LMFDB - Embedded newform 572.2.e.a.131.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(131,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("572.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.e (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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			131.6
Root			$0.599676 - 1.28078i$ of defining polynomial
Character	$\chi$	$=$	572.131
Dual form			572.2.e.a.131.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.599676 + 1.28078i) q^{2} +(-1.28078 + 1.53610i) q^{4} +0.561553 q^{5} +4.53448 q^{7} +(-2.73546 - 0.719224i) q^{8} +3.00000 q^{9} +O(q^{10})$	\(q+(0.599676 + 1.28078i) q^{2} +(-1.28078 + 1.53610i) q^{4} +0.561553 q^{5} +4.53448 q^{7} +(-2.73546 - 0.719224i) q^{8} +3.00000 q^{9} +(0.336750 + 0.719224i) q^{10} +(-1.66757 - 2.86692i) q^{11} +1.00000i q^{13} +(2.71922 + 5.80766i) q^{14} +(-0.719224 - 3.93481i) q^{16} +3.12311i q^{17} +(1.79903 + 3.84233i) q^{18} +5.20798 q^{19} +(-0.719224 + 0.862603i) q^{20} +(2.67188 - 3.85500i) q^{22} +1.19935i q^{23} -4.68466 q^{25} +(-1.28078 + 0.599676i) q^{26} +(-5.80766 + 6.96543i) q^{28} +5.68466i q^{29} -7.60669i q^{31} +(4.60831 - 3.28078i) q^{32} +(-4.00000 + 1.87285i) q^{34} +2.54635 q^{35} +(-3.84233 + 4.60831i) q^{36} -8.24621 q^{37} +(3.12311 + 6.67026i) q^{38} +(-1.53610 - 0.403882i) q^{40} +8.56155i q^{41} -5.47091 q^{43} +(6.53966 + 1.11033i) q^{44} +1.68466 q^{45} +(-1.53610 + 0.719224i) q^{46} +5.73384i q^{47} +13.5616 q^{49} +(-2.80928 - 6.00000i) q^{50} +(-1.53610 - 1.28078i) q^{52} -4.24621 q^{53} +(-0.936426 - 1.60993i) q^{55} +(-12.4039 - 3.26131i) q^{56} +(-7.28078 + 3.40896i) q^{58} -4.53448i q^{59} +0.315342i q^{61} +(9.74247 - 4.56155i) q^{62} +13.6035 q^{63} +(6.96543 + 3.93481i) q^{64} +0.561553i q^{65} -10.1530i q^{67} +(-4.79741 - 4.00000i) q^{68} +(1.52699 + 3.26131i) q^{70} -0.410574i q^{71} +(-8.20637 - 2.15767i) q^{72} -14.8078i q^{73} +(-4.94506 - 10.5616i) q^{74} +(-6.67026 + 8.00000i) q^{76} +(-7.56155 - 13.0000i) q^{77} +4.27156 q^{79} +(-0.403882 - 2.20960i) q^{80} +9.00000 q^{81} +(-10.9654 + 5.13416i) q^{82} -3.33513 q^{83} +1.75379i q^{85} +(-3.28078 - 7.00701i) q^{86} +(2.49960 + 9.04168i) q^{88} -2.00000 q^{89} +(1.01025 + 2.15767i) q^{90} +4.53448i q^{91} +(-1.84233 - 1.53610i) q^{92} +(-7.34376 + 3.43845i) q^{94} +2.92456 q^{95} +12.2462 q^{97} +(8.13254 + 17.3693i) q^{98} +(-5.00270 - 8.60076i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9	$ 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9} + 30 q^{14} - 14 q^{16} - 14 q^{20} - 8 q^{22} + 12 q^{25} - 2 q^{26} - 32 q^{34} - 6 q^{36} - 8 q^{38} - 6 q^{44} - 36 q^{45} + 92 q^{49} + 32 q^{53} - 58 q^{56} - 50 q^{58} - 2 q^{64} - 62 q^{70} - 44 q^{77} + 38 q^{80} + 72 q^{81} - 30 q^{82} - 18 q^{86} + 20 q^{88} - 16 q^{89} + 10 q^{92} + 32 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9 + 30 * q^14 - 14 * q^16 - 14 * q^20 - 8 * q^22 + 12 * q^25 - 2 * q^26 - 32 * q^34 - 6 * q^36 - 8 * q^38 - 6 * q^44 - 36 * q^45 + 92 * q^49 + 32 * q^53 - 58 * q^56 - 50 * q^58 - 2 * q^64 - 62 * q^70 - 44 * q^77 + 38 * q^80 + 72 * q^81 - 30 * q^82 - 18 * q^86 + 20 * q^88 - 16 * q^89 + 10 * q^92 + 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.599676	+	1.28078i	0.424035	+	0.905646i
$2$	0.599676	+	1.28078i	0.424035	+	0.905646i
$3$		0			0		1.00000			$0$
$3$		0			0		−1.00000			$\pi$
$4$	−1.28078	+	1.53610i	−0.640388	+	0.768051i
$5$	0.561553			0.251134			0.125567	−	0.992085i	$-0.459925\pi$
$5$	0.561553			0.251134			0.125567	+	0.992085i	$0.459925\pi$
$6$		0			0
$7$	4.53448			1.71387			0.856937	−	0.515421i	$-0.172364\pi$
$7$	4.53448			1.71387			0.856937	+	0.515421i	$0.172364\pi$
$8$	−2.73546	−	0.719224i	−0.967130	−	0.254284i
$9$	3.00000			1.00000
$10$	0.336750	+	0.719224i	0.106490	+	0.227438i
$11$	−1.66757	−	2.86692i	−0.502790	−	0.864409i
$11$	−1.66757	−	2.86692i	−0.502790	−	0.864409i
$12$		0			0
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	2.71922	+	5.80766i	0.726743	+	1.55216i
$15$		0			0
$16$	−0.719224	−	3.93481i	−0.179806	−	0.983702i
$17$			3.12311i			0.757464i	0.925506	+	0.378732i	$0.123640\pi$
$17$			3.12311i			0.757464i	−0.925506	+	0.378732i	$0.876360\pi$
$18$	1.79903	+	3.84233i	0.424035	+	0.905646i
$19$	5.20798			1.19479			0.597397	−	0.801946i	$-0.296202\pi$
$19$	5.20798			1.19479			0.597397	+	0.801946i	$0.296202\pi$
$20$	−0.719224	+	0.862603i	−0.160823	+	0.192884i
$21$		0			0
$22$	2.67188	−	3.85500i	0.569647	−	0.821889i
$23$			1.19935i			0.250082i	0.992152	+	0.125041i	$0.0399063\pi$
$23$			1.19935i			0.250082i	−0.992152	+	0.125041i	$0.960094\pi$
$24$		0			0
$25$	−4.68466			−0.936932
$26$	−1.28078	+	0.599676i	−0.251181	+	0.117606i
$27$		0			0
$28$	−5.80766	+	6.96543i	−1.09754	+	1.31634i
$29$			5.68466i			1.05561i	0.849364	+	0.527807i	$0.176986\pi$
$29$			5.68466i			1.05561i	−0.849364	+	0.527807i	$0.823014\pi$
$30$		0			0
$31$		−	7.60669i		−	1.36620i	−0.730324	−	0.683101i	$-0.760631\pi$
$31$		−	7.60669i		−	1.36620i	0.730324	−	0.683101i	$-0.239369\pi$
$32$	4.60831	−	3.28078i	0.814642	−	0.579965i
$33$		0			0
$34$	−4.00000	+	1.87285i	−0.685994	+	0.321192i
$35$	2.54635			0.430412
$36$	−3.84233	+	4.60831i	−0.640388	+	0.768051i
$37$	−8.24621			−1.35567			−0.677834	−	0.735215i	$-0.737081\pi$
$37$	−8.24621			−1.35567			−0.677834	+	0.735215i	$0.737081\pi$
$38$	3.12311	+	6.67026i	0.506635	+	1.08206i
$39$		0			0
$40$	−1.53610	−	0.403882i	−0.242879	−	0.0638594i
$41$			8.56155i			1.33709i	0.743672	+	0.668545i	$0.233083\pi$
$41$			8.56155i			1.33709i	−0.743672	+	0.668545i	$0.766917\pi$
$42$		0			0
$43$	−5.47091			−0.834306			−0.417153	−	0.908836i	$-0.636972\pi$
$43$	−5.47091			−0.834306			−0.417153	+	0.908836i	$0.636972\pi$
$44$	6.53966	+	1.11033i	0.985891	+	0.167388i
$45$	1.68466			0.251134
$46$	−1.53610	+	0.719224i	−0.226486	+	0.106044i
$47$			5.73384i			0.836366i	0.908363	+	0.418183i	$0.137333\pi$
$47$			5.73384i			0.836366i	−0.908363	+	0.418183i	$0.862667\pi$
$48$		0			0
$49$	13.5616			1.93736
$50$	−2.80928	−	6.00000i	−0.397292	−	0.848528i
$51$		0			0
$52$	−1.53610	−	1.28078i	−0.213019	−	0.177612i
$53$	−4.24621			−0.583262			−0.291631	−	0.956531i	$-0.594198\pi$
$53$	−4.24621			−0.583262			−0.291631	+	0.956531i	$0.594198\pi$
$54$		0			0
$55$	−0.936426	−	1.60993i	−0.126268	−	0.217082i
$56$	−12.4039	−	3.26131i	−1.65754	−	0.435811i
$57$		0			0
$58$	−7.28078	+	3.40896i	−0.956013	+	0.447618i
$59$		−	4.53448i		−	0.590340i	−0.955445	−	0.295170i	$-0.904624\pi$
$59$		−	4.53448i		−	0.590340i	0.955445	−	0.295170i	$-0.0953762\pi$
$60$		0			0
$61$			0.315342i			0.0403753i	0.999796	+	0.0201877i	$0.00642637\pi$
$61$			0.315342i			0.0403753i	−0.999796	+	0.0201877i	$0.993574\pi$
$62$	9.74247	−	4.56155i	1.23729	−	0.579318i
$63$	13.6035			1.71387
$64$	6.96543	+	3.93481i	0.870679	+	0.491851i
$65$			0.561553i			0.0696521i
$66$		0			0
$67$		−	10.1530i		−	1.24039i	−0.784447	−	0.620196i	$-0.787053\pi$
$67$		−	10.1530i		−	1.24039i	0.784447	−	0.620196i	$-0.212947\pi$
