LMFDB - Embedded newform 8006.2.a.a.1.8

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:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73399 q^{3} +1.00000 q^{4} +1.40012 q^{5} -2.73399 q^{6} +2.82233 q^{7} +1.00000 q^{8} +4.47471 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73399 q^{3} +1.00000 q^{4} +1.40012 q^{5} -2.73399 q^{6} +2.82233 q^{7} +1.00000 q^{8} +4.47471 q^{9} +1.40012 q^{10} +1.99250 q^{11} -2.73399 q^{12} -3.41771 q^{13} +2.82233 q^{14} -3.82791 q^{15} +1.00000 q^{16} -3.91240 q^{17} +4.47471 q^{18} +7.80062 q^{19} +1.40012 q^{20} -7.71623 q^{21} +1.99250 q^{22} -4.09466 q^{23} -2.73399 q^{24} -3.03967 q^{25} -3.41771 q^{26} -4.03183 q^{27} +2.82233 q^{28} -4.79804 q^{29} -3.82791 q^{30} -6.29194 q^{31} +1.00000 q^{32} -5.44746 q^{33} -3.91240 q^{34} +3.95160 q^{35} +4.47471 q^{36} +1.93880 q^{37} +7.80062 q^{38} +9.34399 q^{39} +1.40012 q^{40} -6.35791 q^{41} -7.71623 q^{42} -0.471936 q^{43} +1.99250 q^{44} +6.26512 q^{45} -4.09466 q^{46} +7.42217 q^{47} -2.73399 q^{48} +0.965551 q^{49} -3.03967 q^{50} +10.6965 q^{51} -3.41771 q^{52} -12.0284 q^{53} -4.03183 q^{54} +2.78973 q^{55} +2.82233 q^{56} -21.3268 q^{57} -4.79804 q^{58} -13.3255 q^{59} -3.82791 q^{60} -9.61645 q^{61} -6.29194 q^{62} +12.6291 q^{63} +1.00000 q^{64} -4.78520 q^{65} -5.44746 q^{66} -12.2379 q^{67} -3.91240 q^{68} +11.1948 q^{69} +3.95160 q^{70} -1.62743 q^{71} +4.47471 q^{72} -6.35124 q^{73} +1.93880 q^{74} +8.31042 q^{75} +7.80062 q^{76} +5.62348 q^{77} +9.34399 q^{78} -10.9283 q^{79} +1.40012 q^{80} -2.40112 q^{81} -6.35791 q^{82} +1.54192 q^{83} -7.71623 q^{84} -5.47783 q^{85} -0.471936 q^{86} +13.1178 q^{87} +1.99250 q^{88} +14.4665 q^{89} +6.26512 q^{90} -9.64591 q^{91} -4.09466 q^{92} +17.2021 q^{93} +7.42217 q^{94} +10.9218 q^{95} -2.73399 q^{96} +17.5015 q^{97} +0.965551 q^{98} +8.91583 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9 - 9 * q^10 - 48 * q^11 - 15 * q^12 - 30 * q^13 - 29 * q^14 - 51 * q^15 + 69 * q^16 - 37 * q^17 + 40 * q^18 - 72 * q^19 - 9 * q^20 - 38 * q^21 - 48 * q^22 - 75 * q^23 - 15 * q^24 + 18 * q^25 - 30 * q^26 - 48 * q^27 - 29 * q^28 - 27 * q^29 - 51 * q^30 - 61 * q^31 + 69 * q^32 - 29 * q^33 - 37 * q^34 - 64 * q^35 + 40 * q^36 - 42 * q^37 - 72 * q^38 - 68 * q^39 - 9 * q^40 - 49 * q^41 - 38 * q^42 - 95 * q^43 - 48 * q^44 - 20 * q^45 - 75 * q^46 - 62 * q^47 - 15 * q^48 - 4 * q^49 + 18 * q^50 - 76 * q^51 - 30 * q^52 - 28 * q^53 - 48 * q^54 - 76 * q^55 - 29 * q^56 - 44 * q^57 - 27 * q^58 - 68 * q^59 - 51 * q^60 - 62 * q^61 - 61 * q^62 - 91 * q^63 + 69 * q^64 - 79 * q^65 - 29 * q^66 - 116 * q^67 - 37 * q^68 - 23 * q^69 - 64 * q^70 - 89 * q^71 + 40 * q^72 - 60 * q^73 - 42 * q^74 - 47 * q^75 - 72 * q^76 + 5 * q^77 - 68 * q^78 - 170 * q^79 - 9 * q^80 - 3 * q^81 - 49 * q^82 - 82 * q^83 - 38 * q^84 - 81 * q^85 - 95 * q^86 - 51 * q^87 - 48 * q^88 - 78 * q^89 - 20 * q^90 - 85 * q^91 - 75 * q^92 - 21 * q^93 - 62 * q^94 - 70 * q^95 - 15 * q^96 - 60 * q^97 - 4 * q^98 - 148 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.73399	−1.57847	−0.789235	−	0.614091i	$-0.789523\pi$
$3$	−2.73399	−1.57847	−0.789235	+	0.614091i	$0.789523\pi$
$4$	1.00000	0.500000
$5$	1.40012	0.626152	0.313076	−	0.949728i	$-0.398640\pi$
$5$	1.40012	0.626152	0.313076	+	0.949728i	$0.398640\pi$
$6$	−2.73399	−1.11615
$7$	2.82233	1.06674	0.533370	−	0.845882i	$-0.320925\pi$
$7$	2.82233	1.06674	0.533370	+	0.845882i	$0.320925\pi$
$8$	1.00000	0.353553
$9$	4.47471	1.49157
$10$	1.40012	0.442757
$11$	1.99250	0.600760	0.300380	−	0.953820i	$-0.402887\pi$
$11$	1.99250	0.600760	0.300380	+	0.953820i	$0.402887\pi$
$12$	−2.73399	−0.789235
$13$	−3.41771	−0.947903	−0.473951	−	0.880551i	$-0.657173\pi$
$13$	−3.41771	−0.947903	−0.473951	+	0.880551i	$0.657173\pi$
$14$	2.82233	0.754300
$15$	−3.82791	−0.988363
$16$	1.00000	0.250000
$17$	−3.91240	−0.948897	−0.474449	−	0.880283i	$-0.657353\pi$
$17$	−3.91240	−0.948897	−0.474449	+	0.880283i	$0.657353\pi$
$18$	4.47471	1.05470
$19$	7.80062	1.78959	0.894793	−	0.446481i	$-0.147323\pi$
$19$	7.80062	1.78959	0.894793	+	0.446481i	$0.147323\pi$
$20$	1.40012	0.313076
$21$	−7.71623	−1.68382
$22$	1.99250	0.424801
$23$	−4.09466	−0.853796	−0.426898	−	0.904300i	$-0.640394\pi$
$23$	−4.09466	−0.853796	−0.426898	+	0.904300i	$0.640394\pi$
$24$	−2.73399	−0.558074
$25$	−3.03967	−0.607933
$26$	−3.41771	−0.670268
$27$	−4.03183	−0.775927
$28$	2.82233	0.533370
$29$	−4.79804	−0.890973	−0.445487	−	0.895289i	$-0.646969\pi$
$29$	−4.79804	−0.890973	−0.445487	+	0.895289i	$0.646969\pi$
$30$	−3.82791	−0.698878
$31$	−6.29194	−1.13007	−0.565033	−	0.825068i	$-0.691137\pi$
$31$	−6.29194	−1.13007	−0.565033	+	0.825068i	$0.691137\pi$
$32$	1.00000	0.176777
$33$	−5.44746	−0.948282
$34$	−3.91240	−0.670972
$35$	3.95160	0.667942
$36$	4.47471	0.745784
$37$	1.93880	0.318737	0.159368	−	0.987219i	$-0.449054\pi$
$37$	1.93880	0.318737	0.159368	+	0.987219i	$0.449054\pi$
$38$	7.80062	1.26543
$39$	9.34399	1.49624
$40$	1.40012	0.221378
$41$	−6.35791	−0.992939	−0.496469	−	0.868054i	$-0.665370\pi$
$41$	−6.35791	−0.992939	−0.496469	+	0.868054i	$0.665370\pi$
$42$	−7.71623	−1.19064
$43$	−0.471936	−0.0719696	−0.0359848	−	0.999352i	$-0.511457\pi$
$43$	−0.471936	−0.0719696	−0.0359848	+	0.999352i	$0.511457\pi$
$44$	1.99250	0.300380
$45$	6.26512	0.933949
$46$	−4.09466	−0.603725
$47$	7.42217	1.08263	0.541317	−	0.840818i	$-0.317926\pi$
$47$	7.42217	1.08263	0.541317	+	0.840818i	$0.317926\pi$
$48$	−2.73399	−0.394618
$49$	0.965551	0.137936
$50$	−3.03967	−0.429874
$51$	10.6965	1.49781
$52$	−3.41771	−0.473951
$53$	−12.0284	−1.65222	−0.826111	−	0.563508i	$-0.809451\pi$
$53$	−12.0284	−1.65222	−0.826111	+	0.563508i	$0.809451\pi$
$54$	−4.03183	−0.548663
$55$	2.78973	0.376167
$56$	2.82233	0.377150
$57$	−21.3268	−2.82481
$58$	−4.79804	−0.630013
$59$	−13.3255	−1.73483	−0.867416	−	0.497583i	$-0.834221\pi$
$59$	−13.3255	−1.73483	−0.867416	+	0.497583i	$0.834221\pi$
$60$	−3.82791	−0.494182
$61$	−9.61645	−1.23126	−0.615630	−	0.788035i	$-0.711098\pi$
