LMFDB - Embedded newform 384.2.v.a.37.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.06625543762$
Analytic rank:	$0$
Dimension:	$512$
Relative dimension:	$32$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			37.19
Character	$\chi$	$=$	384.37
Dual form			384.2.v.a.301.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.249021 + 1.39212i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.87598 + 0.693333i) q^{4} +(0.986309 - 0.809443i) q^{5} +(1.11035 - 0.875856i) q^{6} +(1.86960 - 1.24923i) q^{7} +(-1.43236 - 2.43892i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(0.249021 + 1.39212i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.87598 + 0.693333i) q^{4} +(0.986309 - 0.809443i) q^{5} +(1.11035 - 0.875856i) q^{6} +(1.86960 - 1.24923i) q^{7} +(-1.43236 - 2.43892i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(1.37245 + 1.17149i) q^{10} +(-0.801248 - 2.64136i) q^{11} +(1.49579 + 1.32763i) q^{12} +(0.812353 - 0.989855i) q^{13} +(2.20464 + 2.29162i) q^{14} +(-1.17881 - 0.488278i) q^{15} +(3.03858 - 2.60135i) q^{16} +(6.22260 - 2.57749i) q^{17} +(-1.29585 - 0.566365i) q^{18} +(-2.45384 + 0.241682i) q^{19} +(-1.28908 + 2.20234i) q^{20} +(-1.98305 - 1.05996i) q^{21} +(3.47755 - 1.77319i) q^{22} +(4.61128 - 0.917241i) q^{23} +(-1.47573 + 2.41293i) q^{24} +(-0.657844 + 3.30721i) q^{25} +(1.58029 + 0.884395i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-2.64120 + 3.63978i) q^{28} +(3.05321 + 0.926180i) q^{29} +(0.386192 - 1.76263i) q^{30} +(-1.35822 - 1.35822i) q^{31} +(4.37806 + 3.58226i) q^{32} +(-1.95177 + 1.95177i) q^{33} +(5.13772 + 8.02074i) q^{34} +(0.832827 - 2.74546i) q^{35} +(0.465751 - 1.94501i) q^{36} +(-0.392832 + 3.98849i) q^{37} +(-0.947508 - 3.35585i) q^{38} +(-1.25591 - 0.249817i) q^{39} +(-3.38692 - 1.24612i) q^{40} +(0.0227335 + 0.114289i) q^{41} +(0.981768 - 3.02459i) q^{42} +(0.604945 - 1.13177i) q^{43} +(3.33446 + 4.39960i) q^{44} +(0.125063 + 1.26979i) q^{45} +(2.42521 + 6.19103i) q^{46} +(-3.37897 - 8.15756i) q^{47} +(-3.72657 - 1.45352i) q^{48} +(-0.743939 + 1.79603i) q^{49} +(-4.76783 - 0.0922310i) q^{50} +(-5.20645 - 4.27283i) q^{51} +(-0.837656 + 2.42018i) q^{52} +(-7.45329 + 2.26093i) q^{53} +(0.111371 + 1.40982i) q^{54} +(-2.92831 - 1.95663i) q^{55} +(-5.72472 - 2.77048i) q^{56} +(1.36988 + 2.05016i) q^{57} +(-0.529037 + 4.48106i) q^{58} +(-6.40092 - 7.79954i) q^{59} +(2.54995 + 0.0986918i) q^{60} +(-0.976284 + 0.521835i) q^{61} +(1.55257 - 2.22902i) q^{62} +2.24855i q^{63} +(-3.89670 + 6.98683i) q^{64} -1.63386i q^{65} +(-3.20312 - 2.23105i) q^{66} +(0.00283170 - 0.00151358i) q^{67} +(-9.88640 + 9.14964i) q^{68} +(-2.98268 - 3.63440i) q^{69} +(4.02940 + 0.475714i) q^{70} +(-0.720817 - 1.07878i) q^{71} +(2.82367 + 0.164030i) q^{72} +(5.09139 + 3.40196i) q^{73} +(-5.65026 + 0.446351i) q^{74} +(3.22680 - 0.978839i) q^{75} +(4.43578 - 2.15472i) q^{76} +(-4.79768 - 3.93735i) q^{77} +(0.0350248 - 1.81059i) q^{78} +(-5.69280 + 13.7436i) q^{79} +(0.891329 - 5.02529i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.153442 + 0.0601080i) q^{82} +(-0.758662 - 7.70283i) q^{83} +(4.45506 + 0.613549i) q^{84} +(4.05108 - 7.57904i) q^{85} +(1.72620 + 0.560318i) q^{86} +(-0.622454 - 3.12929i) q^{87} +(-5.29440 + 5.73756i) q^{88} +(16.8111 + 3.34393i) q^{89} +(-1.73655 + 0.490307i) q^{90} +(0.282222 - 2.86545i) q^{91} +(-8.01470 + 4.91788i) q^{92} +(-0.557581 + 1.83810i) q^{93} +(10.5148 - 6.73533i) q^{94} +(-2.22462 + 2.22462i) q^{95} +(1.09547 - 5.54977i) q^{96} +(-1.56493 - 1.56493i) q^{97} +(-2.68554 - 0.588401i) q^{98} +(2.64136 + 0.801248i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{25}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.249021	+	1.39212i	0.176085	+	0.984375i
$2$	0.249021	+	1.39212i	0.176085	+	0.984375i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$3$	−0.471397	−	0.881921i	−0.272161	−	0.509177i
$4$	−1.87598	+	0.693333i	−0.937988	+	0.346667i
$5$	0.986309	−	0.809443i	0.441091	−	0.361994i	−0.387480	−	0.921878i	$-0.626654\pi$
$5$	0.986309	−	0.809443i	0.441091	−	0.361994i	0.828571	+	0.559884i	$0.189154\pi$
$6$	1.11035	−	0.875856i	0.453298	−	0.357567i
$7$	1.86960	−	1.24923i	0.706644	−	0.472164i	−0.149593	−	0.988748i	$-0.547796\pi$
$7$	1.86960	−	1.24923i	0.706644	−	0.472164i	0.856237	+	0.516583i	$0.172796\pi$
$8$	−1.43236	−	2.43892i	−0.506415	−	0.862290i
$9$	−0.555570	+	0.831470i	−0.185190	+	0.277157i
$10$	1.37245	+	1.17149i	0.434007	+	0.370457i
$11$	−0.801248	−	2.64136i	−0.241585	−	0.796400i	−0.990949	−	0.134241i	$-0.957140\pi$
$11$	−0.801248	−	2.64136i	−0.241585	−	0.796400i	0.749363	−	0.662159i	$-0.230360\pi$
$12$	1.49579	+	1.32763i	0.431799	+	0.383253i
$13$	0.812353	−	0.989855i	0.225306	−	0.274536i	−0.648072	−	0.761579i	$-0.724424\pi$
$13$	0.812353	−	0.989855i	0.225306	−	0.274536i	0.873378	+	0.487043i	$0.161924\pi$
$14$	2.20464	+	2.29162i	0.589216	+	0.612462i
$15$	−1.17881	−	0.488278i	−0.304367	−	0.126073i
$16$	3.03858	−	2.60135i	0.759644	−	0.650339i
$17$	6.22260	−	2.57749i	1.50920	−	0.625132i	0.533809	−	0.845605i	$-0.320760\pi$
$17$	6.22260	−	2.57749i	1.50920	−	0.625132i	0.975393	+	0.220473i	$0.0707600\pi$
$18$	−1.29585	−	0.566365i	−0.305435	−	0.133493i
$19$	−2.45384	+	0.241682i	−0.562949	+	0.0554457i	−0.375490	−	0.926827i	$-0.622525\pi$
$19$	−2.45384	+	0.241682i	−0.562949	+	0.0554457i	−0.187460	+	0.982272i	$0.560025\pi$
$20$	−1.28908	+	2.20234i	−0.288247	+	0.492457i
$21$	−1.98305	−	1.05996i	−0.432736	−	0.231302i
$22$	3.47755	−	1.77319i	0.741417	−	0.378044i
$23$	4.61128	−	0.917241i	0.961519	−	0.191258i	0.310714	−	0.950503i	$-0.399432\pi$
$23$	4.61128	−	0.917241i	0.961519	−	0.191258i	0.650804	+	0.759245i	$0.274432\pi$
$24$	−1.47573	+	2.41293i	−0.301232	+	0.492537i
$25$	−0.657844	+	3.30721i	−0.131569	+	0.661441i
$26$	1.58029	+	0.884395i	0.309920	+	0.173444i
$27$	0.995185	+	0.0980171i	0.191523	+	0.0188634i
$28$	−2.64120	+	3.63978i	−0.499140	+	0.687855i
$29$	3.05321	+	0.926180i	0.566966	+	0.171987i	0.560738	−	0.827993i	$-0.310517\pi$
$29$	3.05321	+	0.926180i	0.566966	+	0.171987i	0.00622825	+	0.999981i	$0.498017\pi$
$30$	0.386192	−	1.76263i	0.0705086	−	0.321811i
$31$	−1.35822	−	1.35822i	−0.243943	−	0.243943i	0.574536	−	0.818479i	$-0.305182\pi$
$31$	−1.35822	−	1.35822i	−0.243943	−	0.243943i	−0.818479	+	0.574536i	$0.805182\pi$
$32$	4.37806	+	3.58226i	0.773939	+	0.633260i
$33$	−1.95177	+	1.95177i	−0.339759	+	0.339759i
$34$	5.13772	+	8.02074i	0.881112	+	1.37555i
$35$	0.832827	−	2.74546i	0.140773	−	0.464068i
$36$	0.465751	−	1.94501i	0.0776252	−	0.324169i
$37$	−0.392832	+	3.98849i	−0.0645811	+	0.655703i	0.907340	+	0.420397i	$0.138109\pi$
$37$	−0.392832	+	3.98849i	−0.0645811	+	0.655703i	−0.971921	+	0.235306i	$0.924391\pi$
$38$	−0.947508	−	3.35585i	−0.153706	−	0.544390i
$39$	−1.25591	−	0.249817i	−0.201107	−	0.0400027i
$40$	−3.38692	−	1.24612i	−0.535519	−	0.197029i
$41$	0.0227335	+	0.114289i	0.00355037	+	0.0178489i	0.982520	−	0.186158i	$-0.0596036\pi$
$41$	0.0227335	+	0.114289i	0.00355037	+	0.0178489i	−0.978969	+	0.204007i	$0.934604\pi$
$42$	0.981768	−	3.02459i	0.151490	−	0.466704i
$43$	0.604945	−	1.13177i	0.0922532	−	0.172594i	−0.831562	−	0.555431i	$-0.812553\pi$
$43$	0.604945	−	1.13177i	0.0922532	−	0.172594i	0.923816	+	0.382838i	$0.125053\pi$
$44$	3.33446	+	4.39960i	0.502690	+	0.663264i
$45$	0.125063	+	1.26979i	0.0186433	+	0.189289i
$46$	2.42521	+	6.19103i	0.357578	+	0.912817i
$47$	−3.37897	−	8.15756i	−0.492874	−	1.18990i	−0.953251	−	0.302179i	$-0.902286\pi$
$47$	−3.37897	−	8.15756i	−0.492874	−	1.18990i	0.460378	−	0.887723i	$-0.347714\pi$
$48$	−3.72657	−	1.45352i	−0.537883	−	0.209797i
$49$	−0.743939	+	1.79603i	−0.106277	+	0.256575i
$50$	−4.76783	−	0.0922310i	−0.674273	−	0.0130434i
$51$	−5.20645	−	4.27283i	−0.729049	−	0.598315i
$52$	−0.837656	+	2.42018i	−0.116162	+	0.335618i
$53$	−7.45329	+	2.26093i	−1.02379	+	0.310563i	−0.757155	−	0.653235i	$-0.773411\pi$
$53$	−7.45329	+	2.26093i	−1.02379	+	0.310563i	−0.266633	+	0.963798i	$0.585911\pi$
$54$	0.111371	+	1.40982i	0.0151557	+	0.191852i
$55$	−2.92831	−	1.95663i	−0.394853	−	0.263832i
$56$	−5.72472	−	2.77048i	−0.764998	−	0.370220i
$57$	1.36988	+	2.05016i	0.181445	+	0.271551i
$58$	−0.529037	+	4.48106i	−0.0694660	+	0.588392i
$59$	−6.40092	−	7.79954i	−0.833328	−	1.01541i	−0.999570	−	0.0293283i	$-0.990663\pi$
$59$	−6.40092	−	7.79954i	−0.833328	−	1.01541i	0.166242	−	0.986085i	$-0.446837\pi$
$60$	2.54995	+	0.0986918i	0.329198	+	0.0127411i
$61$	−0.976284	+	0.521835i	−0.125000	+	0.0668141i	−0.532712	−	0.846297i	$-0.678827\pi$
$61$	−0.976284	+	0.521835i	−0.125000	+	0.0668141i	0.407711	+	0.913111i	$0.366327\pi$
$62$	1.55257	−	2.22902i	0.197177	−	0.283086i
$63$			2.24855i			0.283291i
$64$	−3.89670	+	6.98683i	−0.487087	+	0.873353i
$65$		−	1.63386i		−	0.202655i
$66$	−3.20312	−	2.23105i	−0.394276	−	0.274624i
$67$	0.00283170	−	0.00151358i	0.000345947	−	0.000184913i	−0.471224	−	0.882014i	$-0.656188\pi$
$67$	0.00283170	−	0.00151358i	0.000345947	−	0.000184913i	0.471570	+	0.881829i	$0.343688\pi$
$68$	−9.88640	+	9.14964i	−1.19890	+	1.10956i
$69$	−2.98268	−	3.63440i	−0.359072	−	0.437531i
$70$	4.02940	+	0.475714i	0.481605	+	0.0568587i
$71$	−0.720817	−	1.07878i	−0.0855452	−	0.128027i	0.786229	−	0.617935i	$-0.212031\pi$
$71$	−0.720817	−	1.07878i	−0.0855452	−	0.128027i	−0.871774	+	0.489908i	$0.837031\pi$
$72$	2.82367	+	0.164030i	0.332772	+	0.0193312i
$73$	5.09139	+	3.40196i	0.595902	+	0.398169i	0.816626	−	0.577167i	$-0.195842\pi$
