LMFDB - Embedded newform 8018.2.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.29667 q^{3} +1.00000 q^{4} -2.85656 q^{5} -2.29667 q^{6} +3.49764 q^{7} +1.00000 q^{8} +2.27470 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.29667 q^{3} +1.00000 q^{4} -2.85656 q^{5} -2.29667 q^{6} +3.49764 q^{7} +1.00000 q^{8} +2.27470 q^{9} -2.85656 q^{10} -4.96410 q^{11} -2.29667 q^{12} -4.70743 q^{13} +3.49764 q^{14} +6.56058 q^{15} +1.00000 q^{16} +3.17293 q^{17} +2.27470 q^{18} -1.00000 q^{19} -2.85656 q^{20} -8.03293 q^{21} -4.96410 q^{22} +3.65618 q^{23} -2.29667 q^{24} +3.15992 q^{25} -4.70743 q^{26} +1.66578 q^{27} +3.49764 q^{28} +3.48985 q^{29} +6.56058 q^{30} +5.19873 q^{31} +1.00000 q^{32} +11.4009 q^{33} +3.17293 q^{34} -9.99122 q^{35} +2.27470 q^{36} +3.75245 q^{37} -1.00000 q^{38} +10.8114 q^{39} -2.85656 q^{40} +1.13949 q^{41} -8.03293 q^{42} -8.13856 q^{43} -4.96410 q^{44} -6.49781 q^{45} +3.65618 q^{46} +8.02556 q^{47} -2.29667 q^{48} +5.23350 q^{49} +3.15992 q^{50} -7.28719 q^{51} -4.70743 q^{52} -9.42716 q^{53} +1.66578 q^{54} +14.1802 q^{55} +3.49764 q^{56} +2.29667 q^{57} +3.48985 q^{58} -8.92132 q^{59} +6.56058 q^{60} +13.0416 q^{61} +5.19873 q^{62} +7.95608 q^{63} +1.00000 q^{64} +13.4470 q^{65} +11.4009 q^{66} -3.77284 q^{67} +3.17293 q^{68} -8.39704 q^{69} -9.99122 q^{70} +8.58402 q^{71} +2.27470 q^{72} +5.50483 q^{73} +3.75245 q^{74} -7.25731 q^{75} -1.00000 q^{76} -17.3626 q^{77} +10.8114 q^{78} -11.0591 q^{79} -2.85656 q^{80} -10.6498 q^{81} +1.13949 q^{82} +8.42263 q^{83} -8.03293 q^{84} -9.06367 q^{85} -8.13856 q^{86} -8.01505 q^{87} -4.96410 q^{88} -14.4964 q^{89} -6.49781 q^{90} -16.4649 q^{91} +3.65618 q^{92} -11.9398 q^{93} +8.02556 q^{94} +2.85656 q^{95} -2.29667 q^{96} -8.13665 q^{97} +5.23350 q^{98} -11.2918 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) $ 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.29667	−1.32598	−0.662992	−	0.748627i	$-0.730714\pi$
$3$	−2.29667	−1.32598	−0.662992	+	0.748627i	$0.730714\pi$
$4$	1.00000	0.500000
$5$	−2.85656	−1.27749	−0.638746	−	0.769418i	$-0.720546\pi$
$5$	−2.85656	−1.27749	−0.638746	+	0.769418i	$0.720546\pi$
$6$	−2.29667	−0.937612
$7$	3.49764	1.32198	0.660992	−	0.750393i	$-0.270136\pi$
$7$	3.49764	1.32198	0.660992	+	0.750393i	$0.270136\pi$
$8$	1.00000	0.353553
$9$	2.27470	0.758233
$10$	−2.85656	−0.903323
$11$	−4.96410	−1.49673	−0.748366	−	0.663286i	$-0.769161\pi$
$11$	−4.96410	−1.49673	−0.748366	+	0.663286i	$0.769161\pi$
$12$	−2.29667	−0.662992
$13$	−4.70743	−1.30561	−0.652803	−	0.757528i	$-0.726407\pi$
$13$	−4.70743	−1.30561	−0.652803	+	0.757528i	$0.726407\pi$
$14$	3.49764	0.934784
$15$	6.56058	1.69393
$16$	1.00000	0.250000
$17$	3.17293	0.769549	0.384775	−	0.923011i	$-0.374279\pi$
$17$	3.17293	0.769549	0.384775	+	0.923011i	$0.374279\pi$
$18$	2.27470	0.536152
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−2.85656	−0.638746
$21$	−8.03293	−1.75293
$22$	−4.96410	−1.05835
$23$	3.65618	0.762365	0.381183	−	0.924500i	$-0.375517\pi$
$23$	3.65618	0.762365	0.381183	+	0.924500i	$0.375517\pi$
$24$	−2.29667	−0.468806
$25$	3.15992	0.631985
$26$	−4.70743	−0.923202
$27$	1.66578	0.320579
$28$	3.49764	0.660992
$29$	3.48985	0.648050	0.324025	−	0.946049i	$-0.394964\pi$
$29$	3.48985	0.648050	0.324025	+	0.946049i	$0.394964\pi$
$30$	6.56058	1.19779
$31$	5.19873	0.933720	0.466860	−	0.884331i	$-0.345385\pi$
$31$	5.19873	0.933720	0.466860	+	0.884331i	$0.345385\pi$
$32$	1.00000	0.176777
$33$	11.4009	1.98464
$34$	3.17293	0.544154
$35$	−9.99122	−1.68882
$36$	2.27470	0.379117
$37$	3.75245	0.616900	0.308450	−	0.951241i	$-0.400190\pi$
$37$	3.75245	0.616900	0.308450	+	0.951241i	$0.400190\pi$
$38$	−1.00000	−0.162221
$39$	10.8114	1.73121
$40$	−2.85656	−0.451662
$41$	1.13949	0.177958	0.0889791	−	0.996033i	$-0.471640\pi$
$41$	1.13949	0.177958	0.0889791	+	0.996033i	$0.471640\pi$
$42$	−8.03293	−1.23951
$43$	−8.13856	−1.24112	−0.620559	−	0.784159i	$-0.713094\pi$
$43$	−8.13856	−1.24112	−0.620559	+	0.784159i	$0.713094\pi$
$44$	−4.96410	−0.748366
$45$	−6.49781	−0.968637
$46$	3.65618	0.539074
$47$	8.02556	1.17065	0.585324	−	0.810799i	$-0.300967\pi$
$47$	8.02556	1.17065	0.585324	+	0.810799i	$0.300967\pi$
$48$	−2.29667	−0.331496
$49$	5.23350	0.747643
$50$	3.15992	0.446881
$51$	−7.28719	−1.02041
$52$	−4.70743	−0.652803
$53$	−9.42716	−1.29492	−0.647460	−	0.762099i	$-0.724169\pi$
$53$	−9.42716	−1.29492	−0.647460	+	0.762099i	$0.724169\pi$
$54$	1.66578	0.226684
$55$	14.1802	1.91206
$56$	3.49764	0.467392
$57$	2.29667	0.304202
$58$	3.48985	0.458240
$59$	−8.92132	−1.16146	−0.580728	−	0.814097i	$-0.697232\pi$
$59$	−8.92132	−1.16146	−0.580728	+	0.814097i	$0.697232\pi$
$60$	6.56058	0.846967
$61$	13.0416	1.66980	0.834900	−	0.550401i	$-0.185525\pi$
$61$	13.0416	1.66980	0.834900	+	0.550401i	$0.185525\pi$
$62$	5.19873	0.660240
$63$	7.95608	1.00237
$64$	1.00000	0.125000
$65$	13.4470	1.66790
$66$	11.4009	1.40335
$67$	−3.77284	−0.460926	−0.230463	−	0.973081i	$-0.574024\pi$
$67$	−3.77284	−0.460926	−0.230463	+	0.973081i	$0.574024\pi$
$68$	3.17293	0.384775
$69$	−8.39704	−1.01088
$70$	−9.99122	−1.19418
$71$	8.58402	1.01874	0.509368	−	0.860549i	$-0.329879\pi$
$71$	8.58402	1.01874	0.509368	+	0.860549i	$0.329879\pi$
$72$	2.27470	0.268076
$73$	5.50483	0.644291	0.322146	−	0.946690i	$-0.395596\pi$
$73$	5.50483	0.644291	0.322146	+	0.946690i	$0.395596\pi$
$74$	3.75245	0.436214
$75$	−7.25731	−0.838002
$76$	−1.00000	−0.114708
$77$	−17.3626	−1.97866
$78$	10.8114	1.22415
$79$	−11.0591	−1.24424	−0.622120	−	0.782922i	$-0.713729\pi$
$79$	−11.0591	−1.24424	−0.622120	+	0.782922i	$0.713729\pi$
$80$	−2.85656	−0.319373
$81$	−10.6498	−1.18332
$82$	1.13949	0.125835
$83$	8.42263	0.924504	0.462252	−	0.886749i	$-0.347042\pi$
$83$	8.42263	0.924504	0.462252	+	0.886749i	$0.347042\pi$
$84$	−8.03293	−0.876465
