LMFDB - Embedded newform 384.2.v.a.229.15

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			229.15
Character	$\chi$	$=$	384.229
Dual form			384.2.v.a.109.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.127742 + 1.40843i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.96736 - 0.359831i) q^{4} +(-1.40713 - 1.71460i) q^{5} +(0.551272 + 1.30234i) q^{6} +(0.0127962 - 0.00855015i) q^{7} +(0.758112 - 2.72493i) q^{8} +(0.555570 - 0.831470i) q^{9} +(2.59464 - 1.76283i) q^{10} +(3.40372 - 1.03251i) q^{11} +(-1.90468 + 0.610066i) q^{12} +(-2.41676 - 1.98339i) q^{13} +(0.0104077 + 0.0191148i) q^{14} +(-2.04924 - 0.848822i) q^{15} +(3.74104 + 1.41584i) q^{16} +(4.96730 - 2.05752i) q^{17} +(1.10010 + 0.888697i) q^{18} +(-0.321304 - 3.26226i) q^{19} +(2.15138 + 3.87957i) q^{20} +(0.00725473 - 0.0135727i) q^{21} +(1.01942 + 4.92581i) q^{22} +(4.07213 - 0.809998i) q^{23} +(-0.615929 - 2.76055i) q^{24} +(0.0156326 - 0.0785902i) q^{25} +(3.10219 - 3.15049i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.0282514 + 0.0122168i) q^{28} +(-0.827213 + 2.72696i) q^{29} +(1.45728 - 2.77778i) q^{30} +(-3.88443 - 3.88443i) q^{31} +(-2.47200 + 5.08814i) q^{32} +(2.51509 - 2.51509i) q^{33} +(2.26335 + 7.25893i) q^{34} +(-0.0326660 - 0.00990914i) q^{35} +(-1.39220 + 1.43589i) q^{36} +(-2.61418 - 0.257475i) q^{37} +(4.63571 - 0.0358090i) q^{38} +(-3.06636 - 0.609936i) q^{39} +(-5.73893 + 2.53449i) q^{40} +(1.20863 + 6.07619i) q^{41} +(0.0181894 + 0.0119516i) q^{42} +(-9.65881 - 5.16274i) q^{43} +(-7.06789 + 0.806554i) q^{44} +(-2.20740 + 0.217410i) q^{45} +(0.620646 + 5.83880i) q^{46} +(2.67337 + 6.45408i) q^{47} +(3.96673 - 0.514858i) q^{48} +(-2.67869 + 6.46694i) q^{49} +(0.108692 + 0.0320567i) q^{50} +(3.41086 - 4.15614i) q^{51} +(4.04097 + 4.77167i) q^{52} +(-0.861628 - 2.84041i) q^{53} +(1.38913 + 0.265177i) q^{54} +(-6.55983 - 4.38314i) q^{55} +(-0.0135976 - 0.0413508i) q^{56} +(-1.82118 - 2.72559i) q^{57} +(-3.73506 - 1.51342i) q^{58} +(5.35526 - 4.39495i) q^{59} +(3.72616 + 2.40732i) q^{60} +(5.71656 + 10.6949i) q^{61} +(5.96715 - 4.97475i) q^{62} -0.0153899i q^{63} +(-6.85053 - 4.13161i) q^{64} +6.93467i q^{65} +(3.22106 + 3.86362i) q^{66} +(2.05001 + 3.83531i) q^{67} +(-10.5128 + 2.26051i) q^{68} +(3.20947 - 2.63395i) q^{69} +(0.0181292 - 0.0447421i) q^{70} +(-1.74600 - 2.61308i) q^{71} +(-1.84452 - 2.14424i) q^{72} +(6.90550 + 4.61411i) q^{73} +(0.696576 - 3.64901i) q^{74} +(-0.0232605 - 0.0766795i) q^{75} +(-0.541739 + 6.53366i) q^{76} +(0.0347266 - 0.0423145i) q^{77} +(1.25076 - 4.24084i) q^{78} +(0.304162 - 0.734312i) q^{79} +(-2.83656 - 8.40666i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-8.71230 + 0.926090i) q^{82} +(-5.51850 + 0.543524i) q^{83} +(-0.0191566 + 0.0240919i) q^{84} +(-10.5175 - 5.62171i) q^{85} +(8.50520 - 12.9443i) q^{86} +(0.555941 + 2.79491i) q^{87} +(-0.233112 - 10.0577i) q^{88} +(-6.60896 - 1.31460i) q^{89} +(-0.0242301 - 3.13674i) q^{90} +(-0.0478837 - 0.00471613i) q^{91} +(-8.30283 + 0.128280i) q^{92} +(-5.25686 - 1.59465i) q^{93} +(-9.43163 + 2.94080i) q^{94} +(-5.14134 + 5.14134i) q^{95} +(0.218426 + 5.65264i) q^{96} +(10.0236 + 10.0236i) q^{97} +(-8.76606 - 4.59886i) q^{98} +(1.03251 - 3.40372i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

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 $

$2$	−0.127742	+	1.40843i	−0.0903270	+	0.995912i
$2$	−0.127742	+	1.40843i	−0.0903270	+	0.995912i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$3$	0.881921	−	0.471397i	0.509177	−	0.272161i
$4$	−1.96736	−	0.359831i	−0.983682	−	0.179916i
$5$	−1.40713	−	1.71460i	−0.629289	−	0.766791i	0.356588	−	0.934262i	$-0.383940\pi$
$5$	−1.40713	−	1.71460i	−0.629289	−	0.766791i	−0.985877	+	0.167471i	$0.946440\pi$
$6$	0.551272	+	1.30234i	0.225056	+	0.531680i
$7$	0.0127962	−	0.00855015i	0.00483651	−	0.00323165i	−0.553150	−	0.833082i	$-0.686574\pi$
$7$	0.0127962	−	0.00855015i	0.00483651	−	0.00323165i	0.557986	+	0.829850i	$0.311574\pi$
$8$	0.758112	−	2.72493i	0.268033	−	0.963410i
$9$	0.555570	−	0.831470i	0.185190	−	0.277157i
$10$	2.59464	−	1.76283i	0.820499	−	0.557455i
$11$	3.40372	−	1.03251i	1.02626	−	0.311313i	0.268108	−	0.963389i	$-0.413602\pi$
$11$	3.40372	−	1.03251i	1.02626	−	0.311313i	0.758154	+	0.652076i	$0.226102\pi$
$12$	−1.90468	+	0.610066i	−0.549835	+	0.176111i
$13$	−2.41676	−	1.98339i	−0.670290	−	0.550092i	0.236523	−	0.971626i	$-0.423992\pi$
$13$	−2.41676	−	1.98339i	−0.670290	−	0.550092i	−0.906813	+	0.421533i	$0.861492\pi$
$14$	0.0104077	+	0.0191148i	0.00278158	+	0.00510865i
$15$	−2.04924	−	0.848822i	−0.529111	−	0.219165i
$16$	3.74104	+	1.41584i	0.935261	+	0.353960i
$17$	4.96730	−	2.05752i	1.20475	−	0.499022i	0.312217	−	0.950011i	$-0.398928\pi$
$17$	4.96730	−	2.05752i	1.20475	−	0.499022i	0.892530	+	0.450989i	$0.148928\pi$
$18$	1.10010	+	0.888697i	0.259296	+	0.209468i
$19$	−0.321304	−	3.26226i	−0.0737122	−	0.748413i	−0.959007	−	0.283383i	$-0.908543\pi$
$19$	−0.321304	−	3.26226i	−0.0737122	−	0.748413i	0.885295	−	0.465030i	$-0.153957\pi$
$20$	2.15138	+	3.87957i	0.481063	+	0.867498i
$21$	0.00725473	−	0.0135727i	0.00158311	−	0.00296180i
$22$	1.01942	+	4.92581i	0.217341	+	1.05019i
$23$	4.07213	−	0.809998i	0.849099	−	0.168896i	0.248684	−	0.968585i	$-0.420002\pi$
$23$	4.07213	−	0.809998i	0.849099	−	0.168896i	0.600415	+	0.799689i	$0.295002\pi$
$24$	−0.615929	−	2.76055i	−0.125726	−	0.563495i
$25$	0.0156326	−	0.0785902i	0.00312651	−	0.0157180i
$26$	3.10219	−	3.15049i	0.608389	−	0.617861i
$27$	0.0980171	−	0.995185i	0.0188634	−	0.191523i
$28$	−0.0282514	+	0.0122168i	−0.00533901	+	0.00230876i
$29$	−0.827213	+	2.72696i	−0.153610	+	0.506383i	−0.999642	−	0.0267482i	$-0.991485\pi$
$29$	−0.827213	+	2.72696i	−0.153610	+	0.506383i	0.846033	+	0.533131i	$0.178985\pi$
$30$	1.45728	−	2.77778i	0.266062	−	0.507151i
$31$	−3.88443	−	3.88443i	−0.697663	−	0.697663i	0.266243	−	0.963906i	$-0.414218\pi$
$31$	−3.88443	−	3.88443i	−0.697663	−	0.697663i	−0.963906	+	0.266243i	$0.914218\pi$
$32$	−2.47200	+	5.08814i	−0.436992	+	0.899465i
$33$	2.51509	−	2.51509i	0.437822	−	0.437822i
$34$	2.26335	+	7.25893i	0.388161	+	1.24490i
$35$	−0.0326660	−	0.00990914i	−0.00552157	−	0.00167495i
$36$	−1.39220	+	1.43589i	−0.232033	+	0.239315i
$37$	−2.61418	−	0.257475i	−0.429769	−	0.0423286i	−0.119180	−	0.992873i	$-0.538026\pi$
$37$	−2.61418	−	0.257475i	−0.429769	−	0.0423286i	−0.310589	+	0.950544i	$0.600526\pi$
$38$	4.63571	−	0.0358090i	0.752012	−	0.00580899i
$39$	−3.06636	−	0.609936i	−0.491010	−	0.0976680i
$40$	−5.73893	+	2.53449i	−0.907405	+	0.400738i
$41$	1.20863	+	6.07619i	0.188756	+	0.948942i	0.952759	+	0.303728i	$0.0982315\pi$
$41$	1.20863	+	6.07619i	0.188756	+	0.948942i	−0.764002	+	0.645213i	$0.776769\pi$
$42$	0.0181894	+	0.0119516i	0.00280669	+	0.00184417i
$43$	−9.65881	−	5.16274i	−1.47295	−	0.787311i	−0.477150	−	0.878822i	$-0.658330\pi$
$43$	−9.65881	−	5.16274i	−1.47295	−	0.787311i	−0.995804	+	0.0915111i	$0.970830\pi$
$44$	−7.06789	+	0.806554i	−1.06552	+	0.121593i
$45$	−2.20740	+	0.217410i	−0.329059	+	0.0324095i
$46$	0.620646	+	5.83880i	0.0915092	+	0.860884i
$47$	2.67337	+	6.45408i	0.389950	+	0.941424i	0.989949	+	0.141423i	$0.0451677\pi$
$47$	2.67337	+	6.45408i	0.389950	+	0.941424i	−0.599999	+	0.800001i	$0.704832\pi$
$48$	3.96673	−	0.514858i	0.572548	−	0.0743133i
$49$	−2.67869	+	6.46694i	−0.382670	+	0.923848i
$50$	0.108692	+	0.0320567i	0.0153714	+	0.00453350i
$51$	3.41086	−	4.15614i	0.477615	−	0.581976i
$52$	4.04097	+	4.77167i	0.560382	+	0.661712i
$53$	−0.861628	−	2.84041i	−0.118354	−	0.390160i	0.877668	−	0.479269i	$-0.159098\pi$
$53$	−0.861628	−	2.84041i	−0.118354	−	0.390160i	−0.996022	+	0.0891089i	$0.971598\pi$
$54$	1.38913	+	0.265177i	0.189037	+	0.0360860i
$55$	−6.55983	−	4.38314i	−0.884527	−	0.591022i
$56$	−0.0135976	−	0.0413508i	−0.00181706	−	0.00552573i
$57$	−1.82118	−	2.72559i	−0.241221	−	0.361013i
$58$	−3.73506	−	1.51342i	−0.490438	−	0.198722i
$59$	5.35526	−	4.39495i	0.697196	−	0.572174i	−0.217626	−	0.976032i	$-0.569831\pi$
$59$	5.35526	−	4.39495i	0.697196	−	0.572174i	0.914821	+	0.403858i	$0.132331\pi$
$60$	3.72616	+	2.40732i	0.481046	+	0.310784i
$61$	5.71656	+	10.6949i	0.731930	+	1.36934i	0.921851	+	0.387545i	$0.126677\pi$
$61$	5.71656	+	10.6949i	0.731930	+	1.36934i	−0.189921	+	0.981799i	$0.560823\pi$
$62$	5.96715	−	4.97475i	0.757829	−	0.631794i
$63$		−	0.0153899i		−	0.00193894i
$64$	−6.85053	−	4.13161i	−0.856316	−	0.516452i
$65$			6.93467i			0.860140i
$66$	3.22106	+	3.86362i	0.396485	+	0.475579i
$67$	2.05001	+	3.83531i	0.250449	+	0.468557i	0.975459	−	0.220181i	$-0.0706648\pi$
$67$	2.05001	+	3.83531i	0.250449	+	0.468557i	−0.725010	+	0.688738i	$0.758165\pi$
$68$	−10.5128	+	2.26051i	−1.27487	+	0.274127i
$69$	3.20947	−	2.63395i	0.386375	−	0.317090i
$70$	0.0181292	−	0.0447421i	0.00216685	−	0.00534770i
$71$	−1.74600	−	2.61308i	−0.207212	−	0.310115i	0.713277	−	0.700882i	$-0.247210\pi$
$71$	−1.74600	−	2.61308i	−0.207212	−	0.310115i	−0.920490	+	0.390766i	$0.872210\pi$
$72$	−1.84452	−	2.14424i	−0.217378	−	0.252701i
$73$	6.90550	+	4.61411i	0.808228	+	0.540040i	0.889652	−	0.456639i	$-0.150947\pi$
$73$	6.90550	+	4.61411i	0.808228	+	0.540040i	−0.0814244	+	0.996680i	$0.525947\pi$
$74$	0.696576	−	3.64901i	0.0809753	−	0.424189i
$75$	−0.0232605	−	0.0766795i	−0.00268589	−	0.00885419i
$76$	−0.541739	+	6.53366i	−0.0621418	+	0.749462i
$77$	0.0347266	−	0.0423145i	0.00395747	−	0.00482219i
$78$	1.25076	−	4.24084i	0.141620	−	0.480181i
