LMFDB - Embedded newform 1274.2.f.z.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1274,2,Mod(79,1274)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1274, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1274.79"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,-2,-4,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1729412175$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.21913473024.16
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 11x^{6} - 2x^{5} + 51x^{4} + 162x^{2} + 112x + 196 $ x^8 - 2x^7 + 11x^6 - 2x^5 + 51x^4 + 162x^2 + 112x + 196
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			79.1
Root			$1.43998 + 2.49412i$ of defining polynomial
Character	$\chi$	$=$	1274.79
Dual form			1274.2.f.z.1145.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.43998 - 2.49412i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.03644 - 3.52722i) q^{5} -2.87996 q^{6} -1.00000 q^{8} +(-2.64709 + 4.58489i) q^{9} +(-2.03644 - 3.52722i) q^{10} +(0.889353 + 1.54040i) q^{11} +(-1.43998 + 2.49412i) q^{12} +1.00000 q^{13} -11.7297 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.74355 - 3.01991i) q^{17} +(2.64709 + 4.58489i) q^{18} +(-3.70711 + 6.42090i) q^{19} -4.07288 q^{20} +1.77871 q^{22} +(-1.52486 + 2.64114i) q^{23} +(1.43998 + 2.49412i) q^{24} +(-5.79417 - 10.0358i) q^{25} +(0.500000 - 0.866025i) q^{26} +6.60713 q^{27} -9.72973 q^{29} +(-5.86487 + 10.1582i) q^{30} +(-1.88935 - 3.27245i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.56130 - 4.43630i) q^{33} -3.48709 q^{34} +5.29417 q^{36} +(-0.147087 + 0.254762i) q^{37} +(3.70711 + 6.42090i) q^{38} +(-1.43998 - 2.49412i) q^{39} +(-2.03644 + 3.52722i) q^{40} +4.56700 q^{41} +7.00437 q^{43} +(0.889353 - 1.54040i) q^{44} +(10.7813 + 18.6737i) q^{45} +(1.52486 + 2.64114i) q^{46} +(1.57639 - 2.73040i) q^{47} +2.87996 q^{48} -11.5883 q^{50} +(-5.02135 + 8.69723i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-6.69511 - 11.5963i) q^{53} +(3.30357 - 5.72194i) q^{54} +7.24445 q^{55} +21.3526 q^{57} +(-4.86487 + 8.42620i) q^{58} +(-6.22258 - 10.7778i) q^{59} +(5.86487 + 10.1582i) q^{60} +(-1.48842 + 2.57802i) q^{61} -3.77871 q^{62} +1.00000 q^{64} +(2.03644 - 3.52722i) q^{65} +(-2.56130 - 4.43630i) q^{66} +(4.99061 + 8.64399i) q^{67} +(-1.74355 + 3.01991i) q^{68} +8.78308 q^{69} +1.38146 q^{71} +(2.64709 - 4.58489i) q^{72} +(-2.54493 - 4.40794i) q^{73} +(0.147087 + 0.254762i) q^{74} +(-16.6870 + 28.9027i) q^{75} +7.41421 q^{76} -2.87996 q^{78} +(3.64927 - 6.32073i) q^{79} +(2.03644 + 3.52722i) q^{80} +(-1.57288 - 2.72431i) q^{81} +(2.28350 - 3.95514i) q^{82} +12.6285 q^{83} -14.2025 q^{85} +(3.50219 - 6.06597i) q^{86} +(14.0106 + 24.2671i) q^{87} +(-0.889353 - 1.54040i) q^{88} +(5.43059 - 9.40606i) q^{89} +21.5625 q^{90} +3.04972 q^{92} +(-5.44126 + 9.42454i) q^{93} +(-1.57639 - 2.73040i) q^{94} +(15.0986 + 26.1515i) q^{95} +(1.43998 - 2.49412i) q^{96} -3.68182 q^{97} -9.41678 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 4 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{11} - 2 q^{12} + 8 q^{13} - 16 q^{15} - 4 q^{16} + 8 q^{17} + 6 q^{18} - 24 q^{19} + 12 q^{22} - 2 q^{23} + 2 q^{24} - 16 q^{25} + 4 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 4 * q^6 - 8 * q^8 - 6 * q^9 + 6 * q^11 - 2 * q^12 + 8 * q^13 - 16 * q^15 - 4 * q^16 + 8 * q^17 + 6 * q^18 - 24 * q^19 + 12 * q^22 - 2 * q^23 + 2 * q^24 - 16 * q^25 + 4 * q^26 + 28 * q^27 - 8 * q^30 - 14 * q^31 + 4 * q^32 - 6 * q^33 + 16 * q^34 + 12 * q^36 + 14 * q^37 + 24 * q^38 - 2 * q^39 + 12 * q^41 + 8 * q^43 + 6 * q^44 + 12 * q^45 + 2 * q^46 + 6 * q^47 + 4 * q^48 - 32 * q^50 - 4 * q^51 - 4 * q^52 - 16 * q^53 + 14 * q^54 + 48 * q^55 + 24 * q^57 - 16 * q^59 + 8 * q^60 - 18 * q^61 - 28 * q^62 + 8 * q^64 + 6 * q^66 + 22 * q^67 + 8 * q^68 + 20 * q^69 + 32 * q^71 + 6 * q^72 - 10 * q^73 - 14 * q^74 - 42 * q^75 + 48 * q^76 - 4 * q^78 - 10 * q^79 + 20 * q^81 + 6 * q^82 + 40 * q^83 - 80 * q^85 + 4 * q^86 + 8 * q^87 - 6 * q^88 + 16 * q^89 + 24 * q^90 + 4 * q^92 + 2 * q^93 - 6 * q^94 + 4 * q^95 + 2 * q^96 + 4 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	−1.43998	−	2.49412i	−0.831373	−	1.43998i	−0.896950	−	0.442133i	$-0.854222\pi$
$3$	−1.43998	−	2.49412i	−0.831373	−	1.43998i	0.0655765	−	0.997848i	$-0.479111\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.03644	−	3.52722i	0.910724	−	1.57742i	0.0976791	−	0.995218i	$-0.468858\pi$
$5$	2.03644	−	3.52722i	0.910724	−	1.57742i	0.813044	−	0.582202i	$-0.197809\pi$
$6$	−2.87996			−1.17574
$7$		0			0
$7$		0			0
$8$	−1.00000			−0.353553
$9$	−2.64709	+	4.58489i	−0.882362	+	1.52830i
$10$	−2.03644	−	3.52722i	−0.643979	−	1.11540i
$11$	0.889353	+	1.54040i	0.268150	+	0.464449i	0.968384	−	0.249464i	$-0.0802544\pi$
$11$	0.889353	+	1.54040i	0.268150	+	0.464449i	−0.700234	+	0.713913i	$0.746921\pi$
$12$	−1.43998	+	2.49412i	−0.415687	+	0.719990i
$13$	1.00000			0.277350
$13$	1.00000			0.277350
$14$		0			0
$15$	−11.7297			−3.02860
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.74355	−	3.01991i	−0.422872	−	0.732436i	0.573347	−	0.819313i	$-0.305645\pi$
$17$	−1.74355	−	3.01991i	−0.422872	−	0.732436i	−0.996219	+	0.0868766i	$0.972311\pi$
$18$	2.64709	+	4.58489i	0.623924	+	1.08067i
$19$	−3.70711	+	6.42090i	−0.850469	+	1.47305i	0.0303174	+	0.999540i	$0.490348\pi$
$19$	−3.70711	+	6.42090i	−0.850469	+	1.47305i	−0.880786	+	0.473515i	$0.842985\pi$
$20$	−4.07288			−0.910724
$21$		0			0
$22$	1.77871			0.379221
$23$	−1.52486	+	2.64114i	−0.317955	+	0.550715i	−0.980061	−	0.198695i	$-0.936330\pi$
$23$	−1.52486	+	2.64114i	−0.317955	+	0.550715i	0.662106	+	0.749410i	$0.269663\pi$
$24$	1.43998	+	2.49412i	0.293935	+	0.509110i
$25$	−5.79417	−	10.0358i	−1.15883	−	2.00716i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	6.60713			1.27154
$28$		0			0
$29$	−9.72973			−1.80677			−0.903383	−	0.428834i	$-0.858924\pi$
$29$	−9.72973			−1.80677			−0.903383	+	0.428834i	$0.858924\pi$
$30$	−5.86487	+	10.1582i	−1.07077	+	1.85463i
$31$	−1.88935	−	3.27245i	−0.339338	−	0.587750i	0.644971	−	0.764207i	$-0.276870\pi$
$31$	−1.88935	−	3.27245i	−0.339338	−	0.587750i	−0.984308	+	0.176457i	$0.943536\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	2.56130	−	4.43630i	0.445865	−	0.772261i
$34$	−3.48709			−0.598032
$35$		0			0
$36$	5.29417			0.882362
$37$	−0.147087	+	0.254762i	−0.0241810	+	0.0418827i	−0.877863	−	0.478912i	$-0.841031\pi$
$37$	−0.147087	+	0.254762i	−0.0241810	+	0.0418827i	0.853682	+	0.520795i	$0.174364\pi$
$38$	3.70711	+	6.42090i	0.601372	+	1.04161i
$39$	−1.43998	−	2.49412i	−0.230581	−	0.399379i
$40$	−2.03644	+	3.52722i	−0.321989	+	0.557702i
$41$	4.56700			0.713246			0.356623	−	0.934248i	$-0.383928\pi$
$41$	4.56700			0.713246			0.356623	+	0.934248i	$0.383928\pi$
$42$		0			0
$43$	7.00437			1.06816			0.534079	−	0.845435i	$-0.320659\pi$
$43$	7.00437			1.06816			0.534079	+	0.845435i	$0.320659\pi$
$44$	0.889353	−	1.54040i	0.134075	−	0.232225i
$45$	10.7813	+	18.6737i	1.60718	+	2.78371i
$46$	1.52486	+	2.64114i	0.224828	+	0.389414i
$47$	1.57639	−	2.73040i	0.229941	−	0.398269i	−0.727850	−	0.685737i	$-0.759480\pi$
$47$	1.57639	−	2.73040i	0.229941	−	0.398269i	0.957790	+	0.287468i	$0.0928134\pi$
$48$	2.87996			0.415687
$49$		0			0
$50$	−11.5883			−1.63884
$51$	−5.02135	+	8.69723i	−0.703129	+	1.21786i
$52$	−0.500000	−	0.866025i	−0.0693375	−	0.120096i
$53$	−6.69511	−	11.5963i	−0.919644	−	1.59287i	−0.799957	−	0.600058i	$-0.795144\pi$
$53$	−6.69511	−	11.5963i	−0.919644	−	1.59287i	−0.119687	−	0.992812i	$-0.538189\pi$
$54$	3.30357	−	5.72194i	0.449558	−	0.778658i
$55$	7.24445			0.976842
$56$		0			0
$57$	21.3526			2.82823
$58$	−4.86487	+	8.42620i	−0.638788	+	1.10641i
$59$	−6.22258	−	10.7778i	−0.810110	−	1.40315i	−0.912786	−	0.408437i	$-0.866074\pi$
$59$	−6.22258	−	10.7778i	−0.810110	−	1.40315i	0.102676	−	0.994715i	$-0.467260\pi$
$60$	5.86487	+	10.1582i	0.757151	+	1.31142i
$61$	−1.48842	+	2.57802i	−0.190573	+	0.330082i	−0.945440	−	0.325796i	$-0.894368\pi$
