LMFDB - Embedded newform 8013.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.9841271397$
Analytic rank:	$0$
Dimension:	$129$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} -8.23349 q^{10} +0.648462 q^{11} +4.34456 q^{12} -2.92940 q^{13} -10.2673 q^{14} +3.26876 q^{15} +6.18609 q^{16} +5.11297 q^{17} -2.51884 q^{18} +0.451729 q^{19} +14.2013 q^{20} +4.07622 q^{21} -1.63337 q^{22} -0.767548 q^{23} -5.90558 q^{24} +5.68479 q^{25} +7.37869 q^{26} +1.00000 q^{27} +17.7094 q^{28} +7.38455 q^{29} -8.23349 q^{30} +9.64925 q^{31} -3.77062 q^{32} +0.648462 q^{33} -12.8788 q^{34} +13.3242 q^{35} +4.34456 q^{36} +5.04246 q^{37} -1.13783 q^{38} -2.92940 q^{39} -19.3039 q^{40} -3.08641 q^{41} -10.2673 q^{42} +2.69609 q^{43} +2.81728 q^{44} +3.26876 q^{45} +1.93333 q^{46} +12.3720 q^{47} +6.18609 q^{48} +9.61554 q^{49} -14.3191 q^{50} +5.11297 q^{51} -12.7270 q^{52} -10.7907 q^{53} -2.51884 q^{54} +2.11967 q^{55} -24.0724 q^{56} +0.451729 q^{57} -18.6005 q^{58} -1.24993 q^{59} +14.2013 q^{60} +8.94667 q^{61} -24.3049 q^{62} +4.07622 q^{63} -2.87458 q^{64} -9.57550 q^{65} -1.63337 q^{66} -12.4383 q^{67} +22.2136 q^{68} -0.767548 q^{69} -33.5615 q^{70} -15.1732 q^{71} -5.90558 q^{72} +9.15289 q^{73} -12.7011 q^{74} +5.68479 q^{75} +1.96257 q^{76} +2.64327 q^{77} +7.37869 q^{78} +5.51966 q^{79} +20.2208 q^{80} +1.00000 q^{81} +7.77417 q^{82} -14.5915 q^{83} +17.7094 q^{84} +16.7131 q^{85} -6.79103 q^{86} +7.38455 q^{87} -3.82954 q^{88} -2.32441 q^{89} -8.23349 q^{90} -11.9409 q^{91} -3.33466 q^{92} +9.64925 q^{93} -31.1632 q^{94} +1.47659 q^{95} -3.77062 q^{96} -0.704230 q^{97} -24.2200 q^{98} +0.648462 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) $ 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * 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 $

$2$	−2.51884	−1.78109	−0.890545	−	0.454895i	$-0.849677\pi$
$2$	−2.51884	−1.78109	−0.890545	+	0.454895i	$0.849677\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	4.34456	2.17228
$5$	3.26876	1.46183	0.730917	−	0.682467i	$-0.239093\pi$
$5$	3.26876	1.46183	0.730917	+	0.682467i	$0.239093\pi$
$6$	−2.51884	−1.02831
$7$	4.07622	1.54066	0.770332	−	0.637642i	$-0.220090\pi$
$7$	4.07622	1.54066	0.770332	+	0.637642i	$0.220090\pi$
$8$	−5.90558	−2.08794
$9$	1.00000	0.333333
$10$	−8.23349	−2.60366
$11$	0.648462	0.195519	0.0977593	−	0.995210i	$-0.468832\pi$
$11$	0.648462	0.195519	0.0977593	+	0.995210i	$0.468832\pi$
$12$	4.34456	1.25417
$13$	−2.92940	−0.812469	−0.406235	−	0.913769i	$-0.633158\pi$
$13$	−2.92940	−0.812469	−0.406235	+	0.913769i	$0.633158\pi$
$14$	−10.2673	−2.74406
$15$	3.26876	0.843990
$16$	6.18609	1.54652
$17$	5.11297	1.24008	0.620039	−	0.784571i	$-0.287117\pi$
$17$	5.11297	1.24008	0.620039	+	0.784571i	$0.287117\pi$
$18$	−2.51884	−0.593697
$19$	0.451729	0.103634	0.0518169	−	0.998657i	$-0.483499\pi$
$19$	0.451729	0.103634	0.0518169	+	0.998657i	$0.483499\pi$
$20$	14.2013	3.17551
$21$	4.07622	0.889503
$22$	−1.63337	−0.348236
$23$	−0.767548	−0.160045	−0.0800224	−	0.996793i	$-0.525499\pi$
$23$	−0.767548	−0.160045	−0.0800224	+	0.996793i	$0.525499\pi$
$24$	−5.90558	−1.20547
$25$	5.68479	1.13696
$26$	7.37869	1.44708
$27$	1.00000	0.192450
$28$	17.7094	3.34676
$29$	7.38455	1.37128	0.685638	−	0.727943i	$-0.259523\pi$
$29$	7.38455	1.37128	0.685638	+	0.727943i	$0.259523\pi$
$30$	−8.23349	−1.50322
$31$	9.64925	1.73306	0.866528	−	0.499129i	$-0.166346\pi$
$31$	9.64925	1.73306	0.866528	+	0.499129i	$0.166346\pi$
$32$	−3.77062	−0.666558
$33$	0.648462	0.112883
$34$	−12.8788	−2.20869
$35$	13.3242	2.25220
$36$	4.34456	0.724094
$37$	5.04246	0.828975	0.414487	−	0.910055i	$-0.363961\pi$
$37$	5.04246	0.828975	0.414487	+	0.910055i	$0.363961\pi$
$38$	−1.13783	−0.184581
$39$	−2.92940	−0.469079
$40$	−19.3039	−3.05222
$41$	−3.08641	−0.482016	−0.241008	−	0.970523i	$-0.577478\pi$
$41$	−3.08641	−0.482016	−0.241008	+	0.970523i	$0.577478\pi$
$42$	−10.2673	−1.58429
$43$	2.69609	0.411150	0.205575	−	0.978641i	$-0.434094\pi$
$43$	2.69609	0.411150	0.205575	+	0.978641i	$0.434094\pi$
$44$	2.81728	0.424721
$45$	3.26876	0.487278
$46$	1.93333	0.285054
$47$	12.3720	1.80465	0.902323	−	0.431061i	$-0.141860\pi$
$47$	12.3720	1.80465	0.902323	+	0.431061i	$0.141860\pi$
$48$	6.18609	0.892885
$49$	9.61554	1.37365
$50$	−14.3191	−2.02502
$51$	5.11297	0.715959
$52$	−12.7270	−1.76491
$53$	−10.7907	−1.48221	−0.741105	−	0.671389i	$-0.765698\pi$
$53$	−10.7907	−1.48221	−0.741105	+	0.671389i	$0.765698\pi$
$54$	−2.51884	−0.342771
$55$	2.11967	0.285816
$56$	−24.0724	−3.21681
$57$	0.451729	0.0598330
$58$	−18.6005	−2.44236
$59$	−1.24993	−0.162727	−0.0813633	−	0.996685i	$-0.525927\pi$
$59$	−1.24993	−0.162727	−0.0813633	+	0.996685i	$0.525927\pi$
$60$	14.2013	1.83338
$61$	8.94667	1.14550	0.572752	−	0.819729i	$-0.305876\pi$
$61$	8.94667	1.14550	0.572752	+	0.819729i	$0.305876\pi$
$62$	−24.3049	−3.08673
$63$	4.07622	0.513555
$64$	−2.87458	−0.359322
$65$	−9.57550	−1.18769
$66$	−1.63337	−0.201054
$67$	−12.4383	−1.51958	−0.759791	−	0.650167i	$-0.774699\pi$
$67$	−12.4383	−1.51958	−0.759791	+	0.650167i	$0.774699\pi$
$68$	22.2136	2.69380
$69$	−0.767548	−0.0924019
$70$	−33.5615	−4.01136
$71$	−15.1732	−1.80073	−0.900363	−	0.435139i	$-0.856699\pi$
$71$	−15.1732	−1.80073	−0.900363	+	0.435139i	$0.856699\pi$
$72$	−5.90558	−0.695979
$73$	9.15289	1.07126	0.535632	−	0.844451i	$-0.320073\pi$
$73$	9.15289	1.07126	0.535632	+	0.844451i	$0.320073\pi$
$74$	−12.7011	−1.47648
$75$	5.68479	0.656423
$76$	1.96257	0.225122
$77$	2.64327	0.301229
$78$	7.37869	0.835472
$79$	5.51966	0.621011	0.310505	−	0.950572i	$-0.399502\pi$
$79$	5.51966	0.621011	0.310505	+	0.950572i	$0.399502\pi$
$80$	20.2208	2.26076
$81$	1.00000	0.111111
$82$	7.77417	0.858513
$83$	−14.5915	−1.60163	−0.800814	−	0.598913i	$-0.795600\pi$
