LMFDB - Embedded newform 2738.2.a.s.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2738,2,Mod(1,2738)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2738, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("2738.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2738 = 2 \cdot 37^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2738.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:	$21.8630400734$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{36})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} + 9x^{2} - 3 $ x^6 - 6x^4 + 9x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-1.96962$ of defining polynomial
Character	$\chi$	$=$	2738.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +0.384754 q^{5} +1.53209 q^{6} -3.26414 q^{7} +1.00000 q^{8} -0.652704 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +0.384754 q^{5} +1.53209 q^{6} -3.26414 q^{7} +1.00000 q^{8} -0.652704 q^{9} +0.384754 q^{10} -2.58472 q^{11} +1.53209 q^{12} +1.36492 q^{13} -3.26414 q^{14} +0.589478 q^{15} +1.00000 q^{16} -3.33213 q^{17} -0.652704 q^{18} -5.98578 q^{19} +0.384754 q^{20} -5.00095 q^{21} -2.58472 q^{22} -7.54605 q^{23} +1.53209 q^{24} -4.85196 q^{25} +1.36492 q^{26} -5.59627 q^{27} -3.26414 q^{28} -3.21297 q^{29} +0.589478 q^{30} +2.53737 q^{31} +1.00000 q^{32} -3.96002 q^{33} -3.33213 q^{34} -1.25589 q^{35} -0.652704 q^{36} -5.98578 q^{38} +2.09118 q^{39} +0.384754 q^{40} +8.26915 q^{41} -5.00095 q^{42} +4.33920 q^{43} -2.58472 q^{44} -0.251131 q^{45} -7.54605 q^{46} +5.22909 q^{47} +1.53209 q^{48} +3.65461 q^{49} -4.85196 q^{50} -5.10511 q^{51} +1.36492 q^{52} -8.67122 q^{53} -5.59627 q^{54} -0.994481 q^{55} -3.26414 q^{56} -9.17075 q^{57} -3.21297 q^{58} +12.9674 q^{59} +0.589478 q^{60} -7.01264 q^{61} +2.53737 q^{62} +2.13052 q^{63} +1.00000 q^{64} +0.525160 q^{65} -3.96002 q^{66} +11.2380 q^{67} -3.33213 q^{68} -11.5612 q^{69} -1.25589 q^{70} +14.9995 q^{71} -0.652704 q^{72} +15.0792 q^{73} -7.43364 q^{75} -5.98578 q^{76} +8.43688 q^{77} +2.09118 q^{78} -1.46329 q^{79} +0.384754 q^{80} -6.61587 q^{81} +8.26915 q^{82} -0.0111178 q^{83} -5.00095 q^{84} -1.28205 q^{85} +4.33920 q^{86} -4.92256 q^{87} -2.58472 q^{88} +0.953262 q^{89} -0.251131 q^{90} -4.45530 q^{91} -7.54605 q^{92} +3.88748 q^{93} +5.22909 q^{94} -2.30306 q^{95} +1.53209 q^{96} -14.8185 q^{97} +3.65461 q^{98} +1.68705 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	$ 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.53209	0.884552	0.442276	−	0.896879i	$-0.354171\pi$
$3$	1.53209	0.884552	0.442276	+	0.896879i	$0.354171\pi$
$4$	1.00000	0.500000
$5$	0.384754	0.172067	0.0860337	−	0.996292i	$-0.472581\pi$
$5$	0.384754	0.172067	0.0860337	+	0.996292i	$0.472581\pi$
$6$	1.53209	0.625473
$7$	−3.26414	−1.23373	−0.616864	−	0.787069i	$-0.711597\pi$
$7$	−3.26414	−1.23373	−0.616864	+	0.787069i	$0.711597\pi$
$8$	1.00000	0.353553
$9$	−0.652704	−0.217568
$10$	0.384754	0.121670
$11$	−2.58472	−0.779321	−0.389661	−	0.920959i	$-0.627408\pi$
$11$	−2.58472	−0.779321	−0.389661	+	0.920959i	$0.627408\pi$
$12$	1.53209	0.442276
$13$	1.36492	0.378561	0.189281	−	0.981923i	$-0.439384\pi$
$13$	1.36492	0.378561	0.189281	+	0.981923i	$0.439384\pi$
$14$	−3.26414	−0.872378
$15$	0.589478	0.152203
$16$	1.00000	0.250000
$17$	−3.33213	−0.808159	−0.404080	−	0.914724i	$-0.632408\pi$
$17$	−3.33213	−0.808159	−0.404080	+	0.914724i	$0.632408\pi$
$18$	−0.652704	−0.153844
$19$	−5.98578	−1.37323	−0.686616	−	0.727020i	$-0.740905\pi$
$19$	−5.98578	−1.37323	−0.686616	+	0.727020i	$0.740905\pi$
$20$	0.384754	0.0860337
$21$	−5.00095	−1.09130
$22$	−2.58472	−0.551063
$23$	−7.54605	−1.57346	−0.786730	−	0.617297i	$-0.788228\pi$
$23$	−7.54605	−1.57346	−0.786730	+	0.617297i	$0.788228\pi$
$24$	1.53209	0.312736
$25$	−4.85196	−0.970393
$26$	1.36492	0.267683
$27$	−5.59627	−1.07700
$28$	−3.26414	−0.616864
$29$	−3.21297	−0.596634	−0.298317	−	0.954467i	$-0.596425\pi$
$29$	−3.21297	−0.596634	−0.298317	+	0.954467i	$0.596425\pi$
$30$	0.589478	0.107623
$31$	2.53737	0.455726	0.227863	−	0.973693i	$-0.426826\pi$
$31$	2.53737	0.455726	0.227863	+	0.973693i	$0.426826\pi$
$32$	1.00000	0.176777
$33$	−3.96002	−0.689350
$34$	−3.33213	−0.571455
$35$	−1.25589	−0.212285
$36$	−0.652704	−0.108784
$37$	0	0
$37$	0	0
$38$	−5.98578	−0.971022
$39$	2.09118	0.334857
$40$	0.384754	0.0608350
$41$	8.26915	1.29142	0.645712	−	0.763581i	$-0.276561\pi$
$41$	8.26915	1.29142	0.645712	+	0.763581i	$0.276561\pi$
$42$	−5.00095	−0.771664
$43$	4.33920	0.661722	0.330861	−	0.943680i	$-0.392661\pi$
$43$	4.33920	0.661722	0.330861	+	0.943680i	$0.392661\pi$
$44$	−2.58472	−0.389661
$45$	−0.251131	−0.0374363
$46$	−7.54605	−1.11260
$47$	5.22909	0.762742	0.381371	−	0.924422i	$-0.375452\pi$
$47$	5.22909	0.762742	0.381371	+	0.924422i	$0.375452\pi$
$48$	1.53209	0.221138
$49$	3.65461	0.522087
$50$	−4.85196	−0.686171
$51$	−5.10511	−0.714859
$52$	1.36492	0.189281
$53$	−8.67122	−1.19108	−0.595542	−	0.803324i	$-0.703063\pi$
$53$	−8.67122	−1.19108	−0.595542	+	0.803324i	$0.703063\pi$
$54$	−5.59627	−0.761555
$55$	−0.994481	−0.134096
$56$	−3.26414	−0.436189
$57$	−9.17075	−1.21470
$58$	−3.21297	−0.421884
$59$	12.9674	1.68821	0.844107	−	0.536174i	$-0.180131\pi$
$59$	12.9674	1.68821	0.844107	+	0.536174i	$0.180131\pi$
$60$	0.589478	0.0761013
$61$	−7.01264	−0.897877	−0.448938	−	0.893563i	$-0.648198\pi$
$61$	−7.01264	−0.897877	−0.448938	+	0.893563i	$0.648198\pi$
$62$	2.53737	0.322247
$63$	2.13052	0.268420
$64$	1.00000	0.125000
$65$	0.525160	0.0651381
$66$	−3.96002	−0.487444
$67$	11.2380	1.37294	0.686470	−	0.727158i	$-0.259159\pi$
$67$	11.2380	1.37294	0.686470	+	0.727158i	$0.259159\pi$
$68$	−3.33213	−0.404080
$69$	−11.5612	−1.39181
$70$	−1.25589	−0.150108
$71$	14.9995	1.78012	0.890059	−	0.455845i	$-0.150663\pi$
$71$	14.9995	1.78012	0.890059	+	0.455845i	$0.150663\pi$
$72$	−0.652704	−0.0769219
$73$	15.0792	1.76489	0.882445	−	0.470416i	$-0.155896\pi$
