LMFDB - Embedded newform 380.2.n.a.31.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("380.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			31.13
Character	$\chi$	$=$	380.31
Dual form			380.2.n.a.331.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.564655 + 1.29660i) q^{2} +(-1.52787 - 2.64635i) q^{3} +(-1.36233 + 1.46426i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.56853 - 3.47531i) q^{6} -2.58057i q^{7} +(-2.66780 - 0.939591i) q^{8} +(-3.16877 + 5.48848i) q^{9} +O(q^{10})$	\(q+(0.564655 + 1.29660i) q^{2} +(-1.52787 - 2.64635i) q^{3} +(-1.36233 + 1.46426i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.56853 - 3.47531i) q^{6} -2.58057i q^{7} +(-2.66780 - 0.939591i) q^{8} +(-3.16877 + 5.48848i) q^{9} +(-0.840559 + 1.13730i) q^{10} -0.0502420i q^{11} +(5.95641 + 1.36800i) q^{12} +(-2.19367 - 1.26651i) q^{13} +(3.34595 - 1.45713i) q^{14} +(1.52787 - 2.64635i) q^{15} +(-0.288118 - 3.98961i) q^{16} +(-3.71766 - 6.43917i) q^{17} +(-8.90561 - 1.00953i) q^{18} +(-4.32524 - 0.540643i) q^{19} +(-1.94925 - 0.447682i) q^{20} +(-6.82908 + 3.94277i) q^{21} +(0.0651436 - 0.0283694i) q^{22} +(-1.82478 - 1.05354i) q^{23} +(1.58957 + 8.49551i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.403494 - 3.55945i) q^{26} +10.1987 q^{27} +(3.77862 + 3.51558i) q^{28} +(-0.821013 - 0.474012i) q^{29} +(4.29397 + 0.486758i) q^{30} -3.30561 q^{31} +(5.01023 - 2.62633i) q^{32} +(-0.132958 + 0.0767632i) q^{33} +(6.24982 - 8.45621i) q^{34} +(2.23484 - 1.29028i) q^{35} +(-3.71965 - 12.1170i) q^{36} +8.51189i q^{37} +(-1.74127 - 5.91337i) q^{38} +7.74028i q^{39} +(-0.520192 - 2.78018i) q^{40} +(9.25357 - 5.34255i) q^{41} +(-8.96826 - 6.62826i) q^{42} +(7.12832 - 4.11554i) q^{43} +(0.0735673 + 0.0684461i) q^{44} -6.33755 q^{45} +(0.335642 - 2.96089i) q^{46} +(-7.59619 - 4.38566i) q^{47} +(-10.1177 + 6.85806i) q^{48} +0.340679 q^{49} +(-1.40521 - 0.159293i) q^{50} +(-11.3602 + 19.6764i) q^{51} +(4.84300 - 1.48669i) q^{52} +(10.5104 + 6.06821i) q^{53} +(5.75873 + 13.2236i) q^{54} +(0.0435108 - 0.0251210i) q^{55} +(-2.42468 + 6.88444i) q^{56} +(5.17768 + 12.2721i) q^{57} +(0.151014 - 1.33218i) q^{58} +(1.90456 + 3.29879i) q^{59} +(1.79348 + 5.84240i) q^{60} +(-0.165545 + 0.286732i) q^{61} +(-1.86653 - 4.28605i) q^{62} +(14.1634 + 8.17723i) q^{63} +(6.23434 + 5.01328i) q^{64} -2.53303i q^{65} +(-0.174606 - 0.129048i) q^{66} +(-2.82453 + 4.89222i) q^{67} +(14.4933 + 3.32865i) q^{68} +6.43867i q^{69} +(2.93489 + 2.16912i) q^{70} +(-3.89538 - 6.74700i) q^{71} +(13.6106 - 11.6648i) q^{72} +(-5.13808 - 8.89942i) q^{73} +(-11.0365 + 4.80628i) q^{74} +3.05574 q^{75} +(6.68404 - 5.59674i) q^{76} -0.129653 q^{77} +(-10.0360 + 4.37059i) q^{78} +(3.09164 + 5.35488i) q^{79} +(3.31104 - 2.24432i) q^{80} +(-6.07592 - 10.5238i) q^{81} +(12.1522 + 8.98145i) q^{82} -3.75388i q^{83} +(3.53021 - 15.3709i) q^{84} +(3.71766 - 6.43917i) q^{85} +(9.36123 + 6.91870i) q^{86} +2.89691i q^{87} +(-0.0472069 + 0.134036i) q^{88} +(-8.19252 - 4.72996i) q^{89} +(-3.57853 - 8.21724i) q^{90} +(-3.26832 + 5.66090i) q^{91} +(4.02860 - 1.23669i) q^{92} +(5.05055 + 8.74780i) q^{93} +(1.39721 - 12.3256i) q^{94} +(-1.69441 - 4.01609i) q^{95} +(-14.6052 - 9.24613i) q^{96} +(-10.4944 + 6.05892i) q^{97} +(0.192366 + 0.441724i) q^{98} +(0.275752 + 0.159205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	$ 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) $ 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.564655	+	1.29660i	0.399271	+	0.916833i
$2$	0.564655	+	1.29660i	0.399271	+	0.916833i
$3$	−1.52787	−	2.64635i	−0.882116	−	1.52787i	−0.848984	−	0.528419i	$-0.822785\pi$
$3$	−1.52787	−	2.64635i	−0.882116	−	1.52787i	−0.0331323	−	0.999451i	$-0.510548\pi$
$4$	−1.36233	+	1.46426i	−0.681165	+	0.732130i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	2.56853	−	3.47531i	1.04860	−	1.41879i
$7$		−	2.58057i		−	0.975362i	−0.873022	−	0.487681i	$-0.837843\pi$
$7$		−	2.58057i		−	0.975362i	0.873022	−	0.487681i	$-0.162157\pi$
$8$	−2.66780	−	0.939591i	−0.943211	−	0.332195i
$9$	−3.16877	+	5.48848i	−1.05626	+	1.82949i
$10$	−0.840559	+	1.13730i	−0.265808	+	0.359647i
$11$		−	0.0502420i		−	0.0151485i	−0.999971	−	0.00757426i	$-0.997589\pi$
$11$		−	0.0502420i		−	0.0151485i	0.999971	−	0.00757426i	$-0.00241099\pi$
$12$	5.95641	+	1.36800i	1.71947	+	0.394907i
$13$	−2.19367	−	1.26651i	−0.608414	−	0.351268i	0.163931	−	0.986472i	$-0.447583\pi$
$13$	−2.19367	−	1.26651i	−0.608414	−	0.351268i	−0.772344	+	0.635204i	$0.780916\pi$
$14$	3.34595	−	1.45713i	0.894244	−	0.389434i
$15$	1.52787	−	2.64635i	0.394494	−	0.683284i
$16$	−0.288118	−	3.98961i	−0.0720294	−	0.997403i
$17$	−3.71766	−	6.43917i	−0.901664	−	1.56173i	−0.825333	−	0.564646i	$-0.809013\pi$
$17$	−3.71766	−	6.43917i	−0.901664	−	1.56173i	−0.0763309	−	0.997083i	$-0.524321\pi$
$18$	−8.90561	−	1.00953i	−2.09907	−	0.237948i
$19$	−4.32524	−	0.540643i	−0.992278	−	0.124032i
$19$	−4.32524	−	0.540643i	−0.992278	−	0.124032i
$20$	−1.94925	−	0.447682i	−0.435866	−	0.100105i
$21$	−6.82908	+	3.94277i	−1.49023	+	0.860383i
$22$	0.0651436	−	0.0283694i	0.0138887	−	0.00604837i
$23$	−1.82478	−	1.05354i	−0.380493	−	0.219678i	0.297540	−	0.954709i	$-0.403834\pi$
$23$	−1.82478	−	1.05354i	−0.380493	−	0.219678i	−0.678033	+	0.735032i	$0.737167\pi$
$24$	1.58957	+	8.49551i	0.324470	+	1.73414i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	0.403494	−	3.55945i	0.0791317	−	0.698065i
$27$	10.1987			1.96274
$28$	3.77862	+	3.51558i	0.714092	+	0.664382i
$29$	−0.821013	−	0.474012i	−0.152458	−	0.0880218i	0.421830	−	0.906675i	$-0.361388\pi$
$29$	−0.821013	−	0.474012i	−0.152458	−	0.0880218i	−0.574288	+	0.818653i	$0.694721\pi$
$30$	4.29397	+	0.486758i	0.783968	+	0.0888695i
$31$	−3.30561			−0.593705			−0.296853	−	0.954923i	$-0.595937\pi$
$31$	−3.30561			−0.593705			−0.296853	+	0.954923i	$0.595937\pi$
$32$	5.01023	−	2.62633i	0.885692	−	0.464273i
$33$	−0.132958	+	0.0767632i	−0.0231450	+	0.0133628i
$34$	6.24982	−	8.45621i	1.07183	−	1.45023i
$35$	2.23484	−	1.29028i	0.377756	−	0.218098i
$36$	−3.71965	−	12.1170i	−0.619941	−	2.01950i
$37$			8.51189i			1.39935i	0.714463	+	0.699673i	$0.246671\pi$
$37$			8.51189i			1.39935i	−0.714463	+	0.699673i	$0.753329\pi$
$38$	−1.74127	−	5.91337i	−0.282472	−	0.959276i
$39$			7.74028i			1.23944i
$40$	−0.520192	−	2.78018i	−0.0822496	−	0.439585i
$41$	9.25357	−	5.34255i	1.44516	−	0.834366i	0.446977	−	0.894546i	$-0.352501\pi$
$41$	9.25357	−	5.34255i	1.44516	−	0.834366i	0.998188	+	0.0601797i	$0.0191674\pi$
$42$	−8.96826	−	6.62826i	−1.38383	−	1.02276i
$43$	7.12832	−	4.11554i	1.08706	−	0.627613i	0.154266	−	0.988029i	$-0.450699\pi$
$43$	7.12832	−	4.11554i	1.08706	−	0.627613i	0.932792	+	0.360416i	$0.117365\pi$
$44$	0.0735673	+	0.0684461i	0.0110907	+	0.0103186i
$45$	−6.33755			−0.944746
$46$	0.335642	−	2.96089i	0.0494877	−	0.436559i
$47$	−7.59619	−	4.38566i	−1.10802	−	0.639714i	−0.169703	−	0.985495i	$-0.554281\pi$
$47$	−7.59619	−	4.38566i	−1.10802	−	0.639714i	−0.938315	+	0.345781i	$0.887614\pi$
$48$	−10.1177	+	6.85806i	−1.46036	+	0.989876i
$49$	0.340679			0.0486685
$50$	−1.40521	−	0.159293i	−0.198727	−	0.0225274i
$51$	−11.3602	+	19.6764i	−1.59075	+	2.75525i
$52$	4.84300	−	1.48669i	0.671604	−	0.206167i
$53$	10.5104	+	6.06821i	1.44372	+	0.833533i	0.998096	−	0.0616866i	$-0.0196479\pi$
$53$	10.5104	+	6.06821i	1.44372	+	0.833533i	0.445626	+	0.895219i	$0.352981\pi$
$54$	5.75873	+	13.2236i	0.783664	+	1.79950i
$55$	0.0435108	−	0.0251210i	0.00586700	−	0.00338731i
$56$	−2.42468	+	6.88444i	−0.324011	+	0.919972i
$57$	5.17768	+	12.2721i	0.685800	+	1.62548i
$58$	0.151014	−	1.33218i	0.0198291	−	0.174923i
$59$	1.90456	+	3.29879i	0.247953	+	0.429467i	0.962958	−	0.269653i	$-0.0869089\pi$
$59$	1.90456	+	3.29879i	0.247953	+	0.429467i	−0.715005	+	0.699119i	$0.753576\pi$
$60$	1.79348	+	5.84240i	0.231537	+	0.754250i
$61$	−0.165545	+	0.286732i	−0.0211959	+	0.0367123i	−0.876429	−	0.481532i	$-0.840081\pi$
$61$	−0.165545	+	0.286732i	−0.0211959	+	0.0367123i	0.855233	+	0.518244i	$0.173414\pi$
$62$	−1.86653	−	4.28605i	−0.237050	−	0.544329i
$63$	14.1634	+	8.17723i	1.78442	+	1.03023i
$64$	6.23434	+	5.01328i	0.779292	+	0.626660i
$65$		−	2.53303i		−	0.314184i
$66$	−0.174606	−	0.129048i	−0.0214925	−	0.0158847i
$67$	−2.82453	+	4.89222i	−0.345071	+	0.597680i	−0.985367	−	0.170448i	$-0.945478\pi$
$67$	−2.82453	+	4.89222i	−0.345071	+	0.597680i	0.640296	+	0.768128i	$0.278812\pi$
$68$	14.4933	+	3.32865i	1.75757	+	0.403658i
$69$			6.43867i			0.775125i
$70$	2.93489	+	2.16912i	0.350786	+	0.259259i
$71$	−3.89538	−	6.74700i	−0.462297	−	0.800722i	0.536778	−	0.843723i	$-0.319641\pi$
$71$	−3.89538	−	6.74700i	−0.462297	−	0.800722i	−0.999075	+	0.0430017i	$0.986308\pi$
$72$	13.6106	−	11.6648i	1.60402	−	1.37471i
$73$	−5.13808	−	8.89942i	−0.601367	−	1.04160i	−0.992614	−	0.121313i	$-0.961290\pi$
$73$	−5.13808	−	8.89942i	−0.601367	−	1.04160i	0.391247	−	0.920286i	$-0.372044\pi$
$74$	−11.0365	+	4.80628i	−1.28297	+	0.558719i
$75$	3.05574			0.352846
$76$	6.68404	−	5.59674i	0.766712	−	0.641991i
$77$	−0.129653			−0.0147753
$78$	−10.0360	+	4.37059i	−1.13636	+	0.494872i
