LMFDB - Embedded newform 8038.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8038,2,Mod(1,8038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8038, 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("8038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8038 = 2 \cdot 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8038.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:	$64.1837531447$
Analytic rank:	$0$
Dimension:	$92$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.15753 q^{3} +1.00000 q^{4} -0.384990 q^{5} -2.15753 q^{6} -2.87024 q^{7} +1.00000 q^{8} +1.65493 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.15753 q^{3} +1.00000 q^{4} -0.384990 q^{5} -2.15753 q^{6} -2.87024 q^{7} +1.00000 q^{8} +1.65493 q^{9} -0.384990 q^{10} -2.43244 q^{11} -2.15753 q^{12} -3.83822 q^{13} -2.87024 q^{14} +0.830627 q^{15} +1.00000 q^{16} -4.11428 q^{17} +1.65493 q^{18} -3.00193 q^{19} -0.384990 q^{20} +6.19262 q^{21} -2.43244 q^{22} -7.18346 q^{23} -2.15753 q^{24} -4.85178 q^{25} -3.83822 q^{26} +2.90202 q^{27} -2.87024 q^{28} +1.67095 q^{29} +0.830627 q^{30} -9.45961 q^{31} +1.00000 q^{32} +5.24806 q^{33} -4.11428 q^{34} +1.10501 q^{35} +1.65493 q^{36} -1.62752 q^{37} -3.00193 q^{38} +8.28108 q^{39} -0.384990 q^{40} -3.17641 q^{41} +6.19262 q^{42} +8.91551 q^{43} -2.43244 q^{44} -0.637133 q^{45} -7.18346 q^{46} -5.87019 q^{47} -2.15753 q^{48} +1.23826 q^{49} -4.85178 q^{50} +8.87668 q^{51} -3.83822 q^{52} -9.47387 q^{53} +2.90202 q^{54} +0.936464 q^{55} -2.87024 q^{56} +6.47675 q^{57} +1.67095 q^{58} +11.9808 q^{59} +0.830627 q^{60} +2.65385 q^{61} -9.45961 q^{62} -4.75005 q^{63} +1.00000 q^{64} +1.47768 q^{65} +5.24806 q^{66} +6.28220 q^{67} -4.11428 q^{68} +15.4985 q^{69} +1.10501 q^{70} +1.92419 q^{71} +1.65493 q^{72} +6.89093 q^{73} -1.62752 q^{74} +10.4679 q^{75} -3.00193 q^{76} +6.98168 q^{77} +8.28108 q^{78} -12.4847 q^{79} -0.384990 q^{80} -11.2260 q^{81} -3.17641 q^{82} +3.60839 q^{83} +6.19262 q^{84} +1.58396 q^{85} +8.91551 q^{86} -3.60512 q^{87} -2.43244 q^{88} -2.72091 q^{89} -0.637133 q^{90} +11.0166 q^{91} -7.18346 q^{92} +20.4094 q^{93} -5.87019 q^{94} +1.15571 q^{95} -2.15753 q^{96} -6.10434 q^{97} +1.23826 q^{98} -4.02553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) $ 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * 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
$3$	−2.15753	−1.24565	−0.622825	−	0.782361i	$-0.714015\pi$
$3$	−2.15753	−1.24565	−0.622825	+	0.782361i	$0.714015\pi$
$4$	1.00000	0.500000
$5$	−0.384990	−0.172173	−0.0860864	−	0.996288i	$-0.527436\pi$
$5$	−0.384990	−0.172173	−0.0860864	+	0.996288i	$0.527436\pi$
$6$	−2.15753	−0.880808
$7$	−2.87024	−1.08485	−0.542424	−	0.840105i	$-0.682493\pi$
$7$	−2.87024	−1.08485	−0.542424	+	0.840105i	$0.682493\pi$
$8$	1.00000	0.353553
$9$	1.65493	0.551645
$10$	−0.384990	−0.121745
$11$	−2.43244	−0.733408	−0.366704	−	0.930338i	$-0.619514\pi$
$11$	−2.43244	−0.733408	−0.366704	+	0.930338i	$0.619514\pi$
$12$	−2.15753	−0.622825
$13$	−3.83822	−1.06453	−0.532266	−	0.846577i	$-0.678659\pi$
$13$	−3.83822	−1.06453	−0.532266	+	0.846577i	$0.678659\pi$
$14$	−2.87024	−0.767103
$15$	0.830627	0.214467
$16$	1.00000	0.250000
$17$	−4.11428	−0.997859	−0.498929	−	0.866643i	$-0.666273\pi$
$17$	−4.11428	−0.997859	−0.498929	+	0.866643i	$0.666273\pi$
$18$	1.65493	0.390072
$19$	−3.00193	−0.688689	−0.344345	−	0.938843i	$-0.611899\pi$
$19$	−3.00193	−0.688689	−0.344345	+	0.938843i	$0.611899\pi$
$20$	−0.384990	−0.0860864
$21$	6.19262	1.35134
$22$	−2.43244	−0.518598
$23$	−7.18346	−1.49786	−0.748928	−	0.662652i	$-0.769431\pi$
$23$	−7.18346	−1.49786	−0.748928	+	0.662652i	$0.769431\pi$
$24$	−2.15753	−0.440404
$25$	−4.85178	−0.970357
$26$	−3.83822	−0.752738
$27$	2.90202	0.558494
$28$	−2.87024	−0.542424
$29$	1.67095	0.310287	0.155144	−	0.987892i	$-0.450416\pi$
$29$	1.67095	0.310287	0.155144	+	0.987892i	$0.450416\pi$
$30$	0.830627	0.151651
$31$	−9.45961	−1.69900	−0.849498	−	0.527592i	$-0.823095\pi$
$31$	−9.45961	−1.69900	−0.849498	+	0.527592i	$0.823095\pi$
$32$	1.00000	0.176777
$33$	5.24806	0.913570
$34$	−4.11428	−0.705593
$35$	1.10501	0.186781
$36$	1.65493	0.275822
$37$	−1.62752	−0.267563	−0.133781	−	0.991011i	$-0.542712\pi$
$37$	−1.62752	−0.267563	−0.133781	+	0.991011i	$0.542712\pi$
$38$	−3.00193	−0.486977
$39$	8.28108	1.32603
$40$	−0.384990	−0.0608723
$41$	−3.17641	−0.496072	−0.248036	−	0.968751i	$-0.579785\pi$
$41$	−3.17641	−0.496072	−0.248036	+	0.968751i	$0.579785\pi$
$42$	6.19262	0.955542
$43$	8.91551	1.35960	0.679801	−	0.733396i	$-0.262066\pi$
$43$	8.91551	1.35960	0.679801	+	0.733396i	$0.262066\pi$
$44$	−2.43244	−0.366704
$45$	−0.637133	−0.0949782
$46$	−7.18346	−1.05914
$47$	−5.87019	−0.856256	−0.428128	−	0.903718i	$-0.640827\pi$
$47$	−5.87019	−0.856256	−0.428128	+	0.903718i	$0.640827\pi$
$48$	−2.15753	−0.311413
$49$	1.23826	0.176895
$50$	−4.85178	−0.686146
$51$	8.87668	1.24298
$52$	−3.83822	−0.532266
$53$	−9.47387	−1.30134	−0.650668	−	0.759362i	$-0.725511\pi$
$53$	−9.47387	−1.30134	−0.650668	+	0.759362i	$0.725511\pi$
$54$	2.90202	0.394915
$55$	0.936464	0.126273
$56$	−2.87024	−0.383552
$57$	6.47675	0.857866
$58$	1.67095	0.219406
$59$	11.9808	1.55977	0.779886	−	0.625921i	$-0.215277\pi$
$59$	11.9808	1.55977	0.779886	+	0.625921i	$0.215277\pi$
$60$	0.830627	0.107234
$61$	2.65385	0.339790	0.169895	−	0.985462i	$-0.445657\pi$
$61$	2.65385	0.339790	0.169895	+	0.985462i	$0.445657\pi$
$62$	−9.45961	−1.20137
$63$	−4.75005	−0.598451
$64$	1.00000	0.125000
$65$	1.47768	0.183283
$66$	5.24806	0.645991
$67$	6.28220	0.767493	0.383747	−	0.923438i	$-0.374634\pi$
$67$	6.28220	0.767493	0.383747	+	0.923438i	$0.374634\pi$
$68$	−4.11428	−0.498929
$69$	15.4985	1.86580
$70$	1.10501	0.132074
$71$	1.92419	0.228359	0.114180	−	0.993460i	$-0.463576\pi$
$71$	1.92419	0.228359	0.114180	+	0.993460i	$0.463576\pi$
$72$	1.65493	0.195036
$73$	6.89093	0.806522	0.403261	−	0.915085i	$-0.367877\pi$
