LMFDB - Embedded newform 384.2.v.a.109.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("384.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			109.9
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.788656 + 1.17389i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-0.756043 - 1.85159i) q^{4} +(-0.453393 + 0.552461i) q^{5} +(1.24890 - 0.663510i) q^{6} +(-1.44548 - 0.965841i) q^{7} +(2.76983 + 0.572759i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})$	\(q+(-0.788656 + 1.17389i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-0.756043 - 1.85159i) q^{4} +(-0.453393 + 0.552461i) q^{5} +(1.24890 - 0.663510i) q^{6} +(-1.44548 - 0.965841i) q^{7} +(2.76983 + 0.572759i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.290958 - 0.967935i) q^{10} +(2.30143 + 0.698132i) q^{11} +(-0.206065 + 1.98936i) q^{12} +(-1.74047 + 1.42836i) q^{13} +(2.27378 - 0.935124i) q^{14} +(0.660285 - 0.273499i) q^{15} +(-2.85680 + 2.79977i) q^{16} +(5.03347 + 2.08493i) q^{17} +(-1.41421 - 0.00356449i) q^{18} +(-0.389496 + 3.95462i) q^{19} +(1.36572 + 0.421815i) q^{20} +(0.819508 + 1.53319i) q^{21} +(-2.63457 + 2.15105i) q^{22} +(-1.78138 - 0.354339i) q^{23} +(-2.17277 - 1.81082i) q^{24} +(0.875804 + 4.40296i) q^{25} +(-0.304115 - 3.16961i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(-0.695498 + 3.40667i) q^{28} +(2.69440 + 8.88225i) q^{29} +(-0.199680 + 0.990799i) q^{30} +(0.759258 - 0.759258i) q^{31} +(-1.03359 - 5.56163i) q^{32} +(-1.70059 - 1.70059i) q^{33} +(-6.41716 + 4.26445i) q^{34} +(1.18896 - 0.360667i) q^{35} +(1.11951 - 1.65732i) q^{36} +(0.701562 - 0.0690978i) q^{37} +(-4.33512 - 3.57606i) q^{38} +(2.20828 - 0.439254i) q^{39} +(-1.57225 + 1.27054i) q^{40} +(-1.73814 + 8.73822i) q^{41} +(-2.44611 - 0.247148i) q^{42} +(-3.05435 + 1.63259i) q^{43} +(-0.447325 - 4.78914i) q^{44} +(-0.711246 - 0.0700516i) q^{45} +(1.82085 - 1.81170i) q^{46} +(3.60433 - 8.70163i) q^{47} +(3.83927 - 1.12249i) q^{48} +(-1.52221 - 3.67494i) q^{49} +(-5.85931 - 2.44433i) q^{50} +(-3.45629 - 4.21150i) q^{51} +(3.96062 + 2.14273i) q^{52} +(-0.661557 + 2.18086i) q^{53} +(1.24554 + 0.669797i) q^{54} +(-1.42914 + 0.954923i) q^{55} +(-3.45055 - 3.50313i) q^{56} +(2.20770 - 3.30406i) q^{57} +(-12.5518 - 3.84211i) q^{58} +(7.60232 + 6.23907i) q^{59} +(-1.00561 - 1.01580i) q^{60} +(0.233796 - 0.437401i) q^{61} +(0.292493 + 1.49008i) q^{62} -1.73847i q^{63} +(7.34389 + 3.17289i) q^{64} -1.60915i q^{65} +(3.33748 - 0.655125i) q^{66} +(-1.98855 + 3.72031i) q^{67} +(0.0549278 - 10.8962i) q^{68} +(1.40400 + 1.15224i) q^{69} +(-0.514297 + 1.68015i) q^{70} +(2.72431 - 4.07722i) q^{71} +(1.06260 + 2.62124i) q^{72} +(0.964879 - 0.644711i) q^{73} +(-0.472178 + 0.878052i) q^{74} +(1.30315 - 4.29592i) q^{75} +(7.61683 - 2.26867i) q^{76} +(-2.65240 - 3.23196i) q^{77} +(-1.22594 + 2.93870i) q^{78} +(-0.799719 - 1.93069i) q^{79} +(-0.251510 - 2.84766i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(-8.88693 - 8.93184i) q^{82} +(-4.07908 - 0.401754i) q^{83} +(2.21927 - 2.67656i) q^{84} +(-3.43398 + 1.83550i) q^{85} +(0.492356 - 4.87303i) q^{86} +(1.81081 - 9.10358i) q^{87} +(5.97471 + 3.25187i) q^{88} +(10.4965 - 2.08788i) q^{89} +(0.643161 - 0.779679i) q^{90} +(3.89539 - 0.383662i) q^{91} +(0.690709 + 3.56629i) q^{92} +(-1.02752 + 0.311694i) q^{93} +(7.37219 + 11.0937i) q^{94} +(-2.00818 - 2.00818i) q^{95} +(-1.71019 + 5.39215i) q^{96} +(13.4124 - 13.4124i) q^{97} +(5.51448 + 1.11136i) q^{98} +(0.698132 + 2.30143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−0.788656	+	1.17389i	−0.557664	+	0.830067i
$2$	−0.788656	+	1.17389i	−0.557664	+	0.830067i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$3$	−0.881921	−	0.471397i	−0.509177	−	0.272161i
$4$	−0.756043	−	1.85159i	−0.378021	−	0.925797i
$5$	−0.453393	+	0.552461i	−0.202763	+	0.247068i	−0.864457	−	0.502706i	$-0.832338\pi$
$5$	−0.453393	+	0.552461i	−0.202763	+	0.247068i	0.661694	+	0.749774i	$0.269838\pi$
$6$	1.24890	−	0.663510i	0.509862	−	0.270877i
$7$	−1.44548	−	0.965841i	−0.546342	−	0.365054i	0.251560	−	0.967842i	$-0.419056\pi$
$7$	−1.44548	−	0.965841i	−0.546342	−	0.365054i	−0.797901	+	0.602788i	$0.794056\pi$
$8$	2.76983	+	0.572759i	0.979282	+	0.202501i
$9$	0.555570	+	0.831470i	0.185190	+	0.277157i
$10$	−0.290958	−	0.967935i	−0.0920089	−	0.306088i
$11$	2.30143	+	0.698132i	0.693908	+	0.210495i	0.617487	−	0.786581i	$-0.288151\pi$
$11$	2.30143	+	0.698132i	0.693908	+	0.210495i	0.0764208	+	0.997076i	$0.475651\pi$
$12$	−0.206065	+	1.98936i	−0.0594859	+	0.574278i
$13$	−1.74047	+	1.42836i	−0.482719	+	0.396157i	−0.844036	−	0.536286i	$-0.819827\pi$
$13$	−1.74047	+	1.42836i	−0.482719	+	0.396157i	0.361318	+	0.932443i	$0.382327\pi$
$14$	2.27378	−	0.935124i	0.607694	−	0.249923i
$15$	0.660285	−	0.273499i	0.170485	−	0.0706171i
$16$	−2.85680	+	2.79977i	−0.714200	+	0.699942i
$17$	5.03347	+	2.08493i	1.22080	+	0.505670i	0.897662	−	0.440684i	$-0.145264\pi$
$17$	5.03347	+	2.08493i	1.22080	+	0.505670i	0.323133	+	0.946354i	$0.395264\pi$
$18$	−1.41421	−	0.00356449i	−0.333332	−	0.000840158i
$19$	−0.389496	+	3.95462i	−0.0893566	+	0.907252i	0.841107	+	0.540868i	$0.181904\pi$
$19$	−0.389496	+	3.95462i	−0.0893566	+	0.907252i	−0.930464	+	0.366384i	$0.880596\pi$
$20$	1.36572	+	0.421815i	0.305384	+	0.0943208i
$21$	0.819508	+	1.53319i	0.178831	+	0.334570i
$22$	−2.63457	+	2.15105i	−0.561692	+	0.458605i
$23$	−1.78138	−	0.354339i	−0.371444	−	0.0738847i	0.00583886	−	0.999983i	$-0.498141\pi$
$23$	−1.78138	−	0.354339i	−0.371444	−	0.0738847i	−0.377283	+	0.926098i	$0.623141\pi$
$24$	−2.17277	−	1.81082i	−0.443516	−	0.369631i
$25$	0.875804	+	4.40296i	0.175161	+	0.880593i
$26$	−0.304115	−	3.16961i	−0.0596418	−	0.621611i
$27$	−0.0980171	−	0.995185i	−0.0188634	−	0.191523i
$28$	−0.695498	+	3.40667i	−0.131437	+	0.643799i
$29$	2.69440	+	8.88225i	0.500338	+	1.64939i	0.735566	+	0.677453i	$0.236916\pi$
$29$	2.69440	+	8.88225i	0.500338	+	1.64939i	−0.235228	+	0.971940i	$0.575584\pi$
$30$	−0.199680	+	0.990799i	−0.0364563	+	0.180894i
$31$	0.759258	−	0.759258i	0.136367	−	0.136367i	−0.635628	−	0.771995i	$-0.719259\pi$
$31$	0.759258	−	0.759258i	0.136367	−	0.136367i	0.771995	+	0.635628i	$0.219259\pi$
$32$	−1.03359	−	5.56163i	−0.182715	−	0.983166i
$33$	−1.70059	−	1.70059i	−0.296034	−	0.296034i
$34$	−6.41716	+	4.26445i	−1.10053	+	0.731347i
$35$	1.18896	−	0.360667i	0.200971	−	0.0609639i
$36$	1.11951	−	1.65732i	0.186585	−	0.276219i
$37$	0.701562	−	0.0690978i	0.115336	−	0.0113596i	−0.0401844	−	0.999192i	$-0.512795\pi$
$37$	0.701562	−	0.0690978i	0.115336	−	0.0113596i	0.155520	+	0.987833i	$0.450295\pi$
$38$	−4.33512	−	3.57606i	−0.703249	−	0.580114i
$39$	2.20828	−	0.439254i	0.353608	−	0.0703370i
$40$	−1.57225	+	1.27054i	−0.248594	+	0.200889i
$41$	−1.73814	+	8.73822i	−0.271452	+	1.36468i	0.568796	+	0.822479i	$0.307409\pi$
$41$	−1.73814	+	8.73822i	−0.271452	+	1.36468i	−0.840248	+	0.542203i	$0.817591\pi$
$42$	−2.44611	−	0.247148i	−0.377443	−	0.0381357i
$43$	−3.05435	+	1.63259i	−0.465785	+	0.248967i	−0.687556	−	0.726132i	$-0.741316\pi$
$43$	−3.05435	+	1.63259i	−0.465785	+	0.248967i	0.221771	+	0.975099i	$0.428816\pi$
$44$	−0.447325	−	4.78914i	−0.0674367	−	0.721989i
$45$	−0.711246	−	0.0700516i	−0.106026	−	0.0104427i
$46$	1.82085	−	1.81170i	0.268470	−	0.267120i
$47$	3.60433	−	8.70163i	0.525746	−	1.26926i	−0.408541	−	0.912740i	$-0.633962\pi$
$47$	3.60433	−	8.70163i	0.525746	−	1.26926i	0.934287	−	0.356523i	$-0.116038\pi$
$48$	3.83927	−	1.12249i	0.554151	−	0.162017i
$49$	−1.52221	−	3.67494i	−0.217459	−	0.524991i
$50$	−5.85931	−	2.44433i	−0.828631	−	0.345680i
$51$	−3.45629	−	4.21150i	−0.483978	−	0.589729i
$52$	3.96062	+	2.14273i	0.549239	+	0.297144i
$53$	−0.661557	+	2.18086i	−0.0908719	+	0.299564i	−0.990581	−	0.136925i	$-0.956278\pi$
$53$	−0.661557	+	2.18086i	−0.0908719	+	0.299564i	0.899710	+	0.436489i	$0.143778\pi$
$54$	1.24554	+	0.669797i	0.169497	+	0.0911478i
$55$	−1.42914	+	0.954923i	−0.192706	+	0.128762i
$56$	−3.45055	−	3.50313i	−0.461099	−	0.468125i
$57$	2.20770	−	3.30406i	0.292417	−	0.437633i
$58$	−12.5518	−	3.84211i	−1.64813	−	0.504494i
$59$	7.60232	+	6.23907i	0.989738	+	0.812257i	0.982224	−	0.187715i	$-0.0601080\pi$
$59$	7.60232	+	6.23907i	0.989738	+	0.812257i	0.00751452	+	0.999972i	$0.497608\pi$
$60$	−1.00561	−	1.01580i	−0.129824	−	0.131140i
$61$	0.233796	−	0.437401i	0.0299345	−	0.0560034i	−0.866509	−	0.499161i	$-0.833642\pi$
$61$	0.233796	−	0.437401i	0.0299345	−	0.0560034i	0.896444	+	0.443157i	$0.146142\pi$
$62$	0.292493	+	1.49008i	0.0371467	+	0.189240i
$63$		−	1.73847i		−	0.219026i
$64$	7.34389	+	3.17289i	0.917987	+	0.396611i
$65$		−	1.60915i		−	0.199590i
$66$	3.33748	−	0.655125i	0.410815	−	0.0806404i
$67$	−1.98855	+	3.72031i	−0.242939	+	0.454508i	−0.973609	−	0.228224i	$-0.926708\pi$
$67$	−1.98855	+	3.72031i	−0.242939	+	0.454508i	0.730669	+	0.682732i	$0.239208\pi$
$68$	0.0549278	−	10.8962i	0.00666098	−	1.32136i
$69$	1.40400	+	1.15224i	0.169022	+	0.138713i
$70$	−0.514297	+	1.68015i	−0.0614703	+	0.200817i
$71$	2.72431	−	4.07722i	0.323317	−	0.483877i	−0.633834	−	0.773469i	$-0.718520\pi$
$71$	2.72431	−	4.07722i	0.323317	−	0.483877i	0.957150	+	0.289592i	$0.0935196\pi$
$72$	1.06260	+	2.62124i	0.125229	+	0.308916i
$73$	0.964879	−	0.644711i	0.112931	−	0.0754578i	−0.497822	−	0.867279i	$-0.665867\pi$
$73$	0.964879	−	0.644711i	0.112931	−	0.0754578i	0.610753	+	0.791821i	$0.290867\pi$
