LMFDB - Embedded newform 3549.2.a.ba.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3549,2,Mod(1,3549)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3549, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("3549.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3549 = 3 \cdot 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3549.a (trivial)

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:	yes
Analytic conductor:	$28.3389076774$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - 13x^{6} + 22x^{5} + 57x^{4} - 72x^{3} - 96x^{2} + 64x + 61 $ x^8 - 2x^7 - 13x^6 + 22x^5 + 57x^4 - 72x^3 - 96x^2 + 64*x + 61
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 273)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-0.756173$ of defining polynomial
Character	$\chi$	$=$	3549.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.756173 q^{2} -1.00000 q^{3} -1.42820 q^{4} -4.01537 q^{5} -0.756173 q^{6} +1.00000 q^{7} -2.59231 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.756173 q^{2} -1.00000 q^{3} -1.42820 q^{4} -4.01537 q^{5} -0.756173 q^{6} +1.00000 q^{7} -2.59231 q^{8} +1.00000 q^{9} -3.03631 q^{10} -0.679275 q^{11} +1.42820 q^{12} +0.756173 q^{14} +4.01537 q^{15} +0.896164 q^{16} +2.97235 q^{17} +0.756173 q^{18} +0.918653 q^{19} +5.73476 q^{20} -1.00000 q^{21} -0.513649 q^{22} +8.59922 q^{23} +2.59231 q^{24} +11.1232 q^{25} -1.00000 q^{27} -1.42820 q^{28} -7.97866 q^{29} +3.03631 q^{30} -3.29616 q^{31} +5.86229 q^{32} +0.679275 q^{33} +2.24761 q^{34} -4.01537 q^{35} -1.42820 q^{36} -5.43258 q^{37} +0.694661 q^{38} +10.4091 q^{40} +9.22234 q^{41} -0.756173 q^{42} +5.06133 q^{43} +0.970141 q^{44} -4.01537 q^{45} +6.50250 q^{46} -3.03541 q^{47} -0.896164 q^{48} +1.00000 q^{49} +8.41105 q^{50} -2.97235 q^{51} +1.32745 q^{53} -0.756173 q^{54} +2.72754 q^{55} -2.59231 q^{56} -0.918653 q^{57} -6.03325 q^{58} -4.83250 q^{59} -5.73476 q^{60} -4.46940 q^{61} -2.49247 q^{62} +1.00000 q^{63} +2.64058 q^{64} +0.513649 q^{66} -4.04076 q^{67} -4.24511 q^{68} -8.59922 q^{69} -3.03631 q^{70} -2.41210 q^{71} -2.59231 q^{72} +7.82146 q^{73} -4.10797 q^{74} -11.1232 q^{75} -1.31202 q^{76} -0.679275 q^{77} +16.1827 q^{79} -3.59843 q^{80} +1.00000 q^{81} +6.97369 q^{82} -4.78597 q^{83} +1.42820 q^{84} -11.9351 q^{85} +3.82724 q^{86} +7.97866 q^{87} +1.76089 q^{88} -4.52542 q^{89} -3.03631 q^{90} -12.2814 q^{92} +3.29616 q^{93} -2.29530 q^{94} -3.68873 q^{95} -5.86229 q^{96} -8.54947 q^{97} +0.756173 q^{98} -0.679275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 8 q^{3} + 14 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 8 * q^3 + 14 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} + 14 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 14 q^{12} - 2 q^{14} + 6 q^{15} + 10 q^{16} - 2 q^{17} - 2 q^{18} - 14 q^{19} + 10 q^{20} - 8 q^{21} + 18 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{25} - 8 q^{27} + 14 q^{28} + 12 q^{29} + 4 q^{30} - 16 q^{31} - 26 q^{32} + 16 q^{33} - 32 q^{34} - 6 q^{35} + 14 q^{36} + 8 q^{37} + 12 q^{38} - 14 q^{40} + 4 q^{41} + 2 q^{42} + 14 q^{43} - 68 q^{44} - 6 q^{45} + 28 q^{46} - 6 q^{47} - 10 q^{48} + 8 q^{49} - 32 q^{50} + 2 q^{51} + 14 q^{53} + 2 q^{54} - 2 q^{55} - 12 q^{56} + 14 q^{57} - 24 q^{58} - 50 q^{59} - 10 q^{60} - 2 q^{61} - 20 q^{62} + 8 q^{63} + 24 q^{64} - 18 q^{66} + 16 q^{67} - 36 q^{68} + 6 q^{69} - 4 q^{70} - 34 q^{71} - 12 q^{72} + 8 q^{73} - 6 q^{74} - 10 q^{75} + 4 q^{76} - 16 q^{77} + 46 q^{79} + 24 q^{80} + 8 q^{81} - 42 q^{82} - 42 q^{83} - 14 q^{84} - 20 q^{85} - 50 q^{86} - 12 q^{87} + 62 q^{88} - 28 q^{89} - 4 q^{90} - 58 q^{92} + 16 q^{93} + 24 q^{94} - 24 q^{95} + 26 q^{96} - 16 q^{97} - 2 q^{98} - 16 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 + 14 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 14 * q^12 - 2 * q^14 + 6 * q^15 + 10 * q^16 - 2 * q^17 - 2 * q^18 - 14 * q^19 + 10 * q^20 - 8 * q^21 + 18 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^25 - 8 * q^27 + 14 * q^28 + 12 * q^29 + 4 * q^30 - 16 * q^31 - 26 * q^32 + 16 * q^33 - 32 * q^34 - 6 * q^35 + 14 * q^36 + 8 * q^37 + 12 * q^38 - 14 * q^40 + 4 * q^41 + 2 * q^42 + 14 * q^43 - 68 * q^44 - 6 * q^45 + 28 * q^46 - 6 * q^47 - 10 * q^48 + 8 * q^49 - 32 * q^50 + 2 * q^51 + 14 * q^53 + 2 * q^54 - 2 * q^55 - 12 * q^56 + 14 * q^57 - 24 * q^58 - 50 * q^59 - 10 * q^60 - 2 * q^61 - 20 * q^62 + 8 * q^63 + 24 * q^64 - 18 * q^66 + 16 * q^67 - 36 * q^68 + 6 * q^69 - 4 * q^70 - 34 * q^71 - 12 * q^72 + 8 * q^73 - 6 * q^74 - 10 * q^75 + 4 * q^76 - 16 * q^77 + 46 * q^79 + 24 * q^80 + 8 * q^81 - 42 * q^82 - 42 * q^83 - 14 * q^84 - 20 * q^85 - 50 * q^86 - 12 * q^87 + 62 * q^88 - 28 * q^89 - 4 * q^90 - 58 * q^92 + 16 * q^93 + 24 * q^94 - 24 * q^95 + 26 * q^96 - 16 * q^97 - 2 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	0.756173	0.534695	0.267348	−	0.963600i	$-0.413853\pi$
$2$	0.756173	0.534695	0.267348	+	0.963600i	$0.413853\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.42820	−0.714101
$5$	−4.01537	−1.79573	−0.897864	−	0.440274i	$-0.854881\pi$
$5$	−4.01537	−1.79573	−0.897864	+	0.440274i	$0.854881\pi$
$6$	−0.756173	−0.308706
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.59231	−0.916522
$9$	1.00000	0.333333
$10$	−3.03631	−0.960167
$11$	−0.679275	−0.204809	−0.102404	−	0.994743i	$-0.532654\pi$
$11$	−0.679275	−0.204809	−0.102404	+	0.994743i	$0.532654\pi$
$12$	1.42820	0.412286
$13$	0	0
$13$	0	0
$14$	0.756173	0.202096
$15$	4.01537	1.03676
$16$	0.896164	0.224041
$17$	2.97235	0.720900	0.360450	−	0.932778i	$-0.382623\pi$
$17$	2.97235	0.720900	0.360450	+	0.932778i	$0.382623\pi$
$18$	0.756173	0.178232
$19$	0.918653	0.210753	0.105377	−	0.994432i	$-0.466395\pi$
$19$	0.918653	0.210753	0.105377	+	0.994432i	$0.466395\pi$
$20$	5.73476	1.28233
$21$	−1.00000	−0.218218
$22$	−0.513649	−0.109510
$23$	8.59922	1.79306	0.896530	−	0.442983i	$-0.146080\pi$
$23$	8.59922	1.79306	0.896530	+	0.442983i	$0.146080\pi$
$24$	2.59231	0.529154
$25$	11.1232	2.22464
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−1.42820	−0.269905
$29$	−7.97866	−1.48160	−0.740800	−	0.671726i	$-0.765553\pi$
