.947524	−	1.06076i
$149$	0.591865	+	1.10730i	0.0484875	+	0.0907137i	0.904998	−	0.425416i	$-0.139872\pi$
$149$	0.591865	+	1.10730i	0.0484875	+	0.0907137i	−0.856510	+	0.516130i	$0.827372\pi$
$150$	4.70874	−	4.91004i	0.384467	−	0.400903i
$151$	−11.3723	−	2.26210i	−0.925466	−	0.184087i	−0.290721	−	0.956808i	$-0.593895\pi$
$151$	−11.3723	−	2.26210i	−0.925466	−	0.184087i	−0.634746	+	0.772721i	$0.718895\pi$
$152$	−7.89443	+	0.496216i	−0.640323	+	0.0402484i
$153$	−0.512256	−	2.57528i	−0.0414134	−	0.208199i
$154$	0.693359	+	3.14080i	0.0558724	+	0.253092i
$155$	0.394898	+	4.00947i	0.0317190	+	0.322048i
$156$	1.30852	+	1.20334i	0.104766	+	0.0963444i
$157$	3.82040	+	12.5942i	0.304901	+	1.00513i	0.966801	+	0.255532i	$0.0822507\pi$
$157$	3.82040	+	12.5942i	0.304901	+	1.00513i	−0.661899	+	0.749593i	$0.730249\pi$
$158$	0.359305	−	4.64193i	0.0285848	−	0.369293i
$159$	−0.0499911	+	0.0499911i	−0.00396456	+	0.00396456i
$160$	−0.257208	−	2.44945i	−0.0203341	−	0.193646i
$161$	0.699247	+	0.699247i	0.0551084	+	0.0551084i
$162$	−1.07419	+	0.919844i	−0.0843964	+	0.0722698i
$163$	9.49178	−	2.87930i	0.743454	−	0.225524i	0.104239	−	0.994552i	$-0.466759\pi$
$163$	9.49178	−	2.87930i	0.743454	−	0.225524i	0.639215	+	0.769028i	$0.279259\pi$
$164$	15.7080	−	7.29065i	1.22659	−	0.569304i
$165$	2.41844	−	0.238196i	0.188276	−	0.0185435i
$166$	−1.09922	−	0.701660i	−0.0853161	−	0.0544594i
$167$	−15.8067	+	3.14416i	−1.22316	+	0.243302i	−0.764098	−	0.645101i	$-0.776815\pi$
$167$	−15.8067	+	3.14416i	−1.22316	+	0.243302i	−0.459065	+	0.888403i	$0.651815\pi$
$168$	0.916221	−	0.699154i	0.0706880	−	0.0539409i
$169$	−2.38204	+	11.9753i	−0.183234	+	0.921179i
$170$	1.61639	−	0.0338272i	0.123971	−	0.00259443i
$171$	−2.46639	+	1.31831i	−0.188610	+	0.100814i
$172$	−6.93186	−	3.34013i	−0.528549	−	0.254683i
$173$	−10.7992	−	1.06362i	−0.821045	−	0.0808659i	−0.321233	−	0.947000i	$-0.604097\pi$
$173$	−10.7992	−	1.06362i	−0.821045	−	0.0808659i	−0.499811	+	0.866134i	$0.666597\pi$
$174$	−6.62358	+	8.42430i	−0.502132	+	0.638644i
$175$	−0.750108	+	1.81092i	−0.0567028	+	0.136893i
$176$	−12.6713	+	18.3822i	−0.955134	+	1.38561i
$177$	1.10907	+	2.67752i	0.0833625	+	0.201255i
$178$	−8.63957	−	2.42459i	−0.647563	−	0.181730i
$179$	15.8582	+	19.3232i	1.18529	+	1.44429i	0.868428	+	0.495815i	$0.165131\pi$
$179$	15.8582	+	19.3232i	1.18529	+	1.44429i	0.316866	+	0.948470i	$0.397369\pi$
$180$	−0.442248	−	0.750106i	−0.0329632	−	0.0559096i
$181$	−1.85088	+	6.10154i	−0.137575	+	0.453524i	−0.998472	−	0.0552549i	$-0.982403\pi$
$181$	−1.85088	+	6.10154i	−0.137575	+	0.453524i	0.860897	+	0.508779i	$0.169903\pi$
$182$	−0.477215	−	0.186069i	−0.0353735	−	0.0137924i
$183$	5.25975	−	3.51445i	0.388812	−	0.259796i
$184$	−0.242949	+	6.85992i	−0.0179104	+	0.505720i
$185$	2.09273	−	3.13200i	0.153861	−	0.230269i
$186$	−12.8857	−	2.28394i	−0.944823	−	0.167467i
$187$	−11.3291	−	9.29754i	−0.828465	−	0.679903i
$188$	11.0345	−	2.67927i	0.804773	−	0.195406i
$189$	0.192082	−	0.359359i	0.0139719	−	0.0261396i
$190$	−0.534225	−	1.63699i	−0.0387567	−	0.118760i
$191$		−	23.5406i		−	1.70334i	−0.524079	−	0.851669i	$-0.675591\pi$
$191$		−	23.5406i		−	1.70334i	0.524079	−	0.851669i	$-0.324409\pi$
$192$	7.88606	+	1.34539i	0.569127	+	0.0970951i
$193$		−	5.08658i		−	0.366140i	−0.983100	−	0.183070i	$-0.941396\pi$
$193$		−	5.08658i		−	0.366140i	0.983100	−	0.183070i	$-0.0586035\pi$
$194$	−18.2429	+	5.95350i	−1.30976	+	0.427436i
$195$	−0.182428	+	0.341299i	−0.0130640	+	0.0244410i
$196$	7.11139	−	11.6722i	0.507957	−	0.833729i
$197$	−5.15617	−	4.23156i	−0.367362	−	0.301486i	0.432542	−	0.901614i	$-0.357617\pi$
$197$	−5.15617	−	4.23156i	−0.367362	−	0.301486i	−0.799905	+	0.600127i	$0.795117\pi$
$198$	−1.37764	+	7.77242i	−0.0979044	+	0.552362i
$199$	−9.66974	+	14.4718i	−0.685470	+	1.02588i	0.311662	+	0.950193i	$0.399114\pi$
$199$	−9.66974	+	14.4718i	−0.685470	+	1.02588i	−0.997132	+	0.0756849i	$0.975886\pi$
$200$	−12.7467	+	4.75861i	−0.901327	+	0.336485i
$201$	6.54665	−	4.37433i	0.461765	−	0.308541i
$202$	9.91047	−	25.4176i	0.697299	−	1.78838i
$203$	0.896306	−	2.95472i	0.0629083	−	0.207381i
$204$	−1.31284	+	5.08473i	−0.0919174	+	0.356002i
$205$	2.39159	+	2.91416i	0.167036	+	0.203534i
$206$	0.566934	−	2.02016i	0.0395001	−	0.140751i
$207$	0.928723	+	2.24214i	0.0645507	+	0.155839i
$208$	−1.31291	−	3.30413i	−0.0910339	−	0.229100i
$209$	−5.97351	+	14.4213i	−0.413197	+	0.997545i
$210$	0.197231	+	0.155072i	0.0136102	+	0.0107010i
$211$	−20.8206	−	2.05065i	−1.43335	−	0.141173i	−0.648669	−	0.761071i	$-0.724674\pi$
$211$	−20.8206	−	2.05065i	−1.43335	−	0.141173i	−0.784682	+	0.619898i	$0.787174\pi$
$212$	0.133472	−	0.0466701i	0.00916690	−	0.00320532i
$213$	−8.87987	+	4.74639i	−0.608439	+	0.325217i
$214$	0.110528	+	5.28141i	0.00755551	+	0.361030i
$215$	0.326789	−	1.64288i	0.0222868	−	0.112043i
$216$	2.73400	−	0.724737i	0.186025	−	0.0493121i
$217$	3.69813	−	0.735604i	0.251045	−	0.0499360i
$218$	−0.958333	+	1.50132i	−0.0649065	+	0.101682i
$219$	−10.3363	+	1.01804i	−0.698464	+	0.0687927i
$220$	−4.56421	−	1.67046i	−0.307719	−	0.112623i
$221$	2.23340	−	0.677496i	0.150235	−	0.0455733i
$222$	7.95820	+	9.29356i	0.534119	+	0.623743i
$223$	−6.13435	−	6.13435i	−0.410786	−	0.410786i	0.471226	−	0.882012i	$-0.343812\pi$
$223$	−6.13435	−	6.13435i	−0.410786	−	0.410786i	−0.882012	+	0.471226i	$0.843812\pi$
$224$	−2.25778	+	0.464255i	−0.150854	+	0.0310194i
$225$	−3.40149	+	3.40149i	−0.226766	+	0.226766i
$226$	9.12730	+	0.706491i	0.607139	+	0.0469951i
$227$	0.860887	+	2.83796i	0.0571391	+	0.188362i	0.980864	−	0.194694i	$-0.0623715\pi$
$227$	0.860887	+	2.83796i	0.0571391	+	0.188362i	−0.923725	+	0.383056i	$0.874871\pi$
$228$	5.58833	−	0.234004i	0.370096	−	0.0154973i
