LMFDB - Embedded newform 76.3.b.a.39.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,3,Mod(39,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("76.39");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	76.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.07085000914$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-19})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 4x^{2} - 5x + 25 $ x^4 - x^3 - 4x^2 - 5x + 25
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			39.4
Root			$-1.63746 + 1.52274i$ of defining polynomial
Character	$\chi$	$=$	76.39
Dual form			76.3.b.a.39.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +3.04547i q^{3} +(-2.00000 - 3.46410i) q^{4} -8.54983 q^{5} +(-5.27492 - 3.04547i) q^{6} -3.04547i q^{7} +8.00000 q^{8} -0.274917 q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +3.04547i q^{3} +(-2.00000 - 3.46410i) q^{4} -8.54983 q^{5} +(-5.27492 - 3.04547i) q^{6} -3.04547i q^{7} +8.00000 q^{8} -0.274917 q^{9} +(8.54983 - 14.8087i) q^{10} +13.0192i q^{11} +(10.5498 - 6.09095i) q^{12} -21.8248 q^{13} +(5.27492 + 3.04547i) q^{14} -26.0383i q^{15} +(-8.00000 + 13.8564i) q^{16} -7.27492 q^{17} +(0.274917 - 0.476171i) q^{18} +4.35890i q^{19} +(17.0997 + 29.6175i) q^{20} +9.27492 q^{21} +(-22.5498 - 13.0192i) q^{22} +31.8257i q^{23} +24.3638i q^{24} +48.0997 q^{25} +(21.8248 - 37.8016i) q^{26} +26.5720i q^{27} +(-10.5498 + 6.09095i) q^{28} +4.37459 q^{29} +(45.0997 + 26.0383i) q^{30} -21.0148i q^{31} +(-16.0000 - 27.7128i) q^{32} -39.6495 q^{33} +(7.27492 - 12.6005i) q^{34} +26.0383i q^{35} +(0.549834 + 0.952341i) q^{36} +24.1993 q^{37} +(-7.54983 - 4.35890i) q^{38} -66.4667i q^{39} -68.3987 q^{40} +6.74917 q^{41} +(-9.27492 + 16.0646i) q^{42} -14.0866i q^{43} +(45.0997 - 26.0383i) q^{44} +2.35050 q^{45} +(-55.1238 - 31.8257i) q^{46} +59.0048i q^{47} +(-42.1993 - 24.3638i) q^{48} +39.7251 q^{49} +(-48.0997 + 83.3111i) q^{50} -22.1556i q^{51} +(43.6495 + 75.6032i) q^{52} -26.9244 q^{53} +(-46.0241 - 26.5720i) q^{54} -111.312i q^{55} -24.3638i q^{56} -13.2749 q^{57} +(-4.37459 + 7.57701i) q^{58} -76.7439i q^{59} +(-90.1993 + 52.0766i) q^{60} -16.9003 q^{61} +(36.3987 + 21.0148i) q^{62} +0.837253i q^{63} +64.0000 q^{64} +186.598 q^{65} +(39.6495 - 68.6750i) q^{66} +31.2186i q^{67} +(14.5498 + 25.2011i) q^{68} -96.9244 q^{69} +(-45.0997 - 26.0383i) q^{70} -25.4312i q^{71} -2.19934 q^{72} -110.924 q^{73} +(-24.1993 + 41.9145i) q^{74} +146.486i q^{75} +(15.0997 - 8.71780i) q^{76} +39.6495 q^{77} +(115.124 + 66.4667i) q^{78} +104.760i q^{79} +(68.3987 - 118.470i) q^{80} -83.3987 q^{81} +(-6.74917 + 11.6899i) q^{82} -0.376903i q^{83} +(-18.5498 - 32.1293i) q^{84} +62.1993 q^{85} +(24.3987 + 14.0866i) q^{86} +13.3227i q^{87} +104.153i q^{88} -47.8488 q^{89} +(-2.35050 + 4.07118i) q^{90} +66.4667i q^{91} +(110.248 - 63.6514i) q^{92} +64.0000 q^{93} +(-102.199 - 59.0048i) q^{94} -37.2679i q^{95} +(84.3987 - 48.7276i) q^{96} +93.6977 q^{97} +(-39.7251 + 68.8059i) q^{98} -3.57919i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9	$ 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9} + 4 q^{10} + 12 q^{12} - 42 q^{13} + 6 q^{14} - 32 q^{16} - 14 q^{17} - 14 q^{18} + 8 q^{20} + 22 q^{21} - 60 q^{22} + 132 q^{25} + 42 q^{26} - 12 q^{28} - 58 q^{29} + 120 q^{30} - 64 q^{32} - 68 q^{33} + 14 q^{34} - 28 q^{36} - 24 q^{37} - 32 q^{40} - 124 q^{41} - 22 q^{42} + 120 q^{44} + 100 q^{45} + 6 q^{46} - 48 q^{48} + 174 q^{49} - 132 q^{50} + 84 q^{52} - 2 q^{53} - 18 q^{54} - 38 q^{57} + 58 q^{58} - 240 q^{60} - 128 q^{61} - 96 q^{62} + 256 q^{64} + 384 q^{65} + 68 q^{66} + 28 q^{68} - 282 q^{69} - 120 q^{70} + 112 q^{72} - 338 q^{73} + 24 q^{74} + 68 q^{77} + 234 q^{78} + 32 q^{80} - 92 q^{81} + 124 q^{82} - 44 q^{84} + 128 q^{85} - 144 q^{86} + 20 q^{89} - 100 q^{90} - 12 q^{92} + 256 q^{93} - 288 q^{94} + 96 q^{96} - 48 q^{97} - 174 q^{98}+O(q^{100}) $ 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9 + 4 * q^10 + 12 * q^12 - 42 * q^13 + 6 * q^14 - 32 * q^16 - 14 * q^17 - 14 * q^18 + 8 * q^20 + 22 * q^21 - 60 * q^22 + 132 * q^25 + 42 * q^26 - 12 * q^28 - 58 * q^29 + 120 * q^30 - 64 * q^32 - 68 * q^33 + 14 * q^34 - 28 * q^36 - 24 * q^37 - 32 * q^40 - 124 * q^41 - 22 * q^42 + 120 * q^44 + 100 * q^45 + 6 * q^46 - 48 * q^48 + 174 * q^49 - 132 * q^50 + 84 * q^52 - 2 * q^53 - 18 * q^54 - 38 * q^57 + 58 * q^58 - 240 * q^60 - 128 * q^61 - 96 * q^62 + 256 * q^64 + 384 * q^65 + 68 * q^66 + 28 * q^68 - 282 * q^69 - 120 * q^70 + 112 * q^72 - 338 * q^73 + 24 * q^74 + 68 * q^77 + 234 * q^78 + 32 * q^80 - 92 * q^81 + 124 * q^82 - 44 * q^84 + 128 * q^85 - 144 * q^86 + 20 * q^89 - 100 * q^90 - 12 * q^92 + 256 * q^93 - 288 * q^94 + 96 * q^96 - 48 * q^97 - 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$2$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$3$			3.04547i			1.01516i	0.861605	+	0.507579i	$0.169460\pi$
$3$			3.04547i			1.01516i	−0.861605	+	0.507579i	$0.830540\pi$
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	−8.54983			−1.70997			−0.854983	−	0.518655i	$-0.826433\pi$
$5$	−8.54983			−1.70997			−0.854983	+	0.518655i	$0.826433\pi$
$6$	−5.27492	−	3.04547i	−0.879153	−	0.507579i
$7$		−	3.04547i		−	0.435068i	−0.976053	−	0.217534i	$-0.930199\pi$
$7$		−	3.04547i		−	0.435068i	0.976053	−	0.217534i	$-0.0698013\pi$
$8$	8.00000			1.00000
$9$	−0.274917			−0.0305464
$10$	8.54983	−	14.8087i	0.854983	−	1.48087i
$11$			13.0192i			1.18356i	0.806100	+	0.591780i	$0.201574\pi$
$11$			13.0192i			1.18356i	−0.806100	+	0.591780i	$0.798426\pi$
$12$	10.5498	−	6.09095i	0.879153	−	0.507579i
$13$	−21.8248			−1.67883			−0.839414	−	0.543493i	$-0.817101\pi$
$13$	−21.8248			−1.67883			−0.839414	+	0.543493i	$0.817101\pi$
$14$	5.27492	+	3.04547i	0.376780	+	0.217534i
$15$		−	26.0383i		−	1.73589i
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	−7.27492			−0.427936			−0.213968	−	0.976841i	$-0.568639\pi$
$17$	−7.27492			−0.427936			−0.213968	+	0.976841i	$0.568639\pi$
$18$	0.274917	−	0.476171i	0.0152732	−	0.0264539i
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	17.0997	+	29.6175i	0.854983	+	1.48087i
$21$	9.27492			0.441663
$22$	−22.5498	−	13.0192i	−1.02499	−	0.591780i
$23$			31.8257i			1.38373i	0.722028	+	0.691863i	$0.243210\pi$
$23$			31.8257i			1.38373i	−0.722028	+	0.691863i	$0.756790\pi$
$24$			24.3638i			1.01516i
$25$	48.0997			1.92399
$26$	21.8248	−	37.8016i	0.839414	−	1.45391i
$27$			26.5720i			0.984149i
$28$	−10.5498	+	6.09095i	−0.376780	+	0.217534i
$29$	4.37459			0.150848			0.0754239	−	0.997152i	$-0.475969\pi$
$29$	4.37459			0.150848			0.0754239	+	0.997152i	$0.475969\pi$
$30$	45.0997	+	26.0383i	1.50332	+	0.867944i
$31$		−	21.0148i		−	0.677896i	−0.940805	−	0.338948i	$-0.889929\pi$
$31$		−	21.0148i		−	0.677896i	0.940805	−	0.338948i	$-0.110071\pi$
$32$	−16.0000	−	27.7128i	−0.500000	−	0.866025i
$33$	−39.6495			−1.20150
$34$	7.27492	−	12.6005i	0.213968	−	0.370604i
$35$			26.0383i			0.743952i
$36$	0.549834	+	0.952341i	0.0152732	+	0.0264539i
$37$	24.1993			0.654036			0.327018	−	0.945018i	$-0.393956\pi$
$37$	24.1993			0.654036			0.327018	+	0.945018i	$0.393956\pi$
$38$	−7.54983	−	4.35890i	−0.198680	−	0.114708i
$39$		−	66.4667i		−	1.70428i
$40$	−68.3987			−1.70997
$41$	6.74917			0.164614			0.0823070	−	0.996607i	$-0.473771\pi$
$41$	6.74917			0.164614			0.0823070	+	0.996607i	$0.473771\pi$
$42$	−9.27492	+	16.0646i	−0.220831	+	0.382491i
$43$		−	14.0866i		−	0.327595i	−0.986494	−	0.163797i	$-0.947626\pi$
$43$		−	14.0866i		−	0.327595i	0.986494	−	0.163797i	$-0.0523744\pi$
$44$	45.0997	−	26.0383i	1.02499	−	0.591780i
$45$	2.35050			0.0522333
$46$	−55.1238	−	31.8257i	−1.19834	−	0.691863i
$47$			59.0048i			1.25542i	0.778447	+	0.627711i	$0.216008\pi$
$47$			59.0048i			1.25542i	−0.778447	+	0.627711i	$0.783992\pi$
$48$	−42.1993	−	24.3638i	−0.879153	−	0.507579i
$49$	39.7251			0.810716
$50$	−48.0997	+	83.3111i	−0.961993	+	1.66622i