$29$	−7.97866	−1.48160	−0.740800	+	0.671726i	$0.765553\pi$
$30$	3.03631	0.554353
$31$	−3.29616	−0.592007	−0.296004	−	0.955187i	$-0.595654\pi$
$31$	−3.29616	−0.592007	−0.296004	+	0.955187i	$0.595654\pi$
$32$	5.86229	1.03632
$33$	0.679275	0.118247
$34$	2.24761	0.385462
$35$	−4.01537	−0.678721
$36$	−1.42820	−0.238034
$37$	−5.43258	−0.893110	−0.446555	−	0.894756i	$-0.647349\pi$
$37$	−5.43258	−0.893110	−0.446555	+	0.894756i	$0.647349\pi$
$38$	0.694661	0.112689
$39$	0	0
$40$	10.4091	1.64582
$41$	9.22234	1.44029	0.720144	−	0.693825i	$-0.244076\pi$
$41$	9.22234	1.44029	0.720144	+	0.693825i	$0.244076\pi$
$42$	−0.756173	−0.116680
$43$	5.06133	0.771846	0.385923	−	0.922531i	$-0.373883\pi$
$43$	5.06133	0.771846	0.385923	+	0.922531i	$0.373883\pi$
$44$	0.970141	0.146254
$45$	−4.01537	−0.598576
$46$	6.50250	0.958741
$47$	−3.03541	−0.442760	−0.221380	−	0.975188i	$-0.571056\pi$
$47$	−3.03541	−0.442760	−0.221380	+	0.975188i	$0.571056\pi$
$48$	−0.896164	−0.129350
$49$	1.00000	0.142857
$50$	8.41105	1.18950
$51$	−2.97235	−0.416212
$52$	0	0
$53$	1.32745	0.182339	0.0911695	−	0.995835i	$-0.470940\pi$
$53$	1.32745	0.182339	0.0911695	+	0.995835i	$0.470940\pi$
$54$	−0.756173	−0.102902
$55$	2.72754	0.367781
$56$	−2.59231	−0.346413
$57$	−0.918653	−0.121679
$58$	−6.03325	−0.792205
$59$	−4.83250	−0.629138	−0.314569	−	0.949235i	$-0.601860\pi$
$59$	−4.83250	−0.629138	−0.314569	+	0.949235i	$0.601860\pi$
$60$	−5.73476	−0.740354
$61$	−4.46940	−0.572247	−0.286124	−	0.958193i	$-0.592367\pi$
$61$	−4.46940	−0.572247	−0.286124	+	0.958193i	$0.592367\pi$
$62$	−2.49247	−0.316543
$63$	1.00000	0.125988
$64$	2.64058	0.330072
$65$	0	0
$66$	0.513649	0.0632259
$67$	−4.04076	−0.493658	−0.246829	−	0.969059i	$-0.579389\pi$
$67$	−4.04076	−0.493658	−0.246829	+	0.969059i	$0.579389\pi$
$68$	−4.24511	−0.514796
$69$	−8.59922	−1.03522
$70$	−3.03631	−0.362909
$71$	−2.41210	−0.286264	−0.143132	−	0.989704i	$-0.545717\pi$
$71$	−2.41210	−0.286264	−0.143132	+	0.989704i	$0.545717\pi$
$72$	−2.59231	−0.305507
$73$	7.82146	0.915433	0.457716	−	0.889098i	$-0.348668\pi$
$73$	7.82146	0.915433	0.457716	+	0.889098i	$0.348668\pi$
$74$	−4.10797	−0.477542
$75$	−11.1232	−1.28439
$76$	−1.31202	−0.150499
$77$	−0.679275	−0.0774105
$78$	0	0
$79$	16.1827	1.82069	0.910346	−	0.413848i	$-0.135815\pi$
$79$	16.1827	1.82069	0.910346	+	0.413848i	$0.135815\pi$
$80$	−3.59843	−0.402317
$81$	1.00000	0.111111
$82$	6.97369	0.770115
$83$	−4.78597	−0.525328	−0.262664	−	0.964887i	$-0.584601\pi$
$83$	−4.78597	−0.525328	−0.262664	+	0.964887i	$0.584601\pi$
$84$	1.42820	0.155830
$85$	−11.9351	−1.29454
$86$	3.82724	0.412702
$87$	7.97866	0.855402
$88$	1.76089	0.187712
$89$	−4.52542	−0.479693	−0.239847	−	0.970811i	$-0.577097\pi$
$89$	−4.52542	−0.479693	−0.239847	+	0.970811i	$0.577097\pi$
$90$	−3.03631	−0.320056
$91$	0	0
$92$	−12.2814	−1.28043
$93$	3.29616	0.341795
$94$	−2.29530	−0.236742
$95$	−3.68873	−0.378456
$96$	−5.86229	−0.598317
$97$	−8.54947	−0.868067	−0.434034	−	0.900897i	$-0.642910\pi$
$97$	−8.54947	−0.868067	−0.434034	+	0.900897i	$0.642910\pi$
$98$	0.756173	0.0763850
$99$	−0.679275	−0.0682697
$100$	−15.8861	−1.58861
$101$	−13.4484	−1.33816	−0.669080	−	0.743190i	$-0.733312\pi$
$101$	−13.4484	−1.33816	−0.669080	+	0.743190i	$0.733312\pi$
$102$	−2.24761	−0.222547
$103$	−12.9919	−1.28013	−0.640066	−	0.768320i	$-0.721093\pi$
$103$	−12.9919	−1.28013	−0.640066	+	0.768320i	$0.721093\pi$
$104$	0	0
$105$	4.01537	0.391860
$106$	1.00378	0.0974958
$107$	−6.04327	−0.584225	−0.292113	−	0.956384i	$-0.594358\pi$
$107$	−6.04327	−0.584225	−0.292113	+	0.956384i	$0.594358\pi$
$108$	1.42820	0.137429
$109$	18.1361	1.73712	0.868561	−	0.495582i	$-0.165045\pi$
$109$	18.1361	1.73712	0.868561	+	0.495582i	$0.165045\pi$
$110$	2.06249	0.196651
$111$	5.43258	0.515637
$112$	0.896164	0.0846795
$113$	−20.5748	−1.93551	−0.967756	−	0.251888i	$-0.918948\pi$
$113$	−20.5748	−1.93551	−0.967756	+	0.251888i	$0.918948\pi$
$114$	−0.694661	−0.0650609
$115$	−34.5290	−3.21985
$116$	11.3951	1.05801
$117$	0	0
$118$	−3.65421	−0.336397
$119$	2.97235	0.272475
$120$	−10.4091	−0.950216
$121$	−10.5386	−0.958053
$122$	−3.37964	−0.305978
$123$	−9.22234	−0.831551
$124$	4.70758	0.422753
$125$	−24.5868	−2.19911
$126$	0.756173	0.0673653
$127$	19.7663	1.75398	0.876989	−	0.480510i	$-0.159548\pi$
$127$	19.7663	1.75398	0.876989	+	0.480510i	$0.159548\pi$
$128$	−9.72784	−0.859827
$129$	−5.06133	−0.445625
$130$	0	0
$131$	−7.92094	−0.692056	−0.346028	−	0.938224i	$-0.612470\pi$
$131$	−7.92094	−0.692056	−0.346028	+	0.938224i	$0.612470\pi$
$132$	−0.970141	−0.0844399
$133$	0.918653	0.0796573
$134$	−3.05552	−0.263957
$135$	4.01537	0.345588
$136$	−7.70526	−0.660721
$137$	−9.75434	−0.833370	−0.416685	−	0.909051i	$-0.636808\pi$
$137$	−9.75434	−0.833370	−0.416685	+	0.909051i	$0.636808\pi$
$138$	−6.50250	−0.553529
$139$	−12.2334	−1.03762	−0.518812	−	0.854888i	$-0.673626\pi$
$139$	−12.2334	−1.03762	−0.518812	+	0.854888i	$0.673626\pi$
$140$	5.73476	0.484675
$141$	3.03541	0.255628
$142$	−1.82397	−0.153064
$143$	0	0
$144$	0.896164	0.0746803
$145$	32.0373	2.66055
$146$	5.91438	0.489478
$147$	−1.00000	−0.0824786
$148$	7.75881	0.637771
$149$	−5.98537	−0.490340	−0.245170	−	0.969480i	$-0.578844\pi$
$149$	−5.98537	−0.490340	−0.245170	+	0.969480i	$0.578844\pi$
$150$	−8.41105	−0.686760
$151$	13.1858	1.07304	0.536521	−	0.843887i	$-0.319738\pi$
$151$	13.1858	1.07304	0.536521	+	0.843887i	$0.319738\pi$
$152$	−2.38144	−0.193160
$153$	2.97235	0.240300
$154$	−0.513649	−0.0413910
$155$	13.2353	1.06308
$156$	0	0
$157$	11.0004	0.877928	0.438964	−	0.898505i	$-0.355346\pi$
$157$	11.0004	0.877928	0.438964	+	0.898505i	$0.355346\pi$
$158$	12.2369	0.973516
$159$	−1.32745	−0.105273
$160$	−23.5392	−1.86094
$161$	8.59922	0.677713
$162$	0.756173	0.0594106
$163$	−6.94883	−0.544274	−0.272137	−	0.962258i	$-0.587730\pi$
$163$	−6.94883	−0.544274	−0.272137	+	0.962258i	$0.587730\pi$
$164$	−13.1714	−1.02851
$165$	−2.72754	−0.212339
$166$	−3.61902	−0.280891
$167$	−2.59708	−0.200968	−0.100484	−	0.994939i	$-0.532039\pi$
$167$	−2.59708	−0.200968	−0.100484	+	0.994939i	$0.532039\pi$
$168$	2.59231	0.200001
$169$	0	0