$61$	−1.48842	+	2.57802i	−0.190573	+	0.330082i	0.754867	+	0.655877i	$0.227701\pi$
$62$	−3.77871			−0.479896
$63$		0			0
$64$	1.00000			0.125000
$65$	2.03644	−	3.52722i	0.252589	−	0.437497i
$66$	−2.56130	−	4.43630i	−0.315274	−	0.546071i
$67$	4.99061	+	8.64399i	0.609700	+	1.05603i	0.991290	+	0.131699i	$0.0420433\pi$
$67$	4.99061	+	8.64399i	0.609700	+	1.05603i	−0.381590	+	0.924332i	$0.624623\pi$
$68$	−1.74355	+	3.01991i	−0.211436	+	0.366218i
$69$	8.78308			1.05736
$70$		0			0
$71$	1.38146			0.163950			0.0819748	−	0.996634i	$-0.473877\pi$
$71$	1.38146			0.163950			0.0819748	+	0.996634i	$0.473877\pi$
$72$	2.64709	−	4.58489i	0.311962	−	0.540334i
$73$	−2.54493	−	4.40794i	−0.297861	−	0.515910i	0.677785	−	0.735260i	$-0.262940\pi$
$73$	−2.54493	−	4.40794i	−0.297861	−	0.515910i	−0.975646	+	0.219349i	$0.929607\pi$
$74$	0.147087	+	0.254762i	0.0170985	+	0.0296155i
$75$	−16.6870	+	28.9027i	−1.92685	+	3.33740i
$76$	7.41421			0.850469
$77$		0			0
$78$	−2.87996			−0.326091
$79$	3.64927	−	6.32073i	0.410575	−	0.711138i	−0.584377	−	0.811482i	$-0.698661\pi$
$79$	3.64927	−	6.32073i	0.410575	−	0.711138i	0.994953	+	0.100345i	$0.0319945\pi$
$80$	2.03644	+	3.52722i	0.227681	+	0.394355i
$81$	−1.57288	−	2.72431i	−0.174764	−	0.302701i
$82$	2.28350	−	3.95514i	0.252171	−	0.436772i
$83$	12.6285			1.38616			0.693078	−	0.720863i	$-0.256254\pi$
$83$	12.6285			1.38616			0.693078	+	0.720863i	$0.256254\pi$
$84$		0			0
$85$	−14.2025			−1.54048
$86$	3.50219	−	6.06597i	0.377651	−	0.654110i
$87$	14.0106	+	24.2671i	1.50210	+	2.60171i
$88$	−0.889353	−	1.54040i	−0.0948053	−	0.164208i
$89$	5.43059	−	9.40606i	0.575641	−	0.997040i	−0.420330	−	0.907371i	$-0.638086\pi$
$89$	5.43059	−	9.40606i	0.575641	−	0.997040i	0.995972	−	0.0896688i	$-0.0285808\pi$
$90$	21.5625			2.27289
$91$		0			0
$92$	3.04972			0.317955
$93$	−5.44126	+	9.42454i	−0.564233	+	0.977279i
$94$	−1.57639	−	2.73040i	−0.162593	−	0.281619i
$95$	15.0986	+	26.1515i	1.54908	+	2.68309i
$96$	1.43998	−	2.49412i	0.146967	−	0.254555i
$97$	−3.68182			−0.373833			−0.186916	−	0.982376i	$-0.559849\pi$
$97$	−3.68182			−0.373833			−0.186916	+	0.982376i	$0.559849\pi$
$98$		0			0
$99$	−9.41678			−0.946422
$100$	−5.79417	+	10.0358i	−0.579417	+	1.00358i
$101$	−8.05021	−	13.9434i	−0.801025	−	1.38742i	−0.918942	−	0.394393i	$-0.870955\pi$
$101$	−8.05021	−	13.9434i	−0.801025	−	1.38742i	0.117916	−	0.993024i	$-0.462379\pi$
$102$	5.02135	+	8.69723i	0.497187	+	0.861154i
$103$	0.776893	−	1.34562i	0.0765496	−	0.132588i	−0.825209	−	0.564827i	$-0.808943\pi$
$103$	0.776893	−	1.34562i	0.0765496	−	0.132588i	0.901759	+	0.432239i	$0.142276\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−13.3902			−1.30057
$107$	6.13770	−	10.6308i	0.593353	−	1.02772i	−0.400424	−	0.916330i	$-0.631137\pi$
$107$	6.13770	−	10.6308i	0.593353	−	1.02772i	0.993777	−	0.111388i	$-0.0355297\pi$
$108$	−3.30357	−	5.72194i	−0.317886	−	0.550594i
$109$	−0.362680	−	0.628180i	−0.0347384	−	0.0601687i	0.848133	−	0.529783i	$-0.177726\pi$
$109$	−0.362680	−	0.628180i	−0.0347384	−	0.0601687i	−0.882872	+	0.469614i	$0.844393\pi$
$110$	3.62223	−	6.27388i	0.345366	−	0.598191i
$111$	0.847211			0.0804137
$112$		0			0
$113$	−0.783079			−0.0736659			−0.0368330	−	0.999321i	$-0.511727\pi$
$113$	−0.783079			−0.0736659			−0.0368330	+	0.999321i	$0.511727\pi$
$114$	10.6763	−	18.4919i	0.999929	−	1.73193i
$115$	6.21058	+	10.7570i	0.579139	+	1.00310i
$116$	4.86487	+	8.42620i	0.451692	+	0.782353i
$117$	−2.64709	+	4.58489i	−0.244723	+	0.423873i
$118$	−12.4452			−1.14567
$119$		0			0
$120$	11.7297			1.07077
$121$	3.91810	−	6.78635i	0.356191	−	0.616941i
$122$	1.48842	+	2.57802i	0.134755	+	0.233403i
$123$	−6.57639	−	11.3906i	−0.592974	−	1.02706i
$124$	−1.88935	+	3.27245i	−0.169669	+	0.293875i
$125$	−26.8336			−2.40007
$126$		0			0
$127$	1.39287			0.123597			0.0617985	−	0.998089i	$-0.480316\pi$
$127$	1.39287			0.123597			0.0617985	+	0.998089i	$0.480316\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−10.0862	−	17.4697i	−0.888037	−	1.53813i
$130$	−2.03644	−	3.52722i	−0.178608	−	0.309357i
$131$	3.57197	−	6.18684i	0.312085	−	0.540547i	−0.666729	−	0.745300i	$-0.732306\pi$
$131$	3.57197	−	6.18684i	0.312085	−	0.540547i	0.978814	+	0.204754i	$0.0656394\pi$
$132$	−5.12260			−0.445865
$133$		0			0
$134$	9.98122			0.862246
$135$	13.4550	−	23.3048i	1.15802	−	2.00576i
$136$	1.74355	+	3.01991i	0.149508	+	0.258955i
$137$	3.46575	+	6.00285i	0.296099	+	0.512858i	0.975240	−	0.221150i	$-0.0709809\pi$
$137$	3.46575	+	6.00285i	0.296099	+	0.512858i	−0.679141	+	0.734008i	$0.737648\pi$
$138$	4.39154	−	7.60637i	0.373833	−	0.647497i
$139$	−11.3928			−0.966322			−0.483161	−	0.875531i	$-0.660512\pi$
$139$	−11.3928			−0.966322			−0.483161	+	0.875531i	$0.660512\pi$
$140$		0			0
$141$	−9.07991			−0.764666
$142$	0.690732	−	1.19638i	0.0579649	−	0.100398i
$143$	0.889353	+	1.54040i	0.0743714	+	0.128815i
$144$	−2.64709	−	4.58489i	−0.220591	−	0.382074i
$145$	−19.8140	+	34.3189i	−1.64546	+	2.85003i
$146$	−5.08985			−0.421239
$147$		0			0
$148$	0.294174			0.0241810
$149$	−5.66437	+	9.81097i	−0.464043	+	0.803746i	−0.999158	−	0.0410332i	$-0.986935\pi$
$149$	−5.66437	+	9.81097i	−0.464043	+	0.803746i	0.535115	+	0.844779i	$0.320268\pi$
$150$	16.6870	+	28.9027i	1.36249	+	2.35990i
$151$	8.41859	+	14.5814i	0.685095	+	1.18662i	0.973407	+	0.229083i	$0.0735726\pi$
$151$	8.41859	+	14.5814i	0.685095	+	1.18662i	−0.288312	+	0.957537i	$0.593094\pi$
$152$	3.70711	−	6.42090i	0.300686	−	0.520804i
$153$	18.4613			1.49251
$154$		0			0
$155$	−15.3902			−1.23617
$156$	−1.43998	+	2.49412i	−0.115291	+	0.199689i
$157$	−8.21997	−	14.2374i	−0.656025	−	1.13627i	−0.981636	−	0.190764i	$-0.938903\pi$
$157$	−8.21997	−	14.2374i	−0.656025	−	1.13627i	0.325611	−	0.945504i	$-0.394430\pi$
$158$	−3.64927	−	6.32073i	−0.290321	−	0.502850i
$159$	−19.2816	+	33.3968i	−1.52913	+	2.64854i
$160$	4.07288			0.321989
$161$		0			0
$162$	−3.14576			−0.247154
$163$	−0.101256	+	0.175380i	−0.00793095	+	0.0137368i	−0.869964	−	0.493116i	$-0.835858\pi$
$163$	−0.101256	+	0.175380i	−0.00793095	+	0.0137368i	0.862033	+	0.506853i	$0.169191\pi$
$164$	−2.28350	−	3.95514i	−0.178312	−	0.308845i
$165$	−10.4319	−	18.0685i	−0.812120	−	1.40663i
$166$	6.31424	−	10.9366i	0.490080	−	0.848843i
$167$	−21.4631			−1.66086			−0.830432	−	0.557120i	$-0.811906\pi$
$167$	−21.4631			−1.66086			−0.830432	+	0.557120i	$0.811906\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$	−7.10126	+	12.2997i	−0.544641	+	0.943347i
$171$	−19.6261	−	33.9934i	−1.50084	−	2.59954i
$172$	−3.50219	−	6.06597i	−0.267039	−	0.462526i
$173$	3.39724	−	5.88420i	0.258288	−	0.447367i	−0.707496	−	0.706718i	$-0.750175\pi$
$173$	3.39724	−	5.88420i	0.258288	−	0.447367i	0.965783	+	0.259350i	$0.0835085\pi$
$174$	28.0213			2.12429
$175$		0			0
$176$	−1.77871			−0.134075
$177$	−17.9208	+	31.0397i	−1.34701	+	2.33309i
$178$	−5.43059	−	9.40606i	−0.407040	−	0.705014i
$179$	−4.16454	−	7.21320i	−0.311273	−	0.539140i	0.667366	−	0.744730i	$-0.267422\pi$
$179$	−4.16454	−	7.21320i	−0.311273	−	0.539140i	−0.978638	+	0.205590i	$0.934089\pi$
$180$	10.7813	−	18.6737i	0.803588	−	1.39186i
$181$	20.0505			1.49034			0.745170	−	0.666875i	$-0.232368\pi$
$181$	20.0505			1.49034			0.745170	+	0.666875i	$0.232368\pi$
$182$		0			0
$183$	8.57319			0.633748
$184$	1.52486	−	2.64114i	0.112414	−	0.194707i
$185$	0.599068	+	1.03762i	0.0440444	+	0.0762871i
$186$	5.44126	+	9.42454i	0.398973	+	0.691041i
$187$	3.10126	−	5.37153i	0.226786	−	0.392805i
$188$	−3.15279			−0.229941
$189$		0			0
$190$	30.1972			2.19074
$191$	4.24264	−	7.34847i	0.306987	−	0.531717i	−0.670715	−	0.741715i	$-0.734013\pi$
$191$	4.24264	−	7.34847i	0.306987	−	0.531717i	0.977702	+	0.209999i	$0.0673460\pi$
$192$	−1.43998	−	2.49412i	−0.103922	−	0.179998i
$193$	3.55741	+	6.16162i	0.256068	+	0.443523i	0.965185	−	0.261568i	$-0.0842396\pi$
$193$	3.55741	+	6.16162i	0.256068	+	0.443523i	−0.709117	+	0.705091i	$0.750906\pi$
$194$	−1.84091	+	3.18855i	−0.132170	+	0.228925i
$195$	−11.7297			−0.839984
$196$		0			0