$73$	6.89093	0.806522	0.403261	+	0.915085i	$0.367877\pi$
$74$	−1.62752	−0.189195
$75$	10.4679	1.20872
$76$	−3.00193	−0.344345
$77$	6.98168	0.795636
$78$	8.28108	0.937648
$79$	−12.4847	−1.40464	−0.702320	−	0.711862i	$-0.747852\pi$
$79$	−12.4847	−1.40464	−0.702320	+	0.711862i	$0.747852\pi$
$80$	−0.384990	−0.0430432
$81$	−11.2260	−1.24733
$82$	−3.17641	−0.350776
$83$	3.60839	0.396072	0.198036	−	0.980195i	$-0.436544\pi$
$83$	3.60839	0.396072	0.198036	+	0.980195i	$0.436544\pi$
$84$	6.19262	0.675670
$85$	1.58396	0.171804
$86$	8.91551	0.961384
$87$	−3.60512	−0.386510
$88$	−2.43244	−0.259299
$89$	−2.72091	−0.288416	−0.144208	−	0.989547i	$-0.546063\pi$
$89$	−2.72091	−0.288416	−0.144208	+	0.989547i	$0.546063\pi$
$90$	−0.637133	−0.0671597
$91$	11.0166	1.15485
$92$	−7.18346	−0.748928
$93$	20.4094	2.11635
$94$	−5.87019	−0.605464
$95$	1.15571	0.118574
$96$	−2.15753	−0.220202
$97$	−6.10434	−0.619802	−0.309901	−	0.950769i	$-0.600296\pi$
$97$	−6.10434	−0.619802	−0.309901	+	0.950769i	$0.600296\pi$
$98$	1.23826	0.125083
$99$	−4.02553	−0.404581
$100$	−4.85178	−0.485178
$101$	1.15627	0.115053	0.0575265	−	0.998344i	$-0.481679\pi$
$101$	1.15627	0.115053	0.0575265	+	0.998344i	$0.481679\pi$
$102$	8.87668	0.878922
$103$	1.00848	0.0993687	0.0496844	−	0.998765i	$-0.484178\pi$
$103$	1.00848	0.0993687	0.0496844	+	0.998765i	$0.484178\pi$
$104$	−3.83822	−0.376369
$105$	−2.38410	−0.232664
$106$	−9.47387	−0.920184
$107$	1.03254	0.0998191	0.0499096	−	0.998754i	$-0.484107\pi$
$107$	1.03254	0.0998191	0.0499096	+	0.998754i	$0.484107\pi$
$108$	2.90202	0.279247
$109$	−18.3488	−1.75750	−0.878748	−	0.477286i	$-0.841621\pi$
$109$	−18.3488	−1.75750	−0.878748	+	0.477286i	$0.841621\pi$
$110$	0.936464	0.0892884
$111$	3.51142	0.333289
$112$	−2.87024	−0.271212
$113$	−13.5818	−1.27767	−0.638834	−	0.769345i	$-0.720583\pi$
$113$	−13.5818	−1.27767	−0.638834	+	0.769345i	$0.720583\pi$
$114$	6.47675	0.606603
$115$	2.76556	0.257890
$116$	1.67095	0.155144
$117$	−6.35201	−0.587243
$118$	11.9808	1.10293
$119$	11.8090	1.08253
$120$	0.830627	0.0758255
$121$	−5.08324	−0.462113
$122$	2.65385	0.240268
$123$	6.85320	0.617932
$124$	−9.45961	−0.849498
$125$	3.79284	0.339242
$126$	−4.75005	−0.423168
$127$	8.28410	0.735095	0.367548	−	0.930005i	$-0.380197\pi$
$127$	8.28410	0.735095	0.367548	+	0.930005i	$0.380197\pi$
$128$	1.00000	0.0883883
$129$	−19.2355	−1.69359
$130$	1.47768	0.129601
$131$	−0.747069	−0.0652717	−0.0326358	−	0.999467i	$-0.510390\pi$
$131$	−0.747069	−0.0652717	−0.0326358	+	0.999467i	$0.510390\pi$
$132$	5.24806	0.456785
$133$	8.61624	0.747123
$134$	6.28220	0.542700
$135$	−1.11725	−0.0961574
$136$	−4.11428	−0.352796
$137$	−23.1978	−1.98192	−0.990960	−	0.134154i	$-0.957168\pi$
$137$	−23.1978	−1.98192	−0.990960	+	0.134154i	$0.957168\pi$
$138$	15.4985	1.31932
$139$	3.23932	0.274755	0.137378	−	0.990519i	$-0.456133\pi$
$139$	3.23932	0.274755	0.137378	+	0.990519i	$0.456133\pi$
$140$	1.10501	0.0933906
$141$	12.6651	1.06660
$142$	1.92419	0.161474
$143$	9.33625	0.780736
$144$	1.65493	0.137911
$145$	−0.643299	−0.0534230
$146$	6.89093	0.570297
$147$	−2.67159	−0.220349
$148$	−1.62752	−0.133781
$149$	−3.71787	−0.304580	−0.152290	−	0.988336i	$-0.548665\pi$
$149$	−3.71787	−0.304580	−0.152290	+	0.988336i	$0.548665\pi$
$150$	10.4679	0.854698
$151$	−0.385892	−0.0314034	−0.0157017	−	0.999877i	$-0.504998\pi$
$151$	−0.385892	−0.0314034	−0.0157017	+	0.999877i	$0.504998\pi$
$152$	−3.00193	−0.243488
$153$	−6.80886	−0.550464
$154$	6.98168	0.562600
$155$	3.64185	0.292521
$156$	8.28108	0.663017
$157$	−10.2144	−0.815200	−0.407600	−	0.913161i	$-0.633634\pi$
$157$	−10.2144	−0.815200	−0.407600	+	0.913161i	$0.633634\pi$
$158$	−12.4847	−0.993230
$159$	20.4402	1.62101
$160$	−0.384990	−0.0304361
$161$	20.6182	1.62494
$162$	−11.2260	−0.881997
$163$	19.4114	1.52042	0.760210	−	0.649677i	$-0.225096\pi$
$163$	19.4114	1.52042	0.760210	+	0.649677i	$0.225096\pi$
$164$	−3.17641	−0.248036
$165$	−2.02045	−0.157292
$166$	3.60839	0.280065
$167$	20.0189	1.54911	0.774556	−	0.632506i	$-0.217974\pi$
$167$	20.0189	1.54911	0.774556	+	0.632506i	$0.217974\pi$
$168$	6.19262	0.477771
$169$	1.73196	0.133228
$170$	1.58396	0.121484
$171$	−4.96799	−0.379912
$172$	8.91551	0.679801
$173$	13.1260	0.997950	0.498975	−	0.866616i	$-0.333710\pi$
$173$	13.1260	0.997950	0.498975	+	0.866616i	$0.333710\pi$
$174$	−3.60512	−0.273304
$175$	13.9258	1.05269
$176$	−2.43244	−0.183352
$177$	−25.8490	−1.94293
$178$	−2.72091	−0.203941
$179$	3.79760	0.283846	0.141923	−	0.989878i	$-0.454672\pi$
$179$	3.79760	0.283846	0.141923	+	0.989878i	$0.454672\pi$
$180$	−0.637133	−0.0474891
$181$	−12.1799	−0.905322	−0.452661	−	0.891683i	$-0.649525\pi$
$181$	−12.1799	−0.905322	−0.452661	+	0.891683i	$0.649525\pi$
$182$	11.0166	0.816606
$183$	−5.72575	−0.423260
$184$	−7.18346	−0.529572
$185$	0.626579	0.0460670
$186$	20.4094	1.49649
$187$	10.0077	0.731838
$188$	−5.87019	−0.428128
$189$	−8.32948	−0.605881
$190$	1.15571	0.0838441
$191$	−7.83127	−0.566651	−0.283325	−	0.959024i	$-0.591438\pi$
$191$	−7.83127	−0.566651	−0.283325	+	0.959024i	$0.591438\pi$
$192$	−2.15753	−0.155706
$193$	14.6471	1.05432	0.527162	−	0.849765i	$-0.323256\pi$
$193$	14.6471	1.05432	0.527162	+	0.849765i	$0.323256\pi$
$194$	−6.10434	−0.438266
$195$	−3.18813	−0.228307
$196$	1.23826	0.0884473
$197$	−3.11052	−0.221615	−0.110808	−	0.993842i	$-0.535344\pi$
$197$	−3.11052	−0.221615	−0.110808	+	0.993842i	$0.535344\pi$
$198$	−4.02553	−0.286082
$199$	2.66896	0.189197	0.0945986	−	0.995515i	$-0.469843\pi$
$199$	2.66896	0.189197	0.0945986	+	0.995515i	$0.469843\pi$
$200$	−4.85178	−0.343073
$201$	−13.5540	−0.956028
$202$	1.15627	0.0813547
$203$	−4.79602	−0.336615
$204$	8.87668	0.621492
$205$	1.22289	0.0854101
$206$	1.00848	0.0702643
$207$	−11.8882	−0.826284
$208$	−3.83822	−0.266133
$209$	7.30201	0.505090
$210$	−2.38410	−0.164518
$211$	−20.7799	−1.43055	−0.715275	−	0.698843i	$-0.753699\pi$
$211$	−20.7799	−1.43055	−0.715275	+	0.698843i	$0.753699\pi$
