LMFDB - Embedded newform 640.2.bm.a.341.45

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [640,2,Mod(21,640)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(640, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 13, 0]))

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

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

chi := DirichletCharacter("640.21");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 640 = 2^{7} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	640.bm (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:	$5.11042572936$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			341.45
Character	$\chi$	$=$	640.341
Dual form			640.2.bm.a.381.45

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.822181 - 1.15066i) q^{2} +(0.201260 - 0.245236i) q^{3} +(-0.648036 - 1.89210i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-0.116711 - 0.433210i) q^{6} +(-2.74012 - 0.545044i) q^{7} +(-2.70997 - 0.809981i) q^{8} +(0.565636 + 2.84364i) q^{9} +O(q^{10})$	\(q+(0.822181 - 1.15066i) q^{2} +(0.201260 - 0.245236i) q^{3} +(-0.648036 - 1.89210i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-0.116711 - 0.433210i) q^{6} +(-2.74012 - 0.545044i) q^{7} +(-2.70997 - 0.809981i) q^{8} +(0.565636 + 2.84364i) q^{9} +(-0.452759 + 1.33978i) q^{10} +(-5.93055 - 0.584108i) q^{11} +(-0.594435 - 0.221883i) q^{12} +(-1.54989 + 5.10930i) q^{13} +(-2.88004 + 2.70482i) q^{14} +(-0.121406 + 0.293099i) q^{15} +(-3.16010 + 2.45230i) q^{16} +(-0.333940 - 0.806201i) q^{17} +(3.73712 + 1.68714i) q^{18} +(0.123550 - 0.0660386i) q^{19} +(1.16938 + 1.62251i) q^{20} +(-0.685142 + 0.562281i) q^{21} +(-5.54810 + 6.34381i) q^{22} +(5.15622 - 7.71682i) q^{23} +(-0.744045 + 0.501565i) q^{24} +(0.831470 - 0.555570i) q^{25} +(4.60477 + 5.98416i) q^{26} +(1.65057 + 0.882247i) q^{27} +(0.744419 + 5.53780i) q^{28} +(-0.760028 - 7.71669i) q^{29} +(0.237440 + 0.380677i) q^{30} +(-2.80087 - 2.80087i) q^{31} +(0.223590 + 5.65243i) q^{32} +(-1.33683 + 1.33683i) q^{33} +(-1.20222 - 0.278593i) q^{34} +(2.78035 - 0.273841i) q^{35} +(5.01391 - 2.91302i) q^{36} +(-1.71200 + 3.20293i) q^{37} +(0.0255921 - 0.196459i) q^{38} +(0.941053 + 1.40839i) q^{39} +(2.82840 - 0.0115584i) q^{40} +(-0.589295 - 0.393755i) q^{41} +(0.0836838 + 1.25066i) q^{42} +(-2.27983 - 2.77798i) q^{43} +(2.73802 + 11.5997i) q^{44} +(-1.36675 - 2.55700i) q^{45} +(-4.64009 - 12.2777i) q^{46} +(-9.23838 + 3.82666i) q^{47} +(-0.0346090 + 1.26852i) q^{48} +(0.744043 + 0.308193i) q^{49} +(0.0443463 - 1.41352i) q^{50} +(-0.264918 - 0.0803621i) q^{51} +(10.6717 - 0.378462i) q^{52} +(-0.302218 + 3.06847i) q^{53} +(2.37223 - 1.17387i) q^{54} +(5.84474 - 1.16259i) q^{55} +(6.98417 + 3.69650i) q^{56} +(0.00867054 - 0.0435897i) q^{57} +(-9.50417 - 5.46999i) q^{58} +(3.63714 + 11.9900i) q^{59} +(0.633248 + 0.0397730i) q^{60} +(-11.5478 - 9.47700i) q^{61} +(-5.52568 + 0.920027i) q^{62} -8.10023i q^{63} +(6.68786 + 4.39005i) q^{64} -5.33920i q^{65} +(0.439119 + 2.63735i) q^{66} +(9.55787 + 7.84394i) q^{67} +(-1.30901 + 1.15430i) q^{68} +(-0.854703 - 2.81758i) q^{69} +(1.97086 - 3.42439i) q^{70} +(1.38132 - 6.94439i) q^{71} +(0.770443 - 8.16434i) q^{72} +(2.85534 - 0.567962i) q^{73} +(2.27791 + 4.60333i) q^{74} +(0.0310958 - 0.315720i) q^{75} +(-0.205016 - 0.190973i) q^{76} +(15.9321 + 4.83294i) q^{77} +(2.39429 + 0.0751161i) q^{78} +(-11.3149 - 4.68677i) q^{79} +(2.31216 - 3.26403i) q^{80} +(-7.48741 + 3.10139i) q^{81} +(-0.937585 + 0.354341i) q^{82} +(-2.31472 - 4.33053i) q^{83} +(1.50789 + 0.931979i) q^{84} +(0.553588 + 0.674549i) q^{85} +(-5.07095 + 0.339306i) q^{86} +(-2.04538 - 1.36668i) q^{87} +(15.5985 + 6.38655i) q^{88} +(4.86037 + 7.27406i) q^{89} +(-4.06595 - 0.529659i) q^{90} +(7.03168 - 13.1553i) q^{91} +(-17.9424 - 4.75531i) q^{92} +(-1.25058 + 0.123171i) q^{93} +(-3.19243 + 13.7764i) q^{94} +(-0.0990595 + 0.0990595i) q^{95} +(1.43118 + 1.08278i) q^{96} +(2.03675 + 2.03675i) q^{97} +(0.966363 - 0.602750i) q^{98} +(-1.69354 - 17.1948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) $ 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{29}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	0.822181	−	1.15066i	0.581370	−	0.813639i
$2$	0.822181	−	1.15066i	0.581370	−	0.813639i
$3$	0.201260	−	0.245236i	0.116198	−	0.141587i	−0.711663	−	0.702521i	$-0.752058\pi$
$3$	0.201260	−	0.245236i	0.116198	−	0.141587i	0.827861	+	0.560934i	$0.189558\pi$
$4$	−0.648036	−	1.89210i	−0.324018	−	0.946051i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$5$	−0.956940	+	0.290285i	−0.427957	+	0.129819i
$6$	−0.116711	−	0.433210i	−0.0476471	−	0.176857i
$7$	−2.74012	−	0.545044i	−1.03567	−	0.206007i	−0.352153	−	0.935943i	$-0.614550\pi$
$7$	−2.74012	−	0.545044i	−1.03567	−	0.206007i	−0.683516	+	0.729935i	$0.739550\pi$
$8$	−2.70997	−	0.809981i	−0.958119	−	0.286372i
$9$	0.565636	+	2.84364i	0.188545	+	0.947881i
$10$	−0.452759	+	1.33978i	−0.143175	+	0.423675i
$11$	−5.93055	−	0.584108i	−1.78813	−	0.176115i	−0.851016	−	0.525140i	$-0.824013\pi$
$11$	−5.93055	−	0.584108i	−1.78813	−	0.176115i	−0.937113	+	0.349025i	$0.886513\pi$
$12$	−0.594435	−	0.221883i	−0.171599	−	0.0640520i
$13$	−1.54989	+	5.10930i	−0.429862	+	1.41706i	0.428278	+	0.903647i	$0.359120\pi$
$13$	−1.54989	+	5.10930i	−0.429862	+	1.41706i	−0.858139	+	0.513417i	$0.828380\pi$
$14$	−2.88004	+	2.70482i	−0.769723	+	0.722895i
$15$	−0.121406	+	0.293099i	−0.0313468	+	0.0756778i
$16$	−3.16010	+	2.45230i	−0.790025	+	0.613075i
$17$	−0.333940	−	0.806201i	−0.0809922	−	0.195533i	0.878196	−	0.478301i	$-0.158747\pi$
$17$	−0.333940	−	0.806201i	−0.0809922	−	0.195533i	−0.959188	+	0.282768i	$0.908747\pi$
$18$	3.73712	+	1.68714i	0.880848	+	0.397662i
$19$	0.123550	−	0.0660386i	0.0283442	−	0.0151503i	−0.457164	−	0.889383i	$-0.651135\pi$
$19$	0.123550	−	0.0660386i	0.0283442	−	0.0151503i	0.485508	+	0.874232i	$0.338635\pi$
$20$	1.16938	+	1.62251i	0.261481	+	0.362805i
$21$	−0.685142	+	0.562281i	−0.149510	+	0.122700i
$22$	−5.54810	+	6.34381i	−1.18286	+	1.35250i
$23$	5.15622	−	7.71682i	1.07515	−	1.60907i	0.327654	−	0.944798i	$-0.393742\pi$
$23$	5.15622	−	7.71682i	1.07515	−	1.60907i	0.747492	−	0.664271i	$-0.231258\pi$
$24$	−0.744045	+	0.501565i	−0.151878	+	0.102382i
$25$	0.831470	−	0.555570i	0.166294	−	0.111114i
$26$	4.60477	+	5.98416i	0.903070	+	1.17359i
$27$	1.65057	+	0.882247i	0.317652	+	0.169788i
$28$	0.744419	+	5.53780i	0.140682	+	1.04655i
$29$	−0.760028	−	7.71669i	−0.141134	−	1.43295i	−0.761257	−	0.648450i	$-0.775418\pi$
$29$	−0.760028	−	7.71669i	−0.141134	−	1.43295i	0.620124	−	0.784504i	$-0.287082\pi$
$30$	0.237440	+	0.380677i	0.0433504	+	0.0695018i
$31$	−2.80087	−	2.80087i	−0.503052	−	0.503052i	0.409333	−	0.912385i	$-0.365761\pi$
$31$	−2.80087	−	2.80087i	−0.503052	−	0.503052i	−0.912385	+	0.409333i	$0.865761\pi$
$32$	0.223590	+	5.65243i	0.0395255	+	0.999219i
$33$	−1.33683	+	1.33683i	−0.232712	+	0.232712i
$34$	−1.20222	−	0.278593i	−0.206179	−	0.0477783i
$35$	2.78035	−	0.273841i	0.469965	−	0.0462875i
$36$	5.01391	−	2.91302i	0.835652	−	0.485504i
$37$	−1.71200	+	3.20293i	−0.281452	+	0.526559i	−0.982432	−	0.186622i	$-0.940246\pi$
$37$	−1.71200	+	3.20293i	−0.281452	+	0.526559i	0.700980	+	0.713181i	$0.252746\pi$
$38$	0.0255921	−	0.196459i	0.00415159	−	0.0318699i
$39$	0.941053	+	1.40839i	0.150689	+	0.225522i
$40$	2.82840	−	0.0115584i	0.447210	−	0.00182755i
$41$	−0.589295	−	0.393755i	−0.0920325	−	0.0614941i	0.508703	−	0.860942i	$-0.330125\pi$
$41$	−0.589295	−	0.393755i	−0.0920325	−	0.0614941i	−0.600735	+	0.799448i	$0.705125\pi$
$42$	0.0836838	+	1.25066i	0.0129127	+	0.192981i
$43$	−2.27983	−	2.77798i	−0.347671	−	0.423639i	0.569587	−	0.821931i	$-0.307103\pi$
$43$	−2.27983	−	2.77798i	−0.347671	−	0.423639i	−0.917259	+	0.398292i	$0.869603\pi$
$44$	2.73802	+	11.5997i	0.412772	+	1.74873i
$45$	−1.36675	−	2.55700i	−0.203742	−	0.381175i
$46$	−4.64009	−	12.2777i	−0.684145	−	1.81024i
$47$	−9.23838	+	3.82666i	−1.34756	+	0.558176i	−0.935611	−	0.353033i	$-0.885150\pi$
$47$	−9.23838	+	3.82666i	−1.34756	+	0.558176i	−0.411945	+	0.911209i	$0.635150\pi$
$48$	−0.0346090	+	1.26852i	−0.00499538	+	0.183095i
$49$	0.744043	+	0.308193i	0.106292	+	0.0440275i
$50$	0.0443463	−	1.41352i	0.00627152	−	0.199902i
$51$	−0.264918	−	0.0803621i	−0.0370960	−	0.0112529i
$52$	10.6717	−	0.378462i	1.47990	−	0.0524833i
$53$	−0.302218	+	3.06847i	−0.0415129	+	0.421487i	0.951858	+	0.306538i	$0.0991706\pi$
$53$	−0.302218	+	3.06847i	−0.0415129	+	0.421487i	−0.993371	+	0.114949i	$0.963329\pi$
$54$	2.37223	−	1.17387i	0.322820	−	0.159744i
$55$	5.84474	−	1.16259i	0.788105	−	0.156764i
$56$	6.98417	+	3.69650i	0.933299	+	0.493966i
$57$	0.00867054	−	0.0435897i	0.00114844	−	0.00577360i
$58$	−9.50417	−	5.46999i	−1.24796	−	0.718244i
$59$	3.63714	+	11.9900i	0.473515	+	1.56097i	0.790452	+	0.612523i	$0.209845\pi$
$59$	3.63714	+	11.9900i	0.473515	+	1.56097i	−0.316937	+	0.948446i	$0.602655\pi$
$60$	0.633248	+	0.0397730i	0.0817520	+	0.00513467i
$61$	−11.5478	−	9.47700i	−1.47854	−	1.21341i	−0.924652	−	0.380814i	$-0.875644\pi$
$61$	−11.5478	−	9.47700i	−1.47854	−	1.21341i	−0.553888	−	0.832591i	$-0.686856\pi$
$62$	−5.52568	+	0.920027i	−0.701762	+	0.116844i
$63$		−	8.10023i		−	1.02053i
$64$	6.68786	+	4.39005i	0.835983	+	0.548756i
$65$		−	5.33920i		−	0.662246i
$66$	0.439119	+	2.63735i	0.0540519	+	0.324635i
$67$	9.55787	+	7.84394i	1.16768	+	0.958290i	0.999622	−	0.0274871i	$-0.00875053\pi$
$67$	9.55787	+	7.84394i	1.16768	+	0.958290i	0.168058	+	0.985777i	$0.446251\pi$
$68$	−1.30901	+	1.15430i	−0.158741	+	0.139979i