$79$	3.09164	+	5.35488i	0.347837	+	0.602471i	0.985865	−	0.167542i	$-0.0535830\pi$
$79$	3.09164	+	5.35488i	0.347837	+	0.602471i	−0.638028	+	0.770013i	$0.720250\pi$
$80$	3.31104	−	2.24432i	0.370186	−	0.250923i
$81$	−6.07592	−	10.5238i	−0.675103	−	1.16931i
$82$	12.1522	+	8.98145i	1.34199	+	0.991835i
$83$		−	3.75388i		−	0.412042i	−0.978548	−	0.206021i	$-0.933949\pi$
$83$		−	3.75388i		−	0.412042i	0.978548	−	0.206021i	$-0.0660515\pi$
$84$	3.53021	−	15.3709i	0.385178	−	1.67710i
$85$	3.71766	−	6.43917i	0.403237	−	0.698426i
$86$	9.36123	+	6.91870i	1.00945	+	0.746062i
$87$			2.89691i			0.310582i
$88$	−0.0472069	+	0.134036i	−0.00503227	+	0.0142882i
$89$	−8.19252	−	4.72996i	−0.868406	−	0.501374i	−0.00158770	−	0.999999i	$-0.500505\pi$
$89$	−8.19252	−	4.72996i	−0.868406	−	0.501374i	−0.866818	+	0.498624i	$0.833839\pi$
$90$	−3.57853	−	8.21724i	−0.377210	−	0.866174i
$91$	−3.26832	+	5.66090i	−0.342613	+	0.593424i
$92$	4.02860	−	1.23669i	0.420011	−	0.128934i
$93$	5.05055	+	8.74780i	0.523717	+	0.907105i
$94$	1.39721	−	12.3256i	0.144111	−	1.27129i
$95$	−1.69441	−	4.01609i	−0.173843	−	0.412042i
$96$	−14.6052	−	9.24613i	−1.49063	−	0.943679i
$97$	−10.4944	+	6.05892i	−1.06554	+	0.615190i	−0.926960	−	0.375161i	$-0.877588\pi$
$97$	−10.4944	+	6.05892i	−1.06554	+	0.615190i	−0.138581	+	0.990351i	$0.544254\pi$
$98$	0.192366	+	0.441724i	0.0194319	+	0.0446208i
$99$	0.275752	+	0.159205i	0.0277141	+	0.0160007i
$100$	−0.586922	−	1.91194i	−0.0586922	−	0.191194i
$101$	3.68519	−	6.38293i	0.366690	−	0.635126i	−0.622356	−	0.782734i	$-0.713824\pi$
$101$	3.68519	−	6.38293i	0.366690	−	0.635126i	0.989046	+	0.147609i	$0.0471576\pi$
$102$	−31.9270	−	3.61920i	−3.16124	−	0.358354i
$103$	11.4675			1.12993			0.564963	−	0.825116i	$-0.308891\pi$
$103$	11.4675			1.12993			0.564963	+	0.825116i	$0.308891\pi$
$104$	4.66227	+	5.43996i	0.457173	+	0.533432i
$105$	−6.82908	−	3.94277i	−0.666450	−	0.384775i
$106$	−1.93325	+	17.0543i	−0.187774	+	1.65646i
$107$	7.01954			0.678605			0.339302	−	0.940677i	$-0.389809\pi$
$107$	7.01954			0.678605			0.339302	+	0.940677i	$0.389809\pi$
$108$	−13.8939	+	14.9335i	−1.33695	+	1.43698i
$109$	−0.132921	+	0.0767422i	−0.0127316	+	0.00735057i	−0.506352	−	0.862327i	$-0.669006\pi$
$109$	−0.132921	+	0.0767422i	−0.0127316	+	0.00735057i	0.493621	+	0.869677i	$0.335673\pi$
$110$	0.0571404	+	0.0422313i	0.00544812	+	0.00402660i
$111$	22.5254	−	13.0051i	2.13802	−	1.23439i
$112$	−10.2955	+	0.743506i	−0.972829	+	0.0702547i
$113$			0.965284i			0.0908063i	0.998969	+	0.0454031i	$0.0144572\pi$
$113$			0.965284i			0.0908063i	−0.998969	+	0.0454031i	$0.985543\pi$
$114$	−12.9884	+	13.6429i	−1.21648	+	1.27777i
$115$		−	2.10707i		−	0.196486i
$116$	1.81257	−	0.556416i	0.168293	−	0.0516619i
$117$	13.9025	−	8.02659i	1.28528	−	0.742059i
$118$	−3.20179	+	4.33213i	−0.294749	+	0.398805i
$119$	−16.6167	+	9.59366i	−1.52325	+	0.879449i
$120$	−6.56254	+	5.62436i	−0.599075	+	0.513432i
$121$	10.9975			0.999771
$122$	−0.465252	−	0.0527403i	−0.0421219	−	0.00477488i
$123$	−28.2765	−	16.3254i	−2.54961	−	1.47202i
$124$	4.50333	−	4.84028i	0.404411	−	0.434670i
$125$	−1.00000			−0.0894427
$126$	−2.60515	+	22.9815i	−0.232085	+	2.04736i
$127$	2.37171	−	4.10792i	0.210455	−	0.364519i	−0.741402	−	0.671061i	$-0.765839\pi$
$127$	2.37171	−	4.10792i	0.210455	−	0.364519i	0.951857	+	0.306542i	$0.0991720\pi$
$128$	−2.97996	+	10.9142i	−0.263394	+	0.964688i
$129$	−21.7823	−	12.5760i	−1.91782	−	1.10726i
$130$	3.28432	−	1.43029i	0.288054	−	0.125445i
$131$	−18.4541	+	10.6545i	−1.61234	+	0.930885i	−0.623515	+	0.781812i	$0.714296\pi$
$131$	−18.4541	+	10.6545i	−1.61234	+	0.930885i	−0.988826	+	0.149074i	$0.952371\pi$
$132$	0.0687309	−	0.299262i	0.00598226	−	0.0260474i
$133$	−1.39516	+	11.1616i	−0.120976	+	0.967831i
$134$	−7.93813	−	0.899855i	−0.685750	−	0.0777356i
$135$	5.09934	+	8.83231i	0.438881	+	0.760164i
$136$	3.86779	+	20.6715i	0.331660	+	1.77257i
$137$	9.73106	−	16.8547i	0.831380	−	1.43999i	−0.0655634	−	0.997848i	$-0.520884\pi$
$137$	9.73106	−	16.8547i	0.831380	−	1.43999i	0.896944	−	0.442145i	$-0.145782\pi$
$138$	−8.34836	+	3.63563i	−0.710660	+	0.309485i
$139$	−8.05921	−	4.65299i	−0.683573	−	0.394661i	0.117627	−	0.993058i	$-0.462471\pi$
$139$	−8.05921	−	4.65299i	−0.683573	−	0.394661i	−0.801200	+	0.598397i	$0.795805\pi$
$140$	−1.15527	+	5.03017i	−0.0976383	+	0.425127i
$141$			26.8029i			2.25721i
$142$	6.54860	−	8.86047i	0.549546	−	0.743554i
$143$	−0.0636322	+	0.110214i	−0.00532119	+	0.00921657i
$144$	22.8099	+	11.0608i	1.90082	+	0.921737i
$145$		−	0.948024i		−	0.0787291i
$146$	8.63772	−	11.6871i	0.714863	−	0.967233i
$147$	−0.520514	−	0.901556i	−0.0429312	−	0.0743591i
$148$	−12.4636	−	11.5960i	−1.02450	−	0.953185i
$149$	−7.62969	−	13.2150i	−0.625049	−	1.08262i	−0.988531	−	0.151015i	$-0.951746\pi$
$149$	−7.62969	−	13.2150i	−0.625049	−	1.08262i	0.363483	−	0.931601i	$-0.381588\pi$
$150$	1.72544	+	3.96206i	0.140881	+	0.323501i
$151$	−1.99840			−0.162628			−0.0813138	−	0.996689i	$-0.525912\pi$
$151$	−1.99840			−0.162628			−0.0813138	+	0.996689i	$0.525912\pi$
$152$	11.0309	+	5.50628i	0.894724	+	0.446619i
$153$	47.1216			3.80956
$154$	−0.0732091	−	0.168107i	−0.00589935	−	0.0135465i
$155$	−1.65281	−	2.86274i	−0.132757	−	0.229941i
$156$	−11.3338	−	10.5448i	−0.907429	−	0.844260i
$157$	−3.51514	−	6.08840i	−0.280538	−	0.485907i	0.690979	−	0.722875i	$-0.257180\pi$
$157$	−3.51514	−	6.08840i	−0.280538	−	0.485907i	−0.971517	+	0.236968i	$0.923846\pi$
$158$	−5.19741	+	7.03227i	−0.413484	+	0.559458i
$159$		−	37.0857i		−	2.94109i
$160$	4.77958	+	3.02582i	0.377859	+	0.239212i
$161$	−2.71872	+	4.70896i	−0.214265	+	0.371118i
$162$	10.2143	−	13.8203i	0.802514	−	1.08583i
$163$			5.59414i			0.438167i	0.975706	+	0.219083i	$0.0703067\pi$
$163$			5.59414i			0.438167i	−0.975706	+	0.219083i	$0.929693\pi$
$164$	−4.78352	+	20.8279i	−0.373530	+	1.62639i
$165$	−0.132958	−	0.0767632i	−0.0103507	−	0.00597601i
$166$	4.86727	−	2.11965i	0.377773	−	0.164516i
$167$	6.06419	−	10.5035i	0.469261	−	0.812784i	−0.530122	−	0.847922i	$-0.677854\pi$
$167$	6.06419	−	10.5035i	0.469261	−	0.812784i	0.999382	+	0.0351380i	$0.0111871\pi$
$168$	21.9232	−	4.10199i	1.69141	−	0.316476i
$169$	−3.29188	−	5.70171i	−0.253222	−	0.438593i
$170$	10.4482	+	1.18439i	0.801341	+	0.0908389i
$171$	16.6730	−	22.0258i	1.27502	−	1.68436i
$172$	−3.68490	+	16.0444i	−0.280971	+	1.22338i
$173$	7.40766	−	4.27681i	0.563194	−	0.325160i	−0.191233	−	0.981545i	$-0.561248\pi$
$173$	7.40766	−	4.27681i	0.563194	−	0.325160i	0.754426	+	0.656385i	$0.227915\pi$
$174$	−3.75613	+	1.63576i	−0.284752	+	0.124006i
$175$	2.23484	+	1.29028i	0.168938	+	0.0975362i
$176$	−0.200446	+	0.0144756i	−0.0151092	+	0.00109114i
$177$	5.81984	−	10.0803i	0.437446	−	0.757679i
$178$	1.50690	−	13.2932i	0.112947	−	0.996367i
$179$	−11.9221			−0.891100			−0.445550	−	0.895257i	$-0.646992\pi$
$179$	−11.9221			−0.891100			−0.445550	+	0.895257i	$0.646992\pi$
$180$	8.63382	−	9.27982i	0.643527	−	0.691677i
$181$	15.7076	+	9.06876i	1.16753	+	0.674076i	0.953098	−	0.302663i	$-0.0978755\pi$
$181$	15.7076	+	9.06876i	1.16753	+	0.674076i	0.214435	+	0.976738i	$0.431209\pi$
$182$	−9.18539	−	1.04124i	−0.680866	−	0.0771820i
$183$	1.01172			0.0747888
$184$	3.87826	+	4.52517i	0.285909	+	0.333600i
$185$	−7.37151	+	4.25594i	−0.541964	+	0.312903i
$186$	−8.49056	+	11.4880i	−0.622558	+	0.842342i
$187$	−0.323517	+	0.186782i	−0.0236579	+	0.0136589i
$188$	16.7703	−	5.14808i	1.22310	−	0.375462i
$189$		−	26.3183i		−	1.91438i
$190$	4.25049	−	4.46467i	0.308363	−	0.323901i
$191$		−	9.84361i		−	0.712259i	−0.934437	−	0.356129i	$-0.884096\pi$
$191$		−	9.84361i		−	0.712259i	0.934437	−	0.356129i	$-0.115904\pi$
$192$	3.74164	−	24.1579i	0.270029	−	1.74344i
$193$	1.06403	−	0.614316i	0.0765903	−	0.0442195i	−0.461216	−	0.887288i	$-0.652587\pi$
$193$	1.06403	−	0.614316i	0.0765903	−	0.0442195i	0.537806	+	0.843069i	$0.319253\pi$
$194$	−13.7817	−	10.1858i	−0.989467	−	0.731295i
$195$	−6.70328	+	3.87014i	−0.480032	+	0.277146i
$196$	−0.464117	+	0.498843i	−0.0331512	+	0.0356317i
$197$	−20.6208			−1.46917			−0.734586	−	0.678516i	$-0.762624\pi$
$197$	−20.6208			−1.46917			−0.734586	+	0.678516i	$0.762624\pi$
$198$	−0.0507206	+	0.447435i	−0.00360456	+	0.0317978i
$199$	22.1489	+	12.7877i	1.57010	+	0.906495i	0.996156	+	0.0875972i	$0.0279188\pi$
$199$	22.1489	+	12.7877i	1.57010	+	0.906495i	0.573939	+	0.818898i	$0.305414\pi$
$200$	2.14761	−	1.84059i	0.151859	−	0.130149i
$201$	17.2620			1.21757
$202$	10.3570	+	1.17405i	0.728713	+	0.0826059i
$203$	−1.22322	+	2.11868i	−0.0858531	+	0.148702i
$204$	−13.3351	−	43.4401i	−0.933643	−	3.04141i
$205$	9.25357	+	5.34255i	0.646297	+	0.373140i
$206$	6.47518	+	14.8687i	0.451147	+	1.03595i
$207$	11.5646	−	6.67684i	0.803797	−	0.464072i
$208$	−4.42086	+	9.11678i	−0.306532	+	0.632135i
$209$	−0.0271630	+	0.217309i	−0.00187890	+	0.0150316i
$210$	1.25611	−	11.0809i	0.0866799	−	0.764652i
$211$	−3.68296	−	6.37908i	−0.253546	−	0.439154i	0.710954	−	0.703239i	$-0.248263\pi$
$211$	−3.68296	−	6.37908i	−0.253546	−	0.439154i	−0.964499	+	0.264085i	$0.914930\pi$
$212$	−23.2041	+	7.12313i	−1.59367	+	0.489219i
