LMFDB - Embedded newform 8026.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$81$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.44759 q^{3} +1.00000 q^{4} +0.910070 q^{5} +2.44759 q^{6} -1.13462 q^{7} -1.00000 q^{8} +2.99071 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.44759 q^{3} +1.00000 q^{4} +0.910070 q^{5} +2.44759 q^{6} -1.13462 q^{7} -1.00000 q^{8} +2.99071 q^{9} -0.910070 q^{10} +1.08567 q^{11} -2.44759 q^{12} +0.0487246 q^{13} +1.13462 q^{14} -2.22748 q^{15} +1.00000 q^{16} +5.38283 q^{17} -2.99071 q^{18} +8.07160 q^{19} +0.910070 q^{20} +2.77708 q^{21} -1.08567 q^{22} -3.40168 q^{23} +2.44759 q^{24} -4.17177 q^{25} -0.0487246 q^{26} +0.0227294 q^{27} -1.13462 q^{28} +3.07113 q^{29} +2.22748 q^{30} -9.22104 q^{31} -1.00000 q^{32} -2.65729 q^{33} -5.38283 q^{34} -1.03258 q^{35} +2.99071 q^{36} -1.93027 q^{37} -8.07160 q^{38} -0.119258 q^{39} -0.910070 q^{40} -9.73126 q^{41} -2.77708 q^{42} -11.9523 q^{43} +1.08567 q^{44} +2.72176 q^{45} +3.40168 q^{46} +10.5796 q^{47} -2.44759 q^{48} -5.71265 q^{49} +4.17177 q^{50} -13.1750 q^{51} +0.0487246 q^{52} +7.11073 q^{53} -0.0227294 q^{54} +0.988040 q^{55} +1.13462 q^{56} -19.7560 q^{57} -3.07113 q^{58} -12.3864 q^{59} -2.22748 q^{60} +7.19444 q^{61} +9.22104 q^{62} -3.39331 q^{63} +1.00000 q^{64} +0.0443428 q^{65} +2.65729 q^{66} -0.822257 q^{67} +5.38283 q^{68} +8.32592 q^{69} +1.03258 q^{70} -2.06749 q^{71} -2.99071 q^{72} +10.5136 q^{73} +1.93027 q^{74} +10.2108 q^{75} +8.07160 q^{76} -1.23182 q^{77} +0.119258 q^{78} -3.84611 q^{79} +0.910070 q^{80} -9.02777 q^{81} +9.73126 q^{82} +15.6774 q^{83} +2.77708 q^{84} +4.89875 q^{85} +11.9523 q^{86} -7.51689 q^{87} -1.08567 q^{88} -8.57779 q^{89} -2.72176 q^{90} -0.0552837 q^{91} -3.40168 q^{92} +22.5693 q^{93} -10.5796 q^{94} +7.34572 q^{95} +2.44759 q^{96} +12.7856 q^{97} +5.71265 q^{98} +3.24694 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) $ 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * 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
$3$	−2.44759	−1.41312	−0.706559	−	0.707654i	$-0.749754\pi$
$3$	−2.44759	−1.41312	−0.706559	+	0.707654i	$0.749754\pi$
$4$	1.00000	0.500000
$5$	0.910070	0.406996	0.203498	−	0.979075i	$-0.434769\pi$
$5$	0.910070	0.406996	0.203498	+	0.979075i	$0.434769\pi$
$6$	2.44759	0.999226
$7$	−1.13462	−0.428845	−0.214422	−	0.976741i	$-0.568787\pi$
$7$	−1.13462	−0.428845	−0.214422	+	0.976741i	$0.568787\pi$
$8$	−1.00000	−0.353553
$9$	2.99071	0.996905
$10$	−0.910070	−0.287789
$11$	1.08567	0.327343	0.163672	−	0.986515i	$-0.447666\pi$
$11$	1.08567	0.327343	0.163672	+	0.986515i	$0.447666\pi$
$12$	−2.44759	−0.706559
$13$	0.0487246	0.0135138	0.00675688	−	0.999977i	$-0.497849\pi$
$13$	0.0487246	0.0135138	0.00675688	+	0.999977i	$0.497849\pi$
$14$	1.13462	0.303239
$15$	−2.22748	−0.575133
$16$	1.00000	0.250000
$17$	5.38283	1.30553	0.652764	−	0.757561i	$-0.273609\pi$
$17$	5.38283	1.30553	0.652764	+	0.757561i	$0.273609\pi$
$18$	−2.99071	−0.704918
$19$	8.07160	1.85175	0.925876	−	0.377827i	$-0.123328\pi$
$19$	8.07160	1.85175	0.925876	+	0.377827i	$0.123328\pi$
$20$	0.910070	0.203498
$21$	2.77708	0.606008
$22$	−1.08567	−0.231467
$23$	−3.40168	−0.709298	−0.354649	−	0.934999i	$-0.615400\pi$
$23$	−3.40168	−0.709298	−0.354649	+	0.934999i	$0.615400\pi$
$24$	2.44759	0.499613
$25$	−4.17177	−0.834355
$26$	−0.0487246	−0.00955567
$27$	0.0227294	0.00437428
$28$	−1.13462	−0.214422
$29$	3.07113	0.570295	0.285148	−	0.958484i	$-0.407957\pi$
$29$	3.07113	0.570295	0.285148	+	0.958484i	$0.407957\pi$
$30$	2.22748	0.406681
$31$	−9.22104	−1.65615	−0.828073	−	0.560620i	$-0.810563\pi$
$31$	−9.22104	−1.65615	−0.828073	+	0.560620i	$0.810563\pi$
$32$	−1.00000	−0.176777
$33$	−2.65729	−0.462575
$34$	−5.38283	−0.923148
$35$	−1.03258	−0.174538
$36$	2.99071	0.498452
$37$	−1.93027	−0.317335	−0.158667	−	0.987332i	$-0.550720\pi$
$37$	−1.93027	−0.317335	−0.158667	+	0.987332i	$0.550720\pi$
$38$	−8.07160	−1.30939
$39$	−0.119258	−0.0190966
$40$	−0.910070	−0.143895
$41$	−9.73126	−1.51977	−0.759884	−	0.650059i	$-0.774744\pi$
$41$	−9.73126	−1.51977	−0.759884	+	0.650059i	$0.774744\pi$
$42$	−2.77708	−0.428513
$43$	−11.9523	−1.82271	−0.911353	−	0.411627i	$-0.864961\pi$
$43$	−11.9523	−1.82271	−0.911353	+	0.411627i	$0.864961\pi$
$44$	1.08567	0.163672
$45$	2.72176	0.405736
$46$	3.40168	0.501550
$47$	10.5796	1.54320	0.771600	−	0.636109i	$-0.219457\pi$
$47$	10.5796	1.54320	0.771600	+	0.636109i	$0.219457\pi$
$48$	−2.44759	−0.353280
$49$	−5.71265	−0.816092
$50$	4.17177	0.589978
$51$	−13.1750	−1.84487
$52$	0.0487246	0.00675688
$53$	7.11073	0.976734	0.488367	−	0.872638i	$-0.337593\pi$
$53$	7.11073	0.976734	0.488367	+	0.872638i	$0.337593\pi$
$54$	−0.0227294	−0.00309308
$55$	0.988040	0.133227
$56$	1.13462	0.151619
$57$	−19.7560	−2.61675
$58$	−3.07113	−0.403260
$59$	−12.3864	−1.61257	−0.806287	−	0.591524i	$-0.798526\pi$
$59$	−12.3864	−1.61257	−0.806287	+	0.591524i	$0.798526\pi$
$60$	−2.22748	−0.287567
$61$	7.19444	0.921153	0.460577	−	0.887620i	$-0.347643\pi$
$61$	7.19444	0.921153	0.460577	+	0.887620i	$0.347643\pi$
$62$	9.22104	1.17107
$63$	−3.39331	−0.427517
$64$	1.00000	0.125000
$65$	0.0443428	0.00550004
$66$	2.65729	0.327090
$67$	−0.822257	−0.100455	−0.0502273	−	0.998738i	$-0.515995\pi$
$67$	−0.822257	−0.100455	−0.0502273	+	0.998738i	$0.515995\pi$
$68$	5.38283	0.652764
$69$	8.32592	1.00232
$70$	1.03258	0.123417
$71$	−2.06749	−0.245366	−0.122683	−	0.992446i	$-0.539150\pi$
$71$	−2.06749	−0.245366	−0.122683	+	0.992446i	$0.539150\pi$
$72$	−2.99071	−0.352459
$73$	10.5136	1.23052	0.615259	−	0.788325i	$-0.289051\pi$
$73$	10.5136	1.23052	0.615259	+	0.788325i	$0.289051\pi$
$74$	1.93027	0.224390
$75$	10.2108	1.17904
$76$	8.07160	0.925876
$77$	−1.23182	−0.140379
$78$	0.119258	0.0135033
$79$	−3.84611	−0.432721	−0.216361	−	0.976314i	$-0.569419\pi$
$79$	−3.84611	−0.432721	−0.216361	+	0.976314i	$0.569419\pi$
$80$	0.910070	0.101749
