LMFDB - Embedded newform 384.2.v.a.109.15

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			109.15
Character	$\chi$	$=$	384.109
Dual form			384.2.v.a.229.15

$q$-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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.127742	−	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	−0.985877	−	0.167471i	$-0.946440\pi$
$5$	−1.40713	+	1.71460i	−0.629289	+	0.766791i	0.356588	+	0.934262i	$0.383940\pi$
$6$	0.551272	−	1.30234i	0.225056	−	0.531680i
$7$	0.0127962	+	0.00855015i	0.00483651	+	0.00323165i	0.557986	−	0.829850i	$-0.311574\pi$
$7$	0.0127962	+	0.00855015i	0.00483651	+	0.00323165i	−0.553150	+	0.833082i	$0.686574\pi$
$8$	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	0.758154	−	0.652076i	$-0.226102\pi$
$11$	3.40372	+	1.03251i	1.02626	+	0.311313i	0.268108	+	0.963389i	$0.413602\pi$
$12$	−1.90468	−	0.610066i	−0.549835	−	0.176111i
$13$	−2.41676	+	1.98339i	−0.670290	+	0.550092i	−0.906813	−	0.421533i	$-0.861492\pi$
$13$	−2.41676	+	1.98339i	−0.670290	+	0.550092i	0.236523	+	0.971626i	$0.423992\pi$
$14$	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	0.892530	−	0.450989i	$-0.148928\pi$
$17$	4.96730	+	2.05752i	1.20475	+	0.499022i	0.312217	+	0.950011i	$0.398928\pi$
$18$	1.10010	−	0.888697i	0.259296	−	0.209468i
$19$	−0.321304	+	3.26226i	−0.0737122	+	0.748413i	0.885295	+	0.465030i	$0.153957\pi$
$19$	−0.321304	+	3.26226i	−0.0737122	+	0.748413i	−0.959007	+	0.283383i	$0.908543\pi$
$20$	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	0.600415	−	0.799689i	$-0.295002\pi$
$23$	4.07213	+	0.809998i	0.849099	+	0.168896i	0.248684	+	0.968585i	$0.420002\pi$
$24$	−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	0.846033	−	0.533131i	$-0.178985\pi$
$29$	−0.827213	−	2.72696i	−0.153610	−	0.506383i	−0.999642	+	0.0267482i	$0.991485\pi$
$30$	1.45728	+	2.77778i	0.266062	+	0.507151i
$31$	−3.88443	+	3.88443i	−0.697663	+	0.697663i	−0.963906	−	0.266243i	$-0.914218\pi$
$31$	−3.88443	+	3.88443i	−0.697663	+	0.697663i	0.266243	+	0.963906i	$0.414218\pi$
$32$	−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	−0.310589	−	0.950544i	$-0.600526\pi$
$37$	−2.61418	+	0.257475i	−0.429769	+	0.0423286i	−0.119180	+	0.992873i	$0.538026\pi$
$38$	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	−0.764002	−	0.645213i	$-0.776769\pi$
$41$	1.20863	−	6.07619i	0.188756	−	0.948942i	0.952759	−	0.303728i	$-0.0982315\pi$
$42$	0.0181894	−	0.0119516i	0.00280669	−	0.00184417i
$43$	−9.65881	+	5.16274i	−1.47295	+	0.787311i	−0.995804	−	0.0915111i	$-0.970830\pi$
$43$	−9.65881	+	5.16274i	−1.47295	+	0.787311i	−0.477150	+	0.878822i	$0.658330\pi$
$44$	−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	−0.599999	−	0.800001i	$-0.704832\pi$
$47$	2.67337	−	6.45408i	0.389950	−	0.941424i	0.989949	−	0.141423i	$-0.0451677\pi$
$48$	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	−0.996022	−	0.0891089i	$-0.971598\pi$
$53$	−0.861628	+	2.84041i	−0.118354	+	0.390160i	0.877668	+	0.479269i	$0.159098\pi$
$54$	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	0.914821	−	0.403858i	$-0.132331\pi$
$59$	5.35526	+	4.39495i	0.697196	+	0.572174i	−0.217626	+	0.976032i	$0.569831\pi$
$60$	3.72616	−	2.40732i	0.481046	−	0.310784i
$61$	5.71656	−	10.6949i	0.731930	−	1.36934i	−0.189921	−	0.981799i	$-0.560823\pi$
$61$	5.71656	−	10.6949i	0.731930	−	1.36934i	0.921851	−	0.387545i	$-0.126677\pi$
$62$	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	−0.725010	−	0.688738i	$-0.758165\pi$
$67$	2.05001	−	3.83531i	0.250449	−	0.468557i	0.975459	+	0.220181i	$0.0706648\pi$
$68$	−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	−0.920490	−	0.390766i	$-0.872210\pi$
$71$	−1.74600	+	2.61308i	−0.207212	+	0.310115i	0.713277	+	0.700882i	$0.247210\pi$
$72$	−1.84452	+	2.14424i	−0.217378	+	0.252701i
$73$	6.90550	−	4.61411i	0.808228	−	0.540040i	−0.0814244	−	0.996680i	$-0.525947\pi$