$212$	−9.47387	−0.650668
$213$	−4.15149	−0.284456
$214$	1.03254	0.0705828
$215$	−3.43238	−0.234087
$216$	2.90202	0.197457
$217$	27.1513	1.84315
$218$	−18.3488	−1.24274
$219$	−14.8674	−1.00464
$220$	0.936464	0.0631364
$221$	15.7915	1.06225
$222$	3.51142	0.235671
$223$	−5.24824	−0.351448	−0.175724	−	0.984439i	$-0.556227\pi$
$223$	−5.24824	−0.351448	−0.175724	+	0.984439i	$0.556227\pi$
$224$	−2.87024	−0.191776
$225$	−8.02938	−0.535292
$226$	−13.5818	−0.903447
$227$	16.1802	1.07391	0.536957	−	0.843609i	$-0.319574\pi$
$227$	16.1802	1.07391	0.536957	+	0.843609i	$0.319574\pi$
$228$	6.47675	0.428933
$229$	−17.2291	−1.13853	−0.569264	−	0.822155i	$-0.692772\pi$
$229$	−17.2291	−1.13853	−0.569264	+	0.822155i	$0.692772\pi$
$230$	2.76556	0.182356
$231$	−15.0632	−0.991084
$232$	1.67095	0.109703
$233$	19.1139	1.25219	0.626097	−	0.779746i	$-0.284652\pi$
$233$	19.1139	1.25219	0.626097	+	0.779746i	$0.284652\pi$
$234$	−6.35201	−0.415244
$235$	2.25997	0.147424
$236$	11.9808	0.779886
$237$	26.9361	1.74969
$238$	11.8090	0.765461
$239$	−0.0755661	−0.00488797	−0.00244398	−	0.999997i	$-0.500778\pi$
$239$	−0.0755661	−0.00488797	−0.00244398	+	0.999997i	$0.500778\pi$
$240$	0.830627	0.0536168
$241$	29.4664	1.89810	0.949049	−	0.315129i	$-0.102048\pi$
$241$	29.4664	1.89810	0.949049	+	0.315129i	$0.102048\pi$
$242$	−5.08324	−0.326763
$243$	15.5144	0.995247
$244$	2.65385	0.169895
$245$	−0.476719	−0.0304564
$246$	6.85320	0.436944
$247$	11.5221	0.733132
$248$	−9.45961	−0.600686
$249$	−7.78521	−0.493367
$250$	3.79284	0.239880
$251$	−17.6220	−1.11229	−0.556145	−	0.831086i	$-0.687720\pi$
$251$	−17.6220	−1.11229	−0.556145	+	0.831086i	$0.687720\pi$
$252$	−4.75005	−0.299225
$253$	17.4733	1.09854
$254$	8.28410	0.519791
$255$	−3.41743	−0.214008
$256$	1.00000	0.0625000
$257$	27.1176	1.69155	0.845776	−	0.533538i	$-0.179138\pi$
$257$	27.1176	1.69155	0.845776	+	0.533538i	$0.179138\pi$
$258$	−19.2355	−1.19755
$259$	4.67137	0.290265
$260$	1.47768	0.0916417
$261$	2.76531	0.171168
$262$	−0.747069	−0.0461541
$263$	−26.6465	−1.64310	−0.821548	−	0.570140i	$-0.806889\pi$
$263$	−26.6465	−1.64310	−0.821548	+	0.570140i	$0.806889\pi$
$264$	5.24806	0.322996
$265$	3.64735	0.224055
$266$	8.61624	0.528296
$267$	5.87045	0.359266
$268$	6.28220	0.383747
$269$	14.3669	0.875965	0.437982	−	0.898984i	$-0.355693\pi$
$269$	14.3669	0.875965	0.437982	+	0.898984i	$0.355693\pi$
$270$	−1.11725	−0.0679936
$271$	−13.4415	−0.816511	−0.408255	−	0.912868i	$-0.633863\pi$
$271$	−13.4415	−0.816511	−0.408255	+	0.912868i	$0.633863\pi$
$272$	−4.11428	−0.249465
$273$	−23.7687	−1.43855
$274$	−23.1978	−1.40143
$275$	11.8017	0.711667
$276$	15.4985	0.932902
$277$	16.2264	0.974951	0.487476	−	0.873137i	$-0.337918\pi$
$277$	16.2264	0.974951	0.487476	+	0.873137i	$0.337918\pi$
$278$	3.23932	0.194281
$279$	−15.6550	−0.937242
$280$	1.10501	0.0660371
$281$	−20.0915	−1.19856	−0.599279	−	0.800541i	$-0.704546\pi$
$281$	−20.0915	−1.19856	−0.599279	+	0.800541i	$0.704546\pi$
$282$	12.6651	0.754197
$283$	17.9448	1.06671	0.533354	−	0.845892i	$-0.320932\pi$
$283$	17.9448	1.06671	0.533354	+	0.845892i	$0.320932\pi$
$284$	1.92419	0.114180
$285$	−2.49348	−0.147701
$286$	9.33625	0.552064
$287$	9.11706	0.538163
$288$	1.65493	0.0975179
$289$	−0.0727174	−0.00427749
$290$	−0.643299	−0.0377758
$291$	13.1703	0.772056
$292$	6.89093	0.403261
$293$	−26.6923	−1.55938	−0.779692	−	0.626164i	$-0.784624\pi$
$293$	−26.6923	−1.55938	−0.779692	+	0.626164i	$0.784624\pi$
$294$	−2.67159	−0.155810
$295$	−4.61250	−0.268550
$296$	−1.62752	−0.0945977
$297$	−7.05898	−0.409604
$298$	−3.71787	−0.215370
$299$	27.5717	1.59451
$300$	10.4679	0.604362
$301$	−25.5896	−1.47496
$302$	−0.385892	−0.0222056
$303$	−2.49468	−0.143316
$304$	−3.00193	−0.172172
$305$	−1.02170	−0.0585026
$306$	−6.80886	−0.389237
$307$	−21.2766	−1.21432	−0.607160	−	0.794579i	$-0.707691\pi$
$307$	−21.2766	−1.21432	−0.607160	+	0.794579i	$0.707691\pi$
$308$	6.98168	0.397818
$309$	−2.17583	−0.123779
$310$	3.64185	0.206843
$311$	−5.52440	−0.313260	−0.156630	−	0.987657i	$-0.550063\pi$
$311$	−5.52440	−0.313260	−0.156630	+	0.987657i	$0.550063\pi$
$312$	8.28108	0.468824
$313$	14.1743	0.801182	0.400591	−	0.916257i	$-0.368805\pi$
$313$	14.1743	0.801182	0.400591	+	0.916257i	$0.368805\pi$
$314$	−10.2144	−0.576434
$315$	1.82872	0.103037
$316$	−12.4847	−0.702320
$317$	−17.8380	−1.00188	−0.500942	−	0.865481i	$-0.667013\pi$
$317$	−17.8380	−1.00188	−0.500942	+	0.865481i	$0.667013\pi$
$318$	20.4402	1.14623
$319$	−4.06448	−0.227567
$320$	−0.384990	−0.0215216
$321$	−2.22773	−0.124340
$322$	20.6182	1.14901
$323$	12.3508	0.687215
$324$	−11.2260	−0.623666
$325$	18.6222	1.03298
$326$	19.4114	1.07510
$327$	39.5881	2.18923
$328$	−3.17641	−0.175388
$329$	16.8488	0.928907
$330$	−2.02045	−0.111222
$331$	25.4838	1.40072	0.700359	−	0.713791i	$-0.253023\pi$
$331$	25.4838	1.40072	0.700359	+	0.713791i	$0.253023\pi$
$332$	3.60839	0.198036
$333$	−2.69344	−0.147600
$334$	20.0189	1.09539
$335$	−2.41858	−0.132141
$336$	6.19262	0.337835
$337$	−1.81270	−0.0987438	−0.0493719	−	0.998780i	$-0.515722\pi$
$337$	−1.81270	−0.0987438	−0.0493719	+	0.998780i	$0.515722\pi$
$338$	1.73196	0.0942063
$339$	29.3031	1.59153
$340$	1.58396	0.0859021
$341$	23.0099	1.24606
$342$	−4.96799	−0.268638
$343$	16.5376	0.892944
$344$	8.91551	0.480692
$345$	−5.96678	−0.321241
$346$	13.1260	0.705657
$347$	3.47753	0.186683	0.0933417	−	0.995634i	$-0.470245\pi$
$347$	3.47753	0.186683	0.0933417	+	0.995634i	$0.470245\pi$
$348$	−3.60512	−0.193255
$349$	−5.26605	−0.281885	−0.140943	−	0.990018i	$-0.545013\pi$
$349$	−5.26605	−0.281885	−0.140943	+	0.990018i	$0.545013\pi$
$350$	13.9258	0.744364
$351$	−11.1386	−0.594534
$352$	−2.43244	−0.129649
$353$	0.918678	0.0488963	0.0244481	−	0.999701i	$-0.492217\pi$
$353$	0.918678	0.0488963	0.0244481	+	0.999701i	$0.492217\pi$
$354$	−25.8490	−1.37386
$355$	−0.740793	−0.0393172
$356$	−2.72091	−0.144208
$357$	−25.4782	−1.34845
$358$	3.79760	0.200709