$83$	−14.5915	−1.60163	−0.800814	+	0.598913i	$0.795600\pi$
$84$	17.7094	1.93225
$85$	16.7131	1.81279
$86$	−6.79103	−0.732295
$87$	7.38455	0.791706
$88$	−3.82954	−0.408231
$89$	−2.32441	−0.246387	−0.123193	−	0.992383i	$-0.539314\pi$
$89$	−2.32441	−0.246387	−0.123193	+	0.992383i	$0.539314\pi$
$90$	−8.23349	−0.867886
$91$	−11.9409	−1.25174
$92$	−3.33466	−0.347662
$93$	9.64925	1.00058
$94$	−31.1632	−3.21424
$95$	1.47659	0.151495
$96$	−3.77062	−0.384838
$97$	−0.704230	−0.0715037	−0.0357519	−	0.999361i	$-0.511383\pi$
$97$	−0.704230	−0.0715037	−0.0357519	+	0.999361i	$0.511383\pi$
$98$	−24.2200	−2.44659
$99$	0.648462	0.0651729
$100$	24.6979	2.46979
$101$	−15.3888	−1.53124	−0.765619	−	0.643294i	$-0.777567\pi$
$101$	−15.3888	−1.53124	−0.765619	+	0.643294i	$0.777567\pi$
$102$	−12.8788	−1.27519
$103$	13.9462	1.37416	0.687078	−	0.726584i	$-0.258893\pi$
$103$	13.9462	1.37416	0.687078	+	0.726584i	$0.258893\pi$
$104$	17.2998	1.69638
$105$	13.3242	1.30031
$106$	27.1799	2.63995
$107$	14.1540	1.36832	0.684158	−	0.729334i	$-0.260170\pi$
$107$	14.1540	1.36832	0.684158	+	0.729334i	$0.260170\pi$
$108$	4.34456	0.418056
$109$	−2.57625	−0.246760	−0.123380	−	0.992359i	$-0.539373\pi$
$109$	−2.57625	−0.246760	−0.123380	+	0.992359i	$0.539373\pi$
$110$	−5.33910	−0.509063
$111$	5.04246	0.478609
$112$	25.2158	2.38267
$113$	−15.2411	−1.43376	−0.716881	−	0.697195i	$-0.754431\pi$
$113$	−15.2411	−1.43376	−0.716881	+	0.697195i	$0.754431\pi$
$114$	−1.13783	−0.106568
$115$	−2.50893	−0.233959
$116$	32.0826	2.97880
$117$	−2.92940	−0.270823
$118$	3.14837	0.289831
$119$	20.8416	1.91054
$120$	−19.3039	−1.76220
$121$	−10.5795	−0.961772
$122$	−22.5352	−2.04024
$123$	−3.08641	−0.278292
$124$	41.9217	3.76468
$125$	2.23840	0.200209
$126$	−10.2673	−0.914688
$127$	−13.3631	−1.18578	−0.592889	−	0.805284i	$-0.702013\pi$
$127$	−13.3631	−1.18578	−0.592889	+	0.805284i	$0.702013\pi$
$128$	14.7819	1.30654
$129$	2.69609	0.237378
$130$	24.1192	2.11539
$131$	−18.2766	−1.59683	−0.798415	−	0.602108i	$-0.794328\pi$
$131$	−18.2766	−1.59683	−0.798415	+	0.602108i	$0.794328\pi$
$132$	2.81728	0.245213
$133$	1.84135	0.159665
$134$	31.3301	2.70651
$135$	3.26876	0.281330
$136$	−30.1950	−2.58920
$137$	−18.7483	−1.60177	−0.800886	−	0.598817i	$-0.795638\pi$
$137$	−18.7483	−1.60177	−0.800886	+	0.598817i	$0.795638\pi$
$138$	1.93333	0.164576
$139$	−19.5104	−1.65485	−0.827425	−	0.561577i	$-0.810195\pi$
$139$	−19.5104	−1.65485	−0.827425	+	0.561577i	$0.810195\pi$
$140$	57.8877	4.89240
$141$	12.3720	1.04191
$142$	38.2189	3.20726
$143$	−1.89960	−0.158853
$144$	6.18609	0.515508
$145$	24.1383	2.00458
$146$	−23.0547	−1.90802
$147$	9.61554	0.793076
$148$	21.9073	1.80077
$149$	13.7429	1.12586	0.562929	−	0.826505i	$-0.309674\pi$
$149$	13.7429	1.12586	0.562929	+	0.826505i	$0.309674\pi$
$150$	−14.3191	−1.16915
$151$	−3.70655	−0.301635	−0.150817	−	0.988562i	$-0.548191\pi$
$151$	−3.70655	−0.301635	−0.150817	+	0.988562i	$0.548191\pi$
$152$	−2.66772	−0.216381
$153$	5.11297	0.413359
$154$	−6.65798	−0.536515
$155$	31.5411	2.53344
$156$	−12.7270	−1.01897
$157$	2.96178	0.236376	0.118188	−	0.992991i	$-0.462291\pi$
$157$	2.96178	0.236376	0.118188	+	0.992991i	$0.462291\pi$
$158$	−13.9032	−1.10608
$159$	−10.7907	−0.855754
$160$	−12.3253	−0.974397
$161$	−3.12869	−0.246575
$162$	−2.51884	−0.197899
$163$	17.3658	1.36019	0.680095	−	0.733124i	$-0.261938\pi$
$163$	17.3658	1.36019	0.680095	+	0.733124i	$0.261938\pi$
$164$	−13.4091	−1.04707
$165$	2.11967	0.165016
$166$	36.7538	2.85264
$167$	−13.9346	−1.07830	−0.539148	−	0.842211i	$-0.681254\pi$
$167$	−13.9346	−1.07830	−0.539148	+	0.842211i	$0.681254\pi$
$168$	−24.0724	−1.85723
$169$	−4.41862	−0.339894
$170$	−42.0976	−3.22874
$171$	0.451729	0.0345446
$172$	11.7133	0.893133
$173$	−19.1201	−1.45368	−0.726838	−	0.686809i	$-0.759011\pi$
$173$	−19.1201	−1.45368	−0.726838	+	0.686809i	$0.759011\pi$
$174$	−18.6005	−1.41010
$175$	23.1724	1.75167
$176$	4.01144	0.302374
$177$	−1.24993	−0.0939502
$178$	5.85481	0.438836
$179$	−1.13929	−0.0851547	−0.0425773	−	0.999093i	$-0.513557\pi$
$179$	−1.13929	−0.0851547	−0.0425773	+	0.999093i	$0.513557\pi$
$180$	14.2013	1.05850
$181$	17.1194	1.27247	0.636237	−	0.771494i	$-0.280490\pi$
$181$	17.1194	1.27247	0.636237	+	0.771494i	$0.280490\pi$
$182$	30.0771	2.22947
$183$	8.94667	0.661357
$184$	4.53281	0.334163
$185$	16.4826	1.21182
$186$	−24.3049	−1.78212
$187$	3.31557	0.242458
$188$	53.7510	3.92020
$189$	4.07622	0.296501
$190$	−3.71931	−0.269827
$191$	8.40422	0.608108	0.304054	−	0.952655i	$-0.401660\pi$
$191$	8.40422	0.608108	0.304054	+	0.952655i	$0.401660\pi$
$192$	−2.87458	−0.207455
$193$	14.1958	1.02184	0.510920	−	0.859628i	$-0.329305\pi$
$193$	14.1958	1.02184	0.510920	+	0.859628i	$0.329305\pi$
$194$	1.77384	0.127355
$195$	−9.57550	−0.685716
$196$	41.7753	2.98395
$197$	5.47194	0.389860	0.194930	−	0.980817i	$-0.437552\pi$
$197$	5.47194	0.389860	0.194930	+	0.980817i	$0.437552\pi$
$198$	−1.63337	−0.116079
$199$	11.6424	0.825309	0.412654	−	0.910888i	$-0.364602\pi$
$199$	11.6424	0.825309	0.412654	+	0.910888i	$0.364602\pi$
$200$	−33.5719	−2.37389
$201$	−12.4383	−0.877331
$202$	38.7618	2.72727
$203$	30.1010	2.11268
$204$	22.2136	1.55526
$205$	−10.0887	−0.704627
$206$	−35.1282	−2.44749
$207$	−0.767548	−0.0533483
$208$	−18.1215	−1.25650
$209$	0.292929	0.0202623
$210$	−33.5615	−2.31596
$211$	−23.0003	−1.58341	−0.791704	−	0.610905i	$-0.790806\pi$
$211$	−23.0003	−1.58341	−0.791704	+	0.610905i	$0.790806\pi$
$212$	−46.8806	−3.21978
$213$	−15.1732	−1.03965
$214$	−35.6516	−2.43709
$215$	8.81287	0.601033
$216$	−5.90558	−0.401824
$217$	39.3324	2.67006
$218$	6.48917	0.439502
$219$	9.15289	0.618495
$220$	9.20902	0.620872
$221$	−14.9779	−1.00752
$222$	−12.7011	−0.852445
$223$	−10.6453	−0.712861	−0.356431	−	0.934322i	$-0.616006\pi$
$223$	−10.6453	−0.712861	−0.356431	+	0.934322i	$0.616006\pi$
