LMFDB - Embedded newform 3549.2.a.bc.1.1

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:	$0$
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			1.1
Root			$-2.29328$ 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)

$f(q)$	$=$	$q-2.29328 q^{2} -1.00000 q^{3} +3.25913 q^{4} -0.692320 q^{5} +2.29328 q^{6} -1.00000 q^{7} -2.88753 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.29328 q^{2} -1.00000 q^{3} +3.25913 q^{4} -0.692320 q^{5} +2.29328 q^{6} -1.00000 q^{7} -2.88753 q^{8} +1.00000 q^{9} +1.58768 q^{10} +6.01573 q^{11} -3.25913 q^{12} +2.29328 q^{14} +0.692320 q^{15} +0.103650 q^{16} -7.99504 q^{17} -2.29328 q^{18} +3.00918 q^{19} -2.25636 q^{20} +1.00000 q^{21} -13.7958 q^{22} +0.653547 q^{23} +2.88753 q^{24} -4.52069 q^{25} -1.00000 q^{27} -3.25913 q^{28} +9.28692 q^{29} -1.58768 q^{30} +1.47475 q^{31} +5.53735 q^{32} -6.01573 q^{33} +18.3348 q^{34} +0.692320 q^{35} +3.25913 q^{36} +4.03636 q^{37} -6.90088 q^{38} +1.99909 q^{40} +9.18247 q^{41} -2.29328 q^{42} -8.12988 q^{43} +19.6060 q^{44} -0.692320 q^{45} -1.49876 q^{46} -0.664432 q^{47} -0.103650 q^{48} +1.00000 q^{49} +10.3672 q^{50} +7.99504 q^{51} +10.3300 q^{53} +2.29328 q^{54} -4.16481 q^{55} +2.88753 q^{56} -3.00918 q^{57} -21.2975 q^{58} -2.04106 q^{59} +2.25636 q^{60} +1.38796 q^{61} -3.38201 q^{62} -1.00000 q^{63} -12.9060 q^{64} +13.7958 q^{66} -7.38012 q^{67} -26.0568 q^{68} -0.653547 q^{69} -1.58768 q^{70} -1.00204 q^{71} -2.88753 q^{72} -10.6068 q^{73} -9.25650 q^{74} +4.52069 q^{75} +9.80729 q^{76} -6.01573 q^{77} +6.08603 q^{79} -0.0717592 q^{80} +1.00000 q^{81} -21.0580 q^{82} -0.377468 q^{83} +3.25913 q^{84} +5.53513 q^{85} +18.6441 q^{86} -9.28692 q^{87} -17.3706 q^{88} +6.63723 q^{89} +1.58768 q^{90} +2.12999 q^{92} -1.47475 q^{93} +1.52373 q^{94} -2.08331 q^{95} -5.53735 q^{96} +0.346177 q^{97} -2.29328 q^{98} +6.01573 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.29328	−1.62159	−0.810796	−	0.585328i	$-0.800966\pi$
$2$	−2.29328	−1.62159	−0.810796	+	0.585328i	$0.800966\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.25913	1.62956
$5$	−0.692320	−0.309615	−0.154807	−	0.987945i	$-0.549476\pi$
$5$	−0.692320	−0.309615	−0.154807	+	0.987945i	$0.549476\pi$
$6$	2.29328	0.936227
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.88753	−1.02089
$9$	1.00000	0.333333
$10$	1.58768	0.502069
$11$	6.01573	1.81381	0.906906	−	0.421333i	$-0.138438\pi$
$11$	6.01573	1.81381	0.906906	+	0.421333i	$0.138438\pi$
$12$	−3.25913	−0.940829
$13$	0	0
$13$	0	0
$14$	2.29328	0.612904
$15$	0.692320	0.178756
$16$	0.103650	0.0259126
$17$	−7.99504	−1.93908	−0.969541	−	0.244930i	$-0.921235\pi$
$17$	−7.99504	−1.93908	−0.969541	+	0.244930i	$0.921235\pi$
$18$	−2.29328	−0.540531
$19$	3.00918	0.690353	0.345176	−	0.938538i	$-0.387819\pi$
$19$	3.00918	0.690353	0.345176	+	0.938538i	$0.387819\pi$
$20$	−2.25636	−0.504537
$21$	1.00000	0.218218
$22$	−13.7958	−2.94126
$23$	0.653547	0.136274	0.0681370	−	0.997676i	$-0.478295\pi$
$23$	0.653547	0.136274	0.0681370	+	0.997676i	$0.478295\pi$
$24$	2.88753	0.589414
$25$	−4.52069	−0.904139
$26$	0	0
$27$	−1.00000	−0.192450
$28$	−3.25913	−0.615917
$29$	9.28692	1.72454	0.862269	−	0.506450i	$-0.169043\pi$
$29$	9.28692	1.72454	0.862269	+	0.506450i	$0.169043\pi$
$30$	−1.58768	−0.289870
$31$	1.47475	0.264873	0.132437	−	0.991191i	$-0.457720\pi$
$31$	1.47475	0.264873	0.132437	+	0.991191i	$0.457720\pi$
$32$	5.53735	0.978875
$33$	−6.01573	−1.04720
$34$	18.3348	3.14440
$35$	0.692320	0.117023
$36$	3.25913	0.543188
$37$	4.03636	0.663574	0.331787	−	0.943354i	$-0.392349\pi$
$37$	4.03636	0.663574	0.331787	+	0.943354i	$0.392349\pi$
$38$	−6.90088	−1.11947
$39$	0	0
$40$	1.99909	0.316084
$41$	9.18247	1.43406	0.717031	−	0.697042i	$-0.245501\pi$
$41$	9.18247	1.43406	0.717031	+	0.697042i	$0.245501\pi$
$42$	−2.29328	−0.353861
$43$	−8.12988	−1.23979	−0.619897	−	0.784683i	$-0.712826\pi$
$43$	−8.12988	−1.23979	−0.619897	+	0.784683i	$0.712826\pi$
$44$	19.6060	2.95572
$45$	−0.692320	−0.103205
$46$	−1.49876	−0.220981
$47$	−0.664432	−0.0969174	−0.0484587	−	0.998825i	$-0.515431\pi$
$47$	−0.664432	−0.0969174	−0.0484587	+	0.998825i	$0.515431\pi$
$48$	−0.103650	−0.0149606
$49$	1.00000	0.142857
$50$	10.3672	1.46614
$51$	7.99504	1.11953
$52$	0	0
$53$	10.3300	1.41894	0.709470	−	0.704735i	$-0.248934\pi$
$53$	10.3300	1.41894	0.709470	+	0.704735i	$0.248934\pi$
$54$	2.29328	0.312076
$55$	−4.16481	−0.561583
$56$	2.88753	0.385862
$57$	−3.00918	−0.398575
$58$	−21.2975	−2.79650
$59$	−2.04106	−0.265724	−0.132862	−	0.991135i	$-0.542417\pi$
$59$	−2.04106	−0.265724	−0.132862	+	0.991135i	$0.542417\pi$
$60$	2.25636	0.291295
$61$	1.38796	0.177710	0.0888550	−	0.996045i	$-0.471679\pi$
$61$	1.38796	0.177710	0.0888550	+	0.996045i	$0.471679\pi$
$62$	−3.38201	−0.429516
$63$	−1.00000	−0.125988
$64$	−12.9060	−1.61325
$65$	0	0
$66$	13.7958	1.69814
$67$	−7.38012	−0.901625	−0.450813	−	0.892619i	$-0.648866\pi$
$67$	−7.38012	−0.901625	−0.450813	+	0.892619i	$0.648866\pi$
$68$	−26.0568	−3.15986
$69$	−0.653547	−0.0786778
$70$	−1.58768	−0.189764
$71$	−1.00204	−0.118920	−0.0594599	−	0.998231i	$-0.518938\pi$
$71$	−1.00204	−0.118920	−0.0594599	+	0.998231i	$0.518938\pi$
$72$	−2.88753	−0.340298
$73$	−10.6068	−1.24144	−0.620718	−	0.784034i	$-0.713159\pi$
$73$	−10.6068	−1.24144	−0.620718	+	0.784034i	$0.713159\pi$
$74$	−9.25650	−1.07605
$75$	4.52069	0.522005
$76$	9.80729	1.12497
$77$	−6.01573	−0.685556
$78$	0	0
$79$	6.08603	0.684731	0.342366	−	0.939567i	$-0.388772\pi$