$51$		−	22.1556i		−	0.434423i
$52$	43.6495	+	75.6032i	0.839414	+	1.45391i
$53$	−26.9244			−0.508008			−0.254004	−	0.967203i	$-0.581748\pi$
$53$	−26.9244			−0.508008			−0.254004	+	0.967203i	$0.581748\pi$
$54$	−46.0241	−	26.5720i	−0.852298	−	0.492074i
$55$		−	111.312i		−	2.02385i
$56$		−	24.3638i		−	0.435068i
$57$	−13.2749			−0.232893
$58$	−4.37459	+	7.57701i	−0.0754239	+	0.130638i
$59$		−	76.7439i		−	1.30074i	−0.759615	−	0.650372i	$-0.774613\pi$
$59$		−	76.7439i		−	1.30074i	0.759615	−	0.650372i	$-0.225387\pi$
$60$	−90.1993	+	52.0766i	−1.50332	+	0.867944i
$61$	−16.9003			−0.277055			−0.138527	−	0.990359i	$-0.544237\pi$
$61$	−16.9003			−0.277055			−0.138527	+	0.990359i	$0.544237\pi$
$62$	36.3987	+	21.0148i	0.587075	+	0.338948i
$63$			0.837253i			0.0132897i
$64$	64.0000			1.00000
$65$	186.598			2.87074
$66$	39.6495	−	68.6750i	0.600750	−	1.04053i
$67$			31.2186i			0.465950i	0.972483	+	0.232975i	$0.0748460\pi$
$67$			31.2186i			0.465950i	−0.972483	+	0.232975i	$0.925154\pi$
$68$	14.5498	+	25.2011i	0.213968	+	0.370604i
$69$	−96.9244			−1.40470
$70$	−45.0997	−	26.0383i	−0.644281	−	0.371976i
$71$		−	25.4312i		−	0.358186i	−0.983832	−	0.179093i	$-0.942684\pi$
$71$		−	25.4312i		−	0.358186i	0.983832	−	0.179093i	$-0.0573164\pi$
$72$	−2.19934			−0.0305464
$73$	−110.924			−1.51951			−0.759756	−	0.650208i	$-0.774682\pi$
$73$	−110.924			−1.51951			−0.759756	+	0.650208i	$0.774682\pi$
$74$	−24.1993	+	41.9145i	−0.327018	+	0.566412i
$75$			146.486i			1.95315i
$76$	15.0997	−	8.71780i	0.198680	−	0.114708i
$77$	39.6495			0.514929
$78$	115.124	+	66.4667i	1.47595	+	0.852138i
$79$			104.760i			1.32608i	0.748584	+	0.663040i	$0.230734\pi$
$79$			104.760i			1.32608i	−0.748584	+	0.663040i	$0.769266\pi$
$80$	68.3987	−	118.470i	0.854983	−	1.48087i
$81$	−83.3987			−1.02961
$82$	−6.74917	+	11.6899i	−0.0823070	+	0.142560i
$83$		−	0.376903i		−	0.00454100i	−0.999997	−	0.00227050i	$-0.999277\pi$
$83$		−	0.376903i		−	0.00454100i	0.999997	−	0.00227050i	$-0.000722723\pi$
$84$	−18.5498	−	32.1293i	−0.220831	−	0.382491i
$85$	62.1993			0.731757
$86$	24.3987	+	14.0866i	0.283706	+	0.163797i
$87$			13.3227i			0.153134i
$88$			104.153i			1.18356i
$89$	−47.8488			−0.537627			−0.268814	−	0.963192i	$-0.586632\pi$
$89$	−47.8488			−0.537627			−0.268814	+	0.963192i	$0.586632\pi$
$90$	−2.35050	+	4.07118i	−0.0261166	+	0.0452353i
$91$			66.4667i			0.730404i
$92$	110.248	−	63.6514i	1.19834	−	0.691863i
$93$	64.0000			0.688172
$94$	−102.199	−	59.0048i	−1.08723	−	0.627711i
$95$		−	37.2679i		−	0.392293i
$96$	84.3987	−	48.7276i	0.879153	−	0.507579i
$97$	93.6977			0.965955			0.482978	−	0.875633i	$-0.339555\pi$
$97$	93.6977			0.965955			0.482978	+	0.875633i	$0.339555\pi$
$98$	−39.7251	+	68.8059i	−0.405358	+	0.702101i
$99$		−	3.57919i		−	0.0361534i
$100$	−96.1993	−	166.622i	−0.961993	−	1.66622i
$101$	82.7010			0.818822			0.409411	−	0.912350i	$-0.365734\pi$
$101$	82.7010			0.818822			0.409411	+	0.912350i	$0.365734\pi$
$102$	38.3746	+	22.1556i	0.376221	+	0.217212i
$103$		−	94.7133i		−	0.919546i	−0.888036	−	0.459773i	$-0.847931\pi$
$103$		−	94.7133i		−	0.919546i	0.888036	−	0.459773i	$-0.152069\pi$
$104$	−174.598			−1.67883
$105$	−79.2990			−0.755229
$106$	26.9244	−	46.6345i	0.254004	−	0.439948i
$107$			77.2043i			0.721536i	0.932656	+	0.360768i	$0.117485\pi$
$107$			77.2043i			0.721536i	−0.932656	+	0.360768i	$0.882515\pi$
$108$	92.0482	−	53.1440i	0.852298	−	0.492074i
$109$	−22.1752			−0.203443			−0.101721	−	0.994813i	$-0.532435\pi$
$109$	−22.1752			−0.203443			−0.101721	+	0.994813i	$0.532435\pi$
$110$	192.797	+	111.312i	1.75270	+	1.01192i
$111$			73.6985i			0.663950i
$112$	42.1993	+	24.3638i	0.376780	+	0.217534i
$113$	−145.698			−1.28936			−0.644680	−	0.764453i	$-0.723009\pi$
$113$	−145.698			−1.28936			−0.644680	+	0.764453i	$0.723009\pi$
$114$	13.2749	−	22.9928i	0.116447	−	0.201692i
$115$		−	272.105i		−	2.36613i
$116$	−8.74917	−	15.1540i	−0.0754239	−	0.130638i
$117$	6.00000			0.0512821
$118$	132.924	+	76.7439i	1.12648	+	0.650372i
$119$			22.1556i			0.186181i
$120$		−	208.306i		−	1.73589i
$121$	−48.4983			−0.400813
$122$	16.9003	−	29.2722i	0.138527	−	0.239936i
$123$			20.5544i			0.167109i
$124$	−72.7974	+	42.0296i	−0.587075	+	0.338948i
$125$	−197.498			−1.57999
$126$	−1.45017	−	0.837253i	−0.0115093	−	0.00664487i
$127$			242.110i			1.90638i	0.302373	+	0.953190i	$0.402221\pi$
$127$			242.110i			1.90638i	−0.302373	+	0.953190i	$0.597779\pi$
$128$	−64.0000	+	110.851i	−0.500000	+	0.866025i
$129$	42.9003			0.332561
$130$	−186.598	+	323.197i	−1.43537	+	2.48613i
$131$			184.173i			1.40590i	0.711240	+	0.702950i	$0.248134\pi$
$131$			184.173i			1.40590i	−0.711240	+	0.702950i	$0.751866\pi$
$132$	79.2990	+	137.350i	0.600750	+	1.04053i
$133$	13.2749			0.0998114
$134$	−54.0723	−	31.2186i	−0.403524	−	0.232975i
$135$		−	227.186i		−	1.68286i
$136$	−58.1993			−0.427936
$137$	−154.973			−1.13119			−0.565593	−	0.824684i	$-0.691353\pi$
$137$	−154.973			−1.13119			−0.565593	+	0.824684i	$0.691353\pi$
$138$	96.9244	−	167.878i	0.702351	−	1.21651i
$139$			71.1867i			0.512135i	0.966659	+	0.256067i	$0.0824269\pi$
$139$			71.1867i			0.512135i	−0.966659	+	0.256067i	$0.917573\pi$
$140$	90.1993	−	52.0766i	0.644281	−	0.371976i
$141$	−179.698			−1.27445
$142$	44.0482	+	25.4312i	0.310198	+	0.179093i
$143$		−	284.140i		−	1.98699i
$144$	2.19934	−	3.80936i	0.0152732	−	0.0264539i
$145$	−37.4020			−0.257945
$146$	110.924	−	192.127i	0.759756	−	1.31594i
$147$			120.982i			0.823005i
$148$	−48.3987	−	83.8290i	−0.327018	−	0.566412i
$149$	56.9485			0.382205			0.191102	−	0.981570i	$-0.438794\pi$
$149$	56.9485			0.382205			0.191102	+	0.981570i	$0.438794\pi$
$150$	−253.722	−	146.486i	−1.69148	−	0.976576i
$151$		−	216.993i		−	1.43704i	−0.695508	−	0.718519i	$-0.744821\pi$
$151$		−	216.993i		−	1.43704i	0.695508	−	0.718519i	$-0.255179\pi$
$152$			34.8712i			0.229416i
$153$	2.00000			0.0130719
$154$	−39.6495	+	68.6750i	−0.257464	+	0.445941i
$155$			179.673i			1.15918i
$156$	−230.248	+	132.933i	−1.47595	+	0.852138i
$157$	308.997			1.96813			0.984066	−	0.177804i	$-0.0568994\pi$
$157$	308.997			1.96813			0.984066	+	0.177804i	$0.0568994\pi$
$158$	−181.450	−	104.760i	−1.14842	−	0.663040i
$159$		−	81.9976i		−	0.515708i
$160$	136.797	+	236.940i	0.854983	+	1.48087i
$161$	96.9244			0.602015
$162$	83.3987	−	144.451i	0.514807	−	0.891671i
$163$			144.278i			0.885142i	0.896734	+	0.442571i	$0.145933\pi$
$163$			144.278i			0.885142i	−0.896734	+	0.442571i	$0.854067\pi$
$164$	−13.4983	−	23.3798i	−0.0823070	−	0.142560i
$165$	338.997			2.05453
$166$	0.652815	+	0.376903i	0.00393262	+	0.00227050i
$167$		−	199.474i		−	1.19445i	−0.802073	−	0.597226i	$-0.796269\pi$
$167$		−	199.474i		−	1.19445i	0.802073	−	0.597226i	$-0.203731\pi$
$168$	74.1993			0.441663
$169$	307.320			1.81846
$170$	−62.1993	+	107.732i	−0.365878	+	0.633720i
$171$		−	1.19834i		−	0.00700782i
$172$	−48.7974	+	28.1732i	−0.283706	+	0.163797i
$173$	−231.897			−1.34045			−0.670223	−	0.742160i	$-0.733801\pi$
$173$	−231.897			−1.34045			−0.670223	+	0.742160i	$0.733801\pi$
$174$	−23.0756	−	13.3227i	−0.132618	−	0.0765672i
$175$		−	146.486i		−	0.837065i
$176$	−180.399	−	104.153i	−1.02499	−	0.591780i
$177$	233.722			1.32046
$178$	47.8488	−	82.8766i	0.268814	−	0.465599i
$179$		−	120.375i		−	0.672484i	−0.941776	−	0.336242i	$-0.890844\pi$
$179$		−	120.375i		−	0.672484i	0.941776	−	0.336242i	$-0.109156\pi$
$180$	−4.70099	−	8.14236i	−0.0261166	−	0.0452353i
$181$	142.000			0.784530			0.392265	−	0.919852i	$-0.371692\pi$
$181$	142.000			0.784530			0.392265	+	0.919852i	$0.371692\pi$
$182$	−115.124	−	66.4667i	−0.632548	−	0.365202i
$183$		−	51.4695i		−	0.281254i
$184$			254.606i			1.38373i
$185$	−206.900			−1.11838
$186$	−64.0000	+	110.851i	−0.344086	+	0.595974i
$187$		−	94.7133i		−	0.506488i
$188$	204.399	−	118.010i	1.08723	−	0.627711i
$189$	80.9244			0.428172
$190$	64.5498	+	37.2679i	0.339736	+	0.196147i
$191$			133.551i			0.699218i	0.936896	+	0.349609i	$0.113686\pi$