$69$	−0.854703	−	2.81758i	−0.102894	−	0.339197i
$70$	1.97086	−	3.42439i	0.235562	−	0.409292i
$71$	1.38132	−	6.94439i	0.163933	−	0.824147i	−0.808053	−	0.589110i	$-0.799479\pi$
$71$	1.38132	−	6.94439i	0.163933	−	0.824147i	0.971986	−	0.235038i	$-0.0755214\pi$
$72$	0.770443	−	8.16434i	0.0907976	−	0.962177i
$73$	2.85534	−	0.567962i	0.334192	−	0.0664750i	−0.0251420	−	0.999684i	$-0.508004\pi$
$73$	2.85534	−	0.567962i	0.334192	−	0.0664750i	0.359334	+	0.933209i	$0.383004\pi$
$74$	2.27791	+	4.60333i	0.264802	+	0.535126i
$75$	0.0310958	−	0.315720i	0.00359063	−	0.0364563i
$76$	−0.205016	−	0.190973i	−0.0235170	−	0.0219061i
$77$	15.9321	+	4.83294i	1.81563	+	0.550765i
$78$	2.39429	+	0.0751161i	0.271100	+	0.00850523i
$79$	−11.3149	−	4.68677i	−1.27302	−	0.527303i	−0.359140	−	0.933284i	$-0.616930\pi$
$79$	−11.3149	−	4.68677i	−1.27302	−	0.527303i	−0.913882	+	0.405981i	$0.866930\pi$
$80$	2.31216	−	3.26403i	0.258507	−	0.364930i
$81$	−7.48741	+	3.10139i	−0.831934	+	0.344598i
$82$	−0.937585	+	0.354341i	−0.103539	+	0.0391304i
$83$	−2.31472	−	4.33053i	−0.254073	−	0.475338i	0.722256	−	0.691625i	$-0.243105\pi$
$83$	−2.31472	−	4.33053i	−0.254073	−	0.475338i	−0.976330	+	0.216288i	$0.930605\pi$
$84$	1.50789	+	0.931979i	0.164524	+	0.101687i
$85$	0.553588	+	0.674549i	0.0600451	+	0.0731651i
$86$	−5.07095	+	0.339306i	−0.546815	+	0.0365883i
$87$	−2.04538	−	1.36668i	−0.219287	−	0.146523i
$88$	15.5985	+	6.38655i	1.66281	+	0.680809i
$89$	4.86037	+	7.27406i	0.515199	+	0.771049i	0.994290	−	0.106716i	$-0.0340336\pi$
$89$	4.86037	+	7.27406i	0.515199	+	0.771049i	−0.479091	+	0.877765i	$0.659034\pi$
$90$	−4.06595	−	0.529659i	−0.428589	−	0.0558310i
$91$	7.03168	−	13.1553i	0.737120	−	1.37905i
$92$	−17.9424	−	4.75531i	−1.87063	−	0.495775i
$93$	−1.25058	+	0.123171i	−0.129679	+	0.0127723i
$94$	−3.19243	+	13.7764i	−0.329274	+	1.42093i
$95$	−0.0990595	+	0.0990595i	−0.0101633	+	0.0101633i
$96$	1.43118	+	1.08278i	0.146069	+	0.110510i
$97$	2.03675	+	2.03675i	0.206800	+	0.206800i	0.802906	−	0.596106i	$-0.203286\pi$
$97$	2.03675	+	2.03675i	0.206800	+	0.206800i	−0.596106	+	0.802906i	$0.703286\pi$
$98$	0.966363	−	0.602750i	0.0976174	−	0.0608870i
$99$	−1.69354	−	17.1948i	−0.170207	−	1.72814i
$100$	−1.59002	−	1.21320i	−0.159002	−	0.121320i
$101$	0.561481	+	0.300118i	0.0558694	+	0.0298628i	0.499095	−	0.866547i	$-0.333666\pi$
$101$	0.561481	+	0.300118i	0.0558694	+	0.0298628i	−0.443225	+	0.896410i	$0.646166\pi$
$102$	−0.310280	+	0.238759i	−0.0307223	+	0.0236406i
$103$	2.67306	−	1.78608i	0.263384	−	0.175988i	−0.416865	−	0.908968i	$-0.636871\pi$
$103$	2.67306	−	1.78608i	0.263384	−	0.175988i	0.680250	+	0.732980i	$0.261871\pi$
$104$	8.33858	−	12.5907i	0.817665	−	1.23462i
$105$	0.492418	−	0.736956i	0.0480551	−	0.0719195i
$106$	3.28229	+	2.87059i	0.318804	+	0.278817i
$107$	2.95218	−	2.42279i	0.285398	−	0.234220i	−0.480791	−	0.876835i	$-0.659651\pi$
$107$	2.95218	−	2.42279i	0.285398	−	0.234220i	0.766189	+	0.642615i	$0.222151\pi$
$108$	0.599673	−	3.69477i	0.0577036	−	0.355529i
$109$	−16.1110	+	8.61152i	−1.54316	+	0.824834i	−0.999892	−	0.0147267i	$-0.995312\pi$
$109$	−16.1110	+	8.61152i	−1.54316	+	0.824834i	−0.543265	+	0.839561i	$0.682812\pi$
$110$	3.46769	−	7.68117i	0.330631	−	0.732371i
$111$	0.440917	+	1.06447i	0.0418500	+	0.101035i
$112$	9.99567	−	4.99721i	0.944502	−	0.472192i
$113$	1.64369	−	3.96821i	0.154625	−	0.373298i	−0.827516	−	0.561442i	$-0.810247\pi$
$113$	1.64369	−	3.96821i	0.154625	−	0.373298i	0.982142	+	0.188143i	$0.0602469\pi$
$114$	−0.0430282	−	0.0458155i	−0.00402996	−	0.00429102i
$115$	−2.69412	+	8.88131i	−0.251228	+	0.828186i
$116$	−14.1082	+	6.43875i	−1.30992	+	0.597823i
$117$	−15.4057	−	1.51733i	−1.42426	−	0.140277i
$118$	16.7868	+	5.67287i	1.54535	+	0.522230i
$119$	0.475620	+	2.39110i	0.0436000	+	0.219192i
$120$	0.566410	−	0.695953i	0.0517059	−	0.0635315i
$121$	24.0416	+	4.78218i	2.18560	+	0.434744i
$122$	−20.3992	+	5.49573i	−1.84685	+	0.497560i
$123$	−0.215164	+	0.0652694i	−0.0194007	+	0.00588515i
$124$	−3.48447	+	7.11460i	−0.312915	+	0.638910i
$125$	−0.634393	+	0.773010i	−0.0567419	+	0.0691402i
$126$	−9.32061	−	6.65986i	−0.830346	−	0.593307i
$127$	3.05181			0.270805			0.135402	−	0.990791i	$-0.456767\pi$
$127$	3.05181			0.270805			0.135402	+	0.990791i	$0.456767\pi$
$128$	10.5501	−	4.08604i	0.932505	−	0.361158i
$129$	−1.14010			−0.100380
$130$	−6.14360	−	4.38979i	−0.538830	−	0.385010i
$131$	0.945772	−	1.15243i	0.0826325	−	0.100688i	−0.730053	−	0.683390i	$-0.760505\pi$
$131$	0.945772	−	1.15243i	0.0826325	−	0.100688i	0.812686	+	0.582702i	$0.198005\pi$
$132$	3.39573	+	1.66310i	0.295560	+	0.144754i
$133$	−0.374535	+	0.113614i	−0.0324763	+	0.00985158i
$134$	16.8840	−	4.54872i	1.45856	−	0.392949i
$135$	−1.83560	−	0.365123i	−0.157983	−	0.0314248i
$136$	0.251958	+	2.45527i	0.0216052	+	0.210537i
$137$	0.948085	+	4.76634i	0.0810004	+	0.407216i	0.999918	+	0.0127680i	$0.00406429\pi$
$137$	0.948085	+	4.76634i	0.0810004	+	0.407216i	−0.918918	+	0.394448i	$0.870936\pi$
$138$	−3.94480	−	1.33309i	−0.335803	−	0.113480i
$139$	−12.0022	−	1.18211i	−1.01801	−	0.100266i	−0.424781	−	0.905296i	$-0.639649\pi$
$139$	−12.0022	−	1.18211i	−1.01801	−	0.100266i	−0.593234	+	0.805030i	$0.702149\pi$
$140$	−2.31990	−	5.08325i	−0.196068	−	0.429613i
$141$	−0.920881	+	3.03574i	−0.0775522	+	0.255655i
$142$	−6.85493	−	7.29898i	−0.575253	−	0.612517i
$143$	12.1761	−	29.3956i	1.01821	−	2.45819i
$144$	−8.76093	−	7.59908i	−0.730078	−	0.633257i
$145$	2.96734	+	7.16379i	0.246424	+	0.594920i
$146$	1.69408	−	3.75249i	0.140203	−	0.310558i
$147$	0.225326	−	0.120439i	0.0185846	−	0.00993367i
$148$	7.16972	+	1.16367i	0.589347	+	0.0956530i
$149$	9.71154	−	7.97005i	0.795600	−	0.652932i	−0.146144	−	0.989263i	$-0.546686\pi$
$149$	9.71154	−	7.97005i	0.795600	−	0.652932i	0.941744	+	0.336331i	$0.109186\pi$
$150$	−0.337721	−	0.295360i	−0.0275748	−	0.0241160i
$151$	10.8975	−	16.3093i	0.886826	−	1.32723i	−0.0575436	−	0.998343i	$-0.518327\pi$
$151$	10.8975	−	16.3093i	0.886826	−	1.32723i	0.944370	−	0.328886i	$-0.106673\pi$
$152$	−0.388305	+	0.0788897i	−0.0314957	+	0.00639880i
$153$	2.10366	−	1.40562i	0.170071	−	0.113638i
$154$	18.6601	−	14.3588i	1.50368	−	1.15707i
$155$	3.49332	+	1.86722i	0.280590	+	0.149979i
$156$	2.05497	−	2.69325i	0.164529	−	0.215633i
$157$	1.71272	+	17.3896i	0.136690	+	1.38784i	0.781695	+	0.623661i	$0.214355\pi$
$157$	1.71272	+	17.3896i	0.136690	+	1.38784i	−0.645005	+	0.764178i	$0.723145\pi$
$158$	−14.6957	+	9.16618i	−1.16913	+	0.729222i
$159$	0.691676	+	0.691676i	0.0548535	+	0.0548535i
$160$	−1.85478	−	5.34414i	−0.146633	−	0.422491i
$161$	−18.3347	+	18.3347i	−1.44498	+	1.44498i
$162$	−2.58737	+	11.1654i	−0.203283	+	0.877234i
$163$	−19.3588	+	1.90668i	−1.51630	+	0.149343i	−0.821645	−	0.569999i	$-0.806943\pi$
$163$	−19.3588	+	1.90668i	−1.51630	+	0.149343i	−0.694656	+	0.719342i	$0.744443\pi$
$164$	−0.363139	+	1.37017i	−0.0283564	+	0.106993i
$165$	0.891204	−	1.66733i	0.0693801	−	0.129801i
$166$	−6.88609	−	0.897030i	−0.534464	−	0.0696230i
$167$	2.74417	+	4.10694i	0.212350	+	0.317805i	0.922320	−	0.386428i	$-0.126291\pi$
$167$	2.74417	+	4.10694i	0.212350	+	0.317805i	−0.709969	+	0.704233i	$0.751291\pi$
$168$	2.31215	−	0.968813i	0.178386	−	0.0747455i
$169$	−12.8937	−	8.61526i	−0.991819	−	0.662712i
$170$	1.23133	−	0.0823900i	0.0944384	−	0.00631903i
$171$	0.257674	+	0.313977i	0.0197048	+	0.0240104i
$172$	−3.77882	+	6.11391i	−0.288132	+	0.466181i
$173$	9.09997	+	17.0249i	0.691858	+	1.29438i	0.945039	+	0.326957i	$0.106023\pi$
$173$	9.09997	+	17.0249i	0.691858	+	1.29438i	−0.253181	+	0.967419i	$0.581477\pi$
$174$	−3.25425	+	1.22988i	−0.246704	+	0.0932366i
$175$	−2.58114	+	1.06914i	−0.195116	+	0.0808196i
$176$	20.1735	−	12.6977i	1.52064	−	0.957122i
$177$	3.67240	+	1.52116i	0.276035	+	0.114337i
$178$	12.3661	+	0.387961i	0.926877	+	0.0290789i
$179$	−3.26098	−	0.989207i	−0.243737	−	0.0739368i	0.166053	−	0.986117i	$-0.446898\pi$
$179$	−3.26098	−	0.989207i	−0.243737	−	0.0739368i	−0.409789	+	0.912180i	$0.634398\pi$
$180$	−3.95241	+	4.24305i	−0.294595	+	0.316258i
$181$	1.18584	−	12.0401i	0.0881430	−	0.894931i	−0.844842	−	0.535016i	$-0.820306\pi$
$181$	1.18584	−	12.0401i	0.0881430	−	0.894931i	0.932985	−	0.359915i	$-0.117194\pi$
$182$	−9.35601	−	18.9071i	−0.693514	−	1.40149i
$183$	−4.64821	+	0.924586i	−0.343605	+	0.0683473i
$184$	−20.2237	+	16.7359i	−1.49091	+	1.23379i
$185$	0.708523	−	3.56199i	0.0520916	−	0.261882i
$186$	−0.886474	+	1.54026i	−0.0649995	+	0.112937i
$187$	1.50954	+	4.97628i	0.110388	+	0.363901i
$188$	13.2272	+	15.0001i	0.964695	+	1.09400i
$189$	−4.04189	−	3.31710i	−0.294005	−	0.241283i
$190$	0.0325389	+	0.195429i	0.00236062	+	0.0141779i
$191$		−	8.52504i		−	0.616850i	−0.951249	−	0.308425i	$-0.900198\pi$
$191$		−	8.52504i		−	0.616850i	0.951249	−	0.308425i	$-0.0998020\pi$
$192$	2.42260	−	0.756563i	0.174836	−	0.0546002i
$193$		−	0.273564i		−	0.0196916i	−0.999952	−	0.00984579i	$-0.996866\pi$
$193$		−	0.273564i		−	0.0196916i	0.999952	−	0.00984579i	$-0.00313406\pi$
$194$	4.01817	−	0.669027i	0.288488	−	0.0480334i
$195$	−1.30936	−	1.07457i	−0.0937656	−	0.0769514i
$196$	0.100965	−	1.60753i	0.00721180	−	0.114823i
$197$	−0.436241	−	1.43809i	−0.0310809	−	0.102460i	0.940028	−	0.341098i	$-0.110799\pi$
$197$	−0.436241	−	1.43809i	−0.0310809	−	0.102460i	−0.971108	+	0.238638i	$0.923299\pi$
$198$	−21.1777	−	12.1885i	−1.50504	−	0.866201i
$199$	0.582858	−	2.93022i	0.0413177	−	0.207718i	−0.954612	−	0.297852i	$-0.903730\pi$
$199$	0.582858	−	2.93022i	0.0413177	−	0.207718i	0.995930	+	0.0901344i	$0.0287297\pi$
$200$	−2.70326	+	0.832103i	−0.191149	+	0.0588386i
