LMFDB - Embedded newform 342.2.h.e.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(121,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("342.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.h (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
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			277.1
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	342.277
Dual form			342.2.h.e.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(1.72474 - 0.158919i) q^{6} +(-0.724745 + 1.25529i) q^{7} +1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(1.72474 - 0.158919i) q^{6} +(-0.724745 + 1.25529i) q^{7} +1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(1.50000 + 2.59808i) q^{10} +(2.72474 - 4.71940i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(2.00000 - 3.46410i) q^{13} +1.44949 q^{14} +(2.17423 - 4.71940i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.00000 + 2.82843i) q^{18} +(1.00000 + 4.24264i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.44949 - 2.04989i) q^{21} -5.44949 q^{22} +(2.44949 - 4.24264i) q^{23} +(-0.724745 + 1.57313i) q^{24} +4.00000 q^{25} -4.00000 q^{26} +(5.00000 - 1.41421i) q^{27} +(-0.724745 - 1.25529i) q^{28} -7.89898 q^{29} +(-5.17423 + 0.476756i) q^{30} +(-0.724745 - 1.25529i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.44949 + 7.70674i) q^{33} -3.00000 q^{34} +(2.17423 - 3.76588i) q^{35} +(2.94949 - 0.548188i) q^{36} +0.898979 q^{37} +(3.17423 - 2.98735i) q^{38} +(4.00000 + 5.65685i) q^{39} -3.00000 q^{40} -1.89898 q^{41} +(-1.05051 + 2.28024i) q^{42} +(-5.89898 - 10.2173i) q^{43} +(2.72474 + 4.71940i) q^{44} +(5.84847 + 6.84072i) q^{45} -4.89898 q^{46} -6.55051 q^{47} +(1.72474 - 0.158919i) q^{48} +(2.44949 + 4.24264i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(3.00000 + 4.24264i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-3.94949 - 6.84072i) q^{53} +(-3.72474 - 3.62302i) q^{54} +(-8.17423 + 14.1582i) q^{55} +(-0.724745 + 1.25529i) q^{56} +(-7.39898 - 1.50170i) q^{57} +(3.94949 + 6.84072i) q^{58} -0.550510 q^{59} +(3.00000 + 4.24264i) q^{60} -5.89898 q^{61} +(-0.724745 + 1.25529i) q^{62} +(4.27526 - 0.794593i) q^{63} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(3.94949 - 8.57277i) q^{66} +(6.89898 - 11.9494i) q^{67} +(1.50000 + 2.59808i) q^{68} +(4.89898 + 6.92820i) q^{69} -4.34847 q^{70} +(5.72474 - 9.91555i) q^{71} +(-1.94949 - 2.28024i) q^{72} +(2.39898 - 4.15515i) q^{73} +(-0.449490 - 0.778539i) q^{74} +(-2.89898 + 6.29253i) q^{75} +(-4.17423 - 1.25529i) q^{76} +(3.94949 + 6.84072i) q^{77} +(2.89898 - 6.29253i) q^{78} +(5.00000 + 8.66025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(0.949490 + 1.64456i) q^{82} +(0.825765 - 1.43027i) q^{83} +(2.50000 - 0.230351i) q^{84} +(-4.50000 + 7.79423i) q^{85} +(-5.89898 + 10.2173i) q^{86} +(5.72474 - 12.4261i) q^{87} +(2.72474 - 4.71940i) q^{88} +(4.50000 + 7.79423i) q^{89} +(3.00000 - 8.48528i) q^{90} +(2.89898 + 5.02118i) q^{91} +(2.44949 + 4.24264i) q^{92} +(2.50000 - 0.230351i) q^{93} +(3.27526 + 5.67291i) q^{94} +(-3.00000 - 12.7279i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(2.00000 + 3.46410i) q^{97} +(2.44949 - 4.24264i) q^{98} +(-16.0732 + 2.98735i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 6 q^{20} + 4 q^{21} - 12 q^{22} + 2 q^{24} + 16 q^{25} - 16 q^{26} + 20 q^{27} + 2 q^{28} - 12 q^{29} - 6 q^{30} + 2 q^{31} - 2 q^{32} + 12 q^{33} - 12 q^{34} - 6 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 12 q^{40} + 12 q^{41} - 14 q^{42} - 4 q^{43} + 6 q^{44} - 6 q^{45} - 36 q^{47} + 2 q^{48} - 8 q^{50} + 12 q^{51} + 8 q^{52} - 6 q^{53} - 10 q^{54} - 18 q^{55} + 2 q^{56} - 10 q^{57} + 6 q^{58} - 12 q^{59} + 12 q^{60} - 4 q^{61} + 2 q^{62} + 22 q^{63} + 4 q^{64} - 24 q^{65} + 6 q^{66} + 8 q^{67} + 6 q^{68} + 12 q^{70} + 18 q^{71} + 2 q^{72} - 10 q^{73} + 8 q^{74} + 8 q^{75} - 2 q^{76} + 6 q^{77} - 8 q^{78} + 20 q^{79} + 6 q^{80} + 14 q^{81} - 6 q^{82} + 18 q^{83} + 10 q^{84} - 18 q^{85} - 4 q^{86} + 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{90} - 8 q^{91} + 10 q^{93} + 18 q^{94} - 12 q^{95} - 4 q^{96} + 8 q^{97} - 30 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 6 * q^20 + 4 * q^21 - 12 * q^22 + 2 * q^24 + 16 * q^25 - 16 * q^26 + 20 * q^27 + 2 * q^28 - 12 * q^29 - 6 * q^30 + 2 * q^31 - 2 * q^32 + 12 * q^33 - 12 * q^34 - 6 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 12 * q^40 + 12 * q^41 - 14 * q^42 - 4 * q^43 + 6 * q^44 - 6 * q^45 - 36 * q^47 + 2 * q^48 - 8 * q^50 + 12 * q^51 + 8 * q^52 - 6 * q^53 - 10 * q^54 - 18 * q^55 + 2 * q^56 - 10 * q^57 + 6 * q^58 - 12 * q^59 + 12 * q^60 - 4 * q^61 + 2 * q^62 + 22 * q^63 + 4 * q^64 - 24 * q^65 + 6 * q^66 + 8 * q^67 + 6 * q^68 + 12 * q^70 + 18 * q^71 + 2 * q^72 - 10 * q^73 + 8 * q^74 + 8 * q^75 - 2 * q^76 + 6 * q^77 - 8 * q^78 + 20 * q^79 + 6 * q^80 + 14 * q^81 - 6 * q^82 + 18 * q^83 + 10 * q^84 - 18 * q^85 - 4 * q^86 + 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^90 - 8 * q^91 + 10 * q^93 + 18 * q^94 - 12 * q^95 - 4 * q^96 + 8 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$3$	−0.724745	+	1.57313i	−0.418432	+	0.908248i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.00000			−1.34164			−0.670820	−	0.741620i	$-0.734058\pi$
$5$	−3.00000			−1.34164			−0.670820	+	0.741620i	$0.734058\pi$
$6$	1.72474	−	0.158919i	0.704124	−	0.0648783i
$7$	−0.724745	+	1.25529i	−0.273928	+	0.474457i	−0.969864	−	0.243647i	$-0.921656\pi$
$7$	−0.724745	+	1.25529i	−0.273928	+	0.474457i	0.695936	+	0.718104i	$0.254990\pi$
$8$	1.00000			0.353553
$9$	−1.94949	−	2.28024i	−0.649830	−	0.760080i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	2.72474	−	4.71940i	0.821541	−	1.42295i	−0.0829925	−	0.996550i	$-0.526448\pi$
$11$	2.72474	−	4.71940i	0.821541	−	1.42295i	0.904534	−	0.426401i	$-0.140219\pi$
$12$	−1.00000	−	1.41421i	−0.288675	−	0.408248i
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	1.44949			0.387392
$15$	2.17423	−	4.71940i	0.561385	−	1.21854i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$	−1.00000	+	2.82843i	−0.235702	+	0.666667i
$19$	1.00000	+	4.24264i	0.229416	+	0.973329i
$19$	1.00000	+	4.24264i	0.229416	+	0.973329i
$20$	1.50000	−	2.59808i	0.335410	−	0.580948i
$21$	−1.44949	−	2.04989i	−0.316305	−	0.447322i
$22$	−5.44949			−1.16184
$23$	2.44949	−	4.24264i	0.510754	−	0.884652i	−0.489168	−	0.872189i	$-0.662700\pi$
$23$	2.44949	−	4.24264i	0.510754	−	0.884652i	0.999922	−	0.0124624i	$-0.00396701\pi$
$24$	−0.724745	+	1.57313i	−0.147938	+	0.321114i
$25$	4.00000			0.800000
$26$	−4.00000			−0.784465
$27$	5.00000	−	1.41421i	0.962250	−	0.272166i
$28$	−0.724745	−	1.25529i	−0.136964	−	0.237228i
$29$	−7.89898			−1.46680			−0.733402	−	0.679795i	$-0.762069\pi$
$29$	−7.89898			−1.46680			−0.733402	+	0.679795i	$0.762069\pi$
$30$	−5.17423	+	0.476756i	−0.944682	+	0.0870433i
$31$	−0.724745	−	1.25529i	−0.130168	−	0.225458i	0.793573	−	0.608475i	$-0.208218\pi$
$31$	−0.724745	−	1.25529i	−0.130168	−	0.225458i	−0.923741	+	0.383017i	$0.874885\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.44949	+	7.70674i	0.948634	+	1.34157i
$34$	−3.00000			−0.514496
$35$	2.17423	−	3.76588i	0.367513	−	0.636551i
$36$	2.94949	−	0.548188i	0.491582	−	0.0913647i
$37$	0.898979			0.147791			0.0738957	−	0.997266i	$-0.476457\pi$
$37$	0.898979			0.147791			0.0738957	+	0.997266i	$0.476457\pi$
$38$	3.17423	−	2.98735i	0.514929	−	0.484611i
$39$	4.00000	+	5.65685i	0.640513	+	0.905822i
$40$	−3.00000			−0.474342
$41$	−1.89898			−0.296571			−0.148285	−	0.988945i	$-0.547375\pi$
$41$	−1.89898			−0.296571			−0.148285	+	0.988945i	$0.547375\pi$
$42$	−1.05051	+	2.28024i	−0.162097	+	0.351849i
$43$	−5.89898	−	10.2173i	−0.899586	−	1.55813i	−0.828024	−	0.560692i	$-0.810535\pi$
$43$	−5.89898	−	10.2173i	−0.899586	−	1.55813i	−0.0715617	−	0.997436i	$-0.522798\pi$
$44$	2.72474	+	4.71940i	0.410771	+	0.711476i
$45$	5.84847	+	6.84072i	0.871838	+	1.01975i
$46$	−4.89898			−0.722315
$47$	−6.55051			−0.955490			−0.477745	−	0.878499i	$-0.658546\pi$
$47$	−6.55051			−0.955490			−0.477745	+	0.878499i	$0.658546\pi$
$48$	1.72474	−	0.158919i	0.248945	−	0.0229379i
$49$	2.44949	+	4.24264i	0.349927	+	0.606092i
$50$	−2.00000	−	3.46410i	−0.282843	−	0.489898i
$51$	3.00000	+	4.24264i	0.420084	+	0.594089i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	−3.94949	−	6.84072i	−0.542504	−	0.939645i	−0.998759	−	0.0497958i	$-0.984143\pi$
$53$	−3.94949	−	6.84072i	−0.542504	−	0.939645i	0.456255	−	0.889849i	$-0.349190\pi$
$54$	−3.72474	−	3.62302i	−0.506874	−	0.493031i
$55$	−8.17423	+	14.1582i	−1.10221	+	1.90909i
$56$	−0.724745	+	1.25529i	−0.0968481	+	0.167746i
$57$	−7.39898	−	1.50170i	−0.980019	−	0.198905i
$58$	3.94949	+	6.84072i	0.518593	+	0.898230i
$59$	−0.550510			−0.0716703			−0.0358352	−	0.999358i	$-0.511409\pi$
$59$	−0.550510			−0.0716703			−0.0358352	+	0.999358i	$0.511409\pi$
$60$	3.00000	+	4.24264i	0.387298	+	0.547723i
$61$	−5.89898			−0.755287			−0.377643	−	0.925951i	$-0.623265\pi$
$61$	−5.89898			−0.755287			−0.377643	+	0.925951i	$0.623265\pi$
