LMFDB - Embedded newform 416.2.bg.a.389.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [416,2,Mod(77,416)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(416, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7, 4]))

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

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

chi := DirichletCharacter("416.77");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 416 = 2^{5} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	416.bg (of order $8$, degree $4$, 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:	$3.32177672409$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$54$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			389.7
Character	$\chi$	$=$	416.389
Dual form			416.2.bg.a.77.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31886 - 0.510506i) q^{2} +(0.324061 + 0.782352i) q^{3} +(1.47877 + 1.34657i) q^{4} +(0.174055 - 0.420207i) q^{5} +(-0.0279946 - 1.19725i) q^{6} +(2.63267 - 2.63267i) q^{7} +(-1.26285 - 2.53085i) q^{8} +(1.61426 - 1.61426i) q^{9} +O(q^{10})$	\(q+(-1.31886 - 0.510506i) q^{2} +(0.324061 + 0.782352i) q^{3} +(1.47877 + 1.34657i) q^{4} +(0.174055 - 0.420207i) q^{5} +(-0.0279946 - 1.19725i) q^{6} +(2.63267 - 2.63267i) q^{7} +(-1.26285 - 2.53085i) q^{8} +(1.61426 - 1.61426i) q^{9} +(-0.444072 + 0.465337i) q^{10} +(-2.03436 - 0.842658i) q^{11} +(-0.574280 + 1.59329i) q^{12} +(-2.76010 + 2.31988i) q^{13} +(-4.81611 + 2.12812i) q^{14} +0.385154 q^{15} +(0.373508 + 3.98252i) q^{16} -4.77309i q^{17} +(-2.95307 + 1.30489i) q^{18} +(-0.598021 - 1.44375i) q^{19} +(0.823225 - 0.387011i) q^{20} +(2.91282 + 1.20653i) q^{21} +(2.25284 + 2.14990i) q^{22} +(3.12684 - 3.12684i) q^{23} +(1.57077 - 1.80814i) q^{24} +(3.38926 + 3.38926i) q^{25} +(4.82449 - 1.65054i) q^{26} +(4.13309 + 1.71198i) q^{27} +(7.43818 - 0.348037i) q^{28} +(-1.02631 - 2.47773i) q^{29} +(-0.507964 - 0.196624i) q^{30} -1.90545i q^{31} +(1.54050 - 5.44306i) q^{32} -1.86465i q^{33} +(-2.43669 + 6.29503i) q^{34} +(-0.648036 - 1.56450i) q^{35} +(4.56083 - 0.213404i) q^{36} +(-2.32688 + 5.61757i) q^{37} +(0.0516613 + 2.20940i) q^{38} +(-2.70940 - 1.40759i) q^{39} +(-1.28329 + 0.0901511i) q^{40} +(2.95080 + 2.95080i) q^{41} +(-3.22565 - 3.07825i) q^{42} +(4.00294 - 9.66394i) q^{43} +(-1.87364 - 3.98549i) q^{44} +(-0.397353 - 0.959295i) q^{45} +(-5.72012 + 2.52758i) q^{46} +1.36571 q^{47} +(-2.99470 + 1.58279i) q^{48} -6.86192i q^{49} +(-2.73971 - 6.20018i) q^{50} +(3.73424 - 1.54677i) q^{51} +(-7.20542 - 0.286105i) q^{52} +(-0.464168 + 1.12060i) q^{53} +(-4.57698 - 4.36783i) q^{54} +(-0.708182 + 0.708182i) q^{55} +(-9.98757 - 3.33822i) q^{56} +(0.935726 - 0.935726i) q^{57} +(0.0886598 + 3.79171i) q^{58} +(0.498001 - 1.20228i) q^{59} +(0.569554 + 0.518637i) q^{60} +(3.55260 + 8.57672i) q^{61} +(-0.972744 + 2.51302i) q^{62} -8.49964i q^{63} +(-4.81041 + 6.39218i) q^{64} +(0.494419 + 1.56360i) q^{65} +(-0.951917 + 2.45921i) q^{66} +(7.70250 - 3.19048i) q^{67} +(6.42729 - 7.05829i) q^{68} +(3.45957 + 1.43300i) q^{69} +(0.0559819 + 2.39418i) q^{70} +(-9.25555 + 9.25555i) q^{71} +(-6.12403 - 2.04688i) q^{72} +(10.4559 + 10.4559i) q^{73} +(5.93662 - 6.22089i) q^{74} +(-1.55327 + 3.74991i) q^{75} +(1.05978 - 2.94025i) q^{76} +(-7.57423 + 3.13735i) q^{77} +(2.85473 + 3.23957i) q^{78} +1.42746i q^{79} +(1.73850 + 0.536229i) q^{80} -3.06041i q^{81} +(-2.38528 - 5.39808i) q^{82} +(-4.61887 - 11.1509i) q^{83} +(2.68271 + 5.70649i) q^{84} +(-2.00569 - 0.830783i) q^{85} +(-10.2128 + 10.7018i) q^{86} +(1.60587 - 1.60587i) q^{87} +(0.436450 + 6.21280i) q^{88} +(-5.78585 + 5.78585i) q^{89} +(0.0343261 + 1.46802i) q^{90} +(-1.15896 + 13.3739i) q^{91} +(8.83436 - 0.413366i) q^{92} +(1.49073 - 0.617482i) q^{93} +(-1.80118 - 0.697204i) q^{94} -0.710764 q^{95} +(4.75760 - 0.558669i) q^{96} +9.17375i q^{97} +(-3.50305 + 9.04989i) q^{98} +(-4.64425 + 1.92371i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9}+O(q^{10}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9	$ 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38} - 28 q^{39} + 32 q^{40} + 32 q^{42} - 8 q^{43} - 112 q^{48} + 16 q^{51} - 12 q^{52} - 8 q^{53} - 40 q^{55} - 48 q^{56} - 8 q^{61} + 56 q^{62} - 8 q^{64} - 8 q^{65} - 56 q^{66} - 8 q^{69} - 8 q^{74} - 16 q^{75} - 8 q^{77} + 84 q^{78} - 88 q^{82} - 8 q^{87} + 72 q^{88} + 88 q^{90} + 44 q^{91} - 80 q^{92} + 24 q^{94} + 112 q^{95}+O(q^{100}) $ 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/416\mathbb{Z}\right)^\times$.

$n$	$261$	$287$	$353$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.31886	−	0.510506i	−0.932573	−	0.360982i
$2$	−1.31886	−	0.510506i	−0.932573	−	0.360982i
$3$	0.324061	+	0.782352i	0.187097	+	0.451691i	0.989398	−	0.145228i	$-0.0463915\pi$
$3$	0.324061	+	0.782352i	0.187097	+	0.451691i	−0.802302	+	0.596919i	$0.796391\pi$
$4$	1.47877	+	1.34657i	0.739384	+	0.673284i
$5$	0.174055	−	0.420207i	0.0778400	−	0.187922i	−0.880169	−	0.474660i	$-0.842571\pi$
$5$	0.174055	−	0.420207i	0.0778400	−	0.187922i	0.958009	+	0.286738i	$0.0925709\pi$
$6$	−0.0279946	−	1.19725i	−0.0114288	−	0.488773i
$7$	2.63267	−	2.63267i	0.995056	−	0.995056i	−0.00493151	−	0.999988i	$-0.501570\pi$
$7$	2.63267	−	2.63267i	0.995056	−	0.995056i	0.999988	+	0.00493151i	$0.00156976\pi$
$8$	−1.26285	−	2.53085i	−0.446486	−	0.894791i
$9$	1.61426	−	1.61426i	0.538087	−	0.538087i
$10$	−0.444072	+	0.465337i	−0.140428	+	0.147152i
$11$	−2.03436	−	0.842658i	−0.613381	−	0.254071i	0.0542922	−	0.998525i	$-0.482710\pi$
$11$	−2.03436	−	0.842658i	−0.613381	−	0.254071i	−0.667673	+	0.744454i	$0.732710\pi$
$12$	−0.574280	+	1.59329i	−0.165780	+	0.459942i
$13$	−2.76010	+	2.31988i	−0.765515	+	0.643419i
$13$	−2.76010	+	2.31988i	−0.765515	+	0.643419i
$14$	−4.81611	+	2.12812i	−1.28716	+	0.568765i
$15$	0.385154			0.0994464
$16$	0.373508	+	3.98252i	0.0933769	+	0.995631i
$17$		−	4.77309i		−	1.15764i	−0.815454	−	0.578822i	$-0.803512\pi$
$17$		−	4.77309i		−	1.15764i	0.815454	−	0.578822i	$-0.196488\pi$
$18$	−2.95307	+	1.30489i	−0.696045	+	0.307566i
$19$	−0.598021	−	1.44375i	−0.137196	−	0.331219i	0.840317	−	0.542095i	$-0.182369\pi$
$19$	−0.598021	−	1.44375i	−0.137196	−	0.331219i	−0.977513	+	0.210875i	$0.932369\pi$
$20$	0.823225	−	0.387011i	0.184079	−	0.0865383i
$21$	2.91282	+	1.20653i	0.635630	+	0.263286i
$22$	2.25284	+	2.14990i	0.480308	+	0.458359i
$23$	3.12684	−	3.12684i	0.651990	−	0.651990i	−0.301482	−	0.953472i	$-0.597481\pi$
$23$	3.12684	−	3.12684i	0.651990	−	0.651990i	0.953472	+	0.301482i	$0.0974812\pi$
$24$	1.57077	−	1.80814i	0.320633	−	0.369086i
$25$	3.38926	+	3.38926i	0.677851	+	0.677851i
$26$	4.82449	−	1.65054i	0.946161	−	0.323697i
$27$	4.13309	+	1.71198i	0.795414	+	0.329471i
$28$	7.43818	−	0.348037i	1.40568	−	0.0657729i
$29$	−1.02631	−	2.47773i	−0.190581	−	0.460103i	0.799489	−	0.600681i	$-0.205104\pi$
$29$	−1.02631	−	2.47773i	−0.190581	−	0.460103i	−0.990070	+	0.140578i	$0.955104\pi$
$30$	−0.507964	−	0.196624i	−0.0927410	−	0.0358984i
$31$		−	1.90545i		−	0.342229i	−0.985251	−	0.171115i	$-0.945263\pi$
$31$		−	1.90545i		−	0.342229i	0.985251	−	0.171115i	$-0.0547369\pi$
$32$	1.54050	−	5.44306i	0.272324	−	0.962206i
$33$		−	1.86465i		−	0.324595i
$34$	−2.43669	+	6.29503i	−0.417889	+	1.07959i
$35$	−0.648036	−	1.56450i	−0.109538	−	0.264448i
$36$	4.56083	−	0.213404i	0.760138	−	0.0355674i
$37$	−2.32688	+	5.61757i	−0.382536	+	0.923524i	0.608938	+	0.793218i	$0.291596\pi$
$37$	−2.32688	+	5.61757i	−0.382536	+	0.923524i	−0.991474	+	0.130306i	$0.958404\pi$
