LMFDB - Embedded newform 8007.2.a.e.1.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.35
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.51096 q^{2} +1.00000 q^{3} +0.283004 q^{4} -0.836006 q^{5} +1.51096 q^{6} +4.41131 q^{7} -2.59431 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.51096 q^{2} +1.00000 q^{3} +0.283004 q^{4} -0.836006 q^{5} +1.51096 q^{6} +4.41131 q^{7} -2.59431 q^{8} +1.00000 q^{9} -1.26317 q^{10} -3.77485 q^{11} +0.283004 q^{12} -5.83823 q^{13} +6.66531 q^{14} -0.836006 q^{15} -4.48592 q^{16} -1.00000 q^{17} +1.51096 q^{18} +4.09394 q^{19} -0.236593 q^{20} +4.41131 q^{21} -5.70365 q^{22} +9.55384 q^{23} -2.59431 q^{24} -4.30109 q^{25} -8.82134 q^{26} +1.00000 q^{27} +1.24842 q^{28} -9.47550 q^{29} -1.26317 q^{30} +0.516268 q^{31} -1.58942 q^{32} -3.77485 q^{33} -1.51096 q^{34} -3.68788 q^{35} +0.283004 q^{36} +1.47853 q^{37} +6.18578 q^{38} -5.83823 q^{39} +2.16886 q^{40} -2.87578 q^{41} +6.66531 q^{42} +3.76117 q^{43} -1.06830 q^{44} -0.836006 q^{45} +14.4355 q^{46} -12.0333 q^{47} -4.48592 q^{48} +12.4596 q^{49} -6.49879 q^{50} -1.00000 q^{51} -1.65224 q^{52} +1.99252 q^{53} +1.51096 q^{54} +3.15579 q^{55} -11.4443 q^{56} +4.09394 q^{57} -14.3171 q^{58} +3.16400 q^{59} -0.236593 q^{60} -6.64046 q^{61} +0.780062 q^{62} +4.41131 q^{63} +6.57028 q^{64} +4.88079 q^{65} -5.70365 q^{66} -2.31978 q^{67} -0.283004 q^{68} +9.55384 q^{69} -5.57224 q^{70} -1.24383 q^{71} -2.59431 q^{72} -11.6516 q^{73} +2.23401 q^{74} -4.30109 q^{75} +1.15860 q^{76} -16.6520 q^{77} -8.82134 q^{78} -5.66365 q^{79} +3.75025 q^{80} +1.00000 q^{81} -4.34520 q^{82} -7.20343 q^{83} +1.24842 q^{84} +0.836006 q^{85} +5.68299 q^{86} -9.47550 q^{87} +9.79314 q^{88} -16.5922 q^{89} -1.26317 q^{90} -25.7542 q^{91} +2.70378 q^{92} +0.516268 q^{93} -18.1819 q^{94} -3.42255 q^{95} -1.58942 q^{96} -10.9846 q^{97} +18.8260 q^{98} -3.77485 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	1.51096	1.06841	0.534205	−	0.845355i	$-0.320611\pi$
$2$	1.51096	1.06841	0.534205	+	0.845355i	$0.320611\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	0.283004	0.141502
$5$	−0.836006	−0.373873	−0.186937	−	0.982372i	$-0.559856\pi$
$5$	−0.836006	−0.373873	−0.186937	+	0.982372i	$0.559856\pi$
$6$	1.51096	0.616847
$7$	4.41131	1.66732	0.833658	−	0.552280i	$-0.186242\pi$
$7$	4.41131	1.66732	0.833658	+	0.552280i	$0.186242\pi$
$8$	−2.59431	−0.917229
$9$	1.00000	0.333333
$10$	−1.26317	−0.399450
$11$	−3.77485	−1.13816	−0.569079	−	0.822283i	$-0.692700\pi$
$11$	−3.77485	−1.13816	−0.569079	+	0.822283i	$0.692700\pi$
$12$	0.283004	0.0816962
$13$	−5.83823	−1.61923	−0.809617	−	0.586959i	$-0.800325\pi$
$13$	−5.83823	−1.61923	−0.809617	+	0.586959i	$0.800325\pi$
$14$	6.66531	1.78138
$15$	−0.836006	−0.215856
$16$	−4.48592	−1.12148
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.51096	0.356137
$19$	4.09394	0.939214	0.469607	−	0.882876i	$-0.344396\pi$
$19$	4.09394	0.939214	0.469607	+	0.882876i	$0.344396\pi$
$20$	−0.236593	−0.0529038
$21$	4.41131	0.962626
$22$	−5.70365	−1.21602
$23$	9.55384	1.99211	0.996057	−	0.0887162i	$-0.0282764\pi$
$23$	9.55384	1.99211	0.996057	+	0.0887162i	$0.0282764\pi$
$24$	−2.59431	−0.529562
$25$	−4.30109	−0.860219
$26$	−8.82134	−1.73001
$27$	1.00000	0.192450
$28$	1.24842	0.235929
$29$	−9.47550	−1.75956	−0.879778	−	0.475385i	$-0.842309\pi$
$29$	−9.47550	−1.75956	−0.879778	+	0.475385i	$0.842309\pi$
$30$	−1.26317	−0.230623
$31$	0.516268	0.0927245	0.0463623	−	0.998925i	$-0.485237\pi$
$31$	0.516268	0.0927245	0.0463623	+	0.998925i	$0.485237\pi$
$32$	−1.58942	−0.280972
$33$	−3.77485	−0.657116
$34$	−1.51096	−0.259128
$35$	−3.68788	−0.623365
$36$	0.283004	0.0471673
$37$	1.47853	0.243070	0.121535	−	0.992587i	$-0.461218\pi$
$37$	1.47853	0.243070	0.121535	+	0.992587i	$0.461218\pi$
$38$	6.18578	1.00347
$39$	−5.83823	−0.934865
$40$	2.16886	0.342927
$41$	−2.87578	−0.449122	−0.224561	−	0.974460i	$-0.572095\pi$
$41$	−2.87578	−0.449122	−0.224561	+	0.974460i	$0.572095\pi$
$42$	6.66531	1.02848
$43$	3.76117	0.573573	0.286787	−	0.957994i	$-0.407413\pi$
$43$	3.76117	0.573573	0.286787	+	0.957994i	$0.407413\pi$
$44$	−1.06830	−0.161052
$45$	−0.836006	−0.124624
$46$	14.4355	2.12840
$47$	−12.0333	−1.75524	−0.877622	−	0.479354i	$-0.840871\pi$
$47$	−12.0333	−1.75524	−0.877622	+	0.479354i	$0.840871\pi$
$48$	−4.48592	−0.647486
$49$	12.4596	1.77995
$50$	−6.49879	−0.919067
$51$	−1.00000	−0.140028
$52$	−1.65224	−0.229125
$53$	1.99252	0.273693	0.136847	−	0.990592i	$-0.456303\pi$
$53$	1.99252	0.273693	0.136847	+	0.990592i	$0.456303\pi$
$54$	1.51096	0.205616
$55$	3.15579	0.425527
$56$	−11.4443	−1.52931
$57$	4.09394	0.542255
$58$	−14.3171	−1.87993
$59$	3.16400	0.411918	0.205959	−	0.978561i	$-0.433969\pi$
$59$	3.16400	0.411918	0.205959	+	0.978561i	$0.433969\pi$
$60$	−0.236593	−0.0305440
$61$	−6.64046	−0.850223	−0.425112	−	0.905141i	$-0.639765\pi$
$61$	−6.64046	−0.850223	−0.425112	+	0.905141i	$0.639765\pi$
$62$	0.780062	0.0990679
$63$	4.41131	0.555772
$64$	6.57028	0.821286
$65$	4.88079	0.605388
$66$	−5.70365	−0.702070
$67$	−2.31978	−0.283407	−0.141703	−	0.989909i	$-0.545258\pi$
$67$	−2.31978	−0.283407	−0.141703	+	0.989909i	$0.545258\pi$
$68$	−0.283004	−0.0343193
$69$	9.55384	1.15015
$70$	−5.57224	−0.666010
$71$	−1.24383	−0.147615	−0.0738077	−	0.997272i	$-0.523515\pi$
$71$	−1.24383	−0.147615	−0.0738077	+	0.997272i	$0.523515\pi$
$72$	−2.59431	−0.305743
$73$	−11.6516	−1.36371	−0.681856	−	0.731487i	$-0.738827\pi$
$73$	−11.6516	−1.36371	−0.681856	+	0.731487i	$0.738827\pi$
$74$	2.23401	0.259698
$75$	−4.30109	−0.496648
