LMFDB - Embedded newform 8006.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8006,2,Mod(1,8006)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8006, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8006.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8006 = 2 \cdot 4003 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8006.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:	$63.9282318582$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	8006.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.23769 q^{3} +1.00000 q^{4} +1.27122 q^{5} +3.23769 q^{6} +2.87873 q^{7} -1.00000 q^{8} +7.48264 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.23769 q^{3} +1.00000 q^{4} +1.27122 q^{5} +3.23769 q^{6} +2.87873 q^{7} -1.00000 q^{8} +7.48264 q^{9} -1.27122 q^{10} -4.77782 q^{11} -3.23769 q^{12} +4.64176 q^{13} -2.87873 q^{14} -4.11580 q^{15} +1.00000 q^{16} -0.530932 q^{17} -7.48264 q^{18} +3.41867 q^{19} +1.27122 q^{20} -9.32043 q^{21} +4.77782 q^{22} -6.14112 q^{23} +3.23769 q^{24} -3.38401 q^{25} -4.64176 q^{26} -14.5134 q^{27} +2.87873 q^{28} -4.08768 q^{29} +4.11580 q^{30} -4.00447 q^{31} -1.00000 q^{32} +15.4691 q^{33} +0.530932 q^{34} +3.65948 q^{35} +7.48264 q^{36} +0.582951 q^{37} -3.41867 q^{38} -15.0286 q^{39} -1.27122 q^{40} +4.29558 q^{41} +9.32043 q^{42} +6.86941 q^{43} -4.77782 q^{44} +9.51204 q^{45} +6.14112 q^{46} -1.94983 q^{47} -3.23769 q^{48} +1.28707 q^{49} +3.38401 q^{50} +1.71899 q^{51} +4.64176 q^{52} -2.49140 q^{53} +14.5134 q^{54} -6.07364 q^{55} -2.87873 q^{56} -11.0686 q^{57} +4.08768 q^{58} +0.0907119 q^{59} -4.11580 q^{60} +0.447273 q^{61} +4.00447 q^{62} +21.5405 q^{63} +1.00000 q^{64} +5.90068 q^{65} -15.4691 q^{66} -8.23989 q^{67} -0.530932 q^{68} +19.8831 q^{69} -3.65948 q^{70} -2.95936 q^{71} -7.48264 q^{72} +5.78588 q^{73} -0.582951 q^{74} +10.9564 q^{75} +3.41867 q^{76} -13.7541 q^{77} +15.0286 q^{78} +6.28125 q^{79} +1.27122 q^{80} +24.5419 q^{81} -4.29558 q^{82} +6.02110 q^{83} -9.32043 q^{84} -0.674929 q^{85} -6.86941 q^{86} +13.2346 q^{87} +4.77782 q^{88} +0.823713 q^{89} -9.51204 q^{90} +13.3624 q^{91} -6.14112 q^{92} +12.9652 q^{93} +1.94983 q^{94} +4.34587 q^{95} +3.23769 q^{96} +7.98473 q^{97} -1.28707 q^{98} -35.7507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) $ 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * 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
$3$	−3.23769	−1.86928	−0.934641	−	0.355594i	$-0.884279\pi$
$3$	−3.23769	−1.86928	−0.934641	+	0.355594i	$0.884279\pi$
$4$	1.00000	0.500000
$5$	1.27122	0.568505	0.284252	−	0.958749i	$-0.408255\pi$
$5$	1.27122	0.568505	0.284252	+	0.958749i	$0.408255\pi$
$6$	3.23769	1.32178
$7$	2.87873	1.08806	0.544028	−	0.839067i	$-0.316898\pi$
$7$	2.87873	1.08806	0.544028	+	0.839067i	$0.316898\pi$
$8$	−1.00000	−0.353553
$9$	7.48264	2.49421
$10$	−1.27122	−0.401994
$11$	−4.77782	−1.44057	−0.720284	−	0.693679i	$-0.755989\pi$
$11$	−4.77782	−1.44057	−0.720284	+	0.693679i	$0.755989\pi$
$12$	−3.23769	−0.934641
$13$	4.64176	1.28739	0.643697	−	0.765281i	$-0.277400\pi$
$13$	4.64176	1.28739	0.643697	+	0.765281i	$0.277400\pi$
$14$	−2.87873	−0.769372
$15$	−4.11580	−1.06270
$16$	1.00000	0.250000
$17$	−0.530932	−0.128770	−0.0643850	−	0.997925i	$-0.520509\pi$
$17$	−0.530932	−0.128770	−0.0643850	+	0.997925i	$0.520509\pi$
$18$	−7.48264	−1.76367
$19$	3.41867	0.784297	0.392149	−	0.919902i	$-0.371732\pi$
$19$	3.41867	0.784297	0.392149	+	0.919902i	$0.371732\pi$
$20$	1.27122	0.284252
$21$	−9.32043	−2.03388
$22$	4.77782	1.01864
$23$	−6.14112	−1.28051	−0.640256	−	0.768161i	$-0.721172\pi$
$23$	−6.14112	−1.28051	−0.640256	+	0.768161i	$0.721172\pi$
$24$	3.23769	0.660891
$25$	−3.38401	−0.676802
$26$	−4.64176	−0.910324
$27$	−14.5134	−2.79310
$28$	2.87873	0.544028
$29$	−4.08768	−0.759062	−0.379531	−	0.925179i	$-0.623915\pi$
$29$	−4.08768	−0.759062	−0.379531	+	0.925179i	$0.623915\pi$
$30$	4.11580	0.751439
$31$	−4.00447	−0.719224	−0.359612	−	0.933102i	$-0.617091\pi$
$31$	−4.00447	−0.719224	−0.359612	+	0.933102i	$0.617091\pi$
$32$	−1.00000	−0.176777
$33$	15.4691	2.69283
$34$	0.530932	0.0910541
$35$	3.65948	0.618565
$36$	7.48264	1.24711
$37$	0.582951	0.0958366	0.0479183	−	0.998851i	$-0.484741\pi$
$37$	0.582951	0.0958366	0.0479183	+	0.998851i	$0.484741\pi$
$38$	−3.41867	−0.554582
$39$	−15.0286	−2.40650
$40$	−1.27122	−0.200997
$41$	4.29558	0.670857	0.335429	−	0.942066i	$-0.391119\pi$
$41$	4.29558	0.670857	0.335429	+	0.942066i	$0.391119\pi$
$42$	9.32043	1.43817
$43$	6.86941	1.04757	0.523787	−	0.851849i	$-0.324519\pi$
$43$	6.86941	1.04757	0.523787	+	0.851849i	$0.324519\pi$
$44$	−4.77782	−0.720284
$45$	9.51204	1.41797
$46$	6.14112	0.905459
$47$	−1.94983	−0.284411	−0.142206	−	0.989837i	$-0.545419\pi$
$47$	−1.94983	−0.284411	−0.142206	+	0.989837i	$0.545419\pi$
$48$	−3.23769	−0.467320
$49$	1.28707	0.183867
$50$	3.38401	0.478572
$51$	1.71899	0.240707
$52$	4.64176	0.643697
$53$	−2.49140	−0.342220	−0.171110	−	0.985252i	$-0.554735\pi$
$53$	−2.49140	−0.342220	−0.171110	+	0.985252i	$0.554735\pi$
$54$	14.5134	1.97502
$55$	−6.07364	−0.818970
$56$	−2.87873	−0.384686
$57$	−11.0686	−1.46607
$58$	4.08768	0.536738
$59$	0.0907119	0.0118097	0.00590484	−	0.999983i	$-0.498120\pi$
$59$	0.0907119	0.0118097	0.00590484	+	0.999983i	$0.498120\pi$
$60$	−4.11580	−0.531348
$61$	0.447273	0.0572674	0.0286337	−	0.999590i	$-0.490884\pi$
$61$	0.447273	0.0572674	0.0286337	+	0.999590i	$0.490884\pi$
$62$	4.00447	0.508568
$63$	21.5405	2.71384
$64$	1.00000	0.125000
$65$	5.90068	0.731889
$66$	−15.4691	−1.90412
$67$	−8.23989	−1.00666	−0.503331	−	0.864093i	$-0.667893\pi$
$67$	−8.23989	−1.00666	−0.503331	+	0.864093i	$0.667893\pi$
$68$	−0.530932	−0.0643850
$69$	19.8831	2.39364
$70$	−3.65948	−0.437392
$71$	−2.95936	−0.351211	−0.175606	−	0.984461i	$-0.556188\pi$
$71$	−2.95936	−0.351211	−0.175606	+	0.984461i	$0.556188\pi$
$72$	−7.48264	−0.881837
$73$	5.78588	0.677186	0.338593	−	0.940933i	$-0.390049\pi$