$229$	−0.655554	−	6.65595i	−0.0433202	−	0.439838i	−0.992242	−	0.124325i	$-0.960323\pi$
$229$	−0.655554	−	6.65595i	−0.0433202	−	0.439838i	0.948921	−	0.315513i	$-0.102177\pi$
$230$	−1.45916	+	0.322123i	−0.0962142	+	0.0212401i
$231$	−0.443704	−	2.23065i	−0.0291936	−	0.146766i
$232$	19.2477	−	9.42799i	1.26368	−	0.618978i
$233$	17.6666	+	3.51411i	1.15738	+	0.230217i	0.736202	−	0.676762i	$-0.236617\pi$
$233$	17.6666	+	3.51411i	1.15738	+	0.230217i	0.421177	+	0.906979i	$0.361617\pi$
$234$	−0.907259	−	0.870064i	−0.0593094	−	0.0568778i
$235$	1.16526	+	2.18005i	0.0760131	+	0.142210i
$236$	0.326305	−	5.78707i	0.0212406	−	0.376706i
$237$	−0.322688	+	3.27631i	−0.0209609	+	0.212819i
$238$	−0.179783	−	1.50237i	−0.0116536	−	0.0973845i
$239$	10.6322	+	4.40400i	0.687739	+	0.284871i	0.699058	−	0.715065i	$-0.253603\pi$
$239$	10.6322	+	4.40400i	0.687739	+	0.284871i	−0.0113186	+	0.999936i	$0.503603\pi$
$240$	0.145594	+	1.73545i	0.00939808	+	0.112023i
$241$	14.8203	−	6.13875i	0.954656	−	0.395432i	0.149677	−	0.988735i	$-0.452177\pi$
$241$	14.8203	−	6.13875i	0.954656	−	0.395432i	0.804979	+	0.593303i	$0.202177\pi$
$242$	13.9589	+	24.8502i	0.897311	+	1.59743i
$243$	0.773010	−	0.634393i	0.0495886	−	0.0406963i
$244$	−12.5279	+	1.76576i	−0.802014	+	0.113041i
$245$	2.84729	+	0.863716i	0.181907	+	0.0551808i
$246$	−11.2126	+	4.92174i	−0.714891	+	0.313799i
$247$	−1.38103	−	2.06685i	−0.0878727	−	0.131511i
$248$	21.2338	+	15.3021i	1.34835	+	0.971683i
$249$	0.766715	+	0.512303i	0.0485886	+	0.0324659i
$250$	−3.46031	−	4.95123i	−0.218849	−	0.313143i
$251$	0.168138	−	0.204877i	0.0106128	−	0.0129317i	−0.767677	−	0.640837i	$-0.778587\pi$
$251$	0.168138	−	0.204877i	0.0106128	−	0.0129317i	0.778290	+	0.627905i	$0.216087\pi$
$252$	−0.658068	+	0.480713i	−0.0414544	+	0.0302821i
$253$	11.9463	+	6.38545i	0.751059	+	0.401449i
$254$	8.22407	+	4.17702i	0.516024	+	0.262090i
$255$	−1.14321			−0.0715905
$256$	−13.0406	−	9.27052i	−0.815038	−	0.579407i
$257$	−15.5574			−0.970446			−0.485223	−	0.874390i	$-0.661262\pi$
$257$	−15.5574			−0.970446			−0.485223	+	0.874390i	$0.661262\pi$
$258$	4.85107	+	2.46387i	0.302015	+	0.153394i
$259$	−3.10906	−	1.66183i	−0.193188	−	0.103261i
$260$	0.624996	−	0.456554i	0.0387606	−	0.0283143i
$261$	4.80719	−	5.85758i	0.297558	−	0.362575i
$262$	10.7852	+	15.4321i	0.666311	+	0.953399i
$263$	15.0190	+	10.0354i	0.926113	+	0.618809i	0.924497	−	0.381190i	$-0.124486\pi$
$263$	15.0190	+	10.0354i	0.926113	+	0.618809i	0.00161607	+	0.999999i	$0.499486\pi$
$264$	9.22996	−	12.8079i	0.568065	−	0.788269i
$265$	0.0171010	+	0.0255934i	0.00105051	+	0.00157219i
$266$	−1.47566	+	0.647734i	−0.0904784	+	0.0397151i
$267$	6.07189	+	1.84189i	0.371594	+	0.112722i
$268$	−15.5930	+	2.19778i	−0.952497	+	0.134251i
$269$	7.58187	−	6.22228i	0.462275	−	0.379379i	−0.374233	−	0.927335i	$-0.622094\pi$
$269$	7.58187	−	6.22228i	0.462275	−	0.379379i	0.836507	+	0.547956i	$0.184594\pi$
$270$	0.301551	+	0.536832i	0.0183518	+	0.0326706i
$271$	15.0603	−	6.23816i	0.914846	−	0.378941i	0.124936	−	0.992165i	$-0.460127\pi$
$271$	15.0603	−	6.23816i	0.914846	−	0.378941i	0.789910	+	0.613223i	$0.210127\pi$
$272$	6.77983	−	8.02159i	0.411088	−	0.486380i
$273$	0.334615	+	0.138602i	0.0202518	+	0.00838859i
$274$	1.50370	+	12.5658i	0.0908417	+	0.759129i
$275$	−2.63175	+	26.7206i	−0.158701	+	1.61131i
$276$	0.273245	−	4.84604i	0.0164474	−	0.291697i
$277$	2.08129	+	3.89382i	0.125053	+	0.233957i	0.936655	−	0.350253i	$-0.113904\pi$
$277$	2.08129	+	3.89382i	0.125053	+	0.233957i	−0.811603	+	0.584210i	$0.801404\pi$
$278$	7.73251	+	7.41549i	0.463765	+	0.444752i
$279$	9.07576	+	1.80528i	0.543351	+	0.108079i
$280$	−0.220729	−	0.450631i	−0.0131911	−	0.0269303i
$281$	3.99247	+	20.0715i	0.238171	+	1.19736i	0.895950	+	0.444154i	$0.146496\pi$
$281$	3.99247	+	20.0715i	0.238171	+	1.19736i	−0.657780	+	0.753211i	$0.728504\pi$
$282$	−7.84050	+	1.73086i	−0.466895	+	0.103071i
$283$	−2.51246	−	25.5095i	−0.149350	−	1.51638i	−0.719300	−	0.694700i	$-0.755537\pi$
$283$	−2.51246	−	25.5095i	−0.149350	−	1.51638i	0.569950	−	0.821680i	$-0.306963\pi$
$284$	20.1199	−	0.842495i	1.19390	−	0.0499929i
$285$	0.353452	+	1.16518i	0.0209367	+	0.0690190i
$286$	−6.99531	−	0.541467i	−0.413642	−	0.0320176i
$287$	2.49481	−	2.49481i	0.147264	−	0.147264i
$288$	−5.55516	−	1.06780i	−0.327341	−	0.0629206i
$289$	−7.14567	−	7.14567i	−0.420333	−	0.420333i
$290$	3.03474	+	3.54396i	0.178206	+	0.208108i
$291$	12.9849	−	3.93894i	0.761190	−	0.230905i
$292$	19.5072	+	7.13948i	1.14157	+	0.417807i
$293$	−10.9732	+	1.08077i	−0.641064	+	0.0631393i	−0.413326	−	0.910583i	$-0.635633\pi$
$293$	−10.9732	+	1.08077i	−0.641064	+	0.0631393i	−0.227738	+	0.973722i	$0.573133\pi$
$294$	−5.20010	+	8.14648i	−0.303276	+	0.475112i
$295$	1.23756	−	0.246166i	0.0720535	−	0.0143323i
$296$	−6.27020	−	23.6537i	−0.364448	−	1.37484i
$297$	1.08891	−	5.47434i	0.0631852	−	0.317654i
$298$	0.0371516	+	1.77524i	0.00215213	+	0.102837i
$299$	−1.90243	+	1.01687i	−0.110020	+	0.0588070i
$300$	9.08170	−	3.17553i	0.524332	−	0.183339i
$301$	−1.56013	−	0.153659i	−0.0899242	−	0.00885676i
$302$	−12.8907	−	10.1353i	−0.741776	−	0.583219i
$303$	−7.38228	+	17.8224i	−0.424101	+	1.02387i
$304$	−10.2719	−	4.43002i	−0.589133	−	0.254079i
$305$	−1.05398	−	2.54453i	−0.0603507	−	0.145700i
$306$	1.00334	−	3.57523i	0.0573574	−	0.204383i
$307$	−14.8658	−	18.1140i	−0.848437	−	1.03382i	−0.998977	−	0.0452194i	$-0.985601\pi$
$307$	−14.8658	−	18.1140i	−0.848437	−	1.03382i	0.150540	−	0.988604i	$-0.451899\pi$
$308$	−1.13715	+	4.40427i	−0.0647953	+	0.250956i
$309$	−0.430683	+	1.41977i	−0.0245007	+	0.0807680i
$310$	−2.06979	+	5.30844i	−0.117556	+	0.301499i
$311$	−27.9260	+	18.6596i	−1.58354	+	1.05809i	−0.622147	+	0.782901i	$0.713739\pi$