$61$	−9.61645	−1.23126	−0.615630	+	0.788035i	$0.711098\pi$
$62$	−6.29194	−0.799078
$63$	12.6291	1.59112
$64$	1.00000	0.125000
$65$	−4.78520	−0.593532
$66$	−5.44746	−0.670536
$67$	−12.2379	−1.49510	−0.747549	−	0.664206i	$-0.768770\pi$
$67$	−12.2379	−1.49510	−0.747549	+	0.664206i	$0.768770\pi$
$68$	−3.91240	−0.474449
$69$	11.1948	1.34769
$70$	3.95160	0.472307
$71$	−1.62743	−0.193140	−0.0965702	−	0.995326i	$-0.530787\pi$
$71$	−1.62743	−0.193140	−0.0965702	+	0.995326i	$0.530787\pi$
$72$	4.47471	0.527349
$73$	−6.35124	−0.743356	−0.371678	−	0.928362i	$-0.621217\pi$
$73$	−6.35124	−0.743356	−0.371678	+	0.928362i	$0.621217\pi$
$74$	1.93880	0.225381
$75$	8.31042	0.959604
$76$	7.80062	0.894793
$77$	5.62348	0.640855
$78$	9.34399	1.05800
$79$	−10.9283	−1.22953	−0.614767	−	0.788709i	$-0.710750\pi$
$79$	−10.9283	−1.22953	−0.614767	+	0.788709i	$0.710750\pi$
$80$	1.40012	0.156538
$81$	−2.40112	−0.266792
$82$	−6.35791	−0.702114
$83$	1.54192	0.169248	0.0846238	−	0.996413i	$-0.473031\pi$
$83$	1.54192	0.169248	0.0846238	+	0.996413i	$0.473031\pi$
$84$	−7.71623	−0.841909
$85$	−5.47783	−0.594154
$86$	−0.471936	−0.0508902
$87$	13.1178	1.40638
$88$	1.99250	0.212401
$89$	14.4665	1.53344	0.766722	−	0.641979i	$-0.221886\pi$
$89$	14.4665	1.53344	0.766722	+	0.641979i	$0.221886\pi$
$90$	6.26512	0.660402
$91$	−9.64591	−1.01117
$92$	−4.09466	−0.426898
$93$	17.2021	1.78378
$94$	7.42217	0.765538
$95$	10.9218	1.12055
$96$	−2.73399	−0.279037
$97$	17.5015	1.77701	0.888506	−	0.458865i	$-0.151744\pi$
$97$	17.5015	1.77701	0.888506	+	0.458865i	$0.151744\pi$
$98$	0.965551	0.0975354
$99$	8.91583	0.896075
$100$	−3.03967	−0.303967
$101$	−1.61987	−0.161183	−0.0805917	−	0.996747i	$-0.525681\pi$
$101$	−1.61987	−0.161183	−0.0805917	+	0.996747i	$0.525681\pi$
$102$	10.6965	1.05911
$103$	0.695444	0.0685241	0.0342621	−	0.999413i	$-0.489092\pi$
$103$	0.695444	0.0685241	0.0342621	+	0.999413i	$0.489092\pi$
$104$	−3.41771	−0.335134
$105$	−10.8036	−1.05433
$106$	−12.0284	−1.16830
$107$	−8.66620	−0.837793	−0.418897	−	0.908034i	$-0.637583\pi$
$107$	−8.66620	−0.837793	−0.418897	+	0.908034i	$0.637583\pi$
$108$	−4.03183	−0.387963
$109$	3.10480	0.297385	0.148693	−	0.988883i	$-0.452493\pi$
$109$	3.10480	0.297385	0.148693	+	0.988883i	$0.452493\pi$
$110$	2.78973	0.265990
$111$	−5.30066	−0.503116
$112$	2.82233	0.266685
$113$	13.4566	1.26589	0.632945	−	0.774197i	$-0.281846\pi$
$113$	13.4566	1.26589	0.632945	+	0.774197i	$0.281846\pi$
$114$	−21.3268	−1.99744
$115$	−5.73302	−0.534606
$116$	−4.79804	−0.445487
$117$	−15.2933	−1.41386
$118$	−13.3255	−1.22671
$119$	−11.0421	−1.01223
$120$	−3.82791	−0.349439
$121$	−7.02996	−0.639087
$122$	−9.61645	−0.870632
$123$	17.3825	1.56732
$124$	−6.29194	−0.565033
$125$	−11.2565	−1.00681
$126$	12.6291	1.12509
$127$	−7.98666	−0.708701	−0.354351	−	0.935113i	$-0.615298\pi$
$127$	−7.98666	−0.708701	−0.354351	+	0.935113i	$0.615298\pi$
$128$	1.00000	0.0883883
$129$	1.29027	0.113602
$130$	−4.78520	−0.419690
$131$	−3.85882	−0.337147	−0.168573	−	0.985689i	$-0.553916\pi$
$131$	−3.85882	−0.337147	−0.168573	+	0.985689i	$0.553916\pi$
$132$	−5.44746	−0.474141
$133$	22.0159	1.90902
$134$	−12.2379	−1.05719
$135$	−5.64505	−0.485848
$136$	−3.91240	−0.335486
$137$	13.9980	1.19593	0.597964	−	0.801523i	$-0.295977\pi$
$137$	13.9980	1.19593	0.597964	+	0.801523i	$0.295977\pi$
$138$	11.1948	0.952962
$139$	3.54704	0.300856	0.150428	−	0.988621i	$-0.451935\pi$
$139$	3.54704	0.300856	0.150428	+	0.988621i	$0.451935\pi$
$140$	3.95160	0.333971
$141$	−20.2921	−1.70891
$142$	−1.62743	−0.136571
$143$	−6.80978	−0.569462
$144$	4.47471	0.372892
$145$	−6.71783	−0.557885
$146$	−6.35124	−0.525632
$147$	−2.63981	−0.217728
$148$	1.93880	0.159368
$149$	5.75523	0.471486	0.235743	−	0.971815i	$-0.424248\pi$
$149$	5.75523	0.471486	0.235743	+	0.971815i	$0.424248\pi$
$150$	8.31042	0.678543
$151$	−2.56523	−0.208756	−0.104378	−	0.994538i	$-0.533285\pi$
$151$	−2.56523	−0.208756	−0.104378	+	0.994538i	$0.533285\pi$
$152$	7.80062	0.632714
$153$	−17.5069	−1.41535
$154$	5.62348	0.453153
$155$	−8.80947	−0.707594
$156$	9.34399	0.748118
$157$	15.6450	1.24861	0.624303	−	0.781182i	$-0.285383\pi$
$157$	15.6450	1.24861	0.624303	+	0.781182i	$0.285383\pi$
$158$	−10.9283	−0.869411
$159$	32.8854	2.60798
$160$	1.40012	0.110689
$161$	−11.5565	−0.910779
$162$	−2.40112	−0.188650
$163$	7.88038	0.617239	0.308620	−	0.951186i	$-0.400133\pi$
$163$	7.88038	0.617239	0.308620	+	0.951186i	$0.400133\pi$
$164$	−6.35791	−0.496469
$165$	−7.62710	−0.593769
$166$	1.54192	0.119676
$167$	3.19095	0.246923	0.123461	−	0.992349i	$-0.460600\pi$
$167$	3.19095	0.246923	0.123461	+	0.992349i	$0.460600\pi$
$168$	−7.71623	−0.595320
$169$	−1.31925	−0.101480
$170$	−5.47783	−0.420131
$171$	34.9055	2.66929
$172$	−0.471936	−0.0359848
$173$	−15.5302	−1.18074	−0.590371	−	0.807132i	$-0.701018\pi$
$173$	−15.5302	−1.18074	−0.590371	+	0.807132i	$0.701018\pi$
$174$	13.1178	0.994457
$175$	−8.57894	−0.648507
$176$	1.99250	0.150190
$177$	36.4318	2.73838
$178$	14.4665	1.08431
$179$	21.4124	1.60044	0.800220	−	0.599706i	$-0.204716\pi$
$179$	21.4124	1.60044	0.800220	+	0.599706i	$0.204716\pi$
$180$	6.26512	0.466975
$181$	−15.6888	−1.16614	−0.583068	−	0.812423i	$-0.698148\pi$
$181$	−15.6888	−1.16614	−0.583068	+	0.812423i	$0.698148\pi$
$182$	−9.64591	−0.715003
$183$	26.2913	1.94351
$184$	−4.09466	−0.301862
$185$	2.71455	0.199578
$186$	17.2021	1.26132
$187$	−7.79545	−0.570060
$188$	7.42217	0.541317
$189$	−11.3792	−0.827712
$190$	10.9218	0.792351
$191$	13.1829	0.953881	0.476941	−	0.878936i	$-0.341746\pi$
$191$	13.1829	0.953881	0.476941	+	0.878936i	$0.341746\pi$
$192$	−2.73399	−0.197309
$193$	−1.59022	−0.114467	−0.0572333	−	0.998361i	$-0.518228\pi$
$193$	−1.59022	−0.114467	−0.0572333	+	0.998361i	$0.518228\pi$
$194$	17.5015	1.25654
$195$	13.0827	0.936872
$196$	0.965551	0.0689679
$197$	9.52983	0.678972	0.339486	−	0.940611i	$-0.389747\pi$
$197$	9.52983	0.678972	0.339486	+	0.940611i	$0.389747\pi$
$198$	8.91583	0.633621