$68$	−4.79741	−	4.00000i	−0.581772	−	0.485071i
$69$		0			0
$70$	1.52699	+	3.26131i	0.182510	+	0.389801i
$71$		−	0.410574i		−	0.0487261i	−0.999703	−	0.0243631i	$-0.992244\pi$
$71$		−	0.410574i		−	0.0487261i	0.999703	−	0.0243631i	$-0.00775577\pi$
$72$	−8.20637	−	2.15767i	−0.967130	−	0.254284i
$73$		−	14.8078i		−	1.73312i	−0.499075	−	0.866559i	$-0.666327\pi$
$73$		−	14.8078i		−	1.73312i	0.499075	−	0.866559i	$-0.333673\pi$
$74$	−4.94506	−	10.5616i	−0.574851	−	1.22776i
$75$		0			0
$76$	−6.67026	+	8.00000i	−0.765132	+	0.917663i
$77$	−7.56155	−	13.0000i	−0.861719	−	1.48149i
$78$		0			0
$79$	4.27156			0.480588			0.240294	−	0.970700i	$-0.422756\pi$
$79$	4.27156			0.480588			0.240294	+	0.970700i	$0.422756\pi$
$80$	−0.403882	−	2.20960i	−0.0451554	−	0.247041i
$81$	9.00000			1.00000
$82$	−10.9654	+	5.13416i	−1.21093	+	0.566973i
$83$	−3.33513			−0.366078			−0.183039	−	0.983106i	$-0.558594\pi$
$83$	−3.33513			−0.366078			−0.183039	+	0.983106i	$0.558594\pi$
$84$		0			0
$85$			1.75379i			0.190225i
$86$	−3.28078	−	7.00701i	−0.353775	−	0.755586i
$87$		0			0
$88$	2.49960	+	9.04168i	0.266458	+	0.963847i
$89$	−2.00000			−0.212000			−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000			−0.212000			−0.106000	+	0.994366i	$0.533804\pi$
$90$	1.01025	+	2.15767i	0.106490	+	0.227438i
$91$			4.53448i			0.475343i
$92$	−1.84233	−	1.53610i	−0.192076	−	0.160150i
$93$		0			0
$94$	−7.34376	+	3.43845i	−0.757451	+	0.354649i
$95$	2.92456			0.300053
$96$		0			0
$97$	12.2462			1.24341			0.621707	−	0.783250i	$-0.286439\pi$
$97$	12.2462			1.24341			0.621707	+	0.783250i	$0.286439\pi$
$98$	8.13254	+	17.3693i	0.821511	+	1.75457i
$99$	−5.00270	−	8.60076i	−0.502790	−	0.864409i
$100$	6.00000	−	7.19612i	0.600000	−	0.719612i
$101$		−	13.1231i		−	1.30580i	−0.757445	−	0.652899i	$-0.773553\pi$
$101$		−	13.1231i		−	1.30580i	0.757445	−	0.652899i	$-0.226447\pi$
$102$		0			0
$103$		−	8.39547i		−	0.827230i	−0.910452	−	0.413615i	$-0.864266\pi$
$103$		−	8.39547i		−	0.827230i	0.910452	−	0.413615i	$-0.135734\pi$
$104$	0.719224	−	2.73546i	0.0705257	−	0.268233i
$105$		0			0
$106$	−2.54635	−	5.43845i	−0.247324	−	0.528229i
$107$	2.54635			0.246165			0.123083	−	0.992396i	$-0.460722\pi$
$107$	2.54635			0.246165			0.123083	+	0.992396i	$0.460722\pi$
$108$		0			0
$109$		−	2.00000i		−	0.191565i	−0.995402	−	0.0957826i	$-0.969465\pi$
$109$		−	2.00000i		−	0.191565i	0.995402	−	0.0957826i	$-0.0305354\pi$
$110$	1.50040	−	2.16479i	0.143058	−	0.206404i
$111$		0			0
$112$	−3.26131	−	17.8423i	−0.308165	−	1.68594i
$113$	7.68466			0.722912			0.361456	−	0.932389i	$-0.382280\pi$
$113$	7.68466			0.722912			0.361456	+	0.932389i	$0.382280\pi$
$114$		0			0
$115$			0.673500i			0.0628042i
$116$	−8.73222	−	7.28078i	−0.810766	−	0.676003i
$117$			3.00000i			0.277350i
$118$	5.80766	−	2.71922i	0.534639	−	0.250325i
$119$			14.1617i			1.29820i
$120$		0			0
$121$	−5.43845	+	9.56155i	−0.494404	+	0.869232i
$122$	−0.403882	+	0.189103i	−0.0365658	+	0.0171206i
$123$		0			0
$124$	11.6847	+	9.74247i	1.04931	+	0.874900i
$125$	−5.43845			−0.486430
$126$	8.15767	+	17.4230i	0.726743	+	1.55216i
$127$	−9.89012			−0.877606			−0.438803	−	0.898583i	$-0.644597\pi$
$127$	−9.89012			−0.877606			−0.438803	+	0.898583i	$0.644597\pi$
$128$	−0.862603	+	11.2808i	−0.0762440	+	0.997089i
$129$		0			0
$130$	−0.719224	+	0.336750i	−0.0630801	+	0.0295349i
$131$	−15.8869			−1.38804			−0.694022	−	0.719954i	$-0.744163\pi$
$131$	−15.8869			−1.38804			−0.694022	+	0.719954i	$0.744163\pi$
$132$		0			0
$133$	23.6155			2.04773
$134$	13.0038	−	6.08854i	1.12336	−	0.525970i
$135$		0			0
$136$	2.24621	−	8.54312i	0.192611	−	0.732566i
$137$	−21.3693			−1.82570			−0.912852	−	0.408291i	$-0.866125\pi$
$137$	−21.3693			−1.82570			−0.912852	+	0.408291i	$0.866125\pi$
$138$		0			0
$139$	−17.6121			−1.49384			−0.746919	−	0.664915i	$-0.768468\pi$
$139$	−17.6121			−1.49384			−0.746919	+	0.664915i	$0.768468\pi$
$140$	−3.26131	+	3.91146i	−0.275631	+	0.330579i
$141$		0			0
$142$	0.525853	−	0.246211i	0.0441286	−	0.0206616i
$143$	2.86692	−	1.66757i	0.239744	−	0.139449i
$144$	−2.15767	−	11.8044i	−0.179806	−	0.983702i
$145$			3.19224i			0.265101i
$146$	18.9654	−	8.87987i	1.56959	−	0.734903i
$147$		0			0
$148$	10.5616	−	12.6670i	0.868154	−	1.04122i
$149$			18.4924i			1.51496i	0.652859	+	0.757479i	$0.273569\pi$
$149$			18.4924i			1.51496i	−0.652859	+	0.757479i	$0.726431\pi$
$150$		0			0
$151$	6.55498			0.533437			0.266719	−	0.963774i	$-0.414061\pi$
$151$	6.55498			0.533437			0.266719	+	0.963774i	$0.414061\pi$
$152$	−14.2462	−	3.74571i	−1.15552	−	0.303817i
$153$			9.36932i			0.757464i
$154$	12.1156	−	17.4805i	0.976304	−	1.40861i
$155$		−	4.27156i		−	0.343100i
$156$		0			0
$157$	8.00000			0.638470			0.319235	−	0.947676i	$-0.396574\pi$
$157$	8.00000			0.638470			0.319235	+	0.947676i	$0.396574\pi$
$158$	2.56155	+	5.47091i	0.203786	+	0.435242i
$159$		0			0
$160$	2.58781	−	1.84233i	0.204584	−	0.145649i
$161$			5.43845i			0.428610i
$162$	5.39709	+	11.5270i	0.424035	+	0.905646i
$163$			6.40734i			0.501861i	0.968005	+	0.250931i	$0.0807366\pi$
$163$			6.40734i			0.501861i	−0.968005	+	0.250931i	$0.919263\pi$
$164$	−13.1514	−	10.9654i	−1.02695	−	0.856257i
$165$		0			0
$166$	−2.00000	−	4.27156i	−0.155230	−	0.331537i
$167$	−0.262926			−0.0203459			−0.0101729	−	0.999948i	$-0.503238\pi$
$167$	−0.262926			−0.0203459			−0.0101729	+	0.999948i	$0.503238\pi$
$168$		0			0
$169$	−1.00000			−0.0769231
$170$	−2.24621	+	1.05171i	−0.172277	+	0.0806621i
$171$	15.6240			1.19479
$172$	7.00701	−	8.40388i	0.534280	−	0.640790i
$173$		−	16.8078i		−	1.27787i	−0.769260	−	0.638935i	$-0.779375\pi$
$173$		−	16.8078i		−	1.27787i	0.769260	−	0.638935i	$-0.220625\pi$
$174$		0			0
$175$	−21.2425			−1.60578
$176$	−10.0814	+	8.62351i	−0.759916	+	0.650021i
$177$		0			0
$178$	−1.19935	−	2.56155i	−0.0898953	−	0.191997i
$179$		−	14.1617i		−	1.05849i	−0.848468	−	0.529247i	$-0.822475\pi$
$179$		−	14.1617i		−	1.05849i	0.848468	−	0.529247i	$-0.177525\pi$
$180$	−2.15767	+	2.58781i	−0.160823	+	0.192884i
$181$	1.75379			0.130358			0.0651790	−	0.997874i	$-0.479238\pi$
$181$	1.75379			0.130358			0.0651790	+	0.997874i	$0.479238\pi$
$182$	−5.80766	+	2.71922i	−0.430492	+	0.201562i
$183$		0			0
$184$	0.862603	−	3.28078i	0.0635919	−	0.241862i
$185$	−4.63068			−0.340455
$186$		0			0
$187$	8.95369	−	5.20798i	0.654759	−	0.380846i
$188$	−8.80776	−	7.34376i	−0.642372	−	0.535599i
$189$		0			0
$190$	1.75379	+	3.74571i	0.127233	+	0.271742i
$191$		−	1.72521i		−	0.124832i	−0.998050	−	0.0624158i	$-0.980120\pi$
$191$		−	1.72521i		−	0.124832i	0.998050	−	0.0624158i	$-0.0198805\pi$
$192$		0			0
$193$			4.24621i			0.305649i	0.988253	+	0.152824i	$0.0488369\pi$
$193$			4.24621i			0.305649i	−0.988253	+	0.152824i	$0.951163\pi$
$194$	7.34376	+	15.6847i	0.527252	+	1.12609i
$195$		0			0
$196$	−17.3693	+	20.8319i	−1.24067	+	1.48800i
$197$		−	5.36932i		−	0.382548i	−0.981537	−	0.191274i	$-0.938738\pi$
$197$		−	5.36932i		−	0.382548i	0.981537	−	0.191274i	$-0.0612619\pi$