$73$	5.78588	0.677186	0.338593	+	0.940933i	$0.390049\pi$
$74$	−0.582951	−0.0677667
$75$	10.9564	1.26513
$76$	3.41867	0.392149
$77$	−13.7541	−1.56742
$78$	15.0286	1.70165
$79$	6.28125	0.706695	0.353348	−	0.935492i	$-0.385043\pi$
$79$	6.28125	0.706695	0.353348	+	0.935492i	$0.385043\pi$
$80$	1.27122	0.142126
$81$	24.5419	2.72688
$82$	−4.29558	−0.474368
$83$	6.02110	0.660901	0.330451	−	0.943823i	$-0.392799\pi$
$83$	6.02110	0.660901	0.330451	+	0.943823i	$0.392799\pi$
$84$	−9.32043	−1.01694
$85$	−0.674929	−0.0732063
$86$	−6.86941	−0.740747
$87$	13.2346	1.41890
$88$	4.77782	0.509318
$89$	0.823713	0.0873134	0.0436567	−	0.999047i	$-0.486099\pi$
$89$	0.823713	0.0873134	0.0436567	+	0.999047i	$0.486099\pi$
$90$	−9.51204	−1.00266
$91$	13.3624	1.40076
$92$	−6.14112	−0.640256
$93$	12.9652	1.34443
$94$	1.94983	0.201109
$95$	4.34587	0.445877
$96$	3.23769	0.330445
$97$	7.98473	0.810726	0.405363	−	0.914156i	$-0.367145\pi$
$97$	7.98473	0.810726	0.405363	+	0.914156i	$0.367145\pi$
$98$	−1.28707	−0.130014
$99$	−35.7507	−3.59308
$100$	−3.38401	−0.338401
$101$	11.2302	1.11744	0.558722	−	0.829355i	$-0.311292\pi$
$101$	11.2302	1.11744	0.558722	+	0.829355i	$0.311292\pi$
$102$	−1.71899	−0.170206
$103$	−3.04249	−0.299785	−0.149893	−	0.988702i	$-0.547893\pi$
$103$	−3.04249	−0.299785	−0.149893	+	0.988702i	$0.547893\pi$
$104$	−4.64176	−0.455162
$105$	−11.8483	−1.15627
$106$	2.49140	0.241986
$107$	9.99496	0.966249	0.483124	−	0.875552i	$-0.339502\pi$
$107$	9.99496	0.966249	0.483124	+	0.875552i	$0.339502\pi$
$108$	−14.5134	−1.39655
$109$	3.29350	0.315460	0.157730	−	0.987482i	$-0.449582\pi$
$109$	3.29350	0.315460	0.157730	+	0.987482i	$0.449582\pi$
$110$	6.07364	0.579099
$111$	−1.88741	−0.179145
$112$	2.87873	0.272014
$113$	−1.01329	−0.0953225	−0.0476612	−	0.998864i	$-0.515177\pi$
$113$	−1.01329	−0.0953225	−0.0476612	+	0.998864i	$0.515177\pi$
$114$	11.0686	1.03667
$115$	−7.80669	−0.727978
$116$	−4.08768	−0.379531
$117$	34.7326	3.21103
$118$	−0.0907119	−0.00835071
$119$	−1.52841	−0.140109
$120$	4.11580	0.375719
$121$	11.8276	1.07524
$122$	−0.447273	−0.0404942
$123$	−13.9078	−1.25402
$124$	−4.00447	−0.359612
$125$	−10.6579	−0.953270
$126$	−21.5405	−1.91898
$127$	17.1526	1.52205	0.761023	−	0.648725i	$-0.224698\pi$
$127$	17.1526	1.52205	0.761023	+	0.648725i	$0.224698\pi$
$128$	−1.00000	−0.0883883
$129$	−22.2410	−1.95821
$130$	−5.90068	−0.517524
$131$	3.77634	0.329940	0.164970	−	0.986299i	$-0.447247\pi$
$131$	3.77634	0.329940	0.164970	+	0.986299i	$0.447247\pi$
$132$	15.4691	1.34641
$133$	9.84143	0.853360
$134$	8.23989	0.711818
$135$	−18.4496	−1.58789
$136$	0.530932	0.0455271
$137$	16.7025	1.42699	0.713494	−	0.700662i	$-0.247112\pi$
$137$	16.7025	1.42699	0.713494	+	0.700662i	$0.247112\pi$
$138$	−19.8831	−1.69256
$139$	22.3948	1.89950	0.949750	−	0.313010i	$-0.101337\pi$
$139$	22.3948	1.89950	0.949750	+	0.313010i	$0.101337\pi$
$140$	3.65948	0.309283
$141$	6.31293	0.531645
$142$	2.95936	0.248344
$143$	−22.1775	−1.85458
$144$	7.48264	0.623553
$145$	−5.19632	−0.431530
$146$	−5.78588	−0.478843
$147$	−4.16714	−0.343700
$148$	0.582951	0.0479183
$149$	−0.723199	−0.0592468	−0.0296234	−	0.999561i	$-0.509431\pi$
$149$	−0.723199	−0.0592468	−0.0296234	+	0.999561i	$0.509431\pi$
$150$	−10.9564	−0.894585
$151$	−11.4215	−0.929465	−0.464732	−	0.885451i	$-0.653849\pi$
$151$	−11.4215	−0.929465	−0.464732	+	0.885451i	$0.653849\pi$
$152$	−3.41867	−0.277291
$153$	−3.97277	−0.321180
$154$	13.7541	1.10833
$155$	−5.09054	−0.408882
$156$	−15.0286	−1.20325
$157$	−2.97232	−0.237217	−0.118609	−	0.992941i	$-0.537843\pi$
$157$	−2.97232	−0.237217	−0.118609	+	0.992941i	$0.537843\pi$
$158$	−6.28125	−0.499709
$159$	8.06637	0.639705
$160$	−1.27122	−0.100498
$161$	−17.6786	−1.39327
$162$	−24.5419	−1.92820
$163$	−23.1375	−1.81227	−0.906134	−	0.422992i	$-0.860980\pi$
$163$	−23.1375	−1.81227	−0.906134	+	0.422992i	$0.860980\pi$
$164$	4.29558	0.335429
$165$	19.6646	1.53088
$166$	−6.02110	−0.467328
$167$	−5.34107	−0.413305	−0.206652	−	0.978414i	$-0.566257\pi$
$167$	−5.34107	−0.413305	−0.206652	+	0.978414i	$0.566257\pi$
$168$	9.32043	0.719087
$169$	8.54596	0.657381
$170$	0.674929	0.0517647
$171$	25.5807	1.95620
$172$	6.86941	0.523787
$173$	−8.03832	−0.611142	−0.305571	−	0.952169i	$-0.598847\pi$
$173$	−8.03832	−0.611142	−0.305571	+	0.952169i	$0.598847\pi$
$174$	−13.2346	−1.00331
$175$	−9.74165	−0.736399
$176$	−4.77782	−0.360142
$177$	−0.293697	−0.0220756
$178$	−0.823713	−0.0617399
$179$	−18.7670	−1.40271	−0.701355	−	0.712812i	$-0.747421\pi$
$179$	−18.7670	−1.40271	−0.701355	+	0.712812i	$0.747421\pi$
$180$	9.51204	0.708986
$181$	24.2638	1.80352	0.901758	−	0.432241i	$-0.142277\pi$
$181$	24.2638	1.80352	0.901758	+	0.432241i	$0.142277\pi$
$182$	−13.3624	−0.990485
$183$	−1.44813	−0.107049
$184$	6.14112	0.452730
$185$	0.741056	0.0544835
$186$	−12.9652	−0.950657
$187$	2.53670	0.185502
$188$	−1.94983	−0.142206
$189$	−41.7801	−3.03905
$190$	−4.34587	−0.315282
$191$	−14.2245	−1.02925	−0.514624	−	0.857416i	$-0.672068\pi$
$191$	−14.2245	−1.02925	−0.514624	+	0.857416i	$0.672068\pi$
$192$	−3.23769	−0.233660
$193$	0.801739	0.0577105	0.0288552	−	0.999584i	$-0.490814\pi$
$193$	0.801739	0.0577105	0.0288552	+	0.999584i	$0.490814\pi$
$194$	−7.98473	−0.573270
$195$	−19.1046	−1.36811
$196$	1.28707	0.0919336
$197$	−1.43630	−0.102332	−0.0511659	−	0.998690i	$-0.516294\pi$
$197$	−1.43630	−0.102332	−0.0511659	+	0.998690i	$0.516294\pi$
$198$	35.7507	2.54069
$199$	−7.34485	−0.520663	−0.260331	−	0.965519i	$-0.583832\pi$
$199$	−7.34485	−0.520663	−0.260331	+	0.965519i	$0.583832\pi$
$200$	3.38401	0.239286
$201$	26.6782	1.88174
$202$	−11.2302	−0.790152
$203$	−11.7673	−0.825903
$204$	1.71899	0.120354
$205$	5.46061	0.381386
$206$	3.04249	0.211980
$207$	−45.9518	−3.19387
$208$	4.64176	0.321848
$209$	−16.3338	−1.12983
$210$	11.8483	0.817608
$211$	6.79221	0.467595	0.233797	−	0.972285i	$-0.424885\pi$
