LMFDB - Embedded newform 8015.2.a.l.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} +O(q^{10})$	\(q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} -0.858241 q^{10} -3.80724 q^{11} +3.98500 q^{12} +4.68905 q^{13} -0.858241 q^{14} +3.15413 q^{15} +0.123083 q^{16} -4.07383 q^{17} +5.96350 q^{18} +7.23547 q^{19} +1.26342 q^{20} +3.15413 q^{21} -3.26753 q^{22} -0.764001 q^{23} +8.83408 q^{24} +1.00000 q^{25} +4.02433 q^{26} -12.4541 q^{27} +1.26342 q^{28} -0.590526 q^{29} +2.70700 q^{30} -6.93316 q^{31} +5.70724 q^{32} +12.0085 q^{33} -3.49633 q^{34} +1.00000 q^{35} -8.77891 q^{36} -2.77423 q^{37} +6.20978 q^{38} -14.7898 q^{39} +2.80080 q^{40} -11.9508 q^{41} +2.70700 q^{42} +3.49226 q^{43} +4.81016 q^{44} -6.94851 q^{45} -0.655697 q^{46} +3.74422 q^{47} -0.388221 q^{48} +1.00000 q^{49} +0.858241 q^{50} +12.8494 q^{51} -5.92425 q^{52} +12.9071 q^{53} -10.6886 q^{54} +3.80724 q^{55} +2.80080 q^{56} -22.8216 q^{57} -0.506814 q^{58} -7.01171 q^{59} -3.98500 q^{60} +4.71799 q^{61} -5.95032 q^{62} -6.94851 q^{63} +4.65202 q^{64} -4.68905 q^{65} +10.3062 q^{66} -15.3211 q^{67} +5.14697 q^{68} +2.40976 q^{69} +0.858241 q^{70} -3.14562 q^{71} -19.4614 q^{72} -13.3099 q^{73} -2.38096 q^{74} -3.15413 q^{75} -9.14146 q^{76} +3.80724 q^{77} -12.6932 q^{78} -14.5011 q^{79} -0.123083 q^{80} +18.4363 q^{81} -10.2567 q^{82} -11.8838 q^{83} -3.98500 q^{84} +4.07383 q^{85} +2.99720 q^{86} +1.86259 q^{87} +10.6633 q^{88} +4.25748 q^{89} -5.96350 q^{90} -4.68905 q^{91} +0.965256 q^{92} +21.8681 q^{93} +3.21344 q^{94} -7.23547 q^{95} -18.0014 q^{96} +13.3856 q^{97} +0.858241 q^{98} -26.4547 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) $ 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * 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 $

$2$	0.858241	0.606868	0.303434	−	0.952852i	$-0.401867\pi$
$2$	0.858241	0.606868	0.303434	+	0.952852i	$0.401867\pi$
$3$	−3.15413	−1.82104	−0.910518	−	0.413470i	$-0.864317\pi$
$3$	−3.15413	−1.82104	−0.910518	+	0.413470i	$0.864317\pi$
$4$	−1.26342	−0.631711
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.70700	−1.10513
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−2.80080	−0.990233
$9$	6.94851	2.31617
$10$	−0.858241	−0.271400
$11$	−3.80724	−1.14793	−0.573963	−	0.818881i	$-0.694595\pi$
$11$	−3.80724	−1.14793	−0.573963	+	0.818881i	$0.694595\pi$
$12$	3.98500	1.15037
$13$	4.68905	1.30051	0.650254	−	0.759717i	$-0.274663\pi$
$13$	4.68905	1.30051	0.650254	+	0.759717i	$0.274663\pi$
$14$	−0.858241	−0.229374
$15$	3.15413	0.814392
$16$	0.123083	0.0307708
$17$	−4.07383	−0.988049	−0.494025	−	0.869448i	$-0.664475\pi$
$17$	−4.07383	−0.988049	−0.494025	+	0.869448i	$0.664475\pi$
$18$	5.96350	1.40561
$19$	7.23547	1.65993	0.829966	−	0.557815i	$-0.188360\pi$
$19$	7.23547	1.65993	0.829966	+	0.557815i	$0.188360\pi$
$20$	1.26342	0.282510
$21$	3.15413	0.688287
$22$	−3.26753	−0.696640
$23$	−0.764001	−0.159305	−0.0796526	−	0.996823i	$-0.525381\pi$
$23$	−0.764001	−0.159305	−0.0796526	+	0.996823i	$0.525381\pi$
$24$	8.83408	1.80325
$25$	1.00000	0.200000
$26$	4.02433	0.789236
$27$	−12.4541	−2.39679
$28$	1.26342	0.238764
$29$	−0.590526	−0.109658	−0.0548290	−	0.998496i	$-0.517461\pi$
$29$	−0.590526	−0.109658	−0.0548290	+	0.998496i	$0.517461\pi$
$30$	2.70700	0.494228
$31$	−6.93316	−1.24523	−0.622617	−	0.782527i	$-0.713930\pi$
$31$	−6.93316	−1.24523	−0.622617	+	0.782527i	$0.713930\pi$
$32$	5.70724	1.00891
$33$	12.0085	2.09042
$34$	−3.49633	−0.599615
$35$	1.00000	0.169031
$36$	−8.77891	−1.46315
$37$	−2.77423	−0.456080	−0.228040	−	0.973652i	$-0.573232\pi$
$37$	−2.77423	−0.456080	−0.228040	+	0.973652i	$0.573232\pi$
$38$	6.20978	1.00736
$39$	−14.7898	−2.36827
$40$	2.80080	0.442846
$41$	−11.9508	−1.86640	−0.933202	−	0.359351i	$-0.882998\pi$
$41$	−11.9508	−1.86640	−0.933202	+	0.359351i	$0.882998\pi$
$42$	2.70700	0.417699
$43$	3.49226	0.532565	0.266283	−	0.963895i	$-0.414205\pi$
$43$	3.49226	0.532565	0.266283	+	0.963895i	$0.414205\pi$
$44$	4.81016	0.725159
$45$	−6.94851	−1.03582
$46$	−0.655697	−0.0966772
$47$	3.74422	0.546151	0.273076	−	0.961993i	$-0.411959\pi$
$47$	3.74422	0.546151	0.273076	+	0.961993i	$0.411959\pi$
$48$	−0.388221	−0.0560348
$49$	1.00000	0.142857
$50$	0.858241	0.121374
$51$	12.8494	1.79927
$52$	−5.92425	−0.821546
$53$	12.9071	1.77292	0.886462	−	0.462801i	$-0.153155\pi$
$53$	12.9071	1.77292	0.886462	+	0.462801i	$0.153155\pi$
$54$	−10.6886	−1.45454
$55$	3.80724	0.513368
$56$	2.80080	0.374273
$57$	−22.8216	−3.02279
$58$	−0.506814	−0.0665479
$59$	−7.01171	−0.912848	−0.456424	−	0.889763i	$-0.650870\pi$
$59$	−7.01171	−0.912848	−0.456424	+	0.889763i	$0.650870\pi$
$60$	−3.98500	−0.514461
$61$	4.71799	0.604077	0.302039	−	0.953296i	$-0.402333\pi$
$61$	4.71799	0.604077	0.302039	+	0.953296i	$0.402333\pi$
$62$	−5.95032	−0.755692
$63$	−6.94851	−0.875430
$64$	4.65202	0.581502
$65$	−4.68905	−0.581605
$66$	10.3062	1.26861
$67$	−15.3211	−1.87177	−0.935887	−	0.352301i	$-0.885399\pi$
$67$	−15.3211	−1.87177	−0.935887	+	0.352301i	$0.885399\pi$
$68$	5.14697	0.624162
$69$	2.40976	0.290100
$70$	0.858241	0.102579
$71$	−3.14562	−0.373316	−0.186658	−	0.982425i	$-0.559766\pi$
$71$	−3.14562	−0.373316	−0.186658	+	0.982425i	$0.559766\pi$
$72$	−19.4614	−2.29355
$73$	−13.3099	−1.55781	−0.778906	−	0.627141i	$-0.784225\pi$
$73$	−13.3099	−1.55781	−0.778906	+	0.627141i	$0.784225\pi$
$74$	−2.38096	−0.276780
$75$	−3.15413	−0.364207
$76$	−9.14146	−1.04860
$77$	3.80724	0.433876
$78$	−12.6932	−1.43723
$79$	−14.5011	−1.63150	−0.815750	−	0.578404i	$-0.803676\pi$
$79$	−14.5011	−1.63150	−0.815750	+	0.578404i	$0.803676\pi$
$80$	−0.123083	−0.0137611
$81$	18.4363	2.04848
$82$	−10.2567	−1.13266
$83$	−11.8838	−1.30442	−0.652210	−	0.758039i	$-0.726158\pi$
$83$	−11.8838	−1.30442	−0.652210	+	0.758039i	$0.726158\pi$