$73$	15.0792	1.76489	0.882445	+	0.470416i	$0.155896\pi$
$74$	0	0
$75$	−7.43364	−0.858363
$76$	−5.98578	−0.686616
$77$	8.43688	0.961471
$78$	2.09118	0.236780
$79$	−1.46329	−0.164633	−0.0823167	−	0.996606i	$-0.526232\pi$
$79$	−1.46329	−0.164633	−0.0823167	+	0.996606i	$0.526232\pi$
$80$	0.384754	0.0430169
$81$	−6.61587	−0.735096
$82$	8.26915	0.913175
$83$	−0.0111178	−0.00122034	−0.000610170	−	1.00000i	$-0.500194\pi$
$83$	−0.0111178	−0.00122034	−0.000610170		1.00000i	$0.500194\pi$
$84$	−5.00095	−0.545649
$85$	−1.28205	−0.139058
$86$	4.33920	0.467908
$87$	−4.92256	−0.527754
$88$	−2.58472	−0.275532
$89$	0.953262	0.101046	0.0505228	−	0.998723i	$-0.483911\pi$
$89$	0.953262	0.101046	0.0505228	+	0.998723i	$0.483911\pi$
$90$	−0.251131	−0.0264715
$91$	−4.45530	−0.467042
$92$	−7.54605	−0.786730
$93$	3.88748	0.403113
$94$	5.22909	0.539340
$95$	−2.30306	−0.236289
$96$	1.53209	0.156368
$97$	−14.8185	−1.50459	−0.752297	−	0.658824i	$-0.771054\pi$
$97$	−14.8185	−1.50459	−0.752297	+	0.658824i	$0.771054\pi$
$98$	3.65461	0.369171
$99$	1.68705	0.169555
$100$	−4.85196	−0.485196
$101$	−1.27252	−0.126621	−0.0633103	−	0.997994i	$-0.520166\pi$
$101$	−1.27252	−0.126621	−0.0633103	+	0.997994i	$0.520166\pi$
$102$	−5.10511	−0.505482
$103$	−10.8461	−1.06870	−0.534350	−	0.845264i	$-0.679443\pi$
$103$	−10.8461	−1.06870	−0.534350	+	0.845264i	$0.679443\pi$
$104$	1.36492	0.133842
$105$	−1.92414	−0.187777
$106$	−8.67122	−0.842224
$107$	−4.75958	−0.460126	−0.230063	−	0.973176i	$-0.573893\pi$
$107$	−4.75958	−0.460126	−0.230063	+	0.973176i	$0.573893\pi$
$108$	−5.59627	−0.538501
$109$	−9.63744	−0.923099	−0.461550	−	0.887114i	$-0.652706\pi$
$109$	−9.63744	−0.923099	−0.461550	+	0.887114i	$0.652706\pi$
$110$	−0.994481	−0.0948201
$111$	0	0
$112$	−3.26414	−0.308432
$113$	−12.9549	−1.21870	−0.609348	−	0.792903i	$-0.708569\pi$
$113$	−12.9549	−1.21870	−0.609348	+	0.792903i	$0.708569\pi$
$114$	−9.17075	−0.858920
$115$	−2.90338	−0.270741
$116$	−3.21297	−0.298317
$117$	−0.890890	−0.0823628
$118$	12.9674	1.19375
$119$	10.8765	0.997050
$120$	0.589478	0.0538117
$121$	−4.31924	−0.392658
$122$	−7.01264	−0.634895
$123$	12.6691	1.14233
$124$	2.53737	0.227863
$125$	−3.79059	−0.339040
$126$	2.13052	0.189801
$127$	11.2408	0.997458	0.498729	−	0.866758i	$-0.333800\pi$
$127$	11.2408	0.997458	0.498729	+	0.866758i	$0.333800\pi$
$128$	1.00000	0.0883883
$129$	6.64804	0.585327
$130$	0.525160	0.0460596
$131$	−8.36959	−0.731254	−0.365627	−	0.930761i	$-0.619145\pi$
$131$	−8.36959	−0.731254	−0.365627	+	0.930761i	$0.619145\pi$
$132$	−3.96002	−0.344675
$133$	19.5384	1.69420
$134$	11.2380	0.970815
$135$	−2.15319	−0.185317
$136$	−3.33213	−0.285728
$137$	−3.98413	−0.340387	−0.170194	−	0.985411i	$-0.554439\pi$
$137$	−3.98413	−0.340387	−0.170194	+	0.985411i	$0.554439\pi$
$138$	−11.5612	−0.984156
$139$	−5.11140	−0.433543	−0.216772	−	0.976222i	$-0.569553\pi$
$139$	−5.11140	−0.433543	−0.216772	+	0.976222i	$0.569553\pi$
$140$	−1.25589	−0.106142
$141$	8.01143	0.674684
$142$	14.9995	1.25873
$143$	−3.52794	−0.295021
$144$	−0.652704	−0.0543920
$145$	−1.23620	−0.102661
$146$	15.0792	1.24797
$147$	5.59918	0.461813
$148$	0	0
$149$	−15.8700	−1.30012	−0.650060	−	0.759883i	$-0.725256\pi$
$149$	−15.8700	−1.30012	−0.650060	+	0.759883i	$0.725256\pi$
$150$	−7.43364	−0.606954
$151$	21.7680	1.77146	0.885729	−	0.464202i	$-0.153659\pi$
$151$	21.7680	1.77146	0.885729	+	0.464202i	$0.153659\pi$
$152$	−5.98578	−0.485511
$153$	2.17489	0.175830
$154$	8.43688	0.679863
$155$	0.976266	0.0784155
$156$	2.09118	0.167429
$157$	−9.75142	−0.778248	−0.389124	−	0.921185i	$-0.627222\pi$
$157$	−9.75142	−0.778248	−0.389124	+	0.921185i	$0.627222\pi$
$158$	−1.46329	−0.116413
$159$	−13.2851	−1.05358
$160$	0.384754	0.0304175
$161$	24.6314	1.94122
$162$	−6.61587	−0.519792
$163$	−13.1647	−1.03114	−0.515571	−	0.856847i	$-0.672420\pi$
$163$	−13.1647	−1.03114	−0.515571	+	0.856847i	$0.672420\pi$
$164$	8.26915	0.645712
$165$	−1.52363	−0.118615
$166$	−0.0111178	−0.000862910 0
$167$	5.60228	0.433518	0.216759	−	0.976225i	$-0.430451\pi$
$167$	5.60228	0.433518	0.216759	+	0.976225i	$0.430451\pi$
$168$	−5.00095	−0.385832
$169$	−11.1370	−0.856691
$170$	−1.28205	−0.0983288
$171$	3.90694	0.298771
$172$	4.33920	0.330861
$173$	10.8354	0.823800	0.411900	−	0.911229i	$-0.364865\pi$
$173$	10.8354	0.823800	0.411900	+	0.911229i	$0.364865\pi$
$174$	−4.92256	−0.373178
$175$	15.8375	1.19720
$176$	−2.58472	−0.194830
$177$	19.8672	1.49331
$178$	0.953262	0.0714500
$179$	−6.07192	−0.453837	−0.226918	−	0.973914i	$-0.572865\pi$
$179$	−6.07192	−0.453837	−0.226918	+	0.973914i	$0.572865\pi$
$180$	−0.251131	−0.0187182
$181$	21.5538	1.60208	0.801042	−	0.598608i	$-0.204279\pi$
$181$	21.5538	1.60208	0.801042	+	0.598608i	$0.204279\pi$
$182$	−4.45530	−0.330249
$183$	−10.7440	−0.794219
$184$	−7.54605	−0.556302
$185$	0	0
$186$	3.88748	0.285044
$187$	8.61260	0.629816
$188$	5.22909	0.381371
$189$	18.2670	1.32873
$190$	−2.30306	−0.167081
$191$	6.62693	0.479508	0.239754	−	0.970834i	$-0.422933\pi$
$191$	6.62693	0.479508	0.239754	+	0.970834i	$0.422933\pi$
$192$	1.53209	0.110569
$193$	−22.8544	−1.64510	−0.822548	−	0.568696i	$-0.807448\pi$
$193$	−22.8544	−1.64510	−0.822548	+	0.568696i	$0.807448\pi$
$194$	−14.8185	−1.06391
$195$	0.804592	0.0576180
$196$	3.65461	0.261043
$197$	−14.7561	−1.05133	−0.525663	−	0.850693i	$-0.676183\pi$
$197$	−14.7561	−1.05133	−0.525663	+	0.850693i	$0.676183\pi$
$198$	1.68705	0.119894
$199$	−1.47478	−0.104544	−0.0522721	−	0.998633i	$-0.516646\pi$
$199$	−1.47478	−0.104544	−0.0522721	+	0.998633i	$0.516646\pi$
$200$	−4.85196	−0.343086
$201$	17.2176	1.21444
$202$	−1.27252	−0.0895342
$203$	10.4876	0.736084
$204$	−5.10511	−0.357430
$205$	3.18159	0.222212
$206$	−10.8461	−0.755685
$207$	4.92533	0.342334
$208$	1.36492	0.0946403
$209$	15.4716	1.07019
$210$	−1.92414	−0.132778
$211$	−2.41952	−0.166567	−0.0832835	−	0.996526i	$-0.526541\pi$
$211$	−2.41952	−0.166567	−0.0832835	+	0.996526i	$0.526541\pi$