$79$	6.08603	0.684731	0.342366	+	0.939567i	$0.388772\pi$
$80$	−0.0717592	−0.00802292
$81$	1.00000	0.111111
$82$	−21.0580	−2.32546
$83$	−0.377468	−0.0414325	−0.0207163	−	0.999785i	$-0.506595\pi$
$83$	−0.377468	−0.0414325	−0.0207163	+	0.999785i	$0.506595\pi$
$84$	3.25913	0.355600
$85$	5.53513	0.600369
$86$	18.6441	2.01044
$87$	−9.28692	−0.995663
$88$	−17.3706	−1.85171
$89$	6.63723	0.703544	0.351772	−	0.936086i	$-0.385579\pi$
$89$	6.63723	0.703544	0.351772	+	0.936086i	$0.385579\pi$
$90$	1.58768	0.167356
$91$	0	0
$92$	2.12999	0.222067
$93$	−1.47475	−0.152925
$94$	1.52373	0.157161
$95$	−2.08331	−0.213744
$96$	−5.53735	−0.565154
$97$	0.346177	0.0351490	0.0175745	−	0.999846i	$-0.494406\pi$
$97$	0.346177	0.0351490	0.0175745	+	0.999846i	$0.494406\pi$
$98$	−2.29328	−0.231656
$99$	6.01573	0.604604
$100$	−14.7335	−1.47335
$101$	−15.2947	−1.52188	−0.760938	−	0.648825i	$-0.775261\pi$
$101$	−15.2947	−1.52188	−0.760938	+	0.648825i	$0.775261\pi$
$102$	−18.3348	−1.81542
$103$	10.6987	1.05418	0.527088	−	0.849811i	$-0.323284\pi$
$103$	10.6987	1.05418	0.527088	+	0.849811i	$0.323284\pi$
$104$	0	0
$105$	−0.692320	−0.0675635
$106$	−23.6897	−2.30094
$107$	−11.6138	−1.12275	−0.561376	−	0.827561i	$-0.689728\pi$
$107$	−11.6138	−1.12275	−0.561376	+	0.827561i	$0.689728\pi$
$108$	−3.25913	−0.313610
$109$	−7.98992	−0.765296	−0.382648	−	0.923894i	$-0.624988\pi$
$109$	−7.98992	−0.765296	−0.382648	+	0.923894i	$0.624988\pi$
$110$	9.55108	0.910659
$111$	−4.03636	−0.383114
$112$	−0.103650	−0.00979403
$113$	7.70366	0.724700	0.362350	−	0.932042i	$-0.381975\pi$
$113$	7.70366	0.724700	0.362350	+	0.932042i	$0.381975\pi$
$114$	6.90088	0.646327
$115$	−0.452464	−0.0421924
$116$	30.2673	2.81024
$117$	0	0
$118$	4.68072	0.430896
$119$	7.99504	0.732904
$120$	−1.99909	−0.182491
$121$	25.1890	2.28991
$122$	−3.18298	−0.288173
$123$	−9.18247	−0.827956
$124$	4.80640	0.431627
$125$	6.59137	0.589550
$126$	2.29328	0.204301
$127$	0.733394	0.0650782	0.0325391	−	0.999470i	$-0.489641\pi$
$127$	0.733394	0.0650782	0.0325391	+	0.999470i	$0.489641\pi$
$128$	18.5223	1.63716
$129$	8.12988	0.715796
$130$	0	0
$131$	−9.82604	−0.858505	−0.429253	−	0.903185i	$-0.641223\pi$
$131$	−9.82604	−0.858505	−0.429253	+	0.903185i	$0.641223\pi$
$132$	−19.6060	−1.70649
$133$	−3.00918	−0.260929
$134$	16.9247	1.46207
$135$	0.692320	0.0595854
$136$	23.0859	1.97960
$137$	5.69875	0.486877	0.243439	−	0.969916i	$-0.421725\pi$
$137$	5.69875	0.486877	0.243439	+	0.969916i	$0.421725\pi$
$138$	1.49876	0.127583
$139$	−9.84044	−0.834655	−0.417328	−	0.908756i	$-0.637033\pi$
$139$	−9.84044	−0.834655	−0.417328	+	0.908756i	$0.637033\pi$
$140$	2.25636	0.190697
$141$	0.664432	0.0559553
$142$	2.29795	0.192840
$143$	0	0
$144$	0.103650	0.00863752
$145$	−6.42952	−0.533943
$146$	24.3244	2.01310
$147$	−1.00000	−0.0824786
$148$	13.1550	1.08134
$149$	−13.6589	−1.11898	−0.559492	−	0.828836i	$-0.689004\pi$
$149$	−13.6589	−1.11898	−0.559492	+	0.828836i	$0.689004\pi$
$150$	−10.3672	−0.846479
$151$	−11.4487	−0.931684	−0.465842	−	0.884868i	$-0.654248\pi$
$151$	−11.4487	−0.931684	−0.465842	+	0.884868i	$0.654248\pi$
$152$	−8.68908	−0.704778
$153$	−7.99504	−0.646361
$154$	13.7958	1.11169
$155$	−1.02100	−0.0820086
$156$	0	0
$157$	−8.49845	−0.678250	−0.339125	−	0.940741i	$-0.610131\pi$
$157$	−8.49845	−0.678250	−0.339125	+	0.940741i	$0.610131\pi$
$158$	−13.9570	−1.11036
$159$	−10.3300	−0.819226
$160$	−3.83362	−0.303074
$161$	−0.653547	−0.0515067
$162$	−2.29328	−0.180177
$163$	15.6768	1.22790	0.613951	−	0.789344i	$-0.289579\pi$
$163$	15.6768	1.22790	0.613951	+	0.789344i	$0.289579\pi$
$164$	29.9268	2.33689
$165$	4.16481	0.324230
$166$	0.865639	0.0671867
$167$	19.4273	1.50333	0.751664	−	0.659546i	$-0.229252\pi$
$167$	19.4273	1.50333	0.751664	+	0.659546i	$0.229252\pi$
$168$	−2.88753	−0.222778
$169$	0	0
$170$	−12.6936	−0.973554
$171$	3.00918	0.230118
$172$	−26.4963	−2.02032
$173$	13.1310	0.998335	0.499167	−	0.866506i	$-0.333639\pi$
$173$	13.1310	0.998335	0.499167	+	0.866506i	$0.333639\pi$
$174$	21.2975	1.61456
$175$	4.52069	0.341732
$176$	0.623532	0.0470005
$177$	2.04106	0.153416
$178$	−15.2210	−1.14086
$179$	9.94455	0.743291	0.371645	−	0.928375i	$-0.378794\pi$
$179$	9.94455	0.743291	0.371645	+	0.928375i	$0.378794\pi$
$180$	−2.25636	−0.168179
$181$	−0.453624	−0.0337176	−0.0168588	−	0.999858i	$-0.505367\pi$
$181$	−0.453624	−0.0337176	−0.0168588	+	0.999858i	$0.505367\pi$
$182$	0	0
$183$	−1.38796	−0.102601
$184$	−1.88713	−0.139121
$185$	−2.79445	−0.205452
$186$	3.38201	0.247981
$187$	−48.0960	−3.51713
$188$	−2.16547	−0.157933
$189$	1.00000	0.0727393
$190$	4.77762	0.346605
$191$	1.23989	0.0897152	0.0448576	−	0.998993i	$-0.485717\pi$
$191$	1.23989	0.0897152	0.0448576	+	0.998993i	$0.485717\pi$
$192$	12.9060	0.931410
$193$	1.59114	0.114533	0.0572663	−	0.998359i	$-0.481762\pi$
$193$	1.59114	0.114533	0.0572663	+	0.998359i	$0.481762\pi$
$194$	−0.793881	−0.0569973
$195$	0	0
$196$	3.25913	0.232795
$197$	11.4208	0.813696	0.406848	−	0.913496i	$-0.366628\pi$
$197$	11.4208	0.813696	0.406848	+	0.913496i	$0.366628\pi$
$198$	−13.7958	−0.980421
$199$	−24.1080	−1.70897	−0.854487	−	0.519473i	$-0.826128\pi$
$199$	−24.1080	−1.70897	−0.854487	+	0.519473i	$0.826128\pi$
$200$	13.0536	0.923030
$201$	7.38012	0.520554
$202$	35.0749	2.46786
$203$	−9.28692	−0.651814
$204$	26.0568	1.82434
$205$	−6.35721	−0.444007
$206$	−24.5351	−1.70944
$207$	0.653547	0.0454246
$208$	0	0
$209$	18.1024	1.25217
$210$	1.58768	0.109561