$199$	10.7477	0.761885	0.380943	−	0.924599i	$-0.375600\pi$
$199$	10.7477	0.761885	0.380943	+	0.924599i	$0.375600\pi$
$200$	−3.03967	−0.214937
$201$	33.4583	2.35997
$202$	−1.61987	−0.113974
$203$	−13.5417	−0.950438
$204$	10.6965	0.748903
$205$	−8.90183	−0.621731
$206$	0.695444	0.0484539
$207$	−18.3224	−1.27350
$208$	−3.41771	−0.236976
$209$	15.5427	1.07511
$210$	−10.8036	−0.745522
$211$	1.78668	0.123000	0.0615001	−	0.998107i	$-0.480412\pi$
$211$	1.78668	0.123000	0.0615001	+	0.998107i	$0.480412\pi$
$212$	−12.0284	−0.826111
$213$	4.44938	0.304867
$214$	−8.66620	−0.592409
$215$	−0.660767	−0.0450639
$216$	−4.03183	−0.274331
$217$	−17.7579	−1.20549
$218$	3.10480	0.210283
$219$	17.3642	1.17337
$220$	2.78973	0.188084
$221$	13.3715	0.899463
$222$	−5.30066	−0.355757
$223$	−21.7588	−1.45708	−0.728539	−	0.685004i	$-0.759800\pi$
$223$	−21.7588	−1.45708	−0.728539	+	0.685004i	$0.759800\pi$
$224$	2.82233	0.188575
$225$	−13.6016	−0.906774
$226$	13.4566	0.895120
$227$	4.27139	0.283502	0.141751	−	0.989902i	$-0.454727\pi$
$227$	4.27139	0.283502	0.141751	+	0.989902i	$0.454727\pi$
$228$	−21.3268	−1.41240
$229$	2.81027	0.185708	0.0928540	−	0.995680i	$-0.470401\pi$
$229$	2.81027	0.185708	0.0928540	+	0.995680i	$0.470401\pi$
$230$	−5.73302	−0.378024
$231$	−15.3745	−1.01157
$232$	−4.79804	−0.315007
$233$	28.5745	1.87198	0.935990	−	0.352025i	$-0.114507\pi$
$233$	28.5745	1.87198	0.935990	+	0.352025i	$0.114507\pi$
$234$	−15.2933	−0.999751
$235$	10.3919	0.677894
$236$	−13.3255	−0.867416
$237$	29.8780	1.94078
$238$	−11.0421	−0.715753
$239$	−9.92291	−0.641860	−0.320930	−	0.947103i	$-0.603995\pi$
$239$	−9.92291	−0.641860	−0.320930	+	0.947103i	$0.603995\pi$
$240$	−3.82791	−0.247091
$241$	−19.6016	−1.26265	−0.631325	−	0.775519i	$-0.717488\pi$
$241$	−19.6016	−1.26265	−0.631325	+	0.775519i	$0.717488\pi$
$242$	−7.02996	−0.451903
$243$	18.6602	1.19705
$244$	−9.61645	−0.615630
$245$	1.35189	0.0863689
$246$	17.3825	1.10827
$247$	−26.6603	−1.69635
$248$	−6.29194	−0.399539
$249$	−4.21559	−0.267152
$250$	−11.2565	−0.711923
$251$	−12.1650	−0.767851	−0.383925	−	0.923364i	$-0.625428\pi$
$251$	−12.1650	−0.767851	−0.383925	+	0.923364i	$0.625428\pi$
$252$	12.6291	0.795559
$253$	−8.15859	−0.512926
$254$	−7.98666	−0.501127
$255$	14.9763	0.937855
$256$	1.00000	0.0625000
$257$	−10.5546	−0.658375	−0.329188	−	0.944265i	$-0.606775\pi$
$257$	−10.5546	−0.658375	−0.329188	+	0.944265i	$0.606775\pi$
$258$	1.29027	0.0803286
$259$	5.47193	0.340009
$260$	−4.78520	−0.296766
$261$	−21.4698	−1.32895
$262$	−3.85882	−0.238399
$263$	−11.2506	−0.693741	−0.346871	−	0.937913i	$-0.612756\pi$
$263$	−11.2506	−0.693741	−0.346871	+	0.937913i	$0.612756\pi$
$264$	−5.44746	−0.335268
$265$	−16.8411	−1.03454
$266$	22.0159	1.34988
$267$	−39.5512	−2.42050
$268$	−12.2379	−0.747549
$269$	21.6700	1.32125	0.660623	−	0.750718i	$-0.270292\pi$
$269$	21.6700	1.32125	0.660623	+	0.750718i	$0.270292\pi$
$270$	−5.64505	−0.343547
$271$	0.228800	0.0138986	0.00694931	−	0.999976i	$-0.497788\pi$
$271$	0.228800	0.0138986	0.00694931	+	0.999976i	$0.497788\pi$
$272$	−3.91240	−0.237224
$273$	26.3718	1.59610
$274$	13.9980	0.845649
$275$	−6.05652	−0.365222
$276$	11.1948	0.673846
$277$	20.2394	1.21607	0.608035	−	0.793910i	$-0.291958\pi$
$277$	20.2394	1.21607	0.608035	+	0.793910i	$0.291958\pi$
$278$	3.54704	0.212737
$279$	−28.1546	−1.68557
$280$	3.95160	0.236153
$281$	−2.63854	−0.157402	−0.0787009	−	0.996898i	$-0.525077\pi$
$281$	−2.63854	−0.157402	−0.0787009	+	0.996898i	$0.525077\pi$
$282$	−20.2921	−1.20838
$283$	−23.3658	−1.38895	−0.694477	−	0.719515i	$-0.744364\pi$
$283$	−23.3658	−1.38895	−0.694477	+	0.719515i	$0.744364\pi$
$284$	−1.62743	−0.0965702
$285$	−29.8601	−1.76876
$286$	−6.80978	−0.402670
$287$	−17.9441	−1.05921
$288$	4.47471	0.263675
$289$	−1.69309	−0.0995936
$290$	−6.71783	−0.394484
$291$	−47.8491	−2.80496
$292$	−6.35124	−0.371678
$293$	−1.11863	−0.0653508	−0.0326754	−	0.999466i	$-0.510403\pi$
$293$	−1.11863	−0.0653508	−0.0326754	+	0.999466i	$0.510403\pi$
$294$	−2.63981	−0.153957
$295$	−18.6573	−1.08627
$296$	1.93880	0.112690
$297$	−8.03341	−0.466146
$298$	5.75523	0.333391
$299$	13.9944	0.809316
$300$	8.31042	0.479802
$301$	−1.33196	−0.0767729
$302$	−2.56523	−0.147613
$303$	4.42872	0.254423
$304$	7.80062	0.447396
$305$	−13.4642	−0.770957
$306$	−17.5069	−1.00080
$307$	1.00536	0.0573790	0.0286895	−	0.999588i	$-0.490867\pi$
$307$	1.00536	0.0573790	0.0286895	+	0.999588i	$0.490867\pi$
$308$	5.62348	0.320428
$309$	−1.90134	−0.108163
$310$	−8.80947	−0.500344
$311$	−23.6992	−1.34386	−0.671930	−	0.740615i	$-0.734534\pi$
$311$	−23.6992	−1.34386	−0.671930	+	0.740615i	$0.734534\pi$
$312$	9.34399	0.528999
$313$	−15.8107	−0.893671	−0.446835	−	0.894616i	$-0.647449\pi$
$313$	−15.8107	−0.893671	−0.446835	+	0.894616i	$0.647449\pi$
$314$	15.6450	0.882898
$315$	17.6822	0.996282
$316$	−10.9283	−0.614767
$317$	23.0300	1.29349	0.646746	−	0.762706i	$-0.276129\pi$
$317$	23.0300	1.29349	0.646746	+	0.762706i	$0.276129\pi$
$318$	32.8854	1.84412
$319$	−9.56007	−0.535261
$320$	1.40012	0.0782691
$321$	23.6933	1.32243
$322$	−11.5565	−0.644018
$323$	−30.5192	−1.69813
$324$	−2.40112	−0.133396
$325$	10.3887	0.576261
$326$	7.88038	0.436454
$327$	−8.48848	−0.469414
$328$	−6.35791	−0.351057
$329$	20.9478	1.15489
$330$	−7.62710	−0.419858
$331$	−21.5205	−1.18287	−0.591437	−	0.806351i	$-0.701439\pi$
$331$	−21.5205	−1.18287	−0.591437	+	0.806351i	$0.701439\pi$
$332$	1.54192	0.0846238
$333$	8.67556	0.475418
$334$	3.19095	0.174601
$335$	−17.1345	−0.936160
$336$	−7.71623	−0.420955
$337$	−8.67159	−0.472372	−0.236186	−	0.971708i	$-0.575897\pi$
$337$	−8.67159	−0.472372	−0.236186	+	0.971708i	$0.575897\pi$
$338$	−1.31925	−0.0717575
$339$	−36.7902	−1.99817
$340$	−5.47783	−0.297077
$341$	−12.5367	−0.678899
$342$	34.9055	1.88747
$343$	−17.0312	−0.919599
$344$	−0.471936	−0.0254451
$345$	15.6740	0.843860
$346$	−15.5302	−0.834910
$347$	12.6562	0.679419	0.339710	−	0.940530i	$-0.389671\pi$
$347$	12.6562	0.679419	0.339710	+	0.940530i	$0.389671\pi$