$81$	−9.02777	−1.00309
$82$	9.73126	1.07464
$83$	15.6774	1.72082	0.860411	−	0.509601i	$-0.170207\pi$
$83$	15.6774	1.72082	0.860411	+	0.509601i	$0.170207\pi$
$84$	2.77708	0.303004
$85$	4.89875	0.531344
$86$	11.9523	1.28885
$87$	−7.51689	−0.805895
$88$	−1.08567	−0.115733
$89$	−8.57779	−0.909244	−0.454622	−	0.890684i	$-0.650226\pi$
$89$	−8.57779	−0.909244	−0.454622	+	0.890684i	$0.650226\pi$
$90$	−2.72176	−0.286899
$91$	−0.0552837	−0.00579530
$92$	−3.40168	−0.354649
$93$	22.5693	2.34033
$94$	−10.5796	−1.09121
$95$	7.34572	0.753655
$96$	2.44759	0.249806
$97$	12.7856	1.29818	0.649092	−	0.760710i	$-0.275149\pi$
$97$	12.7856	1.29818	0.649092	+	0.760710i	$0.275149\pi$
$98$	5.71265	0.577064
$99$	3.24694	0.326330
$100$	−4.17177	−0.417177
$101$	13.0332	1.29686	0.648428	−	0.761276i	$-0.275427\pi$
$101$	13.0332	1.29686	0.648428	+	0.761276i	$0.275427\pi$
$102$	13.1750	1.30452
$103$	−17.8803	−1.76180	−0.880899	−	0.473305i	$-0.843061\pi$
$103$	−17.8803	−1.76180	−0.880899	+	0.473305i	$0.843061\pi$
$104$	−0.0487246	−0.00477784
$105$	2.52734	0.246643
$106$	−7.11073	−0.690655
$107$	−7.58835	−0.733593	−0.366797	−	0.930301i	$-0.619546\pi$
$107$	−7.58835	−0.733593	−0.366797	+	0.930301i	$0.619546\pi$
$108$	0.0227294	0.00218714
$109$	2.94013	0.281613	0.140807	−	0.990037i	$-0.455030\pi$
$109$	2.94013	0.281613	0.140807	+	0.990037i	$0.455030\pi$
$110$	−0.988040	−0.0942059
$111$	4.72452	0.448432
$112$	−1.13462	−0.107211
$113$	8.38348	0.788652	0.394326	−	0.918971i	$-0.370978\pi$
$113$	8.38348	0.788652	0.394326	+	0.918971i	$0.370978\pi$
$114$	19.7560	1.85032
$115$	−3.09576	−0.288681
$116$	3.07113	0.285148
$117$	0.145721	0.0134719
$118$	12.3864	1.14026
$119$	−6.10744	−0.559869
$120$	2.22748	0.203340
$121$	−9.82131	−0.892846
$122$	−7.19444	−0.651354
$123$	23.8182	2.14761
$124$	−9.22104	−0.828073
$125$	−8.34696	−0.746574
$126$	3.39331	0.302300
$127$	−10.9488	−0.971546	−0.485773	−	0.874085i	$-0.661462\pi$
$127$	−10.9488	−0.971546	−0.485773	+	0.874085i	$0.661462\pi$
$128$	−1.00000	−0.0883883
$129$	29.2543	2.57570
$130$	−0.0443428	−0.00388912
$131$	−18.0252	−1.57487	−0.787435	−	0.616397i	$-0.788591\pi$
$131$	−18.0252	−1.57487	−0.787435	+	0.616397i	$0.788591\pi$
$132$	−2.65729	−0.231287
$133$	−9.15817	−0.794114
$134$	0.822257	0.0710322
$135$	0.0206854	0.00178031
$136$	−5.38283	−0.461574
$137$	−17.6524	−1.50814	−0.754072	−	0.656792i	$-0.771913\pi$
$137$	−17.6524	−1.50814	−0.754072	+	0.656792i	$0.771913\pi$
$138$	−8.32592	−0.708749
$139$	5.69278	0.482855	0.241428	−	0.970419i	$-0.422384\pi$
$139$	5.69278	0.482855	0.241428	+	0.970419i	$0.422384\pi$
$140$	−1.03258	−0.0872689
$141$	−25.8947	−2.18072
$142$	2.06749	0.173500
$143$	0.0528990	0.00442364
$144$	2.99071	0.249226
$145$	2.79495	0.232108
$146$	−10.5136	−0.870108
$147$	13.9822	1.15324
$148$	−1.93027	−0.158667
$149$	1.06058	0.0868861	0.0434430	−	0.999056i	$-0.486167\pi$
$149$	1.06058	0.0868861	0.0434430	+	0.999056i	$0.486167\pi$
$150$	−10.2108	−0.833709
$151$	15.7425	1.28110	0.640552	−	0.767914i	$-0.278705\pi$
$151$	15.7425	1.28110	0.640552	+	0.767914i	$0.278705\pi$
$152$	−8.07160	−0.654693
$153$	16.0985	1.30149
$154$	1.23182	0.0992632
$155$	−8.39179	−0.674045
$156$	−0.119258	−0.00954828
$157$	−10.1560	−0.810540	−0.405270	−	0.914197i	$-0.632823\pi$
$157$	−10.1560	−0.810540	−0.405270	+	0.914197i	$0.632823\pi$
$158$	3.84611	0.305980
$159$	−17.4042	−1.38024
$160$	−0.910070	−0.0719474
$161$	3.85960	0.304179
$162$	9.02777	0.709289
$163$	9.10486	0.713148	0.356574	−	0.934267i	$-0.383945\pi$
$163$	9.10486	0.713148	0.356574	+	0.934267i	$0.383945\pi$
$164$	−9.73126	−0.759884
$165$	−2.41832	−0.188266
$166$	−15.6774	−1.21680
$167$	11.1294	0.861222	0.430611	−	0.902538i	$-0.358298\pi$
$167$	11.1294	0.861222	0.430611	+	0.902538i	$0.358298\pi$
$168$	−2.77708	−0.214256
$169$	−12.9976	−0.999817
$170$	−4.89875	−0.375717
$171$	24.1399	1.84602
$172$	−11.9523	−0.911353
$173$	6.71172	0.510283	0.255141	−	0.966904i	$-0.417878\pi$
$173$	6.71172	0.510283	0.255141	+	0.966904i	$0.417878\pi$
$174$	7.51689	0.569854
$175$	4.73336	0.357808
$176$	1.08567	0.0818358
$177$	30.3169	2.27876
$178$	8.57779	0.642933
$179$	14.4469	1.07981	0.539904	−	0.841726i	$-0.318460\pi$
$179$	14.4469	1.07981	0.539904	+	0.841726i	$0.318460\pi$
$180$	2.72176	0.202868
$181$	18.7339	1.39248	0.696238	−	0.717811i	$-0.254856\pi$
$181$	18.7339	1.39248	0.696238	+	0.717811i	$0.254856\pi$
$182$	0.0552837	0.00409790
$183$	−17.6091	−1.30170
$184$	3.40168	0.250775
$185$	−1.75668	−0.129154
$186$	−22.5693	−1.65486
$187$	5.84400	0.427356
$188$	10.5796	0.771600
$189$	−0.0257892	−0.00187589
$190$	−7.34572	−0.532915
$191$	−15.9025	−1.15067	−0.575333	−	0.817919i	$-0.695128\pi$
$191$	−15.9025	−1.15067	−0.575333	+	0.817919i	$0.695128\pi$
$192$	−2.44759	−0.176640
$193$	14.7163	1.05930	0.529651	−	0.848216i	$-0.322323\pi$
$193$	14.7163	1.05930	0.529651	+	0.848216i	$0.322323\pi$
$194$	−12.7856	−0.917954
$195$	−0.108533	−0.00777221
$196$	−5.71265	−0.408046
$197$	−7.73695	−0.551235	−0.275618	−	0.961267i	$-0.588882\pi$
$197$	−7.73695	−0.551235	−0.275618	+	0.961267i	$0.588882\pi$
$198$	−3.24694	−0.230750
$199$	−20.2276	−1.43390	−0.716948	−	0.697127i	$-0.754461\pi$
$199$	−20.2276	−1.43390	−0.716948	+	0.697127i	$0.754461\pi$
$200$	4.17177	0.294989
$201$	2.01255	0.141954
$202$	−13.0332	−0.917016
$203$	−3.48456	−0.244568
$204$	−13.1750	−0.922433
$205$	−8.85613	−0.618539
$206$	17.8803	1.24578
$207$	−10.1734	−0.707103
$208$	0.0487246	0.00337844
$209$	8.76313	0.606159
$210$	−2.52734	−0.174403
$211$	4.52661	0.311625	0.155812	−	0.987787i	$-0.450200\pi$
$211$	4.52661	0.311625	0.155812	+	0.987787i	$0.450200\pi$
$212$	7.11073	0.488367
$213$	5.06037	0.346731
$214$	7.58835	0.518729
$215$	−10.8774	−0.741833
$216$	−0.0227294	−0.00154654
$217$	10.4623	0.710230
$218$	−2.94013	−0.199131
$219$	−25.7329	−1.73887
$220$	0.988040	0.0666136
$221$	0.262276	0.0176426
$222$	−4.72452	−0.317089