$76$	1.15860	0.132901
$77$	−16.6520	−1.89767
$78$	−8.82134	−0.998820
$79$	−5.66365	−0.637211	−0.318605	−	0.947887i	$-0.603214\pi$
$79$	−5.66365	−0.637211	−0.318605	+	0.947887i	$0.603214\pi$
$80$	3.75025	0.419291
$81$	1.00000	0.111111
$82$	−4.34520	−0.479847
$83$	−7.20343	−0.790679	−0.395340	−	0.918535i	$-0.629373\pi$
$83$	−7.20343	−0.790679	−0.395340	+	0.918535i	$0.629373\pi$
$84$	1.24842	0.136214
$85$	0.836006	0.0906775
$86$	5.68299	0.612812
$87$	−9.47550	−1.01588
$88$	9.79314	1.04395
$89$	−16.5922	−1.75877	−0.879385	−	0.476112i	$-0.842046\pi$
$89$	−16.5922	−1.75877	−0.879385	+	0.476112i	$0.842046\pi$
$90$	−1.26317	−0.133150
$91$	−25.7542	−2.69978
$92$	2.70378	0.281888
$93$	0.516268	0.0535345
$94$	−18.1819	−1.87532
$95$	−3.42255	−0.351147
$96$	−1.58942	−0.162219
$97$	−10.9846	−1.11532	−0.557659	−	0.830070i	$-0.688300\pi$
$97$	−10.9846	−1.11532	−0.557659	+	0.830070i	$0.688300\pi$
$98$	18.8260	1.90171
$99$	−3.77485	−0.379386
$100$	−1.21723	−0.121723
$101$	8.99430	0.894966	0.447483	−	0.894292i	$-0.352320\pi$
$101$	8.99430	0.894966	0.447483	+	0.894292i	$0.352320\pi$
$102$	−1.51096	−0.149607
$103$	−3.55553	−0.350337	−0.175169	−	0.984538i	$-0.556047\pi$
$103$	−3.55553	−0.350337	−0.175169	+	0.984538i	$0.556047\pi$
$104$	15.1462	1.48521
$105$	−3.68788	−0.359900
$106$	3.01062	0.292417
$107$	0.213848	0.0206735	0.0103368	−	0.999947i	$-0.496710\pi$
$107$	0.213848	0.0206735	0.0103368	+	0.999947i	$0.496710\pi$
$108$	0.283004	0.0272321
$109$	−2.27426	−0.217835	−0.108917	−	0.994051i	$-0.534738\pi$
$109$	−2.27426	−0.217835	−0.108917	+	0.994051i	$0.534738\pi$
$110$	4.76828	0.454638
$111$	1.47853	0.140336
$112$	−19.7888	−1.86986
$113$	−11.6893	−1.09964	−0.549820	−	0.835283i	$-0.685304\pi$
$113$	−11.6893	−1.09964	−0.549820	+	0.835283i	$0.685304\pi$
$114$	6.18578	0.579351
$115$	−7.98707	−0.744798
$116$	−2.68160	−0.248981
$117$	−5.83823	−0.539745
$118$	4.78068	0.440097
$119$	−4.41131	−0.404384
$120$	2.16886	0.197989
$121$	3.24946	0.295406
$122$	−10.0335	−0.908388
$123$	−2.87578	−0.259301
$124$	0.146106	0.0131207
$125$	7.77577	0.695486
$126$	6.66531	0.593793
$127$	−10.9893	−0.975140	−0.487570	−	0.873084i	$-0.662117\pi$
$127$	−10.9893	−0.975140	−0.487570	+	0.873084i	$0.662117\pi$
$128$	13.1063	1.15844
$129$	3.76117	0.331153
$130$	7.37469	0.646803
$131$	9.00008	0.786341	0.393170	−	0.919466i	$-0.371378\pi$
$131$	9.00008	0.786341	0.393170	+	0.919466i	$0.371378\pi$
$132$	−1.06830	−0.0929833
$133$	18.0596	1.56597
$134$	−3.50510	−0.302795
$135$	−0.836006	−0.0719519
$136$	2.59431	0.222461
$137$	−13.7663	−1.17614	−0.588068	−	0.808811i	$-0.700111\pi$
$137$	−13.7663	−1.17614	−0.588068	+	0.808811i	$0.700111\pi$
$138$	14.4355	1.22883
$139$	9.60376	0.814581	0.407290	−	0.913299i	$-0.366474\pi$
$139$	9.60376	0.814581	0.407290	+	0.913299i	$0.366474\pi$
$140$	−1.04368	−0.0882074
$141$	−12.0333	−1.01339
$142$	−1.87938	−0.157714
$143$	22.0384	1.84295
$144$	−4.48592	−0.373826
$145$	7.92157	0.657850
$146$	−17.6051	−1.45700
$147$	12.4596	1.02765
$148$	0.418431	0.0343948
$149$	6.36857	0.521734	0.260867	−	0.965375i	$-0.415992\pi$
$149$	6.36857	0.521734	0.260867	+	0.965375i	$0.415992\pi$
$150$	−6.49879	−0.530624
$151$	−19.1679	−1.55986	−0.779929	−	0.625868i	$-0.784745\pi$
$151$	−19.1679	−1.55986	−0.779929	+	0.625868i	$0.784745\pi$
$152$	−10.6210	−0.861474
$153$	−1.00000	−0.0808452
$154$	−25.1605	−2.02749
$155$	−0.431603	−0.0346672
$156$	−1.65224	−0.132285
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−8.55756	−0.680803
$159$	1.99252	0.158017
$160$	1.32876	0.105048
$161$	42.1449	3.32149
$162$	1.51096	0.118712
$163$	9.98282	0.781914	0.390957	−	0.920409i	$-0.372144\pi$
$163$	9.98282	0.781914	0.390957	+	0.920409i	$0.372144\pi$
$164$	−0.813858	−0.0635516
$165$	3.15579	0.245678
$166$	−10.8841	−0.844770
$167$	−5.94434	−0.459987	−0.229993	−	0.973192i	$-0.573870\pi$
$167$	−5.94434	−0.459987	−0.229993	+	0.973192i	$0.573870\pi$
$168$	−11.4443	−0.882948
$169$	21.0849	1.62192
$170$	1.26317	0.0968809
$171$	4.09394	0.313071
$172$	1.06443	0.0811618
$173$	2.56947	0.195353	0.0976767	−	0.995218i	$-0.468859\pi$
$173$	2.56947	0.195353	0.0976767	+	0.995218i	$0.468859\pi$
$174$	−14.3171	−1.08538
$175$	−18.9734	−1.43426
$176$	16.9336	1.27642
$177$	3.16400	0.237821
$178$	−25.0702	−1.87909
$179$	−23.5273	−1.75851	−0.879256	−	0.476349i	$-0.841960\pi$
$179$	−23.5273	−1.75851	−0.879256	+	0.476349i	$0.841960\pi$
$180$	−0.236593	−0.0176346
$181$	20.8338	1.54857	0.774283	−	0.632840i	$-0.218111\pi$
$181$	20.8338	1.54857	0.774283	+	0.632840i	$0.218111\pi$
$182$	−38.9136	−2.88447
$183$	−6.64046	−0.490877
$184$	−24.7857	−1.82722
$185$	−1.23606	−0.0908772
$186$	0.780062	0.0571969
$187$	3.77485	0.276044
$188$	−3.40548	−0.248371
$189$	4.41131	0.320875
$190$	−5.17135	−0.375169
$191$	−14.1901	−1.02676	−0.513381	−	0.858161i	$-0.671607\pi$
$191$	−14.1901	−1.02676	−0.513381	+	0.858161i	$0.671607\pi$
$192$	6.57028	0.474169
$193$	3.49012	0.251224	0.125612	−	0.992079i	$-0.459911\pi$
$193$	3.49012	0.251224	0.125612	+	0.992079i	$0.459911\pi$
$194$	−16.5973	−1.19162
$195$	4.88079	0.349521
$196$	3.52612	0.251866
$197$	−8.19739	−0.584040	−0.292020	−	0.956412i	$-0.594327\pi$
$197$	−8.19739	−0.584040	−0.292020	+	0.956412i	$0.594327\pi$
$198$	−5.70365	−0.405341
$199$	8.96818	0.635737	0.317869	−	0.948135i	$-0.397033\pi$
$199$	8.96818	0.635737	0.317869	+	0.948135i	$0.397033\pi$
$200$	11.1584	0.789017
$201$	−2.31978	−0.163625
$202$	13.5900	0.956192
$203$	−41.7993	−2.93374
$204$	−0.283004	−0.0198142
$205$	2.40417	0.167915
$206$	−5.37227	−0.374304
