LMFDB - Embedded newform 8039.2.a.a.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.55932 q^{2} -0.558527 q^{3} +4.55013 q^{4} +0.514137 q^{5} +1.42945 q^{6} +2.79738 q^{7} -6.52662 q^{8} -2.68805 q^{9} +O(q^{10})$	\(q-2.55932 q^{2} -0.558527 q^{3} +4.55013 q^{4} +0.514137 q^{5} +1.42945 q^{6} +2.79738 q^{7} -6.52662 q^{8} -2.68805 q^{9} -1.31584 q^{10} +5.72615 q^{11} -2.54137 q^{12} -2.25357 q^{13} -7.15939 q^{14} -0.287159 q^{15} +7.60346 q^{16} -5.96241 q^{17} +6.87958 q^{18} -3.07089 q^{19} +2.33939 q^{20} -1.56241 q^{21} -14.6551 q^{22} +1.34199 q^{23} +3.64529 q^{24} -4.73566 q^{25} +5.76762 q^{26} +3.17693 q^{27} +12.7284 q^{28} -5.47079 q^{29} +0.734933 q^{30} -1.13081 q^{31} -6.40647 q^{32} -3.19821 q^{33} +15.2597 q^{34} +1.43823 q^{35} -12.2310 q^{36} +3.49632 q^{37} +7.85939 q^{38} +1.25868 q^{39} -3.35557 q^{40} +0.914864 q^{41} +3.99871 q^{42} +10.6855 q^{43} +26.0547 q^{44} -1.38202 q^{45} -3.43459 q^{46} +0.844776 q^{47} -4.24673 q^{48} +0.825313 q^{49} +12.1201 q^{50} +3.33016 q^{51} -10.2541 q^{52} +6.84265 q^{53} -8.13078 q^{54} +2.94402 q^{55} -18.2574 q^{56} +1.71517 q^{57} +14.0015 q^{58} +11.3389 q^{59} -1.30661 q^{60} +5.06197 q^{61} +2.89412 q^{62} -7.51948 q^{63} +1.18930 q^{64} -1.15864 q^{65} +8.18524 q^{66} -13.7596 q^{67} -27.1298 q^{68} -0.749538 q^{69} -3.68091 q^{70} -8.59825 q^{71} +17.5439 q^{72} -1.69293 q^{73} -8.94821 q^{74} +2.64500 q^{75} -13.9730 q^{76} +16.0182 q^{77} -3.22137 q^{78} -3.26461 q^{79} +3.90922 q^{80} +6.28974 q^{81} -2.34143 q^{82} +2.92348 q^{83} -7.10917 q^{84} -3.06549 q^{85} -27.3477 q^{86} +3.05559 q^{87} -37.3724 q^{88} -0.0821052 q^{89} +3.53705 q^{90} -6.30409 q^{91} +6.10624 q^{92} +0.631590 q^{93} -2.16205 q^{94} -1.57886 q^{95} +3.57818 q^{96} -4.63719 q^{97} -2.11224 q^{98} -15.3922 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * 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 $

$2$	−2.55932	−1.80971	−0.904857	−	0.425715i	$-0.860023\pi$
$2$	−2.55932	−1.80971	−0.904857	+	0.425715i	$0.860023\pi$
$3$	−0.558527	−0.322466	−0.161233	−	0.986916i	$-0.551547\pi$
$3$	−0.558527	−0.322466	−0.161233	+	0.986916i	$0.551547\pi$
$4$	4.55013	2.27507
$5$	0.514137	0.229929	0.114964	−	0.993370i	$-0.463325\pi$
$5$	0.514137	0.229929	0.114964	+	0.993370i	$0.463325\pi$
$6$	1.42945	0.583571
$7$	2.79738	1.05731	0.528654	−	0.848837i	$-0.322697\pi$
$7$	2.79738	1.05731	0.528654	+	0.848837i	$0.322697\pi$
$8$	−6.52662	−2.30751
$9$	−2.68805	−0.896016
$10$	−1.31584	−0.416106
$11$	5.72615	1.72650	0.863249	−	0.504778i	$-0.168426\pi$
$11$	5.72615	1.72650	0.863249	+	0.504778i	$0.168426\pi$
$12$	−2.54137	−0.733631
$13$	−2.25357	−0.625028	−0.312514	−	0.949913i	$-0.601171\pi$
$13$	−2.25357	−0.625028	−0.312514	+	0.949913i	$0.601171\pi$
$14$	−7.15939	−1.91343
$15$	−0.287159	−0.0741442
$16$	7.60346	1.90086
$17$	−5.96241	−1.44610	−0.723048	−	0.690798i	$-0.757260\pi$
$17$	−5.96241	−1.44610	−0.723048	+	0.690798i	$0.757260\pi$
$18$	6.87958	1.62153
$19$	−3.07089	−0.704510	−0.352255	−	0.935904i	$-0.614585\pi$
$19$	−3.07089	−0.704510	−0.352255	+	0.935904i	$0.614585\pi$
$20$	2.33939	0.523104
$21$	−1.56241	−0.340946
$22$	−14.6551	−3.12447
$23$	1.34199	0.279824	0.139912	−	0.990164i	$-0.455318\pi$
$23$	1.34199	0.279824	0.139912	+	0.990164i	$0.455318\pi$
$24$	3.64529	0.744092
$25$	−4.73566	−0.947133
$26$	5.76762	1.13112
$27$	3.17693	0.611400
$28$	12.7284	2.40545
$29$	−5.47079	−1.01590	−0.507951	−	0.861386i	$-0.669597\pi$
$29$	−5.47079	−1.01590	−0.507951	+	0.861386i	$0.669597\pi$
$30$	0.734933	0.134180
$31$	−1.13081	−0.203100	−0.101550	−	0.994830i	$-0.532380\pi$
$31$	−1.13081	−0.203100	−0.101550	+	0.994830i	$0.532380\pi$
$32$	−6.40647	−1.13251
$33$	−3.19821	−0.556736
$34$	15.2597	2.61702
$35$	1.43823	0.243106
$36$	−12.2310	−2.03850
$37$	3.49632	0.574791	0.287396	−	0.957812i	$-0.407211\pi$
$37$	3.49632	0.574791	0.287396	+	0.957812i	$0.407211\pi$
$38$	7.85939	1.27496
$39$	1.25868	0.201550
$40$	−3.35557	−0.530563
$41$	0.914864	0.142878	0.0714389	−	0.997445i	$-0.477241\pi$
$41$	0.914864	0.142878	0.0714389	+	0.997445i	$0.477241\pi$
$42$	3.99871	0.617015
$43$	10.6855	1.62953	0.814763	−	0.579795i	$-0.196867\pi$
$43$	10.6855	1.62953	0.814763	+	0.579795i	$0.196867\pi$
$44$	26.0547	3.92790
$45$	−1.38202	−0.206020
$46$	−3.43459	−0.506402
$47$	0.844776	0.123223	0.0616116	−	0.998100i	$-0.480376\pi$
$47$	0.844776	0.123223	0.0616116	+	0.998100i	$0.480376\pi$
$48$	−4.24673	−0.612963
$49$	0.825313	0.117902
$50$	12.1201	1.71404
$51$	3.33016	0.466316
$52$	−10.2541	−1.42198
$53$	6.84265	0.939910	0.469955	−	0.882690i	$-0.344270\pi$
$53$	6.84265	0.939910	0.469955	+	0.882690i	$0.344270\pi$
$54$	−8.13078	−1.10646
$55$	2.94402	0.396972
$56$	−18.2574	−2.43975
$57$	1.71517	0.227180
$58$	14.0015	1.83849
$59$	11.3389	1.47620	0.738101	−	0.674691i	$-0.235723\pi$
$59$	11.3389	1.47620	0.738101	+	0.674691i	$0.235723\pi$
$60$	−1.30661	−0.168683
$61$	5.06197	0.648119	0.324060	−	0.946037i	$-0.394952\pi$
$61$	5.06197	0.648119	0.324060	+	0.946037i	$0.394952\pi$
$62$	2.89412	0.367553
$63$	−7.51948	−0.947365
$64$	1.18930	0.148663
$65$	−1.15864	−0.143712
$66$	8.18524	1.00753
$67$	−13.7596	−1.68100	−0.840500	−	0.541811i	$-0.817739\pi$
$67$	−13.7596	−1.68100	−0.840500	+	0.541811i	$0.817739\pi$
$68$	−27.1298	−3.28997
$69$	−0.749538	−0.0902338
$70$	−3.68091	−0.439952
$71$	−8.59825	−1.02043	−0.510213	−	0.860048i	$-0.670433\pi$
$71$	−8.59825	−1.02043	−0.510213	+	0.860048i	$0.670433\pi$
$72$	17.5439	2.06756
$73$	−1.69293	−0.198143	−0.0990713	−	0.995080i	$-0.531587\pi$
