LMFDB - Embedded newform 666.2.e.d.223.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(223,666)] 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("666.223"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
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} + 21x^{12} + 119x^{10} + 272x^{8} + 283x^{6} + 143x^{4} + 34x^{2} + 3 $ x^14 + 21x^12 + 119x^10 + 272x^8 + 283x^6 + 143x^4 + 34x^2 + 3
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			223.7
Root			$1.87343i$ of defining polynomial
Character	$\chi$	$=$	666.223
Dual form			666.2.e.d.445.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(1.72951 + 0.0937946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.962268 - 1.66670i) q^{5} +(0.945983 - 1.45090i) q^{6} +(1.29333 - 2.24011i) q^{7} -1.00000 q^{8} +(2.98241 + 0.324437i) q^{9} -1.92454 q^{10} +(-0.402694 + 0.697486i) q^{11} +(-0.783526 - 1.54470i) q^{12} +(-1.05799 - 1.83249i) q^{13} +(-1.29333 - 2.24011i) q^{14} +(-1.50792 - 2.97282i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.29698 q^{17} +(1.77217 - 2.42062i) q^{18} +0.553500 q^{19} +(-0.962268 + 1.66670i) q^{20} +(2.44693 - 3.75298i) q^{21} +(0.402694 + 0.697486i) q^{22} +(1.58699 + 2.74875i) q^{23} +(-1.72951 - 0.0937946i) q^{24} +(0.648079 - 1.12251i) q^{25} -2.11598 q^{26} +(5.12767 + 0.840851i) q^{27} -2.58665 q^{28} +(-0.936182 + 1.62151i) q^{29} +(-3.32850 - 0.180511i) q^{30} +(-1.31576 - 2.27896i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.761883 + 1.16854i) q^{33} +(-1.14849 + 1.98924i) q^{34} -4.97811 q^{35} +(-1.21023 - 2.74506i) q^{36} -1.00000 q^{37} +(0.276750 - 0.479345i) q^{38} +(-1.65793 - 3.26855i) q^{39} +(0.962268 + 1.66670i) q^{40} +(0.279742 + 0.484528i) q^{41} +(-2.02671 - 3.99560i) q^{42} +(2.42736 - 4.20431i) q^{43} +0.805387 q^{44} +(-2.32914 - 5.28296i) q^{45} +3.17399 q^{46} +(-1.08331 + 1.87634i) q^{47} +(-0.945983 + 1.45090i) q^{48} +(0.154608 + 0.267789i) q^{49} +(-0.648079 - 1.12251i) q^{50} +(-3.97264 - 0.215444i) q^{51} +(-1.05799 + 1.83249i) q^{52} +4.37849 q^{53} +(3.29203 - 4.02026i) q^{54} +1.55000 q^{55} +(-1.29333 + 2.24011i) q^{56} +(0.957283 + 0.0519153i) q^{57} +(0.936182 + 1.62151i) q^{58} +(5.87961 + 10.1838i) q^{59} +(-1.82058 + 2.79231i) q^{60} +(2.87631 - 4.98192i) q^{61} -2.63151 q^{62} +(4.58400 - 6.26131i) q^{63} +1.00000 q^{64} +(-2.03614 + 3.52670i) q^{65} +(0.631042 + 1.24408i) q^{66} +(3.97077 + 6.87757i) q^{67} +(1.14849 + 1.98924i) q^{68} +(2.48690 + 4.90285i) q^{69} +(-2.48906 + 4.31117i) q^{70} +3.33204 q^{71} +(-2.98241 - 0.324437i) q^{72} +2.44405 q^{73} +(-0.500000 + 0.866025i) q^{74} +(1.22614 - 1.88060i) q^{75} +(-0.276750 - 0.479345i) q^{76} +(1.04163 + 1.80416i) q^{77} +(-3.65961 - 0.198468i) q^{78} +(4.22347 - 7.31527i) q^{79} +1.92454 q^{80} +(8.78948 + 1.93521i) q^{81} +0.559485 q^{82} +(-6.97791 + 12.0861i) q^{83} +(-4.47364 - 0.242614i) q^{84} +(2.21031 + 3.82837i) q^{85} +(-2.42736 - 4.20431i) q^{86} +(-1.77122 + 2.71662i) q^{87} +(0.402694 - 0.697486i) q^{88} -0.682322 q^{89} +(-5.73975 - 0.624391i) q^{90} -5.47331 q^{91} +(1.58699 - 2.74875i) q^{92} +(-2.06186 - 4.06488i) q^{93} +(1.08331 + 1.87634i) q^{94} +(-0.532615 - 0.922517i) q^{95} +(0.783526 + 1.54470i) q^{96} +(-5.61514 + 9.72570i) q^{97} +0.309216 q^{98} +(-1.42729 + 1.94954i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 7 q^{2} - q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 14 q^{8} - q^{9} - 6 q^{10} - q^{11} - q^{12} + 9 q^{13} - 3 q^{14} - q^{15} - 7 q^{16} + 18 q^{17} + q^{18} - 26 q^{19} - 3 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) $ 14 * q + 7 * q^2 - q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 14 * q^8 - q^9 - 6 * q^10 - q^11 - q^12 + 9 * q^13 - 3 * q^14 - q^15 - 7 * q^16 + 18 * q^17 + q^18 - 26 * q^19 - 3 * q^20 - 8 * q^21 + q^22 - 4 * q^23 + q^24 + 2 * q^25 + 18 * q^26 + 29 * q^27 - 6 * q^28 - 3 * q^29 + 10 * q^30 + 19 * q^31 + 7 * q^32 - 17 * q^33 + 9 * q^34 - 6 * q^35 + 2 * q^36 - 14 * q^37 - 13 * q^38 - 18 * q^39 + 3 * q^40 - 24 * q^41 - 16 * q^42 + q^43 + 2 * q^44 + 23 * q^45 - 8 * q^46 - 12 * q^47 + 2 * q^48 + 8 * q^49 - 2 * q^50 - 30 * q^51 + 9 * q^52 + 8 * q^53 + q^54 - 50 * q^55 - 3 * q^56 + 14 * q^57 + 3 * q^58 + 5 * q^59 + 11 * q^60 + 39 * q^61 + 38 * q^62 + 49 * q^63 + 14 * q^64 - 8 * q^65 + 2 * q^66 + 15 * q^67 - 9 * q^68 - 62 * q^69 - 3 * q^70 - 6 * q^71 + q^72 - 14 * q^73 - 7 * q^74 + 13 * q^75 + 13 * q^76 - 5 * q^77 + 3 * q^78 + 18 * q^79 + 6 * q^80 + 35 * q^81 - 48 * q^82 - q^83 - 8 * q^84 + 3 * q^85 - q^86 - 28 * q^87 + q^88 + 26 * q^89 + 13 * q^90 - 46 * q^91 - 4 * q^92 + 13 * q^93 + 12 * q^94 - 20 * q^95 + q^96 + 7 * q^97 + 16 * q^98 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	1.72951	+	0.0937946i	0.998533	+	0.0541523i
$3$	1.72951	+	0.0937946i	0.998533	+	0.0541523i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.962268	−	1.66670i	−0.430339	−	0.745370i	0.566563	−	0.824018i	$-0.308273\pi$
$5$	−0.962268	−	1.66670i	−0.430339	−	0.745370i	−0.996902	+	0.0786486i	$0.974939\pi$
$6$	0.945983	−	1.45090i	0.386196	−	0.592328i
$7$	1.29333	−	2.24011i	0.488832	−	0.846682i	−0.511086	−	0.859530i	$-0.670756\pi$
$7$	1.29333	−	2.24011i	0.488832	−	0.846682i	0.999917	+	0.0128482i	$0.00408983\pi$
$8$	−1.00000			−0.353553
$9$	2.98241	+	0.324437i	0.994135	+	0.108146i
$10$	−1.92454			−0.608592
$11$	−0.402694	+	0.697486i	−0.121417	+	0.210300i	−0.920327	−	0.391151i	$-0.872077\pi$
$11$	−0.402694	+	0.697486i	−0.121417	+	0.210300i	0.798910	+	0.601451i	$0.205410\pi$
$12$	−0.783526	−	1.54470i	−0.226185	−	0.445915i
$13$	−1.05799	−	1.83249i	−0.293434	−	0.508242i	0.681186	−	0.732111i	$-0.261465\pi$
$13$	−1.05799	−	1.83249i	−0.293434	−	0.508242i	−0.974619	+	0.223869i	$0.928131\pi$
$14$	−1.29333	−	2.24011i	−0.345656	−	0.598694i
$15$	−1.50792	−	2.97282i	−0.389345	−	0.767580i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.29698			−0.557099			−0.278549	−	0.960422i	$-0.589854\pi$
$17$	−2.29698			−0.557099			−0.278549	+	0.960422i	$0.589854\pi$
$18$	1.77217	−	2.42062i	0.417705	−	0.570546i
$19$	0.553500			0.126982			0.0634908	−	0.997982i	$-0.479777\pi$
$19$	0.553500			0.126982			0.0634908	+	0.997982i	$0.479777\pi$
$20$	−0.962268	+	1.66670i	−0.215170	+	0.372685i
$21$	2.44693	−	3.75298i	0.533964	−	0.818968i
$22$	0.402694	+	0.697486i	0.0858546	+	0.148704i
$23$	1.58699	+	2.74875i	0.330911	+	0.573155i	0.982691	−	0.185254i	$-0.0593107\pi$
$23$	1.58699	+	2.74875i	0.330911	+	0.573155i	−0.651780	+	0.758408i	$0.725977\pi$
$24$	−1.72951	−	0.0937946i	−0.353035	−	0.0191457i
$25$	0.648079	−	1.12251i	0.129616	−	0.224501i
$26$	−2.11598			−0.414978
$27$	5.12767	+	0.840851i	0.986820	+	0.161822i
$28$	−2.58665			−0.488832
$29$	−0.936182	+	1.62151i	−0.173845	+	0.301108i	−0.939761	−	0.341833i	$-0.888952\pi$
$29$	−0.936182	+	1.62151i	−0.173845	+	0.301108i	0.765916	+	0.642940i	$0.222286\pi$
$30$	−3.32850	−	0.180511i	−0.607699	−	0.0329567i
$31$	−1.31576	−	2.27896i	−0.236317	−	0.409312i	0.723338	−	0.690494i	$-0.242607\pi$
$31$	−1.31576	−	2.27896i	−0.236317	−	0.409312i	−0.959655	+	0.281182i	$0.909274\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.761883	+	1.16854i	−0.132627	+	0.203416i
$34$	−1.14849	+	1.98924i	−0.196964	+	0.341152i
$35$	−4.97811			−0.841455
$36$	−1.21023	−	2.74506i	−0.201705	−	0.457510i
$37$	−1.00000			−0.164399
$37$	−1.00000			−0.164399
$38$	0.276750	−	0.479345i	0.0448948	−	0.0777600i
$39$	−1.65793	−	3.26855i	−0.265481	−	0.523387i
$40$	0.962268	+	1.66670i	0.152148	+	0.263528i
$41$	0.279742	+	0.484528i	0.0436884	+	0.0756705i	0.887043	−	0.461687i	$-0.152756\pi$
$41$	0.279742	+	0.484528i	0.0436884	+	0.0756705i	−0.843354	+	0.537358i	$0.819422\pi$
$42$	−2.02671	−	3.99560i	−0.312728	−	0.616534i
$43$	2.42736	−	4.20431i	0.370169	−	0.641152i	−0.619422	−	0.785058i	$-0.712633\pi$
$43$	2.42736	−	4.20431i	0.370169	−	0.641152i	0.989591	+	0.143906i	$0.0459664\pi$
$44$	0.805387			0.121417
$45$	−2.32914	−	5.28296i	−0.347207	−	0.787538i
$46$	3.17399			0.467979
$47$	−1.08331	+	1.87634i	−0.158016	+	0.273693i	−0.934153	−	0.356872i	$-0.883843\pi$
$47$	−1.08331	+	1.87634i	−0.158016	+	0.273693i	0.776137	+	0.630565i	$0.217177\pi$
$48$	−0.945983	+	1.45090i	−0.136541	+	0.209420i
$49$	0.154608	+	0.267789i	0.0220869	+	0.0382556i
$50$	−0.648079	−	1.12251i	−0.0916522	−	0.158746i
$51$	−3.97264	−	0.215444i	−0.556281	−	0.0301682i
$52$	−1.05799	+	1.83249i	−0.146717	+	0.254121i
$53$	4.37849			0.601432			0.300716	−	0.953714i	$-0.402774\pi$
$53$	4.37849			0.601432			0.300716	+	0.953714i	$0.402774\pi$
$54$	3.29203	−	4.02026i	0.447989	−	0.547089i
$55$	1.55000			0.209002
$56$	−1.29333	+	2.24011i	−0.172828	+	0.299347i
$57$	0.957283	+	0.0519153i	0.126795	+	0.00687635i
$58$	0.936182	+	1.62151i	0.122927	+	0.212915i
$59$	5.87961	+	10.1838i	0.765460	+	1.32582i	0.940003	+	0.341166i	$0.110822\pi$
$59$	5.87961	+	10.1838i	0.765460	+	1.32582i	−0.174543	+	0.984650i	$0.555845\pi$
$60$	−1.82058	+	2.79231i	−0.235036	+	0.360486i
$61$	2.87631	−	4.98192i	0.368274	−	0.637870i	−0.621021	−	0.783794i	$-0.713282\pi$