$73$	6.90550	−	4.61411i	0.808228	−	0.540040i	0.889652	+	0.456639i	$0.150947\pi$
$74$	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	0.940066	−	0.340992i	$-0.110763\pi$
$79$	0.304162	+	0.734312i	0.0342209	+	0.0826166i	−0.905845	+	0.423609i	$0.860763\pi$
$80$	−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	−0.209499	−	0.977809i	$-0.567183\pi$
$83$	−5.51850	−	0.543524i	−0.605734	−	0.0596595i	−0.396235	+	0.918149i	$0.629683\pi$
$84$	−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	−0.532499	−	0.846431i	$-0.678747\pi$
$89$	−6.60896	+	1.31460i	−0.700548	+	0.139348i	−0.168050	+	0.985779i	$0.553747\pi$
$90$	−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	0.0179066	−	0.999840i	$-0.494300\pi$
$97$	10.0236	−	10.0236i	1.01775	−	1.01775i	0.999840	−	0.0179066i	$-0.00570016\pi$
$98$	−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	0.974563	+	0.224115i	$0.0719492\pi$
$101$	0.627601	+	6.37214i	0.0624486	+	0.634052i	−0.912114	+	0.409937i	$0.865551\pi$
$102$	5.41793	−	5.33487i	0.536455	−	0.528231i
$103$	2.14174	+	10.7672i	0.211032	+	1.06093i	0.930469	+	0.366371i	$0.119400\pi$
$103$	2.14174	+	10.7672i	0.211032	+	1.06093i	−0.719437	+	0.694557i	$0.755600\pi$
$104$	−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	0.952230	+	0.305381i	$0.0987839\pi$
$107$	7.00413	+	13.1038i	0.677115	+	1.26679i	−0.275115	+	0.961411i	$0.588716\pi$
$108$	−0.550934	−	1.92262i	−0.0530136	−	0.185004i
$109$	0.611739	−	6.21109i	0.0585939	−	0.594914i	−0.920393	−	0.390993i	$-0.872132\pi$
$109$	0.611739	−	6.21109i	0.0585939	−	0.594914i	0.978987	−	0.203921i	$-0.0653685\pi$
$110$	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	0.178672	−	0.983909i	$-0.442820\pi$
$113$	10.6380	−	4.40641i	1.00074	−	0.414520i	0.822069	+	0.569388i	$0.192820\pi$
$114$	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	0.682755	−	0.730647i	$-0.260781\pi$
$131$	5.20271	+	2.78091i	0.454563	+	0.242969i	−0.228192	+	0.973616i	$0.573281\pi$
$132$	−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	−0.853314	−	0.521397i	$-0.825411\pi$
$137$	−11.8039	−	17.6657i	−1.00847	−	1.50929i	−0.155158	−	0.987890i	$-0.549589\pi$
$138$	3.29975	−	4.85679i	0.280893	−	0.413437i
$139$	15.8982	+	4.82265i	1.34846	+	0.409052i	0.880228	−	0.474552i	$-0.157390\pi$
$139$	15.8982	+	4.82265i	1.34846	+	0.409052i	0.468236	+	0.883603i	$0.344890\pi$
$140$	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	0.830393	−	0.557178i	$-0.188116\pi$
$149$	−1.15016	−	2.15181i	−0.0942252	−	0.176283i	−0.924618	+	0.380895i	$0.875616\pi$
$150$	0.110969	+	0.0229656i	0.00906060	+	0.00187514i
$151$	−8.81999	−	1.75441i	−0.717761	−	0.142772i	−0.177320	−	0.984153i	$-0.556743\pi$
$151$	−8.81999	−	1.75441i	−0.717761	−	0.142772i	−0.540441	+	0.841382i	$0.681743\pi$
$152$	−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	−0.979152	−	0.203128i	$-0.934889\pi$
$157$	−3.48169	−	11.4776i	−0.277869	−	0.916011i	0.701283	−	0.712883i	$-0.252611\pi$
$158$	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	0.304541	−	0.952499i	$-0.401497\pi$
$163$	13.8771	−	4.20957i	1.08694	−	0.329719i	0.782397	+	0.622780i	$0.213997\pi$
$164$	−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	0.820583	−	0.571527i	$-0.193649\pi$
$167$	23.2278	−	4.62029i	1.79742	−	0.357529i	0.976834	+	0.213998i	$0.0686487\pi$
$168$	−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	0.985235	−	0.171210i	$-0.0547676\pi$
$173$	25.2292	+	2.48485i	1.91814	+	0.188920i	0.932902	+	0.360130i	$0.117268\pi$
$174$	−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	−0.999207	−	0.0398206i	$-0.987321\pi$
$179$	−11.2829	−	13.7483i	−0.843327	−	1.02760i	0.155880	−	0.987776i	$-0.450179\pi$
$180$	4.42099	−	0.366567i	0.329521	−	0.0273223i
$181$	−5.73573	+	18.9082i	−0.426333	+	1.40543i	0.436390	+	0.899757i	$0.356257\pi$
$181$	−5.73573	+	18.9082i	−0.426333	+	1.40543i	−0.862724	+	0.505675i	$0.831243\pi$
