LMFDB - Embedded newform 640.2.bm.a.101.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [640,2,Mod(21,640)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://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);

sage: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")

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:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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			101.7
Character	$\chi$	$=$	640.101
Dual form			640.2.bm.a.621.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.33948 - 0.453651i) q^{2} +(1.21479 - 0.649321i) q^{3} +(1.58840 + 1.21531i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-1.92175 + 0.318659i) q^{6} +(-2.42162 + 1.61807i) q^{7} +(-1.57630 - 2.34846i) q^{8} +(-0.612605 + 0.916828i) q^{9} +(-0.499079 - 1.32322i) q^{10} +(0.714160 - 0.216638i) q^{11} +(2.71871 + 0.444969i) q^{12} +(0.881016 + 0.723031i) q^{13} +(3.97775 - 1.06881i) q^{14} +(1.27259 + 0.527123i) q^{15} +(1.04604 + 3.86080i) q^{16} +(-2.54005 + 1.05212i) q^{17} +(1.23649 - 0.950162i) q^{18} +(0.386506 + 3.92426i) q^{19} +(0.0682238 + 1.99884i) q^{20} +(-1.89112 + 3.53803i) q^{21} +(-1.05488 - 0.0337973i) q^{22} +(7.92217 - 1.57582i) q^{23} +(-3.43979 - 1.82937i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.852098 - 1.36816i) q^{26} +(-0.553911 + 5.62395i) q^{27} +(-5.81297 - 0.372867i) q^{28} +(-2.53430 + 8.35447i) q^{29} +(-1.46547 - 1.28338i) q^{30} +(3.63335 + 3.63335i) q^{31} +(0.350307 - 5.64600i) q^{32} +(0.726889 - 0.726889i) q^{33} +(3.87964 - 0.257000i) q^{34} +(-2.78705 - 0.845442i) q^{35} +(-2.08729 + 0.711786i) q^{36} +(-2.86539 - 0.282217i) q^{37} +(1.26253 - 5.43180i) q^{38} +(1.53973 + 0.306272i) q^{39} +(0.815389 - 2.70835i) q^{40} +(-1.11480 - 5.60448i) q^{41} +(4.13814 - 3.88121i) q^{42} +(-10.6679 - 5.70211i) q^{43} +(1.39765 + 0.523818i) q^{44} +(-1.09735 + 0.108079i) q^{45} +(-11.3264 - 1.48313i) q^{46} +(1.83938 + 4.44066i) q^{47} +(3.77762 + 4.01086i) q^{48} +(0.567292 - 1.36957i) q^{49} +(0.706253 - 1.22524i) q^{50} +(-2.40247 + 2.92742i) q^{51} +(0.520700 + 2.21917i) q^{52} +(0.429284 + 1.41516i) q^{53} +(3.29326 - 7.28188i) q^{54} +(0.620522 + 0.414619i) q^{55} +(7.61719 + 3.13650i) q^{56} +(3.01763 + 4.51620i) q^{57} +(7.18465 - 10.0409i) q^{58} +(9.34867 - 7.67226i) q^{59} +(1.38076 + 2.38387i) q^{60} +(6.37176 + 11.9207i) q^{61} +(-3.21852 - 6.51507i) q^{62} -3.21145i q^{63} +(-3.03054 + 7.40377i) q^{64} +1.13972i q^{65} +(-1.30341 + 0.643898i) q^{66} +(-1.54585 - 2.89208i) q^{67} +(-5.31329 - 1.41576i) q^{68} +(8.60059 - 7.05832i) q^{69} +(3.34965 + 2.39680i) q^{70} +(6.65135 + 9.95445i) q^{71} +(3.11878 - 0.00651960i) q^{72} +(1.28181 + 0.856479i) q^{73} +(3.71010 + 1.67791i) q^{74} +(0.399850 + 1.31813i) q^{75} +(-4.15527 + 6.70303i) q^{76} +(-1.37889 + 1.68018i) q^{77} +(-1.92350 - 1.10874i) q^{78} +(-0.303191 + 0.731967i) q^{79} +(-2.32084 + 3.25787i) q^{80} +(1.71295 + 4.13544i) q^{81} +(-1.04923 + 8.01281i) q^{82} +(9.61841 - 0.947330i) q^{83} +(-7.30367 + 3.32152i) q^{84} +(-2.42470 - 1.29603i) q^{85} +(11.7026 + 12.4773i) q^{86} +(2.34608 + 11.7945i) q^{87} +(-1.63450 - 1.33569i) q^{88} +(-9.23251 - 1.83646i) q^{89} +(1.51891 + 0.353043i) q^{90} +(-3.30340 - 0.325357i) q^{91} +(14.4987 + 7.12486i) q^{92} +(6.77299 + 2.05456i) q^{93} +(-0.449302 - 6.78261i) q^{94} +(-2.78830 + 2.78830i) q^{95} +(-3.24051 - 7.08618i) q^{96} +(-8.66696 - 8.66696i) q^{97} +(-1.38118 + 1.57715i) q^{98} +(-0.238878 + 0.787475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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

Character values

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

$n$	$257$	$261$	$511$
$\chi(n)$	$1$	$e\left(\frac{9}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.33948	−	0.453651i	−0.947154	−	0.320780i
$2$	−1.33948	−	0.453651i	−0.947154	−	0.320780i
$3$	1.21479	−	0.649321i	0.701361	−	0.374885i	−0.0818469	−	0.996645i	$-0.526082\pi$
$3$	1.21479	−	0.649321i	0.701361	−	0.374885i	0.783208	+	0.621759i	$0.213582\pi$
$4$	1.58840	+	1.21531i	0.794201	+	0.607655i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$5$	0.634393	+	0.773010i	0.283709	+	0.345701i
$6$	−1.92175	+	0.318659i	−0.784553	+	0.130092i
$7$	−2.42162	+	1.61807i	−0.915286	+	0.611575i	−0.921488	−	0.388406i	$-0.873026\pi$
$7$	−2.42162	+	1.61807i	−0.915286	+	0.611575i	0.00620213	+	0.999981i	$0.498026\pi$
$8$	−1.57630	−	2.34846i	−0.557307	−	0.830306i
$9$	−0.612605	+	0.916828i	−0.204202	+	0.305609i
$10$	−0.499079	−	1.32322i	−0.157823	−	0.418440i
$11$	0.714160	−	0.216638i	0.215327	−	0.0653188i	−0.180778	−	0.983524i	$-0.557862\pi$
$11$	0.714160	−	0.216638i	0.215327	−	0.0653188i	0.396105	+	0.918205i	$0.370362\pi$
$12$	2.71871	+	0.444969i	0.784823	+	0.128452i
$13$	0.881016	+	0.723031i	0.244350	+	0.200533i	0.748595	−	0.663028i	$-0.230729\pi$
$13$	0.881016	+	0.723031i	0.244350	+	0.200533i	−0.504245	+	0.863561i	$0.668229\pi$
$14$	3.97775	−	1.06881i	1.06310	−	0.285650i
$15$	1.27259	+	0.527123i	0.328581	+	0.136103i
$16$	1.04604	+	3.86080i	0.261510	+	0.965201i
$17$	−2.54005	+	1.05212i	−0.616054	+	0.255178i	−0.668814	−	0.743429i	$-0.733198\pi$
$17$	−2.54005	+	1.05212i	−0.616054	+	0.255178i	0.0527608	+	0.998607i	$0.483198\pi$
$18$	1.23649	−	0.950162i	0.291443	−	0.223955i
$19$	0.386506	+	3.92426i	0.0886705	+	0.900287i	0.931896	+	0.362726i	$0.118154\pi$
$19$	0.386506	+	3.92426i	0.0886705	+	0.900287i	−0.843225	+	0.537561i	$0.819346\pi$
$20$	0.0682238	+	1.99884i	0.0152553	+	0.446953i
$21$	−1.89112	+	3.53803i	−0.412676	+	0.772062i
$22$	−1.05488	−	0.0337973i	−0.224901	−	0.00720562i
$23$	7.92217	−	1.57582i	1.65189	−	0.328581i	0.720734	−	0.693212i	$-0.243805\pi$
$23$	7.92217	−	1.57582i	1.65189	−	0.328581i	0.931152	+	0.364631i	$0.118805\pi$
$24$	−3.43979	−	1.82937i	−0.702144	−	0.373419i
$25$	−0.195090	+	0.980785i	−0.0390181	+	0.196157i
$26$	−0.852098	−	1.36816i	−0.167110	−	0.268318i
$27$	−0.553911	+	5.62395i	−0.106600	+	1.08233i
$28$	−5.81297	−	0.372867i	−1.09855	−	0.0704652i
$29$	−2.53430	+	8.35447i	−0.470608	+	1.55139i	0.325085	+	0.945685i	$0.394607\pi$
$29$	−2.53430	+	8.35447i	−0.470608	+	1.55139i	−0.795693	+	0.605701i	$0.792893\pi$
$30$	−1.46547	−	1.28338i	−0.267558	−	0.234312i
$31$	3.63335	+	3.63335i	0.652570	+	0.652570i	0.953611	−	0.301041i	$-0.0973342\pi$
$31$	3.63335	+	3.63335i	0.652570	+	0.652570i	−0.301041	+	0.953611i	$0.597334\pi$
$32$	0.350307	−	5.64600i	0.0619262	−	0.998081i
$33$	0.726889	−	0.726889i	0.126535	−	0.126535i
$34$	3.87964	−	0.257000i	0.665353	−	0.0440752i
$35$	−2.78705	−	0.845442i	−0.471097	−	0.142906i
$36$	−2.08729	+	0.711786i	−0.347882	+	0.118631i
$37$	−2.86539	−	0.282217i	−0.471068	−	0.0463961i	−0.140302	−	0.990109i	$-0.544807\pi$
$37$	−2.86539	−	0.282217i	−0.471068	−	0.0463961i	−0.330766	+	0.943713i	$0.607307\pi$
$38$	1.26253	−	5.43180i	0.204809	−	0.881154i
$39$	1.53973	+	0.306272i	0.246554	+	0.0490427i
$40$	0.815389	−	2.70835i	0.128924	−	0.428227i
$41$	−1.11480	−	5.60448i	−0.174103	−	0.875273i	−0.964784	−	0.263045i	$-0.915273\pi$
$41$	−1.11480	−	5.60448i	−0.174103	−	0.875273i	0.790681	−	0.612228i	$-0.209727\pi$
$42$	4.13814	−	3.88121i	0.638529	−	0.598884i
$43$	−10.6679	−	5.70211i	−1.62684	−	0.869563i	−0.995572	−	0.0939974i	$-0.970035\pi$
$43$	−10.6679	−	5.70211i	−1.62684	−	0.869563i	−0.631266	−	0.775566i	$-0.717465\pi$
$44$	1.39765	+	0.523818i	0.210704	+	0.0789685i
$45$	−1.09735	+	0.108079i	−0.163583	+	0.0161115i
$46$	−11.3264	−	1.48313i	−1.66999	−	0.218675i
$47$	1.83938	+	4.44066i	0.268302	+	0.647738i	0.999404	−	0.0345307i	$-0.0109936\pi$
$47$	1.83938	+	4.44066i	0.268302	+	0.647738i	−0.731102	+	0.682268i	$0.760994\pi$
$48$	3.77762	+	4.01086i	0.545253	+	0.578918i
$49$	0.567292	−	1.36957i	0.0810418	−	0.195652i
$50$	0.706253	−	1.22524i	0.0998793	−	0.173275i
$51$	−2.40247	+	2.92742i	−0.336414	+	0.409921i
$52$	0.520700	+	2.21917i	0.0722081	+	0.307744i
$53$	0.429284	+	1.41516i	0.0589668	+	0.194387i	0.981475	−	0.191590i	$-0.0613643\pi$
$53$	0.429284	+	1.41516i	0.0589668	+	0.194387i	−0.922508	+	0.385977i	$0.873864\pi$
$54$	3.29326	−	7.28188i	0.448156	−	0.990938i
$55$	0.620522	+	0.414619i	0.0836711	+	0.0559072i
$56$	7.61719	+	3.13650i	1.01789	+	0.419133i
$57$	3.01763	+	4.51620i	0.399695	+	0.598185i
$58$	7.18465	−	10.0409i	0.943391	−	1.31844i
$59$	9.34867	−	7.67226i	1.21709	−	0.998843i	0.217352	−	0.976093i	$-0.430258\pi$
$59$	9.34867	−	7.67226i	1.21709	−	0.998843i	0.999741	−	0.0227495i	$-0.00724202\pi$
$60$	1.38076	+	2.38387i	0.178256	+	0.307757i
$61$	6.37176	+	11.9207i	0.815820	+	1.52629i	0.849943	+	0.526875i	$0.176636\pi$
$61$	6.37176	+	11.9207i	0.815820	+	1.52629i	−0.0341227	+	0.999418i	$0.510864\pi$
$62$	−3.21852	−	6.51507i	−0.408753	−	0.827415i
$63$		−	3.21145i		−	0.404604i
$64$	−3.03054	+	7.40377i	−0.378817	+	0.925471i
$65$			1.13972i			0.141365i
$66$	−1.30341	+	0.643898i	−0.160438	+	0.0792584i
$67$	−1.54585	−	2.89208i	−0.188856	−	0.353324i	0.769618	−	0.638504i	$-0.220447\pi$
$67$	−1.54585	−	2.89208i	−0.188856	−	0.353324i	−0.958474	+	0.285180i	$0.907947\pi$
$68$	−5.31329	−	1.41576i	−0.644330	−	0.171686i
$69$	8.60059	−	7.05832i	1.03539	−	0.849722i
$70$	3.34965	+	2.39680i	0.400360	+	0.286472i
$71$	6.65135	+	9.95445i	0.789370	+	1.18138i	0.979860	+	0.199687i	$0.0639925\pi$
$71$	6.65135	+	9.95445i	0.789370	+	1.18138i	−0.190490	+	0.981689i	$0.561008\pi$