$79$	0.304162	−	0.734312i	0.0342209	−	0.0826166i	−0.905845	−	0.423609i	$-0.860763\pi$
$79$	0.304162	−	0.734312i	0.0342209	−	0.0826166i	0.940066	+	0.340992i	$0.110763\pi$
$80$	−2.83656	−	8.40666i	−0.317137	−	0.939893i
$81$	−0.382683	−	0.923880i	−0.0425204	−	0.102653i
$82$	−8.71230	+	0.926090i	−0.962112	+	0.102270i
$83$	−5.51850	+	0.543524i	−0.605734	+	0.0596595i	−0.396235	−	0.918149i	$-0.629683\pi$
$83$	−5.51850	+	0.543524i	−0.605734	+	0.0596595i	−0.209499	+	0.977809i	$0.567183\pi$
$84$	−0.0191566	+	0.0240919i	−0.00209015	+	0.00262864i
$85$	−10.5175	−	5.62171i	−1.14078	−	0.609760i
$86$	8.50520	−	12.9443i	0.917140	−	1.39582i
$87$	0.555941	+	2.79491i	0.0596032	+	0.299645i
$88$	−0.233112	−	10.0577i	−0.0248498	−	1.07215i
$89$	−6.60896	−	1.31460i	−0.700548	−	0.139348i	−0.168050	−	0.985779i	$-0.553747\pi$
$89$	−6.60896	−	1.31460i	−0.700548	−	0.139348i	−0.532499	+	0.846431i	$0.678747\pi$
$90$	−0.0242301	−	3.13674i	−0.00255407	−	0.330642i
$91$	−0.0478837	−	0.00471613i	−0.00501957	−	0.000494385i
$92$	−8.30283	+	0.128280i	−0.865630	+	0.0133741i
$93$	−5.25686	−	1.59465i	−0.545111	−	0.165358i
$94$	−9.43163	+	2.94080i	−0.972798	+	0.303320i
$95$	−5.14134	+	5.14134i	−0.527490	+	0.527490i
$96$	0.218426	+	5.65264i	0.0222930	+	0.576920i
$97$	10.0236	+	10.0236i	1.01775	+	1.01775i	0.999840	+	0.0179066i	$0.00570016\pi$
$97$	10.0236	+	10.0236i	1.01775	+	1.01775i	0.0179066	+	0.999840i	$0.494300\pi$
$98$	−8.76606	−	4.59886i	−0.885506	−	0.464555i
$99$	1.03251	−	3.40372i	0.103771	−	0.342087i
$100$	−0.0590341	+	0.148990i	−0.00590341	+	0.0148990i
$101$	0.627601	−	6.37214i	0.0624486	−	0.634052i	−0.912114	−	0.409937i	$-0.865551\pi$
$101$	0.627601	−	6.37214i	0.0624486	−	0.634052i	0.974563	−	0.224115i	$-0.0719492\pi$
$102$	5.41793	+	5.33487i	0.536455	+	0.528231i
$103$	2.14174	−	10.7672i	0.211032	−	1.06093i	−0.719437	−	0.694557i	$-0.755600\pi$
$103$	2.14174	−	10.7672i	0.211032	−	1.06093i	0.930469	−	0.366371i	$-0.119400\pi$
$104$	−7.23678	+	5.08189i	−0.709624	+	0.498320i
$105$	−0.0334800	+	0.00665959i	−0.00326731	+	0.000649909i
$106$	4.11059	−	0.850706i	0.399255	−	0.0826279i
$107$	7.00413	−	13.1038i	0.677115	−	1.26679i	−0.275115	−	0.961411i	$-0.588716\pi$
$107$	7.00413	−	13.1038i	0.677115	−	1.26679i	0.952230	−	0.305381i	$-0.0987839\pi$
$108$	−0.550934	+	1.92262i	−0.0530136	+	0.185004i
$109$	0.611739	+	6.21109i	0.0585939	+	0.594914i	0.978987	+	0.203921i	$0.0653685\pi$
$109$	0.611739	+	6.21109i	0.0585939	+	0.594914i	−0.920393	+	0.390993i	$0.872132\pi$
$110$	7.01132	−	8.67917i	0.668503	−	0.827526i
$111$	−2.42688	+	1.00525i	−0.230349	+	0.0954136i
$112$	0.0599768	−	0.0138691i	0.00566727	−	0.00131051i
$113$	10.6380	+	4.40641i	1.00074	+	0.414520i	0.822069	−	0.569388i	$-0.192820\pi$
$113$	10.6380	+	4.40641i	1.00074	+	0.414520i	0.178672	+	0.983909i	$0.442820\pi$
$114$	4.07145	−	2.21684i	0.381326	−	0.207626i
$115$	−7.11886	−	5.84230i	−0.663837	−	0.544797i
$116$	2.60867	−	5.06726i	0.242209	−	0.470483i
$117$	−2.99181	+	0.907555i	−0.276593	+	0.0839035i
$118$	5.50590	+	8.10395i	0.506859	+	0.746029i
$119$	0.0459704	−	0.0687996i	0.00421410	−	0.00630685i
$120$	−3.86654	+	4.94053i	−0.352965	+	0.451007i
$121$	1.37309	−	0.917471i	0.124827	−	0.0834065i
$122$	−15.7933	+	6.68519i	−1.42986	+	0.605249i
$123$	3.93021	+	4.78898i	0.354375	+	0.431808i
$124$	6.24434	+	9.03982i	0.560758	+	0.811800i
$125$	−9.93760	+	5.31176i	−0.888846	+	0.475098i
$126$	0.0216756	+	0.00196593i	0.00193101	+	0.000175139i
$127$	−8.91223			−0.790832			−0.395416	−	0.918502i	$-0.629400\pi$
$127$	−8.91223			−0.790832			−0.395416	+	0.918502i	$0.629400\pi$
$128$	6.69420	−	9.12073i	0.591689	−	0.806166i
$129$	−10.9520			−0.964271
$130$	−9.76701	−	0.885846i	−0.856624	−	0.0776939i
$131$	5.20271	−	2.78091i	0.454563	−	0.242969i	−0.228192	−	0.973616i	$-0.573281\pi$
$131$	5.20271	−	2.78091i	0.454563	−	0.242969i	0.682755	+	0.730647i	$0.260781\pi$
$132$	−5.85312	+	4.04310i	−0.509448	+	0.351906i
$133$	−0.0320043	−	0.0389973i	−0.00277512	−	0.00338150i
$134$	−5.66364	+	2.39738i	−0.489264	+	0.207102i
$135$	−1.84426	+	1.23230i	−0.158729	+	0.106059i
$136$	−1.84084	−	15.0954i	−0.157851	−	1.29442i
$137$	−11.8039	+	17.6657i	−1.00847	+	1.50929i	−0.155158	+	0.987890i	$0.549589\pi$
$137$	−11.8039	+	17.6657i	−1.00847	+	1.50929i	−0.853314	+	0.521397i	$0.825411\pi$
$138$	3.29975	+	4.85679i	0.280893	+	0.413437i
$139$	15.8982	−	4.82265i	1.34846	−	0.409052i	0.468236	−	0.883603i	$-0.344890\pi$
$139$	15.8982	−	4.82265i	1.34846	−	0.409052i	0.880228	+	0.474552i	$0.157390\pi$
$140$	0.0607004	+	0.0312491i	0.00513012	+	0.00264103i
$141$	5.40013	+	4.43177i	0.454773	+	0.373222i
$142$	3.90338	−	2.12533i	0.327565	−	0.178354i
$143$	−10.2739	−	4.25557i	−0.859143	−	0.355869i
$144$	3.25564	−	2.32397i	0.271303	−	0.193664i
$145$	5.83963	−	2.41885i	0.484955	−	0.200875i
$146$	−7.38078	+	9.13652i	−0.610838	+	0.756144i
$147$	0.686097	+	6.96606i	0.0565883	+	0.574551i
$148$	5.05040	+	1.44721i	0.415141	+	0.118960i
$149$	−1.15016	+	2.15181i	−0.0942252	+	0.176283i	−0.924618	−	0.380895i	$-0.875616\pi$
$149$	−1.15016	+	2.15181i	−0.0942252	+	0.176283i	0.830393	+	0.557178i	$0.188116\pi$
$150$	0.110969	−	0.0229656i	0.00906060	−	0.00187514i
$151$	−8.81999	+	1.75441i	−0.717761	+	0.142772i	−0.540441	−	0.841382i	$-0.681743\pi$
$151$	−8.81999	+	1.75441i	−0.717761	+	0.142772i	−0.177320	+	0.984153i	$0.556743\pi$
$152$	−9.13302	−	1.59762i	−0.740786	−	0.129584i
$153$	1.04892	−	5.27325i	0.0847998	−	0.426317i
$154$	0.0551611	+	0.0543155i	0.00444501	+	0.00437686i
$155$	−1.19432	+	12.1261i	−0.0959301	+	0.973994i
$156$	5.81317	+	2.30334i	0.465426	+	0.184415i
$157$	−3.48169	+	11.4776i	−0.277869	+	0.916011i	0.701283	+	0.712883i	$0.252611\pi$
$157$	−3.48169	+	11.4776i	−0.277869	+	0.916011i	−0.979152	+	0.203128i	$0.934889\pi$
$158$	0.995375	+	0.522194i	0.0791878	+	0.0415435i
$159$	−2.09885	−	2.09885i	−0.166449	−	0.166449i
$160$	12.2026	−	2.92122i	0.964697	−	0.230942i
$161$	0.0451823	−	0.0451823i	0.00356086	−	0.00356086i
$162$	1.35011	−	0.420966i	0.106074	−	0.0330742i
$163$	13.8771	+	4.20957i	1.08694	+	0.329719i	0.782397	−	0.622780i	$-0.213997\pi$
$163$	13.8771	+	4.20957i	1.08694	+	0.329719i	0.304541	+	0.952499i	$0.401497\pi$
$164$	−0.191411	−	12.3890i	−0.0149467	−	0.967417i
$165$	−7.85145	−	0.773300i	−0.611235	−	0.0602014i
$166$	−0.0605752	−	7.84186i	−0.00470155	−	0.608646i
$167$	23.2278	+	4.62029i	1.79742	+	0.357529i	0.976834	−	0.213998i	$-0.0686487\pi$
$167$	23.2278	+	4.62029i	1.79742	+	0.357529i	0.820583	+	0.571527i	$0.193649\pi$
$168$	−0.0314847	−	0.0300583i	−0.00242910	−	0.00231905i
$169$	−0.629250	−	3.16346i	−0.0484039	−	0.243343i
$170$	9.26131	−	14.0950i	0.710310	−	1.08104i
$171$	−2.89097	−	1.54526i	−0.221078	−	0.118169i
$172$	17.1447	+	13.6325i	1.30727	+	1.03947i
$173$	25.2292	−	2.48485i	1.91814	−	0.188920i	0.932902	−	0.360130i	$-0.117268\pi$
$173$	25.2292	−	2.48485i	1.91814	−	0.188920i	0.985235	+	0.171210i	$0.0547676\pi$
$174$	−4.00745	+	0.425980i	−0.303804	+	0.0322934i
$175$	−0.000471921	−	0.00113932i	−3.56738e−5	−	8.61243e-5i
$176$	14.1953	+	0.956463i	1.07001	+	0.0720961i
$177$	2.65116	−	6.40045i	0.199273	−	0.481088i
$178$	2.69577	−	9.14034i	0.202056	−	0.685098i
$179$	−11.2829	+	13.7483i	−0.843327	+	1.02760i	0.155880	+	0.987776i	$0.450179\pi$
$179$	−11.2829	+	13.7483i	−0.843327	+	1.02760i	−0.999207	+	0.0398206i	$0.987321\pi$
$180$	4.42099	+	0.366567i	0.329521	+	0.0273223i
$181$	−5.73573	−	18.9082i	−0.426333	−	1.40543i	−0.862724	−	0.505675i	$-0.831243\pi$
$181$	−5.73573	−	18.9082i	−0.426333	−	1.40543i	0.436390	−	0.899757i	$-0.356257\pi$
$182$	0.0127591	−	0.0668385i	0.000945767	−	0.00495440i
$183$	10.0831	+	6.73731i	0.745364	+	0.498037i
$184$	0.879945	−	11.7104i	0.0648704	−	0.863300i
$185$	3.23704	+	4.84457i	0.237992	+	0.356180i
$186$	2.91748	−	7.20023i	0.213920	−	0.527947i
$187$	14.7829	−	12.1320i	1.08103	−	0.887180i
$188$	−2.93711	−	13.6595i	−0.214210	−	0.996220i
$189$	−0.00725473	−	0.0135727i	−0.000527704	−	0.000987265i
$190$	−6.58446	−	7.89799i	−0.477687	−	0.572981i
$191$			15.5569i			1.12566i	0.826573	+	0.562830i	$0.190287\pi$
$191$			15.5569i			1.12566i	−0.826573	+	0.562830i	$0.809713\pi$
$192$	−7.98926	−	0.414439i	−0.576575	−	0.0299096i
$193$			14.3931i			1.03603i	0.855370	+	0.518017i	$0.173330\pi$
$193$			14.3931i			1.03603i	−0.855370	+	0.518017i	$0.826670\pi$
$194$	−15.3981	+	12.8372i	−1.10552	+	0.921656i
$195$	3.26898	+	6.11583i	0.234096	+	0.437964i
$196$	7.59697	−	11.7589i	0.542641	−	0.839925i
$197$	15.8702	−	13.0243i	1.13070	−	0.927944i	0.132703	−	0.991156i	$-0.457634\pi$
$197$	15.8702	−	13.0243i	1.13070	−	0.927944i	0.998000	+	0.0632113i	$0.0201342\pi$
$198$	4.66202	+	1.88902i	0.331315	+	0.134246i
$199$	11.6340	+	17.4116i	0.824714	+	1.23427i	0.969569	+	0.244819i	$0.0787286\pi$
$199$	11.6340	+	17.4116i	0.824714	+	1.23427i	−0.144855	+	0.989453i	$0.546271\pi$
$200$	−0.202302	−	0.102178i	−0.0143049	−	0.00722507i
$201$	3.61590	+	2.41607i	0.255046	+	0.170416i
$202$	8.89456	+	1.69792i	0.625819	+	0.119465i
$203$	0.0127307	+	0.0419675i	0.000893520	+	0.00294554i
$204$	−8.20590	+	6.94931i	−0.574528	+	0.486549i
$205$	8.71752	−	10.6223i	0.608858	−	0.741895i
$206$	14.8913	+	4.39192i	1.03753	+	0.306000i
$207$	1.58887	−	3.83587i	0.110434	−	0.266611i
$208$	−6.23306	−	10.8417i	−0.432185	−	0.751735i
$209$	−4.46194	−	10.7721i	−0.308639	−	0.745120i
$210$	−0.00510279	−	0.0480050i	−0.000352126	−	0.00331266i