$311$	−27.9260	+	18.6596i	−1.58354	+	1.05809i	−0.961391	+	0.275186i	$0.911261\pi$
$312$	0.879279	+	2.35529i	0.0497794	+	0.133342i
$313$	−0.247527	+	0.370451i	−0.0139911	+	0.0209391i	−0.838399	−	0.545057i	$-0.816508\pi$
$313$	−0.247527	+	0.370451i	−0.0139911	+	0.0209391i	0.824408	+	0.565996i	$0.191508\pi$
$314$	−3.24834	+	18.3267i	−0.183315	+	1.03423i
$315$	−0.137138	−	0.112547i	−0.00772687	−	0.00634128i
$316$	3.42581	−	5.62291i	0.192717	−	0.316314i
$317$	−10.2393	+	19.1563i	−0.575094	+	1.07593i	0.411295	+	0.911502i	$0.365077\pi$
$317$	−10.2393	+	19.1563i	−0.575094	+	1.07593i	−0.986390	+	0.164424i	$0.947423\pi$
$318$	−0.0950489	+	0.0310188i	−0.00533008	+	0.00173945i
$319$		−	42.2952i		−	2.36808i
$320$	1.24435	−	3.25323i	0.0695611	−	0.181861i
$321$		−	3.73534i		−	0.208486i
$322$	0.433874	+	1.32949i	0.0241788	+	0.0740895i
$323$	3.46155	−	6.47610i	0.192606	−	0.360340i
$324$	−1.94353	+	0.471905i	−0.107974	+	0.0262170i
$325$	−3.30523	−	2.71253i	−0.183341	−	0.150464i
$326$	13.8121	+	2.44816i	0.764983	+	0.135591i
$327$	0.699707	−	1.04719i	0.0386939	−	0.0579095i
$328$	24.4752	+	0.866806i	1.35142	+	0.0478614i
$329$	1.92357	−	1.28529i	0.106050	−	0.0708601i
$330$	3.20196	+	1.24846i	0.176262	+	0.0687257i
$331$	5.45182	−	17.9722i	0.299659	−	0.987844i	−0.669790	−	0.742551i	$-0.733616\pi$
$331$	5.45182	−	17.9722i	0.299659	−	0.987844i	0.969449	−	0.245293i	$-0.0788841\pi$
$332$	−0.936655	−	1.58868i	−0.0514056	−	0.0871901i
$333$	−5.48857	−	6.68784i	−0.300772	−	0.366491i
$334$	−21.9443	−	6.15839i	−1.20074	−	0.336972i
$335$	−1.31186	−	3.16710i	−0.0716744	−	0.173037i
$336$	1.60301	−	0.294803i	0.0874514	−	0.0160828i
$337$	12.2286	−	29.5225i	0.666136	−	1.60820i	−0.121883	−	0.992545i	$-0.538893\pi$
$337$	12.2286	−	29.5225i	0.666136	−	1.60820i	0.788019	−	0.615651i	$-0.211107\pi$
$338$	−10.6727	+	13.5742i	−0.580517	+	0.738339i
$339$	−6.44211	−	0.634492i	−0.349887	−	0.0344609i
$340$	2.05977	+	0.992504i	0.111707	+	0.0538261i
$341$	45.5509	−	24.3475i	2.46672	−	1.31849i
$342$	−3.95414	+	0.0827510i	−0.213815	+	0.00447466i
$343$	1.09972	−	5.52866i	0.0593792	−	0.298520i
$344$	−6.60131	−	8.65083i	−0.355919	−	0.466422i
$345$	1.03632	−	0.206137i	0.0557937	−	0.0110981i
$346$	−12.9355	−	8.25706i	−0.695417	−	0.443902i
$347$	5.39600	−	0.531460i	0.289673	−	0.0285303i	0.0478627	−	0.998854i	$-0.484759\pi$
$347$	5.39600	−	0.531460i	0.289673	−	0.0285303i	0.241810	+	0.970324i	$0.422259\pi$
$348$	−13.7467	+	6.38037i	−0.736901	+	0.342024i
$349$	−19.2413	+	5.83677i	−1.02996	+	0.312435i	−0.759646	−	0.650337i	$-0.774628\pi$
$349$	−19.2413	+	5.83677i	−1.02996	+	0.312435i	−0.270315	+	0.962772i	$0.587128\pi$
$350$	−2.10555	+	1.80301i	−0.112546	+	0.0963750i
$351$	0.628516	+	0.628516i	0.0335477	+	0.0335477i
$352$	−27.7495	+	15.0632i	−1.47905	+	0.802874i
$353$	−17.8202	+	17.8202i	−0.948475	+	0.948475i	−0.998736	−	0.0502612i	$-0.983995\pi$
$353$	−17.8202	+	17.8202i	−0.948475	+	0.948475i	0.0502612	+	0.998736i	$0.483995\pi$
$354$	−0.316301	+	4.08635i	−0.0168112	+	0.217187i
$355$	1.27255	+	4.19504i	0.0675400	+	0.222649i
$356$	−9.34090	−	8.59006i	−0.495067	−	0.455272i
$357$	0.104870	+	1.06477i	0.00555033	+	0.0563534i
$358$	7.62070	+	34.5204i	0.402766	+	1.82446i
$359$	−6.45238	−	32.4383i	−0.340544	−	1.71203i	−0.648998	−	0.760790i	$-0.724812\pi$
$359$	−6.45238	−	32.4383i	−0.340544	−	1.71203i	0.308454	−	0.951239i	$-0.400188\pi$
$360$	−0.0772526	−	1.22903i	−0.00407157	−	0.0647757i
$361$	10.9642	+	2.18091i	0.577061	+	0.114785i
$362$	−6.24129	+	6.50810i	−0.328035	+	0.342058i
$363$	−9.50061	−	17.7744i	−0.498653	−	0.932914i
$364$	−0.482560	−	0.540230i	−0.0252930	−	0.0283157i
$365$	−0.443240	+	4.50029i	−0.0232002	+	0.235556i
$366$	8.88272	−	1.06296i	0.464307	−	0.0555617i
$367$	7.54907	+	3.12693i	0.394058	+	0.163224i	0.570909	−	0.821013i	$-0.306591\pi$
$367$	7.54907	+	3.12693i	0.394058	+	0.163224i	−0.176851	+	0.984238i	$0.556591\pi$
$368$	−4.69953	+	8.49409i	−0.244980	+	0.442785i
$369$	7.99961	−	3.31355i	0.416443	−	0.172496i
$370$	4.64450	−	2.60892i	0.241456	−	0.135631i
$371$	0.0222686	−	0.0182754i	0.00115613	−	0.000948809i
$372$	−14.7849	−	11.1320i	−0.766560	−	0.577167i
$373$	−2.46272	−	0.747059i	−0.127515	−	0.0386813i	0.225882	−	0.974155i	$-0.427474\pi$
$373$	−2.46272	−	0.747059i	−0.127515	−	0.0386813i	−0.353397	+	0.935473i	$0.614974\pi$
$374$	−8.33057	−	18.9786i	−0.430764	−	0.981359i
$375$	2.37302	+	3.55148i	0.122542	+	0.183398i
$376$	15.6292	+	3.68835i	0.806017	+	0.190212i
$377$	5.60029	+	3.74199i	0.288430	+	0.192722i
$378$	0.472335	−	0.330105i	0.0242943	−	0.0169788i
$379$	−22.1580	+	26.9996i	−1.13818	+	1.38688i	−0.227491	+	0.973780i	$0.573052\pi$
$379$	−22.1580	+	26.9996i	−1.13818	+	1.38688i	−0.910688	+	0.413095i	$0.864448\pi$
$380$	0.374746	−	2.40620i	0.0192240	−	0.123436i
$381$	−5.75223	−	3.07463i	−0.294695	−	0.157518i
$382$	15.0757	−	29.6824i	0.771342	−	1.51868i
$383$	−22.8022			−1.16514			−0.582569	−	0.812781i	$-0.697952\pi$
$383$	−22.8022			−1.16514			−0.582569	+	0.812781i	$0.697952\pi$
$384$	9.08193	+	6.74674i	0.463460	+	0.344293i
$385$	−0.990220			−0.0504663
$386$	3.25752	−	6.41367i	0.165803	−	0.326447i
$387$	−3.39302	−	1.81361i	−0.172477	−	0.0921909i
$388$	−26.8152	−	4.17624i	−1.36133	−	0.212016i
$389$	22.1708	−	27.0152i	1.12411	−	1.36973i	0.203573	−	0.979060i	$-0.434745\pi$
$389$	22.1708	−	27.0152i	1.12411	−	1.36973i	0.920532	−	0.390666i	$-0.127755\pi$
$390$	−0.448597	+	0.313515i	−0.0227156	+	0.0158754i
$391$	−5.29839	−	3.54027i	−0.267951	−	0.179039i
$392$	16.4418	−	10.1633i	0.830436	−	0.513322i
$393$	−7.39629	−	11.0693i	−0.373093	−	0.558374i
$394$	−3.79147	−	8.63766i	−0.191012	−	0.435159i
$395$	1.37164	+	0.416083i	0.0690147	+	0.0209354i
