LMFDB - Embedded newform 384.2.v.a.157.32

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			157.32
Character	$\chi$	$=$	384.157
Dual form			384.2.v.a.181.32

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.41167 - 0.0847019i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.98565 - 0.239143i) q^{4} +(1.11591 - 0.596466i) q^{5} +(-0.0540742 + 1.41318i) q^{6} +(-0.322650 - 1.62207i) q^{7} +(2.78284 - 0.505781i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})$	\(q+(1.41167 - 0.0847019i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.98565 - 0.239143i) q^{4} +(1.11591 - 0.596466i) q^{5} +(-0.0540742 + 1.41318i) q^{6} +(-0.322650 - 1.62207i) q^{7} +(2.78284 - 0.505781i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.52478 - 0.936535i) q^{10} +(2.19437 - 2.67384i) q^{11} +(0.0433638 + 1.99953i) q^{12} +(-1.37633 + 2.57494i) q^{13} +(-0.592870 - 2.26251i) q^{14} +(0.484215 + 1.16900i) q^{15} +(3.88562 - 0.949710i) q^{16} +(-1.55074 + 3.74381i) q^{17} +(-1.40107 - 0.192330i) q^{18} +(0.0648022 + 0.213624i) q^{19} +(2.07316 - 1.45123i) q^{20} +(1.64589 - 0.162106i) q^{21} +(2.87125 - 3.96046i) q^{22} +(-3.78613 + 2.52981i) q^{23} +(0.230580 + 2.81901i) q^{24} +(-1.88837 + 2.82615i) q^{25} +(-1.72483 + 3.75155i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-1.02858 - 3.14371i) q^{28} +(-3.94961 + 3.24136i) q^{29} +(0.782571 + 1.60923i) q^{30} +(5.85792 - 5.85792i) q^{31} +(5.40479 - 1.66980i) q^{32} +(2.44588 + 2.44588i) q^{33} +(-1.87203 + 5.41639i) q^{34} +(-1.32756 - 1.61764i) q^{35} +(-1.99415 - 0.152833i) q^{36} +(-11.2249 - 3.40505i) q^{37} +(0.109574 + 0.296079i) q^{38} +(-2.42763 - 1.62209i) q^{39} +(2.80371 - 2.22427i) q^{40} +(2.04941 + 3.06716i) q^{41} +(2.30973 - 0.368251i) q^{42} +(-0.519546 - 5.27504i) q^{43} +(3.71781 - 5.83408i) q^{44} +(-1.21083 + 0.367302i) q^{45} +(-5.13050 + 3.89196i) q^{46} +(-2.35364 - 0.974910i) q^{47} +(0.564279 + 3.96000i) q^{48} +(3.94014 - 1.63206i) q^{49} +(-2.42638 + 4.14955i) q^{50} +(-3.57378 - 1.91023i) q^{51} +(-2.11714 + 5.44207i) q^{52} +(-2.49585 - 2.04829i) q^{53} +(0.328733 - 1.37548i) q^{54} +(0.853857 - 4.29263i) q^{55} +(-1.71830 - 4.35078i) q^{56} +(-0.218947 + 0.0435513i) q^{57} +(-5.30101 + 4.91028i) q^{58} +(3.50455 + 6.55655i) q^{59} +(1.24104 + 2.20543i) q^{60} +(2.87865 + 0.283522i) q^{61} +(7.77330 - 8.76565i) q^{62} +1.65385i q^{63} +(7.48837 - 2.81501i) q^{64} +3.69433i q^{65} +(3.65996 + 3.24562i) q^{66} +(-9.85831 - 0.970958i) q^{67} +(-2.18391 + 7.80474i) q^{68} +(-2.14652 - 4.01586i) q^{69} +(-2.01110 - 2.17113i) q^{70} +(-5.76433 + 1.14660i) q^{71} +(-2.82804 - 0.0468422i) q^{72} +(1.76363 - 8.86634i) q^{73} +(-16.1344 - 3.85604i) q^{74} +(-2.62744 - 2.15629i) q^{75} +(0.179761 + 0.408686i) q^{76} +(-5.04518 - 2.69670i) q^{77} +(-3.56442 - 2.08424i) q^{78} +(-3.18689 + 1.32005i) q^{79} +(3.76953 - 3.37743i) q^{80} +(0.923880 + 0.382683i) q^{81} +(3.15289 + 4.15624i) q^{82} +(-2.47435 + 0.750586i) q^{83} +(3.22939 - 0.715488i) q^{84} +(0.502573 + 5.10271i) q^{85} +(-1.18024 - 7.40263i) q^{86} +(-2.83862 - 4.24830i) q^{87} +(4.75418 - 8.55074i) q^{88} +(5.57553 + 3.72545i) q^{89} +(-1.67819 + 0.621070i) q^{90} +(4.62081 + 1.40171i) q^{91} +(-6.91295 + 5.92875i) q^{92} +(5.25554 + 6.40389i) q^{93} +(-3.40515 - 1.17690i) q^{94} +(0.199733 + 0.199733i) q^{95} +(1.13200 + 5.54243i) q^{96} +(-8.49241 + 8.49241i) q^{97} +(5.42396 - 2.63767i) q^{98} +(-2.67384 + 2.19437i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 512 q+O(q^{10}) $ 512 * q	$ 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) $ 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{27}{32}\right)$	$1$

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 $

$2$	1.41167	−	0.0847019i	0.998205	−	0.0598933i
$2$	1.41167	−	0.0847019i	0.998205	−	0.0598933i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$3$	−0.0980171	+	0.995185i	−0.0565902	+	0.574570i
$4$	1.98565	−	0.239143i	0.992826	−	0.119572i
$5$	1.11591	−	0.596466i	0.499050	−	0.266748i	−0.202610	−	0.979259i	$-0.564943\pi$
$5$	1.11591	−	0.596466i	0.499050	−	0.266748i	0.701660	+	0.712512i	$0.252443\pi$
$6$	−0.0540742	+	1.41318i	−0.0220757	+	0.576928i
$7$	−0.322650	−	1.62207i	−0.121950	−	0.613086i	−0.992625	−	0.121226i	$-0.961317\pi$
$7$	−0.322650	−	1.62207i	−0.121950	−	0.613086i	0.870675	−	0.491860i	$-0.163683\pi$
$8$	2.78284	−	0.505781i	0.983882	−	0.178821i
$9$	−0.980785	−	0.195090i	−0.326928	−	0.0650301i
$10$	1.52478	−	0.936535i	0.482177	−	0.296158i
$11$	2.19437	−	2.67384i	0.661626	−	0.806194i	−0.328776	−	0.944408i	$-0.606636\pi$
$11$	2.19437	−	2.67384i	0.661626	−	0.806194i	0.990402	+	0.138214i	$0.0441362\pi$
$12$	0.0433638	+	1.99953i	0.0125181	+	0.577215i
$13$	−1.37633	+	2.57494i	−0.381726	+	0.714159i	−0.997262	−	0.0739497i	$-0.976440\pi$
$13$	−1.37633	+	2.57494i	−0.381726	+	0.714159i	0.615536	+	0.788109i	$0.288940\pi$
$14$	−0.592870	−	2.26251i	−0.158451	−	0.604681i
$15$	0.484215	+	1.16900i	0.125024	+	0.301834i
$16$	3.88562	−	0.949710i	0.971405	−	0.237427i
$17$	−1.55074	+	3.74381i	−0.376109	+	0.908007i	0.616579	+	0.787293i	$0.288518\pi$
$17$	−1.55074	+	3.74381i	−0.376109	+	0.908007i	−0.992687	+	0.120713i	$0.961482\pi$
$18$	−1.40107	−	0.192330i	−0.330236	−	0.0453325i
$19$	0.0648022	+	0.213624i	0.0148666	+	0.0490088i	0.964060	−	0.265685i	$-0.0855981\pi$
$19$	0.0648022	+	0.213624i	0.0148666	+	0.0490088i	−0.949193	+	0.314694i	$0.898098\pi$
$20$	2.07316	−	1.45123i	0.463574	−	0.324506i
$21$	1.64589	−	0.162106i	0.359162	−	0.0353744i
$22$	2.87125	−	3.96046i	0.612153	−	0.844373i
$23$	−3.78613	+	2.52981i	−0.789463	+	0.527502i	−0.883703	−	0.468047i	$-0.844958\pi$
$23$	−3.78613	+	2.52981i	−0.789463	+	0.527502i	0.0942407	+	0.995549i	$0.469958\pi$
$24$	0.230580	+	2.81901i	0.0470669	+	0.575429i
$25$	−1.88837	+	2.82615i	−0.377674	+	0.565229i
$26$	−1.72483	+	3.75155i	−0.338267	+	0.735740i
$27$	0.290285	−	0.956940i	0.0558653	−	0.184163i
$28$	−1.02858	−	3.14371i	−0.194383	−	0.594106i
$29$	−3.94961	+	3.24136i	−0.733423	+	0.601905i	−0.925176	−	0.379538i	$-0.876083\pi$
$29$	−3.94961	+	3.24136i	−0.733423	+	0.601905i	0.191753	+	0.981443i	$0.438583\pi$
$30$	0.782571	+	1.60923i	0.142877	+	0.293804i
$31$	5.85792	−	5.85792i	1.05211	−	1.05211i	0.0535482	−	0.998565i	$-0.482947\pi$
$31$	5.85792	−	5.85792i	1.05211	−	1.05211i	0.998565	−	0.0535482i	$-0.0170531\pi$
$32$	5.40479	−	1.66980i	0.955441	−	0.295182i
$33$	2.44588	+	2.44588i	0.425773	+	0.425773i
$34$	−1.87203	+	5.41639i	−0.321050	+	0.928903i
$35$	−1.32756	−	1.61764i	−0.224398	−	0.273430i
$36$	−1.99415	−	0.152833i	−0.332359	−	0.0254722i
$37$	−11.2249	−	3.40505i	−1.84537	−	0.559786i	−0.999658	−	0.0261430i	$-0.991677\pi$
$37$	−11.2249	−	3.40505i	−1.84537	−	0.559786i	−0.845710	−	0.533643i	$-0.820823\pi$
$38$	0.109574	+	0.296079i	0.0177753	+	0.0480304i
$39$	−2.42763	−	1.62209i	−0.388733	−	0.259743i
$40$	2.80371	−	2.22427i	0.443306	−	0.351688i
$41$	2.04941	+	3.06716i	0.320064	+	0.479009i	0.956260	−	0.292518i	$-0.0944931\pi$
$41$	2.04941	+	3.06716i	0.320064	+	0.479009i	−0.636196	+	0.771527i	$0.719493\pi$
$42$	2.30973	−	0.368251i	0.356399	−	0.0568223i
$43$	−0.519546	−	5.27504i	−0.0792300	−	0.804435i	−0.949897	−	0.312563i	$-0.898813\pi$
$43$	−0.519546	−	5.27504i	−0.0792300	−	0.804435i	0.870667	−	0.491873i	$-0.163687\pi$
$44$	3.71781	−	5.83408i	0.560481	−	0.879521i
$45$	−1.21083	+	0.367302i	−0.180500	+	0.0547541i
$46$	−5.13050	+	3.89196i	−0.756452	+	0.573839i
$47$	−2.35364	−	0.974910i	−0.343314	−	0.142205i	0.204363	−	0.978895i	$-0.434488\pi$
$47$	−2.35364	−	0.974910i	−0.343314	−	0.142205i	−0.547677	+	0.836690i	$0.684488\pi$
$48$	0.564279	+	3.96000i	0.0814467	+	0.571577i
$49$	3.94014	−	1.63206i	0.562877	−	0.233151i
$50$	−2.42638	+	4.14955i	−0.343143	+	0.586835i
$51$	−3.57378	−	1.91023i	−0.500430	−	0.267485i
$52$	−2.11714	+	5.44207i	−0.293594	+	0.754679i
$53$	−2.49585	−	2.04829i	−0.342831	−	0.281354i	0.447183	−	0.894442i	$-0.352427\pi$
$53$	−2.49585	−	2.04829i	−0.342831	−	0.281354i	−0.790015	+	0.613088i	$0.789927\pi$
$54$	0.328733	−	1.37548i	0.0447349	−	0.187179i
$55$	0.853857	−	4.29263i	0.115134	−	0.578818i
$56$	−1.71830	−	4.35078i	−0.229617	−	0.581397i
$57$	−0.218947	+	0.0435513i	−0.0290003	+	0.00576852i
$58$	−5.30101	+	4.91028i	−0.696057	+	0.644752i
$59$	3.50455	+	6.55655i	0.456253	+	0.853590i	0.999898	+	0.0142743i	$0.00454382\pi$
$59$	3.50455	+	6.55655i	0.456253	+	0.853590i	−0.543645	+	0.839315i	$0.682956\pi$
$60$	1.24104	+	2.20543i	0.160218	+	0.284720i
$61$	2.87865	+	0.283522i	0.368573	+	0.0363013i	0.280609	−	0.959822i	$-0.409464\pi$
$61$	2.87865	+	0.283522i	0.368573	+	0.0363013i	0.0879648	+	0.996124i	$0.471964\pi$
$62$	7.77330	−	8.76565i	0.987210	−	1.11324i
$63$			1.65385i			0.208366i
$64$	7.48837	−	2.81501i	0.936046	−	0.351877i
$65$			3.69433i			0.458225i
$66$	3.65996	+	3.24562i	0.450510	+	0.399508i
$67$	−9.85831	−	0.970958i	−1.20438	−	0.118621i	−0.524156	−	0.851622i	$-0.675619\pi$
$67$	−9.85831	−	0.970958i	−1.20438	−	0.118621i	−0.680228	+	0.733001i	$0.738119\pi$
$68$	−2.18391	+	7.80474i	−0.264839	+	0.946464i
$69$	−2.14652	−	4.01586i	−0.258411	−	0.483453i
$70$	−2.01110	−	2.17113i	−0.240372	−	0.259499i
$71$	−5.76433	+	1.14660i	−0.684100	+	0.136076i	−0.524892	−	0.851169i	$-0.675894\pi$
$71$	−5.76433	+	1.14660i	−0.684100	+	0.136076i	−0.159208	+	0.987245i	$0.550894\pi$
$72$	−2.82804	−	0.0468422i	−0.333288	−	0.00552041i
$73$	1.76363	−	8.86634i	0.206417	−	1.03773i	−0.729090	−	0.684418i	$-0.760056\pi$
