LMFDB - Embedded newform 8022.2.a.ba.1.5

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			1.5
Root			$2.58623$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.58623 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.58623 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.58623 q^{10} +0.737645 q^{11} +1.00000 q^{12} +0.634226 q^{13} +1.00000 q^{14} -1.58623 q^{15} +1.00000 q^{16} -2.00913 q^{17} +1.00000 q^{18} +2.56986 q^{19} -1.58623 q^{20} +1.00000 q^{21} +0.737645 q^{22} -3.56280 q^{23} +1.00000 q^{24} -2.48389 q^{25} +0.634226 q^{26} +1.00000 q^{27} +1.00000 q^{28} +1.67806 q^{29} -1.58623 q^{30} +5.01097 q^{31} +1.00000 q^{32} +0.737645 q^{33} -2.00913 q^{34} -1.58623 q^{35} +1.00000 q^{36} +7.69844 q^{37} +2.56986 q^{38} +0.634226 q^{39} -1.58623 q^{40} -5.27648 q^{41} +1.00000 q^{42} +10.4291 q^{43} +0.737645 q^{44} -1.58623 q^{45} -3.56280 q^{46} +9.57465 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.48389 q^{50} -2.00913 q^{51} +0.634226 q^{52} -4.06450 q^{53} +1.00000 q^{54} -1.17007 q^{55} +1.00000 q^{56} +2.56986 q^{57} +1.67806 q^{58} -1.95373 q^{59} -1.58623 q^{60} +0.508439 q^{61} +5.01097 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00603 q^{65} +0.737645 q^{66} +0.255385 q^{67} -2.00913 q^{68} -3.56280 q^{69} -1.58623 q^{70} -6.03250 q^{71} +1.00000 q^{72} +8.04899 q^{73} +7.69844 q^{74} -2.48389 q^{75} +2.56986 q^{76} +0.737645 q^{77} +0.634226 q^{78} +1.93127 q^{79} -1.58623 q^{80} +1.00000 q^{81} -5.27648 q^{82} +4.94310 q^{83} +1.00000 q^{84} +3.18694 q^{85} +10.4291 q^{86} +1.67806 q^{87} +0.737645 q^{88} +3.51416 q^{89} -1.58623 q^{90} +0.634226 q^{91} -3.56280 q^{92} +5.01097 q^{93} +9.57465 q^{94} -4.07639 q^{95} +1.00000 q^{96} +12.4637 q^{97} +1.00000 q^{98} +0.737645 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−1.58623	−0.709382	−0.354691	−	0.934984i	$-0.615414\pi$
$5$	−1.58623	−0.709382	−0.354691	+	0.934984i	$0.615414\pi$
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.58623	−0.501609
$11$	0.737645	0.222408	0.111204	−	0.993798i	$-0.464529\pi$
$11$	0.737645	0.222408	0.111204	+	0.993798i	$0.464529\pi$
$12$	1.00000	0.288675
$13$	0.634226	0.175903	0.0879513	−	0.996125i	$-0.471968\pi$
$13$	0.634226	0.175903	0.0879513	+	0.996125i	$0.471968\pi$
$14$	1.00000	0.267261
$15$	−1.58623	−0.409562
$16$	1.00000	0.250000
$17$	−2.00913	−0.487286	−0.243643	−	0.969865i	$-0.578343\pi$
$17$	−2.00913	−0.487286	−0.243643	+	0.969865i	$0.578343\pi$
$18$	1.00000	0.235702
$19$	2.56986	0.589567	0.294784	−	0.955564i	$-0.404752\pi$
$19$	2.56986	0.589567	0.294784	+	0.955564i	$0.404752\pi$
$20$	−1.58623	−0.354691
$21$	1.00000	0.218218
$22$	0.737645	0.157266
$23$	−3.56280	−0.742895	−0.371448	−	0.928454i	$-0.621138\pi$
$23$	−3.56280	−0.742895	−0.371448	+	0.928454i	$0.621138\pi$
$24$	1.00000	0.204124
$25$	−2.48389	−0.496777
$26$	0.634226	0.124382
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	1.67806	0.311608	0.155804	−	0.987788i	$-0.450203\pi$
$29$	1.67806	0.311608	0.155804	+	0.987788i	$0.450203\pi$
$30$	−1.58623	−0.289604
$31$	5.01097	0.899997	0.449999	−	0.893029i	$-0.351424\pi$
$31$	5.01097	0.899997	0.449999	+	0.893029i	$0.351424\pi$
$32$	1.00000	0.176777
$33$	0.737645	0.128408
$34$	−2.00913	−0.344563
$35$	−1.58623	−0.268121
$36$	1.00000	0.166667
$37$	7.69844	1.26562	0.632808	−	0.774309i	$-0.281902\pi$
$37$	7.69844	1.26562	0.632808	+	0.774309i	$0.281902\pi$
$38$	2.56986	0.416887
$39$	0.634226	0.101557
$40$	−1.58623	−0.250804
$41$	−5.27648	−0.824048	−0.412024	−	0.911173i	$-0.635178\pi$
$41$	−5.27648	−0.824048	−0.412024	+	0.911173i	$0.635178\pi$
$42$	1.00000	0.154303
$43$	10.4291	1.59042	0.795208	−	0.606337i	$-0.207362\pi$
$43$	10.4291	1.59042	0.795208	+	0.606337i	$0.207362\pi$
$44$	0.737645	0.111204
$45$	−1.58623	−0.236461
$46$	−3.56280	−0.525306
$47$	9.57465	1.39661	0.698303	−	0.715802i	$-0.253939\pi$
$47$	9.57465	1.39661	0.698303	+	0.715802i	$0.253939\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−2.48389	−0.351274
$51$	−2.00913	−0.281335
$52$	0.634226	0.0879513
$53$	−4.06450	−0.558301	−0.279151	−	0.960247i	$-0.590053\pi$
$53$	−4.06450	−0.558301	−0.279151	+	0.960247i	$0.590053\pi$
$54$	1.00000	0.136083
$55$	−1.17007	−0.157773
$56$	1.00000	0.133631
$57$	2.56986	0.340387
$58$	1.67806	0.220340
$59$	−1.95373	−0.254353	−0.127177	−	0.991880i	$-0.540592\pi$
$59$	−1.95373	−0.254353	−0.127177	+	0.991880i	$0.540592\pi$
$60$	−1.58623	−0.204781
$61$	0.508439	0.0650989	0.0325495	−	0.999470i	$-0.489637\pi$
$61$	0.508439	0.0650989	0.0325495	+	0.999470i	$0.489637\pi$
$62$	5.01097	0.636394
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−1.00603	−0.124782
$66$	0.737645	0.0907978
$67$	0.255385	0.0312003	0.0156001	−	0.999878i	$-0.495034\pi$
$67$	0.255385	0.0312003	0.0156001	+	0.999878i	$0.495034\pi$
$68$	−2.00913	−0.243643
$69$	−3.56280	−0.428911
$70$	−1.58623	−0.189590
$71$	−6.03250	−0.715926	−0.357963	−	0.933736i	$-0.616529\pi$
$71$	−6.03250	−0.715926	−0.357963	+	0.933736i	$0.616529\pi$
$72$	1.00000	0.117851
$73$	8.04899	0.942063	0.471031	−	0.882116i	$-0.343882\pi$
$73$	8.04899	0.942063	0.471031	+	0.882116i	$0.343882\pi$
$74$	7.69844	0.894926
$75$	−2.48389	−0.286814
$76$	2.56986	0.294784
$77$	0.737645	0.0840625
$78$	0.634226	0.0718119
$79$	1.93127	0.217285	0.108642	−	0.994081i	$-0.465350\pi$
$79$	1.93127	0.217285	0.108642	+	0.994081i	$0.465350\pi$
$80$	−1.58623	−0.177346
$81$	1.00000	0.111111
$82$	−5.27648	−0.582690
$83$	4.94310	0.542575	0.271288	−	0.962498i	$-0.412551\pi$
