LMFDB - Embedded newform 161.2.e.a.116.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(93,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("161.93");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.e (of order $3$, degree $2$, 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:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 10 x^{12} - 2 x^{11} + 71 x^{10} - 19 x^{9} + 243 x^{8} - 140 x^{7} + 610 x^{6} - 323 x^{5} + \cdots + 121 $ x^14 + 10x^12 - 2x^11 + 71x^10 - 19x^9 + 243x^8 - 140x^7 + 610x^6 - 323x^5 + 766x^4 - 422x^3 + 675x^2 - 264x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.6
Root			$-1.02250 + 1.77102i$ of defining polynomial
Character	$\chi$	$=$	161.116
Dual form			161.2.e.a.93.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.02250 + 1.77102i) q^{2} +(0.443108 - 0.767485i) q^{3} +(-1.09101 + 1.88969i) q^{4} +(0.756483 + 1.31027i) q^{5} +1.81231 q^{6} +(-2.63728 - 0.211547i) q^{7} -0.372248 q^{8} +(1.10731 + 1.91792i) q^{9} +(-1.54701 + 2.67950i) q^{10} +(1.85912 - 3.22009i) q^{11} +(0.966873 + 1.67467i) q^{12} -3.46012 q^{13} +(-2.32197 - 4.88699i) q^{14} +1.34081 q^{15} +(1.80140 + 3.12012i) q^{16} +(0.941342 - 1.63045i) q^{17} +(-2.26445 + 3.92215i) q^{18} +(-3.91984 - 6.78936i) q^{19} -3.30134 q^{20} +(-1.33096 + 1.93033i) q^{21} +7.60380 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.164946 + 0.285695i) q^{24} +(1.35547 - 2.34774i) q^{25} +(-3.53797 - 6.12795i) q^{26} +4.62128 q^{27} +(3.27707 - 4.75285i) q^{28} -8.98292 q^{29} +(1.37098 + 2.37461i) q^{30} +(-0.0489231 + 0.0847374i) q^{31} +(-4.05612 + 7.02541i) q^{32} +(-1.64758 - 2.85369i) q^{33} +3.85009 q^{34} +(-1.71787 - 3.61557i) q^{35} -4.83237 q^{36} +(3.99451 + 6.91870i) q^{37} +(8.01607 - 13.8842i) q^{38} +(-1.53321 + 2.65559i) q^{39} +(-0.281599 - 0.487745i) q^{40} -1.24879 q^{41} +(-4.77957 - 0.383389i) q^{42} +3.32571 q^{43} +(4.05665 + 7.02632i) q^{44} +(-1.67532 + 2.90175i) q^{45} +(1.02250 - 1.77102i) q^{46} +(3.04616 + 5.27610i) q^{47} +3.19286 q^{48} +(6.91050 + 1.11582i) q^{49} +5.54386 q^{50} +(-0.834232 - 1.44493i) q^{51} +(3.77504 - 6.53856i) q^{52} +(0.615844 - 1.06667i) q^{53} +(4.72526 + 8.18439i) q^{54} +5.62557 q^{55} +(0.981723 + 0.0787480i) q^{56} -6.94764 q^{57} +(-9.18504 - 15.9090i) q^{58} +(-0.0156761 + 0.0271518i) q^{59} +(-1.46285 + 2.53373i) q^{60} +(-0.938670 - 1.62582i) q^{61} -0.200096 q^{62} +(-2.51456 - 5.29234i) q^{63} -9.38393 q^{64} +(-2.61752 - 4.53368i) q^{65} +(3.36930 - 5.83580i) q^{66} +(-5.99009 + 10.3751i) q^{67} +(2.05403 + 3.55769i) q^{68} -0.886215 q^{69} +(4.64674 - 6.73932i) q^{70} +0.158944 q^{71} +(-0.412195 - 0.713942i) q^{72} +(-6.98293 + 12.0948i) q^{73} +(-8.16878 + 14.1487i) q^{74} +(-1.20124 - 2.08060i) q^{75} +17.1064 q^{76} +(-5.58422 + 8.09898i) q^{77} -6.27082 q^{78} +(1.53539 + 2.65937i) q^{79} +(-2.72546 + 4.72064i) q^{80} +(-1.27421 + 2.20700i) q^{81} +(-1.27689 - 2.21163i) q^{82} -12.2989 q^{83} +(-2.19564 - 4.62112i) q^{84} +2.84844 q^{85} +(3.40054 + 5.88990i) q^{86} +(-3.98040 + 6.89426i) q^{87} +(-0.692053 + 1.19867i) q^{88} +(-7.12478 - 12.3405i) q^{89} -6.85208 q^{90} +(9.12531 + 0.731978i) q^{91} +2.18203 q^{92} +(0.0433564 + 0.0750955i) q^{93} +(-6.22940 + 10.7896i) q^{94} +(5.93058 - 10.2721i) q^{95} +(3.59460 + 6.22602i) q^{96} +12.9734 q^{97} +(5.08985 + 13.3796i) q^{98} +8.23449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 5 q^{3} - 6 q^{4} - 4 q^{5} + 12 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} + 2 q^{10} - 4 q^{11} - 9 q^{12} + 28 q^{13} - 14 q^{14} - 6 q^{15} + 8 q^{16} - 4 q^{17} - 19 q^{18} - 9 q^{19} + 24 q^{20} - 6 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) $ 14 * q - 5 * q^3 - 6 * q^4 - 4 * q^5 + 12 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 + 2 * q^10 - 4 * q^11 - 9 * q^12 + 28 * q^13 - 14 * q^14 - 6 * q^15 + 8 * q^16 - 4 * q^17 - 19 * q^18 - 9 * q^19 + 24 * q^20 - 6 * q^21 - 20 * q^22 - 7 * q^23 + 4 * q^24 - 3 * q^25 - 14 * q^26 + 40 * q^27 - 16 * q^28 - 10 * q^29 + 17 * q^30 - 10 * q^31 - 19 * q^32 - 3 * q^33 + 40 * q^34 + 15 * q^35 + 8 * q^36 + 5 * q^37 + 17 * q^38 - 18 * q^39 - 4 * q^40 + 46 * q^41 + q^42 - 22 * q^43 + 34 * q^44 - 6 * q^45 - 4 * q^47 + 22 * q^48 - 20 * q^49 - 18 * q^50 - 7 * q^51 - 12 * q^52 - 2 * q^53 - 15 * q^54 + 34 * q^55 + 31 * q^56 - 48 * q^57 + 7 * q^58 - 7 * q^59 - 32 * q^60 - 12 * q^61 - 8 * q^62 + 52 * q^63 - 18 * q^64 - 9 * q^65 + 27 * q^66 - 2 * q^67 + 12 * q^68 + 10 * q^69 - 13 * q^70 - 56 * q^71 + 20 * q^72 - 59 * q^73 - 2 * q^74 + 22 * q^75 + 2 * q^76 + 2 * q^77 - 34 * q^78 + 4 * q^79 + 22 * q^80 - 11 * q^81 - 54 * q^82 - 18 * q^83 - 17 * q^84 + 18 * q^85 + 15 * q^86 - 11 * q^87 + 33 * q^88 - q^89 + 4 * q^90 + 44 * q^91 + 12 * q^92 - 15 * q^93 + 14 * q^94 + 16 * q^95 - 20 * q^96 + 70 * q^97 - 17 * q^98 + 36 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/161\mathbb{Z}\right)^\times$.

$n$	$24$	$120$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.02250	+	1.77102i	0.723017	+	1.25230i	0.959785	+	0.280736i	$0.0905785\pi$
$2$	1.02250	+	1.77102i	0.723017	+	1.25230i	−0.236768	+	0.971566i	$0.576088\pi$
$3$	0.443108	−	0.767485i	0.255828	−	0.443108i	−0.709292	−	0.704915i	$-0.750985\pi$
$3$	0.443108	−	0.767485i	0.255828	−	0.443108i	0.965120	+	0.261807i	$0.0843185\pi$
$4$	−1.09101	+	1.88969i	−0.545507	+	0.944846i
$5$	0.756483	+	1.31027i	0.338310	+	0.585969i	0.984115	−	0.177533i	$-0.0568116\pi$
$5$	0.756483	+	1.31027i	0.338310	+	0.585969i	−0.645805	+	0.763502i	$0.723478\pi$
$6$	1.81231			0.739873
$7$	−2.63728	−	0.211547i	−0.996798	−	0.0799573i
$7$	−2.63728	−	0.211547i	−0.996798	−	0.0799573i
$8$	−0.372248			−0.131610
$9$	1.10731	+	1.91792i	0.369104	+	0.639306i
$10$	−1.54701	+	2.67950i	−0.489207	+	0.847332i
$11$	1.85912	−	3.22009i	0.560545	−	0.970893i	−0.436903	−	0.899508i	$-0.643925\pi$
$11$	1.85912	−	3.22009i	0.560545	−	0.970893i	0.997449	−	0.0713847i	$-0.0227418\pi$
$12$	0.966873	+	1.67467i	0.279112	+	0.483437i
$13$	−3.46012			−0.959665			−0.479832	−	0.877360i	$-0.659303\pi$
$13$	−3.46012			−0.959665			−0.479832	+	0.877360i	$0.659303\pi$
$14$	−2.32197	−	4.88699i	−0.620571	−	1.30610i
$15$	1.34081			0.346197
$16$	1.80140	+	3.12012i	0.450351	+	0.780031i
$17$	0.941342	−	1.63045i	0.228309	−	0.395443i	−0.728998	−	0.684516i	$-0.760014\pi$
$17$	0.941342	−	1.63045i	0.228309	−	0.395443i	0.957307	+	0.289073i	$0.0933470\pi$
$18$	−2.26445	+	3.92215i	−0.533737	+	0.924459i
$19$	−3.91984	−	6.78936i	−0.899272	−	1.55759i	−0.828426	−	0.560098i	$-0.810764\pi$
$19$	−3.91984	−	6.78936i	−0.899272	−	1.55759i	−0.0708458	−	0.997487i	$-0.522570\pi$
$20$	−3.30134			−0.738201
$21$	−1.33096	+	1.93033i	−0.290439	+	0.421234i
$22$	7.60380			1.62114
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$23$	−0.500000	−	0.866025i	−0.104257	−	0.180579i
$24$	−0.164946	+	0.285695i	−0.0336695	+	0.0583172i
$25$	1.35547	−	2.34774i	0.271093	−	0.469547i
$26$	−3.53797	−	6.12795i	−0.693854	−	1.20179i
$27$	4.62128			0.889365
$28$	3.27707	−	4.75285i	0.619308	−	0.898204i
$29$	−8.98292			−1.66809			−0.834043	−	0.551699i	$-0.813980\pi$
$29$	−8.98292			−1.66809			−0.834043	+	0.551699i	$0.813980\pi$
$30$	1.37098	+	2.37461i	0.250306	+	0.433543i
$31$	−0.0489231	+	0.0847374i	−0.00878685	+	0.0152193i	−0.870385	−	0.492371i	$-0.836130\pi$
$31$	−0.0489231	+	0.0847374i	−0.00878685	+	0.0152193i	0.861599	+	0.507590i	$0.169464\pi$
$32$	−4.05612	+	7.02541i	−0.717028	+	1.24193i
$33$	−1.64758	−	2.85369i	−0.286807	−	0.496764i
$34$	3.85009			0.660285
$35$	−1.71787	−	3.61557i	−0.290374	−	0.611144i
$36$	−4.83237			−0.805395
$37$	3.99451	+	6.91870i	0.656694	+	1.13743i	0.981466	+	0.191635i	$0.0613790\pi$
$37$	3.99451	+	6.91870i	0.656694	+	1.13743i	−0.324772	+	0.945792i	$0.605288\pi$
$38$	8.01607	−	13.8842i	1.30038	−	2.25232i
$39$	−1.53321	+	2.65559i	−0.245509	+	0.425235i
$40$	−0.281599	−	0.487745i	−0.0445248	−	0.0771192i
$41$	−1.24879			−0.195028			−0.0975139	−	0.995234i	$-0.531089\pi$
$41$	−1.24879			−0.195028			−0.0975139	+	0.995234i	$0.531089\pi$
$42$	−4.77957	−	0.383389i	−0.737504	−	0.0591582i
$43$	3.32571			0.507165			0.253583	−	0.967314i	$-0.418391\pi$
$43$	3.32571			0.507165			0.253583	+	0.967314i	$0.418391\pi$
$44$	4.05665	+	7.02632i	0.611563	+	1.05926i
$45$	−1.67532	+	2.90175i	−0.249743	+	0.432567i
$46$	1.02250	−	1.77102i	0.150759	−	0.261123i
$47$	3.04616	+	5.27610i	0.444328	+	0.769598i	0.998005	−	0.0631329i	$-0.0201092\pi$
$47$	3.04616	+	5.27610i	0.444328	+	0.769598i	−0.553677	+	0.832731i	$0.686776\pi$
$48$	3.19286			0.460850
$49$	6.91050	+	1.11582i	0.987214	+	0.159403i
$50$	5.54386			0.784020
$51$	−0.834232	−	1.44493i	−0.116816	−	0.202331i
$52$	3.77504	−	6.53856i	0.523504	−	0.906735i
$53$	0.615844	−	1.06667i	0.0845927	−	0.146519i	−0.820625	−	0.571467i	$-0.806374\pi$
$53$	0.615844	−	1.06667i	0.0845927	−	0.146519i	0.905218	+	0.424948i	$0.139708\pi$