$197$	15.5048			1.10467			0.552336	−	0.833621i	$-0.313736\pi$
$197$	15.5048			1.10467			0.552336	+	0.833621i	$0.313736\pi$
$198$	−4.70839	+	8.15517i	−0.334611	+	0.579562i
$199$	1.47903	+	2.56175i	0.104846	+	0.181598i	0.913675	−	0.406445i	$-0.133232\pi$
$199$	1.47903	+	2.56175i	0.104846	+	0.181598i	−0.808830	+	0.588043i	$0.799898\pi$
$200$	5.79417	+	10.0358i	0.409710	+	0.709639i
$201$	14.3728	−	24.8943i	1.01378	−	1.75591i
$202$	−16.1004			−1.13282
$203$		0			0
$204$	10.0427			0.703129
$205$	9.30043	−	16.1088i	0.649570	−	1.12509i
$206$	−0.776893	−	1.34562i	−0.0541287	−	0.0937537i
$207$	−8.07288	−	13.9826i	−0.561104	−	0.971861i
$208$	−0.500000	+	0.866025i	−0.0346688	+	0.0600481i
$209$	−13.1877			−0.912212
$210$		0			0
$211$	−4.66485			−0.321142			−0.160571	−	0.987024i	$-0.551334\pi$
$211$	−4.66485			−0.321142			−0.160571	+	0.987024i	$0.551334\pi$
$212$	−6.69511	+	11.5963i	−0.459822	+	0.796435i
$213$	−1.98928	−	3.44553i	−0.136303	−	0.236084i
$214$	−6.13770	−	10.6308i	−0.419564	−	0.726707i
$215$	14.2640	−	24.7059i	0.972796	−	1.68493i
$216$	−6.60713			−0.449558
$217$		0			0
$218$	−0.725360			−0.0491276
$219$	−7.32929	+	12.6947i	−0.495267	+	0.857828i
$220$	−3.62223	−	6.27388i	−0.244210	−	0.422985i
$221$	−1.74355	−	3.01991i	−0.117284	−	0.203141i
$222$	0.423605	−	0.733706i	0.0284305	−	0.0492431i
$223$	5.74476			0.384698			0.192349	−	0.981327i	$-0.438389\pi$
$223$	5.74476			0.384698			0.192349	+	0.981327i	$0.438389\pi$
$224$		0			0
$225$	61.3507			4.09005
$226$	−0.391540	+	0.678167i	−0.0260448	+	0.0451110i
$227$	−2.55244	−	4.42096i	−0.169411	−	0.293429i	0.768802	−	0.639487i	$-0.220853\pi$
$227$	−2.55244	−	4.42096i	−0.169411	−	0.293429i	−0.938213	+	0.346058i	$0.887520\pi$
$228$	−10.6763	−	18.4919i	−0.707057	−	1.22466i
$229$	1.13770	−	1.97055i	0.0751810	−	0.130217i	−0.825984	−	0.563694i	$-0.809380\pi$
$229$	1.13770	−	1.97055i	0.0751810	−	0.130217i	0.901165	+	0.433476i	$0.142713\pi$
$230$	12.4212			0.819026
$231$		0			0
$232$	9.72973			0.638788
$233$	7.33819	−	12.7101i	0.480741	−	0.832668i	−0.519015	−	0.854765i	$-0.673701\pi$
$233$	7.33819	−	12.7101i	0.480741	−	0.832668i	0.999756	+	0.0220973i	$0.00703436\pi$
$234$	2.64709	+	4.58489i	0.173046	+	0.299724i
$235$	−6.42047	−	11.1206i	−0.418825	−	0.725426i
$236$	−6.22258	+	10.7778i	−0.405055	+	0.701576i
$237$	−21.0195			−1.36537
$238$		0			0
$239$	5.27976			0.341520			0.170760	−	0.985313i	$-0.445378\pi$
$239$	5.27976			0.341520			0.170760	+	0.985313i	$0.445378\pi$
$240$	5.86487	−	10.1582i	0.378576	−	0.655712i
$241$	−9.81643	−	17.0025i	−0.632332	−	1.09523i	−0.987074	−	0.160266i	$-0.948765\pi$
$241$	−9.81643	−	17.0025i	−0.632332	−	1.09523i	0.354742	−	0.934964i	$-0.384569\pi$
$242$	−3.91810	−	6.78635i	−0.251865	−	0.436243i
$243$	5.38087	−	9.31993i	0.345183	−	0.597874i
$244$	2.97684			0.190573
$245$		0			0
$246$	−13.1528			−0.838591
$247$	−3.70711	+	6.42090i	−0.235878	+	0.408552i
$248$	1.88935	+	3.27245i	0.119974	+	0.207801i
$249$	−18.1848	−	31.4969i	−1.15241	−	1.99604i
$250$	−13.4168	+	23.2385i	−0.848551	+	1.46973i
$251$	−2.77689			−0.175276			−0.0876380	−	0.996152i	$-0.527932\pi$
$251$	−2.77689			−0.175276			−0.0876380	+	0.996152i	$0.527932\pi$
$252$		0			0
$253$	−5.42456			−0.341039
$254$	0.696434	−	1.20626i	0.0436981	−	0.0756874i
$255$	20.4513	+	35.4228i	1.28071	+	2.21826i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.59779	−	6.23155i	0.224424	−	0.388713i	−0.731723	−	0.681603i	$-0.761283\pi$
$257$	3.59779	−	6.23155i	0.224424	−	0.388713i	0.956146	+	0.292889i	$0.0946167\pi$
$258$	−20.1723			−1.25587
$259$		0			0
$260$	−4.07288			−0.252589
$261$	25.7555	−	44.6098i	1.59422	−	2.76127i
$262$	−3.57197	−	6.18684i	−0.220677	−	0.382224i
$263$	3.34133	+	5.78736i	0.206035	+	0.356864i	0.950462	−	0.310840i	$-0.100610\pi$
$263$	3.34133	+	5.78736i	0.206035	+	0.356864i	−0.744427	+	0.667704i	$0.767277\pi$
$264$	−2.56130	+	4.43630i	−0.157637	+	0.273036i
$265$	−54.5367			−3.35016
$266$		0			0
$267$	−31.2798			−1.91429
$268$	4.99061	−	8.64399i	0.304850	−	0.528016i
$269$	4.05542	+	7.02420i	0.247264	+	0.428273i	0.962766	−	0.270338i	$-0.0871353\pi$
$269$	4.05542	+	7.02420i	0.247264	+	0.428273i	−0.715502	+	0.698611i	$0.753802\pi$
$270$	−13.4550	−	23.3048i	−0.818847	−	1.41828i
$271$	0.529235	−	0.916662i	0.0321487	−	0.0556833i	−0.849503	−	0.527583i	$-0.823098\pi$
$271$	0.529235	−	0.916662i	0.0321487	−	0.0556833i	0.881652	+	0.471900i	$0.156432\pi$
$272$	3.48709			0.211436
$273$		0			0
$274$	6.93149			0.418747
$275$	10.3061	−	17.8507i	0.621483	−	1.07644i
$276$	−4.39154	−	7.60637i	−0.264340	−	0.457850i
$277$	12.3066	+	21.3157i	0.739433	+	1.28073i	0.952751	+	0.303752i	$0.0982395\pi$
$277$	12.3066	+	21.3157i	0.739433	+	1.28073i	−0.213318	+	0.976983i	$0.568427\pi$
$278$	−5.69639	+	9.86643i	−0.341647	+	0.591749i
$279$	20.0051			1.19768
$280$		0			0
$281$	5.13776			0.306493			0.153247	−	0.988188i	$-0.451027\pi$
$281$	5.13776			0.306493			0.153247	+	0.988188i	$0.451027\pi$
$282$	−4.53995	+	7.86343i	−0.270350	+	0.468261i
$283$	−0.814064	−	1.41000i	−0.0483911	−	0.0838159i	0.840815	−	0.541322i	$-0.182076\pi$
$283$	−0.814064	−	1.41000i	−0.0483911	−	0.0838159i	−0.889206	+	0.457506i	$0.848743\pi$
$284$	−0.690732	−	1.19638i	−0.0409874	−	0.0709922i
$285$	43.4834	−	75.3154i	2.57573	−	4.46130i
$286$	1.77871			0.105177
$287$		0			0
$288$	−5.29417			−0.311962
$289$	2.42009	−	4.19172i	0.142358	−	0.246572i
$290$	19.8140	+	34.3189i	1.16352	+	2.01527i
$291$	5.30175	+	9.18291i	0.310794	+	0.538312i
$292$	−2.54493	+	4.40794i	−0.148931	+	0.257955i
$293$	14.1509			0.826703			0.413352	−	0.910571i	$-0.364358\pi$
$293$	14.1509			0.826703			0.413352	+	0.910571i	$0.364358\pi$
$294$		0			0
$295$	−50.6876			−2.95115
$296$	0.147087	−	0.254762i	0.00854927	−	0.0148078i
$297$	5.87607	+	10.1777i	0.340964	+	0.590567i
$298$	5.66437	+	9.81097i	0.328128	+	0.568334i
$299$	−1.52486	+	2.64114i	−0.0881850	+	0.152741i
$300$	33.3740			1.92685
$301$		0			0
$302$	16.8372			0.968871
$303$	−23.1843	+	40.1563i	−1.33190	+	2.30692i
$304$	−3.70711	−	6.42090i	−0.212617	−	0.368264i
$305$	6.06216	+	10.5000i	0.347118	+	0.601226i
$306$	9.23064	−	15.9879i	0.527681	−	0.913970i
$307$	16.4347			0.937979			0.468989	−	0.883204i	$-0.344618\pi$
$307$	16.4347			0.937979			0.468989	+	0.883204i	$0.344618\pi$
$308$		0			0
$309$	−4.47485			−0.254565
$310$	−7.69511	+	13.3283i	−0.437053	+	0.756997i
$311$	6.25955	+	10.8419i	0.354946	+	0.614785i	0.987109	−	0.160051i	$-0.0511658\pi$
$311$	6.25955	+	10.8419i	0.354946	+	0.614785i	−0.632162	+	0.774836i	$0.717832\pi$
$312$	1.43998	+	2.49412i	0.0815228	+	0.141202i
$313$	−7.96740	+	13.7999i	−0.450344	+	0.780019i	−0.998407	−	0.0564179i	$-0.982032\pi$
$313$	−7.96740	+	13.7999i	−0.450344	+	0.780019i	0.548063	+	0.836437i	$0.315365\pi$
$314$	−16.4399			−0.927759
$315$		0			0
$316$	−7.29855			−0.410575
$317$	6.93538	−	12.0124i	0.389530	−	0.674686i	−0.602856	−	0.797850i	$-0.705971\pi$
$317$	6.93538	−	12.0124i	0.389530	−	0.674686i	0.992386	+	0.123164i	$0.0393041\pi$
$318$	19.2816	+	33.3968i	1.08126	+	1.87280i
$319$	−8.65316	−	14.9877i	−0.484484	−	0.839151i
$320$	2.03644	−	3.52722i	0.113840	−	0.197177i
$321$	−35.3526			−1.97319
$322$		0			0
$323$	25.8541			1.43856
$324$	−1.57288	+	2.72431i	−0.0873822	+	0.151350i
$325$	−5.79417	−	10.0358i	−0.321403	−	0.556686i
$326$	0.101256	+	0.175380i	0.00560803	+	0.00971339i
$327$	−1.04450	+	1.80913i	−0.0577612	+	0.100045i
$328$	−4.56700			−0.252171
$329$		0			0
$330$	−20.8637			−1.14851
$331$	0.115022	−	0.199223i	0.00632216	−	0.0109503i	−0.862847	−	0.505465i	$-0.831321\pi$
$331$	0.115022	−	0.199223i	0.00632216	−	0.0109503i	0.869169	+	0.494515i	$0.164654\pi$
$332$	−6.31424	−	10.9366i	−0.346539	−	0.600223i
$333$	−0.778705	−	1.34876i	−0.0426728	−	0.0739114i
$334$	−10.7315	+	18.5876i	−0.587204	+	1.01707i
$335$	40.6523			2.22107
$336$		0			0
$337$	−7.05710			−0.384425			−0.192212	−	0.981353i	$-0.561566\pi$
$337$	−7.05710			−0.384425			−0.192212	+	0.981353i	$0.561566\pi$
$338$	0.500000	−	0.866025i	0.0271964	−	0.0471056i
