LMFDB - Embedded newform 684.3.g.a.343.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (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:	$18.6376500822$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 76)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.2
Root			$-1.63746 - 1.52274i$ of defining polynomial
Character	$\chi$	$=$	684.343
Dual form			684.3.g.a.343.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +8.54983 q^{5} -3.04547i q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +8.54983 q^{5} -3.04547i q^{7} -8.00000 q^{8} +(8.54983 - 14.8087i) q^{10} -13.0192i q^{11} -21.8248 q^{13} +(-5.27492 - 3.04547i) q^{14} +(-8.00000 + 13.8564i) q^{16} +7.27492 q^{17} +4.35890i q^{19} +(-17.0997 - 29.6175i) q^{20} +(-22.5498 - 13.0192i) q^{22} -31.8257i q^{23} +48.0997 q^{25} +(-21.8248 + 37.8016i) q^{26} +(-10.5498 + 6.09095i) q^{28} -4.37459 q^{29} -21.0148i q^{31} +(16.0000 + 27.7128i) q^{32} +(7.27492 - 12.6005i) q^{34} -26.0383i q^{35} +24.1993 q^{37} +(7.54983 + 4.35890i) q^{38} -68.3987 q^{40} -6.74917 q^{41} -14.0866i q^{43} +(-45.0997 + 26.0383i) q^{44} +(-55.1238 - 31.8257i) q^{46} -59.0048i q^{47} +39.7251 q^{49} +(48.0997 - 83.3111i) q^{50} +(43.6495 + 75.6032i) q^{52} +26.9244 q^{53} -111.312i q^{55} +24.3638i q^{56} +(-4.37459 + 7.57701i) q^{58} +76.7439i q^{59} -16.9003 q^{61} +(-36.3987 - 21.0148i) q^{62} +64.0000 q^{64} -186.598 q^{65} +31.2186i q^{67} +(-14.5498 - 25.2011i) q^{68} +(-45.0997 - 26.0383i) q^{70} +25.4312i q^{71} -110.924 q^{73} +(24.1993 - 41.9145i) q^{74} +(15.0997 - 8.71780i) q^{76} -39.6495 q^{77} +104.760i q^{79} +(-68.3987 + 118.470i) q^{80} +(-6.74917 + 11.6899i) q^{82} +0.376903i q^{83} +62.1993 q^{85} +(-24.3987 - 14.0866i) q^{86} +104.153i q^{88} +47.8488 q^{89} +66.4667i q^{91} +(-110.248 + 63.6514i) q^{92} +(-102.199 - 59.0048i) q^{94} +37.2679i q^{95} +93.6977 q^{97} +(39.7251 - 68.8059i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8}+O(q^{10}) $ 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8	$ 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8} + 4 q^{10} - 42 q^{13} - 6 q^{14} - 32 q^{16} + 14 q^{17} - 8 q^{20} - 60 q^{22} + 132 q^{25} - 42 q^{26} - 12 q^{28} + 58 q^{29} + 64 q^{32} + 14 q^{34} - 24 q^{37} - 32 q^{40} + 124 q^{41} - 120 q^{44} + 6 q^{46} + 174 q^{49} + 132 q^{50} + 84 q^{52} + 2 q^{53} + 58 q^{58} - 128 q^{61} + 96 q^{62} + 256 q^{64} - 384 q^{65} - 28 q^{68} - 120 q^{70} - 338 q^{73} - 24 q^{74} - 68 q^{77} - 32 q^{80} + 124 q^{82} + 128 q^{85} + 144 q^{86} - 20 q^{89} + 12 q^{92} - 288 q^{94} - 48 q^{97} + 174 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8 + 4 * q^10 - 42 * q^13 - 6 * q^14 - 32 * q^16 + 14 * q^17 - 8 * q^20 - 60 * q^22 + 132 * q^25 - 42 * q^26 - 12 * q^28 + 58 * q^29 + 64 * q^32 + 14 * q^34 - 24 * q^37 - 32 * q^40 + 124 * q^41 - 120 * q^44 + 6 * q^46 + 174 * q^49 + 132 * q^50 + 84 * q^52 + 2 * q^53 + 58 * q^58 - 128 * q^61 + 96 * q^62 + 256 * q^64 - 384 * q^65 - 28 * q^68 - 120 * q^70 - 338 * q^73 - 24 * q^74 - 68 * q^77 - 32 * q^80 + 124 * q^82 + 128 * q^85 + 144 * q^86 - 20 * q^89 + 12 * q^92 - 288 * q^94 - 48 * q^97 + 174 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

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
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$5$	8.54983			1.70997			0.854983	−	0.518655i	$-0.173567\pi$
$5$	8.54983			1.70997			0.854983	+	0.518655i	$0.173567\pi$
$6$		0			0
$7$		−	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			0
$10$	8.54983	−	14.8087i	0.854983	−	1.48087i
$11$		−	13.0192i		−	1.18356i	−0.806100	−	0.591780i	$-0.798426\pi$
$11$		−	13.0192i		−	1.18356i	0.806100	−	0.591780i	$-0.201574\pi$
$12$		0			0
$13$	−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
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$17$	7.27492			0.427936			0.213968	−	0.976841i	$-0.431361\pi$
$17$	7.27492			0.427936			0.213968	+	0.976841i	$0.431361\pi$
$18$		0			0
$19$			4.35890i			0.229416i
$19$			4.35890i			0.229416i
$20$	−17.0997	−	29.6175i	−0.854983	−	1.48087i
$21$		0			0
$22$	−22.5498	−	13.0192i	−1.02499	−	0.591780i
$23$		−	31.8257i		−	1.38373i	−0.722028	−	0.691863i	$-0.756790\pi$
$23$		−	31.8257i		−	1.38373i	0.722028	−	0.691863i	$-0.243210\pi$
$24$		0			0
$25$	48.0997			1.92399
$26$	−21.8248	+	37.8016i	−0.839414	+	1.45391i
$27$		0			0
$28$	−10.5498	+	6.09095i	−0.376780	+	0.217534i
$29$	−4.37459			−0.150848			−0.0754239	−	0.997152i	$-0.524031\pi$
$29$	−4.37459			−0.150848			−0.0754239	+	0.997152i	$0.524031\pi$
$30$		0			0
$31$		−	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
$33$		0			0
$34$	7.27492	−	12.6005i	0.213968	−	0.370604i
$35$		−	26.0383i		−	0.743952i
$36$		0			0
$37$	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
$39$		0			0
$40$	−68.3987			−1.70997
$41$	−6.74917			−0.164614			−0.0823070	−	0.996607i	$-0.526229\pi$
$41$	−6.74917			−0.164614			−0.0823070	+	0.996607i	$0.526229\pi$
$42$		0			0
$43$		−	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
$45$		0			0
$46$	−55.1238	−	31.8257i	−1.19834	−	0.691863i
$47$		−	59.0048i		−	1.25542i	−0.778447	−	0.627711i	$-0.783992\pi$
$47$		−	59.0048i		−	1.25542i	0.778447	−	0.627711i	$-0.216008\pi$
$48$		0			0
$49$	39.7251			0.810716
$50$	48.0997	−	83.3111i	0.961993	−	1.66622i
$51$		0			0
$52$	43.6495	+	75.6032i	0.839414	+	1.45391i