$212$	−8.67122	−0.595542
$213$	22.9806	1.57461
$214$	−4.75958	−0.325358
$215$	1.66953	0.113861
$216$	−5.59627	−0.380778
$217$	−8.28234	−0.562242
$218$	−9.63744	−0.652730
$219$	23.1027	1.56114
$220$	−0.994481	−0.0670479
$221$	−4.54809	−0.305938
$222$	0	0
$223$	−6.94726	−0.465223	−0.232611	−	0.972570i	$-0.574727\pi$
$223$	−6.94726	−0.465223	−0.232611	+	0.972570i	$0.574727\pi$
$224$	−3.26414	−0.218095
$225$	3.16689	0.211126
$226$	−12.9549	−0.861749
$227$	21.8490	1.45017	0.725084	−	0.688660i	$-0.241801\pi$
$227$	21.8490	1.45017	0.725084	+	0.688660i	$0.241801\pi$
$228$	−9.17075	−0.607348
$229$	−4.25010	−0.280854	−0.140427	−	0.990091i	$-0.544848\pi$
$229$	−4.25010	−0.280854	−0.140427	+	0.990091i	$0.544848\pi$
$230$	−2.90338	−0.191443
$231$	12.9260	0.850471
$232$	−3.21297	−0.210942
$233$	−17.3443	−1.13626	−0.568131	−	0.822938i	$-0.692333\pi$
$233$	−17.3443	−1.13626	−0.568131	+	0.822938i	$0.692333\pi$
$234$	−0.890890	−0.0582393
$235$	2.01192	0.131243
$236$	12.9674	0.844107
$237$	−2.24190	−0.145627
$238$	10.8765	0.705021
$239$	−18.3584	−1.18750	−0.593752	−	0.804648i	$-0.702354\pi$
$239$	−18.3584	−1.18750	−0.593752	+	0.804648i	$0.702354\pi$
$240$	0.589478	0.0380506
$241$	23.4661	1.51158	0.755792	−	0.654811i	$-0.227252\pi$
$241$	23.4661	1.51158	0.755792	+	0.654811i	$0.227252\pi$
$242$	−4.31924	−0.277651
$243$	6.65270	0.426771
$244$	−7.01264	−0.448938
$245$	1.40613	0.0898341
$246$	12.6691	0.807751
$247$	−8.17013	−0.519853
$248$	2.53737	0.161123
$249$	−0.0170335	−0.00107945
$250$	−3.79059	−0.239738
$251$	−6.10149	−0.385123	−0.192561	−	0.981285i	$-0.561679\pi$
$251$	−6.10149	−0.385123	−0.192561	+	0.981285i	$0.561679\pi$
$252$	2.13052	0.134210
$253$	19.5044	1.22623
$254$	11.2408	0.705309
$255$	−1.96422	−0.123004
$256$	1.00000	0.0625000
$257$	−4.34710	−0.271165	−0.135582	−	0.990766i	$-0.543291\pi$
$257$	−4.34710	−0.271165	−0.135582	+	0.990766i	$0.543291\pi$
$258$	6.64804	0.413889
$259$	0	0
$260$	0.525160	0.0325690
$261$	2.09712	0.129808
$262$	−8.36959	−0.517075
$263$	4.05485	0.250033	0.125016	−	0.992155i	$-0.460102\pi$
$263$	4.05485	0.250033	0.125016	+	0.992155i	$0.460102\pi$
$264$	−3.96002	−0.243722
$265$	−3.33629	−0.204947
$266$	19.5384	1.19798
$267$	1.46048	0.0893801
$268$	11.2380	0.686470
$269$	8.79337	0.536141	0.268071	−	0.963399i	$-0.413614\pi$
$269$	8.79337	0.536141	0.268071	+	0.963399i	$0.413614\pi$
$270$	−2.15319	−0.131039
$271$	−12.9122	−0.784361	−0.392180	−	0.919888i	$-0.628279\pi$
$271$	−12.9122	−0.784361	−0.392180	+	0.919888i	$0.628279\pi$
$272$	−3.33213	−0.202040
$273$	−6.82591	−0.413123
$274$	−3.98413	−0.240690
$275$	12.5410	0.756248
$276$	−11.5612	−0.695904
$277$	−7.77643	−0.467240	−0.233620	−	0.972328i	$-0.575057\pi$
$277$	−7.77643	−0.467240	−0.233620	+	0.972328i	$0.575057\pi$
$278$	−5.11140	−0.306561
$279$	−1.65615	−0.0991513
$280$	−1.25589	−0.0750539
$281$	0.232510	0.0138704	0.00693518	−	0.999976i	$-0.497792\pi$
$281$	0.232510	0.0138704	0.00693518	+	0.999976i	$0.497792\pi$
$282$	8.01143	0.477074
$283$	−12.8330	−0.762843	−0.381421	−	0.924401i	$-0.624565\pi$
$283$	−12.8330	−0.762843	−0.381421	+	0.924401i	$0.624565\pi$
$284$	14.9995	0.890059
$285$	−3.52849	−0.209010
$286$	−3.52794	−0.208611
$287$	−26.9917	−1.59327
$288$	−0.652704	−0.0384609
$289$	−5.89693	−0.346878
$290$	−1.23620	−0.0725925
$291$	−22.7033	−1.33089
$292$	15.0792	0.882445
$293$	−24.6443	−1.43974	−0.719868	−	0.694111i	$-0.755797\pi$
$293$	−24.6443	−1.43974	−0.719868	+	0.694111i	$0.755797\pi$
$294$	5.59918	0.326551
$295$	4.98927	0.290487
$296$	0	0
$297$	14.4648	0.839331
$298$	−15.8700	−0.919324
$299$	−10.2998	−0.595651
$300$	−7.43364	−0.429181
$301$	−14.1638	−0.816385
$302$	21.7680	1.25261
$303$	−1.94961	−0.112002
$304$	−5.98578	−0.343308
$305$	−2.69815	−0.154495
$306$	2.17489	0.124330
$307$	−6.91132	−0.394450	−0.197225	−	0.980358i	$-0.563193\pi$
$307$	−6.91132	−0.394450	−0.197225	+	0.980358i	$0.563193\pi$
$308$	8.43688	0.480736
$309$	−16.6172	−0.945320
$310$	0.976266	0.0554482
$311$	−1.65859	−0.0940501	−0.0470251	−	0.998894i	$-0.514974\pi$
$311$	−1.65859	−0.0940501	−0.0470251	+	0.998894i	$0.514974\pi$
$312$	2.09118	0.118390
$313$	25.9509	1.46683	0.733416	−	0.679780i	$-0.237925\pi$
$313$	25.9509	1.46683	0.733416	+	0.679780i	$0.237925\pi$
$314$	−9.75142	−0.550304
$315$	0.819725	0.0461863
$316$	−1.46329	−0.0823167
$317$	11.3498	0.637470	0.318735	−	0.947844i	$-0.396742\pi$
$317$	11.3498	0.637470	0.318735	+	0.947844i	$0.396742\pi$
$318$	−13.2851	−0.744991
$319$	8.30462	0.464969
$320$	0.384754	0.0215084
$321$	−7.29210	−0.407006
$322$	24.6314	1.37265
$323$	19.9454	1.10979
$324$	−6.61587	−0.367548
$325$	−6.62255	−0.367353
$326$	−13.1647	−0.729127
$327$	−14.7654	−0.816529
$328$	8.26915	0.456588
$329$	−17.0685	−0.941016
$330$	−1.52363	−0.0838733
$331$	12.8377	0.705623	0.352811	−	0.935694i	$-0.385226\pi$
$331$	12.8377	0.705623	0.352811	+	0.935694i	$0.385226\pi$
$332$	−0.0111178	−0.000610170 0
$333$	0	0
$334$	5.60228	0.306543
$335$	4.32387	0.236238
$336$	−5.00095	−0.272824
$337$	−5.71183	−0.311143	−0.155572	−	0.987825i	$-0.549722\pi$
$337$	−5.71183	−0.311143	−0.155572	+	0.987825i	$0.549722\pi$
$338$	−11.1370	−0.605772
$339$	−19.8481	−1.07800
$340$	−1.28205	−0.0695290
$341$	−6.55839	−0.355157
$342$	3.90694	0.211263
$343$	10.9198	0.589615
$344$	4.33920	0.233954
$345$	−4.44823	−0.239485
$346$	10.8354	0.582515
$347$	32.3416	1.73619	0.868095	−	0.496398i	$-0.165344\pi$
$347$	32.3416	1.73619	0.868095	+	0.496398i	$0.165344\pi$
$348$	−4.92256	−0.263877
$349$	−24.9320	−1.33458	−0.667290	−	0.744798i	$-0.732546\pi$
$349$	−24.9320	−1.33458	−0.667290	+	0.744798i	$0.732546\pi$
$350$	15.8375	0.846549
$351$	−7.63847	−0.407711
$352$	−2.58472	−0.137766
$353$	−8.64114	−0.459921	−0.229961	−	0.973200i	$-0.573860\pi$
$353$	−8.64114	−0.459921	−0.229961	+	0.973200i	$0.573860\pi$
$354$	19.8672	1.05593
$355$	5.77114	0.306300
$356$	0.953262	0.0505228