$61$	2.87631	−	4.98192i	0.368274	−	0.637870i	0.989296	+	0.145924i	$0.0466154\pi$
$62$	−2.63151			−0.334202
$63$	4.58400	−	6.26131i	0.577530	−	0.788851i
$64$	1.00000			0.125000
$65$	−2.03614	+	3.52670i	−0.252552	+	0.437433i
$66$	0.631042	+	1.24408i	0.0776759	+	0.153136i
$67$	3.97077	+	6.87757i	0.485106	+	0.840229i	0.999854	−	0.0171133i	$-0.00544759\pi$
$67$	3.97077	+	6.87757i	0.485106	+	0.840229i	−0.514747	+	0.857342i	$0.672114\pi$
$68$	1.14849	+	1.98924i	0.139275	+	0.241231i
$69$	2.48690	+	4.90285i	0.299388	+	0.590233i
$70$	−2.48906	+	4.31117i	−0.297499	+	0.515284i
$71$	3.33204			0.395441			0.197720	−	0.980258i	$-0.436646\pi$
$71$	3.33204			0.395441			0.197720	+	0.980258i	$0.436646\pi$
$72$	−2.98241	−	0.324437i	−0.351480	−	0.0382353i
$73$	2.44405			0.286055			0.143027	−	0.989719i	$-0.454316\pi$
$73$	2.44405			0.286055			0.143027	+	0.989719i	$0.454316\pi$
$74$	−0.500000	+	0.866025i	−0.0581238	+	0.100673i
$75$	1.22614	−	1.88060i	0.141583	−	0.217153i
$76$	−0.276750	−	0.479345i	−0.0317454	−	0.0549846i
$77$	1.04163	+	1.80416i	0.118705	+	0.205603i
$78$	−3.65961	−	0.198468i	−0.414369	−	0.0224720i
$79$	4.22347	−	7.31527i	0.475178	−	0.823032i	−0.524418	−	0.851461i	$-0.675717\pi$
$79$	4.22347	−	7.31527i	0.475178	−	0.823032i	0.999596	+	0.0284289i	$0.00905040\pi$
$80$	1.92454			0.215170
$81$	8.78948	+	1.93521i	0.976609	+	0.215023i
$82$	0.559485			0.0617847
$83$	−6.97791	+	12.0861i	−0.765925	+	1.32662i	0.173831	+	0.984776i	$0.444385\pi$
$83$	−6.97791	+	12.0861i	−0.765925	+	1.32662i	−0.939756	+	0.341846i	$0.888948\pi$
$84$	−4.47364	−	0.242614i	−0.488115	−	0.0264714i
$85$	2.21031	+	3.82837i	0.239742	+	0.415245i
$86$	−2.42736	−	4.20431i	−0.261749	−	0.453363i
$87$	−1.77122	+	2.71662i	−0.189895	+	0.291252i
$88$	0.402694	−	0.697486i	0.0429273	−	0.0743522i
$89$	−0.682322			−0.0723260			−0.0361630	−	0.999346i	$-0.511514\pi$
$89$	−0.682322			−0.0723260			−0.0361630	+	0.999346i	$0.511514\pi$
$90$	−5.73975	−	0.624391i	−0.605023	−	0.0658166i
$91$	−5.47331			−0.573759
$92$	1.58699	−	2.74875i	0.165456	−	0.286577i
$93$	−2.06186	−	4.06488i	−0.213805	−	0.421509i
$94$	1.08331	+	1.87634i	0.111735	+	0.193530i
$95$	−0.532615	−	0.922517i	−0.0546452	−	0.0946482i
$96$	0.783526	+	1.54470i	0.0799683	+	0.157655i
$97$	−5.61514	+	9.72570i	−0.570131	+	0.987495i	0.426421	+	0.904525i	$0.359774\pi$
$97$	−5.61514	+	9.72570i	−0.570131	+	0.987495i	−0.996552	+	0.0829706i	$0.973559\pi$
$98$	0.309216			0.0312355
$99$	−1.42729	+	1.94954i	−0.143448	+	0.195936i
$100$	−1.29616			−0.129616
$101$	−1.04540	+	1.81069i	−0.104022	+	0.180171i	−0.913338	−	0.407202i	$-0.866504\pi$
$101$	−1.04540	+	1.81069i	−0.104022	+	0.180171i	0.809316	+	0.587373i	$0.199838\pi$
$102$	−2.17290	+	3.33269i	−0.215149	+	0.329985i
$103$	2.77854	+	4.81258i	0.273778	+	0.474197i	0.969826	−	0.243798i	$-0.0783933\pi$
$103$	2.77854	+	4.81258i	0.273778	+	0.474197i	−0.696048	+	0.717995i	$0.745060\pi$
$104$	1.05799	+	1.83249i	0.103745	+	0.179691i
$105$	−8.60969	−	0.466920i	−0.840220	−	0.0455667i
$106$	2.18924	−	3.79188i	0.212638	−	0.368300i
$107$	−2.07573			−0.200668			−0.100334	−	0.994954i	$-0.531991\pi$
$107$	−2.07573			−0.200668			−0.100334	+	0.994954i	$0.531991\pi$
$108$	−1.83564	−	4.86112i	−0.176634	−	0.467761i
$109$	−8.12962			−0.778676			−0.389338	−	0.921095i	$-0.627296\pi$
$109$	−8.12962			−0.778676			−0.389338	+	0.921095i	$0.627296\pi$
$110$	0.774999	−	1.34234i	0.0738932	−	0.127987i
$111$	−1.72951	−	0.0937946i	−0.164158	−	0.00890259i
$112$	1.29333	+	2.24011i	0.122208	+	0.211670i
$113$	−2.79503	−	4.84113i	−0.262934	−	0.455416i	0.704086	−	0.710115i	$-0.251357\pi$
$113$	−2.79503	−	4.84113i	−0.262934	−	0.455416i	−0.967020	+	0.254699i	$0.918024\pi$
$114$	0.523601	−	0.803074i	0.0490398	−	0.0752147i
$115$	3.05423	−	5.29008i	0.284808	−	0.493302i
$116$	1.87236			0.173845
$117$	−2.56083	−	5.80849i	−0.236749	−	0.536995i
$118$	11.7592			1.08252
$119$	−2.97074	+	5.14548i	−0.272328	+	0.471685i
$120$	1.50792	+	2.97282i	0.137654	+	0.271381i
$121$	5.17568	+	8.96453i	0.470516	+	0.814958i
$122$	−2.87631	−	4.98192i	−0.260409	−	0.451042i
$123$	0.438371	+	0.864234i	0.0395266	+	0.0779253i
$124$	−1.31576	+	2.27896i	−0.118158	+	0.204656i
$125$	−12.1172			−1.08379
$126$	−3.13045	−	7.10052i	−0.278883	−	0.632564i
$127$	0.0154504			0.00137100			0.000685500	−	1.00000i	$-0.499782\pi$
$127$	0.0154504			0.00137100			0.000685500		1.00000i	$0.499782\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	4.59249	−	7.04373i	0.404346	−	0.620166i
$130$	2.03614	+	3.52670i	0.178581	+	0.309312i
$131$	−0.939116	−	1.62660i	−0.0820509	−	0.142116i	0.822080	−	0.569372i	$-0.192814\pi$
$131$	−0.939116	−	1.62660i	−0.0820509	−	0.142116i	−0.904131	+	0.427256i	$0.859480\pi$
$132$	1.39292	+	0.0755410i	0.121239	+	0.00657500i
$133$	0.715856	−	1.23990i	0.0620726	−	0.107513i
$134$	7.94153			0.686044
$135$	−3.53275	−	9.35539i	−0.304051	−	0.805184i
$136$	2.29698			0.196964
$137$	−5.74407	+	9.94901i	−0.490749	+	0.850002i	−0.999943	−	0.0106497i	$-0.996610\pi$
$137$	−5.74407	+	9.94901i	−0.490749	+	0.850002i	0.509195	+	0.860651i	$0.329943\pi$
$138$	5.48944	+	0.297703i	0.467292	+	0.0253421i
$139$	7.05490	+	12.2194i	0.598388	+	1.03644i	0.993059	+	0.117617i	$0.0375254\pi$
$139$	7.05490	+	12.2194i	0.598388	+	1.03644i	−0.394671	+	0.918823i	$0.629141\pi$
$140$	2.48906	+	4.31117i	0.210364	+	0.364361i
$141$	−2.04958	+	3.14354i	−0.172606	+	0.264734i
$142$	1.66602	−	2.88563i	0.139809	−	0.242157i
$143$	1.70418			0.142511
$144$	−1.77217	+	2.42062i	−0.147681	+	0.201718i
$145$	3.60343			0.299249
$146$	1.22203	−	2.11661i	0.101136	−	0.175172i
$147$	0.242279	+	0.477645i	0.0199828	+	0.0393955i
$148$	0.500000	+	0.866025i	0.0410997	+	0.0711868i
$149$	−0.0771313	−	0.133595i	−0.00631884	−	0.0109446i	0.862849	−	0.505462i	$-0.168678\pi$
$149$	−0.0771313	−	0.133595i	−0.00631884	−	0.0109446i	−0.869168	+	0.494518i	$0.835345\pi$
$150$	−1.01557	−	2.00217i	−0.0829213	−	0.163477i
$151$	10.0141	−	17.3449i	0.814936	−	1.41151i	−0.0944387	−	0.995531i	$-0.530106\pi$
$151$	10.0141	−	17.3449i	0.814936	−	1.41151i	0.909374	−	0.415979i	$-0.136561\pi$
$152$	−0.553500			−0.0448948
$153$	−6.85051	−	0.745225i	−0.553831	−	0.0602478i
$154$	2.08326			0.167874
$155$	−2.53222	+	4.38593i	−0.203393	+	0.352287i
$156$	−2.00168	+	3.07008i	−0.160263	+	0.245803i
$157$	2.50032	+	4.33069i	0.199548	+	0.345627i	0.948382	−	0.317131i	$-0.102719\pi$
$157$	2.50032	+	4.33069i	0.199548	+	0.345627i	−0.748834	+	0.662757i	$0.769386\pi$
$158$	−4.22347	−	7.31527i	−0.336001	−	0.581972i
$159$	7.57264	+	0.410679i	0.600549	+	0.0325689i
$160$	0.962268	−	1.66670i	0.0760740	−	0.131764i
$161$	8.21001			0.647039
$162$	6.07068	−	6.64431i	0.476958	−	0.522026i
$163$	8.30211			0.650272			0.325136	−	0.945667i	$-0.394590\pi$
$163$	8.30211			0.650272			0.325136	+	0.945667i	$0.394590\pi$
$164$	0.279742	−	0.484528i	0.0218442	−	0.0378353i
$165$	2.68074	+	0.145381i	0.208695	+	0.0113179i
$166$	6.97791	+	12.0861i	0.541591	+	0.938063i
$167$	−1.14420	−	1.98181i	−0.0885408	−	0.153357i	0.818354	−	0.574715i	$-0.194887\pi$
$167$	−1.14420	−	1.98181i	−0.0885408	−	0.153357i	−0.906895	+	0.421358i	$0.861554\pi$
$168$	−2.44693	+	3.75298i	−0.188785	+	0.289549i
$169$	4.26131	−	7.38081i	0.327793	−	0.567754i
$170$	4.42062			0.339046
$171$	1.65076	+	0.179576i	0.126237	+	0.0137325i
$172$	−4.85472			−0.370169
$173$	−5.06924	+	8.78018i	−0.385407	+	0.667544i	−0.991826	−	0.127601i	$-0.959272\pi$
$173$	−5.06924	+	8.78018i	−0.385407	+	0.667544i	0.606419	+	0.795146i	$0.292606\pi$
$174$	1.46705	+	2.89223i	0.111216	+	0.219260i
$175$	−1.67636	−	2.90354i	−0.126721	−	0.219487i
$176$	−0.402694	−	0.697486i	−0.0303542	−	0.0525750i
$177$	9.21366	+	18.1644i	0.692541	+	1.36532i
$178$	−0.341161	+	0.590908i	−0.0255711	+	0.0442904i
$179$	−22.0371			−1.64713			−0.823566	−	0.567221i	$-0.808019\pi$
$179$	−22.0371			−1.64713			−0.823566	+	0.567221i	$0.808019\pi$
$180$	−3.41061	+	4.65857i	−0.254212	+	0.347229i
$181$	0.000728061	0		5.41164e−5	0		2.70582e−5	−	1.00000i	$-0.499991\pi$
$181$	0.000728061	0		5.41164e−5	0		2.70582e−5		1.00000i	$0.499991\pi$
$182$	−2.73666	+	4.74003i	−0.202855	+	0.351354i
$183$	5.44189	−	8.34650i	0.402276	−	0.616991i
$184$	−1.58699	−	2.74875i	−0.116995	−	0.202641i
$185$	0.962268	+	1.66670i	0.0707474	+	0.122538i
$186$	−4.55122	−	0.246821i	−0.333712	−	0.0180978i
$187$	0.924978	−	1.60211i	0.0676411	−	0.117158i
$188$	2.16661			0.158016
$189$	8.51535	−	10.3990i	0.619401	−	0.756419i
$190$	−1.06523			−0.0772799
$191$	6.78664	−	11.7548i	0.491064	−	0.850548i	−0.508883	−	0.860836i	$-0.669941\pi$
$191$	6.78664	−	11.7548i	0.491064	−	0.850548i	0.999947	+	0.0102878i	$0.00327475\pi$
$192$	1.72951	+	0.0937946i	0.124817	+	0.00676904i
$193$	13.3058	+	23.0464i	0.957776	+	1.65892i	0.727885	+	0.685700i	$0.240504\pi$
$193$	13.3058	+	23.0464i	0.957776	+	1.65892i	0.229891	+	0.973216i	$0.426163\pi$
$194$	5.61514	+	9.72570i	0.403143	+	0.698265i
$195$	−3.85231	+	5.90848i	−0.275870	+	0.423115i
$196$	0.154608	−	0.267789i	0.0110434	−	0.0191278i
$197$	−3.36092			−0.239455			−0.119728	−	0.992807i	$-0.538202\pi$
