LMFDB - Embedded newform 280.2.b.d.141.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(141,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.141");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	12.0.8272021826830336.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 4x^{9} + 4x^{8} - 12x^{7} + 10x^{6} - 24x^{5} + 16x^{4} - 32x^{3} + 48x^{2} + 64 $ x^12 + 3x^10 - 4x^9 + 4x^8 - 12x^7 + 10x^6 - 24x^5 + 16x^4 - 32x^3 + 48*x^2 + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			141.6
Root			$-1.11909 + 0.864661i$ of defining polynomial
Character	$\chi$	$=$	280.141
Dual form			280.2.b.d.141.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.864661 + 1.11909i) q^{2} +0.903031i q^{3} +(-0.504724 - 1.93527i) q^{4} -1.00000i q^{5} +(-1.01057 - 0.780815i) q^{6} +1.00000 q^{7} +(2.60215 + 1.10852i) q^{8} +2.18454 q^{9} +O(q^{10})$	\(q+(-0.864661 + 1.11909i) q^{2} +0.903031i q^{3} +(-0.504724 - 1.93527i) q^{4} -1.00000i q^{5} +(-1.01057 - 0.780815i) q^{6} +1.00000 q^{7} +(2.60215 + 1.10852i) q^{8} +2.18454 q^{9} +(1.11909 + 0.864661i) q^{10} -1.29182i q^{11} +(1.74760 - 0.455781i) q^{12} +4.20430i q^{13} +(-0.864661 + 1.11909i) q^{14} +0.903031 q^{15} +(-3.49051 + 1.95355i) q^{16} +7.59222 q^{17} +(-1.88888 + 2.44469i) q^{18} +1.10642i q^{19} +(-1.93527 + 0.504724i) q^{20} +0.903031i q^{21} +(1.44567 + 1.11699i) q^{22} -2.12413 q^{23} +(-1.00103 + 2.34982i) q^{24} -1.00000 q^{25} +(-4.70499 - 3.63529i) q^{26} +4.68180i q^{27} +(-0.504724 - 1.93527i) q^{28} -1.25526i q^{29} +(-0.780815 + 1.01057i) q^{30} -3.58278 q^{31} +(0.831908 - 5.59535i) q^{32} +1.16656 q^{33} +(-6.56470 + 8.49638i) q^{34} -1.00000i q^{35} +(-1.10259 - 4.22766i) q^{36} -1.87587i q^{37} +(-1.23818 - 0.956675i) q^{38} -3.79661 q^{39} +(1.10852 - 2.60215i) q^{40} +4.82859 q^{41} +(-1.01057 - 0.780815i) q^{42} +11.3049i q^{43} +(-2.50002 + 0.652014i) q^{44} -2.18454i q^{45} +(1.83665 - 2.37710i) q^{46} +8.05265 q^{47} +(-1.76412 - 3.15204i) q^{48} +1.00000 q^{49} +(0.864661 - 1.11909i) q^{50} +6.85601i q^{51} +(8.13644 - 2.12201i) q^{52} -10.6025i q^{53} +(-5.23935 - 4.04816i) q^{54} -1.29182 q^{55} +(2.60215 + 1.10852i) q^{56} -0.999128 q^{57} +(1.40475 + 1.08537i) q^{58} -10.5375i q^{59} +(-0.455781 - 1.74760i) q^{60} -3.38884i q^{61} +(3.09789 - 4.00945i) q^{62} +2.18454 q^{63} +(5.54238 + 5.76906i) q^{64} +4.20430 q^{65} +(-1.00868 + 1.30548i) q^{66} -9.24944i q^{67} +(-3.83198 - 14.6930i) q^{68} -1.91816i q^{69} +(1.11909 + 0.864661i) q^{70} -13.1131 q^{71} +(5.68449 + 2.42160i) q^{72} -11.1131 q^{73} +(2.09926 + 1.62199i) q^{74} -0.903031i q^{75} +(2.14121 - 0.558435i) q^{76} -1.29182i q^{77} +(3.28278 - 4.24875i) q^{78} -6.94327 q^{79} +(1.95355 + 3.49051i) q^{80} +2.32580 q^{81} +(-4.17509 + 5.40362i) q^{82} +5.74106i q^{83} +(1.74760 - 0.455781i) q^{84} -7.59222i q^{85} +(-12.6512 - 9.77494i) q^{86} +1.13354 q^{87} +(1.43201 - 3.36152i) q^{88} +0.691243 q^{89} +(2.44469 + 1.88888i) q^{90} +4.20430i q^{91} +(1.07210 + 4.11076i) q^{92} -3.23536i q^{93} +(-6.96281 + 9.01164i) q^{94} +1.10642 q^{95} +(5.05277 + 0.751239i) q^{96} +6.79574 q^{97} +(-0.864661 + 1.11909i) q^{98} -2.82203i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	$ 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) $ 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$1$	$1$	$-1$	$1$

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 $

$2$	−0.864661	+	1.11909i	−0.611407	+	0.791316i
$2$	−0.864661	+	1.11909i	−0.611407	+	0.791316i
$3$			0.903031i			0.521365i	0.965425	+	0.260683i	$0.0839476\pi$
$3$			0.903031i			0.521365i	−0.965425	+	0.260683i	$0.916052\pi$
$4$	−0.504724	−	1.93527i	−0.252362	−	0.967633i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−1.01057	−	0.780815i	−0.412565	−	0.318766i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	2.60215	+	1.10852i	0.919999	+	0.391920i
$9$	2.18454			0.728178
$10$	1.11909	+	0.864661i	0.353887	+	0.273430i
$11$		−	1.29182i		−	0.389499i	−0.980853	−	0.194750i	$-0.937611\pi$
$11$		−	1.29182i		−	0.389499i	0.980853	−	0.194750i	$-0.0623895\pi$
$12$	1.74760	−	0.455781i	0.504490	−	0.131573i
$13$			4.20430i			1.16606i	0.812449	+	0.583032i	$0.198134\pi$
$13$			4.20430i			1.16606i	−0.812449	+	0.583032i	$0.801866\pi$
$14$	−0.864661	+	1.11909i	−0.231090	+	0.299089i
$15$	0.903031			0.233162
$16$	−3.49051	+	1.95355i	−0.872627	+	0.488387i
$17$	7.59222			1.84138			0.920692	−	0.390289i	$-0.127625\pi$
$17$	7.59222			1.84138			0.920692	+	0.390289i	$0.127625\pi$
$18$	−1.88888	+	2.44469i	−0.445214	+	0.576219i
$19$			1.10642i			0.253829i	0.991914	+	0.126915i	$0.0405074\pi$
$19$			1.10642i			0.253829i	−0.991914	+	0.126915i	$0.959493\pi$
$20$	−1.93527	+	0.504724i	−0.432739	+	0.112860i
$21$			0.903031i			0.197057i
$22$	1.44567	+	1.11699i	0.308217	+	0.238143i
$23$	−2.12413			−0.442912			−0.221456	−	0.975170i	$-0.571081\pi$
$23$	−2.12413			−0.442912			−0.221456	+	0.975170i	$0.571081\pi$
$24$	−1.00103	+	2.34982i	−0.204333	+	0.479656i
$25$	−1.00000			−0.200000
$26$	−4.70499	−	3.63529i	−0.922725	−	0.712940i
$27$			4.68180i			0.901012i
$28$	−0.504724	−	1.93527i	−0.0953838	−	0.365731i
$29$		−	1.25526i		−	0.233095i	−0.993185	−	0.116548i	$-0.962817\pi$
$29$		−	1.25526i		−	0.233095i	0.993185	−	0.116548i	$-0.0371828\pi$
$30$	−0.780815	+	1.01057i	−0.142557	+	0.184504i
$31$	−3.58278			−0.643485			−0.321743	−	0.946827i	$-0.604269\pi$
$31$	−3.58278			−0.643485			−0.321743	+	0.946827i	$0.604269\pi$
$32$	0.831908	−	5.59535i	0.147062	−	0.989127i
$33$	1.16656			0.203071
$34$	−6.56470	+	8.49638i	−1.12584	+	1.45712i
$35$		−	1.00000i		−	0.169031i
$36$	−1.10259	−	4.22766i	−0.183764	−	0.704609i
$37$		−	1.87587i		−	0.308391i	−0.988040	−	0.154195i	$-0.950721\pi$
$37$		−	1.87587i		−	0.308391i	0.988040	−	0.154195i	$-0.0492785\pi$
$38$	−1.23818	−	0.956675i	−0.200859	−	0.155193i
$39$	−3.79661			−0.607945
$40$	1.10852	−	2.60215i	0.175272	−	0.411436i
$41$	4.82859			0.754098			0.377049	−	0.926193i	$-0.376939\pi$
$41$	4.82859			0.754098			0.377049	+	0.926193i	$0.376939\pi$
$42$	−1.01057	−	0.780815i	−0.155935	−	0.120482i
$43$			11.3049i			1.72399i	0.506919	+	0.861994i	$0.330784\pi$
$43$			11.3049i			1.72399i	−0.506919	+	0.861994i	$0.669216\pi$
$44$	−2.50002	+	0.652014i	−0.376893	+	0.0982948i
$45$		−	2.18454i		−	0.325651i
$46$	1.83665	−	2.37710i	0.270800	−	0.350484i
$47$	8.05265			1.17460			0.587300	−	0.809369i	$-0.300191\pi$
$47$	8.05265			1.17460			0.587300	+	0.809369i	$0.300191\pi$
$48$	−1.76412	−	3.15204i	−0.254628	−	0.454957i
$49$	1.00000			0.142857
$50$	0.864661	−	1.11909i	0.122281	−	0.158263i
$51$			6.85601i			0.960034i
$52$	8.13644	−	2.12201i	1.12832	−	0.294270i
$53$		−	10.6025i		−	1.45637i	−0.685380	−	0.728186i	$-0.740364\pi$
$53$		−	10.6025i		−	1.45637i	0.685380	−	0.728186i	$-0.259636\pi$
$54$	−5.23935	−	4.04816i	−0.712985	−	0.550885i
$55$	−1.29182			−0.174189
$56$	2.60215	+	1.10852i	0.347727	+	0.148132i
$57$	−0.999128			−0.132338
$58$	1.40475	+	1.08537i	0.184452	+	0.142516i
$59$		−	10.5375i		−	1.37187i	−0.727662	−	0.685936i	$-0.759393\pi$
$59$		−	10.5375i		−	1.37187i	0.727662	−	0.685936i	$-0.240607\pi$
$60$	−0.455781	−	1.74760i	−0.0588411	−	0.225615i
$61$		−	3.38884i		−	0.433896i	−0.976183	−	0.216948i	$-0.930390\pi$
$61$		−	3.38884i		−	0.433896i	0.976183	−	0.216948i	$-0.0696102\pi$
$62$	3.09789	−	4.00945i	0.393432	−	0.509200i
$63$	2.18454			0.275226
$64$	5.54238	+	5.76906i	0.692797	+	0.721132i
$65$	4.20430			0.521479
$66$	−1.00868	+	1.30548i	−0.124159	+	0.160694i
$67$		−	9.24944i		−	1.13000i	−0.825091	−	0.565000i	$-0.808876\pi$
$67$		−	9.24944i		−	1.13000i	0.825091	−	0.565000i	$-0.191124\pi$
$68$	−3.83198	−	14.6930i	−0.464695	−	1.78178i
$69$		−	1.91816i		−	0.230919i
$70$	1.11909	+	0.864661i	0.133757	+	0.103347i
$71$	−13.1131			−1.55623			−0.778117	−	0.628120i	$-0.783825\pi$
$71$	−13.1131			−1.55623			−0.778117	+	0.628120i	$0.783825\pi$
$72$	5.68449	+	2.42160i	0.669924	+	0.285388i
