LMFDB - Embedded newform 686.2.c.b.667.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [686,2,Mod(361,686)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(686, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("686.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 686 = 2 \cdot 7^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	686.c (of order $3$, degree $2$, not 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:	$5.47773757866$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			667.3
Root			$-0.623490 + 1.07992i$ of defining polynomial
Character	$\chi$	$=$	686.667
Dual form			686.2.c.b.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(1.62349 + 2.81197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.123490 + 0.213891i) q^{5} -3.24698 q^{6} +1.00000 q^{8} +(-3.77144 + 6.53232i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(1.62349 + 2.81197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.123490 + 0.213891i) q^{5} -3.24698 q^{6} +1.00000 q^{8} +(-3.77144 + 6.53232i) q^{9} +(-0.123490 - 0.213891i) q^{10} +(2.52446 + 4.37249i) q^{11} +(1.62349 - 2.81197i) q^{12} -2.10992 q^{13} -0.801938 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48039 - 4.29615i) q^{17} +(-3.77144 - 6.53232i) q^{18} +(0.253020 - 0.438244i) q^{19} +0.246980 q^{20} -5.04892 q^{22} +(2.46950 - 4.27730i) q^{23} +(1.62349 + 2.81197i) q^{24} +(2.46950 + 4.27730i) q^{25} +(1.05496 - 1.82724i) q^{26} -14.7506 q^{27} -4.66487 q^{29} +(0.400969 - 0.694498i) q^{30} +(4.53803 + 7.86010i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.19687 + 14.1974i) q^{33} +4.96077 q^{34} +7.54288 q^{36} +(1.32155 - 2.28900i) q^{37} +(0.253020 + 0.438244i) q^{38} +(-3.42543 - 5.93301i) q^{39} +(-0.123490 + 0.213891i) q^{40} -6.70171 q^{41} +3.62565 q^{43} +(2.52446 - 4.37249i) q^{44} +(-0.931468 - 1.61335i) q^{45} +(2.46950 + 4.27730i) q^{46} +(-0.458615 + 0.794345i) q^{47} -3.24698 q^{48} -4.93900 q^{50} +(8.05376 - 13.9495i) q^{51} +(1.05496 + 1.82724i) q^{52} +(1.81282 + 3.13990i) q^{53} +(7.37531 - 12.7744i) q^{54} -1.24698 q^{55} +1.64310 q^{57} +(2.33244 - 4.03990i) q^{58} +(-3.83728 - 6.64637i) q^{59} +(0.400969 + 0.694498i) q^{60} +(6.51842 - 11.2902i) q^{61} -9.07606 q^{62} +1.00000 q^{64} +(0.260553 - 0.451291i) q^{65} +(-8.19687 - 14.1974i) q^{66} +(2.73341 + 4.73440i) q^{67} +(-2.48039 + 4.29615i) q^{68} +16.0368 q^{69} +11.2295 q^{71} +(-3.77144 + 6.53232i) q^{72} +(-2.68114 - 4.64386i) q^{73} +(1.32155 + 2.28900i) q^{74} +(-8.01842 + 13.8883i) q^{75} -0.506041 q^{76} +6.85086 q^{78} +(3.28232 - 5.68515i) q^{79} +(-0.123490 - 0.213891i) q^{80} +(-12.6332 - 21.8813i) q^{81} +(3.35086 - 5.80385i) q^{82} +0.753020 q^{83} +1.22521 q^{85} +(-1.81282 + 3.13990i) q^{86} +(-7.57338 - 13.1175i) q^{87} +(2.52446 + 4.37249i) q^{88} +(-4.84601 + 8.39354i) q^{89} +1.86294 q^{90} -4.93900 q^{92} +(-14.7349 + 25.5216i) q^{93} +(-0.458615 - 0.794345i) q^{94} +(0.0624909 + 0.108237i) q^{95} +(1.62349 - 2.81197i) q^{96} +12.2784 q^{97} -38.0834 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 5 q^{3} - 3 q^{4} + 4 q^{5} - 10 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 5 * q^3 - 3 * q^4 + 4 * q^5 - 10 * q^6 + 6 * q^8 - 4 * q^9	$ 6 q - 3 q^{2} + 5 q^{3} - 3 q^{4} + 4 q^{5} - 10 q^{6} + 6 q^{8} - 4 q^{9} + 4 q^{10} + 6 q^{11} + 5 q^{12} - 14 q^{13} + 4 q^{15} - 3 q^{16} - 2 q^{17} - 4 q^{18} + 11 q^{19} - 8 q^{20} - 12 q^{22} + 5 q^{23} + 5 q^{24} + 5 q^{25} + 7 q^{26} - 16 q^{27} - 30 q^{29} - 2 q^{30} + 12 q^{31} - 3 q^{32} - 17 q^{33} + 4 q^{34} + 8 q^{36} + 12 q^{37} + 11 q^{38} - 7 q^{39} + 4 q^{40} + 14 q^{41} - 2 q^{43} + 6 q^{44} - 11 q^{45} + 5 q^{46} + 4 q^{47} - 10 q^{48} - 10 q^{50} + 8 q^{51} + 7 q^{52} - q^{53} + 8 q^{54} + 2 q^{55} + 18 q^{57} + 15 q^{58} - 2 q^{59} - 2 q^{60} + 11 q^{61} - 24 q^{62} + 6 q^{64} - 14 q^{65} - 17 q^{66} + 13 q^{67} - 2 q^{68} + 40 q^{69} + 26 q^{71} - 4 q^{72} - 9 q^{73} + 12 q^{74} - 20 q^{75} - 22 q^{76} + 14 q^{78} - 2 q^{79} + 4 q^{80} - 27 q^{81} - 7 q^{82} + 14 q^{83} + 4 q^{85} + q^{86} - 18 q^{87} + 6 q^{88} - 24 q^{89} + 22 q^{90} - 10 q^{92} - 41 q^{93} + 4 q^{94} - 24 q^{95} + 5 q^{96} + 14 q^{97} - 72 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 5 * q^3 - 3 * q^4 + 4 * q^5 - 10 * q^6 + 6 * q^8 - 4 * q^9 + 4 * q^10 + 6 * q^11 + 5 * q^12 - 14 * q^13 + 4 * q^15 - 3 * q^16 - 2 * q^17 - 4 * q^18 + 11 * q^19 - 8 * q^20 - 12 * q^22 + 5 * q^23 + 5 * q^24 + 5 * q^25 + 7 * q^26 - 16 * q^27 - 30 * q^29 - 2 * q^30 + 12 * q^31 - 3 * q^32 - 17 * q^33 + 4 * q^34 + 8 * q^36 + 12 * q^37 + 11 * q^38 - 7 * q^39 + 4 * q^40 + 14 * q^41 - 2 * q^43 + 6 * q^44 - 11 * q^45 + 5 * q^46 + 4 * q^47 - 10 * q^48 - 10 * q^50 + 8 * q^51 + 7 * q^52 - q^53 + 8 * q^54 + 2 * q^55 + 18 * q^57 + 15 * q^58 - 2 * q^59 - 2 * q^60 + 11 * q^61 - 24 * q^62 + 6 * q^64 - 14 * q^65 - 17 * q^66 + 13 * q^67 - 2 * q^68 + 40 * q^69 + 26 * q^71 - 4 * q^72 - 9 * q^73 + 12 * q^74 - 20 * q^75 - 22 * q^76 + 14 * q^78 - 2 * q^79 + 4 * q^80 - 27 * q^81 - 7 * q^82 + 14 * q^83 + 4 * q^85 + q^86 - 18 * q^87 + 6 * q^88 - 24 * q^89 + 22 * q^90 - 10 * q^92 - 41 * q^93 + 4 * q^94 - 24 * q^95 + 5 * q^96 + 14 * q^97 - 72 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/686\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	1.62349	+	2.81197i	0.937322	+	1.62349i	0.770440	+	0.637513i	$0.220037\pi$
$3$	1.62349	+	2.81197i	0.937322	+	1.62349i	0.166883	+	0.985977i	$0.446630\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.123490	+	0.213891i	−0.0552263	+	0.0956548i	−0.892317	−	0.451410i	$-0.850921\pi$
$5$	−0.123490	+	0.213891i	−0.0552263	+	0.0956548i	0.837091	+	0.547064i	$0.184255\pi$
$6$	−3.24698			−1.32557
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−3.77144	+	6.53232i	−1.25715	+	2.17744i
$10$	−0.123490	−	0.213891i	−0.0390509	−	0.0676382i
$11$	2.52446	+	4.37249i	0.761153	+	1.31836i	0.942257	+	0.334892i	$0.108700\pi$
$11$	2.52446	+	4.37249i	0.761153	+	1.31836i	−0.181104	+	0.983464i	$0.557967\pi$
$12$	1.62349	−	2.81197i	0.468661	−	0.811745i
$13$	−2.10992			−0.585185			−0.292593	−	0.956237i	$-0.594518\pi$
$13$	−2.10992			−0.585185			−0.292593	+	0.956237i	$0.594518\pi$
$14$		0			0
$15$	−0.801938			−0.207059
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.48039	−	4.29615i	−0.601582	−	1.04197i	−0.992582	−	0.121580i	$-0.961204\pi$
$17$	−2.48039	−	4.29615i	−0.601582	−	1.04197i	0.391000	−	0.920391i	$-0.372129\pi$
$18$	−3.77144	−	6.53232i	−0.888937	−	1.53968i
$19$	0.253020	−	0.438244i	0.0580469	−	0.100540i	−0.835542	−	0.549427i	$-0.814846\pi$
$19$	0.253020	−	0.438244i	0.0580469	−	0.100540i	0.893589	+	0.448887i	$0.148179\pi$
$20$	0.246980			0.0552263
$21$		0			0
$22$	−5.04892			−1.07643
$23$	2.46950	−	4.27730i	0.514926	−	0.891879i	−0.484924	−	0.874557i	$-0.661153\pi$
$23$	2.46950	−	4.27730i	0.514926	−	0.891879i	0.999850	−	0.0173222i	$-0.00551411\pi$
$24$	1.62349	+	2.81197i	0.331393	+	0.573990i
$25$	2.46950	+	4.27730i	0.493900	+	0.855460i
$26$	1.05496	−	1.82724i	0.206894	−	0.358351i
$27$	−14.7506			−2.83876
$28$		0			0
$29$	−4.66487			−0.866245			−0.433123	−	0.901335i	$-0.642588\pi$
$29$	−4.66487			−0.866245			−0.433123	+	0.901335i	$0.642588\pi$
$30$	0.400969	−	0.694498i	0.0732066	−	0.126797i
$31$	4.53803	+	7.86010i	0.815055	+	1.41172i	0.909289	+	0.416166i	$0.136626\pi$
$31$	4.53803	+	7.86010i	0.815055	+	1.41172i	−0.0942340	+	0.995550i	$0.530040\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−8.19687	+	14.1974i	−1.42689	+	2.47145i
$34$	4.96077			0.850765
$35$		0			0
$36$	7.54288			1.25715
$37$	1.32155	−	2.28900i	0.217262	−	0.376309i	−0.736708	−	0.676211i	$-0.763621\pi$
$37$	1.32155	−	2.28900i	0.217262	−	0.376309i	0.953970	+	0.299902i	$0.0969541\pi$
$38$	0.253020	+	0.438244i	0.0410453	+	0.0710926i
$39$	−3.42543	−	5.93301i	−0.548507	−	0.950043i
$40$	−0.123490	+	0.213891i	−0.0195255	+	0.0338191i
$41$	−6.70171			−1.04663			−0.523316	−	0.852139i	$-0.675305\pi$
$41$	−6.70171			−1.04663			−0.523316	+	0.852139i	$0.675305\pi$
$42$		0			0
$43$	3.62565			0.552906			0.276453	−	0.961027i	$-0.410841\pi$
$43$	3.62565			0.552906			0.276453	+	0.961027i	$0.410841\pi$
$44$	2.52446	−	4.37249i	0.380576	−	0.659178i
$45$	−0.931468	−	1.61335i	−0.138855	−	0.240504i
$46$	2.46950	+	4.27730i	0.364108	+	0.630654i
$47$	−0.458615	+	0.794345i	−0.0668959	+	0.115867i	−0.897533	−	0.440946i	$-0.854643\pi$