$84$	−3.98500	−0.434799
$85$	4.07383	0.441869
$86$	2.99720	0.323197
$87$	1.86259	0.199691
$88$	10.6633	1.13672
$89$	4.25748	0.451292	0.225646	−	0.974209i	$-0.427551\pi$
$89$	4.25748	0.451292	0.225646	+	0.974209i	$0.427551\pi$
$90$	−5.96350	−0.628608
$91$	−4.68905	−0.491546
$92$	0.965256	0.100635
$93$	21.8681	2.26761
$94$	3.21344	0.331442
$95$	−7.23547	−0.742344
$96$	−18.0014	−1.83726
$97$	13.3856	1.35910	0.679551	−	0.733628i	$-0.262175\pi$
$97$	13.3856	1.35910	0.679551	+	0.733628i	$0.262175\pi$
$98$	0.858241	0.0866954
$99$	−26.4547	−2.65879
$100$	−1.26342	−0.126342
$101$	5.84607	0.581705	0.290853	−	0.956768i	$-0.406061\pi$
$101$	5.84607	0.581705	0.290853	+	0.956768i	$0.406061\pi$
$102$	11.0279	1.09192
$103$	3.79996	0.374421	0.187211	−	0.982320i	$-0.440055\pi$
$103$	3.79996	0.374421	0.187211	+	0.982320i	$0.440055\pi$
$104$	−13.1331	−1.28781
$105$	−3.15413	−0.307811
$106$	11.0774	1.07593
$107$	−1.41474	−0.136768	−0.0683839	−	0.997659i	$-0.521784\pi$
$107$	−1.41474	−0.136768	−0.0683839	+	0.997659i	$0.521784\pi$
$108$	15.7348	1.51408
$109$	−15.0737	−1.44380	−0.721898	−	0.691999i	$-0.756730\pi$
$109$	−15.0737	−1.44380	−0.721898	+	0.691999i	$0.756730\pi$
$110$	3.26753	0.311547
$111$	8.75027	0.830539
$112$	−0.123083	−0.0116303
$113$	−17.9528	−1.68886	−0.844428	−	0.535669i	$-0.820060\pi$
$113$	−17.9528	−1.68886	−0.844428	+	0.535669i	$0.820060\pi$
$114$	−19.5864	−1.83444
$115$	0.764001	0.0712434
$116$	0.746085	0.0692722
$117$	32.5819	3.01220
$118$	−6.01774	−0.553978
$119$	4.07383	0.373447
$120$	−8.83408	−0.806438
$121$	3.49509	0.317736
$122$	4.04917	0.366595
$123$	37.6944	3.39879
$124$	8.75952	0.786628
$125$	−1.00000	−0.0894427
$126$	−5.96350	−0.531270
$127$	−9.17177	−0.813863	−0.406932	−	0.913459i	$-0.633401\pi$
$127$	−9.17177	−0.813863	−0.406932	+	0.913459i	$0.633401\pi$
$128$	−7.42193	−0.656012
$129$	−11.0150	−0.969820
$130$	−4.02433	−0.352957
$131$	0.0451058	0.00394091	0.00197045	−	0.999998i	$-0.499373\pi$
$131$	0.0451058	0.00394091	0.00197045	+	0.999998i	$0.499373\pi$
$132$	−15.1718	−1.32054
$133$	−7.23547	−0.627395
$134$	−13.1492	−1.13592
$135$	12.4541	1.07188
$136$	11.4100	0.978399
$137$	21.8675	1.86827	0.934134	−	0.356924i	$-0.116174\pi$
$137$	21.8675	1.86827	0.934134	+	0.356924i	$0.116174\pi$
$138$	2.06815	0.176053
$139$	9.99513	0.847776	0.423888	−	0.905715i	$-0.360665\pi$
$139$	9.99513	0.847776	0.423888	+	0.905715i	$0.360665\pi$
$140$	−1.26342	−0.106779
$141$	−11.8098	−0.994561
$142$	−2.69969	−0.226553
$143$	−17.8523	−1.49289
$144$	0.855247	0.0712705
$145$	0.590526	0.0490405
$146$	−11.4231	−0.945386
$147$	−3.15413	−0.260148
$148$	3.50502	0.288111
$149$	2.71779	0.222650	0.111325	−	0.993784i	$-0.464491\pi$
$149$	2.71779	0.222650	0.111325	+	0.993784i	$0.464491\pi$
$150$	−2.70700	−0.221026
$151$	−16.8195	−1.36875	−0.684375	−	0.729130i	$-0.739925\pi$
$151$	−16.8195	−1.36875	−0.684375	+	0.729130i	$0.739925\pi$
$152$	−20.2651	−1.64372
$153$	−28.3071	−2.28849
$154$	3.26753	0.263305
$155$	6.93316	0.556885
$156$	18.6858	1.49606
$157$	−10.7254	−0.855978	−0.427989	−	0.903784i	$-0.640778\pi$
$157$	−10.7254	−0.855978	−0.427989	+	0.903784i	$0.640778\pi$
$158$	−12.4454	−0.990105
$159$	−40.7106	−3.22856
$160$	−5.70724	−0.451197
$161$	0.764001	0.0602117
$162$	15.8228	1.24315
$163$	−4.04557	−0.316873	−0.158437	−	0.987369i	$-0.550645\pi$
$163$	−4.04557	−0.316873	−0.158437	+	0.987369i	$0.550645\pi$
$164$	15.0989	1.17903
$165$	−12.0085	−0.934862
$166$	−10.1992	−0.791610
$167$	18.8132	1.45581	0.727904	−	0.685680i	$-0.240495\pi$
$167$	18.8132	1.45581	0.727904	+	0.685680i	$0.240495\pi$
$168$	−8.83408	−0.681564
$169$	8.98716	0.691320
$170$	3.49633	0.268156
$171$	50.2758	3.84468
$172$	−4.41221	−0.336427
$173$	−0.854004	−0.0649287	−0.0324643	−	0.999473i	$-0.510336\pi$
$173$	−0.854004	−0.0649287	−0.0324643	+	0.999473i	$0.510336\pi$
$174$	1.59855	0.121186
$175$	−1.00000	−0.0755929
$176$	−0.468608	−0.0353227
$177$	22.1158	1.66233
$178$	3.65394	0.273874
$179$	−16.9353	−1.26580	−0.632901	−	0.774232i	$-0.718136\pi$
$179$	−16.9353	−1.26580	−0.632901	+	0.774232i	$0.718136\pi$
$180$	8.77891	0.654341
$181$	11.4585	0.851703	0.425852	−	0.904793i	$-0.359975\pi$
$181$	11.4585	0.851703	0.425852	+	0.904793i	$0.359975\pi$
$182$	−4.02433	−0.298303
$183$	−14.8811	−1.10005
$184$	2.13982	0.157749
$185$	2.77423	0.203965
$186$	18.7681	1.37614
$187$	15.5101	1.13421
$188$	−4.73054	−0.345010
$189$	12.4541	0.905903
$190$	−6.20978	−0.450505
$191$	−25.4170	−1.83911	−0.919553	−	0.392966i	$-0.871449\pi$
$191$	−25.4170	−1.83911	−0.919553	+	0.392966i	$0.871449\pi$
$192$	−14.6731	−1.05894
$193$	23.0146	1.65663	0.828313	−	0.560266i	$-0.189301\pi$
$193$	23.0146	1.65663	0.828313	+	0.560266i	$0.189301\pi$
$194$	11.4881	0.824795
$195$	14.7898	1.05912
$196$	−1.26342	−0.0902445
$197$	−5.89035	−0.419670	−0.209835	−	0.977737i	$-0.567293\pi$
$197$	−5.89035	−0.419670	−0.209835	+	0.977737i	$0.567293\pi$
$198$	−22.7045	−1.61354
$199$	6.85706	0.486084	0.243042	−	0.970016i	$-0.421855\pi$
$199$	6.85706	0.486084	0.243042	+	0.970016i	$0.421855\pi$
$200$	−2.80080	−0.198047
$201$	48.3248	3.40857
$202$	5.01733	0.353018
$203$	0.590526	0.0414468
$204$	−16.2342	−1.13662
$205$	11.9508	0.834682
$206$	3.26128	0.227224
$207$	−5.30867	−0.368978
$208$	0.577144	0.0400177
$209$	−27.5472	−1.90548
$210$	−2.70700	−0.186801
$211$	19.6455	1.35245	0.676225	−	0.736695i	$-0.263615\pi$
$211$	19.6455	1.35245	0.676225	+	0.736695i	$0.263615\pi$
$212$	−16.3071	−1.11998
$213$	9.92167	0.679821
$214$	−1.21419	−0.0830000
$215$	−3.49226	−0.238170
$216$	34.8815	2.37338
$217$	6.93316	0.470654
$218$	−12.9368	−0.876194
$219$	41.9813	2.83683
$220$	−4.81016	−0.324301
$221$	−19.1024	−1.28497
$222$	7.50984	0.504027
$223$	−10.0369	−0.672124	−0.336062	−	0.941840i	$-0.609095\pi$
$223$	−10.0369	−0.672124	−0.336062	+	0.941840i	$0.609095\pi$