$211$	−24.8684	+	2.44933i	−1.71201	+	0.168619i	−0.906000	−	0.423277i	$-0.860880\pi$
$211$	−24.8684	+	2.44933i	−1.71201	+	0.168619i	−0.806014	+	0.591896i	$0.798380\pi$
$212$	0.673069	+	5.89815i	0.0462266	+	0.405087i
$213$	−2.77163	−	1.48147i	−0.189909	−	0.101509i
$214$	17.5611	+	11.5387i	1.20045	+	0.788772i
$215$	4.73921	+	23.8256i	0.323212	+	1.62489i
$216$	−2.63750	−	1.02155i	−0.179459	−	0.0695078i
$217$	−0.0829183	−	0.0164935i	−0.00562886	−	0.00111965i
$218$	−8.82604	+	0.0681776i	−0.597775	+	0.00461757i
$219$	8.26518	+	0.814049i	0.558509	+	0.0550084i
$220$	11.3284	+	10.9837i	0.763759	+	0.740518i
$221$	−16.0856	−	4.87953i	−1.08204	−	0.328233i
$222$	−1.10581	−	3.54650i	−0.0742169	−	0.238026i
$223$	4.46643	−	4.46643i	0.299094	−	0.299094i	−0.541565	−	0.840659i	$-0.682168\pi$
$223$	4.46643	−	4.46643i	0.299094	−	0.299094i	0.840659	+	0.541565i	$0.182168\pi$
$224$	0.0118722	+	0.0862449i	0.000793244	+	0.00576248i
$225$	−0.0566604	−	0.0566604i	−0.00377736	−	0.00377736i
$226$	−7.56505	+	14.4200i	−0.503220	+	0.959207i
$227$	−1.53036	+	5.04493i	−0.101574	+	0.334844i	−0.992968	−	0.118385i	$-0.962228\pi$
$227$	−1.53036	+	5.04493i	−0.101574	+	0.334844i	0.891394	+	0.453229i	$0.149728\pi$
$228$	2.60218	+	6.01755i	0.172333	+	0.398522i
$229$	−1.05847	+	10.7468i	−0.0699454	+	0.710167i	0.894709	+	0.446649i	$0.147383\pi$
$229$	−1.05847	+	10.7468i	−0.0699454	+	0.710167i	−0.964654	+	0.263518i	$0.915117\pi$
$230$	9.13786	−	9.28013i	0.602532	−	0.611913i
$231$	0.0106792	−	0.0536881i	0.000702642	−	0.00353242i
$232$	6.80365	+	4.32144i	0.446682	+	0.283716i
$233$	2.67988	−	0.533060i	0.175564	−	0.0349220i	−0.106525	−	0.994310i	$-0.533972\pi$
$233$	2.67988	−	0.533060i	0.175564	−	0.0349220i	0.282090	+	0.959388i	$0.408972\pi$
$234$	−0.896051	−	4.32969i	−0.0585767	−	0.283041i
$235$	7.30436	−	13.6655i	0.476484	−	0.891439i
$236$	−12.1172	+	6.71948i	−0.788762	+	0.437401i
$237$	−0.0779054	−	0.790987i	−0.00506050	−	0.0513801i
$238$	0.0910273	+	0.0735348i	0.00590042	+	0.00476656i
$239$	2.45915	−	1.01861i	0.159069	−	0.0658885i	−0.301728	−	0.953394i	$-0.597564\pi$
$239$	2.45915	−	1.01861i	0.159069	−	0.0658885i	0.460797	+	0.887505i	$0.347564\pi$
$240$	−6.46449	−	6.07687i	−0.417281	−	0.392260i
$241$	9.45803	+	3.91764i	0.609245	+	0.252358i	0.665906	−	0.746036i	$-0.268045\pi$
$241$	9.45803	+	3.91764i	0.609245	+	0.252358i	−0.0566606	+	0.998393i	$0.518045\pi$
$242$	1.11680	+	2.05111i	0.0717903	+	0.131850i
$243$	−0.773010	−	0.634393i	−0.0495886	−	0.0406963i
$244$	−7.39818	−	23.0978i	−0.473620	−	1.47869i
$245$	14.8575	−	4.50697i	0.949209	−	0.287939i
$246$	−7.24700	+	4.92369i	−0.462052	+	0.313923i
$247$	−5.69380	+	8.52137i	−0.362288	+	0.542202i
$248$	−13.5296	+	7.63997i	−0.859133	+	0.485139i
$249$	−4.61066	+	3.08075i	−0.292189	+	0.195234i
$250$	−6.21181	−	14.6750i	−0.392869	−	0.928127i
$251$	2.98165	+	3.63315i	0.188200	+	0.229322i	0.858559	−	0.512714i	$-0.171360\pi$
$251$	2.98165	+	3.63315i	0.188200	+	0.229322i	−0.670359	+	0.742037i	$0.733860\pi$
$252$	−0.00553775	+	0.0302775i	−0.000348846	+	0.00190730i
$253$	13.0241	−	6.96152i	0.818818	−	0.437667i
$254$	1.13846	−	12.5523i	0.0714335	−	0.787600i
$255$	−11.9256			−0.746812
$256$	11.9908	+	10.5934i	0.749425	+	0.662089i
$257$	5.88375			0.367018			0.183509	−	0.983018i	$-0.441254\pi$
$257$	5.88375			0.367018			0.183509	+	0.983018i	$0.441254\pi$
$258$	1.39903	−	15.4252i	0.0870997	−	0.960329i
$259$	−0.0356531	+	0.0190570i	−0.00221537	+	0.00118414i
$260$	2.49531	−	13.6430i	0.154753	−	0.846104i
$261$	1.80781	+	2.20282i	0.111900	+	0.136351i
$262$	3.25212	+	7.68291i	0.200917	+	0.474652i
$263$	−8.53743	+	5.70453i	−0.526440	+	0.351756i	−0.790217	−	0.612828i	$-0.790032\pi$
$263$	−8.53743	+	5.70453i	−0.526440	+	0.351756i	0.263776	+	0.964584i	$0.415032\pi$
$264$	−4.94674	−	8.76019i	−0.304451	−	0.539153i
$265$	−3.65773	+	5.47418i	−0.224692	+	0.336276i
$266$	0.0590134	−	0.0400943i	0.00361834	−	0.00245834i
$267$	−6.44828	+	1.95606i	−0.394628	+	0.119709i
$268$	−2.65306	−	8.28310i	−0.162062	−	0.505971i
$269$	−8.41263	−	6.90406i	−0.512927	−	0.420948i	0.341998	−	0.939701i	$-0.388897\pi$
$269$	−8.41263	−	6.90406i	−0.512927	−	0.420948i	−0.854924	+	0.518753i	$0.826397\pi$
$270$	−1.50002	−	2.75494i	−0.0912883	−	0.167660i
$271$	−20.0427	−	8.30194i	−1.21750	−	0.504307i	−0.320889	−	0.947117i	$-0.603982\pi$
$271$	−20.0427	−	8.30194i	−1.21750	−	0.504307i	−0.896616	+	0.442810i	$0.853982\pi$
$272$	21.4960	−	0.664389i	1.30339	−	0.0402845i
$273$	−0.0444528	+	0.0184129i	−0.00269041	+	0.00111440i
$274$	−23.3732	−	18.8816i	−1.41202	−	1.14068i
$275$	−0.0279361	−	0.283640i	−0.00168461	−	0.0171041i
$276$	−7.26198	+	4.02706i	−0.437120	+	0.242401i
$277$	−7.57138	+	14.1651i	−0.454920	+	0.851096i	0.544999	+	0.838436i	$0.316530\pi$
$277$	−7.57138	+	14.1651i	−0.454920	+	0.851096i	−0.999920	+	0.0126598i	$0.995970\pi$
$278$	4.76152	+	23.0075i	0.285577	+	1.37990i
$279$	−5.38785	+	1.07171i	−0.322562	+	0.0641616i
$280$	−0.0517663	+	0.0815006i	−0.00309363	+	0.00487059i
$281$	−4.43475	+	22.2950i	−0.264555	+	1.33001i	0.588631	+	0.808402i	$0.299667\pi$
$281$	−4.43475	+	22.2950i	−0.264555	+	1.33001i	−0.853186	+	0.521607i	$0.825333\pi$
$282$	−6.93167	+	7.03959i	−0.412775	+	0.419202i
$283$	2.16531	−	21.9847i	0.128714	−	1.30686i	−0.686259	−	0.727358i	$-0.740748\pi$
$283$	2.16531	−	21.9847i	0.128714	−	1.30686i	0.814973	−	0.579499i	$-0.196752\pi$
$284$	2.49476	+	5.76914i	0.148037	+	0.342336i
$285$	−2.11065	+	6.95787i	−0.125024	+	0.412148i
$286$	7.30608	−	13.9264i	0.432018	−	0.823487i
$287$	0.0674182	+	0.0674182i	0.00397957	+	0.00397957i
$288$	2.85727	+	4.88221i	0.168366	+	0.287687i
$289$	8.41983	−	8.41983i	0.495284	−	0.495284i
$290$	2.66083	+	8.53371i	0.156249	+	0.501117i
$291$	13.5652	+	4.11495i	0.795204	+	0.241223i
$292$	−11.9253	−	11.5624i	−0.697877	−	0.676641i
$293$	−14.3500	−	1.41335i	−0.838334	−	0.0825687i	−0.330268	−	0.943887i	$-0.607139\pi$
$293$	−14.3500	−	1.41335i	−0.838334	−	0.0825687i	−0.508066	+	0.861318i	$0.669639\pi$
$294$	−9.89886	+	0.0764647i	−0.577314	+	0.00445951i
$295$	−15.0711	−	2.99784i	−0.877476	−	0.174541i
$296$	−2.68345	+	6.92828i	−0.155972	+	0.402698i
$297$	−0.693913	−	3.48854i	−0.0402649	−	0.202425i
$298$	−2.88375	−	1.89480i	−0.167051	−	0.109763i
$299$	−11.4479	−	6.11904i	−0.662051	−	0.353873i
$300$	0.0181701	+	0.159226i	0.00104905	+	0.00919294i
$301$	−0.167738	+	0.0165208i	−0.00966828	+	0.000952242i
$302$	−1.34428	−	12.6465i	−0.0773547	−	0.727723i
$303$	−2.45031	−	5.91558i	−0.140767	−	0.339841i
$304$	3.41681	−	12.6592i	0.195968	−	0.726052i
$305$	10.2935	−	24.8508i	0.589406	−	1.42295i
$306$	7.29303	+	2.15094i	0.416915	+	0.122961i
$307$	−4.87813	+	5.94402i	−0.278410	+	0.339243i	−0.893376	−	0.449310i	$-0.851670\pi$
$307$	−4.87813	+	5.94402i	−0.278410	+	0.339243i	0.614966	+	0.788554i	$0.289170\pi$
$308$	−0.0835460	+	0.0707524i	−0.00476048	+	0.00403149i
$309$	−3.18680	−	10.5055i	−0.181291	−	0.597635i
$310$	−16.9263	−	3.23113i	−0.961348	−	0.183516i
$311$	23.4566	+	15.6732i	1.33010	+	0.888746i	0.998504	−	0.0546742i	$-0.0174120\pi$
$311$	23.4566	+	15.6732i	1.33010	+	0.888746i	0.331599	+	0.943421i	$0.392412\pi$
$312$	−3.98668	+	7.89322i	−0.225701	+	0.446866i
$313$	−11.7776	−	17.6265i	−0.665711	−	0.996307i	−0.998577	−	0.0533331i	$-0.983015\pi$
$313$	−11.7776	−	17.6265i	−0.665711	−	0.996307i	0.332865	−	0.942974i	$-0.391985\pi$
$314$	−15.7206	−	6.36989i	−0.887167	−	0.359474i
$315$	−0.0263874	+	0.0216556i	−0.00148676	+	0.00122015i
$316$	−0.862626	+	1.33521i	−0.0485265	+	0.0751116i
$317$	−13.4205	−	25.1079i	−0.753768	−	1.41020i	−0.906618	−	0.421952i	$-0.861345\pi$
$317$	−13.4205	−	25.1079i	−0.753768	−	1.41020i	0.152850	−	0.988249i	$-0.451155\pi$
$318$	3.22419	−	2.68797i	0.180804	−	0.150734i
$319$			10.1359i			0.567502i
$320$	2.55556	+	17.5596i	0.142860	+	0.981613i
$321$		−	14.8582i		−	0.829306i
$322$	0.0578645	+	0.0694078i	0.00322466	+	0.00386795i
$323$	−8.30818	−	15.5435i	−0.462279	−	0.864864i
$324$	0.420437	+	1.95531i	0.0233576	+	0.108628i
$325$	−0.193655	+	0.158929i	−0.0107420	+	0.00881577i
$326$	−7.70158	+	19.0072i	−0.426551	+	1.05271i
$327$	3.46739	+	5.18932i	0.191747	+	0.286970i
$328$	17.4735	+	1.31300i	0.964812	+	0.0724983i
$329$	0.0893923	+	0.0597300i	0.00492835	+	0.00329302i
$330$	2.09210	−	10.9595i	0.115166	−	0.603298i
$331$	−0.551783	−	1.81899i	−0.0303288	−	0.0999805i	0.940469	−	0.339879i	$-0.110386\pi$
$331$	−0.551783	−	1.81899i	−0.0303288	−	0.0999805i	−0.970798	+	0.239898i	$0.922886\pi$
$332$	11.0525	+	0.916417i	0.606583	+	0.0502949i
$333$	−1.66644	+	2.03057i	−0.0913206	+	0.111274i
$334$	−9.47452	+	32.1245i	−0.518422	+	1.75778i
$335$	3.69136	−	8.91174i	0.201681	−	0.486900i
$336$	0.0463569	−	0.0405043i	0.00252898	−	0.00220969i
$337$	−7.55810	−	18.2469i	−0.411716	−	0.993971i	−0.984677	−	0.174388i	$-0.944205\pi$
$337$	−7.55810	−	18.2469i	−0.411716	−	0.993971i	0.572961	−	0.819583i	$-0.305795\pi$
$338$	4.53589	−	0.482151i	0.246720	−	0.0262256i
$339$	11.4591	−	1.12862i	0.622371	−	0.0612982i
$340$	18.6688	+	14.8445i	1.01246	+	0.805054i
$341$	−17.2322	−	9.21081i	−0.933177	−	0.498793i
$342$	2.54569	−	3.87435i	0.137655	−	0.209501i
$343$	0.0420331	+	0.211315i	0.00226957	+	0.0114099i
$344$	−21.3906	+	22.4057i	−1.15330	+	1.20803i
$345$	−9.03231	−	1.79664i	−0.486283	−	0.0967278i
$346$	0.276934	+	35.8510i	0.0148881	+	1.92736i
$347$	−34.5392	−	3.40182i	−1.85416	−	0.182619i	−0.891446	−	0.453128i	$-0.850308\pi$
$347$	−34.5392	−	3.40182i	−1.85416	−	0.182619i	−0.962718	+	0.270508i	$0.912808\pi$