$47$	−0.458615	+	0.794345i	−0.0668959	+	0.115867i	0.830638	+	0.556814i	$0.187976\pi$
$48$	−3.24698			−0.468661
$49$		0			0
$50$	−4.93900			−0.698480
$51$	8.05376	−	13.9495i	1.12775	−	1.95332i
$52$	1.05496	+	1.82724i	0.146296	+	0.253393i
$53$	1.81282	+	3.13990i	0.249010	+	0.431299i	0.963251	−	0.268601i	$-0.0865613\pi$
$53$	1.81282	+	3.13990i	0.249010	+	0.431299i	−0.714241	+	0.699900i	$0.753228\pi$
$54$	7.37531	−	12.7744i	1.00365	−	1.73838i
$55$	−1.24698			−0.168143
$56$		0			0
$57$	1.64310			0.217634
$58$	2.33244	−	4.03990i	0.306264	−	0.530465i
$59$	−3.83728	−	6.64637i	−0.499572	−	0.865283i	0.500428	−	0.865778i	$-0.333176\pi$
$59$	−3.83728	−	6.64637i	−0.499572	−	0.865283i	−1.00000		0.000494713i	$0.999843\pi$
$60$	0.400969	+	0.694498i	0.0517649	+	0.0896594i
$61$	6.51842	−	11.2902i	0.834598	−	1.44557i	−0.0597595	−	0.998213i	$-0.519033\pi$
$61$	6.51842	−	11.2902i	0.834598	−	1.44557i	0.894357	−	0.447353i	$-0.147633\pi$
$62$	−9.07606			−1.15266
$63$		0			0
$64$	1.00000			0.125000
$65$	0.260553	−	0.451291i	0.0323176	−	0.0559758i
$66$	−8.19687	−	14.1974i	−1.00896	−	1.74758i
$67$	2.73341	+	4.73440i	0.333939	+	0.578399i	0.983280	−	0.182098i	$-0.0582888\pi$
$67$	2.73341	+	4.73440i	0.333939	+	0.578399i	−0.649342	+	0.760497i	$0.724955\pi$
$68$	−2.48039	+	4.29615i	−0.300791	+	0.520985i
$69$	16.0368			1.93061
$70$		0			0
$71$	11.2295			1.33270			0.666349	−	0.745640i	$-0.267856\pi$
$71$	11.2295			1.33270			0.666349	+	0.745640i	$0.267856\pi$
$72$	−3.77144	+	6.53232i	−0.444468	+	0.769842i
$73$	−2.68114	−	4.64386i	−0.313803	−	0.543523i	0.665379	−	0.746506i	$-0.268270\pi$
$73$	−2.68114	−	4.64386i	−0.313803	−	0.543523i	−0.979182	+	0.202982i	$0.934937\pi$
$74$	1.32155	+	2.28900i	0.153627	+	0.266090i
$75$	−8.01842	+	13.8883i	−0.925887	+	1.60368i
$76$	−0.506041			−0.0580469
$77$		0			0
$78$	6.85086			0.775707
$79$	3.28232	−	5.68515i	0.369290	−	0.639629i	−0.620165	−	0.784472i	$-0.712934\pi$
$79$	3.28232	−	5.68515i	0.369290	−	0.639629i	0.989455	+	0.144842i	$0.0462675\pi$
$80$	−0.123490	−	0.213891i	−0.0138066	−	0.0239137i
$81$	−12.6332	−	21.8813i	−1.40369	−	2.43126i
$82$	3.35086	−	5.80385i	0.370040	−	0.640928i
$83$	0.753020			0.0826547			0.0413274	−	0.999146i	$-0.486841\pi$
$83$	0.753020			0.0826547			0.0413274	+	0.999146i	$0.486841\pi$
$84$		0			0
$85$	1.22521			0.132893
$86$	−1.81282	+	3.13990i	−0.195482	+	0.338584i
$87$	−7.57338	−	13.1175i	−0.811951	−	1.40634i
$88$	2.52446	+	4.37249i	0.269108	+	0.466109i
$89$	−4.84601	+	8.39354i	−0.513676	+	0.889713i	0.486198	+	0.873849i	$0.338383\pi$
$89$	−4.84601	+	8.39354i	−0.513676	+	0.889713i	−0.999874	+	0.0158645i	$0.994950\pi$
$90$	1.86294			0.196371
$91$		0			0
$92$	−4.93900			−0.514926
$93$	−14.7349	+	25.5216i	−1.52794	+	2.64647i
$94$	−0.458615	−	0.794345i	−0.0473026	−	0.0819304i
$95$	0.0624909	+	0.108237i	0.00641143	+	0.0111049i
$96$	1.62349	−	2.81197i	0.165697	−	0.286995i
$97$	12.2784			1.24669			0.623343	−	0.781948i	$-0.285774\pi$
$97$	12.2784			1.24669			0.623343	+	0.781948i	$0.285774\pi$
$98$		0			0
$99$	−38.0834			−3.82752
$100$	2.46950	−	4.27730i	0.246950	−	0.427730i
$101$	7.81431	+	13.5348i	0.777553	+	1.34676i	0.933348	+	0.358973i	$0.116873\pi$
$101$	7.81431	+	13.5348i	0.777553	+	1.34676i	−0.155795	+	0.987789i	$0.549794\pi$
$102$	8.05376	+	13.9495i	0.797441	+	1.38121i
$103$	0.513574	−	0.889535i	0.0506039	−	0.0876485i	−0.839614	−	0.543184i	$-0.817219\pi$
$103$	0.513574	−	0.889535i	0.0506039	−	0.0876485i	0.890218	+	0.455535i	$0.150552\pi$
$104$	−2.10992			−0.206894
$105$		0			0
$106$	−3.62565			−0.352154
$107$	−3.41939	+	5.92255i	−0.330565	+	0.572555i	−0.982623	−	0.185614i	$-0.940572\pi$
$107$	−3.41939	+	5.92255i	−0.330565	+	0.572555i	0.652058	+	0.758169i	$0.273906\pi$
$108$	7.37531	+	12.7744i	0.709690	+	1.22922i
$109$	0.228562	+	0.395881i	0.0218922	+	0.0379185i	0.876764	−	0.480921i	$-0.159698\pi$
$109$	0.228562	+	0.395881i	0.0218922	+	0.0379185i	−0.854872	+	0.518839i	$0.826364\pi$
$110$	0.623490	−	1.07992i	0.0594474	−	0.102966i
$111$	8.58211			0.814577
$112$		0			0
$113$	13.4722			1.26736			0.633678	−	0.773597i	$-0.281544\pi$
$113$	13.4722			1.26736			0.633678	+	0.773597i	$0.281544\pi$
$114$	−0.821552	+	1.42297i	−0.0769454	+	0.133273i
$115$	0.609916	+	1.05641i	0.0568750	+	0.0985104i
$116$	2.33244	+	4.03990i	0.216561	+	0.375095i
$117$	7.95742	−	13.7827i	0.735664	−	1.27421i
$118$	7.67456			0.706501
$119$		0			0
$120$	−0.801938			−0.0732066
$121$	−7.24578	+	12.5501i	−0.658708	+	1.14091i
$122$	6.51842	+	11.2902i	0.590150	+	1.02217i
$123$	−10.8802	−	18.8450i	−0.981031	−	1.69920i
$124$	4.53803	−	7.86010i	0.407527	−	0.705858i
$125$	−2.45473			−0.219558
$126$		0			0
$127$	14.1129			1.25232			0.626159	−	0.779696i	$-0.284626\pi$
$127$	14.1129			1.25232			0.626159	+	0.779696i	$0.284626\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	5.88620	+	10.1952i	0.518251	+	0.897637i
$130$	0.260553	+	0.451291i	0.0228520	+	0.0395809i
$131$	−2.49396	+	4.31966i	−0.217898	+	0.377411i	−0.954165	−	0.299280i	$-0.903253\pi$
$131$	−2.49396	+	4.31966i	−0.217898	+	0.377411i	0.736267	+	0.676691i	$0.236587\pi$
$132$	16.3937			1.42689
$133$		0			0
$134$	−5.46681			−0.472261
$135$	1.82155	−	3.15502i	0.156774	−	0.271541i
$136$	−2.48039	−	4.29615i	−0.212691	−	0.368392i
$137$	7.26540	+	12.5840i	0.620725	+	1.07513i	0.989351	+	0.145549i	$0.0464949\pi$
$137$	7.26540	+	12.5840i	0.620725	+	1.07513i	−0.368626	+	0.929578i	$0.620172\pi$
$138$	−8.01842	+	13.8883i	−0.682573	+	1.18225i
$139$	−13.6649			−1.15904			−0.579520	−	0.814958i	$-0.696760\pi$
$139$	−13.6649			−1.15904			−0.579520	+	0.814958i	$0.696760\pi$
$140$		0			0
$141$	−2.97823			−0.250812
$142$	−5.61476	+	9.72505i	−0.471180	+	0.816108i
$143$	−5.32640	−	9.22559i	−0.445416	−	0.771483i
$144$	−3.77144	−	6.53232i	−0.314287	−	0.544360i
$145$	0.576064	−	0.997773i	0.0478395	−	0.0828605i
$146$	5.36227			0.443785
$147$		0			0
$148$	−2.64310			−0.217262
$149$	−2.72252	+	4.71554i	−0.223038	+	0.386312i	−0.955729	−	0.294249i	$-0.904931\pi$
$149$	−2.72252	+	4.71554i	−0.223038	+	0.386312i	0.732691	+	0.680561i	$0.238264\pi$
$150$	−8.01842	−	13.8883i	−0.654701	−	1.13398i
$151$	3.21110	+	5.56179i	0.261316	+	0.452612i	0.966592	−	0.256320i	$-0.0825102\pi$
$151$	3.21110	+	5.56179i	0.261316	+	0.452612i	−0.705276	+	0.708933i	$0.749177\pi$
$152$	0.253020	−	0.438244i	0.0205227	−	0.0355463i
$153$	37.4185			3.02511
$154$		0			0
$155$	−2.24160			−0.180050
$156$	−3.42543	+	5.93301i	−0.274254	+	0.475021i
$157$	−1.32424	−	2.29365i	−0.105686	−	0.183053i	0.808332	−	0.588726i	$-0.200370\pi$
$157$	−1.32424	−	2.29365i	−0.105686	−	0.183053i	−0.914018	+	0.405673i	$0.867037\pi$
$158$	3.28232	+	5.68515i	0.261128	+	0.452286i
$159$	−5.88620	+	10.1952i	−0.466806	+	0.808532i
$160$	0.246980			0.0195255
$161$		0			0
$162$	25.2664			1.98511
$163$	1.50753	−	2.61112i	0.118079	−	0.204519i	−0.800927	−	0.598762i	$-0.795660\pi$
$163$	1.50753	−	2.61112i	0.118079	−	0.204519i	0.919006	+	0.394243i	$0.128993\pi$
$164$	3.35086	+	5.80385i	0.261658	+	0.453205i
$165$	−2.02446	−	3.50647i	−0.157604	−	0.272978i
$166$	−0.376510	+	0.652135i	−0.0292229	+	0.0506155i
$167$	−13.7017			−1.06027			−0.530135	−	0.847913i	$-0.677859\pi$
$167$	−13.7017			−1.06027			−0.530135	+	0.847913i	$0.677859\pi$
$168$		0			0
$169$	−8.54825			−0.657558
$170$	−0.612605	+	1.06106i	−0.0469846	+	0.0813798i
$171$	1.90850	+	3.30562i	0.145947	+	0.252787i
$172$	−1.81282	−	3.13990i	−0.138226	−	0.239415i
$173$	−2.95324	+	5.11516i	−0.224531	+	0.388898i	−0.956179	−	0.292784i	$-0.905418\pi$
$173$	−2.95324	+	5.11516i	−0.224531	+	0.388898i	0.731648	+	0.681683i	$0.238752\pi$
$174$	15.1468			1.14827
$175$		0			0
$176$	−5.04892			−0.380576
$177$	12.4596	−	21.5806i	0.936519	−	1.62210i
$178$	−4.84601	−	8.39354i	−0.363224	−	0.629122i
$179$	−4.21864	−	7.30689i	−0.315316	−	0.546143i	0.664189	−	0.747565i	$-0.268777\pi$
$179$	−4.21864	−	7.30689i	−0.315316	−	0.546143i	−0.979505	+	0.201422i	$0.935444\pi$
$180$	−0.931468	+	1.61335i	−0.0694276	+	0.120252i
$181$	13.1347			0.976292			0.488146	−	0.872762i	$-0.337673\pi$
$181$	13.1347			0.976292			0.488146	+	0.872762i	$0.337673\pi$
$182$		0			0
$183$	42.3303			3.12915
$184$	2.46950	−	4.27730i	0.182054	−	0.315327i
$185$	0.326396	+	0.565335i	0.0239971	+	0.0415643i
$186$	−14.7349	−	25.5216i	−1.08042	−	1.87133i
$187$	12.5233	−	21.6909i	0.915792	−	1.58620i