$348$	13.1178	0.703188
$349$	−20.6625	−1.10604	−0.553020	−	0.833168i	$-0.686525\pi$
$349$	−20.6625	−1.10604	−0.553020	+	0.833168i	$0.686525\pi$
$350$	−8.57894	−0.458564
$351$	13.7796	0.735503
$352$	1.99250	0.106200
$353$	−11.1394	−0.592893	−0.296447	−	0.955049i	$-0.595802\pi$
$353$	−11.1394	−0.592893	−0.296447	+	0.955049i	$0.595802\pi$
$354$	36.4318	1.93633
$355$	−2.27860	−0.120935
$356$	14.4665	0.766722
$357$	30.1890	1.59777
$358$	21.4124	1.13168
$359$	−29.0165	−1.53143	−0.765717	−	0.643178i	$-0.777616\pi$
$359$	−29.0165	−1.53143	−0.765717	+	0.643178i	$0.777616\pi$
$360$	6.26512	0.330201
$361$	41.8497	2.20262
$362$	−15.6888	−0.824583
$363$	19.2199	1.00878
$364$	−9.64591	−0.505583
$365$	−8.89249	−0.465454
$366$	26.2913	1.37427
$367$	−11.0236	−0.575426	−0.287713	−	0.957717i	$-0.592895\pi$
$367$	−11.0236	−0.575426	−0.287713	+	0.957717i	$0.592895\pi$
$368$	−4.09466	−0.213449
$369$	−28.4498	−1.48104
$370$	2.71455	0.141123
$371$	−33.9480	−1.76249
$372$	17.2021	0.891888
$373$	9.79007	0.506911	0.253455	−	0.967347i	$-0.418433\pi$
$373$	9.79007	0.506911	0.253455	+	0.967347i	$0.418433\pi$
$374$	−7.79545	−0.403093
$375$	30.7751	1.58922
$376$	7.42217	0.382769
$377$	16.3983	0.844556
$378$	−11.3792	−0.585281
$379$	−22.9623	−1.17949	−0.589746	−	0.807589i	$-0.700772\pi$
$379$	−22.9623	−1.17949	−0.589746	+	0.807589i	$0.700772\pi$
$380$	10.9218	0.560277
$381$	21.8354	1.11866
$382$	13.1829	0.674496
$383$	32.9788	1.68514	0.842570	−	0.538587i	$-0.181042\pi$
$383$	32.9788	1.68514	0.842570	+	0.538587i	$0.181042\pi$
$384$	−2.73399	−0.139518
$385$	7.87355	0.401273
$386$	−1.59022	−0.0809401
$387$	−2.11178	−0.107348
$388$	17.5015	0.888506
$389$	−38.9039	−1.97251	−0.986254	−	0.165239i	$-0.947161\pi$
$389$	−38.9039	−1.97251	−0.986254	+	0.165239i	$0.947161\pi$
$390$	13.0827	0.662469
$391$	16.0200	0.810165
$392$	0.965551	0.0487677
$393$	10.5500	0.532176
$394$	9.52983	0.480106
$395$	−15.3010	−0.769875
$396$	8.91583	0.448037
$397$	12.1956	0.612078	0.306039	−	0.952019i	$-0.400996\pi$
$397$	12.1956	0.612078	0.306039	+	0.952019i	$0.400996\pi$
$398$	10.7477	0.538734
$399$	−60.1914	−3.01334
$400$	−3.03967	−0.151983
$401$	−20.5719	−1.02731	−0.513656	−	0.857996i	$-0.671709\pi$
$401$	−20.5719	−1.02731	−0.513656	+	0.857996i	$0.671709\pi$
$402$	33.4583	1.66875
$403$	21.5041	1.07119
$404$	−1.61987	−0.0805917
$405$	−3.36186	−0.167052
$406$	−13.5417	−0.672061
$407$	3.86305	0.191484
$408$	10.6965	0.529555
$409$	−10.0322	−0.496063	−0.248031	−	0.968752i	$-0.579784\pi$
$409$	−10.0322	−0.496063	−0.248031	+	0.968752i	$0.579784\pi$
$410$	−8.90183	−0.439630
$411$	−38.2703	−1.88774
$412$	0.695444	0.0342621
$413$	−37.6090	−1.85062
$414$	−18.3224	−0.900497
$415$	2.15887	0.105975
$416$	−3.41771	−0.167567
$417$	−9.69757	−0.474892
$418$	15.5427	0.760219
$419$	−1.69956	−0.0830290	−0.0415145	−	0.999138i	$-0.513218\pi$
$419$	−1.69956	−0.0830290	−0.0415145	+	0.999138i	$0.513218\pi$
$420$	−10.8036	−0.527164
$421$	−2.15271	−0.104917	−0.0524583	−	0.998623i	$-0.516706\pi$
$421$	−2.15271	−0.104917	−0.0524583	+	0.998623i	$0.516706\pi$
$422$	1.78668	0.0869742
$423$	33.2120	1.61482
$424$	−12.0284	−0.584149
$425$	11.8924	0.576866
$426$	4.44938	0.215573
$427$	−27.1408	−1.31344
$428$	−8.66620	−0.418897
$429$	18.6179	0.898879
$430$	−0.660767	−0.0318650
$431$	−41.0042	−1.97510	−0.987552	−	0.157293i	$-0.949723\pi$
$431$	−41.0042	−1.97510	−0.987552	+	0.157293i	$0.949723\pi$
$432$	−4.03183	−0.193982
$433$	27.6990	1.33113	0.665564	−	0.746340i	$-0.268191\pi$
$433$	27.6990	1.33113	0.665564	+	0.746340i	$0.268191\pi$
$434$	−17.7579	−0.852409
$435$	18.3665	0.880605
$436$	3.10480	0.148693
$437$	−31.9409	−1.52794
$438$	17.3642	0.829695
$439$	32.9297	1.57165	0.785824	−	0.618451i	$-0.212239\pi$
$439$	32.9297	1.57165	0.785824	+	0.618451i	$0.212239\pi$
$440$	2.78973	0.132995
$441$	4.32056	0.205741
$442$	13.3715	0.636016
$443$	7.54226	0.358344	0.179172	−	0.983818i	$-0.442658\pi$
$443$	7.54226	0.358344	0.179172	+	0.983818i	$0.442658\pi$
$444$	−5.30066	−0.251558
$445$	20.2548	0.960170
$446$	−21.7588	−1.03031
$447$	−15.7347	−0.744227
$448$	2.82233	0.133343
$449$	21.6222	1.02041	0.510207	−	0.860052i	$-0.329569\pi$
$449$	21.6222	1.02041	0.510207	+	0.860052i	$0.329569\pi$
$450$	−13.6016	−0.641186
$451$	−12.6681	−0.596518
$452$	13.4566	0.632945
$453$	7.01332	0.329515
$454$	4.27139	0.200466
$455$	−13.5054	−0.633144
$456$	−21.3268	−0.998721
$457$	−35.0443	−1.63930	−0.819651	−	0.572864i	$-0.805832\pi$
$457$	−35.0443	−1.63930	−0.819651	+	0.572864i	$0.805832\pi$
$458$	2.81027	0.131315
$459$	15.7742	0.736275
$460$	−5.73302	−0.267303
$461$	37.2100	1.73304	0.866522	−	0.499138i	$-0.166350\pi$
$461$	37.2100	1.73304	0.866522	+	0.499138i	$0.166350\pi$
$462$	−15.3745	−0.715289
$463$	−8.22444	−0.382222	−0.191111	−	0.981568i	$-0.561209\pi$
$463$	−8.22444	−0.382222	−0.191111	+	0.981568i	$0.561209\pi$
$464$	−4.79804	−0.222743
$465$	24.0850	1.11692
$466$	28.5745	1.32369
$467$	28.4253	1.31537	0.657683	−	0.753295i	$-0.271537\pi$
$467$	28.4253	1.31537	0.657683	+	0.753295i	$0.271537\pi$
$468$	−15.2933	−0.706931
$469$	−34.5394	−1.59488
$470$	10.3919	0.479344
$471$	−42.7733	−1.97089
$472$	−13.3255	−0.613356
$473$	−0.940330	−0.0432364
$474$	29.8780	1.37234
$475$	−23.7113	−1.08795
$476$	−11.0421	−0.506114
$477$	−53.8233	−2.46440
$478$	−9.92291	−0.453863
$479$	−26.8822	−1.22828	−0.614141	−	0.789197i	$-0.710497\pi$
$479$	−26.8822	−1.22828	−0.614141	+	0.789197i	$0.710497\pi$
$480$	−3.82791	−0.174720
$481$	−6.62626	−0.302131
$482$	−19.6016	−0.892828
$483$	31.5953	1.43764
$484$	−7.02996	−0.319544
$485$	24.5042	1.11268
$486$	18.6602	0.846442
$487$	36.2532	1.64279	0.821395	−	0.570359i	$-0.193196\pi$
$487$	36.2532	1.64279	0.821395	+	0.570359i	$0.193196\pi$
$488$	−9.61645	−0.435316
$489$	−21.5449	−0.974294
$490$	1.35189	0.0610720
$491$	−26.6163	−1.20118	−0.600588	−	0.799559i	$-0.705067\pi$
$491$	−26.6163	−1.20118	−0.600588	+	0.799559i	$0.705067\pi$
$492$	17.3825	0.783662
$493$	18.7719	0.845442