$38$	0.0516613	+	2.20940i	0.00838057	+	0.358411i
$39$	−2.70940	−	1.40759i	−0.433852	−	0.225395i
$40$	−1.28329	+	0.0901511i	−0.202906	+	0.0142541i
$41$	2.95080	+	2.95080i	0.460838	+	0.460838i	0.898930	−	0.438092i	$-0.144346\pi$
$41$	2.95080	+	2.95080i	0.460838	+	0.460838i	−0.438092	+	0.898930i	$0.644346\pi$
$42$	−3.22565	−	3.07825i	−0.497729	−	0.474985i
$43$	4.00294	−	9.66394i	0.610442	−	1.47374i	−0.252074	−	0.967708i	$-0.581113\pi$
$43$	4.00294	−	9.66394i	0.610442	−	1.47374i	0.862516	−	0.506030i	$-0.168887\pi$
$44$	−1.87364	−	3.98549i	−0.282462	−	0.600836i
$45$	−0.397353	−	0.959295i	−0.0592339	−	0.143003i
$46$	−5.72012	+	2.52758i	−0.843385	+	0.372672i
$47$	1.36571			0.199210			0.0996048	−	0.995027i	$-0.468242\pi$
$47$	1.36571			0.199210			0.0996048	+	0.995027i	$0.468242\pi$
$48$	−2.99470	+	1.58279i	−0.432247	+	0.228457i
$49$		−	6.86192i		−	0.980274i
$50$	−2.73971	−	6.20018i	−0.387453	−	0.876838i
$51$	3.73424	−	1.54677i	0.522898	−	0.216591i
$52$	−7.20542	−	0.286105i	−0.999213	−	0.0396756i
$53$	−0.464168	+	1.12060i	−0.0637584	+	0.153926i	−0.952547	−	0.304390i	$-0.901547\pi$
$53$	−0.464168	+	1.12060i	−0.0637584	+	0.153926i	0.888789	+	0.458316i	$0.151547\pi$
$54$	−4.57698	−	4.36783i	−0.622848	−	0.594386i
$55$	−0.708182	+	0.708182i	−0.0954912	+	0.0954912i
$56$	−9.98757	−	3.33822i	−1.33465	−	0.446089i
$57$	0.935726	−	0.935726i	0.123940	−	0.123940i
$58$	0.0886598	+	3.79171i	0.0116416	+	0.497876i
$59$	0.498001	−	1.20228i	0.0648342	−	0.156524i	−0.888142	−	0.459570i	$-0.848004\pi$
$59$	0.498001	−	1.20228i	0.0648342	−	0.156524i	0.952976	+	0.303046i	$0.0980036\pi$
$60$	0.569554	+	0.518637i	0.0735291	+	0.0669557i
$61$	3.55260	+	8.57672i	0.454863	+	1.09814i	0.970451	+	0.241300i	$0.0775738\pi$
$61$	3.55260	+	8.57672i	0.454863	+	1.09814i	−0.515587	+	0.856837i	$0.672426\pi$
$62$	−0.972744	+	2.51302i	−0.123539	+	0.319154i
$63$		−	8.49964i		−	1.07085i
$64$	−4.81041	+	6.39218i	−0.601301	+	0.799023i
$65$	0.494419	+	1.56360i	0.0613251	+	0.193941i
$66$	−0.951917	+	2.45921i	−0.117173	+	0.302708i
$67$	7.70250	−	3.19048i	0.941011	−	0.389779i	0.141166	−	0.989986i	$-0.454915\pi$
$67$	7.70250	−	3.19048i	0.941011	−	0.389779i	0.799845	+	0.600207i	$0.204915\pi$
$68$	6.42729	−	7.05829i	0.779424	−	0.855944i
$69$	3.45957	+	1.43300i	0.416483	+	0.172513i
$70$	0.0559819	+	2.39418i	0.00669112	+	0.286159i
$71$	−9.25555	+	9.25555i	−1.09843	+	1.09843i	−0.103837	+	0.994594i	$0.533112\pi$
$71$	−9.25555	+	9.25555i	−1.09843	+	1.09843i	−0.994594	+	0.103837i	$0.966888\pi$
$72$	−6.12403	−	2.04688i	−0.721724	−	0.241227i
$73$	10.4559	+	10.4559i	1.22377	+	1.22377i	0.966281	+	0.257491i	$0.0828958\pi$
$73$	10.4559	+	10.4559i	1.22377	+	1.22377i	0.257491	+	0.966281i	$0.417104\pi$
$74$	5.93662	−	6.22089i	0.690118	−	0.723164i
$75$	−1.55327	+	3.74991i	−0.179356	+	0.433003i
$76$	1.05978	−	2.94025i	0.121565	−	0.337270i
$77$	−7.57423	+	3.13735i	−0.863164	+	0.357534i
$78$	2.85473	+	3.23957i	0.323235	+	0.366810i
$79$			1.42746i			0.160602i	0.996771	+	0.0803008i	$0.0255881\pi$
$79$			1.42746i			0.160602i	−0.996771	+	0.0803008i	$0.974412\pi$
$80$	1.73850	+	0.536229i	0.194370	+	0.0599523i
$81$		−	3.06041i		−	0.340046i
$82$	−2.38528	−	5.39808i	−0.263410	−	0.596119i
$83$	−4.61887	−	11.1509i	−0.506986	−	1.22397i	−0.945610	−	0.325302i	$-0.894534\pi$
$83$	−4.61887	−	11.1509i	−0.506986	−	1.22397i	0.438624	−	0.898671i	$-0.355466\pi$
$84$	2.68271	+	5.70649i	0.292708	+	0.622629i
$85$	−2.00569	−	0.830783i	−0.217547	−	0.0901110i
$86$	−10.2128	+	10.7018i	−1.10127	+	1.15401i
$87$	1.60587	−	1.60587i	0.172167	−	0.172167i
$88$	0.436450	+	6.21280i	0.0465257	+	0.662287i
$89$	−5.78585	+	5.78585i	−0.613299	+	0.613299i	−0.943804	−	0.330505i	$-0.892781\pi$
$89$	−5.78585	+	5.78585i	−0.613299	+	0.613299i	0.330505	+	0.943804i	$0.392781\pi$
$90$	0.0343261	+	1.46802i	0.00361829	+	0.154743i
$91$	−1.15896	+	13.3739i	−0.121492	+	1.40197i
$92$	8.83436	−	0.413366i	0.921046	−	0.0430964i
$93$	1.49073	−	0.617482i	0.154582	−	0.0640299i
$94$	−1.80118	−	0.697204i	−0.185777	−	0.0719111i
$95$	−0.710764			−0.0729228
$96$	4.75760	−	0.558669i	0.485571	−	0.0570190i
$97$			9.17375i			0.931453i	0.884929	+	0.465727i	$0.154207\pi$
$97$			9.17375i			0.931453i	−0.884929	+	0.465727i	$0.845793\pi$
$98$	−3.50305	+	9.04989i	−0.353861	+	0.914177i
$99$	−4.64425	+	1.92371i	−0.466765	+	0.193340i
$100$	0.448057	+	9.57578i	0.0448057	+	0.957578i
$101$	−7.40238	−	3.06617i	−0.736565	−	0.305095i	−0.0173181	−	0.999850i	$-0.505513\pi$
$101$	−7.40238	−	3.06617i	−0.736565	−	0.305095i	−0.719246	+	0.694755i	$0.755513\pi$
$102$	−5.71456	+	0.133621i	−0.565826	+	0.0132304i
$103$	−8.49030	−	8.49030i	−0.836574	−	0.836574i	0.151832	−	0.988406i	$-0.451483\pi$
$103$	−8.49030	−	8.49030i	−0.836574	−	0.836574i	−0.988406	+	0.151832i	$0.951483\pi$
$104$	9.35687	+	4.05574i	0.917516	+	0.397698i
$105$	1.01398	−	1.01398i	0.0989548	−	0.0989548i
$106$	1.18424	−	1.24095i	0.115024	−	0.120532i
$107$	−4.25131	+	10.2636i	−0.410990	+	0.992218i	0.573882	+	0.818938i	$0.305437\pi$
$107$	−4.25131	+	10.2636i	−0.410990	+	0.992218i	−0.984873	+	0.173280i	$0.944563\pi$
$108$	3.80658	+	8.09712i	0.366289	+	0.779146i
$109$	1.70421	+	4.11432i	0.163233	+	0.394080i	0.984240	−	0.176839i	$-0.0565871\pi$
$109$	1.70421	+	4.11432i	0.163233	+	0.394080i	−0.821006	+	0.570919i	$0.806587\pi$
$110$	1.29552	−	0.572459i	0.123523	−	0.0545819i
$111$	−5.14897			−0.488718
$112$	11.4680	+	9.50135i	1.08362	+	0.897793i
$113$			6.33692i			0.596127i	0.954546	+	0.298063i	$0.0963407\pi$
$113$			6.33692i			0.596127i	−0.954546	+	0.298063i	$0.903659\pi$
$114$	−1.71178	+	0.756396i	−0.160323	+	0.0708429i
$115$	−0.769676	−	1.85816i	−0.0717726	−	0.173274i
$116$	1.81876	−	5.04598i	0.168868	−	0.468508i
$117$	−0.710636	+	8.20042i	−0.0656983	+	0.758129i
$118$	−1.27056	+	1.33140i	−0.116965	+	0.122566i
$119$	−12.5660	−	12.5660i	−1.15192	−	1.15192i
$120$	−0.486393	−	0.974768i	−0.0444014	−	0.0889837i
$121$	−4.34964	−	4.34964i	−0.395422	−	0.395422i
$122$	−0.306898	−	13.1251i	−0.0277852	−	1.18829i
$123$	−1.35233	+	3.26480i	−0.121935	+	0.294377i
$124$	2.56582	−	2.81772i	0.230418	−	0.253039i
$125$	4.11514	−	1.70455i	0.368070	−	0.152459i
$126$	−4.33912	+	11.2098i	−0.386559	+	0.998649i
$127$	−7.97744			−0.707883			−0.353941	−	0.935268i	$-0.615159\pi$
$127$	−7.97744			−0.707883			−0.353941	+	0.935268i	$0.615159\pi$
$128$	9.60749	−	5.97463i	0.849190	−	0.528088i
$129$	8.85780			0.779886
$130$	0.146161	−	2.31457i	0.0128191	−	0.203001i
$131$	8.21330	+	19.8287i	0.717599	+	1.73244i	0.680075	+	0.733142i	$0.261947\pi$
$131$	8.21330	+	19.8287i	0.717599	+	1.73244i	0.0375243	+	0.999296i	$0.488053\pi$
$132$	2.51088	−	2.75739i	0.218544	−	0.240000i
$133$	−5.37532	−	2.22653i	−0.466099	−	0.193065i
$134$	−11.7873	+	0.275616i	−1.01826	+	0.0238096i
$135$	1.43878	−	1.43878i	0.123830	−	0.123830i
$136$	−12.0800	+	6.02771i	−1.03585	+	0.516872i
$137$	14.0871	+	14.0871i	1.20354	+	1.20354i	0.973082	+	0.230458i	$0.0740223\pi$
$137$	14.0871	+	14.0871i	1.20354	+	1.20354i	0.230458	+	0.973082i	$0.425978\pi$
$138$	−3.83112	−	3.65605i	−0.326127	−	0.311224i
$139$	−0.531254	+	1.28256i	−0.0450604	+	0.108785i	−0.944807	−	0.327627i	$-0.893751\pi$
$139$	−0.531254	+	1.28256i	−0.0450604	+	0.108785i	0.899747	+	0.436412i	$0.143751\pi$
$140$	1.14841	−	3.18615i	0.0970582	−	0.269279i
$141$	0.442573	+	1.06847i	0.0372714	+	0.0899811i
$142$	16.9318	−	7.48174i	1.42088	−	0.627853i
$143$	7.56989	−	2.39364i	0.633026	−	0.200166i
$144$	7.03177	+	5.82589i	0.585981	+	0.485491i
$145$	−1.21979			−0.101298
$146$	−8.45205	−	19.1277i	−0.699497	−	1.58302i