$211$	0.379483	0.0261247	0.0130623	−	0.999915i	$-0.495842\pi$
$211$	0.379483	0.0261247	0.0130623	+	0.999915i	$0.495842\pi$
$212$	33.6669	2.31225
$213$	1.00204	0.0686584
$214$	26.6338	1.82065
$215$	5.62848	0.383859
$216$	2.88753	0.196471
$217$	−1.47475	−0.100113
$218$	18.3231	1.24100
$219$	10.6068	0.716743
$220$	−13.5736	−0.915135
$221$	0	0
$222$	9.25650	0.621256
$223$	11.0794	0.741934	0.370967	−	0.928646i	$-0.379026\pi$
$223$	11.0794	0.741934	0.370967	+	0.928646i	$0.379026\pi$
$224$	−5.53735	−0.369980
$225$	−4.52069	−0.301380
$226$	−17.6666	−1.17517
$227$	16.2595	1.07918	0.539592	−	0.841927i	$-0.318579\pi$
$227$	16.2595	1.07918	0.539592	+	0.841927i	$0.318579\pi$
$228$	−9.80729	−0.649504
$229$	−10.4004	−0.687278	−0.343639	−	0.939102i	$-0.611660\pi$
$229$	−10.4004	−0.687278	−0.343639	+	0.939102i	$0.611660\pi$
$230$	1.03762	0.0684190
$231$	6.01573	0.395806
$232$	−26.8162	−1.76057
$233$	15.5960	1.02173	0.510863	−	0.859662i	$-0.329326\pi$
$233$	15.5960	1.02173	0.510863	+	0.859662i	$0.329326\pi$
$234$	0	0
$235$	0.460000	0.0300071
$236$	−6.65208	−0.433013
$237$	−6.08603	−0.395330
$238$	−18.3348	−1.18847
$239$	23.1700	1.49874	0.749370	−	0.662151i	$-0.230356\pi$
$239$	23.1700	1.49874	0.749370	+	0.662151i	$0.230356\pi$
$240$	0.0717592	0.00463204
$241$	−10.3316	−0.665518	−0.332759	−	0.943012i	$-0.607980\pi$
$241$	−10.3316	−0.665518	−0.332759	+	0.943012i	$0.607980\pi$
$242$	−57.7655	−3.71331
$243$	−1.00000	−0.0641500
$244$	4.52353	0.289589
$245$	−0.692320	−0.0442307
$246$	21.0580	1.34261
$247$	0	0
$248$	−4.25838	−0.270407
$249$	0.377468	0.0239211
$250$	−15.1158	−0.956010
$251$	−14.8803	−0.939238	−0.469619	−	0.882869i	$-0.655609\pi$
$251$	−14.8803	−0.939238	−0.469619	+	0.882869i	$0.655609\pi$
$252$	−3.25913	−0.205306
$253$	3.93156	0.247175
$254$	−1.68188	−0.105530
$255$	−5.53513	−0.346623
$256$	−16.6649	−1.04155
$257$	−24.0098	−1.49769	−0.748844	−	0.662746i	$-0.769391\pi$
$257$	−24.0098	−1.49769	−0.748844	+	0.662746i	$0.769391\pi$
$258$	−18.6441	−1.16073
$259$	−4.03636	−0.250807
$260$	0	0
$261$	9.28692	0.574846
$262$	22.5338	1.39215
$263$	−7.86137	−0.484753	−0.242376	−	0.970182i	$-0.577927\pi$
$263$	−7.86137	−0.484753	−0.242376	+	0.970182i	$0.577927\pi$
$264$	17.3706	1.06909
$265$	−7.15170	−0.439325
$266$	6.90088	0.423120
$267$	−6.63723	−0.406192
$268$	−24.0527	−1.46926
$269$	−8.68344	−0.529439	−0.264719	−	0.964325i	$-0.585279\pi$
$269$	−8.68344	−0.529439	−0.264719	+	0.964325i	$0.585279\pi$
$270$	−1.58768	−0.0966233
$271$	−2.80089	−0.170142	−0.0850710	−	0.996375i	$-0.527112\pi$
$271$	−2.80089	−0.170142	−0.0850710	+	0.996375i	$0.527112\pi$
$272$	−0.828688	−0.0502466
$273$	0	0
$274$	−13.0688	−0.789517
$275$	−27.1953	−1.63994
$276$	−2.12999	−0.128210
$277$	3.28495	0.197374	0.0986868	−	0.995119i	$-0.468536\pi$
$277$	3.28495	0.197374	0.0986868	+	0.995119i	$0.468536\pi$
$278$	22.5669	1.35347
$279$	1.47475	0.0882910
$280$	−1.99909	−0.119469
$281$	13.9619	0.832895	0.416447	−	0.909160i	$-0.363275\pi$
$281$	13.9619	0.832895	0.416447	+	0.909160i	$0.363275\pi$
$282$	−1.52373	−0.0907367
$283$	8.92062	0.530276	0.265138	−	0.964211i	$-0.414583\pi$
$283$	8.92062	0.530276	0.265138	+	0.964211i	$0.414583\pi$
$284$	−3.26576	−0.193787
$285$	2.08331	0.123405
$286$	0	0
$287$	−9.18247	−0.542024
$288$	5.53735	0.326292
$289$	46.9206	2.76004
$290$	14.7447	0.865838
$291$	−0.346177	−0.0202933
$292$	−34.5690	−2.02300
$293$	5.90904	0.345210	0.172605	−	0.984991i	$-0.444782\pi$
$293$	5.90904	0.345210	0.172605	+	0.984991i	$0.444782\pi$
$294$	2.29328	0.133747
$295$	1.41307	0.0822720
$296$	−11.6551	−0.677439
$297$	−6.01573	−0.349068
$298$	31.3238	1.81454
$299$	0	0
$300$	14.7335	0.850639
$301$	8.12988	0.468598
$302$	26.2551	1.51081
$303$	15.2947	0.878655
$304$	0.311902	0.0178888
$305$	−0.960912	−0.0550216
$306$	18.3348	1.04813
$307$	17.9000	1.02161	0.510804	−	0.859697i	$-0.329348\pi$
$307$	17.9000	1.02161	0.510804	+	0.859697i	$0.329348\pi$
$308$	−19.6060	−1.11716
$309$	−10.6987	−0.608629
$310$	2.34144	0.132985
$311$	14.2495	0.808014	0.404007	−	0.914756i	$-0.367617\pi$
$311$	14.2495	0.808014	0.404007	+	0.914756i	$0.367617\pi$
$312$	0	0
$313$	−9.44689	−0.533970	−0.266985	−	0.963701i	$-0.586027\pi$
$313$	−9.44689	−0.533970	−0.266985	+	0.963701i	$0.586027\pi$
$314$	19.4893	1.09985
$315$	0.692320	0.0390078
$316$	19.8351	1.11581
$317$	15.8830	0.892076	0.446038	−	0.895014i	$-0.352835\pi$
$317$	15.8830	0.892076	0.446038	+	0.895014i	$0.352835\pi$
$318$	23.6897	1.32845
$319$	55.8677	3.12799
$320$	8.93508	0.499486
$321$	11.6138	0.648221
$322$	1.49876	0.0835229
$323$	−24.0585	−1.33865
$324$	3.25913	0.181063
$325$	0	0
$326$	−35.9513	−1.99116
$327$	7.98992	0.441844
$328$	−26.5146	−1.46403
$329$	0.664432	0.0366313
$330$	−9.55108	−0.525769
$331$	−1.92053	−0.105562	−0.0527810	−	0.998606i	$-0.516809\pi$
$331$	−1.92053	−0.105562	−0.0527810	+	0.998606i	$0.516809\pi$
$332$	−1.23022	−0.0675169
$333$	4.03636	0.221191
$334$	−44.5522	−2.43779
$335$	5.10941	0.279157
$336$	0.103650	0.00565459
$337$	23.6637	1.28904	0.644522	−	0.764586i	$-0.277056\pi$
$337$	23.6637	1.28904	0.644522	+	0.764586i	$0.277056\pi$
$338$	0	0
$339$	−7.70366	−0.418406
$340$	18.0397	0.978339
$341$	8.87170	0.480430
$342$	−6.90088	−0.373157
$343$	−1.00000	−0.0539949
$344$	23.4752	1.26570
$345$	0.452464	0.0243598
$346$	−30.1131	−1.61889
$347$	17.3503	0.931415	0.465708	−	0.884939i	$-0.345800\pi$
$347$	17.3503	0.931415	0.465708	+	0.884939i	$0.345800\pi$
$348$	−30.2673	−1.62250
