LMFDB - Embedded newform 8018.2.a.j.1.44

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:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.44
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)

$f(q)$	$=$	$q+1.00000 q^{2} +3.11312 q^{3} +1.00000 q^{4} +3.52936 q^{5} +3.11312 q^{6} +1.63304 q^{7} +1.00000 q^{8} +6.69152 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.11312 q^{3} +1.00000 q^{4} +3.52936 q^{5} +3.11312 q^{6} +1.63304 q^{7} +1.00000 q^{8} +6.69152 q^{9} +3.52936 q^{10} -1.92465 q^{11} +3.11312 q^{12} -4.26478 q^{13} +1.63304 q^{14} +10.9873 q^{15} +1.00000 q^{16} -0.309085 q^{17} +6.69152 q^{18} -1.00000 q^{19} +3.52936 q^{20} +5.08386 q^{21} -1.92465 q^{22} +7.57448 q^{23} +3.11312 q^{24} +7.45636 q^{25} -4.26478 q^{26} +11.4921 q^{27} +1.63304 q^{28} -8.60144 q^{29} +10.9873 q^{30} +0.310414 q^{31} +1.00000 q^{32} -5.99165 q^{33} -0.309085 q^{34} +5.76359 q^{35} +6.69152 q^{36} -2.33119 q^{37} -1.00000 q^{38} -13.2768 q^{39} +3.52936 q^{40} +0.172790 q^{41} +5.08386 q^{42} +5.61447 q^{43} -1.92465 q^{44} +23.6168 q^{45} +7.57448 q^{46} -11.8930 q^{47} +3.11312 q^{48} -4.33317 q^{49} +7.45636 q^{50} -0.962220 q^{51} -4.26478 q^{52} +14.1226 q^{53} +11.4921 q^{54} -6.79276 q^{55} +1.63304 q^{56} -3.11312 q^{57} -8.60144 q^{58} +13.2644 q^{59} +10.9873 q^{60} -13.4563 q^{61} +0.310414 q^{62} +10.9275 q^{63} +1.00000 q^{64} -15.0519 q^{65} -5.99165 q^{66} -4.34927 q^{67} -0.309085 q^{68} +23.5803 q^{69} +5.76359 q^{70} -5.01075 q^{71} +6.69152 q^{72} -5.27188 q^{73} -2.33119 q^{74} +23.2126 q^{75} -1.00000 q^{76} -3.14303 q^{77} -13.2768 q^{78} -12.5042 q^{79} +3.52936 q^{80} +15.7019 q^{81} +0.172790 q^{82} +1.05001 q^{83} +5.08386 q^{84} -1.09087 q^{85} +5.61447 q^{86} -26.7773 q^{87} -1.92465 q^{88} +13.5600 q^{89} +23.6168 q^{90} -6.96456 q^{91} +7.57448 q^{92} +0.966355 q^{93} -11.8930 q^{94} -3.52936 q^{95} +3.11312 q^{96} +0.906098 q^{97} -4.33317 q^{98} -12.8788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	3.11312	1.79736	0.898681	−	0.438604i	$-0.144527\pi$
$3$	3.11312	1.79736	0.898681	+	0.438604i	$0.144527\pi$
$4$	1.00000	0.500000
$5$	3.52936	1.57838	0.789188	−	0.614151i	$-0.210502\pi$
$5$	3.52936	1.57838	0.789188	+	0.614151i	$0.210502\pi$
$6$	3.11312	1.27093
$7$	1.63304	0.617232	0.308616	−	0.951187i	$-0.400134\pi$
$7$	1.63304	0.617232	0.308616	+	0.951187i	$0.400134\pi$
$8$	1.00000	0.353553
$9$	6.69152	2.23051
$10$	3.52936	1.11608
$11$	−1.92465	−0.580302	−0.290151	−	0.956981i	$-0.593706\pi$
$11$	−1.92465	−0.580302	−0.290151	+	0.956981i	$0.593706\pi$
$12$	3.11312	0.898681
$13$	−4.26478	−1.18284	−0.591418	−	0.806365i	$-0.701432\pi$
$13$	−4.26478	−1.18284	−0.591418	+	0.806365i	$0.701432\pi$
$14$	1.63304	0.436449
$15$	10.9873	2.83691
$16$	1.00000	0.250000
$17$	−0.309085	−0.0749642	−0.0374821	−	0.999297i	$-0.511934\pi$
$17$	−0.309085	−0.0749642	−0.0374821	+	0.999297i	$0.511934\pi$
$18$	6.69152	1.57721
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	3.52936	0.789188
$21$	5.08386	1.10939
$22$	−1.92465	−0.410336
$23$	7.57448	1.57939	0.789695	−	0.613500i	$-0.210239\pi$
$23$	7.57448	1.57939	0.789695	+	0.613500i	$0.210239\pi$
$24$	3.11312	0.635463
$25$	7.45636	1.49127
$26$	−4.26478	−0.836392
$27$	11.4921	2.21167
$28$	1.63304	0.308616
$29$	−8.60144	−1.59725	−0.798624	−	0.601830i	$-0.794438\pi$
$29$	−8.60144	−1.59725	−0.798624	+	0.601830i	$0.794438\pi$
$30$	10.9873	2.00600
$31$	0.310414	0.0557519	0.0278760	−	0.999611i	$-0.491126\pi$
$31$	0.310414	0.0557519	0.0278760	+	0.999611i	$0.491126\pi$
$32$	1.00000	0.176777
$33$	−5.99165	−1.04301
$34$	−0.309085	−0.0530077
$35$	5.76359	0.974224
$36$	6.69152	1.11525
$37$	−2.33119	−0.383245	−0.191623	−	0.981469i	$-0.561375\pi$
$37$	−2.33119	−0.383245	−0.191623	+	0.981469i	$0.561375\pi$
$38$	−1.00000	−0.162221
$39$	−13.2768	−2.12598
$40$	3.52936	0.558040
$41$	0.172790	0.0269853	0.0134926	−	0.999909i	$-0.495705\pi$
$41$	0.172790	0.0269853	0.0134926	+	0.999909i	$0.495705\pi$
$42$	5.08386	0.784456
$43$	5.61447	0.856198	0.428099	−	0.903732i	$-0.359183\pi$
$43$	5.61447	0.856198	0.428099	+	0.903732i	$0.359183\pi$
$44$	−1.92465	−0.290151
$45$	23.6168	3.52058
$46$	7.57448	1.11680
$47$	−11.8930	−1.73477	−0.867383	−	0.497642i	$-0.834199\pi$
$47$	−11.8930	−1.73477	−0.867383	+	0.497642i	$0.834199\pi$
$48$	3.11312	0.449340
$49$	−4.33317	−0.619025
$50$	7.45636	1.05449
$51$	−0.962220	−0.134738
$52$	−4.26478	−0.591418
$53$	14.1226	1.93989	0.969945	−	0.243323i	$-0.0782375\pi$
$53$	14.1226	1.93989	0.969945	+	0.243323i	$0.0782375\pi$
$54$	11.4921	1.56388
$55$	−6.79276	−0.915936
$56$	1.63304	0.218224
$57$	−3.11312	−0.412343
$58$	−8.60144	−1.12942
$59$	13.2644	1.72688	0.863438	−	0.504454i	$-0.168306\pi$
$59$	13.2644	1.72688	0.863438	+	0.504454i	$0.168306\pi$
$60$	10.9873	1.41846
$61$	−13.4563	−1.72290	−0.861450	−	0.507842i	$-0.830444\pi$
$61$	−13.4563	−1.72290	−0.861450	+	0.507842i	$0.830444\pi$
$62$	0.310414	0.0394226
$63$	10.9275	1.37674
$64$	1.00000	0.125000
$65$	−15.0519	−1.86696
$66$	−5.99165	−0.737521
$67$	−4.34927	−0.531348	−0.265674	−	0.964063i	$-0.585595\pi$
$67$	−4.34927	−0.531348	−0.265674	+	0.964063i	$0.585595\pi$
$68$	−0.309085	−0.0374821
$69$	23.5803	2.83873
$70$	5.76359	0.688881
$71$	−5.01075	−0.594667	−0.297334	−	0.954774i	$-0.596097\pi$
$71$	−5.01075	−0.594667	−0.297334	+	0.954774i	$0.596097\pi$
$72$	6.69152	0.788603
$73$	−5.27188	−0.617026	−0.308513	−	0.951220i	$-0.599831\pi$
$73$	−5.27188	−0.617026	−0.308513	+	0.951220i	$0.599831\pi$
$74$	−2.33119	−0.270995