$170$	−9.02498	−0.692185
$171$	0.918653	0.0702511
$172$	−7.22860	−0.551176
$173$	−3.75296	−0.285332	−0.142666	−	0.989771i	$-0.545568\pi$
$173$	−3.75296	−0.285332	−0.142666	+	0.989771i	$0.545568\pi$
$174$	6.03325	0.457380
$175$	11.1232	0.840834
$176$	−0.608741	−0.0458856
$177$	4.83250	0.363233
$178$	−3.42200	−0.256490
$179$	19.2089	1.43574	0.717869	−	0.696178i	$-0.245118\pi$
$179$	19.2089	1.43574	0.717869	+	0.696178i	$0.245118\pi$
$180$	5.73476	0.427443
$181$	5.21963	0.387972	0.193986	−	0.981004i	$-0.437858\pi$
$181$	5.21963	0.387972	0.193986	+	0.981004i	$0.437858\pi$
$182$	0	0
$183$	4.46940	0.330387
$184$	−22.2919	−1.64338
$185$	21.8138	1.60378
$186$	2.49247	0.182756
$187$	−2.01904	−0.147647
$188$	4.33518	0.316176
$189$	−1.00000	−0.0727393
$190$	−2.78932	−0.202358
$191$	0.587605	0.0425176	0.0212588	−	0.999774i	$-0.493233\pi$
$191$	0.587605	0.0425176	0.0212588	+	0.999774i	$0.493233\pi$
$192$	−2.64058	−0.190567
$193$	14.9502	1.07614	0.538070	−	0.842900i	$-0.319154\pi$
$193$	14.9502	1.07614	0.538070	+	0.842900i	$0.319154\pi$
$194$	−6.46488	−0.464151
$195$	0	0
$196$	−1.42820	−0.102014
$197$	−21.0291	−1.49826	−0.749130	−	0.662423i	$-0.769528\pi$
$197$	−21.0291	−1.49826	−0.749130	+	0.662423i	$0.769528\pi$
$198$	−0.513649	−0.0365035
$199$	26.1787	1.85576	0.927879	−	0.372882i	$-0.121630\pi$
$199$	26.1787	1.85576	0.927879	+	0.372882i	$0.121630\pi$
$200$	−28.8348	−2.03893
$201$	4.04076	0.285014
$202$	−10.1693	−0.715508
$203$	−7.97866	−0.559992
$204$	4.24511	0.297217
$205$	−37.0311	−2.58636
$206$	−9.82414	−0.684480
$207$	8.59922	0.597687
$208$	0	0
$209$	−0.624017	−0.0431642
$210$	3.03631	0.209526
$211$	12.1928	0.839388	0.419694	−	0.907666i	$-0.362137\pi$
$211$	12.1928	0.839388	0.419694	+	0.907666i	$0.362137\pi$
$212$	−1.89586	−0.130208
$213$	2.41210	0.165274
$214$	−4.56976	−0.312382
$215$	−20.3231	−1.38602
$216$	2.59231	0.176385
$217$	−3.29616	−0.223758
$218$	13.7140	0.928831
$219$	−7.82146	−0.528525
$220$	−3.89547	−0.262633
$221$	0	0
$222$	4.10797	0.275709
$223$	−7.51986	−0.503567	−0.251784	−	0.967784i	$-0.581017\pi$
$223$	−7.51986	−0.503567	−0.251784	+	0.967784i	$0.581017\pi$
$224$	5.86229	0.391690
$225$	11.1232	0.741546
$226$	−15.5581	−1.03491
$227$	−24.8114	−1.64679	−0.823394	−	0.567470i	$-0.807922\pi$
$227$	−24.8114	−1.64679	−0.823394	+	0.567470i	$0.807922\pi$
$228$	1.31202	0.0868907
$229$	−8.08968	−0.534581	−0.267290	−	0.963616i	$-0.586128\pi$
$229$	−8.08968	−0.534581	−0.267290	+	0.963616i	$0.586128\pi$
$230$	−26.1099	−1.72164
$231$	0.679275	0.0446930
$232$	20.6832	1.35792
$233$	−2.29275	−0.150203	−0.0751014	−	0.997176i	$-0.523928\pi$
$233$	−2.29275	−0.150203	−0.0751014	+	0.997176i	$0.523928\pi$
$234$	0	0
$235$	12.1883	0.795077
$236$	6.90179	0.449268
$237$	−16.1827	−1.05118
$238$	2.24761	0.145691
$239$	0.000676538 0	4.37616e−5 0	2.18808e−5	−	1.00000i	$-0.499993\pi$
$239$	0.000676538 0	4.37616e−5 0	2.18808e−5		1.00000i	$0.499993\pi$
$240$	3.59843	0.232278
$241$	−18.7495	−1.20776	−0.603881	−	0.797074i	$-0.706380\pi$
$241$	−18.7495	−1.20776	−0.603881	+	0.797074i	$0.706380\pi$
$242$	−7.96900	−0.512267
$243$	−1.00000	−0.0641500
$244$	6.38320	0.408642
$245$	−4.01537	−0.256532
$246$	−6.97369	−0.444626
$247$	0	0
$248$	8.54467	0.542587
$249$	4.78597	0.303298
$250$	−18.5919	−1.17586
$251$	6.42817	0.405742	0.202871	−	0.979205i	$-0.434973\pi$
$251$	6.42817	0.405742	0.202871	+	0.979205i	$0.434973\pi$
$252$	−1.42820	−0.0899683
$253$	−5.84123	−0.367235
$254$	14.9468	0.937844
$255$	11.9351	0.747403
$256$	−12.6371	−0.789818
$257$	−2.11002	−0.131619	−0.0658096	−	0.997832i	$-0.520963\pi$
$257$	−2.11002	−0.131619	−0.0658096	+	0.997832i	$0.520963\pi$
$258$	−3.82724	−0.238274
$259$	−5.43258	−0.337564
$260$	0	0
$261$	−7.97866	−0.493867
$262$	−5.98961	−0.370039
$263$	−17.5276	−1.08080	−0.540399	−	0.841409i	$-0.681727\pi$
$263$	−17.5276	−1.08080	−0.540399	+	0.841409i	$0.681727\pi$
$264$	−1.76089	−0.108376
$265$	−5.33019	−0.327431
$266$	0.694661	0.0425924
$267$	4.52542	0.276951
$268$	5.77103	0.352522
$269$	27.0426	1.64882	0.824408	−	0.565995i	$-0.191508\pi$
$269$	27.0426	1.64882	0.824408	+	0.565995i	$0.191508\pi$
$270$	3.03631	0.184784
$271$	−16.2920	−0.989666	−0.494833	−	0.868988i	$-0.664771\pi$
$271$	−16.2920	−0.989666	−0.494833	+	0.868988i	$0.664771\pi$
$272$	2.66371	0.161511
$273$	0	0
$274$	−7.37597	−0.445599
$275$	−7.55569	−0.455626
$276$	12.2814	0.739254
$277$	28.0719	1.68668	0.843338	−	0.537384i	$-0.180587\pi$
$277$	28.0719	1.68668	0.843338	+	0.537384i	$0.180587\pi$
$278$	−9.25058	−0.554813
$279$	−3.29616	−0.197336
$280$	10.4091	0.622063
$281$	−8.95674	−0.534314	−0.267157	−	0.963653i	$-0.586084\pi$
$281$	−8.95674	−0.534314	−0.267157	+	0.963653i	$0.586084\pi$
$282$	2.29530	0.136683
$283$	−5.03954	−0.299569	−0.149785	−	0.988719i	$-0.547858\pi$
$283$	−5.03954	−0.299569	−0.149785	+	0.988719i	$0.547858\pi$
$284$	3.44497	0.204421
$285$	3.68873	0.218501
$286$	0	0
$287$	9.22234	0.544378
$288$	5.86229	0.345438
$289$	−8.16515	−0.480303
$290$	24.2257	1.42258
$291$	8.54947	0.501179
$292$	−11.1706	−0.653711
$293$	−4.92561	−0.287757	−0.143879	−	0.989595i	$-0.545957\pi$
$293$	−4.92561	−0.287757	−0.143879	+	0.989595i	$0.545957\pi$
$294$	−0.756173	−0.0441009
$295$	19.4043	1.12976
$296$	14.0829	0.818555
$297$	0.679275	0.0394155
$298$	−4.52598	−0.262183
$299$	0	0
$300$	15.8861	0.917187
$301$	5.06133	0.291730
$302$	9.97073	0.573751
$303$	13.4484	0.772588
$304$	0.823263	0.0472174
$305$	17.9463	1.02760
$306$	2.24761	0.128487
$307$	−11.2027	−0.639371	−0.319685	−	0.947524i	$-0.603577\pi$
$307$	−11.2027	−0.639371	−0.319685	+	0.947524i	$0.603577\pi$
$308$	0.970141	0.0552789
$309$	12.9919	0.739084
$310$	10.0082	0.568426
$311$	9.44321	0.535475	0.267738	−	0.963492i	$-0.413724\pi$
$311$	9.44321	0.535475	0.267738	+	0.963492i	$0.413724\pi$
$312$	0	0
$313$	−28.0752	−1.58690	−0.793451	−	0.608634i	$-0.791718\pi$
$313$	−28.0752	−1.58690	−0.793451	+	0.608634i	$0.791718\pi$
$314$	8.31821	0.469424
$315$	−4.01537	−0.226240
$316$	−23.1121	−1.30016
$317$	8.48965	0.476826	0.238413	−	0.971164i	$-0.423373\pi$
$317$	8.48965	0.476826	0.238413	+	0.971164i	$0.423373\pi$
$318$	−1.00378	−0.0562892