$73$	−1.69293	−0.198143	−0.0990713	+	0.995080i	$0.531587\pi$
$74$	−8.94821	−1.04021
$75$	2.64500	0.305418
$76$	−13.9730	−1.60281
$77$	16.0182	1.82544
$78$	−3.22137	−0.364748
$79$	−3.26461	−0.367297	−0.183649	−	0.982992i	$-0.558791\pi$
$79$	−3.26461	−0.367297	−0.183649	+	0.982992i	$0.558791\pi$
$80$	3.90922	0.437064
$81$	6.28974	0.698860
$82$	−2.34143	−0.258568
$83$	2.92348	0.320894	0.160447	−	0.987044i	$-0.448706\pi$
$83$	2.92348	0.320894	0.160447	+	0.987044i	$0.448706\pi$
$84$	−7.10917	−0.775675
$85$	−3.06549	−0.332499
$86$	−27.3477	−2.94898
$87$	3.05559	0.327593
$88$	−37.3724	−3.98391
$89$	−0.0821052	−0.00870313	−0.00435157	−	0.999991i	$-0.501385\pi$
$89$	−0.0821052	−0.00870313	−0.00435157	+	0.999991i	$0.501385\pi$
$90$	3.53705	0.372837
$91$	−6.30409	−0.660848
$92$	6.10624	0.636619
$93$	0.631590	0.0654928
$94$	−2.16205	−0.222999
$95$	−1.57886	−0.161987
$96$	3.57818	0.365197
$97$	−4.63719	−0.470836	−0.235418	−	0.971894i	$-0.575646\pi$
$97$	−4.63719	−0.470836	−0.235418	+	0.971894i	$0.575646\pi$
$98$	−2.11224	−0.213369
$99$	−15.3922	−1.54697
$100$	−21.5479	−2.15479
$101$	12.7960	1.27325	0.636626	−	0.771172i	$-0.280329\pi$
$101$	12.7960	1.27325	0.636626	+	0.771172i	$0.280329\pi$
$102$	−8.52297	−0.843900
$103$	0.361117	0.0355819	0.0177909	−	0.999842i	$-0.494337\pi$
$103$	0.361117	0.0355819	0.0177909	+	0.999842i	$0.494337\pi$
$104$	14.7082	1.44226
$105$	−0.803292	−0.0783933
$106$	−17.5125	−1.70097
$107$	3.19426	0.308801	0.154400	−	0.988008i	$-0.450655\pi$
$107$	3.19426	0.308801	0.154400	+	0.988008i	$0.450655\pi$
$108$	14.4554	1.39098
$109$	4.24746	0.406832	0.203416	−	0.979092i	$-0.434796\pi$
$109$	4.24746	0.406832	0.203416	+	0.979092i	$0.434796\pi$
$110$	−7.53470	−0.718406
$111$	−1.95279	−0.185350
$112$	21.2697	2.00980
$113$	11.1175	1.04585	0.522923	−	0.852380i	$-0.324841\pi$
$113$	11.1175	1.04585	0.522923	+	0.852380i	$0.324841\pi$
$114$	−4.38968	−0.411131
$115$	0.689967	0.0643397
$116$	−24.8929	−2.31124
$117$	6.05771	0.560035
$118$	−29.0200	−2.67150
$119$	−16.6791	−1.52897
$120$	1.87418	0.171088
$121$	21.7887	1.98079
$122$	−12.9552	−1.17291
$123$	−0.510976	−0.0460732
$124$	−5.14535	−0.462066
$125$	−5.00546	−0.447702
$126$	19.2448	1.71446
$127$	2.56038	0.227197	0.113598	−	0.993527i	$-0.463762\pi$
$127$	2.56038	0.227197	0.113598	+	0.993527i	$0.463762\pi$
$128$	9.76913	0.863477
$129$	−5.96815	−0.525466
$130$	2.96535	0.260078
$131$	−21.2275	−1.85465	−0.927327	−	0.374251i	$-0.877900\pi$
$131$	−21.2275	−1.85465	−0.927327	+	0.374251i	$0.877900\pi$
$132$	−14.5523	−1.26661
$133$	−8.59043	−0.744885
$134$	35.2152	3.04213
$135$	1.63338	0.140579
$136$	38.9144	3.33688
$137$	5.61163	0.479434	0.239717	−	0.970843i	$-0.422945\pi$
$137$	5.61163	0.479434	0.239717	+	0.970843i	$0.422945\pi$
$138$	1.91831	0.163297
$139$	−1.49818	−0.127074	−0.0635370	−	0.997979i	$-0.520238\pi$
$139$	−1.49818	−0.127074	−0.0635370	+	0.997979i	$0.520238\pi$
$140$	6.54416	0.553082
$141$	−0.471830	−0.0397353
$142$	22.0057	1.84668
$143$	−12.9043	−1.07911
$144$	−20.4385	−1.70320
$145$	−2.81274	−0.233585
$146$	4.33276	0.358582
$147$	−0.460959	−0.0380193
$148$	15.9087	1.30769
$149$	−9.14644	−0.749306	−0.374653	−	0.927165i	$-0.622238\pi$
$149$	−9.14644	−0.749306	−0.374653	+	0.927165i	$0.622238\pi$
$150$	−6.76940	−0.552719
$151$	0.931237	0.0757830	0.0378915	−	0.999282i	$-0.487936\pi$
$151$	0.931237	0.0757830	0.0378915	+	0.999282i	$0.487936\pi$
$152$	20.0425	1.62566
$153$	16.0272	1.29573
$154$	−40.9957	−3.30353
$155$	−0.581393	−0.0466986
$156$	5.72717	0.458540
$157$	−15.9422	−1.27232	−0.636162	−	0.771555i	$-0.719479\pi$
$157$	−15.9422	−1.27232	−0.636162	+	0.771555i	$0.719479\pi$
$158$	8.35519	0.664703
$159$	−3.82180	−0.303089
$160$	−3.29380	−0.260398
$161$	3.75405	0.295861
$162$	−16.0975	−1.26474
$163$	−19.2104	−1.50468	−0.752338	−	0.658777i	$-0.771074\pi$
$163$	−19.2104	−1.50468	−0.752338	+	0.658777i	$0.771074\pi$
$164$	4.16275	0.325056
$165$	−1.64432	−0.128010
$166$	−7.48214	−0.580726
$167$	21.2817	1.64683	0.823415	−	0.567440i	$-0.192066\pi$
$167$	21.2817	1.64683	0.823415	+	0.567440i	$0.192066\pi$
$168$	10.1973	0.786735
$169$	−7.92141	−0.609339
$170$	7.84559	0.601729
$171$	8.25469	0.631252
$172$	48.6205	3.70728
$173$	−23.3425	−1.77470	−0.887350	−	0.461097i	$-0.847456\pi$
$173$	−23.3425	−1.77470	−0.887350	+	0.461097i	$0.847456\pi$
$174$	−7.82023	−0.592850
$175$	−13.2474	−1.00141
$176$	43.5385	3.28184
$177$	−6.33309	−0.476024
$178$	0.210134	0.0157502
$179$	−7.68245	−0.574213	−0.287107	−	0.957899i	$-0.592693\pi$
$179$	−7.68245	−0.574213	−0.287107	+	0.957899i	$0.592693\pi$
$180$	−6.28840	−0.468709
$181$	8.21203	0.610396	0.305198	−	0.952289i	$-0.401277\pi$
$181$	8.21203	0.610396	0.305198	+	0.952289i	$0.401277\pi$
$182$	16.1342	1.19595
$183$	−2.82725	−0.208996
$184$	−8.75866	−0.645697
$185$	1.79759	0.132161
$186$	−1.61644	−0.118523
$187$	−34.1416	−2.49668
$188$	3.84384	0.280341
$189$	8.88706	0.646439
$190$	4.04080	0.293151
$191$	−11.0481	−0.799416	−0.399708	−	0.916643i	$-0.630888\pi$
$191$	−11.0481	−0.799416	−0.399708	+	0.916643i	$0.630888\pi$
$192$	−0.664256	−0.0479386
$193$	−18.4774	−1.33003	−0.665016	−	0.746829i	$-0.731575\pi$
$193$	−18.4774	−1.33003	−0.665016	+	0.746829i	$0.731575\pi$
$194$	11.8681	0.852078
$195$	0.647134	0.0463422
$196$	3.75528	0.268235
$197$	−3.34958	−0.238648	−0.119324	−	0.992855i	$-0.538073\pi$
$197$	−3.34958	−0.238648	−0.119324	+	0.992855i	$0.538073\pi$
$198$	39.3935	2.79957
$199$	−18.9266	−1.34167	−0.670836	−	0.741606i	$-0.734065\pi$
$199$	−18.9266	−1.34167	−0.670836	+	0.741606i	$0.734065\pi$
$200$	30.9079	2.18552