$349$	24.6873	1.32148	0.660740	−	0.750614i	$-0.270242\pi$
$349$	24.6873	1.32148	0.660740	+	0.750614i	$0.270242\pi$
$350$	−10.3672	−0.554151
$351$	0	0
$352$	33.3112	1.77550
$353$	20.3166	1.08135	0.540673	−	0.841233i	$-0.318170\pi$
$353$	20.3166	1.08135	0.540673	+	0.841233i	$0.318170\pi$
$354$	−4.68072	−0.248778
$355$	0.693730	0.0368194
$356$	21.6316	1.14647
$357$	−7.99504	−0.423142
$358$	−22.8056	−1.20531
$359$	0.0752273	0.00397035	0.00198517	−	0.999998i	$-0.499368\pi$
$359$	0.0752273	0.00397035	0.00198517	+	0.999998i	$0.499368\pi$
$360$	1.99909	0.105361
$361$	−9.94484	−0.523413
$362$	1.04029	0.0546763
$363$	−25.1890	−1.32208
$364$	0	0
$365$	7.34332	0.384367
$366$	3.18298	0.166377
$367$	36.5624	1.90854	0.954270	−	0.298945i	$-0.0966348\pi$
$367$	36.5624	1.90854	0.954270	+	0.298945i	$0.0966348\pi$
$368$	0.0677403	0.00353121
$369$	9.18247	0.478021
$370$	6.40846	0.333160
$371$	−10.3300	−0.536309
$372$	−4.80640	−0.249200
$373$	17.5447	0.908430	0.454215	−	0.890892i	$-0.349920\pi$
$373$	17.5447	0.908430	0.454215	+	0.890892i	$0.349920\pi$
$374$	110.298	5.70335
$375$	−6.59137	−0.340377
$376$	1.91857	0.0989425
$377$	0	0
$378$	−2.29328	−0.117954
$379$	0.979323	0.0503045	0.0251522	−	0.999684i	$-0.491993\pi$
$379$	0.979323	0.0503045	0.0251522	+	0.999684i	$0.491993\pi$
$380$	−6.78979	−0.348309
$381$	−0.733394	−0.0375729
$382$	−2.84341	−0.145482
$383$	−7.04462	−0.359963	−0.179982	−	0.983670i	$-0.557604\pi$
$383$	−7.04462	−0.359963	−0.179982	+	0.983670i	$0.557604\pi$
$384$	−18.5223	−0.945214
$385$	4.16481	0.212259
$386$	−3.64892	−0.185725
$387$	−8.12988	−0.413265
$388$	1.12824	0.0572775
$389$	32.5771	1.65172	0.825862	−	0.563873i	$-0.190689\pi$
$389$	32.5771	1.65172	0.825862	+	0.563873i	$0.190689\pi$
$390$	0	0
$391$	−5.22513	−0.264246
$392$	−2.88753	−0.145842
$393$	9.82604	0.495658
$394$	−26.1910	−1.31948
$395$	−4.21348	−0.212003
$396$	19.6060	0.985240
$397$	−7.89345	−0.396161	−0.198081	−	0.980186i	$-0.563471\pi$
$397$	−7.89345	−0.396161	−0.198081	+	0.980186i	$0.563471\pi$
$398$	55.2864	2.77126
$399$	3.00918	0.150647
$400$	−0.468571	−0.0234286
$401$	−27.9955	−1.39803	−0.699014	−	0.715108i	$-0.746378\pi$
$401$	−27.9955	−1.39803	−0.699014	+	0.715108i	$0.746378\pi$
$402$	−16.9247	−0.844126
$403$	0	0
$404$	−49.8472	−2.47999
$405$	−0.692320	−0.0344017
$406$	21.2975	1.05698
$407$	24.2817	1.20360
$408$	−23.0859	−1.14292
$409$	2.30233	0.113843	0.0569214	−	0.998379i	$-0.481872\pi$
$409$	2.30233	0.113843	0.0569214	+	0.998379i	$0.481872\pi$
$410$	14.5789	0.719998
$411$	−5.69875	−0.281099
$412$	34.8685	1.71785
$413$	2.04106	0.100434
$414$	−1.49876	−0.0736603
$415$	0.261329	0.0128281
$416$	0	0
$417$	9.84044	0.481889
$418$	−41.5139	−2.03051
$419$	12.5570	0.613449	0.306725	−	0.951798i	$-0.400767\pi$
$419$	12.5570	0.613449	0.306725	+	0.951798i	$0.400767\pi$
$420$	−2.25636	−0.110099
$421$	5.65171	0.275448	0.137724	−	0.990471i	$-0.456021\pi$
$421$	5.65171	0.275448	0.137724	+	0.990471i	$0.456021\pi$
$422$	−0.870260	−0.0423636
$423$	−0.664432	−0.0323058
$424$	−29.8283	−1.44859
$425$	36.1431	1.75320
$426$	−2.29795	−0.111336
$427$	−1.38796	−0.0671680
$428$	−37.8509	−1.82959
$429$	0	0
$430$	−12.9077	−0.622463
$431$	29.7784	1.43438	0.717188	−	0.696880i	$-0.245429\pi$
$431$	29.7784	1.43438	0.717188	+	0.696880i	$0.245429\pi$
$432$	−0.103650	−0.00498688
$433$	21.9107	1.05296	0.526481	−	0.850187i	$-0.323511\pi$
$433$	21.9107	1.05296	0.526481	+	0.850187i	$0.323511\pi$
$434$	3.38201	0.162342
$435$	6.42952	0.308272
$436$	−26.0402	−1.24710
$437$	1.96664	0.0940771
$438$	−24.3244	−1.16227
$439$	32.7713	1.56409	0.782045	−	0.623221i	$-0.214176\pi$
$439$	32.7713	1.56409	0.782045	+	0.623221i	$0.214176\pi$
$440$	12.0260	0.573317
$441$	1.00000	0.0476190
$442$	0	0
$443$	7.38161	0.350711	0.175355	−	0.984505i	$-0.443893\pi$
$443$	7.38161	0.350711	0.175355	+	0.984505i	$0.443893\pi$
$444$	−13.1550	−0.624309
$445$	−4.59508	−0.217828
$446$	−25.4082	−1.20311
$447$	13.6589	0.646046
$448$	12.9060	0.609751
$449$	33.8516	1.59756	0.798779	−	0.601625i	$-0.205480\pi$
$449$	33.8516	1.59756	0.798779	+	0.601625i	$0.205480\pi$
$450$	10.3672	0.488715
$451$	55.2393	2.60112
$452$	25.1072	1.18094
$453$	11.4487	0.537908
$454$	−37.2877	−1.75000
$455$	0	0
$456$	8.68908	0.406904
$457$	−27.7870	−1.29982	−0.649910	−	0.760011i	$-0.725193\pi$
$457$	−27.7870	−1.29982	−0.649910	+	0.760011i	$0.725193\pi$
$458$	23.8510	1.11448
$459$	7.99504	0.373176
$460$	−1.47464	−0.0687553
$461$	−29.8771	−1.39151	−0.695757	−	0.718278i	$-0.744931\pi$
$461$	−29.8771	−1.39151	−0.695757	+	0.718278i	$0.744931\pi$
$462$	−13.7958	−0.641836
$463$	2.45788	0.114228	0.0571138	−	0.998368i	$-0.481810\pi$
$463$	2.45788	0.114228	0.0571138	+	0.998368i	$0.481810\pi$
$464$	0.962592	0.0446872
$465$	1.02100	0.0473477
$466$	−35.7659	−1.65682
$467$	5.12405	0.237113	0.118556	−	0.992947i	$-0.462173\pi$
$467$	5.12405	0.237113	0.118556	+	0.992947i	$0.462173\pi$
$468$	0	0
$469$	7.38012	0.340782
$470$	−1.05491	−0.0486593
$471$	8.49845	0.391588
$472$	5.89362	0.271276
$473$	−48.9072	−2.24875
$474$	13.9570	0.641064
$475$	−13.6036	−0.624175
$476$	26.0568	1.19431
$477$	10.3300	0.472980
$478$	−53.1352	−2.43035
$479$	30.1753	1.37874	0.689372	−	0.724408i	$-0.257887\pi$
$479$	30.1753	1.37874	0.689372	+	0.724408i	$0.257887\pi$
$480$	3.83362	0.174980
$481$	0	0
$482$	23.6933	1.07920
$483$	0.653547	0.0297374
$484$	82.0943	3.73156
$485$	−0.239666	−0.0108827
$486$	2.29328	0.104025
$487$	7.48823	0.339324	0.169662	−	0.985502i	$-0.445732\pi$