$198$	8.01565	−	11.5650i	0.569647	−	0.821889i
$199$			5.99676i			0.425099i	0.977150	+	0.212550i	$0.0681767\pi$
$199$			5.99676i			0.425099i	−0.977150	+	0.212550i	$0.931823\pi$
$200$	12.8147	+	3.36932i	0.906134	+	0.238247i
$201$		0			0
$202$	16.8078	−	7.86962i	1.18259	−	0.553704i
$203$			25.7770i			1.80919i
$204$		0			0
$205$			4.80776i			0.335789i
$206$	10.7527	−	5.03457i	0.749177	−	0.350775i
$207$			3.59806i			0.250082i
$208$	3.93481	−	0.719224i	0.272830	−	0.0498692i
$209$	−8.68466	−	14.9309i	−0.600730	−	1.03279i
$210$		0			0
$211$	17.6121			1.21247			0.606233	−	0.795287i	$-0.292680\pi$
$211$	17.6121			1.21247			0.606233	+	0.795287i	$0.292680\pi$
$212$	5.43845	−	6.52262i	0.373514	−	0.447975i
$213$		0			0
$214$	1.52699	+	3.26131i	0.104383	+	0.222938i
$215$	−3.07221			−0.209523
$216$		0			0
$217$		−	34.4924i		−	2.34150i
$218$	2.56155	−	1.19935i	0.173490	−	0.0812304i
$219$		0			0
$220$	3.67237	+	0.623508i	0.247591	+	0.0420369i
$221$	−3.12311			−0.210083
$222$		0			0
$223$			23.3459i			1.56336i	0.623681	+	0.781679i	$0.285637\pi$
$223$			23.3459i			1.56336i	−0.623681	+	0.781679i	$0.714363\pi$
$224$	20.8963	−	14.8766i	1.39619	−	0.993987i
$225$	−14.0540			−0.936932
$226$	4.60831	+	9.84233i	0.306540	+	0.654702i
$227$	−15.6240			−1.03700			−0.518499	−	0.855078i	$-0.673509\pi$
$227$	−15.6240			−1.03700			−0.518499	+	0.855078i	$0.673509\pi$
$228$		0			0
$229$	5.19224			0.343113			0.171556	−	0.985174i	$-0.445120\pi$
$229$	5.19224			0.343113			0.171556	+	0.985174i	$0.445120\pi$
$230$	−0.862603	+	0.403882i	−0.0568783	+	0.0266312i
$231$		0			0
$232$	4.08854	−	15.5501i	0.268426	−	1.02092i
$233$		−	9.12311i		−	0.597675i	−0.954304	−	0.298837i	$-0.903401\pi$
$233$		−	9.12311i		−	0.597675i	0.954304	−	0.298837i	$-0.0965988\pi$
$234$	−3.84233	+	1.79903i	−0.251181	+	0.117606i
$235$			3.21985i			0.210040i
$236$	6.96543	+	5.80766i	0.453411	+	0.378047i
$237$		0			0
$238$	−18.1379	+	8.49242i	−1.17571	+	0.550482i
$239$	−2.13578			−0.138152			−0.0690760	−	0.997611i	$-0.522005\pi$
$239$	−2.13578			−0.138152			−0.0690760	+	0.997611i	$0.522005\pi$
$240$		0			0
$241$			2.49242i			0.160551i	0.996773	+	0.0802755i	$0.0255800\pi$
$241$			2.49242i			0.160551i	−0.996773	+	0.0802755i	$0.974420\pi$
$242$	−15.5075	−	1.23160i	−0.996861	−	0.0791701i
$243$		0			0
$244$	−0.484397	−	0.403882i	−0.0310103	−	0.0258559i
$245$	7.61553			0.486538
$246$		0			0
$247$			5.20798i			0.331376i
$248$	−5.47091	+	20.8078i	−0.347403	+	1.32129i
$249$		0			0
$250$	−3.26131	−	6.96543i	−0.206263	−	0.440533i
$251$			22.4095i			1.41447i	0.706976	+	0.707237i	$0.250059\pi$
$251$			22.4095i			1.41447i	−0.706976	+	0.707237i	$0.749941\pi$
$252$	−17.4230	+	20.8963i	−1.09754	+	1.31634i
$253$	3.43845	−	2.00000i	0.216173	−	0.125739i
$254$	−5.93087	−	12.6670i	−0.372136	−	0.794800i
$255$		0			0
$256$	−14.9654	+	5.66001i	−0.935340	+	0.353751i
$257$	−30.8078			−1.92174			−0.960868	−	0.277007i	$-0.910657\pi$
$257$	−30.8078			−1.92174			−0.960868	+	0.277007i	$0.910657\pi$
$258$		0			0
$259$	−37.3923			−2.32345
$260$	−0.862603	−	0.719224i	−0.0534964	−	0.0446044i
$261$			17.0540i			1.05561i
$262$	−9.52699	−	20.3475i	−0.588579	−	1.25708i
$263$	26.1552			1.61280			0.806399	−	0.591371i	$-0.201413\pi$
$263$	26.1552			1.61280			0.806399	+	0.591371i	$0.201413\pi$
$264$		0			0
$265$	−2.38447			−0.146477
$266$	14.1617	+	30.2462i	0.868308	+	1.85451i
$267$		0			0
$268$	15.5961	+	13.0038i	0.952685	+	0.794332i
$269$	−2.87689			−0.175407			−0.0877037	−	0.996147i	$-0.527953\pi$
$269$	−2.87689			−0.175407			−0.0877037	+	0.996147i	$0.527953\pi$
$270$		0			0
$271$	13.2252			0.803377			0.401688	−	0.915776i	$-0.368424\pi$
$271$	13.2252			0.803377			0.401688	+	0.915776i	$0.368424\pi$
$272$	12.2888	−	2.24621i	0.745119	−	0.136197i
$273$		0			0
$274$	−12.8147	−	27.3693i	−0.774163	−	1.65344i
$275$	7.81198	+	13.4305i	0.471080	+	0.809892i
$276$		0			0
$277$		−	1.43845i		−	0.0864279i	−0.999066	−	0.0432140i	$-0.986240\pi$
$277$		−	1.43845i		−	0.0864279i	0.999066	−	0.0432140i	$-0.0137597\pi$
$278$	−10.5616	−	22.5571i	−0.633440	−	1.35289i
$279$		−	22.8201i		−	1.36620i
$280$	−6.96543	−	1.83140i	−0.416264	−	0.109447i
$281$		−	4.56155i		−	0.272119i	−0.990701	−	0.136060i	$-0.956556\pi$
$281$		−	4.56155i		−	0.272119i	0.990701	−	0.136060i	$-0.0434439\pi$
$282$		0			0
$283$	−27.3546			−1.62606			−0.813030	−	0.582222i	$-0.802183\pi$
$283$	−27.3546			−1.62606			−0.813030	+	0.582222i	$0.802183\pi$
$284$	0.630683	+	0.525853i	0.0374242	+	0.0312036i
$285$		0			0
$286$	3.85500	+	2.67188i	0.227951	+	0.157992i
$287$			38.8222i			2.29160i
$288$	13.8249	−	9.84233i	0.814642	−	0.579965i
$289$	7.24621			0.426248
$290$	−4.08854	+	1.91431i	−0.240087	+	0.112412i
$291$		0			0
$292$	22.7462	+	18.9654i	1.33112	+	1.10987i
$293$			19.1231i			1.11718i	0.829443	+	0.558592i	$0.188658\pi$
$293$			19.1231i			1.11718i	−0.829443	+	0.558592i	$0.811342\pi$
$294$		0			0
$295$		−	2.54635i		−	0.148254i
$296$	22.5571	+	5.93087i	1.31111	+	0.344725i
$297$		0			0
$298$	−23.6847	+	11.0895i	−1.37202	+	0.642396i
$299$	−1.19935			−0.0693604
$300$		0			0
$301$	−24.8078			−1.42990
$302$	3.93087	+	8.39547i	0.226196	+	0.483105i
$303$		0			0
$304$	−3.74571	−	20.4924i	−0.214831	−	1.17532i
$305$			0.177081i			0.0101396i
$306$	−12.0000	+	5.61856i	−0.685994	+	0.321192i
$307$	4.68213			0.267223			0.133612	−	0.991034i	$-0.457343\pi$
$307$	4.68213			0.267223			0.133612	+	0.991034i	$0.457343\pi$
$308$	29.6540	+	5.03477i	1.68969	+	0.286883i
$309$		0			0
$310$	5.47091	−	2.56155i	0.310727	−	0.145486i
$311$			26.1552i			1.48313i	0.670884	+	0.741563i	$0.265915\pi$
$311$			26.1552i			1.48313i	−0.670884	+	0.741563i	$0.734085\pi$
$312$		0			0
$313$	−31.6847			−1.79092			−0.895461	−	0.445139i	$-0.853154\pi$
$313$	−31.6847			−1.79092			−0.895461	+	0.445139i	$0.853154\pi$
$314$	4.79741	+	10.2462i	0.270734	+	0.578227i
$315$	7.63906			0.430412
$316$	−5.47091	+	6.56155i	−0.307763	+	0.369116i
$317$	34.1771			1.91958			0.959788	−	0.280726i	$-0.0905751\pi$
$317$	34.1771			1.91958			0.959788	+	0.280726i	$0.0905751\pi$
$318$		0			0
$319$	16.2975	−	9.47954i	0.912482	−	0.530753i
$320$	3.91146	+	2.20960i	0.218657	+	0.123521i
$321$		0			0
$322$	−6.96543	+	3.26131i	−0.388169	+	0.181746i
$323$			16.2651i			0.905014i
$324$	−11.5270	+	13.8249i	−0.640388	+	0.768051i
$325$		−	4.68466i		−	0.259858i
$326$	−8.20637	+	3.84233i	−0.454509	+	0.212807i
$327$		0			0
$328$	6.15767	−	23.4197i	0.340000	−	1.29314i
$329$			26.0000i			1.43343i
$330$		0			0
$331$		−	32.5625i		−	1.78980i	−0.446268	−	0.894900i	$-0.647247\pi$
$331$		−	32.5625i		−	1.78980i	0.446268	−	0.894900i	$-0.352753\pi$
$332$	4.27156	−	5.12311i	0.234432	−	0.281167i
$333$	−24.7386			−1.35567
$334$	−0.157671	−	0.336750i	−0.00862736	−	0.0184261i
$335$		−	5.70147i		−	0.311505i
$336$		0			0
$337$		−	3.75379i		−	0.204482i	−0.994760	−	0.102241i	$-0.967399\pi$
$337$		−	3.75379i		−	0.204482i	0.994760	−	0.102241i	$-0.0326013\pi$
$338$	−0.599676	−	1.28078i	−0.0326181	−	0.0696651i
$339$		0			0
$340$	−2.69400	−	2.24621i	−0.146103	−	0.121818i