$339$	1.12762	+	1.95309i	0.0612439	+	0.106077i
$340$	7.10126	+	12.2997i	0.385120	+	0.667047i
$341$	3.36060	−	5.82073i	0.181987	−	0.315210i
$342$	−39.2521			−2.12251
$343$		0			0
$344$	−7.00437			−0.377651
$345$	17.8862	−	30.9798i	0.962961	−	1.66790i
$346$	−3.39724	−	5.88420i	−0.182637	−	0.316336i
$347$	−13.2702	−	22.9846i	−0.712380	−	1.23388i	−0.963961	−	0.266042i	$-0.914284\pi$
$347$	−13.2702	−	22.9846i	−0.712380	−	1.23388i	0.251581	−	0.967836i	$-0.419049\pi$
$348$	14.0106	−	24.2671i	0.751048	−	1.30085i
$349$	8.59573			0.460119			0.230059	−	0.973177i	$-0.426108\pi$
$349$	8.59573			0.460119			0.230059	+	0.973177i	$0.426108\pi$
$350$		0			0
$351$	6.60713			0.352663
$352$	−0.889353	+	1.54040i	−0.0474027	+	0.0821038i
$353$	14.3450	+	24.8462i	0.763506	+	1.32243i	0.941033	+	0.338315i	$0.109857\pi$
$353$	14.3450	+	24.8462i	0.763506	+	1.32243i	−0.177527	+	0.984116i	$0.556810\pi$
$354$	17.9208	+	31.0397i	0.952478	+	1.64974i
$355$	2.81327	−	4.87272i	0.149313	−	0.258617i
$356$	−10.8612			−0.575641
$357$		0			0
$358$	−8.32909			−0.440206
$359$	−12.7662	+	22.1117i	−0.673773	+	1.16701i	0.303053	+	0.952974i	$0.401994\pi$
$359$	−12.7662	+	22.1117i	−0.673773	+	1.16701i	−0.976826	+	0.214035i	$0.931339\pi$
$360$	−10.7813	−	18.6737i	−0.568223	−	0.984191i
$361$	−17.9853	−	31.1514i	−0.946594	−	1.63955i
$362$	10.0252	−	17.3642i	0.526915	−	0.912643i
$363$	−22.5680			−1.18451
$364$		0			0
$365$	−20.7304			−1.08508
$366$	4.28659	−	7.42460i	0.224064	−	0.388090i
$367$	16.3563	+	28.3300i	0.853794	+	1.47881i	0.877760	+	0.479101i	$0.159037\pi$
$367$	16.3563	+	28.3300i	0.853794	+	1.47881i	−0.0239659	+	0.999713i	$0.507629\pi$
$368$	−1.52486	−	2.64114i	−0.0794889	−	0.137679i
$369$	−12.0893	+	20.9392i	−0.629341	+	1.09005i
$370$	1.19814			0.0622882
$371$		0			0
$372$	10.8825			0.564233
$373$	−2.07657	+	3.59672i	−0.107521	+	0.186231i	−0.914765	−	0.403986i	$-0.867625\pi$
$373$	−2.07657	+	3.59672i	−0.107521	+	0.186231i	0.807245	+	0.590217i	$0.200958\pi$
$374$	−3.10126	−	5.37153i	−0.160362	−	0.277755i
$375$	38.6398	+	66.9261i	1.99535	+	3.45605i
$376$	−1.57639	+	2.73040i	−0.0812963	+	0.140809i
$377$	−9.72973			−0.501107
$378$		0			0
$379$	−16.4390			−0.844413			−0.422206	−	0.906500i	$-0.638744\pi$
$379$	−16.4390			−0.844413			−0.422206	+	0.906500i	$0.638744\pi$
$380$	15.0986	−	26.1515i	0.774542	−	1.34155i
$381$	−2.00570	−	3.47398i	−0.102755	−	0.177977i
$382$	−4.24264	−	7.34847i	−0.217072	−	0.375980i
$383$	−15.8945	+	27.5300i	−0.812170	+	1.40672i	0.0991725	+	0.995070i	$0.468380\pi$
$383$	−15.8945	+	27.5300i	−0.812170	+	1.40672i	−0.911342	+	0.411649i	$0.864953\pi$
$384$	−2.87996			−0.146967
$385$		0			0
$386$	7.11482			0.362135
$387$	−18.5412	+	32.1143i	−0.942502	+	1.63246i
$388$	1.84091	+	3.18855i	0.0934581	+	0.161874i
$389$	5.95284	+	10.3106i	0.301821	+	0.522769i	0.976548	−	0.215298i	$-0.0690722\pi$
$389$	5.95284	+	10.3106i	0.301821	+	0.522769i	−0.674727	+	0.738067i	$0.735739\pi$
$390$	−5.86487	+	10.1582i	−0.296979	+	0.514383i
$391$	10.6347			0.537818
$392$		0			0
$393$	−20.5743			−1.03784
$394$	7.75241	−	13.4276i	0.390561	−	0.676471i
$395$	−14.8631	−	25.7436i	−0.747841	−	1.29530i
$396$	4.70839	+	8.15517i	0.236605	+	0.409813i
$397$	−12.7146	+	22.0223i	−0.638126	+	1.10527i	0.347717	+	0.937599i	$0.386957\pi$
$397$	−12.7146	+	22.0223i	−0.638126	+	1.10527i	−0.985844	+	0.167668i	$0.946376\pi$
$398$	2.95806			0.148274
$399$		0			0
$400$	11.5883			0.579417
$401$	14.7217	−	25.4987i	0.735165	−	1.27334i	−0.219486	−	0.975616i	$-0.570438\pi$
$401$	14.7217	−	25.4987i	0.735165	−	1.27334i	0.954651	−	0.297728i	$-0.0962287\pi$
$402$	−14.3728	−	24.8943i	−0.716848	−	1.24162i
$403$	−1.88935	−	3.27245i	−0.0941154	−	0.163013i
$404$	−8.05021	+	13.9434i	−0.400513	+	0.693708i
$405$	−12.8123			−0.636648
$406$		0			0
$407$	−0.523250			−0.0259365
$408$	5.02135	−	8.69723i	0.248594	−	0.430577i
$409$	6.66364	+	11.5418i	0.329496	+	0.570703i	0.982412	−	0.186727i	$-0.0597880\pi$
$409$	6.66364	+	11.5418i	0.329496	+	0.570703i	−0.652916	+	0.757430i	$0.726455\pi$
$410$	−9.30043	−	16.1088i	−0.459315	−	0.795557i
$411$	9.98122	−	17.2880i	0.492337	−	0.852753i
$412$	−1.55379			−0.0765496
$413$		0			0
$414$	−16.1458			−0.793521
$415$	25.7171	−	44.5434i	1.26240	−	2.18655i
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	16.4054	+	28.4149i	0.803375	+	1.39149i
$418$	−6.59385	+	11.4209i	−0.322516	+	0.558614i
$419$	−40.1045			−1.95923			−0.979616	−	0.200880i	$-0.935620\pi$
$419$	−40.1045			−1.95923			−0.979616	+	0.200880i	$0.935620\pi$
$420$		0			0
$421$	−14.8486			−0.723675			−0.361838	−	0.932241i	$-0.617851\pi$
$421$	−14.8486			−0.723675			−0.361838	+	0.932241i	$0.617851\pi$
$422$	−2.33243	+	4.03988i	−0.113541	+	0.196658i
$423$	8.34571	+	14.4552i	0.405782	+	0.702835i
$424$	6.69511	+	11.5963i	0.325143	+	0.563164i
$425$	−20.2048	+	34.9958i	−0.980078	+	1.69754i
$426$	−3.97856			−0.192762
$427$		0			0
$428$	−12.2754			−0.593353
$429$	2.56130	−	4.43630i	0.123661	−	0.214187i
$430$	−14.2640	−	24.7059i	−0.687871	−	1.19143i
$431$	4.77689	+	8.27382i	0.230095	+	0.398536i	0.957836	−	0.287316i	$-0.0927630\pi$
$431$	4.77689	+	8.27382i	0.230095	+	0.398536i	−0.727741	+	0.685852i	$0.759430\pi$
$432$	−3.30357	+	5.72194i	−0.158943	+	0.275297i
$433$	−20.4150			−0.981081			−0.490540	−	0.871419i	$-0.663201\pi$
$433$	−20.4150			−0.981081			−0.490540	+	0.871419i	$0.663201\pi$
$434$		0			0
$435$	114.127			5.47198
$436$	−0.362680	+	0.628180i	−0.0173692	+	0.0300844i
$437$	−11.3056	−	19.5820i	−0.540822	−	0.936732i
$438$	7.32929	+	12.6947i	0.350207	+	0.606576i
$439$	0.641760	−	1.11156i	0.0306296	−	0.0530519i	−0.850304	−	0.526291i	$-0.823582\pi$
$439$	0.641760	−	1.11156i	0.0306296	−	0.0530519i	0.880934	+	0.473239i	$0.156915\pi$
$440$	−7.24445			−0.345366
$441$		0			0
$442$	−3.48709			−0.165864
$443$	−7.35196	+	12.7340i	−0.349302	+	0.605009i	−0.986126	−	0.166001i	$-0.946915\pi$
$443$	−7.35196	+	12.7340i	−0.349302	+	0.605009i	0.636823	+	0.771010i	$0.280248\pi$
$444$	−0.423605	−	0.733706i	−0.0201034	−	0.0348201i
$445$	−22.1181	−	38.3097i	−1.04850	−	1.81606i
$446$	2.87238	−	4.97511i	0.136011	−	0.235578i
$447$	32.6263			1.54317
$448$		0			0
$449$	36.3320			1.71461			0.857306	−	0.514808i	$-0.172137\pi$
$449$	36.3320			1.71461			0.857306	+	0.514808i	$0.172137\pi$
$450$	30.6754	−	53.1313i	1.44605	−	2.50463i
$451$	4.06168	+	7.03503i	0.191257	+	0.331267i
$452$	0.391540	+	0.678167i	0.0184165	+	0.0318983i
$453$	24.2452	−	41.9939i	1.13914	−	1.97305i
$454$	−5.10488			−0.239584
$455$		0			0
$456$	−21.3526			−0.999929
$457$	14.9823	−	25.9500i	0.700840	−	1.21389i	−0.267332	−	0.963605i	$-0.586142\pi$
$457$	14.9823	−	25.9500i	0.700840	−	1.21389i	0.968172	−	0.250286i	$-0.0805247\pi$
$458$	−1.13770	−	1.97055i	−0.0531610	−	0.0920776i
$459$	−11.5198	−	19.9530i	−0.537700	−	0.931324i
$460$	6.21058	−	10.7570i	0.289570	−	0.501549i
$461$	4.50503			0.209820			0.104910	−	0.994482i	$-0.466544\pi$
$461$	4.50503			0.209820			0.104910	+	0.994482i	$0.466544\pi$
$462$		0			0
$463$	−24.0854			−1.11934			−0.559671	−	0.828715i	$-0.689073\pi$
$463$	−24.0854			−1.11934			−0.559671	+	0.828715i	$0.689073\pi$
$464$	4.86487	−	8.42620i	0.225846	−	0.391176i
$465$	22.1616	+	38.3850i	1.02772	+	1.78006i
$466$	−7.33819	−	12.7101i	−0.339935	−	0.588785i
$467$	−18.3852	+	31.8442i	−0.850767	+	1.47357i	0.0297492	+	0.999557i	$0.490529\pi$
$467$	−18.3852	+	31.8442i	−0.850767	+	1.47357i	−0.880517	+	0.474015i	$0.842804\pi$
$468$	5.29417			0.244723
$469$		0			0
$470$	−12.8409			−0.592308
$471$	−23.6732	+	41.0032i	−1.09080	+	1.88933i
$472$	6.22258	+	10.7778i	0.286417	+	0.496089i
$473$	6.22936	+	10.7896i	0.286426	+	0.496105i
$474$	−10.5098	+	18.2035i	−0.482730	+	0.836112i
$475$	85.9185			3.94221
$476$		0			0
$477$	70.8901			3.24584
$478$	2.63988	−	4.57241i	0.120745	−	0.209137i
$479$	12.5180	+	21.6819i	0.571963	+	0.990670i	0.996364	+	0.0851953i	$0.0271514\pi$
$479$	12.5180	+	21.6819i	0.571963	+	0.990670i	−0.424401	+	0.905474i	$0.639515\pi$