$319$	5.41970	0.303445
$320$	−10.6029	−0.592719
$321$	6.04327	0.337303
$322$	6.50250	0.362370
$323$	2.73056	0.151932
$324$	−1.42820	−0.0793445
$325$	0	0
$326$	−5.25452	−0.291021
$327$	−18.1361	−1.00293
$328$	−23.9072	−1.32006
$329$	−3.03541	−0.167348
$330$	−2.06249	−0.113536
$331$	−31.6062	−1.73723	−0.868617	−	0.495484i	$-0.834991\pi$
$331$	−31.6062	−1.73723	−0.868617	+	0.495484i	$0.834991\pi$
$332$	6.83533	0.375137
$333$	−5.43258	−0.297703
$334$	−1.96384	−0.107457
$335$	16.2252	0.886475
$336$	−0.896164	−0.0488898
$337$	−3.80886	−0.207482	−0.103741	−	0.994604i	$-0.533081\pi$
$337$	−3.80886	−0.207482	−0.103741	+	0.994604i	$0.533081\pi$
$338$	0	0
$339$	20.5748	1.11747
$340$	17.0457	0.924432
$341$	2.23899	0.121248
$342$	0.694661	0.0375629
$343$	1.00000	0.0539949
$344$	−13.1206	−0.707414
$345$	34.5290	1.85898
$346$	−2.83789	−0.152566
$347$	−16.0224	−0.860126	−0.430063	−	0.902799i	$-0.641509\pi$
$347$	−16.0224	−0.860126	−0.430063	+	0.902799i	$0.641509\pi$
$348$	−11.3951	−0.610843
$349$	12.3031	0.658568	0.329284	−	0.944231i	$-0.393193\pi$
$349$	12.3031	0.658568	0.329284	+	0.944231i	$0.393193\pi$
$350$	8.41105	0.449590
$351$	0	0
$352$	−3.98210	−0.212247
$353$	−32.1574	−1.71156	−0.855782	−	0.517337i	$-0.826923\pi$
$353$	−32.1574	−1.71156	−0.855782	+	0.517337i	$0.826923\pi$
$354$	3.65421	0.194219
$355$	9.68547	0.514051
$356$	6.46321	0.342549
$357$	−2.97235	−0.157313
$358$	14.5252	0.767682
$359$	26.7993	1.41441	0.707207	−	0.707006i	$-0.249955\pi$
$359$	26.7993	1.41441	0.707207	+	0.707006i	$0.249955\pi$
$360$	10.4091	0.548608
$361$	−18.1561	−0.955583
$362$	3.94694	0.207447
$363$	10.5386	0.553132
$364$	0	0
$365$	−31.4060	−1.64387
$366$	3.37964	0.176657
$367$	5.51238	0.287744	0.143872	−	0.989596i	$-0.454045\pi$
$367$	5.51238	0.287744	0.143872	+	0.989596i	$0.454045\pi$
$368$	7.70631	0.401719
$369$	9.22234	0.480096
$370$	16.4950	0.857535
$371$	1.32745	0.0689176
$372$	−4.70758	−0.244076
$373$	17.4569	0.903886	0.451943	−	0.892047i	$-0.350731\pi$
$373$	17.4569	0.903886	0.451943	+	0.892047i	$0.350731\pi$
$374$	−1.52674	−0.0789461
$375$	24.5868	1.26966
$376$	7.86874	0.405800
$377$	0	0
$378$	−0.756173	−0.0388934
$379$	7.23186	0.371476	0.185738	−	0.982599i	$-0.440532\pi$
$379$	7.23186	0.371476	0.185738	+	0.982599i	$0.440532\pi$
$380$	5.26825	0.270255
$381$	−19.7663	−1.01266
$382$	0.444331	0.0227340
$383$	16.4130	0.838665	0.419333	−	0.907833i	$-0.362264\pi$
$383$	16.4130	0.838665	0.419333	+	0.907833i	$0.362264\pi$
$384$	9.72784	0.496422
$385$	2.72754	0.139008
$386$	11.3050	0.575407
$387$	5.06133	0.257282
$388$	12.2104	0.619888
$389$	20.7408	1.05160	0.525800	−	0.850608i	$-0.323766\pi$
$389$	20.7408	1.05160	0.525800	+	0.850608i	$0.323766\pi$
$390$	0	0
$391$	25.5599	1.29262
$392$	−2.59231	−0.130932
$393$	7.92094	0.399559
$394$	−15.9016	−0.801113
$395$	−64.9794	−3.26947
$396$	0.970141	0.0487514
$397$	6.59996	0.331242	0.165621	−	0.986189i	$-0.447037\pi$
$397$	6.59996	0.331242	0.165621	+	0.986189i	$0.447037\pi$
$398$	19.7956	0.992265
$399$	−0.918653	−0.0459902
$400$	9.96820	0.498410
$401$	−35.8498	−1.79025	−0.895126	−	0.445813i	$-0.852915\pi$
$401$	−35.8498	−1.79025	−0.895126	+	0.445813i	$0.852915\pi$
$402$	3.05552	0.152395
$403$	0	0
$404$	19.2070	0.955582
$405$	−4.01537	−0.199525
$406$	−6.03325	−0.299425
$407$	3.69021	0.182917
$408$	7.70526	0.381467
$409$	−15.4396	−0.763441	−0.381721	−	0.924278i	$-0.624668\pi$
$409$	−15.4396	−0.763441	−0.381721	+	0.924278i	$0.624668\pi$
$410$	−28.0019	−1.38292
$411$	9.75434	0.481146
$412$	18.5551	0.914143
$413$	−4.83250	−0.237792
$414$	6.50250	0.319580
$415$	19.2174	0.943346
$416$	0	0
$417$	12.2334	0.599073
$418$	−0.471865	−0.0230797
$419$	−11.2657	−0.550365	−0.275183	−	0.961392i	$-0.588738\pi$
$419$	−11.2657	−0.550365	−0.275183	+	0.961392i	$0.588738\pi$
$420$	−5.73476	−0.279827
$421$	1.85065	0.0901953	0.0450976	−	0.998983i	$-0.485640\pi$
$421$	1.85065	0.0901953	0.0450976	+	0.998983i	$0.485640\pi$
$422$	9.21988	0.448817
$423$	−3.03541	−0.147587
$424$	−3.44116	−0.167118
$425$	33.0620	1.60374
$426$	1.82397	0.0883714
$427$	−4.46940	−0.216289
$428$	8.63101	0.417196
$429$	0	0
$430$	−15.3678	−0.741101
$431$	−14.3083	−0.689204	−0.344602	−	0.938749i	$-0.611986\pi$
$431$	−14.3083	−0.689204	−0.344602	+	0.938749i	$0.611986\pi$
$432$	−0.896164	−0.0431167
$433$	−25.3730	−1.21935	−0.609674	−	0.792652i	$-0.708700\pi$
$433$	−25.3730	−1.21935	−0.609674	+	0.792652i	$0.708700\pi$
$434$	−2.49247	−0.119642
$435$	−32.0373	−1.53607
$436$	−25.9020	−1.24048
$437$	7.89969	0.377893
$438$	−5.91438	−0.282600
$439$	−28.6525	−1.36751	−0.683754	−	0.729713i	$-0.739654\pi$
$439$	−28.6525	−1.36751	−0.683754	+	0.729713i	$0.739654\pi$
$440$	−7.07064	−0.337079
$441$	1.00000	0.0476190
$442$	0	0
$443$	0.854762	0.0406110	0.0203055	−	0.999794i	$-0.493536\pi$
$443$	0.854762	0.0406110	0.0203055	+	0.999794i	$0.493536\pi$
$444$	−7.75881	−0.368217
$445$	18.1712	0.861398
$446$	−5.68632	−0.269255
$447$	5.98537	0.283098
$448$	2.64058	0.124755
$449$	−4.34533	−0.205069	−0.102534	−	0.994729i	$-0.532695\pi$
$449$	−4.34533	−0.205069	−0.102534	+	0.994729i	$0.532695\pi$
$450$	8.41105	0.396501
$451$	−6.26450	−0.294984
$452$	29.3849	1.38215
$453$	−13.1858	−0.619522
$454$	−18.7617	−0.880530
$455$	0	0
$456$	2.38144	0.111521
$457$	29.9203	1.39961	0.699806	−	0.714333i	$-0.253270\pi$
$457$	29.9203	1.39961	0.699806	+	0.714333i	$0.253270\pi$
$458$	−6.11720	−0.285838
$459$	−2.97235	−0.138737
$460$	49.3144	2.29930
$461$	−21.5390	−1.00317	−0.501586	−	0.865108i	$-0.667250\pi$
$461$	−21.5390	−1.00317	−0.501586	+	0.865108i	$0.667250\pi$
$462$	0.513649	0.0238971
$463$	−15.6213	−0.725984	−0.362992	−	0.931792i	$-0.618245\pi$
$463$	−15.6213	−0.725984	−0.362992	+	0.931792i	$0.618245\pi$
$464$	−7.15019	−0.331939
$465$	−13.2353	−0.613771
$466$	−1.73371	−0.0803127
$467$	39.7675	1.84022	0.920109	−	0.391662i	$-0.128100\pi$
$467$	39.7675	1.84022	0.920109	+	0.391662i	$0.128100\pi$
$468$	0	0
$469$	−4.04076	−0.186585
$470$	9.21647	0.425124
$471$	−11.0004	−0.506872
$472$	12.5274	0.576619
$473$	−3.43803	−0.158081
$474$	−12.2369	−0.562059
$475$	10.2183	0.468850
$476$	−4.24511	−0.194574