$211$	6.79221	0.467595	0.233797	+	0.972285i	$0.424885\pi$
$212$	−2.49140	−0.171110
$213$	9.58149	0.656513
$214$	−9.99496	−0.683241
$215$	8.73250	0.595551
$216$	14.5134	0.987511
$217$	−11.5278	−0.782557
$218$	−3.29350	−0.223064
$219$	−18.7329	−1.26585
$220$	−6.07364	−0.409485
$221$	−2.46446	−0.165778
$222$	1.88741	0.126675
$223$	−15.6545	−1.04830	−0.524151	−	0.851626i	$-0.675617\pi$
$223$	−15.6545	−1.04830	−0.524151	+	0.851626i	$0.675617\pi$
$224$	−2.87873	−0.192343
$225$	−25.3213	−1.68809
$226$	1.01329	0.0674032
$227$	−25.8441	−1.71533	−0.857667	−	0.514206i	$-0.828087\pi$
$227$	−25.8441	−1.71533	−0.857667	+	0.514206i	$0.828087\pi$
$228$	−11.0686	−0.733036
$229$	20.7765	1.37295	0.686476	−	0.727153i	$-0.259157\pi$
$229$	20.7765	1.37295	0.686476	+	0.727153i	$0.259157\pi$
$230$	7.80669	0.514758
$231$	44.5314	2.92995
$232$	4.08768	0.268369
$233$	−11.5367	−0.755794	−0.377897	−	0.925848i	$-0.623353\pi$
$233$	−11.5367	−0.755794	−0.377897	+	0.925848i	$0.623353\pi$
$234$	−34.7326	−2.27054
$235$	−2.47865	−0.161689
$236$	0.0907119	0.00590484
$237$	−20.3367	−1.32101
$238$	1.52841	0.0990721
$239$	−25.9980	−1.68167	−0.840835	−	0.541291i	$-0.817936\pi$
$239$	−25.9980	−1.68167	−0.840835	+	0.541291i	$0.817936\pi$
$240$	−4.11580	−0.265674
$241$	15.4443	0.994856	0.497428	−	0.867505i	$-0.334278\pi$
$241$	15.4443	0.994856	0.497428	+	0.867505i	$0.334278\pi$
$242$	−11.8276	−0.760307
$243$	−35.9190	−2.30421
$244$	0.447273	0.0286337
$245$	1.63614	0.104529
$246$	13.9078	0.886727
$247$	15.8687	1.00970
$248$	4.00447	0.254284
$249$	−19.4944	−1.23541
$250$	10.6579	0.674064
$251$	26.9230	1.69937	0.849683	−	0.527293i	$-0.176793\pi$
$251$	26.9230	1.69937	0.849683	+	0.527293i	$0.176793\pi$
$252$	21.5405	1.35692
$253$	29.3412	1.84467
$254$	−17.1526	−1.07625
$255$	2.18521	0.136843
$256$	1.00000	0.0625000
$257$	26.1372	1.63040	0.815198	−	0.579183i	$-0.196628\pi$
$257$	26.1372	1.63040	0.815198	+	0.579183i	$0.196628\pi$
$258$	22.2410	1.38466
$259$	1.67816	0.104276
$260$	5.90068	0.365945
$261$	−30.5866	−1.89326
$262$	−3.77634	−0.233303
$263$	10.6768	0.658362	0.329181	−	0.944267i	$-0.393227\pi$
$263$	10.6768	0.658362	0.329181	+	0.944267i	$0.393227\pi$
$264$	−15.4691	−0.952058
$265$	−3.16710	−0.194554
$266$	−9.84143	−0.603417
$267$	−2.66693	−0.163213
$268$	−8.23989	−0.503331
$269$	15.6248	0.952660	0.476330	−	0.879266i	$-0.341967\pi$
$269$	15.6248	0.952660	0.476330	+	0.879266i	$0.341967\pi$
$270$	18.4496	1.12281
$271$	15.2841	0.928445	0.464222	−	0.885719i	$-0.346334\pi$
$271$	15.2841	0.928445	0.464222	+	0.885719i	$0.346334\pi$
$272$	−0.530932	−0.0321925
$273$	−43.2632	−2.61841
$274$	−16.7025	−1.00903
$275$	16.1682	0.974980
$276$	19.8831	1.19682
$277$	−17.7797	−1.06828	−0.534140	−	0.845396i	$-0.679364\pi$
$277$	−17.7797	−1.06828	−0.534140	+	0.845396i	$0.679364\pi$
$278$	−22.3948	−1.34315
$279$	−29.9640	−1.79390
$280$	−3.65948	−0.218696
$281$	3.68894	0.220064	0.110032	−	0.993928i	$-0.464905\pi$
$281$	3.68894	0.220064	0.110032	+	0.993928i	$0.464905\pi$
$282$	−6.31293	−0.375930
$283$	−3.35236	−0.199277	−0.0996386	−	0.995024i	$-0.531769\pi$
$283$	−3.35236	−0.199277	−0.0996386	+	0.995024i	$0.531769\pi$
$284$	−2.95936	−0.175606
$285$	−14.0706	−0.833469
$286$	22.1775	1.31138
$287$	12.3658	0.729931
$288$	−7.48264	−0.440919
$289$	−16.7181	−0.983418
$290$	5.19632	0.305138
$291$	−25.8521	−1.51548
$292$	5.78588	0.338593
$293$	32.0613	1.87304	0.936521	−	0.350612i	$-0.114026\pi$
$293$	32.0613	1.87304	0.936521	+	0.350612i	$0.114026\pi$
$294$	4.16714	0.243032
$295$	0.115314	0.00671386
$296$	−0.582951	−0.0338833
$297$	69.3424	4.02365
$298$	0.723199	0.0418938
$299$	−28.5056	−1.64852
$300$	10.9564	0.632567
$301$	19.7752	1.13982
$302$	11.4215	0.657231
$303$	−36.3598	−2.08882
$304$	3.41867	0.196074
$305$	0.568580	0.0325568
$306$	3.97277	0.227108
$307$	15.6317	0.892149	0.446074	−	0.894996i	$-0.352822\pi$
$307$	15.6317	0.892149	0.446074	+	0.894996i	$0.352822\pi$
$308$	−13.7541	−0.783710
$309$	9.85064	0.560383
$310$	5.09054	0.289124
$311$	−13.5882	−0.770514	−0.385257	−	0.922809i	$-0.625887\pi$
$311$	−13.5882	−0.770514	−0.385257	+	0.922809i	$0.625887\pi$
$312$	15.0286	0.850826
$313$	12.3922	0.700451	0.350226	−	0.936665i	$-0.386105\pi$
$313$	12.3922	0.700451	0.350226	+	0.936665i	$0.386105\pi$
$314$	2.97232	0.167738
$315$	27.3826	1.54283
$316$	6.28125	0.353348
$317$	29.6381	1.66464	0.832320	−	0.554295i	$-0.187012\pi$
$317$	29.6381	1.66464	0.832320	+	0.554295i	$0.187012\pi$
$318$	−8.06637	−0.452340
$319$	19.5302	1.09348
$320$	1.27122	0.0710631
$321$	−32.3606	−1.80619
$322$	17.6786	0.985191
$323$	−1.81508	−0.100994
$324$	24.5419	1.36344
$325$	−15.7078	−0.871311
$326$	23.1375	1.28147
$327$	−10.6633	−0.589684
$328$	−4.29558	−0.237184
$329$	−5.61302	−0.309456
$330$	−19.6646	−1.08250
$331$	14.5171	0.797930	0.398965	−	0.916966i	$-0.369369\pi$
$331$	14.5171	0.797930	0.398965	+	0.916966i	$0.369369\pi$
$332$	6.02110	0.330451
$333$	4.36201	0.239037
$334$	5.34107	0.292251
$335$	−10.4747	−0.572293
$336$	−9.32043	−0.508471
$337$	−4.04800	−0.220509	−0.110254	−	0.993903i	$-0.535167\pi$
$337$	−4.04800	−0.220509	−0.110254	+	0.993903i	$0.535167\pi$
$338$	−8.54596	−0.464839
$339$	3.28072	0.178185
$340$	−0.674929	−0.0366032
$341$	19.1327	1.03609
$342$	−25.5807	−1.38325
$343$	−16.4460	−0.887999
$344$	−6.86941	−0.370374
$345$	25.2756	1.36079
$346$	8.03832	0.432143
$347$	−9.79624	−0.525890	−0.262945	−	0.964811i	$-0.584694\pi$
$347$	−9.79624	−0.525890	−0.262945	+	0.964811i	$0.584694\pi$
$348$	13.2346	0.709450
$349$	17.5945	0.941810	0.470905	−	0.882184i	$-0.343927\pi$
$349$	17.5945	0.941810	0.470905	+	0.882184i	$0.343927\pi$
$350$	9.74165	0.520713
$351$	−67.3677	−3.59582
$352$	4.77782	0.254659
$353$	−12.0260	−0.640081	−0.320040	−	0.947404i	$-0.603697\pi$
$353$	−12.0260	−0.640081	−0.320040	+	0.947404i	$0.603697\pi$
$354$	0.293697	0.0156098
$355$	−3.76198	−0.199665
$356$	0.823713	0.0436567
$357$	4.94852	0.261903
$358$	18.7670	0.991866
