LMFDB - Embedded newform 65.2.f.b.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,2,Mod(18,65)]

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, 3]))

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

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

chi := DirichletCharacter("65.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	65.f (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			18.1
Root			$0.561103 - 0.561103i$ of defining polynomial
Character	$\chi$	$=$	65.18
Dual form			65.2.f.b.47.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +O(q^{10})$	\(q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +(2.94844 - 3.45220i) q^{10} +(2.70032 + 2.70032i) q^{11} +(2.82253 + 2.82253i) q^{12} +(3.45220 - 1.04033i) q^{13} +3.28596i q^{14} +(-0.329998 - 4.19286i) q^{15} -3.74065 q^{16} +(2.24812 + 2.24812i) q^{17} +1.09188 q^{18} +(-2.33000 - 2.33000i) q^{19} +(-3.60844 - 3.08188i) 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} +3.43468 q^{28} +4.27844i q^{29} +(-8.51285 + 0.670002i) q^{30} +(3.36032 - 3.36032i) q^{31} +8.09097i q^{32} -7.18285i q^{33} +(4.56441 - 4.56441i) q^{34} +(-2.75188 - 2.35031i) q^{35} -1.14130i q^{36} -7.78220 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} +(-0.780980 + 0.914416i) q^{45} +(9.79129 + 9.79129i) q^{46} +5.36662 q^{47} +(4.97506 + 4.97506i) q^{48} -4.38064 q^{49} +(10.0266 - 1.58812i) q^{50} -5.97999i q^{51} +(-7.32629 + 2.20779i) q^{52} +(-4.61845 - 4.61845i) q^{53} +(6.64877 + 6.64877i) q^{54} +(0.670002 + 8.51285i) q^{55} -0.401567i q^{56} +6.19779i q^{57} +8.68661 q^{58} +(4.47130 - 4.47130i) q^{59} +(0.700324 + 8.89811i) q^{60} -12.1479 q^{61} +(-6.82253 - 6.82253i) q^{62} -0.870382i q^{63} +8.94596 q^{64} +(7.38064 + 3.24441i) q^{65} -14.5835 q^{66} -5.84285i q^{67} +(-4.77097 - 4.77097i) q^{68} +12.8279 q^{69} +(-4.77189 + 5.58720i) q^{70} +(-1.37155 + 1.37155i) q^{71} -0.133436 q^{72} +4.02662i q^{73} +15.8004i q^{74} +(5.52778 - 7.60844i) q^{75} +(4.94474 + 4.94474i) q^{76} +(-4.37033 - 4.37033i) q^{77} +(-6.51285 + 12.1313i) q^{78} +8.63754i q^{79} +(-6.36032 - 5.43219i) q^{80} +10.3242 q^{81} +(-5.83532 - 5.83532i) q^{82} -7.48791 q^{83} +(-4.56811 - 4.56811i) q^{84} +(0.557801 + 7.08726i) 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} -8.93844 q^{93} -10.8960i q^{94} +(-0.578117 - 7.34539i) q^{95} +(10.7610 - 10.7610i) q^{96} -8.63754i q^{97} +8.89410i q^{98} +(-1.45220 + 1.45220i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	$ 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) $ 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	2.03032i		−	1.43565i	−0.696221	−	0.717827i	$-0.745137\pi$
$2$		−	2.03032i		−	1.43565i	0.696221	−	0.717827i	$-0.254863\pi$
$3$	−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
$5$	1.70032	+	1.45220i	0.760408	+	0.649446i
$5$	1.70032	+	1.45220i	0.760408	+	0.649446i
$6$	−2.70032	+	2.70032i	−1.10240	+	1.10240i
$7$	−1.61845			−0.611715			−0.305857	−	0.952077i	$-0.598943\pi$
$7$	−1.61845			−0.611715			−0.305857	+	0.952077i	$0.598943\pi$
$8$			0.248119i			0.0877234i
$9$			0.537789i			0.179263i
$10$	2.94844	−	3.45220i	0.932380	−	1.09168i
$11$	2.70032	+	2.70032i	0.814178	+	0.814178i	0.985257	−	0.171079i	$-0.0547253\pi$
$11$	2.70032	+	2.70032i	0.814178	+	0.814178i	−0.171079	+	0.985257i	$0.554725\pi$
$12$	2.82253	+	2.82253i	0.814794	+	0.814794i
$13$	3.45220	−	1.04033i	0.957469	−	0.288535i
$13$	3.45220	−	1.04033i	0.957469	−	0.288535i
$14$			3.28596i			0.878211i
$15$	−0.329998	−	4.19286i	−0.0852051	−	1.08259i
$16$	−3.74065			−0.935163
$17$	2.24812	+	2.24812i	0.545249	+	0.545249i	0.925063	−	0.379814i	$-0.124012\pi$
$17$	2.24812	+	2.24812i	0.545249	+	0.545249i	−0.379814	+	0.925063i	$0.624012\pi$
$18$	1.09188			0.257360
$19$	−2.33000	−	2.33000i	−0.534538	−	0.534538i	0.387381	−	0.921920i	$-0.373380\pi$
$19$	−2.33000	−	2.33000i	−0.534538	−	0.534538i	−0.921920	+	0.387381i	$0.873380\pi$
$20$	−3.60844	−	3.08188i	−0.806871	−	0.689129i
$21$	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	$0.501777\pi$
$23$	−4.82253	+	4.82253i	−1.00557	+	1.00557i	−0.999984	+	0.00558275i	$0.998223\pi$
$24$	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
$28$	3.43468			0.649093
$29$			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	−0.337717	−	0.941248i	$-0.609655\pi$
$31$	3.36032	−	3.36032i	0.603531	−	0.603531i	0.941248	+	0.337717i	$0.109655\pi$
$32$			8.09097i			1.43029i
$33$		−	7.18285i		−	1.25037i
$34$	4.56441	−	4.56441i	0.782789	−	0.782789i
$35$	−2.75188	−	2.35031i	−0.465153	−	0.397276i
$36$		−	1.14130i		−	0.190217i
$37$	−7.78220			−1.27939			−0.639693	−	0.768630i	$-0.720939\pi$
$37$	−7.78220			−1.27939			−0.639693	+	0.768630i	$0.720939\pi$
$38$	−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	−0.446117	−	0.894974i	$-0.647194\pi$
$41$	2.87409	−	2.87409i	0.448857	−	0.448857i	0.894974	+	0.446117i	$0.147194\pi$
$42$	4.37033	−	4.37033i	0.674356	−	0.674356i
$43$	3.97876	−	3.97876i	0.606756	−	0.606756i	−0.335341	−	0.942097i	$-0.608851\pi$
$43$	3.97876	−	3.97876i	0.606756	−	0.606756i	0.942097	+	0.335341i	$0.108851\pi$
$44$	−5.73065	−	5.73065i	−0.863927	−	0.863927i
$45$	−0.780980	+	0.914416i	−0.116422	+	0.136313i
$46$	9.79129	+	9.79129i	1.44365	+	1.44365i
$47$	5.36662			0.782802			0.391401	−	0.920220i	$-0.371991\pi$
$47$	5.36662			0.782802			0.391401	+	0.920220i	$0.371991\pi$
$48$	4.97506	+	4.97506i	0.718088	+	0.718088i
$49$	−4.38064			−0.625805
$50$	10.0266	−	1.58812i	1.41798	−	0.224595i
$51$		−	5.97999i		−	0.837366i
$52$	−7.32629	+	2.20779i	−1.01597	+	0.306166i
$53$	−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
$57$			6.19779i			0.820917i
$58$	8.68661			1.14061
$59$	4.47130	−	4.47130i	0.582113	−	0.582113i	−0.353370	−	0.935484i	$-0.614964\pi$
$59$	4.47130	−	4.47130i	0.582113	−	0.582113i	0.935484	+	0.353370i	$0.114964\pi$
$60$	0.700324	+	8.89811i	0.0904114	+	1.14874i
$61$	−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
$63$		−	0.870382i		−	0.109658i
$64$	8.94596			1.11825
$65$	7.38064	+	3.24441i	0.915455	+	0.402420i
$66$	−14.5835			−1.79510
$67$		−	5.84285i		−	0.713817i	−0.934139	−	0.356909i	$-0.883831\pi$
$67$		−	5.84285i		−	0.713817i	0.934139	−	0.356909i	$-0.116169\pi$
$68$	−4.77097	−	4.77097i	−0.578566	−	0.578566i
$69$	12.8279			1.54430
$70$	−4.77189	+	5.58720i	−0.570350	+	0.667799i
$71$	−1.37155	+	1.37155i	−0.162773	+	0.162773i	−0.783794	−	0.621021i	$-0.786718\pi$
$71$	−1.37155	+	1.37155i	−0.162773	+	0.162773i	0.621021	+	0.783794i	$0.286718\pi$
$72$	−0.133436			−0.0157256
$73$			4.02662i			0.471280i	0.971840	+	0.235640i	$0.0757186\pi$
$73$			4.02662i			0.471280i	−0.971840	+	0.235640i	$0.924281\pi$
$74$			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
