LMFDB - Embedded newform 4334.2.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.47732$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.47732 q^{3} +1.00000 q^{4} +1.17448 q^{5} +2.47732 q^{6} +0.539926 q^{7} -1.00000 q^{8} +3.13710 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.47732 q^{3} +1.00000 q^{4} +1.17448 q^{5} +2.47732 q^{6} +0.539926 q^{7} -1.00000 q^{8} +3.13710 q^{9} -1.17448 q^{10} +1.00000 q^{11} -2.47732 q^{12} +3.77319 q^{13} -0.539926 q^{14} -2.90957 q^{15} +1.00000 q^{16} -5.84469 q^{17} -3.13710 q^{18} -0.884118 q^{19} +1.17448 q^{20} -1.33757 q^{21} -1.00000 q^{22} +5.41015 q^{23} +2.47732 q^{24} -3.62059 q^{25} -3.77319 q^{26} -0.339631 q^{27} +0.539926 q^{28} -1.87829 q^{29} +2.90957 q^{30} +1.14143 q^{31} -1.00000 q^{32} -2.47732 q^{33} +5.84469 q^{34} +0.634133 q^{35} +3.13710 q^{36} +2.52588 q^{37} +0.884118 q^{38} -9.34739 q^{39} -1.17448 q^{40} -1.15235 q^{41} +1.33757 q^{42} -10.8504 q^{43} +1.00000 q^{44} +3.68447 q^{45} -5.41015 q^{46} +0.607182 q^{47} -2.47732 q^{48} -6.70848 q^{49} +3.62059 q^{50} +14.4791 q^{51} +3.77319 q^{52} +2.28169 q^{53} +0.339631 q^{54} +1.17448 q^{55} -0.539926 q^{56} +2.19024 q^{57} +1.87829 q^{58} -7.45106 q^{59} -2.90957 q^{60} -8.34390 q^{61} -1.14143 q^{62} +1.69380 q^{63} +1.00000 q^{64} +4.43155 q^{65} +2.47732 q^{66} -14.3987 q^{67} -5.84469 q^{68} -13.4026 q^{69} -0.634133 q^{70} -6.18878 q^{71} -3.13710 q^{72} +12.6792 q^{73} -2.52588 q^{74} +8.96935 q^{75} -0.884118 q^{76} +0.539926 q^{77} +9.34739 q^{78} +15.3800 q^{79} +1.17448 q^{80} -8.56992 q^{81} +1.15235 q^{82} +13.5215 q^{83} -1.33757 q^{84} -6.86448 q^{85} +10.8504 q^{86} +4.65311 q^{87} -1.00000 q^{88} -4.22512 q^{89} -3.68447 q^{90} +2.03724 q^{91} +5.41015 q^{92} -2.82769 q^{93} -0.607182 q^{94} -1.03838 q^{95} +2.47732 q^{96} -14.4480 q^{97} +6.70848 q^{98} +3.13710 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * 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
$3$	−2.47732	−1.43028	−0.715140	−	0.698982i	$-0.753637\pi$
$3$	−2.47732	−1.43028	−0.715140	+	0.698982i	$0.753637\pi$
$4$	1.00000	0.500000
$5$	1.17448	0.525245	0.262622	−	0.964899i	$-0.415413\pi$
$5$	1.17448	0.525245	0.262622	+	0.964899i	$0.415413\pi$
$6$	2.47732	1.01136
$7$	0.539926	0.204073	0.102036	−	0.994781i	$-0.467464\pi$
$7$	0.539926	0.204073	0.102036	+	0.994781i	$0.467464\pi$
$8$	−1.00000	−0.353553
$9$	3.13710	1.04570
$10$	−1.17448	−0.371404
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−2.47732	−0.715140
$13$	3.77319	1.04650	0.523248	−	0.852181i	$-0.324720\pi$
$13$	3.77319	1.04650	0.523248	+	0.852181i	$0.324720\pi$
$14$	−0.539926	−0.144301
$15$	−2.90957	−0.751247
$16$	1.00000	0.250000
$17$	−5.84469	−1.41754	−0.708772	−	0.705437i	$-0.750751\pi$
$17$	−5.84469	−1.41754	−0.708772	+	0.705437i	$0.750751\pi$
$18$	−3.13710	−0.739421
$19$	−0.884118	−0.202831	−0.101415	−	0.994844i	$-0.532337\pi$
$19$	−0.884118	−0.202831	−0.101415	+	0.994844i	$0.532337\pi$
$20$	1.17448	0.262622
$21$	−1.33757	−0.291881
$22$	−1.00000	−0.213201
$23$	5.41015	1.12809	0.564047	−	0.825743i	$-0.309244\pi$
$23$	5.41015	1.12809	0.564047	+	0.825743i	$0.309244\pi$
$24$	2.47732	0.505680
$25$	−3.62059	−0.724118
$26$	−3.77319	−0.739984
$27$	−0.339631	−0.0653620
$28$	0.539926	0.102036
$29$	−1.87829	−0.348789	−0.174395	−	0.984676i	$-0.555797\pi$
$29$	−1.87829	−0.348789	−0.174395	+	0.984676i	$0.555797\pi$
$30$	2.90957	0.531212
$31$	1.14143	0.205008	0.102504	−	0.994733i	$-0.467315\pi$
$31$	1.14143	0.205008	0.102504	+	0.994733i	$0.467315\pi$
$32$	−1.00000	−0.176777
$33$	−2.47732	−0.431245
$34$	5.84469	1.00236
$35$	0.634133	0.107188
$36$	3.13710	0.522849
$37$	2.52588	0.415252	0.207626	−	0.978208i	$-0.433426\pi$
$37$	2.52588	0.415252	0.207626	+	0.978208i	$0.433426\pi$
$38$	0.884118	0.143423
$39$	−9.34739	−1.49678
$40$	−1.17448	−0.185702
$41$	−1.15235	−0.179967	−0.0899836	−	0.995943i	$-0.528681\pi$
$41$	−1.15235	−0.179967	−0.0899836	+	0.995943i	$0.528681\pi$
$42$	1.33757	0.206391
$43$	−10.8504	−1.65467	−0.827337	−	0.561707i	$-0.810145\pi$
$43$	−10.8504	−1.65467	−0.827337	+	0.561707i	$0.810145\pi$
$44$	1.00000	0.150756
$45$	3.68447	0.549248
$46$	−5.41015	−0.797683
$47$	0.607182	0.0885667	0.0442833	−	0.999019i	$-0.485900\pi$
$47$	0.607182	0.0885667	0.0442833	+	0.999019i	$0.485900\pi$
$48$	−2.47732	−0.357570
$49$	−6.70848	−0.958354
$50$	3.62059	0.512029
$51$	14.4791	2.02748
$52$	3.77319	0.523248
$53$	2.28169	0.313414	0.156707	−	0.987645i	$-0.449912\pi$
$53$	2.28169	0.313414	0.156707	+	0.987645i	$0.449912\pi$
$54$	0.339631	0.0462179
$55$	1.17448	0.158367
$56$	−0.539926	−0.0721506
$57$	2.19024	0.290104
$58$	1.87829	0.246631
$59$	−7.45106	−0.970045	−0.485023	−	0.874502i	$-0.661189\pi$
$59$	−7.45106	−0.970045	−0.485023	+	0.874502i	$0.661189\pi$
$60$	−2.90957	−0.375623
$61$	−8.34390	−1.06833	−0.534164	−	0.845381i	$-0.679373\pi$
$61$	−8.34390	−1.06833	−0.534164	+	0.845381i	$0.679373\pi$
$62$	−1.14143	−0.144962
$63$	1.69380	0.213399
$64$	1.00000	0.125000
$65$	4.43155	0.549666
$66$	2.47732	0.304937
$67$	−14.3987	−1.75908	−0.879538	−	0.475829i	$-0.842148\pi$
$67$	−14.3987	−1.75908	−0.879538	+	0.475829i	$0.842148\pi$
$68$	−5.84469	−0.708772
$69$	−13.4026	−1.61349
$70$	−0.634133	−0.0757934
$71$	−6.18878	−0.734474	−0.367237	−	0.930127i	$-0.619696\pi$
$71$	−6.18878	−0.734474	−0.367237	+	0.930127i	$0.619696\pi$
$72$	−3.13710	−0.369710
$73$	12.6792	1.48399	0.741996	−	0.670405i	$-0.233879\pi$
$73$	12.6792	1.48399	0.741996	+	0.670405i	$0.233879\pi$
$74$	−2.52588	−0.293628
$75$	8.96935	1.03569