$74$	−0.472178	+	0.878052i	−0.0548895	+	0.102071i
$75$	1.30315	−	4.29592i	0.150475	−	0.496050i
$76$	7.61683	−	2.26867i	0.873710	−	0.260235i
$77$	−2.65240	−	3.23196i	−0.302269	−	0.368316i
$78$	−1.22594	+	2.93870i	−0.138810	+	0.332743i
$79$	−0.799719	−	1.93069i	−0.0899754	−	0.217220i	0.872486	−	0.488640i	$-0.162507\pi$
$79$	−0.799719	−	1.93069i	−0.0899754	−	0.217220i	−0.962461	+	0.271420i	$0.912507\pi$
$80$	−0.251510	−	2.84766i	−0.0281196	−	0.318378i
$81$	−0.382683	+	0.923880i	−0.0425204	+	0.102653i
$82$	−8.88693	−	8.93184i	−0.981398	−	0.986357i
$83$	−4.07908	−	0.401754i	−0.447737	−	0.0440982i	−0.128363	−	0.991727i	$-0.540972\pi$
$83$	−4.07908	−	0.401754i	−0.447737	−	0.0440982i	−0.319373	+	0.947629i	$0.603472\pi$
$84$	2.21927	−	2.67656i	0.242142	−	0.292036i
$85$	−3.43398	+	1.83550i	−0.372467	+	0.199088i
$86$	0.492356	−	4.87303i	0.0530921	−	0.525472i
$87$	1.81081	−	9.10358i	0.194140	−	0.976006i
$88$	5.97471	+	3.25187i	0.636906	+	0.346651i
$89$	10.4965	−	2.08788i	1.11263	−	0.221315i	0.395642	−	0.918405i	$-0.370522\pi$
$89$	10.4965	−	2.08788i	1.11263	−	0.221315i	0.716984	+	0.697090i	$0.245522\pi$
$90$	0.643161	−	0.779679i	0.0677952	−	0.0821853i
$91$	3.89539	−	0.383662i	0.408348	−	0.0402187i
$92$	0.690709	+	3.56629i	0.0720114	+	0.371811i
$93$	−1.02752	+	0.311694i	−0.106549	+	0.0323212i
$94$	7.37219	+	11.0937i	0.760383	+	1.14423i
$95$	−2.00818	−	2.00818i	−0.206035	−	0.206035i
$96$	−1.71019	+	5.39215i	−0.174545	+	0.550334i
$97$	13.4124	−	13.4124i	1.36182	−	1.36182i	0.490230	−	0.871593i	$-0.336913\pi$
$97$	13.4124	−	13.4124i	1.36182	−	1.36182i	0.871593	−	0.490230i	$-0.163087\pi$
$98$	5.51448	+	1.11136i	0.557047	+	0.112264i
$99$	0.698132	+	2.30143i	0.0701649	+	0.231303i
$100$	7.49035	−	4.95046i	0.749035	−	0.495046i
$101$	0.705266	+	7.16068i	0.0701766	+	0.712515i	0.964321	+	0.264736i	$0.0852848\pi$
$101$	0.705266	+	7.16068i	0.0701766	+	0.712515i	−0.894144	+	0.447779i	$0.852215\pi$
$102$	7.66968	−	0.735883i	0.759411	−	0.0728633i
$103$	−1.77920	−	8.94463i	−0.175310	−	0.881341i	−0.963868	−	0.266381i	$-0.914172\pi$
$103$	−1.77920	−	8.94463i	−0.175310	−	0.881341i	0.788558	−	0.614960i	$-0.210828\pi$
$104$	−5.63890	+	2.95945i	−0.552940	+	0.290198i
$105$	−1.21859	−	0.242392i	−0.118922	−	0.0236550i
$106$	−2.03835	−	2.49655i	−0.197982	−	0.242486i
$107$	1.48148	+	2.77165i	0.143220	+	0.267946i	0.943296	−	0.331953i	$-0.107708\pi$
$107$	1.48148	+	2.77165i	0.143220	+	0.267946i	−0.800076	+	0.599899i	$0.795208\pi$
$108$	−1.76857	+	0.933890i	−0.170181	+	0.0898636i
$109$	−1.27775	+	12.9732i	−0.122386	+	1.24261i	0.716221	+	0.697874i	$0.245870\pi$
$109$	−1.27775	+	12.9732i	−0.122386	+	1.24261i	−0.838607	+	0.544737i	$0.816630\pi$
$110$	0.00612670	−	2.43076i	0.000584158	−	0.231764i
$111$	−0.651295	−	0.269775i	−0.0618181	−	0.0256059i
$112$	6.83359	−	1.28780i	0.645713	−	0.121686i
$113$	−9.71429	+	4.02379i	−0.913844	+	0.378526i	−0.789527	−	0.613716i	$-0.789674\pi$
$113$	−9.71429	+	4.02379i	−0.913844	+	0.378526i	−0.124317	+	0.992243i	$0.539674\pi$
$114$	2.13749	+	5.19737i	0.200194	+	0.486778i
$115$	1.00342	−	0.823488i	0.0935697	−	0.0767907i
$116$	14.4092	−	11.7043i	1.33786	−	1.08672i
$117$	−2.15459	−	0.653588i	−0.199192	−	0.0604243i
$118$	−13.3196	+	4.00382i	−1.22617	+	0.368582i
$119$	−5.26208	−	7.87526i	−0.482374	−	0.721924i
$120$	1.98552	−	0.379361i	0.181253	−	0.0346308i
$121$	−4.33696	−	2.89787i	−0.394269	−	0.263442i
$122$	0.329077	+	0.619409i	0.0297932	+	0.0560787i
$123$	5.65207	−	6.88707i	0.509630	−	0.620986i
$124$	−1.97987	−	0.831806i	−0.177797	−	0.0746984i
$125$	−5.98104	−	3.19693i	−0.534960	−	0.285942i
$126$	2.04077	+	1.37105i	0.181807	+	0.122143i
$127$	6.75243			0.599181			0.299590	−	0.954068i	$-0.403150\pi$
$127$	6.75243			0.599181			0.299590	+	0.954068i	$0.403150\pi$
$128$	−9.51643	+	6.11862i	−0.841142	+	0.540815i
$129$	3.46330			0.304926
$130$	1.88897	+	1.26907i	0.165673	+	0.111304i
$131$	6.81974	+	3.64523i	0.595843	+	0.318485i	0.741607	−	0.670834i	$-0.234064\pi$
$131$	6.81974	+	3.64523i	0.595843	+	0.318485i	−0.145764	+	0.989319i	$0.546564\pi$
$132$	−1.86308	+	4.43451i	−0.162160	+	0.385974i
$133$	4.38255	−	5.34015i	0.380015	−	0.463050i
$134$	−2.79896	−	5.26838i	−0.241793	−	0.455119i
$135$	0.594241	+	0.397059i	0.0511441	+	0.0341734i
$136$	12.7477	+	8.65786i	1.09310	+	0.742406i
$137$	6.16824	+	9.23143i	0.526989	+	0.788694i	0.995500	−	0.0947634i	$-0.0302095\pi$
$137$	6.16824	+	9.23143i	0.526989	+	0.788694i	−0.468511	+	0.883458i	$0.655209\pi$
$138$	−2.45988	+	0.739430i	−0.209399	+	0.0629445i
$139$	−11.3790	−	3.45179i	−0.965156	−	0.292777i	−0.231907	−	0.972738i	$-0.574497\pi$
$139$	−11.3790	−	3.45179i	−0.965156	−	0.292777i	−0.733248	+	0.679961i	$0.761997\pi$
$140$	−1.56671	−	1.92879i	−0.132412	−	0.163013i
$141$	−7.28066	+	5.97508i	−0.613142	+	0.503192i
$142$	2.63767	+	6.41358i	0.221348	+	0.538215i
$143$	−5.00275	+	2.07221i	−0.418351	+	0.173287i
$144$	−3.91507	−	0.819874i	−0.326256	−	0.0683228i
$145$	−6.12872	−	2.53860i	−0.508962	−	0.210819i
$146$	−0.00413641	+	1.64112i	−0.000342332	+	0.135820i
$147$	−0.389885	+	3.95857i	−0.0321572	+	0.326498i
$148$	−0.658352	−	1.24677i	−0.0541162	−	0.102484i
$149$	−6.76707	−	12.6603i	−0.554380	−	1.03717i	−0.990530	−	0.137298i	$-0.956158\pi$
$149$	−6.76707	−	12.6603i	−0.554380	−	1.03717i	0.436149	−	0.899874i	$-0.356342\pi$
$150$	4.01520	+	4.91776i	0.327840	+	0.401534i
$151$	−14.2835	−	2.84116i	−1.16237	−	0.231210i	−0.424038	−	0.905645i	$-0.639388\pi$
$151$	−14.2835	−	2.84116i	−1.16237	−	0.231210i	−0.738335	+	0.674434i	$0.764388\pi$
$152$	−3.34388	+	10.7305i	−0.271225	+	0.870361i
$153$	1.06289	+	5.34350i	0.0859294	+	0.431996i
$154$	5.88580	−	0.564725i	0.474291	−	0.0455069i
$155$	0.0752181	+	0.763702i	0.00604166	+	0.0613420i
$156$	−2.48287	−	3.75674i	−0.198789	−	0.300780i
$157$	−3.76094	−	12.3982i	−0.300156	−	0.989481i	−0.969203	−	0.246262i	$-0.920798\pi$
$157$	−3.76094	−	12.3982i	−0.300156	−	0.989481i	0.669048	−	0.743220i	$-0.266702\pi$
$158$	2.89713	+	0.583869i	0.230483	+	0.0464501i
$159$	1.61149	−	1.61149i	0.127800	−	0.127800i
$160$	3.54120	+	1.95058i	0.279957	+	0.154207i
$161$	2.23272	+	2.23272i	0.175963	+	0.175963i
$162$	−0.782729	−	1.17785i	−0.0614970	−	0.0925408i
$163$	−17.2415	+	5.23014i	−1.35045	+	0.409656i	−0.880923	−	0.473260i	$-0.843077\pi$
$163$	−17.2415	+	5.23014i	−1.35045	+	0.409656i	−0.469532	+	0.882916i	$0.655577\pi$
$164$	17.4938	−	3.38814i	1.36603	−	0.264569i
$165$	1.71054	−	0.168473i	0.133165	−	0.0131156i
$166$	3.68860	−	4.47155i	0.286291	−	0.347059i
$167$	−21.8269	+	4.34165i	−1.68902	+	0.335967i	−0.943715	−	0.330759i	$-0.892695\pi$
$167$	−21.8269	+	4.34165i	−1.68902	+	0.335967i	−0.745303	+	0.666726i	$0.767695\pi$
$168$	1.39175	+	4.71606i	0.107376	+	0.363852i
$169$	−1.54717	+	7.77817i	−0.119013	+	0.598321i
$170$	0.553551	−	5.47870i	0.0424554	−	0.420197i
$171$	−3.50454	+	1.87322i	−0.267999	+	0.143248i
$172$	5.33211	+	4.42112i	0.406569	+	0.337107i
$173$	−21.2779	−	2.09569i	−1.61773	−	0.159332i	−0.751762	−	0.659435i	$-0.770796\pi$
$173$	−21.2779	−	2.09569i	−1.61773	−	0.159332i	−0.865966	+	0.500102i	$0.833296\pi$
$174$	9.25851	+	9.30530i	0.701886	+	0.705433i
$175$	2.98660	−	7.21030i	0.225766	−	0.545047i
$176$	−8.52934	+	4.44905i	−0.642923	+	0.335360i
$177$	−3.76358	−	9.08607i	−0.282888	−	0.682951i
$178$	−5.82717	+	13.9684i	−0.436765	+	1.04697i
$179$	0.928743	+	1.13168i	0.0694175	+	0.0845855i	0.806561	−	0.591150i	$-0.201326\pi$
$179$	0.928743	+	1.13168i	0.0694175	+	0.0845855i	−0.737144	+	0.675736i	$0.763826\pi$
$180$	0.408025	+	1.36990i	0.0304124	+	0.102106i
$181$	2.02384	−	6.67171i	0.150431	−	0.495904i	−0.849043	−	0.528323i	$-0.822821\pi$
$181$	2.02384	−	6.67171i	0.150431	−	0.495904i	0.999474	+	0.0324188i	$0.0103210\pi$
$182$	−2.62174	+	4.87534i	−0.194337	+	0.361384i
$183$	−0.412379	+	0.275543i	−0.0304839	+	0.0203687i
$184$	−4.73117	−	2.00176i	−0.348786	−	0.147572i
$185$	−0.279909	+	0.418914i	−0.0205793	+	0.0307991i
$186$	0.444463	−	1.45201i	0.0325896	−	0.106467i
$187$	10.1286	+	8.31235i	0.740679	+	0.607859i
$188$	−18.8369	−	0.0949567i	−1.37382	−	0.00692543i
$189$	−0.819508	+	1.53319i	−0.0596105	+	0.111523i
$190$	3.94115	−	0.773621i	0.285921	−	0.0561244i
$191$			18.5815i			1.34451i	0.740319	+	0.672255i	$0.234674\pi$
$191$			18.5815i			1.34451i	−0.740319	+	0.672255i	$0.765326\pi$
$192$	−4.98105	−	6.26012i	−0.359476	−	0.451786i
$193$		−	25.1958i		−	1.81364i	−0.421522	−	0.906818i	$-0.638504\pi$
$193$		−	25.1958i		−	1.81364i	0.421522	−	0.906818i	$-0.361496\pi$
$194$	5.16693	+	26.3225i	0.370964	+	1.88984i
$195$	−0.758548	+	1.41914i	−0.0543207	+	0.101627i
$196$	−5.65364	+	5.59693i	−0.403831	+	0.399780i
$197$	10.9518	+	8.98789i	0.780281	+	0.640360i	0.937808	−	0.347154i	$-0.112852\pi$
$197$	10.9518	+	8.98789i	0.780281	+	0.640360i	−0.157527	+	0.987515i	$0.550352\pi$
$198$	−3.25222	−	0.995508i	−0.231125	−	0.0707477i
$199$	−4.98796	+	7.46500i	−0.353587	+	0.529180i	−0.965041	−	0.262100i	$-0.915585\pi$
$199$	−4.98796	+	7.46500i	−0.353587	+	0.529180i	0.611454	+	0.791280i	$0.290585\pi$
$200$	−0.0960098	+	12.6971i	−0.00678892	+	0.897819i
$201$	3.50748	−	2.34362i	0.247399	−	0.165306i
$202$	−8.96208	−	4.81941i	−0.630570	−	0.339093i
$203$	4.68413	−	15.4415i	0.328762	−	1.08378i
$204$	−5.18489	+	9.58373i	−0.363015	+	0.670995i
$205$	−4.03946	−	4.92210i	−0.282128	−	0.343774i
$206$	11.9032	+	4.96565i	0.829336	+	0.345974i
$207$	−0.695060	−	1.67802i	−0.0483100	−	0.116631i