$207$	9.55384	0.664038
$208$	26.1898	1.81594
$209$	−15.4540	−1.06897
$210$	−5.57224	−0.384521
$211$	25.5807	1.76105	0.880523	−	0.474004i	$-0.157192\pi$
$211$	25.5807	1.76105	0.880523	+	0.474004i	$0.157192\pi$
$212$	0.563890	0.0387281
$213$	−1.24383	−0.0852258
$214$	0.323117	0.0220878
$215$	−3.14436	−0.214444
$216$	−2.59431	−0.176521
$217$	2.27742	0.154601
$218$	−3.43632	−0.232737
$219$	−11.6516	−0.787339
$220$	0.893102	0.0602129
$221$	5.83823	0.392722
$222$	2.23401	0.149937
$223$	22.9302	1.53552	0.767759	−	0.640738i	$-0.221372\pi$
$223$	22.9302	1.53552	0.767759	+	0.640738i	$0.221372\pi$
$224$	−7.01141	−0.468469
$225$	−4.30109	−0.286740
$226$	−17.6621	−1.17487
$227$	5.09238	0.337993	0.168997	−	0.985617i	$-0.445947\pi$
$227$	5.09238	0.337993	0.168997	+	0.985617i	$0.445947\pi$
$228$	1.15860	0.0767302
$229$	−9.45760	−0.624976	−0.312488	−	0.949922i	$-0.601162\pi$
$229$	−9.45760	−0.624976	−0.312488	+	0.949922i	$0.601162\pi$
$230$	−12.0681	−0.795750
$231$	−16.6520	−1.09562
$232$	24.5824	1.61391
$233$	−0.0450260	−0.00294975	−0.00147487	−	0.999999i	$-0.500469\pi$
$233$	−0.0450260	−0.00294975	−0.00147487	+	0.999999i	$0.500469\pi$
$234$	−8.82134	−0.576669
$235$	10.0599	0.656238
$236$	0.895425	0.0582872
$237$	−5.66365	−0.367894
$238$	−6.66531	−0.432048
$239$	−9.94081	−0.643018	−0.321509	−	0.946907i	$-0.604190\pi$
$239$	−9.94081	−0.643018	−0.321509	+	0.946907i	$0.604190\pi$
$240$	3.75025	0.242078
$241$	24.0300	1.54791	0.773954	−	0.633242i	$-0.218276\pi$
$241$	24.0300	1.54791	0.773954	+	0.633242i	$0.218276\pi$
$242$	4.90981	0.315615
$243$	1.00000	0.0641500
$244$	−1.87928	−0.120308
$245$	−10.4163	−0.665474
$246$	−4.34520	−0.277040
$247$	−23.9013	−1.52081
$248$	−1.33936	−0.0850496
$249$	−7.20343	−0.456499
$250$	11.7489	0.743065
$251$	−20.7510	−1.30979	−0.654895	−	0.755720i	$-0.727287\pi$
$251$	−20.7510	−1.30979	−0.654895	+	0.755720i	$0.727287\pi$
$252$	1.24842	0.0786429
$253$	−36.0643	−2.26734
$254$	−16.6044	−1.04185
$255$	0.836006	0.0523527
$256$	6.66252	0.416407
$257$	28.1129	1.75364	0.876818	−	0.480823i	$-0.159662\pi$
$257$	28.1129	1.75364	0.876818	+	0.480823i	$0.159662\pi$
$258$	5.68299	0.353807
$259$	6.52227	0.405274
$260$	1.38128	0.0856636
$261$	−9.47550	−0.586518
$262$	13.5988	0.840135
$263$	−32.2198	−1.98676	−0.993379	−	0.114881i	$-0.963351\pi$
$263$	−32.2198	−1.98676	−0.993379	+	0.114881i	$0.963351\pi$
$264$	9.79314	0.602726
$265$	−1.66575	−0.102327
$266$	27.2874	1.67310
$267$	−16.5922	−1.01543
$268$	−0.656508	−0.0401026
$269$	6.99553	0.426525	0.213263	−	0.976995i	$-0.431591\pi$
$269$	6.99553	0.426525	0.213263	+	0.976995i	$0.431591\pi$
$270$	−1.26317	−0.0768742
$271$	−14.2680	−0.866722	−0.433361	−	0.901220i	$-0.642672\pi$
$271$	−14.2680	−0.866722	−0.433361	+	0.901220i	$0.642672\pi$
$272$	4.48592	0.271999
$273$	−25.7542	−1.55872
$274$	−20.8004	−1.25660
$275$	16.2360	0.979066
$276$	2.70378	0.162748
$277$	−11.9154	−0.715925	−0.357962	−	0.933736i	$-0.616528\pi$
$277$	−11.9154	−0.715925	−0.357962	+	0.933736i	$0.616528\pi$
$278$	14.5109	0.870307
$279$	0.516268	0.0309082
$280$	9.56751	0.571768
$281$	−1.29000	−0.0769551	−0.0384776	−	0.999259i	$-0.512251\pi$
$281$	−1.29000	−0.0769551	−0.0384776	+	0.999259i	$0.512251\pi$
$282$	−18.1819	−1.08272
$283$	8.98090	0.533859	0.266930	−	0.963716i	$-0.413991\pi$
$283$	8.98090	0.533859	0.266930	+	0.963716i	$0.413991\pi$
$284$	−0.352009	−0.0208879
$285$	−3.42255	−0.202735
$286$	33.2992	1.96902
$287$	−12.6860	−0.748828
$288$	−1.58942	−0.0936574
$289$	1.00000	0.0588235
$290$	11.9692	0.702855
$291$	−10.9846	−0.643929
$292$	−3.29744	−0.192968
$293$	19.2587	1.12511	0.562553	−	0.826761i	$-0.309819\pi$
$293$	19.2587	1.12511	0.562553	+	0.826761i	$0.309819\pi$
$294$	18.8260	1.09795
$295$	−2.64512	−0.154005
$296$	−3.83578	−0.222950
$297$	−3.77485	−0.219039
$298$	9.62266	0.557426
$299$	−55.7775	−3.22570
$300$	−1.21723	−0.0702767
$301$	16.5917	0.956328
$302$	−28.9619	−1.66657
$303$	8.99430	0.516709
$304$	−18.3651	−1.05331
$305$	5.55146	0.317876
$306$	−1.51096	−0.0863759
$307$	−27.4875	−1.56880	−0.784398	−	0.620258i	$-0.787028\pi$
$307$	−27.4875	−1.56880	−0.784398	+	0.620258i	$0.787028\pi$
$308$	−4.71258	−0.268524
$309$	−3.55553	−0.202267
$310$	−0.652136	−0.0370388
$311$	0.632203	0.0358490	0.0179245	−	0.999839i	$-0.494294\pi$
$311$	0.632203	0.0358490	0.0179245	+	0.999839i	$0.494294\pi$
$312$	15.1462	0.857485
$313$	−1.56409	−0.0884074	−0.0442037	−	0.999023i	$-0.514075\pi$
$313$	−1.56409	−0.0884074	−0.0442037	+	0.999023i	$0.514075\pi$
$314$	1.51096	0.0852685
$315$	−3.68788	−0.207788
$316$	−1.60284	−0.0901666
$317$	13.1851	0.740547	0.370274	−	0.928923i	$-0.379264\pi$
$317$	13.1851	0.740547	0.370274	+	0.928923i	$0.379264\pi$
$318$	3.01062	0.168827
$319$	35.7685	2.00265
$320$	−5.49279	−0.307057
$321$	0.213848	0.0119359
$322$	63.6793	3.54871
$323$	−4.09394	−0.227793
$324$	0.283004	0.0157224
$325$	25.1108	1.39290
$326$	15.0836	0.835406
$327$	−2.27426	−0.125767
$328$	7.46068	0.411947
$329$	−53.0827	−2.92655
$330$	4.76828	0.262485
$331$	30.8607	1.69626	0.848128	−	0.529792i	$-0.177730\pi$
$331$	30.8607	1.69626	0.848128	+	0.529792i	$0.177730\pi$
$332$	−2.03860	−0.111883
$333$	1.47853	0.0810232
$334$	−8.98167	−0.491455
$335$	1.93935	0.105958
$336$	−19.7888	−1.07956
$337$	14.6282	0.796850	0.398425	−	0.917201i	$-0.369557\pi$
$337$	14.6282	0.796850	0.398425	+	0.917201i	$0.369557\pi$
$338$	31.8585	1.73287
$339$	−11.6893	−0.634878
$340$	0.236593	0.0128311
$341$	−1.94883	−0.105535
$342$	6.18578	0.334489
$343$	24.0841	1.30042
$344$	−9.75766	−0.526098
$345$	−7.98707	−0.430009