$224$	−15.3699	−1.02694
$225$	5.68479	0.378986
$226$	38.3899	2.55366
$227$	−3.66318	−0.243134	−0.121567	−	0.992583i	$-0.538792\pi$
$227$	−3.66318	−0.243134	−0.121567	+	0.992583i	$0.538792\pi$
$228$	1.96257	0.129974
$229$	10.3781	0.685801	0.342901	−	0.939372i	$-0.388591\pi$
$229$	10.3781	0.685801	0.342901	+	0.939372i	$0.388591\pi$
$230$	6.31959	0.416702
$231$	2.64327	0.173915
$232$	−43.6100	−2.86314
$233$	−10.4755	−0.686273	−0.343137	−	0.939285i	$-0.611489\pi$
$233$	−10.4755	−0.686273	−0.343137	+	0.939285i	$0.611489\pi$
$234$	7.37869	0.482360
$235$	40.4412	2.63809
$236$	−5.43038	−0.353488
$237$	5.51966	0.358541
$238$	−52.4966	−3.40285
$239$	−14.6957	−0.950586	−0.475293	−	0.879828i	$-0.657658\pi$
$239$	−14.6957	−0.950586	−0.475293	+	0.879828i	$0.657658\pi$
$240$	20.2208	1.30525
$241$	−23.0092	−1.48215	−0.741076	−	0.671421i	$-0.765684\pi$
$241$	−23.0092	−1.48215	−0.741076	+	0.671421i	$0.765684\pi$
$242$	26.6481	1.71300
$243$	1.00000	0.0641500
$244$	38.8694	2.48836
$245$	31.4309	2.00805
$246$	7.77417	0.495663
$247$	−1.32330	−0.0841993
$248$	−56.9844	−3.61851
$249$	−14.5915	−0.924701
$250$	−5.63817	−0.356589
$251$	−6.73804	−0.425301	−0.212651	−	0.977128i	$-0.568210\pi$
$251$	−6.73804	−0.425301	−0.212651	+	0.977128i	$0.568210\pi$
$252$	17.7094	1.11559
$253$	−0.497726	−0.0312917
$254$	33.6594	2.11198
$255$	16.7131	1.04661
$256$	−31.4840	−1.96775
$257$	−26.4634	−1.65074	−0.825370	−	0.564592i	$-0.809034\pi$
$257$	−26.4634	−1.65074	−0.825370	+	0.564592i	$0.809034\pi$
$258$	−6.79103	−0.422791
$259$	20.5541	1.27717
$260$	−41.6014	−2.58001
$261$	7.38455	0.457092
$262$	46.0357	2.84410
$263$	26.4099	1.62851	0.814253	−	0.580510i	$-0.197147\pi$
$263$	26.4099	1.62851	0.814253	+	0.580510i	$0.197147\pi$
$264$	−3.82954	−0.235692
$265$	−35.2720	−2.16674
$266$	−4.63806	−0.284378
$267$	−2.32441	−0.142251
$268$	−54.0390	−3.30096
$269$	7.91517	0.482596	0.241298	−	0.970451i	$-0.422427\pi$
$269$	7.91517	0.482596	0.241298	+	0.970451i	$0.422427\pi$
$270$	−8.23349	−0.501074
$271$	0.262801	0.0159640	0.00798201	−	0.999968i	$-0.497459\pi$
$271$	0.262801	0.0159640	0.00798201	+	0.999968i	$0.497459\pi$
$272$	31.6293	1.91781
$273$	−11.9409	−0.722694
$274$	47.2239	2.85290
$275$	3.68637	0.222296
$276$	−3.33466	−0.200723
$277$	22.4788	1.35062	0.675311	−	0.737533i	$-0.264009\pi$
$277$	22.4788	1.35062	0.675311	+	0.737533i	$0.264009\pi$
$278$	49.1436	2.94744
$279$	9.64925	0.577685
$280$	−78.6869	−4.70244
$281$	5.19041	0.309634	0.154817	−	0.987943i	$-0.450521\pi$
$281$	5.19041	0.309634	0.154817	+	0.987943i	$0.450521\pi$
$282$	−31.1632	−1.85574
$283$	12.2072	0.725644	0.362822	−	0.931858i	$-0.381813\pi$
$283$	12.2072	0.725644	0.362822	+	0.931858i	$0.381813\pi$
$284$	−65.9209	−3.91168
$285$	1.47659	0.0874659
$286$	4.78480	0.282931
$287$	−12.5809	−0.742625
$288$	−3.77062	−0.222186
$289$	9.14247	0.537792
$290$	−60.8005	−3.57033
$291$	−0.704230	−0.0412827
$292$	39.7653	2.32709
$293$	19.2073	1.12210	0.561051	−	0.827782i	$-0.310397\pi$
$293$	19.2073	1.12210	0.561051	+	0.827782i	$0.310397\pi$
$294$	−24.2200	−1.41254
$295$	−4.08571	−0.237879
$296$	−29.7786	−1.73085
$297$	0.648462	0.0376276
$298$	−34.6161	−2.00526
$299$	2.24845	0.130031
$300$	24.6979	1.42593
$301$	10.9898	0.633444
$302$	9.33622	0.537239
$303$	−15.3888	−0.884061
$304$	2.79444	0.160272
$305$	29.2445	1.67454
$306$	−12.8788	−0.736230
$307$	−28.4591	−1.62425	−0.812124	−	0.583485i	$-0.801689\pi$
$307$	−28.4591	−1.62425	−0.812124	+	0.583485i	$0.801689\pi$
$308$	11.4839	0.654353
$309$	13.9462	0.793369
$310$	−79.4469	−4.51228
$311$	18.7576	1.06365	0.531823	−	0.846856i	$-0.321507\pi$
$311$	18.7576	1.06365	0.531823	+	0.846856i	$0.321507\pi$
$312$	17.2998	0.979408
$313$	−1.65575	−0.0935886	−0.0467943	−	0.998905i	$-0.514901\pi$
$313$	−1.65575	−0.0935886	−0.0467943	+	0.998905i	$0.514901\pi$
$314$	−7.46026	−0.421007
$315$	13.3242	0.750732
$316$	23.9805	1.34901
$317$	−12.2014	−0.685298	−0.342649	−	0.939464i	$-0.611324\pi$
$317$	−12.2014	−0.685298	−0.342649	+	0.939464i	$0.611324\pi$
$318$	27.1799	1.52418
$319$	4.78860	0.268110
$320$	−9.39630	−0.525269
$321$	14.1540	0.789997
$322$	7.88068	0.439173
$323$	2.30968	0.128514
$324$	4.34456	0.241365
$325$	−16.6530	−0.923743
$326$	−43.7416	−2.42262
$327$	−2.57625	−0.142467
$328$	18.2270	1.00642
$329$	50.4311	2.78035
$330$	−5.33910	−0.293908
$331$	−9.21492	−0.506498	−0.253249	−	0.967401i	$-0.581499\pi$
$331$	−9.21492	−0.506498	−0.253249	+	0.967401i	$0.581499\pi$
$332$	−63.3938	−3.47919
$333$	5.04246	0.276325
$334$	35.0992	1.92054
$335$	−40.6579	−2.22138
$336$	25.2158	1.37564
$337$	−0.296921	−0.0161743	−0.00808716	−	0.999967i	$-0.502574\pi$
$337$	−0.296921	−0.0161743	−0.00808716	+	0.999967i	$0.502574\pi$
$338$	11.1298	0.605381
$339$	−15.2411	−0.827783
$340$	72.6110	3.93788
$341$	6.25717	0.338845
$342$	−1.13783	−0.0615270
$343$	10.6615	0.575667
$344$	−15.9220	−0.858455
$345$	−2.50893	−0.135076
$346$	48.1605	2.58913
$347$	2.31373	0.124208	0.0621038	−	0.998070i	$-0.480219\pi$
$347$	2.31373	0.124208	0.0621038	+	0.998070i	$0.480219\pi$
$348$	32.0826	1.71981
$349$	14.4172	0.771733	0.385867	−	0.922555i	$-0.373902\pi$
$349$	14.4172	0.771733	0.385867	+	0.922555i	$0.373902\pi$
$350$	−58.3676	−3.11988
$351$	−2.92940	−0.156360
$352$	−2.44511	−0.130325
$353$	−20.7594	−1.10491	−0.552457	−	0.833542i	$-0.686309\pi$
$353$	−20.7594	−1.10491	−0.552457	+	0.833542i	$0.686309\pi$
$354$	3.14837	0.167334
$355$	−49.5975	−2.63236
$356$	−10.0985	−0.535221
$357$	20.8416	1.10305
$358$	2.86970	0.151668
$359$	−1.95160	−0.103002	−0.0515008	−	0.998673i	$-0.516400\pi$
$359$	−1.95160	−0.103002	−0.0515008	+	0.998673i	$0.516400\pi$
$360$	−19.3039	−1.01741
$361$	−18.7959	−0.989260
$362$	−43.1210	−2.26639
$363$	−10.5795	−0.555280
$364$	−51.8778	−2.71914
$365$	29.9186	1.56601