$208$	0.973075	−	8.95345i	0.0674706	−	0.620810i
$209$	−3.65725	+	8.82938i	−0.252977	+	0.610741i
$210$	1.24559	−	1.23933i	0.0859538	−	0.0855216i
$211$	18.3471	+	1.80703i	1.26307	+	0.124401i	0.707285	−	0.706928i	$-0.249920\pi$
$211$	18.3471	+	1.80703i	1.26307	+	0.124401i	0.555780	+	0.831329i	$0.312420\pi$
$212$	4.53824	−	0.423890i	0.311687	−	0.0291129i
$213$	−4.32462	+	2.31156i	−0.296318	+	0.158385i
$214$	−4.42199	−	0.446785i	−0.302281	−	0.0305416i
$215$	0.482882	−	2.42761i	0.0329323	−	0.165562i
$216$	0.298510	−	2.81263i	0.0203110	−	0.191375i
$217$	−1.83082	+	0.364172i	−0.124284	+	0.0247216i
$218$	−14.2215	−	11.7314i	−0.963199	−	0.794548i
$219$	−1.15486	+	0.113744i	−0.0780383	+	0.00768610i
$220$	2.84862	+	1.92423i	0.192054	+	0.129732i
$221$	−11.7386	+	3.56087i	−0.789625	+	0.239530i
$222$	0.830334	−	0.551789i	0.0557284	−	0.0370337i
$223$	18.3209	+	18.3209i	1.22686	+	1.22686i	0.965146	+	0.261713i	$0.0842875\pi$
$223$	18.3209	+	18.3209i	1.22686	+	1.22686i	0.261713	+	0.965146i	$0.415713\pi$
$224$	−3.87761	+	9.03753i	−0.259084	+	0.603845i
$225$	−3.17436	+	3.17436i	−0.211624	+	0.211624i
$226$	2.93774	−	14.5769i	0.195416	−	0.969642i
$227$	4.29031	+	14.1433i	0.284758	+	0.938721i	0.976307	+	0.216392i	$0.0694288\pi$
$227$	4.29031	+	14.1433i	0.284758	+	0.938721i	−0.691549	+	0.722330i	$0.743071\pi$
$228$	−7.78689	−	1.58976i	−0.515699	−	0.105284i
$229$	0.895877	+	9.09600i	0.0592012	+	0.601080i	0.978320	+	0.207099i	$0.0664024\pi$
$229$	0.895877	+	9.09600i	0.0592012	+	0.601080i	−0.919119	+	0.393981i	$0.871098\pi$
$230$	0.175330	+	1.82736i	0.0115609	+	0.120493i
$231$	0.815673	+	4.10066i	0.0536673	+	0.269804i
$232$	2.37564	+	26.1456i	0.155969	+	1.71654i
$233$	13.1511	+	2.61592i	0.861560	+	0.171375i	0.606045	−	0.795430i	$-0.292755\pi$
$233$	13.1511	+	2.61592i	0.861560	+	0.171375i	0.255515	+	0.966805i	$0.417755\pi$
$234$	2.46647	−	2.01380i	0.161239	−	0.131646i
$235$	3.17313	+	5.93651i	0.206992	+	0.387255i
$236$	5.80453	−	18.7934i	0.377843	−	1.22335i
$237$	−0.204833	+	2.07970i	−0.0133053	+	0.135091i
$238$	13.3947	+	0.0337610i	0.868248	+	0.00218840i
$239$	−6.92374	−	2.86791i	−0.447859	−	0.185509i	0.147343	−	0.989086i	$-0.452928\pi$
$239$	−6.92374	−	2.86791i	−0.447859	−	0.185509i	−0.595202	+	0.803576i	$0.702928\pi$
$240$	−1.12057	+	2.62998i	−0.0723323	+	0.169764i
$241$	25.7887	−	10.6820i	1.66120	−	0.688090i	0.663029	−	0.748594i	$-0.269271\pi$
$241$	25.7887	−	10.6820i	1.66120	−	0.688090i	0.998168	+	0.0605038i	$0.0192707\pi$
$242$	6.82215	−	2.80570i	0.438545	−	0.180357i
$243$	0.773010	−	0.634393i	0.0495886	−	0.0406963i
$244$	−0.986648	−	0.102201i	−0.0631637	−	0.00654273i
$245$	2.72042	+	0.825230i	0.173801	+	0.0527220i
$246$	3.62713	+	12.0665i	0.231258	+	0.769329i
$247$	−4.97073	−	7.43923i	−0.316280	−	0.473347i
$248$	2.53789	−	1.66814i	0.161156	−	0.105927i
$249$	3.40804	+	2.27718i	0.215976	+	0.144310i
$250$	8.46983	−	4.49981i	0.535679	−	0.284593i
$251$	12.1965	−	14.8614i	0.769835	−	0.938046i	−0.229544	−	0.973298i	$-0.573723\pi$
$251$	12.1965	−	14.8614i	0.769835	−	0.938046i	0.999378	+	0.0352520i	$0.0112234\pi$
$252$	−3.21894	+	1.31436i	−0.202774	+	0.0827967i
$253$	−3.85235	−	2.05913i	−0.242195	−	0.129456i
$254$	−5.32534	+	7.92662i	−0.334142	+	0.497360i
$255$	3.89375			0.243836
$256$	0.322599	−	15.9967i	0.0201624	−	0.999797i
$257$	−4.94760			−0.308623			−0.154311	−	0.988022i	$-0.549316\pi$
$257$	−4.94760			−0.308623			−0.154311	+	0.988022i	$0.549316\pi$
$258$	−2.73135	+	4.06553i	−0.170046	+	0.253109i
$259$	−1.08083	−	0.577717i	−0.0671597	−	0.0358976i
$260$	−2.97949	+	1.21659i	−0.184780	+	0.0754494i
$261$	−5.88839	+	7.17503i	−0.364482	+	0.444123i
$262$	−9.65753	+	5.13080i	−0.596644	+	0.316982i
$263$	−13.1231	−	8.76858i	−0.809205	−	0.540694i	0.0807539	−	0.996734i	$-0.474267\pi$
$263$	−13.1231	−	8.76858i	−0.809205	−	0.540694i	−0.889959	+	0.456040i	$0.849267\pi$
$264$	−3.73630	−	5.68435i	−0.229954	−	0.349848i
$265$	−0.904895	−	1.35427i	−0.0555873	−	0.0831922i
$266$	2.81243	+	9.35618i	0.172441	+	0.573664i
$267$	−10.2413	−	3.10666i	−0.626757	−	0.190125i
$268$	8.39192	+	0.869267i	0.512618	+	0.0530990i
$269$	10.7944	−	8.85872i	0.658145	−	0.540126i	−0.244966	−	0.969532i	$-0.578777\pi$
$269$	10.7944	−	8.85872i	0.658145	−	0.540126i	0.903112	+	0.429406i	$0.141277\pi$
$270$	−0.934756	+	0.384431i	−0.0568874	+	0.0233957i
$271$	2.07784	−	0.860671i	0.126220	−	0.0522821i	−0.318680	−	0.947863i	$-0.603239\pi$
$271$	2.07784	−	0.860671i	0.126220	−	0.0522821i	0.444900	+	0.895580i	$0.353239\pi$
$272$	−20.2169	+	8.13631i	−1.22583	+	0.493337i
$273$	−3.61628	−	1.49791i	−0.218867	−	0.0906579i
$274$	−15.7013	−	0.0395749i	−0.948551	−	0.00239081i
$275$	−1.05825	+	10.7445i	−0.0638146	+	0.647921i
$276$	1.07199	−	3.47078i	0.0645260	−	0.208917i
$277$	−11.0044	−	20.5878i	−0.661191	−	1.23700i	−0.959278	−	0.282462i	$-0.908849\pi$
$277$	−11.0044	−	20.5878i	−0.661191	−	1.23700i	0.298088	−	0.954539i	$-0.403651\pi$
$278$	13.0262	−	10.6355i	0.781257	−	0.637872i
$279$	1.05312	+	0.209479i	0.0630487	+	0.0125412i
$280$	3.49979	−	0.317999i	0.209153	−	0.0190041i
$281$	2.46072	+	12.3709i	0.146794	+	0.737983i	0.982124	+	0.188235i	$0.0602765\pi$
$281$	2.46072	+	12.3709i	0.146794	+	0.737983i	−0.835330	+	0.549749i	$0.814723\pi$
$282$	−1.27216	−	13.2590i	−0.0757561	−	0.789561i
$283$	0.0187229	+	0.190097i	0.00111296	+	0.0113001i	0.995725	−	0.0923655i	$-0.0294428\pi$
$283$	0.0187229	+	0.190097i	0.00111296	+	0.0113001i	−0.994612	+	0.103666i	$0.966943\pi$
$284$	−9.60906	−	1.96177i	−0.570193	−	0.116409i
$285$	0.824406	+	2.71770i	0.0488336	+	0.160983i
$286$	1.51290	−	7.50695i	0.0894599	−	0.443895i
$287$	10.9522	−	10.9522i	0.646488	−	0.646488i
$288$	4.05009	−	3.94927i	0.238654	−	0.232713i
$289$	8.96805	+	8.96805i	0.527532	+	0.527532i
$290$	7.81349	−	5.19237i	0.458824	−	0.304906i
$291$	−18.1512	+	5.50612i	−1.06404	+	0.322775i
$292$	−1.92323	−	1.29913i	−0.112549	−	0.0760261i
$293$	10.9694	−	1.08039i	0.640837	−	0.0631169i	0.227621	−	0.973750i	$-0.426905\pi$
$293$	10.9694	−	1.08039i	0.640837	−	0.0631169i	0.413216	+	0.910633i	$0.364405\pi$
$294$	−4.33945	−	3.57964i	−0.253082	−	0.208769i
$295$	−6.89368	+	1.37124i	−0.401365	+	0.0798365i
$296$	1.98278	+	0.210437i	0.115247	+	0.0122314i
$297$	0.469190	−	2.35878i	0.0272252	−	0.136870i
$298$	20.1987	+	2.04082i	1.17008	+	0.118221i
$299$	3.60656	−	1.92775i	0.208573	−	0.111484i
$300$	−8.93953	+	0.834989i	−0.516124	+	0.0482081i
$301$	5.99184	+	0.590145i	0.345364	+	0.0340154i
$302$	14.6000	−	14.5266i	0.840134	−	0.835909i
$303$	2.75353	−	6.64762i	0.158186	−	0.381896i
$304$	−9.95931	−	12.3881i	−0.571206	−	0.710504i
$305$	0.135645	+	0.327477i	0.00776704	+	0.0187513i
$306$	−7.11094	−	2.96647i	−0.406506	−	0.169582i
$307$	−10.2766	−	12.5221i	−0.586518	−	0.714675i	0.392201	−	0.919880i	$-0.371714\pi$
$307$	−10.2766	−	12.5221i	−0.586518	−	0.714675i	−0.978719	+	0.205205i	$0.934214\pi$
$308$	−3.97894	+	7.35466i	−0.226721	+	0.419071i
$309$	−2.64736	+	8.72717i	−0.150603	+	0.496471i
$310$	−0.955825	−	0.514001i	−0.0542872	−	0.0291933i
$311$	18.9907	−	12.6892i	1.07687	−	0.719538i	0.115083	−	0.993356i	$-0.463286\pi$
$311$	18.9907	−	12.6892i	1.07687	−	0.719538i	0.961782	+	0.273818i	$0.0882864\pi$
$312$	6.36814	+	0.0481532i	0.360525	+	0.00272614i
$313$	12.3362	−	18.4624i	0.697284	−	1.04356i	−0.298728	−	0.954338i	$-0.596562\pi$
$313$	12.3362	−	18.4624i	0.697284	−	1.04356i	0.996012	−	0.0892204i	$-0.0284376\pi$
$314$	17.5202	+	5.36295i	0.988722	+	0.302649i
$315$	0.960435	+	0.788209i	0.0541144	+	0.0444105i
$316$	−2.97023	+	2.94044i	−0.167089	+	0.165413i
$317$	6.93632	−	12.9769i	0.389583	−	0.728858i	−0.608313	−	0.793697i	$-0.708154\pi$
$317$	6.93632	−	12.9769i	0.389583	−	0.728858i	0.997896	+	0.0648394i	$0.0206535\pi$
$318$	0.620804	+	3.16263i	0.0348130	+	0.177352i
$319$			22.3230i			1.24985i
$320$	−5.08256	+	2.61865i	−0.284124	+	0.146387i
$321$		−	3.14274i		−	0.175411i
$322$	−4.38182	+	0.860124i	−0.244190	+	0.0479328i
$323$	−10.2056	+	19.0934i	−0.567856	+	1.06238i
$324$	1.99997	+	0.0100819i	0.111110	+	0.000560103i
$325$	−7.81334	−	6.41224i	−0.433406	−	0.355687i
$326$	7.45797	−	24.3644i	0.413058	−	1.34942i
$327$	7.24242	−	10.8390i	0.400507	−	0.599400i
$328$	−9.81925	+	23.2078i	−0.542177	+	1.28144i
$329$	−13.6144	+	9.09685i	−0.750586	+	0.501525i
$330$	−1.15126	+	2.14086i	−0.0633747	+	0.117850i
$331$	−5.50925	+	18.1616i	−0.302816	+	0.998250i	0.665054	+	0.746796i	$0.268409\pi$
$331$	−5.50925	+	18.1616i	−0.302816	+	0.998250i	−0.967869	+	0.251454i	$0.919091\pi$
$332$	2.34007	+	7.85653i	0.128428	+	0.431183i
$333$	0.447219	+	0.544938i	0.0245075	+	0.0298624i
$334$	12.1173	−	29.0465i	0.663030	−	1.58935i
$335$	−1.15373	−	2.78535i	−0.0630351	−	0.152180i
$336$	−6.63375	−	2.08559i	−0.361901	−	0.113778i
$337$	−0.132912	+	0.320879i	−0.00724019	+	0.0174794i	−0.927458	−	0.373927i	$-0.878011\pi$
$337$	−0.132912	+	0.320879i	−0.00724019	+	0.0174794i	0.920218	+	0.391406i	$0.128011\pi$
$338$	−7.91054	−	7.95052i	−0.430277	−	0.432451i
$339$	10.4640	+	1.03062i	0.568329	+	0.0559755i
$340$	5.99484	+	4.97062i	0.325116	+	0.269570i
$341$	2.27744	−	1.21732i	0.123330	−	0.0659215i
$342$	0.564925	−	5.59127i	0.0305477	−	0.302341i
$343$	−3.72319	+	18.7177i	−0.201033	+	1.01066i
$344$	−9.39511	+	2.77257i	−0.506551	+	0.149487i
$345$	−1.27313	+	0.253241i	−0.0685430	+	0.0136341i
$346$	19.2411	−	23.3252i	1.03441	−	1.25397i
$347$	23.3706	−	2.30180i	1.25460	−	0.123567i	0.551206	−	0.834369i	$-0.314168\pi$