$191$			133.551i			0.699218i	−0.936896	+	0.349609i	$0.886314\pi$
$192$			194.910i			1.01516i
$193$	−16.1993			−0.0839344			−0.0419672	−	0.999119i	$-0.513362\pi$
$193$	−16.1993			−0.0839344			−0.0419672	+	0.999119i	$0.513362\pi$
$194$	−93.6977	+	162.289i	−0.482978	+	0.836542i
$195$			568.280i			2.91425i
$196$	−79.4502	−	137.612i	−0.405358	−	0.702101i
$197$	−0.453477			−0.00230191			−0.00115096	−	0.999999i	$-0.500366\pi$
$197$	−0.453477			−0.00230191			−0.00115096	+	0.999999i	$0.500366\pi$
$198$	6.19934	+	3.57919i	0.0313098	+	0.0180767i
$199$			166.120i			0.834774i	0.908729	+	0.417387i	$0.137054\pi$
$199$			166.120i			0.834774i	−0.908729	+	0.417387i	$0.862946\pi$
$200$	384.797			1.92399
$201$	−95.0756			−0.473013
$202$	−82.7010	+	143.242i	−0.409411	+	0.709120i
$203$		−	13.3227i		−	0.0656290i
$204$	−76.7492	+	44.3112i	−0.376221	+	0.217212i
$205$	−57.7043			−0.281484
$206$	164.048	+	94.7133i	0.796350	+	0.459773i
$207$		−	8.74944i		−	0.0422678i
$208$	174.598	−	302.413i	0.839414	−	1.45391i
$209$	−56.7492			−0.271527
$210$	79.2990	−	137.350i	0.377614	−	0.654047i
$211$		−	164.446i		−	0.779363i	−0.920950	−	0.389681i	$-0.872585\pi$
$211$		−	164.446i		−	0.779363i	0.920950	−	0.389681i	$-0.127415\pi$
$212$	53.8488	+	93.2689i	0.254004	+	0.439948i
$213$	77.4502			0.363616
$214$	−133.722	−	77.2043i	−0.624868	−	0.360768i
$215$			120.438i			0.560176i
$216$			212.576i			0.984149i
$217$	−64.0000			−0.294931
$218$	22.1752	−	38.4087i	0.101721	−	0.176186i
$219$		−	337.818i		−	1.54255i
$220$	−385.595	+	222.623i	−1.75270	+	1.01192i
$221$	158.773			0.718431
$222$	−127.650	−	73.6985i	−0.574998	−	0.331975i
$223$			144.362i			0.647361i	0.946166	+	0.323681i	$0.104920\pi$
$223$			144.362i			0.647361i	−0.946166	+	0.323681i	$0.895080\pi$
$224$	−84.3987	+	48.7276i	−0.376780	+	0.217534i
$225$	−13.2234			−0.0587708
$226$	145.698	−	252.356i	0.644680	−	1.11662i
$227$			94.5564i			0.416548i	0.978070	+	0.208274i	$0.0667846\pi$
$227$			94.5564i			0.416548i	−0.978070	+	0.208274i	$0.933215\pi$
$228$	26.5498	+	45.9857i	0.116447	+	0.201692i
$229$	−82.3987			−0.359820			−0.179910	−	0.983683i	$-0.557581\pi$
$229$	−82.3987			−0.359820			−0.179910	+	0.983683i	$0.557581\pi$
$230$	471.299	+	272.105i	2.04913	+	1.18306i
$231$			120.752i			0.522734i
$232$	34.9967			0.150848
$233$	253.601			1.08842			0.544209	−	0.838950i	$-0.316830\pi$
$233$	253.601			1.08842			0.544209	+	0.838950i	$0.316830\pi$
$234$	−6.00000	+	10.3923i	−0.0256410	+	0.0444116i
$235$		−	504.481i		−	2.14673i
$236$	−265.849	+	153.488i	−1.12648	+	0.650372i
$237$	−319.045			−1.34618
$238$	−38.3746	−	22.1556i	−0.161238	−	0.0930907i
$239$		−	143.744i		−	0.601441i	−0.953712	−	0.300720i	$-0.902773\pi$
$239$		−	143.744i		−	0.601441i	0.953712	−	0.300720i	$-0.0972271\pi$
$240$	360.797	+	208.306i	1.50332	+	0.867944i
$241$	−0.646192			−0.00268129			−0.00134065	−	0.999999i	$-0.500427\pi$
$241$	−0.646192			−0.00268129			−0.00134065	+	0.999999i	$0.500427\pi$
$242$	48.4983	−	84.0016i	0.200406	−	0.347114i
$243$		−	14.8404i		−	0.0610716i
$244$	33.8007	+	58.5445i	0.138527	+	0.239936i
$245$	−339.643			−1.38630
$246$	−35.6013	−	20.5544i	−0.144721	−	0.0835546i
$247$		−	95.1319i		−	0.385149i
$248$		−	168.118i		−	0.677896i
$249$	1.14785			0.00460983
$250$	197.498	−	342.077i	0.789993	−	1.36831i
$251$		−	222.540i		−	0.886613i	−0.896370	−	0.443306i	$-0.853805\pi$
$251$		−	222.540i		−	0.886613i	0.896370	−	0.443306i	$-0.146195\pi$
$252$	2.90033	−	1.67451i	0.0115093	−	0.00664487i
$253$	−414.344			−1.63772
$254$	−419.347	−	242.110i	−1.65097	−	0.953190i
$255$			189.427i			0.742849i
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	64.1512			0.249615			0.124808	−	0.992181i	$-0.460169\pi$
$257$	64.1512			0.249615			0.124808	+	0.992181i	$0.460169\pi$
$258$	−42.9003	+	74.3056i	−0.166280	+	0.288006i
$259$		−	73.6985i		−	0.284550i
$260$	−373.196	−	646.394i	−1.43537	−	2.48613i
$261$	−1.20265			−0.00460785
$262$	−318.997	−	184.173i	−1.21754	−	0.702950i
$263$			90.0666i			0.342459i	0.985231	+	0.171229i	$0.0547739\pi$
$263$			90.0666i			0.342459i	−0.985231	+	0.171229i	$0.945226\pi$
$264$	−317.196			−1.20150
$265$	230.199			0.868677
$266$	−13.2749	+	22.9928i	−0.0499057	+	0.0864392i
$267$		−	145.722i		−	0.545777i
$268$	108.145	−	62.4373i	0.403524	−	0.232975i
$269$	−167.993			−0.624511			−0.312255	−	0.949998i	$-0.601084\pi$
$269$	−167.993			−0.624511			−0.312255	+	0.949998i	$0.601084\pi$
$270$	393.498	+	227.186i	1.45740	+	0.841431i
$271$			192.158i			0.709071i	0.935042	+	0.354536i	$0.115361\pi$
$271$			192.158i			0.709071i	−0.935042	+	0.354536i	$0.884639\pi$
$272$	58.1993	−	100.804i	0.213968	−	0.370604i
$273$	−202.423			−0.741475
$274$	154.973	−	268.420i	0.565593	−	0.979637i
$275$			626.217i			2.27715i
$276$	193.849	+	335.756i	0.702351	+	1.21651i
$277$	241.045			0.870198			0.435099	−	0.900383i	$-0.356713\pi$
$277$	241.045			0.870198			0.435099	+	0.900383i	$0.356713\pi$
$278$	−123.299	−	71.1867i	−0.443522	−	0.256067i
$279$			5.77733i			0.0207073i
$280$			208.306i			0.743952i
$281$	−232.646			−0.827922			−0.413961	−	0.910295i	$-0.635855\pi$
$281$	−232.646			−0.827922			−0.413961	+	0.910295i	$0.635855\pi$
$282$	179.698	−	311.246i	0.637226	−	1.10371i
$283$			110.014i			0.388742i	0.980928	+	0.194371i	$0.0622666\pi$
$283$			110.014i			0.388742i	−0.980928	+	0.194371i	$0.937733\pi$
$284$	−88.0964	+	50.8625i	−0.310198	+	0.179093i
$285$	113.498			0.398240
$286$	492.145	+	284.140i	1.72079	+	0.993496i
$287$		−	20.5544i		−	0.0716182i
$288$	4.39868	+	7.61873i	0.0152732	+	0.0264539i
$289$	−236.076			−0.816871
$290$	37.4020	−	64.7821i	0.128972	−	0.223387i
$291$			285.354i			0.980598i
$292$	221.849	+	384.253i	0.759756	+	1.31594i
$293$	−279.069			−0.952454			−0.476227	−	0.879322i	$-0.657996\pi$
$293$	−279.069			−0.952454			−0.476227	+	0.879322i	$0.657996\pi$
$294$	−209.547	−	120.982i	−0.712743	−	0.411503i
$295$			656.148i			2.22423i
$296$	193.595			0.654036
$297$	−345.945			−1.16480
$298$	−56.9485	+	98.6377i	−0.191102	+	0.330999i
$299$		−	694.588i		−	2.32304i
$300$	507.444	−	292.973i	1.69148	−	0.976576i
$301$	−42.9003			−0.142526
$302$	375.842	+	216.993i	1.24451	+	0.718519i
$303$			251.864i			0.831234i
$304$	−60.3987	−	34.8712i	−0.198680	−	0.114708i
$305$	144.495			0.473754
$306$	−2.00000	+	3.46410i	−0.00653595	+	0.0113206i
$307$		−	270.660i		−	0.881630i	−0.897598	−	0.440815i	$-0.854690\pi$
$307$		−	270.660i		−	0.881630i	0.897598	−	0.440815i	$-0.145310\pi$
$308$	−79.2990	−	137.350i	−0.257464	−	0.445941i
$309$	288.447			0.933485
$310$	−311.203	−	179.673i	−1.00388	−	0.579590i
$311$			346.127i			1.11295i	0.830865	+	0.556474i	$0.187846\pi$
$311$			346.127i			1.11295i	−0.830865	+	0.556474i	$0.812154\pi$
$312$		−	531.734i		−	1.70428i
$313$	526.973			1.68362			0.841809	−	0.539775i	$-0.181491\pi$
$313$	526.973			1.68362			0.841809	+	0.539775i	$0.181491\pi$
$314$	−308.997	+	535.198i	−0.984066	+	1.70445i
$315$		−	7.15838i		−	0.0227250i
$316$	362.900	−	209.521i	1.14842	−	0.663040i
$317$	436.918			1.37829			0.689145	−	0.724624i	$-0.257986\pi$
$317$	436.918			1.37829			0.689145	+	0.724624i	$0.257986\pi$
$318$	142.024	+	81.9976i	0.446617	+	0.257854i
$319$			56.9534i			0.178537i
$320$	−547.189			−1.70997
$321$	−235.124			−0.732473
$322$	−96.9244	+	167.878i	−0.301008	+	0.521360i
$323$		−	31.7106i		−	0.0981753i
$324$	166.797	+	288.901i	0.514807	+	0.891671i
$325$	−1049.76			−3.23004
$326$	−249.897	−	144.278i	−0.766555	−	0.442571i
$327$		−	67.5342i		−	0.206526i
$328$	53.9934			0.164614
$329$	179.698			0.546194
$330$	−338.997	+	587.159i	−1.02726	+	1.77927i
$331$			202.372i			0.611397i	0.952128	+	0.305698i	$0.0988899\pi$
$331$			202.372i			0.611397i	−0.952128	+	0.305698i	$0.901110\pi$
$332$	−1.30563	+	0.753805i	−0.00393262	+	0.00227050i
$333$	−6.65281			−0.0199784
$334$	345.498	+	199.474i	1.03443	+	0.597226i
$335$		−	266.914i		−	0.796759i
$336$	−74.1993	+	128.517i	−0.220831	+	0.382491i