$182$	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	$-0.809713\pi$
$191$		−	15.5569i		−	1.12566i	0.826573	−	0.562830i	$-0.190287\pi$
$192$	−7.98926	+	0.414439i	−0.576575	+	0.0299096i
$193$		−	14.3931i		−	1.03603i	−0.855370	−	0.518017i	$-0.826670\pi$
$193$		−	14.3931i		−	1.03603i	0.855370	−	0.518017i	$-0.173330\pi$
$194$	−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	0.998000	−	0.0632113i	$-0.0201342\pi$
$197$	15.8702	+	13.0243i	1.13070	+	0.927944i	0.132703	+	0.991156i	$0.457634\pi$
$198$	4.66202	−	1.88902i	0.331315	−	0.134246i
$199$	11.6340	−	17.4116i	0.824714	−	1.23427i	−0.144855	−	0.989453i	$-0.546271\pi$
$199$	11.6340	−	17.4116i	0.824714	−	1.23427i	0.969569	−	0.244819i	$-0.0787286\pi$
$200$	−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	−0.806014	−	0.591896i	$-0.798380\pi$
$211$	−24.8684	−	2.44933i	−1.71201	−	0.168619i	−0.906000	+	0.423277i	$0.860880\pi$
$212$	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	0.840659	−	0.541565i	$-0.182168\pi$
$223$	4.46643	+	4.46643i	0.299094	+	0.299094i	−0.541565	+	0.840659i	$0.682168\pi$
$224$	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	0.891394	−	0.453229i	$-0.149728\pi$
$227$	−1.53036	−	5.04493i	−0.101574	−	0.334844i	−0.992968	+	0.118385i	$0.962228\pi$
$228$	2.60218	−	6.01755i	0.172333	−	0.398522i
$229$	−1.05847	−	10.7468i	−0.0699454	−	0.710167i	−0.964654	−	0.263518i	$-0.915117\pi$
$229$	−1.05847	−	10.7468i	−0.0699454	−	0.710167i	0.894709	−	0.446649i	$-0.147383\pi$
$230$	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	0.282090	−	0.959388i	$-0.408972\pi$
$233$	2.67988	+	0.533060i	0.175564	+	0.0349220i	−0.106525	+	0.994310i	$0.533972\pi$
$234$	−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	0.460797	−	0.887505i	$-0.347564\pi$
$239$	2.45915	+	1.01861i	0.159069	+	0.0658885i	−0.301728	+	0.953394i	$0.597564\pi$
$240$	−6.46449	+	6.07687i	−0.417281	+	0.392260i
$241$	9.45803	−	3.91764i	0.609245	−	0.252358i	−0.0566606	−	0.998393i	$-0.518045\pi$
$241$	9.45803	−	3.91764i	0.609245	−	0.252358i	0.665906	+	0.746036i	$0.268045\pi$
$242$	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	−0.670359	−	0.742037i	$-0.733860\pi$
$251$	2.98165	−	3.63315i	0.188200	−	0.229322i	0.858559	+	0.512714i	$0.171360\pi$
$252$	−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	0.263776	−	0.964584i	$-0.415032\pi$
$263$	−8.53743	−	5.70453i	−0.526440	−	0.351756i	−0.790217	+	0.612828i	$0.790032\pi$
$264$	−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	−0.854924	−	0.518753i	$-0.826397\pi$
$269$	−8.41263	+	6.90406i	−0.512927	+	0.420948i	0.341998	+	0.939701i	$0.388897\pi$
$270$	−1.50002	+	2.75494i	−0.0912883	+	0.167660i
$271$	−20.0427	+	8.30194i	−1.21750	+	0.504307i	−0.896616	−	0.442810i	$-0.853982\pi$
$271$	−20.0427	+	8.30194i	−1.21750	+	0.504307i	−0.320889	+	0.947117i	$0.603982\pi$
$272$	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	−0.999920	−	0.0126598i	$-0.995970\pi$
$277$	−7.57138	−	14.1651i	−0.454920	−	0.851096i	0.544999	−	0.838436i	$-0.316530\pi$
$278$	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	−0.853186	−	0.521607i	$-0.825333\pi$
$281$	−4.43475	−	22.2950i	−0.264555	−	1.33001i	0.588631	−	0.808402i	$-0.299667\pi$
$282$	−6.93167	−	7.03959i	−0.412775	−	0.419202i
$283$	2.16531	+	21.9847i	0.128714	+	1.30686i	0.814973	+	0.579499i	$0.196752\pi$
$283$	2.16531	+	21.9847i	0.128714	+	1.30686i	−0.686259	+	0.727358i	$0.740748\pi$
$284$	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	−0.508066	−	0.861318i	$-0.669639\pi$
$293$	−14.3500	+	1.41335i	−0.838334	+	0.0825687i	−0.330268	+	0.943887i	$0.607139\pi$
$294$	−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	0.614966	−	0.788554i	$-0.289170\pi$
$307$	−4.87813	−	5.94402i	−0.278410	−	0.339243i	−0.893376	+	0.449310i	$0.851670\pi$
$308$	−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	0.331599	−	0.943421i	$-0.392412\pi$