$201$	7.68510	0.542065
$202$	−32.7492	−2.30422
$203$	−15.3039	−1.07412
$204$	15.1527	1.06090
$205$	0.470365	0.0328517
$206$	−0.924214	−0.0643930
$207$	−3.60734	−0.250727
$208$	−17.1349	−1.18809
$209$	−17.5844	−1.21634
$210$	2.05588	0.141870
$211$	−20.9303	−1.44090	−0.720449	−	0.693508i	$-0.756064\pi$
$211$	−20.9303	−1.44090	−0.720449	+	0.693508i	$0.756064\pi$
$212$	31.1350	2.13836
$213$	4.80236	0.329052
$214$	−8.17514	−0.558841
$215$	5.49381	0.374675
$216$	−20.7346	−1.41081
$217$	−3.16331	−0.214740
$218$	−10.8706	−0.736251
$219$	0.945548	0.0638942
$220$	13.3957	0.903138
$221$	13.4367	0.903851
$222$	4.99782	0.335431
$223$	20.3983	1.36597	0.682985	−	0.730432i	$-0.260681\pi$
$223$	20.3983	1.36597	0.682985	+	0.730432i	$0.260681\pi$
$224$	−17.9213	−1.19742
$225$	12.7297	0.848646
$226$	−28.4533	−1.89268
$227$	22.5883	1.49924	0.749618	−	0.661871i	$-0.230237\pi$
$227$	22.5883	1.49924	0.749618	+	0.661871i	$0.230237\pi$
$228$	7.80427	0.516850
$229$	−14.8585	−0.981878	−0.490939	−	0.871194i	$-0.663346\pi$
$229$	−14.8585	−0.981878	−0.490939	+	0.871194i	$0.663346\pi$
$230$	−1.76585	−0.116437
$231$	−8.94659	−0.588642
$232$	35.7058	2.34420
$233$	8.52136	0.558253	0.279127	−	0.960254i	$-0.409955\pi$
$233$	8.52136	0.558253	0.279127	+	0.960254i	$0.409955\pi$
$234$	−15.5036	−1.01350
$235$	0.434330	0.0283326
$236$	51.5936	3.35846
$237$	1.82337	0.118441
$238$	42.6872	2.76700
$239$	−9.38103	−0.606809	−0.303404	−	0.952862i	$-0.598123\pi$
$239$	−9.38103	−0.606809	−0.303404	+	0.952862i	$0.598123\pi$
$240$	−2.18340	−0.140938
$241$	−10.3409	−0.666116	−0.333058	−	0.942906i	$-0.608081\pi$
$241$	−10.3409	−0.666116	−0.333058	+	0.942906i	$0.608081\pi$
$242$	−55.7644	−3.58467
$243$	−13.0438	−0.836758
$244$	23.0327	1.47451
$245$	0.424324	0.0271090
$246$	1.30775	0.0833793
$247$	6.92047	0.440339
$248$	7.38039	0.468655
$249$	−1.63284	−0.103477
$250$	12.8106	0.810213
$251$	−4.40768	−0.278210	−0.139105	−	0.990278i	$-0.544423\pi$
$251$	−4.40768	−0.278210	−0.139105	+	0.990278i	$0.544423\pi$
$252$	−34.2146	−2.15532
$253$	7.68443	0.483116
$254$	−6.55284	−0.411162
$255$	1.71216	0.107220
$256$	−27.3810	−1.71131
$257$	6.39792	0.399091	0.199546	−	0.979889i	$-0.436053\pi$
$257$	6.39792	0.399091	0.199546	+	0.979889i	$0.436053\pi$
$258$	15.2744	0.950943
$259$	9.78052	0.607732
$260$	−5.27199	−0.326955
$261$	14.7058	0.910264
$262$	54.3280	3.35640
$263$	−27.1085	−1.67158	−0.835789	−	0.549050i	$-0.814990\pi$
$263$	−27.1085	−1.67158	−0.835789	+	0.549050i	$0.814990\pi$
$264$	20.8735	1.28467
$265$	3.51806	0.216113
$266$	21.9857	1.34803
$267$	0.0458580	0.00280646
$268$	−62.6080	−3.82439
$269$	−2.04410	−0.124631	−0.0623156	−	0.998056i	$-0.519849\pi$
$269$	−2.04410	−0.124631	−0.0623156	+	0.998056i	$0.519849\pi$
$270$	−4.18034	−0.254407
$271$	4.48683	0.272555	0.136278	−	0.990671i	$-0.456486\pi$
$271$	4.48683	0.272555	0.136278	+	0.990671i	$0.456486\pi$
$272$	−45.3349	−2.74883
$273$	3.52100	0.213101
$274$	−14.3620	−0.867639
$275$	−27.1171	−1.63522
$276$	−3.41050	−0.205288
$277$	−9.74186	−0.585332	−0.292666	−	0.956215i	$-0.594542\pi$
$277$	−9.74186	−0.585332	−0.292666	+	0.956215i	$0.594542\pi$
$278$	3.83433	0.229968
$279$	3.03968	0.181981
$280$	−9.38680	−0.560969
$281$	26.2166	1.56395	0.781976	−	0.623309i	$-0.214212\pi$
$281$	26.2166	1.56395	0.781976	+	0.623309i	$0.214212\pi$
$282$	1.20757	0.0719095
$283$	−19.9549	−1.18620	−0.593099	−	0.805130i	$-0.702096\pi$
$283$	−19.9549	−1.18620	−0.593099	+	0.805130i	$0.702096\pi$
$284$	−39.1232	−2.32154
$285$	0.881834	0.0522353
$286$	33.0262	1.95288
$287$	2.55922	0.151066
$288$	17.2209	1.01475
$289$	18.5503	1.09119
$290$	7.19870	0.422722
$291$	2.59000	0.151828
$292$	−7.70306	−0.450788
$293$	−4.19606	−0.245136	−0.122568	−	0.992460i	$-0.539113\pi$
$293$	−4.19606	−0.245136	−0.122568	+	0.992460i	$0.539113\pi$
$294$	1.17974	0.0688041
$295$	5.82975	0.339421
$296$	−22.8191	−1.32634
$297$	18.1915	1.05558
$298$	23.4087	1.35603
$299$	−3.02427	−0.174898
$300$	12.0351	0.694846
$301$	29.8914	1.72291
$302$	−2.38334	−0.137146
$303$	−7.14693	−0.410580
$304$	−23.3494	−1.33918
$305$	2.60255	0.149021
$306$	−41.0189	−2.34489
$307$	16.0560	0.916362	0.458181	−	0.888859i	$-0.348501\pi$
$307$	16.0560	0.916362	0.458181	+	0.888859i	$0.348501\pi$
$308$	72.8849	4.15300
$309$	−0.201693	−0.0114739
$310$	1.48797	0.0845111
$311$	7.85743	0.445554	0.222777	−	0.974869i	$-0.428488\pi$
$311$	7.85743	0.445554	0.222777	+	0.974869i	$0.428488\pi$
$312$	−8.21493	−0.465079
$313$	3.34545	0.189096	0.0945481	−	0.995520i	$-0.469859\pi$
$313$	3.34545	0.189096	0.0945481	+	0.995520i	$0.469859\pi$
$314$	40.8012	2.30255
$315$	−3.86604	−0.217827
$316$	−14.8544	−0.835626
$317$	2.61558	0.146905	0.0734527	−	0.997299i	$-0.476598\pi$
$317$	2.61558	0.146905	0.0734527	+	0.997299i	$0.476598\pi$
$318$	9.78123	0.548504
$319$	−31.3266	−1.75395
$320$	0.611463	0.0341818
$321$	−1.78408	−0.0995776
$322$	−9.60783	−0.535424
$323$	18.3099	1.01879
$324$	28.6192	1.58995
$325$	10.6722	0.591985
$326$	49.1657	2.72303
$327$	−2.37232	−0.131189
$328$	−5.97097	−0.329692
$329$	2.36316	0.130285
$330$	4.20833	0.231661
$331$	−7.67886	−0.422068	−0.211034	−	0.977479i	$-0.567683\pi$
$331$	−7.67886	−0.422068	−0.211034	+	0.977479i	$0.567683\pi$
$332$	13.3022	0.730055
$333$	−9.39827	−0.515022
$334$	−54.4668	−2.98029
$335$	−7.07431	−0.386511
$336$	−11.8797	−0.648092
$337$	15.4324	0.840657	0.420328	−	0.907372i	$-0.361915\pi$
$337$	15.4324	0.840657	0.420328	+	0.907372i	$0.361915\pi$
$338$	20.2735	1.10273
$339$	−6.20942	−0.337250
$340$	−13.9484	−0.756459
$341$	−6.47520	−0.350652