$197$	−3.36092			−0.239455			−0.119728	+	0.992807i	$0.538202\pi$
$198$	0.974705	+	2.21083i	0.0692693	+	0.157117i
$199$	−14.9111			−1.05702			−0.528510	−	0.848927i	$-0.677249\pi$
$199$	−14.9111			−1.05702			−0.528510	+	0.848927i	$0.677249\pi$
$200$	−0.648079	+	1.12251i	−0.0458261	+	0.0793732i
$201$	6.22240	+	12.2673i	0.438894	+	0.865265i
$202$	1.04540	+	1.81069i	0.0735543	+	0.127400i
$203$	2.42158	+	4.19430i	0.169962	+	0.294382i
$204$	1.79974	+	3.54813i	0.126007	+	0.248419i
$205$	0.538374	−	0.932492i	0.0376017	−	0.0651280i
$206$	5.55709			0.387181
$207$	3.84126	+	8.71278i	0.266986	+	0.605580i
$208$	2.11598			0.146717
$209$	−0.222891	+	0.386058i	−0.0154177	+	0.0267042i
$210$	−4.70921	+	7.22275i	−0.324966	+	0.498417i
$211$	−11.1903	−	19.3821i	−0.770371	−	1.33432i	−0.937360	−	0.348363i	$-0.886738\pi$
$211$	−11.1903	−	19.3821i	−0.770371	−	1.33432i	0.166989	−	0.985959i	$-0.446596\pi$
$212$	−2.18924	−	3.79188i	−0.150358	−	0.260428i
$213$	5.76280	+	0.312528i	0.394861	+	0.0214140i
$214$	−1.03786	+	1.79763i	−0.0709470	+	0.122884i
$215$	−9.34309			−0.637194
$216$	−5.12767	−	0.840851i	−0.348894	−	0.0572126i
$217$	−6.80681			−0.462076
$218$	−4.06481	+	7.04045i	−0.275304	+	0.476840i
$219$	4.22701	+	0.229239i	0.285635	+	0.0154905i
$220$	−0.774999	−	1.34234i	−0.0522504	−	0.0905004i
$221$	2.43018	+	4.20919i	0.163472	+	0.283141i
$222$	−0.945983	+	1.45090i	−0.0634902	+	0.0973781i
$223$	5.11873	−	8.86591i	0.342776	−	0.593705i	−0.642171	−	0.766561i	$-0.721966\pi$
$223$	5.11873	−	8.86591i	0.342776	−	0.593705i	0.984947	+	0.172856i	$0.0552995\pi$
$224$	2.58665			0.172828
$225$	2.29702	−	3.13751i	0.153135	−	0.209167i
$226$	−5.59006			−0.371845
$227$	−3.74392	+	6.48467i	−0.248493	+	0.430402i	−0.963108	−	0.269116i	$-0.913269\pi$
$227$	−3.74392	+	6.48467i	−0.248493	+	0.430402i	0.714615	+	0.699518i	$0.246602\pi$
$228$	−0.433682	−	0.854989i	−0.0287213	−	0.0566230i
$229$	11.6632	+	20.2013i	0.770727	+	1.33494i	0.937165	+	0.348887i	$0.113440\pi$
$229$	11.6632	+	20.2013i	0.770727	+	1.33494i	−0.166437	+	0.986052i	$0.553226\pi$
$230$	−3.05423	−	5.29008i	−0.201390	−	0.348817i
$231$	1.63229	+	3.21800i	0.107397	+	0.211729i
$232$	0.936182	−	1.62151i	0.0614634	−	0.106458i
$233$	17.3712			1.13802			0.569012	−	0.822329i	$-0.307326\pi$
$233$	17.3712			1.13802			0.569012	+	0.822329i	$0.307326\pi$
$234$	−6.31071	−	0.686503i	−0.412544	−	0.0448781i
$235$	4.16973			0.272003
$236$	5.87961	−	10.1838i	0.382730	−	0.662908i
$237$	7.99067	−	12.2557i	0.519050	−	0.796092i
$238$	2.97074	+	5.14548i	0.192565	+	0.333532i
$239$	−4.63463	−	8.02742i	−0.299790	−	0.519251i	0.676298	−	0.736628i	$-0.263583\pi$
$239$	−4.63463	−	8.02742i	−0.299790	−	0.519251i	−0.976088	+	0.217377i	$0.930250\pi$
$240$	3.32850	+	0.180511i	0.214854	+	0.0116519i
$241$	2.74777	−	4.75929i	0.177000	−	0.306573i	−0.763852	−	0.645392i	$-0.776694\pi$
$241$	2.74777	−	4.75929i	0.177000	−	0.306573i	0.940852	+	0.338819i	$0.110027\pi$
$242$	10.3514			0.665410
$243$	15.0200	+	4.17136i	0.963532	+	0.267593i
$244$	−5.75263			−0.368274
$245$	0.297549	−	0.515370i	0.0190097	−	0.0329258i
$246$	0.967634	+	0.0524766i	0.0616941	+	0.00334579i
$247$	−0.585598	−	1.01428i	−0.0372607	−	0.0645374i
$248$	1.31576	+	2.27896i	0.0835505	+	0.144714i
$249$	−13.2020	+	20.2485i	−0.836641	+	1.28320i
$250$	−6.05859	+	10.4938i	−0.383179	+	0.663686i
$251$	−25.6223			−1.61727			−0.808633	−	0.588314i	$-0.799792\pi$
$251$	−25.6223			−1.61727			−0.808633	+	0.588314i	$0.799792\pi$
$252$	−7.71445	−	0.839207i	−0.485965	−	0.0528651i
$253$	−2.55629			−0.160713
$254$	0.00772519	−	0.0133804i	0.000484722	−	0.000839563i
$255$	3.46367	+	6.82851i	0.216903	+	0.427618i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−10.3289	−	17.8902i	−0.644301	−	1.11596i	−0.984462	−	0.175596i	$-0.943815\pi$
$257$	−10.3289	−	17.8902i	−0.644301	−	1.11596i	0.340161	−	0.940367i	$-0.389518\pi$
$258$	−3.80380	−	7.49907i	−0.236814	−	0.466872i
$259$	−1.29333	+	2.24011i	−0.0803635	+	0.139194i
$260$	4.07228			0.252552
$261$	−3.31815	+	4.53228i	−0.205389	+	0.280541i
$262$	−1.87823			−0.116038
$263$	13.4798	−	23.3476i	0.831198	−	1.43968i	−0.0658903	−	0.997827i	$-0.520989\pi$
$263$	13.4798	−	23.3476i	0.831198	−	1.43968i	0.897089	−	0.441851i	$-0.145678\pi$
$264$	0.761883	−	1.16854i	0.0468906	−	0.0719185i
$265$	−4.21328	−	7.29762i	−0.258820	−	0.448289i
$266$	−0.715856	−	1.23990i	−0.0438920	−	0.0760231i
$267$	−1.18008	−	0.0639981i	−0.0722198	−	0.00391662i
$268$	3.97077	−	6.87757i	0.242553	−	0.420114i
$269$	26.7977			1.63388			0.816941	−	0.576721i	$-0.195668\pi$
$269$	26.7977			1.63388			0.816941	+	0.576721i	$0.195668\pi$
$270$	−9.86838	−	1.61825i	−0.600571	−	0.0984834i
$271$	−14.7405			−0.895424			−0.447712	−	0.894178i	$-0.647761\pi$
$271$	−14.7405			−0.895424			−0.447712	+	0.894178i	$0.647761\pi$
$272$	1.14849	−	1.98924i	0.0696373	−	0.120615i
$273$	−9.46615	−	0.513367i	−0.572917	−	0.0310704i
$274$	5.74407	+	9.94901i	0.347012	+	0.601042i
$275$	0.521955	+	0.904052i	0.0314751	+	0.0545164i
$276$	3.00254	−	4.60514i	0.180732	−	0.277197i
$277$	−3.64312	+	6.31006i	−0.218894	+	0.379135i	−0.954470	−	0.298307i	$-0.903578\pi$
$277$	−3.64312	+	6.31006i	−0.218894	+	0.379135i	0.735576	+	0.677442i	$0.236911\pi$
$278$	14.1098			0.846249
$279$	−3.18474	−	7.22365i	−0.190665	−	0.432468i
$280$	4.97811			0.297499
$281$	−4.78927	+	8.29526i	−0.285704	+	0.494854i	−0.972780	−	0.231732i	$-0.925561\pi$
$281$	−4.78927	+	8.29526i	−0.285704	+	0.494854i	0.687076	+	0.726586i	$0.258894\pi$
$282$	1.69760	+	3.34676i	0.101090	+	0.199297i
$283$	−15.8605	−	27.4713i	−0.942812	−	1.63300i	−0.760074	−	0.649836i	$-0.774838\pi$
$283$	−15.8605	−	27.4713i	−0.942812	−	1.63300i	−0.182737	−	0.983162i	$-0.558496\pi$
$284$	−1.66602	−	2.88563i	−0.0988602	−	0.171231i
$285$	−0.834636	−	1.64546i	−0.0494396	−	0.0974685i
$286$	0.852092	−	1.47587i	0.0503853	−	0.0872699i
$287$	1.44719			0.0854251
$288$	1.21023	+	2.74506i	0.0713136	+	0.161754i
$289$	−11.7239			−0.689641
$290$	1.80172	−	3.12066i	0.105800	−	0.183252i
$291$	−10.6236	+	16.2940i	−0.622769	+	0.955172i
$292$	−1.22203	−	2.11661i	−0.0715137	−	0.123865i
$293$	8.13337	+	14.0874i	0.475156	+	0.822995i	0.999595	−	0.0284531i	$-0.00905812\pi$
$293$	8.13337	+	14.0874i	0.475156	+	0.822995i	−0.524439	+	0.851448i	$0.675725\pi$
$294$	0.534792	+	0.0290028i	0.0311897	+	0.00169148i
$295$	11.3155	−	19.5991i	0.658815	−	1.14110i
$296$	1.00000			0.0581238
$297$	−2.65136	+	3.23787i	−0.153848	+	0.187880i
$298$	−0.154263			−0.00893619
$299$	3.35805	−	5.81631i	0.194201	−	0.336366i
$300$	−2.24172	−	0.121573i	−0.129426	−	0.00701900i
$301$	−6.27875	−	10.8751i	−0.361901	−	0.626831i
$302$	−10.0141	−	17.3449i	−0.576246	−	0.998088i
$303$	−1.97787	+	3.03355i	−0.113626	+	0.174273i
$304$	−0.276750	+	0.479345i	−0.0158727	+	0.0274923i
$305$	−11.0711			−0.633932
$306$	−4.07064	+	5.56011i	−0.232703	+	0.317850i
$307$	−9.26465			−0.528762			−0.264381	−	0.964418i	$-0.585168\pi$
$307$	−9.26465			−0.528762			−0.264381	+	0.964418i	$0.585168\pi$
$308$	1.04163	−	1.80416i	0.0593524	−	0.102801i
$309$	4.35412	+	8.58401i	0.247697	+	0.488327i
$310$	2.53222	+	4.38593i	0.143820	+	0.249104i
$311$	−16.6966	−	28.9193i	−0.946776	−	1.63986i	−0.752156	−	0.658986i	$-0.770986\pi$
$311$	−16.6966	−	28.9193i	−0.946776	−	1.63986i	−0.194620	−	0.980879i	$-0.562348\pi$
$312$	1.65793	+	3.26855i	0.0938616	+	0.185045i
$313$	−12.7130	+	22.0196i	−0.718582	+	1.24462i	0.242979	+	0.970031i	$0.421875\pi$
$313$	−12.7130	+	22.0196i	−0.718582	+	1.24462i	−0.961562	+	0.274589i	$0.911458\pi$
$314$	5.00065			0.282203
$315$	−14.8467	−	1.61508i	−0.836519	−	0.0909997i
$316$	−8.44695			−0.475178
$317$	−0.115362	+	0.199812i	−0.00647936	+	0.0112226i	−0.869247	−	0.494378i	$-0.835396\pi$
$317$	−0.115362	+	0.199812i	−0.00647936	+	0.0112226i	0.862768	+	0.505601i	$0.168729\pi$
$318$	4.14198	−	6.35276i	0.232271	−	0.356245i
$319$	−0.753989	−	1.30595i	−0.0422153	−	0.0731190i
$320$	−0.962268	−	1.66670i	−0.0537924	−	0.0931712i
$321$	−3.58999	−	0.194692i	−0.200374	−	0.0108667i
$322$	4.10501	−	7.11008i	0.228763	−	0.396229i
$323$	−1.27138			−0.0707412
$324$	−2.71880	−	8.57952i	−0.151045	−	0.476640i
$325$	−2.74265			−0.152135
$326$	4.15106	−	7.18984i	0.229906	−	0.398208i
$327$	−14.0602	−	0.762514i	−0.777533	−	0.0421671i
$328$	−0.279742	−	0.484528i	−0.0154462	−	0.0267536i
$329$	2.80214	+	4.85345i	0.154487	+	0.267579i
$330$	1.46627	−	2.24889i	0.0807156	−	0.123798i
$331$	4.98308	−	8.63095i	0.273895	−	0.474400i	−0.695961	−	0.718080i	$-0.745021\pi$
$331$	4.98308	−	8.63095i	0.273895	−	0.474400i	0.969856	+	0.243680i	$0.0783546\pi$
$332$	13.9558			0.765925
$333$	−2.98241	−	0.324437i	−0.163435	−	0.0177790i
$334$	−2.28840			−0.125216
$335$	7.64188	−	13.2361i	0.417521	−	0.723167i
$336$	2.02671	+	3.99560i	0.110566	+	0.217978i
$337$	−11.3735	−	19.6996i	−0.619557	−	1.07310i	−0.989567	−	0.144076i	$-0.953979\pi$
$337$	−11.3735	−	19.6996i	−0.619557	−	1.07310i	0.370010	−	0.929028i	$-0.379354\pi$
$338$	−4.26131	−	7.38081i	−0.231785	−	0.401463i
$339$	−4.37996	−	8.63494i	−0.237887	−	0.468986i