$359$	4.31446	0.227708	0.113854	−	0.993497i	$-0.463680\pi$
$359$	4.31446	0.227708	0.113854	+	0.993497i	$0.463680\pi$
$360$	−9.51204	−0.501329
$361$	−7.31267	−0.384878
$362$	−24.2638	−1.27528
$363$	−38.2941	−2.00992
$364$	13.3624	0.700378
$365$	7.35510	0.384983
$366$	1.44813	0.0756950
$367$	16.3122	0.851488	0.425744	−	0.904844i	$-0.360012\pi$
$367$	16.3122	0.851488	0.425744	+	0.904844i	$0.360012\pi$
$368$	−6.14112	−0.320128
$369$	32.1423	1.67326
$370$	−0.741056	−0.0385257
$371$	−7.17205	−0.372354
$372$	12.9652	0.672216
$373$	−13.8756	−0.718453	−0.359227	−	0.933250i	$-0.616959\pi$
$373$	−13.8756	−0.718453	−0.359227	+	0.933250i	$0.616959\pi$
$374$	−2.53670	−0.131170
$375$	34.5069	1.78193
$376$	1.94983	0.100555
$377$	−18.9740	−0.977212
$378$	41.7801	2.14894
$379$	1.53050	0.0786166	0.0393083	−	0.999227i	$-0.487485\pi$
$379$	1.53050	0.0786166	0.0393083	+	0.999227i	$0.487485\pi$
$380$	4.34587	0.222938
$381$	−55.5347	−2.84513
$382$	14.2245	0.727788
$383$	26.3519	1.34652	0.673258	−	0.739407i	$-0.264894\pi$
$383$	26.3519	1.34652	0.673258	+	0.739407i	$0.264894\pi$
$384$	3.23769	0.165223
$385$	−17.4844	−0.891086
$386$	−0.801739	−0.0408075
$387$	51.4013	2.61287
$388$	7.98473	0.405363
$389$	−20.0116	−1.01463	−0.507315	−	0.861760i	$-0.669362\pi$
$389$	−20.0116	−1.01463	−0.507315	+	0.861760i	$0.669362\pi$
$390$	19.1046	0.967397
$391$	3.26052	0.164892
$392$	−1.28707	−0.0650069
$393$	−12.2266	−0.616751
$394$	1.43630	0.0723595
$395$	7.98481	0.401760
$396$	−35.7507	−1.79654
$397$	−20.8542	−1.04664	−0.523322	−	0.852135i	$-0.675307\pi$
$397$	−20.8542	−1.04664	−0.523322	+	0.852135i	$0.675307\pi$
$398$	7.34485	0.368164
$399$	−31.8635	−1.59517
$400$	−3.38401	−0.169201
$401$	10.5615	0.527414	0.263707	−	0.964603i	$-0.415055\pi$
$401$	10.5615	0.527414	0.263707	+	0.964603i	$0.415055\pi$
$402$	−26.6782	−1.33059
$403$	−18.5878	−0.925924
$404$	11.2302	0.558722
$405$	31.1981	1.55025
$406$	11.7673	0.584001
$407$	−2.78524	−0.138059
$408$	−1.71899	−0.0851029
$409$	−13.7731	−0.681038	−0.340519	−	0.940238i	$-0.610603\pi$
$409$	−13.7731	−0.681038	−0.340519	+	0.940238i	$0.610603\pi$
$410$	−5.46061	−0.269680
$411$	−54.0774	−2.66744
$412$	−3.04249	−0.149893
$413$	0.261135	0.0128496
$414$	45.9518	2.25841
$415$	7.65411	0.375726
$416$	−4.64176	−0.227581
$417$	−72.5073	−3.55070
$418$	16.3338	0.798913
$419$	1.65852	0.0810239	0.0405119	−	0.999179i	$-0.487101\pi$
$419$	1.65852	0.0810239	0.0405119	+	0.999179i	$0.487101\pi$
$420$	−11.8483	−0.578136
$421$	3.39765	0.165592	0.0827958	−	0.996567i	$-0.473615\pi$
$421$	3.39765	0.165592	0.0827958	+	0.996567i	$0.473615\pi$
$422$	−6.79221	−0.330639
$423$	−14.5898	−0.709382
$424$	2.49140	0.120993
$425$	1.79668	0.0871518
$426$	−9.58149	−0.464225
$427$	1.28758	0.0623102
$428$	9.99496	0.483124
$429$	71.8039	3.46673
$430$	−8.73250	−0.421118
$431$	18.5718	0.894574	0.447287	−	0.894391i	$-0.352390\pi$
$431$	18.5718	0.894574	0.447287	+	0.894391i	$0.352390\pi$
$432$	−14.5134	−0.698276
$433$	−23.5974	−1.13402	−0.567009	−	0.823712i	$-0.691899\pi$
$433$	−23.5974	−1.13402	−0.567009	+	0.823712i	$0.691899\pi$
$434$	11.5278	0.553351
$435$	16.8241	0.806652
$436$	3.29350	0.157730
$437$	−20.9945	−1.00430
$438$	18.7329	0.895092
$439$	29.1618	1.39182	0.695909	−	0.718130i	$-0.255002\pi$
$439$	29.1618	1.39182	0.695909	+	0.718130i	$0.255002\pi$
$440$	6.07364	0.289550
$441$	9.63068	0.458604
$442$	2.46446	0.117222
$443$	17.1972	0.817062	0.408531	−	0.912744i	$-0.366041\pi$
$443$	17.1972	0.817062	0.408531	+	0.912744i	$0.366041\pi$
$444$	−1.88741	−0.0895727
$445$	1.04712	0.0496381
$446$	15.6545	0.741261
$447$	2.34149	0.110749
$448$	2.87873	0.136007
$449$	12.7081	0.599730	0.299865	−	0.953982i	$-0.403058\pi$
$449$	12.7081	0.599730	0.299865	+	0.953982i	$0.403058\pi$
$450$	25.3213	1.19366
$451$	−20.5235	−0.966416
$452$	−1.01329	−0.0476612
$453$	36.9791	1.73743
$454$	25.8441	1.21292
$455$	16.9864	0.796337
$456$	11.0686	0.518335
$457$	−14.3847	−0.672888	−0.336444	−	0.941704i	$-0.609224\pi$
$457$	−14.3847	−0.672888	−0.336444	+	0.941704i	$0.609224\pi$
$458$	−20.7765	−0.970823
$459$	7.70563	0.359668
$460$	−7.80669	−0.363989
$461$	20.1639	0.939126	0.469563	−	0.882899i	$-0.344411\pi$
$461$	20.1639	0.939126	0.469563	+	0.882899i	$0.344411\pi$
$462$	−44.5314	−2.07179
$463$	−7.91941	−0.368046	−0.184023	−	0.982922i	$-0.558912\pi$
$463$	−7.91941	−0.368046	−0.184023	+	0.982922i	$0.558912\pi$
$464$	−4.08768	−0.189766
$465$	16.4816	0.764316
$466$	11.5367	0.534427
$467$	15.6782	0.725501	0.362750	−	0.931886i	$-0.381838\pi$
$467$	15.6782	0.725501	0.362750	+	0.931886i	$0.381838\pi$
$468$	34.7326	1.60552
$469$	−23.7204	−1.09531
$470$	2.47865	0.114332
$471$	9.62346	0.443426
$472$	−0.0907119	−0.00417535
$473$	−32.8208	−1.50910
$474$	20.3367	0.934097
$475$	−11.5688	−0.530814
$476$	−1.52841	−0.0700545
$477$	−18.6422	−0.853569
$478$	25.9980	1.18912
$479$	−5.00632	−0.228745	−0.114372	−	0.993438i	$-0.536486\pi$
$479$	−5.00632	−0.228745	−0.114372	+	0.993438i	$0.536486\pi$
$480$	4.11580	0.187860
$481$	2.70592	0.123379
$482$	−15.4443	−0.703470
$483$	57.2379	2.60441
$484$	11.8276	0.537618
$485$	10.1503	0.460902
$486$	35.9190	1.62932
$487$	31.0747	1.40813	0.704064	−	0.710136i	$-0.251367\pi$
$487$	31.0747	1.40813	0.704064	+	0.710136i	$0.251367\pi$
$488$	−0.447273	−0.0202471
$489$	74.9120	3.38764
$490$	−1.63614	−0.0739134
$491$	6.23502	0.281382	0.140691	−	0.990054i	$-0.455068\pi$
$491$	6.23502	0.281382	0.140691	+	0.990054i	$0.455068\pi$
$492$	−13.9078	−0.627010
$493$	2.17028	0.0977445
$494$	−15.8687	−0.713965
$495$	−45.4469	−2.04268
$496$	−4.00447	−0.179806
$497$	−8.51919	−0.382138
$498$	19.4944	0.873567
$499$	20.2649	0.907183	0.453591	−	0.891210i	$-0.350143\pi$
$499$	20.2649	0.907183	0.453591	+	0.891210i	$0.350143\pi$
$500$	−10.6579	−0.476635
$501$	17.2927	0.772583
$502$	−26.9230	−1.20163
$503$	2.15199	0.0959526	0.0479763	−	0.998848i	$-0.484723\pi$
$503$	2.15199	0.0959526	0.0479763	+	0.998848i	$0.484723\pi$
