LMFDB - Embedded newform 65.2.k.b.8.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(8,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("65.8");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.k (of order $4$, 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:	$0.519027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.619810816.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{5} + 14x^{4} - 8x^{3} + 2x^{2} + 2x + 1 $ x^8 - 2x^5 + 14x^4 - 8x^3 + 2x^2 + 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.4
Root			$0.561103 - 0.561103i$ of defining polynomial
Character	$\chi$	$=$	65.8
Dual form			65.2.k.b.57.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.03032 q^{2} +(-1.33000 - 1.33000i) q^{3} +2.12221 q^{4} +(-1.45220 + 1.70032i) q^{5} +(-2.70032 - 2.70032i) q^{6} +1.61845i q^{7} +0.248119 q^{8} +0.537789i q^{9} +O(q^{10})$	\(q+2.03032 q^{2} +(-1.33000 - 1.33000i) q^{3} +2.12221 q^{4} +(-1.45220 + 1.70032i) q^{5} +(-2.70032 - 2.70032i) q^{6} +1.61845i q^{7} +0.248119 q^{8} +0.537789i q^{9} +(-2.94844 + 3.45220i) q^{10} +(2.70032 - 2.70032i) q^{11} +(-2.82253 - 2.82253i) q^{12} +(-1.04033 + 3.45220i) q^{13} +3.28596i q^{14} +(4.19286 - 0.329998i) q^{15} -3.74065 q^{16} +(-2.24812 - 2.24812i) q^{17} +1.09188i q^{18} +(2.33000 - 2.33000i) q^{19} +(-3.08188 + 3.60844i) q^{20} +(2.15253 - 2.15253i) q^{21} +(5.48253 - 5.48253i) q^{22} +(4.82253 - 4.82253i) q^{23} +(-0.329998 - 0.329998i) q^{24} +(-0.782203 - 4.93844i) q^{25} +(-2.11220 + 7.00909i) q^{26} +(-3.27474 + 3.27474i) q^{27} +3.43468i q^{28} +4.27844i q^{29} +(8.51285 - 0.670002i) q^{30} +(3.36032 + 3.36032i) q^{31} -8.09097 q^{32} -7.18285 q^{33} +(-4.56441 - 4.56441i) q^{34} +(-2.75188 - 2.35031i) q^{35} +1.14130i q^{36} +7.78220i q^{37} +(4.73065 - 4.73065i) q^{38} +(5.97506 - 3.20779i) q^{39} +(-0.360320 + 0.421883i) q^{40} +(2.87409 + 2.87409i) q^{41} +(4.37033 - 4.37033i) q^{42} +(-3.97876 + 3.97876i) q^{43} +(5.73065 - 5.73065i) q^{44} +(-0.914416 - 0.780980i) q^{45} +(9.79129 - 9.79129i) q^{46} -5.36662i q^{47} +(4.97506 + 4.97506i) q^{48} +4.38064 q^{49} +(-1.58812 - 10.0266i) q^{50} +5.97999i q^{51} +(-2.20779 + 7.32629i) q^{52} +(-4.61845 - 4.61845i) q^{53} +(-6.64877 + 6.64877i) q^{54} +(0.670002 + 8.51285i) q^{55} +0.401567i q^{56} -6.19779 q^{57} +8.68661i q^{58} +(-4.47130 - 4.47130i) q^{59} +(8.89811 - 0.700324i) q^{60} -12.1479 q^{61} +(6.82253 + 6.82253i) q^{62} -0.870382 q^{63} -8.94596 q^{64} +(-4.35910 - 6.78220i) q^{65} -14.5835 q^{66} +5.84285 q^{67} +(-4.77097 - 4.77097i) q^{68} -12.8279 q^{69} +(-5.58720 - 4.77189i) q^{70} +(-1.37155 - 1.37155i) q^{71} +0.133436i q^{72} +4.02662 q^{73} +15.8004i q^{74} +(-5.52778 + 7.60844i) q^{75} +(4.94474 - 4.94474i) q^{76} +(4.37033 + 4.37033i) q^{77} +(12.1313 - 6.51285i) q^{78} +8.63754i q^{79} +(5.43219 - 6.36032i) q^{80} +10.3242 q^{81} +(5.83532 + 5.83532i) q^{82} -7.48791i q^{83} +(4.56811 - 4.56811i) q^{84} +(7.08726 - 0.557801i) q^{85} +(-8.07817 + 8.07817i) q^{86} +(5.69032 - 5.69032i) q^{87} +(0.670002 - 0.670002i) q^{88} +(-8.59843 - 8.59843i) q^{89} +(-1.85656 - 1.58564i) q^{90} +(-5.58720 - 1.68371i) q^{91} +(10.2344 - 10.2344i) q^{92} -8.93844i q^{93} -10.8960i q^{94} +(0.578117 + 7.34539i) q^{95} +(10.7610 + 10.7610i) q^{96} +8.63754 q^{97} +8.89410 q^{98} +(1.45220 + 1.45220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6	$ 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 8 q^{16} - 16 q^{17} + 14 q^{19} - 22 q^{20} - 12 q^{21} + 10 q^{22} + 14 q^{23} + 2 q^{24} + 12 q^{25} + 6 q^{26} + 12 q^{27} + 14 q^{30} + 2 q^{31} - 4 q^{32} - 8 q^{33} - 24 q^{35} + 2 q^{38} - 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} + 6 q^{43} + 10 q^{44} + 6 q^{45} + 2 q^{46} - 14 q^{48} - 24 q^{49} - 20 q^{50} - 22 q^{52} - 24 q^{53} - 20 q^{54} + 10 q^{55} - 40 q^{57} + 22 q^{59} + 46 q^{60} + 20 q^{61} + 30 q^{62} + 16 q^{63} - 48 q^{64} - 36 q^{66} - 12 q^{67} + 4 q^{68} - 4 q^{69} + 20 q^{70} - 10 q^{71} - 4 q^{73} - 30 q^{75} + 6 q^{76} + 24 q^{77} + 30 q^{78} + 2 q^{80} - 20 q^{81} - 20 q^{82} + 16 q^{84} - 20 q^{85} - 46 q^{86} + 16 q^{87} + 10 q^{88} - 28 q^{89} + 14 q^{90} + 20 q^{91} + 50 q^{92} - 2 q^{95} + 30 q^{96} + 12 q^{97} + 92 q^{98} - 2 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 8 * q^16 - 16 * q^17 + 14 * q^19 - 22 * q^20 - 12 * q^21 + 10 * q^22 + 14 * q^23 + 2 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 14 * q^30 + 2 * q^31 - 4 * q^32 - 8 * q^33 - 24 * q^35 + 2 * q^38 - 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 + 6 * q^43 + 10 * q^44 + 6 * q^45 + 2 * q^46 - 14 * q^48 - 24 * q^49 - 20 * q^50 - 22 * q^52 - 24 * q^53 - 20 * q^54 + 10 * q^55 - 40 * q^57 + 22 * q^59 + 46 * q^60 + 20 * q^61 + 30 * q^62 + 16 * q^63 - 48 * q^64 - 36 * q^66 - 12 * q^67 + 4 * q^68 - 4 * q^69 + 20 * q^70 - 10 * q^71 - 4 * q^73 - 30 * q^75 + 6 * q^76 + 24 * q^77 + 30 * q^78 + 2 * q^80 - 20 * q^81 - 20 * q^82 + 16 * q^84 - 20 * q^85 - 46 * q^86 + 16 * q^87 + 10 * q^88 - 28 * q^89 + 14 * q^90 + 20 * q^91 + 50 * q^92 - 2 * q^95 + 30 * q^96 + 12 * q^97 + 92 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	2.03032			1.43565			0.717827	−	0.696221i	$-0.245137\pi$
$2$	2.03032			1.43565			0.717827	+	0.696221i	$0.245137\pi$
$3$	−1.33000	−	1.33000i	−0.767875	−	0.767875i	0.209857	−	0.977732i	$-0.432700\pi$
$3$	−1.33000	−	1.33000i	−0.767875	−	0.767875i	−0.977732	+	0.209857i	$0.932700\pi$
$4$	2.12221			1.06110
$5$	−1.45220	+	1.70032i	−0.649446	+	0.760408i
$5$	−1.45220	+	1.70032i	−0.649446	+	0.760408i
$6$	−2.70032	−	2.70032i	−1.10240	−	1.10240i
$7$			1.61845i			0.611715i	0.952077	+	0.305857i	$0.0989431\pi$
$7$			1.61845i			0.611715i	−0.952077	+	0.305857i	$0.901057\pi$
$8$	0.248119			0.0877234
$9$			0.537789i			0.179263i
$10$	−2.94844	+	3.45220i	−0.932380	+	1.09168i
$11$	2.70032	−	2.70032i	0.814178	−	0.814178i	−0.171079	−	0.985257i	$-0.554725\pi$
$11$	2.70032	−	2.70032i	0.814178	−	0.814178i	0.985257	+	0.171079i	$0.0547253\pi$
$12$	−2.82253	−	2.82253i	−0.814794	−	0.814794i
$13$	−1.04033	+	3.45220i	−0.288535	+	0.957469i
$13$	−1.04033	+	3.45220i	−0.288535	+	0.957469i
$14$			3.28596i			0.878211i
$15$	4.19286	−	0.329998i	1.08259	−	0.0852051i
$16$	−3.74065			−0.935163
$17$	−2.24812	−	2.24812i	−0.545249	−	0.545249i	0.379814	−	0.925063i	$-0.375988\pi$
$17$	−2.24812	−	2.24812i	−0.545249	−	0.545249i	−0.925063	+	0.379814i	$0.875988\pi$
$18$			1.09188i			0.257360i
$19$	2.33000	−	2.33000i	0.534538	−	0.534538i	−0.387381	−	0.921920i	$-0.626620\pi$
$19$	2.33000	−	2.33000i	0.534538	−	0.534538i	0.921920	+	0.387381i	$0.126620\pi$
$20$	−3.08188	+	3.60844i	−0.689129	+	0.806871i
$21$	2.15253	−	2.15253i	0.469720	−	0.469720i
$22$	5.48253	−	5.48253i	1.16888	−	1.16888i
$23$	4.82253	−	4.82253i	1.00557	−	1.00557i	0.00558275	−	0.999984i	$-0.498223\pi$
$23$	4.82253	−	4.82253i	1.00557	−	1.00557i	0.999984	−	0.00558275i	$-0.00177705\pi$
$24$	−0.329998	−	0.329998i	−0.0673605	−	0.0673605i
$25$	−0.782203	−	4.93844i	−0.156441	−	0.987687i
$26$	−2.11220	+	7.00909i	−0.414237	+	1.37460i
$27$	−3.27474	+	3.27474i	−0.630223	+	0.630223i
$28$			3.43468i			0.649093i
$29$			4.27844i			0.794487i	0.917713	+	0.397243i	$0.130033\pi$
$29$			4.27844i			0.794487i	−0.917713	+	0.397243i	$0.869967\pi$
$30$	8.51285	−	0.670002i	1.55423	−	0.122325i
$31$	3.36032	+	3.36032i	0.603531	+	0.603531i	0.941248	−	0.337717i	$-0.109655\pi$
$31$	3.36032	+	3.36032i	0.603531	+	0.603531i	−0.337717	+	0.941248i	$0.609655\pi$
$32$	−8.09097			−1.43029
$33$	−7.18285			−1.25037
$34$	−4.56441	−	4.56441i	−0.782789	−	0.782789i
$35$	−2.75188	−	2.35031i	−0.465153	−	0.397276i
$36$			1.14130i			0.190217i
$37$			7.78220i			1.27939i	0.768630	+	0.639693i	$0.220939\pi$
$37$			7.78220i			1.27939i	−0.768630	+	0.639693i	$0.779061\pi$
$38$	4.73065	−	4.73065i	0.767412	−	0.767412i
$39$	5.97506	−	3.20779i	0.956775	−	0.513658i
$40$	−0.360320	+	0.421883i	−0.0569716	+	0.0667055i
$41$	2.87409	+	2.87409i	0.448857	+	0.448857i	0.894974	−	0.446117i	$-0.147194\pi$
$41$	2.87409	+	2.87409i	0.448857	+	0.448857i	−0.446117	+	0.894974i	$0.647194\pi$
$42$	4.37033	−	4.37033i	0.674356	−	0.674356i
$43$	−3.97876	+	3.97876i	−0.606756	+	0.606756i	−0.942097	−	0.335341i	$-0.891149\pi$
$43$	−3.97876	+	3.97876i	−0.606756	+	0.606756i	0.335341	+	0.942097i	$0.391149\pi$
$44$	5.73065	−	5.73065i	0.863927	−	0.863927i
$45$	−0.914416	−	0.780980i	−0.136313	−	0.116422i
$46$	9.79129	−	9.79129i	1.44365	−	1.44365i
$47$		−	5.36662i		−	0.782802i	−0.920220	−	0.391401i	$-0.871991\pi$
$47$		−	5.36662i		−	0.782802i	0.920220	−	0.391401i	$-0.128009\pi$
$48$	4.97506	+	4.97506i	0.718088	+	0.718088i
$49$	4.38064			0.625805
$50$	−1.58812	−	10.0266i	−0.224595	−	1.41798i
$51$			5.97999i			0.837366i
$52$	−2.20779	+	7.32629i	−0.306166	+	1.01597i
$53$	−4.61845	−	4.61845i	−0.634392	−	0.634392i	0.314774	−	0.949167i	$-0.398071\pi$
$53$	−4.61845	−	4.61845i	−0.634392	−	0.634392i	−0.949167	+	0.314774i	$0.898071\pi$