$340$	2.21031	−	3.82837i	0.119871	−	0.207622i
$341$	2.11939			0.114771
$342$	0.980898	−	1.33981i	0.0530409	−	0.0724488i
$343$	18.9064			1.02085
$344$	−2.42736	+	4.20431i	−0.130875	+	0.226681i
$345$	5.77850	−	8.86277i	0.311104	−	0.477155i
$346$	5.06924	+	8.78018i	0.272524	+	0.472025i
$347$	−6.94452	−	12.0283i	−0.372801	−	0.645711i	0.617194	−	0.786811i	$-0.288269\pi$
$347$	−6.94452	−	12.0283i	−0.372801	−	0.645711i	−0.989995	+	0.141100i	$0.954936\pi$
$348$	3.23827	+	0.175618i	0.173590	+	0.00941409i
$349$	−3.29716	+	5.71086i	−0.176493	+	0.305695i	−0.940677	−	0.339303i	$-0.889809\pi$
$349$	−3.29716	+	5.71086i	−0.176493	+	0.305695i	0.764184	+	0.644998i	$0.223142\pi$
$350$	−3.35271			−0.179210
$351$	−3.88417	−	10.2860i	−0.207322	−	0.549028i
$352$	−0.805387			−0.0429273
$353$	13.4857	−	23.3580i	0.717774	−	1.24322i	−0.244106	−	0.969749i	$-0.578495\pi$
$353$	13.4857	−	23.3580i	0.717774	−	1.24322i	0.961880	−	0.273472i	$-0.0881722\pi$
$354$	20.3377	+	1.10295i	1.08094	+	0.0586212i
$355$	−3.20632	−	5.55351i	−0.170174	−	0.294750i
$356$	0.341161	+	0.590908i	0.0180815	+	0.0313181i
$357$	−5.62055	+	8.62051i	−0.297471	+	0.456246i
$358$	−11.0186	+	19.0847i	−0.582349	+	1.00866i
$359$	−30.9863			−1.63540			−0.817698	−	0.575647i	$-0.804750\pi$
$359$	−30.9863			−1.63540			−0.817698	+	0.575647i	$0.804750\pi$
$360$	2.32914	+	5.28296i	0.122756	+	0.278437i
$361$	−18.6936			−0.983876
$362$	0.000364031	0	0.000630520i	1.91330e−5	0	3.31394e-5i
$363$	8.11055	+	15.9897i	0.425694	+	0.839241i
$364$	2.73666	+	4.74003i	0.143440	+	0.248445i
$365$	−2.35183	−	4.07350i	−0.123101	−	0.213217i
$366$	−4.50734	−	8.88607i	−0.235602	−	0.464482i
$367$	4.19902	−	7.27292i	0.219187	−	0.379643i	−0.735373	−	0.677663i	$-0.762993\pi$
$367$	4.19902	−	7.27292i	0.219187	−	0.379643i	0.954560	+	0.298020i	$0.0963262\pi$
$368$	−3.17399			−0.165456
$369$	0.677106	+	1.53582i	0.0352487	+	0.0799515i
$370$	1.92454			0.100052
$371$	5.66282	−	9.80829i	0.293999	−	0.509221i
$372$	−2.48936	+	3.81806i	−0.129068	+	0.197957i
$373$	−9.72736	−	16.8483i	−0.503664	−	0.872371i	−0.999991	−	0.00423568i	$-0.998652\pi$
$373$	−9.72736	−	16.8483i	−0.503664	−	0.872371i	0.496327	−	0.868135i	$-0.334682\pi$
$374$	−0.924978	−	1.60211i	−0.0478295	−	0.0828431i
$375$	−20.9568	−	1.13653i	−1.08220	−	0.0586900i
$376$	1.08331	−	1.87634i	0.0558673	−	0.0967649i
$377$	3.96189			0.204048
$378$	−4.74816	−	12.5740i	−0.244219	−	0.646738i
$379$	−16.4204			−0.843457			−0.421729	−	0.906722i	$-0.638576\pi$
$379$	−16.4204			−0.843457			−0.421729	+	0.906722i	$0.638576\pi$
$380$	−0.532615	+	0.922517i	−0.0273226	+	0.0473241i
$381$	0.0267216	+	0.00144916i	0.00136899	+	7.42428e-5i
$382$	−6.78664	−	11.7548i	−0.347235	−	0.601428i
$383$	13.8398	+	23.9713i	0.707183	+	1.22488i	0.965898	+	0.258923i	$0.0833674\pi$
$383$	13.8398	+	23.9713i	0.707183	+	1.22488i	−0.258716	+	0.965954i	$0.583299\pi$
$384$	0.945983	−	1.45090i	0.0482745	−	0.0740410i
$385$	2.00465	−	3.47216i	0.102167	−	0.176958i
$386$	26.6117			1.35450
$387$	8.60341	−	11.7514i	0.437336	−	0.597359i
$388$	11.2303			0.570131
$389$	1.79780	−	3.11388i	0.0911520	−	0.157880i	−0.816844	−	0.576858i	$-0.804278\pi$
$389$	1.79780	−	3.11388i	0.0911520	−	0.157880i	0.907996	+	0.418979i	$0.137612\pi$
$390$	3.19074	+	6.29044i	0.161569	+	0.318529i
$391$	−3.64529	−	6.31382i	−0.184350	−	0.319304i
$392$	−0.154608	−	0.267789i	−0.00780889	−	0.0135254i
$393$	−1.47164	−	2.90130i	−0.0742346	−	0.146351i
$394$	−1.68046	+	2.91064i	−0.0846603	+	0.146636i
$395$	−16.2565			−0.817951
$396$	2.40199	+	0.261298i	0.120705	+	0.0131307i
$397$	−24.3856			−1.22388			−0.611939	−	0.790905i	$-0.709610\pi$
$397$	−24.3856			−1.22388			−0.611939	+	0.790905i	$0.709610\pi$
$398$	−7.45555	+	12.9134i	−0.373713	+	0.647289i
$399$	1.35438	−	2.07727i	0.0678036	−	0.103994i
$400$	0.648079	+	1.12251i	0.0324040	+	0.0561253i
$401$	12.4644	+	21.5889i	0.622441	+	1.07810i	0.989030	+	0.147716i	$0.0471921\pi$
$401$	12.4644	+	21.5889i	0.622441	+	1.07810i	−0.366589	+	0.930383i	$0.619475\pi$
$402$	13.7350	+	0.744873i	0.685037	+	0.0371509i
$403$	−2.78411	+	4.82223i	−0.138687	+	0.240212i
$404$	2.09081			0.104022
$405$	−5.23244	−	16.5116i	−0.260002	−	0.820468i
$406$	4.84316			0.240362
$407$	0.402694	−	0.697486i	0.0199608	−	0.0345731i
$408$	3.97264	+	0.215444i	0.196675	+	0.0106661i
$409$	−2.55547	−	4.42620i	−0.126360	−	0.218861i	0.795904	−	0.605423i	$-0.206996\pi$
$409$	−2.55547	−	4.42620i	−0.126360	−	0.218861i	−0.922264	+	0.386562i	$0.873663\pi$
$410$	−0.538374	−	0.932492i	−0.0265884	−	0.0460525i
$411$	−10.8676	+	16.6682i	−0.536058	+	0.822179i
$412$	2.77854	−	4.81258i	0.136889	−	0.237099i
$413$	30.4170			1.49672
$414$	9.46612	+	1.02976i	0.465234	+	0.0506099i
$415$	26.8585			1.31843
$416$	1.05799	−	1.83249i	0.0518723	−	0.0898454i
$417$	11.0554	+	21.7953i	0.541385	+	1.06732i
$418$	0.222891	+	0.386058i	0.0109019	+	0.0188827i
$419$	−15.0666	−	26.0961i	−0.736052	−	1.27488i	−0.954260	−	0.298978i	$-0.903354\pi$
$419$	−15.0666	−	26.0961i	−0.736052	−	1.27488i	0.218208	−	0.975902i	$-0.429979\pi$
$420$	3.90048	+	7.68967i	0.190324	+	0.375218i
$421$	−3.57359	+	6.18964i	−0.174166	+	0.301664i	−0.939872	−	0.341526i	$-0.889056\pi$
$421$	−3.57359	+	6.18964i	−0.174166	+	0.301664i	0.765706	+	0.643190i	$0.222390\pi$
$422$	−22.3806			−1.08947
$423$	−3.83961	+	5.24455i	−0.186688	+	0.254999i
$424$	−4.37849			−0.212638
$425$	−1.48862	+	2.57837i	−0.0722088	+	0.125069i
$426$	3.15206	−	4.83447i	0.152718	−	0.234231i
$427$	−7.44003	−	12.8865i	−0.360048	−	0.623622i
$428$	1.03786	+	1.79763i	0.0501671	+	0.0868920i
$429$	2.94740	+	0.159843i	0.142302	+	0.00771731i
$430$	−4.67155	+	8.09136i	−0.225282	+	0.390200i
$431$	1.93814			0.0933568			0.0466784	−	0.998910i	$-0.485136\pi$
$431$	1.93814			0.0933568			0.0466784	+	0.998910i	$0.485136\pi$
$432$	−3.29203	+	4.02026i	−0.158388	+	0.193425i
$433$	−4.66668			−0.224266			−0.112133	−	0.993693i	$-0.535768\pi$
$433$	−4.66668			−0.224266			−0.112133	+	0.993693i	$0.535768\pi$
$434$	−3.40341	+	5.89487i	−0.163369	+	0.282963i
$435$	6.23217	+	0.337982i	0.298810	+	0.0162050i
$436$	4.06481	+	7.04045i	0.194669	+	0.337177i
$437$	0.878401	+	1.52143i	0.0420196	+	0.0727801i
$438$	2.31203	−	3.54608i	0.110473	−	0.169438i
$439$	−2.00860	+	3.47900i	−0.0958653	+	0.166044i	−0.909969	−	0.414675i	$-0.863895\pi$
$439$	−2.00860	+	3.47900i	−0.0958653	+	0.166044i	0.814104	+	0.580719i	$0.197228\pi$
$440$	−1.55000			−0.0738932
$441$	0.374223	+	0.848816i	0.0178201	+	0.0404198i
$442$	4.86036			0.231184
$443$	1.35634	−	2.34925i	0.0644418	−	0.111616i	−0.832004	−	0.554769i	$-0.812807\pi$
$443$	1.35634	−	2.34925i	0.0644418	−	0.111616i	0.896446	+	0.443153i	$0.146140\pi$
$444$	0.783526	+	1.54470i	0.0371845	+	0.0733080i
$445$	0.656577	+	1.13722i	0.0311247	+	0.0539096i
$446$	−5.11873	−	8.86591i	−0.242379	−	0.419813i
$447$	−0.120869	−	0.238289i	−0.00571689	−	0.0112707i
$448$	1.29333	−	2.24011i	0.0611040	−	0.105835i
$449$	−2.45717			−0.115961			−0.0579805	−	0.998318i	$-0.518466\pi$
$449$	−2.45717			−0.115961			−0.0579805	+	0.998318i	$0.518466\pi$
$450$	−1.56865	−	3.55803i	−0.0739470	−	0.167727i
$451$	−0.450602			−0.0212180
$452$	−2.79503	+	4.84113i	−0.131467	+	0.227708i
$453$	18.9463	−	29.0589i	0.890176	−	1.36531i
$454$	3.74392	+	6.48467i	0.175711	+	0.304340i
$455$	5.26680	+	9.12236i	0.246911	+	0.427663i
$456$	−0.957283	−	0.0519153i	−0.0448289	−	0.00243116i
$457$	−20.8731	+	36.1533i	−0.976404	+	1.69118i	−0.301182	+	0.953567i	$0.597381\pi$
$457$	−20.8731	+	36.1533i	−0.976404	+	1.69118i	−0.675222	+	0.737615i	$0.735952\pi$
$458$	23.3264			1.08997
$459$	−11.7781	−	1.93141i	−0.549756	−	0.0901507i
$460$	−6.10846			−0.284808
$461$	−12.3417	+	21.3765i	−0.574812	+	0.995604i	0.421250	+	0.906945i	$0.361592\pi$
$461$	−12.3417	+	21.3765i	−0.574812	+	0.995604i	−0.996062	+	0.0886595i	$0.971742\pi$
$462$	3.60302	+	0.195398i	0.167627	+	0.00909076i
$463$	15.0390	+	26.0482i	0.698920	+	1.21056i	0.968841	+	0.247682i	$0.0796688\pi$
$463$	15.0390	+	26.0482i	0.698920	+	1.21056i	−0.269922	+	0.962882i	$0.586998\pi$
$464$	−0.936182	−	1.62151i	−0.0434612	−	0.0752769i
$465$	−4.79087	+	7.34800i	−0.222171	+	0.340755i
$466$	8.68560	−	15.0439i	0.402352	−	0.696895i
$467$	8.29454			0.383825			0.191913	−	0.981412i	$-0.438531\pi$
$467$	8.29454			0.383825			0.191913	+	0.981412i	$0.438531\pi$
$468$	−3.74989	+	5.12199i	−0.173339	+	0.236764i
$469$	20.5420			0.948542
$470$	2.08486	−	3.61109i	0.0961676	−	0.166567i
$471$	3.91814	+	7.72449i	0.180538	+	0.355926i
$472$	−5.87961	−	10.1838i	−0.270631	−	0.468747i
$473$	1.95497	+	3.38610i	0.0898895	+	0.155693i
$474$	−6.61840	−	13.0480i	−0.303993	−	0.599313i
$475$	0.358712	−	0.621307i	0.0164588	−	0.0285075i
$476$	5.94149			0.272328
$477$	13.0584	+	1.42054i	0.597904	+	0.0650423i
$478$	−9.26927			−0.423966
$479$	20.9811	−	36.3403i	0.958650	−	1.66043i	0.232866	−	0.972509i	$-0.425189\pi$
$479$	20.9811	−	36.3403i	0.958650	−	1.66043i	0.725784	−	0.687923i	$-0.241477\pi$
$480$	1.82058	−	2.79231i	0.0830977	−	0.127451i
$481$	1.05799	+	1.83249i	0.0482402	+	0.0835545i