$201$	3.84724	−	0.765263i	0.271363	−	0.0539775i
$202$	0.806973	−	0.399322i	0.0567784	−	0.0280962i
$203$	−2.12337	+	21.5589i	−0.149031	+	1.51314i
$204$	0.0196234	+	0.553330i	0.00137391	+	0.0387409i
$205$	0.678221	+	0.205736i	0.0473690	+	0.0143692i
$206$	0.142567	−	4.54426i	0.00993314	−	0.316614i
$207$	24.8604	+	10.2975i	1.72792	+	0.715728i
$208$	−7.63173	−	19.9467i	−0.529165	−	1.38305i
$209$	−0.771291	+	0.319479i	−0.0533513	+	0.0220988i
$210$	−0.443129	−	1.17252i	−0.0305788	−	0.0809114i
$211$	4.64823	+	8.69622i	0.319997	+	0.598673i	0.989566	−	0.144077i	$-0.0460213\pi$
$211$	4.64823	+	8.69622i	0.319997	+	0.598673i	−0.669569	+	0.742750i	$0.733521\pi$
$212$	6.00171	−	1.41665i	0.412199	−	0.0972962i
$213$	−1.42501	−	1.73638i	−0.0976400	−	0.118975i
$214$	−0.360582	−	5.38893i	−0.0246489	−	0.368379i
$215$	2.98807	+	1.99656i	0.203785	+	0.136165i
$216$	−3.75838	−	3.72779i	−0.255726	−	0.253644i
$217$	6.14814	+	9.20134i	0.417363	+	0.624627i
$218$	−3.33725	+	25.6185i	−0.226027	+	1.73511i
$219$	0.435381	−	0.814540i	0.0294203	−	0.0550415i
$220$	−5.98735	−	10.3054i	−0.403667	−	0.694793i
$221$	4.63669	−	0.456674i	0.311898	−	0.0307192i
$222$	1.58735	+	0.367840i	0.106536	+	0.0246878i
$223$	−4.54980	+	4.54980i	−0.304677	+	0.304677i	−0.842841	−	0.538163i	$-0.819118\pi$
$223$	−4.54980	+	4.54980i	−0.304677	+	0.304677i	0.538163	+	0.842841i	$0.319118\pi$
$224$	2.46816	−	15.6102i	0.164911	−	1.04300i
$225$	2.05015	+	2.05015i	0.136677	+	0.136677i
$226$	−3.21466	−	5.15392i	−0.213836	−	0.342834i
$227$	−0.325666	−	3.30654i	−0.0216152	−	0.219463i	−0.999924	−	0.0123118i	$-0.996081\pi$
$227$	−0.325666	−	3.30654i	−0.0216152	−	0.219463i	0.978309	−	0.207151i	$-0.0664191\pi$
$228$	−0.0880951	+	0.0118422i	−0.00583424	+	0.000784268i
$229$	−18.3910	−	9.83022i	−1.21531	−	0.649599i	−0.266014	−	0.963969i	$-0.585707\pi$
$229$	−18.3910	−	9.83022i	−1.21531	−	0.649599i	−0.949300	+	0.314370i	$0.898207\pi$
$230$	8.00432	+	10.4021i	0.527789	+	0.685891i
$231$	4.39170	−	2.93444i	0.288953	−	0.193072i
$232$	−4.19073	+	21.5276i	−0.275135	+	1.41336i
$233$	8.08344	−	12.0977i	0.529564	−	0.792548i	−0.466182	−	0.884689i	$-0.654371\pi$
$233$	8.08344	−	12.0977i	0.529564	−	0.792548i	0.995746	+	0.0921405i	$0.0293709\pi$
$234$	−14.4122	+	16.4792i	−0.942155	+	1.07728i
$235$	7.72975	−	6.34365i	0.504234	−	0.413814i
$236$	20.3294	−	14.6518i	1.32333	−	0.953752i
$237$	−3.42660	+	1.83155i	−0.222581	+	0.118972i
$238$	3.14239	+	1.41864i	0.203691	+	0.0919570i
$239$	−6.37733	−	15.3962i	−0.412515	−	0.995900i	−0.984460	−	0.175608i	$-0.943811\pi$
$239$	−6.37733	−	15.3962i	−0.412515	−	0.995900i	0.571945	−	0.820292i	$-0.306189\pi$
$240$	−0.335113	−	1.22394i	−0.0216315	−	0.0790053i
$241$	6.42221	−	15.5046i	0.413691	−	0.998738i	−0.570447	−	0.821334i	$-0.693230\pi$
$241$	6.42221	−	15.5046i	0.413691	−	0.998738i	0.984138	−	0.177404i	$-0.0567698\pi$
$242$	25.2692	−	23.7319i	1.62437	−	1.52555i
$243$	−2.37620	+	7.83328i	−0.152433	+	0.502505i
$244$	−10.4481	+	27.9910i	−0.668870	+	1.79194i
$245$	−0.801468	−	0.0789378i	−0.0512039	−	0.00504315i
$246$	−0.101801	+	0.301244i	−0.00649061	+	0.0192066i
$247$	0.145923	+	0.733604i	0.00928485	+	0.0466781i
$248$	5.32162	+	9.85893i	0.337923	+	0.626043i
$249$	−1.52786	−	0.303911i	−0.0968244	−	0.0192596i
$250$	0.367886	+	1.36553i	0.0232671	+	0.0863634i
$251$	−5.00188	+	1.51730i	−0.315716	+	0.0957714i	−0.444166	−	0.895945i	$-0.646500\pi$
$251$	−5.00188	+	1.51730i	−0.315716	+	0.0957714i	0.128450	+	0.991716i	$0.459000\pi$
$252$	−15.3265	+	5.24924i	−0.965476	+	0.330671i
$253$	−35.0867	+	42.7532i	−2.20588	+	2.68787i
$254$	2.50914	−	3.51160i	0.157438	−	0.220337i
$255$	0.276839			0.0173363
$256$	3.97244	−	15.4990i	0.248278	−	0.968689i
$257$	3.09686			0.193177			0.0965885	−	0.995324i	$-0.469207\pi$
$257$	3.09686			0.193177			0.0965885	+	0.995324i	$0.469207\pi$
$258$	−0.937370	+	1.31187i	−0.0583581	+	0.0816734i
$259$	6.43684	−	7.84332i	0.399966	−	0.487360i
$260$	−10.1023	+	3.45999i	−0.626519	+	0.214580i
$261$	21.5136	−	6.52609i	1.33166	−	0.403955i
$262$	−0.548455	−	2.03577i	−0.0338837	−	0.125770i
$263$	−0.677926	−	0.134848i	−0.0418027	−	0.00831507i	0.174145	−	0.984720i	$-0.444284\pi$
$263$	−0.677926	−	0.134848i	−0.0418027	−	0.00831507i	−0.215947	+	0.976405i	$0.569284\pi$
$264$	4.70557	−	2.53996i	0.289608	−	0.156323i
$265$	−0.601526	−	3.02408i	−0.0369515	−	0.185768i
$266$	−0.177205	+	0.524373i	−0.0108651	+	0.0321514i
$267$	2.76206	+	0.272039i	0.169035	+	0.0166485i
$268$	8.64769	−	23.1676i	0.528242	−	1.41519i
$269$	0.697780	−	2.30027i	0.0425444	−	0.140250i	−0.933095	−	0.359629i	$-0.882903\pi$
$269$	0.697780	−	2.30027i	0.0425444	−	0.140250i	0.975640	+	0.219379i	$0.0704032\pi$
$270$	−1.92933	+	1.81195i	−0.117415	+	0.110272i
$271$	−9.52562	+	22.9969i	−0.578640	+	1.39696i	0.315393	+	0.948961i	$0.397864\pi$
$271$	−9.52562	+	22.9969i	−0.578640	+	1.39696i	−0.894034	+	0.448000i	$0.852136\pi$
$272$	3.03233	+	1.72876i	0.183862	+	0.104821i
$273$	−1.81097	−	4.37207i	−0.109605	−	0.264609i
$274$	6.26394	+	2.82788i	0.378418	+	0.170838i
$275$	−5.25559	+	2.80917i	−0.316924	+	0.169399i
$276$	−4.77727	+	3.44308i	−0.287558	+	0.207249i
$277$	−19.0204	+	15.6096i	−1.14282	+	0.937891i	−0.998665	−	0.0516639i	$-0.983548\pi$
$277$	−19.0204	+	15.6096i	−1.14282	+	0.937891i	−0.144159	+	0.989555i	$0.546048\pi$
$278$	−11.2282	+	12.8386i	−0.673423	+	0.770005i
$279$	6.38041	−	9.54896i	0.381985	−	0.571681i
$280$	−7.75647	−	1.50993i	−0.463538	−	0.0902358i
$281$	0.880809	−	0.588538i	0.0525447	−	0.0351092i	−0.529020	−	0.848609i	$-0.677441\pi$
$281$	0.880809	−	0.588538i	0.0525447	−	0.0351092i	0.581565	+	0.813500i	$0.302441\pi$
$282$	2.73597	+	3.55555i	0.162925	+	0.211730i
$283$	10.5362	+	5.63172i	0.626313	+	0.334771i	0.753834	−	0.657065i	$-0.228202\pi$
$283$	10.5362	+	5.63172i	0.626313	+	0.334771i	−0.127521	+	0.991836i	$0.540702\pi$
$284$	−14.0346	+	1.88661i	−0.832803	+	0.111950i
$285$	0.00435625	+	0.0442297i	0.000258042	+	0.00261994i
$286$	−23.8135	−	38.1791i	−1.40812	−	2.25758i
$287$	1.40013	+	1.40013i	0.0826469	+	0.0826469i
$288$	−15.9470	+	3.83303i	−0.939688	+	0.225863i
$289$	11.4824	−	11.4824i	0.675434	−	0.675434i
$290$	10.6828	+	2.47554i	0.627314	+	0.145368i
$291$	0.909399	−	0.0895680i	0.0533099	−	0.00525057i
$292$	−2.92501	−	5.03453i	−0.171173	−	0.294624i
$293$	11.1872	−	20.9298i	0.653562	−	1.22273i	−0.308843	−	0.951113i	$-0.599942\pi$
$293$	11.1872	−	20.9298i	0.653562	−	1.22273i	0.962406	−	0.271616i	$-0.0875582\pi$
$294$	0.0466742	−	0.358297i	0.00272210	−	0.0208963i
$295$	−6.96105	−	10.4179i	−0.405288	−	0.606556i
$296$	7.23379	−	7.29316i	0.420456	−	0.423906i
$297$	−9.27345	−	6.19632i	−0.538100	−	0.359547i
$298$	−1.18618	−	17.7275i	−0.0687133	−	1.02693i
$299$	31.4360	+	38.3049i	1.81799	+	2.21523i
$300$	−0.617526	+	0.145762i	−0.0356529	+	0.00841557i
$301$	4.73290	+	8.85463i	0.272800	+	0.510372i
$302$	−9.80669	−	25.9485i	−0.564312	−	1.49317i
$303$	0.186603	−	0.0772937i	0.0107201	−	0.00444040i
$304$	−0.228482	+	0.511669i	−0.0131044	+	0.0293462i
$305$	13.8015	+	5.71679i	0.790274	+	0.327342i
$306$	0.112199	−	3.57627i	0.00641396	−	0.204442i
$307$	−17.3752	−	5.27071i	−0.991656	−	0.300815i	−0.247548	−	0.968876i	$-0.579625\pi$
$307$	−17.3752	−	5.27071i	−0.991656	−	0.300815i	−0.744107	+	0.668060i	$0.767125\pi$
$308$	−1.18014	−	33.2770i	−0.0672448	−	1.89614i
$309$	0.0999685	−	1.01500i	0.00568701	−	0.0577412i
$310$	5.02067	−	2.48443i	0.285155	−	0.141106i
$311$	−6.52410	+	1.29772i	−0.369948	+	0.0735872i	−0.376563	−	0.926391i	$-0.622894\pi$
$311$	−6.52410	+	1.29772i	−0.369948	+	0.0735872i	0.00661541	+	0.999978i	$0.497894\pi$
$312$	−1.40946	−	4.57892i	−0.0797949	−	0.259230i
$313$	−2.91544	+	14.6569i	−0.164790	+	0.828456i	0.806624	+	0.591065i	$0.201292\pi$
$313$	−2.91544	+	14.6569i	−0.164790	+	0.828456i	−0.971414	+	0.237391i	$0.923708\pi$
$314$	21.4177	+	12.3266i	1.20867	+	0.695631i
$315$	2.35137	+	7.75144i	0.132485	+	0.436744i
$316$	−1.53541	+	24.4461i	−0.0863733	+	1.37520i
$317$	13.8748	+	11.3867i	0.779285	+	0.639543i	0.937549	−	0.347854i	$-0.113090\pi$
$317$	13.8748	+	11.3867i	0.779285	+	0.639543i	−0.158263	+	0.987397i	$0.550590\pi$
$318$	1.36457	−	0.227201i	0.0765211	−	0.0127408i
$319$			46.2082i			2.58716i
$320$	−7.67425	−	2.25963i	−0.429003	−	0.126317i
$321$		−	1.21159i		−	0.0676245i
$322$	6.02255	+	36.1714i	0.335624	+	2.01575i
$323$	−0.0944985	−	0.0775529i	−0.00525804	−	0.00431516i
$324$	10.7202	+	12.1571i	0.595569	+	0.675396i
$325$	1.54989	+	5.10930i	0.0859723	+	0.283413i
$326$	−13.7225	+	23.8431i	−0.760021	+	1.32055i
$327$	−1.13065	+	5.68416i	−0.0625251	+	0.314335i
$328$	1.27804	+	1.54438i	0.0705678	+	0.0852742i
$329$	27.4000	−	5.45020i	1.51061	−	0.300479i
$330$	−1.18579	−	2.39632i	−0.0652758	−	0.131913i
$331$	0.0853382	−	0.866453i	0.00469061	−	0.0476246i	−0.992554	−	0.121801i	$-0.961133\pi$
$331$	0.0853382	−	0.866453i	0.00469061	−	0.0476246i	0.997245	+	0.0741768i	$0.0236329\pi$
$332$	−6.69379	+	7.18603i	−0.367369	+	0.394384i
$333$	−10.0764	−	3.05663i	−0.552182	−	0.167503i
$334$	6.98190	+	0.219043i	0.382033	+	0.0119855i
$335$	−11.4233	−	4.73168i	−0.624121	−	0.258519i
$336$	0.786233	−	3.45704i	0.0428925	−	0.188597i
$337$	−3.07178	+	1.27237i	−0.167330	+	0.0693105i	−0.464776	−	0.885428i	$-0.653865\pi$
$337$	−3.07178	+	1.27237i	−0.167330	+	0.0693105i	0.297446	+	0.954739i	$0.403865\pi$
$338$	−20.5142	+	7.75290i	−1.11582	+	0.421702i
$339$	−0.642341	−	1.20173i	−0.0348872	−	0.0652693i
$340$	0.917570	−	1.48458i	0.0497622	−	0.0805125i
$341$	14.9747	+	18.2467i	0.810926	+	0.988116i
$342$	0.573136	−	0.0383494i	0.0309916	−	0.00207370i