$73$	−11.1131			−1.30068			−0.650342	−	0.759641i	$-0.725375\pi$
$73$	−11.1131			−1.30068			−0.650342	+	0.759641i	$0.725375\pi$
$74$	2.09926	+	1.62199i	0.244034	+	0.188552i
$75$		−	0.903031i		−	0.104273i
$76$	2.14121	−	0.558435i	0.245614	−	0.0640569i
$77$		−	1.29182i		−	0.147217i
$78$	3.28278	−	4.24875i	0.371702	−	0.481076i
$79$	−6.94327			−0.781179			−0.390589	−	0.920565i	$-0.627729\pi$
$79$	−6.94327			−0.781179			−0.390589	+	0.920565i	$0.627729\pi$
$80$	1.95355	+	3.49051i	0.218413	+	0.390251i
$81$	2.32580			0.258422
$82$	−4.17509	+	5.40362i	−0.461061	+	0.596730i
$83$			5.74106i			0.630164i	0.949065	+	0.315082i	$0.102032\pi$
$83$			5.74106i			0.630164i	−0.949065	+	0.315082i	$0.897968\pi$
$84$	1.74760	−	0.455781i	0.190679	−	0.0497298i
$85$		−	7.59222i		−	0.823492i
$86$	−12.6512	−	9.77494i	−1.36422	−	1.05406i
$87$	1.13354			0.121528
$88$	1.43201	−	3.36152i	0.152653	−	0.358339i
$89$	0.691243			0.0732716			0.0366358	−	0.999329i	$-0.488336\pi$
$89$	0.691243			0.0732716			0.0366358	+	0.999329i	$0.488336\pi$
$90$	2.44469	+	1.88888i	0.257693	+	0.199106i
$91$			4.20430i			0.440731i
$92$	1.07210	+	4.11076i	0.111774	+	0.428577i
$93$		−	3.23536i		−	0.335491i
$94$	−6.96281	+	9.01164i	−0.718159	+	0.929480i
$95$	1.10642			0.113516
$96$	5.05277	+	0.751239i	0.515696	+	0.0766730i
$97$	6.79574			0.690003			0.345002	−	0.938602i	$-0.387878\pi$
$97$	6.79574			0.690003			0.345002	+	0.938602i	$0.387878\pi$
$98$	−0.864661	+	1.11909i	−0.0873439	+	0.113045i
$99$		−	2.82203i		−	0.283625i
$100$	0.504724	+	1.93527i	0.0504724	+	0.193527i
$101$			10.6769i			1.06239i	0.847248	+	0.531197i	$0.178258\pi$
$101$			10.6769i			1.06239i	−0.847248	+	0.531197i	$0.821742\pi$
$102$	−7.67249	−	5.92812i	−0.759690	−	0.586972i
$103$	−6.57062			−0.647422			−0.323711	−	0.946156i	$-0.604931\pi$
$103$	−6.57062			−0.647422			−0.323711	+	0.946156i	$0.604931\pi$
$104$	−4.66054	+	10.9402i	−0.457004	+	1.07278i
$105$	0.903031			0.0881268
$106$	11.8652	+	9.16760i	1.15245	+	0.890436i
$107$		−	5.23055i		−	0.505656i	−0.967511	−	0.252828i	$-0.918639\pi$
$107$		−	5.23055i		−	0.505656i	0.967511	−	0.252828i	$-0.0813607\pi$
$108$	9.06052	−	2.36301i	0.871849	−	0.227381i
$109$		−	6.07063i		−	0.581461i	−0.956805	−	0.290731i	$-0.906102\pi$
$109$		−	6.07063i		−	0.581461i	0.956805	−	0.290731i	$-0.0938983\pi$
$110$	1.11699	−	1.44567i	0.106501	−	0.137839i
$111$	1.69397			0.160784
$112$	−3.49051	+	1.95355i	−0.329822	+	0.184593i
$113$	−18.7147			−1.76053			−0.880267	−	0.474479i	$-0.842636\pi$
$113$	−18.7147			−1.76053			−0.880267	+	0.474479i	$0.842636\pi$
$114$	0.863907	−	1.11811i	0.0809123	−	0.104721i
$115$			2.12413i			0.198076i
$116$	−2.42926	+	0.633558i	−0.225551	+	0.0588244i
$117$			9.18445i			0.849102i
$118$	11.7925	+	9.11140i	1.08558	+	0.838772i
$119$	7.59222			0.695978
$120$	2.34982	+	1.00103i	0.214508	+	0.0913807i
$121$	9.33119			0.848290
$122$	3.79241	+	2.93019i	0.343349	+	0.265287i
$123$			4.36036i			0.393161i
$124$	1.80831	+	6.93362i	0.162391	+	0.622658i
$125$			1.00000i			0.0894427i
$126$	−1.88888	+	2.44469i	−0.168275	+	0.217790i
$127$	−16.2597			−1.44282			−0.721408	−	0.692510i	$-0.756505\pi$
$127$	−16.2597			−1.44282			−0.721408	+	0.692510i	$0.756505\pi$
$128$	−11.2484	+	1.21414i	−0.994225	+	0.107316i
$129$	−10.2087			−0.898827
$130$	−3.63529	+	4.70499i	−0.318836	+	0.412655i
$131$		−	10.2006i		−	0.891229i	−0.895225	−	0.445614i	$-0.852985\pi$
$131$		−	10.2006i		−	0.891229i	0.895225	−	0.445614i	$-0.147015\pi$
$132$	−0.588789	−	2.25760i	−0.0512475	−	0.196499i
$133$			1.10642i			0.0959385i
$134$	10.3510	+	7.99763i	0.894187	+	0.690890i
$135$	4.68180			0.402945
$136$	19.7561	+	8.41611i	1.69407	+	0.721675i
$137$	−19.3320			−1.65164			−0.825821	−	0.563932i	$-0.809288\pi$
$137$	−19.3320			−1.65164			−0.825821	+	0.563932i	$0.809288\pi$
$138$	2.14659	+	1.65856i	0.182730	+	0.141186i
$139$			4.64690i			0.394145i	0.980389	+	0.197073i	$0.0631435\pi$
$139$			4.64690i			0.394145i	−0.980389	+	0.197073i	$0.936857\pi$
$140$	−1.93527	+	0.504724i	−0.163560	+	0.0426569i
$141$			7.27179i			0.612396i
$142$	11.3383	−	14.6747i	0.951493	−	1.23147i
$143$	5.43122			0.454181
$144$	−7.62514	+	4.26760i	−0.635428	+	0.355633i
$145$	−1.25526			−0.104243
$146$	9.60902	−	12.4365i	0.795248	−	1.02925i
$147$			0.903031i			0.0744807i
$148$	−3.63030	+	0.946795i	−0.298409	+	0.0778260i
$149$		−	12.1751i		−	0.997426i	−0.866767	−	0.498713i	$-0.833806\pi$
$149$		−	12.1751i		−	0.997426i	0.866767	−	0.498713i	$-0.166194\pi$
$150$	1.01057	+	0.780815i	0.0825129	+	0.0637533i
$151$	−0.130253			−0.0105998			−0.00529990	−	0.999986i	$-0.501687\pi$
$151$	−0.130253			−0.0105998			−0.00529990	+	0.999986i	$0.501687\pi$
$152$	−1.22648	+	2.87906i	−0.0994808	+	0.233523i
$153$	16.5855			1.34086
$154$	1.44567	+	1.11699i	0.116495	+	0.0900096i
$155$			3.58278i			0.287775i
$156$	1.91624	+	7.34746i	0.153422	+	0.588267i
$157$			20.4348i			1.63087i	0.578848	+	0.815436i	$0.303502\pi$
$157$			20.4348i			1.63087i	−0.578848	+	0.815436i	$0.696498\pi$
$158$	6.00357	−	7.77014i	0.477619	−	0.618159i
$159$	9.57442			0.759301
$160$	−5.59535	−	0.831908i	−0.442351	−	0.0657681i
$161$	−2.12413			−0.167405
$162$	−2.01103	+	2.60278i	−0.158001	+	0.204494i
$163$			17.1574i			1.34387i	0.740609	+	0.671936i	$0.234537\pi$
$163$			17.1574i			1.34387i	−0.740609	+	0.671936i	$0.765463\pi$
$164$	−2.43710	−	9.34460i	−0.190306	−	0.729690i
$165$		−	1.16656i		−	0.0908163i
$166$	−6.42477	−	4.96407i	−0.498658	−	0.385287i
$167$	−2.16201			−0.167301			−0.0836507	−	0.996495i	$-0.526658\pi$
$167$	−2.16201			−0.167301			−0.0836507	+	0.996495i	$0.526658\pi$
$168$	−1.00103	+	2.34982i	−0.0772308	+	0.181293i
$169$	−4.67615			−0.359704
$170$	8.49638	+	6.56470i	0.651643	+	0.503489i
$171$			2.41701i			0.184833i
$172$	21.8781	−	5.70587i	1.66819	−	0.435069i
$173$			22.0578i			1.67702i	0.544885	+	0.838511i	$0.316573\pi$
$173$			22.0578i			1.67702i	−0.544885	+	0.838511i	$0.683427\pi$
$174$	−0.980124	+	1.26853i	−0.0743030	+	0.0961669i
$175$	−1.00000			−0.0755929
$176$	2.52364	+	4.50912i	0.190227	+	0.339888i
$177$	9.51573			0.715246
$178$	−0.597690	+	0.773563i	−0.0447988	+	0.0579810i
$179$		−	9.70563i		−	0.725433i	−0.931900	−	0.362716i	$-0.881849\pi$
$179$		−	9.70563i		−	0.725433i	0.931900	−	0.362716i	$-0.118151\pi$
$180$	−4.22766	+	1.10259i	−0.315111	+	0.0821820i
$181$		−	0.813811i		−	0.0604901i	−0.999543	−	0.0302450i	$-0.990371\pi$
$181$		−	0.813811i		−	0.0604901i	0.999543	−	0.0302450i	$-0.00962876\pi$
$182$	−4.70499	−	3.63529i	−0.348757	−	0.269466i
$183$	3.06022			0.226218
$184$	−5.52731	−	2.35464i	−0.407479	−	0.173586i
$185$	−1.87587			−0.137917
$186$	3.62065	+	2.79749i	0.265479	+	0.205122i
$187$		−	9.80781i		−	0.717218i
$188$	−4.06437	−	15.5840i	−0.296424	−	1.13658i
$189$			4.68180i			0.340550i
$190$	−0.956675	+	1.23818i	−0.0694045	+	0.0898270i
$191$	−12.2412			−0.885740			−0.442870	−	0.896586i	$-0.646040\pi$
$191$	−12.2412			−0.885740			−0.442870	+	0.896586i	$0.646040\pi$
$192$	−5.20964	+	5.00494i	−0.375973	+	0.361200i
$193$	−9.49075			−0.683159			−0.341579	−	0.939853i	$-0.610962\pi$
$193$	−9.49075			−0.683159			−0.341579	+	0.939853i	$0.610962\pi$
$194$	−5.87601	+	7.60505i	−0.421873	+	0.546010i
$195$			3.79661i			0.271881i
$196$	−0.504724	−	1.93527i	−0.0360517	−	0.138233i
$197$		−	13.3086i		−	0.948197i	−0.880472	−	0.474098i	$-0.842774\pi$
$197$		−	13.3086i		−	0.948197i	0.880472	−	0.474098i	$-0.157226\pi$
$198$	3.15811	+	2.44010i	0.224437	+	0.173411i
$199$	−10.3880			−0.736383			−0.368192	−	0.929750i	$-0.620023\pi$
$199$	−10.3880			−0.736383			−0.368192	+	0.929750i	$0.620023\pi$
$200$	−2.60215	−	1.10852i	−0.184000	−	0.0783840i
$201$	8.35253			0.589142
$202$	−11.9485	−	9.23193i	−0.840690	−	0.649556i
$203$		−	1.25526i		−	0.0881018i
$204$	13.2682	−	3.46039i	0.928960	−	0.242276i
$205$		−	4.82859i		−	0.337243i
$206$	5.68135	−	7.35311i	0.395839	−	0.512315i
$207$	−4.64024			−0.322519
$208$	−8.21331	−	14.6751i	−0.569491	−	1.01754i
$209$	1.42930			0.0988664
$210$	−0.780815	+	1.01057i	−0.0538814	+	0.0697361i
