LMFDB - Embedded newform 640.2.bm.a.221.27

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			221.27
Character	$\chi$	$=$	640.221
Dual form			640.2.bm.a.501.27

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.430955 + 1.34695i) q^{2} +(2.54637 + 0.250795i) q^{3} +(-1.62856 - 1.16095i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.43518 + 3.32175i) q^{6} +(0.101830 + 0.511933i) q^{7} +(2.26558 - 1.69327i) q^{8} +(3.47873 + 0.691963i) q^{9} +O(q^{10})$	\(q+(-0.430955 + 1.34695i) q^{2} +(2.54637 + 0.250795i) q^{3} +(-1.62856 - 1.16095i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.43518 + 3.32175i) q^{6} +(0.101830 + 0.511933i) q^{7} +(2.26558 - 1.69327i) q^{8} +(3.47873 + 0.691963i) q^{9} +(-1.39106 + 0.254880i) q^{10} +(1.61214 + 1.32305i) q^{11} +(-3.85574 - 3.36464i) q^{12} +(1.25079 + 0.668559i) q^{13} +(-0.733432 - 0.0834604i) q^{14} +(0.979167 + 2.36392i) q^{15} +(1.30438 + 3.78135i) q^{16} +(0.336905 - 0.813360i) q^{17} +(-2.43122 + 4.38748i) q^{18} +(1.89686 - 0.575408i) q^{19} +(0.256172 - 1.98353i) q^{20} +(0.130906 + 1.32911i) q^{21} +(-2.47684 + 1.60130i) q^{22} +(-0.408366 + 0.272861i) q^{23} +(6.19366 - 3.74348i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-1.43955 + 1.39663i) q^{26} +(1.33905 + 0.406197i) q^{27} +(0.428494 - 0.951930i) q^{28} +(0.0332421 + 0.0405057i) q^{29} +(-3.60606 + 0.300147i) q^{30} +(-2.05462 + 2.05462i) q^{31} +(-5.65542 + 0.127348i) q^{32} +(3.77328 + 3.77328i) q^{33} +(0.950366 + 0.804316i) q^{34} +(-0.403482 + 0.331129i) q^{35} +(-4.86197 - 5.16554i) q^{36} +(-2.50140 + 8.24600i) q^{37} +(-0.0424180 + 2.80296i) q^{38} +(3.01729 + 2.01609i) q^{39} +(2.56131 + 1.19986i) q^{40} +(-2.42693 - 3.63216i) q^{41} +(-1.84666 - 0.396462i) q^{42} +(4.69096 - 0.462019i) q^{43} +(-1.08946 - 4.02627i) q^{44} +(1.02961 + 3.39416i) q^{45} +(-0.191543 - 0.667640i) q^{46} +(-5.31348 - 2.20092i) q^{47} +(2.37309 + 9.95583i) q^{48} +(6.21545 - 2.57452i) q^{49} +(-0.880523 - 1.10665i) q^{50} +(1.06187 - 1.98662i) q^{51} +(-1.26081 - 2.54089i) q^{52} +(-1.47336 + 1.79529i) q^{53} +(-1.12420 + 1.62858i) q^{54} +(-0.406867 + 2.04546i) q^{55} +(1.09754 + 0.987399i) q^{56} +(4.97442 - 0.989474i) q^{57} +(-0.0688850 + 0.0273194i) q^{58} +(8.74956 - 4.67674i) q^{59} +(1.14977 - 4.98654i) q^{60} +(1.06257 - 10.7884i) q^{61} +(-1.88202 - 3.65292i) q^{62} +1.85134i q^{63} +(2.26570 - 7.67246i) q^{64} +1.41825i q^{65} +(-6.70854 + 3.45631i) q^{66} +(-0.232003 + 2.35556i) q^{67} +(-1.49294 + 0.933472i) q^{68} +(-1.10828 + 0.592389i) q^{69} +(-0.272132 - 0.686172i) q^{70} +(-5.15016 + 1.02443i) q^{71} +(9.05302 - 4.32272i) q^{72} +(-0.318018 + 1.59879i) q^{73} +(-10.0290 - 6.92292i) q^{74} +(-1.62321 + 1.97789i) q^{75} +(-3.75717 - 1.26508i) q^{76} +(-0.513147 + 0.960031i) q^{77} +(-4.01589 + 3.19530i) q^{78} +(-8.74439 + 3.62204i) q^{79} +(-2.71997 + 2.93288i) q^{80} +(-6.52284 - 2.70185i) q^{81} +(5.93825 - 1.70366i) q^{82} +(-3.04631 - 10.0423i) q^{83} +(1.32984 - 2.31650i) q^{84} +(0.876136 - 0.0862918i) q^{85} +(-1.39928 + 6.51760i) q^{86} +(0.0744881 + 0.111479i) q^{87} +(5.89270 + 0.267691i) q^{88} +(-4.60308 - 3.07568i) q^{89} +(-5.01548 - 0.0759006i) q^{90} +(-0.214890 + 0.708397i) q^{91} +(0.981825 + 0.0297233i) q^{92} +(-5.74711 + 4.71653i) q^{93} +(5.25440 - 6.20851i) q^{94} +(1.40164 + 1.40164i) q^{95} +(-14.4327 - 1.09408i) q^{96} +(4.36732 - 4.36732i) q^{97} +(0.789177 + 9.48141i) q^{98} +(4.69270 + 5.71807i) 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 $\left(\mathbb{Z}/640\mathbb{Z}\right)^\times$.

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{11}{32}\right)$	$1$

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 $

$2$	−0.430955	+	1.34695i	−0.304731	+	0.952438i
$2$	−0.430955	+	1.34695i	−0.304731	+	0.952438i
$3$	2.54637	+	0.250795i	1.47015	+	0.144797i	0.801147	−	0.598467i	$-0.204223\pi$
$3$	2.54637	+	0.250795i	1.47015	+	0.144797i	0.668998	+	0.743264i	$0.266723\pi$
$4$	−1.62856	−	1.16095i	−0.814278	−	0.580476i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$5$	0.471397	+	0.881921i	0.210815	+	0.394407i
$6$	−1.43518	+	3.32175i	−0.585910	+	1.35610i
$7$	0.101830	+	0.511933i	0.0384880	+	0.193492i	0.995246	−	0.0973927i	$-0.0310503\pi$
$7$	0.101830	+	0.511933i	0.0384880	+	0.193492i	−0.956758	+	0.290885i	$0.906050\pi$
$8$	2.26558	−	1.69327i	0.801003	−	0.598660i
$9$	3.47873	+	0.691963i	1.15958	+	0.230654i
$10$	−1.39106	+	0.254880i	−0.439890	+	0.0806000i
$11$	1.61214	+	1.32305i	0.486078	+	0.398914i	0.845261	−	0.534353i	$-0.179445\pi$
$11$	1.61214	+	1.32305i	0.486078	+	0.398914i	−0.359183	+	0.933267i	$0.616945\pi$
$12$	−3.85574	−	3.36464i	−1.11306	−	0.971289i
$13$	1.25079	+	0.668559i	0.346906	+	0.185425i	0.635642	−	0.771984i	$-0.280735\pi$
$13$	1.25079	+	0.668559i	0.346906	+	0.185425i	−0.288737	+	0.957408i	$0.593235\pi$
$14$	−0.733432	−	0.0834604i	−0.196018	−	0.0223057i
$15$	0.979167	+	2.36392i	0.252820	+	0.610361i
$16$	1.30438	+	3.78135i	0.326096	+	0.945337i
$17$	0.336905	−	0.813360i	0.0817114	−	0.197269i	−0.877744	−	0.479131i	$-0.840952\pi$
$17$	0.336905	−	0.813360i	0.0817114	−	0.197269i	0.959455	+	0.281862i	$0.0909520\pi$
$18$	−2.43122	+	4.38748i	−0.573044	+	1.03414i
$19$	1.89686	−	0.575408i	0.435171	−	0.132008i	−0.0650960	−	0.997879i	$-0.520735\pi$
$19$	1.89686	−	0.575408i	0.435171	−	0.132008i	0.500267	+	0.865871i	$0.333235\pi$
$20$	0.256172	−	1.98353i	0.0572819	−	0.443530i
$21$	0.130906	+	1.32911i	0.0285659	+	0.290035i
$22$	−2.47684	+	1.60130i	−0.528064	+	0.341398i
$23$	−0.408366	+	0.272861i	−0.0851502	+	0.0568955i	−0.597417	−	0.801931i	$-0.703806\pi$
$23$	−0.408366	+	0.272861i	−0.0851502	+	0.0568955i	0.512266	+	0.858827i	$0.328806\pi$
$24$	6.19366	−	3.74348i	1.26428	−	0.764135i
$25$	−0.555570	+	0.831470i	−0.111114	+	0.166294i
$26$	−1.43955	+	1.39663i	−0.282319	+	0.273901i
$27$	1.33905	+	0.406197i	0.257701	+	0.0781726i
$28$	0.428494	−	0.951930i	0.0809777	−	0.179898i
$29$	0.0332421	+	0.0405057i	0.00617291	+	0.00752171i	0.776088	−	0.630625i	$-0.217201\pi$
$29$	0.0332421	+	0.0405057i	0.00617291	+	0.00752171i	−0.769915	+	0.638147i	$0.779701\pi$
$30$	−3.60606	+	0.300147i	−0.658374	+	0.0547991i
$31$	−2.05462	+	2.05462i	−0.369021	+	0.369021i	−0.867120	−	0.498099i	$-0.834032\pi$
$31$	−2.05462	+	2.05462i	−0.369021	+	0.369021i	0.498099	+	0.867120i	$0.334032\pi$
$32$	−5.65542	+	0.127348i	−0.999747	+	0.0225122i
$33$	3.77328	+	3.77328i	0.656844	+	0.656844i
$34$	0.950366	+	0.804316i	0.162986	+	0.137939i
$35$	−0.403482	+	0.331129i	−0.0682009	+	0.0559710i
$36$	−4.86197	−	5.16554i	−0.810328	−	0.860923i
$37$	−2.50140	+	8.24600i	−0.411227	+	1.35563i	0.469885	+	0.882727i	$0.344295\pi$
$37$	−2.50140	+	8.24600i	−0.411227	+	1.35563i	−0.881113	+	0.472907i	$0.843205\pi$
$38$	−0.0424180	+	2.80296i	−0.00688110	+	0.454700i
$39$	3.01729	+	2.01609i	0.483153	+	0.322832i
$40$	2.56131	+	1.19986i	0.404979	+	0.189715i
$41$	−2.42693	−	3.63216i	−0.379023	−	0.567249i	0.592089	−	0.805873i	$-0.298304\pi$
$41$	−2.42693	−	3.63216i	−0.379023	−	0.567249i	−0.971112	+	0.238624i	$0.923304\pi$
$42$	−1.84666	−	0.396462i	−0.284945	−	0.0611754i
$43$	4.69096	−	0.462019i	0.715364	−	0.0704572i	0.266215	−	0.963914i	$-0.414227\pi$
$43$	4.69096	−	0.462019i	0.715364	−	0.0704572i	0.449150	+	0.893457i	$0.351727\pi$
$44$	−1.08946	−	4.02627i	−0.164242	−	0.606983i
$45$	1.02961	+	3.39416i	0.153485	+	0.505971i
$46$	−0.191543	−	0.667640i	−0.0282415	−	0.0984381i
$47$	−5.31348	−	2.20092i	−0.775051	−	0.321037i	−0.0401347	−	0.999194i	$-0.512779\pi$
$47$	−5.31348	−	2.20092i	−0.775051	−	0.321037i	−0.734917	+	0.678158i	$0.762779\pi$
$48$	2.37309	+	9.95583i	0.342527	+	1.43700i
$49$	6.21545	−	2.57452i	0.887922	−	0.367789i
$50$	−0.880523	−	1.10665i	−0.124525	−	0.156504i
$51$	1.06187	−	1.98662i	0.148692	−	0.278182i
$52$	−1.26081	−	2.54089i	−0.174843	−	0.352358i
$53$	−1.47336	+	1.79529i	−0.202381	+	0.246603i	−0.864304	−	0.502970i	$-0.832241\pi$
$53$	−1.47336	+	1.79529i	−0.202381	+	0.246603i	0.661923	+	0.749572i	$0.269741\pi$
$54$	−1.12420	+	1.62858i	−0.152984	+	0.221622i
$55$	−0.406867	+	2.04546i	−0.0548619	+	0.275810i
$56$	1.09754	+	0.987399i	0.146665	+	0.131947i
$57$	4.97442	−	0.989474i	0.658878	−	0.131059i
$58$	−0.0688850	+	0.0273194i	−0.00904505	+	0.00358721i
$59$	8.74956	−	4.67674i	1.13910	−	0.608859i	0.209634	−	0.977780i	$-0.432773\pi$
$59$	8.74956	−	4.67674i	1.13910	−	0.608859i	0.929461	+	0.368921i	$0.120273\pi$
$60$	1.14977	−	4.98654i	0.148434	−	0.643759i
$61$	1.06257	−	10.7884i	0.136048	−	1.38132i	−0.648484	−	0.761229i	$-0.724596\pi$
$61$	1.06257	−	10.7884i	0.136048	−	1.38132i	0.784531	−	0.620089i	$-0.212904\pi$
$62$	−1.88202	−	3.65292i	−0.239017	−	0.463922i
$63$			1.85134i			0.233247i
$64$	2.26570	−	7.67246i	0.283213	−	0.959057i
$65$			1.41825i			0.175912i
$66$	−6.70854	+	3.45631i	−0.825764	+	0.425442i
$67$	−0.232003	+	2.35556i	−0.0283436	+	0.287778i	0.970556	+	0.240876i	$0.0774347\pi$
$67$	−0.232003	+	2.35556i	−0.0283436	+	0.287778i	−0.998900	+	0.0469016i	$0.985065\pi$
$68$	−1.49294	+	0.933472i	−0.181046	+	0.113200i
$69$	−1.10828	+	0.592389i	−0.133421	+	0.0713152i
$70$	−0.272132	−	0.686172i	−0.0325260	−	0.0820133i
$71$	−5.15016	+	1.02443i	−0.611212	+	0.121578i	−0.490984	−	0.871169i	$-0.663363\pi$
$71$	−5.15016	+	1.02443i	−0.611212	+	0.121578i	−0.120228	+	0.992746i	$0.538363\pi$
$72$	9.05302	−	4.32272i	1.06691	−	0.509437i
$73$	−0.318018	+	1.59879i	−0.0372212	+	0.187124i	−0.994923	−	0.100639i	$-0.967911\pi$
