LMFDB - Embedded newform 384.2.v.a.181.4

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			181.4
Character	$\chi$	$=$	384.181
Dual form			384.2.v.a.157.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28206 - 0.596933i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(1.28734 + 1.53060i) q^{4} +(-0.434364 - 0.232173i) q^{5} +(-0.468395 + 1.33439i) q^{6} +(-0.519029 + 2.60933i) q^{7} +(-0.736779 - 2.73078i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})$	\(q+(-1.28206 - 0.596933i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(1.28734 + 1.53060i) q^{4} +(-0.434364 - 0.232173i) q^{5} +(-0.468395 + 1.33439i) q^{6} +(-0.519029 + 2.60933i) q^{7} +(-0.736779 - 2.73078i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(0.418289 + 0.556945i) q^{10} +(0.916620 + 1.11690i) q^{11} +(1.39705 - 1.43117i) q^{12} +(1.88580 + 3.52808i) q^{13} +(2.22302 - 3.03549i) q^{14} +(-0.188479 + 0.455030i) q^{15} +(-0.685499 + 3.94082i) q^{16} +(0.865395 + 2.08925i) q^{17} +(1.37388 + 0.335346i) q^{18} +(-0.820463 + 2.70471i) q^{19} +(-0.203811 - 0.963726i) q^{20} +(2.64764 + 0.260770i) q^{21} +(-0.508442 - 1.97910i) q^{22} +(-1.61348 - 1.07809i) q^{23} +(-2.64541 + 1.00089i) q^{24} +(-2.64308 - 3.95565i) q^{25} +(-0.311674 - 5.64889i) q^{26} +(0.290285 + 0.956940i) q^{27} +(-4.66203 + 2.56468i) q^{28} +(6.40700 + 5.25809i) q^{29} +(0.513264 - 0.470865i) q^{30} +(4.65187 + 4.65187i) q^{31} +(3.23126 - 4.64317i) q^{32} +(1.02168 - 1.02168i) q^{33} +(0.137655 - 3.19512i) q^{34} +(0.831264 - 1.01290i) q^{35} +(-1.56121 - 1.25005i) q^{36} +(6.97766 - 2.11665i) q^{37} +(2.66641 - 2.97783i) q^{38} +(3.32625 - 2.22253i) q^{39} +(-0.313982 + 1.35721i) q^{40} +(5.57407 - 8.34219i) q^{41} +(-3.23877 - 1.91479i) q^{42} +(-0.656241 + 6.66293i) q^{43} +(-0.529535 + 2.84082i) q^{44} +(0.471313 + 0.142971i) q^{45} +(1.42502 + 2.34532i) q^{46} +(-7.80396 + 3.23250i) q^{47} +(3.98904 + 0.295930i) q^{48} +(-0.0720787 - 0.0298560i) q^{49} +(1.02732 + 6.64912i) q^{50} +(1.99436 - 1.06601i) q^{51} +(-2.97242 + 7.42825i) q^{52} +(-1.88878 + 1.55008i) q^{53} +(0.199067 - 1.40013i) q^{54} +(-0.138832 - 0.697957i) q^{55} +(7.50793 - 0.505149i) q^{56} +(2.77210 + 0.551405i) q^{57} +(-5.07541 - 10.5657i) q^{58} +(-1.29781 + 2.42803i) q^{59} +(-0.939108 + 0.297292i) q^{60} +(5.00881 - 0.493324i) q^{61} +(-3.18711 - 8.74081i) q^{62} -2.66045i q^{63} +(-6.91431 + 4.02396i) q^{64} -1.97030i q^{65} +(-1.91973 + 0.699979i) q^{66} +(-5.17367 + 0.509562i) q^{67} +(-2.08375 + 4.01416i) q^{68} +(-0.914753 + 1.71138i) q^{69} +(-1.67036 + 0.802384i) q^{70} +(1.15091 + 0.228930i) q^{71} +(1.25537 + 2.53457i) q^{72} +(-1.75052 - 8.80047i) q^{73} +(-10.2093 - 1.45153i) q^{74} +(-3.67754 + 3.01808i) q^{75} +(-5.19605 + 2.22608i) q^{76} +(-3.39013 + 1.81206i) q^{77} +(-5.59114 + 0.863861i) q^{78} +(-0.912975 - 0.378167i) q^{79} +(1.21271 - 1.55260i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-12.1260 + 7.36782i) q^{82} +(-6.02031 - 1.82624i) q^{83} +(3.00929 + 4.38820i) q^{84} +(0.109169 - 1.10842i) q^{85} +(4.81866 - 8.15052i) q^{86} +(4.60477 - 6.89153i) q^{87} +(2.37467 - 3.32600i) q^{88} +(-15.5192 + 10.3696i) q^{89} +(-0.518906 - 0.464639i) q^{90} +(-10.1847 + 3.08950i) q^{91} +(-0.426968 - 3.85747i) q^{92} +(4.17350 - 5.08543i) q^{93} +(11.9347 + 0.514181i) q^{94} +(0.984339 - 0.984339i) q^{95} +(-4.93753 - 2.76059i) q^{96} +(4.43740 + 4.43740i) q^{97} +(0.0745870 + 0.0813032i) q^{98} +(-1.11690 - 0.916620i) 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 $\left(\mathbb{Z}/384\mathbb{Z}\right)^\times$.

$n$	$127$	$133$	$257$
$\chi(n)$	$1$	$e\left(\frac{5}{32}\right)$	$1$

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 $

$2$	−1.28206	−	0.596933i	−0.906551	−	0.422095i
$2$	−1.28206	−	0.596933i	−0.906551	−	0.422095i
$3$	−0.0980171	−	0.995185i	−0.0565902	−	0.574570i
$3$	−0.0980171	−	0.995185i	−0.0565902	−	0.574570i
$4$	1.28734	+	1.53060i	0.643671	+	0.765302i
$5$	−0.434364	−	0.232173i	−0.194254	−	0.103831i	0.371402	−	0.928472i	$-0.378877\pi$
$5$	−0.434364	−	0.232173i	−0.194254	−	0.103831i	−0.565656	+	0.824641i	$0.691377\pi$
$6$	−0.468395	+	1.33439i	−0.191221	+	0.544764i
$7$	−0.519029	+	2.60933i	−0.196174	+	0.986236i	0.749718	+	0.661757i	$0.230189\pi$
$7$	−0.519029	+	2.60933i	−0.196174	+	0.986236i	−0.945893	+	0.324479i	$0.894811\pi$
$8$	−0.736779	−	2.73078i	−0.260491	−	0.965476i
$9$	−0.980785	+	0.195090i	−0.326928	+	0.0650301i
$10$	0.418289	+	0.556945i	0.132274	+	0.176121i
$11$	0.916620	+	1.11690i	0.276371	+	0.336759i	0.892635	−	0.450781i	$-0.148854\pi$
$11$	0.916620	+	1.11690i	0.276371	+	0.336759i	−0.616263	+	0.787540i	$0.711354\pi$
$12$	1.39705	−	1.43117i	0.403294	−	0.413143i
$13$	1.88580	+	3.52808i	0.523026	+	0.978512i	0.995280	+	0.0970497i	$0.0309406\pi$
$13$	1.88580	+	3.52808i	0.523026	+	0.978512i	−0.472254	+	0.881463i	$0.656559\pi$
$14$	2.22302	−	3.03549i	0.594128	−	0.811269i
$15$	−0.188479	+	0.455030i	−0.0486652	+	0.117488i
$16$	−0.685499	+	3.94082i	−0.171375	+	0.985206i
$17$	0.865395	+	2.08925i	0.209889	+	0.506717i	0.993405	−	0.114654i	$-0.0365759\pi$
$17$	0.865395	+	2.08925i	0.209889	+	0.506717i	−0.783516	+	0.621371i	$0.786576\pi$
$18$	1.37388	+	0.335346i	0.323826	+	0.0790418i
$19$	−0.820463	+	2.70471i	−0.188227	+	0.620502i	0.811137	+	0.584856i	$0.198849\pi$
$19$	−0.820463	+	2.70471i	−0.188227	+	0.620502i	−0.999364	+	0.0356461i	$0.988651\pi$
$20$	−0.203811	−	0.963726i	−0.0455736	−	0.215496i
$21$	2.64764	+	0.260770i	0.577763	+	0.0569047i
$22$	−0.508442	−	1.97910i	−0.108400	−	0.421945i
$23$	−1.61348	−	1.07809i	−0.336434	−	0.224798i	0.375865	−	0.926675i	$-0.377346\pi$
$23$	−1.61348	−	1.07809i	−0.336434	−	0.224798i	−0.712298	+	0.701877i	$0.752346\pi$
$24$	−2.64541	+	1.00089i	−0.539993	+	0.204307i
$25$	−2.64308	−	3.95565i	−0.528617	−	0.791131i
$26$	−0.311674	−	5.64889i	−0.0611243	−	1.10784i
$27$	0.290285	+	0.956940i	0.0558653	+	0.184163i
$28$	−4.66203	+	2.56468i	−0.881040	+	0.484679i
$29$	6.40700	+	5.25809i	1.18975	+	0.976402i	0.999985	−	0.00542747i	$-0.00172763\pi$
$29$	6.40700	+	5.25809i	1.18975	+	0.976402i	0.189764	+	0.981830i	$0.439228\pi$
$30$	0.513264	−	0.470865i	0.0937087	−	0.0859677i
$31$	4.65187	+	4.65187i	0.835500	+	0.835500i	0.988263	−	0.152763i	$-0.0488171\pi$
$31$	4.65187	+	4.65187i	0.835500	+	0.835500i	−0.152763	+	0.988263i	$0.548817\pi$
$32$	3.23126	−	4.64317i	0.571211	−	0.820803i
$33$	1.02168	−	1.02168i	0.177852	−	0.177852i
$34$	0.137655	−	3.19512i	0.0236076	−	0.547958i
$35$	0.831264	−	1.01290i	0.140509	−	0.171211i
$36$	−1.56121	−	1.25005i	−0.260202	−	0.208341i
$37$	6.97766	−	2.11665i	1.14712	−	0.347975i	0.341195	−	0.939992i	$-0.389168\pi$
$37$	6.97766	−	2.11665i	1.14712	−	0.347975i	0.805925	+	0.592017i	$0.201668\pi$
$38$	2.66641	−	2.97783i	0.432549	−	0.483067i
$39$	3.32625	−	2.22253i	0.532626	−	0.355889i
$40$	−0.313982	+	1.35721i	−0.0496449	+	0.214594i
$41$	5.57407	−	8.34219i	0.870524	−	1.30283i	−0.0814577	−	0.996677i	$-0.525958\pi$
$41$	5.57407	−	8.34219i	0.870524	−	1.30283i	0.951982	−	0.306155i	$-0.0990424\pi$
$42$	−3.23877	−	1.91479i	−0.499753	−	0.295458i
$43$	−0.656241	+	6.66293i	−0.100076	+	1.01609i	0.805698	+	0.592326i	$0.201790\pi$
$43$	−0.656241	+	6.66293i	−0.100076	+	1.01609i	−0.905774	+	0.423761i	$0.860710\pi$
$44$	−0.529535	+	2.84082i	−0.0798304	+	0.428270i
$45$	0.471313	+	0.142971i	0.0702592	+	0.0213129i
$46$	1.42502	+	2.34532i	0.210108	+	0.345798i
$47$	−7.80396	+	3.23250i	−1.13832	+	0.471509i	−0.870602	−	0.491987i	$-0.836271\pi$
$47$	−7.80396	+	3.23250i	−1.13832	+	0.471509i	−0.267722	+	0.963496i	$0.586271\pi$
$48$	3.98904	+	0.295930i	0.575768	+	0.0427138i
$49$	−0.0720787	−	0.0298560i	−0.0102970	−	0.00426514i
$50$	1.02732	+	6.64912i	0.145286	+	0.940327i
$51$	1.99436	−	1.06601i	0.279267	−	0.149271i
$52$	−2.97242	+	7.42825i	−0.412201	+	1.03011i
$53$	−1.88878	+	1.55008i	−0.259444	+	0.212920i	−0.755119	−	0.655588i	$-0.772421\pi$
$53$	−1.88878	+	1.55008i	−0.259444	+	0.212920i	0.495675	+	0.868508i	$0.334921\pi$
$54$	0.199067	−	1.40013i	0.0270897	−	0.190534i
$55$	−0.138832	−	0.697957i	−0.0187202	−	0.0941126i
$56$	7.50793	−	0.505149i	1.00329	−	0.0675034i
$57$	2.77210	+	0.551405i	0.367174	+	0.0730354i
$58$	−5.07541	−	10.5657i	−0.666434	−	1.38735i
$59$	−1.29781	+	2.42803i	−0.168961	+	0.316103i	−0.952124	−	0.305714i	$-0.901105\pi$
$59$	−1.29781	+	2.42803i	−0.168961	+	0.316103i	0.783163	+	0.621816i	$0.213605\pi$
$60$	−0.939108	+	0.297292i	−0.121238	+	0.0383802i
$61$	5.00881	−	0.493324i	0.641312	−	0.0631637i	0.227866	−	0.973692i	$-0.426825\pi$
$61$	5.00881	−	0.493324i	0.641312	−	0.0631637i	0.413446	+	0.910529i	$0.364325\pi$
$62$	−3.18711	−	8.74081i	−0.404763	−	1.11008i
$63$		−	2.66045i		−	0.335186i
$64$	−6.91431	+	4.02396i	−0.864289	+	0.502995i
$65$		−	1.97030i		−	0.244386i
$66$	−1.91973	+	0.699979i	−0.236302	+	0.0861615i
$67$	−5.17367	+	0.509562i	−0.632065	+	0.0622529i	−0.408976	−	0.912545i	$-0.634114\pi$
$67$	−5.17367	+	0.509562i	−0.632065	+	0.0622529i	−0.223089	+	0.974798i	$0.571614\pi$
$68$	−2.08375	+	4.01416i	−0.252692	+	0.486788i
$69$	−0.914753	+	1.71138i	−0.110123	+	0.206026i
$70$	−1.67036	+	0.802384i	−0.199646	+	0.0959033i
$71$	1.15091	+	0.228930i	0.136588	+	0.0271690i	0.262911	−	0.964820i	$-0.415318\pi$
$71$	1.15091	+	0.228930i	0.136588	+	0.0271690i	−0.126323	+	0.991989i	$0.540318\pi$
$72$	1.25537	+	2.53457i	0.147947	+	0.298702i
$73$	−1.75052	−	8.80047i	−0.204883	−	1.03002i	−0.937131	−	0.348978i	$-0.886529\pi$