$211$		−	26.4575i		−	1.82141i	−0.413061	−	0.910703i	$-0.635540\pi$
$211$		−	26.4575i		−	1.82141i	0.413061	−	0.910703i	$-0.364460\pi$
$212$	−20.5187	+	5.35135i	−1.40923	+	0.367533i
$213$		−	11.8415i		−	0.811366i
$214$	5.85345	+	4.52265i	0.400134	+	0.309162i
$215$	11.3049			0.770991
$216$	−5.18985	+	12.1827i	−0.353125	+	0.828930i
$217$	−3.58278			−0.243215
$218$	6.79358	+	5.24904i	0.460119	+	0.355510i
$219$		−	10.0354i		−	0.678132i
$220$	0.652014	+	2.50002i	0.0439588	+	0.168551i
$221$			31.9200i			2.14717i
$222$	−1.46471	+	1.89570i	−0.0983046	+	0.127231i
$223$	25.1828			1.68636			0.843182	−	0.537629i	$-0.180680\pi$
$223$	25.1828			1.68636			0.843182	+	0.537629i	$0.180680\pi$
$224$	0.831908	−	5.59535i	0.0555842	−	0.373855i
$225$	−2.18454			−0.145636
$226$	16.1819	−	20.9435i	1.07640	−	1.39314i
$227$		−	4.09910i		−	0.272067i	−0.990704	−	0.136033i	$-0.956565\pi$
$227$		−	4.09910i		−	0.272067i	0.990704	−	0.136033i	$-0.0434355\pi$
$228$	0.504284	+	1.93358i	0.0333970	+	0.128054i
$229$		−	15.2474i		−	1.00758i	−0.863827	−	0.503788i	$-0.831939\pi$
$229$		−	15.2474i		−	1.00758i	0.863827	−	0.503788i	$-0.168061\pi$
$230$	−2.37710	−	1.83665i	−0.156741	−	0.121105i
$231$	1.16656			0.0767538
$232$	1.39147	−	3.26637i	0.0913547	−	0.214448i
$233$	2.79648			0.183204			0.0916018	−	0.995796i	$-0.470801\pi$
$233$	2.79648			0.183204			0.0916018	+	0.995796i	$0.470801\pi$
$234$	−10.2782	−	7.94143i	−0.671908	−	0.519147i
$235$		−	8.05265i		−	0.525297i
$236$	−20.3929	+	5.31855i	−1.32747	+	0.346208i
$237$		−	6.26999i		−	0.407279i
$238$	−6.56470	+	8.49638i	−0.425526	+	0.550738i
$239$	26.3801			1.70639			0.853193	−	0.521596i	$-0.174663\pi$
$239$	26.3801			1.70639			0.853193	+	0.521596i	$0.174663\pi$
$240$	−3.15204	+	1.76412i	−0.203463	+	0.113873i
$241$	−18.1881			−1.17160			−0.585798	−	0.810457i	$-0.699219\pi$
$241$	−18.1881			−1.17160			−0.585798	+	0.810457i	$0.699219\pi$
$242$	−8.06831	+	10.4424i	−0.518651	+	0.671266i
$243$			16.1457i			1.03574i
$244$	−6.55830	+	1.71043i	−0.419852	+	0.109499i
$245$		−	1.00000i		−	0.0638877i
$246$	−4.87964	−	3.77023i	−0.311114	−	0.240381i
$247$	−4.65171			−0.295981
$248$	−9.32292	−	3.97157i	−0.592006	−	0.252195i
$249$	−5.18436			−0.328545
$250$	−1.11909	−	0.864661i	−0.0707775	−	0.0546859i
$251$		−	13.9875i		−	0.882883i	−0.897290	−	0.441441i	$-0.854467\pi$
$251$		−	13.9875i		−	0.882883i	0.897290	−	0.441441i	$-0.145533\pi$
$252$	−1.10259	−	4.22766i	−0.0694564	−	0.266317i
$253$			2.74400i			0.172514i
$254$	14.0591	−	18.1961i	0.882149	−	1.14172i
$255$	6.85601			0.429340
$256$	8.36729	−	13.6378i	0.522956	−	0.852360i
$257$	−7.00696			−0.437082			−0.218541	−	0.975828i	$-0.570130\pi$
$257$	−7.00696			−0.437082			−0.218541	+	0.975828i	$0.570130\pi$
$258$	8.82707	−	11.4245i	0.549550	−	0.711256i
$259$		−	1.87587i		−	0.116561i
$260$	−2.12201	−	8.13644i	−0.131602	−	0.504601i
$261$		−	2.74215i		−	0.169735i
$262$	11.4154	+	8.82004i	0.705243	+	0.544904i
$263$	28.4537			1.75453			0.877266	−	0.480004i	$-0.159365\pi$
$263$	28.4537			1.75453			0.877266	+	0.480004i	$0.159365\pi$
$264$	3.03556	+	1.29315i	0.186826	+	0.0795878i
$265$	−10.6025			−0.651309
$266$	−1.23818	−	0.956675i	−0.0759177	−	0.0586575i
$267$			0.624213i			0.0382012i
$268$	−17.9001	+	4.66841i	−1.09342	+	0.285169i
$269$			19.6931i			1.20071i	0.799733	+	0.600356i	$0.204974\pi$
$269$			19.6931i			1.20071i	−0.799733	+	0.600356i	$0.795026\pi$
$270$	−4.04816	+	5.23935i	−0.246363	+	0.318857i
$271$	14.6110			0.887554			0.443777	−	0.896137i	$-0.353638\pi$
$271$	14.6110			0.887554			0.443777	+	0.896137i	$0.353638\pi$
$272$	−26.5007	+	14.8318i	−1.60684	+	0.899309i
$273$	−3.79661			−0.229782
$274$	16.7156	−	21.6342i	1.00983	−	1.30697i
$275$			1.29182i			0.0778999i
$276$	−3.71214	+	0.968140i	−0.223445	+	0.0582752i
$277$			0.687390i			0.0413012i	0.999787	+	0.0206506i	$0.00657377\pi$
$277$			0.687390i			0.0413012i	−0.999787	+	0.0206506i	$0.993426\pi$
$278$	−5.20030	−	4.01799i	−0.311893	−	0.240983i
$279$	−7.82670			−0.468572
$280$	1.10852	−	2.60215i	0.0662466	−	0.155508i
$281$	0.158684			0.00946630			0.00473315	−	0.999989i	$-0.498493\pi$
$281$	0.158684			0.00946630			0.00473315	+	0.999989i	$0.498493\pi$
$282$	−8.13779	−	6.28763i	−0.484598	−	0.374423i
$283$		−	13.2574i		−	0.788070i	−0.919095	−	0.394035i	$-0.871079\pi$
$283$		−	13.2574i		−	0.788070i	0.919095	−	0.394035i	$-0.128921\pi$
$284$	6.61847	+	25.3773i	0.392734	+	1.50586i
$285$			0.999128i			0.0591833i
$286$	−4.69616	+	6.07802i	−0.277690	+	0.359401i
$287$	4.82859			0.285022
$288$	1.81733	−	12.2232i	0.107087	−	0.720261i
$289$	40.6419			2.39070
$290$	1.08537	−	1.40475i	0.0637352	−	0.0824895i
$291$			6.13676i			0.359744i
$292$	5.60902	+	21.5067i	0.328243	+	1.25859i
$293$		−	22.8027i		−	1.33215i	−0.745885	−	0.666075i	$-0.767973\pi$
$293$		−	22.8027i		−	1.33215i	0.745885	−	0.666075i	$-0.232027\pi$
$294$	−1.01057	−	0.780815i	−0.0589378	−	0.0455381i
$295$	−10.5375			−0.613520
$296$	2.07943	−	4.88129i	0.120864	−	0.283719i
$297$	6.04805			0.350944
$298$	13.6251	+	10.5274i	0.789279	+	0.609834i
$299$		−	8.93050i		−	0.516464i
$300$	−1.74760	+	0.455781i	−0.100898	+	0.0263145i
$301$			11.3049i			0.651606i
$302$	0.112624	−	0.145764i	0.00648080	−	0.00838779i
$303$	−9.64160			−0.553896
$304$	−2.16144	−	3.86196i	−0.123967	−	0.221498i
$305$	−3.38884			−0.194044
$306$	−14.3408	+	18.5606i	−0.819810	+	1.06104i
$307$		−	0.569392i		−	0.0324969i	−0.999868	−	0.0162485i	$-0.994828\pi$
$307$		−	0.569392i		−	0.0324969i	0.999868	−	0.0162485i	$-0.00517228\pi$
$308$	−2.50002	+	0.652014i	−0.142452	+	0.0371519i
$309$		−	5.93347i		−	0.337543i
$310$	−4.00945	−	3.09789i	−0.227721	−	0.175948i
$311$	16.8332			0.954522			0.477261	−	0.878762i	$-0.341630\pi$
$311$	16.8332			0.954522			0.477261	+	0.878762i	$0.341630\pi$
$312$	−9.87936	−	4.20861i	−0.559309	−	0.238266i
$313$	−21.5395			−1.21749			−0.608744	−	0.793367i	$-0.708326\pi$
$313$	−21.5395			−1.21749			−0.608744	+	0.793367i	$0.708326\pi$
$314$	−22.8683	−	17.6691i	−1.29053	−	0.997127i
$315$		−	2.18454i		−	0.123085i
$316$	3.50443	+	13.4371i	0.197140	+	0.755894i
$317$			21.2199i			1.19183i	0.803049	+	0.595914i	$0.203210\pi$
$317$			21.2199i			1.19183i	−0.803049	+	0.595914i	$0.796790\pi$
$318$	−8.27863	+	10.7146i	−0.464242	+	0.600847i
$319$	−1.62157			−0.0907905
$320$	5.76906	−	5.54238i	0.322500	−	0.309828i
$321$	4.72335			0.263632
$322$	1.83665	−	2.37710i	0.102353	−	0.132470i
$323$			8.40016i			0.467398i
$324$	−1.17389	−	4.50104i	−0.0652159	−	0.250058i
$325$		−	4.20430i		−	0.233213i
$326$	−19.2007	−	14.8353i	−1.06343	−	0.821654i
$327$	5.48197			0.303154
$328$	12.5647	+	5.35257i	0.693770	+	0.295546i
$329$	8.05265			0.443957
$330$	1.30548	+	1.00868i	0.0718644	+	0.0555258i
$331$			12.3082i			0.676518i	0.941053	+	0.338259i	$0.109838\pi$
$331$			12.3082i			0.676518i	−0.941053	+	0.338259i	$0.890162\pi$
$332$	11.1105	−	2.89765i	0.609767	−	0.159029i
$333$		−	4.09790i		−	0.224563i
$334$	1.86941	−	2.41949i	0.102289	−	0.132388i
$335$	−9.24944			−0.505351
$336$	−1.76412	−	3.15204i	−0.0962404	−	0.171958i
$337$	−5.91725			−0.322333			−0.161167	−	0.986927i	$-0.551526\pi$
$337$	−5.91725			−0.322333			−0.161167	+	0.986927i	$0.551526\pi$
$338$	4.04329	−	5.23304i	0.219926	−	0.284640i
$339$		−	16.9000i		−	0.917881i
$340$	−14.6930	+	3.83198i	−0.796838	+	0.207818i
$341$			4.62831i			0.250637i
$342$	−2.70485	−	2.08989i	−0.146261	−	0.113008i
$343$	1.00000			0.0539949
$344$	−12.5317	+	29.4172i	−0.675665	+	1.58607i
$345$	−1.91816			−0.103270
$346$	−24.6846	−	19.0725i	−1.32705	−	1.02534i
$347$			24.6755i			1.32465i	0.749215	+	0.662326i	$0.230431\pi$
$347$			24.6755i			1.32465i	−0.749215	+	0.662326i	$0.769569\pi$
$348$	−0.572122	−	2.19369i	−0.0306690	−	0.117594i
$349$			5.85422i			0.313369i	0.987649	+	0.156684i	$0.0500806\pi$
$349$			5.85422i			0.313369i	−0.987649	+	0.156684i	$0.949919\pi$
$350$	0.864661	−	1.11909i	0.0462181	−	0.0598179i
$351$	−19.6837			−1.05064
$352$	−7.22820	−	1.07468i	−0.385265	−	0.0572806i