$357$	16.6638	0.881942
$358$	−6.07192	−0.320911
$359$	3.85848	0.203643	0.101821	−	0.994803i	$-0.467533\pi$
$359$	3.85848	0.203643	0.101821	+	0.994803i	$0.467533\pi$
$360$	−0.251131	−0.0132357
$361$	16.8296	0.885768
$362$	21.5538	1.13284
$363$	−6.61746	−0.347327
$364$	−4.45530	−0.233521
$365$	5.80180	0.303680
$366$	−10.7440	−0.561597
$367$	10.4563	0.545813	0.272906	−	0.962041i	$-0.412015\pi$
$367$	10.4563	0.545813	0.272906	+	0.962041i	$0.412015\pi$
$368$	−7.54605	−0.393365
$369$	−5.39731	−0.280973
$370$	0	0
$371$	28.3041	1.46947
$372$	3.88748	0.201557
$373$	−9.86566	−0.510825	−0.255412	−	0.966832i	$-0.582211\pi$
$373$	−9.86566	−0.510825	−0.255412	+	0.966832i	$0.582211\pi$
$374$	8.61260	0.445347
$375$	−5.80752	−0.299899
$376$	5.22909	0.269670
$377$	−4.38546	−0.225862
$378$	18.2670	0.939553
$379$	2.48121	0.127451	0.0637255	−	0.997967i	$-0.479702\pi$
$379$	2.48121	0.127451	0.0637255	+	0.997967i	$0.479702\pi$
$380$	−2.30306	−0.118144
$381$	17.2219	0.882303
$382$	6.62693	0.339063
$383$	−25.5639	−1.30625	−0.653127	−	0.757249i	$-0.726543\pi$
$383$	−25.5639	−1.30625	−0.653127	+	0.757249i	$0.726543\pi$
$384$	1.53209	0.0781841
$385$	3.24613	0.165438
$386$	−22.8544	−1.16326
$387$	−2.83221	−0.143969
$388$	−14.8185	−0.752297
$389$	−6.37509	−0.323230	−0.161615	−	0.986854i	$-0.551670\pi$
$389$	−6.37509	−0.323230	−0.161615	+	0.986854i	$0.551670\pi$
$390$	0.804592	0.0407421
$391$	25.1444	1.27161
$392$	3.65461	0.184586
$393$	−12.8229	−0.646832
$394$	−14.7561	−0.743400
$395$	−0.563009	−0.0283281
$396$	1.68705	0.0847776
$397$	37.4977	1.88196	0.940979	−	0.338465i	$-0.109908\pi$
$397$	37.4977	1.88196	0.940979	+	0.338465i	$0.109908\pi$
$398$	−1.47478	−0.0739240
$399$	29.9346	1.49861
$400$	−4.85196	−0.242598
$401$	−35.1464	−1.75513	−0.877563	−	0.479462i	$-0.840832\pi$
$401$	−35.1464	−1.75513	−0.877563	+	0.479462i	$0.840832\pi$
$402$	17.2176	0.858737
$403$	3.46332	0.172520
$404$	−1.27252	−0.0633103
$405$	−2.54548	−0.126486
$406$	10.4876	0.520490
$407$	0	0
$408$	−5.10511	−0.252741
$409$	0.450741	0.0222877	0.0111439	−	0.999938i	$-0.496453\pi$
$409$	0.450741	0.0222877	0.0111439	+	0.999938i	$0.496453\pi$
$410$	3.18159	0.157128
$411$	−6.10404	−0.301090
$412$	−10.8461	−0.534350
$413$	−42.3275	−2.08280
$414$	4.92533	0.242067
$415$	−0.00427763	−0.000209981 0
$416$	1.36492	0.0669208
$417$	−7.83112	−0.383492
$418$	15.4716	0.756738
$419$	−15.3113	−0.748006	−0.374003	−	0.927428i	$-0.622015\pi$
$419$	−15.3113	−0.748006	−0.374003	+	0.927428i	$0.622015\pi$
$420$	−1.92414	−0.0938884
$421$	−22.3965	−1.09154	−0.545769	−	0.837936i	$-0.683762\pi$
$421$	−22.3965	−1.09154	−0.545769	+	0.837936i	$0.683762\pi$
$422$	−2.41952	−0.117781
$423$	−3.41305	−0.165948
$424$	−8.67122	−0.421112
$425$	16.1674	0.784232
$426$	22.9806	1.11342
$427$	22.8902	1.10774
$428$	−4.75958	−0.230063
$429$	−5.40511	−0.260961
$430$	1.66953	0.0805117
$431$	−0.102080	−0.00491701	−0.00245851	−	0.999997i	$-0.500783\pi$
$431$	−0.102080	−0.00491701	−0.00245851	+	0.999997i	$0.500783\pi$
$432$	−5.59627	−0.269251
$433$	7.92714	0.380954	0.190477	−	0.981692i	$-0.438997\pi$
$433$	7.92714	0.380954	0.190477	+	0.981692i	$0.438997\pi$
$434$	−8.28234	−0.397565
$435$	−1.89398	−0.0908092
$436$	−9.63744	−0.461550
$437$	45.1690	2.16073
$438$	23.1027	1.10389
$439$	7.57063	0.361326	0.180663	−	0.983545i	$-0.442176\pi$
$439$	7.57063	0.361326	0.180663	+	0.983545i	$0.442176\pi$
$440$	−0.994481	−0.0474100
$441$	−2.38538	−0.113589
$442$	−4.54809	−0.216331
$443$	−15.9856	−0.759499	−0.379749	−	0.925089i	$-0.623990\pi$
$443$	−15.9856	−0.759499	−0.379749	+	0.925089i	$0.623990\pi$
$444$	0	0
$445$	0.366772	0.0173867
$446$	−6.94726	−0.328962
$447$	−24.3142	−1.15002
$448$	−3.26414	−0.154216
$449$	28.6753	1.35327	0.676636	−	0.736318i	$-0.263437\pi$
$449$	28.6753	1.35327	0.676636	+	0.736318i	$0.263437\pi$
$450$	3.16689	0.149289
$451$	−21.3734	−1.00643
$452$	−12.9549	−0.609348
$453$	33.3506	1.56695
$454$	21.8490	1.02542
$455$	−1.71420	−0.0803627
$456$	−9.17075	−0.429460
$457$	−0.105116	−0.00491713	−0.00245857	−	0.999997i	$-0.500783\pi$
$457$	−0.105116	−0.00491713	−0.00245857	+	0.999997i	$0.500783\pi$
$458$	−4.25010	−0.198594
$459$	18.6475	0.870389
$460$	−2.90338	−0.135371
$461$	23.9701	1.11640	0.558199	−	0.829707i	$-0.311493\pi$
$461$	23.9701	1.11640	0.558199	+	0.829707i	$0.311493\pi$
$462$	12.9260	0.601374
$463$	−20.7514	−0.964398	−0.482199	−	0.876062i	$-0.660162\pi$
$463$	−20.7514	−0.964398	−0.482199	+	0.876062i	$0.660162\pi$
$464$	−3.21297	−0.149158
$465$	1.49573	0.0693626
$466$	−17.3443	−0.803459
$467$	−17.4928	−0.809472	−0.404736	−	0.914434i	$-0.632637\pi$
$467$	−17.4928	−0.809472	−0.404736	+	0.914434i	$0.632637\pi$
$468$	−0.890890	−0.0411814
$469$	−36.6824	−1.69384
$470$	2.01192	0.0928028
$471$	−14.9400	−0.688401
$472$	12.9674	0.596874
$473$	−11.2156	−0.515694
$474$	−2.24190	−0.102974
$475$	29.0428	1.33258
$476$	10.8765	0.498525
$477$	5.65974	0.259142
$478$	−18.3584	−0.839692
$479$	6.88046	0.314376	0.157188	−	0.987569i	$-0.449757\pi$
$479$	6.88046	0.314376	0.157188	+	0.987569i	$0.449757\pi$
$480$	0.589478	0.0269059
$481$	0	0
$482$	23.4661	1.06885
$483$	37.7374	1.71711
$484$	−4.31924	−0.196329
$485$	−5.70150	−0.258892
$486$	6.65270	0.301773
$487$	1.70810	0.0774014	0.0387007	−	0.999251i	$-0.487678\pi$
$487$	1.70810	0.0774014	0.0387007	+	0.999251i	$0.487678\pi$
$488$	−7.01264	−0.317447
$489$	−20.1696	−0.912099
$490$	1.40613	0.0635223
$491$	10.6231	0.479412	0.239706	−	0.970846i	$-0.422949\pi$
$491$	10.6231	0.479412	0.239706	+	0.970846i	$0.422949\pi$
$492$	12.6691	0.571166
$493$	10.7060	0.482175
$494$	−8.17013	−0.367591
$495$	0.649101	0.0291749
$496$	2.53737	0.113931
$497$	−48.9606	−2.19618
$498$	−0.0170335	−0.000763289 0
$499$	−35.4707	−1.58789	−0.793944	−	0.607991i	$-0.791976\pi$
$499$	−35.4707	−1.58789	−0.793944	+	0.607991i	$0.791976\pi$
$500$	−3.79059	−0.169520
$501$	8.58320	0.383469
$502$	−6.10149	−0.272323