$347$	23.3706	−	2.30180i	1.25460	−	0.123567i	0.703392	+	0.710802i	$0.251668\pi$
$348$	−18.2252	+	3.52980i	−0.976973	+	0.189217i
$349$	1.30878	−	0.397013i	0.0700573	−	0.0212516i	−0.255062	−	0.966925i	$-0.582096\pi$
$349$	1.30878	−	0.397013i	0.0700573	−	0.0212516i	0.325119	+	0.945673i	$0.394596\pi$
$350$	6.10871	+	9.19240i	0.326524	+	0.491354i
$351$	1.59208	+	1.59208i	0.0849790	+	0.0849790i
$352$	1.50401	−	13.5213i	0.0801639	−	0.720687i
$353$	6.76625	−	6.76625i	0.360131	−	0.360131i	−0.503730	−	0.863861i	$-0.668039\pi$
$353$	6.76625	−	6.76625i	0.360131	−	0.360131i	0.863861	+	0.503730i	$0.168039\pi$
$354$	13.6342	+	2.74776i	0.724651	+	0.146042i
$355$	1.01732	+	3.35366i	0.0539938	+	0.177994i
$356$	−11.8017	−	17.8567i	−0.625489	−	0.946403i
$357$	0.928369	+	9.42589i	0.0491345	+	0.498871i
$358$	−2.06093	+	0.197740i	−0.108923	+	0.0104509i
$359$	3.51207	+	17.6564i	0.185360	+	0.931867i	0.955724	+	0.294263i	$0.0950742\pi$
$359$	3.51207	+	17.6564i	0.185360	+	0.931867i	−0.770365	+	0.637604i	$0.779926\pi$
$360$	−1.92991	−	0.601403i	−0.101715	−	0.0316967i
$361$	3.14759	+	0.626095i	0.165663	+	0.0329524i
$362$	6.23575	+	7.63745i	0.327744	+	0.401416i
$363$	2.45882	+	4.60012i	0.129054	+	0.241444i
$364$	−3.65547	−	6.92261i	−0.191599	−	0.362844i
$365$	−0.0812913	+	0.825365i	−0.00425498	+	0.0432016i
$366$	0.00176786	−	0.701396i	9.24073e−5	−	0.0366626i
$367$	18.9292	+	7.84073i	0.988096	+	0.409283i	0.817419	−	0.576044i	$-0.195404\pi$
$367$	18.9292	+	7.84073i	0.988096	+	0.409283i	0.170678	+	0.985327i	$0.445404\pi$
$368$	6.08111	−	3.97518i	0.317000	−	0.207221i
$369$	−8.23123	+	3.40949i	−0.428501	+	0.177491i
$370$	−0.271007	−	0.658962i	−0.0140890	−	0.0342578i
$371$	3.06264	−	2.51344i	0.159004	−	0.130491i
$372$	1.35398	+	1.66689i	0.0702005	+	0.0864243i
$373$	7.15296	+	2.16983i	0.370366	+	0.112349i	0.469981	−	0.882677i	$-0.344261\pi$
$373$	7.15296	+	2.16983i	0.370366	+	0.112349i	−0.0996144	+	0.995026i	$0.531761\pi$
$374$	−17.7458	+	5.33432i	−0.917614	+	0.275831i
$375$	3.76778	+	5.63888i	0.194567	+	0.291191i
$376$	14.9673	−	22.0376i	0.771880	−	1.13650i
$377$	−17.3766	−	11.6107i	−0.894941	−	0.597980i
$378$	−1.15349	−	2.17118i	−0.0593292	−	0.111673i
$379$	−0.630780	+	0.768607i	−0.0324010	+	0.0394807i	−0.788959	−	0.614446i	$-0.789380\pi$
$379$	−0.630780	+	0.768607i	−0.0324010	+	0.0394807i	0.756558	+	0.653927i	$0.226880\pi$
$380$	−2.20006	+	5.23660i	−0.112861	+	0.268632i
$381$	−5.95511	−	3.18307i	−0.305089	−	0.163074i
$382$	−21.8127	−	14.6544i	−1.11603	−	0.749785i
$383$	−26.5482			−1.35655			−0.678275	−	0.734808i	$-0.737272\pi$
$383$	−26.5482			−1.35655			−0.678275	+	0.734808i	$0.737272\pi$
$384$	11.2770	−	0.910125i	0.575479	−	0.0464446i
$385$	2.98811			0.152288
$386$	29.5772	+	19.8709i	1.50544	+	1.01140i
$387$	−3.05435	−	1.63259i	−0.155262	−	0.0829890i
$388$	−34.9747	−	14.6940i	−1.77557	−	0.745973i
$389$	24.3389	−	29.6570i	1.23403	−	1.50367i	0.437320	−	0.899306i	$-0.355928\pi$
$389$	24.3389	−	29.6570i	1.23403	−	1.50367i	0.796709	−	0.604363i	$-0.206572\pi$
$390$	−1.06769	−	2.00967i	−0.0540644	−	0.101764i
$391$	−8.22775	−	5.49761i	−0.416095	−	0.278026i
$392$	−2.11141	−	11.0508i	−0.106642	−	0.558150i
$393$	−4.29613	−	6.42961i	−0.216711	−	0.324331i
$394$	−19.1880	+	5.76784i	−0.966677	+	0.290580i
$395$	1.42922	+	0.433548i	0.0719117	+	0.0218142i
$396$	3.73350	−	3.03264i	0.187615	−	0.152396i
$397$	−10.5556	+	8.66276i	−0.529770	+	0.434771i	−0.860870	−	0.508824i	$-0.830080\pi$
$397$	−10.5556	+	8.66276i	−0.529770	+	0.434771i	0.331100	+	0.943596i	$0.392580\pi$
$398$	−4.82932	−	11.7426i	−0.242072	−	0.588605i
$399$	−6.38239	+	2.64367i	−0.319519	+	0.132349i
$400$	−14.8293	−	10.1263i	−0.741464	−	0.506317i
$401$	−12.9278	−	5.35487i	−0.645583	−	0.267409i	0.0357744	−	0.999360i	$-0.488610\pi$
$401$	−12.9278	−	5.35487i	−0.645583	−	0.267409i	−0.681358	+	0.731950i	$0.738610\pi$
$402$	−0.0150365	+	5.96572i	−0.000749951	+	0.297543i
$403$	−0.236966	+	2.40596i	−0.0118041	+	0.119849i
$404$	12.7255	−	6.71965i	0.633115	−	0.334315i
$405$	−0.336901	−	0.630298i	−0.0167408	−	0.0313197i
$406$	14.4325	+	17.6767i	0.716273	+	0.877281i
$407$	1.66284	+	0.330759i	0.0824237	+	0.0163951i
$408$	−7.16116	−	13.6448i	−0.354530	−	0.675517i
$409$	−2.41571	−	12.1446i	−0.119449	−	0.600512i	−0.993420	−	0.114532i	$-0.963463\pi$
$409$	−2.41571	−	12.1446i	−0.119449	−	0.600512i	0.873970	−	0.485979i	$-0.161537\pi$
$410$	8.96376	−	0.860047i	0.442689	−	0.0424747i
$411$	−1.08824	−	11.0491i	−0.0536789	−	0.545011i
$412$	−15.2167	+	10.0569i	−0.749672	+	0.495467i
$413$	−4.96309	−	16.3611i	−0.244218	−	0.805077i
$414$	2.51798	+	0.507459i	0.123752	+	0.0249402i
$415$	2.07138	−	2.07138i	0.101680	−	0.101680i
$416$	9.74296	+	8.20348i	0.477688	+	0.402209i
$417$	8.40824	+	8.40824i	0.411753	+	0.411753i
$418$	−7.48042	−	11.2566i	−0.365879	−	0.550576i
$419$	9.04930	−	2.74507i	0.442087	−	0.134106i	−0.0613907	−	0.998114i	$-0.519554\pi$
$419$	9.04930	−	2.74507i	0.442087	−	0.134106i	0.503478	+	0.864008i	$0.332054\pi$
$420$	0.472492	+	2.43959i	0.0230553	+	0.119040i
$421$	20.3260	−	2.00194i	0.990629	−	0.0975684i	0.410300	−	0.911951i	$-0.365424\pi$
$421$	20.3260	−	2.00194i	0.990629	−	0.0975684i	0.580329	+	0.814382i	$0.302924\pi$
$422$	−16.5908	+	20.1124i	−0.807627	+	0.979054i
$423$	9.23760	−	1.83747i	0.449147	−	0.0893410i
$424$	−3.08151	+	5.66170i	−0.149651	+	0.274956i
$425$	−4.77154	+	23.9882i	−0.231454	+	1.16360i
$426$	0.697121	−	6.89966i	0.0337756	−	0.334290i
$427$	−0.760407	+	0.406446i	−0.0367987	+	0.0196693i
$428$	4.01191	−	4.83858i	0.193923	−	0.233882i
$429$	5.38887	+	0.530757i	0.260177	+	0.0256252i
$430$	2.46893	+	2.48140i	0.119062	+	0.119664i
$431$	−4.15848	+	10.0395i	−0.200307	+	0.483584i	−0.991832	−	0.127553i	$-0.959288\pi$
$431$	−4.15848	+	10.0395i	−0.200307	+	0.483584i	0.791525	+	0.611137i	$0.209288\pi$
$432$	3.06630	+	2.56862i	0.147528	+	0.123583i
$433$	−7.17154	−	17.3136i	−0.344642	−	0.832040i	−0.997234	−	0.0743302i	$-0.976318\pi$
$433$	−7.17154	−	17.3136i	−0.344642	−	0.832040i	0.652591	−	0.757710i	$-0.273682\pi$
$434$	1.01639	−	2.43639i	0.0487882	−	0.116950i
$435$	4.20836	+	5.12790i	0.201775	+	0.245864i
$436$	24.9872	−	7.44244i	1.19667	−	0.356428i
$437$	2.09512	−	6.90668i	0.100223	−	0.330391i
$438$	0.777266	−	1.44539i	0.0371392	−	0.0690633i
$439$	31.7465	−	21.2123i	1.51518	−	1.01241i	0.528643	−	0.848844i	$-0.322701\pi$
$439$	31.7465	−	21.2123i	1.51518	−	1.01241i	0.986533	−	0.163563i	$-0.0522988\pi$
$440$	−4.50542	+	1.82642i	−0.214788	+	0.0870711i
$441$	2.20991	−	3.30736i	0.105234	−	0.157493i
$442$	5.07766	−	16.5882i	0.241520	−	0.789019i
$443$	−4.24072	−	3.48027i	−0.201482	−	0.165352i	0.528242	−	0.849094i	$-0.322852\pi$
$443$	−4.24072	−	3.48027i	−0.201482	−	0.165352i	−0.729724	+	0.683742i	$0.760352\pi$
$444$	−0.00710727	+	1.40989i	−0.000337296	+	0.0669106i
$445$	−3.60556	+	6.74552i	−0.170920	+	0.319768i
$446$	−35.9557	+	7.05786i	−1.70255	+	0.334199i
$447$			14.3554i			0.678986i
$448$	−7.55098	−	11.6794i	−0.356750	−	0.551800i
$449$		−	5.43882i		−	0.256674i	−0.991731	−	0.128337i	$-0.959036\pi$
$449$		−	5.43882i		−	0.256674i	0.991731	−	0.128337i	$-0.0409638\pi$
$450$	−1.22288	−	6.22983i	−0.0576469	−	0.293677i
$451$	−10.1006	+	18.8970i	−0.475621	+	0.889824i
$452$	14.7948	+	14.9448i	0.695891	+	0.702943i
$453$	11.2576	+	9.23886i	0.528928	+	0.434080i
$454$	−19.9862	−	6.11781i	−0.938001	−	0.287123i
$455$	−1.55418	+	2.32600i	−0.0728612	+	0.109044i
$456$	8.00738	−	7.88719i	0.374980	−	0.369352i
$457$	−18.9333	+	12.6509i	−0.885664	+	0.591782i	−0.913052	−	0.407843i	$-0.866281\pi$
$457$	−18.9333	+	12.6509i	−0.885664	+	0.591782i	0.0273877	+	0.999625i	$0.491281\pi$
$458$	−11.3843	−	6.12195i	−0.531951	−	0.286060i
$459$	1.58152	−	5.21359i	0.0738193	−	0.243349i
$460$	−2.28340	−	1.23534i	−0.106464	−	0.0575980i
$461$	−25.9885	−	31.6671i	−1.21041	−	1.47488i	−0.836990	−	0.547219i	$-0.815687\pi$
$461$	−25.9885	−	31.6671i	−1.21041	−	1.47488i	−0.373415	−	0.927664i	$-0.621813\pi$
$462$	−5.45702	−	2.27650i	−0.253884	−	0.105912i
$463$	7.34726	+	17.7379i	0.341456	+	0.824348i	0.997569	+	0.0696853i	$0.0221995\pi$
$463$	7.34726	+	17.7379i	0.341456	+	0.824348i	−0.656113	+	0.754663i	$0.727800\pi$
$464$	−32.5656	−	17.8311i	−1.51182	−	0.827789i
$465$	0.293670	−	0.708983i	0.0136186	−	0.0328783i
$466$	−13.4425	+	13.3749i	−0.622714	+	0.619582i
$467$	4.21922	+	0.415557i	0.195242	+	0.0192297i	0.195165	−	0.980770i	$-0.437476\pi$
$467$	4.21922	+	0.415557i	0.195242	+	0.0192297i	7.66273e−5		1.00000i	$0.499976\pi$
$468$	0.418784	+	4.48357i	0.0193583	+	0.207253i
$469$	6.46764	−	3.45702i	0.298648	−	0.159631i
$470$	−9.47132	−	0.956954i	−0.436879	−	0.0441410i
$471$	−2.52760	+	12.7071i	−0.116466	+	0.585512i
$472$	17.4836	+	21.6354i	0.804750	+	0.995852i
$473$	−8.16915	+	1.62494i	−0.375618	+	0.0747150i
$474$	−2.27980	−	1.88062i	−0.104715	−	0.0863798i
$475$	−17.7532	+	1.74854i	−0.814572	+	0.0802283i
$476$	−10.6034	+	15.6973i	−0.486007	+	0.719484i
$477$	−2.18086	+	0.661557i	−0.0998548	+	0.0302906i
$478$	8.82706	−	5.86593i	0.403740	−	0.268301i
$479$	10.3843	+	10.3843i	0.474471	+	0.474471i	0.903358	−	0.428887i	$-0.141094\pi$
$479$	10.3843	+	10.3843i	0.474471	+	0.474471i	−0.428887	+	0.903358i	$0.641094\pi$
$480$	−2.20356	−	3.38957i	−0.100578	−	0.154712i
$481$	−1.12235	+	1.12235i	−0.0511746	+	0.0511746i
$482$	−7.79888	+	38.6976i	−0.355229	+	1.76263i
$483$	−0.916587	−	3.02158i	−0.0417062	−	0.137487i
