LMFDB - Embedded newform 8022.2.a.ba.1.15

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			1.15
Root			$-2.95354$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.95354 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.95354 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.95354 q^{10} +3.91962 q^{11} +1.00000 q^{12} +3.15542 q^{13} +1.00000 q^{14} +3.95354 q^{15} +1.00000 q^{16} -0.274165 q^{17} +1.00000 q^{18} -5.15151 q^{19} +3.95354 q^{20} +1.00000 q^{21} +3.91962 q^{22} -2.79170 q^{23} +1.00000 q^{24} +10.6305 q^{25} +3.15542 q^{26} +1.00000 q^{27} +1.00000 q^{28} -5.61490 q^{29} +3.95354 q^{30} +1.34159 q^{31} +1.00000 q^{32} +3.91962 q^{33} -0.274165 q^{34} +3.95354 q^{35} +1.00000 q^{36} -5.79814 q^{37} -5.15151 q^{38} +3.15542 q^{39} +3.95354 q^{40} +2.13961 q^{41} +1.00000 q^{42} +10.5562 q^{43} +3.91962 q^{44} +3.95354 q^{45} -2.79170 q^{46} -12.7718 q^{47} +1.00000 q^{48} +1.00000 q^{49} +10.6305 q^{50} -0.274165 q^{51} +3.15542 q^{52} -6.70527 q^{53} +1.00000 q^{54} +15.4964 q^{55} +1.00000 q^{56} -5.15151 q^{57} -5.61490 q^{58} +5.03957 q^{59} +3.95354 q^{60} +7.96315 q^{61} +1.34159 q^{62} +1.00000 q^{63} +1.00000 q^{64} +12.4751 q^{65} +3.91962 q^{66} +0.669240 q^{67} -0.274165 q^{68} -2.79170 q^{69} +3.95354 q^{70} +5.21776 q^{71} +1.00000 q^{72} -12.7861 q^{73} -5.79814 q^{74} +10.6305 q^{75} -5.15151 q^{76} +3.91962 q^{77} +3.15542 q^{78} -3.58567 q^{79} +3.95354 q^{80} +1.00000 q^{81} +2.13961 q^{82} +5.76683 q^{83} +1.00000 q^{84} -1.08392 q^{85} +10.5562 q^{86} -5.61490 q^{87} +3.91962 q^{88} -5.53790 q^{89} +3.95354 q^{90} +3.15542 q^{91} -2.79170 q^{92} +1.34159 q^{93} -12.7718 q^{94} -20.3667 q^{95} +1.00000 q^{96} +15.7303 q^{97} +1.00000 q^{98} +3.91962 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	3.95354	1.76808	0.884039	−	0.467414i	$-0.154814\pi$
$5$	3.95354	1.76808	0.884039	+	0.467414i	$0.154814\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	3.95354	1.25022
$11$	3.91962	1.18181	0.590905	−	0.806741i	$-0.298771\pi$
$11$	3.91962	1.18181	0.590905	+	0.806741i	$0.298771\pi$
$12$	1.00000	0.288675
$13$	3.15542	0.875157	0.437578	−	0.899180i	$-0.355836\pi$
$13$	3.15542	0.875157	0.437578	+	0.899180i	$0.355836\pi$
$14$	1.00000	0.267261
$15$	3.95354	1.02080
$16$	1.00000	0.250000
$17$	−0.274165	−0.0664947	−0.0332474	−	0.999447i	$-0.510585\pi$
$17$	−0.274165	−0.0664947	−0.0332474	+	0.999447i	$0.510585\pi$
$18$	1.00000	0.235702
$19$	−5.15151	−1.18184	−0.590919	−	0.806731i	$-0.701235\pi$
$19$	−5.15151	−1.18184	−0.590919	+	0.806731i	$0.701235\pi$
$20$	3.95354	0.884039
$21$	1.00000	0.218218
$22$	3.91962	0.835666
$23$	−2.79170	−0.582111	−0.291055	−	0.956706i	$-0.594006\pi$
$23$	−2.79170	−0.582111	−0.291055	+	0.956706i	$0.594006\pi$
$24$	1.00000	0.204124
$25$	10.6305	2.12610
$26$	3.15542	0.618829
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	−5.61490	−1.04266	−0.521331	−	0.853355i	$-0.674564\pi$
$29$	−5.61490	−1.04266	−0.521331	+	0.853355i	$0.674564\pi$
$30$	3.95354	0.721815
$31$	1.34159	0.240957	0.120478	−	0.992716i	$-0.461557\pi$
$31$	1.34159	0.240957	0.120478	+	0.992716i	$0.461557\pi$
$32$	1.00000	0.176777
$33$	3.91962	0.682318
$34$	−0.274165	−0.0470189
$35$	3.95354	0.668271
$36$	1.00000	0.166667
$37$	−5.79814	−0.953208	−0.476604	−	0.879118i	$-0.658132\pi$
$37$	−5.79814	−0.953208	−0.476604	+	0.879118i	$0.658132\pi$
$38$	−5.15151	−0.835686
$39$	3.15542	0.505272
$40$	3.95354	0.625110
$41$	2.13961	0.334152	0.167076	−	0.985944i	$-0.446568\pi$
$41$	2.13961	0.334152	0.167076	+	0.985944i	$0.446568\pi$
$42$	1.00000	0.154303
$43$	10.5562	1.60981	0.804903	−	0.593407i	$-0.202217\pi$
$43$	10.5562	1.60981	0.804903	+	0.593407i	$0.202217\pi$
$44$	3.91962	0.590905
$45$	3.95354	0.589359
$46$	−2.79170	−0.411614
$47$	−12.7718	−1.86296	−0.931478	−	0.363798i	$-0.881480\pi$
$47$	−12.7718	−1.86296	−0.931478	+	0.363798i	$0.881480\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	10.6305	1.50338
$51$	−0.274165	−0.0383908
$52$	3.15542	0.437578
$53$	−6.70527	−0.921039	−0.460520	−	0.887650i	$-0.652337\pi$
$53$	−6.70527	−0.921039	−0.460520	+	0.887650i	$0.652337\pi$
$54$	1.00000	0.136083
$55$	15.4964	2.08953
$56$	1.00000	0.133631
$57$	−5.15151	−0.682334
$58$	−5.61490	−0.737273
$59$	5.03957	0.656096	0.328048	−	0.944661i	$-0.393609\pi$
$59$	5.03957	0.656096	0.328048	+	0.944661i	$0.393609\pi$
$60$	3.95354	0.510400
$61$	7.96315	1.01958	0.509789	−	0.860300i	$-0.329724\pi$
$61$	7.96315	1.01958	0.509789	+	0.860300i	$0.329724\pi$
$62$	1.34159	0.170382
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	12.4751	1.54734
$66$	3.91962	0.482472
$67$	0.669240	0.0817607	0.0408803	−	0.999164i	$-0.486984\pi$
$67$	0.669240	0.0817607	0.0408803	+	0.999164i	$0.486984\pi$
$68$	−0.274165	−0.0332474
$69$	−2.79170	−0.336082
$70$	3.95354	0.472539
$71$	5.21776	0.619234	0.309617	−	0.950861i	$-0.399799\pi$
$71$	5.21776	0.619234	0.309617	+	0.950861i	$0.399799\pi$
$72$	1.00000	0.117851
$73$	−12.7861	−1.49650	−0.748249	−	0.663418i	$-0.769105\pi$
$73$	−12.7861	−1.49650	−0.748249	+	0.663418i	$0.769105\pi$
$74$	−5.79814	−0.674020
$75$	10.6305	1.22750
$76$	−5.15151	−0.590919
$77$	3.91962	0.446682
$78$	3.15542	0.357281
$79$	−3.58567	−0.403419	−0.201710	−	0.979445i	$-0.564650\pi$
$79$	−3.58567	−0.403419	−0.201710	+	0.979445i	$0.564650\pi$
$80$	3.95354	0.442019
$81$	1.00000	0.111111
$82$	2.13961	0.236281
$83$	5.76683	0.632992	0.316496	−	0.948594i	$-0.397494\pi$