$341$	−21.8078	+	12.6847i	−1.18096	+	0.686913i
$342$	9.36932	+	20.0108i	0.506635	+	1.08206i
$343$	29.7533			1.60653
$344$	14.9654	+	3.93481i	0.806882	+	0.212151i
$345$		0			0
$346$	21.5270	−	10.0792i	1.15730	−	0.541862i
$347$	−21.3578			−1.14655			−0.573273	−	0.819364i	$-0.694327\pi$
$347$	−21.3578			−1.14655			−0.573273	+	0.819364i	$0.694327\pi$
$348$		0			0
$349$			18.0000i			0.963518i	0.876304	+	0.481759i	$0.160002\pi$
$349$			18.0000i			0.963518i	−0.876304	+	0.481759i	$0.839998\pi$
$350$	−12.7386	−	27.2069i	−0.680909	−	1.45427i
$351$		0			0
$352$	−17.0904	−	7.74073i	−0.910920	−	0.412583i
$353$	−3.12311			−0.166226			−0.0831131	−	0.996540i	$-0.526486\pi$
$353$	−3.12311			−0.166226			−0.0831131	+	0.996540i	$0.526486\pi$
$354$		0			0
$355$		−	0.230559i		−	0.0122368i
$356$	2.56155	−	3.07221i	0.135762	−	0.162827i
$357$		0			0
$358$	18.1379	−	8.49242i	0.958620	−	0.448838i
$359$	−6.93319			−0.365920			−0.182960	−	0.983120i	$-0.558568\pi$
$359$	−6.93319			−0.365920			−0.182960	+	0.983120i	$0.558568\pi$
$360$	−4.60831	−	1.21165i	−0.242879	−	0.0638594i
$361$	8.12311			0.427532
$362$	1.05171	+	2.24621i	0.0552764	+	0.118058i
$363$		0			0
$364$	−6.96543	−	5.80766i	−0.365088	−	0.304404i
$365$		−	8.31534i		−	0.435245i
$366$		0			0
$367$		−	15.7392i		−	0.821581i	−0.911730	−	0.410791i	$-0.865253\pi$
$367$		−	15.7392i		−	0.821581i	0.911730	−	0.410791i	$-0.134747\pi$
$368$	4.71922	−	0.862603i	0.246007	−	0.0449663i
$369$			25.6847i			1.33709i
$370$	−2.77691	−	5.93087i	−0.144365	−	0.308331i
$371$	−19.2544			−0.999638
$372$		0			0
$373$			21.0540i			1.09013i	0.838393	+	0.545067i	$0.183496\pi$
$373$			21.0540i			1.09013i	−0.838393	+	0.545067i	$0.816504\pi$
$374$	12.0396	+	8.34457i	0.622552	+	0.431487i
$375$		0			0
$376$	4.12391	−	15.6847i	0.212674	−	0.808874i
$377$	−5.68466			−0.292775
$378$		0			0
$379$		−	35.1089i		−	1.80342i	−0.432339	−	0.901711i	$-0.642311\pi$
$379$		−	35.1089i		−	1.80342i	0.432339	−	0.901711i	$-0.357689\pi$
$380$	−3.74571	+	4.49242i	−0.192151	+	0.230456i
$381$		0			0
$382$	2.20960	−	1.03457i	0.113053	−	0.0529330i
$383$		−	7.08084i		−	0.361814i	−0.983500	−	0.180907i	$-0.942097\pi$
$383$		−	7.08084i		−	0.361814i	0.983500	−	0.180907i	$-0.0579033\pi$
$384$		0			0
$385$	−4.24621	−	7.30019i	−0.216407	−	0.372052i
$386$	−5.43845	+	2.54635i	−0.276810	+	0.129606i
$387$	−16.4127			−0.834306
$388$	−15.6847	+	18.8114i	−0.796268	+	0.955006i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−3.74571			−0.189428
$392$	−37.0970	−	9.75379i	−1.87368	−	0.492641i
$393$		0			0
$394$	6.87689	−	3.21985i	0.346453	−	0.162214i
$395$	2.39871			0.120692
$396$	19.6190	+	3.33099i	0.985891	+	0.167388i
$397$	17.0540			0.855914			0.427957	−	0.903799i	$-0.359233\pi$
$397$	17.0540			0.855914			0.427957	+	0.903799i	$0.359233\pi$
$398$	−7.68051	+	3.59612i	−0.384989	+	0.180257i
$399$		0			0
$400$	3.36932	+	18.4332i	0.168466	+	0.921662i
$401$	31.6155			1.57880			0.789402	−	0.613877i	$-0.210391\pi$
$401$	31.6155			1.57880			0.789402	+	0.613877i	$0.210391\pi$
$402$		0			0
$403$	7.60669			0.378916
$404$	20.1584	+	16.8078i	1.00292	+	0.836218i
$405$	5.05398			0.251134
$406$	−33.0146	+	15.4579i	−1.63849	+	0.767161i
$407$	13.7511	+	23.6412i	0.681617	+	1.17185i
$408$		0			0
$409$		−	29.6847i		−	1.46781i	−0.679251	−	0.733906i	$-0.737695\pi$
$409$		−	29.6847i		−	1.46781i	0.679251	−	0.733906i	$-0.262305\pi$
$410$	−6.15767	+	2.88310i	−0.304106	+	0.142386i
$411$		0			0
$412$	12.8963	+	10.7527i	0.635355	+	0.529748i
$413$		−	20.5616i		−	1.01177i
$414$	−4.60831	+	2.15767i	−0.226486	+	0.106044i
$415$	−1.87285			−0.0919347
$416$	3.28078	+	4.60831i	0.160853	+	0.225941i
$417$		0			0
$418$	13.9151	−	20.0768i	0.680611	−	0.981988i
$419$			12.2888i			0.600348i	0.953884	+	0.300174i	$0.0970448\pi$
$419$			12.2888i			0.600348i	−0.953884	+	0.300174i	$0.902955\pi$
$420$		0			0
$421$	18.3153			0.892635			0.446318	−	0.894875i	$-0.352735\pi$
$421$	18.3153			0.892635			0.446318	+	0.894875i	$0.352735\pi$
$422$	10.5616	+	22.5571i	0.514128	+	1.09806i
$423$			17.2015i			0.836366i
$424$	11.6153	+	3.05398i	0.564090	+	0.148314i
$425$		−	14.6307i		−	0.709692i
$426$		0			0
$427$			1.42991i			0.0691983i
$428$	−3.26131	+	3.91146i	−0.157641	+	0.189068i
$429$		0			0
$430$	−1.84233	−	3.93481i	−0.0888450	−	0.189753i
$431$	23.6412			1.13876			0.569379	−	0.822075i	$-0.307184\pi$
$431$	23.6412			1.13876			0.569379	+	0.822075i	$0.307184\pi$
$432$		0			0
$433$	−13.0540			−0.627334			−0.313667	−	0.949533i	$-0.601558\pi$
$433$	−13.0540			−0.627334			−0.313667	+	0.949533i	$0.601558\pi$
$434$	44.1771	−	20.6843i	2.12057	−	0.992878i
$435$		0			0
$436$	3.07221	+	2.56155i	0.147132	+	0.122676i
$437$			6.24621i			0.298797i
$438$		0			0
$439$	9.59482			0.457936			0.228968	−	0.973434i	$-0.426465\pi$
$439$	9.59482			0.457936			0.228968	+	0.973434i	$0.426465\pi$
$440$	1.40366	+	5.07738i	0.0669167	+	0.242055i
$441$	40.6847			1.93736
$442$	−1.87285	−	4.00000i	−0.0890825	−	0.190261i
$443$		−	33.8772i		−	1.60955i	−0.593578	−	0.804777i	$-0.702285\pi$
$443$		−	33.8772i		−	1.60955i	0.593578	−	0.804777i	$-0.297715\pi$
$444$		0			0
$445$	−1.12311			−0.0532403
$446$	−29.9009	+	14.0000i	−1.41585	+	0.662919i
$447$		0			0
$448$	31.5847	+	17.8423i	1.49223	+	0.842971i
$449$	31.6155			1.49203			0.746015	−	0.665930i	$-0.231965\pi$
$449$	31.6155			1.49203			0.746015	+	0.665930i	$0.231965\pi$
$450$	−8.42784	−	18.0000i	−0.397292	−	0.848528i
$451$	24.5453	−	14.2770i	1.15579	−	0.672276i
$452$	−9.84233	+	11.8044i	−0.462944	+	0.555233i
$453$		0			0
$454$	−9.36932	−	20.0108i	−0.439724	−	0.939153i
$455$			2.54635i			0.119375i
$456$		0			0
$457$			27.3002i			1.27705i	0.769602	+	0.638524i	$0.220455\pi$
$457$			27.3002i			1.27705i	−0.769602	+	0.638524i	$0.779545\pi$
$458$	3.11366	+	6.65009i	0.145492	+	0.310738i
$459$		0			0
$460$	−1.03457	−	0.862603i	−0.0482368	−	0.0402191i
$461$		−	23.6155i		−	1.09988i	−0.835203	−	0.549942i	$-0.814650\pi$
$461$		−	23.6155i		−	1.09988i	0.835203	−	0.549942i	$-0.185350\pi$
$462$		0			0
$463$			28.4386i			1.32166i	0.750538	+	0.660828i	$0.229795\pi$
$463$			28.4386i			1.32166i	−0.750538	+	0.660828i	$0.770205\pi$
$464$	22.3680	−	4.08854i	1.03841	−	0.189806i
$465$		0			0
$466$	11.6847	−	5.47091i	0.541281	−	0.253435i
$467$		−	22.7048i		−	1.05065i	−0.850901	−	0.525326i	$-0.823943\pi$
$467$		−	22.7048i		−	1.05065i	0.850901	−	0.525326i	$-0.176057\pi$
$468$	−4.60831	−	3.84233i	−0.213019	−	0.177612i
$469$		−	46.0388i		−	2.12588i
$470$	−4.12391	+	1.93087i	−0.190222	+	0.0890644i
$471$		0			0
$472$	−3.26131	+	12.4039i	−0.150114	+	0.570935i
$473$	9.12311	+	15.6847i	0.419481	+	0.721181i
$474$		0			0
$475$	−24.3976			−1.11944
$476$	−21.7538	−	18.1379i	−0.997083	−	0.831351i
$477$	−12.7386			−0.583262
$478$	−1.28078	−	2.73546i	−0.0585813	−	0.125117i
$479$	−10.1530			−0.463904			−0.231952	−	0.972727i	$-0.574511\pi$
$479$	−10.1530			−0.463904			−0.231952	+	0.972727i	$0.574511\pi$
$480$		0			0
$481$		−	8.24621i		−	0.375995i
$482$	−3.19224	+	1.49465i	−0.145402	+	0.0680793i