$484$	−2.08674	+	10.2212i	−0.0948519	+	0.464600i
$485$	1.32874	+	13.4909i	0.0603349	+	0.612591i
$486$	0.135069	+	1.40775i	0.00612687	+	0.0638568i
$487$	1.97642	+	9.93613i	0.0895601	+	0.450249i	0.999379	+	0.0352431i	$0.0112205\pi$
$487$	1.97642	+	9.93613i	0.0895601	+	0.450249i	−0.909819	+	0.415006i	$0.863779\pi$
$488$	0.898099	−	1.07762i	0.0406550	−	0.0487814i
$489$	17.6711	+	3.51500i	0.799114	+	0.158954i
$490$	−3.11421	+	2.54265i	−0.140685	+	0.114865i
$491$	−1.62097	−	3.03261i	−0.0731532	−	0.136860i	0.842686	−	0.538406i	$-0.180973\pi$
$491$	−1.62097	−	3.03261i	−0.0731532	−	0.136860i	−0.915839	+	0.401546i	$0.868473\pi$
$492$	−17.0253	−	5.25842i	−0.767558	−	0.237068i
$493$	−4.95670	+	50.3262i	−0.223238	+	2.26658i
$494$	12.6530	+	0.0318918i	0.569288	+	0.00143488i
$495$	−1.58798	−	0.657762i	−0.0713743	−	0.0295642i
$496$	−0.0433012	+	4.29479i	−0.00194428	+	0.192842i
$497$	−7.87590	+	3.26231i	−0.353282	+	0.146334i
$498$	−5.36093	+	2.20476i	−0.240229	+	0.0987975i
$499$	−15.5262	+	12.7420i	−0.695049	+	0.570412i	−0.914192	−	0.405281i	$-0.867174\pi$
$499$	−15.5262	+	12.7420i	−0.695049	+	0.570412i	0.219143	+	0.975693i	$0.429674\pi$
$500$	−1.39750	+	13.4915i	−0.0624980	+	0.603357i
$501$	21.2963	+	6.46015i	0.951447	+	0.288618i
$502$	7.82690	+	26.0379i	0.349332	+	1.16213i
$503$	4.48109	+	6.70643i	0.199802	+	0.299025i	0.917818	−	0.397002i	$-0.129949\pi$
$503$	4.48109	+	6.70643i	0.199802	+	0.299025i	−0.718016	+	0.696027i	$0.754949\pi$
$504$	0.995723	−	4.81526i	0.0443530	−	0.214489i
$505$	−4.27576	−	2.85697i	−0.190269	−	0.127133i
$506$	5.45537	−	2.89830i	0.242521	−	0.128845i
$507$	5.03109	−	6.13040i	0.223439	−	0.272261i
$508$	−5.10512	−	12.5028i	−0.226503	−	0.554720i
$509$	4.92257	+	2.63117i	0.218189	+	0.116624i	0.576871	−	0.816835i	$-0.304274\pi$
$509$	4.92257	+	2.63117i	0.218189	+	0.116624i	−0.358682	+	0.933460i	$0.616774\pi$
$510$	−3.07083	+	4.57084i	−0.135979	+	0.202400i
$511$	−2.01741			−0.0892448
$512$	18.5240	+	12.9946i	0.818654	+	0.574287i
$513$	3.97376			0.175446
$514$	3.90195	−	5.80794i	0.172108	−	0.256177i
$515$	5.74823	+	3.07249i	0.253297	+	0.135390i
$516$	−2.61840	−	6.41262i	−0.115269	−	0.282300i
$517$	14.3700	−	17.5099i	0.631992	−	0.770085i
$518$	1.53058	−	0.813161i	0.0672500	−	0.0357282i
$519$	17.7775	+	11.8786i	0.780347	+	0.521411i
$520$	0.921654	−	4.45707i	0.0404172	−	0.195455i
$521$	6.75556	+	10.1104i	0.295967	+	0.442945i	0.949414	−	0.314026i	$-0.101678\pi$
$521$	6.75556	+	10.1104i	0.295967	+	0.442945i	−0.653448	+	0.756972i	$0.726678\pi$
$522$	−3.77879	−	12.5710i	−0.165393	−	0.550216i
$523$	−23.6997	−	7.18921i	−1.03631	−	0.314362i	−0.274109	−	0.961699i	$-0.588383\pi$
$523$	−23.6997	−	7.18921i	−1.03631	−	0.314362i	−0.762205	+	0.647336i	$0.775883\pi$
$524$	1.59346	−	15.3833i	0.0696108	−	0.672024i
$525$	−6.03286	+	4.95104i	−0.263296	+	0.216081i
$526$	20.6430	−	8.48971i	0.900076	−	0.370169i
$527$	5.40470	−	2.23870i	0.235432	−	0.0975193i
$528$	9.61947	+	0.0969859i	0.418634	+	0.00422077i
$529$	−18.2015	−	7.53929i	−0.791368	−	0.327795i
$530$	2.30342	+	0.00580572i	0.100054	+	0.000252184i
$531$	−0.963969	+	9.78734i	−0.0418327	+	0.424734i
$532$	−13.2012	−	4.07732i	−0.572344	−	0.176774i
$533$	−9.45619	−	17.6913i	−0.409593	−	0.766295i
$534$	11.7237	−	9.57208i	0.507336	−	0.414224i
$535$	−2.20292	−	0.438188i	−0.0952405	−	0.0189445i
$536$	−7.63877	+	9.16565i	−0.329945	+	0.395896i
$537$	−0.285610	−	1.43586i	−0.0123250	−	0.0619618i
$538$	1.88612	+	19.6579i	0.0813164	+	0.847513i
$539$	−0.937671	−	9.52033i	−0.0403883	−	0.410070i
$540$	0.285920	−	1.40049i	0.0123041	−	0.0602673i
$541$	8.90729	+	29.3634i	0.382954	+	1.26243i	0.910714	+	0.413037i	$0.135532\pi$
$541$	8.90729	+	29.3634i	0.382954	+	1.26243i	−0.527760	+	0.849394i	$0.676968\pi$
$542$	−0.628370	+	3.11794i	−0.0269908	+	0.133927i
$543$	−4.92989	+	4.92989i	−0.211562	+	0.211562i
$544$	6.39305	−	30.1492i	0.274100	−	1.29264i
$545$	−6.58788	−	6.58788i	−0.282194	−	0.282194i
$546$	4.61039	−	3.06379i	0.197307	−	0.131118i
$547$	38.5534	−	11.6950i	1.64842	−	0.500044i	0.676719	−	0.736241i	$-0.263401\pi$
$547$	38.5534	−	11.6950i	1.64842	−	0.500044i	0.971705	+	0.236197i	$0.0759012\pi$
$548$	12.4294	−	18.4004i	0.530958	−	0.786028i
$549$	0.493575	−	0.0486129i	0.0210653	−	0.00207475i
$550$	−11.7783	−	9.71602i	−0.502230	−	0.414293i
$551$	−36.1754	+	7.19574i	−1.54112	+	0.306549i
$552$	3.22890	+	3.99565i	0.137431	+	0.170066i
$553$	−0.708762	+	3.56318i	−0.0301396	+	0.151522i
$554$	32.8465	+	3.31871i	1.39552	+	0.140999i
$555$	0.444332	−	0.237501i	0.0188609	−	0.0100813i
$556$	2.21172	+	23.6790i	0.0937976	+	1.00421i
$557$	24.2226	+	2.38572i	1.02635	+	0.101086i	0.597153	−	0.802127i	$-0.296298\pi$
$557$	24.2226	+	2.38572i	1.02635	+	0.101086i	0.429192	+	0.903213i	$0.358798\pi$
$558$	−1.07646	+	1.07104i	−0.0455700	+	0.0453409i
$559$	2.98407	−	7.20419i	0.126213	−	0.304705i
$560$	−2.38684	+	4.35917i	−0.100862	+	0.184209i
$561$	−5.01424	−	12.1054i	−0.211701	−	0.511092i
$562$	−16.4627	−	6.86774i	−0.694437	−	0.289698i
$563$	−17.3329	−	21.1201i	−0.730493	−	0.890108i	0.266792	−	0.963754i	$-0.414036\pi$
$563$	−17.3329	−	21.1201i	−0.730493	−	0.890108i	−0.997284	+	0.0736462i	$0.976536\pi$
$564$	16.5679	+	8.96340i	0.697635	+	0.377427i
$565$	2.18140	−	7.19112i	0.0917723	−	0.302533i
$566$	−0.237919	−	0.127942i	−0.0100005	−	0.00537782i
$567$	1.44548	−	0.965841i	0.0607046	−	0.0405615i
$568$	9.88114	−	9.73283i	0.414604	−	0.408381i
$569$	21.5695	−	32.2810i	0.904241	−	1.35329i	−0.0310898	−	0.999517i	$-0.509898\pi$
$569$	21.5695	−	32.2810i	0.904241	−	1.35329i	0.935330	−	0.353775i	$-0.115102\pi$
$570$	−3.84046	−	1.17557i	−0.160859	−	0.0492392i
$571$	33.4486	+	27.4506i	1.39978	+	1.14877i	0.969216	+	0.246211i	$0.0791857\pi$
$571$	33.4486	+	27.4506i	1.39978	+	1.14877i	0.430565	+	0.902560i	$0.358314\pi$
$572$	7.61918	+	7.69639i	0.318574	+	0.321802i
$573$	8.75926	−	16.3874i	0.365923	−	0.684595i
$574$	4.21917	+	21.4942i	0.176105	+	0.897151i
$575$		−	8.15369i		−	0.340032i
$576$	1.44189	+	7.86899i	0.0600788	+	0.327874i
$577$			0.713433i			0.0297006i	0.999890	+	0.0148503i	$0.00472717\pi$
$577$			0.713433i			0.0297006i	−0.999890	+	0.0148503i	$0.995273\pi$
$578$	−17.6002	+	3.45481i	−0.732073	+	0.143701i
$579$	−11.8772	+	22.2207i	−0.493601	+	0.923463i
$580$	−0.0668798	+	13.2672i	−0.00277703	+	0.550890i
$581$	5.50821	+	4.52047i	0.228519	+	0.187541i
$582$	7.85151	−	25.6500i	0.325455	−	1.06323i
$583$	−3.04506	+	4.55725i	−0.126113	+	0.188742i
$584$	3.04181	−	1.23310i	0.125871	−	0.0510259i
$585$	1.33796	−	0.893995i	0.0553178	−	0.0369622i
$586$	−7.38279	+	13.7289i	−0.304980	+	0.567135i
$587$	11.2514	−	37.0908i	0.464394	−	1.53090i	−0.342103	−	0.939662i	$-0.611139\pi$
$587$	11.2514	−	37.0908i	0.464394	−	1.53090i	0.806497	−	0.591239i	$-0.201361\pi$
$588$	7.62444	−	2.27094i	0.314427	−	0.0936520i
$589$	2.70685	+	3.29831i	0.111534	+	0.135904i
$590$	3.82706	−	9.17386i	0.157557	−	0.377682i
$591$	−5.42174	−	13.0892i	−0.223021	−	0.538419i
$592$	−1.81076	+	2.16161i	−0.0744219	+	0.0888415i
$593$	−12.9539	+	31.2734i	−0.531951	+	1.28424i	0.398278	+	0.917265i	$0.369608\pi$
$593$	−12.9539	+	31.2734i	−0.531951	+	1.28424i	−0.930229	+	0.366980i	$0.880392\pi$
$594$	2.39892	+	2.41104i	0.0984289	+	0.0989264i
$595$	6.73656	+	0.663494i	0.276172	+	0.0272006i
$596$	−18.3255	+	22.1016i	−0.750644	+	0.905317i
$597$	7.91796	−	4.23224i	0.324061	−	0.173214i
$598$	−0.581371	+	5.75404i	−0.0237740	+	0.235300i
$599$	7.89256	−	39.6786i	0.322481	−	1.62122i	−0.390891	−	0.920437i	$-0.627833\pi$
$599$	7.89256	−	39.6786i	0.322481	−	1.62122i	0.713372	−	0.700786i	$-0.247167\pi$
$600$	6.07003	−	11.1526i	0.247808	−	0.455301i
$601$	−18.7737	+	3.73432i	−0.765794	+	0.152326i	−0.562506	−	0.826793i	$-0.690163\pi$
$601$	−18.7737	+	3.73432i	−0.765794	+	0.152326i	−0.203288	+	0.979119i	$0.565163\pi$
$602$	−5.41827	+	6.56835i	−0.220832	+	0.267706i
$603$	−4.19810	+	0.413477i	−0.170960	+	0.0168381i
$604$	5.53824	+	28.5952i	0.225348	+	1.16352i
$605$	3.56730	−	1.08213i	0.145032	−	0.0439948i
$606$	5.63199	+	8.47503i	0.228784	+	0.344275i
$607$	31.1285	+	31.1285i	1.26347	+	1.26347i	0.949402	+	0.314064i	$0.101691\pi$
$607$	31.1285	+	31.1285i	1.26347	+	1.26347i	0.314064	+	0.949402i	$0.398309\pi$
$608$	22.3967	−	1.92123i	0.908307	−	0.0779162i
$609$	−11.4101	+	11.4101i	−0.462361	+	0.462361i
$610$	−0.491400	−	0.0990338i	−0.0198962	−	0.00400976i
$611$	6.15587	+	20.2932i	0.249040	+	0.820975i
$612$	9.09040	−	6.00795i	0.367458	−	0.242857i
$613$	3.84853	+	39.0747i	0.155441	+	1.57821i	0.684105	+	0.729383i	$0.260193\pi$
$613$	3.84853	+	39.0747i	0.155441	+	1.57821i	−0.528665	+	0.848831i	$0.677307\pi$
$614$	22.8043	−	2.18801i	0.920308	−	0.0883009i
$615$	1.24223	+	6.24510i	0.0500914	+	0.251827i
$616$	−5.49556	−	10.4712i	−0.221422	−	0.421895i
$617$	−14.6973	−	2.92347i	−0.591691	−	0.117695i	−0.109842	−	0.993949i	$-0.535035\pi$
$617$	−14.6973	−	2.92347i	−0.591691	−	0.117695i	−0.481849	+	0.876254i	$0.660035\pi$
$618$	−8.15690	−	9.99045i	−0.328118	−	0.401875i
$619$	−14.2138	−	26.5922i	−0.571302	−	1.06883i	−0.987210	−	0.159425i	$-0.949036\pi$
$619$	−14.2138	−	26.5922i	−0.571302	−	1.06883i	0.415908	−	0.909407i	$-0.363464\pi$
$620$	1.35720	−	0.716665i	0.0545064	−	0.0287820i
$621$	−0.178027	+	1.80753i	−0.00714396	+	0.0725339i
$622$	−0.0814127	+	32.3005i	−0.00326435	+	1.29513i
$623$	−17.1891	−	7.11994i	−0.688665	−	0.285254i