$83$	5.76683	0.632992	0.316496	+	0.948594i	$0.397494\pi$
$84$	1.00000	0.109109
$85$	−1.08392	−0.117568
$86$	10.5562	1.13830
$87$	−5.61490	−0.601981
$88$	3.91962	0.417833
$89$	−5.53790	−0.587016	−0.293508	−	0.955957i	$-0.594823\pi$
$89$	−5.53790	−0.587016	−0.293508	+	0.955957i	$0.594823\pi$
$90$	3.95354	0.416740
$91$	3.15542	0.330778
$92$	−2.79170	−0.291055
$93$	1.34159	0.139116
$94$	−12.7718	−1.31731
$95$	−20.3667	−2.08958
$96$	1.00000	0.102062
$97$	15.7303	1.59717	0.798587	−	0.601879i	$-0.205581\pi$
$97$	15.7303	1.59717	0.798587	+	0.601879i	$0.205581\pi$
$98$	1.00000	0.101015
$99$	3.91962	0.393937
$100$	10.6305	1.06305
$101$	1.75182	0.174313	0.0871564	−	0.996195i	$-0.472222\pi$
$101$	1.75182	0.174313	0.0871564	+	0.996195i	$0.472222\pi$
$102$	−0.274165	−0.0271464
$103$	−5.30803	−0.523016	−0.261508	−	0.965201i	$-0.584220\pi$
$103$	−5.30803	−0.523016	−0.261508	+	0.965201i	$0.584220\pi$
$104$	3.15542	0.309415
$105$	3.95354	0.385826
$106$	−6.70527	−0.651273
$107$	5.88089	0.568527	0.284264	−	0.958746i	$-0.408251\pi$
$107$	5.88089	0.568527	0.284264	+	0.958746i	$0.408251\pi$
$108$	1.00000	0.0962250
$109$	−13.7235	−1.31447	−0.657235	−	0.753686i	$-0.728274\pi$
$109$	−13.7235	−1.31447	−0.657235	+	0.753686i	$0.728274\pi$
$110$	15.4964	1.47752
$111$	−5.79814	−0.550335
$112$	1.00000	0.0944911
$113$	−9.27235	−0.872270	−0.436135	−	0.899881i	$-0.643653\pi$
$113$	−9.27235	−0.872270	−0.436135	+	0.899881i	$0.643653\pi$
$114$	−5.15151	−0.482483
$115$	−11.0371	−1.02922
$116$	−5.61490	−0.521331
$117$	3.15542	0.291719
$118$	5.03957	0.463930
$119$	−0.274165	−0.0251327
$120$	3.95354	0.360907
$121$	4.36343	0.396675
$122$	7.96315	0.720950
$123$	2.13961	0.192923
$124$	1.34159	0.120478
$125$	22.2604	1.99103
$126$	1.00000	0.0890871
$127$	−12.0134	−1.06601	−0.533007	−	0.846111i	$-0.678938\pi$
$127$	−12.0134	−1.06601	−0.533007	+	0.846111i	$0.678938\pi$
$128$	1.00000	0.0883883
$129$	10.5562	0.929422
$130$	12.4751	1.09414
$131$	5.34134	0.466675	0.233338	−	0.972396i	$-0.425035\pi$
$131$	5.34134	0.466675	0.233338	+	0.972396i	$0.425035\pi$
$132$	3.91962	0.341159
$133$	−5.15151	−0.446693
$134$	0.669240	0.0578135
$135$	3.95354	0.340267
$136$	−0.274165	−0.0235094
$137$	−9.76686	−0.834439	−0.417219	−	0.908806i	$-0.636995\pi$
$137$	−9.76686	−0.834439	−0.417219	+	0.908806i	$0.636995\pi$
$138$	−2.79170	−0.237646
$139$	−10.3135	−0.874781	−0.437391	−	0.899272i	$-0.644097\pi$
$139$	−10.3135	−0.874781	−0.437391	+	0.899272i	$0.644097\pi$
$140$	3.95354	0.334135
$141$	−12.7718	−1.07558
$142$	5.21776	0.437865
$143$	12.3681	1.03427
$144$	1.00000	0.0833333
$145$	−22.1988	−1.84351
$146$	−12.7861	−1.05818
$147$	1.00000	0.0824786
$148$	−5.79814	−0.476604
$149$	0.618408	0.0506619	0.0253310	−	0.999679i	$-0.491936\pi$
$149$	0.618408	0.0506619	0.0253310	+	0.999679i	$0.491936\pi$
$150$	10.6305	0.867976
$151$	−15.2552	−1.24145	−0.620723	−	0.784030i	$-0.713161\pi$
$151$	−15.2552	−1.24145	−0.620723	+	0.784030i	$0.713161\pi$
$152$	−5.15151	−0.417843
$153$	−0.274165	−0.0221649
$154$	3.91962	0.315852
$155$	5.30403	0.426030
$156$	3.15542	0.252636
$157$	−21.3351	−1.70273	−0.851365	−	0.524575i	$-0.824224\pi$
$157$	−21.3351	−1.70273	−0.851365	+	0.524575i	$0.824224\pi$
$158$	−3.58567	−0.285261
$159$	−6.70527	−0.531762
$160$	3.95354	0.312555
$161$	−2.79170	−0.220017
$162$	1.00000	0.0785674
$163$	16.5167	1.29369	0.646844	−	0.762622i	$-0.276088\pi$
$163$	16.5167	1.29369	0.646844	+	0.762622i	$0.276088\pi$
$164$	2.13961	0.167076
$165$	15.4964	1.20639
$166$	5.76683	0.447593
$167$	−5.85226	−0.452862	−0.226431	−	0.974027i	$-0.572706\pi$
$167$	−5.85226	−0.452862	−0.226431	+	0.974027i	$0.572706\pi$
$168$	1.00000	0.0771517
$169$	−3.04331	−0.234101
$170$	−1.08392	−0.0831330
$171$	−5.15151	−0.393946
$172$	10.5562	0.804903
$173$	10.2434	0.778794	0.389397	−	0.921070i	$-0.372683\pi$
$173$	10.2434	0.778794	0.389397	+	0.921070i	$0.372683\pi$
$174$	−5.61490	−0.425665
$175$	10.6305	0.803590
$176$	3.91962	0.295453
$177$	5.03957	0.378797
$178$	−5.53790	−0.415083
$179$	2.67877	0.200221	0.100110	−	0.994976i	$-0.468080\pi$
$179$	2.67877	0.200221	0.100110	+	0.994976i	$0.468080\pi$
$180$	3.95354	0.294680
$181$	−3.76536	−0.279877	−0.139939	−	0.990160i	$-0.544691\pi$
$181$	−3.76536	−0.279877	−0.139939	+	0.990160i	$0.544691\pi$
$182$	3.15542	0.233895
$183$	7.96315	0.588653
$184$	−2.79170	−0.205807
$185$	−22.9232	−1.68535
$186$	1.34159	0.0983702
$187$	−1.07462	−0.0785842
$188$	−12.7718	−0.931478
$189$	1.00000	0.0727393
$190$	−20.3667	−1.47756
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	20.4545	1.47235	0.736174	−	0.676793i	$-0.236631\pi$
$193$	20.4545	1.47235	0.736174	+	0.676793i	$0.236631\pi$
$194$	15.7303	1.12937
$195$	12.4751	0.893360
$196$	1.00000	0.0714286
$197$	−3.33188	−0.237387	−0.118693	−	0.992931i	$-0.537871\pi$
$197$	−3.33188	−0.237387	−0.118693	+	0.992931i	$0.537871\pi$
$198$	3.91962	0.278555
$199$	14.3010	1.01377	0.506885	−	0.862014i	$-0.330797\pi$
$199$	14.3010	1.01377	0.506885	+	0.862014i	$0.330797\pi$
$200$	10.6305	0.751689
$201$	0.669240	0.0472045
$202$	1.75182	0.123258
$203$	−5.61490	−0.394089
$204$	−0.274165	−0.0191954
$205$	8.45906	0.590806
$206$	−5.30803	−0.369828
$207$	−2.79170	−0.194037
$208$	3.15542	0.218789
$209$	−20.1920	−1.39671
$210$	3.95354	0.272820
$211$	6.34162	0.436575	0.218288	−	0.975884i	$-0.429953\pi$
$211$	6.34162	0.436575	0.218288	+	0.975884i	$0.429953\pi$
$212$	−6.70527	−0.460520
$213$	5.21776	0.357515
$214$	5.88089	0.402009
$215$	41.7344	2.84626