$73$	1.76363	−	8.86634i	0.206417	−	1.03773i	0.935507	−	0.353309i	$-0.114944\pi$
$74$	−16.1344	−	3.85604i	−1.87558	−	0.448256i
$75$	−2.62744	−	2.15629i	−0.303391	−	0.248987i
$76$	0.179761	+	0.408686i	0.0206200	+	0.0468795i
$77$	−5.04518	−	2.69670i	−0.574952	−	0.307318i
$78$	−3.56442	−	2.08424i	−0.403592	−	0.235994i
$79$	−3.18689	+	1.32005i	−0.358554	+	0.148518i	−0.554686	−	0.832060i	$-0.687162\pi$
$79$	−3.18689	+	1.32005i	−0.358554	+	0.148518i	0.196133	+	0.980577i	$0.437162\pi$
$80$	3.76953	−	3.37743i	0.421446	−	0.377608i
$81$	0.923880	+	0.382683i	0.102653	+	0.0425204i
$82$	3.15289	+	4.15624i	0.348179	+	0.458980i
$83$	−2.47435	+	0.750586i	−0.271595	+	0.0823875i	−0.423144	−	0.906062i	$-0.639074\pi$
$83$	−2.47435	+	0.750586i	−0.271595	+	0.0823875i	0.151549	+	0.988450i	$0.451574\pi$
$84$	3.22939	−	0.715488i	0.352356	−	0.0780662i
$85$	0.502573	+	5.10271i	0.0545117	+	0.553466i
$86$	−1.18024	−	7.40263i	−0.127268	−	0.798246i
$87$	−2.83862	−	4.24830i	−0.304332	−	0.455465i
$88$	4.75418	−	8.55074i	0.506798	−	0.911511i
$89$	5.57553	+	3.72545i	0.591005	+	0.394897i	0.814803	−	0.579739i	$-0.196845\pi$
$89$	5.57553	+	3.72545i	0.591005	+	0.394897i	−0.223797	+	0.974636i	$0.571845\pi$
$90$	−1.67819	+	0.621070i	−0.176897	+	0.0654666i
$91$	4.62081	+	1.40171i	0.484393	+	0.146939i
$92$	−6.91295	+	5.92875i	−0.720724	+	0.618115i
$93$	5.25554	+	6.40389i	0.544974	+	0.664052i
$94$	−3.40515	−	1.17690i	−0.351215	−	0.121388i
$95$	0.199733	+	0.199733i	0.0204922	+	0.0204922i
$96$	1.13200	+	5.54243i	0.115534	+	0.565672i
$97$	−8.49241	+	8.49241i	−0.862273	+	0.862273i	−0.991602	−	0.129328i	$-0.958718\pi$
$97$	−8.49241	+	8.49241i	−0.862273	+	0.862273i	0.129328	+	0.991602i	$0.458718\pi$
$98$	5.42396	−	2.63767i	0.547902	−	0.266445i
$99$	−2.67384	+	2.19437i	−0.268731	+	0.220542i
$100$	−3.07379	+	6.06333i	−0.307379	+	0.606333i
$101$	−0.319260	+	1.05246i	−0.0317676	+	0.104724i	−0.971390	−	0.237488i	$-0.923676\pi$
$101$	−0.319260	+	1.05246i	−0.0317676	+	0.104724i	0.939623	+	0.342212i	$0.111176\pi$
$102$	−5.20682	−	2.39391i	−0.515552	−	0.237033i
$103$	10.7916	−	16.1508i	1.06333	−	1.59138i	0.290382	−	0.956911i	$-0.406218\pi$
$103$	10.7916	−	16.1508i	1.06333	−	1.59138i	0.772946	−	0.634472i	$-0.218782\pi$
$104$	−2.52776	+	7.86176i	−0.247867	+	0.770909i
$105$	1.73997	−	1.16261i	0.169804	−	0.113459i
$106$	−3.69682	−	2.68012i	−0.359067	−	0.260316i
$107$	−7.59750	+	0.748289i	−0.734479	+	0.0723398i	−0.458339	−	0.888778i	$-0.651555\pi$
$107$	−7.59750	+	0.748289i	−0.734479	+	0.0723398i	−0.276140	+	0.961117i	$0.589055\pi$
$108$	0.347558	−	1.96957i	0.0334438	−	0.189522i
$109$	−2.77922	−	9.16187i	−0.266201	−	0.877548i	−0.983519	−	0.180802i	$-0.942131\pi$
$109$	−2.77922	−	9.16187i	−0.266201	−	0.877548i	0.717318	−	0.696746i	$-0.245369\pi$
$110$	0.841774	−	6.13212i	0.0802600	−	0.584674i
$111$	4.48889	−	10.8371i	0.426066	−	1.02861i
$112$	−2.79420	−	5.99634i	−0.264027	−	0.566601i
$113$	6.51206	+	15.7215i	0.612603	+	1.47896i	0.860130	+	0.510074i	$0.170382\pi$
$113$	6.51206	+	15.7215i	0.612603	+	1.47896i	−0.247527	+	0.968881i	$0.579618\pi$
$114$	−0.305394	+	0.0800256i	−0.0286027	+	0.00749508i
$115$	−2.71603	+	5.08133i	−0.253271	+	0.473837i
$116$	−7.06739	+	7.38073i	−0.656191	+	0.685283i
$117$	1.85223	−	2.25695i	0.171239	−	0.208655i
$118$	5.50263	+	8.95887i	0.506558	+	0.824731i
$119$	6.57307	+	1.30747i	0.602553	+	0.119855i
$120$	1.93875	+	3.00823i	0.176983	+	0.274612i
$121$	−0.188197	−	0.946132i	−0.0171088	−	0.0860120i
$122$	4.08773	+	0.156414i	0.370086	+	0.0141611i
$123$	−3.25326	+	1.73891i	−0.293337	+	0.156792i
$124$	10.2309	−	13.0327i	0.918762	−	1.17037i
$125$	−1.04166	+	10.5762i	−0.0931692	+	0.945963i
$126$	0.140084	+	2.33470i	0.0124797	+	0.207992i
$127$	12.8451			1.13982			0.569909	−	0.821708i	$-0.306978\pi$
$127$	12.8451			1.13982			0.569909	+	0.821708i	$0.306978\pi$
$128$	10.3327	−	4.60816i	0.913291	−	0.407308i
$129$	5.30056			0.466688
$130$	0.312917	+	5.21519i	0.0274446	+	0.457403i
$131$	−1.02431	+	10.4000i	−0.0894947	+	0.908655i	0.840679	+	0.541534i	$0.182156\pi$
$131$	−1.02431	+	10.4000i	−0.0894947	+	0.908655i	−0.930173	+	0.367120i	$0.880344\pi$
$132$	5.44158	+	4.27175i	0.473629	+	0.371808i
$133$	0.325606	−	0.174040i	0.0282336	−	0.0150912i
$134$	−13.9990	−	0.535660i	−1.20933	−	0.0462740i
$135$	−0.246851	−	1.24100i	−0.0212455	−	0.106809i
$136$	−2.42190	+	11.2027i	−0.207676	+	0.960627i
$137$	19.5291	+	3.88459i	1.66849	+	0.331883i	0.936828	−	0.349789i	$-0.113747\pi$
$137$	19.5291	+	3.88459i	1.66849	+	0.331883i	0.731658	+	0.681672i	$0.238747\pi$
$138$	−3.37034	−	5.48728i	−0.286903	−	0.467108i
$139$	−0.183178	+	0.223203i	−0.0155370	+	0.0189318i	−0.780721	−	0.624880i	$-0.785148\pi$
$139$	−0.183178	+	0.223203i	−0.0155370	+	0.0189318i	0.765184	+	0.643812i	$0.222648\pi$
$140$	−3.02292	−	2.89458i	−0.255483	−	0.244637i
$141$	1.20091	−	2.24675i	0.101135	−	0.189211i
$142$	−8.04024	+	2.10687i	−0.674722	+	0.176805i
$143$	3.86480	+	9.33045i	0.323191	+	0.780251i
$144$	−3.99624	+	0.173414i	−0.333020	+	0.0144512i
$145$	−2.47404	+	5.97286i	−0.205458	+	0.496019i
$146$	1.73867	−	12.6658i	0.143893	−	1.04823i
$147$	1.23800	+	4.08114i	0.102108	+	0.336606i
$148$	−23.1031	−	4.07687i	−1.89906	−	0.335117i
$149$	−3.88769	+	0.382904i	−0.318492	+	0.0313687i	−0.256000	−	0.966677i	$-0.582405\pi$
$149$	−3.88769	+	0.382904i	−0.318492	+	0.0313687i	−0.0624917	+	0.998045i	$0.519905\pi$
$150$	−3.89174	−	2.82143i	−0.317759	−	0.230369i
$151$	6.04299	−	4.03780i	0.491772	−	0.328591i	−0.284835	−	0.958576i	$-0.591939\pi$
$151$	6.04299	−	4.03780i	0.491772	−	0.328591i	0.776607	+	0.629985i	$0.216939\pi$
$152$	0.288381	+	0.561706i	0.0233908	+	0.0455604i
$153$	2.25132	−	3.36934i	0.182008	−	0.272395i
$154$	−7.35057	−	3.37953i	−0.592326	−	0.272331i
$155$	3.04286	−	10.0310i	0.244408	−	0.805705i
$156$	−5.20835	−	2.64036i	−0.417002	−	0.211398i
$157$	11.8729	−	9.74385i	0.947562	−	0.777644i	−0.0274896	−	0.999622i	$-0.508751\pi$
$157$	11.8729	−	9.74385i	0.947562	−	0.777644i	0.975052	+	0.221978i	$0.0712513\pi$
$158$	−4.38705	+	2.13342i	−0.349015	+	0.169726i
$159$	2.28306	−	2.28306i	0.181059	−	0.181059i
$160$	5.03527	−	5.08712i	0.398073	−	0.402172i
$161$	5.32513	+	5.32513i	0.419679	+	0.419679i
$162$	1.33663	+	0.461970i	0.105016	+	0.0362958i
$163$	4.43324	+	5.40192i	0.347238	+	0.423111i	0.917117	−	0.398618i	$-0.130510\pi$
$163$	4.43324	+	5.40192i	0.347238	+	0.423111i	−0.569879	+	0.821729i	$0.693010\pi$
$164$	4.80290	+	5.60020i	0.375043	+	0.437302i
$165$	4.18826	+	1.27050i	0.326056	+	0.0989080i
$166$	−3.42940	+	1.26916i	−0.266173	+	0.0985063i
$167$	−1.92266	−	1.28468i	−0.148780	−	0.0994117i	0.478952	−	0.877841i	$-0.341017\pi$
$167$	−1.92266	−	1.28468i	−0.148780	−	0.0994117i	−0.627732	+	0.778429i	$0.716017\pi$
$168$	4.49825	−	1.28357i	0.347047	−	0.0990298i
$169$	2.48640	+	3.72116i	0.191262	+	0.286243i
$170$	1.14168	+	7.16080i	0.0875628	+	0.549208i
$171$	−0.0218810	−	0.222162i	−0.00167328	−	0.0169891i
$172$	−2.29313	−	10.3501i	−0.174849	−	0.789190i
$173$	10.0879	−	3.06013i	0.766968	−	0.232657i	0.117528	−	0.993070i	$-0.462503\pi$
$173$	10.0879	−	3.06013i	0.766968	−	0.232657i	0.649440	+	0.760412i	$0.275003\pi$
$174$	−4.36705	−	5.75677i	−0.331065	−	0.436420i
$175$	5.19350	+	2.15122i	0.392592	+	0.162617i
$176$	5.98710	−	12.4735i	0.451294	−	0.940229i
$177$	−6.86848	+	2.84502i	−0.516267	+	0.213845i
$178$	8.18639	+	4.78687i	0.613596	+	0.358791i
$179$	−14.8566	−	7.94104i	−1.11044	−	0.593541i	−0.188965	−	0.981984i	$-0.560513\pi$
$179$	−14.8566	−	7.94104i	−1.11044	−	0.593541i	−0.921473	+	0.388442i	$0.873013\pi$
$180$	−2.31645	+	1.01890i	−0.172658	+	0.0759440i
$181$	−8.95514	−	7.34929i	−0.665630	−	0.546268i	0.239769	−	0.970830i	$-0.422928\pi$
$181$	−8.95514	−	7.34929i	−0.665630	−	0.546268i	−0.905399	+	0.424562i	$0.860428\pi$
$182$	6.64181	+	1.58736i	0.492324	+	0.117663i
$183$	−0.564314	+	2.83700i	−0.0417153	+	0.209717i
$184$	−9.25665	+	8.95501i	−0.682410	+	0.660172i
$185$	−14.5570	+	2.89557i	−1.07025	+	0.212886i
$186$	7.96153	+	8.59505i	0.583768	+	0.630220i
$187$	6.60747	+	12.3617i	0.483186	+	0.903977i
$188$	−4.90666	−	1.37297i	−0.357855	−	0.100134i
$189$	−1.64589	−	0.162106i	−0.119721	−	0.0117915i
$190$	0.298876	+	0.265040i	0.0216827	+	0.0192280i
$191$		−	16.4488i		−	1.19019i	−0.803654	−	0.595096i	$-0.797114\pi$
$191$		−	16.4488i		−	1.19019i	0.803654	−	0.595096i	$-0.202886\pi$
$192$	2.06747	+	7.72823i	0.149207	+	0.557737i
$193$		−	9.52497i		−	0.685622i	−0.939404	−	0.342811i	$-0.888621\pi$
$193$		−	9.52497i		−	0.685622i	0.939404	−	0.342811i	$-0.111379\pi$
$194$	−11.2692	+	12.7078i	−0.809081	+	0.912370i
$195$	−3.67654	−	0.362108i	−0.263283	−	0.0259311i
$196$	7.43345	−	4.18296i	0.530960	−	0.298783i
$197$	−1.12756	−	2.10952i	−0.0803353	−	0.150297i	0.838546	−	0.544831i	$-0.183406\pi$
$197$	−1.12756	−	2.10952i	−0.0803353	−	0.150297i	−0.918881	+	0.394534i	$0.870906\pi$
$198$	−3.58873	+	3.32421i	−0.255040	+	0.236241i
$199$	1.44709	−	0.287844i	0.102581	−	0.0204047i	−0.143533	−	0.989646i	$-0.545846\pi$
$199$	1.44709	−	0.287844i	0.102581	−	0.0204047i	0.246114	+	0.969241i	$0.420846\pi$
$200$	−3.82562	+	8.81981i	−0.270512	+	0.623654i
$201$	1.93257	−	9.71567i	0.136313	−	0.685290i
$202$	−0.361546	+	1.51277i	−0.0254383	+	0.106438i
$203$	6.53206	+	5.36072i	0.458461	+	0.376249i
$204$	−7.55310	−	2.93840i	−0.528823	−	0.205729i
$205$	4.11641	+	2.20027i	0.287502	+	0.153673i
$206$	13.8662	−	23.7137i	0.966106	−	1.65221i
$207$	4.20692	−	1.74256i	0.292401	−	0.121117i