$624$	−5.07880	+	7.43753i	−0.203315	+	0.297740i
$625$	−16.2596	+	6.73493i	−0.650383	+	0.269397i
$626$	11.9439	+	29.0419i	0.477373	+	1.16075i
$627$	7.38754	−	6.06280i	0.295030	−	0.242125i
$628$	−20.1129	+	16.3373i	−0.802593	+	0.651928i
$629$	3.67535	+	1.11491i	0.146546	+	0.0444542i
$630$	−1.68273	+	0.505821i	−0.0670414	+	0.0201524i
$631$	8.20010	+	12.2723i	0.326441	+	0.488554i	0.957998	−	0.286776i	$-0.0925836\pi$
$631$	8.20010	+	12.2723i	0.326441	+	0.488554i	−0.631557	+	0.775330i	$0.717584\pi$
$632$	−1.10926	−	5.80573i	−0.0441241	−	0.230940i
$633$	−15.3289	−	10.2424i	−0.609267	−	0.407099i
$634$	9.76315	+	18.3768i	0.387744	+	0.729837i
$635$	−3.06150	+	3.73045i	−0.121492	+	0.148038i
$636$	−4.20219	−	1.76547i	−0.166628	−	0.0700055i
$637$	7.89851	+	4.22184i	0.312950	+	0.167275i
$638$	−26.2047	−	17.6051i	−1.03746	−	0.696994i
$639$	4.90363			0.193985
$640$	0.934385	−	8.03159i	0.0369348	−	0.317477i
$641$	−4.91328			−0.194063			−0.0970314	−	0.995281i	$-0.530935\pi$
$641$	−4.91328			−0.194063			−0.0970314	+	0.995281i	$0.530935\pi$
$642$	3.68924	+	2.47854i	0.145603	+	0.0978203i
$643$	−35.8046	−	19.1380i	−1.41200	−	0.754728i	−0.423489	−	0.905901i	$-0.639195\pi$
$643$	−35.8046	−	19.1380i	−1.41200	−	0.754728i	−0.988507	+	0.151173i	$0.951695\pi$
$644$	2.44606	−	5.82213i	0.0963883	−	0.229424i
$645$	−1.57023	+	1.91333i	−0.0618279	+	0.0753375i
$646$	−14.3648	−	27.0384i	−0.565177	−	1.06381i
$647$	−15.7302	−	10.5106i	−0.618417	−	0.413213i	0.206517	−	0.978443i	$-0.433787\pi$
$647$	−15.7302	−	10.5106i	−0.618417	−	0.413213i	−0.824933	+	0.565230i	$0.808787\pi$
$648$	−1.58913	+	2.33980i	−0.0624268	+	0.0919161i
$649$	13.1405	+	19.6662i	0.515811	+	0.771966i
$650$	13.6893	−	4.11496i	0.536939	−	0.161402i
$651$	1.78631	+	0.541870i	0.0700109	+	0.0212376i
$652$	22.7194	+	27.9700i	0.889759	+	1.09539i
$653$	−18.9810	+	15.5773i	−0.742784	+	0.609587i	−0.927769	−	0.373155i	$-0.878276\pi$
$653$	−18.9810	+	15.5773i	−0.742784	+	0.609587i	0.184986	+	0.982741i	$0.440776\pi$
$654$	7.01208	+	17.0501i	0.274194	+	0.666711i
$655$	−5.10586	+	2.11492i	−0.199503	+	0.0826367i
$656$	−19.4995	−	29.8297i	−0.761327	−	1.16466i
$657$	1.07212	+	0.444085i	0.0418272	+	0.0173254i
$658$	0.0583645	−	23.1561i	0.00227529	−	0.902719i
$659$	2.11088	−	21.4321i	0.0822283	−	0.834878i	−0.862289	−	0.506416i	$-0.830970\pi$
$659$	2.11088	−	21.4321i	0.0822283	−	0.834878i	0.944517	−	0.328462i	$-0.106530\pi$
$660$	−1.60518	−	3.03985i	−0.0624817	−	0.118326i
$661$	4.00290	+	7.48890i	0.155695	+	0.291285i	0.947660	−	0.319282i	$-0.103442\pi$
$661$	4.00290	+	7.48890i	0.155695	+	0.291285i	−0.791965	+	0.610567i	$0.790942\pi$
$662$	−16.9748	−	20.7905i	−0.659744	−	0.808045i
$663$	12.0311	+	2.39314i	0.467250	+	0.0929418i
$664$	−11.0682	−	3.44912i	−0.429531	−	0.133852i
$665$	0.963207	+	4.84237i	0.0373516	+	0.187779i
$666$	−0.992401	+	0.0952180i	−0.0384548	+	0.00368962i
$667$	−1.65243	−	16.7774i	−0.0639824	−	0.649624i
$668$	24.5411	+	37.1321i	0.949522	+	1.43669i
$669$	−7.52118	−	24.7940i	−0.290786	−	0.958592i
$670$	4.17960	+	0.842331i	0.161472	+	0.0325421i
$671$	0.843428	−	0.843428i	0.0325602	−	0.0325602i
$672$	7.68001	−	6.14249i	0.296263	−	0.236952i
$673$	25.3557	+	25.3557i	0.977390	+	0.977390i	0.999750	−	0.0223595i	$-0.00711785\pi$
$673$	25.3557	+	25.3557i	0.977390	+	0.977390i	−0.0223595	+	0.999750i	$0.507118\pi$
$674$	−0.271855	−	0.409088i	−0.0104715	−	0.0157575i
$675$	4.29592	−	1.30315i	0.165350	−	0.0501584i
$676$	15.5717	−	3.01589i	0.598913	−	0.115996i
$677$	29.9955	−	2.95430i	1.15282	−	0.113543i	0.496508	−	0.868032i	$-0.334615\pi$
$677$	29.9955	−	2.95430i	1.15282	−	0.113543i	0.656313	+	0.754489i	$0.272115\pi$
$678$	−9.46237	+	11.4708i	−0.363400	+	0.440535i
$679$	−32.3417	+	6.43316i	−1.24116	+	0.246882i
$680$	−10.5628	+	3.11718i	−0.405066	+	0.119538i
$681$	2.88337	−	14.4957i	0.110491	−	0.555476i
$682$	−0.367120	+	3.63352i	−0.0140577	+	0.139135i
$683$	−4.53596	+	2.42452i	−0.173564	+	0.0927718i	−0.555891	−	0.831255i	$-0.687623\pi$
$683$	−4.53596	+	2.42452i	−0.173564	+	0.0927718i	0.382327	+	0.924027i	$0.375123\pi$
$684$	6.11802	+	5.07275i	0.233928	+	0.193962i
$685$	−7.89664	−	0.777751i	−0.301715	−	0.0297163i
$686$	−19.0363	−	19.1325i	−0.726808	−	0.730481i
$687$	3.49773	−	8.44427i	0.133447	−	0.322169i
$688$	4.15481	−	13.2155i	0.158401	−	0.503834i
$689$	−1.96365	−	4.74066i	−0.0748090	−	0.180605i
$690$	0.706784	−	1.69424i	0.0269068	−	0.0644985i
$691$	−29.9987	−	36.5535i	−1.14120	−	1.39056i	−0.908434	−	0.418029i	$-0.862721\pi$
$691$	−29.9987	−	36.5535i	−1.14120	−	1.39056i	−0.232770	−	0.972532i	$-0.574779\pi$
$692$	12.2066	+	40.9824i	0.464026	+	1.55792i
$693$	1.21368	−	4.00097i	0.0461039	−	0.151984i
$694$	−15.7293	+	29.2499i	−0.597076	+	1.11031i
$695$	7.06614	−	4.72144i	0.268034	−	0.179095i
$696$	10.2298	−	24.1782i	0.387760	−	0.916472i
$697$	−26.9675	+	40.3597i	−1.02147	+	1.52873i
$698$	−0.566125	+	1.84947i	−0.0214281	+	0.0700035i
$699$	−10.3651	−	8.50644i	−0.392045	−	0.321743i
$700$	−15.6085	−	0.0786826i	−0.589948	−	0.00297392i
$701$	13.8683	−	25.9458i	0.523800	−	0.979961i	−0.471383	−	0.881929i	$-0.656245\pi$
$701$	13.8683	−	25.9458i	0.523800	−	0.979961i	0.995183	−	0.0980326i	$-0.0312549\pi$
$702$	−3.12454	+	0.613326i	−0.117928	+	0.0231485i
$703$			2.80132i			0.105654i
$704$	14.6864	+	12.4292i	0.553514	+	0.468443i
$705$		−	6.73133i		−	0.253517i
$706$	2.60660	+	13.2791i	0.0981006	+	0.499765i
$707$	5.89663	−	11.0318i	0.221766	−	0.414894i
$708$	−13.9783	+	13.8381i	−0.525336	+	0.520067i
$709$	−32.1273	−	26.3662i	−1.20656	−	0.990202i	−0.999931	−	0.0117836i	$-0.996249\pi$
$709$	−32.1273	−	26.3662i	−1.20656	−	0.990202i	−0.206634	−	0.978418i	$-0.566251\pi$
$710$	−4.73915	−	1.45066i	−0.177857	−	0.0544423i
$711$	1.16101	−	1.73758i	0.0435413	−	0.0651642i
$712$	30.2693	+	0.228884i	1.13439	+	0.00857777i
$713$	−1.62156	+	1.08349i	−0.0607280	+	0.0405772i
$714$	−11.7971	−	6.34398i	−0.441497	−	0.237418i
$715$	1.12340	−	3.70335i	0.0420127	−	0.138497i
$716$	1.39324	−	2.57525i	0.0520677	−	0.0962417i
$717$	4.75427	+	5.79310i	0.177551	+	0.216347i
$718$	−23.4965	−	9.80201i	−0.876880	−	0.365808i
$719$	3.36745	+	8.12974i	0.125585	+	0.303188i	0.974150	−	0.225903i	$-0.0725331\pi$
$719$	3.36745	+	8.12974i	0.125585	+	0.303188i	−0.848565	+	0.529091i	$0.822533\pi$
$720$	2.22801	−	1.79120i	0.0830332	−	0.0667541i
$721$	−6.06729	+	14.6477i	−0.225958	+	0.545511i
$722$	−3.21734	+	3.20116i	−0.119737	+	0.119135i
$723$	−27.7791	−	2.73600i	−1.03312	−	0.101753i
$724$	−13.8834	+	1.29677i	−0.515973	+	0.0481939i
$725$	−36.7485	+	19.6425i	−1.36480	+	0.729503i
$726$	−7.33920	−	0.741531i	−0.272383	−	0.0275208i
$727$	8.02880	−	40.3635i	0.297772	−	1.49700i	−0.484903	−	0.874568i	$-0.661145\pi$
$727$	8.02880	−	40.3635i	0.297772	−	1.49700i	0.782674	−	0.622431i	$-0.213855\pi$
$728$	11.0093	+	1.16844i	0.408032	+	0.0433053i
$729$	−0.980785	+	0.195090i	−0.0363254	+	0.00722557i
$730$	−0.904778	−	0.746356i	−0.0334873	−	0.0276239i
$731$	−18.7778	+	1.84945i	−0.694523	+	0.0684045i
$732$	0.821969	+	0.555236i	0.0303808	+	0.0205221i
$733$	42.7306	−	12.9622i	1.57829	−	0.478770i	0.624951	−	0.780664i	$-0.285119\pi$
$733$	42.7306	−	12.9622i	1.57829	−	0.478770i	0.953341	+	0.301894i	$0.0976190\pi$
$734$	−24.1328	+	16.0372i	−0.890758	+	0.591943i
$735$	−2.01018	−	2.01018i	−0.0741468	−	0.0741468i
$736$	−0.129479	+	10.2736i	−0.00477265	+	0.378691i
$737$	−7.17377	+	7.17377i	−0.264249	+	0.264249i
$738$	2.48924	−	12.3515i	0.0916303	−	0.454664i
$739$	−6.85788	−	22.6074i	−0.252271	−	0.831627i	−0.988014	−	0.154365i	$-0.950667\pi$
$739$	−6.85788	−	22.6074i	−0.252271	−	0.831627i	0.735743	−	0.677261i	$-0.236833\pi$
$740$	0.987281	+	0.201561i	0.0362932	+	0.00740954i
$741$	0.876968	+	8.90400i	0.0322162	+	0.327097i
$742$	0.535140	+	5.57744i	0.0196456	+	0.204754i
$743$	7.88405	+	39.6358i	0.289238	+	1.45410i	0.802905	+	0.596107i	$0.203286\pi$
$743$	7.88405	+	39.6358i	0.289238	+	1.45410i	−0.513668	+	0.857989i	$0.671714\pi$
$744$	−3.02457	+	0.274819i	−0.110886	+	0.0100754i
$745$	10.0625	+	2.00155i	0.368660	+	0.0733311i
$746$	−8.18837	+	6.68555i	−0.299797	+	0.244775i
$747$	−1.93217	−	3.61483i	−0.0706943	−	0.132260i
$748$	7.73342	−	25.0386i	0.282762	−	0.915502i
$749$	0.535522	−	5.43725i	0.0195676	−	0.198673i
$750$	−9.59092	−	0.0241737i	−0.350211	−	0.000882700i
$751$	−44.1451	−	18.2855i	−1.61088	−	0.667247i	−0.617977	−	0.786196i	$-0.712047\pi$
$751$	−44.1451	−	18.2855i	−1.61088	−	0.667247i	−0.992900	+	0.118949i	$0.962047\pi$
$752$	14.0657	+	34.9501i	0.512923	+	1.27450i
$753$	−17.7620	+	7.35725i	−0.647282	+	0.268113i
$754$	27.3338	−	11.2414i	0.995440	−	0.409388i
$755$	8.04565	−	6.60290i	0.292811	−	0.240304i
$756$	3.45843	+	0.358238i	0.125782	+	0.0130290i
$757$	−35.4850	−	10.7643i	−1.28973	−	0.391234i	−0.430388	−	0.902644i	$-0.641623\pi$
$757$	−35.4850	−	10.7643i	−1.28973	−	0.391234i	−0.859337	+	0.511410i	$0.829123\pi$
$758$	−0.404793	−	1.34663i	−0.0147028	−	0.0489120i
$759$	2.42681	+	3.63197i	0.0880875	+	0.131832i
$760$	−4.41211	−	6.71251i	−0.160044	−	0.243488i
$761$	−6.69219	−	4.47158i	−0.242592	−	0.162095i	0.428331	−	0.903622i	$-0.359102\pi$
$761$	−6.69219	−	4.47158i	−0.242592	−	0.162095i	−0.670923	+	0.741527i	$0.734102\pi$
$762$	8.43311	−	4.48030i	0.305500	−	0.162304i
$763$	14.3771	−	17.5185i	0.520484	−	0.634212i
$764$	34.4054	−	14.0484i	1.24474	−	0.508254i
$765$	−3.43398	−	1.83550i	−0.124156	−	0.0663626i
$766$	20.9374	−	31.1647i	0.756500	−	1.12603i