$494$	−26.6603	−1.19950
$495$	12.4832	0.561079
$496$	−6.29194	−0.282517
$497$	−4.59315	−0.206031
$498$	−4.21559	−0.188905
$499$	−3.77779	−0.169117	−0.0845585	−	0.996419i	$-0.526948\pi$
$499$	−3.77779	−0.169117	−0.0845585	+	0.996419i	$0.526948\pi$
$500$	−11.2565	−0.503406
$501$	−8.72402	−0.389760
$502$	−12.1650	−0.542952
$503$	37.4739	1.67088	0.835440	−	0.549582i	$-0.185213\pi$
$503$	37.4739	1.67088	0.835440	+	0.549582i	$0.185213\pi$
$504$	12.6291	0.562545
$505$	−2.26802	−0.100925
$506$	−8.15859	−0.362694
$507$	3.60680	0.160184
$508$	−7.98666	−0.354351
$509$	38.6436	1.71285	0.856423	−	0.516275i	$-0.172682\pi$
$509$	38.6436	1.71285	0.856423	+	0.516275i	$0.172682\pi$
$510$	14.9763	0.663164
$511$	−17.9253	−0.792968
$512$	1.00000	0.0441942
$513$	−31.4508	−1.38859
$514$	−10.5546	−0.465541
$515$	0.973705	0.0429066
$516$	1.29027	0.0568009
$517$	14.7886	0.650404
$518$	5.47193	0.240423
$519$	42.4595	1.86376
$520$	−4.78520	−0.209845
$521$	18.2963	0.801574	0.400787	−	0.916171i	$-0.368737\pi$
$521$	18.2963	0.801574	0.400787	+	0.916171i	$0.368737\pi$
$522$	−21.4698	−0.939708
$523$	5.16374	0.225795	0.112897	−	0.993607i	$-0.463987\pi$
$523$	5.16374	0.225795	0.112897	+	0.993607i	$0.463987\pi$
$524$	−3.85882	−0.168573
$525$	23.4547	1.02365
$526$	−11.2506	−0.490549
$527$	24.6166	1.07232
$528$	−5.44746	−0.237070
$529$	−6.23375	−0.271032
$530$	−16.8411	−0.731532
$531$	−59.6277	−2.58762
$532$	22.0159	0.954512
$533$	21.7295	0.941209
$534$	−39.5512	−1.71155
$535$	−12.1337	−0.524586
$536$	−12.2379	−0.528597
$537$	−58.5414	−2.52625
$538$	21.6700	0.934261
$539$	1.92386	0.0828663
$540$	−5.64505	−0.242924
$541$	27.5730	1.18545	0.592727	−	0.805403i	$-0.298051\pi$
$541$	27.5730	1.18545	0.592727	+	0.805403i	$0.298051\pi$
$542$	0.228800	0.00982781
$543$	42.8929	1.84071
$544$	−3.91240	−0.167743
$545$	4.34708	0.186209
$546$	26.3718	1.12861
$547$	−7.61462	−0.325578	−0.162789	−	0.986661i	$-0.552049\pi$
$547$	−7.61462	−0.325578	−0.162789	+	0.986661i	$0.552049\pi$
$548$	13.9980	0.597964
$549$	−43.0308	−1.83651
$550$	−6.05652	−0.258251
$551$	−37.4277	−1.59447
$552$	11.1948	0.476481
$553$	−30.8434	−1.31159
$554$	20.2394	0.859891
$555$	−7.42156	−0.315027
$556$	3.54704	0.150428
$557$	−36.9570	−1.56592	−0.782959	−	0.622073i	$-0.786291\pi$
$557$	−36.9570	−1.56592	−0.782959	+	0.622073i	$0.786291\pi$
$558$	−28.1546	−1.19188
$559$	1.61294	0.0682202
$560$	3.95160	0.166986
$561$	21.3127	0.899822
$562$	−2.63854	−0.111300
$563$	10.1554	0.427998	0.213999	−	0.976834i	$-0.431351\pi$
$563$	10.1554	0.427998	0.213999	+	0.976834i	$0.431351\pi$
$564$	−20.2921	−0.854453
$565$	18.8408	0.792640
$566$	−23.3658	−0.982138
$567$	−6.77677	−0.284598
$568$	−1.62743	−0.0682855
$569$	−31.7739	−1.33203	−0.666015	−	0.745938i	$-0.732001\pi$
$569$	−31.7739	−1.33203	−0.666015	+	0.745938i	$0.732001\pi$
$570$	−29.8601	−1.25070
$571$	−24.6893	−1.03321	−0.516607	−	0.856222i	$-0.672805\pi$
$571$	−24.6893	−1.03321	−0.516607	+	0.856222i	$0.672805\pi$
$572$	−6.80978	−0.284731
$573$	−36.0419	−1.50567
$574$	−17.9441	−0.748973
$575$	12.4464	0.519051
$576$	4.47471	0.186446
$577$	33.1097	1.37838	0.689188	−	0.724582i	$-0.257967\pi$
$577$	33.1097	1.37838	0.689188	+	0.724582i	$0.257967\pi$
$578$	−1.69309	−0.0704233
$579$	4.34765	0.180682
$580$	−6.71783	−0.278943
$581$	4.35181	0.180543
$582$	−47.8491	−1.98341
$583$	−23.9664	−0.992589
$584$	−6.35124	−0.262816
$585$	−21.4124	−0.885293
$586$	−1.11863	−0.0462100
$587$	24.6836	1.01880	0.509400	−	0.860530i	$-0.329867\pi$
$587$	24.6836	1.01880	0.509400	+	0.860530i	$0.329867\pi$
$588$	−2.63981	−0.108864
$589$	−49.0811	−2.02235
$590$	−18.6573	−0.768109
$591$	−26.0545	−1.07174
$592$	1.93880	0.0796841
$593$	37.7723	1.55112	0.775561	−	0.631272i	$-0.217467\pi$
$593$	37.7723	1.55112	0.775561	+	0.631272i	$0.217467\pi$
$594$	−8.03341	−0.329615
$595$	−15.4603	−0.633809
$596$	5.75523	0.235743
$597$	−29.3841	−1.20261
$598$	13.9944	0.572273
$599$	−22.2799	−0.910331	−0.455165	−	0.890407i	$-0.650420\pi$
$599$	−22.2799	−0.910331	−0.455165	+	0.890407i	$0.650420\pi$
$600$	8.31042	0.339271
$601$	−10.9401	−0.446255	−0.223127	−	0.974789i	$-0.571627\pi$
$601$	−10.9401	−0.446255	−0.223127	+	0.974789i	$0.571627\pi$
$602$	−1.33196	−0.0542866
$603$	−54.7611	−2.23004
$604$	−2.56523	−0.104378
$605$	−9.84279	−0.400166
$606$	4.42872	0.179904
$607$	−6.44202	−0.261474	−0.130737	−	0.991417i	$-0.541734\pi$
$607$	−6.44202	−0.261474	−0.130737	+	0.991417i	$0.541734\pi$
$608$	7.80062	0.316357
$609$	37.0228	1.50024
$610$	−13.4642	−0.545149
$611$	−25.3668	−1.02623
$612$	−17.5069	−0.707673
$613$	−26.7460	−1.08026	−0.540130	−	0.841582i	$-0.681625\pi$
$613$	−26.7460	−1.08026	−0.540130	+	0.841582i	$0.681625\pi$
$614$	1.00536	0.0405731
$615$	24.3375	0.981384
$616$	5.62348	0.226577
$617$	−33.5084	−1.34900	−0.674500	−	0.738275i	$-0.735641\pi$
$617$	−33.5084	−1.34900	−0.674500	+	0.738275i	$0.735641\pi$
$618$	−1.90134	−0.0764830
$619$	33.0415	1.32805	0.664025	−	0.747710i	$-0.268847\pi$
$619$	33.0415	1.32805	0.664025	+	0.747710i	$0.268847\pi$
$620$	−8.80947	−0.353797
$621$	16.5090	0.662483
$622$	−23.6992	−0.950252
$623$	40.8292	1.63579
$624$	9.34399	0.374059
$625$	−0.562105	−0.0224842
$626$	−15.8107	−0.631921
$627$	−42.4936	−1.69703
$628$	15.6450	0.624303
$629$	−7.58537	−0.302448
$630$	17.6822	0.704478
$631$	−7.53037	−0.299779	−0.149890	−	0.988703i	$-0.547892\pi$
$631$	−7.53037	−0.299779	−0.149890	+	0.988703i	$0.547892\pi$
$632$	−10.9283	−0.434706
$633$	−4.88477	−0.194152
$634$	23.0300	0.914637
$635$	−11.1823	−0.443755
$636$	32.8854	1.30399
$637$	−3.29998	−0.130750
$638$	−9.56007	−0.378487
$639$	−7.28227	−0.288082
$640$	1.40012	0.0553446
$641$	14.3172	0.565497	0.282748	−	0.959194i	$-0.408754\pi$
$641$	14.3172	0.565497	0.282748	+	0.959194i	$0.408754\pi$
$642$	23.6933	0.935101
$643$	32.1525	1.26797	0.633985	−	0.773345i	$-0.281418\pi$
$643$	32.1525	1.26797	0.633985	+	0.773345i	$0.281418\pi$
$644$	−11.5565	−0.455389
$645$	1.80653	0.0711321
$646$	−30.5192	−1.20076