$477$	1.32745	0.0607797
$478$	0.000511580 0	2.33991e−5 0
$479$	34.9676	1.59771	0.798855	−	0.601523i	$-0.205439\pi$
$479$	34.9676	1.59771	0.798855	+	0.601523i	$0.205439\pi$
$480$	23.5392	1.07441
$481$	0	0
$482$	−14.1779	−0.645785
$483$	−8.59922	−0.391278
$484$	15.0512	0.684147
$485$	34.3293	1.55881
$486$	−0.756173	−0.0343007
$487$	25.1459	1.13947	0.569735	−	0.821829i	$-0.307046\pi$
$487$	25.1459	1.13947	0.569735	+	0.821829i	$0.307046\pi$
$488$	11.5861	0.524477
$489$	6.94883	0.314237
$490$	−3.03631	−0.137167
$491$	−2.42782	−0.109566	−0.0547830	−	0.998498i	$-0.517447\pi$
$491$	−2.42782	−0.109566	−0.0547830	+	0.998498i	$0.517447\pi$
$492$	13.1714	0.593811
$493$	−23.7154	−1.06809
$494$	0	0
$495$	2.72754	0.122594
$496$	−2.95390	−0.132634
$497$	−2.41210	−0.108197
$498$	3.61902	0.162172
$499$	−1.45843	−0.0652881	−0.0326440	−	0.999467i	$-0.510393\pi$
$499$	−1.45843	−0.0652881	−0.0326440	+	0.999467i	$0.510393\pi$
$500$	35.1150	1.57039
$501$	2.59708	0.116029
$502$	4.86081	0.216949
$503$	−12.4090	−0.553292	−0.276646	−	0.960972i	$-0.589223\pi$
$503$	−12.4090	−0.553292	−0.276646	+	0.960972i	$0.589223\pi$
$504$	−2.59231	−0.115471
$505$	54.0001	2.40297
$506$	−4.41698	−0.196359
$507$	0	0
$508$	−28.2303	−1.25252
$509$	−3.54760	−0.157245	−0.0786224	−	0.996904i	$-0.525052\pi$
$509$	−3.54760	−0.157245	−0.0786224	+	0.996904i	$0.525052\pi$
$510$	9.02498	0.399633
$511$	7.82146	0.346001
$512$	9.89985	0.437516
$513$	−0.918653	−0.0405595
$514$	−1.59554	−0.0703762
$515$	52.1673	2.29877
$516$	7.22860	0.318222
$517$	2.06188	0.0906813
$518$	−4.10797	−0.180494
$519$	3.75296	0.164737
$520$	0	0
$521$	−27.9069	−1.22262	−0.611312	−	0.791390i	$-0.709358\pi$
$521$	−27.9069	−1.22262	−0.611312	+	0.791390i	$0.709358\pi$
$522$	−6.03325	−0.264068
$523$	−11.4090	−0.498881	−0.249441	−	0.968390i	$-0.580247\pi$
$523$	−11.4090	−0.498881	−0.249441	+	0.968390i	$0.580247\pi$
$524$	11.3127	0.494198
$525$	−11.1232	−0.485456
$526$	−13.2539	−0.577898
$527$	−9.79732	−0.426778
$528$	0.608741	0.0264921
$529$	50.9465	2.21507
$530$	−4.03055	−0.175076
$531$	−4.83250	−0.209713
$532$	−1.31202	−0.0568833
$533$	0	0
$534$	3.42200	0.148084
$535$	24.2660	1.04911
$536$	10.4749	0.452448
$537$	−19.2089	−0.828924
$538$	20.4489	0.881615
$539$	−0.679275	−0.0292584
$540$	−5.73476	−0.246785
$541$	0.700149	0.0301018	0.0150509	−	0.999887i	$-0.495209\pi$
$541$	0.700149	0.0301018	0.0150509	+	0.999887i	$0.495209\pi$
$542$	−12.3195	−0.529170
$543$	−5.21963	−0.223996
$544$	17.4248	0.747080
$545$	−72.8231	−3.11940
$546$	0	0
$547$	−21.4832	−0.918557	−0.459278	−	0.888292i	$-0.651892\pi$
$547$	−21.4832	−0.918557	−0.459278	+	0.888292i	$0.651892\pi$
$548$	13.9312	0.595110
$549$	−4.46940	−0.190749
$550$	−5.71342	−0.243621
$551$	−7.32962	−0.312252
$552$	22.2919	0.948805
$553$	16.1827	0.688157
$554$	21.2272	0.901857
$555$	−21.8138	−0.925944
$556$	17.4718	0.740969
$557$	15.6547	0.663313	0.331656	−	0.943400i	$-0.392393\pi$
$557$	15.6547	0.663313	0.331656	+	0.943400i	$0.392393\pi$
$558$	−2.49247	−0.105514
$559$	0	0
$560$	−3.59843	−0.152061
$561$	2.01904	0.0852440
$562$	−6.77285	−0.285695
$563$	−21.4938	−0.905854	−0.452927	−	0.891548i	$-0.649620\pi$
$563$	−21.4938	−0.905854	−0.452927	+	0.891548i	$0.649620\pi$
$564$	−4.33518	−0.182544
$565$	82.6153	3.47565
$566$	−3.81076	−0.160178
$567$	1.00000	0.0419961
$568$	6.25292	0.262367
$569$	6.10679	0.256010	0.128005	−	0.991774i	$-0.459143\pi$
$569$	6.10679	0.256010	0.128005	+	0.991774i	$0.459143\pi$
$570$	2.78932	0.116832
$571$	−4.49229	−0.187996	−0.0939982	−	0.995572i	$-0.529965\pi$
$571$	−4.49229	−0.187996	−0.0939982	+	0.995572i	$0.529965\pi$
$572$	0	0
$573$	−0.587605	−0.0245475
$574$	6.97369	0.291076
$575$	95.6506	3.98891
$576$	2.64058	0.110024
$577$	8.80521	0.366566	0.183283	−	0.983060i	$-0.441328\pi$
$577$	8.80521	0.366566	0.183283	+	0.983060i	$0.441328\pi$
$578$	−6.17427	−0.256816
$579$	−14.9502	−0.621310
$580$	−45.7557	−1.89990
$581$	−4.78597	−0.198555
$582$	6.46488	0.267978
$583$	−0.901701	−0.0373447
$584$	−20.2757	−0.839014
$585$	0	0
$586$	−3.72461	−0.153862
$587$	−24.4210	−1.00796	−0.503981	−	0.863715i	$-0.668132\pi$
$587$	−24.4210	−1.00796	−0.503981	+	0.863715i	$0.668132\pi$
$588$	1.42820	0.0588980
$589$	−3.02802	−0.124767
$590$	14.6730	0.604078
$591$	21.0291	0.865021
$592$	−4.86848	−0.200093
$593$	−16.0560	−0.659340	−0.329670	−	0.944096i	$-0.606937\pi$
$593$	−16.0560	−0.659340	−0.329670	+	0.944096i	$0.606937\pi$
$594$	0.513649	0.0210753
$595$	−11.9351	−0.489290
$596$	8.54831	0.350153
$597$	−26.1787	−1.07142
$598$	0	0
$599$	−11.3129	−0.462231	−0.231116	−	0.972926i	$-0.574238\pi$
$599$	−11.3129	−0.462231	−0.231116	+	0.972926i	$0.574238\pi$
$600$	28.8348	1.17718
$601$	1.56416	0.0638035	0.0319018	−	0.999491i	$-0.489844\pi$
$601$	1.56416	0.0638035	0.0319018	+	0.999491i	$0.489844\pi$
$602$	3.82724	0.155987
$603$	−4.04076	−0.164553
$604$	−18.8319	−0.766261
$605$	42.3163	1.72040
$606$	10.1693	0.413099
$607$	−38.3912	−1.55825	−0.779126	−	0.626867i	$-0.784337\pi$
$607$	−38.3912	−1.55825	−0.779126	+	0.626867i	$0.784337\pi$
$608$	5.38540	0.218407
$609$	7.97866	0.323312
$610$	13.5705	0.549453
$611$	0	0
$612$	−4.24511	−0.171599
$613$	−4.31167	−0.174147	−0.0870734	−	0.996202i	$-0.527751\pi$
$613$	−4.31167	−0.174147	−0.0870734	+	0.996202i	$0.527751\pi$
$614$	−8.47117	−0.341868
$615$	37.0311	1.49324
$616$	1.76089	0.0709484
$617$	21.7901	0.877235	0.438618	−	0.898674i	$-0.355468\pi$
$617$	21.7901	0.877235	0.438618	+	0.898674i	$0.355468\pi$
$618$	9.82414	0.395185
$619$	19.3477	0.777648	0.388824	−	0.921312i	$-0.372881\pi$
$619$	19.3477	0.777648	0.388824	+	0.921312i	$0.372881\pi$
$620$	−18.9026	−0.759149
$621$	−8.59922	−0.345075
$622$	7.14070	0.286316
$623$	−4.52542	−0.181307
$624$	0	0
$625$	43.1093	1.72437
$626$	−21.2297	−0.848509
$627$	0.624017	0.0249209
$628$	−15.7108	−0.626929
$629$	−16.1475	−0.643843
$630$	−3.03631	−0.120970
$631$	−42.2424	−1.68164	−0.840821	−	0.541313i	$-0.817928\pi$
$631$	−42.2424	−1.68164	−0.840821	+	0.541313i	$0.817928\pi$
$632$	−41.9506	−1.66870
$633$	−12.1928	−0.484621
$634$	6.41965	0.254957
$635$	−79.3691	−3.14967
$636$	1.89586	0.0751759
$637$	0	0