$53$	26.9244			0.508008			0.254004	−	0.967203i	$-0.418252\pi$
$53$	26.9244			0.508008			0.254004	+	0.967203i	$0.418252\pi$
$54$		0			0
$55$		−	111.312i		−	2.02385i
$56$			24.3638i			0.435068i
$57$		0			0
$58$	−4.37459	+	7.57701i	−0.0754239	+	0.130638i
$59$			76.7439i			1.30074i	0.759615	+	0.650372i	$0.225387\pi$
$59$			76.7439i			1.30074i	−0.759615	+	0.650372i	$0.774613\pi$
$60$		0			0
$61$	−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			0
$64$	64.0000			1.00000
$65$	−186.598			−2.87074
$66$		0			0
$67$			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
$69$		0			0
$70$	−45.0997	−	26.0383i	−0.644281	−	0.371976i
$71$			25.4312i			0.358186i	0.983832	+	0.179093i	$0.0573164\pi$
$71$			25.4312i			0.358186i	−0.983832	+	0.179093i	$0.942684\pi$
$72$		0			0
$73$	−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
$75$		0			0
$76$	15.0997	−	8.71780i	0.198680	−	0.114708i
$77$	−39.6495			−0.514929
$78$		0			0
$79$			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
$81$		0			0
$82$	−6.74917	+	11.6899i	−0.0823070	+	0.142560i
$83$			0.376903i			0.00454100i	0.999997	+	0.00227050i	$0.000722723\pi$
$83$			0.376903i			0.00454100i	−0.999997	+	0.00227050i	$0.999277\pi$
$84$		0			0
$85$	62.1993			0.731757
$86$	−24.3987	−	14.0866i	−0.283706	−	0.163797i
$87$		0			0
$88$			104.153i			1.18356i
$89$	47.8488			0.537627			0.268814	−	0.963192i	$-0.413368\pi$
$89$	47.8488			0.537627			0.268814	+	0.963192i	$0.413368\pi$
$90$		0			0
$91$			66.4667i			0.730404i
$92$	−110.248	+	63.6514i	−1.19834	+	0.691863i
$93$		0			0
$94$	−102.199	−	59.0048i	−1.08723	−	0.627711i
$95$			37.2679i			0.392293i
$96$		0			0
$97$	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
$99$		0			0
$100$	−96.1993	−	166.622i	−0.961993	−	1.66622i
$101$	−82.7010			−0.818822			−0.409411	−	0.912350i	$-0.634266\pi$
$101$	−82.7010			−0.818822			−0.409411	+	0.912350i	$0.634266\pi$
$102$		0			0
$103$		−	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
$105$		0			0
$106$	26.9244	−	46.6345i	0.254004	−	0.439948i
$107$		−	77.2043i		−	0.721536i	−0.932656	−	0.360768i	$-0.882515\pi$
$107$		−	77.2043i		−	0.721536i	0.932656	−	0.360768i	$-0.117485\pi$
$108$		0			0
$109$	−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
$111$		0			0
$112$	42.1993	+	24.3638i	0.376780	+	0.217534i
$113$	145.698			1.28936			0.644680	−	0.764453i	$-0.276991\pi$
$113$	145.698			1.28936			0.644680	+	0.764453i	$0.276991\pi$
$114$		0			0
$115$		−	272.105i		−	2.36613i
$116$	8.74917	+	15.1540i	0.0754239	+	0.130638i
$117$		0			0
$118$	132.924	+	76.7439i	1.12648	+	0.650372i
$119$		−	22.1556i		−	0.186181i
$120$		0			0
$121$	−48.4983			−0.400813
$122$	−16.9003	+	29.2722i	−0.138527	+	0.239936i
$123$		0			0
$124$	−72.7974	+	42.0296i	−0.587075	+	0.338948i
$125$	197.498			1.57999
$126$		0			0
$127$			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
$129$		0			0
$130$	−186.598	+	323.197i	−1.43537	+	2.48613i
$131$		−	184.173i		−	1.40590i	−0.711240	−	0.702950i	$-0.751866\pi$
$131$		−	184.173i		−	1.40590i	0.711240	−	0.702950i	$-0.248134\pi$
$132$		0			0
$133$	13.2749			0.0998114
$134$	54.0723	+	31.2186i	0.403524	+	0.232975i
$135$		0			0
$136$	−58.1993			−0.427936
$137$	154.973			1.13119			0.565593	−	0.824684i	$-0.308647\pi$
$137$	154.973			1.13119			0.565593	+	0.824684i	$0.308647\pi$
$138$		0			0
$139$			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
$141$		0			0
$142$	44.0482	+	25.4312i	0.310198	+	0.179093i
$143$			284.140i			1.98699i
$144$		0			0
$145$	−37.4020			−0.257945
$146$	−110.924	+	192.127i	−0.759756	+	1.31594i
$147$		0			0
$148$	−48.3987	−	83.8290i	−0.327018	−	0.566412i
$149$	−56.9485			−0.382205			−0.191102	−	0.981570i	$-0.561206\pi$
$149$	−56.9485			−0.382205			−0.191102	+	0.981570i	$0.561206\pi$
$150$		0			0
$151$		−	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
$153$		0			0
$154$	−39.6495	+	68.6750i	−0.257464	+	0.445941i
$155$		−	179.673i		−	1.15918i
$156$		0			0
$157$	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
$159$		0			0
$160$	136.797	+	236.940i	0.854983	+	1.48087i
$161$	−96.9244			−0.602015
$162$		0			0
$163$			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
$165$		0			0
$166$	0.652815	+	0.376903i	0.00393262	+	0.00227050i
$167$			199.474i			1.19445i	0.802073	+	0.597226i	$0.203731\pi$
$167$			199.474i			1.19445i	−0.802073	+	0.597226i	$0.796269\pi$
$168$		0			0
$169$	307.320			1.81846
$170$	62.1993	−	107.732i	0.365878	−	0.633720i
$171$		0			0
$172$	−48.7974	+	28.1732i	−0.283706	+	0.163797i
$173$	231.897			1.34045			0.670223	−	0.742160i	$-0.266199\pi$
$173$	231.897			1.34045			0.670223	+	0.742160i	$0.266199\pi$
$174$		0			0
$175$		−	146.486i		−	0.837065i
$176$	180.399	+	104.153i	1.02499	+	0.591780i
$177$		0			0
$178$	47.8488	−	82.8766i	0.268814	−	0.465599i
$179$			120.375i			0.672484i	0.941776	+	0.336242i	$0.109156\pi$
$179$			120.375i			0.672484i	−0.941776	+	0.336242i	$0.890844\pi$
$180$		0			0
$181$	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
$183$		0			0
$184$			254.606i			1.38373i
$185$	206.900			1.11838
$186$		0			0
$187$		−	94.7133i		−	0.506488i
$188$	−204.399	+	118.010i	−1.08723	+	0.627711i
$189$		0			0
$190$	64.5498	+	37.2679i	0.339736	+	0.196147i
$191$		−	133.551i		−	0.699218i	−0.936896	−	0.349609i	$-0.886314\pi$
$191$		−	133.551i		−	0.699218i	0.936896	−	0.349609i	$-0.113686\pi$
$192$		0			0
$193$	−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