$76$	−0.884118	−0.101415
$77$	0.539926	0.0615302
$78$	9.34739	1.05838
$79$	15.3800	1.73038	0.865190	−	0.501444i	$-0.167198\pi$
$79$	15.3800	1.73038	0.865190	+	0.501444i	$0.167198\pi$
$80$	1.17448	0.131311
$81$	−8.56992	−0.952213
$82$	1.15235	0.127256
$83$	13.5215	1.48417	0.742087	−	0.670304i	$-0.233836\pi$
$83$	13.5215	1.48417	0.742087	+	0.670304i	$0.233836\pi$
$84$	−1.33757	−0.145940
$85$	−6.86448	−0.744558
$86$	10.8504	1.17003
$87$	4.65311	0.498866
$88$	−1.00000	−0.106600
$89$	−4.22512	−0.447861	−0.223931	−	0.974605i	$-0.571889\pi$
$89$	−4.22512	−0.447861	−0.223931	+	0.974605i	$0.571889\pi$
$90$	−3.68447	−0.388377
$91$	2.03724	0.213561
$92$	5.41015	0.564047
$93$	−2.82769	−0.293218
$94$	−0.607182	−0.0626261
$95$	−1.03838	−0.106536
$96$	2.47732	0.252840
$97$	−14.4480	−1.46698	−0.733489	−	0.679702i	$-0.762109\pi$
$97$	−14.4480	−1.46698	−0.733489	+	0.679702i	$0.762109\pi$
$98$	6.70848	0.677659
$99$	3.13710	0.315290
$100$	−3.62059	−0.362059
$101$	17.9364	1.78474	0.892371	−	0.451302i	$-0.149040\pi$
$101$	17.9364	1.78474	0.892371	+	0.451302i	$0.149040\pi$
$102$	−14.4791	−1.43365
$103$	10.7356	1.05781	0.528905	−	0.848681i	$-0.322603\pi$
$103$	10.7356	1.05781	0.528905	+	0.848681i	$0.322603\pi$
$104$	−3.77319	−0.369992
$105$	−1.57095	−0.153309
$106$	−2.28169	−0.221617
$107$	12.3551	1.19441	0.597205	−	0.802089i	$-0.296278\pi$
$107$	12.3551	1.19441	0.597205	+	0.802089i	$0.296278\pi$
$108$	−0.339631	−0.0326810
$109$	−16.4018	−1.57101	−0.785505	−	0.618855i	$-0.787597\pi$
$109$	−16.4018	−1.57101	−0.785505	+	0.618855i	$0.787597\pi$
$110$	−1.17448	−0.111983
$111$	−6.25741	−0.593927
$112$	0.539926	0.0510182
$113$	7.82432	0.736050	0.368025	−	0.929816i	$-0.380034\pi$
$113$	7.82432	0.736050	0.368025	+	0.929816i	$0.380034\pi$
$114$	−2.19024	−0.205135
$115$	6.35412	0.592525
$116$	−1.87829	−0.174395
$117$	11.8369	1.09432
$118$	7.45106	0.685926
$119$	−3.15570	−0.289282
$120$	2.90957	0.265606
$121$	1.00000	0.0909091
$122$	8.34390	0.755421
$123$	2.85474	0.257403
$124$	1.14143	0.102504
$125$	−10.1247	−0.905584
$126$	−1.69380	−0.150896
$127$	−6.81011	−0.604300	−0.302150	−	0.953260i	$-0.597704\pi$
$127$	−6.81011	−0.604300	−0.302150	+	0.953260i	$0.597704\pi$
$128$	−1.00000	−0.0883883
$129$	26.8799	2.36664
$130$	−4.43155	−0.388673
$131$	10.8126	0.944700	0.472350	−	0.881411i	$-0.343406\pi$
$131$	10.8126	0.944700	0.472350	+	0.881411i	$0.343406\pi$
$132$	−2.47732	−0.215623
$133$	−0.477358	−0.0413922
$134$	14.3987	1.24385
$135$	−0.398891	−0.0343310
$136$	5.84469	0.501178
$137$	−8.34831	−0.713244	−0.356622	−	0.934249i	$-0.616072\pi$
$137$	−8.34831	−0.713244	−0.356622	+	0.934249i	$0.616072\pi$
$138$	13.4026	1.14091
$139$	0.295437	0.0250586	0.0125293	−	0.999922i	$-0.496012\pi$
$139$	0.295437	0.0250586	0.0125293	+	0.999922i	$0.496012\pi$
$140$	0.634133	0.0535940
$141$	−1.50418	−0.126675
$142$	6.18878	0.519351
$143$	3.77319	0.315530
$144$	3.13710	0.261425
$145$	−2.20602	−0.183200
$146$	−12.6792	−1.04934
$147$	16.6190	1.37071
$148$	2.52588	0.207626
$149$	−3.70851	−0.303813	−0.151907	−	0.988395i	$-0.548541\pi$
$149$	−3.70851	−0.303813	−0.151907	+	0.988395i	$0.548541\pi$
$150$	−8.96935	−0.732344
$151$	5.75292	0.468166	0.234083	−	0.972217i	$-0.424791\pi$
$151$	5.75292	0.468166	0.234083	+	0.972217i	$0.424791\pi$
$152$	0.884118	0.0717115
$153$	−18.3353	−1.48232
$154$	−0.539926	−0.0435084
$155$	1.34059	0.107679
$156$	−9.34739	−0.748390
$157$	17.2199	1.37430	0.687151	−	0.726515i	$-0.258861\pi$
$157$	17.2199	1.37430	0.687151	+	0.726515i	$0.258861\pi$
$158$	−15.3800	−1.22356
$159$	−5.65246	−0.448269
$160$	−1.17448	−0.0928510
$161$	2.92108	0.230213
$162$	8.56992	0.673316
$163$	−21.0957	−1.65234	−0.826170	−	0.563421i	$-0.809485\pi$
$163$	−21.0957	−1.65234	−0.826170	+	0.563421i	$0.809485\pi$
$164$	−1.15235	−0.0899836
$165$	−2.90957	−0.226509
$166$	−13.5215	−1.04947
$167$	−12.7388	−0.985756	−0.492878	−	0.870098i	$-0.664055\pi$
$167$	−12.7388	−0.985756	−0.492878	+	0.870098i	$0.664055\pi$
$168$	1.33757	0.103195
$169$	1.23698	0.0951521
$170$	6.86448	0.526482
$171$	−2.77356	−0.212100
$172$	−10.8504	−0.827337
$173$	−18.9753	−1.44267	−0.721334	−	0.692588i	$-0.756471\pi$
$173$	−18.9753	−1.44267	−0.721334	+	0.692588i	$0.756471\pi$
$174$	−4.65311	−0.352751
$175$	−1.95485	−0.147773
$176$	1.00000	0.0753778
$177$	18.4586	1.38744
$178$	4.22512	0.316686
$179$	20.0469	1.49837	0.749187	−	0.662358i	$-0.230444\pi$
$179$	20.0469	1.49837	0.749187	+	0.662358i	$0.230444\pi$
$180$	3.68447	0.274624
$181$	−8.48119	−0.630402	−0.315201	−	0.949025i	$-0.602072\pi$
$181$	−8.48119	−0.630402	−0.315201	+	0.949025i	$0.602072\pi$
$182$	−2.03724	−0.151010
$183$	20.6705	1.52801
$184$	−5.41015	−0.398841
$185$	2.96660	0.218109
$186$	2.82769	0.207336
$187$	−5.84469	−0.427406
$188$	0.607182	0.0442833
$189$	−0.183375	−0.0133386
$190$	1.03838	0.0753321
$191$	1.98035	0.143293	0.0716465	−	0.997430i	$-0.477175\pi$
$191$	1.98035	0.143293	0.0716465	+	0.997430i	$0.477175\pi$
$192$	−2.47732	−0.178785
$193$	11.9118	0.857432	0.428716	−	0.903439i	$-0.358966\pi$
$193$	11.9118	0.857432	0.428716	+	0.903439i	$0.358966\pi$
$194$	14.4480	1.03731
$195$	−10.9783	−0.786176
$196$	−6.70848	−0.479177
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	−3.13710	−0.222944
$199$	17.3954	1.23313	0.616565	−	0.787304i	$-0.288524\pi$
$199$	17.3954	1.23313	0.616565	+	0.787304i	$0.288524\pi$
$200$	3.62059	0.256014
$201$	35.6700	2.51597
$202$	−17.9364	−1.26200
$203$	−1.01414	−0.0711783
$204$	14.4791	1.01374
$205$	−1.35342	−0.0945268
$206$	−10.7356	−0.747985
$207$	16.9722	1.17965