$216$	1.00000	0.0680414
$217$	1.34159	0.0910731
$218$	−13.7235	−0.929471
$219$	−12.7861	−0.864004
$220$	15.4964	1.04477
$221$	−0.865106	−0.0581933
$222$	−5.79814	−0.389146
$223$	8.25256	0.552632	0.276316	−	0.961067i	$-0.410886\pi$
$223$	8.25256	0.552632	0.276316	+	0.961067i	$0.410886\pi$
$224$	1.00000	0.0668153
$225$	10.6305	0.708699
$226$	−9.27235	−0.616788
$227$	−6.73922	−0.447298	−0.223649	−	0.974670i	$-0.571797\pi$
$227$	−6.73922	−0.447298	−0.223649	+	0.974670i	$0.571797\pi$
$228$	−5.15151	−0.341167
$229$	−22.1982	−1.46690	−0.733448	−	0.679746i	$-0.762090\pi$
$229$	−22.1982	−1.46690	−0.733448	+	0.679746i	$0.762090\pi$
$230$	−11.0371	−0.727766
$231$	3.91962	0.257892
$232$	−5.61490	−0.368637
$233$	−1.92106	−0.125853	−0.0629265	−	0.998018i	$-0.520043\pi$
$233$	−1.92106	−0.125853	−0.0629265	+	0.998018i	$0.520043\pi$
$234$	3.15542	0.206276
$235$	−50.4938	−3.29385
$236$	5.03957	0.328048
$237$	−3.58567	−0.232914
$238$	−0.274165	−0.0177715
$239$	8.78042	0.567958	0.283979	−	0.958830i	$-0.408345\pi$
$239$	8.78042	0.567958	0.283979	+	0.958830i	$0.408345\pi$
$240$	3.95354	0.255200
$241$	−1.55607	−0.100235	−0.0501176	−	0.998743i	$-0.515960\pi$
$241$	−1.55607	−0.100235	−0.0501176	+	0.998743i	$0.515960\pi$
$242$	4.36343	0.280492
$243$	1.00000	0.0641500
$244$	7.96315	0.509789
$245$	3.95354	0.252583
$246$	2.13961	0.136417
$247$	−16.2552	−1.03429
$248$	1.34159	0.0851911
$249$	5.76683	0.365458
$250$	22.2604	1.40787
$251$	10.1812	0.642634	0.321317	−	0.946972i	$-0.395875\pi$
$251$	10.1812	0.642634	0.321317	+	0.946972i	$0.395875\pi$
$252$	1.00000	0.0629941
$253$	−10.9424	−0.687944
$254$	−12.0134	−0.753786
$255$	−1.08392	−0.0678778
$256$	1.00000	0.0625000
$257$	3.30493	0.206156	0.103078	−	0.994673i	$-0.467131\pi$
$257$	3.30493	0.206156	0.103078	+	0.994673i	$0.467131\pi$
$258$	10.5562	0.657200
$259$	−5.79814	−0.360279
$260$	12.4751	0.773672
$261$	−5.61490	−0.347554
$262$	5.34134	0.329989
$263$	−10.7404	−0.662282	−0.331141	−	0.943581i	$-0.607434\pi$
$263$	−10.7404	−0.662282	−0.331141	+	0.943581i	$0.607434\pi$
$264$	3.91962	0.241236
$265$	−26.5096	−1.62847
$266$	−5.15151	−0.315859
$267$	−5.53790	−0.338914
$268$	0.669240	0.0408803
$269$	−25.5816	−1.55974	−0.779868	−	0.625943i	$-0.784714\pi$
$269$	−25.5816	−1.55974	−0.779868	+	0.625943i	$0.784714\pi$
$270$	3.95354	0.240605
$271$	−19.3801	−1.17726	−0.588628	−	0.808404i	$-0.700332\pi$
$271$	−19.3801	−1.17726	−0.588628	+	0.808404i	$0.700332\pi$
$272$	−0.274165	−0.0166237
$273$	3.15542	0.190975
$274$	−9.76686	−0.590037
$275$	41.6675	2.51264
$276$	−2.79170	−0.168041
$277$	6.68607	0.401727	0.200863	−	0.979619i	$-0.435625\pi$
$277$	6.68607	0.401727	0.200863	+	0.979619i	$0.435625\pi$
$278$	−10.3135	−0.618564
$279$	1.34159	0.0803189
$280$	3.95354	0.236269
$281$	16.9696	1.01232	0.506162	−	0.862439i	$-0.331064\pi$
$281$	16.9696	1.01232	0.506162	+	0.862439i	$0.331064\pi$
$282$	−12.7718	−0.760549
$283$	26.7828	1.59207	0.796036	−	0.605249i	$-0.206926\pi$
$283$	26.7828	1.59207	0.796036	+	0.605249i	$0.206926\pi$
$284$	5.21776	0.309617
$285$	−20.3667	−1.20642
$286$	12.3681	0.731339
$287$	2.13961	0.126297
$288$	1.00000	0.0589256
$289$	−16.9248	−0.995578
$290$	−22.1988	−1.30356
$291$	15.7303	0.922129
$292$	−12.7861	−0.748249
$293$	−14.6160	−0.853875	−0.426937	−	0.904281i	$-0.640407\pi$
$293$	−14.6160	−0.853875	−0.426937	+	0.904281i	$0.640407\pi$
$294$	1.00000	0.0583212
$295$	19.9242	1.16003
$296$	−5.79814	−0.337010
$297$	3.91962	0.227439
$298$	0.618408	0.0358234
$299$	−8.80900	−0.509438
$300$	10.6305	0.613752
$301$	10.5562	0.608449
$302$	−15.2552	−0.877836
$303$	1.75182	0.100640
$304$	−5.15151	−0.295460
$305$	31.4827	1.80269
$306$	−0.274165	−0.0156730
$307$	18.3068	1.04483	0.522413	−	0.852693i	$-0.325032\pi$
$307$	18.3068	1.04483	0.522413	+	0.852693i	$0.325032\pi$
$308$	3.91962	0.223341
$309$	−5.30803	−0.301964
$310$	5.30403	0.301249
$311$	−8.70439	−0.493580	−0.246790	−	0.969069i	$-0.579376\pi$
$311$	−8.70439	−0.493580	−0.246790	+	0.969069i	$0.579376\pi$
$312$	3.15542	0.178641
$313$	−8.15648	−0.461031	−0.230516	−	0.973069i	$-0.574041\pi$
$313$	−8.15648	−0.461031	−0.230516	+	0.973069i	$0.574041\pi$
$314$	−21.3351	−1.20401
$315$	3.95354	0.222757
$316$	−3.58567	−0.201710
$317$	11.4249	0.641687	0.320843	−	0.947132i	$-0.396034\pi$
$317$	11.4249	0.641687	0.320843	+	0.947132i	$0.396034\pi$
$318$	−6.70527	−0.376013
$319$	−22.0083	−1.23223
$320$	3.95354	0.221010
$321$	5.88089	0.328239
$322$	−2.79170	−0.155576
$323$	1.41236	0.0785860
$324$	1.00000	0.0555556
$325$	33.5437	1.86067
$326$	16.5167	0.914776
$327$	−13.7235	−0.758910
$328$	2.13961	0.118140
$329$	−12.7718	−0.704131
$330$	15.4964	0.853048
$331$	17.6193	0.968445	0.484223	−	0.874945i	$-0.339102\pi$
$331$	17.6193	0.968445	0.484223	+	0.874945i	$0.339102\pi$
$332$	5.76683	0.316496
$333$	−5.79814	−0.317736
$334$	−5.85226	−0.320222
$335$	2.64587	0.144559
$336$	1.00000	0.0545545
$337$	19.7123	1.07380	0.536899	−	0.843647i	$-0.319596\pi$
$337$	19.7123	1.07380	0.536899	+	0.843647i	$0.319596\pi$
$338$	−3.04331	−0.165534
$339$	−9.27235	−0.503605
$340$	−1.08392	−0.0587839
$341$	5.25853	0.284765
$342$	−5.15151	−0.278562
$343$	1.00000	0.0539949
$344$	10.5562	0.569152
$345$	−11.0371	−0.594219
$346$	10.2434	0.550690
$347$	8.82409	0.473702	0.236851	−	0.971546i	$-0.423885\pi$
$347$	8.82409	0.473702	0.236851	+	0.971546i	$0.423885\pi$
$348$	−5.61490	−0.300991
$349$	−35.4020	−1.89502	−0.947512	−	0.319719i	$-0.896412\pi$
