LMFDB - Embedded newform 7942.2.a.bs.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 21 x^{10} + 59 x^{9} + 162 x^{8} - 408 x^{7} - 581 x^{6} + 1236 x^{5} + 972 x^{4} + \cdots + 81 $ x^12 - 3x^11 - 21x^10 + 59x^9 + 162x^8 - 408x^7 - 581x^6 + 1236x^5 + 972x^4 - 1596x^3 - 621x^2 + 648*x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.116160$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.116160 q^{3} +1.00000 q^{4} -0.498551 q^{5} +0.116160 q^{6} -2.29128 q^{7} -1.00000 q^{8} -2.98651 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.116160 q^{3} +1.00000 q^{4} -0.498551 q^{5} +0.116160 q^{6} -2.29128 q^{7} -1.00000 q^{8} -2.98651 q^{9} +0.498551 q^{10} +1.00000 q^{11} -0.116160 q^{12} +0.281152 q^{13} +2.29128 q^{14} +0.0579118 q^{15} +1.00000 q^{16} +1.65358 q^{17} +2.98651 q^{18} -0.498551 q^{20} +0.266155 q^{21} -1.00000 q^{22} +8.04296 q^{23} +0.116160 q^{24} -4.75145 q^{25} -0.281152 q^{26} +0.695394 q^{27} -2.29128 q^{28} -2.32572 q^{29} -0.0579118 q^{30} -3.69373 q^{31} -1.00000 q^{32} -0.116160 q^{33} -1.65358 q^{34} +1.14232 q^{35} -2.98651 q^{36} +5.88414 q^{37} -0.0326587 q^{39} +0.498551 q^{40} +0.535174 q^{41} -0.266155 q^{42} -5.13015 q^{43} +1.00000 q^{44} +1.48893 q^{45} -8.04296 q^{46} +10.6311 q^{47} -0.116160 q^{48} -1.75004 q^{49} +4.75145 q^{50} -0.192080 q^{51} +0.281152 q^{52} +8.71898 q^{53} -0.695394 q^{54} -0.498551 q^{55} +2.29128 q^{56} +2.32572 q^{58} -2.84215 q^{59} +0.0579118 q^{60} -12.4970 q^{61} +3.69373 q^{62} +6.84292 q^{63} +1.00000 q^{64} -0.140169 q^{65} +0.116160 q^{66} -11.7338 q^{67} +1.65358 q^{68} -0.934272 q^{69} -1.14232 q^{70} +5.50926 q^{71} +2.98651 q^{72} +2.38179 q^{73} -5.88414 q^{74} +0.551929 q^{75} -2.29128 q^{77} +0.0326587 q^{78} +14.1034 q^{79} -0.498551 q^{80} +8.87874 q^{81} -0.535174 q^{82} -15.6876 q^{83} +0.266155 q^{84} -0.824392 q^{85} +5.13015 q^{86} +0.270156 q^{87} -1.00000 q^{88} +6.41709 q^{89} -1.48893 q^{90} -0.644199 q^{91} +8.04296 q^{92} +0.429064 q^{93} -10.6311 q^{94} +0.116160 q^{96} +15.4833 q^{97} +1.75004 q^{98} -2.98651 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) $ 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * 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
$3$	−0.116160	−0.0670651	−0.0335325	−	0.999438i	$-0.510676\pi$
$3$	−0.116160	−0.0670651	−0.0335325	+	0.999438i	$0.510676\pi$
$4$	1.00000	0.500000
$5$	−0.498551	−0.222959	−0.111479	−	0.993767i	$-0.535559\pi$
$5$	−0.498551	−0.222959	−0.111479	+	0.993767i	$0.535559\pi$
$6$	0.116160	0.0474222
$7$	−2.29128	−0.866022	−0.433011	−	0.901389i	$-0.642549\pi$
$7$	−2.29128	−0.866022	−0.433011	+	0.901389i	$0.642549\pi$
$8$	−1.00000	−0.353553
$9$	−2.98651	−0.995502
$10$	0.498551	0.157656
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−0.116160	−0.0335325
$13$	0.281152	0.0779777	0.0389888	−	0.999240i	$-0.487586\pi$
$13$	0.281152	0.0779777	0.0389888	+	0.999240i	$0.487586\pi$
$14$	2.29128	0.612370
$15$	0.0579118	0.0149528
$16$	1.00000	0.250000
$17$	1.65358	0.401051	0.200526	−	0.979688i	$-0.435735\pi$
$17$	1.65358	0.401051	0.200526	+	0.979688i	$0.435735\pi$
$18$	2.98651	0.703926
$19$	0	0
$19$	0	0
$20$	−0.498551	−0.111479
$21$	0.266155	0.0580798
$22$	−1.00000	−0.213201
$23$	8.04296	1.67707	0.838537	−	0.544845i	$-0.183412\pi$
$23$	8.04296	1.67707	0.838537	+	0.544845i	$0.183412\pi$
$24$	0.116160	0.0237111
$25$	−4.75145	−0.950289
$26$	−0.281152	−0.0551385
$27$	0.695394	0.133829
$28$	−2.29128	−0.433011
$29$	−2.32572	−0.431875	−0.215937	−	0.976407i	$-0.569281\pi$
$29$	−2.32572	−0.431875	−0.215937	+	0.976407i	$0.569281\pi$
$30$	−0.0579118	−0.0105732
$31$	−3.69373	−0.663413	−0.331707	−	0.943383i	$-0.607624\pi$
$31$	−3.69373	−0.663413	−0.331707	+	0.943383i	$0.607624\pi$
$32$	−1.00000	−0.176777
$33$	−0.116160	−0.0202209
$34$	−1.65358	−0.283586
$35$	1.14232	0.193087
$36$	−2.98651	−0.497751
$37$	5.88414	0.967346	0.483673	−	0.875249i	$-0.339302\pi$
$37$	5.88414	0.967346	0.483673	+	0.875249i	$0.339302\pi$
$38$	0	0
$39$	−0.0326587	−0.00522958
$40$	0.498551	0.0788279
$41$	0.535174	0.0835802	0.0417901	−	0.999126i	$-0.486694\pi$
$41$	0.535174	0.0835802	0.0417901	+	0.999126i	$0.486694\pi$
$42$	−0.266155	−0.0410686
$43$	−5.13015	−0.782340	−0.391170	−	0.920318i	$-0.627930\pi$
$43$	−5.13015	−0.782340	−0.391170	+	0.920318i	$0.627930\pi$
$44$	1.00000	0.150756
$45$	1.48893	0.221956
$46$	−8.04296	−1.18587
$47$	10.6311	1.55070	0.775352	−	0.631529i	$-0.217572\pi$
$47$	10.6311	1.55070	0.775352	+	0.631529i	$0.217572\pi$
$48$	−0.116160	−0.0167663
$49$	−1.75004	−0.250006
$50$	4.75145	0.671956
$51$	−0.192080	−0.0268965
$52$	0.281152	0.0389888
$53$	8.71898	1.19764	0.598822	−	0.800882i	$-0.295636\pi$
$53$	8.71898	1.19764	0.598822	+	0.800882i	$0.295636\pi$
$54$	−0.695394	−0.0946311
$55$	−0.498551	−0.0672246
$56$	2.29128	0.306185
$57$	0	0
$58$	2.32572	0.305382
$59$	−2.84215	−0.370016	−0.185008	−	0.982737i	$-0.559231\pi$
$59$	−2.84215	−0.370016	−0.185008	+	0.982737i	$0.559231\pi$
$60$	0.0579118	0.00747638
$61$	−12.4970	−1.60008	−0.800039	−	0.599948i	$-0.795188\pi$
$61$	−12.4970	−1.60008	−0.800039	+	0.599948i	$0.795188\pi$
$62$	3.69373	0.469104
$63$	6.84292	0.862127
$64$	1.00000	0.125000
$65$	−0.140169	−0.0173858
$66$	0.116160	0.0142983
$67$	−11.7338	−1.43351	−0.716756	−	0.697324i	$-0.754374\pi$
$67$	−11.7338	−1.43351	−0.716756	+	0.697324i	$0.754374\pi$
$68$	1.65358	0.200526
$69$	−0.934272	−0.112473
$70$	−1.14232	−0.136533
$71$	5.50926	0.653829	0.326914	−	0.945054i	$-0.393991\pi$
$71$	5.50926	0.653829	0.326914	+	0.945054i	$0.393991\pi$
$72$	2.98651	0.351963
$73$	2.38179	0.278768	0.139384	−	0.990238i	$-0.455488\pi$
$73$	2.38179	0.278768	0.139384	+	0.990238i	$0.455488\pi$
$74$	−5.88414	−0.684017
$75$	0.551929	0.0637312
$76$	0	0
$77$	−2.29128	−0.261115
$78$	0.0326587	0.00369787
$79$	14.1034	1.58676	0.793379	−	0.608727i	$-0.208320\pi$
