LMFDB - Embedded newform 117.2.e.c.79.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(40,117)] 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("117.40"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 3 x^{10} - x^{9} - 2 x^{8} + 9 x^{7} + 24 x^{6} + 27 x^{5} - 18 x^{4} - 27 x^{3} + \cdots + 729 $ x^12 - x^11 - 3x^10 - x^9 - 2x^8 + 9x^7 + 24x^6 + 27x^5 - 18x^4 - 27x^3 - 243x^2 - 243*x + 729
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$1.70010 + 0.331167i$ of defining polynomial
Character	$\chi$	$=$	117.79
Dual form			117.2.e.c.40.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.129090 - 0.223591i) q^{2} +(-1.13685 - 1.30674i) q^{3} +(0.966671 + 1.67432i) q^{4} +(-1.73641 - 3.00755i) q^{5} +(-0.438932 + 0.0855008i) q^{6} +(2.21165 - 3.83070i) q^{7} +1.01551 q^{8} +(-0.415158 + 2.97114i) q^{9} -0.896615 q^{10} +(-0.0632497 + 0.109552i) q^{11} +(1.08895 - 3.16664i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.571006 - 0.989012i) q^{14} +(-1.95606 + 5.68816i) q^{15} +(-1.80225 + 3.12159i) q^{16} +0.346319 q^{17} +(0.610726 + 0.476370i) q^{18} -0.863955 q^{19} +(3.35707 - 5.81462i) q^{20} +(-7.52005 + 1.46485i) q^{21} +(0.0163299 + 0.0282841i) q^{22} +(4.05879 + 7.03003i) q^{23} +(-1.15448 - 1.32702i) q^{24} +(-3.53023 + 6.11454i) q^{25} +0.258181 q^{26} +(4.35448 - 2.83522i) q^{27} +8.55177 q^{28} +(1.25024 - 2.16549i) q^{29} +(1.01931 + 1.17165i) q^{30} +(3.01390 + 5.22023i) q^{31} +(1.48082 + 2.56485i) q^{32} +(0.215061 - 0.0418924i) q^{33} +(0.0447064 - 0.0774338i) q^{34} -15.3613 q^{35} +(-5.37596 + 2.17700i) q^{36} -2.44616 q^{37} +(-0.111528 + 0.193173i) q^{38} +(0.563250 - 1.63791i) q^{39} +(-1.76335 - 3.05421i) q^{40} +(-2.36645 - 4.09881i) q^{41} +(-0.643238 + 1.87051i) q^{42} +(3.36581 - 5.82976i) q^{43} -0.244567 q^{44} +(9.65672 - 3.91050i) q^{45} +2.09580 q^{46} +(-0.107498 + 0.186192i) q^{47} +(6.12800 - 1.19369i) q^{48} +(-6.28282 - 10.8822i) q^{49} +(0.911438 + 1.57866i) q^{50} +(-0.393711 - 0.452550i) q^{51} +(-0.966671 + 1.67432i) q^{52} -4.02070 q^{53} +(-0.0718083 - 1.33962i) q^{54} +0.439310 q^{55} +(2.24596 - 3.89012i) q^{56} +(0.982185 + 1.12897i) q^{57} +(-0.322789 - 0.559087i) q^{58} +(6.87049 + 11.9000i) q^{59} +(-11.4147 + 2.22350i) q^{60} +(1.36331 - 2.36132i) q^{61} +1.55626 q^{62} +(10.4633 + 8.16147i) q^{63} -6.44436 q^{64} +(1.73641 - 3.00755i) q^{65} +(0.0183956 - 0.0534937i) q^{66} +(-2.00833 - 3.47853i) q^{67} +(0.334776 + 0.579850i) q^{68} +(4.57222 - 13.2959i) q^{69} +(-1.98300 + 3.43466i) q^{70} +8.55239 q^{71} +(-0.421598 + 3.01723i) q^{72} -9.17500 q^{73} +(-0.315775 + 0.546939i) q^{74} +(12.0035 - 2.33819i) q^{75} +(-0.835161 - 1.44654i) q^{76} +(0.279773 + 0.484581i) q^{77} +(-0.293512 - 0.337376i) q^{78} +(-0.216092 + 0.374282i) q^{79} +12.5178 q^{80} +(-8.65529 - 2.46698i) q^{81} -1.22194 q^{82} +(0.520310 - 0.901203i) q^{83} +(-9.72205 - 11.1750i) q^{84} +(-0.601351 - 1.04157i) q^{85} +(-0.868988 - 1.50513i) q^{86} +(-4.25107 + 0.828078i) q^{87} +(-0.0642309 + 0.111251i) q^{88} -10.8984 q^{89} +(0.372237 - 2.66396i) q^{90} +4.42331 q^{91} +(-7.84703 + 13.5915i) q^{92} +(3.39516 - 9.87301i) q^{93} +(0.0277539 + 0.0480712i) q^{94} +(1.50018 + 2.59839i) q^{95} +(1.66814 - 4.85090i) q^{96} +(-0.0894355 + 0.154907i) q^{97} -3.24421 q^{98} +(-0.299234 - 0.233405i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.129090	−	0.223591i	0.0912807	−	0.158103i	−0.816770	−	0.576964i	$-0.804237\pi$
$2$	0.129090	−	0.223591i	0.0912807	−	0.158103i	0.908050	+	0.418861i	$0.137571\pi$
$3$	−1.13685	−	1.30674i	−0.656359	−	0.754449i
$3$	−1.13685	−	1.30674i	−0.656359	−	0.754449i
$4$	0.966671	+	1.67432i	0.483336	+	0.837162i
$5$	−1.73641	−	3.00755i	−0.776546	−	1.34502i	−0.933922	−	0.357478i	$-0.883637\pi$
$5$	−1.73641	−	3.00755i	−0.776546	−	1.34502i	0.157376	−	0.987539i	$-0.449697\pi$
$6$	−0.438932	+	0.0855008i	−0.179193	+	0.0349056i
$7$	2.21165	−	3.83070i	0.835927	−	1.44787i	−0.0573473	−	0.998354i	$-0.518264\pi$
$7$	2.21165	−	3.83070i	0.835927	−	1.44787i	0.893274	−	0.449513i	$-0.148402\pi$
$8$	1.01551			0.359038
$9$	−0.415158	+	2.97114i	−0.138386	+	0.990378i
$10$	−0.896615			−0.283534
$11$	−0.0632497	+	0.109552i	−0.0190705	+	0.0330311i	−0.875403	−	0.483394i	$-0.839404\pi$
$11$	−0.0632497	+	0.109552i	−0.0190705	+	0.0330311i	0.856333	+	0.516425i	$0.172737\pi$
$12$	1.08895	−	3.16664i	0.314354	−	0.914131i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$13$	0.500000	+	0.866025i	0.138675	+	0.240192i
$14$	−0.571006	−	0.989012i	−0.152608	−	0.264325i
$15$	−1.95606	+	5.68816i	−0.505054	+	1.46868i
$16$	−1.80225	+	3.12159i	−0.450562	+	0.780397i
$17$	0.346319			0.0839947			0.0419973	−	0.999118i	$-0.486628\pi$
$17$	0.346319			0.0839947			0.0419973	+	0.999118i	$0.486628\pi$
$18$	0.610726	+	0.476370i	0.143950	+	0.112282i
$19$	−0.863955			−0.198205			−0.0991024	−	0.995077i	$-0.531597\pi$
$19$	−0.863955			−0.198205			−0.0991024	+	0.995077i	$0.531597\pi$
$20$	3.35707	−	5.81462i	0.750665	−	1.30019i
$21$	−7.52005	+	1.46485i	−1.64101	+	0.319657i
$22$	0.0163299	+	0.0282841i	0.00348154	+	0.00603020i
$23$	4.05879	+	7.03003i	0.846316	+	1.46586i	0.884473	+	0.466591i	$0.154518\pi$
$23$	4.05879	+	7.03003i	0.846316	+	1.46586i	−0.0381573	+	0.999272i	$0.512149\pi$
$24$	−1.15448	−	1.32702i	−0.235658	−	0.270876i
$25$	−3.53023	+	6.11454i	−0.706047	+	1.22291i
$26$	0.258181			0.0506334
$27$	4.35448	−	2.83522i	0.838021	−	0.545639i
$28$	8.55177			1.61613
$29$	1.25024	−	2.16549i	0.232165	−	0.402121i	−0.726280	−	0.687399i	$-0.758753\pi$
$29$	1.25024	−	2.16549i	0.232165	−	0.402121i	0.958445	+	0.285278i	$0.0920859\pi$
$30$	1.01931	+	1.17165i	0.186100	+	0.213912i
$31$	3.01390	+	5.22023i	0.541313	+	0.937582i	0.998829	+	0.0483803i	$0.0154059\pi$
$31$	3.01390	+	5.22023i	0.541313	+	0.937582i	−0.457516	+	0.889201i	$0.651261\pi$
$32$	1.48082	+	2.56485i	0.261774	+	0.453406i
$33$	0.215061	−	0.0418924i	0.0374374	−	0.00729253i
$34$	0.0447064	−	0.0774338i	0.00766709	−	0.0132798i
$35$	−15.3613			−2.59654
$36$	−5.37596	+	2.17700i	−0.895994	+	0.362834i
$37$	−2.44616			−0.402146			−0.201073	−	0.979576i	$-0.564443\pi$
$37$	−2.44616			−0.402146			−0.201073	+	0.979576i	$0.564443\pi$
$38$	−0.111528	+	0.193173i	−0.0180923	+	0.0313367i
$39$	0.563250	−	1.63791i	0.0901921	−	0.262276i
$40$	−1.76335	−	3.05421i	−0.278810	−	0.482912i
$41$	−2.36645	−	4.09881i	−0.369577	−	0.640127i	0.619922	−	0.784663i	$-0.287164\pi$
$41$	−2.36645	−	4.09881i	−0.369577	−	0.640127i	−0.989499	+	0.144537i	$0.953831\pi$
$42$	−0.643238	+	1.87051i	−0.0992538	+	0.288627i
$43$	3.36581	−	5.82976i	0.513281	−	0.889030i	−0.486600	−	0.873625i	$-0.661763\pi$
$43$	3.36581	−	5.82976i	0.513281	−	0.889030i	0.999881	−	0.0154046i	$-0.00490364\pi$
$44$	−0.244567			−0.0368698
$45$	9.65672	−	3.91050i	1.43954	−	0.582943i
$46$	2.09580			0.309009
$47$	−0.107498	+	0.186192i	−0.0156802	+	0.0271589i	−0.873759	−	0.486359i	$-0.838325\pi$
$47$	−0.107498	+	0.186192i	−0.0156802	+	0.0271589i	0.858079	+	0.513518i	$0.171658\pi$
$48$	6.12800	−	1.19369i	0.884500	−	0.172294i
$49$	−6.28282	−	10.8822i	−0.897546	−	1.55460i
$50$	0.911438	+	1.57866i	0.128897	+	0.223256i
$51$	−0.393711	−	0.452550i	−0.0551306	−	0.0633697i
$52$	−0.966671	+	1.67432i	−0.134053	+	0.232187i
$53$	−4.02070			−0.552285			−0.276142	−	0.961117i	$-0.589056\pi$
$53$	−4.02070			−0.552285			−0.276142	+	0.961117i	$0.589056\pi$
$54$	−0.0718083	−	1.33962i	−0.00977187	−	0.182300i
$55$	0.439310			0.0592365
$56$	2.24596	−	3.89012i	0.300130	−	0.519840i
$57$	0.982185	+	1.12897i	0.130094	+	0.149535i
$58$	−0.322789	−	0.559087i	−0.0423843	−	0.0734117i
$59$	6.87049	+	11.9000i	0.894461	+	1.54925i	0.834470	+	0.551053i	$0.185774\pi$
$59$	6.87049	+	11.9000i	0.894461	+	1.54925i	0.0599909	+	0.998199i	$0.480893\pi$
$60$	−11.4147	+	2.22350i	−1.47363	+	0.287053i
$61$	1.36331	−	2.36132i	0.174554	−	0.302336i	−0.765453	−	0.643492i	$-0.777485\pi$
$61$	1.36331	−	2.36132i	0.174554	−	0.302336i	0.940007	+	0.341156i	$0.110818\pi$
$62$	1.55626			0.197646
$63$	10.4633	+	8.16147i	1.31826	+	1.02825i
$64$	−6.44436			−0.805545
$65$	1.73641	−	3.00755i	0.215375	−	0.373041i
$66$	0.0183956	−	0.0534937i	0.00226434	−	0.00658462i
$67$	−2.00833	−	3.47853i	−0.245356	−	0.424970i	0.716875	−	0.697201i	$-0.245572\pi$
$67$	−2.00833	−	3.47853i	−0.245356	−	0.424970i	−0.962232	+	0.272232i	$0.912238\pi$
$68$	0.334776	+	0.579850i	0.0405976	+	0.0703171i
$69$	4.57222	−	13.2959i	0.550431	−	1.60063i
$70$	−1.98300	+	3.43466i	−0.237014	+	0.410520i
$71$	8.55239			1.01498			0.507491	−	0.861657i	$-0.330573\pi$
$71$	8.55239			1.01498			0.507491	+	0.861657i	$0.330573\pi$
$72$	−0.421598	+	3.01723i	−0.0496859	+	0.355584i
$73$	−9.17500			−1.07385			−0.536926	−	0.843629i	$-0.680415\pi$
$73$	−9.17500			−1.07385			−0.536926	+	0.843629i	$0.680415\pi$
$74$	−0.315775	+	0.546939i	−0.0367081	+	0.0635803i
$75$	12.0035	−	2.33819i	1.38604	−	0.269991i