$147$	5.36843	−	2.22368i	0.442781	−	0.183406i
$148$	−11.0054	+	5.17379i	−0.904635	+	0.425283i
$149$	−17.4449	−	7.22591i	−1.42914	−	0.591969i	−0.472001	−	0.881598i	$-0.656468\pi$
$149$	−17.4449	−	7.22591i	−1.42914	−	0.591969i	−0.957139	+	0.289628i	$0.906468\pi$
$150$	3.96289	−	4.15265i	0.323568	−	0.339062i
$151$	−4.74261	−	4.74261i	−0.385948	−	0.385948i	0.487291	−	0.873240i	$-0.337985\pi$
$151$	−4.74261	−	4.74261i	−0.385948	−	0.385948i	−0.873240	+	0.487291i	$0.837985\pi$
$152$	−2.89871	+	3.33675i	−0.235116	+	0.270646i
$153$	−7.70502	−	7.70502i	−0.622914	−	0.622914i
$154$	11.5910	−	0.271026i	0.934026	−	0.0218399i
$155$	−0.800685	−	0.331654i	−0.0643125	−	0.0266391i
$156$	−2.11116	−	5.72989i	−0.169028	−	0.458759i
$157$	0.643579	+	1.55374i	0.0513632	+	0.124002i	0.947478	−	0.319820i	$-0.103622\pi$
$157$	0.643579	+	1.55374i	0.0513632	+	0.124002i	−0.896115	+	0.443822i	$0.853622\pi$
$158$	0.728726	−	1.88261i	0.0579743	−	0.149773i
$159$	−1.02712			−0.0814561
$160$	−2.01908	−	1.59472i	−0.159622	−	0.126074i
$161$		−	16.4639i		−	1.29753i
$162$	−1.56236	+	4.03624i	−0.122750	+	0.317117i
$163$	3.88527	−	1.60933i	0.304318	−	0.126053i	−0.225299	−	0.974290i	$-0.572336\pi$
$163$	3.88527	−	1.60933i	0.304318	−	0.126053i	0.529617	+	0.848237i	$0.322336\pi$
$164$	0.390094	+	8.33700i	0.0304612	+	0.651011i
$165$	−0.783541	−	0.324553i	−0.0609986	−	0.0252664i
$166$	0.399010	+	17.0644i	0.0309692	+	1.32446i
$167$	4.18868	−	4.18868i	0.324130	−	0.324130i	−0.526219	−	0.850349i	$-0.676391\pi$
$167$	4.18868	−	4.18868i	0.324130	−	0.324130i	0.850349	+	0.526219i	$0.176391\pi$
$168$	−0.624915	−	8.89558i	−0.0482133	−	0.686309i
$169$	2.23633	−	12.8062i	0.172025	−	0.985093i
$170$	2.22110	+	2.11960i	0.170350	+	0.162566i
$171$	−3.29596	−	1.36523i	−0.252048	−	0.104402i
$172$	18.9326	−	8.90050i	1.44360	−	0.678657i
$173$	−5.17577	+	2.14387i	−0.393507	+	0.162996i	−0.570658	−	0.821188i	$-0.693312\pi$
$173$	−5.17577	+	2.14387i	−0.393507	+	0.162996i	0.177151	+	0.984184i	$0.443312\pi$
$174$	−2.93772	+	1.29811i	−0.222708	+	0.0984092i
$175$	17.8456			1.34900
$176$	2.59606	−	8.41661i	0.195685	−	0.634426i
$177$	1.10199			0.0828306
$178$	10.5844	−	4.67700i	0.793336	−	0.350556i
$179$	10.9140	−	4.52074i	0.815753	−	0.337896i	0.0645059	−	0.997917i	$-0.479453\pi$
$179$	10.9140	−	4.52074i	0.815753	−	0.337896i	0.751247	+	0.660022i	$0.229453\pi$
$180$	0.704164	−	1.95364i	0.0524853	−	0.145616i
$181$	−8.56927	+	20.6880i	−0.636948	+	1.53773i	0.193776	+	0.981046i	$0.437927\pi$
$181$	−8.56927	+	20.6880i	−0.636948	+	1.53773i	−0.830724	+	0.556684i	$0.812073\pi$
$182$	8.35597	−	17.0466i	0.619386	−	1.26358i
$183$	−5.55876	+	5.55876i	−0.410915	+	0.410915i
$184$	−11.8623	−	3.96482i	−0.874499	−	0.292291i
$185$	1.95554	+	1.95554i	0.143774	+	0.143774i
$186$	−2.28129	+	0.0533424i	−0.167273	+	0.00391126i
$187$	−4.02208	+	9.71017i	−0.294124	+	0.710078i
$188$	2.01957	+	1.83902i	0.147292	+	0.134125i
$189$	15.3882	−	6.37399i	1.11932	−	0.463639i
$190$	0.937396	+	0.362849i	0.0680058	+	0.0263238i
$191$	−13.1429			−0.950990			−0.475495	−	0.879718i	$-0.657731\pi$
$191$	−13.1429			−0.950990			−0.475495	+	0.879718i	$0.657731\pi$
$192$	−6.55980	−	1.69198i	−0.473413	−	0.122108i
$193$		−	25.0752i		−	1.80496i	−0.430736	−	0.902478i	$-0.641746\pi$
$193$		−	25.0752i		−	1.80496i	0.430736	−	0.902478i	$-0.358254\pi$
$194$	4.68325	−	12.0989i	0.336238	−	0.868648i
$195$	−1.06307	+	0.893511i	−0.0761277	+	0.0639857i
$196$	9.24004	−	10.1472i	0.660003	−	0.724799i
$197$	4.45408	−	10.7531i	0.317340	−	0.766127i	−0.682053	−	0.731303i	$-0.738913\pi$
$197$	4.45408	−	10.7531i	0.317340	−	0.766127i	0.999393	−	0.0348245i	$-0.0110872\pi$
$198$	7.10717	−	0.166184i	0.505085	−	0.0118102i
$199$	−7.03725	−	7.03725i	−0.498857	−	0.498857i	0.412225	−	0.911082i	$-0.364752\pi$
$199$	−7.03725	−	7.03725i	−0.498857	−	0.498857i	−0.911082	+	0.412225i	$0.864752\pi$
$200$	4.29757	−	12.8578i	0.303884	−	0.909186i
$201$	4.99216	+	4.99216i	0.352120	+	0.352120i
$202$	8.19739	+	7.82280i	0.576766	+	0.550410i
$203$	−9.22498	−	3.82111i	−0.647467	−	0.268190i
$204$	7.60490	+	2.74109i	0.532450	+	0.191915i
$205$	1.75355	−	0.726344i	0.122473	−	0.0507301i
$206$	6.86314	+	15.5318i	0.478178	+	1.08215i
$207$		−	10.0951i		−	0.701655i
$208$	−10.2699	−	10.1257i	−0.712089	−	0.702090i
$209$			3.44103i			0.238021i
$210$	−1.85495	+	0.819656i	−0.128003	+	0.0565616i
$211$	−11.7050	+	4.84836i	−0.805804	+	0.333775i	−0.747278	−	0.664511i	$-0.768640\pi$
$211$	−11.7050	+	4.84836i	−0.805804	+	0.333775i	−0.0585253	+	0.998286i	$0.518640\pi$
$212$	−2.19536	+	1.03207i	−0.150778	+	0.0708832i
$213$	−10.2405	−	4.24174i	−0.701665	−	0.290639i
$214$	10.8465	−	11.3659i	0.741451	−	0.776955i
$215$	−3.36412	−	3.36412i	−0.229431	−	0.229431i
$216$	−0.886712	−	12.6222i	−0.0603331	−	0.858834i
$217$	−5.01643	−	5.01643i	−0.340537	−	0.340537i
$218$	−0.147221	−	6.29620i	−0.00997108	−	0.426433i
$219$	−4.79185	+	11.5686i	−0.323803	+	0.781730i
$220$	−2.00085	+	0.0936211i	−0.134897	+	0.00631194i
$221$	11.0730	+	13.1742i	0.744850	+	0.886194i
$222$	6.79075	+	2.62858i	0.455766	+	0.176419i
$223$			8.17921i			0.547721i	0.961769	+	0.273860i	$0.0883006\pi$
$223$			8.17921i			0.547721i	−0.961769	+	0.273860i	$0.911699\pi$
$224$	−10.2742	−	18.3854i	−0.686471	−	1.22843i
$225$	10.9423			0.729486
$226$	3.23503	−	8.35749i	0.215191	−	0.555932i
$227$	19.1203	−	7.91990i	1.26906	−	0.525662i	0.356382	−	0.934340i	$-0.384010\pi$
$227$	19.1203	−	7.91990i	1.26906	−	0.525662i	0.912679	+	0.408678i	$0.134010\pi$
$228$	2.64374	−	0.123702i	0.175086	−	0.00819239i
$229$	−8.16200	+	19.7048i	−0.539360	+	1.30213i	0.385811	+	0.922578i	$0.373922\pi$
$229$	−8.16200	+	19.7048i	−0.539360	+	1.30213i	−0.925170	+	0.379552i	$0.876078\pi$
$230$	0.0664900	+	2.84357i	0.00438422	+	0.187500i
$231$	−4.90902	−	4.90902i	−0.322990	−	0.322990i
$232$	−4.97469	+	5.72644i	−0.326604	+	0.375959i
$233$	−14.9937	+	14.9937i	−0.982272	+	0.982272i	−0.999846	−	0.0175738i	$-0.994406\pi$
$233$	−14.9937	+	14.9937i	−0.982272	+	0.982272i	0.0175738	+	0.999846i	$0.494406\pi$
$234$	5.12359	−	10.4524i	0.334939	−	0.683294i
$235$	0.237710	−	0.573882i	0.0155065	−	0.0374359i
$236$	2.35538	−	1.10730i	0.153322	−	0.0720792i
$237$	−1.11678	+	0.462583i	−0.0725423	+	0.0300480i
$238$	10.1577	+	22.9877i	0.658428	+	1.49007i
$239$	3.22230			0.208433			0.104217	−	0.994555i	$-0.466766\pi$
$239$	3.22230			0.208433			0.104217	+	0.994555i	$0.466766\pi$
$240$	0.143858	+	1.53389i	0.00928600	+	0.0990119i
$241$	−23.7981			−1.53297			−0.766486	−	0.642261i	$-0.777997\pi$
$241$	−23.7981			−1.53297			−0.766486	+	0.642261i	$0.777997\pi$
$242$	3.51604	+	7.95708i	0.226020	+	0.511500i
$243$	14.7936	−	6.12771i	0.949010	−	0.393093i
$244$	−6.29568	+	17.4668i	−0.403040	+	1.11820i
$245$	−2.88343	−	1.19435i	−0.184215	−	0.0763045i
$246$	3.45022	−	3.61544i	0.219978	−	0.230512i
$247$	4.99993	+	2.59756i	0.318138	+	0.165279i
$248$	−4.82241	+	2.40630i	−0.306224	+	0.152800i
$249$	7.22716	−	7.22716i	0.458002	−	0.458002i
$250$	−6.29747	+	0.147251i	−0.398287	+	0.00931296i
$251$	−12.7453	−	5.27928i	−0.804476	−	0.333225i	−0.0577284	−	0.998332i	$-0.518386\pi$
$251$	−12.7453	−	5.27928i	−0.804476	−	0.333225i	−0.746748	+	0.665107i	$0.768386\pi$
$252$	11.4453	−	12.5690i	0.720989	−	0.791772i
$253$	−8.99595	+	3.72624i	−0.565571	+	0.234267i
$254$	10.5211	+	4.07253i	0.660152	+	0.255533i
$255$		−	1.83838i		−	0.115124i
$256$	−15.7210	+	2.97501i	−0.982562	+	0.185938i
$257$	15.1870			0.947336			0.473668	−	0.880703i	$-0.342930\pi$
$257$	15.1870			0.947336			0.473668	+	0.880703i	$0.342930\pi$
