LMFDB - Embedded newform 3549.2.a.bb.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} - 9x^{6} + 14x^{5} + 25x^{4} - 24x^{3} - 16x^{2} + 8x + 1 $ x^8 - 2x^7 - 9x^6 + 14x^5 + 25x^4 - 24x^3 - 16x^2 + 8*x + 1
Coefficient ring:	$\Z[a_1, a_2]$
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			$-0.106359$ 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)

$f(q)$	$=$	$q+0.106359 q^{2} +1.00000 q^{3} -1.98869 q^{4} +1.41292 q^{5} +0.106359 q^{6} -1.00000 q^{7} -0.424234 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.106359 q^{2} +1.00000 q^{3} -1.98869 q^{4} +1.41292 q^{5} +0.106359 q^{6} -1.00000 q^{7} -0.424234 q^{8} +1.00000 q^{9} +0.150278 q^{10} +3.00048 q^{11} -1.98869 q^{12} -0.106359 q^{14} +1.41292 q^{15} +3.93225 q^{16} -6.36712 q^{17} +0.106359 q^{18} -5.30339 q^{19} -2.80986 q^{20} -1.00000 q^{21} +0.319129 q^{22} -0.671915 q^{23} -0.424234 q^{24} -3.00365 q^{25} +1.00000 q^{27} +1.98869 q^{28} +0.516587 q^{29} +0.150278 q^{30} +0.282012 q^{31} +1.26670 q^{32} +3.00048 q^{33} -0.677203 q^{34} -1.41292 q^{35} -1.98869 q^{36} -6.45321 q^{37} -0.564065 q^{38} -0.599410 q^{40} -3.97193 q^{41} -0.106359 q^{42} +4.94438 q^{43} -5.96701 q^{44} +1.41292 q^{45} -0.0714645 q^{46} +5.91777 q^{47} +3.93225 q^{48} +1.00000 q^{49} -0.319466 q^{50} -6.36712 q^{51} -12.2506 q^{53} +0.106359 q^{54} +4.23944 q^{55} +0.424234 q^{56} -5.30339 q^{57} +0.0549439 q^{58} -2.30204 q^{59} -2.80986 q^{60} +4.03885 q^{61} +0.0299946 q^{62} -1.00000 q^{63} -7.72978 q^{64} +0.319129 q^{66} +2.11412 q^{67} +12.6622 q^{68} -0.671915 q^{69} -0.150278 q^{70} -14.6750 q^{71} -0.424234 q^{72} -6.44186 q^{73} -0.686359 q^{74} -3.00365 q^{75} +10.5468 q^{76} -3.00048 q^{77} +12.6905 q^{79} +5.55597 q^{80} +1.00000 q^{81} -0.422452 q^{82} +8.49842 q^{83} +1.98869 q^{84} -8.99625 q^{85} +0.525881 q^{86} +0.516587 q^{87} -1.27291 q^{88} -11.4231 q^{89} +0.150278 q^{90} +1.33623 q^{92} +0.282012 q^{93} +0.629410 q^{94} -7.49327 q^{95} +1.26670 q^{96} -0.366855 q^{97} +0.106359 q^{98} +3.00048 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 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 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * 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 $

$2$	0.106359	0.0752074	0.0376037	−	0.999293i	$-0.488028\pi$
$2$	0.106359	0.0752074	0.0376037	+	0.999293i	$0.488028\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.98869	−0.994344
$5$	1.41292	0.631878	0.315939	−	0.948780i	$-0.397681\pi$
$5$	1.41292	0.631878	0.315939	+	0.948780i	$0.397681\pi$
$6$	0.106359	0.0434210
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.424234	−0.149989
$9$	1.00000	0.333333
$10$	0.150278	0.0475219
$11$	3.00048	0.904678	0.452339	−	0.891846i	$-0.350590\pi$
$11$	3.00048	0.904678	0.452339	+	0.891846i	$0.350590\pi$
$12$	−1.98869	−0.574085
$13$	0	0
$13$	0	0
$14$	−0.106359	−0.0284257
$15$	1.41292	0.364815
$16$	3.93225	0.983064
$17$	−6.36712	−1.54425	−0.772127	−	0.635468i	$-0.780807\pi$
$17$	−6.36712	−1.54425	−0.772127	+	0.635468i	$0.780807\pi$
$18$	0.106359	0.0250691
$19$	−5.30339	−1.21668	−0.608340	−	0.793676i	$-0.708164\pi$
$19$	−5.30339	−1.21668	−0.608340	+	0.793676i	$0.708164\pi$
$20$	−2.80986	−0.628304
$21$	−1.00000	−0.218218
$22$	0.319129	0.0680385
$23$	−0.671915	−0.140104	−0.0700520	−	0.997543i	$-0.522317\pi$
$23$	−0.671915	−0.140104	−0.0700520	+	0.997543i	$0.522317\pi$
$24$	−0.424234	−0.0865965
$25$	−3.00365	−0.600730
$26$	0	0
$27$	1.00000	0.192450
$28$	1.98869	0.375827
$29$	0.516587	0.0959279	0.0479639	−	0.998849i	$-0.484727\pi$
$29$	0.516587	0.0959279	0.0479639	+	0.998849i	$0.484727\pi$
$30$	0.150278	0.0274368
$31$	0.282012	0.0506508	0.0253254	−	0.999679i	$-0.491938\pi$
$31$	0.282012	0.0506508	0.0253254	+	0.999679i	$0.491938\pi$
$32$	1.26670	0.223923
$33$	3.00048	0.522316
$34$	−0.677203	−0.116139
$35$	−1.41292	−0.238827
$36$	−1.98869	−0.331448
$37$	−6.45321	−1.06090	−0.530451	−	0.847716i	$-0.677977\pi$
$37$	−6.45321	−1.06090	−0.530451	+	0.847716i	$0.677977\pi$
$38$	−0.564065	−0.0915034
$39$	0	0
$40$	−0.599410	−0.0947750
$41$	−3.97193	−0.620311	−0.310155	−	0.950686i	$-0.600381\pi$
$41$	−3.97193	−0.620311	−0.310155	+	0.950686i	$0.600381\pi$
$42$	−0.106359	−0.0164116
$43$	4.94438	0.754011	0.377005	−	0.926211i	$-0.376954\pi$
$43$	4.94438	0.754011	0.377005	+	0.926211i	$0.376954\pi$
$44$	−5.96701	−0.899561
$45$	1.41292	0.210626
$46$	−0.0714645	−0.0105369
$47$	5.91777	0.863195	0.431598	−	0.902066i	$-0.357950\pi$
$47$	5.91777	0.863195	0.431598	+	0.902066i	$0.357950\pi$
$48$	3.93225	0.567572
$49$	1.00000	0.142857
$50$	−0.319466	−0.0451794
$51$	−6.36712	−0.891576
$52$	0	0
$53$	−12.2506	−1.68275	−0.841375	−	0.540451i	$-0.818254\pi$
$53$	−12.2506	−1.68275	−0.841375	+	0.540451i	$0.818254\pi$
$54$	0.106359	0.0144737
$55$	4.23944	0.571646
$56$	0.424234	0.0566907
$57$	−5.30339	−0.702451
$58$	0.0549439	0.00721449
$59$	−2.30204	−0.299699	−0.149850	−	0.988709i	$-0.547879\pi$
$59$	−2.30204	−0.299699	−0.149850	+	0.988709i	$0.547879\pi$
$60$	−2.80986	−0.362751
$61$	4.03885	0.517121	0.258561	−	0.965995i	$-0.416752\pi$
$61$	4.03885	0.517121	0.258561	+	0.965995i	$0.416752\pi$
$62$	0.0299946	0.00380931
$63$	−1.00000	−0.125988
$64$	−7.72978	−0.966223
$65$	0	0
$66$	0.319129	0.0392820
$67$	2.11412	0.258281	0.129140	−	0.991626i	$-0.458778\pi$
$67$	2.11412	0.258281	0.129140	+	0.991626i	$0.458778\pi$
$68$	12.6622	1.53552
$69$	−0.671915	−0.0808891
$70$	−0.150278	−0.0179616
$71$	−14.6750	−1.74160	−0.870801	−	0.491635i	$-0.836400\pi$
$71$	−14.6750	−1.74160	−0.870801	+	0.491635i	$0.836400\pi$
$72$	−0.424234	−0.0499965
$73$	−6.44186	−0.753963	−0.376981	−	0.926221i	$-0.623038\pi$
$73$	−6.44186	−0.753963	−0.376981	+	0.926221i	$0.623038\pi$
$74$	−0.686359	−0.0797877
$75$	−3.00365	−0.346832
$76$	10.5468	1.20980
$77$	−3.00048	−0.341936