$349$	−35.4020	−1.89502	−0.947512	+	0.319719i	$0.896412\pi$
$350$	10.6305	0.568224
$351$	3.15542	0.168424
$352$	3.91962	0.208917
$353$	28.7971	1.53271	0.766357	−	0.642415i	$-0.222067\pi$
$353$	28.7971	1.53271	0.766357	+	0.642415i	$0.222067\pi$
$354$	5.03957	0.267850
$355$	20.6286	1.09485
$356$	−5.53790	−0.293508
$357$	−0.274165	−0.0145103
$358$	2.67877	0.141577
$359$	−7.92516	−0.418274	−0.209137	−	0.977886i	$-0.567065\pi$
$359$	−7.92516	−0.418274	−0.209137	+	0.977886i	$0.567065\pi$
$360$	3.95354	0.208370
$361$	7.53808	0.396741
$362$	−3.76536	−0.197903
$363$	4.36343	0.229021
$364$	3.15542	0.165389
$365$	−50.5503	−2.64593
$366$	7.96315	0.416241
$367$	25.3613	1.32385	0.661925	−	0.749570i	$-0.269740\pi$
$367$	25.3613	1.32385	0.661925	+	0.749570i	$0.269740\pi$
$368$	−2.79170	−0.145528
$369$	2.13961	0.111384
$370$	−22.9232	−1.19172
$371$	−6.70527	−0.348120
$372$	1.34159	0.0695582
$373$	−31.5841	−1.63536	−0.817681	−	0.575672i	$-0.804740\pi$
$373$	−31.5841	−1.63536	−0.817681	+	0.575672i	$0.804740\pi$
$374$	−1.07462	−0.0555674
$375$	22.2604	1.14952
$376$	−12.7718	−0.658654
$377$	−17.7174	−0.912492
$378$	1.00000	0.0514344
$379$	21.8729	1.12353	0.561767	−	0.827296i	$-0.310122\pi$
$379$	21.8729	1.12353	0.561767	+	0.827296i	$0.310122\pi$
$380$	−20.3667	−1.04479
$381$	−12.0134	−0.615463
$382$	−1.00000	−0.0511645
$383$	−31.5775	−1.61353	−0.806767	−	0.590870i	$-0.798785\pi$
$383$	−31.5775	−1.61353	−0.806767	+	0.590870i	$0.798785\pi$
$384$	1.00000	0.0510310
$385$	15.4964	0.789769
$386$	20.4545	1.04111
$387$	10.5562	0.536602
$388$	15.7303	0.798587
$389$	15.1202	0.766627	0.383313	−	0.923618i	$-0.374783\pi$
$389$	15.1202	0.766627	0.383313	+	0.923618i	$0.374783\pi$
$390$	12.4751	0.631701
$391$	0.765387	0.0387073
$392$	1.00000	0.0505076
$393$	5.34134	0.269435
$394$	−3.33188	−0.167858
$395$	−14.1761	−0.713277
$396$	3.91962	0.196968
$397$	−24.5576	−1.23251	−0.616254	−	0.787547i	$-0.711351\pi$
$397$	−24.5576	−1.23251	−0.616254	+	0.787547i	$0.711351\pi$
$398$	14.3010	0.716843
$399$	−5.15151	−0.257898
$400$	10.6305	0.531525
$401$	3.22951	0.161274	0.0806369	−	0.996744i	$-0.474305\pi$
$401$	3.22951	0.161274	0.0806369	+	0.996744i	$0.474305\pi$
$402$	0.669240	0.0333786
$403$	4.23328	0.210875
$404$	1.75182	0.0871564
$405$	3.95354	0.196453
$406$	−5.61490	−0.278663
$407$	−22.7265	−1.12651
$408$	−0.274165	−0.0135732
$409$	−13.9743	−0.690982	−0.345491	−	0.938422i	$-0.612288\pi$
$409$	−13.9743	−0.690982	−0.345491	+	0.938422i	$0.612288\pi$
$410$	8.45906	0.417763
$411$	−9.76686	−0.481764
$412$	−5.30803	−0.261508
$413$	5.03957	0.247981
$414$	−2.79170	−0.137205
$415$	22.7994	1.11918
$416$	3.15542	0.154707
$417$	−10.3135	−0.505055
$418$	−20.1920	−0.987622
$419$	21.9407	1.07187	0.535937	−	0.844258i	$-0.319958\pi$
$419$	21.9407	1.07187	0.535937	+	0.844258i	$0.319958\pi$
$420$	3.95354	0.192913
$421$	27.1875	1.32504	0.662518	−	0.749046i	$-0.269488\pi$
$421$	27.1875	1.32504	0.662518	+	0.749046i	$0.269488\pi$
$422$	6.34162	0.308705
$423$	−12.7718	−0.620985
$424$	−6.70527	−0.325637
$425$	−2.91451	−0.141374
$426$	5.21776	0.252801
$427$	7.96315	0.385364
$428$	5.88089	0.284264
$429$	12.3681	0.597135
$430$	41.7344	2.01261
$431$	−29.4575	−1.41892	−0.709460	−	0.704746i	$-0.751061\pi$
$431$	−29.4575	−1.41892	−0.709460	+	0.704746i	$0.751061\pi$
$432$	1.00000	0.0481125
$433$	34.5087	1.65838	0.829192	−	0.558964i	$-0.188801\pi$
$433$	34.5087	1.65838	0.829192	+	0.558964i	$0.188801\pi$
$434$	1.34159	0.0643984
$435$	−22.1988	−1.06435
$436$	−13.7235	−0.657235
$437$	14.3815	0.687960
$438$	−12.7861	−0.610943
$439$	23.2282	1.10862	0.554310	−	0.832311i	$-0.312982\pi$
$439$	23.2282	1.10862	0.554310	+	0.832311i	$0.312982\pi$
$440$	15.4964	0.738761
$441$	1.00000	0.0476190
$442$	−0.865106	−0.0411489
$443$	21.7951	1.03552	0.517759	−	0.855526i	$-0.326766\pi$
$443$	21.7951	1.03552	0.517759	+	0.855526i	$0.326766\pi$
$444$	−5.79814	−0.275167
$445$	−21.8943	−1.03789
$446$	8.25256	0.390770
$447$	0.618408	0.0292497
$448$	1.00000	0.0472456
$449$	−16.6407	−0.785324	−0.392662	−	0.919683i	$-0.628446\pi$
$449$	−16.6407	−0.785324	−0.392662	+	0.919683i	$0.628446\pi$
$450$	10.6305	0.501126
$451$	8.38648	0.394904
$452$	−9.27235	−0.436135
$453$	−15.2552	−0.716750
$454$	−6.73922	−0.316287
$455$	12.4751	0.584841
$456$	−5.15151	−0.241242
$457$	14.5234	0.679377	0.339688	−	0.940538i	$-0.389678\pi$
$457$	14.5234	0.679377	0.339688	+	0.940538i	$0.389678\pi$
$458$	−22.1982	−1.03725
$459$	−0.274165	−0.0127969
$460$	−11.0371	−0.514608
$461$	7.51767	0.350133	0.175067	−	0.984557i	$-0.443986\pi$
$461$	7.51767	0.350133	0.175067	+	0.984557i	$0.443986\pi$
$462$	3.91962	0.182357
$463$	12.3728	0.575011	0.287505	−	0.957779i	$-0.407174\pi$
$463$	12.3728	0.575011	0.287505	+	0.957779i	$0.407174\pi$
$464$	−5.61490	−0.260665
$465$	5.30403	0.245969
$466$	−1.92106	−0.0889916
$467$	26.2456	1.21450	0.607251	−	0.794510i	$-0.292272\pi$
$467$	26.2456	1.21450	0.607251	+	0.794510i	$0.292272\pi$
$468$	3.15542	0.145859
$469$	0.669240	0.0309026
$470$	−50.4938	−2.32910
$471$	−21.3351	−0.983071
$472$	5.03957	0.231965
$473$	41.3763	1.90248
$474$	−3.58567	−0.164695
$475$	−54.7631	−2.51270
$476$	−0.274165	−0.0125663
$477$	−6.70527	−0.307013
$478$	8.78042	0.401607
$479$	15.5913	0.712386	0.356193	−	0.934412i	$-0.384075\pi$
$479$	15.5913	0.712386	0.356193	+	0.934412i	$0.384075\pi$
$480$	3.95354	0.180454
$481$	−18.2956	−0.834206
$482$	−1.55607	−0.0708770
$483$	−2.79170	−0.127027
$484$	4.36343	0.198338
$485$	62.1906	2.82393