$647$	29.9667	1.17811	0.589056	−	0.808092i	$-0.299500\pi$
$647$	29.9667	1.17811	0.589056	+	0.808092i	$0.299500\pi$
$648$	−2.40112	−0.0943251
$649$	−26.5510	−1.04222
$650$	10.3887	0.407478
$651$	48.5501	1.90283
$652$	7.88038	0.308620
$653$	44.5326	1.74270	0.871348	−	0.490665i	$-0.163246\pi$
$653$	44.5326	1.74270	0.871348	+	0.490665i	$0.163246\pi$
$654$	−8.48848	−0.331926
$655$	−5.40281	−0.211105
$656$	−6.35791	−0.248235
$657$	−28.4199	−1.10877
$658$	20.9478	0.816631
$659$	−25.4939	−0.993103	−0.496552	−	0.868007i	$-0.665401\pi$
$659$	−25.4939	−0.993103	−0.496552	+	0.868007i	$0.665401\pi$
$660$	−7.62710	−0.296884
$661$	−8.48142	−0.329889	−0.164945	−	0.986303i	$-0.552745\pi$
$661$	−8.48142	−0.329889	−0.164945	+	0.986303i	$0.552745\pi$
$662$	−21.5205	−0.836418
$663$	−36.5575	−1.41977
$664$	1.54192	0.0598381
$665$	30.8249	1.19534
$666$	8.67556	0.336171
$667$	19.6463	0.760709
$668$	3.19095	0.123461
$669$	59.4884	2.29995
$670$	−17.1345	−0.661965
$671$	−19.1607	−0.739692
$672$	−7.71623	−0.297660
$673$	−41.0575	−1.58265	−0.791324	−	0.611397i	$-0.790608\pi$
$673$	−41.0575	−1.58265	−0.791324	+	0.611397i	$0.790608\pi$
$674$	−8.67159	−0.334017
$675$	12.2554	0.471711
$676$	−1.31925	−0.0507402
$677$	−5.69049	−0.218703	−0.109352	−	0.994003i	$-0.534877\pi$
$677$	−5.69049	−0.218703	−0.109352	+	0.994003i	$0.534877\pi$
$678$	−36.7902	−1.41292
$679$	49.3951	1.89561
$680$	−5.47783	−0.210065
$681$	−11.6779	−0.447500
$682$	−12.5367	−0.480054
$683$	−38.3264	−1.46652	−0.733259	−	0.679949i	$-0.762002\pi$
$683$	−38.3264	−1.46652	−0.733259	+	0.679949i	$0.762002\pi$
$684$	34.9055	1.33465
$685$	19.5988	0.748833
$686$	−17.0312	−0.650255
$687$	−7.68325	−0.293134
$688$	−0.471936	−0.0179924
$689$	41.1094	1.56615
$690$	15.6740	0.596699
$691$	−0.536877	−0.0204237	−0.0102119	−	0.999948i	$-0.503251\pi$
$691$	−0.536877	−0.0204237	−0.0102119	+	0.999948i	$0.503251\pi$
$692$	−15.5302	−0.590371
$693$	25.1634	0.955879
$694$	12.6562	0.480422
$695$	4.96628	0.188382
$696$	13.1178	0.497229
$697$	24.8747	0.942197
$698$	−20.6625	−0.782088
$699$	−78.1226	−2.95487
$700$	−8.57894	−0.324254
$701$	−4.61549	−0.174325	−0.0871623	−	0.996194i	$-0.527780\pi$
$701$	−4.61549	−0.174325	−0.0871623	+	0.996194i	$0.527780\pi$
$702$	13.7796	0.520079
$703$	15.1238	0.570407
$704$	1.99250	0.0750950
$705$	−28.4114	−1.07004
$706$	−11.1394	−0.419239
$707$	−4.57182	−0.171941
$708$	36.4318	1.36919
$709$	40.6993	1.52850	0.764248	−	0.644923i	$-0.223110\pi$
$709$	40.6993	1.52850	0.764248	+	0.644923i	$0.223110\pi$
$710$	−2.27860	−0.0855142
$711$	−48.9011	−1.83393
$712$	14.4665	0.542154
$713$	25.7634	0.964846
$714$	30.1890	1.12979
$715$	−9.53450	−0.356570
$716$	21.4124	0.800220
$717$	27.1291	1.01316
$718$	−29.0165	−1.08289
$719$	5.91217	0.220487	0.110243	−	0.993905i	$-0.464837\pi$
$719$	5.91217	0.220487	0.110243	+	0.993905i	$0.464837\pi$
$720$	6.26512	0.233487
$721$	1.96277	0.0730975
$722$	41.8497	1.55749
$723$	53.5906	1.99305
$724$	−15.6888	−0.583068
$725$	14.5844	0.541652
$726$	19.2199	0.713316
$727$	36.9577	1.37069	0.685343	−	0.728220i	$-0.259652\pi$
$727$	36.9577	1.37069	0.685343	+	0.728220i	$0.259652\pi$
$728$	−9.64591	−0.357501
$729$	−43.8133	−1.62272
$730$	−8.89249	−0.329126
$731$	1.84640	0.0682918
$732$	26.2913	0.971754
$733$	16.2502	0.600215	0.300108	−	0.953905i	$-0.402977\pi$
$733$	16.2502	0.600215	0.300108	+	0.953905i	$0.402977\pi$
$734$	−11.0236	−0.406888
$735$	−3.69605	−0.136331
$736$	−4.09466	−0.150931
$737$	−24.3840	−0.898195
$738$	−28.4498	−1.04725
$739$	−20.8067	−0.765388	−0.382694	−	0.923875i	$-0.625004\pi$
$739$	−20.8067	−0.765388	−0.382694	+	0.923875i	$0.625004\pi$
$740$	2.71455	0.0997889
$741$	72.8890	2.67764
$742$	−33.9480	−1.24627
$743$	18.1204	0.664772	0.332386	−	0.943143i	$-0.392146\pi$
$743$	18.1204	0.664772	0.332386	+	0.943143i	$0.392146\pi$
$744$	17.2021	0.630660
$745$	8.05800	0.295222
$746$	9.79007	0.358440
$747$	6.89964	0.252445
$748$	−7.79545	−0.285030
$749$	−24.4589	−0.893708
$750$	30.7751	1.12375
$751$	−7.78024	−0.283905	−0.141953	−	0.989873i	$-0.545338\pi$
$751$	−7.78024	−0.283905	−0.141953	+	0.989873i	$0.545338\pi$
$752$	7.42217	0.270659
$753$	33.2591	1.21203
$754$	16.3983	0.597191
$755$	−3.59163	−0.130713
$756$	−11.3792	−0.413856
$757$	23.7081	0.861687	0.430844	−	0.902427i	$-0.358216\pi$
$757$	23.7081	0.861687	0.430844	+	0.902427i	$0.358216\pi$
$758$	−22.9623	−0.834027
$759$	22.3055	0.809639
$760$	10.9218	0.396176
$761$	−47.5543	−1.72384	−0.861921	−	0.507042i	$-0.830739\pi$
$761$	−47.5543	−1.72384	−0.861921	+	0.507042i	$0.830739\pi$
$762$	21.8354	0.791015
$763$	8.76276	0.317233
$764$	13.1829	0.476941
$765$	−24.5117	−0.886222
$766$	32.9788	1.19157
$767$	45.5427	1.64445
$768$	−2.73399	−0.0986544
$769$	−52.3198	−1.88670	−0.943351	−	0.331798i	$-0.892345\pi$
$769$	−52.3198	−1.88670	−0.943351	+	0.331798i	$0.892345\pi$
$770$	7.87355	0.283743
$771$	28.8561	1.03923
$772$	−1.59022	−0.0572333
$773$	−19.4562	−0.699792	−0.349896	−	0.936789i	$-0.613783\pi$
$773$	−19.4562	−0.699792	−0.349896	+	0.936789i	$0.613783\pi$
$774$	−2.11178	−0.0759062
$775$	19.1254	0.687005
$776$	17.5015	0.628269
$777$	−14.9602	−0.536695
$778$	−38.9039	−1.39477
$779$	−49.5957	−1.77695
$780$	13.0827	0.468436
$781$	−3.24265	−0.116031
$782$	16.0200	0.572873
$783$	19.3449	0.691330
$784$	0.965551	0.0344840
$785$	21.9049	0.781818
$786$	10.5500	0.376305
$787$	−32.0655	−1.14301	−0.571505	−	0.820599i	$-0.693640\pi$
$787$	−32.0655	−1.14301	−0.571505	+	0.820599i	$0.693640\pi$
$788$	9.52983	0.339486
$789$	30.7590	1.09505
$790$	−15.3010	−0.544384
$791$	37.9790	1.35038
$792$	8.91583	0.316810
$793$	32.8663	1.16711
$794$	12.1956	0.432805
$795$	46.0435	1.63299
$796$	10.7477	0.380943
$797$	−14.2901	−0.506182	−0.253091	−	0.967442i	$-0.581447\pi$
$797$	−14.2901	−0.506182	−0.253091	+	0.967442i	$0.581447\pi$
$798$	−60.1914	−2.13075
$799$	−29.0385	−1.02731
$800$	−3.03967	−0.107468
$801$	64.7333	2.28724
$802$	−20.5719	−0.726419
$803$	−12.6548	−0.446579
$804$	33.4583	1.17998
$805$	−16.1805	−0.570286