$213$	−11.9033	+	20.6171i	−0.815599	+	1.41266i
$214$	3.96362	+	9.10152i	0.270947	+	0.622167i
$215$	7.12832	+	4.11554i	0.486147	+	0.280677i
$216$	−27.2080	−	9.58257i	−1.85127	−	0.652012i
$217$			8.53035i			0.579078i
$218$	−0.174558	−	0.129013i	−0.0118226	−	0.00873784i
$219$	−15.7006	+	27.1943i	−1.06095	+	1.83762i
$220$	−0.0224924	+	0.0979342i	−0.00151644	+	0.00660272i
$221$			18.8339i			1.26690i
$222$	29.5814	+	21.8630i	1.98537	+	1.46735i
$223$	7.04246	+	12.1979i	0.471598	+	0.816832i	0.999472	−	0.0324908i	$-0.0103440\pi$
$223$	7.04246	+	12.1979i	0.471598	+	0.816832i	−0.527874	+	0.849323i	$0.677011\pi$
$224$	−6.77741	−	12.9292i	−0.452835	−	0.863871i
$225$	−3.16877	−	5.48848i	−0.211252	−	0.365898i
$226$	−1.25158	+	0.545053i	−0.0832542	+	0.0362564i
$227$	−17.5305			−1.16354			−0.581771	−	0.813353i	$-0.697640\pi$
$227$	−17.5305			−1.16354			−0.581771	+	0.813353i	$0.697640\pi$
$228$	−25.0233	−	9.13721i	−1.65721	−	0.605127i
$229$	26.2037			1.73159			0.865793	−	0.500401i	$-0.166814\pi$
$229$	26.2037			1.73159			0.865793	+	0.500401i	$0.166814\pi$
$230$	2.73203	−	1.18977i	0.180144	−	0.0784511i
$231$	0.198092	+	0.343106i	0.0130335	+	0.0225747i
$232$	1.74492	+	2.03599i	0.114560	+	0.133669i
$233$	−11.8519	−	20.5281i	−0.776445	−	1.34484i	−0.933979	−	0.357329i	$-0.883688\pi$
$233$	−11.8519	−	20.5281i	−0.776445	−	1.34484i	0.157533	−	0.987514i	$-0.449646\pi$
$234$	18.2574	+	13.4936i	1.19352	+	0.882107i
$235$		−	8.77132i		−	0.572178i
$236$	−7.42493	−	1.70527i	−0.483322	−	0.111004i
$237$	9.44725	−	16.3631i	0.613665	−	1.06290i
$238$	−21.8218	−	16.1281i	−1.41450	−	1.04543i
$239$			4.14202i			0.267925i	0.990986	+	0.133962i	$0.0427701\pi$
$239$			4.14202i			0.267925i	−0.990986	+	0.133962i	$0.957230\pi$
$240$	−10.9981	−	5.33315i	−0.709925	−	0.344253i
$241$	−6.67304	−	3.85268i	−0.429848	−	0.248173i	0.269434	−	0.963019i	$-0.413163\pi$
$241$	−6.67304	−	3.85268i	−0.429848	−	0.248173i	−0.699282	+	0.714846i	$0.746497\pi$
$242$	6.20978	+	14.2593i	0.399180	+	0.916622i
$243$	−3.26843	+	5.66110i	−0.209670	+	0.363159i
$244$	−0.194324	−	0.633025i	−0.0124403	−	0.0405252i
$245$	0.170340	+	0.295037i	0.0108826	+	0.0188492i
$246$	5.20106	−	45.8815i	0.331607	−	2.92530i
$247$	8.80341	+	6.66397i	0.560147	+	0.424018i
$248$	8.81872	+	3.10592i	0.559989	+	0.197226i
$249$	−9.93407	+	5.73544i	−0.629546	+	0.363469i
$250$	−0.564655	−	1.29660i	−0.0357119	−	0.0820040i
$251$	17.1425	+	9.89724i	1.08203	+	0.624708i	0.931442	−	0.363889i	$-0.118551\pi$
$251$	17.1425	+	9.89724i	1.08203	+	0.624708i	0.150584	+	0.988597i	$0.451884\pi$
$252$	−31.2688	+	9.59879i	−1.96975	+	0.604667i
$253$	−0.0529318	+	0.0916805i	−0.00332779	+	0.00576391i
$254$	6.66552	+	0.755594i	0.418232	+	0.0474102i
$255$	−22.7204			−1.42281
$256$	−15.8340	+	2.29895i	−0.989624	+	0.143685i
$257$	1.68474	+	0.972684i	0.105091	+	0.0606744i	0.551624	−	0.834093i	$-0.314008\pi$
$257$	1.68474	+	0.972684i	0.105091	+	0.0606744i	−0.446533	+	0.894767i	$0.647342\pi$
$258$	4.00654	−	35.3440i	0.249436	−	2.20042i
$259$	21.9655			1.36487
$260$	3.70901	+	3.45082i	0.230023	+	0.214011i
$261$	5.20320	−	3.00407i	0.322070	−	0.185947i
$262$	−24.2347	−	17.9114i	−1.49723	−	1.10657i
$263$	−21.9297	+	12.6611i	−1.35225	+	0.780719i	−0.988564	−	0.150804i	$-0.951814\pi$
$263$	−21.9297	+	12.6611i	−1.35225	+	0.780719i	−0.363682	+	0.931523i	$0.618480\pi$
$264$	0.426831	−	0.0798632i	0.0262696	−	0.00491524i
$265$			12.1364i			0.745534i
$266$	−15.2598	+	4.49347i	−0.935641	+	0.275512i
$267$			28.9070i			1.76908i
$268$	−3.31555	−	10.8007i	−0.202530	−	0.659756i
$269$	−3.90613	+	2.25520i	−0.238161	+	0.137502i	−0.614331	−	0.789048i	$-0.710574\pi$
$269$	−3.90613	+	2.25520i	−0.238161	+	0.137502i	0.376170	+	0.926551i	$0.377241\pi$
$270$	−8.57258	+	11.5990i	−0.521711	+	0.705892i
$271$	15.0198	−	8.67168i	0.912387	−	0.526767i	0.0311886	−	0.999514i	$-0.490071\pi$
$271$	15.0198	−	8.67168i	0.912387	−	0.526767i	0.881198	+	0.472747i	$0.156737\pi$
$272$	−24.6187	+	16.6872i	−1.49273	+	1.01181i
$273$	19.9743			1.20890
$274$	27.3484	+	3.10018i	1.65218	+	0.187289i
$275$	0.0435108	+	0.0251210i	0.00262380	+	0.00151485i
$276$	−9.42789	−	8.77159i	−0.567492	−	0.527988i
$277$	−5.47773			−0.329125			−0.164562	−	0.986367i	$-0.552621\pi$
$277$	−5.47773			−0.329125			−0.164562	+	0.986367i	$0.552621\pi$
$278$	1.48238	−	13.0769i	0.0889071	−	0.784299i
$279$	10.4747	−	18.1428i	0.627106	−	1.08618i
$280$	−7.17444	+	1.34239i	−0.428755	+	0.0802231i
$281$	−8.73176	−	5.04128i	−0.520893	−	0.300738i	0.216407	−	0.976303i	$-0.430566\pi$
$281$	−8.73176	−	5.04128i	−0.520893	−	0.300738i	−0.737300	+	0.675565i	$0.763900\pi$
$282$	−34.7525	+	15.1344i	−2.06948	+	0.901239i
$283$	−23.7158	+	13.6923i	−1.40976	+	0.813924i	−0.995365	−	0.0961733i	$-0.969340\pi$
$283$	−23.7158	+	13.6923i	−1.40976	+	0.813924i	−0.414394	+	0.910098i	$0.636006\pi$
$284$	15.1862	+	3.48778i	0.901133	+	0.206962i
$285$	−8.03913	+	10.6201i	−0.476197	+	0.629078i
$286$	−0.178834	−	0.0202723i	−0.0105747	−	0.00119873i
$287$	−13.7868	−	23.8794i	−0.813809	−	1.40956i
$288$	−1.46176	+	35.8208i	−0.0861349	+	2.11076i
$289$	−19.1419	+	33.1548i	−1.12600	+	1.95028i
$290$	1.22920	−	0.535306i	0.0721814	−	0.0314343i
$291$	32.0680	+	18.5145i	1.87986	+	1.08534i
$292$	20.0308	+	4.60045i	1.17222	+	0.269221i
$293$		−	2.52559i		−	0.147546i	−0.997275	−	0.0737732i	$-0.976496\pi$
$293$		−	2.52559i		−	0.147546i	0.997275	−	0.0737732i	$-0.0235041\pi$
$294$	0.875044	−	1.18396i	0.0510336	−	0.0690502i
$295$	−1.90456	+	3.29879i	−0.110888	+	0.192063i
$296$	7.99769	−	22.7080i	0.464856	−	1.31988i
$297$		−	0.512401i		−	0.0297325i
$298$	12.8264	−	17.3546i	0.743014	−	1.00532i
$299$	2.66864	+	4.62222i	0.154331	+	0.267310i
$300$	−4.16292	+	4.47440i	−0.240347	+	0.258330i
$301$	−10.6204	−	18.3951i	−0.612150	−	1.06028i
$302$	−1.12841	−	2.59112i	−0.0649326	−	0.149102i
$303$	−22.5220			−1.29385
$304$	−0.910777	+	17.4118i	−0.0522366	+	0.998635i
$305$	−0.331090			−0.0189581
$306$	26.6075	+	61.0978i	1.52105	+	3.49273i
$307$	−7.55893	−	13.0924i	−0.431411	−	0.747226i	0.565584	−	0.824691i	$-0.308651\pi$
$307$	−7.55893	−	13.0924i	−0.431411	−	0.747226i	−0.996995	+	0.0774650i	$0.975317\pi$
$308$	0.176630	−	0.189845i	0.0100644	−	0.0108174i
$309$	−17.5208	−	30.3470i	−0.996726	−	1.72638i
$310$	2.77856	−	3.75949i	0.157812	−	0.213525i
$311$		−	2.04039i		−	0.115700i	−0.998325	−	0.0578500i	$-0.981575\pi$
$311$		−	2.04039i		−	0.115700i	0.998325	−	0.0578500i	$-0.0184245\pi$
$312$	7.27269	−	20.6495i	0.411735	−	1.16905i
$313$	−3.19642	+	5.53637i	−0.180672	+	0.312934i	−0.942110	−	0.335305i	$-0.891161\pi$
$313$	−3.19642	+	5.53637i	−0.180672	+	0.312934i	0.761437	+	0.648239i	$0.224494\pi$
$314$	5.90936	−	7.99556i	0.333484	−	0.451216i
$315$			16.3545i			0.921469i
$316$	−12.0528	−	2.76814i	−0.678021	−	0.155720i
$317$	−15.5467	−	8.97591i	−0.873191	−	0.504137i	−0.00478400	−	0.999989i	$-0.501523\pi$
$317$	−15.5467	−	8.97591i	−0.873191	−	0.504137i	−0.868407	+	0.495851i	$0.834856\pi$
$318$	48.0853	−	20.9407i	2.69649	−	1.17429i
$319$	−0.0238153	+	0.0412493i	−0.00133340	+	0.00230952i
$320$	−1.22446	+	7.90574i	−0.0684495	+	0.441944i
$321$	−10.7249	−	18.5761i	−0.598608	−	1.03682i
$322$	−7.64077	−	0.866147i	−0.425803	−	0.0482685i
$323$	12.5985	+	29.8609i	0.700998	+	1.66150i
$324$	23.6870	+	5.44016i	1.31594	+	0.302231i
$325$	2.19367	−	1.26651i	0.121683	−	0.0702536i
$326$	−7.25335	+	3.15876i	−0.401726	+	0.174947i
$327$	0.406173	+	0.234504i	0.0224614	+	0.0129681i
$328$	−29.7065	+	5.55830i	−1.64027	+	0.306906i
$329$	−11.3175	+	19.6025i	−0.623953	+	1.08072i
$330$	0.0244557	−	0.215737i	0.00134624	−	0.0118760i
$331$	10.4333			0.573464			0.286732	−	0.958011i	$-0.407431\pi$
$331$	10.4333			0.573464			0.286732	+	0.958011i	$0.407431\pi$
$332$	5.49666	+	5.11402i	0.301668	+	0.280668i
$333$	−46.7173	−	26.9722i	−2.56009	−	1.47807i
$334$	17.0430	+	1.93197i	0.932549	+	0.105712i
$335$	−5.64905			−0.308641
$336$	17.6977	+	26.1094i	0.965488	+	1.42438i
$337$	−11.0485	+	6.37885i	−0.601850	+	0.347478i	−0.769769	−	0.638323i	$-0.779629\pi$
$337$	−11.0485	+	6.37885i	−0.601850	+	0.347478i	0.167919	+	0.985801i	$0.446295\pi$
$338$	5.53404	−	7.48774i	0.301012	−	0.407280i
$339$	2.55448	−	1.47483i	0.138740	−	0.0801017i
$340$	4.36395	+	14.2159i	0.236668	+	0.770965i
$341$			0.166080i			0.00899376i
$342$	37.9731	+	9.18120i	2.05335	+	0.496462i
$343$		−	18.9431i		−	1.02283i
$344$	−22.8839	+	4.28174i	−1.23381	+	0.230856i
$345$	−5.57605	+	3.21933i	−0.300205	+	0.173323i
$346$	9.72807	+	7.18982i	0.522985	+	0.386527i
$347$	23.5673	−	13.6066i	1.26516	−	0.730440i	0.291091	−	0.956695i	$-0.405982\pi$
$347$	23.5673	−	13.6066i	1.26516	−	0.730440i	0.974068	+	0.226256i	$0.0726485\pi$
$348$	−4.24184	−	3.94655i	−0.227386	−	0.211557i
$349$	10.9057			0.583770			0.291885	−	0.956453i	$-0.405717\pi$
$349$	10.9057			0.583770			0.291885	+	0.956453i	$0.405717\pi$
$350$	−0.411066	+	3.62625i	−0.0219724	+	0.193831i
$351$	−22.3725	−	12.9168i	−1.19416	−	0.689446i
$352$	−0.131952	−	0.251724i	−0.00703305	−	0.0134169i
$353$	3.43193			0.182663			0.0913315	−	0.995821i	$-0.470888\pi$
$353$	3.43193			0.182663			0.0913315	+	0.995821i	$0.470888\pi$