$79$	14.1034	1.58676	0.793379	+	0.608727i	$0.208320\pi$
$80$	−0.498551	−0.0557397
$81$	8.87874	0.986527
$82$	−0.535174	−0.0591001
$83$	−15.6876	−1.72194	−0.860971	−	0.508653i	$-0.830144\pi$
$83$	−15.6876	−1.72194	−0.860971	+	0.508653i	$0.830144\pi$
$84$	0.266155	0.0290399
$85$	−0.824392	−0.0894179
$86$	5.13015	0.553198
$87$	0.270156	0.0289637
$88$	−1.00000	−0.106600
$89$	6.41709	0.680210	0.340105	−	0.940387i	$-0.389537\pi$
$89$	6.41709	0.680210	0.340105	+	0.940387i	$0.389537\pi$
$90$	−1.48893	−0.156947
$91$	−0.644199	−0.0675304
$92$	8.04296	0.838537
$93$	0.429064	0.0444919
$94$	−10.6311	−1.09651
$95$	0	0
$96$	0.116160	0.0118555
$97$	15.4833	1.57209	0.786044	−	0.618170i	$-0.212126\pi$
$97$	15.4833	1.57209	0.786044	+	0.618170i	$0.212126\pi$
$98$	1.75004	0.176781
$99$	−2.98651	−0.300155
$100$	−4.75145	−0.475145
$101$	−0.380477	−0.0378588	−0.0189294	−	0.999821i	$-0.506026\pi$
$101$	−0.380477	−0.0378588	−0.0189294	+	0.999821i	$0.506026\pi$
$102$	0.192080	0.0190187
$103$	−6.42485	−0.633060	−0.316530	−	0.948583i	$-0.602518\pi$
$103$	−6.42485	−0.633060	−0.316530	+	0.948583i	$0.602518\pi$
$104$	−0.281152	−0.0275693
$105$	−0.132692	−0.0129494
$106$	−8.71898	−0.846862
$107$	−10.6754	−1.03203	−0.516014	−	0.856580i	$-0.672585\pi$
$107$	−10.6754	−1.03203	−0.516014	+	0.856580i	$0.672585\pi$
$108$	0.695394	0.0669143
$109$	6.06721	0.581133	0.290567	−	0.956855i	$-0.406156\pi$
$109$	6.06721	0.581133	0.290567	+	0.956855i	$0.406156\pi$
$110$	0.498551	0.0475350
$111$	−0.683502	−0.0648752
$112$	−2.29128	−0.216505
$113$	12.9988	1.22282	0.611411	−	0.791313i	$-0.290602\pi$
$113$	12.9988	1.22282	0.611411	+	0.791313i	$0.290602\pi$
$114$	0	0
$115$	−4.00983	−0.373918
$116$	−2.32572	−0.215937
$117$	−0.839664	−0.0776269
$118$	2.84215	0.261641
$119$	−3.78880	−0.347319
$120$	−0.0579118	−0.00528660
$121$	1.00000	0.0909091
$122$	12.4970	1.13143
$123$	−0.0621659	−0.00560531
$124$	−3.69373	−0.331707
$125$	4.86159	0.434834
$126$	−6.84292	−0.609616
$127$	17.5813	1.56009	0.780043	−	0.625726i	$-0.215197\pi$
$127$	17.5813	1.56009	0.780043	+	0.625726i	$0.215197\pi$
$128$	−1.00000	−0.0883883
$129$	0.595919	0.0524677
$130$	0.140169	0.0122936
$131$	5.13325	0.448494	0.224247	−	0.974532i	$-0.428008\pi$
$131$	5.13325	0.448494	0.224247	+	0.974532i	$0.428008\pi$
$132$	−0.116160	−0.0101104
$133$	0	0
$134$	11.7338	1.01365
$135$	−0.346689	−0.0298383
$136$	−1.65358	−0.141793
$137$	3.01949	0.257972	0.128986	−	0.991646i	$-0.458828\pi$
$137$	3.01949	0.257972	0.128986	+	0.991646i	$0.458828\pi$
$138$	0.934272	0.0795305
$139$	−2.94278	−0.249604	−0.124802	−	0.992182i	$-0.539829\pi$
$139$	−2.94278	−0.249604	−0.124802	+	0.992182i	$0.539829\pi$
$140$	1.14232	0.0965436
$141$	−1.23491	−0.103998
$142$	−5.50926	−0.462327
$143$	0.281152	0.0235112
$144$	−2.98651	−0.248876
$145$	1.15949	0.0962903
$146$	−2.38179	−0.197119
$147$	0.203285	0.0167667
$148$	5.88414	0.483673
$149$	2.60187	0.213153	0.106577	−	0.994304i	$-0.466011\pi$
$149$	2.60187	0.213153	0.106577	+	0.994304i	$0.466011\pi$
$150$	−0.551929	−0.0450648
$151$	15.7549	1.28212	0.641059	−	0.767492i	$-0.278495\pi$
$151$	15.7549	1.28212	0.641059	+	0.767492i	$0.278495\pi$
$152$	0	0
$153$	−4.93842	−0.399247
$154$	2.29128	0.184636
$155$	1.84151	0.147914
$156$	−0.0326587	−0.00261479
$157$	1.39782	0.111558	0.0557791	−	0.998443i	$-0.482236\pi$
$157$	1.39782	0.111558	0.0557791	+	0.998443i	$0.482236\pi$
$158$	−14.1034	−1.12201
$159$	−1.01280	−0.0803201
$160$	0.498551	0.0394139
$161$	−18.4287	−1.45238
$162$	−8.87874	−0.697580
$163$	−16.7244	−1.30995	−0.654977	−	0.755649i	$-0.727322\pi$
$163$	−16.7244	−1.30995	−0.654977	+	0.755649i	$0.727322\pi$
$164$	0.535174	0.0417901
$165$	0.0579118	0.00450843
$166$	15.6876	1.21760
$167$	−9.79562	−0.758008	−0.379004	−	0.925395i	$-0.623733\pi$
$167$	−9.79562	−0.758008	−0.379004	+	0.925395i	$0.623733\pi$
$168$	−0.266155	−0.0205343
$169$	−12.9210	−0.993919
$170$	0.824392	0.0632280
$171$	0	0
$172$	−5.13015	−0.391170
$173$	13.5070	1.02692	0.513460	−	0.858113i	$-0.328363\pi$
$173$	13.5070	1.02692	0.513460	+	0.858113i	$0.328363\pi$
$174$	−0.270156	−0.0204805
$175$	10.8869	0.822971
$176$	1.00000	0.0753778
$177$	0.330144	0.0248151
$178$	−6.41709	−0.480981
$179$	−17.7695	−1.32816	−0.664079	−	0.747662i	$-0.731176\pi$
$179$	−17.7695	−1.32816	−0.664079	+	0.747662i	$0.731176\pi$
$180$	1.48893	0.110978
$181$	−11.3679	−0.844970	−0.422485	−	0.906370i	$-0.638842\pi$
$181$	−11.3679	−0.844970	−0.422485	+	0.906370i	$0.638842\pi$
$182$	0.644199	0.0477512
$183$	1.45165	0.107309
$184$	−8.04296	−0.592935
$185$	−2.93354	−0.215678
$186$	−0.429064	−0.0314605
$187$	1.65358	0.120921
$188$	10.6311	0.775352
$189$	−1.59334	−0.115898
$190$	0	0
$191$	−8.81314	−0.637697	−0.318848	−	0.947806i	$-0.603296\pi$
$191$	−8.81314	−0.637697	−0.318848	+	0.947806i	$0.603296\pi$
$192$	−0.116160	−0.00838314
$193$	1.62372	0.116878	0.0584388	−	0.998291i	$-0.481388\pi$
$193$	1.62372	0.116878	0.0584388	+	0.998291i	$0.481388\pi$
$194$	−15.4833	−1.11163
$195$	0.0162820	0.00116598
$196$	−1.75004	−0.125003
$197$	−20.2131	−1.44012	−0.720062	−	0.693910i	$-0.755887\pi$
$197$	−20.2131	−1.44012	−0.720062	+	0.693910i	$0.755887\pi$
$198$	2.98651	0.212242
$199$	−17.2777	−1.22478	−0.612392	−	0.790554i	$-0.709793\pi$
$199$	−17.2777	−1.22478	−0.612392	+	0.790554i	$0.709793\pi$
$200$	4.75145	0.335978
$201$	1.36300	0.0961387
$202$	0.380477	0.0267702
$203$	5.32887	0.374013
$204$	−0.192080	−0.0134483
$205$	−0.266812	−0.0186349
$206$	6.42485	0.447641
$207$	−24.0204	−1.66953
$208$	0.281152	0.0194944
$209$	0	0
$210$	0.132692	0.00915662
$211$	7.33059	0.504659	0.252329	−	0.967641i	$-0.418803\pi$
$211$	7.33059	0.504659	0.252329	+	0.967641i	$0.418803\pi$
$212$	8.71898	0.598822
$213$	−0.639956	−0.0438491
$214$	10.6754	0.729755
$215$	2.55764	0.174430
$216$	−0.695394	−0.0473155
$217$	8.46336	0.574530
$218$	−6.06721	−0.410923