$83$	4.94310	0.542575	0.271288	+	0.962498i	$0.412551\pi$
$84$	1.00000	0.109109
$85$	3.18694	0.345672
$86$	10.4291	1.12459
$87$	1.67806	0.179907
$88$	0.737645	0.0786332
$89$	3.51416	0.372501	0.186250	−	0.982502i	$-0.440366\pi$
$89$	3.51416	0.372501	0.186250	+	0.982502i	$0.440366\pi$
$90$	−1.58623	−0.167203
$91$	0.634226	0.0664849
$92$	−3.56280	−0.371448
$93$	5.01097	0.519614
$94$	9.57465	0.987550
$95$	−4.07639	−0.418228
$96$	1.00000	0.102062
$97$	12.4637	1.26550	0.632749	−	0.774357i	$-0.281926\pi$
$97$	12.4637	1.26550	0.632749	+	0.774357i	$0.281926\pi$
$98$	1.00000	0.101015
$99$	0.737645	0.0741361
$100$	−2.48389	−0.248389
$101$	16.4860	1.64042	0.820209	−	0.572063i	$-0.193857\pi$
$101$	16.4860	1.64042	0.820209	+	0.572063i	$0.193857\pi$
$102$	−2.00913	−0.198934
$103$	−15.8181	−1.55860	−0.779301	−	0.626650i	$-0.784425\pi$
$103$	−15.8181	−1.55860	−0.779301	+	0.626650i	$0.784425\pi$
$104$	0.634226	0.0621909
$105$	−1.58623	−0.154800
$106$	−4.06450	−0.394779
$107$	−14.2898	−1.38145	−0.690724	−	0.723119i	$-0.742708\pi$
$107$	−14.2898	−1.38145	−0.690724	+	0.723119i	$0.742708\pi$
$108$	1.00000	0.0962250
$109$	16.7212	1.60160	0.800801	−	0.598930i	$-0.204407\pi$
$109$	16.7212	1.60160	0.800801	+	0.598930i	$0.204407\pi$
$110$	−1.17007	−0.111562
$111$	7.69844	0.730704
$112$	1.00000	0.0944911
$113$	1.61752	0.152164	0.0760819	−	0.997102i	$-0.475759\pi$
$113$	1.61752	0.152164	0.0760819	+	0.997102i	$0.475759\pi$
$114$	2.56986	0.240690
$115$	5.65141	0.526997
$116$	1.67806	0.155804
$117$	0.634226	0.0586342
$118$	−1.95373	−0.179855
$119$	−2.00913	−0.184177
$120$	−1.58623	−0.144802
$121$	−10.4559	−0.950535
$122$	0.508439	0.0460319
$123$	−5.27648	−0.475764
$124$	5.01097	0.449999
$125$	11.8711	1.06179
$126$	1.00000	0.0890871
$127$	−0.598140	−0.0530763	−0.0265382	−	0.999648i	$-0.508448\pi$
$127$	−0.598140	−0.0530763	−0.0265382	+	0.999648i	$0.508448\pi$
$128$	1.00000	0.0883883
$129$	10.4291	0.918227
$130$	−1.00603	−0.0882343
$131$	10.2758	0.897800	0.448900	−	0.893582i	$-0.351816\pi$
$131$	10.2758	0.897800	0.448900	+	0.893582i	$0.351816\pi$
$132$	0.737645	0.0642038
$133$	2.56986	0.222835
$134$	0.255385	0.0220619
$135$	−1.58623	−0.136521
$136$	−2.00913	−0.172282
$137$	1.45460	0.124274	0.0621372	−	0.998068i	$-0.480208\pi$
$137$	1.45460	0.124274	0.0621372	+	0.998068i	$0.480208\pi$
$138$	−3.56280	−0.303286
$139$	−2.52391	−0.214075	−0.107038	−	0.994255i	$-0.534137\pi$
$139$	−2.52391	−0.214075	−0.107038	+	0.994255i	$0.534137\pi$
$140$	−1.58623	−0.134061
$141$	9.57465	0.806331
$142$	−6.03250	−0.506236
$143$	0.467833	0.0391222
$144$	1.00000	0.0833333
$145$	−2.66178	−0.221049
$146$	8.04899	0.666139
$147$	1.00000	0.0824786
$148$	7.69844	0.632808
$149$	6.43824	0.527441	0.263721	−	0.964599i	$-0.415050\pi$
$149$	6.43824	0.527441	0.263721	+	0.964599i	$0.415050\pi$
$150$	−2.48389	−0.202808
$151$	3.79758	0.309043	0.154521	−	0.987989i	$-0.450616\pi$
$151$	3.79758	0.309043	0.154521	+	0.987989i	$0.450616\pi$
$152$	2.56986	0.208443
$153$	−2.00913	−0.162429
$154$	0.737645	0.0594411
$155$	−7.94854	−0.638442
$156$	0.634226	0.0507787
$157$	11.2396	0.897019	0.448509	−	0.893778i	$-0.351955\pi$
$157$	11.2396	0.897019	0.448509	+	0.893778i	$0.351955\pi$
$158$	1.93127	0.153644
$159$	−4.06450	−0.322335
$160$	−1.58623	−0.125402
$161$	−3.56280	−0.280788
$162$	1.00000	0.0785674
$163$	14.9780	1.17317	0.586585	−	0.809887i	$-0.300472\pi$
$163$	14.9780	1.17317	0.586585	+	0.809887i	$0.300472\pi$
$164$	−5.27648	−0.412024
$165$	−1.17007	−0.0910900
$166$	4.94310	0.383659
$167$	−2.67688	−0.207143	−0.103572	−	0.994622i	$-0.533027\pi$
$167$	−2.67688	−0.207143	−0.103572	+	0.994622i	$0.533027\pi$
$168$	1.00000	0.0771517
$169$	−12.5978	−0.969058
$170$	3.18694	0.244427
$171$	2.56986	0.196522
$172$	10.4291	0.795208
$173$	5.60901	0.426445	0.213223	−	0.977004i	$-0.431604\pi$
$173$	5.60901	0.426445	0.213223	+	0.977004i	$0.431604\pi$
$174$	1.67806	0.127213
$175$	−2.48389	−0.187764
$176$	0.737645	0.0556021
$177$	−1.95373	−0.146851
$178$	3.51416	0.263398
$179$	−3.78639	−0.283008	−0.141504	−	0.989938i	$-0.545194\pi$
$179$	−3.78639	−0.283008	−0.141504	+	0.989938i	$0.545194\pi$
$180$	−1.58623	−0.118230
$181$	−21.2822	−1.58190	−0.790948	−	0.611884i	$-0.790412\pi$
$181$	−21.2822	−1.58190	−0.790948	+	0.611884i	$0.790412\pi$
$182$	0.634226	0.0470119
$183$	0.508439	0.0375849
$184$	−3.56280	−0.262653
$185$	−12.2115	−0.897806
$186$	5.01097	0.367422
$187$	−1.48203	−0.108377
$188$	9.57465	0.698303
$189$	1.00000	0.0727393
$190$	−4.07639	−0.295732
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	8.24313	0.593354	0.296677	−	0.954978i	$-0.404122\pi$
$193$	8.24313	0.593354	0.296677	+	0.954978i	$0.404122\pi$
$194$	12.4637	0.894842
$195$	−1.00603	−0.0720430
$196$	1.00000	0.0714286
$197$	−17.2367	−1.22806	−0.614031	−	0.789282i	$-0.710453\pi$
$197$	−17.2367	−1.22806	−0.614031	+	0.789282i	$0.710453\pi$
$198$	0.737645	0.0524222
$199$	−4.54892	−0.322464	−0.161232	−	0.986917i	$-0.551547\pi$
$199$	−4.54892	−0.322464	−0.161232	+	0.986917i	$0.551547\pi$
$200$	−2.48389	−0.175637
$201$	0.255385	0.0180135
$202$	16.4860	1.15995
$203$	1.67806	0.117777
$204$	−2.00913	−0.140667
$205$	8.36970	0.584565
$206$	−15.8181	−1.10210
$207$	−3.56280	−0.247632
$208$	0.634226	0.0439756
$209$	1.89565	0.131125
$210$	−1.58623	−0.109460
$211$	1.18055	0.0812724	0.0406362	−	0.999174i	$-0.487062\pi$
$211$	1.18055	0.0812724	0.0406362	+	0.999174i	$0.487062\pi$
$212$	−4.06450	−0.279151
$213$	−6.03250	−0.413340
$214$	−14.2898	−0.976831
$215$	−16.5428	−1.12821
$216$	1.00000	0.0680414