$346$	3.88237	0.208718
$347$	−15.6380	−0.839494	−0.419747	−	0.907641i	$-0.637881\pi$
$347$	−15.6380	−0.839494	−0.419747	+	0.907641i	$0.637881\pi$
$348$	−2.68160	−0.143749
$349$	16.1732	0.865732	0.432866	−	0.901458i	$-0.357502\pi$
$349$	16.1732	0.865732	0.432866	+	0.901458i	$0.357502\pi$
$350$	−28.6681	−1.53238
$351$	−5.83823	−0.311622
$352$	5.99981	0.319791
$353$	−31.2640	−1.66401	−0.832007	−	0.554765i	$-0.812808\pi$
$353$	−31.2640	−1.66401	−0.832007	+	0.554765i	$0.812808\pi$
$354$	4.78068	0.254090
$355$	1.03985	0.0551894
$356$	−4.69566	−0.248869
$357$	−4.41131	−0.233471
$358$	−35.5488	−1.87881
$359$	36.5852	1.93090	0.965448	−	0.260597i	$-0.0839194\pi$
$359$	36.5852	1.93090	0.965448	+	0.260597i	$0.0839194\pi$
$360$	2.16886	0.114309
$361$	−2.23968	−0.117878
$362$	31.4791	1.65450
$363$	3.24946	0.170553
$364$	−7.28855	−0.382024
$365$	9.74077	0.509855
$366$	−10.0335	−0.524458
$367$	7.01003	0.365921	0.182960	−	0.983120i	$-0.441432\pi$
$367$	7.01003	0.365921	0.182960	+	0.983120i	$0.441432\pi$
$368$	−42.8577	−2.23411
$369$	−2.87578	−0.149707
$370$	−1.86764	−0.0970942
$371$	8.78960	0.456333
$372$	0.146106	0.00757525
$373$	−29.0982	−1.50665	−0.753323	−	0.657651i	$-0.771550\pi$
$373$	−29.0982	−1.50665	−0.753323	+	0.657651i	$0.771550\pi$
$374$	5.70365	0.294929
$375$	7.77577	0.401539
$376$	31.2183	1.60996
$377$	55.3201	2.84913
$378$	6.66531	0.342827
$379$	32.4861	1.66870	0.834351	−	0.551234i	$-0.185843\pi$
$379$	32.4861	1.66870	0.834351	+	0.551234i	$0.185843\pi$
$380$	−0.968597	−0.0496880
$381$	−10.9893	−0.562997
$382$	−21.4407	−1.09700
$383$	−7.27241	−0.371603	−0.185801	−	0.982587i	$-0.559488\pi$
$383$	−7.27241	−0.371603	−0.185801	+	0.982587i	$0.559488\pi$
$384$	13.1063	0.668827
$385$	13.9212	0.709488
$386$	5.27344	0.268411
$387$	3.76117	0.191191
$388$	−3.10869	−0.157820
$389$	2.37476	0.120405	0.0602025	−	0.998186i	$-0.480825\pi$
$389$	2.37476	0.120405	0.0602025	+	0.998186i	$0.480825\pi$
$390$	7.37469	0.373432
$391$	−9.55384	−0.483159
$392$	−32.3242	−1.63262
$393$	9.00008	0.453994
$394$	−12.3859	−0.623995
$395$	4.73484	0.238236
$396$	−1.06830	−0.0536839
$397$	15.8906	0.797527	0.398763	−	0.917054i	$-0.369440\pi$
$397$	15.8906	0.797527	0.398763	+	0.917054i	$0.369440\pi$
$398$	13.5506	0.679228
$399$	18.0596	0.904111
$400$	19.2944	0.964718
$401$	9.07651	0.453259	0.226630	−	0.973981i	$-0.427229\pi$
$401$	9.07651	0.453259	0.226630	+	0.973981i	$0.427229\pi$
$402$	−3.50510	−0.174819
$403$	−3.01409	−0.150143
$404$	2.54542	0.126640
$405$	−0.836006	−0.0415414
$406$	−63.1571	−3.13444
$407$	−5.58124	−0.276652
$408$	2.59431	0.128438
$409$	−11.9495	−0.590863	−0.295432	−	0.955364i	$-0.595463\pi$
$409$	−11.9495	−0.590863	−0.295432	+	0.955364i	$0.595463\pi$
$410$	3.63261	0.179402
$411$	−13.7663	−0.679043
$412$	−1.00623	−0.0495734
$413$	13.9574	0.686797
$414$	14.4355	0.709465
$415$	6.02211	0.295614
$416$	9.27939	0.454959
$417$	9.60376	0.470298
$418$	−23.3504	−1.14210
$419$	−13.7153	−0.670038	−0.335019	−	0.942211i	$-0.608743\pi$
$419$	−13.7153	−0.670038	−0.335019	+	0.942211i	$0.608743\pi$
$420$	−1.04368	−0.0509266
$421$	6.16177	0.300306	0.150153	−	0.988663i	$-0.452023\pi$
$421$	6.16177	0.300306	0.150153	+	0.988663i	$0.452023\pi$
$422$	38.6514	1.88152
$423$	−12.0333	−0.585081
$424$	−5.16921	−0.251039
$425$	4.30109	0.208634
$426$	−1.87938	−0.0910562
$427$	−29.2931	−1.41759
$428$	0.0605200	0.00292534
$429$	22.0384	1.06402
$430$	−4.75101	−0.229114
$431$	7.61302	0.366706	0.183353	−	0.983047i	$-0.441305\pi$
$431$	7.61302	0.366706	0.183353	+	0.983047i	$0.441305\pi$
$432$	−4.48592	−0.215829
$433$	1.14271	0.0549150	0.0274575	−	0.999623i	$-0.491259\pi$
$433$	1.14271	0.0549150	0.0274575	+	0.999623i	$0.491259\pi$
$434$	3.44109	0.165178
$435$	7.92157	0.379810
$436$	−0.643626	−0.0308241
$437$	39.1128	1.87102
$438$	−17.6051	−0.841202
$439$	−0.0587339	−0.00280322	−0.00140161	−	0.999999i	$-0.500446\pi$
$439$	−0.0587339	−0.00280322	−0.00140161	+	0.999999i	$0.500446\pi$
$440$	−8.18712	−0.390306
$441$	12.4596	0.593315
$442$	8.82134	0.419588
$443$	14.8539	0.705730	0.352865	−	0.935674i	$-0.385207\pi$
$443$	14.8539	0.705730	0.352865	+	0.935674i	$0.385207\pi$
$444$	0.418431	0.0198579
$445$	13.8712	0.657557
$446$	34.6466	1.64056
$447$	6.36857	0.301223
$448$	28.9835	1.36934
$449$	−32.4901	−1.53330	−0.766652	−	0.642063i	$-0.778079\pi$
$449$	−32.4901	−1.53330	−0.766652	+	0.642063i	$0.778079\pi$
$450$	−6.49879	−0.306356
$451$	10.8556	0.511172
$452$	−3.30813	−0.155601
$453$	−19.1679	−0.900585
$454$	7.69439	0.361116
$455$	21.5307	1.00937
$456$	−10.6210	−0.497372
$457$	31.1587	1.45754	0.728772	−	0.684756i	$-0.240091\pi$
$457$	31.1587	1.45754	0.728772	+	0.684756i	$0.240091\pi$
$458$	−14.2901	−0.667731
$459$	−1.00000	−0.0466760
$460$	−2.26037	−0.105390
$461$	7.72673	0.359870	0.179935	−	0.983679i	$-0.442411\pi$
$461$	7.72673	0.359870	0.179935	+	0.983679i	$0.442411\pi$
$462$	−25.1605	−1.17057
$463$	−38.9910	−1.81207	−0.906034	−	0.423206i	$-0.860905\pi$
$463$	−38.9910	−1.81207	−0.906034	+	0.423206i	$0.860905\pi$
$464$	42.5063	1.97330
$465$	−0.431603	−0.0200151
$466$	−0.0680325	−0.00315154
$467$	6.85955	0.317422	0.158711	−	0.987325i	$-0.449266\pi$
$467$	6.85955	0.317422	0.158711	+	0.987325i	$0.449266\pi$
$468$	−1.65224	−0.0763750
$469$	−10.2333	−0.472529
$470$	15.2002	0.701132
$471$	1.00000	0.0460776
$472$	−8.20841	−0.377823
$473$	−14.1978	−0.652818
$474$	−8.55756	−0.393062
$475$	−17.6084	−0.807929
$476$	−1.24842	−0.0572211
$477$	1.99252	0.0912311
$478$	−15.0202	−0.687007
$479$	−25.8766	−1.18233	−0.591165	−	0.806550i	$-0.701332\pi$