$223$	28.9180	1.93649	0.968247	−	0.249994i	$-0.0804286\pi$
$223$	28.9180	1.93649	0.968247	+	0.249994i	$0.0804286\pi$
$224$	1.13462	0.0758097
$225$	−12.4766	−0.831772
$226$	−8.38348	−0.557661
$227$	7.58439	0.503394	0.251697	−	0.967806i	$-0.419011\pi$
$227$	7.58439	0.503394	0.251697	+	0.967806i	$0.419011\pi$
$228$	−19.7560	−1.30837
$229$	4.73632	0.312985	0.156492	−	0.987679i	$-0.449981\pi$
$229$	4.73632	0.312985	0.156492	+	0.987679i	$0.449981\pi$
$230$	3.09576	0.204129
$231$	3.01500	0.198373
$232$	−3.07113	−0.201630
$233$	−17.6630	−1.15714	−0.578570	−	0.815633i	$-0.696389\pi$
$233$	−17.6630	−1.15714	−0.578570	+	0.815633i	$0.696389\pi$
$234$	−0.145721	−0.00952609
$235$	9.62821	0.628075
$236$	−12.3864	−0.806287
$237$	9.41372	0.611487
$238$	6.10744	0.395887
$239$	−18.2862	−1.18284	−0.591418	−	0.806365i	$-0.701432\pi$
$239$	−18.2862	−1.18284	−0.591418	+	0.806365i	$0.701432\pi$
$240$	−2.22748	−0.143783
$241$	−6.16062	−0.396841	−0.198420	−	0.980117i	$-0.563581\pi$
$241$	−6.16062	−0.396841	−0.198420	+	0.980117i	$0.563581\pi$
$242$	9.82131	0.631338
$243$	22.0281	1.41311
$244$	7.19444	0.460577
$245$	−5.19891	−0.332146
$246$	−23.8182	−1.51859
$247$	0.393285	0.0250241
$248$	9.22104	0.585536
$249$	−38.3720	−2.43172
$250$	8.34696	0.527908
$251$	24.8064	1.56577	0.782884	−	0.622167i	$-0.213748\pi$
$251$	24.8064	1.56577	0.782884	+	0.622167i	$0.213748\pi$
$252$	−3.39331	−0.213759
$253$	−3.69311	−0.232184
$254$	10.9488	0.686986
$255$	−11.9902	−0.750852
$256$	1.00000	0.0625000
$257$	24.1055	1.50366	0.751830	−	0.659356i	$-0.229171\pi$
$257$	24.1055	1.50366	0.751830	+	0.659356i	$0.229171\pi$
$258$	−29.2543	−1.82129
$259$	2.19012	0.136087
$260$	0.0443428	0.00275002
$261$	9.18488	0.568530
$262$	18.0252	1.11360
$263$	−13.9249	−0.858645	−0.429322	−	0.903151i	$-0.641248\pi$
$263$	−13.9249	−0.858645	−0.429322	+	0.903151i	$0.641248\pi$
$264$	2.65729	0.163545
$265$	6.47126	0.397526
$266$	9.15817	0.561523
$267$	20.9950	1.28487
$268$	−0.822257	−0.0502273
$269$	−23.8294	−1.45290	−0.726451	−	0.687218i	$-0.758832\pi$
$269$	−23.8294	−1.45290	−0.726451	+	0.687218i	$0.758832\pi$
$270$	−0.0206854	−0.00125887
$271$	16.6051	1.00869	0.504344	−	0.863503i	$-0.331734\pi$
$271$	16.6051	1.00869	0.504344	+	0.863503i	$0.331734\pi$
$272$	5.38283	0.326382
$273$	0.135312	0.00818945
$274$	17.6524	1.06642
$275$	−4.52919	−0.273120
$276$	8.32592	0.501161
$277$	−5.96770	−0.358564	−0.179282	−	0.983798i	$-0.557378\pi$
$277$	−5.96770	−0.358564	−0.179282	+	0.983798i	$0.557378\pi$
$278$	−5.69278	−0.341430
$279$	−27.5775	−1.65102
$280$	1.03258	0.0617085
$281$	6.94096	0.414063	0.207031	−	0.978334i	$-0.433620\pi$
$281$	6.94096	0.414063	0.207031	+	0.978334i	$0.433620\pi$
$282$	25.8947	1.54200
$283$	−11.8000	−0.701439	−0.350719	−	0.936481i	$-0.614063\pi$
$283$	−11.8000	−0.701439	−0.350719	+	0.936481i	$0.614063\pi$
$284$	−2.06749	−0.122683
$285$	−17.9793	−1.06500
$286$	−0.0528990	−0.00312798
$287$	11.0412	0.651744
$288$	−2.99071	−0.176229
$289$	11.9748	0.704403
$290$	−2.79495	−0.164125
$291$	−31.2940	−1.83449
$292$	10.5136	0.615259
$293$	26.1606	1.52832	0.764160	−	0.645027i	$-0.223154\pi$
$293$	26.1606	1.52832	0.764160	+	0.645027i	$0.223154\pi$
$294$	−13.9822	−0.815461
$295$	−11.2725	−0.656311
$296$	1.93027	0.112195
$297$	0.0246768	0.00143189
$298$	−1.06058	−0.0614377
$299$	−0.165745	−0.00958529
$300$	10.2108	0.589521
$301$	13.5612	0.781657
$302$	−15.7425	−0.905878
$303$	−31.9001	−1.83261
$304$	8.07160	0.462938
$305$	6.54744	0.374905
$306$	−16.0985	−0.920290
$307$	−22.3696	−1.27670	−0.638349	−	0.769747i	$-0.720382\pi$
$307$	−22.3696	−1.27670	−0.638349	+	0.769747i	$0.720382\pi$
$308$	−1.23182	−0.0701897
$309$	43.7637	2.48963
$310$	8.39179	0.476622
$311$	−20.4126	−1.15749	−0.578745	−	0.815508i	$-0.696457\pi$
$311$	−20.4126	−1.15749	−0.578745	+	0.815508i	$0.696457\pi$
$312$	0.119258	0.00675165
$313$	34.8587	1.97033	0.985166	−	0.171603i	$-0.0548947\pi$
$313$	34.8587	1.97033	0.985166	+	0.171603i	$0.0548947\pi$
$314$	10.1560	0.573139
$315$	−3.08815	−0.173998
$316$	−3.84611	−0.216361
$317$	9.73168	0.546585	0.273293	−	0.961931i	$-0.411887\pi$
$317$	9.73168	0.546585	0.273293	+	0.961931i	$0.411887\pi$
$318$	17.4042	0.975978
$319$	3.33425	0.186682
$320$	0.910070	0.0508745
$321$	18.5732	1.03665
$322$	−3.85960	−0.215087
$323$	43.4481	2.41751
$324$	−9.02777	−0.501543
$325$	−0.203268	−0.0112753
$326$	−9.10486	−0.504272
$327$	−7.19624	−0.397953
$328$	9.73126	0.537319
$329$	−12.0038	−0.661793
$330$	2.41832	0.133124
$331$	−20.8701	−1.14712	−0.573562	−	0.819162i	$-0.694439\pi$
$331$	−20.8701	−1.14712	−0.573562	+	0.819162i	$0.694439\pi$
$332$	15.6774	0.860411
$333$	−5.77289	−0.316352
$334$	−11.1294	−0.608976
$335$	−0.748311	−0.0408846
$336$	2.77708	0.151502
$337$	−16.0986	−0.876946	−0.438473	−	0.898744i	$-0.644480\pi$
$337$	−16.0986	−0.876946	−0.438473	+	0.898744i	$0.644480\pi$
$338$	12.9976	0.706978
$339$	−20.5194	−1.11446
$340$	4.89875	0.265672
$341$	−10.0110	−0.542128
$342$	−24.1399	−1.30533
$343$	14.4240	0.778821
$344$	11.9523	0.644424
$345$	7.57717	0.407941
$346$	−6.71172	−0.360824
$347$	−21.3465	−1.14594	−0.572970	−	0.819576i	$-0.694209\pi$
$347$	−21.3465	−1.14594	−0.572970	+	0.819576i	$0.694209\pi$
$348$	−7.51689	−0.402948
$349$	−34.7456	−1.85989	−0.929945	−	0.367700i	$-0.880145\pi$
$349$	−34.7456	−1.85989	−0.929945	+	0.367700i	$0.880145\pi$
$350$	−4.73336	−0.253009
$351$	0.00110748	5.91130e−5 0
$352$	−1.08567	−0.0578666
$353$	12.3338	0.656462	0.328231	−	0.944597i	$-0.393548\pi$
$353$	12.3338	0.656462	0.328231	+	0.944597i	$0.393548\pi$
$354$	−30.3169	−1.61133
$355$	−1.88156	−0.0998627
$356$	−8.57779	−0.454622
$357$	14.9485	0.791161
$358$	−14.4469	−0.763540
$359$	−30.4610	−1.60767	−0.803834	−	0.594853i	$-0.797210\pi$
$359$	−30.4610	−1.60767	−0.803834	+	0.594853i	$0.797210\pi$
$360$	−2.72176	−0.143449
$361$	46.1508	2.42899
$362$	−18.7339	−0.984630
$363$	24.0386	1.26170
$364$	−0.0552837	−0.00289765