$806$	21.5041	0.757448
$807$	−59.2457	−2.08555
$808$	−1.61987	−0.0569869
$809$	4.27046	0.150141	0.0750707	−	0.997178i	$-0.476082\pi$
$809$	4.27046	0.150141	0.0750707	+	0.997178i	$0.476082\pi$
$810$	−3.36186	−0.118124
$811$	2.07560	0.0728843	0.0364422	−	0.999336i	$-0.488398\pi$
$811$	2.07560	0.0728843	0.0364422	+	0.999336i	$0.488398\pi$
$812$	−13.5417	−0.475219
$813$	−0.625538	−0.0219386
$814$	3.86305	0.135400
$815$	11.0335	0.386486
$816$	10.6965	0.374452
$817$	−3.68140	−0.128796
$818$	−10.0322	−0.350769
$819$	−43.1626	−1.50822
$820$	−8.90183	−0.310865
$821$	38.7426	1.35213	0.676063	−	0.736844i	$-0.263685\pi$
$821$	38.7426	1.35213	0.676063	+	0.736844i	$0.263685\pi$
$822$	−38.2703	−1.33483
$823$	−36.6136	−1.27627	−0.638135	−	0.769925i	$-0.720294\pi$
$823$	−36.6136	−1.27627	−0.638135	+	0.769925i	$0.720294\pi$
$824$	0.695444	0.0242269
$825$	16.5585	0.576492
$826$	−37.6090	−1.30858
$827$	−35.7908	−1.24457	−0.622284	−	0.782792i	$-0.713795\pi$
$827$	−35.7908	−1.24457	−0.622284	+	0.782792i	$0.713795\pi$
$828$	−18.3224	−0.636748
$829$	23.2081	0.806052	0.403026	−	0.915189i	$-0.367958\pi$
$829$	23.2081	0.806052	0.403026	+	0.915189i	$0.367958\pi$
$830$	2.15887	0.0749355
$831$	−55.3344	−1.91953
$832$	−3.41771	−0.118488
$833$	−3.77763	−0.130887
$834$	−9.69757	−0.335799
$835$	4.46771	0.154611
$836$	15.5427	0.537556
$837$	25.3681	0.876849
$838$	−1.69956	−0.0587104
$839$	20.8242	0.718930	0.359465	−	0.933159i	$-0.382959\pi$
$839$	20.8242	0.718930	0.359465	+	0.933159i	$0.382959\pi$
$840$	−10.8036	−0.372761
$841$	−5.97883	−0.206166
$842$	−2.15271	−0.0741872
$843$	7.21373	0.248454
$844$	1.78668	0.0615001
$845$	−1.84710	−0.0635422
$846$	33.2120	1.14185
$847$	−19.8409	−0.681741
$848$	−12.0284	−0.413055
$849$	63.8819	2.19242
$850$	11.8924	0.407906
$851$	−7.93873	−0.272136
$852$	4.44938	0.152433
$853$	1.57658	0.0539810	0.0269905	−	0.999636i	$-0.491408\pi$
$853$	1.57658	0.0539810	0.0269905	+	0.999636i	$0.491408\pi$
$854$	−27.1408	−0.928739
$855$	48.8719	1.67138
$856$	−8.66620	−0.296205
$857$	−45.4195	−1.55150	−0.775750	−	0.631040i	$-0.782628\pi$
$857$	−45.4195	−1.55150	−0.775750	+	0.631040i	$0.782628\pi$
$858$	18.6179	0.635603
$859$	−9.46611	−0.322979	−0.161490	−	0.986874i	$-0.551630\pi$
$859$	−9.46611	−0.322979	−0.161490	+	0.986874i	$0.551630\pi$
$860$	−0.660767	−0.0225320
$861$	49.0591	1.67193
$862$	−41.0042	−1.39661
$863$	−38.7550	−1.31924	−0.659618	−	0.751601i	$-0.729282\pi$
$863$	−38.7550	−1.31924	−0.659618	+	0.751601i	$0.729282\pi$
$864$	−4.03183	−0.137166
$865$	−21.7442	−0.739324
$866$	27.6990	0.941250
$867$	4.62889	0.157205
$868$	−17.7579	−0.602744
$869$	−21.7746	−0.738654
$870$	18.3665	0.622682
$871$	41.8257	1.41721
$872$	3.10480	0.105142
$873$	78.3143	2.65054
$874$	−31.9409	−1.08042
$875$	−31.7695	−1.07401
$876$	17.3642	0.586683
$877$	5.44956	0.184018	0.0920092	−	0.995758i	$-0.470671\pi$
$877$	5.44956	0.184018	0.0920092	+	0.995758i	$0.470671\pi$
$878$	32.9297	1.11132
$879$	3.05831	0.103154
$880$	2.78973	0.0940418
$881$	11.2420	0.378754	0.189377	−	0.981904i	$-0.439353\pi$
$881$	11.2420	0.378754	0.189377	+	0.981904i	$0.439353\pi$
$882$	4.32056	0.145481
$883$	−10.5154	−0.353872	−0.176936	−	0.984222i	$-0.556619\pi$
$883$	−10.5154	−0.353872	−0.176936	+	0.984222i	$0.556619\pi$
$884$	13.3715	0.449731
$885$	51.0089	1.71464
$886$	7.54226	0.253387
$887$	4.66364	0.156590	0.0782948	−	0.996930i	$-0.475052\pi$
$887$	4.66364	0.156590	0.0782948	+	0.996930i	$0.475052\pi$
$888$	−5.30066	−0.177878
$889$	−22.5410	−0.756001
$890$	20.2548	0.678943
$891$	−4.78423	−0.160278
$892$	−21.7588	−0.728539
$893$	57.8976	1.93747
$894$	−15.7347	−0.526248
$895$	29.9800	1.00212
$896$	2.82233	0.0942875
$897$	−38.2605	−1.27748
$898$	21.6222	0.721542
$899$	30.1890	1.00686
$900$	−13.6016	−0.453387
$901$	47.0598	1.56779
$902$	−12.6681	−0.421802
$903$	3.64157	0.121184
$904$	13.4566	0.447560
$905$	−21.9661	−0.730179
$906$	7.01332	0.233002
$907$	−8.40084	−0.278945	−0.139473	−	0.990226i	$-0.544541\pi$
$907$	−8.40084	−0.278945	−0.139473	+	0.990226i	$0.544541\pi$
$908$	4.27139	0.141751
$909$	−7.24845	−0.240416
$910$	−13.5054	−0.447701
$911$	7.97925	0.264364	0.132182	−	0.991225i	$-0.457802\pi$
$911$	7.97925	0.264364	0.132182	+	0.991225i	$0.457802\pi$
$912$	−21.3268	−0.706202
$913$	3.07227	0.101677
$914$	−35.0443	−1.15916
$915$	36.8109	1.21693
$916$	2.81027	0.0928540
$917$	−10.8909	−0.359648
$918$	15.7742	0.520625
$919$	36.8022	1.21399	0.606996	−	0.794705i	$-0.292374\pi$
$919$	36.8022	1.21399	0.606996	+	0.794705i	$0.292374\pi$
$920$	−5.73302	−0.189012
$921$	−2.74865	−0.0905710
$922$	37.2100	1.22545
$923$	5.56209	0.183078
$924$	−15.3745	−0.505785
$925$	−5.89330	−0.193771
$926$	−8.22444	−0.270272
$927$	3.11191	0.102208
$928$	−4.79804	−0.157503
$929$	16.2032	0.531610	0.265805	−	0.964027i	$-0.414362\pi$
$929$	16.2032	0.531610	0.265805	+	0.964027i	$0.414362\pi$
$930$	24.0850	0.789779
$931$	7.53190	0.246848
$932$	28.5745	0.935990
$933$	64.7934	2.12124
$934$	28.4253	0.930104
$935$	−10.9146	−0.356944
$936$	−15.2933	−0.499876
$937$	23.7498	0.775873	0.387936	−	0.921686i	$-0.373188\pi$
$937$	23.7498	0.775873	0.387936	+	0.921686i	$0.373188\pi$
$938$	−34.5394	−1.12775
$939$	43.2262	1.41063
$940$	10.3919	0.338947
$941$	21.2962	0.694237	0.347119	−	0.937821i	$-0.387160\pi$
$941$	21.2962	0.694237	0.347119	+	0.937821i	$0.387160\pi$
$942$	−42.7733	−1.39363
$943$	26.0335	0.847767
$944$	−13.3255	−0.433708
$945$	−15.9322	−0.518274
$946$	−0.940330	−0.0305728
$947$	−1.00286	−0.0325884	−0.0162942	−	0.999867i	$-0.505187\pi$
$947$	−1.00286	−0.0325884	−0.0162942	+	0.999867i	$0.505187\pi$
$948$	29.8780	0.970391
$949$	21.7067	0.704629
$950$	−23.7113	−0.769296
$951$	−62.9637	−2.04174
$952$	−11.0421	−0.357877
$953$	−34.7108	−1.12439	−0.562196	−	0.827004i	$-0.690044\pi$
$953$	−34.7108	−1.12439	−0.562196	+	0.827004i	$0.690044\pi$
$954$	−53.8233	−1.74260
$955$	18.4576	0.597275
$956$	−9.92291	−0.320930
$957$	26.1371	0.844894
$958$	−26.8822	−0.868526
$959$	39.5069	1.27575