$72$	3.11878	−	0.00651960i	0.367552	−	0.000768342i
$73$	1.28181	+	0.856479i	0.150025	+	0.100243i	0.628317	−	0.777957i	$-0.283744\pi$
$73$	1.28181	+	0.856479i	0.150025	+	0.100243i	−0.478292	+	0.878201i	$0.658744\pi$
$74$	3.71010	+	1.67791i	0.431291	+	0.195053i
$75$	0.399850	+	1.31813i	0.0461707	+	0.152204i
$76$	−4.15527	+	6.70303i	−0.476642	+	0.768890i
$77$	−1.37889	+	1.68018i	−0.157139	+	0.191474i
$78$	−1.92350	−	1.10874i	−0.217793	−	0.125541i
$79$	−0.303191	+	0.731967i	−0.0341116	+	0.0823528i	−0.940017	−	0.341127i	$-0.889191\pi$
$79$	−0.303191	+	0.731967i	−0.0341116	+	0.0823528i	0.905906	+	0.423480i	$0.139191\pi$
$80$	−2.32084	+	3.25787i	−0.259478	+	0.364241i
$81$	1.71295	+	4.13544i	0.190328	+	0.459493i
$82$	−1.04923	+	8.01281i	−0.115868	+	0.884867i
$83$	9.61841	−	0.947330i	1.05576	−	0.103983i	0.444787	−	0.895636i	$-0.353279\pi$
$83$	9.61841	−	0.947330i	1.05576	−	0.103983i	0.610970	+	0.791653i	$0.290779\pi$
$84$	−7.30367	+	3.32152i	−0.796895	+	0.362408i
$85$	−2.42470	−	1.29603i	−0.262995	−	0.140574i
$86$	11.7026	+	12.4773i	1.26193	+	1.34547i
$87$	2.34608	+	11.7945i	0.251526	+	1.26451i
$88$	−1.63450	−	1.33569i	−0.174238	−	0.142385i
$89$	−9.23251	−	1.83646i	−0.978644	−	0.194664i	−0.320246	−	0.947334i	$-0.603766\pi$
$89$	−9.23251	−	1.83646i	−0.978644	−	0.194664i	−0.658398	+	0.752670i	$0.728766\pi$
$90$	1.51891	+	0.353043i	0.160107	+	0.0372140i
$91$	−3.30340	−	0.325357i	−0.346291	−	0.0341067i
$92$	14.4987	+	7.12486i	1.51159	+	0.742818i
$93$	6.77299	+	2.05456i	0.702326	+	0.213048i
$94$	−0.449302	−	6.78261i	−0.0463420	−	0.699573i
$95$	−2.78830	+	2.78830i	−0.286073	+	0.286073i
$96$	−3.24051	−	7.08618i	−0.330733	−	0.723231i
$97$	−8.66696	−	8.66696i	−0.879996	−	0.879996i	0.113537	−	0.993534i	$-0.463782\pi$
$97$	−8.66696	−	8.66696i	−0.879996	−	0.879996i	−0.993534	+	0.113537i	$0.963782\pi$
$98$	−1.38118	+	1.57715i	−0.139520	+	0.159316i
$99$	−0.238878	+	0.787475i	−0.0240081	+	0.0791442i
$100$	−1.50184	+	1.32079i	−0.150184	+	0.132079i
$101$	0.939268	−	9.53655i	0.0934607	−	0.948922i	−0.828072	−	0.560622i	$-0.810562\pi$
$101$	0.939268	−	9.53655i	0.0934607	−	0.948922i	0.921533	−	0.388301i	$-0.126938\pi$
$102$	4.54609	−	2.83134i	0.450130	−	0.280344i
$103$	2.44911	−	12.3125i	0.241318	−	1.21319i	−0.650044	−	0.759896i	$-0.725250\pi$
$103$	2.44911	−	12.3125i	0.241318	−	1.21319i	0.891362	−	0.453291i	$-0.149750\pi$
$104$	0.309263	−	3.20875i	0.0303257	−	0.314644i
$105$	−3.93465	+	0.782651i	−0.383983	+	0.0763789i
$106$	0.0669720	−	2.09032i	0.00650489	−	0.203030i
$107$	4.02677	−	7.53355i	0.389282	−	0.728296i	−0.608591	−	0.793484i	$-0.708265\pi$
$107$	4.02677	−	7.53355i	0.389282	−	0.728296i	0.997873	+	0.0651886i	$0.0207649\pi$
$108$	−7.71468	+	8.25993i	−0.742346	+	0.794812i
$109$	−0.371840	−	3.77536i	−0.0356159	−	0.361614i	−0.996430	−	0.0844211i	$-0.973096\pi$
$109$	−0.371840	−	3.77536i	−0.0356159	−	0.361614i	0.960814	−	0.277193i	$-0.0894041\pi$
$110$	−0.643082	−	0.836873i	−0.0613155	−	0.0797927i
$111$	−3.66411	+	1.51772i	−0.347782	+	0.144056i
$112$	−8.78018	−	7.65682i	−0.829649	−	0.723502i
$113$	4.92941	+	2.04183i	0.463720	+	0.192079i	0.602296	−	0.798273i	$-0.294253\pi$
$113$	4.92941	+	2.04183i	0.463720	+	0.192079i	−0.138576	+	0.990352i	$0.544253\pi$
$114$	−1.99327	−	7.41830i	−0.186687	−	0.694787i
$115$	6.24389	+	5.12423i	0.582246	+	0.477837i
$116$	−14.1788	+	10.1903i	−1.31646	+	0.946145i
$117$	−1.20261	+	0.364808i	−0.111181	+	0.0337265i
$118$	−16.0029	+	6.03579i	−1.47318	+	0.555639i
$119$	4.44863	−	6.65784i	0.407805	−	0.610323i
$120$	−0.768056	−	3.81953i	−0.0701136	−	0.348674i
$121$	−8.68307	+	5.80184i	−0.789370	+	0.527440i
$122$	−3.12699	−	18.8581i	−0.283104	−	1.70733i
$123$	−4.99336	−	6.08443i	−0.450236	−	0.548614i
$124$	1.35557	+	10.1869i	0.121734	+	0.914809i
$125$	−0.881921	+	0.471397i	−0.0788814	+	0.0421630i
$126$	−1.45688	+	4.30166i	−0.129789	+	0.383223i
$127$	7.40832			0.657382			0.328691	−	0.944438i	$-0.393393\pi$
$127$	7.40832			0.657382			0.328691	+	0.944438i	$0.393393\pi$
$128$	7.41807	−	8.54238i	0.655671	−	0.755047i
$129$	−16.6618			−1.46699
$130$	0.517035	−	1.52663i	0.0453470	−	0.133894i
$131$	12.0043	−	6.41645i	1.04882	−	0.560608i	0.145407	−	0.989372i	$-0.453551\pi$
$131$	12.0043	−	6.41645i	1.04882	−	0.560608i	0.903417	+	0.428764i	$0.141051\pi$
$132$	2.03799	−	0.271196i	0.177384	−	0.0236046i
$133$	−7.28572	−	8.87767i	−0.631752	−	0.769792i
$134$	0.758636	+	4.57515i	0.0655362	+	0.395233i
$135$	−4.69877	+	3.13962i	−0.404406	+	0.270215i
$136$	6.47477	+	4.30675i	0.555207	+	0.369301i
$137$	3.52232	−	5.27153i	0.300932	−	0.450377i	−0.649929	−	0.759995i	$-0.725201\pi$
$137$	3.52232	−	5.27153i	0.300932	−	0.450377i	0.950861	+	0.309618i	$0.100201\pi$
$138$	−14.7223	+	5.55280i	−1.25325	+	0.472686i
$139$	−14.5656	+	4.41842i	−1.23544	+	0.374766i	−0.839423	−	0.543478i	$-0.817107\pi$
$139$	−14.5656	+	4.41842i	−1.23544	+	0.374766i	−0.396014	+	0.918244i	$0.629607\pi$
$140$	−3.39948	−	4.73003i	−0.287308	−	0.399760i
$141$	5.11789	+	4.20014i	0.431004	+	0.353716i
$142$	−4.39349	−	16.3512i	−0.368694	−	1.37216i
$143$	0.785822	+	0.325498i	0.0657138	+	0.0272195i
$144$	−4.18050	−	1.40611i	−0.348375	−	0.117176i
$145$	−8.06583	+	3.34098i	−0.669831	+	0.277453i
$146$	−1.32842	−	1.72873i	−0.109940	−	0.143071i
$147$	−0.200144	−	2.03209i	−0.0165076	−	0.167604i
$148$	−4.20842	−	3.93062i	−0.345930	−	0.323095i
$149$	5.83464	−	10.9159i	0.477993	−	0.894261i	−0.521174	−	0.853450i	$-0.674506\pi$
$149$	5.83464	−	10.9159i	0.477993	−	0.894261i	0.999167	−	0.0408110i	$-0.0129942\pi$
$150$	0.0623799	−	1.94700i	0.00509330	−	0.158971i
$151$	−8.21420	+	1.63391i	−0.668462	+	0.132965i	−0.517644	−	0.855596i	$-0.673191\pi$
$151$	−8.21420	+	1.63391i	−0.668462	+	0.132965i	−0.150818	+	0.988562i	$0.548191\pi$
$152$	8.60672	−	7.09352i	0.698097	−	0.575360i
$153$	0.591432	−	2.97333i	0.0478144	−	0.240379i
$154$	2.60920	−	1.62503i	0.210256	−	0.130949i
$155$	−0.503645	+	5.11360i	−0.0404538	+	0.410734i
$156$	2.07350	+	2.35774i	0.166013	+	0.188770i
$157$	0.429209	−	1.41491i	0.0342546	−	0.112922i	−0.938146	−	0.346240i	$-0.887458\pi$
$157$	0.429209	−	1.41491i	0.0342546	−	0.112922i	0.972401	+	0.233318i	$0.0749582\pi$
$158$	0.738175	−	0.842911i	0.0587260	−	0.0670584i
$159$	1.44039	+	1.44039i	0.114230	+	0.114230i
$160$	4.58665	−	3.31099i	0.362606	−	0.261757i
$161$	−16.6347	+	16.6347i	−1.31100	+	1.31100i
$162$	−0.418420	−	6.31641i	−0.0328742	−	0.496264i
$163$	7.57045	+	2.29647i	0.592963	+	0.179873i	0.572483	−	0.819917i	$-0.305980\pi$
$163$	7.57045	+	2.29647i	0.592963	+	0.179873i	0.0204806	+	0.999790i	$0.493480\pi$
$164$	5.04044	−	10.2570i	0.393592	−	0.800937i
$165$	1.02303	+	0.100759i	0.0796425	+	0.00784410i
$166$	−13.3134	−	3.09447i	−1.03332	−	0.240177i
$167$	−2.71168	−	0.539387i	−0.209836	−	0.0417390i	0.0890528	−	0.996027i	$-0.471616\pi$
$167$	−2.71168	−	0.539387i	−0.209836	−	0.0417390i	−0.298889	+	0.954288i	$0.596616\pi$
$168$	11.2899	−	1.13579i	0.871036	−	0.0876284i
$169$	−2.28276	−	11.4762i	−0.175597	−	0.882785i
$170$	2.65988	+	2.83597i	0.204004	+	0.217509i
$171$	−3.83465	−	2.04966i	−0.293243	−	0.156741i
$172$	−10.0151	−	22.0220i	−0.763642	−	1.67917i
$173$	−25.7045	+	2.53168i	−1.95428	+	0.192480i	−0.995721	−	0.0924142i	$-0.970542\pi$
$173$	−25.7045	+	2.53168i	−1.95428	+	0.192480i	−0.958559	+	0.284894i	$0.908042\pi$
$174$	2.20808	−	16.8628i	0.167394	−	1.27837i
$175$	−1.11455	−	2.69076i	−0.0842520	−	0.203402i
$176$	1.58344	+	2.53062i	0.119356	+	0.190752i
$177$	6.37495	−	15.3905i	0.479171	−	1.15682i
$178$	11.5336	+	6.64823i	0.864482	+	0.498306i
$179$	5.78319	−	7.04684i	0.432256	−	0.526706i	−0.510639	−	0.859795i	$-0.670591\pi$
$179$	5.78319	−	7.04684i	0.432256	−	0.526706i	0.942895	+	0.333090i	$0.108091\pi$
$180$	−1.87438	−	1.16195i	−0.139708	−	0.0866064i
$181$	−3.73735	−	12.3204i	−0.277795	−	0.915769i	−0.979181	−	0.202987i	$-0.934935\pi$
$181$	−3.73735	−	12.3204i	−0.277795	−	0.915769i	0.701386	−	0.712782i	$-0.252565\pi$
$182$	4.27724	+	1.93440i	0.317050	+	0.143387i
$183$	15.4807	+	10.3439i	1.14437	+	0.764643i
$184$	−16.1885	−	16.1209i	−1.19343	−	1.18845i
$185$	−1.59963	−	2.39402i	−0.117607	−	0.176012i
$186$	−8.14021	−	5.82461i	−0.596869	−	0.427081i
$187$	−1.58607	+	1.30166i	−0.115985	+	0.0951866i
$188$	−2.47511	+	9.28898i	−0.180516	+	0.677469i
$189$	−7.75862	−	14.5153i	−0.564356	−	1.05584i
$190$	4.99978	−	2.46995i	0.362722	−	0.179189i
$191$			2.48821i			0.180041i	0.995940	+	0.0900204i	$0.0286932\pi$
$191$			2.48821i			0.180041i	−0.995940	+	0.0900204i	$0.971307\pi$
$192$	1.12594	+	10.9618i	0.0812578	+	0.791103i
$193$			23.1189i			1.66413i	0.554675	+	0.832067i	$0.312842\pi$
$193$			23.1189i			1.66413i	−0.554675	+	0.832067i	$0.687158\pi$
$194$	7.67743	+	15.5410i	0.551207	+	1.11578i
$195$	0.740044	+	1.38453i	0.0529957	+	0.0991479i
$196$	2.56554	−	1.48598i	0.183253	−	0.106142i
$197$	1.76329	−	1.44709i	0.125629	−	0.103101i	−0.569481	−	0.822005i	$-0.692856\pi$
$197$	1.76329	−	1.44709i	0.125629	−	0.103101i	0.695110	+	0.718904i	$0.255356\pi$
$198$	0.677210	−	0.946438i	0.0481272	−	0.0672604i
$199$	9.29355	+	13.9088i	0.658802	+	0.985968i	0.998960	+	0.0455990i	$0.0145197\pi$
$199$	9.29355	+	13.9088i	0.658802	+	0.985968i	−0.340157	+	0.940369i	$0.610480\pi$
$200$	2.61086	−	1.08785i	0.184616	−	0.0769228i
$201$	−3.75578	−	2.50953i	−0.264912	−	0.177009i
$202$	−5.58439	+	12.3479i	−0.392917	+	0.868795i
$203$	−7.38104	−	24.3320i	−0.518047	−	1.70777i
$204$	−7.37383	+	1.73017i	−0.516271	+	0.121136i