$342$	−21.1264	−1.14239
$343$	−17.2729	−0.932650
$344$	−69.7403	−3.76014
$345$	−0.385365	−0.0207474
$346$	59.7411	3.21170
$347$	−21.3805	−1.14777	−0.573883	−	0.818938i	$-0.694563\pi$
$347$	−21.3805	−1.14777	−0.573883	+	0.818938i	$0.694563\pi$
$348$	13.9033	0.745297
$349$	−23.6538	−1.26616	−0.633079	−	0.774087i	$-0.718209\pi$
$349$	−23.6538	−1.26616	−0.633079	+	0.774087i	$0.718209\pi$
$350$	33.9045	1.81227
$351$	−7.15944	−0.382142
$352$	−36.6844	−1.95528
$353$	31.2961	1.66573	0.832863	−	0.553480i	$-0.186700\pi$
$353$	31.2961	1.66573	0.832863	+	0.553480i	$0.186700\pi$
$354$	16.2084	0.861468
$355$	−4.42068	−0.234625
$356$	−0.373590	−0.0198002
$357$	9.31572	0.493040
$358$	19.6619	1.03916
$359$	−8.65053	−0.456558	−0.228279	−	0.973596i	$-0.573310\pi$
$359$	−8.65053	−0.456558	−0.228279	+	0.973596i	$0.573310\pi$
$360$	9.01995	0.475393
$361$	−9.56965	−0.503666
$362$	−21.0172	−1.10464
$363$	−12.1696	−0.638738
$364$	−28.6845	−1.50347
$365$	−0.870398	−0.0455587
$366$	7.23584	0.378223
$367$	−0.239753	−0.0125150	−0.00625751	−	0.999980i	$-0.501992\pi$
$367$	−0.239753	−0.0125150	−0.00625751	+	0.999980i	$0.501992\pi$
$368$	10.2038	0.531908
$369$	−2.45920	−0.128021
$370$	−4.60060	−0.239174
$371$	19.1415	0.993775
$372$	2.87382	0.149001
$373$	19.0426	0.985988	0.492994	−	0.870033i	$-0.335902\pi$
$373$	19.0426	0.985988	0.492994	+	0.870033i	$0.335902\pi$
$374$	87.3794	4.51828
$375$	2.79569	0.144369
$376$	−5.51353	−0.284339
$377$	12.3288	0.634967
$378$	−22.7449	−1.16987
$379$	−7.67720	−0.394351	−0.197176	−	0.980368i	$-0.563177\pi$
$379$	−7.67720	−0.394351	−0.197176	+	0.980368i	$0.563177\pi$
$380$	−7.18401	−0.368532
$381$	−1.43004	−0.0732632
$382$	28.2758	1.44671
$383$	−4.89155	−0.249947	−0.124973	−	0.992160i	$-0.539885\pi$
$383$	−4.89155	−0.249947	−0.124973	+	0.992160i	$0.539885\pi$
$384$	−5.45632	−0.278442
$385$	8.23554	0.419722
$386$	47.2896	2.40698
$387$	−28.7232	−1.46008
$388$	−21.0999	−1.07118
$389$	−1.08387	−0.0549542	−0.0274771	−	0.999622i	$-0.508747\pi$
$389$	−1.08387	−0.0549542	−0.0274771	+	0.999622i	$0.508747\pi$
$390$	−1.65622	−0.0838662
$391$	−8.00150	−0.404653
$392$	−5.38650	−0.272059
$393$	11.8561	0.598062
$394$	8.57265	0.431884
$395$	−1.67845	−0.0844522
$396$	−70.0364	−3.51946
$397$	20.1907	1.01334	0.506672	−	0.862139i	$-0.330875\pi$
$397$	20.1907	1.01334	0.506672	+	0.862139i	$0.330875\pi$
$398$	48.4393	2.42804
$399$	4.79799	0.240200
$400$	−36.0074	−1.80037
$401$	7.70608	0.384823	0.192412	−	0.981314i	$-0.438369\pi$
$401$	7.70608	0.384823	0.192412	+	0.981314i	$0.438369\pi$
$402$	−19.6686	−0.980983
$403$	2.54837	0.126943
$404$	58.2237	2.89674
$405$	3.23379	0.160688
$406$	39.1676	1.94385
$407$	20.0204	0.992376
$408$	−21.7347	−1.07603
$409$	−20.1327	−0.995498	−0.497749	−	0.867321i	$-0.665840\pi$
$409$	−20.1327	−0.995498	−0.497749	+	0.867321i	$0.665840\pi$
$410$	−1.20382	−0.0594523
$411$	−3.13425	−0.154601
$412$	1.64313	0.0809512
$413$	31.7192	1.56080
$414$	9.23234	0.453745
$415$	1.50307	0.0737828
$416$	14.4374	0.707853
$417$	0.836774	0.0409770
$418$	45.0040	2.20122
$419$	−37.6270	−1.83820	−0.919101	−	0.394023i	$-0.871083\pi$
$419$	−37.6270	−1.83820	−0.919101	+	0.394023i	$0.871083\pi$
$420$	−3.65509	−0.178350
$421$	9.45771	0.460941	0.230470	−	0.973079i	$-0.425974\pi$
$421$	9.45771	0.460941	0.230470	+	0.973079i	$0.425974\pi$
$422$	53.5673	2.60762
$423$	−2.27080	−0.110410
$424$	−44.6594	−2.16885
$425$	28.2360	1.36965
$426$	−12.2908	−0.595490
$427$	14.1602	0.685262
$428$	14.5343	0.702542
$429$	7.20739	0.347976
$430$	−14.0604	−0.678055
$431$	39.5092	1.90309	0.951546	−	0.307507i	$-0.0994948\pi$
$431$	39.5092	1.90309	0.951546	+	0.307507i	$0.0994948\pi$
$432$	24.1556	1.16219
$433$	21.6335	1.03964	0.519819	−	0.854276i	$-0.325999\pi$
$433$	21.6335	1.03964	0.519819	+	0.854276i	$0.325999\pi$
$434$	8.09594	0.388617
$435$	1.57099	0.0753232
$436$	19.3265	0.925571
$437$	−4.12110	−0.197139
$438$	−2.41996	−0.115630
$439$	−34.8887	−1.66515	−0.832573	−	0.553916i	$-0.813133\pi$
$439$	−34.8887	−1.66515	−0.832573	+	0.553916i	$0.813133\pi$
$440$	−19.2145	−0.916016
$441$	−2.21848	−0.105642
$442$	−34.3889	−1.63571
$443$	−5.98823	−0.284509	−0.142255	−	0.989830i	$-0.545435\pi$
$443$	−5.98823	−0.284509	−0.142255	+	0.989830i	$0.545435\pi$
$444$	−8.88545	−0.421685
$445$	−0.0422133	−0.00200110
$446$	−52.2058	−2.47202
$447$	5.10854	0.241625
$448$	3.32692	0.157182
$449$	−22.7019	−1.07137	−0.535684	−	0.844418i	$-0.679946\pi$
$449$	−22.7019	−1.07137	−0.535684	+	0.844418i	$0.679946\pi$
$450$	−32.5794	−1.53581
$451$	5.23864	0.246678
$452$	50.5861	2.37937
$453$	−0.520121	−0.0244374
$454$	−57.8107	−2.71319
$455$	−3.24116	−0.151948
$456$	−11.1943	−0.524220
$457$	−7.63124	−0.356974	−0.178487	−	0.983942i	$-0.557120\pi$
$457$	−7.63124	−0.356974	−0.178487	+	0.983942i	$0.557120\pi$
$458$	38.0277	1.77692
$459$	−18.9421	−0.884143
$460$	3.13944	0.146377
$461$	−33.1809	−1.54539	−0.772695	−	0.634778i	$-0.781092\pi$
$461$	−33.1809	−1.54539	−0.772695	+	0.634778i	$0.781092\pi$
$462$	22.8972	1.06527
$463$	−12.8410	−0.596770	−0.298385	−	0.954446i	$-0.596448\pi$
$463$	−12.8410	−0.596770	−0.298385	+	0.954446i	$0.596448\pi$
$464$	−41.5970	−1.93109
$465$	0.324724	0.0150587
$466$	−21.8089	−1.01028
$467$	6.73167	0.311505	0.155752	−	0.987796i	$-0.450220\pi$
$467$	6.73167	0.311505	0.155752	+	0.987796i	$0.450220\pi$
$468$	27.5634	1.27412
$469$	−38.4907	−1.77734
$470$	−1.11159	−0.0512739
$471$	8.90414	0.410281
$472$	−74.0048	−3.40635
$473$	61.1868	2.81337
$474$	−4.66660	−0.214344
$475$	14.5427	0.667264
$476$	−75.8921	−3.47851