$480$	−5.86487	−	10.1582i	−0.267693	−	0.463658i
$481$	−0.147087	+	0.254762i	−0.00670660	+	0.0116162i
$482$	−19.6329			−0.894252
$483$		0			0
$484$	−7.83621			−0.356191
$485$	−7.49781	+	12.9866i	−0.340458	+	0.589691i
$486$	−5.38087	−	9.31993i	−0.244081	−	0.422761i
$487$	−3.88365	−	6.72668i	−0.175985	−	0.304815i	0.764517	−	0.644604i	$-0.222978\pi$
$487$	−3.88365	−	6.72668i	−0.175985	−	0.304815i	−0.940502	+	0.339789i	$0.889644\pi$
$488$	1.48842	−	2.57802i	0.0673777	−	0.116702i
$489$	0.583224			0.0263743
$490$		0			0
$491$	13.9470			0.629419			0.314710	−	0.949188i	$-0.398093\pi$
$491$	13.9470			0.629419			0.314710	+	0.949188i	$0.398093\pi$
$492$	−6.57639	+	11.3906i	−0.296487	+	0.513530i
$493$	16.9642	+	29.3829i	0.764031	+	1.32334i
$494$	3.70711	+	6.42090i	0.166791	+	0.288890i
$495$	−19.1767	+	33.2150i	−0.861928	+	1.49290i
$496$	3.77871			0.169669
$497$		0			0
$498$	−36.3695			−1.62976
$499$	−15.8466	+	27.4471i	−0.709390	+	1.22870i	0.255694	+	0.966758i	$0.417696\pi$
$499$	−15.8466	+	27.4471i	−0.709390	+	1.22870i	−0.965084	+	0.261941i	$0.915637\pi$
$500$	13.4168	+	23.2385i	0.600016	+	1.03926i
$501$	30.9064	+	53.5315i	1.38080	+	2.39161i
$502$	−1.38845	+	2.40486i	−0.0619694	+	0.107334i
$503$	13.1767			0.587520			0.293760	−	0.955879i	$-0.405093\pi$
$503$	13.1767			0.587520			0.293760	+	0.955879i	$0.405093\pi$
$504$		0			0
$505$	−65.5750			−2.91805
$506$	−2.71228	+	4.69780i	−0.120575	+	0.208843i
$507$	−1.43998	−	2.49412i	−0.0639518	−	0.110768i
$508$	−0.696434	−	1.20626i	−0.0308993	−	0.0535191i
$509$	1.88546	−	3.26572i	0.0835717	−	0.144750i	−0.821210	−	0.570626i	$-0.806701\pi$
$509$	1.88546	−	3.26572i	0.0835717	−	0.144750i	0.904782	+	0.425876i	$0.140034\pi$
$510$	40.9027			1.81120
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−24.4933	+	42.4237i	−1.08141	+	1.87305i
$514$	−3.59779	−	6.23155i	−0.158692	−	0.274862i
$515$	−3.16419	−	5.48054i	−0.139431	−	0.241502i
$516$	−10.0862	+	17.4697i	−0.444019	+	0.769063i
$517$	5.60788			0.246634
$518$		0			0
$519$	−19.5678			−0.858933
$520$	−2.03644	+	3.52722i	−0.0893038	+	0.154679i
$521$	10.2696	+	17.7875i	0.449921	+	0.779286i	0.998380	−	0.0568910i	$-0.0181187\pi$
$521$	10.2696	+	17.7875i	0.449921	+	0.779286i	−0.548459	+	0.836177i	$0.684785\pi$
$522$	−25.7555	−	44.6098i	−1.12729	−	1.95252i
$523$	17.3269	−	30.0110i	0.757651	−	1.31229i	−0.186394	−	0.982475i	$-0.559680\pi$
$523$	17.3269	−	30.0110i	0.757651	−	1.31229i	0.944045	−	0.329816i	$-0.106987\pi$
$524$	−7.14395			−0.312085
$525$		0			0
$526$	6.68267			0.291378
$527$	−6.58835	+	11.4114i	−0.286993	+	0.497086i
$528$	2.56130	+	4.43630i	0.111466	+	0.193065i
$529$	6.84960	+	11.8639i	0.297809	+	0.515820i
$530$	−27.2684	+	47.2302i	−1.18446	+	2.05155i
$531$	65.8868			2.85924
$532$		0			0
$533$	4.56700			0.197819
$534$	−15.6399	+	27.0891i	−0.676804	+	1.17226i
$535$	−24.9981	−	43.2980i	−1.08076	−	1.87193i
$536$	−4.99061	−	8.64399i	−0.215561	−	0.373363i
$537$	−11.9937	+	20.7737i	−0.517567	+	0.896453i
$538$	8.11085			0.349683
$539$		0			0
$540$	−26.9101			−1.15802
$541$	−9.19729	+	15.9302i	−0.395423	+	0.684892i	−0.993155	−	0.116804i	$-0.962735\pi$
$541$	−9.19729	+	15.9302i	−0.395423	+	0.684892i	0.597733	+	0.801696i	$0.296068\pi$
$542$	−0.529235	−	0.916662i	−0.0227326	−	0.0393740i
$543$	−28.8723	−	50.0083i	−1.23903	−	2.14606i
$544$	1.74355	−	3.01991i	0.0747539	−	0.129478i
$545$	−2.95430			−0.126548
$546$		0			0
$547$	28.4403			1.21602			0.608010	−	0.793929i	$-0.291968\pi$
$547$	28.4403			1.21602			0.608010	+	0.793929i	$0.291968\pi$
$548$	3.46575	−	6.00285i	0.148049	−	0.256429i
$549$	−7.87996	−	13.6485i	−0.336309	−	0.582503i
$550$	−10.3061	−	17.8507i	−0.439455	−	0.761158i
$551$	36.0692	−	62.4736i	1.53660	−	2.66147i
$552$	−8.78308			−0.373833
$553$		0			0
$554$	24.6132			1.04572
$555$	1.72529	−	2.98830i	0.0732346	−	0.126846i
$556$	5.69639	+	9.86643i	0.241581	+	0.418430i
$557$	8.34341	+	14.4512i	0.353522	+	0.612318i	0.986864	−	0.161554i	$-0.0516507\pi$
$557$	8.34341	+	14.4512i	0.353522	+	0.612318i	−0.633342	+	0.773872i	$0.718317\pi$
$558$	10.0026	−	17.3249i	0.423442	−	0.733423i
$559$	7.00437			0.296253
$560$		0			0
$561$	−17.8630			−0.754176
$562$	2.56888	−	4.44943i	0.108362	−	0.187688i
$563$	5.75550	+	9.96882i	0.242565	+	0.420136i	0.961444	−	0.275000i	$-0.0886778\pi$
$563$	5.75550	+	9.96882i	0.242565	+	0.420136i	−0.718879	+	0.695135i	$0.755344\pi$
$564$	4.53995	+	7.86343i	0.191167	+	0.331110i
$565$	−1.59469	+	2.76209i	−0.0670893	+	0.116202i
$566$	−1.62813			−0.0684354
$567$		0			0
$568$	−1.38146			−0.0579649
$569$	−16.1522	+	27.9765i	−0.677136	+	1.17283i	0.298704	+	0.954346i	$0.403446\pi$
$569$	−16.1522	+	27.9765i	−0.677136	+	1.17283i	−0.975840	+	0.218488i	$0.929888\pi$
$570$	−43.4834	−	75.3154i	−1.82132	−	3.15462i
$571$	−4.94137	−	8.55870i	−0.206790	−	0.358171i	0.743912	−	0.668278i	$-0.232968\pi$
$571$	−4.94137	−	8.55870i	−0.206790	−	0.358171i	−0.950702	+	0.310107i	$0.899635\pi$
$572$	0.889353	−	1.54040i	0.0371857	−	0.0644075i
$573$	−24.4373			−1.02088
$574$		0			0
$575$	35.3412			1.47383
$576$	−2.64709	+	4.58489i	−0.110295	+	0.191037i
$577$	13.4795	+	23.3471i	0.561158	+	0.971953i	0.997396	+	0.0721222i	$0.0229771\pi$
$577$	13.4795	+	23.3471i	0.561158	+	0.971953i	−0.436238	+	0.899831i	$0.643690\pi$
$578$	−2.42009	−	4.19172i	−0.100662	−	0.174353i
$579$	10.2452	−	17.7452i	0.425776	−	0.737466i
$580$	39.6280			1.64546
$581$		0			0
$582$	10.6035			0.439530
$583$	11.9086	−	20.6263i	0.493205	−	0.854256i
$584$	2.54493	+	4.40794i	0.105310	+	0.182402i
$585$	10.7813	+	18.6737i	0.445751	+	0.772063i
$586$	7.07544	−	12.2550i	0.292284	−	0.506250i
$587$	−6.80955			−0.281060			−0.140530	−	0.990076i	$-0.544881\pi$
$587$	−6.80955			−0.281060			−0.140530	+	0.990076i	$0.544881\pi$
$588$		0			0
$589$	28.0161			1.15438
$590$	−25.3438	+	43.8968i	−1.04339	+	1.80720i
$591$	−22.3266	−	38.6709i	−0.918395	−	1.59071i
$592$	−0.147087	−	0.254762i	−0.00604525	−	0.0104707i
$593$	12.8849	−	22.3174i	0.529121	−	0.916464i	−0.470303	−	0.882505i	$-0.655855\pi$
$593$	12.8849	−	22.3174i	0.529121	−	0.916464i	0.999423	−	0.0339587i	$-0.0108115\pi$
$594$	11.7521			0.482196
$595$		0			0
$596$	11.3287			0.464043
$597$	4.25955	−	7.37775i	0.174332	−	0.301951i
$598$	1.52486	+	2.64114i	0.0623562	+	0.108004i
$599$	−6.82085	−	11.8141i	−0.278692	−	0.482709i	0.692368	−	0.721545i	$-0.256568\pi$
$599$	−6.82085	−	11.8141i	−0.278692	−	0.482709i	−0.971060	+	0.238836i	$0.923234\pi$
$600$	16.6870	−	28.9027i	0.681244	−	1.17995i
$601$	−2.52541			−0.103014			−0.0515068	−	0.998673i	$-0.516402\pi$
$601$	−2.52541			−0.103014			−0.0515068	+	0.998673i	$0.516402\pi$
$602$		0			0
$603$	−52.8423			−2.15190
$604$	8.41859	−	14.5814i	0.342547	−	0.593310i
$605$	−15.9580	−	27.6400i	−0.648784	−	1.12373i
$606$	23.1843	+	40.1563i	0.941797	+	1.63124i
$607$	−0.183043	+	0.317040i	−0.00742949	+	0.0128683i	−0.869716	−	0.493552i	$-0.835698\pi$
$607$	−0.183043	+	0.317040i	−0.00742949	+	0.0128683i	0.862287	+	0.506420i	$0.169032\pi$
$608$	−7.41421			−0.300686
$609$		0			0
$610$	12.1243			0.490899
$611$	1.57639	−	2.73040i	0.0637741	−	0.110460i
$612$	−9.23064	−	15.9879i	−0.373127	−	0.646274i
$613$	−4.95673	−	8.58531i	−0.200200	−	0.346757i	0.748392	−	0.663256i	$-0.230826\pi$
$613$	−4.95673	−	8.58531i	−0.200200	−	0.346757i	−0.948593	+	0.316499i	$0.897493\pi$
$614$	8.21736	−	14.2329i	0.331626	−	0.574392i
$615$	−53.5697			−2.16014
$616$		0			0
$617$	31.2835			1.25943			0.629714	−	0.776827i	$-0.283172\pi$
$617$	31.2835			1.25943			0.629714	+	0.776827i	$0.283172\pi$
$618$	−2.23742	+	3.87533i	−0.0900023	+	0.155889i
$619$	−18.8245	−	32.6050i	−0.756620	−	1.31050i	−0.944565	−	0.328325i	$-0.893516\pi$
$619$	−18.8245	−	32.6050i	−0.756620	−	1.31050i	0.187945	−	0.982180i	$-0.439817\pi$
$620$	7.69511	+	13.3283i	0.309043	+	0.535278i
$621$	−10.0750	+	17.4503i	−0.404294	+	0.700258i
$622$	12.5191			0.501970
$623$		0			0
$624$	2.87996			0.115291
$625$	−25.6740	+	44.4687i	−1.02696	+	1.77875i
$626$	7.96740	+	13.7999i	0.318441	+	0.551557i
