LMFDB - Embedded newform 7942.2.a.bo.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} - 14x^{6} + 29x^{5} + 64x^{4} - 50x^{3} - 36x^{2} + 30x - 5 $ x^8 - 3x^7 - 14x^6 + 29x^5 + 64x^4 - 50x^3 - 36x^2 + 30*x - 5
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.960117$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.96012 q^{3} +1.00000 q^{4} +0.342083 q^{5} -1.96012 q^{6} +2.97928 q^{7} -1.00000 q^{8} +0.842060 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.96012 q^{3} +1.00000 q^{4} +0.342083 q^{5} -1.96012 q^{6} +2.97928 q^{7} -1.00000 q^{8} +0.842060 q^{9} -0.342083 q^{10} -1.00000 q^{11} +1.96012 q^{12} +5.18258 q^{13} -2.97928 q^{14} +0.670523 q^{15} +1.00000 q^{16} -1.22326 q^{17} -0.842060 q^{18} +0.342083 q^{20} +5.83974 q^{21} +1.00000 q^{22} +9.22765 q^{23} -1.96012 q^{24} -4.88298 q^{25} -5.18258 q^{26} -4.22982 q^{27} +2.97928 q^{28} +2.96691 q^{29} -0.670523 q^{30} +2.03355 q^{31} -1.00000 q^{32} -1.96012 q^{33} +1.22326 q^{34} +1.01916 q^{35} +0.842060 q^{36} -0.918957 q^{37} +10.1585 q^{39} -0.342083 q^{40} +8.14950 q^{41} -5.83974 q^{42} +8.17418 q^{43} -1.00000 q^{44} +0.288054 q^{45} -9.22765 q^{46} +0.0493107 q^{47} +1.96012 q^{48} +1.87610 q^{49} +4.88298 q^{50} -2.39774 q^{51} +5.18258 q^{52} -4.78039 q^{53} +4.22982 q^{54} -0.342083 q^{55} -2.97928 q^{56} -2.96691 q^{58} -3.40757 q^{59} +0.670523 q^{60} -12.4651 q^{61} -2.03355 q^{62} +2.50873 q^{63} +1.00000 q^{64} +1.77287 q^{65} +1.96012 q^{66} -3.70377 q^{67} -1.22326 q^{68} +18.0873 q^{69} -1.01916 q^{70} +16.0084 q^{71} -0.842060 q^{72} -6.87618 q^{73} +0.918957 q^{74} -9.57121 q^{75} -2.97928 q^{77} -10.1585 q^{78} +3.35069 q^{79} +0.342083 q^{80} -10.8171 q^{81} -8.14950 q^{82} +15.3543 q^{83} +5.83974 q^{84} -0.418457 q^{85} -8.17418 q^{86} +5.81550 q^{87} +1.00000 q^{88} +6.78881 q^{89} -0.288054 q^{90} +15.4404 q^{91} +9.22765 q^{92} +3.98600 q^{93} -0.0493107 q^{94} -1.96012 q^{96} +11.6117 q^{97} -1.87610 q^{98} -0.842060 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	$ 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * q^98 - 15 * 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
$3$	1.96012	1.13167	0.565837	−	0.824517i	$-0.308553\pi$
$3$	1.96012	1.13167	0.565837	+	0.824517i	$0.308553\pi$
$4$	1.00000	0.500000
$5$	0.342083	0.152984	0.0764921	−	0.997070i	$-0.475628\pi$
$5$	0.342083	0.152984	0.0764921	+	0.997070i	$0.475628\pi$
$6$	−1.96012	−0.800215
$7$	2.97928	1.12606	0.563031	−	0.826436i	$-0.309635\pi$
$7$	2.97928	1.12606	0.563031	+	0.826436i	$0.309635\pi$
$8$	−1.00000	−0.353553
$9$	0.842060	0.280687
$10$	−0.342083	−0.108176
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	1.96012	0.565837
$13$	5.18258	1.43739	0.718695	−	0.695326i	$-0.244740\pi$