$366$	−22.5352	−1.17794
$367$	−22.3819	−1.16833	−0.584164	−	0.811636i	$-0.698578\pi$
$367$	−22.3819	−1.16833	−0.584164	+	0.811636i	$0.698578\pi$
$368$	−4.74812	−0.247513
$369$	−3.08641	−0.160672
$370$	−41.5170	−2.15837
$371$	−43.9850	−2.28359
$372$	41.9217	2.17354
$373$	−6.26236	−0.324253	−0.162126	−	0.986770i	$-0.551835\pi$
$373$	−6.26236	−0.324253	−0.162126	+	0.986770i	$0.551835\pi$
$374$	−8.35139	−0.431840
$375$	2.23840	0.115590
$376$	−73.0640	−3.76799
$377$	−21.6323	−1.11412
$378$	−10.2673	−0.528095
$379$	−20.0025	−1.02746	−0.513730	−	0.857952i	$-0.671737\pi$
$379$	−20.0025	−1.02746	−0.513730	+	0.857952i	$0.671737\pi$
$380$	6.41516	0.329091
$381$	−13.3631	−0.684610
$382$	−21.1689	−1.08309
$383$	−20.7570	−1.06063	−0.530317	−	0.847799i	$-0.677927\pi$
$383$	−20.7570	−1.06063	−0.530317	+	0.847799i	$0.677927\pi$
$384$	14.7819	0.754333
$385$	8.64022	0.440346
$386$	−35.7571	−1.81999
$387$	2.69609	0.137050
$388$	−3.05957	−0.155326
$389$	−7.59223	−0.384941	−0.192471	−	0.981303i	$-0.561650\pi$
$389$	−7.59223	−0.384941	−0.192471	+	0.981303i	$0.561650\pi$
$390$	24.1192	1.22132
$391$	−3.92445	−0.198468
$392$	−56.7853	−2.86809
$393$	−18.2766	−0.921930
$394$	−13.7829	−0.694375
$395$	18.0425	0.907814
$396$	2.81728	0.141574
$397$	29.8494	1.49810	0.749050	−	0.662514i	$-0.230510\pi$
$397$	29.8494	1.49810	0.749050	+	0.662514i	$0.230510\pi$
$398$	−29.3254	−1.46995
$399$	1.84135	0.0921826
$400$	35.1666	1.75833
$401$	9.98013	0.498384	0.249192	−	0.968454i	$-0.419835\pi$
$401$	9.98013	0.498384	0.249192	+	0.968454i	$0.419835\pi$
$402$	31.3301	1.56261
$403$	−28.2665	−1.40805
$404$	−66.8574	−3.32628
$405$	3.26876	0.162426
$406$	−75.8197	−3.76287
$407$	3.26984	0.162080
$408$	−30.1950	−1.49488
$409$	33.8654	1.67453	0.837267	−	0.546794i	$-0.184152\pi$
$409$	33.8654	1.67453	0.837267	+	0.546794i	$0.184152\pi$
$410$	25.4119	1.25500
$411$	−18.7483	−0.924783
$412$	60.5899	2.98505
$413$	−5.09497	−0.250707
$414$	1.93333	0.0950180
$415$	−47.6962	−2.34131
$416$	11.0457	0.541558
$417$	−19.5104	−0.955428
$418$	−0.737843	−0.0360891
$419$	32.6422	1.59468	0.797339	−	0.603532i	$-0.206240\pi$
$419$	32.6422	1.59468	0.797339	+	0.603532i	$0.206240\pi$
$420$	57.8877	2.82463
$421$	−9.37994	−0.457150	−0.228575	−	0.973526i	$-0.573407\pi$
$421$	−9.37994	−0.457150	−0.228575	+	0.973526i	$0.573407\pi$
$422$	57.9341	2.82019
$423$	12.3720	0.601549
$424$	63.7250	3.09476
$425$	29.0661	1.40992
$426$	38.2189	1.85171
$427$	36.4686	1.76484
$428$	61.4928	2.97237
$429$	−1.89960	−0.0917138
$430$	−22.1982	−1.07049
$431$	23.4793	1.13096	0.565480	−	0.824762i	$-0.308691\pi$
$431$	23.4793	1.13096	0.565480	+	0.824762i	$0.308691\pi$
$432$	6.18609	0.297628
$433$	−37.1402	−1.78484	−0.892421	−	0.451203i	$-0.850995\pi$
$433$	−37.1402	−1.78484	−0.892421	+	0.451203i	$0.850995\pi$
$434$	−99.0721	−4.75561
$435$	24.1383	1.15734
$436$	−11.1927	−0.536032
$437$	−0.346724	−0.0165861
$438$	−23.0547	−1.10159
$439$	13.3938	0.639253	0.319627	−	0.947544i	$-0.396442\pi$
$439$	13.3938	0.639253	0.319627	+	0.947544i	$0.396442\pi$
$440$	−12.5179	−0.596765
$441$	9.61554	0.457883
$442$	37.7270	1.79449
$443$	−9.99995	−0.475112	−0.237556	−	0.971374i	$-0.576346\pi$
$443$	−9.99995	−0.475112	−0.237556	+	0.971374i	$0.576346\pi$
$444$	21.9073	1.03967
$445$	−7.59792	−0.360176
$446$	26.8138	1.26967
$447$	13.7429	0.650015
$448$	−11.7174	−0.553595
$449$	33.9889	1.60404	0.802019	−	0.597299i	$-0.203759\pi$
$449$	33.9889	1.60404	0.802019	+	0.597299i	$0.203759\pi$
$450$	−14.3191	−0.675008
$451$	−2.00142	−0.0942431
$452$	−66.2159	−3.11454
$453$	−3.70655	−0.174149
$454$	9.22697	0.433043
$455$	−39.0318	−1.82984
$456$	−2.66772	−0.124928
$457$	9.39491	0.439475	0.219738	−	0.975559i	$-0.429480\pi$
$457$	9.39491	0.439475	0.219738	+	0.975559i	$0.429480\pi$
$458$	−26.1407	−1.22147
$459$	5.11297	0.238653
$460$	−10.9002	−0.508224
$461$	−29.2213	−1.36097	−0.680487	−	0.732760i	$-0.738232\pi$
$461$	−29.2213	−1.36097	−0.680487	+	0.732760i	$0.738232\pi$
$462$	−6.65798	−0.309757
$463$	−5.91392	−0.274843	−0.137422	−	0.990513i	$-0.543882\pi$
$463$	−5.91392	−0.274843	−0.137422	+	0.990513i	$0.543882\pi$
$464$	45.6815	2.12071
$465$	31.5411	1.46268
$466$	26.3861	1.22231
$467$	29.8913	1.38321	0.691603	−	0.722278i	$-0.256905\pi$
$467$	29.8913	1.38321	0.691603	+	0.722278i	$0.256905\pi$
$468$	−12.7270	−0.588304
$469$	−50.7013	−2.34117
$470$	−101.865	−4.69868
$471$	2.96178	0.136472
$472$	7.38154	0.339763
$473$	1.74831	0.0803875
$474$	−13.9032	−0.638593
$475$	2.56798	0.117827
$476$	90.5475	4.15024
$477$	−10.7907	−0.494070
$478$	37.0161	1.69308
$479$	−13.7282	−0.627259	−0.313630	−	0.949545i	$-0.601545\pi$
$479$	−13.7282	−0.627259	−0.313630	+	0.949545i	$0.601545\pi$
$480$	−12.3253	−0.562569
$481$	−14.7714	−0.673516
$482$	57.9565	2.63985
$483$	−3.12869	−0.142360
$484$	−45.9633	−2.08924
$485$	−2.30196	−0.104527
$486$	−2.51884	−0.114257
$487$	12.2678	0.555905	0.277953	−	0.960595i	$-0.410344\pi$
$487$	12.2678	0.555905	0.277953	+	0.960595i	$0.410344\pi$
$488$	−52.8353	−2.39174
$489$	17.3658	0.785307
$490$	−79.1694	−3.57651
$491$	31.2069	1.40835	0.704174	−	0.710028i	$-0.251318\pi$
$491$	31.2069	1.40835	0.704174	+	0.710028i	$0.251318\pi$
$492$	−13.4091	−0.604528
$493$	37.7570	1.70049
$494$	3.33317	0.149967
$495$	2.11967	0.0952719
$496$	59.6911	2.68021
$497$	−61.8492	−2.77432
$498$	36.7538	1.64698
$499$	−5.47525	−0.245106	−0.122553	−	0.992462i	$-0.539108\pi$
$499$	−5.47525	−0.245106	−0.122553	+	0.992462i	$0.539108\pi$
$500$	9.72487	0.434909
$501$	−13.9346	−0.622554
$502$	16.9721	0.757500
$503$	−7.58932	−0.338391	−0.169195	−	0.985583i	$-0.554117\pi$
$503$	−7.58932	−0.338391	−0.169195	+	0.985583i	$0.554117\pi$
$504$	−24.0724	−1.07227
$505$	−50.3021	−2.23842
$506$	1.25369	0.0557334
$507$	−4.41862	−0.196238
$508$	−58.0566	−2.57584