$217$	5.01097	0.340167
$218$	16.7212	1.13250
$219$	8.04899	0.543900
$220$	−1.17007	−0.0788863
$221$	−1.27424	−0.0857149
$222$	7.69844	0.516686
$223$	−4.97941	−0.333446	−0.166723	−	0.986004i	$-0.553319\pi$
$223$	−4.97941	−0.333446	−0.166723	+	0.986004i	$0.553319\pi$
$224$	1.00000	0.0668153
$225$	−2.48389	−0.165592
$226$	1.61752	0.107596
$227$	−3.83824	−0.254753	−0.127377	−	0.991854i	$-0.540656\pi$
$227$	−3.83824	−0.254753	−0.127377	+	0.991854i	$0.540656\pi$
$228$	2.56986	0.170193
$229$	22.0758	1.45881	0.729406	−	0.684081i	$-0.239797\pi$
$229$	22.0758	1.45881	0.729406	+	0.684081i	$0.239797\pi$
$230$	5.65141	0.372643
$231$	0.737645	0.0485335
$232$	1.67806	0.110170
$233$	−10.5131	−0.688738	−0.344369	−	0.938834i	$-0.611907\pi$
$233$	−10.5131	−0.688738	−0.344369	+	0.938834i	$0.611907\pi$
$234$	0.634226	0.0414606
$235$	−15.1876	−0.990728
$236$	−1.95373	−0.127177
$237$	1.93127	0.125449
$238$	−2.00913	−0.130233
$239$	27.4246	1.77395	0.886974	−	0.461819i	$-0.152803\pi$
$239$	27.4246	1.77395	0.886974	+	0.461819i	$0.152803\pi$
$240$	−1.58623	−0.102390
$241$	−15.1548	−0.976209	−0.488105	−	0.872785i	$-0.662312\pi$
$241$	−15.1548	−0.976209	−0.488105	+	0.872785i	$0.662312\pi$
$242$	−10.4559	−0.672129
$243$	1.00000	0.0641500
$244$	0.508439	0.0325495
$245$	−1.58623	−0.101340
$246$	−5.27648	−0.336416
$247$	1.62987	0.103706
$248$	5.01097	0.318197
$249$	4.94310	0.313256
$250$	11.8711	0.750797
$251$	2.13325	0.134649	0.0673247	−	0.997731i	$-0.478554\pi$
$251$	2.13325	0.134649	0.0673247	+	0.997731i	$0.478554\pi$
$252$	1.00000	0.0629941
$253$	−2.62808	−0.165226
$254$	−0.598140	−0.0375306
$255$	3.18694	0.199574
$256$	1.00000	0.0625000
$257$	11.9630	0.746231	0.373115	−	0.927785i	$-0.378290\pi$
$257$	11.9630	0.746231	0.373115	+	0.927785i	$0.378290\pi$
$258$	10.4291	0.649285
$259$	7.69844	0.478358
$260$	−1.00603	−0.0623911
$261$	1.67806	0.103869
$262$	10.2758	0.634841
$263$	19.6597	1.21227	0.606136	−	0.795361i	$-0.292719\pi$
$263$	19.6597	1.21227	0.606136	+	0.795361i	$0.292719\pi$
$264$	0.737645	0.0453989
$265$	6.44721	0.396049
$266$	2.56986	0.157568
$267$	3.51416	0.215063
$268$	0.255385	0.0156001
$269$	−1.90913	−0.116402	−0.0582009	−	0.998305i	$-0.518536\pi$
$269$	−1.90913	−0.116402	−0.0582009	+	0.998305i	$0.518536\pi$
$270$	−1.58623	−0.0965347
$271$	10.6912	0.649444	0.324722	−	0.945810i	$-0.394729\pi$
$271$	10.6912	0.649444	0.324722	+	0.945810i	$0.394729\pi$
$272$	−2.00913	−0.121822
$273$	0.634226	0.0383851
$274$	1.45460	0.0878753
$275$	−1.83223	−0.110487
$276$	−3.56280	−0.214455
$277$	−20.3562	−1.22308	−0.611542	−	0.791212i	$-0.709451\pi$
$277$	−20.3562	−1.22308	−0.611542	+	0.791212i	$0.709451\pi$
$278$	−2.52391	−0.151374
$279$	5.01097	0.299999
$280$	−1.58623	−0.0947952
$281$	22.4032	1.33646	0.668230	−	0.743955i	$-0.267052\pi$
$281$	22.4032	1.33646	0.668230	+	0.743955i	$0.267052\pi$
$282$	9.57465	0.570162
$283$	−20.9374	−1.24460	−0.622300	−	0.782779i	$-0.713802\pi$
$283$	−20.9374	−1.24460	−0.622300	+	0.782779i	$0.713802\pi$
$284$	−6.03250	−0.357963
$285$	−4.07639	−0.241464
$286$	0.467833	0.0276636
$287$	−5.27648	−0.311461
$288$	1.00000	0.0589256
$289$	−12.9634	−0.762552
$290$	−2.66178	−0.156305
$291$	12.4637	0.730636
$292$	8.04899	0.471031
$293$	−3.39639	−0.198419	−0.0992096	−	0.995067i	$-0.531631\pi$
$293$	−3.39639	−0.198419	−0.0992096	+	0.995067i	$0.531631\pi$
$294$	1.00000	0.0583212
$295$	3.09905	0.180434
$296$	7.69844	0.447463
$297$	0.737645	0.0428025
$298$	6.43824	0.372957
$299$	−2.25962	−0.130677
$300$	−2.48389	−0.143407
$301$	10.4291	0.601121
$302$	3.79758	0.218526
$303$	16.4860	0.947096
$304$	2.56986	0.147392
$305$	−0.806499	−0.0461800
$306$	−2.00913	−0.114854
$307$	8.27043	0.472018	0.236009	−	0.971751i	$-0.424160\pi$
$307$	8.27043	0.472018	0.236009	+	0.971751i	$0.424160\pi$
$308$	0.737645	0.0420312
$309$	−15.8181	−0.899859
$310$	−7.94854	−0.451447
$311$	−15.7206	−0.891434	−0.445717	−	0.895174i	$-0.647051\pi$
$311$	−15.7206	−0.891434	−0.445717	+	0.895174i	$0.647051\pi$
$312$	0.634226	0.0359060
$313$	22.5102	1.27235	0.636175	−	0.771545i	$-0.280516\pi$
$313$	22.5102	1.27235	0.636175	+	0.771545i	$0.280516\pi$
$314$	11.2396	0.634288
$315$	−1.58623	−0.0893737
$316$	1.93127	0.108642
$317$	−27.4767	−1.54325	−0.771623	−	0.636080i	$-0.780555\pi$
$317$	−27.4767	−1.54325	−0.771623	+	0.636080i	$0.780555\pi$
$318$	−4.06450	−0.227926
$319$	1.23781	0.0693042
$320$	−1.58623	−0.0886728
$321$	−14.2898	−0.797579
$322$	−3.56280	−0.198547
$323$	−5.16320	−0.287288
$324$	1.00000	0.0555556
$325$	−1.57534	−0.0873843
$326$	14.9780	0.829557
$327$	16.7212	0.924686
$328$	−5.27648	−0.291345
$329$	9.57465	0.527868
$330$	−1.17007	−0.0644104
$331$	34.4634	1.89428	0.947141	−	0.320818i	$-0.103958\pi$
$331$	34.4634	1.89428	0.947141	+	0.320818i	$0.103958\pi$
$332$	4.94310	0.271288
$333$	7.69844	0.421872
$334$	−2.67688	−0.146472
$335$	−0.405099	−0.0221329
$336$	1.00000	0.0545545
$337$	−10.8467	−0.590857	−0.295428	−	0.955365i	$-0.595462\pi$
$337$	−10.8467	−0.590857	−0.295428	+	0.955365i	$0.595462\pi$
$338$	−12.5978	−0.685228
$339$	1.61752	0.0878518
$340$	3.18694	0.172836
$341$	3.69632	0.200167
$342$	2.56986	0.138962
$343$	1.00000	0.0539949
$344$	10.4291	0.562297
$345$	5.65141	0.304262
$346$	5.60901	0.301542
$347$	22.0953	1.18614	0.593070	−	0.805151i	$-0.297916\pi$
$347$	22.0953	1.18614	0.593070	+	0.805151i	$0.297916\pi$
$348$	1.67806	0.0899534
$349$	28.8039	1.54184	0.770919	−	0.636933i	$-0.219797\pi$
$349$	28.8039	1.54184	0.770919	+	0.636933i	$0.219797\pi$
$350$	−2.48389	−0.132769
$351$	0.634226	0.0338525