$73$	5.09139	+	3.40196i	0.595902	+	0.398169i	−0.220724	+	0.975336i	$0.570842\pi$
$74$	−5.65026	+	0.446351i	−0.656830	+	0.0518872i
$75$	3.22680	−	0.978839i	0.372599	−	0.113027i
$76$	4.43578	−	2.15472i	0.508819	−	0.247163i
$77$	−4.79768	−	3.93735i	−0.546746	−	0.448703i
$78$	0.0350248	−	1.81059i	0.00396578	−	0.205009i
$79$	−5.69280	+	13.7436i	−0.640491	+	1.54628i	0.185529	+	0.982639i	$0.440600\pi$
$79$	−5.69280	+	13.7436i	−0.640491	+	1.54628i	−0.826019	+	0.563642i	$0.809400\pi$
$80$	0.891329	−	5.02529i	0.0996536	−	0.561845i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−0.153442	+	0.0601080i	−0.0169449	+	0.00663781i
$83$	−0.758662	−	7.70283i	−0.0832740	−	0.845495i	−0.942568	−	0.334014i	$-0.891597\pi$
$83$	−0.758662	−	7.70283i	−0.0832740	−	0.845495i	0.859294	−	0.511482i	$-0.170903\pi$
$84$	4.45506	+	0.613549i	0.486087	+	0.0669437i
$85$	4.05108	−	7.57904i	0.439401	−	0.822062i
$86$	1.72620	+	0.560318i	0.186141	+	0.0604206i
$87$	−0.622454	−	3.12929i	−0.0667341	−	0.335495i
$88$	−5.29440	+	5.73756i	−0.564385	+	0.611626i
$89$	16.8111	+	3.34393i	1.78197	+	0.354456i	0.972536	−	0.232754i	$-0.0747738\pi$
$89$	16.8111	+	3.34393i	1.78197	+	0.354456i	0.809434	+	0.587210i	$0.199774\pi$
$90$	−1.73655	+	0.490307i	−0.183048	+	0.0516829i
$91$	0.282222	−	2.86545i	0.0295849	−	0.300381i
$92$	−8.01470	+	4.91788i	−0.835591	+	0.512724i
$93$	−0.557581	+	1.83810i	−0.0578185	+	0.190602i
$94$	10.5148	−	6.73533i	1.08452	−	0.694696i
$95$	−2.22462	+	2.22462i	−0.228241	+	0.228241i
$96$	1.09547	−	5.54977i	0.111806	−	0.566421i
$97$	−1.56493	−	1.56493i	−0.158895	−	0.158895i	0.623182	−	0.782077i	$-0.285840\pi$
$97$	−1.56493	−	1.56493i	−0.158895	−	0.158895i	−0.782077	+	0.623182i	$0.785840\pi$
$98$	−2.68554	−	0.588401i	−0.271280	−	0.0594374i
$99$	2.64136	+	0.801248i	0.265467	+	0.0805284i
$100$	−1.05890	−	6.66035i	−0.105890	−	0.666035i
$101$	−16.1314	−	1.58881i	−1.60514	−	0.158092i	−0.744610	−	0.667500i	$-0.767365\pi$
$101$	−16.1314	−	1.58881i	−1.60514	−	0.158092i	−0.860525	+	0.509408i	$0.829865\pi$
$102$	4.65175	−	8.31202i	0.460592	−	0.823012i
$103$	−3.61968	+	18.1974i	−0.356658	+	1.79304i	0.219403	+	0.975634i	$0.429589\pi$
$103$	−3.61968	+	18.1974i	−0.356658	+	1.79304i	−0.576061	+	0.817407i	$0.695411\pi$
$104$	−3.57776	−	0.563439i	−0.350828	−	0.0552498i
$105$	−2.81387	+	0.559714i	−0.274606	+	0.0546225i
$106$	−5.00351	−	9.81283i	−0.485984	−	0.953106i
$107$	14.6281	+	7.81889i	1.41415	+	0.755880i	0.988814	−	0.149154i	$-0.0476551\pi$
$107$	14.6281	+	7.81889i	1.41415	+	0.755880i	0.425338	+	0.905034i	$0.360155\pi$
$108$	−1.93490	+	0.506117i	−0.186186	+	0.0487011i
$109$	−3.52115	+	0.346803i	−0.337265	+	0.0332177i	−0.265232	−	0.964185i	$-0.585449\pi$
$109$	−3.52115	+	0.346803i	−0.337265	+	0.0332177i	−0.0720328	+	0.997402i	$0.522949\pi$
$110$	1.99465	−	4.56379i	0.190182	−	0.435140i
$111$	3.70271	−	1.53371i	0.351446	−	0.145574i
$112$	2.43125	−	8.65938i	0.229731	−	0.818235i
$113$	8.97247	+	3.71652i	0.844059	+	0.349621i	0.762453	−	0.647044i	$-0.223995\pi$
$113$	8.97247	+	3.71652i	0.844059	+	0.349621i	0.0816065	+	0.996665i	$0.473995\pi$
$114$	−2.51294	+	2.41756i	−0.235358	+	0.226425i
$115$	3.80569	−	4.63725i	0.354883	−	0.432426i
$116$	−6.36990	+	0.379397i	−0.591430	+	0.0352262i
$117$	0.371715	+	1.22538i	0.0343651	+	0.113286i
$118$	9.26390	−	10.8531i	0.852811	−	0.999106i
$119$	8.41393	−	12.5923i	0.771304	−	1.15434i
$120$	0.497603	+	3.57441i	0.0454247	+	0.326298i
$121$	2.81138	−	1.87851i	0.255580	−	0.170773i
$122$	−0.969570	−	1.22915i	−0.0877808	−	0.111282i
$123$	0.0900772	−	0.0739245i	0.00812199	−	0.00666555i
$124$	3.48968	+	1.60629i	0.313383	+	0.144249i
$125$	5.03551	+	9.42077i	0.450389	+	0.842619i
$126$	−3.13025	+	0.559938i	−0.278865	+	0.0498832i
$127$	−17.1546			−1.52223			−0.761113	−	0.648619i	$-0.775347\pi$
$127$	−17.1546			−1.52223			−0.761113	+	0.648619i	$0.775347\pi$
$128$	−10.6968	−	3.68479i	−0.945476	−	0.325692i
$129$	−1.28330			−0.112988
$130$	2.27452	−	0.406865i	0.199488	−	0.0356844i
$131$	1.77392	+	3.31876i	0.154988	+	0.289962i	0.947417	−	0.320003i	$-0.103684\pi$
$131$	1.77392	+	3.31876i	0.154988	+	0.289962i	−0.792429	+	0.609964i	$0.791184\pi$
$132$	2.30824	−	5.01469i	0.200907	−	0.436473i
$133$	−4.28579	+	3.51726i	−0.371625	+	0.304985i
$134$	0.00281223	+	0.00356514i	0.000242939	+	0.000307981i
$135$	1.06090	−	0.708870i	0.0913076	−	0.0610098i
$136$	−15.1993	−	11.4846i	−1.30333	−	0.984793i
$137$	−7.55474	+	11.3065i	−0.645445	+	0.965977i	0.354081	+	0.935215i	$0.384794\pi$
$137$	−7.55474	+	11.3065i	−0.645445	+	0.965977i	−0.999527	+	0.0307625i	$0.990206\pi$
$138$	4.31676	−	5.05728i	0.367467	−	0.430504i
$139$	−2.91350	−	9.60451i	−0.247120	−	0.814644i	−0.989483	−	0.144647i	$-0.953795\pi$
$139$	−2.91350	−	9.60451i	−0.247120	−	0.814644i	0.742364	−	0.669997i	$-0.233705\pi$
$140$	0.341157	+	5.72785i	0.0288330	+	0.484092i
$141$	−5.60149	+	6.82543i	−0.471730	+	0.574805i
$142$	1.32229	−	1.27210i	0.110964	−	0.106752i
$143$	−3.26546	−	1.35260i	−0.273071	−	0.113110i
$144$	0.474804	+	3.97172i	0.0395670	+	0.330977i
$145$	3.76109	−	1.55790i	0.312342	−	0.129376i
$146$	−3.46806	+	7.93497i	−0.287018	+	0.656702i
$147$	1.93465	−	0.190546i	0.159567	−	0.0157160i
$148$	−2.02841	−	7.75467i	−0.166734	−	0.637430i
$149$	−10.6657	−	5.70093i	−0.873767	−	0.467038i	−0.0273913	−	0.999625i	$-0.508720\pi$
$149$	−10.6657	−	5.70093i	−0.873767	−	0.467038i	−0.846375	+	0.532587i	$0.821220\pi$
$150$	2.16620	+	4.24833i	0.176870	+	0.346875i
$151$	5.49436	−	1.09290i	0.447125	−	0.0889386i	0.0336078	−	0.999435i	$-0.489300\pi$
$151$	5.49436	−	1.09290i	0.447125	−	0.0889386i	0.413517	+	0.910497i	$0.364300\pi$
$152$	4.10422	+	5.63855i	0.332896	+	0.457347i
$153$	−1.31399	+	6.60588i	−0.106230	+	0.534054i
$154$	4.28653	−	7.65942i	0.345419	−	0.617213i
$155$	−2.43902	−	0.240222i	−0.195907	−	0.0192951i
$156$	2.52927	−	0.402117i	0.202504	−	0.0321951i
$157$	5.17234	+	1.56901i	0.412798	+	0.125221i	0.489851	−	0.871806i	$-0.337051\pi$
$157$	5.17234	+	1.56901i	0.412798	+	0.125221i	−0.0770533	+	0.997027i	$0.524551\pi$
$158$	−20.5504	−	4.50259i	−1.63490	−	0.358207i
$159$	5.50742	+	5.50742i	0.436767	+	0.436767i
$160$	7.21775	−	0.0105715i	0.570613	−	0.000835753i
$161$	7.47543	−	7.47543i	0.589146	−	0.589146i
$162$	1.19085	−	0.762806i	0.0935621	−	0.0599317i
$163$	−2.44245	+	8.05167i	−0.191307	+	0.630656i	0.807841	+	0.589400i	$0.200636\pi$
$163$	−2.44245	+	8.05167i	−0.191307	+	0.630656i	−0.999149	+	0.0412556i	$0.986864\pi$
$164$	−0.121888	−	0.198641i	−0.00951783	−	0.0155113i
$165$	−0.345201	+	3.50489i	−0.0268739	+	0.272855i
$166$	10.5343	−	2.97431i	0.817621	−	0.230852i
$167$	7.44052	+	1.48001i	0.575765	+	0.114527i	0.474379	−	0.880321i	$-0.342673\pi$
$167$	7.44052	+	1.48001i	0.575765	+	0.114527i	0.101385	+	0.994847i	$0.467673\pi$
$168$	0.255272	+	6.35475i	0.0196947	+	0.490279i
$169$	2.21628	+	11.1420i	0.170483	+	0.857076i
$170$	11.5597	+	3.75223i	0.886589	+	0.287783i
$171$	1.16233	−	2.17456i	0.0888855	−	0.166293i
$172$	−0.350167	+	2.54261i	−0.0267000	+	0.193872i
$173$	2.10014	+	21.3230i	0.159670	+	1.62116i	0.657202	+	0.753715i	$0.271740\pi$
$173$	2.10014	+	21.3230i	0.159670	+	1.62116i	−0.497531	+	0.867446i	$0.665760\pi$
$174$	4.20133	−	1.64579i	0.318502	−	0.124767i
$175$	2.90155	+	7.00496i	0.219337	+	0.529525i
$176$	−9.30577	−	5.94165i	−0.701449	−	0.447869i
$177$	−3.86121	+	9.32178i	−0.290226	+	0.700668i
$178$	−0.468826	+	24.2357i	−0.0351400	+	1.81654i
$179$	13.7812	+	11.3100i	1.03006	+	0.845346i	0.988106	−	0.153773i	$-0.0491426\pi$
$179$	13.7812	+	11.3100i	1.03006	+	0.845346i	0.0419514	+	0.999120i	$0.486643\pi$
$180$	−1.11500	−	2.29538i	−0.0831073	−	0.171088i
$181$	21.5295	−	6.53089i	1.60027	−	0.485438i	0.640911	−	0.767615i	$-0.278557\pi$
$181$	21.5295	−	6.53089i	1.60027	−	0.485438i	0.959362	+	0.282178i	$0.0910567\pi$
$182$	4.05932	−	0.320672i	0.300897	−	0.0237698i
$183$	0.920434	+	0.615014i	0.0680404	+	0.0454632i
$184$	−8.84209	−	9.93275i	−0.651848	−	0.732252i
$185$	2.84100	+	4.25185i	0.208874	+	0.312603i
$186$	−2.69770	−	0.318492i	−0.197805	−	0.0233530i
$187$	−11.7939	−	14.3709i	−0.862456	−	1.05091i
$188$	11.9948	+	12.9606i	0.874809	+	0.945252i
$189$	1.98305	−	1.05996i	0.144245	−	0.0771008i
$190$	−3.65090	−	2.54295i	−0.264864	−	0.184485i
$191$			13.0547i			0.944602i	0.881437	+	0.472301i	$0.156577\pi$
$191$			13.0547i			0.944602i	−0.881437	+	0.472301i	$0.843423\pi$
$192$	7.99872	+	0.143011i	0.577258	+	0.0103210i
$193$		−	21.4497i		−	1.54398i	−0.635635	−	0.771990i	$-0.719262\pi$
$193$		−	21.4497i		−	1.54398i	0.635635	−	0.771990i	$-0.280738\pi$
$194$	1.78886	−	2.56827i	0.128433	−	0.184391i
$195$	−1.44093	+	0.770194i	−0.103187	+	0.0551548i
$196$	0.150367	−	3.88510i	0.0107405	−	0.277507i
$197$	−8.25304	−	10.0564i	−0.588005	−	0.716486i	0.390984	−	0.920397i	$-0.372135\pi$
$197$	−8.25304	−	10.0564i	−0.588005	−	0.716486i	−0.978989	+	0.203911i	$0.934635\pi$
$198$	−0.457675	+	3.87661i	−0.0325256	+	0.275499i
$199$	11.8422	+	17.7231i	0.839470	+	1.25636i	0.964468	+	0.264198i	$0.0851073\pi$
$199$	11.8422	+	17.7231i	0.839470	+	1.25636i	−0.124999	+	0.992157i	$0.539893\pi$
$200$	9.00829	−	3.13267i	0.636982	−	0.221514i
$201$	−0.00266971	−	0.00178384i	−0.000188307	−	0.000125823i
$202$	−1.80526	−	22.8525i	−0.127018	−	1.60789i
$203$	6.86530	−	2.08257i	0.481850	−	0.146167i
$204$	12.7297	+	4.40592i	0.891256	+	0.308476i
$205$	0.114932	+	0.0943226i	0.00802723	+	0.00658778i
$206$	−26.2342	−	0.507487i	−1.82783	−	0.0353583i