$482$	−2.74777	−	4.75929i	−0.125158	−	0.216779i
$483$	14.1993	+	0.770054i	0.646090	+	0.0350387i
$484$	5.17568	−	8.96453i	0.235258	−	0.407479i
$485$	21.6131			0.981399
$486$	11.1225	−	10.9220i	0.504527	−	0.495432i
$487$	−29.0161			−1.31484			−0.657422	−	0.753522i	$-0.728353\pi$
$487$	−29.0161			−1.31484			−0.657422	+	0.753522i	$0.728353\pi$
$488$	−2.87631	+	4.98192i	−0.130205	+	0.225521i
$489$	14.3586	+	0.778693i	0.649317	+	0.0352137i
$490$	−0.297549	−	0.515370i	−0.0134419	−	0.0232820i
$491$	17.3660	+	30.0787i	0.783715	+	1.35743i	0.929764	+	0.368157i	$0.120011\pi$
$491$	17.3660	+	30.0787i	0.783715	+	1.35743i	−0.146048	+	0.989277i	$0.546656\pi$
$492$	0.529263	−	0.811757i	0.0238610	−	0.0365968i
$493$	2.15039	−	3.72458i	0.0968486	−	0.167747i
$494$	−1.17120			−0.0526946
$495$	4.62272	+	0.502877i	0.207776	+	0.0226026i
$496$	2.63151			0.118158
$497$	4.30942	−	7.46414i	0.193304	−	0.334812i
$498$	10.9348	+	21.5575i	0.489998	+	0.966015i
$499$	1.97276	+	3.41691i	0.0883127	+	0.152962i	0.906798	−	0.421565i	$-0.138519\pi$
$499$	1.97276	+	3.41691i	0.0883127	+	0.152962i	−0.818485	+	0.574527i	$0.805186\pi$
$500$	6.05859	+	10.4938i	0.270949	+	0.469297i
$501$	−1.79302	−	3.53488i	−0.0801063	−	0.157927i
$502$	−12.8112	+	22.1896i	−0.571790	+	0.990369i
$503$	−16.1760			−0.721254			−0.360627	−	0.932710i	$-0.617437\pi$
$503$	−16.1760			−0.721254			−0.360627	+	0.932710i	$0.617437\pi$
$504$	−4.58400	+	6.26131i	−0.204188	+	0.278901i
$505$	4.02383			0.179058
$506$	−1.27814	+	2.21381i	−0.0568205	+	0.0984159i
$507$	8.06226	−	12.3655i	0.358057	−	0.549171i
$508$	−0.00772519	−	0.0133804i	−0.000342750	−	0.000593660i
$509$	2.57815	+	4.46549i	0.114274	+	0.197929i	0.917489	−	0.397760i	$-0.130212\pi$
$509$	2.57815	+	4.46549i	0.114274	+	0.197929i	−0.803215	+	0.595689i	$0.796879\pi$
$510$	7.64550	+	0.414630i	0.338548	+	0.0183601i
$511$	3.16096	−	5.47494i	0.139833	−	0.242197i
$512$	−1.00000			−0.0441942
$513$	2.83816	+	0.465411i	0.125308	+	0.0205484i
$514$	−20.6579			−0.911180
$515$	5.34741	−	9.26198i	0.235635	−	0.408132i
$516$	−8.39629	−	0.455347i	−0.369626	−	0.0200455i
$517$	−0.872481	−	1.51118i	−0.0383717	−	0.0664617i
$518$	1.29333	+	2.24011i	0.0568255	+	0.0984247i
$519$	−9.59083	+	14.7099i	−0.420991	+	0.645694i
$520$	2.03614	−	3.52670i	0.0892907	−	0.154656i
$521$	11.5583			0.506378			0.253189	−	0.967417i	$-0.418521\pi$
$521$	11.5583			0.506378			0.253189	+	0.967417i	$0.418521\pi$
$522$	2.26599	+	5.13975i	0.0991799	+	0.224961i
$523$	−14.2256			−0.622041			−0.311021	−	0.950403i	$-0.600671\pi$
$523$	−14.2256			−0.622041			−0.311021	+	0.950403i	$0.600671\pi$
$524$	−0.939116	+	1.62660i	−0.0410255	+	0.0710582i
$525$	−2.62694	−	5.17893i	−0.114649	−	0.226027i
$526$	−13.4798	−	23.3476i	−0.587746	−	1.01801i
$527$	3.02226	+	5.23471i	0.131652	+	0.228027i
$528$	−0.631042	−	1.24408i	−0.0274626	−	0.0541416i
$529$	6.46290	−	11.1941i	0.280996	−	0.486699i
$530$	−8.42656			−0.366027
$531$	14.2314	+	32.2797i	0.617589	+	1.40082i
$532$	−1.43171			−0.0620726
$533$	0.591930	−	1.02525i	0.0256393	−	0.0444086i
$534$	−0.645465	+	0.989982i	−0.0279320	+	0.0428407i
$535$	1.99741	+	3.45961i	0.0863555	+	0.149572i
$536$	−3.97077	−	6.87757i	−0.171511	−	0.297066i
$537$	−38.1134	−	2.06696i	−1.64471	−	0.0891960i
$538$	13.3988	−	23.2075i	0.577665	−	1.00054i
$539$	−0.249039			−0.0107269
$540$	−6.33564	+	7.73715i	−0.272642	+	0.332954i
$541$	15.1108			0.649666			0.324833	−	0.945771i	$-0.394692\pi$
$541$	15.1108			0.649666			0.324833	+	0.945771i	$0.394692\pi$
$542$	−7.37027	+	12.7657i	−0.316580	+	0.548333i
$543$	0.00125919		6.82882e-5i	5.40370e−5		2.93053e-6i
$544$	−1.14849	−	1.98924i	−0.0492410	−	0.0852880i
$545$	7.82287	+	13.5496i	0.335095	+	0.580402i
$546$	−5.17766	+	7.94124i	−0.221584	+	0.339854i
$547$	3.88367	−	6.72671i	0.166054	−	0.287613i	−0.770975	−	0.636865i	$-0.780231\pi$
$547$	3.88367	−	6.72671i	0.166054	−	0.287613i	0.937029	+	0.349252i	$0.113564\pi$
$548$	11.4881			0.490749
$549$	10.1947	−	13.9249i	0.435097	−	0.594302i
$550$	1.04391			0.0445125
$551$	−0.518176	+	0.897508i	−0.0220751	+	0.0382351i
$552$	−2.48690	−	4.90285i	−0.105850	−	0.208679i
$553$	−10.9247	−	18.9221i	−0.464564	−	0.804649i
$554$	3.64312	+	6.31006i	0.154781	+	0.268089i
$555$	1.50792	+	2.97282i	0.0640078	+	0.126189i
$556$	7.05490	−	12.2194i	0.299194	−	0.518220i
$557$	4.11757			0.174467			0.0872335	−	0.996188i	$-0.472197\pi$
$557$	4.11757			0.174467			0.0872335	+	0.996188i	$0.472197\pi$
$558$	−7.84823	−	0.853760i	−0.332242	−	0.0361425i
$559$	−10.2725			−0.434481
$560$	2.48906	−	4.31117i	0.105182	−	0.182180i
$561$	1.75003	−	2.68410i	0.0738862	−	0.113323i
$562$	4.78927	+	8.29526i	0.202023	+	0.349915i
$563$	1.25854	+	2.17986i	0.0530412	+	0.0918701i	0.891327	−	0.453361i	$-0.149775\pi$
$563$	1.25854	+	2.17986i	0.0530412	+	0.0918701i	−0.838286	+	0.545231i	$0.816442\pi$
$564$	3.74718	+	0.203217i	0.157785	+	0.00855696i
$565$	−5.37914	+	9.31694i	−0.226302	+	0.391967i
$566$	−31.7211			−1.33334
$567$	15.7028	−	17.1865i	0.659454	−	0.721767i
$568$	−3.33204			−0.139809
$569$	19.4892	−	33.7564i	0.817031	−	1.41514i	−0.0908285	−	0.995867i	$-0.528952\pi$
$569$	19.4892	−	33.7564i	0.817031	−	1.41514i	0.907860	−	0.419273i	$-0.137715\pi$
$570$	−1.84233	−	0.0999129i	−0.0771666	−	0.00418489i
$571$	−4.34277	−	7.52190i	−0.181739	−	0.314782i	0.760734	−	0.649064i	$-0.224839\pi$
$571$	−4.34277	−	7.52190i	−0.181739	−	0.314782i	−0.942473	+	0.334283i	$0.891506\pi$
$572$	−0.852092	−	1.47587i	−0.0356278	−	0.0617091i
$573$	12.8401	−	19.6935i	0.536403	−	0.822708i
$574$	0.723597	−	1.25331i	0.0302023	−	0.0523120i
$575$	4.11399			0.171565
$576$	2.98241	+	0.324437i	0.124267	+	0.0135182i
$577$	−39.8730			−1.65994			−0.829968	−	0.557811i	$-0.811641\pi$
$577$	−39.8730			−1.65994			−0.829968	+	0.557811i	$0.811641\pi$
$578$	−5.86195	+	10.1532i	−0.243825	+	0.422317i
$579$	20.8510	+	41.1070i	0.866536	+	1.70835i
$580$	−1.80172	−	3.12066i	−0.0748122	−	0.129579i
$581$	18.0494	+	31.2626i	0.748817	+	1.29699i
$582$	8.79921	+	17.3474i	0.364739	+	0.719071i
$583$	−1.76319	+	3.05393i	−0.0730239	+	0.126481i
$584$	−2.44405			−0.101136
$585$	−7.21679	+	9.85745i	−0.298378	+	0.407555i
$586$	16.2667			0.671973
$587$	−0.972373	+	1.68420i	−0.0401341	+	0.0695143i	−0.885395	−	0.464840i	$-0.846112\pi$
$587$	−0.972373	+	1.68420i	−0.0401341	+	0.0695143i	0.845261	+	0.534354i	$0.179445\pi$
$588$	0.292513	−	0.448642i	0.0120630	−	0.0185017i
$589$	−0.728270	−	1.26140i	−0.0300079	−	0.0519751i
$590$	−11.3155	−	19.5991i	−0.465853	−	0.806881i
$591$	−5.81274	−	0.315236i	−0.239104	−	0.0129671i
$592$	0.500000	−	0.866025i	0.0205499	−	0.0355934i
$593$	−17.1562			−0.704522			−0.352261	−	0.935902i	$-0.614587\pi$
$593$	−17.1562			−0.704522			−0.352261	+	0.935902i	$0.614587\pi$
$594$	1.47840	+	3.91508i	0.0606594	+	0.160638i
$595$	11.4346			0.468773
$596$	−0.0771313	+	0.133595i	−0.00315942	+	0.00547228i
$597$	−25.7889	−	1.39858i	−1.05547	−	0.0572401i
$598$	−3.35805	−	5.81631i	−0.137321	−	0.237847i
$599$	15.6908	+	27.1773i	0.641109	+	1.11043i	0.985185	+	0.171492i	$0.0548588\pi$
$599$	15.6908	+	27.1773i	0.641109	+	1.11043i	−0.344076	+	0.938942i	$0.611808\pi$
$600$	−1.22614	+	1.88060i	−0.0500571	+	0.0767751i
$601$	4.33174	−	7.50280i	0.176696	−	0.306046i	−0.764051	−	0.645156i	$-0.776793\pi$
$601$	4.33174	−	7.50280i	0.176696	−	0.306046i	0.940747	+	0.339110i	$0.110126\pi$
$602$	−12.5575			−0.511805
$603$	9.61109	+	21.8000i	0.391394	+	0.887763i
$604$	−20.0282			−0.814936
$605$	9.96078	−	17.2526i	0.404963	−	0.701417i
$606$	1.63820	+	3.22966i	0.0665474	+	0.131196i
$607$	11.4865	+	19.8953i	0.466224	+	0.807523i	0.999256	−	0.0385717i	$-0.0122808\pi$
$607$	11.4865	+	19.8953i	0.466224	+	0.807523i	−0.533032	+	0.846095i	$0.678947\pi$
$608$	0.276750	+	0.479345i	0.0112237	+	0.0194400i
$609$	3.79474	+	7.48121i	0.153771	+	0.303154i
$610$	−5.53557	+	9.58789i	−0.224129	+	0.388202i
$611$	4.58451			0.185470
$612$	2.77987	+	6.30533i	0.112370	+	0.254878i
$613$	−14.6863			−0.593175			−0.296588	−	0.955006i	$-0.595849\pi$
$613$	−14.6863			−0.593175			−0.296588	+	0.955006i	$0.595849\pi$
$614$	−4.63232	+	8.02342i	−0.186945	+	0.323799i
$615$	1.01859	−	1.56226i	0.0410734	−	0.0629963i
$616$	−1.04163	−	1.80416i	−0.0419685	−	0.0726915i
$617$	11.7505	+	20.3525i	0.473058	+	0.819360i	0.999524	−	0.0308355i	$-0.00981681\pi$
$617$	11.7505	+	20.3525i	0.473058	+	0.819360i	−0.526467	+	0.850196i	$0.676483\pi$
$618$	9.61103	+	0.521225i	0.386612	+	0.0209667i
$619$	9.37013	−	16.2295i	0.376617	−	0.652320i	−0.613950	−	0.789345i	$-0.710420\pi$
$619$	9.37013	−	16.2295i	0.376617	−	0.652320i	0.990568	+	0.137024i	$0.0437538\pi$
$620$	5.06444			0.203393
$621$	5.82628	+	15.4291i	0.233801	+	0.619149i
$622$	−33.3932			−1.33894
$623$	−0.882465	+	1.52848i	−0.0353552	+	0.0612371i
$624$	3.65961	+	0.198468i	0.146502	+	0.00794506i
$625$	8.41959	+	14.5832i	0.336784	+	0.583326i
$626$	12.7130	+	22.0196i	0.508114	+	0.880080i
$627$	−0.421702	+	0.646785i	−0.0168412	+	0.0258301i
$628$	2.50032	−	4.33069i	0.0997738	−	0.172813i
$629$	2.29698			0.0915864
$630$	−8.82208	+	12.0501i	−0.351480	+	0.480088i