$78$	0	0
$79$	12.6905	1.42779	0.713894	−	0.700254i	$-0.246930\pi$
$79$	12.6905	1.42779	0.713894	+	0.700254i	$0.246930\pi$
$80$	5.55597	0.621176
$81$	1.00000	0.111111
$82$	−0.422452	−0.0466520
$83$	8.49842	0.932823	0.466412	−	0.884568i	$-0.345547\pi$
$83$	8.49842	0.932823	0.466412	+	0.884568i	$0.345547\pi$
$84$	1.98869	0.216984
$85$	−8.99625	−0.975780
$86$	0.525881	0.0567072
$87$	0.516587	0.0553840
$88$	−1.27291	−0.135692
$89$	−11.4231	−1.21084	−0.605421	−	0.795905i	$-0.706995\pi$
$89$	−11.4231	−1.21084	−0.605421	+	0.795905i	$0.706995\pi$
$90$	0.150278	0.0158406
$91$	0	0
$92$	1.33623	0.139312
$93$	0.282012	0.0292432
$94$	0.629410	0.0649187
$95$	−7.49327	−0.768794
$96$	1.26670	0.129282
$97$	−0.366855	−0.0372485	−0.0186243	−	0.999827i	$-0.505929\pi$
$97$	−0.366855	−0.0372485	−0.0186243	+	0.999827i	$0.505929\pi$
$98$	0.106359	0.0107439
$99$	3.00048	0.301559
$100$	5.97332	0.597332
$101$	18.3518	1.82608	0.913038	−	0.407876i	$-0.133730\pi$
$101$	18.3518	1.82608	0.913038	+	0.407876i	$0.133730\pi$
$102$	−0.677203	−0.0670531
$103$	−3.99871	−0.394005	−0.197003	−	0.980403i	$-0.563121\pi$
$103$	−3.99871	−0.394005	−0.197003	+	0.980403i	$0.563121\pi$
$104$	0	0
$105$	−1.41292	−0.137887
$106$	−1.30297	−0.126555
$107$	−0.0996570	−0.00963421	−0.00481710	−	0.999988i	$-0.501533\pi$
$107$	−0.0996570	−0.00963421	−0.00481710	+	0.999988i	$0.501533\pi$
$108$	−1.98869	−0.191362
$109$	−4.98762	−0.477727	−0.238864	−	0.971053i	$-0.576775\pi$
$109$	−4.98762	−0.477727	−0.238864	+	0.971053i	$0.576775\pi$
$110$	0.450904	0.0429920
$111$	−6.45321	−0.612512
$112$	−3.93225	−0.371563
$113$	4.02046	0.378213	0.189106	−	0.981957i	$-0.439441\pi$
$113$	4.02046	0.378213	0.189106	+	0.981957i	$0.439441\pi$
$114$	−0.564065	−0.0528295
$115$	−0.949364	−0.0885286
$116$	−1.02733	−0.0953853
$117$	0	0
$118$	−0.244843	−0.0225396
$119$	6.36712	0.583673
$120$	−0.599410	−0.0547184
$121$	−1.99714	−0.181558
$122$	0.429569	0.0388914
$123$	−3.97193	−0.358137
$124$	−0.560833	−0.0503643
$125$	−11.3085	−1.01147
$126$	−0.106359	−0.00947525
$127$	−16.5944	−1.47252	−0.736258	−	0.676701i	$-0.763409\pi$
$127$	−16.5944	−1.47252	−0.736258	+	0.676701i	$0.763409\pi$
$128$	−3.35554	−0.296590
$129$	4.94438	0.435328
$130$	0	0
$131$	−18.6490	−1.62937	−0.814685	−	0.579903i	$-0.803090\pi$
$131$	−18.6490	−1.62937	−0.814685	+	0.579903i	$0.803090\pi$
$132$	−5.96701	−0.519362
$133$	5.30339	0.459862
$134$	0.224856	0.0194246
$135$	1.41292	0.121605
$136$	2.70115	0.231622
$137$	−9.96740	−0.851572	−0.425786	−	0.904824i	$-0.640002\pi$
$137$	−9.96740	−0.851572	−0.425786	+	0.904824i	$0.640002\pi$
$138$	−0.0714645	−0.00608346
$139$	21.5773	1.83017	0.915083	−	0.403265i	$-0.132125\pi$
$139$	21.5773	1.83017	0.915083	+	0.403265i	$0.132125\pi$
$140$	2.80986	0.237477
$141$	5.91777	0.498366
$142$	−1.56082	−0.130981
$143$	0	0
$144$	3.93225	0.327688
$145$	0.729898	0.0606147
$146$	−0.685152	−0.0567036
$147$	1.00000	0.0824786
$148$	12.8334	1.05490
$149$	−22.8086	−1.86856	−0.934278	−	0.356547i	$-0.883954\pi$
$149$	−22.8086	−1.86856	−0.934278	+	0.356547i	$0.883954\pi$
$150$	−0.319466	−0.0260843
$151$	−16.9055	−1.37575	−0.687874	−	0.725830i	$-0.741456\pi$
$151$	−16.9055	−1.37575	−0.687874	+	0.725830i	$0.741456\pi$
$152$	2.24988	0.182489
$153$	−6.36712	−0.514751
$154$	−0.319129	−0.0257161
$155$	0.398460	0.0320051
$156$	0	0
$157$	−11.9666	−0.955042	−0.477521	−	0.878620i	$-0.658464\pi$
$157$	−11.9666	−0.955042	−0.477521	+	0.878620i	$0.658464\pi$
$158$	1.34975	0.107380
$159$	−12.2506	−0.971537
$160$	1.78975	0.141492
$161$	0.671915	0.0529543
$162$	0.106359	0.00835638
$163$	0.280599	0.0219782	0.0109891	−	0.999940i	$-0.496502\pi$
$163$	0.280599	0.0219782	0.0109891	+	0.999940i	$0.496502\pi$
$164$	7.89892	0.616802
$165$	4.23944	0.330040
$166$	0.903887	0.0701552
$167$	−20.8191	−1.61103	−0.805515	−	0.592575i	$-0.798111\pi$
$167$	−20.8191	−1.61103	−0.805515	+	0.592575i	$0.798111\pi$
$168$	0.424234	0.0327304
$169$	0	0
$170$	−0.956835	−0.0733859
$171$	−5.30339	−0.405560
$172$	−9.83283	−0.749746
$173$	−5.56720	−0.423267	−0.211633	−	0.977349i	$-0.567878\pi$
$173$	−5.56720	−0.423267	−0.211633	+	0.977349i	$0.567878\pi$
$174$	0.0549439	0.00416529
$175$	3.00365	0.227055
$176$	11.7986	0.889356
$177$	−2.30204	−0.173032
$178$	−1.21495	−0.0910643
$179$	−6.09328	−0.455433	−0.227716	−	0.973728i	$-0.573126\pi$
$179$	−6.09328	−0.455433	−0.227716	+	0.973728i	$0.573126\pi$
$180$	−2.80986	−0.209435
$181$	15.8856	1.18077	0.590383	−	0.807123i	$-0.298977\pi$
$181$	15.8856	1.18077	0.590383	+	0.807123i	$0.298977\pi$
$182$	0	0
$183$	4.03885	0.298560
$184$	0.285049	0.0210141
$185$	−9.11788	−0.670360
$186$	0.0299946	0.00219931
$187$	−19.1044	−1.39705
$188$	−11.7686	−0.858313
$189$	−1.00000	−0.0727393
$190$	−0.796980	−0.0578190
$191$	5.30672	0.383981	0.191990	−	0.981397i	$-0.438506\pi$
$191$	5.30672	0.383981	0.191990	+	0.981397i	$0.438506\pi$
$192$	−7.72978	−0.557849
$193$	−2.08239	−0.149894	−0.0749469	−	0.997188i	$-0.523879\pi$
$193$	−2.08239	−0.149894	−0.0749469	+	0.997188i	$0.523879\pi$
$194$	−0.0390185	−0.00280137
$195$	0	0
$196$	−1.98869	−0.142049
$197$	9.87467	0.703541	0.351770	−	0.936086i	$-0.385580\pi$
$197$	9.87467	0.703541	0.351770	+	0.936086i	$0.385580\pi$
$198$	0.319129	0.0226795
$199$	−3.31608	−0.235070	−0.117535	−	0.993069i	$-0.537499\pi$
$199$	−3.31608	−0.235070	−0.117535	+	0.993069i	$0.537499\pi$
$200$	1.27425	0.0901032
$201$	2.11412	0.149118
$202$	1.95189	0.137334
$203$	−0.516587	−0.0362573
$204$	12.6622	0.886533
$205$	−5.61202	−0.391961
$206$	−0.425301	−0.0296321
$207$	−0.671915	−0.0467013
$208$	0	0
$209$	−15.9127	−1.10070
$210$	−0.150278	−0.0103701
$211$	−17.4614	−1.20209	−0.601046	−	0.799215i	$-0.705249\pi$
$211$	−17.4614	−1.20209	−0.601046	+	0.799215i	$0.705249\pi$
$212$	24.3626	1.67323
$213$	−14.6750	−1.00551
$214$	−0.0105995	−0.000724564 0