$354$	16.3562	+	1.85412i	0.869324	+	0.0985454i
$355$	3.89538	−	6.74700i	0.206745	−	0.358094i
$356$	18.0868	−	5.55223i	0.958599	−	0.294268i
$357$	50.7763	+	29.3157i	2.68737	+	1.55155i
$358$	−6.73187	−	15.4582i	−0.355791	−	0.816989i
$359$	15.2894	−	8.82735i	0.806945	−	0.465890i	−0.0389488	−	0.999241i	$-0.512401\pi$
$359$	15.2894	−	8.82735i	0.806945	−	0.465890i	0.845894	+	0.533351i	$0.179068\pi$
$360$	16.9073	+	5.95470i	0.891094	+	0.313840i
$361$	18.4154	+	4.67682i	0.969232	+	0.246148i
$362$	−2.88918	+	25.4871i	−0.151852	+	1.33957i
$363$	−16.8027	−	29.1032i	−0.881914	−	1.52752i
$364$	−3.83650	−	12.4977i	−0.201087	−	0.655057i
$365$	5.13808	−	8.89942i	0.268939	−	0.465817i
$366$	0.571275	+	1.31180i	0.0298610	+	0.0685688i
$367$	−28.6713	−	16.5534i	−1.49663	−	0.864079i	−0.496636	−	0.867959i	$-0.665432\pi$
$367$	−28.6713	−	16.5534i	−1.49663	−	0.864079i	−0.999992	+	0.00388005i	$0.998765\pi$
$368$	−3.67745	+	7.58370i	−0.191700	+	0.395328i
$369$			67.7173i			3.52522i
$370$	−9.68061	−	7.15474i	−0.503271	−	0.371957i
$371$	15.6594	−	27.1229i	0.812996	−	1.40815i
$372$	−19.6896	−	4.52207i	−1.02086	−	0.234459i
$373$			3.68872i			0.190994i	0.995430	+	0.0954972i	$0.0304441\pi$
$373$			3.68872i			0.190994i	−0.995430	+	0.0954972i	$0.969556\pi$
$374$	−0.424857	−	0.314003i	−0.0219688	−	0.0162367i
$375$	1.52787	+	2.64635i	0.0788989	+	0.136657i
$376$	16.1444	+	18.8374i	0.832584	+	0.971464i
$377$	1.20069	+	2.07965i	0.0618385	+	0.107107i
$378$	34.1243	−	14.8608i	1.75516	−	0.764356i
$379$	−5.62740			−0.289060			−0.144530	−	0.989500i	$-0.546167\pi$
$379$	−5.62740			−0.289060			−0.144530	+	0.989500i	$0.546167\pi$
$380$	8.18895	+	2.99018i	0.420084	+	0.153393i
$381$	−14.4947			−0.742584
$382$	12.7632	−	5.55824i	0.653022	−	0.284385i
$383$	0.608547	+	1.05403i	0.0310953	+	0.0538586i	0.881154	−	0.472829i	$-0.156767\pi$
$383$	0.608547	+	1.05403i	0.0310953	+	0.0538586i	−0.850059	+	0.526688i	$0.823434\pi$
$384$	33.4358	−	8.78947i	1.70626	−	0.448536i
$385$	−0.0648264	−	0.112283i	−0.00330386	−	0.00572245i
$386$	1.39733	+	1.03274i	0.0711222	+	0.0525650i
$387$			52.1648i			2.65169i
$388$	5.42494	−	23.6207i	0.275409	−	1.19916i
$389$	5.53895	−	9.59374i	0.280836	−	0.486422i	−0.690755	−	0.723089i	$-0.742722\pi$
$389$	5.53895	−	9.59374i	0.280836	−	0.486422i	0.971591	+	0.236667i	$0.0760550\pi$
$390$	−8.80305	−	6.50616i	−0.445760	−	0.329452i
$391$			15.6668i			0.792302i
$392$	−0.908865	−	0.320099i	−0.0459046	−	0.0161674i
$393$	56.3909	+	32.5573i	2.84454	+	1.64230i
$394$	−11.6436	−	26.7369i	−0.586598	−	1.34699i
$395$	−3.09164	+	5.35488i	−0.155557	+	0.269433i
$396$	−0.608783	+	0.186882i	−0.0305925	+	0.00939119i
$397$	−1.75835	−	3.04554i	−0.0882489	−	0.152852i	0.818522	−	0.574475i	$-0.194794\pi$
$397$	−1.75835	−	3.04554i	−0.0882489	−	0.152852i	−0.906771	+	0.421623i	$0.861460\pi$
$398$	−4.07398	+	35.9389i	−0.204210	+	1.80145i
$399$	31.6690	−	13.3613i	1.58543	−	0.668903i
$400$	3.59916	+	1.74529i	0.179958	+	0.0872644i
$401$	−1.93722	+	1.11846i	−0.0967403	+	0.0558530i	−0.547590	−	0.836747i	$-0.684454\pi$
$401$	−1.93722	+	1.11846i	−0.0967403	+	0.0558530i	0.450849	+	0.892600i	$0.351121\pi$
$402$	9.74710	+	22.3819i	0.486141	+	1.11631i
$403$	7.25141	+	4.18661i	0.361219	+	0.208550i
$404$	4.32584	+	14.0917i	0.215218	+	0.701090i
$405$	6.07592	−	10.5238i	0.301915	−	0.522932i
$406$	−3.43777	−	0.389701i	−0.170614	−	0.0193405i
$407$	0.427654			0.0211980
$408$	48.7945	−	41.8189i	2.41569	−	2.07034i
$409$	−3.92165	−	2.26417i	−0.193913	−	0.111956i	0.399900	−	0.916559i	$-0.369045\pi$
$409$	−3.92165	−	2.26417i	−0.193913	−	0.111956i	−0.593813	+	0.804603i	$0.702378\pi$
$410$	−1.70206	+	15.0148i	−0.0840588	+	0.741530i
$411$	−59.4712			−2.93350
$412$	−15.6225	+	16.7914i	−0.769665	+	0.827253i
$413$	8.51276	−	4.91484i	0.418885	−	0.241844i
$414$	15.1872	+	11.2245i	0.746410	+	0.551657i
$415$	3.25095	−	1.87694i	0.159583	−	0.0921353i
$416$	−14.3171	−	0.584244i	−0.701952	−	0.0286449i
$417$			28.4366i			1.39255i
$418$	−0.297099	+	0.0874850i	−0.0145316	+	0.00427903i
$419$			25.1864i			1.23044i	0.788357	+	0.615218i	$0.210932\pi$
$419$			25.1864i			1.23044i	−0.788357	+	0.615218i	$0.789068\pi$
$420$	15.0767	−	4.62820i	0.735667	−	0.225833i
$421$	−4.18408	+	2.41568i	−0.203919	+	0.117733i	−0.598482	−	0.801136i	$-0.704229\pi$
$421$	−4.18408	+	2.41568i	−0.203919	+	0.117733i	0.394563	+	0.918869i	$0.370896\pi$
$422$	6.19149	−	8.37730i	0.301397	−	0.407800i
$423$	48.1412	−	27.7943i	2.34070	−	1.35141i
$424$	−22.3382	−	26.0643i	−1.08484	−	1.26579i
$425$	7.43531			0.360666
$426$	−33.4533	−	3.79222i	−1.62082	−	0.183734i
$427$	0.739931	+	0.427200i	0.0358078	+	0.0206736i
$428$	−9.56293	+	10.2784i	−0.462241	+	0.496827i
$429$	0.388887			0.0187756
$430$	−1.31115	+	11.5664i	−0.0632294	+	0.557782i
$431$	13.7381	−	23.7951i	0.661742	−	1.14617i	−0.318416	−	0.947951i	$-0.603151\pi$
$431$	13.7381	−	23.7951i	0.661742	−	1.14617i	0.980158	−	0.198219i	$-0.0635158\pi$
$432$	−2.93842	−	40.6887i	−0.141375	−	1.95764i
$433$	−27.8134	−	16.0581i	−1.33663	−	0.771703i	−0.350322	−	0.936629i	$-0.613928\pi$
$433$	−27.8134	−	16.0581i	−1.33663	−	0.771703i	−0.986306	+	0.164927i	$0.947261\pi$
$434$	−11.0604	+	4.81671i	−0.530918	+	0.231209i
$435$	−2.50880	+	1.44846i	−0.120288	+	0.0694482i
$436$	0.0687121	−	0.299180i	0.00329071	−	0.0143281i
$437$	7.32302	+	5.54335i	0.350308	+	0.265175i
$438$	−44.1255	−	5.00201i	−2.10840	−	0.239005i
$439$	−1.55374	−	2.69116i	−0.0741560	−	0.128442i	0.826563	−	0.562844i	$-0.190293\pi$
$439$	−1.55374	−	2.69116i	−0.0741560	−	0.128442i	−0.900719	+	0.434402i	$0.856960\pi$
$440$	−0.139682	+	0.0261355i	−0.00665906	+	0.00124596i
$441$	−1.07954	+	1.86981i	−0.0514064	+	0.0890386i
$442$	−24.4199	+	10.6346i	−1.16154	+	0.505838i
$443$	23.1409	+	13.3604i	1.09946	+	0.634772i	0.936078	−	0.351791i	$-0.114427\pi$
$443$	23.1409	+	13.3604i	1.09946	+	0.634772i	0.163379	+	0.986563i	$0.447761\pi$
$444$	−11.6443	+	50.7003i	−0.552612	+	2.40613i
$445$		−	9.45991i		−	0.448443i
$446$	−11.8392	+	16.0188i	−0.560603	+	0.758514i
$447$	−23.3144	+	40.3816i	−1.10273	+	1.90999i
$448$	12.9371	−	16.0881i	0.611221	−	0.760092i
$449$		−	18.9486i		−	0.894240i	−0.894474	−	0.447120i	$-0.852450\pi$
$449$		−	18.9486i		−	0.894240i	0.894474	−	0.447120i	$-0.147550\pi$
$450$	5.32708	−	7.20772i	0.251121	−	0.339775i
$451$	−0.268420	−	0.464917i	−0.0126394	−	0.0218921i
$452$	−1.41343	−	1.31503i	−0.0664820	−	0.0618540i
$453$	3.05330	+	5.28847i	0.143457	+	0.248474i
$454$	−9.89870	−	22.7300i	−0.464569	−	1.06677i
$455$	−6.53665			−0.306443
$456$	−2.28224	−	37.6045i	−0.106876	−	1.76099i
$457$	−0.413466			−0.0193411			−0.00967056	−	0.999953i	$-0.503078\pi$
$457$	−0.413466			−0.0193411			−0.00967056	+	0.999953i	$0.503078\pi$
$458$	14.7960	+	33.9756i	0.691373	+	1.58758i
$459$	−37.9152	−	65.6710i	−1.76973	−	3.06526i
$460$	3.08531	+	2.87053i	0.143853	+	0.133839i
$461$	−8.25054	−	14.2904i	−0.384266	−	0.665568i	0.607401	−	0.794395i	$-0.292212\pi$
$461$	−8.25054	−	14.2904i	−0.384266	−	0.665568i	−0.991667	+	0.128827i	$0.958879\pi$
$462$	−0.333017	+	0.450583i	−0.0154933	+	0.0209630i
$463$			28.5162i			1.32526i	0.748946	+	0.662631i	$0.230560\pi$
$463$			28.5162i			1.32526i	−0.748946	+	0.662631i	$0.769440\pi$
$464$	−1.65457	+	3.41209i	−0.0768117	+	0.158402i
$465$	−5.05055	+	8.74780i	−0.234213	+	0.405670i
$466$	19.9245	−	26.9585i	0.922983	−	1.24883i
$467$		−	20.8226i		−	0.963553i	−0.876294	−	0.481776i	$-0.839992\pi$
$467$		−	20.8226i		−	0.963553i	0.876294	−	0.481776i	$-0.160008\pi$
$468$	−7.18672	+	31.2917i	−0.332206	+	1.44646i
$469$	12.6247	+	7.28888i	0.582955	+	0.336569i
$470$	11.3729	−	4.95277i	0.524591	−	0.228454i
$471$	−10.7413	+	18.6046i	−0.494935	+	0.857252i
$472$	−1.98147	−	10.5900i	−0.0912047	−	0.487446i
$473$	−0.206773	−	0.358141i	−0.00950741	−	0.0164673i
$474$	26.5508	+	3.00976i	1.21952	+	0.138243i
$475$	2.63083	−	3.47545i	0.120711	−	0.159464i
$476$	8.58981	−	37.4009i	0.393713	−	1.71427i
$477$	−66.6105	+	38.4576i	−3.04988	+	1.76085i
$478$	−5.37053	+	2.33881i	−0.245642	+	0.106975i
$479$	33.9439	+	19.5975i	1.55094	+	0.895434i	0.998066	+	0.0621675i	$0.0198013\pi$
$479$	33.9439	+	19.5975i	1.55094	+	0.895434i	0.552872	+	0.833267i	$0.313532\pi$
$480$	0.704808	−	17.2715i	0.0321699	−	0.788333i
$481$	10.7804	−	18.6723i	0.491545	−	0.851381i
$482$	1.22741	−	10.8277i	0.0559070	−	0.493187i
$483$	16.6154			0.756027
$484$	−14.9822	+	16.1032i	−0.681008	+	0.731962i
$485$	−10.4944	−	6.05892i	−0.476524	−	0.275121i
$486$	−9.18570	−	1.04128i	−0.416672	−	0.0472333i
$487$	28.5749			1.29485			0.647426	−	0.762128i	$-0.275846\pi$
$487$	28.5749			1.29485			0.647426	+	0.762128i	$0.275846\pi$
$488$	0.711052	−	0.609400i	0.0321878	−	0.0275863i
$489$	14.8040	−	8.54712i	0.669462	−	0.386514i
$490$	−0.286361	+	0.387456i	−0.0129365	+	0.0175035i
$491$	−11.1686	+	6.44818i	−0.504030	+	0.291002i	−0.730376	−	0.683045i	$-0.760655\pi$
$491$	−11.1686	+	6.44818i	−0.504030	+	0.291002i	0.226346	+	0.974047i	$0.427322\pi$
$492$	62.4266	−	19.1635i	2.81441	−	0.863958i
$493$			7.04885i			0.317464i
$494$	−3.66960	+	15.1773i	−0.165103	+	0.682860i
$495$			0.318411i			0.0143115i