$75$	23.2126	2.68036
$76$	−1.00000	−0.114708
$77$	−3.14303	−0.358181
$78$	−13.2768	−1.50330
$79$	−12.5042	−1.40683	−0.703416	−	0.710778i	$-0.748343\pi$
$79$	−12.5042	−1.40683	−0.703416	+	0.710778i	$0.748343\pi$
$80$	3.52936	0.394594
$81$	15.7019	1.74465
$82$	0.172790	0.0190815
$83$	1.05001	0.115253	0.0576266	−	0.998338i	$-0.481647\pi$
$83$	1.05001	0.115253	0.0576266	+	0.998338i	$0.481647\pi$
$84$	5.08386	0.554694
$85$	−1.09087	−0.118322
$86$	5.61447	0.605424
$87$	−26.7773	−2.87083
$88$	−1.92465	−0.205168
$89$	13.5600	1.43736	0.718678	−	0.695343i	$-0.244748\pi$
$89$	13.5600	1.43736	0.718678	+	0.695343i	$0.244748\pi$
$90$	23.6168	2.48943
$91$	−6.96456	−0.730084
$92$	7.57448	0.789695
$93$	0.966355	0.100206
$94$	−11.8930	−1.22666
$95$	−3.52936	−0.362104
$96$	3.11312	0.317732
$97$	0.906098	0.0920003	0.0460001	−	0.998941i	$-0.485353\pi$
$97$	0.906098	0.0920003	0.0460001	+	0.998941i	$0.485353\pi$
$98$	−4.33317	−0.437717
$99$	−12.8788	−1.29437
$100$	7.45636	0.745636
$101$	−9.76946	−0.972098	−0.486049	−	0.873932i	$-0.661562\pi$
$101$	−9.76946	−0.972098	−0.486049	+	0.873932i	$0.661562\pi$
$102$	−0.962220	−0.0952740
$103$	13.6828	1.34820	0.674102	−	0.738639i	$-0.264531\pi$
$103$	13.6828	1.34820	0.674102	+	0.738639i	$0.264531\pi$
$104$	−4.26478	−0.418196
$105$	17.9427	1.75103
$106$	14.1226	1.37171
$107$	−6.36688	−0.615510	−0.307755	−	0.951466i	$-0.599578\pi$
$107$	−6.36688	−0.615510	−0.307755	+	0.951466i	$0.599578\pi$
$108$	11.4921	1.10583
$109$	7.05225	0.675483	0.337741	−	0.941239i	$-0.390337\pi$
$109$	7.05225	0.675483	0.337741	+	0.941239i	$0.390337\pi$
$110$	−6.79276	−0.647664
$111$	−7.25727	−0.688830
$112$	1.63304	0.154308
$113$	3.10704	0.292286	0.146143	−	0.989263i	$-0.453314\pi$
$113$	3.10704	0.292286	0.146143	+	0.989263i	$0.453314\pi$
$114$	−3.11312	−0.291570
$115$	26.7331	2.49287
$116$	−8.60144	−0.798624
$117$	−28.5379	−2.63833
$118$	13.2644	1.22109
$119$	−0.504749	−0.0462703
$120$	10.9873	1.00300
$121$	−7.29574	−0.663249
$122$	−13.4563	−1.21827
$123$	0.537917	0.0485023
$124$	0.310414	0.0278760
$125$	8.66939	0.775413
$126$	10.9275	0.973502
$127$	−13.5644	−1.20364	−0.601821	−	0.798631i	$-0.705558\pi$
$127$	−13.5644	−1.20364	−0.601821	+	0.798631i	$0.705558\pi$
$128$	1.00000	0.0883883
$129$	17.4785	1.53890
$130$	−15.0519	−1.32014
$131$	12.8647	1.12400	0.561998	−	0.827139i	$-0.310033\pi$
$131$	12.8647	1.12400	0.561998	+	0.827139i	$0.310033\pi$
$132$	−5.99165	−0.521506
$133$	−1.63304	−0.141603
$134$	−4.34927	−0.375720
$135$	40.5599	3.49084
$136$	−0.309085	−0.0265039
$137$	−20.1960	−1.72546	−0.862730	−	0.505665i	$-0.831247\pi$
$137$	−20.1960	−1.72546	−0.862730	+	0.505665i	$0.831247\pi$
$138$	23.5803	2.00729
$139$	1.04794	0.0888850	0.0444425	−	0.999012i	$-0.485849\pi$
$139$	1.04794	0.0888850	0.0444425	+	0.999012i	$0.485849\pi$
$140$	5.76359	0.487112
$141$	−37.0242	−3.11800
$142$	−5.01075	−0.420493
$143$	8.20819	0.686403
$144$	6.69152	0.557627
$145$	−30.3576	−2.52106
$146$	−5.27188	−0.436304
$147$	−13.4897	−1.11261
$148$	−2.33119	−0.191623
$149$	−8.13308	−0.666288	−0.333144	−	0.942876i	$-0.608109\pi$
$149$	−8.13308	−0.666288	−0.333144	+	0.942876i	$0.608109\pi$
$150$	23.2126	1.89530
$151$	−6.61600	−0.538403	−0.269201	−	0.963084i	$-0.586760\pi$
$151$	−6.61600	−0.538403	−0.269201	+	0.963084i	$0.586760\pi$
$152$	−1.00000	−0.0811107
$153$	−2.06825	−0.167208
$154$	−3.14303	−0.253272
$155$	1.09556	0.0879975
$156$	−13.2768	−1.06299
$157$	−1.29134	−0.103060	−0.0515302	−	0.998671i	$-0.516410\pi$
$157$	−1.29134	−0.103060	−0.0515302	+	0.998671i	$0.516410\pi$
$158$	−12.5042	−0.994780
$159$	43.9654	3.48668
$160$	3.52936	0.279020
$161$	12.3694	0.974849
$162$	15.7019	1.23366
$163$	19.2958	1.51136	0.755680	−	0.654941i	$-0.227306\pi$
$163$	19.2958	1.51136	0.755680	+	0.654941i	$0.227306\pi$
$164$	0.172790	0.0134926
$165$	−21.1467	−1.64627
$166$	1.05001	0.0814963
$167$	20.6145	1.59519	0.797597	−	0.603191i	$-0.206104\pi$
$167$	20.6145	1.59519	0.797597	+	0.603191i	$0.206104\pi$
$168$	5.08386	0.392228
$169$	5.18834	0.399103
$170$	−1.09087	−0.0836661
$171$	−6.69152	−0.511713
$172$	5.61447	0.428099
$173$	4.50938	0.342842	0.171421	−	0.985198i	$-0.445164\pi$
$173$	4.50938	0.342842	0.171421	+	0.985198i	$0.445164\pi$
$174$	−26.7773	−2.02998
$175$	12.1766	0.920461
$176$	−1.92465	−0.145076
$177$	41.2937	3.10382
$178$	13.5600	1.01636
$179$	−13.9787	−1.04481	−0.522407	−	0.852696i	$-0.674966\pi$
$179$	−13.9787	−1.04481	−0.522407	+	0.852696i	$0.674966\pi$
$180$	23.6168	1.76029
$181$	−19.7766	−1.46998	−0.734992	−	0.678075i	$-0.762814\pi$
$181$	−19.7766	−1.46998	−0.734992	+	0.678075i	$0.762814\pi$
$182$	−6.96456	−0.516248
$183$	−41.8910	−3.09668
$184$	7.57448	0.558398
$185$	−8.22760	−0.604905
$186$	0.966355	0.0708566
$187$	0.594880	0.0435019
$188$	−11.8930	−0.867383
$189$	18.7672	1.36511
$190$	−3.52936	−0.256046
$191$	14.3546	1.03866	0.519330	−	0.854574i	$-0.326181\pi$
$191$	14.3546	1.03866	0.519330	+	0.854574i	$0.326181\pi$
$192$	3.11312	0.224670
$193$	16.4774	1.18607	0.593034	−	0.805178i	$-0.297930\pi$
$193$	16.4774	1.18607	0.593034	+	0.805178i	$0.297930\pi$
$194$	0.906098	0.0650540
$195$	−46.8585	−3.35560
$196$	−4.33317	−0.309512
$197$	8.42969	0.600591	0.300295	−	0.953846i	$-0.402915\pi$
$197$	8.42969	0.600591	0.300295	+	0.953846i	$0.402915\pi$
$198$	−12.8788	−0.915257
$199$	−20.6646	−1.46488	−0.732438	−	0.680834i	$-0.761618\pi$
$199$	−20.6646	−1.46488	−0.732438	+	0.680834i	$0.761618\pi$
$200$	7.45636	0.527245
$201$	−13.5398	−0.955025
$202$	−9.76946	−0.687377
$203$	−14.0465	−0.985872