$85$	−9.06367	−0.983093
$86$	−8.13856	−0.877603
$87$	−8.01505	−0.859303
$88$	−4.96410	−0.529175
$89$	−14.4964	−1.53662	−0.768309	−	0.640079i	$-0.778902\pi$
$89$	−14.4964	−1.53662	−0.768309	+	0.640079i	$0.778902\pi$
$90$	−6.49781	−0.684929
$91$	−16.4649	−1.72599
$92$	3.65618	0.381183
$93$	−11.9398	−1.23810
$94$	8.02556	0.827774
$95$	2.85656	0.293077
$96$	−2.29667	−0.234403
$97$	−8.13665	−0.826152	−0.413076	−	0.910697i	$-0.635546\pi$
$97$	−8.13665	−0.826152	−0.413076	+	0.910697i	$0.635546\pi$
$98$	5.23350	0.528663
$99$	−11.2918	−1.13487
$100$	3.15992	0.315992
$101$	0.790901	0.0786976	0.0393488	−	0.999226i	$-0.487472\pi$
$101$	0.790901	0.0786976	0.0393488	+	0.999226i	$0.487472\pi$
$102$	−7.28719	−0.721539
$103$	−18.1323	−1.78663	−0.893317	−	0.449428i	$-0.851628\pi$
$103$	−18.1323	−1.78663	−0.893317	+	0.449428i	$0.851628\pi$
$104$	−4.70743	−0.461601
$105$	22.9465	2.23935
$106$	−9.42716	−0.915647
$107$	17.9505	1.73534	0.867669	−	0.497143i	$-0.165618\pi$
$107$	17.9505	1.73534	0.867669	+	0.497143i	$0.165618\pi$
$108$	1.66578	0.160289
$109$	9.46542	0.906623	0.453311	−	0.891352i	$-0.350243\pi$
$109$	9.46542	0.906623	0.453311	+	0.891352i	$0.350243\pi$
$110$	14.1802	1.35203
$111$	−8.61815	−0.817999
$112$	3.49764	0.330496
$113$	6.16757	0.580196	0.290098	−	0.956997i	$-0.406312\pi$
$113$	6.16757	0.580196	0.290098	+	0.956997i	$0.406312\pi$
$114$	2.29667	0.215103
$115$	−10.4441	−0.973916
$116$	3.48985	0.324025
$117$	−10.7080	−0.989953
$118$	−8.92132	−0.821274
$119$	11.0978	1.01733
$120$	6.56058	0.598896
$121$	13.6423	1.24021
$122$	13.0416	1.18073
$123$	−2.61703	−0.235970
$124$	5.19873	0.466860
$125$	5.25628	0.470136
$126$	7.95608	0.708784
$127$	−15.9649	−1.41666	−0.708328	−	0.705883i	$-0.750550\pi$
$127$	−15.9649	−1.41666	−0.708328	+	0.705883i	$0.750550\pi$
$128$	1.00000	0.0883883
$129$	18.6916	1.64570
$130$	13.4470	1.17938
$131$	6.81492	0.595422	0.297711	−	0.954656i	$-0.403777\pi$
$131$	6.81492	0.595422	0.297711	+	0.954656i	$0.403777\pi$
$132$	11.4009	0.992321
$133$	−3.49764	−0.303284
$134$	−3.77284	−0.325924
$135$	−4.75839	−0.409537
$136$	3.17293	0.272077
$137$	5.92554	0.506253	0.253127	−	0.967433i	$-0.418541\pi$
$137$	5.92554	0.506253	0.253127	+	0.967433i	$0.418541\pi$
$138$	−8.39704	−0.714803
$139$	−1.70301	−0.144448	−0.0722238	−	0.997388i	$-0.523010\pi$
$139$	−1.70301	−0.144448	−0.0722238	+	0.997388i	$0.523010\pi$
$140$	−9.99122	−0.844412
$141$	−18.4321	−1.55226
$142$	8.58402	0.720355
$143$	23.3681	1.95414
$144$	2.27470	0.189558
$145$	−9.96897	−0.827878
$146$	5.50483	0.455583
$147$	−12.0196	−0.991362
$148$	3.75245	0.308450
$149$	−9.59643	−0.786170	−0.393085	−	0.919502i	$-0.628592\pi$
$149$	−9.59643	−0.786170	−0.393085	+	0.919502i	$0.628592\pi$
$150$	−7.25731	−0.592557
$151$	6.52834	0.531269	0.265634	−	0.964074i	$-0.414419\pi$
$151$	6.52834	0.531269	0.265634	+	0.964074i	$0.414419\pi$
$152$	−1.00000	−0.0811107
$153$	7.21747	0.583498
$154$	−17.3626	−1.39912
$155$	−14.8505	−1.19282
$156$	10.8114	0.865606
$157$	18.1842	1.45126	0.725630	−	0.688085i	$-0.241548\pi$
$157$	18.1842	1.45126	0.725630	+	0.688085i	$0.241548\pi$
$158$	−11.0591	−0.879811
$159$	21.6511	1.71704
$160$	−2.85656	−0.225831
$161$	12.7880	1.00784
$162$	−10.6498	−0.836731
$163$	−24.1581	−1.89221	−0.946106	−	0.323857i	$-0.895020\pi$
$163$	−24.1581	−1.89221	−0.946106	+	0.323857i	$0.895020\pi$
$164$	1.13949	0.0889791
$165$	−32.5673	−2.53536
$166$	8.42263	0.653723
$167$	3.75715	0.290737	0.145369	−	0.989378i	$-0.453563\pi$
$167$	3.75715	0.290737	0.145369	+	0.989378i	$0.453563\pi$
$168$	−8.03293	−0.619754
$169$	9.15987	0.704605
$170$	−9.06367	−0.695152
$171$	−2.27470	−0.173951
$172$	−8.13856	−0.620559
$173$	−0.250777	−0.0190662	−0.00953311	−	0.999955i	$-0.503035\pi$
$173$	−0.250777	−0.0190662	−0.00953311	+	0.999955i	$0.503035\pi$
$174$	−8.01505	−0.607619
$175$	11.0523	0.835474
$176$	−4.96410	−0.374183
$177$	20.4893	1.54007
$178$	−14.4964	−1.08655
$179$	22.7834	1.70291	0.851455	−	0.524427i	$-0.175720\pi$
$179$	22.7834	1.70291	0.851455	+	0.524427i	$0.175720\pi$
$180$	−6.49781	−0.484318
$181$	−18.3016	−1.36035	−0.680174	−	0.733051i	$-0.738096\pi$
$181$	−18.3016	−1.36035	−0.680174	+	0.733051i	$0.738096\pi$
$182$	−16.4649	−1.22046
$183$	−29.9522	−2.21413
$184$	3.65618	0.269537
$185$	−10.7191	−0.788084
$186$	−11.9398	−0.875467
$187$	−15.7508	−1.15181
$188$	8.02556	0.585324
$189$	5.82629	0.423800
$190$	2.85656	0.207237
$191$	−23.9399	−1.73223	−0.866114	−	0.499846i	$-0.833390\pi$
$191$	−23.9399	−1.73223	−0.866114	+	0.499846i	$0.833390\pi$
$192$	−2.29667	−0.165748
$193$	−22.3369	−1.60785	−0.803923	−	0.594733i	$-0.797258\pi$
$193$	−22.3369	−1.60785	−0.803923	+	0.594733i	$0.797258\pi$
$194$	−8.13665	−0.584178
$195$	−30.8834	−2.21161
$196$	5.23350	0.373821
$197$	14.0343	0.999901	0.499950	−	0.866054i	$-0.333352\pi$
$197$	14.0343	0.999901	0.499950	+	0.866054i	$0.333352\pi$
$198$	−11.2918	−0.802475
$199$	−13.2890	−0.942033	−0.471017	−	0.882124i	$-0.656113\pi$
$199$	−13.2890	−0.942033	−0.471017	+	0.882124i	$0.656113\pi$
$200$	3.15992	0.223440
$201$	8.66498	0.611181
$202$	0.790901	0.0556476
$203$	12.2063	0.856712
$204$	−7.28719	−0.510205
$205$	−3.25502	−0.227340
$206$	−18.1323	−1.26334
$207$	8.31670	0.578051
$208$	−4.70743	−0.326401
$209$	4.96410	0.343374
$210$	22.9465	1.58346
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	−9.42716	−0.647460
$213$	−19.7147	−1.35083
$214$	17.9505	1.22707
$215$	23.2483	1.58552
$216$	1.66578	0.113342
$217$	18.1833	1.23436
$218$	9.46542	0.641079
$219$	−12.6428	−0.854320
$220$	14.1802	0.956031
$221$	−14.9364	−1.00473
$222$	−8.61815	−0.578412
$223$	5.97646	0.400213	0.200107	−	0.979774i	$-0.435871\pi$
$223$	5.97646	0.400213	0.200107	+	0.979774i	$0.435871\pi$
$224$	3.49764	0.233696
$225$	7.18788	0.479192
$226$	6.16757	0.410260