$486$	1.00000	0.0453609
$487$	−5.78894	−0.262322	−0.131161	−	0.991361i	$-0.541870\pi$
$487$	−5.78894	−0.262322	−0.131161	+	0.991361i	$0.541870\pi$
$488$	7.96315	0.360475
$489$	16.5167	0.746911
$490$	3.95354	0.178603
$491$	−23.7644	−1.07247	−0.536237	−	0.844068i	$-0.680155\pi$
$491$	−23.7644	−1.07247	−0.536237	+	0.844068i	$0.680155\pi$
$492$	2.13961	0.0964613
$493$	1.53941	0.0693315
$494$	−16.2552	−0.731356
$495$	15.4964	0.696511
$496$	1.34159	0.0602392
$497$	5.21776	0.234048
$498$	5.76683	0.258418
$499$	−26.4004	−1.18185	−0.590923	−	0.806728i	$-0.701236\pi$
$499$	−26.4004	−1.18185	−0.590923	+	0.806728i	$0.701236\pi$
$500$	22.2604	0.995515
$501$	−5.85226	−0.261460
$502$	10.1812	0.454411
$503$	23.7807	1.06033	0.530163	−	0.847895i	$-0.322131\pi$
$503$	23.7807	1.06033	0.530163	+	0.847895i	$0.322131\pi$
$504$	1.00000	0.0445435
$505$	6.92590	0.308199
$506$	−10.9424	−0.486450
$507$	−3.04331	−0.135158
$508$	−12.0134	−0.533007
$509$	33.9199	1.50347	0.751736	−	0.659464i	$-0.229217\pi$
$509$	33.9199	1.50347	0.751736	+	0.659464i	$0.229217\pi$
$510$	−1.08392	−0.0479969
$511$	−12.7861	−0.565623
$512$	1.00000	0.0441942
$513$	−5.15151	−0.227445
$514$	3.30493	0.145774
$515$	−20.9855	−0.924733
$516$	10.5562	0.464711
$517$	−50.0605	−2.20166
$518$	−5.79814	−0.254756
$519$	10.2434	0.449637
$520$	12.4751	0.547069
$521$	42.5078	1.86230	0.931150	−	0.364637i	$-0.118807\pi$
$521$	42.5078	1.86230	0.931150	+	0.364637i	$0.118807\pi$
$522$	−5.61490	−0.245758
$523$	−24.8596	−1.08703	−0.543516	−	0.839399i	$-0.682907\pi$
$523$	−24.8596	−1.08703	−0.543516	+	0.839399i	$0.682907\pi$
$524$	5.34134	0.233338
$525$	10.6305	0.463953
$526$	−10.7404	−0.468304
$527$	−0.367817	−0.0160224
$528$	3.91962	0.170580
$529$	−15.2064	−0.661147
$530$	−26.5096	−1.15150
$531$	5.03957	0.218699
$532$	−5.15151	−0.223346
$533$	6.75139	0.292435
$534$	−5.53790	−0.239648
$535$	23.2503	1.00520
$536$	0.669240	0.0289068
$537$	2.67877	0.115597
$538$	−25.5816	−1.10290
$539$	3.91962	0.168830
$540$	3.95354	0.170133
$541$	7.01385	0.301549	0.150774	−	0.988568i	$-0.451823\pi$
$541$	7.01385	0.301549	0.150774	+	0.988568i	$0.451823\pi$
$542$	−19.3801	−0.832445
$543$	−3.76536	−0.161587
$544$	−0.274165	−0.0117547
$545$	−54.2563	−2.32409
$546$	3.15542	0.135040
$547$	39.7448	1.69937	0.849683	−	0.527293i	$-0.176793\pi$
$547$	39.7448	1.69937	0.849683	+	0.527293i	$0.176793\pi$
$548$	−9.76686	−0.417219
$549$	7.96315	0.339859
$550$	41.6675	1.77671
$551$	28.9253	1.23226
$552$	−2.79170	−0.118823
$553$	−3.58567	−0.152478
$554$	6.68607	0.284064
$555$	−22.9232	−0.973035
$556$	−10.3135	−0.437391
$557$	−24.1592	−1.02366	−0.511829	−	0.859087i	$-0.671032\pi$
$557$	−24.1592	−1.02366	−0.511829	+	0.859087i	$0.671032\pi$
$558$	1.34159	0.0567941
$559$	33.3093	1.40883
$560$	3.95354	0.167068
$561$	−1.07462	−0.0453706
$562$	16.9696	0.715821
$563$	−15.9743	−0.673237	−0.336618	−	0.941641i	$-0.609283\pi$
$563$	−15.9743	−0.673237	−0.336618	+	0.941641i	$0.609283\pi$
$564$	−12.7718	−0.537789
$565$	−36.6586	−1.54224
$566$	26.7828	1.12577
$567$	1.00000	0.0419961
$568$	5.21776	0.218932
$569$	−42.3700	−1.77624	−0.888122	−	0.459609i	$-0.847990\pi$
$569$	−42.3700	−1.77624	−0.888122	+	0.459609i	$0.847990\pi$
$570$	−20.3667	−0.853068
$571$	−21.2612	−0.889751	−0.444876	−	0.895592i	$-0.646752\pi$
$571$	−21.2612	−0.889751	−0.444876	+	0.895592i	$0.646752\pi$
$572$	12.3681	0.517134
$573$	−1.00000	−0.0417756
$574$	2.13961	0.0893058
$575$	−29.6772	−1.23762
$576$	1.00000	0.0416667
$577$	15.2975	0.636845	0.318422	−	0.947949i	$-0.396847\pi$
$577$	15.2975	0.636845	0.318422	+	0.947949i	$0.396847\pi$
$578$	−16.9248	−0.703980
$579$	20.4545	0.850060
$580$	−22.1988	−0.921753
$581$	5.76683	0.239248
$582$	15.7303	0.652044
$583$	−26.2821	−1.08849
$584$	−12.7861	−0.529092
$585$	12.4751	0.515782
$586$	−14.6160	−0.603780
$587$	−36.3820	−1.50165	−0.750824	−	0.660503i	$-0.770343\pi$
$587$	−36.3820	−1.50165	−0.750824	+	0.660503i	$0.770343\pi$
$588$	1.00000	0.0412393
$589$	−6.91122	−0.284772
$590$	19.9242	0.820264
$591$	−3.33188	−0.137055
$592$	−5.79814	−0.238302
$593$	−19.7015	−0.809044	−0.404522	−	0.914528i	$-0.632562\pi$
$593$	−19.7015	−0.809044	−0.404522	+	0.914528i	$0.632562\pi$
$594$	3.91962	0.160824
$595$	−1.08392	−0.0444365
$596$	0.618408	0.0253310
$597$	14.3010	0.585300
$598$	−8.80900	−0.360227
$599$	−21.0845	−0.861490	−0.430745	−	0.902474i	$-0.641749\pi$
$599$	−21.0845	−0.861490	−0.430745	+	0.902474i	$0.641749\pi$
$600$	10.6305	0.433988
$601$	6.43914	0.262658	0.131329	−	0.991339i	$-0.458076\pi$
$601$	6.43914	0.262658	0.131329	+	0.991339i	$0.458076\pi$
$602$	10.5562	0.430239
$603$	0.669240	0.0272536
$604$	−15.2552	−0.620723
$605$	17.2510	0.701353
$606$	1.75182	0.0711629
$607$	20.2010	0.819932	0.409966	−	0.912101i	$-0.365541\pi$
$607$	20.2010	0.819932	0.409966	+	0.912101i	$0.365541\pi$
$608$	−5.15151	−0.208921
$609$	−5.61490	−0.227527
$610$	31.4827	1.27470
$611$	−40.3004	−1.63038
$612$	−0.274165	−0.0110825
$613$	33.8164	1.36583	0.682916	−	0.730497i	$-0.260712\pi$
$613$	33.8164	1.36583	0.682916	+	0.730497i	$0.260712\pi$
$614$	18.3068	0.738803
$615$	8.45906	0.341102
$616$	3.91962	0.157926
$617$	8.23404	0.331490	0.165745	−	0.986169i	$-0.446997\pi$
$617$	8.23404	0.331490	0.165745	+	0.986169i	$0.446997\pi$
$618$	−5.30803	−0.213520
$619$	−23.2635	−0.935040	−0.467520	−	0.883983i	$-0.654852\pi$
$619$	−23.2635	−0.935040	−0.467520	+	0.883983i	$0.654852\pi$
$620$	5.30403	0.213015
$621$	−2.79170	−0.112027