$73$	−1.75052	−	8.80047i	−0.204883	−	1.03002i	0.732248	−	0.681038i	$-0.238471\pi$
$74$	−10.2093	−	1.45153i	−1.18680	−	0.168737i
$75$	−3.67754	+	3.01808i	−0.424646	+	0.348498i
$76$	−5.19605	+	2.22608i	−0.596028	+	0.255349i
$77$	−3.39013	+	1.81206i	−0.386341	+	0.206504i
$78$	−5.59114	+	0.863861i	−0.633072	+	0.0978130i
$79$	−0.912975	−	0.378167i	−0.102718	−	0.0425471i	0.330733	−	0.943724i	$-0.392704\pi$
$79$	−0.912975	−	0.378167i	−0.102718	−	0.0425471i	−0.433451	+	0.901177i	$0.642704\pi$
$80$	1.21271	−	1.55260i	0.135585	−	0.173586i
$81$	0.923880	−	0.382683i	0.102653	−	0.0425204i
$82$	−12.1260	+	7.36782i	−1.33909	+	0.813640i
$83$	−6.02031	−	1.82624i	−0.660815	−	0.200456i	−0.0579750	−	0.998318i	$-0.518464\pi$
$83$	−6.02031	−	1.82624i	−0.660815	−	0.200456i	−0.602840	+	0.797862i	$0.705964\pi$
$84$	3.00929	+	4.38820i	0.328340	+	0.478791i
$85$	0.109169	−	1.10842i	0.0118411	−	0.120225i
$86$	4.81866	−	8.15052i	0.519609	−	0.878893i
$87$	4.60477	−	6.89153i	0.493683	−	0.738849i
$88$	2.37467	−	3.32600i	0.253141	−	0.354553i
$89$	−15.5192	+	10.3696i	−1.64503	+	1.09917i	−0.741191	+	0.671294i	$0.765739\pi$
$89$	−15.5192	+	10.3696i	−1.64503	+	1.09917i	−0.903836	+	0.427878i	$0.859261\pi$
$90$	−0.518906	−	0.464639i	−0.0546975	−	0.0489773i
$91$	−10.1847	+	3.08950i	−1.06765	+	0.323867i
$92$	−0.426968	−	3.85747i	−0.0445144	−	0.402169i
$93$	4.17350	−	5.08543i	0.432772	−	0.527335i
$94$	11.9347	+	0.514181i	1.23097	+	0.0530338i
$95$	0.984339	−	0.984339i	0.100991	−	0.100991i
$96$	−4.93753	−	2.76059i	−0.503934	−	0.281751i
$97$	4.43740	+	4.43740i	0.450550	+	0.450550i	0.895537	−	0.444987i	$-0.146792\pi$
$97$	4.43740	+	4.43740i	0.450550	+	0.450550i	−0.444987	+	0.895537i	$0.646792\pi$
$98$	0.0745870	+	0.0813032i	0.00753443	+	0.00821287i
$99$	−1.11690	−	0.916620i	−0.112253	−	0.0921237i
$100$	2.65199	−	9.13779i	0.265199	−	0.913779i
$101$	1.97010	+	6.49455i	0.196032	+	0.646231i	0.998755	+	0.0498795i	$0.0158837\pi$
$101$	1.97010	+	6.49455i	0.196032	+	0.646231i	−0.802723	+	0.596352i	$0.796616\pi$
$102$	−3.19323	+	0.176184i	−0.316176	+	0.0174449i
$103$	−7.44913	−	11.1484i	−0.733984	−	1.09849i	−0.991231	−	0.132139i	$-0.957815\pi$
$103$	−7.44913	−	11.1484i	−0.733984	−	1.09849i	0.257247	−	0.966346i	$-0.417185\pi$
$104$	8.24498	−	7.74911i	0.808487	−	0.759862i
$105$	−1.08950	−	0.727980i	−0.106324	−	0.0710435i
$106$	3.34682	−	0.859820i	0.325072	−	0.0835131i
$107$	−14.0817	−	1.38693i	−1.36133	−	0.134079i	−0.609159	−	0.793048i	$-0.708493\pi$
$107$	−14.0817	−	1.38693i	−1.36133	−	0.134079i	−0.752170	+	0.658969i	$0.770993\pi$
$108$	−1.09100	+	1.67622i	−0.104982	+	0.161294i
$109$	−2.69296	+	8.87749i	−0.257939	+	0.850309i	0.728339	+	0.685217i	$0.240292\pi$
$109$	−2.69296	+	8.87749i	−0.257939	+	0.850309i	−0.986278	+	0.165093i	$0.947208\pi$
$110$	−0.238643	+	0.977695i	−0.0227537	+	0.0932196i
$111$	−2.79039	−	6.73660i	−0.264852	−	0.639409i
$112$	−9.92713	−	3.83410i	−0.938026	−	0.362288i
$113$	0.952411	−	2.29932i	0.0895953	−	0.216302i	−0.872730	−	0.488203i	$-0.837652\pi$
$113$	0.952411	−	2.29932i	0.0895953	−	0.216302i	0.962325	+	0.271901i	$0.0876524\pi$
$114$	−3.22484	−	2.36169i	−0.302034	−	0.221193i
$115$	0.450535	+	0.842891i	0.0420126	+	0.0786000i
$116$	0.199949	+	16.5755i	0.0185648	+	1.53900i
$117$	−2.53785	−	3.09238i	−0.234625	−	0.285891i
$118$	3.11324	−	2.33817i	0.286597	−	0.215246i
$119$	−5.90071	+	1.17372i	−0.540917	+	0.107595i
$120$	1.38145	+	0.179440i	0.126109	+	0.0163805i
$121$	1.73871	−	8.74109i	0.158065	−	0.794644i
$122$	−6.71606	−	2.35745i	−0.608043	−	0.213434i
$123$	−8.84838	−	4.72956i	−0.797831	−	0.426450i
$124$	−1.13162	+	13.1087i	−0.101623	+	1.17720i
$125$	0.471044	+	4.78259i	0.0421315	+	0.427768i
$126$	−1.58811	+	3.41086i	−0.141480	+	0.303863i
$127$	14.1616			1.25664			0.628318	−	0.777956i	$-0.283743\pi$
$127$	14.1616			1.25664			0.628318	+	0.777956i	$0.283743\pi$
$128$	11.2666	−	1.03157i	0.995835	−	0.0911787i
$129$	6.69516			0.589476
$130$	−1.17614	+	2.52604i	−0.103154	+	0.221548i
$131$	−0.401558	−	4.07708i	−0.0350843	−	0.356216i	−0.996659	−	0.0816736i	$-0.973974\pi$
$131$	−0.401558	−	4.07708i	−0.0350843	−	0.356216i	0.961575	−	0.274543i	$-0.0885265\pi$
$132$	2.87904	+	0.248536i	0.250589	+	0.0216323i
$133$	−6.63164	−	3.54468i	−0.575036	−	0.307363i
$134$	6.93712	+	2.43505i	0.599276	+	0.210356i
$135$	0.0960860	−	0.483057i	0.00826977	−	0.0415749i
$136$	5.06767	−	3.90252i	0.434549	−	0.334638i
$137$	−2.02429	+	0.402657i	−0.172947	+	0.0344013i	−0.280804	−	0.959765i	$-0.590601\pi$
$137$	−2.02429	+	0.402657i	−0.172947	+	0.0344013i	0.107857	+	0.994166i	$0.465601\pi$
$138$	2.19435	−	1.64804i	0.186795	−	0.140291i
$139$	5.02577	+	6.12392i	0.426281	+	0.519424i	0.941216	−	0.337804i	$-0.109684\pi$
$139$	5.02577	+	6.12392i	0.426281	+	0.519424i	−0.514936	+	0.857229i	$0.672184\pi$
$140$	2.62047	−	0.0316104i	0.221470	−	0.00267157i
$141$	3.98186	+	7.44954i	0.335333	+	0.627364i
$142$	−1.33888	−	0.980517i	−0.112356	−	0.0822832i
$143$	−2.21197	+	5.34016i	−0.184974	+	0.446566i
$144$	−0.0964891	−	3.99884i	−0.00804076	−	0.333236i
$145$	−1.56219	−	3.77145i	−0.129733	−	0.313202i
$146$	−3.00902	+	12.3276i	−0.249028	+	1.02024i
$147$	−0.0226473	+	0.0746580i	−0.00186791	+	0.00615769i
$148$	12.2224	+	7.95519i	1.00467	+	0.653912i
$149$	8.11544	+	0.799301i	0.664842	+	0.0654813i	0.424809	−	0.905283i	$-0.360341\pi$
$149$	8.11544	+	0.799301i	0.664842	+	0.0654813i	0.240034	+	0.970764i	$0.422841\pi$
$150$	6.51640	−	1.67411i	0.532062	−	0.136690i
$151$	−2.94808	−	1.96984i	−0.239911	−	0.160303i	0.429803	−	0.902923i	$-0.358583\pi$
$151$	−2.94808	−	1.96984i	−0.239911	−	0.160303i	−0.669714	+	0.742619i	$0.733583\pi$
$152$	7.99045	+	0.247735i	0.648111	+	0.0200939i
$153$	−1.25636	−	1.88027i	−0.101571	−	0.152011i
$154$	5.42802	−	0.299488i	0.437402	−	0.0241334i
$155$	−0.940569	−	3.10064i	−0.0755483	−	0.249050i
$156$	7.68383	+	2.23001i	0.615199	+	0.178544i
$157$	−17.8247	−	14.6284i	−1.42257	−	1.16747i	−0.959693	−	0.281050i	$-0.909317\pi$
$157$	−17.8247	−	14.6284i	−1.42257	−	1.16747i	−0.462877	−	0.886423i	$-0.653183\pi$
$158$	0.944746	+	1.02982i	0.0751600	+	0.0819278i
$159$	1.72775	+	1.72775i	0.137020	+	0.137020i
$160$	−2.48156	+	1.26662i	−0.196184	+	0.100135i
$161$	3.65055	−	3.65055i	0.287703	−	0.287703i
$162$	−1.41290	−	0.0608719i	−0.111008	−	0.00478255i
$163$	0.176986	−	0.215658i	0.0138626	−	0.0168916i	−0.766033	−	0.642801i	$-0.777772\pi$
$163$	0.176986	−	0.215658i	0.0138626	−	0.0168916i	0.779896	+	0.625910i	$0.215272\pi$
$164$	19.9443	−	2.20755i	1.55739	−	0.172381i
$165$	−0.680989	+	0.206576i	−0.0530149	+	0.0160819i
$166$	6.62824	+	5.93507i	0.514452	+	0.460651i
$167$	0.362060	−	0.241921i	0.0280171	−	0.0187204i	−0.541483	−	0.840712i	$-0.682137\pi$
$167$	0.362060	−	0.241921i	0.0280171	−	0.0187204i	0.569500	+	0.821991i	$0.307137\pi$
$168$	−1.23862	−	7.42226i	−0.0955618	−	0.572640i
$169$	−1.66868	+	2.49736i	−0.128360	+	0.192105i
$170$	−0.801611	+	1.35589i	−0.0614808	+	0.103992i
$171$	0.277037	−	2.81280i	0.0211855	−	0.215100i
$172$	−11.0431	+	7.57302i	−0.842029	+	0.577437i
$173$	18.0968	+	5.48961i	1.37587	+	0.417367i	0.889720	−	0.456506i	$-0.150899\pi$
$173$	18.0968	+	5.48961i	1.37587	+	0.417367i	0.486155	+	0.873873i	$0.338399\pi$
$174$	−10.0174	+	6.08660i	−0.759414	+	0.461424i
$175$	11.6935	−	4.84359i	0.883942	−	0.366141i
$176$	−5.02986	+	2.84660i	−0.379140	+	0.214571i
$177$	2.54355	+	1.05357i	0.191185	+	0.0791913i
$178$	26.0864	−	4.03049i	1.95526	−	0.302098i
$179$	16.8371	−	8.99963i	1.25847	−	0.672664i	0.298937	−	0.954273i	$-0.403368\pi$
$179$	16.8371	−	8.99963i	1.25847	−	0.672664i	0.959529	+	0.281609i	$0.0908680\pi$
$180$	0.387909	+	0.905446i	0.0289130	+	0.0674880i
$181$	13.5190	−	11.0947i	1.00486	−	0.824666i	0.0203123	−	0.999794i	$-0.493534\pi$
$181$	13.5190	−	11.0947i	1.00486	−	0.824666i	0.984546	+	0.175128i	$0.0560339\pi$
$182$	14.9016	+	2.11867i	1.10458	+	0.157047i
$183$	−0.981898	−	4.93633i	−0.0725840	−	0.364904i
$184$	−1.75526	+	5.20037i	−0.129399	+	0.383377i
$185$	−3.52228	−	0.700624i	−0.258963	−	0.0515109i
$186$	−8.38633	+	4.02851i	−0.614916	+	0.295385i
$187$	−1.54025	+	2.88161i	−0.112634	+	0.210724i
$188$	−14.9940	−	7.78343i	−1.09355	−	0.567665i
$189$	−2.64764	+	0.260770i	−0.192588	+	0.0189682i
$190$	−1.84956	+	0.674395i	−0.134181	+	0.0489257i
$191$			10.3660i			0.750055i	0.927014	+	0.375027i	$0.122367\pi$
$191$			10.3660i			0.750055i	−0.927014	+	0.375027i	$0.877633\pi$
$192$	4.68231	+	6.48660i	0.337916	+	0.468130i
$193$		−	17.3721i		−	1.25047i	−0.780436	−	0.625236i	$-0.785003\pi$
$193$		−	17.3721i		−	1.25047i	0.780436	−	0.625236i	$-0.214997\pi$
$194$	−3.04017	−	8.33783i	−0.218272	−	0.598621i
$195$	−1.96081	+	0.193123i	−0.140417	+	0.0138298i
$196$	−0.0470923	−	0.148759i	−0.00336373	−	0.0106256i
$197$	−4.18920	+	7.83744i	−0.298468	+	0.558395i	−0.985795	−	0.167954i	$-0.946284\pi$
$197$	−4.18920	+	7.83744i	−0.298468	+	0.558395i	0.687327	+	0.726348i	$0.258784\pi$
$198$	0.884775	+	1.84188i	0.0628782	+	0.130896i
$199$	24.5854	+	4.89034i	1.74281	+	0.346667i	0.960937	−	0.276767i	$-0.0892630\pi$
$199$	24.5854	+	4.89034i	1.74281	+	0.346667i	0.781876	+	0.623434i	$0.214263\pi$
$200$	−8.85465	+	10.1321i	−0.626118	+	0.716449i
$201$	1.01422	+	5.09881i	0.0715373	+	0.359643i
$202$	1.35103	−	9.50240i	0.0950580	−	0.668586i
$203$	−17.0455	+	13.9889i	−1.19636	+	0.981828i
$204$	4.19907	+	1.68026i	0.293994	+	0.117642i
$205$	−4.35801	+	2.32940i	−0.304376	+	0.162693i