$348$	−0.0880446	−	5.69864i	−0.00471969	−	0.305479i
$349$	6.36230	+	1.92998i	0.340566	+	0.103310i	0.455935	−	0.890013i	$-0.349305\pi$
$349$	6.36230	+	1.92998i	0.340566	+	0.103310i	−0.115369	+	0.993323i	$0.536805\pi$
$350$	0.00166494		0.000519130i	8.89945e−5		2.77487e-5i
$351$	−2.21072	+	2.21072i	−0.118000	+	0.118000i
$352$	−3.16045	+	19.8710i	−0.168453	+	1.05913i
$353$	0.112946	+	0.112946i	0.00601153	+	0.00601153i	0.710106	−	0.704095i	$-0.248647\pi$
$353$	0.112946	+	0.112946i	0.00601153	+	0.00601153i	−0.704095	+	0.710106i	$0.748647\pi$
$354$	8.67594	+	4.55158i	0.461121	+	0.241914i
$355$	−2.02352	+	6.67064i	−0.107397	+	0.354041i
$356$	12.5292	+	4.96441i	0.664046	+	0.263113i
$357$	0.00811039	−	0.0823462i	0.000429247	−	0.00435822i
$358$	−17.9223	−	17.6475i	−0.947221	−	0.932699i
$359$	0.478773	−	2.40695i	0.0252687	−	0.127034i	−0.966092	−	0.258198i	$-0.916871\pi$
$359$	0.478773	−	2.40695i	0.0252687	−	0.127034i	0.991361	+	0.131164i	$0.0418714\pi$
$360$	−1.08103	+	6.17983i	−0.0569752	+	0.325706i
$361$	8.09584	−	1.61036i	0.426097	−	0.0847559i
$362$	27.3636	−	5.66303i	1.43820	−	0.297642i
$363$	0.778467	−	1.45641i	0.0408589	−	0.0764417i
$364$	0.0925076	+	0.0265084i	0.00484871	+	0.00138942i
$365$	−1.80563	−	18.3328i	−0.0945107	−	0.959584i
$366$	−10.7771	+	13.3407i	−0.563327	+	0.697331i
$367$	−16.1275	+	6.68024i	−0.841850	+	0.348705i	−0.761583	−	0.648068i	$-0.775577\pi$
$367$	−16.1275	+	6.68024i	−0.841850	+	0.348705i	−0.0802670	+	0.996773i	$0.525577\pi$
$368$	16.3809	+	2.73525i	0.853911	+	0.142585i
$369$	5.72365	+	2.37081i	0.297961	+	0.123420i
$370$	−7.23676	+	3.94030i	−0.376221	+	0.204846i
$371$	−0.0353115	−	0.0289794i	−0.00183328	−	0.00150453i
$372$	9.76836	+	5.02884i	0.506466	+	0.260733i
$373$	8.16243	−	2.47605i	0.422635	−	0.128205i	−0.0718011	−	0.997419i	$-0.522875\pi$
$373$	8.16243	−	2.47605i	0.422635	−	0.128205i	0.494436	+	0.869214i	$0.335375\pi$
$374$	15.1987	+	22.3705i	0.785907	+	1.15675i
$375$	−6.26023	+	9.36910i	−0.323277	+	0.483818i
$376$	19.6136	−	2.39183i	1.01150	−	0.123349i
$377$	7.40778	−	4.94972i	0.381520	−	0.254924i
$378$	0.0200429	−	0.00848401i	0.00103090	−	0.000436370i
$379$	7.66135	+	9.33538i	0.393537	+	0.479526i	0.931655	−	0.363343i	$-0.118365\pi$
$379$	7.66135	+	9.33538i	0.393537	+	0.479526i	−0.538119	+	0.842869i	$0.680865\pi$
$380$	11.9649	−	8.26487i	0.613786	−	0.423979i
$381$	−7.85988	+	4.20119i	−0.402674	+	0.215234i
$382$	−21.9109	−	1.98727i	−1.12106	−	0.101678i
$383$	23.1386			1.18233			0.591164	−	0.806552i	$-0.298669\pi$
$383$	23.1386			1.18233			0.591164	+	0.806552i	$0.298669\pi$
$384$	1.60427	−	11.1994i	0.0818676	−	0.571516i
$385$	−0.121417			−0.00618801
$386$	−20.2716	−	1.83859i	−1.03180	−	0.0935820i
$387$	−9.65881	+	5.16274i	−0.490985	+	0.262437i
$388$	−16.1133	−	23.3270i	−0.818030	−	1.18425i
$389$	8.25634	+	10.0604i	0.418613	+	0.510081i	0.939032	−	0.343830i	$-0.111724\pi$
$389$	8.25634	+	10.0604i	0.418613	+	0.510081i	−0.520419	+	0.853911i	$0.674224\pi$
$390$	−9.03132	+	3.82289i	−0.457319	+	0.193580i
$391$	18.5609	−	12.4020i	0.938666	−	0.627196i
$392$	15.5912	+	12.2019i	0.787476	+	0.616290i
$393$	3.27747	−	4.90508i	0.165327	−	0.247429i
$394$	16.3166	+	24.0158i	0.822018	+	1.20990i
$395$	−1.68705	+	0.511760i	−0.0848845	+	0.0257494i
$396$	−3.25609	+	6.32483i	−0.163624	+	0.317835i
$397$	18.9922	+	15.5865i	0.953194	+	0.782266i	0.976066	−	0.217473i	$-0.0697813\pi$
$397$	18.9922	+	15.5865i	0.953194	+	0.782266i	−0.0228728	+	0.999738i	$0.507281\pi$
$398$	−26.0091	+	14.1616i	−1.30372	+	0.709855i
$399$	−0.0466084	−	0.0193058i	−0.00233334	−	0.000966501i
$400$	0.169753	−	0.271876i	0.00848765	−	0.0135938i
$401$	−28.3918	+	11.7603i	−1.41782	+	0.587281i	−0.954312	−	0.298812i	$-0.903410\pi$
$401$	−28.3918	+	11.7603i	−1.41782	+	0.587281i	−0.463509	+	0.886092i	$0.653410\pi$
$402$	−3.86477	+	4.78412i	−0.192757	+	0.238610i
$403$	1.68342	+	17.0921i	0.0838572	+	0.851416i
$404$	−3.52761	+	12.3105i	−0.175505	+	0.612470i
$405$	−1.04559	+	1.95617i	−0.0519560	+	0.0972029i
$406$	−0.0607346	+	0.0125693i	−0.00301421	+	0.000623805i
$407$	−9.16380	+	1.82279i	−0.454233	+	0.0903525i
$408$	−8.73939	−	12.4452i	−0.432665	−	0.616128i
$409$	4.30685	−	21.6520i	0.212960	−	1.07062i	−0.715336	−	0.698780i	$-0.753726\pi$
$409$	4.30685	−	21.6520i	0.212960	−	1.07062i	0.928296	−	0.371842i	$-0.121274\pi$
$410$	13.8472	+	13.6349i	0.683866	+	0.673382i
$411$	−2.08251	+	21.1441i	−0.102723	+	1.04296i
$412$	−8.08797	+	20.4124i	−0.398466	+	1.00565i
$413$	0.0309496	−	0.102027i	0.00152293	−	0.00502042i
$414$	5.19959	+	2.72781i	0.255546	+	0.134065i
$415$	8.69719	+	8.69719i	0.426928	+	0.426928i
$416$	16.0660	−	7.39391i	0.787700	−	0.362516i
$417$	11.7475	−	11.7475i	0.575279	−	0.575279i
$418$	15.7417	−	4.90829i	0.769952	−	0.240073i
$419$	5.07465	+	1.53938i	0.247913	+	0.0752036i	0.411795	−	0.911276i	$-0.364902\pi$
$419$	5.07465	+	1.53938i	0.247913	+	0.0752036i	−0.163883	+	0.986480i	$0.552402\pi$
$420$	0.0682637	−	0.00105468i	0.00333093	−	5.14632e-5i
$421$	−15.5994	−	1.53641i	−0.760270	−	0.0748801i	−0.289550	−	0.957163i	$-0.593506\pi$
$421$	−15.5994	−	1.53641i	−0.760270	−	0.0748801i	−0.470720	+	0.882283i	$0.656006\pi$
$422$	−0.272975	−	35.3384i	−0.0132882	−	1.72025i
$423$	6.85161	+	1.36287i	0.333137	+	0.0662650i
$424$	−8.39313	+	0.194532i	−0.407606	+	0.00944729i
$425$	−0.0840495	−	0.422545i	−0.00407700	−	0.0204965i
$426$	2.44060	−	3.71441i	0.118248	−	0.179964i
$427$	0.164593	+	0.0879770i	0.00796523	+	0.00425751i
$428$	−18.4948	+	23.2596i	−0.893981	+	1.12430i
$429$	−11.0668	+	1.08998i	−0.534310	+	0.0526249i
$430$	−34.1622	+	3.63133i	−1.64745	+	0.175118i
$431$	−9.49857	−	22.9316i	−0.457530	−	1.10458i	−0.969394	−	0.245509i	$-0.921045\pi$
$431$	−9.49857	−	22.9316i	−0.457530	−	1.10458i	0.511864	−	0.859066i	$-0.328955\pi$
$432$	1.77571	−	3.58425i	0.0854337	−	0.172447i
$433$	12.2048	−	29.4649i	0.586523	−	1.41599i	−0.300283	−	0.953850i	$-0.597081\pi$
$433$	12.2048	−	29.4649i	0.586523	−	1.41599i	0.886806	−	0.462142i	$-0.152919\pi$
$434$	0.0338221	−	0.114678i	0.00162351	−	0.00550472i
$435$	4.00985	−	4.88602i	0.192258	−	0.234267i
$436$	1.03143	−	12.4396i	0.0493966	−	0.595748i
$437$	−3.95082	−	13.0241i	−0.188993	−	0.623027i
$438$	−2.20234	+	11.5370i	−0.105232	+	0.551257i
$439$	−4.41550	−	2.95034i	−0.210740	−	0.140812i	0.445721	−	0.895172i	$-0.352947\pi$
$439$	−4.41550	−	2.95034i	−0.210740	−	0.140812i	−0.656461	+	0.754360i	$0.727947\pi$
$440$	−16.9169	+	14.5522i	−0.806479	+	0.693749i
$441$	3.88886	+	5.82009i	0.185184	+	0.277147i
$442$	8.92729	−	22.0322i	0.424628	−	1.04797i
$443$	12.2093	−	10.0199i	0.580080	−	0.476059i	−0.298005	−	0.954564i	$-0.596321\pi$
$443$	12.2093	−	10.0199i	0.580080	−	0.476059i	0.878085	+	0.478505i	$0.158821\pi$
$444$	5.13627	−	1.10442i	0.243757	−	0.0524133i
$445$	7.04567	+	13.1815i	0.333997	+	0.624864i
$446$	5.72011	+	6.86121i	0.270855	+	0.324888i
$447$			2.43991i			0.115404i
$448$	−0.122987	+	0.00570411i	−0.00581058	+	0.000269494i
$449$			22.8643i			1.07903i	0.841975	+	0.539517i	$0.181393\pi$
$449$			22.8643i			1.07903i	−0.841975	+	0.539517i	$0.818607\pi$
$450$	0.0870402	−	0.0725644i	0.00410311	−	0.00342072i
$451$	10.3876	+	19.4338i	0.489131	+	0.915100i
$452$	−19.3433	−	12.4969i	−0.909832	−	0.587805i
$453$	−6.95152	+	5.70496i	−0.326611	+	0.268043i
$454$	−6.90996	−	2.79986i	−0.324300	−	0.131404i
$455$	0.0592925	+	0.0887374i	0.00277967	+	0.00416007i
$456$	−8.80772	+	2.89630i	−0.412459	+	0.135631i
$457$	−19.4513	−	12.9969i	−0.909893	−	0.607971i	0.0100813	−	0.999949i	$-0.496791\pi$
$457$	−19.4513	−	12.9969i	−0.909893	−	0.607971i	−0.919975	+	0.391978i	$0.871791\pi$
$458$	−15.0009	−	2.86359i	−0.700946	−	0.133807i
$459$	−1.56073	−	5.14505i	−0.0728488	−	0.240150i
$460$	11.9031	+	14.0555i	0.554987	+	0.655342i
$461$	−3.34479	+	4.07563i	−0.155782	+	0.189821i	−0.845053	−	0.534683i	$-0.820431\pi$
$461$	−3.34479	+	4.07563i	−0.155782	+	0.189821i	0.689271	+	0.724504i	$0.257931\pi$
$462$	0.0742519	+	0.0218992i	0.00345451	+	0.00101884i
$463$	5.61611	−	13.5585i	0.261003	−	0.630116i	−0.737998	−	0.674803i	$-0.764229\pi$
$463$	5.61611	−	13.5585i	0.261003	−	0.630116i	0.999001	+	0.0446861i	$0.0142288\pi$
$464$	−6.95557	+	9.03046i	−0.322904	+	0.419228i
$465$	4.66292	+	11.2573i	0.216238	+	0.522044i
$466$	0.408448	+	3.84252i	0.0189210	+	0.178001i
$467$	−2.43846	+	0.240168i	−0.112839	+	0.0111136i	−0.154279	−	0.988027i	$-0.549305\pi$
$467$	−2.43846	+	0.240168i	−0.112839	+	0.0111136i	0.0414402	+	0.999141i	$0.486805\pi$
$468$	6.21254	−	0.708945i	0.287175	−	0.0327710i
$469$	0.0590249	+	0.0315494i	0.00272551	+	0.00145682i
$470$	18.3139	+	12.0334i	0.844755	+	0.555057i
$471$	2.33992	+	11.7636i	0.107818	+	0.542037i
$472$	−7.91606	−	17.9246i	−0.364366	−	0.825047i
$473$	−38.2065	−	7.59974i	−1.75674	−	0.349437i
$474$	1.12400	−	0.00868247i	0.0516272	−	0.000398799i
$475$	−0.261404	−	0.0257461i	−0.0119940	−	0.00118131i
$476$	−0.115197	+	0.118812i	−0.00528004	+	0.00544575i
$477$	−2.84041	−	0.861628i	−0.130053	−	0.0394512i
$478$	1.12051	+	3.59366i	0.0512509	+	0.164370i
$479$	16.7305	−	16.7305i	0.764438	−	0.764438i	−0.212683	−	0.977121i	$-0.568220\pi$
$479$	16.7305	−	16.7305i	0.764438	−	0.764438i	0.977121	+	0.212683i	$0.0682202\pi$
$480$	9.38464	−	8.32853i	0.428348	−	0.380144i
$481$	5.80719	+	5.80719i	0.264785	+	0.264785i
$482$	−6.72592	+	12.8205i	−0.306357	+	0.583960i
$483$	0.0185484	−	0.0611460i	0.000843983	−	0.00278224i
$484$	−3.03151	+	1.31092i	−0.137796	+	0.0595872i