$73$	−0.318018	+	1.59879i	−0.0372212	+	0.187124i	0.957702	+	0.287762i	$0.0929114\pi$
$74$	−10.0290	−	6.92292i	−1.16584	−	0.804773i
$75$	−1.62321	+	1.97789i	−0.187433	+	0.228387i
$76$	−3.75717	−	1.26508i	−0.430977	−	0.145115i
$77$	−0.513147	+	0.960031i	−0.0584786	+	0.109406i
$78$	−4.01589	+	3.19530i	−0.454710	+	0.361796i
$79$	−8.74439	+	3.62204i	−0.983821	+	0.407512i	−0.815840	−	0.578278i	$-0.803725\pi$
$79$	−8.74439	+	3.62204i	−0.983821	+	0.407512i	−0.167981	+	0.985790i	$0.553725\pi$
$80$	−2.71997	+	2.93288i	−0.304102	+	0.327906i
$81$	−6.52284	−	2.70185i	−0.724760	−	0.300205i
$82$	5.93825	−	1.70366i	0.655770	−	0.188138i
$83$	−3.04631	−	10.0423i	−0.334376	−	1.10229i	−0.949476	−	0.313841i	$-0.898384\pi$
$83$	−3.04631	−	10.0423i	−0.334376	−	1.10229i	0.615099	−	0.788450i	$-0.289116\pi$
$84$	1.32984	−	2.31650i	0.145098	−	0.252751i
$85$	0.876136	−	0.0862918i	0.0950302	−	0.00935966i
$86$	−1.39928	+	6.51760i	−0.150888	+	0.702811i
$87$	0.0744881	+	0.111479i	0.00798596	+	0.0119518i
$88$	5.89270	+	0.267691i	0.628164	+	0.0285360i
$89$	−4.60308	−	3.07568i	−0.487926	−	0.326021i	0.287155	−	0.957884i	$-0.407291\pi$
$89$	−4.60308	−	3.07568i	−0.487926	−	0.326021i	−0.775080	+	0.631863i	$0.782291\pi$
$90$	−5.01548	−	0.0759006i	−0.528678	−	0.00800063i
$91$	−0.214890	+	0.708397i	−0.0225266	+	0.0742602i
$92$	0.981825	+	0.0297233i	0.102362	+	0.00309887i
$93$	−5.74711	+	4.71653i	−0.595947	+	0.489081i
$94$	5.25440	−	6.20851i	0.541950	−	0.640359i
$95$	1.40164	+	1.40164i	0.143805	+	0.143805i
$96$	−14.4327	−	1.09408i	−1.47303	−	0.111664i
$97$	4.36732	−	4.36732i	0.443434	−	0.443434i	−0.449730	−	0.893164i	$-0.648480\pi$
$97$	4.36732	−	4.36732i	0.443434	−	0.443434i	0.893164	+	0.449730i	$0.148480\pi$
$98$	0.789177	+	9.48141i	0.0797189	+	0.957767i
$99$	4.69270	+	5.71807i	0.471634	+	0.574687i
$100$	1.87007	−	0.709104i	0.187007	−	0.0709104i
$101$	−10.0153	−	3.03810i	−0.996556	−	0.302302i	−0.250450	−	0.968129i	$-0.580579\pi$
$101$	−10.0153	−	3.03810i	−0.996556	−	0.302302i	−0.746106	+	0.665827i	$0.768079\pi$
$102$	2.21826	+	2.28643i	0.219641	+	0.226391i
$103$	8.58851	−	12.8536i	0.846251	−	1.26650i	−0.115701	−	0.993284i	$-0.536911\pi$
$103$	8.58851	−	12.8536i	0.846251	−	1.26650i	0.961952	−	0.273220i	$-0.0880887\pi$
$104$	3.96580	−	0.603239i	0.388879	−	0.0591525i
$105$	−1.11046	+	0.741985i	−0.108370	+	0.0724103i
$106$	−1.78322	−	2.75823i	−0.173202	−	0.267903i
$107$	1.43981	+	14.6186i	0.139192	+	1.41324i	0.770369	+	0.637598i	$0.220072\pi$
$107$	1.43981	+	14.6186i	0.139192	+	1.41324i	−0.631178	+	0.775638i	$0.717428\pi$
$108$	−1.70914	−	2.21609i	−0.164462	−	0.213243i
$109$	−5.97451	+	1.81235i	−0.572254	+	0.173591i	−0.563132	−	0.826367i	$-0.690404\pi$
$109$	−5.97451	+	1.81235i	−0.572254	+	0.173591i	−0.00912204	+	0.999958i	$0.502904\pi$
$110$	−2.57979	−	1.42953i	−0.245973	−	0.136300i
$111$	−8.43753	+	20.3700i	−0.800855	+	1.93344i
$112$	−1.80297	+	1.05281i	−0.170365	+	0.0994812i
$113$	−4.35038	−	10.5028i	−0.409250	−	0.988016i	−0.985336	−	0.170627i	$-0.945421\pi$
$113$	−4.35038	−	10.5028i	−0.409250	−	0.988016i	0.576086	−	0.817389i	$-0.304579\pi$
$114$	−0.810981	+	7.12672i	−0.0759553	+	0.667479i
$115$	−0.433144	−	0.231521i	−0.0403909	−	0.0215894i
$116$	−0.00711154	−	0.104558i	−0.000660290	−	0.00970799i
$117$	3.88853	+	3.19123i	0.359495	+	0.295030i
$118$	2.52867	+	13.8007i	0.232783	+	1.27046i
$119$	0.450693	+	0.0896483i	0.0413149	+	0.00821805i
$120$	6.22113	+	3.69766i	0.567908	+	0.337548i
$121$	−1.29746	−	6.52277i	−0.117951	−	0.592979i
$122$	14.0736	+	6.08056i	1.27416	+	0.550508i
$123$	−5.26894	−	9.85748i	−0.475084	−	0.888819i
$124$	5.73138	−	0.960748i	0.514693	−	0.0862777i
$125$	−0.995185	−	0.0980171i	−0.0890120	−	0.00876692i
$126$	−2.49366	−	0.797844i	−0.222153	−	0.0710776i
$127$	9.54937			0.847369			0.423685	−	0.905810i	$-0.360736\pi$
$127$	9.54937			0.847369			0.423685	+	0.905810i	$0.360736\pi$
$128$	9.35801	+	6.35828i	0.827139	+	0.561997i
$129$	12.0608			1.06189
$130$	−1.91032	−	0.611203i	−0.167546	−	0.0536060i
$131$	2.10987	+	0.207804i	0.184340	+	0.0181559i	0.189766	−	0.981829i	$-0.439227\pi$
$131$	2.10987	+	0.207804i	0.184340	+	0.0181559i	−0.00542566	+	0.999985i	$0.501727\pi$
$132$	−1.76440	−	10.5256i	−0.153571	−	0.916135i
$133$	0.487727	+	0.912473i	0.0422913	+	0.0791215i
$134$	−3.07284	−	1.32764i	−0.265453	−	0.114690i
$135$	0.272991	+	1.37242i	0.0234953	+	0.118119i
$136$	−0.613950	−	2.41320i	−0.0526458	−	0.206930i
$137$	−15.0162	−	2.98691i	−1.28292	−	0.255189i	−0.493881	−	0.869530i	$-0.664422\pi$
$137$	−15.0162	−	2.98691i	−1.28292	−	0.255189i	−0.789041	+	0.614340i	$0.789422\pi$
$138$	−0.320299	−	1.74809i	−0.0272657	−	0.148808i
$139$	10.5040	+	8.62039i	0.890936	+	0.731172i	0.963929	−	0.266160i	$-0.0857550\pi$
$139$	10.5040	+	8.62039i	0.890936	+	0.731172i	−0.0729928	+	0.997332i	$0.523255\pi$
$140$	1.04152	−	0.0708389i	0.0880243	−	0.00598698i
$141$	−12.9781	−	6.93694i	−1.09295	−	0.584196i
$142$	0.839631	−	7.37850i	0.0704603	−	0.619190i
$143$	1.13190	+	2.73266i	0.0946546	+	0.228516i
$144$	1.92105	+	14.0569i	0.160087	+	1.17141i
$145$	−0.0200526	+	0.0484112i	−0.00166528	+	0.00402033i
$146$	−2.01643	−	1.11736i	−0.166881	−	0.0924734i
$147$	16.4725	−	4.99688i	1.35863	−	0.412136i
$148$	13.6469	−	10.5251i	1.12177	−	0.865155i
$149$	−1.45480	−	14.7708i	−0.119182	−	1.21007i	−0.849732	−	0.527215i	$-0.823236\pi$
$149$	−1.45480	−	14.7708i	−0.119182	−	1.21007i	0.730550	−	0.682859i	$-0.239264\pi$
$150$	−1.96459	−	3.03877i	−0.160408	−	0.248115i
$151$	3.56430	−	2.38159i	0.290058	−	0.193811i	−0.402024	−	0.915629i	$-0.631693\pi$
$151$	3.56430	−	2.38159i	0.290058	−	0.193811i	0.692083	+	0.721818i	$0.256693\pi$
$152$	3.32318	−	4.51553i	0.269545	−	0.366258i
$153$	1.73482	−	2.59634i	0.140252	−	0.209901i
$154$	−1.07197	−	1.10492i	−0.0863820	−	0.0890366i
$155$	−2.78056	−	0.843472i	−0.223340	−	0.0677493i
$156$	−2.57324	−	6.78624i	−0.206024	−	0.543334i
$157$	−5.97659	−	7.28250i	−0.476984	−	0.581207i	0.477814	−	0.878461i	$-0.341429\pi$
$157$	−5.97659	−	7.28250i	−0.476984	−	0.581207i	−0.954798	+	0.297254i	$0.903929\pi$
$158$	−1.11028	−	13.3392i	−0.0883288	−	1.06121i
$159$	−4.20196	+	4.20196i	−0.333237	+	0.333237i
$160$	−2.77826	−	4.92760i	−0.219641	−	0.389561i
$161$	−0.181270	−	0.181270i	−0.0142861	−	0.0142861i
$162$	6.45031	−	7.62157i	0.506784	−	0.598807i
$163$	17.3290	−	14.2216i	1.35731	−	1.11392i	0.374929	−	0.927054i	$-0.377667\pi$
$163$	17.3290	−	14.2216i	1.35731	−	1.11392i	0.982386	−	0.186865i	$-0.0598329\pi$
$164$	−0.264370	+	8.73273i	−0.0206439	+	0.681912i
$165$	−1.54902	+	5.10645i	−0.120591	+	0.397537i
$166$	14.8394	+	0.224568i	1.15176	+	0.0174299i
$167$	12.1925	+	8.14675i	0.943482	+	0.630415i	0.929237	−	0.369484i	$-0.120465\pi$
$167$	12.1925	+	8.14675i	0.943482	+	0.630415i	0.0142452	+	0.999899i	$0.495465\pi$
$168$	2.54711	+	2.78954i	0.196514	+	0.215218i
$169$	−6.10492	−	9.13666i	−0.469609	−	0.702820i
$170$	−0.261344	+	1.21730i	−0.0200442	+	0.0933626i
$171$	6.99684	−	0.689129i	0.535062	−	0.0526990i
$172$	−8.17586	−	4.69355i	−0.623404	−	0.357880i
$173$	−1.76522	−	5.81917i	−0.134208	−	0.442423i	0.863917	−	0.503634i	$-0.168004\pi$
$173$	−1.76522	−	5.81917i	−0.134208	−	0.442423i	−0.998125	+	0.0612106i	$0.980504\pi$
$174$	−0.182258	+	0.0522892i	−0.0138170	+	0.00396403i
$175$	−0.482230	−	0.199746i	−0.0364532	−	0.0150994i
$176$	−2.90006	+	7.82181i	−0.218600	+	0.589591i
$177$	23.4525	−	9.71434i	1.76280	−	0.730174i
$178$	6.12651	−	4.87464i	0.459202	−	0.365370i
$179$	−3.28458	+	6.14502i	−0.245501	+	0.459301i	−0.974247	−	0.225484i	$-0.927604\pi$
$179$	−3.28458	+	6.14502i	−0.245501	+	0.459301i	0.728746	+	0.684785i	$0.240104\pi$
$180$	2.26368	−	6.72289i	0.168725	−	0.501095i
$181$	7.62786	−	9.29457i	0.566974	−	0.690860i	−0.408050	−	0.912960i	$-0.633791\pi$
$181$	7.62786	−	9.29457i	0.566974	−	0.690860i	0.975024	+	0.222100i	$0.0712911\pi$
$182$	−0.861568	−	0.594734i	−0.0638637	−	0.0440846i
$183$	5.41138	−	27.2048i	0.400021	−	2.01104i
$184$	−0.463158	+	1.30966i	−0.0341445	+	0.0965495i
$185$	−8.45147	+	1.68110i	−0.621365	+	0.123597i
$186$	−3.87619	−	9.77369i	−0.284216	−	0.716642i
$187$	1.61925	−	0.865508i	0.118411	−	0.0632922i
$188$	6.09814	+	9.75301i	0.444753	+	0.711311i
$189$	−0.0715901	+	0.726867i	−0.00520742	+	0.0528718i
$190$	−2.49198	+	1.28390i	−0.180788	+	0.0931436i
$191$			18.7189i			1.35445i	0.735776	+	0.677225i	$0.236818\pi$
$191$			18.7189i			1.35445i	−0.735776	+	0.677225i	$0.763182\pi$
$192$	7.69352	−	18.9687i	0.555232	−	1.36895i
$193$			16.2146i			1.16715i	0.812059	+	0.583575i	$0.198347\pi$
$193$			16.2146i			1.16715i	−0.812059	+	0.583575i	$0.801653\pi$
$194$	4.00045	+	7.76469i	0.287215	+	0.557472i
$195$	−0.355691	+	3.61139i	−0.0254715	+	0.258617i
$196$	−13.1111	−	3.02308i	−0.936507	−	0.215935i
$197$	1.32178	−	0.706504i	0.0941726	−	0.0503363i	−0.423638	−	0.905832i	$-0.639247\pi$
$197$	1.32178	−	0.706504i	0.0941726	−	0.0503363i	0.517811	+	0.855495i	$0.326747\pi$
$198$	−9.72430	+	3.85660i	−0.691076	+	0.274077i
$199$	6.10047	−	1.21346i	0.432451	−	0.0860198i	0.0259350	−	0.999664i	$-0.491744\pi$
$199$	6.10047	−	1.21346i	0.432451	−	0.0860198i	0.406516	+	0.913644i	$0.366744\pi$
$200$	0.149211	+	2.82449i	0.0105508	+	0.199722i
$201$	−1.18153	+	5.93994i	−0.0833385	+	0.418971i
$202$	8.40830	−	12.1808i	0.591606	−	0.857037i
$203$	−0.0173511	+	0.0211424i	−0.00121781	+	0.00148391i
$204$	−4.03568	+	2.00254i	−0.282554	+	0.140206i
$205$	2.05923	−	3.85255i	0.143823	−	0.269074i