$638$	4.09823	0.162251
$639$	−2.41210	−0.0954212
$640$	39.0608	1.54402
$641$	−13.6797	−0.540315	−0.270157	−	0.962816i	$-0.587076\pi$
$641$	−13.6797	−0.540315	−0.270157	+	0.962816i	$0.587076\pi$
$642$	4.56976	0.180354
$643$	26.5143	1.04562	0.522810	−	0.852449i	$-0.324884\pi$
$643$	26.5143	1.04562	0.522810	+	0.852449i	$0.324884\pi$
$644$	−12.2814	−0.483956
$645$	20.3231	0.800222
$646$	2.06477	0.0812374
$647$	−0.218510	−0.00859053	−0.00429526	−	0.999991i	$-0.501367\pi$
$647$	−0.218510	−0.00859053	−0.00429526	+	0.999991i	$0.501367\pi$
$648$	−2.59231	−0.101836
$649$	3.28260	0.128853
$650$	0	0
$651$	3.29616	0.129187
$652$	9.92433	0.388667
$653$	−6.10489	−0.238903	−0.119451	−	0.992840i	$-0.538114\pi$
$653$	−6.10489	−0.238903	−0.119451	+	0.992840i	$0.538114\pi$
$654$	−13.7140	−0.536261
$655$	31.8055	1.24274
$656$	8.26473	0.322684
$657$	7.82146	0.305144
$658$	−2.29530	−0.0894800
$659$	−6.61310	−0.257610	−0.128805	−	0.991670i	$-0.541114\pi$
$659$	−6.61310	−0.257610	−0.128805	+	0.991670i	$0.541114\pi$
$660$	3.89547	0.151631
$661$	14.2706	0.555061	0.277530	−	0.960717i	$-0.410484\pi$
$661$	14.2706	0.555061	0.277530	+	0.960717i	$0.410484\pi$
$662$	−23.8998	−0.928891
$663$	0	0
$664$	12.4067	0.481475
$665$	−3.68873	−0.143043
$666$	−4.10797	−0.159181
$667$	−68.6102	−2.65660
$668$	3.70915	0.143511
$669$	7.51986	0.290735
$670$	12.2690	0.473994
$671$	3.03595	0.117201
$672$	−5.86229	−0.226143
$673$	−26.6850	−1.02863	−0.514316	−	0.857600i	$-0.671954\pi$
$673$	−26.6850	−1.02863	−0.514316	+	0.857600i	$0.671954\pi$
$674$	−2.88016	−0.110940
$675$	−11.1232	−0.428132
$676$	0	0
$677$	−2.49411	−0.0958565	−0.0479282	−	0.998851i	$-0.515262\pi$
$677$	−2.49411	−0.0958565	−0.0479282	+	0.998851i	$0.515262\pi$
$678$	15.5581	0.597505
$679$	−8.54947	−0.328099
$680$	30.9395	1.18647
$681$	24.8114	0.950774
$682$	1.69307	0.0648309
$683$	−1.94415	−0.0743907	−0.0371954	−	0.999308i	$-0.511842\pi$
$683$	−1.94415	−0.0743907	−0.0371954	+	0.999308i	$0.511842\pi$
$684$	−1.31202	−0.0501664
$685$	39.1673	1.49650
$686$	0.756173	0.0288708
$687$	8.08968	0.308640
$688$	4.53578	0.172925
$689$	0	0
$690$	26.1099	0.993988
$691$	−33.1616	−1.26153	−0.630763	−	0.775976i	$-0.717258\pi$
$691$	−33.1616	−1.26153	−0.630763	+	0.775976i	$0.717258\pi$
$692$	5.35998	0.203756
$693$	−0.679275	−0.0258035
$694$	−12.1157	−0.459905
$695$	49.1217	1.86329
$696$	−20.6832	−0.783995
$697$	27.4120	1.03830
$698$	9.30324	0.352133
$699$	2.29275	0.0867196
$700$	−15.8861	−0.600440
$701$	−11.6757	−0.440986	−0.220493	−	0.975389i	$-0.570767\pi$
$701$	−11.6757	−0.440986	−0.220493	+	0.975389i	$0.570767\pi$
$702$	0	0
$703$	−4.99065	−0.188226
$704$	−1.79368	−0.0676017
$705$	−12.1883	−0.459038
$706$	−24.3165	−0.915165
$707$	−13.4484	−0.505777
$708$	−6.90179	−0.259385
$709$	−37.6669	−1.41461	−0.707305	−	0.706908i	$-0.750089\pi$
$709$	−37.6669	−1.41461	−0.707305	+	0.706908i	$0.750089\pi$
$710$	7.32390	0.274861
$711$	16.1827	0.606897
$712$	11.7313	0.439649
$713$	−28.3444	−1.06150
$714$	−2.24761	−0.0841147
$715$	0	0
$716$	−27.4341	−1.02526
$717$	−0.000676538 0	−2.52658e−5 0
$718$	20.2649	0.756281
$719$	−11.3956	−0.424986	−0.212493	−	0.977163i	$-0.568158\pi$
$719$	−11.3956	−0.424986	−0.212493	+	0.977163i	$0.568158\pi$
$720$	−3.59843	−0.134106
$721$	−12.9919	−0.483844
$722$	−13.7291	−0.510946
$723$	18.7495	0.697302
$724$	−7.45468	−0.277051
$725$	−88.7481	−3.29602
$726$	7.96900	0.295757
$727$	−4.63125	−0.171764	−0.0858818	−	0.996305i	$-0.527371\pi$
$727$	−4.63125	−0.171764	−0.0858818	+	0.996305i	$0.527371\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−23.7484	−0.878968
$731$	15.0440	0.556424
$732$	−6.38320	−0.235930
$733$	6.56888	0.242627	0.121314	−	0.992614i	$-0.461289\pi$
$733$	6.56888	0.242627	0.121314	+	0.992614i	$0.461289\pi$
$734$	4.16831	0.153855
$735$	4.01537	0.148109
$736$	50.4111	1.85818
$737$	2.74479	0.101106
$738$	6.97369	0.256705
$739$	−36.2153	−1.33220	−0.666100	−	0.745862i	$-0.732038\pi$
$739$	−36.2153	−1.33220	−0.666100	+	0.745862i	$0.732038\pi$
$740$	−31.1545	−1.14526
$741$	0	0
$742$	1.00378	0.0368499
$743$	−5.84654	−0.214489	−0.107244	−	0.994233i	$-0.534203\pi$
$743$	−5.84654	−0.214489	−0.107244	+	0.994233i	$0.534203\pi$
$744$	−8.54467	−0.313263
$745$	24.0335	0.880518
$746$	13.2005	0.483304
$747$	−4.78597	−0.175109
$748$	2.88360	0.105435
$749$	−6.04327	−0.220816
$750$	18.5919	0.678881
$751$	−24.5323	−0.895197	−0.447598	−	0.894235i	$-0.647721\pi$
$751$	−24.5323	−0.895197	−0.447598	+	0.894235i	$0.647721\pi$
$752$	−2.72023	−0.0991965
$753$	−6.42817	−0.234255
$754$	0	0
$755$	−52.9457	−1.92689
$756$	1.42820	0.0519432
$757$	0.878770	0.0319394	0.0159697	−	0.999872i	$-0.494916\pi$
$757$	0.878770	0.0319394	0.0159697	+	0.999872i	$0.494916\pi$
$758$	5.46854	0.198626
$759$	5.84123	0.212023
$760$	9.56235	0.346863
$761$	−32.4980	−1.17805	−0.589026	−	0.808114i	$-0.700488\pi$
$761$	−32.4980	−1.17805	−0.589026	+	0.808114i	$0.700488\pi$
$762$	−14.9468	−0.541465
$763$	18.1361	0.656571
$764$	−0.839218	−0.0303619
$765$	−11.9351	−0.431513
$766$	12.4111	0.448430
$767$	0	0
$768$	12.6371	0.456001
$769$	−28.7804	−1.03785	−0.518924	−	0.854820i	$-0.673667\pi$
$769$	−28.7804	−1.03785	−0.518924	+	0.854820i	$0.673667\pi$
$770$	2.06249	0.0743270
$771$	2.11002	0.0759904
$772$	−21.3519	−0.768473
$773$	−20.6862	−0.744033	−0.372016	−	0.928226i	$-0.621333\pi$
$773$	−20.6862	−0.744033	−0.372016	+	0.928226i	$0.621333\pi$
$774$	3.82724	0.137567
$775$	−36.6637	−1.31700
$776$	22.1629	0.795602
$777$	5.43258	0.194893
$778$	15.6836	0.562286
$779$	8.47213	0.303546
$780$	0	0
$781$	1.63848	0.0586294
$782$	19.3277	0.691157
$783$	7.97866	0.285134
$784$	0.896164	0.0320059
$785$	−44.1707	−1.57652
$786$	5.98961	0.213642
$787$	43.6433	1.55572	0.777858	−	0.628440i	$-0.216306\pi$
$787$	43.6433	1.55572	0.777858	+	0.628440i	$0.216306\pi$
$788$	30.0338	1.06991
$789$	17.5276	0.623999
$790$	−49.1357	−1.74817
$791$	−20.5748	−0.731555
$792$	1.76089	0.0625706
$793$	0	0
$794$	4.99071	0.177114
$795$	5.33019	0.189042
$796$	−37.3884	−1.32520
$797$	−40.4512	−1.43285	−0.716427	−	0.697662i	$-0.754224\pi$
$797$	−40.4512	−1.43285	−0.716427	+	0.697662i	$0.754224\pi$