$207$	−1.79923	+	4.34373i	−0.125055	+	0.301910i
$208$	−0.106566	−	5.12097i	−0.00738901	−	0.355075i
$209$	2.60450	+	6.28783i	0.180157	+	0.434938i
$210$	−1.47990	−	3.77786i	−0.102123	−	0.260697i
$211$	0.140811	+	1.42968i	0.00969384	+	0.0984232i	0.998814	−	0.0486856i	$-0.0155032\pi$
$211$	0.140811	+	1.42968i	0.00969384	+	0.0984232i	−0.989120	+	0.147109i	$0.953003\pi$
$212$	12.4146	−	9.40907i	0.852640	−	0.646217i
$213$	−0.611607	+	1.14424i	−0.0419066	+	0.0784018i
$214$	−7.24209	+	22.3111i	−0.495059	+	1.52516i
$215$	−0.319442	−	1.60594i	−0.0217858	−	0.109524i
$216$	−1.18641	−	2.56758i	−0.0807247	−	0.174701i
$217$	−4.23605	−	0.842603i	−0.287562	−	0.0571996i
$218$	−1.35963	−	4.81549i	−0.0920859	−	0.326146i
$219$	0.600194	−	6.09388i	0.0405574	−	0.411786i
$220$	6.85003	+	1.64030i	0.461829	+	0.110589i
$221$	2.50361	−	8.25330i	0.168411	−	0.555177i
$222$	3.05716	+	4.77268i	0.205183	+	0.320321i
$223$	−8.41540	+	8.41540i	−0.563537	+	0.563537i	−0.930310	−	0.366773i	$-0.880462\pi$
$223$	−8.41540	+	8.41540i	−0.563537	+	0.563537i	0.366773	+	0.930310i	$0.380462\pi$
$224$	12.6603	+	1.22821i	0.845902	+	0.0820633i
$225$	−2.38436	−	2.38436i	−0.158958	−	0.158958i
$226$	−2.93949	+	13.4162i	−0.195532	+	0.892434i
$227$	3.47304	+	1.05354i	0.230514	+	0.0699257i	0.403428	−	0.915011i	$-0.367818\pi$
$227$	3.47304	+	1.05354i	0.230514	+	0.0699257i	−0.172914	+	0.984937i	$0.555318\pi$
$228$	−3.99130	−	2.89628i	−0.264331	−	0.191811i
$229$	−2.66759	−	0.262735i	−0.176280	−	0.0173620i	0.00949219	−	0.999955i	$-0.496978\pi$
$229$	−2.66759	−	0.262735i	−0.176280	−	0.0173620i	−0.185772	+	0.982593i	$0.559478\pi$
$230$	7.40329	+	4.14319i	0.488159	+	0.273194i
$231$	−1.21083	+	6.08723i	−0.0796665	+	0.400511i
$232$	−2.11441	−	8.77316i	−0.138818	−	0.575986i
$233$	10.0626	−	2.00157i	0.659221	−	0.131127i	0.145867	−	0.989304i	$-0.453403\pi$
$233$	10.0626	−	2.00157i	0.659221	−	0.131127i	0.513354	+	0.858177i	$0.328403\pi$
$234$	−1.61331	+	0.822617i	−0.105465	+	0.0537761i
$235$	−9.93578	−	5.31079i	−0.648139	−	0.346438i
$236$	17.4156	+	10.1938i	1.13366	+	0.663559i
$237$	14.8044	−	1.45810i	0.961648	−	0.0947141i
$238$	19.6252	+	8.57741i	1.27212	+	0.555991i
$239$	−1.32076	+	0.547078i	−0.0854331	+	0.0353876i	−0.424991	−	0.905198i	$-0.639723\pi$
$239$	−1.32076	+	0.547078i	−0.0854331	+	0.0353876i	0.339558	+	0.940585i	$0.389723\pi$
$240$	−4.85208	+	1.58282i	−0.313201	+	0.102171i
$241$	19.9851	+	8.27810i	1.28735	+	0.533239i	0.918196	−	0.396127i	$-0.129646\pi$
$241$	19.9851	+	8.27810i	1.28735	+	0.533239i	0.369158	+	0.929367i	$0.379646\pi$
$242$	3.31519	+	3.44598i	0.213109	+	0.221516i
$243$	−0.634393	+	0.773010i	−0.0406963	+	0.0495886i
$244$	1.46968	−	1.65584i	0.0940867	−	0.106004i
$245$	0.720028	+	2.37361i	0.0460009	+	0.151645i
$246$	0.125343	+	0.106989i	0.00799155	+	0.00682138i
$247$	−1.75415	+	2.62528i	−0.111614	+	0.167042i
$248$	−1.36713	+	5.25804i	−0.0868130	+	0.333886i
$249$	−6.43566	+	4.30017i	−0.407843	+	0.272512i
$250$	−11.8609	+	9.35598i	−0.750147	+	0.591724i
$251$	9.60495	−	7.88258i	0.606259	−	0.497544i	−0.280452	−	0.959868i	$-0.590484\pi$
$251$	9.60495	−	7.88258i	0.606259	−	0.497544i	0.886711	+	0.462324i	$0.152984\pi$
$252$	−1.55900	−	4.21823i	−0.0982076	−	0.265724i
$253$	−6.11754	−	11.4451i	−0.384607	−	0.719548i
$254$	−4.27187	−	23.8812i	−0.268041	−	1.49844i
$255$	−8.59378			−0.538163
$256$	2.46591	−	15.8088i	0.154119	−	0.988052i
$257$	−24.5600			−1.53201			−0.766005	−	0.642835i	$-0.777758\pi$
$257$	−24.5600			−1.53201			−0.766005	+	0.642835i	$0.777758\pi$
$258$	−0.319570	−	1.78651i	−0.0198955	−	0.111223i
$259$	4.24810	+	7.94763i	0.263964	+	0.493842i
$260$	1.13281	+	3.06508i	0.0702537	+	0.190088i
$261$	−2.46636	+	2.02409i	−0.152664	+	0.125288i
$262$	−4.17836	+	3.29594i	−0.258140	+	0.203624i
$263$	−0.816294	+	0.545430i	−0.0503349	+	0.0336327i	−0.580483	−	0.814272i	$-0.697136\pi$
$263$	−0.816294	+	0.545430i	−0.0503349	+	0.0336327i	0.530148	+	0.847905i	$0.322136\pi$
$264$	7.55584	+	1.96458i	0.465030	+	0.120911i
$265$	−5.52115	+	8.26299i	−0.339162	+	0.507591i
$266$	−5.96369	−	5.09045i	−0.365657	−	0.312115i
$267$	−4.97560	−	16.4024i	−0.304502	−	1.00381i
$268$	−0.00426279	+	0.00480274i	−0.000260391	+	0.000293374i
$269$	−0.558577	+	0.680629i	−0.0340571	+	0.0414987i	−0.789760	−	0.613415i	$-0.789795\pi$
$269$	−0.558577	+	0.680629i	−0.0340571	+	0.0414987i	0.755703	+	0.654914i	$0.227295\pi$
$270$	1.25102	+	1.30037i	0.0761344	+	0.0791380i
$271$	−3.57822	−	1.48215i	−0.217362	−	0.0900341i	0.271346	−	0.962482i	$-0.412531\pi$
$271$	−3.57822	−	1.48215i	−0.217362	−	0.0900341i	−0.488707	+	0.872448i	$0.662531\pi$
$272$	12.2029	−	24.0191i	0.739910	−	1.45637i
$273$	−2.66014	+	1.10187i	−0.160999	+	0.0666880i
$274$	−17.6212	−	7.70153i	−1.06454	−	0.465266i
$275$	9.26262	−	0.912288i	0.558557	−	0.0550130i
$276$	8.11529	+	4.75007i	0.488483	+	0.285920i
$277$	−17.5457	−	9.37836i	−1.05422	−	0.563491i	−0.149174	−	0.988811i	$-0.547662\pi$
$277$	−17.5457	−	9.37836i	−1.05422	−	0.563491i	−0.905043	+	0.425320i	$0.860162\pi$
$278$	12.6451	−	6.44766i	0.758401	−	0.386705i
$279$	1.88390	−	0.374731i	0.112786	−	0.0224346i
$280$	−7.88888	+	1.90129i	−0.471451	+	0.113624i
$281$	4.17763	−	21.0024i	0.249217	−	1.25290i	−0.630046	−	0.776558i	$-0.716964\pi$
$281$	4.17763	−	21.0024i	0.249217	−	1.25290i	0.879262	−	0.476338i	$-0.158036\pi$
$282$	−10.8967	−	6.09825i	−0.648888	−	0.363145i
$283$	−22.4889	−	2.21496i	−1.33683	−	0.131666i	−0.595795	−	0.803137i	$-0.703163\pi$
$283$	−22.4889	−	2.21496i	−1.33683	−	0.131666i	−0.741031	+	0.671471i	$0.765663\pi$
$284$	2.10019	+	1.52400i	0.124623	+	0.0904326i
$285$	3.01061	+	0.913259i	0.178333	+	0.0540968i
$286$	1.06980	−	4.88273i	0.0632589	−	0.288722i
$287$	0.185275	+	0.185275i	0.0109365	+	0.0109365i
$288$	−5.41086	+	1.65002i	−0.318838	+	0.0972287i
$289$	20.0565	−	20.0565i	1.17980	−	1.17980i
$290$	3.10537	+	4.84793i	0.182353	+	0.284680i
$291$	−0.642442	+	2.11785i	−0.0376606	+	0.124150i
$292$	−11.9100	−	2.85196i	−0.696981	−	0.166899i
$293$	1.04529	−	10.6130i	0.0610663	−	0.620016i	−0.915135	−	0.403148i	$-0.867916\pi$
$293$	1.04529	−	10.6130i	0.0610663	−	0.620016i	0.976201	−	0.216868i	$-0.0695841\pi$
$294$	0.747030	+	2.64580i	0.0435677	+	0.154306i
$295$	−12.6266	−	2.51158i	−0.735147	−	0.146230i
$296$	10.2903	−	4.75486i	0.598111	−	0.276371i
$297$	−0.538491	−	2.70718i	−0.0312464	−	0.157086i
$298$	5.28037	−	16.2675i	0.305884	−	0.942352i
$299$	2.83805	−	5.30962i	0.164129	−	0.307063i
$300$	−5.37474	+	4.07353i	−0.310311	+	0.235185i
$301$	−0.282836	−	2.87168i	−0.0163024	−	0.165521i
$302$	2.88965	+	7.37663i	0.166281	+	0.424477i
$303$	6.20309	+	14.9756i	0.356358	+	0.860325i
$304$	−6.82748	+	7.11767i	−0.391583	+	0.408227i
$305$	−0.540522	+	1.30494i	−0.0309502	+	0.0747204i
$306$	−9.52336	−	0.184224i	−0.544415	−	0.0105314i
$307$	24.0406	+	19.7296i	1.37207	+	1.12603i	0.978387	+	0.206780i	$0.0662985\pi$
$307$	24.0406	+	19.7296i	1.37207	+	1.12603i	0.393681	+	0.919247i	$0.371202\pi$
$308$	11.7302	+	4.05999i	0.668392	+	0.231340i
$309$	17.7550	−	5.38591i	1.01004	−	0.306394i
$310$	−0.272950	−	3.45522i	−0.0155025	−	0.196243i
$311$	−11.7221	−	7.83245i	−0.664699	−	0.444137i	0.176909	−	0.984227i	$-0.443390\pi$
$311$	−11.7221	−	7.83245i	−0.664699	−	0.444137i	−0.841607	+	0.540090i	$0.818390\pi$
$312$	1.18964	+	3.42091i	0.0673499	+	0.193671i
$313$	−16.4046	−	24.5513i	−0.927245	−	1.38772i	−0.921771	−	0.387735i	$-0.873257\pi$
$313$	−16.4046	−	24.5513i	−0.927245	−	1.38772i	−0.00547421	−	0.999985i	$-0.501743\pi$
$314$	−0.896225	+	7.59122i	−0.0505769	+	0.428397i
$315$	1.82008	+	2.21777i	0.102550	+	0.124957i
$316$	1.15064	−	29.7298i	0.0647287	−	1.67243i
$317$	−5.68241	+	3.03731i	−0.319156	+	0.170592i	−0.623194	−	0.782068i	$-0.714165\pi$
$317$	−5.68241	+	3.03731i	−0.319156	+	0.170592i	0.304038	+	0.952660i	$0.401665\pi$
$318$	−6.29551	+	9.03843i	−0.353034	+	0.506850i
$319$		−	8.80672i		−	0.493082i
$320$	1.81209	+	10.0453i	0.101299	+	0.561550i
$321$		−	16.5866i		−	0.925776i
$322$	12.2682	+	8.54512i	0.683680	+	0.476201i
$323$	−14.6463	+	7.82863i	−0.814944	+	0.435596i
$324$	1.35846	+	1.46785i	0.0754701	+	0.0815472i
$325$	2.73925	+	3.33779i	0.151946	+	0.185147i
$326$	−11.8171	−	1.39513i	−0.654488	−	0.0772693i
$327$	1.96571	+	2.94190i	0.108704	+	0.162687i
$328$	0.246179	−	0.219148i	0.0135930	−	0.0121004i
$329$	−16.5080	−	11.0303i	−0.910116	−	0.608120i
$330$	−4.96517	+	0.392231i	−0.273324	+	0.0215916i
$331$	9.44077	−	2.86383i	0.518912	−	0.157410i	−0.0199555	−	0.999801i	$-0.506352\pi$
$331$	9.44077	−	2.86383i	0.518912	−	0.157410i	0.538867	+	0.842391i	$0.318852\pi$
$332$	6.76386	+	13.9243i	0.371215	+	0.764196i
$333$	−3.09806	−	2.54251i	−0.169773	−	0.139329i
$334$	−0.207501	+	10.7266i	−0.0113539	+	0.586935i
$335$	0.00156778	−	0.00378495i	8.56569e−5	−	0.000206794i
$336$	−8.78298	+	1.93784i	−0.479151	+	0.105718i
$337$	−6.83864	−	16.5099i	−0.372525	−	0.899354i	−0.993321	−	0.115382i	$-0.963191\pi$
$337$	−6.83864	−	16.5099i	−0.372525	−	0.899354i	0.620797	−	0.783972i	$-0.286809\pi$
$338$	−14.9590	+	5.85991i	−0.813665	+	0.318737i
$339$	−0.951916	−	9.66497i	−0.0517010	−	0.524929i
$340$	−2.34493	+	17.0268i	−0.127172	+	0.923410i
$341$	−2.49927	+	4.67581i	−0.135343	+	0.253209i
$342$	3.31669	+	1.07658i	0.179346	+	0.0582150i
$343$	3.92348	+	19.7246i	0.211848	+	1.06503i
$344$	−3.62680	+	0.145690i	−0.195544	+	0.00785506i
$345$	−5.88368	−	1.17034i	−0.316767	−	0.0630088i
$346$	−29.1612	+	8.23353i	−1.56771	+	0.442637i