$62$	−0.724745	+	1.25529i	−0.0920427	+	0.159423i
$63$	4.27526	−	0.794593i	0.538632	−	0.100109i
$64$	1.00000			0.125000
$65$	−6.00000	+	10.3923i	−0.744208	+	1.28901i
$66$	3.94949	−	8.57277i	0.486149	−	1.05523i
$67$	6.89898	−	11.9494i	0.842844	−	1.45985i	−0.0446356	−	0.999003i	$-0.514213\pi$
$67$	6.89898	−	11.9494i	0.842844	−	1.45985i	0.887480	−	0.460846i	$-0.152454\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	4.89898	+	6.92820i	0.589768	+	0.834058i
$70$	−4.34847			−0.519741
$71$	5.72474	−	9.91555i	0.679402	−	1.17676i	−0.295759	−	0.955263i	$-0.595573\pi$
$71$	5.72474	−	9.91555i	0.679402	−	1.17676i	0.975161	−	0.221497i	$-0.0710942\pi$
$72$	−1.94949	−	2.28024i	−0.229750	−	0.268729i
$73$	2.39898	−	4.15515i	0.280779	−	0.486324i	−0.690798	−	0.723048i	$-0.742740\pi$
$73$	2.39898	−	4.15515i	0.280779	−	0.486324i	0.971577	+	0.236724i	$0.0760738\pi$
$74$	−0.449490	−	0.778539i	−0.0522521	−	0.0905033i
$75$	−2.89898	+	6.29253i	−0.334745	+	0.726599i
$76$	−4.17423	−	1.25529i	−0.478818	−	0.143992i
$77$	3.94949	+	6.84072i	0.450086	+	0.779572i
$78$	2.89898	−	6.29253i	0.328245	−	0.712489i
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	1.50000	+	2.59808i	0.167705	+	0.290474i
$81$	−1.39898	+	8.89060i	−0.155442	+	0.987845i
$82$	0.949490	+	1.64456i	0.104854	+	0.181612i
$83$	0.825765	−	1.43027i	0.0906395	−	0.156992i	−0.817141	−	0.576438i	$-0.804442\pi$
$83$	0.825765	−	1.43027i	0.0906395	−	0.156992i	0.907780	+	0.419446i	$0.137776\pi$
$84$	2.50000	−	0.230351i	0.272772	−	0.0251333i
$85$	−4.50000	+	7.79423i	−0.488094	+	0.845403i
$86$	−5.89898	+	10.2173i	−0.636103	+	1.10176i
$87$	5.72474	−	12.4261i	0.613757	−	1.33222i
$88$	2.72474	−	4.71940i	0.290459	−	0.503089i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$	3.00000	−	8.48528i	0.316228	−	0.894427i
$91$	2.89898	+	5.02118i	0.303896	+	0.526363i
$92$	2.44949	+	4.24264i	0.255377	+	0.442326i
$93$	2.50000	−	0.230351i	0.259238	−	0.0238863i
$94$	3.27526	+	5.67291i	0.337817	+	0.585116i
$95$	−3.00000	−	12.7279i	−0.307794	−	1.30586i
$96$	−1.00000	−	1.41421i	−0.102062	−	0.144338i
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	0.949516	−	0.313719i	$-0.101575\pi$
$97$	2.00000	+	3.46410i	0.203069	+	0.351726i	−0.746447	+	0.665445i	$0.768242\pi$
$98$	2.44949	−	4.24264i	0.247436	−	0.428571i
$99$	−16.0732	+	2.98735i	−1.61542	+	0.300240i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	11.6969			1.16389			0.581944	−	0.813229i	$-0.302292\pi$
$101$	11.6969			1.16389			0.581944	+	0.813229i	$0.302292\pi$
$102$	2.17423	−	4.71940i	0.215281	−	0.467290i
$103$	−5.62372	−	9.74058i	−0.554122	−	0.959768i	−0.997971	−	0.0636660i	$-0.979721\pi$
$103$	−5.62372	−	9.74058i	−0.554122	−	0.959768i	0.443849	−	0.896101i	$-0.353613\pi$
$104$	2.00000	−	3.46410i	0.196116	−	0.339683i
$105$	4.34847	+	6.14966i	0.424367	+	0.600146i
$106$	−3.94949	+	6.84072i	−0.383608	+	0.664429i
$107$	4.89898			0.473602			0.236801	−	0.971558i	$-0.423901\pi$
$107$	4.89898			0.473602			0.236801	+	0.971558i	$0.423901\pi$
$108$	−1.27526	+	5.03723i	−0.122711	+	0.484708i
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	−0.841086	−	0.540901i	$-0.818083\pi$
$109$	0.500000	−	0.866025i	0.0478913	−	0.0829502i	0.888977	+	0.457951i	$0.151417\pi$
$110$	16.3485			1.55877
$111$	−0.651531	+	1.41421i	−0.0618406	+	0.134231i
$112$	1.44949			0.136964
$113$	6.94949	+	12.0369i	0.653753	+	1.13233i	0.982205	+	0.187813i	$0.0601398\pi$
$113$	6.94949	+	12.0369i	0.653753	+	1.13233i	−0.328452	+	0.944521i	$0.606527\pi$
$114$	2.39898	+	7.15855i	0.224685	+	0.670460i
$115$	−7.34847	+	12.7279i	−0.685248	+	1.18688i
$116$	3.94949	−	6.84072i	0.366701	−	0.635145i
$117$	−11.7980	+	2.19275i	−1.09072	+	0.202720i
$118$	0.275255	+	0.476756i	0.0253393	+	0.0438889i
$119$	2.17423	+	3.76588i	0.199312	+	0.345218i
$120$	2.17423	−	4.71940i	0.198480	−	0.430820i
$121$	−9.34847	−	16.1920i	−0.849861	−	1.47200i
$122$	2.94949	+	5.10867i	0.267034	+	0.462517i
$123$	1.37628	−	2.98735i	0.124095	−	0.269360i
$124$	1.44949			0.130168
$125$	3.00000			0.268328
$126$	−2.82577	−	3.30518i	−0.251739	−	0.294449i
$127$	1.17423	+	2.03383i	0.104196	+	0.180474i	0.913410	−	0.407042i	$-0.133440\pi$
$127$	1.17423	+	2.03383i	0.104196	+	0.180474i	−0.809213	+	0.587515i	$0.800106\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	20.3485	−	1.87492i	1.79158	−	0.165077i
$130$	12.0000			1.05247
$131$	−14.1464			−1.23598			−0.617990	−	0.786186i	$-0.712053\pi$
$131$	−14.1464			−1.23598			−0.617990	+	0.786186i	$0.712053\pi$
$132$	−9.39898	+	0.866025i	−0.818076	+	0.0753778i
$133$	−6.05051	−	1.81954i	−0.524646	−	0.157774i
$134$	−13.7980			−1.19196
$135$	−15.0000	+	4.24264i	−1.29099	+	0.365148i
$136$	1.50000	−	2.59808i	0.128624	−	0.222783i
$137$	−17.6969			−1.51195			−0.755976	−	0.654600i	$-0.772837\pi$
$137$	−17.6969			−1.51195			−0.755976	+	0.654600i	$0.772837\pi$
$138$	3.55051	−	7.70674i	0.302240	−	0.656041i
$139$	10.4495	−	18.0990i	0.886314	−	1.53514i	0.0421142	−	0.999113i	$-0.486591\pi$
$139$	10.4495	−	18.0990i	0.886314	−	1.53514i	0.844200	−	0.536028i	$-0.180076\pi$
$140$	2.17423	+	3.76588i	0.183756	+	0.318275i
$141$	4.74745	−	10.3048i	0.399807	−	0.867822i
$142$	−11.4495			−0.960820
$143$	−10.8990	−	18.8776i	−0.911418	−	1.57862i
$144$	−1.00000	+	2.82843i	−0.0833333	+	0.235702i
$145$	23.6969			1.96792
$146$	−4.79796			−0.397082
$147$	−8.44949	+	0.778539i	−0.696902	+	0.0642128i
$148$	−0.449490	+	0.778539i	−0.0369478	+	0.0639955i
$149$	−18.7980			−1.53999			−0.769994	−	0.638051i	$-0.779741\pi$
$149$	−18.7980			−1.53999			−0.769994	+	0.638051i	$0.779741\pi$
$150$	6.89898	−	0.635674i	0.563299	−	0.0519026i
$151$	2.82577	−	4.89437i	0.229958	−	0.398298i	−0.727838	−	0.685749i	$-0.759475\pi$
$151$	2.82577	−	4.89437i	0.229958	−	0.398298i	0.957795	+	0.287451i	$0.0928079\pi$
$152$	1.00000	+	4.24264i	0.0811107	+	0.344124i
$153$	−8.84847	+	1.64456i	−0.715356	+	0.132955i
$154$	3.94949	−	6.84072i	0.318259	−	0.551241i
$155$	2.17423	+	3.76588i	0.174639	+	0.302483i
$156$	−6.89898	+	0.635674i	−0.552360	+	0.0508947i
$157$	−11.8990			−0.949642			−0.474821	−	0.880082i	$-0.657487\pi$
$157$	−11.8990			−0.949642			−0.474821	+	0.880082i	$0.657487\pi$
$158$	5.00000	−	8.66025i	0.397779	−	0.688973i
$159$	13.6237	−	1.25529i	1.08043	−	0.0995514i
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$	3.55051	+	6.14966i	0.279819	+	0.484661i
$162$	8.39898	−	3.23375i	0.659886	−	0.254067i
$163$	−11.1010			−0.869499			−0.434750	−	0.900551i	$-0.643163\pi$
$163$	−11.1010			−0.869499			−0.434750	+	0.900551i	$0.643163\pi$
$164$	0.949490	−	1.64456i	0.0741427	−	0.128419i
$165$	−16.3485	−	23.1202i	−1.27273	−	1.79991i
$166$	−1.65153			−0.128184
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$	−1.44949	−	2.04989i	−0.111831	−	0.158152i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	9.00000			0.690268
$171$	7.72474	−	10.5512i	0.590726	−	0.806872i
$172$	11.7980			0.899586
$173$	8.44949	+	14.6349i	0.642403	+	1.11267i	0.984895	+	0.173154i	$0.0553957\pi$
$173$	8.44949	+	14.6349i	0.642403	+	1.11267i	−0.342492	+	0.939521i	$0.611271\pi$
$174$	−13.6237	+	1.25529i	−1.03281	+	0.0951637i
$175$	−2.89898	+	5.02118i	−0.219142	+	0.379566i
$176$	−5.44949			−0.410771
$177$	0.398979	−	0.866025i	0.0299891	−	0.0650945i
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−7.10102			−0.530755			−0.265378	−	0.964145i	$-0.585497\pi$
$179$	−7.10102			−0.530755			−0.265378	+	0.964145i	$0.585497\pi$
$180$	−8.84847	+	1.64456i	−0.659526	+	0.122579i
$181$	−5.50000	−	9.52628i	−0.408812	−	0.708083i	0.585945	−	0.810351i	$-0.300723\pi$
$181$	−5.50000	−	9.52628i	−0.408812	−	0.708083i	−0.994757	+	0.102268i	$0.967390\pi$
$182$	2.89898	−	5.02118i	0.214887	−	0.372195i
$183$	4.27526	−	9.27987i	0.316036	−	0.685988i
$184$	2.44949	−	4.24264i	0.180579	−	0.312772i
$185$	−2.69694			−0.198283
$186$	−1.44949	−	2.04989i	−0.106282	−	0.150305i
$187$	−8.17423	−	14.1582i	−0.597759	−	1.03535i
$188$	3.27526	−	5.67291i	0.238873	−	0.413739i
$189$	−1.84847	+	7.30142i	−0.134456	+	0.531100i
$190$	−9.52270	+	8.96204i	−0.690850	+	0.650175i
$191$	−10.6237	+	18.4008i	−0.768706	+	1.33144i	0.169559	+	0.985520i	$0.445766\pi$
$191$	−10.6237	+	18.4008i	−0.768706	+	1.33144i	−0.938265	+	0.345917i	$0.887568\pi$
$192$	−0.724745	+	1.57313i	−0.0523040	+	0.113531i
$193$	18.5959			1.33856			0.669282	−	0.743009i	$-0.266602\pi$
$193$	18.5959			1.33856			0.669282	+	0.743009i	$0.266602\pi$
$194$	2.00000	−	3.46410i	0.143592	−	0.248708i
$195$	−12.0000	−	16.9706i	−0.859338	−	1.21529i
$196$	−4.89898			−0.349927
$197$	−21.7980			−1.55304			−0.776520	−	0.630092i	$-0.783017\pi$
$197$	−21.7980			−1.55304			−0.776520	+	0.630092i	$0.783017\pi$
$198$	10.6237	+	12.4261i	0.754995	+	0.883087i
$199$	7.17423	+	12.4261i	0.508568	+	0.880866i	0.999951	+	0.00992190i	$0.00315829\pi$
$199$	7.17423	+	12.4261i	0.508568	+	0.880866i	−0.491383	+	0.870944i	$0.663508\pi$
$200$	4.00000			0.282843
$201$	13.7980	+	19.5133i	0.973233	+	1.37636i
$202$	−5.84847	−	10.1298i	−0.411497	−	0.712733i
$203$	5.72474	−	9.91555i	0.401798	−	0.695935i
$204$	−5.17423	+	0.476756i	−0.362269	+	0.0333796i