$798$	−0.694661	−0.0245907
$799$	−9.02230	−0.319186
$800$	65.2073	2.30543
$801$	−4.52542	−0.159898
$802$	−27.1086	−0.957240
$803$	−5.31292	−0.187489
$804$	−5.77103	−0.203528
$805$	−34.5290	−1.21699
$806$	0	0
$807$	−27.0426	−0.951945
$808$	34.8624	1.22645
$809$	23.1616	0.814319	0.407160	−	0.913357i	$-0.366519\pi$
$809$	23.1616	0.814319	0.407160	+	0.913357i	$0.366519\pi$
$810$	−3.03631	−0.106685
$811$	−4.12331	−0.144789	−0.0723945	−	0.997376i	$-0.523064\pi$
$811$	−4.12331	−0.144789	−0.0723945	+	0.997376i	$0.523064\pi$
$812$	11.3951	0.399891
$813$	16.2920	0.571384
$814$	2.79044	0.0978048
$815$	27.9021	0.977368
$816$	−2.66371	−0.0932486
$817$	4.64961	0.162669
$818$	−11.6750	−0.408208
$819$	0	0
$820$	52.8879	1.84692
$821$	−22.1699	−0.773733	−0.386867	−	0.922136i	$-0.626443\pi$
$821$	−22.1699	−0.773733	−0.386867	+	0.922136i	$0.626443\pi$
$822$	7.37597	0.257267
$823$	49.9856	1.74239	0.871195	−	0.490938i	$-0.163346\pi$
$823$	49.9856	1.74239	0.871195	+	0.490938i	$0.163346\pi$
$824$	33.6791	1.17327
$825$	7.55569	0.263056
$826$	−3.65421	−0.127146
$827$	13.2512	0.460788	0.230394	−	0.973097i	$-0.425998\pi$
$827$	13.2512	0.460788	0.230394	+	0.973097i	$0.425998\pi$
$828$	−12.2814	−0.426809
$829$	34.2056	1.18801	0.594005	−	0.804461i	$-0.297546\pi$
$829$	34.2056	1.18801	0.594005	+	0.804461i	$0.297546\pi$
$830$	14.5317	0.504403
$831$	−28.0719	−0.973802
$832$	0	0
$833$	2.97235	0.102986
$834$	9.25058	0.320322
$835$	10.4282	0.360884
$836$	0.891223	0.0308236
$837$	3.29616	0.113932
$838$	−8.51882	−0.294278
$839$	36.2127	1.25020	0.625101	−	0.780544i	$-0.285058\pi$
$839$	36.2127	1.25020	0.625101	+	0.780544i	$0.285058\pi$
$840$	−10.4091	−0.359148
$841$	34.6590	1.19514
$842$	1.39941	0.0482270
$843$	8.95674	0.308487
$844$	−17.4138	−0.599408
$845$	0	0
$846$	−2.29530	−0.0789140
$847$	−10.5386	−0.362110
$848$	1.18961	0.0408514
$849$	5.03954	0.172957
$850$	25.0006	0.857513
$851$	−46.7159	−1.60140
$852$	−3.44497	−0.118023
$853$	19.0258	0.651431	0.325715	−	0.945468i	$-0.394395\pi$
$853$	19.0258	0.651431	0.325715	+	0.945468i	$0.394395\pi$
$854$	−3.37964	−0.115649
$855$	−3.68873	−0.126152
$856$	15.6661	0.535455
$857$	50.1577	1.71335	0.856677	−	0.515854i	$-0.172525\pi$
$857$	50.1577	1.71335	0.856677	+	0.515854i	$0.172525\pi$
$858$	0	0
$859$	−17.8970	−0.610638	−0.305319	−	0.952250i	$-0.598763\pi$
$859$	−17.8970	−0.610638	−0.305319	+	0.952250i	$0.598763\pi$
$860$	29.0255	0.989762
$861$	−9.22234	−0.314297
$862$	−10.8195	−0.368514
$863$	−19.5763	−0.666385	−0.333192	−	0.942859i	$-0.608126\pi$
$863$	−19.5763	−0.666385	−0.333192	+	0.942859i	$0.608126\pi$
$864$	−5.86229	−0.199439
$865$	15.0695	0.512379
$866$	−19.1864	−0.651980
$867$	8.16515	0.277303
$868$	4.70758	0.159786
$869$	−10.9925	−0.372894
$870$	−24.2257	−0.821329
$871$	0	0
$872$	−47.0145	−1.59211
$873$	−8.54947	−0.289356
$874$	5.97354	0.202058
$875$	−24.5868	−0.831187
$876$	11.1706	0.377420
$877$	7.14238	0.241181	0.120591	−	0.992702i	$-0.461521\pi$
$877$	7.14238	0.241181	0.120591	+	0.992702i	$0.461521\pi$
$878$	−21.6662	−0.731200
$879$	4.92561	0.166137
$880$	2.44432	0.0823980
$881$	−37.7674	−1.27242	−0.636209	−	0.771517i	$-0.719498\pi$
$881$	−37.7674	−1.27242	−0.636209	+	0.771517i	$0.719498\pi$
$882$	0.756173	0.0254617
$883$	−5.94028	−0.199906	−0.0999532	−	0.994992i	$-0.531869\pi$
$883$	−5.94028	−0.199906	−0.0999532	+	0.994992i	$0.531869\pi$
$884$	0	0
$885$	−19.4043	−0.652267
$886$	0.646348	0.0217145
$887$	26.3430	0.884510	0.442255	−	0.896889i	$-0.354179\pi$
$887$	26.3430	0.884510	0.442255	+	0.896889i	$0.354179\pi$
$888$	−14.0829	−0.472593
$889$	19.7663	0.662942
$890$	13.7406	0.460586
$891$	−0.679275	−0.0227566
$892$	10.7399	0.359598
$893$	−2.78849	−0.0933132
$894$	4.52598	0.151371
$895$	−77.1307	−2.57819
$896$	−9.72784	−0.324984
$897$	0	0
$898$	−3.28582	−0.109649
$899$	26.2989	0.877118
$900$	−15.8861	−0.529538
$901$	3.94564	0.131448
$902$	−4.73705	−0.157726
$903$	−5.06133	−0.168431
$904$	53.3363	1.77394
$905$	−20.9587	−0.696691
$906$	−9.97073	−0.331255
$907$	42.6973	1.41774	0.708870	−	0.705339i	$-0.249205\pi$
$907$	42.6973	1.41774	0.708870	+	0.705339i	$0.249205\pi$
$908$	35.4356	1.17597
$909$	−13.4484	−0.446054
$910$	0	0
$911$	−1.76256	−0.0583963	−0.0291981	−	0.999574i	$-0.509295\pi$
$911$	−1.76256	−0.0583963	−0.0291981	+	0.999574i	$0.509295\pi$
$912$	−0.823263	−0.0272610
$913$	3.25099	0.107592
$914$	22.6249	0.748366
$915$	−17.9463	−0.593285
$916$	11.5537	0.381745
$917$	−7.92094	−0.261573
$918$	−2.24761	−0.0741822
$919$	−16.1363	−0.532287	−0.266144	−	0.963933i	$-0.585750\pi$
$919$	−16.1363	−0.532287	−0.266144	+	0.963933i	$0.585750\pi$
$920$	89.5101	2.95106
$921$	11.2027	0.369141
$922$	−16.2872	−0.536392
$923$	0	0
$924$	−0.970141	−0.0319153
$925$	−60.4275	−1.98684
$926$	−11.8124	−0.388180
$927$	−12.9919	−0.426710
$928$	−46.7732	−1.53540
$929$	15.8148	0.518865	0.259433	−	0.965761i	$-0.416464\pi$
$929$	15.8148	0.518865	0.259433	+	0.965761i	$0.416464\pi$
$930$	−10.0082	−0.328181
$931$	0.918653	0.0301076
$932$	3.27450	0.107260
$933$	−9.44321	−0.309157
$934$	30.0711	0.983956
$935$	8.10719	0.265134
$936$	0	0
$937$	26.6821	0.871665	0.435833	−	0.900028i	$-0.356454\pi$
$937$	26.6821	0.871665	0.435833	+	0.900028i	$0.356454\pi$
$938$	−3.05552	−0.0997662
$939$	28.0752	0.916199
$940$	−17.4073	−0.567765
$941$	31.6041	1.03026	0.515132	−	0.857111i	$-0.327743\pi$
$941$	31.6041	1.03026	0.515132	+	0.857111i	$0.327743\pi$
$942$	−8.31821	−0.271022
$943$	79.3049	2.58252
$944$	−4.33071	−0.140953
$945$	4.01537	0.130620
$946$	−2.59975	−0.0845252
$947$	35.6370	1.15805	0.579023	−	0.815311i	$-0.303434\pi$
$947$	35.6370	1.15805	0.579023	+	0.815311i	$0.303434\pi$
$948$	23.1121	0.750646
$949$	0	0
$950$	7.72684	0.250692
$951$	−8.48965	−0.275296
$952$	−7.70526	−0.249729
$953$	5.66554	0.183525	0.0917624	−	0.995781i	$-0.470750\pi$
$953$	5.66554	0.183525	0.0917624	+	0.995781i	$0.470750\pi$
$954$	1.00378	0.0324986
$955$	−2.35945	−0.0763500
$956$	−0.000966233 0	−3.12502e−5 0
$957$	−5.41970	−0.175194
$958$	26.4416	0.854288
$959$	−9.75434	−0.314984
$960$	10.6029	0.342207
$961$	−20.1354	−0.649528
$962$	0	0
$963$	−6.04327	−0.194742
$964$	26.7781	0.862464