$359$	−29.1422	−1.53807	−0.769033	−	0.639209i	$-0.779262\pi$
$359$	−29.1422	−1.53807	−0.769033	+	0.639209i	$0.779262\pi$
$360$	−0.637133	−0.0335799
$361$	−9.98843	−0.525707
$362$	−12.1799	−0.640159
$363$	10.9672	0.575631
$364$	11.0166	0.577427
$365$	−2.65294	−0.138861
$366$	−5.72575	−0.299290
$367$	4.73670	0.247254	0.123627	−	0.992329i	$-0.460547\pi$
$367$	4.73670	0.247254	0.123627	+	0.992329i	$0.460547\pi$
$368$	−7.18346	−0.374464
$369$	−5.25675	−0.273656
$370$	0.626579	0.0325743
$371$	27.1923	1.41175
$372$	20.4094	1.05818
$373$	16.1256	0.834951	0.417475	−	0.908688i	$-0.362915\pi$
$373$	16.1256	0.834951	0.417475	+	0.908688i	$0.362915\pi$
$374$	10.0077	0.517487
$375$	−8.18316	−0.422576
$376$	−5.87019	−0.302732
$377$	−6.41348	−0.330311
$378$	−8.32948	−0.428422
$379$	14.7946	0.759949	0.379974	−	0.924997i	$-0.375933\pi$
$379$	14.7946	0.759949	0.379974	+	0.924997i	$0.375933\pi$
$380$	1.15571	0.0592868
$381$	−17.8732	−0.915672
$382$	−7.83127	−0.400683
$383$	−12.7432	−0.651147	−0.325574	−	0.945517i	$-0.605557\pi$
$383$	−12.7432	−0.651147	−0.325574	+	0.945517i	$0.605557\pi$
$384$	−2.15753	−0.110101
$385$	−2.68788	−0.136987
$386$	14.6471	0.745520
$387$	14.7546	0.750018
$388$	−6.10434	−0.309901
$389$	−29.4979	−1.49560	−0.747801	−	0.663923i	$-0.768890\pi$
$389$	−29.4979	−1.49560	−0.747801	+	0.663923i	$0.768890\pi$
$390$	−3.18813	−0.161437
$391$	29.5548	1.49465
$392$	1.23826	0.0625417
$393$	1.61182	0.0813057
$394$	−3.11052	−0.156706
$395$	4.80649	0.241841
$396$	−4.02553	−0.202290
$397$	−1.37947	−0.0692334	−0.0346167	−	0.999401i	$-0.511021\pi$
$397$	−1.37947	−0.0692334	−0.0346167	+	0.999401i	$0.511021\pi$
$398$	2.66896	0.133783
$399$	−18.5898	−0.930654
$400$	−4.85178	−0.242589
$401$	14.0154	0.699898	0.349949	−	0.936769i	$-0.386199\pi$
$401$	14.0154	0.699898	0.349949	+	0.936769i	$0.386199\pi$
$402$	−13.5540	−0.676014
$403$	36.3081	1.80863
$404$	1.15627	0.0575265
$405$	4.32190	0.214757
$406$	−4.79602	−0.238023
$407$	3.95884	0.196233
$408$	8.87668	0.439461
$409$	−22.1596	−1.09572	−0.547860	−	0.836570i	$-0.684557\pi$
$409$	−22.1596	−1.09572	−0.547860	+	0.836570i	$0.684557\pi$
$410$	1.22289	0.0603941
$411$	50.0499	2.46878
$412$	1.00848	0.0496844
$413$	−34.3878	−1.69212
$414$	−11.8882	−0.584271
$415$	−1.38919	−0.0681928
$416$	−3.83822	−0.188184
$417$	−6.98892	−0.342249
$418$	7.30201	0.357153
$419$	−24.5838	−1.20100	−0.600499	−	0.799626i	$-0.705031\pi$
$419$	−24.5838	−1.20100	−0.600499	+	0.799626i	$0.705031\pi$
$420$	−2.38410	−0.116332
$421$	−40.0808	−1.95342	−0.976710	−	0.214563i	$-0.931167\pi$
$421$	−40.0808	−1.95342	−0.976710	+	0.214563i	$0.931167\pi$
$422$	−20.7799	−1.01155
$423$	−9.71478	−0.472349
$424$	−9.47387	−0.460092
$425$	19.9616	0.968279
$426$	−4.15149	−0.201141
$427$	−7.61717	−0.368621
$428$	1.03254	0.0499096
$429$	−20.1432	−0.972524
$430$	−3.43238	−0.165524
$431$	−7.79687	−0.375562	−0.187781	−	0.982211i	$-0.560130\pi$
$431$	−7.79687	−0.375562	−0.187781	+	0.982211i	$0.560130\pi$
$432$	2.90202	0.139623
$433$	22.2054	1.06712	0.533562	−	0.845761i	$-0.320853\pi$
$433$	22.2054	1.06712	0.533562	+	0.845761i	$0.320853\pi$
$434$	27.1513	1.30330
$435$	1.38794	0.0665464
$436$	−18.3488	−0.878748
$437$	21.5642	1.03156
$438$	−14.8674	−0.710391
$439$	33.0204	1.57598	0.787989	−	0.615689i	$-0.211122\pi$
$439$	33.0204	1.57598	0.787989	+	0.615689i	$0.211122\pi$
$440$	0.936464	0.0446442
$441$	2.04924	0.0975830
$442$	15.7915	0.751126
$443$	13.2396	0.629034	0.314517	−	0.949252i	$-0.398157\pi$
$443$	13.2396	0.629034	0.314517	+	0.949252i	$0.398157\pi$
$444$	3.51142	0.166645
$445$	1.04752	0.0496574
$446$	−5.24824	−0.248511
$447$	8.02141	0.379400
$448$	−2.87024	−0.135606
$449$	−24.0015	−1.13270	−0.566351	−	0.824164i	$-0.691645\pi$
$449$	−24.0015	−1.13270	−0.566351	+	0.824164i	$0.691645\pi$
$450$	−8.02938	−0.378509
$451$	7.72643	0.363823
$452$	−13.5818	−0.638834
$453$	0.832573	0.0391177
$454$	16.1802	0.759372
$455$	−4.24129	−0.198835
$456$	6.47675	0.303301
$457$	8.37371	0.391706	0.195853	−	0.980633i	$-0.437253\pi$
$457$	8.37371	0.391706	0.195853	+	0.980633i	$0.437253\pi$
$458$	−17.2291	−0.805061
$459$	−11.9397	−0.557298
$460$	2.76556	0.128945
$461$	31.7374	1.47816	0.739079	−	0.673619i	$-0.235261\pi$
$461$	31.7374	1.47816	0.739079	+	0.673619i	$0.235261\pi$
$462$	−15.0632	−0.700802
$463$	−15.0911	−0.701342	−0.350671	−	0.936499i	$-0.614046\pi$
$463$	−15.0911	−0.701342	−0.350671	+	0.936499i	$0.614046\pi$
$464$	1.67095	0.0775719
$465$	−7.85741	−0.364378
$466$	19.1139	0.885434
$467$	25.3281	1.17204	0.586022	−	0.810295i	$-0.300693\pi$
$467$	25.3281	1.17204	0.586022	+	0.810295i	$0.300693\pi$
$468$	−6.35201	−0.293622
$469$	−18.0314	−0.832613
$470$	2.25997	0.104244
$471$	22.0379	1.01545
$472$	11.9808	0.551463
$473$	−21.6864	−0.997144
$474$	26.9361	1.23722
$475$	14.5647	0.668274
$476$	11.8090	0.541263
$477$	−15.6786	−0.717875
$478$	−0.0755661	−0.00345631
$479$	−10.2215	−0.467034	−0.233517	−	0.972353i	$-0.575023\pi$
$479$	−10.2215	−0.467034	−0.233517	+	0.972353i	$0.575023\pi$
$480$	0.830627	0.0379128
$481$	6.24679	0.284829
$482$	29.4664	1.34216
$483$	−44.4845	−2.02411
$484$	−5.08324	−0.231056
$485$	2.35011	0.106713
$486$	15.5144	0.703746
$487$	−29.8323	−1.35183	−0.675916	−	0.736979i	$-0.736252\pi$
$487$	−29.8323	−1.35183	−0.675916	+	0.736979i	$0.736252\pi$
$488$	2.65385	0.120134
$489$	−41.8807	−1.89391
$490$	−0.476719	−0.0215359
$491$	29.2592	1.32045	0.660225	−	0.751068i	$-0.270461\pi$
$491$	29.2592	1.32045	0.660225	+	0.751068i	$0.270461\pi$
$492$	6.85320	0.308966
$493$	−6.87475	−0.309623
$494$	11.5221	0.518402
$495$	1.54979	0.0696577
$496$	−9.45961	−0.424749
$497$	−5.52288	−0.247735
$498$	−7.78521	−0.348863
$499$	18.4277	0.824936	0.412468	−	0.910972i	$-0.364667\pi$
$499$	18.4277	0.824936	0.412468	+	0.910972i	$0.364667\pi$
$500$	3.79284	0.169621
$501$	−43.1914	−1.92965
$502$	−17.6220	−0.786507
$503$	−1.62029	−0.0722453	−0.0361227	−	0.999347i	$-0.511501\pi$
$503$	−1.62029	−0.0722453	−0.0361227	+	0.999347i	$0.511501\pi$