$78$	−6.51285	+	12.1313i	−0.737435	+	1.37360i
$79$			8.63754i			0.971799i	0.874015	+	0.485899i	$0.161508\pi$
$79$			8.63754i			0.971799i	−0.874015	+	0.485899i	$0.838492\pi$
$80$	−6.36032	−	5.43219i	−0.711105	−	0.607338i
$81$	10.3242			1.14713
$82$	−5.83532	−	5.83532i	−0.644404	−	0.644404i
$83$	−7.48791			−0.821905			−0.410952	−	0.911657i	$-0.634804\pi$
$83$	−7.48791			−0.821905			−0.410952	+	0.911657i	$0.634804\pi$
$84$	−4.56811	−	4.56811i	−0.498422	−	0.498422i
$85$	0.557801	+	7.08726i	0.0605021	+	0.768721i
$86$	−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	$-0.527074\pi$
$89$	8.59843	−	8.59843i	0.911432	−	0.911432i	0.996385	+	0.0849529i	$0.0270740\pi$
$90$	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
$93$	−8.93844			−0.926873
$94$		−	10.8960i		−	1.12383i
$95$	−0.578117	−	7.34539i	−0.0593136	−	0.753621i
$96$	10.7610	−	10.7610i	1.09829	−	1.09829i
$97$		−	8.63754i		−	0.877009i	−0.898729	−	0.438505i	$-0.855508\pi$
$97$		−	8.63754i		−	0.877009i	0.898729	−	0.438505i	$-0.144492\pi$
$98$			8.89410i			0.898440i
$99$	−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	$-0.986951\pi$
$101$		−	0.823754i		−	0.0819665i	0.999160	−	0.0409833i	$-0.0130490\pi$
$102$	−12.1413			−1.20217
$103$	−0.867787	+	0.867787i	−0.0855056	+	0.0855056i	−0.748566	−	0.663060i	$-0.769257\pi$
$103$	−0.867787	+	0.867787i	−0.0855056	+	0.0855056i	0.663060	+	0.748566i	$0.269257\pi$
$104$	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	$-0.361616\pi$
$109$	−5.07187	−	5.07187i	−0.485797	−	0.485797i	−0.906977	+	0.421180i	$0.861616\pi$
$110$	17.2838	−	1.36032i	1.64795	−	0.129701i
$111$	10.3503	+	10.3503i	0.982408	+	0.982408i
$112$	6.05404			0.572053
$113$	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
$115$	−15.2032	+	1.19656i	−1.41770	+	0.111580i
$116$		−	9.07974i		−	0.843032i
$117$	0.559477	+	1.85656i	0.0517237	+	0.171639i
$118$	−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
$122$			24.6642i			2.23299i
$123$	−7.64506			−0.689332
$124$	−7.13129	+	7.13129i	−0.640409	+	0.640409i
$125$	−5.84162	+	9.53286i	−0.522491	+	0.852645i
$126$	−1.76716			−0.157431
$127$	11.4779	+	11.4779i	1.01850	+	1.01850i	0.999826	+	0.0186734i	$0.00594429\pi$
$127$	11.4779	+	11.4779i	1.01850	+	1.01850i	0.0186734	+	0.999826i	$0.494056\pi$
$128$		−	1.98125i		−	0.175119i
$129$	−10.5835			−0.931825
$130$	6.58720	−	14.9851i	0.577736	−	1.31428i
$131$	1.80882			0.158037			0.0790186	−	0.996873i	$-0.474821\pi$
$131$	1.80882			0.158037			0.0790186	+	0.996873i	$0.474821\pi$
$132$			15.2435i			1.32678i
$133$	3.77097	+	3.77097i	0.326985	+	0.326985i
$134$	−11.8629			−1.02479
$135$	−10.3237	+	0.812525i	−0.888522	+	0.0699310i
$136$	−0.557801	+	0.557801i	−0.0478311	+	0.0478311i
$137$	−8.96505			−0.765936			−0.382968	−	0.923762i	$-0.625098\pi$
$137$	−8.96505			−0.765936			−0.382968	+	0.923762i	$0.625098\pi$
$138$		−	26.0448i		−	2.21708i
$139$		−	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
$143$	12.1313	+	6.51285i	1.01447	+	0.544632i
$144$		−	2.01168i		−	0.167640i
$145$	−6.21317	+	7.27474i	−0.515976	+	0.604134i
$146$	8.17533			0.676595
$147$	5.82624	+	5.82624i	0.480540	+	0.480540i
$148$	16.5154			1.35756
$149$	7.78591	+	7.78591i	0.637846	+	0.637846i	0.950024	−	0.312177i	$-0.101058\pi$
$149$	7.78591	+	7.78591i	0.637846	+	0.637846i	−0.312177	+	0.950024i	$0.601058\pi$
$150$	−15.4476	−	11.2232i	−1.26129	−	0.916369i
$151$	1.86038	+	1.86038i	0.151395	+	0.151395i	0.778741	−	0.627346i	$-0.215859\pi$
$151$	1.86038	+	1.86038i	0.151395	+	0.151395i	−0.627346	+	0.778741i	$0.715859\pi$
$152$	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	$0.0614521\pi$
$158$	17.5370			1.39517
$159$			12.2850i			0.974267i
$160$	−11.7497	+	13.7573i	−0.928898	+	1.08761i
$161$	7.80500	−	7.80500i	0.615120	−	0.615120i
$162$		−	20.9613i		−	1.64688i
$163$		−	7.53779i		−	0.590405i	−0.955435	−	0.295203i	$-0.904613\pi$
$163$		−	7.53779i		−	0.590405i	0.955435	−	0.295203i	$-0.0953871\pi$
$164$	−6.09941	+	6.09941i	−0.476284	+	0.476284i
$165$	10.4310	−	12.2132i	0.812050	−	0.950794i
$166$			15.2029i			1.17997i
$167$	18.9086			1.46319			0.731594	−	0.681740i	$-0.238776\pi$
$167$	18.9086			1.46319			0.731594	+	0.681740i	$0.238776\pi$
$168$	−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	−0.592223	−	0.805774i	$-0.701750\pi$
$173$	2.80882	−	2.80882i	0.213551	−	0.213551i	0.805774	+	0.592223i	$0.201750\pi$
$174$	−11.5532	−	11.5532i	−0.875844	−	0.875844i
$175$	−1.26595	−	7.99259i	−0.0956970	−	0.604183i
$176$	−10.1010	−	10.1010i	−0.761389	−	0.761389i
$177$	−11.8936			−0.893980
$178$	−17.4576	−	17.4576i	−1.30850	−	1.30850i
$179$	−21.6632			−1.61919			−0.809593	−	0.586991i	$-0.800312\pi$
$179$	−21.6632			−1.61919			−0.809593	+	0.586991i	$0.800312\pi$
$180$	1.65740	−	1.94058i	0.123535	−	0.144642i
$181$		−	6.82791i		−	0.507515i	−0.967268	−	0.253757i	$-0.918334\pi$
$181$		−	6.82791i		−	0.507515i	0.967268	−	0.253757i	$-0.0816665\pi$
$182$	3.41848	+	11.3438i	0.253395	+	0.840860i
$183$	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
$187$			12.1413i			0.887860i
$188$	−11.3891			−0.830634
$189$	5.29998	−	5.29998i	0.385517	−	0.385517i
$190$	−14.9135	+	1.17376i	−1.08194	+	0.0851538i
$191$	−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
$193$			7.18885i			0.517465i	0.965949	+	0.258732i	$0.0833047\pi$
$193$			7.18885i			0.517465i	−0.965949	+	0.258732i	$0.916695\pi$
$194$	−17.5370			−1.25908
$195$	−5.50117	−	14.1313i	−0.393947	−	1.01196i
$196$	9.29661			0.664044
$197$		−	4.41558i		−	0.314597i	−0.987551	−	0.157299i	$-0.949721\pi$
$197$		−	4.41558i		−	0.314597i	0.987551	−	0.157299i	$-0.0502785\pi$
$198$	2.94844	+	2.94844i	0.209537	+	0.209537i
$199$	0.312468			0.0221503			0.0110751	−	0.999939i	$-0.496475\pi$
$199$	0.312468			0.0221503			0.0110751	+	0.999939i	$0.496475\pi$
$200$	−1.22532	+	0.194079i	−0.0866433	+	0.0137235i
$201$	−7.77097	+	7.77097i	−0.548122	+	0.548122i
$202$	−1.67248			−0.117676
$203$		−	6.92442i		−	0.485999i
$204$			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
$208$	−12.9135	+	3.89150i	−0.895390	+	0.269827i
$209$		−	12.5835i		−	0.870419i
$210$	13.7776	−	1.08436i	0.950743	−	0.0748281i
$211$	−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
$213$	3.64831			0.249978
$214$	6.66908	+	6.66908i	0.455889	+	0.455889i
$215$	12.5432	−	0.987208i	0.855437	−	0.0673270i
$216$	−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
$223$	6.81715			0.456510			0.228255	−	0.973601i	$-0.426698\pi$
$223$	6.81715			0.456510			0.228255	+	0.973601i	$0.426698\pi$
$224$		−	13.0948i		−	0.874932i
$225$	−2.65584	+	0.420660i	−0.177056	+	0.0280440i
$226$	18.7748	−	18.7748i	1.24888	−	1.24888i
$227$			4.56288i			0.302849i	0.988469	+	0.151424i	$0.0483860\pi$
$227$			4.56288i			0.302849i	−0.988469	+	0.151424i	$0.951614\pi$