$509$	16.7244	0.741294	0.370647	−	0.928774i	$-0.379136\pi$
$509$	16.7244	0.741294	0.370647	+	0.928774i	$0.379136\pi$
$510$	−42.0976	−1.86411
$511$	37.3091	1.65046
$512$	49.7395	2.19819
$513$	0.451729	0.0199443
$514$	66.6571	2.94012
$515$	45.5866	2.00879
$516$	11.7133	0.515651
$517$	8.02279	0.352842
$518$	−51.7726	−2.27476
$519$	−19.1201	−0.839280
$520$	56.5489	2.47983
$521$	−40.4749	−1.77324	−0.886620	−	0.462499i	$-0.846953\pi$
$521$	−40.4749	−1.77324	−0.886620	+	0.462499i	$0.846953\pi$
$522$	−18.6005	−0.814122
$523$	34.7864	1.52110	0.760551	−	0.649278i	$-0.224929\pi$
$523$	34.7864	1.52110	0.760551	+	0.649278i	$0.224929\pi$
$524$	−79.4036	−3.46876
$525$	23.1724	1.01133
$526$	−66.5224	−2.90052
$527$	49.3363	2.14912
$528$	4.01144	0.174576
$529$	−22.4109	−0.974386
$530$	88.8447	3.85917
$531$	−1.24993	−0.0542422
$532$	7.99984	0.346837
$533$	9.04132	0.391623
$534$	5.85481	0.253362
$535$	46.2659	2.00025
$536$	73.4554	3.17279
$537$	−1.13929	−0.0491641
$538$	−19.9371	−0.859548
$539$	6.23531	0.268574
$540$	14.2013	0.611128
$541$	31.0638	1.33554	0.667768	−	0.744370i	$-0.267250\pi$
$541$	31.0638	1.33554	0.667768	+	0.744370i	$0.267250\pi$
$542$	−0.661954	−0.0284333
$543$	17.1194	0.734663
$544$	−19.2791	−0.826584
$545$	−8.42114	−0.360722
$546$	30.0771	1.28718
$547$	42.0721	1.79887	0.899436	−	0.437053i	$-0.143978\pi$
$547$	42.0721	1.79887	0.899436	+	0.437053i	$0.143978\pi$
$548$	−81.4529	−3.47950
$549$	8.94667	0.381835
$550$	−9.28538	−0.395930
$551$	3.33582	0.142111
$552$	4.53281	0.192929
$553$	22.4993	0.956770
$554$	−56.6206	−2.40558
$555$	16.4826	0.699646
$556$	−84.7641	−3.59480
$557$	−14.4813	−0.613591	−0.306796	−	0.951775i	$-0.599257\pi$
$557$	−14.4813	−0.613591	−0.306796	+	0.951775i	$0.599257\pi$
$558$	−24.3049	−1.02891
$559$	−7.89793	−0.334047
$560$	82.4245	3.48307
$561$	3.31557	0.139983
$562$	−13.0738	−0.551485
$563$	9.12990	0.384779	0.192390	−	0.981319i	$-0.438376\pi$
$563$	9.12990	0.384779	0.192390	+	0.981319i	$0.438376\pi$
$564$	53.7510	2.26333
$565$	−49.8195	−2.09592
$566$	−30.7481	−1.29244
$567$	4.07622	0.171185
$568$	89.6065	3.75980
$569$	24.3208	1.01958	0.509790	−	0.860299i	$-0.329723\pi$
$569$	24.3208	1.01958	0.509790	+	0.860299i	$0.329723\pi$
$570$	−3.71931	−0.155785
$571$	−28.5261	−1.19378	−0.596891	−	0.802322i	$-0.703598\pi$
$571$	−28.5261	−1.19378	−0.596891	+	0.802322i	$0.703598\pi$
$572$	−8.25295	−0.345073
$573$	8.40422	0.351091
$574$	31.6892	1.32268
$575$	−4.36335	−0.181964
$576$	−2.87458	−0.119774
$577$	−15.0112	−0.624923	−0.312462	−	0.949930i	$-0.601154\pi$
$577$	−15.0112	−0.624923	−0.312462	+	0.949930i	$0.601154\pi$
$578$	−23.0284	−0.957856
$579$	14.1958	0.589959
$580$	104.870	4.35450
$581$	−59.4782	−2.46757
$582$	1.77384	0.0735282
$583$	−6.99733	−0.289800
$584$	−54.0531	−2.23673
$585$	−9.57550	−0.395898
$586$	−48.3801	−1.99856
$587$	−18.0151	−0.743564	−0.371782	−	0.928320i	$-0.621253\pi$
$587$	−18.0151	−0.743564	−0.371782	+	0.928320i	$0.621253\pi$
$588$	41.7753	1.72278
$589$	4.35885	0.179603
$590$	10.2912	0.423684
$591$	5.47194	0.225086
$592$	31.1931	1.28203
$593$	8.31313	0.341379	0.170690	−	0.985325i	$-0.445400\pi$
$593$	8.31313	0.341379	0.170690	+	0.985325i	$0.445400\pi$
$594$	−1.63337	−0.0670181
$595$	68.1261	2.79290
$596$	59.7067	2.44568
$597$	11.6424	0.476492
$598$	−5.66350	−0.231598
$599$	−17.1097	−0.699082	−0.349541	−	0.936921i	$-0.613662\pi$
$599$	−17.1097	−0.699082	−0.349541	+	0.936921i	$0.613662\pi$
$600$	−33.5719	−1.37057
$601$	16.0414	0.654342	0.327171	−	0.944965i	$-0.393905\pi$
$601$	16.0414	0.654342	0.327171	+	0.944965i	$0.393905\pi$
$602$	−27.6817	−1.12822
$603$	−12.4383	−0.506527
$604$	−16.1033	−0.655236
$605$	−34.5818	−1.40595
$606$	38.7618	1.57459
$607$	23.9825	0.973418	0.486709	−	0.873564i	$-0.338197\pi$
$607$	23.9825	0.973418	0.486709	+	0.873564i	$0.338197\pi$
$608$	−1.70330	−0.0690780
$609$	30.1010	1.21975
$610$	−73.6623	−2.98250
$611$	−36.2426	−1.46622
$612$	22.2136	0.897932
$613$	−13.9768	−0.564518	−0.282259	−	0.959338i	$-0.591084\pi$
$613$	−13.9768	−0.564518	−0.282259	+	0.959338i	$0.591084\pi$
$614$	71.6840	2.89293
$615$	−10.0887	−0.406816
$616$	−15.6100	−0.628947
$617$	−42.8632	−1.72561	−0.862803	−	0.505540i	$-0.831293\pi$
$617$	−42.8632	−1.72561	−0.862803	+	0.505540i	$0.831293\pi$
$618$	−35.1282	−1.41306
$619$	37.0699	1.48996	0.744982	−	0.667085i	$-0.232458\pi$
$619$	37.0699	1.48996	0.744982	+	0.667085i	$0.232458\pi$
$620$	137.032	5.50334
$621$	−0.767548	−0.0308006
$622$	−47.2474	−1.89445
$623$	−9.47478	−0.379599
$624$	−18.1215	−0.725442
$625$	−21.1071	−0.844286
$626$	4.17058	0.166690
$627$	0.292929	0.0116985
$628$	12.8676	0.513475
$629$	25.7819	1.02799
$630$	−33.5615	−1.33712
$631$	−31.5036	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$631$	−31.5036	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$632$	−32.5968	−1.29663
$633$	−23.0003	−0.914181
$634$	30.7333	1.22058
$635$	−43.6806	−1.73341
$636$	−46.8806	−1.85894
$637$	−28.1678	−1.11605
$638$	−12.0617	−0.477528
$639$	−15.1732	−0.600242
$640$	48.3183	1.90995
$641$	−21.0790	−0.832569	−0.416285	−	0.909234i	$-0.636668\pi$
$641$	−21.0790	−0.832569	−0.416285	+	0.909234i	$0.636668\pi$
$642$	−35.6516	−1.40706
$643$	−19.5545	−0.771155	−0.385578	−	0.922675i	$-0.625998\pi$
$643$	−19.5545	−0.771155	−0.385578	+	0.922675i	$0.625998\pi$
$644$	−13.5928	−0.535631
$645$	8.81287	0.347006
$646$	−5.81771	−0.228895
$647$	41.6117	1.63593	0.817963	−	0.575271i	$-0.195104\pi$
$647$	41.6117	1.63593	0.817963	+	0.575271i	$0.195104\pi$
$648$	−5.90558	−0.231993
$649$	−0.810530	−0.0318161
$650$	41.9463	1.64527
$651$	39.3324	1.54156
$652$	75.4466	2.95472
$653$	20.8080	0.814281	0.407140	−	0.913366i	$-0.366526\pi$
$653$	20.8080	0.814281	0.407140	+	0.913366i	$0.366526\pi$
$654$	6.48917	0.253746
$655$	−59.7416	−2.33430
$656$	−19.0928	−0.745448