$337$	320.151			0.950003			0.475002	−	0.879985i	$-0.342447\pi$
$337$	320.151			0.950003			0.475002	+	0.879985i	$0.342447\pi$
$338$	−307.320	+	532.293i	−0.909230	+	1.57483i
$339$		−	443.719i		−	1.30890i
$340$	−124.399	−	215.465i	−0.365878	−	0.633720i
$341$	273.595			0.802331
$342$	2.07558	+	1.19834i	0.00606895	+	0.00350391i
$343$		−	270.210i		−	0.787784i
$344$		−	112.693i		−	0.327595i
$345$	828.688			2.40199
$346$	231.897	−	401.657i	0.670223	−	1.16086i
$347$		−	526.040i		−	1.51597i	−0.652275	−	0.757983i	$-0.726185\pi$
$347$		−	526.040i		−	1.51597i	0.652275	−	0.757983i	$-0.273815\pi$
$348$	46.1512	−	26.6454i	0.132618	−	0.0765672i
$349$	471.292			1.35041			0.675204	−	0.737631i	$-0.264056\pi$
$349$	471.292			1.35041			0.675204	+	0.737631i	$0.264056\pi$
$350$	253.722	+	146.486i	0.724919	+	0.418532i
$351$		−	579.928i		−	1.65222i
$352$	360.797	−	208.306i	1.02499	−	0.591780i
$353$	−51.3231			−0.145391			−0.0726956	−	0.997354i	$-0.523160\pi$
$353$	−51.3231			−0.145391			−0.0726956	+	0.997354i	$0.523160\pi$
$354$	−233.722	+	404.818i	−0.660231	+	1.14355i
$355$			217.433i			0.612487i
$356$	95.6977	+	165.753i	0.268814	+	0.465599i
$357$	−67.4743			−0.189004
$358$	208.495	+	120.375i	0.582388	+	0.336242i
$359$			138.554i			0.385944i	0.981204	+	0.192972i	$0.0618127\pi$
$359$			138.554i			0.385944i	−0.981204	+	0.192972i	$0.938187\pi$
$360$	18.8040			0.0522333
$361$	−19.0000			−0.0526316
$362$	−142.000	+	245.951i	−0.392265	+	0.679423i
$363$		−	147.700i		−	0.406888i
$364$	230.248	−	132.933i	0.632548	−	0.365202i
$365$	948.385			2.59832
$366$	89.1478	+	51.4695i	0.243573	+	0.140627i
$367$			710.423i			1.93576i	0.251418	+	0.967878i	$0.419103\pi$
$367$			710.423i			1.93576i	−0.251418	+	0.967878i	$0.580897\pi$
$368$	−440.990	−	254.606i	−1.19834	−	0.691863i
$369$	−1.85546			−0.00502836
$370$	206.900	−	358.362i	0.559190	−	0.968546i
$371$			81.9976i			0.221018i
$372$	−128.000	−	221.703i	−0.344086	−	0.595974i
$373$	−570.767			−1.53021			−0.765103	−	0.643908i	$-0.777312\pi$
$373$	−570.767			−1.53021			−0.765103	+	0.643908i	$0.777312\pi$
$374$	164.048	+	94.7133i	0.438631	+	0.253244i
$375$		−	601.476i		−	1.60394i
$376$			472.039i			1.25542i
$377$	−95.4743			−0.253247
$378$	−80.9244	+	140.165i	−0.214086	+	0.370807i
$379$			297.086i			0.783867i	0.919994	+	0.391933i	$0.128194\pi$
$379$			297.086i			0.783867i	−0.919994	+	0.391933i	$0.871806\pi$
$380$	−129.100	+	74.5357i	−0.339736	+	0.196147i
$381$	−737.341			−1.93528
$382$	−231.316	−	133.551i	−0.605541	−	0.349609i
$383$			724.363i			1.89129i	0.325206	+	0.945643i	$0.394566\pi$
$383$			724.363i			1.89129i	−0.325206	+	0.945643i	$0.605434\pi$
$384$	−337.595	−	194.910i	−0.879153	−	0.507579i
$385$	−338.997			−0.880511
$386$	16.1993	−	28.0581i	0.0419672	−	0.0726893i
$387$			3.87264i			0.0100068i
$388$	−187.395	−	324.578i	−0.482978	−	0.836542i
$389$	333.890			0.858330			0.429165	−	0.903226i	$-0.358808\pi$
$389$	333.890			0.858330			0.429165	+	0.903226i	$0.358808\pi$
$390$	−984.289	−	568.280i	−2.52382	−	1.45713i
$391$		−	231.529i		−	0.592147i
$392$	317.801			0.810716
$393$	−560.894			−1.42721
$394$	0.453477	−	0.785445i	0.00115096	−	0.00199352i
$395$		−	895.683i		−	2.26755i
$396$	−12.3987	+	7.15838i	−0.0313098	+	0.0180767i
$397$	−145.444			−0.366357			−0.183178	−	0.983080i	$-0.558639\pi$
$397$	−145.444			−0.366357			−0.183178	+	0.983080i	$0.558639\pi$
$398$	−287.728	−	166.120i	−0.722936	−	0.417387i
$399$			40.4284i			0.101324i
$400$	−384.797	+	666.489i	−0.961993	+	1.66622i
$401$	513.141			1.27965			0.639827	−	0.768519i	$-0.279006\pi$
$401$	513.141			1.27965			0.639827	+	0.768519i	$0.279006\pi$
$402$	95.0756	−	164.676i	0.236506	−	0.409641i
$403$			458.642i			1.13807i
$404$	−165.402	−	286.485i	−0.409411	−	0.709120i
$405$	713.045			1.76060
$406$	23.0756	+	13.3227i	0.0568364	+	0.0328145i
$407$			315.055i			0.774091i
$408$		−	177.245i		−	0.434423i
$409$	−31.7525			−0.0776344			−0.0388172	−	0.999246i	$-0.512359\pi$
$409$	−31.7525			−0.0776344			−0.0388172	+	0.999246i	$0.512359\pi$
$410$	57.7043	−	99.9468i	0.140742	−	0.243773i
$411$		−	471.965i		−	1.14833i
$412$	−328.096	+	189.427i	−0.796350	+	0.459773i
$413$	−233.722			−0.565912
$414$	15.1545	+	8.74944i	0.0366050	+	0.0211339i
$415$			3.22246i			0.00776495i
$416$	349.196	+	604.825i	0.839414	+	1.45391i
$417$	−216.797			−0.519898
$418$	56.7492	−	98.2924i	0.135764	−	0.235149i
$419$			333.998i			0.797131i	0.917140	+	0.398566i	$0.130492\pi$
$419$			333.998i			0.797131i	−0.917140	+	0.398566i	$0.869508\pi$
$420$	158.598	+	274.700i	0.377614	+	0.654047i
$421$	−414.815			−0.985308			−0.492654	−	0.870225i	$-0.663973\pi$
$421$	−414.815			−0.985308			−0.492654	+	0.870225i	$0.663973\pi$
$422$	284.828	+	164.446i	0.674948	+	0.389681i
$423$		−	16.2214i		−	0.0383486i
$424$	−215.395			−0.508008
$425$	−349.921			−0.823344
$426$	−77.4502	+	134.148i	−0.181808	+	0.314901i
$427$			51.4695i			0.120538i
$428$	267.444	−	154.409i	0.624868	−	0.360768i
$429$	865.341			2.01711
$430$	−208.605	−	120.438i	−0.485127	−	0.280088i
$431$		−	109.784i		−	0.254719i	−0.991857	−	0.127359i	$-0.959350\pi$
$431$		−	109.784i		−	0.254719i	0.991857	−	0.127359i	$-0.0406502\pi$
$432$	−368.193	−	212.576i	−0.852298	−	0.492074i
$433$	186.701			0.431180			0.215590	−	0.976484i	$-0.430833\pi$
$433$	186.701			0.431180			0.215590	+	0.976484i	$0.430833\pi$
$434$	64.0000	−	110.851i	0.147465	−	0.255418i
$435$		−	113.907i		−	0.261855i
$436$	44.3505	+	76.8173i	0.101721	+	0.176186i
$437$	−138.725			−0.317449
$438$	585.117	+	337.818i	1.33588	+	0.771273i
$439$		−	285.961i		−	0.651392i	−0.945475	−	0.325696i	$-0.894401\pi$
$439$		−	285.961i		−	0.651392i	0.945475	−	0.325696i	$-0.105599\pi$
$440$		−	890.493i		−	2.02385i
$441$	−10.9211			−0.0247644
$442$	−158.773	+	275.003i	−0.359216	+	0.622180i
$443$			353.485i			0.797935i	0.916965	+	0.398967i	$0.130631\pi$
$443$			353.485i			0.797935i	−0.916965	+	0.398967i	$0.869369\pi$
$444$	255.299	−	147.397i	0.574998	−	0.331975i
$445$	409.100			0.919325
$446$	−250.042	−	144.362i	−0.560631	−	0.323681i
$447$			173.435i			0.387998i
$448$		−	194.910i		−	0.435068i
$449$	674.990			1.50332			0.751659	−	0.659552i	$-0.229254\pi$
$449$	674.990			1.50332			0.751659	+	0.659552i	$0.229254\pi$
$450$	13.2234	−	22.9036i	0.0293854	−	0.0508970i
$451$			87.8685i			0.194830i
$452$	291.395	+	504.712i	0.644680	+	1.11662i
$453$	660.846			1.45882
$454$	−163.777	−	94.5564i	−0.360741	−	0.208274i
$455$		−	568.280i		−	1.24897i
$456$	−106.199			−0.232893
$457$	−404.725			−0.885613			−0.442806	−	0.896617i	$-0.646017\pi$
$457$	−404.725			−0.885613			−0.442806	+	0.896617i	$0.646017\pi$
$458$	82.3987	−	142.719i	0.179910	−	0.311613i
$459$		−	193.309i		−	0.421153i
$460$	−942.598	+	544.209i	−2.04913	+	1.18306i
$461$	−768.743			−1.66755			−0.833777	−	0.552101i	$-0.813826\pi$
$461$	−768.743			−1.66755			−0.833777	+	0.552101i	$0.813826\pi$
$462$	−209.148	−	120.752i	−0.452701	−	0.261367i
$463$			88.3921i			0.190912i	0.995434	+	0.0954559i	$0.0304309\pi$
$463$			88.3921i			0.190912i	−0.995434	+	0.0954559i	$0.969569\pi$
$464$	−34.9967	+	60.6160i	−0.0754239	+	0.130638i
$465$	−547.189			−1.17675
$466$	−253.601	+	439.250i	−0.544209	+	0.942597i
$467$		−	810.453i		−	1.73545i	−0.497049	−	0.867723i	$-0.665583\pi$
$467$		−	810.453i		−	1.73545i	0.497049	−	0.867723i	$-0.334417\pi$
$468$	−12.0000	−	20.7846i	−0.0256410	−	0.0444116i
$469$	95.0756			0.202720
$470$	873.787	+	504.481i	1.85912	+	1.07336i
$471$			941.042i			1.99797i
$472$		−	613.952i		−	1.30074i
$473$	183.395			0.387728
$474$	319.045	−	552.602i	0.673090	−	1.16583i
$475$			209.662i			0.441393i
$476$	76.7492	−	44.3112i	0.161238	−	0.0930907i
$477$	7.40199			0.0155178
$478$	248.973	+	143.744i	0.520863	+	0.300720i
$479$			122.216i			0.255148i	0.991829	+	0.127574i	$0.0407191\pi$
$479$			122.216i			0.255148i	−0.991829	+	0.127574i	$0.959281\pi$
$480$	−721.595	+	416.613i	−1.50332	+	0.867944i
$481$	−528.145			−1.09801
$482$	0.646192	−	1.11924i	0.00134065	−	0.00232207i