$219$	−0.276670	−0.0186956
$220$	−0.498551	−0.0336123
$221$	0.464907	0.0312730
$222$	0.683502	0.0458737
$223$	4.52822	0.303232	0.151616	−	0.988439i	$-0.451552\pi$
$223$	4.52822	0.303232	0.151616	+	0.988439i	$0.451552\pi$
$224$	2.29128	0.153092
$225$	14.1902	0.946015
$226$	−12.9988	−0.864666
$227$	−23.3452	−1.54947	−0.774737	−	0.632283i	$-0.782118\pi$
$227$	−23.3452	−1.54947	−0.774737	+	0.632283i	$0.782118\pi$
$228$	0	0
$229$	−17.7244	−1.17126	−0.585630	−	0.810579i	$-0.699153\pi$
$229$	−17.7244	−1.17126	−0.585630	+	0.810579i	$0.699153\pi$
$230$	4.00983	0.264400
$231$	0.266155	0.0175117
$232$	2.32572	0.152691
$233$	−16.4045	−1.07469	−0.537347	−	0.843361i	$-0.680573\pi$
$233$	−16.4045	−1.07469	−0.537347	+	0.843361i	$0.680573\pi$
$234$	0.839664	0.0548905
$235$	−5.30015	−0.345743
$236$	−2.84215	−0.185008
$237$	−1.63826	−0.106416
$238$	3.78880	0.245592
$239$	18.2990	1.18367	0.591833	−	0.806060i	$-0.298404\pi$
$239$	18.2990	1.18367	0.591833	+	0.806060i	$0.298404\pi$
$240$	0.0579118	0.00373819
$241$	6.06680	0.390797	0.195399	−	0.980724i	$-0.437400\pi$
$241$	6.06680	0.390797	0.195399	+	0.980724i	$0.437400\pi$
$242$	−1.00000	−0.0642824
$243$	−3.11754	−0.199990
$244$	−12.4970	−0.800039
$245$	0.872486	0.0557411
$246$	0.0621659	0.00396355
$247$	0	0
$248$	3.69373	0.234552
$249$	1.82228	0.115482
$250$	−4.86159	−0.307474
$251$	−17.0918	−1.07882	−0.539411	−	0.842043i	$-0.681353\pi$
$251$	−17.0918	−1.07882	−0.539411	+	0.842043i	$0.681353\pi$
$252$	6.84292	0.431063
$253$	8.04296	0.505657
$254$	−17.5813	−1.10315
$255$	0.0957615	0.00599682
$256$	1.00000	0.0625000
$257$	−24.9996	−1.55943	−0.779716	−	0.626133i	$-0.784637\pi$
$257$	−24.9996	−1.55943	−0.779716	+	0.626133i	$0.784637\pi$
$258$	−0.595919	−0.0371003
$259$	−13.4822	−0.837743
$260$	−0.140169	−0.00869291
$261$	6.94577	0.429932
$262$	−5.13325	−0.317133
$263$	4.06122	0.250425	0.125213	−	0.992130i	$-0.460039\pi$
$263$	4.06122	0.250425	0.125213	+	0.992130i	$0.460039\pi$
$264$	0.116160	0.00714916
$265$	−4.34686	−0.267025
$266$	0	0
$267$	−0.745410	−0.0456183
$268$	−11.7338	−0.716756
$269$	0.576207	0.0351320	0.0175660	−	0.999846i	$-0.494408\pi$
$269$	0.576207	0.0351320	0.0175660	+	0.999846i	$0.494408\pi$
$270$	0.346689	0.0210988
$271$	−26.7182	−1.62301	−0.811507	−	0.584343i	$-0.801352\pi$
$271$	−26.7182	−1.62301	−0.811507	+	0.584343i	$0.801352\pi$
$272$	1.65358	0.100263
$273$	0.0748302	0.00452893
$274$	−3.01949	−0.182414
$275$	−4.75145	−0.286523
$276$	−0.934272	−0.0562365
$277$	−3.12741	−0.187908	−0.0939538	−	0.995577i	$-0.529951\pi$
$277$	−3.12741	−0.187908	−0.0939538	+	0.995577i	$0.529951\pi$
$278$	2.94278	0.176496
$279$	11.0313	0.660429
$280$	−1.14232	−0.0682666
$281$	−24.8620	−1.48314	−0.741572	−	0.670874i	$-0.765919\pi$
$281$	−24.8620	−1.48314	−0.741572	+	0.670874i	$0.765919\pi$
$282$	1.23491	0.0735378
$283$	−1.16115	−0.0690235	−0.0345117	−	0.999404i	$-0.510988\pi$
$283$	−1.16115	−0.0690235	−0.0345117	+	0.999404i	$0.510988\pi$
$284$	5.50926	0.326914
$285$	0	0
$286$	−0.281152	−0.0166249
$287$	−1.22623	−0.0723822
$288$	2.98651	0.175982
$289$	−14.2657	−0.839158
$290$	−1.15949	−0.0680875
$291$	−1.79854	−0.105432
$292$	2.38179	0.139384
$293$	−26.8022	−1.56580	−0.782901	−	0.622146i	$-0.786261\pi$
$293$	−26.8022	−1.56580	−0.782901	+	0.622146i	$0.786261\pi$
$294$	−0.203285	−0.0118558
$295$	1.41695	0.0824983
$296$	−5.88414	−0.342009
$297$	0.695394	0.0403508
$298$	−2.60187	−0.150722
$299$	2.26130	0.130774
$300$	0.551929	0.0318656
$301$	11.7546	0.677524
$302$	−15.7549	−0.906594
$303$	0.0441962	0.00253901
$304$	0	0
$305$	6.23040	0.356751
$306$	4.93842	0.282310
$307$	30.4852	1.73988	0.869941	−	0.493155i	$-0.164157\pi$
$307$	30.4852	1.73988	0.869941	+	0.493155i	$0.164157\pi$
$308$	−2.29128	−0.130558
$309$	0.746312	0.0424562
$310$	−1.84151	−0.104591
$311$	−11.0434	−0.626214	−0.313107	−	0.949718i	$-0.601370\pi$
$311$	−11.0434	−0.626214	−0.313107	+	0.949718i	$0.601370\pi$
$312$	0.0326587	0.00184894
$313$	10.4897	0.592914	0.296457	−	0.955046i	$-0.404195\pi$
$313$	10.4897	0.592914	0.296457	+	0.955046i	$0.404195\pi$
$314$	−1.39782	−0.0788836
$315$	−3.41154	−0.192219
$316$	14.1034	0.793379
$317$	−10.5366	−0.591795	−0.295897	−	0.955220i	$-0.595619\pi$
$317$	−10.5366	−0.591795	−0.295897	+	0.955220i	$0.595619\pi$
$318$	1.01280	0.0567949
$319$	−2.32572	−0.130215
$320$	−0.498551	−0.0278699
$321$	1.24006	0.0692131
$322$	18.4287	1.02699
$323$	0	0
$324$	8.87874	0.493264
$325$	−1.33588	−0.0741013
$326$	16.7244	0.926277
$327$	−0.704768	−0.0389738
$328$	−0.535174	−0.0295500
$329$	−24.3588	−1.34294
$330$	−0.0579118	−0.00318794
$331$	6.07028	0.333653	0.166826	−	0.985986i	$-0.446648\pi$
$331$	6.07028	0.333653	0.166826	+	0.985986i	$0.446648\pi$
$332$	−15.6876	−0.860971
$333$	−17.5730	−0.962996
$334$	9.79562	0.535992
$335$	5.84990	0.319614
$336$	0.266155	0.0145200
$337$	−6.48458	−0.353238	−0.176619	−	0.984279i	$-0.556516\pi$
$337$	−6.48458	−0.353238	−0.176619	+	0.984279i	$0.556516\pi$
$338$	12.9210	0.702807
$339$	−1.50994	−0.0820087
$340$	−0.824392	−0.0447089
$341$	−3.69373	−0.200027
$342$	0	0
$343$	20.0488	1.08253
$344$	5.13015	0.276599
$345$	0.465782	0.0250769
$346$	−13.5070	−0.726142
$347$	19.2179	1.03167	0.515837	−	0.856687i	$-0.327481\pi$
$347$	19.2179	1.03167	0.515837	+	0.856687i	$0.327481\pi$
$348$	0.270156	0.0144819
$349$	29.2730	1.56695	0.783474	−	0.621425i	$-0.213446\pi$
$349$	29.2730	1.56695	0.783474	+	0.621425i	$0.213446\pi$
$350$	−10.8869	−0.581929
$351$	0.195512	0.0104356
$352$	−1.00000	−0.0533002
$353$	−4.70031	−0.250172	−0.125086	−	0.992146i	$-0.539921\pi$
$353$	−4.70031	−0.250172	−0.125086	+	0.992146i	$0.539921\pi$
$354$	−0.330144	−0.0175470
$355$	−2.74665	−0.145777
$356$	6.41709	0.340105
$357$	0.440108	0.0232930
$358$	17.7695	0.939149
$359$	−28.4846	−1.50336	−0.751680	−	0.659529i	$-0.770756\pi$
$359$	−28.4846	−1.50336	−0.751680	+	0.659529i	$0.770756\pi$