$485$	3.08190	−	31.2911i	0.139942	−	1.42086i
$486$	0.992246	−	1.00769i	0.0450092	−	0.0457100i
$487$	6.88044	−	34.5903i	0.311783	−	1.56744i	−0.433791	−	0.901014i	$-0.642824\pi$
$487$	6.88044	−	34.5903i	0.311783	−	1.56744i	0.745573	−	0.666423i	$-0.232176\pi$
$488$	33.4768	−	7.46928i	1.51542	−	0.338119i
$489$	14.2229	−	2.82911i	0.643181	−	0.127937i
$490$	4.44984	+	21.5015i	0.201023	+	0.971338i
$491$	−6.22799	+	11.6517i	−0.281065	+	0.525836i	−0.982352	−	0.187044i	$-0.940109\pi$
$491$	−6.22799	+	11.6517i	−0.281065	+	0.525836i	0.701286	+	0.712880i	$0.252609\pi$
$492$	−6.00894	−	10.8359i	−0.270904	−	0.488519i
$493$	1.50176	+	15.2476i	0.0676358	+	0.686718i
$494$	−11.2744	−	9.10787i	−0.507261	−	0.409782i
$495$	−7.28889	+	3.01916i	−0.327611	+	0.135701i
$496$	−9.03209	−	20.0315i	−0.405553	−	0.899442i
$497$	−0.0446844	−	0.0185089i	−0.00200437	−	0.000830238i
$498$	−3.75005	−	6.88735i	−0.168044	−	0.308629i
$499$	2.92608	+	2.40137i	0.130989	+	0.107500i	0.697607	−	0.716481i	$-0.254248\pi$
$499$	2.92608	+	2.40137i	0.130989	+	0.107500i	−0.566618	+	0.823981i	$0.691748\pi$
$500$	21.4622	−	6.87430i	0.959819	−	0.307428i
$501$	22.6630	−	6.87476i	1.01251	−	0.307141i
$502$	−5.49792	+	3.73534i	−0.245384	+	0.166717i
$503$	22.4592	−	33.6126i	1.00141	−	1.49871i	0.140417	−	0.990092i	$-0.455156\pi$
$503$	22.4592	−	33.6126i	1.00141	−	1.49871i	0.860991	−	0.508620i	$-0.169844\pi$
$504$	−0.0419364	−	0.0116672i	−0.00186799	−	0.000519701i
$505$	−11.8088	+	7.89037i	−0.525484	+	0.351117i
$506$	8.14111	+	19.2328i	0.361917	+	0.855004i
$507$	−2.04619	−	2.49329i	−0.0908746	−	0.110731i
$508$	17.5336	+	3.20690i	0.777928	+	0.142283i
$509$	−11.7519	+	6.28154i	−0.520895	+	0.278424i	−0.710820	−	0.703374i	$-0.751676\pi$
$509$	−11.7519	+	6.28154i	−0.520895	+	0.278424i	0.189924	+	0.981799i	$0.439176\pi$
$510$	1.52340	−	16.7965i	0.0674574	−	0.743760i
$511$	0.127816			0.00565423
$512$	−16.4518	+	15.5350i	−0.727076	+	0.686557i
$513$	−3.27804			−0.144729
$514$	−0.751601	+	8.28687i	−0.0331517	+	0.365518i
$515$	−21.4752	+	11.4787i	−0.946310	+	0.505813i
$516$	21.5466	+	3.94087i	0.948536	+	0.173487i
$517$	15.7633	+	19.2076i	0.693268	+	0.844750i
$518$	−0.0222861	−	0.0526493i	−0.000979193	−	0.00231328i
$519$	21.0788	−	14.0844i	0.925255	−	0.618236i
$520$	18.8965	+	5.25726i	0.828667	+	0.230546i
$521$	−13.7417	+	20.5659i	−0.602034	+	0.901007i	−0.999865	−	0.0164515i	$-0.994763\pi$
$521$	−13.7417	+	20.5659i	−0.602034	+	0.901007i	0.397831	+	0.917459i	$0.369763\pi$
$522$	−3.33345	+	2.26478i	−0.145901	+	0.0991267i
$523$	16.8347	−	5.10674i	0.736129	−	0.223302i	0.100111	−	0.994976i	$-0.468080\pi$
$523$	16.8347	−	5.10674i	0.736129	−	0.223302i	0.636018	+	0.771674i	$0.280580\pi$
$524$	−11.2363	+	3.59896i	−0.490860	+	0.157221i
$525$	−0.000953267	0	0.000782326i	−4.16040e−5	0	3.41435e-5i
$526$	−6.94386	−	12.7531i	−0.302767	−	0.556062i
$527$	−27.2874	−	11.3028i	−1.18866	−	0.492358i
$528$	12.9700	−	5.84811i	0.564449	−	0.254506i
$529$	−5.32304	+	2.20488i	−0.231437	+	0.0958642i
$530$	−7.24276	−	5.85094i	−0.314606	−	0.254149i
$531$	−0.679043	−	6.89444i	−0.0294680	−	0.299193i
$532$	0.0489316	+	0.0882380i	0.00212145	+	0.00382560i
$533$	9.13046	−	17.0819i	0.395484	−	0.739899i
$534$	−1.93127	−	9.33184i	−0.0835742	−	0.403828i
$535$	−32.3235	+	6.42954i	−1.39747	+	0.277973i
$536$	12.0051	−	2.67856i	0.518541	−	0.115696i
$537$	−3.46976	+	17.4437i	−0.149731	+	0.752750i
$538$	10.7986	−	10.9667i	0.465559	−	0.472807i
$539$	−2.44036	+	24.7774i	−0.105114	+	1.06724i
$540$	4.07176	−	1.76076i	0.175221	−	0.0757708i
$541$	−5.59758	+	18.4527i	−0.240659	+	0.793345i	0.750524	+	0.660843i	$0.229801\pi$
$541$	−5.59758	+	18.4527i	−0.240659	+	0.793345i	−0.991183	+	0.132502i	$0.957699\pi$
$542$	14.2530	−	27.1682i	0.612219	−	1.16697i
$543$	−13.9717	−	13.9717i	−0.599583	−	0.599583i
$544$	−1.81019	+	30.3605i	−0.0776111	+	1.30170i
$545$	9.78872	−	9.78872i	0.419303	−	0.419303i
$546$	−0.0202549	−	0.0649609i	−0.000866830	−	0.00278007i
$547$	20.4565	+	6.20540i	0.874656	+	0.265324i	0.695525	−	0.718501i	$-0.255172\pi$
$547$	20.4565	+	6.20540i	0.874656	+	0.265324i	0.179130	+	0.983825i	$0.442672\pi$
$548$	29.5792	−	30.5075i	1.26356	−	1.30322i
$549$	12.0685	+	1.18864i	0.515069	+	0.0507299i
$550$	0.403056	−	0.00311345i	0.0171864	−	0.000132758i
$551$	9.16181	+	1.82240i	0.390306	+	0.0776368i
$552$	−4.74419	−	10.7424i	−0.201926	−	0.457228i
$553$	−0.00238636	−	0.0119970i	−0.000101478	−	0.000510166i
$554$	−18.9834	−	12.4733i	−0.806525	−	0.529938i
$555$	5.13853	+	2.74660i	0.218118	+	0.116587i
$556$	−33.0128	+	3.76726i	−1.40005	+	0.159767i
$557$	19.1748	−	1.88855i	0.812462	−	0.0800205i	0.316751	−	0.948509i	$-0.397408\pi$
$557$	19.1748	−	1.88855i	0.812462	−	0.0800205i	0.495710	+	0.868488i	$0.334908\pi$
$558$	−0.821178	−	7.72533i	−0.0347633	−	0.327039i
$559$	13.1033	+	31.6343i	0.554212	+	1.33799i
$560$	−0.108175	−	0.0833203i	−0.00457124	−	0.00352093i
$561$	7.31836	−	17.6681i	0.308981	−	0.745947i
$562$	−30.8345	−	9.09406i	−1.30068	−	0.383610i
$563$	−7.88595	+	9.60906i	−0.332353	+	0.404973i	−0.912196	−	0.409755i	$-0.865614\pi$
$563$	−7.88595	+	9.60906i	−0.332353	+	0.404973i	0.579842	+	0.814729i	$0.303114\pi$
$564$	−9.02933	−	10.6620i	−0.380203	−	0.448953i
$565$	−7.41389	−	24.4403i	−0.311905	−	1.02821i
$566$	30.6874	+	5.85806i	1.28989	+	0.246233i
$567$	−0.0127962	−	0.00855015i	−0.000537390	−	0.000359073i
$568$	−8.44413	+	2.77674i	−0.354308	+	0.116509i
$569$	−14.6410	−	21.9118i	−0.613781	−	0.918589i	0.386211	−	0.922410i	$-0.373784\pi$
$569$	−14.6410	−	21.9118i	−0.613781	−	0.918589i	−0.999993	+	0.00382173i	$0.998784\pi$
$570$	−9.53007	−	3.86151i	−0.399171	−	0.161741i
$571$	−10.5100	+	8.62531i	−0.439828	+	0.360958i	−0.828094	−	0.560590i	$-0.810574\pi$
$571$	−10.5100	+	8.62531i	−0.439828	+	0.360958i	0.388265	+	0.921548i	$0.373074\pi$
$572$	18.6811	+	12.0691i	0.781097	+	0.504635i
$573$	7.33349	+	13.7200i	0.306361	+	0.573161i
$574$	−0.103566	+	0.0863419i	−0.00432277	+	0.00360384i
$575$		−	0.332692i		−	0.0138742i
$576$	−7.24126	+	3.40061i	−0.301719	+	0.141692i
$577$			23.8530i			0.993015i	0.868032	+	0.496508i	$0.165385\pi$
$577$			23.8530i			0.993015i	−0.868032	+	0.496508i	$0.834615\pi$
$578$	10.7832	+	12.9343i	0.448522	+	0.537997i
$579$	6.78484	+	12.6935i	0.281968	+	0.527526i
$580$	−12.3591	+	2.65749i	−0.513182	+	0.110346i
$581$	−0.0659686	+	0.0541390i	−0.00273684	+	0.00224607i
$582$	−7.52847	+	18.5800i	−0.312065	+	0.770165i
$583$	−5.86548	−	8.77832i	−0.242924	−	0.363561i
$584$	17.8083	−	15.3190i	0.736912	−	0.633906i
$585$	5.76597	+	3.85269i	0.238393	+	0.159289i
$586$	3.82369	−	20.0304i	0.157955	−	0.827449i
$587$	−7.76175	−	25.5871i	−0.320362	−	1.05609i	−0.958243	−	0.285956i	$-0.907689\pi$
$587$	−7.76175	−	25.5871i	−0.320362	−	1.05609i	0.637881	−	0.770135i	$-0.279811\pi$
$588$	1.15680	−	13.9517i	0.0477057	−	0.575356i
$589$	−11.4239	+	13.9201i	−0.470714	+	0.573567i
$590$	6.14747	−	20.8437i	0.253087	−	0.858123i
$591$	7.85663	−	18.9676i	0.323178	−	0.780222i
$592$	−9.41523	−	4.66448i	−0.386964	−	0.191709i
$593$	−8.79110	−	21.2236i	−0.361007	−	0.871549i	−0.995153	−	0.0983353i	$-0.968648\pi$
$593$	−8.79110	−	21.2236i	−0.361007	−	0.871549i	0.634146	−	0.773213i	$-0.281352\pi$
$594$	5.00201	−	0.531698i	0.205235	−	0.0218158i
$595$	−0.182650	+	0.0179895i	−0.00748793	+	0.000737497i
$596$	3.03708	−	3.81952i	0.124404	−	0.156454i
$597$	18.4680	+	9.87137i	0.755847	+	0.404008i
$598$	10.0806	−	15.3420i	0.412228	−	0.627380i
$599$	3.43298	+	17.2588i	0.140268	+	0.705174i	0.985351	+	0.170539i	$0.0545509\pi$
$599$	3.43298	+	17.2588i	0.140268	+	0.705174i	−0.845083	+	0.534635i	$0.820449\pi$
$600$	−0.226581	+	0.00525157i	−0.00925012	+	0.000214394i
$601$	−40.6705	−	8.08988i	−1.65899	−	0.329993i	−0.725395	−	0.688333i	$-0.758343\pi$
$601$	−40.6705	−	8.08988i	−1.65899	−	0.329993i	−0.933591	+	0.358340i	$0.883343\pi$
$602$	−0.00184122	−	0.238358i	−7.50426e−5	−	0.00971477i
$603$	4.32787	+	0.426258i	0.176244	+	0.0173586i
$604$	17.9834	−	0.277846i	0.731735	−	0.0113054i
$605$	−3.50522	−	1.06330i	−0.142507	−	0.0432292i
$606$	8.64470	−	2.69543i	0.351167	−	0.109494i
$607$	21.8304	−	21.8304i	0.886070	−	0.886070i	−0.108073	−	0.994143i	$-0.534468\pi$
$607$	21.8304	−	21.8304i	0.886070	−	0.886070i	0.994143	+	0.108073i	$0.0344681\pi$
$608$	17.3931	+	6.42945i	0.705383	+	0.260749i
$609$	0.0310108	+	0.0310108i	0.00125662	+	0.00125662i
$610$	33.6857	+	17.6722i	1.36390	+	0.715527i
$611$	6.34003	−	20.9003i	0.256490	−	0.845535i
$612$	−3.96108	+	9.99698i	−0.160117	+	0.404104i
$613$	−3.49624	+	35.4979i	−0.141212	+	1.43375i	0.619673	+	0.784860i	$0.287265\pi$
$613$	−3.49624	+	35.4979i	−0.141212	+	1.43375i	−0.760885	+	0.648887i	$0.775235\pi$
$614$	−7.74861	−	7.62982i	−0.312708	−	0.307914i
$615$	2.68083	−	13.4775i	0.108102	−	0.543464i
$616$	−0.0889776	−	0.126707i	−0.00358501	−	0.00510517i
$617$	42.8420	−	8.52180i	1.72475	−	0.343075i	0.769450	−	0.638707i	$-0.220530\pi$
$617$	42.8420	−	8.52180i	1.72475	−	0.343075i	0.955302	+	0.295632i	$0.0955302\pi$
$618$	15.2033	−	3.14640i	0.611568	−	0.126567i
$619$	−1.88976	+	3.53549i	−0.0759559	+	0.142103i	−0.917032	−	0.398813i	$-0.869422\pi$
$619$	−1.88976	+	3.53549i	−0.0759559	+	0.142103i	0.841077	+	0.540916i	$0.181922\pi$
$620$	6.71302	−	23.4268i	0.269602	−	0.940842i
$621$	−0.406959	−	4.13192i	−0.0163307	−	0.165808i
$622$	−25.0711	+	31.0349i	−1.00526	+	1.24439i
$623$	−0.0958096	+	0.0396857i	−0.00383853	+	0.00158997i