$767$	−22.1432			−0.799546
$768$	−7.82532	+	13.9558i	−0.282372	+	0.503587i
$769$	−1.42178			−0.0512707			−0.0256354	−	0.999671i	$-0.508161\pi$
$769$	−1.42178			−0.0512707			−0.0256354	+	0.999671i	$0.508161\pi$
$770$	−2.35659	+	3.50771i	−0.0849256	+	0.126409i
$771$	4.36339	+	2.33228i	0.157144	+	0.0839950i
$772$	−46.6525	+	19.0491i	−1.67906	+	0.685593i
$773$	3.54403	−	4.31842i	0.127470	−	0.155323i	−0.705364	−	0.708845i	$-0.749217\pi$
$773$	3.54403	−	4.31842i	0.127470	−	0.155323i	0.832834	+	0.553522i	$0.186717\pi$
$774$	4.32531	−	2.29793i	0.155470	−	0.0825974i
$775$	4.00795	+	2.67802i	0.143970	+	0.0961975i
$776$	44.8321	−	29.4680i	1.60938	−	1.05784i
$777$	0.680876	+	1.01900i	0.0244263	+	0.0365565i
$778$	15.6191	+	51.9604i	0.559972	+	1.86287i
$779$	−33.8794	−	10.2772i	−1.21385	−	0.368219i
$780$	3.20117	+	0.331589i	0.114620	+	0.0118728i
$781$	9.11626	−	7.48152i	0.326206	−	0.267710i
$782$	12.9425	−	5.32277i	0.462822	−	0.190342i
$783$	8.57539	−	3.55204i	0.306459	−	0.126940i
$784$	14.6376	+	6.23673i	0.522772	+	0.222740i
$785$	8.55468	+	3.54347i	0.305330	+	0.126472i
$786$	10.9358	+	0.0275635i	0.390068	+	0.000983159i
$787$	4.83804	−	49.1214i	0.172457	−	1.75099i	−0.386953	−	0.922099i	$-0.626472\pi$
$787$	4.83804	−	49.1214i	0.172457	−	1.75099i	0.559411	−	0.828891i	$-0.311028\pi$
$788$	8.36191	−	27.0735i	0.297881	−	0.964452i
$789$	7.44006	+	13.9194i	0.264873	+	0.495543i
$790$	−1.63610	+	1.33583i	−0.0582098	+	0.0475265i
$791$	17.9282	+	3.56614i	0.637453	+	0.126797i
$792$	0.615540	+	6.77443i	0.0218722	+	0.240719i
$793$	0.217854	+	1.09523i	0.00773622	+	0.0388926i
$794$	−1.84440	−	19.2231i	−0.0654552	−	0.682201i
$795$	0.159647	+	1.62093i	0.00566210	+	0.0574883i
$796$	17.5933	+	3.59181i	0.623577	+	0.127308i
$797$	−3.00552	−	9.90786i	−0.106461	−	0.350954i	0.887483	−	0.460840i	$-0.152452\pi$
$797$	−3.00552	−	9.90786i	−0.106461	−	0.350954i	−0.993944	+	0.109885i	$0.964952\pi$
$798$	1.93013	−	9.57719i	0.0683258	−	0.339029i
$799$	36.2846	−	36.2846i	1.28366	−	1.28366i
$800$	23.5824	−	9.42176i	0.833764	−	0.333110i
$801$	7.56754	+	7.56754i	0.267386	+	0.267386i
$802$	16.4816	−	10.9527i	0.581986	−	0.386753i
$803$	2.67070	−	0.810147i	0.0942468	−	0.0285895i
$804$	−6.99124	−	4.72255i	−0.246562	−	0.166552i
$805$	−2.24579	+	0.221191i	−0.0791537	+	0.00779596i
$806$	−2.63745	−	2.17565i	−0.0929003	−	0.0766339i
$807$	−13.6958	+	2.72426i	−0.482114	+	0.0958984i
$808$	−2.14788	+	20.2378i	−0.0755621	+	0.711964i
$809$	−1.96753	+	9.89143i	−0.0691746	+	0.347764i	−0.999836	−	0.0181177i	$-0.994233\pi$
$809$	−1.96753	+	9.89143i	−0.0691746	+	0.347764i	0.930661	+	0.365882i	$0.119233\pi$
$810$	1.00560	+	0.101603i	0.0353332	+	0.00356996i
$811$	−36.0172	+	19.2516i	−1.26474	+	0.676016i	−0.960949	−	0.276724i	$-0.910751\pi$
$811$	−36.0172	+	19.2516i	−1.26474	+	0.676016i	−0.303787	+	0.952740i	$0.598251\pi$
$812$	−32.1328	+	3.00134i	−1.12764	+	0.105326i
$813$	−2.23821	−	0.220445i	−0.0784976	−	0.00773133i
$814$	−1.69968	+	1.69113i	−0.0595738	+	0.0592742i
$815$	4.92770	−	11.8965i	0.172610	−	0.416717i
$816$	21.6652	+	2.35460i	0.758433	+	0.0824276i
$817$	−5.26660	−	12.7147i	−0.184255	−	0.444831i
$818$	16.1616	+	6.74213i	0.565077	+	0.235733i
$819$	2.48317	+	3.02575i	0.0867688	+	0.105728i
$820$	−6.05972	+	11.2008i	−0.211615	+	0.391148i
$821$	−2.14148	+	7.05953i	−0.0747383	+	0.246379i	−0.986347	−	0.164680i	$-0.947341\pi$
$821$	−2.14148	+	7.05953i	−0.0747383	+	0.246379i	0.911609	+	0.411059i	$0.134841\pi$
$822$	13.8287	+	7.43645i	0.482330	+	0.259376i
$823$	−18.0824	+	12.0823i	−0.630314	+	0.421162i	−0.829272	−	0.558846i	$-0.811244\pi$
$823$	−18.0824	+	12.0823i	−0.630314	+	0.421162i	0.198958	+	0.980008i	$0.436244\pi$
$824$	0.195044	−	25.7941i	0.00679469	−	0.898582i
$825$	5.99823	−	8.97699i	0.208832	−	0.312539i
$826$	23.1203	+	7.07716i	0.804459	+	0.246246i
$827$	27.8081	+	22.8215i	0.966983	+	0.793583i	0.978478	−	0.206351i	$-0.0661589\pi$
$827$	27.8081	+	22.8215i	0.966983	+	0.793583i	−0.0114947	+	0.999934i	$0.503659\pi$
$828$	−2.58152	+	2.55563i	−0.0897142	+	0.0888142i
$829$	11.9609	−	22.3773i	0.415420	−	0.777197i	−0.583982	−	0.811767i	$-0.698506\pi$
$829$	11.9609	−	22.3773i	0.415420	−	0.777197i	0.999402	+	0.0345699i	$0.0110061\pi$
$830$	0.797967	+	4.06518i	0.0276979	+	0.141104i
$831$			23.3443i			0.809803i
$832$	−17.3138	+	4.96745i	−0.600249	+	0.172215i
$833$		−	21.6714i		−	0.750869i
$834$	−16.5016	+	3.23915i	−0.571402	+	0.112163i
$835$	7.49758	−	14.0270i	0.259465	−	0.485424i
$836$	19.1135	+	0.0963508i	0.661053	+	0.00333236i
$837$	−0.830022	−	0.681182i	−0.0286898	−	0.0235451i
$838$	−3.91436	+	12.7878i	−0.135219	+	0.441748i
$839$	13.0095	−	19.4700i	0.449136	−	0.672180i	−0.535948	−	0.844251i	$-0.680046\pi$
$839$	13.0095	−	19.4700i	0.449136	−	0.672180i	0.985085	+	0.172071i	$0.0550458\pi$
$840$	−3.23645	−	1.36934i	−0.111668	−	0.0472468i
$841$	−47.5220	+	31.7532i	−1.63869	+	1.09494i
$842$	−13.6802	+	25.4394i	−0.471450	+	0.876698i
$843$	3.66142	−	12.0701i	0.126106	−	0.415716i
$844$	−10.5253	−	35.3375i	−0.362295	−	1.21637i
$845$	−3.59565	−	4.38132i	−0.123694	−	0.150722i
$846$	−5.12830	+	12.2931i	−0.176314	+	0.422645i
$847$	3.47013	+	8.37764i	0.119235	+	0.287859i
$848$	−4.21597	−	8.08249i	−0.144777	−	0.277554i
$849$	0.0730989	−	0.176476i	0.00250875	−	0.00605665i
$850$	−24.3964	−	24.5197i	−0.836789	−	0.841018i
$851$	−1.27423	−	0.125501i	−0.0436801	−	0.00430212i
$852$	7.54966	+	6.25980i	0.258647	+	0.214457i
$853$	13.7053	−	7.32566i	0.469262	−	0.250826i	−0.219777	−	0.975550i	$-0.570533\pi$
$853$	13.7053	−	7.32566i	0.469262	−	0.250826i	0.689039	+	0.724724i	$0.258033\pi$
$854$	0.122576	−	1.21318i	0.00419447	−	0.0415142i
$855$	0.554055	−	2.78542i	0.0189483	−	0.0952595i
$856$	2.51595	+	8.52552i	0.0859935	+	0.291396i
$857$	23.1353	−	4.60189i	0.790286	−	0.157198i	0.216586	−	0.976263i	$-0.430508\pi$
$857$	23.1353	−	4.60189i	0.790286	−	0.157198i	0.573700	+	0.819066i	$0.305508\pi$
$858$	−4.87301	+	5.90736i	−0.166362	+	0.201674i
$859$	−16.1217	+	1.58785i	−0.550066	+	0.0541768i	−0.369233	−	0.929337i	$-0.620379\pi$
$859$	−16.1217	+	1.58785i	−0.550066	+	0.0541768i	−0.180833	+	0.983514i	$0.557879\pi$
$860$	−4.86003	+	0.941277i	−0.165726	+	0.0320973i
$861$	−14.8218	+	4.49614i	−0.505126	+	0.153228i
$862$	−8.50563	−	12.7993i	−0.289703	−	0.435946i
$863$	−26.5907	−	26.5907i	−0.905159	−	0.905159i	0.0907172	−	0.995877i	$-0.471084\pi$
$863$	−26.5907	−	26.5907i	−0.905159	−	0.905159i	−0.995877	+	0.0907172i	$0.971084\pi$
$864$	−5.43354	+	1.57375i	−0.184853	+	0.0535400i
$865$	10.8050	−	10.8050i	0.367382	−	0.367382i
$866$	25.9802	+	5.23589i	0.882844	+	0.177923i
$867$	−3.68160	−	12.1366i	−0.125034	−	0.412181i
$868$	2.05848	+	3.11460i	0.0698692	+	0.105716i
$869$	−0.492621	−	5.00167i	−0.0167110	−	0.169670i
$870$	−9.33855	+	0.896007i	−0.316606	+	0.0303775i
$871$	−1.85296	−	9.31544i	−0.0627850	−	0.315642i
$872$	−10.9697	+	35.2018i	−0.371480	+	1.19208i
$873$	18.6035	+	3.70047i	0.629634	+	0.125242i
$874$	6.45536	+	7.90643i	0.218356	+	0.267439i
$875$	5.55776	+	10.3978i	0.187887	+	0.351511i
$876$	1.08373	+	2.05234i	0.0366159	+	0.0693421i
$877$	−3.20960	+	32.5876i	−0.108381	+	1.10041i	0.775068	+	0.631878i	$0.217716\pi$
$877$	−3.20960	+	32.5876i	−0.108381	+	1.10041i	−0.883449	+	0.468528i	$0.844784\pi$
$878$	−0.136096	+	53.9961i	−0.00459302	+	1.82228i
$879$	−10.1834	−	4.21810i	−0.343478	−	0.142273i
$880$	1.40921	−	6.72929i	0.0475045	−	0.226844i
$881$	14.5761	−	6.03760i	0.491080	−	0.203412i	−0.123381	−	0.992359i	$-0.539374\pi$
$881$	14.5761	−	6.03760i	0.491080	−	0.203412i	0.614461	+	0.788947i	$0.289374\pi$
$882$	2.13962	+	5.20256i	0.0720449	+	0.175179i
$883$	41.8706	−	34.3623i	1.40906	−	1.15638i	0.443475	−	0.896287i	$-0.353745\pi$
$883$	41.8706	−	34.3623i	1.40906	−	1.15638i	0.965582	−	0.260097i	$-0.0837546\pi$
$884$	15.4682	+	19.0430i	0.520251	+	0.640485i
$885$	6.72608	+	2.04033i	0.226095	+	0.0685850i
$886$	7.42992	−	2.23341i	0.249613	−	0.0750328i
$887$	26.4828	+	39.6343i	0.889206	+	1.33079i	0.943192	+	0.332249i	$0.107807\pi$
$887$	26.4828	+	39.6343i	0.889206	+	1.33079i	−0.0539859	+	0.998542i	$0.517193\pi$
$888$	−1.64946	−	1.12027i	−0.0553522	−	0.0375936i
$889$	−9.76052	−	6.52177i	−0.327357	−	0.218733i
$890$	−5.07497	−	9.55243i	−0.170113	−	0.320198i
$891$	−1.52571	+	1.85908i	−0.0511132	+	0.0622816i
$892$	20.0715	−	47.7743i	0.672043	−	1.59960i
$893$	33.0078	+	17.6430i	1.10456	+	0.590401i
$894$	−16.8516	−	11.3215i	−0.563603	−	0.378646i
$895$	−1.04629			−0.0349737
$896$	19.6655	+	0.347000i	0.656977	+	0.0115925i
$897$	−4.08943			−0.136542
$898$	6.38458	+	4.28936i	0.213056	+	0.143138i
$899$	8.78967	+	4.69818i	0.293152	+	0.156693i
$900$	8.27758	+	3.47767i	0.275919	+	0.115922i
$901$	−7.87687	+	9.59800i	−0.262417	+	0.319756i
$902$	−14.2171	−	26.7603i	−0.473377	−	0.891020i
$903$	−5.00614	−	3.34499i	−0.166594	−	0.111314i
$904$	−29.2116	+	5.58126i	−0.971563	+	0.185630i
$905$	2.76826	+	4.14300i	0.0920201	+	0.137718i
$906$	−19.7238	+	5.92890i	−0.655279	+	0.196974i
$907$	23.8396	+	7.23165i	0.791580	+	0.240123i	0.660082	−	0.751193i	$-0.270521\pi$
$907$	23.8396	+	7.23165i	0.791580	+	0.240123i	0.131497	+	0.991317i	$0.458021\pi$
$908$	22.9439	−	18.6368i	0.761421	−	0.618485i
$909$	−5.56207	+	4.56467i	−0.184482	+	0.151401i
$910$	−1.50475	−	3.65886i	−0.0498821	−	0.121290i
$911$	−23.1112	+	9.57299i	−0.765709	+	0.317167i	−0.731133	−	0.682235i	$-0.761008\pi$