$215$	6.98602	0.476443
$216$	−0.424234	−0.0288655
$217$	−0.282012	−0.0191442
$218$	−0.530480	−0.0359286
$219$	−6.44186	−0.435301
$220$	−8.43092	−0.568413
$221$	0	0
$222$	−0.686359	−0.0460654
$223$	18.7566	1.25604	0.628018	−	0.778199i	$-0.283867\pi$
$223$	18.7566	1.25604	0.628018	+	0.778199i	$0.283867\pi$
$224$	−1.26670	−0.0846350
$225$	−3.00365	−0.200243
$226$	0.427613	0.0284444
$227$	−16.3261	−1.08360	−0.541800	−	0.840508i	$-0.682257\pi$
$227$	−16.3261	−1.08360	−0.541800	+	0.840508i	$0.682257\pi$
$228$	10.5468	0.698478
$229$	−11.3658	−0.751071	−0.375536	−	0.926808i	$-0.622541\pi$
$229$	−11.3658	−0.751071	−0.375536	+	0.926808i	$0.622541\pi$
$230$	−0.100974	−0.00665801
$231$	−3.00048	−0.197417
$232$	−0.219154	−0.0143882
$233$	30.2591	1.98234	0.991170	−	0.132600i	$-0.0423325\pi$
$233$	30.2591	1.98234	0.991170	+	0.132600i	$0.0423325\pi$
$234$	0	0
$235$	8.36134	0.545434
$236$	4.57803	0.298004
$237$	12.6905	0.824334
$238$	0.677203	0.0438966
$239$	−17.1229	−1.10759	−0.553795	−	0.832653i	$-0.686821\pi$
$239$	−17.1229	−1.10759	−0.553795	+	0.832653i	$0.686821\pi$
$240$	5.55597	0.358636
$241$	−17.3298	−1.11631	−0.558154	−	0.829737i	$-0.688490\pi$
$241$	−17.3298	−1.11631	−0.558154	+	0.829737i	$0.688490\pi$
$242$	−0.212415	−0.0136545
$243$	1.00000	0.0641500
$244$	−8.03201	−0.514197
$245$	1.41292	0.0902683
$246$	−0.422452	−0.0269345
$247$	0	0
$248$	−0.119639	−0.00759708
$249$	8.49842	0.538566
$250$	−1.20277	−0.0760698
$251$	11.3754	0.718011	0.359005	−	0.933335i	$-0.383116\pi$
$251$	11.3754	0.718011	0.359005	+	0.933335i	$0.383116\pi$
$252$	1.98869	0.125276
$253$	−2.01607	−0.126749
$254$	−1.76497	−0.110744
$255$	−8.99625	−0.563367
$256$	15.1027	0.943917
$257$	17.9289	1.11837	0.559187	−	0.829041i	$-0.311113\pi$
$257$	17.9289	1.11837	0.559187	+	0.829041i	$0.311113\pi$
$258$	0.525881	0.0327399
$259$	6.45321	0.400983
$260$	0	0
$261$	0.516587	0.0319760
$262$	−1.98350	−0.122541
$263$	20.7063	1.27681	0.638403	−	0.769702i	$-0.279595\pi$
$263$	20.7063	1.27681	0.638403	+	0.769702i	$0.279595\pi$
$264$	−1.27291	−0.0783419
$265$	−17.3092	−1.06329
$266$	0.564065	0.0345850
$267$	−11.4231	−0.699080
$268$	−4.20432	−0.256820
$269$	−7.56039	−0.460965	−0.230483	−	0.973076i	$-0.574031\pi$
$269$	−7.56039	−0.460965	−0.230483	+	0.973076i	$0.574031\pi$
$270$	0.150278	0.00914560
$271$	−18.6386	−1.13221	−0.566107	−	0.824332i	$-0.691551\pi$
$271$	−18.6386	−1.13221	−0.566107	+	0.824332i	$0.691551\pi$
$272$	−25.0371	−1.51810
$273$	0	0
$274$	−1.06013	−0.0640446
$275$	−9.01239	−0.543467
$276$	1.33623	0.0804316
$277$	17.6041	1.05773	0.528864	−	0.848706i	$-0.322618\pi$
$277$	17.6041	1.05773	0.528864	+	0.848706i	$0.322618\pi$
$278$	2.29495	0.137642
$279$	0.282012	0.0168836
$280$	0.599410	0.0358216
$281$	17.5012	1.04404	0.522018	−	0.852934i	$-0.325179\pi$
$281$	17.5012	1.04404	0.522018	+	0.852934i	$0.325179\pi$
$282$	0.629410	0.0374808
$283$	16.4110	0.975533	0.487766	−	0.872974i	$-0.337812\pi$
$283$	16.4110	0.975533	0.487766	+	0.872974i	$0.337812\pi$
$284$	29.1840	1.73175
$285$	−7.49327	−0.443863
$286$	0	0
$287$	3.97193	0.234455
$288$	1.26670	0.0746411
$289$	23.5403	1.38472
$290$	0.0776315	0.00455868
$291$	−0.366855	−0.0215054
$292$	12.8108	0.749698
$293$	28.0424	1.63826	0.819128	−	0.573610i	$-0.194458\pi$
$293$	28.0424	1.63826	0.819128	+	0.573610i	$0.194458\pi$
$294$	0.106359	0.00620300
$295$	−3.25260	−0.189373
$296$	2.73767	0.159124
$297$	3.00048	0.174105
$298$	−2.42591	−0.140529
$299$	0	0
$300$	5.97332	0.344870
$301$	−4.94438	−0.284989
$302$	−1.79806	−0.103466
$303$	18.3518	1.05428
$304$	−20.8543	−1.19607
$305$	5.70658	0.326758
$306$	−0.677203	−0.0387131
$307$	23.6211	1.34813	0.674063	−	0.738674i	$-0.264548\pi$
$307$	23.6211	1.34813	0.674063	+	0.738674i	$0.264548\pi$
$308$	5.96701	0.340002
$309$	−3.99871	−0.227479
$310$	0.0423800	0.00240702
$311$	−13.2516	−0.751431	−0.375716	−	0.926735i	$-0.622603\pi$
$311$	−13.2516	−0.751431	−0.375716	+	0.926735i	$0.622603\pi$
$312$	0	0
$313$	−11.1849	−0.632210	−0.316105	−	0.948724i	$-0.602375\pi$
$313$	−11.1849	−0.632210	−0.316105	+	0.948724i	$0.602375\pi$
$314$	−1.27276	−0.0718262
$315$	−1.41292	−0.0796091
$316$	−25.2374	−1.41971
$317$	20.3673	1.14394	0.571971	−	0.820274i	$-0.306179\pi$
$317$	20.3673	1.14394	0.571971	+	0.820274i	$0.306179\pi$
$318$	−1.30297	−0.0730668
$319$	1.55001	0.0867838
$320$	−10.9216	−0.610535
$321$	−0.0996570	−0.00556231
$322$	0.0714645	0.00398256
$323$	33.7673	1.87886
$324$	−1.98869	−0.110483
$325$	0	0
$326$	0.0298443	0.00165293
$327$	−4.98762	−0.275816
$328$	1.68503	0.0930401
$329$	−5.91777	−0.326257
$330$	0.450904	0.0248215
$331$	−25.1972	−1.38496	−0.692481	−	0.721436i	$-0.743482\pi$
$331$	−25.1972	−1.38496	−0.692481	+	0.721436i	$0.743482\pi$
$332$	−16.9007	−0.927547
$333$	−6.45321	−0.353634
$334$	−2.21431	−0.121161
$335$	2.98708	0.163202
$336$	−3.93225	−0.214522
$337$	−20.9316	−1.14022	−0.570108	−	0.821570i	$-0.693099\pi$
$337$	−20.9316	−1.14022	−0.570108	+	0.821570i	$0.693099\pi$
$338$	0	0
$339$	4.02046	0.218361
$340$	17.8907	0.970261
$341$	0.846169	0.0458226
$342$	−0.564065	−0.0305011
$343$	−1.00000	−0.0539949
$344$	−2.09758	−0.113094
$345$	−0.949364	−0.0511120
$346$	−0.592124	−0.0318328
$347$	−23.6447	−1.26932	−0.634658	−	0.772793i	$-0.718859\pi$
$347$	−23.6447	−1.26932	−0.634658	+	0.772793i	$0.718859\pi$
$348$	−1.02733	−0.0550707
$349$	−23.8442	−1.27635	−0.638174	−	0.769892i	$-0.720310\pi$
$349$	−23.8442	−1.27635	−0.638174	+	0.769892i	$0.720310\pi$
$350$	0.319466	0.0170762
$351$	0	0
$352$	3.80071	0.202578
$353$	8.56994	0.456132	0.228066	−	0.973646i	$-0.426760\pi$
$353$	8.56994	0.456132	0.228066	+	0.973646i	$0.426760\pi$
$354$	−0.244843	−0.0130133
$355$	−20.7346	−1.10048
$356$	22.7169	1.20399
$357$	6.36712	0.336984
$358$	−0.648077	−0.0342519
$359$	7.78179	0.410707	0.205354	−	0.978688i	$-0.434166\pi$