$396$	−6.71463	+	8.91799i	−0.337423	+	0.448146i
$397$	29.6874	−	24.3638i	1.48997	−	1.22279i	0.575710	−	0.817654i	$-0.304726\pi$
$397$	29.6874	−	24.3638i	1.48997	−	1.22279i	0.914258	−	0.405131i	$-0.132774\pi$
$398$	−21.4605	+	12.0548i	−1.07572	+	0.604255i
$399$	1.05280	−	0.436085i	0.0527060	−	0.0218316i
$400$	−19.1198	−	2.16302i	−0.955990	−	0.108151i
$401$	−13.8586	−	5.74042i	−0.692065	−	0.286663i	0.00879503	−	0.999961i	$-0.497200\pi$
$401$	−13.8586	−	5.74042i	−0.692065	−	0.286663i	−0.700860	+	0.713298i	$0.747200\pi$
$402$	11.0561	−	1.32303i	0.551426	−	0.0659868i
$403$	−0.806199	+	8.18547i	−0.0401596	+	0.407748i
$404$	28.7739	−	25.7023i	1.43156	−	1.27874i
$405$	−0.205239	−	0.383976i	−0.0101984	−	0.0190799i
$406$	3.02240	−	3.15161i	0.149999	−	0.156412i
$407$	−47.3623	−	9.42094i	−2.34766	−	0.466979i
$408$	−4.91169	+	5.57057i	−0.243165	+	0.275784i
$409$	1.88885	+	9.49591i	0.0933978	+	0.469543i	0.998971	+	0.0453526i	$0.0144411\pi$
$409$	1.88885	+	9.49591i	0.0933978	+	0.469543i	−0.905573	+	0.424190i	$0.860559\pi$
$410$	1.14929	+	5.20607i	0.0567592	+	0.257109i
$411$	−0.877133	−	8.90568i	−0.0432658	−	0.439285i
$412$	2.00859	−	2.18415i	0.0989560	−	0.107606i
$413$	−0.342800	−	1.13006i	−0.0168681	−	0.0556067i
$414$	−0.264868	+	3.42188i	−0.0130175	+	0.168176i
$415$	0.283888	−	0.283888i	0.0139355	−	0.0139355i
$416$	0.460566	−	5.00699i	0.0225811	−	0.245488i
$417$	−5.35680	−	5.35680i	−0.262324	−	0.262324i
$418$	−16.7676	+	14.3584i	−0.820132	+	0.702290i
$419$	−0.757046	+	0.229647i	−0.0369841	+	0.0112190i	−0.308723	−	0.951152i	$-0.599901\pi$
$419$	−0.757046	+	0.229647i	−0.0369841	+	0.0112190i	0.271738	+	0.962371i	$0.412401\pi$
$420$	0.149378	+	0.321840i	0.00728890	+	0.0157042i
$421$	−25.6124	+	2.52260i	−1.24827	+	0.122944i	−0.700482	−	0.713670i	$-0.747031\pi$
$421$	−25.6124	+	2.52260i	−1.24827	+	0.122944i	−0.547792	+	0.836615i	$0.684531\pi$
$422$	−24.9395	−	15.9195i	−1.21403	−	0.774949i
$423$	5.56846	−	1.10764i	0.270748	−	0.0538551i
$424$	0.198183	+	0.0266310i	0.00962463	+	0.00129332i
$425$	2.46418	−	12.3883i	0.119530	−	0.600918i
$426$	−14.2363	+	0.297932i	−0.689750	+	0.0144349i
$427$	−2.27325	+	1.21508i	−0.110010	+	0.0588018i
$428$	−3.24292	+	6.73011i	−0.156753	+	0.325312i
$429$	4.93734	+	0.486286i	0.238377	+	0.0234781i
$430$	1.46417	−	1.86222i	0.0706085	−	0.0898045i
$431$	1.60451	−	3.87362i	0.0772864	−	0.186586i	−0.880514	−	0.474020i	$-0.842802\pi$
$431$	1.60451	−	3.87362i	0.0772864	−	0.186586i	0.957800	+	0.287434i	$0.0928023\pi$
$432$	3.91143	+	0.837070i	0.188189	+	0.0402736i
$433$	14.1340	+	34.1225i	0.679237	+	1.63982i	0.765410	+	0.643543i	$0.222536\pi$
$433$	14.1340	+	34.1225i	0.679237	+	1.63982i	−0.0861731	+	0.996280i	$0.527464\pi$
$434$	5.13406	+	1.44081i	0.246443	+	0.0691611i
$435$	−2.09298	−	2.55031i	−0.100351	−	0.122278i
$436$	−2.16983	+	1.27929i	−0.103916	+	0.0612669i
$437$	−1.97017	+	6.49477i	−0.0942458	+	0.310687i
$438$	−13.6850	−	5.33588i	−0.653897	−	0.254958i
$439$	−17.1233	+	11.4414i	−0.817249	+	0.546068i	−0.892474	−	0.451098i	$-0.851032\pi$
$439$	−17.1233	+	11.4414i	−0.817249	+	0.546068i	0.0752252	+	0.997167i	$0.476032\pi$
$440$	−4.68522	−	5.02927i	−0.223359	−	0.239761i
$441$	3.79675	−	5.68223i	0.180798	−	0.270583i
$442$	3.24998	+	0.576049i	0.154586	+	0.0273998i
$443$	−31.1159	−	25.5361i	−1.47836	−	1.21326i	−0.924802	−	0.380448i	$-0.875770\pi$
$443$	−31.1159	−	25.5361i	−1.47836	−	1.21326i	−0.553558	−	0.832811i	$-0.686730\pi$
$444$	4.08277	+	16.8148i	0.193760	+	0.797995i
$445$	1.30227	−	2.43637i	0.0617334	−	0.115495i
$446$	−3.80628	−	11.6633i	−0.180233	−	0.552274i
$447$		−	1.25556i		−	0.0593858i
$448$	−3.14415	−	0.860535i	−0.148547	−	0.0406564i
$449$			16.5637i			0.781689i	0.920457	+	0.390844i	$0.127817\pi$
$449$			16.5637i			0.781689i	−0.920457	+	0.390844i	$0.872183\pi$
$450$	−6.46731	+	2.11058i	−0.304872	+	0.0994938i
$451$	22.7823	−	42.6227i	1.07278	−	2.00703i
$452$	11.0562	+	6.73606i	0.520038	+	0.316838i
$453$	8.96315	+	7.35586i	0.421125	+	0.345609i
$454$	−0.731979	+	4.12971i	−0.0343535	+	0.193817i
$455$	0.0876080	−	0.131115i	0.00410713	−	0.00614675i
$456$	7.19618	+	3.28379i	0.336992	+	0.153777i
$457$	11.5221	−	7.69885i	0.538983	−	0.360137i	−0.256088	−	0.966654i	$-0.582434\pi$
$457$	11.5221	−	7.69885i	0.538983	−	0.360137i	0.795071	+	0.606517i	$0.207434\pi$
$458$	3.43598	−	8.81232i	0.160553	−	0.411773i
$459$	−0.762211	+	2.51267i	−0.0355770	+	0.117282i
$460$	−2.04615	−	0.528302i	−0.0954021	−	0.0246322i
$461$	16.5954	+	20.2216i	0.772926	+	0.941813i	0.999482	−	0.0321849i	$-0.0102466\pi$
$461$	16.5954	+	20.2216i	0.772926	+	0.941813i	−0.226556	+	0.973998i	$0.572747\pi$
$462$	0.869073	−	3.09678i	0.0404329	−	0.144075i
$463$	10.9169	+	26.3556i	0.507349	+	1.22485i	0.945404	+	0.325901i	$0.105668\pi$
$463$	10.9169	+	26.3556i	0.507349	+	1.22485i	−0.438054	+	0.898948i	$0.644332\pi$
$464$	30.3073	+	0.438768i	1.40698	+	0.0203693i
$465$	1.54178	−	3.72219i	0.0714984	−	0.172612i
$466$	20.0254	+	15.7449i	0.927657	+	0.729368i
$467$	21.7922	+	2.14635i	1.00842	+	0.0993211i	0.588718	−	0.808339i	$-0.299633\pi$
$467$	21.7922	+	2.14635i	1.00842	+	0.0993211i	0.419707	+	0.907660i	$0.362133\pi$
$468$	−0.586762	−	1.67808i	−0.0271231	−	0.0775695i
$469$	−2.82945	+	1.51237i	−0.130652	+	0.0698348i
$470$	0.0731437	+	3.49507i	0.00337387	+	0.161215i
$471$	2.56756	−	12.9080i	0.118307	−	0.594769i
$472$	4.11756	−	7.08795i	0.189526	−	0.326249i
$473$	−21.0615	+	4.18939i	−0.968408	+	0.192628i
$474$	−2.50507	+	3.92445i	−0.115062	+	0.180256i
$475$	−13.3881	+	1.31862i	−0.614290	+	0.0605023i
$476$	0.735453	−	2.00948i	0.0337094	−	0.0921044i
$477$	0.0676539	−	0.0205226i	0.00309766	−	0.000939665i
$478$	10.5858	+	12.3620i	0.484181	+	0.565425i