$206$	13.6119	+	17.1076i	0.948388	+	1.19195i
$207$	−1.60940	+	0.666637i	−0.111861	+	0.0463345i
$208$	−0.896550	+	5.60171i	−0.0621645	+	0.388409i
$209$	3.81930	+	1.58201i	0.264186	+	0.109430i
$210$	−0.520859	−	1.81550i	−0.0359427	−	0.125281i
$211$	−5.83874	−	19.2478i	−0.401956	−	1.32507i	−0.891472	−	0.453076i	$-0.850327\pi$
$211$	−5.83874	−	19.2478i	−0.401956	−	1.32507i	0.489516	−	0.871994i	$-0.337173\pi$
$212$	4.48370	−	1.21324i	0.307941	−	0.0833254i
$213$	−13.3711	+	1.31694i	−0.916174	+	0.0902353i
$214$	−20.3111	−	4.36062i	−1.38844	−	0.298086i
$215$	2.61877	+	3.91926i	0.178598	+	0.267291i
$216$	3.72153	−	1.34710i	0.253218	−	0.0916585i
$217$	−1.26105	−	0.842606i	−0.0856056	−	0.0571998i
$218$	0.133603	−	8.82841i	0.00904872	−	0.597935i
$219$	−1.21076	+	3.99134i	−0.0818155	+	0.269710i
$220$	3.03728	−	2.85879i	0.204774	−	0.192740i
$221$	0.965175	−	0.792099i	0.0649247	−	0.0532823i
$222$	−23.8012	−	20.1435i	−1.59743	−	1.35194i
$223$	11.1327	+	11.1327i	0.745499	+	0.745499i	0.973630	−	0.228131i	$-0.0732615\pi$
$223$	11.1327	+	11.1327i	0.745499	+	0.745499i	−0.228131	+	0.973630i	$0.573261\pi$
$224$	−0.641084	−	2.88223i	−0.0428342	−	0.192577i
$225$	−2.50803	+	2.50803i	−0.167202	+	0.167202i
$226$	16.0215	−	1.33354i	1.06574	−	0.0887055i
$227$	11.4378	+	13.9370i	0.759151	+	0.925028i	0.998951	−	0.0457944i	$-0.0145819\pi$
$227$	11.4378	+	13.9370i	0.759151	+	0.925028i	−0.239800	+	0.970822i	$0.577082\pi$
$228$	−9.24985	−	4.16365i	−0.612586	−	0.275745i
$229$	−15.2903	−	4.63826i	−1.01041	−	0.306505i	−0.258672	−	0.965965i	$-0.583285\pi$
$229$	−15.2903	−	4.63826i	−1.01041	−	0.306505i	−0.751739	+	0.659460i	$0.770785\pi$
$230$	0.498513	−	0.483649i	0.0328710	−	0.0318909i
$231$	−1.54743	+	2.31590i	−0.101814	+	0.152375i
$232$	0.143900	+	0.0354810i	0.00944747	+	0.00232944i
$233$	−0.745322	+	0.498008i	−0.0488277	+	0.0326256i	−0.579745	−	0.814798i	$-0.696848\pi$
$233$	−0.745322	+	0.498008i	−0.0488277	+	0.0326256i	0.530917	+	0.847424i	$0.321848\pi$
$234$	−5.97422	+	3.86238i	−0.390547	+	0.252492i
$235$	−0.563723	−	5.72358i	−0.0367733	−	0.373365i
$236$	−19.6786	−	2.54149i	−1.28097	−	0.165437i
$237$	−23.1748	+	7.03000i	−1.50537	+	0.456648i
$238$	−0.314980	+	0.568426i	−0.0204171	+	0.0368456i
$239$	−9.22573	+	22.2729i	−0.596763	+	1.44071i	0.280100	+	0.959971i	$0.409632\pi$
$239$	−9.22573	+	22.2729i	−0.596763	+	1.44071i	−0.876862	+	0.480741i	$0.840368\pi$
$240$	−7.66159	+	6.78603i	−0.494554	+	0.438036i
$241$	0.0863882	+	0.208560i	0.00556475	+	0.0134345i	0.926637	−	0.375956i	$-0.122686\pi$
$241$	0.0863882	+	0.208560i	0.00556475	+	0.0134345i	−0.921073	+	0.389391i	$0.872686\pi$
$242$	9.34500	+	1.06341i	0.600719	+	0.0683584i
$243$	−19.6342	−	10.4947i	−1.25953	−	0.673234i
$244$	−14.2553	+	16.3360i	−0.912602	+	1.04580i
$245$	5.20047	+	4.26792i	0.332246	+	0.272667i
$246$	15.5482	−	2.84886i	0.991319	−	0.181637i
$247$	2.75727	+	0.548454i	0.175441	+	0.0348973i
$248$	−1.17589	+	8.13393i	−0.0746689	+	0.516505i
$249$	−5.23846	−	26.3355i	−0.331974	−	1.66894i
$250$	0.560904	−	1.29822i	0.0354747	−	0.0821069i
$251$	−8.99398	−	16.8265i	−0.567695	−	1.06208i	−0.987964	−	0.154683i	$-0.950564\pi$
$251$	−8.99398	−	16.8265i	−0.567695	−	1.06208i	0.420270	−	0.907399i	$-0.361936\pi$
$252$	2.14931	−	3.01501i	0.135394	−	0.189928i
$253$	−1.01935	−	0.100397i	−0.0640860	−	0.00631192i
$254$	−4.11535	+	12.8625i	−0.258220	+	0.807067i
$255$	2.25260			0.141064
$256$	−12.5972	+	9.86465i	−0.787323	+	0.616541i
$257$	12.4896			0.779078			0.389539	−	0.921010i	$-0.372634\pi$
$257$	12.4896			0.779078			0.389539	+	0.921010i	$0.372634\pi$
$258$	−5.19765	+	16.2453i	−0.323592	+	1.01139i
$259$	−4.47611	−	0.440859i	−0.278132	−	0.0273936i
$260$	1.64652	−	2.30970i	0.102113	−	0.143242i
$261$	0.0876121	+	0.163911i	0.00542305	+	0.0101458i
$262$	−1.18916	+	2.75234i	−0.0734667	+	0.170040i
$263$	−1.19509	−	6.00811i	−0.0736922	−	0.370476i	0.926288	−	0.376817i	$-0.122981\pi$
$263$	−1.19509	−	6.00811i	−0.0736922	−	0.370476i	−0.999980	+	0.00634129i	$0.997981\pi$
$264$	14.9378	+	2.15950i	0.919360	+	0.132908i
$265$	−2.27784	−	0.453091i	−0.139927	−	0.0278332i
$266$	−1.43925	+	0.263709i	−0.0882458	+	0.0161691i
$267$	−10.9498	−	8.98624i	−0.670115	−	0.549949i
$268$	3.11252	−	3.56682i	0.190128	−	0.217878i
$269$	−27.4810	−	14.6889i	−1.67555	−	0.895598i	−0.985052	−	0.172260i	$-0.944893\pi$
$269$	−27.4810	−	14.6889i	−1.67555	−	0.895598i	−0.690494	−	0.723338i	$-0.742607\pi$
$270$	−1.96623	−	0.223745i	−0.119661	−	0.0136167i
$271$	9.88323	+	23.8602i	0.600363	+	1.44941i	0.873208	+	0.487347i	$0.162035\pi$
$271$	9.88323	+	23.8602i	0.600363	+	1.44941i	−0.272845	+	0.962058i	$0.587965\pi$
$272$	3.51505	+	0.213021i	0.213131	+	0.0129163i
$273$	−0.724851	+	1.74995i	−0.0438700	+	0.105912i
$274$	10.4945	−	18.9389i	0.633998	−	1.14414i
$275$	−1.99573	+	0.605398i	−0.120347	+	0.0365069i
$276$	2.49263	+	0.321923i	0.150039	+	0.0193775i
$277$	0.661516	+	6.71649i	0.0397467	+	0.403555i	0.994388	+	0.105796i	$0.0337391\pi$
$277$	0.661516	+	6.71649i	0.0397467	+	0.403555i	−0.954641	+	0.297759i	$0.903761\pi$
$278$	−16.1380	+	10.4333i	−0.967893	+	0.625750i
$279$	−8.56920	+	5.72575i	−0.513024	+	0.342792i
$280$	−0.353431	+	1.43340i	−0.0211215	+	0.0856621i
$281$	−8.16289	+	12.2166i	−0.486957	+	0.728783i	−0.990848	−	0.134984i	$-0.956902\pi$
$281$	−8.16289	+	12.2166i	−0.486957	+	0.728783i	0.503890	+	0.863768i	$0.331902\pi$
$282$	14.9367	−	14.4914i	0.889468	−	0.862948i
$283$	−17.1108	−	5.19050i	−1.01713	−	0.308543i	−0.262668	−	0.964886i	$-0.584602\pi$
$283$	−17.1108	−	5.19050i	−1.01713	−	0.308543i	−0.754463	+	0.656343i	$0.772102\pi$
$284$	9.57663	+	4.31074i	0.568269	+	0.255796i
$285$	3.21757	+	3.92061i	0.190592	+	0.232237i
$286$	−4.16856	+	0.346966i	−0.246492	+	0.0205165i
$287$	1.61229	−	1.61229i	0.0951704	−	0.0951704i
$288$	−19.7618	−	3.47033i	−1.16448	−	0.204491i
$289$	11.4728	+	11.4728i	0.674869	+	0.674869i
$290$	−0.0565658	−	0.0478729i	−0.00332166	−	0.00281119i
$291$	12.2161	−	10.0255i	0.716121	−	0.587705i
$292$	2.37402	−	2.23451i	0.138929	−	0.130765i
$293$	−6.16792	+	20.3329i	−0.360334	+	1.18786i	0.570154	+	0.821538i	$0.306884\pi$
$293$	−6.16792	+	20.3329i	−0.360334	+	1.18786i	−0.930488	+	0.366323i	$0.880616\pi$
$294$	−0.368360	+	24.3411i	−0.0214832	+	1.41960i
$295$	8.24903	+	5.51182i	0.480277	+	0.320911i
$296$	8.29556	+	22.9175i	0.482169	+	1.33205i
$297$	1.62132	+	2.42647i	0.0940784	+	0.140798i
$298$	20.5226	+	4.40603i	1.18884	+	0.255234i
$299$	−0.693202	+	0.0682744i	−0.0400889	+	0.00394841i
$300$	4.93973	−	1.33663i	0.285196	−	0.0771706i
$301$	0.714201	+	2.35441i	0.0411659	+	0.135706i
$302$	1.67183	+	5.82729i	0.0962029	+	0.335323i
$303$	−24.7406	−	10.2479i	−1.42131	−	0.588726i
$304$	4.65005	+	6.42215i	0.266699	+	0.368336i
$305$	10.0154	−	4.14853i	0.573483	−	0.237544i
$306$	2.74951	+	3.45562i	0.157179	+	0.197545i
$307$	−7.82535	+	14.6402i	−0.446616	+	0.835560i	0.553380	+	0.832929i	$0.313338\pi$
$307$	−7.82535	+	14.6402i	−0.446616	+	0.835560i	−0.999997	+	0.00263140i	$0.999162\pi$
$308$	1.95024	−	0.967725i	0.111125	−	0.0551412i
$309$	25.0931	−	30.5761i	1.42750	−	1.73941i
$310$	2.33441	−	3.38177i	0.132586	−	0.192072i
$311$	0.949842	−	4.77518i	0.0538606	−	0.270776i	−0.944466	−	0.328610i	$-0.893420\pi$
$311$	0.949842	−	4.77518i	0.0538606	−	0.270776i	0.998326	+	0.0578349i	$0.0184197\pi$
$312$	10.2497	−	0.541464i	0.580274	−	0.0306544i
$313$	4.63769	−	0.922493i	0.262138	−	0.0521424i	−0.0622717	−	0.998059i	$-0.519835\pi$
$313$	4.63769	−	0.922493i	0.262138	−	0.0521424i	0.324409	+	0.945917i	$0.394835\pi$
$314$	12.3848	−	4.91175i	0.698916	−	0.277186i
$315$	−1.63273	+	0.872715i	−0.0919942	+	0.0491719i
$316$	18.4457	+	4.25311i	1.03765	+	0.239256i
$317$	0.585978	−	5.94953i	0.0329118	−	0.334159i	−0.964603	−	0.263705i	$-0.915055\pi$
$317$	0.585978	−	5.94953i	0.0329118	−	0.334159i	0.997515	−	0.0704535i	$-0.0224447\pi$
$318$	−3.84898	−	7.47070i	−0.215840	−	0.418936i
$319$			0.109282i			0.00611860i
$320$	7.83455	−	1.61860i	0.437965	−	0.0904825i
$321$			37.5855i			2.09782i
$322$	0.322282	−	0.166043i	0.0179601	−	0.00925321i
$323$	0.171049	−	1.73669i	0.00951743	−	0.0966321i
$324$	7.48608	+	11.9728i	0.415894	+	0.665156i
$325$	−1.25079	+	0.668559i	−0.0693811	+	0.0370850i
$326$	11.6877	+	29.4702i	0.647323	+	1.63220i
$327$	−15.6678	+	3.11652i	−0.866432	+	0.172344i
$328$	−11.6486	−	4.11951i	−0.643188	−	0.227462i
$329$	0.585651	−	2.94426i	0.0322880	−	0.162323i
$330$	−6.21058	−	4.28711i	−0.341881	−	0.235998i
$331$	−8.23531	+	10.0348i	−0.452653	+	0.551560i	−0.948470	−	0.316868i	$-0.897369\pi$
$331$	−8.23531	+	10.0348i	−0.452653	+	0.551560i	0.495816	+	0.868427i	$0.334869\pi$
$332$	−6.69759	+	19.8911i	−0.367578	+	1.09167i
$333$	−14.4076	+	26.9547i	−0.789532	+	1.47711i
$334$	−16.2277	+	12.9118i	−0.887940	+	0.706502i
$335$	−2.18679	+	0.905796i	−0.119477	+	0.0494889i
$336$	−4.85506	+	2.22866i	−0.264865	+	0.121584i
$337$	26.9602	+	11.1673i	1.46861	+	0.608320i	0.966543	−	0.256506i	$-0.0825712\pi$
$337$	26.9602	+	11.1673i	1.46861	+	0.608320i	0.502072	+	0.864826i	$0.332571\pi$
$338$	14.9376	−	4.28554i	0.812497	−	0.233102i
$339$	−8.44363	−	27.8349i	−0.458595	−	1.51179i
$340$	−1.52702	−	0.876620i	−0.0828141	−	0.0475414i
$341$	−6.03069	+	0.593971i	−0.326580	+	0.0321654i
$342$	−2.08710	+	9.72139i	−0.112858	+	0.525673i
$343$	3.98081	+	5.95770i	0.214943	+	0.321685i
$344$	9.84542	−	8.98978i	0.530829	−	0.484696i
$345$	−1.04488	−	0.698167i	−0.0562545	−	0.0375880i