$624$	−10.6078	−	6.62326i	−0.424652	−	0.265143i
$625$	22.7209	+	9.41131i	0.908836	+	0.376452i
$626$	26.3302	−	14.3364i	1.05237	−	0.572997i
$627$	−9.01300	−	7.39677i	−0.359944	−	0.295399i
$628$	10.9797	−	21.3278i	0.438139	−	0.851071i
$629$	−13.5152	+	4.09979i	−0.538886	+	0.163469i
$630$	−0.0271297	−	0.0399312i	−0.00108087	−	0.00159090i
$631$	−4.59564	+	6.87786i	−0.182950	+	0.273803i	−0.911597	−	0.411086i	$-0.865150\pi$
$631$	−4.59564	+	6.87786i	−0.182950	+	0.273803i	0.728647	+	0.684890i	$0.240150\pi$
$632$	−1.77036	−	1.38551i	−0.0704213	−	0.0551127i
$633$	−20.7774	+	13.8830i	−0.825828	+	0.551800i
$634$	37.0772	−	15.6945i	1.47252	−	0.623308i
$635$	12.5407	+	15.2809i	0.497662	+	0.606403i
$636$	3.37396	+	4.88442i	0.133786	+	0.193680i
$637$	19.3002	−	10.3162i	0.764702	−	0.408742i
$638$	−14.2757	−	1.29478i	−0.565182	−	0.0512608i
$639$	−3.14272			−0.124324
$640$	−25.0580	+	1.35624i	−0.990505	+	0.0536099i
$641$	−14.1401			−0.558500			−0.279250	−	0.960218i	$-0.590086\pi$
$641$	−14.1401			−0.558500			−0.279250	+	0.960218i	$0.590086\pi$
$642$	20.9268	+	1.89802i	0.825916	+	0.0749088i
$643$	−27.6065	+	14.7560i	−1.08869	+	0.581918i	−0.915234	−	0.402923i	$-0.867994\pi$
$643$	−27.6065	+	14.7560i	−1.08869	+	0.581918i	−0.173458	+	0.984841i	$0.555494\pi$
$644$	−0.105148	+	0.0726320i	−0.00414341	+	0.00286210i
$645$	15.4109	+	18.7783i	0.606805	+	0.739394i
$646$	22.9533	−	9.71595i	0.903085	−	0.382269i
$647$	32.9535	−	22.0188i	1.29554	−	0.865650i	0.299457	−	0.954110i	$-0.403195\pi$
$647$	32.9535	−	22.0188i	1.29554	−	0.865650i	0.996080	+	0.0884599i	$0.0281945\pi$
$648$	−2.80763	+	0.342383i	−0.110294	+	0.0134501i
$649$	13.6900	−	20.4886i	0.537380	−	0.804246i
$650$	−0.199102	−	0.293052i	−0.00780943	−	0.0114944i
$651$	−0.0809024	+	0.0245415i	−0.00317082	+	0.000961856i
$652$	−25.7866	−	13.2752i	−1.00988	−	0.519896i
$653$	34.3114	+	28.1586i	1.34271	+	1.10193i	0.985824	+	0.167784i	$0.0536611\pi$
$653$	34.3114	+	28.1586i	1.34271	+	1.10193i	0.356885	+	0.934148i	$0.383839\pi$
$654$	−7.75173	+	4.22069i	−0.303117	+	0.165042i
$655$	−12.0891	−	5.00745i	−0.472358	−	0.195657i
$656$	−4.08137	+	24.4425i	−0.159351	+	0.954320i
$657$	7.67298	−	3.17825i	0.299351	−	0.123995i
$658$	−0.0955448	+	0.118273i	−0.00372472	+	0.00461076i
$659$	−3.10661	−	31.5420i	−0.121016	−	1.22870i	−0.843430	−	0.537239i	$-0.819467\pi$
$659$	−3.10661	−	31.5420i	−0.121016	−	1.22870i	0.722414	−	0.691461i	$-0.243033\pi$
$660$	15.1684	+	4.34656i	0.590429	+	0.169190i
$661$	−0.562032	+	1.05149i	−0.0218605	+	0.0408982i	−0.892614	−	0.450821i	$-0.851131\pi$
$661$	−0.562032	+	1.05149i	−0.0218605	+	0.0408982i	0.870754	+	0.491719i	$0.163631\pi$
$662$	2.63240	−	0.544789i	0.102311	−	0.0211738i
$663$	−16.4865	+	3.27936i	−0.640281	+	0.127360i
$664$	−2.70257	+	15.4496i	−0.104880	+	0.599560i
$665$	−0.0218304	+	0.109749i	−0.000846547	+	0.00425588i
$666$	−2.64704	−	2.60646i	−0.102571	−	0.100998i
$667$	−1.15969	+	11.7746i	−0.0449035	+	0.455913i
$668$	−44.0349	−	17.4479i	−1.70376	−	0.675078i
$669$	1.83358	−	6.04450i	0.0708902	−	0.233694i
$670$	12.0800	+	6.33744i	0.466693	+	0.244837i
$671$	30.5002	+	30.5002i	1.17745	+	1.17745i
$672$	0.0511259	+	0.0704647i	0.00197222	+	0.00271824i
$673$	−23.8442	+	23.8442i	−0.919126	+	0.919126i	−0.996966	−	0.0778398i	$-0.975198\pi$
$673$	−23.8442	+	23.8442i	−0.919126	+	0.919126i	0.0778398	+	0.996966i	$0.475198\pi$
$674$	26.6650	−	8.31419i	1.02710	−	0.320251i
$675$	−0.0766795	−	0.0232605i	−0.00295140	−	0.000895296i
$676$	0.0996546	+	6.45009i	0.00383287	+	0.248080i
$677$	21.4074	+	2.10844i	0.822752	+	0.0810340i	0.500627	−	0.865663i	$-0.333103\pi$
$677$	21.4074	+	2.10844i	0.822752	+	0.0810340i	0.322125	+	0.946697i	$0.395603\pi$
$678$	0.125783	+	16.2835i	0.00483068	+	0.625364i
$679$	0.213968	+	0.0425609i	0.00821134	+	0.00163334i
$680$	−23.2922	+	24.3975i	−0.893215	+	0.935603i
$681$	1.02850	+	5.17064i	0.0394124	+	0.198139i
$682$	15.1741	−	23.0938i	0.581045	−	0.884307i
$683$	−20.8344	−	11.1362i	−0.797207	−	0.426116i	0.0218976	−	0.999760i	$-0.493029\pi$
$683$	−20.8344	−	11.1362i	−0.797207	−	0.426116i	−0.819105	+	0.573644i	$0.805529\pi$
$684$	5.13157	+	4.08035i	0.196210	+	0.156016i
$685$	46.8993	−	4.61917i	1.79193	−	0.176490i
$686$	−0.302992	+	0.0322071i	−0.0115683	+	0.00122967i
$687$	4.13251	+	9.97677i	0.157665	+	0.380638i
$688$	−28.8244	−	32.9893i	−1.09892	−	1.25771i
$689$	−3.55127	+	8.57353i	−0.135293	+	0.326626i
$690$	3.68425	−	12.4919i	0.140257	−	0.475558i
$691$	−21.9476	+	26.7433i	−0.834928	+	1.01736i	0.164592	+	0.986362i	$0.447369\pi$
$691$	−21.9476	+	26.7433i	−0.834928	+	1.01736i	−0.999519	+	0.0310004i	$0.990131\pi$
$692$	−50.5291	−	4.18962i	−1.92083	−	0.159266i
$693$	−0.0158902	−	0.0523828i	−0.000603617	−	0.00198986i
$694$	9.20333	−	48.2116i	0.349354	−	1.83009i
$695$	−30.6397	−	20.4728i	−1.16223	−	0.776578i
$696$	8.03740	+	0.603949i	0.304657	+	0.0228926i
$697$	18.5055	+	27.6955i	0.700946	+	1.04904i
$698$	−3.53098	+	8.71434i	−0.133650	+	0.329843i
$699$	2.11216	−	1.73340i	0.0798891	−	0.0655633i
$700$	0.000518478		0.00241126i	1.95966e−5		9.11372e-5i
$701$	8.25009	+	15.4348i	0.311602	+	0.582966i	0.988161	−	0.153423i	$-0.0490296\pi$
$701$	8.25009	+	15.4348i	0.311602	+	0.582966i	−0.676559	+	0.736389i	$0.736530\pi$
$702$	−2.83125	−	3.39605i	−0.106859	−	0.128176i
$703$			8.61086i			0.324765i
$704$	−27.5832	−	6.98964i	−1.03958	−	0.263432i
$705$		−	15.4951i		−	0.583581i
$706$	−0.173505	+	0.144649i	−0.00652996	+	0.00544395i
$707$	−0.0464519	−	0.0869053i	−0.00174700	−	0.00326841i
$708$	−7.51887	+	11.6381i	−0.282576	+	0.437385i
$709$	−39.1591	+	32.1370i	−1.47065	+	1.20693i	−0.539662	+	0.841882i	$0.681448\pi$
$709$	−39.1591	+	32.1370i	−1.47065	+	1.20693i	−0.930988	+	0.365050i	$0.881052\pi$
$710$	−9.13667	−	3.70211i	−0.342893	−	0.138938i
$711$	−0.441575	−	0.660864i	−0.0165604	−	0.0247843i
$712$	−8.59254	+	17.0124i	−0.322019	+	0.637565i
$713$	−18.9643	−	12.6715i	−0.710218	−	0.474552i
$714$	0.114943	+	0.0219420i	0.00430163	+	0.000821158i
$715$	7.16010	+	23.6037i	0.267773	+	0.882728i
$716$	27.1447	−	22.9880i	1.01445	−	0.859101i
$717$	1.68860	−	2.05757i	0.0630620	−	0.0768413i
$718$	3.32887	+	0.981787i	0.124232	+	0.0366400i
$719$	8.63841	−	20.8550i	0.322158	−	0.777759i	−0.676970	−	0.736011i	$-0.736707\pi$
$719$	8.63841	−	20.8550i	0.322158	−	0.777759i	0.999128	−	0.0417482i	$-0.0132927\pi$
$720$	−8.56579	−	2.31198i	−0.319228	−	0.0861623i
$721$	−0.0646554	−	0.156092i	−0.00240789	−	0.00581317i
$722$	1.23391	+	11.6082i	0.0459214	+	0.432011i
$723$	10.1880	−	1.00343i	0.378896	−	0.0373180i
$724$	4.48052	+	39.2631i	0.166517	+	1.45920i
$725$	0.201380	+	0.107640i	0.00747908	+	0.00399765i
$726$	1.95181	+	1.28246i	0.0724385	+	0.0475966i
$727$	2.77128	+	13.9322i	0.102781	+	0.516716i	0.997536	+	0.0701580i	$0.0223504\pi$
$727$	2.77128	+	13.9322i	0.102781	+	0.516716i	−0.894755	+	0.446558i	$0.852650\pi$
$728$	−0.0491523	+	0.126904i	−0.00182171	+	0.00470339i
$729$	−0.980785	−	0.195090i	−0.0363254	−	0.00722557i
$730$	26.0512	−	0.201235i	0.964198	−	0.00744804i
$731$	−58.6006	−	5.77166i	−2.16742	−	0.213472i
$732$	−17.4128	−	16.8830i	−0.643597	−	0.624012i
$733$	−47.2797	−	14.3421i	−1.74631	−	0.529739i	−0.754374	−	0.656445i	$-0.772059\pi$
$733$	−47.2797	−	14.3421i	−1.74631	−	0.529739i	−0.991940	+	0.126706i	$0.959559\pi$
$734$	−7.34850	−	23.5679i	−0.271238	−	0.869906i
$735$	10.9786	−	10.9786i	0.404950	−	0.404950i
$736$	−5.94493	+	22.7219i	−0.219133	+	0.837541i
$737$	10.9377	+	10.9377i	0.402894	+	0.402894i
$738$	−4.07028	+	7.75852i	−0.149829	+	0.285595i
$739$	−0.0390667	+	0.128786i	−0.00143709	+	0.00473746i	−0.957656	−	0.287915i	$-0.907038\pi$
$739$	−0.0390667	+	0.128786i	−0.00143709	+	0.00473746i	0.956219	+	0.292653i	$0.0945379\pi$
$740$	−4.62521	−	10.6958i	−0.170026	−	0.393186i
$741$	−1.00454	+	10.1992i	−0.0369025	+	0.374678i
$742$	0.0453262	−	0.0460319i	0.00166398	−	0.00168989i
$743$	−3.60569	+	18.1271i	−0.132280	+	0.665017i	0.856561	+	0.516045i	$0.172596\pi$
$743$	−3.60569	+	18.1271i	−0.132280	+	0.665017i	−0.988841	+	0.148972i	$0.952404\pi$
$744$	−8.33062	+	13.1157i	−0.305415	+	0.480844i
$745$	5.30792	−	1.05581i	0.194467	−	0.0386819i
$746$	2.44466	+	11.8125i	0.0895054	+	0.432487i
$747$	−2.61399	+	4.89043i	−0.0956408	+	0.178931i
$748$	−33.4488	+	18.5487i	−1.22301	+	0.678209i
$749$	−0.0224132	−	0.227565i	−0.000818962	−	0.00831506i
$750$	−12.3961	−	10.0139i	−0.452640	−	0.365658i
$751$	14.0861	−	5.83464i	0.514008	−	0.212909i	−0.110575	−	0.993868i	$-0.535269\pi$
$751$	14.0861	−	5.83464i	0.514008	−	0.212909i	0.624583	+	0.780959i	$0.285269\pi$
$752$	0.863250	+	27.9300i	0.0314795	+	1.01850i
$753$	4.34223	+	1.79861i	0.158240	+	0.0655450i
$754$	6.02507	+	11.0657i	0.219420	+	0.402987i
$755$	15.4190	+	12.6541i	0.561155	+	0.460528i
$756$	0.00938884	+	0.0293128i	0.000341469	+	0.00106610i
$757$	39.8453	−	12.0870i	1.44820	−	0.439308i	0.534320	−	0.845283i	$-0.320568\pi$
$757$	39.8453	−	12.0870i	1.44820	−	0.439308i	0.913884	+	0.405975i	$0.133068\pi$
$758$	−14.1269	+	9.59797i	−0.513113	+	0.348614i
$759$	8.20458	−	12.2790i	0.297808	−	0.445700i
$760$	10.1121	+	17.9075i	0.366804	+	0.649574i
$761$	−19.9768	+	13.3480i	−0.724157	+	0.483866i	−0.862205	−	0.506559i	$-0.830917\pi$
$761$	−19.9768	+	13.3480i	−0.724157	+	0.483866i	0.138048	+	0.990425i	$0.455917\pi$
$762$	−4.91306	−	11.6068i	−0.177982	−	0.420469i
$763$	0.0609337	+	0.0742479i	0.00220595	+	0.00268795i
$764$	5.59787	−	30.6062i	0.202524	−	1.10729i
$765$	−10.5175	+	5.62171i	−0.380260	+	0.203253i