$347$	−2.74446	+	27.8650i	−0.147330	+	1.49587i	0.582830	+	0.812594i	$0.301946\pi$
$347$	−2.74446	+	27.8650i	−0.147330	+	1.49587i	−0.730160	+	0.683276i	$0.760554\pi$
$348$	3.33735	+	5.43890i	0.178901	+	0.291556i
$349$	10.2316	−	33.7292i	0.547686	−	1.80548i	−0.0436390	−	0.999047i	$-0.513895\pi$
$349$	10.2316	−	33.7292i	0.547686	−	1.80548i	0.591325	−	0.806433i	$-0.298605\pi$
$350$	−9.02918	+	5.78368i	−0.482630	+	0.309151i
$351$	0.905464	−	0.905464i	0.0483301	−	0.0483301i
$352$	5.95413	−	14.4343i	0.317356	−	0.769351i
$353$	11.2166	+	11.2166i	0.597001	+	0.597001i	0.939513	−	0.342513i	$-0.111278\pi$
$353$	11.2166	+	11.2166i	0.597001	+	0.597001i	−0.342513	+	0.939513i	$0.611278\pi$
$354$	−13.9385	−	3.05393i	−0.740824	−	0.162315i
$355$	−1.58416	−	0.480549i	−0.0840783	−	0.0255049i
$356$	−33.8556	+	5.38254i	−1.79435	+	0.285274i
$357$	−15.0717	−	1.48444i	−0.797681	−	0.0785648i
$358$	−12.3130	+	22.0015i	−0.650761	+	1.16282i
$359$	1.69377	−	8.51518i	0.0893940	−	0.449414i	−0.910000	−	0.414608i	$-0.863919\pi$
$359$	1.69377	−	8.51518i	0.0893940	−	0.449414i	0.999394	−	0.0348060i	$-0.0110813\pi$
$360$	2.91778	−	2.12381i	0.153781	−	0.111935i
$361$	−12.6720	+	2.52062i	−0.666948	+	0.132664i
$362$	14.4531	+	28.3452i	0.759636	+	1.48979i
$363$	−2.98197	−	1.59390i	−0.156513	−	0.0836579i
$364$	1.45727	+	5.57120i	0.0763817	+	0.292010i
$365$	7.77537	−	0.765807i	0.406981	−	0.0400842i
$366$	−0.626964	+	1.43450i	−0.0327719	+	0.0749827i
$367$	13.7456	−	5.69362i	0.717515	−	0.297205i	0.00610480	−	0.999981i	$-0.498057\pi$
$367$	13.7456	−	5.69362i	0.717515	−	0.297205i	0.711410	+	0.702777i	$0.248057\pi$
$368$	11.6257	−	14.7827i	0.606030	−	0.770601i
$369$	−0.107658	−	0.0445933i	−0.00560443	−	0.00232143i
$370$	−5.21161	+	5.01380i	−0.270939	+	0.260655i
$371$	−11.1103	+	13.5379i	−0.576817	+	0.702854i
$372$	−0.228406	−	3.83482i	−0.0118423	−	0.198826i
$373$	3.11515	+	10.2693i	0.161296	+	0.531722i	0.999916	−	0.0129956i	$-0.00413674\pi$
$373$	3.11515	+	10.2693i	0.161296	+	0.531722i	−0.838619	+	0.544718i	$0.816637\pi$
$374$	17.0691	−	19.9972i	0.882620	−	1.03403i
$375$	5.93466	−	8.88184i	0.306464	−	0.458656i
$376$	−15.0558	+	19.9256i	−0.776442	+	1.02758i
$377$	3.39707	−	2.26985i	0.174958	−	0.116903i
$378$	1.96941	+	2.49668i	0.101296	+	0.128415i
$379$	−14.1953	+	11.6498i	−0.729163	+	0.598409i	−0.923984	−	0.382430i	$-0.875087\pi$
$379$	−14.1953	+	11.6498i	−0.729163	+	0.598409i	0.194821	+	0.980839i	$0.437587\pi$
$380$	2.63093	−	5.71573i	0.134964	−	0.293211i
$381$	8.08663	+	15.1290i	0.414291	+	0.775084i
$382$	−18.1736	+	3.25089i	−0.929843	+	0.166330i
$383$	−18.9651			−0.969069			−0.484535	−	0.874772i	$-0.661011\pi$
$383$	−18.9651			−0.969069			−0.484535	+	0.874772i	$0.661011\pi$
$384$	1.79276	+	11.1708i	0.0914866	+	0.570056i
$385$	−7.91906			−0.403593
$386$	29.8604	−	5.34142i	1.51986	−	0.271871i
$387$	0.604945	+	1.13177i	0.0307511	+	0.0575312i
$388$	4.02079	+	1.85075i	0.204125	+	0.0939578i
$389$	−12.1899	+	10.0040i	−0.618055	+	0.507225i	−0.890522	−	0.454941i	$-0.849660\pi$
$389$	−12.1899	+	10.0040i	−0.618055	+	0.507225i	0.272467	+	0.962165i	$0.412160\pi$
$390$	−1.43102	−	1.81415i	−0.0724627	−	0.0918631i
$391$	26.3300	−	17.5931i	1.33157	−	0.889723i
$392$	5.44596	−	0.758146i	0.275063	−	0.0382921i
$393$	2.09067	−	3.12891i	0.105460	−	0.157832i
$394$	11.9444	−	13.9934i	0.601752	−	0.704980i
$395$	5.50983	+	18.1635i	0.277230	+	0.913904i
$396$	−5.51066	+	0.328221i	−0.276921	+	0.0164937i
$397$	−12.0542	+	14.6881i	−0.604984	+	0.737175i	−0.981969	−	0.189044i	$-0.939461\pi$
$397$	−12.0542	+	14.6881i	−0.604984	+	0.737175i	0.376984	+	0.926220i	$0.376961\pi$
$398$	−21.7236	+	20.8991i	−1.08891	+	1.04758i
$399$	5.12225	+	2.12171i	0.256433	+	0.106218i
$400$	6.60430	+	11.7605i	0.330215	+	0.588024i
$401$	21.4834	−	8.89872i	1.07283	−	0.444381i	0.224841	−	0.974395i	$-0.427814\pi$
$401$	21.4834	−	8.89872i	1.07283	−	0.444381i	0.847988	+	0.530015i	$0.177814\pi$
$402$	0.00181850	−	0.00416076i	9.06986e−5	−	0.000207520i
$403$	−2.44779	+	0.241086i	−0.121933	+	0.0120094i
$404$	31.3637	−	8.20388i	1.56040	−	0.408158i
$405$	−1.12527	−	0.601470i	−0.0559152	−	0.0298873i
$406$	4.60878	+	9.03869i	0.228730	+	0.448583i
$407$	10.8498	−	2.15816i	0.537804	−	0.106976i
$408$	−2.96359	+	18.8184i	−0.146719	+	0.931648i
$409$	−5.24015	+	26.3440i	−0.259109	+	1.30263i	0.603747	+	0.797176i	$0.293674\pi$
$409$	−5.24015	+	26.3440i	−0.259109	+	1.30263i	−0.862856	+	0.505451i	$0.831326\pi$
$410$	−0.102687	+	0.183488i	−0.00507137	+	0.00906181i
$411$	13.5327	+	1.33285i	0.667519	+	0.0657449i
$412$	−5.82641	−	36.6475i	−0.287046	−	1.80549i
$413$	−21.7106	−	6.58584i	−1.06831	−	0.324068i
$414$	−6.49503	−	1.42306i	−0.319213	−	0.0699396i
$415$	−6.98327	−	6.98327i	−0.342795	−	0.342795i
$416$	7.10245	−	1.42358i	0.348226	−	0.0697969i
$417$	−7.09701	+	7.09701i	−0.347542	+	0.347542i
$418$	−8.10481	+	5.19157i	−0.396419	+	0.253928i
$419$	−5.06782	+	16.7064i	−0.247579	+	0.816160i	0.741777	+	0.670647i	$0.233983\pi$
$419$	−5.06782	+	16.7064i	−0.247579	+	0.816160i	−0.989356	+	0.145513i	$0.953517\pi$
$420$	4.89069	−	3.00096i	0.238641	−	0.146432i
$421$	1.63549	−	16.6054i	0.0797089	−	0.809298i	−0.869349	−	0.494198i	$-0.835462\pi$
$421$	1.63549	−	16.6054i	0.0797089	−	0.809298i	0.949058	−	0.315100i	$-0.102038\pi$
$422$	−1.95522	+	0.552046i	−0.0951784	+	0.0268732i
$423$	8.66002	+	1.72258i	0.421064	+	0.0837549i
$424$	16.1900	+	14.9395i	0.786257	+	0.725528i
$425$	4.43077	+	22.2750i	0.214924	+	1.08050i
$426$	−1.74521	−	0.566489i	−0.0845559	−	0.0274465i
$427$	−1.17337	+	2.19523i	−0.0567835	+	0.106234i
$428$	−32.8631	−	4.52589i	−1.58850	−	0.218767i
$429$	0.346442	+	3.51749i	0.0167264	+	0.169826i
$430$	2.15611	−	0.844615i	0.103977	−	0.0407309i
$431$	−8.44778	−	20.3947i	−0.406915	−	0.982380i	−0.985944	−	0.167073i	$-0.946568\pi$
$431$	−8.44778	−	20.3947i	−0.406915	−	0.982380i	0.579029	−	0.815307i	$-0.303432\pi$
$432$	3.27892	−	2.29100i	0.157757	−	0.110226i
$433$	4.72889	−	11.4165i	0.227256	−	0.548644i	−0.768586	−	0.639747i	$-0.779039\pi$
$433$	4.72889	−	11.4165i	0.227256	−	0.548644i	0.995841	+	0.0911029i	$0.0290392\pi$
$434$	0.118135	−	6.10690i	0.00567064	−	0.293141i
$435$	−3.14691	−	2.58260i	−0.150883	−	0.123826i
$436$	6.36515	−	3.09193i	0.304835	−	0.148076i
$437$	−11.0937	+	3.36523i	−0.530682	+	0.160981i
$438$	8.63285	−	0.681964i	0.412493	−	0.0325855i
$439$	−13.0272	−	8.70453i	−0.621756	−	0.415444i	0.204398	−	0.978888i	$-0.434476\pi$
$439$	−13.0272	−	8.70453i	−0.621756	−	0.415444i	−0.826155	+	0.563443i	$0.809476\pi$
$440$	−0.577690	+	9.94452i	−0.0275403	+	0.474086i
$441$	−1.08003	−	1.61638i	−0.0514301	−	0.0769706i
$442$	12.1130	+	1.43007i	0.576157	+	0.0680216i
$443$	−26.4887	−	32.2765i	−1.25851	−	1.53350i	−0.727421	−	0.686191i	$-0.759281\pi$
$443$	−26.4887	−	32.2765i	−1.25851	−	1.53350i	−0.531094	−	0.847313i	$-0.678219\pi$
$444$	−5.88283	+	5.44442i	−0.279187	+	0.258381i
$445$	19.2876	−	10.3095i	0.914321	−	0.488715i
$446$	−13.8108	−	9.61961i	−0.653962	−	0.455502i
$447$			12.0937i			0.572012i
$448$	1.44287	+	17.9305i	0.0681693	+	0.847135i
$449$		−	10.8470i		−	0.511902i	−0.966690	−	0.255951i	$-0.917611\pi$
$449$		−	10.8470i		−	0.511902i	0.966690	−	0.255951i	$-0.0823886\pi$
$450$	2.72555	−	3.91307i	0.128484	−	0.184464i
$451$	0.283663	−	0.151621i	0.0133572	−	0.00713955i
$452$	−19.4089	−	0.751191i	−0.912920	−	0.0353331i
$453$	−3.55387	−	4.33040i	−0.166975	−	0.203460i
$454$	−0.601783	+	5.09723i	−0.0282431	+	0.239225i
$455$	−2.04106	−	3.05466i	−0.0956864	−	0.143205i
$456$	3.03804	−	6.27760i	0.142269	−	0.293975i
$457$	−26.3326	−	17.5949i	−1.23179	−	0.823053i	−0.242658	−	0.970112i	$-0.578019\pi$
$457$	−26.3326	−	17.5949i	−1.23179	−	0.823053i	−0.989128	+	0.147059i	$0.953019\pi$
$458$	−0.298530	−	3.77903i	−0.0139494	−	0.176582i
$459$	6.44528	−	1.95515i	0.300840	−	0.0912587i
$460$	−3.92423	+	11.3380i	−0.182968	+	0.528636i
$461$	1.55470	+	1.27591i	0.0724094	+	0.0594249i	0.669902	−	0.742450i	$-0.266336\pi$
$461$	1.55470	+	1.27591i	0.0724094	+	0.0594249i	−0.597492	+	0.801875i	$0.703836\pi$
$462$	−8.77566	−	0.169760i	−0.408281	−	0.00789796i
$463$	10.6673	−	25.7531i	0.495752	−	1.19685i	−0.456000	−	0.889980i	$-0.650718\pi$
$463$	10.6673	−	25.7531i	0.495752	−	1.19685i	0.951751	−	0.306870i	$-0.0992818\pi$
$464$	11.6867	−	5.12820i	0.542543	−	0.238071i
$465$	0.937889	+	2.26426i	0.0434935	+	0.105003i
$466$	5.29222	+	13.5098i	0.245157	+	0.625831i
$467$	0.413784	+	4.20122i	0.0191477	+	0.194409i	1.00000		0.000343720i	$-0.000109410\pi$
$467$	0.413784	+	4.20122i	0.0191477	+	0.194409i	−0.980852	+	0.194753i	$0.937609\pi$
$468$	−1.54693	−	2.04106i	−0.0715067	−	0.0943482i
$469$	0.00340335	−	0.00636723i	0.000157152	−	0.000294011i
$470$	4.91901	−	15.1543i	0.226897	−	0.699014i
$471$	−1.05448	−	5.30123i	−0.0485878	−	0.244268i
$472$	−9.85407	+	26.7831i	−0.453570	+	1.23279i
$473$	−3.47413	−	0.691047i	−0.159741	−	0.0317744i
$474$	5.71646	+	20.2463i	0.262566	+	0.929945i
$475$	0.814951	−	8.27434i	0.0373925	−	0.379653i
$476$	−7.05365	+	29.4566i	−0.323304	+	1.35014i
$477$	2.26093	−	7.45329i	0.103521	−	0.341263i
$478$	−1.09050	−	1.70242i	−0.0498781	−	0.0778670i
$479$	−3.47279	+	3.47279i	−0.158676	+	0.158676i	−0.781980	−	0.623304i	$-0.785790\pi$
$479$	−3.47279	+	3.47279i	−0.158676	+	0.158676i	0.623304	+	0.781980i	$0.285790\pi$
$480$	−3.41175	−	6.36051i	−0.155724	−	0.290316i
$481$	3.62891	+	3.62891i	0.165464	+	0.165464i
$482$	−6.54736	+	29.8830i	−0.298224	+	1.36113i
$483$	−10.1166	−	3.06885i	−0.460323	−	0.139637i