$227$	−3.95788	−0.262694	−0.131347	−	0.991336i	$-0.541930\pi$
$227$	−3.95788	−0.262694	−0.131347	+	0.991336i	$0.541930\pi$
$228$	2.29667	0.152101
$229$	−24.2782	−1.60435	−0.802173	−	0.597092i	$-0.796323\pi$
$229$	−24.2782	−1.60435	−0.802173	+	0.597092i	$0.796323\pi$
$230$	−10.4441	−0.688662
$231$	39.8763	2.62367
$232$	3.48985	0.229120
$233$	−2.95326	−0.193475	−0.0967373	−	0.995310i	$-0.530841\pi$
$233$	−2.95326	−0.193475	−0.0967373	+	0.995310i	$0.530841\pi$
$234$	−10.7080	−0.700003
$235$	−22.9255	−1.49549
$236$	−8.92132	−0.580728
$237$	25.3990	1.64984
$238$	11.0978	0.719363
$239$	−2.75288	−0.178069	−0.0890345	−	0.996029i	$-0.528378\pi$
$239$	−2.75288	−0.178069	−0.0890345	+	0.996029i	$0.528378\pi$
$240$	6.56058	0.423483
$241$	−10.3594	−0.667308	−0.333654	−	0.942696i	$-0.608282\pi$
$241$	−10.3594	−0.667308	−0.333654	+	0.942696i	$0.608282\pi$
$242$	13.6423	0.876958
$243$	19.4619	1.24848
$244$	13.0416	0.834900
$245$	−14.9498	−0.955107
$246$	−2.61703	−0.166856
$247$	4.70743	0.299526
$248$	5.19873	0.330120
$249$	−19.3440	−1.22588
$250$	5.25628	0.332436
$251$	−10.4588	−0.660153	−0.330076	−	0.943954i	$-0.607074\pi$
$251$	−10.4588	−0.660153	−0.330076	+	0.943954i	$0.607074\pi$
$252$	7.95608	0.501186
$253$	−18.1496	−1.14106
$254$	−15.9649	−1.00173
$255$	20.8163	1.30357
$256$	1.00000	0.0625000
$257$	−1.39997	−0.0873280	−0.0436640	−	0.999046i	$-0.513903\pi$
$257$	−1.39997	−0.0873280	−0.0436640	+	0.999046i	$0.513903\pi$
$258$	18.6916	1.16369
$259$	13.1247	0.815532
$260$	13.4470	0.833950
$261$	7.93837	0.491373
$262$	6.81492	0.421027
$263$	−17.6058	−1.08562	−0.542811	−	0.839855i	$-0.682640\pi$
$263$	−17.6058	−1.08562	−0.542811	+	0.839855i	$0.682640\pi$
$264$	11.4009	0.701677
$265$	26.9292	1.65425
$266$	−3.49764	−0.214454
$267$	33.2935	2.03753
$268$	−3.77284	−0.230463
$269$	−23.0012	−1.40241	−0.701204	−	0.712961i	$-0.747354\pi$
$269$	−23.0012	−1.40241	−0.701204	+	0.712961i	$0.747354\pi$
$270$	−4.75839	−0.289586
$271$	−4.68065	−0.284329	−0.142165	−	0.989843i	$-0.545406\pi$
$271$	−4.68065	−0.284329	−0.142165	+	0.989843i	$0.545406\pi$
$272$	3.17293	0.192387
$273$	37.8145	2.28863
$274$	5.92554	0.357975
$275$	−15.6862	−0.945912
$276$	−8.39704	−0.505442
$277$	−7.27036	−0.436833	−0.218417	−	0.975856i	$-0.570089\pi$
$277$	−7.27036	−0.436833	−0.218417	+	0.975856i	$0.570089\pi$
$278$	−1.70301	−0.102140
$279$	11.8256	0.707977
$280$	−9.99122	−0.597089
$281$	20.9609	1.25042	0.625211	−	0.780455i	$-0.285013\pi$
$281$	20.9609	1.25042	0.625211	+	0.780455i	$0.285013\pi$
$282$	−18.4321	−1.09761
$283$	3.10278	0.184441	0.0922206	−	0.995739i	$-0.470603\pi$
$283$	3.10278	0.184441	0.0922206	+	0.995739i	$0.470603\pi$
$284$	8.58402	0.509368
$285$	−6.56058	−0.388615
$286$	23.3681	1.38179
$287$	3.98552	0.235258
$288$	2.27470	0.134038
$289$	−6.93249	−0.407794
$290$	−9.96897	−0.585398
$291$	18.6872	1.09546
$292$	5.50483	0.322146
$293$	7.61930	0.445124	0.222562	−	0.974919i	$-0.428558\pi$
$293$	7.61930	0.445124	0.222562	+	0.974919i	$0.428558\pi$
$294$	−12.0196	−0.700999
$295$	25.4843	1.48375
$296$	3.75245	0.218107
$297$	−8.26908	−0.479821
$298$	−9.59643	−0.555906
$299$	−17.2112	−0.995348
$300$	−7.25731	−0.419001
$301$	−28.4658	−1.64074
$302$	6.52834	0.375664
$303$	−1.81644	−0.104352
$304$	−1.00000	−0.0573539
$305$	−37.2540	−2.13316
$306$	7.21747	0.412595
$307$	3.97392	0.226804	0.113402	−	0.993549i	$-0.463825\pi$
$307$	3.97392	0.226804	0.113402	+	0.993549i	$0.463825\pi$
$308$	−17.3626	−0.989328
$309$	41.6440	2.36905
$310$	−14.8505	−0.843451
$311$	12.7238	0.721499	0.360749	−	0.932663i	$-0.382521\pi$
$311$	12.7238	0.721499	0.360749	+	0.932663i	$0.382521\pi$
$312$	10.8114	0.612076
$313$	−4.68503	−0.264814	−0.132407	−	0.991195i	$-0.542271\pi$
$313$	−4.68503	−0.264814	−0.132407	+	0.991195i	$0.542271\pi$
$314$	18.1842	1.02620
$315$	−22.7270	−1.28052
$316$	−11.0591	−0.622120
$317$	−6.56798	−0.368895	−0.184447	−	0.982842i	$-0.559049\pi$
$317$	−6.56798	−0.368895	−0.184447	+	0.982842i	$0.559049\pi$
$318$	21.6511	1.21413
$319$	−17.3240	−0.969956
$320$	−2.85656	−0.159686
$321$	−41.2263	−2.30103
$322$	12.7880	0.712647
$323$	−3.17293	−0.176547
$324$	−10.6498	−0.591658
$325$	−14.8751	−0.825123
$326$	−24.1581	−1.33800
$327$	−21.7390	−1.20217
$328$	1.13949	0.0629177
$329$	28.0706	1.54758
$330$	−32.5673	−1.79277
$331$	−30.5546	−1.67943	−0.839715	−	0.543027i	$-0.817278\pi$
$331$	−30.5546	−1.67943	−0.839715	+	0.543027i	$0.817278\pi$
$332$	8.42263	0.462252
$333$	8.53570	0.467754
$334$	3.75715	0.205582
$335$	10.7773	0.588830
$336$	−8.03293	−0.438232
$337$	8.28383	0.451249	0.225624	−	0.974214i	$-0.427558\pi$
$337$	8.28383	0.451249	0.225624	+	0.974214i	$0.427558\pi$
$338$	9.15987	0.498231
$339$	−14.1649	−0.769330
$340$	−9.06367	−0.491547
$341$	−25.8070	−1.39753
$342$	−2.27470	−0.123002
$343$	−6.17859	−0.333612
$344$	−8.13856	−0.438802
$345$	23.9866	1.29140
$346$	−0.250777	−0.0134819
$347$	−10.8011	−0.579834	−0.289917	−	0.957052i	$-0.593628\pi$
$347$	−10.8011	−0.579834	−0.289917	+	0.957052i	$0.593628\pi$
$348$	−8.01505	−0.429652
$349$	17.9136	0.958895	0.479448	−	0.877570i	$-0.340837\pi$
$349$	17.9136	0.958895	0.479448	+	0.877570i	$0.340837\pi$
$350$	11.0523	0.590770
$351$	−7.84152	−0.418550
$352$	−4.96410	−0.264587
$353$	22.8241	1.21480	0.607402	−	0.794394i	$-0.292212\pi$
$353$	22.8241	1.21480	0.607402	+	0.794394i	$0.292212\pi$
$354$	20.4893	1.08900
$355$	−24.5208	−1.30143
$356$	−14.4964	−0.768309
$357$	−25.4880	−1.34897
$358$	22.7834	1.20414
$359$	−27.3860	−1.44538	−0.722688	−	0.691174i	$-0.757094\pi$
$359$	−27.3860	−1.44538	−0.722688	+	0.691174i	$0.757094\pi$
$360$	−6.49781	−0.342465
$361$	1.00000	0.0526316
$362$	−18.3016	−0.961911
$363$	−31.3318	−1.64449
$364$	−16.4649	−0.862995
$365$	−15.7249	−0.823077
$366$	−29.9522	−1.56563
$367$	−11.9582	−0.624214	−0.312107	−	0.950047i	$-0.601035\pi$