$228$		−	13.1530i		−	0.871077i
$229$	−13.5635	+	13.5635i	−0.896300	+	0.896300i	−0.995107	−	0.0988063i	$-0.968498\pi$
$229$	−13.5635	+	13.5635i	−0.896300	+	0.896300i	0.0988063	+	0.995107i	$0.468498\pi$
$230$	2.42941	+	30.8673i	0.160190	+	2.03533i
$231$			11.6250i			0.764872i
$232$	−1.06156			−0.0696950
$233$	−0.665074	+	0.665074i	−0.0435704	+	0.0435704i	−0.728556	−	0.684986i	$-0.759808\pi$
$233$	−0.665074	+	0.665074i	−0.0435704	+	0.0435704i	0.684986	+	0.728556i	$0.259808\pi$
$234$	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	$-0.107402\pi$
$239$	9.47004	+	9.47004i	0.612566	+	0.612566i	−0.331048	+	0.943614i	$0.607402\pi$
$240$	1.23441	+	15.6840i	0.0796807	+	1.01240i
$241$	−11.9072	−	11.9072i	−0.767010	−	0.767010i	0.210569	−	0.977579i	$-0.432468\pi$
$241$	−11.9072	−	11.9072i	−0.767010	−	0.767010i	−0.977579	+	0.210569i	$0.932468\pi$
$242$	7.27565			0.467697
$243$	−3.90689	−	3.90689i	−0.250627	−	0.250627i
$244$	25.7804			1.65042
$245$	−7.44850	−	6.36158i	−0.475867	−	0.406426i
$246$			15.5219i			0.989642i
$247$	−10.4676	−	5.61967i	−0.666037	−	0.357571i
$248$	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	$-0.848117\pi$
$251$		−	14.5519i		−	0.918509i	0.888305	−	0.459254i	$-0.151883\pi$
$252$			1.84713i			0.116358i
$253$	−26.0448			−1.63742
$254$	23.3038	−	23.3038i	1.46221	−	1.46221i
$255$	8.68417	−	10.1679i	0.543824	−	0.636740i
$256$	13.8694			0.866834
$257$	−13.0266	−	13.0266i	−0.812578	−	0.812578i	0.172442	−	0.985020i	$-0.444834\pi$
$257$	−13.0266	−	13.0266i	−0.812578	−	0.812578i	−0.985020	+	0.172442i	$0.944834\pi$
$258$			21.4879i			1.33778i
$259$	12.5951			0.782619
$260$	−15.6632	−	6.88532i	−0.971393	−	0.427009i
$261$	−2.30090			−0.142422
$262$		−	3.67248i		−	0.226887i
$263$	−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
$265$	−1.14592	−	14.5598i	−0.0703936	−	0.894400i
$266$	7.65629	−	7.65629i	0.469437	−	0.469437i
$267$	−22.8718			−1.39973
$268$			12.3997i			0.757434i
$269$			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	0.975136	−	0.221607i	$-0.0711302\pi$
$271$	12.4047	+	12.4047i	0.753529	+	0.753529i	−0.221607	+	0.975136i	$0.571130\pi$
$272$	−8.40943	−	8.40943i	−0.509897	−	0.509897i
$273$	9.67031	+	5.19163i	0.585274	+	0.314212i
$274$			18.2019i			1.09962i
$275$	−11.2232	+	15.4476i	−0.676783	+	0.931524i
$276$	−27.2235			−1.63866
$277$	11.7206	+	11.7206i	0.704225	+	0.704225i	0.965315	−	0.261090i	$-0.0840818\pi$
$277$	11.7206	+	11.7206i	0.704225	+	0.704225i	−0.261090	+	0.965315i	$0.584082\pi$
$278$	−10.9195			−0.654905
$279$	1.80714	+	1.80714i	0.108191	+	0.108191i
$280$	0.583158	−	0.682794i	0.0348503	−	0.0408048i
$281$	−12.5191	−	12.5191i	−0.746830	−	0.746830i	0.227053	−	0.973882i	$-0.427091\pi$
$281$	−12.5191	−	12.5191i	−0.746830	−	0.746830i	−0.973882	+	0.227053i	$0.927091\pi$
$282$	−14.4916	+	14.4916i	−0.862963	+	0.862963i
$283$	12.8558	−	12.8558i	0.764195	−	0.764195i	−0.212883	−	0.977078i	$-0.568285\pi$
$283$	12.8558	−	12.8558i	0.764195	−	0.764195i	0.977078	+	0.212883i	$0.0682852\pi$
$284$	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
$288$	−4.35123			−0.256399
$289$		−	6.89192i		−	0.405407i
$290$	14.7701	+	12.6147i	0.867327	+	0.740763i
$291$	−11.4879	+	11.4879i	−0.673433	+	0.673433i
$292$		−	8.54531i		−	0.500077i
$293$			18.2991i			1.06904i	0.845155	+	0.534521i	$0.179508\pi$
$293$			18.2991i			1.06904i	−0.845155	+	0.534521i	$0.820492\pi$
$294$	11.8291	−	11.8291i	0.689889	−	0.689889i
$295$	14.0959	−	1.10941i	0.820695	−	0.0645926i
$296$		−	1.93091i		−	0.112232i
$297$	−17.6857			−1.02623
$298$	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
$305$	−20.6554	−	17.6412i	−1.18272	−	1.01013i
$306$	2.45469	+	2.45469i	0.140325	+	0.140325i
$307$	18.9366			1.08077			0.540384	−	0.841418i	$-0.318279\pi$
$307$	18.9366			1.08077			0.540384	+	0.841418i	$0.318279\pi$
$308$	9.27474	+	9.27474i	0.528477	+	0.528477i
$309$	2.30831			0.131315
$310$	−1.69280	−	21.5082i	−0.0961446	−	1.22159i
$311$			17.3532i			0.984010i	0.870592	+	0.492005i	$0.163736\pi$
$311$			17.3532i			0.984010i	−0.870592	+	0.492005i	$0.836264\pi$
$312$	0.795914	−	1.48253i	0.0450598	−	0.0839315i
$313$	−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
$317$		−	33.4987i		−	1.88147i	−0.339139	−	0.940736i	$-0.610136\pi$
$317$		−	33.4987i		−	1.88147i	0.339139	−	0.940736i	$-0.389864\pi$
$318$	24.9426			1.39871
$319$	−11.5532	+	11.5532i	−0.646854	+	0.646854i
$320$	15.2110	+	12.9914i	0.850322	+	0.726239i
$321$	8.73740			0.487674
$322$	−15.8467	−	15.8467i	−0.883100	−	0.883100i
$323$		−	10.4762i		−	0.582913i
$324$	−21.9100			−1.21722
$325$	7.83792	+	16.2347i	0.434769	+	0.900542i
$326$	−15.3041			−0.847618
$327$			13.4912i			0.746063i
$328$	0.713116	+	0.713116i	0.0393753	+	0.0393753i
$329$	−8.68558			−0.478852
$330$	−24.7967	−	21.1782i	−1.36501	−	1.16582i
$331$	18.7185	−	18.7185i	1.02886	−	1.02886i	0.0292907	−	0.999571i	$-0.490675\pi$
$331$	18.7185	−	18.7185i	1.02886	−	1.02886i	0.999571	−	0.0292907i	$-0.00932486\pi$
$332$	15.8909			0.872126
$333$		−	4.18518i		−	0.229347i
$334$		−	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	0.958416	−	0.285375i	$-0.0921181\pi$
$337$	12.3554	+	12.3554i	0.673041	+	0.673041i	−0.285375	+	0.958416i	$0.592118\pi$
$338$	−14.5835	−	21.9994i	−0.793238	−	1.19661i
$339$		−	24.5975i		−	1.33595i
$340$	−1.18377	−	15.0406i	−0.0641989	−	0.815693i
$341$	18.1479			0.982764
$342$	−2.54409	−	2.54409i	−0.137569	−	0.137569i
$343$	18.4189			0.994529
$344$	0.987208	+	0.987208i	0.0532267	+	0.0532267i
$345$	21.8116	+	18.6288i	1.17430	+	1.00294i
$346$	−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	$-0.674614\pi$
$349$	6.19870	−	6.19870i	0.331809	−	0.331809i	0.853273	+	0.521464i	$0.174614\pi$
$350$	−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
$353$	3.89028			0.207059			0.103529	−	0.994626i	$-0.466986\pi$
$353$	3.89028			0.207059			0.103529	+	0.994626i	$0.466986\pi$
$354$			24.1479i			1.28345i
$355$	−4.32385	+	0.340308i	−0.229486	+	0.0180616i
$356$	−18.2477	+	18.2477i	−0.967124	+	0.967124i
$357$			9.67828i			0.512229i
$358$			43.9833i			2.32459i
$359$	−16.1238	+	16.1238i	−0.850980	+	0.850980i	−0.990254	−	0.139274i	$-0.955523\pi$
$359$	−16.1238	+	16.1238i	−0.850980	+	0.850980i	0.139274	+	0.990254i	$0.455523\pi$
$360$	−0.226884	−	0.193776i	−0.0119578	−	0.0102129i
$361$		−	8.14222i		−	0.428538i
$362$	−13.8629			−0.728616
$363$	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
$370$	−22.9454	+	26.8658i	−1.19287	+	1.39668i
$371$	7.47470	+	7.47470i	0.388067	+	0.388067i
$372$	18.9692			0.983508
$373$	−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
$375$	20.4480	−	4.90934i	1.05593	−	0.253517i
$376$			1.33156i			0.0686700i
$377$	4.45098	+	14.7701i	0.229237	+	0.760696i