$343$	14.3900	+	9.61506i	0.776985	+	0.519165i
$344$	3.92816	+	9.37487i	0.211792	+	0.505459i
$345$	1.63580	+	2.44815i	0.0880685	+	0.131804i
$346$	27.0716	+	3.52654i	1.45538	+	0.189588i
$347$	−13.5062	+	25.2683i	−0.725051	+	1.35648i	0.201193	+	0.979552i	$0.435518\pi$
$347$	−13.5062	+	25.2683i	−0.725051	+	1.35648i	−0.926244	+	0.376924i	$0.876982\pi$
$348$	−1.26041	+	4.75571i	−0.0675652	+	0.254933i
$349$	16.7181	−	1.64659i	0.894900	−	0.0881400i	0.359899	−	0.932991i	$-0.382811\pi$
$349$	16.7181	−	1.64659i	0.894900	−	0.0881400i	0.535001	+	0.844851i	$0.320311\pi$
$350$	−0.891944	+	3.84904i	−0.0476764	+	0.205740i
$351$	−7.06585	+	7.06585i	−0.377147	+	0.377147i
$352$	1.97562	−	33.6527i	0.105301	−	1.79369i
$353$	22.0343	+	22.0343i	1.17277	+	1.17277i	0.981547	+	0.191220i	$0.0612445\pi$
$353$	22.0343	+	22.0343i	1.17277	+	1.17277i	0.191220	+	0.981547i	$0.438756\pi$
$354$	4.76971	−	2.97502i	0.253507	−	0.158120i
$355$	0.694004	+	7.04634i	0.0368339	+	0.373981i
$356$	10.6136	−	13.9102i	0.562518	−	0.737238i
$357$	0.682108	+	0.364594i	0.0361010	+	0.0192964i
$358$	−3.81935	+	2.93897i	−0.201859	+	0.155329i
$359$	−2.17658	+	1.45435i	−0.114876	+	0.0767575i	−0.611681	−	0.791105i	$-0.709506\pi$
$359$	−2.17658	+	1.45435i	−0.114876	+	0.0767575i	0.496805	+	0.867862i	$0.334506\pi$
$360$	1.63271	+	8.03643i	0.0860516	+	0.423557i
$361$	−10.5449	+	15.7816i	−0.554996	+	0.830611i
$362$	−12.8790	−	11.2636i	−0.676907	−	0.592002i
$363$	6.01138	−	4.93342i	0.315516	−	0.258937i
$364$	−29.4480	−	4.77951i	−1.54350	−	0.250514i
$365$	−2.56752	+	1.37237i	−0.134390	+	0.0718330i
$366$	−2.75778	+	6.10868i	−0.144152	+	0.319306i
$367$	−1.04716	−	2.52806i	−0.0546612	−	0.131964i	0.894190	−	0.447688i	$-0.147753\pi$
$367$	−1.04716	−	2.52806i	−0.0546612	−	0.131964i	−0.948851	+	0.315724i	$0.897753\pi$
$368$	2.62982	+	37.0305i	0.137089	+	1.93035i
$369$	0.786371	−	1.89847i	0.0409368	−	0.0988303i
$370$	−3.51610	−	3.74387i	−0.182793	−	0.194634i
$371$	2.50057	−	8.24327i	0.129823	−	0.427969i
$372$	1.04347	+	2.28640i	0.0541016	+	0.118545i
$373$	−26.1290	−	2.57348i	−1.35291	−	0.133250i	−0.604562	−	0.796558i	$-0.706652\pi$
$373$	−26.1290	−	2.57348i	−1.35291	−	0.133250i	−0.748346	+	0.663308i	$0.769152\pi$
$374$	6.96712	+	2.35444i	0.360261	+	0.121745i
$375$	0.0618920	+	0.311152i	0.00319609	+	0.0160678i
$376$	28.1352	−	2.88722i	1.45096	−	0.148897i
$377$	40.6048	+	8.07680i	2.09126	+	0.415977i
$378$	−7.14002	+	1.92359i	−0.367243	+	0.0989388i
$379$	−18.6710	+	5.66380i	−0.959067	+	0.290930i	−0.730741	−	0.682655i	$-0.760825\pi$
$379$	−18.6710	+	5.66380i	−0.959067	+	0.290930i	−0.228326	+	0.973585i	$0.573325\pi$
$380$	0.251625	+	0.123237i	0.0129081	+	0.00632190i
$381$	0.614208	−	0.748415i	0.0314669	−	0.0383425i
$382$	−9.80942	−	7.00913i	−0.501894	−	0.358618i
$383$	−27.2804			−1.39396			−0.696980	−	0.717090i	$-0.745474\pi$
$383$	−27.2804			−1.39396			−0.696980	+	0.717090i	$0.745474\pi$
$384$	1.12127	−	3.40962i	0.0572194	−	0.173996i
$385$	−16.6490			−0.848510
$386$	−0.314779	−	0.224919i	−0.0160218	−	0.0114481i
$387$	6.61004	−	8.05436i	0.336007	−	0.409426i
$388$	2.53384	−	5.17361i	0.128636	−	0.262650i
$389$	−27.3640	+	8.30078i	−1.38741	+	0.420866i	−0.893663	−	0.448740i	$-0.851873\pi$
$389$	−27.3640	+	8.30078i	−1.38741	+	0.420866i	−0.493747	+	0.869606i	$0.664373\pi$
$390$	−2.31300	+	0.623144i	−0.117123	+	0.0315541i
$391$	−7.94318	−	1.58000i	−0.401704	−	0.0799039i
$392$	−1.76670	−	1.43785i	−0.0892320	−	0.0726226i
$393$	−0.0922705	−	0.463875i	−0.00465443	−	0.0233994i
$394$	−2.01343	−	0.680409i	−0.101435	−	0.0342785i
$395$	12.1881	+	1.20043i	0.613252	+	0.0604001i
$396$	−31.4368	+	14.3472i	−1.57976	+	0.720973i
$397$	6.50476	−	21.4433i	0.326465	−	1.07621i	−0.628082	−	0.778147i	$-0.716160\pi$
$397$	6.50476	−	21.4433i	0.326465	−	1.07621i	0.954546	−	0.298062i	$-0.0963403\pi$
$398$	−2.89248	−	3.07985i	−0.144987	−	0.154379i
$399$	−0.0475167	+	0.114715i	−0.00237881	+	0.00574295i
$400$	−1.26510	+	3.79467i	−0.0632550	+	0.189733i
$401$	−14.0857	−	34.0059i	−0.703407	−	1.69817i	−0.715852	−	0.698252i	$-0.753962\pi$
$401$	−14.0857	−	34.0059i	−0.703407	−	1.69817i	0.0124453	−	0.999923i	$-0.496038\pi$
$402$	2.28257	−	5.05604i	0.113844	−	0.252173i
$403$	18.6515	−	9.96945i	0.929099	−	0.496614i
$404$	0.203994	−	1.25687i	0.0101491	−	0.0625314i
$405$	6.26472	−	5.14132i	0.311296	−	0.255474i
$406$	23.0612	+	20.1686i	1.14451	+	1.00095i
$407$	12.0240	−	17.9952i	0.596007	−	0.891988i
$408$	0.652829	+	0.432358i	0.0323198	+	0.0214049i
$409$	−14.6818	+	9.81005i	−0.725967	+	0.485076i	−0.862817	−	0.505516i	$-0.831302\pi$
$409$	−14.6818	+	9.81005i	−0.725967	+	0.485076i	0.136850	+	0.990592i	$0.456302\pi$
$410$	0.794353	−	0.611250i	0.0392303	−	0.0301875i
$411$	1.35969	+	0.726770i	0.0670686	+	0.0358489i
$412$	−5.11169	−	3.90025i	−0.251835	−	0.192152i
$413$	−3.43110	−	34.8366i	−0.168834	−	1.71420i
$414$	32.2887	−	20.1395i	1.58690	−	0.989801i
$415$	3.47214	+	3.47214i	0.170440	+	0.170440i
$416$	−29.2265	−	7.61825i	−1.43295	−	0.373516i
$417$	−2.70546	+	2.70546i	−0.132487	+	0.132487i
$418$	−0.266529	+	1.15016i	−0.0130364	+	0.0562563i
$419$	−11.1415	+	1.09734i	−0.544297	+	0.0536086i	−0.366430	−	0.930446i	$-0.619420\pi$
$419$	−11.1415	+	1.09734i	−0.544297	+	0.0536086i	−0.177868	+	0.984054i	$0.556920\pi$
$420$	−1.71350	−	0.454131i	−0.0836103	−	0.0221593i
$421$	−4.37958	+	8.19362i	−0.213448	+	0.399332i	−0.965746	−	0.259491i	$-0.916445\pi$
$421$	−4.37958	+	8.19362i	−0.213448	+	0.399332i	0.752298	+	0.658823i	$0.228945\pi$
$422$	13.8281	+	1.80134i	0.673140	+	0.0876880i
$423$	−16.1072	−	24.1062i	−0.783160	−	1.17208i
$424$	3.30441	−	8.07068i	0.160476	−	0.391947i
$425$	−0.725562	−	0.484805i	−0.0351949	−	0.0235165i
$426$	−3.16960	+	0.212083i	−0.153567	+	0.0102754i
$427$	26.4769	+	32.2622i	1.28131	+	1.56128i
$428$	−6.49728	−	4.01577i	−0.314058	−	0.194109i
$429$	−4.75832	−	8.90218i	−0.229734	−	0.429801i
$430$	4.75410	−	1.79671i	0.229263	−	0.0866453i
$431$	3.94158	−	1.63266i	0.189859	−	0.0786424i	−0.285728	−	0.958311i	$-0.592235\pi$
$431$	3.94158	−	1.63266i	0.189859	−	0.0786424i	0.475588	+	0.879668i	$0.342235\pi$
$432$	−7.37949	+	1.25970i	−0.355046	+	0.0606074i
$433$	−13.9597	−	5.78229i	−0.670859	−	0.277879i	0.0211407	−	0.999777i	$-0.493270\pi$
$433$	−13.9597	−	5.78229i	−0.670859	−	0.277879i	−0.692000	+	0.721898i	$0.743270\pi$
$434$	15.6425	+	0.490752i	0.750864	+	0.0235569i
$435$	2.35403	+	0.714086i	0.112867	+	0.0342378i
$436$	26.7344	+	24.9031i	1.28035	+	1.19264i
$437$	0.127440	−	1.29392i	0.00609628	−	0.0618966i
$438$	−0.579297	−	1.17068i	−0.0276799	−	0.0559370i
$439$	16.9804	−	3.37760i	0.810428	−	0.161204i	0.227553	−	0.973766i	$-0.426928\pi$
$439$	16.9804	−	3.37760i	0.810428	−	0.161204i	0.582875	+	0.812562i	$0.301928\pi$
$440$	−16.7807	−	1.58355i	−0.799991	−	0.0754926i
$441$	−0.455533	+	2.29012i	−0.0216920	+	0.109053i
$442$	3.28672	−	5.71072i	0.156333	−	0.271631i
$443$	−5.94048	−	19.5831i	−0.282241	−	0.930423i	−0.977370	−	0.211538i	$-0.932153\pi$
$443$	−5.94048	−	19.5831i	−0.282241	−	0.930423i	0.695129	−	0.718885i	$-0.255347\pi$
$444$	1.72835	−	1.52407i	0.0820239	−	0.0723293i
$445$	−6.76264	−	5.54995i	−0.320580	−	0.263093i
$446$	1.49451	+	8.97603i	0.0707672	+	0.425027i
$447$		−	3.98567i		−	0.188516i
$448$	−15.9328	−	15.6745i	−0.752753	−	0.740548i
$449$			0.130333i			0.00615081i	0.999995	+	0.00307541i	$0.000978934\pi$
$449$			0.130333i			0.00615081i	−0.999995	+	0.00307541i	$0.999021\pi$
$450$	4.04463	−	0.673431i	0.190665	−	0.0317459i
$451$	3.26485	+	2.67939i	0.153736	+	0.126168i
$452$	−8.57344	−	0.538479i	−0.403261	−	0.0253279i
$453$	−1.80639	−	5.95486i	−0.0848715	−	0.279784i
$454$	−4.07246	−	2.34384i	−0.191130	−	0.110002i
$455$	−2.91010	+	14.6301i	−0.136428	+	0.685868i
$456$	−0.0588038	+	0.111104i	−0.00275374	+	0.00520291i
$457$	−4.21965	+	0.839340i	−0.197387	+	0.0392627i	−0.292793	−	0.956176i	$-0.594585\pi$
$457$	−4.21965	+	0.839340i	−0.197387	+	0.0392627i	0.0954067	+	0.995438i	$0.469585\pi$
$458$	−26.4320	+	13.0796i	−1.23509	+	0.611170i
$459$	0.160079	−	1.62531i	0.00747184	−	0.0758628i
$460$	18.5502	−	0.657868i	0.864909	−	0.0306732i
$461$	−9.05709	−	2.74744i	−0.421831	−	0.127961i	0.0722307	−	0.997388i	$-0.476988\pi$
$461$	−9.05709	−	2.74744i	−0.421831	−	0.127961i	−0.494061	+	0.869427i	$0.664488\pi$
$462$	0.234231	−	7.46600i	0.0108974	−	0.347350i
$463$	−20.5065	−	8.49406i	−0.953017	−	0.394752i	−0.148653	−	0.988889i	$-0.547494\pi$
$463$	−20.5065	−	8.49406i	−0.953017	−	0.394752i	−0.804364	+	0.594137i	$0.797494\pi$
$464$	21.3254	+	22.5217i	0.990008	+	1.04554i
$465$	1.16097	−	0.480892i	0.0538389	−	0.0223008i
$466$	−7.27431	−	19.2478i	−0.336976	−	0.891638i
$467$	−17.2934	−	32.3536i	−0.800242	−	1.49715i	−0.866407	−	0.499339i	$-0.833576\pi$
$467$	−17.2934	−	32.3536i	−0.800242	−	1.49715i	0.0661647	−	0.997809i	$-0.478924\pi$
$468$	7.11250	+	30.1324i	0.328776	+	1.39287i
$469$	−21.9144	−	26.7028i	−1.01192	−	1.23302i
$470$	−0.944119	−	14.1099i	−0.0435490	−	0.650843i
$471$	4.60925	+	3.07981i	0.212383	+	0.141910i
$472$	−0.144822	−	35.4386i	−0.00666597	−	1.63120i
$473$	11.8980	+	17.8067i	0.547072	+	0.818751i
$474$	−0.709787	+	5.44871i	−0.0326016	+	0.250268i
$475$	0.0660386	−	0.123550i	0.00303006	−	0.00566884i
$476$	4.21599	−	2.44944i	0.193240	−	0.112270i
$477$	−8.89659	+	0.876238i	−0.407347	+	0.0401202i
$478$	−22.9592	−	5.32036i	−1.05013	−	0.243348i
$479$	−24.1536	+	24.1536i	−1.10361	+	1.10361i	−0.109633	+	0.993972i	$0.534968\pi$
$479$	−24.1536	+	24.1536i	−1.10361	+	1.10361i	−0.993972	+	0.109633i	$0.965032\pi$
$480$	−1.68387	−	0.620703i	−0.0768577	−	0.0283311i