$204$	−0.962220	−0.0673689
$205$	0.609838	0.0425929
$206$	13.6828	0.953324
$207$	50.6848	3.52284
$208$	−4.26478	−0.295709
$209$	1.92465	0.133130
$210$	17.9427	1.23817
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	14.1226	0.969945
$213$	−15.5991	−1.06883
$214$	−6.36688	−0.435231
$215$	19.8155	1.35140
$216$	11.4921	0.781942
$217$	0.506918	0.0344119
$218$	7.05225	0.477639
$219$	−16.4120	−1.10902
$220$	−6.79276	−0.457968
$221$	1.31818	0.0886704
$222$	−7.25727	−0.487076
$223$	24.1397	1.61651	0.808257	−	0.588829i	$-0.200411\pi$
$223$	24.1397	1.61651	0.808257	+	0.588829i	$0.200411\pi$
$224$	1.63304	0.109112
$225$	49.8944	3.32629
$226$	3.10704	0.206677
$227$	6.50611	0.431826	0.215913	−	0.976413i	$-0.430727\pi$
$227$	6.50611	0.431826	0.215913	+	0.976413i	$0.430727\pi$
$228$	−3.11312	−0.206171
$229$	30.1506	1.99241	0.996203	−	0.0870578i	$-0.0277465\pi$
$229$	30.1506	1.99241	0.996203	+	0.0870578i	$0.0277465\pi$
$230$	26.7331	1.76273
$231$	−9.78462	−0.643781
$232$	−8.60144	−0.564712
$233$	−2.75451	−0.180454	−0.0902271	−	0.995921i	$-0.528759\pi$
$233$	−2.75451	−0.180454	−0.0902271	+	0.995921i	$0.528759\pi$
$234$	−28.5379	−1.86558
$235$	−41.9745	−2.73811
$236$	13.2644	0.863438
$237$	−38.9271	−2.52858
$238$	−0.504749	−0.0327180
$239$	−17.2685	−1.11701	−0.558503	−	0.829502i	$-0.688624\pi$
$239$	−17.2685	−1.11701	−0.558503	+	0.829502i	$0.688624\pi$
$240$	10.9873	0.709228
$241$	23.9596	1.54338	0.771688	−	0.636001i	$-0.219413\pi$
$241$	23.9596	1.54338	0.771688	+	0.636001i	$0.219413\pi$
$242$	−7.29574	−0.468988
$243$	14.4054	0.924108
$244$	−13.4563	−0.861450
$245$	−15.2933	−0.977054
$246$	0.537917	0.0342963
$247$	4.26478	0.271361
$248$	0.310414	0.0197113
$249$	3.26880	0.207152
$250$	8.66939	0.548300
$251$	20.4757	1.29241	0.646207	−	0.763162i	$-0.276354\pi$
$251$	20.4757	1.29241	0.646207	+	0.763162i	$0.276354\pi$
$252$	10.9275	0.688370
$253$	−14.5782	−0.916523
$254$	−13.5644	−0.851103
$255$	−3.39602	−0.212667
$256$	1.00000	0.0625000
$257$	−21.9862	−1.37146	−0.685730	−	0.727856i	$-0.740517\pi$
$257$	−21.9862	−1.37146	−0.685730	+	0.727856i	$0.740517\pi$
$258$	17.4785	1.08816
$259$	−3.80693	−0.236551
$260$	−15.0519	−0.933481
$261$	−57.5567	−3.56267
$262$	12.8647	0.794785
$263$	5.34066	0.329319	0.164660	−	0.986350i	$-0.447347\pi$
$263$	5.34066	0.329319	0.164660	+	0.986350i	$0.447347\pi$
$264$	−5.99165	−0.368761
$265$	49.8438	3.06188
$266$	−1.63304	−0.100128
$267$	42.2139	2.58345
$268$	−4.34927	−0.265674
$269$	−12.1715	−0.742110	−0.371055	−	0.928611i	$-0.621004\pi$
$269$	−12.1715	−0.742110	−0.371055	+	0.928611i	$0.621004\pi$
$270$	40.5599	2.46840
$271$	27.9090	1.69535	0.847677	−	0.530513i	$-0.178001\pi$
$271$	27.9090	1.69535	0.847677	+	0.530513i	$0.178001\pi$
$272$	−0.309085	−0.0187411
$273$	−21.6815	−1.31223
$274$	−20.1960	−1.22008
$275$	−14.3509	−0.865389
$276$	23.5803	1.41937
$277$	−5.41780	−0.325524	−0.162762	−	0.986665i	$-0.552040\pi$
$277$	−5.41780	−0.325524	−0.162762	+	0.986665i	$0.552040\pi$
$278$	1.04794	0.0628512
$279$	2.07714	0.124355
$280$	5.76359	0.344440
$281$	31.1547	1.85854	0.929268	−	0.369406i	$-0.120439\pi$
$281$	31.1547	1.85854	0.929268	+	0.369406i	$0.120439\pi$
$282$	−37.0242	−2.20476
$283$	−28.3213	−1.68353	−0.841763	−	0.539847i	$-0.818482\pi$
$283$	−28.3213	−1.68353	−0.841763	+	0.539847i	$0.818482\pi$
$284$	−5.01075	−0.297334
$285$	−10.9873	−0.650832
$286$	8.20819	0.485360
$287$	0.282174	0.0166562
$288$	6.69152	0.394302
$289$	−16.9045	−0.994380
$290$	−30.3576	−1.78266
$291$	2.82079	0.165358
$292$	−5.27188	−0.308513
$293$	−8.77177	−0.512452	−0.256226	−	0.966617i	$-0.582479\pi$
$293$	−8.77177	−0.512452	−0.256226	+	0.966617i	$0.582479\pi$
$294$	−13.4897	−0.786735
$295$	46.8148	2.72566
$296$	−2.33119	−0.135498
$297$	−22.1183	−1.28343
$298$	−8.13308	−0.471137
$299$	−32.3035	−1.86816
$300$	23.2126	1.34018
$301$	9.16866	0.528473
$302$	−6.61600	−0.380708
$303$	−30.4135	−1.74721
$304$	−1.00000	−0.0573539
$305$	−47.4920	−2.71939
$306$	−2.06825	−0.118234
$307$	−7.91178	−0.451549	−0.225775	−	0.974180i	$-0.572491\pi$
$307$	−7.91178	−0.451549	−0.225775	+	0.974180i	$0.572491\pi$
$308$	−3.14303	−0.179091
$309$	42.5961	2.42321
$310$	1.09556	0.0622237
$311$	−15.6665	−0.888366	−0.444183	−	0.895936i	$-0.646506\pi$
$311$	−15.6665	−0.888366	−0.444183	+	0.895936i	$0.646506\pi$
$312$	−13.2768	−0.751649
$313$	−18.0873	−1.02235	−0.511176	−	0.859476i	$-0.670790\pi$
$313$	−18.0873	−1.02235	−0.511176	+	0.859476i	$0.670790\pi$
$314$	−1.29134	−0.0728747
$315$	38.5672	2.17301
$316$	−12.5042	−0.703416
$317$	−24.1556	−1.35671	−0.678357	−	0.734733i	$-0.737308\pi$
$317$	−24.1556	−1.35671	−0.678357	+	0.734733i	$0.737308\pi$
$318$	43.9654	2.46546
$319$	16.5547	0.926887
$320$	3.52936	0.197297
$321$	−19.8209	−1.10629
$322$	12.3694	0.689322
$323$	0.309085	0.0171980
$324$	15.7019	0.872327
$325$	−31.7997	−1.76393
$326$	19.2958	1.06869
$327$	21.9545	1.21409
$328$	0.172790	0.00954074
$329$	−19.4217	−1.07075
$330$	−21.1467	−1.16409
$331$	−11.6693	−0.641403	−0.320702	−	0.947180i	$-0.603919\pi$
$331$	−11.6693	−0.641403	−0.320702	+	0.947180i	$0.603919\pi$
$332$	1.05001	0.0576266
$333$	−15.5992	−0.854831
$334$	20.6145	1.12797
$335$	−15.3501	−0.838668
$336$	5.08386	0.277347
$337$	−32.2474	−1.75663	−0.878313	−	0.478086i	$-0.841331\pi$
$337$	−32.2474	−1.75663	−0.878313	+	0.478086i	$0.841331\pi$
$338$	5.18834	0.282208
$339$	9.67260	0.525343
$340$	−1.09087	−0.0591609
$341$	−0.597436	−0.0323530
$342$	−6.69152	−0.361836
$343$	−18.5075	−0.999314
$344$	5.61447	0.302712
