LMFDB - Embedded newform 8022.2.a.ba.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8022,2,Mod(1,8022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8022, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8022 = 2 \cdot 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8022.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:	$64.0559925015$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 5 x^{15} - 39 x^{14} + 165 x^{13} + 711 x^{12} - 1949 x^{11} - 7497 x^{10} + 8238 x^{9} + \cdots + 30 $ x^16 - 5x^15 - 39x^14 + 165x^13 + 711x^12 - 1949x^11 - 7497x^10 + 8238x^9 + 42708x^8 + 7872x^7 - 97852x^6 - 109082x^5 - 6830x^4 + 49478x^3 + 28368x^2 + 4947*x + 30
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$-1.54551$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.54551 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.54551 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.54551 q^{10} -5.92302 q^{11} +1.00000 q^{12} -4.51330 q^{13} +1.00000 q^{14} +2.54551 q^{15} +1.00000 q^{16} +1.83577 q^{17} +1.00000 q^{18} +8.28261 q^{19} +2.54551 q^{20} +1.00000 q^{21} -5.92302 q^{22} -2.33538 q^{23} +1.00000 q^{24} +1.47962 q^{25} -4.51330 q^{26} +1.00000 q^{27} +1.00000 q^{28} -3.93800 q^{29} +2.54551 q^{30} +10.9124 q^{31} +1.00000 q^{32} -5.92302 q^{33} +1.83577 q^{34} +2.54551 q^{35} +1.00000 q^{36} +4.99953 q^{37} +8.28261 q^{38} -4.51330 q^{39} +2.54551 q^{40} +7.91948 q^{41} +1.00000 q^{42} +9.96682 q^{43} -5.92302 q^{44} +2.54551 q^{45} -2.33538 q^{46} -6.16536 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.47962 q^{50} +1.83577 q^{51} -4.51330 q^{52} +3.22915 q^{53} +1.00000 q^{54} -15.0771 q^{55} +1.00000 q^{56} +8.28261 q^{57} -3.93800 q^{58} -10.2574 q^{59} +2.54551 q^{60} +8.86236 q^{61} +10.9124 q^{62} +1.00000 q^{63} +1.00000 q^{64} -11.4886 q^{65} -5.92302 q^{66} +6.64365 q^{67} +1.83577 q^{68} -2.33538 q^{69} +2.54551 q^{70} +11.8395 q^{71} +1.00000 q^{72} -8.53254 q^{73} +4.99953 q^{74} +1.47962 q^{75} +8.28261 q^{76} -5.92302 q^{77} -4.51330 q^{78} +15.3625 q^{79} +2.54551 q^{80} +1.00000 q^{81} +7.91948 q^{82} -10.7276 q^{83} +1.00000 q^{84} +4.67296 q^{85} +9.96682 q^{86} -3.93800 q^{87} -5.92302 q^{88} -1.20994 q^{89} +2.54551 q^{90} -4.51330 q^{91} -2.33538 q^{92} +10.9124 q^{93} -6.16536 q^{94} +21.0834 q^{95} +1.00000 q^{96} -0.596015 q^{97} +1.00000 q^{98} -5.92302 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * 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
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	2.54551	1.13839	0.569193	−	0.822204i	$-0.307256\pi$
$5$	2.54551	1.13839	0.569193	+	0.822204i	$0.307256\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	2.54551	0.804961
$11$	−5.92302	−1.78586	−0.892929	−	0.450197i	$-0.851354\pi$
$11$	−5.92302	−1.78586	−0.892929	+	0.450197i	$0.851354\pi$
$12$	1.00000	0.288675
$13$	−4.51330	−1.25176	−0.625881	−	0.779918i	$-0.715261\pi$
$13$	−4.51330	−1.25176	−0.625881	+	0.779918i	$0.715261\pi$
$14$	1.00000	0.267261
$15$	2.54551	0.657248
$16$	1.00000	0.250000
$17$	1.83577	0.445239	0.222619	−	0.974905i	$-0.428539\pi$
$17$	1.83577	0.445239	0.222619	+	0.974905i	$0.428539\pi$
$18$	1.00000	0.235702
$19$	8.28261	1.90016	0.950080	−	0.312007i	$-0.101001\pi$
$19$	8.28261	1.90016	0.950080	+	0.312007i	$0.101001\pi$
$20$	2.54551	0.569193
$21$	1.00000	0.218218
$22$	−5.92302	−1.26279
$23$	−2.33538	−0.486961	−0.243481	−	0.969906i	$-0.578289\pi$
$23$	−2.33538	−0.486961	−0.243481	+	0.969906i	$0.578289\pi$
$24$	1.00000	0.204124
$25$	1.47962	0.295923
$26$	−4.51330	−0.885130
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−3.93800	−0.731269	−0.365634	−	0.930759i	$-0.619148\pi$
$29$	−3.93800	−0.731269	−0.365634	+	0.930759i	$0.619148\pi$
$30$	2.54551	0.464744
$31$	10.9124	1.95992	0.979961	−	0.199190i	$-0.0638310\pi$
$31$	10.9124	1.95992	0.979961	+	0.199190i	$0.0638310\pi$
$32$	1.00000	0.176777
$33$	−5.92302	−1.03107
$34$	1.83577	0.314831
$35$	2.54551	0.430270
$36$	1.00000	0.166667
$37$	4.99953	0.821917	0.410959	−	0.911654i	$-0.365194\pi$
$37$	4.99953	0.821917	0.410959	+	0.911654i	$0.365194\pi$
$38$	8.28261	1.34362
$39$	−4.51330	−0.722706
$40$	2.54551	0.402480
$41$	7.91948	1.23681	0.618407	−	0.785858i	$-0.287778\pi$
$41$	7.91948	1.23681	0.618407	+	0.785858i	$0.287778\pi$
$42$	1.00000	0.154303
$43$	9.96682	1.51993	0.759963	−	0.649967i	$-0.225217\pi$
$43$	9.96682	1.51993	0.759963	+	0.649967i	$0.225217\pi$
$44$	−5.92302	−0.892929
$45$	2.54551	0.379462
$46$	−2.33538	−0.344333
$47$	−6.16536	−0.899310	−0.449655	−	0.893202i	$-0.648453\pi$
$47$	−6.16536	−0.899310	−0.449655	+	0.893202i	$0.648453\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.47962	0.209249
$51$	1.83577	0.257059
$52$	−4.51330	−0.625881
$53$	3.22915	0.443558	0.221779	−	0.975097i	$-0.428814\pi$
$53$	3.22915	0.443558	0.221779	+	0.975097i	$0.428814\pi$
$54$	1.00000	0.136083
$55$	−15.0771	−2.03300
$56$	1.00000	0.133631
$57$	8.28261	1.09706
$58$	−3.93800	−0.517085
$59$	−10.2574	−1.33540	−0.667702	−	0.744429i	$-0.732722\pi$
$59$	−10.2574	−1.33540	−0.667702	+	0.744429i	$0.732722\pi$
$60$	2.54551	0.328624
$61$	8.86236	1.13471	0.567354	−	0.823474i	$-0.307967\pi$
$61$	8.86236	1.13471	0.567354	+	0.823474i	$0.307967\pi$
$62$	10.9124	1.38587
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−11.4886	−1.42499
$66$	−5.92302	−0.729074
$67$	6.64365	0.811651	0.405826	−	0.913951i	$-0.366984\pi$
$67$	6.64365	0.811651	0.405826	+	0.913951i	$0.366984\pi$
$68$	1.83577	0.222619
$69$	−2.33538	−0.281147
$70$	2.54551	0.304247
$71$	11.8395	1.40509	0.702543	−	0.711642i	$-0.252048\pi$
$71$	11.8395	1.40509	0.702543	+	0.711642i	$0.252048\pi$
$72$	1.00000	0.117851
$73$	−8.53254	−0.998658	−0.499329	−	0.866412i	$-0.666420\pi$
$73$	−8.53254	−0.998658	−0.499329	+	0.866412i	$0.666420\pi$
$74$	4.99953	0.581183