$477$	−18.3934	−0.842174
$478$	24.0091	1.09815
$479$	24.0282	1.09787	0.548937	−	0.835864i	$-0.315033\pi$
$479$	24.0282	1.09787	0.548937	+	0.835864i	$0.315033\pi$
$480$	1.83968	0.0839693
$481$	−7.87921	−0.359261
$482$	26.4657	1.20548
$483$	−2.09674	−0.0954049
$484$	99.1417	4.50644
$485$	−2.38415	−0.108259
$486$	33.3832	1.51429
$487$	30.6947	1.39091	0.695454	−	0.718571i	$-0.255203\pi$
$487$	30.6947	1.39091	0.695454	+	0.718571i	$0.255203\pi$
$488$	−33.0376	−1.49554
$489$	10.7295	0.485206
$490$	−1.08598	−0.0490596
$491$	−0.246528	−0.0111257	−0.00556283	−	0.999985i	$-0.501771\pi$
$491$	−0.246528	−0.0111257	−0.00556283	+	0.999985i	$0.501771\pi$
$492$	−2.32501	−0.104820
$493$	32.6191	1.46909
$494$	−17.7117	−0.796888
$495$	−7.91367	−0.355693
$496$	−8.59809	−0.386066
$497$	−24.0526	−1.07890
$498$	4.17897	0.187264
$499$	5.43647	0.243370	0.121685	−	0.992569i	$-0.461170\pi$
$499$	5.43647	0.243370	0.121685	+	0.992569i	$0.461170\pi$
$500$	−22.7755	−1.01855
$501$	−11.8864	−0.531046
$502$	11.2807	0.503481
$503$	40.0922	1.78762	0.893812	−	0.448442i	$-0.148021\pi$
$503$	40.0922	1.78762	0.893812	+	0.448442i	$0.148021\pi$
$504$	49.0768	2.18605
$505$	6.57891	0.292758
$506$	−19.6670	−0.874303
$507$	4.42432	0.196491
$508$	11.6501	0.516888
$509$	16.4141	0.727542	0.363771	−	0.931488i	$-0.381489\pi$
$509$	16.4141	0.727542	0.363771	+	0.931488i	$0.381489\pi$
$510$	−4.38197	−0.194037
$511$	−4.73577	−0.209498
$512$	50.5384	2.23350
$513$	−9.75599	−0.430737
$514$	−16.3743	−0.722241
$515$	0.185663	0.00818130
$516$	−27.1559	−1.19547
$517$	4.83731	0.212745
$518$	−25.0315	−1.09982
$519$	13.0374	0.572280
$520$	7.56203	0.331617
$521$	−29.9560	−1.31240	−0.656199	−	0.754588i	$-0.727837\pi$
$521$	−29.9560	−1.31240	−0.656199	+	0.754588i	$0.727837\pi$
$522$	−37.6368	−1.64732
$523$	19.7818	0.864999	0.432499	−	0.901634i	$-0.357632\pi$
$523$	19.7818	0.864999	0.432499	+	0.901634i	$0.357632\pi$
$524$	−96.5880	−4.21947
$525$	7.39905	0.322921
$526$	69.3793	3.02508
$527$	6.74237	0.293702
$528$	−24.3174	−1.05828
$529$	−21.1991	−0.921698
$530$	−9.00385	−0.391102
$531$	−30.4796	−1.32270
$532$	−39.0876	−1.69466
$533$	−2.06171	−0.0893026
$534$	−0.117365	−0.00507890
$535$	1.64229	0.0710022
$536$	89.8035	3.87892
$537$	4.29086	0.185164
$538$	5.23152	0.225547
$539$	4.72586	0.203557
$540$	7.43208	0.319826
$541$	−39.1158	−1.68172	−0.840860	−	0.541252i	$-0.817950\pi$
$541$	−39.1158	−1.68172	−0.840860	+	0.541252i	$0.817950\pi$
$542$	−11.4832	−0.493248
$543$	−4.58664	−0.196832
$544$	38.1980	1.63772
$545$	2.18377	0.0935426
$546$	−9.01138	−0.385652
$547$	−27.4408	−1.17328	−0.586641	−	0.809847i	$-0.699550\pi$
$547$	−27.4408	−1.17328	−0.586641	+	0.809847i	$0.699550\pi$
$548$	25.5337	1.09074
$549$	−13.6068	−0.580725
$550$	69.4014	2.95929
$551$	16.8002	0.715713
$552$	4.89195	0.208215
$553$	−9.13233	−0.388346
$554$	24.9326	1.05928
$555$	−1.00400	−0.0426174
$556$	−6.81693	−0.289102
$557$	−39.4137	−1.67001	−0.835006	−	0.550241i	$-0.814536\pi$
$557$	−39.4137	−1.67001	−0.835006	+	0.550241i	$0.814536\pi$
$558$	−7.77953	−0.329334
$559$	−24.0806	−1.01850
$560$	10.9355	0.462111
$561$	19.0690	0.805094
$562$	−67.0968	−2.83031
$563$	−30.6505	−1.29176	−0.645882	−	0.763437i	$-0.723510\pi$
$563$	−30.6505	−1.29176	−0.645882	+	0.763437i	$0.723510\pi$
$564$	−2.14689	−0.0904004
$565$	5.71592	0.240470
$566$	51.0711	2.14668
$567$	17.5948	0.738911
$568$	56.1175	2.35464
$569$	−14.4198	−0.604509	−0.302254	−	0.953227i	$-0.597739\pi$
$569$	−14.4198	−0.604509	−0.302254	+	0.953227i	$0.597739\pi$
$570$	−2.25690	−0.0945310
$571$	−18.1573	−0.759859	−0.379929	−	0.925015i	$-0.624052\pi$
$571$	−18.1573	−0.759859	−0.379929	+	0.925015i	$0.624052\pi$
$572$	−58.7162	−2.45505
$573$	6.17069	0.257784
$574$	−6.54987	−0.273386
$575$	−6.35522	−0.265031
$576$	−3.19690	−0.133204
$577$	33.9270	1.41240	0.706200	−	0.708013i	$-0.250408\pi$
$577$	33.9270	1.41240	0.706200	+	0.708013i	$0.250408\pi$
$578$	−47.4762	−1.97475
$579$	10.3201	0.428889
$580$	−12.7983	−0.531422
$581$	8.17808	0.339284
$582$	−6.62864	−0.274766
$583$	39.1820	1.62275
$584$	11.0491	0.457216
$585$	3.11449	0.128768
$586$	10.7391	0.443627
$587$	−31.8331	−1.31389	−0.656946	−	0.753938i	$-0.728152\pi$
$587$	−31.8331	−1.31389	−0.656946	+	0.753938i	$0.728152\pi$
$588$	−2.09743	−0.0864965
$589$	3.47260	0.143086
$590$	−14.9202	−0.614256
$591$	1.87083	0.0769556
$592$	26.5841	1.09260
$593$	−25.9105	−1.06402	−0.532008	−	0.846739i	$-0.678563\pi$
$593$	−25.9105	−1.06402	−0.532008	+	0.846739i	$0.678563\pi$
$594$	−46.5581	−1.91030
$595$	−8.57534	−0.351555
$596$	−41.6176	−1.70472
$597$	10.5710	0.432643
$598$	7.74009	0.316516
$599$	−8.38461	−0.342586	−0.171293	−	0.985220i	$-0.554794\pi$
$599$	−8.38461	−0.342586	−0.171293	+	0.985220i	$0.554794\pi$
$600$	−17.2629	−0.704754
$601$	−16.3943	−0.668736	−0.334368	−	0.942443i	$-0.608523\pi$
$601$	−16.3943	−0.668736	−0.334368	+	0.942443i	$0.608523\pi$
$602$	−76.5017	−3.11798
$603$	36.9864	1.50620
$604$	4.23726	0.172411
$605$	11.2024	0.455442
$606$	18.2913	0.743033
$607$	−38.6475	−1.56865	−0.784327	−	0.620348i	$-0.786991\pi$
$607$	−38.6475	−1.56865	−0.784327	+	0.620348i	$0.786991\pi$
$608$	19.6735	0.797867
$609$	8.54762	0.346367
$610$	−6.66076	−0.269686
$611$	−1.90376	−0.0770180
$612$	72.9261	2.94786
$613$	−48.0777	−1.94184	−0.970920	−	0.239403i	$-0.923048\pi$
$613$	−48.0777	−1.94184	−0.970920	+	0.239403i	$0.923048\pi$
$614$	−41.0924	−1.65835
$615$	−0.262712	−0.0105936
$616$	−104.545	−4.21222
$617$	23.2826	0.937324	0.468662	−	0.883378i	$-0.344736\pi$
$617$	23.2826	0.937324	0.468662	+	0.883378i	$0.344736\pi$