$353$	−4.89320			−0.260439			−0.130219	−	0.991485i	$-0.541568\pi$
$353$	−4.89320			−0.260439			−0.130219	+	0.991485i	$0.541568\pi$
$354$	−8.22788	+	10.6490i	−0.437307	+	0.565985i
$355$			13.1131i			0.695969i
$356$	−0.348887	−	1.33774i	−0.0184910	−	0.0709000i
$357$			6.85601i			0.362859i
$358$	10.8615	+	8.39208i	0.574047	+	0.443535i
$359$	4.71373			0.248781			0.124391	−	0.992233i	$-0.460302\pi$
$359$	4.71373			0.248781			0.124391	+	0.992233i	$0.460302\pi$
$360$	2.42160	−	5.68449i	0.127629	−	0.299599i
$361$	17.7758			0.935571
$362$	0.910727	+	0.703670i	0.0478667	+	0.0369841i
$363$			8.42635i			0.442269i
$364$	8.13644	−	2.12201i	0.426465	−	0.111224i
$365$			11.1131i			0.581684i
$366$	−2.64606	+	3.42467i	−0.138312	+	0.179010i
$367$	−5.37925			−0.280794			−0.140397	−	0.990095i	$-0.544838\pi$
$367$	−5.37925			−0.280794			−0.140397	+	0.990095i	$0.544838\pi$
$368$	7.41430	−	4.14960i	0.386497	−	0.216313i
$369$	10.5482			0.549118
$370$	1.62199	−	2.09926i	0.0843232	−	0.109136i
$371$		−	10.6025i		−	0.550457i
$372$	−6.26128	+	1.63296i	−0.324632	+	0.0846651i
$373$		−	26.8589i		−	1.39070i	−0.718670	−	0.695351i	$-0.755249\pi$
$373$		−	26.8589i		−	1.39070i	0.718670	−	0.695351i	$-0.244751\pi$
$374$	10.9758	+	8.48043i	0.567546	+	0.438513i
$375$	−0.903031			−0.0466323
$376$	20.9542	+	8.92651i	1.08063	+	0.460349i
$377$	5.27748			0.271804
$378$	−5.23935	−	4.04816i	−0.269483	−	0.208215i
$379$		−	1.37944i		−	0.0708571i	−0.999372	−	0.0354286i	$-0.988720\pi$
$379$		−	1.37944i		−	0.0708571i	0.999372	−	0.0354286i	$-0.0112796\pi$
$380$	−0.558435	−	2.14121i	−0.0286471	−	0.109842i
$381$		−	14.6830i		−	0.752234i
$382$	10.5845	−	13.6990i	0.541548	−	0.700900i
$383$	17.5157			0.895012			0.447506	−	0.894281i	$-0.352312\pi$
$383$	17.5157			0.895012			0.447506	+	0.894281i	$0.352312\pi$
$384$	−1.09641	−	10.1576i	−0.0559508	−	0.518354i
$385$	−1.29182			−0.0658374
$386$	8.20628	−	10.6210i	0.417688	−	0.540595i
$387$			24.6961i			1.25537i
$388$	−3.42997	−	13.1516i	−0.174130	−	0.667670i
$389$			30.1930i			1.53085i	0.643527	+	0.765423i	$0.277470\pi$
$389$			30.1930i			1.53085i	−0.643527	+	0.765423i	$0.722530\pi$
$390$	−4.24875	−	3.28278i	−0.215144	−	0.166230i
$391$	−16.1269			−0.815572
$392$	2.60215	+	1.10852i	0.131428	+	0.0559886i
$393$	9.21144			0.464655
$394$	14.8935	+	11.5074i	0.750323	+	0.579735i
$395$			6.94327i			0.349354i
$396$	−5.46139	+	1.42435i	−0.274445	+	0.0715762i
$397$			11.6372i			0.584054i	0.956410	+	0.292027i	$0.0943297\pi$
$397$			11.6372i			0.584054i	−0.956410	+	0.292027i	$0.905670\pi$
$398$	8.98207	−	11.6251i	0.450230	−	0.582712i
$399$	−0.999128			−0.0500190
$400$	3.49051	−	1.95355i	0.174525	−	0.0976775i
$401$	−10.0188			−0.500315			−0.250158	−	0.968205i	$-0.580482\pi$
$401$	−10.0188			−0.500315			−0.250158	+	0.968205i	$0.580482\pi$
$402$	−7.22211	+	9.34723i	−0.360206	+	0.466198i
$403$		−	15.0631i		−	0.750345i
$404$	20.6627	−	5.38890i	1.02801	−	0.268108i
$405$		−	2.32580i		−	0.115570i
$406$	1.40475	+	1.08537i	0.0697163	+	0.0538661i
$407$	−2.42329			−0.120118
$408$	−7.60001	+	17.8404i	−0.376256	+	0.883230i
$409$	−24.2484			−1.19900			−0.599502	−	0.800373i	$-0.704635\pi$
$409$	−24.2484			−1.19900			−0.599502	+	0.800373i	$0.704635\pi$
$410$	5.40362	+	4.17509i	0.266866	+	0.206193i
$411$		−	17.4574i		−	0.861108i
$412$	3.31635	+	12.7159i	0.163385	+	0.626467i
$413$		−	10.5375i		−	0.518519i
$414$	4.01224	−	5.19285i	0.197191	−	0.255215i
$415$	5.74106			0.281818
$416$	23.5245	+	3.49759i	1.15339	+	0.171484i
$417$	−4.19630			−0.205493
$418$	−1.23586	+	1.59951i	−0.0604477	+	0.0782346i
$419$			29.7918i			1.45543i	0.685882	+	0.727713i	$0.259417\pi$
$419$			29.7918i			1.45543i	−0.685882	+	0.727713i	$0.740583\pi$
$420$	−0.455781	−	1.74760i	−0.0222398	−	0.0852744i
$421$		−	13.0088i		−	0.634011i	−0.948424	−	0.317006i	$-0.897323\pi$
$421$		−	13.0088i		−	0.634011i	0.948424	−	0.317006i	$-0.102677\pi$
$422$	29.6083	+	22.8767i	1.44131	+	1.11362i
$423$	17.5913			0.855319
$424$	11.7531	−	27.5894i	0.570781	−	1.33986i
$425$	−7.59222			−0.368277
$426$	13.2517	+	10.2389i	0.642047	+	0.496075i
$427$		−	3.38884i		−	0.163997i
$428$	−10.1225	+	2.63998i	−0.489290	+	0.127608i
$429$			4.90456i			0.236794i
$430$	−9.77494	+	12.6512i	−0.471390	+	0.610097i
$431$	14.9975			0.722405			0.361202	−	0.932487i	$-0.382366\pi$
$431$	14.9975			0.722405			0.361202	+	0.932487i	$0.382366\pi$
$432$	−9.14612	−	16.3418i	−0.440043	−	0.786247i
$433$	3.60776			0.173378			0.0866888	−	0.996235i	$-0.472371\pi$
$433$	3.60776			0.173378			0.0866888	+	0.996235i	$0.472371\pi$
$434$	3.09789	−	4.00945i	0.148703	−	0.192460i
$435$		−	1.13354i		−	0.0543489i
$436$	−11.7483	+	3.06399i	−0.562641	+	0.146739i
$437$		−	2.35018i		−	0.112424i
$438$	11.2305	+	8.67724i	0.536616	+	0.414615i
$439$	10.9266			0.521497			0.260748	−	0.965407i	$-0.416031\pi$
$439$	10.9266			0.521497			0.260748	+	0.965407i	$0.416031\pi$
$440$	−3.36152	−	1.43201i	−0.160254	−	0.0682683i
$441$	2.18454			0.104025
$442$	−35.7213	−	27.6000i	−1.69909	−	1.31280i
$443$		−	6.41092i		−	0.304592i	−0.988335	−	0.152296i	$-0.951333\pi$
$443$		−	6.41092i		−	0.304592i	0.988335	−	0.152296i	$-0.0486667\pi$
$444$	−0.854985	−	3.27827i	−0.0405758	−	0.155580i
$445$		−	0.691243i		−	0.0327680i
$446$	−21.7746	+	28.1818i	−1.03106	+	1.33445i
$447$	10.9945			0.520023
$448$	5.54238	+	5.76906i	0.261853	+	0.272562i
$449$	18.6929			0.882173			0.441087	−	0.897465i	$-0.354593\pi$
$449$	18.6929			0.882173			0.441087	+	0.897465i	$0.354593\pi$
$450$	1.88888	−	2.44469i	0.0890427	−	0.115244i
$451$		−	6.23768i		−	0.293721i
$452$	9.44577	+	36.2180i	0.444291	+	1.70355i
$453$		−	0.117622i		−	0.00552637i
$454$	4.58726	+	3.54433i	0.215291	+	0.166344i
$455$	4.20430			0.197101
$456$	−2.59988	−	1.10755i	−0.121751	−	0.0518658i
$457$	21.1856			0.991021			0.495511	−	0.868602i	$-0.334981\pi$
$457$	21.1856			0.991021			0.495511	+	0.868602i	$0.334981\pi$
$458$	17.0632	+	13.1838i	0.797311	+	0.616040i
$459$			35.5452i			1.65911i
$460$	4.11076	−	1.07210i	0.191665	−	0.0499869i
$461$			4.57955i			0.213291i	0.994297	+	0.106645i	$0.0340110\pi$
$461$			4.57955i			0.213291i	−0.994297	+	0.106645i	$0.965989\pi$
$462$	−1.00868	+	1.30548i	−0.0469278	+	0.0607365i
$463$	−40.6437			−1.88888			−0.944438	−	0.328691i	$-0.893393\pi$
$463$	−40.6437			−1.88888			−0.944438	+	0.328691i	$0.893393\pi$
$464$	2.45221	+	4.38148i	0.113841	+	0.203405i
$465$	−3.23536			−0.150036
$466$	−2.41801	+	3.12951i	−0.112012	+	0.144972i
$467$		−	38.7920i		−	1.79508i	−0.440933	−	0.897540i	$-0.645352\pi$
$467$		−	38.7920i		−	1.79508i	0.440933	−	0.897540i	$-0.354648\pi$
$468$	17.7743	−	4.63561i	0.821619	−	0.214281i
$469$		−	9.24944i		−	0.427100i
$470$	9.01164	+	6.96281i	0.415676	+	0.321171i
$471$	−18.4532			−0.850279
$472$	11.6810	−	27.4203i	0.537664	−	1.26212i
$473$	14.6040			0.671492
$474$	7.01668	+	5.42141i	0.322287	+	0.249014i
$475$		−	1.10642i		−	0.0507659i
$476$	−3.83198	−	14.6930i	−0.175638	−	0.673451i
$477$		−	23.1616i		−	1.06050i
$478$	−22.8098	+	29.5217i	−1.04330	+	1.35029i
$479$	3.42244			0.156375			0.0781876	−	0.996939i	$-0.475087\pi$
$479$	3.42244			0.156375			0.0781876	+	0.996939i	$0.475087\pi$
$480$	0.751239	−	5.05277i	0.0342892	−	0.230626i
$481$	7.88671			0.359603
$482$	15.7265	−	20.3541i	0.716323	−	0.927103i
$483$		−	1.91816i		−	0.0872792i
$484$	−4.70967	−	18.0583i	−0.214076	−	0.820833i
$485$		−	6.79574i		−	0.308579i
$486$	−18.0684	−	13.9605i	−0.819601	−	0.633262i
$487$	−14.8752			−0.674060			−0.337030	−	0.941494i	$-0.609422\pi$
$487$	−14.8752			−0.674060			−0.337030	+	0.941494i	$0.609422\pi$
$488$	3.75658	−	8.81827i	0.170053	−	0.399184i
$489$	−15.4937			−0.700648
$490$	1.11909	+	0.864661i	0.0505553	+	0.0390614i
$491$			7.58225i			0.342182i	0.985255	+	0.171091i	$0.0547292\pi$
$491$			7.58225i			0.342182i	−0.985255	+	0.171091i	$0.945271\pi$
$492$	8.43846	−	2.20078i	0.380435	−	0.0992187i
$493$		−	9.53019i		−	0.429218i
$494$	4.02215	−	5.20568i	0.180965	−	0.234215i
$495$	−2.82203			−0.126841