$479$	25.8571	+	25.8571i	1.18144	+	1.18144i	0.979371	+	0.202070i	$0.0647667\pi$
$479$	25.8571	+	25.8571i	1.18144	+	1.18144i	0.202070	+	0.979371i	$0.435233\pi$
$480$	−0.927824	+	2.28147i	−0.0423492	+	0.104134i
$481$	5.43772	−	5.43772i	0.247939	−	0.247939i
$482$	22.6182	+	1.75074i	1.03023	+	0.0797442i
$483$	−0.287058	−	0.946304i	−0.0130616	−	0.0430583i
$484$	1.68638	+	40.2731i	0.0766537	+	1.83059i
$485$	−0.579070	−	5.87940i	−0.0262942	−	0.266970i
$486$	1.38096	−	0.304860i	0.0626418	−	0.0138287i
$487$	0.911682	+	4.58334i	0.0413123	+	0.207691i	0.995928	−	0.0901483i	$-0.0287341\pi$
$487$	0.911682	+	4.58334i	0.0413123	+	0.207691i	−0.954616	+	0.297839i	$0.903734\pi$
$488$	−16.9272	−	5.79657i	−0.766258	−	0.262399i
$489$	−9.72830	−	1.93508i	−0.439929	−	0.0875073i
$490$	3.03702	+	2.91251i	0.137198	+	0.131574i
$491$	1.49417	+	2.79540i	0.0674310	+	0.126155i	0.913378	−	0.407112i	$-0.133464\pi$
$491$	1.49417	+	2.79540i	0.0674310	+	0.126155i	−0.845947	+	0.533267i	$0.820964\pi$
$492$	−17.2900	−	0.974898i	−0.779492	−	0.0439518i
$493$	−1.95023	+	19.8010i	−0.0878340	+	0.891794i
$494$	−0.417696	−	3.49053i	−0.0187930	−	0.157046i
$495$	−2.24516	−	0.929977i	−0.100913	−	0.0417993i
$496$	16.9740	+	32.8928i	0.762156	+	1.47693i
$497$	3.79046	−	1.57006i	0.170025	−	0.0704267i
$498$	0.638666	+	1.13698i	0.0286193	+	0.0509492i
$499$	7.39511	−	6.06901i	0.331051	−	0.271686i	−0.454153	−	0.890924i	$-0.650058\pi$
$499$	7.39511	−	6.06901i	0.331051	−	0.271686i	0.785204	+	0.619237i	$0.212558\pi$
$500$	−1.19227	−	8.45904i	−0.0533200	−	0.378300i
$501$	15.4224	+	4.67835i	0.689024	+	0.209013i
$502$	0.343211	−	0.150651i	0.0153183	−	0.00672389i
$503$	5.45720	+	8.16727i	0.243324	+	0.364161i	0.932950	−	0.360005i	$-0.117225\pi$
$503$	5.45720	+	8.16727i	0.243324	+	0.364161i	−0.689626	+	0.724166i	$0.742225\pi$
$504$	−1.13761	+	0.184695i	−0.0506733	+	0.00822697i
$505$	6.98347	+	4.66621i	0.310761	+	0.207644i
$506$	10.9738	+	15.7020i	0.487845	+	0.698039i
$507$	7.74590	−	9.43841i	0.344008	−	0.419174i
$508$	7.69471	+	10.5336i	0.341398	+	0.467354i
$509$	1.35228	+	0.722808i	0.0599387	+	0.0320379i	0.501094	−	0.865393i	$-0.332931\pi$
$509$	1.35228	+	0.722808i	0.0599387	+	0.0320379i	−0.441155	+	0.897431i	$0.645431\pi$
$510$	−1.44147	−	0.732127i	−0.0638295	−	0.0324191i
$511$	4.23216			0.187220
$512$	−10.5059	−	20.0406i	−0.464302	−	0.885677i
$513$	2.79661			0.123473
$514$	−19.6164	−	9.96319i	−0.865241	−	0.439458i
$515$	0.569689	+	0.304505i	0.0251035	+	0.0134181i
$516$	4.53882	+	6.21339i	0.199811	+	0.273529i
$517$	20.1038	−	24.4965i	0.884164	−	1.07736i
$518$	−2.85596	−	4.08649i	−0.125484	−	0.179550i
$519$	9.02262	+	6.02872i	0.396049	+	0.264631i
$520$	1.08044	−	0.175413i	0.0473805	−	0.00769236i
$521$	−20.8712	−	31.2359i	−0.914383	−	1.36847i	−0.929593	−	0.368587i	$-0.879842\pi$
$521$	−20.8712	−	31.2359i	−0.914383	−	1.36847i	0.0152099	−	0.999884i	$-0.495158\pi$
$522$	9.81266	−	4.30723i	0.429489	−	0.188522i
$523$	11.3829	+	3.45298i	0.497741	+	0.150988i	0.529166	−	0.848518i	$-0.322505\pi$
$523$	11.3829	+	3.45298i	0.497741	+	0.150988i	−0.0314255	+	0.999506i	$0.510005\pi$
$524$	3.71610	+	26.3653i	0.162339	+	1.15178i
$525$	1.51520	−	1.24349i	0.0661287	−	0.0542704i
$526$	12.5107	+	22.2720i	0.545492	+	0.971106i
$527$	−22.4479	+	9.29822i	−0.977845	+	0.405037i
$528$	19.8404	−	10.2384i	0.863442	−	0.445571i
$529$	−15.8079	−	6.54783i	−0.687298	−	0.284688i
$530$	0.00517225	+	0.0432225i	0.000224668	+	0.00187747i
$531$	0.284066	−	2.88417i	0.0123274	−	0.125162i
$532$	−2.27548	−	0.128303i	−0.0986544	−	0.00556264i
$533$	3.62803	+	6.78757i	0.157148	+	0.294002i
$534$	6.47648	+	6.21096i	0.280265	+	0.268775i
$535$	−1.59506	−	0.317278i	−0.0689606	−	0.0137171i
$536$	−21.0688	−	7.21482i	−0.910032	−	0.311633i
$537$	−4.87674	−	24.5170i	−0.210447	−	1.05799i
$538$	13.5448	−	2.99014i	0.583959	−	0.128914i
$539$	−3.73881	−	37.9607i	−0.161042	−	1.63508i
$540$	0.0364305	+	0.870009i	0.00156772	+	0.0374392i
$541$	7.57286	+	24.9644i	0.325583	+	1.07330i	0.955092	+	0.296309i	$0.0957559\pi$
$541$	7.57286	+	24.9644i	0.325583	+	1.07330i	−0.629509	+	0.776993i	$0.716744\pi$
$542$	22.9845	+	1.77910i	0.987269	+	0.0764187i
$543$	4.50858	−	4.50858i	0.193482	−	0.193482i
$544$	13.6858	−	5.77253i	0.586775	−	0.247495i
$545$	−0.387736	−	0.387736i	−0.0166088	−	0.0166088i
$546$	0.333154	+	0.389056i	0.0142577	+	0.0166501i
$547$	−30.1662	+	9.15081i	−1.28981	+	0.391260i	−0.859368	−	0.511357i	$-0.829143\pi$
$547$	−30.1662	+	9.15081i	−1.28981	+	0.391260i	−0.430444	+	0.902617i	$0.641643\pi$
$548$	−6.15131	+	16.8072i	−0.262771	+	0.717970i
$549$	−6.29538	+	0.620041i	−0.268680	+	0.0264627i
$550$	−20.4306	+	32.0066i	−0.871165	+	1.36477i
$551$	20.7845	−	4.13429i	0.885448	−	0.176127i
$552$	3.44801	−	5.93539i	0.146757	−	0.252627i
$553$	0.261708	−	1.31569i	0.0111289	−	0.0559489i
$554$	0.130643	+	6.24261i	0.00555050	+	0.265223i
$555$	−3.32204	+	1.77567i	−0.141013	+	0.0753729i
$556$	5.00093	+	14.3022i	0.212087	+	0.606548i
$557$	−10.1167	−	0.996409i	−0.428659	−	0.0422192i	−0.118612	−	0.992941i	$-0.537845\pi$
$557$	−10.1167	−	0.996409i	−0.428659	−	0.0422192i	−0.310046	+	0.950721i	$0.600345\pi$
$558$	10.2875	+	8.08852i	0.435505	+	0.342414i
$559$	1.30866	−	3.15939i	0.0553506	−	0.133628i
$560$	0.0102725	−	0.709558i	0.000434092	−	0.0299843i
$561$	5.60853	+	13.5402i	0.236792	+	0.571667i
$562$	−7.81996	+	27.8650i	−0.329865	+	1.17541i
$563$	16.2254	+	19.7708i	0.683821	+	0.833238i	0.993043	−	0.117752i	$-0.0375687\pi$
$563$	16.2254	+	19.7708i	0.683821	+	0.833238i	−0.309222	+	0.950990i	$0.600069\pi$
$564$	−10.9946	−	2.83872i	−0.462954	−	0.119532i
$565$	−0.818131	+	2.69702i	−0.0344190	+	0.113464i
$566$	13.1686	−	33.7739i	0.553519	−	1.41962i