$481$	−13.7113	−	13.7113i	−0.625183	−	0.625183i
$482$	−12.5603	−	20.1374i	−0.572105	−	0.917231i
$483$	0.806286	+	8.18636i	0.0366873	+	0.372492i
$484$	−6.53148	−	48.5883i	−0.296885	−	2.20856i
$485$	−2.54028	−	1.35781i	−0.115348	−	0.0616549i
$486$	7.05977	+	9.17457i	0.320238	+	0.416167i
$487$	−12.8300	+	8.57273i	−0.581383	+	0.388467i	−0.811202	−	0.584766i	$-0.801186\pi$
$487$	−12.8300	+	8.57273i	−0.581383	+	0.388467i	0.229820	+	0.973233i	$0.426186\pi$
$488$	23.6179	+	35.0358i	1.06913	+	1.58600i
$489$	−3.42857	+	5.13122i	−0.155046	+	0.232042i
$490$	−0.749783	+	0.857316i	−0.0338717	+	0.0387296i
$491$	−3.39786	+	2.78855i	−0.153343	+	0.125846i	−0.707937	−	0.706276i	$-0.750374\pi$
$491$	−3.39786	+	2.78855i	−0.153343	+	0.125846i	0.554593	+	0.832121i	$0.312874\pi$
$492$	0.262931	+	0.364816i	0.0118538	+	0.0164472i
$493$	−5.96741	+	3.18964i	−0.268758	+	0.143654i
$494$	0.964103	+	0.435248i	0.0433771	+	0.0195827i
$495$	6.61199	+	15.9628i	0.297187	+	0.717473i
$496$	15.7196	+	1.98245i	0.705832	+	0.0890147i
$497$	−7.57000	+	18.2756i	−0.339561	+	0.819772i
$498$	−1.60588	+	1.50818i	−0.0719612	+	0.0675832i
$499$	−11.7943	+	38.8805i	−0.527984	+	1.74053i	0.133968	+	0.990986i	$0.457228\pi$
$499$	−11.7943	+	38.8805i	−0.527984	+	1.74053i	−0.661952	+	0.749546i	$0.730272\pi$
$500$	1.87372	+	0.699398i	0.0837955	+	0.0312780i
$501$	1.55946	+	0.153594i	0.0696717	+	0.00686206i
$502$	−2.36655	+	7.00297i	−0.105624	+	0.312558i
$503$	−3.21043	−	16.1399i	−0.143146	−	0.719644i	−0.983970	−	0.178335i	$-0.942929\pi$
$503$	−3.21043	−	16.1399i	−0.143146	−	0.719644i	0.840824	−	0.541309i	$-0.182071\pi$
$504$	−6.56104	+	21.9514i	−0.292252	+	0.977792i
$505$	−0.624423	−	0.124206i	−0.0277865	−	0.00552707i
$506$	20.3468	+	75.5237i	0.904527	+	3.35744i
$507$	−4.70775	+	1.42808i	−0.209079	+	0.0634233i
$508$	−1.97769	−	5.77434i	−0.0877456	−	0.256195i
$509$	21.5427	−	26.2499i	0.954865	−	1.16351i	−0.0315946	−	0.999501i	$-0.510059\pi$
$509$	21.5427	−	26.2499i	0.954865	−	1.16351i	0.986459	−	0.164005i	$-0.0524415\pi$
$510$	0.227612	−	0.318547i	0.0100788	−	0.0141055i
$511$	−8.13355			−0.359807
$512$	−14.5680	−	17.3139i	−0.643822	−	0.765175i
$513$	0.262189			0.0115759
$514$	2.54618	−	3.56343i	0.112307	−	0.157176i
$515$	−2.03949	+	2.48512i	−0.0898705	+	0.109508i
$516$	0.738827	+	2.15719i	0.0325250	+	0.0949649i
$517$	57.0239	−	17.2980i	2.50791	−	0.760765i
$518$	−3.73274	−	13.8552i	−0.164007	−	0.608764i
$519$	6.00657	+	1.19478i	0.263659	+	0.0524451i
$520$	−4.32465	+	14.4691i	−0.189649	+	0.634511i
$521$	5.94852	+	29.9052i	0.260609	+	1.31017i	0.860238	+	0.509893i	$0.170315\pi$
$521$	5.94852	+	29.9052i	0.260609	+	1.31017i	−0.599629	+	0.800278i	$0.704685\pi$
$522$	10.1788	−	30.1205i	0.445514	−	1.31834i
$523$	14.0744	+	1.38621i	0.615433	+	0.0606148i	0.400930	−	0.916109i	$-0.368687\pi$
$523$	14.0744	+	1.38621i	0.615433	+	0.0606148i	0.214502	+	0.976723i	$0.431187\pi$
$524$	−2.79340	−	1.04268i	−0.122030	−	0.0455498i
$525$	−0.257288	+	0.848164i	−0.0112290	+	0.0370169i
$526$	−0.712542	+	0.669193i	−0.0310683	+	0.0291782i
$527$	−1.32275	+	3.19339i	−0.0576197	+	0.139106i
$528$	0.946204	−	7.50281i	0.0411782	−	0.326518i
$529$	−24.1611	−	58.3300i	−1.05048	−	2.53609i
$530$	−3.97425	−	1.79419i	−0.172630	−	0.0779345i
$531$	−32.0381	+	17.1247i	−1.39033	+	0.743149i
$532$	0.457681	+	0.635032i	0.0198430	+	0.0275321i
$533$	2.92515	−	2.40061i	0.126702	−	0.103982i
$534$	2.58394	−	2.95453i	0.111818	−	0.127855i
$535$	−2.12176	+	3.17544i	−0.0917317	+	0.137286i
$536$	−19.5481	−	28.9985i	−0.844349	−	1.25255i
$537$	−0.898894	+	0.600622i	−0.0387901	+	0.0259187i
$538$	−2.07313	−	2.69415i	−0.0893789	−	0.116153i
$539$	−4.23257	−	2.26236i	−0.182310	−	0.0974465i
$540$	0.498683	+	3.70975i	0.0214599	+	0.159642i
$541$	2.13034	+	21.6297i	0.0915905	+	0.929934i	0.925681	+	0.378306i	$0.123493\pi$
$541$	2.13034	+	21.6297i	0.0915905	+	0.929934i	−0.834090	+	0.551628i	$0.814007\pi$
$542$	18.6298	+	29.8684i	0.800219	+	1.28296i
$543$	−2.71400	−	2.71400i	−0.116469	−	0.116469i
$544$	4.48233	−	2.06783i	0.192179	−	0.0886575i
$545$	12.9175	−	12.9175i	0.553325	−	0.553325i
$546$	−6.51971	−	1.51082i	−0.279018	−	0.0646572i
$547$	18.4593	−	1.81808i	0.789264	−	0.0777357i	0.304650	−	0.952464i	$-0.401460\pi$
$547$	18.4593	−	1.81808i	0.789264	−	0.0777357i	0.484613	+	0.874729i	$0.338960\pi$
$548$	8.40402	−	4.88264i	0.359002	−	0.208576i
$549$	20.4174	−	38.1982i	0.871393	−	1.63026i
$550$	−1.08865	+	8.35704i	−0.0464200	+	0.356345i
$551$	−0.603501	−	0.903203i	−0.0257100	−	0.0384777i
$552$	0.0340322	+	8.32784i	0.00144851	+	0.354457i
$553$	28.4496	+	19.0094i	1.20980	+	0.808363i
$554$	2.32316	+	34.7199i	0.0987018	+	1.47511i
$555$	−0.730930	−	0.890641i	−0.0310263	−	0.0378056i
$556$	5.54119	+	23.4755i	0.234999	+	0.995582i
$557$	−0.930907	−	1.74160i	−0.0394438	−	0.0737941i	0.861427	−	0.507881i	$-0.169571\pi$
$557$	−0.930907	−	1.74160i	−0.0394438	−	0.0737941i	−0.900871	+	0.434087i	$0.857071\pi$
$558$	−5.74175	−	15.1927i	−0.243068	−	0.643156i
$559$	17.7270	−	7.34278i	0.749774	−	0.310566i
$560$	−8.11465	+	7.68362i	−0.342906	+	0.324692i
$561$	1.52417	+	0.631333i	0.0643506	+	0.0266549i
$562$	0.0469779	−	1.49740i	0.00198164	−	0.0631639i
$563$	13.1784	+	3.99762i	0.555403	+	0.168480i	0.555494	−	0.831520i	$-0.312529\pi$
$563$	13.1784	+	3.99762i	0.555403	+	0.168480i	−9.13228e−5		1.00000i	$0.500029\pi$
$564$	6.34069	−	0.224867i	0.266991	−	0.00946861i
$565$	−0.421000	+	4.27448i	−0.0177116	+	0.179829i
$566$	15.1429	−	7.49330i	0.636502	−	0.314967i
$567$	22.2068	−	4.41721i	0.932598	−	0.185505i
$568$	−9.36817	+	17.7002i	−0.393080	+	0.742685i
$569$	4.51959	−	22.7215i	0.189471	−	0.952536i	−0.762649	−	0.646813i	$-0.776102\pi$
$569$	4.51959	−	22.7215i	0.189471	−	0.952536i	0.952120	−	0.305724i	$-0.0988984\pi$
$570$	0.0544750	+	0.0313523i	0.00228171	+	0.00131320i
$571$	−10.2831	−	33.8989i	−0.430336	−	1.41863i	−0.857515	−	0.514460i	$-0.827993\pi$
$571$	−10.2831	−	33.8989i	−0.430336	−	1.41863i	0.427179	−	0.904167i	$-0.359507\pi$
$572$	−63.5101	−	3.98894i	−2.65549	−	0.166786i
$573$	−2.09065	−	1.71575i	−0.0873381	−	0.0716765i
$574$	2.76223	−	0.459912i	0.115293	−	0.0191964i
$575$		−	9.28094i		−	0.387042i
$576$	−8.70084	+	21.5011i	−0.362535	+	0.895877i
$577$			27.0049i			1.12423i	0.827059	+	0.562114i	$0.190012\pi$
$577$			27.0049i			1.12423i	−0.827059	+	0.562114i	$0.809988\pi$
$578$	−3.77171	−	22.6529i	−0.156883	−	0.942236i
$579$	−0.0670878	−	0.0550575i	−0.00278807	−	0.00228811i
$580$	11.6317	−	10.2569i	0.482979	−	0.425895i
$581$	3.98228	+	13.1278i	0.165213	+	0.544634i
$582$	0.644628	−	1.12005i	0.0267207	−	0.0464276i
$583$	3.58464	−	18.0212i	0.148461	−	0.746363i
$584$	−8.19792	−	0.773612i	−0.339232	−	0.0320123i
$585$	15.1828	−	3.02004i	0.627731	−	0.124863i
$586$	−14.8851	−	30.0807i	−0.614899	−	1.24262i
$587$	−1.14651	+	11.6407i	−0.0473214	+	0.480462i	0.942094	+	0.335349i	$0.108854\pi$
$587$	−1.14651	+	11.6407i	−0.0473214	+	0.480462i	−0.989415	+	0.145112i	$0.953646\pi$
$588$	−0.373903	−	0.348291i	−0.0154195	−	0.0143633i
$589$	−0.531012	−	0.161081i	−0.0218800	−	0.00663722i
$590$	−17.7108	−	0.555640i	−0.729140	−	0.0228753i
$591$	−0.440470	−	0.182449i	−0.0181185	−	0.00750494i
$592$	−2.44446	−	14.3199i	−0.100467	−	0.588546i
$593$	38.1017	−	15.7823i	1.56465	−	0.648099i	0.578761	−	0.815497i	$-0.303536\pi$
$593$	38.1017	−	15.7823i	1.56465	−	0.648099i	0.985889	+	0.167398i	$0.0535364\pi$
$594$	−14.7543	+	5.57609i	−0.605377	+	0.228790i
$595$	−1.14924	−	2.15008i	−0.0471143	−	0.0881446i
$596$	−21.3736	−	13.2103i	−0.875496	−	0.541116i
$597$	−0.601291	−	0.732675i	−0.0246092	−	0.0299864i
$598$	69.9219	−	4.67859i	2.85932	−	0.191322i
$599$	2.16545	+	1.44691i	0.0884778	+	0.0591190i	0.599022	−	0.800732i	$-0.295556\pi$
$599$	2.16545	+	1.44691i	0.0884778	+	0.0591190i	−0.510544	+	0.859851i	$0.670556\pi$
$600$	−0.339996	+	0.830406i	−0.0138803	+	0.0339012i
$601$	−15.7964	−	23.6410i	−0.644350	−	0.964337i	−0.999563	−	0.0295521i	$-0.990592\pi$
$601$	−15.7964	−	23.6410i	−0.644350	−	0.964337i	0.355214	−	0.934785i	$-0.384408\pi$
$602$	14.0800	+	1.83415i	0.573857	+	0.0747545i
$603$	−16.8991	+	31.6160i	−0.688185	+	1.28750i
$604$	−37.9208	−	10.0502i	−1.54297	−	0.408936i
$605$	−24.3946	+	2.40266i	−0.991782	+	0.0976820i
$606$	0.0644831	−	0.278266i	0.00261945	−	0.0113038i
$607$	18.6144	−	18.6144i	0.755537	−	0.755537i	−0.219970	−	0.975507i	$-0.570596\pi$
$607$	18.6144	−	18.6144i	0.755537	−	0.755537i	0.975507	+	0.219970i	$0.0705959\pi$
$608$	0.400903	+	0.683590i	0.0162588	+	0.0277232i
$609$	4.85968	+	4.85968i	0.196924	+	0.196924i
$610$	17.9254	−	11.1806i	0.725780	−	0.452691i
$611$	−5.23309	−	53.1325i	−0.211708	−	2.14951i
$612$	−4.02283	−	3.06945i	−0.162613	−	0.124075i
$613$	−36.8785	−	19.7120i	−1.48951	−	0.796160i	−0.492272	−	0.870441i	$-0.663834\pi$
$613$	−36.8785	−	19.7120i	−1.48951	−	0.796160i	−0.997237	+	0.0742816i	$0.976334\pi$
$614$	−20.3504	+	15.6595i	−0.821274	+	0.631965i
$615$	0.186953	−	0.124918i	0.00753866	−	0.00503717i
$616$	−39.2608	−	26.0018i	−1.58186	−	1.04764i
$617$	13.1387	−	19.6635i	0.528944	−	0.791621i	−0.466743	−	0.884393i	$-0.654573\pi$
$617$	13.1387	−	19.6635i	0.528944	−	0.791621i	0.995687	+	0.0927721i	$0.0295728\pi$
$618$	−1.08572	−	0.949541i	−0.0436742	−	0.0381962i
$619$	−12.9390	+	10.6188i	−0.520063	+	0.426805i	−0.857455	−	0.514560i	$-0.827955\pi$
$619$	−12.9390	+	10.6188i	−0.520063	+	0.426805i	0.337391	+	0.941364i	$0.390455\pi$
$620$	1.26917	−	7.81974i	0.0509711	−	0.314048i
$621$	15.3188	−	8.18808i	0.614723	−	0.328576i
$622$	−3.87075	+	8.57399i	−0.155203	+	0.343785i