$195$		0			0
$196$	−79.4502	−	137.612i	−0.405358	−	0.702101i
$197$	0.453477			0.00230191			0.00115096	−	0.999999i	$-0.499634\pi$
$197$	0.453477			0.00230191			0.00115096	+	0.999999i	$0.499634\pi$
$198$		0			0
$199$			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
$201$		0			0
$202$	−82.7010	+	143.242i	−0.409411	+	0.709120i
$203$			13.3227i			0.0656290i
$204$		0			0
$205$	−57.7043			−0.281484
$206$	−164.048	−	94.7133i	−0.796350	−	0.459773i
$207$		0			0
$208$	174.598	−	302.413i	0.839414	−	1.45391i
$209$	56.7492			0.271527
$210$		0			0
$211$		−	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
$213$		0			0
$214$	−133.722	−	77.2043i	−0.624868	−	0.360768i
$215$		−	120.438i		−	0.560176i
$216$		0			0
$217$	−64.0000			−0.294931
$218$	−22.1752	+	38.4087i	−0.101721	+	0.176186i
$219$		0			0
$220$	−385.595	+	222.623i	−1.75270	+	1.01192i
$221$	−158.773			−0.718431
$222$		0			0
$223$			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
$225$		0			0
$226$	145.698	−	252.356i	0.644680	−	1.11662i
$227$		−	94.5564i		−	0.416548i	−0.978070	−	0.208274i	$-0.933215\pi$
$227$		−	94.5564i		−	0.416548i	0.978070	−	0.208274i	$-0.0667846\pi$
$228$		0			0
$229$	−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
$231$		0			0
$232$	34.9967			0.150848
$233$	−253.601			−1.08842			−0.544209	−	0.838950i	$-0.683170\pi$
$233$	−253.601			−1.08842			−0.544209	+	0.838950i	$0.683170\pi$
$234$		0			0
$235$		−	504.481i		−	2.14673i
$236$	265.849	−	153.488i	1.12648	−	0.650372i
$237$		0			0
$238$	−38.3746	−	22.1556i	−0.161238	−	0.0930907i
$239$			143.744i			0.601441i	0.953712	+	0.300720i	$0.0972271\pi$
$239$			143.744i			0.601441i	−0.953712	+	0.300720i	$0.902773\pi$
$240$		0			0
$241$	−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
$243$		0			0
$244$	33.8007	+	58.5445i	0.138527	+	0.239936i
$245$	339.643			1.38630
$246$		0			0
$247$		−	95.1319i		−	0.385149i
$248$			168.118i			0.677896i
$249$		0			0
$250$	197.498	−	342.077i	0.789993	−	1.36831i
$251$			222.540i			0.886613i	0.896370	+	0.443306i	$0.146195\pi$
$251$			222.540i			0.886613i	−0.896370	+	0.443306i	$0.853805\pi$
$252$		0			0
$253$	−414.344			−1.63772
$254$	419.347	+	242.110i	1.65097	+	0.953190i
$255$		0			0
$256$	−128.000	−	221.703i	−0.500000	−	0.866025i
$257$	−64.1512			−0.249615			−0.124808	−	0.992181i	$-0.539831\pi$
$257$	−64.1512			−0.249615			−0.124808	+	0.992181i	$0.539831\pi$
$258$		0			0
$259$		−	73.6985i		−	0.284550i
$260$	373.196	+	646.394i	1.43537	+	2.48613i
$261$		0			0
$262$	−318.997	−	184.173i	−1.21754	−	0.702950i
$263$		−	90.0666i		−	0.342459i	−0.985231	−	0.171229i	$-0.945226\pi$
$263$		−	90.0666i		−	0.342459i	0.985231	−	0.171229i	$-0.0547739\pi$
$264$		0			0
$265$	230.199			0.868677
$266$	13.2749	−	22.9928i	0.0499057	−	0.0864392i
$267$		0			0
$268$	108.145	−	62.4373i	0.403524	−	0.232975i
$269$	167.993			0.624511			0.312255	−	0.949998i	$-0.398916\pi$
$269$	167.993			0.624511			0.312255	+	0.949998i	$0.398916\pi$
$270$		0			0
$271$			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
$273$		0			0
$274$	154.973	−	268.420i	0.565593	−	0.979637i
$275$		−	626.217i		−	2.27715i
$276$		0			0
$277$	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
$279$		0			0
$280$			208.306i			0.743952i
$281$	232.646			0.827922			0.413961	−	0.910295i	$-0.364145\pi$
$281$	232.646			0.827922			0.413961	+	0.910295i	$0.364145\pi$
$282$		0			0
$283$			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
$285$		0			0
$286$	492.145	+	284.140i	1.72079	+	0.993496i
$287$			20.5544i			0.0716182i
$288$		0			0
$289$	−236.076			−0.816871
$290$	−37.4020	+	64.7821i	−0.128972	+	0.223387i
$291$		0			0
$292$	221.849	+	384.253i	0.759756	+	1.31594i
$293$	279.069			0.952454			0.476227	−	0.879322i	$-0.342004\pi$
$293$	279.069			0.952454			0.476227	+	0.879322i	$0.342004\pi$
$294$		0			0
$295$			656.148i			2.22423i
$296$	−193.595			−0.654036
$297$		0			0
$298$	−56.9485	+	98.6377i	−0.191102	+	0.330999i
$299$			694.588i			2.32304i
$300$		0			0
$301$	−42.9003			−0.142526
$302$	−375.842	−	216.993i	−1.24451	−	0.718519i
$303$		0			0
$304$	−60.3987	−	34.8712i	−0.198680	−	0.114708i
$305$	−144.495			−0.473754
$306$		0			0
$307$		−	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
$309$		0			0
$310$	−311.203	−	179.673i	−1.00388	−	0.579590i
$311$		−	346.127i		−	1.11295i	−0.830865	−	0.556474i	$-0.812154\pi$
$311$		−	346.127i		−	1.11295i	0.830865	−	0.556474i	$-0.187846\pi$
$312$		0			0
$313$	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
$315$		0			0
$316$	362.900	−	209.521i	1.14842	−	0.663040i
$317$	−436.918			−1.37829			−0.689145	−	0.724624i	$-0.742014\pi$
$317$	−436.918			−1.37829			−0.689145	+	0.724624i	$0.742014\pi$
$318$		0			0
$319$			56.9534i			0.178537i
$320$	547.189			1.70997
$321$		0			0
$322$	−96.9244	+	167.878i	−0.301008	+	0.521360i
$323$			31.7106i			0.0981753i
$324$		0			0
$325$	−1049.76			−3.23004
$326$	249.897	+	144.278i	0.766555	+	0.442571i
$327$		0			0
$328$	53.9934			0.164614
$329$	−179.698			−0.546194
$330$		0			0
$331$			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
$333$		0			0
$334$	345.498	+	199.474i	1.03443	+	0.597226i
$335$			266.914i			0.796759i
$336$		0			0
$337$	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
$339$		0			0
$340$	−124.399	−	215.465i	−0.365878	−	0.633720i
$341$	−273.595			−0.802331
$342$		0			0
$343$		−	270.210i		−	0.787784i