$504$	−21.5405	−0.959489
$505$	14.2760	0.635272
$506$	−29.3412	−1.30438
$507$	−27.6692	−1.22883
$508$	17.1526	0.761023
$509$	6.21726	0.275575	0.137788	−	0.990462i	$-0.456001\pi$
$509$	6.21726	0.275575	0.137788	+	0.990462i	$0.456001\pi$
$510$	−2.18521	−0.0967628
$511$	16.6560	0.736817
$512$	−1.00000	−0.0441942
$513$	−49.6165	−2.19062
$514$	−26.1372	−1.15286
$515$	−3.86766	−0.170429
$516$	−22.2410	−0.979106
$517$	9.31593	0.409714
$518$	−1.67816	−0.0737340
$519$	26.0256	1.14240
$520$	−5.90068	−0.258762
$521$	−11.8146	−0.517608	−0.258804	−	0.965930i	$-0.583328\pi$
$521$	−11.8146	−0.517608	−0.258804	+	0.965930i	$0.583328\pi$
$522$	30.5866	1.33874
$523$	−9.17308	−0.401111	−0.200555	−	0.979682i	$-0.564275\pi$
$523$	−9.17308	−0.401111	−0.200555	+	0.979682i	$0.564275\pi$
$524$	3.77634	0.164970
$525$	31.5404	1.37654
$526$	−10.6768	−0.465532
$527$	2.12610	0.0926145
$528$	15.4691	0.673207
$529$	14.7134	0.639713
$530$	3.16710	0.137570
$531$	0.678764	0.0294559
$532$	9.84143	0.426680
$533$	19.9391	0.863657
$534$	2.66693	0.115409
$535$	12.7057	0.549317
$536$	8.23989	0.355909
$537$	60.7617	2.62206
$538$	−15.6248	−0.673633
$539$	−6.14940	−0.264873
$540$	−18.4496	−0.793946
$541$	29.7842	1.28052	0.640262	−	0.768156i	$-0.278826\pi$
$541$	29.7842	1.28052	0.640262	+	0.768156i	$0.278826\pi$
$542$	−15.2841	−0.656510
$543$	−78.5587	−3.37128
$544$	0.530932	0.0227635
$545$	4.18675	0.179341
$546$	43.2632	1.85149
$547$	−37.5528	−1.60564	−0.802821	−	0.596221i	$-0.796668\pi$
$547$	−37.5528	−1.60564	−0.802821	+	0.596221i	$0.796668\pi$
$548$	16.7025	0.713494
$549$	3.34678	0.142837
$550$	−16.1682	−0.689415
$551$	−13.9744	−0.595331
$552$	−19.8831	−0.846279
$553$	18.0820	0.768925
$554$	17.7797	0.755388
$555$	−2.39931	−0.101845
$556$	22.3948	0.949750
$557$	−5.46480	−0.231551	−0.115775	−	0.993275i	$-0.536935\pi$
$557$	−5.46480	−0.231551	−0.115775	+	0.993275i	$0.536935\pi$
$558$	29.9640	1.26848
$559$	31.8862	1.34864
$560$	3.65948	0.154641
$561$	−8.21305	−0.346755
$562$	−3.68894	−0.155608
$563$	−4.74390	−0.199932	−0.0999659	−	0.994991i	$-0.531873\pi$
$563$	−4.74390	−0.199932	−0.0999659	+	0.994991i	$0.531873\pi$
$564$	6.31293	0.265822
$565$	−1.28811	−0.0541913
$566$	3.35236	0.140910
$567$	70.6495	2.96700
$568$	2.95936	0.124172
$569$	−17.6534	−0.740071	−0.370036	−	0.929018i	$-0.620654\pi$
$569$	−17.6534	−0.740071	−0.370036	+	0.929018i	$0.620654\pi$
$570$	14.0706	0.589352
$571$	31.9890	1.33870	0.669349	−	0.742948i	$-0.266573\pi$
$571$	31.9890	1.33870	0.669349	+	0.742948i	$0.266573\pi$
$572$	−22.1775	−0.927289
$573$	46.0545	1.92395
$574$	−12.3658	−0.516139
$575$	20.7816	0.866654
$576$	7.48264	0.311777
$577$	−5.59453	−0.232903	−0.116452	−	0.993196i	$-0.537152\pi$
$577$	−5.59453	−0.232903	−0.116452	+	0.993196i	$0.537152\pi$
$578$	16.7181	0.695382
$579$	−2.59578	−0.107877
$580$	−5.19632	−0.215765
$581$	17.3331	0.719098
$582$	25.8521	1.07160
$583$	11.9035	0.492991
$584$	−5.78588	−0.239421
$585$	44.1526	1.82549
$586$	−32.0613	−1.32444
$587$	46.0158	1.89928	0.949638	−	0.313349i	$-0.101451\pi$
$587$	46.0158	1.89928	0.949638	+	0.313349i	$0.101451\pi$
$588$	−4.16714	−0.171850
$589$	−13.6900	−0.564086
$590$	−0.115314	−0.00474742
$591$	4.65028	0.191287
$592$	0.582951	0.0239591
$593$	−32.1453	−1.32005	−0.660025	−	0.751243i	$-0.729454\pi$
$593$	−32.1453	−1.32005	−0.660025	+	0.751243i	$0.729454\pi$
$594$	−69.3424	−2.84515
$595$	−1.94294	−0.0796527
$596$	−0.723199	−0.0296234
$597$	23.7804	0.973265
$598$	28.5056	1.16568
$599$	27.6609	1.13019	0.565097	−	0.825024i	$-0.308839\pi$
$599$	27.6609	1.13019	0.565097	+	0.825024i	$0.308839\pi$
$600$	−10.9564	−0.447292
$601$	−12.5652	−0.512545	−0.256272	−	0.966605i	$-0.582494\pi$
$601$	−12.5652	−0.512545	−0.256272	+	0.966605i	$0.582494\pi$
$602$	−19.7752	−0.805975
$603$	−61.6561	−2.51083
$604$	−11.4215	−0.464732
$605$	15.0354	0.611277
$606$	36.3598	1.47702
$607$	18.8492	0.765065	0.382533	−	0.923942i	$-0.375052\pi$
$607$	18.8492	0.765065	0.382533	+	0.923942i	$0.375052\pi$
$608$	−3.41867	−0.138646
$609$	38.0989	1.54384
$610$	−0.568580	−0.0230211
$611$	−9.05063	−0.366149
$612$	−3.97277	−0.160590
$613$	16.9294	0.683770	0.341885	−	0.939742i	$-0.388935\pi$
$613$	16.9294	0.683770	0.341885	+	0.939742i	$0.388935\pi$
$614$	−15.6317	−0.630844
$615$	−17.6798	−0.712917
$616$	13.7541	0.554167
$617$	−6.99988	−0.281804	−0.140902	−	0.990024i	$-0.545000\pi$
$617$	−6.99988	−0.281804	−0.140902	+	0.990024i	$0.545000\pi$
$618$	−9.85064	−0.396251
$619$	6.33107	0.254467	0.127234	−	0.991873i	$-0.459390\pi$
$619$	6.33107	0.254467	0.127234	+	0.991873i	$0.459390\pi$
$620$	−5.09054	−0.204441
$621$	89.1285	3.57660
$622$	13.5882	0.544836
$623$	2.37124	0.0950019
$624$	−15.0286	−0.601625
$625$	3.37160	0.134864
$626$	−12.3922	−0.495294
$627$	52.8838	2.11198
$628$	−2.97232	−0.118609
$629$	−0.309508	−0.0123409
$630$	−27.3826	−1.09095
$631$	−45.5520	−1.81340	−0.906699	−	0.421779i	$-0.861406\pi$
$631$	−45.5520	−1.81340	−0.906699	+	0.421779i	$0.861406\pi$
$632$	−6.28125	−0.249855
$633$	−21.9911	−0.874066
$634$	−29.6381	−1.17708
$635$	21.8046	0.865290
$636$	8.06637	0.319852
$637$	5.97428	0.236709
$638$	−19.5302	−0.773208
$639$	−22.1438	−0.875996
$640$	−1.27122	−0.0502492
$641$	17.4369	0.688717	0.344358	−	0.938838i	$-0.388097\pi$
$641$	17.4369	0.688717	0.344358	+	0.938838i	$0.388097\pi$
$642$	32.3606	1.27717
$643$	−39.6803	−1.56484	−0.782420	−	0.622751i	$-0.786015\pi$
$643$	−39.6803	−1.56484	−0.782420	+	0.622751i	$0.786015\pi$
$644$	−17.6786	−0.696635
$645$	−28.2731	−1.11325
$646$	1.81508	0.0714135
$647$	8.04605	0.316323	0.158161	−	0.987413i	$-0.449443\pi$
$647$	8.04605	0.316323	0.158161	+	0.987413i	$0.449443\pi$
$648$	−24.5419	−0.964098
$649$	−0.433406	−0.0170127
$650$	15.7078	0.616110
$651$	37.3234	1.46282
$652$	−23.1375	−0.906134
$653$	−8.35807	−0.327077	−0.163538	−	0.986537i	$-0.552291\pi$
$653$	−8.35807	−0.327077	−0.163538	+	0.986537i	$0.552291\pi$