$503$	−30.0880	−1.34156	−0.670778	−	0.741658i	$-0.734040\pi$
$503$	−30.0880	−1.34156	−0.670778	+	0.741658i	$0.734040\pi$
$504$	2.13052	0.0949007
$505$	−0.489608	−0.0217873
$506$	19.5044	0.867076
$507$	−17.0629	−0.757788
$508$	11.2408	0.498729
$509$	24.0909	1.06781	0.533905	−	0.845544i	$-0.320724\pi$
$509$	24.0909	1.06781	0.533905	+	0.845544i	$0.320724\pi$
$510$	−1.96422	−0.0869769
$511$	−49.2207	−2.17740
$512$	1.00000	0.0441942
$513$	33.4980	1.47897
$514$	−4.34710	−0.191742
$515$	−4.17309	−0.183888
$516$	6.64804	0.292664
$517$	−13.5157	−0.594421
$518$	0	0
$519$	16.6008	0.728694
$520$	0.525160	0.0230298
$521$	0.749547	0.0328383	0.0164191	−	0.999865i	$-0.494773\pi$
$521$	0.749547	0.0328383	0.0164191	+	0.999865i	$0.494773\pi$
$522$	2.09712	0.0917884
$523$	−2.03859	−0.0891413	−0.0445706	−	0.999006i	$-0.514192\pi$
$523$	−2.03859	−0.0891413	−0.0445706	+	0.999006i	$0.514192\pi$
$524$	−8.36959	−0.365627
$525$	24.2644	1.05899
$526$	4.05485	0.176800
$527$	−8.45485	−0.368299
$528$	−3.96002	−0.172338
$529$	33.9429	1.47578
$530$	−3.33629	−0.144919
$531$	−8.46389	−0.367301
$532$	19.5384	0.847098
$533$	11.2868	0.488883
$534$	1.46048	0.0632013
$535$	−1.83127	−0.0791727
$536$	11.2380	0.485408
$537$	−9.30273	−0.401442
$538$	8.79337	0.379109
$539$	−9.44612	−0.406873
$540$	−2.15319	−0.0926585
$541$	31.3434	1.34756	0.673778	−	0.738934i	$-0.264670\pi$
$541$	31.3434	1.34756	0.673778	+	0.738934i	$0.264670\pi$
$542$	−12.9122	−0.554627
$543$	33.0224	1.41713
$544$	−3.33213	−0.142864
$545$	−3.70805	−0.158835
$546$	−6.82591	−0.292122
$547$	−18.1663	−0.776737	−0.388368	−	0.921504i	$-0.626961\pi$
$547$	−18.1663	−0.776737	−0.388368	+	0.921504i	$0.626961\pi$
$548$	−3.98413	−0.170194
$549$	4.57718	0.195349
$550$	12.5410	0.534748
$551$	19.2321	0.819317
$552$	−11.5612	−0.492078
$553$	4.77640	0.203113
$554$	−7.77643	−0.330389
$555$	0	0
$556$	−5.11140	−0.216772
$557$	32.9061	1.39427	0.697137	−	0.716938i	$-0.254457\pi$
$557$	32.9061	1.39427	0.697137	+	0.716938i	$0.254457\pi$
$558$	−1.65615	−0.0701105
$559$	5.92267	0.250502
$560$	−1.25589	−0.0530711
$561$	13.1953	0.557105
$562$	0.232510	0.00980782
$563$	34.3008	1.44561	0.722804	−	0.691053i	$-0.242853\pi$
$563$	34.3008	1.44561	0.722804	+	0.691053i	$0.242853\pi$
$564$	8.01143	0.337342
$565$	−4.98446	−0.209698
$566$	−12.8330	−0.539411
$567$	21.5951	0.906910
$568$	14.9995	0.629367
$569$	21.2198	0.889579	0.444789	−	0.895635i	$-0.353278\pi$
$569$	21.2198	0.889579	0.444789	+	0.895635i	$0.353278\pi$
$570$	−3.52849	−0.147792
$571$	16.4467	0.688272	0.344136	−	0.938920i	$-0.388172\pi$
$571$	16.4467	0.688272	0.344136	+	0.938920i	$0.388172\pi$
$572$	−3.52794	−0.147510
$573$	10.1530	0.424150
$574$	−26.9917	−1.12661
$575$	36.6132	1.52687
$576$	−0.652704	−0.0271960
$577$	−36.3216	−1.51209	−0.756044	−	0.654521i	$-0.772870\pi$
$577$	−36.3216	−1.51209	−0.756044	+	0.654521i	$0.772870\pi$
$578$	−5.89693	−0.245280
$579$	−35.0150	−1.45517
$580$	−1.23620	−0.0513306
$581$	0.0362901	0.00150557
$582$	−22.7033	−0.941083
$583$	22.4127	0.928237
$584$	15.0792	0.623983
$585$	−0.342774	−0.0141720
$586$	−24.6443	−1.01805
$587$	37.5244	1.54880	0.774398	−	0.632699i	$-0.218053\pi$
$587$	37.5244	1.54880	0.774398	+	0.632699i	$0.218053\pi$
$588$	5.59918	0.230906
$589$	−15.1882	−0.625817
$590$	4.98927	0.205405
$591$	−22.6076	−0.929953
$592$	0	0
$593$	−10.0159	−0.411302	−0.205651	−	0.978625i	$-0.565931\pi$
$593$	−10.0159	−0.411302	−0.205651	+	0.978625i	$0.565931\pi$
$594$	14.4648	0.593496
$595$	4.18479	0.171560
$596$	−15.8700	−0.650060
$597$	−2.25949	−0.0924748
$598$	−10.2998	−0.421189
$599$	−33.6544	−1.37508	−0.687541	−	0.726145i	$-0.741310\pi$
$599$	−33.6544	−1.37508	−0.687541	+	0.726145i	$0.741310\pi$
$600$	−7.43364	−0.303477
$601$	−42.8067	−1.74612	−0.873061	−	0.487610i	$-0.837869\pi$
$601$	−42.8067	−1.74612	−0.873061	+	0.487610i	$0.837869\pi$
$602$	−14.1638	−0.577272
$603$	−7.33508	−0.298708
$604$	21.7680	0.885729
$605$	−1.66185	−0.0675637
$606$	−1.94961	−0.0791977
$607$	−5.37572	−0.218194	−0.109097	−	0.994031i	$-0.534796\pi$
$607$	−5.37572	−0.218194	−0.109097	+	0.994031i	$0.534796\pi$
$608$	−5.98578	−0.242756
$609$	16.0679	0.651105
$610$	−2.69815	−0.109245
$611$	7.13731	0.288744
$612$	2.17489	0.0879148
$613$	33.4187	1.34977	0.674884	−	0.737924i	$-0.264194\pi$
$613$	33.4187	1.34977	0.674884	+	0.737924i	$0.264194\pi$
$614$	−6.91132	−0.278918
$615$	4.87448	0.196558
$616$	8.43688	0.339931
$617$	5.05959	0.203691	0.101846	−	0.994800i	$-0.467525\pi$
$617$	5.05959	0.203691	0.101846	+	0.994800i	$0.467525\pi$
$618$	−16.6172	−0.668442
$619$	−35.7818	−1.43819	−0.719096	−	0.694911i	$-0.755444\pi$
$619$	−35.7818	−1.43819	−0.719096	+	0.694911i	$0.755444\pi$
$620$	0.976266	0.0392078
$621$	42.2297	1.69462
$622$	−1.65859	−0.0665035
$623$	−3.11158	−0.124663
$624$	2.09118	0.0837143
$625$	22.8014	0.912055
$626$	25.9509	1.03721
$627$	23.7038	0.946638
$628$	−9.75142	−0.389124
$629$	0	0
$630$	0.819725	0.0326586
$631$	6.62105	0.263580	0.131790	−	0.991278i	$-0.457928\pi$
$631$	6.62105	0.263580	0.131790	+	0.991278i	$0.457928\pi$
$632$	−1.46329	−0.0582067
$633$	−3.70693	−0.147337
$634$	11.3498	0.450759
$635$	4.32494	0.171630
$636$	−13.2851	−0.526788
$637$	4.98826	0.197642
$638$	8.30462	0.328783
$639$	−9.79025	−0.387296
$640$	0.384754	0.0152088
$641$	−35.5949	−1.40591	−0.702956	−	0.711233i	$-0.748137\pi$
$641$	−35.5949	−1.40591	−0.702956	+	0.711233i	$0.748137\pi$
$642$	−7.29210	−0.287796
$643$	5.01240	0.197670	0.0988350	−	0.995104i	$-0.468488\pi$
$643$	5.01240	0.197670	0.0988350	+	0.995104i	$0.468488\pi$
$644$	24.6314	0.970612
$645$	2.55786	0.100716
$646$	19.9454	0.784741
$647$	35.2707	1.38663	0.693317	−	0.720633i	$-0.256149\pi$
$647$	35.2707	1.38663	0.693317	+	0.720633i	$0.256149\pi$
$648$	−6.61587	−0.259896
$649$	−33.5171	−1.31566
$650$	−6.62255	−0.259758
$651$	−12.6893	−0.497332
$652$	−13.1647	−0.515571
$653$	2.70516	0.105861	0.0529305	−	0.998598i	$-0.483144\pi$