$208$	3.77319	0.261624
$209$	−0.884118	−0.0611557
$210$	1.57095	0.108406
$211$	−21.2882	−1.46554	−0.732772	−	0.680475i	$-0.761774\pi$
$211$	−21.2882	−1.46554	−0.732772	+	0.680475i	$0.761774\pi$
$212$	2.28169	0.156707
$213$	15.3316	1.05050
$214$	−12.3551	−0.844576
$215$	−12.7436	−0.869108
$216$	0.339631	0.0231090
$217$	0.616289	0.0418364
$218$	16.4018	1.11087
$219$	−31.4105	−2.12252
$220$	1.17448	0.0791836
$221$	−22.0531	−1.48345
$222$	6.25741	0.419970
$223$	−5.17257	−0.346381	−0.173191	−	0.984888i	$-0.555408\pi$
$223$	−5.17257	−0.346381	−0.173191	+	0.984888i	$0.555408\pi$
$224$	−0.539926	−0.0360753
$225$	−11.3581	−0.757209
$226$	−7.82432	−0.520466
$227$	−13.7127	−0.910145	−0.455073	−	0.890454i	$-0.650387\pi$
$227$	−13.7127	−0.910145	−0.455073	+	0.890454i	$0.650387\pi$
$228$	2.19024	0.145052
$229$	−21.0838	−1.39325	−0.696627	−	0.717433i	$-0.745317\pi$
$229$	−21.0838	−1.39325	−0.696627	+	0.717433i	$0.745317\pi$
$230$	−6.35412	−0.418979
$231$	−1.33757	−0.0880054
$232$	1.87829	0.123316
$233$	3.24784	0.212773	0.106386	−	0.994325i	$-0.466072\pi$
$233$	3.24784	0.212773	0.106386	+	0.994325i	$0.466072\pi$
$234$	−11.8369	−0.773800
$235$	0.713125	0.0465192
$236$	−7.45106	−0.485023
$237$	−38.1010	−2.47493
$238$	3.15570	0.204553
$239$	−22.7158	−1.46936	−0.734681	−	0.678412i	$-0.762668\pi$
$239$	−22.7158	−1.46936	−0.734681	+	0.678412i	$0.762668\pi$
$240$	−2.90957	−0.187812
$241$	−22.5489	−1.45250	−0.726250	−	0.687431i	$-0.758738\pi$
$241$	−22.5489	−1.45250	−0.726250	+	0.687431i	$0.758738\pi$
$242$	−1.00000	−0.0642824
$243$	22.2493	1.42729
$244$	−8.34390	−0.534164
$245$	−7.87899	−0.503371
$246$	−2.85474	−0.182012
$247$	−3.33595	−0.212261
$248$	−1.14143	−0.0724811
$249$	−33.4969	−2.12278
$250$	10.1247	0.640344
$251$	8.07513	0.509698	0.254849	−	0.966981i	$-0.417974\pi$
$251$	8.07513	0.509698	0.254849	+	0.966981i	$0.417974\pi$
$252$	1.69380	0.106699
$253$	5.41015	0.340133
$254$	6.81011	0.427304
$255$	17.0055	1.06493
$256$	1.00000	0.0625000
$257$	6.40997	0.399843	0.199922	−	0.979812i	$-0.435931\pi$
$257$	6.40997	0.399843	0.199922	+	0.979812i	$0.435931\pi$
$258$	−26.8799	−1.67347
$259$	1.36379	0.0847416
$260$	4.43155	0.274833
$261$	−5.89237	−0.364728
$262$	−10.8126	−0.668004
$263$	21.3227	1.31482	0.657408	−	0.753535i	$-0.271653\pi$
$263$	21.3227	1.31482	0.657408	+	0.753535i	$0.271653\pi$
$264$	2.47732	0.152468
$265$	2.67980	0.164619
$266$	0.477358	0.0292687
$267$	10.4669	0.640567
$268$	−14.3987	−0.879538
$269$	−11.9333	−0.727584	−0.363792	−	0.931480i	$-0.618518\pi$
$269$	−11.9333	−0.727584	−0.363792	+	0.931480i	$0.618518\pi$
$270$	0.398891	0.0242757
$271$	−2.15131	−0.130683	−0.0653414	−	0.997863i	$-0.520814\pi$
$271$	−2.15131	−0.130683	−0.0653414	+	0.997863i	$0.520814\pi$
$272$	−5.84469	−0.354386
$273$	−5.04689	−0.305452
$274$	8.34831	0.504340
$275$	−3.62059	−0.218330
$276$	−13.4026	−0.806744
$277$	−8.75792	−0.526213	−0.263106	−	0.964767i	$-0.584747\pi$
$277$	−8.75792	−0.526213	−0.263106	+	0.964767i	$0.584747\pi$
$278$	−0.295437	−0.0177191
$279$	3.58079	0.214376
$280$	−0.634133	−0.0378967
$281$	−27.4533	−1.63773	−0.818864	−	0.573987i	$-0.805396\pi$
$281$	−27.4533	−1.63773	−0.818864	+	0.573987i	$0.805396\pi$
$282$	1.50418	0.0895728
$283$	−4.59254	−0.272998	−0.136499	−	0.990640i	$-0.543585\pi$
$283$	−4.59254	−0.272998	−0.136499	+	0.990640i	$0.543585\pi$
$284$	−6.18878	−0.367237
$285$	2.57240	0.152376
$286$	−3.77319	−0.223114
$287$	−0.622184	−0.0367264
$288$	−3.13710	−0.184855
$289$	17.1604	1.00943
$290$	2.20602	0.129542
$291$	35.7924	2.09819
$292$	12.6792	0.741996
$293$	−0.240754	−0.0140650	−0.00703250	−	0.999975i	$-0.502239\pi$
$293$	−0.240754	−0.0140650	−0.00703250	+	0.999975i	$0.502239\pi$
$294$	−16.6190	−0.969241
$295$	−8.75114	−0.509511
$296$	−2.52588	−0.146814
$297$	−0.339631	−0.0197074
$298$	3.70851	0.214828
$299$	20.4135	1.18054
$300$	8.96935	0.517846
$301$	−5.85842	−0.337674
$302$	−5.75292	−0.331043
$303$	−44.4342	−2.55268
$304$	−0.884118	−0.0507077
$305$	−9.79977	−0.561133
$306$	18.3353	1.04816
$307$	30.5370	1.74284	0.871420	−	0.490538i	$-0.163200\pi$
$307$	30.5370	1.74284	0.871420	+	0.490538i	$0.163200\pi$
$308$	0.539926	0.0307651
$309$	−26.5955	−1.51296
$310$	−1.34059	−0.0761406
$311$	−5.18206	−0.293848	−0.146924	−	0.989148i	$-0.546937\pi$
$311$	−5.18206	−0.293848	−0.146924	+	0.989148i	$0.546937\pi$
$312$	9.34739	0.529192
$313$	−28.8064	−1.62823	−0.814117	−	0.580701i	$-0.802779\pi$
$313$	−28.8064	−1.62823	−0.814117	+	0.580701i	$0.802779\pi$
$314$	−17.2199	−0.971778
$315$	1.98934	0.112086
$316$	15.3800	0.865190
$317$	11.6051	0.651805	0.325902	−	0.945403i	$-0.394332\pi$
$317$	11.6051	0.651805	0.325902	+	0.945403i	$0.394332\pi$
$318$	5.65246	0.316974
$319$	−1.87829	−0.105164
$320$	1.17448	0.0656556
$321$	−30.6074	−1.70834
$322$	−2.92108	−0.162785
$323$	5.16739	0.287521
$324$	−8.56992	−0.476106
$325$	−13.6612	−0.757786
$326$	21.0957	1.16838
$327$	40.6325	2.24698
$328$	1.15235	0.0636280
$329$	0.327833	0.0180740
$330$	2.90957	0.160166
$331$	9.28416	0.510304	0.255152	−	0.966901i	$-0.417875\pi$
$331$	9.28416	0.510304	0.255152	+	0.966901i	$0.417875\pi$
$332$	13.5215	0.742087
$333$	7.92393	0.434229
$334$	12.7388	0.697035
$335$	−16.9110	−0.923945
$336$	−1.33757	−0.0729702
$337$	23.1156	1.25919	0.629595	−	0.776924i	$-0.283221\pi$
$337$	23.1156	1.25919	0.629595	+	0.776924i	$0.283221\pi$
$338$	−1.23698	−0.0672827
$339$	−19.3833	−1.05276
$340$	−6.86448	−0.372279
$341$	1.14143	0.0618121
$342$	2.77356	0.149977
$343$	−7.40156	−0.399647
$344$	10.8504	0.585015
$345$	−15.7412	−0.847476