$208$	−2.90246	+	11.3123i	−0.201250	+	0.784370i
$209$	0.713397	+	0.295499i	0.0493467	+	0.0204401i
$210$	2.35780	−	1.78861i	0.162703	−	0.123426i
$211$	19.6349	−	5.95619i	1.35172	−	0.410041i	0.470358	−	0.882476i	$-0.344125\pi$
$211$	19.6349	−	5.95619i	1.35172	−	0.410041i	0.881366	+	0.472435i	$0.156625\pi$
$212$	−5.44572	−	3.47033i	−0.374014	−	0.238343i
$213$	−0.576072	−	5.84896i	−0.0394718	−	0.400764i
$214$	−10.6618	+	1.69986i	−0.728827	+	0.116200i
$215$	−3.72614	−	5.57657i	−0.254121	−	0.380319i
$216$	0.323813	−	2.80983i	0.0220327	−	0.191185i
$217$	−11.3920	−	7.61191i	−0.773342	−	0.516730i
$218$	−4.69939	−	12.6982i	−0.318283	−	0.860029i
$219$	8.65078	+	2.62419i	0.584566	+	0.177326i
$220$	0.668909	−	8.72785i	0.0450978	−	0.588432i
$221$	−7.50574	−	9.14577i	−0.504891	−	0.615211i
$222$	5.41892	−	15.6787i	0.363694	−	1.05229i
$223$	0.898803	+	0.898803i	0.0601883	+	0.0601883i	0.736560	−	0.676372i	$-0.236449\pi$
$223$	0.898803	+	0.898803i	0.0601883	+	0.0601883i	−0.676372	+	0.736560i	$0.736449\pi$
$224$	−4.45240	−	8.22820i	−0.297488	−	0.549770i
$225$	2.40344	−	2.40344i	0.160229	−	0.160229i
$226$	10.5246	+	21.6421i	0.700083	+	1.43961i
$227$	−14.1433	+	11.6071i	−0.938723	+	0.770390i	−0.973425	−	0.229007i	$-0.926452\pi$
$227$	−14.1433	+	11.6071i	−0.938723	+	0.770390i	0.0347015	+	0.999398i	$0.488952\pi$
$228$	−0.424338	+	0.138838i	−0.0281025	+	0.00919474i
$229$	−4.36652	+	14.3945i	−0.288548	+	0.951215i	0.686107	+	0.727501i	$0.259318\pi$
$229$	−4.36652	+	14.3945i	−0.288548	+	0.951215i	−0.974655	+	0.223714i	$0.928182\pi$
$230$	−3.40375	+	7.40325i	−0.224437	+	0.488156i
$231$	3.17823	−	4.75656i	0.209112	−	0.312959i
$232$	−9.35169	+	11.0178i	−0.613969	+	0.723354i
$233$	11.9924	−	8.01305i	0.785647	−	0.524952i	−0.0968342	−	0.995301i	$-0.530872\pi$
$233$	11.9924	−	8.01305i	0.785647	−	0.524952i	0.882481	+	0.470348i	$0.155872\pi$
$234$	2.42358	−	3.34297i	0.158434	−	0.218537i
$235$	−3.20795	+	0.315956i	−0.209264	+	0.0206107i
$236$	8.52676	+	12.1809i	0.555045	+	0.792911i
$237$	−1.00133	−	3.30094i	−0.0650432	−	0.214419i
$238$	9.38979	+	1.28896i	0.608650	+	0.0835511i
$239$	−6.20240	+	14.9739i	−0.401200	+	0.968583i	0.586175	+	0.810184i	$0.300633\pi$
$239$	−6.20240	+	14.9739i	−0.401200	+	0.968583i	−0.987375	+	0.158398i	$0.949367\pi$
$240$	2.99169	+	4.08242i	0.193113	+	0.263519i
$241$	2.06308	+	4.98071i	0.132895	+	0.320836i	0.976293	−	0.216453i	$-0.0694487\pi$
$241$	2.06308	+	4.98071i	0.132895	+	0.320836i	−0.843399	+	0.537288i	$0.819449\pi$
$242$	−0.345813	−	1.31969i	−0.0222297	−	0.0848329i
$243$	−0.471397	+	0.881921i	−0.0302401	+	0.0565753i
$244$	5.78380	−	0.125433i	0.370270	−	0.00803004i
$245$	3.42337	−	4.17139i	0.218711	−	0.266500i
$246$	−4.44526	+	2.73033i	−0.283420	+	0.174079i
$247$	−0.639259	−	0.127156i	−0.0406751	−	0.00809077i
$248$	13.3388	−	19.2645i	0.847016	−	1.22329i
$249$	−0.504443	−	2.53600i	−0.0319678	−	0.160713i
$250$	−0.574666	+	15.0184i	−0.0363451	+	0.949845i
$251$	27.7490	−	14.8322i	1.75150	−	0.936198i	0.820090	−	0.572234i	$-0.193923\pi$
$251$	27.7490	−	14.8322i	1.75150	−	0.936198i	0.931413	−	0.363964i	$-0.118577\pi$
$252$	0.395507	+	3.28397i	0.0249146	+	0.206871i
$253$	−1.54384	+	15.6748i	−0.0970602	+	0.985469i
$254$	18.1331	−	1.08800i	1.13777	−	0.0682675i
$255$	−5.12740			−0.321090
$256$	14.1961	−	7.38043i	0.887256	−	0.461277i
$257$	23.2528			1.45047			0.725235	−	0.688501i	$-0.241731\pi$
$257$	23.2528			1.45047			0.725235	+	0.688501i	$0.241731\pi$
$258$	7.48267	−	0.448968i	0.465850	−	0.0279515i
$259$	−1.90150	+	19.3063i	−0.118154	+	1.19964i
$260$	0.883474	+	7.33565i	0.0547907	+	0.454938i
$261$	4.50607	−	2.40855i	0.278919	−	0.149085i
$262$	−0.565095	+	14.7682i	−0.0349117	+	0.912384i
$263$	1.37401	+	6.90760i	0.0847249	+	0.425941i	0.999746	+	0.0225350i	$0.00717371\pi$
$263$	1.37401	+	6.90760i	0.0847249	+	0.425941i	−0.915021	+	0.403406i	$0.867826\pi$
$264$	8.04357	+	5.56941i	0.495047	+	0.342773i
$265$	−4.00688	−	0.797017i	−0.246140	−	0.0489604i
$266$	0.444908	−	0.273267i	0.0272791	−	0.0167551i
$267$	−4.25401	+	5.18353i	−0.260341	+	0.317227i
$268$	−19.8074	+	0.429562i	−1.20993	+	0.0262397i
$269$	11.9852	−	22.4227i	0.730750	−	1.36714i	−0.191868	−	0.981421i	$-0.561454\pi$
$269$	11.9852	−	22.4227i	0.730750	−	1.36714i	0.922618	−	0.385716i	$-0.126046\pi$
$270$	−0.453588	−	1.73098i	−0.0276045	−	0.105344i
$271$	11.3032	+	27.2883i	0.686620	+	1.65765i	0.751482	+	0.659754i	$0.229339\pi$
$271$	11.3032	+	27.2883i	0.686620	+	1.65765i	−0.0648615	+	0.997894i	$0.520661\pi$
$272$	−2.47004	+	16.0198i	−0.149768	+	0.971341i
$273$	−1.84788	+	4.46117i	−0.111839	+	0.270002i
$274$	27.8978	+	3.82962i	1.68537	+	0.231356i
$275$	3.41289	+	11.2508i	0.205805	+	0.678449i
$276$	−5.22261	−	7.46078i	−0.314364	−	0.449086i
$277$	−22.7036	+	2.23611i	−1.36413	+	0.134355i	−0.753440	−	0.657517i	$-0.771607\pi$
$277$	−22.7036	+	2.23611i	−1.36413	+	0.134355i	−0.610687	+	0.791872i	$0.709107\pi$
$278$	−0.239682	+	0.330606i	−0.0143752	+	0.0198284i
$279$	−6.88818	+	4.60254i	−0.412385	+	0.275547i
$280$	−4.51255	−	3.83016i	−0.269677	−	0.228896i
$281$	11.9565	−	17.8941i	0.713263	−	1.06747i	−0.280916	−	0.959732i	$-0.590638\pi$
$281$	11.9565	−	17.8941i	0.713263	−	1.06747i	0.994179	−	0.107741i	$-0.0343618\pi$
$282$	1.50499	−	3.27340i	0.0896211	−	0.194928i
$283$	−2.45574	+	8.09549i	−0.145979	+	0.481227i	−0.999186	−	0.0403452i	$-0.987154\pi$
$283$	−2.45574	+	8.09549i	−0.145979	+	0.481227i	0.853207	+	0.521572i	$0.174654\pi$
$284$	−11.1717	+	3.65524i	−0.662921	+	0.216899i
$285$	−0.218348	+	0.179194i	−0.0129338	+	0.0106145i
$286$	6.24615	+	12.8442i	0.369342	+	0.759494i
$287$	4.31391	−	4.31391i	0.254642	−	0.254642i
$288$	−5.62670	+	0.583294i	−0.331557	+	0.0343709i
$289$	0.409501	+	0.409501i	0.0240883	+	0.0240883i
$290$	−2.98663	+	8.64130i	−0.175381	+	0.507434i
$291$	−7.61911	−	9.28392i	−0.446640	−	0.544233i
$292$	1.38162	−	18.0272i	0.0808531	−	1.05496i
$293$	−25.9749	−	7.87939i	−1.51747	−	0.460319i	−0.581838	−	0.813304i	$-0.697666\pi$
$293$	−25.9749	−	7.87939i	−1.51747	−	0.460319i	−0.935629	+	0.352986i	$0.885166\pi$
$294$	2.09333	+	5.65638i	0.122086	+	0.329887i
$295$	7.82151	+	5.22617i	0.455386	+	0.304279i
$296$	−32.9594	−	3.79833i	−1.91573	−	0.220774i
$297$	−1.92172	−	2.87605i	−0.111509	−	0.166885i
$298$	−5.45572	+	0.869830i	−0.316041	+	0.0503879i
$299$	−1.30313	−	13.2309i	−0.0753620	−	0.765163i
$300$	−5.73285	−	3.65330i	−0.330986	−	0.210923i
$301$	−8.38886	+	2.54473i	−0.483526	+	0.146676i
$302$	8.18873	−	6.21191i	0.471209	−	0.357455i
$303$	−1.01610	−	0.420882i	−0.0583734	−	0.0241790i
$304$	0.454678	+	0.768520i	0.0260776	+	0.0440776i
$305$	3.38142	−	1.40063i	0.193620	−	0.0801999i
$306$	2.89274	−	4.94710i	0.165367	−	0.282807i
$307$	−6.01774	−	3.21655i	−0.343451	−	0.183578i	0.290649	−	0.956830i	$-0.406129\pi$
$307$	−6.01774	−	3.21655i	−0.343451	−	0.183578i	−0.634099	+	0.773252i	$0.718629\pi$
$308$	−10.6629	−	4.14819i	−0.607573	−	0.236365i
$309$	15.0152	+	12.3227i	0.854187	+	0.701013i
$310$	3.44588	−	14.4182i	0.195713	−	0.818897i
$311$	3.46431	−	17.4163i	0.196443	−	0.987586i	−0.749191	−	0.662354i	$-0.769558\pi$
$311$	3.46431	−	17.4163i	0.196443	−	0.987586i	0.945634	−	0.325232i	$-0.105442\pi$
$312$	−7.57614	−	3.28617i	−0.428914	−	0.186043i
$313$	−13.2953	+	2.64461i	−0.751496	+	0.149482i	−0.555954	−	0.831213i	$-0.687647\pi$
$313$	−13.2953	+	2.64461i	−0.751496	+	0.149482i	−0.195543	+	0.980695i	$0.562647\pi$
$314$	15.9354	−	14.7608i	0.899285	−	0.833001i
$315$	0.986466	+	1.84555i	0.0555810	+	0.103985i
$316$	−6.01238	+	3.38329i	−0.338223	+	0.190325i
$317$	−1.38041	−	0.135959i	−0.0775316	−	0.00763619i	0.0591770	−	0.998248i	$-0.481152\pi$
$317$	−1.38041	−	0.135959i	−0.0775316	−	0.00763619i	−0.136709	+	0.990611i	$0.543652\pi$
$318$	3.02956	−	3.41632i	0.169890	−	0.191578i
$319$			17.6733i			0.989517i
$320$	6.67728	−	7.60785i	0.373271	−	0.425292i
$321$		−	7.63427i		−	0.426103i
$322$	7.96841	+	7.06631i	0.444062	+	0.393790i
$323$	−0.900259	−	0.0886678i	−0.0500918	−	0.00493361i
$324$	1.92602	+	0.538936i	0.107001	+	0.0299409i
$325$	−4.67812	−	8.75215i	−0.259496	−	0.485482i
$326$	6.71585	+	7.25025i	0.371956	+	0.401554i
$327$	9.39016	−	1.86782i	0.519277	−	0.103291i
$328$	7.25448	+	7.49885i	0.400562	+	0.414055i
$329$	−0.821972	+	4.13233i	−0.0453168	+	0.227823i
$330$	6.02008	+	1.43877i	0.331395	+	0.0792018i
$331$	−10.2837	−	8.43963i	−0.565244	−	0.463884i	0.307850	−	0.951435i	$-0.400390\pi$
$331$	−10.2837	−	8.43963i	−0.565244	−	0.463884i	−0.873095	+	0.487551i	$0.837890\pi$
$332$	−4.73370	+	2.08212i	−0.259795	+	0.114271i
$333$	10.3450	+	5.52950i	0.566900	+	0.303015i
$334$	−2.82299	−	1.65070i	−0.154467	−	0.0903223i
$335$	−11.5801	+	4.79664i	−0.632689	+	0.262068i
$336$	6.24134	−	2.19300i	0.340493	−	0.119638i
$337$	−32.0205	−	13.2633i	−1.74427	−	0.722499i	−0.998409	−	0.0563925i	$-0.982040\pi$
$337$	−32.0205	−	13.2633i	−1.74427	−	0.722499i	−0.745857	−	0.666106i	$-0.767960\pi$
$338$	3.82518	+	5.04247i	0.208062	+	0.274274i
$339$	−16.2841	+	4.93973i	−0.884431	+	0.268289i
$340$	2.21821	+	10.0120i	0.120299	+	0.542978i
$341$	−2.80873	−	28.5176i	−0.152102	−	1.54431i
$342$	−0.0497064	−	0.311767i	−0.00268782	−	0.0168584i
$343$	−10.3504	−	15.4905i	−0.558870	−	0.836408i
$344$	−4.11382	−	14.4168i	−0.221803	−	0.777301i
$345$	−4.79065	−	3.20101i	−0.257920	−	0.172337i
$346$	13.9816	−	5.17437i	0.751657	−	0.278176i
$347$	13.1383	+	3.98547i	0.705302	+	0.213951i	0.622506	−	0.782615i	$-0.286115\pi$
$347$	13.1383	+	3.98547i	0.705302	+	0.213951i	0.0827966	+	0.996566i	$0.473615\pi$