$567$	−0.338802	+	0.226380i	−0.0142283	+	0.00950707i
$568$	25.9088	+	11.8228i	1.08711	+	0.496073i
$569$	−17.9140	+	26.8102i	−0.750994	+	1.12394i	0.237308	+	0.971434i	$0.423735\pi$
$569$	−17.9140	+	26.8102i	−0.750994	+	1.12394i	−0.988302	+	0.152507i	$0.951265\pi$
$570$	−0.300527	+	1.69553i	−0.0125877	+	0.0710178i
$571$	27.3889	+	22.4775i	1.14619	+	0.940653i	0.998827	−	0.0484294i	$-0.0154216\pi$
$571$	27.3889	+	22.4775i	1.14619	+	0.940653i	0.147363	+	0.989083i	$0.452922\pi$
$572$	−8.47363	−	5.16263i	−0.354300	−	0.215860i
$573$	−11.0970	+	20.7610i	−0.463582	+	0.867302i
$574$	4.74342	−	1.54800i	0.197987	−	0.0646122i
$575$			11.6743i			0.486852i
$576$	−6.32067	−	4.90399i	−0.263361	−	0.204333i
$577$		−	38.5448i		−	1.60464i	−0.596894	−	0.802320i	$-0.703599\pi$
$577$		−	38.5448i		−	1.60464i	0.596894	−	0.802320i	$-0.296401\pi$
$578$	−4.43379	−	13.5862i	−0.184421	−	0.565110i
$579$	−2.39780	+	4.48596i	−0.0996491	+	0.186430i
$580$	1.55690	+	6.41207i	0.0646469	+	0.266247i
$581$	−0.290451	−	0.238367i	−0.0120499	−	0.00988912i
$582$	18.8953	+	3.34912i	0.783234	+	0.138826i
$583$	0.219233	−	0.328105i	0.00907969	−	0.0135887i
$584$	20.0244	+	21.4949i	0.828617	+	0.889464i
$585$	0.321775	−	0.215003i	0.0133037	−	0.00888928i
$586$	−14.5283	−	5.66467i	−0.600159	−	0.234006i
$587$	−8.87279	+	29.2497i	−0.366219	+	1.20726i	0.559429	+	0.828878i	$0.311021\pi$
$587$	−8.87279	+	29.2497i	−0.366219	+	1.20726i	−0.925648	+	0.378385i	$0.876479\pi$
$588$	−11.7739	+	6.94168i	−0.485549	+	0.286270i
$589$	16.4172	+	20.0044i	0.676460	+	0.824269i
$590$	1.71809	+	0.482160i	0.0707325	+	0.0198502i
$591$	2.55259	+	6.16251i	0.105000	+	0.253492i
$592$	7.24206	−	33.8405i	0.297647	−	1.39084i
$593$	−2.75482	+	6.65073i	−0.113127	+	0.273113i	−0.970295	−	0.241924i	$-0.922222\pi$
$593$	−2.75482	+	6.65073i	−0.113127	+	0.273113i	0.857168	+	0.515036i	$0.172222\pi$
$594$	4.87886	−	6.20525i	0.200182	−	0.254604i
$595$	0.463584	+	0.0456591i	0.0190051	+	0.00187184i
$596$	−1.09004	+	2.26219i	−0.0446498	+	0.0926629i
$597$	15.3499	−	8.20469i	0.628230	−	0.335796i
$598$	−3.04998	+	0.0638291i	−0.124723	+	0.00261017i
$599$	2.66432	−	13.3944i	0.108861	−	0.547281i	−0.887408	−	0.460984i	$-0.847496\pi$
$599$	2.66432	−	13.3944i	0.108861	−	0.547281i	0.996269	−	0.0862973i	$-0.0275035\pi$
$600$	13.4848	+	1.81203i	0.550514	+	0.0739757i
$601$	−20.8617	+	4.14964i	−0.850965	+	0.169267i	−0.601259	−	0.799054i	$-0.705334\pi$
$601$	−20.8617	+	4.14964i	−0.850965	+	0.169267i	−0.249706	+	0.968322i	$0.580334\pi$
$602$	−1.86876	−	1.19288i	−0.0761649	−	0.0486180i
$603$	−7.83567	+	0.771746i	−0.319093	+	0.0314279i
$604$	−9.76311	−	21.0349i	−0.397255	−	0.855900i
$605$	−8.39700	+	2.54720i	−0.341387	+	0.103558i
$606$	−20.7220	+	17.7446i	−0.841775	+	0.720823i
$607$	15.8656	+	15.8656i	0.643963	+	0.643963i	0.951527	−	0.307564i	$-0.0995138\pi$
$607$	15.8656	+	15.8656i	0.643963	+	0.643963i	−0.307564	+	0.951527i	$0.599514\pi$
$608$	−10.1148	−	12.1641i	−0.410208	−	0.493318i
$609$	−2.18332	+	2.18332i	−0.0884725	+	0.0884725i
$610$	0.300590	−	3.88339i	0.0121705	−	0.157234i
$611$	1.46493	+	4.82923i	0.0592647	+	0.195370i
$612$	3.55475	−	3.86546i	0.143692	−	0.156252i
$613$	0.820241	+	8.32805i	0.0331292	+	0.336367i	0.997435	+	0.0715760i	$0.0228029\pi$
$613$	0.820241	+	8.32805i	0.0331292	+	0.336367i	−0.964306	+	0.264791i	$0.914697\pi$
$614$	−7.14382	−	32.3603i	−0.288301	−	1.30595i
$615$	−0.735468	−	3.69745i	−0.0296569	−	0.149095i
$616$	−4.25439	+	4.82509i	−0.171414	+	0.194409i
$617$	−19.8776	−	3.95389i	−0.800241	−	0.159178i	−0.222003	−	0.975046i	$-0.571259\pi$
$617$	−19.8776	−	3.95389i	−0.800241	−	0.159178i	−0.578238	+	0.815868i	$0.696259\pi$
$618$	−1.45229	+	1.51437i	−0.0584197	+	0.0609171i
$619$	7.60419	+	14.2264i	0.305638	+	0.571809i	0.987111	−	0.160034i	$-0.0511604\pi$
$619$	7.60419	+	14.2264i	0.305638	+	0.571809i	−0.681473	+	0.731843i	$0.738660\pi$
$620$	−6.00940	+	5.36789i	−0.241343	+	0.215580i
$621$	0.237875	−	2.41518i	0.00954559	−	0.0969180i
$622$	−47.1617	+	5.64364i	−1.89101	+	0.226290i
$623$	−2.38866	−	0.989414i	−0.0956995	−	0.0396400i
$624$	−0.399676	+	3.53289i	−0.0159998	+	0.141429i
$625$	−20.5032	+	8.49271i	−0.820129	+	0.339708i
$626$	−0.549349	+	0.308582i	−0.0219564	+	0.0123334i
$627$	12.0663	−	9.90259i	0.481883	−	0.395471i
$628$	−15.8325	+	21.0278i	−0.631785	+	0.839101i
$629$	21.7389	+	6.59441i	0.866785	+	0.262936i
$630$	−0.100841	−	0.229735i	−0.00401762	−	0.00915287i
$631$	23.2700	+	34.8260i	0.926363	+	1.38640i	0.922328	+	0.386408i	$0.126284\pi$
$631$	23.2700	+	34.8260i	0.926363	+	1.38640i	0.00403510	+	0.999992i	$0.498716\pi$
$632$	7.92059	−	4.89600i	0.315064	−	0.194752i
$633$	17.3955	+	11.6233i	0.691408	+	0.461984i
$634$	−25.1787	+	17.5968i	−0.999973	+	0.698860i
$635$	−1.80152	+	2.19516i	−0.0714911	+	0.0871122i
$636$	−0.139712	−	0.0217590i	−0.00553994	−	0.000862799i
$637$	5.35715	+	2.86346i	0.212258	+	0.113454i
$638$	27.0864	−	53.3300i	1.07236	−	2.11136i
$639$	10.0688			0.398315
$640$	3.65241	−	3.30510i	0.144374	−	0.130646i
$641$	7.64558			0.301982			0.150991	−	0.988535i	$-0.451753\pi$
$641$	7.64558			0.301982			0.150991	+	0.988535i	$0.451753\pi$
$642$	2.39216	−	4.70989i	0.0944111	−	0.185884i
$643$	−17.2160	−	9.20214i	−0.678933	−	0.362897i	0.0956099	−	0.995419i	$-0.469520\pi$
$643$	−17.2160	−	9.20214i	−0.678933	−	0.362897i	−0.774543	+	0.632522i	$0.782020\pi$
$644$	−0.304352	+	1.95421i	−0.0119931	+	0.0770067i
$645$	−1.06265	+	1.29484i	−0.0418418	+	0.0509843i
$646$	8.51205	−	5.94889i	0.334902	−	0.234056i
$647$	25.0051	+	16.7079i	0.983051	+	0.656854i	0.939626	−	0.342203i	$-0.111173\pi$
$647$	25.0051	+	16.7079i	0.983051	+	0.656854i	0.0434253	+	0.999057i	$0.486173\pi$
$648$	−2.75281	−	0.649637i	−0.108141	−	0.0255202i