$76$	−0.835161	−	1.44654i	−0.0957995	−	0.165930i
$77$	0.279773	+	0.484581i	0.0318831	+	0.0552231i
$78$	−0.293512	−	0.337376i	−0.0332337	−	0.0382003i
$79$	−0.216092	+	0.374282i	−0.0243122	+	0.0421100i	−0.877926	−	0.478797i	$-0.841073\pi$
$79$	−0.216092	+	0.374282i	−0.0243122	+	0.0421100i	0.853613	+	0.520907i	$0.174406\pi$
$80$	12.5178			1.39953
$81$	−8.65529	−	2.46698i	−0.961699	−	0.274109i
$82$	−1.22194			−0.134941
$83$	0.520310	−	0.901203i	0.0571114	−	0.0989198i	−0.836056	−	0.548644i	$-0.815144\pi$
$83$	0.520310	−	0.901203i	0.0571114	−	0.0989198i	0.893168	+	0.449724i	$0.148478\pi$
$84$	−9.72205	−	11.1750i	−1.06076	−	1.21929i
$85$	−0.601351	−	1.04157i	−0.0652257	−	0.112974i
$86$	−0.868988	−	1.50513i	−0.0937053	−	0.162302i
$87$	−4.25107	+	0.828078i	−0.455763	+	0.0887793i
$88$	−0.0642309	+	0.111251i	−0.00684704	+	0.0118594i
$89$	−10.8984			−1.15523			−0.577614	−	0.816310i	$-0.696016\pi$
$89$	−10.8984			−1.15523			−0.577614	+	0.816310i	$0.696016\pi$
$90$	0.372237	−	2.66396i	0.0392372	−	0.280806i
$91$	4.42331			0.463689
$92$	−7.84703	+	13.5915i	−0.818109	+	1.41701i
$93$	3.39516	−	9.87301i	0.352062	−	1.02378i
$94$	0.0277539	+	0.0480712i	0.00286260	+	0.00495817i
$95$	1.50018	+	2.59839i	0.153915	+	0.266589i
$96$	1.66814	−	4.85090i	0.170254	−	0.495093i
$97$	−0.0894355	+	0.154907i	−0.00908080	+	0.0157284i	−0.870530	−	0.492115i	$-0.836224\pi$
$97$	−0.0894355	+	0.154907i	−0.00908080	+	0.0157284i	0.861449	+	0.507844i	$0.169557\pi$
$98$	−3.24421			−0.327715
$99$	−0.299234	−	0.233405i	−0.0300742	−	0.0234581i
$100$	−13.6503			−1.36503
$101$	−6.46044	+	11.1898i	−0.642838	+	1.11343i	0.341958	+	0.939715i	$0.388910\pi$
$101$	−6.46044	+	11.1898i	−0.642838	+	1.11343i	−0.984796	+	0.173713i	$0.944423\pi$
$102$	−0.152010	+	0.0296105i	−0.0150513	+	0.00293188i
$103$	3.06676	+	5.31178i	0.302177	+	0.523385i	0.976629	−	0.214933i	$-0.0689535\pi$
$103$	3.06676	+	5.31178i	0.302177	+	0.523385i	−0.674452	+	0.738319i	$0.735620\pi$
$104$	0.507757	+	0.879460i	0.0497896	+	0.0862382i
$105$	17.4635	+	20.0733i	1.70426	+	1.95896i
$106$	−0.519033	+	0.898991i	−0.0504129	+	0.0873178i
$107$	−15.9671			−1.54360			−0.771801	−	0.635864i	$-0.780644\pi$
$107$	−15.9671			−1.54360			−0.771801	+	0.635864i	$0.780644\pi$
$108$	8.95643	+	4.55009i	0.861833	+	0.437832i
$109$	−3.73167			−0.357429			−0.178715	−	0.983901i	$-0.557194\pi$
$109$	−3.73167			−0.357429			−0.178715	+	0.983901i	$0.557194\pi$
$110$	0.0567106	−	0.0982257i	0.00540715	−	0.00936545i
$111$	2.78090	+	3.19650i	0.263952	+	0.303398i
$112$	7.97190	+	13.8077i	0.753274	+	1.30471i
$113$	7.85519	+	13.6056i	0.738954	+	1.27991i	0.952967	+	0.303075i	$0.0980132\pi$
$113$	7.85519	+	13.6056i	0.738954	+	1.27991i	−0.214013	+	0.976831i	$0.568653\pi$
$114$	0.379218	−	0.0738688i	0.0355170	−	0.00691845i
$115$	14.0954	−	24.4140i	1.31441	−	2.27662i
$116$	4.83430			0.448854
$117$	−2.78066	+	1.12603i	−0.257072	+	0.104102i
$118$	3.54765			0.326588
$119$	0.765937	−	1.32664i	0.0702134	−	0.121613i
$120$	−1.98641	+	5.77641i	−0.181333	+	0.527311i
$121$	5.49200	+	9.51242i	0.499273	+	0.864766i
$122$	−0.351980	−	0.609647i	−0.0318668	−	0.0551949i
$123$	−2.66580	+	7.75206i	−0.240367	+	0.698980i
$124$	−5.82691	+	10.0925i	−0.523272	+	0.906333i
$125$	7.15563			0.640019
$126$	3.17555	−	1.28594i	0.282900	−	0.114561i
$127$	14.0100			1.24319			0.621594	−	0.783340i	$-0.286486\pi$
$127$	14.0100			1.24319			0.621594	+	0.783340i	$0.286486\pi$
$128$	−3.79354	+	6.57061i	−0.335305	+	0.580765i
$129$	−11.4444	+	2.22929i	−1.00762	+	0.196278i
$130$	−0.448307	−	0.776491i	−0.0393192	−	0.0681028i
$131$	−2.92767	−	5.07088i	−0.255792	−	0.443045i	0.709318	−	0.704888i	$-0.249003\pi$
$131$	−2.92767	−	5.07088i	−0.255792	−	0.443045i	−0.965110	+	0.261844i	$0.915670\pi$
$132$	0.278035	+	0.319586i	0.0241998	+	0.0278164i
$133$	−1.91077	+	3.30955i	−0.165685	+	0.286974i
$134$	−1.03702			−0.0895852
$135$	−16.0882	−	8.17322i	−1.38465	−	0.703439i
$136$	0.351691			0.0301573
$137$	8.47896	−	14.6860i	0.724406	−	1.25471i	−0.234812	−	0.972041i	$-0.575447\pi$
$137$	8.47896	−	14.6860i	0.724406	−	1.25471i	0.959218	−	0.282667i	$-0.0912193\pi$
$138$	−2.38261	−	2.73868i	−0.202821	−	0.233132i
$139$	−5.36604	−	9.29425i	−0.455142	−	0.788328i	0.543555	−	0.839374i	$-0.317078\pi$
$139$	−5.36604	−	9.29425i	−0.455142	−	0.788328i	−0.998696	+	0.0510454i	$0.983745\pi$
$140$	−14.8494	−	25.7199i	−1.25500	−	2.17373i
$141$	0.365514	−	0.0711995i	0.0307819	−	0.00599608i
$142$	1.10403	−	1.91224i	0.0926483	−	0.160472i
$143$	−0.126499			−0.0105784
$144$	−8.52644	−	6.65068i	−0.710537	−	0.554223i
$145$	−8.68375			−0.721146
$146$	−1.18440	+	2.05145i	−0.0980220	+	0.169779i
$147$	−7.07760	+	20.5814i	−0.583750	+	1.69753i
$148$	−2.36463	−	4.09566i	−0.194371	−	0.336661i
$149$	−2.98801	−	5.17539i	−0.244787	−	0.423984i	0.717284	−	0.696781i	$-0.245385\pi$
$149$	−2.98801	−	5.17539i	−0.244787	−	0.423984i	−0.962072	+	0.272796i	$0.912052\pi$
$150$	1.02673	−	2.98571i	0.0838325	−	0.243782i
$151$	−9.59560	+	16.6201i	−0.780879	+	1.35252i	0.150551	+	0.988602i	$0.451895\pi$
$151$	−9.59560	+	16.6201i	−0.780879	+	1.35252i	−0.931430	+	0.363920i	$0.881438\pi$
$152$	−0.877358			−0.0711631
$153$	−0.143777	+	1.02896i	−0.0116237	+	0.0831865i
$154$	0.144464			0.0116412
$155$	10.4667	−	18.1289i	0.840709	−	1.45615i
$156$	3.28687	−	0.640258i	0.263160	−	0.0512617i
$157$	−9.50028	−	16.4550i	−0.758205	−	1.31325i	−0.943765	−	0.330617i	$-0.892743\pi$
$157$	−9.50028	−	16.4550i	−0.758205	−	1.31325i	0.185560	−	0.982633i	$-0.440590\pi$
$158$	0.0557907	+	0.0966323i	0.00443847	+	0.00768765i
$159$	4.57091	+	5.25402i	0.362497	+	0.416671i
$160$	5.14262	−	8.90727i	0.406560	−	0.704182i
$161$	35.9065			2.82983
$162$	−1.66891	+	1.61678i	−0.131122	+	0.127026i
$163$	4.70788			0.368750			0.184375	−	0.982856i	$-0.440974\pi$
$163$	4.70788			0.368750			0.184375	+	0.982856i	$0.440974\pi$
$164$	4.57516	−	7.92440i	0.357260	−	0.618792i
$165$	−0.499428	−	0.574065i	−0.0388804	−	0.0446909i
$166$	−0.134334	−	0.232673i	−0.0104263	−	0.0180589i
$167$	−8.06308	−	13.9657i	−0.623940	−	1.08070i	−0.988745	−	0.149612i	$-0.952198\pi$
$167$	−8.06308	−	13.9657i	−0.623940	−	1.08070i	0.364805	−	0.931084i	$-0.381136\pi$
$168$	−7.63671	+	1.48758i	−0.589185	+	0.114769i
$169$	−0.500000	+	0.866025i	−0.0384615	+	0.0666173i
$170$	−0.310515			−0.0238154
$171$	0.358678	−	2.56693i	0.0274288	−	0.196298i
$172$	13.0145			0.992349
$173$	−5.96073	+	10.3243i	−0.453186	+	0.784940i	−0.998582	−	0.0532379i	$-0.983046\pi$
$173$	−5.96073	+	10.3243i	−0.453186	+	0.784940i	0.545396	+	0.838178i	$0.316379\pi$
$174$	−0.363622	+	1.05740i	−0.0275661	+	0.0801612i
$175$	15.6153	+	27.0465i	1.18041	+	2.04452i
$176$	−0.227984	−	0.394879i	−0.0171849	−	0.0297651i
$177$	7.73960	−	22.5065i	0.581744	−	1.69169i
$178$	−1.40688	+	2.43678i	−0.105450	+	0.182645i
$179$	−3.82703			−0.286046			−0.143023	−	0.989719i	$-0.545682\pi$
$179$	−3.82703			−0.286046			−0.143023	+	0.989719i	$0.545682\pi$
$180$	15.8823	+	12.3883i	1.18380	+	0.923370i
$181$	11.3406			0.842940			0.421470	−	0.906842i	$-0.361514\pi$
$181$	11.3406			0.842940			0.421470	+	0.906842i	$0.361514\pi$
$182$	0.571006	−	0.989012i	0.0423258	−	0.0733104i
$183$	−4.63551	+	0.902964i	−0.342667	+	0.0667490i
$184$	4.12175	+	7.13909i	0.303860	+	0.526301i
$185$	4.24753	+	7.35693i	0.312284	+	0.540892i
$186$	−1.76923	−	2.03364i	−0.129726	−	0.149114i
$187$	−0.0219046	+	0.0379398i	−0.00160182	+	0.00277444i
$188$	−0.415661			−0.0303152
$189$	−1.23026	−	22.9512i	−0.0894884	−	1.66946i
$190$	0.774635			0.0561979
$191$	−3.19558	+	5.53491i	−0.231224	+	0.400492i	−0.958169	−	0.286204i	$-0.907606\pi$
$191$	−3.19558	+	5.53491i	−0.231224	+	0.400492i	0.726944	+	0.686696i	$0.240940\pi$
$192$	7.32625	+	8.42113i	0.528727	+	0.607743i
$193$	−6.14567	−	10.6446i	−0.442375	−	0.766215i	0.555491	−	0.831523i	$-0.312531\pi$
$193$	−6.14567	−	10.6446i	−0.442375	−	0.766215i	−0.997865	+	0.0653075i	$0.979197\pi$
$194$	0.0230905	+	0.0399940i	0.00165780	+	0.00287140i
$195$	−5.90413	+	1.15008i	−0.422803	+	0.0823590i
$196$	12.1469	−	21.0390i	0.867632	−	1.50278i
$197$	−6.01862			−0.428809			−0.214404	−	0.976745i	$-0.568781\pi$
$197$	−6.01862			−0.428809			−0.214404	+	0.976745i	$0.568781\pi$
$198$	−0.0908155	+	0.0367758i	−0.00645398	+	0.00261354i
$199$	−11.0716			−0.784846			−0.392423	−	0.919785i	$-0.628363\pi$
$199$	−11.0716			−0.784846			−0.392423	+	0.919785i	$0.628363\pi$
$200$	−3.58500	+	6.20940i	−0.253498	+	0.439071i
$201$	−2.26238	+	6.57892i	−0.159576	+	0.464042i
$202$	1.66796	+	2.88900i	0.117357	+	0.203269i
$203$	−5.53022	−	9.57862i	−0.388145	−	0.672287i
$204$	0.377126	−	1.09667i	0.0264041	−	0.0767821i
$205$	−8.21825	+	14.2344i	−0.573987	+	0.994175i
$206$	1.58355			0.110331
$207$	−22.5722	+	9.14064i	−1.56888	+	0.635318i
$208$	−3.60450			−0.249927
$209$	0.0546449	−	0.0946478i	0.00377987	−	0.00654692i
$210$	6.74259	−	1.31341i	0.465283	−	0.0906337i