$479$	−25.8766	−1.18233	−0.591165	+	0.806550i	$0.701332\pi$
$480$	1.32876	0.0606494
$481$	−8.63203	−0.393586
$482$	36.3084	1.65380
$483$	42.1449	1.91766
$484$	0.919612	0.0418005
$485$	9.18319	0.416987
$486$	1.51096	0.0685386
$487$	14.6344	0.663149	0.331575	−	0.943429i	$-0.392420\pi$
$487$	14.6344	0.663149	0.331575	+	0.943429i	$0.392420\pi$
$488$	17.2274	0.779849
$489$	9.98282	0.451439
$490$	−15.7386	−0.710999
$491$	12.7555	0.575646	0.287823	−	0.957684i	$-0.407068\pi$
$491$	12.7555	0.575646	0.287823	+	0.957684i	$0.407068\pi$
$492$	−0.813858	−0.0366916
$493$	9.47550	0.426755
$494$	−36.1140	−1.62485
$495$	3.15579	0.141842
$496$	−2.31594	−0.103989
$497$	−5.48692	−0.246122
$498$	−10.8841	−0.487728
$499$	−35.5293	−1.59051	−0.795254	−	0.606276i	$-0.792663\pi$
$499$	−35.5293	−1.59051	−0.795254	+	0.606276i	$0.792663\pi$
$500$	2.20057	0.0984126
$501$	−5.94434	−0.265574
$502$	−31.3539	−1.39939
$503$	38.4200	1.71306	0.856532	−	0.516094i	$-0.172615\pi$
$503$	38.4200	1.71306	0.856532	+	0.516094i	$0.172615\pi$
$504$	−11.4443	−0.509770
$505$	−7.51928	−0.334604
$506$	−54.4917	−2.42245
$507$	21.0849	0.936415
$508$	−3.11001	−0.137984
$509$	6.47130	0.286835	0.143418	−	0.989662i	$-0.454191\pi$
$509$	6.47130	0.286835	0.143418	+	0.989662i	$0.454191\pi$
$510$	1.26317	0.0559342
$511$	−51.3986	−2.27374
$512$	−16.1458	−0.713549
$513$	4.09394	0.180752
$514$	42.4775	1.87360
$515$	2.97245	0.130982
$516$	1.06443	0.0468588
$517$	45.4240	1.99775
$518$	9.85490	0.432999
$519$	2.56947	0.112787
$520$	−12.6623	−0.555279
$521$	−21.0109	−0.920504	−0.460252	−	0.887788i	$-0.652241\pi$
$521$	−21.0109	−0.920504	−0.460252	+	0.887788i	$0.652241\pi$
$522$	−14.3171	−0.626643
$523$	−3.17411	−0.138794	−0.0693970	−	0.997589i	$-0.522108\pi$
$523$	−3.17411	−0.138794	−0.0693970	+	0.997589i	$0.522108\pi$
$524$	2.54706	0.111269
$525$	−18.9734	−0.828069
$526$	−48.6829	−2.12267
$527$	−0.516268	−0.0224890
$528$	16.9336	0.736942
$529$	68.2759	2.96852
$530$	−2.51689	−0.109327
$531$	3.16400	0.137306
$532$	5.11094	0.221587
$533$	16.7895	0.727233
$534$	−25.0702	−1.08489
$535$	−0.178778	−0.00772927
$536$	6.01825	0.259949
$537$	−23.5273	−1.01528
$538$	10.5700	0.455704
$539$	−47.0331	−2.02586
$540$	−0.236593	−0.0101813
$541$	8.17313	0.351390	0.175695	−	0.984445i	$-0.443783\pi$
$541$	8.17313	0.351390	0.175695	+	0.984445i	$0.443783\pi$
$542$	−21.5585	−0.926015
$543$	20.8338	0.894065
$544$	1.58942	0.0681457
$545$	1.90130	0.0814426
$546$	−38.9136	−1.66535
$547$	7.10732	0.303887	0.151944	−	0.988389i	$-0.451447\pi$
$547$	7.10732	0.303887	0.151944	+	0.988389i	$0.451447\pi$
$548$	−3.89593	−0.166426
$549$	−6.64046	−0.283408
$550$	24.5319	1.04604
$551$	−38.7921	−1.65260
$552$	−24.7857	−1.05495
$553$	−24.9841	−1.06243
$554$	−18.0036	−0.764902
$555$	−1.23606	−0.0524680
$556$	2.71790	0.115265
$557$	−2.69983	−0.114395	−0.0571977	−	0.998363i	$-0.518217\pi$
$557$	−2.69983	−0.114395	−0.0571977	+	0.998363i	$0.518217\pi$
$558$	0.780062	0.0330226
$559$	−21.9586	−0.928749
$560$	16.5435	0.699091
$561$	3.77485	0.159374
$562$	−1.94914	−0.0822197
$563$	−13.7837	−0.580914	−0.290457	−	0.956888i	$-0.593807\pi$
$563$	−13.7837	−0.580914	−0.290457	+	0.956888i	$0.593807\pi$
$564$	−3.40548	−0.143397
$565$	9.77236	0.411126
$566$	13.5698	0.570381
$567$	4.41131	0.185257
$568$	3.22689	0.135397
$569$	6.78604	0.284486	0.142243	−	0.989832i	$-0.454569\pi$
$569$	6.78604	0.284486	0.142243	+	0.989832i	$0.454569\pi$
$570$	−5.17135	−0.216604
$571$	−16.5982	−0.694615	−0.347307	−	0.937751i	$-0.612904\pi$
$571$	−16.5982	−0.694615	−0.347307	+	0.937751i	$0.612904\pi$
$572$	6.23696	0.260781
$573$	−14.1901	−0.592801
$574$	−19.1680	−0.800056
$575$	−41.0920	−1.71365
$576$	6.57028	0.273762
$577$	1.65006	0.0686929	0.0343465	−	0.999410i	$-0.489065\pi$
$577$	1.65006	0.0686929	0.0343465	+	0.999410i	$0.489065\pi$
$578$	1.51096	0.0628477
$579$	3.49012	0.145044
$580$	2.24184	0.0930872
$581$	−31.7765	−1.31831
$582$	−16.5973	−0.687981
$583$	−7.52144	−0.311506
$584$	30.2278	1.25084
$585$	4.88079	0.201796
$586$	29.0992	1.20208
$587$	24.8695	1.02647	0.513236	−	0.858247i	$-0.328446\pi$
$587$	24.8695	1.02647	0.513236	+	0.858247i	$0.328446\pi$
$588$	3.52612	0.145415
$589$	2.11357	0.0870882
$590$	−3.99668	−0.164541
$591$	−8.19739	−0.337196
$592$	−6.63258	−0.272598
$593$	−11.4183	−0.468893	−0.234447	−	0.972129i	$-0.575328\pi$
$593$	−11.4183	−0.468893	−0.234447	+	0.972129i	$0.575328\pi$
$594$	−5.70365	−0.234023
$595$	3.68788	0.151188
$596$	1.80233	0.0738264
$597$	8.96818	0.367043
$598$	−84.2777	−3.44637
$599$	−34.5489	−1.41163	−0.705816	−	0.708396i	$-0.749419\pi$
$599$	−34.5489	−1.41163	−0.705816	+	0.708396i	$0.749419\pi$
$600$	11.1584	0.455539
$601$	14.4655	0.590060	0.295030	−	0.955488i	$-0.404670\pi$
$601$	14.4655	0.590060	0.295030	+	0.955488i	$0.404670\pi$
$602$	25.0694	1.02175
$603$	−2.31978	−0.0944689
$604$	−5.42458	−0.220723
$605$	−2.71657	−0.110444
$606$	13.5900	0.552058
$607$	−15.1709	−0.615768	−0.307884	−	0.951424i	$-0.599621\pi$
$607$	−15.1709	−0.615768	−0.307884	+	0.951424i	$0.599621\pi$
$608$	−6.50698	−0.263893
$609$	−41.7993	−1.69379
$610$	8.38804	0.339622
$611$	70.2534	2.84215
$612$	−0.283004	−0.0114398
$613$	−20.8498	−0.842117	−0.421058	−	0.907034i	$-0.638341\pi$
$613$	−20.8498	−0.842117	−0.421058	+	0.907034i	$0.638341\pi$
$614$	−41.5326	−1.67612
$615$	2.40417	0.0969455
$616$	43.2005	1.74060
$617$	23.3214	0.938885	0.469443	−	0.882963i	$-0.344455\pi$
$617$	23.3214	0.938885	0.469443	+	0.882963i	$0.344455\pi$
$618$	−5.37227	−0.216105
$619$	−40.9406	−1.64554	−0.822772	−	0.568372i	$-0.807573\pi$