$224$	−5.70724	−0.381331
$225$	6.94851	0.463234
$226$	−15.4078	−1.02491
$227$	28.7335	1.90711	0.953556	−	0.301216i	$-0.0973924\pi$
$227$	28.7335	1.90711	0.953556	+	0.301216i	$0.0973924\pi$
$228$	28.8333	1.90953
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.655697	0.0432354
$231$	−12.0085	−0.790103
$232$	1.65395	0.108587
$233$	10.2643	0.672436	0.336218	−	0.941784i	$-0.390852\pi$
$233$	10.2643	0.672436	0.336218	+	0.941784i	$0.390852\pi$
$234$	27.9631	1.82801
$235$	−3.74422	−0.244246
$236$	8.85876	0.576656
$237$	45.7383	2.97102
$238$	3.49633	0.226633
$239$	12.1795	0.787826	0.393913	−	0.919148i	$-0.371121\pi$
$239$	12.1795	0.787826	0.393913	+	0.919148i	$0.371121\pi$
$240$	0.388221	0.0250595
$241$	−21.3677	−1.37641	−0.688207	−	0.725514i	$-0.741602\pi$
$241$	−21.3677	−1.37641	−0.688207	+	0.725514i	$0.741602\pi$
$242$	2.99963	0.192824
$243$	−20.7881	−1.33355
$244$	−5.96082	−0.381602
$245$	−1.00000	−0.0638877
$246$	32.3509	2.06262
$247$	33.9275	2.15875
$248$	19.4184	1.23307
$249$	37.4831	2.37539
$250$	−0.858241	−0.0542799
$251$	−6.07591	−0.383508	−0.191754	−	0.981443i	$-0.561418\pi$
$251$	−6.07591	−0.383508	−0.191754	+	0.981443i	$0.561418\pi$
$252$	8.77891	0.553019
$253$	2.90874	0.182871
$254$	−7.87159	−0.493907
$255$	−12.8494	−0.804659
$256$	−15.6738	−0.979615
$257$	−2.62208	−0.163561	−0.0817804	−	0.996650i	$-0.526061\pi$
$257$	−2.62208	−0.163561	−0.0817804	+	0.996650i	$0.526061\pi$
$258$	−9.45355	−0.588553
$259$	2.77423	0.172382
$260$	5.92425	0.367406
$261$	−4.10328	−0.253987
$262$	0.0387116	0.00239161
$263$	5.81447	0.358536	0.179268	−	0.983800i	$-0.442627\pi$
$263$	5.81447	0.358536	0.179268	+	0.983800i	$0.442627\pi$
$264$	−33.6335	−2.07000
$265$	−12.9071	−0.792876
$266$	−6.20978	−0.380746
$267$	−13.4286	−0.821818
$268$	19.3571	1.18242
$269$	−20.6446	−1.25872	−0.629362	−	0.777112i	$-0.716684\pi$
$269$	−20.6446	−1.25872	−0.629362	+	0.777112i	$0.716684\pi$
$270$	10.6886	0.650489
$271$	26.0918	1.58497	0.792483	−	0.609894i	$-0.208788\pi$
$271$	26.0918	1.58497	0.792483	+	0.609894i	$0.208788\pi$
$272$	−0.501421	−0.0304031
$273$	14.7898	0.895122
$274$	18.7676	1.13379
$275$	−3.80724	−0.229585
$276$	−3.04454	−0.183260
$277$	−5.67594	−0.341034	−0.170517	−	0.985355i	$-0.554544\pi$
$277$	−5.67594	−0.341034	−0.170517	+	0.985355i	$0.554544\pi$
$278$	8.57823	0.514488
$279$	−48.1752	−2.88417
$280$	−2.80080	−0.167380
$281$	0.770969	0.0459922	0.0229961	−	0.999736i	$-0.492679\pi$
$281$	0.770969	0.0459922	0.0229961	+	0.999736i	$0.492679\pi$
$282$	−10.1356	−0.603567
$283$	9.63994	0.573035	0.286518	−	0.958075i	$-0.407502\pi$
$283$	9.63994	0.573035	0.286518	+	0.958075i	$0.407502\pi$
$284$	3.97424	0.235828
$285$	22.8216	1.35183
$286$	−15.3216	−0.905985
$287$	11.9508	0.705435
$288$	39.6568	2.33680
$289$	−0.403906	−0.0237592
$290$	0.506814	0.0297611
$291$	−42.2199	−2.47497
$292$	16.8161	0.984087
$293$	16.2750	0.950797	0.475399	−	0.879771i	$-0.342304\pi$
$293$	16.2750	0.950797	0.475399	+	0.879771i	$0.342304\pi$
$294$	−2.70700	−0.157875
$295$	7.01171	0.408238
$296$	7.77007	0.451626
$297$	47.4158	2.75134
$298$	2.33251	0.135119
$299$	−3.58244	−0.207178
$300$	3.98500	0.230074
$301$	−3.49226	−0.201291
$302$	−14.4352	−0.830651
$303$	−18.4392	−1.05931
$304$	0.890566	0.0510775
$305$	−4.71799	−0.270152
$306$	−24.2943	−1.38881
$307$	−0.339195	−0.0193589	−0.00967944	−	0.999953i	$-0.503081\pi$
$307$	−0.339195	−0.0193589	−0.00967944	+	0.999953i	$0.503081\pi$
$308$	−4.81016	−0.274084
$309$	−11.9855	−0.681834
$310$	5.95032	0.337956
$311$	−9.36543	−0.531065	−0.265533	−	0.964102i	$-0.585548\pi$
$311$	−9.36543	−0.531065	−0.265533	+	0.964102i	$0.585548\pi$
$312$	41.4234	2.34514
$313$	11.5134	0.650775	0.325388	−	0.945581i	$-0.394505\pi$
$313$	11.5134	0.650775	0.325388	+	0.945581i	$0.394505\pi$
$314$	−9.20496	−0.519466
$315$	6.94851	0.391504
$316$	18.3210	1.03064
$317$	−4.38299	−0.246173	−0.123087	−	0.992396i	$-0.539279\pi$
$317$	−4.38299	−0.246173	−0.123087	+	0.992396i	$0.539279\pi$
$318$	−34.9395	−1.95931
$319$	2.24828	0.125879
$320$	−4.65202	−0.260056
$321$	4.46226	0.249059
$322$	0.655697	0.0365405
$323$	−29.4761	−1.64009
$324$	−23.2928	−1.29405
$325$	4.68905	0.260102
$326$	−3.47207	−0.192300
$327$	47.5443	2.62920
$328$	33.4719	1.84818
$329$	−3.74422	−0.206426
$330$	−10.3062	−0.567338
$331$	−13.3632	−0.734507	−0.367253	−	0.930121i	$-0.619702\pi$
$331$	−13.3632	−0.734507	−0.367253	+	0.930121i	$0.619702\pi$
$332$	15.0143	0.824017
$333$	−19.2768	−1.05636
$334$	16.1462	0.883482
$335$	15.3211	0.837083
$336$	0.388221	0.0211792
$337$	32.6187	1.77685	0.888427	−	0.459017i	$-0.151798\pi$
$337$	32.6187	1.77685	0.888427	+	0.459017i	$0.151798\pi$
$338$	7.71314	0.419540
$339$	56.6254	3.07547
$340$	−5.14697	−0.279134
$341$	26.3962	1.42944
$342$	43.1487	2.33321
$343$	−1.00000	−0.0539949
$344$	−9.78114	−0.527364
$345$	−2.40976	−0.129737
$346$	−0.732941	−0.0394031
$347$	6.22228	0.334030	0.167015	−	0.985954i	$-0.446587\pi$
$347$	6.22228	0.334030	0.167015	+	0.985954i	$0.446587\pi$
$348$	−2.35324	−0.126147
$349$	0.696412	0.0372781	0.0186390	−	0.999826i	$-0.494067\pi$
$349$	0.696412	0.0372781	0.0186390	+	0.999826i	$0.494067\pi$
$350$	−0.858241	−0.0458749
$351$	−58.3979	−3.11705
$352$	−21.7288	−1.15815
$353$	−30.8486	−1.64191	−0.820954	−	0.570995i	$-0.806558\pi$
$353$	−30.8486	−1.64191	−0.820954	+	0.570995i	$0.806558\pi$
$354$	18.9807	1.00881
$355$	3.14562	0.166952
$356$	−5.37899	−0.285086
$357$	−12.8494	−0.680061
$358$	−14.5346	−0.768175
$359$	−35.9257	−1.89609	−0.948043	−	0.318141i	$-0.896941\pi$
$359$	−35.9257	−1.89609	−0.948043	+	0.318141i	$0.896941\pi$
$360$	19.4614	1.02571
$361$	33.3521	1.75537
$362$	9.83415	0.516871
$363$	−11.0240	−0.578608
$364$	5.92425	0.310515
$365$	13.3099	0.696675
$366$	−12.7716	−0.667583
$367$	35.7607	1.86669	0.933347	−	0.358976i	$-0.116874\pi$