$211$	−5.03787	−	8.72584i	−0.346821	−	0.600712i	0.638862	−	0.769321i	$-0.279406\pi$
$211$	−5.03787	−	8.72584i	−0.346821	−	0.600712i	−0.985683	+	0.168610i	$0.946072\pi$
$212$	−3.88669	−	6.73195i	−0.266939	−	0.462352i
$213$	−9.72276	−	11.1758i	−0.666193	−	0.765752i
$214$	−2.06120	+	3.57011i	−0.140901	+	0.244048i
$215$	−23.3777			−1.59435
$216$	4.42204	−	2.87920i	0.300881	−	0.195905i
$217$	26.6628			1.80999
$218$	−0.481722	+	0.834368i	−0.0326264	+	0.0565105i
$219$	10.4306	+	11.9894i	0.704833	+	0.810167i
$220$	0.424668	+	0.735547i	0.0286311	+	0.0495905i
$221$	0.173159	+	0.299921i	0.0116480	+	0.0201749i
$222$	1.07370	−	0.209148i	0.0720618	−	0.0140371i
$223$	−8.78466	+	15.2155i	−0.588264	+	1.01890i	0.406196	+	0.913786i	$0.366855\pi$
$223$	−8.78466	+	15.2155i	−0.588264	+	1.01890i	−0.994460	+	0.105117i	$0.966478\pi$
$224$	13.1002			0.875297
$225$	−16.7015	−	13.0273i	−1.11344	−	0.868487i
$226$	4.05612			0.269809
$227$	11.6006	−	20.0928i	0.769958	−	1.33361i	−0.167627	−	0.985850i	$-0.553610\pi$
$227$	11.6006	−	20.0928i	0.769958	−	1.33361i	0.937585	−	0.347756i	$-0.113056\pi$
$228$	−0.940808	+	2.73584i	−0.0623065	+	0.181185i
$229$	4.57963	+	7.93215i	0.302630	+	0.524171i	0.976731	−	0.214468i	$-0.0688019\pi$
$229$	4.57963	+	7.93215i	0.302630	+	0.524171i	−0.674101	+	0.738640i	$0.735469\pi$
$230$	−3.63917	−	6.30323i	−0.239960	−	0.415623i
$231$	0.315164	−	0.916486i	0.0207363	−	0.0603004i
$232$	1.26964	−	2.19908i	0.0833560	−	0.144377i
$233$	20.1888			1.32261			0.661307	−	0.750116i	$-0.270002\pi$
$233$	20.1888			1.32261			0.661307	+	0.750116i	$0.270002\pi$
$234$	−0.107186	+	0.767090i	−0.00700695	+	0.0501462i
$235$	0.746643			0.0487056
$236$	−13.2830	+	23.0068i	−0.864650	+	1.49762i
$237$	0.734753	−	0.143125i	0.0477273	−	0.00929694i
$238$	−0.197750	−	0.342513i	−0.0128182	−	0.0222018i
$239$	−3.84883	−	6.66638i	−0.248960	−	0.431212i	0.714277	−	0.699863i	$-0.246756\pi$
$239$	−3.84883	−	6.66638i	−0.248960	−	0.431212i	−0.963238	+	0.268651i	$0.913422\pi$
$240$	−14.2308	−	16.3575i	−0.918594	−	1.05587i
$241$	−1.55399	+	2.69159i	−0.100101	+	0.173381i	−0.911726	−	0.410798i	$-0.865250\pi$
$241$	−1.55399	+	2.69159i	−0.100101	+	0.173381i	0.811625	+	0.584179i	$0.198583\pi$
$242$	2.83586			0.182296
$243$	6.61603	+	14.1148i	0.424418	+	0.905466i
$244$	5.27149			0.337472
$245$	−21.8191	+	37.7918i	−1.39397	+	2.41443i
$246$	1.38916	+	1.59677i	0.0885697	+	0.101806i
$247$	−0.431977	−	0.748207i	−0.0274861	−	0.0476073i
$248$	3.06066	+	5.30122i	0.194352	+	0.336628i
$249$	−1.76915	+	0.344618i	−0.112116	+	0.0218393i
$250$	0.923722	−	1.59993i	0.0584213	−	0.101189i
$251$	9.63549			0.608187			0.304093	−	0.952642i	$-0.401646\pi$
$251$	9.63549			0.608187			0.304093	+	0.952642i	$0.401646\pi$
$252$	−3.55034	+	25.4085i	−0.223650	+	1.60058i
$253$	−1.02687			−0.0645587
$254$	1.80856	−	3.13251i	0.113479	−	0.196551i
$255$	−0.677422	+	1.96992i	−0.0424218	+	0.123361i
$256$	−5.46494	−	9.46556i	−0.341559	−	0.591597i
$257$	−2.12898	−	3.68750i	−0.132802	−	0.230020i	0.791954	−	0.610581i	$-0.209064\pi$
$257$	−2.12898	−	3.68750i	−0.132802	−	0.230020i	−0.924756	+	0.380561i	$0.875731\pi$
$258$	−0.978914	+	2.84665i	−0.0609445	+	0.177225i
$259$	−5.41005	+	9.37048i	−0.336164	+	0.582253i
$260$	6.71415			0.416394
$261$	5.91491	+	4.61367i	0.366124	+	0.285579i
$262$	−1.51174			−0.0933954
$263$	9.94611	−	17.2272i	0.613303	−	1.06227i	−0.377376	−	0.926060i	$-0.623174\pi$
$263$	9.94611	−	17.2272i	0.613303	−	1.06227i	0.990680	−	0.136213i	$-0.0434930\pi$
$264$	0.218398	−	0.0425423i	0.0134414	−	0.00261830i
$265$	6.98157	+	12.0924i	0.428875	+	0.742832i
$266$	0.493324	+	0.854462i	0.0302476	+	0.0523904i
$267$	12.3898	+	14.2414i	0.758244	+	0.871560i
$268$	3.88279	−	6.72519i	0.237179	−	0.410806i
$269$	5.80864			0.354159			0.177080	−	0.984197i	$-0.443335\pi$
$269$	5.80864			0.354159			0.177080	+	0.984197i	$0.443335\pi$
$270$	−3.90429	+	2.54210i	−0.237608	+	0.154707i
$271$	−18.1178			−1.10058			−0.550290	−	0.834974i	$-0.685483\pi$
$271$	−18.1178			−1.10058			−0.550290	+	0.834974i	$0.685483\pi$
$272$	−0.624153	+	1.08106i	−0.0378448	+	0.0655492i
$273$	−5.02862	−	5.78013i	−0.304346	−	0.349829i
$274$	−2.18910	−	3.79164i	−0.132249	−	0.229061i
$275$	−0.446573	−	0.773486i	−0.0269293	−	0.0466430i
$276$	26.6814	−	5.19735i	1.60603	−	0.312844i
$277$	−5.60978	+	9.71642i	−0.337059	+	0.583803i	−0.983878	−	0.178840i	$-0.942766\pi$
$277$	−5.60978	+	9.71642i	−0.337059	+	0.583803i	0.646819	+	0.762643i	$0.276099\pi$
$278$	−2.77082			−0.166183
$279$	−16.7613	+	6.78749i	−1.00347	+	0.406357i
$280$	−15.5996			−0.932257
$281$	4.51700	−	7.82368i	0.269462	−	0.466721i	−0.699261	−	0.714866i	$-0.746488\pi$
$281$	4.51700	−	7.82368i	0.269462	−	0.466721i	0.968723	+	0.248145i	$0.0798209\pi$
$282$	0.0312648	−	0.0909169i	0.00186179	−	0.00541402i
$283$	9.31076	+	16.1267i	0.553467	+	0.958633i	0.998021	+	0.0628813i	$0.0200289\pi$
$283$	9.31076	+	16.1267i	0.553467	+	0.958633i	−0.444554	+	0.895752i	$0.646638\pi$
$284$	8.26735	+	14.3195i	0.490577	+	0.849705i
$285$	1.68995	−	4.91432i	0.100104	−	0.291099i
$286$	−0.0163299	+	0.0282841i	−0.000965605	+	0.00167248i
$287$	−20.9351			−1.23576
$288$	−8.23530	+	3.33489i	−0.485270	+	0.196511i
$289$	−16.8801			−0.992945
$290$	−1.12099	+	1.94161i	−0.0658267	+	0.114015i
$291$	0.304098	−	0.0592361i	0.0178265	−	0.00347248i
$292$	−8.86921	−	15.3619i	−0.519031	−	0.898989i
$293$	1.75915	+	3.04694i	0.102771	+	0.178004i	0.912825	−	0.408350i	$-0.133896\pi$
$293$	1.75915	+	3.04694i	0.102771	+	0.178004i	−0.810054	+	0.586355i	$0.800563\pi$
$294$	3.68817	+	4.23935i	0.215098	+	0.247244i
$295$	23.8599	−	41.3266i	1.38918	−	2.40613i
$296$	−2.48410			−0.144386
$297$	0.0351835	+	0.656368i	0.00204155	+	0.0380863i
$298$	−1.54289			−0.0893774
$299$	−4.05879	+	7.03003i	−0.234726	+	0.406557i
$300$	15.5183	+	17.8374i	0.895950	+	1.02985i
$301$	−14.8880	−	25.7868i	−0.858131	−	1.48633i
$302$	2.47740	+	4.29098i	0.142558	+	0.246918i
$303$	21.9668	−	4.27897i	1.26196	−	0.245820i
$304$	1.55706	−	2.69691i	0.0893037	−	0.154678i
$305$	−9.46905			−0.542196
$306$	0.211506	+	0.164976i	0.0120910	+	0.00943105i
$307$	15.8342			0.903707			0.451853	−	0.892092i	$-0.350763\pi$
$307$	15.8342			0.903707			0.451853	+	0.892092i	$0.350763\pi$
$308$	−0.540897	+	0.936861i	−0.0308205	+	0.0533826i
$309$	3.45470	−	10.0461i	0.196531	−	0.571505i
$310$	−2.70231	−	4.68054i	−0.153481	−	0.265837i
$311$	8.04473	+	13.9339i	0.456175	+	0.790117i	0.998755	−	0.0498865i	$-0.0158859\pi$
$311$	8.04473	+	13.9339i	0.456175	+	0.790117i	−0.542580	+	0.840004i	$0.682553\pi$
$312$	0.571988	−	1.66332i	0.0323824	−	0.0941669i
$313$	−2.23621	+	3.87323i	−0.126398	+	0.218928i	−0.922279	−	0.386526i	$-0.873675\pi$
$313$	−2.23621	+	3.87323i	−0.126398	+	0.218928i	0.795880	+	0.605454i	$0.207008\pi$
$314$	−4.90558			−0.276838
$315$	6.37738	−	45.6406i	0.359325	−	2.57156i
$316$	−0.835558			−0.0470038
$317$	−6.48094	+	11.2253i	−0.364006	+	0.630477i	−0.988616	−	0.150460i	$-0.951925\pi$
$317$	−6.48094	+	11.2253i	−0.364006	+	0.630477i	0.624610	+	0.780937i	$0.285258\pi$
$318$	1.76481	−	0.343773i	0.0989658	−	0.0192778i
$319$	0.158155	+	0.273933i	0.00885500	+	0.0153373i
$320$	11.1900	+	19.3817i	0.625543	+	1.08347i
$321$	18.1522	+	20.8650i	1.01316	+	1.16457i
$322$	4.63519	−	8.02838i	0.258309	−	0.447404i
$323$	−0.299204			−0.0166481
$324$	−4.23629	−	16.8765i	−0.235350	−	0.937584i
$325$	−7.06047			−0.391644
$326$	0.607743	−	1.05264i	0.0336597	−	0.0583004i
$327$	4.24234	+	4.87633i	0.234602	+	0.269662i
$328$	−2.40316	−	4.16240i	−0.132692	−	0.229830i
$329$	0.475497	+	0.823585i	0.0262150	+	0.0454057i
$330$	−0.192827	+	0.0375613i	−0.0106148	+	0.00206768i
$331$	−7.08304	+	12.2682i	−0.389319	+	0.674320i	−0.992358	−	0.123391i	$-0.960623\pi$
$331$	−7.08304	+	12.2682i	−0.389319	+	0.674320i	0.603039	+	0.797712i	$0.293956\pi$
$332$	2.01187			0.110416
$333$	1.01554	−	7.26786i	0.0556513	−	0.398276i
$334$	−4.16346			−0.227815
$335$	−6.97456	+	12.0803i	−0.381061	+	0.660017i
$336$	8.98035	−	26.1145i	0.489918	−	1.42466i
$337$	13.0374	+	22.5815i	0.710194	+	1.23009i	0.964784	+	0.263043i	$0.0847260\pi$
$337$	13.0374	+	22.5815i	0.710194	+	1.23009i	−0.254590	+	0.967049i	$0.581941\pi$
$338$	0.129090	+	0.223591i	0.00702159	+	0.0121617i
$339$	8.84887	−	25.7322i	0.480604	−	1.39758i
$340$	1.16262	−	2.01371i	0.0630518	−	0.109209i
$341$	−0.762514			−0.0412925
$342$	−0.527640	−	0.411563i	−0.0285315	−	0.0222548i
$343$	−24.6186			−1.32928
$344$	3.41803	−	5.92020i	0.184288	−	0.319196i
$345$	−47.9272	+	9.33587i	−2.58031	+	0.502627i
$346$	1.53894	+	2.66553i	0.0827342	+	0.143300i
$347$	−12.5166	−	21.6793i	−0.671924	−	1.16381i	−0.977358	−	0.211594i	$-0.932135\pi$
$347$	−12.5166	−	21.6793i	−0.671924	−	1.16381i	0.305433	−	0.952213i	$-0.401199\pi$
$348$	−5.49586	−	6.31720i	−0.294609	−	0.338637i
$349$	−5.96790	+	10.3367i	−0.319454	+	0.553311i	−0.980374	−	0.197145i	$-0.936833\pi$
$349$	−5.96790	+	10.3367i	−0.319454	+	0.553311i	0.660920	+	0.750456i	$0.270166\pi$