$75$	1.47962	0.170851
$76$	8.28261	0.950080
$77$	−5.92302	−0.674991
$78$	−4.51330	−0.511030
$79$	15.3625	1.72841	0.864206	−	0.503138i	$-0.167821\pi$
$79$	15.3625	1.72841	0.864206	+	0.503138i	$0.167821\pi$
$80$	2.54551	0.284597
$81$	1.00000	0.111111
$82$	7.91948	0.874560
$83$	−10.7276	−1.17751	−0.588753	−	0.808313i	$-0.700381\pi$
$83$	−10.7276	−1.17751	−0.588753	+	0.808313i	$0.700381\pi$
$84$	1.00000	0.109109
$85$	4.67296	0.506854
$86$	9.96682	1.07475
$87$	−3.93800	−0.422198
$88$	−5.92302	−0.631396
$89$	−1.20994	−0.128254	−0.0641269	−	0.997942i	$-0.520426\pi$
$89$	−1.20994	−0.128254	−0.0641269	+	0.997942i	$0.520426\pi$
$90$	2.54551	0.268320
$91$	−4.51330	−0.473122
$92$	−2.33538	−0.243481
$93$	10.9124	1.13156
$94$	−6.16536	−0.635909
$95$	21.0834	2.16312
$96$	1.00000	0.102062
$97$	−0.596015	−0.0605162	−0.0302581	−	0.999542i	$-0.509633\pi$
$97$	−0.596015	−0.0605162	−0.0302581	+	0.999542i	$0.509633\pi$
$98$	1.00000	0.101015
$99$	−5.92302	−0.595286
$100$	1.47962	0.147962
$101$	7.14199	0.710655	0.355327	−	0.934742i	$-0.384369\pi$
$101$	7.14199	0.710655	0.355327	+	0.934742i	$0.384369\pi$
$102$	1.83577	0.181768
$103$	−6.21053	−0.611942	−0.305971	−	0.952041i	$-0.598981\pi$
$103$	−6.21053	−0.611942	−0.305971	+	0.952041i	$0.598981\pi$
$104$	−4.51330	−0.442565
$105$	2.54551	0.248416
$106$	3.22915	0.313643
$107$	3.28788	0.317851	0.158926	−	0.987291i	$-0.449197\pi$
$107$	3.28788	0.317851	0.158926	+	0.987291i	$0.449197\pi$
$108$	1.00000	0.0962250
$109$	16.4867	1.57914	0.789568	−	0.613663i	$-0.210305\pi$
$109$	16.4867	1.57914	0.789568	+	0.613663i	$0.210305\pi$
$110$	−15.0771	−1.43755
$111$	4.99953	0.474534
$112$	1.00000	0.0944911
$113$	17.6240	1.65792	0.828962	−	0.559305i	$-0.188932\pi$
$113$	17.6240	1.65792	0.828962	+	0.559305i	$0.188932\pi$
$114$	8.28261	0.775737
$115$	−5.94474	−0.554350
$116$	−3.93800	−0.365634
$117$	−4.51330	−0.417254
$118$	−10.2574	−0.944273
$119$	1.83577	0.168284
$120$	2.54551	0.232372
$121$	24.0822	2.18929
$122$	8.86236	0.802360
$123$	7.91948	0.714075
$124$	10.9124	0.979961
$125$	−8.96117	−0.801511
$126$	1.00000	0.0890871
$127$	−2.51669	−0.223320	−0.111660	−	0.993746i	$-0.535617\pi$
$127$	−2.51669	−0.223320	−0.111660	+	0.993746i	$0.535617\pi$
$128$	1.00000	0.0883883
$129$	9.96682	0.877529
$130$	−11.4886	−1.00762
$131$	−9.63432	−0.841755	−0.420877	−	0.907118i	$-0.638278\pi$
$131$	−9.63432	−0.841755	−0.420877	+	0.907118i	$0.638278\pi$
$132$	−5.92302	−0.515533
$133$	8.28261	0.718193
$134$	6.64365	0.573924
$135$	2.54551	0.219083
$136$	1.83577	0.157416
$137$	−2.82965	−0.241754	−0.120877	−	0.992668i	$-0.538571\pi$
$137$	−2.82965	−0.241754	−0.120877	+	0.992668i	$0.538571\pi$
$138$	−2.33538	−0.198801
$139$	10.0096	0.849002	0.424501	−	0.905428i	$-0.360450\pi$
$139$	10.0096	0.849002	0.424501	+	0.905428i	$0.360450\pi$
$140$	2.54551	0.215135
$141$	−6.16536	−0.519217
$142$	11.8395	0.993545
$143$	26.7324	2.23547
$144$	1.00000	0.0833333
$145$	−10.0242	−0.832466
$146$	−8.53254	−0.706158
$147$	1.00000	0.0824786
$148$	4.99953	0.410959
$149$	−21.3963	−1.75285	−0.876426	−	0.481537i	$-0.840079\pi$
$149$	−21.3963	−1.75285	−0.876426	+	0.481537i	$0.840079\pi$
$150$	1.47962	0.120810
$151$	−24.2475	−1.97323	−0.986617	−	0.163055i	$-0.947865\pi$
$151$	−24.2475	−1.97323	−0.986617	+	0.163055i	$0.947865\pi$
$152$	8.28261	0.671808
$153$	1.83577	0.148413
$154$	−5.92302	−0.477291
$155$	27.7776	2.23115
$156$	−4.51330	−0.361353
$157$	6.47012	0.516372	0.258186	−	0.966095i	$-0.416875\pi$
$157$	6.47012	0.516372	0.258186	+	0.966095i	$0.416875\pi$
$158$	15.3625	1.22217
$159$	3.22915	0.256088
$160$	2.54551	0.201240
$161$	−2.33538	−0.184054
$162$	1.00000	0.0785674
$163$	10.8596	0.850588	0.425294	−	0.905055i	$-0.360171\pi$
$163$	10.8596	0.850588	0.425294	+	0.905055i	$0.360171\pi$
$164$	7.91948	0.618407
$165$	−15.0771	−1.17375
$166$	−10.7276	−0.832622
$167$	−16.4036	−1.26935	−0.634675	−	0.772779i	$-0.718866\pi$
$167$	−16.4036	−1.26935	−0.634675	+	0.772779i	$0.718866\pi$
$168$	1.00000	0.0771517
$169$	7.36984	0.566911
$170$	4.67296	0.358400
$171$	8.28261	0.633387
$172$	9.96682	0.759963
$173$	23.9611	1.82173	0.910864	−	0.412707i	$-0.135417\pi$
$173$	23.9611	1.82173	0.910864	+	0.412707i	$0.135417\pi$
$174$	−3.93800	−0.298539
$175$	1.47962	0.111849
$176$	−5.92302	−0.446465
$177$	−10.2574	−0.770996
$178$	−1.20994	−0.0906892
$179$	1.54375	0.115386	0.0576928	−	0.998334i	$-0.481626\pi$
$179$	1.54375	0.115386	0.0576928	+	0.998334i	$0.481626\pi$
$180$	2.54551	0.189731
$181$	−17.3800	−1.29184	−0.645922	−	0.763403i	$-0.723527\pi$
$181$	−17.3800	−1.29184	−0.645922	+	0.763403i	$0.723527\pi$
$182$	−4.51330	−0.334548
$183$	8.86236	0.655124
$184$	−2.33538	−0.172167
$185$	12.7263	0.935660
$186$	10.9124	0.800135
$187$	−10.8733	−0.795134
$188$	−6.16536	−0.449655
$189$	1.00000	0.0727393
$190$	21.0834	1.52955
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	−11.8744	−0.854735	−0.427368	−	0.904078i	$-0.640559\pi$
$193$	−11.8744	−0.854735	−0.427368	+	0.904078i	$0.640559\pi$
$194$	−0.596015	−0.0427914
$195$	−11.4886	−0.822718
$196$	1.00000	0.0714286
$197$	−13.4872	−0.960926	−0.480463	−	0.877015i	$-0.659531\pi$
$197$	−13.4872	−0.960926	−0.480463	+	0.877015i	$0.659531\pi$
$198$	−5.92302	−0.420931
$199$	−10.6083	−0.752003	−0.376001	−	0.926619i	$-0.622701\pi$
$199$	−10.6083	−0.752003	−0.376001	+	0.926619i	$0.622701\pi$
$200$	1.47962	0.104625
$201$	6.64365	0.468607
$202$	7.14199	0.502509
$203$	−3.93800	−0.276394
$204$	1.83577	0.128529
$205$	20.1591	1.40797
$206$	−6.21053	−0.432708
$207$	−2.33538	−0.162320
$208$	−4.51330	−0.312941
$209$	−49.0581	−3.39342
$210$	2.54551	0.175657
$211$	−16.2027	−1.11544	−0.557721	−	0.830028i	$-0.688324\pi$
$211$	−16.2027	−1.11544	−0.557721	+	0.830028i	$0.688324\pi$
$212$	3.22915	0.221779
$213$	11.8395	0.811226
$214$	3.28788	0.224755
$215$	25.3706	1.73026