$367$	35.7607	1.86669	0.933347	+	0.358976i	$0.116874\pi$
$368$	−0.0940358	−0.00490196
$369$	−83.0404	−4.32291
$370$	2.38096	0.123780
$371$	−12.9071	−0.670103
$372$	−27.6286	−1.43248
$373$	12.8413	0.664900	0.332450	−	0.943121i	$-0.392125\pi$
$373$	12.8413	0.664900	0.332450	+	0.943121i	$0.392125\pi$
$374$	13.3114	0.688314
$375$	3.15413	0.162878
$376$	−10.4868	−0.540817
$377$	−2.76901	−0.142611
$378$	10.6886	0.549763
$379$	25.6885	1.31953	0.659764	−	0.751473i	$-0.270656\pi$
$379$	25.6885	1.31953	0.659764	+	0.751473i	$0.270656\pi$
$380$	9.14146	0.468947
$381$	28.9289	1.48207
$382$	−21.8139	−1.11609
$383$	33.9607	1.73531	0.867655	−	0.497167i	$-0.165626\pi$
$383$	33.9607	1.73531	0.867655	+	0.497167i	$0.165626\pi$
$384$	23.4097	1.19462
$385$	−3.80724	−0.194035
$386$	19.7521	1.00535
$387$	24.2660	1.23351
$388$	−16.9117	−0.858560
$389$	−17.0767	−0.865823	−0.432911	−	0.901436i	$-0.642514\pi$
$389$	−17.0767	−0.865823	−0.432911	+	0.901436i	$0.642514\pi$
$390$	12.6932	0.642748
$391$	3.11241	0.157401
$392$	−2.80080	−0.141462
$393$	−0.142269	−0.00717653
$394$	−5.05533	−0.254684
$395$	14.5011	0.729629
$396$	33.4234	1.67959
$397$	−32.3989	−1.62606	−0.813028	−	0.582225i	$-0.802182\pi$
$397$	−32.3989	−1.62606	−0.813028	+	0.582225i	$0.802182\pi$
$398$	5.88500	0.294989
$399$	22.8216	1.14251
$400$	0.123083	0.00615417
$401$	−14.5152	−0.724853	−0.362427	−	0.932012i	$-0.618052\pi$
$401$	−14.5152	−0.724853	−0.362427	+	0.932012i	$0.618052\pi$
$402$	41.4743	2.06855
$403$	−32.5099	−1.61943
$404$	−7.38606	−0.367470
$405$	−18.4363	−0.916106
$406$	0.506814	0.0251527
$407$	10.5622	0.523547
$408$	−35.9886	−1.78170
$409$	0.122161	0.00604047	0.00302023	−	0.999995i	$-0.499039\pi$
$409$	0.122161	0.00604047	0.00302023	+	0.999995i	$0.499039\pi$
$410$	10.2567	0.506541
$411$	−68.9729	−3.40218
$412$	−4.80096	−0.236526
$413$	7.01171	0.345024
$414$	−4.55612	−0.223921
$415$	11.8838	0.583354
$416$	26.7615	1.31209
$417$	−31.5259	−1.54383
$418$	−23.6421	−1.15637
$419$	−18.8288	−0.919849	−0.459925	−	0.887958i	$-0.652124\pi$
$419$	−18.8288	−0.919849	−0.459925	+	0.887958i	$0.652124\pi$
$420$	3.98500	0.194448
$421$	32.2030	1.56948	0.784739	−	0.619826i	$-0.212797\pi$
$421$	32.2030	1.56948	0.784739	+	0.619826i	$0.212797\pi$
$422$	16.8606	0.820759
$423$	26.0168	1.26498
$424$	−36.1502	−1.75561
$425$	−4.07383	−0.197610
$426$	8.51518	0.412562
$427$	−4.71799	−0.228320
$428$	1.78741	0.0863978
$429$	56.3085	2.71860
$430$	−2.99720	−0.144538
$431$	−20.2546	−0.975629	−0.487815	−	0.872947i	$-0.662206\pi$
$431$	−20.2546	−0.975629	−0.487815	+	0.872947i	$0.662206\pi$
$432$	−1.53289	−0.0737514
$433$	9.84939	0.473331	0.236666	−	0.971591i	$-0.423945\pi$
$433$	9.84939	0.473331	0.236666	+	0.971591i	$0.423945\pi$
$434$	5.95032	0.285625
$435$	−1.86259	−0.0893046
$436$	19.0444	0.912063
$437$	−5.52791	−0.264436
$438$	36.0300	1.72158
$439$	4.62921	0.220940	0.110470	−	0.993879i	$-0.464764\pi$
$439$	4.62921	0.220940	0.110470	+	0.993879i	$0.464764\pi$
$440$	−10.6633	−0.508354
$441$	6.94851	0.330882
$442$	−16.3944	−0.779804
$443$	−25.3536	−1.20459	−0.602294	−	0.798275i	$-0.705746\pi$
$443$	−25.3536	−1.20459	−0.602294	+	0.798275i	$0.705746\pi$
$444$	−11.0553	−0.524661
$445$	−4.25748	−0.201824
$446$	−8.61412	−0.407890
$447$	−8.57224	−0.405453
$448$	−4.65202	−0.219787
$449$	−20.7081	−0.977277	−0.488638	−	0.872486i	$-0.662506\pi$
$449$	−20.7081	−0.977277	−0.488638	+	0.872486i	$0.662506\pi$
$450$	5.96350	0.281122
$451$	45.4997	2.14250
$452$	22.6820	1.06687
$453$	53.0508	2.49254
$454$	24.6603	1.15736
$455$	4.68905	0.219826
$456$	63.9188	2.99327
$457$	25.0559	1.17207	0.586034	−	0.810287i	$-0.300689\pi$
$457$	25.0559	1.17207	0.586034	+	0.810287i	$0.300689\pi$
$458$	0.858241	0.0401030
$459$	50.7359	2.36815
$460$	−0.965256	−0.0450053
$461$	40.5976	1.89082	0.945410	−	0.325883i	$-0.105662\pi$
$461$	40.5976	1.89082	0.945410	+	0.325883i	$0.105662\pi$
$462$	−10.3062	−0.479488
$463$	−12.2642	−0.569966	−0.284983	−	0.958533i	$-0.591988\pi$
$463$	−12.2642	−0.569966	−0.284983	+	0.958533i	$0.591988\pi$
$464$	−0.0726840	−0.00337427
$465$	−21.8681	−1.01411
$466$	8.80924	0.408080
$467$	−40.0594	−1.85373	−0.926863	−	0.375399i	$-0.877506\pi$
$467$	−40.0594	−1.85373	−0.926863	+	0.375399i	$0.877506\pi$
$468$	−41.1647	−1.90284
$469$	15.3211	0.707464
$470$	−3.21344	−0.148225
$471$	33.8292	1.55877
$472$	19.6384	0.903932
$473$	−13.2959	−0.611346
$474$	39.2545	1.80302
$475$	7.23547	0.331986
$476$	−5.14697	−0.235911
$477$	89.6851	4.10640
$478$	10.4529	0.478106
$479$	38.7728	1.77158	0.885788	−	0.464090i	$-0.153618\pi$
$479$	38.7728	1.77158	0.885788	+	0.464090i	$0.153618\pi$
$480$	18.0014	0.821646
$481$	−13.0085	−0.593136
$482$	−18.3386	−0.835302
$483$	−2.40976	−0.109648
$484$	−4.41578	−0.200717
$485$	−13.3856	−0.607809
$486$	−17.8412	−0.809291
$487$	8.02262	0.363540	0.181770	−	0.983341i	$-0.441817\pi$
$487$	8.02262	0.363540	0.181770	+	0.983341i	$0.441817\pi$
$488$	−13.2142	−0.598177
$489$	12.7602	0.577038
$490$	−0.858241	−0.0387714
$491$	−19.9634	−0.900937	−0.450469	−	0.892792i	$-0.648743\pi$
$491$	−19.9634	−0.900937	−0.450469	+	0.892792i	$0.648743\pi$
$492$	−47.6240	−2.14705
$493$	2.40570	0.108347
$494$	29.1179	1.31008
$495$	26.4547	1.18905
$496$	−0.853357	−0.0383169
$497$	3.14562	0.141100
$498$	32.1695	1.44155
$499$	10.0366	0.449300	0.224650	−	0.974439i	$-0.427876\pi$
$499$	10.0366	0.449300	0.224650	+	0.974439i	$0.427876\pi$
$500$	1.26342	0.0565020
$501$	−59.3391	−2.65108
$502$	−5.21459	−0.232739
$503$	−8.19455	−0.365377	−0.182688	−	0.983171i	$-0.558480\pi$
$503$	−8.19455	−0.365377	−0.182688	+	0.983171i	$0.558480\pi$
$504$	19.4614	0.866880
$505$	−5.84607	−0.260147
$506$	2.49640	0.110978
$507$	−28.3466	−1.25892
$508$	11.5878	0.514127
$509$	15.5259	0.688172	0.344086	−	0.938938i	$-0.388189\pi$