$484$	−3.97166	+	5.47326i	−0.180530	+	0.248784i
$485$	−2.81023	−	0.276783i	−0.127606	−	0.0125681i
$486$	−1.23410	−	0.690653i	−0.0559798	−	0.0313287i
$487$	−2.77834	+	13.9677i	−0.125899	+	0.632936i	0.865376	+	0.501123i	$0.167080\pi$
$487$	−2.77834	+	13.9677i	−0.125899	+	0.632936i	−0.991275	+	0.131813i	$0.957920\pi$
$488$	2.67110	+	1.63363i	0.120915	+	0.0739508i
$489$	8.25230	−	1.64148i	0.373182	−	0.0742305i
$490$	−3.12504	+	1.59344i	−0.141175	+	0.0719844i
$491$	7.33481	+	3.92054i	0.331015	+	0.176931i	0.628529	−	0.777786i	$-0.283657\pi$
$491$	7.33481	+	3.92054i	0.331015	+	0.176931i	−0.297514	+	0.954718i	$0.596157\pi$
$492$	−0.117728	+	0.201134i	−0.00530761	+	0.00906783i
$493$	21.3861	−	2.10635i	0.963182	−	0.0948651i
$494$	−4.09151	−	1.78824i	−0.184086	−	0.0804566i
$495$	3.25376	−	1.34775i	0.146246	−	0.0605769i
$496$	−7.66025	−	0.593844i	−0.343955	−	0.0266644i
$497$	−2.69528	−	1.11642i	−0.120900	−	0.0500784i
$498$	−7.58895	−	7.88835i	−0.340069	−	0.353485i
$499$	9.48985	−	11.5634i	0.424824	−	0.517650i	−0.515980	−	0.856601i	$-0.672572\pi$
$499$	9.48985	−	11.5634i	0.424824	−	0.517650i	0.940804	+	0.338951i	$0.110072\pi$
$500$	−15.9782	−	14.1819i	−0.714568	−	0.634232i
$501$	−2.20218	−	7.25963i	−0.0983863	−	0.324336i
$502$	13.3653	+	11.4083i	0.596523	+	0.509176i
$503$	5.41410	−	8.10277i	0.241403	−	0.361285i	−0.690908	−	0.722942i	$-0.742789\pi$
$503$	5.41410	−	8.10277i	0.241403	−	0.361285i	0.932311	+	0.361658i	$0.117789\pi$
$504$	5.48405	−	3.22074i	0.244279	−	0.143463i
$505$	−17.1966	+	11.4904i	−0.765239	+	0.511316i
$506$	14.4095	−	11.3664i	0.640582	−	0.505299i
$507$	8.78161	−	7.20688i	0.390005	−	0.320069i
$508$	32.1817	−	11.8939i	1.42783	−	0.527705i
$509$	−10.0711	−	18.8417i	−0.446394	−	0.835144i	−0.999997	−	0.00236340i	$-0.999248\pi$
$509$	−10.0711	−	18.8417i	−0.446394	−	0.835144i	0.553604	−	0.832780i	$-0.313252\pi$
$510$	−2.14003	−	11.9635i	−0.0947623	−	0.529754i
$511$	13.7687			0.609092
$512$	22.6218	−	0.503901i	0.999752	−	0.0222695i
$513$	−2.46571			−0.108864
$514$	−6.11596	−	34.1904i	−0.269763	−	1.50807i
$515$	11.1596	+	20.8782i	0.491751	+	0.920002i
$516$	2.40745	−	0.889756i	0.105982	−	0.0391693i
$517$	−18.8397	+	15.4613i	−0.828567	+	0.679987i
$518$	−10.0062	+	7.89297i	−0.439645	+	0.346797i
$519$	17.8152	−	11.9038i	0.782002	−	0.522517i
$520$	−3.98485	+	2.34027i	−0.174747	+	0.102628i
$521$	9.43394	−	14.1189i	0.413308	−	0.618560i	−0.565154	−	0.824986i	$-0.691183\pi$
$521$	9.43394	−	14.1189i	0.413308	−	0.618560i	0.978462	+	0.206426i	$0.0661832\pi$
$522$	−3.43195	−	2.92942i	−0.150212	−	0.128217i
$523$	13.0903	+	43.1528i	0.572397	+	1.88694i	0.446197	+	0.894935i	$0.352778\pi$
$523$	13.0903	+	43.1528i	0.572397	+	1.88694i	0.126200	+	0.992005i	$0.459722\pi$
$524$	−5.62883	−	4.99601i	−0.245897	−	0.218252i
$525$	4.81004	−	5.86106i	0.209928	−	0.255797i
$526$	−0.962577	−	1.00055i	−0.0419704	−	0.0436262i
$527$	−11.9524	−	4.95086i	−0.520656	−	0.215663i
$528$	−0.853358	+	11.0078i	−0.0371376	+	0.479054i
$529$	−0.826639	+	0.342405i	−0.0359408	+	0.0148872i
$530$	−12.8779	−	5.62843i	−0.559381	−	0.244483i
$531$	10.0412	−	0.988976i	0.435753	−	0.0429179i
$532$	5.60141	−	9.56978i	0.242852	−	0.414902i
$533$	0.131597	+	0.0703400i	0.00570010	+	0.00304676i
$534$	21.5950	−	11.0112i	0.934505	−	0.476499i
$535$	20.7568	−	4.12878i	0.897393	−	0.178503i
$536$	−0.00774750	−	0.00473832i	−0.000334641	−	0.000204664i
$537$	3.47807	−	17.4854i	0.150090	−	0.754552i
$538$	−1.08661	−	0.608114i	−0.0468472	−	0.0262177i
$539$	5.34004	+	0.525948i	0.230012	+	0.0226542i
$540$	−1.49874	+	2.06538i	−0.0644954	+	0.0888798i
$541$	11.6592	+	3.53678i	0.501268	+	0.152058i	0.530785	−	0.847506i	$-0.321897\pi$
$541$	11.6592	+	3.53678i	0.501268	+	0.152058i	−0.0295176	+	0.999564i	$0.509397\pi$
$542$	1.17227	−	5.35039i	0.0503533	−	0.229819i
$543$	−15.9087	−	15.9087i	−0.682706	−	0.682706i
$544$	36.4761	+	11.0066i	1.56390	+	0.471904i
$545$	−3.19222	+	3.19222i	−0.136740	+	0.136740i
$546$	−2.19636	−	3.42884i	−0.0939955	−	0.146741i
$547$	3.53795	−	11.6630i	0.151272	−	0.498676i	−0.848250	−	0.529596i	$-0.822344\pi$
$547$	3.53795	−	11.6630i	0.151272	−	0.498676i	0.999522	+	0.0309198i	$0.00984365\pi$
$548$	6.33337	−	26.4486i	0.270548	−	1.12983i
$549$	0.108505	−	1.10167i	0.00463087	−	0.0470180i
$550$	3.57660	+	12.6675i	0.152507	+	0.540142i
$551$	−7.71592	−	1.53479i	−0.328709	−	0.0653843i
$552$	−4.59177	+	12.4803i	−0.195439	+	0.531197i
$553$	6.52568	+	32.8068i	0.277500	+	1.39509i
$554$	8.68652	−	26.7610i	0.369055	−	1.13697i
$555$	2.41056	−	4.50985i	0.102323	−	0.191432i
$556$	12.1248	+	15.9978i	0.514205	+	0.678459i
$557$	2.75325	+	27.9543i	0.116659	+	1.18446i	0.858115	+	0.513458i	$0.171636\pi$
$557$	2.75325	+	27.9543i	0.116659	+	1.18446i	−0.741456	+	0.671002i	$0.765864\pi$
$558$	0.990801	+	2.52929i	0.0419439	+	0.107074i
$559$	−0.628861	−	1.51821i	−0.0265980	−	0.0642132i
$560$	−4.61131	−	10.5088i	−0.194864	−	0.444077i
$561$	−7.11441	+	17.1757i	−0.300371	+	0.725159i
$562$	30.2781	+	0.585712i	1.27720	+	0.0247068i
$563$	13.7941	+	11.3205i	0.581352	+	0.477103i	0.878509	−	0.477725i	$-0.158539\pi$
$563$	13.7941	+	11.3205i	0.581352	+	0.477103i	−0.297157	+	0.954828i	$0.596039\pi$
$564$	5.77596	−	16.6881i	0.243212	−	0.702694i
$565$	11.8579	−	3.59707i	0.498867	−	0.151330i
$566$	−2.51673	−	31.8587i	−0.105786	−	1.33912i
$567$	−1.86960	−	1.24923i	−0.0785160	−	0.0524627i
$568$	−1.59859	+	3.30321i	−0.0670753	+	0.138600i
$569$	1.15660	+	1.73097i	0.0484870	+	0.0725659i	0.854921	−	0.518758i	$-0.173605\pi$
$569$	1.15660	+	1.73097i	0.0484870	+	0.0725659i	−0.806434	+	0.591324i	$0.798605\pi$
$570$	−0.521657	+	4.41854i	−0.0218498	+	0.185072i
$571$	−16.5810	−	20.2040i	−0.693893	−	0.845511i	0.300218	−	0.953870i	$-0.402940\pi$
$571$	−16.5810	−	20.2040i	−0.693893	−	0.845511i	−0.994112	+	0.108359i	$0.965440\pi$
$572$	7.06373	+	0.273390i	0.295349	+	0.0114310i
$573$	11.5132	−	6.15393i	0.480970	−	0.257084i
$574$	−0.211788	+	0.304063i	−0.00883984	+	0.0126913i
$575$			15.8539i			0.661152i
$576$	−3.64445	−	7.12166i	−0.151852	−	0.296736i
$577$		−	20.1418i		−	0.838515i	−0.907867	−	0.419257i	$-0.862291\pi$
$577$		−	20.1418i		−	0.838515i	0.907867	−	0.419257i	$-0.137709\pi$
$578$	32.9155	+	22.9265i	1.36911	+	0.953617i
$579$	−18.9169	+	10.1113i	−0.786160	+	0.420211i
$580$	−5.97558	+	5.53027i	−0.248123	+	0.229632i
$581$	−11.0410	−	13.4535i	−0.458058	−	0.558145i
$582$	−3.10827	−	0.366965i	−0.128842	−	0.0152112i
$583$	11.9439	+	17.8753i	0.494664	+	0.740317i
$584$	1.00442	−	17.2903i	0.0415631	−	0.715479i
$585$	1.35850	+	0.907722i	0.0561671	+	0.0375297i
$586$	15.0348	−	1.18769i	0.621081	−	0.0490632i
$587$	20.0027	−	6.06777i	0.825602	−	0.250443i	0.150914	−	0.988547i	$-0.451778\pi$
$587$	20.0027	−	6.06777i	0.825602	−	0.250443i	0.674688	+	0.738103i	$0.264278\pi$
$588$	−3.49724	+	1.69881i	−0.144224	+	0.0700579i
$589$	3.66110	+	3.00459i	0.150853	+	0.123802i
$590$	0.352128	−	18.2031i	0.0144969	−	0.749409i
$591$	−4.97846	+	12.0191i	−0.204787	+	0.494398i
$592$	9.18182	+	13.1412i	0.377370	+	0.540101i
$593$	−1.47699	−	3.56577i	−0.0606527	−	0.146429i	0.890648	−	0.454694i	$-0.150251\pi$
$593$	−1.47699	−	3.56577i	−0.0606527	−	0.146429i	−0.951300	+	0.308266i	$0.900251\pi$
$594$	3.63461	−	1.42379i	0.149130	−	0.0584187i
$595$	−1.89404	−	19.2305i	−0.0776481	−	0.788375i
$596$	23.9612	+	3.29993i	0.981490	+	0.135170i
$597$	10.0480	−	18.7985i	0.411237	−	0.769370i
$598$	8.09835	+	2.62869i	0.331166	+	0.107495i
$599$	−6.67398	−	33.5524i	−0.272692	−	1.37091i	−0.837836	−	0.545921i	$-0.816180\pi$
$599$	−6.67398	−	33.5524i	−0.272692	−	1.37091i	0.565145	−	0.824992i	$-0.308820\pi$
$600$	−7.00925	−	6.46787i	−0.286151	−	0.264050i
$601$	40.4430	+	8.04461i	1.64970	+	0.328147i	0.930399	−	0.366548i	$-0.119460\pi$
$601$	40.4430	+	8.04461i	1.64970	+	0.328147i	0.719305	+	0.694694i	$0.244460\pi$
$602$	3.92728	−	1.10885i	0.160064	−	0.0451933i
$603$	−0.000314716		0.00319537i	−1.28162e−5		0.000130126i
$604$	−9.54955	+	5.85967i	−0.388566	+	0.238427i
$605$	1.25235	−	4.12844i	0.0509152	−	0.167845i
$606$	−19.3031	+	12.3647i	−0.784134	+	0.502280i
$607$	−8.39735	+	8.39735i	−0.340838	+	0.340838i	−0.856682	−	0.515844i	$-0.827478\pi$
$607$	−8.39735	+	8.39735i	−0.340838	+	0.340838i	0.515844	+	0.856682i	$0.327478\pi$
$608$	−11.6088	−	7.73220i	−0.470800	−	0.313582i
$609$	−5.07294	−	5.07294i	−0.205566	−	0.205566i
$610$	−1.95122	−	0.427513i	−0.0790028	−	0.0173095i
$611$	−10.8197	−	3.28213i	−0.437719	−	0.132781i
$612$	−2.11506	−	13.3035i	−0.0854962	−	0.537762i
$613$	20.3821	+	2.00746i	0.823225	+	0.0810806i	0.500853	−	0.865533i	$-0.333020\pi$
$613$	20.3821	+	2.00746i	0.823225	+	0.0810806i	0.322372	+	0.946613i	$0.395520\pi$
$614$	−21.4793	+	38.3804i	−0.866833	+	1.54891i
$615$	0.0290063	−	0.145825i	0.00116965	−	0.00588022i
$616$	−2.73091	+	17.3409i	−0.110031	+	0.698684i
$617$	−38.1030	+	7.57916i	−1.53397	+	0.305126i	−0.888578	−	0.458726i	$-0.848306\pi$
$617$	−38.1030	+	7.57916i	−1.53397	+	0.305126i	−0.645392	+	0.763851i	$0.723306\pi$
$618$	11.9192	+	23.3758i	0.479460	+	0.940311i
$619$	−9.32165	−	4.98253i	−0.374669	−	0.200265i	0.273305	−	0.961928i	$-0.411883\pi$
$619$	−9.32165	−	4.98253i	−0.374669	−	0.200265i	−0.647974	+	0.761663i	$0.724383\pi$
$620$	4.74210	−	1.24040i	0.190447	−	0.0498157i
$621$	4.67898	−	0.460840i	0.187761	−	0.0184929i
$622$	7.98463	−	18.2690i	0.320155	−	0.732518i
$623$	35.6074	−	14.7491i	1.42658	−	0.590909i
$624$	−4.46606	+	2.50799i	−0.178785	+	0.100400i