$496$	0.952405	+	13.1881i	0.0427642	+	0.592163i
$497$	−17.4111	+	10.0523i	−0.780994	+	0.450907i
$498$	−13.0459	−	9.64195i	−0.584600	−	0.432066i
$499$	−1.54787	+	0.893660i	−0.0692920	+	0.0400057i	−0.534246	−	0.845329i	$-0.679404\pi$
$499$	−1.54787	+	0.893660i	−0.0692920	+	0.0400057i	0.464954	+	0.885335i	$0.346071\pi$
$500$	1.36233	−	1.46426i	0.0609252	−	0.0654837i
$501$	−37.0612			−1.65577
$502$	−3.15312	+	27.8155i	−0.140731	+	1.24147i
$503$	10.0449	+	5.79940i	0.447878	+	0.258582i	0.706934	−	0.707280i	$-0.250078\pi$
$503$	10.0449	+	5.79940i	0.447878	+	0.258582i	−0.259056	+	0.965862i	$0.583411\pi$
$504$	−30.1018	−	35.1230i	−1.34084	−	1.56450i
$505$	7.37038			0.327978
$506$	−0.148761	−	0.0168633i	−0.00661323	−	0.000749666i
$507$	−10.0591	+	17.4229i	−0.446742	+	0.773780i
$508$	2.78402	+	9.06915i	0.123521	+	0.402378i
$509$	−2.21815	−	1.28065i	−0.0983179	−	0.0567639i	0.450035	−	0.893011i	$-0.351412\pi$
$509$	−2.21815	−	1.28065i	−0.0983179	−	0.0567639i	−0.548353	+	0.836247i	$0.684745\pi$
$510$	−12.8292	−	29.4592i	−0.568086	−	1.30447i
$511$	−22.9655	+	13.2592i	−1.01594	+	0.586551i
$512$	−11.9216	−	19.2322i	−0.526863	−	0.849950i
$513$	−44.1117	−	5.51384i	−1.94758	−	0.243442i
$514$	−0.309884	+	2.73366i	−0.0136684	+	0.120576i
$515$	5.73375	+	9.93114i	0.252659	+	0.437618i
$516$	48.0892	−	14.7623i	2.11701	−	0.649873i
$517$	−0.220344	+	0.381647i	−0.00969073	+	0.0167848i
$518$	12.4029	+	28.4804i	0.544953	+	1.25136i
$519$	−22.6359	−	13.0688i	−0.993604	−	0.573658i
$520$	−2.38001	+	6.75762i	−0.104370	+	0.296341i
$521$			11.4544i			0.501824i	0.968010	+	0.250912i	$0.0807305\pi$
$521$			11.4544i			0.501824i	−0.968010	+	0.250912i	$0.919269\pi$
$522$	6.83309	+	5.05020i	0.299076	+	0.221041i
$523$	6.56255	−	11.3667i	0.286960	−	0.497030i	−0.686122	−	0.727486i	$-0.740689\pi$
$523$	6.56255	−	11.3667i	0.286960	−	0.497030i	0.973083	+	0.230456i	$0.0740219\pi$
$524$	9.53962	−	41.5365i	0.416740	−	1.81453i
$525$		−	7.88554i		−	0.344153i
$526$	−28.7991	−	21.2849i	−1.25570	−	0.928064i
$527$	12.2891	+	21.2854i	0.535323	+	0.927207i
$528$	0.344563	+	0.508333i	0.0149952	+	0.0221223i
$529$	−9.28012	−	16.0736i	−0.403483	−	0.698854i
$530$	−15.7361	+	6.85289i	−0.683530	+	0.297671i
$531$	−24.1405			−1.04761
$532$	−14.4428	−	17.2486i	−0.626173	−	0.747822i
$533$	−27.0657			−1.17234
$534$	−37.4808	+	16.3225i	−1.62195	+	0.706344i
$535$	3.50977	+	6.07910i	0.151741	+	0.262822i
$536$	12.1320	−	10.3976i	0.524021	−	0.449107i
$537$	18.2154	+	31.5500i	0.786053	+	1.36148i
$538$	−5.12971	−	3.79126i	−0.221157	−	0.163453i
$539$		−	0.0171164i		−	0.000737255i
$540$	−19.8798	−	4.56576i	−0.855489	−	0.196479i
$541$	10.5486	−	18.2706i	0.453518	−	0.785516i	−0.545084	−	0.838382i	$-0.683502\pi$
$541$	10.5486	−	18.2706i	0.453518	−	0.785516i	0.998602	+	0.0528654i	$0.0168354\pi$
$542$	19.7247	+	14.5781i	0.847247	+	0.626183i
$543$		−	55.4235i		−	2.37845i
$544$	−35.5377	−	22.4980i	−1.52367	−	0.964592i
$545$	−0.132921	−	0.0767422i	−0.00569373	−	0.00328727i
$546$	11.2786	+	25.8986i	0.482679	+	1.10836i
$547$	0.958629	−	1.66039i	0.0409880	−	0.0709933i	−0.844804	−	0.535076i	$-0.820283\pi$
$547$	0.958629	−	1.66039i	0.0409880	−	0.0709933i	0.885792	+	0.464083i	$0.153616\pi$
$548$	11.4227	+	37.2104i	0.487956	+	1.58955i
$549$	−1.04915	−	1.81718i	−0.0447766	−	0.0775553i
$550$	−0.00800320	+	0.0706007i	−0.000341257	+	0.00301042i
$551$	3.29481	+	2.49409i	0.140363	+	0.106252i
$552$	6.04971	−	17.1771i	0.257493	−	0.731106i
$553$	13.8186	−	7.97818i	0.587628	−	0.339267i
$554$	−3.09303	−	7.10241i	−0.131410	−	0.301752i
$555$	22.5254	+	13.0051i	0.956151	+	0.552034i
$556$	17.7925	−	5.46188i	0.754570	−	0.231635i
$557$	19.9889	−	34.6217i	0.846956	−	1.46697i	−0.0369559	−	0.999317i	$-0.511766\pi$
$557$	19.9889	−	34.6217i	0.846956	−	1.46697i	0.883912	−	0.467654i	$-0.154901\pi$
$558$	29.4385	+	3.33710i	1.24623	+	0.141271i
$559$	−20.8495			−0.881842
$560$	−5.79162	−	8.54437i	−0.244741	−	0.361066i
$561$	0.988583	+	0.570758i	0.0417380	+	0.0240974i
$562$	1.60608	−	14.1682i	0.0677485	−	0.597648i
$563$	−12.5082			−0.527159			−0.263580	−	0.964638i	$-0.584903\pi$
$563$	−12.5082			−0.527159			−0.263580	+	0.964638i	$0.584903\pi$
$564$	−39.2464	−	36.5143i	−1.65257	−	1.53753i
$565$	−0.835960	+	0.482642i	−0.0351691	+	0.0203049i
$566$	−31.1447	−	23.0184i	−1.30911	−	0.967536i
$567$	−27.1574	+	15.6793i	−1.14050	+	0.658470i
$568$	4.05269	+	21.6597i	0.170047	+	0.908822i
$569$			7.02031i			0.294307i	0.989114	+	0.147153i	$0.0470111\pi$
$569$			7.02031i			0.294307i	−0.989114	+	0.147153i	$0.952989\pi$
$570$	−18.3093	−	4.42685i	−0.766891	−	0.185420i
$571$		−	20.7964i		−	0.870304i	−0.900357	−	0.435152i	$-0.856695\pi$
$571$		−	20.7964i		−	0.870304i	0.900357	−	0.435152i	$-0.143305\pi$
$572$	−0.0746943	−	0.243322i	−0.00312312	−	0.0101738i
$573$	−26.0496	+	15.0398i	−1.08824	+	0.628295i
$574$	23.1772	−	31.3596i	0.967399	−	1.30892i
$575$	1.82478	−	1.05354i	0.0760986	−	0.0439355i
$576$	−47.2705	+	18.3311i	−1.96960	+	0.763794i
$577$	23.4579			0.976566			0.488283	−	0.872685i	$-0.337623\pi$
$577$	23.4579			0.976566			0.488283	+	0.872685i	$0.337623\pi$
$578$	−53.7971	−	6.09836i	−2.23766	−	0.253658i
$579$	−3.25139	−	1.87719i	−0.135123	−	0.0780134i
$580$	1.38815	+	1.29152i	0.0576399	+	0.0536275i
$581$	−9.68713			−0.401890
$582$	−5.89846	+	52.0336i	−0.244499	+	2.15686i
$583$	0.304879	−	0.528066i	0.0126268	−	0.0218702i
$584$	5.34558	+	28.5696i	0.221202	+	1.18222i
$585$	13.9025	+	8.02659i	0.574796	+	0.331859i
$586$	3.27467	−	1.42609i	0.135275	−	0.0589111i
$587$	0.500147	−	0.288760i	0.0206433	−	0.0119184i	−0.489643	−	0.871923i	$-0.662873\pi$
$587$	0.500147	−	0.288760i	0.0206433	−	0.0119184i	0.510286	+	0.860005i	$0.329539\pi$
$588$	2.02922	+	0.466049i	0.0836838	+	0.0192195i
$589$	14.2976	+	1.78716i	0.589121	+	0.0736385i
$590$	−5.35263	−	0.606766i	−0.220364	−	0.0249802i
$591$	31.5059	+	54.5698i	1.29598	+	2.24470i
$592$	33.9591	−	2.45242i	1.39571	−	0.100794i
$593$	15.1226	−	26.1931i	0.621010	−	1.07562i	−0.368288	−	0.929712i	$-0.620056\pi$
$593$	15.1226	−	26.1931i	0.621010	−	1.07562i	0.989298	−	0.145909i	$-0.0466106\pi$
$594$	0.664378	−	0.289330i	0.0272598	−	0.0118714i
$595$	−16.6167	−	9.59366i	−0.681218	−	0.393302i
$596$	29.7444	+	6.83135i	1.21838	+	0.279823i
$597$		−	78.1517i		−	3.19854i
$598$	−4.48630	+	6.07011i	−0.183458	+	0.248225i
$599$	−10.2018	+	17.6700i	−0.416834	+	0.721978i	−0.995619	−	0.0935020i	$-0.970194\pi$
$599$	−10.2018	+	17.6700i	−0.416834	+	0.721978i	0.578785	+	0.815480i	$0.303527\pi$
$600$	−8.15211	−	2.87114i	−0.332808	−	0.117214i
$601$			37.4638i			1.52818i	0.645108	+	0.764091i	$0.276812\pi$
$601$			37.4638i			1.52818i	−0.645108	+	0.764091i	$0.723188\pi$
$602$	17.8542	−	24.1573i	0.727681	−	0.984577i
$603$	−17.9006	−	31.0047i	−0.728967	−	1.26261i
$604$	2.72248	−	2.92618i	0.110776	−	0.119065i
$605$	5.49874	+	9.52409i	0.223555	+	0.387209i
$606$	−12.7171	−	29.2019i	−0.516598	−	1.18625i
$607$	−9.75950			−0.396126			−0.198063	−	0.980189i	$-0.563465\pi$
$607$	−9.75950			−0.396126			−0.198063	+	0.980189i	$0.563465\pi$
$608$	−23.0904	+	8.65074i	−0.936438	+	0.350834i
$609$	7.47568			0.302930
$610$	−0.186952	−	0.429290i	−0.00756945	−	0.0173815i
$611$	11.1090	+	19.2414i	0.449422	+	0.778422i
$612$	−64.1952	+	68.9984i	−2.59494	+	2.78909i
$613$	9.69547	+	16.7930i	0.391596	+	0.678265i	0.992660	−	0.120936i	$-0.0385896\pi$
$613$	9.69547	+	16.7930i	0.391596	+	0.678265i	−0.601064	+	0.799201i	$0.705256\pi$
$614$	12.7074	−	17.1936i	0.512831	−	0.693877i
$615$		−	32.6509i		−	1.31661i
$616$	0.345888	+	0.121820i	0.0139362	+	0.00490829i
$617$	11.1147	−	19.2513i	0.447463	−	0.775028i	−0.550757	−	0.834665i	$-0.685661\pi$
$617$	11.1147	−	19.2513i	0.447463	−	0.775028i	0.998220	+	0.0596372i	$0.0189944\pi$
$618$	29.4546	−	39.8530i	1.18484	−	1.60312i
$619$		−	32.4034i		−	1.30240i	−0.758905	−	0.651202i	$-0.774265\pi$
$619$		−	32.4034i		−	1.30240i	0.758905	−	0.651202i	$-0.225735\pi$
$620$	6.44347	+	1.47986i	0.258776	+	0.0594327i
$621$	−18.6103	−	10.7447i	−0.746807	−	0.431169i
$622$	2.64557	−	1.15212i	0.106077	−	0.0461957i
$623$	−12.2060	+	21.1414i	−0.489022	+	0.847010i
$624$	30.8807	−	2.23011i	1.23622	−	0.0892758i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.98331	−	1.01834i	−0.359045	−	0.0407009i
$627$	0.616576	−	0.260137i	0.0246237	−	0.0103889i
$628$	13.7038	+	3.14732i	0.546840	+	0.125592i
$629$	54.8095	−	31.6443i	2.18540	−	1.26174i
$630$	−21.2051	+	9.23463i	−0.844833	+	0.367916i
$631$	21.2410	+	12.2635i	0.845593	+	0.488203i	0.859161	−	0.511705i	$-0.170986\pi$
$631$	21.2410	+	12.2635i	0.845593	+	0.488203i	−0.0135686	+	0.999908i	$0.504319\pi$
$632$	−3.21649	−	17.1906i	−0.127945	−	0.683807i
$633$	−11.2542	+	19.4928i	−0.447313	+	0.774769i
$634$	2.85960	−	25.2261i	0.113569	−	1.00186i
$635$	4.74342			0.188237
$636$	54.3032	+	50.5230i	2.15326	+	2.00337i
$637$	−0.747337	−	0.431475i	−0.0296106	−	0.0170957i
$638$	−0.0669311	−	0.00758722i	−0.00264983	−	0.000300381i
$639$	49.3743			1.95322
$640$	−10.9420	+	2.87638i	−0.432519	+	0.113699i
$641$	2.82394	−	1.63040i	0.111539	−	0.0643971i	−0.443193	−	0.896426i	$-0.646154\pi$