$311$	23.4566	−	15.6732i	1.33010	−	0.888746i	0.998504	+	0.0546742i	$0.0174120\pi$
$312$	−3.98668	−	7.89322i	−0.225701	−	0.446866i
$313$	−11.7776	+	17.6265i	−0.665711	+	0.996307i	0.332865	+	0.942974i	$0.391985\pi$
$313$	−11.7776	+	17.6265i	−0.665711	+	0.996307i	−0.998577	+	0.0533331i	$0.983015\pi$
$314$	−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	0.152850	+	0.988249i	$0.451155\pi$
$317$	−13.4205	+	25.1079i	−0.753768	+	1.41020i	−0.906618	+	0.421952i	$0.861345\pi$
$318$	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	−0.970798	−	0.239898i	$-0.922886\pi$
$331$	−0.551783	+	1.81899i	−0.0303288	+	0.0999805i	0.940469	+	0.339879i	$0.110386\pi$
$332$	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	0.572961	+	0.819583i	$0.305795\pi$
$337$	−7.55810	+	18.2469i	−0.411716	+	0.993971i	−0.984677	+	0.174388i	$0.944205\pi$
$338$	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	−0.962718	−	0.270508i	$-0.912808\pi$
$347$	−34.5392	+	3.40182i	−1.85416	+	0.182619i	−0.891446	+	0.453128i	$0.850308\pi$
$348$	−0.0880446	+	5.69864i	−0.00471969	+	0.305479i
$349$	6.36230	−	1.92998i	0.340566	−	0.103310i	−0.115369	−	0.993323i	$-0.536805\pi$
$349$	6.36230	−	1.92998i	0.340566	−	0.103310i	0.455935	+	0.890013i	$0.349305\pi$
$350$	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	−0.704095	−	0.710106i	$-0.748647\pi$
$353$	0.112946	−	0.112946i	0.00601153	−	0.00601153i	0.710106	+	0.704095i	$0.248647\pi$
$354$	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	0.991361	−	0.131164i	$-0.0418714\pi$
$359$	0.478773	+	2.40695i	0.0252687	+	0.127034i	−0.966092	+	0.258198i	$0.916871\pi$
$360$	−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	−0.0802670	−	0.996773i	$-0.525577\pi$
$367$	−16.1275	−	6.68024i	−0.841850	−	0.348705i	−0.761583	+	0.648068i	$0.775577\pi$
$368$	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	0.494436	−	0.869214i	$-0.335375\pi$
$373$	8.16243	+	2.47605i	0.422635	+	0.128205i	−0.0718011	+	0.997419i	$0.522875\pi$
$374$	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	−0.538119	−	0.842869i	$-0.680865\pi$
$379$	7.66135	−	9.33538i	0.393537	−	0.479526i	0.931655	+	0.363343i	$0.118365\pi$
$380$	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	−0.520419	−	0.853911i	$-0.674224\pi$
$389$	8.25634	−	10.0604i	0.418613	−	0.510081i	0.939032	+	0.343830i	$0.111724\pi$
$390$	−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	−0.0228728	−	0.999738i	$-0.507281\pi$
$397$	18.9922	−	15.5865i	0.953194	−	0.782266i	0.976066	+	0.217473i	$0.0697813\pi$
$398$	−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	−0.463509	−	0.886092i	$-0.653410\pi$
$401$	−28.3918	−	11.7603i	−1.41782	−	0.587281i	−0.954312	+	0.298812i	$0.903410\pi$
$402$	−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	0.928296	+	0.371842i	$0.121274\pi$
$409$	4.30685	+	21.6520i	0.212960	+	1.07062i	−0.715336	+	0.698780i	$0.753726\pi$
$410$	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	−0.163883	−	0.986480i	$-0.552402\pi$
$419$	5.07465	−	1.53938i	0.247913	−	0.0752036i	0.411795	+	0.911276i	$0.364902\pi$
$420$	0.0682637	+	0.00105468i	0.00333093	+	5.14632e-5i
$421$	−15.5994	+	1.53641i	−0.760270	+	0.0748801i	−0.470720	−	0.882283i	$-0.656006\pi$
$421$	−15.5994	+	1.53641i	−0.760270	+	0.0748801i	−0.289550	+	0.957163i	$0.593506\pi$
$422$	−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	0.511864	+	0.859066i	$0.328955\pi$
$431$	−9.49857	+	22.9316i	−0.457530	+	1.10458i	−0.969394	+	0.245509i	$0.921045\pi$
$432$	1.77571	+	3.58425i	0.0854337	+	0.172447i
$433$	12.2048	+	29.4649i	0.586523	+	1.41599i	0.886806	+	0.462142i	$0.152919\pi$
$433$	12.2048	+	29.4649i	0.586523	+	1.41599i	−0.300283	+	0.953850i	$0.597081\pi$
$434$	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	−0.656461	−	0.754360i	$-0.727947\pi$
$439$	−4.41550	+	2.95034i	−0.210740	+	0.140812i	0.445721	+	0.895172i	$0.352947\pi$