$54$	4.72526	+	8.18439i	0.643026	+	1.11375i
$55$	5.62557			0.758551
$56$	0.981723	+	0.0787480i	0.131188	+	0.0105231i
$57$	−6.94764			−0.920237
$58$	−9.18504	−	15.9090i	−1.20606	−	2.08895i
$59$	−0.0156761	+	0.0271518i	−0.00204085	+	0.00353486i	−0.867044	−	0.498232i	$-0.833983\pi$
$59$	−0.0156761	+	0.0271518i	−0.00204085	+	0.00353486i	0.865003	+	0.501766i	$0.167316\pi$
$60$	−1.46285	+	2.53373i	−0.188853	+	0.327103i
$61$	−0.938670	−	1.62582i	−0.120184	−	0.208165i	0.799656	−	0.600459i	$-0.205015\pi$
$61$	−0.938670	−	1.62582i	−0.120184	−	0.208165i	−0.919840	+	0.392293i	$0.871682\pi$
$62$	−0.200096			−0.0254122
$63$	−2.51456	−	5.29234i	−0.316805	−	0.666772i
$64$	−9.38393			−1.17299
$65$	−2.61752	−	4.53368i	−0.324664	−	0.562334i
$66$	3.36930	−	5.83580i	0.414732	−	0.718337i
$67$	−5.99009	+	10.3751i	−0.731806	+	1.26752i	0.224305	+	0.974519i	$0.427989\pi$
$67$	−5.99009	+	10.3751i	−0.731806	+	1.26752i	−0.956111	+	0.293006i	$0.905345\pi$
$68$	2.05403	+	3.55769i	0.249088	+	0.431434i
$69$	−0.886215			−0.106688
$70$	4.64674	−	6.73932i	0.555391	−	0.805503i
$71$	0.158944			0.0188632			0.00943162	−	0.999956i	$-0.496998\pi$
$71$	0.158944			0.0188632			0.00943162	+	0.999956i	$0.496998\pi$
$72$	−0.412195	−	0.713942i	−0.0485776	−	0.0841389i
$73$	−6.98293	+	12.0948i	−0.817290	+	1.41559i	0.0903811	+	0.995907i	$0.471191\pi$
$73$	−6.98293	+	12.0948i	−0.817290	+	1.41559i	−0.907672	+	0.419681i	$0.862142\pi$
$74$	−8.16878	+	14.1487i	−0.949602	+	1.64476i
$75$	−1.20124	−	2.08060i	−0.138707	−	0.240247i
$76$	17.1064			1.96224
$77$	−5.58422	+	8.09898i	−0.636381	+	0.922965i
$78$	−6.27082			−0.710030
$79$	1.53539	+	2.65937i	0.172745	+	0.299202i	0.939378	−	0.342882i	$-0.111403\pi$
$79$	1.53539	+	2.65937i	0.172745	+	0.299202i	−0.766634	+	0.642085i	$0.778070\pi$
$80$	−2.72546	+	4.72064i	−0.304716	+	0.527784i
$81$	−1.27421	+	2.20700i	−0.141579	+	0.245222i
$82$	−1.27689	−	2.21163i	−0.141008	−	0.244234i
$83$	−12.2989			−1.34998			−0.674989	−	0.737828i	$-0.735852\pi$
$83$	−12.2989			−1.34998			−0.674989	+	0.737828i	$0.735852\pi$
$84$	−2.19564	−	4.62112i	−0.239564	−	0.504206i
$85$	2.84844			0.308956
$86$	3.40054	+	5.88990i	0.366689	+	0.635124i
$87$	−3.98040	+	6.89426i	−0.426744	+	0.739142i
$88$	−0.692053	+	1.19867i	−0.0737731	+	0.127779i
$89$	−7.12478	−	12.3405i	−0.755225	−	1.30809i	−0.945262	−	0.326312i	$-0.894194\pi$
$89$	−7.12478	−	12.3405i	−0.755225	−	1.30809i	0.190037	−	0.981777i	$-0.439139\pi$
$90$	−6.85208			−0.722273
$91$	9.12531	+	0.731978i	0.956592	+	0.0767322i
$92$	2.18203			0.227492
$93$	0.0433564	+	0.0750955i	0.00449585	+	0.00778705i
$94$	−6.22940	+	10.7896i	−0.642513	+	1.11287i
$95$	5.93058	−	10.2721i	0.608465	−	1.05389i
$96$	3.59460	+	6.22602i	0.366872	+	0.635441i
$97$	12.9734			1.31725			0.658625	−	0.752471i	$-0.271138\pi$
$97$	12.9734			1.31725			0.658625	+	0.752471i	$0.271138\pi$
$98$	5.08985	+	13.3796i	0.514152	+	1.35154i
$99$	8.23449			0.827598
$100$	2.95767	+	5.12283i	0.295767	+	0.512283i
$101$	−2.84401	+	4.92597i	−0.282990	+	0.490152i	−0.972120	−	0.234485i	$-0.924660\pi$
$101$	−2.84401	+	4.92597i	−0.282990	+	0.490152i	0.689130	+	0.724638i	$0.257993\pi$
$102$	1.70600	−	2.95489i	0.168920	−	0.292577i
$103$	−2.59465	−	4.49406i	−0.255658	−	0.442813i	0.709416	−	0.704790i	$-0.248959\pi$
$103$	−2.59465	−	4.49406i	−0.255658	−	0.442813i	−0.965074	+	0.261977i	$0.915625\pi$
$104$	1.28802			0.126301
$105$	−3.53610	−	0.283645i	−0.345088	−	0.0276809i
$106$	2.51880			0.244648
$107$	−2.88710	−	5.00061i	−0.279107	−	0.483427i	0.692056	−	0.721844i	$-0.256705\pi$
$107$	−2.88710	−	5.00061i	−0.279107	−	0.483427i	−0.971163	+	0.238416i	$0.923372\pi$
$108$	−5.04188	+	8.73279i	−0.485155	+	0.840313i
$109$	3.01317	−	5.21896i	0.288609	−	0.499886i	−0.684869	−	0.728666i	$-0.740141\pi$
$109$	3.01317	−	5.21896i	0.288609	−	0.499886i	0.973478	+	0.228781i	$0.0734739\pi$
$110$	5.75215	+	9.96301i	0.548446	+	0.949936i
$111$	7.08000			0.672004
$112$	−4.09076	−	8.60972i	−0.386540	−	0.813542i
$113$	8.44589			0.794522			0.397261	−	0.917706i	$-0.369961\pi$
$113$	8.44589			0.794522			0.397261	+	0.917706i	$0.369961\pi$
$114$	−7.10396	−	12.3044i	−0.665347	−	1.15242i
$115$	0.756483	−	1.31027i	0.0705424	−	0.122183i
$116$	9.80050	−	16.9750i	0.909953	−	1.57609i
$117$	−3.83143	−	6.63623i	−0.354216	−	0.613520i
$118$	−0.0641152			−0.00590228
$119$	−2.82750	+	4.10082i	−0.259196	+	0.375922i
$120$	−0.499115			−0.0455628
$121$	−1.41264	−	2.44677i	−0.128422	−	0.222434i
$122$	1.91958	−	3.32481i	0.173791	−	0.301014i
$123$	−0.553347	+	0.958425i	−0.0498936	+	0.0864183i
$124$	−0.106752	−	0.184899i	−0.00958658	−	0.0166044i
$125$	11.6664			1.04347
$126$	6.80171	−	9.86476i	0.605945	−	0.878823i
$127$	0.416632			0.0369701			0.0184851	−	0.999829i	$-0.494116\pi$
$127$	0.416632			0.0369701			0.0184851	+	0.999829i	$0.494116\pi$
$128$	−1.48283	−	2.56833i	−0.131064	−	0.227010i
$129$	1.47365	−	2.55243i	0.129747	−	0.224729i
$130$	5.35284	−	9.27139i	0.469475	−	0.813154i
$131$	7.53823	+	13.0566i	0.658618	+	1.14076i	0.980974	+	0.194142i	$0.0621921\pi$
$131$	7.53823	+	13.0566i	0.658618	+	1.14076i	−0.322355	+	0.946619i	$0.604475\pi$
$132$	7.19013			0.625821
$133$	8.90144	+	18.7347i	0.771853	+	1.62450i
$134$	−24.4995			−2.11643
$135$	3.49592	+	6.05511i	0.300881	+	0.521141i
$136$	−0.350413	+	0.606933i	−0.0300476	+	0.0520440i
$137$	0.0745828	−	0.129181i	0.00637204	−	0.0110367i	−0.862822	−	0.505508i	$-0.831305\pi$
$137$	0.0745828	−	0.129181i	0.00637204	−	0.0110367i	0.869194	+	0.494472i	$0.164638\pi$
$138$	−0.906156	−	1.56951i	−0.0771371	−	0.133605i
$139$	19.6184			1.66401			0.832005	−	0.554768i	$-0.187193\pi$
$139$	19.6184			1.66401			0.832005	+	0.554768i	$0.187193\pi$
$140$	8.70655	+	0.698388i	0.735838	+	0.0590245i
$141$	5.39910			0.454687
$142$	0.162521	+	0.281494i	0.0136384	+	0.0236225i
$143$	−6.43278	+	11.1419i	−0.537936	+	0.931732i
$144$	−3.98943	+	6.90990i	−0.332453	+	0.575825i
$145$	−6.79543	−	11.7700i	−0.564330	−	0.977448i
$146$	−28.5602			−2.36366
$147$	3.91847	−	4.80927i	0.323190	−	0.396662i
$148$	−17.4323			−1.43292
$149$	−4.81856	−	8.34600i	−0.394752	−	0.683731i	0.598317	−	0.801259i	$-0.295836\pi$
$149$	−4.81856	−	8.34600i	−0.394752	−	0.683731i	−0.993070	+	0.117528i	$0.962503\pi$
$150$	2.45653	−	4.25483i	0.200575	−	0.347405i
$151$	8.77911	−	15.2059i	0.714434	−	1.23744i	−0.248744	−	0.968569i	$-0.580018\pi$
$151$	8.77911	−	15.2059i	0.714434	−	1.23744i	0.963178	−	0.268866i	$-0.0866489\pi$
$152$	1.45915	+	2.52733i	0.118353	+	0.204993i
$153$	4.16943			0.337079
$154$	−20.0533	−	1.60856i	−1.61594	−	0.129622i
$155$	−0.148038			−0.0118907
$156$	−3.34550	−	5.79457i	−0.267854	−	0.463937i
$157$	−11.0207	+	19.0884i	−0.879546	+	1.52342i	−0.0277071	+	0.999616i	$0.508821\pi$
$157$	−11.0207	+	19.0884i	−0.879546	+	1.52342i	−0.851839	+	0.523803i	$0.824513\pi$
$158$	−3.13987	+	5.43841i	−0.249794	+	0.432657i
$159$	−0.545771	−	0.945303i	−0.0432824	−	0.0749674i
$160$	−12.2736			−0.970309
$161$	1.13544	+	2.38973i	0.0894848	+	0.188337i
$162$	−5.21152			−0.409456
$163$	−8.10871	−	14.0447i	−0.635123	−	1.10007i	−0.986489	−	0.163828i	$-0.947616\pi$
$163$	−8.10871	−	14.0447i	−0.635123	−	1.10007i	0.351366	−	0.936238i	$-0.385717\pi$
$164$	1.36244	−	2.35982i	0.106389	−	0.184271i
$165$	2.49273	−	4.31754i	0.194059	−	0.336120i
$166$	−12.5756	−	21.7816i	−0.976057	−	1.69058i
$167$	16.6608			1.28925			0.644624	−	0.764499i	$-0.277014\pi$
$167$	16.6608			1.28925			0.644624	+	0.764499i	$0.277014\pi$
$168$	0.495447	−	0.718564i	0.0382245	−	0.0554384i
$169$	−1.02756			−0.0790434
$170$	2.91253	+	5.04465i	0.223381	+	0.386907i
$171$	8.68096	−	15.0359i	0.663849	−	1.14982i
$172$	−3.62839	+	6.28456i	−0.276662	+	0.479193i
$173$	−1.86191	−	3.22493i	−0.141559	−	0.245187i	0.786525	−	0.617558i	$-0.211878\pi$
$173$	−1.86191	−	3.22493i	−0.141559	−	0.245187i	−0.928084	+	0.372372i	$0.878545\pi$
$174$	−16.2798			−1.23417
$175$	−4.07140	+	5.90490i	−0.307769	+	0.446368i
$176$	13.3961			1.00977
$177$	0.0138924	+	0.0240623i	0.00104422	+	0.00180863i
$178$	14.5702	−	25.2363i	1.09208	−	1.89154i
$179$	9.08786	−	15.7406i	0.679259	−	1.17651i	−0.295946	−	0.955205i	$-0.595635\pi$
$179$	9.08786	−	15.7406i	0.679259	−	1.17651i	0.975205	−	0.221306i	$-0.0710318\pi$
$180$	−3.65561	−	6.33169i	−0.272473	−	0.471937i
$181$	−9.63548			−0.716200			−0.358100	−	0.933683i	$-0.616575\pi$
$181$	−9.63548			−0.716200			−0.358100	+	0.933683i	$0.616575\pi$
$182$	8.03428	+	16.9096i	0.595541	+	1.25342i
$183$	−1.66373			−0.122986
$184$	0.186124	+	0.322376i	0.0137212	+	0.0237659i
$185$	−6.04356	+	10.4678i	−0.444332	+	0.769605i
$186$	−0.0886639	+	0.153570i	−0.00650116	+	0.0112603i
$187$	−3.50013	−	6.06241i	−0.255955	−	0.443327i
$188$	−13.2936			−0.969536
$189$	−12.1876	−	0.977618i	−0.886518	−	0.0711112i
$190$	24.2561			1.75972
$191$	−7.18600	−	12.4465i	−0.519961	−	0.900598i	−0.999731	−	0.0232040i	$-0.992613\pi$