$258$	−11.6822	−	4.52196i	−0.727300	−	0.281525i
$259$	8.66333	+	20.9151i	0.538313	+	1.29960i
$260$	−1.37437	+	2.97797i	−0.0852346	+	0.184686i
$261$	−5.65643	−	2.34297i	−0.350124	−	0.145026i
$262$	−0.709522	−	30.3441i	−0.0438344	−	1.87467i
$263$	12.7085	+	12.7085i	0.783637	+	0.783637i	0.980443	−	0.196806i	$-0.0630568\pi$
$263$	12.7085	+	12.7085i	0.783637	+	0.783637i	−0.196806	+	0.980443i	$0.563057\pi$
$264$	−4.71916	+	2.35478i	−0.290444	+	0.144927i
$265$	0.390093	+	0.390093i	0.0239632	+	0.0239632i
$266$	5.95262	+	5.68060i	0.364979	+	0.348300i
$267$	−6.40154	−	2.65160i	−0.391768	−	0.162276i
$268$	15.6864	+	5.65397i	0.958200	+	0.345371i
$269$	11.2281	−	4.65084i	0.684591	−	0.283567i	−0.0131537	−	0.999913i	$-0.504187\pi$
$269$	11.2281	−	4.65084i	0.684591	−	0.283567i	0.697745	+	0.716347i	$0.254187\pi$
$270$	−2.63204	+	1.16304i	−0.160181	+	0.0707801i
$271$	32.1579			1.95345			0.976726	−	0.214492i	$-0.0688095\pi$
$271$	32.1579			1.95345			0.976726	+	0.214492i	$0.0688095\pi$
$272$	19.0089	−	1.78279i	1.15259	−	0.108097i
$273$	−10.8387	+	3.42724i	−0.655987	+	0.207426i
$274$	−11.3873	−	25.7704i	−0.687932	−	1.55684i
$275$	−4.03897	−	9.75093i	−0.243559	−	0.588003i
$276$	3.18627	+	6.77762i	0.191791	+	0.407965i
$277$	4.39442	−	10.6091i	0.264035	−	0.637438i	−0.735145	−	0.677910i	$-0.762886\pi$
$277$	4.39442	−	10.6091i	0.264035	−	0.637438i	0.999181	+	0.0404718i	$0.0128861\pi$
$278$	1.35540	−	1.42031i	0.0812916	−	0.0851842i
$279$	−3.07590	−	3.07590i	−0.184149	−	0.184149i
$280$	−3.14114	+	3.61581i	−0.187719	+	0.216086i
$281$	−1.05901	+	1.05901i	−0.0631752	+	0.0631752i	−0.737989	−	0.674813i	$-0.764224\pi$
$281$	−1.05901	+	1.05901i	−0.0631752	+	0.0631752i	0.674813	+	0.737989i	$0.264224\pi$
$282$	−0.0382326	−	1.63509i	−0.00227672	−	0.0973683i
$283$	2.68510	+	1.11220i	0.159612	+	0.0661136i	0.461059	−	0.887369i	$-0.347470\pi$
$283$	2.68510	+	1.11220i	0.159612	+	0.0661136i	−0.301447	+	0.953483i	$0.597470\pi$
$284$	−26.1500	+	1.22358i	−1.55172	+	0.0726060i
$285$	−0.230331	−	0.556067i	−0.0136436	−	0.0329386i
$286$	−11.2056	−	0.707610i	−0.662599	−	0.0418419i
$287$	15.5370			0.917119
$288$	−6.29975	−	11.2733i	−0.371216	−	0.664285i
$289$	−5.78240			−0.340141
$290$	1.60873	+	0.622712i	0.0944681	+	0.0365669i
$291$	−7.17710	+	2.97285i	−0.420729	+	0.174272i
$292$	1.38226	+	29.5415i	0.0808909	+	1.72878i
$293$	−10.9800	+	26.5081i	−0.641459	+	1.54862i	0.183252	+	0.983066i	$0.441337\pi$
$293$	−10.9800	+	26.5081i	−0.641459	+	1.54862i	−0.824712	+	0.565554i	$0.808663\pi$
$294$	−8.21540	+	0.192097i	−0.479132	+	0.0112033i
$295$	−0.418527	−	0.418527i	−0.0243676	−	0.0243676i
$296$	17.1557	−	1.20519i	0.997157	−	0.0700504i
$297$	−6.96557	−	6.96557i	−0.404183	−	0.404183i
$298$	19.3184	+	18.4357i	1.11909	+	1.06795i
$299$	−1.37651	+	15.8843i	−0.0796055	+	0.918611i
$300$	−7.34643	+	3.45367i	−0.424147	+	0.199398i
$301$	−14.9036	−	35.9804i	−0.859028	−	2.07388i
$302$	3.83370	+	8.67596i	0.220604	+	0.499245i
$303$		−	6.78489i		−	0.389782i
$304$	5.52641	−	2.92089i	0.316961	−	0.167524i
$305$	4.22235			0.241771
$306$	6.22836	+	14.0953i	0.356052	+	0.805773i
$307$	1.38482	+	3.34324i	0.0790357	+	0.190809i	0.958458	−	0.285233i	$-0.0920710\pi$
$307$	1.38482	+	3.34324i	0.0790357	+	0.190809i	−0.879422	+	0.476042i	$0.842071\pi$
$308$	−15.4252	−	5.55981i	−0.878931	−	0.316800i
$309$	3.89103	−	9.39377i	0.221353	−	0.534393i
$310$	0.886677	+	0.846159i	0.0503599	+	0.0480586i
$311$	−15.4889	+	15.4889i	−0.878295	+	0.878295i	−0.993358	−	0.115063i	$-0.963293\pi$
$311$	−15.4889	+	15.4889i	−0.878295	+	0.878295i	0.115063	+	0.993358i	$0.463293\pi$
$312$	−0.140824	+	8.63467i	−0.00797261	+	0.488842i
$313$	7.06224	+	7.06224i	0.399182	+	0.399182i	0.877944	−	0.478763i	$-0.158915\pi$
$313$	7.06224	+	7.06224i	0.399182	+	0.399182i	−0.478763	+	0.877944i	$0.658915\pi$
$314$	−0.0555968	−	2.37771i	−0.00313751	−	0.134182i
$315$	−3.57161	−	1.47941i	−0.201237	−	0.0833553i
$316$	−1.92217	+	2.11088i	−0.108131	+	0.118746i
$317$	17.9537	−	7.43666i	1.00838	−	0.417685i	0.183517	−	0.983017i	$-0.441252\pi$
$317$	17.9537	−	7.43666i	1.00838	−	0.417685i	0.824864	+	0.565332i	$0.191252\pi$
$318$	1.35463	+	0.524352i	0.0759638	+	0.0294042i
$319$			5.90541i			0.330639i
$320$	1.84876	+	3.13396i	0.103349	+	0.175194i
$321$	−9.40742			−0.525071
$322$	−8.40490	+	21.7135i	−0.468387	+	1.21005i
$323$	−6.89116	+	2.85441i	−0.383434	+	0.158824i
$324$	4.12105	−	4.52564i	0.228947	−	0.251424i
$325$	−17.2174	−	1.49203i	−0.955047	−	0.0827630i
$326$	−5.94569	+	0.139025i	−0.329301	+	0.00769990i
$327$	−2.66658	+	2.66658i	−0.147462	+	0.147462i
$328$	3.74161	−	11.1945i	0.206596	−	0.618111i
$329$	3.59547	−	3.59547i	0.198225	−	0.198225i
$330$	0.867692	+	0.828042i	0.0477649	+	0.0455822i
$331$	31.1813	+	12.9157i	1.71388	+	0.709913i	0.999953	+	0.00969293i	$0.00308540\pi$
$331$	31.1813	+	12.9157i	1.71388	+	0.709913i	0.713927	+	0.700220i	$0.246915\pi$
$332$	8.18526	−	22.7092i	0.449224	−	1.24633i
$333$	5.31205	+	12.8244i	0.291098	+	0.702774i
$334$	−7.66261	+	3.38592i	−0.419279	+	0.185269i
$335$		−	3.79197i		−	0.207177i
$336$	−3.71707	+	12.0510i	−0.202783	+	0.657437i
$337$		−	25.2724i		−	1.37668i	−0.725390	−	0.688338i	$-0.758341\pi$
$337$		−	25.2724i		−	1.37668i	0.725390	−	0.688338i	$-0.241659\pi$
$338$	−9.48704	+	15.7479i	−0.516027	+	0.856572i
$339$	−4.95770	+	2.05355i	−0.269265	+	0.111533i
$340$	−1.84724	−	3.92933i	−0.100181	−	0.213098i
$341$	−1.60564	+	3.87637i	−0.0869505	+	0.209917i
$342$	3.64994	+	3.48315i	0.197366	+	0.188347i
$343$	0.363521	+	0.363521i	0.0196283	+	0.0196283i
$344$	−29.5131	+	2.07330i	−1.59124	+	0.111785i
$345$	1.20431	−	1.20431i	0.0648381	−	0.0648381i
$346$	7.92056	−	0.185203i	0.425812	−	0.00995657i
$347$	15.5949	+	6.45963i	0.837180	+	0.346771i	0.759741	−	0.650226i	$-0.225326\pi$
$347$	15.5949	+	6.45963i	0.837180	+	0.346771i	0.0774390	+	0.996997i	$0.475326\pi$
$348$	4.53712	−	0.212295i	0.243215	−	0.0113802i
$349$	0.798682	−	0.330825i	0.0427525	−	0.0177087i	−0.361205	−	0.932487i	$-0.617634\pi$
$349$	0.798682	−	0.330825i	0.0427525	−	0.0177087i	0.403957	+	0.914778i	$0.367634\pi$
$350$	−23.5358	−	9.11028i	−1.25804	−	0.486965i
$351$	−15.3794	+	4.86303i	−0.820889	+	0.259569i
$352$	−7.72055	+	9.77500i	−0.411507	+	0.521009i
$353$		−	10.7419i		−	0.571732i	−0.958270	−	0.285866i	$-0.907719\pi$
$353$		−	10.7419i		−	0.571732i	0.958270	−	0.285866i	$-0.0922812\pi$
$354$	−1.45337	−	0.562572i	−0.0772456	−	0.0299004i
$355$	2.27827	+	5.50023i	0.120918	+	0.291922i
$356$	−16.3470	+	0.764886i	−0.866388	+	0.0405389i
$357$	5.75888	−	13.9032i	0.304792	−	0.735833i
$358$	−16.7019	+	0.390533i	−0.882723	+	0.0206403i
$359$	−18.2124	+	18.2124i	−0.961213	+	0.961213i	−0.999275	−	0.0380622i	$-0.987882\pi$
$359$	−18.2124	+	18.2124i	−0.961213	+	0.961213i	0.0380622	+	0.999275i	$0.487882\pi$
$360$	−1.92603	+	2.21709i	−0.101511	+	0.116851i
$361$	11.7082	−	11.7082i	0.616223	−	0.616223i
$362$	21.8630	−	22.9099i	1.14909	−	1.20412i
$363$	1.99340	−	4.81250i	0.104627	−	0.252591i
$364$	−19.7227	+	18.2163i	−1.03375	+	0.954793i
$365$	6.21356	−	2.57374i	0.325232	−	0.134716i
$366$	10.1690	−	4.49343i	0.531541	−	0.234875i
$367$			30.0980i			1.57110i	0.618796	+	0.785552i	$0.287621\pi$
$367$			30.0980i			1.57110i	−0.618796	+	0.785552i	$0.712379\pi$
$368$	13.6206	+	11.2848i	0.710023	+	0.588261i
$369$	9.52673			0.495942
$370$	−1.58076	−	3.57739i	−0.0821799	−	0.185980i
$371$	1.72817	+	4.17218i	0.0897222	+	0.216609i
$372$	3.03593	+	1.09426i	0.157406	+	0.0567349i
$373$	7.26825	−	17.5471i	0.376336	−	0.908555i	−0.616310	−	0.787503i	$-0.711373\pi$