$365$	9.56807	0.500816
$366$	17.6091	0.920440
$367$	−11.3977	−0.594956	−0.297478	−	0.954729i	$-0.596145\pi$
$367$	−11.3977	−0.594956	−0.297478	+	0.954729i	$0.596145\pi$
$368$	−3.40168	−0.177325
$369$	−29.1034	−1.51506
$370$	1.75668	0.0913256
$371$	−8.06795	−0.418867
$372$	22.5693	1.17017
$373$	−19.8719	−1.02893	−0.514465	−	0.857511i	$-0.672010\pi$
$373$	−19.8719	−1.02893	−0.514465	+	0.857511i	$0.672010\pi$
$374$	−5.84400	−0.302186
$375$	20.4300	1.05500
$376$	−10.5796	−0.545603
$377$	0.149640	0.00770684
$378$	0.0257892	0.00132645
$379$	20.8158	1.06923	0.534617	−	0.845094i	$-0.320456\pi$
$379$	20.8158	1.06923	0.534617	+	0.845094i	$0.320456\pi$
$380$	7.34572	0.376828
$381$	26.7981	1.37291
$382$	15.9025	0.813644
$383$	2.99342	0.152956	0.0764782	−	0.997071i	$-0.475632\pi$
$383$	2.99342	0.152956	0.0764782	+	0.997071i	$0.475632\pi$
$384$	2.44759	0.124903
$385$	−1.12105	−0.0571338
$386$	−14.7163	−0.749039
$387$	−35.7458	−1.81706
$388$	12.7856	0.649092
$389$	−12.3423	−0.625781	−0.312890	−	0.949789i	$-0.601297\pi$
$389$	−12.3423	−0.625781	−0.312890	+	0.949789i	$0.601297\pi$
$390$	0.108533	0.00549579
$391$	−18.3106	−0.926009
$392$	5.71265	0.288532
$393$	44.1184	2.22548
$394$	7.73695	0.389782
$395$	−3.50023	−0.176116
$396$	3.24694	0.163165
$397$	0.189131	0.00949224	0.00474612	−	0.999989i	$-0.498489\pi$
$397$	0.189131	0.00949224	0.00474612	+	0.999989i	$0.498489\pi$
$398$	20.2276	1.01392
$399$	22.4155	1.12218
$400$	−4.17177	−0.208589
$401$	18.3476	0.916233	0.458117	−	0.888892i	$-0.348524\pi$
$401$	18.3476	0.916233	0.458117	+	0.888892i	$0.348524\pi$
$402$	−2.01255	−0.100377
$403$	−0.449291	−0.0223808
$404$	13.0332	0.648428
$405$	−8.21591	−0.408252
$406$	3.48456	0.172936
$407$	−2.09565	−0.103877
$408$	13.1750	0.652259
$409$	−1.28838	−0.0637063	−0.0318531	−	0.999493i	$-0.510141\pi$
$409$	−1.28838	−0.0637063	−0.0318531	+	0.999493i	$0.510141\pi$
$410$	8.85613	0.437373
$411$	43.2058	2.13119
$412$	−17.8803	−0.880899
$413$	14.0538	0.691544
$414$	10.1734	0.499997
$415$	14.2676	0.700367
$416$	−0.0487246	−0.00238892
$417$	−13.9336	−0.682331
$418$	−8.76313	−0.428619
$419$	−7.67913	−0.375150	−0.187575	−	0.982250i	$-0.560063\pi$
$419$	−7.67913	−0.375150	−0.187575	+	0.982250i	$0.560063\pi$
$420$	2.52734	0.123321
$421$	20.2118	0.985061	0.492531	−	0.870295i	$-0.336072\pi$
$421$	20.2118	0.985061	0.492531	+	0.870295i	$0.336072\pi$
$422$	−4.52661	−0.220352
$423$	31.6407	1.53842
$424$	−7.11073	−0.345328
$425$	−22.4559	−1.08927
$426$	−5.06037	−0.245176
$427$	−8.16292	−0.395032
$428$	−7.58835	−0.366797
$429$	−0.129475	−0.00625113
$430$	10.8774	0.524555
$431$	−6.92743	−0.333683	−0.166841	−	0.985984i	$-0.553357\pi$
$431$	−6.92743	−0.333683	−0.166841	+	0.985984i	$0.553357\pi$
$432$	0.0227294	0.00109357
$433$	20.2457	0.972948	0.486474	−	0.873695i	$-0.338283\pi$
$433$	20.2457	0.972948	0.486474	+	0.873695i	$0.338283\pi$
$434$	−10.4623	−0.502208
$435$	−6.84090	−0.327996
$436$	2.94013	0.140807
$437$	−27.4570	−1.31345
$438$	25.7329	1.22957
$439$	−9.40249	−0.448756	−0.224378	−	0.974502i	$-0.572035\pi$
$439$	−9.40249	−0.448756	−0.224378	+	0.974502i	$0.572035\pi$
$440$	−0.988040	−0.0471030
$441$	−17.0849	−0.813566
$442$	−0.262276	−0.0124752
$443$	4.45869	0.211839	0.105919	−	0.994375i	$-0.466221\pi$
$443$	4.45869	0.211839	0.105919	+	0.994375i	$0.466221\pi$
$444$	4.72452	0.224216
$445$	−7.80639	−0.370059
$446$	−28.9180	−1.36931
$447$	−2.59587	−0.122780
$448$	−1.13462	−0.0536056
$449$	−22.6462	−1.06874	−0.534370	−	0.845251i	$-0.679451\pi$
$449$	−22.6462	−1.06874	−0.534370	+	0.845251i	$0.679451\pi$
$450$	12.4766	0.588151
$451$	−10.5650	−0.497486
$452$	8.38348	0.394326
$453$	−38.5312	−1.81035
$454$	−7.58439	−0.355953
$455$	−0.0503120	−0.00235866
$456$	19.7560	0.925160
$457$	−19.7359	−0.923208	−0.461604	−	0.887086i	$-0.652726\pi$
$457$	−19.7359	−0.923208	−0.461604	+	0.887086i	$0.652726\pi$
$458$	−4.73632	−0.221313
$459$	0.122349	0.00571074
$460$	−3.09576	−0.144341
$461$	−33.0477	−1.53919	−0.769593	−	0.638534i	$-0.779541\pi$
$461$	−33.0477	−1.53919	−0.769593	+	0.638534i	$0.779541\pi$
$462$	−3.01500	−0.140271
$463$	−20.2663	−0.941854	−0.470927	−	0.882172i	$-0.656080\pi$
$463$	−20.2663	−0.941854	−0.470927	+	0.882172i	$0.656080\pi$
$464$	3.07113	0.142574
$465$	20.5397	0.952505
$466$	17.6630	0.818221
$467$	−3.50005	−0.161963	−0.0809814	−	0.996716i	$-0.525805\pi$
$467$	−3.50005	−0.161963	−0.0809814	+	0.996716i	$0.525805\pi$
$468$	0.145721	0.00673597
$469$	0.932946	0.0430794
$470$	−9.62821	−0.444116
$471$	24.8579	1.14539
$472$	12.3864	0.570131
$473$	−12.9763	−0.596650
$474$	−9.41372	−0.432386
$475$	−33.6729	−1.54502
$476$	−6.10744	−0.279934
$477$	21.2662	0.973710
$478$	18.2862	0.836392
$479$	−38.0198	−1.73717	−0.868585	−	0.495540i	$-0.834970\pi$
$479$	−38.0198	−1.73717	−0.868585	+	0.495540i	$0.834970\pi$
$480$	2.22748	0.101670
$481$	−0.0940517	−0.00428839
$482$	6.16062	0.280609
$483$	−9.44672	−0.429841
$484$	−9.82131	−0.446423
$485$	11.6358	0.528355
$486$	−22.0281	−0.999216
$487$	2.64149	0.119697	0.0598487	−	0.998207i	$-0.480938\pi$
$487$	2.64149	0.119697	0.0598487	+	0.998207i	$0.480938\pi$
$488$	−7.19444	−0.325677
$489$	−22.2850	−1.00776
$490$	5.19891	0.234863
$491$	25.7930	1.16402	0.582011	−	0.813181i	$-0.302266\pi$
$491$	25.7930	1.16402	0.582011	+	0.813181i	$0.302266\pi$
$492$	23.8182	1.07381
$493$	16.5314	0.744537
$494$	−0.393285	−0.0176947
$495$	2.95494	0.132815
$496$	−9.22104	−0.414037
$497$	2.34580	0.105224
$498$	38.3720	1.71949
$499$	−17.3024	−0.774562	−0.387281	−	0.921962i	$-0.626586\pi$
$499$	−17.3024	−0.774562	−0.387281	+	0.921962i	$0.626586\pi$
$500$	−8.34696	−0.373287
$501$	−27.2403	−1.21701
$502$	−24.8064	−1.10717
$503$	−36.5845	−1.63122	−0.815610	−	0.578602i	$-0.803599\pi$
$503$	−36.5845	−1.63122	−0.815610	+	0.578602i	$0.803599\pi$
$504$	3.39331	0.151150
$505$	11.8612	0.527815
$506$	3.69311	0.164179
$507$	31.8129	1.41286