$622$	−8.70439	−0.349014
$623$	−5.53790	−0.221871
$624$	3.15542	0.126318
$625$	34.8549	1.39420
$626$	−8.15648	−0.325998
$627$	−20.1920	−0.806390
$628$	−21.3351	−0.851365
$629$	1.58965	0.0633833
$630$	3.95354	0.157513
$631$	−3.48657	−0.138798	−0.0693990	−	0.997589i	$-0.522108\pi$
$631$	−3.48657	−0.138798	−0.0693990	+	0.997589i	$0.522108\pi$
$632$	−3.58567	−0.142630
$633$	6.34162	0.252057
$634$	11.4249	0.453741
$635$	−47.4953	−1.88480
$636$	−6.70527	−0.265881
$637$	3.15542	0.125022
$638$	−22.0083	−0.871317
$639$	5.21776	0.206411
$640$	3.95354	0.156277
$641$	26.9629	1.06497	0.532485	−	0.846439i	$-0.321258\pi$
$641$	26.9629	1.06497	0.532485	+	0.846439i	$0.321258\pi$
$642$	5.88089	0.232100
$643$	−30.4570	−1.20111	−0.600554	−	0.799584i	$-0.705053\pi$
$643$	−30.4570	−1.20111	−0.600554	+	0.799584i	$0.705053\pi$
$644$	−2.79170	−0.110009
$645$	41.7344	1.64329
$646$	1.41236	0.0555687
$647$	−15.7981	−0.621086	−0.310543	−	0.950559i	$-0.600511\pi$
$647$	−15.7981	−0.621086	−0.310543	+	0.950559i	$0.600511\pi$
$648$	1.00000	0.0392837
$649$	19.7532	0.775381
$650$	33.5437	1.31569
$651$	1.34159	0.0525811
$652$	16.5167	0.646844
$653$	−26.1704	−1.02413	−0.512064	−	0.858947i	$-0.671119\pi$
$653$	−26.1704	−1.02413	−0.512064	+	0.858947i	$0.671119\pi$
$654$	−13.7235	−0.536630
$655$	21.1172	0.825118
$656$	2.13961	0.0835379
$657$	−12.7861	−0.498833
$658$	−12.7718	−0.497896
$659$	17.1067	0.666383	0.333192	−	0.942859i	$-0.391874\pi$
$659$	17.1067	0.666383	0.333192	+	0.942859i	$0.391874\pi$
$660$	15.4964	0.603196
$661$	1.53826	0.0598316	0.0299158	−	0.999552i	$-0.490476\pi$
$661$	1.53826	0.0598316	0.0299158	+	0.999552i	$0.490476\pi$
$662$	17.6193	0.684794
$663$	−0.865106	−0.0335979
$664$	5.76683	0.223796
$665$	−20.3667	−0.789787
$666$	−5.79814	−0.224673
$667$	15.6752	0.606944
$668$	−5.85226	−0.226431
$669$	8.25256	0.319062
$670$	2.64587	0.102219
$671$	31.2125	1.20495
$672$	1.00000	0.0385758
$673$	−31.1110	−1.19924	−0.599620	−	0.800285i	$-0.704682\pi$
$673$	−31.1110	−1.19924	−0.599620	+	0.800285i	$0.704682\pi$
$674$	19.7123	0.759290
$675$	10.6305	0.409168
$676$	−3.04331	−0.117051
$677$	7.28085	0.279826	0.139913	−	0.990164i	$-0.455318\pi$
$677$	7.28085	0.279826	0.139913	+	0.990164i	$0.455318\pi$
$678$	−9.27235	−0.356103
$679$	15.7303	0.603675
$680$	−1.08392	−0.0415665
$681$	−6.73922	−0.258247
$682$	5.25853	0.201359
$683$	24.0448	0.920048	0.460024	−	0.887906i	$-0.347841\pi$
$683$	24.0448	0.920048	0.460024	+	0.887906i	$0.347841\pi$
$684$	−5.15151	−0.196973
$685$	−38.6137	−1.47535
$686$	1.00000	0.0381802
$687$	−22.1982	−0.846912
$688$	10.5562	0.402451
$689$	−21.1579	−0.806054
$690$	−11.0371	−0.420176
$691$	−15.0895	−0.574031	−0.287016	−	0.957926i	$-0.592663\pi$
$691$	−15.0895	−0.574031	−0.287016	+	0.957926i	$0.592663\pi$
$692$	10.2434	0.389397
$693$	3.91962	0.148894
$694$	8.82409	0.334958
$695$	−40.7749	−1.54668
$696$	−5.61490	−0.212832
$697$	−0.586607	−0.0222193
$698$	−35.4020	−1.33998
$699$	−1.92106	−0.0726613
$700$	10.6305	0.401795
$701$	−4.94251	−0.186676	−0.0933381	−	0.995634i	$-0.529754\pi$
$701$	−4.94251	−0.186676	−0.0933381	+	0.995634i	$0.529754\pi$
$702$	3.15542	0.119094
$703$	29.8692	1.12654
$704$	3.91962	0.147726
$705$	−50.4938	−1.90171
$706$	28.7971	1.08379
$707$	1.75182	0.0658841
$708$	5.03957	0.189399
$709$	44.8108	1.68290	0.841452	−	0.540332i	$-0.181701\pi$
$709$	44.8108	1.68290	0.841452	+	0.540332i	$0.181701\pi$
$710$	20.6286	0.774179
$711$	−3.58567	−0.134473
$712$	−5.53790	−0.207542
$713$	−3.74532	−0.140263
$714$	−0.274165	−0.0102604
$715$	48.8976	1.82867
$716$	2.67877	0.100110
$717$	8.78042	0.327911
$718$	−7.92516	−0.295764
$719$	21.5275	0.802839	0.401420	−	0.915894i	$-0.368517\pi$
$719$	21.5275	0.802839	0.401420	+	0.915894i	$0.368517\pi$
$720$	3.95354	0.147340
$721$	−5.30803	−0.197682
$722$	7.53808	0.280538
$723$	−1.55607	−0.0578708
$724$	−3.76536	−0.139939
$725$	−59.6892	−2.21680
$726$	4.36343	0.161942
$727$	−35.4993	−1.31660	−0.658298	−	0.752757i	$-0.728723\pi$
$727$	−35.4993	−1.31660	−0.658298	+	0.752757i	$0.728723\pi$
$728$	3.15542	0.116948
$729$	1.00000	0.0370370
$730$	−50.5503	−1.87095
$731$	−2.89414	−0.107044
$732$	7.96315	0.294327
$733$	−21.6048	−0.797991	−0.398996	−	0.916953i	$-0.630641\pi$
$733$	−21.6048	−0.797991	−0.398996	+	0.916953i	$0.630641\pi$
$734$	25.3613	0.936104
$735$	3.95354	0.145829
$736$	−2.79170	−0.102904
$737$	2.62317	0.0966256
$738$	2.13961	0.0787603
$739$	−15.0122	−0.552234	−0.276117	−	0.961124i	$-0.589048\pi$
$739$	−15.0122	−0.552234	−0.276117	+	0.961124i	$0.589048\pi$
$740$	−22.9232	−0.842673
$741$	−16.2552	−0.597149
$742$	−6.70527	−0.246158
$743$	3.48225	0.127751	0.0638757	−	0.997958i	$-0.479654\pi$
$743$	3.48225	0.127751	0.0638757	+	0.997958i	$0.479654\pi$
$744$	1.34159	0.0491851
$745$	2.44490	0.0895742
$746$	−31.5841	−1.15638
$747$	5.76683	0.210997
$748$	−1.07462	−0.0392921
$749$	5.88089	0.214883
$750$	22.2604	0.812834
$751$	28.5886	1.04321	0.521606	−	0.853186i	$-0.325333\pi$
$751$	28.5886	1.04321	0.521606	+	0.853186i	$0.325333\pi$
$752$	−12.7718	−0.465739
$753$	10.1812	0.371025
$754$	−17.7174	−0.645229
$755$	−60.3119	−2.19497
$756$	1.00000	0.0363696
$757$	−9.34847	−0.339776	−0.169888	−	0.985463i	$-0.554341\pi$
$757$	−9.34847	−0.339776	−0.169888	+	0.985463i	$0.554341\pi$
$758$	21.8729	0.794458
$759$	−10.9424	−0.397185
$760$	−20.3667	−0.738779
$761$	−8.72228	−0.316182	−0.158091	−	0.987425i	$-0.550534\pi$
$761$	−8.72228	−0.316182	−0.158091	+	0.987425i	$0.550534\pi$