$657$	9.15289	0.357088
$658$	−127.028	−4.95206
$659$	−30.2150	−1.17701	−0.588505	−	0.808494i	$-0.700283\pi$
$659$	−30.2150	−1.17701	−0.588505	+	0.808494i	$0.700283\pi$
$660$	9.20902	0.358461
$661$	3.16792	0.123218	0.0616090	−	0.998100i	$-0.480377\pi$
$661$	3.16792	0.123218	0.0616090	+	0.998100i	$0.480377\pi$
$662$	23.2109	0.902118
$663$	−14.9779	−0.581695
$664$	86.1714	3.34410
$665$	6.01892	0.233404
$666$	−12.7011	−0.492159
$667$	−5.66799	−0.219466
$668$	−60.5399	−2.34236
$669$	−10.6453	−0.411571
$670$	102.411	3.95647
$671$	5.80158	0.223967
$672$	−15.3699	−0.592906
$673$	6.05639	0.233457	0.116728	−	0.993164i	$-0.462759\pi$
$673$	6.05639	0.233457	0.116728	+	0.993164i	$0.462759\pi$
$674$	0.747897	0.0288079
$675$	5.68479	0.218808
$676$	−19.1970	−0.738345
$677$	32.4954	1.24890	0.624450	−	0.781064i	$-0.285323\pi$
$677$	32.4954	1.24890	0.624450	+	0.781064i	$0.285323\pi$
$678$	38.3899	1.47436
$679$	−2.87059	−0.110163
$680$	−98.7003	−3.78498
$681$	−3.66318	−0.140373
$682$	−15.7608	−0.603513
$683$	−21.7372	−0.831751	−0.415876	−	0.909422i	$-0.636525\pi$
$683$	−21.7372	−0.831751	−0.415876	+	0.909422i	$0.636525\pi$
$684$	1.96257	0.0750406
$685$	−61.2835	−2.34152
$686$	−26.8546	−1.02532
$687$	10.3781	0.395947
$688$	16.6783	0.635853
$689$	31.6101	1.20425
$690$	6.31959	0.240583
$691$	0.576970	0.0219490	0.0109745	−	0.999940i	$-0.496507\pi$
$691$	0.576970	0.0219490	0.0109745	+	0.999940i	$0.496507\pi$
$692$	−83.0685	−3.15779
$693$	2.64327	0.100410
$694$	−5.82792	−0.221225
$695$	−63.7748	−2.41911
$696$	−43.6100	−1.65303
$697$	−15.7807	−0.597737
$698$	−36.3146	−1.37453
$699$	−10.4755	−0.396220
$700$	100.674	3.80512
$701$	7.41499	0.280060	0.140030	−	0.990147i	$-0.455280\pi$
$701$	7.41499	0.280060	0.140030	+	0.990147i	$0.455280\pi$
$702$	7.37869	0.278491
$703$	2.27783	0.0859098
$704$	−1.86405	−0.0702542
$705$	40.4412	1.52310
$706$	52.2897	1.96795
$707$	−62.7279	−2.35913
$708$	−5.43038	−0.204086
$709$	−21.1226	−0.793277	−0.396638	−	0.917975i	$-0.629823\pi$
$709$	−21.1226	−0.793277	−0.396638	+	0.917975i	$0.629823\pi$
$710$	124.928	4.68847
$711$	5.51966	0.207004
$712$	13.7270	0.514440
$713$	−7.40626	−0.277367
$714$	−52.4966	−1.96464
$715$	−6.20935	−0.232217
$716$	−4.94972	−0.184980
$717$	−14.6957	−0.548821
$718$	4.91578	0.183455
$719$	−20.1583	−0.751779	−0.375890	−	0.926664i	$-0.622663\pi$
$719$	−20.1583	−0.751779	−0.375890	+	0.926664i	$0.622663\pi$
$720$	20.2208	0.753586
$721$	56.8476	2.11711
$722$	47.3440	1.76196
$723$	−23.0092	−0.855721
$724$	74.3762	2.76417
$725$	41.9796	1.55908
$726$	26.6481	0.989003
$727$	27.5569	1.02203	0.511014	−	0.859572i	$-0.329270\pi$
$727$	27.5569	1.02203	0.511014	+	0.859572i	$0.329270\pi$
$728$	70.5177	2.61356
$729$	1.00000	0.0370370
$730$	−75.3601	−2.78920
$731$	13.7850	0.509858
$732$	38.8694	1.43665
$733$	34.0174	1.25646	0.628231	−	0.778027i	$-0.283779\pi$
$733$	34.0174	1.25646	0.628231	+	0.778027i	$0.283779\pi$
$734$	56.3766	2.08090
$735$	31.4309	1.15935
$736$	2.89413	0.106679
$737$	−8.06578	−0.297107
$738$	7.77417	0.286171
$739$	−8.96461	−0.329769	−0.164884	−	0.986313i	$-0.552725\pi$
$739$	−8.96461	−0.329769	−0.164884	+	0.986313i	$0.552725\pi$
$740$	71.6095	2.63242
$741$	−1.32330	−0.0486125
$742$	110.791	4.06728
$743$	−41.3662	−1.51758	−0.758789	−	0.651336i	$-0.774209\pi$
$743$	−41.3662	−1.51758	−0.758789	+	0.651336i	$0.774209\pi$
$744$	−56.9844	−2.08915
$745$	44.9221	1.64582
$746$	15.7739	0.577523
$747$	−14.5915	−0.533876
$748$	14.4047	0.526687
$749$	57.6946	2.10812
$750$	−5.63817	−0.205877
$751$	30.9437	1.12915	0.564576	−	0.825381i	$-0.309040\pi$
$751$	30.9437	1.12915	0.564576	+	0.825381i	$0.309040\pi$
$752$	76.5345	2.79093
$753$	−6.73804	−0.245548
$754$	54.4883	1.98435
$755$	−12.1158	−0.440940
$756$	17.7094	0.644084
$757$	6.65268	0.241796	0.120898	−	0.992665i	$-0.461423\pi$
$757$	6.65268	0.241796	0.120898	+	0.992665i	$0.461423\pi$
$758$	50.3832	1.83000
$759$	−0.497726	−0.0180663
$760$	−8.72014	−0.316313
$761$	1.37325	0.0497804	0.0248902	−	0.999690i	$-0.492076\pi$
$761$	1.37325	0.0497804	0.0248902	+	0.999690i	$0.492076\pi$
$762$	33.6594	1.21935
$763$	−10.5014	−0.380175
$764$	36.5126	1.32098
$765$	16.7131	0.604262
$766$	52.2836	1.88908
$767$	3.66153	0.132210
$768$	−31.4840	−1.13608
$769$	−3.70178	−0.133490	−0.0667448	−	0.997770i	$-0.521261\pi$
$769$	−3.70178	−0.133490	−0.0667448	+	0.997770i	$0.521261\pi$
$770$	−21.7633	−0.784296
$771$	−26.4634	−0.953056
$772$	61.6747	2.21972
$773$	34.7777	1.25087	0.625434	−	0.780277i	$-0.284922\pi$
$773$	34.7777	1.25087	0.625434	+	0.780277i	$0.284922\pi$
$774$	−6.79103	−0.244098
$775$	54.8539	1.97041
$776$	4.15889	0.149295
$777$	20.5541	0.737376
$778$	19.1236	0.685615
$779$	−1.39422	−0.0499531
$780$	−41.6014	−1.48957
$781$	−9.83924	−0.352076
$782$	9.88507	0.353489
$783$	7.38455	0.263902
$784$	59.4826	2.12438
$785$	9.68135	0.345542
$786$	46.0357	1.64204
$787$	−5.47712	−0.195238	−0.0976192	−	0.995224i	$-0.531123\pi$
$787$	−5.47712	−0.195238	−0.0976192	+	0.995224i	$0.531123\pi$
$788$	23.7732	0.846884
$789$	26.4099	0.940218
$790$	−45.4461	−1.61690
$791$	−62.1261	−2.20895
$792$	−3.82954	−0.136077
$793$	−26.2084	−0.930687
$794$	−75.1860	−2.66825
$795$	−35.2720	−1.25097
$796$	50.5812	1.79280
$797$	−8.91974	−0.315954	−0.157977	−	0.987443i	$-0.550497\pi$
$797$	−8.91974	−0.315954	−0.157977	+	0.987443i	$0.550497\pi$
$798$	−4.63806	−0.164186
$799$	63.2578	2.23790
$800$	−21.4352	−0.757848
$801$	−2.32441	−0.0821288
$802$	−25.1384	−0.887666
$803$	5.93530	0.209452
$804$	−54.0390	−1.90581
$805$	−10.2269	−0.360452
$806$	71.1988	2.50787
$807$	7.91517	0.278627
$808$	90.8795	3.19713
$809$	−18.2549	−0.641807	−0.320904	−	0.947112i	$-0.603987\pi$
$809$	−18.2549	−0.641807	−0.320904	+	0.947112i	$0.603987\pi$
$810$	−8.23349	−0.289295
$811$	32.4981	1.14116	0.570582	−	0.821241i	$-0.306718\pi$