$360$	−1.48893	−0.0784733
$361$	0	0
$362$	11.3679	0.597484
$363$	−0.116160	−0.00609683
$364$	−0.644199	−0.0337652
$365$	−1.18745	−0.0621538
$366$	−1.45165	−0.0758792
$367$	1.29074	0.0673763	0.0336881	−	0.999432i	$-0.489275\pi$
$367$	1.29074	0.0673763	0.0336881	+	0.999432i	$0.489275\pi$
$368$	8.04296	0.419268
$369$	−1.59830	−0.0832042
$370$	2.93354	0.152508
$371$	−19.9776	−1.03719
$372$	0.429064	0.0222459
$373$	−8.35563	−0.432638	−0.216319	−	0.976323i	$-0.569405\pi$
$373$	−8.35563	−0.432638	−0.216319	+	0.976323i	$0.569405\pi$
$374$	−1.65358	−0.0855044
$375$	−0.564724	−0.0291622
$376$	−10.6311	−0.548257
$377$	−0.653881	−0.0336766
$378$	1.59334	0.0819526
$379$	11.2112	0.575879	0.287940	−	0.957649i	$-0.407030\pi$
$379$	11.2112	0.575879	0.287940	+	0.957649i	$0.407030\pi$
$380$	0	0
$381$	−2.04224	−0.104627
$382$	8.81314	0.450920
$383$	23.5595	1.20383	0.601917	−	0.798559i	$-0.294404\pi$
$383$	23.5595	1.20383	0.601917	+	0.798559i	$0.294404\pi$
$384$	0.116160	0.00592777
$385$	1.14232	0.0582180
$386$	−1.62372	−0.0826450
$387$	15.3212	0.778821
$388$	15.4833	0.786044
$389$	32.3109	1.63823	0.819113	−	0.573632i	$-0.194466\pi$
$389$	32.3109	1.63823	0.819113	+	0.573632i	$0.194466\pi$
$390$	−0.0162820	−0.000824473 0
$391$	13.2996	0.672592
$392$	1.75004	0.0883905
$393$	−0.596279	−0.0300783
$394$	20.2131	1.01832
$395$	−7.03128	−0.353782
$396$	−2.98651	−0.150078
$397$	−21.6587	−1.08702	−0.543511	−	0.839402i	$-0.682905\pi$
$397$	−21.6587	−1.08702	−0.543511	+	0.839402i	$0.682905\pi$
$398$	17.2777	0.866053
$399$	0	0
$400$	−4.75145	−0.237572
$401$	15.2032	0.759210	0.379605	−	0.925149i	$-0.376060\pi$
$401$	15.2032	0.759210	0.379605	+	0.925149i	$0.376060\pi$
$402$	−1.36300	−0.0679803
$403$	−1.03850	−0.0517314
$404$	−0.380477	−0.0189294
$405$	−4.42651	−0.219955
$406$	−5.32887	−0.264467
$407$	5.88414	0.291666
$408$	0.192080	0.00950936
$409$	−35.8741	−1.77386	−0.886931	−	0.461902i	$-0.847167\pi$
$409$	−35.8741	−1.77386	−0.886931	+	0.461902i	$0.847167\pi$
$410$	0.266812	0.0131769
$411$	−0.350744	−0.0173009
$412$	−6.42485	−0.316530
$413$	6.51215	0.320442
$414$	24.0204	1.18054
$415$	7.82109	0.383922
$416$	−0.281152	−0.0137846
$417$	0.341834	0.0167397
$418$	0	0
$419$	5.02288	0.245384	0.122692	−	0.992445i	$-0.460847\pi$
$419$	5.02288	0.245384	0.122692	+	0.992445i	$0.460847\pi$
$420$	−0.132692	−0.00647471
$421$	5.74864	0.280172	0.140086	−	0.990139i	$-0.455262\pi$
$421$	5.74864	0.280172	0.140086	+	0.990139i	$0.455262\pi$
$422$	−7.33059	−0.356848
$423$	−31.7498	−1.54373
$424$	−8.71898	−0.423431
$425$	−7.85688	−0.381115
$426$	0.639956	0.0310060
$427$	28.6341	1.38570
$428$	−10.6754	−0.516014
$429$	−0.0326587	−0.00157678
$430$	−2.55764	−0.123340
$431$	−25.8934	−1.24724	−0.623622	−	0.781726i	$-0.714339\pi$
$431$	−25.8934	−1.24724	−0.623622	+	0.781726i	$0.714339\pi$
$432$	0.695394	0.0334571
$433$	9.54377	0.458644	0.229322	−	0.973351i	$-0.426349\pi$
$433$	9.54377	0.458644	0.229322	+	0.973351i	$0.426349\pi$
$434$	−8.46336	−0.406254
$435$	−0.134686	−0.00645772
$436$	6.06721	0.290567
$437$	0	0
$438$	0.276670	0.0132198
$439$	0.635179	0.0303154	0.0151577	−	0.999885i	$-0.495175\pi$
$439$	0.635179	0.0303154	0.0151577	+	0.999885i	$0.495175\pi$
$440$	0.498551	0.0237675
$441$	5.22652	0.248882
$442$	−0.464907	−0.0221134
$443$	17.6440	0.838290	0.419145	−	0.907919i	$-0.362330\pi$
$443$	17.6440	0.838290	0.419145	+	0.907919i	$0.362330\pi$
$444$	−0.683502	−0.0324376
$445$	−3.19925	−0.151659
$446$	−4.52822	−0.214418
$447$	−0.302233	−0.0142951
$448$	−2.29128	−0.108253
$449$	−20.9736	−0.989808	−0.494904	−	0.868948i	$-0.664797\pi$
$449$	−20.9736	−0.989808	−0.494904	+	0.868948i	$0.664797\pi$
$450$	−14.1902	−0.668934
$451$	0.535174	0.0252004
$452$	12.9988	0.611411
$453$	−1.83010	−0.0859854
$454$	23.3452	1.09564
$455$	0.321166	0.0150565
$456$	0	0
$457$	−22.9647	−1.07424	−0.537121	−	0.843505i	$-0.680488\pi$
$457$	−22.9647	−1.07424	−0.537121	+	0.843505i	$0.680488\pi$
$458$	17.7244	0.828206
$459$	1.14989	0.0536721
$460$	−4.00983	−0.186959
$461$	−25.6578	−1.19500	−0.597502	−	0.801867i	$-0.703840\pi$
$461$	−25.6578	−1.19500	−0.597502	+	0.801867i	$0.703840\pi$
$462$	−0.266155	−0.0123827
$463$	14.4251	0.670393	0.335197	−	0.942148i	$-0.391197\pi$
$463$	14.4251	0.670393	0.335197	+	0.942148i	$0.391197\pi$
$464$	−2.32572	−0.107969
$465$	−0.213910	−0.00991986
$466$	16.4045	0.759923
$467$	−6.26939	−0.290113	−0.145056	−	0.989423i	$-0.546336\pi$
$467$	−6.26939	−0.290113	−0.145056	+	0.989423i	$0.546336\pi$
$468$	−0.839664	−0.0388135
$469$	26.8854	1.24145
$470$	5.30015	0.244477
$471$	−0.162371	−0.00748167
$472$	2.84215	0.130820
$473$	−5.13015	−0.235884
$474$	1.63826	0.0752476
$475$	0	0
$476$	−3.78880	−0.173659
$477$	−26.0393	−1.19226
$478$	−18.2990	−0.836979
$479$	9.22842	0.421657	0.210829	−	0.977523i	$-0.432384\pi$
$479$	9.22842	0.421657	0.210829	+	0.977523i	$0.432384\pi$
$480$	−0.0579118	−0.00264330
$481$	1.65434	0.0754314
$482$	−6.06680	−0.276335
$483$	2.14068	0.0974041
$484$	1.00000	0.0454545
$485$	−7.71920	−0.350511
$486$	3.11754	0.141414
$487$	−34.5755	−1.56676	−0.783382	−	0.621541i	$-0.786507\pi$
$487$	−34.5755	−1.56676	−0.783382	+	0.621541i	$0.786507\pi$
$488$	12.4970	0.565713
$489$	1.94270	0.0878521
$490$	−0.872486	−0.0394149
$491$	−19.5615	−0.882800	−0.441400	−	0.897311i	$-0.645518\pi$
$491$	−19.5615	−0.882800	−0.441400	+	0.897311i	$0.645518\pi$
$492$	−0.0621659	−0.00280266
$493$	−3.84575	−0.173204
$494$	0	0
$495$	1.48893	0.0669223
$496$	−3.69373	−0.165853
$497$	−12.6232	−0.566230
$498$	−1.82228	−0.0816583
$499$	7.82554	0.350319	0.175160	−	0.984540i	$-0.443956\pi$
$499$	7.82554	0.350319	0.175160	+	0.984540i	$0.443956\pi$
$500$	4.86159	0.217417
$501$	1.13786	0.0508359
$502$	17.0918	0.762842
$503$	−11.2496	−0.501595	−0.250798	−	0.968040i	$-0.580693\pi$
$503$	−11.2496	−0.501595	−0.250798	+	0.968040i	$0.580693\pi$
$504$	−6.84292	−0.304808