$641$	2.82394	−	1.63040i	0.111539	−	0.0643971i	0.554732	+	0.832029i	$0.312821\pi$
$642$	18.0299	−	24.3950i	0.711583	−	0.962796i
$643$	−5.33210	+	3.07849i	−0.210277	+	0.121404i	−0.601440	−	0.798918i	$-0.705406\pi$
$643$	−5.33210	+	3.07849i	−0.210277	+	0.121404i	0.391163	+	0.920321i	$0.372073\pi$
$644$	−3.19136	−	10.3961i	−0.125757	−	0.409663i
$645$		−	25.1520i		−	0.990359i
$646$	−31.6038	+	33.1962i	−1.24343	+	1.30609i
$647$			11.0103i			0.432861i	0.976298	+	0.216431i	$0.0694415\pi$
$647$			11.0103i			0.432861i	−0.976298	+	0.216431i	$0.930559\pi$
$648$	6.32129	+	33.7843i	0.248324	+	1.32717i
$649$	0.165738	−	0.0956889i	0.00650578	−	0.00375612i
$650$	2.88082	+	2.12916i	0.112995	+	0.0835125i
$651$	22.5743	−	13.0333i	0.884756	−	0.510814i
$652$	−8.19128	−	7.62106i	−0.320795	−	0.298464i
$653$	5.25014			0.205454			0.102727	−	0.994710i	$-0.467243\pi$
$653$	5.25014			0.205454			0.102727	+	0.994710i	$0.467243\pi$
$654$	−0.0747098	+	0.659057i	−0.00292138	+	0.0257712i
$655$	−18.4541	−	10.6545i	−0.721061	−	0.416305i
$656$	−23.9808	−	35.3788i	−0.936293	−	1.38131i
$657$	65.1257			2.54079
$658$	−31.8070	−	3.60559i	−1.23997	−	0.140561i
$659$	12.7141	−	22.0214i	0.495271	−	0.857834i	−0.504715	−	0.863286i	$-0.668402\pi$
$659$	12.7141	−	22.0214i	0.495271	−	0.857834i	0.999985	+	0.00545256i	$0.00173561\pi$
$660$	0.293534	−	0.0901080i	0.0114258	−	0.00350745i
$661$	38.7398	+	22.3664i	1.50680	+	0.869953i	0.999969	+	0.00790992i	$0.00251783\pi$
$661$	38.7398	+	22.3664i	1.50680	+	0.869953i	0.506835	+	0.862043i	$0.330816\pi$
$662$	5.89119	+	13.5277i	0.228968	+	0.525770i
$663$	49.8410	−	28.7757i	1.93566	−	1.11756i
$664$	−3.52711	+	10.0146i	−0.136878	+	0.388642i
$665$	−10.3638	+	4.37254i	−0.401890	+	0.169560i
$666$	8.59298	−	75.8035i	0.332971	−	2.93733i
$667$	0.998778	+	1.72993i	0.0386728	+	0.0669833i
$668$	7.11841	+	23.1887i	0.275420	+	0.897200i
$669$	21.5199	−	37.2736i	0.832009	−	1.44108i
$670$	−3.18977	−	7.32455i	−0.123231	−	0.282972i
$671$	0.0144060	+	0.00831730i	0.000556137	+	0.000321086i
$672$	−23.8603	+	37.6896i	−0.920429	+	1.45391i
$673$			19.7141i			0.759922i	0.925002	+	0.379961i	$0.124063\pi$
$673$			19.7141i			0.759922i	−0.925002	+	0.379961i	$0.875937\pi$
$674$	−14.5094	−	10.7236i	−0.558881	−	0.413058i
$675$	−5.09934	+	8.83231i	−0.196274	+	0.339956i
$676$	12.8334	+	2.94743i	0.493593	+	0.113363i
$677$			49.3518i			1.89674i	0.317163	+	0.948371i	$0.397270\pi$
$677$			49.3518i			1.89674i	−0.317163	+	0.948371i	$0.602730\pi$
$678$	3.35466	+	2.47936i	0.128835	+	0.0952192i
$679$	15.6354	+	27.0814i	0.600033	+	1.03929i
$680$	−15.9682	+	13.6854i	−0.612351	+	0.524810i
$681$	26.7844	+	46.3919i	1.02638	+	1.77774i
$682$	−0.215339	+	0.0937782i	−0.00824578	+	0.00359095i
$683$	27.5765			1.05518			0.527592	−	0.849498i	$-0.323095\pi$
$683$	27.5765			1.05518			0.527592	+	0.849498i	$0.323095\pi$
$684$	9.53738	+	54.4200i	0.364671	+	2.08080i
$685$	19.4621			0.743609
$686$	24.5616	−	10.6963i	0.937766	−	0.408387i
$687$	−40.0358	−	69.3440i	−1.52746	−	2.64564i
$688$	−18.4732	−	27.2534i	−0.704283	−	1.03903i
$689$	−15.3710	−	26.6233i	−0.585587	−	1.01427i
$690$	−7.32273	−	5.41208i	−0.278771	−	0.206034i
$691$		−	2.98647i		−	0.113611i	−0.998385	−	0.0568054i	$-0.981909\pi$
$691$		−	2.98647i		−	0.113611i	0.998385	−	0.0568054i	$-0.0180915\pi$
$692$	−3.82930	+	16.6732i	−0.145568	+	0.633819i
$693$	0.410840	−	0.711596i	0.0156065	−	0.0270313i
$694$	30.9497	+	22.8743i	1.17483	+	0.868295i
$695$		−	9.30598i		−	0.352996i
$696$	2.72191	−	7.72839i	0.103174	−	0.292944i
$697$	−68.8032	−	39.7235i	−2.60611	−	1.50464i
$698$	6.15798	+	14.1403i	0.233083	+	0.535220i
$699$	−36.2164	+	62.7286i	−1.36983	+	2.37261i
$700$	−4.93389	+	1.51459i	−0.186484	+	0.0572462i
$701$	6.46897	+	11.2046i	0.244330	+	0.423191i	0.961943	−	0.273250i	$-0.0880988\pi$
$701$	6.46897	+	11.2046i	0.244330	+	0.423191i	−0.717613	+	0.696442i	$0.754765\pi$
$702$	4.11510	−	36.3016i	0.155315	−	1.37012i
$703$	4.60189	−	36.8160i	0.173564	−	1.38854i
$704$	0.251877	−	0.313225i	0.00949298	−	0.0118051i
$705$	−23.2120	+	13.4014i	−0.874213	+	0.504727i
$706$	1.93785	+	4.44983i	0.0729321	+	0.167471i
$707$	−16.4716	−	9.50987i	−0.619478	−	0.357656i
$708$	6.83159	+	22.2544i	0.256747	+	0.836371i
$709$	−13.5042	+	23.3899i	−0.507160	+	0.878426i	0.492806	+	0.870139i	$0.335971\pi$
$709$	−13.5042	+	23.3899i	−0.507160	+	0.878426i	−0.999966	+	0.00828708i	$0.997362\pi$
$710$	10.9477	+	1.24101i	0.410860	+	0.0465745i
$711$	−39.1868			−1.46962
$712$	17.4118	+	20.3162i	0.652535	+	0.761382i
$713$	6.03201	+	3.48258i	0.225901	+	0.130424i
$714$	−9.33958	+	82.3897i	−0.349525	+	3.08336i
$715$	−0.127264			−0.00475942
$716$	16.2418	−	17.4571i	0.606986	−	0.652401i
$717$	10.9612	−	6.32846i	0.409354	−	0.236341i
$718$	20.0788	+	14.8398i	0.749333	+	0.553817i
$719$	34.2942	−	19.7998i	1.27896	−	0.738406i	0.302301	−	0.953213i	$-0.402245\pi$
$719$	34.2942	−	19.7998i	1.27896	−	0.738406i	0.976657	+	0.214806i	$0.0689120\pi$
$720$	1.82596	+	25.2843i	0.0680494	+	0.942292i
$721$		−	29.5926i		−	1.10209i
$722$	4.33440	+	26.5182i	0.161310	+	0.986904i
$723$			23.5456i			0.875669i
$724$	−34.6779	+	10.6453i	−1.28879	+	0.395630i
$725$	0.821013	−	0.474012i	0.0304916	−	0.0176044i
$726$	28.2473	−	38.2196i	1.04836	−	1.41846i
$727$	−19.2742	+	11.1280i	−0.714840	+	0.412713i	−0.812851	−	0.582472i	$-0.802085\pi$
$727$	−19.2742	+	11.1280i	−0.714840	+	0.412713i	0.0980105	+	0.995185i	$0.468752\pi$
$728$	14.0382	−	12.0313i	0.520289	−	0.445909i
$729$	−16.4806			−0.610391
$730$	14.4402	+	1.63692i	0.534456	+	0.0605852i
$731$	−53.0013	−	30.6003i	−1.96032	−	1.13179i
$732$	−1.37830	+	1.48143i	−0.0509435	+	0.0547552i
$733$	−26.6721			−0.985158			−0.492579	−	0.870268i	$-0.663946\pi$
$733$	−26.6721			−0.985158			−0.492579	+	0.870268i	$0.663946\pi$
$734$	5.27367	−	46.5220i	0.194655	−	1.71716i
$735$	0.520514	−	0.901556i	0.0191994	−	0.0332544i
$736$	−11.9095	−	0.485998i	−0.438990	−	0.0179141i
$737$	0.245795	+	0.141910i	0.00905397	+	0.00522731i
$738$	−87.8021	+	38.2369i	−3.23204	+	1.40752i
$739$	−6.20163	+	3.58051i	−0.228131	+	0.131711i	−0.609709	−	0.792625i	$-0.708714\pi$
$739$	−6.20163	+	3.58051i	−0.228131	+	0.131711i	0.381579	+	0.924336i	$0.375381\pi$
$740$	3.81062	−	16.5918i	0.140081	−	0.609927i
$741$	4.18473	−	33.4786i	0.153730	−	1.22987i
$742$	44.0097	+	4.98887i	1.61565	+	0.183147i
$743$	0.492717	+	0.853411i	0.0180760	+	0.0313086i	0.874922	−	0.484264i	$-0.160913\pi$
$743$	0.492717	+	0.853411i	0.0180760	+	0.0313086i	−0.856846	+	0.515573i	$0.827579\pi$
$744$	−5.25451	−	28.0828i	−0.192640	−	1.02957i
$745$	7.62969	−	13.2150i	0.279530	−	0.484161i
$746$	−4.78278	+	2.08285i	−0.175110	+	0.0762586i
$747$	20.6031	+	11.8952i	0.753827	+	0.435222i
$748$	0.167238	−	0.728172i	0.00611483	−	0.0266246i
$749$		−	18.1144i		−	0.661885i
$750$	−2.56853	+	3.47531i	−0.0937894	+	0.126900i
$751$	−10.3899	+	17.9958i	−0.379132	+	0.656676i	−0.990936	−	0.134333i	$-0.957111\pi$
$751$	−10.3899	+	17.9958i	−0.379132	+	0.656676i	0.611804	+	0.791009i	$0.290444\pi$
$752$	−15.3085	+	31.5694i	−0.558243	+	1.15122i
$753$		−	60.4868i		−	2.20426i
$754$	−2.01849	+	2.73109i	−0.0735092	+	0.0994604i
$755$	−0.999201	−	1.73067i	−0.0363647	−	0.0629854i
$756$	38.5369	+	35.8543i	1.40157	+	1.30401i
$757$	24.5380	+	42.5011i	0.891849	+	1.54473i	0.837657	+	0.546197i	$0.183925\pi$
$757$	24.5380	+	42.5011i	0.891849	+	1.54473i	0.0541924	+	0.998531i	$0.482742\pi$
$758$	−3.17754	−	7.29647i	−0.115413	−	0.265020i
$759$	0.323491			0.0117420
$760$	0.746871	+	12.3062i	0.0270918	+	0.446392i
$761$	−26.2427			−0.951296			−0.475648	−	0.879636i	$-0.657786\pi$
$761$	−26.2427			−0.951296			−0.475648	+	0.879636i	$0.657786\pi$
$762$	−8.18448	−	18.7937i	−0.296493	−	0.680825i
$763$	0.198038	+	0.343012i	0.00716947	+	0.0124179i
$764$	14.4136	+	13.4102i	0.521466	+	0.485165i
$765$	23.5608	+	40.8085i	0.851843	+	1.47544i
$766$	−1.02304	+	1.38421i	−0.0369639	+	0.0500134i
$767$		−	9.64861i		−	0.348391i
$768$	30.2761	+	38.3897i	1.09249	+	1.38527i
$769$	−11.0566	+	19.1505i	−0.398710	+	0.690586i	−0.993567	−	0.113245i	$-0.963875\pi$
$769$	−11.0566	+	19.1505i	−0.398710	+	0.690586i	0.594857	+	0.803832i	$0.297209\pi$
$770$	0.108981	−	0.147455i	0.00392739	−	0.00531389i
$771$		−	5.94454i		−	0.214087i
$772$	−0.550036	+	2.39491i	−0.0197962	+	0.0861948i
$773$	18.5394	+	10.7037i	0.666816	+	0.384987i	0.794869	−	0.606781i	$-0.207539\pi$
$773$	18.5394	+	10.7037i	0.666816	+	0.384987i	−0.128053	+	0.991767i	$0.540873\pi$
$774$	−67.6367	+	29.4551i	−2.43115	+	1.05874i
$775$	1.65281	−	2.86274i	0.0593705	−	0.102833i
$776$	33.6898	−	6.30361i	1.20939	−	0.226286i
$777$	−33.5604	−	58.1283i	−1.20397	−	2.08534i
$778$	15.5668	+	1.76463i	0.558097	+	0.0632651i
$779$	−42.9123	+	18.1049i	−1.53749	+	0.648677i
$780$	3.46518	−	15.0877i	0.124073	−	0.540228i
$781$	−0.338983	+	0.195712i	−0.0121298	+	0.00700312i
$782$	−20.3135	+	8.84631i	−0.726408	+	0.316344i
$783$	−8.37324	−	4.83429i	−0.299235	−	0.172763i
$784$	−0.0981557	−	1.35918i	−0.00350556	−	0.0485421i
$785$	3.51514	−	6.08840i	0.125461	−	0.217304i
$786$	−10.3723	+	91.4999i	−0.369968	+	3.26369i
$787$	4.08708			0.145689			0.0728444	−	0.997343i	$-0.476792\pi$