$216$	1.00000	0.0680414
$217$	10.9124	0.740781
$218$	16.4867	1.11662
$219$	−8.53254	−0.576576
$220$	−15.0771	−1.01650
$221$	−8.28536	−0.557333
$222$	4.99953	0.335546
$223$	−3.10167	−0.207703	−0.103852	−	0.994593i	$-0.533117\pi$
$223$	−3.10167	−0.207703	−0.103852	+	0.994593i	$0.533117\pi$
$224$	1.00000	0.0668153
$225$	1.47962	0.0986411
$226$	17.6240	1.17233
$227$	16.2595	1.07918	0.539592	−	0.841927i	$-0.318579\pi$
$227$	16.2595	1.07918	0.539592	+	0.841927i	$0.318579\pi$
$228$	8.28261	0.548529
$229$	2.51876	0.166444	0.0832221	−	0.996531i	$-0.473479\pi$
$229$	2.51876	0.166444	0.0832221	+	0.996531i	$0.473479\pi$
$230$	−5.94474	−0.391985
$231$	−5.92302	−0.389706
$232$	−3.93800	−0.258543
$233$	17.9635	1.17683	0.588414	−	0.808560i	$-0.299753\pi$
$233$	17.9635	1.17683	0.588414	+	0.808560i	$0.299753\pi$
$234$	−4.51330	−0.295043
$235$	−15.6940	−1.02376
$236$	−10.2574	−0.667702
$237$	15.3625	0.997900
$238$	1.83577	0.118995
$239$	−18.3352	−1.18601	−0.593003	−	0.805201i	$-0.702058\pi$
$239$	−18.3352	−1.18601	−0.593003	+	0.805201i	$0.702058\pi$
$240$	2.54551	0.164312
$241$	−10.2347	−0.659276	−0.329638	−	0.944107i	$-0.606927\pi$
$241$	−10.2347	−0.659276	−0.329638	+	0.944107i	$0.606927\pi$
$242$	24.0822	1.54806
$243$	1.00000	0.0641500
$244$	8.86236	0.567354
$245$	2.54551	0.162627
$246$	7.91948	0.504927
$247$	−37.3818	−2.37855
$248$	10.9124	0.692937
$249$	−10.7276	−0.679833
$250$	−8.96117	−0.566754
$251$	−19.9049	−1.25639	−0.628194	−	0.778056i	$-0.716206\pi$
$251$	−19.9049	−1.25639	−0.628194	+	0.778056i	$0.716206\pi$
$252$	1.00000	0.0629941
$253$	13.8325	0.869644
$254$	−2.51669	−0.157911
$255$	4.67296	0.292632
$256$	1.00000	0.0625000
$257$	8.94897	0.558222	0.279111	−	0.960259i	$-0.409960\pi$
$257$	8.94897	0.558222	0.279111	+	0.960259i	$0.409960\pi$
$258$	9.96682	0.620507
$259$	4.99953	0.310656
$260$	−11.4886	−0.712495
$261$	−3.93800	−0.243756
$262$	−9.63432	−0.595211
$263$	−10.1507	−0.625917	−0.312959	−	0.949767i	$-0.601320\pi$
$263$	−10.1507	−0.625917	−0.312959	+	0.949767i	$0.601320\pi$
$264$	−5.92302	−0.364537
$265$	8.21983	0.504940
$266$	8.28261	0.507839
$267$	−1.20994	−0.0740474
$268$	6.64365	0.405826
$269$	8.13109	0.495761	0.247881	−	0.968791i	$-0.420266\pi$
$269$	8.13109	0.495761	0.247881	+	0.968791i	$0.420266\pi$
$270$	2.54551	0.154915
$271$	−10.2839	−0.624703	−0.312352	−	0.949967i	$-0.601117\pi$
$271$	−10.2839	−0.624703	−0.312352	+	0.949967i	$0.601117\pi$
$272$	1.83577	0.111310
$273$	−4.51330	−0.273157
$274$	−2.82965	−0.170946
$275$	−8.76380	−0.528477
$276$	−2.33538	−0.140574
$277$	17.8590	1.07304	0.536522	−	0.843887i	$-0.319738\pi$
$277$	17.8590	1.07304	0.536522	+	0.843887i	$0.319738\pi$
$278$	10.0096	0.600335
$279$	10.9124	0.653307
$280$	2.54551	0.152123
$281$	−4.19912	−0.250498	−0.125249	−	0.992125i	$-0.539973\pi$
$281$	−4.19912	−0.250498	−0.125249	+	0.992125i	$0.539973\pi$
$282$	−6.16536	−0.367142
$283$	9.40882	0.559296	0.279648	−	0.960103i	$-0.409782\pi$
$283$	9.40882	0.559296	0.279648	+	0.960103i	$0.409782\pi$
$284$	11.8395	0.702543
$285$	21.0834	1.24888
$286$	26.7324	1.58072
$287$	7.91948	0.467472
$288$	1.00000	0.0589256
$289$	−13.6300	−0.801762
$290$	−10.0242	−0.588643
$291$	−0.596015	−0.0349390
$292$	−8.53254	−0.499329
$293$	−12.2989	−0.718509	−0.359254	−	0.933240i	$-0.616969\pi$
$293$	−12.2989	−0.718509	−0.359254	+	0.933240i	$0.616969\pi$
$294$	1.00000	0.0583212
$295$	−26.1104	−1.52021
$296$	4.99953	0.290592
$297$	−5.92302	−0.343689
$298$	−21.3963	−1.23945
$299$	10.5403	0.609560
$300$	1.47962	0.0854257
$301$	9.96682	0.574478
$302$	−24.2475	−1.39529
$303$	7.14199	0.410297
$304$	8.28261	0.475040
$305$	22.5592	1.29174
$306$	1.83577	0.104944
$307$	−12.9009	−0.736291	−0.368145	−	0.929768i	$-0.620007\pi$
$307$	−12.9009	−0.736291	−0.368145	+	0.929768i	$0.620007\pi$
$308$	−5.92302	−0.337496
$309$	−6.21053	−0.353305
$310$	27.7776	1.57766
$311$	26.8325	1.52153	0.760766	−	0.649027i	$-0.224824\pi$
$311$	26.8325	1.52153	0.760766	+	0.649027i	$0.224824\pi$
$312$	−4.51330	−0.255515
$313$	−16.7649	−0.947606	−0.473803	−	0.880631i	$-0.657119\pi$
$313$	−16.7649	−0.947606	−0.473803	+	0.880631i	$0.657119\pi$
$314$	6.47012	0.365130
$315$	2.54551	0.143423
$316$	15.3625	0.864206
$317$	−29.8067	−1.67411	−0.837056	−	0.547117i	$-0.815725\pi$
$317$	−29.8067	−1.67411	−0.837056	+	0.547117i	$0.815725\pi$
$318$	3.22915	0.181082
$319$	23.3249	1.30594
$320$	2.54551	0.142298
$321$	3.28788	0.183511
$322$	−2.33538	−0.130146
$323$	15.2049	0.846025
$324$	1.00000	0.0555556
$325$	−6.67795	−0.370426
$326$	10.8596	0.601457
$327$	16.4867	0.911714
$328$	7.91948	0.437280
$329$	−6.16536	−0.339907
$330$	−15.0771	−0.829967
$331$	−21.7324	−1.19452	−0.597260	−	0.802048i	$-0.703744\pi$
$331$	−21.7324	−1.19452	−0.597260	+	0.802048i	$0.703744\pi$
$332$	−10.7276	−0.588753
$333$	4.99953	0.273972
$334$	−16.4036	−0.897567
$335$	16.9115	0.923973
$336$	1.00000	0.0545545
$337$	−12.9495	−0.705402	−0.352701	−	0.935736i	$-0.614737\pi$
$337$	−12.9495	−0.705402	−0.352701	+	0.935736i	$0.614737\pi$
$338$	7.36984	0.400866
$339$	17.6240	0.957203
$340$	4.67296	0.253427
$341$	−64.6343	−3.50014
$342$	8.28261	0.447872
$343$	1.00000	0.0539949
$344$	9.96682	0.537375
$345$	−5.94474	−0.320054
$346$	23.9611	1.28816
$347$	−2.38016	−0.127773	−0.0638867	−	0.997957i	$-0.520350\pi$
$347$	−2.38016	−0.127773	−0.0638867	+	0.997957i	$0.520350\pi$
$348$	−3.93800	−0.211099
$349$	−23.3710	−1.25102	−0.625512	−	0.780215i	$-0.715110\pi$
$349$	−23.3710	−1.25102	−0.625512	+	0.780215i	$0.715110\pi$
$350$	1.47962	0.0790888
$351$	−4.51330	−0.240902
$352$	−5.92302	−0.315698
$353$	−10.8594	−0.577989	−0.288995	−	0.957331i	$-0.593321\pi$
$353$	−10.8594	−0.577989	−0.288995	+	0.957331i	$0.593321\pi$
$354$	−10.2574	−0.545177
$355$	30.1374	1.59953
$356$	−1.20994	−0.0641269
$357$	1.83577	0.0971591
$358$	1.54375	0.0815900