$191$	−7.18600	−	12.4465i	−0.519961	−	0.900598i	0.479770	−	0.877394i	$-0.340720\pi$
$192$	−4.15809	+	7.20202i	−0.300084	+	0.519761i
$193$	−5.48564	+	9.50140i	−0.394865	+	0.683926i	−0.993084	−	0.117407i	$-0.962542\pi$
$193$	−5.48564	+	9.50140i	−0.394865	+	0.683926i	0.598219	+	0.801333i	$0.295875\pi$
$194$	13.2653	+	22.9762i	0.952395	+	1.64960i
$195$	−4.63938			−0.332233
$196$	−9.64800	+	11.8413i	−0.689143	+	0.845810i
$197$	5.10847			0.363964			0.181982	−	0.983302i	$-0.441749\pi$
$197$	5.10847			0.363964			0.181982	+	0.983302i	$0.441749\pi$
$198$	8.41977	+	14.5835i	0.598367	+	1.03640i
$199$	2.24792	−	3.89352i	0.159351	−	0.276004i	−0.775284	−	0.631613i	$-0.782393\pi$
$199$	2.24792	−	3.89352i	0.159351	−	0.276004i	0.934635	+	0.355609i	$0.115727\pi$
$200$	−0.504570	+	0.873941i	−0.0356785	+	0.0617969i
$201$	5.30851	+	9.19461i	0.374433	+	0.648537i
$202$	−11.6320			−0.818425
$203$	23.6905	+	1.90031i	1.66275	+	0.133376i
$204$	3.64063			0.254895
$205$	−0.944686	−	1.63624i	−0.0659798	−	0.114280i
$206$	5.30605	−	9.19035i	0.369690	−	0.640322i
$207$	1.10731	−	1.91792i	0.0769635	−	0.133305i
$208$	−6.23308	−	10.7960i	−0.432186	−	0.748568i
$209$	−29.1498			−2.01633
$210$	−3.11332	−	6.55254i	−0.214840	−	0.452169i
$211$	2.58550			0.177993			0.0889965	−	0.996032i	$-0.471634\pi$
$211$	2.58550			0.177993			0.0889965	+	0.996032i	$0.471634\pi$
$212$	1.34379	+	2.32751i	0.0922919	+	0.159854i
$213$	0.0704295	−	0.121987i	0.00482575	−	0.00835844i
$214$	5.90413	−	10.2263i	0.403598	−	0.699052i
$215$	2.51584	+	4.35756i	0.171579	+	0.297183i
$216$	−1.72026			−0.117049
$217$	0.146950	−	0.213127i	0.00997561	−	0.0144680i
$218$	12.3239			0.834677
$219$	6.18838	+	10.7186i	0.418172	+	0.724295i
$220$	−6.13757	+	10.6306i	−0.413795	+	0.716714i
$221$	−3.25716	+	5.64156i	−0.219100	+	0.379492i
$222$	7.23930	+	12.5388i	0.485870	+	0.841551i
$223$	5.65862			0.378929			0.189465	−	0.981888i	$-0.439325\pi$
$223$	5.65862			0.378929			0.189465	+	0.981888i	$0.439325\pi$
$224$	12.1833	−	17.6699i	0.814033	−	1.18062i
$225$	6.00369			0.400246
$226$	8.63592	+	14.9579i	0.574453	+	0.994982i
$227$	5.27962	−	9.14457i	0.350421	−	0.606946i	−0.635902	−	0.771769i	$-0.719372\pi$
$227$	5.27962	−	9.14457i	0.350421	−	0.606946i	0.986323	+	0.164823i	$0.0527053\pi$
$228$	7.57997	−	13.1289i	0.501996	−	0.869482i
$229$	5.78632	+	10.0222i	0.382371	+	0.662285i	0.991401	−	0.130862i	$-0.0417744\pi$
$229$	5.78632	+	10.0222i	0.382371	+	0.662285i	−0.609030	+	0.793147i	$0.708441\pi$
$230$	3.09402			0.204013
$231$	3.74144	+	7.87452i	0.246169	+	0.518106i
$232$	3.34388			0.219536
$233$	5.45551	+	9.44923i	0.357403	+	0.619039i	0.987526	−	0.157455i	$-0.0503291\pi$
$233$	5.45551	+	9.44923i	0.357403	+	0.619039i	−0.630123	+	0.776495i	$0.716996\pi$
$234$	7.83528	−	13.5711i	0.512208	−	0.887171i
$235$	−4.60874	+	7.98256i	−0.300641	+	0.520725i
$236$	−0.0342057	−	0.0592459i	−0.00222660	−	0.00385658i
$237$	2.72137			0.176772
$238$	−10.1538	−	0.814475i	−0.658171	−	0.0527946i
$239$	−17.8912			−1.15729			−0.578644	−	0.815580i	$-0.696418\pi$
$239$	−17.8912			−1.15729			−0.578644	+	0.815580i	$0.696418\pi$
$240$	2.41535	+	4.18351i	0.155910	+	0.270044i
$241$	−1.67268	+	2.89718i	−0.107747	+	0.186623i	−0.914857	−	0.403777i	$-0.867697\pi$
$241$	−1.67268	+	2.89718i	−0.107747	+	0.186623i	0.807110	+	0.590401i	$0.201030\pi$
$242$	2.88886	−	5.00365i	0.185703	−	0.321647i
$243$	8.06114	+	13.9623i	0.517122	+	0.895682i
$244$	4.09641			0.262246
$245$	3.76565	+	9.89869i	0.240579	+	0.632404i
$246$	−2.26319			−0.144296
$247$	13.5631	+	23.4920i	0.863000	+	1.49476i
$248$	0.0182115	−	0.0315433i	0.00115643	−	0.00200300i
$249$	−5.44973	+	9.43921i	−0.345363	+	0.598186i
$250$	11.9289	+	20.6614i	0.754449	+	1.30674i
$251$	−19.2286			−1.21370			−0.606851	−	0.794816i	$-0.707567\pi$
$251$	−19.2286			−1.21370			−0.606851	+	0.794816i	$0.707567\pi$
$252$	12.7443	+	1.02227i	0.802816	+	0.0643972i
$253$	−3.71824			−0.233764
$254$	0.426007	+	0.737865i	0.0267300	+	0.0462978i
$255$	1.26216	−	2.18613i	0.0790398	−	0.136901i
$256$	−6.35155	+	11.0012i	−0.396972	+	0.687575i
$257$	−4.39701	−	7.61585i	−0.274278	−	0.475064i	0.695675	−	0.718357i	$-0.255106\pi$
$257$	−4.39701	−	7.61585i	−0.274278	−	0.475064i	−0.969953	+	0.243293i	$0.921772\pi$
$258$	6.02721			0.375238
$259$	−9.07102	−	19.0916i	−0.563646	−	1.18629i
$260$	11.4230			0.708426
$261$	−9.94689	−	17.2285i	−0.615697	−	1.06642i
$262$	−15.4157	+	26.7008i	−0.952385	+	1.64958i
$263$	−5.28547	+	9.15471i	−0.325916	+	0.564503i	−0.981697	−	0.190448i	$-0.939006\pi$
$263$	−5.28547	+	9.15471i	−0.325916	+	0.564503i	0.655781	+	0.754951i	$0.272339\pi$
$264$	0.613308	+	1.06228i	0.0377465	+	0.0653789i
$265$	1.86350			0.114474
$266$	−24.0778	+	34.9209i	−1.47630	+	2.14114i
$267$	−12.6282			−0.772832
$268$	−13.0705	−	22.6388i	−0.798410	−	1.38289i
$269$	15.4306	−	26.7266i	0.940821	−	1.62955i	0.176911	−	0.984227i	$-0.443390\pi$
$269$	15.4306	−	26.7266i	0.940821	−	1.62955i	0.763910	−	0.645323i	$-0.223277\pi$
$270$	−7.14916	+	12.3827i	−0.435084	+	0.753587i
$271$	5.15958	+	8.93665i	0.313422	+	0.542863i	0.979101	−	0.203376i	$-0.0651913\pi$
$271$	5.15958	+	8.93665i	0.313422	+	0.542863i	−0.665679	+	0.746238i	$0.731858\pi$
$272$	6.78295			0.411277
$273$	4.60528	−	6.67919i	0.278724	−	0.404243i
$274$	0.305044			0.0184284
$275$	−5.03995	−	8.72944i	−0.303920	−	0.526405i
$276$	0.966873	−	1.67467i	0.0581989	−	0.100804i
$277$	10.6735	−	18.4871i	0.641310	−	1.11078i	−0.343831	−	0.939032i	$-0.611725\pi$
$277$	10.6735	−	18.4871i	0.641310	−	1.11078i	0.985141	−	0.171750i	$-0.0549421\pi$
$278$	20.0598	+	34.7446i	1.20311	+	2.08384i
$279$	−0.216693			−0.0129730
$280$	0.639476	+	1.34589i	0.0382160	+	0.0804323i
$281$	5.64761			0.336908			0.168454	−	0.985709i	$-0.446122\pi$
$281$	5.64761			0.336908			0.168454	+	0.985709i	$0.446122\pi$
$282$	5.52059	+	9.56194i	0.328746	+	0.569405i
$283$	−8.27078	+	14.3254i	−0.491647	+	0.851557i	−0.999954	−	0.00961857i	$-0.996938\pi$
$283$	−8.27078	+	14.3254i	−0.491647	+	0.851557i	0.508307	+	0.861176i	$0.330272\pi$
$284$	−0.173411	+	0.300356i	−0.0102900	+	0.0178229i
$285$	−5.25577	−	9.10326i	−0.311325	−	0.539231i
$286$	−26.3101			−1.55575
$287$	3.29340	+	0.264177i	0.194403	+	0.0155939i
$288$	−17.9656			−1.05863
$289$	6.72775	+	11.6528i	0.395750	+	0.685459i
$290$	13.8967	−	24.0697i	0.816040	−	1.41342i
$291$	5.74862	−	9.95690i	0.336990	−	0.583684i
$292$	−15.2370	−	26.3912i	−0.891675	−	1.54443i
$293$	−15.8804			−0.927744			−0.463872	−	0.885902i	$-0.653540\pi$
$293$	−15.8804			−0.927744			−0.463872	+	0.885902i	$0.653540\pi$
$294$	12.5240	+	2.02221i	0.730413	+	0.117938i
$295$	−0.0474348			−0.00276176
$296$	−1.48695	−	2.57547i	−0.0864272	−	0.149696i
$297$	8.59150	−	14.8809i	0.498530	−	0.863479i
$298$	9.85397	−	17.0676i	0.570825	−	0.988698i
$299$	1.73006	+	2.99655i	0.100052	+	0.173295i
$300$	5.24226			0.302662
$301$	−8.77082	−	0.703543i	−0.505542	−	0.0405516i
$302$	35.9066			2.06619
$303$	2.52040	+	4.36547i	0.144793	+	0.250790i
$304$	14.1224	−	24.4608i	0.809976	−	1.40292i
$305$	1.42018	−	2.45982i	0.0813191	−	0.140849i
$306$	4.26325	+	7.38416i	0.243714	+	0.422124i
$307$	−14.4841			−0.826650			−0.413325	−	0.910584i	$-0.635633\pi$
$307$	−14.4841			−0.826650			−0.413325	+	0.910584i	$0.635633\pi$
$308$	−9.21212	−	19.3886i	−0.524910	−	1.10477i
$309$	−4.59883			−0.261618
$310$	−0.151369	−	0.262179i	−0.00859718	−	0.0148908i
$311$	−6.55236	+	11.3490i	−0.371550	+	0.643544i	−0.989804	−	0.142434i	$-0.954507\pi$
$311$	−6.55236	+	11.3490i	−0.371550	+	0.643544i	0.618254	+	0.785978i	$0.287840\pi$
$312$	0.570733	−	0.988539i	0.0323114	−	0.0559650i
$313$	7.66422	+	13.2748i	0.433207	+	0.750337i	0.997147	−	0.0754788i	$-0.0240485\pi$
$313$	7.66422	+	13.2748i	0.433207	+	0.750337i	−0.563940	+	0.825816i	$0.690715\pi$
$314$	−45.0746			−2.54371
$315$	5.03216	−	7.29831i	0.283530	−	0.411213i
$316$	−6.70052			−0.376934
$317$	−16.3703	−	28.3541i	−0.919446	−	1.59253i	−0.800259	−	0.599655i	$-0.795304\pi$
$317$	−16.3703	−	28.3541i	−0.919446	−	1.59253i	−0.119187	−	0.992872i	$-0.538029\pi$
$318$	1.11610	−	1.93314i	0.0625879	−	0.108405i
$319$	−16.7003	+	28.9258i	−0.935038	+	1.61953i
$320$	−7.09878	−	12.2955i	−0.396834	−	0.687337i
$321$	−5.11719			−0.285614
$322$	−3.07127	+	4.45438i	−0.171155	+	0.248233i
$323$	−14.7596			−0.821247
$324$	−2.78036	−	4.81573i	−0.154465	−	0.267540i
$325$	−4.69008	+	8.12345i	−0.260159	+	0.450608i
$326$	16.5823	−	28.7214i	0.918410	−	1.59073i
$327$	−2.67031	−	4.62512i	−0.147669	−	0.255770i
$328$	0.464859			0.0256675
$329$	−6.91743	−	14.5590i	−0.381370	−	0.802662i
$330$	10.1953			0.561232
$331$	−15.9151	−	27.5657i	−0.874772	−	1.51515i	−0.857005	−	0.515308i	$-0.827678\pi$
$331$	−15.9151	−	27.5657i	−0.874772	−	1.51515i	−0.0177670	−	0.999842i	$-0.505656\pi$
$332$	13.4183	−	23.2411i	0.736423	−	1.27552i
$333$	−8.84634	+	15.3223i	−0.484776	+	0.839657i
$334$	17.0356	+	29.5066i	0.932149	+	1.61453i