$787$	4.08708			0.145689			0.0728444	+	0.997343i	$0.476792\pi$
$788$	28.0923	−	30.1942i	1.00075	−	1.07563i
$789$	67.0116	+	38.6891i	2.38567	+	1.37737i
$790$	−8.68883	−	0.984954i	−0.309135	−	0.0350431i
$791$	2.49098			0.0885690
$792$	−0.586064	−	0.683822i	−0.0208249	−	0.0242986i
$793$	0.726301	−	0.419330i	0.0257917	−	0.0148908i
$794$	2.95599	−	3.99955i	0.104904	−	0.141939i
$795$	32.1172	−	18.5429i	1.13908	−	0.657648i
$796$	−48.8986	+	15.0108i	−1.73317	+	0.532042i
$797$		−	15.0515i		−	0.533153i	−0.963814	−	0.266576i	$-0.914108\pi$
$797$		−	15.0515i		−	0.533153i	0.963814	−	0.266576i	$-0.0858925\pi$
$798$	35.2063	+	33.5174i	1.24629	+	1.18650i
$799$			65.2175i			2.30723i
$800$	−0.230650	+	5.65215i	−0.00815473	+	0.199834i
$801$	51.9205	−	29.9763i	1.83452	−	1.05916i
$802$	−2.54405	−	1.88026i	−0.0898335	−	0.0663942i
$803$	−0.447124	+	0.258147i	−0.0157787	+	0.00910982i
$804$	−23.5166	+	25.2761i	−0.829366	+	0.891420i
$805$	−5.43744			−0.191645
$806$	−1.33379	+	11.7662i	−0.0469809	+	0.414445i
$807$	11.9361	+	6.89132i	0.420171	+	0.242586i
$808$	−15.8287	+	13.5658i	−0.556852	+	0.477245i
$809$	10.1525			0.356942			0.178471	−	0.983945i	$-0.442885\pi$
$809$	10.1525			0.356942			0.178471	+	0.983945i	$0.442885\pi$
$810$	17.0759	+	1.93570i	0.599987	+	0.0680137i
$811$	−15.4802	+	26.8126i	−0.543585	+	0.941517i	0.455110	+	0.890435i	$0.349600\pi$
$811$	−15.4802	+	26.8126i	−0.543585	+	0.941517i	−0.998694	+	0.0510813i	$0.983733\pi$
$812$	−1.43587	−	4.67745i	−0.0503891	−	0.164146i
$813$	−45.8966	−	26.4984i	−1.60966	−	0.929339i
$814$	0.241477	+	0.554495i	0.00846377	+	0.0194350i
$815$	−4.84467	+	2.79707i	−0.169701	+	0.0979771i
$816$	81.7744	+	39.6536i	2.86267	+	1.38815i
$817$	−33.0567	+	13.9468i	−1.15651	+	0.487937i
$818$	0.721332	−	6.36328i	0.0252208	−	0.222487i
$819$	−20.7132	−	35.8762i	−0.723776	−	1.25362i
$820$	−20.4293	+	6.27132i	−0.713422	+	0.219004i
$821$	−0.831540	+	1.44027i	−0.0290209	+	0.0502657i	−0.880171	−	0.474657i	$-0.842572\pi$
$821$	−0.831540	+	1.44027i	−0.0290209	+	0.0502657i	0.851150	+	0.524922i	$0.175906\pi$
$822$	−33.5807	−	77.1102i	−1.17126	−	2.68953i
$823$	−42.5216	−	24.5498i	−1.48221	−	0.855753i	−0.482412	−	0.875944i	$-0.660239\pi$
$823$	−42.5216	−	24.5498i	−1.48221	−	0.855753i	−0.999796	+	0.0201909i	$0.993573\pi$
$824$	−30.5930	−	10.7747i	−1.06576	−	0.375356i
$825$		−	0.153526i		−	0.00534510i
$826$	11.1793	+	8.26243i	0.388979	+	0.287487i
$827$	28.0653	−	48.6105i	0.975925	−	1.69035i	0.299078	−	0.954229i	$-0.403321\pi$
$827$	28.0653	−	48.6105i	0.975925	−	1.69035i	0.676847	−	0.736124i	$-0.263346\pi$
$828$	−5.97820	+	26.0297i	−0.207757	+	0.904594i
$829$		−	0.980616i		−	0.0340582i	−0.999855	−	0.0170291i	$-0.994579\pi$
$829$		−	0.980616i		−	0.0340582i	0.999855	−	0.0170291i	$-0.00542079\pi$
$830$	4.26930	+	3.15536i	0.148190	+	0.109524i
$831$	8.36926	+	14.4960i	0.290326	+	0.502860i
$832$	−7.32667	−	18.8934i	−0.254007	−	0.655009i
$833$	−1.26653	−	2.19369i	−0.0438826	−	0.0760069i
$834$	−36.8709	+	16.0569i	−1.27673	+	0.556005i
$835$	12.1284			0.419720
$836$	−0.281192	−	0.335820i	−0.00972521	−	0.0116146i
$837$	−33.7128			−1.16529
$838$	−32.6566	+	14.2216i	−1.12810	+	0.491278i
$839$	−16.1989	−	28.0573i	−0.559247	−	0.968644i	−0.997559	−	0.0698217i	$-0.977757\pi$
$839$	−16.1989	−	28.0573i	−0.559247	−	0.968644i	0.438312	−	0.898823i	$-0.355576\pi$
$840$	14.5140	+	16.9351i	0.500782	+	0.584315i
$841$	−14.0506	−	24.3364i	−0.484504	−	0.839186i
$842$	−5.49472	−	4.06104i	−0.189361	−	0.139953i
$843$			30.8097i			1.06114i
$844$	14.3580	+	3.29759i	0.494224	+	0.113508i
$845$	3.29188	−	5.70171i	0.113244	−	0.196145i
$846$	63.2212	+	46.7255i	2.17359	+	1.60646i
$847$		−	28.3797i		−	0.975138i
$848$	21.1815	−	43.6810i	0.727377	−	1.50001i
$849$	72.4693	+	41.8402i	2.48714	+	1.43595i
$850$	4.19839	+	9.64061i	0.144004	+	0.330670i
$851$	8.96759	−	15.5323i	0.307405	−	0.532441i
$852$	−13.9726	−	45.5168i	−0.478693	−	1.55938i
$853$	−8.65003	−	14.9823i	−0.296172	−	0.512984i	0.679085	−	0.734059i	$-0.262377\pi$
$853$	−8.65003	−	14.9823i	−0.296172	−	0.512984i	−0.975257	+	0.221075i	$0.929043\pi$
$854$	−0.136100	+	1.20061i	−0.00465724	+	0.0410841i
$855$	27.4114	+	3.42635i	0.937450	+	0.117179i
$856$	−18.7267	−	6.59549i	−0.640067	−	0.225429i
$857$	24.6152	−	14.2116i	0.840841	−	0.485460i	−0.0167093	−	0.999860i	$-0.505319\pi$
$857$	24.6152	−	14.2116i	0.840841	−	0.485460i	0.857550	+	0.514401i	$0.171986\pi$
$858$	0.219587	+	0.504230i	0.00749657	+	0.0172141i
$859$	−10.8861	−	6.28509i	−0.371428	−	0.214444i	0.302654	−	0.953101i	$-0.402127\pi$
$859$	−10.8861	−	6.28509i	−0.371428	−	0.214444i	−0.674082	+	0.738656i	$0.735461\pi$
$860$	−15.7373	+	4.83100i	−0.536639	+	0.164736i
$861$	−42.1289	+	72.9693i	−1.43575	+	2.48679i
$862$	38.6100	+	4.37677i	1.31506	+	0.149073i
$863$	35.2016			1.19828			0.599138	−	0.800646i	$-0.295510\pi$
$863$	35.2016			1.19828			0.599138	+	0.800646i	$0.295510\pi$
$864$	51.0977	−	26.7850i	1.73838	−	0.911245i
$865$	7.40766	+	4.27681i	0.251868	+	0.145416i
$866$	5.11588	−	45.1301i	0.173845	−	1.53358i
$867$	116.986			3.97304
$868$	−12.4907	−	11.6211i	−0.423960	−	0.394447i
$869$	0.269040	−	0.155330i	0.00912655	−	0.00526922i
$870$	−3.29467	−	2.43503i	−0.111700	−	0.0825551i
$871$	12.3921	−	7.15461i	0.419892	−	0.242425i
$872$	0.426714	−	0.0798413i	0.0144504	−	0.00270377i
$873$		−	76.7974i		−	2.59920i
$874$	−3.05252	+	12.6251i	−0.103253	+	0.427050i
$875$			2.58057i			0.0872391i
$876$	−18.4301	−	60.0374i	−0.622696	−	2.02848i
$877$	−15.6227	+	9.01978i	−0.527542	+	0.304576i	−0.740015	−	0.672591i	$-0.765182\pi$
$877$	−15.6227	+	9.01978i	−0.527542	+	0.304576i	0.212473	+	0.977167i	$0.431848\pi$
$878$	2.61202	−	3.53415i	0.0881514	−	0.119272i
$879$	−6.68359	+	3.85877i	−0.225432	+	0.130153i
$880$	−0.112759	−	0.166353i	−0.00380111	−	0.00560777i
$881$	−23.4300			−0.789378			−0.394689	−	0.918815i	$-0.629148\pi$
$881$	−23.4300			−0.789378			−0.394689	+	0.918815i	$0.629148\pi$
$882$	−3.03396	−	0.343925i	−0.102159	−	0.0115806i
$883$	10.2159	+	5.89815i	0.343792	+	0.198489i	0.661948	−	0.749550i	$-0.269730\pi$
$883$	10.2159	+	5.89815i	0.343792	+	0.198489i	−0.318155	+	0.948039i	$0.603063\pi$
$884$	−27.5777	−	25.6579i	−0.927538	−	0.862970i
$885$	11.6397			0.391264
$886$	−4.25644	+	37.5485i	−0.142998	+	1.26147i
$887$	−5.50168	+	9.52919i	−0.184728	+	0.319959i	−0.943485	−	0.331415i	$-0.892474\pi$
$887$	−5.50168	+	9.52919i	−0.184728	+	0.319959i	0.758757	+	0.651374i	$0.225807\pi$
$888$	−72.3128	+	13.5303i	−2.42666	+	0.454046i
$889$	−10.6008	−	6.12036i	−0.355538	−	0.205270i
$890$	12.2657	−	5.34159i	0.411147	−	0.179050i
$891$	−0.528737	+	0.305266i	−0.0177134	+	0.0102268i
$892$	−27.4551	−	6.30556i	−0.919263	−	0.211126i
$893$	30.4843	+	23.0759i	1.02012	+	0.772204i
$894$	−65.5233	−	7.42763i	−2.19143	−	0.248417i
$895$	−5.96105	−	10.3248i	−0.199256	−	0.345121i
$896$	28.1648	+	7.68998i	0.940921	+	0.256904i
$897$	8.15467	−	14.1243i	0.272276	−	0.471597i
$898$	24.5687	−	10.6994i	0.819869	−	0.357045i
$899$	2.71395	+	1.56690i	0.0905153	+	0.0522590i
$900$	12.3535	+	2.83720i	0.411782	+	0.0945734i
$901$		−	90.2381i		−	3.00627i
$902$	0.451246	−	0.610551i	0.0150248	−	0.0203291i
$903$	−32.4532	+	56.2106i	−1.07998	+	1.87057i
$904$	0.906972	−	2.57519i	0.0301654	−	0.0856494i
$905$			18.1375i			0.602912i
$906$	−5.13295	+	6.94506i	−0.170531	+	0.230734i
$907$	5.31536	+	9.20648i	0.176494	+	0.305696i	0.940677	−	0.339303i	$-0.110191\pi$
$907$	5.31536	+	9.20648i	0.176494	+	0.305696i	−0.764183	+	0.644999i	$0.776858\pi$
$908$	23.8824	−	25.6693i	0.792564	−	0.851864i
$909$	23.3551	+	40.4521i	0.774638	+	1.34171i
$910$	−3.69095	−	8.47540i	−0.122354	−	0.280957i
$911$	7.20132			0.238590			0.119295	−	0.992859i	$-0.461937\pi$
$911$	7.20132			0.238590			0.119295	+	0.992859i	$0.461937\pi$
$912$	47.4692	−	24.1927i	1.57186	−	0.801101i
$913$	−0.188602			−0.00624182
$914$	−0.233466	−	0.536099i	−0.00772236	−	0.0177326i
$915$	0.505862	+	0.876179i	0.0167233	+	0.0289656i
$916$	−35.6980	+	38.3690i	−1.17950	+	1.26775i
$917$	27.4946	+	47.6220i	0.907950	+	1.57262i
$918$	63.7398	−	86.2421i	2.10373	−	2.84641i
$919$		−	2.31313i		−	0.0763032i	−0.999272	−	0.0381516i	$-0.987853\pi$
$919$		−	2.31313i		−	0.0763032i	0.999272	−	0.0381516i	$-0.0121470\pi$
$920$	−1.97979	+	5.62126i	−0.0652716	+	0.185327i
$921$	−23.0981	+	40.0071i	−0.761109	+	1.31828i
$922$	13.8701	−	18.7667i	0.456788	−	0.618050i
$923$			19.7342i			0.649560i
$924$	−0.772264	−	0.177365i	−0.0254056	−	0.00583487i
$925$	−7.37151	−	4.25594i	−0.242374	−	0.139935i
$926$	−36.9741	+	16.1018i	−1.21504	+	0.529139i
$927$	−36.3379	+	62.9390i	−1.19349	+	2.06719i
$928$	−5.35837	−	0.218662i	−0.175897	−	0.00717794i
$929$	28.2066	+	48.8553i	0.925429	+	1.60289i	0.790870	+	0.611984i	$0.209628\pi$
$929$	28.2066	+	48.8553i	0.925429	+	1.60289i	0.134559	+	0.990906i	$0.457038\pi$
$930$	−14.1942	−	1.60903i	−0.465446	−	0.0527623i
$931$	−1.47352	−	0.184186i	−0.0482927	−	0.00603645i
$932$	46.2048	+	10.6118i	1.51349	+	0.347600i
$933$	−5.39958	+	3.11745i	−0.176774	+	0.102061i
$934$	26.9985	−	11.7576i	0.883417	−	0.384719i
$935$	−0.323517	−	0.186782i	−0.0105801	−	0.00610844i