$205$	5.69694			0.397891
$206$	−5.62372	+	9.74058i	−0.391823	+	0.678658i
$207$	−14.4495	+	2.68556i	−1.00431	+	0.186660i
$208$	−4.00000			−0.277350
$209$	22.7474	+	6.84072i	1.57347	+	0.473182i
$210$	3.15153	−	6.84072i	0.217476	−	0.472054i
$211$	21.0454			1.44883			0.724413	−	0.689366i	$-0.242111\pi$
$211$	21.0454			1.44883			0.724413	+	0.689366i	$0.242111\pi$
$212$	7.89898			0.542504
$213$	11.4495	+	16.1920i	0.784506	+	1.10946i
$214$	−2.44949	−	4.24264i	−0.167444	−	0.290021i
$215$	17.6969	+	30.6520i	1.20692	+	2.09045i
$216$	5.00000	−	1.41421i	0.340207	−	0.0962250i
$217$	2.10102			0.142627
$218$	−1.00000			−0.0677285
$219$	4.79796	+	6.78534i	0.324216	+	0.458511i
$220$	−8.17423	−	14.1582i	−0.551107	−	0.954545i
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	1.55051	−	0.142865i	0.104063	−	0.00958844i
$223$	4.44949	+	7.70674i	0.297960	+	0.516082i	0.975669	−	0.219248i	$-0.0703605\pi$
$223$	4.44949	+	7.70674i	0.297960	+	0.516082i	−0.677709	+	0.735330i	$0.737027\pi$
$224$	−0.724745	−	1.25529i	−0.0484241	−	0.0838729i
$225$	−7.79796	−	9.12096i	−0.519864	−	0.608064i
$226$	6.94949	−	12.0369i	0.462273	−	0.800681i
$227$	6.27526	−	10.8691i	0.416503	−	0.721405i	−0.579082	−	0.815270i	$-0.696589\pi$
$227$	6.27526	−	10.8691i	0.416503	−	0.721405i	0.995585	+	0.0938647i	$0.0299221\pi$
$228$	5.00000	−	5.65685i	0.331133	−	0.374634i
$229$	−6.29796	−	10.9084i	−0.416181	−	0.720846i	0.579371	−	0.815064i	$-0.303298\pi$
$229$	−6.29796	−	10.9084i	−0.416181	−	0.720846i	−0.995552	+	0.0942177i	$0.969965\pi$
$230$	14.6969			0.969087
$231$	−13.6237	+	1.25529i	−0.896375	+	0.0825923i
$232$	−7.89898			−0.518593
$233$	−5.05051	+	8.74774i	−0.330870	+	0.573084i	−0.982683	−	0.185296i	$-0.940675\pi$
$233$	−5.05051	+	8.74774i	−0.330870	+	0.573084i	0.651813	+	0.758380i	$0.274009\pi$
$234$	7.79796	+	9.12096i	0.509769	+	0.596256i
$235$	19.6515			1.28192
$236$	0.275255	−	0.476756i	0.0179176	−	0.0310342i
$237$	−17.2474	+	1.58919i	−1.12034	+	0.103229i
$238$	2.17423	−	3.76588i	0.140935	−	0.244106i
$239$	0.275255	+	0.476756i	0.0178048	+	0.0308388i	0.874791	−	0.484501i	$-0.160999\pi$
$239$	0.275255	+	0.476756i	0.0178048	+	0.0308388i	−0.856986	+	0.515340i	$0.827666\pi$
$240$	−5.17423	+	0.476756i	−0.333995	+	0.0307745i
$241$	−3.20204			−0.206262			−0.103131	−	0.994668i	$-0.532886\pi$
$241$	−3.20204			−0.206262			−0.103131	+	0.994668i	$0.532886\pi$
$242$	−9.34847	+	16.1920i	−0.600942	+	1.04086i
$243$	−12.9722	−	8.64420i	−0.832167	−	0.554526i
$244$	2.94949	−	5.10867i	0.188822	−	0.327049i
$245$	−7.34847	−	12.7279i	−0.469476	−	0.813157i
$246$	−3.27526	+	0.301783i	−0.208823	+	0.0192410i
$247$	16.6969	+	5.02118i	1.06240	+	0.319490i
$248$	−0.724745	−	1.25529i	−0.0460213	−	0.0797113i
$249$	1.65153	+	2.33562i	0.104662	+	0.148014i
$250$	−1.50000	−	2.59808i	−0.0948683	−	0.164317i
$251$	11.1742	+	19.3543i	0.705311	+	1.22164i	0.966579	+	0.256369i	$0.0825262\pi$
$251$	11.1742	+	19.3543i	0.705311	+	1.22164i	−0.261268	+	0.965266i	$0.584141\pi$
$252$	−1.44949	+	4.09978i	−0.0913093	+	0.258262i
$253$	−13.3485	−	23.1202i	−0.839211	−	1.45356i
$254$	1.17423	−	2.03383i	0.0736780	−	0.127614i
$255$	−9.00000	−	12.7279i	−0.563602	−	0.797053i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	10.8990	−	18.8776i	0.679860	−	1.17755i	−0.295163	−	0.955447i	$-0.595374\pi$
$257$	10.8990	−	18.8776i	0.679860	−	1.17755i	0.975023	−	0.222105i	$-0.0712927\pi$
$258$	−11.7980	−	16.6848i	−0.734509	−	1.03875i
$259$	−0.651531	+	1.12848i	−0.0404842	+	0.0701206i
$260$	−6.00000	−	10.3923i	−0.372104	−	0.644503i
$261$	15.3990	+	18.0116i	0.953173	+	1.11489i
$262$	7.07321	+	12.2512i	0.436985	+	0.756880i
$263$	−4.89898	−	8.48528i	−0.302084	−	0.523225i	0.674524	−	0.738253i	$-0.264349\pi$
$263$	−4.89898	−	8.48528i	−0.302084	−	0.523225i	−0.976608	+	0.215028i	$0.931016\pi$
$264$	5.44949	+	7.70674i	0.335393	+	0.474317i
$265$	11.8485	+	20.5222i	0.727846	+	1.26067i
$266$	1.44949	+	6.14966i	0.0888739	+	0.377060i
$267$	−15.5227	+	1.43027i	−0.949974	+	0.0875310i
$268$	6.89898	+	11.9494i	0.421422	+	0.729925i
$269$	−2.05051	+	3.55159i	−0.125022	+	0.216544i	−0.921741	−	0.387805i	$-0.873233\pi$
$269$	−2.05051	+	3.55159i	−0.125022	+	0.216544i	0.796720	+	0.604349i	$0.206567\pi$
$270$	11.1742	+	10.8691i	0.680042	+	0.661470i
$271$	2.82577	−	4.89437i	0.171653	−	0.297312i	−0.767345	−	0.641235i	$-0.778423\pi$
$271$	2.82577	−	4.89437i	0.171653	−	0.297312i	0.938998	+	0.343923i	$0.111756\pi$
$272$	−3.00000			−0.181902
$273$	−10.0000	+	0.921404i	−0.605228	+	0.0557659i
$274$	8.84847	+	15.3260i	0.534556	+	0.925877i
$275$	10.8990	−	18.8776i	0.657233	−	1.13836i
$276$	−8.44949	+	0.778539i	−0.508600	+	0.0468625i
$277$	−0.848469	+	1.46959i	−0.0509796	+	0.0882992i	−0.890389	−	0.455200i	$-0.849568\pi$
$277$	−0.848469	+	1.46959i	−0.0509796	+	0.0882992i	0.839410	+	0.543499i	$0.182901\pi$
$278$	−20.8990			−1.25344
$279$	−1.44949	+	4.09978i	−0.0867787	+	0.245447i
$280$	2.17423	−	3.76588i	0.129935	−	0.225055i
$281$	21.0000			1.25275			0.626377	−	0.779520i	$-0.284537\pi$
$281$	21.0000			1.25275			0.626377	+	0.779520i	$0.284537\pi$
$282$	−11.2980	+	1.04100i	−0.672784	+	0.0619905i
$283$	9.65153			0.573724			0.286862	−	0.957972i	$-0.407388\pi$
$283$	9.65153			0.573724			0.286862	+	0.957972i	$0.407388\pi$
$284$	5.72474	+	9.91555i	0.339701	+	0.588380i
$285$	22.1969	+	4.50510i	1.31483	+	0.266859i
$286$	−10.8990	+	18.8776i	−0.644470	+	1.11626i
$287$	1.37628	−	2.38378i	0.0812390	−	0.140710i
$288$	2.94949	−	0.548188i	0.173800	−	0.0323023i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	−11.8485	−	20.5222i	−0.695766	−	1.20510i
$291$	−6.89898	+	0.635674i	−0.404425	+	0.0372639i
$292$	2.39898	+	4.15515i	0.140390	+	0.243162i
$293$	−0.151531	−	0.262459i	−0.00885252	−	0.0153330i	0.861565	−	0.507647i	$-0.169485\pi$
$293$	−0.151531	−	0.262459i	−0.00885252	−	0.0153330i	−0.870418	+	0.492314i	$0.836151\pi$
$294$	4.89898	+	6.92820i	0.285714	+	0.404061i
$295$	1.65153			0.0961558
$296$	0.898979			0.0522521
$297$	6.94949	−	27.4504i	0.403250	−	1.59283i
$298$	9.39898	+	16.2795i	0.544468	+	0.943047i
$299$	−9.79796	−	16.9706i	−0.566631	−	0.981433i
$300$	−4.00000	−	5.65685i	−0.230940	−	0.326599i
$301$	17.1010			0.985686
$302$	−5.65153			−0.325209
$303$	−8.47730	+	18.4008i	−0.487008	+	1.05710i
$304$	3.17423	−	2.98735i	0.182055	−	0.171336i
$305$	17.6969			1.01332
$306$	5.84847	+	6.84072i	0.334335	+	0.391058i
$307$	4.17423	−	7.22999i	0.238236	−	0.412637i	−0.721972	−	0.691922i	$-0.756764\pi$
$307$	4.17423	−	7.22999i	0.238236	−	0.412637i	0.960208	+	0.279285i	$0.0900974\pi$
$308$	−7.89898			−0.450086
$309$	19.3990	−	1.78743i	1.10357	−	0.101683i
$310$	2.17423	−	3.76588i	0.123488	−	0.213888i
$311$	14.1742	+	24.5505i	0.803747	+	1.39213i	0.917134	+	0.398580i	$0.130497\pi$
$311$	14.1742	+	24.5505i	0.803747	+	1.39213i	−0.113387	+	0.993551i	$0.536170\pi$
$312$	4.00000	+	5.65685i	0.226455	+	0.320256i
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	5.94949	+	10.3048i	0.335749	+	0.581535i
$315$	−12.8258	+	2.38378i	−0.722650	+	0.134311i
$316$	−10.0000			−0.562544
$317$	−17.6969			−0.993959			−0.496980	−	0.867762i	$-0.665558\pi$
$317$	−17.6969			−0.993959			−0.496980	+	0.867762i	$0.665558\pi$
$318$	−7.89898	−	11.1708i	−0.442953	−	0.626430i
$319$	−21.5227	+	37.2784i	−1.20504	+	2.08719i
$320$	−3.00000			−0.167705
$321$	−3.55051	+	7.70674i	−0.198170	+	0.430148i
$322$	3.55051	−	6.14966i	0.197862	−	0.342707i
$323$	12.5227	+	3.76588i	0.696782	+	0.209539i
$324$	−7.00000	−	5.65685i	−0.388889	−	0.314270i
$325$	8.00000	−	13.8564i	0.443760	−	0.768615i
$326$	5.55051	+	9.61377i	0.307414	+	0.532457i
$327$	1.00000	+	1.41421i	0.0553001	+	0.0782062i
$328$	−1.89898			−0.104854
$329$	4.74745	−	8.22282i	0.261735	−	0.453339i
$330$	−11.8485	+	25.7183i	−0.652237	+	1.41575i
$331$	7.17423	−	12.4261i	0.394332	−	0.683002i	−0.598684	−	0.800985i	$-0.704309\pi$
$331$	7.17423	−	12.4261i	0.394332	−	0.683002i	0.993016	+	0.117983i	$0.0376428\pi$
$332$	0.825765	+	1.43027i	0.0453198	+	0.0784961i
$333$	−1.75255	−	2.04989i	−0.0960392	−	0.112333i
$334$	6.00000			0.328305
$335$	−20.6969	+	35.8481i	−1.13079	+	1.95859i
$336$	−1.05051	+	2.28024i	−0.0573100	+	0.124397i
$337$	−11.8990			−0.648179			−0.324089	−	0.946026i	$-0.605058\pi$
$337$	−11.8990			−0.648179			−0.324089	+	0.946026i	$0.605058\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	−23.9722	+	2.20881i	−1.30199	+	0.119966i
$340$	−4.50000	−	7.79423i	−0.244047	−	0.422701i
$341$	−7.89898			−0.427754
$342$	−13.0000	−	1.41421i	−0.702959	−	0.0764719i
$343$	−17.2474			−0.931275
$344$	−5.89898	−	10.2173i	−0.318052	−	0.550882i
$345$	−14.6969	−	20.7846i	−0.791257	−	1.11901i
$346$	8.44949	−	14.6349i	0.454247	−	0.786780i
$347$	17.4495			0.936738			0.468369	−	0.883533i	$-0.344842\pi$
$347$	17.4495			0.936738			0.468369	+	0.883533i	$0.344842\pi$
$348$	7.89898	+	11.1708i	0.423430	+	0.598820i
$349$	−13.9495	+	24.1612i	−0.746699	+	1.29332i	0.202698	+	0.979241i	$0.435029\pi$
$349$	−13.9495	+	24.1612i	−0.746699	+	1.29332i	−0.949397	+	0.314079i	$0.898304\pi$
$350$	5.79796			0.309914
$351$	5.10102	−	20.1489i	0.272272	−	1.07547i