$618$	0.516198	0.0207645
$619$	39.7918	1.59937	0.799683	−	0.600423i	$-0.205001\pi$
$619$	39.7918	1.59937	0.799683	+	0.600423i	$0.205001\pi$
$620$	−2.64542	−0.106242
$621$	4.26341	0.171085
$622$	−20.1097	−0.806326
$623$	−0.229679	−0.00920190
$624$	9.57032	0.383120
$625$	21.1048	0.844193
$626$	−8.56210	−0.342210
$627$	9.82133	0.392226
$628$	−72.5391	−2.89463
$629$	−20.8465	−0.831204
$630$	9.89445	0.394204
$631$	21.6190	0.860640	0.430320	−	0.902676i	$-0.358401\pi$
$631$	21.6190	0.860640	0.430320	+	0.902676i	$0.358401\pi$
$632$	21.3068	0.847541
$633$	11.6901	0.464640
$634$	−6.69410	−0.265857
$635$	1.31639	0.0522392
$636$	−17.3897	−0.689547
$637$	−1.85990	−0.0736920
$638$	80.1748	3.17415
$639$	23.1125	0.914317
$640$	5.02267	0.198538
$641$	−31.8572	−1.25828	−0.629141	−	0.777291i	$-0.716593\pi$
$641$	−31.8572	−1.25828	−0.629141	+	0.777291i	$0.716593\pi$
$642$	4.56603	0.180207
$643$	5.35731	0.211272	0.105636	−	0.994405i	$-0.466312\pi$
$643$	5.35731	0.211272	0.105636	+	0.994405i	$0.466312\pi$
$644$	17.0814	0.673103
$645$	−3.06844	−0.120820
$646$	−46.8609	−1.84372
$647$	−3.06890	−0.120651	−0.0603254	−	0.998179i	$-0.519214\pi$
$647$	−3.06890	−0.120651	−0.0603254	+	0.998179i	$0.519214\pi$
$648$	−41.0508	−1.61263
$649$	64.9283	2.54866
$650$	−27.3135	−1.07132
$651$	1.76679	0.0692461
$652$	−87.4100	−3.42324
$653$	23.5999	0.923535	0.461768	−	0.887001i	$-0.347215\pi$
$653$	23.5999	0.923535	0.461768	+	0.887001i	$0.347215\pi$
$654$	6.07153	0.237416
$655$	−10.9138	−0.426439
$656$	6.95613	0.271591
$657$	4.55068	0.177539
$658$	−6.04808	−0.235779
$659$	34.2711	1.33501	0.667506	−	0.744605i	$-0.267362\pi$
$659$	34.2711	1.33501	0.667506	+	0.744605i	$0.267362\pi$
$660$	−7.48186	−0.291231
$661$	11.0633	0.430314	0.215157	−	0.976579i	$-0.430974\pi$
$661$	11.0633	0.430314	0.215157	+	0.976579i	$0.430974\pi$
$662$	19.6527	0.763824
$663$	−7.50477	−0.291461
$664$	−19.0805	−0.740465
$665$	−4.41666	−0.171271
$666$	24.0532	0.932043
$667$	−7.34176	−0.284274
$668$	96.8347	3.74665
$669$	−11.3930	−0.440478
$670$	18.1054	0.699474
$671$	28.9856	1.11898
$672$	10.0095	0.386126
$673$	−11.1966	−0.431598	−0.215799	−	0.976438i	$-0.569236\pi$
$673$	−11.1966	−0.431598	−0.215799	+	0.976438i	$0.569236\pi$
$674$	−39.4965	−1.52135
$675$	−15.0449	−0.579077
$676$	−36.0435	−1.38629
$677$	−40.8652	−1.57058	−0.785288	−	0.619130i	$-0.787485\pi$
$677$	−40.8652	−1.57058	−0.785288	+	0.619130i	$0.787485\pi$
$678$	15.8919	0.610325
$679$	−12.9720	−0.497819
$680$	20.0073	0.767245
$681$	−12.6162	−0.483452
$682$	16.5721	0.634580
$683$	40.5160	1.55030	0.775150	−	0.631777i	$-0.217674\pi$
$683$	40.5160	1.55030	0.775150	+	0.631777i	$0.217674\pi$
$684$	37.5600	1.43614
$685$	2.88515	0.110236
$686$	44.2070	1.68783
$687$	8.29887	0.316622
$688$	81.2468	3.09751
$689$	−15.4204	−0.587471
$690$	0.986274	0.0375468
$691$	−20.9687	−0.797686	−0.398843	−	0.917019i	$-0.630588\pi$
$691$	−20.9687	−0.797686	−0.398843	+	0.917019i	$0.630588\pi$
$692$	−106.212	−4.03756
$693$	−43.0576	−1.63562
$694$	54.7196	2.07713
$695$	−0.770270	−0.0292180
$696$	−19.9426	−0.755924
$697$	−5.45479	−0.206615
$698$	60.5377	2.29139
$699$	−4.75941	−0.180017
$700$	−60.2776	−2.27828
$701$	38.7387	1.46314	0.731571	−	0.681765i	$-0.238788\pi$
$701$	38.7387	1.46314	0.731571	+	0.681765i	$0.238788\pi$
$702$	18.3233	0.691569
$703$	−10.7368	−0.404946
$704$	6.81011	0.256666
$705$	−0.242585	−0.00913629
$706$	−80.0969	−3.01449
$707$	35.7953	1.34622
$708$	−28.8164	−1.08299
$709$	−2.40356	−0.0902676	−0.0451338	−	0.998981i	$-0.514371\pi$
$709$	−2.40356	−0.0902676	−0.0451338	+	0.998981i	$0.514371\pi$
$710$	11.3139	0.424605
$711$	8.77542	0.329104
$712$	0.535869	0.0200826
$713$	−1.51754	−0.0568324
$714$	−23.8419	−0.892262
$715$	−6.63457	−0.248119
$716$	−34.9562	−1.30637
$717$	5.23956	0.195675
$718$	22.1395	0.826239
$719$	1.51866	0.0566365	0.0283182	−	0.999599i	$-0.490985\pi$
$719$	1.51866	0.0566365	0.0283182	+	0.999599i	$0.490985\pi$
$720$	−10.5082	−0.391616
$721$	1.01018	0.0376210
$722$	24.4918	0.911491
$723$	5.77567	0.214800
$724$	37.3659	1.38869
$725$	25.9078	0.962193
$726$	31.1459	1.15593
$727$	−15.4365	−0.572509	−0.286254	−	0.958154i	$-0.592410\pi$
$727$	−15.4365	−0.572509	−0.286254	+	0.958154i	$0.592410\pi$
$728$	41.1444	1.52491
$729$	−11.5839	−0.429035
$730$	2.22763	0.0824483
$731$	−63.7114	−2.35645
$732$	−12.8644	−0.475480
$733$	−11.5624	−0.427067	−0.213533	−	0.976936i	$-0.568497\pi$
$733$	−11.5624	−0.427067	−0.213533	+	0.976936i	$0.568497\pi$
$734$	0.613606	0.0226486
$735$	−0.236996	−0.00874174
$736$	−8.59742	−0.316905
$737$	−78.7894	−2.90224
$738$	6.29388	0.231681
$739$	25.5411	0.939546	0.469773	−	0.882787i	$-0.344336\pi$
$739$	25.5411	0.939546	0.469773	+	0.882787i	$0.344336\pi$
$740$	8.17926	0.300676
$741$	−3.86527	−0.141994
$742$	−48.9892	−1.79845
$743$	−7.33534	−0.269108	−0.134554	−	0.990906i	$-0.542960\pi$
$743$	−7.33534	−0.269108	−0.134554	+	0.990906i	$0.542960\pi$
$744$	−4.12215	−0.151125
$745$	−4.70252	−0.172287
$746$	−48.7362	−1.78436
$747$	−7.85846	−0.287526
$748$	−155.349	−5.68012
$749$	8.93554	0.326498
$750$	−7.15506	−0.261266
$751$	−39.6386	−1.44643	−0.723217	−	0.690621i	$-0.757337\pi$
$751$	−39.6386	−1.44643	−0.723217	+	0.690621i	$0.757337\pi$
$752$	6.42322	0.234231
$753$	2.46181	0.0897133
$754$	−31.5535	−1.14911
$755$	0.478783	0.0174247
$756$	40.4373	1.47069
$757$	−12.7209	−0.462349	−0.231174	−	0.972912i	$-0.574257\pi$
$757$	−12.7209	−0.462349	−0.231174	+	0.972912i	$0.574257\pi$
$758$	19.6484	0.713664
$759$	−4.29196	−0.155788
$760$	10.3046	0.373787