$367$	−11.9582	−0.624214	−0.312107	+	0.950047i	$0.601035\pi$
$368$	3.65618	0.190591
$369$	2.59199	0.134934
$370$	−10.7191	−0.557260
$371$	−32.9728	−1.71186
$372$	−11.9398	−0.619049
$373$	−31.8087	−1.64699	−0.823496	−	0.567322i	$-0.807979\pi$
$373$	−31.8087	−1.64699	−0.823496	+	0.567322i	$0.807979\pi$
$374$	−15.7508	−0.814452
$375$	−12.0720	−0.623393
$376$	8.02556	0.413887
$377$	−16.4282	−0.846097
$378$	5.82629	0.299672
$379$	3.05690	0.157022	0.0785112	−	0.996913i	$-0.474983\pi$
$379$	3.05690	0.157022	0.0785112	+	0.996913i	$0.474983\pi$
$380$	2.85656	0.146538
$381$	36.6661	1.87846
$382$	−23.9399	−1.22487
$383$	7.90743	0.404051	0.202025	−	0.979380i	$-0.435248\pi$
$383$	7.90743	0.404051	0.202025	+	0.979380i	$0.435248\pi$
$384$	−2.29667	−0.117202
$385$	49.5974	2.52772
$386$	−22.3369	−1.13692
$387$	−18.5128	−0.941057
$388$	−8.13665	−0.413076
$389$	−24.2681	−1.23044	−0.615221	−	0.788355i	$-0.710933\pi$
$389$	−24.2681	−1.23044	−0.615221	+	0.788355i	$0.710933\pi$
$390$	−30.8834	−1.56384
$391$	11.6008	0.586678
$392$	5.23350	0.264332
$393$	−15.6516	−0.789520
$394$	14.0343	0.707036
$395$	31.5908	1.58951
$396$	−11.2918	−0.567436
$397$	11.1413	0.559167	0.279583	−	0.960121i	$-0.409804\pi$
$397$	11.1413	0.559167	0.279583	+	0.960121i	$0.409804\pi$
$398$	−13.2890	−0.666118
$399$	8.03293	0.402150
$400$	3.15992	0.157996
$401$	−17.2546	−0.861655	−0.430827	−	0.902434i	$-0.641778\pi$
$401$	−17.2546	−0.861655	−0.430827	+	0.902434i	$0.641778\pi$
$402$	8.66498	0.432170
$403$	−24.4726	−1.21907
$404$	0.790901	0.0393488
$405$	30.4219	1.51168
$406$	12.2063	0.605787
$407$	−18.6275	−0.923333
$408$	−7.28719	−0.360769
$409$	18.8255	0.930862	0.465431	−	0.885084i	$-0.345899\pi$
$409$	18.8255	0.930862	0.465431	+	0.885084i	$0.345899\pi$
$410$	−3.25502	−0.160754
$411$	−13.6090	−0.671284
$412$	−18.1323	−0.893317
$413$	−31.2036	−1.53543
$414$	8.31670	0.408744
$415$	−24.0597	−1.18105
$416$	−4.70743	−0.230801
$417$	3.91126	0.191535
$418$	4.96410	0.242802
$419$	1.03853	0.0507354	0.0253677	−	0.999678i	$-0.491924\pi$
$419$	1.03853	0.0507354	0.0253677	+	0.999678i	$0.491924\pi$
$420$	22.9465	1.11968
$421$	−27.3319	−1.33207	−0.666037	−	0.745919i	$-0.732011\pi$
$421$	−27.3319	−1.33207	−0.666037	+	0.745919i	$0.732011\pi$
$422$	1.00000	0.0486792
$423$	18.2557	0.887625
$424$	−9.42716	−0.457823
$425$	10.0262	0.486344
$426$	−19.7147	−0.955179
$427$	45.6147	2.20745
$428$	17.9505	0.867669
$429$	−53.6689	−2.59116
$430$	23.2483	1.12113
$431$	−15.7053	−0.756497	−0.378249	−	0.925704i	$-0.623474\pi$
$431$	−15.7053	−0.756497	−0.378249	+	0.925704i	$0.623474\pi$
$432$	1.66578	0.0801447
$433$	−2.96793	−0.142630	−0.0713149	−	0.997454i	$-0.522720\pi$
$433$	−2.96793	−0.142630	−0.0713149	+	0.997454i	$0.522720\pi$
$434$	18.1833	0.872826
$435$	22.8955	1.09775
$436$	9.46542	0.453311
$437$	−3.65618	−0.174899
$438$	−12.6428	−0.604095
$439$	13.1705	0.628592	0.314296	−	0.949325i	$-0.398232\pi$
$439$	13.1705	0.628592	0.314296	+	0.949325i	$0.398232\pi$
$440$	14.1802	0.676016
$441$	11.9046	0.566888
$442$	−14.9364	−0.710450
$443$	10.0008	0.475151	0.237576	−	0.971369i	$-0.423647\pi$
$443$	10.0008	0.475151	0.237576	+	0.971369i	$0.423647\pi$
$444$	−8.61815	−0.408999
$445$	41.4099	1.96302
$446$	5.97646	0.282993
$447$	22.0399	1.04245
$448$	3.49764	0.165248
$449$	−13.3322	−0.629185	−0.314592	−	0.949227i	$-0.601868\pi$
$449$	−13.3322	−0.629185	−0.314592	+	0.949227i	$0.601868\pi$
$450$	7.18788	0.338840
$451$	−5.65653	−0.266356
$452$	6.16757	0.290098
$453$	−14.9934	−0.704453
$454$	−3.95788	−0.185753
$455$	47.0329	2.20494
$456$	2.29667	0.107551
$457$	32.0040	1.49708	0.748541	−	0.663089i	$-0.230755\pi$
$457$	32.0040	1.49708	0.748541	+	0.663089i	$0.230755\pi$
$458$	−24.2782	−1.13444
$459$	5.28540	0.246701
$460$	−10.4441	−0.486958
$461$	−25.9269	−1.20754	−0.603769	−	0.797159i	$-0.706335\pi$
$461$	−25.9269	−1.20754	−0.603769	+	0.797159i	$0.706335\pi$
$462$	39.8763	1.85521
$463$	−18.1605	−0.843988	−0.421994	−	0.906599i	$-0.638670\pi$
$463$	−18.1605	−0.843988	−0.421994	+	0.906599i	$0.638670\pi$
$464$	3.48985	0.162012
$465$	34.1067	1.58166
$466$	−2.95326	−0.136807
$467$	23.9286	1.10728	0.553642	−	0.832755i	$-0.313238\pi$
$467$	23.9286	1.10728	0.553642	+	0.832755i	$0.313238\pi$
$468$	−10.7080	−0.494977
$469$	−13.1961	−0.609337
$470$	−22.9255	−1.05747
$471$	−41.7632	−1.92435
$472$	−8.92132	−0.410637
$473$	40.4006	1.85762
$474$	25.3990	1.16662
$475$	−3.15992	−0.144987
$476$	11.0978	0.508666
$477$	−21.4440	−0.981851
$478$	−2.75288	−0.125914
$479$	−16.8945	−0.771929	−0.385964	−	0.922514i	$-0.626131\pi$
$479$	−16.8945	−0.771929	−0.385964	+	0.922514i	$0.626131\pi$
$480$	6.56058	0.299448
$481$	−17.6644	−0.805427
$482$	−10.3594	−0.471858
$483$	−29.3698	−1.33637
$484$	13.6423	0.620103
$485$	23.2428	1.05540
$486$	19.4619	0.882808
$487$	31.3277	1.41959	0.709797	−	0.704406i	$-0.248786\pi$
$487$	31.3277	1.41959	0.709797	+	0.704406i	$0.248786\pi$
$488$	13.0416	0.590364
$489$	55.4833	2.50904
$490$	−14.9498	−0.675363
$491$	−19.6552	−0.887028	−0.443514	−	0.896268i	$-0.646268\pi$
$491$	−19.6552	−0.887028	−0.443514	+	0.896268i	$0.646268\pi$
$492$	−2.61703	−0.117985
$493$	11.0731	0.498706
$494$	4.70743	0.211797
$495$	32.2558	1.44979
$496$	5.19873	0.233430
$497$	30.0238	1.34675
$498$	−19.3440	−0.866826
$499$	−18.0509	−0.808069	−0.404034	−	0.914744i	$-0.632392\pi$
$499$	−18.0509	−0.808069	−0.404034	+	0.914744i	$0.632392\pi$
$500$	5.25628	0.235068
$501$	−8.62895	−0.385513
$502$	−10.4588	−0.466798
$503$	−1.04534	−0.0466095	−0.0233047	−	0.999728i	$-0.507419\pi$
$503$	−1.04534	−0.0466095	−0.0233047	+	0.999728i	$0.507419\pi$
$504$	7.95608	0.354392
$505$	−2.25925	−0.100535
$506$	−18.1496	−0.806849
$507$	−21.0372	−0.934295
$508$	−15.9649	−0.708328
$509$	−28.1349	−1.24706	−0.623529	−	0.781800i	$-0.714302\pi$