$352$	0.737645	0.0393166
$353$	8.50271	0.452553	0.226277	−	0.974063i	$-0.427345\pi$
$353$	8.50271	0.452553	0.226277	+	0.974063i	$0.427345\pi$
$354$	−1.95373	−0.103839
$355$	9.56891	0.507865
$356$	3.51416	0.186250
$357$	−2.00913	−0.106335
$358$	−3.78639	−0.200117
$359$	−25.2282	−1.33149	−0.665746	−	0.746179i	$-0.731886\pi$
$359$	−25.2282	−1.33149	−0.665746	+	0.746179i	$0.731886\pi$
$360$	−1.58623	−0.0836015
$361$	−12.3958	−0.652411
$362$	−21.2822	−1.11857
$363$	−10.4559	−0.548791
$364$	0.634226	0.0332425
$365$	−12.7675	−0.668282
$366$	0.508439	0.0265765
$367$	−3.05206	−0.159316	−0.0796582	−	0.996822i	$-0.525383\pi$
$367$	−3.05206	−0.159316	−0.0796582	+	0.996822i	$0.525383\pi$
$368$	−3.56280	−0.185724
$369$	−5.27648	−0.274683
$370$	−12.2115	−0.634845
$371$	−4.06450	−0.211018
$372$	5.01097	0.259807
$373$	−36.3185	−1.88050	−0.940250	−	0.340485i	$-0.889409\pi$
$373$	−36.3185	−1.88050	−0.940250	+	0.340485i	$0.889409\pi$
$374$	−1.48203	−0.0766338
$375$	11.8711	0.613023
$376$	9.57465	0.493775
$377$	1.06427	0.0548126
$378$	1.00000	0.0514344
$379$	13.2112	0.678614	0.339307	−	0.940676i	$-0.389807\pi$
$379$	13.2112	0.678614	0.339307	+	0.940676i	$0.389807\pi$
$380$	−4.07639	−0.209114
$381$	−0.598140	−0.0306436
$382$	−1.00000	−0.0511645
$383$	−15.1893	−0.776139	−0.388070	−	0.921630i	$-0.626858\pi$
$383$	−15.1893	−0.776139	−0.388070	+	0.921630i	$0.626858\pi$
$384$	1.00000	0.0510310
$385$	−1.17007	−0.0596324
$386$	8.24313	0.419564
$387$	10.4291	0.530139
$388$	12.4637	0.632749
$389$	−18.2391	−0.924758	−0.462379	−	0.886682i	$-0.653004\pi$
$389$	−18.2391	−0.924758	−0.462379	+	0.886682i	$0.653004\pi$
$390$	−1.00603	−0.0509421
$391$	7.15814	0.362003
$392$	1.00000	0.0505076
$393$	10.2758	0.518345
$394$	−17.2367	−0.868371
$395$	−3.06343	−0.154138
$396$	0.737645	0.0370681
$397$	14.2963	0.717513	0.358756	−	0.933431i	$-0.383201\pi$
$397$	14.2963	0.717513	0.358756	+	0.933431i	$0.383201\pi$
$398$	−4.54892	−0.228017
$399$	2.56986	0.128654
$400$	−2.48389	−0.124194
$401$	−12.9023	−0.644308	−0.322154	−	0.946687i	$-0.604407\pi$
$401$	−12.9023	−0.644308	−0.322154	+	0.946687i	$0.604407\pi$
$402$	0.255385	0.0127375
$403$	3.17809	0.158312
$404$	16.4860	0.820209
$405$	−1.58623	−0.0788202
$406$	1.67806	0.0832807
$407$	5.67872	0.281484
$408$	−2.00913	−0.0994669
$409$	15.7848	0.780507	0.390254	−	0.920707i	$-0.372387\pi$
$409$	15.7848	0.780507	0.390254	+	0.920707i	$0.372387\pi$
$410$	8.36970	0.413350
$411$	1.45460	0.0717499
$412$	−15.8181	−0.779301
$413$	−1.95373	−0.0961366
$414$	−3.56280	−0.175102
$415$	−7.84087	−0.384893
$416$	0.634226	0.0310955
$417$	−2.52391	−0.123596
$418$	1.89565	0.0927191
$419$	39.7195	1.94042	0.970212	−	0.242258i	$-0.0778881\pi$
$419$	39.7195	1.94042	0.970212	+	0.242258i	$0.0778881\pi$
$420$	−1.58623	−0.0773999
$421$	38.9983	1.90066	0.950331	−	0.311240i	$-0.100744\pi$
$421$	38.9983	1.90066	0.950331	+	0.311240i	$0.100744\pi$
$422$	1.18055	0.0574683
$423$	9.57465	0.465535
$424$	−4.06450	−0.197389
$425$	4.99045	0.242073
$426$	−6.03250	−0.292276
$427$	0.508439	0.0246051
$428$	−14.2898	−0.690724
$429$	0.467833	0.0225872
$430$	−16.5428	−0.797767
$431$	−40.0271	−1.92804	−0.964019	−	0.265834i	$-0.914353\pi$
$431$	−40.0271	−1.92804	−0.964019	+	0.265834i	$0.914353\pi$
$432$	1.00000	0.0481125
$433$	24.1281	1.15952	0.579762	−	0.814786i	$-0.303146\pi$
$433$	24.1281	1.15952	0.579762	+	0.814786i	$0.303146\pi$
$434$	5.01097	0.240534
$435$	−2.66178	−0.127623
$436$	16.7212	0.800801
$437$	−9.15591	−0.437987
$438$	8.04899	0.384595
$439$	4.20457	0.200673	0.100337	−	0.994954i	$-0.468008\pi$
$439$	4.20457	0.200673	0.100337	+	0.994954i	$0.468008\pi$
$440$	−1.17007	−0.0557810
$441$	1.00000	0.0476190
$442$	−1.27424	−0.0606096
$443$	15.3742	0.730452	0.365226	−	0.930919i	$-0.380992\pi$
$443$	15.3742	0.730452	0.365226	+	0.930919i	$0.380992\pi$
$444$	7.69844	0.365352
$445$	−5.57426	−0.264245
$446$	−4.97941	−0.235782
$447$	6.43824	0.304518
$448$	1.00000	0.0472456
$449$	22.7013	1.07134	0.535671	−	0.844427i	$-0.320059\pi$
$449$	22.7013	1.07134	0.535671	+	0.844427i	$0.320059\pi$
$450$	−2.48389	−0.117091
$451$	−3.89217	−0.183275
$452$	1.61752	0.0760819
$453$	3.79758	0.178426
$454$	−3.83824	−0.180138
$455$	−1.00603	−0.0471632
$456$	2.56986	0.120345
$457$	−33.4700	−1.56566	−0.782831	−	0.622234i	$-0.786225\pi$
$457$	−33.4700	−1.56566	−0.782831	+	0.622234i	$0.786225\pi$
$458$	22.0758	1.03154
$459$	−2.00913	−0.0937783
$460$	5.65141	0.263498
$461$	−4.14941	−0.193257	−0.0966286	−	0.995321i	$-0.530806\pi$
$461$	−4.14941	−0.193257	−0.0966286	+	0.995321i	$0.530806\pi$
$462$	0.737645	0.0343184
$463$	−22.0252	−1.02360	−0.511799	−	0.859105i	$-0.671021\pi$
$463$	−22.0252	−1.02360	−0.511799	+	0.859105i	$0.671021\pi$
$464$	1.67806	0.0779019
$465$	−7.94854	−0.368605
$466$	−10.5131	−0.487011
$467$	−5.04837	−0.233611	−0.116805	−	0.993155i	$-0.537265\pi$
$467$	−5.04837	−0.233611	−0.116805	+	0.993155i	$0.537265\pi$
$468$	0.634226	0.0293171
$469$	0.255385	0.0117926
$470$	−15.1876	−0.700550
$471$	11.2396	0.517894
$472$	−1.95373	−0.0899275
$473$	7.69294	0.353722
$474$	1.93127	0.0887061
$475$	−6.38325	−0.292883
$476$	−2.00913	−0.0920884
$477$	−4.06450	−0.186100
$478$	27.4246	1.25437
$479$	−11.6676	−0.533108	−0.266554	−	0.963820i	$-0.585885\pi$
$479$	−11.6676	−0.533108	−0.266554	+	0.963820i	$0.585885\pi$
$480$	−1.58623	−0.0724010
$481$	4.88255	0.222625
$482$	−15.1548	−0.690284
$483$	−3.56280	−0.162113
$484$	−10.4559	−0.475267
$485$	−19.7703	−0.897722
$486$	1.00000	0.0453609
$487$	42.3684	1.91990	0.959948	−	0.280177i	$-0.0903933\pi$