$188$	0.917231			0.0668959
$189$		0			0
$190$	−0.124982			−0.00906713
$191$	5.09030	−	8.81666i	0.368321	−	0.637951i	−0.620982	−	0.783825i	$-0.713266\pi$
$191$	5.09030	−	8.81666i	0.368321	−	0.637951i	0.989303	+	0.145874i	$0.0465993\pi$
$192$	1.62349	+	2.81197i	0.117165	+	0.202936i
$193$	5.04772	+	8.74291i	0.363343	+	0.629328i	0.988509	−	0.151164i	$-0.0483020\pi$
$193$	5.04772	+	8.74291i	0.363343	+	0.629328i	−0.625166	+	0.780492i	$0.714969\pi$
$194$	−6.13922	+	10.6334i	−0.440770	+	0.763436i
$195$	1.69202			0.121168
$196$		0			0
$197$	−2.38942			−0.170239			−0.0851196	−	0.996371i	$-0.527127\pi$
$197$	−2.38942			−0.170239			−0.0851196	+	0.996371i	$0.527127\pi$
$198$	19.0417	−	32.9812i	1.35323	−	2.34387i
$199$	9.81282	+	16.9963i	0.695613	+	1.20484i	0.969974	+	0.243210i	$0.0782003\pi$
$199$	9.81282	+	16.9963i	0.695613	+	1.20484i	−0.274361	+	0.961627i	$0.588466\pi$
$200$	2.46950	+	4.27730i	0.174620	+	0.302451i
$201$	−8.87531	+	15.3725i	−0.626016	+	1.08429i
$202$	−15.6286			−1.09963
$203$		0			0
$204$	−16.1075			−1.12775
$205$	0.827593	−	1.43343i	0.0578016	−	0.100115i
$206$	0.513574	+	0.889535i	0.0357824	+	0.0619769i
$207$	18.6271	+	32.2631i	1.29468	+	2.24244i
$208$	1.05496	−	1.82724i	0.0731482	−	0.126696i
$209$	2.55496			0.176730
$210$		0			0
$211$	−11.0978			−0.764006			−0.382003	−	0.924161i	$-0.624766\pi$
$211$	−11.0978			−0.764006			−0.382003	+	0.924161i	$0.624766\pi$
$212$	1.81282	−	3.13990i	0.124505	−	0.215649i
$213$	18.2310	+	31.5770i	1.24917	+	2.16362i
$214$	−3.41939	−	5.92255i	−0.233744	−	0.404857i
$215$	−0.447730	+	0.775492i	−0.0305350	+	0.0528881i
$216$	−14.7506			−1.00365
$217$		0			0
$218$	−0.457123			−0.0309603
$219$	8.70560	−	15.0785i	0.588270	−	1.01891i
$220$	0.623490	+	1.07992i	0.0420357	+	0.0728079i
$221$	5.23341	+	9.06453i	0.352037	+	0.609746i
$222$	−4.29105	+	7.43232i	−0.287997	+	0.498825i
$223$	24.3250			1.62892			0.814460	−	0.580220i	$-0.197033\pi$
$223$	24.3250			1.62892			0.814460	+	0.580220i	$0.197033\pi$
$224$		0			0
$225$	−37.2543			−2.48362
$226$	−6.73609	+	11.6673i	−0.448078	+	0.776094i
$227$	−8.29470	−	14.3668i	−0.550539	−	0.953561i	−0.998236	−	0.0593756i	$-0.981089\pi$
$227$	−8.29470	−	14.3668i	−0.550539	−	0.953561i	0.447697	−	0.894185i	$-0.352244\pi$
$228$	−0.821552	−	1.42297i	−0.0544086	−	0.0942385i
$229$	12.6310	−	21.8776i	0.834681	−	1.44571i	−0.0596080	−	0.998222i	$-0.518985\pi$
$229$	12.6310	−	21.8776i	0.834681	−	1.44571i	0.894290	−	0.447489i	$-0.147682\pi$
$230$	−1.21983			−0.0804334
$231$		0			0
$232$	−4.66487			−0.306264
$233$	2.37651	−	4.11624i	0.155690	−	0.269664i	−0.777620	−	0.628735i	$-0.783573\pi$
$233$	2.37651	−	4.11624i	0.155690	−	0.269664i	0.933310	+	0.359071i	$0.116906\pi$
$234$	7.95742	+	13.7827i	0.520193	+	0.901000i
$235$	−0.113269	−	0.196187i	−0.00738883	−	0.0127978i
$236$	−3.83728	+	6.64637i	−0.249786	+	0.432642i
$237$	21.3153			1.38458
$238$		0			0
$239$	−3.56033			−0.230299			−0.115149	−	0.993348i	$-0.536735\pi$
$239$	−3.56033			−0.230299			−0.115149	+	0.993348i	$0.536735\pi$
$240$	0.400969	−	0.694498i	0.0258824	−	0.0448297i
$241$	−1.85354	−	3.21043i	−0.119397	−	0.206802i	0.800132	−	0.599824i	$-0.204763\pi$
$241$	−1.85354	−	3.21043i	−0.119397	−	0.206802i	−0.919529	+	0.393022i	$0.871430\pi$
$242$	−7.24578	−	12.5501i	−0.465777	−	0.806749i
$243$	18.8937	−	32.7249i	1.21203	−	2.09930i
$244$	−13.0368			−0.834598
$245$		0			0
$246$	21.7603			1.38739
$247$	−0.533852	+	0.924659i	−0.0339682	+	0.0588346i
$248$	4.53803	+	7.86010i	0.288165	+	0.499117i
$249$	1.22252	+	2.11747i	0.0774741	+	0.134189i
$250$	1.22737	−	2.12586i	0.0776254	−	0.134451i
$251$	−18.2107			−1.14945			−0.574726	−	0.818346i	$-0.694891\pi$
$251$	−18.2107			−1.14945			−0.574726	+	0.818346i	$0.694891\pi$
$252$		0			0
$253$	24.9366			1.56775
$254$	−7.05645	+	12.2221i	−0.442761	+	0.766885i
$255$	1.98911	+	3.44525i	0.124563	+	0.215750i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.99784	+	3.46037i	−0.124622	+	0.215852i	−0.921585	−	0.388176i	$-0.873105\pi$
$257$	−1.99784	+	3.46037i	−0.124622	+	0.215852i	0.796963	+	0.604028i	$0.206439\pi$
$258$	−11.7724			−0.732917
$259$		0			0
$260$	−0.521106			−0.0323176
$261$	17.5933	−	30.4725i	1.08900	−	1.88620i
$262$	−2.49396	−	4.31966i	−0.154077	−	0.266870i
$263$	−6.05161	−	10.4817i	−0.373158	−	0.646329i	0.616891	−	0.787048i	$-0.288392\pi$
$263$	−6.05161	−	10.4817i	−0.373158	−	0.646329i	−0.990049	+	0.140720i	$0.955058\pi$
$264$	−8.19687	+	14.1974i	−0.504482	+	0.873789i
$265$	−0.895461			−0.0550077
$266$		0			0
$267$	−31.4698			−1.92592
$268$	2.73341	−	4.73440i	0.166969	−	0.289199i
$269$	−13.9046	−	24.0835i	−0.847779	−	1.46840i	−0.883185	−	0.469024i	$-0.844606\pi$
$269$	−13.9046	−	24.0835i	−0.847779	−	1.46840i	0.0354059	−	0.999373i	$-0.488728\pi$
$270$	1.82155	+	3.15502i	0.110856	+	0.192008i
$271$	7.14526	−	12.3760i	0.434044	−	0.751786i	−0.563173	−	0.826339i	$-0.690420\pi$
$271$	7.14526	−	12.3760i	0.434044	−	0.751786i	0.997217	+	0.0745531i	$0.0237530\pi$
$272$	4.96077			0.300791
$273$		0			0
$274$	−14.5308			−0.877837
$275$	−12.4683	+	21.5957i	−0.751867	+	1.30227i
$276$	−8.01842	−	13.8883i	−0.482652	−	0.835978i
$277$	−8.61625	−	14.9238i	−0.517700	−	0.896683i	−0.999789	−	0.0205608i	$-0.993455\pi$
$277$	−8.61625	−	14.9238i	−0.517700	−	0.896683i	0.482088	−	0.876123i	$-0.339878\pi$
$278$	6.83244	−	11.8341i	0.409782	−	0.709764i
$279$	−68.4596			−4.09857
$280$		0			0
$281$	17.6461			1.05268			0.526339	−	0.850275i	$-0.323564\pi$
$281$	17.6461			1.05268			0.526339	+	0.850275i	$0.323564\pi$
$282$	1.48911	−	2.57922i	0.0886755	−	0.153590i
$283$	3.43147	+	5.94348i	0.203980	+	0.353303i	0.949807	−	0.312836i	$-0.101279\pi$
$283$	3.43147	+	5.94348i	0.203980	+	0.353303i	−0.745828	+	0.666139i	$0.767946\pi$
$284$	−5.61476	−	9.72505i	−0.333175	−	0.577076i
$285$	−0.202907	+	0.351445i	−0.0120191	+	0.0208178i
$286$	10.6528			0.629913
$287$		0			0
$288$	7.54288			0.444468
$289$	−3.80463	+	6.58981i	−0.223802	+	0.387636i
$290$	0.576064	+	0.997773i	0.0338277	+	0.0585912i
$291$	19.9339	+	34.5266i	1.16855	+	2.02398i
$292$	−2.68114	+	4.64386i	−0.156902	+	0.271762i
$293$	−11.4886			−0.671170			−0.335585	−	0.942010i	$-0.608934\pi$
$293$	−11.4886			−0.671170			−0.335585	+	0.942010i	$0.608934\pi$
$294$		0			0
$295$	1.89546			0.110358
$296$	1.32155	−	2.28900i	0.0768137	−	0.133045i
$297$	−37.2373	−	64.4970i	−2.16073	−	3.74249i
$298$	−2.72252	−	4.71554i	−0.157711	−	0.273164i
$299$	−5.21044	+	9.02475i	−0.301327	+	0.521915i
$300$	16.0368			0.925887
$301$		0			0
$302$	−6.42221			−0.369556
$303$	−25.3729	+	43.9472i	−1.45764	+	2.52470i
$304$	0.253020	+	0.438244i	0.0145117	+	0.0251350i
$305$	1.60992	+	2.78846i	0.0921835	+	0.159667i
$306$	−18.7092	+	32.4054i	−1.06954	+	1.85249i
$307$	12.6300			0.720830			0.360415	−	0.932792i	$-0.382635\pi$
$307$	12.6300			0.720830			0.360415	+	0.932792i	$0.382635\pi$
$308$		0			0
$309$	3.33513			0.189729
$310$	1.12080	−	1.94128i	0.0636572	−	0.110258i
$311$	−0.169719	−	0.293961i	−0.00962387	−	0.0166690i	0.861173	−	0.508311i	$-0.169730\pi$
$311$	−0.169719	−	0.293961i	−0.00962387	−	0.0166690i	−0.870797	+	0.491642i	$0.836397\pi$
$312$	−3.42543	−	5.93301i	−0.193927	−	0.335891i
$313$	10.8497	−	18.7922i	0.613259	−	1.06220i	−0.377428	−	0.926039i	$-0.623192\pi$
$313$	10.8497	−	18.7922i	0.613259	−	1.06220i	0.990687	−	0.136157i	$-0.0434751\pi$
$314$	2.64848			0.149462
$315$		0			0
$316$	−6.56465			−0.369290
$317$	5.36563	−	9.29354i	0.301364	−	0.521977i	−0.675082	−	0.737743i	$-0.735892\pi$
$317$	5.36563	−	9.29354i	0.301364	−	0.521977i	0.976445	+	0.215766i	$0.0692249\pi$
$318$	−5.88620	−	10.1952i	−0.330082	−	0.571718i
$319$	−11.7763	−	20.3971i	−0.659345	−	1.14202i
$320$	−0.123490	+	0.213891i	−0.00690329	+	0.0119568i
$321$	−22.2054			−1.23938
$322$		0			0
$323$	−2.51035			−0.139680
$324$	−12.6332	+	21.8813i	−0.701843	+	1.21563i
$325$	−5.21044	−	9.02475i	−0.289023	−	0.500603i
$326$	1.50753	+	2.61112i	0.0834945	+	0.144617i
$327$	−0.742135	+	1.28542i	−0.0410402	+	0.0710837i
$328$	−6.70171			−0.370040
$329$		0			0
$330$	4.04892			0.222886
$331$	−12.7485	+	22.0810i	−0.700719	+	1.21368i	0.267495	+	0.963559i	$0.413804\pi$
$331$	−12.7485	+	22.0810i	−0.700719	+	1.21368i	−0.968214	+	0.250122i	$0.919529\pi$
$332$	−0.376510	−	0.652135i	−0.0206637	−	0.0357905i
$333$	9.96830	+	17.2656i	0.546260	+	0.946150i
$334$	6.85086	−	11.8660i	0.374862	−	0.649280i
$335$	−1.35019			−0.0737688