$509$	−28.1349	−1.24706	−0.623529	+	0.781800i	$0.714302\pi$
$510$	20.8163	0.921760
$511$	19.2539	0.851743
$512$	1.00000	0.0441942
$513$	−1.66578	−0.0735459
$514$	−1.39997	−0.0617502
$515$	51.7961	2.28241
$516$	18.6916	0.822852
$517$	−39.8397	−1.75215
$518$	13.1247	0.576668
$519$	0.575952	0.0252815
$520$	13.4470	0.589692
$521$	24.0028	1.05158	0.525791	−	0.850614i	$-0.323769\pi$
$521$	24.0028	1.05158	0.525791	+	0.850614i	$0.323769\pi$
$522$	7.93837	0.347453
$523$	−12.5747	−0.549854	−0.274927	−	0.961465i	$-0.588654\pi$
$523$	−12.5747	−0.549854	−0.274927	+	0.961465i	$0.588654\pi$
$524$	6.81492	0.297711
$525$	−25.3835	−1.10783
$526$	−17.6058	−0.767650
$527$	16.4952	0.718544
$528$	11.4009	0.496160
$529$	−9.63237	−0.418799
$530$	26.9292	1.16973
$531$	−20.2933	−0.880655
$532$	−3.49764	−0.151642
$533$	−5.36406	−0.232343
$534$	33.2935	1.44075
$535$	−51.2766	−2.21688
$536$	−3.77284	−0.162962
$537$	−52.3260	−2.25803
$538$	−23.0012	−0.991652
$539$	−25.9796	−1.11902
$540$	−4.75839	−0.204768
$541$	−11.1054	−0.477458	−0.238729	−	0.971086i	$-0.576731\pi$
$541$	−11.1054	−0.477458	−0.238729	+	0.971086i	$0.576731\pi$
$542$	−4.68065	−0.201051
$543$	42.0328	1.80380
$544$	3.17293	0.136038
$545$	−27.0385	−1.15820
$546$	37.8145	1.61831
$547$	−35.0817	−1.49998	−0.749992	−	0.661447i	$-0.769943\pi$
$547$	−35.0817	−1.49998	−0.749992	+	0.661447i	$0.769943\pi$
$548$	5.92554	0.253127
$549$	29.6656	1.26610
$550$	−15.6862	−0.668861
$551$	−3.48985	−0.148673
$552$	−8.39704	−0.357402
$553$	−38.6806	−1.64487
$554$	−7.27036	−0.308888
$555$	24.6183	1.04499
$556$	−1.70301	−0.0722238
$557$	−29.3710	−1.24449	−0.622245	−	0.782822i	$-0.713779\pi$
$557$	−29.3710	−1.24449	−0.622245	+	0.782822i	$0.713779\pi$
$558$	11.8256	0.500616
$559$	38.3117	1.62041
$560$	−9.99122	−0.422206
$561$	36.1743	1.52728
$562$	20.9609	0.884182
$563$	12.9127	0.544206	0.272103	−	0.962268i	$-0.412281\pi$
$563$	12.9127	0.544206	0.272103	+	0.962268i	$0.412281\pi$
$564$	−18.4321	−0.776131
$565$	−17.6180	−0.741195
$566$	3.10278	0.130420
$567$	−37.2493	−1.56432
$568$	8.58402	0.360178
$569$	9.10279	0.381609	0.190804	−	0.981628i	$-0.438890\pi$
$569$	9.10279	0.381609	0.190804	+	0.981628i	$0.438890\pi$
$570$	−6.56058	−0.274792
$571$	23.1145	0.967312	0.483656	−	0.875258i	$-0.339309\pi$
$571$	23.1145	0.967312	0.483656	+	0.875258i	$0.339309\pi$
$572$	23.3681	0.977070
$573$	54.9820	2.29691
$574$	3.98552	0.166353
$575$	11.5532	0.481804
$576$	2.27470	0.0947791
$577$	−38.7352	−1.61257	−0.806284	−	0.591528i	$-0.798525\pi$
$577$	−38.7352	−1.61257	−0.806284	+	0.591528i	$0.798525\pi$
$578$	−6.93249	−0.288354
$579$	51.3006	2.13198
$580$	−9.96897	−0.413939
$581$	29.4594	1.22218
$582$	18.6872	0.774610
$583$	46.7973	1.93815
$584$	5.50483	0.227791
$585$	30.5880	1.26466
$586$	7.61930	0.314750
$587$	5.52389	0.227995	0.113998	−	0.993481i	$-0.463634\pi$
$587$	5.52389	0.227995	0.113998	+	0.993481i	$0.463634\pi$
$588$	−12.0196	−0.495681
$589$	−5.19873	−0.214210
$590$	25.4843	1.04917
$591$	−32.2321	−1.32585
$592$	3.75245	0.154225
$593$	19.8956	0.817014	0.408507	−	0.912755i	$-0.366049\pi$
$593$	19.8956	0.817014	0.408507	+	0.912755i	$0.366049\pi$
$594$	−8.26908	−0.339284
$595$	−31.7015	−1.29963
$596$	−9.59643	−0.393085
$597$	30.5205	1.24912
$598$	−17.2112	−0.703818
$599$	29.5300	1.20656	0.603282	−	0.797528i	$-0.293859\pi$
$599$	29.5300	1.20656	0.603282	+	0.797528i	$0.293859\pi$
$600$	−7.25731	−0.296278
$601$	16.8803	0.688561	0.344281	−	0.938867i	$-0.388123\pi$
$601$	16.8803	0.688561	0.344281	+	0.938867i	$0.388123\pi$
$602$	−28.4658	−1.16018
$603$	−8.58209	−0.349490
$604$	6.52834	0.265634
$605$	−38.9699	−1.58435
$606$	−1.81644	−0.0737878
$607$	−26.9471	−1.09375	−0.546874	−	0.837215i	$-0.684183\pi$
$607$	−26.9471	−1.09375	−0.546874	+	0.837215i	$0.684183\pi$
$608$	−1.00000	−0.0405554
$609$	−28.0338	−1.13599
$610$	−37.2540	−1.50837
$611$	−37.7798	−1.52841
$612$	7.21747	0.291749
$613$	−33.7660	−1.36379	−0.681897	−	0.731448i	$-0.738845\pi$
$613$	−33.7660	−1.36379	−0.681897	+	0.731448i	$0.738845\pi$
$614$	3.97392	0.160374
$615$	7.47570	0.301449
$616$	−17.3626	−0.699561
$617$	−17.1976	−0.692351	−0.346176	−	0.938170i	$-0.612520\pi$
$617$	−17.1976	−0.692351	−0.346176	+	0.938170i	$0.612520\pi$
$618$	41.6440	1.67517
$619$	20.0529	0.805993	0.402996	−	0.915202i	$-0.367969\pi$
$619$	20.0529	0.805993	0.402996	+	0.915202i	$0.367969\pi$
$620$	−14.8505	−0.596410
$621$	6.09037	0.244398
$622$	12.7238	0.510177
$623$	−50.7033	−2.03139
$624$	10.8114	0.432803
$625$	−30.8145	−1.23258
$626$	−4.68503	−0.187252
$627$	−11.4009	−0.455308
$628$	18.1842	0.725630
$629$	11.9063	0.474735
$630$	−22.7270	−0.905466
$631$	23.0837	0.918949	0.459474	−	0.888191i	$-0.348038\pi$
$631$	23.0837	0.918949	0.459474	+	0.888191i	$0.348038\pi$
$632$	−11.0591	−0.439906
$633$	−2.29667	−0.0912845
$634$	−6.56798	−0.260848
$635$	45.6047	1.80977
$636$	21.6511	0.858521
$637$	−24.6363	−0.976126
$638$	−17.3240	−0.685863
$639$	19.5261	0.772439
$640$	−2.85656	−0.112915
$641$	−24.1776	−0.954958	−0.477479	−	0.878643i	$-0.658449\pi$
$641$	−24.1776	−0.954958	−0.477479	+	0.878643i	$0.658449\pi$
$642$	−41.2263	−1.62707
$643$	31.7796	1.25327	0.626633	−	0.779314i	$-0.284432\pi$
$643$	31.7796	1.25327	0.626633	+	0.779314i	$0.284432\pi$
$644$	12.7880	0.503918
$645$	−53.3936	−2.10237
$646$	−3.17293	−0.124837
$647$	−25.6992	−1.01034	−0.505170	−	0.863020i	$-0.668570\pi$
$647$	−25.6992	−1.01034	−0.505170	+	0.863020i	$0.668570\pi$
$648$	−10.6498	−0.418365
$649$	44.2863	1.73839
$650$	−14.8751	−0.583450
$651$	−41.7611	−1.63675
$652$	−24.1581	−0.946106
$653$	−8.02200	−0.313925	−0.156962	−	0.987605i	$-0.550170\pi$
$653$	−8.02200	−0.313925	−0.156962	+	0.987605i	$0.550170\pi$
$654$	−21.7390	−0.850060
$655$	−19.4672	−0.760647
$656$	1.13949	0.0444896
$657$	12.5218	0.488523
$658$	28.0706	1.09430