$359$	−22.7526	−1.20084	−0.600418	−	0.799687i	$-0.704999\pi$
$359$	−22.7526	−1.20084	−0.600418	+	0.799687i	$0.704999\pi$
$360$	2.54551	0.134160
$361$	49.6015	2.61061
$362$	−17.3800	−0.913472
$363$	24.0822	1.26399
$364$	−4.51330	−0.236561
$365$	−21.7197	−1.13686
$366$	8.86236	0.463243
$367$	34.4165	1.79653	0.898264	−	0.439456i	$-0.144829\pi$
$367$	34.4165	1.79653	0.898264	+	0.439456i	$0.144829\pi$
$368$	−2.33538	−0.121740
$369$	7.91948	0.412272
$370$	12.7263	0.661611
$371$	3.22915	0.167649
$372$	10.9124	0.565781
$373$	−8.85066	−0.458270	−0.229135	−	0.973395i	$-0.573590\pi$
$373$	−8.85066	−0.458270	−0.229135	+	0.973395i	$0.573590\pi$
$374$	−10.8733	−0.562244
$375$	−8.96117	−0.462753
$376$	−6.16536	−0.317954
$377$	17.7734	0.915375
$378$	1.00000	0.0514344
$379$	−26.9767	−1.38570	−0.692851	−	0.721081i	$-0.743646\pi$
$379$	−26.9767	−1.38570	−0.692851	+	0.721081i	$0.743646\pi$
$380$	21.0834	1.08156
$381$	−2.51669	−0.128934
$382$	−1.00000	−0.0511645
$383$	−4.52758	−0.231348	−0.115674	−	0.993287i	$-0.536903\pi$
$383$	−4.52758	−0.231348	−0.115674	+	0.993287i	$0.536903\pi$
$384$	1.00000	0.0510310
$385$	−15.0771	−0.768401
$386$	−11.8744	−0.604389
$387$	9.96682	0.506642
$388$	−0.596015	−0.0302581
$389$	−30.7330	−1.55822	−0.779112	−	0.626885i	$-0.784330\pi$
$389$	−30.7330	−1.55822	−0.779112	+	0.626885i	$0.784330\pi$
$390$	−11.4886	−0.581750
$391$	−4.28722	−0.216814
$392$	1.00000	0.0505076
$393$	−9.63432	−0.485987
$394$	−13.4872	−0.679478
$395$	39.1053	1.96760
$396$	−5.92302	−0.297643
$397$	−7.97730	−0.400369	−0.200185	−	0.979758i	$-0.564154\pi$
$397$	−7.97730	−0.400369	−0.200185	+	0.979758i	$0.564154\pi$
$398$	−10.6083	−0.531746
$399$	8.28261	0.414649
$400$	1.47962	0.0739808
$401$	−10.7539	−0.537022	−0.268511	−	0.963277i	$-0.586532\pi$
$401$	−10.7539	−0.537022	−0.268511	+	0.963277i	$0.586532\pi$
$402$	6.64365	0.331355
$403$	−49.2508	−2.45336
$404$	7.14199	0.355327
$405$	2.54551	0.126487
$406$	−3.93800	−0.195440
$407$	−29.6123	−1.46783
$408$	1.83577	0.0908840
$409$	2.38002	0.117685	0.0588423	−	0.998267i	$-0.481259\pi$
$409$	2.38002	0.117685	0.0588423	+	0.998267i	$0.481259\pi$
$410$	20.1591	0.995587
$411$	−2.82965	−0.139577
$412$	−6.21053	−0.305971
$413$	−10.2574	−0.504735
$414$	−2.33538	−0.114778
$415$	−27.3072	−1.34046
$416$	−4.51330	−0.221283
$417$	10.0096	0.490171
$418$	−49.0581	−2.39951
$419$	11.4257	0.558184	0.279092	−	0.960264i	$-0.409967\pi$
$419$	11.4257	0.558184	0.279092	+	0.960264i	$0.409967\pi$
$420$	2.54551	0.124208
$421$	−21.7006	−1.05762	−0.528812	−	0.848739i	$-0.677362\pi$
$421$	−21.7006	−1.05762	−0.528812	+	0.848739i	$0.677362\pi$
$422$	−16.2027	−0.788737
$423$	−6.16536	−0.299770
$424$	3.22915	0.156821
$425$	2.71623	0.131757
$426$	11.8395	0.573624
$427$	8.86236	0.428879
$428$	3.28788	0.158926
$429$	26.7324	1.29065
$430$	25.3706	1.22348
$431$	−14.6416	−0.705261	−0.352631	−	0.935763i	$-0.614713\pi$
$431$	−14.6416	−0.705261	−0.352631	+	0.935763i	$0.614713\pi$
$432$	1.00000	0.0481125
$433$	−10.0735	−0.484104	−0.242052	−	0.970263i	$-0.577820\pi$
$433$	−10.0735	−0.484104	−0.242052	+	0.970263i	$0.577820\pi$
$434$	10.9124	0.523811
$435$	−10.0242	−0.480625
$436$	16.4867	0.789568
$437$	−19.3431	−0.925304
$438$	−8.53254	−0.407701
$439$	−16.3848	−0.782005	−0.391002	−	0.920390i	$-0.627872\pi$
$439$	−16.3848	−0.782005	−0.391002	+	0.920390i	$0.627872\pi$
$440$	−15.0771	−0.718773
$441$	1.00000	0.0476190
$442$	−8.28536	−0.394094
$443$	11.6177	0.551975	0.275987	−	0.961161i	$-0.410995\pi$
$443$	11.6177	0.551975	0.275987	+	0.961161i	$0.410995\pi$
$444$	4.99953	0.237267
$445$	−3.07993	−0.146002
$446$	−3.10167	−0.146868
$447$	−21.3963	−1.01201
$448$	1.00000	0.0472456
$449$	−17.9367	−0.846485	−0.423242	−	0.906016i	$-0.639108\pi$
$449$	−17.9367	−0.846485	−0.423242	+	0.906016i	$0.639108\pi$
$450$	1.47962	0.0697498
$451$	−46.9072	−2.20878
$452$	17.6240	0.828962
$453$	−24.2475	−1.13925
$454$	16.2595	0.763098
$455$	−11.4886	−0.538596
$456$	8.28261	0.387869
$457$	−22.8421	−1.06851	−0.534255	−	0.845323i	$-0.679408\pi$
$457$	−22.8421	−1.06851	−0.534255	+	0.845323i	$0.679408\pi$
$458$	2.51876	0.117694
$459$	1.83577	0.0856863
$460$	−5.94474	−0.277175
$461$	−2.06471	−0.0961631	−0.0480816	−	0.998843i	$-0.515311\pi$
$461$	−2.06471	−0.0961631	−0.0480816	+	0.998843i	$0.515311\pi$
$462$	−5.92302	−0.275564
$463$	30.6037	1.42227	0.711137	−	0.703054i	$-0.248181\pi$
$463$	30.6037	1.42227	0.711137	+	0.703054i	$0.248181\pi$
$464$	−3.93800	−0.182817
$465$	27.7776	1.28815
$466$	17.9635	0.832143
$467$	−15.9172	−0.736559	−0.368279	−	0.929715i	$-0.620053\pi$
$467$	−15.9172	−0.736559	−0.368279	+	0.929715i	$0.620053\pi$
$468$	−4.51330	−0.208627
$469$	6.64365	0.306775
$470$	−15.6940	−0.723910
$471$	6.47012	0.298128
$472$	−10.2574	−0.472137
$473$	−59.0337	−2.71437
$474$	15.3625	0.705622
$475$	12.2551	0.562302
$476$	1.83577	0.0841422
$477$	3.22915	0.147853
$478$	−18.3352	−0.838632
$479$	32.6867	1.49349	0.746746	−	0.665109i	$-0.231615\pi$
$479$	32.6867	1.49349	0.746746	+	0.665109i	$0.231615\pi$
$480$	2.54551	0.116186
$481$	−22.5644	−1.02885
$482$	−10.2347	−0.466179
$483$	−2.33538	−0.106264
$484$	24.0822	1.09465
$485$	−1.51716	−0.0688908
$486$	1.00000	0.0453609
$487$	24.2105	1.09708	0.548542	−	0.836123i	$-0.315183\pi$
$487$	24.2105	1.09708	0.548542	+	0.836123i	$0.315183\pi$
$488$	8.86236	0.401180
$489$	10.8596	0.491087
$490$	2.54551	0.114994
$491$	29.1266	1.31446	0.657232	−	0.753689i	$-0.271727\pi$
$491$	29.1266	1.31446	0.657232	+	0.753689i	$0.271727\pi$
$492$	7.91948	0.357038
$493$	−7.22926	−0.325589
$494$	−37.3818	−1.68189
$495$	−15.0771	−0.677666
$496$	10.9124	0.489980
$497$	11.8395	0.531072
$498$	−10.7276	−0.480715
$499$	41.7975	1.87111	0.935556	−	0.353178i	$-0.114899\pi$
$499$	41.7975	1.87111	0.935556	+	0.353178i	$0.114899\pi$
$500$	−8.96117	−0.400756
$501$	−16.4036	−0.732860
$502$	−19.9049	−0.888401