$336$		0			0
$337$	17.0586			0.929241			0.464621	−	0.885510i	$-0.346191\pi$
$337$	17.0586			0.929241			0.464621	+	0.885510i	$0.346191\pi$
$338$	4.27413	−	7.40300i	0.232482	−	0.402670i
$339$	21.8720	+	37.8833i	1.18792	+	2.05754i
$340$	−0.612605	−	1.06106i	−0.0332232	−	0.0575442i
$341$	−22.9121	+	39.6850i	−1.24076	+	2.14906i
$342$	−3.81700			−0.206400
$343$		0			0
$344$	3.62565			0.195482
$345$	−1.98039	+	3.43013i	−0.106620	+	0.184672i
$346$	−2.95324	−	5.11516i	−0.158767	−	0.274993i
$347$	−12.3998	−	21.4770i	−0.665655	−	1.15295i	−0.979107	−	0.203344i	$-0.934819\pi$
$347$	−12.3998	−	21.4770i	−0.665655	−	1.15295i	0.313453	−	0.949604i	$-0.398514\pi$
$348$	−7.57338	+	13.1175i	−0.405976	+	0.703170i
$349$	−18.1002			−0.968883			−0.484441	−	0.874824i	$-0.660977\pi$
$349$	−18.1002			−0.968883			−0.484441	+	0.874824i	$0.660977\pi$
$350$		0			0
$351$	31.1226			1.66120
$352$	2.52446	−	4.37249i	0.134554	−	0.233055i
$353$	−4.01961	−	6.96218i	−0.213942	−	0.370559i	0.739002	−	0.673703i	$-0.235297\pi$
$353$	−4.01961	−	6.96218i	−0.213942	−	0.370559i	−0.952945	+	0.303144i	$0.901964\pi$
$354$	12.4596	+	21.5806i	0.662219	+	1.14700i
$355$	−1.38673	+	2.40189i	−0.0736001	+	0.127479i
$356$	9.69202			0.513676
$357$		0			0
$358$	8.43727			0.445924
$359$	−6.78501	+	11.7520i	−0.358099	+	0.620246i	−0.987643	−	0.156719i	$-0.949908\pi$
$359$	−6.78501	+	11.7520i	−0.358099	+	0.620246i	0.629544	+	0.776965i	$0.283242\pi$
$360$	−0.931468	−	1.61335i	−0.0490927	−	0.0850310i
$361$	9.37196	+	16.2327i	0.493261	+	0.854353i
$362$	−6.56734	+	11.3750i	−0.345171	+	0.597855i
$363$	−47.0538			−2.46969
$364$		0			0
$365$	1.32437			0.0693208
$366$	−21.1652	+	36.6591i	−1.10632	+	1.91620i
$367$	3.95712	+	6.85394i	0.206560	+	0.357773i	0.950629	−	0.310331i	$-0.100440\pi$
$367$	3.95712	+	6.85394i	0.206560	+	0.357773i	−0.744069	+	0.668103i	$0.767106\pi$
$368$	2.46950	+	4.27730i	0.128732	+	0.222970i
$369$	25.2751	−	43.7777i	1.31577	−	2.27898i
$370$	−0.652793			−0.0339371
$371$		0			0
$372$	29.4698			1.52794
$373$	3.13318	−	5.42682i	0.162230	−	0.280990i	−0.773438	−	0.633872i	$-0.781465\pi$
$373$	3.13318	−	5.42682i	0.162230	−	0.280990i	0.935668	+	0.352881i	$0.114798\pi$
$374$	12.5233	+	21.6909i	0.647562	+	1.12161i
$375$	−3.98523	−	6.90262i	−0.205796	−	0.356450i
$376$	−0.458615	+	0.794345i	−0.0236513	+	0.0409652i
$377$	9.84249			0.506914
$378$		0			0
$379$	−31.5749			−1.62190			−0.810948	−	0.585119i	$-0.801048\pi$
$379$	−31.5749			−1.62190			−0.810948	+	0.585119i	$0.801048\pi$
$380$	0.0624909	−	0.108237i	0.00320571	−	0.00555246i
$381$	22.9121	+	39.6850i	1.17382	+	2.03312i
$382$	5.09030	+	8.81666i	0.260443	+	0.451100i
$383$	17.1528	−	29.7095i	0.876467	−	1.51808i	0.0212748	−	0.999774i	$-0.493228\pi$
$383$	17.1528	−	29.7095i	0.876467	−	1.51808i	0.855192	−	0.518311i	$-0.173439\pi$
$384$	−3.24698			−0.165697
$385$		0			0
$386$	−10.0954			−0.513844
$387$	−13.6739	+	23.6839i	−0.695083	+	1.20392i
$388$	−6.13922	−	10.6334i	−0.311672	−	0.539831i
$389$	−11.3448	−	19.6498i	−0.575205	−	0.996284i	−0.996019	−	0.0891374i	$-0.971589\pi$
$389$	−11.3448	−	19.6498i	−0.575205	−	0.996284i	0.420814	−	0.907147i	$-0.361744\pi$
$390$	−0.846011	+	1.46533i	−0.0428394	+	0.0742001i
$391$	−24.5013			−1.23908
$392$		0			0
$393$	−16.1957			−0.816963
$394$	1.19471	−	2.06930i	0.0601886	−	0.104250i
$395$	0.810667	+	1.40412i	0.0407891	+	0.0706488i
$396$	19.0417	+	32.9812i	0.956880	+	1.65737i
$397$	2.38135	−	4.12463i	0.119517	−	0.207009i	−0.800060	−	0.599921i	$-0.795199\pi$
$397$	2.38135	−	4.12463i	0.119517	−	0.207009i	0.919576	+	0.392912i	$0.128532\pi$
$398$	−19.6256			−0.983745
$399$		0			0
$400$	−4.93900			−0.246950
$401$	5.91335	−	10.2422i	0.295298	−	0.511472i	−0.679756	−	0.733438i	$-0.737914\pi$
$401$	5.91335	−	10.2422i	0.295298	−	0.511472i	0.975054	+	0.221967i	$0.0712476\pi$
$402$	−8.87531	−	15.3725i	−0.442660	−	0.766710i
$403$	−9.57487	−	16.5842i	−0.476958	−	0.826116i
$404$	7.81431	−	13.5348i	0.388777	−	0.673381i
$405$	6.24027			0.310082
$406$		0			0
$407$	13.3448			0.661478
$408$	8.05376	−	13.9495i	0.398721	−	0.690604i
$409$	0.132219	+	0.229010i	0.00653781	+	0.0113238i	0.869276	−	0.494327i	$-0.164586\pi$
$409$	0.132219	+	0.229010i	0.00653781	+	0.0113238i	−0.862738	+	0.505651i	$0.831252\pi$
$410$	0.827593	+	1.43343i	0.0408719	+	0.0707922i
$411$	−23.5906	+	40.8601i	−1.16364	+	2.01548i
$412$	−1.02715			−0.0506039
$413$		0			0
$414$	−37.2543			−1.83095
$415$	−0.0929903	+	0.161064i	−0.00456472	+	0.00790632i
$416$	1.05496	+	1.82724i	0.0517236	+	0.0895879i
$417$	−22.1848	−	38.4252i	−1.08639	−	1.88169i
$418$	−1.27748	+	2.21266i	−0.0624835	+	0.108225i
$419$	32.3672			1.58124			0.790620	−	0.612307i	$-0.209758\pi$
$419$	32.3672			1.58124			0.790620	+	0.612307i	$0.209758\pi$
$420$		0			0
$421$	−2.95646			−0.144089			−0.0720445	−	0.997401i	$-0.522952\pi$
$421$	−2.95646			−0.144089			−0.0720445	+	0.997401i	$0.522952\pi$
$422$	5.54892	−	9.61101i	0.270117	−	0.467856i
$423$	−3.45928	−	5.99165i	−0.168196	−	0.291324i
$424$	1.81282	+	3.13990i	0.0880385	+	0.152487i
$425$	12.2506	−	21.2187i	0.594243	−	1.02926i
$426$	−36.4620			−1.76659
$427$		0			0
$428$	6.83877			0.330565
$429$	17.2947	−	29.9553i	0.834996	−	1.44626i
$430$	−0.447730	−	0.775492i	−0.0215915	−	0.0373975i
$431$	−16.7126	−	28.9471i	−0.805017	−	1.39433i	−0.916279	−	0.400540i	$-0.868823\pi$
$431$	−16.7126	−	28.9471i	−0.805017	−	1.39433i	0.111262	−	0.993791i	$-0.464511\pi$
$432$	7.37531	−	12.7744i	0.354845	−	0.614609i
$433$	−0.670251			−0.0322102			−0.0161051	−	0.999870i	$-0.505127\pi$
$433$	−0.670251			−0.0322102			−0.0161051	+	0.999870i	$0.505127\pi$
$434$		0			0
$435$	3.74094			0.179364
$436$	0.228562	−	0.395881i	0.0109461	−	0.0189592i
$437$	−1.24967	−	2.16449i	−0.0597797	−	0.103542i
$438$	8.70560	+	15.0785i	0.415969	+	0.720480i
$439$	−7.14556	+	12.3765i	−0.341039	+	0.590696i	−0.984626	−	0.174676i	$-0.944112\pi$
$439$	−7.14556	+	12.3765i	−0.341039	+	0.590696i	0.643587	+	0.765373i	$0.277445\pi$
$440$	−1.24698			−0.0594474
$441$		0			0
$442$	−10.4668			−0.497855
$443$	−4.54072	+	7.86476i	−0.215736	+	0.373666i	−0.953500	−	0.301393i	$-0.902548\pi$
$443$	−4.54072	+	7.86476i	−0.215736	+	0.373666i	0.737764	+	0.675059i	$0.235882\pi$
$444$	−4.29105	−	7.43232i	−0.203644	−	0.352722i
$445$	−1.19687	−	2.07303i	−0.0567369	−	0.0982712i
$446$	−12.1625	+	21.0660i	−0.575910	+	0.997506i
$447$	−17.6799			−0.836232
$448$		0			0
$449$	−19.4843			−0.919520			−0.459760	−	0.888043i	$-0.652064\pi$
$449$	−19.4843			−0.919520			−0.459760	+	0.888043i	$0.652064\pi$
$450$	18.6271	−	32.2631i	0.878092	−	1.52090i
$451$	−16.9182	−	29.3032i	−0.796646	−	1.37983i
$452$	−6.73609	−	11.6673i	−0.316839	−	0.548782i
$453$	−10.4264	+	18.0590i	−0.489874	+	0.848487i
$454$	16.5894			0.778579
$455$		0			0
$456$	1.64310			0.0769454
$457$	16.0966	−	27.8802i	0.752969	−	1.30418i	−0.193409	−	0.981118i	$-0.561954\pi$
$457$	16.0966	−	27.8802i	0.752969	−	1.30418i	0.946378	−	0.323062i	$-0.104712\pi$
$458$	12.6310	+	21.8776i	0.590209	+	1.02227i
$459$	36.5872	+	63.3710i	1.70775	+	2.95790i
$460$	0.609916	−	1.05641i	0.0284375	−	0.0492552i
$461$	30.9571			1.44181			0.720907	−	0.693032i	$-0.243726\pi$
$461$	30.9571			1.44181			0.720907	+	0.693032i	$0.243726\pi$
$462$		0			0
$463$	22.0315			1.02389			0.511944	−	0.859019i	$-0.328925\pi$
$463$	22.0315			1.02389			0.511944	+	0.859019i	$0.328925\pi$
$464$	2.33244	−	4.03990i	0.108281	−	0.187548i
$465$	−3.63922	−	6.30331i	−0.168765	−	0.292309i
$466$	2.37651	+	4.11624i	0.110090	+	0.190681i
$467$	−4.74482	+	8.21828i	−0.219564	+	0.380296i	−0.954675	−	0.297651i	$-0.903797\pi$
$467$	−4.74482	+	8.21828i	−0.219564	+	0.380296i	0.735111	+	0.677947i	$0.237130\pi$
$468$	−15.9148			−0.735664
$469$		0			0
$470$	0.226537			0.0104494
$471$	4.29978	−	7.44744i	0.198123	−	0.343160i
$472$	−3.83728	−	6.64637i	−0.176625	−	0.305924i
$473$	9.15279	+	15.8531i	0.420846	+	0.728926i
$474$	−10.6576	+	18.4596i	−0.489521	+	0.847876i
$475$	2.49934			0.114677
$476$		0			0
$477$	−27.3478			−1.25217
$478$	1.78017	−	3.08334i	0.0814230	−	0.141029i
$479$	−4.29859	−	7.44537i	−0.196407	−	0.340188i	0.750954	−	0.660355i	$-0.229594\pi$
$479$	−4.29859	−	7.44537i	−0.196407	−	0.340188i	−0.947361	+	0.320167i	$0.896261\pi$
$480$	0.400969	+	0.694498i	0.0183016	+	0.0316994i
$481$	−2.78836	+	4.82959i	−0.127138	+	0.220210i
$482$	3.70709			0.168853
$483$		0			0
$484$	14.4916			0.658708