$373$	7.26825	−	17.5471i	0.376336	−	0.908555i	0.992646	−	0.121052i	$-0.0386266\pi$
$374$	10.2616	−	10.7530i	0.530617	−	0.556026i
$375$	2.66711	+	2.66711i	0.137729	+	0.137729i
$376$	−1.72469	−	3.45641i	−0.0889442	−	0.178251i
$377$	8.58075	+	4.45787i	0.441931	+	0.229592i
$378$	−23.5488	+	0.550630i	−1.21122	+	0.0283213i
$379$	−5.15020	+	12.4337i	−0.264548	+	0.638676i	−0.999209	−	0.0397584i	$-0.987341\pi$
$379$	−5.15020	+	12.4337i	−0.264548	+	0.638676i	0.734661	+	0.678434i	$0.237341\pi$
$380$	−1.05105	−	0.957092i	−0.0539179	−	0.0490978i
$381$	−2.58517	−	6.24116i	−0.132442	−	0.319744i
$382$	17.3337	+	6.70955i	0.886867	+	0.343290i
$383$			31.9824i			1.63422i	0.576479	+	0.817112i	$0.304426\pi$
$383$			31.9824i			1.63422i	−0.576479	+	0.817112i	$0.695574\pi$
$384$	7.78767	+	5.58029i	0.397413	+	0.284768i
$385$			3.72882i			0.190038i
$386$	−12.8011	+	33.0707i	−0.651557	+	1.68325i
$387$	−9.13834	−	22.0619i	−0.464528	−	1.12147i
$388$	−12.3531	+	13.5658i	−0.627133	+	0.688701i
$389$	32.8613	+	13.6116i	1.66613	+	0.690135i	0.998521	−	0.0543748i	$-0.0173166\pi$
$389$	32.8613	+	13.6116i	1.66613	+	0.690135i	0.667612	+	0.744509i	$0.267317\pi$
$390$	1.85817	−	0.635713i	0.0940923	−	0.0321906i
$391$	−14.9247	−	14.9247i	−0.754773	−	0.754773i
$392$	−17.3665	+	8.66559i	−0.877140	+	0.437678i
$393$	−12.8514	+	12.8514i	−0.648266	+	0.648266i
$394$	−11.3638	+	11.9080i	−0.572501	+	0.599915i
$395$	0.599828	+	0.248457i	0.0301806	+	0.0125012i
$396$	−9.45818	−	3.40908i	−0.475291	−	0.171313i
$397$	−5.60355	−	13.5282i	−0.281234	−	0.678959i	0.718631	−	0.695392i	$-0.244769\pi$
$397$	−5.60355	−	13.5282i	−0.281234	−	0.678959i	−0.999865	+	0.0164328i	$0.994769\pi$
$398$	5.68857	+	12.8737i	0.285142	+	0.645299i
$399$		−	4.92692i		−	0.246655i
$400$	−12.2319	+	14.7637i	−0.611594	+	0.738185i
$401$	−8.87282			−0.443087			−0.221544	−	0.975150i	$-0.571110\pi$
$401$	−8.87282			−0.443087			−0.221544	+	0.975150i	$0.571110\pi$
$402$	−4.03542	−	9.13247i	−0.201268	−	0.455486i
$403$	4.42042	+	5.25924i	0.220197	+	0.261982i
$404$	−6.81760	−	14.5020i	−0.339188	−	0.721500i
$405$	−1.28601	−	0.532681i	−0.0639022	−	0.0264691i
$406$	10.2157	+	9.74891i	0.506998	+	0.483830i
$407$	9.46739	−	9.46739i	0.469281	−	0.469281i
$408$	−8.63044	−	7.49745i	−0.427270	−	0.371179i
$409$	−3.52806	+	3.52806i	−0.174451	+	0.174451i	−0.788932	−	0.614481i	$-0.789366\pi$
$409$	−3.52806	+	3.52806i	−0.174451	+	0.174451i	0.614481	+	0.788932i	$0.289366\pi$
$410$	−2.68349	+	0.0627467i	−0.132528	+	0.00309884i
$411$	−6.45598	+	15.5861i	−0.318450	+	0.768806i
$412$	−1.12241	−	23.9879i	−0.0552973	−	1.18180i
$413$	−1.85414	−	4.47629i	−0.0912362	−	0.220264i
$414$	−5.15359	+	13.3139i	−0.253285	+	0.654345i
$415$	−5.48964			−0.269476
$416$	8.37530	+	18.5972i	0.410633	+	0.911801i
$417$	−1.17557			−0.0575680
$418$	1.75667	−	4.53823i	0.0859214	−	0.221972i
$419$	−6.43484	−	15.5351i	−0.314362	−	0.758938i	−0.999533	−	0.0305554i	$-0.990272\pi$
$419$	−6.43484	−	15.5351i	−0.314362	−	0.758938i	0.685171	−	0.728383i	$-0.259728\pi$
$420$	2.86485	−	0.134048i	0.139790	−	0.00654088i
$421$	−1.14862	+	2.77302i	−0.0559805	+	0.135149i	−0.949395	−	0.314084i	$-0.898303\pi$
$421$	−1.14862	+	2.77302i	−0.0559805	+	0.135149i	0.893415	+	0.449233i	$0.148303\pi$
$422$	17.9123	−	0.418835i	0.871957	−	0.0203886i
$423$	2.20462	−	2.20462i	0.107192	−	0.107192i
$424$	3.42225	−	0.240413i	0.166199	−	0.0116755i
$425$	16.1772	−	16.1772i	0.784711	−	0.784711i
$426$	11.3403	+	10.8221i	0.549438	+	0.524330i
$427$	31.9325	+	13.2269i	1.54532	+	0.640094i
$428$	−20.1073	+	9.45277i	−0.971924	+	0.456917i
$429$	4.32577	+	5.14664i	0.208850	+	0.248482i
$430$	2.71939	+	6.15420i	0.131141	+	0.296782i
$431$	−6.01180			−0.289578			−0.144789	−	0.989463i	$-0.546250\pi$
$431$	−6.01180			−0.289578			−0.144789	+	0.989463i	$0.546250\pi$
$432$	−5.27427	+	17.0996i	−0.253759	+	0.822704i
$433$		−	35.1333i		−	1.68840i	−0.536031	−	0.844198i	$-0.680077\pi$
$433$		−	35.1333i		−	1.68840i	0.536031	−	0.844198i	$-0.319923\pi$
$434$	4.05504	+	9.17687i	0.194648	+	0.440504i
$435$	−0.395287	−	0.954308i	−0.0189526	−	0.0457556i
$436$	−3.02009	+	8.37895i	−0.144636	+	0.401279i
$437$	−6.38429	−	2.64446i	−0.305402	−	0.126502i
$438$	12.2256	−	12.8110i	0.584161	−	0.612133i
$439$	23.9687	−	23.9687i	1.14396	−	1.14396i	0.156244	−	0.987718i	$-0.450061\pi$
$439$	23.9687	−	23.9687i	1.14396	−	1.14396i	0.987718	−	0.156244i	$-0.0499387\pi$
$440$	2.68663	+	0.897973i	0.128080	+	0.0428092i
$441$	−11.0769	−	11.0769i	−0.527473	−	0.527473i
$442$	−7.87818	−	23.0277i	−0.374727	−	1.09532i
$443$	−22.0314	−	9.12572i	−1.04675	−	0.433576i	−0.208016	−	0.978125i	$-0.566701\pi$
$443$	−22.0314	−	9.12572i	−1.04675	−	0.433576i	−0.838729	+	0.544549i	$0.816701\pi$
$444$	−7.61413	−	6.93344i	−0.361351	−	0.329046i
$445$	1.42420	+	3.43832i	0.0675134	+	0.162992i
$446$	4.17554	−	10.7872i	0.197717	−	0.510789i
$447$		−	15.9897i		−	0.756285i
$448$	4.16428	+	29.4927i	0.196744	+	1.39340i
$449$			22.1167i			1.04375i	0.853022	+	0.521875i	$0.174767\pi$
$449$			22.1167i			1.04375i	−0.853022	+	0.521875i	$0.825233\pi$
$450$	−14.4313	−	5.58610i	−0.680299	−	0.263331i
$451$	−3.51646	−	8.48949i	−0.165584	−	0.399755i
$452$	−8.53309	+	9.37083i	−0.401363	+	0.440767i
$453$	2.17350	−	5.24729i	0.102120	−	0.246539i
$454$	−29.2601	+	0.684177i	−1.37325	+	0.0321100i
$455$	5.41809	+	2.81481i	0.254004	+	0.131960i
$456$	−3.54987	−	1.18650i	−0.166238	−	0.0555629i
$457$	6.66019	+	6.66019i	0.311551	+	0.311551i	0.845510	−	0.533959i	$-0.179296\pi$
$457$	6.66019	+	6.66019i	0.311551	+	0.311551i	−0.533959	+	0.845510i	$0.679296\pi$
$458$	20.8239	−	21.8211i	0.973038	−	1.01963i
$459$	8.17146	−	19.7276i	0.381411	−	0.920807i
$460$	1.36397	−	3.78421i	0.0635954	−	0.176440i
$461$	−7.77024	−	18.7590i	−0.361896	−	0.873695i	−0.995023	−	0.0996467i	$-0.968229\pi$
$461$	−7.77024	−	18.7590i	−0.361896	−	0.873695i	0.633127	−	0.774048i	$-0.281771\pi$
$462$	3.96821	+	8.98038i	0.184618	+	0.417805i
$463$	−1.69268			−0.0786656			−0.0393328	−	0.999226i	$-0.512523\pi$
$463$	−1.69268			−0.0786656			−0.0393328	+	0.999226i	$0.512523\pi$
$464$	9.48428	−	5.01275i	0.440297	−	0.232711i
$465$		−	0.733893i		−	0.0340335i
$466$	27.4290	−	12.1202i	1.27062	−	0.561457i
$467$	−0.497912	+	0.206242i	−0.0230406	+	0.00954373i	−0.394174	−	0.919036i	$-0.628969\pi$
$467$	−0.497912	+	0.206242i	−0.0230406	+	0.00954373i	0.371133	+	0.928580i	$0.378969\pi$
$468$	−12.0933	+	11.1696i	−0.559012	+	0.516315i
$469$	11.8787	−	28.6777i	0.548506	−	1.32421i
$470$	−0.606475	+	0.635516i	−0.0279746	+	0.0293142i
$471$	−1.00701	+	1.00701i	−0.0464006	+	0.0464006i
$472$	−3.67170	+	0.257937i	−0.169003	+	0.0118725i
$473$	−16.2868	+	16.2868i	−0.748867	+	0.748867i
$474$	1.70902	−	0.0399612i	0.0784978	−	0.00183548i
$475$	2.86640	−	6.92009i	0.131519	−	0.317515i
$476$	−1.66121	−	35.5031i	−0.0761417	−	1.62728i
$477$	1.05965	+	2.55823i	0.0485182	+	0.117133i
$478$	−4.24975	−	1.64500i	−0.194379	−	0.0752407i
$479$			4.66766i			0.213271i	0.994298	+	0.106635i	$0.0340078\pi$
$479$			4.66766i			0.213271i	−0.994298	+	0.106635i	$0.965992\pi$
$480$	0.593330	−	2.09642i	0.0270817	−	0.0956879i
$481$	−6.60968	−	20.9031i	−0.301375	−	0.953102i
$482$	31.3863	+	12.1491i	1.42961	+	0.553375i
$483$	12.8805	−	5.33529i	0.586085	−	0.242764i
$484$	−0.575020	−	12.2892i	−0.0261373	−	0.558600i
$485$	3.85487	+	1.59674i	0.175041	+	0.0725043i
$486$	−22.6389	+	0.529354i	−1.02692	+	0.0240120i
$487$	−7.50622	+	7.50622i	−0.340140	+	0.340140i	−0.856420	−	0.516280i	$-0.827316\pi$
$487$	−7.50622	+	7.50622i	−0.340140	+	0.340140i	0.516280	+	0.856420i	$0.327316\pi$