$205$	3.62510	−	4.41720i	0.253188	−	0.308511i
$206$	−8.86611	+	15.3813i	−0.617731	+	1.07167i
$207$	−3.40840	+	8.22861i	−0.236900	+	0.571928i
$208$	−1.86990	+	4.15775i	−0.129654	+	0.288288i
$209$	1.12617	+	2.71882i	0.0778989	+	0.188064i
$210$	5.62543	+	0.736614i	0.388191	+	0.0508312i
$211$	3.18645	−	0.313838i	0.219364	−	0.0216055i	0.0122620	−	0.999925i	$-0.496097\pi$
$211$	3.18645	−	0.313838i	0.219364	−	0.0216055i	0.207102	+	0.978319i	$0.433597\pi$
$212$	−1.03798	+	2.76956i	−0.0712890	+	0.190214i
$213$	14.5437	+	7.77374i	0.996514	+	0.532648i
$214$	−8.81136	+	8.26428i	−0.602332	+	0.564934i
$215$	−2.35985	−	11.8638i	−0.160941	−	0.809103i
$216$	14.0808	−	7.56422i	0.958075	−	0.514680i
$217$	−14.6776	−	2.91956i	−0.996383	−	0.198193i
$218$	−1.21462	+	5.22570i	−0.0822646	+	0.353929i
$219$	2.11327	+	0.208139i	0.142801	+	0.0140647i
$220$	0.481746	+	1.41271i	0.0324793	+	0.0952448i
$221$	−2.99855	−	0.909600i	−0.201704	−	0.0611863i
$222$	5.59651	−	0.370731i	0.375613	−	0.0248819i
$223$	4.14792	−	4.14792i	0.277765	−	0.277765i	−0.554451	−	0.832216i	$-0.687072\pi$
$223$	4.14792	−	4.14792i	0.277765	−	0.277765i	0.832216	+	0.554451i	$0.187072\pi$
$224$	8.28733	+	14.2393i	0.553721	+	0.951402i
$225$	−0.779698	−	0.779698i	−0.0519799	−	0.0519799i
$226$	−5.67655	−	4.97121i	−0.377599	−	0.330680i
$227$	1.19446	−	3.93761i	0.0792792	−	0.261349i	−0.908337	−	0.418240i	$-0.862647\pi$
$227$	1.19446	−	3.93761i	0.0792792	−	0.261349i	0.987616	+	0.156891i	$0.0501472\pi$
$228$	−0.695378	+	10.8409i	−0.0460526	+	0.717956i
$229$	0.711652	−	7.22553i	0.0470273	−	0.477476i	−0.942611	−	0.333893i	$-0.891638\pi$
$229$	0.711652	−	7.22553i	0.0470273	−	0.477476i	0.989638	−	0.143583i	$-0.0458625\pi$
$230$	−6.03895	−	9.69634i	−0.398196	−	0.639358i
$231$	−0.584088	+	2.93641i	−0.0384302	+	0.193202i
$232$	23.6150	−	7.21746i	1.55040	−	0.473850i
$233$	9.33960	−	1.85776i	0.611857	−	0.121706i	0.120572	−	0.992705i	$-0.461527\pi$
$233$	9.33960	−	1.85776i	0.611857	−	0.121706i	0.491286	+	0.870999i	$0.336527\pi$
$234$	1.77636	+	0.0569131i	0.116125	+	0.00372052i
$235$	−2.26579	+	4.23899i	−0.147804	+	0.276521i
$236$	24.1736	−	0.825089i	1.57357	−	0.0537087i
$237$	0.106967	+	1.08606i	0.00694827	+	0.0705470i
$238$	−8.97918	+	6.89991i	−0.582033	+	0.447255i
$239$	25.6155	−	10.6103i	1.65693	−	0.686322i	0.659091	−	0.752063i	$-0.270941\pi$
$239$	25.6155	−	10.6103i	1.65693	−	0.686322i	0.997837	+	0.0657414i	$0.0209412\pi$
$240$	−0.703940	+	5.46461i	−0.0454391	+	0.352739i
$241$	−18.4112	−	7.62618i	−1.18597	−	0.491246i	−0.299530	−	0.954087i	$-0.596830\pi$
$241$	−18.4112	−	7.62618i	−1.18597	−	0.491246i	−0.886441	+	0.462841i	$0.846830\pi$
$242$	14.2628	−	3.83236i	0.916847	−	0.246353i
$243$	−8.33912	−	6.84374i	−0.534955	−	0.439026i
$244$	−4.36646	+	26.6786i	−0.279534	+	1.70792i
$245$	1.41857	−	0.430320i	0.0906294	−	0.0274921i
$246$	3.92829	+	10.4152i	0.250459	+	0.664049i
$247$	−2.49685	+	3.73679i	−0.158870	+	0.237766i
$248$	2.80553	−	14.2601i	0.178151	−	0.905515i
$249$	11.0693	−	7.39624i	0.701486	−	0.468718i
$250$	1.39516	−	0.231341i	0.0882379	−	0.0146313i
$251$	15.0963	+	18.3949i	0.952870	+	1.16108i	0.986848	+	0.161653i	$0.0516825\pi$
$251$	15.0963	+	18.3949i	0.952870	+	1.16108i	−0.0339776	+	0.999423i	$0.510817\pi$
$252$	3.90291	−	5.10107i	0.245860	−	0.321337i
$253$	5.31631	−	2.84163i	0.334234	−	0.178652i
$254$	−9.92328	−	3.36079i	−0.622642	−	0.210875i
$255$	−3.78704			−0.237154
$256$	−13.8116	+	8.07712i	−0.863225	+	0.504820i
$257$	−7.92942			−0.494624			−0.247312	−	0.968936i	$-0.579547\pi$
$257$	−7.92942			−0.494624			−0.247312	+	0.968936i	$0.579547\pi$
$258$	22.3181	+	7.55863i	1.38946	+	0.470580i
$259$	7.39554	−	3.95300i	0.459537	−	0.245627i
$260$	−1.38511	+	1.81033i	−0.0859012	+	0.112272i
$261$	−6.10708	−	7.44150i	−0.378019	−	0.460617i
$262$	−18.9904	+	3.14892i	−1.17323	+	0.194541i
$263$	−19.1247	+	12.7787i	−1.17928	+	0.787968i	−0.981346	−	0.192249i	$-0.938422\pi$
$263$	−19.1247	+	12.7787i	−1.17928	+	0.787968i	−0.197930	+	0.980216i	$0.563422\pi$
$264$	−2.85287	−	0.561274i	−0.175582	−	0.0345440i
$265$	−0.821599	+	1.22961i	−0.0504704	+	0.0755343i
$266$	5.73169	+	15.1966i	0.351433	+	0.931764i
$267$	−12.4080	+	3.76394i	−0.759360	+	0.230349i
$268$	1.05935	−	6.47247i	0.0647098	−	0.395369i
$269$	1.39699	+	1.14648i	0.0851758	+	0.0699020i	0.676018	−	0.736885i	$-0.263704\pi$
$269$	1.39699	+	1.14648i	0.0851758	+	0.0699020i	−0.590842	+	0.806787i	$0.701204\pi$
$270$	7.71819	−	2.07385i	0.469714	−	0.126210i
$271$	12.6299	+	5.23146i	0.767209	+	0.317788i	0.731741	−	0.681583i	$-0.238708\pi$
$271$	12.6299	+	5.23146i	0.767209	+	0.317788i	0.0354676	+	0.999371i	$0.488708\pi$
$272$	−6.71905	−	8.70608i	−0.407402	−	0.527884i
$273$	−4.22422	+	1.74973i	−0.255661	+	0.105898i
$274$	−7.10951	+	5.46319i	−0.429501	+	0.330044i
$275$	0.0731497	+	0.742701i	0.00441109	+	0.0447866i
$276$	22.2392	−	0.759065i	1.33864	−	0.0456903i
$277$	−7.40179	+	13.8478i	−0.444730	+	0.832032i	0.555270	+	0.831670i	$0.312615\pi$
$277$	−7.40179	+	13.8478i	−0.444730	+	0.832032i	−1.00000		0.000361569i	$0.999885\pi$
$278$	21.5147	+	0.689311i	1.29037	+	0.0413421i
$279$	−5.55697	+	1.10535i	−0.332687	+	0.0661756i
$280$	2.40774	+	7.87795i	0.143890	+	0.470797i
$281$	−0.246420	+	1.23884i	−0.0147002	+	0.0739030i	−0.987439	−	0.158000i	$-0.949495\pi$
$281$	−0.246420	+	1.23884i	−0.0147002	+	0.0739030i	0.972739	+	0.231903i	$0.0744953\pi$
$282$	−4.94990	−	7.94773i	−0.294762	−	0.473280i
$283$	1.07552	−	10.9199i	0.0639331	−	0.649123i	−0.908806	−	0.417220i	$-0.863005\pi$
$283$	1.07552	−	10.9199i	0.0639331	−	0.649123i	0.972739	−	0.231904i	$-0.0744954\pi$
$284$	−1.53273	+	23.8951i	−0.0909507	+	1.41791i
$285$	−1.57671	+	5.19771i	−0.0933960	+	0.307885i
$286$	−0.904929	−	0.792487i	−0.0535096	−	0.0468607i
$287$	11.7681	+	11.7681i	0.694649	+	0.694649i
$288$	4.96181	+	3.77994i	0.292377	+	0.222735i
$289$	−6.67591	+	6.67591i	−0.392700	+	0.392700i
$290$	12.3196	−	0.816094i	0.723434	−	0.0479227i
$291$	−16.1562	−	4.90093i	−0.947093	−	0.287298i
$292$	0.995144	+	2.91823i	0.0582364	+	0.170777i
$293$	15.9915	+	1.57503i	0.934236	+	0.0920142i	0.553667	−	0.832738i	$-0.313228\pi$
$293$	15.9915	+	1.57503i	0.934236	+	0.0920142i	0.380569	+	0.924753i	$0.375728\pi$
$294$	−0.653773	+	2.81274i	−0.0381288	+	0.164042i
$295$	11.8615	+	2.35939i	0.690601	+	0.137369i
$296$	3.85395	+	7.17413i	0.224006	+	0.416988i
$297$	0.822781	+	4.13640i	0.0477426	+	0.240018i
$298$	−12.7674	+	11.9746i	−0.739593	+	0.693673i
$299$	8.11892	+	4.33965i	0.469529	+	0.250969i
$300$	−0.966812	+	2.57966i	−0.0558189	+	0.148937i
$301$	35.0600	−	3.45311i	2.02083	−	0.199034i
$302$	11.7440	+	1.53780i	0.675789	+	0.0884903i
$303$	−5.05126	−	12.1948i	−0.290188	−	0.700575i
$304$	−14.7465	+	5.59716i	−0.845769	+	0.321019i
$305$	−5.17264	+	12.4879i	−0.296185	+	0.715053i
$306$	−2.14106	+	3.71440i	−0.122396	+	0.212338i
$307$	16.0786	−	19.5919i	0.917657	−	1.11817i	−0.0749976	−	0.997184i	$-0.523895\pi$
$307$	16.0786	−	19.5919i	0.917657	−	1.11817i	0.992654	−	0.120984i	$-0.0386051\pi$
$308$	−4.23216	+	0.993023i	−0.241150	+	0.0565827i
$309$	−5.01960	−	16.5474i	−0.285555	−	0.941350i
$310$	2.99441	−	6.62107i	0.170071	−	0.376052i
$311$	−15.0256	−	10.0398i	−0.852022	−	0.569303i	0.0510970	−	0.998694i	$-0.483728\pi$
$311$	−15.0256	−	10.0398i	−0.852022	−	0.569303i	−0.903119	+	0.429391i	$0.858728\pi$
$312$	−1.70782	−	4.09878i	−0.0966861	−	0.232048i
$313$	11.7933	+	17.6499i	0.666594	+	0.997629i	0.998523	+	0.0543244i	$0.0173005\pi$
$313$	11.7933	+	17.6499i	0.666594	+	0.997629i	−0.331929	+	0.943304i	$0.607699\pi$
$314$	−1.21679	+	1.70053i	−0.0686676	+	0.0959667i
$315$	2.48248	−	2.03732i	0.139872	−	0.114790i
$316$	−1.37116	+	0.794187i	−0.0771336	+	0.0446765i
$317$	1.99788	+	3.73777i	0.112212	+	0.209934i	0.931758	−	0.363079i	$-0.118274\pi$
$317$	1.99788	+	3.73777i	0.112212	+	0.209934i	−0.819546	+	0.573013i	$0.805774\pi$
$318$	−1.27593	−	2.58280i	−0.0715507	−	0.144836i
$319$			6.51545i			0.364795i
$320$	−7.64575	+	2.35426i	−0.427410	+	0.131607i
$321$		−	11.7664i		−	0.656735i
$322$	29.8281	−	14.7355i	1.66226	−	0.821175i
$323$	−5.11056	−	9.56118i	−0.284359	−	0.531998i
$324$	−2.30498	+	8.65051i	−0.128054	+	0.480584i
$325$	−0.881016	+	0.723031i	−0.0488700	+	0.0401066i
$326$	−9.09865	−	6.51041i	−0.503928	−	0.360578i
$327$	−2.90313	−	4.34484i	−0.160543	−	0.240270i
$328$	−11.4046	+	11.4524i	−0.629716	+	0.632355i
$329$	−11.6396	−	7.77734i	−0.641713	−	0.428779i
$330$	−1.32461	−	0.599062i	−0.0729175	−	0.0329773i
$331$	−3.73997	−	12.3290i	−0.205567	−	0.677664i	−0.997729	−	0.0673531i	$-0.978545\pi$
$331$	−3.73997	−	12.3290i	−0.205567	−	0.677664i	0.792162	−	0.610311i	$-0.208955\pi$
$332$	16.4292	+	10.1846i	0.901669	+	0.558953i
$333$	2.01410	−	2.45419i	0.110372	−	0.134489i
$334$	3.38754	+	1.95265i	0.185358	+	0.106844i
$335$	1.25493	−	3.02967i	0.0685643	−	0.165529i
$336$	−15.6378	−	3.60031i	−0.853114	−	0.196413i
$337$	9.77926	+	23.6092i	0.532710	+	1.28608i	0.929722	+	0.368263i	$0.120047\pi$
$337$	9.77926	+	23.6092i	0.532710	+	1.28608i	−0.397011	+	0.917814i	$0.629953\pi$
$338$	−2.14848	+	16.4077i	−0.116862	+	0.892461i
$339$	7.31401	−	0.720367i	0.397243	−	0.0391250i
$340$	−2.27632	−	5.00537i	−0.123451	−	0.271454i
$341$	3.38192	+	1.80767i	0.183141	+	0.0978910i
$342$	4.20659	+	4.48507i	0.227466	+	0.242525i
$343$	−3.13505	−	15.7610i	−0.169277	−	0.851013i
$344$	3.42465	+	34.0414i	0.184645	+	1.83539i