$348$	−6.65246	−	7.75680i	−0.356609	−	0.415808i
$349$	19.1243	+	23.3030i	1.02370	+	1.24738i	0.968528	+	0.248903i	$0.0800701\pi$
$349$	19.1243	+	23.3030i	1.02370	+	1.24738i	0.0551701	+	0.998477i	$0.482430\pi$
$350$	7.51374	+	2.59692i	0.401626	+	0.138811i
$351$	2.06453	+	2.06453i	0.110197	+	0.110197i
$352$	7.39530	−	18.1157i	0.394171	−	0.965571i
$353$	−20.8702	+	20.8702i	−1.11081	+	1.11081i	−0.117765	+	0.993042i	$0.537573\pi$
$353$	−20.8702	+	20.8702i	−1.11081	+	1.11081i	−0.993042	+	0.117765i	$0.962427\pi$
$354$	−9.45508	+	4.59801i	−0.502532	+	0.244382i
$355$	−5.74856	+	4.71772i	−0.305102	+	0.250391i
$356$	11.9620	+	6.06410i	0.633984	+	0.321397i
$357$	−1.94544	+	6.41327i	−0.102964	+	0.339426i
$358$	−21.6454	−	9.95178i	−1.14399	−	0.525968i
$359$	−7.25713	+	10.8611i	−0.383017	+	0.573225i	−0.972018	−	0.234907i	$-0.924521\pi$
$359$	−7.25713	+	10.8611i	−0.383017	+	0.573225i	0.589001	+	0.808132i	$0.299521\pi$
$360$	−3.18377	+	1.63456i	−0.167800	+	0.0861487i
$361$	15.7565	−	10.5281i	0.829289	−	0.554113i
$362$	−13.2642	−	9.61629i	−0.697153	−	0.505421i
$363$	0.960022	−	0.0945540i	0.0503881	−	0.00496280i
$364$	9.51053	+	1.67827i	0.498487	+	0.0879651i
$365$	−3.32042	−	10.9460i	−0.173799	−	0.572938i
$366$	−0.556329	+	4.05272i	−0.0290798	+	0.211839i
$367$	0.0242433	−	0.0585285i	0.00126549	−	0.00305517i	−0.923246	−	0.384210i	$-0.874474\pi$
$367$	0.0242433	−	0.0585285i	0.00126549	−	0.00305517i	0.924511	+	0.381155i	$0.124474\pi$
$368$	−12.3089	+	13.4256i	−0.641645	+	0.699858i
$369$	−1.41166	−	3.40804i	−0.0734879	−	0.177416i
$370$	−20.3045	+	5.32060i	−1.05558	+	0.276605i
$371$	−2.51719	+	4.70933i	−0.130686	+	0.244496i
$372$	11.9671	+	11.4591i	0.620466	+	0.594125i
$373$	6.36888	−	7.76050i	0.329768	−	0.401824i	−0.581561	−	0.813503i	$-0.697558\pi$
$373$	6.36888	−	7.76050i	0.329768	−	0.401824i	0.911329	+	0.411680i	$0.135058\pi$
$374$	10.3747	+	16.8910i	0.536461	+	0.873415i
$375$	−10.4232	−	2.07329i	−0.538249	−	0.107064i
$376$	−7.04289	−	1.52259i	−0.363210	−	0.0785216i
$377$	−2.91032	−	14.6312i	−0.149889	−	0.753544i
$378$	−2.33719	−	0.0894307i	−0.120212	−	0.00459982i
$379$	−14.9318	+	7.98124i	−0.766998	+	0.409969i	−0.807994	−	0.589191i	$-0.799447\pi$
$379$	−14.9318	+	7.98124i	−0.766998	+	0.409969i	0.0409966	+	0.999159i	$0.486947\pi$
$380$	0.444365	+	0.348835i	0.0227954	+	0.0178949i
$381$	−1.25904	+	12.7832i	−0.0645026	+	0.654905i
$382$	−1.39324	−	23.2203i	−0.0712846	−	1.18806i
$383$	−22.3931			−1.14423			−0.572117	−	0.820172i	$-0.693878\pi$
$383$	−22.3931			−1.14423			−0.572117	+	0.820172i	$0.693878\pi$
$384$	3.57319	+	10.7346i	0.182344	+	0.547799i
$385$	−7.23845			−0.368906
$386$	−0.806783	−	13.4462i	−0.0410642	−	0.684391i
$387$	−0.519546	+	5.27504i	−0.0264100	+	0.268145i
$388$	−14.8321	+	18.8939i	−0.752984	+	0.959190i
$389$	−9.57962	+	5.12041i	−0.485706	+	0.259615i	−0.696025	−	0.718018i	$-0.745050\pi$
$389$	−9.57962	+	5.12041i	−0.485706	+	0.259615i	0.210319	+	0.977633i	$0.432550\pi$
$390$	−5.22075	−	0.199768i	−0.264363	−	0.0101157i
$391$	−3.59984	−	18.0976i	−0.182052	−	0.915236i
$392$	10.1393	−	6.53460i	0.512112	−	0.330047i
$393$	−10.2495	−	2.03876i	−0.517021	−	0.102842i
$394$	−1.77043	−	2.88244i	−0.0891929	−	0.145215i
$395$	−2.76892	+	3.37393i	−0.139319	+	0.169761i
$396$	−4.78455	+	4.99667i	−0.240433	+	0.251092i
$397$	8.11460	−	15.1814i	0.407260	−	0.761930i	−0.591763	−	0.806112i	$-0.701568\pi$
$397$	8.11460	−	15.1814i	0.407260	−	0.761930i	0.999024	+	0.0441815i	$0.0140680\pi$
$398$	2.01844	−	0.528913i	0.101175	−	0.0265120i
$399$	0.141287	+	0.341097i	0.00707319	+	0.0170762i
$400$	−4.65347	+	12.7747i	−0.232674	+	0.638737i
$401$	−9.72203	+	23.4711i	−0.485495	+	1.17209i	0.471469	+	0.881882i	$0.343724\pi$
$401$	−9.72203	+	23.4711i	−0.485495	+	1.17209i	−0.956964	+	0.290206i	$0.906276\pi$
$402$	1.90522	−	13.8791i	0.0950237	−	0.692224i
$403$	7.02133	+	23.1462i	0.349757	+	1.15300i
$404$	−0.382251	+	2.16617i	−0.0190177	+	0.107771i
$405$	1.25922	−	0.124023i	0.0625713	−	0.00616273i
$406$	9.67521	+	7.01432i	0.480172	+	0.348115i
$407$	−33.7362	+	22.5418i	−1.67224	+	1.11735i
$408$	−10.9114	−	3.50830i	−0.540195	−	0.173687i
$409$	4.94278	−	7.39739i	0.244405	−	0.365777i	−0.688904	−	0.724853i	$-0.741908\pi$
$409$	4.94278	−	7.39739i	0.244405	−	0.365777i	0.933309	+	0.359075i	$0.116908\pi$
$410$	5.99739	+	2.75739i	0.296190	+	0.136178i
$411$	−5.78007	+	19.0543i	−0.285110	+	0.939881i
$412$	17.5660	−	34.6505i	0.865415	−	1.70711i
$413$	9.50445	−	7.80010i	0.467684	−	0.383818i
$414$	5.79121	−	2.81627i	0.284622	−	0.138412i
$415$	−2.31345	+	2.31345i	−0.113563	+	0.113563i
$416$	−3.13916	+	16.2152i	−0.153910	+	0.795016i
$417$	−0.204174	−	0.204174i	−0.00999842	−	0.00999842i
$418$	1.03211	+	0.356722i	0.0504824	+	0.0174478i
$419$	−22.8993	−	27.9029i	−1.11870	−	1.36315i	−0.924049	−	0.382274i	$-0.875141\pi$
$419$	−22.8993	−	27.9029i	−1.11870	−	1.36315i	−0.194656	−	0.980872i	$-0.562359\pi$
$420$	3.17694	−	2.72464i	0.155019	−	0.132949i
$421$	−20.4745	−	6.21087i	−0.997867	−	0.302700i	−0.251227	−	0.967928i	$-0.580834\pi$
$421$	−20.4745	−	6.21087i	−0.997867	−	0.302700i	−0.746640	+	0.665229i	$0.768334\pi$
$422$	27.2136	−	10.0713i	1.32474	−	0.490264i
$423$	2.11822	+	1.41535i	0.102991	+	0.0688167i
$424$	−7.98153	−	4.43771i	−0.387617	−	0.215514i
$425$	−7.65218	−	11.4523i	−0.371185	−	0.555518i
$426$	−1.30864	−	8.20803i	−0.0634040	−	0.397680i
$427$	−0.468904	−	4.76086i	−0.0226918	−	0.230394i
$428$	−14.9070	+	3.30273i	−0.720559	+	0.159644i
$429$	−9.66434	+	2.93164i	−0.466599	+	0.141541i
$430$	−5.73245	−	7.55669i	−0.276443	−	0.364416i
$431$	19.0851	+	7.90530i	0.919297	+	0.380785i	0.791608	−	0.611029i	$-0.209244\pi$
$431$	19.0851	+	7.90530i	0.919297	+	0.380785i	0.127689	+	0.991814i	$0.459244\pi$
$432$	0.219121	−	3.99399i	0.0105424	−	0.192161i
$433$	−12.4506	+	5.15720i	−0.598337	+	0.247839i	−0.661233	−	0.750181i	$-0.729966\pi$
$433$	−12.4506	+	5.15720i	−0.598337	+	0.247839i	0.0628960	+	0.998020i	$0.479966\pi$
$434$	−16.7266	−	9.78062i	−0.802902	−	0.469485i
$435$	−5.70160	−	3.04757i	−0.273371	−	0.146120i
$436$	−7.70957	−	17.5276i	−0.369221	−	0.839422i
$437$	−0.785779	−	0.644872i	−0.0375889	−	0.0308484i
$438$	12.4344	+	2.97176i	0.594137	+	0.141996i
$439$	−0.708069	+	3.55971i	−0.0337943	+	0.169895i	−0.993997	−	0.109409i	$-0.965104\pi$
$439$	−0.708069	+	3.55971i	−0.0337943	+	0.169895i	0.960202	+	0.279305i	$0.0901040\pi$
$440$	0.205015	−	12.3775i	0.00977373	−	0.590076i
$441$	−4.18283	+	0.832016i	−0.199182	+	0.0396198i
$442$	−11.3703	−	12.2751i	−0.540831	−	0.583867i
$443$	−1.91485	−	3.58243i	−0.0909772	−	0.170206i	0.832317	−	0.554300i	$-0.187014\pi$
$443$	−1.91485	−	3.58243i	−0.0909772	−	0.170206i	−0.923294	+	0.384094i	$0.874514\pi$
$444$	6.32174	−	22.5922i	0.300016	−	1.07218i
$445$	8.44389	+	0.831651i	0.400279	+	0.0394240i
$446$	1.34495	+	1.19269i	0.0636851	+	0.0564754i
$447$		−	3.90650i		−	0.184771i
$448$	−6.98228	−	11.2384i	−0.329882	−	0.530965i
$449$		−	30.7144i		−	1.44950i	−0.689010	−	0.724752i	$-0.741954\pi$
$449$		−	30.7144i		−	1.44950i	0.689010	−	0.724752i	$-0.258046\pi$
$450$	3.18930	−	3.59645i	0.150345	−	0.169538i
$451$	12.6982	+	1.25067i	0.597937	+	0.0588916i
$452$	16.6904	+	29.6601i	0.785049	+	1.39509i
$453$	3.42604	+	6.40967i	0.160969	+	0.301152i
$454$	−18.9826	+	17.5834i	−0.890897	+	0.825230i
$455$	5.99247	−	1.19198i	0.280932	−	0.0558808i
$456$	−0.587268	+	0.231936i	−0.0275013	+	0.0108614i
$457$	−5.80102	+	29.1637i	−0.271360	+	1.36422i	0.569065	+	0.822292i	$0.307305\pi$
$457$	−5.80102	+	29.1637i	−0.271360	+	1.36422i	−0.840425	+	0.541927i	$0.817695\pi$
$458$	−4.94487	+	20.6902i	−0.231059	+	0.966790i
$459$	3.13245	+	2.57073i	0.146210	+	0.119991i
$460$	−4.17792	+	10.7393i	−0.194797	+	0.500721i
$461$	9.09765	+	4.86280i	0.423720	+	0.226483i	0.669453	−	0.742855i	$-0.266529\pi$
$461$	9.09765	+	4.86280i	0.423720	+	0.226483i	−0.245733	+	0.969338i	$0.579029\pi$
$462$	4.08374	−	6.98392i	0.189993	−	0.324921i
$463$	−28.6354	+	11.8612i	−1.33080	+	0.551236i	−0.930884	−	0.365315i	$-0.880961\pi$
$463$	−28.6354	+	11.8612i	−1.33080	+	0.551236i	−0.399917	+	0.916551i	$0.630961\pi$
$464$	−12.2683	+	16.3457i	−0.569542	+	0.758828i
$465$	9.68440	+	4.01141i	0.449103	+	0.186025i
$466$	16.2506	−	12.3276i	0.752795	−	0.571065i
$467$	34.1423	−	10.3570i	1.57992	−	0.479263i	0.626124	−	0.779723i	$-0.284640\pi$
$467$	34.1423	−	10.3570i	1.57992	−	0.479263i	0.953794	+	0.300460i	$0.0971403\pi$
$468$	3.13815	−	4.92447i	0.145061	−	0.227634i
$469$	1.60582	+	16.3042i	0.0741499	+	0.752857i
$470$	−4.50182	+	0.717746i	−0.207653	+	0.0331072i
$471$	8.53318	+	12.7708i	0.393188	+	0.588448i
$472$	13.0688	+	16.4733i	0.601539	+	0.758244i
$473$	−15.2447	−	10.1862i	−0.700951	−	0.468361i
$474$	−1.69315	−	4.57503i	−0.0777687	−	0.210138i
$475$	−0.726104	−	0.220261i	−0.0333159	−	0.0101063i
$476$	13.3645	+	1.02427i	0.612561	+	0.0469471i
$477$	2.04829	+	2.49585i	0.0937848	+	0.114277i
$478$	−7.48746	+	21.6637i	−0.342468	+	0.990873i
$479$	16.1665	+	16.1665i	0.738668	+	0.738668i	0.972320	−	0.233653i	$-0.0750678\pi$
$479$	16.1665	+	16.1665i	0.738668	+	0.738668i	−0.233653	+	0.972320i	$0.575068\pi$
$480$	4.56908	+	5.50965i	0.208549	+	0.251480i
$481$	24.2170	−	24.2170i	1.10420	−	1.10420i
$482$	3.33427	+	6.85640i	0.151872	+	0.312300i
$483$	−5.82145	+	4.77754i	−0.264885	+	0.217386i
$484$	−0.599955	−	1.83368i	−0.0272707	−	0.0833492i
$485$	−4.41132	+	14.5422i	−0.200308	+	0.660326i
$486$	−0.590758	+	1.28491i	−0.0267973	+	0.0582849i