$13$	5.18258	1.43739	0.718695	+	0.695326i	$0.244740\pi$
$14$	−2.97928	−0.796246
$15$	0.670523	0.173128
$16$	1.00000	0.250000
$17$	−1.22326	−0.296684	−0.148342	−	0.988936i	$-0.547394\pi$
$17$	−1.22326	−0.296684	−0.148342	+	0.988936i	$0.547394\pi$
$18$	−0.842060	−0.198475
$19$	0	0
$19$	0	0
$20$	0.342083	0.0764921
$21$	5.83974	1.27433
$22$	1.00000	0.213201
$23$	9.22765	1.92410	0.962049	−	0.272875i	$-0.0879745\pi$
$23$	9.22765	1.92410	0.962049	+	0.272875i	$0.0879745\pi$
$24$	−1.96012	−0.400107
$25$	−4.88298	−0.976596
$26$	−5.18258	−1.01639
$27$	−4.22982	−0.814029
$28$	2.97928	0.563031
$29$	2.96691	0.550942	0.275471	−	0.961309i	$-0.411166\pi$
$29$	2.96691	0.550942	0.275471	+	0.961309i	$0.411166\pi$
$30$	−0.670523	−0.122420
$31$	2.03355	0.365237	0.182618	−	0.983184i	$-0.441543\pi$
$31$	2.03355	0.365237	0.182618	+	0.983184i	$0.441543\pi$
$32$	−1.00000	−0.176777
$33$	−1.96012	−0.341213
$34$	1.22326	0.209788
$35$	1.01916	0.172270
$36$	0.842060	0.140343
$37$	−0.918957	−0.151076	−0.0755378	−	0.997143i	$-0.524067\pi$
$37$	−0.918957	−0.151076	−0.0755378	+	0.997143i	$0.524067\pi$
$38$	0	0
$39$	10.1585	1.62666
$40$	−0.342083	−0.0540881
$41$	8.14950	1.27274	0.636369	−	0.771385i	$-0.280436\pi$
$41$	8.14950	1.27274	0.636369	+	0.771385i	$0.280436\pi$
$42$	−5.83974	−0.901091
$43$	8.17418	1.24655	0.623275	−	0.782003i	$-0.285802\pi$
$43$	8.17418	1.24655	0.623275	+	0.782003i	$0.285802\pi$
$44$	−1.00000	−0.150756
$45$	0.288054	0.0429406
$46$	−9.22765	−1.36054
$47$	0.0493107	0.00719271	0.00359635	−	0.999994i	$-0.498855\pi$
$47$	0.0493107	0.00719271	0.00359635	+	0.999994i	$0.498855\pi$
$48$	1.96012	0.282919
$49$	1.87610	0.268014
$50$	4.88298	0.690558
$51$	−2.39774	−0.335750
$52$	5.18258	0.718695
$53$	−4.78039	−0.656637	−0.328319	−	0.944567i	$-0.606482\pi$
$53$	−4.78039	−0.656637	−0.328319	+	0.944567i	$0.606482\pi$
$54$	4.22982	0.575605
$55$	−0.342083	−0.0461265
$56$	−2.97928	−0.398123
$57$	0	0
$58$	−2.96691	−0.389575
$59$	−3.40757	−0.443628	−0.221814	−	0.975089i	$-0.571198\pi$
$59$	−3.40757	−0.443628	−0.221814	+	0.975089i	$0.571198\pi$
$60$	0.670523	0.0865642
$61$	−12.4651	−1.59599	−0.797994	−	0.602666i	$-0.794105\pi$
$61$	−12.4651	−1.59599	−0.797994	+	0.602666i	$0.794105\pi$
$62$	−2.03355	−0.258262
$63$	2.50873	0.316070
$64$	1.00000	0.125000
$65$	1.77287	0.219898
$66$	1.96012	0.241274
$67$	−3.70377	−0.452487	−0.226244	−	0.974071i	$-0.572645\pi$
$67$	−3.70377	−0.452487	−0.226244	+	0.974071i	$0.572645\pi$
$68$	−1.22326	−0.148342
$69$	18.0873	2.17745
$70$	−1.01916	−0.121813
$71$	16.0084	1.89985	0.949924	−	0.312482i	$-0.101160\pi$
$71$	16.0084	1.89985	0.949924	+	0.312482i	$0.101160\pi$
$72$	−0.842060	−0.0992377
$73$	−6.87618	−0.804795	−0.402398	−	0.915465i	$-0.631823\pi$
$73$	−6.87618	−0.804795	−0.402398	+	0.915465i	$0.631823\pi$