$488$	17.2200	−	19.8222i	0.779513	−	0.897310i
$489$	2.51813	+	2.51813i	0.113874	+	0.113874i
$490$	3.19310	+	3.04719i	0.144250	+	0.137658i
$491$	−2.81860	+	6.80471i	−0.127202	+	0.307092i	−0.974632	−	0.223815i	$-0.928149\pi$
$491$	−2.81860	+	6.80471i	−0.127202	+	0.307092i	0.847430	+	0.530907i	$0.178149\pi$
$492$	−6.39605	+	3.00689i	−0.288356	+	0.135561i
$493$	−11.8264	+	4.89867i	−0.532636	+	0.220625i
$494$	−5.26812	−	5.97831i	−0.237024	−	0.268977i
$495$			2.28638i			0.102765i
$496$	7.58851	−	0.711701i	0.340734	−	0.0319563i
$497$			48.7336i			2.18600i
$498$	−13.2211	+	5.84208i	−0.592451	+	0.261790i
$499$	−10.5156	−	25.3870i	−0.470745	−	1.13648i	−0.963835	−	0.266500i	$-0.914133\pi$
$499$	−10.5156	−	25.3870i	−0.470745	−	1.13648i	0.493090	−	0.869978i	$-0.335867\pi$
$500$	8.38063	+	3.02069i	0.374793	+	0.135089i
$501$	4.63441	+	1.91963i	0.207050	+	0.0857629i
$502$	14.1141	+	13.4692i	0.629944	+	0.601158i
$503$	14.3069	−	14.3069i	0.637914	−	0.637914i	−0.312127	−	0.950040i	$-0.601041\pi$
$503$	14.3069	−	14.3069i	0.637914	−	0.637914i	0.950040	+	0.312127i	$0.101041\pi$
$504$	−21.5113	+	10.7338i	−0.958190	+	0.478121i
$505$	−2.57685	+	2.57685i	−0.114668	+	0.114668i
$506$	13.7666	−	0.321899i	0.612002	−	0.0143102i
$507$	10.7437	−	2.40039i	0.477143	−	0.106605i
$508$	−11.7968	−	10.7422i	−0.523397	−	0.476606i
$509$	1.98819	−	0.823535i	0.0881249	−	0.0365025i	−0.338186	−	0.941079i	$-0.609813\pi$
$509$	1.98819	−	0.823535i	0.0881249	−	0.0365025i	0.426310	+	0.904577i	$0.359813\pi$
$510$	−0.938502	+	2.42456i	−0.0415576	+	0.107361i
$511$	55.0540			2.43544
$512$	22.2525	+	4.10205i	0.983430	+	0.181287i
$513$		−	6.99096i		−	0.308659i
$514$	−20.0294	−	7.75303i	−0.883460	−	0.341971i
$515$	−5.04547	+	2.08990i	−0.222330	+	0.0920920i
$516$	13.0986	+	11.9276i	0.576635	+	0.525085i
$517$	−2.77834	−	1.15083i	−0.122191	−	0.0506133i
$518$	−0.748399	−	32.0067i	−0.0328828	−	1.40630i
$519$	−3.35453	−	3.35453i	−0.147247	−	0.147247i
$520$	3.33287	−	3.22590i	0.146156	−	0.141465i
$521$	−23.0964	+	23.0964i	−1.01187	+	1.01187i	−0.0119427	+	0.999929i	$0.503802\pi$
$521$	−23.0964	+	23.0964i	−1.01187	+	1.01187i	−0.999929	+	0.0119427i	$0.996198\pi$
$522$	6.26393	+	5.97769i	0.274165	+	0.261636i
$523$	0.685452	−	1.65483i	0.0299727	−	0.0723605i	−0.908184	−	0.418570i	$-0.862531\pi$
$523$	0.685452	−	1.65483i	0.0299727	−	0.0723605i	0.938157	+	0.346210i	$0.112531\pi$
$524$	−14.5551	+	40.3818i	−0.635842	+	1.76409i
$525$	5.78306	+	13.9615i	0.252393	+	0.609331i
$526$	−10.2729	−	23.2484i	−0.447919	−	1.01368i
$527$	−9.09490			−0.396180
$528$	7.42603	−	0.696462i	0.323176	−	0.0303096i
$529$			3.44579i			0.149817i
$530$	−0.315333	−	0.713622i	−0.0136972	−	0.0309978i
$531$	−1.13689	−	2.74470i	−0.0493369	−	0.119110i
$532$	−4.95067	−	10.5308i	−0.214639	−	0.456566i
$533$	−14.9900	−	1.29901i	−0.649289	−	0.0562665i
$534$	7.08906	+	6.76511i	0.306773	+	0.292755i
$535$	3.57287	+	3.57287i	0.154468	+	0.154468i
$536$	−17.8018	−	15.4648i	−0.768919	−	0.667977i
$537$	7.07361	+	7.07361i	0.305249	+	0.305249i
$538$	−17.1826	+	0.401772i	−0.740793	+	0.0173216i
$539$	−5.78225	+	13.9596i	−0.249059	+	0.601282i
$540$	4.06502	−	0.190205i	0.174931	−	0.00818513i
$541$	38.2619	−	15.8486i	1.64501	−	0.681385i	0.648219	−	0.761454i	$-0.275514\pi$
$541$	38.2619	−	15.8486i	1.64501	−	0.681385i	0.996789	+	0.0800693i	$0.0255142\pi$
$542$	−42.4116	−	16.4168i	−1.82174	−	0.705161i
$543$	−18.9623			−0.813750
$544$	−25.9802	−	7.35294i	−1.11389	−	0.315255i
$545$	2.02549			0.0867626
$546$	16.0443	+	1.01317i	0.686633	+	0.0433595i
$547$	−12.7506	−	30.7827i	−0.545177	−	1.31617i	−0.921029	−	0.389494i	$-0.872650\pi$
$547$	−12.7506	−	30.7827i	−0.545177	−	1.31617i	0.375852	−	0.926680i	$-0.377350\pi$
$548$	1.86230	+	39.8007i	0.0795536	+	1.70020i
$549$	19.5799	+	8.11026i	0.835649	+	0.346137i
$550$	0.348914	+	14.9220i	0.0148778	+	0.636276i
$551$	−2.96347	+	2.96347i	−0.126248	+	0.126248i
$552$	−0.742215	−	10.5653i	−0.0315908	−	0.449690i
$553$	3.75803	+	3.75803i	0.159808	+	0.159808i
$554$	−11.2116	+	11.7485i	−0.476336	+	0.499145i
$555$	−0.896206	+	2.16363i	−0.0380418	+	0.0918411i
$556$	−2.51266	+	1.18124i	−0.106560	+	0.0500957i
$557$	1.28592	+	3.10449i	0.0544862	+	0.131541i	0.948779	−	0.315942i	$-0.102320\pi$
$557$	1.28592	+	3.10449i	0.0544862	+	0.131541i	−0.894292	+	0.447483i	$0.852320\pi$
$558$	2.48641	+	5.62693i	0.105258	+	0.238207i
$559$	11.3707	+	35.9598i	0.480928	+	1.52094i
$560$	5.98860	−	3.16517i	0.253065	−	0.133753i
$561$	−8.90017			−0.375765
$562$	1.93731	−	0.856052i	0.0817206	−	0.0361104i
$563$	−15.7221	+	6.51229i	−0.662606	+	0.274460i	−0.688535	−	0.725203i	$-0.741746\pi$
$563$	−15.7221	+	6.51229i	−0.662606	+	0.274460i	0.0259287	+	0.999664i	$0.491746\pi$
$564$	−0.784300	+	2.17597i	−0.0330250	+	0.0916249i
$565$	2.66282	+	1.10298i	0.112026	+	0.0464025i
$566$	−2.97347	−	2.83759i	−0.124984	−	0.119273i
$567$	−8.05706	−	8.05706i	−0.338365	−	0.338365i
$568$	35.1128	+	11.7360i	1.47330	+	0.492433i
$569$	15.2245	+	15.2245i	0.638246	+	0.638246i	0.950123	−	0.311877i	$-0.100958\pi$
$569$	15.2245	+	15.2245i	0.638246	+	0.638246i	−0.311877	+	0.950123i	$0.600958\pi$
$570$	0.0198976	+	0.850958i	0.000833417	+	0.0356427i
$571$	10.3898	+	4.30361i	0.434801	+	0.180100i	0.589338	−	0.807887i	$-0.299389\pi$
$571$	10.3898	+	4.30361i	0.434801	+	0.180100i	−0.154537	+	0.987987i	$0.549389\pi$
$572$	14.4173	+	6.65375i	0.602818	+	0.278207i
$573$	−4.25911	−	10.2824i	−0.177927	−	0.429554i
$574$	−20.4911	−	7.93172i	−0.855280	−	0.331063i
$575$	21.1953			0.883905
$576$	2.55339	+	18.0839i	0.106391	+	0.753496i
$577$		−	13.1232i		−	0.546324i	−0.961968	−	0.273162i	$-0.911930\pi$
$577$		−	13.1232i		−	0.546324i	0.961968	−	0.273162i	$-0.0880695\pi$
$578$	7.62616	+	2.95195i	0.317207	+	0.122785i
$579$	19.6177	−	8.12590i	0.815282	−	0.337701i
$580$	−1.80379	−	1.64254i	−0.0748984	−	0.0682026i
$581$	−41.5167	−	17.1968i	−1.72240	−	0.713442i
$582$	10.9832	−	0.256816i	0.455269	−	0.0106454i
$583$	1.88857	−	1.88857i	0.0782164	−	0.0782164i
$584$	13.2581	−	39.6666i	0.548623	−	1.64142i
$585$	3.32218	+	1.72594i	0.137355	+	0.0713589i
$586$	28.0136	−	29.3550i	1.15723	−	1.21265i
$587$	4.73123	+	1.95974i	0.195279	+	0.0808871i	0.478180	−	0.878262i	$-0.341297\pi$
$587$	4.73123	+	1.95974i	0.195279	+	0.0808871i	−0.282901	+	0.959149i	$0.591297\pi$
$588$	10.9330	+	3.94066i	0.450869	+	0.162510i
$589$	−2.75100	+	1.13950i	−0.113353	+	0.0469523i
$590$	0.338317	+	0.765638i	0.0139283	+	0.0315208i
$591$	9.85610			0.405426
$592$	−23.2412	−	7.16863i	−0.955209	−	0.294629i
$593$	27.9181			1.14646			0.573229	−	0.819395i	$-0.305691\pi$
$593$	27.9181			1.14646			0.573229	+	0.819395i	$0.305691\pi$
$594$	5.63063	+	12.7426i	0.231027	+	0.522833i
$595$	−7.46749	+	3.09314i	−0.306137	+	0.126806i
$596$	−16.0668	−	34.1762i	−0.658120	−	1.39991i
$597$	3.22511	−	7.78610i	0.131995	−	0.318664i
$598$	9.92443	−	20.2464i	0.405840	−	0.827935i
$599$	11.7315	−	11.7315i	0.479335	−	0.479335i	−0.425584	−	0.904919i	$-0.639931\pi$
$599$	11.7315	−	11.7315i	0.479335	−	0.479335i	0.904919	+	0.425584i	$0.139931\pi$
$600$	11.4520	−	0.804505i	0.467527	−	0.0328438i
$601$	7.74754	+	7.74754i	0.316029	+	0.316029i	0.847240	−	0.531211i	$-0.178263\pi$
$601$	7.74754	+	7.74754i	0.316029	+	0.316029i	−0.531211	+	0.847240i	$0.678263\pi$
$602$	1.28747	+	55.0614i	0.0524736	+	2.24413i
$603$	7.28358	−	17.5841i	0.296610	−	0.716081i
$604$	−0.626970	−	13.3995i	−0.0255111	−	0.545217i
$605$	−2.58483	+	1.07067i	−0.105088	+	0.0435290i
$606$	−3.46373	+	8.94830i	−0.140704	+	0.363500i