$960$	−3.82791	−0.123545
$961$	8.58856	0.277050
$962$	−6.62626	−0.213639
$963$	−38.7787	−1.24963
$964$	−19.6016	−0.631325
$965$	−2.22650	−0.0716735
$966$	31.5953	1.01656
$967$	17.1825	0.552553	0.276276	−	0.961078i	$-0.410900\pi$
$967$	17.1825	0.552553	0.276276	+	0.961078i	$0.410900\pi$
$968$	−7.02996	−0.225952
$969$	83.4392	2.68045
$970$	24.5042	0.786784
$971$	23.4069	0.751162	0.375581	−	0.926790i	$-0.377443\pi$
$971$	23.4069	0.751162	0.375581	+	0.926790i	$0.377443\pi$
$972$	18.6602	0.598525
$973$	10.0109	0.320935
$974$	36.2532	1.16163
$975$	−28.4026	−0.909612
$976$	−9.61645	−0.307815
$977$	−33.7753	−1.08057	−0.540285	−	0.841482i	$-0.681683\pi$
$977$	−33.7753	−1.08057	−0.540285	+	0.841482i	$0.681683\pi$
$978$	−21.5449	−0.688930
$979$	28.8244	0.921232
$980$	1.35189	0.0431844
$981$	13.8930	0.443571
$982$	−26.6163	−0.849360
$983$	49.3229	1.57316	0.786578	−	0.617490i	$-0.211851\pi$
$983$	49.3229	1.57316	0.786578	+	0.617490i	$0.211851\pi$
$984$	17.3825	0.554133
$985$	13.3429	0.425140
$986$	18.7719	0.597818
$987$	−57.2711	−1.82296
$988$	−26.6603	−0.848177
$989$	1.93242	0.0614473
$990$	12.4832	0.396743
$991$	19.7225	0.626506	0.313253	−	0.949670i	$-0.398581\pi$
$991$	19.7225	0.626506	0.313253	+	0.949670i	$0.398581\pi$
$992$	−6.29194	−0.199769
$993$	58.8369	1.86713
$994$	−4.59315	−0.145686
$995$	15.0481	0.477056
$996$	−4.21559	−0.133576
$997$	7.19787	0.227959	0.113979	−	0.993483i	$-0.463640\pi$
$997$	7.19787	0.227959	0.113979	+	0.993483i	$0.463640\pi$
$998$	−3.77779	−0.119584
$999$	−7.81691	−0.247316

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8006.2.a.a.1.8	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8006.2.a.a.1.8	✓	69	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73399 q^{3} +1.00000 q^{4} +1.40012 q^{5} -2.73399 q^{6} +2.82233 q^{7} +1.00000 q^{8} +4.47471 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73399 q^{3} +1.00000 q^{4} +1.40012 q^{5} -2.73399 q^{6} +2.82233 q^{7} +1.00000 q^{8} +4.47471 q^{9} +1.40012 q^{10} +1.99250 q^{11} -2.73399 q^{12} -3.41771 q^{13} +2.82233 q^{14} -3.82791 q^{15} +1.00000 q^{16} -3.91240 q^{17} +4.47471 q^{18} +7.80062 q^{19} +1.40012 q^{20} -7.71623 q^{21} +1.99250 q^{22} -4.09466 q^{23} -2.73399 q^{24} -3.03967 q^{25} -3.41771 q^{26} -4.03183 q^{27} +2.82233 q^{28} -4.79804 q^{29} -3.82791 q^{30} -6.29194 q^{31} +1.00000 q^{32} -5.44746 q^{33} -3.91240 q^{34} +3.95160 q^{35} +4.47471 q^{36} +1.93880 q^{37} +7.80062 q^{38} +9.34399 q^{39} +1.40012 q^{40} -6.35791 q^{41} -7.71623 q^{42} -0.471936 q^{43} +1.99250 q^{44} +6.26512 q^{45} -4.09466 q^{46} +7.42217 q^{47} -2.73399 q^{48} +0.965551 q^{49} -3.03967 q^{50} +10.6965 q^{51} -3.41771 q^{52} -12.0284 q^{53} -4.03183 q^{54} +2.78973 q^{55} +2.82233 q^{56} -21.3268 q^{57} -4.79804 q^{58} -13.3255 q^{59} -3.82791 q^{60} -9.61645 q^{61} -6.29194 q^{62} +12.6291 q^{63} +1.00000 q^{64} -4.78520 q^{65} -5.44746 q^{66} -12.2379 q^{67} -3.91240 q^{68} +11.1948 q^{69} +3.95160 q^{70} -1.62743 q^{71} +4.47471 q^{72} -6.35124 q^{73} +1.93880 q^{74} +8.31042 q^{75} +7.80062 q^{76} +5.62348 q^{77} +9.34399 q^{78} -10.9283 q^{79} +1.40012 q^{80} -2.40112 q^{81} -6.35791 q^{82} +1.54192 q^{83} -7.71623 q^{84} -5.47783 q^{85} -0.471936 q^{86} +13.1178 q^{87} +1.99250 q^{88} +14.4665 q^{89} +6.26512 q^{90} -9.64591 q^{91} -4.09466 q^{92} +17.2021 q^{93} +7.42217 q^{94} +10.9218 q^{95} -2.73399 q^{96} +17.5015 q^{97} +0.965551 q^{98} +8.91583 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9	\( 69 q + 69 q^{2} - 15 q^{3} + 69 q^{4} - 9 q^{5} - 15 q^{6} - 29 q^{7} + 69 q^{8} + 40 q^{9} - 9 q^{10} - 48 q^{11} - 15 q^{12} - 30 q^{13} - 29 q^{14} - 51 q^{15} + 69 q^{16} - 37 q^{17} + 40 q^{18} - 72 q^{19} - 9 q^{20} - 38 q^{21} - 48 q^{22} - 75 q^{23} - 15 q^{24} + 18 q^{25} - 30 q^{26} - 48 q^{27} - 29 q^{28} - 27 q^{29} - 51 q^{30} - 61 q^{31} + 69 q^{32} - 29 q^{33} - 37 q^{34} - 64 q^{35} + 40 q^{36} - 42 q^{37} - 72 q^{38} - 68 q^{39} - 9 q^{40} - 49 q^{41} - 38 q^{42} - 95 q^{43} - 48 q^{44} - 20 q^{45} - 75 q^{46} - 62 q^{47} - 15 q^{48} - 4 q^{49} + 18 q^{50} - 76 q^{51} - 30 q^{52} - 28 q^{53} - 48 q^{54} - 76 q^{55} - 29 q^{56} - 44 q^{57} - 27 q^{58} - 68 q^{59} - 51 q^{60} - 62 q^{61} - 61 q^{62} - 91 q^{63} + 69 q^{64} - 79 q^{65} - 29 q^{66} - 116 q^{67} - 37 q^{68} - 23 q^{69} - 64 q^{70} - 89 q^{71} + 40 q^{72} - 60 q^{73} - 42 q^{74} - 47 q^{75} - 72 q^{76} + 5 q^{77} - 68 q^{78} - 170 q^{79} - 9 q^{80} - 3 q^{81} - 49 q^{82} - 82 q^{83} - 38 q^{84} - 81 q^{85} - 95 q^{86} - 51 q^{87} - 48 q^{88} - 78 q^{89} - 20 q^{90} - 85 q^{91} - 75 q^{92} - 21 q^{93} - 62 q^{94} - 70 q^{95} - 15 q^{96} - 60 q^{97} - 4 q^{98} - 148 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 15 * q^3 + 69 * q^4 - 9 * q^5 - 15 * q^6 - 29 * q^7 + 69 * q^8 + 40 * q^9 - 9 * q^10 - 48 * q^11 - 15 * q^12 - 30 * q^13 - 29 * q^14 - 51 * q^15 + 69 * q^16 - 37 * q^17 + 40 * q^18 - 72 * q^19 - 9 * q^20 - 38 * q^21 - 48 * q^22 - 75 * q^23 - 15 * q^24 + 18 * q^25 - 30 * q^26 - 48 * q^27 - 29 * q^28 - 27 * q^29 - 51 * q^30 - 61 * q^31 + 69 * q^32 - 29 * q^33 - 37 * q^34 - 64 * q^35 + 40 * q^36 - 42 * q^37 - 72 * q^38 - 68 * q^39 - 9 * q^40 - 49 * q^41 - 38 * q^42 - 95 * q^43 - 48 * q^44 - 20 * q^45 - 75 * q^46 - 62 * q^47 - 15 * q^48 - 4 * q^49 + 18 * q^50 - 76 * q^51 - 30 * q^52 - 28 * q^53 - 48 * q^54 - 76 * q^55 - 29 * q^56 - 44 * q^57 - 27 * q^58 - 68 * q^59 - 51 * q^60 - 62 * q^61 - 61 * q^62 - 91 * q^63 + 69 * q^64 - 79 * q^65 - 29 * q^66 - 116 * q^67 - 37 * q^68 - 23 * q^69 - 64 * q^70 - 89 * q^71 + 40 * q^72 - 60 * q^73 - 42 * q^74 - 47 * q^75 - 72 * q^76 + 5 * q^77 - 68 * q^78 - 170 * q^79 - 9 * q^80 - 3 * q^81 - 49 * q^82 - 82 * q^83 - 38 * q^84 - 81 * q^85 - 95 * q^86 - 51 * q^87 - 48 * q^88 - 78 * q^89 - 20 * q^90 - 85 * q^91 - 75 * q^92 - 21 * q^93 - 62 * q^94 - 70 * q^95 - 15 * q^96 - 60 * q^97 - 4 * q^98 - 148 * q^99

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