$345$	10.9123	+	2.17059i	0.587499	+	0.116861i
$346$	35.5792	+	8.26976i	1.91275	+	0.444585i
$347$	−27.9315	−	2.75101i	−1.49944	−	0.147682i	−0.685262	−	0.728296i	$-0.740312\pi$
$347$	−27.9315	−	2.75101i	−1.49944	−	0.147682i	−0.814179	+	0.580614i	$0.802812\pi$
$348$	−10.6075	+	21.5857i	−0.568622	+	1.15711i
$349$	22.5616	+	6.84398i	1.20769	+	0.366350i	0.829041	−	0.559188i	$-0.188887\pi$
$349$	22.5616	+	6.84398i	1.20769	+	0.366350i	0.378654	+	0.925538i	$0.376387\pi$
$350$	0.272249	+	4.10983i	0.0145523	+	0.219680i
$351$	−4.55430	+	4.55430i	−0.243091	+	0.243091i
$352$	−0.972962	−	4.10803i	−0.0518591	−	0.218959i
$353$	15.1589	+	15.1589i	0.806826	+	0.806826i	0.984152	−	0.177326i	$-0.0567449\pi$
$353$	15.1589	+	15.1589i	0.806826	+	0.806826i	−0.177326	+	0.984152i	$0.556745\pi$
$354$	−15.5210	+	17.7232i	−0.824933	+	0.941979i
$355$	−3.47532	+	11.4566i	−0.184451	+	0.608053i
$356$	−12.4331	−	14.1374i	−0.658951	−	0.749281i
$357$	1.08109	−	10.9765i	0.0572174	−	0.580938i
$358$	−10.9433	+	6.81554i	−0.578369	+	0.360212i
$359$	−3.18919	+	16.0331i	−0.168319	+	0.846196i	0.800673	+	0.599102i	$0.204476\pi$
$359$	−3.18919	+	16.0331i	−0.168319	+	0.846196i	−0.968992	+	0.247094i	$0.920524\pi$
$360$	1.98358	+	2.40672i	0.104544	+	0.126845i
$361$	3.38449	−	0.673217i	0.178131	−	0.0354325i
$362$	−0.583059	+	18.1984i	−0.0306449	+	0.956485i
$363$	−6.78088	+	12.6861i	−0.355904	+	0.665850i
$364$	−4.85172	−	4.53146i	−0.254299	−	0.237513i
$365$	0.151105	+	1.53420i	0.00790922	+	0.0803036i
$366$	−16.0436	−	20.8783i	−0.838612	−	1.09133i
$367$	0.0207405	−	0.00859100i	0.00108265	−	0.000448447i	−0.382142	−	0.924104i	$-0.624813\pi$
$367$	0.0207405	−	0.00859100i	0.00108265	−	0.000448447i	0.383225	+	0.923655i	$0.374813\pi$
$368$	14.3708	+	28.9376i	0.749131	+	1.50847i
$369$	5.82128	+	2.41125i	0.303044	+	0.125525i
$370$	1.05662	+	3.93240i	0.0549312	+	0.204436i
$371$	−3.32940	−	2.73237i	−0.172854	−	0.141857i
$372$	8.26129	+	11.4948i	0.428328	+	0.595975i
$373$	−2.14811	+	0.651623i	−0.111225	+	0.0337398i	−0.345407	−	0.938453i	$-0.612259\pi$
$373$	−2.14811	+	0.651623i	−0.111225	+	0.0337398i	0.234181	+	0.972193i	$0.424759\pi$
$374$	2.71501	−	1.02402i	0.140390	−	0.0529507i
$375$	−0.765265	+	1.14530i	−0.0395181	+	0.0591430i
$376$	7.52930	−	11.3196i	0.388294	−	0.583761i
$377$	−8.27330	+	5.52804i	−0.426097	+	0.284709i
$378$	3.80759	+	22.9627i	0.195842	+	1.18107i
$379$	4.13366	+	5.03688i	0.212332	+	0.258727i	0.868275	−	0.496083i	$-0.165229\pi$
$379$	4.13366	+	5.03688i	0.212332	+	0.258727i	−0.655943	+	0.754810i	$0.727729\pi$
$380$	−7.81758	+	1.04029i	−0.401034	+	0.0533658i
$381$	8.99958	−	4.81037i	0.461062	−	0.246443i
$382$	1.12878	−	3.33291i	0.0577534	−	0.170526i
$383$	−5.56329			−0.284271			−0.142135	−	0.989847i	$-0.545397\pi$
$383$	−5.56329			−0.284271			−0.142135	+	0.989847i	$0.545397\pi$
$384$	3.46468	−	15.1939i	0.176806	−	0.775362i
$385$	−2.17355			−0.110774
$386$	10.4879	−	30.9672i	0.533820	−	1.57619i
$387$	11.7631	−	6.28748i	0.597950	−	0.319611i
$388$	−3.23357	−	24.2997i	−0.164160	−	1.23363i
$389$	−20.9432	−	25.5193i	−1.06186	−	1.29388i	−0.954029	−	0.299713i	$-0.903109\pi$
$389$	−20.9432	−	25.5193i	−1.06186	−	1.29388i	−0.107832	−	0.994169i	$-0.534391\pi$
$390$	−0.363182	−	2.19026i	−0.0183904	−	0.110908i
$391$	−18.4648	+	12.3378i	−0.933804	+	0.623948i
$392$	−4.11060	+	0.826585i	−0.207616	+	0.0417488i
$393$	10.4165	−	15.5893i	0.525441	−	0.786378i
$394$	−3.01836	+	1.13843i	−0.152063	+	0.0573534i
$395$	−0.758161	+	0.229985i	−0.0381472	+	0.0115718i
$396$	−1.33646	+	0.960516i	−0.0671597	+	0.0482677i
$397$	7.41928	+	6.08884i	0.372363	+	0.305590i	0.801899	−	0.597459i	$-0.203823\pi$
$397$	7.41928	+	6.08884i	0.372363	+	0.305590i	−0.429536	+	0.903050i	$0.641323\pi$
$398$	−6.13878	−	22.8465i	−0.307709	−	1.14519i
$399$	−14.6151	−	6.05377i	−0.731670	−	0.303068i
$400$	−3.99069	+	0.272737i	−0.199535	+	0.0136368i
$401$	9.14748	−	3.78901i	0.456803	−	0.189214i	−0.142403	−	0.989809i	$-0.545483\pi$
$401$	9.14748	−	3.78901i	0.456803	−	0.189214i	0.599206	+	0.800595i	$0.295483\pi$
$402$	3.89233	+	5.06527i	0.194132	+	0.252633i
$403$	0.574015	+	5.82807i	0.0285937	+	0.290317i
$404$	13.0818	−	14.0064i	0.650844	−	0.696843i
$405$	−2.11005	+	3.94763i	−0.104849	+	0.196159i
$406$	−1.15150	+	35.9406i	−0.0571482	+	1.78370i
$407$	−2.10749	+	0.419205i	−0.104464	+	0.0207792i
$408$	10.6620	+	1.02761i	0.527846	+	0.0508744i
$409$	1.67002	−	8.39575i	0.0825771	−	0.415143i	−0.917280	−	0.398243i	$-0.869620\pi$
$409$	1.67002	−	8.39575i	0.0825771	−	0.415143i	0.999857	−	0.0169004i	$-0.00537981\pi$
$410$	−6.85961	+	4.27221i	−0.338772	+	0.210989i
$411$	0.855983	−	8.69094i	0.0422225	−	0.428692i
$412$	18.8537	−	16.5808i	0.928855	−	0.816877i
$413$	−10.2246	+	33.7061i	−0.503122	+	1.65857i
$414$	8.29840	−	9.47582i	0.407844	−	0.465711i
$415$	6.83415	+	6.83415i	0.335475	+	0.335475i
$416$	4.39086	−	4.72093i	0.215280	−	0.231463i
$417$	−14.8252	+	14.8252i	−0.725994	+	0.725994i
$418$	−0.275087	−	4.15268i	−0.0134550	−	0.203114i
$419$	5.98212	+	1.81466i	0.292246	+	0.0886518i	0.433003	−	0.901392i	$-0.357454\pi$
$419$	5.98212	+	1.81466i	0.292246	+	0.0886518i	−0.140758	+	0.990044i	$0.544954\pi$
$420$	−7.20097	−	3.53866i	−0.351371	−	0.172669i
$421$	30.8357	+	3.03705i	1.50284	+	0.148017i	0.815685	−	0.578496i	$-0.196360\pi$
$421$	30.8357	+	3.03705i	1.50284	+	0.148017i	0.687153	+	0.726513i	$0.258860\pi$
$422$	−4.41055	−	1.02516i	−0.214702	−	0.0499038i
$423$	−5.19814	−	1.03397i	−0.252742	−	0.0502735i
$424$	2.64677	−	3.23888i	0.128538	−	0.157294i
$425$	−0.536369	−	2.69651i	−0.0260177	−	0.130800i
$426$	−15.9543	−	17.0105i	−0.772990	−	0.824161i
$427$	−34.7186	−	18.5575i	−1.68015	−	0.898059i
$428$	15.5517	−	7.07253i	0.751721	−	0.341864i
$429$	1.16596	−	0.114837i	0.0562933	−	0.00554441i
$430$	−2.22104	+	16.9618i	−0.107108	+	0.817971i
$431$	−12.3864	−	29.9035i	−0.596633	−	1.44040i	−0.876992	−	0.480505i	$-0.840453\pi$
$431$	−12.3864	−	29.9035i	−0.596633	−	1.44040i	0.280359	−	0.959895i	$-0.409547\pi$
$432$	−22.2924	+	3.74435i	−1.07254	+	0.180150i
$433$	6.82021	−	16.4655i	0.327759	−	0.791279i	−0.671000	−	0.741458i	$-0.734135\pi$
$433$	6.82021	−	16.4655i	0.327759	−	0.791279i	0.998758	−	0.0498214i	$-0.0158652\pi$
$434$	18.3359	+	10.5692i	0.880152	+	0.507339i
$435$	−7.62896	+	9.29591i	−0.365780	+	0.445705i
$436$	3.99760	−	6.44869i	0.191450	−	0.308836i
$437$	9.24588	+	30.4796i	0.442290	+	1.45804i
$438$	−2.73625	−	1.23748i	−0.130743	−	0.0591292i
$439$	26.2827	+	17.5616i	1.25441	+	0.838167i	0.991932	−	0.126772i	$-0.0404616\pi$
$439$	26.2827	+	17.5616i	1.25441	+	0.838167i	0.262474	+	0.964939i	$0.415462\pi$
$440$	−0.00441255	−	2.11084i	−0.000210360	−	0.100630i
$441$	0.908129	+	1.35911i	0.0432442	+	0.0647196i
$442$	3.60385	+	2.57868i	0.171418	+	0.122655i
$443$	−5.71321	+	4.68871i	−0.271443	+	0.222768i	−0.760260	−	0.649619i	$-0.774929\pi$
$443$	−5.71321	+	4.68871i	−0.271443	+	0.222768i	0.488817	+	0.872386i	$0.337429\pi$
$444$	−7.66459	−	2.04228i	−0.363745	−	0.0969221i
$445$	−4.43744	−	8.30186i	−0.210355	−	0.393546i
$446$	−7.43775	+	3.67434i	−0.352188	+	0.173985i
$447$		−	17.0491i		−	0.806393i
$448$	−4.64104	−	22.8328i	−0.219268	−	1.07875i
$449$		−	30.3726i		−	1.43337i	−0.697397	−	0.716685i	$-0.745659\pi$
$449$		−	30.3726i		−	1.43337i	0.697397	−	0.716685i	$-0.254341\pi$
$450$	0.690677	+	1.39810i	0.0325588	+	0.0659070i
$451$	−2.01029	−	3.76099i	−0.0946609	−	0.177098i
$452$	5.34842	+	9.23400i	0.251569	+	0.434331i
$453$	−8.91763	+	7.31851i	−0.418987	+	0.343854i
$454$	−3.38626	+	4.73248i	−0.158925	+	0.222106i
$455$	−1.84415	−	2.75997i	−0.0864552	−	0.129389i
$456$	5.84942	−	14.2057i	0.273924	−	0.665242i
$457$	33.4849	+	22.3739i	1.56636	+	1.04661i	0.969758	+	0.244069i	$0.0784823\pi$
$457$	33.4849	+	22.3739i	1.56636	+	1.04661i	0.596600	+	0.802538i	$0.296518\pi$
$458$	−4.23111	+	9.35559i	−0.197707	+	0.437158i
$459$	−4.51014	−	14.8679i	−0.210515	−	0.693976i
$460$	3.69028	+	15.7276i	0.172060	+	0.733303i
$461$	23.5434	−	28.6877i	1.09652	−	1.33612i	0.159364	−	0.987220i	$-0.449056\pi$
$461$	23.5434	−	28.6877i	1.09652	−	1.33612i	0.937160	−	0.348899i	$-0.113444\pi$
$462$	2.11448	−	3.66828i	0.0983744	−	0.170664i
$463$	7.26074	−	17.5290i	0.337435	−	0.814641i	−0.660525	−	0.750804i	$-0.729666\pi$
$463$	7.26074	−	17.5290i	0.337435	−	0.814641i	0.997960	−	0.0638371i	$-0.0203338\pi$
$464$	−34.9059	−	1.04532i	−1.62047	−	0.0485275i
$465$	2.70854	+	6.53899i	0.125605	+	0.303238i
$466$	−13.3530	−	1.74849i	−0.618564	−	0.0809970i
$467$	5.98621	−	0.589591i	0.277009	−	0.0272830i	0.0414412	−	0.999141i	$-0.486805\pi$
$467$	5.98621	−	0.589591i	0.277009	−	0.0272830i	0.235568	+	0.971858i	$0.424305\pi$
$468$	−2.35358	−	0.882083i	−0.108794	−	0.0407743i
$469$	8.42306	+	4.50222i	0.388941	+	0.207893i
$470$	4.95799	−	4.65016i	0.228695	−	0.214496i
$471$	−0.397332	−	1.99752i	−0.0183081	−	0.0920410i
$472$	−32.7543	−	9.86119i	−1.50764	−	0.453898i
$473$	−8.85387	−	1.76115i	−0.407102	−	0.0809775i
$474$	0.349410	−	1.50328i	0.0160490	−	0.0690477i
$475$	−3.92426	−	0.386506i	−0.180057	−	0.0177341i
$476$	15.1576	−	5.16887i	0.694745	−	0.236915i
$477$	−1.56044	−	0.473354i	−0.0714477	−	0.0216734i
$478$	−39.1247	+	2.59175i	−1.78952	+	0.118544i
$479$	4.14577	−	4.14577i	0.189425	−	0.189425i	−0.606022	−	0.795448i	$-0.707236\pi$
$479$	4.14577	−	4.14577i	0.189425	−	0.189425i	0.795448	+	0.606022i	$0.207236\pi$
$480$	3.42193	−	7.00038i	0.156189	−	0.319522i
$481$	−2.32041	−	2.32041i	−0.105801	−	0.105801i