$505$	0.189687	0.00844096
$506$	−8.04296	−0.357553
$507$	1.50090	0.0666573
$508$	17.5813	0.780043
$509$	15.2535	0.676101	0.338051	−	0.941128i	$-0.390233\pi$
$509$	15.2535	0.676101	0.338051	+	0.941128i	$0.390233\pi$
$510$	−0.0957615	−0.00424039
$511$	−5.45735	−0.241419
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	24.9996	1.10269
$515$	3.20312	0.141146
$516$	0.595919	0.0262339
$517$	10.6311	0.467555
$518$	13.4822	0.592374
$519$	−1.56898	−0.0688705
$520$	0.140169	0.00614681
$521$	−11.6055	−0.508446	−0.254223	−	0.967146i	$-0.581820\pi$
$521$	−11.6055	−0.508446	−0.254223	+	0.967146i	$0.581820\pi$
$522$	−6.94577	−0.304008
$523$	−22.2527	−0.973043	−0.486521	−	0.873669i	$-0.661734\pi$
$523$	−22.2527	−0.973043	−0.486521	+	0.873669i	$0.661734\pi$
$524$	5.13325	0.224247
$525$	−1.26462	−0.0551927
$526$	−4.06122	−0.177077
$527$	−6.10786	−0.266063
$528$	−0.116160	−0.00505522
$529$	41.6892	1.81257
$530$	4.34686	0.188815
$531$	8.48809	0.368352
$532$	0	0
$533$	0.150466	0.00651739
$534$	0.745410	0.0322570
$535$	5.32223	0.230100
$536$	11.7338	0.506823
$537$	2.06411	0.0890730
$538$	−0.576207	−0.0248421
$539$	−1.75004	−0.0753797
$540$	−0.346689	−0.0149191
$541$	−19.8053	−0.851495	−0.425747	−	0.904842i	$-0.639989\pi$
$541$	−19.8053	−0.851495	−0.425747	+	0.904842i	$0.639989\pi$
$542$	26.7182	1.14764
$543$	1.32050	0.0566680
$544$	−1.65358	−0.0708965
$545$	−3.02482	−0.129569
$546$	−0.0748302	−0.00320244
$547$	−6.19583	−0.264914	−0.132457	−	0.991189i	$-0.542287\pi$
$547$	−6.19583	−0.264914	−0.132457	+	0.991189i	$0.542287\pi$
$548$	3.01949	0.128986
$549$	37.3224	1.59288
$550$	4.75145	0.202602
$551$	0	0
$552$	0.934272	0.0397652
$553$	−32.3149	−1.37417
$554$	3.12741	0.132871
$555$	0.340761	0.0144645
$556$	−2.94278	−0.124802
$557$	−10.4271	−0.441810	−0.220905	−	0.975295i	$-0.570901\pi$
$557$	−10.4271	−0.441810	−0.220905	+	0.975295i	$0.570901\pi$
$558$	−11.0313	−0.466994
$559$	−1.44235	−0.0610051
$560$	1.14232	0.0482718
$561$	−0.192080	−0.00810961
$562$	24.8620	1.04874
$563$	−4.62498	−0.194920	−0.0974598	−	0.995239i	$-0.531072\pi$
$563$	−4.62498	−0.194920	−0.0974598	+	0.995239i	$0.531072\pi$
$564$	−1.23491	−0.0519991
$565$	−6.48055	−0.272639
$566$	1.16115	0.0488070
$567$	−20.3437	−0.854354
$568$	−5.50926	−0.231163
$569$	−6.32419	−0.265124	−0.132562	−	0.991175i	$-0.542320\pi$
$569$	−6.32419	−0.265124	−0.132562	+	0.991175i	$0.542320\pi$
$570$	0	0
$571$	1.48702	0.0622299	0.0311150	−	0.999516i	$-0.490094\pi$
$571$	1.48702	0.0622299	0.0311150	+	0.999516i	$0.490094\pi$
$572$	0.281152	0.0117556
$573$	1.02374	0.0427672
$574$	1.22623	0.0511820
$575$	−38.2157	−1.59370
$576$	−2.98651	−0.124438
$577$	−39.2241	−1.63292	−0.816461	−	0.577401i	$-0.804067\pi$
$577$	−39.2241	−1.63292	−0.816461	+	0.577401i	$0.804067\pi$
$578$	14.2657	0.593374
$579$	−0.188611	−0.00783841
$580$	1.15949	0.0481452
$581$	35.9448	1.49124
$582$	1.79854	0.0745519
$583$	8.71898	0.361103
$584$	−2.38179	−0.0985594
$585$	0.418615	0.0173076
$586$	26.8022	1.10719
$587$	−30.0482	−1.24022	−0.620112	−	0.784513i	$-0.712913\pi$
$587$	−30.0482	−1.24022	−0.620112	+	0.784513i	$0.712913\pi$
$588$	0.203285	0.00838334
$589$	0	0
$590$	−1.41695	−0.0583351
$591$	2.34796	0.0965821
$592$	5.88414	0.241837
$593$	−31.2053	−1.28145	−0.640723	−	0.767772i	$-0.721365\pi$
$593$	−31.2053	−1.28145	−0.640723	+	0.767772i	$0.721365\pi$
$594$	−0.695394	−0.0285323
$595$	1.88891	0.0774378
$596$	2.60187	0.106577
$597$	2.00698	0.0821402
$598$	−2.26130	−0.0924714
$599$	28.7348	1.17407	0.587037	−	0.809560i	$-0.300294\pi$
$599$	28.7348	1.17407	0.587037	+	0.809560i	$0.300294\pi$
$600$	−0.551929	−0.0225324
$601$	14.2810	0.582535	0.291267	−	0.956642i	$-0.405923\pi$
$601$	14.2810	0.582535	0.291267	+	0.956642i	$0.405923\pi$
$602$	−11.7546	−0.479082
$603$	35.0431	1.42707
$604$	15.7549	0.641059
$605$	−0.498551	−0.0202690
$606$	−0.0441962	−0.00179535
$607$	−10.4197	−0.422924	−0.211462	−	0.977386i	$-0.567822\pi$
$607$	−10.4197	−0.422924	−0.211462	+	0.977386i	$0.567822\pi$
$608$	0	0
$609$	−0.619002	−0.0250832
$610$	−6.23040	−0.252261
$611$	2.98896	0.120920
$612$	−4.93842	−0.199624
$613$	−24.6139	−0.994146	−0.497073	−	0.867709i	$-0.665592\pi$
$613$	−24.6139	−0.994146	−0.497073	+	0.867709i	$0.665592\pi$
$614$	−30.4852	−1.23028
$615$	0.0309929	0.00124975
$616$	2.29128	0.0923182
$617$	32.5839	1.31178	0.655888	−	0.754858i	$-0.272294\pi$
$617$	32.5839	1.31178	0.655888	+	0.754858i	$0.272294\pi$
$618$	−0.746312	−0.0300211
$619$	−13.0992	−0.526503	−0.263252	−	0.964727i	$-0.584795\pi$
$619$	−13.0992	−0.526503	−0.263252	+	0.964727i	$0.584795\pi$
$620$	1.84151	0.0739569
$621$	5.59302	0.224440
$622$	11.0434	0.442800
$623$	−14.7033	−0.589077
$624$	−0.0326587	−0.00130739
$625$	21.3335	0.853339
$626$	−10.4897	−0.419254
$627$	0	0
$628$	1.39782	0.0557791
$629$	9.72987	0.387955
$630$	3.41154	0.135919
$631$	15.0145	0.597719	0.298860	−	0.954297i	$-0.403394\pi$
$631$	15.0145	0.597719	0.298860	+	0.954297i	$0.403394\pi$
$632$	−14.1034	−0.561004
$633$	−0.851523	−0.0338450
$634$	10.5366	0.418462
$635$	−8.76516	−0.347835
$636$	−1.01280	−0.0401601
$637$	−0.492029	−0.0194949
$638$	2.32572	0.0920760
$639$	−16.4534	−0.650888
$640$	0.498551	0.0197070
$641$	−10.5045	−0.414903	−0.207452	−	0.978245i	$-0.566517\pi$
$641$	−10.5045	−0.414903	−0.207452	+	0.978245i	$0.566517\pi$
$642$	−1.24006	−0.0489411
$643$	42.9906	1.69538	0.847691	−	0.530490i	$-0.177992\pi$
$643$	42.9906	1.69538	0.847691	+	0.530490i	$0.177992\pi$
$644$	−18.4287	−0.726191
$645$	−0.297096	−0.0116981
$646$	0	0
$647$	−0.291739	−0.0114694	−0.00573472	−	0.999984i	$-0.501825\pi$
$647$	−0.291739	−0.0114694	−0.00573472	+	0.999984i	$0.501825\pi$
$648$	−8.87874	−0.348790
$649$	−2.84215	−0.111564
$650$	1.33588	0.0523976
$651$	−0.983105	−0.0385309
$652$	−16.7244	−0.654977
$653$	−16.7418	−0.655158	−0.327579	−	0.944824i	$-0.606233\pi$