$503$	28.2307	1.25874	0.629372	−	0.777105i	$-0.283312\pi$
$503$	28.2307	1.25874	0.629372	+	0.777105i	$0.283312\pi$
$504$	1.00000	0.0445435
$505$	18.1800	0.808999
$506$	13.8325	0.614931
$507$	7.36984	0.327306
$508$	−2.51669	−0.111660
$509$	−4.31187	−0.191120	−0.0955601	−	0.995424i	$-0.530464\pi$
$509$	−4.31187	−0.191120	−0.0955601	+	0.995424i	$0.530464\pi$
$510$	4.67296	0.206922
$511$	−8.53254	−0.377457
$512$	1.00000	0.0441942
$513$	8.28261	0.365686
$514$	8.94897	0.394722
$515$	−15.8090	−0.696626
$516$	9.96682	0.438765
$517$	36.5176	1.60604
$518$	4.99953	0.219667
$519$	23.9611	1.05177
$520$	−11.4886	−0.503810
$521$	−16.0975	−0.705246	−0.352623	−	0.935766i	$-0.614710\pi$
$521$	−16.0975	−0.705246	−0.352623	+	0.935766i	$0.614710\pi$
$522$	−3.93800	−0.172362
$523$	−36.4787	−1.59510	−0.797550	−	0.603252i	$-0.793871\pi$
$523$	−36.4787	−1.59510	−0.797550	+	0.603252i	$0.793871\pi$
$524$	−9.63432	−0.420877
$525$	1.47962	0.0645758
$526$	−10.1507	−0.442590
$527$	20.0326	0.872633
$528$	−5.92302	−0.257766
$529$	−17.5460	−0.762869
$530$	8.21983	0.357047
$531$	−10.2574	−0.445135
$532$	8.28261	0.359096
$533$	−35.7429	−1.54820
$534$	−1.20994	−0.0523594
$535$	8.36932	0.361837
$536$	6.64365	0.286962
$537$	1.54375	0.0666179
$538$	8.13109	0.350556
$539$	−5.92302	−0.255123
$540$	2.54551	0.109541
$541$	2.24534	0.0965348	0.0482674	−	0.998834i	$-0.484630\pi$
$541$	2.24534	0.0965348	0.0482674	+	0.998834i	$0.484630\pi$
$542$	−10.2839	−0.441732
$543$	−17.3800	−0.745847
$544$	1.83577	0.0787078
$545$	41.9669	1.79767
$546$	−4.51330	−0.193151
$547$	21.9270	0.937530	0.468765	−	0.883323i	$-0.344699\pi$
$547$	21.9270	0.937530	0.468765	+	0.883323i	$0.344699\pi$
$548$	−2.82965	−0.120877
$549$	8.86236	0.378236
$550$	−8.76380	−0.373690
$551$	−32.6169	−1.38953
$552$	−2.33538	−0.0994005
$553$	15.3625	0.653279
$554$	17.8590	0.758756
$555$	12.7263	0.540203
$556$	10.0096	0.424501
$557$	0.440780	0.0186765	0.00933823	−	0.999956i	$-0.497028\pi$
$557$	0.440780	0.0186765	0.00933823	+	0.999956i	$0.497028\pi$
$558$	10.9124	0.461958
$559$	−44.9832	−1.90259
$560$	2.54551	0.107567
$561$	−10.8733	−0.459071
$562$	−4.19912	−0.177129
$563$	−3.47202	−0.146328	−0.0731640	−	0.997320i	$-0.523310\pi$
$563$	−3.47202	−0.146328	−0.0731640	+	0.997320i	$0.523310\pi$
$564$	−6.16536	−0.259609
$565$	44.8620	1.88736
$566$	9.40882	0.395482
$567$	1.00000	0.0419961
$568$	11.8395	0.496773
$569$	4.75777	0.199456	0.0997280	−	0.995015i	$-0.468203\pi$
$569$	4.75777	0.199456	0.0997280	+	0.995015i	$0.468203\pi$
$570$	21.0834	0.883088
$571$	28.1398	1.17762	0.588808	−	0.808273i	$-0.299598\pi$
$571$	28.1398	1.17762	0.588808	+	0.808273i	$0.299598\pi$
$572$	26.7324	1.11774
$573$	−1.00000	−0.0417756
$574$	7.91948	0.330553
$575$	−3.45547	−0.144103
$576$	1.00000	0.0416667
$577$	−34.8001	−1.44875	−0.724373	−	0.689408i	$-0.757871\pi$
$577$	−34.8001	−1.44875	−0.724373	+	0.689408i	$0.757871\pi$
$578$	−13.6300	−0.566932
$579$	−11.8744	−0.493482
$580$	−10.0242	−0.416233
$581$	−10.7276	−0.445055
$582$	−0.596015	−0.0247056
$583$	−19.1263	−0.792131
$584$	−8.53254	−0.353079
$585$	−11.4886	−0.474997
$586$	−12.2989	−0.508062
$587$	−7.55194	−0.311702	−0.155851	−	0.987781i	$-0.549812\pi$
$587$	−7.55194	−0.311702	−0.155851	+	0.987781i	$0.549812\pi$
$588$	1.00000	0.0412393
$589$	90.3830	3.72417
$590$	−26.1104	−1.07495
$591$	−13.4872	−0.554791
$592$	4.99953	0.205479
$593$	1.50825	0.0619364	0.0309682	−	0.999520i	$-0.490141\pi$
$593$	1.50825	0.0619364	0.0309682	+	0.999520i	$0.490141\pi$
$594$	−5.92302	−0.243025
$595$	4.67296	0.191573
$596$	−21.3963	−0.876426
$597$	−10.6083	−0.434169
$598$	10.5403	0.431024
$599$	42.0421	1.71779	0.858897	−	0.512148i	$-0.171150\pi$
$599$	42.0421	1.71779	0.858897	+	0.512148i	$0.171150\pi$
$600$	1.47962	0.0604051
$601$	−1.27167	−0.0518727	−0.0259363	−	0.999664i	$-0.508257\pi$
$601$	−1.27167	−0.0518727	−0.0259363	+	0.999664i	$0.508257\pi$
$602$	9.96682	0.406217
$603$	6.64365	0.270550
$604$	−24.2475	−0.986617
$605$	61.3014	2.49226
$606$	7.14199	0.290124
$607$	14.8333	0.602063	0.301032	−	0.953614i	$-0.402669\pi$
$607$	14.8333	0.602063	0.301032	+	0.953614i	$0.402669\pi$
$608$	8.28261	0.335904
$609$	−3.93800	−0.159576
$610$	22.5592	0.913396
$611$	27.8261	1.12572
$612$	1.83577	0.0742065
$613$	3.95780	0.159854	0.0799270	−	0.996801i	$-0.474531\pi$
$613$	3.95780	0.159854	0.0799270	+	0.996801i	$0.474531\pi$
$614$	−12.9009	−0.520636
$615$	20.1591	0.812893
$616$	−5.92302	−0.238645
$617$	17.6524	0.710657	0.355329	−	0.934741i	$-0.384369\pi$
$617$	17.6524	0.710657	0.355329	+	0.934741i	$0.384369\pi$
$618$	−6.21053	−0.249824
$619$	10.1732	0.408896	0.204448	−	0.978877i	$-0.434460\pi$
$619$	10.1732	0.408896	0.204448	+	0.978877i	$0.434460\pi$
$620$	27.7776	1.11557
$621$	−2.33538	−0.0937157
$622$	26.8325	1.07589
$623$	−1.20994	−0.0484754
$624$	−4.51330	−0.180676
$625$	−30.2088	−1.20835
$626$	−16.7649	−0.670059
$627$	−49.0581	−1.95919
$628$	6.47012	0.258186
$629$	9.17797	0.365950
$630$	2.54551	0.101416
$631$	−11.3552	−0.452042	−0.226021	−	0.974122i	$-0.572572\pi$
$631$	−11.3552	−0.452042	−0.226021	+	0.974122i	$0.572572\pi$
$632$	15.3625	0.611086
$633$	−16.2027	−0.644001
$634$	−29.8067	−1.18378
$635$	−6.40626	−0.254225
$636$	3.22915	0.128044
$637$	−4.51330	−0.178823
$638$	23.3249	0.923441
$639$	11.8395	0.468362
$640$	2.54551	0.100620
$641$	16.0351	0.633348	0.316674	−	0.948534i	$-0.397434\pi$
$641$	16.0351	0.633348	0.316674	+	0.948534i	$0.397434\pi$
$642$	3.28788	0.129762
$643$	35.5588	1.40230	0.701152	−	0.713012i	$-0.252669\pi$
$643$	35.5588	1.40230	0.701152	+	0.713012i	$0.252669\pi$
$644$	−2.33538	−0.0920270
$645$	25.3706	0.998967
$646$	15.2049	0.598230
$647$	25.8430	1.01599	0.507996	−	0.861359i	$-0.330386\pi$
$647$	25.8430	1.01599	0.507996	+	0.861359i	$0.330386\pi$
$648$	1.00000	0.0392837
$649$	60.7550	2.38484
$650$	−6.67795	−0.261931