$504$	−4.75005	−0.211584
$505$	−0.445151	−0.0198090
$506$	17.4733	0.776784
$507$	−3.73676	−0.165955
$508$	8.28410	0.367548
$509$	10.3626	0.459314	0.229657	−	0.973272i	$-0.426240\pi$
$509$	10.3626	0.459314	0.229657	+	0.973272i	$0.426240\pi$
$510$	−3.41743	−0.151326
$511$	−19.7786	−0.874954
$512$	1.00000	0.0441942
$513$	−8.71165	−0.384629
$514$	27.1176	1.19611
$515$	−0.388256	−0.0171086
$516$	−19.2355	−0.846795
$517$	14.2789	0.627985
$518$	4.67137	0.205248
$519$	−28.3197	−1.24310
$520$	1.47768	0.0648004
$521$	25.0693	1.09831	0.549154	−	0.835721i	$-0.314950\pi$
$521$	25.0693	1.09831	0.549154	+	0.835721i	$0.314950\pi$
$522$	2.76531	0.121034
$523$	−30.6444	−1.33998	−0.669992	−	0.742368i	$-0.733703\pi$
$523$	−30.6444	−1.33998	−0.669992	+	0.742368i	$0.733703\pi$
$524$	−0.747069	−0.0326358
$525$	−30.0453	−1.31128
$526$	−26.6465	−1.16184
$527$	38.9194	1.69536
$528$	5.24806	0.228392
$529$	28.6021	1.24357
$530$	3.64735	0.158431
$531$	19.8275	0.860440
$532$	8.61624	0.373562
$533$	12.1918	0.528085
$534$	5.87045	0.254039
$535$	−0.397516	−0.0171861
$536$	6.28220	0.271350
$537$	−8.19343	−0.353572
$538$	14.3669	0.619401
$539$	−3.01200	−0.129736
$540$	−1.11725	−0.0480787
$541$	21.1617	0.909811	0.454906	−	0.890540i	$-0.349673\pi$
$541$	21.1617	0.909811	0.454906	+	0.890540i	$0.349673\pi$
$542$	−13.4415	−0.577360
$543$	26.2784	1.12771
$544$	−4.11428	−0.176398
$545$	7.06410	0.302593
$546$	−23.7687	−1.01721
$547$	−0.835398	−0.0357191	−0.0178595	−	0.999841i	$-0.505685\pi$
$547$	−0.835398	−0.0357191	−0.0178595	+	0.999841i	$0.505685\pi$
$548$	−23.1978	−0.990960
$549$	4.39194	0.187443
$550$	11.8017	0.503225
$551$	−5.01607	−0.213692
$552$	15.4985	0.659661
$553$	35.8341	1.52382
$554$	16.2264	0.689395
$555$	−1.35186	−0.0573834
$556$	3.23932	0.137378
$557$	10.9244	0.462882	0.231441	−	0.972849i	$-0.425656\pi$
$557$	10.9244	0.462882	0.231441	+	0.972849i	$0.425656\pi$
$558$	−15.6550	−0.662730
$559$	−34.2197	−1.44734
$560$	1.10501	0.0466953
$561$	−21.5920	−0.911614
$562$	−20.0915	−0.847508
$563$	−41.9275	−1.76703	−0.883517	−	0.468399i	$-0.844831\pi$
$563$	−41.9275	−1.76703	−0.883517	+	0.468399i	$0.844831\pi$
$564$	12.6651	0.533298
$565$	5.22885	0.219979
$566$	17.9448	0.754276
$567$	32.2213	1.35317
$568$	1.92419	0.0807372
$569$	24.4528	1.02511	0.512557	−	0.858653i	$-0.328698\pi$
$569$	24.4528	1.02511	0.512557	+	0.858653i	$0.328698\pi$
$570$	−2.49348	−0.104440
$571$	−31.2732	−1.30874	−0.654371	−	0.756174i	$-0.727067\pi$
$571$	−31.2732	−1.30874	−0.654371	+	0.756174i	$0.727067\pi$
$572$	9.33625	0.390368
$573$	16.8962	0.705849
$574$	9.11706	0.380539
$575$	34.8526	1.45345
$576$	1.65493	0.0689556
$577$	15.6684	0.652286	0.326143	−	0.945321i	$-0.394251\pi$
$577$	15.6684	0.652286	0.326143	+	0.945321i	$0.394251\pi$
$578$	−0.0727174	−0.00302464
$579$	−31.6016	−1.31332
$580$	−0.643299	−0.0267115
$581$	−10.3569	−0.429678
$582$	13.1703	0.545926
$583$	23.0446	0.954411
$584$	6.89093	0.285149
$585$	2.44546	0.101107
$586$	−26.6923	−1.10265
$587$	−14.5106	−0.598918	−0.299459	−	0.954109i	$-0.596806\pi$
$587$	−14.5106	−0.598918	−0.299459	+	0.954109i	$0.596806\pi$
$588$	−2.67159	−0.110174
$589$	28.3971	1.17008
$590$	−4.61250	−0.189894
$591$	6.71104	0.276055
$592$	−1.62752	−0.0668907
$593$	32.8996	1.35102	0.675512	−	0.737349i	$-0.263923\pi$
$593$	32.8996	1.35102	0.675512	+	0.737349i	$0.263923\pi$
$594$	−7.05898	−0.289634
$595$	−4.54633	−0.186381
$596$	−3.71787	−0.152290
$597$	−5.75835	−0.235674
$598$	27.5717	1.12749
$599$	10.2296	0.417969	0.208985	−	0.977919i	$-0.432984\pi$
$599$	10.2296	0.417969	0.208985	+	0.977919i	$0.432984\pi$
$600$	10.4679	0.427349
$601$	−0.866931	−0.0353628	−0.0176814	−	0.999844i	$-0.505628\pi$
$601$	−0.866931	−0.0353628	−0.0176814	+	0.999844i	$0.505628\pi$
$602$	−25.5896	−1.04296
$603$	10.3966	0.423384
$604$	−0.385892	−0.0157017
$605$	1.95700	0.0795632
$606$	−2.49468	−0.101340
$607$	22.6189	0.918073	0.459037	−	0.888417i	$-0.348195\pi$
$607$	22.6189	0.918073	0.459037	+	0.888417i	$0.348195\pi$
$608$	−3.00193	−0.121744
$609$	10.3476	0.419304
$610$	−1.02170	−0.0413676
$611$	22.5311	0.911511
$612$	−6.80886	−0.275232
$613$	−22.0430	−0.890309	−0.445154	−	0.895454i	$-0.646851\pi$
$613$	−22.0430	−0.890309	−0.445154	+	0.895454i	$0.646851\pi$
$614$	−21.2766	−0.858654
$615$	−2.63841	−0.106391
$616$	6.98168	0.281300
$617$	−8.85897	−0.356649	−0.178324	−	0.983972i	$-0.557068\pi$
$617$	−8.85897	−0.356649	−0.178324	+	0.983972i	$0.557068\pi$
$618$	−2.17583	−0.0875248
$619$	−44.2087	−1.77690	−0.888448	−	0.458976i	$-0.848216\pi$
$619$	−44.2087	−1.77690	−0.888448	+	0.458976i	$0.848216\pi$
$620$	3.64185	0.146260
$621$	−20.8465	−0.836543
$622$	−5.52440	−0.221508
$623$	7.80966	0.312888
$624$	8.28108	0.331509
$625$	22.7987	0.911948
$626$	14.1743	0.566521
$627$	−15.7543	−0.629166
$628$	−10.2144	−0.407600
$629$	6.69607	0.266990
$630$	1.82872	0.0728581
$631$	39.7500	1.58242	0.791212	−	0.611542i	$-0.209450\pi$
$631$	39.7500	1.58242	0.791212	+	0.611542i	$0.209450\pi$
$632$	−12.4847	−0.496615
$633$	44.8333	1.78196
$634$	−17.8380	−0.708438
$635$	−3.18930	−0.126563
$636$	20.4402	0.810505
$637$	−4.75273	−0.188310
$638$	−4.06448	−0.160914
$639$	3.18441	0.125973
$640$	−0.384990	−0.0152181
$641$	−24.1051	−0.952096	−0.476048	−	0.879419i	$-0.657931\pi$
$641$	−24.1051	−0.952096	−0.476048	+	0.879419i	$0.657931\pi$
$642$	−2.22773	−0.0879214
$643$	39.4003	1.55380	0.776899	−	0.629626i	$-0.216792\pi$
$643$	39.4003	1.55380	0.776899	+	0.629626i	$0.216792\pi$
$644$	20.6182	0.812472
$645$	7.40547	0.291590
$646$	12.3508	0.485934
$647$	45.4137	1.78540	0.892698	−	0.450656i	$-0.148810\pi$
$647$	45.4137	1.78540	0.892698	+	0.450656i	$0.148810\pi$
$648$	−11.2260	−0.440999
$649$	−29.1427	−1.14395
$650$	18.6222	0.730424
$651$	−58.5798	−2.29592
$652$	19.4114	0.760210
$653$	26.0631	1.01993	0.509963	−	0.860196i	$-0.329659\pi$
$653$	26.0631	1.01993	0.509963	+	0.860196i	$0.329659\pi$
$654$	39.5881	1.54802
$655$	0.287614	0.0112380