$649$	−8.98700	−	13.4500i	−0.352771	−	0.527959i
$650$	−2.43042	−	5.53694i	−0.0953290	−	0.217177i
$651$	−3.60822	−	1.09454i	−0.141417	−	0.0428985i
$652$	15.8479	+	11.9324i	0.620651	+	0.467308i
$653$	8.39465	−	6.88931i	0.328508	−	0.269600i	−0.455652	−	0.890158i	$-0.650594\pi$
$653$	8.39465	−	6.88931i	0.328508	−	0.269600i	0.784160	+	0.620558i	$0.213094\pi$
$654$	1.55289	−	0.872295i	0.0607229	−	0.0341094i
$655$	−5.35506	+	2.21814i	−0.209240	+	0.0866699i
$656$	30.3057	+	16.7672i	1.18324	+	0.654650i
$657$	9.59572	+	3.97468i	0.374365	+	0.155067i
$658$	3.24854	−	0.388739i	0.126641	−	0.0151546i
$659$	−0.212622	+	2.15879i	−0.00828259	+	0.0840945i	−0.998437	−	0.0558823i	$-0.982203\pi$
$659$	−0.212622	+	2.15879i	−0.00828259	+	0.0840945i	0.990155	+	0.139977i	$0.0447028\pi$
$660$	3.23782	+	3.62477i	0.126032	+	0.141094i
$661$	7.02242	+	13.1380i	0.273140	+	0.511010i	0.980669	−	0.195675i	$-0.0626898\pi$
$661$	7.02242	+	13.1380i	0.273140	+	0.511010i	−0.707528	+	0.706685i	$0.750190\pi$
$662$	18.3839	−	19.1698i	0.714509	−	0.745055i
$663$	−2.28906	−	0.455322i	−0.0888996	−	0.0176832i
$664$	−0.163616	−	2.60301i	−0.00634954	−	0.101017i
$665$	−0.0967924	−	0.486608i	−0.00375345	−	0.0188699i
$666$	−2.63755	−	11.9477i	−0.102203	−	0.462962i
$667$	−1.80253	−	18.3013i	−0.0697940	−	0.708631i
$668$	−23.7256	−	21.8185i	−0.917973	−	0.844185i
$669$	2.51830	+	8.30172i	0.0973631	+	0.320963i
$670$	0.374136	−	4.83353i	0.0144541	−	0.186736i
$671$	−24.9667	+	24.9667i	−0.963830	+	0.963830i
$672$	2.21003	+	0.654874i	0.0852539	+	0.0252623i
$673$	−25.8555	−	25.8555i	−0.996656	−	0.996656i	0.00333808	−	0.999994i	$-0.498937\pi$
$673$	−25.8555	−	25.8555i	−0.996656	−	0.996656i	−0.999994	+	0.00333808i	$0.998937\pi$
$674$	34.3257	−	29.3936i	1.32218	−	1.13220i
$675$	4.60330	−	1.39640i	0.177181	−	0.0537473i
$676$	−22.1503	+	10.2808i	−0.851934	+	0.395415i
$677$	−21.9258	+	2.15950i	−0.842677	+	0.0829964i	−0.510137	−	0.860093i	$-0.670405\pi$
$677$	−21.9258	+	2.15950i	−0.842677	+	0.0829964i	−0.332539	+	0.943089i	$0.607905\pi$
$678$	−7.71652	−	4.92565i	−0.296351	−	0.189168i
$679$	−5.42286	+	1.07867i	−0.208110	+	0.0413957i
$680$	1.96155	+	2.57055i	0.0752219	+	0.0985762i
$681$	0.578572	−	2.90868i	0.0221709	−	0.111461i
$682$	73.0276	−	1.52830i	2.79637	−	0.0585215i
$683$	−5.62836	+	3.00842i	−0.215363	+	0.115114i	−0.575551	−	0.817766i	$-0.695213\pi$
$683$	−5.62836	+	3.00842i	−0.215363	+	0.115114i	0.360188	+	0.932880i	$0.382713\pi$
$684$	−5.03877	−	2.42795i	−0.192662	−	0.0928348i
$685$	−3.87741	−	0.381891i	−0.148148	−	0.0145913i
$686$	4.92727	−	6.26682i	0.188124	−	0.239268i
$687$	−2.55945	+	6.17905i	−0.0976490	+	0.235745i
$688$	−2.78348	−	15.1354i	−0.106119	−	0.577032i
$689$	0.0240480	+	0.0580570i	0.000916156	+	0.00221180i
$690$	1.43871	+	0.403756i	0.0547708	+	0.0153707i
$691$	3.62929	+	4.42230i	0.138065	+	0.168232i	0.837453	−	0.546510i	$-0.184044\pi$
$691$	3.62929	+	4.42230i	0.138065	+	0.168232i	−0.699388	+	0.714742i	$0.746544\pi$
$692$	−11.0225	−	18.6954i	−0.419011	−	0.710693i
$693$	−0.660209	+	2.17642i	−0.0250793	+	0.0826753i
$694$	7.14418	+	2.78556i	0.271189	+	0.105738i
$695$	−2.74246	+	1.83246i	−0.104028	+	0.0695090i
$696$	−21.4193	−	0.758580i	−0.811897	−	0.0287539i
$697$	−12.6312	+	18.9039i	−0.478440	+	0.716036i
$698$	−27.9993	−	4.96278i	−1.05979	−	0.187844i
$699$	−13.9240	−	11.4272i	−0.526655	−	0.432215i
$700$	−3.80956	+	0.924994i	−0.143988	+	0.0349615i
$701$	7.03260	−	13.1571i	0.265617	−	0.496935i	−0.713388	−	0.700769i	$-0.752840\pi$
$701$	7.03260	−	13.1571i	0.265617	−	0.496935i	0.979005	+	0.203834i	$0.0653403\pi$
$702$	0.389986	+	1.19501i	0.0147191	+	0.0451026i
$703$		−	24.1954i		−	0.912547i
$704$	−44.6360	+	1.22212i	−1.68228	+	0.0460606i
$705$		−	2.47193i		−	0.0930982i
$706$	−33.8819	+	11.0572i	−1.27516	+	0.416144i
$707$	3.70541	−	6.93234i	0.139356	−	0.260718i
$708$	−3.01578	+	4.94992i	−0.113340	+	0.186029i
$709$	12.6979	+	10.4209i	0.476879	+	0.391365i	0.841899	−	0.539635i	$-0.181438\pi$
$709$	12.6979	+	10.4209i	0.476879	+	0.391365i	−0.365020	+	0.931000i	$0.618938\pi$
$710$	−1.08200	+	6.10448i	−0.0406068	+	0.229097i
$711$	1.82903	−	2.73733i	0.0685939	−	0.102658i
$712$	−6.27675	−	16.8133i	−0.235231	−	0.630103i
$713$	18.6725	−	12.4765i	0.699289	−	0.467250i
$714$	−0.549660	+	1.40972i	−0.0205705	+	0.0527576i
$715$	0.627029	−	2.06704i	0.0234496	−	0.0773029i
$716$	−12.4984	+	48.4072i	−0.467088	+	1.80906i
$717$	−7.30073	−	8.89596i	−0.272651	−	0.332226i
$718$	12.6381	−	45.0337i	0.471651	−	1.68064i
$719$	−2.39809	−	5.78950i	−0.0894336	−	0.215912i	0.872834	−	0.488018i	$-0.162280\pi$
$719$	−2.39809	−	5.78950i	−0.0894336	−	0.215912i	−0.962267	+	0.272106i	$0.912280\pi$
$720$	0.689681	−	1.59916i	0.0257029	−	0.0595972i
$721$	0.231352	−	0.558532i	0.00861598	−	0.0208008i
$722$	12.4280	+	9.77151i	0.462524	+	0.363658i
$723$	−15.9641	−	1.57232i	−0.593711	−	0.0584754i
$724$	−12.0375	+	4.20906i	−0.447371	+	0.156429i
$725$	32.1475	−	17.1832i	1.19393	−	0.638168i
$726$	−0.596356	−	28.4961i	−0.0221329	−	1.05759i
$727$	−7.46408	+	37.5245i	−0.276828	+	1.39171i	0.552765	+	0.833337i	$0.313573\pi$
$727$	−7.46408	+	37.5245i	−0.276828	+	1.39171i	−0.829593	+	0.558369i	$0.811427\pi$
$728$	−0.262489	−	0.990214i	−0.00972849	−	0.0366998i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−3.44093	+	5.39056i	−0.127354	+	0.199514i
$731$	10.0534	−	0.990171i	0.371838	−	0.0366228i
$732$	11.8810	+	4.34833i	0.439133	+	0.160719i
$733$	−13.0218	+	3.95013i	−0.480972	+	0.145901i	−0.521455	−	0.853279i	$-0.674610\pi$
$733$	−13.0218	+	3.95013i	−0.480972	+	0.145901i	0.0404827	+	0.999180i	$0.487110\pi$
$734$	7.51610	+	8.77728i	0.277424	+	0.323975i
$735$	−2.10393	−	2.10393i	−0.0776048	−	0.0776048i