$936$	−44.6307	+	8.35074i	−1.45880	+	0.272952i
$937$	−3.97929	+	6.89233i	−0.129998	+	0.225163i	−0.923675	−	0.383176i	$-0.874830\pi$
$937$	−3.97929	+	6.89233i	−0.129998	+	0.225163i	0.793678	+	0.608338i	$0.208164\pi$
$938$	−2.32214	+	20.4849i	−0.0758204	+	0.668854i
$939$	19.5349			0.637496
$940$	12.8435	+	11.9494i	0.418909	+	0.389747i
$941$	10.1295	+	5.84828i	0.330213	+	0.190648i	0.655936	−	0.754817i	$-0.272274\pi$
$941$	10.1295	+	5.84828i	0.330213	+	0.190648i	−0.325723	+	0.945465i	$0.605608\pi$
$942$	−30.1878	−	3.42204i	−0.983571	−	0.111496i
$943$	−22.5143			−0.733166
$944$	12.6122	−	8.54889i	0.410491	−	0.278243i
$945$	22.7924	−	13.1592i	0.741435	−	0.428068i
$946$	0.347609	−	0.470327i	0.0113017	−	0.0152916i
$947$	−48.3203	+	27.8977i	−1.57020	+	0.906555i	−0.574055	+	0.818817i	$0.694631\pi$
$947$	−48.3203	+	27.8977i	−1.57020	+	0.906555i	−0.996144	+	0.0877381i	$0.972036\pi$
$948$	11.0896	+	36.1252i	0.360174	+	1.17329i
$949$			26.0298i			0.844964i
$950$	5.99177	+	1.44870i	0.194399	+	0.0470020i
$951$			54.8561i			1.77883i
$952$	53.3442	−	9.98109i	1.72890	−	0.323489i
$953$	−40.7256	+	23.5129i	−1.31923	+	0.761659i	−0.983605	−	0.180336i	$-0.942282\pi$
$953$	−40.7256	+	23.5129i	−1.31923	+	0.761659i	−0.335627	+	0.941995i	$0.608948\pi$
$954$	−87.4759	−	64.6517i	−2.83214	−	2.09318i
$955$	8.52482	−	4.92181i	0.275857	−	0.159266i
$956$	−6.06499	−	5.64279i	−0.196156	−	0.182501i
$957$	0.145547			0.00470486
$958$	−6.24350	+	55.0774i	−0.201718	+	1.77947i
$959$	−43.4946	−	25.1116i	−1.40451	−	0.810897i
$960$	22.7922	−	8.83859i	0.735614	−	0.285264i
$961$	−20.0729			−0.647514
$962$	30.2976	+	3.43450i	0.976834	+	0.110733i
$963$	−22.2433	+	38.5266i	−0.716781	+	1.24150i
$964$	14.7322	−	4.52245i	0.474492	−	0.145658i
$965$	1.06403	+	0.614316i	0.0342522	+	0.0197755i
$966$	9.38198	+	21.5435i	0.301860	+	0.693151i
$967$	22.0126	−	12.7090i	0.707877	−	0.408693i	−0.102397	−	0.994744i	$-0.532651\pi$
$967$	22.0126	−	12.7090i	0.707877	−	0.408693i	0.810275	+	0.586050i	$0.199318\pi$
$968$	−29.3391	−	10.3331i	−0.942994	−	0.332119i
$969$	59.7735	−	78.9635i	1.92020	−	2.53667i
$970$	1.93029	−	17.0282i	0.0619778	−	0.546741i
$971$	−13.9518	−	24.1652i	−0.447733	−	0.775497i	0.550505	−	0.834832i	$-0.314435\pi$
$971$	−13.9518	−	24.1652i	−0.447733	−	0.775497i	−0.998238	+	0.0593349i	$0.981102\pi$
$972$	−3.83663	−	12.4981i	−0.123060	−	0.400877i
$973$	−12.0073	+	20.7973i	−0.384938	+	0.666732i
$974$	16.1350	+	37.0501i	0.516997	+	1.18716i
$975$	−6.70328	−	3.87014i	−0.214677	−	0.123944i
$976$	1.19165	+	0.577847i	0.0381437	+	0.0184964i
$977$		−	48.5640i		−	1.55370i	−0.629686	−	0.776849i	$-0.716817\pi$
$977$		−	48.5640i		−	1.55370i	0.629686	−	0.776849i	$-0.283183\pi$
$978$	19.4413	+	14.3687i	0.621666	+	0.459461i
$979$	−0.237642	+	0.411609i	−0.00759508	+	0.0131551i
$980$	−0.664070	−	0.152516i	−0.0212129	−	0.00487194i
$981$		−	0.972714i		−	0.0310564i
$982$	−14.6671	−	10.8401i	−0.468045	−	0.345923i
$983$	22.5166	+	38.9998i	0.718166	+	1.24390i	0.961726	+	0.274015i	$0.0883517\pi$
$983$	22.5166	+	38.9998i	0.718166	+	1.24390i	−0.243559	+	0.969886i	$0.578315\pi$
$984$	60.0969	+	70.1214i	1.91582	+	2.23539i
$985$	−10.3104	−	17.8581i	−0.328517	−	0.569008i
$986$	−9.13952	+	3.98017i	−0.291062	+	0.126754i
$987$	69.1666			2.20160
$988$	−21.7509	+	3.81196i	−0.691989	+	0.121275i
$989$	−17.3435			−0.551490
$990$	−0.412851	+	0.179792i	−0.0131213	+	0.00571417i
$991$	11.6111	+	20.1110i	0.368838	+	0.638847i	0.989384	−	0.145323i	$-0.0464223\pi$
$991$	11.6111	+	20.1110i	0.368838	+	0.638847i	−0.620546	+	0.784170i	$0.713089\pi$
$992$	−16.5619	+	8.68161i	−0.525840	+	0.275642i
$993$	−15.9407	−	27.6100i	−0.505861	−	0.876178i
$994$	−22.8650	−	16.8991i	−0.725235	−	0.536006i
$995$			25.5754i			0.810794i
$996$	5.13530	−	22.3596i	0.162718	−	0.708492i
$997$	−10.9096	+	18.8959i	−0.345509	+	0.598439i	−0.985446	−	0.169988i	$-0.945627\pi$
$997$	−10.9096	+	18.8959i	−0.345509	+	0.598439i	0.639937	+	0.768427i	$0.278960\pi$
$998$	−2.03273	−	1.50235i	−0.0643449	−	0.0475560i
$999$			86.8100i			2.74655i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	380.2.n.a.31.13	yes	40
4.3	odd	2	inner	380.2.n.a.31.7	✓	40
19.8	odd	6	inner	380.2.n.a.331.7	yes	40
76.27	even	6	inner	380.2.n.a.331.13	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
380.2.n.a.31.7	✓	40	4.3	odd	2	inner
380.2.n.a.31.13	yes	40	1.1	even	1	trivial
380.2.n.a.331.7	yes	40	19.8	odd	6	inner
380.2.n.a.331.13	yes	40	76.27	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.564655 + 1.29660i) q^{2} +(-1.52787 - 2.64635i) q^{3} +(-1.36233 + 1.46426i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.56853 - 3.47531i) q^{6} -2.58057i q^{7} +(-2.66780 - 0.939591i) q^{8} +(-3.16877 + 5.48848i) q^{9} +O(q^{10})\)	\(q+(0.564655 + 1.29660i) q^{2} +(-1.52787 - 2.64635i) q^{3} +(-1.36233 + 1.46426i) q^{4} +(0.500000 + 0.866025i) q^{5} +(2.56853 - 3.47531i) q^{6} -2.58057i q^{7} +(-2.66780 - 0.939591i) q^{8} +(-3.16877 + 5.48848i) q^{9} +(-0.840559 + 1.13730i) q^{10} -0.0502420i q^{11} +(5.95641 + 1.36800i) q^{12} +(-2.19367 - 1.26651i) q^{13} +(3.34595 - 1.45713i) q^{14} +(1.52787 - 2.64635i) q^{15} +(-0.288118 - 3.98961i) q^{16} +(-3.71766 - 6.43917i) q^{17} +(-8.90561 - 1.00953i) q^{18} +(-4.32524 - 0.540643i) q^{19} +(-1.94925 - 0.447682i) q^{20} +(-6.82908 + 3.94277i) q^{21} +(0.0651436 - 0.0283694i) q^{22} +(-1.82478 - 1.05354i) q^{23} +(1.58957 + 8.49551i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.403494 - 3.55945i) q^{26} +10.1987 q^{27} +(3.77862 + 3.51558i) q^{28} +(-0.821013 - 0.474012i) q^{29} +(4.29397 + 0.486758i) q^{30} -3.30561 q^{31} +(5.01023 - 2.62633i) q^{32} +(-0.132958 + 0.0767632i) q^{33} +(6.24982 - 8.45621i) q^{34} +(2.23484 - 1.29028i) q^{35} +(-3.71965 - 12.1170i) q^{36} +8.51189i q^{37} +(-1.74127 - 5.91337i) q^{38} +7.74028i q^{39} +(-0.520192 - 2.78018i) q^{40} +(9.25357 - 5.34255i) q^{41} +(-8.96826 - 6.62826i) q^{42} +(7.12832 - 4.11554i) q^{43} +(0.0735673 + 0.0684461i) q^{44} -6.33755 q^{45} +(0.335642 - 2.96089i) q^{46} +(-7.59619 - 4.38566i) q^{47} +(-10.1177 + 6.85806i) q^{48} +0.340679 q^{49} +(-1.40521 - 0.159293i) q^{50} +(-11.3602 + 19.6764i) q^{51} +(4.84300 - 1.48669i) q^{52} +(10.5104 + 6.06821i) q^{53} +(5.75873 + 13.2236i) q^{54} +(0.0435108 - 0.0251210i) q^{55} +(-2.42468 + 6.88444i) q^{56} +(5.17768 + 12.2721i) q^{57} +(0.151014 - 1.33218i) q^{58} +(1.90456 + 3.29879i) q^{59} +(1.79348 + 5.84240i) q^{60} +(-0.165545 + 0.286732i) q^{61} +(-1.86653 - 4.28605i) q^{62} +(14.1634 + 8.17723i) q^{63} +(6.23434 + 5.01328i) q^{64} -2.53303i q^{65} +(-0.174606 - 0.129048i) q^{66} +(-2.82453 + 4.89222i) q^{67} +(14.4933 + 3.32865i) q^{68} +6.43867i q^{69} +(2.93489 + 2.16912i) q^{70} +(-3.89538 - 6.74700i) q^{71} +(13.6106 - 11.6648i) q^{72} +(-5.13808 - 8.89942i) q^{73} +(-11.0365 + 4.80628i) q^{74} +3.05574 q^{75} +(6.68404 - 5.59674i) q^{76} -0.129653 q^{77} +(-10.0360 + 4.37059i) q^{78} +(3.09164 + 5.35488i) q^{79} +(3.31104 - 2.24432i) q^{80} +(-6.07592 - 10.5238i) q^{81} +(12.1522 + 8.98145i) q^{82} -3.75388i q^{83} +(3.53021 - 15.3709i) q^{84} +(3.71766 - 6.43917i) q^{85} +(9.36123 + 6.91870i) q^{86} +2.89691i q^{87} +(-0.0472069 + 0.134036i) q^{88} +(-8.19252 - 4.72996i) q^{89} +(-3.57853 - 8.21724i) q^{90} +(-3.26832 + 5.66090i) q^{91} +(4.02860 - 1.23669i) q^{92} +(5.05055 + 8.74780i) q^{93} +(1.39721 - 12.3256i) q^{94} +(-1.69441 - 4.01609i) q^{95} +(-14.6052 - 9.24613i) q^{96} +(-10.4944 + 6.05892i) q^{97} +(0.192366 + 0.441724i) q^{98} +(0.275752 + 0.159205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9}+O(q^{10}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9	\( 40 q - 3 q^{2} + q^{4} + 20 q^{5} + 3 q^{6} - 22 q^{9} - 3 q^{10} + 12 q^{13} + 18 q^{14} - 7 q^{16} + 4 q^{17} + 2 q^{20} + 12 q^{21} - 8 q^{24} - 20 q^{25} + 2 q^{26} + 8 q^{28} + 6 q^{30} - 18 q^{32} - 6 q^{33} - 27 q^{34} - 14 q^{36} + 38 q^{38} + 36 q^{41} - 21 q^{42} - 8 q^{44} - 44 q^{45} - 18 q^{48} - 60 q^{49} - 33 q^{52} + 42 q^{53} + 9 q^{54} + 12 q^{57} - 62 q^{58} + 3 q^{60} + 12 q^{61} - 23 q^{62} + 64 q^{64} + 2 q^{66} + 72 q^{68} + 18 q^{70} + 42 q^{72} - 18 q^{73} + 6 q^{74} - 62 q^{76} - 28 q^{77} - 24 q^{78} + 7 q^{80} - 48 q^{81} - q^{82} - 4 q^{85} + 78 q^{86} - 18 q^{89} + 39 q^{90} + 16 q^{92} + 8 q^{96} + 30 q^{97} - 12 q^{98}+O(q^{100}) \) 40 * q - 3 * q^2 + q^4 + 20 * q^5 + 3 * q^6 - 22 * q^9 - 3 * q^10 + 12 * q^13 + 18 * q^14 - 7 * q^16 + 4 * q^17 + 2 * q^20 + 12 * q^21 - 8 * q^24 - 20 * q^25 + 2 * q^26 + 8 * q^28 + 6 * q^30 - 18 * q^32 - 6 * q^33 - 27 * q^34 - 14 * q^36 + 38 * q^38 + 36 * q^41 - 21 * q^42 - 8 * q^44 - 44 * q^45 - 18 * q^48 - 60 * q^49 - 33 * q^52 + 42 * q^53 + 9 * q^54 + 12 * q^57 - 62 * q^58 + 3 * q^60 + 12 * q^61 - 23 * q^62 + 64 * q^64 + 2 * q^66 + 72 * q^68 + 18 * q^70 + 42 * q^72 - 18 * q^73 + 6 * q^74 - 62 * q^76 - 28 * q^77 - 24 * q^78 + 7 * q^80 - 48 * q^81 - q^82 - 4 * q^85 + 78 * q^86 - 18 * q^89 + 39 * q^90 + 16 * q^92 + 8 * q^96 + 30 * q^97 - 12 * q^98

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