$496$	12.5057	−	6.99913i	0.561523	−	0.314270i
$497$	−13.1131			−0.588201
$498$	4.48271	−	5.80176i	0.200875	−	0.259983i
$499$			22.4671i			1.00576i	0.864355	+	0.502882i	$0.167727\pi$
$499$			22.4671i			1.00576i	−0.864355	+	0.502882i	$0.832273\pi$
$500$	1.93527	−	0.504724i	0.0865477	−	0.0225719i
$501$		−	1.95236i		−	0.0872252i
$502$	15.6533	+	12.0944i	0.698639	+	0.539801i
$503$	−19.9356			−0.888885			−0.444443	−	0.895807i	$-0.646598\pi$
$503$	−19.9356			−0.888885			−0.444443	+	0.895807i	$0.646598\pi$
$504$	5.68449	+	2.42160i	0.253207	+	0.107866i
$505$	10.6769			0.475117
$506$	−3.07079	−	2.37263i	−0.136513	−	0.105476i
$507$		−	4.22271i		−	0.187537i
$508$	8.20666	+	31.4669i	0.364112	+	1.39612i
$509$			8.88133i			0.393658i	0.980438	+	0.196829i	$0.0630644\pi$
$509$			8.88133i			0.393658i	−0.980438	+	0.196829i	$0.936936\pi$
$510$	−5.92812	+	7.67249i	−0.262502	+	0.339744i
$511$	−11.1131			−0.491613
$512$	8.02701	+	21.1558i	0.354747	+	0.934962i
$513$	−5.18002			−0.228703
$514$	6.05864	−	7.84141i	0.267235	−	0.345870i
$515$			6.57062i			0.289536i
$516$	5.15258	+	19.7566i	0.226830	+	0.869735i
$517$		−	10.4026i		−	0.457506i
$518$	2.09926	+	1.62199i	0.0922364	+	0.0712661i
$519$	−19.9188			−0.874340
$520$	10.9402	+	4.66054i	0.479761	+	0.204378i
$521$	−30.7217			−1.34594			−0.672970	−	0.739669i	$-0.734982\pi$
$521$	−30.7217			−1.34594			−0.672970	+	0.739669i	$0.734982\pi$
$522$	3.06872	+	2.37103i	0.134314	+	0.103777i
$523$			35.7861i			1.56482i	0.622765	+	0.782409i	$0.286009\pi$
$523$			35.7861i			1.56482i	−0.622765	+	0.782409i	$0.713991\pi$
$524$	−19.7408	+	5.14847i	−0.862382	+	0.224912i
$525$		−	0.903031i		−	0.0394115i
$526$	−24.6028	+	31.8423i	−1.07273	+	1.38839i
$527$	−27.2012			−1.18490
$528$	−4.07187	+	2.27893i	−0.177206	+	0.0991775i
$529$	−18.4881			−0.803829
$530$	9.16760	−	11.8652i	0.398215	−	0.515391i
$531$		−	23.0196i		−	0.998967i
$532$	2.14121	−	0.558435i	0.0928332	−	0.0242112i
$533$			20.3008i			0.879327i
$534$	−0.698551	−	0.539733i	−0.0302293	−	0.0233565i
$535$	−5.23055			−0.226136
$536$	10.2532	−	24.0685i	0.442869	−	1.03960i
$537$	8.76448			0.378215
$538$	−22.0384	−	17.0279i	−0.950142	−	0.734124i
$539$		−	1.29182i		−	0.0556428i
$540$	−2.36301	−	9.06052i	−0.101688	−	0.389903i
$541$			3.84635i			0.165368i	0.996576	+	0.0826838i	$0.0263492\pi$
$541$			3.84635i			0.165368i	−0.996576	+	0.0826838i	$0.973651\pi$
$542$	−12.6335	+	16.3510i	−0.542657	+	0.702336i
$543$	0.734896			0.0315374
$544$	6.31603	−	42.4811i	0.270798	−	1.82136i
$545$	−6.07063			−0.260037
$546$	3.28278	−	4.24875i	0.140490	−	0.181830i
$547$			23.6081i			1.00941i	0.863293	+	0.504704i	$0.168398\pi$
$547$			23.6081i			1.00941i	−0.863293	+	0.504704i	$0.831602\pi$
$548$	9.75731	+	37.4125i	0.416811	+	1.59818i
$549$		−	7.40303i		−	0.315954i
$550$	−1.44567	−	1.11699i	−0.0616434	−	0.0476286i
$551$	1.38884			0.0591665
$552$	2.12631	−	4.99134i	0.0905018	−	0.212445i
$553$	−6.94327			−0.295258
$554$	−0.769251	−	0.594359i	−0.0326823	−	0.0252519i
$555$		−	1.69397i		−	0.0719048i
$556$	8.99299	−	2.34540i	0.381388	−	0.0994672i
$557$		−	4.66983i		−	0.197867i	−0.995094	−	0.0989335i	$-0.968457\pi$
$557$		−	4.66983i		−	0.197867i	0.995094	−	0.0989335i	$-0.0315431\pi$
$558$	6.76744	−	8.75878i	0.286489	−	0.370789i
$559$	−47.5294			−2.01028
$560$	1.95355	+	3.49051i	0.0825525	+	0.147501i
$561$	8.85676			0.373933
$562$	−0.137208	+	0.177582i	−0.00578777	+	0.00749084i
$563$		−	22.5505i		−	0.950391i	−0.879880	−	0.475195i	$-0.842377\pi$
$563$		−	22.5505i		−	0.950391i	0.879880	−	0.475195i	$-0.157623\pi$
$564$	14.0729	−	3.67025i	0.592574	−	0.154545i
$565$			18.7147i			0.787334i
$566$	14.8362	+	11.4631i	0.623613	+	0.481832i
$567$	2.32580			0.0976744
$568$	−34.1222	−	14.5360i	−1.43173	−	0.609919i
$569$	−16.6949			−0.699888			−0.349944	−	0.936771i	$-0.613799\pi$
$569$	−16.6949			−0.699888			−0.349944	+	0.936771i	$0.613799\pi$
$570$	−1.11811	−	0.863907i	−0.0468327	−	0.0361851i
$571$		−	25.4090i		−	1.06333i	−0.846954	−	0.531667i	$-0.821566\pi$
$571$		−	25.4090i		−	1.06333i	0.846954	−	0.531667i	$-0.178434\pi$
$572$	−2.74126	−	10.5108i	−0.114618	−	0.439481i
$573$		−	11.0542i		−	0.461794i
$574$	−4.17509	+	5.40362i	−0.174265	+	0.225543i
$575$	2.12413			0.0885825
$576$	12.1075	+	12.6027i	0.504480	+	0.525113i
$577$	19.3383			0.805066			0.402533	−	0.915406i	$-0.368130\pi$
$577$	19.3383			0.805066			0.402533	+	0.915406i	$0.368130\pi$
$578$	−35.1414	+	45.4819i	−1.46169	+	1.89180i
$579$		−	8.57044i		−	0.356175i
$580$	0.633558	+	2.42926i	0.0263071	+	0.100869i
$581$			5.74106i			0.238179i
$582$	−6.86759	−	5.30622i	−0.284671	−	0.219950i
$583$	−13.6966			−0.567256
$584$	−28.9178	−	12.3190i	−1.19663	−	0.509764i
$585$	9.18445			0.379730
$586$	25.5183	+	19.7166i	1.05415	+	0.814487i
$587$		−	36.3623i		−	1.50083i	−0.660965	−	0.750417i	$-0.729853\pi$
$587$		−	36.3623i		−	1.50083i	0.660965	−	0.750417i	$-0.270147\pi$
$588$	1.74760	−	0.455781i	0.0720700	−	0.0187961i
$589$		−	3.96404i		−	0.163336i
$590$	9.11140	−	11.7925i	0.375110	−	0.485488i
$591$	12.0181			0.494357
$592$	3.66460	+	6.54773i	0.150614	+	0.269110i
$593$	−20.0914			−0.825054			−0.412527	−	0.910945i	$-0.635354\pi$
$593$	−20.0914			−0.825054			−0.412527	+	0.910945i	$0.635354\pi$
$594$	−5.22951	+	6.76831i	−0.214570	+	0.277707i
$595$		−	7.59222i		−	0.311251i
$596$	−23.5621	+	6.14508i	−0.965142	+	0.251712i
$597$		−	9.38065i		−	0.383925i
$598$	9.99403	+	7.72185i	0.408686	+	0.315770i
$599$	2.61777			0.106959			0.0534796	−	0.998569i	$-0.482969\pi$
$599$	2.61777			0.106959			0.0534796	+	0.998569i	$0.482969\pi$
$600$	1.00103	−	2.34982i	0.0408667	−	0.0959311i
$601$	45.5595			1.85841			0.929206	−	0.369562i	$-0.120492\pi$
$601$	45.5595			1.85841			0.929206	+	0.369562i	$0.120492\pi$
$602$	−12.6512	−	9.77494i	−0.515626	−	0.398397i
$603$		−	20.2057i		−	0.822841i
$604$	0.0657416	+	0.252073i	0.00267499	+	0.0102567i
$605$		−	9.33119i		−	0.379367i
$606$	8.33672	−	10.7898i	0.338656	−	0.438306i
$607$	−29.1244			−1.18212			−0.591062	−	0.806626i	$-0.701291\pi$
$607$	−29.1244			−1.18212			−0.591062	+	0.806626i	$0.701291\pi$
$608$	6.19079	+	0.920437i	0.251070	+	0.0373287i
$609$	1.13354			0.0459332
$610$	2.93019	−	3.79241i	0.118640	−	0.153550i
$611$			33.8558i			1.36966i
$612$	−8.37108	−	32.0973i	−0.338381	−	1.29746i
$613$		−	24.8079i		−	1.00198i	−0.865452	−	0.500991i	$-0.832969\pi$
$613$		−	24.8079i		−	1.00198i	0.865452	−	0.500991i	$-0.167031\pi$
$614$	0.637201	+	0.492331i	0.0257153	+	0.0198689i
$615$	4.36036			0.175827
$616$	1.43201	−	3.36152i	0.0576973	−	0.135440i
$617$	25.0278			1.00758			0.503790	−	0.863826i	$-0.331939\pi$
$617$	25.0278			1.00758			0.503790	+	0.863826i	$0.331939\pi$
$618$	6.64008	+	5.13044i	0.267103	+	0.206376i
$619$			25.9218i			1.04188i	0.853592	+	0.520942i	$0.174419\pi$
$619$			25.9218i			1.04188i	−0.853592	+	0.520942i	$0.825581\pi$
$620$	6.93362	−	1.80831i	0.278461	−	0.0726236i
$621$		−	9.94475i		−	0.399069i
$622$	−14.5550	+	18.8378i	−0.583602	+	0.755328i
$623$	0.691243			0.0276941
$624$	13.2521	−	7.41687i	0.530509	−	0.296913i
$625$	1.00000			0.0400000
$626$	18.6244	−	24.1047i	0.744381	−	0.963417i
$627$			1.29070i			0.0515455i
$628$	39.5467	−	10.3139i	1.57808	−	0.411570i
$629$		−	14.2420i		−	0.567866i
$630$	2.44469	+	1.88888i	0.0973988	+	0.0752549i
$631$	36.3672			1.44776			0.723878	−	0.689928i	$-0.242358\pi$
$631$	36.3672			1.44776			0.723878	+	0.689928i	$0.242358\pi$
$632$	−18.0674	−	7.69673i	−0.718684	−	0.306160i
$633$	23.8919			0.949618
$634$	−23.7469	−	18.3480i	−0.943112	−	0.728692i
$635$			16.2597i			0.645247i
$636$	−4.83244	−	18.5291i	−0.191619	−	0.734725i
$637$			4.20430i			0.166581i
$638$	1.40211	−	1.81468i	0.0555100	−	0.0718440i
$639$	−28.6459			−1.13322
$640$	1.21414	+	11.2484i	0.0479932	+	0.444631i
$641$	2.48804			0.0982718			0.0491359	−	0.998792i	$-0.484353\pi$
$641$	2.48804			0.0982718			0.0491359	+	0.998792i	$0.484353\pi$
$642$	−4.08409	+	5.28585i	−0.161186	+	0.208616i