$350$	8.06314			0.430993
$351$	4.63261	+	2.35348i	0.247271	+	0.125620i
$352$	−0.374646			−0.0199687
$353$	7.42385	−	12.8585i	0.395132	−	0.684388i	−0.597986	−	0.801506i	$-0.704032\pi$
$353$	7.42385	−	12.8585i	0.395132	−	0.684388i	0.993118	+	0.117118i	$0.0373657\pi$
$354$	−4.03314	−	4.63587i	−0.214359	−	0.246394i
$355$	−14.8505	−	25.7217i	−0.788180	−	1.36517i
$356$	−10.5352	−	18.2475i	−0.558363	−	0.967113i
$357$	−2.60433	+	0.507306i	−0.137836	+	0.0268495i
$358$	−0.494033	+	0.855690i	−0.0261105	+	0.0452246i
$359$	35.0911			1.85204			0.926019	−	0.377477i	$-0.123208\pi$
$359$	35.0911			1.85204			0.926019	+	0.377477i	$0.123208\pi$
$360$	9.80652	−	3.97116i	0.516849	−	0.209299i
$361$	−18.2536			−0.960715
$362$	1.46396	−	2.53566i	0.0769442	−	0.133271i
$363$	6.18673	−	17.9908i	0.324719	−	0.944272i
$364$	4.27588	+	7.40605i	0.224117	+	0.388182i
$365$	15.9316	+	27.5943i	0.833896	+	1.44435i
$366$	−0.396505	+	1.15302i	−0.0207257	+	0.0602695i
$367$	6.82647	−	11.8238i	0.356339	−	0.617197i	−0.631007	−	0.775777i	$-0.717358\pi$
$367$	6.82647	−	11.8238i	0.356339	−	0.617197i	0.987346	+	0.158580i	$0.0506916\pi$
$368$	−29.2598			−1.52527
$369$	13.1606	−	5.32939i	0.685112	−	0.277437i
$370$	2.19326			0.114022
$371$	−8.89239	+	15.4021i	−0.461670	+	0.799635i
$372$	19.8126	−	3.85935i	1.02724	−	0.200098i
$373$	8.89873	+	15.4130i	0.460759	+	0.798057i	0.998999	−	0.0447342i	$-0.0142441\pi$
$373$	8.89873	+	15.4130i	0.460759	+	0.798057i	−0.538240	+	0.842791i	$0.680911\pi$
$374$	0.00565534	+	0.00979533i	0.000292431	+	0.000506505i
$375$	−8.13485	−	9.35057i	−0.420082	−	0.482861i
$376$	−0.109166	+	0.189081i	−0.00562979	+	0.00975109i
$377$	2.50049			0.128782
$378$	−5.29050	−	2.68771i	−0.272114	−	0.138241i
$379$	21.8610			1.12292			0.561461	−	0.827503i	$-0.310240\pi$
$379$	21.8610			1.12292			0.561461	+	0.827503i	$0.310240\pi$
$380$	−2.90036	+	5.02357i	−0.148785	+	0.257704i
$381$	−15.9272	−	18.3075i	−0.815977	−	0.937921i
$382$	0.825038	+	1.42901i	0.0422126	+	0.0731144i
$383$	4.25617	+	7.37190i	0.217480	+	0.376687i	0.954037	−	0.299689i	$-0.0968829\pi$
$383$	4.25617	+	7.37190i	0.217480	+	0.376687i	−0.736557	+	0.676376i	$0.763550\pi$
$384$	12.8988	−	2.51259i	0.658238	−	0.128220i
$385$	0.971601	−	1.68286i	0.0495174	−	0.0857666i
$386$	−3.17338			−0.161521
$387$	15.9237	+	12.4206i	0.809445	+	0.631372i
$388$	−0.345819			−0.0175563
$389$	6.27691	−	10.8719i	0.318252	−	0.551229i	−0.661871	−	0.749618i	$-0.730237\pi$
$389$	6.27691	−	10.8719i	0.318252	−	0.551229i	0.980123	+	0.198389i	$0.0635708\pi$
$390$	−0.505018	+	1.46857i	−0.0255726	+	0.0743642i
$391$	1.40564	+	2.43463i	0.0710860	+	0.123125i
$392$	−6.38029	−	11.0510i	−0.322253	−	0.558159i
$393$	−3.29802	+	9.59053i	−0.166363	+	0.483778i
$394$	−0.776946	+	1.34571i	−0.0391420	+	0.0677959i
$395$	1.50089			0.0755182
$396$	0.101534	−	0.726641i	0.00510227	−	0.0365151i
$397$	5.98359			0.300308			0.150154	−	0.988663i	$-0.452023\pi$
$397$	5.98359			0.300308			0.150154	+	0.988663i	$0.452023\pi$
$398$	−1.42924	+	2.47551i	−0.0716413	+	0.124086i
$399$	6.49698	−	1.26557i	0.325256	−	0.0633575i
$400$	−12.7247	−	22.0399i	−0.636236	−	1.10199i
$401$	−11.2778	−	19.5337i	−0.563185	−	0.975466i	−0.997216	−	0.0745676i	$-0.976242\pi$
$401$	−11.2778	−	19.5337i	−0.563185	−	0.975466i	0.434031	−	0.900898i	$-0.357091\pi$
$402$	1.17894	+	1.35512i	0.0588000	+	0.0675874i
$403$	−3.01390	+	5.22023i	−0.150133	+	0.260038i
$404$	−24.9805			−1.24283
$405$	7.60955	+	30.3149i	0.378122	+	1.50636i
$406$	−2.85559			−0.141721
$407$	0.154719	−	0.267981i	0.00766912	−	0.0132833i
$408$	−0.399819	−	0.459570i	−0.0197940	−	0.0227521i
$409$	−1.36458	−	2.36351i	−0.0674739	−	0.116868i	0.830315	−	0.557295i	$-0.188161\pi$
$409$	−1.36458	−	2.36351i	−0.0674739	−	0.116868i	−0.897789	+	0.440426i	$0.854827\pi$
$410$	2.12179	+	3.67505i	0.104788	+	0.181498i
$411$	−28.8301	+	5.61589i	−1.42208	+	0.277012i
$412$	−5.92909	+	10.2695i	−0.292105	+	0.505941i
$413$	60.7805			2.99082
$414$	−0.870089	+	6.22691i	−0.0427625	+	0.306036i
$415$	−3.61388			−0.177398
$416$	−1.48082	+	2.56485i	−0.0726031	+	0.125752i
$417$	−6.04484	+	17.5782i	−0.296017	+	0.860807i
$418$	−0.0141083	−	0.0244362i	−0.000690058	−	0.00119521i
$419$	16.2360	+	28.1216i	0.793180	+	1.37383i	0.923989	+	0.382420i	$0.124909\pi$
$419$	16.2360	+	28.1216i	0.793180	+	1.37383i	−0.130809	+	0.991408i	$0.541757\pi$
$420$	−16.7278	+	48.6439i	−0.816233	+	2.37358i
$421$	−6.69111	+	11.5894i	−0.326105	+	0.564830i	−0.981735	−	0.190252i	$-0.939070\pi$
$421$	−6.69111	+	11.5894i	−0.326105	+	0.564830i	0.655630	+	0.755082i	$0.272403\pi$
$422$	−2.60136			−0.126632
$423$	−0.508573	−	0.396690i	−0.0247277	−	0.0192877i
$424$	−4.08307			−0.198291
$425$	−1.22259	+	2.11758i	−0.0593041	+	0.102718i
$426$	−3.75392	+	0.731237i	−0.181878	+	0.0354285i
$427$	−6.03033	−	10.4448i	−0.291828	−	0.505461i
$428$	−15.4350	−	26.7342i	−0.746078	−	1.29225i
$429$	0.143811	+	0.165302i	0.00694324	+	0.00798087i
$430$	−3.01784	+	5.22705i	−0.145533	+	0.252071i
$431$	−14.6522			−0.705772			−0.352886	−	0.935666i	$-0.614800\pi$
$431$	−14.6522			−0.705772			−0.352886	+	0.935666i	$0.614800\pi$
$432$	1.00253	+	18.7027i	0.0482340	+	0.899833i
$433$	6.62721			0.318483			0.159242	−	0.987240i	$-0.449095\pi$
$433$	6.62721			0.318483			0.159242	+	0.987240i	$0.449095\pi$
$434$	3.44192	−	5.96157i	0.165217	−	0.286165i
$435$	9.87209	+	11.3474i	0.473331	+	0.544068i
$436$	−3.60730	−	6.24802i	−0.172758	−	0.299226i
$437$	−3.50661	−	6.07363i	−0.167744	−	0.290541i
$438$	4.02720	−	0.784470i	0.192427	−	0.0374834i
$439$	15.9958	−	27.7055i	0.763438	−	1.32231i	−0.177631	−	0.984097i	$-0.556843\pi$
$439$	15.9958	−	27.7055i	0.763438	−	1.32231i	0.941069	−	0.338216i	$-0.109823\pi$
$440$	0.446125			0.0212682
$441$	34.9408	−	14.1493i	1.66385	−	0.673776i
$442$	0.0894128			0.00425293
$443$	10.5559	−	18.2834i	0.501527	−	0.868670i	−0.498472	−	0.866906i	$-0.666105\pi$
$443$	10.5559	−	18.2834i	0.501527	−	0.868670i	0.999998	−	0.00176387i	$-0.000561458\pi$
$444$	−2.66375	+	7.74610i	−0.126416	+	0.367614i
$445$	18.9241	+	32.7775i	0.897087	+	1.55380i
$446$	2.26803	+	3.92834i	0.107394	+	0.186012i
$447$	−3.36599	+	9.78819i	−0.159206	+	0.462965i
$448$	−14.2527	+	24.6864i	−0.673377	+	1.16632i
$449$	−7.87220			−0.371512			−0.185756	−	0.982596i	$-0.559473\pi$
$449$	−7.87220			−0.371512			−0.185756	+	0.982596i	$0.559473\pi$
$450$	−5.06879	+	2.05261i	−0.238945	+	0.0967611i
$451$	0.598709			0.0281921
$452$	−15.1868	+	26.3043i	−0.714326	+	1.23725i
$453$	32.6269	−	6.35548i	1.53295	−	0.298607i
$454$	−2.99505	−	5.18758i	−0.140565	−	0.243465i
$455$	−7.68067	−	13.3033i	−0.360075	−	0.623669i
$456$	0.997421	+	1.14648i	0.0467085	+	0.0536889i
$457$	12.6044	−	21.8315i	0.589609	−	1.02123i	−0.404674	−	0.914461i	$-0.632615\pi$
$457$	12.6044	−	21.8315i	0.589609	−	1.02123i	0.994283	−	0.106773i	$-0.0340517\pi$
$458$	2.36474			0.110497
$459$	1.50804	−	0.981890i	0.0703893	−	0.0458307i
$460$	54.5026			2.54120
$461$	−5.65188	+	9.78934i	−0.263234	+	0.455935i	−0.967099	−	0.254398i	$-0.918123\pi$
$461$	−5.65188	+	9.78934i	−0.263234	+	0.455935i	0.703865	+	0.710333i	$0.251456\pi$
$462$	−0.164233	−	0.188777i	−0.00764083	−	0.00878272i
$463$	−15.1397	−	26.2227i	−0.703602	−	1.21867i	−0.967194	−	0.254040i	$-0.918241\pi$
$463$	−15.1397	−	26.2227i	−0.703602	−	1.21867i	0.263592	−	0.964634i	$-0.415093\pi$
$464$	4.50651	+	7.80550i	0.209209	+	0.362361i
$465$	−35.5889	+	6.93247i	−1.65040	+	0.321485i
$466$	2.60618	−	4.51404i	0.120729	−	0.209109i
$467$	−30.8192			−1.42614			−0.713070	−	0.701093i	$-0.752696\pi$
$467$	−30.8192			−1.42614			−0.713070	+	0.701093i	$0.752696\pi$
$468$	−4.57332	−	3.56722i	−0.211402	−	0.164895i
$469$	−17.7669			−0.820400
$470$	0.0963843	−	0.166943i	0.00444588	−	0.00770049i
$471$	−10.7021	+	31.1212i	−0.493125	+	1.43399i
$472$	6.97707	+	12.0846i	0.321146	+	0.556241i
$473$	0.425773	+	0.737461i	0.0195771	+	0.0339085i
$474$	0.0628482	−	0.182760i	0.00288671	−	0.00839446i
$475$	3.04996	−	5.28269i	0.139942	−	0.242386i
$476$	2.96164			0.135746
$477$	1.66922	−	11.9460i	0.0764285	−	0.546971i
$478$	−1.98739			−0.0909011
$479$	6.39593	−	11.0781i	0.292237	−	0.506170i	−0.682101	−	0.731258i	$-0.738934\pi$
$479$	6.39593	−	11.0781i	0.292237	−	0.506170i	0.974338	+	0.225088i	$0.0722669\pi$
$480$	−17.4859	+	3.40612i	−0.798118	+	0.155468i
$481$	−1.22308	−	2.11843i	−0.0557675	−	0.0965922i
$482$	0.401210	+	0.694917i	0.0182746	+	0.0316526i
$483$	−40.8202	−	46.9207i	−1.85739	−	2.13496i
$484$	−10.6179	+	18.3908i	−0.482633	+	0.835944i
$485$	0.621187			0.0282066
$486$	4.01001	+	0.342803i	0.181898	+	0.0155499i
$487$	7.29411			0.330528			0.165264	−	0.986249i	$-0.447152\pi$
$487$	7.29411			0.330528			0.165264	+	0.986249i	$0.447152\pi$
$488$	1.38446	−	2.39795i	0.0626715	−	0.108550i
$489$	−5.35214	−	6.15200i	−0.242032	−	0.278203i
$490$	5.63327	+	9.75711i	0.254485	+	0.440782i
$491$	−2.41978	−	4.19118i	−0.109203	−	0.189146i	0.806244	−	0.591582i	$-0.201497\pi$