$623$	−9.35334	−	22.5809i	−0.374733	−	0.904687i
$624$	−6.42761	−	2.14289i	−0.257310	−	0.0857843i
$625$	0.382683	−	0.923880i	0.0153073	−	0.0369552i
$626$	14.4681	+	15.4053i	0.578261	+	0.615719i
$627$	−0.0768822	+	0.253447i	−0.00307038	+	0.0101217i
$628$	31.7929	−	14.5097i	1.26868	−	0.579001i
$629$	3.15392	+	0.310634i	0.125755	+	0.0123858i
$630$	10.8525	+	3.66746i	0.432375	+	0.146115i
$631$	2.58092	+	12.9752i	0.102745	+	0.516534i	0.997543	+	0.0700620i	$0.0223197\pi$
$631$	2.58092	+	12.9752i	0.102745	+	0.516534i	−0.894798	+	0.446472i	$0.852680\pi$
$632$	26.8667	+	21.8658i	1.06870	+	0.869776i
$633$	3.06813	+	0.610289i	0.121947	+	0.0242568i
$634$	24.5098	−	6.60319i	0.973410	−	0.262246i
$635$	−2.92040	+	0.885895i	−0.115893	+	0.0351557i
$636$	0.860491	−	1.75695i	0.0341207	−	0.0696677i
$637$	−2.72783	+	3.32387i	−0.108081	+	0.131697i
$638$	53.1699	+	37.9915i	2.10502	+	1.50410i
$639$	20.5287			0.812102
$640$	−8.90969	+	6.97262i	−0.352186	+	0.275617i
$641$	−4.83150			−0.190833			−0.0954164	−	0.995437i	$-0.530418\pi$
$641$	−4.83150			−0.190833			−0.0954164	+	0.995437i	$0.530418\pi$
$642$	−1.39413	−	0.996148i	−0.0550219	−	0.0393148i
$643$	7.98495	−	9.72969i	0.314896	−	0.383701i	−0.591377	−	0.806395i	$-0.701415\pi$
$643$	7.98495	−	9.72969i	0.314896	−	0.383701i	0.906273	+	0.422694i	$0.138915\pi$
$644$	46.5726	+	22.8095i	1.83522	+	0.898822i
$645$	1.09101	−	0.330954i	0.0429584	−	0.0130313i
$646$	−0.166932	+	0.0449731i	−0.00656785	+	0.00176944i
$647$	46.2690	+	9.20348i	1.81902	+	0.361826i	0.982523	−	0.186140i	$-0.0595978\pi$
$647$	46.2690	+	9.20348i	1.81902	+	0.361826i	0.836500	+	0.547966i	$0.184598\pi$
$648$	22.8027	−	2.34000i	0.895775	−	0.0919238i
$649$	−14.5668	−	73.2320i	−0.571795	−	2.87461i
$650$	7.15335	+	2.41737i	0.280578	+	0.0948172i
$651$	3.49387	+	0.344117i	0.136936	+	0.0134870i
$652$	16.1529	+	35.3933i	0.632595	+	1.38611i
$653$	−10.4050	+	34.3008i	−0.407181	+	1.34229i	0.478536	+	0.878068i	$0.341168\pi$
$653$	−10.4050	+	34.3008i	−0.407181	+	1.34229i	−0.885716	+	0.464227i	$0.846332\pi$
$654$	5.61094	+	5.97440i	0.219405	+	0.233618i
$655$	−0.570516	+	1.37735i	−0.0222919	+	0.0538174i
$656$	2.82784	−	0.200826i	0.110408	−	0.00784094i
$657$	3.23016	+	7.79831i	0.126021	+	0.304241i
$658$	16.2564	−	36.0091i	0.633742	−	1.40378i
$659$	11.1622	−	5.96630i	0.434816	−	0.232414i	−0.239441	−	0.970911i	$-0.576964\pi$
$659$	11.1622	−	5.96630i	0.434816	−	0.232414i	0.674257	+	0.738497i	$0.264464\pi$
$660$	−3.73228	−	0.605762i	−0.145279	−	0.0235792i
$661$	30.8304	−	25.3019i	1.19916	−	0.984129i	0.199173	−	0.979964i	$-0.436174\pi$
$661$	30.8304	−	25.3019i	1.19916	−	0.984129i	0.999991	−	0.00416461i	$-0.00132564\pi$
$662$	−0.926829	−	0.810577i	−0.0360222	−	0.0315040i
$663$	0.821188	−	1.22899i	0.0318923	−	0.0477302i
$664$	2.76516	+	13.6105i	0.107309	+	0.528189i
$665$	0.325427	−	0.217443i	0.0126195	−	0.00843210i
$666$	−11.8018	+	9.08137i	−0.457309	+	0.351896i
$667$	−63.4672	−	33.9239i	−2.45746	−	1.31354i
$668$	5.99243	−	7.85370i	0.231854	−	0.303869i
$669$	0.200082	+	2.03147i	0.00773562	+	0.0785411i
$670$	−14.8366	+	9.25402i	−0.573187	+	0.357514i
$671$	62.9490	+	62.9490i	2.43012	+	2.43012i
$672$	−3.33145	−	3.74700i	−0.128513	−	0.144544i
$673$	−17.6656	+	17.6656i	−0.680961	+	0.680961i	−0.960217	−	0.279256i	$-0.909912\pi$
$673$	−17.6656	+	17.6656i	−0.680961	+	0.680961i	0.279256	+	0.960217i	$0.409912\pi$
$674$	−1.06149	+	4.58069i	−0.0408871	+	0.176442i
$675$	1.86255	−	0.183445i	0.0716895	−	0.00706079i
$676$	−7.94540	+	29.9791i	−0.305592	+	1.15304i
$677$	12.0115	−	22.4720i	0.461640	−	0.863668i	−0.538143	−	0.842854i	$-0.680874\pi$
$677$	12.0115	−	22.4720i	0.461640	−	0.863668i	0.999783	−	0.0208148i	$-0.00662603\pi$
$678$	−1.91091	−	0.248928i	−0.0733880	−	0.00956003i
$679$	−4.47082	−	6.69105i	−0.171574	−	0.256779i
$680$	−0.953834	−	2.27640i	−0.0365779	−	0.0872961i
$681$	−0.876426	−	0.585609i	−0.0335847	−	0.0224406i
$682$	33.3077	−	2.22867i	1.27542	−	0.0853403i
$683$	−10.5374	−	12.8398i	−0.403202	−	0.491303i	0.531339	−	0.847159i	$-0.321689\pi$
$683$	−10.5374	−	12.8398i	−0.403202	−	0.491303i	−0.934541	+	0.355857i	$0.884189\pi$
$684$	0.427094	−	0.691014i	0.0163304	−	0.0264216i
$685$	−2.29086	−	4.28589i	−0.0875292	−	0.163756i
$686$	22.8948	−	8.65262i	0.874128	−	0.330359i
$687$	−6.11211	+	2.53172i	−0.233191	+	0.0965910i
$688$	14.0169	+	3.18787i	0.534391	+	0.121536i
$689$	−15.2093	−	6.29992i	−0.579430	−	0.240008i
$690$	4.16191	+	0.130572i	0.158441	+	0.00497078i
$691$	−28.2132	−	8.55838i	−1.07328	−	0.325576i	−0.296296	−	0.955096i	$-0.595752\pi$
$691$	−28.2132	−	8.55838i	−1.07328	−	0.325576i	−0.776984	+	0.629520i	$0.783252\pi$
$692$	26.3156	−	28.2508i	1.00037	−	1.07393i
$693$	−4.73141	+	48.0388i	−0.179731	+	1.82484i
$694$	17.9707	+	36.3162i	0.682159	+	1.37854i
$695$	11.8286	−	2.35285i	0.448683	−	0.0892485i
$696$	4.43592	+	5.36036i	0.168143	+	0.203184i
$697$	−0.120656	+	0.606581i	−0.00457019	+	0.0229759i
$698$	11.8507	−	20.5907i	0.448554	−	0.779368i
$699$	−1.33992	−	4.41714i	−0.0506806	−	0.167072i
$700$	3.69560	+	4.19094i	0.139680	+	0.158402i
$701$	−15.0289	−	12.3339i	−0.567634	−	0.465845i	0.306269	−	0.951945i	$-0.400919\pi$
$701$	−15.0289	−	12.3339i	−0.567634	−	0.465845i	−0.873903	+	0.486100i	$0.838419\pi$
$702$	2.32098	+	13.9398i	0.0875998	+	0.526124i
$703$			0.508779i			0.0191890i
$704$	−37.0984	−	29.9419i	−1.39820	−	1.12848i
$705$		−	3.17234i		−	0.119477i
$706$	43.4702	−	7.23780i	1.63602	−	0.272398i
$707$	−1.37495	−	1.12839i	−0.0517103	−	0.0424375i
$708$	0.498338	−	7.93432i	0.0187287	−	0.298190i
$709$	4.01896	+	13.2487i	0.150935	+	0.497567i	0.999503	−	0.0315196i	$-0.0100347\pi$
$709$	4.01896	+	13.2487i	0.150935	+	0.497567i	−0.848568	+	0.529087i	$0.822535\pi$
$710$	8.67854	+	4.99481i	0.325700	+	0.187452i
$711$	6.92741	−	34.8264i	0.259798	−	1.30609i
$712$	−7.27960	−	23.6493i	−0.272815	−	0.886295i
$713$	−36.0558	+	7.17194i	−1.35030	+	0.268591i
$714$	0.980340	−	0.485112i	0.0366883	−	0.0181548i
$715$	−3.11867	+	31.6644i	−0.116632	+	1.18418i
$716$	0.241551	+	6.81114i	0.00902719	+	0.254544i
$717$	−5.05922	−	1.53470i	−0.188940	−	0.0573143i
$718$	−0.116088	+	3.70025i	−0.00433236	+	0.138092i
$719$	−32.4434	−	13.4385i	−1.20994	−	0.501172i	−0.315739	−	0.948846i	$-0.602252\pi$
$719$	−32.4434	−	13.4385i	−1.20994	−	0.501172i	−0.894197	+	0.447674i	$0.852252\pi$
$720$	10.5896	+	4.72871i	0.394651	+	0.176228i
$721$	−8.29800	+	3.43715i	−0.309034	+	0.128006i
$722$	9.48941	+	25.1090i	0.353159	+	0.934459i
$723$	−2.50975	−	4.69541i	−0.0933386	−	0.174624i
$724$	−23.5495	+	5.55866i	−0.875210	+	0.206586i
$725$	−4.91911	−	5.99395i	−0.182691	−	0.222610i
$726$	−0.734236	−	10.9732i	−0.0272500	−	0.407254i
$727$	22.3012	+	14.9012i	0.827107	+	0.552655i	0.895530	−	0.445001i	$-0.146797\pi$
$727$	22.3012	+	14.9012i	0.827107	+	0.552655i	−0.0684231	+	0.997656i	$0.521797\pi$
$728$	−29.7112	+	29.9550i	−1.10117	+	1.11021i
$729$	−12.0648	−	18.0562i	−0.446844	−	0.668749i
$730$	−0.531838	+	4.08268i	−0.0196842	+	0.151107i
$731$	−1.47829	+	2.76568i	−0.0546765	+	0.102292i
$732$	4.76162	+	8.19571i	0.175994	+	0.302922i
$733$	9.66649	−	0.952067i	0.357040	−	0.0351654i	0.0820928	−	0.996625i	$-0.473840\pi$
$733$	9.66649	−	0.952067i	0.357040	−	0.0351654i	0.274947	+	0.961459i	$0.411340\pi$
$734$	−3.76989	−	0.873603i	−0.139149	−	0.0322453i
$735$	−0.180662	+	0.180662i	−0.00666382	+	0.00666382i
$736$	44.7717	+	27.4198i	1.65031	+	1.01071i
$737$	−52.1017	−	52.1017i	−1.91919	−	1.91919i
$738$	−1.53795	−	2.46573i	−0.0566127	−	0.0907648i
$739$	−1.15477	−	11.7245i	−0.0424788	−	0.431295i	−0.992779	−	0.119959i	$-0.961724\pi$
$739$	−1.15477	−	11.7245i	−0.0424788	−	0.431295i	0.950300	−	0.311336i	$-0.100776\pi$
$740$	−7.19879	+	0.967698i	−0.264633	+	0.0355733i
$741$	0.209275	+	0.111860i	0.00768789	+	0.00410926i
$742$	−7.42928	−	9.65477i	−0.272738	−	0.354438i
$743$	−3.88766	+	2.59765i	−0.142624	+	0.0952986i	−0.624835	−	0.780757i	$-0.714834\pi$
$743$	−3.88766	+	2.59765i	−0.142624	+	0.0952986i	0.482211	+	0.876055i	$0.339834\pi$
$744$	3.48880	+	0.679156i	0.127905	+	0.0248991i
$745$	−6.97978	+	10.4460i	−0.255719	+	0.382711i
$746$	−24.4440	+	27.9497i	−0.894957	+	1.02331i
$747$	11.0052	−	9.03174i	0.402659	−	0.330454i
$748$	8.43739	−	6.08101i	0.308501	−	0.222344i
$749$	−9.40986	+	5.02967i	−0.343829	+	0.183780i
$750$	0.408917	+	0.184607i	0.0149315	+	0.00674089i
$751$	−0.812653	−	1.96192i	−0.0296541	−	0.0715914i	0.908359	−	0.418192i	$-0.137336\pi$
$751$	−0.812653	−	1.96192i	−0.0296541	−	0.0715914i	−0.938013	+	0.346600i	$0.887336\pi$
$752$	19.8101	−	34.7479i	0.722398	−	1.26713i
$753$	−0.634582	+	1.53202i	−0.0231254	+	0.0558297i
$754$	42.6782	−	40.0818i	1.55425	−	1.45969i
$755$	−5.69393	+	18.7704i	−0.207223	+	0.683124i
$756$	−3.65699	+	9.79727i	−0.133003	+	0.356323i
$757$	−8.66651	−	0.853577i	−0.314990	−	0.0310238i	−0.0607130	−	0.998155i	$-0.519337\pi$
$757$	−8.66651	−	0.853577i	−0.314990	−	0.0310238i	−0.254277	+	0.967131i	$0.581837\pi$
$758$	−8.83387	+	26.1407i	−0.320861	+	0.949472i
$759$	3.42309	+	17.2090i	0.124250	+	0.624649i
$760$	0.348685	−	0.188212i	0.0126481	−	0.00682716i
$761$	23.5946	+	4.69326i	0.855305	+	0.170131i	0.603220	−	0.797575i	$-0.293884\pi$
$761$	23.5946	+	4.69326i	0.855305	+	0.170131i	0.252084	+	0.967705i	$0.418884\pi$
$762$	−0.356181	−	1.32208i	−0.0129031	−	0.0478938i
$763$	48.8399	−	14.8154i	1.76812	−	0.536354i
$764$	−16.1302	+	5.52454i	−0.583572	+	0.199871i
$765$	−1.60505	+	1.95576i	−0.0580306	+	0.0707105i
$766$	−22.4294	+	31.3904i	−0.810407	+	1.13418i
$767$	−66.8978			−2.41554
$768$	−3.00143	−	4.09352i	−0.108305	−	0.147712i