$487$	42.3684	1.91990	0.959948	+	0.280177i	$0.0903933\pi$
$488$	0.508439	0.0230160
$489$	14.9780	0.677330
$490$	−1.58623	−0.0716584
$491$	−36.1422	−1.63108	−0.815538	−	0.578704i	$-0.803559\pi$
$491$	−36.1422	−1.63108	−0.815538	+	0.578704i	$0.803559\pi$
$492$	−5.27648	−0.237882
$493$	−3.37144	−0.151842
$494$	1.62987	0.0733315
$495$	−1.17007	−0.0525908
$496$	5.01097	0.224999
$497$	−6.03250	−0.270595
$498$	4.94310	0.221506
$499$	−38.0641	−1.70398	−0.851991	−	0.523557i	$-0.824605\pi$
$499$	−38.0641	−1.70398	−0.851991	+	0.523557i	$0.824605\pi$
$500$	11.8711	0.530893
$501$	−2.67688	−0.119594
$502$	2.13325	0.0952115
$503$	−26.4854	−1.18093	−0.590463	−	0.807065i	$-0.701055\pi$
$503$	−26.4854	−1.18093	−0.590463	+	0.807065i	$0.701055\pi$
$504$	1.00000	0.0445435
$505$	−26.1505	−1.16368
$506$	−2.62808	−0.116832
$507$	−12.5978	−0.559486
$508$	−0.598140	−0.0265382
$509$	22.7970	1.01046	0.505231	−	0.862984i	$-0.331407\pi$
$509$	22.7970	1.01046	0.505231	+	0.862984i	$0.331407\pi$
$510$	3.18694	0.141120
$511$	8.04899	0.356066
$512$	1.00000	0.0441942
$513$	2.56986	0.113462
$514$	11.9630	0.527665
$515$	25.0910	1.10564
$516$	10.4291	0.459113
$517$	7.06269	0.310617
$518$	7.69844	0.338250
$519$	5.60901	0.246208
$520$	−1.00603	−0.0441171
$521$	38.8072	1.70018	0.850088	−	0.526640i	$-0.176549\pi$
$521$	38.8072	1.70018	0.850088	+	0.526640i	$0.176549\pi$
$522$	1.67806	0.0734466
$523$	−0.825056	−0.0360772	−0.0180386	−	0.999837i	$-0.505742\pi$
$523$	−0.825056	−0.0360772	−0.0180386	+	0.999837i	$0.505742\pi$
$524$	10.2758	0.448900
$525$	−2.48389	−0.108406
$526$	19.6597	0.857206
$527$	−10.0677	−0.438556
$528$	0.737645	0.0321019
$529$	−10.3065	−0.448107
$530$	6.44721	0.280049
$531$	−1.95373	−0.0847845
$532$	2.56986	0.111418
$533$	−3.34648	−0.144952
$534$	3.51416	0.152073
$535$	22.6669	0.979974
$536$	0.255385	0.0110310
$537$	−3.78639	−0.163395
$538$	−1.90913	−0.0823086
$539$	0.737645	0.0317726
$540$	−1.58623	−0.0682603
$541$	8.03453	0.345432	0.172716	−	0.984972i	$-0.444746\pi$
$541$	8.03453	0.345432	0.172716	+	0.984972i	$0.444746\pi$
$542$	10.6912	0.459226
$543$	−21.2822	−0.913308
$544$	−2.00913	−0.0861409
$545$	−26.5236	−1.13615
$546$	0.634226	0.0271424
$547$	−23.0017	−0.983481	−0.491741	−	0.870742i	$-0.663639\pi$
$547$	−23.0017	−0.983481	−0.491741	+	0.870742i	$0.663639\pi$
$548$	1.45460	0.0621372
$549$	0.508439	0.0216996
$550$	−1.83223	−0.0781264
$551$	4.31238	0.183714
$552$	−3.56280	−0.151643
$553$	1.93127	0.0821259
$554$	−20.3562	−0.864851
$555$	−12.2115	−0.518348
$556$	−2.52391	−0.107038
$557$	−6.63976	−0.281336	−0.140668	−	0.990057i	$-0.544925\pi$
$557$	−6.63976	−0.281336	−0.140668	+	0.990057i	$0.544925\pi$
$558$	5.01097	0.212131
$559$	6.61437	0.279758
$560$	−1.58623	−0.0670303
$561$	−1.48203	−0.0625712
$562$	22.4032	0.945020
$563$	−23.4151	−0.986830	−0.493415	−	0.869794i	$-0.664252\pi$
$563$	−23.4151	−0.986830	−0.493415	+	0.869794i	$0.664252\pi$
$564$	9.57465	0.403166
$565$	−2.56576	−0.107942
$566$	−20.9374	−0.880066
$567$	1.00000	0.0419961
$568$	−6.03250	−0.253118
$569$	−0.799000	−0.0334958	−0.0167479	−	0.999860i	$-0.505331\pi$
$569$	−0.799000	−0.0334958	−0.0167479	+	0.999860i	$0.505331\pi$
$570$	−4.07639	−0.170741
$571$	−33.0680	−1.38385	−0.691927	−	0.721968i	$-0.743238\pi$
$571$	−33.0680	−1.38385	−0.691927	+	0.721968i	$0.743238\pi$
$572$	0.467833	0.0195611
$573$	−1.00000	−0.0417756
$574$	−5.27648	−0.220236
$575$	8.84959	0.369053
$576$	1.00000	0.0416667
$577$	17.2322	0.717387	0.358693	−	0.933455i	$-0.383222\pi$
$577$	17.2322	0.717387	0.358693	+	0.933455i	$0.383222\pi$
$578$	−12.9634	−0.539206
$579$	8.24313	0.342573
$580$	−2.66178	−0.110524
$581$	4.94310	0.205074
$582$	12.4637	0.516637
$583$	−2.99815	−0.124171
$584$	8.04899	0.333069
$585$	−1.00603	−0.0415940
$586$	−3.39639	−0.140304
$587$	6.95963	0.287255	0.143627	−	0.989632i	$-0.454123\pi$
$587$	6.95963	0.287255	0.143627	+	0.989632i	$0.454123\pi$
$588$	1.00000	0.0412393
$589$	12.8775	0.530609
$590$	3.09905	0.127586
$591$	−17.2367	−0.709022
$592$	7.69844	0.316404
$593$	−30.0114	−1.23242	−0.616210	−	0.787582i	$-0.711333\pi$
$593$	−30.0114	−1.23242	−0.616210	+	0.787582i	$0.711333\pi$
$594$	0.737645	0.0302659
$595$	3.18694	0.130652
$596$	6.43824	0.263721
$597$	−4.54892	−0.186175
$598$	−2.25962	−0.0924027
$599$	−46.7965	−1.91205	−0.956026	−	0.293282i	$-0.905252\pi$
$599$	−46.7965	−1.91205	−0.956026	+	0.293282i	$0.905252\pi$
$600$	−2.48389	−0.101404
$601$	43.9175	1.79143	0.895716	−	0.444627i	$-0.146664\pi$
$601$	43.9175	1.79143	0.895716	+	0.444627i	$0.146664\pi$
$602$	10.4291	0.425056
$603$	0.255385	0.0104001
$604$	3.79758	0.154521
$605$	16.5854	0.674292
$606$	16.4860	0.669698
$607$	−39.2232	−1.59202	−0.796010	−	0.605284i	$-0.793060\pi$
$607$	−39.2232	−1.59202	−0.796010	+	0.605284i	$0.793060\pi$
$608$	2.56986	0.104222
$609$	1.67806	0.0679984
$610$	−0.806499	−0.0326542
$611$	6.07249	0.245667
$612$	−2.00913	−0.0812144
$613$	21.2948	0.860089	0.430045	−	0.902808i	$-0.358498\pi$
$613$	21.2948	0.860089	0.430045	+	0.902808i	$0.358498\pi$
$614$	8.27043	0.333767
$615$	8.36970	0.337499
$616$	0.737645	0.0297206
$617$	38.3798	1.54511	0.772556	−	0.634947i	$-0.218978\pi$
$617$	38.3798	1.54511	0.772556	+	0.634947i	$0.218978\pi$
$618$	−15.8181	−0.636296
$619$	−18.8962	−0.759504	−0.379752	−	0.925088i	$-0.623991\pi$
$619$	−18.8962	−0.759504	−0.379752	+	0.925088i	$0.623991\pi$
$620$	−7.94854	−0.319221
$621$	−3.56280	−0.142970
$622$	−15.7206	−0.630339
$623$	3.51416	0.140792
$624$	0.634226	0.0253893
$625$	−6.41089	−0.256436