$487$	7.48823	0.339324	0.169662	+	0.985502i	$0.445732\pi$
$488$	−4.00777	−0.181423
$489$	−15.6768	−0.708930
$490$	1.58768	0.0717242
$491$	−20.4619	−0.923433	−0.461717	−	0.887027i	$-0.652766\pi$
$491$	−20.4619	−0.923433	−0.461717	+	0.887027i	$0.652766\pi$
$492$	−29.9268	−1.34921
$493$	−74.2493	−3.34402
$494$	0	0
$495$	−4.16481	−0.187194
$496$	0.152858	0.00686354
$497$	1.00204	0.0449475
$498$	−0.865639	−0.0387902
$499$	−4.96188	−0.222124	−0.111062	−	0.993813i	$-0.535425\pi$
$499$	−4.96188	−0.222124	−0.111062	+	0.993813i	$0.535425\pi$
$500$	21.4821	0.960709
$501$	−19.4273	−0.867947
$502$	34.1247	1.52306
$503$	−5.89196	−0.262710	−0.131355	−	0.991335i	$-0.541933\pi$
$503$	−5.89196	−0.262710	−0.131355	+	0.991335i	$0.541933\pi$
$504$	2.88753	0.128621
$505$	10.5888	0.471195
$506$	−9.01617	−0.400818
$507$	0	0
$508$	2.39022	0.106049
$509$	−12.3670	−0.548156	−0.274078	−	0.961707i	$-0.588373\pi$
$509$	−12.3670	−0.548156	−0.274078	+	0.961707i	$0.588373\pi$
$510$	12.6936	0.562081
$511$	10.6068	0.469218
$512$	1.17253	0.0518192
$513$	−3.00918	−0.132858
$514$	55.0611	2.42864
$515$	−7.40693	−0.326389
$516$	26.4963	1.16643
$517$	−3.99705	−0.175790
$518$	9.25650	0.406707
$519$	−13.1310	−0.576389
$520$	0	0
$521$	1.39280	0.0610196	0.0305098	−	0.999534i	$-0.490287\pi$
$521$	1.39280	0.0610196	0.0305098	+	0.999534i	$0.490287\pi$
$522$	−21.2975	−0.932166
$523$	19.9919	0.874184	0.437092	−	0.899417i	$-0.356008\pi$
$523$	19.9919	0.874184	0.437092	+	0.899417i	$0.356008\pi$
$524$	−32.0243	−1.39899
$525$	−4.52069	−0.197299
$526$	18.0283	0.786071
$527$	−11.7907	−0.513610
$528$	−0.623532	−0.0271358
$529$	−22.5729	−0.981429
$530$	16.4008	0.712407
$531$	−2.04106	−0.0885745
$532$	−9.80729	−0.425200
$533$	0	0
$534$	15.2210	0.658677
$535$	8.04049	0.347621
$536$	21.3103	0.920465
$537$	−9.94455	−0.429139
$538$	19.9136	0.858534
$539$	6.01573	0.259116
$540$	2.25636	0.0970982
$541$	13.5238	0.581434	0.290717	−	0.956809i	$-0.406106\pi$
$541$	13.5238	0.581434	0.290717	+	0.956809i	$0.406106\pi$
$542$	6.42322	0.275901
$543$	0.453624	0.0194669
$544$	−44.2714	−1.89812
$545$	5.53159	0.236947
$546$	0	0
$547$	23.9335	1.02332	0.511660	−	0.859188i	$-0.329031\pi$
$547$	23.9335	1.02332	0.511660	+	0.859188i	$0.329031\pi$
$548$	18.5730	0.793397
$549$	1.38796	0.0592366
$550$	62.3663	2.65931
$551$	27.9460	1.19054
$552$	1.88713	0.0803217
$553$	−6.08603	−0.258804
$554$	−7.53331	−0.320060
$555$	2.79445	0.118618
$556$	−32.0712	−1.36012
$557$	−13.5761	−0.575238	−0.287619	−	0.957745i	$-0.592864\pi$
$557$	−13.5761	−0.575238	−0.287619	+	0.957745i	$0.592864\pi$
$558$	−3.38201	−0.143172
$559$	0	0
$560$	0.0717592	0.00303238
$561$	48.0960	2.03062
$562$	−32.0184	−1.35062
$563$	−32.6958	−1.37797	−0.688983	−	0.724778i	$-0.741942\pi$
$563$	−32.6958	−1.37797	−0.688983	+	0.724778i	$0.741942\pi$
$564$	2.16547	0.0911827
$565$	−5.33340	−0.224378
$566$	−20.4575	−0.859891
$567$	−1.00000	−0.0419961
$568$	2.89341	0.121405
$569$	30.5183	1.27939	0.639696	−	0.768628i	$-0.279060\pi$
$569$	30.5183	1.27939	0.639696	+	0.768628i	$0.279060\pi$
$570$	−4.77762	−0.200113
$571$	26.4381	1.10640	0.553201	−	0.833048i	$-0.313406\pi$
$571$	26.4381	1.10640	0.553201	+	0.833048i	$0.313406\pi$
$572$	0	0
$573$	−1.23989	−0.0517971
$574$	21.0580	0.878943
$575$	−2.95448	−0.123211
$576$	−12.9060	−0.537750
$577$	20.6254	0.858648	0.429324	−	0.903151i	$-0.358752\pi$
$577$	20.6254	0.858648	0.429324	+	0.903151i	$0.358752\pi$
$578$	−107.602	−4.47566
$579$	−1.59114	−0.0661255
$580$	−20.9546	−0.870094
$581$	0.377468	0.0156600
$582$	0.793881	0.0329074
$583$	62.1428	2.57369
$584$	30.6275	1.26737
$585$	0	0
$586$	−13.5511	−0.559790
$587$	−7.55831	−0.311965	−0.155982	−	0.987760i	$-0.549854\pi$
$587$	−7.55831	−0.311965	−0.155982	+	0.987760i	$0.549854\pi$
$588$	−3.25913	−0.134404
$589$	4.43779	0.182856
$590$	−3.24056	−0.133412
$591$	−11.4208	−0.469788
$592$	0.418370	0.0171949
$593$	−27.0632	−1.11135	−0.555676	−	0.831399i	$-0.687540\pi$
$593$	−27.0632	−1.11135	−0.555676	+	0.831399i	$0.687540\pi$
$594$	13.7958	0.566046
$595$	−5.53513	−0.226918
$596$	−44.5162	−1.82346
$597$	24.1080	0.986676
$598$	0	0
$599$	−46.2708	−1.89057	−0.945286	−	0.326242i	$-0.894218\pi$
$599$	−46.2708	−1.89057	−0.945286	+	0.326242i	$0.894218\pi$
$600$	−13.0536	−0.532912
$601$	−18.9337	−0.772321	−0.386161	−	0.922432i	$-0.626199\pi$
$601$	−18.9337	−0.772321	−0.386161	+	0.922432i	$0.626199\pi$
$602$	−18.6441	−0.759876
$603$	−7.38012	−0.300542
$604$	−37.3128	−1.51824
$605$	−17.4389	−0.708991
$606$	−35.0749	−1.42482
$607$	−4.00591	−0.162595	−0.0812974	−	0.996690i	$-0.525906\pi$
$607$	−4.00591	−0.162595	−0.0812974	+	0.996690i	$0.525906\pi$
$608$	16.6629	0.675769
$609$	9.28692	0.376325
$610$	2.20364	0.0892227
$611$	0	0
$612$	−26.0568	−1.05329
$613$	−6.50306	−0.262656	−0.131328	−	0.991339i	$-0.541924\pi$
$613$	−6.50306	−0.262656	−0.131328	+	0.991339i	$0.541924\pi$
$614$	−41.0498	−1.65663
$615$	6.35721	0.256348
$616$	17.3706	0.699881
$617$	17.1220	0.689305	0.344652	−	0.938730i	$-0.387997\pi$
$617$	17.1220	0.689305	0.344652	+	0.938730i	$0.387997\pi$
$618$	24.5351	0.986948
$619$	23.5838	0.947912	0.473956	−	0.880548i	$-0.342826\pi$
$619$	23.5838	0.947912	0.473956	+	0.880548i	$0.342826\pi$
$620$	−3.32757	−0.133638
$621$	−0.653547	−0.0262259
$622$	−32.6780	−1.31027
$623$	−6.63723	−0.265915
$624$	0	0
$625$	18.0401	0.721605
$626$	21.6644	0.865882
$627$	−18.1024	−0.722941
$628$	−27.6975	−1.10525
$629$	−32.2709	−1.28672