$491$	−2.41978	−	4.19118i	−0.109203	−	0.189146i	−0.915448	+	0.402437i	$0.868163\pi$
$492$	−15.5564	+	3.03028i	−0.701338	+	0.136615i
$493$	0.432983	−	0.749949i	0.0195006	−	0.0337760i
$494$	−0.223057			−0.0100358
$495$	−0.182383	+	1.30525i	−0.00819750	+	0.0586665i
$496$	−21.7272			−0.975581
$497$	18.9149	−	32.7616i	0.848451	−	1.46956i
$498$	−0.151327	+	0.440054i	−0.00678113	+	0.0197193i
$499$	1.05749	+	1.83163i	0.0473398	+	0.0819949i	0.888724	−	0.458442i	$-0.151592\pi$
$499$	1.05749	+	1.83163i	0.0473398	+	0.0819949i	−0.841385	+	0.540437i	$0.818259\pi$
$500$	6.91714	+	11.9808i	0.309344	+	0.535799i
$501$	−9.08306	+	26.4132i	−0.405801	+	1.18005i
$502$	1.24385	−	2.15441i	0.0555157	−	0.0961560i
$503$	2.80951			0.125270			0.0626349	−	0.998037i	$-0.480050\pi$
$503$	2.80951			0.125270			0.0626349	+	0.998037i	$0.480050\pi$
$504$	10.6257	+	8.28808i	0.473304	+	0.369180i
$505$	44.8719			1.99677
$506$	−0.132559	+	0.229599i	−0.00589296	+	0.0102069i
$507$	1.70010	−	0.331167i	0.0755039	−	0.0147076i
$508$	13.5431	+	23.4573i	0.600877	+	1.04075i
$509$	8.57868	+	14.8587i	0.380243	+	0.658601i	0.991097	−	0.133143i	$-0.0425069\pi$
$509$	8.57868	+	14.8587i	0.380243	+	0.658601i	−0.610853	+	0.791744i	$0.709174\pi$
$510$	0.353008	+	0.405763i	0.0156314	+	0.0179675i
$511$	−20.2919	+	35.1466i	−0.897662	+	1.55480i
$512$	−17.9961			−0.795321
$513$	−3.76208	+	2.44950i	−0.166100	+	0.108148i
$514$	−1.09932			−0.0484890
$515$	10.6503	−	18.4468i	0.469308	−	0.812865i
$516$	−14.7955	−	17.0067i	−0.651337	−	0.748677i
$517$	−0.0135984	−	0.0235532i	−0.000598059	−	0.00103587i
$518$	1.39677	+	2.41928i	0.0613706	+	0.106297i
$519$	20.2676	−	3.94799i	0.889650	−	0.173297i
$520$	1.76335	−	3.05421i	0.0773279	−	0.133936i
$521$	−38.3213			−1.67889			−0.839444	−	0.543447i	$-0.817119\pi$
$521$	−38.3213			−1.67889			−0.839444	+	0.543447i	$0.817119\pi$
$522$	1.79513	−	0.726941i	0.0785708	−	0.0318173i
$523$	2.55236			0.111607			0.0558034	−	0.998442i	$-0.482228\pi$
$523$	2.55236			0.111607			0.0558034	+	0.998442i	$0.482228\pi$
$524$	5.66019	−	9.80374i	0.247267	−	0.428279i
$525$	17.5906	−	51.1529i	0.767718	−	2.23250i
$526$	−2.56789	−	4.44772i	−0.111965	−	0.193930i
$527$	1.04377	+	1.80787i	0.0454674	+	0.0787518i
$528$	−0.256823	+	0.746833i	−0.0111768	+	0.0325017i
$529$	−21.4475	+	37.1482i	−0.932502	+	1.61514i
$530$	3.60501			0.156592
$531$	−38.2089	+	15.4727i	−1.65813	+	0.671460i
$532$	−7.38834			−0.320325
$533$	2.36645	−	4.09881i	0.102502	−	0.177539i
$534$	4.78366	−	0.931822i	0.207009	−	0.0403239i
$535$	27.7255	+	48.0220i	1.19868	+	2.07617i
$536$	−2.03948	−	3.53249i	−0.0880923	−	0.152580i
$537$	4.35075	+	5.00095i	0.187749	+	0.215807i
$538$	0.749840	−	1.29876i	0.0323279	−	0.0559935i
$539$	1.58955			0.0684667
$540$	−1.86742	−	34.8377i	−0.0803609	−	1.49918i
$541$	36.7134			1.57843			0.789216	−	0.614115i	$-0.210487\pi$
$541$	36.7134			1.57843			0.789216	+	0.614115i	$0.210487\pi$
$542$	−2.33884	+	4.05098i	−0.100462	+	0.174005i
$543$	−12.8925	−	14.8193i	−0.553271	−	0.635955i
$544$	0.512836	+	0.888257i	0.0219876	+	0.0380837i
$545$	6.47970	+	11.2232i	0.277560	+	0.480748i
$546$	−1.94153	+	0.378196i	−0.0830899	+	0.0161853i
$547$	3.05186	−	5.28597i	0.130488	−	0.226012i	−0.793377	−	0.608731i	$-0.791679\pi$
$547$	3.05186	−	5.28597i	0.130488	−	0.226012i	0.923865	+	0.382719i	$0.125012\pi$
$548$	32.7855			1.40053
$549$	6.44981	+	5.03090i	0.275271	+	0.214713i
$550$	−0.230593			−0.00983251
$551$	−1.08016	+	1.87088i	−0.0460162	+	0.0797023i
$552$	4.64315	−	13.5021i	0.197626	−	0.574689i
$553$	0.955840	+	1.65556i	0.0406464	+	0.0704017i
$554$	1.44834	+	2.50859i	0.0615339	+	0.106580i
$555$	4.78484	−	13.9141i	0.203105	−	0.590622i
$556$	10.3744	−	17.9690i	0.439972	−	0.762054i
$557$	13.9705			0.591948			0.295974	−	0.955196i	$-0.404356\pi$
$557$	13.9705			0.591948			0.295974	+	0.955196i	$0.404356\pi$
$558$	−0.646095	+	4.62387i	−0.0273514	+	0.195744i
$559$	6.73162			0.284717
$560$	27.6850	−	47.9518i	1.16990	−	2.02633i
$561$	0.0744798	−	0.0145081i	0.00314454	−	0.000612533i
$562$	−1.16620	−	2.01992i	−0.0491933	−	0.0852053i
$563$	7.16514	+	12.4104i	0.301975	+	0.523035i	0.976583	−	0.215140i	$-0.0690209\pi$
$563$	7.16514	+	12.4104i	0.301975	+	0.523035i	−0.674609	+	0.738176i	$0.735688\pi$
$564$	0.472543	+	0.543163i	0.0198977	+	0.0228713i
$565$	27.2796	−	47.2497i	1.14766	−	1.98781i
$566$	4.80772			0.202083
$567$	−28.5928	+	27.6997i	−1.20078	+	1.16328i
$568$	8.68507			0.364417
$569$	8.61432	−	14.9204i	0.361131	−	0.625497i	−0.627016	−	0.779006i	$-0.715724\pi$
$569$	8.61432	−	14.9204i	0.361131	−	0.625497i	0.988147	+	0.153509i	$0.0490574\pi$
$570$	−0.880641	−	1.01225i	−0.0368860	−	0.0423984i
$571$	2.40564	+	4.16669i	0.100673	+	0.174371i	0.911962	−	0.410275i	$-0.134567\pi$
$571$	2.40564	+	4.16669i	0.100673	+	0.174371i	−0.811289	+	0.584645i	$0.801234\pi$
$572$	−0.122283	−	0.211801i	−0.00511293	−	0.00885585i
$573$	10.8656	−	2.11654i	0.453917	−	0.0884198i
$574$	−2.70251	+	4.68089i	−0.112801	+	0.195377i
$575$	−57.3139			−2.39015
$576$	2.67543	−	19.1471i	0.111476	−	0.797794i
$577$	−34.1265			−1.42071			−0.710353	−	0.703845i	$-0.751465\pi$
$577$	−34.1265			−1.42071			−0.710353	+	0.703845i	$0.751465\pi$
$578$	−2.17905	+	3.77423i	−0.0906367	+	0.156987i
$579$	−6.92309	+	20.1321i	−0.287714	+	0.836661i
$580$	−8.39433	−	14.5394i	−0.348556	−	0.603716i
$581$	−2.30149	−	3.98630i	−0.0954819	−	0.165379i
$582$	0.0260115	−	0.0756404i	0.00107821	−	0.00313540i
$583$	0.254308	−	0.440474i	0.0105324	−	0.0182426i
$584$	−9.31734			−0.385554
$585$	8.21495	+	6.40771i	0.339646	+	0.264926i
$586$	0.908359			0.0375240
$587$	5.05262	−	8.75140i	0.208544	−	0.361209i	−0.742712	−	0.669611i	$-0.766461\pi$
$587$	5.05262	−	8.75140i	0.208544	−	0.361209i	0.951256	+	0.308402i	$0.0997942\pi$
$588$	−41.3017	+	8.04526i	−1.70325	+	0.331781i
$589$	−2.60388	−	4.51005i	−0.107291	−	0.185833i
$590$	−6.16018	−	10.6697i	−0.253611	−	0.439266i
$591$	6.84225	+	7.86479i	0.281453	+	0.323514i
$592$	4.40858	−	7.63589i	0.181192	−	0.313833i
$593$	−38.0081			−1.56081			−0.780403	−	0.625277i	$-0.784986\pi$
$593$	−38.0081			−1.56081			−0.780403	+	0.625277i	$0.784986\pi$
$594$	0.151300	+	0.0768641i	0.00620791	+	0.00315377i
$595$	−5.31992			−0.218096
$596$	5.77685	−	10.0058i	0.236629	−	0.409853i
$597$	12.5867	+	14.4678i	0.515141	+	0.592126i
$598$	1.04790	+	1.81502i	0.0428519	+	0.0742216i
$599$	14.6376	+	25.3531i	0.598078	+	1.03590i	0.993105	+	0.117231i	$0.0374019\pi$
$599$	14.6376	+	25.3531i	0.598078	+	1.03590i	−0.395027	+	0.918670i	$0.629265\pi$
$600$	12.1897	−	2.37446i	0.497642	−	0.0969370i
$601$	22.8635	−	39.6007i	0.932621	−	1.61535i	0.153798	−	0.988102i	$-0.450849\pi$
$601$	22.8635	−	39.6007i	0.932621	−	1.61535i	0.778823	−	0.627244i	$-0.215817\pi$
$602$	−7.68760			−0.313323
$603$	11.1689	−	4.52288i	0.454835	−	0.184186i
$604$	−37.1032			−1.50971
$605$	19.0727	−	33.0349i	0.775416	−	1.34306i
$606$	1.87896	−	5.46394i	0.0763275	−	0.221958i
$607$	−19.4032	−	33.6074i	−0.787552	−	1.36408i	−0.927462	−	0.373916i	$-0.878015\pi$
$607$	−19.4032	−	33.6074i	−0.787552	−	1.36408i	0.139910	−	0.990164i	$-0.455319\pi$
$608$	−1.27936	−	2.21592i	−0.0518849	−	0.0898674i
$609$	−6.22979	+	18.1160i	−0.252444	+	0.734097i
$610$	−1.22236	+	2.11719i	−0.0494920	+	0.0857227i
$611$	−0.214996			−0.00869781
$612$	−1.86180	+	0.753937i	−0.0752587	+	0.0304761i
$613$	−36.9472			−1.49228			−0.746142	−	0.665787i	$-0.768096\pi$
$613$	−36.9472			−1.49228			−0.746142	+	0.665787i	$0.768096\pi$
$614$	2.04405	−	3.54039i	0.0824910	−	0.142879i
$615$	27.9436	−	5.44322i	1.12680	−	0.219492i
$616$	0.284113	+	0.492098i	0.0114472	+	0.0198272i
$617$	−3.13825	−	5.43561i	−0.126341	−	0.218830i	0.795915	−	0.605408i	$-0.206990\pi$
$617$	−3.13825	−	5.43561i	−0.126341	−	0.218830i	−0.922256	+	0.386579i	$0.873657\pi$
$618$	−1.80026	−	2.06930i	−0.0724171	−	0.0832395i
$619$	−7.04204	+	12.1972i	−0.283043	+	0.490246i	−0.972133	−	0.234431i	$-0.924677\pi$
$619$	−7.04204	+	12.1972i	−0.283043	+	0.490246i	0.689089	+	0.724676i	$0.258011\pi$
$620$	40.4716			1.62538
$621$	37.6056	+	19.1046i	1.50906	+	0.766640i
$622$	4.15399			0.166560
$623$	−24.1035	+	41.7485i	−0.965686	+	1.67262i
$624$	4.09776	+	4.71016i	0.164042	+	0.188557i
$625$	5.22607	+	9.05182i	0.209043	+	0.362073i
$626$	0.577347	+	0.999994i	0.0230754	+	0.0399678i
$627$	−0.185803	+	0.0361931i	−0.00742027	+	0.00144541i
$628$	18.3673	−	31.8131i	0.732935	−	1.26948i
$629$	−0.847150			−0.0337781
$630$	−9.38158	−	7.31769i	−0.373771	−	0.291544i
$631$	7.83048			0.311727			0.155863	−	0.987779i	$-0.450184\pi$
$631$	7.83048			0.311727			0.155863	+	0.987779i	$0.450184\pi$
$632$	−0.219444	+	0.380088i	−0.00872901	+	0.0151191i
$633$	−5.67515	+	16.5031i	−0.225567	+	0.655941i
$634$	1.67325	+	2.89816i	0.0664534	+	0.115101i
$635$	−24.3271	−	42.1358i	−0.965392	−	1.67211i
$636$	−4.37835	+	12.7321i	−0.173613	+	0.504861i
$637$	6.28282	−	10.8822i	0.248935	−	0.431167i