$619$	−40.9406	−1.64554	−0.822772	+	0.568372i	$0.807573\pi$
$620$	−0.122145	−0.00490548
$621$	9.55384	0.383382
$622$	0.955235	0.0383014
$623$	−73.1933	−2.93243
$624$	26.1898	1.04843
$625$	15.0049	0.600196
$626$	−2.36327	−0.0944554
$627$	−15.4540	−0.617173
$628$	0.283004	0.0112931
$629$	−1.47853	−0.0589530
$630$	−5.57224	−0.222003
$631$	11.3310	0.451082	0.225541	−	0.974234i	$-0.427585\pi$
$631$	11.3310	0.451082	0.225541	+	0.974234i	$0.427585\pi$
$632$	14.6933	0.584468
$633$	25.5807	1.01674
$634$	19.9221	0.791209
$635$	9.18709	0.364578
$636$	0.563890	0.0223597
$637$	−72.7421	−2.88215
$638$	54.0449	2.13966
$639$	−1.24383	−0.0492052
$640$	−10.9569	−0.433110
$641$	−30.2058	−1.19306	−0.596529	−	0.802592i	$-0.703454\pi$
$641$	−30.2058	−1.19306	−0.596529	+	0.802592i	$0.703454\pi$
$642$	0.323117	0.0127524
$643$	8.37905	0.330438	0.165219	−	0.986257i	$-0.447167\pi$
$643$	8.37905	0.330438	0.165219	+	0.986257i	$0.447167\pi$
$644$	11.9272	0.469997
$645$	−3.14436	−0.123809
$646$	−6.18578	−0.243376
$647$	4.77231	0.187619	0.0938095	−	0.995590i	$-0.470096\pi$
$647$	4.77231	0.187619	0.0938095	+	0.995590i	$0.470096\pi$
$648$	−2.59431	−0.101914
$649$	−11.9436	−0.468828
$650$	37.9414	1.48818
$651$	2.27742	0.0892590
$652$	2.82518	0.110642
$653$	−43.2636	−1.69303	−0.846517	−	0.532361i	$-0.821305\pi$
$653$	−43.2636	−1.69303	−0.846517	+	0.532361i	$0.821305\pi$
$654$	−3.43632	−0.134371
$655$	−7.52412	−0.293992
$656$	12.9005	0.503681
$657$	−11.6516	−0.454571
$658$	−80.2060	−3.12675
$659$	10.6321	0.414169	0.207084	−	0.978323i	$-0.433603\pi$
$659$	10.6321	0.414169	0.207084	+	0.978323i	$0.433603\pi$
$660$	0.893102	0.0347640
$661$	−32.2932	−1.25606	−0.628031	−	0.778188i	$-0.716139\pi$
$661$	−32.2932	−1.25606	−0.628031	+	0.778188i	$0.716139\pi$
$662$	46.6293	1.81230
$663$	5.83823	0.226738
$664$	18.6880	0.725234
$665$	−15.0979	−0.585473
$666$	2.23401	0.0865661
$667$	−90.5274	−3.50523
$668$	−1.68227	−0.0650891
$669$	22.9302	0.886532
$670$	2.93029	0.113207
$671$	25.0667	0.967689
$672$	−7.01141	−0.270471
$673$	26.5996	1.02534	0.512670	−	0.858586i	$-0.328656\pi$
$673$	26.5996	1.02534	0.512670	+	0.858586i	$0.328656\pi$
$674$	22.1027	0.851364
$675$	−4.30109	−0.165549
$676$	5.96712	0.229505
$677$	−41.1386	−1.58108	−0.790542	−	0.612408i	$-0.790201\pi$
$677$	−41.1386	−1.58108	−0.790542	+	0.612408i	$0.790201\pi$
$678$	−17.6621	−0.678311
$679$	−48.4565	−1.85959
$680$	−2.16886	−0.0831720
$681$	5.09238	0.195140
$682$	−2.94461	−0.112755
$683$	16.2080	0.620184	0.310092	−	0.950707i	$-0.399640\pi$
$683$	16.2080	0.620184	0.310092	+	0.950707i	$0.399640\pi$
$684$	1.15860	0.0443002
$685$	11.5087	0.439726
$686$	36.3901	1.38938
$687$	−9.45760	−0.360830
$688$	−16.8723	−0.643251
$689$	−11.6328	−0.443173
$690$	−12.0681	−0.459426
$691$	18.9584	0.721211	0.360605	−	0.932718i	$-0.382570\pi$
$691$	18.9584	0.721211	0.360605	+	0.932718i	$0.382570\pi$
$692$	0.727171	0.0276429
$693$	−16.6520	−0.632557
$694$	−23.6285	−0.896925
$695$	−8.02880	−0.304550
$696$	24.5824	0.931794
$697$	2.87578	0.108928
$698$	24.4371	0.924958
$699$	−0.0450260	−0.00170304
$700$	−5.36956	−0.202950
$701$	34.0497	1.28604	0.643020	−	0.765849i	$-0.277681\pi$
$701$	34.0497	1.28604	0.643020	+	0.765849i	$0.277681\pi$
$702$	−8.82134	−0.332940
$703$	6.05303	0.228294
$704$	−24.8018	−0.934754
$705$	10.0599	0.378879
$706$	−47.2387	−1.77785
$707$	39.6766	1.49219
$708$	0.895425	0.0336521
$709$	38.6939	1.45318	0.726591	−	0.687071i	$-0.241104\pi$
$709$	38.6939	1.45318	0.726591	+	0.687071i	$0.241104\pi$
$710$	1.57117	0.0589650
$711$	−5.66365	−0.212404
$712$	43.0454	1.61319
$713$	4.93235	0.184718
$714$	−6.66531	−0.249443
$715$	−18.4242	−0.689028
$716$	−6.65832	−0.248833
$717$	−9.94081	−0.371246
$718$	55.2789	2.06299
$719$	9.08974	0.338990	0.169495	−	0.985531i	$-0.445786\pi$
$719$	9.08974	0.338990	0.169495	+	0.985531i	$0.445786\pi$
$720$	3.75025	0.139764
$721$	−15.6845	−0.584123
$722$	−3.38406	−0.125942
$723$	24.0300	0.893685
$724$	5.89605	0.219125
$725$	40.7550	1.51360
$726$	4.90981	0.182220
$727$	7.42933	0.275539	0.137769	−	0.990464i	$-0.456007\pi$
$727$	7.42933	0.275539	0.137769	+	0.990464i	$0.456007\pi$
$728$	66.8145	2.47631
$729$	1.00000	0.0370370
$730$	14.7179	0.544735
$731$	−3.76117	−0.139112
$732$	−1.87928	−0.0694601
$733$	36.4667	1.34693	0.673464	−	0.739220i	$-0.264806\pi$
$733$	36.4667	1.34693	0.673464	+	0.739220i	$0.264806\pi$
$734$	10.5919	0.390954
$735$	−10.4163	−0.384211
$736$	−15.1850	−0.559728
$737$	8.75682	0.322562
$738$	−4.34520	−0.159949
$739$	−19.6819	−0.724009	−0.362004	−	0.932176i	$-0.617907\pi$
$739$	−19.6819	−0.724009	−0.362004	+	0.932176i	$0.617907\pi$
$740$	−0.349811	−0.0128593
$741$	−23.9013	−0.878038
$742$	13.2807	0.487551
$743$	43.5913	1.59921	0.799605	−	0.600526i	$-0.205042\pi$
$743$	43.5913	1.59921	0.799605	+	0.600526i	$0.205042\pi$
$744$	−1.33936	−0.0491034
$745$	−5.32416	−0.195062
$746$	−43.9662	−1.60972
$747$	−7.20343	−0.263560
$748$	1.06830	0.0390608
$749$	0.943351	0.0344693
$750$	11.7489	0.429009
$751$	14.5529	0.531045	0.265522	−	0.964105i	$-0.414456\pi$
$751$	14.5529	0.531045	0.265522	+	0.964105i	$0.414456\pi$
$752$	53.9806	1.96847
$753$	−20.7510	−0.756207
$754$	83.5866	3.04404
$755$	16.0244	0.583189
$756$	1.24842	0.0454045
$757$	22.7994	0.828657	0.414329	−	0.910127i	$-0.364016\pi$
$757$	22.7994	0.828657	0.414329	+	0.910127i	$0.364016\pi$
$758$	49.0853	1.78286
$759$	−36.0643	−1.30905
$760$	8.87918	0.322082
$761$	−24.3697	−0.883400	−0.441700	−	0.897163i	$-0.645624\pi$
$761$	−24.3697	−0.883400	−0.441700	+	0.897163i	$0.645624\pi$