$643$			23.6996i			0.934621i	0.884093	+	0.467310i	$0.154777\pi$
$643$			23.6996i			0.934621i	−0.884093	+	0.467310i	$0.845223\pi$
$644$	1.07210	+	4.11076i	0.0422467	+	0.161987i
$645$			10.2087i			0.401968i
$646$	−9.40053	−	7.26329i	−0.369859	−	0.285770i
$647$	4.02817			0.158364			0.0791819	−	0.996860i	$-0.474769\pi$
$647$	4.02817			0.158364			0.0791819	+	0.996860i	$0.474769\pi$
$648$	6.05208	+	2.57819i	0.237748	+	0.101281i
$649$	−13.6126			−0.534343
$650$	4.70499	+	3.63529i	0.184545	+	0.142588i
$651$		−	3.23536i		−	0.126804i
$652$	33.2042	−	8.65975i	1.30038	−	0.339142i
$653$		−	38.4349i		−	1.50407i	−0.659121	−	0.752037i	$-0.729071\pi$
$653$		−	38.4349i		−	1.50407i	0.659121	−	0.752037i	$-0.270929\pi$
$654$	−4.74004	+	6.13481i	−0.185350	+	0.239890i
$655$	−10.2006			−0.398570
$656$	−16.8542	+	9.43288i	−0.658047	+	0.368292i
$657$	−24.2769			−0.947131
$658$	−6.96281	+	9.01164i	−0.271439	+	0.351310i
$659$			5.31482i			0.207036i	0.994628	+	0.103518i	$0.0330099\pi$
$659$			5.31482i			0.207036i	−0.994628	+	0.103518i	$0.966990\pi$
$660$	−2.25760	+	0.588789i	−0.0878768	+	0.0229186i
$661$		−	39.9262i		−	1.55295i	−0.630149	−	0.776474i	$-0.717006\pi$
$661$		−	39.9262i		−	1.55295i	0.630149	−	0.776474i	$-0.282994\pi$
$662$	−13.7740	−	10.6424i	−0.535340	−	0.413628i
$663$	−28.8247			−1.11946
$664$	−6.36407	+	14.9391i	−0.246974	+	0.579750i
$665$	1.10642			0.0429050
$666$	4.58592	+	3.54329i	0.177701	+	0.137300i
$667$			2.66633i			0.103241i
$668$	1.09122	+	4.18407i	0.0422205	+	0.161886i
$669$			22.7408i			0.879211i
$670$	7.99763	−	10.3510i	0.308975	−	0.399892i
$671$	−4.37778			−0.169002
$672$	5.05277	+	0.751239i	0.194915	+	0.0289797i
$673$	−6.50925			−0.250913			−0.125457	−	0.992099i	$-0.540040\pi$
$673$	−6.50925			−0.250913			−0.125457	+	0.992099i	$0.540040\pi$
$674$	5.11642	−	6.62194i	0.197077	−	0.255067i
$675$		−	4.68180i		−	0.180202i
$676$	2.36017	+	9.04960i	0.0907756	+	0.348062i
$677$		−	41.9029i		−	1.61046i	−0.592962	−	0.805230i	$-0.702042\pi$
$677$		−	41.9029i		−	1.61046i	0.592962	−	0.805230i	$-0.297958\pi$
$678$	18.9126	+	14.6127i	0.726334	+	0.561199i
$679$	6.79574			0.260797
$680$	8.41611	−	19.7561i	0.322743	−	0.757612i
$681$	3.70162			0.141846
$682$	−5.17950	−	4.00192i	−0.198333	−	0.153241i
$683$		−	48.8906i		−	1.87075i	−0.353660	−	0.935374i	$-0.615063\pi$
$683$		−	48.8906i		−	1.87075i	0.353660	−	0.935374i	$-0.384937\pi$
$684$	4.67755	−	1.21992i	0.178851	−	0.0466448i
$685$			19.3320i			0.738637i
$686$	−0.864661	+	1.11909i	−0.0330129	+	0.0427270i
$687$	13.7689			0.525315
$688$	−22.0848	−	39.4600i	−0.841974	−	1.50440i
$689$	44.5763			1.69822
$690$	1.65856	−	2.14659i	0.0631401	−	0.0817193i
$691$		−	15.5309i		−	0.590822i	−0.955370	−	0.295411i	$-0.904543\pi$
$691$		−	15.5309i		−	0.590822i	0.955370	−	0.295411i	$-0.0954565\pi$
$692$	42.6876	−	11.1331i	1.62274	−	0.423216i
$693$		−	2.82203i		−	0.107200i
$694$	−27.6142	−	21.3360i	−1.04822	−	0.809903i
$695$	4.64690			0.176267
$696$	2.94963	+	1.25654i	0.111805	+	0.0476292i
$697$	36.6597			1.38858
$698$	−6.55139	−	5.06191i	−0.247974	−	0.191596i
$699$			2.52531i			0.0955159i
$700$	0.504724	+	1.93527i	0.0190768	+	0.0731462i
$701$			25.1364i			0.949388i	0.880151	+	0.474694i	$0.157441\pi$
$701$			25.1364i			0.949388i	−0.880151	+	0.474694i	$0.842559\pi$
$702$	17.0197	−	22.0278i	0.642367	−	0.831386i
$703$	2.07549			0.0782786
$704$	7.45261	−	7.15978i	0.280881	−	0.269844i
$705$	7.27179			0.273872
$706$	4.23095	−	5.47593i	0.159234	−	0.206089i
$707$			10.6769i			0.401548i
$708$	−4.80281	−	18.4155i	−0.180501	−	0.692095i
$709$			5.70165i			0.214130i	0.994252	+	0.107065i	$0.0341453\pi$
$709$			5.70165i			0.214130i	−0.994252	+	0.107065i	$0.965855\pi$
$710$	−14.6747	−	11.3383i	−0.550731	−	0.425520i
$711$	−15.1678			−0.568838
$712$	1.79872	+	0.766254i	0.0674098	+	0.0287166i
$713$	7.61029			0.285008
$714$	−7.67249	−	5.92812i	−0.287136	−	0.221854i
$715$		−	5.43122i		−	0.203116i
$716$	−18.7830	+	4.89866i	−0.701953	+	0.183072i
$717$			23.8220i			0.889650i
$718$	−4.07578	+	5.27509i	−0.152107	+	0.196865i
$719$	−35.9242			−1.33975			−0.669873	−	0.742476i	$-0.733651\pi$
$719$	−35.9242			−1.33975			−0.669873	+	0.742476i	$0.733651\pi$
$720$	4.26760	+	7.62514i	0.159044	+	0.284172i
$721$	−6.57062			−0.244703
$722$	−15.3701	+	19.8928i	−0.572015	+	0.740332i
$723$		−	16.4244i		−	0.610830i
$724$	−1.57494	+	0.410749i	−0.0585322	+	0.0152654i
$725$			1.25526i			0.0466191i
$726$	−9.42985	−	7.28594i	−0.349974	−	0.270406i
$727$	19.4840			0.722620			0.361310	−	0.932446i	$-0.382330\pi$
$727$	19.4840			0.722620			0.361310	+	0.932446i	$0.382330\pi$
$728$	−4.66054	+	10.9402i	−0.172731	+	0.405472i
$729$	−7.60262			−0.281579
$730$	−12.4365	−	9.60902i	−0.460296	−	0.355646i
$731$			85.8297i			3.17452i
$732$	−1.54457	−	5.92235i	−0.0570889	−	0.218896i
$733$			20.1460i			0.744108i	0.928211	+	0.372054i	$0.121346\pi$
$733$			20.1460i			0.744108i	−0.928211	+	0.372054i	$0.878654\pi$
$734$	4.65122	−	6.01986i	0.171680	−	0.222197i
$735$	0.903031			0.0333088
$736$	−1.76708	+	11.8853i	−0.0651356	+	0.438097i
$737$	−11.9487			−0.440134
$738$	−9.12063	+	11.8044i	−0.335735	+	0.434526i
$739$		−	3.57962i		−	0.131679i	−0.997830	−	0.0658393i	$-0.979028\pi$
$739$		−	3.57962i		−	0.131679i	0.997830	−	0.0658393i	$-0.0209725\pi$
$740$	0.946795	+	3.63030i	0.0348049	+	0.133453i
$741$		−	4.20064i		−	0.154314i
$742$	11.8652	+	9.16760i	0.435585	+	0.336553i
$743$	42.1184			1.54517			0.772586	−	0.634910i	$-0.218963\pi$
$743$	42.1184			1.54517			0.772586	+	0.634910i	$0.218963\pi$
$744$	3.58645	−	8.41889i	0.131486	−	0.308651i
$745$	−12.1751			−0.446062
$746$	30.0575	+	23.2239i	1.10049	+	0.850286i
$747$			12.5416i			0.458872i
$748$	−18.9807	+	4.95024i	−0.694004	+	0.180999i
$749$		−	5.23055i		−	0.191120i
$750$	0.780815	−	1.01057i	0.0285113	−	0.0369009i
$751$	21.8252			0.796413			0.398207	−	0.917296i	$-0.369633\pi$
$751$	21.8252			0.796413			0.398207	+	0.917296i	$0.369633\pi$
$752$	−28.1079	+	15.7313i	−1.02499	+	0.573660i
$753$	12.6311			0.460304
$754$	−4.56323	+	5.90597i	−0.166183	+	0.215083i
$755$			0.130253i			0.00474038i
$756$	9.06052	−	2.36301i	0.329528	−	0.0859420i
$757$		−	8.07681i		−	0.293557i	−0.989169	−	0.146778i	$-0.953110\pi$
$757$		−	8.07681i		−	0.293557i	0.989169	−	0.146778i	$-0.0468904\pi$
$758$	1.54372	+	1.19275i	0.0560704	+	0.0433226i
$759$	−2.47792			−0.0899428
$760$	2.87906	+	1.22648i	0.104435	+	0.0444892i
$761$	−41.4460			−1.50242			−0.751208	−	0.660065i	$-0.770529\pi$
$761$	−41.4460			−1.50242			−0.751208	+	0.660065i	$0.770529\pi$
$762$	16.4316	+	12.6958i	0.595255	+	0.459921i
$763$		−	6.07063i		−	0.219772i
$764$	6.17841	+	23.6899i	0.223527	+	0.857072i
$765$		−	16.5855i		−	0.599649i
$766$	−15.1452	+	19.6017i	−0.547217	+	0.708237i
$767$	44.3030			1.59969
$768$	12.3153	+	7.55592i	0.444391	+	0.272651i
$769$	−8.25246			−0.297591			−0.148796	−	0.988868i	$-0.547540\pi$
$769$	−8.25246			−0.297591			−0.148796	+	0.988868i	$0.547540\pi$
$770$	1.11699	−	1.44567i	0.0402535	−	0.0520982i
$771$		−	6.32750i		−	0.227879i
$772$	4.79021	+	18.3671i	0.172403	+	0.661047i
$773$			25.5920i			0.920479i	0.887795	+	0.460240i	$0.152236\pi$
$773$			25.5920i			0.920479i	−0.887795	+	0.460240i	$0.847764\pi$
$774$	−27.6371	−	21.3537i	−0.993395	−	0.767543i
$775$	3.58278			0.128697
$776$	17.6835	+	7.53320i	0.634802	+	0.270426i
$777$	1.69397			0.0607707
$778$	−33.7887	−	26.1067i	−1.21138	−	0.935971i
$779$			5.34243i			0.191412i
$780$	7.34746	−	1.91624i	0.263081	−	0.0686124i
$781$			16.9398i			0.606152i
$782$	13.9443	−	18.0474i	0.498647	−	0.645375i
$783$	5.87686			0.210022
$784$	−3.49051	+	1.95355i	−0.124661	+	0.0697696i
$785$	20.4348			0.729348
$786$	−7.96477	+	10.3084i	−0.284094	+	0.367689i
$787$		−	44.4731i		−	1.58529i	−0.609681	−	0.792647i	$-0.708702\pi$
$787$		−	44.4731i		−	1.58529i	0.609681	−	0.792647i	$-0.291298\pi$
$788$	−25.7556	+	6.71716i	−0.917507	+	0.239289i
$789$			25.6946i			0.914752i
$790$	−7.77014	−	6.00357i	−0.276449	−	0.213598i
$791$	−18.7147			−0.665419