$811$	32.4981	1.14116	0.570582	+	0.821241i	$0.306718\pi$
$812$	130.776	4.58933
$813$	0.262801	0.00921683
$814$	−8.23621	−0.288679
$815$	56.7645	1.98837
$816$	31.6293	1.10725
$817$	1.21790	0.0426090
$818$	−85.3015	−2.98250
$819$	−11.9409	−0.417248
$820$	−43.8311	−1.53065
$821$	26.4401	0.922765	0.461383	−	0.887201i	$-0.347354\pi$
$821$	26.4401	0.922765	0.461383	+	0.887201i	$0.347354\pi$
$822$	47.2239	1.64712
$823$	13.7959	0.480894	0.240447	−	0.970662i	$-0.422706\pi$
$823$	13.7959	0.480894	0.240447	+	0.970662i	$0.422706\pi$
$824$	−82.3601	−2.86915
$825$	3.68637	0.128343
$826$	12.8334	0.446532
$827$	44.8415	1.55929	0.779646	−	0.626221i	$-0.215399\pi$
$827$	44.8415	1.55929	0.779646	+	0.626221i	$0.215399\pi$
$828$	−3.33466	−0.115887
$829$	−39.7665	−1.38115	−0.690574	−	0.723262i	$-0.742642\pi$
$829$	−39.7665	−1.38115	−0.690574	+	0.723262i	$0.742642\pi$
$830$	120.139	4.17009
$831$	22.4788	0.779782
$832$	8.42079	0.291938
$833$	49.1640	1.70343
$834$	49.1436	1.70170
$835$	−45.5490	−1.57629
$836$	1.27265	0.0440155
$837$	9.64925	0.333527
$838$	−82.2206	−2.84026
$839$	17.3221	0.598024	0.299012	−	0.954249i	$-0.403343\pi$
$839$	17.3221	0.598024	0.299012	+	0.954249i	$0.403343\pi$
$840$	−78.6869	−2.71496
$841$	25.5315	0.880397
$842$	23.6266	0.814226
$843$	5.19041	0.178767
$844$	−99.9263	−3.43960
$845$	−14.4434	−0.496868
$846$	−31.1632	−1.07141
$847$	−43.1243	−1.48177
$848$	−66.7519	−2.29227
$849$	12.2072	0.418951
$850$	−73.2130	−2.51119
$851$	−3.87033	−0.132673
$852$	−65.9209	−2.25841
$853$	41.4809	1.42028	0.710139	−	0.704062i	$-0.248632\pi$
$853$	41.4809	1.42028	0.710139	+	0.704062i	$0.248632\pi$
$854$	−91.8585	−3.14333
$855$	1.47659	0.0504985
$856$	−83.5874	−2.85696
$857$	45.4569	1.55278	0.776389	−	0.630254i	$-0.217049\pi$
$857$	45.4569	1.55278	0.776389	+	0.630254i	$0.217049\pi$
$858$	4.78480	0.163350
$859$	−27.6751	−0.944264	−0.472132	−	0.881528i	$-0.656515\pi$
$859$	−27.6751	−0.944264	−0.472132	+	0.881528i	$0.656515\pi$
$860$	38.2881	1.30561
$861$	−12.5809	−0.428755
$862$	−59.1407	−2.01434
$863$	25.7930	0.878003	0.439001	−	0.898486i	$-0.355332\pi$
$863$	25.7930	0.878003	0.439001	+	0.898486i	$0.355332\pi$
$864$	−3.77062	−0.128279
$865$	−62.4990	−2.12503
$866$	93.5502	3.17896
$867$	9.14247	0.310495
$868$	170.882	5.80012
$869$	3.57929	0.121419
$870$	−60.8005	−2.06133
$871$	36.4368	1.23461
$872$	15.2142	0.515219
$873$	−0.704230	−0.0238346
$874$	0.873342	0.0295412
$875$	9.12420	0.308454
$876$	39.7653	1.34354
$877$	−50.9301	−1.71979	−0.859893	−	0.510474i	$-0.829470\pi$
$877$	−50.9301	−1.71979	−0.859893	+	0.510474i	$0.829470\pi$
$878$	−33.7370	−1.13857
$879$	19.2073	0.647845
$880$	13.1124	0.442020
$881$	−49.3800	−1.66365	−0.831827	−	0.555035i	$-0.812705\pi$
$881$	−49.3800	−1.66365	−0.831827	+	0.555035i	$0.812705\pi$
$882$	−24.2200	−0.815530
$883$	8.67623	0.291978	0.145989	−	0.989286i	$-0.453364\pi$
$883$	8.67623	0.291978	0.145989	+	0.989286i	$0.453364\pi$
$884$	−65.0726	−2.18863
$885$	−4.08571	−0.137340
$886$	25.1883	0.846217
$887$	−32.3831	−1.08732	−0.543660	−	0.839306i	$-0.682962\pi$
$887$	−32.3831	−1.08732	−0.543660	+	0.839306i	$0.682962\pi$
$888$	−29.7786	−0.999305
$889$	−54.4707	−1.82689
$890$	19.1380	0.641506
$891$	0.648462	0.0217243
$892$	−46.2491	−1.54854
$893$	5.58881	0.187022
$894$	−34.6161	−1.15773
$895$	−3.72407	−0.124482
$896$	60.2540	2.01295
$897$	2.24845	0.0750737
$898$	−85.6127	−2.85693
$899$	71.2553	2.37650
$900$	24.6979	0.823263
$901$	−55.1723	−1.83806
$902$	5.04125	0.167855
$903$	10.9898	0.365719
$904$	90.0075	2.99361
$905$	55.9591	1.86014
$906$	9.33622	0.310175
$907$	−26.3106	−0.873628	−0.436814	−	0.899552i	$-0.643893\pi$
$907$	−26.3106	−0.873628	−0.436814	+	0.899552i	$0.643893\pi$
$908$	−15.9149	−0.528155
$909$	−15.3888	−0.510413
$910$	98.3149	3.25911
$911$	−58.8835	−1.95090	−0.975448	−	0.220230i	$-0.929319\pi$
$911$	−58.8835	−1.95090	−0.975448	+	0.220230i	$0.929319\pi$
$912$	2.79444	0.0925331
$913$	−9.46206	−0.313148
$914$	−23.6643	−0.782745
$915$	29.2445	0.966794
$916$	45.0881	1.48975
$917$	−74.4992	−2.46018
$918$	−12.8788	−0.425062
$919$	18.7209	0.617544	0.308772	−	0.951136i	$-0.400082\pi$
$919$	18.7209	0.617544	0.308772	+	0.951136i	$0.400082\pi$
$920$	14.8167	0.488491
$921$	−28.4591	−0.937760
$922$	73.6039	2.42402
$923$	44.4483	1.46303
$924$	11.4839	0.377791
$925$	28.6653	0.942509
$926$	14.8962	0.489520
$927$	13.9462	0.458052
$928$	−27.8443	−0.914035
$929$	6.85266	0.224828	0.112414	−	0.993661i	$-0.464142\pi$
$929$	6.85266	0.224828	0.112414	+	0.993661i	$0.464142\pi$
$930$	−79.4469	−2.60517
$931$	4.34362	0.142356
$932$	−45.5115	−1.49078
$933$	18.7576	0.614096
$934$	−75.2915	−2.46361
$935$	10.8378	0.354434
$936$	17.2998	0.565462
$937$	−10.2142	−0.333683	−0.166841	−	0.985984i	$-0.553357\pi$
$937$	−10.2142	−0.333683	−0.166841	+	0.985984i	$0.553357\pi$
$938$	127.708	4.16983
$939$	−1.65575	−0.0540334
$940$	175.699	5.73068
$941$	38.1858	1.24482	0.622410	−	0.782691i	$-0.286154\pi$
$941$	38.1858	1.24482	0.622410	+	0.782691i	$0.286154\pi$
$942$	−7.46026	−0.243068
$943$	2.36896	0.0771441
$944$	−7.73216	−0.251660
$945$	13.3242	0.433435
$946$	−4.40372	−0.143177
$947$	54.6170	1.77481	0.887407	−	0.460987i	$-0.152505\pi$
$947$	54.6170	1.77481	0.887407	+	0.460987i	$0.152505\pi$
$948$	23.9805	0.778851
$949$	−26.8125	−0.870369
$950$	−6.46835	−0.209861
$951$	−12.2014	−0.395657
$952$	−123.082	−3.98910
$953$	−17.0279	−0.551589	−0.275795	−	0.961217i	$-0.588941\pi$
$953$	−17.0279	−0.551589	−0.275795	+	0.961217i	$0.588941\pi$
$954$	27.1799	0.879983
$955$	27.4714	0.888952
$956$	−63.8464	−2.06494
$957$	4.78860	0.154793
$958$	34.5792	1.11720
$959$	−76.4219	−2.46779
$960$	−9.39630	−0.303264
$961$	62.1080	2.00348
$962$	37.2067	1.19959
$963$	14.1540	0.456105
$964$	−99.9648	−3.21965