$378$	−10.7607	−	10.7607i	−0.553469	−	0.553469i
$379$	−5.31888	−	5.31888i	−0.273213	−	0.273213i	0.557179	−	0.830392i	$-0.311884\pi$
$379$	−5.31888	−	5.31888i	−0.273213	−	0.273213i	−0.830392	+	0.557179i	$0.811884\pi$
$380$	1.22688	+	15.5884i	0.0629378	+	0.799669i
$381$		−	30.5312i		−	1.56416i
$382$			38.4645i			1.96802i
$383$	14.8685			0.759747			0.379874	−	0.925038i	$-0.375968\pi$
$383$	14.8685			0.759747			0.379874	+	0.925038i	$0.375968\pi$
$384$	−2.63506	+	2.63506i	−0.134470	+	0.134470i
$385$	−1.08436	−	13.7776i	−0.0552642	−	0.702170i
$386$	14.5957			0.742900
$387$	2.13974	+	2.13974i	0.108769	+	0.108769i
$388$			18.3306i			0.930597i
$389$	28.9078			1.46568			0.732841	−	0.680400i	$-0.238194\pi$
$389$	28.9078			1.46568			0.732841	+	0.680400i	$0.238194\pi$
$390$	−28.6911	+	11.1691i	−1.45283	+	0.565571i
$391$	−21.6832			−1.09657
$392$		−	1.08692i		−	0.0548977i
$393$	−2.40573	−	2.40573i	−0.121353	−	0.121353i
$394$	−8.96505			−0.451653
$395$	−12.5435	+	14.6866i	−0.631131	+	0.738964i
$396$	3.08188	−	3.08188i	0.154870	−	0.154870i
$397$	−14.6060			−0.733052			−0.366526	−	0.930408i	$-0.619453\pi$
$397$	−14.6060			−0.733052			−0.366526	+	0.930408i	$0.619453\pi$
$398$		−	0.634411i		−	0.0318002i
$399$		−	10.0308i		−	0.502167i
$400$	−2.92595	−	18.4730i	−0.146297	−	0.923649i
$401$	8.22532	+	8.22532i	0.410753	+	0.410753i	0.882001	−	0.471248i	$-0.156196\pi$
$401$	8.22532	+	8.22532i	0.410753	+	0.410753i	−0.471248	+	0.882001i	$0.656196\pi$
$402$	15.7776	+	15.7776i	0.786914	+	0.786914i
$403$	8.10468	−	15.0963i	0.403723	−	0.752003i
$404$			1.74818i			0.0869750i
$405$	17.5544	+	14.9928i	0.872285	+	0.744997i
$406$	−14.0588			−0.697727
$407$	−21.0145	−	21.0145i	−1.04165	−	1.04165i
$408$	1.48375			0.0734565
$409$	26.1042	+	26.1042i	1.29077	+	1.29077i	0.934312	+	0.356456i	$0.116015\pi$
$409$	26.1042	+	26.1042i	1.29077	+	1.29077i	0.356456	+	0.934312i	$0.383985\pi$
$410$	−1.44786	−	18.3960i	−0.0715045	−	0.908515i
$411$	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
$418$	−25.5486			−1.24962
$419$			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	−0.228372	+	0.973574i	$0.573340\pi$
$421$	−24.6619	+	24.6619i	−1.20195	+	1.20195i	−0.973574	+	0.228372i	$0.926660\pi$
$422$			21.7614i			1.05933i
$423$			2.88611i			0.140327i
$424$	1.14592	−	1.14592i	0.0556510	−	0.0556510i
$425$	−9.34371	+	12.8607i	−0.453236	+	0.623835i
$426$		−	7.40725i		−	0.358883i
$427$	19.6607			0.951449
$428$	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	−0.186384	−	0.982477i	$-0.559677\pi$
$431$	16.5273	−	16.5273i	0.796093	−	0.796093i	0.982477	+	0.186384i	$0.0596769\pi$
$432$	12.2496	−	12.2496i	0.589361	−	0.589361i
$433$	−25.0489	+	25.0489i	−1.20378	+	1.20378i	−0.230766	+	0.973009i	$0.574123\pi$
$433$	−25.0489	+	25.0489i	−1.20378	+	1.20378i	−0.973009	+	0.230766i	$0.925877\pi$
$434$	11.0419	+	11.0419i	0.530028	+	0.530028i
$435$	17.9389	−	1.41188i	0.860104	−	0.0676943i
$436$	10.7636	+	10.7636i	0.515481	+	0.515481i
$437$	22.4730			1.07503
$438$	−10.8732	−	10.8732i	−0.519540	−	0.519540i
$439$	−18.1493			−0.866220			−0.433110	−	0.901341i	$-0.642584\pi$
$439$	−18.1493			−0.866220			−0.433110	+	0.901341i	$0.642584\pi$
$440$	−2.11220	+	0.166240i	−0.100695	+	0.00792520i
$441$		−	2.35586i		−	0.112184i
$442$	11.0088	−	20.5057i	0.523634	−	0.975359i
$443$	−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
$447$		−	20.7105i		−	0.979572i
$448$	−14.4785			−0.684047
$449$	−3.27565	+	3.27565i	−0.154588	+	0.154588i	−0.780163	−	0.625576i	$-0.784864\pi$
$449$	−3.27565	+	3.27565i	−0.154588	+	0.154588i	0.625576	+	0.780163i	$0.284864\pi$
$450$	0.854075	+	5.39220i	0.0402615	+	0.254191i
$451$	15.5219			0.730899
$452$	−19.6245	−	19.6245i	−0.923057	−	0.923057i
$453$		−	4.94859i		−	0.232505i
$454$	9.26411			0.434786
$455$	−11.9452	−	5.25091i	−0.559997	−	0.246166i
$456$	−1.53779			−0.0720136
$457$		−	13.8670i		−	0.648672i	−0.945942	−	0.324336i	$-0.894859\pi$
$457$		−	13.8670i		−	0.648672i	0.945942	−	0.324336i	$-0.105141\pi$
$458$	27.5382	+	27.5382i	1.28678	+	1.28678i
$459$	−14.7240			−0.687257
$460$	32.2643	−	2.53935i	1.50433	−	0.118398i
$461$	−6.02325	+	6.02325i	−0.280531	+	0.280531i	−0.833321	−	0.552790i	$-0.813563\pi$
$461$	−6.02325	+	6.02325i	−0.280531	+	0.280531i	0.552790	+	0.833321i	$0.313563\pi$
$462$	23.6026			1.09809
$463$			16.6916i			0.775723i	0.921718	+	0.387862i	$0.126786\pi$
$463$			16.6916i			0.775723i	−0.921718	+	0.387862i	$0.873214\pi$
$464$		−	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	0.826377	−	0.563117i	$-0.190398\pi$
$467$	5.68909	+	5.68909i	0.263260	+	0.263260i	−0.563117	+	0.826377i	$0.690398\pi$
$468$	−1.18733	−	3.94000i	−0.0548842	−	0.182127i
$469$			9.45633i			0.436653i
$470$	15.8232	−	18.5267i	0.729869	−	0.854572i
$471$	−26.3158			−1.21257
$472$	1.10941	+	1.10941i	0.0510649	+	0.0510649i
$473$	21.4879			0.988015
$474$	−23.3242	−	23.3242i	−1.07131	−	1.07131i
$475$	9.68402	−	13.3291i	0.444333	−	0.611580i
$476$	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	$-0.832520\pi$
$479$	−7.93443	+	7.93443i	−0.362533	+	0.362533i	0.502212	+	0.864745i	$0.332520\pi$
$480$	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
$483$	−20.7613			−0.944671
$484$		−	7.60492i		−	0.345678i
$485$	12.5435	−	14.6866i	0.569570	−	0.666885i
$486$	−7.93225	+	7.93225i	−0.359814	+	0.359814i
$487$		−	18.1005i		−	0.820210i	−0.912038	−	0.410105i	$-0.865492\pi$
$487$		−	18.1005i		−	0.820210i	0.912038	−	0.410105i	$-0.134508\pi$
$488$		−	3.01413i		−	0.136443i
$489$	−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	$0.202984\pi$
$491$			26.3839i			1.19069i	−0.803471	+	0.595344i	$0.797016\pi$
$492$	16.2244			0.731453
$493$	−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	$-0.359721\pi$
$499$	−10.6751	−	10.6751i	−0.477882	−	0.477882i	−0.904454	+	0.426572i	$0.859721\pi$
$500$	12.3971	−	20.2307i	0.554417	−	0.904744i
$501$	−25.1484	−	25.1484i	−1.12355	−	1.12355i
$502$	−29.5451			−1.31866
$503$	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
$505$	1.19626	−	1.40065i	0.0532328	−	0.0623280i
$506$			52.8793i			2.35077i
$507$	−23.9643	−	4.85793i	−1.06429	−	0.215748i
$508$	−24.3585	−	24.3585i	−1.08073	−	1.08073i
$509$	21.2626	+	21.2626i	0.942448	+	0.942448i	0.998432	−	0.0559841i	$-0.0178296\pi$
$509$	21.2626	+	21.2626i	0.942448	+	0.942448i	−0.0559841	+	0.998432i	$0.517830\pi$
$510$	−20.6441	−	17.6317i	−0.914138	−	0.780743i
$511$		−	6.51686i		−	0.288289i
$512$		−	32.1217i		−	1.41959i
$513$	15.2603			0.673757
$514$	−26.4482	+	26.4482i	−1.16658	+	1.16658i
$515$	−2.73572	+	0.215315i	−0.120550	+	0.00948789i
$516$	22.4604			0.988763
$517$	14.4916	+	14.4916i	0.637340	+	0.637340i
$518$		−	25.5720i		−	1.12357i
$519$	−7.47145			−0.327960
$520$	−0.805001	+	1.83128i	−0.0353016	+	0.0803068i