$651$	10.9124	0.427690
$652$	10.8596	0.425294
$653$	1.63178	0.0638564	0.0319282	−	0.999490i	$-0.489835\pi$
$653$	1.63178	0.0638564	0.0319282	+	0.999490i	$0.489835\pi$
$654$	16.4867	0.644679
$655$	−24.5243	−0.958242
$656$	7.91948	0.309204
$657$	−8.53254	−0.332886
$658$	−6.16536	−0.240351
$659$	47.9638	1.86841	0.934203	−	0.356743i	$-0.116113\pi$
$659$	47.9638	1.86841	0.934203	+	0.356743i	$0.116113\pi$
$660$	−15.0771	−0.586876
$661$	4.70460	0.182988	0.0914938	−	0.995806i	$-0.470836\pi$
$661$	4.70460	0.182988	0.0914938	+	0.995806i	$0.470836\pi$
$662$	−21.7324	−0.844653
$663$	−8.28536	−0.321777
$664$	−10.7276	−0.416311
$665$	21.0834	0.817581
$666$	4.99953	0.193728
$667$	9.19675	0.356099
$668$	−16.4036	−0.634675
$669$	−3.10167	−0.119918
$670$	16.9115	0.653347
$671$	−52.4919	−2.02643
$672$	1.00000	0.0385758
$673$	−41.6593	−1.60585	−0.802925	−	0.596081i	$-0.796724\pi$
$673$	−41.6593	−1.60585	−0.802925	+	0.596081i	$0.796724\pi$
$674$	−12.9495	−0.498795
$675$	1.47962	0.0569505
$676$	7.36984	0.283455
$677$	40.1639	1.54363	0.771813	−	0.635850i	$-0.219350\pi$
$677$	40.1639	1.54363	0.771813	+	0.635850i	$0.219350\pi$
$678$	17.6240	0.676845
$679$	−0.596015	−0.0228730
$680$	4.67296	0.179200
$681$	16.2595	0.623067
$682$	−64.6343	−2.47497
$683$	25.7258	0.984370	0.492185	−	0.870491i	$-0.336198\pi$
$683$	25.7258	0.984370	0.492185	+	0.870491i	$0.336198\pi$
$684$	8.28261	0.316693
$685$	−7.20291	−0.275209
$686$	1.00000	0.0381802
$687$	2.51876	0.0960966
$688$	9.96682	0.379981
$689$	−14.5741	−0.555229
$690$	−5.94474	−0.226312
$691$	6.77234	0.257632	0.128816	−	0.991669i	$-0.458882\pi$
$691$	6.77234	0.257632	0.128816	+	0.991669i	$0.458882\pi$
$692$	23.9611	0.910864
$693$	−5.92302	−0.224997
$694$	−2.38016	−0.0903495
$695$	25.4795	0.966492
$696$	−3.93800	−0.149270
$697$	14.5383	0.550678
$698$	−23.3710	−0.884607
$699$	17.9635	0.679442
$700$	1.47962	0.0559243
$701$	−49.3537	−1.86406	−0.932031	−	0.362378i	$-0.881965\pi$
$701$	−49.3537	−1.86406	−0.932031	+	0.362378i	$0.881965\pi$
$702$	−4.51330	−0.170343
$703$	41.4091	1.56177
$704$	−5.92302	−0.223232
$705$	−15.6940	−0.591070
$706$	−10.8594	−0.408700
$707$	7.14199	0.268602
$708$	−10.2574	−0.385498
$709$	28.2450	1.06076	0.530381	−	0.847760i	$-0.322049\pi$
$709$	28.2450	1.06076	0.530381	+	0.847760i	$0.322049\pi$
$710$	30.1374	1.13104
$711$	15.3625	0.576138
$712$	−1.20994	−0.0453446
$713$	−25.4846	−0.954406
$714$	1.83577	0.0687018
$715$	68.0474	2.54483
$716$	1.54375	0.0576928
$717$	−18.3352	−0.684740
$718$	−22.7526	−0.849119
$719$	2.43645	0.0908642	0.0454321	−	0.998967i	$-0.485534\pi$
$719$	2.43645	0.0908642	0.0454321	+	0.998967i	$0.485534\pi$
$720$	2.54551	0.0948655
$721$	−6.21053	−0.231292
$722$	49.6015	1.84598
$723$	−10.2347	−0.380633
$724$	−17.3800	−0.645922
$725$	−5.82674	−0.216400
$726$	24.0822	0.893774
$727$	7.55033	0.280026	0.140013	−	0.990150i	$-0.455286\pi$
$727$	7.55033	0.280026	0.140013	+	0.990150i	$0.455286\pi$
$728$	−4.51330	−0.167274
$729$	1.00000	0.0370370
$730$	−21.7197	−0.803881
$731$	18.2968	0.676730
$732$	8.86236	0.327562
$733$	−4.14473	−0.153089	−0.0765446	−	0.997066i	$-0.524389\pi$
$733$	−4.14473	−0.153089	−0.0765446	+	0.997066i	$0.524389\pi$
$734$	34.4165	1.27034
$735$	2.54551	0.0938925
$736$	−2.33538	−0.0860834
$737$	−39.3505	−1.44949
$738$	7.91948	0.291520
$739$	6.45140	0.237319	0.118659	−	0.992935i	$-0.462140\pi$
$739$	6.45140	0.237319	0.118659	+	0.992935i	$0.462140\pi$
$740$	12.7263	0.467830
$741$	−37.3818	−1.37326
$742$	3.22915	0.118546
$743$	25.4326	0.933032	0.466516	−	0.884513i	$-0.345509\pi$
$743$	25.4326	0.933032	0.466516	+	0.884513i	$0.345509\pi$
$744$	10.9124	0.400067
$745$	−54.4644	−1.99542
$746$	−8.85066	−0.324046
$747$	−10.7276	−0.392502
$748$	−10.8733	−0.397567
$749$	3.28788	0.120136
$750$	−8.96117	−0.327216
$751$	−7.75607	−0.283023	−0.141512	−	0.989937i	$-0.545196\pi$
$751$	−7.75607	−0.283023	−0.141512	+	0.989937i	$0.545196\pi$
$752$	−6.16536	−0.224828
$753$	−19.9049	−0.725376
$754$	17.7734	0.647268
$755$	−61.7222	−2.24630
$756$	1.00000	0.0363696
$757$	−47.8175	−1.73796	−0.868979	−	0.494849i	$-0.835223\pi$
$757$	−47.8175	−1.73796	−0.868979	+	0.494849i	$0.835223\pi$
$758$	−26.9767	−0.979839
$759$	13.8325	0.502089
$760$	21.0834	0.764777
$761$	43.2565	1.56805	0.784024	−	0.620730i	$-0.213164\pi$
$761$	43.2565	1.56805	0.784024	+	0.620730i	$0.213164\pi$
$762$	−2.51669	−0.0911700
$763$	16.4867	0.596857
$764$	−1.00000	−0.0361787
$765$	4.67296	0.168951
$766$	−4.52758	−0.163588
$767$	46.2948	1.67161
$768$	1.00000	0.0360844
$769$	7.95390	0.286825	0.143413	−	0.989663i	$-0.454192\pi$
$769$	7.95390	0.286825	0.143413	+	0.989663i	$0.454192\pi$
$770$	−15.0771	−0.543341
$771$	8.94897	0.322289
$772$	−11.8744	−0.427368
$773$	15.0453	0.541142	0.270571	−	0.962700i	$-0.412788\pi$
$773$	15.0453	0.541142	0.270571	+	0.962700i	$0.412788\pi$
$774$	9.96682	0.358250
$775$	16.1461	0.579987
$776$	−0.596015	−0.0213957
$777$	4.99953	0.179357
$778$	−30.7330	−1.10183
$779$	65.5939	2.35015
$780$	−11.4886	−0.411359
$781$	−70.1254	−2.50928
$782$	−4.28722	−0.153311
$783$	−3.93800	−0.140733
$784$	1.00000	0.0357143
$785$	16.4698	0.587831
$786$	−9.63432	−0.343645
$787$	24.5921	0.876615	0.438308	−	0.898825i	$-0.355578\pi$
$787$	24.5921	0.876615	0.438308	+	0.898825i	$0.355578\pi$
$788$	−13.4872	−0.480463
$789$	−10.1507	−0.361373
$790$	39.1053	1.39130
$791$	17.6240	0.626637
$792$	−5.92302	−0.210465
$793$	−39.9984	−1.42039
$794$	−7.97730	−0.283104
$795$	8.21983	0.291527
$796$	−10.6083	−0.376001
$797$	−10.6962	−0.378880	−0.189440	−	0.981892i	$-0.560667\pi$
$797$	−10.6962	−0.378880	−0.189440	+	0.981892i	$0.560667\pi$
$798$	8.28261	0.293201
$799$	−11.3182	−0.400408
$800$	1.47962	0.0523124
$801$	−1.20994	−0.0427513
$802$	−10.7539	−0.379732
$803$	50.5384	1.78346
$804$	6.64365	0.234304
$805$	−5.94474	−0.209525
$806$	−49.2508	−1.73479