$509$	15.5259	0.688172	0.344086	+	0.938938i	$0.388189\pi$
$510$	−11.0279	−0.488322
$511$	13.3099	0.588797
$512$	1.39193	0.0615152
$513$	−90.1113	−3.97851
$514$	−2.25038	−0.0992598
$515$	−3.79996	−0.167446
$516$	13.9167	0.612646
$517$	−14.2552	−0.626942
$518$	2.38096	0.104613
$519$	2.69364	0.118237
$520$	13.1331	0.575924
$521$	19.8743	0.870711	0.435355	−	0.900259i	$-0.356623\pi$
$521$	19.8743	0.870711	0.435355	+	0.900259i	$0.356623\pi$
$522$	−3.52160	−0.154136
$523$	−22.1053	−0.966598	−0.483299	−	0.875455i	$-0.660562\pi$
$523$	−22.1053	−0.966598	−0.483299	+	0.875455i	$0.660562\pi$
$524$	−0.0569876	−0.00248952
$525$	3.15413	0.137657
$526$	4.99022	0.217584
$527$	28.2445	1.23035
$528$	1.47805	0.0643239
$529$	−22.4163	−0.974622
$530$	−11.0774	−0.481171
$531$	−48.7210	−2.11431
$532$	9.14146	0.396333
$533$	−56.0380	−2.42727
$534$	−11.5250	−0.498735
$535$	1.41474	0.0611644
$536$	42.9115	1.85349
$537$	53.4160	2.30507
$538$	−17.7180	−0.763879
$539$	−3.80724	−0.163990
$540$	−15.7348	−0.677118
$541$	16.5788	0.712779	0.356389	−	0.934337i	$-0.384008\pi$
$541$	16.5788	0.712779	0.356389	+	0.934337i	$0.384008\pi$
$542$	22.3931	0.961865
$543$	−36.1415	−1.55098
$544$	−23.2503	−0.996850
$545$	15.0737	0.645685
$546$	12.6932	0.543221
$547$	−41.0499	−1.75517	−0.877583	−	0.479424i	$-0.840845\pi$
$547$	−41.0499	−1.75517	−0.877583	+	0.479424i	$0.840845\pi$
$548$	−27.6279	−1.18021
$549$	32.7830	1.39915
$550$	−3.26753	−0.139328
$551$	−4.27274	−0.182025
$552$	−6.74925	−0.287267
$553$	14.5011	0.616649
$554$	−4.87132	−0.206963
$555$	−8.75027	−0.371428
$556$	−12.6281	−0.535550
$557$	−14.8735	−0.630212	−0.315106	−	0.949056i	$-0.602040\pi$
$557$	−14.8735	−0.630212	−0.315106	+	0.949056i	$0.602040\pi$
$558$	−41.3459	−1.75031
$559$	16.3754	0.692605
$560$	0.123083	0.00520122
$561$	−48.9207	−2.06543
$562$	0.661677	0.0279112
$563$	25.9023	1.09165	0.545825	−	0.837899i	$-0.316216\pi$
$563$	25.9023	1.09165	0.545825	+	0.837899i	$0.316216\pi$
$564$	14.9207	0.628275
$565$	17.9528	0.755280
$566$	8.27339	0.347757
$567$	−18.4363	−0.774251
$568$	8.81025	0.369670
$569$	−23.9155	−1.00259	−0.501296	−	0.865276i	$-0.667143\pi$
$569$	−23.9155	−1.00259	−0.501296	+	0.865276i	$0.667143\pi$
$570$	19.5864	0.820385
$571$	14.5900	0.610572	0.305286	−	0.952261i	$-0.401248\pi$
$571$	14.5900	0.610572	0.305286	+	0.952261i	$0.401248\pi$
$572$	22.5551	0.943074
$573$	80.1683	3.34908
$574$	10.2567	0.428106
$575$	−0.764001	−0.0318610
$576$	32.3246	1.34686
$577$	25.6298	1.06698	0.533491	−	0.845806i	$-0.320880\pi$
$577$	25.6298	1.06698	0.533491	+	0.845806i	$0.320880\pi$
$578$	−0.346649	−0.0144187
$579$	−72.5909	−3.01677
$580$	−0.746085	−0.0309795
$581$	11.8838	0.493024
$582$	−36.2348	−1.50198
$583$	−49.1404	−2.03519
$584$	37.2785	1.54260
$585$	−32.5819	−1.34710
$586$	13.9679	0.577008
$587$	−40.9084	−1.68847	−0.844236	−	0.535972i	$-0.819945\pi$
$587$	−40.9084	−1.68847	−0.844236	+	0.535972i	$0.819945\pi$
$588$	3.98500	0.164338
$589$	−50.1647	−2.06700
$590$	6.01774	0.247746
$591$	18.5789	0.764234
$592$	−0.341461	−0.0140340
$593$	−9.06565	−0.372282	−0.186141	−	0.982523i	$-0.559598\pi$
$593$	−9.06565	−0.372282	−0.186141	+	0.982523i	$0.559598\pi$
$594$	40.6942	1.66970
$595$	−4.07383	−0.167011
$596$	−3.43371	−0.140650
$597$	−21.6280	−0.885176
$598$	−3.07459	−0.125729
$599$	13.2235	0.540300	0.270150	−	0.962818i	$-0.412927\pi$
$599$	13.2235	0.540300	0.270150	+	0.962818i	$0.412927\pi$
$600$	8.83408	0.360650
$601$	38.3644	1.56492	0.782458	−	0.622704i	$-0.213966\pi$
$601$	38.3644	1.56492	0.782458	+	0.622704i	$0.213966\pi$
$602$	−2.99720	−0.122157
$603$	−106.459	−4.33535
$604$	21.2501	0.864656
$605$	−3.49509	−0.142096
$606$	−15.8253	−0.642859
$607$	15.1679	0.615646	0.307823	−	0.951444i	$-0.400400\pi$
$607$	15.1679	0.615646	0.307823	+	0.951444i	$0.400400\pi$
$608$	41.2946	1.67472
$609$	−1.86259	−0.0754761
$610$	−4.04917	−0.163946
$611$	17.5568	0.710274
$612$	35.7638	1.44567
$613$	20.8571	0.842412	0.421206	−	0.906965i	$-0.361607\pi$
$613$	20.8571	0.842412	0.421206	+	0.906965i	$0.361607\pi$
$614$	−0.291111	−0.0117483
$615$	−37.6944	−1.51998
$616$	−10.6633	−0.429638
$617$	−0.696274	−0.0280309	−0.0140155	−	0.999902i	$-0.504461\pi$
$617$	−0.696274	−0.0280309	−0.0140155	+	0.999902i	$0.504461\pi$
$618$	−10.2865	−0.413783
$619$	−4.20837	−0.169149	−0.0845743	−	0.996417i	$-0.526953\pi$
$619$	−4.20837	−0.169149	−0.0845743	+	0.996417i	$0.526953\pi$
$620$	−8.75952	−0.351791
$621$	9.51495	0.381822
$622$	−8.03780	−0.322286
$623$	−4.25748	−0.170572
$624$	−1.82038	−0.0728737
$625$	1.00000	0.0400000
$626$	9.88126	0.394935
$627$	86.8873	3.46995
$628$	13.5507	0.540731
$629$	11.3017	0.450630
$630$	5.96350	0.237591
$631$	−7.57622	−0.301605	−0.150802	−	0.988564i	$-0.548186\pi$
$631$	−7.57622	−0.301605	−0.150802	+	0.988564i	$0.548186\pi$
$632$	40.6147	1.61557
$633$	−61.9643	−2.46286
$634$	−3.76166	−0.149395
$635$	9.17177	0.363971
$636$	51.4347	2.03952
$637$	4.68905	0.185787
$638$	1.92956	0.0763921
$639$	−21.8573	−0.864663
$640$	7.42193	0.293377
$641$	−18.5034	−0.730842	−0.365421	−	0.930842i	$-0.619075\pi$
$641$	−18.5034	−0.730842	−0.365421	+	0.930842i	$0.619075\pi$
$642$	3.82969	0.151146
$643$	−27.0357	−1.06619	−0.533093	−	0.846057i	$-0.678970\pi$
$643$	−27.0357	−1.06619	−0.533093	+	0.846057i	$0.678970\pi$
$644$	−0.965256	−0.0380364
$645$	11.0150	0.433717
$646$	−25.2976	−0.995320
$647$	34.7167	1.36485	0.682427	−	0.730954i	$-0.260925\pi$
$647$	34.7167	1.36485	0.682427	+	0.730954i	$0.260925\pi$
$648$	−51.6364	−2.02847
$649$	26.6953	1.04788
$650$	4.02433	0.157847
$651$	−21.8681	−0.857077
$652$	5.11126	0.200172
$653$	29.4351	1.15188	0.575941	−	0.817491i	$-0.304636\pi$
$653$	29.4351	1.15188	0.575941	+	0.817491i	$0.304636\pi$
$654$	40.8044	1.59558
$655$	−0.0451058	−0.00176243
$656$	−1.47095	−0.0574309