$654$	10.6633	0.416970
$655$	4.80053	0.187572
$656$	4.29558	0.167714
$657$	43.2936	1.68905
$658$	5.61302	0.218818
$659$	26.8448	1.04572	0.522862	−	0.852417i	$-0.324864\pi$
$659$	26.8448	1.04572	0.522862	+	0.852417i	$0.324864\pi$
$660$	19.6646	0.765442
$661$	49.8671	1.93961	0.969803	−	0.243891i	$-0.0784241\pi$
$661$	49.8671	1.93961	0.969803	+	0.243891i	$0.0784241\pi$
$662$	−14.5171	−0.564222
$663$	7.97916	0.309885
$664$	−6.02110	−0.233664
$665$	12.5106	0.485139
$666$	−4.36201	−0.169024
$667$	25.1029	0.971989
$668$	−5.34107	−0.206652
$669$	50.6843	1.95957
$670$	10.4747	0.404672
$671$	−2.13699	−0.0824976
$672$	9.32043	0.359543
$673$	−9.70817	−0.374222	−0.187111	−	0.982339i	$-0.559912\pi$
$673$	−9.70817	−0.374222	−0.187111	+	0.982339i	$0.559912\pi$
$674$	4.04800	0.155923
$675$	49.1135	1.89038
$676$	8.54596	0.328691
$677$	−14.2178	−0.546436	−0.273218	−	0.961952i	$-0.588088\pi$
$677$	−14.2178	−0.546436	−0.273218	+	0.961952i	$0.588088\pi$
$678$	−3.28072	−0.125995
$679$	22.9859	0.882116
$680$	0.674929	0.0258824
$681$	83.6752	3.20644
$682$	−19.1327	−0.732627
$683$	−3.64804	−0.139588	−0.0697942	−	0.997561i	$-0.522234\pi$
$683$	−3.64804	−0.139588	−0.0697942	+	0.997561i	$0.522234\pi$
$684$	25.5807	0.978102
$685$	21.2324	0.811249
$686$	16.4460	0.627910
$687$	−67.2679	−2.56643
$688$	6.86941	0.261894
$689$	−11.5645	−0.440571
$690$	−25.2756	−0.962227
$691$	44.3107	1.68566	0.842830	−	0.538180i	$-0.180888\pi$
$691$	44.3107	1.68566	0.842830	+	0.538180i	$0.180888\pi$
$692$	−8.03832	−0.305571
$693$	−102.917	−3.90948
$694$	9.79624	0.371860
$695$	28.4686	1.07987
$696$	−13.2346	−0.501657
$697$	−2.28066	−0.0863863
$698$	−17.5945	−0.665960
$699$	37.3523	1.41279
$700$	−9.74165	−0.368200
$701$	−29.2961	−1.10650	−0.553250	−	0.833015i	$-0.686612\pi$
$701$	−29.2961	−1.10650	−0.553250	+	0.833015i	$0.686612\pi$
$702$	67.3677	2.54263
$703$	1.99292	0.0751644
$704$	−4.77782	−0.180071
$705$	8.02510	0.302243
$706$	12.0260	0.452606
$707$	32.3286	1.21584
$708$	−0.293697	−0.0110378
$709$	38.3932	1.44189	0.720943	−	0.692994i	$-0.243709\pi$
$709$	38.3932	1.44189	0.720943	+	0.692994i	$0.243709\pi$
$710$	3.76198	0.141185
$711$	47.0003	1.76265
$712$	−0.823713	−0.0308699
$713$	24.5920	0.920976
$714$	−4.94852	−0.185194
$715$	−28.1924	−1.05434
$716$	−18.7670	−0.701355
$717$	84.1735	3.14352
$718$	−4.31446	−0.161014
$719$	49.8913	1.86063	0.930316	−	0.366760i	$-0.119533\pi$
$719$	49.8913	1.86063	0.930316	+	0.366760i	$0.119533\pi$
$720$	9.51204	0.354493
$721$	−8.75850	−0.326184
$722$	7.31267	0.272150
$723$	−50.0039	−1.85967
$724$	24.2638	0.901758
$725$	13.8327	0.513735
$726$	38.2941	1.42123
$727$	7.03530	0.260925	0.130462	−	0.991453i	$-0.458354\pi$
$727$	7.03530	0.260925	0.130462	+	0.991453i	$0.458354\pi$
$728$	−13.3624	−0.495242
$729$	42.6688	1.58033
$730$	−7.35510	−0.272224
$731$	−3.64719	−0.134896
$732$	−1.44813	−0.0535245
$733$	−12.4105	−0.458394	−0.229197	−	0.973380i	$-0.573610\pi$
$733$	−12.4105	−0.458394	−0.229197	+	0.973380i	$0.573610\pi$
$734$	−16.3122	−0.602093
$735$	−5.29733	−0.195395
$736$	6.14112	0.226365
$737$	39.3688	1.45017
$738$	−32.1423	−1.18317
$739$	32.7380	1.20429	0.602144	−	0.798388i	$-0.294313\pi$
$739$	32.7380	1.20429	0.602144	+	0.798388i	$0.294313\pi$
$740$	0.741056	0.0272418
$741$	−51.3778	−1.88741
$742$	7.17205	0.263294
$743$	−0.241082	−0.00884443	−0.00442222	−	0.999990i	$-0.501408\pi$
$743$	−0.241082	−0.00884443	−0.00442222	+	0.999990i	$0.501408\pi$
$744$	−12.9652	−0.475329
$745$	−0.919342	−0.0336821
$746$	13.8756	0.508023
$747$	45.0537	1.64843
$748$	2.53670	0.0927510
$749$	28.7728	1.05133
$750$	−34.5069	−1.26001
$751$	−31.1565	−1.13692	−0.568459	−	0.822711i	$-0.692460\pi$
$751$	−31.1565	−1.13692	−0.568459	+	0.822711i	$0.692460\pi$
$752$	−1.94983	−0.0711029
$753$	−87.1684	−3.17659
$754$	18.9740	0.690993
$755$	−14.5191	−0.528405
$756$	−41.7801	−1.51953
$757$	36.6393	1.33168	0.665838	−	0.746096i	$-0.268074\pi$
$757$	36.6393	1.33168	0.665838	+	0.746096i	$0.268074\pi$
$758$	−1.53050	−0.0555903
$759$	−94.9977	−3.44820
$760$	−4.34587	−0.157641
$761$	32.4160	1.17508	0.587540	−	0.809195i	$-0.300097\pi$
$761$	32.4160	1.17508	0.587540	+	0.809195i	$0.300097\pi$
$762$	55.5347	2.01181
$763$	9.48110	0.343239
$764$	−14.2245	−0.514624
$765$	−5.05025	−0.182592
$766$	−26.3519	−0.952131
$767$	0.421063	0.0152037
$768$	−3.23769	−0.116830
$769$	8.59067	0.309788	0.154894	−	0.987931i	$-0.450496\pi$
$769$	8.59067	0.309788	0.154894	+	0.987931i	$0.450496\pi$
$770$	17.4844	0.630093
$771$	−84.6242	−3.04767
$772$	0.801739	0.0288552
$773$	18.8092	0.676520	0.338260	−	0.941053i	$-0.390162\pi$
$773$	18.8092	0.676520	0.338260	+	0.941053i	$0.390162\pi$
$774$	−51.4013	−1.84758
$775$	13.5512	0.486773
$776$	−7.98473	−0.286635
$777$	−5.43335	−0.194920
$778$	20.0116	0.717452
$779$	14.6852	0.526152
$780$	−19.1046	−0.684053
$781$	14.1393	0.505944
$782$	−3.26052	−0.116596
$783$	59.3260	2.12014
$784$	1.28707	0.0459668
$785$	−3.77846	−0.134859
$786$	12.2266	0.436108
$787$	−22.4370	−0.799792	−0.399896	−	0.916561i	$-0.630954\pi$
$787$	−22.4370	−0.799792	−0.399896	+	0.916561i	$0.630954\pi$
$788$	−1.43630	−0.0511659
$789$	−34.5683	−1.23066
$790$	−7.98481	−0.284087
$791$	−2.91699	−0.103716
$792$	35.7507	1.27035
$793$	2.07613	0.0737257
$794$	20.8542	0.740089
$795$	10.2541	0.363675
$796$	−7.34485	−0.260331
$797$	3.86955	0.137067	0.0685333	−	0.997649i	$-0.478168\pi$
$797$	3.86955	0.137067	0.0685333	+	0.997649i	$0.478168\pi$
$798$	31.8635	1.12796
$799$	1.03523	0.0366237
$800$	3.38401	0.119643
$801$	6.16354	0.217778
$802$	−10.5615	−0.372938
$803$	−27.6439	−0.975533
$804$	26.6782	0.940868
$805$	−22.4733	−0.792081
$806$	18.5878	0.654727
$807$	−50.5882	−1.78079
$808$	−11.2302	−0.395076
$809$	−27.9083	−0.981202	−0.490601	−	0.871384i	$-0.663223\pi$
$809$	−27.9083	−0.981202	−0.490601	+	0.871384i	$0.663223\pi$
$810$	−31.1981	−1.09619
$811$	−26.5142	−0.931039	−0.465520	−	0.885038i	$-0.654133\pi$