$625$	−2.98446	−	1.23620i	−0.119378	−	0.0494482i
$626$	30.0931	−	28.9510i	1.20276	−	1.15711i
$627$	4.31761	−	5.26103i	0.172429	−	0.210105i
$628$	−10.7910	+	0.642725i	−0.430609	+	0.0256475i
$629$	7.83584	+	25.8313i	0.312435	+	1.02996i
$630$	−2.63415	+	3.08603i	−0.104947	+	0.122950i
$631$	−15.0166	+	22.4740i	−0.597803	+	0.894675i	−0.999780	−	0.0209746i	$-0.993323\pi$
$631$	−15.0166	+	22.4740i	−0.597803	+	0.894675i	0.401977	+	0.915650i	$0.368323\pi$
$632$	41.6738	−	5.80152i	1.65770	−	0.230772i
$633$	1.19449	−	0.798131i	0.0474766	−	0.0317229i
$634$	−5.64334	−	7.15422i	−0.224125	−	0.284131i
$635$	−16.9198	+	13.8857i	−0.671440	+	0.551037i
$636$	−14.1503	−	6.51331i	−0.561095	−	0.258270i
$637$	1.17347	+	2.19540i	0.0464944	+	0.0869849i
$638$	12.2600	−	2.19306i	0.485377	−	0.0868241i
$639$	1.29744			0.0513258
$640$	−13.5330	+	5.02414i	−0.534939	+	0.198597i
$641$	−8.54991			−0.337701			−0.168851	−	0.985642i	$-0.554006\pi$
$641$	−8.54991			−0.337701			−0.168851	+	0.985642i	$0.554006\pi$
$642$	23.0905	−	4.13043i	0.911310	−	0.163015i
$643$	18.0456	+	33.7609i	0.711648	+	1.33140i	0.934295	+	0.356501i	$0.116030\pi$
$643$	18.0456	+	33.7609i	0.711648	+	1.33140i	−0.222647	+	0.974899i	$0.571470\pi$
$644$	−8.84076	+	19.2067i	−0.348375	+	0.756850i
$645$	−1.26573	+	1.03876i	−0.0498382	+	0.0409011i
$646$	−14.5456	−	18.4399i	−0.572289	−	0.725508i
$647$	0.228947	−	0.152978i	0.00900085	−	0.00601417i	−0.551062	−	0.834465i	$-0.685777\pi$
$647$	0.228947	−	0.152978i	0.00900085	−	0.00601417i	0.560063	+	0.828450i	$0.310777\pi$
$648$	−1.70513	+	2.25666i	−0.0669839	+	0.0886501i
$649$	−15.4727	+	23.1565i	−0.607355	+	0.908971i
$650$	−3.96446	+	4.64454i	−0.155499	+	0.182174i
$651$	1.25375	+	4.13306i	0.0491384	+	0.161988i
$652$	−1.00052	−	16.7982i	−0.0391832	−	0.657867i
$653$	−16.9375	+	20.6384i	−0.662814	+	0.807641i	−0.990554	−	0.137127i	$-0.956213\pi$
$653$	−16.9375	+	20.6384i	−0.662814	+	0.807641i	0.327739	+	0.944768i	$0.393713\pi$
$654$	−3.60596	+	3.46909i	−0.141004	+	0.135652i
$655$	4.43597	+	1.83744i	0.173328	+	0.0717948i
$656$	0.366383	+	0.288138i	0.0143049	+	0.0112499i
$657$	−5.65725	+	2.34331i	−0.220710	+	0.0914212i
$658$	11.2446	−	25.7278i	0.438361	−	1.00298i
$659$	−38.0415	+	3.74676i	−1.48189	+	0.145953i	−0.806378	−	0.591400i	$-0.798575\pi$
$659$	−38.0415	+	3.74676i	−1.48189	+	0.145953i	−0.675507	+	0.737353i	$0.736075\pi$
$660$	−1.78246	−	6.81442i	−0.0693824	−	0.265251i
$661$	39.1116	+	20.9056i	1.52127	+	0.813133i	0.999209	−	0.0397771i	$-0.0126648\pi$
$661$	39.1116	+	20.9056i	1.52127	+	0.813133i	0.522057	+	0.852911i	$0.325165\pi$
$662$	6.33773	+	12.4295i	0.246323	+	0.483086i
$663$	−8.45896	+	1.68259i	−0.328519	+	0.0653464i
$664$	−17.6999	+	12.8835i	−0.686890	+	0.499978i
$665$	−1.38009	+	6.93820i	−0.0535178	+	0.269052i
$666$	2.76799	−	4.94600i	0.107257	−	0.191654i
$667$	14.9287	+	1.47035i	0.578043	+	0.0569322i
$668$	−14.9844	+	2.38229i	−0.579763	+	0.0921737i
$669$	11.3887	+	3.45473i	0.440313	+	0.133568i
$670$	0.00565950	+	0.00124000i	0.000218646	+	4.79052e-5i
$671$	2.16060	+	2.16060i	0.0834090	+	0.0834090i
$672$	−4.88484	−	11.7444i	−0.188437	−	0.453049i
$673$	2.44223	−	2.44223i	0.0941412	−	0.0941412i	−0.658468	−	0.752609i	$-0.728795\pi$
$673$	2.44223	−	2.44223i	0.0941412	−	0.0941412i	0.752609	+	0.658468i	$0.228795\pi$
$674$	21.2808	−	13.6315i	0.819706	−	0.525066i
$675$	−0.978839	+	3.22680i	−0.0376755	+	0.124200i
$676$	−11.8828	−	19.3655i	−0.457031	−	0.744826i
$677$	−0.480261	+	4.87617i	−0.0184579	+	0.187407i	−0.999992	−	0.00387839i	$-0.998765\pi$
$677$	−0.480261	+	4.87617i	−0.0184579	+	0.187407i	0.981535	+	0.191285i	$0.0612655\pi$
$678$	13.2177	−	3.73196i	0.507623	−	0.143325i
$679$	−4.88076	−	0.970843i	−0.187306	−	0.0372575i
$680$	−24.2873	+	0.975627i	−0.931375	+	0.0374136i
$681$	−0.708045	−	3.55958i	−0.0271324	−	0.136404i
$682$	−7.13164	−	2.31490i	−0.273085	−	0.0886421i
$683$	−22.9156	+	42.8721i	−0.876842	+	1.64046i	−0.114368	+	0.993438i	$0.536484\pi$
$683$	−22.9156	+	42.8721i	−0.876842	+	1.64046i	−0.762475	+	0.647018i	$0.776016\pi$
$684$	−0.672804	+	4.88531i	−0.0257253	+	0.186795i
$685$	1.70063	+	17.2668i	0.0649778	+	0.659731i
$686$	−26.4820	+	10.3738i	−1.01109	+	0.396073i
$687$	1.02578	+	2.47646i	0.0391361	+	0.0944828i
$688$	−1.10597	−	5.01265i	−0.0421646	−	0.191106i
$689$	−3.81671	+	9.21435i	−0.145405	+	0.351039i
$690$	0.164084	−	8.48221i	0.00624655	−	0.322912i
$691$	−3.21773	−	2.64073i	−0.122408	−	0.100458i	0.571198	−	0.820813i	$-0.306479\pi$
$691$	−3.21773	−	2.64073i	−0.122408	−	0.100458i	−0.693606	+	0.720355i	$0.743979\pi$
$692$	−18.7238	−	38.5454i	−0.711771	−	1.46528i
$693$	5.93924	−	1.80165i	0.225613	−	0.0684390i
$694$	−39.4747	+	3.11836i	−1.49844	+	0.118371i
$695$	−10.6479	−	7.11471i	−0.403898	−	0.269876i
$696$	−6.74051	+	6.00038i	−0.255498	+	0.227444i
$697$	0.436039	+	0.652578i	0.0165162	+	0.0247182i
$698$	49.5028	+	5.84434i	1.87371	+	0.221212i
$699$	−6.50869	−	7.93087i	−0.246181	−	0.299973i
$700$	−10.3000	−	11.1294i	−0.389304	−	0.420652i
$701$	19.3344	−	10.3344i	0.730249	−	0.390326i	−0.0639750	−	0.997951i	$-0.520378\pi$
$701$	19.3344	−	10.3344i	0.730249	−	0.390326i	0.794224	+	0.607625i	$0.207878\pi$
$702$	1.48599	+	1.03503i	0.0560851	+	0.0390648i
$703$		−	9.88205i		−	0.372708i
$704$	21.5769	+	4.69440i	0.813212	+	0.176927i
$705$			11.2661i			0.424305i
$706$	−12.8217	+	18.4080i	−0.482550	+	0.692795i
$707$	−32.1441	+	17.1814i	−1.20890	+	0.646173i
$708$	0.780436	−	20.1645i	0.0293306	−	0.757830i
$709$	5.39026	+	6.56806i	0.202436	+	0.246669i	0.864326	−	0.502932i	$-0.167745\pi$
$709$	5.39026	+	6.56806i	0.202436	+	0.246669i	−0.661890	+	0.749601i	$0.730245\pi$
$710$	0.274491	−	2.32500i	0.0103015	−	0.0872556i
$711$	−8.26467	−	12.3690i	−0.309949	−	0.463872i
$712$	−15.9239	−	45.7906i	−0.596773	−	1.71608i
$713$	−7.50893	−	5.01731i	−0.281212	−	0.187900i
$714$	−1.68668	−	21.3513i	−0.0631223	−	0.799052i
$715$	−4.31560	+	1.30912i	−0.161394	+	0.0489584i
$716$	−33.6948	−	11.6622i	−1.25924	−	0.435838i
$717$	1.10508	+	0.906919i	0.0412701	+	0.0338695i
$718$	12.2759	+	0.237471i	0.458133	+	0.00886232i
$719$	6.84230	−	16.5188i	0.255175	−	0.616046i	−0.743432	−	0.668811i	$-0.766803\pi$
$719$	6.84230	−	16.5188i	0.255175	−	0.616046i	0.998607	+	0.0527649i	$0.0168034\pi$
$720$	3.68318	+	3.53302i	0.137264	+	0.131668i
$721$	15.9653	+	38.5437i	0.594580	+	1.43544i
$722$	−6.66459	−	17.0132i	−0.248030	−	0.633166i
$723$	−2.12028	−	21.5276i	−0.0788540	−	0.800618i
$724$	−35.8607	+	27.1789i	−1.33275	+	1.01010i
$725$	−5.07160	+	9.48830i	−0.188355	+	0.352387i
$726$	1.47632	−	4.54816i	0.0547912	−	0.168798i
$727$	−2.78283	−	13.9902i	−0.103209	−	0.518869i	−0.997455	−	0.0712930i	$-0.977287\pi$
$727$	−2.78283	−	13.9902i	−0.103209	−	0.518869i	0.894246	−	0.447576i	$-0.147713\pi$
$728$	−7.39286	+	3.41604i	−0.273998	+	0.126607i
$729$	0.980785	+	0.195090i	0.0363254	+	0.00722557i
$730$	3.00233	+	10.6335i	0.111121	+	0.393564i
$731$	0.847203	−	8.60180i	0.0313349	−	0.318149i
$732$	−2.15312	−	0.515585i	−0.0795817	−	0.0190566i
$733$	5.40287	−	17.8109i	0.199560	−	0.657860i	−0.798853	−	0.601527i	$-0.794559\pi$
$733$	5.40287	−	17.8109i	0.199560	−	0.657860i	0.998412	−	0.0563327i	$-0.0179407\pi$
$734$	11.3491	+	17.7177i	0.418904	+	0.653971i
$735$	1.75392	−	1.75392i	0.0646944	−	0.0646944i
$736$	23.4743	+	12.5031i	0.865273	+	0.460870i
$737$	−0.00626679	−	0.00626679i	−0.000230840	−	0.000230840i
$738$	0.0352700	−	0.160977i	0.00129831	−	0.00592563i
$739$	−2.04800	−	0.621254i	−0.0753369	−	0.0228532i	0.252391	−	0.967625i	$-0.418783\pi$
$739$	−2.04800	−	0.621254i	−0.0753369	−	0.0228532i	−0.327728	+	0.944772i	$0.606283\pi$
$740$	−8.27760	−	6.00662i	−0.304291	−	0.220808i
$741$	3.14219	+	0.309479i	0.115431	+	0.0113690i
$742$	−21.6131	−	12.0956i	−0.793440	−	0.444043i
$743$	−9.68830	+	48.7064i	−0.355429	+	1.78686i	0.226908	+	0.973916i	$0.427138\pi$
$743$	−9.68830	+	48.7064i	−0.355429	+	1.78686i	−0.582337	+	0.812947i	$0.697862\pi$
$744$	5.28164	−	1.27292i	0.193634	−	0.0466675i
$745$	−15.1342	+	3.01039i	−0.554475	+	0.110292i
$746$	−13.5203	+	6.89391i	−0.495012	+	0.252404i
$747$	6.82616	+	3.64866i	0.249756	+	0.133497i
$748$	32.0890	+	18.7824i	1.17329	+	0.686753i
$749$	37.1163	−	3.65564i	1.35620	−	0.133574i
$750$	13.8424	+	6.04997i	0.505453	+	0.220914i
$751$	49.1840	−	20.3727i	1.79475	−	0.743409i	0.806367	−	0.591416i	$-0.201431\pi$
$751$	49.1840	−	20.3727i	1.79475	−	0.743409i	0.988382	−	0.151993i	$-0.0485692\pi$
$752$	−31.4880	−	15.9975i	−1.14825	−	0.583368i
$753$	−11.4796	−	4.75499i	−0.418338	−	0.173281i
$754$	4.00583	+	4.16387i	0.145884	+	0.151639i
$755$	4.53450	−	5.52530i	0.165027	−	0.201086i
$756$	−2.98524	+	3.36337i	−0.108572	+	0.122325i
$757$	12.7599	+	42.0637i	0.463765	+	1.52883i	0.807560	+	0.589785i	$0.200788\pi$
$757$	12.7599	+	42.0637i	0.463765	+	1.52883i	−0.343795	+	0.939045i	$0.611712\pi$
$758$	−19.7528	−	16.8605i	−0.717453	−	0.612399i
$759$	−7.20990	+	10.7904i	−0.261703	+	0.391666i
$760$	8.61211	+	2.23922i	0.312394	+	0.0812250i
$761$	43.1027	−	28.8003i	1.56247	−	1.04401i	0.591053	−	0.806633i	$-0.298713\pi$
$761$	43.1027	−	28.8003i	1.56247	−	1.04401i	0.971418	−	0.237376i	$-0.0762874\pi$
$762$	−19.0476	+	15.0250i	−0.690023	+	0.544298i
$763$	−6.14992	+	5.04711i	−0.222642	+	0.182718i
$764$	−9.05123	−	24.4902i	−0.327462	−	0.886026i
$765$	4.05108	+	7.57904i	0.146467	+	0.274021i
$766$	−4.72270	−	26.4016i	−0.170638	−	0.953927i
$767$	−12.9202			−0.466522
$768$	−15.1046	+	5.27749i	−0.545039	+	0.190435i