$346$	18.9753	1.02012
$347$	22.4255	1.20386	0.601932	−	0.798548i	$-0.294398\pi$
$347$	22.4255	1.20386	0.601932	+	0.798548i	$0.294398\pi$
$348$	4.65311	0.249433
$349$	−30.9220	−1.65522	−0.827608	−	0.561306i	$-0.810299\pi$
$349$	−30.9220	−1.65522	−0.827608	+	0.561306i	$0.810299\pi$
$350$	1.95485	0.104491
$351$	−1.28149	−0.0684010
$352$	−1.00000	−0.0533002
$353$	0.158420	0.00843184	0.00421592	−	0.999991i	$-0.498658\pi$
$353$	0.158420	0.00843184	0.00421592	+	0.999991i	$0.498658\pi$
$354$	−18.4586	−0.981065
$355$	−7.26862	−0.385778
$356$	−4.22512	−0.223931
$357$	7.81766	0.413754
$358$	−20.0469	−1.05951
$359$	−13.5023	−0.712626	−0.356313	−	0.934367i	$-0.615966\pi$
$359$	−13.5023	−0.712626	−0.356313	+	0.934367i	$0.615966\pi$
$360$	−3.68447	−0.194188
$361$	−18.2183	−0.958860
$362$	8.48119	0.445762
$363$	−2.47732	−0.130025
$364$	2.03724	0.106781
$365$	14.8915	0.779459
$366$	−20.6705	−1.08046
$367$	−25.4621	−1.32911	−0.664555	−	0.747239i	$-0.731379\pi$
$367$	−25.4621	−1.32911	−0.664555	+	0.747239i	$0.731379\pi$
$368$	5.41015	0.282023
$369$	−3.61504	−0.188191
$370$	−2.96660	−0.154226
$371$	1.23194	0.0639592
$372$	−2.82769	−0.146609
$373$	23.3957	1.21138	0.605691	−	0.795700i	$-0.292897\pi$
$373$	23.3957	1.21138	0.605691	+	0.795700i	$0.292897\pi$
$374$	5.84469	0.302222
$375$	25.0822	1.29524
$376$	−0.607182	−0.0313130
$377$	−7.08714	−0.365006
$378$	0.183375	0.00943181
$379$	3.72885	0.191538	0.0957691	−	0.995404i	$-0.469469\pi$
$379$	3.72885	0.191538	0.0957691	+	0.995404i	$0.469469\pi$
$380$	−1.03838	−0.0532679
$381$	16.8708	0.864317
$382$	−1.98035	−0.101324
$383$	−24.1680	−1.23493	−0.617464	−	0.786599i	$-0.711840\pi$
$383$	−24.1680	−1.23493	−0.617464	+	0.786599i	$0.711840\pi$
$384$	2.47732	0.126420
$385$	0.634133	0.0323184
$386$	−11.9118	−0.606296
$387$	−34.0388	−1.73029
$388$	−14.4480	−0.733489
$389$	−25.4423	−1.28998	−0.644988	−	0.764193i	$-0.723138\pi$
$389$	−25.4423	−1.28998	−0.644988	+	0.764193i	$0.723138\pi$
$390$	10.9783	0.555910
$391$	−31.6206	−1.59912
$392$	6.70848	0.338829
$393$	−26.7862	−1.35118
$394$	−1.00000	−0.0503793
$395$	18.0635	0.908873
$396$	3.13710	0.157645
$397$	−19.7031	−0.988868	−0.494434	−	0.869215i	$-0.664625\pi$
$397$	−19.7031	−0.988868	−0.494434	+	0.869215i	$0.664625\pi$
$398$	−17.3954	−0.871955
$399$	1.18257	0.0592024
$400$	−3.62059	−0.181030
$401$	4.76826	0.238116	0.119058	−	0.992887i	$-0.462013\pi$
$401$	4.76826	0.238116	0.119058	+	0.992887i	$0.462013\pi$
$402$	−35.6700	−1.77906
$403$	4.30685	0.214539
$404$	17.9364	0.892371
$405$	−10.0652	−0.500145
$406$	1.01414	0.0503307
$407$	2.52588	0.125203
$408$	−14.4791	−0.716824
$409$	−31.6504	−1.56501	−0.782506	−	0.622643i	$-0.786059\pi$
$409$	−31.6504	−1.56501	−0.782506	+	0.622643i	$0.786059\pi$
$410$	1.35342	0.0668405
$411$	20.6814	1.02014
$412$	10.7356	0.528905
$413$	−4.02302	−0.197960
$414$	−16.9722	−0.834136
$415$	15.8807	0.779554
$416$	−3.77319	−0.184996
$417$	−0.731890	−0.0358408
$418$	0.884118	0.0432436
$419$	−4.15370	−0.202922	−0.101461	−	0.994840i	$-0.532352\pi$
$419$	−4.15370	−0.202922	−0.101461	+	0.994840i	$0.532352\pi$
$420$	−1.57095	−0.0766544
$421$	−35.5667	−1.73341	−0.866707	−	0.498818i	$-0.833768\pi$
$421$	−35.5667	−1.73341	−0.866707	+	0.498818i	$0.833768\pi$
$422$	21.2882	1.03630
$423$	1.90479	0.0926140
$424$	−2.28169	−0.110809
$425$	21.1612	1.02647
$426$	−15.3316	−0.742817
$427$	−4.50509	−0.218016
$428$	12.3551	0.597205
$429$	−9.34739	−0.451296
$430$	12.7436	0.614552
$431$	−9.40098	−0.452829	−0.226415	−	0.974031i	$-0.572700\pi$
$431$	−9.40098	−0.452829	−0.226415	+	0.974031i	$0.572700\pi$
$432$	−0.339631	−0.0163405
$433$	7.91627	0.380432	0.190216	−	0.981742i	$-0.439081\pi$
$433$	7.91627	0.380432	0.190216	+	0.981742i	$0.439081\pi$
$434$	−0.616289	−0.0295828
$435$	5.46500	0.262027
$436$	−16.4018	−0.785505
$437$	−4.78321	−0.228812
$438$	31.4105	1.50085
$439$	−18.4842	−0.882201	−0.441101	−	0.897458i	$-0.645412\pi$
$439$	−18.4842	−0.882201	−0.441101	+	0.897458i	$0.645412\pi$
$440$	−1.17448	−0.0559913
$441$	−21.0451	−1.00215
$442$	22.0531	1.04896
$443$	19.4468	0.923945	0.461973	−	0.886894i	$-0.347142\pi$
$443$	19.4468	0.923945	0.461973	+	0.886894i	$0.347142\pi$
$444$	−6.25741	−0.296963
$445$	−4.96233	−0.235237
$446$	5.17257	0.244928
$447$	9.18716	0.434538
$448$	0.539926	0.0255091
$449$	−28.5274	−1.34629	−0.673146	−	0.739510i	$-0.735057\pi$
$449$	−28.5274	−1.34629	−0.673146	+	0.739510i	$0.735057\pi$
$450$	11.3581	0.535428
$451$	−1.15235	−0.0542621
$452$	7.82432	0.368025
$453$	−14.2518	−0.669608
$454$	13.7127	0.643570
$455$	2.39271	0.112172
$456$	−2.19024	−0.102567
$457$	−17.8937	−0.837032	−0.418516	−	0.908209i	$-0.637450\pi$
$457$	−17.8937	−0.837032	−0.418516	+	0.908209i	$0.637450\pi$
$458$	21.0838	0.985180
$459$	1.98504	0.0926536
$460$	6.35412	0.296263
$461$	−39.2738	−1.82916	−0.914582	−	0.404400i	$-0.867480\pi$
$461$	−39.2738	−1.82916	−0.914582	+	0.404400i	$0.867480\pi$
$462$	1.33757	0.0622292
$463$	25.6911	1.19397	0.596984	−	0.802253i	$-0.296366\pi$
$463$	25.6911	1.19397	0.596984	+	0.802253i	$0.296366\pi$
$464$	−1.87829	−0.0871973
$465$	−3.32108	−0.154011
$466$	−3.24784	−0.150453
$467$	−13.9249	−0.644370	−0.322185	−	0.946677i	$-0.604417\pi$
$467$	−13.9249	−0.644370	−0.322185	+	0.946677i	$0.604417\pi$
$468$	11.8369	0.547159
$469$	−7.77420	−0.358979
$470$	−0.713125	−0.0328940
$471$	−42.6593	−1.96563
$472$	7.45106	0.342963
$473$	−10.8504	−0.498903
$474$	38.1010	1.75004
$475$	3.20103	0.146873
$476$	−3.15570	−0.144641
$477$	7.15787	0.327736
$478$	22.7158	1.03900
$479$	13.5517	0.619191	0.309596	−	0.950868i	$-0.399806\pi$