$965$	46.4028	1.49376
$966$	7.88068	0.253557
$967$	13.5986	0.437303	0.218651	−	0.975803i	$-0.429834\pi$
$967$	13.5986	0.437303	0.218651	+	0.975803i	$0.429834\pi$
$968$	62.4780	2.00812
$969$	2.30968	0.0741976
$970$	5.79827	0.186171
$971$	48.4625	1.55523	0.777617	−	0.628738i	$-0.216428\pi$
$971$	48.4625	1.55523	0.777617	+	0.628738i	$0.216428\pi$
$972$	4.34456	0.139352
$973$	−79.5286	−2.54957
$974$	−30.9005	−0.990117
$975$	−16.6530	−0.533323
$976$	55.3449	1.77155
$977$	−33.2269	−1.06302	−0.531512	−	0.847051i	$-0.678376\pi$
$977$	−33.2269	−1.06302	−0.531512	+	0.847051i	$0.678376\pi$
$978$	−43.7416	−1.39870
$979$	−1.50729	−0.0481732
$980$	136.553	4.36204
$981$	−2.57625	−0.0822533
$982$	−78.6052	−2.50839
$983$	1.85585	0.0591923	0.0295962	−	0.999562i	$-0.490578\pi$
$983$	1.85585	0.0591923	0.0295962	+	0.999562i	$0.490578\pi$
$984$	18.2270	0.581056
$985$	17.8865	0.569910
$986$	−95.1038	−3.02872
$987$	50.4311	1.60524
$988$	−5.74914	−0.182905
$989$	−2.06938	−0.0658024
$990$	−5.33910	−0.169688
$991$	−16.0289	−0.509175	−0.254587	−	0.967050i	$-0.581940\pi$
$991$	−16.0289	−0.509175	−0.254587	+	0.967050i	$0.581940\pi$
$992$	−36.3837	−1.15518
$993$	−9.21492	−0.292427
$994$	155.788	4.94131
$995$	38.0562	1.20646
$996$	−63.3938	−2.00871
$997$	30.4200	0.963411	0.481706	−	0.876333i	$-0.340017\pi$
$997$	30.4200	0.963411	0.481706	+	0.876333i	$0.340017\pi$
$998$	13.7913	0.436555
$999$	5.04246	0.159536

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.d.1.11	✓	129

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.d.1.11	✓	129	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.51884 q^{2} +1.00000 q^{3} +4.34456 q^{4} +3.26876 q^{5} -2.51884 q^{6} +4.07622 q^{7} -5.90558 q^{8} +1.00000 q^{9} -8.23349 q^{10} +0.648462 q^{11} +4.34456 q^{12} -2.92940 q^{13} -10.2673 q^{14} +3.26876 q^{15} +6.18609 q^{16} +5.11297 q^{17} -2.51884 q^{18} +0.451729 q^{19} +14.2013 q^{20} +4.07622 q^{21} -1.63337 q^{22} -0.767548 q^{23} -5.90558 q^{24} +5.68479 q^{25} +7.37869 q^{26} +1.00000 q^{27} +17.7094 q^{28} +7.38455 q^{29} -8.23349 q^{30} +9.64925 q^{31} -3.77062 q^{32} +0.648462 q^{33} -12.8788 q^{34} +13.3242 q^{35} +4.34456 q^{36} +5.04246 q^{37} -1.13783 q^{38} -2.92940 q^{39} -19.3039 q^{40} -3.08641 q^{41} -10.2673 q^{42} +2.69609 q^{43} +2.81728 q^{44} +3.26876 q^{45} +1.93333 q^{46} +12.3720 q^{47} +6.18609 q^{48} +9.61554 q^{49} -14.3191 q^{50} +5.11297 q^{51} -12.7270 q^{52} -10.7907 q^{53} -2.51884 q^{54} +2.11967 q^{55} -24.0724 q^{56} +0.451729 q^{57} -18.6005 q^{58} -1.24993 q^{59} +14.2013 q^{60} +8.94667 q^{61} -24.3049 q^{62} +4.07622 q^{63} -2.87458 q^{64} -9.57550 q^{65} -1.63337 q^{66} -12.4383 q^{67} +22.2136 q^{68} -0.767548 q^{69} -33.5615 q^{70} -15.1732 q^{71} -5.90558 q^{72} +9.15289 q^{73} -12.7011 q^{74} +5.68479 q^{75} +1.96257 q^{76} +2.64327 q^{77} +7.37869 q^{78} +5.51966 q^{79} +20.2208 q^{80} +1.00000 q^{81} +7.77417 q^{82} -14.5915 q^{83} +17.7094 q^{84} +16.7131 q^{85} -6.79103 q^{86} +7.38455 q^{87} -3.82954 q^{88} -2.32441 q^{89} -8.23349 q^{90} -11.9409 q^{91} -3.33466 q^{92} +9.64925 q^{93} -31.1632 q^{94} +1.47659 q^{95} -3.77062 q^{96} -0.704230 q^{97} -24.2200 q^{98} +0.648462 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9}+O(q^{10}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9	\( 129 q + 15 q^{2} + 129 q^{3} + 151 q^{4} + 16 q^{5} + 15 q^{6} + 61 q^{7} + 42 q^{8} + 129 q^{9} + 41 q^{10} + 51 q^{11} + 151 q^{12} + 56 q^{13} + 5 q^{14} + 16 q^{15} + 195 q^{16} + 18 q^{17} + 15 q^{18} + 93 q^{19} + 44 q^{20} + 61 q^{21} + 46 q^{22} + 50 q^{23} + 42 q^{24} + 193 q^{25} + q^{26} + 129 q^{27} + 145 q^{28} + 24 q^{29} + 41 q^{30} + 67 q^{31} + 89 q^{32} + 51 q^{33} + 73 q^{34} + 56 q^{35} + 151 q^{36} + 95 q^{37} + 9 q^{38} + 56 q^{39} + 103 q^{40} + 7 q^{41} + 5 q^{42} + 150 q^{43} + 69 q^{44} + 16 q^{45} + 72 q^{46} + 53 q^{47} + 195 q^{48} + 240 q^{49} + 17 q^{50} + 18 q^{51} + 124 q^{52} + 34 q^{53} + 15 q^{54} + 66 q^{55} - 17 q^{56} + 93 q^{57} + 57 q^{58} + 49 q^{59} + 44 q^{60} + 113 q^{61} + 27 q^{62} + 61 q^{63} + 262 q^{64} + 22 q^{65} + 46 q^{66} + 185 q^{67} + 2 q^{68} + 50 q^{69} + 25 q^{70} + 41 q^{71} + 42 q^{72} + 153 q^{73} - q^{74} + 193 q^{75} + 190 q^{76} + 39 q^{77} + q^{78} + 101 q^{79} + 48 q^{80} + 129 q^{81} + 15 q^{82} + 162 q^{83} + 145 q^{84} + 99 q^{85} + 13 q^{86} + 24 q^{87} + 86 q^{88} - 4 q^{89} + 41 q^{90} + 117 q^{91} + 56 q^{92} + 67 q^{93} + 49 q^{94} + 71 q^{95} + 89 q^{96} + 159 q^{97} + 40 q^{98} + 51 q^{99}+O(q^{100}) \) 129 * q + 15 * q^2 + 129 * q^3 + 151 * q^4 + 16 * q^5 + 15 * q^6 + 61 * q^7 + 42 * q^8 + 129 * q^9 + 41 * q^10 + 51 * q^11 + 151 * q^12 + 56 * q^13 + 5 * q^14 + 16 * q^15 + 195 * q^16 + 18 * q^17 + 15 * q^18 + 93 * q^19 + 44 * q^20 + 61 * q^21 + 46 * q^22 + 50 * q^23 + 42 * q^24 + 193 * q^25 + q^26 + 129 * q^27 + 145 * q^28 + 24 * q^29 + 41 * q^30 + 67 * q^31 + 89 * q^32 + 51 * q^33 + 73 * q^34 + 56 * q^35 + 151 * q^36 + 95 * q^37 + 9 * q^38 + 56 * q^39 + 103 * q^40 + 7 * q^41 + 5 * q^42 + 150 * q^43 + 69 * q^44 + 16 * q^45 + 72 * q^46 + 53 * q^47 + 195 * q^48 + 240 * q^49 + 17 * q^50 + 18 * q^51 + 124 * q^52 + 34 * q^53 + 15 * q^54 + 66 * q^55 - 17 * q^56 + 93 * q^57 + 57 * q^58 + 49 * q^59 + 44 * q^60 + 113 * q^61 + 27 * q^62 + 61 * q^63 + 262 * q^64 + 22 * q^65 + 46 * q^66 + 185 * q^67 + 2 * q^68 + 50 * q^69 + 25 * q^70 + 41 * q^71 + 42 * q^72 + 153 * q^73 - q^74 + 193 * q^75 + 190 * q^76 + 39 * q^77 + q^78 + 101 * q^79 + 48 * q^80 + 129 * q^81 + 15 * q^82 + 162 * q^83 + 145 * q^84 + 99 * q^85 + 13 * q^86 + 24 * q^87 + 86 * q^88 - 4 * q^89 + 41 * q^90 + 117 * q^91 + 56 * q^92 + 67 * q^93 + 49 * q^94 + 71 * q^95 + 89 * q^96 + 159 * q^97 + 40 * q^98 + 51 * q^99

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