$627$	18.9900	+	32.8917i	0.758389	+	1.31357i
$628$	−8.21997	+	14.2374i	−0.328012	+	0.568134i
$629$	1.02581			0.0409019
$630$		0			0
$631$	6.19207			0.246503			0.123251	−	0.992375i	$-0.460668\pi$
$631$	6.19207			0.246503			0.123251	+	0.992375i	$0.460668\pi$
$632$	−3.64927	+	6.32073i	−0.145160	+	0.251425i
$633$	6.71730	+	11.6347i	0.266989	+	0.462438i
$634$	−6.93538	−	12.0124i	−0.275439	−	0.477075i
$635$	2.83649	−	4.91295i	0.112563	−	0.194964i
$636$	38.5633			1.52913
$637$		0			0
$638$	−17.3063			−0.685164
$639$	−3.65685	+	6.33386i	−0.144663	+	0.250564i
$640$	−2.03644	−	3.52722i	−0.0804974	−	0.139426i
$641$	−2.15071	−	3.72514i	−0.0849480	−	0.147134i	0.820421	−	0.571760i	$-0.193739\pi$
$641$	−2.15071	−	3.72514i	−0.0849480	−	0.147134i	−0.905369	+	0.424626i	$0.860406\pi$
$642$	−17.6763	+	30.6163i	−0.697629	+	1.20833i
$643$	−12.4113			−0.489455			−0.244728	−	0.969592i	$-0.578699\pi$
$643$	−12.4113			−0.489455			−0.244728	+	0.969592i	$0.578699\pi$
$644$		0			0
$645$	−82.1594			−3.23503
$646$	12.9270	−	22.3903i	0.508607	−	0.880933i
$647$	11.5217	+	19.9562i	0.452966	+	0.784559i	0.998569	−	0.0534843i	$-0.0170327\pi$
$647$	11.5217	+	19.9562i	0.452966	+	0.784559i	−0.545603	+	0.838044i	$0.683699\pi$
$648$	1.57288	+	2.72431i	0.0617885	+	0.107021i
$649$	11.0681	−	19.1706i	0.434462	−	0.752510i
$650$	−11.5883			−0.454532
$651$		0			0
$652$	0.202511			0.00793095
$653$	12.1446	−	21.0351i	0.475256	−	0.823168i	−0.524342	−	0.851508i	$-0.675689\pi$
$653$	12.1446	−	21.0351i	0.475256	−	0.823168i	0.999598	+	0.0283398i	$0.00902205\pi$
$654$	1.04450	+	1.80913i	0.0408433	+	0.0707427i
$655$	−14.5482	−	25.1983i	−0.568446	−	0.984577i
$656$	−2.28350	+	3.95514i	−0.0891558	+	0.154422i
$657$	26.9466			1.05129
$658$		0			0
$659$	−0.990314			−0.0385772			−0.0192886	−	0.999814i	$-0.506140\pi$
$659$	−0.990314			−0.0385772			−0.0192886	+	0.999814i	$0.506140\pi$
$660$	−10.4319	+	18.0685i	−0.406060	+	0.703317i
$661$	−23.7020	−	41.0531i	−0.921903	−	1.59678i	−0.796468	−	0.604680i	$-0.793301\pi$
$661$	−23.7020	−	41.0531i	−0.921903	−	1.59678i	−0.125434	−	0.992102i	$-0.540032\pi$
$662$	−0.115022	−	0.199223i	−0.00447044	−	0.00774303i
$663$	−5.02135	+	8.69723i	−0.195013	+	0.337772i
$664$	−12.6285			−0.490080
$665$		0			0
$666$	−1.55741			−0.0603484
$667$	14.8365	−	25.6976i	0.574471	−	0.995013i
$668$	10.7315	+	18.5876i	0.415216	+	0.719175i
$669$	−8.27234	−	14.3281i	−0.319827	−	0.553957i
$670$	20.3261	−	35.2059i	0.785268	−	1.36012i
$671$	−5.29492			−0.204408
$672$		0			0
$673$	41.4037			1.59599			0.797997	−	0.602661i	$-0.205893\pi$
$673$	41.4037			1.59599			0.797997	+	0.602661i	$0.205893\pi$
$674$	−3.52855	+	6.11163i	−0.135915	+	0.235411i
$675$	−38.2829	−	66.3079i	−1.47351	−	2.55219i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	11.3728	−	19.6982i	0.437091	−	0.757063i	−0.560373	−	0.828240i	$-0.689342\pi$
$677$	11.3728	−	19.6982i	0.437091	−	0.757063i	0.997464	+	0.0711773i	$0.0226756\pi$
$678$	2.25524			0.0866119
$679$		0			0
$680$	14.2025			0.544641
$681$	−7.35093	+	12.7322i	−0.281688	+	0.487898i
$682$	−3.36060	−	5.82073i	−0.128684	−	0.222887i
$683$	13.6216	+	23.5934i	0.521218	+	0.902776i	0.999695	+	0.0246761i	$0.00785546\pi$
$683$	13.6216	+	23.5934i	0.521218	+	0.902776i	−0.478478	+	0.878100i	$0.658811\pi$
$684$	−19.6261	+	33.9934i	−0.750422	+	1.29977i
$685$	28.2311			1.07866
$686$		0			0
$687$	−6.55304			−0.250014
$688$	−3.50219	+	6.06597i	−0.133520	+	0.231263i
$689$	−6.69511	−	11.5963i	−0.255063	−	0.441782i
$690$	−17.8862	−	30.9798i	−0.680916	−	1.17938i
$691$	24.0447	−	41.6466i	0.914702	−	1.58431i	0.107365	−	0.994220i	$-0.465759\pi$
$691$	24.0447	−	41.6466i	0.914702	−	1.58431i	0.807337	−	0.590090i	$-0.200908\pi$
$692$	−6.79448			−0.258288
$693$		0			0
$694$	−26.5403			−1.00746
$695$	−23.2007	+	40.1848i	−0.880053	+	1.52430i
$696$	−14.0106	−	24.2671i	−0.531071	−	0.919843i
$697$	−7.96278	−	13.7919i	−0.301612	−	0.522407i
$698$	4.29786	−	7.44412i	0.162677	−	0.281764i
$699$	−42.2674			−1.59870
$700$		0			0
$701$	0.0656322			0.00247890			0.00123945	−	0.999999i	$-0.499605\pi$
$701$	0.0656322			0.00247890			0.00123945	+	0.999999i	$0.499605\pi$
$702$	3.30357	−	5.72194i	0.124685	−	0.215961i
$703$	−1.09054	−	1.88886i	−0.0411303	−	0.0712398i
$704$	0.889353	+	1.54040i	0.0335187	+	0.0580562i
$705$	−18.4907	+	32.0268i	−0.696400	+	1.20620i
$706$	28.6900			1.07976
$707$		0			0
$708$	35.8415			1.34701
$709$	2.69274	−	4.66397i	0.101128	−	0.175159i	−0.811022	−	0.585016i	$-0.801088\pi$
$709$	2.69274	−	4.66397i	0.101128	−	0.175159i	0.912150	+	0.409857i	$0.134421\pi$
$710$	−2.81327	−	4.87272i	−0.105580	−	0.182870i
$711$	19.3199	+	33.4630i	0.724553	+	1.25496i
$712$	−5.43059	+	9.40606i	−0.203520	+	0.352507i
$713$	11.5240			0.431577
$714$		0			0
$715$	7.24445			0.270927
$716$	−4.16454	+	7.21320i	−0.155636	+	0.269570i
$717$	−7.60276	−	13.1684i	−0.283930	−	0.491782i
$718$	12.7662	+	22.1117i	0.476429	+	0.825200i
$719$	−10.9794	+	19.0169i	−0.409463	+	0.709210i	−0.994830	−	0.101558i	$-0.967617\pi$
$719$	−10.9794	+	19.0169i	−0.409463	+	0.709210i	0.585367	+	0.810769i	$0.300950\pi$
$720$	−21.5625			−0.803588
$721$		0			0
$722$	−35.9706			−1.33869
$723$	−28.2709	+	48.9667i	−1.05141	+	1.82109i
$724$	−10.0252	−	17.3642i	−0.372585	−	0.645336i
$725$	56.3758	+	97.6457i	2.09374	+	3.62647i
$726$	−11.2840	+	19.5444i	−0.418788	+	0.725362i
$727$	−2.73773			−0.101537			−0.0507684	−	0.998710i	$-0.516167\pi$
$727$	−2.73773			−0.101537			−0.0507684	+	0.998710i	$0.516167\pi$
$728$		0			0
$729$	−40.4306			−1.49743
$730$	−10.3652	+	17.9530i	−0.383632	+	0.664471i
$731$	−12.2125	−	21.1526i	−0.451694	−	0.782357i
$732$	−4.28659	−	7.42460i	−0.158437	−	0.274421i
$733$	−2.39543	+	4.14901i	−0.0884772	+	0.153247i	−0.906868	−	0.421416i	$-0.861533\pi$
$733$	−2.39543	+	4.14901i	−0.0884772	+	0.153247i	0.818390	+	0.574663i	$0.194867\pi$
$734$	32.7127			1.20745
$735$		0			0
$736$	−3.04972			−0.112414
$737$	−8.87682	+	15.3751i	−0.326982	+	0.566349i
$738$	12.0893	+	20.9392i	0.445012	+	0.770783i
$739$	−2.22823	−	3.85941i	−0.0819668	−	0.141971i	0.822128	−	0.569303i	$-0.192787\pi$
$739$	−2.22823	−	3.85941i	−0.0819668	−	0.141971i	−0.904095	+	0.427332i	$0.859453\pi$
$740$	0.599068	−	1.03762i	0.0220222	−	0.0381436i
$741$	21.3526			0.784409
$742$		0			0
$743$	39.8769			1.46294			0.731470	−	0.681874i	$-0.238835\pi$
$743$	39.8769			1.46294			0.731470	+	0.681874i	$0.238835\pi$
$744$	5.44126	−	9.42454i	0.199486	−	0.345520i
$745$	23.0703	+	39.9589i	0.845230	+	1.46398i
$746$	2.07657	+	3.59672i	0.0760286	+	0.131685i
$747$	−33.4287	+	57.9002i	−1.22309	+	2.11846i
$748$	−6.20251			−0.226786
$749$		0			0
$750$	77.2796			2.82185
$751$	12.2892	−	21.2854i	0.448438	−	0.776717i	−0.549847	−	0.835265i	$-0.685314\pi$
$751$	12.2892	−	21.2854i	0.448438	−	0.776717i	0.998285	+	0.0585486i	$0.0186473\pi$
$752$	1.57639	+	2.73040i	0.0574852	+	0.0995673i
$753$	3.99867	+	6.92590i	0.145720	+	0.252394i
$754$	−4.86487	+	8.42620i	−0.177168	+	0.306864i
$755$	68.5758			2.49573
$756$		0			0
$757$	−31.3276			−1.13862			−0.569310	−	0.822123i	$-0.692790\pi$
$757$	−31.3276			−1.13862			−0.569310	+	0.822123i	$0.692790\pi$
$758$	−8.21948	+	14.2366i	−0.298545	+	0.517095i
$759$	7.81125	+	13.5295i	0.283531	+	0.491089i
$760$	−15.0986	−	26.1515i	−0.547684	−	0.948616i
$761$	1.34838	−	2.33547i	0.0488789	−	0.0846607i	−0.840551	−	0.541733i	$-0.817769\pi$
$761$	1.34838	−	2.33547i	0.0488789	−	0.0846607i	0.889430	+	0.457072i	$0.151102\pi$
$762$	−4.01140			−0.145318
$763$		0			0
$764$	−8.48528			−0.306987
$765$	37.5953	−	65.1169i	1.35926	−	2.35431i
$766$	15.8945	+	27.5300i	0.574291	+	0.994701i
$767$	−6.22258	−	10.7778i	−0.224684	−	0.389164i
$768$	−1.43998	+	2.49412i	−0.0519608	+	0.0899988i
$769$	16.6046			0.598776			0.299388	−	0.954131i	$-0.403217\pi$
$769$	16.6046			0.598776			0.299388	+	0.954131i	$0.403217\pi$
$770$		0			0
$771$	−20.7230			−0.746320
$772$	3.55741	−	6.16162i	0.128034	−	0.221761i
$773$	−12.1439	−	21.0339i	−0.436787	−	0.756538i	0.560652	−	0.828051i	$-0.310550\pi$