$653$	−16.7418	−0.655158	−0.327579	+	0.944824i	$0.606233\pi$
$654$	0.704768	0.0275586
$655$	−2.55919	−0.0999957
$656$	0.535174	0.0208950
$657$	−7.11325	−0.277514
$658$	24.3588	0.949605
$659$	−23.3216	−0.908480	−0.454240	−	0.890879i	$-0.650089\pi$
$659$	−23.3216	−0.908480	−0.454240	+	0.890879i	$0.650089\pi$
$660$	0.0579118	0.00225421
$661$	−41.7610	−1.62431	−0.812157	−	0.583438i	$-0.801707\pi$
$661$	−41.7610	−1.62431	−0.812157	+	0.583438i	$0.801707\pi$
$662$	−6.07028	−0.235928
$663$	−0.0540037	−0.00209733
$664$	15.6876	0.608799
$665$	0	0
$666$	17.5730	0.680941
$667$	−18.7057	−0.724286
$668$	−9.79562	−0.379004
$669$	−0.525999	−0.0203363
$670$	−5.84990	−0.226001
$671$	−12.4970	−0.482441
$672$	−0.266155	−0.0102672
$673$	−14.5308	−0.560121	−0.280060	−	0.959982i	$-0.590355\pi$
$673$	−14.5308	−0.560121	−0.280060	+	0.959982i	$0.590355\pi$
$674$	6.48458	0.249777
$675$	−3.30413	−0.127176
$676$	−12.9210	−0.496960
$677$	−10.5860	−0.406853	−0.203426	−	0.979090i	$-0.565208\pi$
$677$	−10.5860	−0.406853	−0.203426	+	0.979090i	$0.565208\pi$
$678$	1.50994	0.0579889
$679$	−35.4765	−1.36146
$680$	0.824392	0.0316140
$681$	2.71178	0.103916
$682$	3.69373	0.141440
$683$	19.6157	0.750575	0.375288	−	0.926908i	$-0.377544\pi$
$683$	19.6157	0.750575	0.375288	+	0.926908i	$0.377544\pi$
$684$	0	0
$685$	−1.50537	−0.0575172
$686$	−20.0488	−0.765466
$687$	2.05887	0.0785506
$688$	−5.13015	−0.195585
$689$	2.45136	0.0933895
$690$	−0.465782	−0.0177320
$691$	12.8441	0.488613	0.244307	−	0.969698i	$-0.421440\pi$
$691$	12.8441	0.488613	0.244307	+	0.969698i	$0.421440\pi$
$692$	13.5070	0.513460
$693$	6.84292	0.259941
$694$	−19.2179	−0.729503
$695$	1.46713	0.0556513
$696$	−0.270156	−0.0102402
$697$	0.884951	0.0335199
$698$	−29.2730	−1.10800
$699$	1.90555	0.0720744
$700$	10.8869	0.411486
$701$	27.9107	1.05417	0.527087	−	0.849811i	$-0.323284\pi$
$701$	27.9107	1.05417	0.527087	+	0.849811i	$0.323284\pi$
$702$	−0.195512	−0.00737911
$703$	0	0
$704$	1.00000	0.0376889
$705$	0.615666	0.0231873
$706$	4.70031	0.176898
$707$	0.871778	0.0327866
$708$	0.330144	0.0124076
$709$	37.0592	1.39179	0.695894	−	0.718145i	$-0.255008\pi$
$709$	37.0592	1.39179	0.695894	+	0.718145i	$0.255008\pi$
$710$	2.74665	0.103080
$711$	−42.1200	−1.57962
$712$	−6.41709	−0.240491
$713$	−29.7085	−1.11259
$714$	−0.440108	−0.0164706
$715$	−0.140169	−0.00524202
$716$	−17.7695	−0.664079
$717$	−2.12562	−0.0793827
$718$	28.4846	1.06304
$719$	34.5573	1.28877	0.644385	−	0.764701i	$-0.277113\pi$
$719$	34.5573	1.28877	0.644385	+	0.764701i	$0.277113\pi$
$720$	1.48893	0.0554890
$721$	14.7211	0.548243
$722$	0	0
$723$	−0.704721	−0.0262089
$724$	−11.3679	−0.422485
$725$	11.0505	0.410406
$726$	0.116160	0.00431111
$727$	−12.5155	−0.464174	−0.232087	−	0.972695i	$-0.574555\pi$
$727$	−12.5155	−0.464174	−0.232087	+	0.972695i	$0.574555\pi$
$728$	0.644199	0.0238756
$729$	−26.2741	−0.973115
$730$	1.18745	0.0439494
$731$	−8.48309	−0.313758
$732$	1.45165	0.0536547
$733$	14.8661	0.549091	0.274546	−	0.961574i	$-0.411473\pi$
$733$	14.8661	0.549091	0.274546	+	0.961574i	$0.411473\pi$
$734$	−1.29074	−0.0476422
$735$	−0.101348	−0.00373828
$736$	−8.04296	−0.296467
$737$	−11.7338	−0.432220
$738$	1.59830	0.0588343
$739$	−9.81013	−0.360871	−0.180436	−	0.983587i	$-0.557751\pi$
$739$	−9.81013	−0.360871	−0.180436	+	0.983587i	$0.557751\pi$
$740$	−2.93354	−0.107839
$741$	0	0
$742$	19.9776	0.733401
$743$	10.9782	0.402750	0.201375	−	0.979514i	$-0.435459\pi$
$743$	10.9782	0.402750	0.201375	+	0.979514i	$0.435459\pi$
$744$	−0.429064	−0.0157303
$745$	−1.29716	−0.0475244
$746$	8.35563	0.305921
$747$	46.8513	1.71420
$748$	1.65358	0.0604607
$749$	24.4603	0.893760
$750$	0.564724	0.0206208
$751$	26.2778	0.958891	0.479445	−	0.877572i	$-0.340838\pi$
$751$	26.2778	0.958891	0.479445	+	0.877572i	$0.340838\pi$
$752$	10.6311	0.387676
$753$	1.98538	0.0723513
$754$	0.653881	0.0238130
$755$	−7.85464	−0.285860
$756$	−1.59334	−0.0579492
$757$	−45.6128	−1.65783	−0.828913	−	0.559377i	$-0.811040\pi$
$757$	−45.6128	−1.65783	−0.828913	+	0.559377i	$0.811040\pi$
$758$	−11.2112	−0.407208
$759$	−0.934272	−0.0339119
$760$	0	0
$761$	−36.9343	−1.33887	−0.669433	−	0.742872i	$-0.733463\pi$
$761$	−36.9343	−1.33887	−0.669433	+	0.742872i	$0.733463\pi$
$762$	2.04224	0.0739826
$763$	−13.9017	−0.503274
$764$	−8.81314	−0.318848
$765$	2.46205	0.0890157
$766$	−23.5595	−0.851239
$767$	−0.799076	−0.0288530
$768$	−0.116160	−0.00419157
$769$	0.908733	0.0327697	0.0163849	−	0.999866i	$-0.494784\pi$
$769$	0.908733	0.0327697	0.0163849	+	0.999866i	$0.494784\pi$
$770$	−1.14232	−0.0411663
$771$	2.90396	0.104583
$772$	1.62372	0.0584388
$773$	4.28492	0.154118	0.0770590	−	0.997027i	$-0.475447\pi$
$773$	4.28492	0.154118	0.0770590	+	0.997027i	$0.475447\pi$
$774$	−15.3212	−0.550710
$775$	17.5506	0.630435
$776$	−15.4833	−0.555817
$777$	1.56609	0.0561833
$778$	−32.3109	−1.15840
$779$	0	0
$780$	0.0162820	0.000582991 0
$781$	5.50926	0.197137
$782$	−13.2996	−0.475594
$783$	−1.61729	−0.0577972
$784$	−1.75004	−0.0625015
$785$	−0.696885	−0.0248729
$786$	0.596279	0.0212686
$787$	27.9756	0.997223	0.498612	−	0.866825i	$-0.333843\pi$
$787$	27.9756	0.997223	0.498612	+	0.866825i	$0.333843\pi$
$788$	−20.2131	−0.720062
$789$	−0.471752	−0.0167948
$790$	7.03128	0.250162
$791$	−29.7838	−1.05899
$792$	2.98651	0.106121
$793$	−3.51356	−0.124770
$794$	21.6587	0.768640
$795$	0.504932	0.0179081
$796$	−17.2777	−0.612392
$797$	−51.6959	−1.83116	−0.915581	−	0.402135i	$-0.868268\pi$
$797$	−51.6959	−1.83116	−0.915581	+	0.402135i	$0.868268\pi$
$798$	0	0
$799$	17.5793	0.621912
$800$	4.75145	0.167989
$801$	−19.1647	−0.677151
$802$	−15.2032	−0.536842
$803$	2.38179	0.0840517
$804$	1.36300	0.0480693
$805$	9.18763	0.323821
$806$	1.03850	0.0365796
$807$	−0.0669323	−0.00235613
$808$	0.380477	0.0133851
$809$	16.2645	0.571828	0.285914	−	0.958255i	$-0.407703\pi$
$809$	16.2645	0.571828	0.285914	+	0.958255i	$0.407703\pi$