$656$	−3.17641	−0.124018
$657$	11.4040	0.444914
$658$	16.8488	0.656836
$659$	12.3243	0.480088	0.240044	−	0.970762i	$-0.422838\pi$
$659$	12.3243	0.480088	0.240044	+	0.970762i	$0.422838\pi$
$660$	−2.02045	−0.0786459
$661$	−46.3746	−1.80376	−0.901881	−	0.431985i	$-0.857813\pi$
$661$	−46.3746	−1.80376	−0.901881	+	0.431985i	$0.857813\pi$
$662$	25.4838	0.990457
$663$	−34.0707	−1.32320
$664$	3.60839	0.140033
$665$	−3.31717	−0.128634
$666$	−2.69344	−0.104369
$667$	−12.0032	−0.464766
$668$	20.0189	0.774556
$669$	11.3232	0.437781
$670$	−2.41858	−0.0934381
$671$	−6.45532	−0.249205
$672$	6.19262	0.238886
$673$	−20.7612	−0.800285	−0.400143	−	0.916453i	$-0.631039\pi$
$673$	−20.7612	−0.800285	−0.400143	+	0.916453i	$0.631039\pi$
$674$	−1.81270	−0.0698224
$675$	−14.0800	−0.541938
$676$	1.73196	0.0666139
$677$	−38.7571	−1.48956	−0.744778	−	0.667313i	$-0.767444\pi$
$677$	−38.7571	−1.48956	−0.744778	+	0.667313i	$0.767444\pi$
$678$	29.3031	1.12538
$679$	17.5209	0.672391
$680$	1.58396	0.0607419
$681$	−34.9092	−1.33772
$682$	23.0099	0.881095
$683$	−4.64452	−0.177718	−0.0888589	−	0.996044i	$-0.528322\pi$
$683$	−4.64452	−0.177718	−0.0888589	+	0.996044i	$0.528322\pi$
$684$	−4.96799	−0.189956
$685$	8.93092	0.341233
$686$	16.5376	0.631407
$687$	37.1722	1.41821
$688$	8.91551	0.339901
$689$	36.3628	1.38531
$690$	−5.96678	−0.227151
$691$	−10.1261	−0.385216	−0.192608	−	0.981276i	$-0.561695\pi$
$691$	−10.1261	−0.385216	−0.192608	+	0.981276i	$0.561695\pi$
$692$	13.1260	0.498975
$693$	11.5542	0.438908
$694$	3.47753	0.132005
$695$	−1.24710	−0.0473053
$696$	−3.60512	−0.136652
$697$	13.0686	0.495010
$698$	−5.26605	−0.199323
$699$	−41.2388	−1.55979
$700$	13.9258	0.526345
$701$	9.76015	0.368636	0.184318	−	0.982867i	$-0.440992\pi$
$701$	9.76015	0.368636	0.184318	+	0.982867i	$0.440992\pi$
$702$	−11.1386	−0.420399
$703$	4.88570	0.184268
$704$	−2.43244	−0.0916760
$705$	−4.87594	−0.183639
$706$	0.918678	0.0345749
$707$	−3.31876	−0.124815
$708$	−25.8490	−0.971465
$709$	8.79718	0.330385	0.165193	−	0.986261i	$-0.447175\pi$
$709$	8.79718	0.330385	0.165193	+	0.986261i	$0.447175\pi$
$710$	−0.740793	−0.0278015
$711$	−20.6614	−0.774862
$712$	−2.72091	−0.101971
$713$	67.9527	2.54485
$714$	−25.4782	−0.953496
$715$	−3.59436	−0.134421
$716$	3.79760	0.141923
$717$	0.163036	0.00608870
$718$	−29.1422	−1.08758
$719$	2.46582	0.0919596	0.0459798	−	0.998942i	$-0.485359\pi$
$719$	2.46582	0.0919596	0.0459798	+	0.998942i	$0.485359\pi$
$720$	−0.637133	−0.0237445
$721$	−2.89458	−0.107800
$722$	−9.98843	−0.371731
$723$	−63.5746	−2.36437
$724$	−12.1799	−0.452661
$725$	−8.10708	−0.301089
$726$	10.9672	0.407033
$727$	−29.2352	−1.08427	−0.542137	−	0.840290i	$-0.682385\pi$
$727$	−29.2352	−1.08427	−0.542137	+	0.840290i	$0.682385\pi$
$728$	11.0166	0.408303
$729$	0.205295	0.00760350
$730$	−2.65294	−0.0981896
$731$	−36.6809	−1.35669
$732$	−5.72575	−0.211630
$733$	−21.4262	−0.791396	−0.395698	−	0.918381i	$-0.629497\pi$
$733$	−21.4262	−0.791396	−0.395698	+	0.918381i	$0.629497\pi$
$734$	4.73670	0.174835
$735$	1.02853	0.0379381
$736$	−7.18346	−0.264786
$737$	−15.2811	−0.562886
$738$	−5.25675	−0.193504
$739$	−6.44144	−0.236952	−0.118476	−	0.992957i	$-0.537801\pi$
$739$	−6.44144	−0.236952	−0.118476	+	0.992957i	$0.537801\pi$
$740$	0.626579	0.0230335
$741$	−24.8592	−0.913226
$742$	27.1923	0.998259
$743$	13.0494	0.478738	0.239369	−	0.970929i	$-0.423059\pi$
$743$	13.0494	0.478738	0.239369	+	0.970929i	$0.423059\pi$
$744$	20.4094	0.748244
$745$	1.43134	0.0524403
$746$	16.1256	0.590399
$747$	5.97165	0.218491
$748$	10.0077	0.365919
$749$	−2.96363	−0.108289
$750$	−8.18316	−0.298807
$751$	15.4619	0.564211	0.282106	−	0.959383i	$-0.408967\pi$
$751$	15.4619	0.564211	0.282106	+	0.959383i	$0.408967\pi$
$752$	−5.87019	−0.214064
$753$	38.0199	1.38552
$754$	−6.41348	−0.233565
$755$	0.148564	0.00540681
$756$	−8.32948	−0.302940
$757$	−40.5597	−1.47417	−0.737084	−	0.675801i	$-0.763798\pi$
$757$	−40.5597	−1.47417	−0.737084	+	0.675801i	$0.763798\pi$
$758$	14.7946	0.537365
$759$	−37.6992	−1.36840
$760$	1.15571	0.0419221
$761$	−46.0197	−1.66821	−0.834106	−	0.551605i	$-0.814016\pi$
$761$	−46.0197	−1.66821	−0.834106	+	0.551605i	$0.814016\pi$
$762$	−17.8732	−0.647478
$763$	52.6654	1.90662
$764$	−7.83127	−0.283325
$765$	2.62134	0.0947748
$766$	−12.7432	−0.460431
$767$	−45.9851	−1.66043
$768$	−2.15753	−0.0778531
$769$	7.04897	0.254192	0.127096	−	0.991890i	$-0.459434\pi$
$769$	7.04897	0.254192	0.127096	+	0.991890i	$0.459434\pi$
$770$	−2.68788	−0.0968643
$771$	−58.5071	−2.10708
$772$	14.6471	0.527162
$773$	−16.1663	−0.581460	−0.290730	−	0.956805i	$-0.593898\pi$
$773$	−16.1663	−0.581460	−0.290730	+	0.956805i	$0.593898\pi$
$774$	14.7546	0.530343
$775$	45.8960	1.64863
$776$	−6.10434	−0.219133
$777$	−10.0786	−0.361568
$778$	−29.4979	−1.05755
$779$	9.53536	0.341640
$780$	−3.18813	−0.114153
$781$	−4.68047	−0.167480
$782$	29.5548	1.05688
$783$	4.84913	0.173294
$784$	1.23826	0.0442237
$785$	3.93245	0.140355
$786$	1.61182	0.0574918
$787$	30.6760	1.09348	0.546741	−	0.837301i	$-0.315868\pi$
$787$	30.6760	1.09348	0.546741	+	0.837301i	$0.315868\pi$
$788$	−3.11052	−0.110808
$789$	57.4907	2.04672
$790$	4.80649	0.171007
$791$	38.9830	1.38607
$792$	−4.02553	−0.143041
$793$	−10.1861	−0.361717
$794$	−1.37947	−0.0489554
$795$	−7.86926	−0.279094
$796$	2.66896	0.0945986
$797$	10.3338	0.366043	0.183022	−	0.983109i	$-0.441412\pi$
$797$	10.3338	0.366043	0.183022	+	0.983109i	$0.441412\pi$
$798$	−18.5898	−0.658072
$799$	24.1516	0.854422
$800$	−4.85178	−0.171536
$801$	−4.50293	−0.159103
$802$	14.0154	0.494903
$803$	−16.7618	−0.591510
$804$	−13.5540	−0.478014
$805$	−7.93781	−0.279771
$806$	36.3081	1.27890
$807$	−30.9970	−1.09115
$808$	1.15627	0.0406774
$809$	−30.2519	−1.06360	−0.531800	−	0.846870i	$-0.678484\pi$
$809$	−30.2519	−1.06360	−0.531800	+	0.846870i	$0.678484\pi$
$810$	4.32190	0.151856
$811$	18.3429	0.644106	0.322053	−	0.946722i	$-0.395627\pi$
$811$	18.3429	0.644106	0.322053	+	0.946722i	$0.395627\pi$