$346$	8.59887	+	0.130129i	0.462278	+	0.00699578i
$347$	−5.94110	+	19.5852i	−0.318935	+	1.05139i	0.640146	+	0.768254i	$0.278874\pi$
$347$	−5.94110	+	19.5852i	−0.318935	+	1.05139i	−0.959080	+	0.283134i	$0.908626\pi$
$348$	0.00811412	−	0.268027i	0.000434962	−	0.0143678i
$349$	−7.55550	+	6.20064i	−0.404436	+	0.331912i	−0.814520	−	0.580136i	$-0.803000\pi$
$349$	−7.55550	+	6.20064i	−0.404436	+	0.331912i	0.410083	+	0.912048i	$0.365500\pi$
$350$	0.476868	−	0.563459i	0.0254897	−	0.0301181i
$351$	1.40330	+	1.40330i	0.0749026	+	0.0749026i
$352$	−9.28581	−	7.27709i	−0.494935	−	0.387870i
$353$	−24.5831	+	24.5831i	−1.30843	+	1.30843i	−0.385876	+	0.922550i	$0.626101\pi$
$353$	−24.5831	+	24.5831i	−1.30843	+	1.30843i	−0.922550	+	0.385876i	$0.873899\pi$
$354$	2.97777	+	35.7758i	0.158266	+	1.90146i
$355$	−3.33124	−	4.05912i	−0.176804	−	0.215436i
$356$	3.92565	+	10.3529i	0.208059	+	0.548701i
$357$	1.12515	+	0.341309i	0.0595490	+	0.0180640i
$358$	−6.86154	−	7.07240i	−0.362644	−	0.373788i
$359$	5.09033	−	7.61822i	0.268657	−	0.402074i	−0.672471	−	0.740123i	$-0.734767\pi$
$359$	5.09033	−	7.61822i	0.268657	−	0.402074i	0.941128	+	0.338049i	$0.109767\pi$
$360$	8.07986	+	5.94633i	0.425846	+	0.313399i
$361$	−12.5309	+	8.37289i	−0.659522	+	0.440679i
$362$	9.23207	+	14.2799i	0.485227	+	0.750534i
$363$	−1.66793	−	16.9348i	−0.0875435	−	0.888844i
$364$	1.17237	−	0.904187i	0.0614491	−	0.0473923i
$365$	−1.55992	+	0.473195i	−0.0816497	+	0.0247682i
$366$	34.3115	+	19.0129i	1.79349	+	0.993822i
$367$	−7.88938	+	19.0466i	−0.411822	+	0.994227i	0.572826	+	0.819677i	$0.305847\pi$
$367$	−7.88938	+	19.0466i	−0.411822	+	0.994227i	−0.984648	+	0.174550i	$0.944153\pi$
$368$	−1.56445	−	1.18826i	−0.0815525	−	0.0619422i
$369$	−5.92933	−	14.3147i	−0.308669	−	0.745192i
$370$	1.37784	−	12.1082i	0.0716307	−	0.629475i
$371$	−1.06910	−	0.571446i	−0.0555050	−	0.0296680i
$372$	14.8351	−	1.00901i	0.769166	−	0.0523149i
$373$	15.1438	+	12.4282i	0.784117	+	0.643508i	0.938803	−	0.344456i	$-0.111936\pi$
$373$	15.1438	+	12.4282i	0.784117	+	0.643508i	−0.154686	+	0.987964i	$0.549436\pi$
$374$	0.467972	+	2.55405i	0.0241982	+	0.132067i
$375$	−2.50952	−	0.499175i	−0.129591	−	0.0257773i
$376$	−15.7649	+	4.01079i	−0.813010	+	0.206841i
$377$	0.0144984	+	0.0728883i	0.000746704	+	0.00375394i
$378$	−0.948202	−	0.409676i	−0.0487702	−	0.0210714i
$379$	−5.93125	−	11.0966i	−0.304668	−	0.569994i	0.682269	−	0.731101i	$-0.260993\pi$
$379$	−5.93125	−	11.0966i	−0.304668	−	0.569994i	−0.986937	+	0.161108i	$0.948493\pi$
$380$	−0.655412	−	3.90988i	−0.0336219	−	0.200573i
$381$	24.3162	+	2.39494i	1.24576	+	0.122696i
$382$	−25.2134	−	8.06699i	−1.29003	−	0.412743i
$383$	13.6536			0.697666			0.348833	−	0.937185i	$-0.386578\pi$
$383$	13.6536			0.697666			0.348833	+	0.937185i	$0.386578\pi$
$384$	22.2343	+	18.5374i	1.13464	+	0.945985i
$385$	−1.08857			−0.0554786
$386$	−21.8402	−	6.98775i	−1.11164	−	0.355667i
$387$	16.6383	+	1.63873i	0.845771	+	0.0833012i
$388$	−12.1827	+	2.04217i	−0.618482	+	0.103676i
$389$	−12.6995	−	23.7591i	−0.643891	−	1.20464i	−0.966149	−	0.257984i	$-0.916942\pi$
$389$	−12.6995	−	23.7591i	−0.643891	−	1.20464i	0.322258	−	0.946652i	$-0.395558\pi$
$390$	−4.71108	−	2.03544i	−0.238555	−	0.103069i
$391$	0.0843541	+	0.424077i	0.00426597	+	0.0214465i
$392$	9.72225	−	16.3572i	0.491048	−	0.826163i
$393$	5.32039	+	1.05829i	0.268378	+	0.0533838i
$394$	0.382000	+	2.08484i	0.0192449	+	0.105033i
$395$	−7.31643	−	6.00444i	−0.368130	−	0.302116i
$396$	−1.00391	−	14.7602i	−0.0504486	−	0.741727i
$397$	−31.0678	−	16.6061i	−1.55925	−	0.833437i	−0.999990	−	0.00444415i	$-0.998585\pi$
$397$	−31.0678	−	16.6061i	−1.55925	−	0.833437i	−0.559260	−	0.828992i	$-0.688915\pi$
$398$	−0.994560	+	8.73998i	−0.0498528	+	0.438095i
$399$	1.01309	+	2.44581i	0.0507178	+	0.122444i
$400$	−3.86875	−	1.01625i	−0.193438	−	0.0508125i
$401$	−7.71300	+	18.6208i	−0.385169	+	0.929879i	0.605779	+	0.795633i	$0.292861\pi$
$401$	−7.71300	+	18.6208i	−0.385169	+	0.929879i	−0.990948	+	0.134247i	$0.957139\pi$
$402$	−7.49162	−	4.15131i	−0.373648	−	0.207048i
$403$	−3.94353	+	1.19626i	−0.196441	+	0.0595897i
$404$	12.7833	+	16.5749i	0.635994	+	0.824634i
$405$	−0.692027	−	7.02627i	−0.0343871	−	0.349138i
$406$	−0.0210002	−	0.0324826i	−0.00104222	−	0.00161208i
$407$	−14.9424	+	9.98422i	−0.740669	+	0.494900i
$408$	−0.958124	−	6.29887i	−0.0474342	−	0.311841i
$409$	−0.631930	+	0.945750i	−0.0312469	+	0.0467643i	−0.846764	−	0.531968i	$-0.821453\pi$
$409$	−0.631930	+	0.945750i	−0.0312469	+	0.0467643i	0.815517	+	0.578733i	$0.196453\pi$
$410$	4.30177	+	4.43397i	0.212449	+	0.218978i
$411$	−37.4877	−	11.3718i	−1.84913	−	0.560928i
$412$	−28.9093	+	10.9620i	−1.42426	+	0.540058i
$413$	3.28514	+	4.00295i	0.161651	+	0.196972i
$414$	−0.204346	−	2.45508i	−0.0100431	−	0.120661i
$415$	7.42054	−	7.42054i	0.364260	−	0.364260i
$416$	−7.15886	−	3.62170i	−0.350992	−	0.177568i
$417$	24.5850	+	24.5850i	1.20393	+	1.20393i
$418$	−3.77683	+	4.46264i	−0.184731	+	0.218275i
$419$	−14.3810	+	11.8022i	−0.702559	+	0.576575i	−0.916386	−	0.400296i	$-0.868907\pi$
$419$	−14.3810	+	11.8022i	−0.702559	+	0.576575i	0.213827	+	0.976872i	$0.431407\pi$
$420$	2.66985	+	0.0808258i	0.130275	+	0.00394389i
$421$	7.16322	−	23.6140i	0.349114	−	1.15087i	−0.590039	−	0.807375i	$-0.700888\pi$
$421$	7.16322	−	23.6140i	0.349114	−	1.15087i	0.939153	−	0.343499i	$-0.111612\pi$
$422$	28.4420	+	0.430421i	1.38454	+	0.0209526i
$423$	−16.9612	−	11.3331i	−0.824683	−	0.551036i
$424$	−0.298104	+	6.56217i	−0.0144772	+	0.318687i
$425$	0.489110	+	0.732005i	0.0237253	+	0.0355075i
$426$	3.98850	−	18.5778i	0.193244	−	0.900097i
$427$	5.63115	−	0.554620i	0.272511	−	0.0268400i
$428$	14.6267	−	25.4788i	0.707009	−	1.23156i
$429$	2.19691	+	7.24223i	0.106068	+	0.349658i
$430$	−6.40762	+	1.83832i	−0.309003	+	0.0886519i
$431$	5.47811	+	2.26911i	0.263871	+	0.109299i	0.510697	−	0.859761i	$-0.329387\pi$
$431$	5.47811	+	2.26911i	0.263871	+	0.109299i	−0.246825	+	0.969060i	$0.579387\pi$
$432$	0.210665	+	5.59325i	0.0101356	+	0.269106i
$433$	24.5724	−	10.1782i	1.18088	−	0.489135i	0.296103	−	0.955156i	$-0.404313\pi$
$433$	24.5724	−	10.1782i	1.18088	−	0.489135i	0.884774	+	0.466021i	$0.154313\pi$
$434$	1.67840	−	1.33545i	0.0805660	−	0.0641034i
$435$	−0.0632025	+	0.118244i	−0.00303033	+	0.00566935i
$436$	11.8339	+	3.98461i	0.566739	+	0.190828i
$437$	−0.617608	+	0.752558i	−0.0295442	+	0.0359997i
$438$	−4.85435	−	3.35092i	−0.231950	−	0.160113i
$439$	4.13663	−	20.7963i	0.197431	−	0.992552i	−0.747246	−	0.664548i	$-0.768624\pi$
$439$	4.13663	−	20.7963i	0.197431	−	0.992552i	0.944676	−	0.328004i	$-0.106376\pi$
$440$	2.54172	+	5.32308i	0.121172	+	0.253768i
$441$	23.4034	−	4.65522i	1.11445	−	0.221677i
$442$	0.650971	+	1.64140i	0.0309635	+	0.0780736i
$443$	−23.8131	+	12.7284i	−1.13140	+	0.604744i	−0.927342	−	0.374215i	$-0.877912\pi$
$443$	−23.8131	+	12.7284i	−1.13140	+	0.604744i	−0.204055	+	0.978959i	$0.565412\pi$
$444$	37.3896	−	23.3781i	1.77443	−	1.10948i
$445$	0.542631	−	5.50942i	0.0257232	−	0.261172i
$446$	−19.7929	+	10.1975i	−0.937219	+	0.482865i
$447$		−	37.9768i		−	1.79624i
$448$	4.15850	+	0.378602i	0.196470	+	0.0178873i
$449$		−	15.5915i		−	0.735806i	−0.929864	−	0.367903i	$-0.880076\pi$
$449$		−	15.5915i		−	0.735806i	0.929864	−	0.367903i	$-0.119924\pi$
$450$	−2.29734	−	4.45903i	−0.108298	−	0.210201i
$451$	0.892972	−	9.06650i	0.0420484	−	0.426925i
$452$	−5.10835	+	22.1549i	−0.240277	+	1.04208i
$453$	9.67330	−	5.17048i	0.454491	−	0.242931i
$454$	−23.7016	+	9.39990i	−1.11237	+	0.441159i
$455$	−0.726049	+	0.144420i	−0.0340377	+	0.00677052i
$456$	9.59451	−	10.6648i	0.449304	−	0.499423i
$457$	−6.59073	+	33.1339i	−0.308302	+	1.54994i	0.446985	+	0.894542i	$0.352498\pi$
$457$	−6.59073	+	33.1339i	−0.308302	+	1.54994i	−0.755286	+	0.655395i	$0.772502\pi$
$458$	12.8369	−	18.5964i	0.599831	−	0.868953i
$459$	0.781517	−	0.952281i	0.0364781	−	0.0444487i
$460$	0.436615	+	0.879904i	0.0203573	+	0.0410257i
$461$	11.6145	−	21.7293i	0.540943	−	1.01203i	−0.451839	−	0.892099i	$-0.649232\pi$
$461$	11.6145	−	21.7293i	0.540943	−	1.01203i	0.992782	−	0.119933i	$-0.0382681\pi$
$462$	−2.45253	−	3.08237i	−0.114102	−	0.143405i
$463$	17.2426	−	7.14211i	0.801330	−	0.331922i	0.0558412	−	0.998440i	$-0.482216\pi$
$463$	17.2426	−	7.14211i	0.801330	−	0.331922i	0.745489	+	0.666518i	$0.232216\pi$
$464$	−0.109806	+	0.178535i	−0.00509759	+	0.00828828i
$465$	−6.86878	−	2.84514i	−0.318532	−	0.131940i
$466$	−0.349592	−	1.21853i	−0.0161946	−	0.0564474i
$467$	3.45900	+	11.4028i	0.160063	+	0.527658i	0.999884	−	0.0152053i	$-0.00484017\pi$
$467$	3.45900	+	11.4028i	0.160063	+	0.527658i	−0.839821	+	0.542863i	$0.817340\pi$
$468$	−2.62782	−	9.71150i	−0.121471	−	0.448914i
$469$	−1.22951	+	0.121097i	−0.0567737	+	0.00559172i
$470$	7.95232	+	1.70730i	0.366813	+	0.0787518i
$471$	−13.3922	−	20.0428i	−0.617079	−	0.923524i
$472$	11.9039	−	25.4108i	0.547920	−	1.16963i
$473$	8.17374	+	5.46152i	0.375829	+	0.251121i
$474$	0.518239	−	34.2450i	0.0238035	−	1.57292i
$475$	−0.575408	+	1.89686i	−0.0264015	+	0.0870341i
$476$	−0.629900	−	0.669229i	−0.0288714	−	0.0306741i
$477$	−6.36770	+	5.22583i	−0.291557	+	0.239275i
$478$	−26.0246	−	22.0252i	−1.19034	−	1.00741i
$479$	−14.4069	−	14.4069i	−0.658267	−	0.658267i	0.296703	−	0.954970i	$-0.404113\pi$
$479$	−14.4069	−	14.4069i	−0.658267	−	0.658267i	−0.954970	+	0.296703i	$0.904113\pi$
$480$	−5.83865	−	13.2443i	−0.266496	−	0.604515i
$481$	−8.64165	+	8.64165i	−0.394025	+	0.394025i