$810$	4.42651	0.155532
$811$	46.9741	1.64948	0.824742	−	0.565509i	$-0.191320\pi$
$811$	46.9741	1.64948	0.824742	+	0.565509i	$0.191320\pi$
$812$	5.32887	0.187007
$813$	3.10359	0.108848
$814$	−5.88414	−0.206239
$815$	8.33795	0.292066
$816$	−0.192080	−0.00672413
$817$	0	0
$818$	35.8741	1.25431
$819$	1.92390	0.0672266
$820$	−0.266812	−0.00931747
$821$	−25.0551	−0.874430	−0.437215	−	0.899357i	$-0.644035\pi$
$821$	−25.0551	−0.874430	−0.437215	+	0.899357i	$0.644035\pi$
$822$	0.350744	0.0122336
$823$	−42.3112	−1.47488	−0.737438	−	0.675415i	$-0.763964\pi$
$823$	−42.3112	−1.47488	−0.737438	+	0.675415i	$0.763964\pi$
$824$	6.42485	0.223820
$825$	0.551929	0.0192157
$826$	−6.51215	−0.226587
$827$	13.9959	0.486686	0.243343	−	0.969940i	$-0.421756\pi$
$827$	13.9959	0.486686	0.243343	+	0.969940i	$0.421756\pi$
$828$	−24.0204	−0.834765
$829$	−11.7480	−0.408025	−0.204012	−	0.978968i	$-0.565398\pi$
$829$	−11.7480	−0.408025	−0.204012	+	0.978968i	$0.565398\pi$
$830$	−7.82109	−0.271474
$831$	0.363280	0.0126020
$832$	0.281152	0.00974721
$833$	−2.89383	−0.100265
$834$	−0.341834	−0.0118367
$835$	4.88362	0.169004
$836$	0	0
$837$	−2.56860	−0.0887836
$838$	−5.02288	−0.173512
$839$	−20.5061	−0.707948	−0.353974	−	0.935255i	$-0.615170\pi$
$839$	−20.5061	−0.707948	−0.353974	+	0.935255i	$0.615170\pi$
$840$	0.132692	0.00457831
$841$	−23.5910	−0.813484
$842$	−5.74864	−0.198111
$843$	2.88798	0.0994672
$844$	7.33059	0.252329
$845$	6.44176	0.221603
$846$	31.7498	1.09158
$847$	−2.29128	−0.0787293
$848$	8.71898	0.299411
$849$	0.134880	0.00462907
$850$	7.85688	0.269489
$851$	47.3259	1.62231
$852$	−0.639956	−0.0219245
$853$	−55.5880	−1.90330	−0.951648	−	0.307191i	$-0.900611\pi$
$853$	−55.5880	−1.90330	−0.951648	+	0.307191i	$0.900611\pi$
$854$	−28.6341	−0.979839
$855$	0	0
$856$	10.6754	0.364877
$857$	40.9286	1.39809	0.699047	−	0.715076i	$-0.253608\pi$
$857$	40.9286	1.39809	0.699047	+	0.715076i	$0.253608\pi$
$858$	0.0326587	0.00111495
$859$	−1.62330	−0.0553864	−0.0276932	−	0.999616i	$-0.508816\pi$
$859$	−1.62330	−0.0553864	−0.0276932	+	0.999616i	$0.508816\pi$
$860$	2.55764	0.0872148
$861$	0.142439	0.00485432
$862$	25.8934	0.881934
$863$	28.6326	0.974665	0.487332	−	0.873217i	$-0.337970\pi$
$863$	28.6326	0.974665	0.487332	+	0.873217i	$0.337970\pi$
$864$	−0.695394	−0.0236578
$865$	−6.73395	−0.228961
$866$	−9.54377	−0.324311
$867$	1.65710	0.0562782
$868$	8.46336	0.287265
$869$	14.1034	0.478426
$870$	0.134686	0.00456630
$871$	−3.29899	−0.111782
$872$	−6.06721	−0.205462
$873$	−46.2409	−1.56502
$874$	0	0
$875$	−11.1393	−0.376576
$876$	−0.276670	−0.00934780
$877$	−17.7920	−0.600793	−0.300397	−	0.953814i	$-0.597119\pi$
$877$	−17.7920	−0.600793	−0.300397	+	0.953814i	$0.597119\pi$
$878$	−0.635179	−0.0214363
$879$	3.11335	0.105011
$880$	−0.498551	−0.0168062
$881$	16.4217	0.553262	0.276631	−	0.960976i	$-0.410782\pi$
$881$	16.4217	0.553262	0.276631	+	0.960976i	$0.410782\pi$
$882$	−5.22652	−0.175986
$883$	26.0571	0.876892	0.438446	−	0.898757i	$-0.355529\pi$
$883$	26.0571	0.876892	0.438446	+	0.898757i	$0.355529\pi$
$884$	0.464907	0.0156365
$885$	−0.164594	−0.00553276
$886$	−17.6440	−0.592760
$887$	−44.6815	−1.50026	−0.750130	−	0.661291i	$-0.770009\pi$
$887$	−44.6815	−1.50026	−0.750130	+	0.661291i	$0.770009\pi$
$888$	0.683502	0.0229368
$889$	−40.2836	−1.35107
$890$	3.19925	0.107239
$891$	8.87874	0.297449
$892$	4.52822	0.151616
$893$	0	0
$894$	0.302233	0.0101082
$895$	8.85902	0.296125
$896$	2.29128	0.0765462
$897$	−0.262673	−0.00877039
$898$	20.9736	0.699900
$899$	8.59057	0.286512
$900$	14.1902	0.473008
$901$	14.4175	0.480316
$902$	−0.535174	−0.0178193
$903$	−1.36542	−0.0454382
$904$	−12.9988	−0.432333
$905$	5.66748	0.188393
$906$	1.83010	0.0608008
$907$	−19.9543	−0.662570	−0.331285	−	0.943531i	$-0.607482\pi$
$907$	−19.9543	−0.662570	−0.331285	+	0.943531i	$0.607482\pi$
$908$	−23.3452	−0.774737
$909$	1.13630	0.0376886
$910$	−0.321166	−0.0106465
$911$	3.88096	0.128582	0.0642910	−	0.997931i	$-0.479521\pi$
$911$	3.88096	0.128582	0.0642910	+	0.997931i	$0.479521\pi$
$912$	0	0
$913$	−15.6876	−0.519185
$914$	22.9647	0.759604
$915$	−0.723724	−0.0239256
$916$	−17.7244	−0.585630
$917$	−11.7617	−0.388405
$918$	−1.14989	−0.0379519
$919$	18.4756	0.609454	0.304727	−	0.952440i	$-0.401435\pi$
$919$	18.4756	0.609454	0.304727	+	0.952440i	$0.401435\pi$
$920$	4.00983	0.132200
$921$	−3.54117	−0.116685
$922$	25.6578	0.844995
$923$	1.54894	0.0509840
$924$	0.266155	0.00875586
$925$	−27.9582	−0.919259
$926$	−14.4251	−0.474040
$927$	19.1879	0.630212
$928$	2.32572	0.0763454
$929$	40.8696	1.34089	0.670444	−	0.741960i	$-0.266104\pi$
$929$	40.8696	1.34089	0.670444	+	0.741960i	$0.266104\pi$
$930$	0.213910	0.00701440
$931$	0	0
$932$	−16.4045	−0.537347
$933$	1.28280	0.0419971
$934$	6.26939	0.205141
$935$	−0.824392	−0.0269605
$936$	0.839664	0.0274453
$937$	−45.2015	−1.47667	−0.738335	−	0.674435i	$-0.764387\pi$
$937$	−45.2015	−1.47667	−0.738335	+	0.674435i	$0.764387\pi$
$938$	−26.8854	−0.877840
$939$	−1.21849	−0.0397638
$940$	−5.30015	−0.172872
$941$	10.4566	0.340876	0.170438	−	0.985368i	$-0.445482\pi$
$941$	10.4566	0.340876	0.170438	+	0.985368i	$0.445482\pi$
$942$	0.162371	0.00529034
$943$	4.30438	0.140170
$944$	−2.84215	−0.0925040
$945$	0.794362	0.0258406
$946$	5.13015	0.166795
$947$	−37.2519	−1.21052	−0.605262	−	0.796026i	$-0.706932\pi$
$947$	−37.2519	−1.21052	−0.605262	+	0.796026i	$0.706932\pi$
$948$	−1.63826	−0.0532081
$949$	0.669647	0.0217377
$950$	0	0
$951$	1.22393	0.0396888
$952$	3.78880	0.122796
$953$	−21.3523	−0.691668	−0.345834	−	0.938296i	$-0.612404\pi$
$953$	−21.3523	−0.691668	−0.345834	+	0.938296i	$0.612404\pi$
$954$	26.0393	0.843053
$955$	4.39380	0.142180
$956$	18.2990	0.591833
$957$	0.270156	0.00873289
$958$	−9.22842	−0.298157
$959$	−6.91849	−0.223410
$960$	0.0579118	0.00186909
$961$	−17.3564	−0.559883
$962$	−1.65434	−0.0533381