$352$	2.72474	+	4.71940i	0.145229	+	0.251545i
$353$	3.94949	−	6.84072i	0.210210	−	0.364095i	−0.741570	−	0.670875i	$-0.765919\pi$
$353$	3.94949	−	6.84072i	0.210210	−	0.364095i	0.951780	+	0.306781i	$0.0992519\pi$
$354$	−0.949490	+	0.0874863i	−0.0504648	+	0.00464985i
$355$	−17.1742	+	29.7466i	−0.911514	+	1.57879i
$356$	−9.00000			−0.476999
$357$	−7.50000	+	0.691053i	−0.396942	+	0.0365744i
$358$	3.55051	+	6.14966i	0.187650	+	0.325020i
$359$	9.27526	−	16.0652i	0.489529	−	0.847890i	−0.510398	−	0.859938i	$-0.670502\pi$
$359$	9.27526	−	16.0652i	0.489529	−	0.847890i	0.999927	+	0.0120487i	$0.00383531\pi$
$360$	5.84847	+	6.84072i	0.308241	+	0.360537i
$361$	−17.0000	+	8.48528i	−0.894737	+	0.446594i
$362$	−5.50000	+	9.52628i	−0.289074	+	0.500690i
$363$	32.2474	−	2.97129i	1.69255	−	0.155952i
$364$	−5.79796			−0.303896
$365$	−7.19694	+	12.4655i	−0.376705	+	0.652472i
$366$	−10.1742	+	0.937458i	−0.531816	+	0.0490017i
$367$	13.4495			0.702058			0.351029	−	0.936365i	$-0.385832\pi$
$367$	13.4495			0.702058			0.351029	+	0.936365i	$0.385832\pi$
$368$	−4.89898			−0.255377
$369$	3.70204	+	4.33013i	0.192721	+	0.225417i
$370$	1.34847	+	2.33562i	0.0701036	+	0.121423i
$371$	11.4495			0.594428
$372$	−1.05051	+	2.28024i	−0.0544664	+	0.118225i
$373$	1.84847	+	3.20164i	0.0957101	+	0.165775i	0.909905	−	0.414817i	$-0.136154\pi$
$373$	1.84847	+	3.20164i	0.0957101	+	0.165775i	−0.814195	+	0.580592i	$0.802821\pi$
$374$	−8.17423	+	14.1582i	−0.422680	+	0.732103i
$375$	−2.17423	+	4.71940i	−0.112277	+	0.243709i
$376$	−6.55051			−0.337817
$377$	−15.7980	+	27.3629i	−0.813636	+	1.40926i
$378$	7.24745	−	2.04989i	0.372769	−	0.105435i
$379$	−23.5959			−1.21204			−0.606020	−	0.795449i	$-0.707235\pi$
$379$	−23.5959			−1.21204			−0.606020	+	0.795449i	$0.707235\pi$
$380$	12.5227	+	3.76588i	0.642401	+	0.193186i
$381$	−4.05051	+	0.373215i	−0.207514	+	0.0191204i
$382$	21.2474			1.08711
$383$	34.8434			1.78041			0.890206	−	0.455557i	$-0.150560\pi$
$383$	34.8434			1.78041			0.890206	+	0.455557i	$0.150560\pi$
$384$	1.72474	−	0.158919i	0.0880155	−	0.00810978i
$385$	−11.8485	−	20.5222i	−0.603854	−	1.04591i
$386$	−9.29796	−	16.1045i	−0.473254	−	0.819699i
$387$	−11.7980	+	33.3697i	−0.599724	+	1.69628i
$388$	−4.00000			−0.203069
$389$	0.797959			0.0404581			0.0202291	−	0.999795i	$-0.493560\pi$
$389$	0.797959			0.0404581			0.0202291	+	0.999795i	$0.493560\pi$
$390$	−8.69694	+	18.8776i	−0.440387	+	0.955904i
$391$	−7.34847	−	12.7279i	−0.371628	−	0.643679i
$392$	2.44949	+	4.24264i	0.123718	+	0.214286i
$393$	10.2526	−	22.2542i	0.517173	−	1.12258i
$394$	10.8990	+	18.8776i	0.549083	+	0.951039i
$395$	−15.0000	−	25.9808i	−0.754732	−	1.30723i
$396$	5.44949	−	15.4135i	0.273847	−	0.774557i
$397$	7.29796	−	12.6404i	0.366274	−	0.634405i	−0.622706	−	0.782456i	$-0.713967\pi$
$397$	7.29796	−	12.6404i	0.366274	−	0.634405i	0.988980	+	0.148051i	$0.0472999\pi$
$398$	7.17423	−	12.4261i	0.359612	−	0.622866i
$399$	7.24745	−	8.19955i	0.362826	−	0.410491i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−30.7980			−1.53798			−0.768988	−	0.639263i	$-0.779240\pi$
$401$	−30.7980			−1.53798			−0.768988	+	0.639263i	$0.779240\pi$
$402$	10.0000	−	21.7060i	0.498755	−	1.08260i
$403$	−5.79796			−0.288817
$404$	−5.84847	+	10.1298i	−0.290972	+	0.503979i
$405$	4.19694	−	26.6718i	0.208548	−	1.32533i
$406$	−11.4495			−0.568229
$407$	2.44949	−	4.24264i	0.121417	−	0.210300i
$408$	3.00000	+	4.24264i	0.148522	+	0.210042i
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$	−2.84847	−	4.93369i	−0.140676	−	0.243658i
$411$	12.8258	−	27.8396i	0.632648	−	1.37323i
$412$	11.2474			0.554122
$413$	0.398979	−	0.691053i	0.0196325	−	0.0340045i
$414$	9.55051	+	11.1708i	0.469382	+	0.549017i
$415$	−2.47730	+	4.29080i	−0.121606	+	0.210627i
$416$	2.00000	+	3.46410i	0.0980581	+	0.169842i
$417$	20.8990	+	29.5556i	1.02343	+	1.44734i
$418$	−5.44949	−	23.1202i	−0.266543	−	1.13085i
$419$	4.62372	+	8.00853i	0.225884	+	0.391242i	0.956584	−	0.291456i	$-0.0941397\pi$
$419$	4.62372	+	8.00853i	0.225884	+	0.391242i	−0.730700	+	0.682698i	$0.760806\pi$
$420$	−7.50000	+	0.691053i	−0.365963	+	0.0337199i
$421$	−5.34847	−	9.26382i	−0.260668	−	0.451491i	0.705751	−	0.708460i	$-0.250610\pi$
$421$	−5.34847	−	9.26382i	−0.260668	−	0.451491i	−0.966420	+	0.256969i	$0.917276\pi$
$422$	−10.5227	−	18.2259i	−0.512237	−	0.887221i
$423$	12.7702	+	14.9367i	0.620906	+	0.726249i
$424$	−3.94949	−	6.84072i	−0.191804	−	0.332215i
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	8.29796	−	18.0116i	0.402037	−	0.872663i
$427$	4.27526	−	7.40496i	0.206894	−	0.358351i
$428$	−2.44949	+	4.24264i	−0.118401	+	0.205076i
$429$	37.5959	−	3.46410i	1.81515	−	0.167248i
$430$	17.6969	−	30.6520i	0.853422	−	1.47817i
$431$	−7.62372	−	13.2047i	−0.367222	−	0.636047i	0.621908	−	0.783090i	$-0.286358\pi$
$431$	−7.62372	−	13.2047i	−0.367222	−	0.636047i	−0.989130	+	0.147043i	$0.953024\pi$
$432$	−3.72474	−	3.62302i	−0.179207	−	0.174313i
$433$	−1.39898	−	2.42310i	−0.0672307	−	0.116447i	0.830451	−	0.557092i	$-0.188083\pi$
$433$	−1.39898	−	2.42310i	−0.0672307	−	0.116447i	−0.897681	+	0.440645i	$0.854750\pi$
$434$	−1.05051	−	1.81954i	−0.0504261	−	0.0873406i
$435$	−17.1742	+	37.2784i	−0.823442	+	1.78736i
$436$	0.500000	+	0.866025i	0.0239457	+	0.0414751i
$437$	20.4495	+	6.14966i	0.978232	+	0.294178i
$438$	3.47730	−	7.54782i	0.166152	−	0.360649i
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	0.991322	−	0.131453i	$-0.0419644\pi$
$439$	8.00000	+	13.8564i	0.381819	+	0.661330i	−0.609503	+	0.792784i	$0.708631\pi$
$440$	−8.17423	+	14.1582i	−0.389691	+	0.674965i
$441$	4.89898	−	13.8564i	0.233285	−	0.659829i
$442$	−6.00000	+	10.3923i	−0.285391	+	0.494312i
$443$	−3.85357			−0.183089			−0.0915444	−	0.995801i	$-0.529180\pi$
$443$	−3.85357			−0.183089			−0.0915444	+	0.995801i	$0.529180\pi$
$444$	−0.898979	−	1.27135i	−0.0426637	−	0.0603356i
$445$	−13.5000	−	23.3827i	−0.639961	−	1.10845i
$446$	4.44949	−	7.70674i	0.210689	−	0.364925i
$447$	13.6237	−	29.5717i	0.644380	−	1.39869i
$448$	−0.724745	+	1.25529i	−0.0342410	+	0.0593071i
$449$	21.7980			1.02871			0.514355	−	0.857578i	$-0.328032\pi$
$449$	21.7980			1.02871			0.514355	+	0.857578i	$0.328032\pi$
$450$	−4.00000	+	11.3137i	−0.188562	+	0.533333i
$451$	−5.17423	+	8.96204i	−0.243645	+	0.422006i
$452$	−13.8990			−0.653753
$453$	5.65153	+	7.99247i	0.265532	+	0.375519i
$454$	−12.5505			−0.589025
$455$	−8.69694	−	15.0635i	−0.407719	−	0.706190i
$456$	−7.39898	−	1.50170i	−0.346489	−	0.0703235i
$457$	20.3990	−	35.3321i	0.954224	−	1.65276i	0.218090	−	0.975929i	$-0.430017\pi$
$457$	20.3990	−	35.3321i	0.954224	−	1.65276i	0.736134	−	0.676836i	$-0.236649\pi$
$458$	−6.29796	+	10.9084i	−0.294284	+	0.509715i
$459$	3.82577	−	15.1117i	0.178571	−	0.705354i
$460$	−7.34847	−	12.7279i	−0.342624	−	0.593442i
$461$	−14.6969	−	25.4558i	−0.684505	−	1.18560i	−0.973592	−	0.228294i	$-0.926685\pi$
$461$	−14.6969	−	25.4558i	−0.684505	−	1.18560i	0.289088	−	0.957303i	$-0.406648\pi$
$462$	7.89898	+	11.1708i	0.367494	+	0.519715i
$463$	−12.1742	−	21.0864i	−0.565785	−	0.979968i	−0.996976	−	0.0777074i	$-0.975240\pi$
$463$	−12.1742	−	21.0864i	−0.565785	−	0.979968i	0.431192	−	0.902260i	$-0.358093\pi$
$464$	3.94949	+	6.84072i	0.183350	+	0.317572i
$465$	−7.50000	+	0.691053i	−0.347804	+	0.0320468i
$466$	10.1010			0.467921
$467$	18.0000			0.832941			0.416470	−	0.909149i	$-0.363267\pi$
$467$	18.0000			0.832941			0.416470	+	0.909149i	$0.363267\pi$
$468$	4.00000	−	11.3137i	0.184900	−	0.522976i
$469$	10.0000	+	17.3205i	0.461757	+	0.799787i
$470$	−9.82577	−	17.0187i	−0.453229	−	0.785015i
$471$	8.62372	−	18.7187i	0.397360	−	0.862511i
$472$	−0.550510			−0.0253393
$473$	−64.2929			−2.95619
$474$	10.0000	+	14.1421i	0.459315	+	0.649570i
$475$	4.00000	+	16.9706i	0.183533	+	0.778663i
$476$	−4.34847			−0.199312
$477$	−7.89898	+	22.3417i	−0.361669	+	1.02296i
$478$	0.275255	−	0.476756i	0.0125899	−	0.0218063i
$479$	0.550510			0.0251535			0.0125767	−	0.999921i	$-0.495997\pi$
$479$	0.550510			0.0251535			0.0125767	+	0.999921i	$0.495997\pi$
$480$	3.00000	+	4.24264i	0.136931	+	0.193649i
$481$	1.79796	−	3.11416i	0.0819799	−	0.141993i
$482$	1.60102	+	2.77305i	0.0729245	+	0.126309i
$483$	−12.2474	+	1.12848i	−0.557278	+	0.0513478i
$484$	18.6969			0.849861
$485$	−6.00000	−	10.3923i	−0.272446	−	0.471890i
$486$	−1.00000	+	15.5563i	−0.0453609	+	0.705650i
$487$	37.3939			1.69448			0.847239	−	0.531212i	$-0.178263\pi$
$487$	37.3939			1.69448			0.847239	+	0.531212i	$0.178263\pi$
$488$	−5.89898			−0.267034
$489$	8.04541	−	17.4634i	0.363826	−	0.789721i
$490$	−7.34847	+	12.7279i	−0.331970	+	0.574989i
$491$	33.7423			1.52277			0.761385	−	0.648300i	$-0.224520\pi$
$491$	33.7423			1.52277			0.761385	+	0.648300i	$0.224520\pi$
$492$	1.89898	+	2.68556i	0.0856126	+	0.121075i
$493$	−11.8485	+	20.5222i	−0.533628	+	0.924271i
$494$	−4.00000	−	16.9706i	−0.179969	−	0.763542i
$495$	48.2196	−	8.96204i	2.16731	−	0.402814i
$496$	−0.724745	+	1.25529i	−0.0325420	+	0.0563644i
$497$	8.29796	+	14.3725i	0.372214	+	0.644694i
$498$	1.19694	−	2.59808i	0.0536361	−	0.116423i