$792$	3.12827	−	7.34336i	0.111158	−	0.260935i
$793$	14.2477			0.505950
$794$	−13.0231	−	10.0622i	−0.462171	−	0.357095i
$795$		−	9.57442i		−	0.339570i
$796$	5.24305	+	20.1035i	0.185835	+	0.712549i
$797$			2.52806i			0.0895484i	0.998997	+	0.0447742i	$0.0142568\pi$
$797$			2.52806i			0.0895484i	−0.998997	+	0.0447742i	$0.985743\pi$
$798$	0.863907	−	1.11811i	0.0305820	−	0.0395808i
$799$	61.1375			2.16289
$800$	−0.831908	+	5.59535i	−0.0294124	+	0.197825i
$801$	1.51004			0.0533548
$802$	8.66287	−	11.2119i	0.305896	−	0.395907i
$803$			14.3561i			0.506616i
$804$	−4.21572	−	16.1644i	−0.148677	−	0.570073i
$805$			2.12413i			0.0748658i
$806$	16.8569	+	13.0244i	0.593760	+	0.458767i
$807$	−17.7835			−0.626009
$808$	−11.8356	+	27.7830i	−0.416374	+	0.977403i
$809$	−51.5175			−1.81126			−0.905629	−	0.424071i	$-0.860601\pi$
$809$	−51.5175			−1.81126			−0.905629	+	0.424071i	$0.860601\pi$
$810$	2.60278	+	2.01103i	0.0914524	+	0.0706603i
$811$			12.7638i			0.448196i	0.974567	+	0.224098i	$0.0719436\pi$
$811$			12.7638i			0.448196i	−0.974567	+	0.224098i	$0.928056\pi$
$812$	−2.42926	+	0.633558i	−0.0852502	+	0.0222335i
$813$			13.1942i			0.462740i
$814$	2.09532	−	2.71188i	0.0734410	−	0.0950513i
$815$	17.1574			0.600998
$816$	−13.3936	−	23.9310i	−0.468868	−	0.837751i
$817$	−12.5080			−0.437599
$818$	20.9666	−	27.1361i	0.733080	−	0.948791i
$819$			9.18445i			0.320931i
$820$	−9.34460	+	2.43710i	−0.326327	+	0.0851073i
$821$		−	4.79645i		−	0.167397i	−0.996491	−	0.0836985i	$-0.973327\pi$
$821$		−	4.79645i		−	0.167397i	0.996491	−	0.0836985i	$-0.0266733\pi$
$822$	19.5364	+	15.0947i	0.681409	+	0.526488i
$823$	2.96067			0.103203			0.0516013	−	0.998668i	$-0.483568\pi$
$823$	2.96067			0.103203			0.0516013	+	0.998668i	$0.483568\pi$
$824$	−17.0977	−	7.28364i	−0.595628	−	0.253738i
$825$	−1.16656			−0.0406143
$826$	11.7925	+	9.11140i	0.410312	+	0.317026i
$827$			15.2469i			0.530187i	0.964223	+	0.265093i	$0.0854028\pi$
$827$			15.2469i			0.530187i	−0.964223	+	0.265093i	$0.914597\pi$
$828$	2.34204	+	8.98010i	0.0813915	+	0.312080i
$829$			33.4093i			1.16035i	0.814491	+	0.580176i	$0.197016\pi$
$829$			33.4093i			1.16035i	−0.814491	+	0.580176i	$0.802984\pi$
$830$	−4.96407	+	6.42477i	−0.172305	+	0.223007i
$831$	−0.620734			−0.0215330
$832$	−24.2549	+	23.3018i	−0.840886	+	0.807846i
$833$	7.59222			0.263055
$834$	3.62837	−	4.69603i	0.125640	−	0.162610i
$835$			2.16201i			0.0748195i
$836$	−0.721399	−	2.76607i	−0.0249501	−	0.0956664i
$837$		−	16.7738i		−	0.579788i
$838$	−33.3397	−	25.7598i	−1.15170	−	0.889858i
$839$	−17.3962			−0.600583			−0.300291	−	0.953847i	$-0.597084\pi$
$839$	−17.3962			−0.600583			−0.300291	+	0.953847i	$0.597084\pi$
$840$	2.34982	+	1.00103i	0.0810766	+	0.0345387i
$841$	27.4243			0.945667
$842$	14.5580	+	11.2482i	0.501703	+	0.387639i
$843$			0.143297i			0.00493540i
$844$	−51.2022	+	13.3537i	−1.76245	+	0.459654i
$845$			4.67615i			0.160865i
$846$	−15.2105	+	19.6863i	−0.522948	+	0.676827i
$847$	9.33119			0.320624
$848$	20.7126	+	37.0083i	0.711273	+	1.27087i
$849$	11.9718			0.410872
$850$	6.56470	−	8.49638i	0.225167	−	0.291423i
$851$			3.98459i			0.136590i
$852$	−22.9164	+	5.97668i	−0.785104	+	0.204758i
$853$			21.3807i			0.732063i	0.930603	+	0.366031i	$0.119284\pi$
$853$			21.3807i			0.732063i	−0.930603	+	0.366031i	$0.880716\pi$
$854$	3.79241	+	2.93019i	0.129774	+	0.100269i
$855$	2.41701			0.0826599
$856$	5.79815	−	13.6107i	0.198177	−	0.465203i
$857$	−7.81682			−0.267017			−0.133509	−	0.991048i	$-0.542624\pi$
$857$	−7.81682			−0.267017			−0.133509	+	0.991048i	$0.542624\pi$
$858$	−5.48864	−	4.24078i	−0.187379	−	0.144778i
$859$			23.6235i			0.806024i	0.915195	+	0.403012i	$0.132037\pi$
$859$			23.6235i			0.806024i	−0.915195	+	0.403012i	$0.867963\pi$
$860$	−5.70587	−	21.8781i	−0.194569	−	0.746036i
$861$			4.36036i			0.148601i
$862$	−12.9678	+	16.7836i	−0.441684	+	0.571650i
$863$	4.05556			0.138053			0.0690264	−	0.997615i	$-0.478011\pi$
$863$	4.05556			0.138053			0.0690264	+	0.997615i	$0.478011\pi$
$864$	26.1963	+	3.89482i	0.891215	+	0.132505i
$865$	22.0578			0.749987
$866$	−3.11948	+	4.03740i	−0.106004	+	0.137196i
$867$			36.7008i			1.24643i
$868$	1.80831	+	6.93362i	0.0613781	+	0.235343i
$869$			8.96948i			0.304269i
$870$	1.26853	+	0.980124i	0.0430071	+	0.0332293i
$871$	38.8875			1.31765
$872$	6.72940	−	15.7967i	0.227886	−	0.534944i
$873$	14.8455			0.502445
$874$	2.63006	+	2.03210i	0.0889630	+	0.0687370i
$875$			1.00000i			0.0338062i
$876$	−19.4212	+	5.06512i	−0.656183	+	0.171135i
$877$			23.0415i			0.778056i	0.921226	+	0.389028i	$0.127189\pi$
$877$			23.0415i			0.778056i	−0.921226	+	0.389028i	$0.872811\pi$
$878$	−9.44777	+	12.2278i	−0.318847	+	0.412669i
$879$	20.5916			0.694537
$880$	4.50912	−	2.52364i	0.152002	−	0.0850719i
$881$	0.692738			0.0233389			0.0116695	−	0.999932i	$-0.496285\pi$
$881$	0.692738			0.0233389			0.0116695	+	0.999932i	$0.496285\pi$
$882$	−1.88888	+	2.44469i	−0.0636020	+	0.0823170i
$883$			41.4841i			1.39605i	0.716073	+	0.698025i	$0.245938\pi$
$883$			41.4841i			1.39605i	−0.716073	+	0.698025i	$0.754062\pi$
$884$	61.7737	−	16.1108i	2.07767	−	0.541864i
$885$		−	9.51573i		−	0.319868i
$886$	7.17440	+	5.54327i	0.241029	+	0.186230i
$887$	48.7720			1.63760			0.818801	−	0.574077i	$-0.194639\pi$
$887$	48.7720			1.63760			0.818801	+	0.574077i	$0.194639\pi$
$888$	4.40796	+	1.87779i	0.147921	+	0.0630145i
$889$	−16.2597			−0.545333
$890$	0.773563	+	0.597690i	0.0259299	+	0.0200346i
$891$		−	3.00452i		−	0.100655i
$892$	−12.7103	−	48.7354i	−0.425574	−	1.63178i
$893$			8.90959i			0.298148i
$894$	−9.50653	+	12.3039i	−0.317946	+	0.411502i
$895$	−9.70563			−0.324423
$896$	−11.2484	+	1.21414i	−0.375782	+	0.0405616i
$897$	8.06451			0.269266
$898$	−16.1630	+	20.9191i	−0.539367	+	0.698078i
$899$			4.49730i			0.149993i
$900$	1.10259	+	4.22766i	0.0367529	+	0.140922i
$901$		−	80.4969i		−	2.68174i
$902$	6.98052	+	5.39348i	0.232426	+	0.179583i
$903$	−10.2087			−0.339725
$904$	−48.6985	−	20.7456i	−1.61969	−	0.689988i
$905$	−0.813811			−0.0270520
$906$	0.131630	+	0.101703i	0.00437310	+	0.00337886i
$907$			40.6893i			1.35106i	0.737330	+	0.675532i	$0.236086\pi$
$907$			40.6893i			1.35106i	−0.737330	+	0.675532i	$0.763914\pi$
$908$	−7.93285	+	2.06891i	−0.263261	+	0.0686593i
$909$			23.3241i			0.773613i
$910$	−3.63529	+	4.70499i	−0.120509	+	0.155969i
$911$	−20.6156			−0.683024			−0.341512	−	0.939877i	$-0.610939\pi$
$911$	−20.6156			−0.683024			−0.341512	+	0.939877i	$0.610939\pi$
$912$	3.48747	−	1.95185i	0.115482	−	0.0646321i
$913$	7.41644			0.245448
$914$	−18.3184	+	23.7086i	−0.605918	+	0.784211i
$915$		−	3.06022i		−	0.101168i
$916$	−29.5078	+	7.69572i	−0.974964	+	0.254274i
$917$		−	10.2006i		−	0.336853i
$918$	−39.7783	−	30.7346i	−1.31288	−	1.01439i
$919$	40.1522			1.32450			0.662250	−	0.749283i	$-0.269602\pi$
$919$	40.1522			1.32450			0.662250	+	0.749283i	$0.269602\pi$
$920$	−2.35464	+	5.52731i	−0.0776301	+	0.182230i
$921$	0.514179			0.0169428
$922$	−5.12492	−	3.95975i	−0.168780	−	0.130408i
$923$		−	55.1312i		−	1.81467i
$924$	−0.588789	−	2.25760i	−0.0193697	−	0.0742695i
$925$			1.87587i			0.0616781i
$926$	35.1431	−	45.4840i	1.15487	−	1.49470i
$927$	−14.3537			−0.471439
$928$	−7.02360	−	1.04426i	−0.230561	−	0.0342795i
$929$	22.3942			0.734729			0.367364	−	0.930077i	$-0.380260\pi$
$929$	22.3942			0.734729			0.367364	+	0.930077i	$0.380260\pi$
$930$	2.79749	−	3.62065i	0.0917332	−	0.118726i
$931$			1.10642i			0.0362613i
$932$	−1.41145	−	5.41193i	−0.0462336	−	0.177274i
$933$			15.2009i			0.497654i
$934$	43.4117	+	33.5419i	1.42048	+	1.09753i
$935$	−9.80781			−0.320750
$936$	−10.1811	+	23.8993i	−0.332780	+	0.781174i
$937$	−13.8200			−0.451479			−0.225740	−	0.974188i	$-0.572480\pi$
$937$	−13.8200			−0.451479			−0.225740	+	0.974188i	$0.572480\pi$
$938$	10.3510	+	7.99763i	0.337971	+	0.261132i
$939$		−	19.4509i		−	0.634755i
$940$	−15.5840	+	4.06437i	−0.508295	+	0.132565i
$941$		−	4.76294i		−	0.155268i	−0.996982	−	0.0776338i	$-0.975264\pi$