$74$	0.918957	0.106827
$75$	−9.57121	−1.10519
$76$	0	0
$77$	−2.97928	−0.339520
$78$	−10.1585	−1.15022
$79$	3.35069	0.376982	0.188491	−	0.982075i	$-0.439640\pi$
$79$	3.35069	0.376982	0.188491	+	0.982075i	$0.439640\pi$
$80$	0.342083	0.0382461
$81$	−10.8171	−1.20190
$82$	−8.14950	−0.899962
$83$	15.3543	1.68535	0.842676	−	0.538421i	$-0.180979\pi$
$83$	15.3543	1.68535	0.842676	+	0.538421i	$0.180979\pi$
$84$	5.83974	0.637167
$85$	−0.418457	−0.0453881
$86$	−8.17418	−0.881444
$87$	5.81550	0.623487
$88$	1.00000	0.106600
$89$	6.78881	0.719612	0.359806	−	0.933027i	$-0.382843\pi$
$89$	6.78881	0.719612	0.359806	+	0.933027i	$0.382843\pi$
$90$	−0.288054	−0.0303636
$91$	15.4404	1.61859
$92$	9.22765	0.962049
$93$	3.98600	0.413329
$94$	−0.0493107	−0.00508601
$95$	0	0
$96$	−1.96012	−0.200054
$97$	11.6117	1.17899	0.589495	−	0.807772i	$-0.299327\pi$
$97$	11.6117	1.17899	0.589495	+	0.807772i	$0.299327\pi$
$98$	−1.87610	−0.189515
$99$	−0.842060	−0.0846302
$100$	−4.88298	−0.488298
$101$	−19.0543	−1.89598	−0.947988	−	0.318307i	$-0.896886\pi$
$101$	−19.0543	−1.89598	−0.947988	+	0.318307i	$0.896886\pi$
$102$	2.39774	0.237411
$103$	−5.53494	−0.545373	−0.272687	−	0.962103i	$-0.587912\pi$
$103$	−5.53494	−0.545373	−0.272687	+	0.962103i	$0.587912\pi$
$104$	−5.18258	−0.508194
$105$	1.99768	0.194953
$106$	4.78039	0.464313
$107$	10.8363	1.04759	0.523793	−	0.851845i	$-0.324516\pi$
$107$	10.8363	1.04759	0.523793	+	0.851845i	$0.324516\pi$
$108$	−4.22982	−0.407014
$109$	1.70640	0.163444	0.0817218	−	0.996655i	$-0.473958\pi$
$109$	1.70640	0.163444	0.0817218	+	0.996655i	$0.473958\pi$
$110$	0.342083	0.0326164
$111$	−1.80126	−0.170968
$112$	2.97928	0.281515
$113$	−7.25202	−0.682213	−0.341106	−	0.940025i	$-0.610802\pi$
$113$	−7.25202	−0.682213	−0.341106	+	0.940025i	$0.610802\pi$
$114$	0	0
$115$	3.15663	0.294357
$116$	2.96691	0.275471
$117$	4.36404	0.403456
$118$	3.40757	0.313692
$119$	−3.64444	−0.334085
$120$	−0.670523	−0.0612101
$121$	1.00000	0.0909091
$122$	12.4651	1.12853
$123$	15.9740	1.44033
$124$	2.03355	0.182618
$125$	−3.38080	−0.302388
$126$	−2.50873	−0.223495
$127$	−7.99969	−0.709858	−0.354929	−	0.934893i	$-0.615495\pi$
$127$	−7.99969	−0.709858	−0.354929	+	0.934893i	$0.615495\pi$
$128$	−1.00000	−0.0883883
$129$	16.0223	1.41069
$130$	−1.77287	−0.155491
$131$	3.63042	0.317191	0.158595	−	0.987344i	$-0.449303\pi$
$131$	3.63042	0.317191	0.158595	+	0.987344i	$0.449303\pi$
$132$	−1.96012	−0.170606
$133$	0	0
$134$	3.70377	0.319957
$135$	−1.44695	−0.124534
$136$	1.22326	0.104894
$137$	2.45225	0.209510	0.104755	−	0.994498i	$-0.466594\pi$
$137$	2.45225	0.209510	0.104755	+	0.994498i	$0.466594\pi$
$138$	−18.0873	−1.53969
$139$	−19.2371	−1.63167	−0.815834	−	0.578286i	$-0.803722\pi$
$139$	−19.2371	−1.63167	−0.815834	+	0.578286i	$0.803722\pi$