$773$	−12.1439	−	21.0339i	−0.436787	−	0.756538i	−0.997440	+	0.0715134i	$0.977217\pi$
$774$	18.5412	+	32.1143i	0.666449	+	1.15432i
$775$	−21.8945	+	37.9223i	−0.786473	+	1.36221i
$776$	3.68182			0.132170
$777$		0			0
$778$	11.9057			0.426839
$779$	−16.9304	+	29.3243i	−0.606593	+	1.05065i
$780$	5.86487	+	10.1582i	0.209996	+	0.363724i
$781$	1.22861	+	2.12801i	0.0439631	+	0.0761462i
$782$	5.31733	−	9.20989i	0.190147	−	0.329345i
$783$	−64.2856			−2.29738
$784$		0			0
$785$	−66.9579			−2.38983
$786$	−10.2871	+	17.8179i	−0.366930	+	0.635542i
$787$	−10.6846	−	18.5063i	−0.380866	−	0.659679i	0.610320	−	0.792155i	$-0.291041\pi$
$787$	−10.6846	−	18.5063i	−0.380866	−	0.659679i	−0.991186	+	0.132475i	$0.957707\pi$
$788$	−7.75241	−	13.4276i	−0.276168	−	0.478337i
$789$	9.62291	−	16.6674i	0.342585	−	0.593374i
$790$	−29.7261			−1.05761
$791$		0			0
$792$	9.41678			0.334611
$793$	−1.48842	+	2.57802i	−0.0528554	+	0.0915482i
$794$	12.7146	+	22.0223i	0.451223	+	0.781542i
$795$	78.5318	+	136.021i	2.78524	+	4.82417i
$796$	1.47903	−	2.56175i	0.0524228	−	0.0907990i
$797$	0.537876			0.0190526			0.00952628	−	0.999955i	$-0.496968\pi$
$797$	0.537876			0.0190526			0.00952628	+	0.999955i	$0.496968\pi$
$798$		0			0
$799$	−10.9941			−0.388942
$800$	5.79417	−	10.0358i	0.204855	−	0.354819i
$801$	28.7505	+	49.7973i	1.01585	+	1.75950i
$802$	−14.7217	−	25.4987i	−0.519840	−	0.900390i
$803$	4.52667	−	7.84043i	0.159743	−	0.276683i
$804$	−28.7455			−1.01378
$805$		0			0
$806$	−3.77871			−0.133099
$807$	11.6795	−	20.2294i	0.411137	−	0.712109i
$808$	8.05021	+	13.9434i	0.283205	+	0.490526i
$809$	−8.27901	−	14.3397i	−0.291075	−	0.504156i	0.682989	−	0.730428i	$-0.260679\pi$
$809$	−8.27901	−	14.3397i	−0.291075	−	0.504156i	−0.974064	+	0.226272i	$0.927346\pi$
$810$	−6.40615	+	11.0958i	−0.225089	+	0.389866i
$811$	19.1866			0.673734			0.336867	−	0.941552i	$-0.390633\pi$
$811$	19.1866			0.673734			0.336867	+	0.941552i	$0.390633\pi$
$812$		0			0
$813$	−3.04835			−0.106910
$814$	−0.261625	+	0.453147i	−0.00916994	+	0.0158828i
$815$	0.412402	+	0.714301i	0.0144458	+	0.0250209i
$816$	−5.02135	−	8.69723i	−0.175782	−	0.304464i
$817$	−25.9660	+	44.9744i	−0.908434	+	1.57345i
$818$	13.3273			0.465977
$819$		0			0
$820$	−18.6009			−0.649570
$821$	21.3431	−	36.9673i	0.744878	−	1.29017i	−0.205374	−	0.978684i	$-0.565841\pi$
$821$	21.3431	−	36.9673i	0.744878	−	1.29017i	0.950252	−	0.311482i	$-0.100826\pi$
$822$	−9.98122	−	17.2880i	−0.348135	−	0.602987i
$823$	5.50351	+	9.53237i	0.191840	+	0.332277i	0.945860	−	0.324574i	$-0.105221\pi$
$823$	5.50351	+	9.53237i	0.191840	+	0.332277i	−0.754020	+	0.656852i	$0.771888\pi$
$824$	−0.776893	+	1.34562i	−0.0270644	+	0.0468769i
$825$	−59.3625			−2.06674
$826$		0			0
$827$	18.2076			0.633142			0.316571	−	0.948569i	$-0.397469\pi$
$827$	18.2076			0.633142			0.316571	+	0.948569i	$0.397469\pi$
$828$	−8.07288	+	13.9826i	−0.280552	+	0.485930i
$829$	−4.74596	−	8.22024i	−0.164834	−	0.285501i	0.771762	−	0.635911i	$-0.219375\pi$
$829$	−4.74596	−	8.22024i	−0.164834	−	0.285501i	−0.936596	+	0.350410i	$0.886042\pi$
$830$	−25.7171	−	44.5434i	−0.892655	−	1.54612i
$831$	35.4426	−	61.3883i	1.22949	−	2.12954i
$832$	1.00000			0.0346688
$833$		0			0
$834$	32.8107			1.13614
$835$	−43.7083	+	75.7050i	−1.51259	+	2.61988i
$836$	6.59385	+	11.4209i	0.228053	+	0.395000i
$837$	−12.4832	−	21.6215i	−0.431483	−	0.747350i
$838$	−20.0522	+	34.7315i	−0.692693	+	1.19978i
$839$	−36.0098			−1.24320			−0.621599	−	0.783336i	$-0.713517\pi$
$839$	−36.0098			−1.24320			−0.621599	+	0.783336i	$0.713517\pi$
$840$		0			0
$841$	65.6677			2.26440
$842$	−7.42429	+	12.8592i	−0.255858	+	0.443159i
$843$	−7.39828	−	12.8142i	−0.254810	−	0.441344i
$844$	2.33243	+	4.03988i	0.0802854	+	0.139058i
$845$	2.03644	−	3.52722i	0.0700557	−	0.121340i
$846$	16.6914			0.573863
$847$		0			0
$848$	13.3902			0.459822
$849$	−2.34447	+	4.06075i	−0.0804621	+	0.139364i
$850$	20.2048	+	34.9958i	0.693020	+	1.20035i
$851$	−0.448575	−	0.776955i	−0.0153770	−	0.0266337i
$852$	−1.98928	+	3.44553i	−0.0681516	+	0.118042i
$853$	−27.3815			−0.937523			−0.468762	−	0.883325i	$-0.655300\pi$
$853$	−27.3815			−0.937523			−0.468762	+	0.883325i	$0.655300\pi$
$854$		0			0
$855$	−159.869			−5.46741
$856$	−6.13770	+	10.6308i	−0.209782	+	0.363353i
$857$	3.61460	+	6.26067i	0.123472	+	0.213860i	0.921135	−	0.389244i	$-0.127264\pi$
$857$	3.61460	+	6.26067i	0.123472	+	0.213860i	−0.797662	+	0.603104i	$0.793930\pi$
$858$	−2.56130	−	4.43630i	−0.0874414	−	0.151453i
$859$	10.1314	−	17.5481i	0.345679	−	0.598733i	−0.639798	−	0.768543i	$-0.720982\pi$
$859$	10.1314	−	17.5481i	0.345679	−	0.598733i	0.985477	+	0.169810i	$0.0543153\pi$
$860$	−28.5280			−0.972796
$861$		0			0
$862$	9.55379			0.325403
$863$	−12.3910	+	21.4618i	−0.421793	+	0.730567i	−0.996115	−	0.0880623i	$-0.971933\pi$
$863$	−12.3910	+	21.4618i	−0.421793	+	0.730567i	0.574322	+	0.818630i	$0.305266\pi$
$864$	3.30357	+	5.72194i	0.112390	+	0.194665i
$865$	−13.8366	−	23.9656i	−0.470457	−	0.814856i
$866$	−10.2075	+	17.6799i	−0.346864	+	0.600787i
$867$	−13.9395			−0.473411
$868$		0			0
$869$	12.9820			0.440383
$870$	57.0636	−	98.8370i	1.93464	−	3.35089i
$871$	4.99061	+	8.64399i	0.169100	+	0.292890i
$872$	0.362680	+	0.628180i	0.0122819	+	0.0212729i
$873$	9.74611	−	16.8808i	0.329856	−	0.571327i
$874$	−22.6113			−0.764838
$875$		0			0
$876$	14.6586			0.495267
$877$	13.3691	−	23.1560i	0.451444	−	0.781923i	−0.547032	−	0.837111i	$-0.684243\pi$
$877$	13.3691	−	23.1560i	0.451444	−	0.781923i	0.998476	+	0.0551883i	$0.0175759\pi$
$878$	−0.641760	−	1.11156i	−0.0216584	−	0.0375134i
$879$	−20.3770	−	35.2940i	−0.687299	−	1.19044i
$880$	−3.62223	+	6.27388i	−0.122105	+	0.211492i
$881$	44.1409			1.48715			0.743573	−	0.668655i	$-0.233130\pi$
$881$	44.1409			1.48715			0.743573	+	0.668655i	$0.233130\pi$
$882$		0			0
$883$	−33.5058			−1.12756			−0.563780	−	0.825925i	$-0.690653\pi$
$883$	−33.5058			−1.12756			−0.563780	+	0.825925i	$0.690653\pi$
$884$	−1.74355	+	3.01991i	−0.0586418	+	0.101571i
$885$	72.9892	+	126.421i	2.45350	+	4.24959i
$886$	7.35196	+	12.7340i	0.246994	+	0.427806i
$887$	−25.5832	+	44.3114i	−0.859000	+	1.48783i	0.0138845	+	0.999904i	$0.495580\pi$
$887$	−25.5832	+	44.3114i	−0.859000	+	1.48783i	−0.872884	+	0.487927i	$0.837753\pi$
$888$	−0.847211			−0.0284305
$889$		0			0
$890$	−44.2363			−1.48280
$891$	2.79769	−	4.84574i	0.0937261	−	0.162338i
$892$	−2.87238	−	4.97511i	−0.0961744	−	0.166579i
$893$	11.6877	+	20.2437i	0.391115	+	0.677431i
$894$	16.3132	−	28.2552i	0.545594	−	0.944996i
$895$	−33.9234			−1.13393
$896$		0			0
$897$	8.78308			0.293258
$898$	18.1660	−	31.4644i	0.606207	−	1.04998i
$899$	18.3829	+	31.8401i	0.613104	+	1.06193i
$900$	−30.6754	−	53.1313i	−1.02251	−	1.77104i
$901$	−23.3465	+	40.4373i	−0.777783	+	1.34716i
$902$	8.12335			0.270478
$903$		0			0
$904$	0.783079			0.0260448
$905$	40.8316	−	70.7224i	1.35729	−	2.35089i
$906$	−24.2452	−	41.9939i	−0.805493	−	1.39515i
$907$	0.164543	+	0.284997i	0.00546356	+	0.00946316i	0.868744	−	0.495261i	$-0.164928\pi$
$907$	0.164543	+	0.284997i	0.00546356	+	0.00946316i	−0.863281	+	0.504724i	$0.831594\pi$
$908$	−2.55244	+	4.42096i	−0.0847057	+	0.146715i
$909$	85.2384			2.82718
$910$		0			0
$911$	−3.64811			−0.120867			−0.0604336	−	0.998172i	$-0.519248\pi$
$911$	−3.64811			−0.120867			−0.0604336	+	0.998172i	$0.519248\pi$
$912$	−10.6763	+	18.4919i	−0.353528	+	0.612329i
$913$	11.2312	+	19.4530i	0.371697	+	0.643799i
$914$	−14.9823	−	25.9500i	−0.495569	−	0.858350i
$915$	17.4588	−	30.2395i	0.577170	−	0.999687i
$916$	−2.27539			−0.0751810
$917$		0			0
$918$	−23.0397			−0.760423
$919$	−16.2678	+	28.1767i	−0.536626	+	0.929463i	0.462457	+	0.886642i	$0.346968\pi$
$919$	−16.2678	+	28.1767i	−0.536626	+	0.929463i	−0.999083	+	0.0428211i	$0.986365\pi$
$920$	−6.21058	−	10.7570i	−0.204757	−	0.354649i
$921$	−23.6657	−	40.9901i	−0.779810	−	1.35067i
$922$	2.25252	−	3.90147i	0.0741827	−	0.128488i
$923$	1.38146			0.0454714
$924$		0			0
$925$	3.40900			0.112087
$926$	−12.0427	+	20.8586i	−0.395747	+	0.685455i