$482$	−0.318149	+	0.0264808i	−0.0144913	+	0.00120617i
$483$	−0.416119	−	0.507043i	−0.0189341	−	0.0230712i
$484$	−5.45963	+	12.1290i	−0.248165	+	0.551317i
$485$	5.91038	+	1.79289i	0.268376	+	0.0814111i
$486$	22.5973	−	21.9235i	1.02503	−	0.994471i
$487$	−14.9263	+	22.3388i	−0.676375	+	1.01227i	0.321488	+	0.946914i	$0.395817\pi$
$487$	−14.9263	+	22.3388i	−0.676375	+	1.01227i	−0.997862	+	0.0653525i	$0.979183\pi$
$488$	−15.8604	−	26.2413i	−0.717965	−	1.18789i
$489$	47.6928	−	31.8673i	2.15674	−	1.44109i
$490$	−7.98985	+	5.16550i	−0.360944	+	0.233353i
$491$	−0.955078	−	9.69707i	−0.0431021	−	0.437623i	−0.992383	−	0.123193i	$-0.960687\pi$
$491$	−0.955078	−	9.69707i	−0.0431021	−	0.437623i	0.949281	−	0.314430i	$-0.101813\pi$
$492$	−2.86331	+	22.1704i	−0.129088	+	0.999520i
$493$	0.0441451	−	0.0133913i	0.00198820	−	0.000603113i
$494$	−1.92700	+	3.47754i	−0.0866998	+	0.156462i
$495$	−2.83076	+	6.83407i	−0.127233	+	0.307168i
$496$	−10.4492	−	5.08922i	−0.469185	−	0.228513i
$497$	−1.04888	−	2.53222i	−0.0470486	−	0.113585i
$498$	37.7302	+	4.29348i	1.69073	+	0.192395i
$499$	−26.5351	−	14.1833i	−1.18787	−	0.634931i	−0.245467	−	0.969405i	$-0.578941\pi$
$499$	−26.5351	−	14.1833i	−1.18787	−	0.634931i	−0.942405	+	0.334474i	$0.891441\pi$
$500$	1.50692	+	1.31499i	0.0673915	+	0.0588080i
$501$	29.0034	+	23.8024i	1.29577	+	1.06341i
$502$	26.5405	−	4.86296i	1.18456	−	0.217044i
$503$	19.4398	+	3.86682i	0.866778	+	0.172413i	0.608399	−	0.793631i	$-0.291812\pi$
$503$	19.4398	+	3.86682i	0.866778	+	0.172413i	0.258378	+	0.966044i	$0.416812\pi$
$504$	3.13481	+	4.19435i	0.139635	+	0.186831i
$505$	−2.04180	−	10.2648i	−0.0908589	−	0.456779i
$506$	0.574525	−	1.32975i	0.0255407	−	0.0591145i
$507$	−13.2539	−	24.7964i	−0.588628	−	1.10125i
$508$	−15.5517	−	11.0864i	−0.689994	−	0.491877i
$509$	36.4373	+	3.58876i	1.61505	+	0.159069i	0.864812	−	0.502095i	$-0.167437\pi$
$509$	36.4373	+	3.58876i	1.61505	+	0.159069i	0.750241	+	0.661164i	$0.229937\pi$
$510$	−0.970772	+	3.03415i	−0.0429865	+	0.134354i
$511$	−0.850854			−0.0376396
$512$	−7.85838	−	21.2190i	−0.347295	−	0.937756i
$513$	2.77373			0.122463
$514$	−5.38245	+	16.8228i	−0.237410	+	0.742024i
$515$	15.3845	+	1.51524i	0.677921	+	0.0667694i
$516$	−19.6416	−	14.0020i	−0.864675	−	0.616402i
$517$	−5.65415	−	10.5782i	−0.248669	−	0.465227i
$518$	2.52282	−	5.83911i	0.110846	−	0.256556i
$519$	−3.03549	−	15.2604i	−0.133243	−	0.669859i
$520$	2.40148	+	3.21316i	0.105312	+	0.140906i
$521$	−9.78594	−	1.94654i	−0.428730	−	0.0852797i	−0.0239914	−	0.999712i	$-0.507637\pi$
$521$	−9.78594	−	1.94654i	−0.428730	−	0.0852797i	−0.404738	+	0.914432i	$0.632637\pi$
$522$	−0.258537	+	0.0473710i	−0.0113158	+	0.00207337i
$523$	0.727402	+	0.596963i	0.0318071	+	0.0261034i	0.650163	−	0.759795i	$-0.274701\pi$
$523$	0.727402	+	0.596963i	0.0318071	+	0.0261034i	−0.618355	+	0.785899i	$0.712201\pi$
$524$	−3.19479	−	2.78788i	−0.139565	−	0.121789i
$525$	−1.17784	−	0.629568i	−0.0514051	−	0.0274766i
$526$	8.60766	+	0.979502i	0.375312	+	0.0427083i
$527$	0.978935	+	2.36336i	0.0426431	+	0.102950i
$528$	−9.34628	+	19.1899i	−0.406745	+	0.835133i
$529$	−8.70941	+	21.0264i	−0.378670	+	0.914190i
$530$	1.59194	−	2.87288i	0.0691495	−	0.124790i
$531$	33.6735	−	10.2147i	1.46130	−	0.443282i
$532$	0.265047	−	2.05224i	0.0114912	−	0.0889759i
$533$	−0.607259	−	6.16561i	−0.0263033	−	0.267062i
$534$	16.8229	−	10.8761i	0.727998	−	0.470656i
$535$	−12.2138	+	8.16097i	−0.528047	+	0.352830i
$536$	3.46297	+	5.72955i	0.149578	+	0.247479i
$537$	−9.90490	+	14.8237i	−0.427428	+	0.639691i
$538$	31.6283	−	30.6853i	1.36359	−	1.32294i
$539$	13.4264	+	4.07285i	0.578315	+	0.175430i
$540$	1.14873	−	2.55199i	0.0494335	−	0.109820i
$541$	5.81215	+	7.08213i	0.249884	+	0.304485i	0.882812	−	0.469726i	$-0.155647\pi$
$541$	5.81215	+	7.08213i	0.249884	+	0.304485i	−0.632928	+	0.774210i	$0.718147\pi$
$542$	−36.3978	+	3.02954i	−1.56342	+	0.130130i
$543$	21.7544	−	21.7544i	0.933569	−	0.933569i
$544$	−1.80176	+	4.64280i	−0.0772498	+	0.199058i
$545$	−4.41471	−	4.41471i	−0.189105	−	0.189105i
$546$	−2.04471	−	1.73049i	−0.0875056	−	0.0740580i
$547$	4.60942	−	3.78285i	0.197084	−	0.161743i	−0.530675	−	0.847575i	$-0.678062\pi$
$547$	4.60942	−	3.78285i	0.197084	−	0.161743i	0.727760	+	0.685832i	$0.240562\pi$
$548$	20.9871	+	22.2975i	0.896523	+	0.952500i
$549$	11.1616	−	36.7948i	0.476365	−	1.57036i
$550$	0.0446288	−	2.94905i	0.00190298	−	0.125748i
$551$	0.0863631	+	0.0577060i	0.00367919	+	0.00245836i
$552$	−1.50783	+	3.21872i	−0.0641774	+	0.136998i
$553$	−2.74468	−	4.10771i	−0.116716	−	0.174677i
$554$	−9.33187	−	2.00348i	−0.396473	−	0.0851195i
$555$	−21.9422	+	2.16111i	−0.931393	+	0.0917342i
$556$	−7.09845	−	26.2334i	−0.301041	−	1.11254i
$557$	6.25303	+	20.6135i	0.264949	+	0.873421i	0.983955	+	0.178417i	$0.0570975\pi$
$557$	6.25303	+	20.6135i	0.264949	+	0.873421i	−0.719006	+	0.695004i	$0.755402\pi$
$558$	−4.01937	−	14.0098i	−0.170153	−	0.593083i
$559$	6.17627	+	2.55829i	0.261228	+	0.108204i
$560$	−1.77841	−	1.09379i	−0.0751515	−	0.0462209i
$561$	4.34027	−	1.79780i	0.183246	−	0.0759032i
$562$	−12.9374	−	16.2598i	−0.545730	−	0.685880i
$563$	−14.1338	+	26.4424i	−0.595668	+	1.11442i	0.385763	+	0.922598i	$0.373938\pi$
$563$	−14.1338	+	26.4424i	−0.595668	+	1.11442i	−0.981430	+	0.191818i	$0.938562\pi$
$564$	13.0821	+	26.3641i	0.550856	+	1.11013i
$565$	7.21185	−	8.78766i	0.303405	−	0.369700i
$566$	14.3653	−	20.8105i	0.603820	−	0.874731i
$567$	0.718945	−	3.61438i	0.0301929	−	0.151790i
$568$	−9.93346	+	11.0415i	−0.416799	+	0.463292i
$569$	2.38592	−	0.474590i	0.100023	−	0.0198958i	−0.144825	−	0.989457i	$-0.546262\pi$
$569$	2.38592	−	0.474590i	0.100023	−	0.0198958i	0.244848	+	0.969561i	$0.421262\pi$
$570$	−6.66750	+	2.64429i	−0.279271	+	0.110757i
$571$	23.3043	−	12.4564i	0.975254	−	0.521284i	0.0948411	−	0.995492i	$-0.469766\pi$
$571$	23.3043	−	12.4564i	0.975254	−	0.521284i	0.880413	+	0.474208i	$0.157266\pi$
$572$	1.32912	−	5.76437i	0.0555731	−	0.241020i
$573$	−4.69460	+	47.6651i	−0.196120	+	1.99124i
$574$	1.47685	+	2.86650i	0.0616425	+	0.119645i
$575$		−	0.491137i		−	0.0204818i
$576$	13.1908	−	25.1226i	0.549618	−	1.04678i
$577$			19.1714i			0.798115i	0.916926	+	0.399058i	$0.130663\pi$
$577$			19.1714i			0.798115i	−0.916926	+	0.399058i	$0.869337\pi$
$578$	−20.3975	+	10.5090i	−0.848424	+	0.437117i
$579$	−4.06654	+	41.2882i	−0.168999	+	1.71588i
$580$	0.0888598	−	0.0555602i	0.00368970	−	0.00230701i
$581$	4.83080	−	2.58212i	0.200415	−	0.107124i
$582$	8.23926	+	20.7750i	0.341528	+	0.861153i
$583$	−4.75052	+	0.944937i	−0.196746	+	0.0391353i
$584$	1.98667	+	4.16066i	0.0822091	+	0.172169i
$585$	−0.981377	+	4.93371i	−0.0405749	+	0.203984i
$586$	−24.7293	−	17.0705i	−1.02156	−	0.705174i
$587$	−5.14906	+	6.27414i	−0.212524	+	0.258962i	−0.868351	−	0.495950i	$-0.834820\pi$
$587$	−5.14906	+	6.27414i	−0.212524	+	0.258962i	0.655827	+	0.754911i	$0.272320\pi$
$588$	−32.6275	−	10.9861i	−1.34554	−	0.453058i
$589$	−2.71509	+	5.07958i	−0.111873	+	0.209301i
$590$	−10.9791	+	8.73569i	−0.452003	+	0.359642i
$591$	3.54291	−	1.46752i	0.145736	−	0.0603658i
$592$	−34.4438	+	1.29729i	−1.41563	+	0.0533184i
$593$	−17.6061	−	7.29270i	−0.722997	−	0.299475i	−0.00932631	−	0.999957i	$-0.502969\pi$
$593$	−17.6061	−	7.29270i	−0.722997	−	0.299475i	−0.713671	+	0.700481i	$0.752969\pi$
$594$	−3.96706	+	1.13813i	−0.162770	+	0.0466982i
$595$	0.133392	+	0.439735i	0.00546855	+	0.0180274i
$596$	−14.7790	+	25.7441i	−0.605372	+	1.05452i
$597$	15.8384	−	1.55994i	0.648221	−	0.0638442i
$598$	0.206777	−	0.963132i	0.00845573	−	0.0393854i
$599$	−1.86095	−	2.78511i	−0.0760364	−	0.113797i	0.791502	−	0.611166i	$-0.209299\pi$
$599$	−1.86095	−	2.78511i	−0.0760364	−	0.113797i	−0.867539	+	0.497370i	$0.834299\pi$
$600$	−0.328424	+	7.22961i	−0.0134078	+	0.295147i
$601$	31.1510	+	20.8144i	1.27068	+	0.849039i	0.993726	−	0.111845i	$-0.0356762\pi$
$601$	31.1510	+	20.8144i	1.27068	+	0.849039i	0.276951	+	0.960884i	$0.410676\pi$
$602$	−3.47906	−	0.0526496i	−0.141796	−	0.00214584i
$603$	−2.43704	+	8.03383i	−0.0992438	+	0.327163i
$604$	−8.56956	−	0.259430i	−0.348690	−	0.0105561i
$605$	5.14095	−	4.21907i	0.209009	−	0.171530i
$606$	24.4655	−	28.9080i	0.993843	−	1.17431i
$607$	−24.2798	−	24.2798i	−0.985487	−	0.985487i	0.0144095	−	0.999896i	$-0.495413\pi$
$607$	−24.2798	−	24.2798i	−0.985487	−	0.985487i	−0.999896	+	0.0144095i	$0.995413\pi$
$608$	−10.6543	+	3.49573i	−0.432088	+	0.141771i
$609$	−0.0494848	+	0.0494848i	−0.00200522	+	0.00200522i
$610$	1.27166	+	15.2781i	0.0514881	+	0.618594i
$611$	−5.17459	−	6.30525i	−0.209341	−	0.255083i
$612$	−5.83947	+	2.21424i	−0.236046	+	0.0895053i
$613$	33.5943	+	10.1907i	1.35686	+	0.411600i	0.883154	−	0.469082i	$-0.155415\pi$
$613$	33.5943	+	10.1907i	1.35686	+	0.411600i	0.473708	+	0.880682i	$0.342915\pi$
$614$	−16.3473	−	16.8496i	−0.659721	−	0.679996i
$615$	6.20977	−	9.29357i	0.250402	−	0.374753i
$616$	0.463012	+	3.04392i	0.0186553	+	0.122643i
$617$	0.148112	−	0.0989654i	0.00596277	−	0.00398420i	−0.552585	−	0.833456i	$-0.686359\pi$
$617$	0.148112	−	0.0989654i	0.00596277	−	0.00398420i	0.558548	+	0.829472i	$0.311359\pi$
$618$	30.3704	+	46.9761i	1.22168	+	1.88966i
$619$	1.11799	+	11.3512i	0.0449360	+	0.456243i	0.991154	+	0.132714i	$0.0423692\pi$
$619$	1.11799	+	11.3512i	0.0449360	+	0.456243i	−0.946218	+	0.323529i	$0.895131\pi$
$620$	3.54906	+	4.60173i	0.142534	+	0.184810i
$621$	−0.657658	+	0.199498i	−0.0263909	+	0.00800559i
$622$	6.02259	+	3.33728i	0.241484	+	0.133813i