$630$	−1.58768	−0.0632548
$631$	38.8948	1.54838	0.774189	−	0.632955i	$-0.218158\pi$
$631$	38.8948	1.54838	0.774189	+	0.632955i	$0.218158\pi$
$632$	−17.5736	−0.699039
$633$	−0.379483	−0.0150831
$634$	−36.4240	−1.44658
$635$	−0.507744	−0.0201492
$636$	−33.6669	−1.33498
$637$	0	0
$638$	−128.120	−5.07232
$639$	−1.00204	−0.0396399
$640$	−12.8234	−0.506889
$641$	−39.6685	−1.56681	−0.783406	−	0.621510i	$-0.786520\pi$
$641$	−39.6685	−1.56681	−0.783406	+	0.621510i	$0.786520\pi$
$642$	−26.6338	−1.05115
$643$	25.9081	1.02172	0.510858	−	0.859665i	$-0.329328\pi$
$643$	25.9081	1.02172	0.510858	+	0.859665i	$0.329328\pi$
$644$	−2.12999	−0.0839334
$645$	−5.62848	−0.221621
$646$	55.1728	2.17075
$647$	2.29613	0.0902700	0.0451350	−	0.998981i	$-0.485628\pi$
$647$	2.29613	0.0902700	0.0451350	+	0.998981i	$0.485628\pi$
$648$	−2.88753	−0.113433
$649$	−12.2785	−0.481973
$650$	0	0
$651$	1.47475	0.0578000
$652$	51.0927	2.00095
$653$	−23.7837	−0.930727	−0.465363	−	0.885120i	$-0.654076\pi$
$653$	−23.7837	−0.930727	−0.465363	+	0.885120i	$0.654076\pi$
$654$	−18.3231	−0.716491
$655$	6.80276	0.265806
$656$	0.951766	0.0371602
$657$	−10.6068	−0.413812
$658$	−1.52373	−0.0594011
$659$	−16.0842	−0.626553	−0.313276	−	0.949662i	$-0.601427\pi$
$659$	−16.0842	−0.626553	−0.313276	+	0.949662i	$0.601427\pi$
$660$	13.5736	0.528354
$661$	4.06663	0.158174	0.0790868	−	0.996868i	$-0.474800\pi$
$661$	4.06663	0.158174	0.0790868	+	0.996868i	$0.474800\pi$
$662$	4.40431	0.171178
$663$	0	0
$664$	1.08995	0.0422982
$665$	2.08331	0.0807875
$666$	−9.25650	−0.358682
$667$	6.06944	0.235010
$668$	63.3159	2.44977
$669$	−11.0794	−0.428356
$670$	−11.7173	−0.452679
$671$	8.34959	0.322332
$672$	5.53735	0.213608
$673$	36.4509	1.40508	0.702539	−	0.711645i	$-0.252050\pi$
$673$	36.4509	1.40508	0.702539	+	0.711645i	$0.252050\pi$
$674$	−54.2675	−2.09030
$675$	4.52069	0.174002
$676$	0	0
$677$	25.4552	0.978324	0.489162	−	0.872193i	$-0.337303\pi$
$677$	25.4552	0.978324	0.489162	+	0.872193i	$0.337303\pi$
$678$	17.6666	0.678484
$679$	−0.346177	−0.0132851
$680$	−15.9828	−0.612913
$681$	−16.2595	−0.623067
$682$	−20.3453	−0.779061
$683$	2.13120	0.0815481	0.0407741	−	0.999168i	$-0.487018\pi$
$683$	2.13120	0.0815481	0.0407741	+	0.999168i	$0.487018\pi$
$684$	9.80729	0.374991
$685$	−3.94536	−0.150745
$686$	2.29328	0.0875578
$687$	10.4004	0.396800
$688$	−0.842664	−0.0321263
$689$	0	0
$690$	−1.03762	−0.0395017
$691$	25.7764	0.980580	0.490290	−	0.871559i	$-0.336891\pi$
$691$	25.7764	0.980580	0.490290	+	0.871559i	$0.336891\pi$
$692$	42.7957	1.62685
$693$	−6.01573	−0.228519
$694$	−39.7892	−1.51038
$695$	6.81274	0.258422
$696$	26.8162	1.01647
$697$	−73.4142	−2.78076
$698$	−56.6149	−2.14290
$699$	−15.5960	−0.589893
$700$	14.7335	0.556874
$701$	−8.75888	−0.330819	−0.165409	−	0.986225i	$-0.552894\pi$
$701$	−8.75888	−0.330819	−0.165409	+	0.986225i	$0.552894\pi$
$702$	0	0
$703$	12.1461	0.458100
$704$	−77.6390	−2.92613
$705$	−0.460000	−0.0173246
$706$	−46.5917	−1.75350
$707$	15.2947	0.575215
$708$	6.65208	0.250000
$709$	−19.1517	−0.719257	−0.359628	−	0.933096i	$-0.617097\pi$
$709$	−19.1517	−0.719257	−0.359628	+	0.933096i	$0.617097\pi$
$710$	−1.59092	−0.0597060
$711$	6.08603	0.228244
$712$	−19.1652	−0.718245
$713$	0.963818	0.0360953
$714$	18.3348	0.686165
$715$	0	0
$716$	32.4105	1.21124
$717$	−23.1700	−0.865298
$718$	−0.172517	−0.00643828
$719$	32.4855	1.21151	0.605753	−	0.795653i	$-0.292872\pi$
$719$	32.4855	1.21151	0.605753	+	0.795653i	$0.292872\pi$
$720$	−0.0717592	−0.00267431
$721$	−10.6987	−0.398441
$722$	22.8063	0.848762
$723$	10.3316	0.384237
$724$	−1.47842	−0.0549450
$725$	−41.9833	−1.55922
$726$	57.7655	2.14388
$727$	−34.2511	−1.27030	−0.635151	−	0.772388i	$-0.719062\pi$
$727$	−34.2511	−1.27030	−0.635151	+	0.772388i	$0.719062\pi$
$728$	0	0
$729$	1.00000	0.0370370
$730$	−16.8403	−0.623287
$731$	64.9987	2.40406
$732$	−4.52353	−0.167195
$733$	−10.0339	−0.370611	−0.185306	−	0.982681i	$-0.559328\pi$
$733$	−10.0339	−0.370611	−0.185306	+	0.982681i	$0.559328\pi$
$734$	−83.8477	−3.09488
$735$	0.692320	0.0255366
$736$	3.61892	0.133395
$737$	−44.3968	−1.63538
$738$	−21.0580	−0.775155
$739$	38.3868	1.41208	0.706041	−	0.708171i	$-0.250479\pi$
$739$	38.3868	1.41208	0.706041	+	0.708171i	$0.250479\pi$
$740$	−9.10748	−0.334798
$741$	0	0
$742$	23.6897	0.869675
$743$	−7.74752	−0.284229	−0.142114	−	0.989850i	$-0.545390\pi$
$743$	−7.74752	−0.284229	−0.142114	+	0.989850i	$0.545390\pi$
$744$	4.25838	0.156120
$745$	9.45636	0.346454
$746$	−40.2349	−1.47310
$747$	−0.377468	−0.0138108
$748$	−156.751	−5.73138
$749$	11.6138	0.424360
$750$	15.1158	0.551952
$751$	−28.0733	−1.02441	−0.512205	−	0.858863i	$-0.671171\pi$
$751$	−28.0733	−1.02441	−0.512205	+	0.858863i	$0.671171\pi$
$752$	−0.0688686	−0.00251138
$753$	14.8803	0.542269
$754$	0	0
$755$	7.92618	0.288463
$756$	3.25913	0.118533
$757$	−52.7817	−1.91838	−0.959192	−	0.282755i	$-0.908752\pi$
$757$	−52.7817	−1.91838	−0.959192	+	0.282755i	$0.908752\pi$
$758$	−2.24586	−0.0815733
$759$	−3.93156	−0.142707
$760$	6.01563	0.218210
$761$	−15.6373	−0.566853	−0.283427	−	0.958994i	$-0.591471\pi$
$761$	−15.6373	−0.566853	−0.283427	+	0.958994i	$0.591471\pi$
$762$	1.68188	0.0609280
$763$	7.98992	0.289255
$764$	4.04095	0.146197
$765$	5.53513	0.200123
$766$	16.1553	0.583714
$767$	0	0
$768$	16.6649	0.601342
$769$	−53.0578	−1.91331	−0.956656	−	0.291219i	$-0.905939\pi$
$769$	−53.0578	−1.91331	−0.956656	+	0.291219i	$0.905939\pi$
$770$	−9.55108	−0.344197