$631$	20.0099			0.796583			0.398292	−	0.917259i	$-0.369603\pi$
$631$	20.0099			0.796583			0.398292	+	0.917259i	$0.369603\pi$
$632$	−4.22347	+	7.31527i	−0.168001	+	0.290986i
$633$	−17.5358	−	34.5712i	−0.696984	−	1.37408i
$634$	0.115362	+	0.199812i	0.00458160	+	0.00793556i
$635$	−0.0148674	−	0.0257511i	−0.000589995	−	0.00102190i
$636$	−3.43066	−	6.76344i	−0.136035	−	0.268188i
$637$	0.327148	−	0.566637i	0.0129621	−	0.0224510i
$638$	−1.50798			−0.0597014
$639$	9.93750	+	1.08104i	0.393122	+	0.0427652i
$640$	−1.92454			−0.0760740
$641$	−6.82312	+	11.8180i	−0.269497	+	0.466783i	−0.968732	−	0.248109i	$-0.920191\pi$
$641$	−6.82312	+	11.8180i	−0.269497	+	0.466783i	0.699235	+	0.714892i	$0.253524\pi$
$642$	−1.96361	+	3.01168i	−0.0774973	+	0.118862i
$643$	10.2230	+	17.7067i	0.403155	+	0.698284i	0.994105	−	0.108424i	$-0.0345804\pi$
$643$	10.2230	+	17.7067i	0.403155	+	0.698284i	−0.590950	+	0.806708i	$0.701247\pi$
$644$	−4.10501	−	7.11008i	−0.161760	−	0.280176i
$645$	−16.1590	−	0.876332i	−0.636259	−	0.0345055i
$646$	−0.635688	+	1.10104i	−0.0250108	+	0.0433200i
$647$	−5.59342			−0.219900			−0.109950	−	0.993937i	$-0.535069\pi$
$647$	−5.59342			−0.219900			−0.109950	+	0.993937i	$0.535069\pi$
$648$	−8.78948	−	1.93521i	−0.345283	−	0.0760221i
$649$	−9.47073			−0.371759
$650$	−1.37132	+	2.37520i	−0.0537877	+	0.0931631i
$651$	−11.7724	−	0.638442i	−0.461398	−	0.0250225i
$652$	−4.15106	−	7.18984i	−0.162568	−	0.281576i
$653$	18.7924	+	32.5494i	0.735404	+	1.27376i	0.954546	+	0.298064i	$0.0963409\pi$
$653$	18.7924	+	32.5494i	0.735404	+	1.27376i	−0.219142	+	0.975693i	$0.570326\pi$
$654$	−7.69048	+	11.7953i	−0.300722	+	0.461232i
$655$	−1.80736	+	3.13044i	−0.0706195	+	0.122317i
$656$	−0.559485			−0.0218442
$657$	7.28915	+	0.792941i	0.284377	+	0.0309356i
$658$	5.60428			0.218478
$659$	16.7317	−	28.9801i	0.651774	−	1.12891i	−0.330918	−	0.943660i	$-0.607358\pi$
$659$	16.7317	−	28.9801i	0.651774	−	1.12891i	0.982692	−	0.185247i	$-0.0593084\pi$
$660$	−1.21446	−	2.39428i	−0.0472729	−	0.0931970i
$661$	−9.41779	−	16.3121i	−0.366310	−	0.634467i	0.622676	−	0.782480i	$-0.286046\pi$
$661$	−9.41779	−	16.3121i	−0.366310	−	0.634467i	−0.988985	+	0.148013i	$0.952712\pi$
$662$	−4.98308	−	8.63095i	−0.193673	−	0.335451i
$663$	3.80822	+	7.50778i	0.147899	+	0.291578i
$664$	6.97791	−	12.0861i	0.270795	−	0.469031i
$665$	−2.75538			−0.106849
$666$	−1.77217	+	2.42062i	−0.0686703	+	0.0937971i
$667$	−5.94286			−0.230108
$668$	−1.14420	+	1.98181i	−0.0442704	+	0.0766786i
$669$	9.68447	−	14.8536i	0.374423	−	0.574272i
$670$	−7.64188	−	13.2361i	−0.295232	−	0.511356i
$671$	2.31655	+	4.01238i	0.0894293	+	0.154896i
$672$	4.47364	+	0.242614i	0.172575	+	0.00935905i
$673$	−5.75948	+	9.97571i	−0.222012	+	0.384535i	−0.955419	−	0.295254i	$-0.904596\pi$
$673$	−5.75948	+	9.97571i	−0.222012	+	0.384535i	0.733407	+	0.679790i	$0.237929\pi$
$674$	−22.7471			−0.876185
$675$	4.26699	−	5.21090i	0.164237	−	0.200568i
$676$	−8.52262			−0.327793
$677$	−18.5671	+	32.1591i	−0.713591	+	1.23598i	0.249909	+	0.968269i	$0.419599\pi$
$677$	−18.5671	+	32.1591i	−0.713591	+	1.23598i	−0.963500	+	0.267707i	$0.913734\pi$
$678$	−9.66806	−	0.524317i	−0.371300	−	0.0201363i
$679$	14.5244	+	25.1570i	0.557396	+	0.965438i
$680$	−2.21031	−	3.82837i	−0.0847614	−	0.146811i
$681$	−7.08338	+	10.8641i	−0.271436	+	0.416314i
$682$	1.05969	−	1.83544i	0.0405777	−	0.0702827i
$683$	9.54593			0.365265			0.182632	−	0.983181i	$-0.441538\pi$
$683$	9.54593			0.365265			0.182632	+	0.983181i	$0.441538\pi$
$684$	−0.669863	−	1.51939i	−0.0256128	−	0.0580953i
$685$	22.1093			0.844754
$686$	9.45321	−	16.3734i	0.360925	−	0.625141i
$687$	18.2769	+	36.0323i	0.697306	+	1.37472i
$688$	2.42736	+	4.20431i	0.0925423	+	0.160288i
$689$	−4.63240	−	8.02355i	−0.176480	−	0.305673i
$690$	−4.78613	−	9.43571i	−0.182205	−	0.359211i
$691$	−8.99008	+	15.5713i	−0.341999	+	0.592359i	−0.984804	−	0.173671i	$-0.944437\pi$
$691$	−8.99008	+	15.5713i	−0.341999	+	0.592359i	0.642805	+	0.766030i	$0.277770\pi$
$692$	10.1385			0.385407
$693$	2.52123	+	5.71867i	0.0957735	+	0.217234i
$694$	−13.8890			−0.527221
$695$	13.5774	−	23.5168i	0.515020	−	0.892041i
$696$	1.77122	−	2.71662i	0.0671381	−	0.102973i
$697$	−0.642562	−	1.11295i	−0.0243388	−	0.0421560i
$698$	3.29716	+	5.71086i	0.124800	+	0.216159i
$699$	30.0436	+	1.62932i	1.13635	+	0.0616267i
$700$	−1.67636	+	2.90354i	−0.0633604	+	0.109743i
$701$	−13.9334			−0.526256			−0.263128	−	0.964761i	$-0.584754\pi$
$701$	−13.9334			−0.526256			−0.263128	+	0.964761i	$0.584754\pi$
$702$	−10.8500	−	1.77922i	−0.409509	−	0.0671525i
$703$	−0.553500			−0.0208756
$704$	−0.402694	+	0.697486i	−0.0151771	+	0.0262875i
$705$	7.21158	+	0.391098i	0.271604	+	0.0147296i
$706$	−13.4857	−	23.3580i	−0.507543	−	0.879090i
$707$	2.70410	+	4.68363i	0.101698	+	0.176146i
$708$	11.1240	−	17.0615i	0.418066	−	0.641209i
$709$	−7.26914	+	12.5905i	−0.272998	+	0.472847i	−0.969628	−	0.244584i	$-0.921349\pi$
$709$	−7.26914	+	12.5905i	−0.272998	+	0.472847i	0.696630	+	0.717431i	$0.254682\pi$
$710$	−6.41264			−0.240662
$711$	14.9695	−	20.4468i	0.561398	−	0.766817i
$712$	0.682322			0.0255711
$713$	4.17619	−	7.23337i	0.156400	−	0.270892i
$714$	4.65531	+	9.17779i	0.174221	+	0.343470i
$715$	−1.63988	−	2.84036i	−0.0613281	−	0.106223i
$716$	11.0186	+	19.0847i	0.411783	+	0.713229i
$717$	−7.26271	−	14.3182i	−0.271231	−	0.534723i
$718$	−15.4932	+	26.8350i	−0.578200	+	1.00147i
$719$	2.00668			0.0748367			0.0374183	−	0.999300i	$-0.488087\pi$
$719$	2.00668			0.0748367			0.0374183	+	0.999300i	$0.488087\pi$
$720$	5.73975	+	0.624391i	0.213908	+	0.0232697i
$721$	14.3743			0.535326
$722$	−9.34682	+	16.1892i	−0.347853	+	0.602498i
$723$	5.19870	−	7.97350i	0.193342	−	0.296538i
$724$	−0.000364031	0	0.000630520i	−1.35291e−5	0	2.34331e-5i
$725$	1.21344	+	2.10174i	0.0450660	+	0.0780567i
$726$	17.9028	+	0.970901i	0.664434	+	0.0360335i
$727$	6.28143	−	10.8798i	0.232965	−	0.403508i	−0.725714	−	0.687996i	$-0.758490\pi$
$727$	6.28143	−	10.8798i	0.232965	−	0.403508i	0.958679	+	0.284489i	$0.0918238\pi$
$728$	5.47331			0.202855
$729$	25.5859	+	8.62320i	0.947627	+	0.319378i
$730$	−4.70367			−0.174091
$731$	−5.57559	+	9.65721i	−0.206221	+	0.357185i
$732$	−9.94923	−	0.539565i	−0.367734	−	0.0199429i
$733$	11.4519	+	19.8353i	0.422986	+	0.732634i	0.996230	−	0.0867513i	$-0.0276486\pi$
$733$	11.4519	+	19.8353i	0.422986	+	0.732634i	−0.573244	+	0.819385i	$0.694315\pi$
$734$	−4.19902	−	7.27292i	−0.154989	−	0.268448i
$735$	0.562952	−	0.863428i	0.0207648	−	0.0318480i
$736$	−1.58699	+	2.74875i	−0.0584974	+	0.101320i
$737$	−6.39601			−0.235600
$738$	1.66861	+	0.181518i	0.0614224	+	0.00668176i
$739$	42.0492			1.54681			0.773403	−	0.633915i	$-0.218553\pi$
$739$	42.0492			1.54681			0.773403	+	0.633915i	$0.218553\pi$
$740$	0.962268	−	1.66670i	0.0353737	−	0.0612690i
$741$	−0.917662	−	1.80914i	−0.0337112	−	0.0664605i
$742$	−5.66282	−	9.80829i	−0.207889	−	0.360074i
$743$	−15.2813	−	26.4679i	−0.560615	−	0.971014i	−0.997443	−	0.0714689i	$-0.977231\pi$
$743$	−15.2813	−	26.4679i	−0.560615	−	0.971014i	0.436827	−	0.899545i	$-0.356102\pi$
$744$	2.06186	+	4.06488i	0.0755914	+	0.149026i
$745$	−0.148442	+	0.257109i	−0.00543849	+	0.00941974i
$746$	−19.4547			−0.712288
$747$	−24.7321	+	33.7817i	−0.904901	+	1.23601i
$748$	−1.84996			−0.0676411
$749$	−2.68460	+	4.64986i	−0.0980931	+	0.169902i
$750$	−11.4627	+	17.5808i	−0.418557	+	0.641962i
$751$	−1.69182	−	2.93032i	−0.0617355	−	0.106929i	0.833506	−	0.552511i	$-0.186330\pi$
$751$	−1.69182	−	2.93032i	−0.0617355	−	0.106929i	−0.895241	+	0.445582i	$0.852997\pi$
$752$	−1.08331	−	1.87634i	−0.0395041	−	0.0684231i
$753$	−44.3140	−	2.40323i	−1.61489	−	0.0875787i
$754$	1.98094	−	3.43109i	0.0721417	−	0.124953i
$755$	−38.5450			−1.40280
$756$	−13.2635	−	2.17499i	−0.482389	−	0.0791036i
$757$	−17.5912			−0.639361			−0.319681	−	0.947525i	$-0.603576\pi$
$757$	−17.5912			−0.639361			−0.319681	+	0.947525i	$0.603576\pi$
$758$	−8.21018	+	14.2204i	−0.298207	+	0.516510i
$759$	−4.42113	−	0.239766i	−0.160477	−	0.00870296i
$760$	0.532615	+	0.922517i	0.0193200	+	0.0334632i
$761$	−7.51006	−	13.0078i	−0.272240	−	0.471533i	0.697195	−	0.716881i	$-0.254431\pi$
$761$	−7.51006	−	13.0078i	−0.272240	−	0.471533i	−0.969435	+	0.245348i	$0.921098\pi$
$762$	0.0146158	−	0.0224170i	0.000529475	−	0.000812082i
$763$	−10.5143	+	18.2112i	−0.380642	+	0.659291i
$764$	−13.5733			−0.491064
$765$	5.34997	+	12.1348i	0.193429	+	0.438736i
$766$	27.6797			1.00011
$767$	12.4411	−	21.5487i	0.449224	−	0.778078i
$768$	−0.783526	−	1.54470i	−0.0282731	−	0.0557394i
$769$	18.2269	+	31.5700i	0.657280	+	1.13844i	0.981317	+	0.192398i	$0.0616265\pi$
$769$	18.2269	+	31.5700i	0.657280	+	1.13844i	−0.324037	+	0.946044i	$0.605040\pi$
$770$	−2.00465	−	3.47216i	−0.0722427	−	0.125128i
$771$	−16.1860	−	31.9101i	−0.582924	−	1.14922i
$772$	13.3058	−	23.0464i	0.478888	−	0.829458i
$773$	6.77555			0.243699			0.121850	−	0.992549i	$-0.461117\pi$
$773$	6.77555			0.243699			0.121850	+	0.992549i	$0.461117\pi$
$774$	−5.87534	−	13.3265i	−0.211185	−	0.479011i