$482$	21.2018	+	18.5674i	0.965716	+	0.845721i
$483$	−9.40646	+	31.0090i	−0.428009	+	1.41096i
$484$	−20.8433	−	1.33697i	−0.947421	−	0.0607713i
$485$	1.20139	−	12.1979i	0.0545523	−	0.553879i
$486$	8.06540	+	12.9501i	0.365854	+	0.587428i
$487$	−6.24218	+	31.3815i	−0.282860	+	1.42203i	0.534140	+	0.845396i	$0.320635\pi$
$487$	−6.24218	+	31.3815i	−0.282860	+	1.42203i	−0.817000	+	0.576637i	$0.804365\pi$
$488$	17.9515	−	33.7545i	0.812628	−	1.52799i
$489$	10.6877	−	2.12591i	0.483313	−	0.0961370i
$490$	−2.09536	−	0.0671335i	−0.0946589	−	0.00303278i
$491$	13.2233	−	24.7390i	0.596757	−	1.11645i	−0.384386	−	0.923172i	$-0.625587\pi$
$491$	13.2233	−	24.7390i	0.596757	−	1.11645i	0.981143	−	0.193281i	$-0.0619131\pi$
$492$	−0.536995	−	15.7330i	−0.0242096	−	0.709298i
$493$	−2.35268	−	23.8872i	−0.105960	−	1.07583i
$494$	5.03967	−	3.87266i	0.226745	−	0.174239i
$495$	−0.760269	+	0.314914i	−0.0341715	+	0.0141543i
$496$	−10.2270	+	17.8283i	−0.459207	+	0.800514i
$497$	−32.2141	−	13.3435i	−1.44500	−	0.598538i
$498$	−18.1823	+	4.88552i	−0.814770	+	0.218926i
$499$	2.71567	+	2.22869i	0.121570	+	0.0997698i	0.693214	−	0.720732i	$-0.256194\pi$
$499$	2.71567	+	2.22869i	0.121570	+	0.0997698i	−0.571644	+	0.820502i	$0.693694\pi$
$500$	−1.97374	−	0.323041i	−0.0882683	−	0.0144468i
$501$	−3.64437	+	1.10551i	−0.162818	+	0.0493904i
$502$	−11.8763	−	31.4880i	−0.530065	−	1.40538i
$503$	0.929719	−	1.39142i	0.0414541	−	0.0620405i	−0.810164	−	0.586204i	$-0.800622\pi$
$503$	0.929719	−	1.39142i	0.0414541	−	0.0620405i	0.851618	+	0.524163i	$0.175622\pi$
$504$	−7.54196	+	5.06221i	−0.335946	+	0.225489i
$505$	7.96772	−	5.32386i	0.354559	−	0.236909i
$506$	−8.41019	+	1.39455i	−0.373878	+	0.0619952i
$507$	−10.2248	−	12.4590i	−0.454100	−	0.553323i
$508$	11.7674	+	9.00341i	0.522093	+	0.399462i
$509$	17.1901	−	9.18832i	0.761940	−	0.407265i	−0.0441755	−	0.999024i	$-0.514066\pi$
$509$	17.1901	−	9.18832i	0.761940	−	0.407265i	0.806115	+	0.591758i	$0.201566\pi$
$510$	5.07266	+	1.71800i	0.224621	+	0.0760741i
$511$	−4.48991			−0.198622
$512$	22.1645	−	4.55348i	0.979543	−	0.201237i
$513$	−22.2840			−0.983861
$514$	10.6213	+	3.59719i	0.468485	+	0.158665i
$515$	11.0714	−	5.91778i	0.487864	−	0.260769i
$516$	−26.4656	−	20.2492i	−1.16508	−	0.891423i
$517$	2.27563	+	2.77286i	0.100082	+	0.121950i
$518$	−11.6994	+	1.93996i	−0.514044	+	0.0852370i
$519$	−29.5818	+	19.7660i	−1.29850	+	0.867629i
$520$	2.67659	−	1.79655i	0.117376	−	0.0787837i
$521$	−2.02468	+	3.03015i	−0.0887028	+	0.132753i	−0.873167	−	0.487421i	$-0.837938\pi$
$521$	−2.02468	+	3.03015i	−0.0887028	+	0.132753i	0.784465	+	0.620174i	$0.212938\pi$
$522$	4.80446	+	12.7382i	0.210285	+	0.557536i
$523$	−19.0420	+	5.77633i	−0.832649	+	0.252581i	−0.677697	−	0.735341i	$-0.737022\pi$
$523$	−19.0420	+	5.77633i	−0.832649	+	0.252581i	−0.154951	+	0.987922i	$0.549522\pi$
$524$	26.8657	+	4.39709i	1.17363	+	0.192088i
$525$	−3.10111	−	2.54502i	−0.135344	−	0.111074i
$526$	31.4141	−	8.44085i	1.36972	−	0.368039i
$527$	−13.0517	−	5.40617i	−0.568539	−	0.235497i
$528$	3.56673	+	2.04602i	0.155222	+	0.0890416i
$529$	39.0283	−	16.1661i	1.69688	−	0.702872i
$530$	1.65833	−	1.27432i	0.0720331	−	0.0553528i
$531$	1.30710	+	13.2712i	0.0567232	+	0.575920i
$532$	−0.783520	−	22.9557i	−0.0339699	−	0.995256i
$533$	3.07006	−	5.74368i	0.132979	−	0.248786i
$534$	18.3278	+	0.587206i	0.793122	+	0.0254109i
$535$	8.37806	−	1.66650i	0.362215	−	0.0720491i
$536$	−4.35521	+	8.18916i	−0.188117	+	0.353718i
$537$	2.44973	−	12.3156i	0.105713	−	0.531458i
$538$	−1.35113	−	2.16943i	−0.0582515	−	0.0935306i
$539$	0.108438	−	1.10099i	0.00467074	−	0.0474228i
$540$	−11.2792	−	0.723490i	−0.485377	−	0.0311340i
$541$	−4.07787	+	13.4429i	−0.175321	+	0.577957i	0.824604	+	0.565711i	$0.191398\pi$
$541$	−4.07787	+	13.4429i	−0.175321	+	0.577957i	−0.999925	+	0.0122461i	$0.996102\pi$
$542$	−14.5442	−	12.7370i	−0.624725	−	0.547099i
$543$	−12.5400	−	12.5400i	−0.538143	−	0.538143i
$544$	5.05049	+	14.7097i	0.216538	+	0.630673i
$545$	2.68250	−	2.68250i	0.114906	−	0.114906i
$546$	6.45201	−	0.427402i	0.276120	−	0.0182911i
$547$	2.56860	+	0.779176i	0.109825	+	0.0333152i	0.344719	−	0.938706i	$-0.387974\pi$
$547$	2.56860	+	0.779176i	0.109825	+	0.0333152i	−0.234894	+	0.972021i	$0.575474\pi$
$548$	12.0014	−	4.09259i	0.512675	−	0.174827i
$549$	−14.8326	−	1.46089i	−0.633041	−	0.0623491i
$550$	0.238945	−	1.02802i	0.0101886	−	0.0438348i
$551$	−33.7646	−	6.71620i	−1.43842	−	0.286120i
$552$	−30.1333	−	9.07210i	−1.28256	−	0.386134i
$553$	−0.450165	−	2.26313i	−0.0191430	−	0.0962381i
$554$	16.1966	−	15.1910i	0.688127	−	0.645402i
$555$	−3.49770	−	1.86956i	−0.148469	−	0.0793585i
$556$	−28.5058	−	10.6835i	−1.20891	−	0.453081i
$557$	−24.8363	+	2.44616i	−1.05235	+	0.103647i	−0.609371	−	0.792885i	$-0.708578\pi$
$557$	−24.8363	+	2.44616i	−1.05235	+	0.103647i	−0.442978	+	0.896533i	$0.646078\pi$
$558$	7.94488	+	1.04033i	0.336334	+	0.0440408i
$559$	−5.27579	−	12.7369i	−0.223142	−	0.538712i
$560$	0.348717	−	11.6446i	0.0147360	−	0.492075i
$561$	−1.08156	+	2.61112i	−0.0456635	+	0.110241i
$562$	0.892075	−	1.54761i	0.0376299	−	0.0652820i
$563$	−9.13000	+	11.1249i	−0.384784	+	0.468860i	−0.928997	−	0.370086i	$-0.879328\pi$
$563$	−9.13000	+	11.1249i	−0.384784	+	0.468860i	0.544214	+	0.838947i	$0.316828\pi$
$564$	3.02479	+	12.8913i	0.127366	+	0.542823i
$565$	1.54883	+	5.10580i	0.0651597	+	0.214803i
$566$	−6.39448	+	14.1391i	−0.268780	+	0.594311i
$567$	−10.8396	−	7.24277i	−0.455219	−	0.304168i
$568$	12.8931	−	31.3117i	0.540982	−	1.31381i
$569$	14.2936	+	21.3919i	0.599220	+	0.896796i	0.999811	−	0.0194608i	$-0.00619495\pi$
$569$	14.2936	+	21.3919i	0.599220	+	0.896796i	−0.400590	+	0.916257i	$0.631195\pi$
$570$	4.46991	−	6.24694i	0.187224	−	0.261655i
$571$	26.6399	−	21.8628i	1.11484	−	0.914929i	0.117898	−	0.993026i	$-0.462384\pi$
$571$	26.6399	−	21.8628i	1.11484	−	0.914929i	0.996946	+	0.0780969i	$0.0248844\pi$
$572$	0.852620	+	1.47204i	0.0356498	+	0.0615491i
$573$	1.61565	+	3.02267i	0.0674947	+	0.126274i
$574$	−10.4245	−	21.1017i	−0.435110	−	0.880768i
$575$			8.07737i			0.336850i
$576$	−4.93146	−	7.31407i	−0.205477	−	0.304753i
$577$			21.7029i			0.903503i	0.892144	+	0.451751i	$0.149201\pi$
$577$			21.7029i			0.903503i	−0.892144	+	0.451751i	$0.850799\pi$
$578$	11.9708	−	5.91370i	0.497918	−	0.245977i
$579$	15.0116	+	28.0847i	0.623860	+	1.16716i
$580$	−16.8721	−	4.49568i	−0.700576	−	0.186673i
$581$	−21.7593	+	17.8574i	−0.902727	+	0.740849i
$582$	19.4176	+	13.8940i	0.804884	+	0.575923i
$583$	0.613155	+	0.917652i	0.0253943	+	0.0380053i
$584$	−0.00911501	−	4.36036i	−0.000377182	−	0.180433i
$585$	−1.04493	−	0.698198i	−0.0432024	−	0.0288669i
$586$	−20.7058	−	9.36429i	−0.855349	−	0.386835i
$587$	−0.317675	−	1.04723i	−0.0131118	−	0.0432240i	0.950140	−	0.311823i	$-0.100939\pi$
$587$	−0.317675	−	1.04723i	−0.0131118	−	0.0432240i	−0.963252	+	0.268599i	$0.913439\pi$
$588$	2.15172	−	3.47102i	0.0887353	−	0.143142i
$589$	−12.8539	+	15.6625i	−0.529636	+	0.645364i
$590$	−14.8178	−	8.54132i	−0.610041	−	0.351641i
$591$	1.20240	−	2.90286i	0.0494602	−	0.119408i
$592$	−1.90774	−	11.3579i	−0.0784075	−	0.466808i
$593$	17.6443	+	42.5970i	0.724563	+	1.74925i	0.659915	+	0.751341i	$0.270592\pi$
$593$	17.6443	+	42.5970i	0.724563	+	1.74925i	0.0646478	+	0.997908i	$0.479408\pi$
$594$	0.774384	−	5.91387i	0.0317734	−	0.242649i
$595$	7.96876	−	0.784855i	0.326687	−	0.0321759i
$596$	22.5339	−	10.2479i	0.923025	−	0.419768i
$597$	20.3210	+	10.8618i	0.831684	+	0.444544i
$598$	−8.90643	−	9.49603i	−0.364211	−	0.388321i
$599$	6.79727	+	34.1722i	0.277729	+	1.39624i	0.827755	+	0.561090i	$0.189618\pi$
$599$	6.79727	+	34.1722i	0.277729	+	1.39624i	−0.550026	+	0.835148i	$0.685382\pi$
$600$	2.46529	−	3.01680i	0.100645	−	0.123160i
$601$	20.5349	+	4.08465i	0.837638	+	0.166616i	0.595227	−	0.803557i	$-0.297062\pi$
$601$	20.5349	+	4.08465i	0.837638	+	0.166616i	0.242410	+	0.970174i	$0.422062\pi$
$602$	−48.5286	−	11.2796i	−1.97788	−	0.459724i
$603$	3.59853	+	0.354425i	0.146544	+	0.0144333i
$604$	−15.0332	−	7.38751i	−0.611691	−	0.300593i
$605$	−9.99337	−	3.03146i	−0.406288	−	0.123246i
$606$	1.23386	+	18.6262i	0.0501222	+	0.756638i
$607$	−21.2982	+	21.2982i	−0.864468	+	0.864468i	−0.991853	−	0.127385i	$-0.959341\pi$
$607$	−21.2982	+	21.2982i	−0.864468	+	0.864468i	0.127385	+	0.991853i	$0.459341\pi$
$608$	22.2918	−	0.807514i	0.904050	−	0.0327490i
$609$	−24.7657	−	24.7657i	−1.00356	−	1.00356i
$610$	12.5938	−	14.3806i	0.509907	−	0.582255i
$611$	−1.59021	+	5.24223i	−0.0643331	+	0.212078i
$612$	4.55295	−	4.00407i	0.184042	−	0.161855i
$613$	3.52960	−	35.8367i	0.142559	−	1.44743i	−0.611823	−	0.790995i	$-0.709564\pi$
$613$	3.52960	−	35.8367i	0.142559	−	1.44743i	0.754383	−	0.656435i	$-0.227936\pi$
$614$	−30.4249	+	18.9488i	−1.22785	+	0.764712i
$615$	1.53557	−	7.71984i	0.0619202	−	0.311294i
$616$	6.11938	+	0.589792i	0.246557	+	0.0237634i
$617$	−6.94030	+	1.38051i	−0.279406	+	0.0555773i	−0.332804	−	0.942996i	$-0.607995\pi$
$617$	−6.94030	+	1.38051i	−0.279406	+	0.0555773i	0.0533981	+	0.998573i	$0.482995\pi$
$618$	−0.783100	+	24.4420i	−0.0315009	+	0.983203i
$619$	−5.07658	+	9.49761i	−0.204045	+	0.381741i	−0.963041	−	0.269354i	$-0.913190\pi$
$619$	−5.07658	+	9.49761i	−0.204045	+	0.381741i	0.758996	+	0.651095i	$0.225690\pi$
$620$	−7.01460	+	7.51036i	−0.281713	+	0.301623i
$621$	4.47415	+	45.4268i	0.179541	+	1.82291i
$622$	15.5719	+	20.2644i	0.624375	+	0.812528i