$335$	−18.1256			−0.990307
$336$	−8.42048	−	0.675441i	−0.459375	−	0.0368483i
$337$	30.6355			1.66882			0.834410	−	0.551144i	$-0.185809\pi$
$337$	30.6355			1.66882			0.834410	+	0.551144i	$0.185809\pi$
$338$	−1.05068	−	1.81984i	−0.0571497	−	0.0989862i
$339$	3.74244	−	6.48209i	0.203261	−	0.352059i
$340$	−3.10768	+	5.38267i	−0.168538	+	0.291916i
$341$	0.181908	+	0.315074i	0.00985086	+	0.0170622i
$342$	35.5051			1.91990
$343$	−17.9889	−	4.40462i	−0.971308	−	0.237827i
$344$	−1.23799			−0.0667478
$345$	−0.670407	−	1.16118i	−0.0360935	−	0.0625158i
$346$	3.80761	−	6.59498i	0.204698	−	0.354548i
$347$	6.92855	−	12.0006i	0.371944	−	0.644226i	−0.617920	−	0.786241i	$-0.712025\pi$
$347$	6.92855	−	12.0006i	0.371944	−	0.644226i	0.989865	+	0.142015i	$0.0453580\pi$
$348$	−8.68535	−	15.0435i	−0.465584	−	0.806414i
$349$	22.8620			1.22377			0.611887	−	0.790945i	$-0.290411\pi$
$349$	22.8620			1.22377			0.611887	+	0.790945i	$0.290411\pi$
$350$	−14.6207	−	1.17279i	−0.781510	−	0.0626881i
$351$	−15.9902			−0.853493
$352$	15.0816	+	26.1221i	0.803853	+	1.39231i
$353$	−4.14830	+	7.18507i	−0.220792	+	0.382423i	−0.955049	−	0.296449i	$-0.904198\pi$
$353$	−4.14830	+	7.18507i	−0.220792	+	0.382423i	0.734257	+	0.678872i	$0.237531\pi$
$354$	−0.0284099	+	0.0492075i	−0.00150997	+	0.00261535i
$355$	0.120239	+	0.208260i	0.00638161	+	0.0110533i
$356$	31.0929			1.64792
$357$	1.89443	+	3.98717i	0.100264	+	0.211023i
$358$	37.1694			1.96446
$359$	−12.8677	−	22.2875i	−0.679131	−	1.17629i	−0.975243	−	0.221136i	$-0.929024\pi$
$359$	−12.8677	−	22.2875i	−0.679131	−	1.17629i	0.296112	−	0.955153i	$-0.404310\pi$
$360$	0.623636	−	1.08017i	0.0328685	−	0.0569300i
$361$	−21.2302	+	36.7719i	−1.11738	+	1.93536i
$362$	−9.85229	−	17.0647i	−0.517825	−	0.896899i
$363$	−2.50382			−0.131416
$364$	−11.3391	+	16.4454i	−0.594328	+	0.861974i
$365$	−21.1299			−1.10599
$366$	−1.70116	−	2.94650i	−0.0889212	−	0.154016i
$367$	−0.616910	+	1.06852i	−0.0322024	+	0.0557763i	−0.881677	−	0.471853i	$-0.843585\pi$
$367$	−0.616910	+	1.06852i	−0.0322024	+	0.0557763i	0.849475	+	0.527629i	$0.176919\pi$
$368$	1.80140	−	3.12012i	0.0939047	−	0.162648i
$369$	−1.38280	−	2.39507i	−0.0719855	−	0.124683i
$370$	−24.7182			−1.28504
$371$	−1.84981	+	2.68284i	−0.0960372	+	0.139286i
$372$	−0.189210			−0.00981008
$373$	16.9774	+	29.4057i	0.879055	+	1.52257i	0.852379	+	0.522924i	$0.175159\pi$
$373$	16.9774	+	29.4057i	0.879055	+	1.52257i	0.0266759	+	0.999644i	$0.491508\pi$
$374$	7.15777	−	12.3976i	0.370120	−	0.641066i
$375$	5.16946	−	8.95377i	0.266950	−	0.462371i
$376$	−1.13393	−	1.96402i	−0.0584778	−	0.101287i
$377$	31.0820			1.60080
$378$	−10.7304	−	22.5841i	−0.551915	−	1.16160i
$379$	−25.2824			−1.29867			−0.649335	−	0.760502i	$-0.724953\pi$
$379$	−25.2824			−1.29867			−0.649335	+	0.760502i	$0.724953\pi$
$380$	12.9407	+	22.4139i	0.663844	+	1.14981i
$381$	0.184613	−	0.319759i	0.00945801	−	0.0163817i
$382$	14.6954	−	25.4531i	0.751881	−	1.30230i
$383$	14.9944	+	25.9711i	0.766180	+	1.32706i	0.939620	+	0.342218i	$0.111178\pi$
$383$	14.9944	+	25.9711i	0.766180	+	1.32706i	−0.173440	+	0.984844i	$0.555488\pi$
$384$	−2.62821			−0.134120
$385$	−14.8362	−	1.19007i	−0.756123	−	0.0606517i
$386$	−22.4363			−1.14198
$387$	3.68259	+	6.37844i	0.187197	+	0.324234i
$388$	−14.1542	+	24.5158i	−0.718570	+	1.24460i
$389$	11.0221	−	19.0908i	0.558842	−	0.967942i	−0.438752	−	0.898608i	$-0.644579\pi$
$389$	11.0221	−	19.0908i	0.558842	−	0.967942i	0.997593	−	0.0693341i	$-0.0220874\pi$
$390$	−4.74377	−	8.21644i	−0.240210	−	0.416056i
$391$	−1.88268			−0.0952114
$392$	−2.57242	−	0.415361i	−0.129927	−	0.0209789i
$393$	13.3610			0.673973
$394$	5.22341	+	9.04722i	0.263152	+	0.455792i
$395$	−2.32299	+	4.02354i	−0.116882	+	0.202446i
$396$	−8.98395	+	15.5607i	−0.451460	+	0.781952i
$397$	−6.86442	−	11.8895i	−0.344515	−	0.596718i	0.640750	−	0.767749i	$-0.278623\pi$
$397$	−6.86442	−	11.8895i	−0.344515	−	0.596718i	−0.985266	+	0.171031i	$0.945290\pi$
$398$	9.19401			0.460854
$399$	18.3229	+	1.46975i	0.917291	+	0.0735797i
$400$	9.76697			0.488349
$401$	2.90649	+	5.03419i	0.145143	+	0.251395i	0.929426	−	0.369008i	$-0.120302\pi$
$401$	2.90649	+	5.03419i	0.145143	+	0.251395i	−0.784283	+	0.620403i	$0.786969\pi$
$402$	−10.8559	+	18.8030i	−0.541443	+	0.937807i
$403$	0.169280	−	0.293201i	0.00843244	−	0.0146054i
$404$	−6.20571	−	10.7486i	−0.308746	−	0.534763i
$405$	−3.85567			−0.191590
$406$	20.8580	+	43.8995i	1.03517	+	2.17869i
$407$	29.7051			1.47243
$408$	0.310541	+	0.537873i	0.0153741	+	0.0266287i
$409$	14.7647	−	25.5732i	0.730068	−	1.26451i	−0.226786	−	0.973945i	$-0.572822\pi$
$409$	14.7647	−	25.5732i	0.730068	−	1.26451i	0.956854	−	0.290570i	$-0.0938449\pi$
$410$	1.93188	−	3.34612i	0.0954090	−	0.165253i
$411$	−0.0660964	−	0.114482i	−0.00326029	−	0.00564700i
$412$	11.3232			0.557853
$413$	0.0470861	−	0.0682906i	0.00231696	−	0.00336036i
$414$	4.52890			0.222584
$415$	−9.30390	−	16.1148i	−0.456711	−	0.791046i
$416$	14.0347	−	24.3088i	0.688106	−	1.19184i
$417$	8.69306	−	15.0568i	0.425701	−	0.737336i
$418$	−29.8056	−	51.6249i	−1.45784	−	2.52506i
$419$	14.6409			0.715255			0.357628	−	0.933864i	$-0.383586\pi$
$419$	14.6409			0.715255			0.357628	+	0.933864i	$0.383586\pi$
$420$	4.39394	−	6.37268i	0.214402	−	0.310955i
$421$	−4.25571			−0.207411			−0.103705	−	0.994608i	$-0.533070\pi$
$421$	−4.25571			−0.207411			−0.103705	+	0.994608i	$0.533070\pi$
$422$	2.64367	+	4.57897i	0.128692	+	0.222901i
$423$	−6.74609	+	11.6846i	−0.328006	+	0.568123i
$424$	−0.229247	+	0.397067i	−0.0111332	+	0.0192833i
$425$	−2.55191	−	4.42005i	−0.123786	−	0.214404i
$426$	0.288057			0.0139564
$427$	2.13160	+	4.48633i	0.103155	+	0.217109i
$428$	12.5995			0.609019
$429$	5.70082	+	9.87412i	0.275238	+	0.476727i
$430$	−5.14490	+	8.91122i	−0.248109	+	0.429737i
$431$	0.326349	−	0.565253i	0.0157197	−	0.0272273i	−0.858059	−	0.513552i	$-0.828329\pi$
$431$	0.326349	−	0.565253i	0.0157197	−	0.0272273i	0.873778	+	0.486325i	$0.161663\pi$
$432$	8.32479	+	14.4190i	0.400527	+	0.693733i
$433$	−6.56790			−0.315633			−0.157817	−	0.987468i	$-0.550445\pi$
$433$	−6.56790			−0.315633			−0.157817	+	0.987468i	$0.550445\pi$
$434$	0.527708	+	0.0423297i	0.0253308	+	0.00203189i
$435$	−12.0444			−0.577486
$436$	6.57482	+	11.3879i	0.314877	+	0.545382i
$437$	−3.91984	+	6.78936i	−0.187511	+	0.324779i
$438$	−12.6552	+	21.9195i	−0.604691	+	1.04736i
$439$	7.00651	+	12.1356i	0.334403	+	0.579202i	0.983370	−	0.181614i	$-0.0581321\pi$
$439$	7.00651	+	12.1356i	0.334403	+	0.579202i	−0.648967	+	0.760816i	$0.724799\pi$
$440$	−2.09411			−0.0998326
$441$	5.51202	+	14.4893i	0.262477	+	0.689968i
$442$	−13.3218			−0.633652
$443$	−18.5502	−	32.1299i	−0.881347	−	1.52654i	−0.849844	−	0.527034i	$-0.823304\pi$
$443$	−18.5502	−	32.1299i	−0.881347	−	1.52654i	−0.0315030	−	0.999504i	$-0.510029\pi$
$444$	−7.72438	+	13.3790i	−0.366583	+	0.634940i
$445$	10.7796	−	18.6707i	0.511000	−	0.885078i
$446$	5.78594	+	10.0215i	0.273972	+	0.474534i
$447$	−8.54057			−0.403955
$448$	24.7480	+	1.98514i	1.16924	+	0.0937891i
$449$	4.57195			0.215764			0.107882	−	0.994164i	$-0.465593\pi$
$449$	4.57195			0.215764			0.107882	+	0.994164i	$0.465593\pi$
$450$	6.13878	+	10.6327i	0.289385	+	0.501229i
$451$	−2.32164	+	4.02120i	−0.109322	+	0.189351i
$452$	−9.21458	+	15.9601i	−0.433417	+	0.750701i
$453$	−7.78018	−	13.4757i	−0.365545	−	0.633142i
$454$	21.5937			1.01344
$455$	5.94405	+	12.5103i	0.278662	+	0.586493i
$456$	2.58625			0.121112
$457$	11.5646	+	20.0305i	0.540969	+	0.936986i	0.998849	+	0.0479716i	$0.0152757\pi$
$457$	11.5646	+	20.0305i	0.540969	+	0.936986i	−0.457880	+	0.889014i	$0.651391\pi$
$458$	−11.8330	+	20.4954i	−0.552921	+	0.957687i
$459$	4.35020	−	7.53477i	0.203050	−	0.351693i
$460$	1.65067	+	2.85904i	0.0769628	+	0.133303i
$461$	21.5238			1.00246			0.501232	−	0.865313i	$-0.332880\pi$
$461$	21.5238			1.00246			0.501232	+	0.865313i	$0.332880\pi$
$462$	−10.1203	+	14.6779i	−0.470841	+	0.682877i
$463$	3.69564			0.171751			0.0858754	−	0.996306i	$-0.472631\pi$
$463$	3.69564			0.171751			0.0858754	+	0.996306i	$0.472631\pi$
$464$	−16.1819	−	28.0278i	−0.751225	−	1.30116i
$465$	−0.0655968	+	0.113617i	−0.00304198	+	0.00526886i
$466$	−11.1565	+	19.3237i	−0.516816	+	0.895152i
$467$	−9.87212	−	17.0990i	−0.456827	−	0.791248i	0.541964	−	0.840402i	$-0.317681\pi$
$467$	−9.87212	−	17.0990i	−0.456827	−	0.791248i	−0.998791	+	0.0491540i	$0.984347\pi$
$468$	16.7206			0.772909
$469$	17.9924	−	26.0950i	0.830811	−	1.20495i
$470$	−18.8497			−0.869473
$471$	9.76670	+	16.9164i	0.450026	+	0.779468i
$472$	0.00583539	−	0.0101072i	0.000268596	−	0.000465221i
$473$	6.18288	−	10.7091i	0.284289	−	0.492403i
$474$	2.78260	+	4.81960i	0.127809	+	0.221372i
$475$	−21.2528			−0.975147
$476$	−4.66445	−	9.81716i	−0.213795	−	0.449969i
$477$	2.72773			0.124894
$478$	−18.2938	−	31.6858i	−0.836739	−	1.44927i