$483$		0			0
$484$	−7.72209	−	20.6002i	−0.351004	−	0.936374i
$485$	6.87689			0.312264
$486$		0			0
$487$			17.2015i			0.779475i	0.920926	+	0.389737i	$0.127434\pi$
$487$			17.2015i			0.779475i	−0.920926	+	0.389737i	$0.872566\pi$
$488$	0.226801	−	0.862603i	0.0102668	−	0.0390482i
$489$		0			0
$490$	4.56685	+	9.75379i	0.206309	+	0.440631i
$491$	3.07221			0.138647			0.0693233	−	0.997594i	$-0.477916\pi$
$491$	3.07221			0.138647			0.0693233	+	0.997594i	$0.477916\pi$
$492$		0			0
$493$	−17.7538			−0.799590
$494$	−6.67026	+	3.12311i	−0.300109	+	0.140515i
$495$	−2.80928	−	4.82978i	−0.126268	−	0.217082i
$496$	−29.9309	+	5.47091i	−1.34394	+	0.245651i
$497$		−	1.86174i		−	0.0835104i
$498$		0			0
$499$			10.6789i			0.478053i	0.971013	+	0.239027i	$0.0768283\pi$
$499$			10.6789i			0.478053i	−0.971013	+	0.239027i	$0.923172\pi$
$500$	6.96543	−	8.35401i	0.311504	−	0.373603i
$501$		0			0
$502$	−28.7016	+	13.4384i	−1.28101	+	0.599787i
$503$	−27.5022			−1.22626			−0.613131	−	0.789981i	$-0.710090\pi$
$503$	−27.5022			−1.22626			−0.613131	+	0.789981i	$0.710090\pi$
$504$	−37.2116	−	9.78393i	−1.65754	−	0.435811i
$505$		−	7.36932i		−	0.327930i
$506$	4.62351	+	3.20453i	0.205540	+	0.142459i
$507$		0			0
$508$	12.6670	−	15.1922i	0.562008	−	0.674046i
$509$	−14.0000			−0.620539			−0.310270	−	0.950649i	$-0.600419\pi$
$509$	−14.0000			−0.620539			−0.310270	+	0.950649i	$0.600419\pi$
$510$		0			0
$511$		−	67.1456i		−	2.97035i
$512$	−16.2236	−	15.7732i	−0.716990	−	0.697083i
$513$		0			0
$514$	−18.4747	−	39.4579i	−0.814884	−	1.74041i
$515$		−	4.71450i		−	0.207746i
$516$		0			0
$517$	16.4384	−	9.56155i	0.722962	−	0.420517i
$518$	−22.4233	−	47.8912i	−0.985223	−	2.10422i
$519$		0			0
$520$	0.403882	−	1.53610i	0.0177114	−	0.0673626i
$521$	−20.1771			−0.883974			−0.441987	−	0.897021i	$-0.645726\pi$
$521$	−20.1771			−0.883974			−0.441987	+	0.897021i	$0.645726\pi$
$522$	−21.8423	+	10.2269i	−0.956013	+	0.447618i
$523$	−8.01726			−0.350570			−0.175285	−	0.984518i	$-0.556085\pi$
$523$	−8.01726			−0.350570			−0.175285	+	0.984518i	$0.556085\pi$
$524$	20.3475	−	24.4039i	0.888887	−	1.06609i
$525$		0			0
$526$	15.6847	+	33.4990i	0.683884	+	1.46062i
$527$	23.7565			1.03485
$528$		0			0
$529$	21.5616			0.937459
$530$	−1.42991	−	3.05398i	−0.0621114	−	0.132656i
$531$		−	13.6035i		−	0.590340i
$532$	−30.2462	+	36.2759i	−1.31134	+	1.57276i
$533$	−8.56155			−0.370842
$534$		0			0
$535$	1.42991			0.0618205
$536$	−7.30231	+	27.7732i	−0.315412	+	1.19962i
$537$		0			0
$538$	−1.72521	−	3.68466i	−0.0743789	−	0.158857i
$539$	−22.6148	−	38.8799i	−0.974088	−	1.67467i
$540$		0			0
$541$			23.7538i			1.02126i	0.859802	+	0.510628i	$0.170587\pi$
$541$			23.7538i			1.02126i	−0.859802	+	0.510628i	$0.829413\pi$
$542$	7.93087	+	16.9386i	0.340660	+	0.727575i
$543$		0			0
$544$	10.2462	+	14.3922i	0.439303	+	0.617062i
$545$		−	1.12311i		−	0.0481086i
$546$		0			0
$547$	20.9796			0.897022			0.448511	−	0.893777i	$-0.351954\pi$
$547$	20.9796			0.897022			0.448511	+	0.893777i	$0.351954\pi$
$548$	27.3693	−	32.8255i	1.16916	−	1.40223i
$549$			0.946025i			0.0403753i
$550$	−12.5169	+	18.0594i	−0.533720	+	0.770054i
$551$			29.6056i			1.26124i
$552$		0			0
$553$	19.3693			0.823667
$554$	1.84233	−	0.862603i	0.0782731	−	0.0366485i
$555$		0			0
$556$	22.5571	−	27.0540i	0.956636	−	1.14734i
$557$			36.2462i			1.53580i	0.640569	+	0.767901i	$0.278699\pi$
$557$			36.2462i			1.53580i	−0.640569	+	0.767901i	$0.721301\pi$
$558$	29.2274	−	13.6847i	1.23729	−	0.579318i
$559$		−	5.47091i		−	0.231395i
$560$	−1.83140	−	10.0194i	−0.0773906	−	0.423397i
$561$		0			0
$562$	5.84233	−	2.73546i	0.246444	−	0.115388i
$563$	−3.45041			−0.145418			−0.0727088	−	0.997353i	$-0.523164\pi$
$563$	−3.45041			−0.145418			−0.0727088	+	0.997353i	$0.523164\pi$
$564$		0			0
$565$	4.31534			0.181548
$566$	−16.4039	−	35.0351i	−0.689507	−	1.47263i
$567$	40.8104			1.71387
$568$	−0.295294	+	1.12311i	−0.0123903	+	0.0471245i
$569$		−	44.9848i		−	1.88586i	−0.332987	−	0.942931i	$-0.608057\pi$
$569$		−	44.9848i		−	1.88586i	0.332987	−	0.942931i	$-0.391943\pi$
$570$		0			0
$571$	−33.2037			−1.38953			−0.694765	−	0.719237i	$-0.744492\pi$
$571$	−33.2037			−1.38953			−0.694765	+	0.719237i	$0.744492\pi$
$572$	−1.11033	+	6.53966i	−0.0464252	+	0.273437i
$573$		0			0
$574$	−49.7226	+	23.2808i	−2.07538	+	0.971721i
$575$		−	5.61856i		−	0.234310i
$576$	20.8963	+	11.8044i	0.870679	+	0.491851i
$577$	−26.0000			−1.08239			−0.541197	−	0.840896i	$-0.682029\pi$
$577$	−26.0000			−1.08239			−0.541197	+	0.840896i	$0.682029\pi$
$578$	4.34538	+	9.28078i	0.180744	+	0.386029i
$579$		0			0
$580$	−4.90360	−	4.08854i	−0.203611	−	0.169767i
$581$	−15.1231			−0.627412
$582$		0			0
$583$	7.08084	+	12.1735i	0.293258	+	0.504177i
$584$	−10.6501	+	40.5060i	−0.440704	+	1.67615i
$585$			1.68466i			0.0696521i
$586$	−24.4924	+	11.4677i	−1.01177	+	0.473725i
$587$		−	1.31463i		−	0.0542607i	−0.999632	−	0.0271303i	$-0.991363\pi$
$587$		−	1.31463i		−	0.0542607i	0.999632	−	0.0271303i	$-0.00863691\pi$
$588$		0			0
$589$		−	39.6155i		−	1.63233i
$590$	3.26131	−	1.52699i	0.134266	−	0.0628651i
$591$		0			0
$592$	5.93087	+	32.4473i	0.243757	+	1.33357i
$593$			20.7386i			0.851634i	0.904809	+	0.425817i	$0.140013\pi$
$593$			20.7386i			0.851634i	−0.904809	+	0.425817i	$0.859987\pi$
$594$		0			0
$595$			7.95253i			0.326022i
$596$	−28.4063	−	23.6847i	−1.16357	−	0.970161i
$597$		0			0
$598$	−0.719224	−	1.53610i	−0.0294112	−	0.0628159i
$599$			12.9623i			0.529626i	0.964300	+	0.264813i	$0.0853103\pi$
$599$			12.9623i			0.529626i	−0.964300	+	0.264813i	$0.914690\pi$
$600$		0			0
$601$			40.7386i			1.66176i	0.556449	+	0.830882i	$0.312163\pi$
$601$			40.7386i			1.66176i	−0.556449	+	0.830882i	$0.687837\pi$
$602$	−14.8766	−	31.7732i	−0.606326	−	1.29498i
$603$		−	30.4591i		−	1.24039i
$604$	−8.39547	+	10.0691i	−0.341607	+	0.409707i
$605$	−3.05398	+	5.36932i	−0.124162	+	0.218294i
$606$		0			0
$607$	12.5194			0.508146			0.254073	−	0.967185i	$-0.418230\pi$
$607$	12.5194			0.508146			0.254073	+	0.967185i	$0.418230\pi$
$608$	24.0000	−	17.0862i	0.973329	−	0.692938i
$609$		0			0
$610$	−0.226801	+	0.106191i	−0.00918291	+	0.00429956i
$611$	−5.73384			−0.231966
$612$	−14.3922	−	12.0000i	−0.581772	−	0.485071i
$613$			17.3693i			0.701540i	0.936462	+	0.350770i	$0.114080\pi$
$613$			17.3693i			0.701540i	−0.936462	+	0.350770i	$0.885920\pi$
$614$	2.80776	+	5.99676i	0.113312	+	0.242010i
$615$		0			0
$616$	11.3344	+	40.9994i	0.456675	+	1.65191i
$617$	41.3693			1.66547			0.832733	−	0.553675i	$-0.186775\pi$
$617$	41.3693			1.66547			0.832733	+	0.553675i	$0.186775\pi$
$618$		0			0
$619$		−	9.33190i		−	0.375081i	−0.982257	−	0.187540i	$-0.939948\pi$
$619$		−	9.33190i		−	0.375081i	0.982257	−	0.187540i	$-0.0600515\pi$
$620$	6.56155	+	5.47091i	0.263518	+	0.219717i
$621$		0			0
$622$	−33.4990	+	15.6847i	−1.34319	+	0.628898i
$623$	−9.06897			−0.363341
$624$		0			0
$625$	20.3693			0.814773
$626$	−19.0005	−	40.5810i	−0.759414	−	1.62194i
$627$		0			0