$807$	8.13109	0.286228
$808$	7.14199	0.251254
$809$	−17.2243	−0.605574	−0.302787	−	0.953058i	$-0.597917\pi$
$809$	−17.2243	−0.605574	−0.302787	+	0.953058i	$0.597917\pi$
$810$	2.54551	0.0894401
$811$	−22.1000	−0.776037	−0.388019	−	0.921651i	$-0.626840\pi$
$811$	−22.1000	−0.776037	−0.388019	+	0.921651i	$0.626840\pi$
$812$	−3.93800	−0.138197
$813$	−10.2839	−0.360673
$814$	−29.6123	−1.03791
$815$	27.6432	0.968298
$816$	1.83577	0.0642647
$817$	82.5512	2.88810
$818$	2.38002	0.0832156
$819$	−4.51330	−0.157707
$820$	20.1591	0.703986
$821$	−43.6194	−1.52233	−0.761164	−	0.648559i	$-0.775372\pi$
$821$	−43.6194	−1.52233	−0.761164	+	0.648559i	$0.775372\pi$
$822$	−2.82965	−0.0986955
$823$	0.658857	0.0229663	0.0114832	−	0.999934i	$-0.496345\pi$
$823$	0.658857	0.0229663	0.0114832	+	0.999934i	$0.496345\pi$
$824$	−6.21053	−0.216354
$825$	−8.76380	−0.305116
$826$	−10.2574	−0.356902
$827$	20.7157	0.720356	0.360178	−	0.932884i	$-0.382716\pi$
$827$	20.7157	0.720356	0.360178	+	0.932884i	$0.382716\pi$
$828$	−2.33538	−0.0811602
$829$	−8.46018	−0.293834	−0.146917	−	0.989149i	$-0.546935\pi$
$829$	−8.46018	−0.293834	−0.146917	+	0.989149i	$0.546935\pi$
$830$	−27.3072	−0.947846
$831$	17.8590	0.619522
$832$	−4.51330	−0.156470
$833$	1.83577	0.0636055
$834$	10.0096	0.346604
$835$	−41.7556	−1.44501
$836$	−49.0581	−1.69671
$837$	10.9124	0.377187
$838$	11.4257	0.394696
$839$	15.5793	0.537858	0.268929	−	0.963160i	$-0.413330\pi$
$839$	15.5793	0.537858	0.268929	+	0.963160i	$0.413330\pi$
$840$	2.54551	0.0878284
$841$	−13.4921	−0.465246
$842$	−21.7006	−0.747853
$843$	−4.19912	−0.144625
$844$	−16.2027	−0.557721
$845$	18.7600	0.645363
$846$	−6.16536	−0.211970
$847$	24.0822	0.827474
$848$	3.22915	0.110889
$849$	9.40882	0.322910
$850$	2.71623	0.0931660
$851$	−11.6758	−0.400242
$852$	11.8395	0.405613
$853$	−5.55700	−0.190268	−0.0951341	−	0.995464i	$-0.530328\pi$
$853$	−5.55700	−0.190268	−0.0951341	+	0.995464i	$0.530328\pi$
$854$	8.86236	0.303264
$855$	21.0834	0.721039
$856$	3.28788	0.112377
$857$	56.9206	1.94437	0.972185	−	0.234213i	$-0.0752514\pi$
$857$	56.9206	1.94437	0.972185	+	0.234213i	$0.0752514\pi$
$858$	26.7324	0.912627
$859$	7.89053	0.269221	0.134611	−	0.990899i	$-0.457022\pi$
$859$	7.89053	0.269221	0.134611	+	0.990899i	$0.457022\pi$
$860$	25.3706	0.865131
$861$	7.91948	0.269895
$862$	−14.6416	−0.498695
$863$	5.92109	0.201556	0.100778	−	0.994909i	$-0.467867\pi$
$863$	5.92109	0.201556	0.100778	+	0.994909i	$0.467867\pi$
$864$	1.00000	0.0340207
$865$	60.9932	2.07383
$866$	−10.0735	−0.342313
$867$	−13.6300	−0.462898
$868$	10.9124	0.370390
$869$	−90.9922	−3.08670
$870$	−10.0242	−0.339853
$871$	−29.9848	−1.01599
$872$	16.4867	0.558309
$873$	−0.596015	−0.0201721
$874$	−19.3431	−0.654289
$875$	−8.96117	−0.302943
$876$	−8.53254	−0.288288
$877$	−29.7726	−1.00535	−0.502674	−	0.864476i	$-0.667650\pi$
$877$	−29.7726	−1.00535	−0.502674	+	0.864476i	$0.667650\pi$
$878$	−16.3848	−0.552961
$879$	−12.2989	−0.414831
$880$	−15.0771	−0.508249
$881$	7.28834	0.245550	0.122775	−	0.992435i	$-0.460821\pi$
$881$	7.28834	0.245550	0.122775	+	0.992435i	$0.460821\pi$
$882$	1.00000	0.0336718
$883$	24.8876	0.837533	0.418767	−	0.908094i	$-0.362463\pi$
$883$	24.8876	0.837533	0.418767	+	0.908094i	$0.362463\pi$
$884$	−8.28536	−0.278667
$885$	−26.1104	−0.877691
$886$	11.6177	0.390305
$887$	−11.3387	−0.380715	−0.190357	−	0.981715i	$-0.560965\pi$
$887$	−11.3387	−0.380715	−0.190357	+	0.981715i	$0.560965\pi$
$888$	4.99953	0.167773
$889$	−2.51669	−0.0844071
$890$	−3.07993	−0.103239
$891$	−5.92302	−0.198429
$892$	−3.10167	−0.103852
$893$	−51.0653	−1.70883
$894$	−21.3963	−0.715599
$895$	3.92964	0.131353
$896$	1.00000	0.0334077
$897$	10.5403	0.351930
$898$	−17.9367	−0.598555
$899$	−42.9730	−1.43323
$900$	1.47962	0.0493206
$901$	5.92796	0.197489
$902$	−46.9072	−1.56184
$903$	9.96682	0.331675
$904$	17.6240	0.586165
$905$	−44.2409	−1.47062
$906$	−24.2475	−0.805569
$907$	−37.3301	−1.23953	−0.619763	−	0.784789i	$-0.712771\pi$
$907$	−37.3301	−1.23953	−0.619763	+	0.784789i	$0.712771\pi$
$908$	16.2595	0.539592
$909$	7.14199	0.236885
$910$	−11.4886	−0.380845
$911$	−47.4000	−1.57043	−0.785216	−	0.619222i	$-0.787448\pi$
$911$	−47.4000	−1.57043	−0.785216	+	0.619222i	$0.787448\pi$
$912$	8.28261	0.274264
$913$	63.5397	2.10286
$914$	−22.8421	−0.755551
$915$	22.5592	0.745784
$916$	2.51876	0.0832221
$917$	−9.63432	−0.318153
$918$	1.83577	0.0605893
$919$	27.6618	0.912477	0.456239	−	0.889858i	$-0.349196\pi$
$919$	27.6618	0.912477	0.456239	+	0.889858i	$0.349196\pi$
$920$	−5.94474	−0.195992
$921$	−12.9009	−0.425098
$922$	−2.06471	−0.0679976
$923$	−53.4350	−1.75883
$924$	−5.92302	−0.194853
$925$	7.39739	0.243225
$926$	30.6037	1.00570
$927$	−6.21053	−0.203981
$928$	−3.93800	−0.129271
$929$	−43.9673	−1.44252	−0.721260	−	0.692665i	$-0.756437\pi$
$929$	−43.9673	−1.44252	−0.721260	+	0.692665i	$0.756437\pi$
$930$	27.7776	0.910862
$931$	8.28261	0.271451
$932$	17.9635	0.588414
$933$	26.8325	0.878457
$934$	−15.9172	−0.520826
$935$	−27.6781	−0.905169
$936$	−4.51330	−0.147522
$937$	37.1030	1.21210	0.606052	−	0.795425i	$-0.292752\pi$
$937$	37.1030	1.21210	0.606052	+	0.795425i	$0.292752\pi$
$938$	6.64365	0.216923
$939$	−16.7649	−0.547101
$940$	−15.6940	−0.511881
$941$	−23.9301	−0.780100	−0.390050	−	0.920794i	$-0.627542\pi$
$941$	−23.9301	−0.780100	−0.390050	+	0.920794i	$0.627542\pi$
$942$	6.47012	0.210808
$943$	−18.4950	−0.602281
$944$	−10.2574	−0.333851
$945$	2.54551	0.0828054
$946$	−59.0337	−1.91935
$947$	8.48514	0.275730	0.137865	−	0.990451i	$-0.455976\pi$
$947$	8.48514	0.275730	0.137865	+	0.990451i	$0.455976\pi$
$948$	15.3625	0.498950
$949$	38.5099	1.25008
$950$	12.2551	0.397607
$951$	−29.8067	−0.966550
$952$	1.83577	0.0594975
$953$	−20.0421	−0.649229	−0.324614	−	0.945846i	$-0.605235\pi$
$953$	−20.0421	−0.649229	−0.324614	+	0.945846i	$0.605235\pi$