$345$	83.2232	4.48059
$346$	4.50938	0.242426
$347$	−7.09419	−0.380836	−0.190418	−	0.981703i	$-0.560984\pi$
$347$	−7.09419	−0.380836	−0.190418	+	0.981703i	$0.560984\pi$
$348$	−26.7773	−1.43542
$349$	−16.5448	−0.885621	−0.442811	−	0.896615i	$-0.646019\pi$
$349$	−16.5448	−0.885621	−0.442811	+	0.896615i	$0.646019\pi$
$350$	12.1766	0.650864
$351$	−49.0115	−2.61604
$352$	−1.92465	−0.102584
$353$	24.2666	1.29158	0.645790	−	0.763515i	$-0.276528\pi$
$353$	24.2666	1.29158	0.645790	+	0.763515i	$0.276528\pi$
$354$	41.2937	2.19473
$355$	−17.6847	−0.938609
$356$	13.5600	0.718678
$357$	−1.57135	−0.0831644
$358$	−13.9787	−0.738795
$359$	−4.21485	−0.222451	−0.111226	−	0.993795i	$-0.535478\pi$
$359$	−4.21485	−0.222451	−0.111226	+	0.993795i	$0.535478\pi$
$360$	23.6168	1.24471
$361$	1.00000	0.0526316
$362$	−19.7766	−1.03944
$363$	−22.7125	−1.19210
$364$	−6.96456	−0.365042
$365$	−18.6063	−0.973900
$366$	−41.8910	−2.18968
$367$	12.0527	0.629143	0.314572	−	0.949234i	$-0.398139\pi$
$367$	12.0527	0.629143	0.314572	+	0.949234i	$0.398139\pi$
$368$	7.57448	0.394847
$369$	1.15623	0.0601909
$370$	−8.22760	−0.427733
$371$	23.0628	1.19736
$372$	0.966355	0.0501032
$373$	−12.1662	−0.629944	−0.314972	−	0.949101i	$-0.601995\pi$
$373$	−12.1662	−0.629944	−0.314972	+	0.949101i	$0.601995\pi$
$374$	0.594880	0.0307605
$375$	26.9888	1.39370
$376$	−11.8930	−0.613332
$377$	36.6833	1.88928
$378$	18.7672	0.965279
$379$	−11.2197	−0.576317	−0.288159	−	0.957583i	$-0.593043\pi$
$379$	−11.2197	−0.576317	−0.288159	+	0.957583i	$0.593043\pi$
$380$	−3.52936	−0.181052
$381$	−42.2275	−2.16338
$382$	14.3546	0.734444
$383$	−19.2478	−0.983516	−0.491758	−	0.870732i	$-0.663646\pi$
$383$	−19.2478	−0.983516	−0.491758	+	0.870732i	$0.663646\pi$
$384$	3.11312	0.158866
$385$	−11.0929	−0.565345
$386$	16.4774	0.838676
$387$	37.5693	1.90976
$388$	0.906098	0.0460001
$389$	30.9962	1.57157	0.785786	−	0.618499i	$-0.212259\pi$
$389$	30.9962	1.57157	0.785786	+	0.618499i	$0.212259\pi$
$390$	−46.8585	−2.37277
$391$	−2.34116	−0.118398
$392$	−4.33317	−0.218858
$393$	40.0494	2.02023
$394$	8.42969	0.424682
$395$	−44.1318	−2.22051
$396$	−12.8788	−0.647184
$397$	−29.3191	−1.47148	−0.735741	−	0.677263i	$-0.763166\pi$
$397$	−29.3191	−1.47148	−0.735741	+	0.677263i	$0.763166\pi$
$398$	−20.6646	−1.03582
$399$	−5.08386	−0.254511
$400$	7.45636	0.372818
$401$	−18.6408	−0.930875	−0.465437	−	0.885081i	$-0.654103\pi$
$401$	−18.6408	−0.930875	−0.465437	+	0.885081i	$0.654103\pi$
$402$	−13.5398	−0.675305
$403$	−1.32385	−0.0659454
$404$	−9.76946	−0.486049
$405$	55.4176	2.75372
$406$	−14.0465	−0.697117
$407$	4.48671	0.222398
$408$	−0.962220	−0.0476370
$409$	12.4855	0.617368	0.308684	−	0.951165i	$-0.400111\pi$
$409$	12.4855	0.617368	0.308684	+	0.951165i	$0.400111\pi$
$410$	0.609838	0.0301178
$411$	−62.8725	−3.10127
$412$	13.6828	0.674102
$413$	21.6613	1.06588
$414$	50.6848	2.49102
$415$	3.70585	0.181913
$416$	−4.26478	−0.209098
$417$	3.26236	0.159758
$418$	1.92465	0.0941375
$419$	6.12703	0.299325	0.149662	−	0.988737i	$-0.452181\pi$
$419$	6.12703	0.299325	0.149662	+	0.988737i	$0.452181\pi$
$420$	17.9427	0.875516
$421$	24.3699	1.18772	0.593858	−	0.804570i	$-0.297604\pi$
$421$	24.3699	1.18772	0.593858	+	0.804570i	$0.297604\pi$
$422$	−1.00000	−0.0486792
$423$	−79.5819	−3.86941
$424$	14.1226	0.685855
$425$	−2.30465	−0.111792
$426$	−15.5991	−0.755778
$427$	−21.9747	−1.06343
$428$	−6.36688	−0.307755
$429$	25.5531	1.23371
$430$	19.8155	0.955586
$431$	−9.53430	−0.459251	−0.229626	−	0.973279i	$-0.573750\pi$
$431$	−9.53430	−0.459251	−0.229626	+	0.973279i	$0.573750\pi$
$432$	11.4921	0.552916
$433$	9.17426	0.440887	0.220443	−	0.975400i	$-0.429250\pi$
$433$	9.17426	0.440887	0.220443	+	0.975400i	$0.429250\pi$
$434$	0.506918	0.0243329
$435$	−94.5068	−4.53125
$436$	7.05225	0.337741
$437$	−7.57448	−0.362337
$438$	−16.4120	−0.784195
$439$	6.25958	0.298754	0.149377	−	0.988780i	$-0.452273\pi$
$439$	6.25958	0.298754	0.149377	+	0.988780i	$0.452273\pi$
$440$	−6.79276	−0.323832
$441$	−28.9955	−1.38074
$442$	1.31818	0.0626995
$443$	6.69676	0.318173	0.159086	−	0.987265i	$-0.449145\pi$
$443$	6.69676	0.318173	0.159086	+	0.987265i	$0.449145\pi$
$444$	−7.25727	−0.344415
$445$	47.8581	2.26869
$446$	24.1397	1.14305
$447$	−25.3193	−1.19756
$448$	1.63304	0.0771540
$449$	10.7787	0.508680	0.254340	−	0.967115i	$-0.418142\pi$
$449$	10.7787	0.508680	0.254340	+	0.967115i	$0.418142\pi$
$450$	49.8944	2.35205
$451$	−0.332560	−0.0156596
$452$	3.10704	0.146143
$453$	−20.5964	−0.967704
$454$	6.50611	0.305347
$455$	−24.5804	−1.15235
$456$	−3.11312	−0.145785
$457$	−18.0259	−0.843217	−0.421609	−	0.906778i	$-0.638534\pi$
$457$	−18.0259	−0.843217	−0.421609	+	0.906778i	$0.638534\pi$
$458$	30.1506	1.40884
$459$	−3.55205	−0.165796
$460$	26.7331	1.24644
$461$	32.9146	1.53299	0.766493	−	0.642253i	$-0.222000\pi$
$461$	32.9146	1.53299	0.766493	+	0.642253i	$0.222000\pi$
$462$	−9.78462	−0.455222
$463$	−32.3992	−1.50572	−0.752858	−	0.658183i	$-0.771325\pi$
$463$	−32.3992	−1.50572	−0.752858	+	0.658183i	$0.771325\pi$
$464$	−8.60144	−0.399312
$465$	3.41061	0.158163
$466$	−2.75451	−0.127600
$467$	31.6876	1.46633	0.733164	−	0.680052i	$-0.238043\pi$
$467$	31.6876	1.46633	0.733164	+	0.680052i	$0.238043\pi$
$468$	−28.5379	−1.31916
$469$	−7.10255	−0.327965
$470$	−41.9745	−1.93614
$471$	−4.02011	−0.185237
$472$	13.2644	0.610543
$473$	−10.8059	−0.496854
$474$	−38.9271	−1.78798
$475$	−7.45636	−0.342121
$476$	−0.504749	−0.0231351
$477$	94.5018	4.32694
$478$	−17.2685	−0.789843
$479$	−20.8692	−0.953540	−0.476770	−	0.879028i	$-0.658192\pi$