$344$			112.693i			0.327595i
$345$		0			0
$346$	231.897	−	401.657i	0.670223	−	1.16086i
$347$			526.040i			1.51597i	0.652275	+	0.757983i	$0.273815\pi$
$347$			526.040i			1.51597i	−0.652275	+	0.757983i	$0.726185\pi$
$348$		0			0
$349$	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
$351$		0			0
$352$	360.797	−	208.306i	1.02499	−	0.591780i
$353$	51.3231			0.145391			0.0726956	−	0.997354i	$-0.476840\pi$
$353$	51.3231			0.145391			0.0726956	+	0.997354i	$0.476840\pi$
$354$		0			0
$355$			217.433i			0.612487i
$356$	−95.6977	−	165.753i	−0.268814	−	0.465599i
$357$		0			0
$358$	208.495	+	120.375i	0.582388	+	0.336242i
$359$		−	138.554i		−	0.385944i	−0.981204	−	0.192972i	$-0.938187\pi$
$359$		−	138.554i		−	0.385944i	0.981204	−	0.192972i	$-0.0618127\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	142.000	−	245.951i	0.392265	−	0.679423i
$363$		0			0
$364$	230.248	−	132.933i	0.632548	−	0.365202i
$365$	−948.385			−2.59832
$366$		0			0
$367$			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
$369$		0			0
$370$	206.900	−	358.362i	0.559190	−	0.968546i
$371$		−	81.9976i		−	0.221018i
$372$		0			0
$373$	−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
$375$		0			0
$376$			472.039i			1.25542i
$377$	95.4743			0.253247
$378$		0			0
$379$			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
$381$		0			0
$382$	−231.316	−	133.551i	−0.605541	−	0.349609i
$383$		−	724.363i		−	1.89129i	−0.325206	−	0.945643i	$-0.605434\pi$
$383$		−	724.363i		−	1.89129i	0.325206	−	0.945643i	$-0.394566\pi$
$384$		0			0
$385$	−338.997			−0.880511
$386$	−16.1993	+	28.0581i	−0.0419672	+	0.0726893i
$387$		0			0
$388$	−187.395	−	324.578i	−0.482978	−	0.836542i
$389$	−333.890			−0.858330			−0.429165	−	0.903226i	$-0.641192\pi$
$389$	−333.890			−0.858330			−0.429165	+	0.903226i	$0.641192\pi$
$390$		0			0
$391$		−	231.529i		−	0.592147i
$392$	−317.801			−0.810716
$393$		0			0
$394$	0.453477	−	0.785445i	0.00115096	−	0.00199352i
$395$			895.683i			2.26755i
$396$		0			0
$397$	−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
$399$		0			0
$400$	−384.797	+	666.489i	−0.961993	+	1.66622i
$401$	−513.141			−1.27965			−0.639827	−	0.768519i	$-0.720994\pi$
$401$	−513.141			−1.27965			−0.639827	+	0.768519i	$0.720994\pi$
$402$		0			0
$403$			458.642i			1.13807i
$404$	165.402	+	286.485i	0.409411	+	0.709120i
$405$		0			0
$406$	23.0756	+	13.3227i	0.0568364	+	0.0328145i
$407$		−	315.055i		−	0.774091i
$408$		0			0
$409$	−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
$411$		0			0
$412$	−328.096	+	189.427i	−0.796350	+	0.459773i
$413$	233.722			0.565912
$414$		0			0
$415$			3.22246i			0.00776495i
$416$	−349.196	−	604.825i	−0.839414	−	1.45391i
$417$		0			0
$418$	56.7492	−	98.2924i	0.135764	−	0.235149i
$419$		−	333.998i		−	0.797131i	−0.917140	−	0.398566i	$-0.869508\pi$
$419$		−	333.998i		−	0.797131i	0.917140	−	0.398566i	$-0.130492\pi$
$420$		0			0
$421$	−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
$423$		0			0
$424$	−215.395			−0.508008
$425$	349.921			0.823344
$426$		0			0
$427$			51.4695i			0.120538i
$428$	−267.444	+	154.409i	−0.624868	+	0.360768i
$429$		0			0
$430$	−208.605	−	120.438i	−0.485127	−	0.280088i
$431$			109.784i			0.254719i	0.991857	+	0.127359i	$0.0406502\pi$
$431$			109.784i			0.254719i	−0.991857	+	0.127359i	$0.959350\pi$
$432$		0			0
$433$	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
$435$		0			0
$436$	44.3505	+	76.8173i	0.101721	+	0.176186i
$437$	138.725			0.317449
$438$		0			0
$439$		−	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
$441$		0			0
$442$	−158.773	+	275.003i	−0.359216	+	0.622180i
$443$		−	353.485i		−	0.797935i	−0.916965	−	0.398967i	$-0.869369\pi$
$443$		−	353.485i		−	0.797935i	0.916965	−	0.398967i	$-0.130631\pi$
$444$		0			0
$445$	409.100			0.919325
$446$	250.042	+	144.362i	0.560631	+	0.323681i
$447$		0			0
$448$		−	194.910i		−	0.435068i
$449$	−674.990			−1.50332			−0.751659	−	0.659552i	$-0.770746\pi$
$449$	−674.990			−1.50332			−0.751659	+	0.659552i	$0.770746\pi$
$450$		0			0
$451$			87.8685i			0.194830i
$452$	−291.395	−	504.712i	−0.644680	−	1.11662i
$453$		0			0
$454$	−163.777	−	94.5564i	−0.360741	−	0.208274i
$455$			568.280i			1.24897i
$456$		0			0
$457$	−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
$459$		0			0
$460$	−942.598	+	544.209i	−2.04913	+	1.18306i
$461$	768.743			1.66755			0.833777	−	0.552101i	$-0.186174\pi$
$461$	768.743			1.66755			0.833777	+	0.552101i	$0.186174\pi$
$462$		0			0
$463$			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
$465$		0			0
$466$	−253.601	+	439.250i	−0.544209	+	0.942597i
$467$			810.453i			1.73545i	0.497049	+	0.867723i	$0.334417\pi$
$467$			810.453i			1.73545i	−0.497049	+	0.867723i	$0.665583\pi$
$468$		0			0
$469$	95.0756			0.202720
$470$	−873.787	−	504.481i	−1.85912	−	1.07336i
$471$		0			0
$472$		−	613.952i		−	1.30074i
$473$	−183.395			−0.387728
$474$		0			0
$475$			209.662i			0.441393i
$476$	−76.7492	+	44.3112i	−0.161238	+	0.0930907i
$477$		0			0
$478$	248.973	+	143.744i	0.520863	+	0.300720i
$479$		−	122.216i		−	0.255148i	−0.991829	−	0.127574i	$-0.959281\pi$
$479$		−	122.216i		−	0.255148i	0.991829	−	0.127574i	$-0.0407191\pi$
$480$		0			0
$481$	−528.145			−1.09801
$482$	−0.646192	+	1.11924i	−0.00134065	+	0.00232207i
$483$		0			0
$484$	96.9967	+	168.003i	0.200406	+	0.347114i
$485$	801.100			1.65175
$486$		0			0