$499$	−29.0454			−1.30025			−0.650126	−	0.759827i	$-0.725284\pi$
$499$	−29.0454			−1.30025			−0.650126	+	0.759827i	$0.725284\pi$
$500$	−1.50000	+	2.59808i	−0.0670820	+	0.116190i
$501$	−6.00000	−	8.48528i	−0.268060	−	0.379094i
$502$	11.1742	−	19.3543i	0.498730	−	0.863827i
$503$	8.72474	+	15.1117i	0.389017	+	0.673797i	0.992318	−	0.123717i	$-0.0394813\pi$
$503$	8.72474	+	15.1117i	0.389017	+	0.673797i	−0.603300	+	0.797514i	$0.706148\pi$
$504$	4.27526	−	0.794593i	0.190435	−	0.0353940i
$505$	−35.0908			−1.56152
$506$	−13.3485	+	23.1202i	−0.593412	+	1.02782i
$507$	5.17423	−	0.476756i	0.229796	−	0.0211735i
$508$	−2.34847			−0.104196
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	−0.933921	−	0.357480i	$-0.883636\pi$
$509$	−3.55051	+	6.14966i	−0.157374	+	0.272579i	0.776547	+	0.630059i	$0.216969\pi$
$510$	−6.52270	+	14.1582i	−0.288830	+	0.626935i
$511$	3.47730	+	6.02285i	0.153827	+	0.266435i
$512$	1.00000			0.0441942
$513$	11.0000	+	19.7990i	0.485662	+	0.874147i
$514$	−21.7980			−0.961467
$515$	16.8712	+	29.2217i	0.743433	+	1.28766i
$516$	−8.55051	+	18.5597i	−0.376415	+	0.817047i
$517$	−17.8485	+	30.9145i	−0.784975	+	1.35962i
$518$	1.30306			0.0572532
$519$	−29.1464	+	2.68556i	−1.27939	+	0.117883i
$520$	−6.00000	+	10.3923i	−0.263117	+	0.455733i
$521$	19.1010			0.836831			0.418415	−	0.908256i	$-0.362586\pi$
$521$	19.1010			0.836831			0.418415	+	0.908256i	$0.362586\pi$
$522$	7.89898	−	22.3417i	0.345729	−	0.977869i
$523$	10.9722	+	19.0044i	0.479781	+	0.831004i	0.999731	−	0.0231921i	$-0.00738295\pi$
$523$	10.9722	+	19.0044i	0.479781	+	0.831004i	−0.519950	+	0.854196i	$0.674050\pi$
$524$	7.07321	−	12.2512i	0.308995	−	0.535195i
$525$	−5.79796	−	8.19955i	−0.253044	−	0.357858i
$526$	−4.89898	+	8.48528i	−0.213606	+	0.369976i
$527$	−4.34847			−0.189422
$528$	3.94949	−	8.57277i	0.171879	−	0.373082i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	11.8485	−	20.5222i	0.514665	−	0.891425i
$531$	1.07321	+	1.25529i	0.0465735	+	0.0544752i
$532$	4.60102	−	4.33013i	0.199480	−	0.187735i
$533$	−3.79796	+	6.57826i	−0.164508	+	0.284936i
$534$	9.00000	+	12.7279i	0.389468	+	0.550791i
$535$	−14.6969			−0.635404
$536$	6.89898	−	11.9494i	0.297991	−	0.516135i
$537$	5.14643	−	11.1708i	0.222085	−	0.482057i
$538$	4.10102			0.176808
$539$	26.6969			1.14992
$540$	3.82577	−	15.1117i	0.164635	−	0.650304i
$541$	1.05051	+	1.81954i	0.0451650	+	0.0782280i	0.887724	−	0.460376i	$-0.152285\pi$
$541$	1.05051	+	1.81954i	0.0451650	+	0.0782280i	−0.842559	+	0.538604i	$0.818952\pi$
$542$	−5.65153			−0.242754
$543$	18.9722	−	1.74810i	0.814175	−	0.0750184i
$544$	1.50000	+	2.59808i	0.0643120	+	0.111392i
$545$	−1.50000	+	2.59808i	−0.0642529	+	0.111289i
$546$	5.79796	+	8.19955i	0.248130	+	0.350908i
$547$	36.8434			1.57531			0.787654	−	0.616117i	$-0.211295\pi$
$547$	36.8434			1.57531			0.787654	+	0.616117i	$0.211295\pi$
$548$	8.84847	−	15.3260i	0.377988	−	0.654694i
$549$	11.5000	+	13.4511i	0.490808	+	0.574078i
$550$	−21.7980			−0.929468
$551$	−7.89898	−	33.5125i	−0.336508	−	1.42768i
$552$	4.89898	+	6.92820i	0.208514	+	0.294884i
$553$	−14.4949			−0.616386
$554$	1.69694			0.0720960
$555$	1.95459	−	4.24264i	0.0829678	−	0.180090i
$556$	10.4495	+	18.0990i	0.443157	+	0.767571i
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	0.896053	−	0.443947i	$-0.146422\pi$
$557$	1.50000	+	2.59808i	0.0635570	+	0.110084i	−0.832496	+	0.554031i	$0.813089\pi$
$558$	4.27526	−	0.794593i	0.180986	−	0.0336378i
$559$	−47.1918			−1.99600
$560$	−4.34847			−0.183756
$561$	28.1969	−	2.59808i	1.19048	−	0.109691i
$562$	−10.5000	−	18.1865i	−0.442916	−	0.767153i
$563$	−17.7247	−	30.7002i	−0.747009	−	1.29386i	−0.949250	−	0.314522i	$-0.898156\pi$
$563$	−17.7247	−	30.7002i	−0.747009	−	1.29386i	0.202241	−	0.979336i	$-0.435177\pi$
$564$	6.55051	+	9.26382i	0.275826	+	0.390077i
$565$	−20.8485	−	36.1106i	−0.877102	−	1.51918i
$566$	−4.82577	−	8.35847i	−0.202842	−	0.351333i
$567$	−10.1464	−	8.19955i	−0.426110	−	0.344349i
$568$	5.72474	−	9.91555i	0.240205	−	0.416047i
$569$	11.8485	−	20.5222i	0.496714	−	0.860333i	−0.503279	−	0.864124i	$-0.667873\pi$
$569$	11.8485	−	20.5222i	0.496714	−	0.860333i	0.999993	+	0.00379058i	$0.00120658\pi$
$570$	−7.19694	−	21.4757i	−0.301447	−	0.899517i
$571$	19.4217	+	33.6393i	0.812772	+	1.40776i	0.910917	+	0.412590i	$0.135376\pi$
$571$	19.4217	+	33.6393i	0.812772	+	1.40776i	−0.0981445	+	0.995172i	$0.531291\pi$
$572$	21.7980			0.911418
$573$	−21.2474	−	30.0484i	−0.887625	−	1.25529i
$574$	−2.75255			−0.114889
$575$	9.79796	−	16.9706i	0.408603	−	0.707721i
$576$	−1.94949	−	2.28024i	−0.0812287	−	0.0950100i
$577$	8.00000			0.333044			0.166522	−	0.986038i	$-0.446746\pi$
$577$	8.00000			0.333044			0.166522	+	0.986038i	$0.446746\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−13.4773	+	29.2538i	−0.560097	+	1.21575i
$580$	−11.8485	+	20.5222i	−0.491981	+	0.852136i
$581$	1.19694	+	2.07316i	0.0496574	+	0.0860091i
$582$	4.00000	+	5.65685i	0.165805	+	0.234484i
$583$	−43.0454			−1.78276
$584$	2.39898	−	4.15515i	0.0992705	−	0.171942i
$585$	35.3939	−	6.57826i	1.46336	−	0.271977i
$586$	−0.151531	+	0.262459i	−0.00625968	+	0.0108421i
$587$	−12.2474	−	21.2132i	−0.505506	−	0.875563i	−0.999980	−	0.00636985i	$-0.997972\pi$
$587$	−12.2474	−	21.2132i	−0.505506	−	0.875563i	0.494473	−	0.869193i	$-0.335361\pi$
$588$	3.55051	−	7.70674i	0.146421	−	0.317821i
$589$	4.60102	−	4.33013i	0.189582	−	0.178420i
$590$	−0.825765	−	1.43027i	−0.0339962	−	0.0588832i
$591$	15.7980	−	34.2911i	0.649841	−	1.41055i
$592$	−0.449490	−	0.778539i	−0.0184739	−	0.0319978i
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	0.669934	−	0.742421i	$-0.266322\pi$
$593$	−7.50000	−	12.9904i	−0.307988	−	0.533451i	−0.977922	+	0.208970i	$0.932989\pi$
$594$	−27.2474	+	7.70674i	−1.11798	+	0.316211i
$595$	−6.52270	−	11.2977i	−0.267405	−	0.463159i
$596$	9.39898	−	16.2795i	0.384997	−	0.666835i
$597$	−24.7474	+	2.28024i	−1.01285	+	0.0933240i
$598$	−9.79796	+	16.9706i	−0.400668	+	0.693978i
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	−0.798206	−	0.602384i	$-0.794218\pi$
$599$	3.00000	−	5.19615i	0.122577	−	0.212309i	0.920783	+	0.390075i	$0.127551\pi$
$600$	−2.89898	+	6.29253i	−0.118350	+	0.256891i
$601$	−19.3990	+	33.6000i	−0.791301	+	1.37057i	0.133861	+	0.991000i	$0.457262\pi$
$601$	−19.3990	+	33.6000i	−0.791301	+	1.37057i	−0.925162	+	0.379573i	$0.876071\pi$
$602$	−8.55051	−	14.8099i	−0.348493	−	0.603607i
$603$	−40.6969	+	7.56388i	−1.65731	+	0.308025i
$604$	2.82577	+	4.89437i	0.114979	+	0.199149i
$605$	28.0454	+	48.5761i	1.14021	+	1.97490i
$606$	20.1742	−	1.85886i	0.819522	−	0.0755111i
$607$	−9.72474	−	16.8438i	−0.394715	−	0.683667i	0.598350	−	0.801235i	$-0.295823\pi$
$607$	−9.72474	−	16.8438i	−0.394715	−	0.683667i	−0.993065	+	0.117568i	$0.962490\pi$
$608$	−4.17423	−	1.25529i	−0.169288	−	0.0509089i
$609$	11.4495	+	16.1920i	0.463957	+	0.656134i
$610$	−8.84847	−	15.3260i	−0.358264	−	0.620532i
$611$	−13.1010	+	22.6916i	−0.530011	+	0.918005i
$612$	3.00000	−	8.48528i	0.121268	−	0.342997i
$613$	−9.84847	+	17.0580i	−0.397776	+	0.688968i	−0.993451	−	0.114257i	$-0.963551\pi$
$613$	−9.84847	+	17.0580i	−0.397776	+	0.688968i	0.595675	+	0.803225i	$0.296885\pi$
$614$	−8.34847			−0.336917
$615$	−4.12883	+	8.96204i	−0.166490	+	0.361384i
$616$	3.94949	+	6.84072i	0.159129	+	0.275620i
$617$	4.65153	−	8.05669i	0.187264	−	0.324350i	−0.757073	−	0.653330i	$-0.773371\pi$
$617$	4.65153	−	8.05669i	0.187264	−	0.324350i	0.944337	+	0.328980i	$0.106705\pi$
$618$	−11.2474	−	15.9063i	−0.452439	−	0.639845i
$619$	2.27526	−	3.94086i	0.0914502	−	0.158396i	−0.816671	−	0.577103i	$-0.804183\pi$
$619$	2.27526	−	3.94086i	0.0914502	−	0.158396i	0.908122	+	0.418707i	$0.137516\pi$
$620$	−4.34847			−0.174639
$621$	6.24745	−	24.6773i	0.250701	−	0.990266i
$622$	14.1742	−	24.5505i	0.568335	−	0.984385i
$623$	−13.0454			−0.522653
$624$	2.89898	−	6.29253i	0.116052	−	0.251903i
$625$	−29.0000			−1.16000
$626$	0.500000	+	0.866025i	0.0199840	+	0.0346133i
$627$	−27.2474	+	30.8270i	−1.08816	+	1.23111i
$628$	5.94949	−	10.3048i	0.237410	−	0.411207i
$629$	1.34847	−	2.33562i	0.0537670	−	0.0931272i
$630$	8.47730	+	9.91555i	0.337744	+	0.395045i
$631$	−17.6237	−	30.5252i	−0.701589	−	1.21519i	−0.967908	−	0.251304i	$-0.919141\pi$
$631$	−17.6237	−	30.5252i	−0.701589	−	1.21519i	0.266319	−	0.963885i	$-0.414193\pi$
$632$	5.00000	+	8.66025i	0.198889	+	0.344486i
$633$	−15.2526	+	33.1072i	−0.606234	+	1.31589i
$634$	8.84847	+	15.3260i	0.351418	+	0.608673i
$635$	−3.52270	−	6.10150i	−0.139794	−	0.242131i
$636$	−5.72474	+	12.4261i	−0.227001	+	0.492728i
$637$	19.5959			0.776419
$638$	43.0454			1.70418
$639$	−33.7702	+	6.27647i	−1.33593	+	0.248294i
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	0.631721	−	0.775196i	$-0.282349\pi$
$641$	−9.00000	−	15.5885i	−0.355479	−	0.615707i	−0.987200	+	0.159489i	$0.949015\pi$
$642$	8.44949	−	0.778539i	0.333475	−	0.0307265i
$643$	42.3485			1.67006			0.835030	−	0.550204i	$-0.185450\pi$
$643$	42.3485			1.67006			0.835030	+	0.550204i	$0.185450\pi$
$644$	−7.10102			−0.279819