$479$	−20.8692	−0.953540	−0.476770	+	0.879028i	$0.658192\pi$
$480$	10.9873	0.501500
$481$	9.94201	0.453316
$482$	23.9596	1.09133
$483$	38.5076	1.75216
$484$	−7.29574	−0.331625
$485$	3.19794	0.145211
$486$	14.4054	0.653443
$487$	38.8107	1.75868	0.879340	−	0.476195i	$-0.157984\pi$
$487$	38.8107	1.75868	0.879340	+	0.476195i	$0.157984\pi$
$488$	−13.4563	−0.609137
$489$	60.0700	2.71646
$490$	−15.2933	−0.690882
$491$	−27.4306	−1.23793	−0.618964	−	0.785420i	$-0.712447\pi$
$491$	−27.4306	−1.23793	−0.618964	+	0.785420i	$0.712447\pi$
$492$	0.537917	0.0242512
$493$	2.65858	0.119736
$494$	4.26478	0.191881
$495$	−45.4539	−2.04300
$496$	0.310414	0.0139380
$497$	−8.18277	−0.367047
$498$	3.26880	0.146478
$499$	9.01439	0.403539	0.201770	−	0.979433i	$-0.435331\pi$
$499$	9.01439	0.403539	0.201770	+	0.979433i	$0.435331\pi$
$500$	8.66939	0.387707
$501$	64.1753	2.86714
$502$	20.4757	0.913875
$503$	17.3326	0.772824	0.386412	−	0.922326i	$-0.373714\pi$
$503$	17.3326	0.772824	0.386412	+	0.922326i	$0.373714\pi$
$504$	10.9275	0.486751
$505$	−34.4799	−1.53434
$506$	−14.5782	−0.648080
$507$	16.1519	0.717332
$508$	−13.5644	−0.601821
$509$	24.7204	1.09571	0.547855	−	0.836573i	$-0.315444\pi$
$509$	24.7204	1.09571	0.547855	+	0.836573i	$0.315444\pi$
$510$	−3.39602	−0.150378
$511$	−8.60919	−0.380848
$512$	1.00000	0.0441942
$513$	−11.4921	−0.507391
$514$	−21.9862	−0.969768
$515$	48.2914	2.12797
$516$	17.4785	0.769449
$517$	22.8897	1.00669
$518$	−3.80693	−0.167267
$519$	14.0382	0.616210
$520$	−15.0519	−0.660071
$521$	−15.3117	−0.670819	−0.335410	−	0.942072i	$-0.608875\pi$
$521$	−15.3117	−0.670819	−0.335410	+	0.942072i	$0.608875\pi$
$522$	−57.5567	−2.51919
$523$	12.5363	0.548173	0.274086	−	0.961705i	$-0.411625\pi$
$523$	12.5363	0.548173	0.274086	+	0.961705i	$0.411625\pi$
$524$	12.8647	0.561998
$525$	37.9071	1.65440
$526$	5.34066	0.232864
$527$	−0.0959443	−0.00417940
$528$	−5.99165	−0.260753
$529$	34.3728	1.49447
$530$	49.8438	2.16507
$531$	88.7590	3.85181
$532$	−1.63304	−0.0708013
$533$	−0.736912	−0.0319192
$534$	42.2139	1.82677
$535$	−22.4710	−0.971506
$536$	−4.34927	−0.187860
$537$	−43.5172	−1.87791
$538$	−12.1715	−0.524751
$539$	8.33982	0.359222
$540$	40.5599	1.74542
$541$	−14.6344	−0.629183	−0.314592	−	0.949227i	$-0.601868\pi$
$541$	−14.6344	−0.629183	−0.314592	+	0.949227i	$0.601868\pi$
$542$	27.9090	1.19880
$543$	−61.5670	−2.64209
$544$	−0.309085	−0.0132519
$545$	24.8899	1.06617
$546$	−21.6815	−0.927883
$547$	7.60975	0.325369	0.162685	−	0.986678i	$-0.447985\pi$
$547$	7.60975	0.325369	0.162685	+	0.986678i	$0.447985\pi$
$548$	−20.1960	−0.862730
$549$	−90.0430	−3.84294
$550$	−14.3509	−0.611922
$551$	8.60144	0.366434
$552$	23.5803	1.00364
$553$	−20.4199	−0.868341
$554$	−5.41780	−0.230180
$555$	−25.6135	−1.08723
$556$	1.04794	0.0444425
$557$	27.1342	1.14971	0.574857	−	0.818254i	$-0.305058\pi$
$557$	27.1342	1.14971	0.574857	+	0.818254i	$0.305058\pi$
$558$	2.07714	0.0879323
$559$	−23.9445	−1.01274
$560$	5.76359	0.243556
$561$	1.85193	0.0781886
$562$	31.1547	1.31418
$563$	11.3240	0.477251	0.238625	−	0.971112i	$-0.423303\pi$
$563$	11.3240	0.477251	0.238625	+	0.971112i	$0.423303\pi$
$564$	−37.0242	−1.55900
$565$	10.9659	0.461337
$566$	−28.3213	−1.19043
$567$	25.6418	1.07686
$568$	−5.01075	−0.210247
$569$	7.93649	0.332715	0.166357	−	0.986066i	$-0.446799\pi$
$569$	7.93649	0.332715	0.166357	+	0.986066i	$0.446799\pi$
$570$	−10.9873	−0.460208
$571$	3.02325	0.126519	0.0632595	−	0.997997i	$-0.479850\pi$
$571$	3.02325	0.126519	0.0632595	+	0.997997i	$0.479850\pi$
$572$	8.20819	0.343201
$573$	44.6875	1.86685
$574$	0.282174	0.0117777
$575$	56.4781	2.35530
$576$	6.69152	0.278813
$577$	−36.9371	−1.53771	−0.768856	−	0.639422i	$-0.779174\pi$
$577$	−36.9371	−1.53771	−0.768856	+	0.639422i	$0.779174\pi$
$578$	−16.9045	−0.703133
$579$	51.2961	2.13179
$580$	−30.3576	−1.26053
$581$	1.71470	0.0711379
$582$	2.82079	0.116926
$583$	−27.1810	−1.12572
$584$	−5.27188	−0.218152
$585$	−100.720	−4.16427
$586$	−8.77177	−0.362359
$587$	−8.17180	−0.337286	−0.168643	−	0.985677i	$-0.553939\pi$
$587$	−8.17180	−0.337286	−0.168643	+	0.985677i	$0.553939\pi$
$588$	−13.4897	−0.556306
$589$	−0.310414	−0.0127904
$590$	46.8148	1.92733
$591$	26.2427	1.07948
$592$	−2.33119	−0.0958113
$593$	−8.16114	−0.335138	−0.167569	−	0.985860i	$-0.553592\pi$
$593$	−8.16114	−0.335138	−0.167569	+	0.985860i	$0.553592\pi$
$594$	−22.1183	−0.907525
$595$	−1.78144	−0.0730319
$596$	−8.13308	−0.333144
$597$	−64.3314	−2.63291
$598$	−32.3035	−1.32099
$599$	1.96329	0.0802179	0.0401090	−	0.999195i	$-0.487229\pi$
$599$	1.96329	0.0802179	0.0401090	+	0.999195i	$0.487229\pi$
$600$	23.2126	0.947649
$601$	40.0325	1.63296	0.816481	−	0.577373i	$-0.195922\pi$
$601$	40.0325	1.63296	0.816481	+	0.577373i	$0.195922\pi$
$602$	9.16866	0.373687
$603$	−29.1033	−1.18518
$604$	−6.61600	−0.269201
$605$	−25.7493	−1.04686
$606$	−30.4135	−1.23546
$607$	−42.8081	−1.73753	−0.868765	−	0.495225i	$-0.835086\pi$
$607$	−42.8081	−1.73753	−0.868765	+	0.495225i	$0.835086\pi$
$608$	−1.00000	−0.0405554
$609$	−43.7285	−1.77197
$610$	−47.4920	−1.92290
$611$	50.7208	2.05194
$612$	−2.06825	−0.0836041
$613$	−34.8309	−1.40681	−0.703404	−	0.710790i	$-0.748337\pi$
$613$	−34.8309	−1.40681	−0.703404	+	0.710790i	$0.748337\pi$
$614$	−7.91178	−0.319294
$615$	1.89850	0.0765549
$616$	−3.14303	−0.126636
$617$	26.1277	1.05186	0.525930	−	0.850528i	$-0.323717\pi$
$617$	26.1277	1.05186	0.525930	+	0.850528i	$0.323717\pi$
$618$	42.5961	1.71347
$619$	2.78517	0.111946	0.0559728	−	0.998432i	$-0.482174\pi$