$487$		−	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
$489$		0			0
$490$	339.643	−	588.279i	0.693149	−	1.20057i
$491$			292.596i			0.595918i	0.954579	+	0.297959i	$0.0963059\pi$
$491$			292.596i			0.595918i	−0.954579	+	0.297959i	$0.903694\pi$
$492$		0			0
$493$	−31.8248			−0.0645532
$494$	−164.773	−	95.1319i	−0.333549	−	0.192575i
$495$		0			0
$496$	291.189	+	168.118i	0.587075	+	0.338948i
$497$	77.4502			0.155835
$498$		0			0
$499$		−	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
$501$		0			0
$502$	385.450	+	222.540i	0.767829	+	0.443306i
$503$		−	652.642i		−	1.29750i	−0.761002	−	0.648750i	$-0.775292\pi$
$503$		−	652.642i		−	1.29750i	0.761002	−	0.648750i	$-0.224708\pi$
$504$		0			0
$505$	−707.080			−1.40016
$506$	−414.344	+	717.665i	−0.818861	+	1.41831i
$507$		0			0
$508$	838.694	−	484.220i	1.65097	−	0.953190i
$509$	−448.296			−0.880738			−0.440369	−	0.897817i	$-0.645152\pi$
$509$	−448.296			−0.880738			−0.440369	+	0.897817i	$0.645152\pi$
$510$		0			0
$511$			337.818i			0.661091i
$512$	−512.000			−1.00000
$513$		0			0
$514$	−64.1512	+	111.113i	−0.124808	+	0.216173i
$515$		−	809.783i		−	1.57239i
$516$		0			0
$517$	−768.193			−1.48587
$518$	−127.650	−	73.6985i	−0.246428	−	0.142275i
$519$		0			0
$520$	1492.78			2.87074
$521$	−573.444			−1.10066			−0.550330	−	0.834947i	$-0.685498\pi$
$521$	−573.444			−1.10066			−0.550330	+	0.834947i	$0.685498\pi$
$522$		0			0
$523$		−	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
$525$		0			0
$526$	−156.000	−	90.0666i	−0.296578	−	0.171229i
$527$		−	152.881i		−	0.290096i
$528$		0			0
$529$	−483.876			−0.914700
$530$	230.199	−	398.717i	0.434338	−	0.752296i
$531$		0			0
$532$	−26.5498	−	45.9857i	−0.0499057	−	0.0864392i
$533$	147.299			0.276358
$534$		0			0
$535$		−	660.084i		−	1.23380i
$536$		−	249.749i		−	0.465950i
$537$		0			0
$538$	167.993	−	290.973i	0.312255	−	0.540842i
$539$		−	517.187i		−	0.959530i
$540$		0			0
$541$	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
$543$		0			0
$544$	116.399	+	201.608i	0.213968	+	0.370604i
$545$	−189.595			−0.347880
$546$		0			0
$547$		−	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
$549$		0			0
$550$	−1084.64	−	626.217i	−1.97207	−	1.13858i
$551$		−	19.0684i		−	0.0346069i
$552$		0			0
$553$	319.045			0.576935
$554$	241.045	−	417.502i	0.435099	−	0.753614i
$555$		0			0
$556$	246.598	−	142.373i	0.443522	−	0.256067i
$557$	178.145			0.319829			0.159914	−	0.987131i	$-0.448878\pi$
$557$	178.145			0.319829			0.159914	+	0.987131i	$0.448878\pi$
$558$		0			0
$559$			307.436i			0.549975i
$560$	360.797	+	208.306i	0.644281	+	0.371976i
$561$		0			0
$562$	232.646	−	402.955i	0.413961	−	0.717002i
$563$		−	338.895i		−	0.601945i	−0.953633	−	0.300973i	$-0.902689\pi$
$563$		−	338.895i		−	0.601945i	0.953633	−	0.300973i	$-0.0973112\pi$
$564$		0			0
$565$	1245.69			2.20476
$566$	190.550	+	110.014i	0.336660	+	0.194371i
$567$		0			0
$568$		−	203.450i		−	0.358186i
$569$	137.251			0.241214			0.120607	−	0.992700i	$-0.461516\pi$
$569$	137.251			0.241214			0.120607	+	0.992700i	$0.461516\pi$
$570$		0			0
$571$			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
$573$		0			0
$574$	35.6013	+	20.5544i	0.0620232	+	0.0358091i
$575$		−	1530.81i		−	2.66227i
$576$		0			0
$577$	−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
$579$		0			0
$580$	74.8040	+	129.564i	0.128972	+	0.223387i
$581$	1.14785			0.00197564
$582$		0			0
$583$		−	350.533i		−	0.601258i
$584$	887.395			1.51951
$585$		0			0
$586$	279.069	−	483.362i	0.476227	−	0.824849i
$587$			857.359i			1.46058i	0.683138	+	0.730289i	$0.260615\pi$
$587$			857.359i			1.46058i	−0.683138	+	0.730289i	$0.739385\pi$
$588$		0			0
$589$	91.6013			0.155520
$590$	1136.48	+	656.148i	1.92624	+	1.11212i
$591$		0			0
$592$	−193.595	+	335.316i	−0.327018	+	0.566412i
$593$	494.385			0.833702			0.416851	−	0.908975i	$-0.363134\pi$
$593$	494.385			0.833702			0.416851	+	0.908975i	$0.363134\pi$
$594$		0			0
$595$		−	189.427i		−	0.318364i
$596$	113.897	+	197.275i	0.191102	+	0.330999i
$597$		0			0
$598$	1203.06	+	694.588i	2.01181	+	1.16152i
$599$			287.049i			0.479213i	0.970870	+	0.239607i	$0.0770184\pi$
$599$			287.049i			0.479213i	−0.970870	+	0.239607i	$0.922982\pi$
$600$		0			0
$601$	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
$603$		0			0
$604$	−751.684	+	433.985i	−1.24451	+	0.718519i
$605$	−414.653			−0.685377
$606$		0			0
$607$			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
$609$		0			0
$610$	−144.495	+	250.273i	−0.236877	+	0.410283i
$611$			1287.77i			2.10764i
$612$		0			0
$613$	−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
$615$		0			0
$616$	317.196			0.514929
$617$	−821.382			−1.33125			−0.665626	−	0.746286i	$-0.731835\pi$
$617$	−821.382			−1.33125			−0.665626	+	0.746286i	$0.731835\pi$
$618$		0			0
$619$			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
$621$		0			0
$622$	−599.509	−	346.127i	−0.963841	−	0.556474i
$623$		−	145.722i		−	0.233904i
$624$		0			0
$625$	486.086			0.777738
$626$	526.973	−	912.743i	0.841809	−	1.45806i
$627$		0			0
$628$	−617.993	−	1070.40i	−0.984066	−	1.70445i
$629$	176.048			0.279886
$630$		0			0
$631$			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
$633$		0			0
$634$	−436.918	+	756.764i	−0.689145	+	1.19363i
$635$			2070.00i			3.25985i
$636$		0			0
$637$	−866.990			−1.36105
$638$	98.6462	+	56.9534i	0.154618	+	0.0892687i
$639$		0			0