$645$	−61.0454	+	5.62475i	−2.40366	+	0.221474i
$646$	−3.00000	−	12.7279i	−0.118033	−	0.500773i
$647$	4.89898			0.192599			0.0962994	−	0.995352i	$-0.469299\pi$
$647$	4.89898			0.192599			0.0962994	+	0.995352i	$0.469299\pi$
$648$	−1.39898	+	8.89060i	−0.0549571	+	0.349256i
$649$	−1.50000	+	2.59808i	−0.0588802	+	0.101983i
$650$	−16.0000			−0.627572
$651$	−1.52270	+	3.30518i	−0.0596795	+	0.129540i
$652$	5.55051	−	9.61377i	0.217375	−	0.376504i
$653$	−10.7474	−	18.6151i	−0.420580	−	0.728466i	0.575416	−	0.817861i	$-0.304840\pi$
$653$	−10.7474	−	18.6151i	−0.420580	−	0.728466i	−0.995996	+	0.0893946i	$0.971507\pi$
$654$	0.724745	−	1.57313i	0.0283398	−	0.0615143i
$655$	42.4393			1.65824
$656$	0.949490	+	1.64456i	0.0370713	+	0.0642095i
$657$	−14.1515	+	2.63018i	−0.552104	+	0.102613i
$658$	−9.49490			−0.370150
$659$	22.8434			0.889851			0.444926	−	0.895568i	$-0.353230\pi$
$659$	22.8434			0.889851			0.444926	+	0.895568i	$0.353230\pi$
$660$	28.1969	−	2.59808i	1.09756	−	0.101130i
$661$	10.6969	−	18.5276i	0.416063	−	0.720642i	−0.579477	−	0.814989i	$-0.696743\pi$
$661$	10.6969	−	18.5276i	0.416063	−	0.720642i	0.995539	+	0.0943471i	$0.0300764\pi$
$662$	−14.3485			−0.557669
$663$	20.6969	−	1.90702i	0.803802	−	0.0740627i
$664$	0.825765	−	1.43027i	0.0320459	−	0.0555051i
$665$	18.1515	+	5.45861i	0.703886	+	0.211676i
$666$	−0.898979	+	2.54270i	−0.0348347	+	0.0985275i
$667$	−19.3485	+	33.5125i	−0.749176	+	1.29761i
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	−15.3485	+	1.41421i	−0.593406	+	0.0546767i
$670$	41.3939			1.59918
$671$	−16.0732	+	27.8396i	−0.620500	+	1.07474i
$672$	2.50000	−	0.230351i	0.0964396	−	0.00888598i
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	−0.952343	−	0.305028i	$-0.901334\pi$
$673$	−5.50000	+	9.52628i	−0.212009	+	0.367211i	0.740334	+	0.672239i	$0.234667\pi$
$674$	5.94949	+	10.3048i	0.229166	+	0.396927i
$675$	20.0000	−	5.65685i	0.769800	−	0.217732i
$676$	3.00000			0.115385
$677$	12.3990	−	21.4757i	0.476531	−	0.825377i	−0.523107	−	0.852267i	$-0.675227\pi$
$677$	12.3990	−	21.4757i	0.476531	−	0.825377i	0.999638	+	0.0268903i	$0.00856049\pi$
$678$	13.8990	+	19.6561i	0.533787	+	0.754889i
$679$	−5.79796			−0.222505
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$	12.5505	+	17.7491i	0.480937	+	0.680147i
$682$	3.94949	+	6.84072i	0.151234	+	0.261945i
$683$	−2.20204			−0.0842588			−0.0421294	−	0.999112i	$-0.513414\pi$
$683$	−2.20204			−0.0842588			−0.0421294	+	0.999112i	$0.513414\pi$
$684$	5.27526	+	11.9654i	0.201704	+	0.457510i
$685$	53.0908			2.02850
$686$	8.62372	+	14.9367i	0.329255	+	0.570287i
$687$	21.7247	−	2.00173i	0.828851	−	0.0763706i
$688$	−5.89898	+	10.2173i	−0.224896	+	0.389532i
$689$	−31.5959			−1.20371
$690$	−10.6515	+	23.1202i	−0.405497	+	0.880172i
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	0.208593	+	0.978003i	$0.433112\pi$
$691$	−19.5227	+	33.8143i	−0.742679	+	1.28636i	−0.951271	+	0.308355i	$0.900222\pi$
$692$	−16.8990			−0.642403
$693$	7.89898	−	22.3417i	0.300057	−	0.848691i
$694$	−8.72474	−	15.1117i	−0.331187	−	0.573632i
$695$	−31.3485	+	54.2971i	−1.18912	+	2.05961i
$696$	5.72474	−	12.4261i	0.216996	−	0.471012i
$697$	−2.84847	+	4.93369i	−0.107893	+	0.186877i
$698$	27.8990			1.05599
$699$	−10.1010	−	14.2850i	−0.382056	−	0.540308i
$700$	−2.89898	−	5.02118i	−0.109571	−	0.189783i
$701$	3.15153	−	5.45861i	0.119032	−	0.206169i	−0.800353	−	0.599530i	$-0.795354\pi$
$701$	3.15153	−	5.45861i	0.119032	−	0.206169i	0.919384	+	0.393361i	$0.128688\pi$
$702$	−20.0000	+	5.65685i	−0.754851	+	0.213504i
$703$	0.898979	+	3.81405i	0.0339057	+	0.143850i
$704$	2.72474	−	4.71940i	0.102693	−	0.177869i
$705$	−14.2423	+	30.9145i	−0.536398	+	1.16431i
$706$	−7.89898			−0.297282
$707$	−8.47730	+	14.6831i	−0.318822	+	0.552215i
$708$	0.550510	+	0.778539i	0.0206894	+	0.0292593i
$709$	−12.3939			−0.465462			−0.232731	−	0.972541i	$-0.574766\pi$
$709$	−12.3939			−0.465462			−0.232731	+	0.972541i	$0.574766\pi$
$710$	34.3485			1.28908
$711$	10.0000	−	28.2843i	0.375029	−	1.06074i
$712$	4.50000	+	7.79423i	0.168645	+	0.292101i
$713$	−7.10102			−0.265935
$714$	4.34847	+	6.14966i	0.162737	+	0.230145i
$715$	32.6969	+	56.6328i	1.22280	+	2.11795i
$716$	3.55051	−	6.14966i	0.132689	−	0.229824i
$717$	−0.949490	+	0.0874863i	−0.0354593	+	0.00326724i
$718$	−18.5505			−0.692299
$719$	−7.62372	+	13.2047i	−0.284317	+	0.492451i	−0.972443	−	0.233139i	$-0.925100\pi$
$719$	−7.62372	+	13.2047i	−0.284317	+	0.492451i	0.688126	+	0.725591i	$0.258433\pi$
$720$	3.00000	−	8.48528i	0.111803	−	0.316228i
$721$	16.3031			0.607158
$722$	15.8485	+	10.4798i	0.589819	+	0.390017i
$723$	2.32066	−	5.03723i	0.0863064	−	0.187337i
$724$	11.0000			0.408812
$725$	−31.5959			−1.17344
$726$	−18.6969	−	26.4415i	−0.693908	−	0.981335i
$727$	15.3485	+	26.5843i	0.569243	+	0.985958i	0.996641	+	0.0818945i	$0.0260971\pi$
$727$	15.3485	+	26.5843i	0.569243	+	0.985958i	−0.427398	+	0.904064i	$0.640570\pi$
$728$	2.89898	+	5.02118i	0.107443	+	0.186097i
$729$	23.0000	−	14.1421i	0.851852	−	0.523783i
$730$	14.3939			0.532741
$731$	−35.3939			−1.30909
$732$	5.89898	+	8.34242i	0.218033	+	0.308345i
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	0.571636	−	0.820507i	$-0.306309\pi$
$733$	−11.5000	−	19.9186i	−0.424762	−	0.735710i	−0.996398	+	0.0847976i	$0.972976\pi$
$734$	−6.72474	−	11.6476i	−0.248215	−	0.429921i
$735$	25.3485	−	2.33562i	0.934992	−	0.0861505i
$736$	2.44949	+	4.24264i	0.0902894	+	0.156386i
$737$	−37.5959	−	65.1180i	−1.38486	−	2.39865i
$738$	1.89898	−	5.37113i	0.0699024	−	0.197714i
$739$	−2.62372	+	4.54442i	−0.0965153	+	0.167169i	−0.910240	−	0.414081i	$-0.864103\pi$
$739$	−2.62372	+	4.54442i	−0.0965153	+	0.167169i	0.813725	+	0.581250i	$0.197436\pi$
$740$	1.34847	−	2.33562i	0.0495707	−	0.0858590i
$741$	−20.0000	+	22.6274i	−0.734718	+	0.831239i
$742$	−5.72474	−	9.91555i	−0.210162	−	0.364011i
$743$	−6.55051			−0.240315			−0.120157	−	0.992755i	$-0.538340\pi$
$743$	−6.55051			−0.240315			−0.120157	+	0.992755i	$0.538340\pi$
$744$	2.50000	−	0.230351i	0.0916544	−	0.00844507i
$745$	56.3939			2.06611
$746$	1.84847	−	3.20164i	0.0676773	−	0.117220i
$747$	−4.87117	+	0.905350i	−0.178227	+	0.0331250i
$748$	16.3485			0.597759
$749$	−3.55051	+	6.14966i	−0.129733	+	0.224704i
$750$	5.17423	−	0.476756i	0.188936	−	0.0174087i
$751$	−18.4495	+	31.9555i	−0.673231	+	1.16607i	0.303751	+	0.952751i	$0.401761\pi$
$751$	−18.4495	+	31.9555i	−0.673231	+	1.16607i	−0.976982	+	0.213320i	$0.931572\pi$
$752$	3.27526	+	5.67291i	0.119436	+	0.206870i
$753$	−38.5454	+	3.55159i	−1.40467	+	0.129427i
$754$	31.5959			1.15066
$755$	−8.47730	+	14.6831i	−0.308520	+	0.534373i
$756$	−5.39898	−	5.25153i	−0.196359	−	0.190996i
$757$	26.6464	−	46.1530i	0.968481	−	1.67746i	0.268524	−	0.963273i	$-0.413464\pi$
$757$	26.6464	−	46.1530i	0.968481	−	1.67746i	0.699957	−	0.714185i	$-0.253203\pi$
$758$	11.7980	+	20.4347i	0.428521	+	0.742220i
$759$	46.0454	−	4.24264i	1.67134	−	0.153998i
$760$	−3.00000	−	12.7279i	−0.108821	−	0.461690i
$761$	4.74745	+	8.22282i	0.172095	+	0.298077i	0.939152	−	0.343502i	$-0.111613\pi$
$761$	4.74745	+	8.22282i	0.172095	+	0.298077i	−0.767057	+	0.641579i	$0.778280\pi$
$762$	2.34847	+	3.32124i	0.0850761	+	0.120316i
$763$	0.724745	+	1.25529i	0.0262375	+	0.0454447i
$764$	−10.6237	−	18.4008i	−0.384353	−	0.665719i
$765$	26.5454	−	4.93369i	0.959751	−	0.178378i
$766$	−17.4217	−	30.1752i	−0.629471	−	1.09028i
$767$	−1.10102	+	1.90702i	−0.0397555	+	0.0688586i
$768$	−1.00000	−	1.41421i	−0.0360844	−	0.0510310i
$769$	−11.3485	+	19.6561i	−0.409236	+	0.708818i	−0.994804	−	0.101805i	$-0.967538\pi$
$769$	−11.3485	+	19.6561i	−0.409236	+	0.708818i	0.585568	+	0.810623i	$0.300871\pi$
$770$	−11.8485	+	20.5222i	−0.426989	+	0.739567i
$771$	21.7980	+	30.8270i	0.785034	+	1.11021i
$772$	−9.29796	+	16.1045i	−0.334641	+	0.579615i
$773$	−1.50000	−	2.59808i	−0.0539513	−	0.0934463i	0.837788	−	0.545995i	$-0.183848\pi$
$773$	−1.50000	−	2.59808i	−0.0539513	−	0.0934463i	−0.891740	+	0.452549i	$0.850515\pi$
$774$	34.7980	−	6.46750i	1.25079	−	0.232470i
$775$	−2.89898	−	5.02118i	−0.104134	−	0.180366i
$776$	2.00000	+	3.46410i	0.0717958	+	0.124354i
$777$	−1.30306	−	1.84281i	−0.0467471	−	0.0661103i
$778$	−0.398979	−	0.691053i	−0.0143041	−	0.0247754i
$779$	−1.89898	−	8.05669i	−0.0680380	−	0.288661i
$780$	20.6969	−	1.90702i	0.741069	−	0.0682824i
$781$	−31.1969	−	54.0347i	−1.11631	−	1.93351i
$782$	−7.34847	+	12.7279i	−0.262781	+	0.455150i
$783$	−39.4949	+	11.1708i	−1.41143	+	0.399213i
$784$	2.44949	−	4.24264i	0.0874818	−	0.151523i
$785$	35.6969			1.27408
$786$	−24.3990	+	2.24813i	−0.870283	+	0.0801882i
$787$	−6.72474	−	11.6476i	−0.239711	−	0.415192i	0.720920	−	0.693018i	$-0.243719\pi$
$787$	−6.72474	−	11.6476i	−0.239711	−	0.415192i	−0.960631	+	0.277826i	$0.910386\pi$
$788$	10.8990	−	18.8776i	0.388260	−	0.672486i
$789$	16.8990	−	1.55708i	0.601620	−	0.0554334i
$790$	−15.0000	+	25.9808i	−0.533676	+	0.924354i
$791$	−20.1464			−0.716325
$792$	−16.0732	+	2.98735i	−0.571137	+	0.106151i
$793$	−11.7980	+	20.4347i	−0.418958	+	0.725656i
$794$	−14.5959			−0.517990
$795$	−40.8712	+	3.76588i	−1.44955	+	0.133562i