$623$	1.10581	−	2.66966i	0.0443034	−	0.106958i
$624$	−3.68783	+	14.0392i	−0.147631	+	0.562016i
$625$	−0.382683	−	0.923880i	−0.0153073	−	0.0369552i
$626$	−0.756082	+	6.64429i	−0.0302191	+	0.265559i
$627$	9.32858	+	4.98623i	0.372547	+	0.199131i
$628$	1.27858	+	18.7985i	0.0510209	+	0.750141i
$629$	5.86424	+	4.81265i	0.233822	+	0.191893i
$630$	−0.471869	−	2.57531i	−0.0187997	−	0.102603i
$631$	21.6416	+	4.30477i	0.861537	+	0.171370i	0.606035	−	0.795438i	$-0.292759\pi$
$631$	21.6416	+	4.30477i	0.861537	+	0.171370i	0.255502	+	0.966808i	$0.417759\pi$
$632$	−13.6780	+	23.0126i	−0.544083	+	0.915392i
$633$	−10.0403	−	50.4762i	−0.399068	−	2.00625i
$634$	7.76120	+	3.35326i	0.308236	+	0.133175i
$635$	4.50154	+	8.42179i	0.178638	+	0.334209i
$636$	11.7214	−	1.96485i	0.464784	−	0.0779115i
$637$	9.49542	+	0.935217i	0.376222	+	0.0370547i
$638$	−0.147197	−	0.0470955i	−0.00582759	−	0.00186453i
$639$	−18.6249			−0.736789
$640$	−1.19616	+	11.2503i	−0.0472825	+	0.444707i
$641$	−24.1822			−0.955138			−0.477569	−	0.878594i	$-0.658482\pi$
$641$	−24.1822			−0.955138			−0.477569	+	0.878594i	$0.658482\pi$
$642$	−50.6258	−	16.1977i	−1.99804	−	0.639271i
$643$	17.1017	+	1.68437i	0.674424	+	0.0664250i	0.429431	−	0.903100i	$-0.358714\pi$
$643$	17.1017	+	1.68437i	0.674424	+	0.0664250i	0.244993	+	0.969525i	$0.421214\pi$
$644$	0.0847626	+	0.505655i	0.00334012	+	0.0199256i
$645$	5.68541	+	10.6367i	0.223863	+	0.418818i
$646$	2.26552	+	0.978832i	0.0891359	+	0.0385116i
$647$	1.77732	+	8.93521i	0.0698738	+	0.351279i	0.999867	−	0.0162969i	$-0.00518770\pi$
$647$	1.77732	+	8.93521i	0.0698738	+	0.351279i	−0.929993	+	0.367576i	$0.880188\pi$
$648$	−19.3529	+	4.92365i	−0.760256	+	0.193419i
$649$	20.2930	+	4.03654i	0.796571	+	0.158448i
$650$	−0.361483	−	1.97287i	−0.0141785	−	0.0773822i
$651$	−2.99977	−	2.46185i	−0.117570	−	0.0964875i
$652$	−44.7318	+	3.04244i	−1.75183	+	0.119151i
$653$	20.9831	+	11.2157i	0.821133	+	0.438905i	0.827766	−	0.561073i	$-0.189611\pi$
$653$	20.9831	+	11.2157i	0.821133	+	0.438905i	−0.00663333	+	0.999978i	$0.502111\pi$
$654$	2.55432	−	22.4469i	0.0998820	−	0.877742i
$655$	0.811320	+	1.95870i	0.0317009	+	0.0765327i
$656$	10.5688	−	13.9148i	0.412643	−	0.543282i
$657$	−2.21260	+	5.34169i	−0.0863217	+	0.208399i
$658$	3.71339	+	2.05769i	0.144763	+	0.0802171i
$659$	14.1054	−	4.27882i	0.549467	−	0.166679i	−0.00333072	−	0.999994i	$-0.501060\pi$
$659$	14.1054	−	4.27882i	0.549467	−	0.166679i	0.552798	+	0.833315i	$0.313560\pi$
$660$	8.45101	−	6.51779i	0.328955	−	0.253705i
$661$	−0.141628	−	1.43797i	−0.00550869	−	0.0559307i	0.992037	−	0.125944i	$-0.0401959\pi$
$661$	−0.141628	−	1.43797i	−0.00550869	−	0.0559307i	−0.997546	+	0.0700131i	$0.977696\pi$
$662$	−9.96727	−	15.4171i	−0.387389	−	0.599202i
$663$	2.65634	−	1.77491i	0.103164	−	0.0689319i
$664$	−23.9060	−	17.5935i	−0.927734	−	0.682761i
$665$	−0.574817	+	0.860274i	−0.0222904	+	0.0333600i
$666$	−30.0977	−	31.0226i	−1.16626	−	1.20210i
$667$	−0.0246274	−	0.00747064i	−0.000953576	−	0.000289264i
$668$	−10.3981	−	27.4223i	−0.402316	−	1.06100i
$669$	25.5559	+	31.1399i	0.988047	+	1.20394i
$670$	−0.277656	−	3.33585i	−0.0107268	−	0.128875i
$671$	15.9866	−	15.9866i	0.617157	−	0.617157i
$672$	−0.909586	−	7.49999i	−0.0350880	−	0.289318i
$673$	18.7301	+	18.7301i	0.721991	+	0.721991i	0.969011	−	0.247019i	$-0.0794512\pi$
$673$	18.7301	+	18.7301i	0.721991	+	0.721991i	−0.247019	+	0.969011i	$0.579451\pi$
$674$	−26.6604	+	31.5015i	−1.02692	+	1.21339i
$675$	−1.08168	+	0.887710i	−0.0416338	+	0.0341680i
$676$	−0.665020	+	21.9671i	−0.0255777	+	0.844887i
$677$	1.01061	−	3.33155i	0.0388410	−	0.128042i	−0.935376	−	0.353655i	$-0.884939\pi$
$677$	1.01061	−	3.33155i	0.0388410	−	0.128042i	0.974217	+	0.225613i	$0.0724386\pi$
$678$	41.1311	+	0.622449i	1.57963	+	0.0239050i
$679$	2.68050	+	1.79105i	0.102868	+	0.0687342i
$680$	1.83884	−	1.67903i	0.0705163	−	0.0643879i
$681$	25.6294	+	38.3571i	0.982121	+	1.46985i
$682$	1.79891	−	8.37902i	0.0688838	−	0.320849i
$683$	29.6663	−	2.92187i	1.13515	−	0.111802i	0.487061	−	0.873368i	$-0.338069\pi$
$683$	29.6663	−	2.92187i	1.13515	−	0.111802i	0.648088	+	0.761565i	$0.275569\pi$
$684$	−12.1948	−	7.00071i	−0.466279	−	0.267679i
$685$	−4.44438	−	14.6511i	−0.169811	−	0.559791i
$686$	−9.74028	+	2.79445i	−0.371886	+	0.106693i
$687$	−37.7715	−	15.6455i	−1.44107	−	0.596911i
$688$	7.86586	+	17.1355i	0.299883	+	0.653284i
$689$	−3.04312	+	1.26050i	−0.115934	+	0.0480212i
$690$	1.39069	−	1.10652i	0.0529428	−	0.0421247i
$691$	6.61397	−	12.3739i	0.251607	−	0.470724i	−0.724132	−	0.689662i	$-0.757759\pi$
$691$	6.61397	−	12.3739i	0.251607	−	0.470724i	0.975739	+	0.218938i	$0.0702592\pi$
$692$	−3.88100	+	11.5262i	−0.147534	+	0.438159i
$693$	−2.44941	+	2.98461i	−0.0930453	+	0.113376i
$694$	−23.8199	−	16.4427i	−0.904192	−	0.624156i
$695$	−2.65097	+	13.3273i	−0.100557	+	0.505534i
$696$	0.357523	+	0.126437i	0.0135519	+	0.00479258i
$697$	−3.77190	+	0.750278i	−0.142871	+	0.0284188i
$698$	−5.09587	−	12.8491i	−0.192882	−	0.486345i
$699$	−2.02276	+	1.08119i	−0.0765079	+	0.0408943i
$700$	0.553442	+	0.885143i	0.0209182	+	0.0334553i
$701$	2.76346	−	28.0579i	0.104375	−	1.05973i	−0.790211	−	0.612835i	$-0.790029\pi$
$701$	2.76346	−	28.0579i	0.104375	−	1.05973i	0.894585	−	0.446897i	$-0.147471\pi$
$702$	−2.49494	+	1.28542i	−0.0941653	+	0.0485149i
$703$			17.0809i			0.644217i
$704$	13.8036	−	9.37143i	0.520245	−	0.353199i
$705$		−	14.7157i		−	0.554226i
$706$	−22.5180	−	43.7065i	−0.847477	−	1.64491i
$707$	0.535449	−	5.43651i	0.0201376	−	0.204461i
$708$	−49.4715	−	11.4069i	−1.85925	−	0.428696i
$709$	−8.63542	+	4.61573i	−0.324310	+	0.173347i	−0.625515	−	0.780212i	$-0.715111\pi$
$709$	−8.63542	+	4.61573i	−0.324310	+	0.173347i	0.301205	+	0.953559i	$0.402611\pi$
$710$	6.90305	−	2.73771i	0.259067	−	0.102744i
$711$	−32.9257	+	6.54933i	−1.23481	+	0.245619i
$712$	−15.6366	+	0.826041i	−0.586006	+	0.0309572i
$713$	0.278410	−	1.39966i	0.0104266	−	0.0524178i
$714$	−0.944614	+	1.36843i	−0.0353513	+	0.0512121i
$715$	−1.87641	+	2.28642i	−0.0701739	+	0.0855071i
$716$	12.4832	−	6.19427i	0.466519	−	0.231491i
$717$	−29.0780	+	54.4011i	−1.08594	+	2.03165i
$718$	8.06767	+	10.1395i	0.301083	+	0.378404i
$719$	26.8291	−	11.1130i	1.00056	−	0.414445i	0.178557	−	0.983930i	$-0.442857\pi$
$719$	26.8291	−	11.1130i	1.00056	−	0.414445i	0.822002	+	0.569485i	$0.192857\pi$
$720$	−11.4915	+	8.32058i	−0.428262	+	0.310090i
$721$	7.45475	+	3.08786i	0.277629	+	0.114998i
$722$	−5.87761	−	20.4869i	−0.218742	−	0.762443i
$723$	0.167670	+	0.552735i	0.00623573	+	0.0205564i
$724$	−23.2129	+	6.28115i	−0.862702	+	0.233437i
$725$	−0.0521476	+	0.00513609i	−0.00193671	+	0.000190750i
$726$	23.5291	+	5.05151i	0.873247	+	0.187479i
$727$	18.6622	+	27.9300i	0.692144	+	1.03587i	0.996523	+	0.0833162i	$0.0265512\pi$
$727$	18.6622	+	27.9300i	0.692144	+	1.03587i	−0.304379	+	0.952551i	$0.598449\pi$
$728$	0.712655	+	1.96880i	0.0264127	+	0.0729684i
$729$	−29.7526	−	19.8800i	−1.10195	−	0.736297i
$730$	0.0348831	−	2.30506i	0.00129108	−	0.0853139i
$731$	1.20462	−	3.97109i	0.0445544	−	0.146876i
$732$	−40.3962	+	38.0222i	−1.49309	+	1.40534i
$733$	3.29083	−	2.70071i	0.121550	−	0.0997532i	−0.571655	−	0.820494i	$-0.693698\pi$
$733$	3.29083	−	2.70071i	0.121550	−	0.0997532i	0.693204	+	0.720741i	$0.256198\pi$
$734$	−22.2549	−	18.8349i	−0.821444	−	0.695207i
$735$	12.1719	+	12.1719i	0.448969	+	0.448969i
$736$	2.27473	−	1.59515i	0.0838477	−	0.0587980i
$737$	−3.49054	+	3.49054i	−0.128576	+	0.128576i
$738$	21.8364	−	1.81754i	0.803810	−	0.0669044i
$739$	17.6147	+	21.4636i	0.647969	+	0.789553i	0.988587	−	0.150649i	$-0.0481364\pi$
$739$	17.6147	+	21.4636i	0.647969	+	0.789553i	−0.340618	+	0.940202i	$0.610636\pi$
$740$	15.7154	+	7.07398i	0.577708	+	0.260045i
$741$	6.88346	+	2.08807i	0.252870	+	0.0767073i
$742$	1.23045	−	1.19376i	0.0451711	−	0.0438243i
$743$	7.95397	−	11.9040i	0.291803	−	0.436714i	−0.656384	−	0.754427i	$-0.727915\pi$
$743$	7.95397	−	11.9040i	0.291803	−	0.436714i	0.948187	+	0.317713i	$0.102915\pi$
$744$	−5.03419	+	20.4171i	−0.184562	+	0.748526i
$745$	12.3409	−	8.24594i	0.452137	−	0.302108i
$746$	−23.2665	+	15.0420i	−0.851847	+	0.550726i
$747$	−3.64837	−	37.0426i	−0.133487	−	1.35532i
$748$	−3.64185	−	0.470345i	−0.133159	−	0.0171975i
$749$	−7.33714	+	2.22570i	−0.268093	+	0.0813252i
$750$	1.75386	−	3.16508i	0.0640418	−	0.115573i
$751$	−15.5402	+	37.5173i	−0.567070	+	1.36903i	0.336944	+	0.941525i	$0.390607\pi$
$751$	−15.5402	+	37.5173i	−0.567070	+	1.36903i	−0.904014	+	0.427503i	$0.859393\pi$
$752$	1.39161	−	22.9630i	0.0507469	−	0.837373i
$753$	−18.6819	−	45.1022i	−0.680808	−	1.64362i
$754$	−0.104425	−	0.0118830i	−0.00380294	−	0.000432752i
$755$	3.78057	+	2.02076i	0.137589	+	0.0735428i
$756$	0.960446	−	1.10063i	0.0349311	−	0.0400295i
$757$	15.9080	+	13.0553i	0.578185	+	0.474505i	0.877452	−	0.479665i	$-0.159242\pi$
$757$	15.9080	+	13.0553i	0.578185	+	0.474505i	−0.299266	+	0.954170i	$0.596742\pi$
$758$	17.5027	−	3.20697i	0.635726	−	0.116482i
$759$	−2.57046	−	0.511296i	−0.0933018	−	0.0185589i
$760$	5.54888	+	0.802178i	0.201279	+	0.0290980i
$761$	−0.799965	−	4.02170i	−0.0289987	−	0.145786i	0.963573	−	0.267444i	$-0.0861790\pi$
$761$	−0.799965	−	4.02170i	−0.0289987	−	0.145786i	−0.992572	+	0.121658i	$0.961179\pi$
$762$	−13.7051	+	31.7206i	−0.496482	+	1.14912i
$763$	−1.53618	−	2.87399i	−0.0556135	−	0.104046i
$764$	21.7317	−	30.4847i	0.786225	−	1.10290i
$765$	3.10755	+	0.306067i	0.112354	+	0.0110659i