$521$	−0.104827			−0.00459254			−0.00229627	−	0.999997i	$-0.500731\pi$
$521$	−0.104827			−0.00459254			−0.00229627	+	0.999997i	$0.500731\pi$
$522$			4.67157i			0.204469i
$523$	−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
$525$	−8.94641	+	12.3138i	−0.390453	+	0.537420i
$526$	−22.4211	+	22.4211i	−0.977605	+	0.977605i
$527$	15.1088			0.658150
$528$			26.8685i			1.16930i
$529$		−	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
$533$	6.93195	−	12.9119i	0.300256	−	0.559278i
$534$			46.4371i			2.00953i
$535$	−10.3552	+	0.815007i	−0.447696	+	0.0352358i
$536$	1.44972			0.0626185
$537$	28.8121	+	28.8121i	1.24333	+	1.24333i
$538$	3.58502			0.154561
$539$	−11.8291	−	11.8291i	−0.509517	−	0.509517i
$540$	21.9090	−	1.72435i	0.942814	−	0.0742040i
$541$	18.8179	+	18.8179i	0.809047	+	0.809047i	0.984490	−	0.175443i	$-0.0561358\pi$
$541$	18.8179	+	18.8179i	0.809047	+	0.809047i	−0.175443	+	0.984490i	$0.556136\pi$
$542$	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	$0.118169\pi$
$548$	19.0257			0.812737
$549$		−	6.53301i		−	0.278822i
$550$	31.3636	+	22.7867i	1.33735	+	0.971627i
$551$	9.96876	−	9.96876i	0.424683	−	0.424683i
$552$			3.18285i			0.135471i
$553$		−	13.9794i		−	0.594464i
$554$	23.7967	−	23.7967i	1.01102	−	1.01102i
$555$	2.56811	+	32.6297i	0.109010	+	1.38505i
$556$			11.4136i			0.484046i
$557$	−37.1686			−1.57489			−0.787443	−	0.616388i	$-0.788595\pi$
$557$	−37.1686			−1.57489			−0.787443	+	0.616388i	$0.788595\pi$
$558$	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	$0.605953\pi$
$563$	−30.1782	+	30.1782i	−1.27186	+	1.27186i	−0.945112	+	0.326747i	$0.894047\pi$
$564$	15.1475	+	15.1475i	0.637823	+	0.637823i
$565$	2.29441	+	29.1521i	0.0965264	+	1.22644i
$566$	−26.1013	−	26.1013i	−1.09712	−	1.09712i
$567$	−16.7091			−0.701715
$568$	−0.340308	−	0.340308i	−0.0142790	−	0.0142790i
$569$	37.6216			1.57718			0.788589	−	0.614920i	$-0.210812\pi$
$569$	37.6216			1.57718			0.788589	+	0.614920i	$0.210812\pi$
$570$	21.3960	+	18.2738i	0.896181	+	0.765406i
$571$		−	21.9027i		−	0.916599i	−0.888798	−	0.458299i	$-0.848459\pi$
$571$		−	21.9027i		−	0.916599i	0.888798	−	0.458299i	$-0.151541\pi$
$572$	−25.7451	−	13.8216i	−1.07646	−	0.577911i
$573$	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
$577$			0.139587i			0.00581108i	0.999996	+	0.00290554i	$0.000924863\pi$
$577$			0.139587i			0.00581108i	−0.999996	+	0.00290554i	$0.999075\pi$
$578$	−13.9928			−0.582024
$579$	9.56115	−	9.56115i	0.397348	−	0.397348i
$580$	13.1856	−	15.4385i	0.547504	−	0.641049i
$581$	12.1188			0.502771
$582$	23.3242	+	23.3242i	0.966817	+	0.966817i
$583$		−	24.9426i		−	1.03302i
$584$	−0.999081			−0.0413422
$585$	−1.74481	+	3.96923i	−0.0721390	+	0.164107i
$586$	37.1530			1.53478
$587$			2.38675i			0.0985115i	0.998786	+	0.0492558i	$0.0156849\pi$
$587$			2.38675i			0.0985115i	−0.998786	+	0.0492558i	$0.984315\pi$
$588$	−12.3645	−	12.3645i	−0.509902	−	0.509902i
$589$	−15.6591			−0.645221
$590$	−2.25247	−	28.6192i	−0.0927327	−	1.17823i
$591$	−5.87272	+	5.87272i	−0.241571	+	0.241571i
$592$	29.1105			1.19643
$593$		−	35.9052i		−	1.47445i	−0.675647	−	0.737225i	$-0.736136\pi$
$593$		−	35.9052i		−	1.47445i	0.675647	−	0.737225i	$-0.263864\pi$
$594$			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
$598$	43.9877	+	23.6154i	1.79879	+	0.965705i
$599$		−	31.9707i		−	1.30629i	−0.757233	−	0.653144i	$-0.773449\pi$
$599$		−	31.9707i		−	1.30629i	0.757233	−	0.653144i	$-0.226551\pi$
$600$	1.88780	+	1.37155i	0.0770691	+	0.0559932i
$601$	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
$603$	3.14222			0.127961
$604$	−3.94810	−	3.94810i	−0.160646	−	0.160646i
$605$	−5.20397	+	6.09311i	−0.211572	+	0.247720i
$606$	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
$613$	3.63491			0.146812			0.0734062	−	0.997302i	$-0.476613\pi$
$613$	3.63491			0.146812			0.0734062	+	0.997302i	$0.476613\pi$
$614$		−	38.4474i		−	1.55161i
$615$	−12.9991	−	11.1022i	−0.524174	−	0.447684i
$616$	1.08436	−	1.08436i	0.0436902	−	0.0436902i
$617$			29.1618i			1.17401i	0.809583	+	0.587005i	$0.199693\pi$
$617$			29.1618i			1.17401i	−0.809583	+	0.587005i	$0.800307\pi$
$618$		−	4.68661i		−	0.188523i
$619$	28.1188	−	28.1188i	1.13019	−	1.13019i	0.140045	−	0.990145i	$-0.455275\pi$
$619$	28.1188	−	28.1188i	1.13019	−	1.13019i	0.990145	−	0.140045i	$-0.0447247\pi$
$620$	−22.4816	+	1.76941i	−0.902883	+	0.0710612i
$621$		−	31.5850i		−	1.26746i
$622$	35.2326			1.41270
$623$	−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
$630$	−3.00474	−	2.56627i	−0.119712	−	0.102243i
$631$	−15.9754	−	15.9754i	−0.635971	−	0.635971i	0.313588	−	0.949559i	$-0.398469\pi$
$631$	−15.9754	−	15.9754i	−0.635971	−	0.635971i	−0.949559	+	0.313588i	$0.898469\pi$
$632$	−2.14314			−0.0852495
$633$	14.2552	+	14.2552i	0.566592	+	0.566592i
$634$	−68.0131			−2.70114
$635$	2.84789	+	36.1844i	0.113015	+	1.43593i
$636$		−	26.0714i		−	1.03380i
$637$	−15.1229	+	4.55730i	−0.599189	+	0.180567i
$638$	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	$0.297117\pi$
$641$			40.6941i			1.60732i	−0.595088	+	0.803661i	$0.702883\pi$
$642$		−	17.7397i		−	0.700131i
$643$	−3.29115			−0.129790			−0.0648952	−	0.997892i	$-0.520671\pi$
$643$	−3.29115			−0.129790			−0.0648952	+	0.997892i	$0.520671\pi$
$644$	−16.5638	+	16.5638i	−0.652706	+	0.652706i
$645$	−17.9954	−	15.3694i	−0.708567	−	0.605170i
$646$	−21.2701			−0.836861
$647$	34.7828	+	34.7828i	1.36745	+	1.36745i	0.864052	+	0.503403i	$0.167919\pi$
$647$	34.7828	+	34.7828i	1.36745	+	1.36745i	0.503403	+	0.864052i	$0.332081\pi$
$648$			2.56162i			0.100630i
$649$	24.1479			0.947888
$650$	32.9618	−	15.9135i	1.29287	−	0.624179i
$651$	14.4664			0.566982
$652$			15.9967i			0.626481i
$653$	−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
$655$	3.07558	+	2.62678i	0.120173	+	0.102637i
$656$	−10.7510	+	10.7510i	−0.419755	+	0.419755i
$657$	−2.16547			−0.0844830
$658$			17.6345i			0.687465i
$659$		−	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	0.575076	−	0.818100i	$-0.304972\pi$
$661$	−6.24812	−	6.24812i	−0.243024	−	0.243024i	−0.818100	+	0.575076i	$0.804972\pi$
$662$	−38.0046	−	38.0046i	−1.47709	−	1.47709i
$663$	−6.22115	−	20.6441i	−0.241609	−	0.801752i
$664$		−	1.85789i		−	0.0721002i
$665$	0.935651	+	11.8881i	0.0362830	+	0.461001i
$666$	−8.49727			−0.329263
$667$	−20.6329	−	20.6329i	−0.798910	−	0.798910i
$668$	−40.1279			−1.55259
$669$	−9.06679	−	9.06679i	−0.350543	−	0.350543i
$670$	−20.1707	−	17.2273i	−0.779262	−	0.665549i
$671$	−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	−0.524697	−	0.851289i	$-0.675821\pi$
$673$	8.47252	−	8.47252i	0.326592	−	0.326592i	0.851289	+	0.524697i	$0.175821\pi$
$674$	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	$0.256767\pi$