$640$	547.189	−	947.760i	0.854983	−	1.48087i
$641$	483.196			0.753816			0.376908	−	0.926251i	$-0.376987\pi$
$641$	483.196			0.753816			0.376908	+	0.926251i	$0.376987\pi$
$642$		0			0
$643$		−	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
$645$		0			0
$646$	54.9244	+	31.7106i	0.0850223	+	0.0490877i
$647$		−	654.317i		−	1.01131i	−0.862736	−	0.505654i	$-0.831251\pi$
$647$		−	654.317i		−	1.01131i	0.862736	−	0.505654i	$-0.168749\pi$
$648$		0			0
$649$	999.141			1.53951
$650$	−1049.76	+	1818.24i	−1.61502	+	2.79730i
$651$		0			0
$652$	499.794	−	288.556i	0.766555	−	0.442571i
$653$	−276.042			−0.422728			−0.211364	−	0.977407i	$-0.567791\pi$
$653$	−276.042			−0.422728			−0.211364	+	0.977407i	$0.567791\pi$
$654$		0			0
$655$		−	1574.65i		−	2.40404i
$656$	53.9934	−	93.5193i	0.0823070	−	0.142560i
$657$		0			0
$658$	−179.698	+	311.246i	−0.273097	+	0.473018i
$659$			84.1756i			0.127732i	0.997958	+	0.0638662i	$0.0203431\pi$
$659$			84.1756i			0.127732i	−0.997958	+	0.0638662i	$0.979657\pi$
$660$		0			0
$661$	−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
$663$		0			0
$664$		−	3.01522i		−	0.00454100i
$665$	113.498			0.170674
$666$		0			0
$667$			139.224i			0.208732i
$668$	690.997	−	398.947i	1.03443	−	0.597226i
$669$		0			0
$670$	462.309	+	266.914i	0.690013	+	0.398379i
$671$			220.028i			0.327911i
$672$		0			0
$673$	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
$675$		0			0
$676$	−614.640	−	1064.59i	−0.909230	−	1.57483i
$677$	458.767			0.677646			0.338823	−	0.940850i	$-0.389971\pi$
$677$	458.767			0.677646			0.338823	+	0.940850i	$0.389971\pi$
$678$		0			0
$679$		−	285.354i		−	0.420256i
$680$	−497.595			−0.731757
$681$		0			0
$682$	−273.595	+	473.880i	−0.401165	+	0.694839i
$683$			628.038i			0.919529i	0.888041	+	0.459764i	$0.152066\pi$
$683$			628.038i			0.919529i	−0.888041	+	0.459764i	$0.847934\pi$
$684$		0			0
$685$	1324.99			1.93429
$686$	−468.017	−	270.210i	−0.682241	−	0.393892i
$687$		0			0
$688$	195.189	+	112.693i	0.283706	+	0.163797i
$689$	−587.619			−0.852857
$690$		0			0
$691$		−	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
$693$		0			0
$694$	911.128	+	526.040i	1.31286	+	0.757983i
$695$			608.635i			0.875733i
$696$		0			0
$697$	−49.0997			−0.0704443
$698$	471.292	−	816.302i	0.675204	−	1.16949i
$699$		0			0
$700$	−507.444	+	292.973i	−0.724919	+	0.418532i
$701$	−270.048			−0.385233			−0.192616	−	0.981274i	$-0.561697\pi$
$701$	−270.048			−0.385233			−0.192616	+	0.981274i	$0.561697\pi$
$702$		0			0
$703$			105.482i			0.150046i
$704$		−	833.226i		−	1.18356i
$705$		0			0
$706$	51.3231	−	88.8942i	0.0726956	−	0.125912i
$707$			251.864i			0.356243i
$708$		0			0
$709$	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
$711$		0			0
$712$	−382.791			−0.537627
$713$	−668.811			−0.938023
$714$		0			0
$715$			2429.35i			3.39769i
$716$	416.990	−	240.749i	0.582388	−	0.336242i
$717$		0			0
$718$	−239.983	−	138.554i	−0.334238	−	0.192972i
$719$		−	858.647i		−	1.19422i	−0.802158	−	0.597112i	$-0.796315\pi$
$719$		−	858.647i		−	1.19422i	0.802158	−	0.597112i	$-0.203685\pi$
$720$		0			0
$721$	−288.447			−0.400065
$722$	−19.0000	+	32.9090i	−0.0263158	+	0.0455803i
$723$		0			0
$724$	−284.000	−	491.902i	−0.392265	−	0.679423i
$725$	−210.416			−0.290229
$726$		0			0
$727$		−	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
$729$		0			0
$730$	−948.385	+	1642.65i	−1.29916	+	2.25021i
$731$		−	102.479i		−	0.140190i
$732$		0			0
$733$	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
$735$		0			0
$736$	881.980	−	509.211i	1.19834	−	0.691863i
$737$	406.440			0.551479
$738$		0			0
$739$			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
$741$		0			0
$742$	−142.024	−	81.9976i	−0.191407	−	0.110509i
$743$			567.986i			0.764450i	0.924069	+	0.382225i	$0.124842\pi$
$743$			567.986i			0.764450i	−0.924069	+	0.382225i	$0.875158\pi$
$744$		0			0
$745$	−486.900			−0.653557
$746$	−570.767	+	988.597i	−0.765103	+	1.32520i
$747$		0			0
$748$	−328.096	+	189.427i	−0.438631	+	0.253244i
$749$	−235.124			−0.313917
$750$		0			0
$751$		−	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
$753$		0			0
$754$	95.4743	−	165.366i	0.126624	−	0.219319i
$755$		−	1855.25i		−	2.45729i
$756$		0			0
$757$	−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
$759$		0			0
$760$		−	298.143i		−	0.392293i
$761$	−794.705			−1.04429			−0.522145	−	0.852857i	$-0.674868\pi$
$761$	−794.705			−1.04429			−0.522145	+	0.852857i	$0.674868\pi$
$762$		0			0
$763$			67.5342i			0.0885114i
$764$	−462.633	+	267.101i	−0.605541	+	0.349609i
$765$		0			0
$766$	−1254.63	−	724.363i	−1.63790	−	0.945643i
$767$		−	1674.92i		−	2.18373i
$768$		0			0
$769$	−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
$771$		0			0
$772$	32.3987	+	56.1162i	0.0419672	+	0.0726893i
$773$	167.262			0.216380			0.108190	−	0.994130i	$-0.465495\pi$
$773$	167.262			0.216380			0.108190	+	0.994130i	$0.465495\pi$
$774$		0			0
$775$		−	1010.80i		−	1.30426i
$776$	−749.581			−0.965955
$777$		0			0
$778$	−333.890	+	578.315i	−0.429165	+	0.743336i
$779$		−	29.4190i		−	0.0377650i
$780$		0			0
$781$	331.093			0.423935
$782$	−401.021	−	231.529i	−0.512814	−	0.296073i
$783$		0			0
$784$	−317.801	+	550.447i	−0.405358	+	0.702101i
$785$	2641.87			3.36544
$786$		0			0
$787$		−	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
$789$		0			0
$790$	1551.37	+	895.683i	1.96376	+	1.13378i