$775$	−3.41086			−0.122522
$776$	5.61514	−	9.72570i	0.201572	−	0.349132i
$777$	−2.44693	+	3.75298i	−0.0877832	+	0.134637i
$778$	−1.79780	−	3.11388i	−0.0644542	−	0.111638i
$779$	0.154837	+	0.268186i	0.00554762	+	0.00960876i
$780$	7.04305	+	0.381958i	0.252182	+	0.0136763i
$781$	−1.34179	+	2.32405i	−0.0480131	+	0.0831612i
$782$	−7.29057			−0.260710
$783$	−6.16388	+	7.52740i	−0.220279	+	0.269007i
$784$	−0.309216			−0.0110434
$785$	4.81197	−	8.33457i	0.171746	−	0.297474i
$786$	−3.24842	−	0.176168i	−0.115867	−	0.00628370i
$787$	12.6297	+	21.8753i	0.450200	+	0.779770i	0.998398	−	0.0565789i	$-0.0180192\pi$
$787$	12.6297	+	21.8753i	0.450200	+	0.779770i	−0.548198	+	0.836349i	$0.684686\pi$
$788$	1.68046	+	2.91064i	0.0598639	+	0.103687i
$789$	25.5033	−	39.1156i	0.907941	−	1.39255i
$790$	−8.12823	+	14.0785i	−0.289189	+	0.500891i
$791$	−14.4596			−0.514123
$792$	1.42729	−	1.94954i	0.0507164	−	0.0692738i
$793$	−12.1725			−0.432257
$794$	−12.1928	+	21.1185i	−0.432706	+	0.749469i
$795$	−6.60243	−	13.0165i	−0.234164	−	0.461647i
$796$	7.45555	+	12.9134i	0.264255	+	0.457703i
$797$	−15.8818	−	27.5081i	−0.562562	−	0.974385i	−0.997272	−	0.0738149i	$-0.976483\pi$
$797$	−15.8818	−	27.5081i	−0.562562	−	0.974385i	0.434710	−	0.900570i	$-0.356851\pi$
$798$	−1.12178	−	2.21156i	−0.0397107	−	0.0782884i
$799$	2.48833	−	4.30991i	0.0880308	−	0.152474i
$800$	1.29616			0.0458261
$801$	−2.03496	−	0.221371i	−0.0719018	−	0.00782174i
$802$	24.9287			0.880264
$803$	−0.984204	+	1.70469i	−0.0347318	+	0.0601573i
$804$	7.51256	−	11.5224i	0.264947	−	0.406363i
$805$	−7.90023	−	13.6836i	−0.278447	−	0.482284i
$806$	2.78411	+	4.82223i	0.0980662	+	0.169856i
$807$	46.3468	+	2.51348i	1.63149	+	0.0884785i
$808$	1.04540	−	1.81069i	0.0367772	−	0.0636999i
$809$	16.7917			0.590364			0.295182	−	0.955441i	$-0.404620\pi$
$809$	16.7917			0.590364			0.295182	+	0.955441i	$0.404620\pi$
$810$	−16.9157	−	3.72438i	−0.594356	−	0.130861i
$811$	4.99851			0.175522			0.0877608	−	0.996142i	$-0.472029\pi$
$811$	4.99851			0.175522			0.0877608	+	0.996142i	$0.472029\pi$
$812$	2.42158	−	4.19430i	0.0849808	−	0.147191i
$813$	−25.4939	−	1.38258i	−0.894111	−	0.0484893i
$814$	−0.402694	−	0.697486i	−0.0141144	−	0.0244469i
$815$	−7.98886	−	13.8371i	−0.279838	−	0.484693i
$816$	2.17290	−	3.33269i	0.0760667	−	0.116667i
$817$	1.34354	−	2.32709i	0.0470047	−	0.0814145i
$818$	−5.11093			−0.178700
$819$	−16.3236	−	1.77575i	−0.570394	−	0.0620496i
$820$	−1.07675			−0.0376017
$821$	−10.1758	+	17.6250i	−0.355138	+	0.615118i	−0.987142	−	0.159848i	$-0.948900\pi$
$821$	−10.1758	+	17.6250i	−0.355138	+	0.615118i	0.632003	+	0.774966i	$0.282233\pi$
$822$	9.00125	+	17.7457i	0.313955	+	0.618952i
$823$	5.51817	+	9.55775i	0.192351	+	0.333162i	0.946029	−	0.324082i	$-0.105055\pi$
$823$	5.51817	+	9.55775i	0.192351	+	0.333162i	−0.753678	+	0.657244i	$0.771722\pi$
$824$	−2.77854	−	4.81258i	−0.0967951	−	0.167654i
$825$	0.817931	+	1.61252i	0.0284767	+	0.0561409i
$826$	15.2085	−	26.3419i	0.529172	−	0.916553i
$827$	−18.5480			−0.644977			−0.322488	−	0.946573i	$-0.604519\pi$
$827$	−18.5480			−0.644977			−0.322488	+	0.946573i	$0.604519\pi$
$828$	5.62486	−	7.68302i	0.195477	−	0.267003i
$829$	35.0272			1.21654			0.608272	−	0.793729i	$-0.291863\pi$
$829$	35.0272			1.21654			0.608272	+	0.793729i	$0.291863\pi$
$830$	13.4292	−	23.2601i	0.466136	−	0.807371i
$831$	−6.89266	+	10.5716i	−0.239104	+	0.366725i
$832$	−1.05799	−	1.83249i	−0.0366792	−	0.0635303i
$833$	−0.355131	−	0.615105i	−0.0123046	−	0.0213121i
$834$	24.4030	+	1.32342i	0.845007	+	0.0458264i
$835$	−2.20205	+	3.81407i	−0.0762052	+	0.131991i
$836$	0.445782			0.0154177
$837$	−4.83049	−	12.7921i	−0.166966	−	0.442159i
$838$	−30.1332			−1.04094
$839$	1.01560	−	1.75907i	0.0350625	−	0.0607300i	−0.847962	−	0.530058i	$-0.822170\pi$
$839$	1.01560	−	1.75907i	0.0350625	−	0.0607300i	0.883024	+	0.469328i	$0.155504\pi$
$840$	8.60969	+	0.466920i	0.297063	+	0.0161103i
$841$	12.7471	+	22.0787i	0.439556	+	0.761334i
$842$	3.57359	+	6.18964i	0.123154	+	0.213309i
$843$	−9.06114	+	13.8975i	−0.312082	+	0.478656i
$844$	−11.1903	+	19.3821i	−0.385186	+	0.667161i
$845$	−16.4021			−0.564249
$846$	2.62210	+	5.94748i	0.0901498	+	0.204478i
$847$	26.7754			0.920013
$848$	−2.18924	+	3.79188i	−0.0751790	+	0.130214i
$849$	−24.8543	−	48.9995i	−0.852998	−	1.68166i
$850$	1.48862	+	2.57837i	0.0510593	+	0.0884374i
$851$	−1.58699	−	2.74875i	−0.0544014	−	0.0942261i
$852$	−2.61074	−	5.14700i	−0.0894426	−	0.176333i
$853$	−17.7314	+	30.7116i	−0.607110	+	1.05155i	0.384604	+	0.923082i	$0.374338\pi$
$853$	−17.7314	+	30.7116i	−0.607110	+	1.05155i	−0.991714	+	0.128464i	$0.958995\pi$
$854$	−14.8801			−0.509185
$855$	−1.28918	−	2.92412i	−0.0440889	−	0.100003i
$856$	2.07573			0.0709470
$857$	10.4853	−	18.1611i	0.358171	−	0.620371i	−0.629484	−	0.777013i	$-0.716734\pi$
$857$	10.4853	−	18.1611i	0.358171	−	0.620371i	0.987655	+	0.156642i	$0.0500670\pi$
$858$	1.61213	−	2.47260i	0.0550372	−	0.0844133i
$859$	20.7046	+	35.8614i	0.706432	+	1.22358i	0.966172	+	0.257897i	$0.0830295\pi$
$859$	20.7046	+	35.8614i	0.706432	+	1.22358i	−0.259741	+	0.965678i	$0.583637\pi$
$860$	4.67155	+	8.09136i	0.159298	+	0.275913i
$861$	2.50294	+	0.135739i	0.0852998	+	0.00462597i
$862$	0.969069	−	1.67848i	0.0330066	−	0.0571691i
$863$	1.99139			0.0677875			0.0338938	−	0.999425i	$-0.489209\pi$
$863$	1.99139			0.0677875			0.0338938	+	0.999425i	$0.489209\pi$
$864$	1.83564	+	4.86112i	0.0624496	+	0.165379i
$865$	19.5119			0.663423
$866$	−2.33334	+	4.04146i	−0.0792900	+	0.137334i
$867$	−20.2766	−	1.09964i	−0.688629	−	0.0373457i
$868$	3.40341	+	5.89487i	0.115519	+	0.200085i
$869$	3.40153	+	5.89163i	0.115389	+	0.199860i
$870$	3.40879	−	5.22823i	0.115569	−	0.177253i
$871$	8.40207	−	14.5528i	0.284693	−	0.493103i
$872$	8.12962			0.275304
$873$	−19.9020	+	27.1842i	−0.673580	+	0.920046i
$874$	1.75680			0.0594247
$875$	−15.6715	+	27.1438i	−0.529793	+	0.917629i
$876$	−1.91498	−	3.77532i	−0.0647011	−	0.127556i
$877$	16.0229	+	27.7525i	0.541056	+	0.937136i	0.998844	+	0.0480746i	$0.0153085\pi$
$877$	16.0229	+	27.7525i	0.541056	+	0.937136i	−0.457788	+	0.889061i	$0.651358\pi$
$878$	2.00860	+	3.47900i	0.0677870	+	0.117411i
$879$	12.7454	+	25.1272i	0.429892	+	0.847518i
$880$	−0.774999	+	1.34234i	−0.0261252	+	0.0452502i
$881$	13.1016			0.441405			0.220702	−	0.975341i	$-0.429165\pi$
$881$	13.1016			0.441405			0.220702	+	0.975341i	$0.429165\pi$
$882$	0.922208	+	0.100321i	0.0310523	+	0.00337799i
$883$	6.22984			0.209651			0.104825	−	0.994491i	$-0.466572\pi$
$883$	6.22984			0.209651			0.104825	+	0.994491i	$0.466572\pi$
$884$	2.43018	−	4.20919i	0.0817358	−	0.141571i
$885$	21.4086	−	32.8354i	0.719642	−	1.10375i
$886$	−1.35634	−	2.34925i	−0.0455672	−	0.0789247i
$887$	−14.6180	−	25.3191i	−0.490823	−	0.850131i	0.509121	−	0.860695i	$-0.329971\pi$
$887$	−14.6180	−	25.3191i	−0.490823	−	0.850131i	−0.999944	+	0.0105641i	$0.996637\pi$
$888$	1.72951	+	0.0937946i	0.0580385	+	0.00314754i
$889$	0.0199824	−	0.0346105i	0.000670188	−	0.00116080i
$890$	1.31315			0.0440170
$891$	−4.88925	+	5.35124i	−0.163796	+	0.179273i
$892$	−10.2375			−0.342776
$893$	−0.599610	+	1.03855i	−0.0200652	+	0.0347539i
$894$	−0.266798	−	0.0144690i	−0.00892308	−	0.000483915i
$895$	21.2056	+	36.7292i	0.708826	+	1.22772i
$896$	−1.29333	−	2.24011i	−0.0432070	−	0.0748368i
$897$	6.35332	−	9.74440i	0.212131	−	0.325356i
$898$	−1.22859	+	2.12797i	−0.0409984	+	0.0710114i
$899$	4.92715			0.164329
$900$	−3.86567	−	0.420522i	−0.128856	−	0.0140174i
$901$	−10.0573			−0.335057
$902$	−0.225301	+	0.390233i	−0.00750170	+	0.0129933i
$903$	−9.83913	−	19.3975i	−0.327426	−	0.645509i
$904$	2.79503	+	4.84113i	0.0929613	+	0.161014i
$905$	−0.000700590	−	0.00121346i	−2.32884e−5	−	4.03367e-5i
$906$	−15.6926	−	30.9375i	−0.521352	−	1.02783i
$907$	−13.2984	+	23.0335i	−0.441566	+	0.764815i	−0.997806	−	0.0662067i	$-0.978910\pi$
$907$	−13.2984	+	23.0335i	−0.441566	+	0.764815i	0.556240	+	0.831022i	$0.312244\pi$
$908$	7.48785			0.248493
$909$	−3.70527	+	5.06105i	−0.122896	+	0.167864i
$910$	10.5336			0.349185
$911$	−9.55675	+	16.5528i	−0.316629	+	0.548418i	−0.979782	−	0.200066i	$-0.935884\pi$
$911$	−9.55675	+	16.5528i	−0.316629	+	0.548418i	0.663153	+	0.748484i	$0.269218\pi$
$912$	−0.523601	+	0.803074i	−0.0173382	+	0.0265924i
$913$	−5.61992	−	9.73399i	−0.185992	−	0.322148i
$914$	20.8731	+	36.1533i	0.690422	+	1.19585i
$915$	−19.1477	−	1.03841i	−0.633002	−	0.0343289i
$916$	11.6632	−	20.2013i	0.385364	−	0.667469i
$917$	−4.85834			−0.160436
$918$	−7.56172	+	9.23445i	−0.249574	+	0.304782i
$919$	22.0210			0.726405			0.363202	−	0.931710i	$-0.381683\pi$
$919$	22.0210			0.726405			0.363202	+	0.931710i	$0.381683\pi$
$920$	−3.05423	+	5.29008i	−0.100695	+	0.174409i
$921$	−16.0233	−	0.868974i	−0.527986	−	0.0286337i
$922$	12.3417	+	21.3765i	0.406454	+	0.703999i
$923$	−3.52527	−	6.10595i	−0.116036	−	0.200980i
$924$	1.97073	−	3.02260i	0.0648322	−	0.0994364i
$925$	−0.648079	+	1.12251i	−0.0213087	+	0.0369078i
$926$	30.0779			0.988422
$927$	6.72536	+	15.2545i	0.220890	+	0.501024i