$927$	4.11301	+	7.12394i	0.135089	+	0.233981i
$928$	−4.86487	−	8.42620i	−0.159697	−	0.276603i
$929$	4.99273	−	8.64767i	0.163806	−	0.283721i	−0.772424	−	0.635107i	$-0.780956\pi$
$929$	4.99273	−	8.64767i	0.163806	−	0.283721i	0.936231	+	0.351386i	$0.114289\pi$
$930$	44.3232			1.45342
$931$		0			0
$932$	−14.6764			−0.480741
$933$	18.0272	−	31.2241i	0.590186	−	1.02223i
$934$	18.3852	+	31.8442i	0.601583	+	1.04197i
$935$	−12.6310	−	21.8776i	−0.413079	−	0.715474i
$936$	2.64709	−	4.58489i	0.0865228	−	0.149862i
$937$	−38.1800			−1.24729			−0.623643	−	0.781709i	$-0.714348\pi$
$937$	−38.1800			−1.24729			−0.623643	+	0.781709i	$0.714348\pi$
$938$		0			0
$939$	45.8916			1.49762
$940$	−6.42047	+	11.1206i	−0.209412	+	0.362713i
$941$	3.60525	+	6.24448i	0.117528	+	0.203564i	0.918787	−	0.394753i	$-0.129170\pi$
$941$	3.60525	+	6.24448i	0.117528	+	0.203564i	−0.801260	+	0.598317i	$0.795836\pi$
$942$	23.6732	+	41.0032i	0.771314	+	1.33595i
$943$	−6.96404	+	12.0621i	−0.226780	+	0.392795i
$944$	12.4452			0.405055
$945$		0			0
$946$	12.4587			0.405068
$947$	21.8887	−	37.9124i	0.711287	−	1.23199i	−0.253087	−	0.967444i	$-0.581446\pi$
$947$	21.8887	−	37.9124i	0.711287	−	1.23199i	0.964374	−	0.264542i	$-0.0852209\pi$
$948$	10.5098	+	18.2035i	0.341341	+	0.591221i
$949$	−2.54493	−	4.40794i	−0.0826118	−	0.143088i
$950$	42.9592	−	74.4076i	1.39378	−	2.41410i
$951$	−39.9473			−1.29538
$952$		0			0
$953$	26.9227			0.872113			0.436057	−	0.899919i	$-0.356375\pi$
$953$	26.9227			0.872113			0.436057	+	0.899919i	$0.356375\pi$
$954$	35.4451	−	61.3926i	1.14758	−	1.98766i
$955$	−17.2798	−	29.9294i	−0.559160	−	0.968494i
$956$	−2.63988	−	4.57241i	−0.0853799	−	0.147882i
$957$	−24.9208	+	43.1640i	−0.805574	+	1.39530i
$958$	25.0361			0.808878
$959$		0			0
$960$	−11.7297			−0.378576
$961$	8.36069	−	14.4811i	0.269700	−	0.467134i
$962$	0.147087	+	0.254762i	0.00474228	+	0.00821387i
$963$	32.4940	+	56.2813i	1.04711	+	1.81364i
$964$	−9.81643	+	17.0025i	−0.316166	+	0.547615i
$965$	28.9778			0.932829
$966$		0			0
$967$	−11.8218			−0.380163			−0.190082	−	0.981768i	$-0.560875\pi$
$967$	−11.8218			−0.380163			−0.190082	+	0.981768i	$0.560875\pi$
$968$	−3.91810	+	6.78635i	−0.125933	+	0.218122i
$969$	−37.2293	−	64.4831i	−1.19598	−	2.07150i
$970$	7.49781	+	12.9866i	0.240740	+	0.416974i
$971$	−14.0435	+	24.3240i	−0.450677	+	0.780595i	−0.998428	−	0.0560458i	$-0.982151\pi$
$971$	−14.0435	+	24.3240i	−0.450677	+	0.780595i	0.547751	+	0.836641i	$0.315484\pi$
$972$	−10.7617			−0.345183
$973$		0			0
$974$	−7.76730			−0.248880
$975$	−16.6870	+	28.9027i	−0.534412	+	0.925628i
$976$	−1.48842	−	2.57802i	−0.0476432	−	0.0825204i
$977$	−12.0541	−	20.8783i	−0.385645	−	0.667956i	0.606214	−	0.795302i	$-0.292688\pi$
$977$	−12.0541	−	20.8783i	−0.385645	−	0.667956i	−0.991858	+	0.127346i	$0.959354\pi$
$978$	0.291612	−	0.505087i	0.00932472	−	0.0161509i
$979$	19.3188			0.617433
$980$		0			0
$981$	3.84018			0.122608
$982$	6.97350	−	12.0785i	0.222533	−	0.385439i
$983$	3.53606	+	6.12464i	0.112783	+	0.195346i	0.916891	−	0.399137i	$-0.130690\pi$
$983$	3.53606	+	6.12464i	0.112783	+	0.195346i	−0.804108	+	0.594483i	$0.797357\pi$
$984$	6.57639	+	11.3906i	0.209648	+	0.363121i
$985$	31.5746	−	54.6889i	1.00605	−	1.74253i
$986$	33.9285			1.08050
$987$		0			0
$988$	7.41421			0.235878
$989$	−10.6807	+	18.4995i	−0.339626	+	0.588250i
$990$	19.1767	+	33.2150i	0.609475	+	1.05564i
$991$	−3.45720	−	5.98804i	−0.109822	−	0.190217i	0.805876	−	0.592084i	$-0.201695\pi$
$991$	−3.45720	−	5.98804i	−0.109822	−	0.190217i	−0.915698	+	0.401867i	$0.868361\pi$
$992$	1.88935	−	3.27245i	0.0599870	−	0.103901i
$993$	−0.662515			−0.0210243
$994$		0			0
$995$	12.0478			0.381941
$996$	−18.1848	+	31.4969i	−0.576206	+	0.998018i
$997$	25.7877	+	44.6656i	0.816705	+	1.41458i	0.908097	+	0.418760i	$0.137535\pi$
$997$	25.7877	+	44.6656i	0.816705	+	1.41458i	−0.0913916	+	0.995815i	$0.529132\pi$
$998$	15.8466	+	27.4471i	0.501614	+	0.868821i
$999$	−0.971825	+	1.68325i	−0.0307472	+	0.0532557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.z.79.1		8
7.2	even	3		1274.2.a.u.1.4	yes	4
7.3	odd	6		1274.2.f.ba.1145.4		8
7.4	even	3	inner	1274.2.f.z.1145.1		8
7.5	odd	6		1274.2.a.t.1.1	✓	4
7.6	odd	2		1274.2.f.ba.79.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1274.2.a.t.1.1	✓	4	7.5	odd	6
1274.2.a.u.1.4	yes	4	7.2	even	3
1274.2.f.z.79.1		8	1.1	even	1	trivial
1274.2.f.z.1145.1		8	7.4	even	3	inner
1274.2.f.ba.79.4		8	7.6	odd	2
1274.2.f.ba.1145.4		8	7.3	odd	6

Overview	Random
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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.43998 - 2.49412i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(2.03644 - 3.52722i) q^{5} -2.87996 q^{6} -1.00000 q^{8} +(-2.64709 + 4.58489i) q^{9} +(-2.03644 - 3.52722i) q^{10} +(0.889353 + 1.54040i) q^{11} +(-1.43998 + 2.49412i) q^{12} +1.00000 q^{13} -11.7297 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.74355 - 3.01991i) q^{17} +(2.64709 + 4.58489i) q^{18} +(-3.70711 + 6.42090i) q^{19} -4.07288 q^{20} +1.77871 q^{22} +(-1.52486 + 2.64114i) q^{23} +(1.43998 + 2.49412i) q^{24} +(-5.79417 - 10.0358i) q^{25} +(0.500000 - 0.866025i) q^{26} +6.60713 q^{27} -9.72973 q^{29} +(-5.86487 + 10.1582i) q^{30} +(-1.88935 - 3.27245i) q^{31} +(0.500000 + 0.866025i) q^{32} +(2.56130 - 4.43630i) q^{33} -3.48709 q^{34} +5.29417 q^{36} +(-0.147087 + 0.254762i) q^{37} +(3.70711 + 6.42090i) q^{38} +(-1.43998 - 2.49412i) q^{39} +(-2.03644 + 3.52722i) q^{40} +4.56700 q^{41} +7.00437 q^{43} +(0.889353 - 1.54040i) q^{44} +(10.7813 + 18.6737i) q^{45} +(1.52486 + 2.64114i) q^{46} +(1.57639 - 2.73040i) q^{47} +2.87996 q^{48} -11.5883 q^{50} +(-5.02135 + 8.69723i) q^{51} +(-0.500000 - 0.866025i) q^{52} +(-6.69511 - 11.5963i) q^{53} +(3.30357 - 5.72194i) q^{54} +7.24445 q^{55} +21.3526 q^{57} +(-4.86487 + 8.42620i) q^{58} +(-6.22258 - 10.7778i) q^{59} +(5.86487 + 10.1582i) q^{60} +(-1.48842 + 2.57802i) q^{61} -3.77871 q^{62} +1.00000 q^{64} +(2.03644 - 3.52722i) q^{65} +(-2.56130 - 4.43630i) q^{66} +(4.99061 + 8.64399i) q^{67} +(-1.74355 + 3.01991i) q^{68} +8.78308 q^{69} +1.38146 q^{71} +(2.64709 - 4.58489i) q^{72} +(-2.54493 - 4.40794i) q^{73} +(0.147087 + 0.254762i) q^{74} +(-16.6870 + 28.9027i) q^{75} +7.41421 q^{76} -2.87996 q^{78} +(3.64927 - 6.32073i) q^{79} +(2.03644 + 3.52722i) q^{80} +(-1.57288 - 2.72431i) q^{81} +(2.28350 - 3.95514i) q^{82} +12.6285 q^{83} -14.2025 q^{85} +(3.50219 - 6.06597i) q^{86} +(14.0106 + 24.2671i) q^{87} +(-0.889353 - 1.54040i) q^{88} +(5.43059 - 9.40606i) q^{89} +21.5625 q^{90} +3.04972 q^{92} +(-5.44126 + 9.42454i) q^{93} +(-1.57639 - 2.73040i) q^{94} +(15.0986 + 26.1515i) q^{95} +(1.43998 - 2.49412i) q^{96} -3.68182 q^{97} -9.41678 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} - 2 q^{3} - 4 q^{4} - 4 q^{6} - 8 q^{8} - 6 q^{9} + 6 q^{11} - 2 q^{12} + 8 q^{13} - 16 q^{15} - 4 q^{16} + 8 q^{17} + 6 q^{18} - 24 q^{19} + 12 q^{22} - 2 q^{23} + 2 q^{24} - 16 q^{25} + 4 q^{26}+ \cdots + 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^2 - 2 * q^3 - 4 * q^4 - 4 * q^6 - 8 * q^8 - 6 * q^9 + 6 * q^11 - 2 * q^12 + 8 * q^13 - 16 * q^15 - 4 * q^16 + 8 * q^17 + 6 * q^18 - 24 * q^19 + 12 * q^22 - 2 * q^23 + 2 * q^24 - 16 * q^25 + 4 * q^26 + 28 * q^27 - 8 * q^30 - 14 * q^31 + 4 * q^32 - 6 * q^33 + 16 * q^34 + 12 * q^36 + 14 * q^37 + 24 * q^38 - 2 * q^39 + 12 * q^41 + 8 * q^43 + 6 * q^44 + 12 * q^45 + 2 * q^46 + 6 * q^47 + 4 * q^48 - 32 * q^50 - 4 * q^51 - 4 * q^52 - 16 * q^53 + 14 * q^54 + 48 * q^55 + 24 * q^57 - 16 * q^59 + 8 * q^60 - 18 * q^61 - 28 * q^62 + 8 * q^64 + 6 * q^66 + 22 * q^67 + 8 * q^68 + 20 * q^69 + 32 * q^71 + 6 * q^72 - 10 * q^73 - 14 * q^74 - 42 * q^75 + 48 * q^76 - 4 * q^78 - 10 * q^79 + 20 * q^81 + 6 * q^82 + 40 * q^83 - 80 * q^85 + 4 * q^86 + 8 * q^87 - 6 * q^88 + 16 * q^89 + 24 * q^90 + 4 * q^92 + 2 * q^93 - 6 * q^94 + 4 * q^95 + 2 * q^96 + 4 * q^97 + 8 * q^99

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