$485$	−1.51626	+	2.62624i	−0.0688499	+	0.119252i
$486$	18.8937	+	32.7249i	0.857037	+	1.48443i
$487$	−12.8656	−	22.2839i	−0.582997	−	1.00978i	−0.995122	−	0.0986532i	$-0.968547\pi$
$487$	−12.8656	−	22.2839i	−0.582997	−	1.00978i	0.412125	−	0.911127i	$-0.364787\pi$
$488$	6.51842	−	11.2902i	0.295075	−	0.511085i
$489$	9.78986			0.442713
$490$		0			0
$491$	−17.3448			−0.782761			−0.391380	−	0.920229i	$-0.628002\pi$
$491$	−17.3448			−0.782761			−0.391380	+	0.920229i	$0.628002\pi$
$492$	−10.8802	+	18.8450i	−0.490515	+	0.849598i
$493$	11.5707	+	20.0410i	0.521118	+	0.902602i
$494$	−0.533852	−	0.924659i	−0.0240191	−	0.0416024i
$495$	4.70291	−	8.14567i	0.211380	−	0.366121i
$496$	−9.07606			−0.407527
$497$		0			0
$498$	−2.44504			−0.109565
$499$	18.0492	−	31.2622i	0.807994	−	1.39949i	−0.106258	−	0.994339i	$-0.533887\pi$
$499$	18.0492	−	31.2622i	0.807994	−	1.39949i	0.914251	−	0.405148i	$-0.132780\pi$
$500$	1.22737	+	2.12586i	0.0548894	+	0.0950713i
$501$	−22.2446	−	38.5288i	−0.993815	−	1.72134i
$502$	9.10537	−	15.7710i	0.406392	−	0.703892i
$503$	−7.33513			−0.327057			−0.163529	−	0.986539i	$-0.552288\pi$
$503$	−7.33513			−0.327057			−0.163529	+	0.986539i	$0.552288\pi$
$504$		0			0
$505$	−3.85995			−0.171766
$506$	−12.4683	+	21.5957i	−0.554284	+	0.960048i
$507$	−13.8780	−	24.0374i	−0.616344	−	1.06754i
$508$	−7.05645	−	12.2221i	−0.313079	−	0.542269i
$509$	−1.13049	+	1.95807i	−0.0501081	+	0.0867898i	−0.889992	−	0.455977i	$-0.849290\pi$
$509$	−1.13049	+	1.95807i	−0.0501081	+	0.0867898i	0.839883	+	0.542767i	$0.182623\pi$
$510$	−3.97823			−0.176159
$511$		0			0
$512$	1.00000			0.0441942
$513$	−3.73221	+	6.46438i	−0.164781	+	0.285409i
$514$	−1.99784	−	3.46037i	−0.0881211	−	0.152630i
$515$	0.126842	+	0.219697i	0.00558933	+	0.00968101i
$516$	5.88620	−	10.1952i	0.259125	−	0.448818i
$517$	−4.63102			−0.203672
$518$		0			0
$519$	−19.1782			−0.841830
$520$	0.260553	−	0.451291i	0.0114260	−	0.0197904i
$521$	−4.98158	−	8.62835i	−0.218247	−	0.378015i	0.736025	−	0.676954i	$-0.236701\pi$
$521$	−4.98158	−	8.62835i	−0.218247	−	0.378015i	−0.954272	+	0.298939i	$0.903367\pi$
$522$	17.5933	+	30.4725i	0.770037	+	1.33374i
$523$	15.6570	−	27.1187i	0.684632	−	1.18582i	−0.288921	−	0.957353i	$-0.593296\pi$
$523$	15.6570	−	27.1187i	0.684632	−	1.18582i	0.973552	−	0.228464i	$-0.0733702\pi$
$524$	4.98792			0.217898
$525$		0			0
$526$	12.1032			0.527725
$527$	22.5121	−	38.9922i	0.980644	−	1.69853i
$528$	−8.19687	−	14.1974i	−0.356723	−	0.617862i
$529$	−0.696866	−	1.20701i	−0.0302985	−	0.0524786i
$530$	0.447730	−	0.775492i	0.0194482	−	0.0336852i
$531$	57.8883			2.51214
$532$		0			0
$533$	14.1400			0.612473
$534$	15.7349	−	27.2536i	0.680916	−	1.17938i
$535$	−0.844519	−	1.46275i	−0.0365117	−	0.0632402i
$536$	2.73341	+	4.73440i	0.118065	+	0.204495i
$537$	13.6978	−	23.7253i	0.591105	−	1.02382i
$538$	27.8092			1.19894
$539$		0			0
$540$	−3.64310			−0.156774
$541$	15.1310	−	26.2077i	0.650533	−	1.12676i	−0.332460	−	0.943117i	$-0.607879\pi$
$541$	15.1310	−	26.2077i	0.650533	−	1.12676i	0.982994	−	0.183640i	$-0.0587880\pi$
$542$	7.14526	+	12.3760i	0.306915	+	0.531593i
$543$	21.3240	+	36.9343i	0.915101	+	1.58500i
$544$	−2.48039	+	4.29615i	−0.106346	+	0.184196i
$545$	−0.112900			−0.00483611
$546$		0			0
$547$	23.2760			0.995212			0.497606	−	0.867403i	$-0.334213\pi$
$547$	23.2760			0.995212			0.497606	+	0.867403i	$0.334213\pi$
$548$	7.26540	−	12.5840i	0.310362	−	0.537563i
$549$	49.1676	+	85.1608i	2.09842	+	3.63458i
$550$	−12.4683	−	21.5957i	−0.531650	−	0.920845i
$551$	−1.18031	+	2.04435i	−0.0502828	+	0.0870924i
$552$	16.0368			0.682573
$553$		0			0
$554$	17.2325			0.732139
$555$	−1.05980	+	1.83563i	−0.0449861	+	0.0779182i
$556$	6.83244	+	11.8341i	0.289760	+	0.501879i
$557$	10.8768	+	18.8392i	0.460865	+	0.798242i	0.999004	−	0.0446143i	$-0.0142059\pi$
$557$	10.8768	+	18.8392i	0.460865	+	0.798242i	−0.538139	+	0.842856i	$0.680873\pi$
$558$	34.2298	−	59.2878i	1.44906	−	2.50985i
$559$	−7.64981			−0.323552
$560$		0			0
$561$	81.3256			3.43357
$562$	−8.82304	+	15.2820i	−0.372178	+	0.644631i
$563$	18.6613	+	32.3223i	0.786479	+	1.36222i	0.928111	+	0.372303i	$0.121432\pi$
$563$	18.6613	+	32.3223i	0.786479	+	1.36222i	−0.141632	+	0.989919i	$0.545235\pi$
$564$	1.48911	+	2.57922i	0.0627030	+	0.108605i
$565$	−1.66368	+	2.88157i	−0.0699915	+	0.121229i
$566$	−6.86294			−0.288471
$567$		0			0
$568$	11.2295			0.471180
$569$	10.5679	−	18.3041i	0.443028	−	0.767347i	−0.554884	−	0.831927i	$-0.687238\pi$
$569$	10.5679	−	18.3041i	0.443028	−	0.767347i	0.997913	+	0.0645803i	$0.0205709\pi$
$570$	−0.202907	−	0.351445i	−0.00849882	−	0.0147204i
$571$	−23.0710	−	39.9601i	−0.965491	−	1.67228i	−0.708291	−	0.705920i	$-0.750534\pi$
$571$	−23.0710	−	39.9601i	−0.965491	−	1.67228i	−0.257199	−	0.966358i	$-0.582800\pi$
$572$	−5.32640	+	9.22559i	−0.222708	+	0.385741i
$573$	33.0562			1.38094
$574$		0			0
$575$	24.3937			1.01729
$576$	−3.77144	+	6.53232i	−0.157143	+	0.272180i
$577$	15.0417	+	26.0530i	0.626193	+	1.08460i	0.988309	+	0.152465i	$0.0487213\pi$
$577$	15.0417	+	26.0530i	0.626193	+	1.08460i	−0.362115	+	0.932133i	$0.617945\pi$
$578$	−3.80463	−	6.58981i	−0.158252	−	0.274100i
$579$	−16.3898	+	28.3880i	−0.681139	+	1.17977i
$580$	−1.15213			−0.0478395
$581$		0			0
$582$	−39.8678			−1.65258
$583$	−9.15279	+	15.8531i	−0.379070	+	0.656568i
$584$	−2.68114	−	4.64386i	−0.110946	−	0.192164i
$585$	1.96532	+	3.40403i	0.0812560	+	0.140740i
$586$	5.74429	−	9.94940i	0.237294	−	0.411006i
$587$	−7.40880			−0.305794			−0.152897	−	0.988242i	$-0.548860\pi$
$587$	−7.40880			−0.305794			−0.152897	+	0.988242i	$0.548860\pi$
$588$		0			0
$589$	4.59286			0.189245
$590$	−0.947730	+	1.64152i	−0.0390174	+	0.0675802i
$591$	−3.87920	−	6.71897i	−0.159569	−	0.276381i
$592$	1.32155	+	2.28900i	0.0543155	+	0.0940771i
$593$	−4.76779	+	8.25806i	−0.195790	+	0.339118i	−0.947159	−	0.320764i	$-0.896060\pi$
$593$	−4.76779	+	8.25806i	−0.195790	+	0.339118i	0.751369	+	0.659882i	$0.229394\pi$
$594$	74.4747			3.05573
$595$		0			0
$596$	5.44504			0.223038
$597$	−31.8620	+	55.1867i	−1.30403	+	2.25864i
$598$	−5.21044	−	9.02475i	−0.213071	−	0.369049i
$599$	4.15010	+	7.18819i	0.169569	+	0.293702i	0.938268	−	0.345908i	$-0.112429\pi$
$599$	4.15010	+	7.18819i	0.169569	+	0.293702i	−0.768700	+	0.639610i	$0.779096\pi$
$600$	−8.01842	+	13.8883i	−0.327351	+	0.566988i
$601$	−46.9342			−1.91449			−0.957243	−	0.289284i	$-0.906583\pi$
$601$	−46.9342			−1.91449			−0.957243	+	0.289284i	$0.906583\pi$
$602$		0			0
$603$	−41.2355			−1.67924
$604$	3.21110	−	5.56179i	0.130658	−	0.226306i
$605$	−1.78956	−	3.09961i	−0.0727560	−	0.126017i
$606$	−25.3729	−	43.9472i	−1.03070	−	1.78523i
$607$	−14.6528	+	25.3794i	−0.594739	+	1.03012i	0.398845	+	0.917018i	$0.369411\pi$
$607$	−14.6528	+	25.3794i	−0.594739	+	1.03012i	−0.993584	+	0.113099i	$0.963922\pi$
$608$	−0.506041			−0.0205227
$609$		0			0
$610$	−3.21983			−0.130367
$611$	0.967640	−	1.67600i	0.0391465	−	0.0678038i
$612$	−18.7092	−	32.4054i	−0.756276	−	1.30991i
$613$	6.75816	+	11.7055i	0.272960	+	0.472780i	0.969618	−	0.244623i	$-0.0786642\pi$
$613$	6.75816	+	11.7055i	0.272960	+	0.472780i	−0.696659	+	0.717403i	$0.745331\pi$
$614$	−6.31498	+	10.9379i	−0.254852	+	0.441416i
$615$	5.37435			0.216715
$616$		0			0
$617$	−18.4698			−0.743566			−0.371783	−	0.928320i	$-0.621253\pi$
$617$	−18.4698			−0.743566			−0.371783	+	0.928320i	$0.621253\pi$
$618$	−1.66756	+	2.88830i	−0.0670792	+	0.116185i
$619$	6.64795	+	11.5146i	0.267204	+	0.462810i	0.968139	−	0.250415i	$-0.0805670\pi$
$619$	6.64795	+	11.5146i	0.267204	+	0.462810i	−0.700935	+	0.713225i	$0.747234\pi$
$620$	1.12080	+	1.94128i	0.0450125	+	0.0779639i
$621$	−36.4267	+	63.0929i	−1.46175	+	2.53183i
$622$	0.339437			0.0136102
$623$		0			0
$624$	6.85086			0.274254
$625$	−12.0444	+	20.8615i	−0.481775	+	0.834458i
$626$	10.8497	+	18.7922i	0.433640	+	0.751086i
$627$	4.14795	+	7.18446i	0.165653	+	0.286920i
$628$	−1.32424	+	2.29365i	−0.0528429	+	0.0915267i
$629$	−13.1118			−0.522803
$630$		0			0
$631$	−30.7318			−1.22342			−0.611708	−	0.791084i	$-0.709517\pi$
$631$	−30.7318			−1.22342			−0.611708	+	0.791084i	$0.709517\pi$
$632$	3.28232	−	5.68515i	0.130564	−	0.226143i
$633$	−18.0172	−	31.2067i	−0.716120	−	1.24036i
$634$	5.36563	+	9.29354i	0.213096	+	0.369093i
$635$	−1.74280	+	3.01862i	−0.0691609	+	0.119790i
$636$	11.7724			0.466806
$637$		0			0
$638$	23.5526			0.932455