$626$	22.5102	0.899687
$627$	1.89565	0.0757048
$628$	11.2396	0.448509
$629$	−15.4672	−0.616718
$630$	−1.58623	−0.0631968
$631$	0.0333993	0.00132961	0.000664803	−	1.00000i	$-0.499788\pi$
$631$	0.0333993	0.00132961	0.000664803		1.00000i	$0.499788\pi$
$632$	1.93127	0.0768218
$633$	1.18055	0.0469227
$634$	−27.4767	−1.09124
$635$	0.948785	0.0376514
$636$	−4.06450	−0.161168
$637$	0.634226	0.0251289
$638$	1.23781	0.0490054
$639$	−6.03250	−0.238642
$640$	−1.58623	−0.0627011
$641$	−32.3078	−1.27608	−0.638040	−	0.770003i	$-0.720255\pi$
$641$	−32.3078	−1.27608	−0.638040	+	0.770003i	$0.720255\pi$
$642$	−14.2898	−0.563974
$643$	33.2040	1.30944	0.654718	−	0.755873i	$-0.272787\pi$
$643$	33.2040	1.30944	0.654718	+	0.755873i	$0.272787\pi$
$644$	−3.56280	−0.140394
$645$	−16.5428	−0.651374
$646$	−5.16320	−0.203143
$647$	10.3329	0.406227	0.203114	−	0.979155i	$-0.434894\pi$
$647$	10.3329	0.406227	0.203114	+	0.979155i	$0.434894\pi$
$648$	1.00000	0.0392837
$649$	−1.44116	−0.0565703
$650$	−1.57534	−0.0617901
$651$	5.01097	0.196395
$652$	14.9780	0.586585
$653$	0.0538450	0.00210712	0.00105356	−	0.999999i	$-0.499665\pi$
$653$	0.0538450	0.00210712	0.00105356	+	0.999999i	$0.499665\pi$
$654$	16.7212	0.653851
$655$	−16.2997	−0.636883
$656$	−5.27648	−0.206012
$657$	8.04899	0.314021
$658$	9.57465	0.373259
$659$	−9.08223	−0.353794	−0.176897	−	0.984229i	$-0.556606\pi$
$659$	−9.08223	−0.353794	−0.176897	+	0.984229i	$0.556606\pi$
$660$	−1.17007	−0.0455450
$661$	−8.08344	−0.314409	−0.157205	−	0.987566i	$-0.550248\pi$
$661$	−8.08344	−0.314409	−0.157205	+	0.987566i	$0.550248\pi$
$662$	34.4634	1.33946
$663$	−1.27424	−0.0494875
$664$	4.94310	0.191829
$665$	−4.07639	−0.158075
$666$	7.69844	0.298309
$667$	−5.97859	−0.231492
$668$	−2.67688	−0.103572
$669$	−4.97941	−0.192515
$670$	−0.405099	−0.0156503
$671$	0.375048	0.0144785
$672$	1.00000	0.0385758
$673$	26.8763	1.03601	0.518003	−	0.855379i	$-0.326676\pi$
$673$	26.8763	1.03601	0.518003	+	0.855379i	$0.326676\pi$
$674$	−10.8467	−0.417799
$675$	−2.48389	−0.0956048
$676$	−12.5978	−0.484529
$677$	−25.1607	−0.967004	−0.483502	−	0.875343i	$-0.660635\pi$
$677$	−25.1607	−0.967004	−0.483502	+	0.875343i	$0.660635\pi$
$678$	1.61752	0.0621206
$679$	12.4637	0.478313
$680$	3.18694	0.122214
$681$	−3.83824	−0.147082
$682$	3.69632	0.141539
$683$	−45.3004	−1.73337	−0.866685	−	0.498856i	$-0.833754\pi$
$683$	−45.3004	−1.73337	−0.866685	+	0.498856i	$0.833754\pi$
$684$	2.56986	0.0982612
$685$	−2.30732	−0.0881581
$686$	1.00000	0.0381802
$687$	22.0758	0.842245
$688$	10.4291	0.397604
$689$	−2.57781	−0.0982066
$690$	5.65141	0.215145
$691$	−4.49897	−0.171149	−0.0855745	−	0.996332i	$-0.527273\pi$
$691$	−4.49897	−0.171149	−0.0855745	+	0.996332i	$0.527273\pi$
$692$	5.60901	0.213223
$693$	0.737645	0.0280208
$694$	22.0953	0.838728
$695$	4.00349	0.151861
$696$	1.67806	0.0636067
$697$	10.6012	0.401547
$698$	28.8039	1.09024
$699$	−10.5131	−0.397643
$700$	−2.48389	−0.0938820
$701$	40.4462	1.52763	0.763816	−	0.645434i	$-0.223323\pi$
$701$	40.4462	1.52763	0.763816	+	0.645434i	$0.223323\pi$
$702$	0.634226	0.0239373
$703$	19.7840	0.746166
$704$	0.737645	0.0278010
$705$	−15.1876	−0.571997
$706$	8.50271	0.320004
$707$	16.4860	0.620020
$708$	−1.95373	−0.0734255
$709$	−11.0316	−0.414301	−0.207150	−	0.978309i	$-0.566419\pi$
$709$	−11.0316	−0.414301	−0.207150	+	0.978309i	$0.566419\pi$
$710$	9.56891	0.359115
$711$	1.93127	0.0724283
$712$	3.51416	0.131699
$713$	−17.8531	−0.668604
$714$	−2.00913	−0.0751899
$715$	−0.742090	−0.0277526
$716$	−3.78639	−0.141504
$717$	27.4246	1.02419
$718$	−25.2282	−0.941507
$719$	−2.03588	−0.0759255	−0.0379628	−	0.999279i	$-0.512087\pi$
$719$	−2.03588	−0.0759255	−0.0379628	+	0.999279i	$0.512087\pi$
$720$	−1.58623	−0.0591152
$721$	−15.8181	−0.589096
$722$	−12.3958	−0.461324
$723$	−15.1548	−0.563615
$724$	−21.2822	−0.790948
$725$	−4.16811	−0.154800
$726$	−10.4559	−0.388054
$727$	−51.2613	−1.90118	−0.950588	−	0.310454i	$-0.899519\pi$
$727$	−51.2613	−1.90118	−0.950588	+	0.310454i	$0.899519\pi$
$728$	0.634226	0.0235060
$729$	1.00000	0.0370370
$730$	−12.7675	−0.472547
$731$	−20.9534	−0.774988
$732$	0.508439	0.0187924
$733$	12.6254	0.466329	0.233164	−	0.972437i	$-0.425092\pi$
$733$	12.6254	0.466329	0.233164	+	0.972437i	$0.425092\pi$
$734$	−3.05206	−0.112654
$735$	−1.58623	−0.0585089
$736$	−3.56280	−0.131327
$737$	0.188384	0.00693920
$738$	−5.27648	−0.194230
$739$	4.58142	0.168530	0.0842652	−	0.996443i	$-0.473146\pi$
$739$	4.58142	0.168530	0.0842652	+	0.996443i	$0.473146\pi$
$740$	−12.2115	−0.448903
$741$	1.62987	0.0598749
$742$	−4.06450	−0.149212
$743$	8.96383	0.328851	0.164426	−	0.986389i	$-0.447423\pi$
$743$	8.96383	0.328851	0.164426	+	0.986389i	$0.447423\pi$
$744$	5.01097	0.183711
$745$	−10.2125	−0.374157
$746$	−36.3185	−1.32971
$747$	4.94310	0.180858
$748$	−1.48203	−0.0541883
$749$	−14.2898	−0.522138
$750$	11.8711	0.433473
$751$	26.5438	0.968596	0.484298	−	0.874903i	$-0.339075\pi$
$751$	26.5438	0.968596	0.484298	+	0.874903i	$0.339075\pi$
$752$	9.57465	0.349152
$753$	2.13325	0.0777398
$754$	1.06427	0.0387584
$755$	−6.02382	−0.219229
$756$	1.00000	0.0363696
$757$	16.0492	0.583317	0.291658	−	0.956523i	$-0.405793\pi$
$757$	16.0492	0.583317	0.291658	+	0.956523i	$0.405793\pi$
$758$	13.2112	0.479853
$759$	−2.62808	−0.0953933
$760$	−4.07639	−0.147866
$761$	−23.2236	−0.841855	−0.420927	−	0.907094i	$-0.638295\pi$
$761$	−23.2236	−0.841855	−0.420927	+	0.907094i	$0.638295\pi$
$762$	−0.598140	−0.0216683
$763$	16.7212	0.605349
$764$	−1.00000	−0.0361787
$765$	3.18694	0.115224