$479$	−18.4457	+	31.9489i	−0.842807	+	1.45978i	0.0447052	+	0.999000i	$0.485765\pi$
$479$	−18.4457	+	31.9489i	−0.842807	+	1.45978i	−0.887512	+	0.460784i	$0.847568\pi$
$480$	−5.43850	+	9.41977i	−0.248233	+	0.429952i
$481$	−13.8215	−	23.9395i	−0.630206	−	1.09155i
$482$	−6.84128			−0.311612
$483$	2.33720	+	0.187476i	0.106346	+	0.00853046i
$484$	6.16486			0.280221
$485$	9.81417	+	16.9986i	0.445639	+	0.771869i
$486$	−16.4850	+	28.5529i	−0.747777	+	1.29519i
$487$	−10.7847	+	18.6796i	−0.488699	+	0.846452i	−0.999915	−	0.0130001i	$-0.995862\pi$
$487$	−10.7847	+	18.6796i	−0.488699	+	0.846452i	0.511216	+	0.859452i	$0.329195\pi$
$488$	0.349418	+	0.605210i	0.0158174	+	0.0273966i
$489$	−14.3721			−0.649930
$490$	−13.6804	+	16.7905i	−0.618019	+	0.758516i
$491$	−3.74105			−0.168831			−0.0844156	−	0.996431i	$-0.526902\pi$
$491$	−3.74105			−0.168831			−0.0844156	+	0.996431i	$0.526902\pi$
$492$	−1.20742	−	2.09131i	−0.0544347	−	0.0942836i
$493$	−8.45600	+	14.6462i	−0.380839	+	0.659633i
$494$	−27.7366	+	48.0411i	−1.24793	+	2.16147i
$495$	6.22925	+	10.7894i	0.279984	+	0.484947i
$496$	−0.352521			−0.0158287
$497$	−0.419181	−	0.0336242i	−0.0188028	−	0.00150825i
$498$	−22.2894			−0.998812
$499$	13.8137	+	23.9261i	0.618388	+	1.07108i	0.989780	+	0.142603i	$0.0455472\pi$
$499$	13.8137	+	23.9261i	0.618388	+	1.07108i	−0.371392	+	0.928476i	$0.621119\pi$
$500$	−12.7282	+	22.0459i	−0.569222	+	0.985921i
$501$	7.38251	−	12.7869i	0.329826	−	0.571276i
$502$	−19.6613	−	34.0544i	−0.877527	−	1.51992i
$503$	35.6054			1.58757			0.793783	−	0.608201i	$-0.208109\pi$
$503$	35.6054			1.58757			0.793783	+	0.608201i	$0.208109\pi$
$504$	0.936040	+	1.97006i	0.0416945	+	0.0877536i
$505$	−8.60578			−0.382952
$506$	−3.80190	−	6.58508i	−0.169015	−	0.292743i
$507$	−0.455321	+	0.788640i	−0.0202215	+	0.0350247i
$508$	−0.454552	+	0.787307i	−0.0201675	+	0.0349311i
$509$	3.82914	+	6.63226i	0.169723	+	0.293970i	0.938323	−	0.345761i	$-0.112379\pi$
$509$	3.82914	+	6.63226i	0.169723	+	0.293970i	−0.768599	+	0.639731i	$0.779046\pi$
$510$	5.16225			0.228588
$511$	20.9746	−	30.4201i	0.927860	−	1.34571i
$512$	−31.9091			−1.41020
$513$	−18.1147	−	31.3755i	−0.799782	−	1.38526i
$514$	8.99190	−	15.5744i	0.396616	−	0.686958i
$515$	3.92561	−	6.79936i	0.172983	−	0.299616i
$516$	3.21554	+	5.56947i	0.141556	+	0.245182i
$517$	22.6527			0.996264
$518$	24.5365	−	35.5861i	1.07807	−	1.56356i
$519$	−3.30011			−0.144859
$520$	0.974368	+	1.68765i	0.0427289	+	0.0740086i
$521$	−5.61264	+	9.72137i	−0.245894	+	0.425901i	−0.962383	−	0.271698i	$-0.912415\pi$
$521$	−5.61264	+	9.72137i	−0.245894	+	0.425901i	0.716489	+	0.697599i	$0.245748\pi$
$522$	20.3414	−	35.2323i	0.890319	−	1.54208i
$523$	0.0675806	+	0.117053i	0.00295509	+	0.00511837i	0.867499	−	0.497439i	$-0.165726\pi$
$523$	0.0675806	+	0.117053i	0.00295509	+	0.00511837i	−0.864544	+	0.502557i	$0.832393\pi$
$524$	−32.8973			−1.43712
$525$	2.72785	+	5.74124i	0.119053	+	0.250568i
$526$	−21.6176			−0.942572
$527$	0.0921068	+	0.159534i	0.00401223	+	0.00694939i
$528$	5.93591	−	10.2813i	0.258328	−	0.447436i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	1.90543	+	3.30031i	0.0827667	+	0.143356i
$531$	−0.0694332			−0.00301315
$532$	−45.1143	−	3.61881i	−1.95595	−	0.156895i
$533$	4.32095			0.187161
$534$	−12.9123	−	22.3648i	−0.558771	−	0.967819i
$535$	4.36809	−	7.56575i	0.188849	−	0.327096i
$536$	2.22980	−	3.86213i	0.0963127	−	0.166818i
$537$	−8.05380	−	13.9496i	−0.347547	−	0.601969i
$538$	63.1112			2.72092
$539$	16.4405	−	20.1780i	0.708141	−	0.869127i
$540$	−15.2564			−0.656530
$541$	1.90578	+	3.30091i	0.0819360	+	0.141917i	0.904081	−	0.427360i	$-0.140556\pi$
$541$	1.90578	+	3.30091i	0.0819360	+	0.141917i	−0.822145	+	0.569277i	$0.807223\pi$
$542$	−10.5513	+	18.2755i	−0.453219	+	0.784998i
$543$	−4.26956	+	7.39509i	−0.183224	+	0.317354i
$544$	7.63639	+	13.2266i	0.327408	+	0.567087i
$545$	9.11764			0.390557
$546$	16.5379	+	1.32657i	0.707757	+	0.0567721i
$547$	−10.7277			−0.458683			−0.229341	−	0.973346i	$-0.573657\pi$
$547$	−10.7277			−0.458683			−0.229341	+	0.973346i	$0.573657\pi$
$548$	0.162742	+	0.281877i	0.00695198	+	0.0120412i
$549$	2.07880	−	3.60059i	0.0887210	−	0.153669i
$550$	10.3067	−	17.8517i	0.439479	−	0.761200i
$551$	35.2116	+	60.9883i	1.50006	+	2.59819i
$552$	0.329892			0.0140411
$553$	−3.48667	−	7.33831i	−0.148268	−	0.312057i
$554$	43.6547			1.85471
$555$	5.35590	+	9.27669i	0.227345	+	0.393773i
$556$	−21.4039	+	37.0727i	−0.907729	+	1.57223i
$557$	−15.6929	+	27.1810i	−0.664931	+	1.15170i	0.314372	+	0.949300i	$0.398206\pi$
$557$	−15.6929	+	27.1810i	−0.664931	+	1.15170i	−0.979304	+	0.202395i	$0.935127\pi$
$558$	−0.221568	−	0.383767i	−0.00937973	−	0.0162462i
$559$	−11.5073			−0.486709
$560$	8.18645	−	11.8731i	0.345941	−	0.501730i
$561$	−6.20374			−0.261922
$562$	5.77469	+	10.0020i	0.243590	+	0.421911i
$563$	14.8248	−	25.6773i	0.624789	−	1.08217i	−0.363792	−	0.931480i	$-0.618518\pi$
$563$	14.8248	−	25.6773i	0.624789	−	1.08217i	0.988582	−	0.150687i	$-0.0481485\pi$
$564$	−5.89050	+	10.2026i	−0.248035	+	0.429609i
$565$	6.38917	+	11.0664i	0.268794	+	0.465566i
$566$	−33.8275			−1.42188
$567$	3.82733	−	5.55091i	0.160733	−	0.233116i
$568$	−0.0591668			−0.00248258
$569$	−7.81122	−	13.5294i	−0.327464	−	0.567184i	0.654544	−	0.756024i	$-0.272861\pi$
$569$	−7.81122	−	13.5294i	−0.327464	−	0.567184i	−0.982008	+	0.188840i	$0.939527\pi$
$570$	10.7481	−	18.6162i	0.450187	−	0.779746i
$571$	−4.18981	+	7.25697i	−0.175338	+	0.303695i	−0.940278	−	0.340407i	$-0.889435\pi$
$571$	−4.18981	+	7.25697i	−0.175338	+	0.303695i	0.764940	+	0.644101i	$0.222769\pi$
$572$	−14.0365	−	24.3119i	−0.586895	−	1.01653i
$573$	−12.7367			−0.532083
$574$	2.89964	+	6.10281i	0.121029	+	0.254726i
$575$	−2.71093			−0.113054
$576$	−10.3909	−	17.9976i	−0.432955	−	0.749901i
$577$	2.16297	−	3.74638i	0.0900457	−	0.155964i	−0.817484	−	0.575951i	$-0.804632\pi$
$577$	2.16297	−	3.74638i	0.0900457	−	0.155964i	0.907530	+	0.419987i	$0.137965\pi$
$578$	−13.7583	+	23.8300i	−0.572268	+	0.991197i
$579$	4.86146	+	8.42029i	0.202035	+	0.349935i
$580$	29.6556			1.23138
$581$	32.4356	+	2.60179i	1.34566	+	0.107941i
$582$	23.5119			0.974598
$583$	−2.28986	−	3.96615i	−0.0948361	−	0.164261i
$584$	2.59938	−	4.50226i	0.107563	−	0.186305i
$585$	5.79683	−	10.0404i	0.239669	−	0.415119i
$586$	−16.2377	−	28.1246i	−0.670775	−	1.16182i
$587$	−8.87385			−0.366263			−0.183132	−	0.983088i	$-0.558623\pi$
$587$	−8.87385			−0.366263			−0.183132	+	0.983088i	$0.558623\pi$
$588$	4.81294	+	12.6517i	0.198482	+	0.521747i
$589$	0.767083			0.0316071
$590$	−0.0485021	−	0.0840081i	−0.00199680	−	0.00345856i
$591$	2.26360	−	3.92068i	0.0931122	−	0.161275i
$592$	−14.3915	+	24.9268i	−0.591486	+	1.02448i
$593$	8.24706	+	14.2843i	0.338666	+	0.586587i	0.984182	−	0.177160i	$-0.0566910\pi$
$593$	8.24706	+	14.2843i	0.338666	+	0.586587i	−0.645516	+	0.763747i	$0.723358\pi$
$594$	35.1393			1.44178
$595$	−7.51213	−	0.602578i	−0.307967	−	0.0247033i
$596$	21.0285			0.861360
$597$	−1.99214	−	3.45049i	−0.0815330	−	0.141219i
$598$	−3.53797	+	6.12795i	−0.144679	+	0.250591i
$599$	−14.7100	+	25.4786i	−0.601036	+	1.04103i	0.391628	+	0.920124i	$0.371912\pi$
$599$	−14.7100	+	25.4786i	−0.601036	+	1.04103i	−0.992664	+	0.120902i	$0.961421\pi$
$600$	0.447158	+	0.774500i	0.0182551	+	0.0316188i
$601$	41.9446			1.71095			0.855477	−	0.517841i	$-0.173264\pi$
$601$	41.9446			1.71095			0.855477	+	0.517841i	$0.173264\pi$
$602$	−7.72218	−	16.2527i	−0.314732	−	0.662410i
$603$	−26.5316			−1.08045
$604$	19.1563	+	33.1796i	0.779457	+	1.35006i
$605$	2.13728	−	3.70188i	0.0868930	−	0.150503i
$606$	−5.15423	+	8.92739i	−0.209376	+	0.362650i
$607$	−8.59096	−	14.8800i	−0.348696	−	0.603960i	0.637322	−	0.770598i	$-0.280042\pi$
$607$	−8.59096	−	14.8800i	−0.348696	−	0.603960i	−0.986018	+	0.166638i	$0.946709\pi$
$608$	63.5973			2.57921
$609$	11.9559	−	17.3400i	0.484477	−	0.702654i
$610$	5.80852			0.235180
$611$	−10.5401	−	18.2559i	−0.426406	−	0.738557i
$612$	−4.54891	+	7.87894i	−0.183879	+	0.318487i
$613$	13.6447	−	23.6333i	0.551103	−	0.954539i	−0.447092	−	0.894488i	$-0.647540\pi$
$613$	13.6447	−	23.6333i	0.551103	−	0.954539i	0.998195	−	0.0600509i	$-0.0191263\pi$
$614$	−14.8100	−	25.6516i	−0.597682	−	1.03522i
$615$	−1.67439			−0.0675180
$616$	2.07871	−	3.01483i	0.0837538	−	0.121471i
$617$	28.5612			1.14983			0.574915	−	0.818213i	$-0.305035\pi$
$617$	28.5612			1.14983			0.574915	+	0.818213i	$0.305035\pi$
$618$	−4.70230	−	8.14463i	−0.189154	−	0.327625i
$619$	11.6594	−	20.1946i	0.468629	−	0.811689i	−0.530728	−	0.847542i	$-0.678081\pi$
$619$	11.6594	−	20.1946i	0.468629	−	0.811689i	0.999357	+	0.0358530i	$0.0114148\pi$
$620$	0.161512	−	0.279746i	0.00648647	−	0.0112349i
$621$	−2.31064	−	4.00214i	−0.0927228	−	0.160601i
$622$	−26.7992			−1.07455
$623$	16.1795	+	34.0525i	0.648216	+	1.36429i
$624$	−11.0477			−0.442262
$625$	2.04809	+	3.54739i	0.0819235	+	0.141896i