$811$	−26.5142	−0.931039	−0.465520	+	0.885038i	$0.654133\pi$
$812$	−11.7673	−0.412951
$813$	−49.4853	−1.73552
$814$	2.78524	0.0976225
$815$	−29.4127	−1.03028
$816$	1.71899	0.0601768
$817$	23.4843	0.821610
$818$	13.7731	0.481566
$819$	99.9857	3.49378
$820$	5.46061	0.190693
$821$	20.6296	0.719977	0.359988	−	0.932957i	$-0.382781\pi$
$821$	20.6296	0.719977	0.359988	+	0.932957i	$0.382781\pi$
$822$	54.0774	1.88617
$823$	−13.9230	−0.485326	−0.242663	−	0.970111i	$-0.578021\pi$
$823$	−13.9230	−0.485326	−0.242663	+	0.970111i	$0.578021\pi$
$824$	3.04249	0.105990
$825$	−52.3477	−1.82251
$826$	−0.261135	−0.00908604
$827$	8.98801	0.312544	0.156272	−	0.987714i	$-0.450052\pi$
$827$	8.98801	0.312544	0.156272	+	0.987714i	$0.450052\pi$
$828$	−45.9518	−1.59694
$829$	15.1471	0.526080	0.263040	−	0.964785i	$-0.415275\pi$
$829$	15.1471	0.526080	0.263040	+	0.964785i	$0.415275\pi$
$830$	−7.65411	−0.265678
$831$	57.5652	1.99692
$832$	4.64176	0.160924
$833$	−0.683347	−0.0236766
$834$	72.5073	2.51072
$835$	−6.78965	−0.234966
$836$	−16.3338	−0.564917
$837$	58.1184	2.00887
$838$	−1.65852	−0.0572925
$839$	43.9519	1.51739	0.758693	−	0.651448i	$-0.225838\pi$
$839$	43.9519	1.51739	0.758693	+	0.651448i	$0.225838\pi$
$840$	11.8483	0.408804
$841$	−12.2909	−0.423824
$842$	−3.39765	−0.117091
$843$	−11.9436	−0.411361
$844$	6.79221	0.233797
$845$	10.8637	0.373724
$846$	14.5898	0.501609
$847$	34.0484	1.16992
$848$	−2.49140	−0.0855549
$849$	10.8539	0.372505
$850$	−1.79668	−0.0616257
$851$	−3.57997	−0.122720
$852$	9.58149	0.328256
$853$	−36.6016	−1.25322	−0.626608	−	0.779335i	$-0.715557\pi$
$853$	−36.6016	−1.25322	−0.626608	+	0.779335i	$0.715557\pi$
$854$	−1.28758	−0.0440600
$855$	32.5186	1.11211
$856$	−9.99496	−0.341621
$857$	15.4579	0.528033	0.264017	−	0.964518i	$-0.414953\pi$
$857$	15.4579	0.528033	0.264017	+	0.964518i	$0.414953\pi$
$858$	−71.8039	−2.45135
$859$	−43.4546	−1.48265	−0.741326	−	0.671145i	$-0.765803\pi$
$859$	−43.4546	−1.48265	−0.741326	+	0.671145i	$0.765803\pi$
$860$	8.73250	0.297776
$861$	−40.0367	−1.36445
$862$	−18.5718	−0.632559
$863$	40.3437	1.37332	0.686658	−	0.726980i	$-0.259077\pi$
$863$	40.3437	1.37332	0.686658	+	0.726980i	$0.259077\pi$
$864$	14.5134	0.493755
$865$	−10.2184	−0.347437
$866$	23.5974	0.801871
$867$	54.1281	1.83829
$868$	−11.5278	−0.391278
$869$	−30.0107	−1.01804
$870$	−16.8241	−0.570389
$871$	−38.2476	−1.29597
$872$	−3.29350	−0.111532
$873$	59.7468	2.02212
$874$	20.9945	0.710149
$875$	−30.6811	−1.03721
$876$	−18.7329	−0.632926
$877$	−21.2304	−0.716899	−0.358450	−	0.933549i	$-0.616695\pi$
$877$	−21.2304	−0.716899	−0.358450	+	0.933549i	$0.616695\pi$
$878$	−29.1618	−0.984164
$879$	−103.805	−3.50124
$880$	−6.07364	−0.204742
$881$	19.8623	0.669178	0.334589	−	0.942364i	$-0.391403\pi$
$881$	19.8623	0.669178	0.334589	+	0.942364i	$0.391403\pi$
$882$	−9.63068	−0.324282
$883$	25.8039	0.868372	0.434186	−	0.900823i	$-0.357036\pi$
$883$	25.8039	0.868372	0.434186	+	0.900823i	$0.357036\pi$
$884$	−2.46446	−0.0828888
$885$	−0.373352	−0.0125501
$886$	−17.1972	−0.577750
$887$	−22.7316	−0.763251	−0.381625	−	0.924317i	$-0.624636\pi$
$887$	−22.7316	−0.763251	−0.381625	+	0.924317i	$0.624636\pi$
$888$	1.88741	0.0633375
$889$	49.3776	1.65607
$890$	−1.04712	−0.0350994
$891$	−117.257	−3.92826
$892$	−15.6545	−0.524151
$893$	−6.66582	−0.223063
$894$	−2.34149	−0.0783113
$895$	−23.8569	−0.797447
$896$	−2.87873	−0.0961715
$897$	92.2924	3.08155
$898$	−12.7081	−0.424073
$899$	16.3690	0.545936
$900$	−25.3213	−0.844044
$901$	1.32276	0.0440676
$902$	20.5235	0.683359
$903$	−64.0258	−2.13065
$904$	1.01329	0.0337016
$905$	30.8445	1.02531
$906$	−36.9791	−1.22855
$907$	−9.71840	−0.322694	−0.161347	−	0.986898i	$-0.551584\pi$
$907$	−9.71840	−0.322694	−0.161347	+	0.986898i	$0.551584\pi$
$908$	−25.8441	−0.857667
$909$	84.0313	2.78714
$910$	−16.9864	−0.563095
$911$	−51.5967	−1.70948	−0.854738	−	0.519060i	$-0.826282\pi$
$911$	−51.5967	−1.70948	−0.854738	+	0.519060i	$0.826282\pi$
$912$	−11.0686	−0.366518
$913$	−28.7677	−0.952074
$914$	14.3847	0.475803
$915$	−1.84089	−0.0608578
$916$	20.7765	0.686476
$917$	10.8710	0.358993
$918$	−7.70563	−0.254324
$919$	−17.8692	−0.589451	−0.294725	−	0.955582i	$-0.595228\pi$
$919$	−17.8692	−0.589451	−0.294725	+	0.955582i	$0.595228\pi$
$920$	7.80669	0.257379
$921$	−50.6106	−1.66768
$922$	−20.1639	−0.664062
$923$	−13.7366	−0.452147
$924$	44.5314	1.46497
$925$	−1.97271	−0.0648624
$926$	7.91941	0.260248
$927$	−22.7658	−0.747729
$928$	4.08768	0.134185
$929$	22.6470	0.743024	0.371512	−	0.928428i	$-0.378839\pi$
$929$	22.6470	0.743024	0.371512	+	0.928428i	$0.378839\pi$
$930$	−16.4816	−0.540453
$931$	4.40007	0.144207
$932$	−11.5367	−0.377897
$933$	43.9943	1.44031
$934$	−15.6782	−0.513006
$935$	3.22469	0.105459
$936$	−34.7326	−1.13527
$937$	44.2187	1.44456	0.722281	−	0.691600i	$-0.243094\pi$
$937$	44.2187	1.44456	0.722281	+	0.691600i	$0.243094\pi$
$938$	23.7204	0.774498
$939$	−40.1222	−1.30934
$940$	−2.47865	−0.0808446
$941$	7.34137	0.239322	0.119661	−	0.992815i	$-0.461819\pi$
$941$	7.34137	0.239322	0.119661	+	0.992815i	$0.461819\pi$
$942$	−9.62346	−0.313549
$943$	−26.3797	−0.859041
$944$	0.0907119	0.00295242
$945$	−53.1115	−1.72772
$946$	32.8208	1.06710
$947$	−22.8730	−0.743272	−0.371636	−	0.928378i	$-0.621203\pi$
$947$	−22.8730	−0.743272	−0.371636	+	0.928378i	$0.621203\pi$
$948$	−20.3367	−0.660506
$949$	26.8567	0.871805
$950$	11.5688	0.375342
$951$	−95.9589	−3.11168
$952$	1.52841	0.0495360
$953$	−22.7903	−0.738251	−0.369126	−	0.929380i	$-0.620343\pi$
$953$	−22.7903	−0.738251	−0.369126	+	0.929380i	$0.620343\pi$
$954$	18.6422	0.603564
$955$	−18.0824	−0.585132
$956$	−25.9980	−0.840835
$957$	−63.2327	−2.04402
$958$	5.00632	0.161747
$959$	48.0818	1.55264
$960$	−4.11580	−0.132837
$961$	−14.9642	−0.482716
$962$	−2.70592	−0.0872424
$963$	74.7886	2.41003
$964$	15.4443	0.497428
$965$	1.01918	0.0328087
$966$	−57.2379	−1.84160
$967$	6.89324	0.221672	0.110836	−	0.993839i	$-0.464647\pi$