$628$	−10.2462	+	12.2888i	−0.408868	+	0.490377i
$629$		−	25.7538i		−	1.02687i
$630$	4.58096	+	9.78393i	0.182510	+	0.389801i
$631$		−	36.9817i		−	1.47222i	−0.676862	−	0.736110i	$-0.736661\pi$
$631$		−	36.9817i		−	1.47222i	0.676862	−	0.736110i	$-0.263339\pi$
$632$	−11.6847	−	3.07221i	−0.464791	−	0.122206i
$633$		0			0
$634$	20.4952	+	43.7732i	0.813968	+	1.73846i
$635$	−5.55382			−0.220397
$636$		0			0
$637$			13.5616i			0.537328i
$638$	21.9144	+	15.1887i	0.867598	+	0.601328i
$639$		−	1.23172i		−	0.0487261i
$640$	−0.484397	+	6.33475i	−0.0191475	+	0.250403i
$641$	−1.43845			−0.0568152			−0.0284076	−	0.999596i	$-0.509044\pi$
$641$	−1.43845			−0.0568152			−0.0284076	+	0.999596i	$0.509044\pi$
$642$		0			0
$643$			4.68213i			0.184645i	0.995729	+	0.0923226i	$0.0294291\pi$
$643$			4.68213i			0.184645i	−0.995729	+	0.0923226i	$0.970571\pi$
$644$	−8.35401	−	6.96543i	−0.329194	−	0.274477i
$645$		0			0
$646$	−20.8319	+	9.75379i	−0.819622	+	0.383758i
$647$		−	40.5474i		−	1.59408i	−0.603924	−	0.797042i	$-0.706397\pi$
$647$		−	40.5474i		−	1.59408i	0.603924	−	0.797042i	$-0.293603\pi$
$648$	−24.6191	−	6.47301i	−0.967130	−	0.254284i
$649$	−13.0000	+	7.56155i	−0.510295	+	0.296817i
$650$	6.00000	−	2.80928i	0.235339	−	0.110189i
$651$		0			0
$652$	−9.84233	−	8.20637i	−0.385455	−	0.321386i
$653$	−29.7538			−1.16436			−0.582178	−	0.813061i	$-0.697799\pi$
$653$	−29.7538			−1.16436			−0.582178	+	0.813061i	$0.697799\pi$
$654$		0			0
$655$	−8.92132			−0.348585
$656$	33.6881	−	6.15767i	1.31530	−	0.240417i
$657$		−	44.4233i		−	1.73312i
$658$	−33.3002	+	15.5916i	−1.29818	+	0.607823i
$659$	5.32326			0.207365			0.103682	−	0.994610i	$-0.466937\pi$
$659$	5.32326			0.207365			0.103682	+	0.994610i	$0.466937\pi$
$660$		0			0
$661$	14.0000			0.544537			0.272268	−	0.962221i	$-0.412226\pi$
$661$	14.0000			0.544537			0.272268	+	0.962221i	$0.412226\pi$
$662$	41.7053	−	19.5270i	1.62092	−	0.758938i
$663$		0			0
$664$	9.12311	+	2.39871i	0.354045	+	0.0930878i
$665$	13.2614			0.514254
$666$	−14.8352	−	31.6847i	−0.574851	−	1.22776i
$667$	−6.81791			−0.263991
$668$	0.336750	−	0.403882i	0.0130292	−	0.0156267i
$669$		0			0
$670$	7.30231	−	3.41904i	0.282113	−	0.132089i
$671$	0.904059	−	0.525853i	0.0349008	−	0.0203003i
$672$		0			0
$673$			44.2462i			1.70557i	0.522265	+	0.852783i	$0.325087\pi$
$673$			44.2462i			1.70557i	−0.522265	+	0.852783i	$0.674913\pi$
$674$	4.80776	−	2.25106i	0.185188	−	0.0867075i
$675$		0			0
$676$	1.28078	−	1.53610i	0.0492606	−	0.0590809i
$677$			27.3693i			1.05189i	0.850519	+	0.525944i	$0.176288\pi$
$677$			27.3693i			1.05189i	−0.850519	+	0.525944i	$0.823712\pi$
$678$		0			0
$679$	55.5303			2.13106
$680$	1.26137	−	4.79741i	0.0483712	−	0.183972i
$681$		0			0
$682$	−29.3238	−	20.3242i	−1.12287	−	0.778253i
$683$			31.5108i			1.20573i	0.797844	+	0.602864i	$0.205974\pi$
$683$			31.5108i			1.20573i	−0.797844	+	0.602864i	$0.794026\pi$
$684$	−20.0108	+	24.0000i	−0.765132	+	0.917663i
$685$	−12.0000			−0.458496
$686$	17.8423	+	38.1073i	0.681223	+	1.45494i
$687$		0			0
$688$	3.93481	+	21.5270i	0.150013	+	0.820709i
$689$		−	4.24621i		−	0.161768i
$690$		0			0
$691$			47.3977i			1.80309i	0.432681	+	0.901547i	$0.357568\pi$
$691$			47.3977i			1.80309i	−0.432681	+	0.901547i	$0.642432\pi$
$692$	25.8185	+	21.5270i	0.981470	+	0.818333i
$693$	−22.6847	−	39.0000i	−0.861719	−	1.48149i
$694$	−12.8078	−	27.3546i	−0.486176	−	1.03836i
$695$	−9.89012			−0.375154
$696$		0			0
$697$	−26.7386			−1.01280
$698$	−23.0540	+	10.7942i	−0.872606	+	0.408566i
$699$		0			0
$700$	27.2069	−	32.6307i	1.02832	−	1.23332i
$701$			6.80776i			0.257126i	0.991701	+	0.128563i	$0.0410364\pi$
$701$			6.80776i			0.257126i	−0.991701	+	0.128563i	$0.958964\pi$
$702$		0			0
$703$	−42.9461			−1.61974
$704$	−0.334546	−	26.5309i	−0.0126087	−	0.999921i
$705$		0			0
$706$	−1.87285	−	4.00000i	−0.0704857	−	0.150542i
$707$		−	59.5065i		−	2.23797i
$708$		0			0
$709$	−0.0691303			−0.00259624			−0.00129812	−	0.999999i	$-0.500413\pi$
$709$	−0.0691303			−0.00259624			−0.00129812	+	0.999999i	$0.500413\pi$
$710$	0.295294	−	0.138261i	0.0110822	−	0.00518883i
$711$	12.8147			0.480588
$712$	5.47091	+	1.43845i	0.205031	+	0.0539081i
$713$	9.12311			0.341663
$714$		0			0
$715$	1.60993	−	0.936426i	0.0602078	−	0.0350204i
$716$	21.7538	+	18.1379i	0.812977	+	0.677847i
$717$		0			0
$718$	−4.15767	−	8.87987i	−0.155163	−	0.331394i
$719$			9.44718i			0.352320i	0.984362	+	0.176160i	$0.0563676\pi$
$719$			9.44718i			0.352320i	−0.984362	+	0.176160i	$0.943632\pi$
$720$	−1.21165	−	6.62881i	−0.0451554	−	0.247041i
$721$		−	38.0691i		−	1.41777i
$722$	4.87123	+	10.4039i	0.181289	+	0.387192i
$723$		0			0
$724$	−2.24621	+	2.69400i	−0.0834798	+	0.100122i
$725$		−	26.6307i		−	0.989039i
$726$		0			0
$727$		−	42.1897i		−	1.56473i	−0.622820	−	0.782365i	$-0.714013\pi$
$727$		−	42.1897i		−	1.56473i	0.622820	−	0.782365i	$-0.285987\pi$
$728$	3.26131	−	12.4039i	0.120872	−	0.459718i
$729$	27.0000			1.00000
$730$	10.6501	−	4.98651i	0.394178	−	0.184559i
$731$		−	17.0862i		−	0.631957i
$732$		0			0
$733$			13.8617i			0.511995i	0.966677	+	0.255998i	$0.0824039\pi$
$733$			13.8617i			0.511995i	−0.966677	+	0.255998i	$0.917596\pi$
$734$	20.1584	−	9.43845i	0.744062	−	0.348379i
$735$		0			0
$736$	3.93481	+	5.52699i	0.145039	+	0.203727i
$737$	−29.1080	+	16.9309i	−1.07221	+	0.623657i
$738$	−32.8963	+	15.4025i	−1.21093	+	0.566973i
$739$	23.8718			0.878138			0.439069	−	0.898453i	$-0.355308\pi$
$739$	23.8718			0.878138			0.439069	+	0.898453i	$0.355308\pi$
$740$	5.93087	−	7.11321i	0.218023	−	0.261487i
$741$		0			0
$742$	−11.5464	−	24.6606i	−0.423882	−	0.905318i
$743$	35.2565			1.29344			0.646719	−	0.762729i	$-0.276141\pi$
$743$	35.2565			1.29344			0.646719	+	0.762729i	$0.276141\pi$
$744$		0			0
$745$			10.3845i			0.380458i
$746$	−26.9654	+	12.6256i	−0.987275	+	0.462255i
$747$	−10.0054			−0.366078
$748$	−3.46768	+	20.4241i	−0.126791	+	0.746777i
$749$	11.5464			0.421896
$750$		0			0
$751$		−	26.8287i		−	0.978993i	−0.872005	−	0.489497i	$-0.837181\pi$
$751$		−	26.8287i		−	0.978993i	0.872005	−	0.489497i	$-0.162819\pi$
$752$	22.5616	−	4.12391i	0.822735	−	0.150384i
$753$		0			0
$754$	−3.40896	−	7.28078i	−0.124147	−	0.265150i
$755$	3.68097			0.133964
$756$		0			0
$757$	16.2462			0.590479			0.295239	−	0.955423i	$-0.404601\pi$
$757$	16.2462			0.590479			0.295239	+	0.955423i	$0.404601\pi$
$758$	44.9666	−	21.0540i	1.63326	−	0.764715i
$759$		0			0
$760$	−8.00000	−	2.10341i	−0.290191	−	0.0762988i
$761$			13.6847i			0.496068i	0.968751	+	0.248034i	$0.0797846\pi$
$761$			13.6847i			0.496068i	−0.968751	+	0.248034i	$0.920215\pi$
$762$		0			0
$763$		−	9.06897i		−	0.328319i
$764$	2.65009	+	2.20960i	0.0958770	+	0.0799406i
$765$			5.26137i			0.190225i
$766$	9.06897	−	4.24621i	0.327675	−	0.153422i
$767$	4.53448			0.163731
$768$		0			0
$769$		−	9.05398i		−	0.326495i	−0.986585	−	0.163247i	$-0.947803\pi$
$769$		−	9.05398i		−	0.326495i	0.986585	−	0.163247i	$-0.0521969\pi$
$770$	6.80355	−	9.81620i	0.245183	−	0.353751i
$771$		0			0