$657$	−92.4843	−3.60816
$658$	−3.21344	−0.125273
$659$	−19.9080	−0.775506	−0.387753	−	0.921763i	$-0.626749\pi$
$659$	−19.9080	−0.775506	−0.387753	+	0.921763i	$0.626749\pi$
$660$	15.1718	0.590563
$661$	36.2107	1.40843	0.704217	−	0.709985i	$-0.251298\pi$
$661$	36.2107	1.40843	0.704217	+	0.709985i	$0.251298\pi$
$662$	−11.4688	−0.445748
$663$	60.2513	2.33997
$664$	33.2842	1.29168
$665$	7.23547	0.280580
$666$	−16.5441	−0.641071
$667$	0.451163	0.0174691
$668$	−23.7690	−0.919650
$669$	31.6578	1.22396
$670$	13.1492	0.507999
$671$	−17.9625	−0.693436
$672$	18.0014	0.694417
$673$	23.8379	0.918885	0.459443	−	0.888207i	$-0.348049\pi$
$673$	23.8379	0.918885	0.459443	+	0.888207i	$0.348049\pi$
$674$	27.9947	1.07832
$675$	−12.4541	−0.479359
$676$	−11.3546	−0.436715
$677$	28.3256	1.08864	0.544321	−	0.838877i	$-0.316787\pi$
$677$	28.3256	1.08864	0.544321	+	0.838877i	$0.316787\pi$
$678$	48.5982	1.86640
$679$	−13.3856	−0.513692
$680$	−11.4100	−0.437553
$681$	−90.6292	−3.47292
$682$	22.6543	0.867479
$683$	−51.5505	−1.97252	−0.986262	−	0.165189i	$-0.947176\pi$
$683$	−51.5505	−1.97252	−0.986262	+	0.165189i	$0.947176\pi$
$684$	−63.5196	−2.42873
$685$	−21.8675	−0.835514
$686$	−0.858241	−0.0327678
$687$	−3.15413	−0.120337
$688$	0.429840	0.0163875
$689$	60.5219	2.30570
$690$	−2.06815	−0.0787331
$691$	39.8340	1.51536	0.757679	−	0.652628i	$-0.226334\pi$
$691$	39.8340	1.51536	0.757679	+	0.652628i	$0.226334\pi$
$692$	1.07897	0.0410162
$693$	26.4547	1.00493
$694$	5.34022	0.202712
$695$	−9.99513	−0.379137
$696$	−5.21676	−0.197741
$697$	48.6856	1.84410
$698$	0.597689	0.0226229
$699$	−32.3749	−1.22453
$700$	1.26342	0.0477529
$701$	14.8070	0.559252	0.279626	−	0.960109i	$-0.409790\pi$
$701$	14.8070	0.559252	0.279626	+	0.960109i	$0.409790\pi$
$702$	−50.1194	−1.89164
$703$	−20.0729	−0.757062
$704$	−17.7114	−0.667522
$705$	11.8098	0.444781
$706$	−26.4756	−0.996421
$707$	−5.84607	−0.219864
$708$	−27.9417	−1.05011
$709$	38.6138	1.45017	0.725087	−	0.688658i	$-0.241800\pi$
$709$	38.6138	1.45017	0.725087	+	0.688658i	$0.241800\pi$
$710$	2.69969	0.101318
$711$	−100.761	−3.77883
$712$	−11.9243	−0.446884
$713$	5.29694	0.198372
$714$	−11.0279	−0.412707
$715$	17.8523	0.667640
$716$	21.3964	0.799622
$717$	−38.4157	−1.43466
$718$	−30.8329	−1.15067
$719$	−18.2248	−0.679672	−0.339836	−	0.940485i	$-0.610372\pi$
$719$	−18.2248	−0.679672	−0.339836	+	0.940485i	$0.610372\pi$
$720$	−0.855247	−0.0318732
$721$	−3.79996	−0.141518
$722$	28.6241	1.06528
$723$	67.3964	2.50650
$724$	−14.4769	−0.538031
$725$	−0.590526	−0.0219316
$726$	−9.46122	−0.351139
$727$	14.7747	0.547965	0.273983	−	0.961735i	$-0.411659\pi$
$727$	14.7747	0.547965	0.273983	+	0.961735i	$0.411659\pi$
$728$	13.1331	0.486745
$729$	10.2593	0.379974
$730$	11.4231	0.422789
$731$	−14.2269	−0.526200
$732$	18.8012	0.694912
$733$	12.2286	0.451673	0.225837	−	0.974165i	$-0.427488\pi$
$733$	12.2286	0.451673	0.225837	+	0.974165i	$0.427488\pi$
$734$	30.6913	1.13284
$735$	3.15413	0.116342
$736$	−4.36034	−0.160724
$737$	58.3313	2.14866
$738$	−71.2687	−2.62344
$739$	−27.8081	−1.02294	−0.511469	−	0.859302i	$-0.670899\pi$
$739$	−27.8081	−1.02294	−0.511469	+	0.859302i	$0.670899\pi$
$740$	−3.50502	−0.128847
$741$	−107.012	−3.93117
$742$	−11.0774	−0.406664
$743$	−7.94065	−0.291314	−0.145657	−	0.989335i	$-0.546530\pi$
$743$	−7.94065	−0.291314	−0.145657	+	0.989335i	$0.546530\pi$
$744$	−61.2482	−2.24547
$745$	−2.71779	−0.0995719
$746$	11.0210	0.403506
$747$	−82.5749	−3.02126
$748$	−19.5958	−0.716492
$749$	1.41474	0.0516934
$750$	2.70700	0.0988456
$751$	8.25956	0.301396	0.150698	−	0.988580i	$-0.451848\pi$
$751$	8.25956	0.301396	0.150698	+	0.988580i	$0.451848\pi$
$752$	0.460852	0.0168055
$753$	19.1642	0.698382
$754$	−2.37647	−0.0865461
$755$	16.8195	0.612124
$756$	−15.7348	−0.572269
$757$	25.6148	0.930986	0.465493	−	0.885052i	$-0.345877\pi$
$757$	25.6148	0.930986	0.465493	+	0.885052i	$0.345877\pi$
$758$	22.0469	0.800779
$759$	−9.17452	−0.333014
$760$	20.2651	0.735093
$761$	35.4025	1.28334	0.641669	−	0.766981i	$-0.278242\pi$
$761$	35.4025	1.28334	0.641669	+	0.766981i	$0.278242\pi$
$762$	24.8280	0.899423
$763$	15.0737	0.545704
$764$	32.1124	1.16178
$765$	28.3071	1.02344
$766$	29.1464	1.05310
$767$	−32.8783	−1.18717
$768$	49.4373	1.78391
$769$	43.7943	1.57926	0.789631	−	0.613582i	$-0.210272\pi$
$769$	43.7943	1.57926	0.789631	+	0.613582i	$0.210272\pi$
$770$	−3.26753	−0.117754
$771$	8.27037	0.297850
$772$	−29.0772	−1.04651
$773$	15.4427	0.555437	0.277718	−	0.960663i	$-0.410422\pi$
$773$	15.4427	0.555437	0.277718	+	0.960663i	$0.410422\pi$
$774$	20.8261	0.748579
$775$	−6.93316	−0.249047
$776$	−37.4904	−1.34583
$777$	−8.75027	−0.313914
$778$	−14.6559	−0.525440
$779$	−86.4698	−3.09810
$780$	−18.6858	−0.669060
$781$	11.9761	0.428539
$782$	2.67120	0.0955218
$783$	7.35448	0.262828
$784$	0.123083	0.00439584
$785$	10.7254	0.382805
$786$	−0.122101	−0.00435521
$787$	4.07908	0.145404	0.0727018	−	0.997354i	$-0.476838\pi$
$787$	4.07908	0.145404	0.0727018	+	0.997354i	$0.476838\pi$
$788$	7.44200	0.265110
$789$	−18.3396	−0.652906
$790$	12.4454	0.442789
$791$	17.9528	0.638328
$792$	74.0943	2.63283
$793$	22.1229	0.785607
$794$	−27.8061	−0.986801
$795$	40.7106	1.44386
$796$	−8.66336	−0.307065
$797$	−14.6474	−0.518838	−0.259419	−	0.965765i	$-0.583531\pi$
$797$	−14.6474	−0.518838	−0.259419	+	0.965765i	$0.583531\pi$
$798$	19.5864	0.693352
$799$	−15.2533	−0.539624
$800$	5.70724	0.201781
$801$	29.5831	1.04527
$802$	−12.4575	−0.439890
$803$	50.6742	1.78825
$804$	−61.0546	−2.15323
$805$	−0.764001	−0.0269275
$806$	−27.9013	−0.982783
$807$	65.1157	2.29218
$808$	−16.3737	−0.576024
$809$	23.1089	0.812466	0.406233	−	0.913769i	$-0.366842\pi$
$809$	23.1089	0.812466	0.406233	+	0.913769i	$0.366842\pi$
$810$	−15.8228	−0.555956
$811$	−10.7872	−0.378791	−0.189395	−	0.981901i	$-0.560653\pi$