$483$			295.181i			0.611141i
$484$	96.9967	+	168.003i	0.200406	+	0.347114i
$485$	−801.100			−1.65175
$486$	25.7043	+	14.8404i	0.0528895	+	0.0305358i
$487$		−	882.727i		−	1.81258i	−0.422654	−	0.906291i	$-0.638902\pi$
$487$		−	882.727i		−	1.81258i	0.422654	−	0.906291i	$-0.361098\pi$
$488$	−135.203			−0.277055
$489$	−439.395			−0.898559
$490$	339.643	−	588.279i	0.693149	−	1.20057i
$491$		−	292.596i		−	0.595918i	−0.954579	−	0.297959i	$-0.903694\pi$
$491$		−	292.596i		−	0.595918i	0.954579	−	0.297959i	$-0.0963059\pi$
$492$	71.2026	−	41.1089i	0.144721	−	0.0835546i
$493$	−31.8248			−0.0645532
$494$	164.773	+	95.1319i	0.333549	+	0.192575i
$495$			30.6015i			0.0618212i
$496$	291.189	+	168.118i	0.587075	+	0.338948i
$497$	−77.4502			−0.155835
$498$	−1.14785	+	1.98813i	−0.00230491	+	0.00399223i
$499$		−	254.669i		−	0.510359i	−0.966894	−	0.255179i	$-0.917865\pi$
$499$		−	254.669i		−	0.510359i	0.966894	−	0.255179i	$-0.0821345\pi$
$500$	394.997	+	684.154i	0.789993	+	1.36831i
$501$	607.492			1.21256
$502$	385.450	+	222.540i	0.767829	+	0.443306i
$503$			652.642i			1.29750i	0.761002	+	0.648750i	$0.224708\pi$
$503$			652.642i			1.29750i	−0.761002	+	0.648750i	$0.775292\pi$
$504$			6.69803i			0.0132897i
$505$	−707.080			−1.40016
$506$	414.344	−	717.665i	0.818861	−	1.41831i
$507$			935.935i			1.84603i
$508$	838.694	−	484.220i	1.65097	−	0.953190i
$509$	448.296			0.880738			0.440369	−	0.897817i	$-0.354848\pi$
$509$	448.296			0.880738			0.440369	+	0.897817i	$0.354848\pi$
$510$	−328.096	−	189.427i	−0.643326	−	0.371425i
$511$			337.818i			0.661091i
$512$	512.000			1.00000
$513$	−115.825			−0.225779
$514$	−64.1512	+	111.113i	−0.124808	+	0.216173i
$515$			809.783i			1.57239i
$516$	−85.8007	−	148.611i	−0.166280	−	0.288006i
$517$	−768.193			−1.48587
$518$	127.650	+	73.6985i	0.246428	+	0.142275i
$519$		−	706.237i		−	1.36076i
$520$	1492.78			2.87074
$521$	573.444			1.10066			0.550330	−	0.834947i	$-0.314502\pi$
$521$	573.444			1.10066			0.550330	+	0.834947i	$0.314502\pi$
$522$	1.20265	−	2.08305i	0.00230393	−	0.00399052i
$523$		−	348.408i		−	0.666173i	−0.942896	−	0.333086i	$-0.891910\pi$
$523$		−	348.408i		−	0.666173i	0.942896	−	0.333086i	$-0.108090\pi$
$524$	637.993	−	368.346i	1.21754	−	0.702950i
$525$	446.120			0.849753
$526$	−156.000	−	90.0666i	−0.296578	−	0.171229i
$527$			152.881i			0.290096i
$528$	317.196	−	549.400i	0.600750	−	1.04053i
$529$	−483.876			−0.914700
$530$	−230.199	+	398.717i	−0.434338	+	0.752296i
$531$			21.0982i			0.0397330i
$532$	−26.5498	−	45.9857i	−0.0499057	−	0.0864392i
$533$	−147.299			−0.276358
$534$	252.399	+	145.722i	0.472657	+	0.272888i
$535$		−	660.084i		−	1.23380i
$536$			249.749i			0.465950i
$537$	366.598			0.682678
$538$	167.993	−	290.973i	0.312255	−	0.540842i
$539$			517.187i			0.959530i
$540$	−786.997	+	454.373i	−1.45740	+	0.841431i
$541$	57.1063			0.105557			0.0527785	−	0.998606i	$-0.483192\pi$
$541$	57.1063			0.105557			0.0527785	+	0.998606i	$0.483192\pi$
$542$	−332.828	−	192.158i	−0.614074	−	0.354536i
$543$			432.457i			0.796423i
$544$	116.399	+	201.608i	0.213968	+	0.370604i
$545$	189.595			0.347880
$546$	202.423	−	350.607i	0.370738	−	0.642136i
$547$		−	84.4159i		−	0.154325i	−0.997019	−	0.0771626i	$-0.975414\pi$
$547$		−	84.4159i		−	0.154325i	0.997019	−	0.0771626i	$-0.0245861\pi$
$548$	309.945	+	536.841i	0.565593	+	0.979637i
$549$	4.64619			0.00846301
$550$	−1084.64	−	626.217i	−1.97207	−	1.13858i
$551$			19.0684i			0.0346069i
$552$	−775.395			−1.40470
$553$	319.045			0.576935
$554$	−241.045	+	417.502i	−0.435099	+	0.753614i
$555$		−	630.110i		−	1.13533i
$556$	246.598	−	142.373i	0.443522	−	0.256067i
$557$	−178.145			−0.319829			−0.159914	−	0.987131i	$-0.551122\pi$
$557$	−178.145			−0.319829			−0.159914	+	0.987131i	$0.551122\pi$
$558$	−10.0066	−	5.77733i	−0.0179330	−	0.0103536i
$559$			307.436i			0.549975i
$560$	−360.797	−	208.306i	−0.644281	−	0.371976i
$561$	288.447			0.514166
$562$	232.646	−	402.955i	0.413961	−	0.717002i
$563$			338.895i			0.601945i	0.953633	+	0.300973i	$0.0973112\pi$
$563$			338.895i			0.601945i	−0.953633	+	0.300973i	$0.902689\pi$
$564$	359.395	+	622.491i	0.637226	+	1.10371i
$565$	1245.69			2.20476
$566$	−190.550	−	110.014i	−0.336660	−	0.194371i
$567$			253.989i			0.447952i
$568$		−	203.450i		−	0.358186i
$569$	−137.251			−0.241214			−0.120607	−	0.992700i	$-0.538484\pi$
$569$	−137.251			−0.241214			−0.120607	+	0.992700i	$0.538484\pi$
$570$	−113.498	+	196.585i	−0.199120	+	0.344886i
$571$			370.083i			0.648132i	0.946034	+	0.324066i	$0.105050\pi$
$571$			370.083i			0.648132i	−0.946034	+	0.324066i	$0.894950\pi$
$572$	−984.289	+	568.280i	−1.72079	+	0.993496i
$573$	−406.725			−0.709817
$574$	35.6013	+	20.5544i	0.0620232	+	0.0358091i
$575$			1530.81i			2.66227i
$576$	−17.5947			−0.0305464
$577$	−845.654			−1.46560			−0.732802	−	0.680442i	$-0.761788\pi$
$577$	−845.654			−1.46560			−0.732802	+	0.680442i	$0.761788\pi$
$578$	236.076	−	408.895i	0.408435	−	0.707431i
$579$		−	49.3347i		−	0.0852067i
$580$	74.8040	+	129.564i	0.128972	+	0.223387i
$581$	−1.14785			−0.00197564
$582$	−494.248	−	285.354i	−0.849223	−	0.490299i
$583$		−	350.533i		−	0.601258i
$584$	−887.395			−1.51951
$585$	−51.2990			−0.0876906
$586$	279.069	−	483.362i	0.476227	−	0.824849i
$587$		−	857.359i		−	1.46058i	−0.683138	−	0.730289i	$-0.739385\pi$
$587$		−	857.359i		−	1.46058i	0.683138	−	0.730289i	$-0.260615\pi$
$588$	419.093	−	241.963i	0.712743	−	0.411503i
$589$	91.6013			0.155520
$590$	−1136.48	−	656.148i	−1.92624	−	1.11212i
$591$		−	1.38105i		−	0.00233681i
$592$	−193.595	+	335.316i	−0.327018	+	0.566412i
$593$	−494.385			−0.833702			−0.416851	−	0.908975i	$-0.636866\pi$
$593$	−494.385			−0.833702			−0.416851	+	0.908975i	$0.636866\pi$
$594$	345.945	−	599.195i	0.582399	−	1.00875i
$595$		−	189.427i		−	0.318364i
$596$	−113.897	−	197.275i	−0.191102	−	0.330999i
$597$	−505.914			−0.847428
$598$	1203.06	+	694.588i	2.01181	+	1.16152i
$599$		−	287.049i		−	0.479213i	−0.970870	−	0.239607i	$-0.922982\pi$
$599$		−	287.049i		−	0.479213i	0.970870	−	0.239607i	$-0.0770184\pi$
$600$			1171.89i			1.95315i
$601$	260.550			0.433527			0.216764	−	0.976224i	$-0.430450\pi$
$601$	260.550			0.433527			0.216764	+	0.976224i	$0.430450\pi$
$602$	42.9003	−	74.3056i	0.0712630	−	0.123431i
$603$		−	8.58254i		−	0.0142331i
$604$	−751.684	+	433.985i	−1.24451	+	0.718519i
$605$	414.653			0.685377
$606$	−436.241	−	251.864i	−0.719869	−	0.415617i
$607$			243.157i			0.400589i	0.979736	+	0.200294i	$0.0641899\pi$
$607$			243.157i			0.400589i	−0.979736	+	0.200294i	$0.935810\pi$
$608$	120.797	−	69.7424i	0.198680	−	0.114708i
$609$	40.5739			0.0666238
$610$	−144.495	+	250.273i	−0.236877	+	0.410283i
$611$		−	1287.77i		−	2.10764i
$612$	−4.00000	−	6.92820i	−0.00653595	−	0.0113206i
$613$	−274.907			−0.448462			−0.224231	−	0.974536i	$-0.571987\pi$
$613$	−274.907			−0.448462			−0.224231	+	0.974536i	$0.571987\pi$
$614$	468.797	+	270.660i	0.763514	+	0.440815i
$615$		−	175.737i		−	0.285751i
$616$	317.196			0.514929
$617$	821.382			1.33125			0.665626	−	0.746286i	$-0.268165\pi$
$617$	821.382			1.33125			0.665626	+	0.746286i	$0.268165\pi$
$618$	−288.447	+	499.605i	−0.466742	+	0.808422i
$619$			1015.87i			1.64115i	0.571540	+	0.820574i	$0.306346\pi$
$619$			1015.87i			1.64115i	−0.571540	+	0.820574i	$0.693654\pi$
$620$	622.405	−	359.346i	1.00388	−	0.579590i
$621$	−845.674			−1.36179
$622$	−599.509	−	346.127i	−0.963841	−	0.556474i
$623$			145.722i			0.233904i
$624$	920.990	+	531.734i	1.47595	+	0.852138i
$625$	486.086			0.777738
$626$	−526.973	+	912.743i	−0.841809	+	1.45806i
$627$		−	172.828i		−	0.275643i
$628$	−617.993	−	1070.40i	−0.984066	−	1.70445i
$629$	−176.048			−0.279886
$630$	12.3987	+	7.15838i	0.0196804	+	0.0113625i
$631$			43.7674i			0.0693619i	0.999398	+	0.0346809i	$0.0110415\pi$
$631$			43.7674i			0.0693619i	−0.999398	+	0.0346809i	$0.988958\pi$
$632$			838.082i			1.32608i
$633$	500.815			0.791177