$508$	−10.9488	−0.485773
$509$	31.1189	1.37932	0.689661	−	0.724132i	$-0.257759\pi$
$509$	31.1189	1.37932	0.689661	+	0.724132i	$0.257759\pi$
$510$	11.9902	0.530933
$511$	−11.9288	−0.527701
$512$	−1.00000	−0.0441942
$513$	0.183463	0.00810008
$514$	−24.1055	−1.06325
$515$	−16.2723	−0.717044
$516$	29.2543	1.28785
$517$	11.4860	0.505156
$518$	−2.19012	−0.0962283
$519$	−16.4276	−0.721090
$520$	−0.0443428	−0.00194456
$521$	−12.6352	−0.553556	−0.276778	−	0.960934i	$-0.589267\pi$
$521$	−12.6352	−0.553556	−0.276778	+	0.960934i	$0.589267\pi$
$522$	−9.18488	−0.402011
$523$	−42.0964	−1.84075	−0.920373	−	0.391042i	$-0.872115\pi$
$523$	−42.0964	−1.84075	−0.920373	+	0.391042i	$0.872115\pi$
$524$	−18.0252	−0.787435
$525$	−11.5853	−0.505626
$526$	13.9249	0.607153
$527$	−49.6353	−2.16215
$528$	−2.65729	−0.115644
$529$	−11.4286	−0.496896
$530$	−6.47126	−0.281094
$531$	−37.0442	−1.60758
$532$	−9.15817	−0.397057
$533$	−0.474152	−0.0205378
$534$	−20.9950	−0.908541
$535$	−6.90593	−0.298569
$536$	0.822257	0.0355161
$537$	−35.3600	−1.52590
$538$	23.8294	1.02736
$539$	−6.20207	−0.267142
$540$	0.0206854	0.000890156 0
$541$	39.8135	1.71172	0.855859	−	0.517210i	$-0.173029\pi$
$541$	39.8135	1.71172	0.855859	+	0.517210i	$0.173029\pi$
$542$	−16.6051	−0.713250
$543$	−45.8529	−1.96773
$544$	−5.38283	−0.230787
$545$	2.67572	0.114615
$546$	−0.135312	−0.00579082
$547$	2.82527	0.120800	0.0604000	−	0.998174i	$-0.480762\pi$
$547$	2.82527	0.120800	0.0604000	+	0.998174i	$0.480762\pi$
$548$	−17.6524	−0.754072
$549$	21.5165	0.918302
$550$	4.52919	0.193125
$551$	24.7890	1.05605
$552$	−8.32592	−0.354375
$553$	4.36386	0.185570
$554$	5.96770	0.253543
$555$	4.29965	0.182510
$556$	5.69278	0.241428
$557$	−8.49144	−0.359794	−0.179897	−	0.983685i	$-0.557576\pi$
$557$	−8.49144	−0.359794	−0.179897	+	0.983685i	$0.557576\pi$
$558$	27.5775	1.16745
$559$	−0.582369	−0.0246316
$560$	−1.03258	−0.0436345
$561$	−14.3037	−0.603904
$562$	−6.94096	−0.292787
$563$	−8.19666	−0.345448	−0.172724	−	0.984970i	$-0.555257\pi$
$563$	−8.19666	−0.345448	−0.172724	+	0.984970i	$0.555257\pi$
$564$	−25.8947	−1.09036
$565$	7.62956	0.320978
$566$	11.8000	0.495992
$567$	10.2431	0.430168
$568$	2.06749	0.0867498
$569$	−27.2249	−1.14133	−0.570665	−	0.821183i	$-0.693314\pi$
$569$	−27.2249	−1.14133	−0.570665	+	0.821183i	$0.693314\pi$
$570$	17.9793	0.753072
$571$	−36.2921	−1.51878	−0.759388	−	0.650637i	$-0.774502\pi$
$571$	−36.2921	−1.51878	−0.759388	+	0.650637i	$0.774502\pi$
$572$	0.0528990	0.00221182
$573$	38.9229	1.62603
$574$	−11.0412	−0.460853
$575$	14.1910	0.591806
$576$	2.99071	0.124613
$577$	−12.4305	−0.517487	−0.258744	−	0.965946i	$-0.583309\pi$
$577$	−12.4305	−0.517487	−0.258744	+	0.965946i	$0.583309\pi$
$578$	−11.9748	−0.498088
$579$	−36.0195	−1.49692
$580$	2.79495	0.116054
$581$	−17.7879	−0.737965
$582$	31.2940	1.29718
$583$	7.71994	0.319727
$584$	−10.5136	−0.435054
$585$	0.132617	0.00548302
$586$	−26.1606	−1.08069
$587$	−0.218546	−0.00902038	−0.00451019	−	0.999990i	$-0.501436\pi$
$587$	−0.218546	−0.00902038	−0.00451019	+	0.999990i	$0.501436\pi$
$588$	13.9822	0.576618
$589$	−74.4285	−3.06677
$590$	11.2725	0.464082
$591$	18.9369	0.778961
$592$	−1.93027	−0.0793337
$593$	25.0044	1.02681	0.513403	−	0.858148i	$-0.328385\pi$
$593$	25.0044	1.02681	0.513403	+	0.858148i	$0.328385\pi$
$594$	−0.0246768	−0.00101250
$595$	−5.55820	−0.227864
$596$	1.06058	0.0434430
$597$	49.5089	2.02626
$598$	0.165745	0.00677782
$599$	−15.6866	−0.640937	−0.320468	−	0.947259i	$-0.603840\pi$
$599$	−15.6866	−0.640937	−0.320468	+	0.947259i	$0.603840\pi$
$600$	−10.2108	−0.416854
$601$	−48.9474	−1.99661	−0.998304	−	0.0582164i	$-0.981459\pi$
$601$	−48.9474	−1.99661	−0.998304	+	0.0582164i	$0.981459\pi$
$602$	−13.5612	−0.552715
$603$	−2.45913	−0.100144
$604$	15.7425	0.640552
$605$	−8.93808	−0.363385
$606$	31.9001	1.29585
$607$	−2.84906	−0.115640	−0.0578200	−	0.998327i	$-0.518415\pi$
$607$	−2.84906	−0.115640	−0.0578200	+	0.998327i	$0.518415\pi$
$608$	−8.07160	−0.327347
$609$	8.52878	0.345604
$610$	−6.54744	−0.265098
$611$	0.515488	0.0208544
$612$	16.0985	0.650743
$613$	32.7383	1.32229	0.661143	−	0.750260i	$-0.270072\pi$
$613$	32.7383	1.32229	0.661143	+	0.750260i	$0.270072\pi$
$614$	22.3696	0.902762
$615$	21.6762	0.874069
$616$	1.23182	0.0496316
$617$	13.1121	0.527872	0.263936	−	0.964540i	$-0.414979\pi$
$617$	13.1121	0.527872	0.263936	+	0.964540i	$0.414979\pi$
$618$	−43.7637	−1.76043
$619$	29.8471	1.19966	0.599829	−	0.800128i	$-0.295235\pi$
$619$	29.8471	1.19966	0.599829	+	0.800128i	$0.295235\pi$
$620$	−8.39179	−0.337022
$621$	−0.0773181	−0.00310267
$622$	20.4126	0.818469
$623$	9.73250	0.389925
$624$	−0.119258	−0.00477414
$625$	13.2625	0.530502
$626$	−34.8587	−1.39324
$627$	−21.4486	−0.856574
$628$	−10.1560	−0.405270
$629$	−10.3903	−0.414289
$630$	3.08815	0.123035
$631$	8.66878	0.345098	0.172549	−	0.985001i	$-0.444800\pi$
$631$	8.66878	0.345098	0.172549	+	0.985001i	$0.444800\pi$
$632$	3.84611	0.152990
$633$	−11.0793	−0.440363
$634$	−9.73168	−0.386494
$635$	−9.96414	−0.395415
$636$	−17.4042	−0.690120
$637$	−0.278346	−0.0110285
$638$	−3.33425	−0.132004
$639$	−6.18326	−0.244606
$640$	−0.910070	−0.0359737
$641$	−20.6921	−0.817287	−0.408644	−	0.912694i	$-0.633998\pi$
$641$	−20.6921	−0.817287	−0.408644	+	0.912694i	$0.633998\pi$
$642$	−18.5732	−0.733025
$643$	3.80078	0.149888	0.0749441	−	0.997188i	$-0.476122\pi$
$643$	3.80078	0.149888	0.0749441	+	0.997188i	$0.476122\pi$
$644$	3.85960	0.152089
$645$	26.6235	1.04830
$646$	−43.4481	−1.70944
$647$	−9.70291	−0.381461	−0.190730	−	0.981642i	$-0.561086\pi$
$647$	−9.70291	−0.381461	−0.190730	+	0.981642i	$0.561086\pi$
$648$	9.02777	0.354644
$649$	−13.4476	−0.527865
$650$	0.203268	0.00797282
$651$	−25.6075	−1.00364
$652$	9.10486	0.356574
$653$	−17.6370	−0.690188	−0.345094	−	0.938568i	$-0.612153\pi$
$653$	−17.6370	−0.690188	−0.345094	+	0.938568i	$0.612153\pi$
$654$	7.19624	0.281395
$655$	−16.4042	−0.640965