$736$	−11.3654	+	7.70057i	−0.418933	+	0.283847i
$737$	−31.0753	+	31.0753i	−1.14467	+	1.14467i
$738$	12.2088	+	0.945009i	0.449410	+	0.0347863i
$739$	−5.25608	−	17.3270i	−0.193348	−	0.637383i	−0.998988	−	0.0449776i	$-0.985678\pi$
$739$	−5.25608	−	17.3270i	−0.193348	−	0.637383i	0.805640	−	0.592406i	$-0.201822\pi$
$740$	7.52704	−	0.315185i	0.276700	−	0.0115864i
$741$	0.243649	+	2.47381i	0.00895069	+	0.0908778i
$742$	0.0397823	−	0.00878229i	0.00146045	−	0.000322408i
$743$	1.67217	+	8.40656i	0.0613459	+	0.308407i	0.999260	−	0.0384605i	$-0.0122454\pi$
$743$	1.67217	+	8.40656i	0.0613459	+	0.308407i	−0.937914	+	0.346867i	$0.887245\pi$
$744$	−11.5132	−	23.5048i	−0.422093	−	0.861726i
$745$	−0.536148	−	0.106646i	−0.0196429	−	0.00390722i
$746$	−2.62682	−	2.51913i	−0.0961749	−	0.0922319i
$747$	−0.434685	−	0.813238i	−0.0159043	−	0.0297548i
$748$	1.65012	−	29.2651i	0.0603343	−	1.07004i
$749$	−0.149187	+	1.51472i	−0.00545118	+	0.0553467i
$750$	0.717728	+	5.99778i	0.0262077	+	0.219008i
$751$	46.4143	+	19.2254i	1.69368	+	0.701546i	0.999828	−	0.0185679i	$-0.00591067\pi$
$751$	46.4143	+	19.2254i	1.69368	+	0.701546i	0.693855	+	0.720114i	$0.255911\pi$
$752$	17.3448	+	14.6598i	0.632501	+	0.534589i
$753$	−0.244863	+	0.101425i	−0.00892329	+	0.00369615i
$754$	4.66498	+	8.30478i	0.169889	+	0.302442i
$755$	3.90243	−	3.20264i	0.142024	−	0.116556i
$756$	0.806971	−	0.113740i	0.0293492	−	0.00413667i
$757$	−49.7251	−	15.0839i	−1.80729	−	0.548235i	−0.808121	−	0.589016i	$-0.799516\pi$
$757$	−49.7251	−	15.0839i	−1.80729	−	0.548235i	−0.999168	+	0.0407806i	$0.987016\pi$
$758$	−45.2299	+	19.8535i	−1.64282	+	0.721112i
$759$	−7.52564	−	11.2629i	−0.273164	−	0.408818i
$760$	2.01348	−	2.79399i	0.0730367	−	0.101349i
$761$	12.5211	+	8.36632i	0.453889	+	0.303279i	0.761420	−	0.648259i	$-0.224503\pi$
$761$	12.5211	+	8.36632i	0.453889	+	0.303279i	−0.307531	+	0.951538i	$0.599503\pi$
$762$	−5.28395	−	7.56061i	−0.191417	−	0.273892i
$763$	−0.325563	+	0.396700i	−0.0117862	+	0.0143615i
$764$	38.0180	−	27.7718i	1.37544	−	1.00475i
$765$	1.00822	+	0.538905i	0.0364523	+	0.0194842i
$766$	−28.7513	−	14.6028i	−1.03883	−	0.527622i
$767$	2.57602			0.0930147
$768$	7.13070	+	14.3232i	0.257307	+

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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26090 + 0.640414i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.17974 + 1.61500i) q^{4} +(-0.276206 + 0.336558i) q^{5} +(-0.810126 - 1.15918i) q^{6} +(0.338802 + 0.226380i) q^{7} +(0.453269 + 2.79187i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(1.26090 + 0.640414i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(1.17974 + 1.61500i) q^{4} +(-0.276206 + 0.336558i) q^{5} +(-0.810126 - 1.15918i) q^{6} +(0.338802 + 0.226380i) q^{7} +(0.453269 + 2.79187i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.563804 + 0.247480i) q^{10} +(5.34125 + 1.62025i) q^{11} +(-0.279134 - 1.98043i) q^{12} +(-0.687095 + 0.563884i) q^{13} +(0.282218 + 0.502416i) q^{14} +(0.402244 - 0.166615i) q^{15} +(-1.21643 + 3.81055i) q^{16} +(-2.42587 - 1.00483i) q^{17} +(0.168034 + 1.40420i) q^{18} +(-0.274116 + 2.78314i) q^{19} +(-0.869391 - 0.0490207i) q^{20} +(-0.192082 - 0.359359i) q^{21} +(5.69715 + 5.46359i) q^{22} +(2.38024 + 0.473459i) q^{23} +(0.916332 - 2.67588i) q^{24} +(0.938470 + 4.71801i) q^{25} +(-1.22748 + 0.270977i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(0.0340950 + 0.814233i) q^{28} +(-2.19967 - 7.25133i) q^{29} +(0.613892 + 0.0475178i) q^{30} +(6.54326 - 6.54326i) q^{31} +(-3.97412 + 4.02571i) q^{32} +(-3.94678 - 3.94678i) q^{33} +(-2.41527 - 2.82054i) q^{34} +(-0.169769 + 0.0514989i) q^{35} +(-0.687392 + 1.87816i) q^{36} +(-8.61002 + 0.848013i) q^{37} +(-2.12800 + 3.33372i) q^{38} +(0.871777 - 0.173407i) q^{39} +(-1.06482 - 0.618580i) q^{40} +(1.68923 - 8.49234i) q^{41} +(-0.0120570 - 0.576128i) q^{42} +(-3.39302 + 1.81361i) q^{43} +(3.68459 + 10.5376i) q^{44} +(-0.433289 - 0.0426753i) q^{45} +(2.69803 + 2.12132i) q^{46} +(2.17271 - 5.24538i) q^{47} +(2.86907 - 2.78719i) q^{48} +(-2.61525 - 6.31376i) q^{49} +(-1.83816 + 6.54995i) q^{50} +(1.66575 + 2.02972i) q^{51} +(-1.72126 - 0.444419i) q^{52} +(0.0205226 - 0.0676539i) q^{53} +(0.513740 - 1.31760i) q^{54} +(-2.02059 + 1.35012i) q^{55} +(-0.478456 + 1.04850i) q^{56} +(1.55371 - 2.32530i) q^{57} +(1.87029 - 10.5519i) q^{58} +(-2.24028 - 1.83855i) q^{59} +(0.743626 + 0.453060i) q^{60} +(-2.98198 + 5.57890i) q^{61} +(12.4408 - 4.06000i) q^{62} +0.407473i q^{63} +(-7.58910 + 2.53094i) q^{64} -0.386995i q^{65} +(-2.44893 - 7.50407i) q^{66} +(-3.71158 + 6.94388i) q^{67} +(-1.23910 - 5.10320i) q^{68} +(-1.87600 - 1.53959i) q^{69} +(-0.247042 - 0.0437875i) q^{70} +(5.59391 - 8.37188i) q^{71} +(-2.06953 + 1.92796i) q^{72} +(8.63592 - 5.77034i) q^{73} +(-11.3995 - 4.44472i) q^{74} +(1.39640 - 4.60330i) q^{75} +(-4.81815 + 2.84069i) q^{76} +(1.44283 + 1.75810i) q^{77} +(1.21028 + 0.339649i) q^{78} +(-1.25986 - 3.04156i) q^{79} +(-0.946487 - 1.46189i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(7.56857 - 9.62619i) q^{82} +(-0.917680 - 0.0903836i) q^{83} +(0.353758 - 0.734162i) q^{84} +(1.00822 - 0.538905i) q^{85} +(-5.43972 + 0.113841i) q^{86} +(-1.47832 + 7.43202i) q^{87} +(-2.10251 + 15.6465i) q^{88} +(-6.22319 + 1.23787i) q^{89} +(-0.519005 - 0.331294i) q^{90} +(-0.360441 + 0.0355003i) q^{91} +(2.04343 + 4.40263i) q^{92} +(-8.85511 + 2.68617i) q^{93} +(6.09878 - 5.22247i) q^{94} +(-0.860977 - 0.860977i) q^{95} +(5.40257 - 1.67697i) q^{96} +(-9.59489 + 9.59489i) q^{97} +(0.745856 - 9.63586i) q^{98} +(1.62025 + 5.34125i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

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