$769$	−29.5679			−1.06625			−0.533124	−	0.846037i	$-0.678982\pi$
$769$	−29.5679			−1.06625			−0.533124	+	0.846037i	$0.678982\pi$
$770$	−1.97201	−	11.0242i	−0.0710664	−	0.397286i
$771$	11.5775	+	21.6600i	0.416953	+	0.780065i
$772$	14.8718	+	40.2391i	0.535246	+	1.44824i
$773$	−6.92877	+	5.68630i	−0.249211	+	0.204522i	−0.750702	−	0.660641i	$-0.770285\pi$
$773$	−6.92877	+	5.68630i	−0.249211	+	0.204522i	0.501492	+	0.865162i	$0.332785\pi$
$774$	−1.42491	+	1.12399i	−0.0512175	+	0.0404009i
$775$	5.38540	−	3.59841i	0.193449	−	0.129259i
$776$	−1.57520	+	6.05829i	−0.0565465	+	0.217480i
$777$	5.00664	−	7.49297i	0.179612	−	0.268809i
$778$	−16.9623	−	14.4786i	−0.608129	−	0.519083i
$779$	−0.0834058	−	0.274952i	−0.00298832	−	0.00985118i
$780$	2.16915	−	2.44391i	0.0776682	−	0.0875061i
$781$	−2.27189	+	2.76831i	−0.0812946	+	0.0990578i
$782$	31.0484	+	32.2734i	1.11029	+	1.15409i
$783$	2.94772	+	1.22099i	0.105343	+	0.0436345i
$784$	2.41159	+	7.39262i	0.0861281	+	0.264022i
$785$	6.37155	−	2.63918i	0.227410	−	0.0941965i
$786$	4.87642	+	2.13129i	0.173936	+	0.0760206i
$787$	−1.14670	+	0.112940i	−0.0408754	+	0.00402588i	−0.118434	−	0.992962i	$-0.537787\pi$
$787$	−1.14670	+	0.112940i	−0.0408754	+	0.00402588i	0.0775587	+	0.996988i	$0.475287\pi$
$788$	22.4549	+	13.1434i	0.799924	+	0.468214i
$789$	0.865825	+	0.462793i	0.0308242	+	0.0164759i
$790$	−23.9136	+	12.1934i	−0.850808	+	0.433822i
$791$	21.4178	−	4.26026i	0.761528	−	0.151477i
$792$	−1.82919	−	7.58975i	−0.0649976	−	0.269690i
$793$	−0.276547	+	1.39029i	−0.00982046	+	0.0493708i
$794$	−23.4493	−	13.1232i	−0.832185	−	0.465726i
$795$	9.88996	+	0.974076i	0.350761	+	0.0345469i
$796$	−34.5036	−	25.0375i	−1.22295	−	0.887430i
$797$	−20.5681	−	6.23928i	−0.728561	−	0.221007i	−0.0958513	−	0.995396i	$-0.530557\pi$
$797$	−20.5681	−	6.23928i	−0.728561	−	0.221007i	−0.632710	+	0.774389i	$0.718057\pi$
$798$	−1.67811	+	7.65912i	−0.0594045	+	0.271130i
$799$	−42.0520	−	42.0520i	−1.48769	−	1.48769i
$800$	−14.7274	+	12.1226i	−0.520691	+	0.428598i
$801$	−12.1201	+	12.1201i	−0.428243	+	0.428243i
$802$	17.7379	+	27.6914i	0.626346	+	0.977818i
$803$	4.90633	−	16.1740i	0.173141	−	0.570768i
$804$	0.00624511	+	0.00149545i	0.000220248	+	5.27404e-5i
$805$	1.32215	−	13.4240i	0.0465996	−	0.473134i
$806$	−0.945172	−	3.34757i	−0.0332923	−	0.117913i
$807$	0.863572	+	0.171775i	0.0303992	+	0.00604678i
$808$	19.2310	+	41.6190i	0.676544	+	1.46415i
$809$	5.59765	+	28.1413i	0.196803	+	0.989396i	0.945286	+	0.326242i	$0.105782\pi$
$809$	5.59765	+	28.1413i	0.196803	+	0.989396i	−0.748483	+	0.663154i	$0.769218\pi$
$810$	0.557100	−	1.71629i	0.0195745	−	0.0603042i
$811$	−0.668067	+	1.24987i	−0.0234590	+	0.0438887i	−0.893378	−	0.449306i	$-0.851671\pi$
$811$	−0.668067	+	1.24987i	−0.0234590	+	0.0438887i	0.869919	+	0.493195i	$0.164171\pi$
$812$	−11.4352	+	8.66679i	−0.401298	+	0.304145i
$813$	0.379624	+	3.85439i	0.0133140	+	0.135179i
$814$	5.70623	+	14.5667i	0.200003	+	0.510564i
$815$	4.10836	+	9.91845i	0.143910	+	0.347428i
$816$	−26.9354	+	0.560516i	−0.942926	+	0.0196220i
$817$	−1.21091	+	2.92339i	−0.0423643	+	0.102276i
$818$	−37.9788	−	0.734679i	−1.32790	−	0.0256874i
$819$	2.22574	+	1.82662i	0.0777737	+	0.0638272i
$820$	−0.281008	−	0.0972605i	−0.00981321	−	0.00339648i
$821$	15.7043	−	4.76385i	0.548084	−	0.166259i	−0.00408510	−	0.999992i	$-0.501300\pi$
$821$	15.7043	−	4.76385i	0.548084	−	0.166259i	0.552169	+	0.833732i	$0.313800\pi$
$822$	1.51444	+	19.1710i	0.0528222	+	0.668666i
$823$	−24.6562	−	16.4747i	−0.859460	−	0.574273i	0.0458861	−	0.998947i	$-0.485389\pi$
$823$	−24.6562	−	16.4747i	−0.859460	−	0.574273i	−0.905347	+	0.424674i	$0.860389\pi$
$824$	49.5667	−	17.2370i	1.72674	−	0.600481i
$825$	−5.17093	−	7.73885i	−0.180029	−	0.269432i
$826$	3.76185	−	31.8637i	0.130892	−	1.10868i
$827$	−12.9617	−	15.7939i	−0.450724	−	0.549208i	0.497229	−	0.867619i	$-0.334351\pi$
$827$	−12.9617	−	15.7939i	−0.450724	−	0.549208i	−0.947953	+	0.318411i	$0.896851\pi$
$828$	0.363665	−	9.39621i	0.0126382	−	0.326541i
$829$	−37.3977	+	19.9895i	−1.29888	+	0.694264i	−0.968365	−	0.249538i	$-0.919721\pi$
$829$	−37.3977	+	19.9895i	−1.29888	+	0.694264i	−0.330511	+	0.943802i	$0.607221\pi$
$830$	7.98254	−	11.4605i	0.277078	−	0.397800i
$831$			19.8948i			0.690144i
$832$	3.75045	+	9.53293i	0.130024	+	0.330495i
$833$			13.0935i			0.453661i
$834$	−11.6472	−	8.11256i	−0.403309	−	0.280915i
$835$	8.53663	−	4.56293i	0.295422	−	0.157907i
$836$	−9.24554	−	9.99003i	−0.319764	−	0.345512i
$837$	−1.21855	−	1.48481i	−0.0421192	−	0.0513224i
$838$	−24.5192	−	2.89476i	−0.847002	−	0.0999977i
$839$	−21.8838	−	32.7515i	−0.755514	−	1.13071i	−0.987443	−	0.157974i	$-0.949504\pi$
$839$	−21.8838	−	32.7515i	−0.755514	−	1.13071i	0.231929	−	0.972733i	$-0.425496\pi$
$840$	5.39558	+	6.06111i	0.186165	+	0.209128i
$841$	−15.6484	−	10.4559i	−0.539598	−	0.360548i
$842$	23.5239	−	1.85831i	0.810688	−	0.0640415i
$843$	−20.4918	+	6.21611i	−0.705774	+	0.214094i
$844$	−1.25540	−	2.58442i	−0.0432128	−	0.0889593i
$845$	11.2047	+	9.19549i	0.385455	+	0.316334i
$846$	−0.241510	+	12.4847i	−0.00830328	+	0.429233i
$847$	2.90949	−	7.02412i	0.0999711	−	0.241352i
$848$	−16.7659	+	26.2587i	−0.575744	+	0.901726i
$849$	8.64777	+	20.8776i	0.296791	+	0.716516i
$850$	−29.9061	+	11.7151i	−1.02577	+	0.401825i
$851$	1.84695	+	18.7524i	0.0633125	+	0.642823i
$852$	0.354023	−	2.57061i	0.0121286	−	0.0880676i
$853$	7.17421	−	13.4220i	0.245640	−	0.459560i	−0.728641	−	0.684896i	$-0.759848\pi$
$853$	7.17421	−	13.4220i	0.245640	−	0.459560i	0.974281	+	0.225335i	$0.0723478\pi$
$854$	−3.34821	−	1.08681i	−0.114573	−	0.0371900i
$855$	−0.613770	−	3.08563i	−0.0209905	−	0.105526i
$856$	−1.88303	−	46.8763i	−0.0643608	−	1.60220i
$857$	29.4254	+	5.85308i	1.00515	+	0.199937i	0.670107	−	0.742264i	$-0.266248\pi$
$857$	29.4254	+	5.85308i	1.00515	+	0.199937i	0.335046	+	0.942202i	$0.391248\pi$
$858$	−4.81048	+	1.35822i	−0.164227	+	0.0463688i
$859$	−2.67173	+	27.1265i	−0.0911581	+	0.925544i	0.835463	+	0.549547i	$0.185200\pi$
$859$	−2.67173	+	27.1265i	−0.0911581	+	0.925544i	−0.926621	+	0.375997i	$0.877300\pi$
$860$	1.71272	+	2.79123i	0.0584033	+	0.0951803i
$861$	0.0760601	−	0.250737i	0.00259212	−	0.00854508i
$862$	26.2882	−	16.8390i	0.895379	−	0.573539i
$863$	22.6147	−	22.6147i	0.769815	−	0.769815i	−0.208259	−	0.978074i	$-0.566780\pi$
$863$	22.6147	−	22.6147i	0.769815	−	0.769815i	0.978074	+	0.208259i	$0.0667797\pi$
$864$	4.00585	+	3.99414i	0.136282	+	0.135883i
$865$	19.3312	+	19.3312i	0.657279	+	0.657279i
$866$	17.0707	+	3.74020i	0.580088	+	0.127097i
$867$	−27.1429	−	8.23369i	−0.921820	−	0.279631i
$868$	8.53094	−	1.35629i	0.289559	−	0.0460356i
$869$	40.8633	+	4.02468i	1.38619	+	0.136528i
$870$	2.81164	−	5.02399i	0.0953234	−	0.170329i
$871$	0.000802120	−	0.00403253i	2.71788e−5	−	0.000136637i
$872$	5.88938	+	8.09107i	0.199439	+	0.273998i
$873$	2.17062	−	0.431763i	0.0734644	−	0.0146130i
$874$	−7.44735	−	14.6057i	−0.251910	−	0.494044i
$875$	21.1831	+	11.3226i	0.716120	+	0.382774i
$876$	3.09914	+	11.8481i	0.104710	+	0.400310i
$877$	−47.5837	+	4.68658i	−1.60679	+	0.158255i	−0.861240	−	0.508198i	$-0.830312\pi$
$877$	−47.5837	+	4.68658i	−1.60679	+	0.158255i	−0.745547	+	0.666453i	$0.767812\pi$
$878$	8.87365	−	20.3031i	0.299471	−	0.685195i
$879$	−9.85255	+	4.08106i	−0.332318	+	0.137651i
$880$	−13.9878	+	1.67218i	−0.471528	+	0.0563693i
$881$	−21.7742	−	9.01916i	−0.733590	−	0.303863i	−0.0155639	−	0.999879i	$-0.504954\pi$
$881$	−21.7742	−	9.01916i	−0.733590	−	0.303863i	−0.718027	+	0.696016i	$0.754954\pi$
$882$	1.98124	−	1.90604i	0.0667119	−	0.0641798i
$883$	34.9103	−	42.5384i	1.17483	−	1.43153i	0.295479	−	0.955349i	$-0.404521\pi$
$883$	34.9103	−	42.5384i	1.17483	−	1.43153i	0.879347	−	0.476181i	$-0.157979\pi$
$884$	1.02557	+	17.2188i	0.0344937	+	0.579132i
$885$	3.73710	+	12.3196i	0.125621	+	0.414118i
$886$	38.3365	−	44.9129i	1.28794	−	1.50888i
$887$	17.0674	−	25.5432i	0.573069	−	0.857658i	−0.425819	−	0.904808i	$-0.640014\pi$
$887$	17.0674	−	25.5432i	0.573069	−	0.857658i	0.998888	+	0.0471503i	$0.0150140\pi$
$888$	−9.04422	−	6.83380i	−0.303504	−	0.229327i
$889$	−32.0724	+	21.4301i	−1.07567	+	0.718741i
$890$	19.1550	+	24.2833i	0.642077	+	0.813980i
$891$	−2.13367	+	1.75106i	−0.0714808	+	0.0586628i
$892$	9.95242	−	21.6218i	0.333232	−	0.723951i
$893$	10.2630	+	19.2007i	0.343438	+	0.642527i
$894$	−16.8358	+	3.01159i	−0.563074	+	0.100723i
$895$	22.7473			0.760359
$896$	−24.6020	+	6.47372i	−0.821895	+	0.216272i
$897$	−6.02052			−0.201019
$898$	15.1003	−	2.70114i	0.503904	−	0.0901382i
$899$	−2.88896	−	5.40487i	−0.0963523	−	0.180263i
$900$	6.12617	+	2.81985i	0.204206	+	0.0939950i
$901$	−40.5513	+	33.2796i	−1.35096	+	1.10871i
$902$	0.281712	+	0.357135i	0.00937998	+	0.0118913i
$903$	−2.39927	+	1.60314i	−0.0798426	+	0.0533491i
$904$	−3.78749	−	27.2066i	−0.125970	−	0.904877i
$905$	15.9483	−	23.8684i	0.530140	−	0.793411i
$906$	5.14344	−	6.02576i	0.170879	−	0.200193i
$907$	−9.96347	−	32.8451i	−0.330831	−	1.09061i	−0.951787	−	0.306759i	$-0.900755\pi$
$907$	−9.96347	−	32.8451i	−0.330831	−	1.09061i	0.620956	−	0.783846i	$-0.286745\pi$
$908$	−7.24580	+	0.431567i	−0.240460	+	0.0143221i
$909$	10.2832	−	12.5301i	0.341071	−	0.415597i
$910$	3.74418	−	3.60207i	0.124118	−	0.119407i
$911$	−10.5503	−	4.37006i	−0.349546	−	0.144787i	0.201001	−	0.979591i	$-0.435581\pi$
$911$	−10.5503	−	4.37006i	−0.349546	−	0.144787i	−0.550547	+	0.834804i	$0.685581\pi$
$912$	9.49568	+	2.66605i	0.314433	+	0.0882818i