$678$	−49.9409			−1.91797
$679$			13.9794i			0.536479i
$680$	−1.75848	+	0.138401i	−0.0674348	+	0.00530744i
$681$	6.06862	−	6.06862i	0.232550	−	0.232550i
$682$		−	36.8461i		−	1.41091i
$683$		−	16.4856i		−	0.630803i	−0.948958	−	0.315401i	$-0.897861\pi$
$683$		−	16.4856i		−	0.630803i	0.948958	−	0.315401i	$-0.102139\pi$
$684$	−2.65923	+	2.65923i	−0.101678	+	0.101678i
$685$	−15.2435	−	13.0191i	−0.582424	−	0.497434i
$686$		−	37.3964i		−	1.42780i
$687$	36.0788			1.37649
$688$	−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	0.207018	−	0.978337i	$-0.433624\pi$
$691$	31.1593	−	31.1593i	1.18535	−	1.18535i	0.978337	−	0.207018i	$-0.0663758\pi$
$692$	−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
$695$	7.81023	−	9.14466i	0.296259	−	0.346877i
$696$	1.41188	+	1.41188i	0.0535171	+	0.0535171i
$697$	12.9226			0.489478
$698$	−12.5854	−	12.5854i	−0.476363	−	0.476363i
$699$	1.76909			0.0669133
$700$	2.68661	+	16.9619i	0.101544	+	0.641101i
$701$			16.2976i			0.615554i	0.951459	+	0.307777i	$0.0995850\pi$
$701$			16.2976i			0.615554i	−0.951459	+	0.307777i	$0.900415\pi$
$702$	29.8698	+	16.0360i	1.12736	+	0.605240i
$703$	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
$707$			1.33320i			0.0501401i
$708$	25.2407			0.948605
$709$	−1.04907	+	1.04907i	−0.0393988	+	0.0393988i	−0.726532	−	0.687133i	$-0.758869\pi$
$709$	−1.04907	+	1.04907i	−0.0393988	+	0.0393988i	0.687133	+	0.726532i	$0.258869\pi$
$710$	0.690934	+	8.77880i	0.0259303	+	0.329463i
$711$	−4.64517			−0.174208
$712$	2.13344	+	2.13344i	0.0799539	+	0.0799539i
$713$			32.4105i			1.21378i
$714$	19.6500			0.735384
$715$	11.1691	+	28.6911i	0.417702	+	1.07299i
$716$	45.9739			1.71812
$717$		−	25.1903i		−	0.940748i
$718$	32.7364	+	32.7364i	1.22171	+	1.22171i
$719$	48.2826			1.80064			0.900319	−	0.435232i	$-0.143333\pi$
$719$	48.2826			1.80064			0.900319	+	0.435232i	$0.143333\pi$
$720$	2.92137	−	3.42051i	0.108873	−	0.127475i
$721$	1.40447	−	1.40447i	0.0523050	−	0.0523050i
$722$	−16.5313			−0.615232
$723$			31.6731i			1.17793i
$724$			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	0.400462	−	0.916313i	$-0.368850\pi$
$727$	−13.9089	−	13.9089i	−0.515851	−	0.515851i	−0.916313	+	0.400462i	$0.868850\pi$
$728$	−0.417762	−	1.38629i	−0.0154833	−	0.0513794i
$729$		−	20.5801i		−	0.762227i
$730$	13.9007	+	11.8722i	0.514488	+	0.439412i
$731$	17.8895			0.661666
$732$	−34.2878	−	34.2878i	−1.26731	−	1.26731i
$733$	38.3390			1.41608			0.708041	−	0.706171i	$-0.249579\pi$
$733$	38.3390			1.41608			0.708041	+	0.706171i	$0.249579\pi$
$734$	−13.3735	−	13.3735i	−0.493626	−	0.493626i
$735$	1.44560	+	18.3674i	0.0533218	+	0.677491i
$736$	−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	$-0.870006\pi$
$739$	−14.1532	+	14.1532i	−0.520633	+	0.520633i	0.397130	+	0.917763i	$0.370006\pi$
$740$	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
$743$	19.6941			0.722508			0.361254	−	0.932467i	$-0.382349\pi$
$743$	19.6941			0.722508			0.361254	+	0.932467i	$0.382349\pi$
$744$		−	2.21780i		−	0.0813084i
$745$	1.93183	+	24.5453i	0.0707769	+	0.899270i
$746$	−19.3251	+	19.3251i	−0.707541	+	0.707541i
$747$		−	4.02692i		−	0.147337i
$748$		−	25.7663i		−	0.942111i
$749$	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	$0.196003\pi$
$751$			31.6564i			1.15516i	−0.816334	+	0.577580i	$0.803997\pi$
$752$	−20.0747			−0.732047
$753$	−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
$760$	1.82253	−	0.143442i	0.0661101	−	0.00520319i
$761$	20.3483	+	20.3483i	0.737626	+	0.737626i	0.972118	−	0.234492i	$-0.0753427\pi$
$761$	20.3483	+	20.3483i	0.737626	+	0.737626i	−0.234492	+	0.972118i	$0.575343\pi$
$762$	−61.9881			−2.24559
$763$	8.20855	+	8.20855i	0.297169	+	0.297169i
$764$	40.2053			1.45458
$765$	−3.81145	+	0.299980i	−0.137803	+	0.0108458i
$766$		−	30.1879i		−	1.09073i
$767$	10.7842	−	20.0875i	0.389396	−	0.725316i
$768$	−18.4462	−	18.4462i	−0.665620	−	0.665620i
$769$	−30.9403	−	30.9403i	−1.11573	−	1.11573i	−0.992360	−	0.123374i	$-0.960628\pi$
$769$	−30.9403	−	30.9403i	−1.11573	−	1.11573i	−0.123374	−	0.992360i	$-0.539372\pi$
$770$	−27.9729	+	2.20160i	−1.00807	+	0.0793403i
$771$			34.6507i			1.24792i
$772$		−	15.2562i		−	0.549083i
$773$	−35.7878			−1.28720			−0.643598	−	0.765363i	$-0.722559\pi$
$773$	−35.7878			−1.28720			−0.643598	+	0.765363i	$0.722559\pi$
$774$	4.34435	−	4.34435i	0.156155	−	0.156155i
$775$	19.2232	+	13.9663i	0.690517	+	0.501683i
$776$	2.14314			0.0769342
$777$	−16.7514	−	16.7514i	−0.600954	−	0.600954i
$778$		−	58.6921i		−	2.10421i
$779$	−13.3932			−0.479863
$780$	11.6746	+	29.9895i	0.418018	+	1.07380i
$781$	−7.40725			−0.265052
$782$			44.0240i			1.57429i
$783$	−14.0108	−	14.0108i	−0.500704	−	0.500704i
$784$	16.3864			0.585230
$785$	31.1885	−	2.45469i	1.11317	−	0.0876116i
$786$	−4.88440	+	4.88440i	−0.174221	+	0.174221i
$787$	8.98893			0.320421			0.160210	−	0.987083i	$-0.448783\pi$
$787$	8.98893			0.320421			0.160210	+	0.987083i	$0.448783\pi$
$788$			9.37078i			0.333820i
$789$			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
$793$	−41.9371	+	12.6378i	−1.48923	+	0.448782i
$794$			29.6548i			1.05241i
$795$	−17.8404	+	20.8886i	−0.632734	+	0.740841i
$796$	−0.663123			−0.0235038
$797$	6.02120	+	6.02120i	0.213282	+	0.213282i	0.805660	−	0.592378i	$-0.201811\pi$
$797$	6.02120	+	6.02120i	0.213282	+	0.213282i	−0.592378	+	0.805660i	$0.701811\pi$
$798$	−20.3657			−0.720938
$799$	12.0648	+	12.0648i	0.426822	+	0.426822i
$800$	−39.9567	+	6.32878i	−1.41268	+	0.223756i
$801$	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
$808$	0.204389			0.00719038
$809$			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	−0.911692	−	0.410875i	$-0.865223\pi$
$811$	−14.2623	+	14.2623i	−0.500817	+	0.500817i	0.410875	+	0.911692i	$0.365223\pi$
$812$			14.6951i			0.515695i
$813$		−	32.9963i		−	1.15723i
$814$	−42.6661	+	42.6661i	−1.49545	+	1.49545i
$815$	10.9464	−	12.8167i	0.383436	−	0.448949i
$816$			22.3691i			0.783073i
$817$	−18.5410			−0.648668
$818$	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	−0.243453	+	0.969913i	$0.578280\pi$
$821$	−34.7667	+	34.7667i	−1.21337	+	1.21337i	−0.969913	+	0.243453i	$0.921720\pi$
$822$	24.2085	−	24.2085i	0.844370	−	0.844370i
$823$	4.53102	−	4.53102i	0.157941	−	0.157941i	−0.623712	−	0.781654i	$-0.714376\pi$
$823$	4.53102	−	4.53102i	0.157941	−	0.157941i	0.781654	+	0.623712i	$0.214376\pi$
$824$	−0.215315	−	0.215315i	−0.00750084	−	0.00750084i
$825$	35.4721	−	5.61845i	1.23498	−	0.195609i
$826$	14.6925	+	14.6925i	0.511218	+	0.511218i
$827$	−35.6597			−1.24001			−0.620004	−	0.784598i	$-0.712869\pi$
$827$	−35.6597			−1.24001			−0.620004	+	0.784598i	$0.712869\pi$
$828$	5.50395	+	5.50395i	0.191276	+	0.191276i
$829$	−44.9117			−1.55985			−0.779924	−	0.625874i	$-0.784742\pi$