$766$	−5.88409	+	18.3907i	−0.212601	+	0.664484i
$767$	14.0705			0.508056
$768$	−34.5510	+	21.9597i	−1.24675	+	0.792403i
$769$	−8.93944			−0.322365			−0.161182	−	0.986925i	$-0.551531\pi$
$769$	−8.93944			−0.322365			−0.161182	+	0.986925i	$0.551531\pi$
$770$	0.469124	−	1.46625i	0.0169061	−	0.0528399i
$771$	31.8030	+	3.13233i	1.14536	+	0.112808i
$772$	18.8243	−	26.4063i	0.677502	−	0.950384i
$773$	−17.1679	−	32.1190i	−0.617488	−	1.15524i	−0.975183	−	0.221400i	$-0.928937\pi$
$773$	−17.1679	−	32.1190i	−0.617488	−	1.15524i	0.357695	−	0.933838i	$-0.383563\pi$
$774$	−9.37764	+	21.7047i	−0.337072	+	0.780160i
$775$	−0.566869	−	2.84984i	−0.0203625	−	0.102369i
$776$	2.49948	−	17.2896i	0.0897260	−	0.620659i
$777$	−11.2873	−	2.24518i	−0.404928	−	0.0805452i
$778$	37.4753	−	6.86651i	1.34356	−	0.246176i
$779$	−6.69354	−	5.49325i	−0.239821	−	0.196816i
$780$	4.77191	−	5.46840i	0.170862	−	0.195800i
$781$	−9.65814	−	5.16238i	−0.345595	−	0.184725i
$782$	−0.607564	−	0.0691373i	−0.0217264	−	0.00247234i
$783$	0.0280597	+	0.0677420i	0.00100277	+	0.00242090i
$784$	17.8425	+	20.1446i	0.637232	+	0.719450i
$785$	3.60524	−	8.70383i	0.128677	−	0.310653i
$786$	−3.71832	+	6.71023i	−0.132628	+	0.239346i
$787$	32.6415	−	9.90169i	1.16354	−	0.352957i	0.351293	−	0.936266i	$-0.385742\pi$
$787$	32.6415	−	9.90169i	1.16354	−	0.352957i	0.812251	+	0.583309i	$0.198242\pi$
$788$	−2.97280	−	0.383937i	−0.105902	−	0.0136772i
$789$	−1.53633	−	15.5986i	−0.0546946	−	0.555324i
$790$	11.2407	−	7.26723i	0.399928	−	0.258557i
$791$	4.93370	−	3.29660i	0.175422	−	0.117213i
$792$	20.3139	+	5.00875i	0.721822	+	0.177978i
$793$	8.54175	−	12.7836i	0.303326	−	0.453960i
$794$	35.7565	−	34.6904i	1.26895	−	1.23112i
$795$	−5.68659	−	1.72501i	−0.201683	−	0.0611798i
$796$	−11.3437	−	5.10616i	−0.402067	−	0.180983i
$797$	−35.0406	−	42.6971i	−1.24120	−	1.51241i	−0.780911	−	0.624642i	$-0.785245\pi$
$797$	−35.0406	−	42.6971i	−1.24120	−	1.51241i	−0.460292	−	0.887768i	$-0.652255\pi$
$798$	−3.73098	+	0.310545i	−0.132075	+	0.0109932i
$799$	−3.58028	+	3.58028i	−0.126661	+	0.126661i
$800$	3.03610	−	4.77306i	0.107342	−	0.168753i
$801$	−13.8846	−	13.8846i	−0.490589	−	0.490589i
$802$	−21.7574	−	18.4138i	−0.768280	−	0.650213i
$803$	−2.62796	+	2.15671i	−0.0927386	+	0.0761086i
$804$	8.82016	−	8.30182i	0.311063	−	0.292783i
$805$	0.0744159	−	0.245316i	0.00262282	−	0.00864627i
$806$	0.0881857	−	5.82727i	0.00310621	−	0.205257i
$807$	−66.2928	−	44.2954i	−2.33362	−	1.55927i
$808$	−27.8347	+	10.0755i	−0.979221	+	0.354453i
$809$	−0.282331	−	0.422538i	−0.00992622	−	0.0148556i	0.826473	−	0.562976i	$-0.190344\pi$
$809$	−0.282331	−	0.422538i	−0.00992622	−	0.0148556i	−0.836400	+	0.548120i	$0.815344\pi$
$810$	9.76228	+	2.09588i	0.343011	+	0.0736418i
$811$	43.2498	−	4.25973i	1.51871	−	0.149580i	0.695998	−	0.718044i	$-0.254962\pi$
$811$	43.2498	−	4.25973i	1.51871	−	0.149580i	0.822708	+	0.568464i	$0.192462\pi$
$812$	0.0528026	−	0.0142878i	0.00185301	−	0.000501402i
$813$	19.1823	+	63.2356i	0.672753	+	2.21777i
$814$	−7.00873	−	24.4295i	−0.245656	−	0.856253i
$815$	20.7112	+	8.57884i	0.725480	+	0.300504i
$816$	8.89718	+	1.42399i	0.311464	+	0.0498495i
$817$	8.63226	−	3.57560i	0.302005	−	0.125094i
$818$	−1.00155	−	1.25875i	−0.0350182	−	0.0440113i
$819$	−1.23773	+	2.31563i	−0.0432497	+	0.0809146i
$820$	−7.82620	+	3.88343i	−0.273303	+	0.135615i
$821$	−13.0265	+	15.8729i	−0.454629	+	0.553967i	−0.948997	−	0.315286i	$-0.897900\pi$
$821$	−13.0265	+	15.8729i	−0.454629	+	0.553967i	0.494368	+	0.869253i	$0.335400\pi$
$822$	31.4727	−	45.5934i	1.09774	−	1.59025i
$823$	9.05946	−	45.5450i	0.315793	−	1.58760i	−0.418144	−	0.908381i	$-0.637319\pi$
$823$	9.05946	−	45.5450i	0.315793	−	1.58760i	0.733937	−	0.679217i	$-0.237681\pi$
$824$	−2.30663	−	43.6635i	−0.0803553	−	1.52109i
$825$	−5.23369	+	1.04105i	−0.182214	+	0.0362446i
$826$	−6.80753	+	2.69983i	−0.236864	+	0.0939390i
$827$	5.79955	−	3.09993i	0.201670	−	0.107795i	−0.367470	−	0.930035i	$-0.619776\pi$
$827$	5.79955	−	3.09993i	0.201670	−	0.107795i	0.569141	+	0.822240i	$0.307276\pi$
$828$	3.39494	+	0.782785i	0.117982	+	0.0272037i
$829$	−4.77543	+	48.4858i	−0.165858	+	1.68398i	0.447585	+	0.894241i	$0.352284\pi$
$829$	−4.77543	+	48.4858i	−0.165858	+	1.68398i	−0.613443	+	0.789739i	$0.710216\pi$
$830$	6.79718	+	13.1930i	0.235934	+	0.457936i
$831$			17.2686i			0.599039i
$832$	7.96340	−	8.08185i	0.276081	−	0.280188i
$833$		−	5.92277i		−	0.205212i
$834$	−43.7099	+	22.5198i	−1.51355	+	0.779797i
$835$	−1.43730	+	14.5932i	−0.0497398	+	0.505017i
$836$	−4.38331	−	7.01040i	−0.151600	−	0.242460i
$837$	−3.58582	+	1.91666i	−0.123944	+	0.0662495i
$838$	−9.69941	−	24.4568i	−0.335061	−	0.844845i
$839$	23.6098	−	4.69628i	0.815100	−	0.162134i	0.230100	−	0.973167i	$-0.426095\pi$
$839$	23.6098	−	4.69628i	0.815100	−	0.162134i	0.585000	+	0.811033i	$0.301095\pi$
$840$	−1.25946	+	3.56133i	−0.0434553	+	0.122878i
$841$	5.65708	−	28.4401i	0.195072	−	0.980692i
$842$	28.7198	+	19.8251i	0.989751	+	0.683217i
$843$	−23.8496	+	29.0608i	−0.821424	+	1.00091i
$844$	−12.8370	+	38.1245i	−0.441868	+	1.31230i
$845$	5.17997	−	9.69105i	0.178196	−	0.333382i
$846$	22.5747	−	17.9619i	0.776134	−	0.617542i
$847$	3.20710	−	1.32842i	0.110197	−	0.0456452i
$848$	−8.71045	−	3.22953i	−0.299118	−	0.110903i
$849$	−42.2686	−	17.5082i	−1.45065	−	0.600881i
$850$	−1.19676	+	0.343346i	−0.0410485	+	0.0117767i
$851$	−1.22853	−	4.04992i	−0.0421134	−	0.138829i
$852$	23.3045	+	13.3785i	0.798399	+	0.458340i
$853$	−42.7674	+	4.21222i	−1.46433	+	0.144224i	−0.798550	−	0.601928i	$-0.794399\pi$
$853$	−42.7674	+	4.21222i	−1.46433	+	0.144224i	−0.665776	+	0.746152i	$0.731899\pi$
$854$	−1.67973	+	7.82391i	−0.0574791	+	0.267729i
$855$	3.90605	+	5.84581i	0.133584	+	0.199923i
$856$	28.0152	+	30.6817i	0.957541	+	1.04868i
$857$	−22.2229	−	14.8489i	−0.759120	−	0.507228i	0.114746	−	0.993395i	$-0.463395\pi$
$857$	−22.2229	−	14.8489i	−0.759120	−	0.507228i	−0.873866	+	0.486167i	$0.838395\pi$
$858$	−10.7017	−	0.161952i	−0.365350	−	0.00552894i
$859$	−8.38169	+	27.6307i	−0.285979	+	0.942748i	0.689802	+	0.723998i	$0.257698\pi$
$859$	−8.38169	+	27.6307i	−0.285979	+	0.942748i	−0.975781	+	0.218750i	$0.929802\pi$
$860$	0.285267	−	9.42299i	0.00972752	−	0.321321i
$861$	4.50983	−	3.70112i	0.153695	−	0.126134i
$862$	−5.41720	+	6.40087i	−0.184511	+	0.218014i
$863$	13.4851	+	13.4851i	0.459038	+	0.459038i	0.898340	−	0.439301i	$-0.144774\pi$
$863$	13.4851	+	13.4851i	0.459038	+	0.459038i	−0.439301	+	0.898340i	$0.644774\pi$
$864$	−7.62463	−	2.12669i	−0.259395	−	0.0723514i
$865$	4.29993	−	4.29993i	0.146202	−	0.146202i
$866$	3.11997	+	37.4843i	0.106021	+	1.27377i
$867$	26.3366	+	32.0912i	0.894436	+	1.08987i
$868$	1.07546	+	2.83625i	0.0365036	+	0.0962685i
$869$	−18.8893	−	5.73001i	−0.640776	−	0.194377i
$870$	−0.132031	−	0.136088i	−0.00447627	−	0.00461383i
$871$	−1.86502	+	2.79120i	−0.0631937	+	0.0945761i
$872$	−10.4669	+	14.2224i	−0.354455	+	0.481633i
$873$	18.2148	−	12.1707i	0.616476	−	0.411916i
$874$	−0.747497	−	1.15621i	−0.0252845	−	0.0391093i
$875$	−0.0511612	−	0.519449i	−0.00172956	−	0.0175606i
$876$	6.60553	−	5.09448i	0.223180	−	0.172126i
$877$	25.0772	−	7.60708i	0.846796	−	0.256873i	0.163073	−	0.986614i	$-0.447860\pi$
$877$	25.0772	−	7.60708i	0.846796	−	0.256873i	0.683723	+	0.729741i	$0.260360\pi$
$878$	26.2289	+	14.5341i	0.885181	+	0.490502i
$879$	−20.8052	+	50.2282i	−0.701741	+	1.69415i
$880$	−8.26530	+	1.12956i	−0.278623	+	0.0380773i
$881$	−18.8188	−	45.4326i	−0.634022	−	1.53066i	−0.834524	−	0.550971i	$-0.814257\pi$
$881$	−18.8188	−	45.4326i	−0.634022	−	1.53066i	0.200502	−	0.979693i	$-0.435743\pi$
$882$	−3.81545	+	33.5294i	−0.128473	+	1.12899i
$883$	−22.4941	−	12.0233i	−0.756987	−	0.404618i	0.0472835	−	0.998882i	$-0.484944\pi$
$883$	−22.4941	−	12.0233i	−0.756987	−	0.404618i	−0.804270	+	0.594264i	$0.797444\pi$
$884$	−2.49143	+	0.169455i	−0.0837958	+	0.00569938i
$885$	19.6227	+	16.1039i	0.659610	+	0.541328i
$886$	−6.88212	−	37.5605i	−0.231209	−	1.26187i
$887$	20.6915	+	4.11579i	0.694752	+	0.138195i	0.529820	−	0.848110i	$-0.322260\pi$
$887$	20.6915	+	4.11579i	0.694752	+	0.138195i	0.164932	+	0.986305i	$0.447260\pi$
$888$	15.3759	+	60.4368i	0.515982	+	2.02813i
$889$	0.972409	+	4.88863i	0.0326136	+	0.163959i
$890$	7.18707	+	3.10521i	0.240911	+	0.104087i
$891$	−6.94104	−	12.9858i	−0.232534	−	0.435040i
$892$	−5.20568	−	31.0547i	−0.174299	−	1.03979i
$893$	−11.3454	−	1.11742i	−0.379659	−	0.0373931i
$894$	51.1529	+	16.3663i	1.71081	+	0.547372i
$895$	−6.96777			−0.232907
$896$	−2.30208	+	5.43813i	−0.0769073	+	0.181675i
$897$	−1.78227			−0.0595083
$898$	21.0009	+	6.71922i	0.700810	+	0.224223i
$899$	−0.151524	−	0.0149238i	−0.00505360	−	0.000497736i
$900$	6.99615	−	1.17276i	0.233205	−	0.0390920i
$901$	0.963839	+	1.80322i	0.0321101	+	0.0600738i
$902$	11.8273	+	5.11004i	0.393806	+	0.170146i
$903$	1.22814	+	6.17430i	0.0408701	+	0.205468i
$904$	−27.6401	−	16.4285i	−0.919296	−	0.546403i
$905$	11.7928	+	2.34574i	0.392007	+	0.0779750i
$906$	2.79563	+	15.2577i	0.0928786	+	0.506903i
$907$	−7.10180	−	5.82829i	−0.235811	−	0.193525i	0.509065	−	0.860728i	$-0.329991\pi$
$907$	−7.10180	−	5.82829i	−0.235811	−	0.193525i	−0.744876	+	0.667203i	$0.767491\pi$
$908$	−2.44690	−	35.9758i	−0.0812031	−	1.19390i
$909$	−32.7382	−	17.4989i	−1.08586	−	0.580402i
$910$	0.118368	−	1.04019i	0.00392385	−	0.0344820i
$911$	−20.9753	−	50.6388i	−0.694942	−	1.67774i	−0.734577	−	0.678525i	$-0.762620\pi$