$913$	−19.7381	+	8.17577i	−0.653234	+	0.270579i
$914$	17.9367	−	41.0395i	0.593294	−	1.35747i
$915$	1.40565	−	0.138445i	0.0464694	−	0.00457684i
$916$	5.18651	−	1.35665i	0.171367	−	0.0448249i
$917$	7.46241	+	3.98874i	0.246431	+	0.131720i
$918$	4.32681	+	8.48570i	0.142806	+	0.280070i
$919$	−47.0362	+	9.35608i	−1.55158	+	0.308629i	−0.895153	−	0.445760i	$-0.852934\pi$
$919$	−47.0362	+	9.35608i	−1.55158	+	0.308629i	−0.656429	+	0.754388i	$0.727934\pi$
$920$	−16.7610	−	2.63959i	−0.552594	−	0.0870246i
$921$	6.06730	−	30.5024i	0.199924	−	1.00509i
$922$	−1.38906	+	2.48205i	−0.0457462	+	0.0817419i
$923$	−1.65339	−	0.162845i	−0.0544221	−	0.00536011i
$924$	−1.94900	−	12.2590i	−0.0641174	−	0.403292i
$925$	−12.9323	−	3.92298i	−0.425212	−	0.128987i
$926$	38.5078	+	8.43705i	1.26544	+	0.277259i
$927$	−13.1196	−	13.1196i	−0.430903	−	0.430903i
$928$	10.0493	+	14.9923i	0.329884	+	0.492145i
$929$	−16.6468	+	16.6468i	−0.546165	+	0.546165i	−0.925329	−	0.379164i	$-0.876212\pi$
$929$	−16.6468	+	16.6468i	−0.546165	+	0.546165i	0.379164	+	0.925329i	$0.376212\pi$
$930$	−2.91856	+	1.86950i	−0.0957035	+	0.0613033i
$931$	1.39144	−	4.58696i	0.0456026	−	0.150332i
$932$	−17.4894	+	10.7316i	−0.572884	+	0.351526i
$933$	−1.38185	+	14.0301i	−0.0452397	+	0.459326i
$934$	−5.74555	+	1.62223i	−0.188000	+	0.0530810i
$935$	−23.2649	−	4.62767i	−0.760843	−	0.151341i
$936$	2.45618	−	2.66177i	0.0802828	−	0.0870027i
$937$	−0.311285	−	1.56494i	−0.0101692	−	0.0511242i	0.975367	−	0.220586i	$-0.0707970\pi$
$937$	−0.311285	−	1.56494i	−0.0101692	−	0.0511242i	−0.985537	+	0.169462i	$0.945797\pi$
$938$	0.00971143	+	0.00315229i	0.000317089	+	0.000102926i
$939$	−13.9192	+	26.0410i	−0.454236	+	0.849816i
$940$	22.3214	+	3.07410i	0.728045	+	0.100266i
$941$	4.76335	+	48.3631i	0.155281	+	1.57659i	0.685080	+	0.728468i	$0.259767\pi$
$941$	4.76335	+	48.3631i	0.155281	+	1.57659i	−0.529799	+	0.848123i	$0.677733\pi$
$942$	7.11734	−	2.78808i	0.231895	−	0.0908404i
$943$	0.209661	+	0.506166i	0.00682749	+	0.0164830i
$944$	−39.7390	−	7.04845i	−1.29340	−	0.229408i
$945$	1.09792	−	2.65061i	0.0357153	−	0.0862244i
$946$	0.0968861	−	5.00847i	0.00315004	−	0.162840i
$947$	−17.4072	−	14.2857i	−0.565658	−	0.464224i	0.307577	−	0.951523i	$-0.400482\pi$
$947$	−17.4072	−	14.2857i	−0.565658	−	0.464224i	−0.873235	+	0.487300i	$0.837982\pi$
$948$	−26.7617	+	12.9997i	−0.869181	+	0.422212i
$949$	7.50345	−	2.27615i	0.243572	−	0.0738868i
$950$	11.7218	−	0.925980i	0.380305	−	0.0300427i
$951$	5.35734	+	3.57966i	0.173724	+	0.116078i
$952$	−42.7635	−	2.48419i	−1.38597	−	0.0805130i
$953$	19.5709	+	29.2899i	0.633964	+	0.948794i	0.999836	+	0.0181290i	$0.00577097\pi$
$953$	19.5709	+	29.2899i	0.633964	+	0.948794i	−0.365871	+	0.930665i	$0.619229\pi$
$954$	10.9389	+	1.29145i	0.354159	+	0.0418123i
$955$	10.5670	+	12.8759i	0.341940	+	0.416655i
$956$	2.09842	−	1.94204i	0.0678676	−	0.0628099i
$957$	−7.76683	+	4.15146i	−0.251066	+	0.134198i
$958$	−5.69933	−	3.96973i	−0.184137	−	0.128256i
$959$			30.5762i			0.987358i
$960$	8.00497	−	6.33345i	0.258359	−	0.204411i
$961$		−	27.3105i		−	0.880984i
$962$	−4.14819	+	5.95554i	−0.133743	+	0.192014i
$963$	−14.6281	+	7.81889i	−0.471384	+	0.251960i
$964$	−43.2311	−	1.67319i	−1.39238	−	0.0538897i
$965$	−17.3623	−	21.1560i	−0.558911	−	0.681035i
$966$	1.75294	−	14.8477i	0.0563998	−	0.477718i
$967$	18.2307	+	27.2841i	0.586258	+	0.877397i	0.999447	−	0.0332479i	$-0.0105851\pi$
$967$	18.2307	+	27.2841i	0.586258	+	0.877397i	−0.413189	+	0.910645i	$0.635585\pi$
$968$	−8.60844	−	4.16605i	−0.276686	−	0.133902i
$969$	13.8085	+	9.22652i	0.443592	+	0.296399i
$970$	−0.314492	−	3.98109i	−0.0100977	−	0.127825i
$971$	51.6324	−	15.6625i	1.65696	−	0.502634i	0.683205	−	0.730226i	$-0.260585\pi$
$971$	51.6324	−	15.6625i	1.65696	−	0.502634i	0.973757	+	0.227592i	$0.0730853\pi$
$972$	0.654153	−	1.89000i	0.0209820	−	0.0606216i
$973$	−17.4453	−	14.3170i	−0.559271	−	0.458982i
$974$	−20.1365	−	0.389529i	−0.645215	−	0.0124813i
$975$	1.65239	−	3.98923i	0.0529189	−	0.127758i
$976$	−1.60904	+	4.12530i	−0.0515040	+	0.132047i
$977$	−22.4816	−	54.2753i	−0.719250	−	1.73642i	−0.675477	−	0.737381i	$-0.736062\pi$
$977$	−22.4816	−	54.2753i	−0.719250	−	1.73642i	−0.0437721	−	0.999042i	$-0.513938\pi$
$978$	4.34014	+	11.0794i	0.138782	+	0.354280i
$979$	−4.63731	−	47.0834i	−0.148209	−	1.50479i
$980$	−2.99646	−	3.95363i	−0.0957184	−	0.126294i
$981$	1.66789	−	3.12040i	0.0532516	−	0.0996268i
$982$	−3.63132	+	11.1872i	−0.115880	+	0.356998i
$983$	−4.69529	−	23.6048i	−0.149756	−	0.752876i	−0.980546	−	0.196289i	$-0.937111\pi$
$983$	−4.69529	−	23.6048i	−0.149756	−	0.752876i	0.830790	−	0.556587i	$-0.187889\pi$
$984$	−0.309319	−	0.113805i	−0.00986073	−	0.00362797i
$985$	−16.2801	−	3.23831i	−0.518727	−	0.103181i
$986$	8.25788	+	29.2474i	0.262984	+	0.931428i
$987$	−1.94603	+	19.7584i	−0.0619429	+	0.628917i
$988$	1.47056	−	6.14117i	0.0467847	−	0.195377i
$989$	1.75146	−	5.77380i	0.0556933	−	0.183596i
$990$	2.68648	+	4.19399i	0.0853820	+	0.133294i
$991$	17.4263	−	17.4263i	0.553563	−	0.553563i	−0.373904	−	0.927467i	$-0.621981\pi$
$991$	17.4263	−	17.4263i	0.553563	−	0.553563i	0.927467	+	0.373904i	$0.121981\pi$
$992$	−1.08087	−	10.8118i	−0.0343175	−	0.343276i
$993$	−6.97602	−	6.97602i	−0.221377	−	0.221377i
$994$	0.883008	−	4.03016i	0.0280073	−	0.127829i
$995$	26.0259	+	7.89486i	0.825075	+	0.250284i
$996$	9.09169	−	12.5291i	0.288081	−	0.396999i
$997$	19.5733	+	1.92780i	0.619892	+	0.0610540i	0.403088	−	0.915161i	$-0.367937\pi$
$997$	19.5733	+	1.92780i	0.619892	+	0.0610540i	0.216804	+	0.976215i	$0.430437\pi$
$998$	18.4608	+	10.3314i	0.584367	+	0.327036i
$999$	−0.781880	+	3.93078i	−0.0247376	+	0.124364i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.37.19	✓	512
128.45	even	32	inner	384.2.v.a.301.19	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.37.19	✓	512	1.1	even	1	trivial
384.2.v.a.301.19	yes	512	128.45	even	32	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:	\( N \)	\(=\)	\( 384 = 2^{7} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	384.v (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.249021 + 1.39212i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.87598 + 0.693333i) q^{4} +(0.986309 - 0.809443i) q^{5} +(1.11035 - 0.875856i) q^{6} +(1.86960 - 1.24923i) q^{7} +(-1.43236 - 2.43892i) q^{8} +(-0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(0.249021 + 1.39212i) q^{2} +(-0.471397 - 0.881921i) q^{3} +(-1.87598 + 0.693333i) q^{4} +(0.986309 - 0.809443i) q^{5} +(1.11035 - 0.875856i) q^{6} +(1.86960 - 1.24923i) q^{7} +(-1.43236 - 2.43892i) q^{8} +(-0.555570 + 0.831470i) q^{9} +(1.37245 + 1.17149i) q^{10} +(-0.801248 - 2.64136i) q^{11} +(1.49579 + 1.32763i) q^{12} +(0.812353 - 0.989855i) q^{13} +(2.20464 + 2.29162i) q^{14} +(-1.17881 - 0.488278i) q^{15} +(3.03858 - 2.60135i) q^{16} +(6.22260 - 2.57749i) q^{17} +(-1.29585 - 0.566365i) q^{18} +(-2.45384 + 0.241682i) q^{19} +(-1.28908 + 2.20234i) q^{20} +(-1.98305 - 1.05996i) q^{21} +(3.47755 - 1.77319i) q^{22} +(4.61128 - 0.917241i) q^{23} +(-1.47573 + 2.41293i) q^{24} +(-0.657844 + 3.30721i) q^{25} +(1.58029 + 0.884395i) q^{26} +(0.995185 + 0.0980171i) q^{27} +(-2.64120 + 3.63978i) q^{28} +(3.05321 + 0.926180i) q^{29} +(0.386192 - 1.76263i) q^{30} +(-1.35822 - 1.35822i) q^{31} +(4.37806 + 3.58226i) q^{32} +(-1.95177 + 1.95177i) q^{33} +(5.13772 + 8.02074i) q^{34} +(0.832827 - 2.74546i) q^{35} +(0.465751 - 1.94501i) q^{36} +(-0.392832 + 3.98849i) q^{37} +(-0.947508 - 3.35585i) q^{38} +(-1.25591 - 0.249817i) q^{39} +(-3.38692 - 1.24612i) q^{40} +(0.0227335 + 0.114289i) q^{41} +(0.981768 - 3.02459i) q^{42} +(0.604945 - 1.13177i) q^{43} +(3.33446 + 4.39960i) q^{44} +(0.125063 + 1.26979i) q^{45} +(2.42521 + 6.19103i) q^{46} +(-3.37897 - 8.15756i) q^{47} +(-3.72657 - 1.45352i) q^{48} +(-0.743939 + 1.79603i) q^{49} +(-4.76783 - 0.0922310i) q^{50} +(-5.20645 - 4.27283i) q^{51} +(-0.837656 + 2.42018i) q^{52} +(-7.45329 + 2.26093i) q^{53} +(0.111371 + 1.40982i) q^{54} +(-2.92831 - 1.95663i) q^{55} +(-5.72472 - 2.77048i) q^{56} +(1.36988 + 2.05016i) q^{57} +(-0.529037 + 4.48106i) q^{58} +(-6.40092 - 7.79954i) q^{59} +(2.54995 + 0.0986918i) q^{60} +(-0.976284 + 0.521835i) q^{61} +(1.55257 - 2.22902i) q^{62} +2.24855i q^{63} +(-3.89670 + 6.98683i) q^{64} -1.63386i q^{65} +(-3.20312 - 2.23105i) q^{66} +(0.00283170 - 0.00151358i) q^{67} +(-9.88640 + 9.14964i) q^{68} +(-2.98268 - 3.63440i) q^{69} +(4.02940 + 0.475714i) q^{70} +(-0.720817 - 1.07878i) q^{71} +(2.82367 + 0.164030i) q^{72} +(5.09139 + 3.40196i) q^{73} +(-5.65026 + 0.446351i) q^{74} +(3.22680 - 0.978839i) q^{75} +(4.43578 - 2.15472i) q^{76} +(-4.79768 - 3.93735i) q^{77} +(0.0350248 - 1.81059i) q^{78} +(-5.69280 + 13.7436i) q^{79} +(0.891329 - 5.02529i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-0.153442 + 0.0601080i) q^{82} +(-0.758662 - 7.70283i) q^{83} +(4.45506 + 0.613549i) q^{84} +(4.05108 - 7.57904i) q^{85} +(1.72620 + 0.560318i) q^{86} +(-0.622454 - 3.12929i) q^{87} +(-5.29440 + 5.73756i) q^{88} +(16.8111 + 3.34393i) q^{89} +(-1.73655 + 0.490307i) q^{90} +(0.282222 - 2.86545i) q^{91} +(-8.01470 + 4.91788i) q^{92} +(-0.557581 + 1.83810i) q^{93} +(10.5148 - 6.73533i) q^{94} +(-2.22462 + 2.22462i) q^{95} +(1.09547 - 5.54977i) q^{96} +(-1.56493 - 1.56493i) q^{97} +(-2.68554 - 0.588401i) q^{98} +(2.64136 + 0.801248i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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