$487$	21.8231	−	32.6606i	0.988901	−	1.47999i	0.115312	−	0.993329i	$-0.463213\pi$
$487$	21.8231	−	32.6606i	0.988901	−	1.47999i	0.873589	−	0.486665i	$-0.161787\pi$
$488$	8.15422	−	0.666970i	0.369124	−	0.0301923i
$489$	−5.81044	+	3.88241i	−0.262757	+	0.175569i
$490$	4.47936	−	6.17861i	0.202357	−	0.279121i
$491$	−15.5222	+	1.52880i	−0.700507	+	0.0689939i	−0.441999	−	0.897015i	$-0.645731\pi$
$491$	−15.5222	+	1.52880i	−0.700507	+	0.0689939i	−0.258508	+	0.966009i	$0.583231\pi$
$492$	−6.04400	+	4.23086i	−0.272485	+	0.190742i
$493$	−6.01022	−	19.8131i	−0.270687	−	0.892335i
$494$	−0.913196	−	0.125357i	−0.0410866	−	0.00564008i
$495$	−1.67490	+	4.04357i	−0.0752812	+	0.181745i
$496$	17.1983	−	28.3250i	0.772228	−	1.27183i
$497$	3.71972	+	8.98021i	0.166852	+	0.402817i
$498$	−0.926913	−	3.53729i	−0.0415360	−	0.158510i
$499$	13.3816	−	25.0351i	0.599041	−	1.12073i	−0.381492	−	0.924372i	$-0.624590\pi$
$499$	13.3816	−	25.0351i	0.599041	−	1.12073i	0.980533	−	0.196354i	$-0.0629103\pi$
$500$	0.460843	+	21.2497i	0.0206095	+	0.950316i
$501$	1.46695	−	1.78748i	0.0655385	−	0.0798589i
$502$	37.9163	−	23.2886i	1.69229	−	1.03942i
$503$	−36.7559	−	7.31120i	−1.63886	−	0.325990i	−0.712227	−	0.701949i	$-0.752313\pi$
$503$	−36.7559	−	7.31120i	−1.63886	−	0.325990i	−0.926636	+	0.375959i	$0.877313\pi$
$504$	0.836486	+	4.60240i	0.0372601	+	0.205007i
$505$	0.271491	+	1.36488i	0.0120812	+	0.0607362i
$506$	−0.851706	+	22.2585i	−0.0378630	+	0.989513i
$507$	−3.94696	+	2.10969i	−0.175290	+	0.0936947i
$508$	25.5059	−	3.07182i	1.13164	−	0.136290i
$509$	−1.07355	+	10.9000i	−0.0475845	+	0.483133i	0.941629	+	0.336652i	$0.109295\pi$
$509$	−1.07355	+	10.9000i	−0.0475845	+	0.483133i	−0.989213	+	0.146481i	$0.953205\pi$
$510$	−7.23822	+	0.434301i	−0.320514	+	0.0192312i
$511$	−14.9509			−0.661388
$512$	19.4151	−	11.6212i	0.858036	−	0.513589i
$513$	0.223237			0.00985615
$514$	32.8254	−	1.96956i	1.44787	−	0.0868735i
$515$	2.40906	−	24.4596i	0.106156	−	1.07782i
$516$	10.5251	−	1.26759i	0.463340	−	0.0558027i
$517$	−7.77151	+	4.15396i	−0.341790	+	0.182691i
$518$	−1.04902	+	27.4153i	−0.0460915	+	1.20456i
$519$	2.05661	+	10.3393i	0.0902750	+	0.453843i
$520$	1.86852	+	10.2807i	0.0819401	+	0.450839i
$521$	14.6877	+	2.92156i	0.643479	+	0.127996i	0.506034	−	0.862513i	$-0.331111\pi$
$521$	14.6877	+	2.92156i	0.643479	+	0.127996i	0.137445	+	0.990509i	$0.456111\pi$
$522$	6.15710	−	3.78176i	0.269489	−	0.165523i
$523$	23.0637	−	28.1032i	1.00850	−	1.22887i	0.0351912	−	0.999381i	$-0.488796\pi$
$523$	23.0637	−	28.1032i	1.00850	−	1.22887i	0.973312	−	0.229484i	$-0.0737040\pi$
$524$	0.453167	+	20.8958i	0.0197967	+	0.912837i
$525$	−2.64991	+	4.95763i	−0.115652	+	0.216369i
$526$	2.52474	+	9.63490i	0.110084	+	0.420102i
$527$	12.8468	+	31.0150i	0.559617	+	1.35104i
$528$	11.8266	+	7.18089i	0.514689	+	0.312508i
$529$	−0.866884	+	2.09284i	−0.0376906	+	0.0909932i
$530$	−5.72391	−	0.785739i	−0.248631	−	0.0341303i
$531$	−2.15809	−	7.11427i	−0.0936531	−	0.308733i
$532$	0.604919	−	0.423449i	0.0262266	−	0.0183588i
$533$	−10.7184	+	1.05567i	−0.464266	+	0.0457262i
$534$	−5.56623	+	7.67778i	−0.240874	+	0.332250i
$535$	−8.03179	+	5.36667i	−0.347245	+	0.232022i
$536$	−27.9252	+	2.28412i	−1.20618	+	0.0986591i
$537$	9.35901	−	14.0068i	0.403871	−	0.604436i
$538$	15.0199	−	32.6687i	0.647556	−	1.40845i
$539$	4.28224	−	14.1166i	0.184449	−	0.608047i
$540$	−0.786937	−	2.40517i	−0.0338644	−	0.103502i
$541$	27.8725	−	22.8744i	1.19833	−	0.983446i	0.198338	−	0.980134i	$-0.436446\pi$
$541$	27.8725	−	22.8744i	1.19833	−	0.983446i	0.999995	−	0.00331236i	$-0.00105436\pi$
$542$	18.2678	+	37.5648i	0.784670	+	1.61355i
$543$	8.19166	−	8.19166i	0.351538	−	0.351538i
$544$	−2.12999	+	22.8239i	−0.0913225	+	0.978567i
$545$	−8.56610	−	8.56610i	−0.366931	−	0.366931i
$546$	−2.23073	+	6.45424i	−0.0954665	+	0.276216i
$547$	12.9121	+	15.7335i	0.552082	+	0.672714i	0.972036	−	0.234831i	$-0.0754538\pi$
$547$	12.9121	+	15.7335i	0.552082	+	0.672714i	−0.419954	+	0.907545i	$0.637954\pi$
$548$	39.7070	+	3.04317i	1.69620	+	0.129998i
$549$	−2.76803	−	0.839671i	−0.118136	−	0.0358363i
$550$	5.77086	+	15.5934i	0.246070	+	0.664904i
$551$	−0.948376	−	0.633684i	−0.0404022	−	0.0269959i
$552$	−8.00457	−	10.0898i	−0.340697	−	0.429451i
$553$	3.16948	+	4.74346i	0.134780	+	0.201712i
$554$	−31.8607	+	5.07970i	−1.35363	+	0.215816i
$555$	−1.45479	−	14.7707i	−0.0617523	−	0.626982i
$556$	−0.310350	+	0.487009i	−0.0131618	+	0.0206538i
$557$	−7.41891	+	2.25050i	−0.314349	+	0.0953568i	−0.443517	−	0.896266i	$-0.646269\pi$
$557$	−7.41891	+	2.25050i	−0.314349	+	0.0953568i	0.129168	+	0.991623i	$0.458769\pi$
$558$	−9.33403	+	7.08073i	−0.395141	+	0.299751i
$559$	14.2980	+	5.92241i	0.604739	+	0.250491i
$560$	−6.69468	−	5.02472i	−0.282902	−	0.212333i
$561$	−12.9498	+	5.36399i	−0.546742	+	0.226468i
$562$	15.3630	−	26.2734i	0.648048	−	1.10828i
$563$	25.4595	+	13.6084i	1.07299	+	0.573526i	0.910637	−	0.413207i	$-0.135591\pi$
$563$	25.4595	+	13.6084i	1.07299	+	0.573526i	0.162354	+	0.986733i	$0.448091\pi$
$564$	1.84730	−	4.74845i	0.0777853	−	0.199946i
$565$	16.6442	+	13.6595i	0.700227	+	0.574662i
$566$	−2.78100	+	11.6362i	−0.116894	+	0.489106i
$567$	0.322650	−	1.62207i	0.0135500	−	0.0681207i
$568$	−15.4613	+	6.10628i	−0.648740	+	0.256214i
$569$	−10.7368	+	2.13568i	−0.450110	+	0.0895324i	−0.414940	−	0.909849i	$-0.636197\pi$
$569$	−10.7368	+	2.13568i	−0.450110	+	0.0895324i	−0.0351701	+	0.999381i	$0.511197\pi$
$570$	−0.293059	+	0.271458i	−0.0122749	+	0.0113701i
$571$	−7.17860	−	13.4302i	−0.300415	−	0.562037i	0.685743	−	0.727843i	$-0.259477\pi$
$571$	−7.17860	−	13.4302i	−0.300415	−	0.562037i	−0.986158	+	0.165807i	$0.946977\pi$
$572$	9.90545	+	17.6028i	0.414168	+	0.736009i
$573$	16.3696	+	1.61226i	0.683849	+	0.0673533i
$574$	5.72444	−	6.45523i	0.238934	−	0.269436i
$575$		−	15.4774i		−	0.645451i
$576$	−7.89367	+	1.30001i	−0.328903	+	0.0541673i
$577$		−	20.4928i		−	0.853126i	−0.904458	−	0.426563i	$-0.859724\pi$
$577$		−	20.4928i		−	0.853126i	0.904458	−	0.426563i	$-0.140276\pi$
$578$	0.612768	+	0.543397i	0.0254878	+	0.0226023i
$579$	9.47910	+	0.933610i	0.393938	+	0.0387995i
$580$	−3.48421	+	12.4517i	−0.144674	+	0.517028i
$581$	2.01585	+	3.77140i	0.0836317	+	0.156464i
$582$	−11.5421	−	12.4605i	−0.478434	−	0.516505i
$583$	−10.9536	+	2.17881i	−0.453652	+	0.0902370i
$584$	0.423456	−	25.5656i	0.0175227	−	1.05791i
$585$	0.720728	−	3.62334i	0.0297984	−	0.149807i
$586$	−37.3354	−	8.92301i	−1.54231	−	0.368606i
$587$	19.7249	+	16.1878i	0.814134	+	0.668143i	0.946373	−	0.323075i	$-0.104717\pi$
$587$	19.7249	+	16.1878i	0.814134	+	0.668143i	−0.132239	+	0.991218i	$0.542217\pi$
$588$	3.43421	+	7.80765i	0.141624	+	0.321982i
$589$	1.63100	+	0.871788i	0.0672042	+	0.0359214i
$590$	11.4841	+	6.71515i	0.472793	+	0.276458i
$591$	2.20988	−	0.915361i	0.0909022	−	0.0376529i
$592$	−46.8496	−	2.57029i	−1.92551	−	0.105638i
$593$	24.3845	+	10.1004i	1.00135	+	0.414774i	0.822293	−	0.569064i	$-0.192695\pi$
$593$	24.3845	+	10.1004i	1.00135	+	0.414774i	0.179060	+	0.983838i	$0.442695\pi$
$594$	−2.95645	−	3.89728i	−0.121304	−	0.159907i
$595$	8.11481	−	2.46160i	0.332675	−	0.100916i
$596$	−7.62802	+	1.69003i	−0.312456	+	0.0692262i
$597$	0.144618	+	1.46834i	0.00591884	+	0.0600950i
$598$	−2.96028	−	18.5674i	−0.121055	−	0.759276i
$599$	11.8047	+	17.6669i	0.482325	+	0.721851i	0.990212	−	0.139573i	$-0.0445730\pi$
$599$	11.8047	+	17.6669i	0.482325	+	0.721851i	−0.507886	+	0.861424i	$0.669573\pi$
$600$	−8.40236	−	4.67169i	−0.343025	−	0.190721i
$601$	33.8025	+	22.5861i	1.37883	+	0.921306i	0.999991	−	0.00415558i	$-0.00132277\pi$
$601$	33.8025	+	22.5861i	1.37883	+	0.921306i	0.378841	+	0.925462i	$0.376323\pi$
$602$	−11.6268	+	4.30289i	−0.473873	+	0.175373i
$603$	9.47946	+	2.87556i	0.386033	+	0.117102i
$604$	11.0337	−	9.46280i	0.448953	−	0.385036i
$605$	−0.774346	−	0.943544i	−0.0314816	−	0.0383605i
$606$	−1.47005	−	0.508083i	−0.0597168	−	0.0206395i
$607$	5.55278	+	5.55278i	0.225380	+	0.225380i	0.810760	−	0.585379i	$-0.199054\pi$
$607$	5.55278	+	5.55278i	0.225380	+	0.225380i	−0.585379	+	0.810760i	$0.699054\pi$
$608$	0.706953	+	1.04639i	0.0286707	+	0.0424366i
$609$	−5.97516	+	5.97516i	−0.242126	+	0.242126i
$610$	4.65483	−	2.26365i	0.188469	−	0.0916525i
$611$	5.74973	−	4.71868i	0.232609	−	0.190897i
$612$	3.66458	−	7.22872i	0.148132	−	0.292204i
$613$	−5.17235	+	17.0509i	−0.208909	+	0.688681i	0.788386	+	0.615181i	$0.210917\pi$
$613$	−5.17235	+	17.0509i	−0.208909	+	0.688681i	−0.997295	+	0.0735005i	$0.976583\pi$
$614$	−8.76754	−	4.03101i	−0.353829	−	0.162678i
$615$	−2.59315	+	3.88092i	−0.104566	+	0.156494i
$616$	−15.4039	−	4.95274i	−0.620639	−	0.199551i
$617$	12.1974	−	8.15004i	0.491049	−	0.328108i	−0.285272	−	0.958447i	$-0.592084\pi$
$617$	12.1974	−	8.15004i	0.491049	−	0.328108i	0.776321	+	0.630338i	$0.217084\pi$
$618$	22.2404	+	16.1238i	0.894640	+	0.648595i
$619$	−38.7265	+	3.81422i	−1.55655	+	0.153307i	−0.839361	−	0.543574i	$-0.817071\pi$
$619$	−38.7265	+	3.81422i	−1.55655	+	0.153307i	−0.717187	+	0.696881i	$0.754571\pi$
$620$	3.64322	−	20.6456i	0.146315	−	0.829149i
$621$	1.32182	+	4.35747i	0.0530429	+	0.174859i
$622$	3.41529	−	24.8795i	0.136941	−	0.997578i
$623$	4.24401	−	10.2459i	0.170033	−	0.410495i
$624$	−10.9734	−	3.99729i	−0.439287	−	0.160020i
$625$	−1.35773	−	3.27785i	−0.0543092	−	0.131114i
$626$	−18.5447	+	4.85946i	−0.741194	+	0.194223i
$627$	−0.364001	+	0.680998i	−0.0145368	+	0.0271964i
$628$	21.2453	−	22.1872i	0.847780	−	0.885366i