$479$	13.5517	0.619191	0.309596	+	0.950868i	$0.399806\pi$
$480$	2.90957	0.132803
$481$	9.53063	0.434559
$482$	22.5489	1.02707
$483$	−7.23643	−0.329269
$484$	1.00000	0.0454545
$485$	−16.9690	−0.770522
$486$	−22.2493	−1.00925
$487$	27.5587	1.24880	0.624401	−	0.781104i	$-0.285343\pi$
$487$	27.5587	1.24880	0.624401	+	0.781104i	$0.285343\pi$
$488$	8.34390	0.377711
$489$	52.2607	2.36331
$490$	7.87899	0.355937
$491$	15.9053	0.717794	0.358897	−	0.933377i	$-0.383153\pi$
$491$	15.9053	0.717794	0.358897	+	0.933377i	$0.383153\pi$
$492$	2.85474	0.128702
$493$	10.9780	0.494424
$494$	3.33595	0.150091
$495$	3.68447	0.165604
$496$	1.14143	0.0512519
$497$	−3.34148	−0.149886
$498$	33.4969	1.50103
$499$	−25.2344	−1.12965	−0.564823	−	0.825212i	$-0.691056\pi$
$499$	−25.2344	−1.12965	−0.564823	+	0.825212i	$0.691056\pi$
$500$	−10.1247	−0.452792
$501$	31.5580	1.40991
$502$	−8.07513	−0.360411
$503$	−29.1228	−1.29852	−0.649261	−	0.760565i	$-0.724922\pi$
$503$	−29.1228	−1.29852	−0.649261	+	0.760565i	$0.724922\pi$
$504$	−1.69380	−0.0754478
$505$	21.0660	0.937426
$506$	−5.41015	−0.240510
$507$	−3.06438	−0.136094
$508$	−6.81011	−0.302150
$509$	−31.0295	−1.37536	−0.687680	−	0.726014i	$-0.741371\pi$
$509$	−31.0295	−1.37536	−0.687680	+	0.726014i	$0.741371\pi$
$510$	−17.0055	−0.753016
$511$	6.84584	0.302842
$512$	−1.00000	−0.0441942
$513$	0.300274	0.0132574
$514$	−6.40997	−0.282732
$515$	12.6088	0.555609
$516$	26.8799	1.18332
$517$	0.607182	0.0267039
$518$	−1.36379	−0.0599214
$519$	47.0079	2.06342
$520$	−4.43155	−0.194336
$521$	−42.3633	−1.85597	−0.927985	−	0.372619i	$-0.878460\pi$
$521$	−42.3633	−1.85597	−0.927985	+	0.372619i	$0.878460\pi$
$522$	5.89237	0.257902
$523$	26.7650	1.17035	0.585176	−	0.810906i	$-0.301025\pi$
$523$	26.7650	1.17035	0.585176	+	0.810906i	$0.301025\pi$
$524$	10.8126	0.472350
$525$	4.84278	0.211356
$526$	−21.3227	−0.929715
$527$	−6.67132	−0.290607
$528$	−2.47732	−0.107811
$529$	6.26969	0.272595
$530$	−2.67980	−0.116403
$531$	−23.3747	−1.01438
$532$	−0.477358	−0.0206961
$533$	−4.34805	−0.188335
$534$	−10.4669	−0.452949
$535$	14.5108	0.627358
$536$	14.3987	0.621927
$537$	−49.6625	−2.14309
$538$	11.9333	0.514480
$539$	−6.70848	−0.288955
$540$	−0.398891	−0.0171655
$541$	−13.7426	−0.590838	−0.295419	−	0.955368i	$-0.595459\pi$
$541$	−13.7426	−0.590838	−0.295419	+	0.955368i	$0.595459\pi$
$542$	2.15131	0.0924067
$543$	21.0106	0.901651
$544$	5.84469	0.250589
$545$	−19.2637	−0.825165
$546$	5.04689	0.215987
$547$	−39.3492	−1.68245	−0.841224	−	0.540687i	$-0.818164\pi$
$547$	−39.3492	−1.68245	−0.841224	+	0.540687i	$0.818164\pi$
$548$	−8.34831	−0.356622
$549$	−26.1756	−1.11715
$550$	3.62059	0.154382
$551$	1.66063	0.0707451
$552$	13.4026	0.570454
$553$	8.30403	0.353123
$554$	8.75792	0.372088
$555$	−7.34922	−0.311957
$556$	0.295437	0.0125293
$557$	34.1475	1.44688	0.723439	−	0.690389i	$-0.242560\pi$
$557$	34.1475	1.44688	0.723439	+	0.690389i	$0.242560\pi$
$558$	−3.58079	−0.151587
$559$	−40.9407	−1.73161
$560$	0.634133	0.0267970
$561$	14.4791	0.611310
$562$	27.4533	1.15805
$563$	11.7652	0.495845	0.247922	−	0.968780i	$-0.420252\pi$
$563$	11.7652	0.495845	0.247922	+	0.968780i	$0.420252\pi$
$564$	−1.50418	−0.0633375
$565$	9.18953	0.386607
$566$	4.59254	0.193039
$567$	−4.62712	−0.194321
$568$	6.18878	0.259676
$569$	17.9116	0.750892	0.375446	−	0.926844i	$-0.377490\pi$
$569$	17.9116	0.750892	0.375446	+	0.926844i	$0.377490\pi$
$570$	−2.57240	−0.107746
$571$	−37.4522	−1.56733	−0.783663	−	0.621187i	$-0.786651\pi$
$571$	−37.4522	−1.56733	−0.783663	+	0.621187i	$0.786651\pi$
$572$	3.77319	0.157765
$573$	−4.90595	−0.204949
$574$	0.622184	0.0259695
$575$	−19.5879	−0.816873
$576$	3.13710	0.130712
$577$	−28.8280	−1.20012	−0.600062	−	0.799954i	$-0.704857\pi$
$577$	−28.8280	−1.20012	−0.600062	+	0.799954i	$0.704857\pi$
$578$	−17.1604	−0.713777
$579$	−29.5094	−1.22637
$580$	−2.20602	−0.0915998
$581$	7.30058	0.302879
$582$	−35.7924	−1.48364
$583$	2.28169	0.0944978
$584$	−12.6792	−0.524670
$585$	13.9022	0.574785
$586$	0.240754	0.00994545
$587$	−0.316448	−0.0130612	−0.00653061	−	0.999979i	$-0.502079\pi$
$587$	−0.316448	−0.0130612	−0.00653061	+	0.999979i	$0.502079\pi$
$588$	16.6190	0.685357
$589$	−1.00916	−0.0415818
$590$	8.75114	0.360279
$591$	−2.47732	−0.101903
$592$	2.52588	0.103813
$593$	−47.0430	−1.93182	−0.965912	−	0.258869i	$-0.916650\pi$
$593$	−47.0430	−1.93182	−0.965912	+	0.258869i	$0.916650\pi$
$594$	0.339631	0.0139352
$595$	−3.70631	−0.151944
$596$	−3.70851	−0.151907
$597$	−43.0940	−1.76372
$598$	−20.4135	−0.834771
$599$	21.1359	0.863591	0.431796	−	0.901971i	$-0.357880\pi$
$599$	21.1359	0.863591	0.431796	+	0.901971i	$0.357880\pi$
$600$	−8.96935	−0.366172
$601$	41.2331	1.68193	0.840966	−	0.541088i	$-0.181987\pi$
$601$	41.2331	1.68193	0.840966	+	0.541088i	$0.181987\pi$
$602$	5.85842	0.238771
$603$	−45.1700	−1.83946
$604$	5.75292	0.234083
$605$	1.17448	0.0477495
$606$	44.4342	1.80502
$607$	1.50077	0.0609142	0.0304571	−	0.999536i	$-0.490304\pi$
$607$	1.50077	0.0609142	0.0304571	+	0.999536i	$0.490304\pi$
$608$	0.884118	0.0358557
$609$	2.51233	0.101805
$610$	9.79977	0.396781
$611$	2.29102	0.0926846
$612$	−18.3353	−0.741162
$613$	9.46197	0.382165	0.191083	−	0.981574i	$-0.438800\pi$
$613$	9.46197	0.382165	0.191083	+	0.981574i	$0.438800\pi$
$614$	−30.5370	−1.23237
$615$	3.35284	0.135200
$616$	−0.539926	−0.0217542
$617$	37.1697	1.49640	0.748198	−	0.663476i	$-0.230919\pi$
$617$	37.1697	1.49640	0.748198	+	0.663476i	$0.230919\pi$
$618$	26.5955	1.06983
$619$	13.5189	0.543372	0.271686	−	0.962386i	$-0.412419\pi$