$762$	−16.6044	−0.601512
$763$	−10.0325	−0.363200
$764$	−4.01586	−0.145289
$765$	0.836006	0.0302258
$766$	−10.9883	−0.397024
$767$	−18.4722	−0.666991
$768$	6.66252	0.240413
$769$	44.7701	1.61445	0.807226	−	0.590243i	$-0.200968\pi$
$769$	44.7701	1.61445	0.807226	+	0.590243i	$0.200968\pi$
$770$	21.0343	0.758025
$771$	28.1129	1.01246
$772$	0.987718	0.0355488
$773$	−3.77189	−0.135665	−0.0678327	−	0.997697i	$-0.521608\pi$
$773$	−3.77189	−0.135665	−0.0678327	+	0.997697i	$0.521608\pi$
$774$	5.68299	0.204271
$775$	−2.22052	−0.0797634
$776$	28.4975	1.02300
$777$	6.52227	0.233985
$778$	3.58817	0.128642
$779$	−11.7733	−0.421821
$780$	1.38128	0.0494579
$781$	4.69527	0.168010
$782$	−14.4355	−0.516212
$783$	−9.47550	−0.338627
$784$	−55.8928	−1.99617
$785$	−0.836006	−0.0298383
$786$	13.5988	0.485052
$787$	14.4137	0.513791	0.256896	−	0.966439i	$-0.417300\pi$
$787$	14.4137	0.513791	0.256896	+	0.966439i	$0.417300\pi$
$788$	−2.31990	−0.0826428
$789$	−32.2198	−1.14706
$790$	7.15417	0.254534
$791$	−51.5653	−1.83345
$792$	9.79314	0.347984
$793$	38.7685	1.37671
$794$	24.0101	0.852086
$795$	−1.66575	−0.0590782
$796$	2.53803	0.0899581
$797$	−21.1470	−0.749065	−0.374533	−	0.927214i	$-0.622197\pi$
$797$	−21.1470	−0.749065	−0.374533	+	0.927214i	$0.622197\pi$
$798$	27.2874	0.965963
$799$	12.0333	0.425709
$800$	6.83624	0.241697
$801$	−16.5922	−0.586257
$802$	13.7143	0.484267
$803$	43.9828	1.55212
$804$	−0.656508	−0.0231533
$805$	−35.2334	−1.24181
$806$	−4.55418	−0.160414
$807$	6.99553	0.246254
$808$	−23.3340	−0.820889
$809$	−40.1442	−1.41140	−0.705698	−	0.708513i	$-0.749366\pi$
$809$	−40.1442	−1.41140	−0.705698	+	0.708513i	$0.749366\pi$
$810$	−1.26317	−0.0443833
$811$	−15.6088	−0.548100	−0.274050	−	0.961716i	$-0.588363\pi$
$811$	−15.6088	−0.548100	−0.274050	+	0.961716i	$0.588363\pi$
$812$	−11.8294	−0.415130
$813$	−14.2680	−0.500402
$814$	−8.43304	−0.295578
$815$	−8.34569	−0.292337
$816$	4.48592	0.157039
$817$	15.3980	0.538708
$818$	−18.0552	−0.631285
$819$	−25.7542	−0.899925
$820$	0.680390	0.0237602
$821$	6.49905	0.226818	0.113409	−	0.993548i	$-0.463823\pi$
$821$	6.49905	0.226818	0.113409	+	0.993548i	$0.463823\pi$
$822$	−20.8004	−0.725497
$823$	−30.4232	−1.06049	−0.530244	−	0.847845i	$-0.677900\pi$
$823$	−30.4232	−1.06049	−0.530244	+	0.847845i	$0.677900\pi$
$824$	9.22417	0.321339
$825$	16.2360	0.565264
$826$	21.0890	0.733782
$827$	10.9265	0.379951	0.189976	−	0.981789i	$-0.439159\pi$
$827$	10.9265	0.379951	0.189976	+	0.981789i	$0.439159\pi$
$828$	2.70378	0.0939627
$829$	3.20613	0.111354	0.0556768	−	0.998449i	$-0.482268\pi$
$829$	3.20613	0.111354	0.0556768	+	0.998449i	$0.482268\pi$
$830$	9.09917	0.315837
$831$	−11.9154	−0.413339
$832$	−38.3588	−1.32985
$833$	−12.4596	−0.431700
$834$	14.5109	0.502472
$835$	4.96950	0.171977
$836$	−4.37354	−0.151262
$837$	0.516268	0.0178448
$838$	−20.7233	−0.715876
$839$	−34.1114	−1.17765	−0.588827	−	0.808259i	$-0.700410\pi$
$839$	−34.1114	−1.17765	−0.588827	+	0.808259i	$0.700410\pi$
$840$	9.56751	0.330110
$841$	60.7850	2.09604
$842$	9.31020	0.320851
$843$	−1.29000	−0.0444301
$844$	7.23943	0.249191
$845$	−17.6271	−0.606391
$846$	−18.1819	−0.625107
$847$	14.3344	0.492535
$848$	−8.93826	−0.306941
$849$	8.98090	0.308224
$850$	6.49879	0.222907
$851$	14.1257	0.484222
$852$	−0.352009	−0.0120596
$853$	−14.6199	−0.500577	−0.250289	−	0.968171i	$-0.580525\pi$
$853$	−14.6199	−0.500577	−0.250289	+	0.968171i	$0.580525\pi$
$854$	−44.2607	−1.51457
$855$	−3.42255	−0.117049
$856$	−0.554790	−0.0189623
$857$	−15.4409	−0.527449	−0.263725	−	0.964598i	$-0.584951\pi$
$857$	−15.4409	−0.527449	−0.263725	+	0.964598i	$0.584951\pi$
$858$	33.2992	1.13682
$859$	−4.08598	−0.139412	−0.0697059	−	0.997568i	$-0.522206\pi$
$859$	−4.08598	−0.139412	−0.0697059	+	0.997568i	$0.522206\pi$
$860$	−0.889867	−0.0303442
$861$	−12.6860	−0.432336
$862$	11.5030	0.391793
$863$	19.9392	0.678740	0.339370	−	0.940653i	$-0.389786\pi$
$863$	19.9392	0.678740	0.339370	+	0.940653i	$0.389786\pi$
$864$	−1.58942	−0.0540731
$865$	−2.14809	−0.0730374
$866$	1.72659	0.0586718
$867$	1.00000	0.0339618
$868$	0.644519	0.0218764
$869$	21.3794	0.725247
$870$	11.9692	0.405793
$871$	13.5434	0.458902
$872$	5.90016	0.199804
$873$	−10.9846	−0.371773
$874$	59.0980	1.99902
$875$	34.3013	1.15960
$876$	−3.29744	−0.111410
$877$	−13.5270	−0.456774	−0.228387	−	0.973570i	$-0.573345\pi$
$877$	−13.5270	−0.456774	−0.228387	+	0.973570i	$0.573345\pi$
$878$	−0.0887447	−0.00299499
$879$	19.2587	0.649580
$880$	−14.1566	−0.477220
$881$	−22.5559	−0.759929	−0.379964	−	0.925001i	$-0.624064\pi$
$881$	−22.5559	−0.759929	−0.379964	+	0.925001i	$0.624064\pi$
$882$	18.8260	0.633904
$883$	41.7701	1.40567	0.702837	−	0.711351i	$-0.251916\pi$
$883$	41.7701	1.40567	0.702837	+	0.711351i	$0.251916\pi$
$884$	1.65224	0.0555709
$885$	−2.64512	−0.0889148
$886$	22.4437	0.754010
$887$	−7.76674	−0.260782	−0.130391	−	0.991463i	$-0.541623\pi$
$887$	−7.76674	−0.260782	−0.130391	+	0.991463i	$0.541623\pi$
$888$	−3.83578	−0.128720
$889$	−48.4770	−1.62587
$890$	20.9588	0.702541
$891$	−3.77485	−0.126462
$892$	6.48933	0.217279
$893$	−49.2637	−1.64855
$894$	9.62266	0.321830
$895$	19.6689	0.657460
$896$	57.8158	1.93149
$897$	−55.7775	−1.86236
$898$	−49.0913	−1.63820
$899$	−4.89190	−0.163154
$900$	−1.21723	−0.0405742
$901$	−1.99252	−0.0663803
$902$	16.4024	0.546142
$903$	16.5917	0.552137
$904$	30.3258	1.00862
$905$	−17.4172	−0.578967
$906$	−28.9619	−0.962195
$907$	−25.5683	−0.848982	−0.424491	−	0.905432i	$-0.639547\pi$
$907$	−25.5683	−0.848982	−0.424491	+	0.905432i	$0.639547\pi$