$766$	−15.1893	−0.548813
$767$	−1.23910	−0.0447414
$768$	1.00000	0.0360844
$769$	5.83918	0.210566	0.105283	−	0.994442i	$-0.466425\pi$
$769$	5.83918	0.210566	0.105283	+	0.994442i	$0.466425\pi$
$770$	−1.17007	−0.0421665
$771$	11.9630	0.430837
$772$	8.24313	0.296677
$773$	−7.30652	−0.262797	−0.131399	−	0.991330i	$-0.541947\pi$
$773$	−7.30652	−0.262797	−0.131399	+	0.991330i	$0.541947\pi$
$774$	10.4291	0.374865
$775$	−12.4467	−0.447098
$776$	12.4637	0.447421
$777$	7.69844	0.276180
$778$	−18.2391	−0.653903
$779$	−13.5598	−0.485832
$780$	−1.00603	−0.0360215
$781$	−4.44984	−0.159228
$782$	7.15814	0.255974
$783$	1.67806	0.0599689
$784$	1.00000	0.0357143
$785$	−17.8286	−0.636329
$786$	10.2758	0.366525
$787$	0.279280	0.00995526	0.00497763	−	0.999988i	$-0.498416\pi$
$787$	0.279280	0.00995526	0.00497763	+	0.999988i	$0.498416\pi$
$788$	−17.2367	−0.614031
$789$	19.6597	0.699905
$790$	−3.06343	−0.108992
$791$	1.61752	0.0575125
$792$	0.737645	0.0262111
$793$	0.322465	0.0114511
$794$	14.2963	0.507358
$795$	6.44721	0.228659
$796$	−4.54892	−0.161232
$797$	4.74574	0.168103	0.0840513	−	0.996461i	$-0.473214\pi$
$797$	4.74574	0.168103	0.0840513	+	0.996461i	$0.473214\pi$
$798$	2.56986	0.0909722
$799$	−19.2367	−0.680547
$800$	−2.48389	−0.0878186
$801$	3.51416	0.124167
$802$	−12.9023	−0.455595
$803$	5.93730	0.209523
$804$	0.255385	0.00900674
$805$	5.65141	0.199186
$806$	3.17809	0.111943
$807$	−1.90913	−0.0672047
$808$	16.4860	0.579976
$809$	−30.1122	−1.05869	−0.529344	−	0.848407i	$-0.677562\pi$
$809$	−30.1122	−1.05869	−0.529344	+	0.848407i	$0.677562\pi$
$810$	−1.58623	−0.0557343
$811$	1.73138	0.0607969	0.0303985	−	0.999538i	$-0.490322\pi$
$811$	1.73138	0.0607969	0.0303985	+	0.999538i	$0.490322\pi$
$812$	1.67806	0.0588883
$813$	10.6912	0.374956
$814$	5.67872	0.199039
$815$	−23.7586	−0.832226
$816$	−2.00913	−0.0703337
$817$	26.8012	0.937657
$818$	15.7848	0.551902
$819$	0.634226	0.0221616
$820$	8.36970	0.292283
$821$	−27.8190	−0.970889	−0.485444	−	0.874268i	$-0.661342\pi$
$821$	−27.8190	−0.970889	−0.485444	+	0.874268i	$0.661342\pi$
$822$	1.45460	0.0507348
$823$	−26.9660	−0.939977	−0.469989	−	0.882672i	$-0.655742\pi$
$823$	−26.9660	−0.939977	−0.469989	+	0.882672i	$0.655742\pi$
$824$	−15.8181	−0.551049
$825$	−1.83223	−0.0637899
$826$	−1.95373	−0.0679788
$827$	17.6179	0.612635	0.306317	−	0.951929i	$-0.400903\pi$
$827$	17.6179	0.612635	0.306317	+	0.951929i	$0.400903\pi$
$828$	−3.56280	−0.123816
$829$	−36.5951	−1.27100	−0.635501	−	0.772100i	$-0.719206\pi$
$829$	−36.5951	−1.27100	−0.635501	+	0.772100i	$0.719206\pi$
$830$	−7.84087	−0.272161
$831$	−20.3562	−0.706148
$832$	0.634226	0.0219878
$833$	−2.00913	−0.0696123
$834$	−2.52391	−0.0873958
$835$	4.24613	0.146944
$836$	1.89565	0.0655623
$837$	5.01097	0.173205
$838$	39.7195	1.37209
$839$	−50.1853	−1.73259	−0.866295	−	0.499533i	$-0.833505\pi$
$839$	−50.1853	−1.73259	−0.866295	+	0.499533i	$0.833505\pi$
$840$	−1.58623	−0.0547300
$841$	−26.1841	−0.902901
$842$	38.9983	1.34397
$843$	22.4032	0.771606
$844$	1.18055	0.0406362
$845$	19.9829	0.687433
$846$	9.57465	0.329183
$847$	−10.4559	−0.359268
$848$	−4.06450	−0.139575
$849$	−20.9374	−0.718571
$850$	4.99045	0.171171
$851$	−27.4280	−0.940220
$852$	−6.03250	−0.206670
$853$	−21.5339	−0.737306	−0.368653	−	0.929567i	$-0.620181\pi$
$853$	−21.5339	−0.737306	−0.368653	+	0.929567i	$0.620181\pi$
$854$	0.508439	0.0173984
$855$	−4.07639	−0.139409
$856$	−14.2898	−0.488416
$857$	−55.4218	−1.89317	−0.946586	−	0.322452i	$-0.895493\pi$
$857$	−55.4218	−1.89317	−0.946586	+	0.322452i	$0.895493\pi$
$858$	0.467833	0.0159716
$859$	47.9886	1.63735	0.818675	−	0.574257i	$-0.194709\pi$
$859$	47.9886	1.63735	0.818675	+	0.574257i	$0.194709\pi$
$860$	−16.5428	−0.564106
$861$	−5.27648	−0.179822
$862$	−40.0271	−1.36333
$863$	39.4215	1.34193	0.670963	−	0.741491i	$-0.265881\pi$
$863$	39.4215	1.34193	0.670963	+	0.741491i	$0.265881\pi$
$864$	1.00000	0.0340207
$865$	−8.89716	−0.302513
$866$	24.1281	0.819907
$867$	−12.9634	−0.440260
$868$	5.01097	0.170083
$869$	1.42459	0.0483259
$870$	−2.66178	−0.0902429
$871$	0.161972	0.00548821
$872$	16.7212	0.566252
$873$	12.4637	0.421833
$874$	−9.15591	−0.309703
$875$	11.8711	0.401318
$876$	8.04899	0.271950
$877$	−46.2881	−1.56304	−0.781520	−	0.623881i	$-0.785555\pi$
$877$	−46.2881	−1.56304	−0.781520	+	0.623881i	$0.785555\pi$
$878$	4.20457	0.141897
$879$	−3.39639	−0.114557
$880$	−1.17007	−0.0394431
$881$	−5.40990	−0.182264	−0.0911320	−	0.995839i	$-0.529049\pi$
$881$	−5.40990	−0.182264	−0.0911320	+	0.995839i	$0.529049\pi$
$882$	1.00000	0.0336718
$883$	−6.75207	−0.227225	−0.113613	−	0.993525i	$-0.536242\pi$
$883$	−6.75207	−0.227225	−0.113613	+	0.993525i	$0.536242\pi$
$884$	−1.27424	−0.0428574
$885$	3.09905	0.104174
$886$	15.3742	0.516508
$887$	40.6450	1.36472	0.682362	−	0.731014i	$-0.260953\pi$
$887$	40.6450	1.36472	0.682362	+	0.731014i	$0.260953\pi$
$888$	7.69844	0.258343
$889$	−0.598140	−0.0200610
$890$	−5.57426	−0.186850
$891$	0.737645	0.0247120
$892$	−4.97941	−0.166723
$893$	24.6055	0.823393
$894$	6.43824	0.215327
$895$	6.00607	0.200761
$896$	1.00000	0.0334077
$897$	−2.25962	−0.0754465
$898$	22.7013	0.757553
$899$	8.40871	0.280446
$900$	−2.48389	−0.0827962
$901$	8.16611	0.272053
$902$	−3.89217	−0.129595
$903$	10.4291	0.347057
$904$	1.61752	0.0537980
$905$	33.7584	1.12217
$906$	3.79758	0.126166
$907$	27.5996	0.916430	0.458215	−	0.888841i	$-0.348489\pi$
$907$	27.5996	0.916430	0.458215	+	0.888841i	$0.348489\pi$
$908$	−3.83824	−0.127377
$909$	16.4860	0.546806
$910$	−1.00603	−0.0333494