$638$	0.0816653			0.00323316
$639$	−3.55059	+	25.4103i	−0.140459	+	1.00522i
$640$	26.3486			1.04152
$641$	15.7922	−	27.3529i	0.623754	−	1.08037i	−0.365026	−	0.930997i	$-0.618940\pi$
$641$	15.7922	−	27.3529i	0.623754	−	1.08037i	0.988780	−	0.149376i	$-0.0477266\pi$
$642$	7.00849	−	1.36520i	0.276603	−	0.0538803i
$643$	−15.7929	−	27.3540i	−0.622809	−	1.07874i	−0.988960	−	0.148182i	$-0.952658\pi$
$643$	−15.7929	−	27.3540i	−0.622809	−	1.07874i	0.366151	−	0.930556i	$-0.380675\pi$
$644$	34.7098	+	60.1192i	1.36776	+	2.36903i
$645$	26.5769	+	30.5487i	1.04646	+	1.20285i
$646$	−0.0386243	+	0.0668993i	−0.00151965	+	0.00263212i
$647$	−33.6109			−1.32138			−0.660691	−	0.750658i	$-0.729737\pi$
$647$	−33.6109			−1.32138			−0.660691	+	0.750658i	$0.729737\pi$
$648$	−8.78956	−	2.50525i	−0.345286	−	0.0984156i
$649$	−1.73823			−0.0682313
$650$	−0.911438	+	1.57866i	−0.0357495	+	0.0619200i
$651$	−30.3116	−	34.8415i	−1.18800	−	1.36555i
$652$	4.55098	+	7.88252i	0.178230	+	0.308703i
$653$	−11.3303	−	19.6246i	−0.443389	−	0.767972i	0.554550	−	0.832151i	$-0.312890\pi$
$653$	−11.3303	−	19.6246i	−0.443389	−	0.767972i	−0.997938	+	0.0641790i	$0.979557\pi$
$654$	1.63795	−	0.319061i	0.0640489	−	0.0124763i
$655$	−10.1673	+	17.6102i	−0.397268	+	0.688089i
$656$	17.0597			0.666071
$657$	3.80908	−	27.2602i	0.148606	−	1.06352i
$658$	0.245528			0.00957169
$659$	−7.75617	+	13.4341i	−0.302137	+	0.523317i	−0.976620	−	0.214973i	$-0.931033\pi$
$659$	−7.75617	+	13.4341i	−0.302137	+	0.523317i	0.674482	+	0.738291i	$0.264367\pi$
$660$	0.478388	−	1.39114i	0.0186212	−	0.0541499i
$661$	13.8979	+	24.0719i	0.540566	+	0.936287i	0.998872	+	0.0474928i	$0.0151231\pi$
$661$	13.8979	+	24.0719i	0.540566	+	0.936287i	−0.458306	+	0.888795i	$0.651544\pi$
$662$	1.82870	+	3.16741i	0.0710746	+	0.123105i
$663$	0.195064	−	0.567239i	0.00757566	−	0.0220297i
$664$	0.528381	−	0.915183i	0.0205052	−	0.0355160i
$665$	13.2715			0.514647
$666$	−1.49393	−	1.16528i	−0.0578887	−	0.0451535i
$667$	20.2979			0.785939
$668$	15.5887	−	27.0004i	0.603145	−	1.04468i
$669$	29.8695	−	5.81837i	1.15482	−	0.224951i
$670$	1.80070	+	3.11890i	0.0695670	+	0.120494i
$671$	0.172458	+	0.298706i	0.00665766	+	0.0115314i
$672$	−14.8930	−	17.1187i	−0.574509	−	0.660366i
$673$	−18.1337	+	31.4085i	−0.699004	+	1.21071i	0.269809	+	0.962914i	$0.413040\pi$
$673$	−18.1337	+	31.4085i	−0.699004	+	1.21071i	−0.968812	+	0.247796i	$0.920294\pi$
$674$	6.73202			0.259308
$675$	1.96374	+	36.6347i	0.0755844	+	1.41007i
$676$	−1.93334			−0.0743593
$677$	−2.57859	+	4.46625i	−0.0991033	+	0.171652i	−0.911314	−	0.411713i	$-0.864931\pi$
$677$	−2.57859	+	4.46625i	−0.0991033	+	0.171652i	0.812210	+	0.583365i	$0.198264\pi$
$678$	−4.61118	−	5.30030i	−0.177091	−	0.203557i
$679$	0.395601	+	0.685201i	0.0151818	+	0.0262956i
$680$	−0.610680	−	1.05773i	−0.0234185	−	0.0405621i
$681$	−39.4442	+	7.68345i	−1.51151	+	0.294431i
$682$	−0.0984332	+	0.170491i	−0.00376920	+	0.00652845i
$683$	−8.03083			−0.307291			−0.153646	−	0.988126i	$-0.549101\pi$
$683$	−8.03083			−0.307291			−0.153646	+	0.988126i	$0.549101\pi$
$684$	4.64459	−	1.88083i	0.177590	−	0.0719154i
$685$	−58.8917			−2.25014
$686$	−3.17802	+	5.50449i	−0.121337	+	0.210163i
$687$	5.15895	−	15.0020i	0.196826	−	0.572364i
$688$	12.1321	+	21.0134i	0.462531	+	0.801127i
$689$	−2.01035	−	3.48202i	−0.0765881	−	0.132655i
$690$	−4.09952	+	11.9213i	−0.156066	+	0.453835i
$691$	11.1712	−	19.3491i	0.424973	−	0.736075i	−0.571445	−	0.820640i	$-0.693617\pi$
$691$	11.1712	−	19.3491i	0.424973	−	0.736075i	0.996418	+	0.0845656i	$0.0269503\pi$
$692$	−23.0482			−0.876163
$693$	−1.55591	+	0.630066i	−0.0591040	+	0.0239342i
$694$	−6.46307			−0.245335
$695$	−18.6353	+	32.2773i	−0.706877	+	1.22435i
$696$	−4.31702	+	0.840925i	−0.163636	+	0.0318752i
$697$	−0.819546	−	1.41950i	−0.0310425	−	0.0537672i
$698$	1.54080	+	2.66874i	0.0583200	+	0.101013i
$699$	−22.9516	−	26.3816i	−0.868109	−	0.997844i
$700$	−30.1897	+	52.2902i	−1.14106	+	1.97638i
$701$	−17.7526			−0.670507			−0.335253	−	0.942128i	$-0.608822\pi$
$701$	−17.7526			−0.670507			−0.335253	+	0.942128i	$0.608822\pi$
$702$	1.12424	−	0.731999i	0.0424318	−	0.0276275i
$703$	2.11337			0.0797072
$704$	0.407604	−	0.705991i	0.0153622	−	0.0266080i
$705$	−0.848818	−	0.975670i	−0.0319683	−	0.0367459i
$706$	−1.91669	−	3.31981i	−0.0721357	−	0.124943i
$707$	28.5765	+	49.4960i	1.07473	+	1.86149i
$708$	45.1648	−	8.79777i	1.69740	−	0.330641i
$709$	−9.36197	+	16.2154i	−0.351596	+	0.608983i	−0.986529	−	0.163585i	$-0.947694\pi$
$709$	−9.36197	+	16.2154i	−0.351596	+	0.608983i	0.634933	+	0.772567i	$0.281028\pi$
$710$	−7.66820			−0.287782
$711$	−1.02233	−	0.797423i	−0.0383403	−	0.0299057i
$712$	−11.0675			−0.414771
$713$	−24.4656	+	42.3757i	−0.916244	+	1.58698i
$714$	−0.222766	+	0.647794i	−0.00833679	+	0.0242431i
$715$	0.219655	+	0.380453i	0.00821462	+	0.0142281i
$716$	−3.69948	−	6.40769i	−0.138256	−	0.239467i
$717$	−4.33571	+	12.6081i	−0.161920	+	0.470858i
$718$	4.52992	−	7.84606i	0.169055	−	0.292812i
$719$	25.9370			0.967287			0.483643	−	0.875265i	$-0.339313\pi$
$719$	25.9370			0.967287			0.483643	+	0.875265i	$0.339313\pi$
$720$	−5.19685	+	37.1920i	−0.193675	+	1.38606i
$721$	27.1304			1.01039
$722$	−2.35636	+	4.08134i	−0.0876947	+	0.151892i
$723$	5.28387	−	1.02926i	0.196509	−	0.0382786i
$724$	10.9626	+	18.9878i	0.407423	+	0.705678i
$725$	8.82731	+	15.2894i	0.327838	+	0.567832i
$726$	−3.22393	−	3.70574i	−0.119651	−	0.137533i
$727$	18.6904	−	32.3727i	0.693189	−	1.20064i	−0.277599	−	0.960697i	$-0.589539\pi$
$727$	18.6904	−	32.3727i	0.693189	−	1.20064i	0.970788	−	0.239941i	$-0.0771280\pi$
$728$	4.49193			0.166482
$729$	10.9230	−	24.6918i	0.404557	−	0.914513i
$730$	8.22644			0.304474
$731$	1.16564	−	2.01895i	0.0431129	−	0.0746737i
$732$	−5.99287	−	6.88848i	−0.221503	−	0.254606i
$733$	−15.5642	−	26.9579i	−0.574875	−	0.995713i	−0.996055	−	0.0887358i	$-0.971717\pi$
$733$	−15.5642	−	26.9579i	−0.574875	−	0.995713i	0.421180	−	0.906977i	$-0.361616\pi$
$734$	−1.76246	−	3.05268i	−0.0650537	−	0.112676i
$735$	74.1892	−	14.4515i	2.73651	−	0.533052i
$736$	−12.0207	+	20.8204i	−0.443088	+	0.767450i
$737$	0.508105			0.0187163
$738$	0.507299	−	3.63056i	0.0186739	−	0.133643i
$739$	23.1713			0.852369			0.426184	−	0.904636i	$-0.359858\pi$
$739$	23.1713			0.852369			0.426184	+	0.904636i	$0.359858\pi$
$740$	−8.21193	+	14.2235i	−0.301876	+	0.522865i
$741$	−0.486622	+	1.41508i	−0.0178765	+	0.0519843i
$742$	2.29584	+	3.97652i	0.0842830	+	0.145982i
$743$	−7.95031	−	13.7703i	−0.291669	−	0.505185i	0.682536	−	0.730852i	$-0.260877\pi$
$743$	−7.95031	−	13.7703i	−0.291669	−	0.505185i	−0.974204	+	0.225667i	$0.927544\pi$
$744$	3.44783	−	10.0262i	0.126404	−	0.367577i
$745$	−10.3768	+	17.9732i	−0.380177	+	0.658486i
$746$	4.59496			0.168233
$747$	2.46158	+	1.92005i	0.0900647	+	0.0702510i
$748$	−0.0846981			−0.00309687
$749$	−35.3138	+	61.1653i	−1.29034	+	2.23493i
$750$	−3.14083	+	0.611812i	−0.114687	+	0.0223402i
$751$	4.97369	+	8.61468i	0.181492	+	0.314354i	0.942389	−	0.334519i	$-0.108574\pi$
$751$	4.97369	+	8.61468i	0.181492	+	0.314354i	−0.760897	+	0.648873i	$0.775241\pi$
$752$	−0.387477	−	0.671129i	−0.0141298	−	0.0244736i
$753$	−10.9541	−	12.5911i	−0.399189	−	0.458846i
$754$	0.322789	−	0.559087i	0.0117553	−	0.0203608i
$755$	66.6476			2.42555
$756$	37.2385	−	24.2462i	1.35435	−	0.881824i
$757$	−43.8603			−1.59413			−0.797064	−	0.603894i	$-0.793615\pi$
$757$	−43.8603			−1.59413			−0.797064	+	0.603894i	$0.793615\pi$
$758$	2.82204	−	4.88791i	0.102501	−	0.177537i
$759$	1.16739	+	1.34185i	0.0423737	+	0.0487062i
$760$	1.52345	+	2.63870i	0.0552614	+	0.0957156i
$761$	−23.8404	−	41.2927i	−0.864213	−	1.49686i	−0.867827	−	0.496867i	$-0.834484\pi$
$761$	−23.8404	−	41.2927i	−0.864213	−	1.49686i	0.00361442	−	0.999993i	$-0.498849\pi$
$762$	−6.14944	+	1.19787i	−0.222771	+	0.0433941i
$763$	−8.25316	+	14.2949i	−0.298784	+	0.517510i
$764$	−12.3563			−0.447036
$765$	3.34430	−	1.35428i	0.120914	−	0.0489641i
$766$	2.19772			0.0794069
$767$	−6.87049	+	11.9000i	−0.248079	+	0.429685i
$768$	−6.15625	+	17.9022i	−0.222145	+	0.645989i
$769$	−7.85242	−	13.6008i	−0.283165	−	0.490457i	0.688997	−	0.724764i	$-0.258051\pi$
$769$	−7.85242	−	13.6008i	−0.283165	−	0.490457i	−0.972163	+	0.234307i	$0.924718\pi$
$770$	−0.250849	−	0.434482i	−0.00903996	−	0.0156577i
$771$	−2.39829	+	6.97414i	−0.0863723	+	0.251168i
$772$	11.8817	−	20.5797i	0.427631	−	0.740678i
$773$	−11.8142			−0.424929			−0.212464	−	0.977169i	$-0.568149\pi$
$773$	−11.8142			−0.424929			−0.212464	+	0.977169i	$0.568149\pi$
$774$	4.83271	−	1.95701i	0.173708	−	0.0703434i
$775$	−42.5591			−1.52877
$776$	−0.0908229	+	0.157310i	−0.00326035	+	0.00564710i
$777$	18.3952	−	3.58325i	0.659925	−	0.128549i
$778$	−1.62058	−	2.80692i	−0.0581005	−	0.100633i
$779$	2.04451	+	3.54119i	0.0732520	+	0.126876i
$780$	−7.63296	−	8.77367i	−0.273304	−	0.314148i
$781$	−0.540937	+	0.936930i	−0.0193562	+	0.0335260i