$54$	−6.64877	+	6.64877i	−0.904783	+	0.904783i
$55$	0.670002	+	8.51285i	0.0903431	+	1.14787i
$56$			0.401567i			0.0536617i
$57$	−6.19779			−0.820917
$58$			8.68661i			1.14061i
$59$	−4.47130	−	4.47130i	−0.582113	−	0.582113i	0.353370	−	0.935484i	$-0.385036\pi$
$59$	−4.47130	−	4.47130i	−0.582113	−	0.582113i	−0.935484	+	0.353370i	$0.885036\pi$
$60$	8.89811	−	0.700324i	1.14874	−	0.0904114i
$61$	−12.1479			−1.55538			−0.777690	−	0.628648i	$-0.783609\pi$
$61$	−12.1479			−1.55538			−0.777690	+	0.628648i	$0.783609\pi$
$62$	6.82253	+	6.82253i	0.866462	+	0.866462i
$63$	−0.870382			−0.109658
$64$	−8.94596			−1.11825
$65$	−4.35910	−	6.78220i	−0.540679	−	0.841229i
$66$	−14.5835			−1.79510
$67$	5.84285			0.713817			0.356909	−	0.934139i	$-0.383831\pi$
$67$	5.84285			0.713817			0.356909	+	0.934139i	$0.383831\pi$
$68$	−4.77097	−	4.77097i	−0.578566	−	0.578566i
$69$	−12.8279			−1.54430
$70$	−5.58720	−	4.77189i	−0.667799	−	0.570350i
$71$	−1.37155	−	1.37155i	−0.162773	−	0.162773i	0.621021	−	0.783794i	$-0.286718\pi$
$71$	−1.37155	−	1.37155i	−0.162773	−	0.162773i	−0.783794	+	0.621021i	$0.786718\pi$
$72$			0.133436i			0.0157256i
$73$	4.02662			0.471280			0.235640	−	0.971840i	$-0.424281\pi$
$73$	4.02662			0.471280			0.235640	+	0.971840i	$0.424281\pi$
$74$			15.8004i			1.83676i
$75$	−5.52778	+	7.60844i	−0.638293	+	0.878547i
$76$	4.94474	−	4.94474i	0.567200	−	0.567200i
$77$	4.37033	+	4.37033i	0.498045	+	0.498045i
$78$	12.1313	−	6.51285i	1.37360	−	0.737435i
$79$			8.63754i			0.971799i	0.874015	+	0.485899i	$0.161508\pi$
$79$			8.63754i			0.971799i	−0.874015	+	0.485899i	$0.838492\pi$
$80$	5.43219	−	6.36032i	0.607338	−	0.711105i
$81$	10.3242			1.14713
$82$	5.83532	+	5.83532i	0.644404	+	0.644404i
$83$		−	7.48791i		−	0.821905i	−0.911657	−	0.410952i	$-0.865196\pi$
$83$		−	7.48791i		−	0.821905i	0.911657	−	0.410952i	$-0.134804\pi$
$84$	4.56811	−	4.56811i	0.498422	−	0.498422i
$85$	7.08726	−	0.557801i	0.768721	−	0.0605021i
$86$	−8.07817	+	8.07817i	−0.871092	+	0.871092i
$87$	5.69032	−	5.69032i	0.610066	−	0.610066i
$88$	0.670002	−	0.670002i	0.0714225	−	0.0714225i
$89$	−8.59843	−	8.59843i	−0.911432	−	0.911432i	0.0849529	−	0.996385i	$-0.472926\pi$
$89$	−8.59843	−	8.59843i	−0.911432	−	0.911432i	−0.996385	+	0.0849529i	$0.972926\pi$
$90$	−1.85656	−	1.58564i	−0.195698	−	0.167141i
$91$	−5.58720	−	1.68371i	−0.585698	−	0.176501i
$92$	10.2344	−	10.2344i	1.06701	−	1.06701i
$93$		−	8.93844i		−	0.926873i
$94$		−	10.8960i		−	1.12383i
$95$	0.578117	+	7.34539i	0.0593136	+	0.753621i
$96$	10.7610	+	10.7610i	1.09829	+	1.09829i
$97$	8.63754			0.877009			0.438505	−	0.898729i	$-0.355508\pi$
$97$	8.63754			0.877009			0.438505	+	0.898729i	$0.355508\pi$
$98$	8.89410			0.898440
$99$	1.45220	+	1.45220i	0.145952	+	0.145952i
$100$	−1.66000	−	10.4804i	−0.166000	−	1.04804i
$101$			0.823754i			0.0819665i	0.999160	+	0.0409833i	$0.0130490\pi$
$101$			0.823754i			0.0819665i	−0.999160	+	0.0409833i	$0.986951\pi$
$102$			12.1413i			1.20217i
$103$	0.867787	−	0.867787i	0.0855056	−	0.0855056i	−0.663060	−	0.748566i	$-0.730743\pi$
$103$	0.867787	−	0.867787i	0.0855056	−	0.0855056i	0.748566	+	0.663060i	$0.230743\pi$
$104$	−0.258125	+	0.856558i	−0.0253113	+	0.0839924i
$105$	0.534084	+	6.78591i	0.0521212	+	0.662237i
$106$	−9.37693	−	9.37693i	−0.910768	−	0.910768i
$107$	−3.28474	+	3.28474i	−0.317548	+	0.317548i	−0.847825	−	0.530277i	$-0.822088\pi$
$107$	−3.28474	+	3.28474i	−0.317548	+	0.317548i	0.530277	+	0.847825i	$0.322088\pi$
$108$	−6.94967	+	6.94967i	−0.668732	+	0.668732i
$109$	5.07187	−	5.07187i	0.485797	−	0.485797i	−0.421180	−	0.906977i	$-0.638384\pi$
$109$	5.07187	−	5.07187i	0.485797	−	0.485797i	0.906977	+	0.421180i	$0.138384\pi$
$110$	1.36032	+	17.2838i	0.129701	+	1.64795i
$111$	10.3503	−	10.3503i	0.982408	−	0.982408i
$112$		−	6.05404i		−	0.572053i
$113$	9.24720	+	9.24720i	0.869903	+	0.869903i	0.992461	−	0.122558i	$-0.0391097\pi$
$113$	9.24720	+	9.24720i	0.869903	+	0.869903i	−0.122558	+	0.992461i	$0.539110\pi$
$114$	−12.5835			−1.17855
$115$	1.19656	+	15.2032i	0.111580	+	1.41770i
$116$			9.07974i			0.843032i
$117$	−1.85656	−	0.559477i	−0.171639	−	0.0517237i
$118$	−9.07817	−	9.07817i	−0.835714	−	0.835714i
$119$	3.63846	−	3.63846i	0.333537	−	0.333537i
$120$	1.04033	−	0.0818788i	0.0949685	−	0.00747448i
$121$		−	3.58350i		−	0.325773i
$122$	−24.6642			−2.23299
$123$		−	7.64506i		−	0.689332i
$124$	7.13129	+	7.13129i	0.640409	+	0.640409i
$125$	9.53286	+	5.84162i	0.852645	+	0.522491i
$126$	−1.76716			−0.157431
$127$	−11.4779	−	11.4779i	−1.01850	−	1.01850i	−0.999826	−	0.0186734i	$-0.994056\pi$
$127$	−11.4779	−	11.4779i	−1.01850	−	1.01850i	−0.0186734	−	0.999826i	$-0.505944\pi$
$128$	−1.98125			−0.175119
$129$	10.5835			0.931825
$130$	−8.85037	−	13.7701i	−0.776229	−	1.20771i
$131$	1.80882			0.158037			0.0790186	−	0.996873i	$-0.474821\pi$
$131$	1.80882			0.158037			0.0790186	+	0.996873i	$0.474821\pi$
$132$	−15.2435			−1.32678
$133$	3.77097	+	3.77097i	0.326985	+	0.326985i
$134$	11.8629			1.02479
$135$	−0.812525	−	10.3237i	−0.0699310	−	0.888522i
$136$	−0.557801	−	0.557801i	−0.0478311	−	0.0478311i
$137$			8.96505i			0.765936i	0.923762	+	0.382968i	$0.125098\pi$
$137$			8.96505i			0.765936i	−0.923762	+	0.382968i	$0.874902\pi$
$138$	−26.0448			−2.21708
$139$		−	5.37819i		−	0.456172i	−0.973641	−	0.228086i	$-0.926753\pi$
$139$		−	5.37819i		−	0.456172i	0.973641	−	0.228086i	$-0.0732468\pi$
$140$	−5.84006	−	4.98785i	−0.493575	−	0.421550i
$141$	−7.13759	+	7.13759i	−0.601094	+	0.601094i
$142$	−2.78469	−	2.78469i	−0.233686	−	0.233686i
$143$	6.51285	+	12.1313i	0.544632	+	1.01447i
$144$		−	2.01168i		−	0.167640i
$145$	−7.27474	−	6.21317i	−0.604134	−	0.515976i
$146$	8.17533			0.676595
$147$	−5.82624	−	5.82624i	−0.480540	−	0.480540i
$148$			16.5154i			1.35756i
$149$	−7.78591	+	7.78591i	−0.637846	+	0.637846i	−0.950024	−	0.312177i	$-0.898942\pi$
$149$	−7.78591	+	7.78591i	−0.637846	+	0.637846i	0.312177	+	0.950024i	$0.398942\pi$
$150$	−11.2232	+	15.4476i	−0.916369	+	1.26129i
$151$	1.86038	−	1.86038i	0.151395	−	0.151395i	−0.627346	−	0.778741i	$-0.715859\pi$
$151$	1.86038	−	1.86038i	0.151395	−	0.151395i	0.778741	+	0.627346i	$0.215859\pi$
$152$	0.578117	−	0.578117i	0.0468915	−	0.0468915i
$153$	1.20901	−	1.20901i	0.0977430	−	0.0977430i
$154$	8.87317	+	8.87317i	0.715020	+	0.715020i
$155$	−10.5935	+	0.833760i	−0.850891	+	0.0669692i
$156$	12.6803	−	6.80760i	1.01524	−	0.545044i
$157$	9.89318	−	9.89318i	0.789562	−	0.789562i	−0.191860	−	0.981422i	$-0.561452\pi$
$157$	9.89318	−	9.89318i	0.789562	−	0.789562i	0.981422	+	0.191860i	$0.0614521\pi$
$158$			17.5370i			1.39517i
$159$			12.2850i			0.974267i
$160$	11.7497	−	13.7573i	0.928898	−	1.08761i
$161$	7.80500	+	7.80500i	0.615120	+	0.615120i
$162$	20.9613			1.64688
$163$	−7.53779			−0.590405			−0.295203	−	0.955435i	$-0.595387\pi$
$163$	−7.53779			−0.590405			−0.295203	+	0.955435i	$0.595387\pi$
$164$	6.09941	+	6.09941i	0.476284	+	0.476284i
$165$	10.4310	−	12.2132i	0.812050	−	0.950794i
$166$		−	15.2029i		−	1.17997i
$167$		−	18.9086i		−	1.46319i	−0.681740	−	0.731594i	$-0.738776\pi$
$167$		−	18.9086i		−	1.46319i	0.681740	−	0.731594i	$-0.261224\pi$
$168$	0.534084	−	0.534084i	0.0412054	−	0.0412054i
$169$	−10.8354	−	7.18285i	−0.833495	−	0.552527i
$170$	14.3894	−	1.13252i	1.10362	−	0.0868600i
$171$	1.25305	+	1.25305i	0.0958229	+	0.0958229i
$172$	−8.44376	+	8.44376i	−0.643831	+	0.643831i
$173$	−2.80882	+	2.80882i	−0.213551	+	0.213551i	−0.805774	−	0.592223i	$-0.798250\pi$
$173$	−2.80882	+	2.80882i	−0.213551	+	0.213551i	0.592223	+	0.805774i	$0.298250\pi$
$174$	11.5532	−	11.5532i	0.875844	−	0.875844i
$175$	7.99259	−	1.26595i	0.604183	−	0.0956970i
$176$	−10.1010	+	10.1010i	−0.761389	+	0.761389i
$177$			11.8936i			0.893980i
$178$	−17.4576	−	17.4576i	−1.30850	−	1.30850i
$179$	21.6632			1.61919			0.809593	−	0.586991i	$-0.199688\pi$
$179$	21.6632			1.61919			0.809593	+	0.586991i	$0.199688\pi$
$180$	−1.94058	−	1.65740i	−0.144642	−	0.123535i
$181$			6.82791i			0.507515i	0.967268	+	0.253757i	$0.0816665\pi$
$181$			6.82791i			0.507515i	−0.967268	+	0.253757i	$0.918334\pi$
$182$	−11.3438	−	3.41848i	−0.840860	−	0.253395i
$183$	16.1567	+	16.1567i	1.19434	+	1.19434i
$184$	1.19656	−	1.19656i	0.0882117	−	0.0882117i
$185$	−13.2323	−	11.3014i	−0.972855	−	0.830892i
$186$		−	18.1479i		−	1.33067i
$187$	−12.1413			−0.887860
$188$		−	11.3891i		−	0.830634i
$189$	−5.29998	−	5.29998i	−0.385517	−	0.385517i
$190$	1.17376	+	14.9135i	0.0851538	+	1.08194i
$191$	−18.9450			−1.37082			−0.685408	−	0.728160i	$-0.740376\pi$
$191$	−18.9450			−1.37082			−0.685408	+	0.728160i	$0.740376\pi$
$192$	11.8981	+	11.8981i	0.858672	+	0.858672i
$193$	7.18885			0.517465			0.258732	−	0.965949i	$-0.416695\pi$
$193$	7.18885			0.517465			0.258732	+	0.965949i	$0.416695\pi$
$194$	17.5370			1.25908
$195$	−3.22273	+	14.8179i	−0.230784	+	1.06113i
$196$	9.29661			0.664044
$197$	4.41558			0.314597			0.157299	−	0.987551i	$-0.449721\pi$
$197$	4.41558			0.314597			0.157299	+	0.987551i	$0.449721\pi$
$198$	2.94844	+	2.94844i	0.209537	+	0.209537i