$653$	2.70516	0.105861	0.0529305	+	0.998598i	$0.483144\pi$
$654$	−14.7654	−0.577373
$655$	−3.22024	−0.125825
$656$	8.26915	0.322856
$657$	−9.84227	−0.383983
$658$	−17.0685	−0.665399
$659$	−27.8599	−1.08527	−0.542634	−	0.839969i	$-0.682573\pi$
$659$	−27.8599	−1.08527	−0.542634	+	0.839969i	$0.682573\pi$
$660$	−1.52363	−0.0593074
$661$	−10.6125	−0.412777	−0.206388	−	0.978470i	$-0.566171\pi$
$661$	−10.6125	−0.412777	−0.206388	+	0.978470i	$0.566171\pi$
$662$	12.8377	0.498951
$663$	−6.96809	−0.270618
$664$	−0.0111178	−0.000431455 0
$665$	7.51750	0.291516
$666$	0	0
$667$	24.2452	0.938779
$668$	5.60228	0.216759
$669$	−10.6438	−0.411514
$670$	4.32387	0.167046
$671$	18.1257	0.699735
$672$	−5.00095	−0.192916
$673$	−0.657395	−0.0253407	−0.0126704	−	0.999920i	$-0.504033\pi$
$673$	−0.657395	−0.0253407	−0.0126704	+	0.999920i	$0.504033\pi$
$674$	−5.71183	−0.220011
$675$	27.1529	1.04512
$676$	−11.1370	−0.428346
$677$	32.0071	1.23013	0.615067	−	0.788475i	$-0.289129\pi$
$677$	32.0071	1.23013	0.615067	+	0.788475i	$0.289129\pi$
$678$	−19.8481	−0.762261
$679$	48.3698	1.85626
$680$	−1.28205	−0.0491644
$681$	33.4746	1.28275
$682$	−6.55839	−0.251134
$683$	−3.99530	−0.152876	−0.0764379	−	0.997074i	$-0.524355\pi$
$683$	−3.99530	−0.152876	−0.0764379	+	0.997074i	$0.524355\pi$
$684$	3.90694	0.149386
$685$	−1.53291	−0.0585695
$686$	10.9198	0.416921
$687$	−6.51153	−0.248430
$688$	4.33920	0.165430
$689$	−11.8355	−0.450898
$690$	−4.44823	−0.169341
$691$	4.39613	0.167237	0.0836184	−	0.996498i	$-0.473352\pi$
$691$	4.39613	0.167237	0.0836184	+	0.996498i	$0.473352\pi$
$692$	10.8354	0.411900
$693$	−5.50678	−0.209185
$694$	32.3416	1.22767
$695$	−1.96663	−0.0745987
$696$	−4.92256	−0.186589
$697$	−27.5539	−1.04368
$698$	−24.9320	−0.943691
$699$	−26.5730	−1.00508
$700$	15.8375	0.598601
$701$	−14.3530	−0.542106	−0.271053	−	0.962564i	$-0.587372\pi$
$701$	−14.3530	−0.542106	−0.271053	+	0.962564i	$0.587372\pi$
$702$	−7.63847	−0.288295
$703$	0	0
$704$	−2.58472	−0.0974152
$705$	3.08244	0.116091
$706$	−8.64114	−0.325214
$707$	4.15368	0.156215
$708$	19.8672	0.746657
$709$	6.87475	0.258187	0.129093	−	0.991632i	$-0.458793\pi$
$709$	6.87475	0.258187	0.129093	+	0.991632i	$0.458793\pi$
$710$	5.77114	0.216587
$711$	0.955097	0.0358190
$712$	0.953262	0.0357250
$713$	−19.1471	−0.717066
$714$	16.6638	0.623627
$715$	−1.35739	−0.0507635
$716$	−6.07192	−0.226918
$717$	−28.1266	−1.05041
$718$	3.85848	0.143997
$719$	−17.0965	−0.637592	−0.318796	−	0.947823i	$-0.603279\pi$
$719$	−17.0965	−0.637592	−0.318796	+	0.947823i	$0.603279\pi$
$720$	−0.251131	−0.00935909
$721$	35.4032	1.31849
$722$	16.8296	0.626333
$723$	35.9522	1.33708
$724$	21.5538	0.801042
$725$	15.5892	0.578969
$726$	−6.61746	−0.245597
$727$	−42.6268	−1.58094	−0.790470	−	0.612501i	$-0.790163\pi$
$727$	−42.6268	−1.58094	−0.790470	+	0.612501i	$0.790163\pi$
$728$	−4.45530	−0.165124
$729$	30.0401	1.11260
$730$	5.80180	0.214734
$731$	−14.4588	−0.534777
$732$	−10.7440	−0.397109
$733$	−42.6192	−1.57418	−0.787088	−	0.616841i	$-0.788412\pi$
$733$	−42.6192	−1.57418	−0.787088	+	0.616841i	$0.788412\pi$
$734$	10.4563	0.385948
$735$	2.15431	0.0794630
$736$	−7.54605	−0.278151
$737$	−29.0470	−1.06996
$738$	−5.39731	−0.198678
$739$	−1.69175	−0.0622321	−0.0311161	−	0.999516i	$-0.509906\pi$
$739$	−1.69175	−0.0622321	−0.0311161	+	0.999516i	$0.509906\pi$
$740$	0	0
$741$	−12.5174	−0.459837
$742$	28.3041	1.03908
$743$	12.8065	0.469823	0.234912	−	0.972017i	$-0.424520\pi$
$743$	12.8065	0.469823	0.234912	+	0.972017i	$0.424520\pi$
$744$	3.88748	0.142522
$745$	−6.10605	−0.223708
$746$	−9.86566	−0.361208
$747$	0.00725664	0.000265507 0
$748$	8.61260	0.314908
$749$	15.5359	0.567671
$750$	−5.80752	−0.212061
$751$	48.4720	1.76877	0.884384	−	0.466759i	$-0.154579\pi$
$751$	48.4720	1.76877	0.884384	+	0.466759i	$0.154579\pi$
$752$	5.22909	0.190685
$753$	−9.34802	−0.340661
$754$	−4.38546	−0.159709
$755$	8.37535	0.304810
$756$	18.2670	0.664364
$757$	32.1365	1.16802	0.584010	−	0.811746i	$-0.301483\pi$
$757$	32.1365	1.16802	0.584010	+	0.811746i	$0.301483\pi$
$758$	2.48121	0.0901215
$759$	29.8825	1.08467
$760$	−2.30306	−0.0835406
$761$	−10.3730	−0.376022	−0.188011	−	0.982167i	$-0.560204\pi$
$761$	−10.3730	−0.376022	−0.188011	+	0.982167i	$0.560204\pi$
$762$	17.2219	0.623883
$763$	31.4579	1.13885
$764$	6.62693	0.239754
$765$	0.836799	0.0302545
$766$	−25.5639	−0.923661
$767$	17.6995	0.639093
$768$	1.53209	0.0552845
$769$	−33.9273	−1.22345	−0.611725	−	0.791070i	$-0.709524\pi$
$769$	−33.9273	−1.22345	−0.611725	+	0.791070i	$0.709524\pi$
$770$	3.24613	0.116982
$771$	−6.66015	−0.239859
$772$	−22.8544	−0.822548
$773$	−28.9843	−1.04249	−0.521247	−	0.853406i	$-0.674533\pi$
$773$	−28.9843	−1.04249	−0.521247	+	0.853406i	$0.674533\pi$
$774$	−2.83221	−0.101802
$775$	−12.3112	−0.442233
$776$	−14.8185	−0.531954
$777$	0	0
$778$	−6.37509	−0.228558
$779$	−49.4973	−1.77343
$780$	0.804592	0.0288090
$781$	−38.7696	−1.38728
$782$	25.1444	0.899162
$783$	17.9806	0.642576
$784$	3.65461	0.130522
$785$	−3.75190	−0.133911
$786$	−12.8229	−0.457379
$787$	−16.7100	−0.595647	−0.297823	−	0.954621i	$-0.596261\pi$
$787$	−16.7100	−0.595647	−0.297823	+	0.954621i	$0.596261\pi$
$788$	−14.7561	−0.525663
$789$	6.21239	0.221167
$790$	−0.563009	−0.0200310
$791$	42.2867	1.50354
$792$	1.68705	0.0599468
$793$	−9.57171	−0.339901
$794$	37.4977	1.33075
$795$	−5.11150	−0.181286
$796$	−1.47478	−0.0522721
$797$	−5.21454	−0.184709	−0.0923543	−	0.995726i	$-0.529439\pi$
$797$	−5.21454	−0.184709	−0.0923543	+	0.995726i	$0.529439\pi$
$798$	29.9346	1.05967
$799$	−17.4240	−0.616417
$800$	−4.85196	−0.171543
$801$	−0.622198	−0.0219843
$802$	−35.1464	−1.24106
$803$	−38.9755	−1.37542
$804$	17.2176	0.607219
$805$	9.47703	0.334021
$806$	3.46332	0.121990
$807$	13.4722	0.474245
$808$	−1.27252	−0.0447671
$809$	50.5612	1.77764	0.888818	−	0.458260i	$-0.151527\pi$
$809$	50.5612	1.77764	0.888818	+	0.458260i	$0.151527\pi$
$810$	−2.54548	−0.0894392