$619$	13.5189	0.543372	0.271686	+	0.962386i	$0.412419\pi$
$620$	1.34059	0.0538396
$621$	−1.83745	−0.0737345
$622$	5.18206	0.207782
$623$	−2.28125	−0.0913963
$624$	−9.34739	−0.374195
$625$	6.21162	0.248465
$626$	28.8064	1.15134
$627$	2.19024	0.0874698
$628$	17.2199	0.687151
$629$	−14.7630	−0.588639
$630$	−1.98934	−0.0792571
$631$	9.69831	0.386084	0.193042	−	0.981191i	$-0.438165\pi$
$631$	9.69831	0.386084	0.193042	+	0.981191i	$0.438165\pi$
$632$	−15.3800	−0.611782
$633$	52.7377	2.09614
$634$	−11.6051	−0.460896
$635$	−7.99836	−0.317405
$636$	−5.65246	−0.224135
$637$	−25.3124	−1.00291
$638$	1.87829	0.0743621
$639$	−19.4148	−0.768038
$640$	−1.17448	−0.0464255
$641$	13.8442	0.546811	0.273406	−	0.961899i	$-0.411850\pi$
$641$	13.8442	0.546811	0.273406	+	0.961899i	$0.411850\pi$
$642$	30.6074	1.20798
$643$	−15.5032	−0.611388	−0.305694	−	0.952130i	$-0.598888\pi$
$643$	−15.5032	−0.611388	−0.305694	+	0.952130i	$0.598888\pi$
$644$	2.92108	0.115107
$645$	31.5700	1.24307
$646$	−5.16739	−0.203308
$647$	−2.71766	−0.106842	−0.0534211	−	0.998572i	$-0.517013\pi$
$647$	−2.71766	−0.106842	−0.0534211	+	0.998572i	$0.517013\pi$
$648$	8.56992	0.336658
$649$	−7.45106	−0.292480
$650$	13.6612	0.535836
$651$	−1.52674	−0.0598378
$652$	−21.0957	−0.826170
$653$	2.12189	0.0830359	0.0415180	−	0.999138i	$-0.486781\pi$
$653$	2.12189	0.0830359	0.0415180	+	0.999138i	$0.486781\pi$
$654$	−40.6325	−1.58886
$655$	12.6992	0.496198
$656$	−1.15235	−0.0449918
$657$	39.7760	1.55181
$658$	−0.327833	−0.0127803
$659$	7.37349	0.287230	0.143615	−	0.989634i	$-0.454127\pi$
$659$	7.37349	0.287230	0.143615	+	0.989634i	$0.454127\pi$
$660$	−2.90957	−0.113255
$661$	28.7791	1.11938	0.559688	−	0.828704i	$-0.310921\pi$
$661$	28.7791	1.11938	0.559688	+	0.828704i	$0.310921\pi$
$662$	−9.28416	−0.360839
$663$	54.6326	2.12175
$664$	−13.5215	−0.524734
$665$	−0.560649	−0.0217410
$666$	−7.92393	−0.307046
$667$	−10.1618	−0.393467
$668$	−12.7388	−0.492878
$669$	12.8141	0.495422
$670$	16.9110	0.653328
$671$	−8.34390	−0.322113
$672$	1.33757	0.0515977
$673$	−14.0466	−0.541458	−0.270729	−	0.962656i	$-0.587265\pi$
$673$	−14.0466	−0.541458	−0.270729	+	0.962656i	$0.587265\pi$
$674$	−23.1156	−0.890381
$675$	1.22966	0.0473298
$676$	1.23698	0.0475761
$677$	−21.5963	−0.830013	−0.415006	−	0.909819i	$-0.636221\pi$
$677$	−21.5963	−0.830013	−0.415006	+	0.909819i	$0.636221\pi$
$678$	19.3833	0.744412
$679$	−7.80087	−0.299370
$680$	6.86448	0.263241
$681$	33.9707	1.30176
$682$	−1.14143	−0.0437078
$683$	11.8798	0.454566	0.227283	−	0.973829i	$-0.427016\pi$
$683$	11.8798	0.454566	0.227283	+	0.973829i	$0.427016\pi$
$684$	−2.77356	−0.106050
$685$	−9.80495	−0.374628
$686$	7.40156	0.282593
$687$	52.2312	1.99274
$688$	−10.8504	−0.413668
$689$	8.60924	0.327986
$690$	15.7412	0.599256
$691$	−27.1893	−1.03433	−0.517165	−	0.855886i	$-0.673013\pi$
$691$	−27.1893	−1.03433	−0.517165	+	0.855886i	$0.673013\pi$
$692$	−18.9753	−0.721334
$693$	1.69380	0.0643421
$694$	−22.4255	−0.851260
$695$	0.346985	0.0131619
$696$	−4.65311	−0.176376
$697$	6.73514	0.255111
$698$	30.9220	1.17041
$699$	−8.04592	−0.304325
$700$	−1.95485	−0.0738864
$701$	41.4364	1.56503	0.782515	−	0.622632i	$-0.213936\pi$
$701$	41.4364	1.56503	0.782515	+	0.622632i	$0.213936\pi$
$702$	1.28149	0.0483668
$703$	−2.23318	−0.0842259
$704$	1.00000	0.0376889
$705$	−1.76664	−0.0665354
$706$	−0.158420	−0.00596221
$707$	9.68434	0.364217
$708$	18.4586	0.693718
$709$	12.5616	0.471762	0.235881	−	0.971782i	$-0.424202\pi$
$709$	12.5616	0.471762	0.235881	+	0.971782i	$0.424202\pi$
$710$	7.26862	0.272786
$711$	48.2484	1.80946
$712$	4.22512	0.158343
$713$	6.17532	0.231268
$714$	−7.81766	−0.292568
$715$	4.43155	0.165731
$716$	20.0469	0.749187
$717$	56.2742	2.10160
$718$	13.5023	0.503903
$719$	18.7025	0.697484	0.348742	−	0.937219i	$-0.386609\pi$
$719$	18.7025	0.697484	0.348742	+	0.937219i	$0.386609\pi$
$720$	3.68447	0.137312
$721$	5.79643	0.215870
$722$	18.2183	0.678016
$723$	55.8606	2.07748
$724$	−8.48119	−0.315201
$725$	6.80051	0.252565
$726$	2.47732	0.0919418
$727$	−35.7845	−1.32718	−0.663588	−	0.748099i	$-0.730967\pi$
$727$	−35.7845	−1.32718	−0.663588	+	0.748099i	$0.730967\pi$
$728$	−2.03724	−0.0755052
$729$	−29.4088	−1.08921
$730$	−14.8915	−0.551160
$731$	63.4173	2.34557
$732$	20.6705	0.764003
$733$	35.1916	1.29983	0.649916	−	0.760006i	$-0.274804\pi$
$733$	35.1916	1.29983	0.649916	+	0.760006i	$0.274804\pi$
$734$	25.4621	0.939823
$735$	19.5188	0.719960
$736$	−5.41015	−0.199421
$737$	−14.3987	−0.530381
$738$	3.61504	0.133071
$739$	33.9222	1.24785	0.623925	−	0.781485i	$-0.285537\pi$
$739$	33.9222	1.24785	0.623925	+	0.781485i	$0.285537\pi$
$740$	2.96660	0.109055
$741$	8.26420	0.303593
$742$	−1.23194	−0.0452260
$743$	−17.2746	−0.633744	−0.316872	−	0.948468i	$-0.602633\pi$
$743$	−17.2746	−0.633744	−0.316872	+	0.948468i	$0.602633\pi$
$744$	2.82769	0.103668
$745$	−4.35558	−0.159576
$746$	−23.3957	−0.856576
$747$	42.4181	1.55200
$748$	−5.84469	−0.213703
$749$	6.67082	0.243746
$750$	−25.0822	−0.915871
$751$	−12.0602	−0.440082	−0.220041	−	0.975491i	$-0.570619\pi$
$751$	−12.0602	−0.440082	−0.220041	+	0.975491i	$0.570619\pi$
$752$	0.607182	0.0221417
$753$	−20.0047	−0.729010
$754$	7.08714	0.258098
$755$	6.75670	0.245901
$756$	−0.183375	−0.00666930
$757$	−1.22428	−0.0444973	−0.0222487	−	0.999752i	$-0.507083\pi$
$757$	−1.22428	−0.0444973	−0.0222487	+	0.999752i	$0.507083\pi$
$758$	−3.72885	−0.135438
$759$	−13.4026	−0.486485
$760$	1.03838	0.0376661
$761$	−11.5768	−0.419657	−0.209829	−	0.977738i	$-0.567291\pi$