$440$	−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	0.878085	−	0.478505i	$-0.158821\pi$
$443$	12.2093	+	10.0199i	0.580080	+	0.476059i	−0.298005	+	0.954564i	$0.596321\pi$
$444$	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	$-0.818607\pi$
$449$		−	22.8643i		−	1.07903i	0.841975	−	0.539517i	$-0.181393\pi$
$450$	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	−0.919975	−	0.391978i	$-0.871791\pi$
$457$	−19.4513	+	12.9969i	−0.909893	+	0.607971i	0.0100813	+	0.999949i	$0.496791\pi$
$458$	−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	0.689271	−	0.724504i	$-0.257931\pi$
$461$	−3.34479	−	4.07563i	−0.155782	−	0.189821i	−0.845053	+	0.534683i	$0.820431\pi$
$462$	0.0742519	−	0.0218992i	0.00345451	−	0.00101884i
$463$	5.61611	+	13.5585i	0.261003	+	0.630116i	0.999001	−	0.0446861i	$-0.0142288\pi$
$463$	5.61611	+	13.5585i	0.261003	+	0.630116i	−0.737998	+	0.674803i	$0.764229\pi$
$464$	−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	0.0414402	−	0.999141i	$-0.486805\pi$
$467$	−2.43846	−	0.240168i	−0.112839	−	0.0111136i	−0.154279	+	0.988027i	$0.549305\pi$
$468$	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	0.977121	−	0.212683i	$-0.0682202\pi$
$479$	16.7305	+	16.7305i	0.764438	+	0.764438i	−0.212683	+	0.977121i	$0.568220\pi$
$480$	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	0.745573	+	0.666423i	$0.232176\pi$
$487$	6.88044	+	34.5903i	0.311783	+	1.56744i	−0.433791	+	0.901014i	$0.642824\pi$
$488$	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	0.701286	−	0.712880i	$-0.252609\pi$
$491$	−6.22799	−	11.6517i	−0.281065	−	0.525836i	−0.982352	+	0.187044i	$0.940109\pi$
$492$	−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	−0.566618	−	0.823981i	$-0.691748\pi$
$499$	2.92608	−	2.40137i	0.130989	−	0.107500i	0.697607	+	0.716481i	$0.254248\pi$
$500$	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	0.860991	+	0.508620i	$0.169844\pi$
$503$	22.4592	+	33.6126i	1.00141	+	1.49871i	0.140417	+	0.990092i	$0.455156\pi$
$504$	−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	0.189924	−	0.981799i	$-0.439176\pi$
$509$	−11.7519	−	6.28154i	−0.520895	−	0.278424i	−0.710820	+	0.703374i	$0.751676\pi$
$510$	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	0.397831	−	0.917459i	$-0.369763\pi$
$521$	−13.7417	−	20.5659i	−0.602034	−	0.901007i	−0.999865	+	0.0164515i	$0.994763\pi$
$522$	−3.33345	−	2.26478i	−0.145901	−	0.0991267i
$523$	16.8347	+	5.10674i	0.736129	+	0.223302i	0.636018	−	0.771674i	$-0.280580\pi$
$523$	16.8347	+	5.10674i	0.736129	+	0.223302i	0.100111	+	0.994976i	$0.468080\pi$
$524$	−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	−0.991183	−	0.132502i	$-0.957699\pi$
$541$	−5.59758	−	18.4527i	−0.240659	−	0.793345i	0.750524	−	0.660843i	$-0.229801\pi$
$542$	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	0.179130	−	0.983825i	$-0.442672\pi$
$547$	20.4565	−	6.20540i	0.874656	−	0.265324i	0.695525	+	0.718501i	$0.255172\pi$
$548$	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	0.495710	−	0.868488i	$-0.334908\pi$
$557$	19.1748	+	1.88855i	0.812462	+	0.0800205i	0.316751	+	0.948509i	$0.397408\pi$
$558$	−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	0.579842	−	0.814729i	$-0.303114\pi$
$563$	−7.88595	−	9.60906i	−0.332353	−	0.404973i	−0.912196	+	0.409755i	$0.865614\pi$
$564$	−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	−0.999993	−	0.00382173i	$-0.998784\pi$
$569$	−14.6410	+	21.9118i	−0.613781	+	0.918589i	0.386211	+	0.922410i	$0.373784\pi$
$570$	−9.53007	+	3.86151i	−0.399171	+	0.161741i
$571$	−10.5100	−	8.62531i	−0.439828	−	0.360958i	0.388265	−	0.921548i	$-0.373074\pi$
$571$	−10.5100	−	8.62531i	−0.439828	−	0.360958i	−0.828094	+	0.560590i	$0.810574\pi$
$572$	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	$-0.834615\pi$
$577$		−	23.8530i		−	0.993015i	0.868032	−	0.496508i	$-0.165385\pi$