$619$	2.78517	0.111946	0.0559728	+	0.998432i	$0.482174\pi$
$620$	1.09556	0.0439988
$621$	87.0471	3.49308
$622$	−15.6665	−0.628170
$623$	22.1440	0.887182
$624$	−13.2768	−0.531496
$625$	−6.68446	−0.267378
$626$	−18.0873	−0.722913
$627$	5.99165	0.239284
$628$	−1.29134	−0.0515302
$629$	0.720536	0.0287297
$630$	38.5672	1.53655
$631$	13.9211	0.554190	0.277095	−	0.960843i	$-0.410628\pi$
$631$	13.9211	0.554190	0.277095	+	0.960843i	$0.410628\pi$
$632$	−12.5042	−0.497390
$633$	−3.11312	−0.123735
$634$	−24.1556	−0.959342
$635$	−47.8734	−1.89980
$636$	43.9654	1.74334
$637$	18.4800	0.732205
$638$	16.5547	0.655408
$639$	−33.5296	−1.32641
$640$	3.52936	0.139510
$641$	38.7602	1.53093	0.765467	−	0.643475i	$-0.222508\pi$
$641$	38.7602	1.53093	0.765467	+	0.643475i	$0.222508\pi$
$642$	−19.8209	−0.782267
$643$	−11.8855	−0.468718	−0.234359	−	0.972150i	$-0.575299\pi$
$643$	−11.8855	−0.468718	−0.234359	+	0.972150i	$0.575299\pi$
$644$	12.3694	0.487425
$645$	61.6879	2.42896
$646$	0.309085	0.0121608
$647$	22.0782	0.867982	0.433991	−	0.900917i	$-0.357105\pi$
$647$	22.0782	0.867982	0.433991	+	0.900917i	$0.357105\pi$
$648$	15.7019	0.616828
$649$	−25.5292	−1.00211
$650$	−31.7997	−1.24729
$651$	1.57810	0.0618505
$652$	19.2958	0.755680
$653$	−33.0148	−1.29197	−0.645984	−	0.763351i	$-0.723553\pi$
$653$	−33.0148	−1.29197	−0.645984	+	0.763351i	$0.723553\pi$
$654$	21.9545	0.858489
$655$	45.4042	1.77409
$656$	0.172790	0.00674632
$657$	−35.2769	−1.37628
$658$	−19.4217	−0.757136
$659$	44.4698	1.73230	0.866149	−	0.499786i	$-0.166588\pi$
$659$	44.4698	1.73230	0.866149	+	0.499786i	$0.166588\pi$
$660$	−21.1467	−0.823134
$661$	6.41192	0.249395	0.124697	−	0.992195i	$-0.460204\pi$
$661$	6.41192	0.249395	0.124697	+	0.992195i	$0.460204\pi$
$662$	−11.6693	−0.453541
$663$	4.10366	0.159373
$664$	1.05001	0.0407482
$665$	−5.76359	−0.223502
$666$	−15.5992	−0.604457
$667$	−65.1515	−2.52268
$668$	20.6145	0.797597
$669$	75.1498	2.90546
$670$	−15.3501	−0.593028
$671$	25.8986	0.999803
$672$	5.08386	0.196114
$673$	25.5064	0.983201	0.491600	−	0.870821i	$-0.336412\pi$
$673$	25.5064	0.983201	0.491600	+	0.870821i	$0.336412\pi$
$674$	−32.2474	−1.24212
$675$	85.6896	3.29820
$676$	5.18834	0.199551
$677$	40.5939	1.56015	0.780075	−	0.625685i	$-0.215181\pi$
$677$	40.5939	1.56015	0.780075	+	0.625685i	$0.215181\pi$
$678$	9.67260	0.371474
$679$	1.47970	0.0567855
$680$	−1.09087	−0.0418331
$681$	20.2543	0.776147
$682$	−0.597436	−0.0228770
$683$	−45.9516	−1.75829	−0.879145	−	0.476555i	$-0.841885\pi$
$683$	−45.9516	−1.75829	−0.879145	+	0.476555i	$0.841885\pi$
$684$	−6.69152	−0.255857
$685$	−71.2788	−2.72342
$686$	−18.5075	−0.706621
$687$	93.8624	3.58107
$688$	5.61447	0.214050
$689$	−60.2298	−2.29457
$690$	83.2232	3.16825
$691$	−33.7808	−1.28508	−0.642542	−	0.766251i	$-0.722120\pi$
$691$	−33.7808	−1.28508	−0.642542	+	0.766251i	$0.722120\pi$
$692$	4.50938	0.171421
$693$	−21.0316	−0.798925
$694$	−7.09419	−0.269292
$695$	3.69855	0.140294
$696$	−26.7773	−1.01499
$697$	−0.0534069	−0.00202293
$698$	−16.5448	−0.626229
$699$	−8.57513	−0.324341
$700$	12.1766	0.460230
$701$	17.2106	0.650034	0.325017	−	0.945708i	$-0.394630\pi$
$701$	17.2106	0.650034	0.325017	+	0.945708i	$0.394630\pi$
$702$	−49.0115	−1.84982
$703$	2.33119	0.0879225
$704$	−1.92465	−0.0725378
$705$	−130.672	−4.92138
$706$	24.2666	0.913286
$707$	−15.9539	−0.600010
$708$	41.2937	1.55191
$709$	46.1998	1.73507	0.867535	−	0.497376i	$-0.165703\pi$
$709$	46.1998	1.73507	0.867535	+	0.497376i	$0.165703\pi$
$710$	−17.6847	−0.663697
$711$	−83.6721	−3.13795
$712$	13.5600	0.508182
$713$	2.35122	0.0880540
$714$	−1.57135	−0.0588061
$715$	28.9696	1.08340
$716$	−13.9787	−0.522407
$717$	−53.7589	−2.00766
$718$	−4.21485	−0.157297
$719$	−13.6674	−0.509709	−0.254854	−	0.966979i	$-0.582028\pi$
$719$	−13.6674	−0.509709	−0.254854	+	0.966979i	$0.582028\pi$
$720$	23.6168	0.880145
$721$	22.3445	0.832154
$722$	1.00000	0.0372161
$723$	74.5893	2.77400
$724$	−19.7766	−0.734992
$725$	−64.1355	−2.38193
$726$	−22.7125	−0.842941
$727$	25.8217	0.957674	0.478837	−	0.877904i	$-0.341059\pi$
$727$	25.8217	0.957674	0.478837	+	0.877904i	$0.341059\pi$
$728$	−6.96456	−0.258124
$729$	−2.25985	−0.0836983
$730$	−18.6063	−0.688651
$731$	−1.73535	−0.0641842
$732$	−41.8910	−1.54834
$733$	27.8643	1.02919	0.514596	−	0.857433i	$-0.327942\pi$
$733$	27.8643	1.02919	0.514596	+	0.857433i	$0.327942\pi$
$734$	12.0527	0.444872
$735$	−47.6100	−1.75612
$736$	7.57448	0.279199
$737$	8.37081	0.308343
$738$	1.15623	0.0425614
$739$	1.60865	0.0591752	0.0295876	−	0.999562i	$-0.490581\pi$
$739$	1.60865	0.0591752	0.0295876	+	0.999562i	$0.490581\pi$
$740$	−8.22760	−0.302453
$741$	13.2768	0.487734
$742$	23.0628	0.846663
$743$	−20.1915	−0.740755	−0.370377	−	0.928881i	$-0.620772\pi$
$743$	−20.1915	−0.740755	−0.370377	+	0.928881i	$0.620772\pi$
$744$	0.966355	0.0354283
$745$	−28.7045	−1.05165
$746$	−12.1662	−0.445438
$747$	7.02614	0.257073
$748$	0.594880	0.0217510
$749$	−10.3974	−0.379912
$750$	26.9888	0.985493
$751$	32.0381	1.16909	0.584544	−	0.811362i	$-0.301273\pi$
$751$	32.0381	1.16909	0.584544	+	0.811362i	$0.301273\pi$
$752$	−11.8930	−0.433691
$753$	63.7433	2.32294
$754$	36.6833	1.33593
$755$	−23.3502	−0.849802
$756$	18.7672	0.682555
$757$	−7.73030	−0.280963	−0.140481	−	0.990083i	$-0.544865\pi$
$757$	−7.73030	−0.280963	−0.140481	+	0.990083i	$0.544865\pi$
$758$	−11.2197	−0.407518
$759$	−45.3837	−1.64732
$760$	−3.52936	−0.128023
$761$	1.61935	0.0587015	0.0293507	−	0.999569i	$-0.490656\pi$