$782$	0.725816			0.0259551
$783$	−0.695466	−	12.9743i	−0.0248539	−	0.463664i
$784$	45.2929			1.61760
$785$	−32.9928	+	57.1451i	−1.17756	+	2.03960i
$786$	1.71861	+	1.97545i	0.0613009	+	0.0704621i
$787$	−7.21696	−	12.5001i	−0.257257	−	0.445582i	0.708249	−	0.705962i	$-0.249485\pi$
$787$	−7.21696	−	12.5001i	−0.257257	−	0.445582i	−0.965506	+	0.260381i	$0.916152\pi$
$788$	−5.81803	−	10.0771i	−0.207259	−	0.358983i
$789$	−33.8187	+	6.58764i	−1.20398	+	0.234526i
$790$	0.193751	−	0.335586i	0.00689335	−	0.0119396i
$791$	69.4918			2.47084
$792$	−0.303876	−	0.237026i	−0.0107978	−	0.00842234i
$793$	2.72662			0.0968250
$794$	0.772423	−	1.33788i	0.0274123	−	0.0474795i
$795$	7.86474	−	22.8704i	0.278933	−	0.811129i
$796$	−10.7026	−	18.5375i	−0.379344	−	0.657043i
$797$	16.5103	+	28.5967i	0.584826	+	1.01295i	0.994897	+	0.100895i	$0.0321706\pi$
$797$	16.5103	+	28.5967i	0.584826	+	1.01295i	−0.410071	+	0.912054i	$0.634496\pi$
$798$	0.555729	−	1.61604i	0.0196726	−	0.0572072i
$799$	−0.0372286	+	0.0644818i	−0.00131705	+	0.00228120i
$800$	−20.9106			−0.739300
$801$	4.52456	−	32.3806i	0.159867	−	1.14411i
$802$	−5.82341			−0.205632
$803$	0.580316	−	1.00514i	0.0204789	−	0.0354705i
$804$	−13.2022	+	2.57170i	−0.465607	+	0.0906968i
$805$	−62.3485	−	107.991i	−2.19749	−	3.80617i
$806$	0.778132	+	1.34776i	0.0274085	+	0.0474730i
$807$	−6.60354	−	7.59041i	−0.232455	−	0.267195i
$808$	−6.56067	+	11.3634i	−0.230803	+	0.399763i
$809$	33.4952			1.17763			0.588815	−	0.808268i	$-0.299595\pi$
$809$	33.4952			1.17763			0.588815	+	0.808268i	$0.299595\pi$
$810$	7.76046	+	2.21193i	0.272675	+	0.0777193i
$811$	4.18463			0.146942			0.0734710	−	0.997297i	$-0.476592\pi$
$811$	4.18463			0.146942			0.0734710	+	0.997297i	$0.476592\pi$
$812$	10.6918	−	18.5188i	0.375209	−	0.649881i
$813$	20.5972	+	23.6754i	0.722375	+	0.830331i
$814$	−0.0399454	−	0.0691874i	−0.00140008	−	0.00242502i
$815$	−8.17481	−	14.1592i	−0.286351	−	0.495975i
$816$	2.12224	−	0.413397i	0.0742933	−	0.0144718i
$817$	−2.90791	+	5.03665i	−0.101735	+	0.176210i
$818$	−0.704614			−0.0246363
$819$	−1.83637	+	13.1422i	−0.0641680	+	0.459227i
$820$	−31.7774			−1.10971
$821$	−19.0814	+	33.0499i	−0.665944	+	1.15345i	0.313084	+	0.949725i	$0.398638\pi$
$821$	−19.0814	+	33.0499i	−0.665944	+	1.15345i	−0.979028	+	0.203724i	$0.934696\pi$
$822$	−2.46602	+	7.17111i	−0.0860124	+	0.250121i
$823$	−22.2367	−	38.5150i	−0.775121	−	1.34255i	−0.934726	−	0.355368i	$-0.884355\pi$
$823$	−22.2367	−	38.5150i	−0.775121	−	1.34255i	0.159605	−	0.987181i	$-0.448978\pi$
$824$	3.11433	+	5.39418i	0.108493	+	0.187915i
$825$	−0.503064	+	1.46289i	−0.0175144	+	0.0509313i
$826$	7.84618	−	13.5900i	0.273004	−	0.472856i
$827$	−38.7632			−1.34793			−0.673964	−	0.738764i	$-0.735410\pi$
$827$	−38.7632			−1.34793			−0.673964	+	0.738764i	$0.735410\pi$
$828$	−37.1243	−	28.9572i	−1.29016	−	1.00633i
$829$	−8.74501			−0.303727			−0.151863	−	0.988402i	$-0.548527\pi$
$829$	−8.74501			−0.303727			−0.151863	+	0.988402i	$0.548527\pi$
$830$	−0.466517	+	0.808032i	−0.0161930	+	0.0280472i
$831$	19.0743	−	3.71554i	0.661681	−	0.128891i
$832$	−3.22218	−	5.58098i	−0.111709	−	0.193486i
$833$	−2.17586	−	3.76870i	−0.0753891	−	0.130578i
$834$	3.14999	+	3.62075i	0.109075	+	0.125376i
$835$	−28.0016	+	48.5002i	−0.969036	+	1.67842i
$836$	0.211295			0.00730778
$837$	27.9245	+	14.1863i	0.965212	+	0.490352i
$838$	8.38364			0.289608
$839$	17.5080	−	30.3247i	0.604442	−	1.04692i	−0.387697	−	0.921787i	$-0.626729\pi$
$839$	17.5080	−	30.3247i	0.604442	−	1.04692i	0.992139	−	0.125138i	$-0.0399372\pi$
$840$	17.7344	+	20.3847i	0.611895	+	0.703340i
$841$	11.3738	+	19.7000i	0.392199	+	0.679309i
$842$	1.72752	+	2.99215i	0.0595342	+	0.103116i
$843$	−15.3587	+	2.99176i	−0.528981	+	0.103042i
$844$	9.73992	−	16.8700i	0.335262	−	0.580691i
$845$	3.47282			0.119469
$846$	−0.154348	+	0.0625035i	−0.00530660	+	0.00214892i
$847$	48.5856			1.66942
$848$	7.24630	−	12.5510i	0.248839	−	0.431002i
$849$	10.4886	−	30.5004i	0.359967	−	1.04677i
$850$	0.315648	+	0.546719i	0.0108266	+	0.0187523i
$851$	−9.92843	−	17.1965i	−0.340342	−	0.589490i
$852$	9.31317	−	27.0824i	0.319064	−	0.927827i
$853$	15.2934	−	26.4889i	0.523635	−	0.906963i	−0.475986	−	0.879453i	$-0.657909\pi$
$853$	15.2934	−	26.4889i	0.523635	−	0.906963i	0.999622	−	0.0275101i	$-0.00875785\pi$
$854$	−3.11383			−0.106553
$855$	−8.34297	+	3.37849i	−0.285324	+	0.115542i
$856$	−16.2148			−0.554212
$857$	16.5262	−	28.6243i	0.564526	−	0.977787i	−0.432568	−	0.901601i	$-0.642392\pi$
$857$	16.5262	−	28.6243i	0.564526	−	0.977787i	0.997094	−	0.0761860i	$-0.0242743\pi$
$858$	0.0555247	−	0.0108158i	0.00189558	−	0.000369246i
$859$	2.95877	+	5.12474i	0.100952	+	0.174854i	0.912077	−	0.410019i	$-0.134478\pi$
$859$	2.95877	+	5.12474i	0.100952	+	0.174854i	−0.811125	+	0.584873i	$0.801144\pi$
$860$	−22.5986	−	39.1419i	−0.770604	−	1.33473i
$861$	23.8000	+	27.3568i	0.811101	+	0.932316i
$862$	−1.89146	+	3.27610i	−0.0644233	+	0.111584i
$863$	23.2448			0.791262			0.395631	−	0.918410i	$-0.370526\pi$
$863$	23.2448			0.791262			0.395631	+	0.918410i	$0.370526\pi$
$864$	13.7201	+	6.97016i	0.466768	+	0.237130i
$865$	41.4010			1.40768
$866$	0.855509	−	1.48178i	0.0290714	−	0.0503531i
$867$	19.1900	+	22.0579i	0.651728	+	0.749126i
$868$	25.7742	+	44.6422i	0.874834	+	1.51526i
$869$	−0.0273355	−	0.0473464i	−0.000927292	−	0.00160612i
$870$	3.81158	−	0.742467i	0.129225	−	0.0251720i
$871$	2.00833	−	3.47853i	0.0680496	−	0.117865i
$872$	−3.78956			−0.128331
$873$	−0.423119	−	0.330036i	−0.0143204	−	0.0111700i
$874$	−1.81068			−0.0612471
$875$	15.8258	−	27.4110i	0.535009	−	0.926662i
$876$	−9.99116	+	29.0539i	−0.337570	+	0.981642i
$877$	4.42022	+	7.65604i	0.149260	+	0.258526i	0.930954	−	0.365136i	$-0.118978\pi$
$877$	4.42022	+	7.65604i	0.149260	+	0.258526i	−0.781694	+	0.623662i	$0.785644\pi$
$878$	−4.12981	−	7.15303i	−0.139374	−	0.241403i
$879$	1.98168	−	5.76267i	0.0668406	−	0.194370i
$880$	−0.791746	+	1.37134i	−0.0266897	+	0.0462280i
$881$	9.48167			0.319445			0.159723	−	0.987162i	$-0.448940\pi$
$881$	9.48167			0.319445			0.159723	+	0.987162i	$0.448940\pi$
$882$	1.34686	−	9.63898i	0.0453511	−	0.324561i
$883$	−13.6316			−0.458739			−0.229369	−	0.973339i	$-0.573666\pi$
$883$	−13.6316			−0.458739			−0.229369	+	0.973339i	$0.573666\pi$
$884$	−0.334776	+	0.579850i	−0.0112598	+	0.0195025i
$885$	−81.1284	+	15.8032i	−2.72710	+	0.531220i
$886$	−2.72533	−	4.72042i	−0.0915594	−	0.158586i
$887$	25.0936	+	43.4634i	0.842560	+	1.45936i	0.887724	+	0.460377i	$0.152286\pi$
$887$	25.0936	+	43.4634i	0.842560	+	1.45936i	−0.0451636	+	0.998980i	$0.514381\pi$
$888$	2.82405	+	3.24609i	0.0947688	+	0.108932i
$889$	30.9853	−	53.6681i	1.03921	−	1.79997i
$890$	9.77167			0.327547
$891$	0.817707	−	0.792166i	0.0273942	−	0.0265386i
$892$	−33.9675			−1.13732
$893$	0.0928735	−	0.160862i	0.00310789	−	0.00538303i
$894$	1.75403	+	2.01617i	0.0586637	+	0.0674307i
$895$	6.64530	+	11.5100i	0.222128	+	0.384737i
$896$	16.7800	+	29.0638i	0.560581	+	0.970954i
$897$	13.8007	−	2.68827i	0.460791	−	0.0897587i
$898$	−1.01623	+	1.76015i	−0.0339119	+	0.0587371i
$899$	15.0725			0.502695
$900$	5.66703	−	40.5569i	0.188901	−	1.35190i
$901$	−1.39244			−0.0463890
$902$	0.0772876	−	0.133866i	0.00257339	−	0.00445725i
$903$	−16.7713	+	48.7705i	−0.558115	+	1.62298i
$904$	7.97705	+	13.8167i	0.265313	+	0.459535i
$905$	−19.6919	−	34.1074i	−0.654582	−	1.13377i
$906$	2.79079	−	8.11551i	0.0927177	−	0.269620i
$907$	−27.6176	+	47.8351i	−0.917028	+	1.58834i	−0.113124	+	0.993581i	$0.536086\pi$
$907$	−27.6176	+	47.8351i	−0.917028	+	1.58834i	−0.803905	+	0.594758i	$0.797248\pi$
$908$	44.8558			1.48859
$909$	−30.5644	−	23.8404i	−1.01376	−	0.790736i
$910$	−3.96600			−0.131472
$911$	−1.94875	+	3.37533i	−0.0645649	+	0.111830i	−0.896501	−	0.443042i	$-0.853899\pi$
$911$	−1.94875	+	3.37533i	−0.0645649	+	0.111830i	0.831936	+	0.554872i	$0.187233\pi$
$912$	−5.29431	+	1.03129i	−0.175312	+	0.0341496i
$913$	0.0658189	+	0.114002i	0.00217829	+	0.00377290i
$914$	−3.25422	−	5.63647i	−0.107640	−	0.186438i
$915$	10.7649	+	12.3736i	0.355875	+	0.409059i
$916$	−8.85399	+	15.3356i	−0.292544	+	0.506701i
$917$	−25.9000			−0.855293
$918$	−0.0248685	−	0.463937i	−0.000820784	−	0.0153122i
$919$	47.2360			1.55817			0.779087	−	0.626916i	$-0.215683\pi$
$919$	47.2360			1.55817			0.779087	+	0.626916i	$0.215683\pi$
$920$	14.3141	−	24.7928i	0.471922	−	0.817393i
$921$	−18.0011	−	20.6913i	−0.593156	−	0.681801i
$922$	1.45921	+	2.52742i	0.0480564	+	0.0832361i
$923$	4.27620	+	7.40659i	0.140753	+	0.243791i
$924$	1.83915	−	0.358254i	0.0605037	−	0.0117857i
$925$	8.63550	−	14.9571i	0.283934	−	0.491787i
$926$	−7.81756			−0.256901
$927$	−17.0552	+	6.90652i	−0.560166	+	0.226840i
$928$	7.40555			0.243099
$929$	−20.7302	+	35.9057i	−0.680136	+	1.17803i	0.294804	+	0.955558i	$0.404746\pi$
$929$	−20.7302	+	35.9057i	−0.680136	+	1.17803i	−0.974939	+	0.222472i	$0.928588\pi$