$206$	2.89536	+	18.7395i	0.201729	+	1.30564i
$207$	1.79280	+	0.742603i	0.124608	+	0.0516145i
$208$	−15.1962	+	5.01310i	−1.05367	+	0.347596i
$209$	−3.77295	+	1.56281i	−0.260980	+	0.108102i
$210$	0.962245	+	1.58367i	0.0664012	+	0.109284i
$211$	4.77293	+	1.44785i	0.328582	+	0.0996743i	0.450266	−	0.892895i	$-0.351329\pi$
$211$	4.77293	+	1.44785i	0.328582	+	0.0996743i	−0.121683	+	0.992569i	$0.538829\pi$
$212$	−4.80408	−	0.895490i	−0.329945	−	0.0615025i
$213$	0.115019	−	1.16781i	0.00788097	−	0.0800168i
$214$	17.2256	+	10.1839i	1.17752	+	0.696160i
$215$	1.83200	−	2.74178i	0.124941	−	0.186988i
$216$	2.39932	−	1.49776i	0.163253	−	0.101909i
$217$	−14.5527	+	9.72382i	−0.987904	+	0.660096i
$218$	8.75179	−	9.77394i	0.592746	−	0.661975i
$219$	−8.58651	+	2.60469i	−0.580223	+	0.176009i
$220$	0.889572	−	1.11101i	0.0599749	−	0.0749041i
$221$	−5.73907	+	6.99308i	−0.386052	+	0.470405i
$222$	−0.443856	+	10.3024i	−0.0297897	+	0.691450i
$223$	3.06444	−	3.06444i	0.205210	−	0.205210i	−0.597018	−	0.802228i	$-0.703648\pi$
$223$	3.06444	−	3.06444i	0.205210	−	0.205210i	0.802228	+	0.597018i	$0.203648\pi$
$224$	10.4385	+	10.8414i	0.697449	+	0.724369i
$225$	3.36401	+	3.36401i	0.224267	+	0.224267i
$226$	−2.59359	+	2.37934i	−0.172523	+	0.158271i
$227$	3.34427	+	2.74457i	0.221967	+	0.182164i	0.738804	−	0.673920i	$-0.235391\pi$
$227$	3.34427	+	2.74457i	0.221967	+	0.182164i	−0.516837	+	0.856084i	$0.672891\pi$
$228$	2.72466	+	4.95284i	0.180445	+	0.328010i
$229$	−3.91848	−	12.9175i	−0.258940	−	0.853612i	−0.985958	−	0.166993i	$-0.946594\pi$
$229$	−3.91848	−	12.9175i	−0.258940	−	0.853612i	0.727018	−	0.686619i	$-0.240906\pi$
$230$	−0.0744619	−	1.34957i	−0.00490987	−	0.0889882i
$231$	2.13563	+	3.19619i	0.140514	+	0.210294i
$232$	9.63814	−	21.3701i	0.632775	−	1.40302i
$233$	−17.7873	−	11.8851i	−1.16529	−	0.778619i	−0.186289	−	0.982495i	$-0.559646\pi$
$233$	−17.7873	−	11.8851i	−1.16529	−	0.778619i	−0.978997	+	0.203876i	$0.934646\pi$
$234$	1.40773	+	5.47954i	0.0920261	+	0.358209i
$235$	4.14026	+	0.407780i	0.270081	+	0.0266006i
$236$	−5.38708	+	1.13927i	−0.350669	+	0.0741605i
$237$	−0.286859	+	0.945646i	−0.0186335	+	0.0614263i
$238$	8.26569	+	2.01755i	0.535785	+	0.130778i
$239$	−7.37289	−	17.7997i	−0.476913	−	1.15137i	−0.961049	−	0.276377i	$-0.910866\pi$
$239$	−7.37289	−	17.7997i	−0.476913	−	1.15137i	0.484137	−	0.874992i	$-0.339134\pi$
$240$	−1.66399	−	1.05469i	−0.107410	−	0.0680797i
$241$	0.435972	−	1.05253i	0.0280834	−	0.0677994i	−0.909216	−	0.416325i	$-0.863318\pi$
$241$	0.435972	−	1.05253i	0.0280834	−	0.0677994i	0.937299	+	0.348526i	$0.113318\pi$
$242$	−7.44697	+	10.1687i	−0.478709	+	0.653668i
$243$	−0.471397	−	0.881921i	−0.0302401	−	0.0565753i
$244$	7.20313	+	7.03142i	0.461133	+	0.450141i
$245$	0.0243767	+	0.0297031i	0.00155737	+	0.00189766i
$246$	8.52090	+	11.3454i	0.543273	+	0.723359i
$247$	−11.0896	+	2.20587i	−0.705616	+	0.140356i
$248$	9.27583	−	16.1306i	0.589016	−	1.02430i
$249$	−1.22735	+	6.17033i	−0.0777804	+	0.391029i
$250$	2.25098	−	6.41274i	0.142364	−	0.405577i
$251$	12.6464	+	6.75965i	0.798235	+	0.426665i	0.819479	−	0.573109i	$-0.194263\pi$
$251$	12.6464	+	6.75965i	0.798235	+	0.426665i	−0.0212445	+	0.999774i	$0.506763\pi$
$252$	4.07210	−	3.42492i	0.256518	−	0.215749i
$253$	−0.274821	−	2.79030i	−0.0172778	−	0.175425i
$254$	−18.1560	−	8.45351i	−1.13921	−	0.530421i
$255$	−1.11378			−0.0697476
$256$	−15.0602	−	5.40286i	−0.941261	−	0.337679i
$257$	−6.50313			−0.405654			−0.202827	−	0.979215i	$-0.565013\pi$
$257$	−6.50313			−0.405654			−0.202827	+	0.979215i	$0.565013\pi$
$258$	−8.58358	−	3.99656i	−0.534391	−	0.248815i
$259$	1.90144	+	19.3057i	0.118150	+	1.19960i
$260$	3.01575	−	2.53645i	0.187029	−	0.157304i
$261$	−7.30969	−	3.90711i	−0.452458	−	0.241844i
$262$	−1.91892	+	5.46676i	−0.118552	+	0.337737i
$263$	3.03519	−	15.2589i	0.187158	−	0.940904i	−0.767011	−	0.641634i	$-0.778257\pi$
$263$	3.03519	−	15.2589i	0.187158	−	0.940904i	0.954168	−	0.299270i	$-0.0967432\pi$
$264$	−3.54274	−	2.03723i	−0.218041	−	0.125383i
$265$	1.18031	−	0.234778i	0.0725057	−	0.0144223i
$266$	6.38620	+	8.50313i	0.391563	+	0.521360i
$267$	11.8408	+	14.4280i	0.724644	+	0.882981i
$268$	−7.44022	−	7.26286i	−0.454484	−	0.443650i
$269$	11.4591	+	21.4384i	0.698671	+	1.30712i	0.941487	+	0.337049i	$0.109429\pi$
$269$	11.4591	+	21.4384i	0.698671	+	1.30712i	−0.242816	+	0.970072i	$0.578071\pi$
$270$	−0.411540	+	0.561950i	−0.0250455	+	0.0341992i
$271$	3.73979	−	9.02866i	0.227176	−	0.548452i	−0.768655	−	0.639663i	$-0.779074\pi$
$271$	3.73979	−	9.02866i	0.227176	−	0.548452i	0.995832	+	0.0912111i	$0.0290738\pi$
$272$	−8.82659	+	1.97819i	−0.535190	+	0.119945i
$273$	4.07290	+	9.83285i	0.246503	+	0.595111i
$274$	2.83562	+	0.692137i	0.171306	+	0.0418135i
$275$	1.99538	−	6.57790i	0.120326	−	0.396662i
$276$	−3.79705	+	0.803010i	−0.228555	+	0.0483355i
$277$	15.4012	+	1.51689i	0.925369	+	0.0911409i	0.549464	−	0.835517i	$-0.314832\pi$
$277$	15.4012	+	1.51689i	0.925369	+	0.0911409i	0.375905	+	0.926658i	$0.377332\pi$
$278$	−2.78776	−	10.8513i	−0.167199	−	0.650816i
$279$	−5.47002	−	3.65495i	−0.327481	−	0.218816i
$280$	−3.37846	−	1.52372i	−0.201901	−	0.0910595i
$281$	−16.6418	−	24.9062i	−0.992767	−	1.48578i	−0.869821	−	0.493367i	$-0.835766\pi$
$281$	−16.6418	−	24.9062i	−0.992767	−	1.48578i	−0.122945	−	0.992413i	$-0.539234\pi$
$282$	−0.658101	−	11.9276i	−0.0391893	−	0.710280i
$283$	−7.87390	−	25.9568i	−0.468055	−	1.54297i	−0.800196	−	0.599739i	$-0.795271\pi$
$283$	−7.87390	−	25.9568i	−0.468055	−	1.54297i	0.332141	−	0.943230i	$-0.392229\pi$
$284$	1.13121	+	2.05630i	0.0671252	+	0.122019i
$285$	−1.07608	−	0.883117i	−0.0637415	−	0.0523113i
$286$	6.02358	−	5.52599i	0.356182	−	0.326759i
$287$	18.8745	+	18.8745i	1.11412	+	1.11412i
$288$	−2.26333	+	5.18433i	−0.133368	+	0.305490i
$289$	8.40477	−	8.40477i	0.494398	−	0.494398i
$290$	−0.248491	+	5.76774i	−0.0145919	+	0.338694i
$291$	3.98109	−	4.85097i	0.233376	−	0.284369i
$292$	11.2165	−	14.0086i	0.656397	−	0.819790i
$293$	7.21140	−	2.18755i	0.421294	−	0.127798i	−0.0725173	−	0.997367i	$-0.523103\pi$
$293$	7.21140	−	2.18755i	0.421294	−	0.127798i	0.493812	+	0.869569i	$0.335603\pi$
$294$	0.0736009	−	0.0821970i	0.00429249	−	0.00479383i
$295$	1.12745	−	0.753335i	0.0656424	−	0.0438608i
$296$	−10.9211	−	17.4950i	−0.634776	−	1.01687i
$297$	−0.802730	+	1.20137i	−0.0465791	+	0.0697106i
$298$	−9.92733	−	5.86912i	−0.575075	−	0.339989i
$299$	0.760899	−	7.72554i	0.0440040	−	0.446780i
$300$	−9.35373	−	1.74356i	−0.540038	−	0.100664i
$301$	−17.0452	−	5.17060i	−0.982469	−	0.298029i
$302$	2.60374	+	4.28525i	0.149828	+	0.246589i
$303$	6.27017	−	2.59719i	0.360212	−	0.149205i
$304$	−10.0963	−	5.08737i	−0.579065	−	0.291781i
$305$	−2.29018	−	0.948625i	−0.131136	−	0.0543181i
$306$	0.488327	+	3.16058i	0.0279158	+	0.180678i
$307$	18.7442	−	10.0190i	1.06979	−	0.571812i	0.160096	−	0.987101i	$-0.448820\pi$
$307$	18.7442	−	10.0190i	1.06979	−	0.571812i	0.909689	+	0.415289i	$0.136320\pi$
$308$	−7.13781	−	2.85620i	−0.406714	−	0.162747i
$309$	−10.3646	+	8.50599i	−0.589620	+	0.483889i
$310$	−0.645011	+	4.53666i	−0.0366342	+	0.257665i
$311$	−0.442616	−	2.22518i	−0.0250985	−	0.126178i	0.966205	−	0.257776i	$-0.0829895\pi$
$311$	−0.442616	−	2.22518i	−0.0250985	−	0.126178i	−0.991303	+	0.131597i	$0.957990\pi$
$312$	−8.51994	−	7.44574i	−0.482347	−	0.421532i
$313$	−3.25665	−	0.647788i	−0.184077	−	0.0366151i	0.102191	−	0.994765i	$-0.467415\pi$
$313$	−3.25665	−	0.647788i	−0.184077	−	0.0366151i	−0.286268	+	0.958150i	$0.592415\pi$
$314$	14.1202	+	29.3946i	0.796848	+	1.65883i
$315$	−0.617685	+	1.15561i	−0.0348026	+	0.0651111i
$316$	−0.596488	−	1.88423i	−0.0335551	−	0.105996i
$317$	−4.56557	+	0.449669i	−0.256428	+	0.0252559i	−0.225414	−	0.974263i	$-0.572374\pi$
$317$	−4.56557	+	0.449669i	−0.256428	+	0.0252559i	−0.0310136	+	0.999519i	$0.509874\pi$
$318$	−1.18373	−	3.24643i	−0.0663801	−	0.182051i
$319$			11.9757i			0.670509i
$320$	3.93759	−	0.142551i	0.220118	−	0.00796886i
$321$			14.1498i			0.789766i
$322$	−6.85934	+	2.50108i	−0.382256	+	0.139380i
$323$	−6.36083	+	0.626487i	−0.353926	+	0.0348587i
$324$	1.77509	+	0.921449i	0.0986159	+	0.0511916i
$325$	8.97153	−	16.7846i	0.497651	−	0.931039i
$326$	−0.355640	+	0.170837i	−0.0196971	+	0.00946180i
$327$	9.09870	+	1.80984i	0.503159	+	0.100085i
$328$	−26.8875	−	9.07522i	−1.48462	−	0.501095i
$329$	−4.38421	−	22.0409i	−0.241709	−	1.21515i
$330$	0.996378	+	0.141663i	0.0548488	+	0.00779827i
$331$	−24.0287	+	19.7198i	−1.32074	+	1.08390i	−0.330604	+	0.943770i	$0.607252\pi$
$331$	−24.0287	+	19.7198i	−1.32074	+	1.08390i	−0.990133	+	0.140131i	$0.955248\pi$
$332$	−4.95495	−	11.5657i	−0.271938	−	0.634751i
$333$	−6.43065	+	3.43726i	−0.352398	+	0.188360i
$334$	−0.608593	+	0.0940309i	−0.0333007	+	0.00514514i
$335$	2.36556	+	0.979849i	0.129245	+	0.0535349i
$336$	−2.84261	+	10.2551i	−0.155077	+	0.559464i
$337$	−2.68954	+	1.11404i	−0.146509	+	0.0606859i	−0.454733	−	0.890628i	$-0.650265\pi$
$337$	−2.68954	+	1.11404i	−0.146509	+	0.0606859i	0.308224	+	0.951314i	$0.400265\pi$
$338$	3.63010	−	2.20567i	0.197451	−	0.119972i
$339$	−2.38160	−	0.722452i	−0.129351	−	0.0392382i
$340$	1.83708	−	1.25982i	0.0996299	−	0.0683231i
$341$	−0.931698	+	9.45968i	−0.0504542	+	0.512271i
$342$	−2.03423	+	3.44080i	−0.109999	+	0.186057i
$343$	−10.2312	+	15.3120i	−0.552431	+	0.826772i
$344$	18.6785	−	3.11705i	1.00708	−	0.168060i
$345$	0.794672	−	0.530983i	0.0427837	−	0.0285872i