$629$	30.1547	−	36.7437i	1.20235	−	1.46507i
$630$	1.54889	+	2.52176i	0.0617093	+	0.100469i
$631$	−41.2322	−	8.20159i	−1.64143	−	0.326500i	−0.713897	−	0.700250i	$-0.753072\pi$
$631$	−41.2322	−	8.20159i	−1.64143	−	0.326500i	−0.927529	+	0.373750i	$0.878072\pi$
$632$	−8.20095	+	5.28537i	−0.326216	+	0.210241i
$633$	4.00295	+	20.1242i	0.159103	+	0.799864i
$634$	−1.96021	−	0.0750058i	−0.0778497	−	0.00297886i
$635$	14.3340	−	7.66166i	0.568826	−	0.304044i
$636$	3.98739	−	5.07935i	0.158110	−	0.201409i
$637$	−1.22049	+	12.3919i	−0.0483577	+	0.490984i
$638$	1.49697	+	24.9490i	0.0592655	+	0.987741i
$639$	5.87726			0.232501
$640$	8.78175	−	11.3054i	0.347129	−	0.446885i
$641$	21.6962			0.856950			0.428475	−	0.903554i	$-0.359051\pi$
$641$	21.6962			0.856950			0.428475	+	0.903554i	$0.359051\pi$
$642$	−0.646637	−	10.7771i	−0.0255207	−	0.425338i
$643$	−3.33123	+	33.8225i	−0.131371	+	1.33383i	0.672974	+	0.739666i	$0.265017\pi$
$643$	−3.33123	+	33.8225i	−0.131371	+	1.33383i	−0.804345	+	0.594163i	$0.797483\pi$
$644$	11.8473	+	9.30039i	0.466850	+	0.366487i
$645$	5.91494	−	3.16160i	0.232901	−	0.124488i
$646$	−1.27838	−	0.0489164i	−0.0502973	−	0.00192459i
$647$	1.24790	+	6.27364i	0.0490602	+	0.246642i	0.997531	−	0.0702209i	$-0.0223704\pi$
$647$	1.24790	+	6.27364i	0.0490602	+	0.246642i	−0.948471	+	0.316863i	$0.897370\pi$
$648$	2.76456	+	0.597665i	0.108602	+	0.0234785i
$649$	25.2214	+	5.01685i	0.990027	+	0.196929i
$650$	−7.34531	−	11.9589i	−0.288107	−	0.469068i
$651$	8.69187	−	10.5911i	0.340661	−	0.415097i
$652$	10.0947	+	9.66615i	0.395339	+	0.378556i
$653$	−14.1539	+	26.4802i	−0.553886	+	1.03625i	0.436732	+	0.899592i	$0.356136\pi$
$653$	−14.1539	+	26.4802i	−0.553886	+	1.03625i	−0.990618	+	0.136657i	$0.956364\pi$
$654$	13.0976	−	3.43212i	0.512159	−	0.134206i
$655$	5.06022	+	12.2164i	0.197719	+	0.477336i
$656$	10.8761	+	9.97146i	0.424642	+	0.389320i
$657$	−3.45948	+	8.35191i	−0.134967	+	0.325839i
$658$	−0.810341	+	5.90313i	−0.0315904	+	0.230128i
$659$	−10.2532	−	33.8004i	−0.399409	−	1.31668i	−0.894202	−	0.447664i	$-0.852256\pi$
$659$	−10.2532	−	33.8004i	−0.399409	−	1.31668i	0.494793	−	0.869011i	$-0.335244\pi$
$660$	8.62026	+	1.52117i	0.335543	+	0.0592113i
$661$	20.7313	−	2.04185i	0.806353	−	0.0794189i	0.313563	−	0.949567i	$-0.398477\pi$
$661$	20.7313	−	2.04185i	0.806353	−	0.0794189i	0.492790	+	0.870148i	$0.335977\pi$
$662$	−15.2321	−	11.0430i	−0.592013	−	0.429197i
$663$	9.83742	−	6.57316i	0.382054	−	0.255280i
$664$	−6.50608	+	3.34024i	−0.252485	+	0.129626i
$665$	0.259537	−	0.388425i	0.0100644	−	0.0150625i
$666$	15.0721	+	6.92961i	0.584031	+	0.268517i
$667$	6.75370	−	22.2640i	0.261504	−	0.862064i
$668$	−4.12496	−	2.09114i	−0.159599	−	0.0809086i
$669$	−0.982573	+	0.806377i	−0.0379885	+	0.0311763i
$670$	−15.9411	+	7.75215i	−0.615857	+	0.299492i
$671$	7.07490	−	7.07490i	0.273124	−	0.273124i
$672$	8.62499	−	3.62445i	0.332716	−	0.139816i
$673$	−16.6723	−	16.6723i	−0.642669	−	0.642669i	0.308542	−	0.951211i	$-0.400159\pi$
$673$	−16.6723	−	16.6723i	−0.642669	−	0.642669i	−0.951211	+	0.308542i	$0.900159\pi$
$674$	−46.3259	−	16.0113i	−1.78441	−	0.616732i
$675$	2.15629	+	2.62744i	0.0829956	+	0.101130i
$676$	5.82702	+	6.79433i	0.224116	+	0.261320i
$677$	39.1786	+	11.8847i	1.50576	+	0.456766i	0.932061	−	0.362302i	$-0.118009\pi$
$677$	39.1786	+	11.8847i	1.50576	+	0.456766i	0.573696	+	0.819069i	$0.305509\pi$
$678$	−22.5694	+	8.35258i	−0.866774	+	0.320779i
$679$	16.5154	+	11.0352i	0.633802	+	0.423493i
$680$	3.97943	+	13.9458i	0.152604	+	0.534798i
$681$	−10.1649	−	15.2129i	−0.389521	−	0.582959i
$682$	−6.38051	−	40.0196i	−0.244322	−	1.53243i
$683$	−4.37976	−	44.4684i	−0.167587	−	1.70154i	−0.600113	−	0.799915i	$-0.704878\pi$
$683$	−4.37976	−	44.4684i	−0.167587	−	1.70154i	0.432526	−	0.901621i	$-0.357622\pi$
$684$	−0.0965766	−	0.435903i	−0.00369270	−	0.0166672i
$685$	24.1098	−	7.31361i	0.921186	−	0.279439i
$686$	−15.9235	−	20.9908i	−0.607962	−	0.801434i
$687$	−13.8972	−	5.75641i	−0.530211	−	0.219621i
$688$	−7.02851	−	20.0034i	−0.267959	−	0.762621i
$689$	8.70934	−	3.60753i	0.331799	−	0.137436i
$690$	−7.03397	−	4.11301i	−0.267779	−	0.156580i
$691$	−26.6975	−	14.2701i	−1.01562	−	0.542861i	−0.122402	−	0.992481i	$-0.539060\pi$
$691$	−26.6975	−	14.2701i	−1.01562	−	0.542861i	−0.893220	+	0.449619i	$0.851560\pi$
$692$	19.2992	−	8.48880i	0.733646	−	0.322696i
$693$	4.42214	+	3.62915i	0.167983	+	0.137860i
$694$	18.8846	+	4.51334i	0.716850	+	0.171324i
$695$	−0.0712770	+	0.358334i	−0.00270369	+	0.0135924i
$696$	−10.0481	−	10.3866i	−0.380873	−	0.393703i
$697$	−14.6609	+	2.91624i	−0.555323	+	0.110461i
$698$	28.9711	+	31.2764i	1.09657	+	1.18383i
$699$	6.79901	+	12.7200i	0.257162	+	0.481116i
$700$	10.8269	+	3.02958i	0.409219	+	0.114507i
$701$	−38.7997	−	3.82143i	−1.46544	−	0.144334i	−0.666394	−	0.745599i	$-0.732163\pi$
$701$	−38.7997	−	3.82143i	−1.46544	−	0.144334i	−0.799049	+	0.601266i	$0.794663\pi$
$702$	3.08932	+	2.73958i	0.116599	+	0.103399i
$703$		−	2.61857i		−	0.0987614i
$704$	8.90532	−	26.1999i	0.335632	−	0.987445i
$705$		−	3.22347i		−	0.121403i
$706$	−27.6941	+	31.2296i	−1.04228	+	1.17534i
$707$	1.81018	+	0.178287i	0.0680787	+	0.00670517i
$708$	−12.9580	+	7.29176i	−0.486993	+	0.274041i
$709$	−7.43045	−	13.9014i	−0.279056	−	0.522078i	0.702876	−	0.711313i	$-0.251899\pi$
$709$	−7.43045	−	13.9014i	−0.279056	−	0.522078i	−0.981932	+	0.189235i	$0.939399\pi$
$710$	−7.71549	+	7.14680i	−0.289557	+	0.268215i
$711$	3.38319	−	0.672958i	0.126879	−	0.0252379i
$712$	17.4001	+	7.54733i	0.652095	+	0.282848i
$713$	−7.35941	+	36.9983i	−0.275612	+	1.38560i
$714$	−2.20312	+	9.21823i	−0.0824496	+	0.344984i
$715$	9.87805	+	8.10671i	0.369418	+	0.303174i
$716$	−31.3992	−	12.2153i	−1.17344	−	0.456506i
$717$	−14.2939	−	7.64024i	−0.533815	−	0.285330i
$718$	−9.32475	+	15.9470i	−0.347997	+	0.595136i
$719$	−29.5606	+	12.2444i	−1.10242	+	0.456639i	−0.858322	−	0.513111i	$-0.828493\pi$
$719$	−29.5606	+	12.2444i	−1.10242	+	0.456639i	−0.244101	+	0.969750i	$0.578493\pi$
$720$	−4.35600	+	2.57713i	−0.162339	+	0.0960441i
$721$	−29.6796	−	12.2937i	−1.10533	−	0.457842i
$722$	21.3513	−	16.1969i	0.794612	−	0.602787i
$723$	−5.15895	+	1.56495i	−0.191863	+	0.0582011i
$724$	−19.5393	−	12.4516i	−0.726173	−	0.462759i
$725$	−1.70223	−	17.2830i	−0.0632193	−	0.641876i
$726$	1.34723	−	0.214795i	0.0500004	−	0.00797180i
$727$	11.5959	+	17.3544i	0.430066	+	0.643640i	0.981697	−	0.190449i	$-0.0609943\pi$
$727$	11.5959	+	17.3544i	0.430066	+	0.643640i	−0.551631	+	0.834088i	$0.685994\pi$
$728$	13.5679	+	1.56361i	0.502861	+	0.0579511i
$729$	−0.831470	−	0.555570i	−0.0307952	−	0.0205767i
$730$	−5.61450	−	15.1709i	−0.207802	−	0.561500i
$731$	20.5544	+	6.23511i	0.760232	+	0.230614i
$732$	−0.442082	+	5.76824i	−0.0163398	+	0.213200i
$733$	19.8424	+	24.1780i	0.732894	+	0.893034i	0.997452	−	0.0713355i	$-0.0227261\pi$
$733$	19.8424	+	24.1780i	0.732894	+	0.893034i	−0.264558	+	0.964370i	$0.585226\pi$
$734$	0.0292662	−	0.0846767i	0.00108024	−	0.00312547i
$735$	3.81575	+	3.81575i	0.140746	+	0.140746i
$736$	−16.2390	+	19.9952i	−0.598576	+	0.737032i
$737$	−24.2289	+	24.2289i	−0.892483	+	0.892483i
$738$	−2.28147	−	4.69148i	−0.0839820	−	0.172696i
$739$	23.3990	−	19.2030i	0.860745	−	0.706395i	−0.0966063	−	0.995323i	$-0.530799\pi$
$739$	23.3990	−	19.2030i	0.860745	−	0.706395i	0.957351	+	0.288928i	$0.0932988\pi$
$740$	−28.2127	+	9.23079i	−1.03712	+	0.339331i
$741$	0.189202	−	0.623717i	0.00695053	−	0.0229128i
$742$	−3.15456	+	6.86126i	−0.115808	+	0.251885i
$743$	5.89949	−	8.82921i	0.216431	−	0.323912i	−0.707328	−	0.706885i	$-0.750100\pi$
$743$	5.89949	−	8.82921i	0.216431	−	0.323912i	0.923760	+	0.382973i	$0.125100\pi$
$744$	17.8643	+	15.1628i	0.654936	+	0.555896i
$745$	−4.10992	+	2.74616i	−0.150576	+	0.100611i
$746$	8.33346	−	11.4948i	0.305109	−	0.420853i
$747$	2.57324	−	0.253442i	0.0941498	−	0.00927295i
$748$	16.0763	+	22.9659i	0.587809	+	0.839716i
$749$	3.66512	+	12.0823i	0.133920	+	0.441477i
$750$	−14.8897	−	2.04396i	−0.543696	−	0.0746347i
$751$	5.29408	−	12.7811i	0.193184	−	0.466387i	−0.797373	−	0.603486i	$-0.793778\pi$
$751$	5.29408	−	12.7811i	0.193184	−	0.466387i	0.990557	+	0.137099i	$0.0437779\pi$
$752$	−10.0712	−	1.55286i	−0.367260	−	0.0566268i
$753$	12.0409	+	29.0692i	0.438794	+	1.05934i
$754$	−5.34772	−	20.4079i	−0.194752	−	0.743214i
$755$	4.33502	−	8.11025i	0.157768	−	0.295162i
$756$	−3.30693	+	0.0717173i	−0.120272	+	0.00260833i
$757$	−0.324852	+	0.395833i	−0.0118069	+	0.0143868i	−0.778880	−	0.627172i	$-0.784212\pi$
$757$	−0.324852	+	0.395833i	−0.0118069	+	0.0143868i	0.767074	+	0.641559i	$0.221712\pi$
$758$	−20.4029	+	12.5317i	−0.741066	+	0.455171i
$759$	−15.4480	−	3.07281i	−0.560728	−	0.111536i
$760$	0.656845	+	0.454803i	0.0238263	+	0.0164974i
$761$	−1.88487	−	9.47588i	−0.0683264	−	0.343500i	0.931467	−	0.363826i	$-0.118530\pi$
$761$	−1.88487	−	9.47588i	−0.0683264	−	0.343500i	−0.999793	+	0.0203257i	$0.993530\pi$
$762$	−0.694589	+	18.1524i	−0.0251623	+	0.657593i
$763$	−13.9645	+	7.46418i	−0.505549	+	0.270222i
$764$	−3.93362	−	32.6616i	−0.142313	−	1.18165i
$765$	0.502573	−	5.10271i	0.0181706	−	0.184489i
$766$	−31.6118	+	1.89674i	−1.14218	+	0.0685320i
$767$	−21.7061			−0.783763
$768$	5.95343	+	14.8512i	0.214826	+	0.535895i
$769$	−16.5098			−0.595358			−0.297679	−	0.954666i	$-0.596212\pi$
$769$	−16.5098			−0.595358			−0.297679	+	0.954666i	$0.596212\pi$
$770$	−10.2183	+	0.613111i	−0.368243	+	0.0220950i
$771$	−2.27917	+	23.1408i	−0.0820825	+	0.833397i