$626$	−15.6733	+	27.1470i	−0.626432	+	1.08501i
$627$	−12.9165	+	22.3720i	−0.515835	+	0.893452i
$628$	−24.0474	−	41.6514i	−0.959598	−	1.66207i
$629$	15.0408			0.599716
$630$	18.0709	+	1.44954i	0.719960	+	0.0577509i
$631$	−8.32633			−0.331466			−0.165733	−	0.986171i	$-0.552999\pi$
$631$	−8.32633			−0.331466			−0.165733	+	0.986171i	$0.552999\pi$
$632$	−0.571545	−	0.989945i	−0.0227348	−	0.0393779i
$633$	1.14565	−	1.98433i	0.0455356	−	0.0788700i
$634$	33.4772	−	57.9842i	1.32955	−	2.30285i
$635$	0.315175	+	0.545900i	0.0125073	+	0.0216634i
$636$	2.38177			0.0944435
$637$	−23.9112	−	3.86086i	−0.947394	−	0.152973i
$638$	−68.3043			−2.70419
$639$	0.176001	+	0.304843i	0.00696249	+	0.0120594i
$640$	2.24346	−	3.88580i	0.0886807	−	0.153600i
$641$	6.38867	−	11.0655i	0.252337	−	0.437061i	−0.711832	−	0.702350i	$-0.752134\pi$
$641$	6.38867	−	11.0655i	0.252337	−	0.437061i	0.964169	+	0.265289i	$0.0854674\pi$
$642$	−5.23233	−	9.06266i	−0.206504	−	0.357675i
$643$	−44.8214			−1.76759			−0.883793	−	0.467879i	$-0.845018\pi$
$643$	−44.8214			−1.76759			−0.883793	+	0.467879i	$0.845018\pi$
$644$	−5.75462	−	0.461602i	−0.226764	−	0.0181897i
$645$	4.45915			0.175579
$646$	−15.0917	−	26.1396i	−0.593776	−	1.02845i
$647$	4.56646	−	7.90933i	0.179526	−	0.310948i	−0.762192	−	0.647351i	$-0.775877\pi$
$647$	4.56646	−	7.90933i	0.179526	−	0.310948i	0.941718	+	0.336403i	$0.109210\pi$
$648$	0.474322	−	0.821550i	0.0186331	−	0.0322735i
$649$	0.0582874	+	0.100957i	0.00228798	+	0.00396290i
$650$	−19.1824			−0.752397
$651$	−0.0984568	−	0.207220i	−0.00385883	−	0.00812159i
$652$	35.3869			1.38586
$653$	5.74912	+	9.95777i	0.224980	+	0.389678i	0.956314	−	0.292343i	$-0.0944348\pi$
$653$	5.74912	+	9.95777i	0.224980	+	0.389678i	−0.731333	+	0.682020i	$0.761102\pi$
$654$	5.46080	−	9.45838i	0.213534	−	0.369852i
$655$	−11.4051	+	19.7542i	−0.445634	+	0.771860i
$656$	−2.24957	−	3.89637i	−0.0878310	−	0.152128i
$657$	−30.9291			−1.20666
$658$	18.7112	−	27.1375i	0.729438	−	1.05793i
$659$	−32.6074			−1.27021			−0.635103	−	0.772428i	$-0.719042\pi$
$659$	−32.6074			−1.27021			−0.635103	+	0.772428i	$0.719042\pi$
$660$	5.43921	+	9.42099i	0.211721	+	0.366712i
$661$	1.09549	−	1.89744i	0.0426095	−	0.0738017i	−0.843934	−	0.536447i	$-0.819766\pi$
$661$	1.09549	−	1.89744i	0.0426095	−	0.0738017i	0.886544	+	0.462645i	$0.153100\pi$
$662$	32.5464	−	56.3720i	1.26495	−	2.19096i
$663$	2.88654	+	4.99964i	0.112104	+	0.194170i
$664$	4.57824			0.177670
$665$	−17.8136	+	25.8357i	−0.690783	+	1.00187i
$666$	−36.1815			−1.40201
$667$	4.49146	+	7.77944i	0.173910	+	0.301221i
$668$	−18.1771	+	31.4837i	−0.703294	+	1.21814i
$669$	2.50738	−	4.34290i	0.0969408	−	0.167906i
$670$	−18.5334	−	32.1009i	−0.716009	−	1.24016i
$671$	−6.98040			−0.269475
$672$	−8.16286	−	17.1802i	−0.314889	−	0.662741i
$673$	−3.08634			−0.118969			−0.0594847	−	0.998229i	$-0.518946\pi$
$673$	−3.08634			−0.118969			−0.0594847	+	0.998229i	$0.518946\pi$
$674$	31.3248	+	54.2561i	1.20658	+	2.08987i
$675$	6.26399	−	10.8495i	0.241101	−	0.417599i
$676$	1.12109	−	1.94178i	0.0431187	−	0.0746838i
$677$	5.91089	+	10.2380i	0.227174	+	0.393477i	0.956969	−	0.290189i	$-0.0937180\pi$
$677$	5.91089	+	10.2380i	0.227174	+	0.393477i	−0.729795	+	0.683666i	$0.760385\pi$
$678$	15.3066			0.587845
$679$	−34.2145	−	2.74449i	−1.31303	−	0.105324i
$680$	−1.06033			−0.0406616
$681$	−4.67888	−	8.10406i	−0.179295	−	0.310548i
$682$	−0.372002	+	0.644326i	−0.0142447	+	0.0246725i
$683$	7.87365	−	13.6376i	0.301277	−	0.521827i	−0.675148	−	0.737682i	$-0.735920\pi$
$683$	7.87365	−	13.6376i	0.301277	−	0.521827i	0.976425	+	0.215855i	$0.0692538\pi$
$684$	18.9421	+	32.8087i	0.724269	+	1.25447i
$685$	0.225682			0.00862288
$686$	−10.5929	−	36.3624i	−0.404440	−	1.38832i
$687$	10.2558			0.391285
$688$	5.99094	+	10.3766i	0.228403	+	0.395605i
$689$	−2.13090	+	3.69082i	−0.0811807	+	0.140609i
$690$	1.37098	−	2.37461i	0.0521924	−	0.0903999i
$691$	11.0465	+	19.1330i	0.420227	+	0.727855i	0.995961	−	0.0897819i	$-0.0286170\pi$
$691$	11.0465	+	19.1330i	0.420227	+	0.727855i	−0.575734	+	0.817637i	$0.695284\pi$
$692$	8.12549			0.308885
$693$	−21.7167	−	1.74198i	−0.824948	−	0.0661724i
$694$	28.3378			1.07569
$695$	14.8410	+	25.7053i	0.562951	+	0.975059i
$696$	1.48170	−	2.56637i	0.0561636	−	0.0972782i
$697$	−1.17554	+	2.03609i	−0.0445266	+	0.0771223i
$698$	23.3764	+	40.4891i	0.884810	+	1.53254i
$699$	9.66952			0.365735
$700$	−6.71648	−	14.1360i	−0.253859	−	0.534291i
$701$	2.71631			0.102594			0.0512969	−	0.998683i	$-0.483665\pi$
$701$	2.71631			0.102594			0.0512969	+	0.998683i	$0.483665\pi$
$702$	−16.3500	−	28.3190i	−0.617090	−	1.06883i
$703$	31.3157	−	54.2403i	1.18109	−	2.04571i
$704$	−17.4458	+	30.2171i	−0.657515	+	1.13885i
$705$	4.08433	+	7.07427i	0.153825	+	0.266432i
$706$	−16.9666			−0.638545
$707$	8.54253	−	12.3895i	0.321275	−	0.465956i
$708$	−0.0606272			−0.00227851
$709$	−9.63195	−	16.6830i	−0.361735	−	0.626544i	0.626511	−	0.779412i	$-0.284482\pi$
$709$	−9.63195	−	16.6830i	−0.361735	−	0.626544i	−0.988247	+	0.152868i	$0.951149\pi$
$710$	−0.245888	+	0.425891i	−0.00922803	+	0.0159834i
$711$	−3.40030	+	5.88950i	−0.127521	+	0.220873i
$712$	2.65219	+	4.59372i	0.0993949	+	0.172157i
$713$	0.0978463			0.00366437
$714$	−5.12431	+	7.43196i	−0.191772	+	0.278134i
$715$	−19.4651			−0.727955
$716$	19.8300	+	34.3465i	0.741081	+	1.28359i
$717$	−7.92774	+	13.7313i	−0.296067	+	0.512803i
$718$	26.3144	−	45.5779i	0.982046	−	1.70095i
$719$	−2.50869	−	4.34518i	−0.0935583	−	0.162048i	0.815448	−	0.578831i	$-0.196491\pi$
$719$	−2.50869	−	4.34518i	−0.0935583	−	0.162048i	−0.909006	+	0.416783i	$0.863157\pi$
$720$	−12.0717			−0.449888
$721$	5.89210	+	12.4010i	0.219433	+	0.461837i
$722$	−86.8317			−3.23154
$723$	1.48236	+	2.56752i	0.0551295	+	0.0954871i
$724$	10.5124	−	18.2081i	0.390692	−	0.676699i
$725$	−12.1761	+	21.0895i	−0.452207	+	0.783246i
$726$	−2.56015	−	4.43431i	−0.0950161	−	0.164573i
$727$	16.1209			0.597892			0.298946	−	0.954270i	$-0.403365\pi$
$727$	16.1209			0.597892			0.298946	+	0.954270i	$0.403365\pi$
$728$	−3.39688	−	0.272478i	−0.125897	−	0.0100987i
$729$	6.64255			0.246021
$730$	−21.6053	−	37.4215i	−0.799649	−	1.38503i
$731$	3.13063	−	5.42240i	0.115790	−	0.200555i
$732$	1.81515	−	3.14393i	0.0670899	−	0.116203i
$733$	−3.87132	−	6.70533i	−0.142991	−	0.247667i	0.785631	−	0.618695i	$-0.212339\pi$
$733$	−3.87132	−	6.70533i	−0.142991	−	0.247667i	−0.928621	+	0.371029i	$0.879005\pi$
$734$	−2.52316			−0.0931317
$735$	9.26569	+	1.49610i	0.341770	+	0.0551846i
$736$	8.11224			0.299021
$737$	22.2726	+	38.5772i	0.820421	+	1.42101i
$738$	2.82782	−	4.89793i	0.104093	−	0.180295i
$739$	−4.20053	+	7.27554i	−0.154519	+	0.267635i	−0.932884	−	0.360177i	$-0.882716\pi$
$739$	−4.20053	+	7.27554i	−0.154519	+	0.267635i	0.778365	+	0.627812i	$0.216049\pi$
$740$	−13.1872	−	22.8409i	−0.484772	−	0.839650i
$741$	24.0397			0.883119
$742$	−6.64279	−	0.532846i	−0.243865	−	0.0195614i
$743$	−32.4828			−1.19168			−0.595839	−	0.803104i	$-0.703180\pi$
$743$	−32.4828			−1.19168			−0.595839	+	0.803104i	$0.703180\pi$
$744$	−0.0161394	−	0.0279542i	−0.000591697	−	0.00102485i
$745$	7.29033	−	12.6272i	0.267097	−	0.462625i
$746$	−34.7187	+	60.1346i	−1.27114	+	2.20169i
$747$	−13.6187	−	23.5883i	−0.498282	−	0.863050i
$748$	15.2748			0.558501
$749$	6.55624	+	13.7988i	0.239560	+	0.504196i
$750$	21.1431			0.772037
$751$	1.71971	+	2.97863i	0.0627532	+	0.108692i	0.895695	−	0.444669i	$-0.146679\pi$
$751$	1.71971	+	2.97863i	0.0627532	+	0.108692i	−0.832942	+	0.553360i	$0.813345\pi$
$752$	−10.9747	+	19.0088i	−0.400207	+	0.693179i
$753$	−8.52036	+	14.7577i	−0.310499	+	0.537800i
$754$	31.7814	+	55.0469i	1.15741	+	2.00469i
$755$	26.5650			0.966799
$756$	15.1442	−	21.9642i	0.550791	−	0.798831i
$757$	49.6866			1.80589			0.902946	−	0.429755i	$-0.141400\pi$
$757$	49.6866			1.80589			0.902946	+	0.429755i	$0.141400\pi$
$758$	−25.8513	−	44.7757i	−0.938961	−	1.62633i
$759$	−1.64758	+	2.85369i	−0.0598033	+	0.103582i
$760$	−2.20765	+	3.82376i	−0.0800798	+	0.138702i
$761$	−24.4628	−	42.3708i	−0.886776	−	1.53594i	−0.843664	−	0.536872i	$-0.819606\pi$
$761$	−24.4628	−	42.3708i	−0.886776	−	1.53594i	−0.0431124	−	0.999070i	$-0.513727\pi$
$762$	0.755067			0.0273532
$763$	−9.05062	+	13.1264i	−0.327655	+	0.475209i
$764$	31.3601			1.13457
$765$	3.15411	+	5.46307i	0.114037	+	0.197518i
$766$	−30.6636	+	53.1110i	−1.10792	+	1.91898i
$767$	0.0542411	−	0.0939484i	0.00195853	−	0.00339228i
$768$	5.62884	+	9.74943i	0.203113	+	0.351802i
$769$	−34.2752			−1.23600			−0.617998	−	0.786179i	$-0.712056\pi$
$769$	−34.2752			−1.23600			−0.617998	+	0.786179i	$0.712056\pi$
$770$	−13.0624	−	27.4921i	−0.470735	−	0.990746i
$771$	−7.79340			−0.280673
$772$	−11.9698	−	20.7323i	−0.430803	−	0.746173i
$773$	−6.91486	+	11.9769i	−0.248710	+	0.430779i	−0.963168	−	0.268900i	$-0.913340\pi$
$773$	−6.91486	+	11.9769i	−0.248710	+	0.430779i	0.714458	+	0.699678i	$0.246673\pi$