$771$	24.0098	0.864690
$772$	5.18572	0.186638
$773$	16.9972	0.611348	0.305674	−	0.952136i	$-0.401118\pi$
$773$	16.9972	0.611348	0.305674	+	0.952136i	$0.401118\pi$
$774$	18.6441	0.670147
$775$	−6.66689	−0.239482
$776$	−0.999596	−0.0358834
$777$	4.03636	0.144804
$778$	−74.7083	−2.67842
$779$	27.6317	0.990009
$780$	0	0
$781$	−6.02798	−0.215698
$782$	11.9827	0.428500
$783$	−9.28692	−0.331888
$784$	0.103650	0.00370180
$785$	5.88365	0.209996
$786$	−22.5338	−0.803756
$787$	−21.7213	−0.774282	−0.387141	−	0.922021i	$-0.626537\pi$
$787$	−21.7213	−0.774282	−0.387141	+	0.922021i	$0.626537\pi$
$788$	37.2217	1.32597
$789$	7.86137	0.279872
$790$	9.66268	0.343783
$791$	−7.70366	−0.273911
$792$	−17.3706	−0.617237
$793$	0	0
$794$	18.1019	0.642412
$795$	7.15170	0.253645
$796$	−78.5711	−2.78488
$797$	−16.5076	−0.584731	−0.292365	−	0.956307i	$-0.594442\pi$
$797$	−16.5076	−0.584731	−0.292365	+	0.956307i	$0.594442\pi$
$798$	−6.90088	−0.244289
$799$	5.31216	0.187931
$800$	−25.0327	−0.885039
$801$	6.63723	0.234515
$802$	64.2015	2.26703
$803$	−63.8078	−2.25173
$804$	24.0527	0.848275
$805$	0.452464	0.0159472
$806$	0	0
$807$	8.68344	0.305672
$808$	44.1637	1.55367
$809$	12.3957	0.435811	0.217905	−	0.975970i	$-0.430078\pi$
$809$	12.3957	0.435811	0.217905	+	0.975970i	$0.430078\pi$
$810$	1.58768	0.0557855
$811$	42.7478	1.50108	0.750539	−	0.660826i	$-0.229794\pi$
$811$	42.7478	1.50108	0.750539	+	0.660826i	$0.229794\pi$
$812$	−30.2673	−1.06217
$813$	2.80089	0.0982315
$814$	−55.6846	−1.95175
$815$	−10.8534	−0.380177
$816$	0.828688	0.0290099
$817$	−24.4643	−0.855896
$818$	−5.27988	−0.184607
$819$	0	0
$820$	−20.7190	−0.723537
$821$	22.9828	0.802105	0.401052	−	0.916055i	$-0.368645\pi$
$821$	22.9828	0.802105	0.401052	+	0.916055i	$0.368645\pi$
$822$	13.0688	0.455828
$823$	55.6264	1.93902	0.969508	−	0.245060i	$-0.0788076\pi$
$823$	55.6264	1.93902	0.969508	+	0.245060i	$0.0788076\pi$
$824$	−30.8928	−1.07620
$825$	27.1953	0.946818
$826$	−4.68072	−0.162863
$827$	18.5823	0.646170	0.323085	−	0.946370i	$-0.395280\pi$
$827$	18.5823	0.646170	0.323085	+	0.946370i	$0.395280\pi$
$828$	2.12999	0.0740223
$829$	−0.532642	−0.0184994	−0.00924972	−	0.999957i	$-0.502944\pi$
$829$	−0.532642	−0.0184994	−0.00924972	+	0.999957i	$0.502944\pi$
$830$	−0.599300	−0.0208020
$831$	−3.28495	−0.113954
$832$	0	0
$833$	−7.99504	−0.277012
$834$	−22.5669	−0.781427
$835$	−13.4499	−0.465453
$836$	58.9981	2.04049
$837$	−1.47475	−0.0509748
$838$	−28.7967	−0.994765
$839$	12.9162	0.445917	0.222959	−	0.974828i	$-0.428429\pi$
$839$	12.9162	0.445917	0.222959	+	0.974828i	$0.428429\pi$
$840$	1.99909	0.0689753
$841$	57.2470	1.97403
$842$	−12.9610	−0.446664
$843$	−13.9619	−0.480872
$844$	1.23678	0.0425718
$845$	0	0
$846$	1.52373	0.0523869
$847$	−25.1890	−0.865506
$848$	1.07071	0.0367684
$849$	−8.92062	−0.306155
$850$	−82.8862	−2.84297
$851$	2.63795	0.0904278
$852$	3.26576	0.111883
$853$	9.35074	0.320163	0.160082	−	0.987104i	$-0.448824\pi$
$853$	9.35074	0.320163	0.160082	+	0.987104i	$0.448824\pi$
$854$	3.18298	0.108919
$855$	−2.08331	−0.0712479
$856$	33.5353	1.14621
$857$	−9.28116	−0.317038	−0.158519	−	0.987356i	$-0.550672\pi$
$857$	−9.28116	−0.317038	−0.158519	+	0.987356i	$0.550672\pi$
$858$	0	0
$859$	28.7220	0.979983	0.489991	−	0.871727i	$-0.337000\pi$
$859$	28.7220	0.979983	0.489991	+	0.871727i	$0.337000\pi$
$860$	18.3439	0.625522
$861$	9.18247	0.312938
$862$	−68.2902	−2.32597
$863$	34.3446	1.16910	0.584551	−	0.811357i	$-0.301271\pi$
$863$	34.3446	1.16910	0.584551	+	0.811357i	$0.301271\pi$
$864$	−5.53735	−0.188385
$865$	−9.09089	−0.309099
$866$	−50.2474	−1.70748
$867$	−46.9206	−1.59351
$868$	−4.80640	−0.163140
$869$	36.6119	1.24197
$870$	−14.7447	−0.499892
$871$	0	0
$872$	23.0711	0.781287
$873$	0.346177	0.0117163
$874$	−4.51005	−0.152555
$875$	−6.59137	−0.222829
$876$	34.5690	1.16798
$877$	52.0522	1.75768	0.878839	−	0.477119i	$-0.158319\pi$
$877$	52.0522	1.75768	0.878839	+	0.477119i	$0.158319\pi$
$878$	−75.1538	−2.53632
$879$	−5.90904	−0.199307
$880$	−0.431684	−0.0145521
$881$	23.4179	0.788969	0.394484	−	0.918903i	$-0.370923\pi$
$881$	23.4179	0.788969	0.394484	+	0.918903i	$0.370923\pi$
$882$	−2.29328	−0.0772187
$883$	21.6246	0.727725	0.363863	−	0.931453i	$-0.381458\pi$
$883$	21.6246	0.727725	0.363863	+	0.931453i	$0.381458\pi$
$884$	0	0
$885$	−1.41307	−0.0474998
$886$	−16.9281	−0.568710
$887$	−3.93562	−0.132145	−0.0660726	−	0.997815i	$-0.521047\pi$
$887$	−3.93562	−0.132145	−0.0660726	+	0.997815i	$0.521047\pi$
$888$	11.6551	0.391120
$889$	−0.733394	−0.0245973
$890$	10.5378	0.353228
$891$	6.01573	0.201535
$892$	36.1093	1.20903
$893$	−1.99940	−0.0669072
$894$	−31.3238	−1.04762
$895$	−6.88481	−0.230134
$896$	−18.5223	−0.618788
$897$	0	0
$898$	−77.6312	−2.59059
$899$	13.6959	0.456784
$900$	−14.7335	−0.491117
$901$	−82.5891	−2.75144
$902$	−126.679	−4.21795
$903$	−8.12988	−0.270545
$904$	−22.2445	−0.739842
$905$	0.314053	0.0104395
$906$	−26.2551	−0.872267
$907$	−23.8933	−0.793365	−0.396683	−	0.917956i	$-0.629839\pi$
$907$	−23.8933	−0.793365	−0.396683	+	0.917956i	$0.629839\pi$
$908$	52.9919	1.75860
$909$	−15.2947	−0.507292
$910$	0	0
$911$	9.66281	0.320143	0.160072	−	0.987105i	$-0.448827\pi$
$911$	9.66281	0.320143	0.160072	+	0.987105i	$0.448827\pi$
$912$	−0.311902	−0.0103281
$913$	−2.27075	−0.0751508
$914$	63.7233	2.10778
$915$	0.960912	0.0317668
$916$	−33.8962	−1.11996
$917$	9.82604	0.324484
$918$	−18.3348	−0.605140
$919$	−26.5839	−0.876923	−0.438461	−	0.898750i	$-0.644476\pi$