$761$	21.3131	0.772600	0.386300	−	0.922373i	$-0.373753\pi$
$761$	21.3131	0.772600	0.386300	+	0.922373i	$0.373753\pi$
$762$	3.65994	0.132586
$763$	11.8817	0.430148
$764$	−50.2706	−1.81872
$765$	8.24019	0.297925
$766$	12.5191	0.452332
$767$	−25.5531	−0.922668
$768$	15.2930	0.551838
$769$	1.95899	0.0706431	0.0353216	−	0.999376i	$-0.488754\pi$
$769$	1.95899	0.0706431	0.0353216	+	0.999376i	$0.488754\pi$
$770$	−21.0774	−0.759577
$771$	−3.57341	−0.128693
$772$	−84.0746	−3.02591
$773$	35.6255	1.28136	0.640680	−	0.767808i	$-0.278652\pi$
$773$	35.6255	1.28136	0.640680	+	0.767808i	$0.278652\pi$
$774$	73.5119	2.64233
$775$	5.35515	0.192363
$776$	30.2652	1.08646
$777$	−5.46268	−0.195973
$778$	2.77396	0.0994514
$779$	−2.80944	−0.100659
$780$	2.94455	0.105432
$781$	−49.2349	−1.76176
$782$	20.4784	0.732307
$783$	−17.3803	−0.621122
$784$	6.27523	0.224115
$785$	−8.19646	−0.292544
$786$	−30.3437	−1.08232
$787$	−11.9685	−0.426632	−0.213316	−	0.976983i	$-0.568426\pi$
$787$	−11.9685	−0.426632	−0.213316	+	0.976983i	$0.568426\pi$
$788$	−15.2410	−0.542939
$789$	15.1408	0.539027
$790$	4.29571	0.152834
$791$	31.0998	1.10578
$792$	100.459	3.56964
$793$	−11.4075	−0.405093
$794$	−51.6746	−1.83386
$795$	−1.96493	−0.0696889
$796$	−86.1186	−3.05239
$797$	33.4889	1.18624	0.593119	−	0.805115i	$-0.297896\pi$
$797$	33.4889	1.18624	0.593119	+	0.805115i	$0.297896\pi$
$798$	−12.2796	−0.434693
$799$	−5.03690	−0.178193
$800$	30.3389	1.07264
$801$	0.220703	0.00779815
$802$	−19.7224	−0.696421
$803$	−9.69397	−0.342093
$804$	34.9682	1.23323
$805$	1.93010	0.0680270
$806$	−6.52210	−0.229731
$807$	1.14169	0.0401893
$808$	−83.5148	−2.93804
$809$	29.7786	1.04696	0.523480	−	0.852038i	$-0.324633\pi$
$809$	29.7786	1.04696	0.523480	+	0.852038i	$0.324633\pi$
$810$	−8.27631	−0.290800
$811$	41.8184	1.46844	0.734220	−	0.678911i	$-0.237548\pi$
$811$	41.8184	1.46844	0.734220	+	0.678911i	$0.237548\pi$
$812$	−69.6347	−2.44370
$813$	−2.50601	−0.0878898
$814$	−51.2388	−1.79592
$815$	−9.87678	−0.345969
$816$	25.3208	0.886404
$817$	−32.8140	−1.14802
$818$	51.5261	1.80157
$819$	16.9457	0.592130
$820$	2.14022	0.0747399
$821$	−23.4531	−0.818519	−0.409259	−	0.912418i	$-0.634213\pi$
$821$	−23.4531	−0.818519	−0.409259	+	0.912418i	$0.634213\pi$
$822$	8.02155	0.279784
$823$	−34.2926	−1.19536	−0.597682	−	0.801733i	$-0.703911\pi$
$823$	−34.2926	−1.19536	−0.597682	+	0.801733i	$0.703911\pi$
$824$	−2.35687	−0.0821055
$825$	15.1456	0.527303
$826$	−81.1797	−2.82460
$827$	−2.80259	−0.0974555	−0.0487277	−	0.998812i	$-0.515517\pi$
$827$	−2.80259	−0.0974555	−0.0487277	+	0.998812i	$0.515517\pi$
$828$	−16.4139	−0.570421
$829$	−20.7819	−0.721784	−0.360892	−	0.932608i	$-0.617528\pi$
$829$	−20.7819	−0.721784	−0.360892	+	0.932608i	$0.617528\pi$
$830$	−3.84684	−0.133526
$831$	5.44109	0.188749
$832$	−2.68017	−0.0929183
$833$	−4.92085	−0.170497
$834$	−2.14158	−0.0741567
$835$	10.9417	0.378654
$836$	−80.0112	−2.76724
$837$	−3.59251	−0.124175
$838$	96.2997	3.32662
$839$	−22.0634	−0.761715	−0.380857	−	0.924634i	$-0.624371\pi$
$839$	−22.0634	−0.761715	−0.380857	+	0.924634i	$0.624371\pi$
$840$	5.24278	0.180893
$841$	0.929597	0.0320551
$842$	−24.2053	−0.834171
$843$	−14.6427	−0.504321
$844$	−95.2355	−3.27814
$845$	−4.07269	−0.140105
$846$	5.81171	0.199811
$847$	60.9513	2.09431
$848$	52.0278	1.78664
$849$	11.1454	0.382508
$850$	−72.2649	−2.47867
$851$	4.69203	0.160841
$852$	21.8514	0.748616
$853$	1.04366	0.0357343	0.0178671	−	0.999840i	$-0.494312\pi$
$853$	1.04366	0.0357343	0.0178671	+	0.999840i	$0.494312\pi$
$854$	−36.2406	−1.24013
$855$	4.24404	0.145143
$856$	−20.8477	−0.712560
$857$	−28.9967	−0.990507	−0.495254	−	0.868748i	$-0.664925\pi$
$857$	−28.9967	−0.990507	−0.495254	+	0.868748i	$0.664925\pi$
$858$	−18.4460	−0.629737
$859$	−52.1582	−1.77962	−0.889808	−	0.456335i	$-0.849162\pi$
$859$	−52.1582	−1.77962	−0.889808	+	0.456335i	$0.849162\pi$
$860$	24.9976	0.852411
$861$	−1.42939	−0.0487136
$862$	−101.117	−3.44405
$863$	−42.1940	−1.43630	−0.718150	−	0.695888i	$-0.755011\pi$
$863$	−42.1940	−1.43630	−0.718150	+	0.695888i	$0.755011\pi$
$864$	−20.3529	−0.692419
$865$	−12.0013	−0.408055
$866$	−55.3670	−1.88145
$867$	−10.3608	−0.351873
$868$	−14.3935	−0.488547
$869$	−18.6936	−0.634138
$870$	−4.02067	−0.136313
$871$	31.0082	1.05067
$872$	−27.7215	−0.938769
$873$	12.4650	0.421876
$874$	10.5472	0.356766
$875$	−14.0022	−0.473359
$876$	4.30237	0.145364
$877$	−42.0780	−1.42087	−0.710436	−	0.703762i	$-0.751502\pi$
$877$	−42.0780	−1.42087	−0.710436	+	0.703762i	$0.751502\pi$
$878$	89.2914	3.01344
$879$	2.34361	0.0790480
$880$	22.3847	0.754590
$881$	−47.2208	−1.59091	−0.795455	−	0.606013i	$-0.792768\pi$
$881$	−47.2208	−1.59091	−0.795455	+	0.606013i	$0.792768\pi$
$882$	5.67781	0.191182
$883$	−39.5063	−1.32949	−0.664746	−	0.747069i	$-0.731460\pi$
$883$	−39.5063	−1.32949	−0.664746	+	0.747069i	$0.731460\pi$
$884$	61.1389	2.05632
$885$	−3.25607	−0.109452
$886$	15.3258	0.514881
$887$	−19.5273	−0.655663	−0.327831	−	0.944736i	$-0.606318\pi$
$887$	−19.5273	−0.655663	−0.327831	+	0.944736i	$0.606318\pi$
$888$	12.7451	0.427698
$889$	7.16234	0.240217
$890$	0.108037	0.00362142
$891$	36.0160	1.20658
$892$	92.8149	3.10767
$893$	−2.59421	−0.0868120
$894$	−13.0744	−0.437273
$895$	−3.94983	−0.132028
$896$	27.3279	0.912962
$897$	1.68914	0.0563987
$898$	58.1015	1.93887
$899$	6.18645	0.206330
$900$	57.9218	1.93073
$901$	−40.7987	−1.35920
$902$	−13.4074	−0.446417
$903$	−16.6951	−0.555580
$904$	−72.5597	−2.41330
$905$	4.22211	0.140348
$906$	1.33116	0.0442248
$907$	−22.1573	−0.735721	−0.367860	−	0.929881i	$-0.619910\pi$