$761$	1.61935	0.0587015	0.0293507	+	0.999569i	$0.490656\pi$
$762$	−42.2275	−1.52974
$763$	11.5166	0.416930
$764$	14.3546	0.519330
$765$	−7.29960	−0.263917
$766$	−19.2478	−0.695451
$767$	−56.5697	−2.04261
$768$	3.11312	0.112335
$769$	−19.8835	−0.717019	−0.358509	−	0.933526i	$-0.616715\pi$
$769$	−19.8835	−0.717019	−0.358509	+	0.933526i	$0.616715\pi$
$770$	−11.0929	−0.399759
$771$	−68.4456	−2.46501
$772$	16.4774	0.593034
$773$	5.56540	0.200173	0.100087	−	0.994979i	$-0.468088\pi$
$773$	5.56540	0.200173	0.100087	+	0.994979i	$0.468088\pi$
$774$	37.5693	1.35040
$775$	2.31456	0.0831413
$776$	0.906098	0.0325270
$777$	−11.8514	−0.425168
$778$	30.9962	1.11127
$779$	−0.172790	−0.00619085
$780$	−46.8585	−1.67780
$781$	9.64392	0.345087
$782$	−2.34116	−0.0837198
$783$	−98.8491	−3.53258
$784$	−4.33317	−0.154756
$785$	−4.55761	−0.162668
$786$	40.0494	1.42852
$787$	−25.1116	−0.895132	−0.447566	−	0.894251i	$-0.647709\pi$
$787$	−25.1116	−0.895132	−0.447566	+	0.894251i	$0.647709\pi$
$788$	8.42969	0.300295
$789$	16.6261	0.591905
$790$	−44.1318	−1.57014
$791$	5.07393	0.180408
$792$	−12.8788	−0.457628
$793$	57.3881	2.03791
$794$	−29.3191	−1.04050
$795$	155.170	5.50330
$796$	−20.6646	−0.732438
$797$	−37.6288	−1.33288	−0.666441	−	0.745558i	$-0.732183\pi$
$797$	−37.6288	−1.33288	−0.666441	+	0.745558i	$0.732183\pi$
$798$	−5.08386	−0.179967
$799$	3.67594	0.130045
$800$	7.45636	0.263622
$801$	90.7370	3.20603
$802$	−18.6408	−0.658228
$803$	10.1465	0.358062
$804$	−13.5398	−0.477512
$805$	43.6562	1.53868
$806$	−1.32385	−0.0466305
$807$	−37.8914	−1.33384
$808$	−9.76946	−0.343688
$809$	12.4845	0.438933	0.219467	−	0.975620i	$-0.429568\pi$
$809$	12.4845	0.438933	0.219467	+	0.975620i	$0.429568\pi$
$810$	55.4176	1.94717
$811$	34.0480	1.19559	0.597793	−	0.801651i	$-0.296044\pi$
$811$	34.0480	1.19559	0.597793	+	0.801651i	$0.296044\pi$
$812$	−14.0465	−0.492936
$813$	86.8842	3.04716
$814$	4.48671	0.157259
$815$	68.1016	2.38550
$816$	−0.962220	−0.0336844
$817$	−5.61447	−0.196425
$818$	12.4855	0.436545
$819$	−46.6035	−1.62846
$820$	0.609838	0.0212965
$821$	48.2683	1.68458	0.842288	−	0.539027i	$-0.181208\pi$
$821$	48.2683	1.68458	0.842288	+	0.539027i	$0.181208\pi$
$822$	−62.8725	−2.19293
$823$	16.9035	0.589218	0.294609	−	0.955618i	$-0.404811\pi$
$823$	16.9035	0.589218	0.294609	+	0.955618i	$0.404811\pi$
$824$	13.6828	0.476662
$825$	−44.6759	−1.55542
$826$	21.6613	0.753693
$827$	−15.8986	−0.552849	−0.276425	−	0.961036i	$-0.589150\pi$
$827$	−15.8986	−0.552849	−0.276425	+	0.961036i	$0.589150\pi$
$828$	50.6848	1.76142
$829$	1.57410	0.0546707	0.0273353	−	0.999626i	$-0.491298\pi$
$829$	1.57410	0.0546707	0.0273353	+	0.999626i	$0.491298\pi$
$830$	3.70585	0.128632
$831$	−16.8663	−0.585085
$832$	−4.26478	−0.147855
$833$	1.33932	0.0464047
$834$	3.26236	0.112966
$835$	72.7558	2.51782
$836$	1.92465	0.0665652
$837$	3.56732	0.123305
$838$	6.12703	0.211655
$839$	−3.34485	−0.115477	−0.0577385	−	0.998332i	$-0.518389\pi$
$839$	−3.34485	−0.115477	−0.0577385	+	0.998332i	$0.518389\pi$
$840$	17.9427	0.619084
$841$	44.9848	1.55120
$842$	24.3699	0.839841
$843$	96.9885	3.34046
$844$	−1.00000	−0.0344214
$845$	18.3115	0.629935
$846$	−79.5819	−2.73608
$847$	−11.9142	−0.409378
$848$	14.1226	0.484973
$849$	−88.1676	−3.02591
$850$	−2.30465	−0.0790489
$851$	−17.6576	−0.605293
$852$	−15.5991	−0.534416
$853$	−2.73227	−0.0935512	−0.0467756	−	0.998905i	$-0.514895\pi$
$853$	−2.73227	−0.0935512	−0.0467756	+	0.998905i	$0.514895\pi$
$854$	−21.9747	−0.751958
$855$	−23.6168	−0.807676
$856$	−6.36688	−0.217616
$857$	2.75116	0.0939779	0.0469889	−	0.998895i	$-0.485037\pi$
$857$	2.75116	0.0939779	0.0469889	+	0.998895i	$0.485037\pi$
$858$	25.5531	0.872368
$859$	−3.27473	−0.111732	−0.0558662	−	0.998438i	$-0.517792\pi$
$859$	−3.27473	−0.111732	−0.0558662	+	0.998438i	$0.517792\pi$
$860$	19.8155	0.675702
$861$	0.878440	0.0299372
$862$	−9.53430	−0.324740
$863$	−22.9906	−0.782608	−0.391304	−	0.920261i	$-0.627976\pi$
$863$	−22.9906	−0.782608	−0.391304	+	0.920261i	$0.627976\pi$
$864$	11.4921	0.390971
$865$	15.9152	0.541133
$866$	9.17426	0.311754
$867$	−52.6256	−1.78726
$868$	0.506918	0.0172059
$869$	24.0661	0.816388
$870$	−94.5068	−3.20408
$871$	18.5487	0.628498
$872$	7.05225	0.238819
$873$	6.06317	0.205207
$874$	−7.57448	−0.256211
$875$	14.1575	0.478610
$876$	−16.4120	−0.554510
$877$	33.3480	1.12608	0.563041	−	0.826429i	$-0.309631\pi$
$877$	33.3480	1.12608	0.563041	+	0.826429i	$0.309631\pi$
$878$	6.25958	0.211251
$879$	−27.3076	−0.921062
$880$	−6.79276	−0.228984
$881$	−2.67399	−0.0900890	−0.0450445	−	0.998985i	$-0.514343\pi$
$881$	−2.67399	−0.0900890	−0.0450445	+	0.998985i	$0.514343\pi$
$882$	−28.9955	−0.976330
$883$	9.43466	0.317501	0.158751	−	0.987319i	$-0.449253\pi$
$883$	9.43466	0.317501	0.158751	+	0.987319i	$0.449253\pi$
$884$	1.31818	0.0443352
$885$	145.740	4.89900
$886$	6.69676	0.224982
$887$	52.4640	1.76157	0.880785	−	0.473516i	$-0.157016\pi$
$887$	52.4640	1.76157	0.880785	+	0.473516i	$0.157016\pi$
$888$	−7.25727	−0.243538
$889$	−22.1512	−0.742926
$890$	47.8581	1.60421
$891$	−30.2206	−1.01243
$892$	24.1397	0.808257
$893$	11.8930	0.397982
$894$	−25.3193	−0.846803
$895$	−49.3357	−1.64911
$896$	1.63304	0.0545561
$897$	−100.565	−3.35776
$898$	10.7787	0.359691
$899$	−2.67001	−0.0890497
$900$	49.8944	1.66315
$901$	−4.36509	−0.145422
$902$	−0.332560	−0.0110730
$903$	28.5431	0.949856
$904$	3.10704	0.103339
$905$	−69.7988	−2.32019
$906$	−20.5964	−0.684270
$907$	−36.8949	−1.22508	−0.612538	−	0.790441i	$-0.709851\pi$
$907$	−36.8949	−1.22508	−0.612538	+	0.790441i	$0.709851\pi$