$656$	−9.73126	−0.379942
$657$	31.4430	1.22671
$658$	12.0038	0.467958
$659$	−9.43569	−0.367562	−0.183781	−	0.982967i	$-0.558834\pi$
$659$	−9.43569	−0.367562	−0.183781	+	0.982967i	$0.558834\pi$
$660$	−2.41832	−0.0941330
$661$	23.0595	0.896910	0.448455	−	0.893806i	$-0.351975\pi$
$661$	23.0595	0.896910	0.448455	+	0.893806i	$0.351975\pi$
$662$	20.8701	0.811140
$663$	−0.641945	−0.0249311
$664$	−15.6774	−0.608402
$665$	−8.33458	−0.323201
$666$	5.77289	0.223695
$667$	−10.4470	−0.404510
$668$	11.1294	0.430611
$669$	−70.7796	−2.73650
$670$	0.748311	0.0289098
$671$	7.81082	0.301533
$672$	−2.77708	−0.107128
$673$	37.4441	1.44336	0.721682	−	0.692225i	$-0.243370\pi$
$673$	37.4441	1.44336	0.721682	+	0.692225i	$0.243370\pi$
$674$	16.0986	0.620094
$675$	−0.0948220	−0.00364970
$676$	−12.9976	−0.499909
$677$	−28.9796	−1.11378	−0.556889	−	0.830587i	$-0.688005\pi$
$677$	−28.9796	−1.11378	−0.556889	+	0.830587i	$0.688005\pi$
$678$	20.5194	0.788041
$679$	−14.5068	−0.556719
$680$	−4.89875	−0.187859
$681$	−18.5635	−0.711355
$682$	10.0110	0.383343
$683$	−36.4558	−1.39494	−0.697471	−	0.716613i	$-0.745691\pi$
$683$	−36.4558	−1.39494	−0.697471	+	0.716613i	$0.745691\pi$
$684$	24.1399	0.923010
$685$	−16.0649	−0.613808
$686$	−14.4240	−0.550710
$687$	−11.5926	−0.442284
$688$	−11.9523	−0.455676
$689$	0.346467	0.0131993
$690$	−7.57717	−0.288458
$691$	−5.44076	−0.206976	−0.103488	−	0.994631i	$-0.533000\pi$
$691$	−5.44076	−0.206976	−0.103488	+	0.994631i	$0.533000\pi$
$692$	6.71172	0.255141
$693$	−3.68403	−0.139945
$694$	21.3465	0.810302
$695$	5.18083	0.196520
$696$	7.51689	0.284927
$697$	−52.3817	−1.98410
$698$	34.7456	1.31514
$699$	43.2318	1.63518
$700$	4.73336	0.178904
$701$	−30.9295	−1.16819	−0.584095	−	0.811686i	$-0.698550\pi$
$701$	−30.9295	−1.16819	−0.584095	+	0.811686i	$0.698550\pi$
$702$	−0.00110748	−4.17992e−5 0
$703$	−15.5804	−0.587626
$704$	1.08567	0.0409179
$705$	−23.5660	−0.887545
$706$	−12.3338	−0.464189
$707$	−14.7877	−0.556150
$708$	30.3169	1.13938
$709$	35.2450	1.32365	0.661826	−	0.749657i	$-0.269782\pi$
$709$	35.2450	1.32365	0.661826	+	0.749657i	$0.269782\pi$
$710$	1.88156	0.0706136
$711$	−11.5026	−0.431382
$712$	8.57779	0.321466
$713$	31.3670	1.17470
$714$	−14.9485	−0.559435
$715$	0.0481418	0.00180040
$716$	14.4469	0.539904
$717$	44.7572	1.67149
$718$	30.4610	1.13679
$719$	5.43232	0.202591	0.101296	−	0.994856i	$-0.467701\pi$
$719$	5.43232	0.202591	0.101296	+	0.994856i	$0.467701\pi$
$720$	2.72176	0.101434
$721$	20.2873	0.755537
$722$	−46.1508	−1.71755
$723$	15.0787	0.560783
$724$	18.7339	0.696238
$725$	−12.8121	−0.475829
$726$	−24.0386	−0.892155
$727$	17.8288	0.661233	0.330617	−	0.943765i	$-0.392743\pi$
$727$	17.8288	0.661233	0.330617	+	0.943765i	$0.392743\pi$
$728$	0.0552837	0.00204895
$729$	−26.8326	−0.993799
$730$	−9.56807	−0.354130
$731$	−64.3371	−2.37959
$732$	−17.6091	−0.650850
$733$	−22.8672	−0.844620	−0.422310	−	0.906452i	$-0.638781\pi$
$733$	−22.8672	−0.844620	−0.422310	+	0.906452i	$0.638781\pi$
$734$	11.3977	0.420697
$735$	12.7248	0.469362
$736$	3.40168	0.125387
$737$	−0.892703	−0.0328831
$738$	29.1034	1.07131
$739$	−21.8228	−0.802765	−0.401383	−	0.915910i	$-0.631470\pi$
$739$	−21.8228	−0.802765	−0.401383	+	0.915910i	$0.631470\pi$
$740$	−1.75668	−0.0645769
$741$	−0.962603	−0.0353621
$742$	8.06795	0.296184
$743$	36.5836	1.34212	0.671062	−	0.741402i	$-0.265839\pi$
$743$	36.5836	1.34212	0.671062	+	0.741402i	$0.265839\pi$
$744$	−22.5693	−0.827432
$745$	0.965202	0.0353623
$746$	19.8719	0.727564
$747$	46.8867	1.71549
$748$	5.84400	0.213678
$749$	8.60986	0.314597
$750$	−20.4300	−0.745996
$751$	−29.9067	−1.09131	−0.545655	−	0.838010i	$-0.683719\pi$
$751$	−29.9067	−1.09131	−0.545655	+	0.838010i	$0.683719\pi$
$752$	10.5796	0.385800
$753$	−60.7161	−2.21262
$754$	−0.149640	−0.00544956
$755$	14.3268	0.521404
$756$	−0.0257892	−0.000937943 0
$757$	30.1331	1.09521	0.547604	−	0.836738i	$-0.315540\pi$
$757$	30.1331	1.09521	0.547604	+	0.836738i	$0.315540\pi$
$758$	−20.8158	−0.756063
$759$	9.03924	0.328104
$760$	−7.34572	−0.266457
$761$	−6.63047	−0.240354	−0.120177	−	0.992752i	$-0.538346\pi$
$761$	−6.63047	−0.240354	−0.120177	+	0.992752i	$0.538346\pi$
$762$	−26.7981	−0.970793
$763$	−3.33592	−0.120768
$764$	−15.9025	−0.575333
$765$	14.6508	0.529699
$766$	−2.99342	−0.108157
$767$	−0.603523	−0.0217919
$768$	−2.44759	−0.0883199
$769$	9.81181	0.353823	0.176911	−	0.984227i	$-0.443389\pi$
$769$	9.81181	0.353823	0.176911	+	0.984227i	$0.443389\pi$
$770$	1.12105	0.0403997
$771$	−59.0005	−2.12485
$772$	14.7163	0.529651
$773$	4.42529	0.159167	0.0795833	−	0.996828i	$-0.474641\pi$
$773$	4.42529	0.159167	0.0795833	+	0.996828i	$0.474641\pi$
$774$	35.7458	1.28486
$775$	38.4681	1.38181
$776$	−12.7856	−0.458977
$777$	−5.36052	−0.192308
$778$	12.3423	0.442494
$779$	−78.5469	−2.81423
$780$	−0.108533	−0.00388611
$781$	−2.24462	−0.0803188
$782$	18.3106	0.654787
$783$	0.0698051	0.00249463
$784$	−5.71265	−0.204023
$785$	−9.24271	−0.329886
$786$	−44.1184	−1.57365
$787$	25.2309	0.899384	0.449692	−	0.893184i	$-0.351534\pi$
$787$	25.2309	0.899384	0.449692	+	0.893184i	$0.351534\pi$
$788$	−7.73695	−0.275618
$789$	34.0824	1.21337
$790$	3.50023	0.124533
$791$	−9.51203	−0.338209
$792$	−3.24694	−0.115375
$793$	0.350546	0.0124482
$794$	−0.189131	−0.00671202
$795$	−15.8390	−0.561752
$796$	−20.2276	−0.716948
$797$	3.29307	0.116646	0.0583232	−	0.998298i	$-0.481425\pi$
$797$	3.29307	0.116646	0.0583232	+	0.998298i	$0.481425\pi$
$798$	−22.4155	−0.793499
$799$	56.9484	2.01469
$800$	4.17177	0.147494
$801$	−25.6537	−0.906430
$802$	−18.3476	−0.647875
$803$	11.4143	0.402802
$804$	2.01255	0.0709772
$805$	3.51250	0.123799
$806$	0.449291	0.0158256
$807$	58.3246	2.05312
$808$	−13.0332	−0.458508
$809$	10.7813	0.379050	0.189525	−	0.981876i	$-0.439305\pi$
$809$	10.7813	0.379050	0.189525	+	0.981876i	$0.439305\pi$
$810$	8.21591	0.288678
$811$	−19.5475	−0.686407	−0.343203	−	0.939261i	$-0.611512\pi$