$623$	25.3291	−	10.4917i	1.01479	−	0.420340i
$624$	0.428168	+	6.26497i	0.0171405	+	0.250800i
$625$	−0.923880	−	0.382683i	−0.0369552	−	0.0153073i
$626$	−7.78993	−	28.9916i	−0.311348	−	1.15874i
$627$	3.13345	+	2.57156i	0.125138	+	0.102698i
$628$	2.40132	−	1.72583i	0.0958229	−	0.0688681i
$629$	7.57518	−	2.29791i	0.302042	−	0.0916235i
$630$	−4.24946	+	1.60277i	−0.169303	+	0.0638557i
$631$	5.79930	−	8.67927i	0.230867	−	0.345516i	−0.697891	−	0.716204i	$-0.745878\pi$
$631$	5.79930	−	8.67927i	0.230867	−	0.345516i	0.928758	+	0.370688i	$0.120878\pi$
$632$	2.19692	−	0.441770i	0.0873887	−	0.0175727i
$633$	3.66709	−	2.45027i	0.145754	−	0.0973896i
$634$	−0.980473	−	5.91300i	−0.0389396	−	0.234835i
$635$	4.69979	+	5.72671i	0.186505	+	0.227257i
$636$	0.537396	+	4.03843i	0.0213091	+	0.160134i
$637$	1.49003	−	0.796439i	0.0590372	−	0.0315561i
$638$	2.95574	−	8.72730i	0.117019	−	0.345517i
$639$	−13.2012			−0.522230
$640$	11.3093	+	0.315015i	0.447040	+	0.0124521i
$641$	−41.8076			−1.65130			−0.825651	−	0.564181i	$-0.809192\pi$
$641$	−41.8076			−1.65130			−0.825651	+	0.564181i	$0.809192\pi$
$642$	−5.33782	+	15.7608i	−0.210667	+	0.622029i
$643$	−5.35570	+	2.86268i	−0.211208	+	0.112893i	−0.573609	−	0.819129i	$-0.694457\pi$
$643$	−5.35570	+	2.86268i	−0.211208	+	0.112893i	0.362401	+	0.932022i	$0.381957\pi$
$644$	−46.6389	+	6.20626i	−1.83783	+	0.244561i
$645$	−10.5701	−	12.8797i	−0.416198	−	0.507139i
$646$	2.50804	+	15.1254i	0.0986776	+	0.595101i
$647$	−28.6916	+	19.1711i	−1.12798	+	0.753694i	−0.972213	−	0.234100i	$-0.924786\pi$
$647$	−28.6916	+	19.1711i	−1.12798	+	0.753694i	−0.155770	+	0.987793i	$0.549786\pi$
$648$	7.01178	−	10.5415i	0.275449	−	0.414110i
$649$	5.01434	−	7.50449i	0.196830	−	0.294577i
$650$	1.50811	−	0.568811i	0.0591528	−	0.0223106i
$651$	−19.7260	+	5.98383i	−0.773124	+	0.234525i
$652$	9.23399	+	12.8482i	0.361631	+	0.503173i
$653$	31.5415	+	25.8854i	1.23431	+	1.01297i	0.999158	+	0.0410159i	$0.0130594\pi$
$653$	31.5415	+	25.8854i	1.23431	+	1.01297i	0.235154	+	0.971958i	$0.424441\pi$
$654$	1.91764	+	7.13682i	0.0749855	+	0.279072i
$655$	12.5755	+	5.20892i	0.491364	+	0.203529i
$656$	20.4717	−	10.1665i	0.799285	−	0.396937i
$657$	−1.57049	+	0.650517i	−0.0612705	+	0.0253791i
$658$	12.0628	+	15.6979i	0.470257	+	0.611968i
$659$	−4.33429	−	44.0068i	−0.168840	−	1.71426i	−0.590108	−	0.807324i	$-0.700915\pi$
$659$	−4.33429	−	44.0068i	−0.168840	−	1.71426i	0.421268	−	0.906936i	$-0.361585\pi$
$660$	1.50252	+	1.40334i	0.0584856	+	0.0546250i
$661$	11.1323	−	20.8271i	0.432997	−	0.810080i	−0.566909	−	0.823780i	$-0.691861\pi$
$661$	11.1323	−	20.8271i	0.432997	−	0.810080i	0.999906	+	0.0137000i	$0.00436099\pi$
$662$	−0.583466	+	18.2111i	−0.0226771	+	0.707794i
$663$	−4.23324	+	0.842044i	−0.164405	+	0.0327023i
$664$	−17.3863	−	21.0952i	−0.674719	−	0.818652i
$665$	2.24052	−	11.2639i	0.0868837	−	0.436794i
$666$	−3.81118	+	2.37363i	−0.147680	+	0.0919763i
$667$	−6.91204	+	70.1791i	−0.267635	+	2.71734i
$668$	−3.65172	−	4.15230i	−0.141289	−	0.160657i
$669$	2.34553	−	7.73219i	0.0906836	−	0.298944i
$670$	−3.05537	+	3.48888i	−0.118039	+	0.134787i
$671$	7.13294	+	7.13294i	0.275364	+	0.275364i
$672$	19.3133	+	11.9167i	0.745025	+	0.459695i
$673$	4.54675	−	4.54675i	0.175264	−	0.175264i	−0.614023	−	0.789288i	$-0.710450\pi$
$673$	4.54675	−	4.54675i	0.175264	−	0.175264i	0.789288	+	0.614023i	$0.210450\pi$
$674$	−2.38876	−	36.0604i	−0.0920116	−	1.38900i
$675$	−5.40783	−	1.64045i	−0.208147	−	0.0631408i
$676$	10.3212	−	21.0031i	0.396970	−	0.807811i
$677$	−18.1584	−	1.78845i	−0.697885	−	0.0687357i	−0.257148	−	0.966372i	$-0.582783\pi$
$677$	−18.1584	−	1.78845i	−0.697885	−	0.0687357i	−0.440737	+	0.897636i	$0.645283\pi$
$678$	−10.1238	−	2.35309i	−0.388800	−	0.0903699i
$679$	35.0119	+	6.96429i	1.34363	+	0.267265i
$680$	0.778386	+	7.73724i	0.0298497	+	0.296710i
$681$	−1.10575	−	5.55898i	−0.0423724	−	0.213020i
$682$	−3.70995	−	3.95555i	−0.142061	−	0.151466i
$683$	10.3296	+	5.52127i	0.395250	+	0.211265i	0.657034	−	0.753861i	$-0.271811\pi$
$683$	10.3296	+	5.52127i	0.395250	+	0.211265i	−0.261784	+	0.965126i	$0.584311\pi$
$684$	−3.59998	−	7.91597i	−0.137649	−	0.302675i
$685$	6.30949	−	0.621430i	0.241073	−	0.0237436i
$686$	−2.95065	+	22.5337i	−0.112656	+	0.860341i
$687$	−3.82717	−	9.23962i	−0.146016	−	0.352513i
$688$	10.8557	−	47.1513i	0.413868	−	1.79763i
$689$	−0.644999	+	1.55717i	−0.0245725	+	0.0593233i
$690$	−13.6321	−	7.85784i	−0.518965	−	0.299143i
$691$	16.8219	−	20.4975i	0.639934	−	0.779762i	−0.347520	−	0.937673i	$-0.612976\pi$
$691$	16.8219	−	20.4975i	0.639934	−	0.779762i	0.987453	+	0.157911i	$0.0504760\pi$
$692$	−43.9059	−	27.2177i	−1.66905	−	1.03466i
$693$	−0.695721	−	2.29349i	−0.0264283	−	0.0871223i
$694$	36.1656	+	16.3561i	1.37283	+	0.620868i
$695$	−12.6558	−	8.45634i	−0.480062	−	0.320767i
$696$	24.0009	−	24.1014i	0.909750	−	0.913562i
$697$	8.72827	+	13.0628i	0.330607	+	0.494788i
$698$	−27.1160	−	19.4024i	−1.02635	−	0.734394i
$699$	10.1394	−	8.32119i	0.383507	−	0.314736i
$700$	1.49976	−	5.62853i	0.0566855	−	0.212738i
$701$	17.0878	+	31.9691i	0.645399	+	1.20746i	0.965582	+	0.260100i	$0.0837556\pi$
$701$	17.0878	+	31.9691i	0.645399	+	1.20746i	−0.320183	+	0.947356i	$0.603744\pi$
$702$	8.16645	−	4.03432i	0.308223	−	0.152266i
$703$		−	11.3536i		−	0.428210i
$704$	−0.560351	+	5.94400i	−0.0211190	+	0.224023i
$705$			6.62072i			0.249351i
$706$	−13.4281	−	27.1818i	−0.505375	−	1.02300i
$707$	13.1563	+	24.6137i	0.494794	+	0.925694i
$708$	28.8302	−	16.6987i	1.08351	−	0.627577i
$709$	−12.3875	+	10.1661i	−0.465221	+	0.381797i	−0.837600	−	0.546284i	$-0.816042\pi$
$709$	−12.3875	+	10.1661i	−0.465221	+	0.381797i	0.372379	+	0.928081i	$0.378542\pi$
$710$	9.85241	−	13.7693i	0.369754	−	0.516752i
$711$	−0.485352	−	0.726380i	−0.0182021	−	0.0272414i
$712$	10.2404	+	24.5770i	0.383774	+	0.921062i
$713$	34.5095	+	23.0585i	1.29239	+	0.863549i
$714$	−6.42759	+	14.2123i	−0.240547	+	0.531883i
$715$	0.246907	+	0.813943i	0.00923379	+	0.0304397i
$716$	17.7501	−	4.16484i	0.663354	−	0.155647i
$717$	24.2280	−	29.5220i	0.904813	−	1.10252i
$718$	11.5453	−	20.0292i	0.430866	−	0.747484i
$719$	−4.95280	+	11.9571i	−0.184708	+	0.445925i	−0.988926	−	0.148410i	$-0.952585\pi$
$719$	−4.95280	+	11.9571i	−0.184708	+	0.445925i	0.804218	+	0.594335i	$0.202585\pi$
$720$	−1.56515	−	4.12359i	−0.0583296	−	0.153677i
$721$	13.9917	+	33.7791i	0.521080	+	1.25800i
$722$	−4.83885	−	0.633617i	−0.180083	−	0.0235808i
$723$	−27.3177	+	2.69056i	−1.01596	+	0.100063i
$724$	9.03670	−	24.1118i	0.335846	−	0.896108i
$725$	−7.69952	−	4.11548i	−0.285953	−	0.152845i
$726$	14.8379	−	13.9167i	0.550687	−	0.516495i
$727$	6.44311	+	32.3917i	0.238962	+	1.20134i	0.894809	+	0.446448i	$0.147311\pi$
$727$	6.44311	+	32.3917i	0.238962	+	1.20134i	−0.655848	+	0.754893i	$0.727689\pi$
$728$	4.44308	+	8.27078i	0.164671	+	0.306535i
$729$	−27.7446	−	5.51874i	−1.02758	−	0.204398i
$730$	0.493588	−	2.12357i	0.0182685	−	0.0785970i
$731$	33.0964	+	3.25971i	1.22411	+	0.120565i
$732$	12.0186	+	35.2442i	0.444220	+	1.30266i
$733$	−44.5870	−	13.5253i	−1.64686	−	0.499569i	−0.675534	−	0.737329i	$-0.736087\pi$
$733$	−44.5870	−	13.5253i	−1.64686	−	0.499569i	−0.971324	+	0.237760i	$0.923587\pi$
$734$	−0.0316788	+	0.00209851i	−0.00116928	+	7.74573e-5i
$735$	1.44386	−	1.44386i	0.0532576	−	0.0532576i
$736$	−6.12187	−	45.2806i	−0.225655	−	1.66906i
$737$	−1.73052	−	1.73052i	−0.0637444	−	0.0637444i
$738$	−6.70361	−	5.87065i	−0.246763	−	0.216101i
$739$	−13.6785	+	45.0920i	−0.503172	+	1.65874i	0.225786	+	0.974177i	$0.427505\pi$
$739$	−13.6785	+	45.0920i	−0.503172	+	1.65874i	−0.728958	+	0.684559i	$0.759995\pi$
$740$	0.368617	−	5.74671i	0.0135506	−	0.211253i
$741$	−0.606775	+	6.16069i	−0.0222904	+	0.226318i
$742$	3.22012	+	5.17033i	0.118214	+	0.189809i
$743$	3.47584	−	17.4742i	0.127516	−	0.641067i	−0.863171	−	0.504911i	$-0.831525\pi$
$743$	3.47584	−	17.4742i	0.127516	−	0.641067i	0.990687	−	0.136156i	$-0.0434748\pi$
$744$	−5.85122	−	19.1447i	−0.214516	−	0.701879i
$745$	12.1395	−	2.41470i	0.444758	−	0.0884678i
$746$	3.17296	+	0.101659i	0.116170	+	0.00372199i
$747$	−5.02374	+	9.39876i	−0.183809	+	0.343883i
$748$	−4.10124	+	0.139983i	−0.149956	+	0.00511827i
$749$	2.43855	+	24.7590i	0.0891026	+	0.904674i
$750$	1.54462	−	1.18694i	0.0564016	−	0.0433409i
$751$	36.5553	−	15.1417i	1.33392	−	0.552529i	0.402151	−	0.915573i	$-0.368263\pi$
$751$	36.5553	−	15.1417i	1.33392	−	0.552529i	0.931772	+	0.363045i	$0.118263\pi$
$752$	−15.2205	+	11.7466i	−0.555033	+	0.428355i
$753$	30.2831	+	12.5437i	1.10358	+	0.457116i
$754$	13.5897	−	3.65150i	0.494908	−	0.132980i
$755$	−6.47406	−	5.31312i	−0.235615	−	0.193364i
$756$	5.31685	−	32.4853i	0.193372	−	1.18148i
$757$	30.1984	−	9.16057i	1.09758	−	0.332947i	0.310983	−	0.950415i	$-0.399342\pi$
$757$	30.1984	−	9.16057i	1.09758	−	0.332947i	0.786595	+	0.617469i	$0.211842\pi$
$758$	−3.25196	−	8.62203i	−0.118117	−	0.313166i
$759$	4.61309	−	6.90398i	0.167445	−	0.250599i
$760$	10.9434	+	2.15301i	0.396959	+	0.0780978i
$761$	0.409023	−	0.273300i	0.0148271	−	0.00990713i	−0.548135	−	0.836390i	$-0.684662\pi$
$761$	0.409023	−	0.273300i	0.0148271	−	0.00990713i	0.562962	+	0.826483i	$0.309662\pi$
$762$	−14.2370	+	2.36072i	−0.515751	+	0.0855200i
$763$	7.00927	+	8.54082i	0.253753	+	0.309198i
$764$	−3.02395	+	3.95228i	−0.109403	+	0.142989i
$765$	2.67361	−	1.42908i	0.0966647	−	0.0516684i
$766$	7.45190	+	2.52379i	0.269248	+	0.0911882i