$346$	−19.9242	−	17.8406i	−1.07113	−	0.959115i
$347$	14.0768	−	4.27016i	0.755685	−	0.229234i	0.111144	−	0.993804i	$-0.464549\pi$
$347$	14.0768	−	4.27016i	0.755685	−	0.229234i	0.644541	+	0.764570i	$0.277049\pi$
$348$	16.4761	−	1.82367i	0.883213	−	0.0977591i
$349$	−17.8253	+	21.7202i	−0.954168	+	1.16266i	0.0324280	+	0.999474i	$0.489676\pi$
$349$	−17.8253	+	21.7202i	−0.954168	+	1.16266i	−0.986596	+	0.163183i	$0.947824\pi$
$350$	−17.8830	−	0.770450i	−0.955886	−	0.0411823i
$351$	−2.82874	+	2.82874i	−0.150987	+	0.150987i
$352$	8.14780	−	0.647013i	0.434279	−	0.0344859i
$353$	24.2156	+	24.2156i	1.28886	+	1.28886i	0.935477	+	0.353387i	$0.114970\pi$
$353$	24.2156	+	24.2156i	1.28886	+	1.28886i	0.353387	+	0.935477i	$0.385030\pi$
$354$	−2.63206	−	2.86907i	−0.139893	−	0.152489i
$355$	−0.446763	−	0.366649i	−0.0237117	−	0.0194597i
$356$	−35.8502	−	10.4045i	−1.90006	−	0.551438i
$357$	1.74644	+	5.75725i	0.0924316	+	0.304706i
$358$	−26.9583	+	1.48741i	−1.42479	+	0.0786121i
$359$	−15.5277	−	23.2389i	−0.819523	−	1.22650i	−0.971246	−	0.238079i	$-0.923482\pi$
$359$	−15.5277	−	23.2389i	−0.819523	−	1.22650i	0.151723	−	0.988423i	$-0.451518\pi$
$360$	0.0431694	−	1.39239i	0.00227523	−	0.0733854i
$361$	9.15565	+	6.11761i	0.481876	+	0.321980i
$362$	−23.9549	+	6.15417i	−1.25904	+	0.323456i
$363$	−8.86942	−	0.873561i	−0.465524	−	0.0458501i
$364$	−17.8400	−	11.6115i	−0.935071	−	0.608609i
$365$	−1.28286	+	4.22903i	−0.0671481	+	0.221358i
$366$	−1.68781	+	6.91479i	−0.0882233	+	0.361442i
$367$	9.67364	+	23.3542i	0.504960	+	1.21908i	0.946752	+	0.321963i	$0.104343\pi$
$367$	9.67364	+	23.3542i	0.504960	+	1.21908i	−0.441792	+	0.897117i	$0.645657\pi$
$368$	5.35461	−	5.61941i	0.279128	−	0.292932i
$369$	−3.83949	+	9.26935i	−0.199876	+	0.482543i
$370$	4.09754	+	3.00080i	0.213021	+	0.156004i
$371$	−3.06435	−	5.73300i	−0.159093	−	0.297643i
$372$	13.1565	−	0.158706i	0.682133	−	0.00822850i
$373$	−16.4838	−	20.0856i	−0.853498	−	1.03999i	−0.998719	−	0.0505915i	$-0.983889\pi$
$373$	−16.4838	−	20.0856i	−0.853498	−	1.03999i	0.145221	−	0.989399i	$-0.453611\pi$
$374$	3.69482	−	2.77496i	0.191055	−	0.143490i
$375$	4.71339	−	0.937552i	0.243398	−	0.0484150i
$376$	14.5770	+	18.9292i	0.751754	+	0.976201i
$377$	−6.46864	+	32.5201i	−0.333152	+	1.67487i
$378$	3.55009	+	1.24614i	0.182597	+	0.0640947i
$379$	2.53046	+	1.35256i	0.129981	+	0.0694762i	0.535105	−	0.844785i	$-0.320272\pi$
$379$	2.53046	+	1.35256i	0.129981	+	0.0694762i	−0.405125	+	0.914261i	$0.632772\pi$
$380$	2.77381	+	0.239452i	0.142294	+	0.0122836i
$381$	−1.38808	−	14.0934i	−0.0711134	−	0.722026i
$382$	6.18778	−	13.2898i	0.316595	−	0.679963i
$383$	14.9514			0.763981			0.381991	−	0.924166i	$-0.375239\pi$
$383$	14.9514			0.763981			0.381991	+	0.924166i	$0.375239\pi$
$384$	−2.13092	−	11.1112i	−0.108743	−	0.567017i
$385$	1.89326			0.0964896
$386$	−10.3700	+	22.2720i	−0.527818	+	1.13362i
$387$	−0.656241	−	6.66293i	−0.0333586	−	0.338696i
$388$	−1.07945	+	12.5044i	−0.0548008	+	0.634812i
$389$	−15.9232	−	8.51112i	−0.807337	−	0.431531i	0.0154497	−	0.999881i	$-0.495082\pi$
$389$	−15.9232	−	8.51112i	−0.807337	−	0.431531i	−0.822787	+	0.568350i	$0.807582\pi$
$390$	2.62916	+	0.922879i	0.133133	+	0.0467318i
$391$	0.856106	−	4.30394i	0.0432951	−	0.217659i
$392$	−0.0284240	+	0.218828i	−0.00143563	+	0.0110525i
$393$	−4.01809	+	0.799248i	−0.202686	+	0.0403167i
$394$	10.0492	−	7.54738i	0.506272	−	0.380231i
$395$	0.308764	+	0.376230i	0.0155356	+	0.0189302i
$396$	−0.0348562	−	2.88954i	−0.00175159	−	0.145205i
$397$	11.4579	+	21.4361i	0.575053	+	1.07585i	0.986399	+	0.164369i	$0.0525588\pi$
$397$	11.4579	+	21.4361i	0.575053	+	1.07585i	−0.411346	+	0.911479i	$0.634941\pi$
$398$	−28.6007	−	20.9455i	−1.43362	−	1.04990i
$399$	−2.87760	+	6.94714i	−0.144060	+	0.347792i
$400$	17.4004	−	7.70433i	0.870018	−	0.385216i
$401$	−7.95427	−	19.2033i	−0.397217	−	0.958967i	−0.988323	−	0.152373i	$-0.951308\pi$
$401$	−7.95427	−	19.2033i	−0.397217	−	0.958967i	0.591106	−	0.806594i	$-0.298692\pi$
$402$	1.74336	−	7.14239i	0.0869511	−	0.356230i
$403$	−7.63967	+	25.1846i	−0.380559	+	1.25453i
$404$	−7.40439	+	11.3761i	−0.368382	+	0.565984i
$405$	−0.490149	−	0.0482755i	−0.0243557	−	0.00239883i
$406$	30.2038	−	7.75954i	1.49899	−	0.385100i
$407$	8.75996	+	5.85322i	0.434215	+	0.290133i
$408$	−4.38044	−	4.66076i	−0.216864	−	0.230742i
$409$	19.8185	+	29.6605i	0.979962	+	1.46662i	0.881900	+	0.471436i	$0.156264\pi$
$409$	19.8185	+	29.6605i	0.979962	+	1.46662i	0.0980618	+	0.995180i	$0.468736\pi$
$410$	6.97771	−	0.384991i	0.344605	−	0.0190134i
$411$	0.599133	+	1.97508i	0.0295531	+	0.0974234i
$412$	7.47422	−	25.7535i	0.368228	−	1.26878i
$413$	−5.66195	−	4.64664i	−0.278606	−	0.228646i
$414$	−1.85519	−	2.02224i	−0.0911777	−	0.0993878i
$415$	2.19101	+	2.19101i	0.107552	+	0.107552i
$416$	22.4749	+	2.64406i	1.10192	+	0.129635i
$417$	5.60182	−	5.60182i	0.274322	−	0.274322i
$418$	5.77003	+	0.248589i	0.282221	+	0.0121589i
$419$	18.8965	−	23.0255i	0.923155	−	1.12487i	−0.0687175	−	0.997636i	$-0.521891\pi$
$419$	18.8965	−	23.0255i	0.923155	−	1.12487i	0.991873	−	0.127232i	$-0.0406093\pi$
$420$	−0.288309	−	2.60475i	−0.0140680	−	0.127099i
$421$	−13.4045	+	4.06621i	−0.653296	+	0.198175i	−0.599497	−	0.800377i	$-0.704633\pi$
$421$	−13.4045	+	4.06621i	−0.653296	+	0.198175i	−0.0537984	+	0.998552i	$0.517133\pi$
$422$	−5.25490	−	4.70535i	−0.255805	−	0.229053i
$423$	7.02338	−	4.69287i	0.341488	−	0.228175i
$424$	5.62455	+	4.01578i	0.273152	+	0.195024i
$425$	5.97703	−	8.94526i	0.289929	−	0.433909i
$426$	−0.844563	+	1.42854i	−0.0409192	+	0.0692128i
$427$	−1.31247	+	13.3257i	−0.0635147	+	0.644876i
$428$	−16.0051	−	23.3389i	−0.773637	−	1.12813i
$429$	5.53125	+	1.67789i	0.267051	+	0.0810092i
$430$	−3.98538	+	2.42154i	−0.192192	+	0.116777i
$431$	−16.1560	+	6.69204i	−0.778208	+	0.322344i	−0.736192	−	0.676773i	$-0.763378\pi$
$431$	−16.1560	+	6.69204i	−0.778208	+	0.322344i	−0.0420161	+	0.999117i	$0.513378\pi$
$432$	−3.97012	+	0.487979i	−0.191013	+	0.0234779i
$433$	−32.5441	−	13.4802i	−1.56397	−	0.647818i	−0.578197	−	0.815897i	$-0.696243\pi$
$433$	−32.5441	−	13.4802i	−1.56397	−	0.647818i	−0.985773	+	0.168080i	$0.946243\pi$
$434$	24.4619	−	3.77950i	1.17421	−	0.181422i
$435$	−3.60017	+	1.92433i	−0.172615	+	0.0922647i
$436$	−17.0547	+	7.30652i	−0.816771	+	0.349919i
$437$	4.23972	−	3.47945i	0.202814	−	0.166445i
$438$	12.5632	+	1.78621i	0.600294	+	0.0853483i
$439$	−6.17593	−	31.0485i	−0.294761	−	1.48186i	−0.790000	−	0.613107i	$-0.789920\pi$
$439$	−6.17593	−	31.0485i	−0.294761	−	1.48186i	0.495239	−	0.868757i	$-0.335080\pi$
$440$	−1.80368	+	0.893361i	−0.0859870	+	0.0425893i
$441$	0.0765183	+	0.0152204i	0.00364373	+	0.000724783i
$442$	11.5322	−	5.53969i	0.548531	−	0.263496i
$443$	13.1436	−	24.5899i	0.624471	−	1.16830i	−0.348485	−	0.937314i	$-0.613304\pi$
$443$	13.1436	−	24.5899i	0.624471	−	1.16830i	0.972956	−	0.230989i	$-0.0741961\pi$
$444$	6.71888	−	12.9433i	0.318864	−	0.614261i
$445$	9.14850	−	0.901049i	0.433680	−	0.0427138i
$446$	−5.75806	+	2.09952i	−0.272652	+	0.0994154i
$447$		−	8.15470i		−	0.385704i
$448$	−6.91113	−	20.1303i	−0.326520	−	0.951068i
$449$			7.36597i			0.347622i	0.984779	+	0.173811i	$0.0556081\pi$
$449$			7.36597i			0.347622i	−0.984779	+	0.173811i	$0.944392\pi$
$450$	−2.30476	−	6.32094i	−0.108648	−	0.297972i
$451$	14.4267	−	1.42091i	0.679328	−	0.0669080i
$452$	4.74543	−	1.50225i	0.223206	−	0.0706600i
$453$	−1.67139	+	3.12696i	−0.0785289	+	0.146917i
$454$	−2.64922	−	5.51500i	−0.124334	−	0.258832i
$455$	5.14117	+	1.02264i	0.241022	+	0.0479422i
$456$	−0.536660	−	7.97626i	−0.0251314	−	0.373523i
$457$	5.89343	+	29.6283i	0.275683	+	1.38595i	0.831904	+	0.554919i	$0.187251\pi$
$457$	5.89343	+	29.6283i	0.275683	+	1.38595i	−0.556221	+	0.831034i	$0.687749\pi$
$458$	−2.68716	+	18.9000i	−0.125563	+	0.883140i
$459$	−1.74808	+	1.43461i	−0.0815932	+	0.0669618i
$460$	−0.710140	+	1.77468i	−0.0331105	+	0.0827448i
$461$	9.48343	−	5.06900i	0.441688	−	0.236087i	−0.235534	−	0.971866i	$-0.575684\pi$
$461$	9.48343	−	5.06900i	0.441688	−	0.236087i	0.677221	+	0.735779i	$0.263184\pi$
$462$	−0.830085	−	5.37253i	−0.0386190	−	0.249953i
$463$	27.6722	+	11.4622i	1.28604	+	0.532694i	0.917802	−	0.397039i	$-0.129962\pi$
$463$	27.6722	+	11.4622i	1.28604	+	0.532694i	0.368235	+	0.929733i	$0.379962\pi$
$464$	−25.1132	+	21.6444i	−1.16585	+	1.00482i
$465$	−2.99352	+	1.23996i	−0.138821	+	0.0575016i
$466$	15.7098	+	25.8552i	0.727740	+	1.19772i
$467$	31.4606	+	9.54347i	1.45582	+	0.441619i	0.916348	−	0.400382i	$-0.131123\pi$
$467$	31.4606	+	9.54347i	1.45582	+	0.441619i	0.539475	+	0.842001i	$0.318623\pi$
$468$	1.46613	−	7.86541i	0.0677719	−	0.363579i
$469$	1.35567	−	13.7643i	0.0625989	−	0.635577i
$470$	−5.06463	−	2.99425i	−0.233614	−	0.138115i
$471$	−12.8108	+	19.1728i	−0.590292	+	0.883434i
$472$	7.58662	+	1.75511i	0.349203	+	0.0807855i
$473$	−8.04337	+	5.37441i	−0.369835	+	0.247116i
$474$	0.932256	−	1.04114i	0.0428199	−	0.0478210i
$475$	12.8674	−	3.90329i	0.590398	−	0.179095i
$476$	−9.39275	−	7.52067i	−0.430516	−	0.344709i
$477$	1.55008	−	1.88878i	0.0709735	−	0.0864814i
$478$	−1.17278	+	27.2214i	−0.0536415	+	1.24508i
$479$	−16.5691	+	16.5691i	−0.757060	+	0.757060i	−0.975786	−	0.218726i	$-0.929810\pi$
$479$	−16.5691	+	16.5691i	−0.757060	+	0.757060i	0.218726	+	0.975786i	$0.429810\pi$
$480$	1.50375	+	2.34546i	0.0686366	+	0.107055i
$481$	20.6262	+	20.6262i	0.940472	+	0.940472i
$482$	−1.18723	+	1.08916i	−0.0540769	+	0.0496098i