$359$	7.78179	0.410707	0.205354	+	0.978688i	$0.434166\pi$
$360$	−0.599410	−0.0315917
$361$	9.12592	0.480312
$362$	1.68958	0.0888024
$363$	−1.99714	−0.104823
$364$	0	0
$365$	−9.10185	−0.476412
$366$	0.429569	0.0224539
$367$	−21.3602	−1.11499	−0.557497	−	0.830179i	$-0.688238\pi$
$367$	−21.3602	−1.11499	−0.557497	+	0.830179i	$0.688238\pi$
$368$	−2.64214	−0.137731
$369$	−3.97193	−0.206770
$370$	−0.969772	−0.0504161
$371$	12.2506	0.636020
$372$	−0.560833	−0.0290778
$373$	1.96703	0.101849	0.0509245	−	0.998703i	$-0.483783\pi$
$373$	1.96703	0.101849	0.0509245	+	0.998703i	$0.483783\pi$
$374$	−2.03193	−0.105069
$375$	−11.3085	−0.583970
$376$	−2.51052	−0.129470
$377$	0	0
$378$	−0.106359	−0.00547054
$379$	−32.2453	−1.65633	−0.828166	−	0.560483i	$-0.810615\pi$
$379$	−32.2453	−1.65633	−0.828166	+	0.560483i	$0.810615\pi$
$380$	14.9018	0.764445
$381$	−16.5944	−0.850157
$382$	0.564420	0.0288782
$383$	34.2143	1.74827	0.874134	−	0.485685i	$-0.161430\pi$
$383$	34.2143	1.74827	0.874134	+	0.485685i	$0.161430\pi$
$384$	−3.35554	−0.171236
$385$	−4.23944	−0.216062
$386$	−0.221482	−0.0112731
$387$	4.94438	0.251337
$388$	0.729561	0.0370378
$389$	−0.953360	−0.0483373	−0.0241686	−	0.999708i	$-0.507694\pi$
$389$	−0.953360	−0.0483373	−0.0241686	+	0.999708i	$0.507694\pi$
$390$	0	0
$391$	4.27817	0.216356
$392$	−0.424234	−0.0214271
$393$	−18.6490	−0.940718
$394$	1.05026	0.0529115
$395$	17.9306	0.902188
$396$	−5.96701	−0.299854
$397$	4.58647	0.230188	0.115094	−	0.993355i	$-0.463283\pi$
$397$	4.58647	0.230188	0.115094	+	0.993355i	$0.463283\pi$
$398$	−0.352696	−0.0176790
$399$	5.30339	0.265501
$400$	−11.8111	−0.590556
$401$	31.6754	1.58180	0.790898	−	0.611949i	$-0.209614\pi$
$401$	31.6754	1.58180	0.790898	+	0.611949i	$0.209614\pi$
$402$	0.224856	0.0112148
$403$	0	0
$404$	−36.4961	−1.81575
$405$	1.41292	0.0702087
$406$	−0.0549439	−0.00272682
$407$	−19.3627	−0.959774
$408$	2.70115	0.133727
$409$	−10.8835	−0.538155	−0.269077	−	0.963119i	$-0.586719\pi$
$409$	−10.8835	−0.538155	−0.269077	+	0.963119i	$0.586719\pi$
$410$	−0.596891	−0.0294784
$411$	−9.96740	−0.491656
$412$	7.95219	0.391776
$413$	2.30204	0.113276
$414$	−0.0714645	−0.00351229
$415$	12.0076	0.589430
$416$	0	0
$417$	21.5773	1.05665
$418$	−1.69246	−0.0827811
$419$	16.8251	0.821960	0.410980	−	0.911644i	$-0.365187\pi$
$419$	16.8251	0.821960	0.410980	+	0.911644i	$0.365187\pi$
$420$	2.80986	0.137107
$421$	6.12271	0.298403	0.149201	−	0.988807i	$-0.452330\pi$
$421$	6.12271	0.298403	0.149201	+	0.988807i	$0.452330\pi$
$422$	−1.85718	−0.0904062
$423$	5.91777	0.287732
$424$	5.19713	0.252395
$425$	19.1246	0.927680
$426$	−1.56082	−0.0756222
$427$	−4.03885	−0.195454
$428$	0.198187	0.00957971
$429$	0	0
$430$	0.743029	0.0358320
$431$	−1.09067	−0.0525356	−0.0262678	−	0.999655i	$-0.508362\pi$
$431$	−1.09067	−0.0525356	−0.0262678	+	0.999655i	$0.508362\pi$
$432$	3.93225	0.189191
$433$	8.33979	0.400785	0.200392	−	0.979716i	$-0.435778\pi$
$433$	8.33979	0.400785	0.200392	+	0.979716i	$0.435778\pi$
$434$	−0.0299946	−0.00143979
$435$	0.729898	0.0349959
$436$	9.91881	0.475025
$437$	3.56343	0.170462
$438$	−0.685152	−0.0327378
$439$	−5.74464	−0.274177	−0.137088	−	0.990559i	$-0.543774\pi$
$439$	−5.74464	−0.274177	−0.137088	+	0.990559i	$0.543774\pi$
$440$	−1.79852	−0.0857409
$441$	1.00000	0.0476190
$442$	0	0
$443$	−16.9750	−0.806505	−0.403252	−	0.915089i	$-0.632120\pi$
$443$	−16.9750	−0.806505	−0.403252	+	0.915089i	$0.632120\pi$
$444$	12.8334	0.609047
$445$	−16.1399	−0.765104
$446$	1.99494	0.0944632
$447$	−22.8086	−1.07881
$448$	7.72978	0.365198
$449$	3.47196	0.163852	0.0819260	−	0.996638i	$-0.473893\pi$
$449$	3.47196	0.163852	0.0819260	+	0.996638i	$0.473893\pi$
$450$	−0.319466	−0.0150598
$451$	−11.9177	−0.561181
$452$	−7.99544	−0.376074
$453$	−16.9055	−0.794289
$454$	−1.73643	−0.0814947
$455$	0	0
$456$	2.24988	0.105360
$457$	−9.68784	−0.453178	−0.226589	−	0.973990i	$-0.572757\pi$
$457$	−9.68784	−0.453178	−0.226589	+	0.973990i	$0.572757\pi$
$458$	−1.20886	−0.0564861
$459$	−6.36712	−0.297192
$460$	1.88799	0.0880279
$461$	11.0928	0.516645	0.258322	−	0.966059i	$-0.416830\pi$
$461$	11.0928	0.516645	0.258322	+	0.966059i	$0.416830\pi$
$462$	−0.319129	−0.0148472
$463$	31.1633	1.44828	0.724140	−	0.689653i	$-0.242237\pi$
$463$	31.1633	1.44828	0.724140	+	0.689653i	$0.242237\pi$
$464$	2.03135	0.0943032
$465$	0.398460	0.0184782
$466$	3.21834	0.149087
$467$	27.7222	1.28283	0.641415	−	0.767194i	$-0.278348\pi$
$467$	27.7222	1.28283	0.641415	+	0.767194i	$0.278348\pi$
$468$	0	0
$469$	−2.11412	−0.0976209
$470$	0.889307	0.0410207
$471$	−11.9666	−0.551393
$472$	0.976602	0.0449518
$473$	14.8355	0.682137
$474$	1.34975	0.0619960
$475$	15.9295	0.730897
$476$	−12.6622	−0.580372
$477$	−12.2506	−0.560917
$478$	−1.82118	−0.0832990
$479$	−5.72530	−0.261596	−0.130798	−	0.991409i	$-0.541754\pi$
$479$	−5.72530	−0.261596	−0.130798	+	0.991409i	$0.541754\pi$
$480$	1.78975	0.0816905
$481$	0	0
$482$	−1.84318	−0.0839547
$483$	0.671915	0.0305732
$484$	3.97169	0.180531
$485$	−0.518338	−0.0235365
$486$	0.106359	0.00482456
$487$	3.57737	0.162106	0.0810530	−	0.996710i	$-0.474172\pi$
$487$	3.57737	0.162106	0.0810530	+	0.996710i	$0.474172\pi$
$488$	−1.71342	−0.0775628
$489$	0.280599	0.0126891
$490$	0.150278	0.00678885
$491$	3.46609	0.156422	0.0782112	−	0.996937i	$-0.475079\pi$
$491$	3.46609	0.156422	0.0782112	+	0.996937i	$0.475079\pi$
$492$	7.89892	0.356111
$493$	−3.28918	−0.148137
$494$	0	0
$495$	4.23944	0.190549
$496$	1.10894	0.0497929
$497$	14.6750	0.658264
$498$	0.903887	0.0405041
$499$	34.0041	1.52223	0.761117	−	0.648615i	$-0.224651\pi$
$499$	34.0041	1.52223	0.761117	+	0.648615i	$0.224651\pi$
$500$	22.4891	1.00575
$501$	−20.8191	−0.930129
$502$	1.20988	0.0539998
$503$	−31.9103	−1.42281	−0.711405	−	0.702782i	$-0.751941\pi$
$503$	−31.9103	−1.42281	−0.711405	+	0.702782i	$0.751941\pi$