$911$	−20.9753	−	50.6388i	−0.694942	−	1.67774i	0.0396351	−	0.999214i	$-0.487380\pi$
$912$	10.2301	+	17.5194i	0.338752	+	0.580124i
$913$	8.37542	−	20.2201i	0.277186	−	0.669186i
$914$	−41.7894	−	23.1566i	−1.38227	−	0.765953i
$915$	26.5434	−	8.05186i	0.877499	−	0.266186i
$916$	19.5163	+	25.3050i	0.644837	+	0.836099i
$917$	0.108466	+	1.10127i	0.00358186	+	0.0363672i
$918$	0.945878	+	1.46306i	0.0312186	+	0.0482881i
$919$	−39.5904	+	26.4534i	−1.30597	+	0.872618i	−0.996920	−	0.0784292i	$-0.975010\pi$
$919$	−39.5904	+	26.4534i	−1.30597	+	0.872618i	−0.309045	+	0.951047i	$0.600010\pi$
$920$	−1.37335	+	0.208901i	−0.0452780	+	0.00688725i
$921$	−23.5979	+	35.3168i	−0.777577	+	1.16373i
$922$	24.2629	+	25.0086i	0.799056	+	0.823613i
$923$	−7.12664	−	2.16184i	−0.234576	−	0.0711579i
$924$	5.20873	−	1.97507i	0.171354	−	0.0649751i
$925$	−5.46660	−	6.66107i	−0.179741	−	0.219015i
$926$	2.18929	+	26.3028i	0.0719446	+	0.864365i
$927$	38.7713	−	38.7713i	1.27342	−	1.27342i
$928$	−0.193157	−	0.224843i	−0.00634068	−	0.00738084i
$929$	1.45174	+	1.45174i	0.0476299	+	0.0476299i	0.730521	−	0.682891i	$-0.239277\pi$
$929$	1.45174	+	1.45174i	0.0476299	+	0.0476299i	−0.682891	+	0.730521i	$0.739277\pi$
$930$	6.79240	−	8.02578i	0.222732	−	0.263176i
$931$	10.3085	−	8.45994i	0.337846	−	0.277263i
$932$	1.79196	+	0.0542489i	0.0586977	+	0.00177698i
$933$	3.61624	−	11.9211i	0.118390	−	0.390281i
$934$	−16.8497	−	0.254991i	−0.551338	−	0.00834355i
$935$	1.52662	+	1.02005i	0.0499258	+	0.0333594i
$936$	14.2134	+	0.645680i	0.464579	+	0.0211047i
$937$	−9.06512	−	13.5669i	−0.296145	−	0.443212i	0.653322	−	0.757080i	$-0.273375\pi$
$937$	−9.06512	−	13.5669i	−0.296145	−	0.443212i	−0.949466	+	0.313869i	$0.898375\pi$
$938$	0.366754	−	1.70828i	0.0119750	−	0.0557774i
$939$	12.0406	−	1.18590i	0.392930	−	0.0387003i
$940$	−5.72674	+	9.97562i	−0.186786	+	0.325369i
$941$	5.35444	+	17.6512i	0.174550	+	0.575413i	0.999941	+	0.0108522i	$0.00345444\pi$
$941$	5.35444	+	17.6512i	0.174550	+	0.575413i	−0.825391	+	0.564561i	$0.809046\pi$
$942$	32.7681	−	9.40106i	1.06764	−	0.306303i
$943$	1.98215	+	0.821035i	0.0645478	+	0.0267366i
$944$	29.0971	+	26.9849i	0.947031	+	0.878282i
$945$	−0.674787	+	0.279506i	−0.0219508	+	0.00909232i
$946$	−10.8789	+	8.65596i	−0.353704	+	0.281430i
$947$	−4.89051	+	9.14950i	−0.158920	+	0.297319i	−0.948762	−	0.315992i	$-0.897663\pi$
$947$	−4.89051	+	9.14950i	−0.158920	+	0.297319i	0.789842	+	0.613311i	$0.210163\pi$
$948$	45.9030	+	15.4561i	1.49086	+	0.501991i
$949$	−1.46665	+	1.78712i	−0.0476096	+	0.0580125i
$950$	−2.30701	−	1.59251i	−0.0748493	−	0.0516678i
$951$	2.98423	−	15.0027i	0.0967702	−	0.486497i
$952$	1.17288	−	0.560037i	0.0380132	−	0.0181509i
$953$	−46.2684	+	9.20335i	−1.49878	+	0.298126i	−0.875249	−	0.483673i	$-0.839302\pi$
$953$	−46.2684	+	9.20335i	−1.49878	+	0.298126i	−0.623531	+	0.781799i	$0.714302\pi$
$954$	−4.29475	−	10.8291i	−0.139048	−	0.350604i
$955$	−16.5086	+	8.82401i	−0.534205	+	0.285538i
$956$	40.8823	−	25.5620i	1.32223	−	0.826733i
$957$	−0.0274073	+	0.278271i	−0.000885953	+	0.00899523i
$958$	25.6141	−	13.1966i	0.827553	−	0.426364i
$959$		−	7.99145i		−	0.258057i
$960$	20.3556	−	2.15668i	0.656973	−	0.0696067i
$961$			22.5571i			0.727647i
$962$	−7.91571	−	15.3640i	−0.255213	−	0.495357i
$963$	−5.10684	+	51.8506i	−0.164565	+	1.67086i
$964$	0.101440	−	0.439943i	0.00326715	−	0.0141696i
$965$	−14.3000	+	7.64349i	−0.460332	+	0.246053i
$966$	0.862290	−	0.341979i	0.0277437	−	0.0110030i
$967$	10.0005	−	1.98922i	0.321594	−	0.0639690i	−0.0316537	−	0.999499i	$-0.510077\pi$
$967$	10.0005	−	1.98922i	0.321594	−	0.0639690i	0.353247	+	0.935530i	$0.385077\pi$
$968$	−13.9843	−	12.5809i	−0.449472	−	0.404366i
$969$	0.871108	−	4.37936i	0.0279840	−	0.140685i
$970$	−4.96205	+	7.18833i	−0.159322	+	0.230803i
$971$	−11.2655	+	13.7271i	−0.361528	+	0.440523i	−0.921730	−	0.387833i	$-0.873224\pi$
$971$	−11.2655	+	13.7271i	−0.361528	+	0.440523i	0.560202	+	0.828356i	$0.310724\pi$
$972$	19.7915	+	39.8855i	0.634812	+	1.27933i
$973$	−3.34344	+	6.25514i	−0.107186	+	0.200531i
$974$	−23.6567	−	29.7320i	−0.758009	−	0.952675i
$975$	−3.35263	+	1.38871i	−0.107370	+	0.0444742i
$976$	42.1808	−	10.0543i	1.35018	−	0.321831i
$977$	38.2335	+	15.8368i	1.22320	+	0.506666i	0.898425	−	0.439126i	$-0.144712\pi$
$977$	38.2335	+	15.8368i	1.22320	+	0.506666i	0.324774	+	0.945792i	$0.394712\pi$
$978$	22.3702	+	77.9732i	0.715321	+	2.49331i
$979$	−3.35153	−	11.0485i	−0.107115	−	0.353112i
$980$	−3.51441	−	12.9880i	−0.112264	−	0.414887i
$981$	−22.0378	+	2.17053i	−0.703612	+	0.0692997i
$982$	13.4731	+	2.89256i	0.429943	+	0.0923053i
$983$	24.2436	+	36.2830i	0.773249	+	1.15725i	0.983730	+	0.179651i	$0.0574969\pi$
$983$	24.2436	+	36.2830i	0.773249	+	1.15725i	−0.210481	+	0.977598i	$0.567503\pi$
$984$	−28.6285	−	13.4112i	−0.912644	−	0.427534i
$985$	1.24616	+	0.832659i	0.0397060	+	0.0265307i
$986$	−0.000987180		0.0652324i	−3.14382e−5		0.00207742i
$987$	2.22969	−	7.35030i	0.0709718	−	0.233963i
$988$	−3.85363	−	4.09424i	−0.122600	−	0.130255i
$989$	−1.78956	+	1.46865i	−0.0569047	+	0.0467005i
$990$	−7.98522	−	6.75808i	−0.253787	−	0.214786i
$991$	−17.2399	−	17.2399i	−0.547645	−	0.547645i	0.378114	−	0.925759i	$-0.376573\pi$
$991$	−17.2399	−	17.2399i	−0.547645	−	0.547645i	−0.925759	+	0.378114i	$0.876573\pi$
$992$	11.3581	−	11.8814i	0.360620	−	0.377235i
$993$	−23.4868	+	23.4868i	−0.745330	+	0.745330i
$994$	3.86279	−	0.321516i	0.122520	−	0.0101979i
$995$	3.94591	+	4.80811i	0.125094	+	0.152427i
$996$	−22.0431	+	48.9704i	−0.698463	+	1.55169i
$997$	1.28980	+	0.391257i	0.0408485	+	0.0123912i	0.310643	−	0.950527i	$-0.399456\pi$
$997$	1.28980	+	0.391257i	0.0408485	+	0.0123912i	−0.269794	+	0.962918i	$0.586956\pi$
$998$	30.5396	−	29.6291i	0.966715	−	0.937892i
$999$	−6.69900	+	10.0258i	−0.211947	+	0.317201i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.221.27	✓	1024
128.117	even	32	inner	640.2.bm.a.501.27	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.221.27	✓	1024	1.1	even	1	trivial
640.2.bm.a.501.27	yes	1024	128.117	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)

\(f(q)\)	\(=\)	\(q+(-0.430955 + 1.34695i) q^{2} +(2.54637 + 0.250795i) q^{3} +(-1.62856 - 1.16095i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.43518 + 3.32175i) q^{6} +(0.101830 + 0.511933i) q^{7} +(2.26558 - 1.69327i) q^{8} +(3.47873 + 0.691963i) q^{9} +O(q^{10})\)	\(q+(-0.430955 + 1.34695i) q^{2} +(2.54637 + 0.250795i) q^{3} +(-1.62856 - 1.16095i) q^{4} +(0.471397 + 0.881921i) q^{5} +(-1.43518 + 3.32175i) q^{6} +(0.101830 + 0.511933i) q^{7} +(2.26558 - 1.69327i) q^{8} +(3.47873 + 0.691963i) q^{9} +(-1.39106 + 0.254880i) q^{10} +(1.61214 + 1.32305i) q^{11} +(-3.85574 - 3.36464i) q^{12} +(1.25079 + 0.668559i) q^{13} +(-0.733432 - 0.0834604i) q^{14} +(0.979167 + 2.36392i) q^{15} +(1.30438 + 3.78135i) q^{16} +(0.336905 - 0.813360i) q^{17} +(-2.43122 + 4.38748i) q^{18} +(1.89686 - 0.575408i) q^{19} +(0.256172 - 1.98353i) q^{20} +(0.130906 + 1.32911i) q^{21} +(-2.47684 + 1.60130i) q^{22} +(-0.408366 + 0.272861i) q^{23} +(6.19366 - 3.74348i) q^{24} +(-0.555570 + 0.831470i) q^{25} +(-1.43955 + 1.39663i) q^{26} +(1.33905 + 0.406197i) q^{27} +(0.428494 - 0.951930i) q^{28} +(0.0332421 + 0.0405057i) q^{29} +(-3.60606 + 0.300147i) q^{30} +(-2.05462 + 2.05462i) q^{31} +(-5.65542 + 0.127348i) q^{32} +(3.77328 + 3.77328i) q^{33} +(0.950366 + 0.804316i) q^{34} +(-0.403482 + 0.331129i) q^{35} +(-4.86197 - 5.16554i) q^{36} +(-2.50140 + 8.24600i) q^{37} +(-0.0424180 + 2.80296i) q^{38} +(3.01729 + 2.01609i) q^{39} +(2.56131 + 1.19986i) q^{40} +(-2.42693 - 3.63216i) q^{41} +(-1.84666 - 0.396462i) q^{42} +(4.69096 - 0.462019i) q^{43} +(-1.08946 - 4.02627i) q^{44} +(1.02961 + 3.39416i) q^{45} +(-0.191543 - 0.667640i) q^{46} +(-5.31348 - 2.20092i) q^{47} +(2.37309 + 9.95583i) q^{48} +(6.21545 - 2.57452i) q^{49} +(-0.880523 - 1.10665i) q^{50} +(1.06187 - 1.98662i) q^{51} +(-1.26081 - 2.54089i) q^{52} +(-1.47336 + 1.79529i) q^{53} +(-1.12420 + 1.62858i) q^{54} +(-0.406867 + 2.04546i) q^{55} +(1.09754 + 0.987399i) q^{56} +(4.97442 - 0.989474i) q^{57} +(-0.0688850 + 0.0273194i) q^{58} +(8.74956 - 4.67674i) q^{59} +(1.14977 - 4.98654i) q^{60} +(1.06257 - 10.7884i) q^{61} +(-1.88202 - 3.65292i) q^{62} +1.85134i q^{63} +(2.26570 - 7.67246i) q^{64} +1.41825i q^{65} +(-6.70854 + 3.45631i) q^{66} +(-0.232003 + 2.35556i) q^{67} +(-1.49294 + 0.933472i) q^{68} +(-1.10828 + 0.592389i) q^{69} +(-0.272132 - 0.686172i) q^{70} +(-5.15016 + 1.02443i) q^{71} +(9.05302 - 4.32272i) q^{72} +(-0.318018 + 1.59879i) q^{73} +(-10.0290 - 6.92292i) q^{74} +(-1.62321 + 1.97789i) q^{75} +(-3.75717 - 1.26508i) q^{76} +(-0.513147 + 0.960031i) q^{77} +(-4.01589 + 3.19530i) q^{78} +(-8.74439 + 3.62204i) q^{79} +(-2.71997 + 2.93288i) q^{80} +(-6.52284 - 2.70185i) q^{81} +(5.93825 - 1.70366i) q^{82} +(-3.04631 - 10.0423i) q^{83} +(1.32984 - 2.31650i) q^{84} +(0.876136 - 0.0862918i) q^{85} +(-1.39928 + 6.51760i) q^{86} +(0.0744881 + 0.111479i) q^{87} +(5.89270 + 0.267691i) q^{88} +(-4.60308 - 3.07568i) q^{89} +(-5.01548 - 0.0759006i) q^{90} +(-0.214890 + 0.708397i) q^{91} +(0.981825 + 0.0297233i) q^{92} +(-5.74711 + 4.71653i) q^{93} +(5.25440 - 6.20851i) q^{94} +(1.40164 + 1.40164i) q^{95} +(-14.4327 - 1.09408i) q^{96} +(4.36732 - 4.36732i) q^{97} +(0.789177 + 9.48141i) q^{98} +(4.69270 + 5.71807i) 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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