$954$	3.22915	0.104548
$955$	−2.54551	−0.0823707
$956$	−18.3352	−0.593003
$957$	23.3249	0.753986
$958$	32.6867	1.05606
$959$	−2.82965	−0.0913743
$960$	2.54551	0.0821560
$961$	88.0801	2.84129
$962$	−22.5644	−0.727504
$963$	3.28788	0.105950
$964$	−10.2347	−0.329638
$965$	−30.2263	−0.973019
$966$	−2.33538	−0.0751397
$967$	58.7698	1.88991	0.944955	−	0.327201i	$-0.106105\pi$
$967$	58.7698	1.88991	0.944955	+	0.327201i	$0.106105\pi$
$968$	24.0822	0.774031
$969$	15.2049	0.488453
$970$	−1.51716	−0.0487131
$971$	1.34439	0.0431436	0.0215718	−	0.999767i	$-0.493133\pi$
$971$	1.34439	0.0431436	0.0215718	+	0.999767i	$0.493133\pi$
$972$	1.00000	0.0320750
$973$	10.0096	0.320893
$974$	24.2105	0.775756
$975$	−6.67795	−0.213865
$976$	8.86236	0.283677
$977$	−3.19685	−0.102276	−0.0511381	−	0.998692i	$-0.516285\pi$
$977$	−3.19685	−0.102276	−0.0511381	+	0.998692i	$0.516285\pi$
$978$	10.8596	0.347251
$979$	7.16653	0.229043
$980$	2.54551	0.0813133
$981$	16.4867	0.526379
$982$	29.1266	0.929466
$983$	−44.6466	−1.42400	−0.712002	−	0.702177i	$-0.752211\pi$
$983$	−44.6466	−1.42400	−0.712002	+	0.702177i	$0.752211\pi$
$984$	7.91948	0.252464
$985$	−34.3319	−1.09391
$986$	−7.22926	−0.230226
$987$	−6.16536	−0.196246
$988$	−37.3818	−1.18927
$989$	−23.2763	−0.740145
$990$	−15.0771	−0.479182
$991$	40.0962	1.27370	0.636849	−	0.770988i	$-0.280237\pi$
$991$	40.0962	1.27370	0.636849	+	0.770988i	$0.280237\pi$
$992$	10.9124	0.346469
$993$	−21.7324	−0.689656
$994$	11.8395	0.375525
$995$	−27.0035	−0.856070
$996$	−10.7276	−0.339917
$997$	−48.7751	−1.54472	−0.772361	−	0.635184i	$-0.780924\pi$
$997$	−48.7751	−1.54472	−0.772361	+	0.635184i	$0.780924\pi$
$998$	41.7975	1.32308
$999$	4.99953	0.158178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.12	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.12	✓	16	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:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.54551 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +2.54551 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +2.54551 q^{10} -5.92302 q^{11} +1.00000 q^{12} -4.51330 q^{13} +1.00000 q^{14} +2.54551 q^{15} +1.00000 q^{16} +1.83577 q^{17} +1.00000 q^{18} +8.28261 q^{19} +2.54551 q^{20} +1.00000 q^{21} -5.92302 q^{22} -2.33538 q^{23} +1.00000 q^{24} +1.47962 q^{25} -4.51330 q^{26} +1.00000 q^{27} +1.00000 q^{28} -3.93800 q^{29} +2.54551 q^{30} +10.9124 q^{31} +1.00000 q^{32} -5.92302 q^{33} +1.83577 q^{34} +2.54551 q^{35} +1.00000 q^{36} +4.99953 q^{37} +8.28261 q^{38} -4.51330 q^{39} +2.54551 q^{40} +7.91948 q^{41} +1.00000 q^{42} +9.96682 q^{43} -5.92302 q^{44} +2.54551 q^{45} -2.33538 q^{46} -6.16536 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.47962 q^{50} +1.83577 q^{51} -4.51330 q^{52} +3.22915 q^{53} +1.00000 q^{54} -15.0771 q^{55} +1.00000 q^{56} +8.28261 q^{57} -3.93800 q^{58} -10.2574 q^{59} +2.54551 q^{60} +8.86236 q^{61} +10.9124 q^{62} +1.00000 q^{63} +1.00000 q^{64} -11.4886 q^{65} -5.92302 q^{66} +6.64365 q^{67} +1.83577 q^{68} -2.33538 q^{69} +2.54551 q^{70} +11.8395 q^{71} +1.00000 q^{72} -8.53254 q^{73} +4.99953 q^{74} +1.47962 q^{75} +8.28261 q^{76} -5.92302 q^{77} -4.51330 q^{78} +15.3625 q^{79} +2.54551 q^{80} +1.00000 q^{81} +7.91948 q^{82} -10.7276 q^{83} +1.00000 q^{84} +4.67296 q^{85} +9.96682 q^{86} -3.93800 q^{87} -5.92302 q^{88} -1.20994 q^{89} +2.54551 q^{90} -4.51330 q^{91} -2.33538 q^{92} +10.9124 q^{93} -6.16536 q^{94} +21.0834 q^{95} +1.00000 q^{96} -0.596015 q^{97} +1.00000 q^{98} -5.92302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9} + 11 q^{10} + 8 q^{11} + 16 q^{12} + 6 q^{13} + 16 q^{14} + 11 q^{15} + 16 q^{16} + 14 q^{17} + 16 q^{18} + 29 q^{19} + 11 q^{20} + 16 q^{21} + 8 q^{22} + 9 q^{23} + 16 q^{24} + 29 q^{25} + 6 q^{26} + 16 q^{27} + 16 q^{28} + 11 q^{30} + 14 q^{31} + 16 q^{32} + 8 q^{33} + 14 q^{34} + 11 q^{35} + 16 q^{36} + 11 q^{37} + 29 q^{38} + 6 q^{39} + 11 q^{40} + 14 q^{41} + 16 q^{42} + 28 q^{43} + 8 q^{44} + 11 q^{45} + 9 q^{46} - q^{47} + 16 q^{48} + 16 q^{49} + 29 q^{50} + 14 q^{51} + 6 q^{52} - 4 q^{53} + 16 q^{54} + 17 q^{55} + 16 q^{56} + 29 q^{57} + 25 q^{59} + 11 q^{60} + 16 q^{61} + 14 q^{62} + 16 q^{63} + 16 q^{64} + 6 q^{65} + 8 q^{66} + 26 q^{67} + 14 q^{68} + 9 q^{69} + 11 q^{70} + 9 q^{71} + 16 q^{72} + 31 q^{73} + 11 q^{74} + 29 q^{75} + 29 q^{76} + 8 q^{77} + 6 q^{78} + 9 q^{79} + 11 q^{80} + 16 q^{81} + 14 q^{82} + 13 q^{83} + 16 q^{84} + 20 q^{85} + 28 q^{86} + 8 q^{88} + 21 q^{89} + 11 q^{90} + 6 q^{91} + 9 q^{92} + 14 q^{93} - q^{94} - 37 q^{95} + 16 q^{96} + 18 q^{97} + 16 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q + 16 * q^2 + 16 * q^3 + 16 * q^4 + 11 * q^5 + 16 * q^6 + 16 * q^7 + 16 * q^8 + 16 * q^9 + 11 * q^10 + 8 * q^11 + 16 * q^12 + 6 * q^13 + 16 * q^14 + 11 * q^15 + 16 * q^16 + 14 * q^17 + 16 * q^18 + 29 * q^19 + 11 * q^20 + 16 * q^21 + 8 * q^22 + 9 * q^23 + 16 * q^24 + 29 * q^25 + 6 * q^26 + 16 * q^27 + 16 * q^28 + 11 * q^30 + 14 * q^31 + 16 * q^32 + 8 * q^33 + 14 * q^34 + 11 * q^35 + 16 * q^36 + 11 * q^37 + 29 * q^38 + 6 * q^39 + 11 * q^40 + 14 * q^41 + 16 * q^42 + 28 * q^43 + 8 * q^44 + 11 * q^45 + 9 * q^46 - q^47 + 16 * q^48 + 16 * q^49 + 29 * q^50 + 14 * q^51 + 6 * q^52 - 4 * q^53 + 16 * q^54 + 17 * q^55 + 16 * q^56 + 29 * q^57 + 25 * q^59 + 11 * q^60 + 16 * q^61 + 14 * q^62 + 16 * q^63 + 16 * q^64 + 6 * q^65 + 8 * q^66 + 26 * q^67 + 14 * q^68 + 9 * q^69 + 11 * q^70 + 9 * q^71 + 16 * q^72 + 31 * q^73 + 11 * q^74 + 29 * q^75 + 29 * q^76 + 8 * q^77 + 6 * q^78 + 9 * q^79 + 11 * q^80 + 16 * q^81 + 14 * q^82 + 13 * q^83 + 16 * q^84 + 20 * q^85 + 28 * q^86 + 8 * q^88 + 21 * q^89 + 11 * q^90 + 6 * q^91 + 9 * q^92 + 14 * q^93 - q^94 - 37 * q^95 + 16 * q^96 + 18 * q^97 + 16 * q^98 + 8 * q^99

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