$967$	6.89324	0.221672	0.110836	+	0.993839i	$0.464647\pi$
$968$	−11.8276	−0.380154
$969$	5.87668	0.188786
$970$	−10.1503	−0.325907
$971$	−6.86869	−0.220427	−0.110213	−	0.993908i	$-0.535153\pi$
$971$	−6.86869	−0.220427	−0.110213	+	0.993908i	$0.535153\pi$
$972$	−35.9190	−1.15210
$973$	64.4684	2.06676
$974$	−31.0747	−0.995697
$975$	50.8569	1.62872
$976$	0.447273	0.0143169
$977$	43.4598	1.39040	0.695202	−	0.718815i	$-0.255315\pi$
$977$	43.4598	1.39040	0.695202	+	0.718815i	$0.255315\pi$
$978$	−74.9120	−2.39542
$979$	−3.93555	−0.125781
$980$	1.63614	0.0522647
$981$	24.6441	0.786825
$982$	−6.23502	−0.198967
$983$	16.8493	0.537409	0.268704	−	0.963223i	$-0.413404\pi$
$983$	16.8493	0.537409	0.268704	+	0.963223i	$0.413404\pi$
$984$	13.9078	0.443363
$985$	−1.82584	−0.0581761
$986$	−2.17028	−0.0691158
$987$	18.1732	0.578460
$988$	15.8687	0.504850
$989$	−42.1859	−1.34143
$990$	45.4469	1.44440
$991$	33.6994	1.07050	0.535248	−	0.844695i	$-0.320218\pi$
$991$	33.6994	1.07050	0.535248	+	0.844695i	$0.320218\pi$
$992$	4.00447	0.127142
$993$	−47.0018	−1.49156
$994$	8.51919	0.270212
$995$	−9.33689	−0.295999
$996$	−19.4944	−0.617705
$997$	12.0612	0.381982	0.190991	−	0.981592i	$-0.438830\pi$
$997$	12.0612	0.381982	0.190991	+	0.981592i	$0.438830\pi$
$998$	−20.2649	−0.641475
$999$	−8.46059	−0.267681

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.c.1.3	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.c.1.3	✓	92	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:	\( N \)	\(=\)	\( 8006 = 2 \cdot 4003 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8006.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.23769 q^{3} +1.00000 q^{4} +1.27122 q^{5} +3.23769 q^{6} +2.87873 q^{7} -1.00000 q^{8} +7.48264 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.23769 q^{3} +1.00000 q^{4} +1.27122 q^{5} +3.23769 q^{6} +2.87873 q^{7} -1.00000 q^{8} +7.48264 q^{9} -1.27122 q^{10} -4.77782 q^{11} -3.23769 q^{12} +4.64176 q^{13} -2.87873 q^{14} -4.11580 q^{15} +1.00000 q^{16} -0.530932 q^{17} -7.48264 q^{18} +3.41867 q^{19} +1.27122 q^{20} -9.32043 q^{21} +4.77782 q^{22} -6.14112 q^{23} +3.23769 q^{24} -3.38401 q^{25} -4.64176 q^{26} -14.5134 q^{27} +2.87873 q^{28} -4.08768 q^{29} +4.11580 q^{30} -4.00447 q^{31} -1.00000 q^{32} +15.4691 q^{33} +0.530932 q^{34} +3.65948 q^{35} +7.48264 q^{36} +0.582951 q^{37} -3.41867 q^{38} -15.0286 q^{39} -1.27122 q^{40} +4.29558 q^{41} +9.32043 q^{42} +6.86941 q^{43} -4.77782 q^{44} +9.51204 q^{45} +6.14112 q^{46} -1.94983 q^{47} -3.23769 q^{48} +1.28707 q^{49} +3.38401 q^{50} +1.71899 q^{51} +4.64176 q^{52} -2.49140 q^{53} +14.5134 q^{54} -6.07364 q^{55} -2.87873 q^{56} -11.0686 q^{57} +4.08768 q^{58} +0.0907119 q^{59} -4.11580 q^{60} +0.447273 q^{61} +4.00447 q^{62} +21.5405 q^{63} +1.00000 q^{64} +5.90068 q^{65} -15.4691 q^{66} -8.23989 q^{67} -0.530932 q^{68} +19.8831 q^{69} -3.65948 q^{70} -2.95936 q^{71} -7.48264 q^{72} +5.78588 q^{73} -0.582951 q^{74} +10.9564 q^{75} +3.41867 q^{76} -13.7541 q^{77} +15.0286 q^{78} +6.28125 q^{79} +1.27122 q^{80} +24.5419 q^{81} -4.29558 q^{82} +6.02110 q^{83} -9.32043 q^{84} -0.674929 q^{85} -6.86941 q^{86} +13.2346 q^{87} +4.77782 q^{88} +0.823713 q^{89} -9.51204 q^{90} +13.3624 q^{91} -6.14112 q^{92} +12.9652 q^{93} +1.94983 q^{94} +4.34587 q^{95} +3.23769 q^{96} +7.98473 q^{97} -1.28707 q^{98} -35.7507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9}+O(q^{10}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9	\( 92 q - 92 q^{2} - 2 q^{3} + 92 q^{4} + 10 q^{5} + 2 q^{6} + 8 q^{7} - 92 q^{8} + 104 q^{9} - 10 q^{10} + 4 q^{11} - 2 q^{12} + 40 q^{13} - 8 q^{14} + 15 q^{15} + 92 q^{16} - 14 q^{17} - 104 q^{18} + 64 q^{19} + 10 q^{20} + 54 q^{21} - 4 q^{22} - 49 q^{23} + 2 q^{24} + 116 q^{25} - 40 q^{26} - 8 q^{27} + 8 q^{28} + 39 q^{29} - 15 q^{30} + 53 q^{31} - 92 q^{32} + q^{33} + 14 q^{34} - 22 q^{35} + 104 q^{36} + 58 q^{37} - 64 q^{38} + 58 q^{39} - 10 q^{40} + 27 q^{41} - 54 q^{42} + 40 q^{43} + 4 q^{44} + 43 q^{45} + 49 q^{46} - 28 q^{47} - 2 q^{48} + 148 q^{49} - 116 q^{50} + 48 q^{51} + 40 q^{52} + 32 q^{53} + 8 q^{54} + 36 q^{55} - 8 q^{56} + 48 q^{57} - 39 q^{58} + 8 q^{59} + 15 q^{60} + 99 q^{61} - 53 q^{62} + 92 q^{64} + 13 q^{65} - q^{66} + 48 q^{67} - 14 q^{68} + 63 q^{69} + 22 q^{70} - 13 q^{71} - 104 q^{72} + 49 q^{73} - 58 q^{74} + 16 q^{75} + 64 q^{76} + 41 q^{77} - 58 q^{78} + 143 q^{79} + 10 q^{80} + 124 q^{81} - 27 q^{82} - 24 q^{83} + 54 q^{84} + 121 q^{85} - 40 q^{86} + 5 q^{87} - 4 q^{88} + 25 q^{89} - 43 q^{90} + 67 q^{91} - 49 q^{92} + 43 q^{93} + 28 q^{94} - 38 q^{95} + 2 q^{96} + 74 q^{97} - 148 q^{98} + 86 q^{99}+O(q^{100}) \) 92 * q - 92 * q^2 - 2 * q^3 + 92 * q^4 + 10 * q^5 + 2 * q^6 + 8 * q^7 - 92 * q^8 + 104 * q^9 - 10 * q^10 + 4 * q^11 - 2 * q^12 + 40 * q^13 - 8 * q^14 + 15 * q^15 + 92 * q^16 - 14 * q^17 - 104 * q^18 + 64 * q^19 + 10 * q^20 + 54 * q^21 - 4 * q^22 - 49 * q^23 + 2 * q^24 + 116 * q^25 - 40 * q^26 - 8 * q^27 + 8 * q^28 + 39 * q^29 - 15 * q^30 + 53 * q^31 - 92 * q^32 + q^33 + 14 * q^34 - 22 * q^35 + 104 * q^36 + 58 * q^37 - 64 * q^38 + 58 * q^39 - 10 * q^40 + 27 * q^41 - 54 * q^42 + 40 * q^43 + 4 * q^44 + 43 * q^45 + 49 * q^46 - 28 * q^47 - 2 * q^48 + 148 * q^49 - 116 * q^50 + 48 * q^51 + 40 * q^52 + 32 * q^53 + 8 * q^54 + 36 * q^55 - 8 * q^56 + 48 * q^57 - 39 * q^58 + 8 * q^59 + 15 * q^60 + 99 * q^61 - 53 * q^62 + 92 * q^64 + 13 * q^65 - q^66 + 48 * q^67 - 14 * q^68 + 63 * q^69 + 22 * q^70 - 13 * q^71 - 104 * q^72 + 49 * q^73 - 58 * q^74 + 16 * q^75 + 64 * q^76 + 41 * q^77 - 58 * q^78 + 143 * q^79 + 10 * q^80 + 124 * q^81 - 27 * q^82 - 24 * q^83 + 54 * q^84 + 121 * q^85 - 40 * q^86 + 5 * q^87 - 4 * q^88 + 25 * q^89 - 43 * q^90 + 67 * q^91 - 49 * q^92 + 43 * q^93 + 28 * q^94 - 38 * q^95 + 2 * q^96 + 74 * q^97 - 148 * q^98 + 86 * q^99

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