$829$	−44.9117			−1.55985			−0.779924	+	0.625874i	$0.784742\pi$
$830$	−22.0777	+	25.8498i	−0.766327	+	0.897259i
$831$		−	31.1769i		−	1.08151i
$832$	30.8833	−	9.30673i	1.07069	−	0.322653i
$833$	−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
$837$			22.0083i			0.760719i
$838$	46.4695			1.60526
$839$	−1.42941	+	1.42941i	−0.0493486	+	0.0493486i	−0.731350	−	0.682002i	$-0.761110\pi$
$839$	−1.42941	+	1.42941i	−0.0493486	+	0.0493486i	0.682002	+	0.731350i	$0.261110\pi$
$840$	−1.68371	+	0.132516i	−0.0580936	+	0.00457225i
$841$	10.6949			0.368791
$842$	50.0715	+	50.0715i	1.72558	+	1.72558i
$843$			33.3009i			1.14694i
$844$	22.7462			0.782957
$845$	28.8547	+	3.52210i	0.992633	+	0.121164i
$846$	5.85973			0.201462
$847$		−	5.79970i		−	0.199280i
$848$	17.2760	+	17.2760i	0.593260	+	0.593260i
$849$	−34.1962			−1.17361
$850$	26.1113	+	18.9707i	0.895611	+	0.650691i
$851$	37.5299	−	37.5299i	1.28651	−	1.28651i
$852$	−7.74248			−0.265253
$853$		−	29.8662i		−	1.02260i	−0.859402	−	0.511300i	$-0.829164\pi$
$853$		−	29.8662i		−	1.02260i	0.859402	−	0.511300i	$-0.170836\pi$
$854$		−	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	0.534880	−	0.844928i	$-0.320357\pi$
$857$	−9.07650	−	9.07650i	−0.310047	−	0.310047i	−0.844928	+	0.534880i	$0.820357\pi$
$858$	−50.3452	+	15.1716i	−1.71876	+	0.517951i
$859$		−	55.1497i		−	1.88168i	−0.338845	−	0.940842i	$-0.610036\pi$
$859$		−	55.1497i		−	1.88168i	0.338845	−	0.940842i	$-0.389964\pi$
$860$	−26.6192	+	2.09506i	−0.907707	+	0.0714409i
$861$	12.3731			0.421675
$862$	−33.5558	−	33.5558i	−1.14291	−	1.14291i
$863$	−14.0772			−0.479193			−0.239596	−	0.970873i	$-0.577015\pi$
$863$	−14.0772			−0.479193			−0.239596	+	0.970873i	$0.577015\pi$
$864$	−26.4958	−	26.4958i	−0.901404	−	0.901404i
$865$	8.85488	−	0.696922i	0.301075	−	0.0236961i
$866$	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
$873$	4.64517			0.157215
$874$		−	45.6274i		−	1.54337i
$875$	9.45435	−	15.4284i	0.319615	−	0.521576i
$876$	−11.3652	+	11.3652i	−0.383996	+	0.383996i
$877$		−	3.88489i		−	0.131183i	−0.997847	−	0.0655917i	$-0.979107\pi$
$877$		−	3.88489i		−	0.131183i	0.997847	−	0.0655917i	$-0.0208935\pi$
$878$			36.8490i			1.24359i
$879$	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	$-0.929752\pi$
$881$		−	12.9948i		−	0.437806i	0.975747	−	0.218903i	$-0.0702478\pi$
$882$	−4.78315			−0.161057
$883$	2.20501	−	2.20501i	0.0742043	−	0.0742043i	−0.669031	−	0.743235i	$-0.733290\pi$
$883$	2.20501	−	2.20501i	0.0742043	−	0.0742043i	0.743235	+	0.669031i	$0.233290\pi$
$884$	−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
$890$	−4.33156	−	55.0355i	−0.145194	−	1.84480i
$891$	27.8785	+	27.8785i	0.933967	+	0.933967i
$892$	−14.4674			−0.484404
$893$	−12.5042	−	12.5042i	−0.418438	−	0.418438i
$894$	−42.0489			−1.40633
$895$	−36.8345	−	31.4595i	−1.23124	−	1.05157i
$896$			3.20654i			0.107123i
$897$	44.2846	−	13.3452i	1.47862	−	0.445584i
$898$	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
$902$		−	31.5145i		−	1.04932i
$903$	17.1288			0.570011
$904$	−2.29441	+	2.29441i	−0.0763109	+	0.0763109i
$905$	9.91553	−	11.6097i	0.329603	−	0.385918i
$906$	−10.0472			−0.333797
$907$	24.5036	+	24.5036i	0.813629	+	0.813629i	0.985176	−	0.171547i	$-0.0548766\pi$
$907$	24.5036	+	24.5036i	0.813629	+	0.813629i	−0.171547	+	0.985176i	$0.554877\pi$
$908$		−	9.68337i		−	0.321354i
$909$	0.443006			0.0146936
$910$	−10.6610	+	24.2525i	−0.353410	+	0.803963i
$911$	−33.7082			−1.11680			−0.558400	−	0.829572i	$-0.688585\pi$
$911$	−33.7082			−1.11680			−0.558400	+	0.829572i	$0.688585\pi$
$912$		−	23.1838i		−	0.767691i
$913$	−20.2198	−	20.2198i	−0.669177	−	0.669177i
$914$	−28.1545			−0.931268
$915$	4.00878	+	50.9344i	0.132526	+	1.68384i
$916$	28.7845	−	28.7845i	0.951067	−	0.951067i
$917$	−2.92747			−0.0966737
$918$			29.8944i			0.986664i
$919$			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
$923$	−3.30801	+	6.16173i	−0.108884	+	0.202816i
$924$		−	24.6708i		−	0.811608i
$925$	−6.08726	−	38.4319i	−0.200148	−	1.26363i
$926$	33.8893			1.11367
$927$	−0.466686	−	0.466686i	−0.0153280	−	0.0153280i
$928$	−34.6167			−1.13635
$929$	9.76693	+	9.76693i	0.320443	+	0.320443i	0.848937	−	0.528494i	$-0.177243\pi$
$929$	9.76693	+	9.76693i	0.320443	+	0.320443i	−0.528494	+	0.848937i	$0.677243\pi$
$930$	−26.3545	+	30.8573i	−0.864197	+	1.01185i
$931$	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	$0.304009\pi$
$938$	19.1994			0.626882
$939$			14.7514i			0.481394i
$940$	−19.3651	−	16.5393i	−0.631621	−	0.539452i
$941$	19.3372	−	19.3372i	0.630376	−	0.630376i	−0.317786	−	0.948162i	$-0.602939\pi$
$941$	19.3372	−	19.3372i	0.630376	−	0.630376i	0.948162	+	0.317786i	$0.102939\pi$
$942$			53.4296i			1.74083i
$943$			27.7208i			0.902712i
$944$	−16.7256	+	16.7256i	−0.544371	+	0.544371i
$945$	16.7083	−	1.31503i	0.543522	−	0.0427778i
$946$		−	43.6274i		−	1.41845i
$947$	−7.99987			−0.259961			−0.129980	−	0.991517i	$-0.541491\pi$
$947$	−7.99987			−0.259961			−0.129980	+	0.991517i	$0.541491\pi$
$948$	−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	$-0.437176\pi$
$953$	36.3248	−	36.3248i	1.17667	−	1.17667i	0.980586	−	0.196088i	$-0.0628238\pi$
$954$	−5.04281	−	5.04281i	−0.163267	−	0.163267i
$955$	−32.2127	−	27.5121i	−1.04238	−	0.890270i
$956$	−20.0974	−	20.0974i	−0.649996	−	0.649996i
$957$	30.7314			0.993405
$958$	16.1094	+	16.1094i	0.520472	+	0.520472i
$959$	14.5094			0.468534
$960$	−2.95215	−	37.5091i	−0.0952802	−	1.21060i
$961$			8.41650i			0.271500i
$962$	16.4376	+	54.5461i	0.529969	+	1.75864i
$963$	−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
$967$		−	12.9501i		−	0.416448i	−0.978081	−	0.208224i	$-0.933232\pi$
$967$		−	12.9501i		−	0.416448i	0.978081	−	0.208224i	$-0.0667683\pi$
$968$	−0.889135			−0.0285779
$969$	−13.9334	+	13.9334i	−0.447604	+	0.447604i
$970$	−29.8185	−	25.4673i	−0.957416	−	0.817705i
$971$	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
$973$			8.70430i			0.279047i
$974$	−36.7498			−1.17754
$975$	11.1678	−	32.0166i	0.357655	−	1.02535i
$976$	45.4411			1.45453
$977$		−	37.8354i		−	1.21046i	−0.796050	−	0.605231i	$-0.793081\pi$
$977$		−	37.8354i		−	1.21046i	0.796050	−	0.605231i	$-0.206919\pi$
$978$	20.3545	+	20.3545i	0.650864	+	0.650864i
$979$	46.4371			1.48414
$980$	15.8073	+	13.5006i	0.504944	+	0.431260i
$981$	2.72760	−	2.72760i	0.0870855	−	0.0870855i
$982$	53.5678			1.70942
$983$		−	42.4511i		−	1.35398i	−0.735992	−	0.676990i	$-0.763284\pi$
$983$		−	42.4511i		−	1.35398i	0.735992	−	0.676990i	$-0.236716\pi$
$984$		−	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
$988$	22.2144	+	11.9261i	0.706734	+	0.379420i
$989$			38.3754i			1.22027i
$990$	0.731565	+	9.29505i	0.0232507	+	0.295416i
$991$	−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