$811$	−19.5475	−0.686407	−0.343203	+	0.939261i	$0.611512\pi$
$812$	−3.48456	−0.122284
$813$	−40.6425	−1.42540
$814$	2.09565	0.0734524
$815$	8.28606	0.290248
$816$	−13.1750	−0.461216
$817$	−96.4740	−3.37520
$818$	1.28838	0.0450471
$819$	−0.165338	−0.00577736
$820$	−8.85613	−0.309269
$821$	−33.7853	−1.17911	−0.589557	−	0.807727i	$-0.700698\pi$
$821$	−33.7853	−1.17911	−0.589557	+	0.807727i	$0.700698\pi$
$822$	−43.2058	−1.50698
$823$	−25.0633	−0.873653	−0.436827	−	0.899546i	$-0.643898\pi$
$823$	−25.0633	−0.873653	−0.436827	+	0.899546i	$0.643898\pi$
$824$	17.8803	0.622889
$825$	11.0856	0.385951
$826$	−14.0538	−0.488995
$827$	39.3982	1.37001	0.685005	−	0.728538i	$-0.259800\pi$
$827$	39.3982	1.37001	0.685005	+	0.728538i	$0.259800\pi$
$828$	−10.1734	−0.353551
$829$	50.1596	1.74212	0.871058	−	0.491181i	$-0.163435\pi$
$829$	50.1596	1.74212	0.871058	+	0.491181i	$0.163435\pi$
$830$	−14.2676	−0.495234
$831$	14.6065	0.506694
$832$	0.0487246	0.00168922
$833$	−30.7502	−1.06543
$834$	13.9336	0.482481
$835$	10.1286	0.350514
$836$	8.76313	0.303079
$837$	−0.209589	−0.00724445
$838$	7.67913	0.265271
$839$	−1.39646	−0.0482112	−0.0241056	−	0.999709i	$-0.507674\pi$
$839$	−1.39646	−0.0482112	−0.0241056	+	0.999709i	$0.507674\pi$
$840$	−2.52734	−0.0872014
$841$	−19.5681	−0.674763
$842$	−20.2118	−0.696543
$843$	−16.9886	−0.585120
$844$	4.52661	0.155812
$845$	−11.8287	−0.406921
$846$	−31.6407	−1.08783
$847$	11.1434	0.382892
$848$	7.11073	0.244183
$849$	28.8817	0.991216
$850$	22.4559	0.770232
$851$	6.56616	0.225085
$852$	5.06037	0.173365
$853$	−27.6999	−0.948428	−0.474214	−	0.880410i	$-0.657268\pi$
$853$	−27.6999	−0.948428	−0.474214	+	0.880410i	$0.657268\pi$
$854$	8.16292	0.279330
$855$	21.9690	0.751322
$856$	7.58835	0.259364
$857$	−50.1196	−1.71205	−0.856027	−	0.516931i	$-0.827074\pi$
$857$	−50.1196	−1.71205	−0.856027	+	0.516931i	$0.827074\pi$
$858$	0.129475	0.00442021
$859$	−41.9628	−1.43175	−0.715876	−	0.698227i	$-0.753972\pi$
$859$	−41.9628	−1.43175	−0.715876	+	0.698227i	$0.753972\pi$
$860$	−10.8774	−0.370917
$861$	−27.0245	−0.920992
$862$	6.92743	0.235949
$863$	−24.9557	−0.849502	−0.424751	−	0.905310i	$-0.639638\pi$
$863$	−24.9557	−0.849502	−0.424751	+	0.905310i	$0.639638\pi$
$864$	−0.0227294	−0.000773271 0
$865$	6.10814	0.207683
$866$	−20.2457	−0.687978
$867$	−29.3096	−0.995405
$868$	10.4623	0.355115
$869$	−4.17563	−0.141648
$870$	6.84090	0.231928
$871$	−0.0400641	−0.00135752
$872$	−2.94013	−0.0995653
$873$	38.2381	1.29416
$874$	27.4570	0.928746
$875$	9.47059	0.320164
$876$	−25.7329	−0.869434
$877$	−29.9038	−1.00978	−0.504890	−	0.863184i	$-0.668467\pi$
$877$	−29.9038	−1.00978	−0.504890	+	0.863184i	$0.668467\pi$
$878$	9.40249	0.317319
$879$	−64.0306	−2.15970
$880$	0.988040	0.0333068
$881$	2.81636	0.0948857	0.0474428	−	0.998874i	$-0.484893\pi$
$881$	2.81636	0.0948857	0.0474428	+	0.998874i	$0.484893\pi$
$882$	17.0849	0.575278
$883$	7.11950	0.239590	0.119795	−	0.992799i	$-0.461776\pi$
$883$	7.11950	0.239590	0.119795	+	0.992799i	$0.461776\pi$
$884$	0.262276	0.00882130
$885$	27.5905	0.927445
$886$	−4.45869	−0.149793
$887$	44.3183	1.48806	0.744031	−	0.668146i	$-0.232912\pi$
$887$	44.3183	1.48806	0.744031	+	0.668146i	$0.232912\pi$
$888$	−4.72452	−0.158545
$889$	12.4226	0.416642
$890$	7.80639	0.261671
$891$	−9.80122	−0.328353
$892$	28.9180	0.968247
$893$	85.3947	2.85762
$894$	2.59587	0.0868188
$895$	13.1477	0.439478
$896$	1.13462	0.0379049
$897$	0.405677	0.0135452
$898$	22.6462	0.755713
$899$	−28.3190	−0.944493
$900$	−12.4766	−0.415886
$901$	38.2758	1.27515
$902$	10.5650	0.351776
$903$	−33.1924	−1.10457
$904$	−8.38348	−0.278830
$905$	17.0491	0.566732
$906$	38.5312	1.28011
$907$	−18.9151	−0.628066	−0.314033	−	0.949412i	$-0.601680\pi$
$907$	−18.9151	−0.628066	−0.314033	+	0.949412i	$0.601680\pi$
$908$	7.58439	0.251697
$909$	38.9787	1.29284
$910$	0.0503120	0.00166783
$911$	−18.3532	−0.608069	−0.304035	−	0.952661i	$-0.598334\pi$
$911$	−18.3532	−0.608069	−0.304035	+	0.952661i	$0.598334\pi$
$912$	−19.7560	−0.654187
$913$	17.0206	0.563299
$914$	19.7359	0.652806
$915$	−16.0255	−0.529786
$916$	4.73632	0.156492
$917$	20.4517	0.675375
$918$	−0.122349	−0.00403810
$919$	−5.61543	−0.185236	−0.0926180	−	0.995702i	$-0.529524\pi$
$919$	−5.61543	−0.185236	−0.0926180	+	0.995702i	$0.529524\pi$
$920$	3.09576	0.102064
$921$	54.7516	1.80413
$922$	33.0477	1.08837
$923$	−0.100737	−0.00331581
$924$	3.01500	0.0991863
$925$	8.05266	0.264770
$926$	20.2663	0.665991
$927$	−53.4748	−1.75634
$928$	−3.07113	−0.100815
$929$	37.1097	1.21753	0.608765	−	0.793351i	$-0.291665\pi$
$929$	37.1097	1.21753	0.608765	+	0.793351i	$0.291665\pi$
$930$	−20.5397	−0.673523
$931$	−46.1102	−1.51120
$932$	−17.6630	−0.578570
$933$	49.9617	1.63567
$934$	3.50005	0.114525
$935$	5.31845	0.173932
$936$	−0.145721	−0.00476305
$937$	23.6693	0.773242	0.386621	−	0.922239i	$-0.373642\pi$
$937$	23.6693	0.773242	0.386621	+	0.922239i	$0.373642\pi$
$938$	−0.932946	−0.0304618
$939$	−85.3200	−2.78431
$940$	9.62821	0.314038
$941$	8.74151	0.284965	0.142483	−	0.989797i	$-0.454492\pi$
$941$	8.74151	0.284965	0.142483	+	0.989797i	$0.454492\pi$
$942$	−24.8579	−0.809913
$943$	33.1026	1.07797
$944$	−12.3864	−0.403144
$945$	−0.0234699	−0.000763477 0
$946$	12.9763	0.421895
$947$	−36.2954	−1.17944	−0.589721	−	0.807607i	$-0.700762\pi$
$947$	−36.2954	−1.17944	−0.589721	+	0.807607i	$0.700762\pi$
$948$	9.41372	0.305743
$949$	0.512268	0.0166289
$950$	33.6729	1.09249
$951$	−23.8192	−0.772390
$952$	6.10744	0.197943
$953$	12.2221	0.395913	0.197956	−	0.980211i	$-0.436570\pi$
$953$	12.2221	0.395913	0.197956	+	0.980211i	$0.436570\pi$
$954$	−21.2662	−0.688517
$955$	−14.4724	−0.468316
$956$	−18.2862	−0.591418
$957$	−8.16090	−0.263804
$958$	38.0198	1.22836
$959$	20.0287	0.646759
$960$	−2.22748	−0.0718917
$961$	54.0275	1.74282
$962$	0.0940517	0.00303235
$963$	−22.6946	−0.731322
$964$	−6.16062	−0.198420