$908$	1.44116	0.0478267
$909$	8.99430	0.298322
$910$	32.5320	1.07843
$911$	48.4695	1.60587	0.802933	−	0.596069i	$-0.203272\pi$
$911$	48.4695	1.60587	0.802933	+	0.596069i	$0.203272\pi$
$912$	−18.3651	−0.608128
$913$	27.1918	0.899919
$914$	47.0797	1.55726
$915$	5.55146	0.183526
$916$	−2.67654	−0.0884353
$917$	39.7021	1.31108
$918$	−1.51096	−0.0498692
$919$	−7.05992	−0.232885	−0.116443	−	0.993197i	$-0.537149\pi$
$919$	−7.05992	−0.232885	−0.116443	+	0.993197i	$0.537149\pi$
$920$	20.7210	0.683150
$921$	−27.4875	−0.905745
$922$	11.6748	0.384489
$923$	7.26177	0.239024
$924$	−4.71258	−0.155033
$925$	−6.35932	−0.209093
$926$	−58.9139	−1.93603
$927$	−3.55553	−0.116779
$928$	15.0605	0.494386
$929$	33.1564	1.08783	0.543913	−	0.839141i	$-0.316942\pi$
$929$	33.1564	1.08783	0.543913	+	0.839141i	$0.316942\pi$
$930$	−0.652136	−0.0213844
$931$	51.0089	1.67175
$932$	−0.0127425	−0.000417396 0
$933$	0.632203	0.0206974
$934$	10.3645	0.339137
$935$	−3.15579	−0.103205
$936$	15.1462	0.495069
$937$	−23.7316	−0.775279	−0.387640	−	0.921811i	$-0.626709\pi$
$937$	−23.7316	−0.775279	−0.387640	+	0.921811i	$0.626709\pi$
$938$	−15.4621	−0.504855
$939$	−1.56409	−0.0510420
$940$	2.84700	0.0928590
$941$	18.1442	0.591484	0.295742	−	0.955268i	$-0.404433\pi$
$941$	18.1442	0.591484	0.295742	+	0.955268i	$0.404433\pi$
$942$	1.51096	0.0492298
$943$	−27.4748	−0.894702
$944$	−14.1934	−0.461957
$945$	−3.68788	−0.119967
$946$	−21.4524	−0.697478
$947$	32.5579	1.05799	0.528995	−	0.848625i	$-0.322569\pi$
$947$	32.5579	1.05799	0.528995	+	0.848625i	$0.322569\pi$
$948$	−1.60284	−0.0520577
$949$	68.0245	2.20817
$950$	−26.6056	−0.863201
$951$	13.1851	0.427555
$952$	11.4443	0.370912
$953$	−33.7945	−1.09471	−0.547355	−	0.836900i	$-0.684365\pi$
$953$	−33.7945	−1.09471	−0.547355	+	0.836900i	$0.684365\pi$
$954$	3.01062	0.0974723
$955$	11.8630	0.383879
$956$	−2.81329	−0.0909883
$957$	35.7685	1.15623
$958$	−39.0985	−1.26321
$959$	−60.7275	−1.96099
$960$	−5.49279	−0.177279
$961$	−30.7335	−0.991402
$962$	−13.0427	−0.420512
$963$	0.213848	0.00689117
$964$	6.80058	0.219032
$965$	−2.91776	−0.0939260
$966$	63.6793	2.04885
$967$	−49.4418	−1.58994	−0.794971	−	0.606647i	$-0.792514\pi$
$967$	−49.4418	−1.58994	−0.794971	+	0.606647i	$0.792514\pi$
$968$	−8.43013	−0.270955
$969$	−4.09394	−0.131516
$970$	13.8754	0.445514
$971$	−40.4352	−1.29763	−0.648814	−	0.760947i	$-0.724735\pi$
$971$	−40.4352	−1.29763	−0.648814	+	0.760947i	$0.724735\pi$
$972$	0.283004	0.00907736
$973$	42.3651	1.35816
$974$	22.1121	0.708516
$975$	25.1108	0.804189
$976$	29.7885	0.953508
$977$	46.9397	1.50173	0.750867	−	0.660453i	$-0.229636\pi$
$977$	46.9397	1.50173	0.750867	+	0.660453i	$0.229636\pi$
$978$	15.0836	0.482322
$979$	62.6330	2.00176
$980$	−2.94786	−0.0941659
$981$	−2.27426	−0.0726117
$982$	19.2730	0.615027
$983$	29.8622	0.952456	0.476228	−	0.879322i	$-0.342004\pi$
$983$	29.8622	0.952456	0.476228	+	0.879322i	$0.342004\pi$
$984$	7.46068	0.237838
$985$	6.85306	0.218357
$986$	14.3171	0.455950
$987$	−53.0827	−1.68964
$988$	−6.76418	−0.215197
$989$	35.9336	1.14262
$990$	4.76828	0.151546
$991$	−42.2662	−1.34263	−0.671315	−	0.741173i	$-0.734270\pi$
$991$	−42.2662	−1.34263	−0.671315	+	0.741173i	$0.734270\pi$
$992$	−0.820566	−0.0260530
$993$	30.8607	0.979334
$994$	−8.29052	−0.262959
$995$	−7.49744	−0.237685
$996$	−2.03860	−0.0645955
$997$	8.80520	0.278864	0.139432	−	0.990232i	$-0.455472\pi$
$997$	8.80520	0.278864	0.139432	+	0.990232i	$0.455472\pi$
$998$	−53.6833	−1.69932
$999$	1.47853	0.0467788

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.35	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.35	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q+1.51096 q^{2} +1.00000 q^{3} +0.283004 q^{4} -0.836006 q^{5} +1.51096 q^{6} +4.41131 q^{7} -2.59431 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.51096 q^{2} +1.00000 q^{3} +0.283004 q^{4} -0.836006 q^{5} +1.51096 q^{6} +4.41131 q^{7} -2.59431 q^{8} +1.00000 q^{9} -1.26317 q^{10} -3.77485 q^{11} +0.283004 q^{12} -5.83823 q^{13} +6.66531 q^{14} -0.836006 q^{15} -4.48592 q^{16} -1.00000 q^{17} +1.51096 q^{18} +4.09394 q^{19} -0.236593 q^{20} +4.41131 q^{21} -5.70365 q^{22} +9.55384 q^{23} -2.59431 q^{24} -4.30109 q^{25} -8.82134 q^{26} +1.00000 q^{27} +1.24842 q^{28} -9.47550 q^{29} -1.26317 q^{30} +0.516268 q^{31} -1.58942 q^{32} -3.77485 q^{33} -1.51096 q^{34} -3.68788 q^{35} +0.283004 q^{36} +1.47853 q^{37} +6.18578 q^{38} -5.83823 q^{39} +2.16886 q^{40} -2.87578 q^{41} +6.66531 q^{42} +3.76117 q^{43} -1.06830 q^{44} -0.836006 q^{45} +14.4355 q^{46} -12.0333 q^{47} -4.48592 q^{48} +12.4596 q^{49} -6.49879 q^{50} -1.00000 q^{51} -1.65224 q^{52} +1.99252 q^{53} +1.51096 q^{54} +3.15579 q^{55} -11.4443 q^{56} +4.09394 q^{57} -14.3171 q^{58} +3.16400 q^{59} -0.236593 q^{60} -6.64046 q^{61} +0.780062 q^{62} +4.41131 q^{63} +6.57028 q^{64} +4.88079 q^{65} -5.70365 q^{66} -2.31978 q^{67} -0.283004 q^{68} +9.55384 q^{69} -5.57224 q^{70} -1.24383 q^{71} -2.59431 q^{72} -11.6516 q^{73} +2.23401 q^{74} -4.30109 q^{75} +1.15860 q^{76} -16.6520 q^{77} -8.82134 q^{78} -5.66365 q^{79} +3.75025 q^{80} +1.00000 q^{81} -4.34520 q^{82} -7.20343 q^{83} +1.24842 q^{84} +0.836006 q^{85} +5.68299 q^{86} -9.47550 q^{87} +9.79314 q^{88} -16.5922 q^{89} -1.26317 q^{90} -25.7542 q^{91} +2.70378 q^{92} +0.516268 q^{93} -18.1819 q^{94} -3.42255 q^{95} -1.58942 q^{96} -10.9846 q^{97} +18.8260 q^{98} -3.77485 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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