$769$	−1.60304			−0.0578071			−0.0289035	−	0.999582i	$-0.509202\pi$
$769$	−1.60304			−0.0578071			−0.0289035	+	0.999582i	$0.509202\pi$
$770$	−13.6885	+	19.1573i	−0.493298	+	0.690382i
$771$	0.623275	−	0.759462i	0.0224467	−	0.0273514i
$772$	−0.517611	+	0.177279i	−0.0186292	+	0.00638043i
$773$	41.6707	−	12.6407i	1.49879	−	0.454653i	0.568874	−	0.822425i	$-0.307379\pi$
$773$	41.6707	−	12.6407i	1.49879	−	0.454653i	0.929916	+	0.367772i	$0.119879\pi$
$774$	−3.83318	−	14.2281i	−0.137781	−	0.511417i
$775$	−3.88492	−	0.772759i	−0.139551	−	0.0277583i
$776$	−3.86979	−	7.16924i	−0.138917	−	0.257361i
$777$	−0.627985	−	3.15709i	−0.0225288	−	0.113260i
$778$	−12.9468	+	38.3114i	−0.464165	+	1.37353i
$779$	−0.0988102	−	0.00973195i	−0.00354024	−	0.000348683i
$780$	−1.18468	+	3.17381i	−0.0424182	+	0.113641i
$781$	−12.2483	+	40.3772i	−0.438278	+	1.44481i
$782$	−8.34877	+	7.84085i	−0.298551	+	0.280388i
$783$	5.55355	−	13.4075i	0.198468	−	0.479143i
$784$	−3.10703	+	0.850698i	−0.110965	+	0.0303821i
$785$	−6.68690	−	16.1436i	−0.238666	−	0.576190i
$786$	−0.609625	−	0.275217i	−0.0217446	−	0.00981668i
$787$	−2.99389	+	1.60027i	−0.106721	+	0.0570434i	−0.523893	−	0.851784i	$-0.675521\pi$
$787$	−2.99389	+	1.60027i	−0.106721	+	0.0570434i	0.417173	+	0.908827i	$0.363021\pi$
$788$	−2.43832	+	1.75735i	−0.0868615	+	0.0626030i
$789$	−0.169509	+	0.139112i	−0.00603468	+	0.00495253i
$790$	11.4021	−	13.0374i	0.405670	−	0.463851i
$791$	−6.66676	+	9.97751i	−0.237043	+	0.354760i
$792$	−9.33801	+	47.9690i	−0.331812	+	1.70450i
$793$	66.3185	−	44.3126i	2.35504	−	1.57359i
$794$	−19.3259	−	25.1151i	−0.685850	−	0.891300i
$795$	−0.862676	−	0.461110i	−0.0305960	−	0.0163539i
$796$	−5.92199	+	0.796065i	−0.209900	+	0.0282158i
$797$	−4.01291	−	40.7438i	−0.142145	−	1.44322i	−0.756399	−	0.654110i	$-0.773043\pi$
$797$	−4.01291	−	40.7438i	−0.142145	−	1.44322i	0.614255	−	0.789108i	$-0.289457\pi$
$798$	0.0929311	+	0.148992i	0.00328973	+	0.00527427i
$799$	6.17012	+	6.17012i	0.218283	+	0.218283i
$800$	3.32623	+	4.57561i	0.117600	+	0.161772i
$801$	−17.9356	+	17.9356i	−0.633725	+	0.633725i
$802$	−50.7102	−	11.7512i	−1.79064	−	0.414948i
$803$	−17.2655	+	1.70050i	−0.609286	+	0.0600094i
$804$	−3.94110	−	6.78344i	−0.138992	−	0.239234i
$805$	12.2229	−	22.8675i	0.430801	−	0.805972i
$806$	3.86349	−	29.6583i	0.136086	−	1.04467i
$807$	−0.423675	−	0.634074i	−0.0149140	−	0.0223205i
$808$	−1.27851	−	1.26810i	−0.0449777	−	0.0446116i
$809$	18.9656	+	12.6724i	0.666797	+	0.445539i	0.842350	−	0.538931i	$-0.181172\pi$
$809$	18.9656	+	12.6724i	0.666797	+	0.445539i	−0.175554	+	0.984470i	$0.556172\pi$
$810$	−0.765178	−	11.4357i	−0.0268856	−	0.401808i
$811$	15.8115	+	19.2663i	0.555215	+	0.676532i	0.972677	−	0.232163i	$-0.0745802\pi$
$811$	15.8115	+	19.2663i	0.555215	+	0.676532i	−0.417462	+	0.908695i	$0.637080\pi$
$812$	42.1677	−	9.95334i	1.47980	−	0.349294i
$813$	3.72254	+	6.96438i	0.130555	+	0.244251i
$814$	−10.8204	−	28.6308i	−0.379256	−	1.00351i
$815$	17.9718	−	7.44415i	0.629524	−	0.260757i
$816$	1.03424	−	0.395707i	0.0362056	−	0.0138525i
$817$	−0.465127	−	0.192662i	−0.0162727	−	0.00674038i
$818$	−0.783051	+	24.9594i	−0.0273788	+	0.872684i
$819$	41.3865	+	12.5544i	1.44616	+	0.438688i
$820$	−0.0502381	−	1.41659i	−0.00175439	−	0.0494694i
$821$	−1.48253	+	15.0524i	−0.0517408	+	0.525333i	0.934025	+	0.357208i	$0.116271\pi$
$821$	−1.48253	+	15.0524i	−0.0517408	+	0.525333i	−0.985766	+	0.168125i	$0.946229\pi$
$822$	1.95418	−	0.967005i	0.0681598	−	0.0337282i
$823$	−30.2094	+	6.00902i	−1.05303	+	0.209461i	−0.691112	−	0.722747i	$-0.742879\pi$
$823$	−30.2094	+	6.00902i	−1.05303	+	0.209461i	−0.361921	+	0.932209i	$0.617879\pi$
$824$	−8.69060	+	2.67509i	−0.302751	+	0.0931913i
$825$	−0.368830	+	1.85423i	−0.0128410	+	0.0645561i
$826$	−42.9060	−	24.6939i	−1.49289	−	0.859212i
$827$	−7.97497	−	26.2900i	−0.277317	−	0.914192i	−0.979371	−	0.202068i	$-0.935234\pi$
$827$	−7.97497	−	26.2900i	−0.277317	−	0.914192i	0.702054	−	0.712123i	$-0.252266\pi$
$828$	3.37351	−	53.7116i	0.117238	−	1.86661i
$829$	22.4943	+	18.4606i	0.781260	+	0.641163i	0.938062	−	0.346467i	$-0.112619\pi$
$829$	22.4943	+	18.4606i	0.781260	+	0.641163i	−0.156802	+	0.987630i	$0.550119\pi$
$830$	6.84997	−	1.14052i	0.237766	−	0.0395881i
$831$			7.80607i			0.270790i
$832$	−32.7955	+	27.3662i	−1.13698	+	0.948751i
$833$		−	0.702766i		−	0.0243494i
$834$	0.888687	+	5.33745i	0.0307727	+	0.184821i
$835$	−3.81819	−	3.13351i	−0.132134	−	0.108440i
$836$	1.10431	+	1.25233i	0.0381934	+	0.0433126i
$837$	−2.15197	−	7.09409i	−0.0743829	−	0.245208i
$838$	−7.89765	+	13.7223i	−0.272820	+	0.474028i
$839$	−8.63944	+	43.4334i	−0.298266	+	1.49949i	0.483184	+	0.875519i	$0.339480\pi$
$839$	−8.63944	+	43.4334i	−0.298266	+	1.49949i	−0.781450	+	0.623968i	$0.785520\pi$
$840$	−1.93136	+	1.59828i	−0.0666382	+	0.0551458i
$841$	−30.5269	+	6.07219i	−1.05265	+	0.209386i
$842$	5.82726	+	11.7760i	0.200821	+	0.405829i
$843$	0.0329410	−	0.334455i	0.00113455	−	0.0115193i
$844$	13.4419	−	14.4304i	0.462690	−	0.496714i
$845$	14.8393	+	4.50146i	0.510489	+	0.154855i
$846$	−40.9810	−	1.28570i	−1.40896	−	0.0442032i
$847$	−63.2705	−	26.2075i	−2.17400	−	0.900501i
$848$	−6.56978	−	10.4378i	−0.225607	−	0.358436i
$849$	3.50162	−	1.45042i	0.120175	−	0.0497782i
$850$	−1.15439	+	0.436278i	−0.0395952	+	0.0149642i
$851$	15.8890	+	29.7263i	0.544668	+	1.01900i
$852$	−2.36195	+	3.82150i	−0.0809190	+	0.130922i
$853$	−1.73827	−	2.11808i	−0.0595171	−	0.0725218i	0.742401	−	0.669956i	$-0.233687\pi$
$853$	−1.73827	−	2.11808i	−0.0595171	−	0.0725218i	−0.801918	+	0.597434i	$0.796187\pi$
$854$	58.8916	−	3.94053i	2.01523	−	0.134842i
$855$	−0.337722	−	0.225658i	−0.0115498	−	0.00771735i
$856$	−9.96273	+	4.17448i	−0.340519	+	0.142681i
$857$	−28.0372	−	41.9607i	−0.957734	−	1.43335i	−0.900434	−	0.434993i	$-0.856751\pi$
$857$	−28.0372	−	41.9607i	−0.957734	−	1.43335i	−0.0573005	−	0.998357i	$-0.518249\pi$
$858$	−14.1556	−	1.84400i	−0.483264	−	0.0629533i
$859$	5.92972	−	11.0937i	0.202320	−	0.378513i	−0.760215	−	0.649671i	$-0.774907\pi$
$859$	5.92972	−	11.0937i	0.202320	−	0.378513i	0.962535	+	0.271158i	$0.0874066\pi$
$860$	1.84133	−	6.94758i	0.0627887	−	0.236910i
$861$	0.625152	−	0.0615721i	0.0213051	−	0.00209837i
$862$	1.36206	−	5.87776i	0.0463921	−	0.200197i
$863$	−3.40807	+	3.40807i	−0.116012	+	0.116012i	−0.762730	−	0.646717i	$-0.776141\pi$
$863$	−3.40807	+	3.40807i	−0.116012	+	0.116012i	0.646717	+	0.762730i	$0.276141\pi$
$864$	−4.61779	+	9.52698i	−0.157100	+	0.324115i
$865$	−13.6502	−	13.6502i	−0.464120	−	0.464120i
$866$	−18.1308	+	11.3088i	−0.616111	+	0.384287i
$867$	−0.504949	−	5.12683i	−0.0171490	−	0.174116i
$868$	13.4257	−	17.5957i	0.455696	−	0.597237i
$869$	64.3658	+	34.4042i	2.18346	+	1.16708i
$870$	2.75711	−	2.12158i	0.0934747	−	0.0719282i
$871$	−54.8907	+	36.6768i	−1.85990	+	1.24274i
$872$	50.6356	−	10.2873i	1.71474	−	0.348373i
$873$	−4.63972	+	6.94383i	−0.157031	+	0.235013i
$874$	−1.38408	−	1.21048i	−0.0468173	−	0.0409450i
$875$	2.15964	−	1.77237i	0.0730092	−	0.0599171i
$876$	−1.82334	−	0.295933i	−0.0616048	−	0.00999866i
$877$	12.8405	−	6.86337i	0.433592	−	0.231760i	−0.240136	−	0.970739i	$-0.577192\pi$
$877$	12.8405	−	6.86337i	0.433592	−	0.231760i	0.673728	+	0.738980i	$0.264692\pi$
$878$	10.0745	−	22.3156i	0.339997	−	0.753116i
$879$	−2.88120	−	6.95583i	−0.0971804	−	0.234614i
$880$	−15.6189	+	18.0070i	−0.526514	+	0.607015i
$881$	−11.1527	+	26.9249i	−0.375743	+	0.907123i	0.617011	+	0.786955i	$0.288343\pi$
$881$	−11.1527	+	26.9249i	−0.375743	+	0.907123i	−0.992754	+	0.120168i	$0.961657\pi$
$882$	2.26062	+	2.40706i	0.0761189	+	0.0810498i
$883$	1.12954	−	3.72359i	0.0380120	−	0.125309i	−0.935881	−	0.352316i	$-0.885394\pi$
$883$	1.12954	−	3.72359i	0.0380120	−	0.125309i	0.973893	+	0.227007i	$0.0728942\pi$
$884$	−3.86882	−	8.47715i	−0.130122	−	0.285117i
$885$	−3.95584	−	0.389616i	−0.132974	−	0.0130968i
$886$	−27.4177	−	9.26541i	−0.921115	−	0.311278i
$887$	6.99711	+	35.1768i	0.234940	+	1.18112i	0.900526	+	0.434802i	$0.143182\pi$
$887$	6.99711	+	35.1768i	0.234940	+	1.18112i	−0.665586	+	0.746321i	$0.731818\pi$
$888$	−0.332672	−	3.24181i	−0.0111637	−	0.108788i
$889$	−8.36235	−	1.66337i	−0.280464	−	0.0557878i
$890$	−11.9462	+	3.21843i	−0.400438	+	0.107882i
$891$	46.2160	−	14.0195i	1.54829	−	0.469670i
$892$	11.5571	+	5.66025i	0.386961	+	0.189519i
$893$	−0.888690	+	1.08287i	−0.0297389	+	0.0362369i
$894$	−4.58615	−	3.27694i	−0.153384	−	0.109597i
$895$	3.40771			0.113907
$896$	−31.1356	+	5.44598i	−1.04017	+	0.181937i
$897$	15.7205			0.524894
$898$	0.149969	+	0.107158i	0.00500455	+	0.00357590i
$899$	−19.4847	+	23.7422i	−0.649852	+	0.791847i
$900$	2.55052	−	5.20767i	0.0850175	−	0.173589i
$901$	2.57473	−	0.781036i	0.0857767	−	0.0260201i
$902$	5.76737	−	1.55379i	0.192032	−	0.0517354i
$903$	3.12402	+	0.621406i	0.103961	+	0.0206791i
$904$	−7.66852	+	9.42238i	−0.255051	+	0.313384i
$905$	2.36027	+	11.8659i	0.0784579	+	0.394434i
$906$	−8.33720	−	2.81744i	−0.276985	−	0.0936031i
$907$	11.9968	+	1.18158i	0.398346	+	0.0392337i	0.295207	−	0.955433i	$-0.404611\pi$
$907$	11.9968	+	1.18158i	0.398346	+	0.0392337i	0.103139	+	0.994667i	$0.467111\pi$
$908$	−6.04526	+	2.75895i	−0.200619	+	0.0915589i
$909$	−0.535834	+	1.76641i	−0.0177725	+	0.0585881i
$910$	14.4416	+	15.3771i	0.478734	+	0.509746i
$911$	−12.0993	+	29.2102i	−0.400867	+	0.967778i	0.586590	+	0.809884i	$0.300470\pi$
$911$	−12.0993	+	29.2102i	−0.400867	+	0.967778i	−0.987456	+	0.157893i	$0.949530\pi$
$912$	0.0794954	+	0.159011i	0.00263236	+	0.00526537i
$913$	11.1981	+	27.0345i	0.370602	+	0.894712i