$811$	−10.7872	−0.378791	−0.189395	+	0.981901i	$0.560653\pi$
$812$	−0.746085	−0.0261824
$813$	−82.2969	−2.88628
$814$	9.06488	0.317724
$815$	4.04557	0.141710
$816$	1.58154	0.0553651
$817$	25.2682	0.884021
$818$	0.104843	0.00366577
$819$	−32.5819	−1.13850
$820$	−15.0989	−0.527278
$821$	−40.2600	−1.40508	−0.702541	−	0.711643i	$-0.747951\pi$
$821$	−40.2600	−1.40508	−0.702541	+	0.711643i	$0.747951\pi$
$822$	−59.1953	−2.06467
$823$	14.3262	0.499381	0.249690	−	0.968326i	$-0.419671\pi$
$823$	14.3262	0.499381	0.249690	+	0.968326i	$0.419671\pi$
$824$	−10.6429	−0.370764
$825$	12.0085	0.418083
$826$	6.01774	0.209384
$827$	−24.6400	−0.856818	−0.428409	−	0.903585i	$-0.640926\pi$
$827$	−24.6400	−0.856818	−0.428409	+	0.903585i	$0.640926\pi$
$828$	6.70709	0.233088
$829$	−38.6902	−1.34376	−0.671882	−	0.740658i	$-0.734514\pi$
$829$	−38.6902	−1.34376	−0.671882	+	0.740658i	$0.734514\pi$
$830$	10.1992	0.354019
$831$	17.9026	0.621035
$832$	21.8135	0.756248
$833$	−4.07383	−0.141150
$834$	−27.0568	−0.936901
$835$	−18.8132	−0.651057
$836$	34.8038	1.20371
$837$	86.3464	2.98457
$838$	−16.1597	−0.558227
$839$	−7.89509	−0.272569	−0.136284	−	0.990670i	$-0.543516\pi$
$839$	−7.89509	−0.272569	−0.136284	+	0.990670i	$0.543516\pi$
$840$	8.83408	0.304805
$841$	−28.6513	−0.987975
$842$	27.6379	0.952466
$843$	−2.43173	−0.0837534
$844$	−24.8206	−0.854359
$845$	−8.98716	−0.309168
$846$	22.3287	0.767675
$847$	−3.49509	−0.120093
$848$	1.58865	0.0545544
$849$	−30.4056	−1.04352
$850$	−3.49633	−0.119923
$851$	2.11951	0.0726560
$852$	−12.5353	−0.429451
$853$	−20.8660	−0.714439	−0.357219	−	0.934021i	$-0.616275\pi$
$853$	−20.8660	−0.714439	−0.357219	+	0.934021i	$0.616275\pi$
$854$	−4.04917	−0.138560
$855$	−50.2758	−1.71939
$856$	3.96240	0.135432
$857$	−5.77917	−0.197413	−0.0987064	−	0.995117i	$-0.531470\pi$
$857$	−5.77917	−0.197413	−0.0987064	+	0.995117i	$0.531470\pi$
$858$	48.3263	1.64983
$859$	−27.0660	−0.923479	−0.461740	−	0.887015i	$-0.652775\pi$
$859$	−27.0660	−0.923479	−0.461740	+	0.887015i	$0.652775\pi$
$860$	4.41221	0.150455
$861$	−37.6944	−1.28462
$862$	−17.3833	−0.592078
$863$	32.7795	1.11583	0.557913	−	0.829899i	$-0.311602\pi$
$863$	32.7795	1.11583	0.557913	+	0.829899i	$0.311602\pi$
$864$	−71.0786	−2.41814
$865$	0.854004	0.0290370
$866$	8.45314	0.287250
$867$	1.27397	0.0432663
$868$	−8.75952	−0.297317
$869$	55.2092	1.87284
$870$	−1.59855	−0.0541961
$871$	−71.8415	−2.43426
$872$	42.2184	1.42970
$873$	93.0100	3.14791
$874$	−4.74427	−0.160477
$875$	1.00000	0.0338062
$876$	−53.0401	−1.79206
$877$	−31.8055	−1.07400	−0.536998	−	0.843583i	$-0.680442\pi$
$877$	−31.8055	−1.07400	−0.536998	+	0.843583i	$0.680442\pi$
$878$	3.97298	0.134081
$879$	−51.3335	−1.73144
$880$	0.468608	0.0157968
$881$	21.4210	0.721692	0.360846	−	0.932625i	$-0.382488\pi$
$881$	21.4210	0.721692	0.360846	+	0.932625i	$0.382488\pi$
$882$	5.96350	0.200801
$883$	12.1792	0.409862	0.204931	−	0.978776i	$-0.434303\pi$
$883$	12.1792	0.409862	0.204931	+	0.978776i	$0.434303\pi$
$884$	24.1344	0.811727
$885$	−22.1158	−0.743416
$886$	−21.7595	−0.731025
$887$	41.1229	1.38077	0.690386	−	0.723441i	$-0.257441\pi$
$887$	41.1229	1.38077	0.690386	+	0.723441i	$0.257441\pi$
$888$	−24.5078	−0.822427
$889$	9.17177	0.307611
$890$	−3.65394	−0.122480
$891$	−70.1914	−2.35150
$892$	12.6809	0.424588
$893$	27.0912	0.906573
$894$	−7.35704	−0.246056
$895$	16.9353	0.566084
$896$	7.42193	0.247949
$897$	11.2995	0.377278
$898$	−17.7726	−0.593078
$899$	4.09422	0.136550
$900$	−8.77891	−0.292630
$901$	−52.5813	−1.75174
$902$	39.0497	1.30021
$903$	11.0150	0.366558
$904$	50.2822	1.67236
$905$	−11.4585	−0.380893
$906$	45.5304	1.51264
$907$	17.3948	0.577586	0.288793	−	0.957391i	$-0.406746\pi$
$907$	17.3948	0.577586	0.288793	+	0.957391i	$0.406746\pi$
$908$	−36.3026	−1.20474
$909$	40.6215	1.34733
$910$	4.02433	0.133405
$911$	−18.4553	−0.611451	−0.305726	−	0.952120i	$-0.598899\pi$
$911$	−18.4553	−0.611451	−0.305726	+	0.952120i	$0.598899\pi$
$912$	−2.80896	−0.0930139
$913$	45.2446	1.49738
$914$	21.5040	0.711290
$915$	14.8811	0.491956
$916$	−1.26342	−0.0417447
$917$	−0.0451058	−0.00148952
$918$	43.5436	1.43715
$919$	−23.1891	−0.764938	−0.382469	−	0.923968i	$-0.624926\pi$
$919$	−23.1891	−0.764938	−0.382469	+	0.923968i	$0.624926\pi$
$920$	−2.13982	−0.0705476
$921$	1.06986	0.0352532
$922$	34.8425	1.14748
$923$	−14.7499	−0.485500
$924$	15.1718	0.499117
$925$	−2.77423	−0.0912161
$926$	−10.5256	−0.345894
$927$	26.4041	0.867223
$928$	−3.37028	−0.110635
$929$	−22.6059	−0.741674	−0.370837	−	0.928698i	$-0.620929\pi$
$929$	−22.6059	−0.741674	−0.370837	+	0.928698i	$0.620929\pi$
$930$	−18.7681	−0.615429
$931$	7.23547	0.237133
$932$	−12.9681	−0.424786
$933$	29.5398	0.967088
$934$	−34.3806	−1.12497
$935$	−15.5101	−0.507233
$936$	−91.2555	−2.98278
$937$	−8.49316	−0.277459	−0.138730	−	0.990330i	$-0.544302\pi$
$937$	−8.49316	−0.277459	−0.138730	+	0.990330i	$0.544302\pi$
$938$	13.1492	0.429337
$939$	−36.3147	−1.18509
$940$	4.73054	0.154293
$941$	−37.0113	−1.20653	−0.603267	−	0.797539i	$-0.706135\pi$
$941$	−37.0113	−1.20653	−0.603267	+	0.797539i	$0.706135\pi$
$942$	29.0336	0.945966
$943$	9.13044	0.297328
$944$	−0.863026	−0.0280891
$945$	−12.4541	−0.405132
$946$	−11.4111	−0.371006
$947$	16.5147	0.536655	0.268327	−	0.963328i	$-0.413529\pi$
$947$	16.5147	0.536655	0.268327	+	0.963328i	$0.413529\pi$
$948$	−57.7868	−1.87683
$949$	−62.4110	−2.02595
$950$	6.20978	0.201472
$951$	13.8245	0.448290
$952$	−11.4100	−0.369800
$953$	19.4260	0.629271	0.314635	−	0.949213i	$-0.398118\pi$
$953$	19.4260	0.629271	0.314635	+	0.949213i	$0.398118\pi$
$954$	76.9714	2.49204
$955$	25.4170	0.822473
$956$	−15.3879	−0.497679
$957$	−7.09135	−0.229231
$958$	33.2764	1.07511
$959$	−21.8675	−0.706139
$960$	14.6731	0.473571
$961$	17.0688	0.550605
$962$	−11.1644	−0.359955