$483$	−3.99078	−	3.27515i	−0.181587	−	0.149025i
$484$	15.6175	−	8.59149i	0.709884	−	0.390522i
$485$	−0.897205	−	2.95769i	−0.0407400	−	0.134302i
$486$	0.0779099	+	1.41207i	0.00353407	+	0.0640526i
$487$	−17.2675	−	25.8426i	−0.782464	−	1.17104i	−0.981578	−	0.191064i	$-0.938806\pi$
$487$	−17.2675	−	25.8426i	−0.782464	−	1.17104i	0.199113	−	0.979976i	$-0.436194\pi$
$488$	−5.03754	−	13.3145i	−0.228039	−	0.602718i
$489$	−0.231967	−	0.154996i	−0.0104899	−	0.00700914i
$490$	−0.0135216	−	0.0526323i	−0.000610842	−	0.00237768i
$491$	30.1305	+	2.96759i	1.35977	+	0.133926i	0.751462	−	0.659776i	$-0.229349\pi$
$491$	30.1305	+	2.96759i	1.35977	+	0.133926i	0.608307	+	0.793702i	$0.291849\pi$
$492$	−4.15181	−	19.6319i	−0.187178	−	0.885075i
$493$	−5.44087	+	17.9361i	−0.245044	+	0.807803i
$494$	15.5343	+	3.79172i	0.698921	+	0.170598i
$495$	0.272329	+	0.657462i	0.0122403	+	0.0295507i
$496$	−21.5210	+	15.1433i	−0.966323	+	0.679956i
$497$	−1.19471	+	2.88429i	−0.0535901	+	0.129378i
$498$	5.25681	−	7.17807i	0.235563	−	0.321657i
$499$	3.23236	+	6.04731i	0.144700	+	0.270715i	0.943822	−	0.330454i	$-0.107202\pi$
$499$	3.23236	+	6.04731i	0.144700	+	0.270715i	−0.799122	+	0.601169i	$0.794702\pi$
$500$	−6.71386	+	6.87781i	−0.300253	+	0.307585i
$501$	−0.276244	−	0.336605i	−0.0123417	−	0.0150384i
$502$	−12.1784	−	16.2153i	−0.543547	−	0.723725i
$503$	−0.955393	+	0.190039i	−0.0425989	+	0.00847344i	−0.216344	−	0.976317i	$-0.569413\pi$
$503$	−0.955393	+	0.190039i	−0.0425989	+	0.00847344i	0.173745	+	0.984791i	$0.444413\pi$
$504$	−7.26511	+	1.96017i	−0.323614	+	0.0873128i
$505$	0.652115	−	3.27840i	0.0290187	−	0.145887i
$506$	−1.31329	+	3.74138i	−0.0583828	+	0.166325i
$507$	2.64889	+	1.41586i	0.117641	+	0.0628807i
$508$	18.2308	+	21.6758i	0.808861	+	0.961707i
$509$	0.750657	+	7.62155i	0.0332723	+	0.337819i	0.997382	+	0.0723145i	$0.0230385\pi$
$509$	0.750657	+	7.62155i	0.0332723	+	0.337819i	−0.964110	+	0.265505i	$0.914461\pi$
$510$	1.42793	+	0.664851i	0.0632298	+	0.0294401i
$511$	23.8719			1.05603
$512$	16.0829	+	15.9167i	0.710769	+	0.703425i
$513$	−2.82641			−0.124789
$514$	8.33738	+	3.88193i	0.367746	+	0.171225i
$515$	0.647281	+	6.57195i	0.0285226	+	0.289595i
$516$	8.61897	+	10.2476i	0.379429	+	0.451128i
$517$	−10.7637	−	5.75330i	−0.473385	−	0.253030i
$518$	9.08643	−	25.8860i	0.399235	−	1.13737i
$519$	3.68938	−	18.5477i	0.161946	−	0.814156i
$520$	−5.38046	+	1.45168i	−0.235949	+	0.0636602i
$521$	25.1791	−	5.00843i	1.10312	−	0.219424i	0.390240	−	0.920713i	$-0.372392\pi$
$521$	25.1791	−	5.00843i	1.10312	−	0.219424i	0.712876	+	0.701290i	$0.247392\pi$
$522$	7.03916	+	9.37253i	0.308096	+	0.410225i
$523$	−16.2186	−	19.7624i	−0.709189	−	0.864149i	0.286387	−	0.958114i	$-0.407546\pi$
$523$	−16.2186	−	19.7624i	−0.709189	−	0.864149i	−0.995575	+	0.0939652i	$0.970046\pi$
$524$	5.72346	−	5.86323i	0.250030	−	0.256136i
$525$	−5.96643	−	11.1624i	−0.260396	−	0.487167i
$526$	−12.9998	+	17.7510i	−0.566819	+	0.773980i
$527$	−5.69320	+	13.7446i	−0.248000	+	0.598725i
$528$	3.32591	+	4.72663i	0.144741	+	0.205700i
$529$	−7.36069	−	17.7703i	−0.320030	−	0.772620i
$530$	−1.65337	−	0.403566i	−0.0718177	−	0.0175298i
$531$	0.799188	−	2.63457i	0.0346818	−	0.114331i
$532$	−3.11168	−	14.7136i	−0.134908	−	0.637917i
$533$	39.9435	+	3.93409i	1.73014	+	0.170404i
$534$	−6.56799	−	25.5657i	−0.284225	−	1.10634i
$535$	5.79458	+	3.87181i	0.250521	+	0.167393i
$536$	5.20335	+	13.7527i	0.224751	+	0.594027i
$537$	−10.6066	−	15.8739i	−0.457710	−	0.685011i
$538$	−1.89389	−	34.3255i	−0.0816514	−	1.47988i
$539$	−0.0327225	−	0.107872i	−0.00140946	−	0.00464636i
$540$	0.863065	−	0.474790i	0.0371404	−	0.0204317i
$541$	−23.1784	−	19.0220i	−0.996517	−	0.817820i	−0.0132354	−	0.999912i	$-0.504213\pi$
$541$	−23.1784	−	19.0220i	−0.996517	−	0.817820i	−0.983281	+	0.182092i	$0.941713\pi$
$542$	−10.1841	+	9.34286i	−0.437446	+	0.401310i
$543$	−12.3664	−	12.3664i	−0.530693	−	0.530693i
$544$	12.4970	+	2.73272i	0.535806	+	0.117165i
$545$	3.23084	−	3.23084i	0.138394	−	0.138394i
$546$	0.647859	−	15.0375i	0.0277258	−	0.643547i
$547$	−20.4954	+	24.9737i	−0.876319	+	1.06780i	0.120855	+	0.992670i	$0.461436\pi$
$547$	−20.4954	+	24.9737i	−0.876319	+	1.06780i	−0.997174	+	0.0751277i	$0.976064\pi$
$548$	−3.22227	−	2.58003i	−0.137648	−	0.110214i
$549$	−4.81632	+	1.46102i	−0.205556	+	0.0623546i
$550$	−6.48476	+	7.24214i	−0.276511	+	0.308806i
$551$	−19.4783	+	13.0150i	−0.829803	+	0.554456i
$552$	5.34738	+	1.23708i	0.227599	+	0.0526535i
$553$	1.46062	−	2.18598i	0.0621120	−	0.0929572i
$554$	−18.8398	−	11.1382i	−0.800424	−	0.473218i
$555$	−0.352007	+	3.57399i	−0.0149419	+	0.151707i
$556$	−2.90341	+	15.5761i	−0.123132	+	0.660572i
$557$	10.7879	+	3.27247i	0.457097	+	0.138659i	0.510433	−	0.859918i	$-0.329485\pi$
$557$	10.7879	+	3.27247i	0.457097	+	0.138659i	−0.0533355	+	0.998577i	$0.516985\pi$
$558$	4.83112	+	7.95109i	0.204517	+	0.336596i
$559$	−24.7448	+	10.2496i	−1.04660	+	0.433514i
$560$	3.42182	+	3.97020i	0.144598	+	0.167772i
$561$	3.01870	+	1.25039i	0.127450	+	0.0527914i
$562$	6.46841	+	41.8652i	0.272853	+	1.76598i
$563$	32.7352	−	17.4974i	1.37963	−	0.737425i	0.396103	−	0.918206i	$-0.370362\pi$
$563$	32.7352	−	17.4974i	1.37963	−	0.737425i	0.983523	+	0.180781i	$0.0578625\pi$
$564$	−6.27628	+	15.6848i	−0.264279	+	0.660447i
$565$	−0.947533	+	0.777620i	−0.0398630	+	0.0327147i
$566$	−5.39965	+	37.9782i	−0.226964	+	1.59634i
$567$	0.519029	+	2.60933i	0.0217972	+	0.109582i
$568$	−0.222808	−	3.31155i	−0.00934882	−	0.138950i
$569$	21.9136	+	4.35889i	0.918666	+	0.182734i	0.631706	−	0.775208i	$-0.282355\pi$
$569$	21.9136	+	4.35889i	0.918666	+	0.182734i	0.286961	+	0.957942i	$0.407355\pi$
$570$	0.852436	+	1.77455i	0.0357046	+	0.0743279i
$571$	14.9934	−	28.0507i	0.627454	−	1.17388i	−0.344517	−	0.938780i	$-0.611957\pi$
$571$	14.9934	−	28.0507i	0.627454	−	1.17388i	0.971970	−	0.235103i	$-0.0755428\pi$
$572$	−11.0212	+	3.48897i	−0.460821	+	0.145881i
$573$	10.3160	−	1.01604i	0.430959	−	0.0424458i
$574$	−12.9314	−	35.4649i	−0.539744	−	1.48028i
$575$			9.23185i			0.384995i
$576$	5.99642	−	5.29556i	0.249851	−	0.220648i
$577$			2.08304i			0.0867183i	0.999060	+	0.0433591i	$0.0138060\pi$
$577$			2.08304i			0.0867183i	−0.999060	+	0.0433591i	$0.986194\pi$
$578$	−15.7925	+	5.75831i	−0.656880	+	0.239514i
$579$	−17.2885	+	1.70276i	−0.718484	+	0.0707645i
$580$	3.76153	−	7.24624i	0.156189	−	0.300884i
$581$	7.88999	−	14.7611i	0.327332	−	0.612395i
$582$	−7.99969	+	3.84278i	−0.331598	+	0.159288i
$583$	−3.46259	−	0.688752i	−0.143406	−	0.0285252i
$584$	−22.7424	+	11.2643i	−0.941087	+	0.466120i
$585$	0.384387	+	1.93244i	0.0158924	+	0.0798966i
$586$	−10.5512	−	1.50015i	−0.435868	−	0.0619707i
$587$	−7.68357	+	6.30574i	−0.317135	+	0.260266i	−0.779470	−	0.626439i	$-0.784512\pi$
$587$	−7.68357	+	6.30574i	−0.317135	+	0.260266i	0.462335	+	0.886705i	$0.347012\pi$
$588$	−0.143427	+	0.0614464i	−0.00591482	+	0.00253401i
$589$	−16.3986	+	8.76524i	−0.675693	+	0.361166i
$590$	−1.89514	+	0.292809i	−0.0780217	+	0.0120548i
$591$	8.21032	+	3.40082i	0.337727	+	0.139891i
$592$	3.55817	+	28.9487i	0.146240	+	1.18978i
$593$	28.6594	−	11.8711i	1.17690	−	0.487488i	0.293432	−	0.955980i	$-0.405203\pi$
$593$	28.6594	−	11.8711i	1.17690	−	0.487488i	0.883468	+	0.468492i	$0.155203\pi$
$594$	1.74628	−	1.06105i	0.0716509	−	0.0435354i
$595$	2.83557	+	0.860160i	0.116247	+	0.0352631i
$596$	9.22393	+	13.4505i	0.377827	+	0.550954i
$597$	2.45700	−	24.9464i	0.100558	−	1.02099i
$598$	−5.58715	+	9.45038i	−0.228475	+	0.386455i
$599$	−21.0487	+	31.5016i	−0.860027	+	1.28712i	0.0964568	+	0.995337i	$0.469249\pi$
$599$	−21.0487	+	31.5016i	−0.860027	+	1.28712i	−0.956484	+	0.291785i	$0.905751\pi$
$600$	10.9512	+	7.81889i	0.447082	+	0.319205i
$601$	−8.82262	+	5.89509i	−0.359882	+	0.240466i	−0.722345	−	0.691533i	$-0.756936\pi$
$601$	−8.82262	+	5.89509i	−0.359882	+	0.240466i	0.362463	+	0.931998i	$0.381936\pi$
$602$	18.7664	+	16.8038i	0.764862	+	0.684874i
$603$	4.97485	−	1.50910i	0.202592	−	0.0614555i
$604$	−0.780135	−	7.04820i	−0.0317433	−	0.286787i
$605$	−2.78467	+	3.39314i	−0.113213	+	0.137951i
$606$	−9.58906	−	0.413124i	−0.389529	−	0.0167820i
$607$	−6.53237	+	6.53237i	−0.265141	+	0.265141i	−0.827139	−	0.561998i	$-0.810033\pi$
$607$	−6.53237	+	6.53237i	−0.265141	+	0.265141i	0.561998	+	0.827139i	$0.310033\pi$
$608$	9.90727	+	12.5491i	0.401793	+	0.508935i
$609$	15.5923	+	15.5923i	0.631832	+	0.631832i
$610$	2.36988	+	2.58328i	0.0959537	+	0.104594i
$611$	−26.1212	−	21.4371i	−1.05675	−	0.867253i
$612$	1.26059	−	4.34354i	0.0509564	−	0.175577i
$613$	6.79555	+	22.4019i	0.274470	+	0.904805i	0.980483	+	0.196606i	$0.0629920\pi$
$613$	6.79555	+	22.4019i	0.274470	+	0.904805i	−0.706013	+	0.708199i	$0.749508\pi$
$614$	−30.0117	+	1.65588i	−1.21117	+	0.0668259i
$615$	2.74535	+	4.10870i	0.110703	+	0.165679i
$616$	7.44612	+	7.92261i	0.300013	+	0.319211i
$617$	−24.2117	−	16.1778i	−0.974728	−	0.651293i	−0.0372389	−	0.999306i	$-0.511856\pi$
$617$	−24.2117	−	16.1778i	−0.974728	−	0.651293i	−0.937489	+	0.348014i	$0.886856\pi$
$618$	18.3655	−	4.71821i	0.738769	−	0.189794i
$619$	33.9761	+	3.34636i	1.36562	+	0.134502i	0.754115	−	0.656742i	$-0.228066\pi$
$619$	33.9761	+	3.34636i	1.36562	+	0.134502i	0.611501	+	0.791243i	$0.290566\pi$
$620$	3.53502	−	5.43123i	0.141970	−	0.218123i
$621$	0.563302	−	1.85696i	0.0226045	−	0.0745171i
$622$	−0.760825	+	3.11702i	−0.0305063	+	0.124981i
$623$	−19.0028	−	45.8768i	−0.761331	−	1.83801i