$199$	−0.312468			−0.0221503			−0.0110751	−	0.999939i	$-0.503525\pi$
$199$	−0.312468			−0.0221503			−0.0110751	+	0.999939i	$0.503525\pi$
$200$	−0.194079	−	1.22532i	−0.0137235	−	0.0866433i
$201$	−7.77097	−	7.77097i	−0.548122	−	0.548122i
$202$			1.67248i			0.117676i
$203$	−6.92442			−0.485999
$204$			12.6908i			0.888532i
$205$	−9.06064	+	0.713116i	−0.632823	+	0.0498062i
$206$	1.76189	−	1.76189i	0.122756	−	0.122756i
$207$	2.59350	+	2.59350i	0.180261	+	0.180261i
$208$	3.89150	−	12.9135i	0.269827	−	0.895390i
$209$		−	12.5835i		−	0.870419i
$210$	1.08436	+	13.7776i	0.0748281	+	0.950743i
$211$	−10.7182			−0.737871			−0.368935	−	0.929455i	$-0.620278\pi$
$211$	−10.7182			−0.737871			−0.368935	+	0.929455i	$0.620278\pi$
$212$	−9.80130	−	9.80130i	−0.673156	−	0.673156i
$213$			3.64831i			0.249978i
$214$	−6.66908	+	6.66908i	−0.455889	+	0.455889i
$215$	−0.987208	−	12.5432i	−0.0673270	−	0.855437i
$216$	−0.812525	+	0.812525i	−0.0552853	+	0.0552853i
$217$	−5.43849	+	5.43849i	−0.369189	+	0.369189i
$218$	10.2975	−	10.2975i	0.697437	−	0.697437i
$219$	−5.35539	−	5.35539i	−0.361884	−	0.361884i
$220$	1.42188	+	18.0660i	0.0958633	+	1.21801i
$221$	10.0997	−	5.42219i	0.679383	−	0.364736i
$222$	21.0145	−	21.0145i	1.41040	−	1.41040i
$223$			6.81715i			0.456510i	0.973601	+	0.228255i	$0.0733020\pi$
$223$			6.81715i			0.456510i	−0.973601	+	0.228255i	$0.926698\pi$
$224$		−	13.0948i		−	0.874932i
$225$	2.65584	−	0.420660i	0.177056	−	0.0280440i
$226$	18.7748	+	18.7748i	1.24888	+	1.24888i
$227$	−4.56288			−0.302849			−0.151424	−	0.988469i	$-0.548386\pi$
$227$	−4.56288			−0.302849			−0.151424	+	0.988469i	$0.548386\pi$
$228$	−13.1530			−0.871077
$229$	13.5635	+	13.5635i	0.896300	+	0.896300i	0.995107	−	0.0988063i	$-0.0315024\pi$
$229$	13.5635	+	13.5635i	0.896300	+	0.896300i	−0.0988063	+	0.995107i	$0.531502\pi$
$230$	2.42941	+	30.8673i	0.160190	+	2.03533i
$231$		−	11.6250i		−	0.764872i
$232$			1.06156i			0.0696950i
$233$	0.665074	−	0.665074i	0.0435704	−	0.0435704i	−0.684986	−	0.728556i	$-0.740192\pi$
$233$	0.665074	−	0.665074i	0.0435704	−	0.0435704i	0.728556	+	0.684986i	$0.240192\pi$
$234$	−3.76941	−	1.13592i	−0.246414	−	0.0742573i
$235$	9.12499	+	7.79343i	0.595249	+	0.508387i
$236$	−9.48902	−	9.48902i	−0.617682	−	0.617682i
$237$	11.4879	−	11.4879i	0.746220	−	0.746220i
$238$	7.38724	−	7.38724i	0.478844	−	0.478844i
$239$	−9.47004	+	9.47004i	−0.612566	+	0.612566i	−0.943614	−	0.331048i	$-0.892598\pi$
$239$	−9.47004	+	9.47004i	−0.612566	+	0.612566i	0.331048	+	0.943614i	$0.392598\pi$
$240$	−15.6840	+	1.23441i	−1.01240	+	0.0796807i
$241$	−11.9072	+	11.9072i	−0.767010	+	0.767010i	−0.977579	−	0.210569i	$-0.932468\pi$
$241$	−11.9072	+	11.9072i	−0.767010	+	0.767010i	0.210569	+	0.977579i	$0.432468\pi$
$242$		−	7.27565i		−	0.467697i
$243$	−3.90689	−	3.90689i	−0.250627	−	0.250627i
$244$	−25.7804			−1.65042
$245$	−6.36158	+	7.44850i	−0.406426	+	0.475867i
$246$		−	15.5219i		−	0.989642i
$247$	5.61967	+	10.4676i	0.357571	+	0.666037i
$248$	0.833760	+	0.833760i	0.0529438	+	0.0529438i
$249$	−9.95890	+	9.95890i	−0.631120	+	0.631120i
$250$	19.3548	+	11.8604i	1.22410	+	0.750116i
$251$			14.5519i			0.918509i	0.888305	+	0.459254i	$0.151883\pi$
$251$			14.5519i			0.918509i	−0.888305	+	0.459254i	$0.848117\pi$
$252$	−1.84713			−0.116358
$253$		−	26.0448i		−	1.63742i
$254$	−23.3038	−	23.3038i	−1.46221	−	1.46221i
$255$	−10.1679	−	8.68417i	−0.636740	−	0.543824i
$256$	13.8694			0.866834
$257$	13.0266	+	13.0266i	0.812578	+	0.812578i	0.985020	−	0.172442i	$-0.0551656\pi$
$257$	13.0266	+	13.0266i	0.812578	+	0.812578i	−0.172442	+	0.985020i	$0.555166\pi$
$258$	21.4879			1.33778
$259$	−12.5951			−0.782619
$260$	−9.25091	−	14.3932i	−0.573717	−	0.892631i
$261$	−2.30090			−0.142422
$262$	3.67248			0.226887
$263$	−11.0431	−	11.0431i	−0.680948	−	0.680948i	0.279266	−	0.960214i	$-0.409909\pi$
$263$	−11.0431	−	11.0431i	−0.680948	−	0.680948i	−0.960214	+	0.279266i	$0.909909\pi$
$264$	−1.78220			−0.109687
$265$	14.5598	−	1.14592i	0.894400	−	0.0703936i
$266$	7.65629	+	7.65629i	0.469437	+	0.469437i
$267$			22.8718i			1.39973i
$268$	12.3997			0.757434
$269$			1.76574i			0.107659i	0.998550	+	0.0538296i	$0.0171428\pi$
$269$			1.76574i			0.107659i	−0.998550	+	0.0538296i	$0.982857\pi$
$270$	−1.64969	−	20.9604i	−0.100397	−	1.27561i
$271$	12.4047	−	12.4047i	0.753529	−	0.753529i	−0.221607	−	0.975136i	$-0.571130\pi$
$271$	12.4047	−	12.4047i	0.753529	−	0.753529i	0.975136	+	0.221607i	$0.0711302\pi$
$272$	8.40943	+	8.40943i	0.509897	+	0.509897i
$273$	5.19163	+	9.67031i	0.314212	+	0.585274i
$274$			18.2019i			1.09962i
$275$	−15.4476	−	11.2232i	−0.931524	−	0.676783i
$276$	−27.2235			−1.63866
$277$	−11.7206	−	11.7206i	−0.704225	−	0.704225i	0.261090	−	0.965315i	$-0.415918\pi$
$277$	−11.7206	−	11.7206i	−0.704225	−	0.704225i	−0.965315	+	0.261090i	$0.915918\pi$
$278$		−	10.9195i		−	0.654905i
$279$	−1.80714	+	1.80714i	−0.108191	+	0.108191i
$280$	−0.682794	−	0.583158i	−0.0408048	−	0.0348503i
$281$	−12.5191	+	12.5191i	−0.746830	+	0.746830i	−0.973882	−	0.227053i	$-0.927091\pi$
$281$	−12.5191	+	12.5191i	−0.746830	+	0.746830i	0.227053	+	0.973882i	$0.427091\pi$
$282$	−14.4916	+	14.4916i	−0.862963	+	0.862963i
$283$	−12.8558	+	12.8558i	−0.764195	+	0.764195i	−0.977078	−	0.212883i	$-0.931715\pi$
$283$	−12.8558	+	12.8558i	−0.764195	+	0.764195i	0.212883	+	0.977078i	$0.431715\pi$
$284$	−2.91071	−	2.91071i	−0.172719	−	0.172719i
$285$	9.00045	−	10.5382i	0.533141	−	0.624232i
$286$	13.2232	+	24.6304i	0.781903	+	1.45643i
$287$	−4.65155	+	4.65155i	−0.274572	+	0.274572i
$288$		−	4.35123i		−	0.256399i
$289$		−	6.89192i		−	0.405407i
$290$	−14.7701	−	12.6147i	−0.867327	−	0.740763i
$291$	−11.4879	−	11.4879i	−0.673433	−	0.673433i
$292$	8.54531			0.500077
$293$	18.2991			1.06904			0.534521	−	0.845155i	$-0.320492\pi$
$293$	18.2991			1.06904			0.534521	+	0.845155i	$0.320492\pi$
$294$	−11.8291	−	11.8291i	−0.689889	−	0.689889i
$295$	14.0959	−	1.10941i	0.820695	−	0.0645926i
$296$			1.93091i			0.112232i
$297$			17.6857i			1.02623i
$298$	−15.8079	+	15.8079i	−0.915727	+	0.915727i
$299$	11.6313	+	21.6654i	0.672658	+	1.25294i
$300$	−11.7311	+	16.1467i	−0.677295	+	0.932229i
$301$	−6.43941	−	6.43941i	−0.371162	−	0.371162i
$302$	3.77716	−	3.77716i	0.217351	−	0.217351i
$303$	1.09559	−	1.09559i	0.0629400	−	0.0629400i
$304$	−8.71571	+	8.71571i	−0.499880	+	0.499880i
$305$	17.6412	−	20.6554i	1.01013	−	1.18272i
$306$	2.45469	−	2.45469i	0.140325	−	0.140325i
$307$		−	18.9366i		−	1.08077i	−0.841418	−	0.540384i	$-0.818279\pi$
$307$		−	18.9366i		−	1.08077i	0.841418	−	0.540384i	$-0.181721\pi$
$308$	9.27474	+	9.27474i	0.528477	+	0.528477i
$309$	−2.30831			−0.131315
$310$	−21.5082	+	1.69280i	−1.22159	+	0.0961446i
$311$		−	17.3532i		−	0.984010i	−0.870592	−	0.492005i	$-0.836264\pi$
$311$		−	17.3532i		−	0.984010i	0.870592	−	0.492005i	$-0.163736\pi$
$312$	1.48253	−	0.795914i	0.0839315	−	0.0450598i
$313$	−5.54565	−	5.54565i	−0.313459	−	0.313459i	0.532789	−	0.846248i	$-0.321144\pi$
$313$	−5.54565	−	5.54565i	−0.313459	−	0.313459i	−0.846248	+	0.532789i	$0.821144\pi$
$314$	20.0863	−	20.0863i	1.13354	−	1.13354i
$315$	1.26397	−	1.47993i	0.0712168	−	0.0833847i
$316$			18.3306i			1.03118i
$317$	33.4987			1.88147			0.940736	−	0.339139i	$-0.110136\pi$
$317$	33.4987			1.88147			0.940736	+	0.339139i	$0.110136\pi$
$318$			24.9426i			1.39871i
$319$	11.5532	+	11.5532i	0.646854	+	0.646854i
$320$	12.9914	−	15.2110i	0.726239	−	0.850322i
$321$	8.73740			0.487674
$322$	15.8467	+	15.8467i	0.883100	+	0.883100i
$323$	−10.4762			−0.582913
$324$	21.9100			1.21722
$325$	17.8622	+	2.43727i	0.990819	+	0.135195i
$326$	−15.3041			−0.847618
$327$	−13.4912			−0.746063
$328$	0.713116	+	0.713116i	0.0393753	+	0.0393753i
$329$	8.68558			0.478852
$330$	21.1782	−	24.7967i	1.16582	−	1.36501i
$331$	18.7185	+	18.7185i	1.02886	+	1.02886i	0.999571	+	0.0292907i	$0.00932486\pi$
$331$	18.7185	+	18.7185i	1.02886	+	1.02886i	0.0292907	+	0.999571i	$0.490675\pi$
$332$		−	15.8909i		−	0.872126i
$333$	−4.18518			−0.229347
$334$		−	38.3905i		−	2.10063i
$335$	−8.48501	+	9.93473i	−0.463586	+	0.542792i
$336$	−8.05186	+	8.05186i	−0.439265	+	0.439265i
$337$	−12.3554	−	12.3554i	−0.673041	−	0.673041i	0.285375	−	0.958416i	$-0.407882\pi$
$337$	−12.3554	−	12.3554i	−0.673041	−	0.673041i	−0.958416	+	0.285375i	$0.907882\pi$
$338$	−21.9994	−	14.5835i	−1.19661	−	0.793238i
$339$		−	24.5975i		−	1.33595i
$340$	15.0406	−	1.18377i	0.815693	−	0.0641989i
$341$	18.1479			0.982764
$342$	2.54409	+	2.54409i	0.137569	+	0.137569i
$343$			18.4189i			0.994529i
$344$	−0.987208	+	0.987208i	−0.0532267	+	0.0532267i
$345$	18.6288	−	21.8116i	1.00294	−	1.17430i
$346$	−5.70281	+	5.70281i	−0.306585	+	0.306585i
$347$	−0.962458	+	0.962458i	−0.0516675	+	0.0516675i	−0.732468	−	0.680801i	$-0.761632\pi$
$347$	−0.962458	+	0.962458i	−0.0516675	+	0.0516675i	0.680801	+	0.732468i	$0.261632\pi$
$348$	12.0760	−	12.0760i	0.647343	−	0.647343i
$349$	−6.19870	−	6.19870i	−0.331809	−	0.331809i	0.521464	−	0.853273i	$-0.325386\pi$