$812$	−4.79602	−0.168307
$813$	29.0004	1.01709
$814$	3.95884	0.138757
$815$	−7.47321	−0.261775
$816$	8.87668	0.310746
$817$	−26.7637	−0.936344
$818$	−22.1596	−0.774791
$819$	18.2318	0.637070
$820$	1.22289	0.0427050
$821$	−25.3803	−0.885779	−0.442890	−	0.896576i	$-0.646047\pi$
$821$	−25.3803	−0.885779	−0.442890	+	0.896576i	$0.646047\pi$
$822$	50.0499	1.74569
$823$	−48.5642	−1.69284	−0.846421	−	0.532514i	$-0.821247\pi$
$823$	−48.5642	−1.69284	−0.846421	+	0.532514i	$0.821247\pi$
$824$	1.00848	0.0351322
$825$	−25.4624	−0.886488
$826$	−34.3878	−1.19651
$827$	−26.4216	−0.918770	−0.459385	−	0.888237i	$-0.651930\pi$
$827$	−26.4216	−0.918770	−0.459385	+	0.888237i	$0.651930\pi$
$828$	−11.8882	−0.413142
$829$	−25.6207	−0.889844	−0.444922	−	0.895569i	$-0.646769\pi$
$829$	−25.6207	−0.889844	−0.444922	+	0.895569i	$0.646769\pi$
$830$	−1.38919	−0.0482196
$831$	−35.0090	−1.21445
$832$	−3.83822	−0.133066
$833$	−5.09456	−0.176516
$834$	−6.98892	−0.242007
$835$	−7.70709	−0.266715
$836$	7.30201	0.252545
$837$	−27.4520	−0.948879
$838$	−24.5838	−0.849234
$839$	24.8277	0.857147	0.428574	−	0.903507i	$-0.359016\pi$
$839$	24.8277	0.857147	0.428574	+	0.903507i	$0.359016\pi$
$840$	−2.38410	−0.0822592
$841$	−26.2079	−0.903722
$842$	−40.0808	−1.38128
$843$	43.3480	1.49298
$844$	−20.7799	−0.715275
$845$	−0.666788	−0.0229382
$846$	−9.71478	−0.334001
$847$	14.5901	0.501322
$848$	−9.47387	−0.325334
$849$	−38.7164	−1.32874
$850$	19.9616	0.684677
$851$	11.6912	0.400770
$852$	−4.15149	−0.142228
$853$	−4.04711	−0.138571	−0.0692853	−	0.997597i	$-0.522072\pi$
$853$	−4.04711	−0.138571	−0.0692853	+	0.997597i	$0.522072\pi$
$854$	−7.61717	−0.260654
$855$	1.91263	0.0654105
$856$	1.03254	0.0352914
$857$	0.598709	0.0204515	0.0102257	−	0.999948i	$-0.496745\pi$
$857$	0.598709	0.0204515	0.0102257	+	0.999948i	$0.496745\pi$
$858$	−20.1432	−0.687678
$859$	8.10527	0.276548	0.138274	−	0.990394i	$-0.455844\pi$
$859$	8.10527	0.276548	0.138274	+	0.990394i	$0.455844\pi$
$860$	−3.43238	−0.117043
$861$	−19.6703	−0.670363
$862$	−7.79687	−0.265563
$863$	5.64722	0.192234	0.0961169	−	0.995370i	$-0.469358\pi$
$863$	5.64722	0.192234	0.0961169	+	0.995370i	$0.469358\pi$
$864$	2.90202	0.0987287
$865$	−5.05337	−0.171820
$866$	22.2054	0.754571
$867$	0.156890	0.00532826
$868$	27.1513	0.921576
$869$	30.3683	1.03017
$870$	1.38794	0.0470554
$871$	−24.1125	−0.817021
$872$	−18.3488	−0.621369
$873$	−10.1023	−0.341910
$874$	21.5642	0.729421
$875$	−10.8863	−0.368026
$876$	−14.8674	−0.502322
$877$	−32.5149	−1.09795	−0.548975	−	0.835839i	$-0.684982\pi$
$877$	−32.5149	−1.09795	−0.548975	+	0.835839i	$0.684982\pi$
$878$	33.0204	1.11439
$879$	57.5895	1.94245
$880$	0.936464	0.0315682
$881$	−18.8819	−0.636146	−0.318073	−	0.948066i	$-0.603036\pi$
$881$	−18.8819	−0.636146	−0.318073	+	0.948066i	$0.603036\pi$
$882$	2.04924	0.0690016
$883$	−29.6567	−0.998027	−0.499013	−	0.866594i	$-0.666304\pi$
$883$	−29.6567	−0.998027	−0.499013	+	0.866594i	$0.666304\pi$
$884$	15.7915	0.531126
$885$	9.95161	0.334520
$886$	13.2396	0.444794
$887$	−17.2055	−0.577705	−0.288852	−	0.957374i	$-0.593274\pi$
$887$	−17.2055	−0.577705	−0.288852	+	0.957374i	$0.593274\pi$
$888$	3.51142	0.117836
$889$	−23.7773	−0.797466
$890$	1.04752	0.0351131
$891$	27.3065	0.914804
$892$	−5.24824	−0.175724
$893$	17.6219	0.589694
$894$	8.02141	0.268276
$895$	−1.46204	−0.0488705
$896$	−2.87024	−0.0958879
$897$	−59.4868	−1.98621
$898$	−24.0015	−0.800941
$899$	−15.8065	−0.527177
$900$	−8.02938	−0.267646
$901$	38.9781	1.29855
$902$	7.72643	0.257262
$903$	55.2104	1.83729
$904$	−13.5818	−0.451724
$905$	4.68912	0.155872
$906$	0.832573	0.0276604
$907$	−48.4361	−1.60829	−0.804147	−	0.594430i	$-0.797378\pi$
$907$	−48.4361	−1.60829	−0.804147	+	0.594430i	$0.797378\pi$
$908$	16.1802	0.536957
$909$	1.91355	0.0634683
$910$	−4.24129	−0.140597
$911$	−19.3652	−0.641598	−0.320799	−	0.947147i	$-0.603951\pi$
$911$	−19.3652	−0.641598	−0.320799	+	0.947147i	$0.603951\pi$
$912$	6.47675	0.214467
$913$	−8.77719	−0.290482
$914$	8.37371	0.276978
$915$	2.20436	0.0728738
$916$	−17.2291	−0.569264
$917$	2.14426	0.0708099
$918$	−11.9397	−0.394069
$919$	47.1684	1.55594	0.777971	−	0.628300i	$-0.216249\pi$
$919$	47.1684	1.55594	0.777971	+	0.628300i	$0.216249\pi$
$920$	2.76556	0.0911778
$921$	45.9049	1.51262
$922$	31.7374	1.04522
$923$	−7.38547	−0.243096
$924$	−15.0632	−0.495542
$925$	7.89637	0.259631
$926$	−15.0911	−0.495923
$927$	1.66897	0.0548162
$928$	1.67095	0.0548516
$929$	−9.42015	−0.309065	−0.154532	−	0.987988i	$-0.549387\pi$
$929$	−9.42015	−0.309065	−0.154532	+	0.987988i	$0.549387\pi$
$930$	−7.85741	−0.257654
$931$	−3.71717	−0.121825
$932$	19.1139	0.626097
$933$	11.9191	0.390212
$934$	25.3281	0.828760
$935$	−3.85288	−0.126002
$936$	−6.35201	−0.207622
$937$	−11.2662	−0.368051	−0.184026	−	0.982921i	$-0.558913\pi$
$937$	−11.2662	−0.368051	−0.184026	+	0.982921i	$0.558913\pi$
$938$	−18.0314	−0.588747
$939$	−30.5816	−0.997992
$940$	2.25997	0.0737119
$941$	3.66928	0.119615	0.0598076	−	0.998210i	$-0.480951\pi$
$941$	3.66928	0.119615	0.0598076	+	0.998210i	$0.480951\pi$
$942$	22.0379	0.718035
$943$	22.8176	0.743044
$944$	11.9808	0.389943
$945$	3.20677	0.104316
$946$	−21.6864	−0.705087
$947$	−22.2061	−0.721603	−0.360801	−	0.932643i	$-0.617497\pi$
$947$	−22.2061	−0.721603	−0.360801	+	0.932643i	$0.617497\pi$
$948$	26.9361	0.874845
$949$	−26.4489	−0.858568
$950$	14.5647	0.472541
$951$	38.4861	1.24800
$952$	11.8090	0.382730
$953$	−4.97579	−0.161182	−0.0805908	−	0.996747i	$-0.525681\pi$
$953$	−4.97579	−0.161182	−0.0805908	+	0.996747i	$0.525681\pi$
$954$	−15.6786	−0.507615
$955$	3.01496	0.0975618
$956$	−0.0755661	−0.00244398
$957$	8.76924	0.283469
$958$	−10.2215	−0.330243
$959$	66.5832	2.15008
$960$	0.830627	0.0268084
$961$	58.4841	1.88659
$962$	6.24679	0.201404
$963$	1.70878	0.0550647
$964$	29.4664	0.949049
$965$	−5.63900	−0.181526
$966$	−44.4845	−1.43126
$967$	−44.1567	−1.41998	−0.709992	−	0.704210i	$-0.751301\pi$