$963$	−9.83032	−0.316778
$964$	26.9964	0.869497
$965$	−23.0146	−0.740866
$966$	−2.06815	−0.0665416
$967$	9.05670	0.291244	0.145622	−	0.989340i	$-0.453482\pi$
$967$	9.05670	0.291244	0.145622	+	0.989340i	$0.453482\pi$
$968$	−9.78907	−0.314633
$969$	92.9713	2.98667
$970$	−11.4881	−0.368860
$971$	15.1364	0.485751	0.242876	−	0.970057i	$-0.421909\pi$
$971$	15.1364	0.485751	0.242876	+	0.970057i	$0.421909\pi$
$972$	26.2641	0.842422
$973$	−9.99513	−0.320429
$974$	6.88534	0.220620
$975$	−14.7898	−0.473654
$976$	0.580707	0.0185880
$977$	−24.0438	−0.769231	−0.384615	−	0.923077i	$-0.625666\pi$
$977$	−24.0438	−0.769231	−0.384615	+	0.923077i	$0.625666\pi$
$978$	10.9513	0.350186
$979$	−16.2092	−0.518050
$980$	1.26342	0.0403586
$981$	−104.740	−3.34408
$982$	−17.1334	−0.546750
$983$	−46.6467	−1.48780	−0.743900	−	0.668291i	$-0.767026\pi$
$983$	−46.6467	−1.48780	−0.743900	+	0.668291i	$0.767026\pi$
$984$	−105.575	−3.36559
$985$	5.89035	0.187682
$986$	2.06467	0.0657526
$987$	11.8098	0.375909
$988$	−42.8647	−1.36371
$989$	−2.66809	−0.0848404
$990$	22.7045	0.721596
$991$	−21.9043	−0.695814	−0.347907	−	0.937529i	$-0.613108\pi$
$991$	−21.9043	−0.695814	−0.347907	+	0.937529i	$0.613108\pi$
$992$	−39.5692	−1.25632
$993$	42.1491	1.33756
$994$	2.69969	0.0856291
$995$	−6.85706	−0.217383
$996$	−47.3570	−1.50056
$997$	24.7170	0.782794	0.391397	−	0.920222i	$-0.371992\pi$
$997$	24.7170	0.782794	0.391397	+	0.920222i	$0.371992\pi$
$998$	8.61383	0.272666
$999$	34.5505	1.09313

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.l.1.39	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.l.1.39	✓	62	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} +O(q^{10})\)	\(q+0.858241 q^{2} -3.15413 q^{3} -1.26342 q^{4} -1.00000 q^{5} -2.70700 q^{6} -1.00000 q^{7} -2.80080 q^{8} +6.94851 q^{9} -0.858241 q^{10} -3.80724 q^{11} +3.98500 q^{12} +4.68905 q^{13} -0.858241 q^{14} +3.15413 q^{15} +0.123083 q^{16} -4.07383 q^{17} +5.96350 q^{18} +7.23547 q^{19} +1.26342 q^{20} +3.15413 q^{21} -3.26753 q^{22} -0.764001 q^{23} +8.83408 q^{24} +1.00000 q^{25} +4.02433 q^{26} -12.4541 q^{27} +1.26342 q^{28} -0.590526 q^{29} +2.70700 q^{30} -6.93316 q^{31} +5.70724 q^{32} +12.0085 q^{33} -3.49633 q^{34} +1.00000 q^{35} -8.77891 q^{36} -2.77423 q^{37} +6.20978 q^{38} -14.7898 q^{39} +2.80080 q^{40} -11.9508 q^{41} +2.70700 q^{42} +3.49226 q^{43} +4.81016 q^{44} -6.94851 q^{45} -0.655697 q^{46} +3.74422 q^{47} -0.388221 q^{48} +1.00000 q^{49} +0.858241 q^{50} +12.8494 q^{51} -5.92425 q^{52} +12.9071 q^{53} -10.6886 q^{54} +3.80724 q^{55} +2.80080 q^{56} -22.8216 q^{57} -0.506814 q^{58} -7.01171 q^{59} -3.98500 q^{60} +4.71799 q^{61} -5.95032 q^{62} -6.94851 q^{63} +4.65202 q^{64} -4.68905 q^{65} +10.3062 q^{66} -15.3211 q^{67} +5.14697 q^{68} +2.40976 q^{69} +0.858241 q^{70} -3.14562 q^{71} -19.4614 q^{72} -13.3099 q^{73} -2.38096 q^{74} -3.15413 q^{75} -9.14146 q^{76} +3.80724 q^{77} -12.6932 q^{78} -14.5011 q^{79} -0.123083 q^{80} +18.4363 q^{81} -10.2567 q^{82} -11.8838 q^{83} -3.98500 q^{84} +4.07383 q^{85} +2.99720 q^{86} +1.86259 q^{87} +10.6633 q^{88} +4.25748 q^{89} -5.96350 q^{90} -4.68905 q^{91} +0.965256 q^{92} +21.8681 q^{93} +3.21344 q^{94} -7.23547 q^{95} -18.0014 q^{96} +13.3856 q^{97} +0.858241 q^{98} -26.4547 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9}+O(q^{10}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9	\( 62 q + 2 q^{2} + 11 q^{3} + 64 q^{4} - 62 q^{5} + 3 q^{6} - 62 q^{7} + 15 q^{8} + 69 q^{9} - 2 q^{10} - 13 q^{11} + 37 q^{12} + 31 q^{13} - 2 q^{14} - 11 q^{15} + 64 q^{16} + 30 q^{17} + 18 q^{18} + 20 q^{19} - 64 q^{20} - 11 q^{21} + 7 q^{22} + 29 q^{24} + 62 q^{25} + 59 q^{27} - 64 q^{28} - 29 q^{29} - 3 q^{30} + 20 q^{31} + 22 q^{32} + 72 q^{33} + 13 q^{34} + 62 q^{35} + 53 q^{36} + 35 q^{37} + 34 q^{38} - 6 q^{39} - 15 q^{40} + 13 q^{41} - 3 q^{42} - 4 q^{43} - 44 q^{44} - 69 q^{45} - 19 q^{46} + 58 q^{47} + 64 q^{48} + 62 q^{49} + 2 q^{50} - 30 q^{51} + 82 q^{52} + 18 q^{53} + 22 q^{54} + 13 q^{55} - 15 q^{56} + 21 q^{57} + 18 q^{58} - 11 q^{59} - 37 q^{60} + 24 q^{61} + 48 q^{62} - 69 q^{63} + 65 q^{64} - 31 q^{65} + 25 q^{66} - 6 q^{67} + 65 q^{68} + 27 q^{69} + 2 q^{70} - 35 q^{71} + 53 q^{72} + 116 q^{73} - 69 q^{74} + 11 q^{75} + 65 q^{76} + 13 q^{77} + 102 q^{78} - 83 q^{79} - 64 q^{80} + 126 q^{81} + 71 q^{82} + 84 q^{83} - 37 q^{84} - 30 q^{85} + 24 q^{86} + 49 q^{87} + 20 q^{88} - 16 q^{89} - 18 q^{90} - 31 q^{91} + 19 q^{92} + 65 q^{93} + 54 q^{94} - 20 q^{95} + 17 q^{96} + 155 q^{97} + 2 q^{98} + 6 q^{99}+O(q^{100}) \) 62 * q + 2 * q^2 + 11 * q^3 + 64 * q^4 - 62 * q^5 + 3 * q^6 - 62 * q^7 + 15 * q^8 + 69 * q^9 - 2 * q^10 - 13 * q^11 + 37 * q^12 + 31 * q^13 - 2 * q^14 - 11 * q^15 + 64 * q^16 + 30 * q^17 + 18 * q^18 + 20 * q^19 - 64 * q^20 - 11 * q^21 + 7 * q^22 + 29 * q^24 + 62 * q^25 + 59 * q^27 - 64 * q^28 - 29 * q^29 - 3 * q^30 + 20 * q^31 + 22 * q^32 + 72 * q^33 + 13 * q^34 + 62 * q^35 + 53 * q^36 + 35 * q^37 + 34 * q^38 - 6 * q^39 - 15 * q^40 + 13 * q^41 - 3 * q^42 - 4 * q^43 - 44 * q^44 - 69 * q^45 - 19 * q^46 + 58 * q^47 + 64 * q^48 + 62 * q^49 + 2 * q^50 - 30 * q^51 + 82 * q^52 + 18 * q^53 + 22 * q^54 + 13 * q^55 - 15 * q^56 + 21 * q^57 + 18 * q^58 - 11 * q^59 - 37 * q^60 + 24 * q^61 + 48 * q^62 - 69 * q^63 + 65 * q^64 - 31 * q^65 + 25 * q^66 - 6 * q^67 + 65 * q^68 + 27 * q^69 + 2 * q^70 - 35 * q^71 + 53 * q^72 + 116 * q^73 - 69 * q^74 + 11 * q^75 + 65 * q^76 + 13 * q^77 + 102 * q^78 - 83 * q^79 - 64 * q^80 + 126 * q^81 + 71 * q^82 + 84 * q^83 - 37 * q^84 - 30 * q^85 + 24 * q^86 + 49 * q^87 + 20 * q^88 - 16 * q^89 - 18 * q^90 - 31 * q^91 + 19 * q^92 + 65 * q^93 + 54 * q^94 - 20 * q^95 + 17 * q^96 + 155 * q^97 + 2 * q^98 + 6 * q^99

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