$624$	6.47845	+	14.6317i	0.259346	+	0.585737i
$625$	−8.19715	+	19.7897i	−0.327886	+	0.791587i
$626$	3.78853	+	2.77450i	0.151420	+	0.110891i
$627$	1.92510	+	3.60160i	0.0768809	+	0.143834i
$628$	−0.556273	−	46.1144i	−0.0221977	−	1.84016i
$629$	10.4606	+	12.7463i	0.417093	+	0.508230i
$630$	1.48173	−	1.11284i	0.0590334	−	0.0443365i
$631$	−42.1581	+	8.38576i	−1.67829	+	0.333832i	−0.940135	−	0.340803i	$-0.889301\pi$
$631$	−42.1581	+	8.38576i	−1.67829	+	0.333832i	−0.738152	+	0.674635i	$0.764301\pi$
$632$	−0.360029	+	2.77176i	−0.0143212	+	0.110255i
$633$	0.973052	−	4.89186i	0.0386753	−	0.194434i
$634$	6.12174	+	2.14883i	0.243125	+	0.0853411i
$635$	−6.15129	−	3.28793i	−0.244106	−	0.130478i
$636$	−0.420296	+	4.86872i	−0.0166658	+	0.193057i
$637$	−0.0305916	−	0.310601i	−0.00121208	−	0.0123065i
$638$	7.14867	−	15.3535i	0.283019	−	0.607851i
$639$	−1.17346			−0.0464213
$640$	−5.13330	−	2.16771i	−0.202912	−	0.0856865i
$641$	−3.91889			−0.154787			−0.0773933	−	0.997001i	$-0.524660\pi$
$641$	−3.91889			−0.154787			−0.0773933	+	0.997001i	$0.524660\pi$
$642$	8.44649	−	18.1409i	0.333357	−	0.715964i
$643$	−1.16580	−	11.8365i	−0.0459745	−	0.466787i	−0.990417	−	0.138110i	$-0.955897\pi$
$643$	−1.16580	−	11.8365i	−0.0459745	−	0.466787i	0.944442	−	0.328677i	$-0.106603\pi$
$644$	10.2870	+	0.888039i	0.405366	+	0.0349936i
$645$	−2.90814	−	1.55443i	−0.114508	−	0.0612058i
$646$	8.52891	+	2.99379i	0.335566	+	0.117789i
$647$	−4.73645	+	23.8117i	−0.186209	+	0.936136i	0.768784	+	0.639508i	$0.220862\pi$
$647$	−4.73645	+	23.8117i	−0.186209	+	0.936136i	−0.954993	+	0.296628i	$0.904138\pi$
$648$	−1.72572	−	2.24096i	−0.0677926	−	0.0880332i
$649$	−3.90148	+	0.776052i	−0.153146	+	0.0304627i
$650$	−21.5213	+	16.1634i	−0.844134	+	0.633979i
$651$	11.1034	+	13.5296i	0.435177	+	0.530265i
$652$	0.557929	−	0.00673023i	0.0218502	−	0.000263576i
$653$	−7.37339	−	13.7946i	−0.288543	−	0.539826i	0.695331	−	0.718690i	$-0.255258\pi$
$653$	−7.37339	−	13.7946i	−0.288543	−	0.539826i	−0.983874	+	0.178864i	$0.942758\pi$
$654$	−10.5847	−	7.75164i	−0.413895	−	0.303113i
$655$	−0.772165	+	1.86417i	−0.0301710	+	0.0728392i
$656$	29.0541	+	27.6850i	1.13437	+	1.08092i
$657$	3.43377	+	8.28986i	0.133964	+	0.323418i
$658$	−7.53613	+	30.8748i	−0.293789	+	1.20362i
$659$	13.9483	−	45.9815i	0.543350	−	1.79119i	−0.0654429	−	0.997856i	$-0.520846\pi$
$659$	13.9483	−	45.9815i	0.543350	−	1.79119i	0.608793	−	0.793329i	$-0.291654\pi$
$660$	−1.19285	−	0.776391i	−0.0464317	−	0.0302210i
$661$	22.5086	+	2.21691i	0.875484	+	0.0862277i	0.525768	−	0.850628i	$-0.323778\pi$
$661$	22.5086	+	2.21691i	0.875484	+	0.0862277i	0.349716	+	0.936856i	$0.386278\pi$
$662$	42.5776	−	10.9385i	1.65483	−	0.425135i
$663$	7.52193	+	5.02599i	0.292128	+	0.195193i
$664$	−0.551425	+	17.7857i	−0.0213994	+	0.690219i
$665$	2.05757	+	3.07937i	0.0797891	+	0.119413i
$666$	10.2963	−	0.568091i	0.398973	−	0.0220131i
$667$	−4.66886	−	15.3912i	−0.180779	−	0.595948i
$668$	0.836381	+	0.242736i	0.0323606	+	0.00939174i
$669$	−3.35005	−	2.74932i	−0.129521	−	0.106295i
$670$	−2.44789	−	2.66831i	−0.0945701	−	0.103086i
$671$	5.14217	+	5.14217i	0.198511	+	0.198511i
$672$	9.76601	−	11.4508i	0.376732	−	0.441725i
$673$	−9.25626	+	9.25626i	−0.356803	+	0.356803i	−0.862633	−	0.505830i	$-0.831186\pi$
$673$	−9.25626	+	9.25626i	−0.356803	+	0.356803i	0.505830	+	0.862633i	$0.331186\pi$
$674$	4.11316	+	0.177207i	0.158433	+	0.00682574i
$675$	3.01808	−	3.67754i	0.116166	−	0.141549i
$676$	−5.97063	+	0.660864i	−0.229640	+	0.0254179i
$677$	−19.6957	+	5.97462i	−0.756967	+	0.229623i	−0.645098	−	0.764100i	$-0.723184\pi$
$677$	−19.6957	+	5.97462i	−0.756967	+	0.229623i	−0.111869	+	0.993723i	$0.535684\pi$
$678$	2.62210	+	2.34788i	0.100701	+	0.0901699i
$679$	−13.8818	+	9.27552i	−0.532734	+	0.355962i
$680$	−3.10727	+	0.518540i	−0.119158	+	0.0198851i
$681$	2.40356	−	3.59718i	0.0921046	−	0.137844i
$682$	6.84129	−	11.5717i	0.261966	−	0.443103i
$683$	1.52620	−	15.4958i	0.0583985	−	0.592930i	−0.920801	−	0.390032i	$-0.872464\pi$
$683$	1.52620	−	15.4958i	0.0583985	−	0.592930i	0.979200	−	0.202898i	$-0.0650361\pi$
$684$	4.66192	−	3.19700i	0.178253	−	0.122240i
$685$	0.972766	+	0.295085i	0.0371675	+	0.0112746i
$686$	22.2572	−	13.5236i	0.849784	−	0.516333i
$687$	−12.4712	+	5.16574i	−0.475806	+	0.197085i
$688$	−25.8076	−	7.15356i	−0.983904	−	0.272727i
$689$	−9.03067	−	3.74063i	−0.344041	−	0.142507i
$690$	−1.33578	+	0.206385i	−0.0508521	+	0.00785693i
$691$	0.0903652	−	0.0483012i	0.00343765	−	0.00183746i	−0.469677	−	0.882838i	$-0.655630\pi$
$691$	0.0903652	−	0.0483012i	0.00343765	−	0.00183746i	0.473115	+	0.881001i	$0.343130\pi$
$692$	14.8944	+	34.7661i	0.566199	+	1.32161i
$693$	2.97147	−	2.43862i	0.112877	−	0.0926357i
$694$	−20.5963	−	2.92833i	−0.781826	−	0.111158i
$695$	−0.761210	−	3.82686i	−0.0288743	−	0.145161i
$696$	−22.2119	−	7.49708i	−0.841942	−	0.284176i
$697$	22.2527	+	4.42633i	0.842880	+	0.167659i
$698$	35.8186	−	17.2061i	1.35575	−	0.651259i
$699$	−10.0844	+	18.8666i	−0.381428	+	0.713601i
$700$	22.4671	+	11.6627i	0.849177	+	0.440809i
$701$	13.7625	−	1.35548i	0.519801	−	0.0511959i	0.165285	−	0.986246i	$-0.447146\pi$
$701$	13.7625	−	1.35548i	0.519801	−	0.0511959i	0.354516	+	0.935050i	$0.384646\pi$
$702$	5.31518	−	1.93804i	0.200608	−	0.0731466i
$703$			20.6092i			0.777289i
$704$	−10.8322	−	4.03418i	−0.408253	−	0.152044i
$705$		−	4.16029i		−	0.156686i
$706$	−16.5907	−	45.5008i	−0.624398	−	1.71245i
$707$	−17.9690	+	1.76979i	−0.675793	+	0.0665598i
$708$	1.66182	+	5.24947i	0.0624548	+	0.197287i
$709$	−3.52612	+	6.59691i	−0.132426	+	0.247752i	−0.939391	−	0.342847i	$-0.888609\pi$
$709$	−3.52612	+	6.59691i	−0.132426	+	0.247752i	0.806965	+	0.590599i	$0.201109\pi$
$710$	0.353911	+	0.736752i	0.0132820	+	0.0276498i
$711$	0.969209	+	0.192788i	0.0363482	+	0.00723010i
$712$	39.7512	+	34.7393i	1.48974	+	1.30191i
$713$	−2.49055	−	12.5208i	−0.0932718	−	0.468909i
$714$	1.19765	−	8.42364i	0.0448210	−	0.315247i
$715$	2.20064	−	1.80602i	0.0822992	−	0.0675412i
$716$	35.4500	+	14.1854i	1.32483	+	0.530132i
$717$	−16.9914	+	9.08207i	−0.634554	+	0.339176i
$718$	6.03539	+	39.0626i	0.225239	+	1.45780i
$719$	−27.9684	−	11.5849i	−1.04304	−	0.432043i	−0.205641	−	0.978628i	$-0.565928\pi$
$719$	−27.9684	−	11.5849i	−1.04304	−	0.432043i	−0.837404	+	0.546584i	$0.815928\pi$
$720$	−0.886509	+	1.75935i	−0.0330382	+	0.0655673i
$721$	32.9562	−	13.6509i	1.22735	−	0.508387i
$722$	−8.08627	−	13.3084i	−0.300940	−	0.495289i
$723$	−1.09019	−	0.330707i	−0.0405448	−	0.0122991i
$724$	34.3852	+	6.40948i	1.27792	+	0.238206i
$725$	3.86494	−	39.2414i	0.143540	−	1.45739i
$726$	10.8496	+	6.41440i	0.402668	+	0.238061i
$727$	−13.2802	+	19.8753i	−0.492536	+	0.737133i	−0.991587	−	0.129440i	$-0.958682\pi$
$727$	−13.2802	+	19.8753i	−0.492536	+	0.737133i	0.499051	+	0.866573i	$0.333682\pi$
$728$	15.9406	+	25.5359i	0.590799	+	0.946425i
$729$	−0.831470	+	0.555570i	−0.0307952	+	0.0205767i
$730$	4.16915	−	4.65608i	0.154307	−	0.172329i
$731$	−14.4884	+	4.39501i	−0.535873	+	0.162555i
$732$	6.29153	−	7.85765i	0.232542	−	0.290427i
$733$	6.65579	−	8.11010i	0.245837	−	0.299553i	−0.635443	−	0.772148i	$-0.719182\pi$
$733$	6.65579	−	8.11010i	0.245837	−	0.299553i	0.881280	+	0.472595i	$0.156682\pi$
$734$	1.53875	−	35.7160i	0.0567961	−	1.31830i
$735$	0.0271707	−	0.0271707i	0.00100221	−	0.00100221i
$736$	−10.2193	+	4.00806i	−0.376689	+	0.147739i
$737$	−5.31142	−	5.31142i	−0.195649	−	0.195649i
$738$	10.4556	−	9.59192i	0.384877	−	0.353083i
$739$	−20.0355	−	16.4427i	−0.737019	−	0.604856i	0.189157	−	0.981947i	$-0.439424\pi$
$739$	−20.0355	−	16.4427i	−0.737019	−	0.604856i	−0.926176	+	0.377091i	$0.876924\pi$
$740$	−3.46200	−	6.29316i	−0.127266	−	0.231341i
$741$	3.28222	+	10.8200i	0.120575	+	0.397483i
$742$	0.506460	+	9.17925i	0.0185927	+	0.336981i
$743$	26.1282	+	39.1036i	0.958550	+	1.43457i	0.899802	+	0.436298i	$0.143711\pi$
$743$	26.1282	+	39.1036i	0.958550	+	1.43457i	0.0587475	+	0.998273i	$0.481289\pi$
$744$	−16.9621	−	7.65008i	−0.621862	−	0.280466i
$745$	−3.33948	−	2.23137i	−0.122349	−	0.0817511i
$746$	9.14344	+	35.5906i	0.334765	+	1.30306i
$747$	6.26092	+	0.616647i	0.229075	+	0.0225619i
$748$	−6.39344	+	1.35210i	−0.233767	+	0.0494377i
$749$	10.9278	−	36.0240i	0.399292	−	1.31629i
$750$	−6.60249	−	1.61158i	−0.241089	−	0.0588467i
$751$	−19.9279	−	48.1101i	−0.727178	−	1.75556i	−0.651779	−	0.758409i	$-0.725977\pi$
$751$	−19.9279	−	48.1101i	−0.727178	−	1.75556i	−0.0753992	−	0.997153i	$-0.524023\pi$
$752$	−7.38913	−	32.9699i	−0.269454	−	1.20229i
$753$	5.48753	−	13.2481i	0.199977	−	0.482787i
$754$	27.7055	−	37.8312i	1.00897	−	1.37773i
$755$	0.823196	+	1.54009i	0.0299592	+	0.0560496i
$756$	−3.80756	−	3.71679i	−0.138480	−	0.135178i
$757$	−6.43586	−	7.84212i	−0.233915	−	0.285027i	0.642802	−	0.766032i	$-0.277772\pi$
$757$	−6.43586	−	7.84212i	−0.233915	−	0.285027i	−0.876718	+	0.481006i	$0.840272\pi$
$758$	−2.43680	−	3.24457i	−0.0885087	−	0.117848i
$759$	−2.74993	+	0.546995i	−0.0998161	+	0.0198547i
$760$	−3.41325	−	1.96277i	−0.123812	−	0.0711972i
$761$	2.47540	−	12.4447i	0.0897332	−	0.451119i	−0.909629	−	0.415421i	$-0.863634\pi$
$761$	2.47540	−	12.4447i	0.0897332	−	0.451119i	0.999363	−	0.0356987i	$-0.0113656\pi$
$762$	−6.63321	+	18.8971i	−0.240296	+	0.684570i
$763$	−21.7666	−	11.6345i	−0.788005	−	0.421197i
$764$	−15.8662	+	13.3445i	−0.574019	+	0.482789i
$765$	0.109169	+	1.10842i	0.00394703	+	0.0400749i
$766$	−19.1686	−	8.92499i	−0.692588	−	0.322473i