$639$	−42.3514	+	73.3549i	−1.67540	+	2.90187i
$640$	−0.123490	−	0.213891i	−0.00488136	−	0.00845477i
$641$	−1.84817	−	3.20112i	−0.0729982	−	0.126437i	0.827216	−	0.561884i	$-0.189923\pi$
$641$	−1.84817	−	3.20112i	−0.0729982	−	0.126437i	−0.900214	+	0.435448i	$0.856590\pi$
$642$	11.1027	−	19.2304i	0.438188	−	0.758964i
$643$	10.4340			0.411478			0.205739	−	0.978607i	$-0.434040\pi$
$643$	10.4340			0.411478			0.205739	+	0.978607i	$0.434040\pi$
$644$		0			0
$645$	−2.90754			−0.114484
$646$	1.25518	−	2.17403i	0.0493843	−	0.0855360i
$647$	−22.6712	−	39.2677i	−0.891297	−	1.54377i	−0.838321	−	0.545176i	$-0.816463\pi$
$647$	−22.6712	−	39.2677i	−0.891297	−	1.54377i	−0.0529759	−	0.998596i	$-0.516871\pi$
$648$	−12.6332	−	21.8813i	−0.496278	−	0.859579i
$649$	19.3741	−	33.5570i	0.760501	−	1.31723i
$650$	10.4209			0.408740
$651$		0			0
$652$	−3.01507			−0.118079
$653$	−13.2860	+	23.0120i	−0.519920	+	0.900528i	0.479812	+	0.877372i	$0.340705\pi$
$653$	−13.2860	+	23.0120i	−0.519920	+	0.900528i	−0.999732	+	0.0231567i	$0.992628\pi$
$654$	−0.742135	−	1.28542i	−0.0290198	−	0.0502637i
$655$	−0.615957	−	1.06687i	−0.0240674	−	0.0416860i
$656$	3.35086	−	5.80385i	0.130829	−	0.226602i
$657$	40.4470			1.57799
$658$		0			0
$659$	−24.1497			−0.940740			−0.470370	−	0.882469i	$-0.655880\pi$
$659$	−24.1497			−0.940740			−0.470370	+	0.882469i	$0.655880\pi$
$660$	−2.02446	+	3.50647i	−0.0788019	+	0.136489i
$661$	−1.01208	−	1.75298i	−0.0393654	−	0.0681829i	0.845671	−	0.533704i	$-0.179200\pi$
$661$	−1.01208	−	1.75298i	−0.0393654	−	0.0681829i	−0.885037	+	0.465521i	$0.845867\pi$
$662$	−12.7485	−	22.0810i	−0.495483	−	0.858202i
$663$	−16.9928	+	29.4323i	−0.659944	+	1.14306i
$664$	0.753020			0.0292229
$665$		0			0
$666$	−19.9366			−0.772528
$667$	−11.5199	+	19.9531i	−0.446053	+	0.772586i
$668$	6.85086	+	11.8660i	0.265068	+	0.459110i
$669$	39.4913	+	68.4010i	1.52682	+	2.64454i
$670$	0.675096	−	1.16930i	0.0260812	−	0.0451740i
$671$	65.8219			2.54103
$672$		0			0
$673$	−44.8219			−1.72776			−0.863879	−	0.503700i	$-0.831972\pi$
$673$	−44.8219			−1.72776			−0.863879	+	0.503700i	$0.831972\pi$
$674$	−8.52930	+	14.7732i	−0.328536	+	0.569042i
$675$	−36.4267	−	63.0929i	−1.40206	−	2.42845i
$676$	4.27413	+	7.40300i	0.164389	+	0.284731i
$677$	−14.3656	+	24.8820i	−0.552116	+	0.956293i	0.446006	+	0.895030i	$0.352846\pi$
$677$	−14.3656	+	24.8820i	−0.552116	+	0.956293i	−0.998122	+	0.0612626i	$0.980487\pi$
$678$	−43.7439			−1.67998
$679$		0			0
$680$	1.22521			0.0469846
$681$	26.9327	−	46.6488i	1.03206	−	1.78759i
$682$	−22.9121	−	39.6850i	−0.877352	−	1.51962i
$683$	−1.77359	−	3.07196i	−0.0678647	−	0.117545i	0.830096	−	0.557620i	$-0.188285\pi$
$683$	−1.77359	−	3.07196i	−0.0678647	−	0.117545i	−0.897961	+	0.440075i	$0.854952\pi$
$684$	1.90850	−	3.30562i	0.0729734	−	0.126394i
$685$	−3.58881			−0.137121
$686$		0			0
$687$	82.0253			3.12946
$688$	−1.81282	+	3.13990i	−0.0691132	+	0.119708i
$689$	−3.82490	−	6.62493i	−0.145717	−	0.252390i
$690$	−1.98039	−	3.43013i	−0.0753920	−	0.130583i
$691$	18.8632	−	32.6721i	0.717591	−	1.24290i	−0.244360	−	0.969684i	$-0.578578\pi$
$691$	18.8632	−	32.6721i	0.717591	−	1.24290i	0.961952	−	0.273220i	$-0.0880887\pi$
$692$	5.90648			0.224531
$693$		0			0
$694$	24.7995			0.941378
$695$	1.68747	−	2.92279i	0.0640095	−	0.110868i
$696$	−7.57338	−	13.1175i	−0.287068	−	0.497216i
$697$	16.6228	+	28.7916i	0.629634	+	1.09056i
$698$	9.05011	−	15.6753i	0.342552	−	0.593317i
$699$	15.4330			0.583728
$700$		0			0
$701$	−44.1312			−1.66681			−0.833406	−	0.552661i	$-0.813613\pi$
$701$	−44.1312			−1.66681			−0.833406	+	0.552661i	$0.813613\pi$
$702$	−15.5613	+	26.9530i	−0.587323	+	1.01727i
$703$	−0.668759	−	1.15833i	−0.0252227	−	0.0436871i
$704$	2.52446	+	4.37249i	0.0951441	+	0.164794i
$705$	0.367781	−	0.637015i	0.0138514	−	0.0239914i
$706$	8.03923			0.302560
$707$		0			0
$708$	−24.9191			−0.936519
$709$	−5.48792	+	9.50535i	−0.206103	+	0.356981i	−0.950484	−	0.310775i	$-0.899412\pi$
$709$	−5.48792	+	9.50535i	−0.206103	+	0.356981i	0.744381	+	0.667756i	$0.232745\pi$
$710$	−1.38673	−	2.40189i	−0.0520431	−	0.0901413i
$711$	24.7582	+	42.8824i	0.928504	+	1.60822i
$712$	−4.84601	+	8.39354i	−0.181612	+	0.314561i
$713$	44.8267			1.67877
$714$		0			0
$715$	2.63102			0.0983947
$716$	−4.21864	+	7.30689i	−0.157658	+	0.273071i
$717$	−5.78017	−	10.0115i	−0.215864	−	0.373888i
$718$	−6.78501	−	11.7520i	−0.253214	−	0.438580i
$719$	8.11088	−	14.0484i	0.302485	−	0.523919i	−0.674213	−	0.738537i	$-0.735517\pi$
$719$	8.11088	−	14.0484i	0.302485	−	0.523919i	0.976698	+	0.214618i	$0.0688506\pi$
$720$	1.86294			0.0694276
$721$		0			0
$722$	−18.7439			−0.697577
$723$	6.01842	−	10.4242i	0.223827	−	0.387680i
$724$	−6.56734	−	11.3750i	−0.244073	−	0.422747i
$725$	−11.5199	−	19.9531i	−0.427839	−	0.741038i
$726$	23.5269	−	40.7498i	0.873166	−	1.51237i
$727$	−15.8025			−0.586083			−0.293042	−	0.956100i	$-0.594667\pi$
$727$	−15.8025			−0.586083			−0.293042	+	0.956100i	$0.594667\pi$
$728$		0			0
$729$	46.8961			1.73689
$730$	−0.662186	+	1.14694i	−0.0245086	+	0.0424501i
$731$	−8.99300	−	15.5763i	−0.332618	−	0.576111i
$732$	−21.1652	−	36.6591i	−0.782287	−	1.35496i
$733$	−23.9937	+	41.5583i	−0.886228	+	1.53499i	−0.0419291	+	0.999121i	$0.513350\pi$
$733$	−23.9937	+	41.5583i	−0.886228	+	1.53499i	−0.844299	+	0.535872i	$0.819983\pi$
$734$	−7.91425			−0.292120
$735$		0			0
$736$	−4.93900			−0.182054
$737$	−13.8007	+	23.9036i	−0.508357	+	0.880500i
$738$	25.2751	+	43.7777i	0.930389	+	1.61148i
$739$	−11.1256	−	19.2702i	−0.409263	−	0.708865i	0.585544	−	0.810641i	$-0.300881\pi$
$739$	−11.1256	−	19.2702i	−0.409263	−	0.708865i	−0.994807	+	0.101776i	$0.967548\pi$
$740$	0.326396	−	0.565335i	0.0119986	−	0.0207821i
$741$	−3.46681			−0.127357
$742$		0			0
$743$	−9.69501			−0.355675			−0.177838	−	0.984060i	$-0.556910\pi$
$743$	−9.69501			−0.355675			−0.177838	+	0.984060i	$0.556910\pi$
$744$	−14.7349	+	25.5216i	−0.540208	+	0.935667i
$745$	−0.672407	−	1.16464i	−0.0246351	−	0.0426692i
$746$	3.13318	+	5.42682i	0.114714	+	0.198690i
$747$	−2.83997	+	4.91897i	−0.103909	+	0.179976i
$748$	−25.0465			−0.915792
$749$		0			0
$750$	7.97046			0.291040
$751$	5.31402	−	9.20415i	0.193911	−	0.335864i	−0.752632	−	0.658442i	$-0.771216\pi$
$751$	5.31402	−	9.20415i	0.193911	−	0.335864i	0.946543	+	0.322577i	$0.104549\pi$
$752$	−0.458615	−	0.794345i	−0.0167240	−	0.0289668i
$753$	−29.5649	−	51.2080i	−1.07741	−	1.86612i
$754$	−4.92125	+	8.52385i	−0.179221	+	0.310420i
$755$	−1.58615			−0.0577261
$756$		0			0
$757$	−41.0823			−1.49316			−0.746581	−	0.665295i	$-0.768306\pi$
$757$	−41.0823			−1.49316			−0.746581	+	0.665295i	$0.768306\pi$
$758$	15.7875	−	27.3447i	0.573426	−	0.993204i
$759$	40.4843	+	70.1209i	1.46949	+	2.54523i
$760$	0.0624909	+	0.108237i	0.00226678	+	0.00392618i
$761$	−11.5707	+	20.0410i	−0.419437	+	0.726486i	−0.995883	−	0.0906490i	$-0.971106\pi$
$761$	−11.5707	+	20.0410i	−0.419437	+	0.726486i	0.576446	+	0.817135i	$0.304439\pi$
$762$	−45.8243			−1.66004
$763$		0			0
$764$	−10.1806			−0.368321
$765$	−4.62080	+	8.00346i	−0.167065	+	0.289366i
$766$	17.1528	+	29.7095i	0.619756	+	1.07345i
$767$	8.09634	+	14.0233i	0.292342	+	0.506351i
$768$	1.62349	−	2.81197i	0.0585826	−	0.101468i
$769$	38.7928			1.39891			0.699453	−	0.714679i	$-0.253427\pi$
$769$	38.7928			1.39891			0.699453	+	0.714679i	$0.253427\pi$
$770$		0			0
$771$	−12.9739			−0.467244
$772$	5.04772	−	8.74291i	0.181671	−	0.314664i
$773$	−14.2664	−	24.7101i	−0.513125	−	0.888759i	−0.999884	−	0.0152226i	$-0.995154\pi$
$773$	−14.2664	−	24.7101i	−0.513125	−	0.888759i	0.486759	−	0.873536i	$-0.338179\pi$
$774$	−13.6739	−	23.6839i	−0.491498	−	0.851300i
$775$	−22.4133	+	38.8211i	−0.805111	+	1.39449i
$776$	12.2784			0.440770
$777$		0			0
$778$	22.6896			0.813463
$779$	−1.69567	+	2.93699i	−0.0607537	+	0.105228i
$780$	−0.846011	−	1.46533i	−0.0302920	−	0.0524674i
$781$	28.3485	+	49.1010i	1.01439	+	1.75697i
$782$	12.2506	−	21.2187i	0.438082	−	0.758779i
$783$	68.8098			2.45906
$784$		0			0
$785$	0.654121			0.0233466
$786$	8.09783	−	14.0259i	0.288840	−	0.500286i
$787$	16.7853	+	29.0730i	0.598332	+	1.03634i	0.993067	+	0.117546i	$0.0375028\pi$
$787$	16.7853	+	29.0730i	0.598332	+	1.03634i	−0.394736	+	0.918795i	$0.629164\pi$
$788$	1.19471	+	2.06930i	0.0425598	+	0.0737157i
$789$	19.6494	−	34.0338i	0.699539	−	1.21164i
$790$	−1.62133			−0.0576845
$791$		0			0