$928$	−1.87236			−0.0614634
$929$	13.7419	−	23.8017i	0.450857	−	0.780907i	−0.547583	−	0.836752i	$-0.684452\pi$
$929$	13.7419	−	23.8017i	0.450857	−	0.780907i	0.998439	+	0.0558447i	$0.0177852\pi$
$930$	3.96812	+	7.82302i	0.130120	+	0.256527i
$931$	0.0855755	+	0.148221i	0.00280462	+	0.00485775i
$932$	−8.68560	−	15.0439i	−0.284506	−	0.492779i
$933$	−26.1644	−	51.5823i	−0.856584	−	1.68873i
$934$	4.14727	−	7.18328i	0.135703	−	0.235044i
$935$	−3.56031			−0.116435
$936$	2.56083	+	5.80849i	0.0837033	+	0.189856i
$937$	31.3831			1.02524			0.512620	−	0.858615i	$-0.328675\pi$
$937$	31.3831			1.02524			0.512620	+	0.858615i	$0.328675\pi$
$938$	10.2710	−	17.7899i	0.335360	−	0.580861i
$939$	−24.0526	+	36.8907i	−0.784927	+	1.20388i
$940$	−2.08486	−	3.61109i	−0.0680007	−	0.117781i
$941$	−17.6011	−	30.4861i	−0.573781	−	0.993817i	−0.996173	−	0.0874043i	$-0.972143\pi$
$941$	−17.6011	−	30.4861i	−0.573781	−	0.993817i	0.422392	−	0.906413i	$-0.361191\pi$
$942$	8.64867	+	0.469034i	0.281789	+	0.0152819i
$943$	−0.887899	+	1.53789i	−0.0289140	+	0.0500804i
$944$	−11.7592			−0.382730
$945$	−25.5261	−	4.18585i	−0.830364	−	0.136166i
$946$	3.90993			0.127123
$947$	6.69370	−	11.5938i	0.217516	−	0.376749i	−0.736532	−	0.676403i	$-0.763538\pi$
$947$	6.69370	−	11.5938i	0.217516	−	0.376749i	0.954048	+	0.299654i	$0.0968712\pi$
$948$	−14.6091	−	0.792278i	−0.474481	−	0.0257320i
$949$	−2.58578	−	4.47871i	−0.0839381	−	0.145385i
$950$	−0.358712	−	0.621307i	−0.0116381	−	0.0201579i
$951$	−0.218261	+	0.334757i	−0.00707758	+	0.0108552i
$952$	2.97074	−	5.14548i	0.0962823	−	0.166766i
$953$	19.7162			0.638670			0.319335	−	0.947642i	$-0.396541\pi$
$953$	19.7162			0.638670			0.319335	+	0.947642i	$0.396541\pi$
$954$	7.75944	−	10.5987i	0.251221	−	0.343144i
$955$	−26.1223			−0.845297
$956$	−4.63463	+	8.02742i	−0.149895	+	0.259625i
$957$	−1.18154	−	2.32937i	−0.0381938	−	0.0752978i
$958$	−20.9811	−	36.3403i	−0.677868	−	1.17410i
$959$	14.8579	+	25.7347i	0.479787	+	0.831016i
$960$	−1.50792	−	2.97282i	−0.0486681	−	0.0959475i
$961$	12.0376	−	20.8497i	0.388309	−	0.672571i
$962$	2.11598			0.0682220
$963$	−6.19067	−	0.673444i	−0.199491	−	0.0217014i
$964$	−5.49555			−0.177000
$965$	25.6076	−	44.3536i	0.824337	−	1.42779i
$966$	7.76653	−	11.9119i	0.249884	−	0.383260i
$967$	−23.0512	−	39.9258i	−0.741276	−	1.28393i	−0.951914	−	0.306364i	$-0.900887\pi$
$967$	−23.0512	−	39.9258i	−0.741276	−	1.28393i	0.210638	−	0.977564i	$-0.432446\pi$
$968$	−5.17568	−	8.96453i	−0.166353	−	0.288131i
$969$	−2.19886	−	0.119248i	−0.0706374	−	0.00383080i
$970$	10.8065	−	18.7175i	0.346977	−	0.600982i
$971$	−40.5515			−1.30136			−0.650680	−	0.759352i	$-0.725516\pi$
$971$	−40.5515			−1.30136			−0.650680	+	0.759352i	$0.725516\pi$
$972$	−3.89748	−	15.0934i	−0.125012	−	0.484120i
$973$	36.4972			1.17005
$974$	−14.5080	+	25.1287i	−0.464868	+	0.805175i
$975$	−4.74343	−	0.257245i	−0.151911	−	0.00823845i
$976$	2.87631	+	4.98192i	0.0920686	+	0.159467i
$977$	−10.3797	−	17.9782i	−0.332076	−	0.575173i	0.650843	−	0.759213i	$-0.274416\pi$
$977$	−10.3797	−	17.9782i	−0.332076	−	0.575173i	−0.982919	+	0.184040i	$0.941082\pi$
$978$	7.85366	−	12.0455i	0.251132	−	0.385174i
$979$	0.274767	−	0.475910i	0.00878158	−	0.0152101i
$980$	−0.595098			−0.0190097
$981$	−24.2458	−	2.63755i	−0.774109	−	0.0842105i
$982$	34.7319			1.10834
$983$	−2.97915	+	5.16003i	−0.0950200	+	0.164579i	−0.909617	−	0.415448i	$-0.863625\pi$
$983$	−2.97915	+	5.16003i	−0.0950200	+	0.164579i	0.814597	+	0.580027i	$0.196958\pi$
$984$	−0.438371	−	0.864234i	−0.0139748	−	0.0275508i
$985$	3.23411	+	5.60163i	0.103047	+	0.178483i
$986$	−2.15039	−	3.72458i	−0.0684823	−	0.118615i
$987$	4.39110	+	8.65691i	0.139770	+	0.275553i
$988$	−0.585598	+	1.01428i	−0.0186303	+	0.0322687i
$989$	15.4088			0.489972
$990$	2.74686	−	3.75195i	0.0873011	−	0.119245i
$991$	34.9205			1.10928			0.554642	−	0.832089i	$-0.312855\pi$
$991$	34.9205			1.10928			0.554642	+	0.832089i	$0.312855\pi$
$992$	1.31576	−	2.27896i	0.0417753	−	0.0723569i
$993$	9.42782	−	14.4599i	0.299183	−	0.458872i
$994$	−4.30942	−	7.46414i	−0.136687	−	0.236748i
$995$	14.3485	+	24.8523i	0.454877	+	0.787870i
$996$	24.1367	+	1.30898i	0.764801	+	0.0414766i
$997$	−10.8969	+	18.8740i	−0.345109	+	0.597746i	−0.985374	−	0.170408i	$-0.945491\pi$
$997$	−10.8969	+	18.8740i	−0.345109	+	0.597746i	0.640265	+	0.768154i	$0.278825\pi$
$998$	3.94551			0.124893
$999$	−5.12767	−	0.840851i	−0.162232	−	0.0266033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.e.d.223.7	✓	14
3.2	odd	2		1998.2.e.d.667.5		14
9.2	odd	6		5994.2.a.v.1.3		7
9.4	even	3	inner	666.2.e.d.445.7	yes	14
9.5	odd	6		1998.2.e.d.1333.5		14
9.7	even	3		5994.2.a.u.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.e.d.223.7	✓	14	1.1	even	1	trivial
666.2.e.d.445.7	yes	14	9.4	even	3	inner
1998.2.e.d.667.5		14	3.2	odd	2
1998.2.e.d.1333.5		14	9.5	odd	6
5994.2.a.u.1.5		7	9.7	even	3
5994.2.a.v.1.3		7	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(1.72951 + 0.0937946i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.962268 - 1.66670i) q^{5} +(0.945983 - 1.45090i) q^{6} +(1.29333 - 2.24011i) q^{7} -1.00000 q^{8} +(2.98241 + 0.324437i) q^{9} -1.92454 q^{10} +(-0.402694 + 0.697486i) q^{11} +(-0.783526 - 1.54470i) q^{12} +(-1.05799 - 1.83249i) q^{13} +(-1.29333 - 2.24011i) q^{14} +(-1.50792 - 2.97282i) q^{15} +(-0.500000 + 0.866025i) q^{16} -2.29698 q^{17} +(1.77217 - 2.42062i) q^{18} +0.553500 q^{19} +(-0.962268 + 1.66670i) q^{20} +(2.44693 - 3.75298i) q^{21} +(0.402694 + 0.697486i) q^{22} +(1.58699 + 2.74875i) q^{23} +(-1.72951 - 0.0937946i) q^{24} +(0.648079 - 1.12251i) q^{25} -2.11598 q^{26} +(5.12767 + 0.840851i) q^{27} -2.58665 q^{28} +(-0.936182 + 1.62151i) q^{29} +(-3.32850 - 0.180511i) q^{30} +(-1.31576 - 2.27896i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.761883 + 1.16854i) q^{33} +(-1.14849 + 1.98924i) q^{34} -4.97811 q^{35} +(-1.21023 - 2.74506i) q^{36} -1.00000 q^{37} +(0.276750 - 0.479345i) q^{38} +(-1.65793 - 3.26855i) q^{39} +(0.962268 + 1.66670i) q^{40} +(0.279742 + 0.484528i) q^{41} +(-2.02671 - 3.99560i) q^{42} +(2.42736 - 4.20431i) q^{43} +0.805387 q^{44} +(-2.32914 - 5.28296i) q^{45} +3.17399 q^{46} +(-1.08331 + 1.87634i) q^{47} +(-0.945983 + 1.45090i) q^{48} +(0.154608 + 0.267789i) q^{49} +(-0.648079 - 1.12251i) q^{50} +(-3.97264 - 0.215444i) q^{51} +(-1.05799 + 1.83249i) q^{52} +4.37849 q^{53} +(3.29203 - 4.02026i) q^{54} +1.55000 q^{55} +(-1.29333 + 2.24011i) q^{56} +(0.957283 + 0.0519153i) q^{57} +(0.936182 + 1.62151i) q^{58} +(5.87961 + 10.1838i) q^{59} +(-1.82058 + 2.79231i) q^{60} +(2.87631 - 4.98192i) q^{61} -2.63151 q^{62} +(4.58400 - 6.26131i) q^{63} +1.00000 q^{64} +(-2.03614 + 3.52670i) q^{65} +(0.631042 + 1.24408i) q^{66} +(3.97077 + 6.87757i) q^{67} +(1.14849 + 1.98924i) q^{68} +(2.48690 + 4.90285i) q^{69} +(-2.48906 + 4.31117i) q^{70} +3.33204 q^{71} +(-2.98241 - 0.324437i) q^{72} +2.44405 q^{73} +(-0.500000 + 0.866025i) q^{74} +(1.22614 - 1.88060i) q^{75} +(-0.276750 - 0.479345i) q^{76} +(1.04163 + 1.80416i) q^{77} +(-3.65961 - 0.198468i) q^{78} +(4.22347 - 7.31527i) q^{79} +1.92454 q^{80} +(8.78948 + 1.93521i) q^{81} +0.559485 q^{82} +(-6.97791 + 12.0861i) q^{83} +(-4.47364 - 0.242614i) q^{84} +(2.21031 + 3.82837i) q^{85} +(-2.42736 - 4.20431i) q^{86} +(-1.77122 + 2.71662i) q^{87} +(0.402694 - 0.697486i) q^{88} -0.682322 q^{89} +(-5.73975 - 0.624391i) q^{90} -5.47331 q^{91} +(1.58699 - 2.74875i) q^{92} +(-2.06186 - 4.06488i) q^{93} +(1.08331 + 1.87634i) q^{94} +(-0.532615 - 0.922517i) q^{95} +(0.783526 + 1.54470i) q^{96} +(-5.61514 + 9.72570i) q^{97} +0.309216 q^{98} +(-1.42729 + 1.94954i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 7 q^{2} - q^{3} - 7 q^{4} - 3 q^{5} - 2 q^{6} + 3 q^{7} - 14 q^{8} - q^{9} - 6 q^{10} - q^{11} - q^{12} + 9 q^{13} - 3 q^{14} - q^{15} - 7 q^{16} + 18 q^{17} + q^{18} - 26 q^{19} - 3 q^{20}+ \cdots + 4 q^{99}+O(q^{100}) \) 14 * q + 7 * q^2 - q^3 - 7 * q^4 - 3 * q^5 - 2 * q^6 + 3 * q^7 - 14 * q^8 - q^9 - 6 * q^10 - q^11 - q^12 + 9 * q^13 - 3 * q^14 - q^15 - 7 * q^16 + 18 * q^17 + q^18 - 26 * q^19 - 3 * q^20 - 8 * q^21 + q^22 - 4 * q^23 + q^24 + 2 * q^25 + 18 * q^26 + 29 * q^27 - 6 * q^28 - 3 * q^29 + 10 * q^30 + 19 * q^31 + 7 * q^32 - 17 * q^33 + 9 * q^34 - 6 * q^35 + 2 * q^36 - 14 * q^37 - 13 * q^38 - 18 * q^39 + 3 * q^40 - 24 * q^41 - 16 * q^42 + q^43 + 2 * q^44 + 23 * q^45 - 8 * q^46 - 12 * q^47 + 2 * q^48 + 8 * q^49 - 2 * q^50 - 30 * q^51 + 9 * q^52 + 8 * q^53 + q^54 - 50 * q^55 - 3 * q^56 + 14 * q^57 + 3 * q^58 + 5 * q^59 + 11 * q^60 + 39 * q^61 + 38 * q^62 + 49 * q^63 + 14 * q^64 - 8 * q^65 + 2 * q^66 + 15 * q^67 - 9 * q^68 - 62 * q^69 - 3 * q^70 - 6 * q^71 + q^72 - 14 * q^73 - 7 * q^74 + 13 * q^75 + 13 * q^76 - 5 * q^77 + 3 * q^78 + 18 * q^79 + 6 * q^80 + 35 * q^81 - 48 * q^82 - q^83 - 8 * q^84 + 3 * q^85 - q^86 - 28 * q^87 + q^88 + 26 * q^89 + 13 * q^90 - 46 * q^91 - 4 * q^92 + 13 * q^93 + 12 * q^94 - 20 * q^95 + q^96 + 7 * q^97 + 16 * q^98 + 4 * q^99

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