$349$	−6.19870	−	6.19870i	−0.331809	−	0.331809i	−0.853273	+	0.521464i	$0.825386\pi$
$350$	16.2275	−	2.57029i	0.867398	−	0.137388i
$351$	−7.89826	−	14.7119i	−0.421578	−	0.785261i
$352$	−21.8482	+	21.8482i	−1.16451	+	1.16451i
$353$			3.89028i			0.207059i	0.994626	+	0.103529i	$0.0330136\pi$
$353$			3.89028i			0.207059i	−0.994626	+	0.103529i	$0.966986\pi$
$354$			24.1479i			1.28345i
$355$	4.32385	−	0.340308i	0.229486	−	0.0180616i
$356$	−18.2477	−	18.2477i	−0.967124	−	0.967124i
$357$	−9.67828			−0.512229
$358$	43.9833			2.32459
$359$	16.1238	+	16.1238i	0.850980	+	0.850980i	0.990254	−	0.139274i	$-0.0444768\pi$
$359$	16.1238	+	16.1238i	0.850980	+	0.850980i	−0.139274	+	0.990254i	$0.544477\pi$
$360$	−0.226884	−	0.193776i	−0.0119578	−	0.0102129i
$361$			8.14222i			0.428538i
$362$			13.8629i			0.728616i
$363$	−4.76605	+	4.76605i	−0.250153	+	0.250153i
$364$	−11.8572	−	3.57319i	−0.621486	−	0.187286i
$365$	−5.84747	+	6.84655i	−0.306071	+	0.358365i
$366$	32.8033	+	32.8033i	1.71465	+	1.71465i
$367$	6.58690	−	6.58690i	0.343833	−	0.343833i	−0.513973	−	0.857806i	$-0.671827\pi$
$367$	6.58690	−	6.58690i	0.343833	−	0.343833i	0.857806	+	0.513973i	$0.171827\pi$
$368$	−18.0394	+	18.0394i	−0.940369	+	0.940369i
$369$	−1.54565	+	1.54565i	−0.0804635	+	0.0804635i
$370$	−26.8658	−	22.9454i	−1.39668	−	1.19287i
$371$	7.47470	−	7.47470i	0.388067	−	0.388067i
$372$		−	18.9692i		−	0.983508i
$373$	−9.51823	−	9.51823i	−0.492835	−	0.492835i	0.416363	−	0.909198i	$-0.363305\pi$
$373$	−9.51823	−	9.51823i	−0.492835	−	0.492835i	−0.909198	+	0.416363i	$0.863305\pi$
$374$	−24.6507			−1.27466
$375$	−4.90934	−	20.4480i	−0.253517	−	1.05593i
$376$		−	1.33156i		−	0.0686700i
$377$	−14.7701	−	4.45098i	−0.760696	−	0.229237i
$378$	−10.7607	−	10.7607i	−0.553469	−	0.553469i
$379$	5.31888	−	5.31888i	0.273213	−	0.273213i	−0.557179	−	0.830392i	$-0.688116\pi$
$379$	5.31888	−	5.31888i	0.273213	−	0.273213i	0.830392	+	0.557179i	$0.188116\pi$
$380$	1.22688	+	15.5884i	0.0629378	+	0.799669i
$381$			30.5312i			1.56416i
$382$	−38.4645			−1.96802
$383$			14.8685i			0.759747i	0.925038	+	0.379874i	$0.124032\pi$
$383$			14.8685i			0.759747i	−0.925038	+	0.379874i	$0.875968\pi$
$384$	2.63506	+	2.63506i	0.134470	+	0.134470i
$385$	−13.7776	+	1.08436i	−0.702170	+	0.0552642i
$386$	14.5957			0.742900
$387$	−2.13974	−	2.13974i	−0.108769	−	0.108769i
$388$	18.3306			0.930597
$389$	−28.9078			−1.46568			−0.732841	−	0.680400i	$-0.761806\pi$
$389$	−28.9078			−1.46568			−0.732841	+	0.680400i	$0.761806\pi$
$390$	−6.54317	+	30.0851i	−0.331326	+	1.52342i
$391$	−21.6832			−1.09657
$392$	1.08692			0.0548977
$393$	−2.40573	−	2.40573i	−0.121353	−	0.121353i
$394$	8.96505			0.451653
$395$	−14.6866	−	12.5435i	−0.738964	−	0.631131i
$396$	3.08188	+	3.08188i	0.154870	+	0.154870i
$397$			14.6060i			0.733052i	0.930408	+	0.366526i	$0.119453\pi$
$397$			14.6060i			0.733052i	−0.930408	+	0.366526i	$0.880547\pi$
$398$	−0.634411			−0.0318002
$399$		−	10.0308i		−	0.502167i
$400$	2.92595	+	18.4730i	0.146297	+	0.923649i
$401$	8.22532	−	8.22532i	0.410753	−	0.410753i	−0.471248	−	0.882001i	$-0.656196\pi$
$401$	8.22532	−	8.22532i	0.410753	−	0.410753i	0.882001	+	0.471248i	$0.156196\pi$
$402$	−15.7776	−	15.7776i	−0.786914	−	0.786914i
$403$	−15.0963	+	8.10468i	−0.752003	+	0.403723i
$404$			1.74818i			0.0869750i
$405$	−14.9928	+	17.5544i	−0.744997	+	0.872285i
$406$	−14.0588			−0.697727
$407$	21.0145	+	21.0145i	1.04165	+	1.04165i
$408$			1.48375i			0.0734565i
$409$	−26.1042	+	26.1042i	−1.29077	+	1.29077i	−0.356456	+	0.934312i	$0.616015\pi$
$409$	−26.1042	+	26.1042i	−1.29077	+	1.29077i	−0.934312	+	0.356456i	$0.883985\pi$
$410$	−18.3960	+	1.44786i	−0.908515	+	0.0715045i
$411$	11.9235	−	11.9235i	0.588143	−	0.588143i
$412$	1.84162	−	1.84162i	0.0907303	−	0.0907303i
$413$	7.23655	−	7.23655i	0.356087	−	0.356087i
$414$	5.26565	+	5.26565i	0.258793	+	0.258793i
$415$	12.7319	+	10.8740i	0.624983	+	0.533782i
$416$	8.41726	−	27.9317i	0.412690	−	1.36946i
$417$	−7.15298	+	7.15298i	−0.350283	+	0.350283i
$418$		−	25.5486i		−	1.24962i
$419$			22.8877i			1.11814i	0.829121	+	0.559070i	$0.188842\pi$
$419$			22.8877i			1.11814i	−0.829121	+	0.559070i	$0.811158\pi$
$420$	1.13344	+	14.4011i	0.0553060	+	0.702702i
$421$	−24.6619	−	24.6619i	−1.20195	−	1.20195i	−0.973574	−	0.228372i	$-0.926660\pi$
$421$	−24.6619	−	24.6619i	−1.20195	−	1.20195i	−0.228372	−	0.973574i	$-0.573340\pi$
$422$	−21.7614			−1.05933
$423$	2.88611			0.140327
$424$	−1.14592	−	1.14592i	−0.0556510	−	0.0556510i
$425$	−9.34371	+	12.8607i	−0.453236	+	0.623835i
$426$			7.40725i			0.358883i
$427$		−	19.6607i		−	0.951449i
$428$	−6.97090	+	6.97090i	−0.336951	+	0.336951i
$429$	7.47252	−	24.7967i	0.360777	−	1.19719i
$430$	−2.00435	−	25.4667i	−0.0966583	−	1.22811i
$431$	16.5273	+	16.5273i	0.796093	+	0.796093i	0.982477	−	0.186384i	$-0.0596769\pi$
$431$	16.5273	+	16.5273i	0.796093	+	0.796093i	−0.186384	+	0.982477i	$0.559677\pi$
$432$	12.2496	−	12.2496i	0.589361	−	0.589361i
$433$	25.0489	−	25.0489i	1.20378	−	1.20378i	0.230766	−	0.973009i	$-0.425877\pi$
$433$	25.0489	−	25.0489i	1.20378	−	1.20378i	0.973009	−	0.230766i	$-0.0741233\pi$
$434$	−11.0419	+	11.0419i	−0.530028	+	0.530028i
$435$	1.41188	+	17.9389i	0.0676943	+	0.860104i
$436$	10.7636	−	10.7636i	0.515481	−	0.515481i
$437$		−	22.4730i		−	1.07503i
$438$	−10.8732	−	10.8732i	−0.519540	−	0.519540i
$439$	18.1493			0.866220			0.433110	−	0.901341i	$-0.357416\pi$
$439$	18.1493			0.866220			0.433110	+	0.901341i	$0.357416\pi$
$440$	0.166240	+	2.11220i	0.00792520	+	0.100695i
$441$			2.35586i			0.112184i
$442$	20.5057	−	11.0088i	0.975359	−	0.523634i
$443$	−7.30257	−	7.30257i	−0.346956	−	0.346956i	0.512019	−	0.858974i	$-0.328898\pi$
$443$	−7.30257	−	7.30257i	−0.346956	−	0.346956i	−0.858974	+	0.512019i	$0.828898\pi$
$444$	21.9655	−	21.9655i	1.04244	−	1.04244i
$445$	27.1068	−	2.13344i	1.28499	−	0.101135i
$446$			13.8410i			0.655391i
$447$	20.7105			0.979572
$448$		−	14.4785i		−	0.684047i
$449$	3.27565	+	3.27565i	0.154588	+	0.154588i	0.780163	−	0.625576i	$-0.215136\pi$
$449$	3.27565	+	3.27565i	0.154588	+	0.154588i	−0.625576	+	0.780163i	$0.715136\pi$
$450$	5.39220	−	0.854075i	0.254191	−	0.0402615i
$451$	15.5219			0.730899
$452$	19.6245	+	19.6245i	0.923057	+	0.923057i
$453$	−4.94859			−0.232505
$454$	−9.26411			−0.434786
$455$	10.9766	−	7.05496i	0.514592	−	0.330742i
$456$	−1.53779			−0.0720136
$457$	13.8670			0.648672			0.324336	−	0.945942i	$-0.394859\pi$
$457$	13.8670			0.648672			0.324336	+	0.945942i	$0.394859\pi$
$458$	27.5382	+	27.5382i	1.28678	+	1.28678i
$459$	14.7240			0.687257
$460$	2.53935	+	32.2643i	0.118398	+	1.50433i
$461$	−6.02325	−	6.02325i	−0.280531	−	0.280531i	0.552790	−	0.833321i	$-0.313563\pi$
$461$	−6.02325	−	6.02325i	−0.280531	−	0.280531i	−0.833321	+	0.552790i	$0.813563\pi$
$462$		−	23.6026i		−	1.09809i
$463$	16.6916			0.775723			0.387862	−	0.921718i	$-0.373214\pi$
$463$	16.6916			0.775723			0.387862	+	0.921718i	$0.373214\pi$
$464$		−	16.0042i		−	0.742974i
$465$	15.1982	+	12.9804i	0.704801	+	0.601954i
$466$	1.35031	−	1.35031i	0.0625521	−	0.0625521i
$467$	−5.68909	−	5.68909i	−0.263260	−	0.263260i	0.563117	−	0.826377i	$-0.309602\pi$
$467$	−5.68909	−	5.68909i	−0.263260	−	0.263260i	−0.826377	+	0.563117i	$0.809602\pi$
$468$	−3.94000	−	1.18733i	−0.182127	−	0.0548842i
$469$			9.45633i			0.436653i
$470$	18.5267	+	15.8232i	0.854572	+	0.729869i
$471$	−26.3158			−1.21257
$472$	−1.10941	−	1.10941i	−0.0510649	−	0.0510649i
$473$			21.4879i			0.988015i
$474$	23.3242	−	23.3242i	1.07131	−	1.07131i
$475$	−13.3291	−	9.68402i	−0.611580	−	0.444333i
$476$	7.72156	−	7.72156i	0.353917	−	0.353917i
$477$	2.48375	−	2.48375i	0.113723	−	0.113723i
$478$	−19.2272	+	19.2272i	−0.879433	+	0.879433i
$479$	7.93443	+	7.93443i	0.362533	+	0.362533i	0.864745	−	0.502212i	$-0.167480\pi$
$479$	7.93443	+	7.93443i	0.362533	+	0.362533i	−0.502212	+	0.864745i	$0.667480\pi$
$480$	−33.9243	+	2.67000i	−1.54842	+	0.121868i
$481$	−26.8658	−	8.09604i	−1.22497	−	0.369148i
$482$	−24.1754	+	24.1754i	−1.10116	+	1.10116i
$483$		−	20.7613i		−	0.944671i
$484$		−	7.60492i		−	0.345678i
$485$	−12.5435	+	14.6866i	−0.569570	+	0.666885i
$486$	−7.93225	−	7.93225i	−0.359814	−	0.359814i
$487$	18.1005			0.820210			0.410105	−	0.912038i	$-0.365492\pi$
$487$	18.1005			0.820210			0.410105	+	0.912038i	$0.365492\pi$
$488$	−3.01413			−0.136443
$489$	10.0252	+	10.0252i	0.453357	+	0.453357i
$490$	−12.9161	+	15.1229i	−0.583488	+	0.683181i
$491$		−	26.3839i		−	1.19069i	−0.803471	−	0.595344i	$-0.797016\pi$
$491$		−	26.3839i		−	1.19069i	0.803471	−	0.595344i	$-0.202984\pi$
$492$		−	16.2244i		−	0.731453i
$493$	9.61845	−	9.61845i	0.433193	−	0.433193i
$494$	11.4097	+	21.2526i	0.513348	+	0.956199i
$495$	−4.57812	+	0.360320i	−0.205771	+	0.0161952i
$496$	−12.5698	−	12.5698i	−0.564400	−	0.564400i
$497$	2.21978	−	2.21978i	0.0995706	−	0.0995706i
$498$	−20.2198	+	20.2198i	−0.906070	+	0.906070i
$499$	10.6751	−	10.6751i	0.477882	−	0.477882i	−0.426572	−	0.904454i	$-0.640279\pi$