$659$	33.1069	1.28966	0.644830	−	0.764326i	$-0.276928\pi$
$659$	33.1069	1.28966	0.644830	+	0.764326i	$0.276928\pi$
$660$	−32.5673	−1.26768
$661$	−32.2877	−1.25585	−0.627923	−	0.778275i	$-0.716095\pi$
$661$	−32.2877	−1.25585	−0.627923	+	0.778275i	$0.716095\pi$
$662$	−30.5546	−1.18754
$663$	34.3039	1.33225
$664$	8.42263	0.326862
$665$	9.99122	0.387443
$666$	8.53570	0.330752
$667$	12.7595	0.494051
$668$	3.75715	0.145369
$669$	−13.7260	−0.530676
$670$	10.7773	0.416365
$671$	−64.7396	−2.49924
$672$	−8.03293	−0.309877
$673$	−32.9315	−1.26942	−0.634708	−	0.772752i	$-0.718880\pi$
$673$	−32.9315	−1.26942	−0.634708	+	0.772752i	$0.718880\pi$
$674$	8.28383	0.319081
$675$	5.26373	0.202601
$676$	9.15987	0.352303
$677$	21.5812	0.829433	0.414716	−	0.909951i	$-0.363881\pi$
$677$	21.5812	0.829433	0.414716	+	0.909951i	$0.363881\pi$
$678$	−14.1649	−0.543999
$679$	−28.4591	−1.09216
$680$	−9.06367	−0.347576
$681$	9.08995	0.348328
$682$	−25.8070	−0.988201
$683$	−30.9969	−1.18606	−0.593032	−	0.805179i	$-0.702069\pi$
$683$	−30.9969	−1.18606	−0.593032	+	0.805179i	$0.702069\pi$
$684$	−2.27470	−0.0869753
$685$	−16.9267	−0.646734
$686$	−6.17859	−0.235899
$687$	55.7589	2.12734
$688$	−8.13856	−0.310280
$689$	44.3777	1.69065
$690$	23.9866	0.913155
$691$	−13.2562	−0.504291	−0.252145	−	0.967689i	$-0.581136\pi$
$691$	−13.2562	−0.504291	−0.252145	+	0.967689i	$0.581136\pi$
$692$	−0.250777	−0.00953311
$693$	−39.4948	−1.50028
$694$	−10.8011	−0.410005
$695$	4.86475	0.184531
$696$	−8.01505	−0.303810
$697$	3.61552	0.136948
$698$	17.9136	0.678041
$699$	6.78267	0.256544
$700$	11.0523	0.417737
$701$	−41.8304	−1.57991	−0.789956	−	0.613163i	$-0.789897\pi$
$701$	−41.8304	−1.57991	−0.789956	+	0.613163i	$0.789897\pi$
$702$	−7.84152	−0.295959
$703$	−3.75245	−0.141526
$704$	−4.96410	−0.187091
$705$	52.6523	1.98300
$706$	22.8241	0.858997
$707$	2.76629	0.104037
$708$	20.4893	0.770037
$709$	40.5771	1.52391	0.761953	−	0.647632i	$-0.224240\pi$
$709$	40.5771	1.52391	0.761953	+	0.647632i	$0.224240\pi$
$710$	−24.5208	−0.920248
$711$	−25.1560	−0.943425
$712$	−14.4964	−0.543277
$713$	19.0075	0.711836
$714$	−25.4880	−0.953863
$715$	−66.7524	−2.49640
$716$	22.7834	0.851455
$717$	6.32246	0.236117
$718$	−27.3860	−1.02204
$719$	9.78044	0.364749	0.182374	−	0.983229i	$-0.441622\pi$
$719$	9.78044	0.364749	0.182374	+	0.983229i	$0.441622\pi$
$720$	−6.49781	−0.242159
$721$	−63.4205	−2.36190
$722$	1.00000	0.0372161
$723$	23.7921	0.884840
$724$	−18.3016	−0.680174
$725$	11.0277	0.409558
$726$	−31.3318	−1.16283
$727$	−21.5004	−0.797404	−0.398702	−	0.917081i	$-0.630539\pi$
$727$	−21.5004	−0.797404	−0.398702	+	0.917081i	$0.630539\pi$
$728$	−16.4649	−0.610230
$729$	−12.7480	−0.472147
$730$	−15.7249	−0.582003
$731$	−25.8231	−0.955102
$732$	−29.9522	−1.10706
$733$	46.8109	1.72900	0.864499	−	0.502634i	$-0.167636\pi$
$733$	46.8109	1.72900	0.864499	+	0.502634i	$0.167636\pi$
$734$	−11.9582	−0.441386
$735$	34.3348	1.26646
$736$	3.65618	0.134768
$737$	18.7288	0.689883
$738$	2.59199	0.0954126
$739$	−15.9553	−0.586926	−0.293463	−	0.955970i	$-0.594808\pi$
$739$	−15.9553	−0.586926	−0.293463	+	0.955970i	$0.594808\pi$
$740$	−10.7191	−0.394042
$741$	−10.8114	−0.397167
$742$	−32.9728	−1.21047
$743$	26.1783	0.960387	0.480194	−	0.877162i	$-0.340566\pi$
$743$	26.1783	0.960387	0.480194	+	0.877162i	$0.340566\pi$
$744$	−11.9398	−0.437733
$745$	27.4128	1.00433
$746$	−31.8087	−1.16460
$747$	19.1590	0.700990
$748$	−15.7508	−0.575905
$749$	62.7843	2.29409
$750$	−12.0720	−0.440805
$751$	35.4669	1.29421	0.647103	−	0.762403i	$-0.275980\pi$
$751$	35.4669	1.29421	0.647103	+	0.762403i	$0.275980\pi$
$752$	8.02556	0.292662
$753$	24.0204	0.875352
$754$	−16.4282	−0.598281
$755$	−18.6486	−0.678691
$756$	5.82629	0.211900
$757$	15.8348	0.575527	0.287764	−	0.957701i	$-0.407088\pi$
$757$	15.8348	0.575527	0.287764	+	0.957701i	$0.407088\pi$
$758$	3.05690	0.111032
$759$	41.6837	1.51302
$760$	2.85656	0.103618
$761$	−8.72008	−0.316103	−0.158051	−	0.987431i	$-0.550521\pi$
$761$	−8.72008	−0.316103	−0.158051	+	0.987431i	$0.550521\pi$
$762$	36.6661	1.32827
$763$	33.1066	1.19854
$764$	−23.9399	−0.866114
$765$	−20.6171	−0.745414
$766$	7.90743	0.285707
$767$	41.9965	1.51640
$768$	−2.29667	−0.0828740
$769$	39.6308	1.42912	0.714562	−	0.699572i	$-0.246626\pi$
$769$	39.6308	1.42912	0.714562	+	0.699572i	$0.246626\pi$
$770$	49.5974	1.78737
$771$	3.21528	0.115795
$772$	−22.3369	−0.803923
$773$	−7.83045	−0.281642	−0.140821	−	0.990035i	$-0.544974\pi$
$773$	−7.83045	−0.281642	−0.140821	+	0.990035i	$0.544974\pi$
$774$	−18.5128	−0.665428
$775$	16.4276	0.590097
$776$	−8.13665	−0.292089
$777$	−30.1432	−1.08138
$778$	−24.2681	−0.870054
$779$	−1.13949	−0.0408264
$780$	−30.8834	−1.10580
$781$	−42.6119	−1.52477
$782$	11.6008	0.414844
$783$	5.81332	0.207751
$784$	5.23350	0.186911
$785$	−51.9443	−1.85397
$786$	−15.6516	−0.558275
$787$	−29.6382	−1.05649	−0.528245	−	0.849092i	$-0.677150\pi$
$787$	−29.6382	−1.05649	−0.528245	+	0.849092i	$0.677150\pi$
$788$	14.0343	0.499950
$789$	40.4348	1.43952
$790$	31.5908	1.12395
$791$	21.5719	0.767010
$792$	−11.2918	−0.401238
$793$	−61.3922	−2.18010
$794$	11.1413	0.395390
$795$	−61.8476	−2.19351
$796$	−13.2890	−0.471017
$797$	30.2310	1.07084	0.535419	−	0.844587i	$-0.320154\pi$
$797$	30.2310	1.07084	0.535419	+	0.844587i	$0.320154\pi$
$798$	8.03293	0.284363
$799$	25.4646	0.900872
$800$	3.15992	0.111720
$801$	−32.9750	−1.16511
$802$	−17.2546	−0.609282
$803$	−27.3265	−0.964331
$804$	8.66498	0.305590
$805$	−36.5297	−1.28750
$806$	−24.4726	−0.862012
$807$	52.8262	1.85957
$808$	0.790901	0.0278238
$809$	−19.2065	−0.675265	−0.337633	−	0.941278i	$-0.609626\pi$
$809$	−19.2065	−0.675265	−0.337633	+	0.941278i	$0.609626\pi$
$810$	30.4219	1.06892
$811$	−35.7429	−1.25510	−0.627551	−	0.778575i	$-0.715943\pi$