$811$	36.0684	1.26653	0.633267	−	0.773934i	$-0.281714\pi$
$811$	36.0684	1.26653	0.633267	+	0.773934i	$0.281714\pi$
$812$	10.4876	0.368042
$813$	−19.7826	−0.693808
$814$	0	0
$815$	−5.06519	−0.177426
$816$	−5.10511	−0.178715
$817$	−25.9735	−0.908698
$818$	0.450741	0.0157598
$819$	2.90799	0.101613
$820$	3.18159	0.111106
$821$	51.1334	1.78457	0.892285	−	0.451473i	$-0.149101\pi$
$821$	51.1334	1.78457	0.892285	+	0.451473i	$0.149101\pi$
$822$	−6.10404	−0.212903
$823$	8.08213	0.281725	0.140863	−	0.990029i	$-0.455012\pi$
$823$	8.08213	0.281725	0.140863	+	0.990029i	$0.455012\pi$
$824$	−10.8461	−0.377842
$825$	19.2139	0.668940
$826$	−42.3275	−1.47276
$827$	−25.8525	−0.898981	−0.449490	−	0.893285i	$-0.648394\pi$
$827$	−25.8525	−0.898981	−0.449490	+	0.893285i	$0.648394\pi$
$828$	4.92533	0.171167
$829$	−8.19775	−0.284720	−0.142360	−	0.989815i	$-0.545469\pi$
$829$	−8.19775	−0.284720	−0.142360	+	0.989815i	$0.545469\pi$
$830$	−0.00427763	−0.000148479 0
$831$	−11.9142	−0.413298
$832$	1.36492	0.0473202
$833$	−12.1776	−0.421929
$834$	−7.83112	−0.271170
$835$	2.15550	0.0745943
$836$	15.4716	0.535095
$837$	−14.1998	−0.490817
$838$	−15.3113	−0.528920
$839$	52.8482	1.82452	0.912261	−	0.409610i	$-0.134335\pi$
$839$	52.8482	1.82452	0.912261	+	0.409610i	$0.134335\pi$
$840$	−1.92414	−0.0663891
$841$	−18.6768	−0.644028
$842$	−22.3965	−0.771833
$843$	0.356225	0.0122691
$844$	−2.41952	−0.0832835
$845$	−4.28501	−0.147409
$846$	−3.41305	−0.117343
$847$	14.0986	0.484434
$848$	−8.67122	−0.297771
$849$	−19.6613	−0.674774
$850$	16.1674	0.554536
$851$	0	0
$852$	22.9806	0.787303
$853$	−32.9906	−1.12958	−0.564788	−	0.825236i	$-0.691042\pi$
$853$	−32.9906	−1.12958	−0.564788	+	0.825236i	$0.691042\pi$
$854$	22.8902	0.783288
$855$	1.50321	0.0514088
$856$	−4.75958	−0.162679
$857$	38.4078	1.31199	0.655993	−	0.754767i	$-0.272250\pi$
$857$	38.4078	1.31199	0.655993	+	0.754767i	$0.272250\pi$
$858$	−5.40511	−0.184528
$859$	−20.7158	−0.706814	−0.353407	−	0.935470i	$-0.614977\pi$
$859$	−20.7158	−0.706814	−0.353407	+	0.935470i	$0.614977\pi$
$860$	1.66953	0.0569304
$861$	−41.3536	−1.40933
$862$	−0.102080	−0.00347685
$863$	35.3661	1.20388	0.601938	−	0.798543i	$-0.294396\pi$
$863$	35.3661	1.20388	0.601938	+	0.798543i	$0.294396\pi$
$864$	−5.59627	−0.190389
$865$	4.16897	0.141749
$866$	7.92714	0.269375
$867$	−9.03462	−0.306832
$868$	−8.28234	−0.281121
$869$	3.78220	0.128302
$870$	−1.89398	−0.0642118
$871$	15.3390	0.519742
$872$	−9.63744	−0.326365
$873$	9.67211	0.327351
$874$	45.1690	1.52786
$875$	12.3730	0.418284
$876$	23.1027	0.780568
$877$	26.3702	0.890459	0.445230	−	0.895416i	$-0.353122\pi$
$877$	26.3702	0.890459	0.445230	+	0.895416i	$0.353122\pi$
$878$	7.57063	0.255496
$879$	−37.7573	−1.27352
$880$	−0.994481	−0.0335240
$881$	−33.7205	−1.13607	−0.568037	−	0.823003i	$-0.692297\pi$
$881$	−33.7205	−1.13607	−0.568037	+	0.823003i	$0.692297\pi$
$882$	−2.38538	−0.0803198
$883$	−57.8576	−1.94706	−0.973531	−	0.228555i	$-0.926600\pi$
$883$	−57.8576	−1.94706	−0.973531	+	0.228555i	$0.926600\pi$
$884$	−4.54809	−0.152969
$885$	7.64401	0.256951
$886$	−15.9856	−0.537047
$887$	44.4679	1.49309	0.746544	−	0.665336i	$-0.231712\pi$
$887$	44.4679	1.49309	0.746544	+	0.665336i	$0.231712\pi$
$888$	0	0
$889$	−36.6915	−1.23059
$890$	0.366772	0.0122942
$891$	17.1001	0.572876
$892$	−6.94726	−0.232611
$893$	−31.3002	−1.04742
$894$	−24.3142	−0.813190
$895$	−2.33620	−0.0780905
$896$	−3.26414	−0.109047
$897$	−15.7802	−0.526884
$898$	28.6753	0.956908
$899$	−8.15251	−0.271901
$900$	3.16689	0.105563
$901$	28.8936	0.962586
$902$	−21.3734	−0.711657
$903$	−21.7001	−0.722135
$904$	−12.9549	−0.430874
$905$	8.29294	0.275667
$906$	33.3506	1.10800
$907$	−13.0951	−0.434815	−0.217407	−	0.976081i	$-0.569760\pi$
$907$	−13.0951	−0.434815	−0.217407	+	0.976081i	$0.569760\pi$
$908$	21.8490	0.725084
$909$	0.830579	0.0275486
$910$	−1.71420	−0.0568250
$911$	38.4466	1.27379	0.636896	−	0.770950i	$-0.280218\pi$
$911$	38.4466	1.27379	0.636896	+	0.770950i	$0.280218\pi$
$912$	−9.17075	−0.303674
$913$	0.0287364	0.000951036 0
$914$	−0.105116	−0.00347694
$915$	−4.13380	−0.136659
$916$	−4.25010	−0.140427
$917$	27.3195	0.902169
$918$	18.6475	0.615458
$919$	14.8613	0.490229	0.245115	−	0.969494i	$-0.421174\pi$
$919$	14.8613	0.490229	0.245115	+	0.969494i	$0.421174\pi$
$920$	−2.90338	−0.0957215
$921$	−10.5888	−0.348911
$922$	23.9701	0.789413
$923$	20.4732	0.673884
$924$	12.9260	0.425236
$925$	0	0
$926$	−20.7514	−0.681933
$927$	7.07930	0.232515
$928$	−3.21297	−0.105471
$929$	−7.26526	−0.238366	−0.119183	−	0.992872i	$-0.538027\pi$
$929$	−7.26526	−0.238366	−0.119183	+	0.992872i	$0.538027\pi$
$930$	1.49573	0.0490468
$931$	−21.8757	−0.716947
$932$	−17.3443	−0.568131
$933$	−2.54111	−0.0831922
$934$	−17.4928	−0.572383
$935$	3.31374	0.108371
$936$	−0.890890	−0.0291196
$937$	−26.3830	−0.861897	−0.430948	−	0.902377i	$-0.641821\pi$
$937$	−26.3830	−0.861897	−0.430948	+	0.902377i	$0.641821\pi$
$938$	−36.6824	−1.19772
$939$	39.7591	1.29749
$940$	2.01192	0.0656215
$941$	36.1584	1.17873	0.589366	−	0.807866i	$-0.299378\pi$
$941$	36.1584	1.17873	0.589366	+	0.807866i	$0.299378\pi$
$942$	−14.9400	−0.486773
$943$	−62.3994	−2.03201
$944$	12.9674	0.422054
$945$	7.02831	0.228631
$946$	−11.2156	−0.364651
$947$	−47.1144	−1.53101	−0.765506	−	0.643428i	$-0.777511\pi$
$947$	−47.1144	−1.53101	−0.765506	+	0.643428i	$0.777511\pi$
$948$	−2.24190	−0.0728134
$949$	20.5820	0.668119
$950$	29.0428	0.942273
$951$	17.3889	0.563875
$952$	10.8765	0.352510
$953$	−9.35174	−0.302933	−0.151466	−	0.988462i	$-0.548399\pi$
$953$	−9.35174	−0.302933	−0.151466	+	0.988462i	$0.548399\pi$
$954$	5.65974	0.183241
$955$	2.54974	0.0825077
$956$	−18.3584	−0.593752
$957$	12.7234	0.411290
$958$	6.88046	0.222298
$959$	13.0048	0.419945
$960$	0.589478	0.0190253
$961$	−24.5617	−0.792314
$962$	0	0
$963$	3.10660	0.100109
$964$	23.4661	0.755792
$965$	−8.79333	−0.283067
$966$	37.7374	1.21418