$504$	0.424234	0.0188969
$505$	25.9297	1.15386
$506$	−0.214427	−0.00953246
$507$	0	0
$508$	33.0011	1.46419
$509$	16.5134	0.731944	0.365972	−	0.930626i	$-0.380737\pi$
$509$	16.5134	0.731944	0.365972	+	0.930626i	$0.380737\pi$
$510$	−0.956835	−0.0423694
$511$	6.44186	0.284971
$512$	8.31738	0.367580
$513$	−5.30339	−0.234150
$514$	1.90691	0.0841101
$515$	−5.64987	−0.248963
$516$	−9.83283	−0.432866
$517$	17.7561	0.780913
$518$	0.686359	0.0301569
$519$	−5.56720	−0.244373
$520$	0	0
$521$	14.4961	0.635087	0.317544	−	0.948244i	$-0.397142\pi$
$521$	14.4961	0.635087	0.317544	+	0.948244i	$0.397142\pi$
$522$	0.0549439	0.00240483
$523$	3.83088	0.167513	0.0837564	−	0.996486i	$-0.473308\pi$
$523$	3.83088	0.167513	0.0837564	+	0.996486i	$0.473308\pi$
$524$	37.0870	1.62015
$525$	3.00365	0.131090
$526$	2.20231	0.0960253
$527$	−1.79560	−0.0782177
$528$	11.7986	0.513470
$529$	−22.5485	−0.980371
$530$	−1.84099	−0.0799675
$531$	−2.30204	−0.0998998
$532$	−10.5468	−0.457261
$533$	0	0
$534$	−1.21495	−0.0525760
$535$	−0.140808	−0.00608764
$536$	−0.896881	−0.0387394
$537$	−6.09328	−0.262944
$538$	−0.804119	−0.0346680
$539$	3.00048	0.129240
$540$	−2.80986	−0.120917
$541$	−0.948185	−0.0407656	−0.0203828	−	0.999792i	$-0.506489\pi$
$541$	−0.948185	−0.0407656	−0.0203828	+	0.999792i	$0.506489\pi$
$542$	−1.98239	−0.0851509
$543$	15.8856	0.681716
$544$	−8.06524	−0.345794
$545$	−7.04711	−0.301865
$546$	0	0
$547$	30.4804	1.30325	0.651624	−	0.758542i	$-0.274088\pi$
$547$	30.4804	1.30325	0.651624	+	0.758542i	$0.274088\pi$
$548$	19.8220	0.846756
$549$	4.03885	0.172374
$550$	−0.958552	−0.0408728
$551$	−2.73966	−0.116714
$552$	0.285049	0.0121325
$553$	−12.6905	−0.539653
$554$	1.87236	0.0795491
$555$	−9.11788	−0.387033
$556$	−42.9106	−1.81981
$557$	−12.6446	−0.535771	−0.267885	−	0.963451i	$-0.586325\pi$
$557$	−12.6446	−0.535771	−0.267885	+	0.963451i	$0.586325\pi$
$558$	0.0299946	0.00126977
$559$	0	0
$560$	−5.55597	−0.234783
$561$	−19.1044	−0.806589
$562$	1.86142	0.0785193
$563$	−15.9114	−0.670587	−0.335293	−	0.942114i	$-0.608835\pi$
$563$	−15.9114	−0.670587	−0.335293	+	0.942114i	$0.608835\pi$
$564$	−11.7686	−0.495547
$565$	5.68059	0.238984
$566$	1.74546	0.0733673
$567$	−1.00000	−0.0419961
$568$	6.22564	0.261222
$569$	37.6223	1.57721	0.788605	−	0.614900i	$-0.210804\pi$
$569$	37.6223	1.57721	0.788605	+	0.614900i	$0.210804\pi$
$570$	−0.796980	−0.0333818
$571$	−4.29214	−0.179620	−0.0898102	−	0.995959i	$-0.528626\pi$
$571$	−4.29214	−0.179620	−0.0898102	+	0.995959i	$0.528626\pi$
$572$	0	0
$573$	5.30672	0.221692
$574$	0.422452	0.0176328
$575$	2.01820	0.0841647
$576$	−7.72978	−0.322074
$577$	−22.9788	−0.956621	−0.478310	−	0.878191i	$-0.658751\pi$
$577$	−22.9788	−0.956621	−0.478310	+	0.878191i	$0.658751\pi$
$578$	2.50373	0.104141
$579$	−2.08239	−0.0865412
$580$	−1.45154	−0.0602719
$581$	−8.49842	−0.352574
$582$	−0.0390185	−0.00161737
$583$	−36.7577	−1.52235
$584$	2.73286	0.113086
$585$	0	0
$586$	2.98258	0.123209
$587$	−2.79631	−0.115416	−0.0577081	−	0.998334i	$-0.518379\pi$
$587$	−2.79631	−0.115416	−0.0577081	+	0.998334i	$0.518379\pi$
$588$	−1.98869	−0.0820121
$589$	−1.49562	−0.0616258
$590$	−0.345944	−0.0142423
$591$	9.87467	0.406190
$592$	−25.3757	−1.04293
$593$	28.7209	1.17943	0.589713	−	0.807613i	$-0.299241\pi$
$593$	28.7209	1.17943	0.589713	+	0.807613i	$0.299241\pi$
$594$	0.319129	0.0130940
$595$	8.99625	0.368810
$596$	45.3592	1.85799
$597$	−3.31608	−0.135718
$598$	0	0
$599$	−5.19953	−0.212447	−0.106223	−	0.994342i	$-0.533876\pi$
$599$	−5.19953	−0.212447	−0.106223	+	0.994342i	$0.533876\pi$
$600$	1.27425	0.0520211
$601$	8.40738	0.342944	0.171472	−	0.985189i	$-0.445148\pi$
$601$	8.40738	0.342944	0.171472	+	0.985189i	$0.445148\pi$
$602$	−0.525881	−0.0214333
$603$	2.11412	0.0860935
$604$	33.6197	1.36797
$605$	−2.82180	−0.114723
$606$	1.95189	0.0792901
$607$	7.87133	0.319487	0.159744	−	0.987159i	$-0.448933\pi$
$607$	7.87133	0.319487	0.159744	+	0.987159i	$0.448933\pi$
$608$	−6.71781	−0.272443
$609$	−0.516587	−0.0209332
$610$	0.606948	0.0245746
$611$	0	0
$612$	12.6622	0.511840
$613$	−18.5692	−0.750005	−0.375002	−	0.927024i	$-0.622358\pi$
$613$	−18.5692	−0.750005	−0.375002	+	0.927024i	$0.622358\pi$
$614$	2.51232	0.101389
$615$	−5.61202	−0.226299
$616$	1.27291	0.0512868
$617$	−46.6445	−1.87784	−0.938918	−	0.344141i	$-0.888170\pi$
$617$	−46.6445	−1.87784	−0.938918	+	0.344141i	$0.888170\pi$
$618$	−0.425301	−0.0171081
$619$	9.30626	0.374050	0.187025	−	0.982355i	$-0.440115\pi$
$619$	9.30626	0.374050	0.187025	+	0.982355i	$0.440115\pi$
$620$	−0.792413	−0.0318241
$621$	−0.671915	−0.0269630
$622$	−1.40944	−0.0565132
$623$	11.4231	0.457655
$624$	0	0
$625$	−0.959821	−0.0383929
$626$	−1.18962	−0.0475469
$627$	−15.9127	−0.635492
$628$	23.7979	0.949640
$629$	41.0884	1.63830
$630$	−0.150278	−0.00598720
$631$	−32.6539	−1.29993	−0.649966	−	0.759963i	$-0.725217\pi$
$631$	−32.6539	−1.29993	−0.649966	+	0.759963i	$0.725217\pi$
$632$	−5.38373	−0.214153
$633$	−17.4614	−0.694028
$634$	2.16625	0.0860329
$635$	−23.4466	−0.930450
$636$	24.3626	0.966041
$637$	0	0
$638$	0.164858	0.00652679
$639$	−14.6750	−0.580534
$640$	−4.74111	−0.187409
$641$	18.5085	0.731041	0.365520	−	0.930803i	$-0.380891\pi$
$641$	18.5085	0.731041	0.365520	+	0.930803i	$0.380891\pi$
$642$	−0.0105995	−0.000418327 0
$643$	25.0781	0.988984	0.494492	−	0.869182i	$-0.335354\pi$
$643$	25.0781	0.988984	0.494492	+	0.869182i	$0.335354\pi$
$644$	−1.33623	−0.0526548
$645$	6.98602	0.275074
$646$	3.59147	0.141305
$647$	−6.58749	−0.258981	−0.129491	−	0.991581i	$-0.541334\pi$
$647$	−6.58749	−0.258981	−0.129491	+	0.991581i	$0.541334\pi$
$648$	−0.424234	−0.0166655
$649$	−6.90720	−0.271131
$650$	0	0
$651$	−0.282012	−0.0110529
$652$	−0.558024	−0.0218539
$653$	28.5706	1.11805	0.559027	−	0.829150i	$-0.311175\pi$
$653$	28.5706	1.11805	0.559027	+	0.829150i	$0.311175\pi$