$766$	−2.95577	+	32.5892i	−0.106796	+	1.17749i
$767$	−21.6593			−0.782072
$768$	15.5687	+	3.69014i	0.561785	+	0.133156i
$769$	0.538482			0.0194182			0.00970908	−	0.999953i	$-0.496909\pi$
$769$	0.538482			0.0194182			0.00970908	+	0.999953i	$0.496909\pi$
$770$	0.0155101	−	0.171008i	0.000558944	−	0.00616271i
$771$	5.18901	−	2.77358i	0.186877	−	0.0998881i
$772$	5.17907	−	28.3164i	0.186399	−	1.01913i
$773$	25.6148	+	31.2118i	0.921301	+	1.12261i	0.992141	+	0.125121i	$0.0399319\pi$
$773$	25.6148	+	31.2118i	0.921301	+	1.12261i	−0.0708404	+	0.997488i	$0.522568\pi$
$774$	−6.03754	−	14.2633i	−0.217015	−	0.512683i
$775$	−0.366001	+	0.244554i	−0.0131472	+	0.00878465i
$776$	34.9128	−	19.7147i	1.25330	−	0.707717i
$777$	−0.0224598	+	0.0336135i	−0.000805741	+	0.00120588i
$778$	−15.2240	+	10.3434i	−0.545808	+	0.370827i
$779$	19.4338	−	5.89516i	0.696286	−	0.211216i
$780$	−4.23061	−	13.2083i	−0.151480	−	0.472935i
$781$	−8.64094	−	7.09143i	−0.309197	−	0.253751i
$782$	15.0964	+	27.7260i	0.539846	+	0.991482i
$783$	2.63274	+	1.09052i	0.0940866	+	0.0389719i
$784$	−19.1772	+	20.4005i	−0.684902	+	0.728589i
$785$	24.5786	−	10.1808i	0.877249	−	0.363369i
$786$	6.48981	+	5.24268i	0.231484	+	0.187000i
$787$	0.134929	+	1.36996i	0.00480969	+	0.0488336i	0.997290	−	0.0735708i	$-0.0234395\pi$
$787$	0.134929	+	1.36996i	0.00480969	+	0.0488336i	−0.992480	+	0.122404i	$0.960939\pi$
$788$	−35.9090	+	19.9130i	−1.27920	+	0.709371i
$789$	−4.84025	+	9.05546i	−0.172317	+	0.322383i
$790$	−0.505273	−	2.44146i	−0.0179768	−	0.0868634i
$791$	0.173802	−	0.0345713i	0.00617968	−	0.00122921i
$792$	−8.49216	−	5.39392i	−0.301756	−	0.191665i
$793$	7.39660	−	37.1852i	0.262661	−	1.32049i
$794$	−24.3787	+	24.7582i	−0.865167	+	0.878637i
$795$	−0.645319	+	6.55203i	−0.0228871	+	0.232377i
$796$	−16.6231	−	38.4411i	−0.589192	−	1.36251i
$797$	−9.99512	+	32.9495i	−0.354045	+	1.16713i	0.581388	+	0.813627i	$0.302510\pi$
$797$	−9.99512	+	32.9495i	−0.354045	+	1.16713i	−0.935433	+	0.353504i	$0.884990\pi$
$798$	0.0331448	−	0.0631787i	0.00117331	−	0.00223650i
$799$	26.5588	+	26.5588i	0.939583	+	0.939583i
$800$	0.361235	+	0.273816i	0.0127716	+	0.00968085i
$801$	−4.76479	+	4.76479i	−0.168356	+	0.168356i
$802$	−12.9367	−	41.4903i	−0.456812	−	1.46507i
$803$	28.2685	+	8.57516i	0.997574	+	0.302611i
$804$	−6.24442	−	6.05440i	−0.220224	−	0.213522i
$805$	−0.141047	−	0.0138919i	−0.00497125	−	0.000489625i
$806$	−24.2881	+	0.187615i	−0.855510	+	0.00660847i
$807$	−10.6738	−	2.12316i	−0.375737	−	0.0747386i
$808$	−16.8879	−	6.54097i	−0.594113	−	0.230111i
$809$	1.42882	+	7.18316i	0.0502346	+	0.252547i	0.997740	−	0.0671934i	$-0.0214045\pi$
$809$	1.42882	+	7.18316i	0.0502346	+	0.252547i	−0.947505	+	0.319740i	$0.896404\pi$
$810$	−2.62157	−	1.72253i	−0.0921125	−	0.0605237i
$811$	−40.6948	−	21.7518i	−1.42899	−	0.763809i	−0.438153	−	0.898900i	$-0.644367\pi$
$811$	−40.6948	−	21.7518i	−1.42899	−	0.763809i	−0.990833	+	0.135091i	$0.956867\pi$
$812$	−0.00994470	−	0.0871462i	−0.000348991	−	0.00305823i
$813$	−21.5895	+	2.12639i	−0.757179	+	0.0745756i
$814$	−1.39668	−	13.1394i	−0.0489537	−	0.460537i
$815$	−12.3092	−	29.7171i	−0.431173	−	1.04094i
$816$	18.6446	−	10.7191i	0.652691	−	0.375243i
$817$	−13.7388	+	33.1683i	−0.480659	+	1.16041i
$818$	29.9452	+	8.83177i	1.04701	+	0.308796i
$819$	−0.0305241	+	0.0371937i	−0.00106660	+	0.00129965i
$820$	−20.9728	+	17.7611i	−0.732401	+	0.620246i
$821$	14.1558	+	46.6654i	0.494041	+	1.62863i	0.749637	+	0.661850i	$0.230228\pi$
$821$	14.1558	+	46.6654i	0.494041	+	1.62863i	−0.255596	+	0.966784i	$0.582272\pi$
$822$	−29.5140	−	5.63406i	−1.02942	−	0.196510i
$823$	−31.7619	−	21.2226i	−1.10715	−	0.739775i	−0.139038	−	0.990287i	$-0.544401\pi$
$823$	−31.7619	−	21.2226i	−1.10715	−	0.739775i	−0.968113	+	0.250512i	$0.919401\pi$
$824$	−27.7163	−	13.9989i	−0.965545	−	0.487674i
$825$	−0.158344	−	0.236979i	−0.00551285	−	0.00825056i
$826$	0.139745	+	0.0566235i	0.00486234	+	0.00197018i
$827$	−35.1620	+	28.8567i	−1.22270	+	1.00345i	−0.223112	+	0.974793i	$0.571622\pi$
$827$	−35.1620	+	28.8567i	−1.22270	+	1.00345i	−0.999589	+	0.0286525i	$0.990878\pi$
$828$	−4.50615	+	6.97482i	−0.156599	+	0.242392i
$829$	7.13557	+	13.3497i	0.247828	+	0.463654i	0.974820	−	0.222992i	$-0.0715823\pi$
$829$	7.13557	+	13.3497i	0.247828	+	0.463654i	−0.726992	+	0.686646i	$0.759082\pi$
$830$	−13.3604	+	11.1384i	−0.463746	+	0.386620i
$831$			16.0616i			0.557171i
$832$	8.36153	+	23.5724i	0.289884	+	0.817225i
$833$			37.6347i			1.30396i
$834$	15.0450	+	18.0463i	0.520964	+	0.624891i
$835$	−24.7626	−	46.3276i	−0.856946	−	1.60323i
$836$	4.90213	+	22.7981i	0.169544	+	0.788490i
$837$	−4.24646	+	3.48498i	−0.146779	+	0.120459i
$838$	−2.81636	+	6.95066i	−0.0972894	+	0.240107i
$839$	24.2384	+	36.2754i	0.836804	+	1.25237i	0.965427	+	0.260672i	$0.0839442\pi$
$839$	24.2384	+	36.2754i	0.836804	+	1.25237i	−0.128623	+	0.991694i	$0.541056\pi$
$840$	−0.00723468	+	0.0962795i	−0.000249620	+	0.00332196i
$841$	17.3606	+	11.6000i	0.598642	+	0.400000i
$842$	4.15663	−	21.7745i	0.143247	−	0.750398i
$843$	6.59869	+	21.7530i	0.227271	+	0.749212i
$844$	49.8066	+	4.12972i	1.71441	+	0.142151i
$845$	−4.53861	+	5.53032i	−0.156133	+	0.190249i
$846$	−2.79475	+	9.47593i	−0.0960854	+	0.325789i
$847$	0.00972586	−	0.0234803i	0.000334185	−	0.000806793i
$848$	0.798168	−	11.8460i	0.0274092	−	0.406794i
$849$	−8.45390	−	20.4095i	−0.290137	−	0.700453i
$850$	0.605863	−	0.0644013i	0.0207809	−	0.00220895i
$851$	−10.8539	+	1.06901i	−0.372066	+	0.0366453i
$852$	4.91974	+	3.91191i	0.168547	+	0.134020i
$853$	−47.8430	−	25.5726i	−1.63811	−	0.875589i	−0.993844	−	0.110790i	$-0.964662\pi$
$853$	−47.8430	−	25.5726i	−1.63811	−	0.875589i	−0.644269	−	0.764799i	$-0.722838\pi$
$854$	−0.144935	+	0.220580i	−0.00495958	+	0.00754811i
$855$	1.41849	+	7.13124i	0.0485114	+	0.243883i
$856$	−30.3971	−	29.0199i	−1.03895	−	0.991881i
$857$	57.2228	+	11.3823i	1.95469	+	0.388813i	0.993669	+	0.112345i	$0.0358363\pi$
$857$	57.2228	+	11.3823i	1.95469	+	0.388813i	0.961023	+	0.276467i	$0.0891637\pi$
$858$	−0.121478	−	15.7261i	−0.00414717	−	0.536879i
$859$	44.4519	+	4.37813i	1.51668	+	0.149380i	0.821812	−	0.569759i	$-0.192963\pi$
$859$	44.4519	+	4.37813i	1.51668	+	0.149380i	0.694867	+	0.719139i	$0.255463\pi$
$860$	−0.750551	−	48.5790i	−0.0255936	−	1.65653i
$861$	0.0912383	+	0.0276768i	0.00310939	+	0.000943224i
$862$	33.5110	−	10.4488i	1.14139	−	0.355887i
$863$	8.60931	−	8.60931i	0.293064	−	0.293064i	−0.545225	−	0.838290i	$-0.683556\pi$
$863$	8.60931	−	8.60931i	0.293064	−	0.293064i	0.838290	+	0.545225i	$0.183556\pi$
$864$	4.82135	+	2.95882i	0.164026	+	0.100661i
$865$	−39.7613	−	39.7613i	−1.35193	−	1.35193i
$866$	39.9403	+	20.9535i	1.35723	+	0.712028i
$867$	3.45655	−	11.3947i	0.117390	−	0.386985i
$868$	0.157196	+	0.0622853i	0.00533557	+	0.00211410i
$869$	0.277100	−	2.81345i	0.00939998	−	0.0954396i
$870$	6.36941	+	6.27176i	0.215943	+	0.212632i
$871$	2.65250	−	13.3350i	0.0898764	−	0.451839i
$872$	17.3886	+	3.04175i	0.588851	+	0.103007i
$873$	13.9032	−	2.76552i	0.470552	−	0.0935985i
$874$	18.8482	−	3.90074i	0.637551	−	0.131944i
$875$	−0.0817472	+	0.152938i	−0.00276356	+	0.00517026i
$876$	−15.9677	−	4.57560i	−0.539499	−	0.154595i
$877$	−4.32776	−	43.9404i	−0.146138	−	1.48376i	−0.736397	−	0.676550i	$-0.763474\pi$
$877$	−4.32776	−	43.9404i	−0.146138	−	1.48376i	0.590259	−	0.807214i	$-0.299026\pi$
$878$	4.71940	−	5.84205i	0.159272	−	0.197160i
$879$	−13.3218	+	5.51806i	−0.449333	+	0.186120i
$880$	−18.3348	−	25.6852i	−0.618066	−	0.865847i
$881$	−24.9099	−	10.3180i	−0.839237	−	0.347623i	−0.0786843	−	0.996900i	$-0.525072\pi$
$881$	−24.9099	−	10.3180i	−0.839237	−	0.347623i	−0.760553	+	0.649276i	$0.775072\pi$
$882$	−8.69397	+	4.73373i	−0.292741	+	0.159393i
$883$	9.04106	+	7.41980i	0.304256	+	0.249696i	0.774115	−	0.633045i	$-0.218195\pi$
$883$	9.04106	+	7.41980i	0.304256	+	0.249696i	−0.469859	+	0.882741i	$0.655695\pi$
$884$	29.8905	+	15.3879i	1.00533	+	0.517552i
$885$	−14.7047	+	4.46063i	−0.494294	+	0.149943i
$886$	12.5527	+	18.4759i	0.421716	+	0.620710i
$887$	15.5610	−	23.2887i	0.522487	−	0.781957i	−0.472567	−	0.881295i	$-0.656672\pi$
$887$	15.5610	−	23.2887i	0.522487	−	0.781957i	0.995054	+	0.0993376i	$0.0316724\pi$
$888$	0.899381	+	7.37517i	0.0301813	+	0.247494i
$889$	−0.114043	+	0.0762009i	−0.00382487	+	0.00255570i
$890$	−19.4653	+	8.23952i	−0.652479	+	0.276189i
$891$	−2.25646	−	2.74951i	−0.0755943	−	0.0921119i
$892$	−10.3942	+	7.17993i	−0.348025	+	0.240402i
$893$	20.1959	−	10.7949i	0.675830	−	0.361238i
$894$	−3.43645	−	0.311678i	−0.114932	−	0.0104241i
$895$	39.4494			1.31865
$896$	0.00767669	−	0.173947i	0.000256460	−	0.00581117i
$897$	−12.9807			−0.433412
$898$	−32.2028	−	2.92073i	−1.07462	−	0.0974659i
$899$	13.8059	−	7.37941i	0.460453	−	0.246117i
$900$	0.0910834	+	0.131860i	0.00303611	+	0.00439533i
$901$	−10.1242	−	12.3363i	−0.337285	−	0.410983i
$902$	−28.6981	+	12.1477i	−0.955541	+	0.404473i
$903$	−0.140144	+	0.0936413i	−0.00466371	+	0.00311619i
$904$	20.0720	−	25.6473i	0.667585	−	0.853018i
$905$	−24.3490	+	36.4408i	−0.809387	+	1.21133i
$906$	−7.14706	−	10.5195i	−0.237445	−	0.349487i
$907$	−1.50458	+	0.456409i	−0.0499588	+	0.0151548i	−0.315165	−	0.949037i	$-0.602060\pi$
$907$	−1.50458	+	0.456409i	−0.0499588	+	0.0151548i	0.265206	+	0.964192i	$0.414560\pi$
$908$	4.82611	−	9.37455i	0.160160	−	0.311105i
$909$	−4.94956	−	4.06200i	−0.164167	−	0.134728i
$910$	−0.132555	+	0.0721739i	−0.00439415	+	0.00239254i