$578$	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	0.637881	+	0.770135i	$0.279811\pi$
$587$	−7.76175	+	25.5871i	−0.320362	+	1.05609i	−0.958243	+	0.285956i	$0.907689\pi$
$588$	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	0.634146	+	0.773213i	$0.281352\pi$
$593$	−8.79110	+	21.2236i	−0.361007	+	0.871549i	−0.995153	+	0.0983353i	$0.968648\pi$
$594$	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	−0.845083	−	0.534635i	$-0.820449\pi$
$599$	3.43298	−	17.2588i	0.140268	−	0.705174i	0.985351	−	0.170539i	$-0.0545509\pi$
$600$	−0.226581	−	0.00525157i	−0.00925012	−	0.000214394i
$601$	−40.6705	+	8.08988i	−1.65899	+	0.329993i	−0.933591	−	0.358340i	$-0.883343\pi$
$601$	−40.6705	+	8.08988i	−1.65899	+	0.329993i	−0.725395	+	0.688333i	$0.758343\pi$
$602$	−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	0.994143	−	0.108073i	$-0.0344681\pi$
$607$	21.8304	+	21.8304i	0.886070	+	0.886070i	−0.108073	+	0.994143i	$0.534468\pi$
$608$	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	−0.760885	−	0.648887i	$-0.775235\pi$
$613$	−3.49624	−	35.4979i	−0.141212	−	1.43375i	0.619673	−	0.784860i	$-0.287265\pi$
$614$	−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	0.955302	−	0.295632i	$-0.0955302\pi$
$617$	42.8420	+	8.52180i	1.72475	+	0.343075i	0.769450	+	0.638707i	$0.220530\pi$
$618$	15.2033	+	3.14640i	0.611568	+	0.126567i
$619$	−1.88976	−	3.53549i	−0.0759559	−	0.142103i	0.841077	−	0.540916i	$-0.181922\pi$
$619$	−1.88976	−	3.53549i	−0.0759559	−	0.142103i	−0.917032	+	0.398813i	$0.869422\pi$
$620$	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	0.728647	−	0.684890i	$-0.240150\pi$
$631$	−4.59564	−	6.87786i	−0.182950	−	0.273803i	−0.911597	+	0.411086i	$0.865150\pi$
$632$	−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	−0.173458	−	0.984841i	$-0.555494\pi$
$643$	−27.6065	−	14.7560i	−1.08869	−	0.581918i	−0.915234	+	0.402923i	$0.867994\pi$
$644$	−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	0.996080	−	0.0884599i	$-0.0281945\pi$
$647$	32.9535	+	22.0188i	1.29554	+	0.865650i	0.299457	+	0.954110i	$0.403195\pi$
$648$	−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	0.356885	−	0.934148i	$-0.383839\pi$
$653$	34.3114	−	28.1586i	1.34271	−	1.10193i	0.985824	−	0.167784i	$-0.0536611\pi$
$654$	−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	0.722414	+	0.691461i	$0.243033\pi$
$659$	−3.10661	+	31.5420i	−0.121016	+	1.22870i	−0.843430	+	0.537239i	$0.819467\pi$
$660$	15.1684	−	4.34656i	0.590429	−	0.169190i
$661$	−0.562032	−	1.05149i	−0.0218605	−	0.0408982i	0.870754	−	0.491719i	$-0.163631\pi$
$661$	−0.562032	−	1.05149i	−0.0218605	−	0.0408982i	−0.892614	+	0.450821i	$0.851131\pi$
$662$	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	0.0778398	−	0.996966i	$-0.475198\pi$
$673$	−23.8442	−	23.8442i	−0.919126	−	0.919126i	−0.996966	+	0.0778398i	$0.975198\pi$
$674$	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	0.322125	−	0.946697i	$-0.395603\pi$
$677$	21.4074	−	2.10844i	0.822752	−	0.0810340i	0.500627	+	0.865663i	$0.333103\pi$
$678$	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	−0.819105	−	0.573644i	$-0.805529\pi$
$683$	−20.8344	+	11.1362i	−0.797207	+	0.426116i	0.0218976	+	0.999760i	$0.493029\pi$
$684$	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	−0.999519	−	0.0310004i	$-0.990131\pi$
$691$	−21.9476	−	26.7433i	−0.834928	−	1.01736i	0.164592	−	0.986362i	$-0.447369\pi$
$692$	−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	−0.676559	−	0.736389i	$-0.736530\pi$
$701$	8.25009	−	15.4348i	0.311602	−	0.582966i	0.988161	+	0.153423i	$0.0490296\pi$
$702$	−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	−0.930988	−	0.365050i	$-0.881052\pi$
$709$	−39.1591	−	32.1370i	−1.47065	−	1.20693i	−0.539662	−	0.841882i	$-0.681448\pi$
$710$	−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	0.999128	+	0.0417482i	$0.0132927\pi$