$791$		−	443.719i		−	0.560959i
$792$		0			0
$793$	368.846			0.465127
$794$	−145.444	+	251.916i	−0.183178	+	0.317274i
$795$		0			0
$796$	575.457	−	332.240i	0.722936	−	0.417387i
$797$	224.217			0.281326			0.140663	−	0.990058i	$-0.455077\pi$
$797$	224.217			0.281326			0.140663	+	0.990058i	$0.455077\pi$
$798$		0			0
$799$		−	429.255i		−	0.537240i
$800$	769.595	+	1332.98i	0.961993	+	1.66622i
$801$		0			0
$802$	−513.141	+	888.787i	−0.639827	+	1.10821i
$803$			1444.14i			1.79843i
$804$		0			0
$805$	−828.688			−1.02943
$806$	794.392	+	458.642i	0.985598	+	0.569035i
$807$		0			0
$808$	661.608			0.818822
$809$	−163.179			−0.201704			−0.100852	−	0.994901i	$-0.532157\pi$
$809$	−163.179			−0.201704			−0.100852	+	0.994901i	$0.532157\pi$
$810$		0			0
$811$			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
$813$		0			0
$814$	−545.691	−	315.055i	−0.670382	−	0.387045i
$815$			1233.55i			1.51356i
$816$		0			0
$817$	61.4020			0.0751554
$818$	−31.7525	+	54.9969i	−0.0388172	+	0.0672334i
$819$		0			0
$820$	115.409	+	199.894i	0.140742	+	0.243773i
$821$	−1305.65			−1.59032			−0.795158	−	0.606402i	$-0.792612\pi$
$821$	−1305.65			−1.59032			−0.795158	+	0.606402i	$0.792612\pi$
$822$		0			0
$823$		−	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
$825$		0			0
$826$	233.722	−	404.818i	0.282956	−	0.490094i
$827$			203.586i			0.246175i	0.992396	+	0.123087i	$0.0392795\pi$
$827$			203.586i			0.246175i	−0.992396	+	0.123087i	$0.960720\pi$
$828$		0			0
$829$	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
$831$		0			0
$832$	−1396.78			−1.67883
$833$	288.997			0.346935
$834$		0			0
$835$			1705.47i			2.04247i
$836$	−113.498	−	196.585i	−0.135764	−	0.235149i
$837$		0			0
$838$	−578.502	−	333.998i	−0.690336	−	0.398566i
$839$		−	844.027i		−	1.00599i	−0.864289	−	0.502996i	$-0.832231\pi$
$839$		−	844.027i		−	1.00599i	0.864289	−	0.502996i	$-0.167769\pi$
$840$		0			0
$841$	−821.863			−0.977245
$842$	−414.815	+	718.480i	−0.492654	+	0.853302i
$843$		0			0
$844$	−569.656	+	328.891i	−0.674948	+	0.389681i
$845$	2627.53			3.10951
$846$		0			0
$847$			147.700i			0.174381i
$848$	−215.395	+	373.076i	−0.254004	+	0.439948i
$849$		0			0
$850$	349.921	−	606.081i	0.411672	−	0.713037i
$851$		−	770.161i		−	0.905007i
$852$		0			0
$853$	−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
$855$		0			0
$856$			617.634i			0.721536i
$857$	−183.065			−0.213611			−0.106806	−	0.994280i	$-0.534062\pi$
$857$	−183.065			−0.213611			−0.106806	+	0.994280i	$0.534062\pi$
$858$		0			0
$859$			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
$861$		0			0
$862$	190.151	+	109.784i	0.220593	+	0.127359i
$863$			480.224i			0.556459i	0.960515	+	0.278229i	$0.0897476\pi$
$863$			480.224i			0.556459i	−0.960515	+	0.278229i	$0.910252\pi$
$864$		0			0
$865$	1982.68			2.29212
$866$	186.701	−	323.376i	0.215590	−	0.373413i
$867$		0			0
$868$	128.000	+	221.703i	0.147465	+	0.255418i
$869$	1363.89			1.56949
$870$		0			0
$871$		−	681.339i		−	0.782249i
$872$	177.402			0.203443
$873$		0			0
$874$	138.725	−	240.279i	0.158724	−	0.274919i
$875$		−	601.476i		−	0.687401i
$876$		0			0
$877$	−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
$879$		0			0
$880$	1542.38	+	890.493i	1.75270	+	1.01192i
$881$	−773.890			−0.878423			−0.439211	−	0.898384i	$-0.644742\pi$
$881$	−773.890			−0.878423			−0.439211	+	0.898384i	$0.644742\pi$
$882$		0			0
$883$		−	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
$885$		0			0
$886$	−612.254	−	353.485i	−0.691032	−	0.398967i
$887$			1167.14i			1.31583i	0.753093	+	0.657915i	$0.228561\pi$
$887$			1167.14i			1.31583i	−0.753093	+	0.657915i	$0.771439\pi$
$888$		0			0
$889$	737.341			0.829404
$890$	409.100	−	708.581i	0.459663	−	0.796159i
$891$		0			0
$892$	500.083	−	288.723i	0.560631	−	0.323681i
$893$	257.196			0.288013
$894$		0			0
$895$			1029.18i			1.14993i
$896$	−337.595	−	194.910i	−0.376780	−	0.217534i
$897$		0			0
$898$	−674.990	+	1169.12i	−0.751659	+	1.30191i
$899$			91.9310i			0.102259i
$900$		0			0
$901$	195.873			0.217395
$902$	152.193	+	87.8685i	0.168728	+	0.0974152i
$903$		0			0
$904$	−1165.58			−1.28936
$905$	1214.08			1.34152
$906$		0			0
$907$			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
$909$		0			0
$910$	984.289	+	568.280i	1.08164	+	0.624483i
$911$		−	149.365i		−	0.163957i	−0.996634	−	0.0819785i	$-0.973876\pi$
$911$		−	149.365i		−	0.163957i	0.996634	−	0.0819785i	$-0.0261239\pi$
$912$		0			0
$913$	4.90695			0.00537454
$914$	−404.725	+	701.004i	−0.442806	+	0.766963i
$915$		0			0
$916$	164.797	+	285.437i	0.179910	+	0.311613i
$917$	−560.894			−0.611662
$918$		0			0
$919$		−	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
$921$		0			0
$922$	768.743	−	1331.50i	0.833777	−	1.44414i
$923$		−	555.030i		−	0.601333i
$924$		0			0
$925$	1163.98			1.25836
$926$	153.100	+	88.3921i	0.165334	+	0.0954559i
$927$		0			0
$928$	−69.9934	−	121.232i	−0.0754239	−	0.130638i
$929$	1326.61			1.42800			0.713998	−	0.700147i	$-0.246882\pi$
$929$	1326.61			1.42800			0.713998	+	0.700147i	$0.246882\pi$
$930$		0			0
$931$			173.158i			0.185991i
$932$	507.203	+	878.501i	0.544209	+	0.942597i
$933$		0			0
$934$	1403.75	+	810.453i	1.50294	+	0.867723i
$935$		−	809.783i		−	0.866078i
$936$		0			0
$937$	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
$939$		0			0
$940$	−1747.57	+	1008.96i	−1.85912	+	1.07336i