$772$	−2.27783	−	18.9133i	−0.0819809	−	0.680703i
$773$	−21.4866	+	11.4848i	−0.772818	+	0.413080i	−0.810150	−	0.586223i	$-0.800614\pi$
$773$	−21.4866	+	11.4848i	−0.772818	+	0.413080i	0.0373314	+	0.999303i	$0.488114\pi$
$774$	−0.286624	+	7.49064i	−0.0103025	+	0.269246i
$775$	5.49341	+	27.6173i	0.197329	+	0.992041i
$776$	−19.3377	+	27.9283i	−0.694183	+	1.00257i
$777$	−19.0270	−	3.78470i	−0.682588	−	0.135775i
$778$	−13.0896	+	8.03977i	−0.469285	+	0.288240i
$779$	−0.522413	+	0.636562i	−0.0187174	+	0.0228072i
$780$	−7.38692	+	0.160200i	−0.264494	+	0.00573609i
$781$	−9.58322	+	17.9289i	−0.342915	+	0.641548i
$782$	−6.61470	−	25.2430i	−0.236541	−	0.902689i
$783$	1.95528	+	4.72045i	0.0698758	+	0.168695i
$784$	13.7599	−	10.0836i	0.491425	−	0.360127i
$785$	7.43722	−	17.9550i	0.265446	−	0.640843i
$786$	−14.6417	−	2.00991i	−0.522253	−	0.0716912i
$787$	−6.71893	−	22.1493i	−0.239504	−	0.789539i	−0.991470	−	0.130337i	$-0.958394\pi$
$787$	−6.71893	−	22.1493i	−0.239504	−	0.789539i	0.751966	−	0.659202i	$-0.229106\pi$
$788$	−2.74342	−	3.91911i	−0.0977302	−	0.139613i
$789$	−7.00901	+	0.690328i	−0.249527	+	0.0245763i
$790$	−3.62303	+	4.99743i	−0.128902	+	0.177801i
$791$	23.4003	−	15.6356i	0.832020	−	0.555938i
$792$	−6.33100	+	7.45894i	−0.224962	+	0.265042i
$793$	−4.69203	+	7.02212i	−0.166619	+	0.249363i
$794$	10.1693	−	22.1185i	0.360895	−	0.784955i
$795$	1.18592	−	3.90946i	0.0420603	−	0.138654i
$796$	2.80458	−	0.917619i	0.0994057	−	0.0325242i
$797$	−6.53412	+	5.36241i	−0.231450	+	0.189946i	−0.742969	−	0.669326i	$-0.766583\pi$
$797$	−6.53412	+	5.36241i	−0.231450	+	0.189946i	0.511519	+	0.859272i	$0.329083\pi$
$798$	0.228343	+	0.469550i	0.00808324	+	0.0166219i
$799$	7.29975	−	7.29975i	0.258247	−	0.258247i
$800$	−5.48714	+	18.4279i	−0.194000	+	0.651526i
$801$	−4.74160	−	4.74160i	−0.167536	−	0.167536i
$802$	−11.7363	+	33.9570i	−0.414423	+	1.19906i
$803$	−19.8372	−	24.1716i	−0.700038	−	0.852999i
$804$	1.51397	−	19.7541i	0.0533935	−	0.696673i
$805$	9.11862	+	2.76610i	0.321389	+	0.0974924i
$806$	11.8724	+	32.0802i	0.418186	+	1.12998i
$807$	21.1400	+	14.1253i	0.744163	+	0.497234i
$808$	−0.356135	+	3.09030i	−0.0125288	+	0.108716i
$809$	15.3186	+	22.9259i	0.538573	+	0.806032i	0.996555	−	0.0829295i	$-0.0264276\pi$
$809$	15.3186	+	22.9259i	0.538573	+	0.806032i	−0.457982	+	0.888961i	$0.651428\pi$
$810$	1.76711	−	0.281738i	0.0620898	−	0.00989927i
$811$	−1.64683	−	16.7206i	−0.0578281	−	0.587139i	−0.979813	−	0.199914i	$-0.935934\pi$
$811$	−1.64683	−	16.7206i	−0.0578281	−	0.587139i	0.921985	−	0.387225i	$-0.126566\pi$
$812$	14.2524	+	9.08243i	0.500160	+	0.318731i
$813$	−28.2648	+	8.57404i	−0.991291	+	0.300705i
$814$	−45.7152	+	34.6792i	−1.60232	+	1.21550i
$815$	8.16915	+	3.38377i	0.286153	+	0.118528i
$816$	−15.7005	−	4.02836i	−0.549628	−	0.141021i
$817$	1.09321	−	0.452822i	0.0382465	−	0.0158422i
$818$	6.35102	−	10.8614i	0.222058	−	0.379759i
$819$	−4.25856	−	2.27625i	−0.148806	−	0.0795386i
$820$	8.69993	+	3.38455i	0.303815	+	0.118194i
$821$	36.0334	+	29.5719i	1.25758	+	1.03207i	0.997793	+	0.0663979i	$0.0211507\pi$
$821$	36.0334	+	29.5719i	1.25758	+	1.03207i	0.259782	+	0.965667i	$0.416349\pi$
$822$	−6.54564	+	27.3881i	−0.228305	+	0.955270i
$823$	5.72730	−	28.7931i	0.199641	−	1.00366i	−0.742857	−	0.669451i	$-0.766530\pi$
$823$	5.72730	−	28.7931i	0.199641	−	1.00366i	0.942498	−	0.334213i	$-0.108470\pi$
$824$	21.8625	−	50.4032i	0.761617	−	1.75588i
$825$	−11.5311	+	2.29369i	−0.401463	+	0.0798559i
$826$	12.7565	−	11.8163i	0.443856	−	0.411140i
$827$	12.6431	+	23.6535i	0.439642	+	0.822513i	0.999983	−	0.00574899i	$-0.00182997\pi$
$827$	12.6431	+	23.6535i	0.439642	+	0.822513i	−0.560341	+	0.828262i	$0.689330\pi$
$828$	7.93676	−	4.46618i	0.275821	−	0.155211i
$829$	8.86383	+	0.873011i	0.307853	+	0.0303209i	0.250764	−	0.968048i	$-0.419318\pi$
$829$	8.86383	+	0.873011i	0.307853	+	0.0303209i	0.0570891	+	0.998369i	$0.481818\pi$
$830$	−3.06988	+	3.46179i	−0.106557	+	0.120161i
$831$		−	22.8135i		−	0.791390i
$832$	−3.05801	+	23.1565i	−0.106017	+	0.802807i
$833$			17.2820i			0.598786i
$834$	−0.305521	−	0.270933i	−0.0105793	−	0.00938164i
$835$	−2.91178	−	0.286786i	−0.100766	−	0.00992463i
$836$	1.48722	+	0.416153i	0.0514367	+	0.0143930i
$837$	−3.90522	−	7.30614i	−0.134984	−	0.252537i
$838$	−34.6898	−	37.4502i	−1.19834	−	1.29370i
$839$	−34.5231	+	6.86707i	−1.19187	+	0.237078i	−0.750883	−	0.660436i	$-0.770372\pi$
$839$	−34.5231	+	6.86707i	−1.19187	+	0.237078i	−0.440987	+	0.897513i	$0.645372\pi$
$840$	4.25403	−	4.11540i	0.146778	−	0.141995i
$841$	−0.564635	+	2.83861i	−0.0194702	+	0.0978831i
$842$	−29.4294	−	7.03350i	−1.01420	−	0.242391i
$843$	16.6360	+	13.6528i	0.572975	+	0.470228i
$844$	37.5637	−	16.5225i	1.29300	−	0.568727i
$845$	4.99414	+	2.66943i	0.171804	+	0.0918310i
$846$	3.11012	+	1.81860i	0.106928	+	0.0625247i
$847$	−1.47397	+	0.610540i	−0.0506463	+	0.0209784i
$848$	−11.6432	−	5.58855i	−0.399829	−	0.191912i
$849$	−7.81580	−	3.23741i	−0.268238	−	0.111108i
$850$	−11.7724	−	15.5188i	−0.403791	−	0.532289i
$851$	51.1132	−	15.5050i	1.75214	−	0.531505i
$852$	−2.54262	−	11.4762i	−0.0871086	−	0.393169i
$853$	3.63306	+	36.8871i	0.124394	+	1.26299i	0.831357	+	0.555739i	$0.187565\pi$
$853$	3.63306	+	36.8871i	0.124394	+	1.26299i	−0.706963	+	0.707250i	$0.749935\pi$
$854$	−1.06519	−	6.68107i	−0.0364502	−	0.228621i
$855$	−0.156929	−	0.234861i	−0.00536686	−	0.00803208i
$856$	−20.7642	+	5.92504i	−0.709704	+	0.202514i
$857$	−45.8152	−	30.6128i	−1.56502	−	1.04571i	−0.970339	−	0.241749i	$-0.922279\pi$
$857$	−45.8152	−	30.6128i	−1.56502	−	1.04571i	−0.594680	−	0.803963i	$-0.702721\pi$
$858$	−13.3946	+	4.95712i	−0.457284	+	0.169233i
$859$	−11.6782	−	3.54254i	−0.398455	−	0.120870i	0.0846964	−	0.996407i	$-0.473008\pi$
$859$	−11.6782	−	3.54254i	−0.398455	−	0.120870i	−0.483152	+	0.875537i	$0.660508\pi$
$860$	−8.73242	−	10.1820i	−0.297773	−	0.347205i
$861$	3.87030	+	4.71597i	0.131899	+	0.160720i
$862$	27.6115	+	9.54317i	0.940453	+	0.325042i
$863$	−35.2711	−	35.2711i	−1.20064	−	1.20064i	−0.973972	−	0.226669i	$-0.927216\pi$
$863$	−35.2711	−	35.2711i	−1.20064	−	1.20064i	−0.226669	−	0.973972i	$-0.572784\pi$
$864$	−0.0289722	−	5.65678i	−0.000985653	−	0.192448i
$865$	9.43190	−	9.43190i	0.320694	−	0.320694i
$866$	−17.1393	+	8.33487i	−0.582418	+	0.283231i
$867$	−0.447668	+	0.367391i	−0.0152036	+	0.0124773i
$868$	−24.4409	−	12.3903i	−0.829580	−	0.420553i
$869$	−3.46359	+	11.4179i	−0.117494	+	0.387327i
$870$	−8.30694	−	3.81924i	−0.281632	−	0.129484i
$871$	16.0685	−	24.0482i	0.544459	−	0.814841i
$872$	−12.3680	−	24.0903i	−0.418834	−	0.815801i
$873$	9.98601	−	6.67244i	0.337975	−	0.225828i
$874$	−1.16389	−	0.843792i	−0.0393690	−	0.0285417i
$875$	17.4914	−	1.72276i	0.591318	−	0.0582398i
$876$	17.8050	+	3.14194i	0.601575	+	0.106156i
$877$	5.07012	+	16.7139i	0.171206	+	0.564390i	0.999988	+	0.00481900i	$0.00153394\pi$
$877$	5.07012	+	16.7139i	0.171206	+	0.564390i	−0.828783	+	0.559571i	$0.810966\pi$
$878$	−0.698050	+	5.08512i	−0.0235580	+	0.171615i
$879$	10.3874	−	25.0775i	0.350359	−	0.845842i
$880$	−0.758987	−	17.4904i	−0.0255855	−	0.589603i
$881$	−9.19240	−	22.1924i	−0.309700	−	0.747681i	−0.999715	−	0.0238861i	$-0.992396\pi$
$881$	−9.19240	−	22.1924i	−0.309700	−	0.747681i	0.690015	−	0.723795i	$-0.257604\pi$
$882$	−5.83432	+	1.52883i	−0.196452	+	0.0514784i
$883$	−14.3348	+	26.8185i	−0.482404	+	0.902514i	0.516526	+	0.856271i	$0.327225\pi$
$883$	−14.3348	+	26.8185i	−0.482404	+	0.902514i	−0.998930	+	0.0462430i	$0.985275\pi$
$884$	−17.0909	−	16.3654i	−0.574830	−	0.550427i
$885$	−5.96764	+	7.27159i	−0.200600	+	0.244432i
$886$	−3.00658	−	4.89503i	−0.101008	−	0.164452i
$887$	15.9848	+	3.17958i	0.536718	+	0.106760i	0.456005	−	0.889977i	$-0.349280\pi$
$887$	15.9848	+	3.17958i	0.536718	+	0.106760i	0.0807138	+	0.996737i	$0.474280\pi$
$888$	7.01063	−	32.4284i	0.235261	−	1.08822i
$889$	−4.14448	−	20.8357i	−0.139001	−	0.698806i
$890$	11.9905	+	0.458806i	0.401922	+	0.0153792i
$891$	3.05056	−	1.63056i	0.102198	−	0.0546258i
$892$	1.99965	+	1.56977i	0.0669533	+	0.0525597i
$893$	0.0557433	−	0.565971i	0.00186538	−	0.0189395i
$894$	−0.330888	−	5.51470i	−0.0110665	−	0.184439i
$895$	−21.3152			−0.712489
$896$	−10.8086	−	15.2736i	−0.361091	−	0.510255i
$897$	13.2949			0.443905
$898$	−2.60157	−	43.3588i	−0.0868156	−	1.44690i
$899$	−4.14886	+	42.1241i	−0.138372	+	1.40492i
$900$	4.19763	−	5.34716i	0.139921	−	0.178239i
$901$	11.5388	−	6.16762i	0.384414	−	0.205473i
$902$	18.0317	+	0.689970i	0.600391	+	0.0229735i
$903$	−1.71023	−	8.59789i	−0.0569128	−	0.286120i
$904$	26.0737	+	40.4567i	0.867197	+	1.34557i
$905$	−14.3767	−	2.85971i	−0.477898	−	0.0950598i
$906$	5.37936	+	8.75817i	0.178717	+	0.290971i
$907$	7.42445	−	9.04672i	0.246525	−	0.300391i	−0.635016	−	0.772499i	$-0.719007\pi$
$907$	7.42445	−	9.04672i	0.246525	−	0.300391i	0.881541	+	0.472107i	$0.156507\pi$
$908$	−25.3079	+	26.4299i	−0.839872	+	0.877108i
$909$	0.518451	−	0.969953i	0.0171959	−	0.0321713i
$910$	8.35846	−	2.19026i	0.277080	−	0.0726064i
$911$	2.19635	+	5.30245i	0.0727682	+	0.175678i	0.956078	−	0.293111i	$-0.0946905\pi$
$911$	2.19635	+	5.30245i	0.0727682	+	0.175678i	−0.883310	+	0.468789i	$0.844691\pi$
$912$	−0.809385	+	0.377160i	−0.0268014	+	0.0124890i
$913$	−3.42268	+	8.26308i	−0.113274	+	0.273468i
$914$	−5.71893	+	41.6610i	−0.189165	+	1.37802i
$915$	1.06245	+	3.50243i	0.0351235	+	0.115787i
$916$	−5.22805	+	29.6267i	−0.172740	+	0.978893i
$917$	17.2001	−	1.69406i	0.567997	−	0.0559429i
$918$	4.63974	+	3.36371i	0.153134	+	0.111019i