$719$	8.63841	+	20.8550i	0.322158	+	0.777759i	−0.676970	+	0.736011i	$0.736707\pi$
$720$	−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	−0.894755	−	0.446558i	$-0.852650\pi$
$727$	2.77128	−	13.9322i	0.102781	−	0.516716i	0.997536	−	0.0701580i	$-0.0223504\pi$
$728$	−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	−0.991940	−	0.126706i	$-0.959559\pi$
$733$	−47.2797	+	14.3421i	−1.74631	+	0.529739i	−0.754374	+	0.656445i	$0.772059\pi$
$734$	−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	0.956219	−	0.292653i	$-0.0945379\pi$
$739$	−0.0390667	−	0.128786i	−0.00143709	−	0.00473746i	−0.957656	+	0.287915i	$0.907038\pi$
$740$	−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	−0.988841	−	0.148972i	$-0.952404\pi$
$743$	−3.60569	−	18.1271i	−0.132280	−	0.665017i	0.856561	−	0.516045i	$-0.172596\pi$
$744$	−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	0.624583	−	0.780959i	$-0.285269\pi$
$751$	14.0861	+	5.83464i	0.514008	+	0.212909i	−0.110575	+	0.993868i	$0.535269\pi$
$752$	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	0.913884	−	0.405975i	$-0.133068\pi$
$757$	39.8453	+	12.0870i	1.44820	+	0.439308i	0.534320	+	0.845283i	$0.320568\pi$
$758$	−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	0.138048	−	0.990425i	$-0.455917\pi$
$761$	−19.9768	−	13.3480i	−0.724157	−	0.483866i	−0.862205	+	0.506559i	$0.830917\pi$
$762$	−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	−0.0708404	−	0.997488i	$-0.522568\pi$
$773$	25.6148	−	31.2118i	0.921301	−	1.12261i	0.992141	−	0.125121i	$-0.0399319\pi$
$774$	−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	−0.992480	−	0.122404i	$-0.960939\pi$
$787$	0.134929	−	1.36996i	0.00480969	−	0.0488336i	0.997290	+	0.0735708i	$0.0234395\pi$
$788$	−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	−0.935433	−	0.353504i	$-0.884990\pi$
$797$	−9.99512	−	32.9495i	−0.354045	−	1.16713i	0.581388	−	0.813627i	$-0.302510\pi$
$798$	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	−0.947505	−	0.319740i	$-0.896404\pi$
$809$	1.42882	−	7.18316i	0.0502346	−	0.252547i	0.997740	+	0.0671934i	$0.0214045\pi$
$810$	−2.62157	+	1.72253i	−0.0921125	+	0.0605237i
$811$	−40.6948	+	21.7518i	−1.42899	+	0.763809i	−0.990833	−	0.135091i	$-0.956867\pi$
$811$	−40.6948	+	21.7518i	−1.42899	+	0.763809i	−0.438153	+	0.898900i	$0.644367\pi$
$812$	−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	−0.255596	−	0.966784i	$-0.582272\pi$
$821$	14.1558	−	46.6654i	0.494041	−	1.62863i	0.749637	−	0.661850i	$-0.230228\pi$
$822$	−29.5140	+	5.63406i	−1.02942	+	0.196510i
$823$	−31.7619	+	21.2226i	−1.10715	+	0.739775i	−0.968113	−	0.250512i	$-0.919401\pi$
$823$	−31.7619	+	21.2226i	−1.10715	+	0.739775i	−0.139038	+	0.990287i	$0.544401\pi$
$824$	−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	−0.999589	−	0.0286525i	$-0.990878\pi$
$827$	−35.1620	−	28.8567i	−1.22270	−	1.00345i	−0.223112	−	0.974793i	$-0.571622\pi$
$828$	−4.50615	−	6.97482i	−0.156599	−	0.242392i
$829$	7.13557	−	13.3497i	0.247828	−	0.463654i	−0.726992	−	0.686646i	$-0.759082\pi$
$829$	7.13557	−	13.3497i	0.247828	−	0.463654i	0.974820	+	0.222992i	$0.0715823\pi$
$830$	−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	−0.128623	−	0.991694i	$-0.541056\pi$
$839$	24.2384	−	36.2754i	0.836804	−	1.25237i	0.965427	−	0.260672i	$-0.0839442\pi$
$840$	−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	−0.644269	+	0.764799i	$0.722838\pi$
$853$	−47.8430	+	25.5726i	−1.63811	+	0.875589i	−0.993844	+	0.110790i	$0.964662\pi$
$854$	−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	0.961023	−	0.276467i	$-0.0891637\pi$
$857$	57.2228	−	11.3823i	1.95469	−	0.388813i	0.993669	−	0.112345i	$-0.0358363\pi$
$858$	−0.121478	+	15.7261i	−0.00414717	+	0.536879i
$859$	44.4519	−	4.37813i	1.51668	−	0.149380i	0.694867	−	0.719139i	$-0.255463\pi$
$859$	44.4519	−	4.37813i	1.51668	−	0.149380i	0.821812	+	0.569759i	$0.192963\pi$