$908$	6.50611	0.215913
$909$	−65.3726	−2.16827
$910$	−24.5804	−0.814833
$911$	10.5838	0.350658	0.175329	−	0.984510i	$-0.443901\pi$
$911$	10.5838	0.350658	0.175329	+	0.984510i	$0.443901\pi$
$912$	−3.11312	−0.103086
$913$	−2.02089	−0.0668817
$914$	−18.0259	−0.596244
$915$	−147.848	−4.88772
$916$	30.1506	0.996203
$917$	21.0086	0.693766
$918$	−3.55205	−0.117235
$919$	3.12362	0.103039	0.0515194	−	0.998672i	$-0.483594\pi$
$919$	3.12362	0.103039	0.0515194	+	0.998672i	$0.483594\pi$
$920$	26.7331	0.881363
$921$	−24.6303	−0.811597
$922$	32.9146	1.08398
$923$	21.3698	0.703394
$924$	−9.78462	−0.321890
$925$	−17.3822	−0.571523
$926$	−32.3992	−1.06470
$927$	91.5585	3.00718
$928$	−8.60144	−0.282356
$929$	5.08269	0.166758	0.0833789	−	0.996518i	$-0.473429\pi$
$929$	5.08269	0.166758	0.0833789	+	0.996518i	$0.473429\pi$
$930$	3.41061	0.111838
$931$	4.33317	0.142014
$932$	−2.75451	−0.0902271
$933$	−48.7717	−1.59671
$934$	31.6876	1.03685
$935$	2.09954	0.0686624
$936$	−28.5379	−0.932789
$937$	49.4387	1.61509	0.807547	−	0.589804i	$-0.200795\pi$
$937$	49.4387	1.61509	0.807547	+	0.589804i	$0.200795\pi$
$938$	−7.10255	−0.231906
$939$	−56.3078	−1.83754
$940$	−41.9745	−1.36906
$941$	−50.3828	−1.64243	−0.821215	−	0.570618i	$-0.806704\pi$
$941$	−50.3828	−1.64243	−0.821215	+	0.570618i	$0.806704\pi$
$942$	−4.02011	−0.130982
$943$	1.30880	0.0426203
$944$	13.2644	0.431719
$945$	66.2360	2.15466
$946$	−10.8059	−0.351329
$947$	32.7345	1.06373	0.531863	−	0.846830i	$-0.321492\pi$
$947$	32.7345	1.06373	0.531863	+	0.846830i	$0.321492\pi$
$948$	−38.9271	−1.26429
$949$	22.4834	0.729842
$950$	−7.45636	−0.241916
$951$	−75.1993	−2.43850
$952$	−0.504749	−0.0163590
$953$	−33.1484	−1.07378	−0.536891	−	0.843652i	$-0.680401\pi$
$953$	−33.1484	−1.07378	−0.536891	+	0.843652i	$0.680401\pi$
$954$	94.5018	3.05961
$955$	50.6624	1.63940
$956$	−17.2685	−0.558503
$957$	51.5369	1.66595
$958$	−20.8692	−0.674254
$959$	−32.9809	−1.06501
$960$	10.9873	0.354614
$961$	−30.9036	−0.996892
$962$	9.94201	0.320543
$963$	−42.6041	−1.37290
$964$	23.9596	0.771688
$965$	58.1546	1.87206
$966$	38.5076	1.23896
$967$	−8.55158	−0.275000	−0.137500	−	0.990502i	$-0.543907\pi$
$967$	−8.55158	−0.275000	−0.137500	+	0.990502i	$0.543907\pi$
$968$	−7.29574	−0.234494
$969$	0.962220	0.0309110
$970$	3.19794	0.102680
$971$	1.17139	0.0375916	0.0187958	−	0.999823i	$-0.494017\pi$
$971$	1.17139	0.0375916	0.0187958	+	0.999823i	$0.494017\pi$
$972$	14.4054	0.462054
$973$	1.71133	0.0548626
$974$	38.8107	1.24357
$975$	−98.9964	−3.17042
$976$	−13.4563	−0.430725
$977$	9.74081	0.311636	0.155818	−	0.987786i	$-0.450199\pi$
$977$	9.74081	0.311636	0.155818	+	0.987786i	$0.450199\pi$
$978$	60.0700	1.92083
$979$	−26.0982	−0.834101
$980$	−15.2933	−0.488527
$981$	47.1903	1.50667
$982$	−27.4306	−0.875347
$983$	−20.2302	−0.645243	−0.322622	−	0.946528i	$-0.604564\pi$
$983$	−20.2302	−0.645243	−0.322622	+	0.946528i	$0.604564\pi$
$984$	0.537917	0.0171482
$985$	29.7514	0.947959
$986$	2.65858	0.0846665
$987$	−60.4621	−1.92453
$988$	4.26478	0.135681
$989$	42.5267	1.35227
$990$	−45.4539	−1.44462
$991$	9.00990	0.286209	0.143104	−	0.989708i	$-0.454292\pi$
$991$	9.00990	0.286209	0.143104	+	0.989708i	$0.454292\pi$
$992$	0.310414	0.00985564
$993$	−36.3280	−1.15283
$994$	−8.18277	−0.259542
$995$	−72.9328	−2.31213
$996$	3.26880	0.103576
$997$	5.41771	0.171581	0.0857903	−	0.996313i	$-0.472658\pi$
$997$	5.41771	0.171581	0.0857903	+	0.996313i	$0.472658\pi$
$998$	9.01439	0.285345
$999$	−26.7904	−0.847610

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.44	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.44	✓	47	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.11312 q^{3} +1.00000 q^{4} +3.52936 q^{5} +3.11312 q^{6} +1.63304 q^{7} +1.00000 q^{8} +6.69152 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.11312 q^{3} +1.00000 q^{4} +3.52936 q^{5} +3.11312 q^{6} +1.63304 q^{7} +1.00000 q^{8} +6.69152 q^{9} +3.52936 q^{10} -1.92465 q^{11} +3.11312 q^{12} -4.26478 q^{13} +1.63304 q^{14} +10.9873 q^{15} +1.00000 q^{16} -0.309085 q^{17} +6.69152 q^{18} -1.00000 q^{19} +3.52936 q^{20} +5.08386 q^{21} -1.92465 q^{22} +7.57448 q^{23} +3.11312 q^{24} +7.45636 q^{25} -4.26478 q^{26} +11.4921 q^{27} +1.63304 q^{28} -8.60144 q^{29} +10.9873 q^{30} +0.310414 q^{31} +1.00000 q^{32} -5.99165 q^{33} -0.309085 q^{34} +5.76359 q^{35} +6.69152 q^{36} -2.33119 q^{37} -1.00000 q^{38} -13.2768 q^{39} +3.52936 q^{40} +0.172790 q^{41} +5.08386 q^{42} +5.61447 q^{43} -1.92465 q^{44} +23.6168 q^{45} +7.57448 q^{46} -11.8930 q^{47} +3.11312 q^{48} -4.33317 q^{49} +7.45636 q^{50} -0.962220 q^{51} -4.26478 q^{52} +14.1226 q^{53} +11.4921 q^{54} -6.79276 q^{55} +1.63304 q^{56} -3.11312 q^{57} -8.60144 q^{58} +13.2644 q^{59} +10.9873 q^{60} -13.4563 q^{61} +0.310414 q^{62} +10.9275 q^{63} +1.00000 q^{64} -15.0519 q^{65} -5.99165 q^{66} -4.34927 q^{67} -0.309085 q^{68} +23.5803 q^{69} +5.76359 q^{70} -5.01075 q^{71} +6.69152 q^{72} -5.27188 q^{73} -2.33119 q^{74} +23.2126 q^{75} -1.00000 q^{76} -3.14303 q^{77} -13.2768 q^{78} -12.5042 q^{79} +3.52936 q^{80} +15.7019 q^{81} +0.172790 q^{82} +1.05001 q^{83} +5.08386 q^{84} -1.09087 q^{85} +5.61447 q^{86} -26.7773 q^{87} -1.92465 q^{88} +13.5600 q^{89} +23.6168 q^{90} -6.96456 q^{91} +7.57448 q^{92} +0.966355 q^{93} -11.8930 q^{94} -3.52936 q^{95} +3.11312 q^{96} +0.906098 q^{97} -4.33317 q^{98} -12.8788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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