$634$	−436.918	+	756.764i	−0.689145	+	1.19363i
$635$		−	2070.00i		−	3.25985i
$636$	−284.048	+	163.995i	−0.446617	+	0.257854i
$637$	−866.990			−1.36105
$638$	−98.6462	−	56.9534i	−0.154618	−	0.0892687i
$639$			6.99148i			0.0109413i
$640$	547.189	−	947.760i	0.854983	−	1.48087i
$641$	−483.196			−0.753816			−0.376908	−	0.926251i	$-0.623013\pi$
$641$	−483.196			−0.753816			−0.376908	+	0.926251i	$0.623013\pi$
$642$	235.124	−	407.246i	0.366236	−	0.634340i
$643$		−	625.463i		−	0.972727i	−0.873757	−	0.486363i	$-0.838323\pi$
$643$		−	625.463i		−	0.972727i	0.873757	−	0.486363i	$-0.161677\pi$
$644$	−193.849	−	335.756i	−0.301008	−	0.521360i
$645$	−366.791			−0.568668
$646$	54.9244	+	31.7106i	0.0850223	+	0.0490877i
$647$			654.317i			1.01131i	0.862736	+	0.505654i	$0.168749\pi$
$647$			654.317i			1.01131i	−0.862736	+	0.505654i	$0.831251\pi$
$648$	−667.189			−1.02961
$649$	999.141			1.53951
$650$	1049.76	−	1818.24i	1.61502	−	2.79730i
$651$		−	194.910i		−	0.299402i
$652$	499.794	−	288.556i	0.766555	−	0.442571i
$653$	276.042			0.422728			0.211364	−	0.977407i	$-0.432209\pi$
$653$	276.042			0.422728			0.211364	+	0.977407i	$0.432209\pi$
$654$	116.973	+	67.5342i	0.178857	+	0.103263i
$655$		−	1574.65i		−	2.40404i
$656$	−53.9934	+	93.5193i	−0.0823070	+	0.142560i
$657$	30.4950			0.0464156
$658$	−179.698	+	311.246i	−0.273097	+	0.473018i
$659$		−	84.1756i		−	0.127732i	−0.997958	−	0.0638662i	$-0.979657\pi$
$659$		−	84.1756i		−	0.127732i	0.997958	−	0.0638662i	$-0.0203431\pi$
$660$	−677.993	−	1174.32i	−1.02726	−	1.77927i
$661$	−165.282			−0.250048			−0.125024	−	0.992154i	$-0.539901\pi$
$661$	−165.282			−0.250048			−0.125024	+	0.992154i	$0.539901\pi$
$662$	−350.519	−	202.372i	−0.529485	−	0.305698i
$663$			483.540i			0.729321i
$664$		−	3.01522i		−	0.00454100i
$665$	−113.498			−0.170674
$666$	6.65281	−	11.5230i	0.00998921	−	0.0173018i
$667$			139.224i			0.208732i
$668$	−690.997	+	398.947i	−1.03443	+	0.597226i
$669$	−439.650			−0.657174
$670$	462.309	+	266.914i	0.690013	+	0.398379i
$671$		−	220.028i		−	0.327911i
$672$	−148.399	−	257.034i	−0.220831	−	0.382491i
$673$	487.836			0.724867			0.362434	−	0.932010i	$-0.381946\pi$
$673$	487.836			0.724867			0.362434	+	0.932010i	$0.381946\pi$
$674$	−320.151	+	554.518i	−0.475002	+	0.822727i
$675$			1278.11i			1.89349i
$676$	−614.640	−	1064.59i	−0.909230	−	1.57483i
$677$	−458.767			−0.677646			−0.338823	−	0.940850i	$-0.610029\pi$
$677$	−458.767			−0.677646			−0.338823	+	0.940850i	$0.610029\pi$
$678$	768.543	+	443.719i	1.13354	+	0.654452i
$679$		−	285.354i		−	0.420256i
$680$	497.595			0.731757
$681$	−287.969			−0.422862
$682$	−273.595	+	473.880i	−0.401165	+	0.694839i
$683$		−	628.038i		−	0.919529i	−0.888041	−	0.459764i	$-0.847934\pi$
$683$		−	628.038i		−	0.919529i	0.888041	−	0.459764i	$-0.152066\pi$
$684$	−4.15116	+	2.39667i	−0.00606895	+	0.00350391i
$685$	1324.99			1.93429
$686$	468.017	+	270.210i	0.682241	+	0.393892i
$687$		−	250.943i		−	0.365274i
$688$	195.189	+	112.693i	0.283706	+	0.163797i
$689$	587.619			0.852857
$690$	−828.688	+	1435.33i	−1.20100	+	2.08019i
$691$		−	304.297i		−	0.440372i	−0.975458	−	0.220186i	$-0.929334\pi$
$691$		−	304.297i		−	0.440372i	0.975458	−	0.220186i	$-0.0706665\pi$
$692$	463.794	+	803.315i	0.670223	+	1.16086i
$693$	−10.9003			−0.0157292
$694$	911.128	+	526.040i	1.31286	+	0.757983i
$695$		−	608.635i		−	0.875733i
$696$			106.582i			0.153134i
$697$	−49.0997			−0.0704443
$698$	−471.292	+	816.302i	−0.675204	+	1.16949i
$699$			772.336i			1.10492i
$700$	−507.444	+	292.973i	−0.724919	+	0.418532i
$701$	270.048			0.385233			0.192616	−	0.981274i	$-0.438303\pi$
$701$	270.048			0.385233			0.192616	+	0.981274i	$0.438303\pi$
$702$	1004.46	+	579.928i	1.43086	+	0.826108i
$703$			105.482i			0.150046i
$704$			833.226i			1.18356i
$705$	1536.39			2.17927
$706$	51.3231	−	88.8942i	0.0726956	−	0.125912i
$707$		−	251.864i		−	0.356243i
$708$	−467.444	−	809.636i	−0.660231	−	1.14355i
$709$	339.086			0.478260			0.239130	−	0.970988i	$-0.423138\pi$
$709$	339.086			0.478260			0.239130	+	0.970988i	$0.423138\pi$
$710$	−376.605	−	217.433i	−0.530429	−	0.306243i
$711$		−	28.8004i		−	0.0405069i
$712$	−382.791			−0.537627
$713$	668.811			0.938023
$714$	67.4743	−	116.869i	0.0945018	−	0.163682i
$715$			2429.35i			3.39769i
$716$	−416.990	+	240.749i	−0.582388	+	0.336242i
$717$	437.770			0.610558
$718$	−239.983	−	138.554i	−0.334238	−	0.192972i
$719$			858.647i			1.19422i	0.802158	+	0.597112i	$0.203685\pi$
$719$			858.647i			1.19422i	−0.802158	+	0.597112i	$0.796315\pi$
$720$	−18.8040	+	32.5694i	−0.0261166	+	0.0452353i
$721$	−288.447			−0.400065
$722$	19.0000	−	32.9090i	0.0263158	−	0.0455803i
$723$		−	1.96796i		−	0.00272194i
$724$	−284.000	−	491.902i	−0.392265	−	0.679423i
$725$	210.416			0.290229
$726$	255.825	+	147.700i	0.352376	+	0.203444i
$727$		−	66.2164i		−	0.0910817i	−0.998962	−	0.0455408i	$-0.985499\pi$
$727$		−	66.2164i		−	0.0910817i	0.998962	−	0.0455408i	$-0.0145011\pi$
$728$			531.734i			0.730404i
$729$	−705.392			−0.967616
$730$	−948.385	+	1642.65i	−1.29916	+	2.25021i
$731$			102.479i			0.140190i
$732$	−178.296	+	102.939i	−0.243573	+	0.140627i
$733$	153.238			0.209055			0.104528	−	0.994522i	$-0.466667\pi$
$733$	153.238			0.209055			0.104528	+	0.994522i	$0.466667\pi$
$734$	−1230.49	−	710.423i	−1.67641	−	0.967878i
$735$		−	1034.37i		−	1.40731i
$736$	881.980	−	509.211i	1.19834	−	0.691863i
$737$	−406.440			−0.551479
$738$	1.85546	−	3.21376i	0.00251418	−	0.00435468i
$739$			1339.49i			1.81256i	0.422673	+	0.906282i	$0.361092\pi$
$739$			1339.49i			1.81256i	−0.422673	+	0.906282i	$0.638908\pi$
$740$	413.801	+	716.724i	0.559190	+	0.968546i
$741$	289.722			0.390988
$742$	−142.024	−	81.9976i	−0.191407	−	0.110509i
$743$		−	567.986i		−	0.764450i	−0.924069	−	0.382225i	$-0.875158\pi$
$743$		−	567.986i		−	0.764450i	0.924069	−	0.382225i	$-0.124842\pi$
$744$	512.000			0.688172
$745$	−486.900			−0.653557
$746$	570.767	−	988.597i	0.765103	−	1.32520i
$747$			0.103617i			0.000138711i
$748$	−328.096	+	189.427i	−0.438631	+	0.253244i
$749$	235.124			0.313917
$750$	1041.79	+	601.476i	1.38905	+	0.801968i
$751$		−	774.912i		−	1.03184i	−0.856637	−	0.515920i	$-0.827450\pi$
$751$		−	774.912i		−	1.03184i	0.856637	−	0.515920i	$-0.172550\pi$
$752$	−817.595	−	472.039i	−1.08723	−	0.627711i
$753$	677.739			0.900052
$754$	95.4743	−	165.366i	0.126624	−	0.219319i
$755$			1855.25i			2.45729i
$756$	−161.849	−	280.330i	−0.214086	−	0.370807i
$757$	−166.000			−0.219287			−0.109643	−	0.993971i	$-0.534971\pi$
$757$	−166.000			−0.219287			−0.109643	+	0.993971i	$0.534971\pi$
$758$	−514.567	−	297.086i	−0.678849	−	0.391933i
$759$		−	1261.87i		−	1.66255i
$760$		−	298.143i		−	0.392293i
$761$	794.705			1.04429			0.522145	−	0.852857i	$-0.325132\pi$
$761$	794.705			1.04429			0.522145	+	0.852857i	$0.325132\pi$
$762$	737.341	−	1277.11i	0.967639	−	1.67600i
$763$			67.5342i			0.0885114i
$764$	462.633	−	267.101i	0.605541	−	0.349609i
$765$	−17.0997			−0.0223525
$766$	−1254.63	−	724.363i	−1.63790	−	0.945643i
$767$			1674.92i			2.18373i
$768$	675.189	−	389.821i	0.879153	−	0.507579i
$769$	−982.512			−1.27765			−0.638825	−	0.769352i	$-0.720579\pi$
$769$	−982.512			−1.27765			−0.638825	+	0.769352i	$0.720579\pi$
$770$	338.997	−	587.159i	0.440255	−	0.762545i
$771$			195.371i			0.253399i
$772$	32.3987	+	56.1162i	0.0419672	+	0.0726893i
$773$	−167.262			−0.216380			−0.108190	−	0.994130i	$-0.534505\pi$
$773$	−167.262			−0.216380			−0.108190	+	0.994130i	$0.534505\pi$
$774$	−6.70762	−	3.87264i	−0.00866617	−	0.00500342i
$775$		−	1010.80i		−	1.30426i
$776$	749.581			0.965955
$777$	224.447			0.288863
$778$	−333.890	+	578.315i	−0.429165	+	0.743336i
$779$			29.4190i			0.0377650i
$780$	1968.58	−	1136.56i	2.52382	−	1.45713i
$781$	331.093			0.423935
$782$	401.021	+	231.529i	0.512814	+	0.296073i
$783$			116.242i			0.148457i
$784$	−317.801	+	550.447i	−0.405358	+	0.702101i
$785$	−2641.87			−3.36544
$786$	560.894	−	971.496i	0.713605	−	1.23600i