$941$		−	4.76294i		−	0.155268i	0.996982	−	0.0776338i	$-0.0247365\pi$
$942$	15.9558	−	20.6508i	0.519867	−	0.672840i
$943$	−10.2566			−0.333999
$944$	20.5856	+	36.7814i	0.670005	+	1.19713i
$945$	4.68180			0.152299
$946$	−12.6275	+	16.3432i	−0.410555	+	0.531363i
$947$		−	48.4745i		−	1.57521i	−0.616181	−	0.787605i	$-0.711321\pi$
$947$		−	48.4745i		−	1.57521i	0.616181	−	0.787605i	$-0.288679\pi$
$948$	−12.1341	+	3.16461i	−0.394097	+	0.102782i
$949$		−	46.7226i		−	1.51668i
$950$	1.23818	+	0.956675i	0.0401718	+	0.0310386i
$951$	−19.1622			−0.621377
$952$	19.7561	+	8.41611i	0.640299	+	0.272768i
$953$	9.83000			0.318425			0.159212	−	0.987244i	$-0.449105\pi$
$953$	9.83000			0.318425			0.159212	+	0.987244i	$0.449105\pi$
$954$	25.9199	+	20.0269i	0.839189	+	0.648396i
$955$			12.2412i			0.396115i
$956$	−13.3147	−	51.0525i	−0.430627	−	1.65116i
$957$		−	1.46433i		−	0.0473350i
$958$	−2.95925	+	3.83001i	−0.0956089	+	0.123742i
$959$	−19.3320			−0.624262
$960$	5.00494	+	5.20964i	0.161534	+	0.168140i
$961$	−18.1637			−0.585926
$962$	−6.81933	+	8.82594i	−0.219864	+	0.284560i
$963$		−	11.4263i		−	0.368208i
$964$	9.17995	+	35.1988i	0.295666	+	1.13368i
$965$			9.49075i			0.305518i
$966$	2.14659	+	1.65856i	0.0690654	+	0.0533631i
$967$	50.6548			1.62895			0.814475	−	0.580199i	$-0.197025\pi$
$967$	50.6548			1.62895			0.814475	+	0.580199i	$0.197025\pi$
$968$	24.2812	+	10.3438i	0.780426	+	0.332462i
$969$	−7.58560			−0.243685
$970$	7.60505	+	5.87601i	0.244183	+	0.188667i
$971$		−	2.90161i		−	0.0931170i	−0.998916	−	0.0465585i	$-0.985175\pi$
$971$		−	2.90161i		−	0.0931170i	0.998916	−	0.0465585i	$-0.0148254\pi$
$972$	31.2461	−	8.14910i	1.00222	−	0.261382i
$973$			4.64690i			0.148973i
$974$	12.8620	−	16.6467i	0.412126	−	0.533395i
$975$	3.79661			0.121589
$976$	6.62026	+	11.8288i	0.211909	+	0.378629i
$977$	−18.4101			−0.588992			−0.294496	−	0.955653i	$-0.595152\pi$
$977$	−18.4101			−0.588992			−0.294496	+	0.955653i	$0.595152\pi$
$978$	13.3968	−	17.3388i	0.428382	−	0.554434i
$979$		−	0.892964i		−	0.0285392i
$980$	−1.93527	+	0.504724i	−0.0618198	+	0.0161228i
$981$		−	13.2615i		−	0.423407i
$982$	−8.48522	−	6.55607i	−0.270774	−	0.209213i
$983$	−6.24328			−0.199130			−0.0995649	−	0.995031i	$-0.531745\pi$
$983$	−6.24328			−0.199130			−0.0995649	+	0.995031i	$0.531745\pi$
$984$	−4.83354	+	11.3463i	−0.154087	+	0.361707i
$985$	−13.3086			−0.424047
$986$	10.6651	+	8.24038i	0.339647	+	0.262427i
$987$			7.27179i			0.231464i
$988$	2.34783	+	9.00229i	0.0746944	+	0.286401i
$989$		−	24.0132i		−	0.763575i
$990$	2.44010	−	3.15811i	0.0775515	−	0.100371i
$991$	−50.9148			−1.61736			−0.808682	−	0.588247i	$-0.799818\pi$
$991$	−50.9148			−1.61736			−0.808682	+	0.588247i	$0.799818\pi$
$992$	−2.98054	+	20.0469i	−0.0946323	+	0.636489i
$993$	−11.1147			−0.352713
$994$	11.3383	−	14.6747i	0.359630	−	0.465453i
$995$			10.3880i			0.329321i
$996$	2.61667	+	10.0331i	0.0829123	+	0.317911i
$997$			57.9532i			1.83540i	0.397278	+	0.917698i	$0.369955\pi$
$997$			57.9532i			1.83540i	−0.397278	+	0.917698i	$0.630045\pi$
$998$	−25.1427	−	19.4264i	−0.795878	−	0.614932i
$999$	8.78243			0.277864

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.b.d.141.6	yes	12
4.3	odd	2		1120.2.b.d.561.5		12
8.3	odd	2		1120.2.b.d.561.8		12
8.5	even	2	inner	280.2.b.d.141.5	✓	12
16.3	odd	4		8960.2.a.cd.1.4		6
16.5	even	4		8960.2.a.cf.1.4		6
16.11	odd	4		8960.2.a.cg.1.3		6
16.13	even	4		8960.2.a.ca.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.b.d.141.5	✓	12	8.5	even	2	inner
280.2.b.d.141.6	yes	12	1.1	even	1	trivial
1120.2.b.d.561.5		12	4.3	odd	2
1120.2.b.d.561.8		12	8.3	odd	2
8960.2.a.ca.1.3		6	16.13	even	4
8960.2.a.cd.1.4		6	16.3	odd	4
8960.2.a.cf.1.4		6	16.5	even	4
8960.2.a.cg.1.3		6	16.11	odd	4

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.864661 + 1.11909i) q^{2} +0.903031i q^{3} +(-0.504724 - 1.93527i) q^{4} -1.00000i q^{5} +(-1.01057 - 0.780815i) q^{6} +1.00000 q^{7} +(2.60215 + 1.10852i) q^{8} +2.18454 q^{9} +O(q^{10})\)	\(q+(-0.864661 + 1.11909i) q^{2} +0.903031i q^{3} +(-0.504724 - 1.93527i) q^{4} -1.00000i q^{5} +(-1.01057 - 0.780815i) q^{6} +1.00000 q^{7} +(2.60215 + 1.10852i) q^{8} +2.18454 q^{9} +(1.11909 + 0.864661i) q^{10} -1.29182i q^{11} +(1.74760 - 0.455781i) q^{12} +4.20430i q^{13} +(-0.864661 + 1.11909i) q^{14} +0.903031 q^{15} +(-3.49051 + 1.95355i) q^{16} +7.59222 q^{17} +(-1.88888 + 2.44469i) q^{18} +1.10642i q^{19} +(-1.93527 + 0.504724i) q^{20} +0.903031i q^{21} +(1.44567 + 1.11699i) q^{22} -2.12413 q^{23} +(-1.00103 + 2.34982i) q^{24} -1.00000 q^{25} +(-4.70499 - 3.63529i) q^{26} +4.68180i q^{27} +(-0.504724 - 1.93527i) q^{28} -1.25526i q^{29} +(-0.780815 + 1.01057i) q^{30} -3.58278 q^{31} +(0.831908 - 5.59535i) q^{32} +1.16656 q^{33} +(-6.56470 + 8.49638i) q^{34} -1.00000i q^{35} +(-1.10259 - 4.22766i) q^{36} -1.87587i q^{37} +(-1.23818 - 0.956675i) q^{38} -3.79661 q^{39} +(1.10852 - 2.60215i) q^{40} +4.82859 q^{41} +(-1.01057 - 0.780815i) q^{42} +11.3049i q^{43} +(-2.50002 + 0.652014i) q^{44} -2.18454i q^{45} +(1.83665 - 2.37710i) q^{46} +8.05265 q^{47} +(-1.76412 - 3.15204i) q^{48} +1.00000 q^{49} +(0.864661 - 1.11909i) q^{50} +6.85601i q^{51} +(8.13644 - 2.12201i) q^{52} -10.6025i q^{53} +(-5.23935 - 4.04816i) q^{54} -1.29182 q^{55} +(2.60215 + 1.10852i) q^{56} -0.999128 q^{57} +(1.40475 + 1.08537i) q^{58} -10.5375i q^{59} +(-0.455781 - 1.74760i) q^{60} -3.38884i q^{61} +(3.09789 - 4.00945i) q^{62} +2.18454 q^{63} +(5.54238 + 5.76906i) q^{64} +4.20430 q^{65} +(-1.00868 + 1.30548i) q^{66} -9.24944i q^{67} +(-3.83198 - 14.6930i) q^{68} -1.91816i q^{69} +(1.11909 + 0.864661i) q^{70} -13.1131 q^{71} +(5.68449 + 2.42160i) q^{72} -11.1131 q^{73} +(2.09926 + 1.62199i) q^{74} -0.903031i q^{75} +(2.14121 - 0.558435i) q^{76} -1.29182i q^{77} +(3.28278 - 4.24875i) q^{78} -6.94327 q^{79} +(1.95355 + 3.49051i) q^{80} +2.32580 q^{81} +(-4.17509 + 5.40362i) q^{82} +5.74106i q^{83} +(1.74760 - 0.455781i) q^{84} -7.59222i q^{85} +(-12.6512 - 9.77494i) q^{86} +1.13354 q^{87} +(1.43201 - 3.36152i) q^{88} +0.691243 q^{89} +(2.44469 + 1.88888i) q^{90} +4.20430i q^{91} +(1.07210 + 4.11076i) q^{92} -3.23536i q^{93} +(-6.96281 + 9.01164i) q^{94} +1.10642 q^{95} +(5.05277 + 0.751239i) q^{96} +6.79574 q^{97} +(-0.864661 + 1.11909i) q^{98} -2.82203i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9	\( 12 q - 2 q^{2} + 6 q^{4} + 12 q^{7} + 10 q^{8} - 20 q^{9} + 16 q^{12} - 2 q^{14} + 2 q^{16} - 2 q^{18} + 4 q^{20} + 12 q^{22} + 8 q^{23} - 24 q^{24} - 12 q^{25} + 6 q^{28} + 12 q^{30} + 24 q^{31} - 2 q^{32} - 24 q^{33} - 20 q^{34} - 18 q^{36} + 12 q^{38} - 48 q^{39} + 12 q^{40} - 16 q^{41} + 16 q^{44} - 48 q^{46} - 16 q^{47} + 20 q^{48} + 12 q^{49} + 2 q^{50} + 4 q^{52} + 44 q^{54} - 8 q^{55} + 10 q^{56} + 40 q^{57} + 4 q^{58} - 8 q^{60} + 8 q^{62} - 20 q^{63} - 6 q^{64} + 8 q^{65} + 64 q^{66} - 56 q^{68} - 32 q^{71} - 46 q^{72} - 8 q^{73} - 32 q^{74} - 12 q^{76} - 24 q^{78} + 8 q^{80} + 60 q^{81} - 28 q^{82} + 16 q^{84} - 76 q^{86} + 48 q^{87} - 40 q^{88} - 48 q^{89} + 24 q^{90} + 12 q^{94} + 28 q^{96} + 32 q^{97} - 2 q^{98}+O(q^{100}) \) 12 * q - 2 * q^2 + 6 * q^4 + 12 * q^7 + 10 * q^8 - 20 * q^9 + 16 * q^12 - 2 * q^14 + 2 * q^16 - 2 * q^18 + 4 * q^20 + 12 * q^22 + 8 * q^23 - 24 * q^24 - 12 * q^25 + 6 * q^28 + 12 * q^30 + 24 * q^31 - 2 * q^32 - 24 * q^33 - 20 * q^34 - 18 * q^36 + 12 * q^38 - 48 * q^39 + 12 * q^40 - 16 * q^41 + 16 * q^44 - 48 * q^46 - 16 * q^47 + 20 * q^48 + 12 * q^49 + 2 * q^50 + 4 * q^52 + 44 * q^54 - 8 * q^55 + 10 * q^56 + 40 * q^57 + 4 * q^58 - 8 * q^60 + 8 * q^62 - 20 * q^63 - 6 * q^64 + 8 * q^65 + 64 * q^66 - 56 * q^68 - 32 * q^71 - 46 * q^72 - 8 * q^73 - 32 * q^74 - 12 * q^76 - 24 * q^78 + 8 * q^80 + 60 * q^81 - 28 * q^82 + 16 * q^84 - 76 * q^86 + 48 * q^87 - 40 * q^88 - 48 * q^89 + 24 * q^90 + 12 * q^94 + 28 * q^96 + 32 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

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