$967$	−44.1567	−1.41998	−0.709992	+	0.704210i	$0.751301\pi$
$968$	−5.08324	−0.163382
$969$	−26.6471	−0.856029
$970$	2.35011	0.0754575
$971$	20.5052	0.658044	0.329022	−	0.944322i	$-0.393281\pi$
$971$	20.5052	0.658044	0.329022	+	0.944322i	$0.393281\pi$
$972$	15.5144	0.497623
$973$	−9.29761	−0.298068
$974$	−29.8323	−0.955889
$975$	−40.1780	−1.28673
$976$	2.65385	0.0849476
$977$	−11.7096	−0.374624	−0.187312	−	0.982300i	$-0.559978\pi$
$977$	−11.7096	−0.374624	−0.187312	+	0.982300i	$0.559978\pi$
$978$	−41.8807	−1.33920
$979$	6.61845	0.211527
$980$	−0.476719	−0.0152282
$981$	−30.3661	−0.969514
$982$	29.2592	0.933699
$983$	44.9891	1.43493	0.717465	−	0.696594i	$-0.245302\pi$
$983$	44.9891	1.43493	0.717465	+	0.696594i	$0.245302\pi$
$984$	6.85320	0.218472
$985$	1.19752	0.0381561
$986$	−6.87475	−0.218937
$987$	−36.3519	−1.15709
$988$	11.5221	0.366566
$989$	−64.0442	−2.03649
$990$	1.54979	0.0492555
$991$	−19.4032	−0.616362	−0.308181	−	0.951328i	$-0.599720\pi$
$991$	−19.4032	−0.616362	−0.308181	+	0.951328i	$0.599720\pi$
$992$	−9.45961	−0.300343
$993$	−54.9821	−1.74480
$994$	−5.52288	−0.175175
$995$	−1.02752	−0.0325746
$996$	−7.78521	−0.246684
$997$	−37.0339	−1.17287	−0.586437	−	0.809995i	$-0.699470\pi$
$997$	−37.0339	−1.17287	−0.586437	+	0.809995i	$0.699470\pi$
$998$	18.4277	0.583318
$999$	−4.72309	−0.149432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8038.2.a.d.1.16	✓	92

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8038.2.a.d.1.16	✓	92	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8038 = 2 \cdot 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.15753 q^{3} +1.00000 q^{4} -0.384990 q^{5} -2.15753 q^{6} -2.87024 q^{7} +1.00000 q^{8} +1.65493 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.15753 q^{3} +1.00000 q^{4} -0.384990 q^{5} -2.15753 q^{6} -2.87024 q^{7} +1.00000 q^{8} +1.65493 q^{9} -0.384990 q^{10} -2.43244 q^{11} -2.15753 q^{12} -3.83822 q^{13} -2.87024 q^{14} +0.830627 q^{15} +1.00000 q^{16} -4.11428 q^{17} +1.65493 q^{18} -3.00193 q^{19} -0.384990 q^{20} +6.19262 q^{21} -2.43244 q^{22} -7.18346 q^{23} -2.15753 q^{24} -4.85178 q^{25} -3.83822 q^{26} +2.90202 q^{27} -2.87024 q^{28} +1.67095 q^{29} +0.830627 q^{30} -9.45961 q^{31} +1.00000 q^{32} +5.24806 q^{33} -4.11428 q^{34} +1.10501 q^{35} +1.65493 q^{36} -1.62752 q^{37} -3.00193 q^{38} +8.28108 q^{39} -0.384990 q^{40} -3.17641 q^{41} +6.19262 q^{42} +8.91551 q^{43} -2.43244 q^{44} -0.637133 q^{45} -7.18346 q^{46} -5.87019 q^{47} -2.15753 q^{48} +1.23826 q^{49} -4.85178 q^{50} +8.87668 q^{51} -3.83822 q^{52} -9.47387 q^{53} +2.90202 q^{54} +0.936464 q^{55} -2.87024 q^{56} +6.47675 q^{57} +1.67095 q^{58} +11.9808 q^{59} +0.830627 q^{60} +2.65385 q^{61} -9.45961 q^{62} -4.75005 q^{63} +1.00000 q^{64} +1.47768 q^{65} +5.24806 q^{66} +6.28220 q^{67} -4.11428 q^{68} +15.4985 q^{69} +1.10501 q^{70} +1.92419 q^{71} +1.65493 q^{72} +6.89093 q^{73} -1.62752 q^{74} +10.4679 q^{75} -3.00193 q^{76} +6.98168 q^{77} +8.28108 q^{78} -12.4847 q^{79} -0.384990 q^{80} -11.2260 q^{81} -3.17641 q^{82} +3.60839 q^{83} +6.19262 q^{84} +1.58396 q^{85} +8.91551 q^{86} -3.60512 q^{87} -2.43244 q^{88} -2.72091 q^{89} -0.637133 q^{90} +11.0166 q^{91} -7.18346 q^{92} +20.4094 q^{93} -5.87019 q^{94} +1.15571 q^{95} -2.15753 q^{96} -6.10434 q^{97} +1.23826 q^{98} -4.02553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9}+O(q^{10}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9	\( 92 q + 92 q^{2} + 31 q^{3} + 92 q^{4} + 28 q^{5} + 31 q^{6} + 29 q^{7} + 92 q^{8} + 113 q^{9} + 28 q^{10} + 37 q^{11} + 31 q^{12} + 20 q^{13} + 29 q^{14} + 30 q^{15} + 92 q^{16} + 52 q^{17} + 113 q^{18} + 61 q^{19} + 28 q^{20} + 5 q^{21} + 37 q^{22} + 71 q^{23} + 31 q^{24} + 118 q^{25} + 20 q^{26} + 112 q^{27} + 29 q^{28} + 30 q^{29} + 30 q^{30} + 89 q^{31} + 92 q^{32} + 52 q^{33} + 52 q^{34} + 58 q^{35} + 113 q^{36} + 15 q^{37} + 61 q^{38} + 43 q^{39} + 28 q^{40} + 75 q^{41} + 5 q^{42} + 46 q^{43} + 37 q^{44} + 63 q^{45} + 71 q^{46} + 92 q^{47} + 31 q^{48} + 131 q^{49} + 118 q^{50} + 45 q^{51} + 20 q^{52} + 72 q^{53} + 112 q^{54} + 86 q^{55} + 29 q^{56} + 44 q^{57} + 30 q^{58} + 95 q^{59} + 30 q^{60} - 4 q^{61} + 89 q^{62} + 67 q^{63} + 92 q^{64} + 55 q^{65} + 52 q^{66} + 40 q^{67} + 52 q^{68} + 25 q^{69} + 58 q^{70} + 84 q^{71} + 113 q^{72} + 87 q^{73} + 15 q^{74} + 132 q^{75} + 61 q^{76} + 96 q^{77} + 43 q^{78} + 68 q^{79} + 28 q^{80} + 156 q^{81} + 75 q^{82} + 120 q^{83} + 5 q^{84} - 14 q^{85} + 46 q^{86} + 73 q^{87} + 37 q^{88} + 86 q^{89} + 63 q^{90} + 93 q^{91} + 71 q^{92} + 29 q^{93} + 92 q^{94} + 67 q^{95} + 31 q^{96} + 65 q^{97} + 131 q^{98} + 94 q^{99}+O(q^{100}) \) 92 * q + 92 * q^2 + 31 * q^3 + 92 * q^4 + 28 * q^5 + 31 * q^6 + 29 * q^7 + 92 * q^8 + 113 * q^9 + 28 * q^10 + 37 * q^11 + 31 * q^12 + 20 * q^13 + 29 * q^14 + 30 * q^15 + 92 * q^16 + 52 * q^17 + 113 * q^18 + 61 * q^19 + 28 * q^20 + 5 * q^21 + 37 * q^22 + 71 * q^23 + 31 * q^24 + 118 * q^25 + 20 * q^26 + 112 * q^27 + 29 * q^28 + 30 * q^29 + 30 * q^30 + 89 * q^31 + 92 * q^32 + 52 * q^33 + 52 * q^34 + 58 * q^35 + 113 * q^36 + 15 * q^37 + 61 * q^38 + 43 * q^39 + 28 * q^40 + 75 * q^41 + 5 * q^42 + 46 * q^43 + 37 * q^44 + 63 * q^45 + 71 * q^46 + 92 * q^47 + 31 * q^48 + 131 * q^49 + 118 * q^50 + 45 * q^51 + 20 * q^52 + 72 * q^53 + 112 * q^54 + 86 * q^55 + 29 * q^56 + 44 * q^57 + 30 * q^58 + 95 * q^59 + 30 * q^60 - 4 * q^61 + 89 * q^62 + 67 * q^63 + 92 * q^64 + 55 * q^65 + 52 * q^66 + 40 * q^67 + 52 * q^68 + 25 * q^69 + 58 * q^70 + 84 * q^71 + 113 * q^72 + 87 * q^73 + 15 * q^74 + 132 * q^75 + 61 * q^76 + 96 * q^77 + 43 * q^78 + 68 * q^79 + 28 * q^80 + 156 * q^81 + 75 * q^82 + 120 * q^83 + 5 * q^84 - 14 * q^85 + 46 * q^86 + 73 * q^87 + 37 * q^88 + 86 * q^89 + 63 * q^90 + 93 * q^91 + 71 * q^92 + 29 * q^93 + 92 * q^94 + 67 * q^95 + 31 * q^96 + 65 * q^97 + 131 * q^98 + 94 * q^99

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