$911$	−37.5661	−	15.5604i	−1.24462	−	0.515539i	−0.339465	−	0.940619i	$-0.610246\pi$
$911$	−37.5661	−	15.5604i	−1.24462	−	0.515539i	−0.905156	+	0.425080i	$0.860246\pi$
$912$	−2.95412	−	12.7751i	−0.0978208	−	0.423024i
$913$	−18.2222	+	7.54790i	−0.603068	+	0.249799i
$914$	20.7901	−	25.7356i	0.687674	−	0.851258i
$915$	−2.63649	−	26.7688i	−0.0871598	−	0.884948i
$916$	5.94941	−	20.7620i	0.196574	−	0.685995i
$917$	0.0427978	−	0.0800691i	0.00141331	−	0.00264411i
$918$	7.44583	−	1.54095i	0.245749	−	0.0508590i
$919$	50.6601	−	10.0769i	1.67112	−	0.332407i	0.733401	−	0.679796i	$-0.237932\pi$
$919$	50.6601	−	10.0769i	1.67112	−	0.332407i	0.937721	+	0.347389i	$0.112932\pi$
$920$	−21.3168	+	14.9693i	−0.702793	+	0.493523i
$921$	−1.50014	+	7.54169i	−0.0494312	+	0.248507i
$922$	−5.31299	−	5.23153i	−0.174974	−	0.172291i
$923$	−0.963068	+	9.77819i	−0.0316998	+	0.321853i
$924$	−0.0403286	+	0.101781i	−0.00132671	+	0.00334836i
$925$	−0.0611014	+	0.201424i	−0.00200900	+	0.00662279i
$926$	18.3788	+	9.64190i	0.603965	+	0.316852i
$927$	−7.76275	−	7.76275i	−0.254962	−	0.254962i
$928$	−11.8303	−	10.9500i	−0.388348	−	0.359452i
$929$	−6.61376	+	6.61376i	−0.216991	+	0.216991i	−0.807229	−	0.590238i	$-0.799034\pi$
$929$	−6.61376	+	6.61376i	−0.216991	+	0.216991i	0.590238	+	0.807229i	$0.299034\pi$
$930$	−16.4508	+	5.12939i	−0.539443	+	0.168199i
$931$	21.9575	+	6.66073i	0.719628	+	0.218297i
$932$	−5.46410	+	0.0844210i	−0.178983	+	0.00276530i
$933$	28.0752	+	2.76517i	0.919141	+	0.0905274i
$934$	−0.0267664	−	3.46509i	−0.000875824	−	0.113381i
$935$	−41.6030	−	8.27536i	−1.36056	−	0.270633i
$936$	0.204901	+	8.84051i	0.00669739	+	0.288961i
$937$	−6.91772	−	34.7777i	−0.225992	−	1.13614i	−0.912519	−	0.409034i	$-0.865866\pi$
$937$	−6.91772	−	34.7777i	−0.225992	−	1.13614i	0.686527	−	0.727104i	$-0.259134\pi$
$938$	−0.0519752	+	0.0791023i	−0.00169705	+	0.00258278i
$939$	−18.6960	−	9.99323i	−0.610121	−	0.326117i
$940$	−19.2876	+	24.2567i	−0.629092	+	0.791165i
$941$	−14.2050	+	1.39907i	−0.463069	+	0.0456084i	−0.326862	−	0.945072i	$-0.605991\pi$
$941$	−14.2050	+	1.39907i	−0.463069	+	0.0456084i	−0.136207	+	0.990680i	$0.543491\pi$
$942$	−16.8671	+	1.79292i	−0.549560	+	0.0584165i
$943$	9.84340	+	23.7641i	0.320545	+	0.773865i
$944$	26.2568	−	8.85952i	0.854586	−	0.288353i
$945$	−0.0130633	+	0.0315375i	−0.000424948	+	0.00102591i
$946$	15.5843	−	52.8404i	0.506689	−	1.71799i
$947$	−9.99572	+	12.1798i	−0.324817	+	0.395791i	−0.909659	−	0.415357i	$-0.863657\pi$
$947$	−9.99572	+	12.1798i	−0.324817	+	0.395791i	0.584841	+	0.811148i	$0.301157\pi$
$948$	−0.131353	+	1.58419i	−0.00426616	+	0.0514521i
$949$	−7.53740	−	24.8475i	−0.244674	−	0.806583i
$950$	0.0696538	−	0.364881i	0.00225987	−	0.0118383i
$951$	−23.6716	−	15.8168i	−0.767604	−	0.512896i
$952$	−0.152624	−	0.177424i	−0.00494656	−	0.00575035i
$953$	16.0514	+	24.0227i	0.519957	+	0.778171i	0.994794	−	0.101903i	$-0.0324931\pi$
$953$	16.0514	+	24.0227i	0.519957	+	0.778171i	−0.474837	+	0.880074i	$0.657493\pi$
$954$	1.57638	−	3.89045i	0.0510373	−	0.125958i
$955$	26.6739	−	21.8907i	0.863146	−	0.708366i
$956$	−5.20456	+	1.11910i	−0.168328	+	0.0361944i
$957$	4.77803	+	8.93907i	0.154452	+	0.288959i
$958$	21.4267	+	25.7010i	0.692264	+	0.830363i
$959$			0.326979i			0.0105587i
$960$	10.5314	+	14.2815i	0.339898	+	0.460935i
$961$		−	0.822473i		−	0.0265314i
$962$	−8.92086	+	7.43722i	−0.287620	+	0.239785i
$963$	−7.00413	−	13.1038i	−0.225705	−	0.422264i
$964$	−17.1977	−	11.1107i	−0.553900	−	0.357852i
$965$	24.6783	−	20.2530i	0.794422	−	0.651966i
$966$	0.0837506	+	0.0339351i	0.00269463	+	0.00109184i
$967$	1.70444	+	2.55087i	0.0548110	+	0.0820304i	0.857863	−	0.513879i	$-0.171792\pi$
$967$	1.70444	+	2.55087i	0.0548110	+	0.0820304i	−0.803052	+	0.595909i	$0.796792\pi$
$968$	−1.45909	−	4.43713i	−0.0468969	−	0.142615i
$969$	−14.6543	−	9.79170i	−0.470764	−	0.314555i
$970$	43.6777	+	8.33784i	1.40241	+	0.267712i
$971$	−0.469014	−	1.54613i	−0.0150514	−	0.0496177i	0.949093	−	0.314996i	$-0.102003\pi$
$971$	−0.469014	−	1.54613i	−0.0150514	−	0.0496177i	−0.964144	+	0.265378i	$0.914503\pi$
$972$	1.29252	+	1.52624i	0.0414576	+	0.0489540i
$973$	0.162202	−	0.197643i	0.00519995	−	0.00633615i
$974$	47.8392	+	14.1093i	1.53287	+	0.452090i
$975$	−0.0958700	+	0.231451i	−0.00307030	+	0.00741236i
$976$	6.24360	+	48.1039i	0.199853	+	1.53977i
$977$	−5.50772	−	13.2968i	−0.176208	−	0.425403i	0.810958	−	0.585105i	$-0.198947\pi$
$977$	−5.50772	−	13.2968i	−0.176208	−	0.425403i	−0.987165	+	0.159702i	$0.948947\pi$
$978$	2.16775	+	20.3934i	0.0693170	+	0.652108i
$979$	−23.8524	+	2.34926i	−0.762326	+	0.0750826i
$980$	−30.8518	+	3.52066i	−0.985525	+	0.112463i
$981$	5.50419	+	2.94205i	0.175735	+	0.0939325i
$982$	−15.6151	−	10.2601i	−0.498299	−	0.327413i
$983$	2.91609	+	14.6602i	0.0930088	+	0.467587i	0.999017	+	0.0443270i	$0.0141143\pi$
$983$	2.91609	+	14.6602i	0.0930088	+	0.467587i	−0.906008	+	0.423260i	$0.860886\pi$
$984$	16.0292	−	7.07899i	0.510992	−	0.225670i
$985$	−44.6629	−	8.88401i	−1.42308	−	0.283068i
$986$	−21.6671	+	0.167369i	−0.690020	+	0.00533012i
$987$	0.106993	+	0.0105379i	0.00340564	+	0.000335426i
$988$	14.2680	−	14.7158i	0.453927	−	0.468173i
$989$	−43.5138	−	13.1998i	−1.38366	−	0.419728i
$990$	−3.32118	−	10.6516i	−0.105554	−	0.338530i
$991$	−26.3239	+	26.3239i	−0.836207	+	0.836207i	−0.988357	−	0.152150i	$-0.951380\pi$
$991$	−26.3239	+	26.3239i	−0.836207	+	0.836207i	0.152150	+	0.988357i	$0.451380\pi$
$992$	29.3668	−	10.1622i	0.932397	−	0.322651i
$993$	−1.34409	−	1.34409i	−0.0426535	−	0.0426535i
$994$	0.0317766	−	0.0605707i	0.00100789	−	0.00192118i
$995$	13.4832	−	44.4481i	0.427445	−	1.40910i
$996$	10.1794	−	4.40189i	0.322547	−	0.139479i
$997$	−3.22683	+	32.7626i	−0.102195	+	1.03760i	0.798160	+	0.602445i	$0.205807\pi$
$997$	−3.22683	+	32.7626i	−0.102195	+	1.03760i	−0.900355	+	0.435156i	$0.856693\pi$
$998$	−3.75595	+	3.81443i	−0.118893	+	0.120744i
$999$	−0.512470	+	2.57636i	−0.0162138	+	0.0815124i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.229.15	yes	512
128.109	even	32	inner	384.2.v.a.109.15	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.15	✓	512	128.109	even	32	inner
384.2.v.a.229.15	yes	512	1.1	even	1	trivial

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+(-0.127742 + 1.40843i) q^{2} +(0.881921 - 0.471397i) q^{3} +(-1.96736 - 0.359831i) q^{4} +(-1.40713 - 1.71460i) q^{5} +(0.551272 + 1.30234i) q^{6} +(0.0127962 - 0.00855015i) q^{7} +(0.758112 - 2.72493i) q^{8} +(0.555570 - 0.831470i) q^{9} +(2.59464 - 1.76283i) q^{10} +(3.40372 - 1.03251i) q^{11} +(-1.90468 + 0.610066i) q^{12} +(-2.41676 - 1.98339i) q^{13} +(0.0104077 + 0.0191148i) q^{14} +(-2.04924 - 0.848822i) q^{15} +(3.74104 + 1.41584i) q^{16} +(4.96730 - 2.05752i) q^{17} +(1.10010 + 0.888697i) q^{18} +(-0.321304 - 3.26226i) q^{19} +(2.15138 + 3.87957i) q^{20} +(0.00725473 - 0.0135727i) q^{21} +(1.01942 + 4.92581i) q^{22} +(4.07213 - 0.809998i) q^{23} +(-0.615929 - 2.76055i) q^{24} +(0.0156326 - 0.0785902i) q^{25} +(3.10219 - 3.15049i) q^{26} +(0.0980171 - 0.995185i) q^{27} +(-0.0282514 + 0.0122168i) q^{28} +(-0.827213 + 2.72696i) q^{29} +(1.45728 - 2.77778i) q^{30} +(-3.88443 - 3.88443i) q^{31} +(-2.47200 + 5.08814i) q^{32} +(2.51509 - 2.51509i) q^{33} +(2.26335 + 7.25893i) q^{34} +(-0.0326660 - 0.00990914i) q^{35} +(-1.39220 + 1.43589i) q^{36} +(-2.61418 - 0.257475i) q^{37} +(4.63571 - 0.0358090i) q^{38} +(-3.06636 - 0.609936i) q^{39} +(-5.73893 + 2.53449i) q^{40} +(1.20863 + 6.07619i) q^{41} +(0.0181894 + 0.0119516i) q^{42} +(-9.65881 - 5.16274i) q^{43} +(-7.06789 + 0.806554i) q^{44} +(-2.20740 + 0.217410i) q^{45} +(0.620646 + 5.83880i) q^{46} +(2.67337 + 6.45408i) q^{47} +(3.96673 - 0.514858i) q^{48} +(-2.67869 + 6.46694i) q^{49} +(0.108692 + 0.0320567i) q^{50} +(3.41086 - 4.15614i) q^{51} +(4.04097 + 4.77167i) q^{52} +(-0.861628 - 2.84041i) q^{53} +(1.38913 + 0.265177i) q^{54} +(-6.55983 - 4.38314i) q^{55} +(-0.0135976 - 0.0413508i) q^{56} +(-1.82118 - 2.72559i) q^{57} +(-3.73506 - 1.51342i) q^{58} +(5.35526 - 4.39495i) q^{59} +(3.72616 + 2.40732i) q^{60} +(5.71656 + 10.6949i) q^{61} +(5.96715 - 4.97475i) q^{62} -0.0153899i q^{63} +(-6.85053 - 4.13161i) q^{64} +6.93467i q^{65} +(3.22106 + 3.86362i) q^{66} +(2.05001 + 3.83531i) q^{67} +(-10.5128 + 2.26051i) q^{68} +(3.20947 - 2.63395i) q^{69} +(0.0181292 - 0.0447421i) q^{70} +(-1.74600 - 2.61308i) q^{71} +(-1.84452 - 2.14424i) q^{72} +(6.90550 + 4.61411i) q^{73} +(0.696576 - 3.64901i) q^{74} +(-0.0232605 - 0.0766795i) q^{75} +(-0.541739 + 6.53366i) q^{76} +(0.0347266 - 0.0423145i) q^{77} +(1.25076 - 4.24084i) q^{78} +(0.304162 - 0.734312i) q^{79} +(-2.83656 - 8.40666i) q^{80} +(-0.382683 - 0.923880i) q^{81} +(-8.71230 + 0.926090i) q^{82} +(-5.51850 + 0.543524i) q^{83} +(-0.0191566 + 0.0240919i) q^{84} +(-10.5175 - 5.62171i) q^{85} +(8.50520 - 12.9443i) q^{86} +(0.555941 + 2.79491i) q^{87} +(-0.233112 - 10.0577i) q^{88} +(-6.60896 - 1.31460i) q^{89} +(-0.0242301 - 3.13674i) q^{90} +(-0.0478837 - 0.00471613i) q^{91} +(-8.30283 + 0.128280i) q^{92} +(-5.25686 - 1.59465i) q^{93} +(-9.43163 + 2.94080i) q^{94} +(-5.14134 + 5.14134i) q^{95} +(0.218426 + 5.65264i) q^{96} +(10.0236 + 10.0236i) q^{97} +(-8.76606 - 4.59886i) q^{98} +(1.03251 - 3.40372i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 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

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