$499$	10.6751	−	10.6751i	0.477882	−	0.477882i	0.904454	+	0.426572i	$0.140279\pi$
$500$	20.2307	+	12.3971i	0.904744	+	0.554417i
$501$	−25.1484	+	25.1484i	−1.12355	+	1.12355i
$502$			29.5451i			1.31866i
$503$	0.564102	+	0.564102i	0.0251521	+	0.0251521i	0.719571	−	0.694419i	$-0.244338\pi$
$503$	0.564102	+	0.564102i	0.0251521	+	0.0251521i	−0.694419	+	0.719571i	$0.744338\pi$
$504$	−0.215958			−0.00961955
$505$	−1.40065	−	1.19626i	−0.0623280	−	0.0532328i
$506$		−	52.8793i		−	2.35077i
$507$	4.85793	+	23.9643i	0.215748	+	1.06429i
$508$	−24.3585	−	24.3585i	−1.08073	−	1.08073i
$509$	−21.2626	+	21.2626i	−0.942448	+	0.942448i	−0.998432	−	0.0559841i	$-0.982170\pi$
$509$	−21.2626	+	21.2626i	−0.942448	+	0.942448i	0.0559841	+	0.998432i	$0.482170\pi$
$510$	−20.6441	−	17.6317i	−0.914138	−	0.780743i
$511$			6.51686i			0.288289i
$512$	32.1217			1.41959
$513$			15.2603i			0.673757i
$514$	26.4482	+	26.4482i	1.16658	+	1.16658i
$515$	0.215315	+	2.73572i	0.00948789	+	0.120550i
$516$	22.4604			0.988763
$517$	−14.4916	−	14.4916i	−0.637340	−	0.637340i
$518$	−25.5720			−1.12357
$519$	7.47145			0.327960
$520$	−1.08158	−	1.68279i	−0.0474302	−	0.0737954i
$521$	−0.104827			−0.00459254			−0.00229627	−	0.999997i	$-0.500731\pi$
$521$	−0.104827			−0.00459254			−0.00229627	+	0.999997i	$0.500731\pi$
$522$	−4.67157			−0.204469
$523$	−5.70495	−	5.70495i	−0.249460	−	0.249460i	0.571289	−	0.820749i	$-0.306444\pi$
$523$	−5.70495	−	5.70495i	−0.249460	−	0.249460i	−0.820749	+	0.571289i	$0.806444\pi$
$524$	3.83869			0.167694
$525$	−12.3138	−	8.94641i	−0.537420	−	0.390453i
$526$	−22.4211	−	22.4211i	−0.977605	−	0.977605i
$527$		−	15.1088i		−	0.658150i
$528$	26.8685			1.16930
$529$		−	23.5136i		−	1.02233i
$530$	29.5610	−	2.32660i	1.28405	−	0.101061i
$531$	2.40462	−	2.40462i	0.104351	−	0.104351i
$532$	8.00279	+	8.00279i	0.346965	+	0.346965i
$533$	−12.9119	+	6.93195i	−0.559278	+	0.300256i
$534$			46.4371i			2.00953i
$535$	−0.815007	−	10.3552i	−0.0352358	−	0.447696i
$536$	1.44972			0.0626185
$537$	−28.8121	−	28.8121i	−1.24333	−	1.24333i
$538$			3.58502i			0.154561i
$539$	11.8291	−	11.8291i	0.509517	−	0.509517i
$540$	−1.72435	−	21.9090i	−0.0742040	−	0.942814i
$541$	18.8179	−	18.8179i	0.809047	−	0.809047i	−0.175443	−	0.984490i	$-0.556136\pi$
$541$	18.8179	−	18.8179i	0.809047	−	0.809047i	0.984490	+	0.175443i	$0.0561358\pi$
$542$	25.1854	−	25.1854i	1.08181	−	1.08181i
$543$	9.08111	−	9.08111i	0.389708	−	0.389708i
$544$	18.1895	+	18.1895i	0.779866	+	0.779866i
$545$	1.25843	+	15.9892i	0.0539052	+	0.684903i
$546$	10.5407	+	19.6338i	0.451100	+	0.840250i
$547$	13.3103	−	13.3103i	0.569108	−	0.569108i	−0.362770	−	0.931879i	$-0.618169\pi$
$547$	13.3103	−	13.3103i	0.569108	−	0.569108i	0.931879	+	0.362770i	$0.118169\pi$
$548$			19.0257i			0.812737i
$549$		−	6.53301i		−	0.278822i
$550$	−31.3636	−	22.7867i	−1.33735	−	0.971627i
$551$	9.96876	+	9.96876i	0.424683	+	0.424683i
$552$	−3.18285			−0.135471
$553$	−13.9794			−0.594464
$554$	−23.7967	−	23.7967i	−1.01102	−	1.01102i
$555$	2.56811	+	32.6297i	0.109010	+	1.38505i
$556$		−	11.4136i		−	0.484046i
$557$			37.1686i			1.57489i	0.616388	+	0.787443i	$0.288595\pi$
$557$			37.1686i			1.57489i	−0.616388	+	0.787443i	$0.711405\pi$
$558$	−3.66908	+	3.66908i	−0.155325	+	0.155325i
$559$	−9.59629	−	17.8747i	−0.405880	−	0.756021i
$560$	10.2938	+	8.79171i	0.434994	+	0.371517i
$561$	16.1479	+	16.1479i	0.681765	+	0.681765i
$562$	−25.4179	+	25.4179i	−1.07219	+	1.07219i
$563$	30.1782	−	30.1782i	1.27186	−	1.27186i	0.326747	−	0.945112i	$-0.394047\pi$
$563$	30.1782	−	30.1782i	1.27186	−	1.27186i	0.945112	−	0.326747i	$-0.105953\pi$
$564$	−15.1475	+	15.1475i	−0.637823	+	0.637823i
$565$	−29.1521	+	2.29441i	−1.22644	+	0.0965264i
$566$	−26.1013	+	26.1013i	−1.09712	+	1.09712i
$567$			16.7091i			0.701715i
$568$	−0.340308	−	0.340308i	−0.0142790	−	0.0142790i
$569$	−37.6216			−1.57718			−0.788589	−	0.614920i	$-0.789188\pi$
$569$	−37.6216			−1.57718			−0.788589	+	0.614920i	$0.789188\pi$
$570$	18.2738	−	21.3960i	0.765406	−	0.896181i
$571$			21.9027i			0.916599i	0.888798	+	0.458299i	$0.151541\pi$
$571$			21.9027i			0.916599i	−0.888798	+	0.458299i	$0.848459\pi$
$572$	13.8216	+	25.7451i	0.577911	+	1.07646i
$573$	25.1969	+	25.1969i	1.05261	+	1.05261i
$574$	−9.44415	+	9.44415i	−0.394191	+	0.394191i
$575$	−27.5880	−	20.0436i	−1.15050	−	0.835875i
$576$		−	4.81104i		−	0.200460i
$577$	−0.139587			−0.00581108			−0.00290554	−	0.999996i	$-0.500925\pi$
$577$	−0.139587			−0.00581108			−0.00290554	+	0.999996i	$0.500925\pi$
$578$		−	13.9928i		−	0.582024i
$579$	−9.56115	−	9.56115i	−0.397348	−	0.397348i
$580$	−15.4385	−	13.1856i	−0.641049	−	0.547504i
$581$	12.1188			0.502771
$582$	−23.3242	−	23.3242i	−0.966817	−	0.966817i
$583$	−24.9426			−1.03302
$584$	0.999081			0.0413422
$585$	3.64739	−	2.34427i	0.150801	−	0.0969238i
$586$	37.1530			1.53478
$587$	−2.38675			−0.0985115			−0.0492558	−	0.998786i	$-0.515685\pi$
$587$	−2.38675			−0.0985115			−0.0492558	+	0.998786i	$0.515685\pi$
$588$	−12.3645	−	12.3645i	−0.509902	−	0.509902i
$589$	15.6591			0.645221
$590$	28.6192	−	2.25247i	1.17823	−	0.0927327i
$591$	−5.87272	−	5.87272i	−0.241571	−	0.241571i
$592$		−	29.1105i		−	1.19643i
$593$	−35.9052			−1.47445			−0.737225	−	0.675647i	$-0.763864\pi$
$593$	−35.9052			−1.47445			−0.737225	+	0.675647i	$0.763864\pi$
$594$			35.9076i			1.47331i
$595$	0.902771	+	11.4703i	0.0370100	+	0.470238i
$596$	−16.5233	+	16.5233i	−0.676821	+	0.676821i
$597$	0.415582	+	0.415582i	0.0170087	+	0.0170087i
$598$	23.6154	+	43.9877i	0.965705	+	1.79879i
$599$		−	31.9707i		−	1.30629i	−0.757233	−	0.653144i	$-0.773449\pi$
$599$		−	31.9707i		−	1.30629i	0.757233	−	0.653144i	$-0.226551\pi$
$600$	−1.37155	+	1.88780i	−0.0559932	+	0.0770691i
$601$	44.8777			1.83060			0.915299	−	0.402775i	$-0.131954\pi$
$601$	44.8777			1.83060			0.915299	+	0.402775i	$0.131954\pi$
$602$	−13.0741	−	13.0741i	−0.532860	−	0.532860i
$603$			3.14222i			0.127961i
$604$	3.94810	−	3.94810i	0.160646	−	0.160646i
$605$	6.09311	+	5.20397i	0.247720	+	0.211572i
$606$	2.22440	−	2.22440i	0.0903601	−	0.0903601i
$607$	−25.9355	+	25.9355i	−1.05269	+	1.05269i	−0.0541565	+	0.998532i	$0.517247\pi$
$607$	−25.9355	+	25.9355i	−1.05269	+	1.05269i	−0.998532	+	0.0541565i	$0.982753\pi$
$608$	−18.8519	+	18.8519i	−0.764547	+	0.764547i
$609$	9.20947	+	9.20947i	0.373186	+	0.373186i
$610$	35.8174	−	41.9371i	1.45020	−	1.69798i
$611$	18.5267	+	5.58305i	0.749509	+	0.225866i
$612$	2.56578	−	2.56578i	0.103715	−	0.103715i
$613$			3.63491i			0.146812i	0.997302	+	0.0734062i	$0.0233870\pi$
$613$			3.63491i			0.146812i	−0.997302	+	0.0734062i	$0.976613\pi$
$614$		−	38.4474i		−	1.55161i
$615$	12.9991	+	11.1022i	0.524174	+	0.447684i
$616$	1.08436	+	1.08436i	0.0436902	+	0.0436902i
$617$	−29.1618			−1.17401			−0.587005	−	0.809583i	$-0.699693\pi$
$617$	−29.1618			−1.17401			−0.587005	+	0.809583i	$0.699693\pi$
$618$	−4.68661			−0.188523
$619$	−28.1188	−	28.1188i	−1.13019	−	1.13019i	−0.990145	−	0.140045i	$-0.955275\pi$
$619$	−28.1188	−	28.1188i	−1.13019	−	1.13019i	−0.140045	−	0.990145i	$-0.544725\pi$
$620$	−22.4816	+	1.76941i	−0.902883	+	0.0710612i
$621$			31.5850i			1.26746i
$622$		−	35.2326i		−	1.41270i
$623$	13.9161	−	13.9161i	0.557536	−	0.557536i
$624$	−22.3506	+	11.9992i	−0.894741	+	0.480354i
$625$	−23.7763	+	7.72572i	−0.951053	+	0.309029i
$626$	−11.2595	−	11.2595i	−0.450019	−	0.450019i
$627$	−16.7360	+	16.7360i	−0.668373	+	0.668373i
$628$	20.9954	−	20.9954i	0.837807	−	0.837807i
$629$	17.4953	−	17.4953i	0.697584	−	0.697584i
$630$	2.56627	−	3.00474i	0.102243	−	0.119712i
$631$	−15.9754	+	15.9754i	−0.635971	+	0.635971i	−0.949559	−	0.313588i	$-0.898469\pi$
$631$	−15.9754	+	15.9754i	−0.635971	+	0.635971i	0.313588	+	0.949559i	$0.398469\pi$
$632$			2.14314i			0.0852495i
$633$	14.2552	+	14.2552i	0.566592	+	0.566592i
$634$	68.0131			2.70114
$635$	36.1844	−	2.84789i	1.43593	−	0.113015i
$636$			26.0714i			1.03380i
$637$	−4.55730	+	15.1229i	−0.180567	+	0.599189i
$638$	23.4567	+	23.4567i	0.928658	+	0.928658i
$639$	0.737604	−	0.737604i	0.0291792	−	0.0291792i
$640$	2.87718	−	3.36876i	0.113730	−	0.133162i
$641$		−	40.6941i		−	1.60732i	−0.595088	−	0.803661i	$-0.702883\pi$
$641$		−	40.6941i		−	1.60732i	0.595088	−	0.803661i	$-0.297117\pi$
$642$	17.7397			0.700131
$643$		−	3.29115i		−	0.129790i	−0.997892	−	0.0648952i	$-0.979329\pi$
$643$		−	3.29115i		−	0.129790i	0.997892	−	0.0648952i	$-0.0206713\pi$
$644$	16.5638	+	16.5638i	0.652706	+	0.652706i
$645$	−15.3694	+	17.9954i	−0.605170	+	0.708567i
$646$	−21.2701			−0.836861
$647$	−34.7828	−	34.7828i	−1.36745	−	1.36745i	−0.864052	−	0.503403i	$-0.832081\pi$
$647$	−34.7828	−	34.7828i	−1.36745	−	1.36745i	−0.503403	−	0.864052i	$-0.667919\pi$
$648$	2.56162			0.100630
$649$	−24.1479			−0.947888
$650$	36.2661	+	4.94844i	1.42247	+	0.194094i
$651$	14.4664			0.566982
$652$	−15.9967			−0.626481
$653$	−9.10093	−	9.10093i	−0.356147	−	0.356147i	0.506243	−	0.862391i	$-0.331034\pi$
$653$	−9.10093	−	9.10093i	−0.356147	−	0.356147i	−0.862391	+	0.506243i	$0.831034\pi$