$930$	−3.04415	+	8.85228i	−0.0998216	+	0.290278i
$931$	5.42808	+	9.40171i	0.177898	+	0.308128i
$932$	19.5159	+	33.8026i	0.639266	+	1.10724i
$933$	9.06238	−	26.3531i	0.296689	−	0.862761i
$934$	−3.97846	+	6.89089i	−0.130179	+	0.225477i
$935$	0.152141			0.00497555
$936$	−2.82379	+	1.14350i	−0.0922986	+	0.0373764i
$937$	40.5189			1.32369			0.661847	−	0.749639i	$-0.269773\pi$
$937$	40.5189			1.32369			0.661847	+	0.749639i	$0.269773\pi$
$938$	−2.29354	+	3.97252i	−0.0748866	+	0.129707i
$939$	7.60356	−	1.48112i	0.248133	−	0.0483345i
$940$	0.721758	+	1.25012i	0.0235411	+	0.0407745i
$941$	−26.3131	−	45.5757i	−0.857783	−	1.48572i	−0.874039	−	0.485857i	$-0.838508\pi$
$941$	−26.3131	−	45.5757i	−0.857783	−	1.48572i	0.0162551	−	0.999868i	$-0.494826\pi$
$942$	5.57689	+	6.41033i	0.181705	+	0.208860i
$943$	19.2098	−	33.2724i	0.625558	−	1.08350i
$944$	−49.5293			−1.61204
$945$	−66.8907	+	43.5528i	−2.17595	+	1.41677i
$946$	0.219853			0.00714804
$947$	29.4464	−	51.0027i	0.956880	−	1.65737i	0.226875	−	0.973924i	$-0.427149\pi$
$947$	29.4464	−	51.0027i	0.956880	−	1.65737i	0.730006	−	0.683441i	$-0.239517\pi$
$948$	0.949902	+	1.09186i	0.0308514	+	0.0354620i
$949$	−4.58750	−	7.94578i	−0.148917	−	0.257931i
$950$	−0.787442	−	1.36389i	−0.0255480	−	0.0442504i
$951$	22.0365	−	4.29254i	0.714581	−	0.139195i
$952$	0.777819	−	1.34722i	0.0252093	−	0.0436637i
$953$	−48.3782			−1.56712			−0.783562	−	0.621313i	$-0.786600\pi$
$953$	−48.3782			−1.56712			−0.783562	+	0.621313i	$0.786600\pi$
$954$	−2.45554	−	1.91534i	−0.0795012	−	0.0620114i
$955$	22.1954			0.718225
$956$	7.44112	−	12.8884i	0.240663	−	0.416840i
$957$	0.178162	−	0.518088i	0.00575915	−	0.0167474i
$958$	−1.65131	−	2.86014i	−0.0533513	−	0.0924071i
$959$	−37.5050	−	64.9606i	−1.21110	−	2.09769i
$960$	12.6056	−	36.6566i	0.406843	−	1.18309i
$961$	−2.66723	+	4.61978i	−0.0860396	+	0.149025i
$962$	−0.631550			−0.0203620
$963$	6.62889	−	47.4406i	0.213613	−	1.52875i
$964$	−6.00879			−0.193530
$965$	−21.3428	+	36.9668i	−0.687048	+	1.19000i
$966$	−15.7605	+	3.07004i	−0.507087	+	0.0987769i
$967$	3.33999	+	5.78503i	0.107407	+	0.186034i	0.914719	−	0.404091i	$-0.132412\pi$
$967$	3.33999	+	5.78503i	0.107407	+	0.186034i	−0.807312	+	0.590125i	$0.799079\pi$
$968$	5.57720	+	9.65999i	0.179258	+	0.310484i
$969$	0.340149	+	0.390983i	0.0109272	+	0.0125602i
$970$	0.0801892	−	0.138892i	0.00257472	−	0.00445955i
$971$	−10.4893			−0.336618			−0.168309	−	0.985734i	$-0.553831\pi$
$971$	−10.4893			−0.336618			−0.168309	+	0.985734i	$0.553831\pi$
$972$	−17.2373	+	24.7218i	−0.552885	+	0.792951i
$973$	−47.4713			−1.52186
$974$	0.941599	−	1.63090i	0.0301708	−	0.0522573i
$975$	8.02667	+	9.22622i	0.257059	+	0.295476i
$976$	4.91405	+	8.51138i	0.157295	+	0.272443i
$977$	−14.5581	−	25.2153i	−0.465754	−	0.806709i	0.533482	−	0.845812i	$-0.320883\pi$
$977$	−14.5581	−	25.2153i	−0.465754	−	0.806709i	−0.999235	+	0.0391027i	$0.987550\pi$
$978$	−2.06644	+	0.402528i	−0.0660775	+	0.0128714i
$979$	0.689321	−	1.19394i	0.0220308	−	0.0381584i
$980$	−84.3676			−2.69503
$981$	1.54923	−	11.0873i	0.0494632	−	0.353990i
$982$	−1.24948			−0.0398726
$983$	−26.9267	+	46.6385i	−0.858829	+	1.48754i	0.0142175	+	0.999899i	$0.495474\pi$
$983$	−26.9267	+	46.6385i	−0.858829	+	1.48754i	−0.873047	+	0.487637i	$0.837859\pi$
$984$	−2.70716	+	7.87232i	−0.0863011	+	0.250960i
$985$	10.4508	+	18.1013i	0.332990	+	0.576755i
$986$	−0.111788	−	0.193622i	−0.00356005	−	0.00616619i
$987$	0.535647	−	1.55764i	0.0170498	−	0.0495803i
$988$	0.835161	−	1.44654i	0.0265700	−	0.0460206i
$989$	54.6445			1.73759
$990$	0.268298	+	0.209274i	0.00852707	+	0.00665117i
$991$	−16.0335			−0.509322			−0.254661	−	0.967030i	$-0.581964\pi$
$991$	−16.0335			−0.509322			−0.254661	+	0.967030i	$0.581964\pi$
$992$	−8.92609	+	15.4604i	−0.283404	+	0.490870i
$993$	24.0837	−	4.69133i	0.764273	−	0.148875i
$994$	−4.88347	−	8.45842i	−0.154894	−	0.268285i
$995$	19.2249	+	33.2984i	0.609469	+	1.05563i
$996$	−2.28719	−	2.62900i	−0.0724725	−	0.0833031i
$997$	17.0632	−	29.5544i	0.540397	−	0.935996i	−0.458484	−	0.888703i	$-0.651607\pi$
$997$	17.0632	−	29.5544i	0.540397	−	0.935996i	0.998881	−	0.0472930i	$-0.0150595\pi$
$998$	0.546048			0.0172848
$999$	−10.6517	+	6.93539i	−0.337006	+	0.219426i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.e.c.79.3	yes	12
3.2	odd	2		351.2.e.c.235.4		12
9.2	odd	6		1053.2.a.m.1.3		6
9.4	even	3	inner	117.2.e.c.40.3	✓	12
9.5	odd	6		351.2.e.c.118.4		12
9.7	even	3		1053.2.a.l.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.e.c.40.3	✓	12	9.4	even	3	inner
117.2.e.c.79.3	yes	12	1.1	even	1	trivial
351.2.e.c.118.4		12	9.5	odd	6
351.2.e.c.235.4		12	3.2	odd	2
1053.2.a.l.1.4		6	9.7	even	3
1053.2.a.m.1.3		6	9.2	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.129090 - 0.223591i) q^{2} +(-1.13685 - 1.30674i) q^{3} +(0.966671 + 1.67432i) q^{4} +(-1.73641 - 3.00755i) q^{5} +(-0.438932 + 0.0855008i) q^{6} +(2.21165 - 3.83070i) q^{7} +1.01551 q^{8} +(-0.415158 + 2.97114i) q^{9} -0.896615 q^{10} +(-0.0632497 + 0.109552i) q^{11} +(1.08895 - 3.16664i) q^{12} +(0.500000 + 0.866025i) q^{13} +(-0.571006 - 0.989012i) q^{14} +(-1.95606 + 5.68816i) q^{15} +(-1.80225 + 3.12159i) q^{16} +0.346319 q^{17} +(0.610726 + 0.476370i) q^{18} -0.863955 q^{19} +(3.35707 - 5.81462i) q^{20} +(-7.52005 + 1.46485i) q^{21} +(0.0163299 + 0.0282841i) q^{22} +(4.05879 + 7.03003i) q^{23} +(-1.15448 - 1.32702i) q^{24} +(-3.53023 + 6.11454i) q^{25} +0.258181 q^{26} +(4.35448 - 2.83522i) q^{27} +8.55177 q^{28} +(1.25024 - 2.16549i) q^{29} +(1.01931 + 1.17165i) q^{30} +(3.01390 + 5.22023i) q^{31} +(1.48082 + 2.56485i) q^{32} +(0.215061 - 0.0418924i) q^{33} +(0.0447064 - 0.0774338i) q^{34} -15.3613 q^{35} +(-5.37596 + 2.17700i) q^{36} -2.44616 q^{37} +(-0.111528 + 0.193173i) q^{38} +(0.563250 - 1.63791i) q^{39} +(-1.76335 - 3.05421i) q^{40} +(-2.36645 - 4.09881i) q^{41} +(-0.643238 + 1.87051i) q^{42} +(3.36581 - 5.82976i) q^{43} -0.244567 q^{44} +(9.65672 - 3.91050i) q^{45} +2.09580 q^{46} +(-0.107498 + 0.186192i) q^{47} +(6.12800 - 1.19369i) q^{48} +(-6.28282 - 10.8822i) q^{49} +(0.911438 + 1.57866i) q^{50} +(-0.393711 - 0.452550i) q^{51} +(-0.966671 + 1.67432i) q^{52} -4.02070 q^{53} +(-0.0718083 - 1.33962i) q^{54} +0.439310 q^{55} +(2.24596 - 3.89012i) q^{56} +(0.982185 + 1.12897i) q^{57} +(-0.322789 - 0.559087i) q^{58} +(6.87049 + 11.9000i) q^{59} +(-11.4147 + 2.22350i) q^{60} +(1.36331 - 2.36132i) q^{61} +1.55626 q^{62} +(10.4633 + 8.16147i) q^{63} -6.44436 q^{64} +(1.73641 - 3.00755i) q^{65} +(0.0183956 - 0.0534937i) q^{66} +(-2.00833 - 3.47853i) q^{67} +(0.334776 + 0.579850i) q^{68} +(4.57222 - 13.2959i) q^{69} +(-1.98300 + 3.43466i) q^{70} +8.55239 q^{71} +(-0.421598 + 3.01723i) q^{72} -9.17500 q^{73} +(-0.315775 + 0.546939i) q^{74} +(12.0035 - 2.33819i) q^{75} +(-0.835161 - 1.44654i) q^{76} +(0.279773 + 0.484581i) q^{77} +(-0.293512 - 0.337376i) q^{78} +(-0.216092 + 0.374282i) q^{79} +12.5178 q^{80} +(-8.65529 - 2.46698i) q^{81} -1.22194 q^{82} +(0.520310 - 0.901203i) q^{83} +(-9.72205 - 11.1750i) q^{84} +(-0.601351 - 1.04157i) q^{85} +(-0.868988 - 1.50513i) q^{86} +(-4.25107 + 0.828078i) q^{87} +(-0.0642309 + 0.111251i) q^{88} -10.8984 q^{89} +(0.372237 - 2.66396i) q^{90} +4.42331 q^{91} +(-7.84703 + 13.5915i) q^{92} +(3.39516 - 9.87301i) q^{93} +(0.0277539 + 0.0480712i) q^{94} +(1.50018 + 2.59839i) q^{95} +(1.66814 - 4.85090i) q^{96} +(-0.0894355 + 0.154907i) q^{97} -3.24421 q^{98} +(-0.299234 - 0.233405i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} - 2 q^{3} - 6 q^{4} + 3 q^{5} - 7 q^{6} - 12 q^{8} - 2 q^{9} - 12 q^{10} + 7 q^{11} + 7 q^{12} + 6 q^{13} + 13 q^{14} - 12 q^{15} - 6 q^{16} - 28 q^{17} + 26 q^{18} - 6 q^{19} + 17 q^{20}+ \cdots - 11 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 - 2 * q^3 - 6 * q^4 + 3 * q^5 - 7 * q^6 - 12 * q^8 - 2 * q^9 - 12 * q^10 + 7 * q^11 + 7 * q^12 + 6 * q^13 + 13 * q^14 - 12 * q^15 - 6 * q^16 - 28 * q^17 + 26 * q^18 - 6 * q^19 + 17 * q^20 - 18 * q^21 + 3 * q^22 + 17 * q^23 - 30 * q^24 - 3 * q^25 + 4 * q^26 + 13 * q^27 + 30 * q^28 + 14 * q^29 - 7 * q^30 - 6 * q^31 + 9 * q^32 + 19 * q^33 - 3 * q^34 - 26 * q^35 + 43 * q^36 - 18 * q^37 - 4 * q^38 - q^39 + 6 * q^40 - 4 * q^41 - 17 * q^42 + 3 * q^43 - 26 * q^44 + 18 * q^45 + 9 * q^47 - 3 * q^48 - 21 * q^50 - 4 * q^51 + 6 * q^52 - 56 * q^53 + 35 * q^54 + 30 * q^55 + 16 * q^56 - 30 * q^57 - 18 * q^58 + 17 * q^59 - 31 * q^60 + 6 * q^61 + 8 * q^62 - 60 * q^64 - 3 * q^65 - 19 * q^66 + 12 * q^67 + 22 * q^68 - 13 * q^69 - 9 * q^70 + 2 * q^71 - 18 * q^73 - 27 * q^74 + 18 * q^75 + 3 * q^76 + 15 * q^77 - 2 * q^78 + 6 * q^79 + 48 * q^80 - 2 * q^81 + 54 * q^82 + 28 * q^83 + 31 * q^84 - 27 * q^85 - 6 * q^86 + 23 * q^87 + 9 * q^88 + 18 * q^89 + 26 * q^90 + 44 * q^92 + 2 * q^93 + 24 * q^94 + 32 * q^95 - 57 * q^96 - 34 * q^98 - 11 * q^99

Introduction

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