$654$	−0.530480	−0.0207434
$655$	−26.3496	−1.02956
$656$	−15.6186	−0.609805
$657$	−6.44186	−0.251321
$658$	−0.629410	−0.0245370
$659$	−27.5572	−1.07348	−0.536738	−	0.843749i	$-0.680344\pi$
$659$	−27.5572	−1.07348	−0.536738	+	0.843749i	$0.680344\pi$
$660$	−8.43092	−0.328173
$661$	39.2159	1.52532	0.762662	−	0.646798i	$-0.223892\pi$
$661$	39.2159	1.52532	0.762662	+	0.646798i	$0.223892\pi$
$662$	−2.67995	−0.104159
$663$	0	0
$664$	−3.60532	−0.139914
$665$	7.49327	0.290577
$666$	−0.686359	−0.0265959
$667$	−0.347103	−0.0134399
$668$	41.4027	1.60192
$669$	18.7566	0.725172
$670$	0.317704	0.0122740
$671$	12.1185	0.467828
$672$	−1.26670	−0.0488640
$673$	0.0744211	0.00286872	0.00143436	−	0.999999i	$-0.499543\pi$
$673$	0.0744211	0.00286872	0.00143436	+	0.999999i	$0.499543\pi$
$674$	−2.22627	−0.0857527
$675$	−3.00365	−0.115611
$676$	0	0
$677$	35.6966	1.37193	0.685966	−	0.727633i	$-0.259380\pi$
$677$	35.6966	1.37193	0.685966	+	0.727633i	$0.259380\pi$
$678$	0.427613	0.0164224
$679$	0.366855	0.0140786
$680$	3.81652	0.146357
$681$	−16.3261	−0.625616
$682$	0.0899980	0.00344620
$683$	16.6706	0.637881	0.318941	−	0.947775i	$-0.396673\pi$
$683$	16.6706	0.637881	0.318941	+	0.947775i	$0.396673\pi$
$684$	10.5468	0.403266
$685$	−14.0832	−0.538090
$686$	−0.106359	−0.00406082
$687$	−11.3658	−0.433631
$688$	19.4426	0.741241
$689$	0	0
$690$	−0.100974	−0.00384400
$691$	−47.7874	−1.81792	−0.908959	−	0.416885i	$-0.863122\pi$
$691$	−47.7874	−1.81792	−0.908959	+	0.416885i	$0.863122\pi$
$692$	11.0714	0.420873
$693$	−3.00048	−0.113979
$694$	−2.51484	−0.0954619
$695$	30.4871	1.15644
$696$	−0.219154	−0.00830702
$697$	25.2898	0.957918
$698$	−2.53605	−0.0959909
$699$	30.2591	1.14450
$700$	−5.97332	−0.225770
$701$	−30.5430	−1.15359	−0.576797	−	0.816887i	$-0.695698\pi$
$701$	−30.5430	−1.15359	−0.576797	+	0.816887i	$0.695698\pi$
$702$	0	0
$703$	34.2239	1.29078
$704$	−23.1930	−0.874120
$705$	8.36134	0.314906
$706$	0.911494	0.0343045
$707$	−18.3518	−0.690192
$708$	4.57803	0.172053
$709$	29.7888	1.11874	0.559370	−	0.828918i	$-0.311043\pi$
$709$	29.7888	1.11874	0.559370	+	0.828918i	$0.311043\pi$
$710$	−2.20532	−0.0827643
$711$	12.6905	0.475929
$712$	4.84606	0.181614
$713$	−0.189488	−0.00709637
$714$	0.677203	0.0253437
$715$	0	0
$716$	12.1176	0.452857
$717$	−17.1229	−0.639467
$718$	0.827667	0.0308882
$719$	15.0565	0.561512	0.280756	−	0.959779i	$-0.409415\pi$
$719$	15.0565	0.561512	0.280756	+	0.959779i	$0.409415\pi$
$720$	5.55597	0.207059
$721$	3.99871	0.148920
$722$	0.970627	0.0361230
$723$	−17.3298	−0.644501
$724$	−31.5915	−1.17409
$725$	−1.55165	−0.0576268
$726$	−0.212415	−0.00788345
$727$	34.6564	1.28533	0.642667	−	0.766146i	$-0.277828\pi$
$727$	34.6564	1.28533	0.642667	+	0.766146i	$0.277828\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−0.968067	−0.0358298
$731$	−31.4815	−1.16438
$732$	−8.03201	−0.296871
$733$	34.3778	1.26977	0.634886	−	0.772605i	$-0.281047\pi$
$733$	34.3778	1.26977	0.634886	+	0.772605i	$0.281047\pi$
$734$	−2.27186	−0.0838558
$735$	1.41292	0.0521164
$736$	−0.851115	−0.0313725
$737$	6.34336	0.233661
$738$	−0.422452	−0.0155507
$739$	19.9101	0.732406	0.366203	−	0.930535i	$-0.380658\pi$
$739$	19.9101	0.732406	0.366203	+	0.930535i	$0.380658\pi$
$740$	18.1326	0.666568
$741$	0	0
$742$	1.30297	0.0478334
$743$	−25.9071	−0.950441	−0.475220	−	0.879867i	$-0.657632\pi$
$743$	−25.9071	−0.950441	−0.475220	+	0.879867i	$0.657632\pi$
$744$	−0.119639	−0.00438618
$745$	−32.2268	−1.18070
$746$	0.209212	0.00765980
$747$	8.49842	0.310941
$748$	37.9927	1.38915
$749$	0.0996570	0.00364139
$750$	−1.20277	−0.0439189
$751$	−2.22226	−0.0810915	−0.0405457	−	0.999178i	$-0.512910\pi$
$751$	−2.22226	−0.0810915	−0.0405457	+	0.999178i	$0.512910\pi$
$752$	23.2702	0.848576
$753$	11.3754	0.414544
$754$	0	0
$755$	−23.8861	−0.869305
$756$	1.98869	0.0723279
$757$	−53.9782	−1.96187	−0.980936	−	0.194330i	$-0.937747\pi$
$757$	−53.9782	−1.96187	−0.980936	+	0.194330i	$0.937747\pi$
$758$	−3.42959	−0.124568
$759$	−2.01607	−0.0731785
$760$	3.17890	0.115311
$761$	43.7649	1.58647	0.793237	−	0.608913i	$-0.208394\pi$
$761$	43.7649	1.58647	0.793237	+	0.608913i	$0.208394\pi$
$762$	−1.76497	−0.0639381
$763$	4.98762	0.180564
$764$	−10.5534	−0.381809
$765$	−8.99625	−0.325260
$766$	3.63901	0.131483
$767$	0	0
$768$	15.1027	0.544971
$769$	−15.3047	−0.551903	−0.275951	−	0.961172i	$-0.588993\pi$
$769$	−15.3047	−0.551903	−0.275951	+	0.961172i	$0.588993\pi$
$770$	−0.450904	−0.0162495
$771$	17.9289	0.645694
$772$	4.14123	0.149046
$773$	1.69082	0.0608145	0.0304072	−	0.999538i	$-0.490320\pi$
$773$	1.69082	0.0608145	0.0304072	+	0.999538i	$0.490320\pi$
$774$	0.525881	0.0189024
$775$	−0.847064	−0.0304274
$776$	0.155633	0.00558689
$777$	6.45321	0.231508
$778$	−0.101399	−0.00363532
$779$	21.0647	0.754720
$780$	0	0
$781$	−44.0320	−1.57559
$782$	0.455023	0.0162716
$783$	0.516587	0.0184613
$784$	3.93225	0.140438
$785$	−16.9079	−0.603470
$786$	−1.98350	−0.0707490
$787$	−4.48551	−0.159891	−0.0799455	−	0.996799i	$-0.525475\pi$
$787$	−4.48551	−0.159891	−0.0799455	+	0.996799i	$0.525475\pi$
$788$	−19.6376	−0.699562
$789$	20.7063	0.737164
$790$	1.90709	0.0678512
$791$	−4.02046	−0.142951
$792$	−1.27291	−0.0452307
$793$	0	0
$794$	0.487814	0.0173119
$795$	−17.3092	−0.613893
$796$	6.59464	0.233741
$797$	−5.08453	−0.180103	−0.0900516	−	0.995937i	$-0.528703\pi$
$797$	−5.08453	−0.180103	−0.0900516	+	0.995937i	$0.528703\pi$
$798$	0.564065	0.0199677
$799$	−37.6792	−1.33299
$800$	−3.80473	−0.134517
$801$	−11.4231	−0.403614
$802$	3.36898	0.118963
$803$	−19.3286	−0.682093
$804$	−4.20432	−0.148275
$805$	0.949364	0.0334607
$806$	0	0
$807$	−7.56039	−0.266138
$808$	−7.78548	−0.273892
$809$	−42.8271	−1.50572	−0.752860	−	0.658181i	$-0.771326\pi$
$809$	−42.8271	−1.50572	−0.752860	+	0.658181i	$0.771326\pi$
$810$	0.150278	0.00528021