$654$	−27.3914			−1.07109
$655$	−2.62678	+	3.07558i	−0.102637	+	0.120173i
$656$	−10.7510	−	10.7510i	−0.419755	−	0.419755i
$657$			2.16547i			0.0844830i
$658$	17.6345			0.687465
$659$		−	1.05740i		−	0.0411906i	−0.999788	−	0.0205953i	$-0.993444\pi$
$659$		−	1.05740i		−	0.0411906i	0.999788	−	0.0205953i	$-0.00655616\pi$
$660$	22.1367	−	25.9189i	0.861669	−	1.00889i
$661$	−6.24812	+	6.24812i	−0.243024	+	0.243024i	−0.818100	−	0.575076i	$-0.804972\pi$
$661$	−6.24812	+	6.24812i	−0.243024	+	0.243024i	0.575076	+	0.818100i	$0.304972\pi$
$662$	38.0046	+	38.0046i	1.47709	+	1.47709i
$663$	−20.6441	−	6.22115i	−0.801752	−	0.241609i
$664$		−	1.85789i		−	0.0721002i
$665$	−11.8881	+	0.935651i	−0.461001	+	0.0362830i
$666$	−8.49727			−0.329263
$667$	20.6329	+	20.6329i	0.798910	+	0.798910i
$668$		−	40.1279i		−	1.55259i
$669$	9.06679	−	9.06679i	0.350543	−	0.350543i
$670$	−17.2273	+	20.1707i	−0.665549	+	0.779262i
$671$	−32.8033	+	32.8033i	−1.26636	+	1.26636i
$672$	−17.4160	+	17.4160i	−0.671838	+	0.671838i
$673$	−8.47252	+	8.47252i	−0.326592	+	0.326592i	−0.851289	−	0.524697i	$-0.824179\pi$
$673$	−8.47252	+	8.47252i	−0.326592	+	0.326592i	0.524697	+	0.851289i	$0.324179\pi$
$674$	−25.0854	−	25.0854i	−0.966254	−	0.966254i
$675$	18.7336	+	13.6106i	0.721056	+	0.523871i
$676$	−22.9950	−	15.2435i	−0.884424	−	0.586288i
$677$	−0.782203	+	0.782203i	−0.0300625	+	0.0300625i	−0.721978	−	0.691916i	$-0.756767\pi$
$677$	−0.782203	+	0.782203i	−0.0300625	+	0.0300625i	0.691916	+	0.721978i	$0.256767\pi$
$678$		−	49.9409i		−	1.91797i
$679$			13.9794i			0.536479i
$680$	1.75848	−	0.138401i	0.0674348	−	0.00530744i
$681$	6.06862	+	6.06862i	0.232550	+	0.232550i
$682$	36.8461			1.41091
$683$	−16.4856			−0.630803			−0.315401	−	0.948958i	$-0.602139\pi$
$683$	−16.4856			−0.630803			−0.315401	+	0.948958i	$0.602139\pi$
$684$	2.65923	+	2.65923i	0.101678	+	0.101678i
$685$	−15.2435	−	13.0191i	−0.582424	−	0.497434i
$686$			37.3964i			1.42780i
$687$		−	36.0788i		−	1.37649i
$688$	14.8832	−	14.8832i	0.567416	−	0.567416i
$689$	20.7485	−	11.1391i	0.790455	−	0.424367i
$690$	37.8224	−	44.2846i	1.43987	−	1.68589i
$691$	31.1593	+	31.1593i	1.18535	+	1.18535i	0.978337	+	0.207018i	$0.0663758\pi$
$691$	31.1593	+	31.1593i	1.18535	+	1.18535i	0.207018	+	0.978337i	$0.433624\pi$
$692$	−5.96089	+	5.96089i	−0.226599	+	0.226599i
$693$	−2.35031	+	2.35031i	−0.0892810	+	0.0892810i
$694$	−1.95410	+	1.95410i	−0.0741766	+	0.0741766i
$695$	9.14466	+	7.81023i	0.346877	+	0.296259i
$696$	1.41188	−	1.41188i	0.0535171	−	0.0535171i
$697$		−	12.9226i		−	0.489478i
$698$	−12.5854	−	12.5854i	−0.476363	−	0.476363i
$699$	−1.76909			−0.0669133
$700$	16.9619	−	2.68661i	0.641101	−	0.101544i
$701$		−	16.2976i		−	0.615554i	−0.951459	−	0.307777i	$-0.900415\pi$
$701$		−	16.2976i		−	0.615554i	0.951459	−	0.307777i	$-0.0995850\pi$
$702$	−16.0360	−	29.8698i	−0.605240	−	1.12736i
$703$	18.1325	+	18.1325i	0.683881	+	0.683881i
$704$	−24.1570	+	24.1570i	−0.910451	+	0.910451i
$705$	−1.77097	−	22.5015i	−0.0666987	−	0.847454i
$706$			7.89852i			0.297265i
$707$	−1.33320			−0.0501401
$708$			25.2407i			0.948605i
$709$	1.04907	+	1.04907i	0.0393988	+	0.0393988i	0.726532	−	0.687133i	$-0.241131\pi$
$709$	1.04907	+	1.04907i	0.0393988	+	0.0393988i	−0.687133	+	0.726532i	$0.741131\pi$
$710$	8.77880	−	0.690934i	0.329463	−	0.0259303i
$711$	−4.64517			−0.174208
$712$	−2.13344	−	2.13344i	−0.0799539	−	0.0799539i
$713$	32.4105			1.21378
$714$	−19.6500			−0.735384
$715$	−30.0851	−	6.54317i	−1.12512	−	0.244701i
$716$	45.9739			1.71812
$717$	25.1903			0.940748
$718$	32.7364	+	32.7364i	1.22171	+	1.22171i
$719$	−48.2826			−1.80064			−0.900319	−	0.435232i	$-0.856667\pi$
$719$	−48.2826			−1.80064			−0.900319	+	0.435232i	$0.856667\pi$
$720$	3.42051	+	2.92137i	0.127475	+	0.108873i
$721$	1.40447	+	1.40447i	0.0523050	+	0.0523050i
$722$			16.5313i			0.615232i
$723$	31.6731			1.17793
$724$			14.4902i			0.538526i
$725$	21.1288	−	3.34661i	0.784704	−	0.124290i
$726$	−9.67661	+	9.67661i	−0.359133	+	0.359133i
$727$	13.9089	+	13.9089i	0.515851	+	0.515851i	0.916313	−	0.400462i	$-0.131150\pi$
$727$	13.9089	+	13.9089i	0.515851	+	0.515851i	−0.400462	+	0.916313i	$0.631150\pi$
$728$	−1.38629	−	0.417762i	−0.0513794	−	0.0154833i
$729$		−	20.5801i		−	0.762227i
$730$	−11.8722	+	13.9007i	−0.439412	+	0.514488i
$731$	17.8895			0.661666
$732$	34.2878	+	34.2878i	1.26731	+	1.26731i
$733$			38.3390i			1.41608i	0.706171	+	0.708041i	$0.250421\pi$
$733$			38.3390i			1.41608i	−0.706171	+	0.708041i	$0.749579\pi$
$734$	13.3735	−	13.3735i	0.493626	−	0.493626i
$735$	18.3674	−	1.44560i	0.677491	−	0.0533218i
$736$	−39.0189	+	39.0189i	−1.43826	+	1.43826i
$737$	15.7776	−	15.7776i	0.581175	−	0.581175i
$738$	−3.13817	+	3.13817i	−0.115518	+	0.115518i
$739$	14.1532	+	14.1532i	0.520633	+	0.520633i	0.917763	−	0.397130i	$-0.129994\pi$
$739$	14.1532	+	14.1532i	0.520633	+	0.520633i	−0.397130	+	0.917763i	$0.629994\pi$
$740$	−28.0816	−	23.9838i	−1.03230	−	0.881662i
$741$	6.44773	−	21.3960i	0.236863	−	0.786003i
$742$	15.1760	−	15.1760i	0.557130	−	0.557130i
$743$			19.6941i			0.722508i	0.932467	+	0.361254i	$0.117651\pi$
$743$			19.6941i			0.722508i	−0.932467	+	0.361254i	$0.882349\pi$
$744$		−	2.21780i		−	0.0813084i
$745$	−1.93183	−	24.5453i	−0.0707769	−	0.899270i
$746$	−19.3251	−	19.3251i	−0.707541	−	0.707541i
$747$	4.02692			0.147337
$748$	−25.7663			−0.942111
$749$	−5.31617	−	5.31617i	−0.194249	−	0.194249i
$750$	−9.96754	−	41.5161i	−0.363963	−	1.51595i
$751$		−	31.6564i		−	1.15516i	−0.816334	−	0.577580i	$-0.803997\pi$
$751$		−	31.6564i		−	1.15516i	0.816334	−	0.577580i	$-0.196003\pi$
$752$			20.0747i			0.732047i
$753$	19.3540	−	19.3540i	0.705300	−	0.705300i
$754$	−29.9880	−	9.03693i	−1.09210	−	0.329105i
$755$	0.461595	+	5.86489i	0.0167992	+	0.213445i
$756$	−11.2477	−	11.2477i	−0.409073	−	0.409073i
$757$	−7.76808	+	7.76808i	−0.282335	+	0.282335i	−0.834040	−	0.551704i	$-0.813978\pi$
$757$	−7.76808	+	7.76808i	−0.282335	+	0.282335i	0.551704	+	0.834040i	$0.313978\pi$
$758$	10.7990	−	10.7990i	0.392239	−	0.392239i
$759$	−34.6395	+	34.6395i	−1.25733	+	1.25733i
$760$	0.143442	+	1.82253i	0.00520319	+	0.0661101i
$761$	20.3483	−	20.3483i	0.737626	−	0.737626i	−0.234492	−	0.972118i	$-0.575343\pi$
$761$	20.3483	−	20.3483i	0.737626	−	0.737626i	0.972118	+	0.234492i	$0.0753427\pi$
$762$			61.9881i			2.24559i
$763$	8.20855	+	8.20855i	0.297169	+	0.297169i
$764$	−40.2053			−1.45458
$765$	0.299980	+	3.81145i	0.0108458	+	0.137803i
$766$			30.1879i			1.09073i
$767$	20.0875	−	10.7842i	0.725316	−	0.389396i
$768$	−18.4462	−	18.4462i	−0.665620	−	0.665620i
$769$	30.9403	−	30.9403i	1.11573	−	1.11573i	0.123374	−	0.992360i	$-0.460628\pi$
$769$	30.9403	−	30.9403i	1.11573	−	1.11573i	0.992360	−	0.123374i	$-0.0393715\pi$
$770$	−27.9729	+	2.20160i	−1.00807	+	0.0793403i
$771$		−	34.6507i		−	1.24792i
$772$	15.2562			0.549083
$773$		−	35.7878i		−	1.28720i	−0.765363	−	0.643598i	$-0.777441\pi$
$773$		−	35.7878i		−	1.28720i	0.765363	−	0.643598i	$-0.222559\pi$
$774$	−4.34435	−	4.34435i	−0.156155	−	0.156155i
$775$	13.9663	−	19.2232i	0.501683	−	0.690517i
$776$	2.14314			0.0769342
$777$	16.7514	+	16.7514i	0.600954	+	0.600954i
$778$	−58.6921			−2.10421
$779$	13.3932			0.479863
$780$	−6.83929	+	31.4467i	−0.244886	+	1.12597i
$781$	−7.40725			−0.265052
$782$	−44.0240			−1.57429
$783$	−14.0108	−	14.0108i	−0.500704	−	0.500704i
$784$	−16.3864			−0.585230
$785$	2.45469	+	31.1885i	0.0876116	+	1.11317i
$786$	−4.88440	−	4.88440i	−0.174221	−	0.174221i
$787$		−	8.98893i		−	0.320421i	−0.987083	−	0.160210i	$-0.948783\pi$
$787$		−	8.98893i		−	0.320421i	0.987083	−	0.160210i	$-0.0512172\pi$
$788$	9.37078			0.333820
$789$			29.3746i			1.04576i
$790$	−29.8185	−	25.4673i	−1.06090	−	0.906085i
$791$	−14.9661	+	14.9661i	−0.532133	+	0.532133i
$792$	0.360320	+	0.360320i	0.0128034	+	0.0128034i
$793$	12.6378	−	41.9371i	0.448782	−	1.48923i
$794$			29.6548i			1.05241i
$795$	−20.8886	−	17.8404i	−0.740841	−	0.632734i
$796$	−0.663123			−0.0235038
$797$	−6.02120	−	6.02120i	−0.213282	−	0.213282i	0.592378	−	0.805660i	$-0.298189\pi$
$797$	−6.02120	−	6.02120i	−0.213282	−	0.213282i	−0.805660	+	0.592378i	$0.798189\pi$
$798$		−	20.3657i		−	0.720938i
$799$	−12.0648	+	12.0648i	−0.426822	+	0.426822i
$800$	6.32878	+	39.9567i	0.223756	+	1.41268i
$801$	4.62414	−	4.62414i	0.163386	−	0.163386i
$802$	16.7000	−	16.7000i	0.589699	−	0.589699i
$803$	10.8732	−	10.8732i	0.383706	−	0.383706i
$804$	−16.4916	−	16.4916i	−0.581614	−	0.581614i
$805$	−24.6055	+	1.93657i	−0.867230	+	0.0682551i
$806$	−30.6504	+	16.4551i	−1.07962	+	0.579606i
$807$	2.34843	−	2.34843i	0.0826688	−	0.0826688i
$808$			0.204389i			0.00719038i
$809$			35.3904i			1.24426i	0.782914	+	0.622130i	$0.213732\pi$
$809$			35.3904i			1.24426i	−0.782914	+	0.622130i	$0.786268\pi$
$810$	−30.4402	+	35.6411i	−1.06956	+	1.25230i
$811$	−14.2623	−	14.2623i	−0.500817	−	0.500817i	0.410875	−	0.911692i	$-0.365223\pi$
$811$	−14.2623	−	14.2623i	−0.500817	−	0.500817i	−0.911692	+	0.410875i	$0.865223\pi$