$967$	−49.9460	−1.60615	−0.803077	−	0.595875i	$-0.796805\pi$
$967$	−49.9460	−1.60615	−0.803077	+	0.595875i	$0.796805\pi$
$968$	−4.31924	−0.138826
$969$	30.5581	0.981668
$970$	−5.70150	−0.183064
$971$	37.6187	1.20724	0.603621	−	0.797271i	$-0.293724\pi$
$971$	37.6187	1.20724	0.603621	+	0.797271i	$0.293724\pi$
$972$	6.65270	0.213386
$973$	16.6843	0.534875
$974$	1.70810	0.0547311
$975$	−10.1463	−0.324943
$976$	−7.01264	−0.224469
$977$	−28.1356	−0.900136	−0.450068	−	0.892994i	$-0.648600\pi$
$977$	−28.1356	−0.900136	−0.450068	+	0.892994i	$0.648600\pi$
$978$	−20.1696	−0.644951
$979$	−2.46391	−0.0787470
$980$	1.40613	0.0449171
$981$	6.29039	0.200837
$982$	10.6231	0.338995
$983$	32.9418	1.05068	0.525340	−	0.850893i	$-0.323938\pi$
$983$	32.9418	1.05068	0.525340	+	0.850893i	$0.323938\pi$
$984$	12.6691	0.403875
$985$	−5.67746	−0.180899
$986$	10.7060	0.340949
$987$	−26.1504	−0.832378
$988$	−8.17013	−0.259926
$989$	−32.7438	−1.04119
$990$	0.649101	0.0206298
$991$	−38.9993	−1.23885	−0.619426	−	0.785055i	$-0.712635\pi$
$991$	−38.9993	−1.23885	−0.619426	+	0.785055i	$0.712635\pi$
$992$	2.53737	0.0805617
$993$	19.6685	0.624160
$994$	−48.9606	−1.55294
$995$	−0.567428	−0.0179887
$996$	−0.0170335	−0.000539727 0
$997$	7.98046	0.252744	0.126372	−	0.991983i	$-0.459667\pi$
$997$	7.98046	0.252744	0.126372	+	0.991983i	$0.459667\pi$
$998$	−35.4707	−1.12281
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2738.2.a.s.1.6		6
37.2	odd	36		74.2.h.a.41.2	✓	12
37.19	odd	36		74.2.h.a.65.2	yes	12
37.36	even	2		2738.2.a.r.1.5		6
111.2	even	36		666.2.bj.c.559.1		12
111.56	even	36		666.2.bj.c.361.1		12
148.19	even	36		592.2.bq.b.65.2		12
148.39	even	36		592.2.bq.b.337.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.41.2	✓	12	37.2	odd	36
74.2.h.a.65.2	yes	12	37.19	odd	36
592.2.bq.b.65.2		12	148.19	even	36
592.2.bq.b.337.2		12	148.39	even	36
666.2.bj.c.361.1		12	111.56	even	36
666.2.bj.c.559.1		12	111.2	even	36
2738.2.a.r.1.5		6	37.36	even	2
2738.2.a.s.1.6		6	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:	\( N \)	\(=\)	\( 2738 = 2 \cdot 37^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2738.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +0.384754 q^{5} +1.53209 q^{6} -3.26414 q^{7} +1.00000 q^{8} -0.652704 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.53209 q^{3} +1.00000 q^{4} +0.384754 q^{5} +1.53209 q^{6} -3.26414 q^{7} +1.00000 q^{8} -0.652704 q^{9} +0.384754 q^{10} -2.58472 q^{11} +1.53209 q^{12} +1.36492 q^{13} -3.26414 q^{14} +0.589478 q^{15} +1.00000 q^{16} -3.33213 q^{17} -0.652704 q^{18} -5.98578 q^{19} +0.384754 q^{20} -5.00095 q^{21} -2.58472 q^{22} -7.54605 q^{23} +1.53209 q^{24} -4.85196 q^{25} +1.36492 q^{26} -5.59627 q^{27} -3.26414 q^{28} -3.21297 q^{29} +0.589478 q^{30} +2.53737 q^{31} +1.00000 q^{32} -3.96002 q^{33} -3.33213 q^{34} -1.25589 q^{35} -0.652704 q^{36} -5.98578 q^{38} +2.09118 q^{39} +0.384754 q^{40} +8.26915 q^{41} -5.00095 q^{42} +4.33920 q^{43} -2.58472 q^{44} -0.251131 q^{45} -7.54605 q^{46} +5.22909 q^{47} +1.53209 q^{48} +3.65461 q^{49} -4.85196 q^{50} -5.10511 q^{51} +1.36492 q^{52} -8.67122 q^{53} -5.59627 q^{54} -0.994481 q^{55} -3.26414 q^{56} -9.17075 q^{57} -3.21297 q^{58} +12.9674 q^{59} +0.589478 q^{60} -7.01264 q^{61} +2.53737 q^{62} +2.13052 q^{63} +1.00000 q^{64} +0.525160 q^{65} -3.96002 q^{66} +11.2380 q^{67} -3.33213 q^{68} -11.5612 q^{69} -1.25589 q^{70} +14.9995 q^{71} -0.652704 q^{72} +15.0792 q^{73} -7.43364 q^{75} -5.98578 q^{76} +8.43688 q^{77} +2.09118 q^{78} -1.46329 q^{79} +0.384754 q^{80} -6.61587 q^{81} +8.26915 q^{82} -0.0111178 q^{83} -5.00095 q^{84} -1.28205 q^{85} +4.33920 q^{86} -4.92256 q^{87} -2.58472 q^{88} +0.953262 q^{89} -0.251131 q^{90} -4.45530 q^{91} -7.54605 q^{92} +3.88748 q^{93} +5.22909 q^{94} -2.30306 q^{95} +1.53209 q^{96} -14.8185 q^{97} +3.65461 q^{98} +1.68705 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9	\( 6 q + 6 q^{2} + 6 q^{4} - 6 q^{5} + 6 q^{8} - 6 q^{9} - 6 q^{10} - 6 q^{11} - 12 q^{13} + 6 q^{15} + 6 q^{16} - 12 q^{17} - 6 q^{18} - 12 q^{19} - 6 q^{20} - 12 q^{21} - 6 q^{22} + 6 q^{23} + 6 q^{25} - 12 q^{26} - 6 q^{27} + 6 q^{29} + 6 q^{30} - 18 q^{31} + 6 q^{32} + 6 q^{33} - 12 q^{34} - 24 q^{35} - 6 q^{36} - 12 q^{38} - 6 q^{39} - 6 q^{40} - 12 q^{41} - 12 q^{42} - 6 q^{44} - 6 q^{45} + 6 q^{46} - 6 q^{47} - 12 q^{49} + 6 q^{50} - 24 q^{51} - 12 q^{52} - 24 q^{53} - 6 q^{54} - 36 q^{55} - 24 q^{57} + 6 q^{58} - 12 q^{59} + 6 q^{60} - 12 q^{61} - 18 q^{62} + 6 q^{63} + 6 q^{64} + 18 q^{65} + 6 q^{66} + 18 q^{67} - 12 q^{68} - 24 q^{69} - 24 q^{70} + 24 q^{71} - 6 q^{72} - 18 q^{75} - 12 q^{76} + 30 q^{77} - 6 q^{78} - 12 q^{79} - 6 q^{80} - 18 q^{81} - 12 q^{82} - 6 q^{83} - 12 q^{84} + 18 q^{85} - 6 q^{87} - 6 q^{88} - 6 q^{90} - 12 q^{91} + 6 q^{92} + 36 q^{93} - 6 q^{94} + 18 q^{95} + 12 q^{97} - 12 q^{98} + 12 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 6 * q^4 - 6 * q^5 + 6 * q^8 - 6 * q^9 - 6 * q^10 - 6 * q^11 - 12 * q^13 + 6 * q^15 + 6 * q^16 - 12 * q^17 - 6 * q^18 - 12 * q^19 - 6 * q^20 - 12 * q^21 - 6 * q^22 + 6 * q^23 + 6 * q^25 - 12 * q^26 - 6 * q^27 + 6 * q^29 + 6 * q^30 - 18 * q^31 + 6 * q^32 + 6 * q^33 - 12 * q^34 - 24 * q^35 - 6 * q^36 - 12 * q^38 - 6 * q^39 - 6 * q^40 - 12 * q^41 - 12 * q^42 - 6 * q^44 - 6 * q^45 + 6 * q^46 - 6 * q^47 - 12 * q^49 + 6 * q^50 - 24 * q^51 - 12 * q^52 - 24 * q^53 - 6 * q^54 - 36 * q^55 - 24 * q^57 + 6 * q^58 - 12 * q^59 + 6 * q^60 - 12 * q^61 - 18 * q^62 + 6 * q^63 + 6 * q^64 + 18 * q^65 + 6 * q^66 + 18 * q^67 - 12 * q^68 - 24 * q^69 - 24 * q^70 + 24 * q^71 - 6 * q^72 - 18 * q^75 - 12 * q^76 + 30 * q^77 - 6 * q^78 - 12 * q^79 - 6 * q^80 - 18 * q^81 - 12 * q^82 - 6 * q^83 - 12 * q^84 + 18 * q^85 - 6 * q^87 - 6 * q^88 - 6 * q^90 - 12 * q^91 + 6 * q^92 + 36 * q^93 - 6 * q^94 + 18 * q^95 + 12 * q^97 - 12 * q^98 + 12 * q^99

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