$941$	−875.963			−0.930885			−0.465442	−	0.885078i	$-0.654105\pi$
$941$	−875.963			−0.930885			−0.465442	+	0.885078i	$0.654105\pi$
$942$		0			0
$943$			214.797i			0.227781i
$944$	−1063.40	−	613.952i	−1.12648	−	0.650372i
$945$		0			0
$946$	−183.395	+	317.650i	−0.193864	+	0.335782i
$947$		−	676.892i		−	0.714775i	−0.933956	−	0.357388i	$-0.883667\pi$
$947$		−	676.892i		−	0.714775i	0.933956	−	0.357388i	$-0.116333\pi$
$948$		0			0
$949$	2420.90			2.55100
$950$	363.145	+	209.662i	0.382257	+	0.220696i
$951$		0			0
$952$			177.245i			0.186181i
$953$	1133.40			1.18929			0.594646	−	0.803988i	$-0.297292\pi$
$953$	1133.40			1.18929			0.594646	+	0.803988i	$0.297292\pi$
$954$		0			0
$955$		−	1141.84i		−	1.19564i
$956$	497.945	−	287.489i	0.520863	−	0.300720i
$957$		0			0
$958$	−211.684	−	122.216i	−0.220965	−	0.127574i
$959$		−	471.965i		−	0.492143i
$960$		0			0
$961$	519.379			0.540457
$962$	−528.145	+	914.773i	−0.549007	+	0.950908i
$963$		0			0
$964$	1.29238	+	2.23847i	0.00134065	+	0.00232207i
$965$	−138.502			−0.143525
$966$		0			0
$967$		−	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
$969$		0			0
$970$	801.100	−	1387.55i	0.825876	−	1.43046i
$971$		−	875.819i		−	0.901977i	−0.892530	−	0.450988i	$-0.851072\pi$
$971$		−	875.819i		−	0.901977i	0.892530	−	0.450988i	$-0.148928\pi$
$972$		0			0
$973$	216.797			0.222813
$974$	−1528.93	−	882.727i	−1.56974	−	0.906291i
$975$		0			0
$976$	135.203	−	234.178i	0.138527	−	0.239936i
$977$	−218.131			−0.223266			−0.111633	−	0.993749i	$-0.535608\pi$
$977$	−218.131			−0.223266			−0.111633	+	0.993749i	$0.535608\pi$
$978$		0			0
$979$		−	622.951i		−	0.636314i
$980$	−679.286	−	1176.56i	−0.693149	−	1.20057i
$981$		0			0
$982$	506.791	+	292.596i	0.516080	+	0.297959i
$983$			84.0793i			0.0855334i	0.999085	+	0.0427667i	$0.0136172\pi$
$983$			84.0793i			0.0855334i	−0.999085	+	0.0427667i	$0.986383\pi$
$984$		0			0
$985$	3.87715			0.00393619
$986$	−31.8248	+	55.1221i	−0.0322766	+	0.0559048i
$987$		0			0
$988$	−329.547	+	190.264i	−0.333549	+	0.192575i
$989$	−448.316			−0.453302
$990$		0			0
$991$			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
$993$		0			0
$994$	77.4502	−	134.148i	0.0779177	−	0.134957i
$995$			1420.30i			1.42744i
$996$		0			0
$997$	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
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.3.b.a.39.1	✓	4	12.11	even	2
76.3.b.a.39.4	yes	4	3.2	odd	2
684.3.g.a.343.2		4	1.1	even	1	trivial
684.3.g.a.343.4		4	4.3	odd	2	inner
1216.3.d.a.191.1		4	24.5	odd	2
1216.3.d.a.191.4		4	24.11	even	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +8.54983 q^{5} -3.04547i q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +8.54983 q^{5} -3.04547i q^{7} -8.00000 q^{8} +(8.54983 - 14.8087i) q^{10} -13.0192i q^{11} -21.8248 q^{13} +(-5.27492 - 3.04547i) q^{14} +(-8.00000 + 13.8564i) q^{16} +7.27492 q^{17} +4.35890i q^{19} +(-17.0997 - 29.6175i) q^{20} +(-22.5498 - 13.0192i) q^{22} -31.8257i q^{23} +48.0997 q^{25} +(-21.8248 + 37.8016i) q^{26} +(-10.5498 + 6.09095i) q^{28} -4.37459 q^{29} -21.0148i q^{31} +(16.0000 + 27.7128i) q^{32} +(7.27492 - 12.6005i) q^{34} -26.0383i q^{35} +24.1993 q^{37} +(7.54983 + 4.35890i) q^{38} -68.3987 q^{40} -6.74917 q^{41} -14.0866i q^{43} +(-45.0997 + 26.0383i) q^{44} +(-55.1238 - 31.8257i) q^{46} -59.0048i q^{47} +39.7251 q^{49} +(48.0997 - 83.3111i) q^{50} +(43.6495 + 75.6032i) q^{52} +26.9244 q^{53} -111.312i q^{55} +24.3638i q^{56} +(-4.37459 + 7.57701i) q^{58} +76.7439i q^{59} -16.9003 q^{61} +(-36.3987 - 21.0148i) q^{62} +64.0000 q^{64} -186.598 q^{65} +31.2186i q^{67} +(-14.5498 - 25.2011i) q^{68} +(-45.0997 - 26.0383i) q^{70} +25.4312i q^{71} -110.924 q^{73} +(24.1993 - 41.9145i) q^{74} +(15.0997 - 8.71780i) q^{76} -39.6495 q^{77} +104.760i q^{79} +(-68.3987 + 118.470i) q^{80} +(-6.74917 + 11.6899i) q^{82} +0.376903i q^{83} +62.1993 q^{85} +(-24.3987 - 14.0866i) q^{86} +104.153i q^{88} +47.8488 q^{89} +66.4667i q^{91} +(-110.248 + 63.6514i) q^{92} +(-102.199 - 59.0048i) q^{94} +37.2679i q^{95} +93.6977 q^{97} +(39.7251 - 68.8059i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8}+O(q^{10}) \) 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8	\( 4 q + 4 q^{2} - 8 q^{4} + 4 q^{5} - 32 q^{8} + 4 q^{10} - 42 q^{13} - 6 q^{14} - 32 q^{16} + 14 q^{17} - 8 q^{20} - 60 q^{22} + 132 q^{25} - 42 q^{26} - 12 q^{28} + 58 q^{29} + 64 q^{32} + 14 q^{34} - 24 q^{37} - 32 q^{40} + 124 q^{41} - 120 q^{44} + 6 q^{46} + 174 q^{49} + 132 q^{50} + 84 q^{52} + 2 q^{53} + 58 q^{58} - 128 q^{61} + 96 q^{62} + 256 q^{64} - 384 q^{65} - 28 q^{68} - 120 q^{70} - 338 q^{73} - 24 q^{74} - 68 q^{77} - 32 q^{80} + 124 q^{82} + 128 q^{85} + 144 q^{86} - 20 q^{89} + 12 q^{92} - 288 q^{94} - 48 q^{97} + 174 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 - 8 * q^4 + 4 * q^5 - 32 * q^8 + 4 * q^10 - 42 * q^13 - 6 * q^14 - 32 * q^16 + 14 * q^17 - 8 * q^20 - 60 * q^22 + 132 * q^25 - 42 * q^26 - 12 * q^28 + 58 * q^29 + 64 * q^32 + 14 * q^34 - 24 * q^37 - 32 * q^40 + 124 * q^41 - 120 * q^44 + 6 * q^46 + 174 * q^49 + 132 * q^50 + 84 * q^52 + 2 * q^53 + 58 * q^58 - 128 * q^61 + 96 * q^62 + 256 * q^64 - 384 * q^65 - 28 * q^68 - 120 * q^70 - 338 * q^73 - 24 * q^74 - 68 * q^77 - 32 * q^80 + 124 * q^82 + 128 * q^85 + 144 * q^86 - 20 * q^89 + 12 * q^92 - 288 * q^94 - 48 * q^97 + 174 * q^98

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