$860$	−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	0.838290	−	0.545225i	$-0.183556\pi$
$863$	8.60931	+	8.60931i	0.293064	+	0.293064i	−0.545225	+	0.838290i	$0.683556\pi$
$864$	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	0.590259	+	0.807214i	$0.299026\pi$
$877$	−4.32776	+	43.9404i	−0.146138	+	1.48376i	−0.736397	+	0.676550i	$0.763474\pi$
$878$	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	−0.760553	−	0.649276i	$-0.775072\pi$
$881$	−24.9099	+	10.3180i	−0.839237	+	0.347623i	−0.0786843	+	0.996900i	$0.525072\pi$
$882$	−8.69397	−	4.73373i	−0.292741	−	0.159393i
$883$	9.04106	−	7.41980i	0.304256	−	0.249696i	−0.469859	−	0.882741i	$-0.655695\pi$
$883$	9.04106	−	7.41980i	0.304256	−	0.249696i	0.774115	+	0.633045i	$0.218195\pi$
$884$	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	0.995054	−	0.0993376i	$-0.0316724\pi$
$887$	15.5610	+	23.2887i	0.522487	+	0.781957i	−0.472567	+	0.881295i	$0.656672\pi$
$888$	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	0.265206	−	0.964192i	$-0.414560\pi$
$907$	−1.50458	−	0.456409i	−0.0499588	−	0.0151548i	−0.315165	+	0.949037i	$0.602060\pi$
$908$	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	−0.905156	−	0.425080i	$-0.860246\pi$
$911$	−37.5661	+	15.5604i	−1.24462	+	0.515539i	−0.339465	+	0.940619i	$0.610246\pi$
$912$	−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	0.937721	−	0.347389i	$-0.112932\pi$
$919$	50.6601	+	10.0769i	1.67112	+	0.332407i	0.733401	+	0.679796i	$0.237932\pi$
$920$	−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	0.590238	−	0.807229i	$-0.299034\pi$
$929$	−6.61376	−	6.61376i	−0.216991	−	0.216991i	−0.807229	+	0.590238i	$0.799034\pi$
$930$	−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	0.686527	+	0.727104i	$0.259134\pi$
$937$	−6.91772	+	34.7777i	−0.225992	+	1.13614i	−0.912519	+	0.409034i	$0.865866\pi$
$938$	−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	−0.136207	−	0.990680i	$-0.543491\pi$
$941$	−14.2050	−	1.39907i	−0.463069	−	0.0456084i	−0.326862	+	0.945072i	$0.605991\pi$
$942$	−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	0.584841	−	0.811148i	$-0.301157\pi$
$947$	−9.99572	−	12.1798i	−0.324817	−	0.395791i	−0.909659	+	0.415357i	$0.863657\pi$
$948$	−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	−0.474837	−	0.880074i	$-0.657493\pi$
$953$	16.0514	−	24.0227i	0.519957	−	0.778171i	0.994794	+	0.101903i	$0.0324931\pi$
$954$	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	−0.803052	−	0.595909i	$-0.796792\pi$
$967$	1.70444	−	2.55087i	0.0548110	−	0.0820304i	0.857863	+	0.513879i	$0.171792\pi$
$968$	−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	−0.964144	−	0.265378i	$-0.914503\pi$
$971$	−0.469014	+	1.54613i	−0.0150514	+	0.0496177i	0.949093	+	0.314996i	$0.102003\pi$
$972$	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	−0.987165	−	0.159702i	$-0.948947\pi$
$977$	−5.50772	+	13.2968i	−0.176208	+	0.425403i	0.810958	+	0.585105i	$0.198947\pi$
$978$	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	−0.906008	−	0.423260i	$-0.860886\pi$
$983$	2.91609	−	14.6602i	0.0930088	−	0.467587i	0.999017	−	0.0443270i	$-0.0141143\pi$
$984$	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	0.152150	−	0.988357i	$-0.451380\pi$
$991$	−26.3239	−	26.3239i	−0.836207	−	0.836207i	−0.988357	+	0.152150i	$0.951380\pi$
$992$	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	−0.900355	−	0.435156i	$-0.856693\pi$
$997$	−3.22683	−	32.7626i	−0.102195	−	1.03760i	0.798160	−	0.602445i	$-0.205807\pi$
$998$	−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.109.15	✓	512
128.101	even	32	inner	384.2.v.a.229.15	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.109.15	✓	512	1.1	even	1	trivial
384.2.v.a.229.15	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+(-0.127742 - 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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