$762$	−12.0134	−0.435198
$763$	−13.7235	−0.496823
$764$	−1.00000	−0.0361787
$765$	−1.08392	−0.0391893
$766$	−31.5775	−1.14094
$767$	15.9020	0.574187
$768$	1.00000	0.0360844
$769$	−22.2660	−0.802932	−0.401466	−	0.915874i	$-0.631499\pi$
$769$	−22.2660	−0.802932	−0.401466	+	0.915874i	$0.631499\pi$
$770$	15.4964	0.558451
$771$	3.30493	0.119024
$772$	20.4545	0.736174
$773$	24.6598	0.886953	0.443476	−	0.896286i	$-0.353745\pi$
$773$	24.6598	0.886953	0.443476	+	0.896286i	$0.353745\pi$
$774$	10.5562	0.379435
$775$	14.2618	0.512298
$776$	15.7303	0.564686
$777$	−5.79814	−0.208007
$778$	15.1202	0.542087
$779$	−11.0223	−0.394913
$780$	12.4751	0.446680
$781$	20.4516	0.731817
$782$	0.765387	0.0273702
$783$	−5.61490	−0.200660
$784$	1.00000	0.0357143
$785$	−84.3493	−3.01056
$786$	5.34134	0.190519
$787$	29.5056	1.05176	0.525881	−	0.850558i	$-0.323736\pi$
$787$	29.5056	1.05176	0.525881	+	0.850558i	$0.323736\pi$
$788$	−3.33188	−0.118693
$789$	−10.7404	−0.382369
$790$	−14.1761	−0.504363
$791$	−9.27235	−0.329687
$792$	3.91962	0.139278
$793$	25.1271	0.892290
$794$	−24.5576	−0.871515
$795$	−26.5096	−0.940197
$796$	14.3010	0.506885
$797$	−49.2468	−1.74441	−0.872206	−	0.489139i	$-0.837311\pi$
$797$	−49.2468	−1.74441	−0.872206	+	0.489139i	$0.837311\pi$
$798$	−5.15151	−0.182362
$799$	3.50157	0.123877
$800$	10.6305	0.375845
$801$	−5.53790	−0.195672
$802$	3.22951	0.114038
$803$	−50.1166	−1.76858
$804$	0.669240	0.0236023
$805$	−11.0371	−0.389007
$806$	4.23328	0.149111
$807$	−25.5816	−0.900515
$808$	1.75182	0.0616289
$809$	6.94469	0.244162	0.122081	−	0.992520i	$-0.461043\pi$
$809$	6.94469	0.244162	0.122081	+	0.992520i	$0.461043\pi$
$810$	3.95354	0.138913
$811$	33.3288	1.17033	0.585166	−	0.810913i	$-0.301029\pi$
$811$	33.3288	1.17033	0.585166	+	0.810913i	$0.301029\pi$
$812$	−5.61490	−0.197045
$813$	−19.3801	−0.679689
$814$	−22.7265	−0.796564
$815$	65.2995	2.28734
$816$	−0.274165	−0.00959769
$817$	−54.3804	−1.90253
$818$	−13.9743	−0.488598
$819$	3.15542	0.110259
$820$	8.45906	0.295403
$821$	52.1947	1.82161	0.910804	−	0.412838i	$-0.135463\pi$
$821$	52.1947	1.82161	0.910804	+	0.412838i	$0.135463\pi$
$822$	−9.76686	−0.340658
$823$	9.24937	0.322413	0.161206	−	0.986921i	$-0.448462\pi$
$823$	9.24937	0.322413	0.161206	+	0.986921i	$0.448462\pi$
$824$	−5.30803	−0.184914
$825$	41.6675	1.45068
$826$	5.03957	0.175349
$827$	−7.12833	−0.247876	−0.123938	−	0.992290i	$-0.539552\pi$
$827$	−7.12833	−0.247876	−0.123938	+	0.992290i	$0.539552\pi$
$828$	−2.79170	−0.0970184
$829$	34.2434	1.18932	0.594660	−	0.803977i	$-0.297286\pi$
$829$	34.2434	1.18932	0.594660	+	0.803977i	$0.297286\pi$
$830$	22.7994	0.791379
$831$	6.68607	0.231937
$832$	3.15542	0.109395
$833$	−0.274165	−0.00949925
$834$	−10.3135	−0.357128
$835$	−23.1372	−0.800695
$836$	−20.1920	−0.698354
$837$	1.34159	0.0463722
$838$	21.9407	0.757929
$839$	37.0012	1.27742	0.638711	−	0.769447i	$-0.279468\pi$
$839$	37.0012	1.27742	0.638711	+	0.769447i	$0.279468\pi$
$840$	3.95354	0.136410
$841$	2.52716	0.0871434
$842$	27.1875	0.936942
$843$	16.9696	0.584465
$844$	6.34162	0.218288
$845$	−12.0319	−0.413909
$846$	−12.7718	−0.439103
$847$	4.36343	0.149929
$848$	−6.70527	−0.230260
$849$	26.7828	0.919183
$850$	−2.91451	−0.0999668
$851$	16.1867	0.554873
$852$	5.21776	0.178757
$853$	47.9806	1.64283	0.821413	−	0.570334i	$-0.193186\pi$
$853$	47.9806	1.64283	0.821413	+	0.570334i	$0.193186\pi$
$854$	7.96315	0.272493
$855$	−20.3667	−0.696527
$856$	5.88089	0.201005
$857$	14.1969	0.484957	0.242479	−	0.970157i	$-0.422040\pi$
$857$	14.1969	0.484957	0.242479	+	0.970157i	$0.422040\pi$
$858$	12.3681	0.422239
$859$	−4.09987	−0.139886	−0.0699430	−	0.997551i	$-0.522282\pi$
$859$	−4.09987	−0.139886	−0.0699430	+	0.997551i	$0.522282\pi$
$860$	41.7344	1.42313
$861$	2.13961	0.0729179
$862$	−29.4575	−1.00333
$863$	4.75896	0.161997	0.0809984	−	0.996714i	$-0.474189\pi$
$863$	4.75896	0.161997	0.0809984	+	0.996714i	$0.474189\pi$
$864$	1.00000	0.0340207
$865$	40.4978	1.37697
$866$	34.5087	1.17265
$867$	−16.9248	−0.574797
$868$	1.34159	0.0455365
$869$	−14.0545	−0.476765
$870$	−22.1988	−0.752608
$871$	2.11173	0.0715534
$872$	−13.7235	−0.464735
$873$	15.7303	0.532391
$874$	14.3815	0.486461
$875$	22.2604	0.752538
$876$	−12.7861	−0.432002
$877$	−15.9188	−0.537540	−0.268770	−	0.963204i	$-0.586617\pi$
$877$	−15.9188	−0.537540	−0.268770	+	0.963204i	$0.586617\pi$
$878$	23.2282	0.783912
$879$	−14.6160	−0.492985
$880$	15.4964	0.522383
$881$	−46.9082	−1.58038	−0.790188	−	0.612865i	$-0.790017\pi$
$881$	−46.9082	−1.58038	−0.790188	+	0.612865i	$0.790017\pi$
$882$	1.00000	0.0336718
$883$	24.5051	0.824662	0.412331	−	0.911034i	$-0.364715\pi$
$883$	24.5051	0.824662	0.412331	+	0.911034i	$0.364715\pi$
$884$	−0.865106	−0.0290967
$885$	19.9242	0.669743
$886$	21.7951	0.732222
$887$	0.917316	0.0308005	0.0154002	−	0.999881i	$-0.495098\pi$
$887$	0.917316	0.0308005	0.0154002	+	0.999881i	$0.495098\pi$
$888$	−5.79814	−0.194573
$889$	−12.0134	−0.402915
$890$	−21.8943	−0.733900
$891$	3.91962	0.131312
$892$	8.25256	0.276316
$893$	65.7940	2.20171
$894$	0.618408	0.0206826
$895$	10.5906	0.354005
$896$	1.00000	0.0334077
$897$	−8.80900	−0.294124
$898$	−16.6407	−0.555308
$899$	−7.53290	−0.251236
$900$	10.6305	0.354350
$901$	1.83835	0.0612443
$902$	8.38648	0.279239
$903$	10.5562	0.351288
$904$	−9.27235	−0.308394
$905$	−14.8865	−0.494845
$906$	−15.2552	−0.506819
$907$	22.2827	0.739886	0.369943	−	0.929054i	$-0.379377\pi$
$907$	22.2827	0.739886	0.369943	+	0.929054i	$0.379377\pi$