$767$	13.7836			0.497697
$768$	−11.5336	+	18.7802i	−0.416183	+	0.677672i
$769$	2.25361			0.0812673			0.0406336	−	0.999174i	$-0.487062\pi$
$769$	2.25361			0.0812673			0.0406336	+	0.999174i	$0.487062\pi$
$770$	2.91142	+	0.986034i	0.104920	+	0.0355342i
$771$	−9.63261	+	5.14874i	−0.346910	+	0.185427i
$772$	−28.0966	+	36.7221i	−1.01122	+	1.32166i
$773$	3.00306	+	3.65924i	0.108013	+	0.131614i	0.824211	−	0.566283i	$-0.191619\pi$
$773$	3.00306	+	3.65924i	0.108013	+	0.131614i	−0.716198	+	0.697897i	$0.754119\pi$
$774$	−18.6087	+	3.08563i	−0.668875	+	0.110911i
$775$	−4.27237	+	2.85471i	−0.153468	+	0.102544i
$776$	−6.69227	+	34.0158i	−0.240238	+	1.22109i
$777$	6.41729	−	9.60416i	0.230219	−	0.344547i
$778$	16.4761	+	43.6835i	0.590696	+	1.56613i
$779$	21.5626	−	6.54094i	0.772560	−	0.234353i
$780$	−0.507141	+	3.09857i	−0.0181585	+	0.110946i
$781$	6.90664	+	5.66813i	0.247139	+	0.202822i
$782$	30.3302	−	8.14961i	1.08461	−	0.291429i
$783$	−45.5814	−	18.8804i	−1.62895	−	0.674731i
$784$	5.88103	+	0.757583i	0.210037	+	0.0270565i
$785$	1.36603	−	0.565828i	0.0487557	−	0.0201953i
$786$	−21.0247	+	16.1561i	−0.749927	+	0.576270i
$787$	−2.04992	−	20.8132i	−0.0730719	−	0.741912i	−0.959999	−	0.280003i	$-0.909665\pi$
$787$	−2.04992	−	20.8132i	−0.0730719	−	0.741912i	0.886927	−	0.461909i	$-0.152835\pi$
$788$	4.55948	−	0.155623i	0.162425	−	0.00554384i
$789$	−14.9350	+	27.9415i	−0.531702	+	0.994744i
$790$	1.11987	+	0.0358797i	0.0398433	+	0.00127654i
$791$	−15.2410	+	3.03162i	−0.541907	+	0.107792i
$792$	2.22590	−	0.680303i	0.0790938	−	0.0241735i
$793$	−3.00543	+	15.1093i	−0.106726	+	0.536548i
$794$	−7.17575	−	11.5216i	−0.254658	−	0.408887i
$795$	−0.199662	+	2.02720i	−0.00708129	+	0.0718975i
$796$	−2.14159	+	33.3873i	−0.0759068	+	1.18338i
$797$	−6.91898	+	22.8088i	−0.245083	+	0.807930i	0.744953	+	0.667117i	$0.232472\pi$
$797$	−6.91898	+	22.8088i	−0.245083	+	0.807930i	−0.990036	+	0.140813i	$0.955028\pi$
$798$	16.8303	+	14.7390i	0.595786	+	0.521756i
$799$	−9.34427	−	9.34427i	−0.330576	−	0.330576i
$800$	5.46917	+	1.44506i	0.193364	+	0.0510904i
$801$	7.33959	−	7.33959i	0.259332	−	0.259332i
$802$	−13.9717	+	0.925533i	−0.493359	+	0.0326817i
$803$	1.10096	+	0.333974i	0.0388522	+	0.0117857i
$804$	−2.91582	−	8.55057i	−0.102833	−	0.301556i
$805$	−23.4117	−	2.30585i	−0.825155	−	0.0812706i
$806$	1.87503	−	8.06698i	0.0660451	−	0.284147i
$807$	2.44148	+	0.485641i	0.0859442	+	0.0170954i
$808$	−23.8768	+	12.8267i	−0.839983	+	0.451240i
$809$	2.79528	+	14.0528i	0.0982770	+	0.494072i	0.998303	+	0.0582353i	$0.0185474\pi$
$809$	2.79528	+	14.0528i	0.0982770	+	0.494072i	−0.900026	+	0.435836i	$0.856453\pi$
$810$	4.61721	−	4.33053i	0.162232	−	0.152159i
$811$	−21.7890	−	11.6465i	−0.765117	−	0.408963i	0.0421794	−	0.999110i	$-0.486570\pi$
$811$	−21.7890	−	11.6465i	−0.765117	−	0.408963i	−0.807296	+	0.590147i	$0.799070\pi$
$812$	17.8469	−	47.6193i	0.626304	−	1.67111i
$813$	18.7396	−	1.84569i	0.657225	−	0.0647310i
$814$	3.01311	+	0.394547i	0.105609	+	0.0138289i
$815$	3.02745	+	7.30890i	0.106047	+	0.256020i
$816$	−13.8153	−	6.21328i	−0.483632	−	0.217508i
$817$	18.2534	−	44.0675i	0.638604	−	1.54173i
$818$	−6.04569	+	10.4883i	−0.211383	+	0.366715i
$819$	2.32198	−	2.82934i	0.0811365	−	0.0988651i
$820$	11.1264	−	2.61066i	0.388550	−	0.0911684i
$821$	−2.28898	−	7.54575i	−0.0798859	−	0.263348i	0.907895	−	0.419198i	$-0.137689\pi$
$821$	−2.28898	−	7.54575i	−0.0798859	−	0.263348i	−0.987781	+	0.155849i	$0.950189\pi$
$822$	−5.08922	+	11.2530i	−0.177507	+	0.392494i
$823$	10.5185	+	7.02820i	0.366650	+	0.244988i	0.725223	−	0.688514i	$-0.241737\pi$
$823$	10.5185	+	7.02820i	0.366650	+	0.244988i	−0.358573	+	0.933502i	$0.616737\pi$
$824$	−32.7760	+	13.6566i	−1.14181	+	0.475750i
$825$	0.571113	+	0.854731i	0.0198836	+	0.0297579i
$826$	28.9865	−	40.5102i	1.00857	−	1.40953i
$827$	18.4116	−	15.1100i	0.640233	−	0.525426i	−0.257323	−	0.966325i	$-0.582841\pi$
$827$	18.4116	−	15.1100i	0.640233	−	0.525426i	0.897556	+	0.440900i	$0.145341\pi$
$828$	−15.4142	+	8.92808i	−0.535682	+	0.310272i
$829$	8.20033	+	15.3417i	0.284809	+	0.532841i	0.983122	−	0.182952i	$-0.0585654\pi$
$829$	8.20033	+	15.3417i	0.284809	+	0.532841i	−0.698312	+	0.715793i	$0.746065\pi$
$830$	−6.05387	−	12.2545i	−0.210133	−	0.425360i
$831$			21.6283i			0.750278i
$832$	−8.02311	+	4.33167i	−0.278151	+	0.150174i
$833$			4.07563i			0.141212i
$834$	26.5835	−	13.1326i	0.920512	−	0.454744i
$835$	−1.30332	−	2.43834i	−0.0451033	−	0.0843823i
$836$	−1.51539	+	5.68722i	−0.0524110	+	0.196697i
$837$	−22.4464	+	18.4213i	−0.775860	+	0.636732i
$838$	−7.18970	−	5.14449i	−0.248364	−	0.177713i
$839$	−2.28686	−	3.42253i	−0.0789513	−	0.118159i	0.789892	−	0.613245i	$-0.210136\pi$
$839$	−2.28686	−	3.42253i	−0.0789513	−	0.118159i	−0.868844	+	0.495087i	$0.835136\pi$
$840$	8.04022	+	8.00668i	0.277414	+	0.276257i
$841$	−39.2618	−	26.2339i	−1.35386	−	0.904618i
$842$	−39.9259	−	18.0567i	−1.37594	−	0.622274i
$843$	0.505054	+	1.66494i	0.0173950	+	0.0573436i
$844$	5.44277	+	3.37402i	0.187348	+	0.116139i
$845$	7.42306	−	9.04502i	0.255361	−	0.311158i
$846$	6.49373	+	3.74313i	0.223259	+	0.128691i
$847$	11.6393	−	28.0997i	0.399931	−	0.965518i
$848$	−5.01461	+	3.13770i	−0.172202	+	0.107749i
$849$	−5.78401	−	13.9638i	−0.198507	−	0.479238i
$850$	−0.504819	+	3.85524i	−0.0173151	+	0.132233i
$851$	−23.1449	+	2.27957i	−0.793395	+	0.0781426i
$852$	13.6537	+	30.0229i	0.467766	+	1.02857i
$853$	−42.0124	−	22.4561i	−1.43848	−	0.768882i	−0.446438	−	0.894814i	$-0.647308\pi$
$853$	−42.0124	−	22.4561i	−1.43848	−	0.768882i	−0.992039	+	0.125932i	$0.959808\pi$
$854$	38.0862	+	40.6075i	1.30328	+	1.38956i
$855$	−0.848264	−	4.26451i	−0.0290100	−	0.145843i
$856$	−24.0396	+	2.41845i	−0.821658	+	0.0826609i
$857$	38.2563	+	7.60965i	1.30681	+	0.259941i	0.798897	−	0.601468i	$-0.205417\pi$
$857$	38.2563	+	7.60965i	1.30681	+	0.259941i	0.507913	+	0.861408i	$0.330417\pi$
$858$	−1.61388	−	0.375119i	−0.0550970	−	0.0128063i
$859$	−33.4496	−	3.29450i	−1.14129	−	0.112407i	−0.490341	−	0.871531i	$-0.663128\pi$
$859$	−33.4496	−	3.29450i	−1.14129	−	0.112407i	−0.650946	+	0.759124i	$0.725628\pi$
$860$	10.6698	−	21.7124i	0.363836	−	0.740386i
$861$	21.9371	+	6.65454i	0.747614	+	0.226786i
$862$	3.02561	+	45.6742i	0.103053	+	1.55567i
$863$	12.9810	−	12.9810i	0.441879	−	0.441879i	−0.450764	−	0.892643i	$-0.648848\pi$
$863$	12.9810	−	12.9810i	0.441879	−	0.441879i	0.892643	+	0.450764i	$0.148848\pi$
$864$	31.5588	+	5.09749i	1.07365	+	0.173420i
$865$	−18.2638	−	18.2638i	−0.620988	−	0.620988i
$866$	−16.6051	+	18.9611i	−0.564264	+	0.644325i
$867$	−3.77504	+	12.4447i	−0.128207	+	0.422643i
$868$	−19.7658	−	22.4753i	−0.670895	−	0.762862i
$869$	−0.0579547	+	0.588424i	−0.00196598	+	0.0199609i
$870$	14.4359	−	8.99078i	0.489423	−	0.304816i
$871$	0.729147	−	3.66567i	0.0247062	−	0.124206i
$872$	−8.28015	+	6.82436i	−0.280401	+	0.231102i
$873$	13.2555	−	2.63669i	0.448632	−	0.0892384i
$874$	1.44244	−	45.0211i	0.0487911	−	1.52286i
$875$	1.37292	−	2.56856i	0.0464133	−	0.0868331i
$876$	3.10376	+	2.89888i	0.104866	+	0.0979441i
$877$	0.603438	+	6.12681i	0.0203767	+	0.206888i	0.999982	+	0.00595763i	$0.00189638\pi$
$877$	0.603438	+	6.12681i	0.0203767	+	0.206888i	−0.979606	+	0.200930i	$0.935604\pi$
$878$	−27.2383	−	35.4465i	−0.919249	−	1.19626i
$879$	20.4491	−	8.47030i	0.689732	−	0.285696i
$880$	−0.951672	+	2.82942i	−0.0320809	+	0.0953797i
$881$	−2.68517	−	1.11223i	−0.0904657	−	0.0374721i	0.336992	−	0.941508i	$-0.390591\pi$
$881$	−2.68517	−	1.11223i	−0.0904657	−	0.0374721i	−0.427457	+	0.904036i	$0.640591\pi$
$882$	−0.599857	−	2.23247i	−0.0201982	−	0.0751713i
$883$	1.53268	+	1.25783i	0.0515787	+	0.0423295i	0.659829	−	0.751415i	$-0.270629\pi$
$883$	1.53268	+	1.25783i	0.0515787	+	0.0423295i	−0.608251	+	0.793745i	$0.708129\pi$
$884$	−3.65745	−	5.08898i	−0.123013	−	0.171161i
$885$	15.9412	−	4.83572i	0.535859	−	0.162551i
$886$	9.77976	−	3.68862i	0.328558	−	0.123922i
$887$	13.4935	−	20.1945i	0.453068	−	0.678065i	−0.532675	−	0.846320i	$-0.678813\pi$
$887$	13.4935	−	20.1945i	0.453068	−	0.678065i	0.985743	+	0.168255i	$0.0538132\pi$
$888$	9.34007	+	6.21263i	0.313432	+	0.208482i
$889$	−17.9401	+	11.9872i	−0.601693	+	0.402038i
$890$	2.17770	+	13.1332i	0.0729968	+	0.440226i
$891$	2.11922	+	2.58227i	0.0709964	+	0.0865094i
$892$	11.6296	−	1.54755i	0.389387	−	0.0518159i
$893$	−16.7154	+	8.93456i	−0.559359	+	0.298984i
$894$	−7.73432	+	22.8368i	−0.258674	+	0.763778i
$895$	9.11610			0.304718
$896$	−4.14153	+	32.6894i	−0.138359	+	1.09208i
$897$	12.6806			0.423394
$898$	−13.7785	+	40.6834i	−0.459796	+	1.35762i
$899$	−39.5627	+	21.1467i	−1.31949	+	0.705283i
$900$	−0.290899	−	2.18605i	−0.00969662	−	0.0728683i
$901$	−2.57933	−	3.14293i	−0.0859300	−	0.104706i
$902$	0.986564	+	5.94973i	0.0328490	+	0.198104i
$903$	40.3485	−	26.9600i	1.34271	−	0.897173i
$904$	−2.97508	−	14.7951i	−0.0989499	−	0.492076i
$905$	7.15285	−	10.7050i	0.237769	−	0.355846i
$906$	15.2650	−	5.75749i	0.507146	−	0.191280i
$907$	33.8468	−	10.2673i	1.12386	−	0.340921i	0.326967	−	0.945036i	$-0.393973\pi$
$907$	33.8468	−	10.2673i	1.12386	−	0.340921i	0.796897	+	0.604115i	$0.206473\pi$
$908$	6.68271	−	4.80287i	0.221773	−	0.159389i
$909$	8.16797	+	6.70328i	0.270915	+	0.222334i
$910$	1.21814	+	4.53352i	0.0403809	+	0.150285i
$911$	−42.1882	−	17.4749i	−1.39776	−	0.578970i	−0.448588	−	0.893738i	$-0.648073\pi$
$911$	−42.1882	−	17.4749i	−1.39776	−	0.578970i	−0.949168	+	0.314769i	$0.898073\pi$