$774$	−7.53090	+	13.0439i	−0.270693	+	0.468854i
$775$	0.132627	+	0.229717i	0.00476412	+	0.00825169i
$776$	−4.82933			−0.173363
$777$	−18.6719	−	1.49775i	−0.669852	−	0.0537316i
$778$	45.0803			1.61621
$779$	4.89504	+	8.47846i	0.175383	+	0.303772i
$780$	5.06163	−	8.76700i	0.181235	−	0.313909i
$781$	0.295497	−	0.511815i	0.0105737	−	0.0183142i
$782$	−1.92504	−	3.33428i	−0.0688395	−	0.119233i
$783$	−41.5126			−1.48354
$784$	8.96711	+	23.5716i	0.320254	+	0.841844i
$785$	−33.3479			−1.19024
$786$	13.6616	+	23.6626i	0.487294	+	0.844018i
$787$	−8.80794	+	15.2558i	−0.313969	+	0.543811i	−0.979218	−	0.202811i	$-0.934992\pi$
$787$	−8.80794	+	15.2558i	−0.313969	+	0.543811i	0.665249	+	0.746622i	$0.268326\pi$
$788$	−5.57342	+	9.65344i	−0.198545	+	0.343890i
$789$	4.68407	+	8.11304i	0.166757	+	0.288832i
$790$	−9.50103			−0.338031
$791$	−22.2742	−	1.78670i	−0.791978	−	0.0635278i
$792$	−3.06527			−0.108920
$793$	3.24791	+	5.62555i	0.115337	+	0.199769i
$794$	14.0377	−	24.3141i	0.498181	−	0.862874i
$795$	0.825733	−	1.43021i	0.0292857	−	0.0507244i
$796$	4.90503	+	8.49576i	0.173854	+	0.301124i
$797$	−32.3522			−1.14598			−0.572988	−	0.819564i	$-0.694216\pi$
$797$	−32.3522			−1.14598			−0.572988	+	0.819564i	$0.694216\pi$
$798$	16.1322	+	33.9530i	0.571073	+	1.20192i
$799$	11.4699			0.405776
$800$	10.9959	+	19.0454i	0.388763	+	0.673357i
$801$	15.7787	−	27.3295i	0.557513	−	0.965641i
$802$	−5.94377	+	10.2949i	−0.209882	+	0.363526i
$803$	25.9642	+	44.9713i	0.916257	+	1.58700i
$804$	−23.1666			−0.817024
$805$	−2.27224	+	3.29551i	−0.0800860	+	0.116151i
$806$	0.692355			0.0243872
$807$	−13.6748	−	23.6855i	−0.481377	−	0.833770i
$808$	1.05868	−	1.83368i	0.0372441	−	0.0645087i
$809$	−7.53742	+	13.0552i	−0.265002	+	0.458996i	−0.967564	−	0.252626i	$-0.918706\pi$
$809$	−7.53742	+	13.0552i	−0.265002	+	0.458996i	0.702562	+	0.711622i	$0.252039\pi$
$810$	−3.94243	−	6.82848i	−0.138523	−	0.239928i
$811$	36.2016			1.27121			0.635605	−	0.772014i	$-0.280751\pi$
$811$	36.2016			1.27121			0.635605	+	0.772014i	$0.280751\pi$
$812$	−29.4377	+	42.6945i	−1.03306	+	1.49828i
$813$	9.14499			0.320729
$814$	30.3735	+	52.6084i	1.06459	+	1.84392i
$815$	12.2682	−	21.2492i	0.429737	−	0.744326i
$816$	3.00558	−	5.20581i	0.105216	−	0.182240i
$817$	−13.0362	−	22.5794i	−0.456080	−	0.789953i
$818$	60.3877			2.11141
$819$	8.70068	+	18.3121i	0.304026	+	0.639878i
$820$	4.12267			0.143970
$821$	4.36683	+	7.56356i	0.152403	+	0.263970i	0.932110	−	0.362174i	$-0.117965\pi$
$821$	4.36683	+	7.56356i	0.152403	+	0.263970i	−0.779707	+	0.626144i	$0.784632\pi$
$822$	0.135167	−	0.234116i	0.00471450	−	0.00816575i
$823$	−24.7466	+	42.8624i	−0.862613	+	1.49409i	0.00678427	+	0.999977i	$0.497840\pi$
$823$	−24.7466	+	42.8624i	−0.862613	+	1.49409i	−0.869398	+	0.494113i	$0.835493\pi$
$824$	0.965852	+	1.67290i	0.0336470	+	0.0582784i
$825$	−8.93296			−0.311006
$826$	0.169090	+	0.0135634i	0.00588339	+	0.000471930i
$827$	26.4116			0.918423			0.459211	−	0.888327i	$-0.348132\pi$
$827$	26.4116			0.918423			0.459211	+	0.888327i	$0.348132\pi$
$828$	2.41618	+	4.18495i	0.0839682	+	0.145437i
$829$	19.6103	−	33.9660i	0.681093	−	1.17969i	−0.293554	−	0.955942i	$-0.594838\pi$
$829$	19.6103	−	33.9660i	0.681093	−	1.17969i	0.974648	−	0.223746i	$-0.0718285\pi$
$830$	19.0265	−	32.9548i	0.660419	−	1.14388i
$831$	−9.45904	−	16.3835i	−0.328131	−	0.568339i
$832$	32.4695			1.12568
$833$	8.32443	−	10.2169i	0.288424	−	0.353993i
$834$	35.5546			1.23116
$835$	12.6036	+	21.8301i	0.436165	+	0.755460i
$836$	31.8028	−	55.0841i	1.09992	−	1.90512i
$837$	−0.226087	+	0.391595i	−0.00781472	+	0.0135355i
$838$	14.9703	+	25.9294i	0.517142	+	0.895716i
$839$	−14.8912			−0.514101			−0.257050	−	0.966398i	$-0.582751\pi$
$839$	−14.8912			−0.514101			−0.257050	+	0.966398i	$0.582751\pi$
$840$	1.31631	+	0.105586i	0.0454169	+	0.00364308i
$841$	51.6929			1.78251
$842$	−4.35147	−	7.53696i	−0.149961	−	0.259741i
$843$	2.50250	−	4.33446i	0.0861907	−	0.149287i
$844$	−2.82081	+	4.88579i	−0.0970964	+	0.168176i
$845$	−0.777335	−	1.34638i	−0.0267411	−	0.0463170i
$846$	−27.5915			−0.948616
$847$	3.20793	+	6.75167i	0.110226	+	0.231990i
$848$	4.43754			0.152386
$849$	7.32969	+	12.6954i	0.251554	+	0.435705i
$850$	5.21867	−	9.03900i	0.178999	−	0.310035i
$851$	3.99451	−	6.91870i	0.136930	−	0.237170i
$852$	0.153679	+	0.266180i	0.00526496	+	0.00911918i
$853$	−42.1641			−1.44367			−0.721836	−	0.692064i	$-0.756702\pi$
$853$	−42.1641			−1.44367			−0.721836	+	0.692064i	$0.756702\pi$
$854$	−5.76583	+	8.36238i	−0.197303	+	0.286155i
$855$	26.2680			0.898346
$856$	1.07472	+	1.86147i	0.0367331	+	0.0636237i
$857$	−22.7241	+	39.3593i	−0.776240	+	1.34449i	0.157855	+	0.987462i	$0.449542\pi$
$857$	−22.7241	+	39.3593i	−0.776240	+	1.34449i	−0.934095	+	0.357025i	$0.883791\pi$
$858$	−11.6582	+	20.1926i	−0.398004	+	0.689363i
$859$	0.359104	+	0.621987i	0.0122525	+	0.0212219i	0.872087	−	0.489352i	$-0.162766\pi$
$859$	0.359104	+	0.621987i	0.0122525	+	0.0212219i	−0.859834	+	0.510573i	$0.829433\pi$
$860$	−10.9793			−0.374390
$861$	1.66208	−	2.41058i	0.0566437	−	0.0821523i
$862$	1.33477			0.0454623
$863$	12.1628	+	21.0665i	0.414025	+	0.717113i	0.995326	−	0.0965765i	$-0.0307892\pi$
$863$	12.1628	+	21.0665i	0.414025	+	0.717113i	−0.581300	+	0.813689i	$0.697456\pi$
$864$	−18.7445	+	32.4664i	−0.637700	+	1.10453i
$865$	2.81701	−	4.87920i	0.0957812	−	0.165898i
$866$	−6.71568	−	11.6319i	−0.228208	−	0.395268i
$867$	11.9245			0.404976
$868$	0.242419	+	0.510214i	0.00822824	+	0.0173178i
$869$	11.4179			0.387325
$870$	−12.3154	−	21.3310i	−0.417532	−	0.723187i
$871$	20.7264	−	35.8992i	0.702288	−	1.21640i
$872$	−1.12165	+	1.94275i	−0.0379837	+	0.0657897i
$873$	14.3656	+	24.8820i	0.486202	+	0.842127i
$874$	−16.0321			−0.542295
$875$	−30.7675	−	2.46799i	−1.04013	−	0.0834332i
$876$	−27.0064			−0.912463
$877$	−20.0394	−	34.7093i	−0.676684	−	1.17205i	−0.975974	−	0.217889i	$-0.930083\pi$
$877$	−20.0394	−	34.7093i	−0.676684	−	1.17205i	0.299290	−	0.954162i	$-0.403250\pi$
$878$	−14.3283	+	24.8174i	−0.483558	+	0.837546i
$879$	−7.03673	+	12.1880i	−0.237343	+	0.411090i
$880$	10.1339	+	17.5525i	0.341614	+	0.591694i
$881$	35.8620			1.20822			0.604111	−	0.796901i	$-0.293529\pi$
$881$	35.8620			1.20822			0.604111	+	0.796901i	$0.293529\pi$
$882$	−20.0249	+	24.5773i	−0.674273	+	0.827559i
$883$	27.0684			0.910925			0.455463	−	0.890255i	$-0.349474\pi$
$883$	27.0684			0.910925			0.455463	+	0.890255i	$0.349474\pi$
$884$	−7.10721	−	12.3100i	−0.239041	−	0.414032i
$885$	−0.0210187	+	0.0364055i	−0.000706536	+	0.00122376i
$886$	37.9352	−	65.7057i	1.27446	−	2.20743i
$887$	−28.5904	−	49.5200i	−0.959970	−	1.66272i	−0.722560	−	0.691308i	$-0.757035\pi$
$887$	−28.5904	−	49.5200i	−0.959970	−	1.66272i	−0.237410	−	0.971410i	$-0.576299\pi$
$888$	−2.63552			−0.0884421
$889$	−1.09878	−	0.0881373i	−0.0368518	−	0.00295603i
$890$	44.0884			1.47785
$891$	4.73782	+	8.20614i	0.158723	+	0.274916i
$892$	−6.17363	+	10.6930i	−0.206709	+	0.358030i
$893$	23.8809	−	41.3629i	0.799143	−	1.38416i
$894$	−8.73274	−	15.1255i	−0.292066	−	0.505874i
$895$	27.4993			0.919199
$896$	3.36730	+	7.08709i	0.112494	+	0.236763i
$897$	3.06641			0.102385
$898$	4.67482	+	8.09703i	0.156001	+	0.270201i
$899$	0.439473	−	0.761189i	0.0146572	−	0.0253871i
$900$	−6.55011	+	11.3451i	−0.218337	+	0.378171i
$901$	−1.15944	−	2.00821i	−0.0386266	−	0.0669032i
$902$	−9.49553			−0.316166
$903$	−4.42638	+	6.41973i	−0.147301	+	0.213635i
$904$	−3.14397			−0.104567
$905$	−7.28908	−	12.6251i	−0.242297	−	0.419671i
$906$	15.9105	−	27.5577i	0.528590	−	0.915545i
$907$	−7.98765	+	13.8350i	−0.265225	+	0.459384i	−0.967623	−	0.252401i	$-0.918780\pi$
$907$	−7.98765	+	13.8350i	−0.265225	+	0.459384i	0.702397	+	0.711785i	$0.252113\pi$
$908$	11.5203	+	19.9537i	0.382314	+	0.662187i
$909$	−12.5968			−0.417810
$910$	−16.0783	+	23.3189i	−0.532989	+	0.773013i
$911$	−12.2417			−0.405587			−0.202793	−	0.979222i	$-0.565002\pi$
$911$	−12.2417			−0.405587			−0.202793	+	0.979222i	$0.565002\pi$
$912$	−12.5155	−	21.6775i	−0.414430	−	0.717814i
$913$	−22.8651	+	39.6035i	−0.756724	+	1.31068i
$914$	−23.6496	+	40.9623i	−0.782260	+	1.35491i
$915$	−1.25858	−	2.17993i	−0.0416074	−	0.0720662i
$916$	−25.2518			−0.834344
$917$	−17.1183	−	36.0286i	−0.565298	−	1.18977i
$918$	17.7923			0.587235
$919$	−6.50353	−	11.2645i	−0.214532	−	0.371580i	0.738596	−	0.674148i	$-0.235489\pi$
$919$	−6.50353	−	11.2645i	−0.214532	−	0.371580i	−0.953128	+	0.302569i	$0.902156\pi$
$920$	−0.281599	+	0.487745i	−0.00928406	+	0.0160805i
$921$	−6.41801	+	11.1163i	−0.211481	+	0.366295i
$922$	22.0081	+	38.1191i	0.724798	+	1.25539i
$923$	−0.549967			−0.0181024
$924$	−18.9624	−	1.52105i	−0.623817	−	0.0500389i
$925$	21.6577			0.712101
$926$	3.77879	+	6.54506i	0.124179	+	0.215084i
$927$	5.74616	−	9.95264i	0.188729	−	0.326888i
$928$	36.4358	−	63.1087i	1.19606	−	2.07164i