$761$	−11.5768	−0.419657	−0.209829	+	0.977738i	$0.567291\pi$
$762$	−16.8708	−0.611165
$763$	−8.85577	−0.320600
$764$	1.98035	0.0716465
$765$	−21.5345	−0.778583
$766$	24.1680	0.873226
$767$	−28.1143	−1.01515
$768$	−2.47732	−0.0893925
$769$	53.8959	1.94354	0.971768	−	0.235940i	$-0.0758169\pi$
$769$	53.8959	1.94354	0.971768	+	0.235940i	$0.0758169\pi$
$770$	−0.634133	−0.0228526
$771$	−15.8795	−0.571887
$772$	11.9118	0.428716
$773$	48.7571	1.75367	0.876836	−	0.480790i	$-0.159650\pi$
$773$	48.7571	1.75367	0.876836	+	0.480790i	$0.159650\pi$
$774$	34.0388	1.22350
$775$	−4.13266	−0.148450
$776$	14.4480	0.518655
$777$	−3.37853	−0.121204
$778$	25.4423	0.912151
$779$	1.01882	0.0365028
$780$	−10.9783	−0.393088
$781$	−6.18878	−0.221452
$782$	31.6206	1.13075
$783$	0.637924	0.0227976
$784$	−6.70848	−0.239589
$785$	20.2245	0.721844
$786$	26.7862	0.955432
$787$	−15.8791	−0.566029	−0.283014	−	0.959116i	$-0.591334\pi$
$787$	−15.8791	−0.566029	−0.283014	+	0.959116i	$0.591334\pi$
$788$	1.00000	0.0356235
$789$	−52.8232	−1.88055
$790$	−18.0635	−0.642670
$791$	4.22455	0.150208
$792$	−3.13710	−0.111472
$793$	−31.4831	−1.11800
$794$	19.7031	0.699235
$795$	−6.63872	−0.235451
$796$	17.3954	0.616565
$797$	−52.3754	−1.85523	−0.927615	−	0.373537i	$-0.878145\pi$
$797$	−52.3754	−1.85523	−0.927615	+	0.373537i	$0.878145\pi$
$798$	−1.18257	−0.0418624
$799$	−3.54879	−0.125547
$800$	3.62059	0.128007
$801$	−13.2546	−0.468328
$802$	−4.76826	−0.168373
$803$	12.6792	0.447440
$804$	35.6700	1.25798
$805$	3.43075	0.120918
$806$	−4.30685	−0.151702
$807$	29.5625	1.04065
$808$	−17.9364	−0.631002
$809$	44.6334	1.56923	0.784613	−	0.619986i	$-0.212862\pi$
$809$	44.6334	1.56923	0.784613	+	0.619986i	$0.212862\pi$
$810$	10.0652	0.353656
$811$	46.5397	1.63423	0.817115	−	0.576475i	$-0.195572\pi$
$811$	46.5397	1.63423	0.817115	+	0.576475i	$0.195572\pi$
$812$	−1.01414	−0.0355892
$813$	5.32948	0.186913
$814$	−2.52588	−0.0885321
$815$	−24.7765	−0.867883
$816$	14.4791	0.506871
$817$	9.59305	0.335618
$818$	31.6504	1.10663
$819$	6.39103	0.223321
$820$	−1.35342	−0.0472634
$821$	−17.4852	−0.610237	−0.305119	−	0.952314i	$-0.598696\pi$
$821$	−17.4852	−0.610237	−0.305119	+	0.952314i	$0.598696\pi$
$822$	−20.6814	−0.721347
$823$	−40.3592	−1.40683	−0.703417	−	0.710778i	$-0.748343\pi$
$823$	−40.3592	−1.40683	−0.703417	+	0.710778i	$0.748343\pi$
$824$	−10.7356	−0.373992
$825$	8.96935	0.312273
$826$	4.02302	0.139979
$827$	37.1226	1.29088	0.645439	−	0.763812i	$-0.276674\pi$
$827$	37.1226	1.29088	0.645439	+	0.763812i	$0.276674\pi$
$828$	16.9722	0.589823
$829$	26.0075	0.903277	0.451639	−	0.892201i	$-0.350840\pi$
$829$	26.0075	0.903277	0.451639	+	0.892201i	$0.350840\pi$
$830$	−15.8807	−0.551228
$831$	21.6961	0.752631
$832$	3.77319	0.130812
$833$	39.2090	1.35851
$834$	0.731890	0.0253433
$835$	−14.9615	−0.517763
$836$	−0.884118	−0.0305779
$837$	−0.387666	−0.0133997
$838$	4.15370	0.143487
$839$	31.9226	1.10209	0.551046	−	0.834475i	$-0.314229\pi$
$839$	31.9226	1.10209	0.551046	+	0.834475i	$0.314229\pi$
$840$	1.57095	0.0542029
$841$	−25.4720	−0.878346
$842$	35.5667	1.22571
$843$	68.0106	2.34241
$844$	−21.2882	−0.732772
$845$	1.45281	0.0499781
$846$	−1.90479	−0.0654880
$847$	0.539926	0.0185521
$848$	2.28169	0.0783534
$849$	11.3772	0.390463
$850$	−21.1612	−0.725824
$851$	13.6654	0.468443
$852$	15.3316	0.525251
$853$	16.5369	0.566213	0.283107	−	0.959088i	$-0.408635\pi$
$853$	16.5369	0.566213	0.283107	+	0.959088i	$0.408635\pi$
$854$	4.50509	0.154161
$855$	−3.25750	−0.111404
$856$	−12.3551	−0.422288
$857$	−27.1295	−0.926725	−0.463362	−	0.886169i	$-0.653357\pi$
$857$	−27.1295	−0.926725	−0.463362	+	0.886169i	$0.653357\pi$
$858$	9.34739	0.319115
$859$	−13.2556	−0.452274	−0.226137	−	0.974096i	$-0.572610\pi$
$859$	−13.2556	−0.452274	−0.226137	+	0.974096i	$0.572610\pi$
$860$	−12.7436	−0.434554
$861$	1.54135	0.0525290
$862$	9.40098	0.320199
$863$	35.5277	1.20938	0.604689	−	0.796462i	$-0.293297\pi$
$863$	35.5277	1.20938	0.604689	+	0.796462i	$0.293297\pi$
$864$	0.339631	0.0115545
$865$	−22.2862	−0.757753
$866$	−7.91627	−0.269006
$867$	−42.5116	−1.44377
$868$	0.616289	0.0209182
$869$	15.3800	0.521729
$870$	−5.46500	−0.185281
$871$	−54.3289	−1.84086
$872$	16.4018	0.555436
$873$	−45.3249	−1.53402
$874$	4.78321	0.161794
$875$	−5.46660	−0.184805
$876$	−31.4105	−1.06126
$877$	37.6943	1.27285	0.636423	−	0.771340i	$-0.280413\pi$
$877$	37.6943	1.27285	0.636423	+	0.771340i	$0.280413\pi$
$878$	18.4842	0.623811
$879$	0.596424	0.0201169
$880$	1.17448	0.0395918
$881$	28.3534	0.955252	0.477626	−	0.878563i	$-0.341497\pi$
$881$	28.3534	0.955252	0.477626	+	0.878563i	$0.341497\pi$
$882$	21.0451	0.708627
$883$	−28.1102	−0.945983	−0.472992	−	0.881067i	$-0.656826\pi$
$883$	−28.1102	−0.945983	−0.472992	+	0.881067i	$0.656826\pi$
$884$	−22.0531	−0.741727
$885$	21.6793	0.728743
$886$	−19.4468	−0.653328
$887$	49.3466	1.65690	0.828448	−	0.560066i	$-0.189224\pi$
$887$	49.3466	1.65690	0.828448	+	0.560066i	$0.189224\pi$
$888$	6.25741	0.209985
$889$	−3.67695	−0.123321
$890$	4.96233	0.166338
$891$	−8.56992	−0.287103
$892$	−5.17257	−0.173191
$893$	−0.536821	−0.0179640
$894$	−9.18716	−0.307265
$895$	23.5447	0.787013
$896$	−0.539926	−0.0180376
$897$	−50.5708	−1.68851
$898$	28.5274	0.951972
$899$	−2.14394	−0.0715044
$900$	−11.3581	−0.378605
$901$	−13.3357	−0.444278
$902$	1.15235	0.0383691
$903$	14.5132	0.482968
$904$	−7.82432	−0.260233
$905$	−9.96102	−0.331115
$906$	14.2518	0.473484
$907$	−54.3605	−1.80501	−0.902505	−	0.430679i	$-0.858274\pi$
$907$	−54.3605	−1.80501	−0.902505	+	0.430679i	$0.858274\pi$