$767$	−11.0137			−0.397681
$768$	−3.90069	+	15.5172i	−0.140754	+	0.559930i
$769$	23.3694			0.842721			0.421360	−	0.906893i	$-0.361553\pi$
$769$	23.3694			0.842721			0.421360	+	0.906893i	$0.361553\pi$
$770$	−2.42727	−	1.13015i	−0.0874728	−	0.0407278i
$771$	0.637418	+	6.47181i	0.0229560	+	0.233077i
$772$	26.5898	−	22.3638i	0.956988	−	0.804892i
$773$	−16.3860	−	8.75851i	−0.589364	−	0.315022i	0.149621	−	0.988743i	$-0.452195\pi$
$773$	−16.3860	−	8.75851i	−0.589364	−	0.315022i	−0.738985	+	0.673722i	$0.764695\pi$
$774$	−3.13598	+	8.93398i	−0.112720	+	0.321125i
$775$	6.10590	−	30.6964i	0.219330	−	1.10265i
$776$	8.84817	−	15.3869i	0.317631	−	0.552359i
$777$	19.0263	−	3.78457i	0.682566	−	0.135771i
$778$	15.3339	+	20.4168i	0.549746	+	0.731978i
$779$	17.9898	+	21.9207i	0.644553	+	0.785390i
$780$	−2.81983	−	2.75261i	−0.100966	−	0.0985594i
$781$	0.799253	+	1.49530i	0.0285995	+	0.0535060i
$782$	−3.66674	+	5.00685i	−0.131122	+	0.179045i
$783$	−3.17182	+	7.65746i	−0.113352	+	0.273655i
$784$	0.167067	−	0.263583i	0.00596668	−	0.00941369i
$785$	4.34612	+	10.4925i	0.155120	+	0.374492i
$786$	5.62852	+	1.37385i	0.200763	+	0.0490036i
$787$	−12.4192	+	40.9406i	−0.442697	+	1.45938i	0.397756	+	0.917491i	$0.369789\pi$
$787$	−12.4192	+	40.9406i	−0.442697	+	1.45938i	−0.840453	+	0.541885i	$0.817711\pi$
$788$	−17.3890	+	3.67746i	−0.619456	+	0.131004i
$789$	−15.4829	−	1.52494i	−0.551207	−	0.0542891i
$790$	−0.171269	−	0.666660i	−0.00609348	−	0.0237187i
$791$	5.50537	+	3.67857i	0.195749	+	0.130795i
$792$	−1.68017	+	3.72537i	−0.0597024	+	0.132375i
$793$	11.1861	+	16.7411i	0.397229	+	0.594495i
$794$	−1.89369	−	34.3219i	−0.0672046	−	1.21804i
$795$	−0.349337	−	1.15161i	−0.0123897	−	0.0408434i
$796$	24.1647	+	43.9261i	0.856494	+	1.55692i
$797$	−39.7140	−	32.5924i	−1.40674	−	1.15448i	−0.966519	−	0.256593i	$-0.917400\pi$
$797$	−39.7140	−	32.5924i	−1.40674	−	1.15448i	−0.440222	−	0.897889i	$-0.645100\pi$
$798$	7.83623	−	7.18890i	0.277399	−	0.254484i
$799$	−13.5070	−	13.5070i	−0.477844	−	0.477844i
$800$	−26.9072	−	0.509458i	−0.951314	−	0.0180121i
$801$	13.1980	−	13.1980i	0.466327	−	0.466327i
$802$	−1.26525	+	29.3679i	−0.0446776	+	1.03702i
$803$	8.22472	−	10.0218i	0.290244	−	0.353663i
$804$	−6.49862	+	8.11628i	−0.229189	+	0.286239i
$805$	−2.43322	+	0.738111i	−0.0857599	+	0.0260150i
$806$	24.8280	−	27.7278i	0.874530	−	0.976668i
$807$	20.2120	−	13.5052i	0.711495	−	0.475406i
$808$	16.2836	−	10.1649i	0.572857	−	0.357602i
$809$	13.3936	−	20.0449i	0.470894	−	0.704743i	−0.517664	−	0.855584i	$-0.673198\pi$
$809$	13.3936	−	20.0449i	0.470894	−	0.704743i	0.988558	+	0.150841i	$0.0481982\pi$
$810$	0.599582	+	0.354478i	0.0210672	+	0.0124551i
$811$	4.49728	−	45.6616i	0.157921	−	1.60340i	−0.510677	−	0.859773i	$-0.670605\pi$
$811$	4.49728	−	45.6616i	0.157921	−	1.60340i	0.668598	−	0.743624i	$-0.266895\pi$
$812$	−43.3549	−	8.08145i	−1.52146	−	0.283603i
$813$	−9.35175	−	2.83682i	−0.327980	−	0.0994917i
$814$	−7.73679	−	12.7333i	−0.271175	−	0.446301i
$815$	−0.126946	+	0.0525829i	−0.00444673	+	0.00184190i
$816$	2.83382	+	8.59019i	0.0992036	+	0.300717i
$817$	−17.4828	−	7.24162i	−0.611647	−	0.253352i
$818$	−7.70314	−	49.8568i	−0.269334	−	1.74320i
$819$	9.38629	−	5.01707i	0.327983	−	0.175311i
$820$	−9.17564	−	3.67164i	−0.320427	−	0.128219i
$821$	−27.1118	+	22.2501i	−0.946208	+	0.776533i	−0.974805	−	0.223058i	$-0.928396\pi$
$821$	−27.1118	+	22.2501i	−0.946208	+	0.776533i	0.0285969	+	0.999591i	$0.490896\pi$
$822$	0.410865	−	2.88980i	0.0143306	−	0.100794i
$823$	4.84746	+	24.3698i	0.168972	+	0.849479i	0.968531	+	0.248892i	$0.0800665\pi$
$823$	4.84746	+	24.3698i	0.168972	+	0.849479i	−0.799559	+	0.600587i	$0.794934\pi$
$824$	−24.9555	+	28.5558i	−0.869365	+	0.994790i
$825$	−6.74181	−	1.34103i	−0.234720	−	0.0466886i
$826$	4.48521	+	9.33706i	0.156060	+	0.324878i
$827$	2.47505	−	4.63050i	0.0860661	−	0.161018i	−0.835206	−	0.549938i	$-0.814652\pi$
$827$	2.47505	−	4.63050i	0.0860661	−	0.161018i	0.921272	+	0.388919i	$0.127152\pi$
$828$	1.17132	+	3.70006i	0.0407062	+	0.128586i
$829$	41.6585	−	4.10300i	1.44686	−	0.142503i	0.656120	−	0.754656i	$-0.272196\pi$
$829$	41.6585	−	4.10300i	1.44686	−	0.142503i	0.790739	+	0.612153i	$0.209696\pi$
$830$	−1.50111	−	4.11688i	−0.0521044	−	0.142899i
$831$		−	15.4757i		−	0.536847i
$832$	−27.2358	−	16.8059i	−0.944232	−	0.582638i
$833$		−	0.176428i		−	0.00611285i
$834$	−10.5258	+	3.83795i	−0.364478	+	0.132897i
$835$	−0.213434	+	0.0210214i	−0.00738617	+	0.000727475i
$836$	−7.24912	−	3.76303i	−0.250716	−	0.130147i
$837$	−3.10119	+	5.80193i	−0.107193	+	0.200544i
$838$	−37.9711	+	18.2400i	−1.31169	+	0.630091i
$839$	−23.5402	−	4.68244i	−0.812698	−	0.161656i	−0.228790	−	0.973476i	$-0.573477\pi$
$839$	−23.5402	−	4.68244i	−0.812698	−	0.161656i	−0.583908	+	0.811820i	$0.698477\pi$
$840$	−1.18523	+	3.51154i	−0.0408944	+	0.121160i
$841$	7.74452	+	38.9343i	0.267052	+	1.34256i
$842$	19.6126	+	2.78847i	0.675895	+	0.0960971i
$843$	−23.1551	+	19.0029i	−0.797504	+	0.654495i
$844$	3.92831	+	9.16935i	0.135218	+	0.315622i
$845$	1.30463	−	0.697342i	0.0448808	−	0.0239893i
$846$	−11.8057	+	1.82404i	−0.405888	+	0.0627119i
$847$	21.9060	+	9.07375i	0.752698	+	0.311778i
$848$	−4.81385	−	8.50594i	−0.165308	−	0.292095i
$849$	−25.0600	+	10.3802i	−0.860057	+	0.356247i
$850$	−13.0026	+	7.90045i	−0.445986	+	0.270983i
$851$	−13.5403	−	4.10739i	−0.464154	−	0.140800i
$852$	1.93552	−	1.32732i	0.0663098	−	0.0454732i
$853$	2.30787	−	23.4322i	0.0790200	−	0.802303i	−0.871242	−	0.490853i	$-0.836685\pi$
$853$	2.30787	−	23.4322i	0.0790200	−	0.802303i	0.950262	−	0.311450i	$-0.100815\pi$
$854$	9.63721	−	16.3009i	0.329778	−	0.557804i
$855$	−0.773390	+	1.15746i	−0.0264494	+	0.0395843i
$856$	6.58770	+	39.4758i	0.225163	+	1.34926i
$857$	−28.2428	+	18.8712i	−0.964756	+	0.644629i	−0.934895	−	0.354925i	$-0.884506\pi$
$857$	−28.2428	+	18.8712i	−0.964756	+	0.644629i	−0.0298608	+	0.999554i	$0.509506\pi$
$858$	−6.08980	−	5.45294i	−0.207902	−	0.186160i
$859$	−40.5554	+	12.3024i	−1.38373	+	0.419751i	−0.892409	−	0.451226i	$-0.850987\pi$
$859$	−40.5554	+	12.3024i	−1.38373	+	0.419751i	−0.491323	+	0.870977i	$0.663487\pi$
$860$	6.55498	−	0.725543i	0.223523	−	0.0247408i
$861$	16.9336	−	20.6336i	0.577094	−	0.703191i
$862$	24.7077	+	1.06448i	0.841546	+	0.0362562i
$863$	−29.3450	+	29.3450i	−0.998915	+	0.998915i	−0.999999	−	0.00108481i	$-0.999655\pi$
$863$	−29.3450	+	29.3450i	−0.998915	+	0.998915i	0.00108481	+	0.999999i	$0.499655\pi$
$864$	5.38122	+	1.74428i	0.183073	+	0.0593416i
$865$	−6.58607	−	6.58607i	−0.223933	−	0.223933i
$866$	33.6766	+	36.7091i	1.14438	+	1.24742i
$867$	−9.18811	−	7.54048i	−0.312044	−	0.256088i
$868$	−33.6177	−	9.75658i	−1.14106	−	0.331160i
$869$	−0.414475	−	1.36634i	−0.0140601	−	0.0463499i
$870$	5.76433	−	0.318043i	0.195429	−	0.0107827i
$871$	−11.5543	−	17.2922i	−0.391501	−	0.585923i
$872$	26.2266	+	0.813125i	0.888144	+	0.0275359i
$873$	−5.21783	−	3.48644i	−0.176597	−	0.117998i
$874$	−7.51257	+	1.93003i	−0.254116	+	0.0652841i
$875$	−12.7239	−	1.25319i	−0.430145	−	0.0423656i
$876$	−15.0405	−	9.78942i	−0.508172	−	0.330754i
$877$	6.21429	−	20.4858i	0.209842	−	0.691755i	−0.787325	−	0.616538i	$-0.788535\pi$
$877$	6.21429	−	20.4858i	0.209842	−	0.691755i	0.997167	−	0.0752176i	$-0.0239651\pi$
$878$	−10.6160	+	43.4925i	−0.358271	+	1.46780i
$879$	−2.88386	−	6.96226i	−0.0972702	−	0.234831i
$880$	2.84570	−	0.0686647i	0.0959284	−	0.00231469i
$881$	−1.72475	+	4.16392i	−0.0581084	+	0.140286i	−0.950267	−	0.311436i	$-0.899190\pi$
$881$	−1.72475	+	4.16392i	−0.0581084	+	0.140286i	0.892159	+	0.451722i	$0.149190\pi$
$882$	−0.0890153	−	0.0651898i	−0.00299730	−	0.00219505i
$883$	16.8072	+	31.4441i	0.565608	+	1.05818i	0.988389	+	0.151946i	$0.0485541\pi$
$883$	16.8072	+	31.4441i	0.565608	+	1.05818i	−0.422781	+	0.906232i	$0.638946\pi$
$884$	−18.0918	+	0.218239i	−0.608492	+	0.00734018i
$885$	−0.860216	−	1.04818i	−0.0289159	−	0.0352341i
$886$	−31.5294	+	23.6799i	−1.05925	+	0.795541i
$887$	27.6517	−	5.50027i	0.928455	−	0.184681i	0.292374	−	0.956304i	$-0.405555\pi$
$887$	27.6517	−	5.50027i	0.928455	−	0.184681i	0.636080	+	0.771623i	$0.280555\pi$
$888$	−16.3403	+	12.5833i	−0.548343	+	0.422269i
$889$	−7.35027	+	36.9523i	−0.246520	+	1.23934i
$890$	−12.2668	−	4.30584i	−0.411183	−	0.144332i
$891$	1.27427	+	0.681110i	0.0426895	+	0.0228180i
$892$	8.63544	+	0.745462i	0.289136	+	0.0249599i
$893$	−2.34011	−	23.7596i	−0.0783089	−	0.795083i
$894$	−4.86781	+	10.4548i	−0.162804	+	0.349661i
$895$	−9.40292			−0.314305
$896$	−3.15597	+	29.9337i	−0.105434	+	1.00001i
$897$	−7.76292			−0.259196
$898$	4.39699	−	9.44360i	0.146730	−	0.315137i
$899$	5.34458	+	54.2644i	0.178252	+	1.80982i
$900$	−0.818335	+	9.47959i	−0.0272778	+	0.315986i
$901$	−4.87305	−	2.60470i	−0.162345	−	0.0867752i
$902$	−19.3441	−	6.79010i	−0.644088	−	0.226086i
$903$	−3.47498	+	17.4699i	−0.115640	+	0.581363i
$904$	−6.98066	−	0.906731i	−0.232173	−	0.0301574i
$905$	−8.44806	+	1.68042i	−0.280823	+	0.0558592i
$906$	4.00941	−	3.01123i	0.133204	−	0.100041i
$907$	−3.47017	−	4.22841i	−0.115225	−	0.140402i	0.712204	−	0.701973i	$-0.247697\pi$
$907$	−3.47017	−	4.22841i	−0.115225	−	0.140402i	−0.827429	+	0.561571i	$0.810197\pi$
$908$	0.104368	+	8.65195i	0.00346356	+	0.287125i
$909$	−3.19927	−	5.98541i	−0.106113	−	0.198523i
$910$	−5.98083	−	4.38002i	−0.198263	−	0.145196i
$911$	6.26941	−	15.1357i	0.207715	−	0.501468i	−0.785348	−	0.619055i	$-0.787516\pi$