$965$	13.3929	0.431131
$966$	9.44672	0.303943
$967$	3.17194	0.102003	0.0510013	−	0.998699i	$-0.483759\pi$
$967$	3.17194	0.102003	0.0510013	+	0.998699i	$0.483759\pi$
$968$	9.82131	0.315669
$969$	−106.343	−3.41624
$970$	−11.6358	−0.373603
$971$	−27.5984	−0.885675	−0.442837	−	0.896602i	$-0.646028\pi$
$971$	−27.5984	−0.885675	−0.442837	+	0.896602i	$0.646028\pi$
$972$	22.0281	0.706553
$973$	−6.45912	−0.207070
$974$	−2.64149	−0.0846389
$975$	0.497517	0.0159333
$976$	7.19444	0.230288
$977$	17.7441	0.567683	0.283842	−	0.958871i	$-0.408391\pi$
$977$	17.7441	0.567683	0.283842	+	0.958871i	$0.408391\pi$
$978$	22.2850	0.712596
$979$	−9.31269	−0.297635
$980$	−5.19891	−0.166073
$981$	8.79308	0.280742
$982$	−25.7930	−0.823088
$983$	−39.9670	−1.27475	−0.637375	−	0.770554i	$-0.719980\pi$
$983$	−39.9670	−1.27475	−0.637375	+	0.770554i	$0.719980\pi$
$984$	−23.8182	−0.759296
$985$	−7.04117	−0.224350
$986$	−16.5314	−0.526467
$987$	29.3805	0.935191
$988$	0.393285	0.0125121
$989$	40.6578	1.29284
$990$	−2.95494	−0.0939143
$991$	33.0696	1.05049	0.525246	−	0.850950i	$-0.323973\pi$
$991$	33.0696	1.05049	0.525246	+	0.850950i	$0.323973\pi$
$992$	9.22104	0.292768
$993$	51.0815	1.62102
$994$	−2.34580	−0.0744044
$995$	−18.4085	−0.583589
$996$	−38.3720	−1.21586
$997$	9.82751	0.311240	0.155620	−	0.987817i	$-0.450262\pi$
$997$	9.82751	0.311240	0.155620	+	0.987817i	$0.450262\pi$
$998$	17.3024	0.547698
$999$	−0.0438740	−0.00138811

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.b.1.14	✓	81

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.b.1.14	✓	81	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.44759 q^{3} +1.00000 q^{4} +0.910070 q^{5} +2.44759 q^{6} -1.13462 q^{7} -1.00000 q^{8} +2.99071 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.44759 q^{3} +1.00000 q^{4} +0.910070 q^{5} +2.44759 q^{6} -1.13462 q^{7} -1.00000 q^{8} +2.99071 q^{9} -0.910070 q^{10} +1.08567 q^{11} -2.44759 q^{12} +0.0487246 q^{13} +1.13462 q^{14} -2.22748 q^{15} +1.00000 q^{16} +5.38283 q^{17} -2.99071 q^{18} +8.07160 q^{19} +0.910070 q^{20} +2.77708 q^{21} -1.08567 q^{22} -3.40168 q^{23} +2.44759 q^{24} -4.17177 q^{25} -0.0487246 q^{26} +0.0227294 q^{27} -1.13462 q^{28} +3.07113 q^{29} +2.22748 q^{30} -9.22104 q^{31} -1.00000 q^{32} -2.65729 q^{33} -5.38283 q^{34} -1.03258 q^{35} +2.99071 q^{36} -1.93027 q^{37} -8.07160 q^{38} -0.119258 q^{39} -0.910070 q^{40} -9.73126 q^{41} -2.77708 q^{42} -11.9523 q^{43} +1.08567 q^{44} +2.72176 q^{45} +3.40168 q^{46} +10.5796 q^{47} -2.44759 q^{48} -5.71265 q^{49} +4.17177 q^{50} -13.1750 q^{51} +0.0487246 q^{52} +7.11073 q^{53} -0.0227294 q^{54} +0.988040 q^{55} +1.13462 q^{56} -19.7560 q^{57} -3.07113 q^{58} -12.3864 q^{59} -2.22748 q^{60} +7.19444 q^{61} +9.22104 q^{62} -3.39331 q^{63} +1.00000 q^{64} +0.0443428 q^{65} +2.65729 q^{66} -0.822257 q^{67} +5.38283 q^{68} +8.32592 q^{69} +1.03258 q^{70} -2.06749 q^{71} -2.99071 q^{72} +10.5136 q^{73} +1.93027 q^{74} +10.2108 q^{75} +8.07160 q^{76} -1.23182 q^{77} +0.119258 q^{78} -3.84611 q^{79} +0.910070 q^{80} -9.02777 q^{81} +9.73126 q^{82} +15.6774 q^{83} +2.77708 q^{84} +4.89875 q^{85} +11.9523 q^{86} -7.51689 q^{87} -1.08567 q^{88} -8.57779 q^{89} -2.72176 q^{90} -0.0552837 q^{91} -3.40168 q^{92} +22.5693 q^{93} -10.5796 q^{94} +7.34572 q^{95} +2.44759 q^{96} +12.7856 q^{97} +5.71265 q^{98} +3.24694 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9}+O(q^{10}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9	\( 81 q - 81 q^{2} - 10 q^{3} + 81 q^{4} - 26 q^{5} + 10 q^{6} + 3 q^{7} - 81 q^{8} + 59 q^{9} + 26 q^{10} - 41 q^{11} - 10 q^{12} + 33 q^{13} - 3 q^{14} - 7 q^{15} + 81 q^{16} - 9 q^{17} - 59 q^{18} - 32 q^{19} - 26 q^{20} - 23 q^{21} + 41 q^{22} - 28 q^{23} + 10 q^{24} + 81 q^{25} - 33 q^{26} - 37 q^{27} + 3 q^{28} - 35 q^{29} + 7 q^{30} - 29 q^{31} - 81 q^{32} - 7 q^{33} + 9 q^{34} - 67 q^{35} + 59 q^{36} + 13 q^{37} + 32 q^{38} - 42 q^{39} + 26 q^{40} - 66 q^{41} + 23 q^{42} - 22 q^{43} - 41 q^{44} - 65 q^{45} + 28 q^{46} - 71 q^{47} - 10 q^{48} + 64 q^{49} - 81 q^{50} - 43 q^{51} + 33 q^{52} - 37 q^{53} + 37 q^{54} + 12 q^{55} - 3 q^{56} - q^{57} + 35 q^{58} - 162 q^{59} - 7 q^{60} + 19 q^{61} + 29 q^{62} - 16 q^{63} + 81 q^{64} - 45 q^{65} + 7 q^{66} - 43 q^{67} - 9 q^{68} - 21 q^{69} + 67 q^{70} - 99 q^{71} - 59 q^{72} + 53 q^{73} - 13 q^{74} - 61 q^{75} - 32 q^{76} - 31 q^{77} + 42 q^{78} + 4 q^{79} - 26 q^{80} + q^{81} + 66 q^{82} - 112 q^{83} - 23 q^{84} + 17 q^{85} + 22 q^{86} - 15 q^{87} + 41 q^{88} - 111 q^{89} + 65 q^{90} - 49 q^{91} - 28 q^{92} - 19 q^{93} + 71 q^{94} - 53 q^{95} + 10 q^{96} + 50 q^{97} - 64 q^{98} - 97 q^{99}+O(q^{100}) \) 81 * q - 81 * q^2 - 10 * q^3 + 81 * q^4 - 26 * q^5 + 10 * q^6 + 3 * q^7 - 81 * q^8 + 59 * q^9 + 26 * q^10 - 41 * q^11 - 10 * q^12 + 33 * q^13 - 3 * q^14 - 7 * q^15 + 81 * q^16 - 9 * q^17 - 59 * q^18 - 32 * q^19 - 26 * q^20 - 23 * q^21 + 41 * q^22 - 28 * q^23 + 10 * q^24 + 81 * q^25 - 33 * q^26 - 37 * q^27 + 3 * q^28 - 35 * q^29 + 7 * q^30 - 29 * q^31 - 81 * q^32 - 7 * q^33 + 9 * q^34 - 67 * q^35 + 59 * q^36 + 13 * q^37 + 32 * q^38 - 42 * q^39 + 26 * q^40 - 66 * q^41 + 23 * q^42 - 22 * q^43 - 41 * q^44 - 65 * q^45 + 28 * q^46 - 71 * q^47 - 10 * q^48 + 64 * q^49 - 81 * q^50 - 43 * q^51 + 33 * q^52 - 37 * q^53 + 37 * q^54 + 12 * q^55 - 3 * q^56 - q^57 + 35 * q^58 - 162 * q^59 - 7 * q^60 + 19 * q^61 + 29 * q^62 - 16 * q^63 + 81 * q^64 - 45 * q^65 + 7 * q^66 - 43 * q^67 - 9 * q^68 - 21 * q^69 + 67 * q^70 - 99 * q^71 - 59 * q^72 + 53 * q^73 - 13 * q^74 - 61 * q^75 - 32 * q^76 - 31 * q^77 + 42 * q^78 + 4 * q^79 - 26 * q^80 + q^81 + 66 * q^82 - 112 * q^83 - 23 * q^84 + 17 * q^85 + 22 * q^86 - 15 * q^87 + 41 * q^88 - 111 * q^89 + 65 * q^90 - 49 * q^91 - 28 * q^92 - 19 * q^93 + 71 * q^94 - 53 * q^95 + 10 * q^96 + 50 * q^97 - 64 * q^98 - 97 * q^99

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