$911$	−15.3748	−0.509390	−0.254695	−	0.967021i	$-0.581975\pi$
$911$	−15.3748	−0.509390	−0.254695	+	0.967021i	$0.581975\pi$
$912$	2.56986	0.0850967
$913$	3.64625	0.120673
$914$	−33.4700	−1.10709
$915$	−0.806499	−0.0266620
$916$	22.0758	0.729406
$917$	10.2758	0.339337
$918$	−2.00913	−0.0663113
$919$	−41.4546	−1.36746	−0.683731	−	0.729734i	$-0.739644\pi$
$919$	−41.4546	−1.36746	−0.683731	+	0.729734i	$0.739644\pi$
$920$	5.65141	0.186321
$921$	8.27043	0.272520
$922$	−4.14941	−0.136654
$923$	−3.82597	−0.125933
$924$	0.737645	0.0242667
$925$	−19.1221	−0.628729
$926$	−22.0252	−0.723793
$927$	−15.8181	−0.519534
$928$	1.67806	0.0550850
$929$	−48.7027	−1.59788	−0.798942	−	0.601408i	$-0.794607\pi$
$929$	−48.7027	−1.59788	−0.798942	+	0.601408i	$0.794607\pi$
$930$	−7.94854	−0.260643
$931$	2.56986	0.0842239
$932$	−10.5131	−0.344369
$933$	−15.7206	−0.514670
$934$	−5.04837	−0.165188
$935$	2.35083	0.0768804
$936$	0.634226	0.0207303
$937$	−19.7433	−0.644984	−0.322492	−	0.946572i	$-0.604521\pi$
$937$	−19.7433	−0.644984	−0.322492	+	0.946572i	$0.604521\pi$
$938$	0.255385	0.00833862
$939$	22.5102	0.734591
$940$	−15.1876	−0.495364
$941$	29.9508	0.976367	0.488184	−	0.872741i	$-0.337660\pi$
$941$	29.9508	0.976367	0.488184	+	0.872741i	$0.337660\pi$
$942$	11.2396	0.366206
$943$	18.7991	0.612181
$944$	−1.95373	−0.0635884
$945$	−1.58623	−0.0516000
$946$	7.69294	0.250119
$947$	15.1372	0.491894	0.245947	−	0.969283i	$-0.420901\pi$
$947$	15.1372	0.491894	0.245947	+	0.969283i	$0.420901\pi$
$948$	1.93127	0.0627247
$949$	5.10487	0.165711
$950$	−6.38325	−0.207100
$951$	−27.4767	−0.890993
$952$	−2.00913	−0.0651164
$953$	15.9054	0.515226	0.257613	−	0.966248i	$-0.417064\pi$
$953$	15.9054	0.515226	0.257613	+	0.966248i	$0.417064\pi$
$954$	−4.06450	−0.131593
$955$	1.58623	0.0513291
$956$	27.4246	0.886974
$957$	1.23781	0.0400128
$958$	−11.6676	−0.376964
$959$	1.45460	0.0469713
$960$	−1.58623	−0.0511952
$961$	−5.89015	−0.190005
$962$	4.88255	0.157420
$963$	−14.2898	−0.460483
$964$	−15.1548	−0.488105
$965$	−13.0755	−0.420914
$966$	−3.56280	−0.114631
$967$	−10.2797	−0.330573	−0.165286	−	0.986246i	$-0.552855\pi$
$967$	−10.2797	−0.330573	−0.165286	+	0.986246i	$0.552855\pi$
$968$	−10.4559	−0.336065
$969$	−5.16320	−0.165866
$970$	−19.7703	−0.634785
$971$	−28.6995	−0.921011	−0.460506	−	0.887657i	$-0.652332\pi$
$971$	−28.6995	−0.921011	−0.460506	+	0.887657i	$0.652332\pi$
$972$	1.00000	0.0320750
$973$	−2.52391	−0.0809128
$974$	42.3684	1.35757
$975$	−1.57534	−0.0504514
$976$	0.508439	0.0162747
$977$	−23.1778	−0.741524	−0.370762	−	0.928728i	$-0.620903\pi$
$977$	−23.1778	−0.741524	−0.370762	+	0.928728i	$0.620903\pi$
$978$	14.9780	0.478945
$979$	2.59221	0.0828473
$980$	−1.58623	−0.0506702
$981$	16.7212	0.533868
$982$	−36.1422	−1.15334
$983$	2.00344	0.0638998	0.0319499	−	0.999489i	$-0.489828\pi$
$983$	2.00344	0.0638998	0.0319499	+	0.999489i	$0.489828\pi$
$984$	−5.27648	−0.168208
$985$	27.3413	0.871165
$986$	−3.37144	−0.107369
$987$	9.57465	0.304764
$988$	1.62987	0.0518532
$989$	−37.1566	−1.18151
$990$	−1.17007	−0.0371873
$991$	−36.0975	−1.14667	−0.573337	−	0.819320i	$-0.694351\pi$
$991$	−36.0975	−1.14667	−0.573337	+	0.819320i	$0.694351\pi$
$992$	5.01097	0.159099
$993$	34.4634	1.09366
$994$	−6.03250	−0.191339
$995$	7.21561	0.228750
$996$	4.94310	0.156628
$997$	25.2376	0.799284	0.399642	−	0.916671i	$-0.369134\pi$
$997$	25.2376	0.799284	0.399642	+	0.916671i	$0.369134\pi$
$998$	−38.0641	−1.20490
$999$	7.69844	0.243568

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.ba.1.5	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.ba.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.58623 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} -1.58623 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.58623 q^{10} +0.737645 q^{11} +1.00000 q^{12} +0.634226 q^{13} +1.00000 q^{14} -1.58623 q^{15} +1.00000 q^{16} -2.00913 q^{17} +1.00000 q^{18} +2.56986 q^{19} -1.58623 q^{20} +1.00000 q^{21} +0.737645 q^{22} -3.56280 q^{23} +1.00000 q^{24} -2.48389 q^{25} +0.634226 q^{26} +1.00000 q^{27} +1.00000 q^{28} +1.67806 q^{29} -1.58623 q^{30} +5.01097 q^{31} +1.00000 q^{32} +0.737645 q^{33} -2.00913 q^{34} -1.58623 q^{35} +1.00000 q^{36} +7.69844 q^{37} +2.56986 q^{38} +0.634226 q^{39} -1.58623 q^{40} -5.27648 q^{41} +1.00000 q^{42} +10.4291 q^{43} +0.737645 q^{44} -1.58623 q^{45} -3.56280 q^{46} +9.57465 q^{47} +1.00000 q^{48} +1.00000 q^{49} -2.48389 q^{50} -2.00913 q^{51} +0.634226 q^{52} -4.06450 q^{53} +1.00000 q^{54} -1.17007 q^{55} +1.00000 q^{56} +2.56986 q^{57} +1.67806 q^{58} -1.95373 q^{59} -1.58623 q^{60} +0.508439 q^{61} +5.01097 q^{62} +1.00000 q^{63} +1.00000 q^{64} -1.00603 q^{65} +0.737645 q^{66} +0.255385 q^{67} -2.00913 q^{68} -3.56280 q^{69} -1.58623 q^{70} -6.03250 q^{71} +1.00000 q^{72} +8.04899 q^{73} +7.69844 q^{74} -2.48389 q^{75} +2.56986 q^{76} +0.737645 q^{77} +0.634226 q^{78} +1.93127 q^{79} -1.58623 q^{80} +1.00000 q^{81} -5.27648 q^{82} +4.94310 q^{83} +1.00000 q^{84} +3.18694 q^{85} +10.4291 q^{86} +1.67806 q^{87} +0.737645 q^{88} +3.51416 q^{89} -1.58623 q^{90} +0.634226 q^{91} -3.56280 q^{92} +5.01097 q^{93} +9.57465 q^{94} -4.07639 q^{95} +1.00000 q^{96} +12.4637 q^{97} +1.00000 q^{98} +0.737645 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{2} + 16 q^{3} + 16 q^{4} + 11 q^{5} + 16 q^{6} + 16 q^{7} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 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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