$812$	−14.6951			−0.515695
$813$	−32.9963			−1.15723
$814$	42.6661	+	42.6661i	1.49545	+	1.49545i
$815$	10.9464	−	12.8167i	0.383436	−	0.448949i
$816$		−	22.3691i		−	0.783073i
$817$			18.5410i			0.648668i
$818$	−52.9999	+	52.9999i	−1.85310	+	1.85310i
$819$	0.905483	−	3.00474i	0.0316401	−	0.104994i
$820$	−19.2286	+	1.51338i	−0.671490	+	0.0528495i
$821$	−34.7667	−	34.7667i	−1.21337	−	1.21337i	−0.969913	−	0.243453i	$-0.921720\pi$
$821$	−34.7667	−	34.7667i	−1.21337	−	1.21337i	−0.243453	−	0.969913i	$-0.578280\pi$
$822$	24.2085	−	24.2085i	0.844370	−	0.844370i
$823$	−4.53102	+	4.53102i	−0.157941	+	0.157941i	−0.781654	−	0.623712i	$-0.785624\pi$
$823$	−4.53102	+	4.53102i	−0.157941	+	0.157941i	0.623712	+	0.781654i	$0.285624\pi$
$824$	0.215315	−	0.215315i	0.00750084	−	0.00750084i
$825$	5.61845	+	35.4721i	0.195609	+	1.23498i
$826$	14.6925	−	14.6925i	0.511218	−	0.511218i
$827$			35.6597i			1.24001i	0.784598	+	0.620004i	$0.212869\pi$
$827$			35.6597i			1.24001i	−0.784598	+	0.620004i	$0.787131\pi$
$828$	5.50395	+	5.50395i	0.191276	+	0.191276i
$829$	44.9117			1.55985			0.779924	−	0.625874i	$-0.215258\pi$
$829$	44.9117			1.55985			0.779924	+	0.625874i	$0.215258\pi$
$830$	25.8498	+	22.0777i	0.897259	+	0.766327i
$831$			31.1769i			1.08151i
$832$	9.30673	−	30.8833i	0.322653	−	1.07069i
$833$	−9.84819	−	9.84819i	−0.341220	−	0.341220i
$834$	−14.5229	+	14.5229i	−0.502885	+	0.502885i
$835$	32.1507	+	27.4591i	1.11262	+	0.950262i
$836$		−	26.7048i		−	0.923604i
$837$	−22.0083			−0.760719
$838$			46.4695i			1.60526i
$839$	1.42941	+	1.42941i	0.0493486	+	0.0493486i	0.731350	−	0.682002i	$-0.238890\pi$
$839$	1.42941	+	1.42941i	0.0493486	+	0.0493486i	−0.682002	+	0.731350i	$0.738890\pi$
$840$	0.132516	+	1.68371i	0.00457225	+	0.0580936i
$841$	10.6949			0.368791
$842$	−50.0715	−	50.0715i	−1.72558	−	1.72558i
$843$	33.3009			1.14694
$844$	−22.7462			−0.782957
$845$	27.9484	−	7.99278i	0.961456	−	0.274960i
$846$	5.85973			0.201462
$847$	5.79970			0.199280
$848$	17.2760	+	17.2760i	0.593260	+	0.593260i
$849$	34.1962			1.17361
$850$	−18.9707	+	26.1113i	−0.650691	+	0.895611i
$851$	37.5299	+	37.5299i	1.28651	+	1.28651i
$852$			7.74248i			0.265253i
$853$	−29.8662			−1.02260			−0.511300	−	0.859402i	$-0.670836\pi$
$853$	−29.8662			−1.02260			−0.511300	+	0.859402i	$0.670836\pi$
$854$		−	39.9176i		−	1.36595i
$855$	−3.95027	+	0.310905i	−0.135096	+	0.0106327i
$856$	−0.815007	+	0.815007i	−0.0278564	+	0.0278564i
$857$	9.07650	+	9.07650i	0.310047	+	0.310047i	0.844928	−	0.534880i	$-0.179643\pi$
$857$	9.07650	+	9.07650i	0.310047	+	0.310047i	−0.534880	+	0.844928i	$0.679643\pi$
$858$	15.1716	−	50.3452i	0.517951	−	1.71876i
$859$		−	55.1497i		−	1.88168i	−0.338845	−	0.940842i	$-0.610036\pi$
$859$		−	55.1497i		−	1.88168i	0.338845	−	0.940842i	$-0.389964\pi$
$860$	−2.09506	−	26.6192i	−0.0714409	−	0.907707i
$861$	12.3731			0.421675
$862$	33.5558	+	33.5558i	1.14291	+	1.14291i
$863$		−	14.0772i		−	0.479193i	−0.970873	−	0.239596i	$-0.922985\pi$
$863$		−	14.0772i		−	0.479193i	0.970873	−	0.239596i	$-0.0770151\pi$
$864$	26.4958	−	26.4958i	0.901404	−	0.901404i
$865$	−0.696922	−	8.85488i	−0.0236961	−	0.301075i
$866$	50.8574	−	50.8574i	1.72821	−	1.72821i
$867$	−9.16624	+	9.16624i	−0.311302	+	0.311302i
$868$	−11.5416	+	11.5416i	−0.391748	+	0.391748i
$869$	23.3242	+	23.3242i	0.791218	+	0.791218i
$870$	2.86656	+	36.4217i	0.0971856	+	1.23481i
$871$	−6.07848	+	20.1707i	−0.205961	+	0.683458i
$872$	1.25843	−	1.25843i	0.0426158	−	0.0426158i
$873$			4.64517i			0.157215i
$874$		−	45.6274i		−	1.54337i
$875$	−9.45435	+	15.4284i	−0.319615	+	0.521576i
$876$	−11.3652	−	11.3652i	−0.383996	−	0.383996i
$877$	3.88489			0.131183			0.0655917	−	0.997847i	$-0.479107\pi$
$877$	3.88489			0.131183			0.0655917	+	0.997847i	$0.479107\pi$
$878$	36.8490			1.24359
$879$	−24.3377	−	24.3377i	−0.820891	−	0.820891i
$880$	−2.50624	−	31.8436i	−0.0844855	−	1.07345i
$881$			12.9948i			0.437806i	0.975747	+	0.218903i	$0.0702478\pi$
$881$			12.9948i			0.437806i	−0.975747	+	0.218903i	$0.929752\pi$
$882$			4.78315i			0.161057i
$883$	−2.20501	+	2.20501i	−0.0742043	+	0.0742043i	−0.743235	−	0.669031i	$-0.766710\pi$
$883$	−2.20501	+	2.20501i	−0.0742043	+	0.0742043i	0.669031	+	0.743235i	$0.266710\pi$
$884$	21.4338	−	11.5070i	0.720895	−	0.387022i
$885$	−20.2230	−	17.2720i	−0.679790	−	0.580592i
$886$	−14.8266	−	14.8266i	−0.498109	−	0.498109i
$887$	−2.71582	+	2.71582i	−0.0911884	+	0.0911884i	−0.751230	−	0.660041i	$-0.770539\pi$
$887$	−2.71582	+	2.71582i	−0.0911884	+	0.0911884i	0.660041	+	0.751230i	$0.270539\pi$
$888$	2.56811	−	2.56811i	0.0861802	−	0.0861802i
$889$	18.5764	−	18.5764i	0.623031	−	0.623031i
$890$	55.0355	−	4.33156i	1.84480	−	0.145194i
$891$	27.8785	−	27.8785i	0.933967	−	0.933967i
$892$			14.4674i			0.484404i
$893$	−12.5042	−	12.5042i	−0.418438	−	0.418438i
$894$	42.0489			1.40633
$895$	−31.4595	+	36.8345i	−1.05157	+	1.23124i
$896$		−	3.20654i		−	0.107123i
$897$	13.3452	−	44.2846i	0.445584	−	1.47862i
$898$	6.65063	+	6.65063i	0.221935	+	0.221935i
$899$	−14.3769	+	14.3769i	−0.479497	+	0.479497i
$900$	5.63624	−	0.892728i	0.187875	−	0.0297576i
$901$			20.7656i			0.691803i
$902$	31.5145			1.04932
$903$			17.1288i			0.570011i
$904$	2.29441	+	2.29441i	0.0763109	+	0.0763109i
$905$	−11.6097	−	9.91553i	−0.385918	−	0.329603i
$906$	−10.0472			−0.333797
$907$	−24.5036	−	24.5036i	−0.813629	−	0.813629i	0.171547	−	0.985176i	$-0.445123\pi$
$907$	−24.5036	−	24.5036i	−0.813629	−	0.813629i	−0.985176	+	0.171547i	$0.945123\pi$
$908$	−9.68337			−0.321354
$909$	−0.443006			−0.0146936
$910$	22.2861	−	14.3238i	0.738776	−	0.474831i
$911$	−33.7082			−1.11680			−0.558400	−	0.829572i	$-0.688585\pi$
$911$	−33.7082			−1.11680			−0.558400	+	0.829572i	$0.688585\pi$
$912$	23.1838			0.767691
$913$	−20.2198	−	20.2198i	−0.669177	−	0.669177i
$914$	28.1545			0.931268
$915$	−50.9344	+	4.00878i	−1.68384	+	0.132526i
$916$	28.7845	+	28.7845i	0.951067	+	0.951067i
$917$			2.92747i			0.0966737i
$918$	29.8944			0.986664
$919$			47.9735i			1.58250i	0.611493	+	0.791250i	$0.290569\pi$
$919$			47.9735i			1.58250i	−0.611493	+	0.791250i	$0.709431\pi$
$920$	0.296890	+	3.77220i	0.00978817	+	0.124366i
$921$	−25.1856	+	25.1856i	−0.829895	+	0.829895i
$922$	−12.2291	−	12.2291i	−0.402745	−	0.402745i
$923$	6.16173	−	3.30801i	0.202816	−	0.108884i
$924$		−	24.6708i		−	0.811608i
$925$	38.4319	−	6.08726i	1.26363	−	0.200148i
$926$	33.8893			1.11367
$927$	0.466686	+	0.466686i	0.0153280	+	0.0153280i
$928$		−	34.6167i		−	1.13635i
$929$	−9.76693	+	9.76693i	−0.320443	+	0.320443i	−0.848937	−	0.528494i	$-0.822757\pi$
$929$	−9.76693	+	9.76693i	−0.320443	+	0.320443i	0.528494	+	0.848937i	$0.322757\pi$
$930$	30.8573	+	26.3545i	1.01185	+	0.864197i
$931$	10.2069	−	10.2069i	0.334517	−	0.334517i
$932$	1.41142	−	1.41142i	0.0462327	−	0.0462327i
$933$	−23.0797	+	23.0797i	−0.755597	+	0.755597i
$934$	−11.5507	−	11.5507i	−0.377950	−	0.377950i
$935$	17.6317	−	20.6441i	0.576617	−	0.675136i
$936$	−0.460648	−	0.138817i	−0.0150567	−	0.00453737i
$937$	−7.31002	+	7.31002i	−0.238808	+	0.238808i	−0.816356	−	0.577548i	$-0.804009\pi$
$937$	−7.31002	+	7.31002i	−0.238808	+	0.238808i	0.577548	+	0.816356i	$0.304009\pi$
$938$			19.1994i			0.626882i
$939$			14.7514i			0.481394i
$940$	19.3651	+	16.5393i	0.631621	+	0.539452i
$941$	19.3372	+	19.3372i	0.630376	+	0.630376i	0.948162	−	0.317786i	$-0.102939\pi$
$941$	19.3372	+	19.3372i	0.630376	+	0.630376i	−0.317786	+	0.948162i	$0.602939\pi$
$942$	−53.4296			−1.74083
$943$	27.7208			0.902712
$944$	16.7256	+	16.7256i	0.544371	+	0.544371i
$945$	16.7083	−	1.31503i	0.543522	−	0.0427778i
$946$			43.6274i			1.41845i
$947$			7.99987i			0.259961i	0.991517	+	0.129980i	$0.0414915\pi$
$947$			7.99987i			0.259961i	−0.991517	+	0.129980i	$0.958509\pi$
$948$	24.3797	−	24.3797i	0.791816	−	0.791816i
$949$	−4.18900	+	13.9007i	−0.135981	+	0.451236i
$950$	−27.0623	−	19.6617i	−0.878018	−	0.637909i
$951$	−44.5532	−	44.5532i	−1.44474	−	1.44474i
$952$	0.902771	−	0.902771i	0.0292590	−	0.0292590i
$953$	−36.3248	+	36.3248i	−1.17667	+	1.17667i	−0.196088	+	0.980586i	$0.562824\pi$
$953$	−36.3248	+	36.3248i	−1.17667	+	1.17667i	−0.980586	+	0.196088i	$0.937176\pi$
$954$	5.04281	−	5.04281i	0.163267	−	0.163267i
$955$	27.5121	−	32.2127i	0.890270	−	1.04238i
$956$	−20.0974	+	20.0974i	−0.649996	+	0.649996i
$957$		−	30.7314i		−	0.993405i
$958$	16.1094	+	16.1094i	0.520472	+	0.520472i
$959$	−14.5094			−0.468534
$960$	−37.5091	+	2.95215i	−1.21060	+	0.0952802i
$961$		−	8.41650i		−	0.271500i
$962$	−54.5461	−	16.4376i	−1.75864	−	0.529969i
$963$	−1.76650	−	1.76650i	−0.0569246	−	0.0569246i
$964$	−25.2695	+	25.2695i	−0.813877	+	0.813877i
$965$	−10.4397	+	12.2234i	−0.336065	+	0.393484i
$966$		−	42.1521i		−	1.35622i
$967$	12.9501			0.416448			0.208224	−	0.978081i	$-0.433232\pi$
$967$	12.9501			0.416448			0.208224	+	0.978081i	$0.433232\pi$
$968$		−	0.889135i		−	0.0285779i
$969$	13.9334	+	13.9334i	0.447604	+	0.447604i
$970$	−25.4673	+	29.8185i	−0.817705	+	0.957416i