$912$	−14.2796	+	16.3746i	−0.472845	+	0.542217i
$913$	6.66385	−	2.76026i	0.220541	−	0.0913512i
$914$	−34.7024	−	45.1598i	−1.14785	−	1.49375i
$915$	1.82494	+	18.5289i	0.0603305	+	0.612546i
$916$	9.91165	−	10.6122i	0.327490	−	0.350636i
$917$	−18.6876	+	34.9621i	−0.617120	+	1.15455i
$918$	−0.703619	+	21.9613i	−0.0232229	+	0.724831i
$919$	5.94432	−	1.18240i	0.196085	−	0.0390038i	−0.0960706	−	0.995375i	$-0.530627\pi$
$919$	5.94432	−	1.18240i	0.196085	−	0.0390038i	0.292156	+	0.956371i	$0.405627\pi$
$920$	2.19179	−	22.7409i	0.0722612	−	0.749745i
$921$	6.81082	−	34.2403i	0.224424	−	1.12826i
$922$	−44.5500	+	27.7461i	−1.46718	+	0.913768i
$923$	−1.33743	+	13.5792i	−0.0440221	+	0.446964i
$924$	−4.49642	+	3.95435i	−0.147921	+	0.130089i
$925$	0.835805	−	2.75528i	0.0274811	−	0.0905930i
$926$	−17.6776	+	20.1858i	−0.580924	+	0.663348i
$927$	9.78811	+	9.78811i	0.321484	+	0.321484i
$928$	46.2815	+	17.2353i	1.51927	+	0.565776i
$929$	−0.287670	+	0.287670i	−0.00943816	+	0.00943816i	−0.711810	−	0.702372i	$-0.752124\pi$
$929$	−0.287670	+	0.287670i	−0.00943816	+	0.00943816i	0.702372	+	0.711810i	$0.252124\pi$
$930$	−0.661609	−	9.98757i	−0.0216950	−	0.327505i
$931$	5.59379	+	1.69686i	0.183329	+	0.0556123i
$932$	17.0928	+	8.39964i	0.559893	+	0.275139i
$933$	−24.7720	−	2.43983i	−0.810998	−	0.0798764i
$934$	−8.28587	−	1.92591i	−0.271122	−	0.0630176i
$935$	−2.01239	−	0.400289i	−0.0658122	−	0.0130909i
$936$	2.75241	+	2.24923i	0.0899654	+	0.0735185i
$937$	6.72971	+	33.8325i	0.219850	+	1.10526i	0.920196	+	0.391458i	$0.128029\pi$
$937$	6.72971	+	33.8325i	0.219850	+	1.10526i	−0.700346	+	0.713804i	$0.746971\pi$
$938$	−9.24007	−	9.85175i	−0.301699	−	0.321671i
$939$	25.7868	+	13.7833i	0.841520	+	0.449802i
$940$	−8.75067	+	3.97959i	−0.285415	+	0.129800i
$941$	21.9322	−	2.16013i	0.714968	−	0.0704183i	0.266009	−	0.963970i	$-0.414295\pi$
$941$	21.9322	−	2.16013i	0.714968	−	0.0704183i	0.448959	+	0.893552i	$0.351795\pi$
$942$	−0.373960	+	2.85589i	−0.0121843	+	0.0930498i
$943$	−17.6633	−	42.6429i	−0.575196	−	1.38865i
$944$	39.4002	+	28.0679i	1.28237	+	0.913532i
$945$	6.29850	−	15.2059i	0.204890	−	0.494649i
$946$	11.0606	+	6.37558i	0.359612	+	0.207288i
$947$	33.0155	−	40.2295i	1.07286	−	1.30728i	0.123759	−	0.992312i	$-0.460505\pi$
$947$	33.0155	−	40.2295i	1.07286	−	1.30728i	0.949101	−	0.314972i	$-0.101995\pi$
$948$	−1.14999	+	1.85509i	−0.0373499	+	0.0602506i
$949$	0.510036	+	1.68136i	0.0165565	+	0.0545793i
$950$	5.08112	+	2.29796i	0.164853	+	0.0745557i
$951$	4.85402	+	3.24335i	0.157402	+	0.105173i
$952$	−22.6481	+	0.0473442i	−0.734028	+	0.00153443i
$953$	13.6098	+	20.3686i	0.440866	+	0.659803i	0.983654	−	0.180067i	$-0.0576314\pi$
$953$	13.6098	+	20.3686i	0.440866	+	0.659803i	−0.542788	+	0.839870i	$0.682631\pi$
$954$	1.87544	+	1.34194i	0.0607195	+	0.0434470i
$955$	−1.92341	+	1.57851i	−0.0622402	+	0.0510792i
$956$	53.5825	+	14.2774i	1.73298	+	0.461763i
$957$	4.23062	+	7.91493i	0.136756	+	0.255853i
$958$	−7.43390	+	3.67243i	−0.240178	+	0.118651i
$959$			18.4650i			0.596267i
$960$	−7.75933	+	7.82449i	−0.250431	+	0.252534i
$961$		−	4.59747i		−	0.148306i
$962$	2.05548	+	4.16079i	0.0662713	+	0.134149i
$963$	4.44015	+	8.30694i	0.143082	+	0.267687i
$964$	−19.9763	−	34.4888i	−0.643392	−	1.11081i
$965$	−17.8711	+	14.6665i	−0.575292	+	0.472130i
$966$	26.6670	−	37.2686i	0.857996	−	1.19910i
$967$	19.9383	+	29.8398i	0.641173	+	0.959584i	0.999661	+	0.0260492i	$0.00829265\pi$
$967$	19.9383	+	29.8398i	0.641173	+	0.959584i	−0.358487	+	0.933535i	$0.616707\pi$
$968$	27.3126	+	11.2464i	0.877859	+	0.361473i
$969$	−12.4165	−	8.29647i	−0.398877	−	0.266521i
$970$	−7.14283	+	15.7938i	−0.229342	+	0.507109i
$971$	−4.56206	−	15.0391i	−0.146404	−	0.482628i	0.852812	−	0.522217i	$-0.174895\pi$
$971$	−4.56206	−	15.0391i	−0.146404	−	0.482628i	−0.999216	+	0.0395894i	$0.987395\pi$
$972$	−4.92861	−	21.0052i	−0.158085	−	0.673743i
$973$	28.1230	−	34.2680i	0.901581	−	1.09858i
$974$	22.5975	−	39.2031i	0.724071	−	1.25615i
$975$	−0.600774	+	1.45040i	−0.0192402	+	0.0464498i
$976$	−39.3584	+	37.0697i	−1.25983	+	1.18657i
$977$	−21.3928	−	51.6469i	−0.684418	−	1.65233i	−0.755736	−	0.654877i	$-0.772720\pi$
$977$	−21.3928	−	51.6469i	−0.684418	−	1.65233i	0.0713177	−	0.997454i	$-0.477280\pi$
$978$	−15.2803	−	2.00086i	−0.488611	−	0.0639805i
$979$	−6.99133	+	0.688586i	−0.223444	+	0.0220073i
$980$	2.77624	+	1.04049i	0.0886837	+	0.0332372i
$981$	3.68915	+	1.97189i	0.117785	+	0.0629576i
$982$	−28.9351	+	27.1386i	−0.923356	+	0.866026i
$983$	1.75450	+	8.82045i	0.0559597	+	0.281329i	0.998626	−	0.0524092i	$-0.0166900\pi$
$983$	1.75450	+	8.82045i	0.0559597	+	0.281329i	−0.942666	+	0.333738i	$0.891690\pi$
$984$	−6.41799	+	21.3176i	−0.204598	+	0.679581i
$985$	2.23724	+	0.445014i	0.0712842	+	0.0141793i
$986$	−7.68508	+	33.0637i	−0.244743	+	1.05296i
$987$	−19.1897	−	1.89002i	−0.610815	−	0.0601601i
$988$	−8.50736	+	2.90109i	−0.270655	+	0.0922959i
$989$	−93.4983	−	28.3624i	−2.97307	−	0.901872i
$990$	1.16122	−	0.0769233i	0.0369061	−	0.00244478i
$991$	−7.51398	+	7.51398i	−0.238689	+	0.238689i	−0.816307	−	0.577618i	$-0.803982\pi$
$991$	−7.51398	+	7.51398i	−0.238689	+	0.238689i	0.577618	+	0.816307i	$0.303982\pi$
$992$	21.7867	−	19.2411i	0.691728	−	0.610906i
$993$	−12.5488	−	12.5488i	−0.398223	−	0.398223i
$994$	37.0968	+	32.4873i	1.17664	+	1.03043i
$995$	−4.85587	+	16.0077i	−0.153941	+	0.507477i
$996$	26.5712	+	1.70438i	0.841939	+	0.0540053i
$997$	4.12179	−	41.8492i	0.130538	−	1.32538i	−0.677183	−	0.735814i	$-0.736800\pi$
$997$	4.12179	−	41.8492i	0.130538	−	1.32538i	0.807722	−	0.589564i	$-0.200700\pi$
$998$	−2.62653	−	4.21724i	−0.0831413	−	0.133495i
$999$	3.17435	−	15.9585i	0.100432	−	0.504905i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	640.2.bm.a.101.7	✓	1024
128.109	even	32	inner	640.2.bm.a.621.7	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
640.2.bm.a.101.7	✓	1024	1.1	even	1	trivial
640.2.bm.a.621.7	yes	1024	128.109	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 640 = 2^{7} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	640.bm (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.33948 - 0.453651i) q^{2} +(1.21479 - 0.649321i) q^{3} +(1.58840 + 1.21531i) q^{4} +(0.634393 + 0.773010i) q^{5} +(-1.92175 + 0.318659i) q^{6} +(-2.42162 + 1.61807i) q^{7} +(-1.57630 - 2.34846i) q^{8} +(-0.612605 + 0.916828i) q^{9} +(-0.499079 - 1.32322i) q^{10} +(0.714160 - 0.216638i) q^{11} +(2.71871 + 0.444969i) q^{12} +(0.881016 + 0.723031i) q^{13} +(3.97775 - 1.06881i) q^{14} +(1.27259 + 0.527123i) q^{15} +(1.04604 + 3.86080i) q^{16} +(-2.54005 + 1.05212i) q^{17} +(1.23649 - 0.950162i) q^{18} +(0.386506 + 3.92426i) q^{19} +(0.0682238 + 1.99884i) q^{20} +(-1.89112 + 3.53803i) q^{21} +(-1.05488 - 0.0337973i) q^{22} +(7.92217 - 1.57582i) q^{23} +(-3.43979 - 1.82937i) q^{24} +(-0.195090 + 0.980785i) q^{25} +(-0.852098 - 1.36816i) q^{26} +(-0.553911 + 5.62395i) q^{27} +(-5.81297 - 0.372867i) q^{28} +(-2.53430 + 8.35447i) q^{29} +(-1.46547 - 1.28338i) q^{30} +(3.63335 + 3.63335i) q^{31} +(0.350307 - 5.64600i) q^{32} +(0.726889 - 0.726889i) q^{33} +(3.87964 - 0.257000i) q^{34} +(-2.78705 - 0.845442i) q^{35} +(-2.08729 + 0.711786i) q^{36} +(-2.86539 - 0.282217i) q^{37} +(1.26253 - 5.43180i) q^{38} +(1.53973 + 0.306272i) q^{39} +(0.815389 - 2.70835i) q^{40} +(-1.11480 - 5.60448i) q^{41} +(4.13814 - 3.88121i) q^{42} +(-10.6679 - 5.70211i) q^{43} +(1.39765 + 0.523818i) q^{44} +(-1.09735 + 0.108079i) q^{45} +(-11.3264 - 1.48313i) q^{46} +(1.83938 + 4.44066i) q^{47} +(3.77762 + 4.01086i) q^{48} +(0.567292 - 1.36957i) q^{49} +(0.706253 - 1.22524i) q^{50} +(-2.40247 + 2.92742i) q^{51} +(0.520700 + 2.21917i) q^{52} +(0.429284 + 1.41516i) q^{53} +(3.29326 - 7.28188i) q^{54} +(0.620522 + 0.414619i) q^{55} +(7.61719 + 3.13650i) q^{56} +(3.01763 + 4.51620i) q^{57} +(7.18465 - 10.0409i) q^{58} +(9.34867 - 7.67226i) q^{59} +(1.38076 + 2.38387i) q^{60} +(6.37176 + 11.9207i) q^{61} +(-3.21852 - 6.51507i) q^{62} -3.21145i q^{63} +(-3.03054 + 7.40377i) q^{64} +1.13972i q^{65} +(-1.30341 + 0.643898i) q^{66} +(-1.54585 - 2.89208i) q^{67} +(-5.31329 - 1.41576i) q^{68} +(8.60059 - 7.05832i) q^{69} +(3.34965 + 2.39680i) q^{70} +(6.65135 + 9.95445i) q^{71} +(3.11878 - 0.00651960i) q^{72} +(1.28181 + 0.856479i) q^{73} +(3.71010 + 1.67791i) q^{74} +(0.399850 + 1.31813i) q^{75} +(-4.15527 + 6.70303i) q^{76} +(-1.37889 + 1.68018i) q^{77} +(-1.92350 - 1.10874i) q^{78} +(-0.303191 + 0.731967i) q^{79} +(-2.32084 + 3.25787i) q^{80} +(1.71295 + 4.13544i) q^{81} +(-1.04923 + 8.01281i) q^{82} +(9.61841 - 0.947330i) q^{83} +(-7.30367 + 3.32152i) q^{84} +(-2.42470 - 1.29603i) q^{85} +(11.7026 + 12.4773i) q^{86} +(2.34608 + 11.7945i) q^{87} +(-1.63450 - 1.33569i) q^{88} +(-9.23251 - 1.83646i) q^{89} +(1.51891 + 0.353043i) q^{90} +(-3.30340 - 0.325357i) q^{91} +(14.4987 + 7.12486i) q^{92} +(6.77299 + 2.05456i) q^{93} +(-0.449302 - 6.78261i) q^{94} +(-2.78830 + 2.78830i) q^{95} +(-3.24051 - 7.08618i) q^{96} +(-8.66696 - 8.66696i) q^{97} +(-1.38118 + 1.57715i) q^{98} +(-0.238878 + 0.787475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 192 q^{52} - 128 q^{54} - 32 q^{56} - 288 q^{58} - 192 q^{62} - 192 q^{64} - 192 q^{66} - 192 q^{68} - 288 q^{72} - 32 q^{74} - 128 q^{76} - 192 q^{78}+O(q^{100}) \) 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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