$911$	−23.1112	+	9.57299i	−0.765709	+	0.317167i	−0.0345762	+	0.999402i	$0.511008\pi$
$912$	2.94364	+	15.6201i	0.0974736	+	0.517232i
$913$	−9.10724	−	3.77234i	−0.301406	−	0.124846i
$914$	0.0811667	−	32.2029i	0.00268476	−	1.06518i
$915$	0.0347430	−	0.352752i	0.00114857	−	0.0116616i
$916$	16.1648	−	8.53576i	0.534099	−	0.282030i
$917$	−6.33711	−	11.8559i	−0.209270	−	0.391516i
$918$	4.87291	+	5.96827i	0.160830	+	0.196982i
$919$	−47.2885	−	9.40628i	−1.55991	−	0.310284i	−0.661668	−	0.749797i	$-0.730151\pi$
$919$	−47.2885	−	9.40628i	−1.55991	−	0.310284i	−0.898237	+	0.439512i	$0.855151\pi$
$920$	3.25097	−	1.70620i	0.107181	−	0.0562518i
$921$	3.16030	+	15.8879i	0.104135	+	0.523524i
$922$	57.6697	−	5.53324i	1.89925	−	0.182228i
$923$	1.08218	+	10.9876i	0.0356205	+	0.361661i
$924$	6.97608	−	4.61057i	0.229496	−	0.151677i
$925$	0.918665	+	3.02843i	0.0302055	+	0.0995743i
$926$	−26.6168	−	5.36418i	−0.874682	−	0.176278i
$927$	6.44872	−	6.44872i	0.211804	−	0.211804i
$928$	46.6149	−	24.1659i	1.53021	−	0.793284i
$929$	28.9168	+	28.9168i	0.948728	+	0.948728i	0.998748	−	0.0500200i	$-0.0159285\pi$
$929$	28.9168	+	28.9168i	0.948728	+	0.948728i	−0.0500200	+	0.998748i	$0.515929\pi$
$930$	0.600664	+	0.903881i	0.0196965	+	0.0296394i
$931$	15.1259	−	4.58839i	0.495731	−	0.150378i
$932$	−5.09919	−	26.3283i	−0.167030	−	0.862413i
$933$	−22.7300	+	2.23871i	−0.744146	+	0.0732920i
$934$	−3.81533	+	4.62517i	−0.124841	+	0.151340i
$935$	−9.18449	+	1.82691i	−0.300365	+	0.0597463i
$936$	−5.59350	−	3.04439i	−0.182829	−	0.0995090i
$937$	3.56167	−	17.9057i	0.116355	−	0.584955i	−0.877983	−	0.478691i	$-0.841111\pi$
$937$	3.56167	−	17.9057i	0.116355	−	0.584955i	0.994338	−	0.106264i	$-0.0338888\pi$
$938$	−1.04257	+	10.3187i	−0.0340411	+	0.336918i
$939$	−19.5827	+	10.4672i	−0.639057	+	0.341583i
$940$	8.59298	−	10.3636i	0.280272	−	0.338023i
$941$	26.3304	+	2.59331i	0.858345	+	0.0845396i	0.517607	−	0.855619i	$-0.326823\pi$
$941$	26.3304	+	2.59331i	0.858345	+	0.0845396i	0.340738	+	0.940158i	$0.389323\pi$
$942$	−12.9234	−	12.9887i	−0.421066	−	0.423193i
$943$	6.19258	−	14.9502i	0.201658	−	0.486846i
$944$	−39.1862	+	3.46099i	−1.27540	+	0.112645i
$945$	−0.475469	−	1.14788i	−0.0154670	−	0.0373407i
$946$	4.53514	−	10.8712i	0.147450	−	0.353454i
$947$	−11.0774	−	13.4979i	−0.359969	−	0.438623i	0.561263	−	0.827637i	$-0.310316\pi$
$947$	−11.0774	−	13.4979i	−0.359969	−	0.438623i	−0.921232	+	0.389015i	$0.872816\pi$
$948$	4.00563	−	1.19308i	0.130097	−	0.0387493i
$949$	−0.758457	+	2.50030i	−0.0246205	+	0.0811631i
$950$	11.9486	−	22.2193i	0.387663	−	0.720889i
$951$	−12.2346	+	8.17488i	−0.396733	+	0.265089i
$952$	−10.0644	−	24.8270i	−0.326190	−	0.804649i
$953$	28.6022	−	42.8063i	0.926518	−	1.38663i	0.00428723	−	0.999991i	$-0.498635\pi$
$953$	28.6022	−	42.8063i	0.926518	−	1.38663i	0.922230	−	0.386641i	$-0.126365\pi$
$954$	0.943354	−	3.08184i	0.0305422	−	0.0997781i
$955$	−10.2655	−	8.42472i	−0.332185	−	0.272618i
$956$	−0.0755555	+	14.9882i	−0.00244364	+	0.484753i
$957$	10.5230	−	19.6871i	0.340159	−	0.636393i
$958$	−20.3797	+	4.00040i	−0.658439	+	0.129247i
$959$		−	19.3014i		−	0.623275i
$960$	5.71684	+	0.0864616i	0.184510	+	0.00279053i
$961$			29.8471i			0.962808i
$962$	−0.432368	−	2.20266i	−0.0139401	−	0.0710166i
$963$	−1.48148	+	2.77165i	−0.0477400	+	0.0893152i
$964$	−39.2761	−	39.6741i	−1.26500	−	1.27782i
$965$	13.9197	+	11.4236i	0.448091	+	0.367739i
$966$	4.26988	+	1.30702i	0.137381	+	0.0420526i
$967$	32.1758	−	48.1545i	1.03470	−	1.54855i	0.214295	−	0.976769i	$-0.431254\pi$
$967$	32.1758	−	48.1545i	1.03470	−	1.54855i	0.820410	−	0.571776i	$-0.193746\pi$
$968$	−10.3529	−	10.5106i	−0.332754	−	0.337824i
$969$	18.0011	−	12.0280i	0.578279	−	0.386394i
$970$	−16.8848	−	9.07989i	−0.542138	−	0.291538i
$971$	12.5414	−	41.3435i	0.402473	−	1.32678i	−0.488437	−	0.872599i	$-0.662433\pi$
$971$	12.5414	−	41.3435i	0.402473	−	1.32678i	0.890911	−	0.454178i	$-0.150067\pi$
$972$	−1.75907	−	0.951673i	−0.0564221	−	0.0305249i
$973$	13.1143	+	15.9798i	0.420425	+	0.512290i
$974$	−13.2227	−	5.51609i	−0.423681	−	0.176747i
$975$	3.86804	+	9.33828i	0.123876	+	0.299064i
$976$	0.556714	+	1.90414i	0.0178200	+	0.0609500i
$977$	−12.5955	+	30.4082i	−0.402965	+	0.972843i	0.583977	+	0.811770i	$0.301496\pi$
$977$	−12.5955	+	30.4082i	−0.402965	+	0.972843i	−0.986942	+	0.161074i	$0.948504\pi$
$978$	−18.0626	+	17.9718i	−0.577579	+	0.574675i
$979$	25.6146	+	2.52281i	0.818645	+	0.0806295i
$980$	−0.528762	−	5.66102i	−0.0168907	−	0.180835i
$981$	−11.4967	+	6.14513i	−0.367062	+	0.196199i
$982$	4.83834	+	0.488852i	0.154398	+	0.0155999i
$983$	−5.91957	+	29.7597i	−0.188805	+	0.949186i	0.763910	+	0.645322i	$0.223277\pi$
$983$	−5.91957	+	29.7597i	−0.188805	+	0.949186i	−0.952715	+	0.303864i	$0.901723\pi$
$984$	19.5999	−	15.8387i	0.624822	−	0.504920i
$985$	−9.93091	+	1.97538i	−0.316425	+	0.0629408i
$986$	−55.1683	−	45.5087i	−1.75692	−	1.44929i
$987$	16.2950	−	1.60492i	0.518677	−	0.0510852i
$988$	−10.0163	+	14.8282i	−0.318662	+	0.471746i
$989$	6.01946	−	1.82598i	0.191408	−	0.0580629i
$990$	2.02451	−	1.34537i	0.0643432	−	0.0427586i
$991$	33.0339	+	33.0339i	1.04936	+	1.04936i	0.998717	+	0.0506383i	$0.0161256\pi$
$991$	33.0339	+	33.0339i	1.04936	+	1.04936i	0.0506383	+	0.998717i	$0.483874\pi$
$992$	−5.00747	−	3.43795i	−0.158987	−	0.109155i
$993$	13.4200	−	13.4200i	0.425872	−	0.425872i
$994$	2.38179	−	11.8183i	0.0755457	−	0.374853i
$995$	−1.86262	−	6.14023i	−0.0590490	−	0.194658i
$996$	1.63979	−	8.03195i	0.0519586	−	0.254502i
$997$	0.856344	+	8.69461i	0.0271207	+	0.275361i	0.999175	+	0.0406059i	$0.0129288\pi$
$997$	0.856344	+	8.69461i	0.0271207	+	0.275361i	−0.972055	+	0.234755i	$0.924571\pi$
$998$	−2.71292	−	28.2752i	−0.0858761	−	0.895036i
$999$	−0.137530	−	0.691411i	−0.00435126	−	0.0218753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.109.9	✓	512
128.101	even	32	inner	384.2.v.a.229.9	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.9	✓	512	1.1	even	1	trivial
384.2.v.a.229.9	yes	512	128.101	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)

\(f(q)\)	\(=\)	\(q+(-0.788656 + 1.17389i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-0.756043 - 1.85159i) q^{4} +(-0.453393 + 0.552461i) q^{5} +(1.24890 - 0.663510i) q^{6} +(-1.44548 - 0.965841i) q^{7} +(2.76983 + 0.572759i) q^{8} +(0.555570 + 0.831470i) q^{9} +O(q^{10})\)	\(q+(-0.788656 + 1.17389i) q^{2} +(-0.881921 - 0.471397i) q^{3} +(-0.756043 - 1.85159i) q^{4} +(-0.453393 + 0.552461i) q^{5} +(1.24890 - 0.663510i) q^{6} +(-1.44548 - 0.965841i) q^{7} +(2.76983 + 0.572759i) q^{8} +(0.555570 + 0.831470i) q^{9} +(-0.290958 - 0.967935i) q^{10} +(2.30143 + 0.698132i) q^{11} +(-0.206065 + 1.98936i) q^{12} +(-1.74047 + 1.42836i) q^{13} +(2.27378 - 0.935124i) q^{14} +(0.660285 - 0.273499i) q^{15} +(-2.85680 + 2.79977i) q^{16} +(5.03347 + 2.08493i) q^{17} +(-1.41421 - 0.00356449i) q^{18} +(-0.389496 + 3.95462i) q^{19} +(1.36572 + 0.421815i) q^{20} +(0.819508 + 1.53319i) q^{21} +(-2.63457 + 2.15105i) q^{22} +(-1.78138 - 0.354339i) q^{23} +(-2.17277 - 1.81082i) q^{24} +(0.875804 + 4.40296i) q^{25} +(-0.304115 - 3.16961i) q^{26} +(-0.0980171 - 0.995185i) q^{27} +(-0.695498 + 3.40667i) q^{28} +(2.69440 + 8.88225i) q^{29} +(-0.199680 + 0.990799i) q^{30} +(0.759258 - 0.759258i) q^{31} +(-1.03359 - 5.56163i) q^{32} +(-1.70059 - 1.70059i) q^{33} +(-6.41716 + 4.26445i) q^{34} +(1.18896 - 0.360667i) q^{35} +(1.11951 - 1.65732i) q^{36} +(0.701562 - 0.0690978i) q^{37} +(-4.33512 - 3.57606i) q^{38} +(2.20828 - 0.439254i) q^{39} +(-1.57225 + 1.27054i) q^{40} +(-1.73814 + 8.73822i) q^{41} +(-2.44611 - 0.247148i) q^{42} +(-3.05435 + 1.63259i) q^{43} +(-0.447325 - 4.78914i) q^{44} +(-0.711246 - 0.0700516i) q^{45} +(1.82085 - 1.81170i) q^{46} +(3.60433 - 8.70163i) q^{47} +(3.83927 - 1.12249i) q^{48} +(-1.52221 - 3.67494i) q^{49} +(-5.85931 - 2.44433i) q^{50} +(-3.45629 - 4.21150i) q^{51} +(3.96062 + 2.14273i) q^{52} +(-0.661557 + 2.18086i) q^{53} +(1.24554 + 0.669797i) q^{54} +(-1.42914 + 0.954923i) q^{55} +(-3.45055 - 3.50313i) q^{56} +(2.20770 - 3.30406i) q^{57} +(-12.5518 - 3.84211i) q^{58} +(7.60232 + 6.23907i) q^{59} +(-1.00561 - 1.01580i) q^{60} +(0.233796 - 0.437401i) q^{61} +(0.292493 + 1.49008i) q^{62} -1.73847i q^{63} +(7.34389 + 3.17289i) q^{64} -1.60915i q^{65} +(3.33748 - 0.655125i) q^{66} +(-1.98855 + 3.72031i) q^{67} +(0.0549278 - 10.8962i) q^{68} +(1.40400 + 1.15224i) q^{69} +(-0.514297 + 1.68015i) q^{70} +(2.72431 - 4.07722i) q^{71} +(1.06260 + 2.62124i) q^{72} +(0.964879 - 0.644711i) q^{73} +(-0.472178 + 0.878052i) q^{74} +(1.30315 - 4.29592i) q^{75} +(7.61683 - 2.26867i) q^{76} +(-2.65240 - 3.23196i) q^{77} +(-1.22594 + 2.93870i) q^{78} +(-0.799719 - 1.93069i) q^{79} +(-0.251510 - 2.84766i) q^{80} +(-0.382683 + 0.923880i) q^{81} +(-8.88693 - 8.93184i) q^{82} +(-4.07908 - 0.401754i) q^{83} +(2.21927 - 2.67656i) q^{84} +(-3.43398 + 1.83550i) q^{85} +(0.492356 - 4.87303i) q^{86} +(1.81081 - 9.10358i) q^{87} +(5.97471 + 3.25187i) q^{88} +(10.4965 - 2.08788i) q^{89} +(0.643161 - 0.779679i) q^{90} +(3.89539 - 0.383662i) q^{91} +(0.690709 + 3.56629i) q^{92} +(-1.02752 + 0.311694i) q^{93} +(7.37219 + 11.0937i) q^{94} +(-2.00818 - 2.00818i) q^{95} +(-1.71019 + 5.39215i) q^{96} +(13.4124 - 13.4124i) q^{97} +(5.51448 + 1.11136i) q^{98} +(0.698132 + 2.30143i) 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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