$811$	−35.7429	−1.25510	−0.627551	+	0.778575i	$0.715943\pi$
$812$	12.2063	0.428356
$813$	10.7499	0.377016
$814$	−18.6275	−0.652895
$815$	69.0091	2.41729
$816$	−7.28719	−0.255103
$817$	8.13856	0.284732
$818$	18.8255	0.658219
$819$	−37.4527	−1.30870
$820$	−3.25502	−0.113670
$821$	−28.6396	−0.999528	−0.499764	−	0.866162i	$-0.666580\pi$
$821$	−28.6396	−0.999528	−0.499764	+	0.866162i	$0.666580\pi$
$822$	−13.6090	−0.474669
$823$	−4.73374	−0.165008	−0.0825039	−	0.996591i	$-0.526292\pi$
$823$	−4.73374	−0.165008	−0.0825039	+	0.996591i	$0.526292\pi$
$824$	−18.1323	−0.631670
$825$	36.0260	1.25426
$826$	−31.2036	−1.08571
$827$	30.4029	1.05721	0.528607	−	0.848867i	$-0.322715\pi$
$827$	30.4029	1.05721	0.528607	+	0.848867i	$0.322715\pi$
$828$	8.31670	0.289025
$829$	−29.1112	−1.01107	−0.505536	−	0.862805i	$-0.668705\pi$
$829$	−29.1112	−1.01107	−0.505536	+	0.862805i	$0.668705\pi$
$830$	−24.0597	−0.835126
$831$	16.6976	0.579234
$832$	−4.70743	−0.163201
$833$	16.6055	0.575348
$834$	3.91126	0.135436
$835$	−10.7325	−0.371415
$836$	4.96410	0.171687
$837$	8.65993	0.299331
$838$	1.03853	0.0358753
$839$	16.1664	0.558125	0.279062	−	0.960273i	$-0.409976\pi$
$839$	16.1664	0.558125	0.279062	+	0.960273i	$0.409976\pi$
$840$	22.9465	0.791731
$841$	−16.8209	−0.580032
$842$	−27.3319	−0.941919
$843$	−48.1403	−1.65804
$844$	1.00000	0.0344214
$845$	−26.1657	−0.900127
$846$	18.2557	0.627646
$847$	47.7157	1.63953
$848$	−9.42716	−0.323730
$849$	−7.12607	−0.244566
$850$	10.0262	0.343897
$851$	13.7196	0.470303
$852$	−19.7147	−0.675414
$853$	−4.41529	−0.151177	−0.0755884	−	0.997139i	$-0.524083\pi$
$853$	−4.41529	−0.151177	−0.0755884	+	0.997139i	$0.524083\pi$
$854$	45.6147	1.56090
$855$	6.49781	0.222220
$856$	17.9505	0.613534
$857$	17.5373	0.599062	0.299531	−	0.954087i	$-0.403170\pi$
$857$	17.5373	0.599062	0.299531	+	0.954087i	$0.403170\pi$
$858$	−53.6689	−1.83223
$859$	5.74764	0.196107	0.0980535	−	0.995181i	$-0.468738\pi$
$859$	5.74764	0.196107	0.0980535	+	0.995181i	$0.468738\pi$
$860$	23.2483	0.792759
$861$	−9.15344	−0.311948
$862$	−15.7053	−0.534924
$863$	−33.9609	−1.15604	−0.578020	−	0.816022i	$-0.696175\pi$
$863$	−33.9609	−1.15604	−0.578020	+	0.816022i	$0.696175\pi$
$864$	1.66578	0.0566709
$865$	0.716359	0.0243569
$866$	−2.96793	−0.100854
$867$	15.9217	0.540728
$868$	18.1833	0.617181
$869$	54.8982	1.86229
$870$	22.8955	0.776228
$871$	17.7604	0.601788
$872$	9.46542	0.320540
$873$	−18.5084	−0.626416
$874$	−3.65618	−0.123672
$875$	18.3846	0.621513
$876$	−12.6428	−0.427160
$877$	7.36654	0.248750	0.124375	−	0.992235i	$-0.460307\pi$
$877$	7.36654	0.248750	0.124375	+	0.992235i	$0.460307\pi$
$878$	13.1705	0.444482
$879$	−17.4990	−0.590227
$880$	14.1802	0.478016
$881$	35.0676	1.18146	0.590729	−	0.806870i	$-0.298840\pi$
$881$	35.0676	1.18146	0.590729	+	0.806870i	$0.298840\pi$
$882$	11.9046	0.400850
$883$	18.8297	0.633669	0.316834	−	0.948481i	$-0.397380\pi$
$883$	18.8297	0.633669	0.316834	+	0.948481i	$0.397380\pi$
$884$	−14.9364	−0.502364
$885$	−58.5290	−1.96743
$886$	10.0008	0.335983
$887$	−34.7821	−1.16787	−0.583934	−	0.811801i	$-0.698487\pi$
$887$	−34.7821	−1.16787	−0.583934	+	0.811801i	$0.698487\pi$
$888$	−8.61815	−0.289206
$889$	−55.8395	−1.87280
$890$	41.4099	1.38806
$891$	52.8668	1.77111
$892$	5.97646	0.200107
$893$	−8.02556	−0.268565
$894$	22.0399	0.737123
$895$	−65.0821	−2.17545
$896$	3.49764	0.116848
$897$	39.5284	1.31982
$898$	−13.3322	−0.444901
$899$	18.1428	0.605097
$900$	7.18788	0.239596
$901$	−29.9118	−0.996505
$902$	−5.65653	−0.188342
$903$	65.3765	2.17559
$904$	6.16757	0.205130
$905$	52.2796	1.73783
$906$	−14.9934	−0.498124
$907$	23.5172	0.780876	0.390438	−	0.920629i	$-0.372324\pi$
$907$	23.5172	0.780876	0.390438	+	0.920629i	$0.372324\pi$
$908$	−3.95788	−0.131347
$909$	1.79906	0.0596711
$910$	47.0329	1.55913
$911$	35.4147	1.17334	0.586670	−	0.809826i	$-0.300439\pi$
$911$	35.4147	1.17334	0.586670	+	0.809826i	$0.300439\pi$
$912$	2.29667	0.0760504
$913$	−41.8108	−1.38373
$914$	32.0040	1.05860
$915$	85.5601	2.82853
$916$	−24.2782	−0.802173
$917$	23.8362	0.787139
$918$	5.28540	0.174444
$919$	−12.9174	−0.426106	−0.213053	−	0.977041i	$-0.568341\pi$
$919$	−12.9174	−0.426106	−0.213053	+	0.977041i	$0.568341\pi$
$920$	−10.4441	−0.344331
$921$	−9.12679	−0.300738
$922$	−25.9269	−0.853858
$923$	−40.4087	−1.33007
$924$	39.8763	1.31183
$925$	11.8575	0.389871
$926$	−18.1605	−0.596790
$927$	−41.2456	−1.35468
$928$	3.48985	0.114560
$929$	−0.317477	−0.0104161	−0.00520804	−	0.999986i	$-0.501658\pi$
$929$	−0.317477	−0.0104161	−0.00520804	+	0.999986i	$0.501658\pi$
$930$	34.1067	1.11840
$931$	−5.23350	−0.171521
$932$	−2.95326	−0.0967373
$933$	−29.2223	−0.956696
$934$	23.9286	0.782967
$935$	44.9929	1.47143
$936$	−10.7080	−0.350001
$937$	47.6101	1.55535	0.777677	−	0.628665i	$-0.216398\pi$
$937$	47.6101	1.55535	0.777677	+	0.628665i	$0.216398\pi$
$938$	−13.1961	−0.430867
$939$	10.7600	0.351139
$940$	−22.9255	−0.747747
$941$	−39.0653	−1.27349	−0.636747	−	0.771073i	$-0.719720\pi$
$941$	−39.0653	−1.27349	−0.636747	+	0.771073i	$0.719720\pi$
$942$	−41.7632	−1.36072
$943$	4.16617	0.135669
$944$	−8.92132	−0.290364
$945$	−16.6431	−0.541401
$946$	40.4006	1.31354
$947$	20.9336	0.680251	0.340126	−	0.940380i	$-0.389530\pi$
$947$	20.9336	0.680251	0.340126	+	0.940380i	$0.389530\pi$
$948$	25.3990	0.824922
$949$	−25.9136	−0.841190
$950$	−3.15992	−0.102521
$951$	15.0845	0.489148
$952$	11.0978	0.359681
$953$	−51.6676	−1.67368	−0.836839	−	0.547449i	$-0.815599\pi$
$953$	−51.6676	−1.67368	−0.836839	+	0.547449i	$0.815599\pi$
$954$	−21.4440	−0.694274
$955$	68.3856	2.21291
$956$	−2.75288	−0.0890345
$957$	39.7875	1.28615
$958$	−16.8945	−0.545836
$959$	20.7254	0.669259
$960$	6.56058	0.211742
$961$	−3.97319	−0.128167
$962$	−17.6644	−0.569523
$963$	40.8319	1.31579
$964$	−10.3594	−0.333654
$965$	63.8067	2.05401