$772$	−6.52262	−	5.43845i	−0.234754	−	0.195734i
$773$	8.73863			0.314307			0.157153	−	0.987574i	$-0.449768\pi$
$773$	8.73863			0.314307			0.157153	+	0.987574i	$0.449768\pi$
$774$	−9.84233	−	21.0210i	−0.353775	−	0.755586i
$775$			35.6347i			1.28004i
$776$	−33.4990	−	8.80776i	−1.20254	−	0.316180i
$777$		0			0
$778$	7.19612	+	15.3693i	0.257993	+	0.551017i
$779$			44.5884i			1.59755i
$780$		0			0
$781$	−1.17708	+	0.684658i	−0.0421193	+	0.0244990i
$782$	−2.24621	−	4.79741i	−0.0803244	−	0.171555i
$783$		0			0
$784$	−9.75379	−	53.3621i	−0.348350	−	1.90579i
$785$	4.49242			0.160341
$786$		0			0
$787$	27.3869			0.976238			0.488119	−	0.872777i	$-0.337683\pi$
$787$	27.3869			0.976238			0.488119	+	0.872777i	$0.337683\pi$
$788$	8.24782	+	6.87689i	0.293817	+	0.244979i
$789$		0			0
$790$	1.43845	+	3.07221i	0.0511777	+	0.109304i
$791$	34.8460			1.23898
$792$	7.49879	+	27.1250i	0.266458	+	0.963847i
$793$	−0.315342			−0.0111981
$794$	10.2269	+	21.8423i	0.362938	+	0.775155i
$795$		0			0
$796$	−9.21165	−	7.68051i	−0.326498	−	0.272229i
$797$	28.0000			0.991811			0.495905	−	0.868377i	$-0.334836\pi$
$797$	28.0000			0.991811			0.495905	+	0.868377i	$0.334836\pi$
$798$		0			0
$799$	−17.9074			−0.633518
$800$	−21.5884	+	15.3693i	−0.763263	+	0.543387i
$801$	−6.00000			−0.212000
$802$	18.9591	+	40.4924i	0.669469	+	1.42984i
$803$	−42.4527	+	24.6929i	−1.49812	+	0.871394i
$804$		0			0
$805$			3.05398i			0.107638i
$806$	4.56155	+	9.74247i	0.160674	+	0.343164i
$807$		0			0
$808$	−9.43845	+	35.8977i	−0.332043	+	1.26288i
$809$			35.1231i			1.23486i	0.786625	+	0.617431i	$0.211827\pi$
$809$			35.1231i			1.23486i	−0.786625	+	0.617431i	$0.788173\pi$
$810$	3.03075	+	6.47301i	0.106490	+	0.227438i
$811$	26.2705			0.922481			0.461241	−	0.887275i	$-0.347404\pi$
$811$	26.2705			0.922481			0.461241	+	0.887275i	$0.347404\pi$
$812$	−39.5961	−	33.0146i	−1.38955	−	1.15858i
$813$		0			0
$814$	−22.0329	+	31.7892i	−0.772253	+	1.11421i
$815$			3.59806i			0.126034i
$816$		0			0
$817$	−28.4924			−0.996824
$818$	38.0194	−	17.8012i	1.32932	−	0.622404i
$819$			13.6035i			0.475343i
$820$	−7.38522	−	6.15767i	−0.257903	−	0.215035i
$821$		−	37.2311i		−	1.29937i	−0.760202	−	0.649686i	$-0.774900\pi$
$821$		−	37.2311i		−	1.29937i	0.760202	−	0.649686i	$-0.225100\pi$
$822$		0			0
$823$			43.9149i			1.53078i	0.643568	+	0.765389i	$0.277454\pi$
$823$			43.9149i			1.53078i	−0.643568	+	0.765389i	$0.722546\pi$
$824$	−6.03822	+	22.9654i	−0.210351	+	0.800039i
$825$		0			0
$826$	26.3348	−	12.3303i	0.916303	−	0.429025i
$827$	−19.0744			−0.663281			−0.331640	−	0.943406i	$-0.607602\pi$
$827$	−19.0744			−0.663281			−0.331640	+	0.943406i	$0.607602\pi$
$828$	−5.52699	−	4.60831i	−0.192076	−	0.160150i
$829$	54.9848			1.90970			0.954851	−	0.297084i	$-0.0960142\pi$
$829$	54.9848			1.90970			0.954851	+	0.297084i	$0.0960142\pi$
$830$	−1.12311	−	2.39871i	−0.0389836	−	0.0832603i
$831$		0			0
$832$	−3.93481	+	6.96543i	−0.136415	+	0.241483i
$833$			42.3542i			1.46748i
$834$		0			0
$835$	−0.147647			−0.00510954
$836$	34.0585	+	5.78258i	1.17794	+	0.199995i
$837$		0			0
$838$	−15.7392	+	7.36932i	−0.543703	+	0.254569i
$839$			24.3976i			0.842300i	0.906991	+	0.421150i	$0.138373\pi$
$839$			24.3976i			0.842300i	−0.906991	+	0.421150i	$0.861627\pi$
$840$		0			0
$841$	−3.31534			−0.114322
$842$	10.9833	+	23.4579i	0.378509	+	0.808411i
$843$		0			0
$844$	−22.5571	+	27.0540i	−0.776449	+	0.931236i
$845$	−0.561553			−0.0193180
$846$	−22.0313	+	10.3153i	−0.757451	+	0.354649i
$847$	−24.6606	+	43.3567i	−0.847347	+	1.48975i
$848$	3.05398	+	16.7080i	0.104874	+	0.573756i
$849$		0			0
$850$	18.7386	−	8.77368i	0.642730	−	0.300935i
$851$		−	9.89012i		−	0.339029i
$852$		0			0
$853$			15.7538i			0.539399i	0.962944	+	0.269700i	$0.0869244\pi$
$853$			15.7538i			0.539399i	−0.962944	+	0.269700i	$0.913076\pi$
$854$	−1.83140	+	0.857484i	−0.0626691	+	0.0293425i
$855$	8.77368			0.300053
$856$	−6.96543	−	1.83140i	−0.238074	−	0.0625959i
$857$			12.0000i			0.409912i	0.978771	+	0.204956i	$0.0657052\pi$
$857$			12.0000i			0.409912i	−0.978771	+	0.204956i	$0.934295\pi$
$858$		0			0
$859$			40.6122i			1.38567i	0.721096	+	0.692835i	$0.243638\pi$
$859$			40.6122i			1.38567i	−0.721096	+	0.692835i	$0.756362\pi$
$860$	3.93481	−	4.71922i	0.134176	−	0.160924i
$861$		0			0
$862$	14.1771	+	30.2791i	0.482873	+	1.03131i
$863$			28.7339i			0.978114i	0.872252	+	0.489057i	$0.162659\pi$
$863$			28.7339i			0.978114i	−0.872252	+	0.489057i	$0.837341\pi$
$864$		0			0
$865$		−	9.43845i		−	0.320917i
$866$	−7.82816	−	16.7192i	−0.266012	−	0.568142i
$867$		0			0
$868$	52.9839	+	44.1771i	1.79839	+	1.49947i
$869$	−7.12311	−	12.2462i	−0.241635	−	0.415424i
$870$		0			0
$871$	10.1530			0.344023
$872$	−1.43845	+	5.47091i	−0.0487120	+	0.185268i
$873$	36.7386			1.24341
$874$	−8.00000	+	3.74571i	−0.270604	+	0.126700i
$875$	−24.6606			−0.833679
$876$		0			0
$877$			55.6155i			1.87800i	0.343913	+	0.939001i	$0.388247\pi$
$877$			55.6155i			1.87800i	−0.343913	+	0.939001i	$0.611753\pi$
$878$	5.75379	+	12.2888i	0.194181	+	0.414728i
$879$		0			0
$880$	−5.66125	+	4.84256i	−0.190841	+	0.163243i
$881$	7.43845			0.250608			0.125304	−	0.992118i	$-0.460009\pi$
$881$	7.43845			0.250608			0.125304	+	0.992118i	$0.460009\pi$
$882$	24.3976	+	52.1080i	0.821511	+	1.75457i
$883$		−	11.4677i		−	0.385918i	−0.981207	−	0.192959i	$-0.938192\pi$
$883$		−	11.4677i		−	0.385918i	0.981207	−	0.192959i	$-0.0618084\pi$
$884$	4.00000	−	4.79741i	0.134535	−	0.161354i
$885$		0			0
$886$	43.3891	−	20.3153i	1.45768	−	0.682507i
$887$	32.5949			1.09443			0.547215	−	0.836992i	$-0.315688\pi$
$887$	32.5949			1.09443			0.547215	+	0.836992i	$0.315688\pi$
$888$		0			0
$889$	−44.8466			−1.50411
$890$	−0.673500	−	1.43845i	−0.0225758	−	0.0482169i
$891$	−15.0081	−	25.8023i	−0.502790	−	0.864409i
$892$	−35.8617	−	29.9009i	−1.20074	−	1.00116i
$893$			29.8617i			0.999285i
$894$		0			0
$895$		−	7.95253i		−	0.265824i
$896$	−3.91146	+	51.1525i	−0.130673	+	1.70889i
$897$		0			0
$898$	18.9591	+	40.4924i	0.632673	+	1.35125i
$899$	43.2414			1.44218
$900$	18.0000	−	21.5884i	0.600000	−	0.719612i
$901$		−	13.2614i		−	0.441800i
$902$	33.0048	+	22.8755i	1.09894	+	0.761669i
$903$		0			0
$904$	−21.0210	−	5.52699i	−0.699149	−	0.183825i
$905$	0.984845			0.0327374
$906$		0			0
$907$		−	22.7048i		−	0.753900i	−0.926234	−	0.376950i	$-0.876973\pi$
$907$		−	22.7048i		−	0.753900i	0.926234	−	0.376950i	$-0.123027\pi$
$908$	20.0108	−	24.0000i	0.664081	−	0.796468i
$909$		−	39.3693i		−	1.30580i
$910$	−3.26131	+	1.52699i	−0.108111	+	0.0506191i
$911$		−	58.4548i		−	1.93669i	−0.249607	−	0.968347i	$-0.580301\pi$
$911$		−	58.4548i		−	1.93669i	0.249607	−	0.968347i	$-0.419699\pi$
$912$		0			0
$913$	5.56155	+	9.56155i	0.184061	+	0.316441i
$914$	−34.9654	+	16.3713i	−1.15655	+	0.541514i
$915$		0			0
$916$	−6.65009	+	7.97581i	−0.219725	+	0.263528i
$917$	−72.0388			−2.37893
$918$		0			0
$919$	−10.7113			−0.353332			−0.176666	−	0.984271i	$-0.556531\pi$
$919$	−10.7113			−0.353332			−0.176666	+	0.984271i	$0.556531\pi$