$811$	−7.34880	−0.258051	−0.129026	−	0.991641i	$-0.541185\pi$
$811$	−7.34880	−0.258051	−0.129026	+	0.991641i	$0.541185\pi$
$812$	1.02733	0.0360523
$813$	−18.6386	−0.653684
$814$	−2.05941	−0.0721821
$815$	0.396465	0.0138876
$816$	−25.0371	−0.876476
$817$	−26.2220	−0.917390
$818$	−1.15756	−0.0404733
$819$	0	0
$820$	11.1606	0.389744
$821$	47.4489	1.65598	0.827989	−	0.560744i	$-0.189485\pi$
$821$	47.4489	1.65598	0.827989	+	0.560744i	$0.189485\pi$
$822$	−1.06013	−0.0369762
$823$	−34.8823	−1.21592	−0.607960	−	0.793968i	$-0.708012\pi$
$823$	−34.8823	−1.21592	−0.607960	+	0.793968i	$0.708012\pi$
$824$	1.69639	0.0590966
$825$	−9.01239	−0.313771
$826$	0.244843	0.00851918
$827$	10.6148	0.369111	0.184556	−	0.982822i	$-0.440915\pi$
$827$	10.6148	0.369111	0.184556	+	0.982822i	$0.440915\pi$
$828$	1.33623	0.0464372
$829$	22.1291	0.768576	0.384288	−	0.923213i	$-0.374447\pi$
$829$	22.1291	0.768576	0.384288	+	0.923213i	$0.374447\pi$
$830$	1.27712	0.0443295
$831$	17.6041	0.610680
$832$	0	0
$833$	−6.36712	−0.220608
$834$	2.29495	0.0794677
$835$	−29.4158	−1.01797
$836$	31.6454	1.09448
$837$	0.282012	0.00974774
$838$	1.78951	0.0618175
$839$	−6.74356	−0.232813	−0.116407	−	0.993202i	$-0.537138\pi$
$839$	−6.74356	−0.232813	−0.116407	+	0.993202i	$0.537138\pi$
$840$	0.599410	0.0206816
$841$	−28.7331	−0.990798
$842$	0.651208	0.0224421
$843$	17.5012	0.602775
$844$	34.7253	1.19529
$845$	0	0
$846$	0.629410	0.0216396
$847$	1.99714	0.0686226
$848$	−48.1725	−1.65425
$849$	16.4110	0.563224
$850$	2.03408	0.0697685
$851$	4.33601	0.148636
$852$	29.1840	0.999828
$853$	−44.1129	−1.51040	−0.755199	−	0.655496i	$-0.772460\pi$
$853$	−44.1129	−1.51040	−0.755199	+	0.655496i	$0.772460\pi$
$854$	−0.429569	−0.0146996
$855$	−7.49327	−0.256265
$856$	0.0422779	0.00144503
$857$	57.0811	1.94985	0.974927	−	0.222526i	$-0.0714302\pi$
$857$	57.0811	1.94985	0.974927	+	0.222526i	$0.0714302\pi$
$858$	0	0
$859$	−24.1100	−0.822624	−0.411312	−	0.911495i	$-0.634929\pi$
$859$	−24.1100	−0.822624	−0.411312	+	0.911495i	$0.634929\pi$
$860$	−13.8930	−0.473748
$861$	3.97193	0.135363
$862$	−0.116003	−0.00395107
$863$	−4.28266	−0.145783	−0.0728917	−	0.997340i	$-0.523223\pi$
$863$	−4.28266	−0.145783	−0.0728917	+	0.997340i	$0.523223\pi$
$864$	1.26670	0.0430940
$865$	−7.86602	−0.267453
$866$	0.887014	0.0301420
$867$	23.5403	0.799469
$868$	0.560833	0.0190359
$869$	38.0774	1.29169
$870$	0.0776315	0.00263195
$871$	0	0
$872$	2.11592	0.0716540
$873$	−0.366855	−0.0124162
$874$	0.379004	0.0128200
$875$	11.3085	0.382298
$876$	12.8108	0.432838
$877$	43.3557	1.46402	0.732009	−	0.681295i	$-0.238583\pi$
$877$	43.3557	1.46402	0.732009	+	0.681295i	$0.238583\pi$
$878$	−0.610996	−0.0206201
$879$	28.0424	0.945848
$880$	16.6706	0.561964
$881$	8.99919	0.303190	0.151595	−	0.988443i	$-0.451559\pi$
$881$	8.99919	0.303190	0.151595	+	0.988443i	$0.451559\pi$
$882$	0.106359	0.00358131
$883$	57.3615	1.93037	0.965183	−	0.261574i	$-0.0842415\pi$
$883$	57.3615	1.93037	0.965183	+	0.261574i	$0.0842415\pi$
$884$	0	0
$885$	−3.25260	−0.109335
$886$	−1.80545	−0.0606551
$887$	23.7321	0.796847	0.398423	−	0.917202i	$-0.369557\pi$
$887$	23.7321	0.796847	0.398423	+	0.917202i	$0.369557\pi$
$888$	2.73767	0.0918703
$889$	16.5944	0.556558
$890$	−1.71663	−0.0575415
$891$	3.00048	0.100520
$892$	−37.3010	−1.24893
$893$	−31.3842	−1.05023
$894$	−2.42591	−0.0811346
$895$	−8.60932	−0.287778
$896$	3.35554	0.112101
$897$	0	0
$898$	0.369275	0.0123229
$899$	0.145684	0.00485882
$900$	5.97332	0.199111
$901$	78.0012	2.59860
$902$	−1.26756	−0.0422050
$903$	−4.94438	−0.164539
$904$	−1.70562	−0.0567280
$905$	22.4451	0.746100
$906$	−1.79806	−0.0597364
$907$	14.1384	0.469459	0.234729	−	0.972061i	$-0.424580\pi$
$907$	14.1384	0.469459	0.234729	+	0.972061i	$0.424580\pi$
$908$	32.4675	1.07747
$909$	18.3518	0.608692
$910$	0	0
$911$	26.2323	0.869113	0.434557	−	0.900644i	$-0.356905\pi$
$911$	26.2323	0.869113	0.434557	+	0.900644i	$0.356905\pi$
$912$	−20.8543	−0.690554
$913$	25.4993	0.843904
$914$	−1.03039	−0.0340824
$915$	5.70658	0.188654
$916$	22.6030	0.746823
$917$	18.6490	0.615844
$918$	−0.677203	−0.0223510
$919$	−55.0924	−1.81733	−0.908665	−	0.417526i	$-0.862897\pi$
$919$	−55.0924	−1.81733	−0.908665	+	0.417526i	$0.862897\pi$
$920$	0.402753	0.0132784
$921$	23.6211	0.778341
$922$	1.17983	0.0388555
$923$	0	0
$924$	5.96701	0.196300
$925$	19.3832	0.637315
$926$	3.31451	0.108921
$927$	−3.99871	−0.131335
$928$	0.654362	0.0214805
$929$	−35.1033	−1.15170	−0.575851	−	0.817555i	$-0.695329\pi$
$929$	−35.1033	−1.15170	−0.575851	+	0.817555i	$0.695329\pi$
$930$	0.0423800	0.00138969
$931$	−5.30339	−0.173812
$932$	−60.1759	−1.97113
$933$	−13.2516	−0.433839
$934$	2.94852	0.0964784
$935$	−26.9930	−0.882767
$936$	0	0
$937$	22.6413	0.739658	0.369829	−	0.929100i	$-0.379416\pi$
$937$	22.6413	0.739658	0.369829	+	0.929100i	$0.379416\pi$
$938$	−0.224856	−0.00734182
$939$	−11.1849	−0.365007
$940$	−16.6281	−0.542349
$941$	13.4907	0.439785	0.219892	−	0.975524i	$-0.429429\pi$
$941$	13.4907	0.439785	0.219892	+	0.975524i	$0.429429\pi$
$942$	−1.27276	−0.0414689
$943$	2.66880	0.0869080
$944$	−9.05219	−0.294624
$945$	−1.41292	−0.0459624
$946$	1.57789	0.0513018
$947$	−27.2352	−0.885026	−0.442513	−	0.896762i	$-0.645913\pi$
$947$	−27.2352	−0.885026	−0.442513	+	0.896762i	$0.645913\pi$
$948$	−25.2374	−0.819671
$949$	0	0
$950$	1.69425	0.0549689
$951$	20.3673	0.660455
$952$	−2.70115	−0.0875449
$953$	−57.9455	−1.87704	−0.938519	−	0.345227i	$-0.887802\pi$
$953$	−57.9455	−1.87704	−0.938519	+	0.345227i	$0.887802\pi$
$954$	−1.30297	−0.0421851
$955$	7.49799	0.242629
$956$	34.0521	1.10132
$957$	1.55001	0.0501047
$958$	−0.608939	−0.0196739
$959$	9.96740	0.321864
$960$	−10.9216	−0.352492
$961$	−30.9205	−0.997435
$962$	0	0
$963$	−0.0996570	−0.00321140
$964$	34.4635	1.10999
$965$	−2.94226	−0.0947146
$966$	0.0714645	0.00229933