$963$	31.8821	1.02739
$964$	6.06680	0.195399
$965$	−0.809505	−0.0260589
$966$	−2.14068	−0.0688751
$967$	23.5891	0.758575	0.379287	−	0.925279i	$-0.376169\pi$
$967$	23.5891	0.758575	0.379287	+	0.925279i	$0.376169\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	7.71920	0.247849
$971$	20.2354	0.649385	0.324692	−	0.945820i	$-0.394739\pi$
$971$	20.2354	0.649385	0.324692	+	0.945820i	$0.394739\pi$
$972$	−3.11754	−0.0999950
$973$	6.74273	0.216162
$974$	34.5755	1.10787
$975$	0.155176	0.00496961
$976$	−12.4970	−0.400019
$977$	5.21980	0.166996	0.0834980	−	0.996508i	$-0.473391\pi$
$977$	5.21980	0.166996	0.0834980	+	0.996508i	$0.473391\pi$
$978$	−1.94270	−0.0621209
$979$	6.41709	0.205091
$980$	0.872486	0.0278705
$981$	−18.1198	−0.578520
$982$	19.5615	0.624234
$983$	−40.5282	−1.29265	−0.646325	−	0.763062i	$-0.723695\pi$
$983$	−40.5282	−1.29265	−0.646325	+	0.763062i	$0.723695\pi$
$984$	0.0621659	0.00198178
$985$	10.0773	0.321088
$986$	3.84575	0.122474
$987$	2.82952	0.0900647
$988$	0	0
$989$	−41.2616	−1.31204
$990$	−1.48893	−0.0473212
$991$	−3.36817	−0.106993	−0.0534967	−	0.998568i	$-0.517037\pi$
$991$	−3.36817	−0.106993	−0.0534967	+	0.998568i	$0.517037\pi$
$992$	3.69373	0.117276
$993$	−0.705125	−0.0223765
$994$	12.6232	0.400385
$995$	8.61382	0.273076
$996$	1.82228	0.0577411
$997$	−25.3751	−0.803638	−0.401819	−	0.915719i	$-0.631622\pi$
$997$	−25.3751	−0.803638	−0.401819	+	0.915719i	$0.631622\pi$
$998$	−7.82554	−0.247713
$999$	4.09179	0.129459

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bs.1.6		12
19.14	odd	18		418.2.j.b.177.2	yes	24
19.15	odd	18		418.2.j.b.111.2	✓	24
19.18	odd	2		7942.2.a.bw.1.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.j.b.111.2	✓	24	19.15	odd	18
418.2.j.b.177.2	yes	24	19.14	odd	18
7942.2.a.bs.1.6		12	1.1	even	1	trivial
7942.2.a.bw.1.7		12	19.18	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.116160 q^{3} +1.00000 q^{4} -0.498551 q^{5} +0.116160 q^{6} -2.29128 q^{7} -1.00000 q^{8} -2.98651 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.116160 q^{3} +1.00000 q^{4} -0.498551 q^{5} +0.116160 q^{6} -2.29128 q^{7} -1.00000 q^{8} -2.98651 q^{9} +0.498551 q^{10} +1.00000 q^{11} -0.116160 q^{12} +0.281152 q^{13} +2.29128 q^{14} +0.0579118 q^{15} +1.00000 q^{16} +1.65358 q^{17} +2.98651 q^{18} -0.498551 q^{20} +0.266155 q^{21} -1.00000 q^{22} +8.04296 q^{23} +0.116160 q^{24} -4.75145 q^{25} -0.281152 q^{26} +0.695394 q^{27} -2.29128 q^{28} -2.32572 q^{29} -0.0579118 q^{30} -3.69373 q^{31} -1.00000 q^{32} -0.116160 q^{33} -1.65358 q^{34} +1.14232 q^{35} -2.98651 q^{36} +5.88414 q^{37} -0.0326587 q^{39} +0.498551 q^{40} +0.535174 q^{41} -0.266155 q^{42} -5.13015 q^{43} +1.00000 q^{44} +1.48893 q^{45} -8.04296 q^{46} +10.6311 q^{47} -0.116160 q^{48} -1.75004 q^{49} +4.75145 q^{50} -0.192080 q^{51} +0.281152 q^{52} +8.71898 q^{53} -0.695394 q^{54} -0.498551 q^{55} +2.29128 q^{56} +2.32572 q^{58} -2.84215 q^{59} +0.0579118 q^{60} -12.4970 q^{61} +3.69373 q^{62} +6.84292 q^{63} +1.00000 q^{64} -0.140169 q^{65} +0.116160 q^{66} -11.7338 q^{67} +1.65358 q^{68} -0.934272 q^{69} -1.14232 q^{70} +5.50926 q^{71} +2.98651 q^{72} +2.38179 q^{73} -5.88414 q^{74} +0.551929 q^{75} -2.29128 q^{77} +0.0326587 q^{78} +14.1034 q^{79} -0.498551 q^{80} +8.87874 q^{81} -0.535174 q^{82} -15.6876 q^{83} +0.266155 q^{84} -0.824392 q^{85} +5.13015 q^{86} +0.270156 q^{87} -1.00000 q^{88} +6.41709 q^{89} -1.48893 q^{90} -0.644199 q^{91} +8.04296 q^{92} +0.429064 q^{93} -10.6311 q^{94} +0.116160 q^{96} +15.4833 q^{97} +1.75004 q^{98} -2.98651 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9}+O(q^{10}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9	\( 12 q - 12 q^{2} + 3 q^{3} + 12 q^{4} - 9 q^{5} - 3 q^{6} - 12 q^{7} - 12 q^{8} + 15 q^{9} + 9 q^{10} + 12 q^{11} + 3 q^{12} + 12 q^{14} + 21 q^{15} + 12 q^{16} - 33 q^{17} - 15 q^{18} - 9 q^{20} - 9 q^{21} - 12 q^{22} - 18 q^{23} - 3 q^{24} + 15 q^{25} + 21 q^{27} - 12 q^{28} - 15 q^{29} - 21 q^{30} + 9 q^{31} - 12 q^{32} + 3 q^{33} + 33 q^{34} - 30 q^{35} + 15 q^{36} + 9 q^{37} - 6 q^{39} + 9 q^{40} - 15 q^{41} + 9 q^{42} - 21 q^{43} + 12 q^{44} + 18 q^{46} - 27 q^{47} + 3 q^{48} + 18 q^{49} - 15 q^{50} - 6 q^{51} + 6 q^{53} - 21 q^{54} - 9 q^{55} + 12 q^{56} + 15 q^{58} + 48 q^{59} + 21 q^{60} + 12 q^{61} - 9 q^{62} - 66 q^{63} + 12 q^{64} - 36 q^{65} - 3 q^{66} - 3 q^{67} - 33 q^{68} - 24 q^{69} + 30 q^{70} - 3 q^{71} - 15 q^{72} - 30 q^{73} - 9 q^{74} + 21 q^{75} - 12 q^{77} + 6 q^{78} + 12 q^{79} - 9 q^{80} + 12 q^{81} + 15 q^{82} - 66 q^{83} - 9 q^{84} + 15 q^{85} + 21 q^{86} - 51 q^{87} - 12 q^{88} + 30 q^{89} + 54 q^{91} - 18 q^{92} - 66 q^{93} + 27 q^{94} - 3 q^{96} + 36 q^{97} - 18 q^{98} + 15 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 + 3 * q^3 + 12 * q^4 - 9 * q^5 - 3 * q^6 - 12 * q^7 - 12 * q^8 + 15 * q^9 + 9 * q^10 + 12 * q^11 + 3 * q^12 + 12 * q^14 + 21 * q^15 + 12 * q^16 - 33 * q^17 - 15 * q^18 - 9 * q^20 - 9 * q^21 - 12 * q^22 - 18 * q^23 - 3 * q^24 + 15 * q^25 + 21 * q^27 - 12 * q^28 - 15 * q^29 - 21 * q^30 + 9 * q^31 - 12 * q^32 + 3 * q^33 + 33 * q^34 - 30 * q^35 + 15 * q^36 + 9 * q^37 - 6 * q^39 + 9 * q^40 - 15 * q^41 + 9 * q^42 - 21 * q^43 + 12 * q^44 + 18 * q^46 - 27 * q^47 + 3 * q^48 + 18 * q^49 - 15 * q^50 - 6 * q^51 + 6 * q^53 - 21 * q^54 - 9 * q^55 + 12 * q^56 + 15 * q^58 + 48 * q^59 + 21 * q^60 + 12 * q^61 - 9 * q^62 - 66 * q^63 + 12 * q^64 - 36 * q^65 - 3 * q^66 - 3 * q^67 - 33 * q^68 - 24 * q^69 + 30 * q^70 - 3 * q^71 - 15 * q^72 - 30 * q^73 - 9 * q^74 + 21 * q^75 - 12 * q^77 + 6 * q^78 + 12 * q^79 - 9 * q^80 + 12 * q^81 + 15 * q^82 - 66 * q^83 - 9 * q^84 + 15 * q^85 + 21 * q^86 - 51 * q^87 - 12 * q^88 + 30 * q^89 + 54 * q^91 - 18 * q^92 - 66 * q^93 + 27 * q^94 - 3 * q^96 + 36 * q^97 - 18 * q^98 + 15 * q^99

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