$908$	−6.73922	−0.223649
$909$	1.75182	0.0581043
$910$	12.4751	0.413545
$911$	18.5570	0.614821	0.307411	−	0.951577i	$-0.400537\pi$
$911$	18.5570	0.614821	0.307411	+	0.951577i	$0.400537\pi$
$912$	−5.15151	−0.170584
$913$	22.6038	0.748076
$914$	14.5234	0.480392
$915$	31.4827	1.04078
$916$	−22.1982	−0.733448
$917$	5.34134	0.176387
$918$	−0.274165	−0.00904879
$919$	50.6530	1.67089	0.835444	−	0.549576i	$-0.185211\pi$
$919$	50.6530	1.67089	0.835444	+	0.549576i	$0.185211\pi$
$920$	−11.0371	−0.363883
$921$	18.3068	0.603230
$922$	7.51767	0.247581
$923$	16.4642	0.541927
$924$	3.91962	0.128946
$925$	−61.6371	−2.02661
$926$	12.3728	0.406594
$927$	−5.30803	−0.174339
$928$	−5.61490	−0.184318
$929$	58.8371	1.93038	0.965192	−	0.261542i	$-0.0842311\pi$
$929$	58.8371	1.93038	0.965192	+	0.261542i	$0.0842311\pi$
$930$	5.30403	0.173926
$931$	−5.15151	−0.168834
$932$	−1.92106	−0.0629265
$933$	−8.70439	−0.284969
$934$	26.2456	0.858783
$935$	−4.24856	−0.138943
$936$	3.15542	0.103138
$937$	3.32845	0.108736	0.0543679	−	0.998521i	$-0.482686\pi$
$937$	3.32845	0.108736	0.0543679	+	0.998521i	$0.482686\pi$
$938$	0.669240	0.0218515
$939$	−8.15648	−0.266177
$940$	−50.4938	−1.64693
$941$	2.01569	0.0657095	0.0328548	−	0.999460i	$-0.489540\pi$
$941$	2.01569	0.0657095	0.0328548	+	0.999460i	$0.489540\pi$
$942$	−21.3351	−0.695136
$943$	−5.97317	−0.194513
$944$	5.03957	0.164024
$945$	3.95354	0.128609
$946$	41.3763	1.34526
$947$	−54.9886	−1.78689	−0.893444	−	0.449174i	$-0.851718\pi$
$947$	−54.9886	−1.78689	−0.893444	+	0.449174i	$0.851718\pi$
$948$	−3.58567	−0.116457
$949$	−40.3455	−1.30967
$950$	−54.7631	−1.77675
$951$	11.4249	0.370478
$952$	−0.274165	−0.00888573
$953$	−56.3324	−1.82479	−0.912393	−	0.409315i	$-0.865768\pi$
$953$	−56.3324	−1.82479	−0.912393	+	0.409315i	$0.865768\pi$
$954$	−6.70527	−0.217091
$955$	−3.95354	−0.127934
$956$	8.78042	0.283979
$957$	−22.0083	−0.711427
$958$	15.5913	0.503733
$959$	−9.76686	−0.315388
$960$	3.95354	0.127600
$961$	−29.2001	−0.941940
$962$	−18.2956	−0.589873
$963$	5.88089	0.189509
$964$	−1.55607	−0.0501176
$965$	80.8677	2.60322
$966$	−2.79170	−0.0898216
$967$	−4.79124	−0.154076	−0.0770379	−	0.997028i	$-0.524546\pi$
$967$	−4.79124	−0.154076	−0.0770379	+	0.997028i	$0.524546\pi$
$968$	4.36343	0.140246
$969$	1.41236	0.0453717
$970$	62.1906	1.99682
$971$	42.6905	1.37000	0.685001	−	0.728542i	$-0.259802\pi$
$971$	42.6905	1.37000	0.685001	+	0.728542i	$0.259802\pi$
$972$	1.00000	0.0320750
$973$	−10.3135	−0.330636
$974$	−5.78894	−0.185490
$975$	33.5437	1.07426
$976$	7.96315	0.254894
$977$	−48.2130	−1.54247	−0.771235	−	0.636550i	$-0.780361\pi$
$977$	−48.2130	−1.54247	−0.771235	+	0.636550i	$0.780361\pi$
$978$	16.5167	0.528146
$979$	−21.7065	−0.693742
$980$	3.95354	0.126291
$981$	−13.7235	−0.438157
$982$	−23.7644	−0.758353
$983$	−25.8728	−0.825214	−0.412607	−	0.910909i	$-0.635382\pi$
$983$	−25.8728	−0.825214	−0.412607	+	0.910909i	$0.635382\pi$
$984$	2.13961	0.0682084
$985$	−13.1727	−0.419719
$986$	1.53941	0.0490248
$987$	−12.7718	−0.406530
$988$	−16.2552	−0.517147
$989$	−29.4698	−0.937085
$990$	15.4964	0.492507
$991$	−23.7458	−0.754309	−0.377155	−	0.926150i	$-0.623097\pi$
$991$	−23.7458	−0.754309	−0.377155	+	0.926150i	$0.623097\pi$
$992$	1.34159	0.0425955
$993$	17.6193	0.559132
$994$	5.21776	0.165497
$995$	56.5395	1.79242
$996$	5.76683	0.182729
$997$	4.71686	0.149385	0.0746923	−	0.997207i	$-0.476203\pi$
$997$	4.71686	0.149385	0.0746923	+	0.997207i	$0.476203\pi$
$998$	−26.4004	−0.835691
$999$	−5.79814	−0.183445

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.15	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.15	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.95354 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.95354 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.95354 q^{10} +3.91962 q^{11} +1.00000 q^{12} +3.15542 q^{13} +1.00000 q^{14} +3.95354 q^{15} +1.00000 q^{16} -0.274165 q^{17} +1.00000 q^{18} -5.15151 q^{19} +3.95354 q^{20} +1.00000 q^{21} +3.91962 q^{22} -2.79170 q^{23} +1.00000 q^{24} +10.6305 q^{25} +3.15542 q^{26} +1.00000 q^{27} +1.00000 q^{28} -5.61490 q^{29} +3.95354 q^{30} +1.34159 q^{31} +1.00000 q^{32} +3.91962 q^{33} -0.274165 q^{34} +3.95354 q^{35} +1.00000 q^{36} -5.79814 q^{37} -5.15151 q^{38} +3.15542 q^{39} +3.95354 q^{40} +2.13961 q^{41} +1.00000 q^{42} +10.5562 q^{43} +3.91962 q^{44} +3.95354 q^{45} -2.79170 q^{46} -12.7718 q^{47} +1.00000 q^{48} +1.00000 q^{49} +10.6305 q^{50} -0.274165 q^{51} +3.15542 q^{52} -6.70527 q^{53} +1.00000 q^{54} +15.4964 q^{55} +1.00000 q^{56} -5.15151 q^{57} -5.61490 q^{58} +5.03957 q^{59} +3.95354 q^{60} +7.96315 q^{61} +1.34159 q^{62} +1.00000 q^{63} +1.00000 q^{64} +12.4751 q^{65} +3.91962 q^{66} +0.669240 q^{67} -0.274165 q^{68} -2.79170 q^{69} +3.95354 q^{70} +5.21776 q^{71} +1.00000 q^{72} -12.7861 q^{73} -5.79814 q^{74} +10.6305 q^{75} -5.15151 q^{76} +3.91962 q^{77} +3.15542 q^{78} -3.58567 q^{79} +3.95354 q^{80} +1.00000 q^{81} +2.13961 q^{82} +5.76683 q^{83} +1.00000 q^{84} -1.08392 q^{85} +10.5562 q^{86} -5.61490 q^{87} +3.91962 q^{88} -5.53790 q^{89} +3.95354 q^{90} +3.15542 q^{91} -2.79170 q^{92} +1.34159 q^{93} -12.7718 q^{94} -20.3667 q^{95} +1.00000 q^{96} +15.7303 q^{97} +1.00000 q^{98} +3.91962 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 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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