$792$	−38.0834			−1.35323
$793$	−13.7533	+	23.8214i	−0.488395	+	0.845924i
$794$	2.38135	+	4.12463i	0.0845111	+	0.146378i
$795$	−1.45377	−	2.51801i	−0.0515599	−	0.0893044i
$796$	9.81282	−	16.9963i	0.347806	−	0.602418i
$797$	−20.0224			−0.709228			−0.354614	−	0.935013i	$-0.615388\pi$
$797$	−20.0224			−0.709228			−0.354614	+	0.935013i	$0.615388\pi$
$798$		0			0
$799$	4.55017			0.160974
$800$	2.46950	−	4.27730i	0.0873100	−	0.151225i
$801$	−36.5529	−	63.3114i	−1.29153	−	2.23700i
$802$	5.91335	+	10.2422i	0.208808	+	0.361665i
$803$	13.5368	−	23.4465i	0.477705	−	0.827409i
$804$	17.7506			0.626016
$805$		0			0
$806$	19.1497			0.674521
$807$	45.1480	−	78.1986i	1.58929	−	2.75272i
$808$	7.81431	+	13.5348i	0.274907	+	0.476152i
$809$	5.90193	+	10.2224i	0.207501	+	0.359402i	0.950927	−	0.309417i	$-0.100134\pi$
$809$	5.90193	+	10.2224i	0.207501	+	0.359402i	−0.743426	+	0.668818i	$0.766800\pi$
$810$	−3.12014	+	5.40424i	−0.109630	+	0.189886i
$811$	4.55496			0.159946			0.0799731	−	0.996797i	$-0.474517\pi$
$811$	4.55496			0.159946			0.0799731	+	0.996797i	$0.474517\pi$
$812$		0			0
$813$	46.4010			1.62736
$814$	−6.67241	+	11.5569i	−0.233868	+	0.405071i
$815$	0.372330	+	0.644894i	0.0130421	+	0.0225897i
$816$	8.05376	+	13.9495i	0.281938	+	0.488331i
$817$	0.917362	−	1.58892i	0.0320944	−	0.0555892i
$818$	−0.264438			−0.00924586
$819$		0			0
$820$	−1.65519			−0.0578016
$821$	−15.8490	+	27.4513i	−0.553134	+	0.958056i	0.444912	+	0.895574i	$0.353235\pi$
$821$	−15.8490	+	27.4513i	−0.553134	+	0.958056i	−0.998046	+	0.0624816i	$0.980099\pi$
$822$	−23.5906	−	40.8601i	−0.822817	−	1.42516i
$823$	23.7289	+	41.0996i	0.827136	+	1.43264i	0.900276	+	0.435320i	$0.143365\pi$
$823$	23.7289	+	41.0996i	0.827136	+	1.43264i	−0.0731399	+	0.997322i	$0.523302\pi$
$824$	0.513574	−	0.889535i	0.0178912	−	0.0309884i
$825$	−80.9687			−2.81897
$826$		0			0
$827$	34.4704			1.19865			0.599326	−	0.800505i	$-0.295435\pi$
$827$	34.4704			1.19865			0.599326	+	0.800505i	$0.295435\pi$
$828$	18.6271	−	32.2631i	0.647338	−	1.12122i
$829$	16.3122	+	28.2535i	0.566545	+	0.981284i	0.996904	+	0.0786266i	$0.0250535\pi$
$829$	16.3122	+	28.2535i	0.566545	+	0.981284i	−0.430359	+	0.902658i	$0.641613\pi$
$830$	−0.0929903	−	0.161064i	−0.00322774	−	0.00559061i
$831$	27.9768	−	48.4572i	0.970504	−	1.68096i
$832$	−2.10992			−0.0731482
$833$		0			0
$834$	44.3696			1.53639
$835$	1.69202	−	2.93067i	0.0585548	−	0.101420i
$836$	−1.27748	−	2.21266i	−0.0441825	−	0.0765264i
$837$	−66.9388	−	115.941i	−2.31374	−	4.00752i
$838$	−16.1836	+	28.0308i	−0.559053	+	0.968308i
$839$	−6.24698			−0.215670			−0.107835	−	0.994169i	$-0.534392\pi$
$839$	−6.24698			−0.215670			−0.107835	+	0.994169i	$0.534392\pi$
$840$		0			0
$841$	−7.23895			−0.249619
$842$	1.47823	−	2.56037i	0.0509432	−	0.0882361i
$843$	28.6482	+	49.6202i	0.986698	+	1.70901i
$844$	5.54892	+	9.61101i	0.191002	+	0.330824i
$845$	1.05562	−	1.82839i	0.0363145	−	0.0628986i
$846$	6.91856			0.237865
$847$		0			0
$848$	−3.62565			−0.124505
$849$	−11.1419	+	19.2984i	−0.382389	+	0.662318i
$850$	12.2506	+	21.2187i	0.420193	+	0.727796i
$851$	−6.52715	−	11.3054i	−0.223748	−	0.387542i
$852$	18.2310	−	31.5770i	0.624584	−	1.08181i
$853$	−7.59658			−0.260102			−0.130051	−	0.991507i	$-0.541514\pi$
$853$	−7.59658			−0.260102			−0.130051	+	0.991507i	$0.541514\pi$
$854$		0			0
$855$	−0.942722			−0.0322404
$856$	−3.41939	+	5.92255i	−0.116872	+	0.202429i
$857$	−21.6761	−	37.5440i	−0.740440	−	1.28248i	−0.952295	−	0.305179i	$-0.901284\pi$
$857$	−21.6761	−	37.5440i	−0.740440	−	1.28248i	0.211855	−	0.977301i	$-0.432049\pi$
$858$	17.2947	+	29.9553i	0.590431	+	1.02266i
$859$	−21.0194	+	36.4066i	−0.717172	+	1.24218i	0.244944	+	0.969537i	$0.421230\pi$
$859$	−21.0194	+	36.4066i	−0.717172	+	1.24218i	−0.962116	+	0.272641i	$0.912103\pi$
$860$	0.895461			0.0305350
$861$		0			0
$862$	33.4252			1.13847
$863$	21.4755	−	37.1967i	0.731036	−	1.26619i	−0.225405	−	0.974265i	$-0.572370\pi$
$863$	21.4755	−	37.1967i	0.731036	−	1.26619i	0.956441	−	0.291926i	$-0.0942962\pi$
$864$	7.37531	+	12.7744i	0.250913	+	0.434595i
$865$	−0.729390	−	1.26334i	−0.0248000	−	0.0429548i
$866$	0.335126	−	0.580455i	0.0113880	−	0.0197246i
$867$	−24.7071			−0.839097
$868$		0			0
$869$	33.1444			1.12435
$870$	−1.87047	+	3.23975i	−0.0634149	+	0.109838i
$871$	−5.76726	−	9.98918i	−0.195416	−	0.338471i
$872$	0.228562	+	0.395881i	0.00774008	+	0.0134062i
$873$	−46.3074	+	80.2067i	−1.56727	+	2.71459i
$874$	2.49934			0.0845413
$875$		0			0
$876$	−17.4112			−0.588270
$877$	17.9066	−	31.0152i	0.604664	−	1.04731i	−0.387440	−	0.921895i	$-0.626641\pi$
$877$	17.9066	−	31.0152i	0.604664	−	1.04731i	0.992104	−	0.125414i	$-0.0400261\pi$
$878$	−7.14556	−	12.3765i	−0.241151	−	0.417685i
$879$	−18.6516	−	32.3055i	−0.629103	−	1.08964i
$880$	0.623490	−	1.07992i	0.0210178	−	0.0364040i
$881$	−3.75600			−0.126543			−0.0632715	−	0.997996i	$-0.520153\pi$
$881$	−3.75600			−0.126543			−0.0632715	+	0.997996i	$0.520153\pi$
$882$		0			0
$883$	−7.84979			−0.264166			−0.132083	−	0.991239i	$-0.542167\pi$
$883$	−7.84979			−0.264166			−0.132083	+	0.991239i	$0.542167\pi$
$884$	5.23341	−	9.06453i	0.176018	−	0.304873i
$885$	3.07726	+	5.32997i	0.103441	+	0.179165i
$886$	−4.54072	−	7.86476i	−0.152548	−	0.264222i
$887$	24.4834	−	42.4064i	0.822071	−	1.42387i	−0.0820662	−	0.996627i	$-0.526152\pi$
$887$	24.4834	−	42.4064i	0.822071	−	1.42387i	0.904137	−	0.427242i	$-0.140515\pi$
$888$	8.58211			0.287997
$889$		0			0
$890$	2.39373			0.0802381
$891$	63.7839	−	110.477i	2.13684	−	3.70112i
$892$	−12.1625	−	21.0660i	−0.407230	−	0.705343i
$893$	0.232078	+	0.401971i	0.00776620	+	0.0134514i
$894$	8.83997	−	15.3113i	0.295653	−	0.512086i
$895$	2.08383			0.0696549
$896$		0			0
$897$	−33.8364			−1.12976
$898$	9.74214	−	16.8739i	0.325099	−	0.563088i
$899$	−21.1694	−	36.6664i	−0.706037	−	1.22289i
$900$	18.6271	+	32.2631i	0.620905	+	1.07544i
$901$	8.99300	−	15.5763i	0.299600	−	0.518923i
$902$	33.8364			1.12663
$903$		0			0
$904$	13.4722			0.448078
$905$	−1.62200	+	2.80938i	−0.0539170	+	0.0933870i
$906$	−10.4264	−	18.0590i	−0.346394	−	0.599971i
$907$	4.35905	+	7.55010i	0.144740	+	0.250697i	0.929276	−	0.369386i	$-0.120432\pi$
$907$	4.35905	+	7.55010i	0.144740	+	0.250697i	−0.784536	+	0.620083i	$0.787099\pi$
$908$	−8.29470	+	14.3668i	−0.275269	+	0.476780i
$909$	−117.885			−3.90999
$910$		0			0
$911$	−42.5187			−1.40871			−0.704354	−	0.709849i	$-0.748763\pi$
$911$	−42.5187			−1.40871			−0.704354	+	0.709849i	$0.748763\pi$
$912$	−0.821552	+	1.42297i	−0.0272043	+	0.0471192i
$913$	1.90097	+	3.29257i	0.0629129	+	0.108968i
$914$	16.0966	+	27.8802i	0.532429	+	0.922195i
$915$	−5.22737	+	9.05406i	−0.172811	+	0.299318i
$916$	−25.2620			−0.834681
$917$		0			0
$918$	−73.1745			−2.41512
$919$	11.5785	−	20.0546i	0.381940	−	0.661539i	−0.609400	−	0.792863i	$-0.708589\pi$
$919$	11.5785	−	20.0546i	0.381940	−	0.661539i	0.991340	+	0.131324i	$0.0419228\pi$
$920$	0.609916	+	1.05641i	0.0201083	+	0.0348287i
$921$	20.5046	+	35.5150i	0.675650	+	1.17026i
$922$	−15.4785	+	26.8096i	−0.509758	+	0.882927i
$923$	−23.6933			−0.779876
$924$		0			0
$925$	13.0543			0.429223
$926$	−11.0157	+	19.0798i	−0.361999	+	0.627001i
$927$	3.87382	+	6.70966i	0.127233	+	0.220374i
$928$	2.33244	+	4.03990i	0.0765660	+	0.132616i
$929$	−12.0274	+	20.8321i	−0.394608	+	0.683480i	−0.993051	−	0.117685i	$-0.962453\pi$
$929$	−12.0274	+	20.8321i	−0.394608	+	0.683480i	0.598443	+	0.801165i	$0.295786\pi$
$930$	7.27844			0.238669
$931$		0			0
$932$	−4.75302			−0.155690
$933$	0.551073	−	0.954487i	0.0180413	−	0.0312485i
$934$	−4.74482	−	8.21828i	−0.155255	−	0.268910i
$935$	3.09299	+	5.35722i	0.101152	+	0.175200i
$936$	7.95742	−	13.7827i	0.260096	−	0.450500i
$937$	−7.52840			−0.245942			−0.122971	−	0.992410i	$-0.539242\pi$
$937$	−7.52840			−0.245942			−0.122971	+	0.992410i	$0.539242\pi$
$938$		0			0
$939$	70.4572			2.29929
$940$	−0.113269	+	0.196187i	−0.00369442	+	0.00639892i
$941$	9.21917	+	15.9681i	0.300536	+	0.520544i	0.976258	−	0.216613i	$-0.0695010\pi$
$941$	9.21917	+	15.9681i	0.300536	+	0.520544i	−0.675721	+	0.737157i	$0.736168\pi$
$942$	4.29978	+	7.44744i	0.140094	+	0.242651i
$943$	−16.5499	+	28.6652i	−0.538938	+	0.933468i
$944$	7.67456			0.249786
$945$		0			0
$946$	−18.3056			−0.595166
$947$	−1.76420	+	3.05569i	−0.0573288	+	0.0992964i	−0.893266	−	0.449529i	$-0.851592\pi$
$947$	−1.76420	+	3.05569i	−0.0573288	+	0.0992964i	0.835937	+	0.548826i	$0.184925\pi$