$966$	−29.3698	−0.944959
$967$	41.1527	1.32338	0.661691	−	0.749777i	$-0.269839\pi$
$967$	41.1527	1.32338	0.661691	+	0.749777i	$0.269839\pi$
$968$	13.6423	0.438479
$969$	7.28719	0.234098
$970$	23.2428	0.746282
$971$	52.2825	1.67783	0.838913	−	0.544265i	$-0.183191\pi$
$971$	52.2825	1.67783	0.838913	+	0.544265i	$0.183191\pi$
$972$	19.4619	0.624239
$973$	−5.95653	−0.190958
$974$	31.3277	1.00381
$975$	34.1633	1.09410
$976$	13.0416	0.417450
$977$	−39.2088	−1.25440	−0.627201	−	0.778858i	$-0.715799\pi$
$977$	−39.2088	−1.25440	−0.627201	+	0.778858i	$0.715799\pi$
$978$	55.4833	1.77416
$979$	71.9617	2.29990
$980$	−14.9498	−0.477554
$981$	21.5310	0.687431
$982$	−19.6552	−0.627223
$983$	27.9291	0.890800	0.445400	−	0.895332i	$-0.353061\pi$
$983$	27.9291	0.890800	0.445400	+	0.895332i	$0.353061\pi$
$984$	−2.61703	−0.0834279
$985$	−40.0897	−1.27736
$986$	11.0731	0.352639
$987$	−64.4688	−2.05207
$988$	4.70743	0.149763
$989$	−29.7560	−0.946186
$990$	32.2558	1.02516
$991$	16.1436	0.512819	0.256409	−	0.966568i	$-0.417461\pi$
$991$	16.1436	0.512819	0.256409	+	0.966568i	$0.417461\pi$
$992$	5.19873	0.165060
$993$	70.1738	2.22690
$994$	30.0238	0.952298
$995$	37.9608	1.20344
$996$	−19.3440	−0.612939
$997$	50.5880	1.60214	0.801069	−	0.598572i	$-0.204265\pi$
$997$	50.5880	1.60214	0.801069	+	0.598572i	$0.204265\pi$
$998$	−18.0509	−0.571391
$999$	6.25075	0.197765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.e.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.e.1.6	✓	32	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.29667 q^{3} +1.00000 q^{4} -2.85656 q^{5} -2.29667 q^{6} +3.49764 q^{7} +1.00000 q^{8} +2.27470 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.29667 q^{3} +1.00000 q^{4} -2.85656 q^{5} -2.29667 q^{6} +3.49764 q^{7} +1.00000 q^{8} +2.27470 q^{9} -2.85656 q^{10} -4.96410 q^{11} -2.29667 q^{12} -4.70743 q^{13} +3.49764 q^{14} +6.56058 q^{15} +1.00000 q^{16} +3.17293 q^{17} +2.27470 q^{18} -1.00000 q^{19} -2.85656 q^{20} -8.03293 q^{21} -4.96410 q^{22} +3.65618 q^{23} -2.29667 q^{24} +3.15992 q^{25} -4.70743 q^{26} +1.66578 q^{27} +3.49764 q^{28} +3.48985 q^{29} +6.56058 q^{30} +5.19873 q^{31} +1.00000 q^{32} +11.4009 q^{33} +3.17293 q^{34} -9.99122 q^{35} +2.27470 q^{36} +3.75245 q^{37} -1.00000 q^{38} +10.8114 q^{39} -2.85656 q^{40} +1.13949 q^{41} -8.03293 q^{42} -8.13856 q^{43} -4.96410 q^{44} -6.49781 q^{45} +3.65618 q^{46} +8.02556 q^{47} -2.29667 q^{48} +5.23350 q^{49} +3.15992 q^{50} -7.28719 q^{51} -4.70743 q^{52} -9.42716 q^{53} +1.66578 q^{54} +14.1802 q^{55} +3.49764 q^{56} +2.29667 q^{57} +3.48985 q^{58} -8.92132 q^{59} +6.56058 q^{60} +13.0416 q^{61} +5.19873 q^{62} +7.95608 q^{63} +1.00000 q^{64} +13.4470 q^{65} +11.4009 q^{66} -3.77284 q^{67} +3.17293 q^{68} -8.39704 q^{69} -9.99122 q^{70} +8.58402 q^{71} +2.27470 q^{72} +5.50483 q^{73} +3.75245 q^{74} -7.25731 q^{75} -1.00000 q^{76} -17.3626 q^{77} +10.8114 q^{78} -11.0591 q^{79} -2.85656 q^{80} -10.6498 q^{81} +1.13949 q^{82} +8.42263 q^{83} -8.03293 q^{84} -9.06367 q^{85} -8.13856 q^{86} -8.01505 q^{87} -4.96410 q^{88} -14.4964 q^{89} -6.49781 q^{90} -16.4649 q^{91} +3.65618 q^{92} -11.9398 q^{93} +8.02556 q^{94} +2.85656 q^{95} -2.29667 q^{96} -8.13665 q^{97} +5.23350 q^{98} -11.2918 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9}+O(q^{10}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9	\( 32 q + 32 q^{2} - 7 q^{3} + 32 q^{4} - 6 q^{5} - 7 q^{6} - 5 q^{7} + 32 q^{8} + 15 q^{9} - 6 q^{10} - 21 q^{11} - 7 q^{12} - 19 q^{13} - 5 q^{14} - 14 q^{15} + 32 q^{16} - 14 q^{17} + 15 q^{18} - 32 q^{19} - 6 q^{20} - 26 q^{21} - 21 q^{22} - 13 q^{23} - 7 q^{24} - 10 q^{25} - 19 q^{26} - 25 q^{27} - 5 q^{28} - 42 q^{29} - 14 q^{30} - 15 q^{31} + 32 q^{32} - 32 q^{33} - 14 q^{34} - 22 q^{35} + 15 q^{36} - 54 q^{37} - 32 q^{38} - 32 q^{39} - 6 q^{40} - 16 q^{41} - 26 q^{42} - 37 q^{43} - 21 q^{44} - 46 q^{45} - 13 q^{46} - 9 q^{47} - 7 q^{48} - 7 q^{49} - 10 q^{50} - 32 q^{51} - 19 q^{52} - 53 q^{53} - 25 q^{54} - 17 q^{55} - 5 q^{56} + 7 q^{57} - 42 q^{58} - 34 q^{59} - 14 q^{60} - 33 q^{61} - 15 q^{62} + 18 q^{63} + 32 q^{64} - 50 q^{65} - 32 q^{66} - 53 q^{67} - 14 q^{68} - 40 q^{69} - 22 q^{70} - 27 q^{71} + 15 q^{72} - 43 q^{73} - 54 q^{74} + 5 q^{75} - 32 q^{76} - 56 q^{77} - 32 q^{78} - 11 q^{79} - 6 q^{80} - 8 q^{81} - 16 q^{82} - 17 q^{83} - 26 q^{84} - 30 q^{85} - 37 q^{86} + 3 q^{87} - 21 q^{88} - 21 q^{89} - 46 q^{90} - 67 q^{91} - 13 q^{92} - 31 q^{93} - 9 q^{94} + 6 q^{95} - 7 q^{96} - 51 q^{97} - 7 q^{98} - 32 q^{99}+O(q^{100}) \) 32 * q + 32 * q^2 - 7 * q^3 + 32 * q^4 - 6 * q^5 - 7 * q^6 - 5 * q^7 + 32 * q^8 + 15 * q^9 - 6 * q^10 - 21 * q^11 - 7 * q^12 - 19 * q^13 - 5 * q^14 - 14 * q^15 + 32 * q^16 - 14 * q^17 + 15 * q^18 - 32 * q^19 - 6 * q^20 - 26 * q^21 - 21 * q^22 - 13 * q^23 - 7 * q^24 - 10 * q^25 - 19 * q^26 - 25 * q^27 - 5 * q^28 - 42 * q^29 - 14 * q^30 - 15 * q^31 + 32 * q^32 - 32 * q^33 - 14 * q^34 - 22 * q^35 + 15 * q^36 - 54 * q^37 - 32 * q^38 - 32 * q^39 - 6 * q^40 - 16 * q^41 - 26 * q^42 - 37 * q^43 - 21 * q^44 - 46 * q^45 - 13 * q^46 - 9 * q^47 - 7 * q^48 - 7 * q^49 - 10 * q^50 - 32 * q^51 - 19 * q^52 - 53 * q^53 - 25 * q^54 - 17 * q^55 - 5 * q^56 + 7 * q^57 - 42 * q^58 - 34 * q^59 - 14 * q^60 - 33 * q^61 - 15 * q^62 + 18 * q^63 + 32 * q^64 - 50 * q^65 - 32 * q^66 - 53 * q^67 - 14 * q^68 - 40 * q^69 - 22 * q^70 - 27 * q^71 + 15 * q^72 - 43 * q^73 - 54 * q^74 + 5 * q^75 - 32 * q^76 - 56 * q^77 - 32 * q^78 - 11 * q^79 - 6 * q^80 - 8 * q^81 - 16 * q^82 - 17 * q^83 - 26 * q^84 - 30 * q^85 - 37 * q^86 + 3 * q^87 - 21 * q^88 - 21 * q^89 - 46 * q^90 - 67 * q^91 - 13 * q^92 - 31 * q^93 - 9 * q^94 + 6 * q^95 - 7 * q^96 - 51 * q^97 - 7 * q^98 - 32 * q^99

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