$929$	−22.3927	−	38.7853i	−0.734682	−	1.27251i	−0.954863	−	0.297047i	$-0.903998\pi$
$929$	−22.3927	−	38.7853i	−0.734682	−	1.27251i	0.220181	−	0.975459i	$-0.429335\pi$
$930$	−0.268291			−0.00879761
$931$	−19.5123	−	51.2916i	−0.639491	−	1.68102i
$932$	−23.8082			−0.779863
$933$	5.80680	+	10.0577i	0.190106	+	0.329274i
$934$	20.1885	−	34.9675i	0.660587	−	1.14417i
$935$	5.29558	−	9.17222i	0.173184	−	0.299964i
$936$	1.42624	+	2.47033i	0.0466182	+	0.0807451i
$937$	31.7090			1.03589			0.517943	−	0.855415i	$-0.326698\pi$
$937$	31.7090			1.03589			0.517943	+	0.855415i	$0.326698\pi$
$938$	64.6120	+	5.18279i	2.10966	+	0.169224i
$939$	13.5843			0.443307
$940$	−10.0564	−	17.4182i	−0.328003	−	0.568118i
$941$	−7.51121	+	13.0098i	−0.244858	+	0.424107i	−0.962092	−	0.272726i	$-0.912075\pi$
$941$	−7.51121	+	13.0098i	−0.244858	+	0.424107i	0.717233	+	0.696833i	$0.245408\pi$
$942$	−19.9729	+	34.5941i	−0.650753	+	1.12714i
$943$	0.624394	+	1.08148i	0.0203331	+	0.0352179i
$944$	−0.112956			−0.00367640
$945$	−7.93878	−	16.7086i	−0.258248	−	0.543530i
$946$	25.2880			0.822184
$947$	14.1428	+	24.4961i	0.459580	+	0.796015i	0.998939	−	0.0460606i	$-0.0146667\pi$
$947$	14.1428	+	24.4961i	0.459580	+	0.796015i	−0.539359	+	0.842076i	$0.681333\pi$
$948$	−2.96905	+	5.14255i	−0.0964303	+	0.167022i
$949$	24.1618	−	41.8494i	0.784325	−	1.35849i
$950$	−21.7310	−	37.6392i	−0.705048	−	1.22118i
$951$	−29.0152			−0.940881
$952$	1.05253	−	1.52652i	0.0341127	−	0.0494749i
$953$	−21.1837			−0.686209			−0.343104	−	0.939297i	$-0.611478\pi$
$953$	−21.1837			−0.686209			−0.343104	+	0.939297i	$0.611478\pi$
$954$	2.78910	+	4.83086i	0.0903005	+	0.156405i
$955$	10.8722	−	18.8312i	0.351815	−	0.609362i
$956$	19.5196	−	33.8089i	0.631309	−	1.09346i
$957$	14.8001	+	25.6345i	0.478419	+	0.828645i
$958$	−75.4431			−2.43746
$959$	−0.224024	+	0.324909i	−0.00723410	+	0.0104919i
$960$	−12.5821			−0.406086
$961$	15.4952	+	26.8385i	0.499846	+	0.865758i
$962$	28.2650	−	48.9564i	0.911299	−	1.57842i
$963$	6.39384	−	11.0745i	0.206039	−	0.356870i
$964$	−3.64985	−	6.32172i	−0.117554	−	0.203609i
$965$	−16.5992			−0.534346
$966$	2.05776	+	4.33093i	0.0662074	+	0.139345i
$967$	−30.9508			−0.995310			−0.497655	−	0.867375i	$-0.665805\pi$
$967$	−30.9508			−0.995310			−0.497655	+	0.867375i	$0.665805\pi$
$968$	0.525854	+	0.910807i	0.0169016	+	0.0292744i
$969$	−6.54010	+	11.3278i	−0.210098	+	0.363901i
$970$	−20.0700	+	34.7622i	−0.644408	+	1.11615i
$971$	−25.4824	−	44.1367i	−0.817768	−	1.41642i	−0.907323	−	0.420434i	$-0.861878\pi$
$971$	−25.4824	−	44.1367i	−0.817768	−	1.41642i	0.0895552	−	0.995982i	$-0.471455\pi$
$972$	−35.1793			−1.12838
$973$	−51.7392	−	4.15021i	−1.65868	−	0.133050i
$974$	−44.1093			−1.41335
$975$	4.15642	+	7.19913i	0.133112	+	0.230557i
$976$	3.38185	−	5.85753i	0.108250	−	0.187495i
$977$	−0.186816	+	0.323575i	−0.00597677	+	0.0103521i	−0.868998	−	0.494815i	$-0.835236\pi$
$977$	−0.186816	+	0.323575i	−0.00597677	+	0.0103521i	0.863022	+	0.505167i	$0.168569\pi$
$978$	−14.6955	−	25.4534i	−0.469911	−	0.813909i
$979$	−52.9833			−1.69335
$980$	−22.8139	−	3.68369i	−0.728762	−	0.117671i
$981$	13.3461			0.426107
$982$	−3.82523	−	6.62548i	−0.122068	−	0.211428i
$983$	−8.39099	+	14.5336i	−0.267631	+	0.463551i	−0.968250	−	0.249985i	$-0.919574\pi$
$983$	−8.39099	+	14.5336i	−0.267631	+	0.463551i	0.700618	+	0.713536i	$0.252908\pi$
$984$	0.205982	−	0.356772i	0.00656648	−	0.0113735i
$985$	3.86447	+	6.69346i	0.123132	+	0.213271i
$986$	−34.5851			−1.10141
$987$	−14.2390	−	1.14216i	−0.453231	−	0.0363555i
$988$	−59.1902			−1.88309
$989$	−1.66285	−	2.88015i	−0.0528757	−	0.0915833i
$990$	−12.7388	+	22.0643i	−0.404867	+	0.701250i
$991$	11.2778	−	19.5338i	0.358252	−	0.620510i	−0.629417	−	0.777068i	$-0.716706\pi$
$991$	11.2778	−	19.5338i	0.358252	−	0.620510i	0.987669	+	0.156557i	$0.0500396\pi$
$992$	−0.396876	−	0.687410i	−0.0126008	−	0.0218253i
$993$	−28.2084			−0.895166
$994$	−0.369064	−	0.776760i	−0.0117060	−	0.0246373i
$995$	6.80206			0.215640
$996$	−11.8915	−	20.5966i	−0.376796	−	0.652629i
$997$	−13.6719	+	23.6805i	−0.432995	+	0.749969i	−0.997130	−	0.0757137i	$-0.975876\pi$
$997$	−13.6719	+	23.6805i	−0.432995	+	0.749969i	0.564135	+	0.825683i	$0.309210\pi$
$998$	−28.2491	+	48.9289i	−0.894210	+	1.54882i
$999$	18.4598	+	31.9732i	0.584041	+	1.01159i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.e.a.116.6	yes	14
7.2	even	3	inner	161.2.e.a.93.6	✓	14
7.3	odd	6		1127.2.a.k.1.2		7
7.4	even	3		1127.2.a.n.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.e.a.93.6	✓	14	7.2	even	3	inner
161.2.e.a.116.6	yes	14	1.1	even	1	trivial
1127.2.a.k.1.2		7	7.3	odd	6
1127.2.a.n.1.2		7	7.4	even	3

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:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.02250 + 1.77102i) q^{2} +(0.443108 - 0.767485i) q^{3} +(-1.09101 + 1.88969i) q^{4} +(0.756483 + 1.31027i) q^{5} +1.81231 q^{6} +(-2.63728 - 0.211547i) q^{7} -0.372248 q^{8} +(1.10731 + 1.91792i) q^{9} +(-1.54701 + 2.67950i) q^{10} +(1.85912 - 3.22009i) q^{11} +(0.966873 + 1.67467i) q^{12} -3.46012 q^{13} +(-2.32197 - 4.88699i) q^{14} +1.34081 q^{15} +(1.80140 + 3.12012i) q^{16} +(0.941342 - 1.63045i) q^{17} +(-2.26445 + 3.92215i) q^{18} +(-3.91984 - 6.78936i) q^{19} -3.30134 q^{20} +(-1.33096 + 1.93033i) q^{21} +7.60380 q^{22} +(-0.500000 - 0.866025i) q^{23} +(-0.164946 + 0.285695i) q^{24} +(1.35547 - 2.34774i) q^{25} +(-3.53797 - 6.12795i) q^{26} +4.62128 q^{27} +(3.27707 - 4.75285i) q^{28} -8.98292 q^{29} +(1.37098 + 2.37461i) q^{30} +(-0.0489231 + 0.0847374i) q^{31} +(-4.05612 + 7.02541i) q^{32} +(-1.64758 - 2.85369i) q^{33} +3.85009 q^{34} +(-1.71787 - 3.61557i) q^{35} -4.83237 q^{36} +(3.99451 + 6.91870i) q^{37} +(8.01607 - 13.8842i) q^{38} +(-1.53321 + 2.65559i) q^{39} +(-0.281599 - 0.487745i) q^{40} -1.24879 q^{41} +(-4.77957 - 0.383389i) q^{42} +3.32571 q^{43} +(4.05665 + 7.02632i) q^{44} +(-1.67532 + 2.90175i) q^{45} +(1.02250 - 1.77102i) q^{46} +(3.04616 + 5.27610i) q^{47} +3.19286 q^{48} +(6.91050 + 1.11582i) q^{49} +5.54386 q^{50} +(-0.834232 - 1.44493i) q^{51} +(3.77504 - 6.53856i) q^{52} +(0.615844 - 1.06667i) q^{53} +(4.72526 + 8.18439i) q^{54} +5.62557 q^{55} +(0.981723 + 0.0787480i) q^{56} -6.94764 q^{57} +(-9.18504 - 15.9090i) q^{58} +(-0.0156761 + 0.0271518i) q^{59} +(-1.46285 + 2.53373i) q^{60} +(-0.938670 - 1.62582i) q^{61} -0.200096 q^{62} +(-2.51456 - 5.29234i) q^{63} -9.38393 q^{64} +(-2.61752 - 4.53368i) q^{65} +(3.36930 - 5.83580i) q^{66} +(-5.99009 + 10.3751i) q^{67} +(2.05403 + 3.55769i) q^{68} -0.886215 q^{69} +(4.64674 - 6.73932i) q^{70} +0.158944 q^{71} +(-0.412195 - 0.713942i) q^{72} +(-6.98293 + 12.0948i) q^{73} +(-8.16878 + 14.1487i) q^{74} +(-1.20124 - 2.08060i) q^{75} +17.1064 q^{76} +(-5.58422 + 8.09898i) q^{77} -6.27082 q^{78} +(1.53539 + 2.65937i) q^{79} +(-2.72546 + 4.72064i) q^{80} +(-1.27421 + 2.20700i) q^{81} +(-1.27689 - 2.21163i) q^{82} -12.2989 q^{83} +(-2.19564 - 4.62112i) q^{84} +2.84844 q^{85} +(3.40054 + 5.88990i) q^{86} +(-3.98040 + 6.89426i) q^{87} +(-0.692053 + 1.19867i) q^{88} +(-7.12478 - 12.3405i) q^{89} -6.85208 q^{90} +(9.12531 + 0.731978i) q^{91} +2.18203 q^{92} +(0.0433564 + 0.0750955i) q^{93} +(-6.22940 + 10.7896i) q^{94} +(5.93058 - 10.2721i) q^{95} +(3.59460 + 6.22602i) q^{96} +12.9734 q^{97} +(5.08985 + 13.3796i) q^{98} +8.23449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 5 q^{3} - 6 q^{4} - 4 q^{5} + 12 q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} + 2 q^{10} - 4 q^{11} - 9 q^{12} + 28 q^{13} - 14 q^{14} - 6 q^{15} + 8 q^{16} - 4 q^{17} - 19 q^{18} - 9 q^{19} + 24 q^{20} - 6 q^{21}+ \cdots + 36 q^{99}+O(q^{100}) \) 14 * q - 5 * q^3 - 6 * q^4 - 4 * q^5 + 12 * q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 + 2 * q^10 - 4 * q^11 - 9 * q^12 + 28 * q^13 - 14 * q^14 - 6 * q^15 + 8 * q^16 - 4 * q^17 - 19 * q^18 - 9 * q^19 + 24 * q^20 - 6 * q^21 - 20 * q^22 - 7 * q^23 + 4 * q^24 - 3 * q^25 - 14 * q^26 + 40 * q^27 - 16 * q^28 - 10 * q^29 + 17 * q^30 - 10 * q^31 - 19 * q^32 - 3 * q^33 + 40 * q^34 + 15 * q^35 + 8 * q^36 + 5 * q^37 + 17 * q^38 - 18 * q^39 - 4 * q^40 + 46 * q^41 + q^42 - 22 * q^43 + 34 * q^44 - 6 * q^45 - 4 * q^47 + 22 * q^48 - 20 * q^49 - 18 * q^50 - 7 * q^51 - 12 * q^52 - 2 * q^53 - 15 * q^54 + 34 * q^55 + 31 * q^56 - 48 * q^57 + 7 * q^58 - 7 * q^59 - 32 * q^60 - 12 * q^61 - 8 * q^62 + 52 * q^63 - 18 * q^64 - 9 * q^65 + 27 * q^66 - 2 * q^67 + 12 * q^68 + 10 * q^69 - 13 * q^70 - 56 * q^71 + 20 * q^72 - 59 * q^73 - 2 * q^74 + 22 * q^75 + 2 * q^76 + 2 * q^77 - 34 * q^78 + 4 * q^79 + 22 * q^80 - 11 * q^81 - 54 * q^82 - 18 * q^83 - 17 * q^84 + 18 * q^85 + 15 * q^86 - 11 * q^87 + 33 * q^88 - q^89 + 4 * q^90 + 44 * q^91 + 12 * q^92 - 15 * q^93 + 14 * q^94 + 16 * q^95 - 20 * q^96 + 70 * q^97 - 17 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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