$607$	−34.8012			−1.41254			−0.706268	−	0.707945i	$-0.749623\pi$
$607$	−34.8012			−1.41254			−0.706268	+	0.707945i	$0.749623\pi$
$608$	−8.77967	+	1.03097i	−0.356063	+	0.0418113i
$609$		−	8.45545i		−	0.342632i
$610$	−5.56868	−	2.15553i	−0.225469	−	0.0872750i
$611$	−3.76950	+	3.16828i	−0.152498	+	0.128175i
$612$	−1.01860	−	21.7693i	−0.0411744	−	0.879970i
$613$	−11.6857	+	28.2118i	−0.471982	+	1.13947i	0.491304	+	0.870988i	$0.336520\pi$
$613$	−11.6857	+	28.2118i	−0.471982	+	1.13947i	−0.963286	+	0.268477i	$0.913480\pi$
$614$	−0.119630	−	5.11622i	−0.00482788	−	0.206474i
$615$	1.13651	+	1.13651i	0.0458286	+	0.0458286i
$616$	17.5053	+	15.2072i	0.705309	+	0.612717i
$617$	−24.7162	−	24.7162i	−0.995035	−	0.995035i	0.00495260	−	0.999988i	$-0.498424\pi$
$617$	−24.7162	−	24.7162i	−0.995035	−	0.995035i	−0.999988	+	0.00495260i	$0.998424\pi$
$618$	−9.92729	+	10.4027i	−0.399334	+	0.418456i
$619$	−14.9171	−	6.17885i	−0.599567	−	0.248349i	0.0621933	−	0.998064i	$-0.480190\pi$
$619$	−14.9171	−	6.17885i	−0.599567	−	0.248349i	−0.661761	+	0.749715i	$0.730190\pi$
$620$	−0.737431	−	1.56862i	−0.0296159	−	0.0629971i
$621$	18.2766	−	7.57042i	0.733415	−	0.303790i
$622$	28.3348	−	12.5205i	1.13612	−	0.502025i
$623$			30.4645i			1.22053i
$624$	4.59378	−	11.3160i	0.183898	−	0.453003i
$625$			21.9398i			0.877590i
$626$	−5.70877	−	12.9194i	−0.228168	−	0.516363i
$627$	−2.69210	+	1.11510i	−0.107512	+	0.0445329i
$628$	−1.14051	+	3.16424i	−0.0455113	+	0.126267i
$629$	26.8132	+	11.1064i	1.06911	+	0.442841i
$630$	3.95519	+	3.77446i	0.157579	+	0.150378i
$631$	−29.3183	−	29.3183i	−1.16714	−	1.16714i	−0.982876	−	0.184266i	$-0.941009\pi$
$631$	−29.3183	−	29.3183i	−1.16714	−	1.16714i	−0.184266	−	0.982876i	$-0.558991\pi$
$632$	3.61269	−	1.80267i	0.143705	−	0.0717064i
$633$	−7.58624	−	7.58624i	−0.301526	−	0.301526i
$634$	−27.4748	+	0.642431i	−1.09116	+	0.0255142i
$635$	−1.38852	+	3.35218i	−0.0551016	+	0.133027i
$636$	−1.51888	−	1.38309i	−0.0602273	−	0.0548431i
$637$	15.9188	+	18.9396i	0.630727	+	0.750414i
$638$	3.01475	−	7.78839i	0.119355	−	0.308345i
$639$			29.8818i			1.18210i
$640$	−0.838346	−	5.07705i	−0.0331386	−	0.200688i
$641$	20.3654			0.804385			0.402192	−	0.915555i	$-0.368248\pi$
$641$	20.3654			0.804385			0.402192	+	0.915555i	$0.368248\pi$
$642$	12.4070	+	4.80254i	0.489667	+	0.189541i
$643$	19.8915	−	8.23933i	0.784444	−	0.324927i	0.0457366	−	0.998954i	$-0.485437\pi$
$643$	19.8915	−	8.23933i	0.784444	−	0.324927i	0.738707	+	0.674026i	$0.235437\pi$
$644$	22.1697	−	24.3462i	0.873609	−	0.959376i
$645$	1.54175	−	3.72211i	0.0607063	−	0.146558i
$646$	10.5456	−	0.246584i	0.414913	−	0.00970172i
$647$	30.6117	+	30.6117i	1.20347	+	1.20347i	0.973104	+	0.230368i	$0.0739928\pi$
$647$	30.6117	+	30.6117i	1.20347	+	1.20347i	0.230368	+	0.973104i	$0.426007\pi$
$648$	−7.74544	+	3.86485i	−0.304270	+	0.151825i
$649$	−2.02622	+	2.02622i	−0.0795362	+	0.0795362i
$650$	21.9455	+	10.7573i	0.860775	+	0.421937i
$651$	2.29898	−	5.55024i	0.0901043	−	0.217531i
$652$	7.91249	+	2.85195i	0.309877	+	0.111691i
$653$	−1.79603	+	0.743938i	−0.0702839	+	0.0291125i	−0.417548	−	0.908655i	$-0.637111\pi$
$653$	−1.79603	+	0.743938i	−0.0702839	+	0.0291125i	0.347265	+	0.937767i	$0.387111\pi$
$654$	4.87814	−	2.15553i	0.190750	−	0.0842880i
$655$	9.76171			0.381422
$656$	−10.6495	+	12.8538i	−0.415793	+	0.501856i
$657$	33.7571			1.31699
$658$	−6.57742	+	2.90640i	−0.256414	+	0.113303i
$659$	−13.4376	+	5.56602i	−0.523453	+	0.216821i	−0.628733	−	0.777621i	$-0.716426\pi$
$659$	−13.4376	+	5.56602i	−0.523453	+	0.216821i	0.105280	+	0.994443i	$0.466426\pi$
$660$	−0.721642	−	1.53503i	−0.0280899	−	0.0597510i
$661$	−34.8486	−	14.4348i	−1.35545	−	0.561448i	−0.417649	−	0.908608i	$-0.637146\pi$
$661$	−34.8486	−	14.4348i	−1.35545	−	0.561448i	−0.937806	+	0.347161i	$0.887146\pi$
$662$	−34.5302	−	32.9522i	−1.34205	−	1.28073i
$663$	−6.71855	+	12.9322i	−0.260927	+	0.502246i
$664$	−22.3884	+	25.7716i	−0.868838	+	1.00013i
$665$	−1.87121	+	1.87121i	−0.0725623	+	0.0725623i
$666$	−0.458892	−	19.6254i	−0.0177817	−	0.760469i
$667$	−10.9566	−	4.53835i	−0.424239	−	0.175726i
$668$	11.8344	−	0.553740i	0.457887	−	0.0214249i
$669$	−6.39902	+	2.65056i	−0.247400	+	0.102477i
$670$	−1.93582	+	5.00106i	−0.0747873	+	0.193208i
$671$		−	20.4417i		−	0.789144i
$672$	11.0544	−	13.9960i	0.426433	−	0.539907i
$673$	−23.3132			−0.898658			−0.449329	−	0.893366i	$-0.648337\pi$
$673$	−23.3132			−0.898658			−0.449329	+	0.893366i	$0.648337\pi$
$674$	−12.9017	+	33.3307i	−0.496955	+	1.28385i
$675$	8.20576	+	19.8105i	0.315840	+	0.762505i
$676$	20.5514	−	15.9260i	0.790440	−	0.612540i
$677$	3.14253	+	1.30168i	0.120777	+	0.0500276i	0.442254	−	0.896890i	$-0.354179\pi$
$677$	3.14253	+	1.30168i	0.120777	+	0.0500276i	−0.321476	+	0.946918i	$0.604179\pi$
$678$	7.58684	−	0.177400i	0.291371	−	0.00681299i
$679$	24.1515	+	24.1515i	0.926848	+	0.926848i
$680$	0.430299	+	6.12525i	0.0165012	+	0.234893i
$681$	12.3923	+	12.3923i	0.474874	+	0.474874i
$682$	4.09652	−	4.29268i	0.156864	−	0.164375i
$683$	−42.3682	−	17.5495i	−1.62117	−	0.671512i	−0.626972	−	0.779042i	$-0.715706\pi$
$683$	−42.3682	−	17.5495i	−1.62117	−	0.671512i	−0.994202	+	0.107530i	$0.965706\pi$
$684$	−3.03558	−	6.45709i	−0.116068	−	0.246893i
$685$	8.37142	−	3.46756i	0.319856	−	0.132489i
$686$	−0.293853	−	0.665012i	−0.0112194	−	0.0253903i
$687$	−18.0611			−0.689073
$688$	39.9820	+	12.3322i	1.52430	+	0.470162i
$689$	−1.31851	−	4.16979i	−0.0502311	−	0.158856i
$690$	−2.20313	+	0.973509i	−0.0838717	+	0.0370609i
$691$	−1.34453	−	3.24597i	−0.0511482	−	0.123483i	0.896240	−	0.443569i	$-0.146288\pi$
$691$	−1.34453	−	3.24597i	−0.0511482	−	0.123483i	−0.947388	+	0.320087i	$0.896288\pi$
$692$	−10.5406	−	3.79924i	−0.400695	−	0.144425i
$693$	−7.16229	+	17.2913i	−0.272073	+	0.656842i
$694$	−17.2698	−	16.4806i	−0.655553	−	0.625597i
$695$	0.446473	+	0.446473i	0.0169357	+	0.0169357i
$696$	−6.09219	−	2.03624i	−0.230924	−	0.0771835i
$697$	14.0844	−	14.0844i	0.533486	−	0.533486i
$698$	−1.22224	+	0.0285790i	−0.0462623	+	0.00108173i
$699$	−16.5892	−	6.87149i	−0.627463	−	0.259904i
$700$	26.3895	+	24.0303i	0.997429	+	0.908260i
$701$	−5.12063	−	12.3623i	−0.193404	−	0.466918i	0.797194	−	0.603723i	$-0.206317\pi$
$701$	−5.12063	−	12.3623i	−0.193404	−	0.466918i	−0.990598	+	0.136805i	$0.956317\pi$
$702$	22.7658	+	1.43761i	0.859239	+	0.0542593i
$703$	9.50190			0.358371
$704$	15.1725	−	8.95044i	0.571835	−	0.337332i
$705$	0.526010			0.0198107
$706$	−5.48378	+	14.1670i	−0.206385	+	0.533181i
$707$	−27.5603	+	11.4158i	−1.03651	+	0.429336i
$708$	1.62959	+	1.48390i	0.0612436	+	0.0557685i
$709$	4.61619	−	11.1445i	0.173365	−	0.418539i	−0.813184	−	0.582006i	$-0.802268\pi$
$709$	4.61619	−	11.1445i	0.173365	−	0.418539i	0.986549	+	0.163467i	$0.0522678\pi$
$710$	−0.196813	−	8.41708i	−0.00738625	−	0.315887i
$711$	2.30429	+	2.30429i	0.0864177	+	0.0864177i
$712$	21.9498	+	7.33645i	0.822604	+	0.274945i
$713$	−5.95804	−	5.95804i	−0.223130	−	0.223130i
$714$	−14.6928	+	15.3963i	−0.549863	+	0.576194i
$715$	0.311758	−	3.59755i	0.0116591	−	0.134541i
$716$	22.2268	+	8.01136i	0.830654	+	0.299399i
$717$	1.04422	+	2.52097i	0.0389972	+	0.0941475i
$718$	33.3171	−	14.7220i	1.24338	−	0.549420i
$719$		−	4.72434i		−	0.176188i	−0.996112	−	0.0880941i	$-0.971922\pi$
$719$		−	4.72434i		−	0.176188i	0.996112	−	0.0880941i	$-0.0280776\pi$
$720$	3.67200	−	1.94077i	0.136847	−	0.0723283i
$721$	−44.7043			−1.66488
$722$	−21.4186	+	9.46437i	−0.797118	+	0.352227i
$723$	−7.71204	−	18.6185i	−0.286814	−	0.692430i
$724$	−40.5298	+	19.0537i	−1.50628	+	0.708125i