$920$	0.484397	−	1.84233i	0.0159701	−	0.0607398i
$921$		0			0
$922$	30.2462	−	14.1617i	0.996106	−	0.466390i
$923$	0.410574			0.0135142
$924$		0			0
$925$	38.6307			1.27017
$926$	−36.4235	+	17.0540i	−1.19695	+	0.560428i
$927$		−	25.1864i		−	0.827230i
$928$	18.6501	+	26.1967i	0.612219	+	0.859947i
$929$	−23.1231			−0.758644			−0.379322	−	0.925265i	$-0.623843\pi$
$929$	−23.1231			−0.758644			−0.379322	+	0.925265i	$0.623843\pi$
$930$		0			0
$931$	70.6284			2.31475
$932$	14.0140	+	11.6847i	0.459045	+	0.382744i
$933$		0			0
$934$	29.0798	−	13.6155i	0.951519	−	0.445514i
$935$	5.02797	−	2.92456i	0.164432	−	0.0956433i
$936$	2.15767	−	8.20637i	0.0705257	−	0.268233i
$937$		−	5.12311i		−	0.167365i	−0.996492	−	0.0836823i	$-0.973332\pi$
$937$		−	5.12311i		−	0.167365i	0.996492	−	0.0836823i	$-0.0266681\pi$
$938$	58.9654	−	27.6084i	1.92529	−	0.901446i
$939$		0			0
$940$	−4.94602	−	4.12391i	−0.161322	−	0.134507i
$941$		−	2.49242i		−	0.0812507i	−0.999174	−	0.0406253i	$-0.987065\pi$
$941$		−	2.49242i		−	0.0812507i	0.999174	−	0.0406253i	$-0.0129350\pi$
$942$		0			0
$943$	−10.2683			−0.334383
$944$	−17.8423	+	3.26131i	−0.580718	+	0.106147i
$945$		0			0
$946$	−14.6176	+	21.0904i	−0.475260	+	0.685707i
$947$		−	1.75757i		−	0.0571135i	−0.999592	−	0.0285567i	$-0.990909\pi$
$947$		−	1.75757i		−	0.0571135i	0.999592	−	0.0285567i	$-0.00909113\pi$
$948$		0			0
$949$	14.8078			0.480680
$950$	−14.6307	−	31.2479i	−0.474682	−	1.01382i
$951$		0			0
$952$	10.1854	−	38.7386i	0.330111	−	1.25553i
$953$			22.2462i			0.720625i	0.932832	+	0.360313i	$0.117330\pi$
$953$			22.2462i			0.720625i	−0.932832	+	0.360313i	$0.882670\pi$
$954$	−7.63906	−	16.3153i	−0.247324	−	0.528229i
$955$		−	0.968794i		−	0.0313494i
$956$	2.73546	−	3.28078i	0.0884710	−	0.106108i
$957$		0			0
$958$	−6.08854	−	13.0038i	−0.196712	−	0.420133i
$959$	−96.8988			−3.12903
$960$		0			0
$961$	−26.8617			−0.866508
$962$	10.5616	−	4.94506i	0.340518	−	0.159435i
$963$	7.63906			0.246165
$964$	−3.82862	−	3.19224i	−0.123311	−	0.102815i
$965$			2.38447i			0.0767589i
$966$		0			0
$967$	−28.0604			−0.902362			−0.451181	−	0.892432i	$-0.648997\pi$
$967$	−28.0604			−0.902362			−0.451181	+	0.892432i	$0.648997\pi$
$968$	21.7535	−	22.2437i	0.699185	−	0.714941i
$969$		0			0
$970$	4.12391	+	8.80776i	0.132411	+	0.282800i
$971$			22.9354i			0.736030i	0.929820	+	0.368015i	$0.119963\pi$
$971$			22.9354i			0.736030i	−0.929820	+	0.368015i	$0.880037\pi$
$972$		0			0
$973$	−79.8617			−2.56025
$974$	−22.0313	+	10.3153i	−0.705928	+	0.330525i
$975$		0			0
$976$	1.24081	−	0.226801i	0.0397173	−	0.00725973i
$977$	−48.8769			−1.56371			−0.781855	−	0.623460i	$-0.785726\pi$
$977$	−48.8769			−1.56371			−0.781855	+	0.623460i	$0.785726\pi$
$978$		0			0
$979$	3.33513	+	5.73384i	0.106591	+	0.183254i
$980$	−9.75379	+	11.6982i	−0.311573	+	0.373686i
$981$		−	6.00000i		−	0.191565i
$982$	1.84233	+	3.93481i	0.0587911	+	0.125565i
$983$			12.9300i			0.412402i	0.978510	+	0.206201i	$0.0661100\pi$
$983$			12.9300i			0.412402i	−0.978510	+	0.206201i	$0.933890\pi$
$984$		0			0
$985$		−	3.01515i		−	0.0960708i
$986$	−10.6465	−	22.7386i	−0.339055	−	0.724146i
$987$		0			0
$988$	−8.00000	−	6.67026i	−0.254514	−	0.212209i
$989$		−	6.56155i		−	0.208645i
$990$	4.50121	−	6.49436i	0.143058	−	0.206404i
$991$			35.6024i			1.13095i	0.824767	+	0.565473i	$0.191307\pi$
$991$			35.6024i			1.13095i	−0.824767	+	0.565473i	$0.808693\pi$
$992$	−24.9559	−	35.0540i	−0.792349	−	1.11296i
$993$		0			0
$994$	2.38447	−	1.11644i	0.0756309	−	0.0354114i
$995$			3.36750i			0.106757i
$996$		0			0
$997$			38.4233i			1.21688i	0.793601	+	0.608439i	$0.208204\pi$
$997$			38.4233i			1.21688i	−0.793601	+	0.608439i	$0.791796\pi$
$998$	−13.6773	+	6.40388i	−0.432947	+	0.202711i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.e.a.131.6	yes	8
4.3	odd	2	inner	572.2.e.a.131.4	yes	8
11.10	odd	2	inner	572.2.e.a.131.3	✓	8
44.43	even	2	inner	572.2.e.a.131.5	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.e.a.131.3	✓	8	11.10	odd	2	inner
572.2.e.a.131.4	yes	8	4.3	odd	2	inner
572.2.e.a.131.5	yes	8	44.43	even	2	inner
572.2.e.a.131.6	yes	8	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.599676 + 1.28078i) q^{2} +(-1.28078 + 1.53610i) q^{4} +0.561553 q^{5} +4.53448 q^{7} +(-2.73546 - 0.719224i) q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q+(0.599676 + 1.28078i) q^{2} +(-1.28078 + 1.53610i) q^{4} +0.561553 q^{5} +4.53448 q^{7} +(-2.73546 - 0.719224i) q^{8} +3.00000 q^{9} +(0.336750 + 0.719224i) q^{10} +(-1.66757 - 2.86692i) q^{11} +1.00000i q^{13} +(2.71922 + 5.80766i) q^{14} +(-0.719224 - 3.93481i) q^{16} +3.12311i q^{17} +(1.79903 + 3.84233i) q^{18} +5.20798 q^{19} +(-0.719224 + 0.862603i) q^{20} +(2.67188 - 3.85500i) q^{22} +1.19935i q^{23} -4.68466 q^{25} +(-1.28078 + 0.599676i) q^{26} +(-5.80766 + 6.96543i) q^{28} +5.68466i q^{29} -7.60669i q^{31} +(4.60831 - 3.28078i) q^{32} +(-4.00000 + 1.87285i) q^{34} +2.54635 q^{35} +(-3.84233 + 4.60831i) q^{36} -8.24621 q^{37} +(3.12311 + 6.67026i) q^{38} +(-1.53610 - 0.403882i) q^{40} +8.56155i q^{41} -5.47091 q^{43} +(6.53966 + 1.11033i) q^{44} +1.68466 q^{45} +(-1.53610 + 0.719224i) q^{46} +5.73384i q^{47} +13.5616 q^{49} +(-2.80928 - 6.00000i) q^{50} +(-1.53610 - 1.28078i) q^{52} -4.24621 q^{53} +(-0.936426 - 1.60993i) q^{55} +(-12.4039 - 3.26131i) q^{56} +(-7.28078 + 3.40896i) q^{58} -4.53448i q^{59} +0.315342i q^{61} +(9.74247 - 4.56155i) q^{62} +13.6035 q^{63} +(6.96543 + 3.93481i) q^{64} +0.561553i q^{65} -10.1530i q^{67} +(-4.79741 - 4.00000i) q^{68} +(1.52699 + 3.26131i) q^{70} -0.410574i q^{71} +(-8.20637 - 2.15767i) q^{72} -14.8078i q^{73} +(-4.94506 - 10.5616i) q^{74} +(-6.67026 + 8.00000i) q^{76} +(-7.56155 - 13.0000i) q^{77} +4.27156 q^{79} +(-0.403882 - 2.20960i) q^{80} +9.00000 q^{81} +(-10.9654 + 5.13416i) q^{82} -3.33513 q^{83} +1.75379i q^{85} +(-3.28078 - 7.00701i) q^{86} +(2.49960 + 9.04168i) q^{88} -2.00000 q^{89} +(1.01025 + 2.15767i) q^{90} +4.53448i q^{91} +(-1.84233 - 1.53610i) q^{92} +(-7.34376 + 3.43845i) q^{94} +2.92456 q^{95} +12.2462 q^{97} +(8.13254 + 17.3693i) q^{98} +(-5.00270 - 8.60076i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9	\( 8 q - 2 q^{4} - 12 q^{5} + 24 q^{9} + 30 q^{14} - 14 q^{16} - 14 q^{20} - 8 q^{22} + 12 q^{25} - 2 q^{26} - 32 q^{34} - 6 q^{36} - 8 q^{38} - 6 q^{44} - 36 q^{45} + 92 q^{49} + 32 q^{53} - 58 q^{56} - 50 q^{58} - 2 q^{64} - 62 q^{70} - 44 q^{77} + 38 q^{80} + 72 q^{81} - 30 q^{82} - 18 q^{86} + 20 q^{88} - 16 q^{89} + 10 q^{92} + 32 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 - 12 * q^5 + 24 * q^9 + 30 * q^14 - 14 * q^16 - 14 * q^20 - 8 * q^22 + 12 * q^25 - 2 * q^26 - 32 * q^34 - 6 * q^36 - 8 * q^38 - 6 * q^44 - 36 * q^45 + 92 * q^49 + 32 * q^53 - 58 * q^56 - 50 * q^58 - 2 * q^64 - 62 * q^70 - 44 * q^77 + 38 * q^80 + 72 * q^81 - 30 * q^82 - 18 * q^86 + 20 * q^88 - 16 * q^89 + 10 * q^92 + 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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