$911$	6.26941	−	15.1357i	0.207715	−	0.501468i	0.993063	+	0.117587i	$0.0375159\pi$
$912$	−4.07326	+	10.5464i	−0.134879	+	0.349225i
$913$	−3.47860	−	8.39808i	−0.115125	−	0.277936i
$914$	10.1304	−	41.5032i	0.335083	−	1.37280i
$915$	−0.719580	+	2.37214i	−0.0237886	+	0.0784204i
$916$	14.7271	−	22.6269i	0.486598	−	0.747613i
$917$	10.8469	+	1.06833i	0.358196	+	0.0352792i
$918$	3.09750	−	0.795767i	0.102233	−	0.0262642i
$919$	−27.3583	−	18.2802i	−0.902467	−	0.603009i	0.0154071	−	0.999881i	$-0.495096\pi$
$919$	−27.3583	−	18.2802i	−0.902467	−	0.603009i	−0.917874	+	0.396872i	$0.870096\pi$
$920$	1.96980	−	1.85133i	0.0649425	−	0.0610367i
$921$	−11.8080	−	17.6719i	−0.389086	−	0.582308i
$922$	−15.1842	+	0.837777i	−0.500064	+	0.0275907i
$923$	1.36270	+	4.49221i	0.0448537	+	0.147863i
$924$	−2.14282	+	7.38339i	−0.0704937	+	0.242896i
$925$	−26.8153	−	22.0067i	−0.881681	−	0.723577i
$926$	−28.6352	−	31.2136i	−0.941011	−	1.02574i
$927$	9.48094	+	9.48094i	0.311395	+	0.311395i
$928$	45.1168	−	12.7585i	1.48103	−	0.418819i
$929$	−9.44386	+	9.44386i	−0.309843	+	0.309843i	−0.844849	−	0.535006i	$-0.820310\pi$
$929$	−9.44386	+	9.44386i	−0.309843	+	0.309843i	0.535006	+	0.844849i	$0.320310\pi$
$930$	4.57803	+	0.197235i	0.150120	+	0.00646758i
$931$	0.139890	−	0.170456i	0.00458470	−	0.00558647i
$932$	−4.70697	−	42.5255i	−0.154182	−	1.39297i
$933$	−2.17108	+	0.658591i	−0.0710781	+	0.0215613i
$934$	−34.6375	−	31.0152i	−1.13337	−	1.01485i
$935$	1.33806	−	0.894064i	0.0437593	−	0.0292390i
$936$	−6.57478	+	9.20872i	−0.214904	+	0.300997i
$937$	26.8736	−	40.2192i	0.877923	−	1.31390i	−0.0707003	−	0.997498i	$-0.522523\pi$
$937$	26.8736	−	40.2192i	0.877923	−	1.31390i	0.948623	−	0.316407i	$-0.102477\pi$
$938$	−9.95441	+	16.8374i	−0.325023	+	0.549761i
$939$	−0.325461	+	3.30446i	−0.0106210	+	0.107837i
$940$	4.70578	+	6.86205i	0.153486	+	0.223815i
$941$	6.33610	+	1.92203i	0.206551	+	0.0626565i	0.391865	−	0.920023i	$-0.371830\pi$
$941$	6.33610	+	1.92203i	0.206551	+	0.0626565i	−0.185314	+	0.982679i	$0.559330\pi$
$942$	27.8691	−	16.9334i	0.908023	−	0.551719i
$943$	−17.9873	+	7.45059i	−0.585747	+	0.242625i
$944$	−8.67880	−	6.77886i	−0.282471	−	0.220633i
$945$	1.21059	+	0.501441i	0.0393804	+	0.0163119i
$946$	13.5202	−	2.08895i	0.439581	−	0.0679176i
$947$	−0.370176	+	0.197863i	−0.0120291	+	0.00642968i	−0.477400	−	0.878686i	$-0.658421\pi$
$947$	−0.370176	+	0.197863i	−0.0120291	+	0.00642968i	0.465371	+	0.885116i	$0.345921\pi$
$948$	−1.81669	+	0.778303i	−0.0590035	+	0.0252781i
$949$	27.7476	−	22.7719i	0.900725	−	0.739206i
$950$	−18.8268	−	2.67675i	−0.610822	−	0.0868451i
$951$	0.895007	+	4.49951i	0.0290226	+	0.145906i
$952$	7.55270	+	15.2488i	0.244785	+	0.494215i
$953$	36.0204	+	7.16490i	1.16681	+	0.232094i	0.740230	−	0.672354i	$-0.234717\pi$
$953$	36.0204	+	7.16490i	1.16681	+	0.232094i	0.426585	+	0.904448i	$0.359717\pi$
$954$	−3.11477	+	1.49623i	−0.100844	+	0.0484423i
$955$	2.40669	−	4.50261i	0.0778787	−	0.145701i
$956$	17.7529	−	34.1993i	0.574170	−	1.10609i
$957$	11.9180	−	1.17382i	0.385254	−	0.0379442i
$958$	31.1331	−	11.3519i	1.00587	−	0.366763i
$959$		−	5.49105i		−	0.177315i
$960$	−0.527816	−	3.90465i	−0.0170352	−	0.126022i
$961$			12.2797i			0.396121i
$962$	−14.1315	−	38.7563i	−0.455617	−	1.24955i
$963$	14.0817	−	1.38693i	0.453776	−	0.0446930i
$964$	2.17225	−	0.687665i	0.0699635	−	0.0221482i
$965$	−4.03333	+	7.54582i	−0.129837	+	0.242909i
$966$	3.16137	+	6.58116i	0.101715	+	0.211745i
$967$	41.5837	+	8.27152i	1.33724	+	0.265994i	0.811352	−	0.584558i	$-0.198732\pi$
$967$	41.5837	+	8.27152i	1.33724	+	0.265994i	0.525890	+	0.850552i	$0.323732\pi$
$968$	−25.1510	+	1.69221i	−0.808384	+	0.0543898i
$969$	1.24694	+	6.26879i	0.0400575	+	0.201383i
$970$	−0.615273	+	4.32750i	−0.0197552	+	0.138948i
$971$	−17.1055	+	14.0382i	−0.548943	+	0.450506i	−0.867528	−	0.497389i	$-0.834292\pi$
$971$	−17.1055	+	14.0382i	−0.548943	+	0.450506i	0.318585	+	0.947894i	$0.396792\pi$
$972$	0.743023	−	1.85686i	0.0238325	−	0.0595587i
$973$	−18.5879	+	9.93543i	−0.595900	+	0.318515i
$974$	6.71160	+	43.4392i	0.215053	+	1.39188i
$975$	−17.5831	−	7.28316i	−0.563110	−	0.233248i
$976$	−1.48943	+	20.0770i	−0.0476754	+	0.642649i
$977$	24.0330	−	9.95478i	0.768882	−	0.318482i	0.0364628	−	0.999335i	$-0.488391\pi$
$977$	24.0330	−	9.95478i	0.768882	−	0.318482i	0.732420	+	0.680853i	$0.238391\pi$
$978$	0.204873	+	0.337182i	0.00655113	+	0.0107819i
$979$	−25.8070	−	7.82846i	−0.824795	−	0.250199i
$980$	−0.0140825	+	0.0755491i	−0.000449849	+	0.00241333i
$981$	0.909301	−	9.23228i	0.0290317	−	0.294764i
$982$	−36.8576	−	21.7905i	−1.17617	−	0.695363i
$983$	1.75731	−	2.63001i	0.0560496	−	0.0838842i	−0.802386	−	0.596805i	$-0.796437\pi$
$983$	1.75731	−	2.63001i	0.0560496	−	0.0838842i	0.858436	+	0.512921i	$0.171437\pi$
$984$	−6.39608	+	27.6476i	−0.203899	+	0.881373i
$985$	3.63928	−	2.43169i	0.115957	−	0.0774800i
$986$	17.6822	−	19.7473i	0.563115	−	0.628883i
$987$	−21.5050	+	6.52348i	−0.684513	+	0.207645i
$988$	−17.6525	−	14.1341i	−0.561600	−	0.449667i
$989$	8.24208	−	10.0430i	0.262083	−	0.319349i
$990$	0.0433183	−	1.00547i	0.00137675	−	0.0319558i
$991$	21.8776	−	21.8776i	0.694964	−	0.694964i	−0.268356	−	0.963320i	$-0.586480\pi$
$991$	21.8776	−	21.8776i	0.694964	−	0.694964i	0.963320	+	0.268356i	$0.0864802\pi$
$992$	36.6308	−	6.56801i	1.16303	−	0.208535i
$993$	21.9801	+	21.9801i	0.697518	+	0.697518i
$994$	3.25341	−	2.98466i	0.103192	−	0.0946676i
$995$	−9.54362	−	7.83225i	−0.302553	−	0.248299i
$996$	−11.0244	+	6.06473i	−0.349320	+	0.192168i
$997$	10.7309	+	35.3750i	0.339851	+	1.12034i	0.945777	+	0.324817i	$0.105303\pi$
$997$	10.7309	+	35.3750i	0.339851	+	1.12034i	−0.605926	+	0.795521i	$0.707197\pi$
$998$	−0.534227	−	9.68250i	−0.0169106	−	0.306494i
$999$	4.05102	+	6.06278i	0.128169	+	0.191818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	384.2.v.a.181.4	yes	512
128.29	even	32	inner	384.2.v.a.157.4	✓	512

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
384.2.v.a.157.4	✓	512	128.29	even	32	inner
384.2.v.a.181.4	yes	512	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.28206 - 0.596933i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(1.28734 + 1.53060i) q^{4} +(-0.434364 - 0.232173i) q^{5} +(-0.468395 + 1.33439i) q^{6} +(-0.519029 + 2.60933i) q^{7} +(-0.736779 - 2.73078i) q^{8} +(-0.980785 + 0.195090i) q^{9} +O(q^{10})\)	\(q+(-1.28206 - 0.596933i) q^{2} +(-0.0980171 - 0.995185i) q^{3} +(1.28734 + 1.53060i) q^{4} +(-0.434364 - 0.232173i) q^{5} +(-0.468395 + 1.33439i) q^{6} +(-0.519029 + 2.60933i) q^{7} +(-0.736779 - 2.73078i) q^{8} +(-0.980785 + 0.195090i) q^{9} +(0.418289 + 0.556945i) q^{10} +(0.916620 + 1.11690i) q^{11} +(1.39705 - 1.43117i) q^{12} +(1.88580 + 3.52808i) q^{13} +(2.22302 - 3.03549i) q^{14} +(-0.188479 + 0.455030i) q^{15} +(-0.685499 + 3.94082i) q^{16} +(0.865395 + 2.08925i) q^{17} +(1.37388 + 0.335346i) q^{18} +(-0.820463 + 2.70471i) q^{19} +(-0.203811 - 0.963726i) q^{20} +(2.64764 + 0.260770i) q^{21} +(-0.508442 - 1.97910i) q^{22} +(-1.61348 - 1.07809i) q^{23} +(-2.64541 + 1.00089i) q^{24} +(-2.64308 - 3.95565i) q^{25} +(-0.311674 - 5.64889i) q^{26} +(0.290285 + 0.956940i) q^{27} +(-4.66203 + 2.56468i) q^{28} +(6.40700 + 5.25809i) q^{29} +(0.513264 - 0.470865i) q^{30} +(4.65187 + 4.65187i) q^{31} +(3.23126 - 4.64317i) q^{32} +(1.02168 - 1.02168i) q^{33} +(0.137655 - 3.19512i) q^{34} +(0.831264 - 1.01290i) q^{35} +(-1.56121 - 1.25005i) q^{36} +(6.97766 - 2.11665i) q^{37} +(2.66641 - 2.97783i) q^{38} +(3.32625 - 2.22253i) q^{39} +(-0.313982 + 1.35721i) q^{40} +(5.57407 - 8.34219i) q^{41} +(-3.23877 - 1.91479i) q^{42} +(-0.656241 + 6.66293i) q^{43} +(-0.529535 + 2.84082i) q^{44} +(0.471313 + 0.142971i) q^{45} +(1.42502 + 2.34532i) q^{46} +(-7.80396 + 3.23250i) q^{47} +(3.98904 + 0.295930i) q^{48} +(-0.0720787 - 0.0298560i) q^{49} +(1.02732 + 6.64912i) q^{50} +(1.99436 - 1.06601i) q^{51} +(-2.97242 + 7.42825i) q^{52} +(-1.88878 + 1.55008i) q^{53} +(0.199067 - 1.40013i) q^{54} +(-0.138832 - 0.697957i) q^{55} +(7.50793 - 0.505149i) q^{56} +(2.77210 + 0.551405i) q^{57} +(-5.07541 - 10.5657i) q^{58} +(-1.29781 + 2.42803i) q^{59} +(-0.939108 + 0.297292i) q^{60} +(5.00881 - 0.493324i) q^{61} +(-3.18711 - 8.74081i) q^{62} -2.66045i q^{63} +(-6.91431 + 4.02396i) q^{64} -1.97030i q^{65} +(-1.91973 + 0.699979i) q^{66} +(-5.17367 + 0.509562i) q^{67} +(-2.08375 + 4.01416i) q^{68} +(-0.914753 + 1.71138i) q^{69} +(-1.67036 + 0.802384i) q^{70} +(1.15091 + 0.228930i) q^{71} +(1.25537 + 2.53457i) q^{72} +(-1.75052 - 8.80047i) q^{73} +(-10.2093 - 1.45153i) q^{74} +(-3.67754 + 3.01808i) q^{75} +(-5.19605 + 2.22608i) q^{76} +(-3.39013 + 1.81206i) q^{77} +(-5.59114 + 0.863861i) q^{78} +(-0.912975 - 0.378167i) q^{79} +(1.21271 - 1.55260i) q^{80} +(0.923880 - 0.382683i) q^{81} +(-12.1260 + 7.36782i) q^{82} +(-6.02031 - 1.82624i) q^{83} +(3.00929 + 4.38820i) q^{84} +(0.109169 - 1.10842i) q^{85} +(4.81866 - 8.15052i) q^{86} +(4.60477 - 6.89153i) q^{87} +(2.37467 - 3.32600i) q^{88} +(-15.5192 + 10.3696i) q^{89} +(-0.518906 - 0.464639i) q^{90} +(-10.1847 + 3.08950i) q^{91} +(-0.426968 - 3.85747i) q^{92} +(4.17350 - 5.08543i) q^{93} +(11.9347 + 0.514181i) q^{94} +(0.984339 - 0.984339i) q^{95} +(-4.93753 - 2.76059i) q^{96} +(4.43740 + 4.43740i) q^{97} +(0.0745870 + 0.0813032i) q^{98} +(-1.11690 - 0.916620i) 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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