$971$	4.36013			0.139923			0.0699616	−	0.997550i	$-0.477712\pi$
$971$	4.36013			0.139923			0.0699616	+	0.997550i	$0.477712\pi$
$972$	−8.29123	−	8.29123i	−0.265941	−	0.265941i
$973$	8.70430			0.279047
$974$	36.7498			1.17754
$975$	−20.5152	−	26.9983i	−0.657012	−	0.864638i
$976$	45.4411			1.45453
$977$	37.8354			1.21046			0.605231	−	0.796050i	$-0.293081\pi$
$977$	37.8354			1.21046			0.605231	+	0.796050i	$0.293081\pi$
$978$	20.3545	+	20.3545i	0.650864	+	0.650864i
$979$	−46.4371			−1.48414
$980$	−13.5006	+	15.8073i	−0.431260	+	0.504944i
$981$	2.72760	+	2.72760i	0.0870855	+	0.0870855i
$982$		−	53.5678i		−	1.70942i
$983$	−42.4511			−1.35398			−0.676990	−	0.735992i	$-0.736716\pi$
$983$	−42.4511			−1.35398			−0.676990	+	0.735992i	$0.736716\pi$
$984$		−	1.89689i		−	0.0604705i
$985$	−6.41233	+	7.50792i	−0.204314	+	0.239222i
$986$	19.5285	−	19.5285i	0.621915	−	0.621915i
$987$	−11.5518	−	11.5518i	−0.367698	−	0.367698i
$988$	11.9261	+	22.2144i	0.379420	+	0.706734i
$989$			38.3754i			1.22027i
$990$	−9.29505	+	0.731565i	−0.295416	+	0.0232507i
$991$	−53.6484			−1.70420			−0.852099	−	0.523381i	$-0.824671\pi$
$991$	−53.6484			−1.70420			−0.852099	+	0.523381i	$0.824671\pi$
$992$	−27.1882	−	27.1882i	−0.863227	−	0.863227i
$993$		−	49.7911i		−	1.58007i
$994$	4.50686	−	4.50686i	0.142949	−	0.142949i
$995$	0.453768	−	0.531297i	0.0143854	−	0.0168433i
$996$	−21.1348	+	21.1348i	−0.669683	+	0.669683i
$997$	−30.6973	+	30.6973i	−0.972192	+	0.972192i	−0.999624	−	0.0274316i	$-0.991267\pi$
$997$	−30.6973	+	30.6973i	−0.972192	+	0.972192i	0.0274316	+	0.999624i	$0.491267\pi$
$998$	21.6738	−	21.6738i	0.686074	−	0.686074i
$999$	−25.4847	−	25.4847i	−0.806299	−	0.806299i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.2.k.b.8.4	yes	8
3.2	odd	2		585.2.w.e.73.1		8
4.3	odd	2		1040.2.bg.n.593.3		8
5.2	odd	4		65.2.f.b.47.4	yes	8
5.3	odd	4		325.2.f.b.307.1		8
5.4	even	2		325.2.k.b.268.1		8
13.2	odd	12		845.2.t.c.188.4		16
13.3	even	3		845.2.o.d.488.1		16
13.4	even	6		845.2.o.c.258.4		16
13.5	odd	4		65.2.f.b.18.1	✓	8
13.6	odd	12		845.2.t.c.418.1		16
13.7	odd	12		845.2.t.d.418.4		16
13.8	odd	4		845.2.f.b.408.4		8
13.9	even	3		845.2.o.d.258.1		16
13.10	even	6		845.2.o.c.488.4		16
13.11	odd	12		845.2.t.d.188.1		16
13.12	even	2		845.2.k.b.268.1		8
15.2	even	4		585.2.n.e.307.1		8
20.7	even	4		1040.2.cd.n.177.3		8
39.5	even	4		585.2.n.e.343.4		8
52.31	even	4		1040.2.cd.n.993.3		8
65.2	even	12		845.2.o.d.357.1		16
65.7	even	12		845.2.o.c.587.4		16
65.12	odd	4		845.2.f.b.437.1		8
65.17	odd	12		845.2.t.d.427.1		16
65.18	even	4		325.2.k.b.57.1		8
65.22	odd	12		845.2.t.c.427.4		16
65.32	even	12		845.2.o.d.587.1		16
65.37	even	12		845.2.o.c.357.4		16
65.42	odd	12		845.2.t.c.657.1		16
65.44	odd	4		325.2.f.b.18.4		8
65.47	even	4		845.2.k.b.577.1		8
65.57	even	4	inner	65.2.k.b.57.4	yes	8
65.62	odd	12		845.2.t.d.657.4		16
195.122	odd	4		585.2.w.e.577.1		8
260.187	odd	4		1040.2.bg.n.577.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.1	✓	8	13.5	odd	4
65.2.f.b.47.4	yes	8	5.2	odd	4
65.2.k.b.8.4	yes	8	1.1	even	1	trivial
65.2.k.b.57.4	yes	8	65.57	even	4	inner
325.2.f.b.18.4		8	65.44	odd	4
325.2.f.b.307.1		8	5.3	odd	4
325.2.k.b.57.1		8	65.18	even	4
325.2.k.b.268.1		8	5.4	even	2
585.2.n.e.307.1		8	15.2	even	4
585.2.n.e.343.4		8	39.5	even	4
585.2.w.e.73.1		8	3.2	odd	2
585.2.w.e.577.1		8	195.122	odd	4
845.2.f.b.408.4		8	13.8	odd	4
845.2.f.b.437.1		8	65.12	odd	4
845.2.k.b.268.1		8	13.12	even	2
845.2.k.b.577.1		8	65.47	even	4
845.2.o.c.258.4		16	13.4	even	6
845.2.o.c.357.4		16	65.37	even	12
845.2.o.c.488.4		16	13.10	even	6
845.2.o.c.587.4		16	65.7	even	12
845.2.o.d.258.1		16	13.9	even	3
845.2.o.d.357.1		16	65.2	even	12
845.2.o.d.488.1		16	13.3	even	3
845.2.o.d.587.1		16	65.32	even	12
845.2.t.c.188.4		16	13.2	odd	12
845.2.t.c.418.1		16	13.6	odd	12
845.2.t.c.427.4		16	65.22	odd	12
845.2.t.c.657.1		16	65.42	odd	12
845.2.t.d.188.1		16	13.11	odd	12
845.2.t.d.418.4		16	13.7	odd	12
845.2.t.d.427.1		16	65.17	odd	12
845.2.t.d.657.4		16	65.62	odd	12
1040.2.bg.n.577.3		8	260.187	odd	4
1040.2.bg.n.593.3		8	4.3	odd	2
1040.2.cd.n.177.3		8	20.7	even	4
1040.2.cd.n.993.3		8	52.31	even	4

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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	65.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.03032 q^{2} +(-1.33000 - 1.33000i) q^{3} +2.12221 q^{4} +(-1.45220 + 1.70032i) q^{5} +(-2.70032 - 2.70032i) q^{6} +1.61845i q^{7} +0.248119 q^{8} +0.537789i q^{9} +O(q^{10})\)	\(q+2.03032 q^{2} +(-1.33000 - 1.33000i) q^{3} +2.12221 q^{4} +(-1.45220 + 1.70032i) q^{5} +(-2.70032 - 2.70032i) q^{6} +1.61845i q^{7} +0.248119 q^{8} +0.537789i q^{9} +(-2.94844 + 3.45220i) q^{10} +(2.70032 - 2.70032i) q^{11} +(-2.82253 - 2.82253i) q^{12} +(-1.04033 + 3.45220i) q^{13} +3.28596i q^{14} +(4.19286 - 0.329998i) q^{15} -3.74065 q^{16} +(-2.24812 - 2.24812i) q^{17} +1.09188i q^{18} +(2.33000 - 2.33000i) q^{19} +(-3.08188 + 3.60844i) q^{20} +(2.15253 - 2.15253i) q^{21} +(5.48253 - 5.48253i) q^{22} +(4.82253 - 4.82253i) q^{23} +(-0.329998 - 0.329998i) q^{24} +(-0.782203 - 4.93844i) q^{25} +(-2.11220 + 7.00909i) q^{26} +(-3.27474 + 3.27474i) q^{27} +3.43468i q^{28} +4.27844i q^{29} +(8.51285 - 0.670002i) q^{30} +(3.36032 + 3.36032i) q^{31} -8.09097 q^{32} -7.18285 q^{33} +(-4.56441 - 4.56441i) q^{34} +(-2.75188 - 2.35031i) q^{35} +1.14130i q^{36} +7.78220i q^{37} +(4.73065 - 4.73065i) q^{38} +(5.97506 - 3.20779i) q^{39} +(-0.360320 + 0.421883i) q^{40} +(2.87409 + 2.87409i) q^{41} +(4.37033 - 4.37033i) q^{42} +(-3.97876 + 3.97876i) q^{43} +(5.73065 - 5.73065i) q^{44} +(-0.914416 - 0.780980i) q^{45} +(9.79129 - 9.79129i) q^{46} -5.36662i q^{47} +(4.97506 + 4.97506i) q^{48} +4.38064 q^{49} +(-1.58812 - 10.0266i) q^{50} +5.97999i q^{51} +(-2.20779 + 7.32629i) q^{52} +(-4.61845 - 4.61845i) q^{53} +(-6.64877 + 6.64877i) q^{54} +(0.670002 + 8.51285i) q^{55} +0.401567i q^{56} -6.19779 q^{57} +8.68661i q^{58} +(-4.47130 - 4.47130i) q^{59} +(8.89811 - 0.700324i) q^{60} -12.1479 q^{61} +(6.82253 + 6.82253i) q^{62} -0.870382 q^{63} -8.94596 q^{64} +(-4.35910 - 6.78220i) q^{65} -14.5835 q^{66} +5.84285 q^{67} +(-4.77097 - 4.77097i) q^{68} -12.8279 q^{69} +(-5.58720 - 4.77189i) q^{70} +(-1.37155 - 1.37155i) q^{71} +0.133436i q^{72} +4.02662 q^{73} +15.8004i q^{74} +(-5.52778 + 7.60844i) q^{75} +(4.94474 - 4.94474i) q^{76} +(4.37033 + 4.37033i) q^{77} +(12.1313 - 6.51285i) q^{78} +8.63754i q^{79} +(5.43219 - 6.36032i) q^{80} +10.3242 q^{81} +(5.83532 + 5.83532i) q^{82} -7.48791i q^{83} +(4.56811 - 4.56811i) q^{84} +(7.08726 - 0.557801i) q^{85} +(-8.07817 + 8.07817i) q^{86} +(5.69032 - 5.69032i) q^{87} +(0.670002 - 0.670002i) q^{88} +(-8.59843 - 8.59843i) q^{89} +(-1.85656 - 1.58564i) q^{90} +(-5.58720 - 1.68371i) q^{91} +(10.2344 - 10.2344i) q^{92} -8.93844i q^{93} -10.8960i q^{94} +(0.578117 + 7.34539i) q^{95} +(10.7610 + 10.7610i) q^{96} +8.63754 q^{97} +8.89410 q^{98} +(1.45220 + 1.45220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6	\( 8 q - 4 q^{2} - 6 q^{3} + 8 q^{4} + 2 q^{5} - 6 q^{6} - 6 q^{10} + 6 q^{11} + 2 q^{12} - 2 q^{13} - 2 q^{15} - 8 q^{16} - 16 q^{17} + 14 q^{19} - 22 q^{20} - 12 q^{21} + 10 q^{22} + 14 q^{23} + 2 q^{24} + 12 q^{25} + 6 q^{26} + 12 q^{27} + 14 q^{30} + 2 q^{31} - 4 q^{32} - 8 q^{33} - 24 q^{35} + 2 q^{38} - 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} + 6 q^{43} + 10 q^{44} + 6 q^{45} + 2 q^{46} - 14 q^{48} - 24 q^{49} - 20 q^{50} - 22 q^{52} - 24 q^{53} - 20 q^{54} + 10 q^{55} - 40 q^{57} + 22 q^{59} + 46 q^{60} + 20 q^{61} + 30 q^{62} + 16 q^{63} - 48 q^{64} - 36 q^{66} - 12 q^{67} + 4 q^{68} - 4 q^{69} + 20 q^{70} - 10 q^{71} - 4 q^{73} - 30 q^{75} + 6 q^{76} + 24 q^{77} + 30 q^{78} + 2 q^{80} - 20 q^{81} - 20 q^{82} + 16 q^{84} - 20 q^{85} - 46 q^{86} + 16 q^{87} + 10 q^{88} - 28 q^{89} + 14 q^{90} + 20 q^{91} + 50 q^{92} - 2 q^{95} + 30 q^{96} + 12 q^{97} + 92 q^{98} - 2 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 6 * q^3 + 8 * q^4 + 2 * q^5 - 6 * q^6 - 6 * q^10 + 6 * q^11 + 2 * q^12 - 2 * q^13 - 2 * q^15 - 8 * q^16 - 16 * q^17 + 14 * q^19 - 22 * q^20 - 12 * q^21 + 10 * q^22 + 14 * q^23 + 2 * q^24 + 12 * q^25 + 6 * q^26 + 12 * q^27 + 14 * q^30 + 2 * q^31 - 4 * q^32 - 8 * q^33 - 24 * q^35 + 2 * q^38 - 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 + 6 * q^43 + 10 * q^44 + 6 * q^45 + 2 * q^46 - 14 * q^48 - 24 * q^49 - 20 * q^50 - 22 * q^52 - 24 * q^53 - 20 * q^54 + 10 * q^55 - 40 * q^57 + 22 * q^59 + 46 * q^60 + 20 * q^61 + 30 * q^62 + 16 * q^63 - 48 * q^64 - 36 * q^66 - 12 * q^67 + 4 * q^68 - 4 * q^69 + 20 * q^70 - 10 * q^71 - 4 * q^73 - 30 * q^75 + 6 * q^76 + 24 * q^77 + 30 * q^78 + 2 * q^80 - 20 * q^81 - 20 * q^82 + 16 * q^84 - 20 * q^85 - 46 * q^86 + 16 * q^87 + 10 * q^88 - 28 * q^89 + 14 * q^90 + 20 * q^91 + 50 * q^92 - 2 * q^95 + 30 * q^96 + 12 * q^97 + 92 * q^98 - 2 * q^99

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