$967$	−61.3188	−1.97188	−0.985940	−	0.167101i	$-0.946559\pi$
$967$	−61.3188	−1.97188	−0.985940	+	0.167101i	$0.946559\pi$
$968$	0.847256	0.0272318
$969$	33.7673	1.08476
$970$	−0.0551301	−0.00177012
$971$	−18.3504	−0.588894	−0.294447	−	0.955668i	$-0.595135\pi$
$971$	−18.3504	−0.588894	−0.294447	+	0.955668i	$0.595135\pi$
$972$	−1.98869	−0.0637872
$973$	−21.5773	−0.691738
$974$	0.380487	0.0121916
$975$	0	0
$976$	15.8818	0.508363
$977$	4.81588	0.154074	0.0770368	−	0.997028i	$-0.475454\pi$
$977$	4.81588	0.154074	0.0770368	+	0.997028i	$0.475454\pi$
$978$	0.0298443	0.000954317 0
$979$	−34.2746	−1.09542
$980$	−2.80986	−0.0897577
$981$	−4.98762	−0.159242
$982$	0.368651	0.0117641
$983$	46.0686	1.46936	0.734679	−	0.678414i	$-0.237333\pi$
$983$	46.0686	1.46936	0.734679	+	0.678414i	$0.237333\pi$
$984$	1.68503	0.0537167
$985$	13.9521	0.444552
$986$	−0.349835	−0.0111410
$987$	−5.91777	−0.188365
$988$	0	0
$989$	−3.32220	−0.105640
$990$	0.450904	0.0143307
$991$	−12.8242	−0.407375	−0.203688	−	0.979036i	$-0.565293\pi$
$991$	−12.8242	−0.407375	−0.203688	+	0.979036i	$0.565293\pi$
$992$	0.357224	0.0113419
$993$	−25.1972	−0.799608
$994$	1.56082	0.0495064
$995$	−4.68536	−0.148536
$996$	−16.9007	−0.535519
$997$	30.1107	0.953614	0.476807	−	0.879008i	$-0.341794\pi$
$997$	30.1107	0.953614	0.476807	+	0.879008i	$0.341794\pi$
$998$	3.61666	0.114483
$999$	−6.45321	−0.204171

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bb.1.5		8
13.2	odd	12		273.2.bd.a.43.5	✓	16
13.7	odd	12		273.2.bd.a.127.5	yes	16
13.12	even	2		3549.2.a.bd.1.4		8
39.2	even	12		819.2.ct.b.316.4		16
39.20	even	12		819.2.ct.b.127.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.a.43.5	✓	16	13.2	odd	12
273.2.bd.a.127.5	yes	16	13.7	odd	12
819.2.ct.b.127.4		16	39.20	even	12
819.2.ct.b.316.4		16	39.2	even	12
3549.2.a.bb.1.5		8	1.1	even	1	trivial
3549.2.a.bd.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)

\(f(q)\)	\(=\)	\(q+0.106359 q^{2} +1.00000 q^{3} -1.98869 q^{4} +1.41292 q^{5} +0.106359 q^{6} -1.00000 q^{7} -0.424234 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.106359 q^{2} +1.00000 q^{3} -1.98869 q^{4} +1.41292 q^{5} +0.106359 q^{6} -1.00000 q^{7} -0.424234 q^{8} +1.00000 q^{9} +0.150278 q^{10} +3.00048 q^{11} -1.98869 q^{12} -0.106359 q^{14} +1.41292 q^{15} +3.93225 q^{16} -6.36712 q^{17} +0.106359 q^{18} -5.30339 q^{19} -2.80986 q^{20} -1.00000 q^{21} +0.319129 q^{22} -0.671915 q^{23} -0.424234 q^{24} -3.00365 q^{25} +1.00000 q^{27} +1.98869 q^{28} +0.516587 q^{29} +0.150278 q^{30} +0.282012 q^{31} +1.26670 q^{32} +3.00048 q^{33} -0.677203 q^{34} -1.41292 q^{35} -1.98869 q^{36} -6.45321 q^{37} -0.564065 q^{38} -0.599410 q^{40} -3.97193 q^{41} -0.106359 q^{42} +4.94438 q^{43} -5.96701 q^{44} +1.41292 q^{45} -0.0714645 q^{46} +5.91777 q^{47} +3.93225 q^{48} +1.00000 q^{49} -0.319466 q^{50} -6.36712 q^{51} -12.2506 q^{53} +0.106359 q^{54} +4.23944 q^{55} +0.424234 q^{56} -5.30339 q^{57} +0.0549439 q^{58} -2.30204 q^{59} -2.80986 q^{60} +4.03885 q^{61} +0.0299946 q^{62} -1.00000 q^{63} -7.72978 q^{64} +0.319129 q^{66} +2.11412 q^{67} +12.6622 q^{68} -0.671915 q^{69} -0.150278 q^{70} -14.6750 q^{71} -0.424234 q^{72} -6.44186 q^{73} -0.686359 q^{74} -3.00365 q^{75} +10.5468 q^{76} -3.00048 q^{77} +12.6905 q^{79} +5.55597 q^{80} +1.00000 q^{81} -0.422452 q^{82} +8.49842 q^{83} +1.98869 q^{84} -8.99625 q^{85} +0.525881 q^{86} +0.516587 q^{87} -1.27291 q^{88} -11.4231 q^{89} +0.150278 q^{90} +1.33623 q^{92} +0.282012 q^{93} +0.629410 q^{94} -7.49327 q^{95} +1.26670 q^{96} -0.366855 q^{97} +0.106359 q^{98} +3.00048 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9	\( 8 q - 2 q^{2} + 8 q^{3} + 6 q^{4} - 2 q^{5} - 2 q^{6} - 8 q^{7} - 12 q^{8} + 8 q^{9} - 4 q^{10} - 8 q^{11} + 6 q^{12} + 2 q^{14} - 2 q^{15} + 10 q^{16} + 10 q^{17} - 2 q^{18} - 18 q^{19} - 2 q^{20} - 8 q^{21} + 2 q^{22} - 2 q^{23} - 12 q^{24} - 6 q^{25} + 8 q^{27} - 6 q^{28} - 12 q^{29} - 4 q^{30} - 16 q^{31} - 26 q^{32} - 8 q^{33} - 24 q^{34} + 2 q^{35} + 6 q^{36} - 24 q^{37} + 16 q^{38} - 30 q^{40} + 4 q^{41} + 2 q^{42} - 10 q^{43} + 20 q^{44} - 2 q^{45} - 12 q^{46} - 10 q^{47} + 10 q^{48} + 8 q^{49} + 16 q^{50} + 10 q^{51} + 6 q^{53} - 2 q^{54} - 10 q^{55} + 12 q^{56} - 18 q^{57} - 16 q^{58} - 6 q^{59} - 2 q^{60} + 6 q^{61} + 16 q^{62} - 8 q^{63} - 8 q^{64} + 2 q^{66} - 24 q^{67} + 20 q^{68} - 2 q^{69} + 4 q^{70} - 42 q^{71} - 12 q^{72} - 32 q^{73} - 18 q^{74} - 6 q^{75} - 28 q^{76} + 8 q^{77} - 2 q^{79} + 40 q^{80} + 8 q^{81} - 18 q^{82} + 2 q^{83} - 6 q^{84} - 4 q^{85} - 26 q^{86} - 12 q^{87} - 2 q^{88} - 12 q^{89} - 4 q^{90} - 10 q^{92} - 16 q^{93} - 16 q^{94} - 4 q^{95} - 26 q^{96} - 64 q^{97} - 2 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 + 8 * q^3 + 6 * q^4 - 2 * q^5 - 2 * q^6 - 8 * q^7 - 12 * q^8 + 8 * q^9 - 4 * q^10 - 8 * q^11 + 6 * q^12 + 2 * q^14 - 2 * q^15 + 10 * q^16 + 10 * q^17 - 2 * q^18 - 18 * q^19 - 2 * q^20 - 8 * q^21 + 2 * q^22 - 2 * q^23 - 12 * q^24 - 6 * q^25 + 8 * q^27 - 6 * q^28 - 12 * q^29 - 4 * q^30 - 16 * q^31 - 26 * q^32 - 8 * q^33 - 24 * q^34 + 2 * q^35 + 6 * q^36 - 24 * q^37 + 16 * q^38 - 30 * q^40 + 4 * q^41 + 2 * q^42 - 10 * q^43 + 20 * q^44 - 2 * q^45 - 12 * q^46 - 10 * q^47 + 10 * q^48 + 8 * q^49 + 16 * q^50 + 10 * q^51 + 6 * q^53 - 2 * q^54 - 10 * q^55 + 12 * q^56 - 18 * q^57 - 16 * q^58 - 6 * q^59 - 2 * q^60 + 6 * q^61 + 16 * q^62 - 8 * q^63 - 8 * q^64 + 2 * q^66 - 24 * q^67 + 20 * q^68 - 2 * q^69 + 4 * q^70 - 42 * q^71 - 12 * q^72 - 32 * q^73 - 18 * q^74 - 6 * q^75 - 28 * q^76 + 8 * q^77 - 2 * q^79 + 40 * q^80 + 8 * q^81 - 18 * q^82 + 2 * q^83 - 6 * q^84 - 4 * q^85 - 26 * q^86 - 12 * q^87 - 2 * q^88 - 12 * q^89 - 4 * q^90 - 10 * q^92 - 16 * q^93 - 16 * q^94 - 4 * q^95 - 26 * q^96 - 64 * q^97 - 2 * q^98 - 8 * q^99

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