$919$	−26.5839	−0.876923	−0.438461	+	0.898750i	$0.644476\pi$
$920$	1.30650	0.0430740
$921$	−17.9000	−0.589826
$922$	68.5164	2.25647
$923$	0	0
$924$	19.6060	0.644991
$925$	−18.2471	−0.599963
$926$	−5.63661	−0.185231
$927$	10.6987	0.351392
$928$	51.4250	1.68811
$929$	−43.9772	−1.44284	−0.721422	−	0.692496i	$-0.756511\pi$
$929$	−43.9772	−1.44284	−0.721422	+	0.692496i	$0.756511\pi$
$930$	−2.34144	−0.0767787
$931$	3.00918	0.0986219
$932$	50.8292	1.66497
$933$	−14.2495	−0.466507
$934$	−11.7509	−0.384500
$935$	33.2978	1.08896
$936$	0	0
$937$	−4.79340	−0.156594	−0.0782968	−	0.996930i	$-0.524948\pi$
$937$	−4.79340	−0.156594	−0.0782968	+	0.996930i	$0.524948\pi$
$938$	−16.9247	−0.552610
$939$	9.44689	0.308288
$940$	1.49920	0.0488984
$941$	2.57174	0.0838362	0.0419181	−	0.999121i	$-0.486653\pi$
$941$	2.57174	0.0838362	0.0419181	+	0.999121i	$0.486653\pi$
$942$	−19.4893	−0.634996
$943$	6.00118	0.195425
$944$	−0.211557	−0.00688558
$945$	−0.692320	−0.0225212
$946$	112.158	3.64656
$947$	39.9699	1.29885	0.649424	−	0.760426i	$-0.275010\pi$
$947$	39.9699	1.29885	0.649424	+	0.760426i	$0.275010\pi$
$948$	−19.8351	−0.644215
$949$	0	0
$950$	31.1968	1.01216
$951$	−15.8830	−0.515040
$952$	−23.0859	−0.748218
$953$	−3.40528	−0.110308	−0.0551540	−	0.998478i	$-0.517565\pi$
$953$	−3.40528	−0.110308	−0.0551540	+	0.998478i	$0.517565\pi$
$954$	−23.6897	−0.766981
$955$	−0.858400	−0.0277772
$956$	75.5138	2.44229
$957$	−55.8677	−1.80594
$958$	−69.2003	−2.23576
$959$	−5.69875	−0.184022
$960$	−8.93508	−0.288378
$961$	−28.8251	−0.929842
$962$	0	0
$963$	−11.6138	−0.374251
$964$	−33.6720	−1.08450
$965$	−1.10158	−0.0354610
$966$	−1.49876	−0.0482220
$967$	−16.2860	−0.523723	−0.261861	−	0.965105i	$-0.584336\pi$
$967$	−16.2860	−0.523723	−0.261861	+	0.965105i	$0.584336\pi$
$968$	−72.7340	−2.33776
$969$	24.0585	0.772870
$970$	0.549620	0.0176472
$971$	0.0337391	0.00108274	0.000541369	−	1.00000i	$-0.499828\pi$
$971$	0.0337391	0.00108274	0.000541369		1.00000i	$0.499828\pi$
$972$	−3.25913	−0.104537
$973$	9.84044	0.315470
$974$	−17.1726	−0.550245
$975$	0	0
$976$	0.143862	0.00460492
$977$	50.6625	1.62084	0.810418	−	0.585852i	$-0.199240\pi$
$977$	50.6625	1.62084	0.810418	+	0.585852i	$0.199240\pi$
$978$	35.9513	1.14960
$979$	39.9278	1.27610
$980$	−2.25636	−0.0720767
$981$	−7.98992	−0.255099
$982$	46.9249	1.49743
$983$	−3.36456	−0.107313	−0.0536564	−	0.998559i	$-0.517088\pi$
$983$	−3.36456	−0.107313	−0.0536564	+	0.998559i	$0.517088\pi$
$984$	26.5146	0.845256
$985$	−7.90683	−0.251933
$986$	170.274	5.42264
$987$	−0.664432	−0.0211491
$988$	0	0
$989$	−5.31325	−0.168952
$990$	9.55108	0.303553
$991$	−19.7140	−0.626236	−0.313118	−	0.949714i	$-0.601374\pi$
$991$	−19.7140	−0.626236	−0.313118	+	0.949714i	$0.601374\pi$
$992$	8.16622	0.259278
$993$	1.92053	0.0609462
$994$	−2.29795	−0.0728865
$995$	16.6905	0.529124
$996$	1.23022	0.0389809
$997$	30.5432	0.967313	0.483657	−	0.875258i	$-0.339308\pi$
$997$	30.5432	0.967313	0.483657	+	0.875258i	$0.339308\pi$
$998$	11.3790	0.360195
$999$	−4.03636	−0.127705

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3549.2.a.bc.1.1		8
13.2	odd	12		273.2.bd.b.43.2	✓	16
13.7	odd	12		273.2.bd.b.127.2	yes	16
13.12	even	2		3549.2.a.ba.1.8		8
39.2	even	12		819.2.ct.c.316.7		16
39.20	even	12		819.2.ct.c.127.7		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bd.b.43.2	✓	16	13.2	odd	12
273.2.bd.b.127.2	yes	16	13.7	odd	12
819.2.ct.c.127.7		16	39.20	even	12
819.2.ct.c.316.7		16	39.2	even	12
3549.2.a.ba.1.8		8	13.12	even	2
3549.2.a.bc.1.1		8	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q-2.29328 q^{2} -1.00000 q^{3} +3.25913 q^{4} -0.692320 q^{5} +2.29328 q^{6} -1.00000 q^{7} -2.88753 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.29328 q^{2} -1.00000 q^{3} +3.25913 q^{4} -0.692320 q^{5} +2.29328 q^{6} -1.00000 q^{7} -2.88753 q^{8} +1.00000 q^{9} +1.58768 q^{10} +6.01573 q^{11} -3.25913 q^{12} +2.29328 q^{14} +0.692320 q^{15} +0.103650 q^{16} -7.99504 q^{17} -2.29328 q^{18} +3.00918 q^{19} -2.25636 q^{20} +1.00000 q^{21} -13.7958 q^{22} +0.653547 q^{23} +2.88753 q^{24} -4.52069 q^{25} -1.00000 q^{27} -3.25913 q^{28} +9.28692 q^{29} -1.58768 q^{30} +1.47475 q^{31} +5.53735 q^{32} -6.01573 q^{33} +18.3348 q^{34} +0.692320 q^{35} +3.25913 q^{36} +4.03636 q^{37} -6.90088 q^{38} +1.99909 q^{40} +9.18247 q^{41} -2.29328 q^{42} -8.12988 q^{43} +19.6060 q^{44} -0.692320 q^{45} -1.49876 q^{46} -0.664432 q^{47} -0.103650 q^{48} +1.00000 q^{49} +10.3672 q^{50} +7.99504 q^{51} +10.3300 q^{53} +2.29328 q^{54} -4.16481 q^{55} +2.88753 q^{56} -3.00918 q^{57} -21.2975 q^{58} -2.04106 q^{59} +2.25636 q^{60} +1.38796 q^{61} -3.38201 q^{62} -1.00000 q^{63} -12.9060 q^{64} +13.7958 q^{66} -7.38012 q^{67} -26.0568 q^{68} -0.653547 q^{69} -1.58768 q^{70} -1.00204 q^{71} -2.88753 q^{72} -10.6068 q^{73} -9.25650 q^{74} +4.52069 q^{75} +9.80729 q^{76} -6.01573 q^{77} +6.08603 q^{79} -0.0717592 q^{80} +1.00000 q^{81} -21.0580 q^{82} -0.377468 q^{83} +3.25913 q^{84} +5.53513 q^{85} +18.6441 q^{86} -9.28692 q^{87} -17.3706 q^{88} +6.63723 q^{89} +1.58768 q^{90} +2.12999 q^{92} -1.47475 q^{93} +1.52373 q^{94} -2.08331 q^{95} -5.53735 q^{96} +0.346177 q^{97} -2.29328 q^{98} +6.01573 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{2} - 8 q^{3} + 14 q^{4} + 6 q^{5} - 2 q^{6} - 8 q^{7} + 12 q^{8} + 8 q^{9}+O(q^{10}) \) 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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