$725$	4.91923	−	11.8761i	0.182696	−	0.441066i
$726$	−5.08582	+	5.32936i	−0.188753	+	0.197791i
$727$	−17.8390	+	17.8390i	−0.661613	+	0.661613i	−0.955760	−	0.294147i	$-0.904964\pi$
$727$	−17.8390	+	17.8390i	−0.661613	+	0.661613i	0.294147	+	0.955760i	$0.404964\pi$
$728$	35.3110	−	13.9561i	1.30871	−	0.517248i
$729$	3.09594	+	3.09594i	0.114664	+	0.114664i
$730$	−9.50870	+	0.222338i	−0.351933	+	0.00822909i
$731$	−46.1269	−	19.1064i	−1.70606	−	0.706675i
$732$	−15.7054	+	0.734864i	−0.580487	+	0.0271614i
$733$	−10.0369	+	4.15740i	−0.370720	+	0.153557i	−0.560262	−	0.828315i	$-0.689300\pi$
$733$	−10.0369	+	4.15740i	−0.370720	+	0.153557i	0.189542	+	0.981873i	$0.439300\pi$
$734$	15.3652	−	39.6950i	0.567140	−	1.46517i
$735$		−	2.64290i		−	0.0974848i
$736$	−12.2027	−	21.8364i	−0.449796	−	0.804902i
$737$	−18.3581			−0.676230
$738$	−12.5644	−	4.86345i	−0.462502	−	0.179026i
$739$	−2.23357	+	0.925176i	−0.0821633	+	0.0340331i	−0.423387	−	0.905949i	$-0.639159\pi$
$739$	−2.23357	+	0.925176i	−0.0821633	+	0.0340331i	0.341223	+	0.939982i	$0.389159\pi$
$740$	0.258521	+	5.52506i	0.00950342	+	0.203105i
$741$	−0.411929	+	4.75347i	−0.0151326	+	0.174623i
$742$	−0.149292	−	6.38475i	−0.00548067	−	0.234391i
$743$	26.4798	−	26.4798i	0.971448	−	0.971448i	−0.0281553	−	0.999604i	$-0.508963\pi$
$743$	26.4798	−	26.4798i	0.971448	−	0.971448i	0.999604	+	0.0281553i	$0.00896329\pi$
$744$	−3.44533	−	2.99304i	−0.126312	−	0.109730i
$745$	−6.07276	+	6.07276i	−0.222489	+	0.222489i
$746$	−18.5437	+	19.4316i	−0.678933	+	0.711443i
$747$	−25.4566	−	10.5445i	−0.931407	−	0.385801i
$748$	−19.0231	+	8.94307i	−0.695554	+	0.326991i
$749$	15.8283	+	38.2130i	0.578354	+	1.39627i
$750$	−2.15596	−	4.87912i	−0.0787247	−	0.178160i
$751$		−	11.7260i		−	0.427887i	−0.976846	−	0.213944i	$-0.931369\pi$
$751$		−	11.7260i		−	0.427887i	0.976846	−	0.213944i	$-0.0686309\pi$
$752$	0.510104	+	5.43898i	0.0186016	+	0.198339i
$753$		−	11.6821i		−	0.425720i
$754$	−9.04101	−	10.2598i	−0.329254	−	0.373641i
$755$	−2.81836	+	1.16740i	−0.102571	+	0.0424861i
$756$	31.3385	+	11.2956i	1.13977	+	0.410816i
$757$	3.48173	−	8.40563i	0.126546	−	0.305508i	−0.847891	−	0.530170i	$-0.822128\pi$
$757$	3.48173	−	8.40563i	0.126546	−	0.305508i	0.974437	+	0.224662i	$0.0721280\pi$
$758$	13.1399	−	13.7691i	0.477261	−	0.500114i
$759$	−5.83047	−	5.83047i	−0.211633	−	0.211633i
$760$	0.897589	+	1.79884i	0.0325590	+	0.0652507i
$761$	9.64890	−	9.64890i	0.349772	−	0.349772i	−0.510252	−	0.860025i	$-0.670448\pi$
$761$	9.64890	−	9.64890i	0.349772	−	0.349772i	0.860025	+	0.510252i	$0.170448\pi$
$762$	0.223325	+	9.55094i	0.00809022	+	0.345994i
$763$	15.3183	+	6.34503i	0.554558	+	0.229706i
$764$	−19.4354	−	17.6979i	−0.703147	−	0.640286i
$765$	−4.57880	+	1.89660i	−0.165547	+	0.0685718i
$766$	16.3272	−	42.1802i	0.589925	−	1.52403i
$767$	1.41461	+	4.47372i	0.0510787	+	0.161537i
$768$	−7.42205	−	11.3353i	−0.267820	−	0.409026i
$769$			8.27933i			0.298560i	0.988795	+	0.149280i	$0.0476956\pi$

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:	\( N \)	\(=\)	\( 416 = 2^{5} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	416.bg (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31886 - 0.510506i) q^{2} +(0.324061 + 0.782352i) q^{3} +(1.47877 + 1.34657i) q^{4} +(0.174055 - 0.420207i) q^{5} +(-0.0279946 - 1.19725i) q^{6} +(2.63267 - 2.63267i) q^{7} +(-1.26285 - 2.53085i) q^{8} +(1.61426 - 1.61426i) q^{9} +O(q^{10})\)	\(q+(-1.31886 - 0.510506i) q^{2} +(0.324061 + 0.782352i) q^{3} +(1.47877 + 1.34657i) q^{4} +(0.174055 - 0.420207i) q^{5} +(-0.0279946 - 1.19725i) q^{6} +(2.63267 - 2.63267i) q^{7} +(-1.26285 - 2.53085i) q^{8} +(1.61426 - 1.61426i) q^{9} +(-0.444072 + 0.465337i) q^{10} +(-2.03436 - 0.842658i) q^{11} +(-0.574280 + 1.59329i) q^{12} +(-2.76010 + 2.31988i) q^{13} +(-4.81611 + 2.12812i) q^{14} +0.385154 q^{15} +(0.373508 + 3.98252i) q^{16} -4.77309i q^{17} +(-2.95307 + 1.30489i) q^{18} +(-0.598021 - 1.44375i) q^{19} +(0.823225 - 0.387011i) q^{20} +(2.91282 + 1.20653i) q^{21} +(2.25284 + 2.14990i) q^{22} +(3.12684 - 3.12684i) q^{23} +(1.57077 - 1.80814i) q^{24} +(3.38926 + 3.38926i) q^{25} +(4.82449 - 1.65054i) q^{26} +(4.13309 + 1.71198i) q^{27} +(7.43818 - 0.348037i) q^{28} +(-1.02631 - 2.47773i) q^{29} +(-0.507964 - 0.196624i) q^{30} -1.90545i q^{31} +(1.54050 - 5.44306i) q^{32} -1.86465i q^{33} +(-2.43669 + 6.29503i) q^{34} +(-0.648036 - 1.56450i) q^{35} +(4.56083 - 0.213404i) q^{36} +(-2.32688 + 5.61757i) q^{37} +(0.0516613 + 2.20940i) q^{38} +(-2.70940 - 1.40759i) q^{39} +(-1.28329 + 0.0901511i) q^{40} +(2.95080 + 2.95080i) q^{41} +(-3.22565 - 3.07825i) q^{42} +(4.00294 - 9.66394i) q^{43} +(-1.87364 - 3.98549i) q^{44} +(-0.397353 - 0.959295i) q^{45} +(-5.72012 + 2.52758i) q^{46} +1.36571 q^{47} +(-2.99470 + 1.58279i) q^{48} -6.86192i q^{49} +(-2.73971 - 6.20018i) q^{50} +(3.73424 - 1.54677i) q^{51} +(-7.20542 - 0.286105i) q^{52} +(-0.464168 + 1.12060i) q^{53} +(-4.57698 - 4.36783i) q^{54} +(-0.708182 + 0.708182i) q^{55} +(-9.98757 - 3.33822i) q^{56} +(0.935726 - 0.935726i) q^{57} +(0.0886598 + 3.79171i) q^{58} +(0.498001 - 1.20228i) q^{59} +(0.569554 + 0.518637i) q^{60} +(3.55260 + 8.57672i) q^{61} +(-0.972744 + 2.51302i) q^{62} -8.49964i q^{63} +(-4.81041 + 6.39218i) q^{64} +(0.494419 + 1.56360i) q^{65} +(-0.951917 + 2.45921i) q^{66} +(7.70250 - 3.19048i) q^{67} +(6.42729 - 7.05829i) q^{68} +(3.45957 + 1.43300i) q^{69} +(0.0559819 + 2.39418i) q^{70} +(-9.25555 + 9.25555i) q^{71} +(-6.12403 - 2.04688i) q^{72} +(10.4559 + 10.4559i) q^{73} +(5.93662 - 6.22089i) q^{74} +(-1.55327 + 3.74991i) q^{75} +(1.05978 - 2.94025i) q^{76} +(-7.57423 + 3.13735i) q^{77} +(2.85473 + 3.23957i) q^{78} +1.42746i q^{79} +(1.73850 + 0.536229i) q^{80} -3.06041i q^{81} +(-2.38528 - 5.39808i) q^{82} +(-4.61887 - 11.1509i) q^{83} +(2.68271 + 5.70649i) q^{84} +(-2.00569 - 0.830783i) q^{85} +(-10.2128 + 10.7018i) q^{86} +(1.60587 - 1.60587i) q^{87} +(0.436450 + 6.21280i) q^{88} +(-5.78585 + 5.78585i) q^{89} +(0.0343261 + 1.46802i) q^{90} +(-1.15896 + 13.3739i) q^{91} +(8.83436 - 0.413366i) q^{92} +(1.49073 - 0.617482i) q^{93} +(-1.80118 - 0.697204i) q^{94} -0.710764 q^{95} +(4.75760 - 0.558669i) q^{96} +9.17375i q^{97} +(-3.50305 + 9.04989i) q^{98} +(-4.64425 + 1.92371i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9}+O(q^{10}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9	\( 216 q - 8 q^{3} - 8 q^{4} - 8 q^{9} - 8 q^{10} - 24 q^{12} - 4 q^{13} + 24 q^{14} - 8 q^{16} + 8 q^{22} - 8 q^{23} - 8 q^{25} + 16 q^{26} - 56 q^{27} - 8 q^{29} - 24 q^{30} - 8 q^{35} + 16 q^{36} - 48 q^{38} - 28 q^{39} + 32 q^{40} + 32 q^{42} - 8 q^{43} - 112 q^{48} + 16 q^{51} - 12 q^{52} - 8 q^{53} - 40 q^{55} - 48 q^{56} - 8 q^{61} + 56 q^{62} - 8 q^{64} - 8 q^{65} - 56 q^{66} - 8 q^{69} - 8 q^{74} - 16 q^{75} - 8 q^{77} + 84 q^{78} - 88 q^{82} - 8 q^{87} + 72 q^{88} + 88 q^{90} + 44 q^{91} - 80 q^{92} + 24 q^{94} + 112 q^{95}+O(q^{100}) \) 216 * q - 8 * q^3 - 8 * q^4 - 8 * q^9 - 8 * q^10 - 24 * q^12 - 4 * q^13 + 24 * q^14 - 8 * q^16 + 8 * q^22 - 8 * q^23 - 8 * q^25 + 16 * q^26 - 56 * q^27 - 8 * q^29 - 24 * q^30 - 8 * q^35 + 16 * q^36 - 48 * q^38 - 28 * q^39 + 32 * q^40 + 32 * q^42 - 8 * q^43 - 112 * q^48 + 16 * q^51 - 12 * q^52 - 8 * q^53 - 40 * q^55 - 48 * q^56 - 8 * q^61 + 56 * q^62 - 8 * q^64 - 8 * q^65 - 56 * q^66 - 8 * q^69 - 8 * q^74 - 16 * q^75 - 8 * q^77 + 84 * q^78 - 88 * q^82 - 8 * q^87 + 72 * q^88 + 88 * q^90 + 44 * q^91 - 80 * q^92 + 24 * q^94 + 112 * q^95

Introduction

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