$907$	−22.1573	−0.735721	−0.367860	+	0.929881i	$0.619910\pi$
$908$	102.780	3.41086
$909$	−34.3964	−1.14085
$910$	8.29519	0.274983
$911$	26.4329	0.875762	0.437881	−	0.899033i	$-0.355729\pi$
$911$	26.4329	0.875762	0.437881	+	0.899033i	$0.355729\pi$
$912$	13.0412	0.431839
$913$	16.7403	0.554023
$914$	19.5308	0.646022
$915$	−1.45359	−0.0480543
$916$	−67.6082	−2.23384
$917$	−59.3813	−1.96094
$918$	48.4790	1.60005
$919$	−23.7322	−0.782853	−0.391427	−	0.920209i	$-0.628018\pi$
$919$	−23.7322	−0.782853	−0.391427	+	0.920209i	$0.628018\pi$
$920$	−4.50315	−0.148464
$921$	−8.96769	−0.295495
$922$	84.9207	2.79671
$923$	19.3768	0.637795
$924$	−40.7082	−1.33920
$925$	−16.5574	−0.544404
$926$	32.8641	1.07998
$927$	−0.970699	−0.0318819
$928$	35.0485	1.15052
$929$	32.1406	1.05450	0.527249	−	0.849711i	$-0.323224\pi$
$929$	32.1406	1.05450	0.527249	+	0.849711i	$0.323224\pi$
$930$	−0.831073	−0.0272519
$931$	−2.53444	−0.0830630
$932$	38.7734	1.27006
$933$	−4.38859	−0.143676
$934$	−17.2285	−0.563735
$935$	−17.5535	−0.574060
$936$	−39.5364	−1.29229
$937$	−3.02648	−0.0988708	−0.0494354	−	0.998777i	$-0.515742\pi$
$937$	−3.02648	−0.0988708	−0.0494354	+	0.998777i	$0.515742\pi$
$938$	98.5102	3.21647
$939$	−1.86853	−0.0609770
$940$	1.97626	0.0644586
$941$	17.3329	0.565036	0.282518	−	0.959262i	$-0.408830\pi$
$941$	17.3329	0.565036	0.282518	+	0.959262i	$0.408830\pi$
$942$	−22.7886	−0.742492
$943$	1.22774	0.0399807
$944$	86.2150	2.80606
$945$	4.56916	0.148635
$946$	−156.597	−5.09140
$947$	−34.2899	−1.11427	−0.557136	−	0.830421i	$-0.688100\pi$
$947$	−34.2899	−1.11427	−0.557136	+	0.830421i	$0.688100\pi$
$948$	8.29658	0.269461
$949$	3.81514	0.123845
$950$	−37.2194	−1.20756
$951$	−1.46087	−0.0473719
$952$	108.858	3.52811
$953$	26.7970	0.868038	0.434019	−	0.900904i	$-0.357095\pi$
$953$	26.7970	0.868038	0.434019	+	0.900904i	$0.357095\pi$
$954$	47.0746	1.52410
$955$	−5.68026	−0.183809
$956$	−42.6850	−1.38053
$957$	17.4967	0.565589
$958$	−61.4958	−1.98684
$959$	15.6978	0.506910
$960$	−0.341519	−0.0110225
$961$	−29.7213	−0.958750
$962$	20.1654	0.650160
$963$	−8.58632	−0.276690
$964$	−47.0525	−1.51546
$965$	−9.49990	−0.305813
$966$	5.36623	0.172656
$967$	53.9931	1.73630	0.868151	−	0.496300i	$-0.165309\pi$
$967$	53.9931	1.73630	0.868151	+	0.496300i	$0.165309\pi$
$968$	−142.207	−4.57070
$969$	−10.2266	−0.328525
$970$	6.10182	0.195917
$971$	−48.6505	−1.56127	−0.780634	−	0.624989i	$-0.785104\pi$
$971$	−48.6505	−1.56127	−0.780634	+	0.624989i	$0.785104\pi$
$972$	−59.3509	−1.90368
$973$	−4.19098	−0.134357
$974$	−78.5576	−2.51715
$975$	−5.96069	−0.190895
$976$	38.4885	1.23199
$977$	20.3814	0.652058	0.326029	−	0.945360i	$-0.394289\pi$
$977$	20.3814	0.652058	0.326029	+	0.945360i	$0.394289\pi$
$978$	−27.4603	−0.878085
$979$	−0.470146	−0.0150259
$980$	1.93073	0.0616749
$981$	−11.4174	−0.364528
$982$	0.630945	0.0201343
$983$	11.7214	0.373854	0.186927	−	0.982374i	$-0.440147\pi$
$983$	11.7214	0.373854	0.186927	+	0.982374i	$0.440147\pi$
$984$	3.33495	0.106314
$985$	−1.72214	−0.0548720
$986$	−83.4828	−2.65864
$987$	−1.31989	−0.0420124
$988$	31.4891	1.00180
$989$	14.3399	0.455981
$990$	20.2536	0.643703
$991$	43.2622	1.37427	0.687134	−	0.726531i	$-0.258869\pi$
$991$	43.2622	1.37427	0.687134	+	0.726531i	$0.258869\pi$
$992$	7.24452	0.230014
$993$	4.28885	0.136103
$994$	61.5583	1.95251
$995$	−9.73087	−0.308489
$996$	−7.42966	−0.235418
$997$	−41.0019	−1.29854	−0.649272	−	0.760556i	$-0.724926\pi$
$997$	−41.0019	−1.29854	−0.649272	+	0.760556i	$0.724926\pi$
$998$	−13.9137	−0.440430
$999$	11.1076	0.351427

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.15	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.15	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.55932 q^{2} -0.558527 q^{3} +4.55013 q^{4} +0.514137 q^{5} +1.42945 q^{6} +2.79738 q^{7} -6.52662 q^{8} -2.68805 q^{9} +O(q^{10})\)	\(q-2.55932 q^{2} -0.558527 q^{3} +4.55013 q^{4} +0.514137 q^{5} +1.42945 q^{6} +2.79738 q^{7} -6.52662 q^{8} -2.68805 q^{9} -1.31584 q^{10} +5.72615 q^{11} -2.54137 q^{12} -2.25357 q^{13} -7.15939 q^{14} -0.287159 q^{15} +7.60346 q^{16} -5.96241 q^{17} +6.87958 q^{18} -3.07089 q^{19} +2.33939 q^{20} -1.56241 q^{21} -14.6551 q^{22} +1.34199 q^{23} +3.64529 q^{24} -4.73566 q^{25} +5.76762 q^{26} +3.17693 q^{27} +12.7284 q^{28} -5.47079 q^{29} +0.734933 q^{30} -1.13081 q^{31} -6.40647 q^{32} -3.19821 q^{33} +15.2597 q^{34} +1.43823 q^{35} -12.2310 q^{36} +3.49632 q^{37} +7.85939 q^{38} +1.25868 q^{39} -3.35557 q^{40} +0.914864 q^{41} +3.99871 q^{42} +10.6855 q^{43} +26.0547 q^{44} -1.38202 q^{45} -3.43459 q^{46} +0.844776 q^{47} -4.24673 q^{48} +0.825313 q^{49} +12.1201 q^{50} +3.33016 q^{51} -10.2541 q^{52} +6.84265 q^{53} -8.13078 q^{54} +2.94402 q^{55} -18.2574 q^{56} +1.71517 q^{57} +14.0015 q^{58} +11.3389 q^{59} -1.30661 q^{60} +5.06197 q^{61} +2.89412 q^{62} -7.51948 q^{63} +1.18930 q^{64} -1.15864 q^{65} +8.18524 q^{66} -13.7596 q^{67} -27.1298 q^{68} -0.749538 q^{69} -3.68091 q^{70} -8.59825 q^{71} +17.5439 q^{72} -1.69293 q^{73} -8.94821 q^{74} +2.64500 q^{75} -13.9730 q^{76} +16.0182 q^{77} -3.22137 q^{78} -3.26461 q^{79} +3.90922 q^{80} +6.28974 q^{81} -2.34143 q^{82} +2.92348 q^{83} -7.10917 q^{84} -3.06549 q^{85} -27.3477 q^{86} +3.05559 q^{87} -37.3724 q^{88} -0.0821052 q^{89} +3.53705 q^{90} -6.30409 q^{91} +6.10624 q^{92} +0.631590 q^{93} -2.16205 q^{94} -1.57886 q^{95} +3.57818 q^{96} -4.63719 q^{97} -2.11224 q^{98} -15.3922 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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