$787$		−	110.401i		−	0.140281i	−0.997537	−	0.0701404i	$-0.977655\pi$
$787$		−	110.401i		−	0.140281i	0.997537	−	0.0701404i	$-0.0223447\pi$
$788$	0.906954	+	1.57089i	0.00115096	+	0.00199352i
$789$	−274.296			−0.347650
$790$	1551.37	+	895.683i	1.96376	+	1.13378i
$791$			443.719i			0.560959i
$792$		−	28.6335i		−	0.0361534i
$793$	368.846			0.465127
$794$	145.444	−	251.916i	0.183178	−	0.317274i
$795$			701.066i			0.881844i
$796$	575.457	−	332.240i	0.722936	−	0.417387i
$797$	−224.217			−0.281326			−0.140663	−	0.990058i	$-0.544923\pi$
$797$	−224.217			−0.281326			−0.140663	+	0.990058i	$0.544923\pi$
$798$	−70.0241	−	40.4284i	−0.0877495	−	0.0506622i
$799$		−	429.255i		−	0.537240i
$800$	−769.595	−	1332.98i	−0.961993	−	1.66622i
$801$	13.1545			0.0164226
$802$	−513.141	+	888.787i	−0.639827	+	1.10821i
$803$		−	1444.14i		−	1.79843i
$804$	190.151	+	329.351i	0.236506	+	0.409641i
$805$	−828.688			−1.02943
$806$	−794.392	−	458.642i	−0.985598	−	0.569035i
$807$		−	511.620i		−	0.633977i
$808$	661.608			0.818822
$809$	163.179			0.201704			0.100852	−	0.994901i	$-0.467843\pi$
$809$	163.179			0.201704			0.100852	+	0.994901i	$0.467843\pi$
$810$	−713.045	+	1235.03i	−0.880302	+	1.52473i
$811$			79.1723i			0.0976230i	0.998808	+	0.0488115i	$0.0155434\pi$
$811$			79.1723i			0.0976230i	−0.998808	+	0.0488115i	$0.984457\pi$
$812$	−46.1512	+	26.6454i	−0.0568364	+	0.0328145i
$813$	−585.213			−0.719820
$814$	−545.691	−	315.055i	−0.670382	−	0.387045i
$815$		−	1233.55i		−	1.51356i
$816$	306.997	+	177.245i	0.376221	+	0.217212i
$817$	61.4020			0.0751554
$818$	31.7525	−	54.9969i	0.0388172	−	0.0672334i
$819$		−	18.2728i		−	0.0223112i
$820$	115.409	+	199.894i	0.140742	+	0.243773i
$821$	1305.65			1.59032			0.795158	−	0.606402i	$-0.207388\pi$
$821$	1305.65			1.59032			0.795158	+	0.606402i	$0.207388\pi$
$822$	817.468	+	471.965i	0.994486	+	0.574167i
$823$		−	920.017i		−	1.11788i	−0.829207	−	0.558941i	$-0.811208\pi$
$823$		−	920.017i		−	1.11788i	0.829207	−	0.558941i	$-0.188792\pi$
$824$		−	757.706i		−	0.919546i
$825$	−1907.13			−2.31167
$826$	233.722	−	404.818i	0.282956	−	0.490094i
$827$		−	203.586i		−	0.246175i	−0.992396	−	0.123087i	$-0.960720\pi$
$827$		−	203.586i		−	0.246175i	0.992396	−	0.123087i	$-0.0392795\pi$
$828$	−30.3089	+	17.4989i	−0.0366050	+	0.0211339i
$829$	654.416			0.789404			0.394702	−	0.918809i	$-0.370848\pi$
$829$	654.416			0.789404			0.394702	+	0.918809i	$0.370848\pi$
$830$	−5.58146	−	3.22246i	−0.00672465	−	0.00388248i
$831$			734.096i			0.883389i
$832$	−1396.78			−1.67883
$833$	−288.997			−0.346935
$834$	216.797	−	375.504i	0.259949	−	0.450245i
$835$			1705.47i			2.04247i
$836$	113.498	+	196.585i	0.135764	+	0.235149i
$837$	558.405			0.667151
$838$	−578.502	−	333.998i	−0.690336	−	0.398566i
$839$			844.027i			1.00599i	0.864289	+	0.502996i	$0.167769\pi$
$839$			844.027i			1.00599i	−0.864289	+	0.502996i	$0.832231\pi$
$840$	−634.392			−0.755229
$841$	−821.863			−0.977245
$842$	414.815	−	718.480i	0.492654	−	0.853302i
$843$		−	708.518i		−	0.840472i
$844$	−569.656	+	328.891i	−0.674948	+	0.389681i
$845$	−2627.53			−3.10951
$846$	28.0964	+	16.2214i	0.0332108	+	0.0191743i
$847$			147.700i			0.174381i
$848$	215.395	−	373.076i	0.254004	−	0.439948i
$849$	−335.045			−0.394635
$850$	349.921	−	606.081i	0.411672	−	0.713037i
$851$			770.161i			0.905007i
$852$	−154.900	−	268.295i	−0.181808	−	0.314901i
$853$	−60.8871			−0.0713799			−0.0356900	−	0.999363i	$-0.511363\pi$
$853$	−60.8871			−0.0713799			−0.0356900	+	0.999363i	$0.511363\pi$
$854$	−89.1478	−	51.4695i	−0.104389	−	0.0602688i
$855$			10.2456i			0.0119831i
$856$			617.634i			0.721536i
$857$	183.065			0.213611			0.106806	−	0.994280i	$-0.465938\pi$
$857$	183.065			0.213611			0.106806	+	0.994280i	$0.465938\pi$
$858$	−865.341	+	1498.81i	−1.00856	+	1.74687i
$859$			1107.72i			1.28954i	0.764376	+	0.644770i	$0.223047\pi$
$859$			1107.72i			1.28954i	−0.764376	+	0.644770i	$0.776953\pi$
$860$	417.209	−	240.876i	0.485127	−	0.280088i
$861$	62.5980			0.0727038
$862$	190.151	+	109.784i	0.220593	+	0.127359i
$863$		−	480.224i		−	0.556459i	−0.960515	−	0.278229i	$-0.910252\pi$
$863$		−	480.224i		−	0.556459i	0.960515	−	0.278229i	$-0.0897476\pi$
$864$	736.385	−	425.152i	0.852298	−	0.492074i
$865$	1982.68			2.29212
$866$	−186.701	+	323.376i	−0.215590	+	0.373413i
$867$		−	718.962i		−	0.829253i
$868$	128.000	+	221.703i	0.147465	+	0.255418i
$869$	−1363.89			−1.56949
$870$	197.292	+	113.907i	0.226773	+	0.130927i
$871$		−	681.339i		−	0.782249i
$872$	−177.402			−0.203443
$873$	−25.7591			−0.0295064
$874$	138.725	−	240.279i	0.158724	−	0.274919i
$875$			601.476i			0.687401i
$876$	−1170.23	+	675.635i	−1.33588	+	0.771273i
$877$	−749.571			−0.854699			−0.427349	−	0.904087i	$-0.640553\pi$
$877$	−749.571			−0.854699			−0.427349	+	0.904087i	$0.640553\pi$
$878$	495.299	+	285.961i	0.564122	+	0.325696i
$879$		−	849.897i		−	0.966891i
$880$	1542.38	+	890.493i	1.75270	+	1.01192i
$881$	773.890			0.878423			0.439211	−	0.898384i	$-0.355258\pi$
$881$	773.890			0.878423			0.439211	+	0.898384i	$0.355258\pi$
$882$	10.9211	−	18.9159i	0.0123822	−	0.0214466i
$883$		−	480.621i		−	0.544305i	−0.962254	−	0.272152i	$-0.912265\pi$
$883$		−	480.621i		−	0.544305i	0.962254	−	0.272152i	$-0.0877355\pi$
$884$	−317.547	−	550.007i	−0.359216	−	0.622180i
$885$	−1998.28			−2.25795
$886$	−612.254	−	353.485i	−0.691032	−	0.398967i
$887$		−	1167.14i		−	1.31583i	−0.753093	−	0.657915i	$-0.771439\pi$
$887$		−	1167.14i		−	1.31583i	0.753093	−	0.657915i	$-0.228561\pi$
$888$			589.588i			0.663950i
$889$	737.341			0.829404
$890$	−409.100	+	708.581i	−0.459663	+	0.796159i
$891$		−	1085.78i		−	1.21861i
$892$	500.083	−	288.723i	0.560631	−	0.323681i
$893$	−257.196			−0.288013
$894$	−300.399	−	173.435i	−0.336016	−	0.193999i
$895$			1029.18i			1.14993i
$896$	337.595	+	194.910i	0.376780	+	0.217534i
$897$	2115.35			2.35825
$898$	−674.990	+	1169.12i	−0.751659	+	1.30191i
$899$		−	91.9310i		−	0.102259i
$900$	26.4469	+	45.8073i	0.0293854	+	0.0508970i
$901$	195.873			0.217395
$902$	−152.193	−	87.8685i	−0.168728	−	0.0974152i
$903$		−	130.652i		−	0.144686i
$904$	−1165.58			−1.28936
$905$	−1214.08			−1.34152
$906$	−660.846	+	1144.62i	−0.729410	+	1.26338i
$907$			482.055i			0.531483i	0.964044	+	0.265742i	$0.0856168\pi$
$907$			482.055i			0.531483i	−0.964044	+	0.265742i	$0.914383\pi$
$908$	327.553	−	189.113i	0.360741	−	0.208274i
$909$	−22.7359			−0.0250120
$910$	984.289	+	568.280i	1.08164	+	0.624483i
$911$			149.365i			0.163957i	0.996634	+	0.0819785i	$0.0261239\pi$
$911$			149.365i			0.163957i	−0.996634	+	0.0819785i	$0.973876\pi$
$912$	106.199	−	183.943i	0.116447	−	0.201692i
$913$	4.90695			0.00537454
$914$	404.725	−	701.004i	0.442806	−	0.766963i
$915$			440.056i			0.480936i
$916$	164.797	+	285.437i	0.179910	+	0.311613i
$917$	560.894			0.611662
$918$	334.821	+	193.309i	0.364729	+	0.210577i
$919$		−	109.313i		−	0.118948i	−0.998230	−	0.0594741i	$-0.981058\pi$
$919$		−	109.313i		−	0.118948i	0.998230	−	0.0594741i	$-0.0189424\pi$
$920$		−	2176.84i		−	2.36613i
$921$	824.289			0.894994
$922$	768.743	−	1331.50i	0.833777	−	1.44414i
$923$			555.030i			0.601333i
$924$	418.296	−	241.503i	0.452701	−	0.261367i
$925$	1163.98			1.25836
$926$	−153.100	−	88.3921i	−0.165334	−	0.0954559i
$927$			26.0383i			0.0280888i
$928$	−69.9934	−	121.232i	−0.0754239	−	0.130638i
$929$	−1326.61			−1.42800			−0.713998	−	0.700147i	$-0.753118\pi$
$929$	−1326.61			−1.42800			−0.713998	+	0.700147i	$0.753118\pi$
$930$	547.189	−	947.760i	0.588376	−	1.01910i
$931$			173.158i			0.185991i
$932$	−507.203	−	878.501i	−0.544209	−	0.942597i
$933$	−1054.12			−1.12982
$934$	1403.75	+	810.453i	1.50294	+	0.867723i
$935$			809.783i			0.866078i
$936$	48.0000			0.0512821
$937$	1120.95			1.19632			0.598160	−	0.801376i	$-0.295899\pi$
$937$	1120.95			1.19632			0.598160	+	0.801376i	$0.295899\pi$
$938$	−95.0756	+	164.676i	−0.101360	+	0.175560i
$939$			1604.88i			1.70914i