$993$	−49.7911			−1.58007
$994$	−4.50686	−	4.50686i	−0.142949	−	0.142949i
$995$	0.531297	+	0.453768i	0.0168433	+	0.0143854i
$996$	−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.f.b.18.1	✓	8
3.2	odd	2		585.2.n.e.343.4		8
4.3	odd	2		1040.2.cd.n.993.3		8
5.2	odd	4		65.2.k.b.57.4	yes	8
5.3	odd	4		325.2.k.b.57.1		8
5.4	even	2		325.2.f.b.18.4		8
13.2	odd	12		845.2.o.c.488.4		16
13.3	even	3		845.2.t.c.188.4		16
13.4	even	6		845.2.t.d.418.4		16
13.5	odd	4		845.2.k.b.268.1		8
13.6	odd	12		845.2.o.c.258.4		16
13.7	odd	12		845.2.o.d.258.1		16
13.8	odd	4		65.2.k.b.8.4	yes	8
13.9	even	3		845.2.t.c.418.1		16
13.10	even	6		845.2.t.d.188.1		16
13.11	odd	12		845.2.o.d.488.1		16
13.12	even	2		845.2.f.b.408.4		8
15.2	even	4		585.2.w.e.577.1		8
20.7	even	4		1040.2.bg.n.577.3		8
39.8	even	4		585.2.w.e.73.1		8
52.47	even	4		1040.2.bg.n.593.3		8
65.2	even	12		845.2.t.d.657.4		16
65.7	even	12		845.2.t.c.427.4		16
65.8	even	4		325.2.f.b.307.1		8
65.12	odd	4		845.2.k.b.577.1		8
65.17	odd	12		845.2.o.c.587.4		16
65.22	odd	12		845.2.o.d.587.1		16
65.32	even	12		845.2.t.d.427.1		16
65.34	odd	4		325.2.k.b.268.1		8
65.37	even	12		845.2.t.c.657.1		16
65.42	odd	12		845.2.o.d.357.1		16
65.47	even	4	inner	65.2.f.b.47.4	yes	8
65.57	even	4		845.2.f.b.437.1		8
65.62	odd	12		845.2.o.c.357.4		16
195.47	odd	4		585.2.n.e.307.1		8
260.47	odd	4		1040.2.cd.n.177.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.f.b.18.1	✓	8	1.1	even	1	trivial
65.2.f.b.47.4	yes	8	65.47	even	4	inner
65.2.k.b.8.4	yes	8	13.8	odd	4
65.2.k.b.57.4	yes	8	5.2	odd	4
325.2.f.b.18.4		8	5.4	even	2
325.2.f.b.307.1		8	65.8	even	4
325.2.k.b.57.1		8	5.3	odd	4
325.2.k.b.268.1		8	65.34	odd	4
585.2.n.e.307.1		8	195.47	odd	4
585.2.n.e.343.4		8	3.2	odd	2
585.2.w.e.73.1		8	39.8	even	4
585.2.w.e.577.1		8	15.2	even	4
845.2.f.b.408.4		8	13.12	even	2
845.2.f.b.437.1		8	65.57	even	4
845.2.k.b.268.1		8	13.5	odd	4
845.2.k.b.577.1		8	65.12	odd	4
845.2.o.c.258.4		16	13.6	odd	12
845.2.o.c.357.4		16	65.62	odd	12
845.2.o.c.488.4		16	13.2	odd	12
845.2.o.c.587.4		16	65.17	odd	12
845.2.o.d.258.1		16	13.7	odd	12
845.2.o.d.357.1		16	65.42	odd	12
845.2.o.d.488.1		16	13.11	odd	12
845.2.o.d.587.1		16	65.22	odd	12
845.2.t.c.188.4		16	13.3	even	3
845.2.t.c.418.1		16	13.9	even	3
845.2.t.c.427.4		16	65.7	even	12
845.2.t.c.657.1		16	65.37	even	12
845.2.t.d.188.1		16	13.10	even	6
845.2.t.d.418.4		16	13.4	even	6
845.2.t.d.427.1		16	65.32	even	12
845.2.t.d.657.4		16	65.2	even	12
1040.2.bg.n.577.3		8	20.7	even	4
1040.2.bg.n.593.3		8	52.47	even	4
1040.2.cd.n.177.3		8	260.47	odd	4
1040.2.cd.n.993.3		8	4.3	odd	2

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.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +O(q^{10})\)	\(q-2.03032i q^{2} +(-1.33000 - 1.33000i) q^{3} -2.12221 q^{4} +(1.70032 + 1.45220i) q^{5} +(-2.70032 + 2.70032i) q^{6} -1.61845 q^{7} +0.248119i q^{8} +0.537789i q^{9} +(2.94844 - 3.45220i) q^{10} +(2.70032 + 2.70032i) q^{11} +(2.82253 + 2.82253i) q^{12} +(3.45220 - 1.04033i) q^{13} +3.28596i q^{14} +(-0.329998 - 4.19286i) q^{15} -3.74065 q^{16} +(2.24812 + 2.24812i) q^{17} +1.09188 q^{18} +(-2.33000 - 2.33000i) q^{19} +(-3.60844 - 3.08188i) 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} +3.43468 q^{28} +4.27844i q^{29} +(-8.51285 + 0.670002i) q^{30} +(3.36032 - 3.36032i) q^{31} +8.09097i q^{32} -7.18285i q^{33} +(4.56441 - 4.56441i) q^{34} +(-2.75188 - 2.35031i) q^{35} -1.14130i q^{36} -7.78220 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} +(-0.780980 + 0.914416i) q^{45} +(9.79129 + 9.79129i) q^{46} +5.36662 q^{47} +(4.97506 + 4.97506i) q^{48} -4.38064 q^{49} +(10.0266 - 1.58812i) q^{50} -5.97999i q^{51} +(-7.32629 + 2.20779i) q^{52} +(-4.61845 - 4.61845i) q^{53} +(6.64877 + 6.64877i) q^{54} +(0.670002 + 8.51285i) q^{55} -0.401567i q^{56} +6.19779i q^{57} +8.68661 q^{58} +(4.47130 - 4.47130i) q^{59} +(0.700324 + 8.89811i) q^{60} -12.1479 q^{61} +(-6.82253 - 6.82253i) q^{62} -0.870382i q^{63} +8.94596 q^{64} +(7.38064 + 3.24441i) q^{65} -14.5835 q^{66} -5.84285i q^{67} +(-4.77097 - 4.77097i) q^{68} +12.8279 q^{69} +(-4.77189 + 5.58720i) q^{70} +(-1.37155 + 1.37155i) q^{71} -0.133436 q^{72} +4.02662i q^{73} +15.8004i q^{74} +(5.52778 - 7.60844i) q^{75} +(4.94474 + 4.94474i) q^{76} +(-4.37033 - 4.37033i) q^{77} +(-6.51285 + 12.1313i) q^{78} +8.63754i q^{79} +(-6.36032 - 5.43219i) q^{80} +10.3242 q^{81} +(-5.83532 - 5.83532i) q^{82} -7.48791 q^{83} +(-4.56811 - 4.56811i) q^{84} +(0.557801 + 7.08726i) 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} -8.93844 q^{93} -10.8960i q^{94} +(-0.578117 - 7.34539i) q^{95} +(10.7610 - 10.7610i) q^{96} -8.63754i q^{97} +8.89410i q^{98} +(-1.45220 + 1.45220i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6}+O(q^{10}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6	\( 8 q - 6 q^{3} - 8 q^{4} - 2 q^{5} - 6 q^{6} + 6 q^{10} + 6 q^{11} - 2 q^{12} + 14 q^{13} + 2 q^{15} - 8 q^{16} + 16 q^{17} + 20 q^{18} - 14 q^{19} - 2 q^{20} - 12 q^{21} + 10 q^{22} - 14 q^{23} - 2 q^{24} - 12 q^{25} + 6 q^{26} + 12 q^{27} - 8 q^{28} - 14 q^{30} + 2 q^{31} - 24 q^{35} - 44 q^{37} - 2 q^{38} + 6 q^{39} + 22 q^{40} + 16 q^{41} + 24 q^{42} - 6 q^{43} - 10 q^{44} + 22 q^{45} + 2 q^{46} + 16 q^{47} - 14 q^{48} + 24 q^{49} + 44 q^{50} - 38 q^{52} - 24 q^{53} + 20 q^{54} + 10 q^{55} + 24 q^{58} - 22 q^{59} - 10 q^{60} + 20 q^{61} - 30 q^{62} + 48 q^{64} - 36 q^{66} + 4 q^{68} + 4 q^{69} - 68 q^{70} - 10 q^{71} - 16 q^{72} + 30 q^{75} + 6 q^{76} - 24 q^{77} + 2 q^{78} - 26 q^{80} - 20 q^{81} + 20 q^{82} + 48 q^{83} - 16 q^{84} + 32 q^{85} - 46 q^{86} + 16 q^{87} - 10 q^{88} + 28 q^{89} - 14 q^{90} + 20 q^{91} + 50 q^{92} - 40 q^{93} + 2 q^{95} + 30 q^{96} + 2 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 8 * q^4 - 2 * q^5 - 6 * q^6 + 6 * q^10 + 6 * q^11 - 2 * q^12 + 14 * q^13 + 2 * q^15 - 8 * q^16 + 16 * q^17 + 20 * q^18 - 14 * q^19 - 2 * q^20 - 12 * q^21 + 10 * q^22 - 14 * q^23 - 2 * q^24 - 12 * q^25 + 6 * q^26 + 12 * q^27 - 8 * q^28 - 14 * q^30 + 2 * q^31 - 24 * q^35 - 44 * q^37 - 2 * q^38 + 6 * q^39 + 22 * q^40 + 16 * q^41 + 24 * q^42 - 6 * q^43 - 10 * q^44 + 22 * q^45 + 2 * q^46 + 16 * q^47 - 14 * q^48 + 24 * q^49 + 44 * q^50 - 38 * q^52 - 24 * q^53 + 20 * q^54 + 10 * q^55 + 24 * q^58 - 22 * q^59 - 10 * q^60 + 20 * q^61 - 30 * q^62 + 48 * q^64 - 36 * q^66 + 4 * q^68 + 4 * q^69 - 68 * q^70 - 10 * q^71 - 16 * q^72 + 30 * q^75 + 6 * q^76 - 24 * q^77 + 2 * q^78 - 26 * q^80 - 20 * q^81 + 20 * q^82 + 48 * q^83 - 16 * q^84 + 32 * q^85 - 46 * q^86 + 16 * q^87 - 10 * q^88 + 28 * q^89 - 14 * q^90 + 20 * q^91 + 50 * q^92 - 40 * q^93 + 2 * q^95 + 30 * q^96 + 2 * q^99

Introduction

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