$965$	−60.0306	−1.93245
$966$	−6.50250	−0.209214
$967$	−44.0071	−1.41517	−0.707587	−	0.706627i	$-0.750216\pi$
$967$	−44.0071	−1.41517	−0.707587	+	0.706627i	$0.750216\pi$
$968$	27.3193	0.878077
$969$	−2.73056	−0.0877181
$970$	25.9589	0.833489
$971$	−13.4908	−0.432940	−0.216470	−	0.976289i	$-0.569454\pi$
$971$	−13.4908	−0.432940	−0.216470	+	0.976289i	$0.569454\pi$
$972$	1.42820	0.0458096
$973$	−12.2334	−0.392185
$974$	19.0147	0.609269
$975$	0	0
$976$	−4.00531	−0.128207
$977$	2.32159	0.0742742	0.0371371	−	0.999310i	$-0.488176\pi$
$977$	2.32159	0.0742742	0.0371371	+	0.999310i	$0.488176\pi$
$978$	5.25452	0.168021
$979$	3.07400	0.0982455
$980$	5.73476	0.183190
$981$	18.1361	0.579041
$982$	−1.83585	−0.0585844
$983$	−39.6806	−1.26561	−0.632807	−	0.774310i	$-0.718097\pi$
$983$	−39.6806	−1.26561	−0.632807	+	0.774310i	$0.718097\pi$
$984$	23.9072	0.762134
$985$	84.4395	2.69047
$986$	−17.9329	−0.571101
$987$	3.03541	0.0966182
$988$	0	0
$989$	43.5235	1.38397
$990$	2.06249	0.0655503
$991$	−42.2961	−1.34358	−0.671791	−	0.740741i	$-0.734475\pi$
$991$	−42.2961	−1.34358	−0.671791	+	0.740741i	$0.734475\pi$
$992$	−19.3230	−0.613506
$993$	31.6062	1.00299
$994$	−1.82397	−0.0578527
$995$	−105.117	−3.33243
$996$	−6.83533	−0.216586
$997$	15.2020	0.481453	0.240726	−	0.970593i	$-0.422614\pi$
$997$	15.2020	0.481453	0.240726	+	0.970593i	$0.422614\pi$
$998$	−1.10282	−0.0349092
$999$	5.43258	0.171879

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.ba.1.5		8
13.6	odd	12		273.2.bd.b.127.4	yes	16
13.11	odd	12		273.2.bd.b.43.4	✓	16
13.12	even	2		3549.2.a.bc.1.4		8
39.11	even	12		819.2.ct.c.316.5		16
39.32	even	12		819.2.ct.c.127.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.4	✓	16	13.11	odd	12
273.2.bd.b.127.4	yes	16	13.6	odd	12
819.2.ct.c.127.5		16	39.32	even	12
819.2.ct.c.316.5		16	39.11	even	12
3549.2.a.ba.1.5		8	1.1	even	1	trivial
3549.2.a.bc.1.4		8	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 3549 = 3 \cdot 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3549.a (trivial)

\(f(q)\)	\(=\)	\(q+0.756173 q^{2} -1.00000 q^{3} -1.42820 q^{4} -4.01537 q^{5} -0.756173 q^{6} +1.00000 q^{7} -2.59231 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.756173 q^{2} -1.00000 q^{3} -1.42820 q^{4} -4.01537 q^{5} -0.756173 q^{6} +1.00000 q^{7} -2.59231 q^{8} +1.00000 q^{9} -3.03631 q^{10} -0.679275 q^{11} +1.42820 q^{12} +0.756173 q^{14} +4.01537 q^{15} +0.896164 q^{16} +2.97235 q^{17} +0.756173 q^{18} +0.918653 q^{19} +5.73476 q^{20} -1.00000 q^{21} -0.513649 q^{22} +8.59922 q^{23} +2.59231 q^{24} +11.1232 q^{25} -1.00000 q^{27} -1.42820 q^{28} -7.97866 q^{29} +3.03631 q^{30} -3.29616 q^{31} +5.86229 q^{32} +0.679275 q^{33} +2.24761 q^{34} -4.01537 q^{35} -1.42820 q^{36} -5.43258 q^{37} +0.694661 q^{38} +10.4091 q^{40} +9.22234 q^{41} -0.756173 q^{42} +5.06133 q^{43} +0.970141 q^{44} -4.01537 q^{45} +6.50250 q^{46} -3.03541 q^{47} -0.896164 q^{48} +1.00000 q^{49} +8.41105 q^{50} -2.97235 q^{51} +1.32745 q^{53} -0.756173 q^{54} +2.72754 q^{55} -2.59231 q^{56} -0.918653 q^{57} -6.03325 q^{58} -4.83250 q^{59} -5.73476 q^{60} -4.46940 q^{61} -2.49247 q^{62} +1.00000 q^{63} +2.64058 q^{64} +0.513649 q^{66} -4.04076 q^{67} -4.24511 q^{68} -8.59922 q^{69} -3.03631 q^{70} -2.41210 q^{71} -2.59231 q^{72} +7.82146 q^{73} -4.10797 q^{74} -11.1232 q^{75} -1.31202 q^{76} -0.679275 q^{77} +16.1827 q^{79} -3.59843 q^{80} +1.00000 q^{81} +6.97369 q^{82} -4.78597 q^{83} +1.42820 q^{84} -11.9351 q^{85} +3.82724 q^{86} +7.97866 q^{87} +1.76089 q^{88} -4.52542 q^{89} -3.03631 q^{90} -12.2814 q^{92} +3.29616 q^{93} -2.29530 q^{94} -3.68873 q^{95} -5.86229 q^{96} -8.54947 q^{97} +0.756173 q^{98} -0.679275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 8 q^{3} + 14 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 8 * q^3 + 14 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} - 8 q^{3} + 14 q^{4} - 6 q^{5} + 2 q^{6} + 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 16 q^{11} - 14 q^{12} - 2 q^{14} + 6 q^{15} + 10 q^{16} - 2 q^{17} - 2 q^{18} - 14 q^{19} + 10 q^{20} - 8 q^{21} + 18 q^{22} - 6 q^{23} + 12 q^{24} + 10 q^{25} - 8 q^{27} + 14 q^{28} + 12 q^{29} + 4 q^{30} - 16 q^{31} - 26 q^{32} + 16 q^{33} - 32 q^{34} - 6 q^{35} + 14 q^{36} + 8 q^{37} + 12 q^{38} - 14 q^{40} + 4 q^{41} + 2 q^{42} + 14 q^{43} - 68 q^{44} - 6 q^{45} + 28 q^{46} - 6 q^{47} - 10 q^{48} + 8 q^{49} - 32 q^{50} + 2 q^{51} + 14 q^{53} + 2 q^{54} - 2 q^{55} - 12 q^{56} + 14 q^{57} - 24 q^{58} - 50 q^{59} - 10 q^{60} - 2 q^{61} - 20 q^{62} + 8 q^{63} + 24 q^{64} - 18 q^{66} + 16 q^{67} - 36 q^{68} + 6 q^{69} - 4 q^{70} - 34 q^{71} - 12 q^{72} + 8 q^{73} - 6 q^{74} - 10 q^{75} + 4 q^{76} - 16 q^{77} + 46 q^{79} + 24 q^{80} + 8 q^{81} - 42 q^{82} - 42 q^{83} - 14 q^{84} - 20 q^{85} - 50 q^{86} - 12 q^{87} + 62 q^{88} - 28 q^{89} - 4 q^{90} - 58 q^{92} + 16 q^{93} + 24 q^{94} - 24 q^{95} + 26 q^{96} - 16 q^{97} - 2 q^{98} - 16 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 8 * q^3 + 14 * q^4 - 6 * q^5 + 2 * q^6 + 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 16 * q^11 - 14 * q^12 - 2 * q^14 + 6 * q^15 + 10 * q^16 - 2 * q^17 - 2 * q^18 - 14 * q^19 + 10 * q^20 - 8 * q^21 + 18 * q^22 - 6 * q^23 + 12 * q^24 + 10 * q^25 - 8 * q^27 + 14 * q^28 + 12 * q^29 + 4 * q^30 - 16 * q^31 - 26 * q^32 + 16 * q^33 - 32 * q^34 - 6 * q^35 + 14 * q^36 + 8 * q^37 + 12 * q^38 - 14 * q^40 + 4 * q^41 + 2 * q^42 + 14 * q^43 - 68 * q^44 - 6 * q^45 + 28 * q^46 - 6 * q^47 - 10 * q^48 + 8 * q^49 - 32 * q^50 + 2 * q^51 + 14 * q^53 + 2 * q^54 - 2 * q^55 - 12 * q^56 + 14 * q^57 - 24 * q^58 - 50 * q^59 - 10 * q^60 - 2 * q^61 - 20 * q^62 + 8 * q^63 + 24 * q^64 - 18 * q^66 + 16 * q^67 - 36 * q^68 + 6 * q^69 - 4 * q^70 - 34 * q^71 - 12 * q^72 + 8 * q^73 - 6 * q^74 - 10 * q^75 + 4 * q^76 - 16 * q^77 + 46 * q^79 + 24 * q^80 + 8 * q^81 - 42 * q^82 - 42 * q^83 - 14 * q^84 - 20 * q^85 - 50 * q^86 - 12 * q^87 + 62 * q^88 - 28 * q^89 - 4 * q^90 - 58 * q^92 + 16 * q^93 + 24 * q^94 - 24 * q^95 + 26 * q^96 - 16 * q^97 - 2 * q^98 - 16 * q^99

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