$948$	−10.6576	−	18.4596i	−0.346144	−	0.599539i
$949$	5.65697	+	9.79816i	0.183633	+	0.318062i
$950$	−1.24967	+	2.16449i	−0.0405446	+	0.0702253i
$951$	34.8442			1.12990
$952$		0			0
$953$	11.0935			0.359354			0.179677	−	0.983726i	$-0.442495\pi$
$953$	11.0935			0.359354			0.179677	+	0.983726i	$0.442495\pi$
$954$	13.6739	−	23.6839i	0.442709	−	0.766794i
$955$	1.25720	+	2.17754i	0.0406821	+	0.0704634i
$956$	1.78017	+	3.08334i	0.0575747	+	0.0997224i
$957$	38.2373	−	66.2290i	1.23604	−	2.14088i
$958$	8.59717			0.277762
$959$		0			0
$960$	−0.801938			−0.0258824
$961$	−25.6875	+	44.4920i	−0.828628	+	1.43523i
$962$	−2.78836	−	4.82959i	−0.0899005	−	0.155712i
$963$	−25.7920	−	44.6731i	−0.831136	−	1.43957i
$964$	−1.85354	+	3.21043i	−0.0596986	+	0.103401i
$965$	−2.49337			−0.0802644
$966$		0			0
$967$	−23.6418			−0.760268			−0.380134	−	0.924931i	$-0.624122\pi$
$967$	−23.6418			−0.760268			−0.380134	+	0.924931i	$0.624122\pi$
$968$	−7.24578	+	12.5501i	−0.232888	+	0.403374i
$969$	−4.07553	−	7.05903i	−0.130925	−	0.226769i
$970$	−1.51626	−	2.62624i	−0.0486842	−	0.0843236i
$971$	17.1978	−	29.7875i	0.551904	−	0.955927i	−0.446233	−	0.894917i	$-0.647235\pi$
$971$	17.1978	−	29.7875i	0.551904	−	0.955927i	0.998137	−	0.0610096i	$-0.0194320\pi$
$972$	−37.7875			−1.21203
$973$		0			0
$974$	25.7313			0.824482
$975$	16.9182	−	29.3032i	0.541816	−	0.938452i
$976$	6.51842	+	11.2902i	0.208649	+	0.361391i
$977$	6.78405	+	11.7503i	0.217041	+	0.375926i	0.953902	−	0.300118i	$-0.0970261\pi$
$977$	6.78405	+	11.7503i	0.217041	+	0.375926i	−0.736861	+	0.676044i	$0.763693\pi$
$978$	−4.89493	+	8.47826i	−0.156523	+	0.271105i
$979$	−48.9342			−1.56394
$980$		0			0
$981$	−3.44803			−0.110087
$982$	8.67241	−	15.0210i	0.276748	−	0.479341i
$983$	15.2322	+	26.3830i	0.485832	+	0.841486i	0.999867	−	0.0162832i	$-0.00518334\pi$
$983$	15.2322	+	26.3830i	0.485832	+	0.841486i	−0.514035	+	0.857769i	$0.671850\pi$
$984$	−10.8802	−	18.8450i	−0.346847	−	0.600756i
$985$	0.295069	−	0.511074i	0.00940168	−	0.0162842i
$986$	−23.1414			−0.736972
$987$		0			0
$988$	1.06770			0.0339682
$989$	8.95353	−	15.5080i	0.284706	−	0.493125i
$990$	4.70291	+	8.14567i	0.149468	+	0.258886i
$991$	−29.4974	−	51.0909i	−0.937015	−	1.62296i	−0.771001	−	0.636834i	$-0.780244\pi$
$991$	−29.4974	−	51.0909i	−0.937015	−	1.62296i	−0.166014	−	0.986123i	$-0.553090\pi$
$992$	4.53803	−	7.86010i	0.144083	−	0.249558i
$993$	−82.7881			−2.62720
$994$		0			0
$995$	−4.84713			−0.153664
$996$	1.22252	−	2.11747i	0.0387371	−	0.0670946i
$997$	11.0419	+	19.1252i	0.349701	+	0.605700i	0.986196	−	0.165581i	$-0.0529498\pi$
$997$	11.0419	+	19.1252i	0.349701	+	0.605700i	−0.636495	+	0.771281i	$0.719617\pi$
$998$	18.0492	+	31.2622i	0.571338	+	0.989586i
$999$	−19.4937	+	33.7641i	−0.616754	+	1.06825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	686.2.c.b.667.3		6
7.2	even	3		686.2.a.c.1.1	✓	3
7.3	odd	6		686.2.c.a.361.1		6
7.4	even	3	inner	686.2.c.b.361.3		6
7.5	odd	6		686.2.a.d.1.3	yes	3
7.6	odd	2		686.2.c.a.667.1		6
21.2	odd	6		6174.2.a.e.1.1		3
21.5	even	6		6174.2.a.c.1.3		3
28.19	even	6		5488.2.a.a.1.1		3
28.23	odd	6		5488.2.a.f.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
686.2.a.c.1.1	✓	3	7.2	even	3
686.2.a.d.1.3	yes	3	7.5	odd	6
686.2.c.a.361.1		6	7.3	odd	6
686.2.c.a.667.1		6	7.6	odd	2
686.2.c.b.361.3		6	7.4	even	3	inner
686.2.c.b.667.3		6	1.1	even	1	trivial
5488.2.a.a.1.1		3	28.19	even	6
5488.2.a.f.1.3		3	28.23	odd	6
6174.2.a.c.1.3		3	21.5	even	6
6174.2.a.e.1.1		3	21.2	odd	6

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:	\( N \)	\(=\)	\( 686 = 2 \cdot 7^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	686.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.62349 + 2.81197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.123490 + 0.213891i) q^{5} -3.24698 q^{6} +1.00000 q^{8} +(-3.77144 + 6.53232i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(1.62349 + 2.81197i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.123490 + 0.213891i) q^{5} -3.24698 q^{6} +1.00000 q^{8} +(-3.77144 + 6.53232i) q^{9} +(-0.123490 - 0.213891i) q^{10} +(2.52446 + 4.37249i) q^{11} +(1.62349 - 2.81197i) q^{12} -2.10992 q^{13} -0.801938 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.48039 - 4.29615i) q^{17} +(-3.77144 - 6.53232i) q^{18} +(0.253020 - 0.438244i) q^{19} +0.246980 q^{20} -5.04892 q^{22} +(2.46950 - 4.27730i) q^{23} +(1.62349 + 2.81197i) q^{24} +(2.46950 + 4.27730i) q^{25} +(1.05496 - 1.82724i) q^{26} -14.7506 q^{27} -4.66487 q^{29} +(0.400969 - 0.694498i) q^{30} +(4.53803 + 7.86010i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-8.19687 + 14.1974i) q^{33} +4.96077 q^{34} +7.54288 q^{36} +(1.32155 - 2.28900i) q^{37} +(0.253020 + 0.438244i) q^{38} +(-3.42543 - 5.93301i) q^{39} +(-0.123490 + 0.213891i) q^{40} -6.70171 q^{41} +3.62565 q^{43} +(2.52446 - 4.37249i) q^{44} +(-0.931468 - 1.61335i) q^{45} +(2.46950 + 4.27730i) q^{46} +(-0.458615 + 0.794345i) q^{47} -3.24698 q^{48} -4.93900 q^{50} +(8.05376 - 13.9495i) q^{51} +(1.05496 + 1.82724i) q^{52} +(1.81282 + 3.13990i) q^{53} +(7.37531 - 12.7744i) q^{54} -1.24698 q^{55} +1.64310 q^{57} +(2.33244 - 4.03990i) q^{58} +(-3.83728 - 6.64637i) q^{59} +(0.400969 + 0.694498i) q^{60} +(6.51842 - 11.2902i) q^{61} -9.07606 q^{62} +1.00000 q^{64} +(0.260553 - 0.451291i) q^{65} +(-8.19687 - 14.1974i) q^{66} +(2.73341 + 4.73440i) q^{67} +(-2.48039 + 4.29615i) q^{68} +16.0368 q^{69} +11.2295 q^{71} +(-3.77144 + 6.53232i) q^{72} +(-2.68114 - 4.64386i) q^{73} +(1.32155 + 2.28900i) q^{74} +(-8.01842 + 13.8883i) q^{75} -0.506041 q^{76} +6.85086 q^{78} +(3.28232 - 5.68515i) q^{79} +(-0.123490 - 0.213891i) q^{80} +(-12.6332 - 21.8813i) q^{81} +(3.35086 - 5.80385i) q^{82} +0.753020 q^{83} +1.22521 q^{85} +(-1.81282 + 3.13990i) q^{86} +(-7.57338 - 13.1175i) q^{87} +(2.52446 + 4.37249i) q^{88} +(-4.84601 + 8.39354i) q^{89} +1.86294 q^{90} -4.93900 q^{92} +(-14.7349 + 25.5216i) q^{93} +(-0.458615 - 0.794345i) q^{94} +(0.0624909 + 0.108237i) q^{95} +(1.62349 - 2.81197i) q^{96} +12.2784 q^{97} -38.0834 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 5 q^{3} - 3 q^{4} + 4 q^{5} - 10 q^{6} + 6 q^{8} - 4 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 5 * q^3 - 3 * q^4 + 4 * q^5 - 10 * q^6 + 6 * q^8 - 4 * q^9	\( 6 q - 3 q^{2} + 5 q^{3} - 3 q^{4} + 4 q^{5} - 10 q^{6} + 6 q^{8} - 4 q^{9} + 4 q^{10} + 6 q^{11} + 5 q^{12} - 14 q^{13} + 4 q^{15} - 3 q^{16} - 2 q^{17} - 4 q^{18} + 11 q^{19} - 8 q^{20} - 12 q^{22} + 5 q^{23} + 5 q^{24} + 5 q^{25} + 7 q^{26} - 16 q^{27} - 30 q^{29} - 2 q^{30} + 12 q^{31} - 3 q^{32} - 17 q^{33} + 4 q^{34} + 8 q^{36} + 12 q^{37} + 11 q^{38} - 7 q^{39} + 4 q^{40} + 14 q^{41} - 2 q^{43} + 6 q^{44} - 11 q^{45} + 5 q^{46} + 4 q^{47} - 10 q^{48} - 10 q^{50} + 8 q^{51} + 7 q^{52} - q^{53} + 8 q^{54} + 2 q^{55} + 18 q^{57} + 15 q^{58} - 2 q^{59} - 2 q^{60} + 11 q^{61} - 24 q^{62} + 6 q^{64} - 14 q^{65} - 17 q^{66} + 13 q^{67} - 2 q^{68} + 40 q^{69} + 26 q^{71} - 4 q^{72} - 9 q^{73} + 12 q^{74} - 20 q^{75} - 22 q^{76} + 14 q^{78} - 2 q^{79} + 4 q^{80} - 27 q^{81} - 7 q^{82} + 14 q^{83} + 4 q^{85} + q^{86} - 18 q^{87} + 6 q^{88} - 24 q^{89} + 22 q^{90} - 10 q^{92} - 41 q^{93} + 4 q^{94} - 24 q^{95} + 5 q^{96} + 14 q^{97} - 72 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 5 * q^3 - 3 * q^4 + 4 * q^5 - 10 * q^6 + 6 * q^8 - 4 * q^9 + 4 * q^10 + 6 * q^11 + 5 * q^12 - 14 * q^13 + 4 * q^15 - 3 * q^16 - 2 * q^17 - 4 * q^18 + 11 * q^19 - 8 * q^20 - 12 * q^22 + 5 * q^23 + 5 * q^24 + 5 * q^25 + 7 * q^26 - 16 * q^27 - 30 * q^29 - 2 * q^30 + 12 * q^31 - 3 * q^32 - 17 * q^33 + 4 * q^34 + 8 * q^36 + 12 * q^37 + 11 * q^38 - 7 * q^39 + 4 * q^40 + 14 * q^41 - 2 * q^43 + 6 * q^44 - 11 * q^45 + 5 * q^46 + 4 * q^47 - 10 * q^48 - 10 * q^50 + 8 * q^51 + 7 * q^52 - q^53 + 8 * q^54 + 2 * q^55 + 18 * q^57 + 15 * q^58 - 2 * q^59 - 2 * q^60 + 11 * q^61 - 24 * q^62 + 6 * q^64 - 14 * q^65 - 17 * q^66 + 13 * q^67 - 2 * q^68 + 40 * q^69 + 26 * q^71 - 4 * q^72 - 9 * q^73 + 12 * q^74 - 20 * q^75 - 22 * q^76 + 14 * q^78 - 2 * q^79 + 4 * q^80 - 27 * q^81 - 7 * q^82 + 14 * q^83 + 4 * q^85 + q^86 - 18 * q^87 + 6 * q^88 - 24 * q^89 + 22 * q^90 - 10 * q^92 - 41 * q^93 + 4 * q^94 - 24 * q^95 + 5 * q^96 + 14 * q^97 - 72 * q^99

Introduction

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