$940$	−1747.57	+	1008.96i	−1.85912	+	1.07336i
$941$	875.963			0.930885			0.465442	−	0.885078i	$-0.345895\pi$
$941$	875.963			0.930885			0.465442	+	0.885078i	$0.345895\pi$
$942$	−1629.93	−	941.042i	−1.73029	−	0.998983i
$943$			214.797i			0.227781i
$944$	1063.40	+	613.952i	1.12648	+	0.650372i
$945$	−691.890			−0.732159
$946$	−183.395	+	317.650i	−0.193864	+	0.335782i
$947$			676.892i			0.714775i	0.933956	+	0.357388i	$0.116333\pi$
$947$			676.892i			0.714775i	−0.933956	+	0.357388i	$0.883667\pi$
$948$	638.090	+	1105.20i	0.673090	+	1.16583i
$949$	2420.90			2.55100
$950$	−363.145	−	209.662i	−0.382257	−	0.220696i
$951$			1330.62i			1.39918i
$952$			177.245i			0.186181i
$953$	−1133.40			−1.18929			−0.594646	−	0.803988i	$-0.702708\pi$
$953$	−1133.40			−1.18929			−0.594646	+	0.803988i	$0.702708\pi$
$954$	−7.40199	+	12.8206i	−0.00775890	+	0.0134388i
$955$		−	1141.84i		−	1.19564i
$956$	−497.945	+	287.489i	−0.520863	+	0.300720i
$957$	−173.450			−0.181244
$958$	−211.684	−	122.216i	−0.220965	−	0.127574i
$959$			471.965i			0.492143i
$960$		−	1666.45i		−	1.73589i
$961$	519.379			0.540457
$962$	528.145	−	914.773i	0.549007	−	0.950908i
$963$		−	21.2248i		−	0.0220403i
$964$	1.29238	+	2.23847i	0.00134065	+	0.00232207i
$965$	138.502			0.143525
$966$	−511.268	−	295.181i	−0.529263	−	0.305570i
$967$		−	388.083i		−	0.401327i	−0.979660	−	0.200663i	$-0.935690\pi$
$967$		−	388.083i		−	0.401327i	0.979660	−	0.200663i	$-0.0643097\pi$
$968$	−387.987			−0.400813
$969$	96.5739			0.0996635
$970$	801.100	−	1387.55i	0.825876	−	1.43046i
$971$			875.819i			0.901977i	0.892530	+	0.450988i	$0.148928\pi$
$971$			875.819i			0.901977i	−0.892530	+	0.450988i	$0.851072\pi$
$972$	−51.4086	+	29.6808i	−0.0528895	+	0.0305358i
$973$	216.797			0.222813
$974$	1528.93	+	882.727i	1.56974	+	0.906291i
$975$		−	3197.03i		−	3.27900i
$976$	135.203	−	234.178i	0.138527	−	0.239936i
$977$	218.131			0.223266			0.111633	−	0.993749i	$-0.464392\pi$
$977$	218.131			0.223266			0.111633	+	0.993749i	$0.464392\pi$
$978$	439.395	−	761.055i	0.449280	−	0.778175i
$979$		−	622.951i		−	0.636314i
$980$	679.286	+	1176.56i	0.693149	+	1.20057i
$981$	6.09636			0.00621443
$982$	506.791	+	292.596i	0.516080	+	0.297959i
$983$		−	84.0793i		−	0.0855334i	−0.999085	−	0.0427667i	$-0.986383\pi$
$983$		−	84.0793i		−	0.0855334i	0.999085	−	0.0427667i	$-0.0136172\pi$
$984$			164.435i			0.167109i
$985$	3.87715			0.00393619
$986$	31.8248	−	55.1221i	0.0322766	−	0.0559048i
$987$			547.265i			0.554473i
$988$	−329.547	+	190.264i	−0.333549	+	0.192575i
$989$	448.316			0.453302
$990$	−53.0033	−	30.6015i	−0.0535387	−	0.0309106i
$991$			318.571i			0.321464i	0.986998	+	0.160732i	$0.0513855\pi$
$991$			318.571i			0.321464i	−0.986998	+	0.160732i	$0.948615\pi$
$992$	−582.379	+	336.237i	−0.587075	+	0.338948i
$993$	−616.320			−0.620664
$994$	77.4502	−	134.148i	0.0779177	−	0.134957i
$995$		−	1420.30i		−	1.42744i
$996$	−2.29570	−	3.97626i	−0.00230491	−	0.00399223i
$997$	1539.22			1.54385			0.771925	−	0.635714i	$-0.219294\pi$
$997$	1539.22			1.54385			0.771925	+	0.635714i	$0.219294\pi$
$998$	441.100	+	254.669i	0.441984	+	0.255179i
$999$			643.025i			0.643669i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.3.b.a.39.4	yes	4
3.2	odd	2		684.3.g.a.343.2		4
4.3	odd	2	inner	76.3.b.a.39.1	✓	4
8.3	odd	2		1216.3.d.a.191.4		4
8.5	even	2		1216.3.d.a.191.1		4
12.11	even	2		684.3.g.a.343.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.a.39.1	✓	4	4.3	odd	2	inner
76.3.b.a.39.4	yes	4	1.1	even	1	trivial
684.3.g.a.343.2		4	3.2	odd	2
684.3.g.a.343.4		4	12.11	even	2
1216.3.d.a.191.1		4	8.5	even	2
1216.3.d.a.191.4		4	8.3	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:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	76.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +3.04547i q^{3} +(-2.00000 - 3.46410i) q^{4} -8.54983 q^{5} +(-5.27492 - 3.04547i) q^{6} -3.04547i q^{7} +8.00000 q^{8} -0.274917 q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +3.04547i q^{3} +(-2.00000 - 3.46410i) q^{4} -8.54983 q^{5} +(-5.27492 - 3.04547i) q^{6} -3.04547i q^{7} +8.00000 q^{8} -0.274917 q^{9} +(8.54983 - 14.8087i) q^{10} +13.0192i q^{11} +(10.5498 - 6.09095i) q^{12} -21.8248 q^{13} +(5.27492 + 3.04547i) q^{14} -26.0383i q^{15} +(-8.00000 + 13.8564i) q^{16} -7.27492 q^{17} +(0.274917 - 0.476171i) q^{18} +4.35890i q^{19} +(17.0997 + 29.6175i) q^{20} +9.27492 q^{21} +(-22.5498 - 13.0192i) q^{22} +31.8257i q^{23} +24.3638i q^{24} +48.0997 q^{25} +(21.8248 - 37.8016i) q^{26} +26.5720i q^{27} +(-10.5498 + 6.09095i) q^{28} +4.37459 q^{29} +(45.0997 + 26.0383i) q^{30} -21.0148i q^{31} +(-16.0000 - 27.7128i) q^{32} -39.6495 q^{33} +(7.27492 - 12.6005i) q^{34} +26.0383i q^{35} +(0.549834 + 0.952341i) q^{36} +24.1993 q^{37} +(-7.54983 - 4.35890i) q^{38} -66.4667i q^{39} -68.3987 q^{40} +6.74917 q^{41} +(-9.27492 + 16.0646i) q^{42} -14.0866i q^{43} +(45.0997 - 26.0383i) q^{44} +2.35050 q^{45} +(-55.1238 - 31.8257i) q^{46} +59.0048i q^{47} +(-42.1993 - 24.3638i) q^{48} +39.7251 q^{49} +(-48.0997 + 83.3111i) q^{50} -22.1556i q^{51} +(43.6495 + 75.6032i) q^{52} -26.9244 q^{53} +(-46.0241 - 26.5720i) q^{54} -111.312i q^{55} -24.3638i q^{56} -13.2749 q^{57} +(-4.37459 + 7.57701i) q^{58} -76.7439i q^{59} +(-90.1993 + 52.0766i) q^{60} -16.9003 q^{61} +(36.3987 + 21.0148i) q^{62} +0.837253i q^{63} +64.0000 q^{64} +186.598 q^{65} +(39.6495 - 68.6750i) q^{66} +31.2186i q^{67} +(14.5498 + 25.2011i) q^{68} -96.9244 q^{69} +(-45.0997 - 26.0383i) q^{70} -25.4312i q^{71} -2.19934 q^{72} -110.924 q^{73} +(-24.1993 + 41.9145i) q^{74} +146.486i q^{75} +(15.0997 - 8.71780i) q^{76} +39.6495 q^{77} +(115.124 + 66.4667i) q^{78} +104.760i q^{79} +(68.3987 - 118.470i) q^{80} -83.3987 q^{81} +(-6.74917 + 11.6899i) q^{82} -0.376903i q^{83} +(-18.5498 - 32.1293i) q^{84} +62.1993 q^{85} +(24.3987 + 14.0866i) q^{86} +13.3227i q^{87} +104.153i q^{88} -47.8488 q^{89} +(-2.35050 + 4.07118i) q^{90} +66.4667i q^{91} +(110.248 - 63.6514i) q^{92} +64.0000 q^{93} +(-102.199 - 59.0048i) q^{94} -37.2679i q^{95} +(84.3987 - 48.7276i) q^{96} +93.6977 q^{97} +(-39.7251 + 68.8059i) q^{98} -3.57919i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9	\( 4 q - 4 q^{2} - 8 q^{4} - 4 q^{5} - 6 q^{6} + 32 q^{8} + 14 q^{9} + 4 q^{10} + 12 q^{12} - 42 q^{13} + 6 q^{14} - 32 q^{16} - 14 q^{17} - 14 q^{18} + 8 q^{20} + 22 q^{21} - 60 q^{22} + 132 q^{25} + 42 q^{26} - 12 q^{28} - 58 q^{29} + 120 q^{30} - 64 q^{32} - 68 q^{33} + 14 q^{34} - 28 q^{36} - 24 q^{37} - 32 q^{40} - 124 q^{41} - 22 q^{42} + 120 q^{44} + 100 q^{45} + 6 q^{46} - 48 q^{48} + 174 q^{49} - 132 q^{50} + 84 q^{52} - 2 q^{53} - 18 q^{54} - 38 q^{57} + 58 q^{58} - 240 q^{60} - 128 q^{61} - 96 q^{62} + 256 q^{64} + 384 q^{65} + 68 q^{66} + 28 q^{68} - 282 q^{69} - 120 q^{70} + 112 q^{72} - 338 q^{73} + 24 q^{74} + 68 q^{77} + 234 q^{78} + 32 q^{80} - 92 q^{81} + 124 q^{82} - 44 q^{84} + 128 q^{85} - 144 q^{86} + 20 q^{89} - 100 q^{90} - 12 q^{92} + 256 q^{93} - 288 q^{94} + 96 q^{96} - 48 q^{97} - 174 q^{98}+O(q^{100}) \) 4 * q - 4 * q^2 - 8 * q^4 - 4 * q^5 - 6 * q^6 + 32 * q^8 + 14 * q^9 + 4 * q^10 + 12 * q^12 - 42 * q^13 + 6 * q^14 - 32 * q^16 - 14 * q^17 - 14 * q^18 + 8 * q^20 + 22 * q^21 - 60 * q^22 + 132 * q^25 + 42 * q^26 - 12 * q^28 - 58 * q^29 + 120 * q^30 - 64 * q^32 - 68 * q^33 + 14 * q^34 - 28 * q^36 - 24 * q^37 - 32 * q^40 - 124 * q^41 - 22 * q^42 + 120 * q^44 + 100 * q^45 + 6 * q^46 - 48 * q^48 + 174 * q^49 - 132 * q^50 + 84 * q^52 - 2 * q^53 - 18 * q^54 - 38 * q^57 + 58 * q^58 - 240 * q^60 - 128 * q^61 - 96 * q^62 + 256 * q^64 + 384 * q^65 + 68 * q^66 + 28 * q^68 - 282 * q^69 - 120 * q^70 + 112 * q^72 - 338 * q^73 + 24 * q^74 + 68 * q^77 + 234 * q^78 + 32 * q^80 - 92 * q^81 + 124 * q^82 - 44 * q^84 + 128 * q^85 - 144 * q^86 + 20 * q^89 - 100 * q^90 - 12 * q^92 + 256 * q^93 - 288 * q^94 + 96 * q^96 - 48 * q^97 - 174 * q^98

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