$796$	−14.3485			−0.508568
$797$	24.9495	+	43.2138i	0.883756	+	1.53071i	0.847133	+	0.531382i	$0.178327\pi$
$797$	24.9495	+	43.2138i	0.883756	+	1.53071i	0.0366237	+	0.999329i	$0.488340\pi$
$798$	−10.7247	−	2.17670i	−0.379652	−	0.0770543i
$799$	−9.82577	+	17.0187i	−0.347611	+	0.602079i
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	9.00000	−	25.4558i	0.317999	−	0.899438i
$802$	15.3990	+	26.6718i	0.543757	+	0.941815i
$803$	−13.0732	−	22.6435i	−0.461344	−	0.799071i
$804$	−23.7980	+	2.19275i	−0.839289	+	0.0773324i
$805$	−10.6515	−	18.4490i	−0.375417	−	0.650242i
$806$	2.89898	+	5.02118i	0.102112	+	0.176864i
$807$	−4.10102	−	5.79972i	−0.144363	−	0.204160i
$808$	11.6969			0.411497
$809$	−48.4949			−1.70499			−0.852495	−	0.522736i	$-0.824912\pi$
$809$	−48.4949			−1.70499			−0.852495	+	0.522736i	$0.824912\pi$
$810$	−25.1969	+	9.70125i	−0.885330	+	0.340867i
$811$	5.52270	+	9.56560i	0.193928	+	0.335894i	0.946549	−	0.322561i	$-0.104544\pi$
$811$	5.52270	+	9.56560i	0.193928	+	0.335894i	−0.752620	+	0.658455i	$0.771210\pi$
$812$	5.72474	+	9.91555i	0.200899	+	0.347968i
$813$	5.65153	+	7.99247i	0.198208	+	0.280308i
$814$	−4.89898			−0.171709
$815$	33.3031			1.16656
$816$	2.17423	−	4.71940i	0.0761134	−	0.165212i
$817$	37.4495	−	35.2446i	1.31019	−	1.23305i
$818$	14.0000			0.489499
$819$	5.79796	−	16.3991i	0.202597	−	0.573031i
$820$	−2.84847	+	4.93369i	−0.0994729	+	0.172292i
$821$	43.2929			1.51093			0.755466	−	0.655188i	$-0.227411\pi$
$821$	43.2929			1.51093			0.755466	+	0.655188i	$0.227411\pi$
$822$	−30.5227	+	2.81237i	−1.06460	+	0.0980928i
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	−0.692240	−	0.721668i	$-0.743376\pi$
$823$	8.00000	−	13.8564i	0.278862	−	0.483004i	0.971102	+	0.238664i	$0.0767093\pi$
$824$	−5.62372	−	9.74058i	−0.195912	−	0.339329i
$825$	21.7980	+	30.8270i	0.758908	+	1.07326i
$826$	−0.797959			−0.0277645
$827$	1.07321	+	1.85886i	0.0373193	+	0.0646389i	0.884082	−	0.467332i	$-0.154785\pi$
$827$	1.07321	+	1.85886i	0.0373193	+	0.0646389i	−0.846762	+	0.531971i	$0.821451\pi$
$828$	4.89898	−	13.8564i	0.170251	−	0.481543i
$829$	13.3939			0.465189			0.232594	−	0.972574i	$-0.425279\pi$
$829$	13.3939			0.465189			0.232594	+	0.972574i	$0.425279\pi$
$830$	4.95459			0.171976
$831$	−1.69694	−	2.39983i	−0.0588661	−	0.0832493i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	14.6969			0.509219
$834$	15.1464	−	32.8769i	0.524478	−	1.13843i
$835$	9.00000	−	15.5885i	0.311458	−	0.539461i
$836$	−17.2980	+	16.2795i	−0.598262	+	0.563039i
$837$	−5.39898	−	5.25153i	−0.186616	−	0.181519i
$838$	4.62372	−	8.00853i	0.159724	−	0.276650i
$839$	9.79796	+	16.9706i	0.338263	+	0.585889i	0.984106	−	0.177581i	$-0.0568273\pi$
$839$	9.79796	+	16.9706i	0.338263	+	0.585889i	−0.645843	+	0.763470i	$0.723494\pi$
$840$	4.34847	+	6.14966i	0.150036	+	0.212184i
$841$	33.3939			1.15151
$842$	−5.34847	+	9.26382i	−0.184320	+	0.319252i
$843$	−15.2196	+	33.0358i	−0.524192	+	1.13781i
$844$	−10.5227	+	18.2259i	−0.362206	+	0.627360i
$845$	4.50000	+	7.79423i	0.154805	+	0.268130i
$846$	6.55051	−	18.5276i	0.225211	−	0.636993i
$847$	27.1010			0.931202
$848$	−3.94949	+	6.84072i	−0.135626	+	0.234911i
$849$	−6.99490	+	15.1831i	−0.240064	+	0.521084i
$850$	−12.0000			−0.411597
$851$	2.20204	−	3.81405i	0.0754850	−	0.130744i
$852$	−19.7474	+	1.81954i	−0.676536	+	0.0623363i
$853$	15.5959	+	27.0129i	0.533994	+	0.924905i	0.999211	+	0.0397083i	$0.0126429\pi$
$853$	15.5959	+	27.0129i	0.533994	+	0.924905i	−0.465217	+	0.885197i	$0.654024\pi$
$854$	−8.55051			−0.292592
$855$	−23.1742	+	31.6537i	−0.792542	+	1.08253i
$856$	4.89898			0.167444
$857$	26.4495	+	45.8119i	0.903497	+	1.56490i	0.822922	+	0.568155i	$0.192343\pi$
$857$	26.4495	+	45.8119i	0.903497	+	1.56490i	0.0805757	+	0.996748i	$0.474324\pi$
$858$	−21.7980	−	30.8270i	−0.744170	−	1.05242i
$859$	−7.79796	+	13.5065i	−0.266063	+	0.460835i	−0.967842	−	0.251561i	$-0.919056\pi$
$859$	−7.79796	+	13.5065i	−0.266063	+	0.460835i	0.701779	+	0.712395i	$0.252390\pi$
$860$	−35.3939			−1.20692
$861$	2.75255	+	3.89270i	0.0938067	+	0.132663i
$862$	−7.62372	+	13.2047i	−0.259665	+	0.449753i
$863$	−7.10102			−0.241722			−0.120861	−	0.992669i	$-0.538565\pi$
$863$	−7.10102			−0.241722			−0.120861	+	0.992669i	$0.538565\pi$
$864$	−1.27526	+	5.03723i	−0.0433851	+	0.171370i
$865$	−25.3485	−	43.9048i	−0.861874	−	1.49281i
$866$	−1.39898	+	2.42310i	−0.0475393	+	0.0823404i
$867$	−13.7980	+	1.27135i	−0.468603	+	0.0431773i
$868$	−1.05051	+	1.81954i	−0.0356566	+	0.0617591i
$869$	54.4949			1.84861
$870$	40.8712	−	3.76588i	1.38566	−	0.127675i
$871$	−27.5959	−	47.7975i	−0.935052	−	1.61956i
$872$	0.500000	−	0.866025i	0.0169321	−	0.0293273i
$873$	4.00000	−	11.3137i	0.135379	−	0.382911i
$874$	−4.89898	−	20.7846i	−0.165710	−	0.703050i
$875$	−2.17423	+	3.76588i	−0.0735025	+	0.127310i
$876$	−8.27526	+	0.762485i	−0.279595	+	0.0257620i
$877$	33.2929			1.12422			0.562110	−	0.827063i	$-0.309990\pi$
$877$	33.2929			1.12422			0.562110	+	0.827063i	$0.309990\pi$
$878$	8.00000	−	13.8564i	0.269987	−	0.467631i
$879$	0.522704	−	0.0481621i	0.0176304	−	0.00162447i
$880$	16.3485			0.551107
$881$	21.7980			0.734392			0.367196	−	0.930144i	$-0.380318\pi$
$881$	21.7980			0.734392			0.367196	+	0.930144i	$0.380318\pi$
$882$	−14.4495	+	2.68556i	−0.486540	+	0.0904276i
$883$	−12.1742	−	21.0864i	−0.409696	−	0.709614i	0.585160	−	0.810918i	$-0.301032\pi$
$883$	−12.1742	−	21.0864i	−0.409696	−	0.709614i	−0.994855	+	0.101304i	$0.967698\pi$
$884$	12.0000			0.403604
$885$	−1.19694	+	2.59808i	−0.0402346	+	0.0873334i
$886$	1.92679	+	3.33729i	0.0647316	+	0.112118i
$887$	−9.55051	+	16.5420i	−0.320675	+	0.555425i	−0.980627	−	0.195882i	$-0.937243\pi$
$887$	−9.55051	+	16.5420i	−0.320675	+	0.555425i	0.659953	+	0.751307i	$0.270576\pi$
$888$	−0.651531	+	1.41421i	−0.0218639	+	0.0474579i
$889$	−3.40408			−0.114169
$890$	−13.5000	+	23.3827i	−0.452521	+	0.783789i
$891$	38.1464	+	30.8270i	1.27795	+	1.03274i
$892$	−8.89898			−0.297960
$893$	−6.55051	−	27.7915i	−0.219204	−	0.930006i
$894$	−32.4217	+	2.98735i	−1.08434	+	0.0999118i
$895$	21.3031			0.712083
$896$	1.44949			0.0484241
$897$	33.7980	−	3.11416i	1.12848	−	0.103979i
$898$	−10.8990	−	18.8776i	−0.363704	−	0.629953i
$899$	5.72474	+	9.91555i	0.190931	+	0.330702i
$900$	11.7980	−	2.19275i	0.393265	−	0.0730918i
$901$	−23.6969			−0.789459
$902$	10.3485			0.344566
$903$	−12.3939	+	26.9022i	−0.412442	+	0.895248i
$904$	6.94949	+	12.0369i	0.231137	+	0.400340i
$905$	16.5000	+	28.5788i	0.548479	+	0.949993i
$906$	4.09592	−	8.89060i	0.136078	−	0.295371i
$907$	7.69694	+	13.3315i	0.255573	+	0.442665i	0.965051	−	0.262063i	$-0.0844027\pi$
$907$	7.69694	+	13.3315i	0.255573	+	0.442665i	−0.709478	+	0.704727i	$0.751069\pi$
$908$	6.27526	+	10.8691i	0.208252	+	0.360702i
$909$	−22.8031	−	26.6718i	−0.756330	−	0.884648i
$910$	−8.69694	+	15.0635i	−0.288301	+	0.499351i
$911$	25.6237	−	44.3816i	0.848952	−	1.47043i	−0.0331927	−	0.999449i	$-0.510567\pi$
$911$	25.6237	−	44.3816i	0.848952	−	1.47043i	0.882145	−	0.470979i	$-0.156099\pi$
$912$	2.39898	+	7.15855i	0.0794381	+	0.237043i
$913$	−4.50000	−	7.79423i	−0.148928	−	0.257951i
$914$	−40.7980			−1.34948
$915$	−12.8258	+	27.8396i	−0.424007	+	0.920350i
$916$	12.5959			0.416181
$917$	10.2526	−	17.7579i	0.338569	−	0.586419i
$918$	−15.0000	+	4.24264i	−0.495074	+	0.140028i
$919$	−22.0000			−0.725713			−0.362857	−	0.931845i	$-0.618198\pi$
$919$	−22.0000			−0.725713			−0.362857	+	0.931845i	$0.618198\pi$
$920$	−7.34847	+	12.7279i	−0.242272	+	0.419627i
$921$	8.34847	+	11.8065i	0.275091	+	0.389038i
$922$	−14.6969	+	25.4558i	−0.484018	+	0.838344i
$923$	−22.8990	−	39.6622i	−0.753729	−	1.30550i
$924$	5.72474	−	12.4261i	0.188330	−	0.408790i
$925$	3.59592			0.118233
$926$	−12.1742	+	21.0864i	−0.400070	+	0.692942i
$927$	−11.2474	+	31.8126i	−0.369415	+	1.04486i
$928$	3.94949	−	6.84072i	0.129648	−	0.224558i
$929$	−12.7980	−	22.1667i	−0.419887	−	0.727266i	0.576040	−	0.817421i	$-0.304597\pi$
$929$	−12.7980	−	22.1667i	−0.419887	−	0.727266i	−0.995928	+	0.0901549i	$0.971264\pi$
$930$	4.34847	+	6.14966i	0.142592	+	0.201655i
$931$	−15.5505	+	14.6349i	−0.509647	+	0.479641i
$932$	−5.05051	−	8.74774i	−0.165435	−	0.286542i
$933$	−48.8939	+	4.50510i	−1.60071	+	0.147490i
$934$	−9.00000	−	15.5885i	−0.294489	−	0.510070i
$935$	24.5227	+	42.4746i	0.801978	+	1.38907i
$936$	−11.7980	+	2.19275i	−0.385628	+	0.0716724i
$937$	−21.2980	−	36.8891i	−0.695774	−	1.20512i	−0.969919	−	0.243428i	$-0.921728\pi$
$937$	−21.2980	−	36.8891i	−0.695774	−	1.20512i	0.274145	−	0.961688i	$-0.411605\pi$
$938$	10.0000	−	17.3205i	0.326512	−	0.565535i
$939$	0.724745	−	1.57313i	0.0236512	−	0.0513372i
$940$	−9.82577	+	17.0187i	−0.320481	+	0.555090i
$941$	−20.4495	+	35.4196i	−0.666634	+	1.15464i	0.312205	+	0.950015i	$0.398932\pi$
$941$	−20.4495	+	35.4196i	−0.666634	+	1.15464i	−0.978839	+	0.204630i	$0.934401\pi$
$942$	−20.5227	+	1.89097i	−0.668666	+	0.0616111i
$943$	−4.65153	+	8.05669i	−0.151475	+	0.262362i
$944$	0.275255	+	0.476756i	0.00895879	+	0.0155171i
$945$	5.54541	−	21.9043i	0.180392	−	0.712546i