$919$	−19.9874	+	13.3551i	−0.659322	+	0.440545i	−0.839699	−	0.543053i	$-0.817268\pi$
$919$	−19.9874	+	13.3551i	−0.659322	+	0.440545i	0.180377	+	0.983598i	$0.442268\pi$
$920$	−4.98823	+	15.5142i	−0.164457	+	0.511490i
$921$	3.79090	−	5.67349i	0.124915	−	0.186948i
$922$	13.2548	+	6.09410i	0.436524	+	0.200698i
$923$	4.98122	−	16.4209i	0.163959	−	0.540500i
$924$	5.17336	−	10.2049i	0.170191	−	0.335717i
$925$	30.8200	−	25.2933i	1.01335	−	0.831639i
$926$	−39.4192	+	19.1696i	−1.29540	+	0.629952i
$927$	−13.7351	+	13.7351i	−0.451120	+	0.451120i
$928$	−15.9344	+	24.1139i	−0.523071	+	0.791578i
$929$	7.23770	+	7.23770i	0.237461	+	0.237461i	0.815798	−	0.578337i	$-0.196298\pi$
$929$	7.23770	+	7.23770i	0.237461	+	0.237461i	−0.578337	+	0.815798i	$0.696298\pi$
$930$	14.0110	+	4.84252i	0.459439	+	0.158792i
$931$	0.603977	+	0.735948i	0.0197946	+	0.0241197i
$932$	21.8964	−	18.7790i	0.717241	−	0.615127i
$933$	16.9928	+	5.15472i	0.556321	+	0.168758i
$934$	47.3206	−	17.5126i	1.54838	−	0.573029i
$935$	14.7467	+	9.85341i	0.482267	+	0.322241i
$936$	4.01294	−	7.21755i	0.131167	−	0.235913i
$937$	−3.86623	−	5.78622i	−0.126304	−	0.189028i	0.762928	−	0.646483i	$-0.223761\pi$
$937$	−3.86623	−	5.78622i	−0.126304	−	0.189028i	−0.889233	+	0.457456i	$0.848761\pi$
$938$	3.64789	+	22.8802i	0.119108	+	0.747064i
$939$	−1.32870	−	13.4905i	−0.0433605	−	0.440247i
$940$	−6.29431	+	1.39454i	−0.205298	+	0.0454848i
$941$	−22.9070	+	6.94875i	−0.746746	+	0.226523i	−0.640650	−	0.767833i	$-0.721335\pi$
$941$	−22.9070	+	6.94875i	−0.746746	+	0.226523i	−0.106096	+	0.994356i	$0.533835\pi$
$942$	13.1278	+	17.3055i	0.427727	+	0.563842i
$943$	−15.5187	−	6.42804i	−0.505357	−	0.209326i
$944$	19.8442	+	22.1480i	0.645872	+	0.720854i
$945$	−1.93335	+	0.800820i	−0.0628919	+	0.0260507i
$946$	−22.3833	−	13.0883i	−0.727745	−	0.425538i
$947$	−10.0779	−	5.38673i	−0.327487	−	0.175045i	0.299457	−	0.954110i	$-0.403194\pi$
$947$	−10.0779	−	5.38673i	−0.327487	−	0.175045i	−0.626944	+	0.779064i	$0.715694\pi$
$948$	−2.77768	−	6.31505i	−0.0902150	−	0.205103i
$949$	20.4029	+	16.7443i	0.662308	+	0.543542i
$950$	−1.04368	−	0.249435i	−0.0338614	−	0.00809273i
$951$	0.270608	−	1.36044i	0.00877506	−	0.0441152i
$952$	18.9531	+	0.313929i	0.614273	+	0.0101745i
$953$	−33.7220	+	6.70771i	−1.09236	+	0.217284i	−0.708221	−	0.705991i	$-0.750502\pi$
$953$	−33.7220	+	6.70771i	−1.09236	+	0.217284i	−0.384140	+	0.923275i	$0.625502\pi$
$954$	3.10292	+	3.34983i	0.100461	+	0.108455i
$955$	−9.81114	−	18.3554i	−0.317481	−	0.593965i
$956$	−8.73490	+	31.2163i	−0.282507	+	1.00961i
$957$	−17.5882	−	1.73229i	−0.568547	−	0.0559970i
$958$	24.1912	+	21.4525i	0.781583	+	0.693100i
$959$		−	32.9310i		−	1.06340i
$960$	6.91673	+	7.39083i	0.223237	+	0.238538i
$961$		−	37.6304i		−	1.21389i
$962$	32.1353	−	36.2378i	1.03608	−	1.16835i
$963$	7.59750	+	0.748289i	0.244826	+	0.0241133i
$964$	5.28766	+	9.39659i	0.170304	+	0.302644i
$965$	−5.68132	−	10.6290i	−0.182888	−	0.342159i
$966$	−7.81332	+	7.23742i	−0.251390	+	0.232860i
$967$	−12.8395	+	2.55394i	−0.412892	+	0.0821293i	−0.397165	−	0.917747i	$-0.630006\pi$
$967$	−12.8395	+	2.55394i	−0.412892	+	0.0821293i	−0.0157264	+	0.999876i	$0.505006\pi$
$968$	−1.00226	−	2.53774i	−0.0322138	−	0.0815662i
$969$	0.176482	−	0.887233i	0.00566941	−	0.0285020i
$970$	−4.99560	+	20.9025i	−0.160399	+	0.671138i
$971$	3.99431	+	3.27804i	0.128183	+	0.105197i	0.696301	−	0.717750i	$-0.254828\pi$
$971$	3.99431	+	3.27804i	0.128183	+	0.105197i	−0.568117	+	0.822948i	$0.692328\pi$
$972$	−0.725124	+	1.86392i	−0.0232584	+	0.0597852i
$973$	0.421154	+	0.225111i	0.0135016	+	0.00721674i
$974$	28.0408	−	47.9546i	0.898484	−	1.53657i
$975$	9.16854	−	3.79774i	0.293628	−	0.121625i
$976$	11.4546	−	1.63222i	0.366653	−	0.0522462i
$977$	−31.0666	−	12.8682i	−0.993908	−	0.411690i	−0.174348	−	0.984684i	$-0.555782\pi$
$977$	−31.0666	−	12.8682i	−0.993908	−	0.411690i	−0.819560	+	0.572994i	$0.805782\pi$
$978$	−7.87360	+	5.97286i	−0.251770	+	0.190991i
$979$	22.1960	−	6.73309i	0.709388	−	0.215191i
$980$	5.80006	−	9.10159i	0.185276	−	0.290740i
$981$	0.938429	+	9.52803i	0.0299617	+	0.304206i
$982$	−21.7828	+	3.47293i	−0.695117	+	0.110826i
$983$	9.49278	+	14.2069i	0.302773	+	0.453131i	0.951392	−	0.307981i	$-0.0996534\pi$
$983$	9.49278	+	14.2069i	0.302773	+	0.453131i	−0.648620	+	0.761113i	$0.724653\pi$
$984$	−8.17380	+	6.48453i	−0.260571	+	0.206719i
$985$	−2.51651	−	1.68148i	−0.0801826	−	0.0535763i
$986$	−10.1627	−	27.4605i	−0.323646	−	0.874521i
$987$	−4.03187	−	1.22305i	−0.128336	−	0.0389302i
$988$	−1.29975	−	0.0996140i	−0.0413507	−	0.00316914i
$989$	15.3119	+	18.6576i	0.486890	+	0.593278i
$990$	−2.02192	+	5.85007i	−0.0642607	+	0.185927i
$991$	−24.1529	−	24.1529i	−0.767242	−	0.767242i	0.210378	−	0.977620i	$-0.432531\pi$
$991$	−24.1529	−	24.1529i	−0.767242	−	0.767242i	−0.977620	+	0.210378i	$0.932531\pi$
$992$	21.8793	−	41.4424i	0.694667	−	1.31580i
$993$	9.40697	−	9.40697i	0.298521	−	0.298521i
$994$	6.01168	+	12.3621i	0.190679	+	0.392101i
$995$	1.44313	−	1.18435i	0.0457503	−	0.0375463i
$996$	−1.60812	−	4.91499i	−0.0509551	−	0.155737i
$997$	−15.7552	+	51.9380i	−0.498973	+	1.64489i	0.239712	+	0.970844i	$0.422947\pi$
$997$	−15.7552	+	51.9380i	−0.498973	+	1.64489i	−0.738685	+	0.674050i	$0.764553\pi$
$998$	16.7699	−	36.4749i	0.530841	−	1.15459i
$999$	−6.51685	+	9.75316i	−0.206184	+	0.308576i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.157.32	✓	512
128.53	even	32	inner	384.2.v.a.181.32	yes	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.32	✓	512	1.1	even	1	trivial
384.2.v.a.181.32	yes	512	128.53	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)

\(f(q)\)	\(=\)	\(q+(1.41167 - 0.0847019i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.98565 - 0.239143i) q^{4} +(1.11591 - 0.596466i) q^{5} +(-0.0540742 + 1.41318i) q^{6} +(-0.322650 - 1.62207i) q^{7} +(2.78284 - 0.505781i) q^{8} +(-0.980785 - 0.195090i) q^{9} +O(q^{10})\)	\(q+(1.41167 - 0.0847019i) q^{2} +(-0.0980171 + 0.995185i) q^{3} +(1.98565 - 0.239143i) q^{4} +(1.11591 - 0.596466i) q^{5} +(-0.0540742 + 1.41318i) q^{6} +(-0.322650 - 1.62207i) q^{7} +(2.78284 - 0.505781i) q^{8} +(-0.980785 - 0.195090i) q^{9} +(1.52478 - 0.936535i) q^{10} +(2.19437 - 2.67384i) q^{11} +(0.0433638 + 1.99953i) q^{12} +(-1.37633 + 2.57494i) q^{13} +(-0.592870 - 2.26251i) q^{14} +(0.484215 + 1.16900i) q^{15} +(3.88562 - 0.949710i) q^{16} +(-1.55074 + 3.74381i) q^{17} +(-1.40107 - 0.192330i) q^{18} +(0.0648022 + 0.213624i) q^{19} +(2.07316 - 1.45123i) q^{20} +(1.64589 - 0.162106i) q^{21} +(2.87125 - 3.96046i) q^{22} +(-3.78613 + 2.52981i) q^{23} +(0.230580 + 2.81901i) q^{24} +(-1.88837 + 2.82615i) q^{25} +(-1.72483 + 3.75155i) q^{26} +(0.290285 - 0.956940i) q^{27} +(-1.02858 - 3.14371i) q^{28} +(-3.94961 + 3.24136i) q^{29} +(0.782571 + 1.60923i) q^{30} +(5.85792 - 5.85792i) q^{31} +(5.40479 - 1.66980i) q^{32} +(2.44588 + 2.44588i) q^{33} +(-1.87203 + 5.41639i) q^{34} +(-1.32756 - 1.61764i) q^{35} +(-1.99415 - 0.152833i) q^{36} +(-11.2249 - 3.40505i) q^{37} +(0.109574 + 0.296079i) q^{38} +(-2.42763 - 1.62209i) q^{39} +(2.80371 - 2.22427i) q^{40} +(2.04941 + 3.06716i) q^{41} +(2.30973 - 0.368251i) q^{42} +(-0.519546 - 5.27504i) q^{43} +(3.71781 - 5.83408i) q^{44} +(-1.21083 + 0.367302i) q^{45} +(-5.13050 + 3.89196i) q^{46} +(-2.35364 - 0.974910i) q^{47} +(0.564279 + 3.96000i) q^{48} +(3.94014 - 1.63206i) q^{49} +(-2.42638 + 4.14955i) q^{50} +(-3.57378 - 1.91023i) q^{51} +(-2.11714 + 5.44207i) q^{52} +(-2.49585 - 2.04829i) q^{53} +(0.328733 - 1.37548i) q^{54} +(0.853857 - 4.29263i) q^{55} +(-1.71830 - 4.35078i) q^{56} +(-0.218947 + 0.0435513i) q^{57} +(-5.30101 + 4.91028i) q^{58} +(3.50455 + 6.55655i) q^{59} +(1.24104 + 2.20543i) q^{60} +(2.87865 + 0.283522i) q^{61} +(7.77330 - 8.76565i) q^{62} +1.65385i q^{63} +(7.48837 - 2.81501i) q^{64} +3.69433i q^{65} +(3.65996 + 3.24562i) q^{66} +(-9.85831 - 0.970958i) q^{67} +(-2.18391 + 7.80474i) q^{68} +(-2.14652 - 4.01586i) q^{69} +(-2.01110 - 2.17113i) q^{70} +(-5.76433 + 1.14660i) q^{71} +(-2.82804 - 0.0468422i) q^{72} +(1.76363 - 8.86634i) q^{73} +(-16.1344 - 3.85604i) q^{74} +(-2.62744 - 2.15629i) q^{75} +(0.179761 + 0.408686i) q^{76} +(-5.04518 - 2.69670i) q^{77} +(-3.56442 - 2.08424i) q^{78} +(-3.18689 + 1.32005i) q^{79} +(3.76953 - 3.37743i) q^{80} +(0.923880 + 0.382683i) q^{81} +(3.15289 + 4.15624i) q^{82} +(-2.47435 + 0.750586i) q^{83} +(3.22939 - 0.715488i) q^{84} +(0.502573 + 5.10271i) q^{85} +(-1.18024 - 7.40263i) q^{86} +(-2.83862 - 4.24830i) q^{87} +(4.75418 - 8.55074i) q^{88} +(5.57553 + 3.72545i) q^{89} +(-1.67819 + 0.621070i) q^{90} +(4.62081 + 1.40171i) q^{91} +(-6.91295 + 5.92875i) q^{92} +(5.25554 + 6.40389i) q^{93} +(-3.40515 - 1.17690i) q^{94} +(0.199733 + 0.199733i) q^{95} +(1.13200 + 5.54243i) q^{96} +(-8.49241 + 8.49241i) q^{97} +(5.42396 - 2.63767i) q^{98} +(-2.67384 + 2.19437i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 512 q+O(q^{10}) \) 512 * q	\( 512 q - 96 q^{50} - 96 q^{52} - 32 q^{54} - 224 q^{56} - 192 q^{60} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 192 q^{70} - 224 q^{74} - 32 q^{76} - 96 q^{78} - 96 q^{80}+O(q^{100}) \) 512 * q - 96 * q^50 - 96 * q^52 - 32 * q^54 - 224 * q^56 - 192 * q^60 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 192 * q^70 - 224 * q^74 - 32 * q^76 - 96 * q^78 - 96 * q^80

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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