$908$	−13.7127	−0.455073
$909$	56.2683	1.86630
$910$	−2.39271	−0.0793174
$911$	19.1457	0.634326	0.317163	−	0.948371i	$-0.397270\pi$
$911$	19.1457	0.634326	0.317163	+	0.948371i	$0.397270\pi$
$912$	2.19024	0.0725261
$913$	13.5215	0.447495
$914$	17.8937	0.591871
$915$	24.2771	0.802577
$916$	−21.0838	−0.696627
$917$	5.83799	0.192787
$918$	−1.98504	−0.0655160
$919$	−19.9997	−0.659730	−0.329865	−	0.944028i	$-0.607003\pi$
$919$	−19.9997	−0.659730	−0.329865	+	0.944028i	$0.607003\pi$
$920$	−6.35412	−0.209489
$921$	−75.6498	−2.49275
$922$	39.2738	1.29341
$923$	−23.3515	−0.768623
$924$	−1.33757	−0.0440027
$925$	−9.14518	−0.300692
$926$	−25.6911	−0.844263
$927$	33.6786	1.10615
$928$	1.87829	0.0616578
$929$	−42.3670	−1.39002	−0.695008	−	0.719002i	$-0.744599\pi$
$929$	−42.3670	−1.39002	−0.695008	+	0.719002i	$0.744599\pi$
$930$	3.32108	0.108902
$931$	5.93109	0.194384
$932$	3.24784	0.106386
$933$	12.8376	0.420285
$934$	13.9249	0.455638
$935$	−6.86448	−0.224493
$936$	−11.8369	−0.386900
$937$	38.0785	1.24397	0.621985	−	0.783029i	$-0.286326\pi$
$937$	38.0785	1.24397	0.621985	+	0.783029i	$0.286326\pi$
$938$	7.77420	0.253837
$939$	71.3626	2.32883
$940$	0.713125	0.0232596
$941$	−7.40740	−0.241474	−0.120737	−	0.992685i	$-0.538526\pi$
$941$	−7.40740	−0.241474	−0.120737	+	0.992685i	$0.538526\pi$
$942$	42.6593	1.38991
$943$	−6.23439	−0.203020
$944$	−7.45106	−0.242511
$945$	−0.215371	−0.00700603
$946$	10.8504	0.352777
$947$	33.7478	1.09666	0.548328	−	0.836263i	$-0.315264\pi$
$947$	33.7478	1.09666	0.548328	+	0.836263i	$0.315264\pi$
$948$	−38.1010	−1.23746
$949$	47.8412	1.55299
$950$	−3.20103	−0.103855
$951$	−28.7494	−0.932263
$952$	3.15570	0.102277
$953$	29.5012	0.955637	0.477818	−	0.878459i	$-0.341428\pi$
$953$	29.5012	0.955637	0.477818	+	0.878459i	$0.341428\pi$
$954$	−7.15787	−0.231745
$955$	2.32589	0.0752639
$956$	−22.7158	−0.734681
$957$	4.65311	0.150414
$958$	−13.5517	−0.437834
$959$	−4.50747	−0.145554
$960$	−2.90957	−0.0939058
$961$	−29.6971	−0.957972
$962$	−9.53063	−0.307280
$963$	38.7591	1.24899
$964$	−22.5489	−0.726250
$965$	13.9902	0.450361
$966$	7.23643	0.232828
$967$	−47.1369	−1.51582	−0.757909	−	0.652360i	$-0.773779\pi$
$967$	−47.1369	−1.51582	−0.757909	+	0.652360i	$0.773779\pi$
$968$	−1.00000	−0.0321412
$969$	−12.8013	−0.411236
$970$	16.9690	0.544841
$971$	16.8301	0.540105	0.270052	−	0.962846i	$-0.412959\pi$
$971$	16.8301	0.540105	0.270052	+	0.962846i	$0.412959\pi$
$972$	22.2493	0.713646
$973$	0.159514	0.00511378
$974$	−27.5587	−0.883037
$975$	33.8431	1.08385
$976$	−8.34390	−0.267082
$977$	−1.63026	−0.0521568	−0.0260784	−	0.999660i	$-0.508302\pi$
$977$	−1.63026	−0.0521568	−0.0260784	+	0.999660i	$0.508302\pi$
$978$	−52.2607	−1.67111
$979$	−4.22512	−0.135035
$980$	−7.87899	−0.251685
$981$	−51.4541	−1.64280
$982$	−15.9053	−0.507557
$983$	−51.3995	−1.63939	−0.819695	−	0.572801i	$-0.805857\pi$
$983$	−51.3995	−1.63939	−0.819695	+	0.572801i	$0.805857\pi$
$984$	−2.85474	−0.0910058
$985$	1.17448	0.0374221
$986$	−10.9780	−0.349611
$987$	−0.812147	−0.0258509
$988$	−3.33595	−0.106131
$989$	−58.7023	−1.86663
$990$	−3.68447	−0.117100
$991$	−51.2733	−1.62875	−0.814376	−	0.580338i	$-0.802920\pi$
$991$	−51.2733	−1.62875	−0.814376	+	0.580338i	$0.802920\pi$
$992$	−1.14143	−0.0362406
$993$	−22.9998	−0.729877
$994$	3.34148	0.105985
$995$	20.4306	0.647695
$996$	−33.4969	−1.06139
$997$	43.6887	1.38364	0.691818	−	0.722072i	$-0.256810\pi$
$997$	43.6887	1.38364	0.691818	+	0.722072i	$0.256810\pi$
$998$	25.2344	0.798781
$999$	−0.857867	−0.0271417

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.2	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.2	✓	15	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.47732 q^{3} +1.00000 q^{4} +1.17448 q^{5} +2.47732 q^{6} +0.539926 q^{7} -1.00000 q^{8} +3.13710 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.47732 q^{3} +1.00000 q^{4} +1.17448 q^{5} +2.47732 q^{6} +0.539926 q^{7} -1.00000 q^{8} +3.13710 q^{9} -1.17448 q^{10} +1.00000 q^{11} -2.47732 q^{12} +3.77319 q^{13} -0.539926 q^{14} -2.90957 q^{15} +1.00000 q^{16} -5.84469 q^{17} -3.13710 q^{18} -0.884118 q^{19} +1.17448 q^{20} -1.33757 q^{21} -1.00000 q^{22} +5.41015 q^{23} +2.47732 q^{24} -3.62059 q^{25} -3.77319 q^{26} -0.339631 q^{27} +0.539926 q^{28} -1.87829 q^{29} +2.90957 q^{30} +1.14143 q^{31} -1.00000 q^{32} -2.47732 q^{33} +5.84469 q^{34} +0.634133 q^{35} +3.13710 q^{36} +2.52588 q^{37} +0.884118 q^{38} -9.34739 q^{39} -1.17448 q^{40} -1.15235 q^{41} +1.33757 q^{42} -10.8504 q^{43} +1.00000 q^{44} +3.68447 q^{45} -5.41015 q^{46} +0.607182 q^{47} -2.47732 q^{48} -6.70848 q^{49} +3.62059 q^{50} +14.4791 q^{51} +3.77319 q^{52} +2.28169 q^{53} +0.339631 q^{54} +1.17448 q^{55} -0.539926 q^{56} +2.19024 q^{57} +1.87829 q^{58} -7.45106 q^{59} -2.90957 q^{60} -8.34390 q^{61} -1.14143 q^{62} +1.69380 q^{63} +1.00000 q^{64} +4.43155 q^{65} +2.47732 q^{66} -14.3987 q^{67} -5.84469 q^{68} -13.4026 q^{69} -0.634133 q^{70} -6.18878 q^{71} -3.13710 q^{72} +12.6792 q^{73} -2.52588 q^{74} +8.96935 q^{75} -0.884118 q^{76} +0.539926 q^{77} +9.34739 q^{78} +15.3800 q^{79} +1.17448 q^{80} -8.56992 q^{81} +1.15235 q^{82} +13.5215 q^{83} -1.33757 q^{84} -6.86448 q^{85} +10.8504 q^{86} +4.65311 q^{87} -1.00000 q^{88} -4.22512 q^{89} -3.68447 q^{90} +2.03724 q^{91} +5.41015 q^{92} -2.82769 q^{93} -0.607182 q^{94} -1.03838 q^{95} +2.47732 q^{96} -14.4480 q^{97} +6.70848 q^{98} +3.13710 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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