$914$	−2.50352	+	5.54547i	−0.0828090	+	0.183428i
$915$	4.17966	−	2.23408i	0.138175	−	0.0738563i
$916$	−6.68171	+	41.1681i	−0.220770	+	1.36023i
$917$	−3.21966	+	2.64230i	−0.106322	+	0.0872565i
$918$	−1.73856	−	1.52049i	−0.0573811	−	0.0501837i
$919$	0.369829	−	0.553489i	0.0121995	−	0.0182579i	−0.825320	−	0.564666i	$-0.809005\pi$
$919$	0.369829	−	0.553489i	0.0121995	−	0.0182579i	0.837519	+	0.546408i	$0.184005\pi$
$920$	14.4947	−	21.8859i	0.477875	−	0.721556i
$921$	−4.78951	+	3.20024i	−0.157820	+	0.105452i
$922$	−10.6079	+	8.16274i	−0.349354	+	0.268825i
$923$	33.3400	+	17.8206i	1.09740	+	0.586573i
$924$	−8.39825	−	6.40793i	−0.276282	−	0.210805i
$925$	0.355976	+	3.61428i	0.0117044	+	0.118837i
$926$	−26.6338	+	16.6123i	−0.875241	+	0.545915i
$927$	6.59095	+	6.59095i	0.216475	+	0.216475i
$928$	43.4482	−	6.02138i	1.42626	−	0.197662i
$929$	−23.5581	+	23.5581i	−0.772916	+	0.772916i	−0.978615	−	0.205699i	$-0.934053\pi$
$929$	−23.5581	+	23.5581i	−0.772916	+	0.772916i	0.205699	+	0.978615i	$0.434053\pi$
$930$	0.401189	−	1.73127i	0.0131555	−	0.0567705i
$931$	0.112279	−	0.0110585i	0.00367979	−	0.000362428i
$932$	−28.1285	−	7.45493i	−0.921379	−	0.244194i
$933$	−0.994792	+	1.86113i	−0.0325680	+	0.0609305i
$934$	−51.4463	−	6.70176i	−1.68337	−	0.219288i
$935$	−2.88907	−	4.32380i	−0.0944828	−	0.141404i
$936$	40.5199	+	16.5902i	1.32444	+	0.542269i
$937$	−7.24243	−	4.83924i	−0.236600	−	0.158091i	0.431618	−	0.902056i	$-0.357943\pi$
$937$	−7.24243	−	4.83924i	−0.236600	−	0.158091i	−0.668218	+	0.743965i	$0.732943\pi$
$938$	−48.7435	+	3.26151i	−1.59153	+	0.106492i
$939$	3.00764	+	3.66482i	0.0981505	+	0.119597i
$940$	−17.0120	−	10.5146i	−0.554870	−	0.342947i
$941$	13.9166	+	26.0362i	0.453670	+	0.848756i	0.999938	+	0.0111458i	$0.00354789\pi$
$941$	13.9166	+	26.0362i	0.453670	+	0.848756i	−0.546268	+	0.837610i	$0.683952\pi$
$942$	7.33345	−	2.77153i	0.238937	−	0.0903012i
$943$	−6.07707	+	2.51720i	−0.197897	+	0.0819714i
$944$	−40.8969	−	28.9703i	−1.33108	−	0.942904i
$945$	4.83075	+	2.00096i	0.157144	+	0.0650914i
$946$	30.2717	+	0.949716i	0.984219	+	0.0308779i
$947$	−26.5391	−	8.05055i	−0.862405	−	0.261608i	−0.172059	−	0.985087i	$-0.555042\pi$
$947$	−26.5391	−	8.05055i	−0.862405	−	0.261608i	−0.690346	+	0.723479i	$0.742542\pi$
$948$	5.68604	+	5.29655i	0.184674	+	0.172024i
$949$	−1.52357	+	15.4691i	−0.0494571	+	0.502147i
$950$	−0.0878678	−	0.177568i	−0.00285081	−	0.00576107i
$951$	5.58488	−	1.11090i	0.181102	−	0.0360234i
$952$	0.647834	−	6.86506i	0.0209964	−	0.222498i
$953$	2.40018	−	12.0665i	0.0777495	−	0.390873i	−0.922241	−	0.386614i	$-0.873644\pi$
$953$	2.40018	−	12.0665i	0.0777495	−	0.390873i	0.999991	−	0.00425871i	$-0.00135559\pi$
$954$	−6.30636	+	10.9574i	−0.204176	+	0.354758i
$955$	2.47469	+	8.15796i	0.0800791	+	0.263985i
$956$	−24.9985	+	22.0439i	−0.808510	+	0.712950i
$957$	11.3319	+	9.29986i	0.366309	+	0.300622i
$958$	7.93393	+	47.6512i	0.256334	+	1.53954i
$959$		−	13.5771i		−	0.438428i
$960$	−2.09866	+	1.42723i	−0.0677340	+	0.0460636i
$961$		−	15.3102i		−	0.493878i
$962$	−27.0503	+	4.50388i	−0.872136	+	0.145211i
$963$	8.55941	+	7.02453i	0.275823	+	0.226362i
$964$	−33.4981	−	2.10394i	−1.07890	−	0.0677634i
$965$	0.0794115	+	0.261785i	0.00255635	+	0.00842714i
$966$	10.0826	+	5.80291i	0.324403	+	0.186706i
$967$	−6.51323	+	32.7442i	−0.209451	+	1.05298i	0.722769	+	0.691090i	$0.242869\pi$
$967$	−6.51323	+	32.7442i	−0.209451	+	1.05298i	−0.932220	+	0.361892i	$0.882131\pi$
$968$	−61.2786	−	32.4328i	−1.96957	−	1.04243i
$969$	−0.0380375	+	0.00756614i	−0.00122194	+	0.000243059i
$970$	−3.65094	+	1.80663i	−0.117225	+	0.0580075i
$971$	0.616463	−	6.25906i	0.0197832	−	0.200863i	−0.980213	−	0.197948i	$-0.936572\pi$
$971$	0.616463	−	6.25906i	0.0197832	−	0.200863i	0.999996	−	0.00291457i	$-0.000927739\pi$
$972$	16.3612	−	0.580237i	0.524786	−	0.0186111i
$973$	32.2432	+	9.78088i	1.03367	+	0.313561i
$974$	−0.684287	+	21.8113i	−0.0219260	+	0.698879i
$975$	1.56491	+	0.648209i	0.0501174	+	0.0207593i
$976$	59.7325	+	1.62968i	1.91199	+	0.0521648i
$977$	−21.7768	+	9.02026i	−0.696703	+	0.288584i	−0.702790	−	0.711398i	$-0.748063\pi$
$977$	−21.7768	+	9.02026i	−0.696703	+	0.288584i	0.00608672	+	0.999981i	$0.498063\pi$
$978$	3.08538	+	8.16392i	0.0986597	+	0.261053i
$979$	−24.5759	−	45.9782i	−0.785448	−	1.46947i
$980$	0.370022	+	1.56761i	0.0118199	+	0.0500756i
$981$	−33.6011	−	40.9430i	−1.07280	−	1.30721i
$982$	0.415018	+	6.20248i	0.0132437	+	0.197929i
$983$	22.2202	+	14.8470i	0.708713	+	0.473547i	0.856946	−	0.515406i	$-0.172359\pi$
$983$	22.2202	+	14.8470i	0.708713	+	0.473547i	−0.148233	+	0.988952i	$0.547359\pi$
$984$	0.635956	−	0.00259887i	0.0202735	−	8.28489e-5i
$985$	0.834913	+	1.24954i	0.0266025	+	0.0398135i
$986$	−1.23609	+	9.48892i	−0.0393652	+	0.302189i
$987$	4.17794	−	7.81637i	0.132985	−	0.248798i
$988$	1.29349	−	0.751503i	0.0411514	−	0.0239085i
$989$	−33.1925	+	3.26918i	−1.05546	+	0.103954i
$990$	23.8040	+	5.51613i	0.756540	+	0.175314i
$991$	21.7627	−	21.7627i	0.691315	−	0.691315i	−0.271206	−	0.962521i	$-0.587422\pi$
$991$	21.7627	−	21.7627i	0.691315	−	0.691315i	0.962521	+	0.271206i	$0.0874224\pi$
$992$	15.2055	−	16.4580i	0.482775	−	0.522542i
$993$	−0.195310	−	0.195310i	−0.00619799	−	0.00619799i
$994$	14.8051	+	23.7363i	0.469589	+	0.752871i
$995$	0.292839	+	2.97324i	0.00928362	+	0.0942582i
$996$	0.415080	+	3.08782i	0.0131523	+	0.0978413i
$997$	−5.36565	−	2.86800i	−0.169932	−	0.0908304i	0.384238	−	0.923234i	$-0.374464\pi$
$997$	−5.36565	−	2.86800i	−0.169932	−	0.0908304i	−0.554170	+	0.832404i	$0.686964\pi$
$998$	35.0412	+	45.5380i	1.10921	+	1.44148i
$999$	−5.65156	+	3.77625i	−0.178807	+	0.119475i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.341.45	✓	1024
128.125	even	32	inner	640.2.bm.a.381.45	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.341.45	✓	1024	1.1	even	1	trivial
640.2.bm.a.381.45	yes	1024	128.125	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:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.822181 - 1.15066i) q^{2} +(0.201260 - 0.245236i) q^{3} +(-0.648036 - 1.89210i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-0.116711 - 0.433210i) q^{6} +(-2.74012 - 0.545044i) q^{7} +(-2.70997 - 0.809981i) q^{8} +(0.565636 + 2.84364i) q^{9} +O(q^{10})\)	\(q+(0.822181 - 1.15066i) q^{2} +(0.201260 - 0.245236i) q^{3} +(-0.648036 - 1.89210i) q^{4} +(-0.956940 + 0.290285i) q^{5} +(-0.116711 - 0.433210i) q^{6} +(-2.74012 - 0.545044i) q^{7} +(-2.70997 - 0.809981i) q^{8} +(0.565636 + 2.84364i) q^{9} +(-0.452759 + 1.33978i) q^{10} +(-5.93055 - 0.584108i) q^{11} +(-0.594435 - 0.221883i) q^{12} +(-1.54989 + 5.10930i) q^{13} +(-2.88004 + 2.70482i) q^{14} +(-0.121406 + 0.293099i) q^{15} +(-3.16010 + 2.45230i) q^{16} +(-0.333940 - 0.806201i) q^{17} +(3.73712 + 1.68714i) q^{18} +(0.123550 - 0.0660386i) q^{19} +(1.16938 + 1.62251i) q^{20} +(-0.685142 + 0.562281i) q^{21} +(-5.54810 + 6.34381i) q^{22} +(5.15622 - 7.71682i) q^{23} +(-0.744045 + 0.501565i) q^{24} +(0.831470 - 0.555570i) q^{25} +(4.60477 + 5.98416i) q^{26} +(1.65057 + 0.882247i) q^{27} +(0.744419 + 5.53780i) q^{28} +(-0.760028 - 7.71669i) q^{29} +(0.237440 + 0.380677i) q^{30} +(-2.80087 - 2.80087i) q^{31} +(0.223590 + 5.65243i) q^{32} +(-1.33683 + 1.33683i) q^{33} +(-1.20222 - 0.278593i) q^{34} +(2.78035 - 0.273841i) q^{35} +(5.01391 - 2.91302i) q^{36} +(-1.71200 + 3.20293i) q^{37} +(0.0255921 - 0.196459i) q^{38} +(0.941053 + 1.40839i) q^{39} +(2.82840 - 0.0115584i) q^{40} +(-0.589295 - 0.393755i) q^{41} +(0.0836838 + 1.25066i) q^{42} +(-2.27983 - 2.77798i) q^{43} +(2.73802 + 11.5997i) q^{44} +(-1.36675 - 2.55700i) q^{45} +(-4.64009 - 12.2777i) q^{46} +(-9.23838 + 3.82666i) q^{47} +(-0.0346090 + 1.26852i) q^{48} +(0.744043 + 0.308193i) q^{49} +(0.0443463 - 1.41352i) q^{50} +(-0.264918 - 0.0803621i) q^{51} +(10.6717 - 0.378462i) q^{52} +(-0.302218 + 3.06847i) q^{53} +(2.37223 - 1.17387i) q^{54} +(5.84474 - 1.16259i) q^{55} +(6.98417 + 3.69650i) q^{56} +(0.00867054 - 0.0435897i) q^{57} +(-9.50417 - 5.46999i) q^{58} +(3.63714 + 11.9900i) q^{59} +(0.633248 + 0.0397730i) q^{60} +(-11.5478 - 9.47700i) q^{61} +(-5.52568 + 0.920027i) q^{62} -8.10023i q^{63} +(6.68786 + 4.39005i) q^{64} -5.33920i q^{65} +(0.439119 + 2.63735i) q^{66} +(9.55787 + 7.84394i) q^{67} +(-1.30901 + 1.15430i) q^{68} +(-0.854703 - 2.81758i) q^{69} +(1.97086 - 3.42439i) q^{70} +(1.38132 - 6.94439i) q^{71} +(0.770443 - 8.16434i) q^{72} +(2.85534 - 0.567962i) q^{73} +(2.27791 + 4.60333i) q^{74} +(0.0310958 - 0.315720i) q^{75} +(-0.205016 - 0.190973i) q^{76} +(15.9321 + 4.83294i) q^{77} +(2.39429 + 0.0751161i) q^{78} +(-11.3149 - 4.68677i) q^{79} +(2.31216 - 3.26403i) q^{80} +(-7.48741 + 3.10139i) q^{81} +(-0.937585 + 0.354341i) q^{82} +(-2.31472 - 4.33053i) q^{83} +(1.50789 + 0.931979i) q^{84} +(0.553588 + 0.674549i) q^{85} +(-5.07095 + 0.339306i) q^{86} +(-2.04538 - 1.36668i) q^{87} +(15.5985 + 6.38655i) q^{88} +(4.86037 + 7.27406i) q^{89} +(-4.06595 - 0.529659i) q^{90} +(7.03168 - 13.1553i) q^{91} +(-17.9424 - 4.75531i) q^{92} +(-1.25058 + 0.123171i) q^{93} +(-3.19243 + 13.7764i) q^{94} +(-0.0990595 + 0.0990595i) q^{95} +(1.43118 + 1.08278i) q^{96} +(2.03675 + 2.03675i) q^{97} +(0.966363 - 0.602750i) q^{98} +(-1.69354 - 17.1948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 1024 * q - 192 * q^52 - 128 * q^54 - 32 * q^56 - 288 * q^58 - 192 * q^62 - 192 * q^64 - 192 * q^66 - 192 * q^68 - 288 * q^72 - 32 * q^74 - 128 * q^76 - 192 * q^78

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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