$946$	32.1464	+	55.6792i	1.04517	+	1.81029i
$947$	−1.10102	−	1.90702i	−0.0357784	−	0.0619699i	0.847582	−	0.530665i	$-0.178058\pi$
$947$	−1.10102	−	1.90702i	−0.0357784	−	0.0619699i	−0.883360	+	0.468695i	$0.844724\pi$
$948$	7.24745	−	15.7313i	0.235386	−	0.510930i
$949$	−9.59592	−	16.6206i	−0.311497	−	0.539528i
$950$	12.6969	−	11.9494i	0.411943	−	0.387689i
$951$	12.8258	−	27.8396i	0.415904	−	0.902762i
$952$	2.17423	+	3.76588i	0.0704673	+	0.122053i
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	−0.905074	−	0.425255i	$-0.860184\pi$
$953$	−2.60102	+	4.50510i	−0.0842553	+	0.145934i	0.820818	+	0.571189i	$0.193518\pi$
$954$	23.2980	−	4.33013i	0.754299	−	0.140193i
$955$	31.8712	−	55.2025i	1.03133	−	1.78631i
$956$	−0.550510			−0.0178048
$957$	−43.0454	−	60.8754i	−1.39146	−	1.96782i
$958$	−0.275255	−	0.476756i	−0.00889309	−	0.0154033i
$959$	12.8258	−	22.2149i	0.414166	−	0.717356i
$960$	2.17423	−	4.71940i	0.0701731	−	0.152318i
$961$	14.4495	−	25.0273i	0.466113	−	0.807331i
$962$	−3.59592			−0.115937
$963$	−9.55051	−	11.1708i	−0.307761	−	0.359975i
$964$	1.60102	−	2.77305i	0.0515654	−	0.0893139i
$965$	−55.7878			−1.79587
$966$	7.10102	+	10.0424i	0.228472	+	0.323108i
$967$	−33.4495			−1.07566			−0.537832	−	0.843052i	$-0.680756\pi$
$967$	−33.4495			−1.07566			−0.537832	+	0.843052i	$0.680756\pi$
$968$	−9.34847	−	16.1920i	−0.300471	−	0.520431i
$969$	−15.0000	+	16.9706i	−0.481869	+	0.545173i
$970$	−6.00000	+	10.3923i	−0.192648	+	0.333677i
$971$	−10.8712	+	18.8294i	−0.348873	+	0.604265i	−0.986049	−	0.166453i	$-0.946769\pi$
$971$	−10.8712	+	18.8294i	−0.348873	+	0.604265i	0.637177	+	0.770718i	$0.280102\pi$
$972$	13.9722	−	6.91215i	0.448158	−	0.221707i
$973$	15.1464	+	26.2344i	0.485572	+	0.841036i
$974$	−18.6969	−	32.3840i	−0.599089	−	1.03765i
$975$	16.0000	+	22.6274i	0.512410	+	0.724657i
$976$	2.94949	+	5.10867i	0.0944109	+	0.163524i
$977$	11.2980	+	19.5686i	0.361454	+	0.626056i	0.988200	−	0.153167i	$-0.0489472\pi$
$977$	11.2980	+	19.5686i	0.361454	+	0.626056i	−0.626747	+	0.779223i	$0.715614\pi$
$978$	−19.1464	+	1.76416i	−0.612235	+	0.0564116i
$979$	49.0454			1.56750
$980$	14.6969			0.469476
$981$	−2.94949	+	0.548188i	−0.0941700	+	0.0175023i
$982$	−16.8712	−	29.2217i	−0.538381	−	0.932503i
$983$	18.2474	+	31.6055i	0.582003	+	1.00806i	0.995242	+	0.0974363i	$0.0310642\pi$
$983$	18.2474	+	31.6055i	0.582003	+	1.00806i	−0.413239	+	0.910623i	$0.635602\pi$
$984$	1.37628	−	2.98735i	0.0438741	−	0.0952331i
$985$	65.3939			2.08362
$986$	23.6969			0.754664
$987$	9.49490	+	13.4278i	0.302226	+	0.427412i
$988$	−12.6969	+	11.9494i	−0.403943	+	0.380161i
$989$	−57.7980			−1.83787
$990$	−31.8712	−	37.2784i	−1.01293	−	1.18479i
$991$	27.6237	−	47.8457i	0.877497	−	1.51987i	0.0234172	−	0.999726i	$-0.492545\pi$
$991$	27.6237	−	47.8457i	0.877497	−	1.51987i	0.854079	−	0.520143i	$-0.174121\pi$
$992$	1.44949			0.0460213
$993$	14.3485	+	20.2918i	0.455335	+	0.643941i
$994$	8.29796	−	14.3725i	0.263195	−	0.455868i
$995$	−21.5227	−	37.2784i	−0.682316	−	1.18181i
$996$	−2.84847	+	0.262459i	−0.0902572	+	0.00831633i
$997$	−3.69694			−0.117083			−0.0585416	−	0.998285i	$-0.518645\pi$
$997$	−3.69694			−0.117083			−0.0585416	+	0.998285i	$0.518645\pi$
$998$	14.5227	+	25.1541i	0.459708	+	0.796238i
$999$	4.49490	−	1.27135i	0.142212	−	0.0402237i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.h.e.277.1	yes	4
3.2	odd	2		1026.2.h.e.505.1		4
9.4	even	3		342.2.f.e.49.2	yes	4
9.5	odd	6		1026.2.f.e.847.1		4
19.7	even	3		342.2.f.e.7.1	✓	4
57.26	odd	6		1026.2.f.e.235.1		4
171.121	even	3	inner	342.2.h.e.121.1	yes	4
171.140	odd	6		1026.2.h.e.577.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
342.2.f.e.7.1	✓	4	19.7	even	3
342.2.f.e.49.2	yes	4	9.4	even	3
342.2.h.e.121.1	yes	4	171.121	even	3	inner
342.2.h.e.277.1	yes	4	1.1	even	1	trivial
1026.2.f.e.235.1		4	57.26	odd	6
1026.2.f.e.847.1		4	9.5	odd	6
1026.2.h.e.505.1		4	3.2	odd	2
1026.2.h.e.577.1		4	171.140	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(1.72474 - 0.158919i) q^{6} +(-0.724745 + 1.25529i) q^{7} +1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.724745 + 1.57313i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.00000 q^{5} +(1.72474 - 0.158919i) q^{6} +(-0.724745 + 1.25529i) q^{7} +1.00000 q^{8} +(-1.94949 - 2.28024i) q^{9} +(1.50000 + 2.59808i) q^{10} +(2.72474 - 4.71940i) q^{11} +(-1.00000 - 1.41421i) q^{12} +(2.00000 - 3.46410i) q^{13} +1.44949 q^{14} +(2.17423 - 4.71940i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.50000 - 2.59808i) q^{17} +(-1.00000 + 2.82843i) q^{18} +(1.00000 + 4.24264i) q^{19} +(1.50000 - 2.59808i) q^{20} +(-1.44949 - 2.04989i) q^{21} -5.44949 q^{22} +(2.44949 - 4.24264i) q^{23} +(-0.724745 + 1.57313i) q^{24} +4.00000 q^{25} -4.00000 q^{26} +(5.00000 - 1.41421i) q^{27} +(-0.724745 - 1.25529i) q^{28} -7.89898 q^{29} +(-5.17423 + 0.476756i) q^{30} +(-0.724745 - 1.25529i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.44949 + 7.70674i) q^{33} -3.00000 q^{34} +(2.17423 - 3.76588i) q^{35} +(2.94949 - 0.548188i) q^{36} +0.898979 q^{37} +(3.17423 - 2.98735i) q^{38} +(4.00000 + 5.65685i) q^{39} -3.00000 q^{40} -1.89898 q^{41} +(-1.05051 + 2.28024i) q^{42} +(-5.89898 - 10.2173i) q^{43} +(2.72474 + 4.71940i) q^{44} +(5.84847 + 6.84072i) q^{45} -4.89898 q^{46} -6.55051 q^{47} +(1.72474 - 0.158919i) q^{48} +(2.44949 + 4.24264i) q^{49} +(-2.00000 - 3.46410i) q^{50} +(3.00000 + 4.24264i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-3.94949 - 6.84072i) q^{53} +(-3.72474 - 3.62302i) q^{54} +(-8.17423 + 14.1582i) q^{55} +(-0.724745 + 1.25529i) q^{56} +(-7.39898 - 1.50170i) q^{57} +(3.94949 + 6.84072i) q^{58} -0.550510 q^{59} +(3.00000 + 4.24264i) q^{60} -5.89898 q^{61} +(-0.724745 + 1.25529i) q^{62} +(4.27526 - 0.794593i) q^{63} +1.00000 q^{64} +(-6.00000 + 10.3923i) q^{65} +(3.94949 - 8.57277i) q^{66} +(6.89898 - 11.9494i) q^{67} +(1.50000 + 2.59808i) q^{68} +(4.89898 + 6.92820i) q^{69} -4.34847 q^{70} +(5.72474 - 9.91555i) q^{71} +(-1.94949 - 2.28024i) q^{72} +(2.39898 - 4.15515i) q^{73} +(-0.449490 - 0.778539i) q^{74} +(-2.89898 + 6.29253i) q^{75} +(-4.17423 - 1.25529i) q^{76} +(3.94949 + 6.84072i) q^{77} +(2.89898 - 6.29253i) q^{78} +(5.00000 + 8.66025i) q^{79} +(1.50000 + 2.59808i) q^{80} +(-1.39898 + 8.89060i) q^{81} +(0.949490 + 1.64456i) q^{82} +(0.825765 - 1.43027i) q^{83} +(2.50000 - 0.230351i) q^{84} +(-4.50000 + 7.79423i) q^{85} +(-5.89898 + 10.2173i) q^{86} +(5.72474 - 12.4261i) q^{87} +(2.72474 - 4.71940i) q^{88} +(4.50000 + 7.79423i) q^{89} +(3.00000 - 8.48528i) q^{90} +(2.89898 + 5.02118i) q^{91} +(2.44949 + 4.24264i) q^{92} +(2.50000 - 0.230351i) q^{93} +(3.27526 + 5.67291i) q^{94} +(-3.00000 - 12.7279i) q^{95} +(-1.00000 - 1.41421i) q^{96} +(2.00000 + 3.46410i) q^{97} +(2.44949 - 4.24264i) q^{98} +(-16.0732 + 2.98735i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 12 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} + 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{15} - 2 q^{16} + 6 q^{17} - 4 q^{18} + 4 q^{19} + 6 q^{20} + 4 q^{21} - 12 q^{22} + 2 q^{24} + 16 q^{25} - 16 q^{26} + 20 q^{27} + 2 q^{28} - 12 q^{29} - 6 q^{30} + 2 q^{31} - 2 q^{32} + 12 q^{33} - 12 q^{34} - 6 q^{35} + 2 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 12 q^{40} + 12 q^{41} - 14 q^{42} - 4 q^{43} + 6 q^{44} - 6 q^{45} - 36 q^{47} + 2 q^{48} - 8 q^{50} + 12 q^{51} + 8 q^{52} - 6 q^{53} - 10 q^{54} - 18 q^{55} + 2 q^{56} - 10 q^{57} + 6 q^{58} - 12 q^{59} + 12 q^{60} - 4 q^{61} + 2 q^{62} + 22 q^{63} + 4 q^{64} - 24 q^{65} + 6 q^{66} + 8 q^{67} + 6 q^{68} + 12 q^{70} + 18 q^{71} + 2 q^{72} - 10 q^{73} + 8 q^{74} + 8 q^{75} - 2 q^{76} + 6 q^{77} - 8 q^{78} + 20 q^{79} + 6 q^{80} + 14 q^{81} - 6 q^{82} + 18 q^{83} + 10 q^{84} - 18 q^{85} - 4 q^{86} + 18 q^{87} + 6 q^{88} + 18 q^{89} + 12 q^{90} - 8 q^{91} + 10 q^{93} + 18 q^{94} - 12 q^{95} - 4 q^{96} + 8 q^{97} - 30 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 12 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 + 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^15 - 2 * q^16 + 6 * q^17 - 4 * q^18 + 4 * q^19 + 6 * q^20 + 4 * q^21 - 12 * q^22 + 2 * q^24 + 16 * q^25 - 16 * q^26 + 20 * q^27 + 2 * q^28 - 12 * q^29 - 6 * q^30 + 2 * q^31 - 2 * q^32 + 12 * q^33 - 12 * q^34 - 6 * q^35 + 2 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 12 * q^40 + 12 * q^41 - 14 * q^42 - 4 * q^43 + 6 * q^44 - 6 * q^45 - 36 * q^47 + 2 * q^48 - 8 * q^50 + 12 * q^51 + 8 * q^52 - 6 * q^53 - 10 * q^54 - 18 * q^55 + 2 * q^56 - 10 * q^57 + 6 * q^58 - 12 * q^59 + 12 * q^60 - 4 * q^61 + 2 * q^62 + 22 * q^63 + 4 * q^64 - 24 * q^65 + 6 * q^66 + 8 * q^67 + 6 * q^68 + 12 * q^70 + 18 * q^71 + 2 * q^72 - 10 * q^73 + 8 * q^74 + 8 * q^75 - 2 * q^76 + 6 * q^77 - 8 * q^78 + 20 * q^79 + 6 * q^80 + 14 * q^81 - 6 * q^82 + 18 * q^83 + 10 * q^84 - 18 * q^85 - 4 * q^86 + 18 * q^87 + 6 * q^88 + 18 * q^89 + 12 * q^90 - 8 * q^91 + 10 * q^93 + 18 * q^94 - 12 * q^95 - 4 * q^96 + 8 * q^97 - 30 * q^99

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