$140$	1.01916	0.0861349
$141$	0.0966548	0.00813980
$142$	−16.0084	−1.34339
$143$	−5.18258	−0.433389
$144$	0.842060	0.0701716
$145$	1.01493	0.0842854
$146$	6.87618	0.569076
$147$	3.67738	0.303305
$148$	−0.918957	−0.0755378
$149$	7.52808	0.616724	0.308362	−	0.951269i	$-0.400219\pi$
$149$	7.52808	0.616724	0.308362	+	0.951269i	$0.400219\pi$
$150$	9.57121	0.781486
$151$	−14.0329	−1.14198	−0.570992	−	0.820955i	$-0.693441\pi$
$151$	−14.0329	−1.14198	−0.570992	+	0.820955i	$0.693441\pi$
$152$	0	0
$153$	−1.03006	−0.0832753
$154$	2.97928	0.240077
$155$	0.695644	0.0558755
$156$	10.1585	0.813329
$157$	21.9511	1.75189	0.875945	−	0.482410i	$-0.160239\pi$
$157$	21.9511	1.75189	0.875945	+	0.482410i	$0.160239\pi$
$158$	−3.35069	−0.266566
$159$	−9.37013	−0.743100
$160$	−0.342083	−0.0270441
$161$	27.4918	2.16665
$162$	10.8171	0.849873
$163$	−5.45282	−0.427098	−0.213549	−	0.976932i	$-0.568502\pi$
$163$	−5.45282	−0.427098	−0.213549	+	0.976932i	$0.568502\pi$
$164$	8.14950	0.636369
$165$	−0.670523	−0.0522002
$166$	−15.3543	−1.19172
$167$	16.0782	1.24417	0.622083	−	0.782951i	$-0.286287\pi$
$167$	16.0782	1.24417	0.622083	+	0.782951i	$0.286287\pi$
$168$	−5.83974	−0.450545
$169$	13.8592	1.06609
$170$	0.418457	0.0320942
$171$	0	0
$172$	8.17418	0.623275
$173$	−12.0015	−0.912460	−0.456230	−	0.889862i	$-0.650801\pi$
$173$	−12.0015	−0.912460	−0.456230	+	0.889862i	$0.650801\pi$
$174$	−5.81550	−0.440872
$175$	−14.5478	−1.09971
$176$	−1.00000	−0.0753778
$177$	−6.67923	−0.502042
$178$	−6.78881	−0.508843
$179$	23.2730	1.73951	0.869754	−	0.493486i	$-0.164278\pi$
$179$	23.2730	1.73951	0.869754	+	0.493486i	$0.164278\pi$
$180$	0.288054	0.0214703
$181$	−2.00003	−0.148661	−0.0743306	−	0.997234i	$-0.523682\pi$
$181$	−2.00003	−0.148661	−0.0743306	+	0.997234i	$0.523682\pi$
$182$	−15.4404	−1.14452
$183$	−24.4330	−1.80614
$184$	−9.22765	−0.680272
$185$	−0.314360	−0.0231122
$186$	−3.98600	−0.292268
$187$	1.22326	0.0894537
$188$	0.0493107	0.00359635
$189$	−12.6018	−0.916646
$190$	0	0
$191$	−5.19018	−0.375548	−0.187774	−	0.982212i	$-0.560127\pi$
$191$	−5.19018	−0.375548	−0.187774	+	0.982212i	$0.560127\pi$
$192$	1.96012	0.141459
$193$	−12.5071	−0.900278	−0.450139	−	0.892959i	$-0.648626\pi$
$193$	−12.5071	−0.900278	−0.450139	+	0.892959i	$0.648626\pi$
$194$	−11.6117	−0.833671
$195$	3.47504	0.248853
$196$	1.87610	0.134007
$197$	19.5451	1.39253	0.696264	−	0.717786i	$-0.254844\pi$
$197$	19.5451	1.39253	0.696264	+	0.717786i	$0.254844\pi$
$198$	0.842060	0.0598426
$199$	−13.2151	−0.936794	−0.468397	−	0.883518i	$-0.655168\pi$
$199$	−13.2151	−0.936794	−0.468397	+	0.883518i	$0.655168\pi$
$200$	4.88298	0.345279
$201$	−7.25982	−0.512068
$202$	19.0543	1.34066
$203$	8.83926	0.620394
$204$	−2.39774	−0.167875
$205$	2.78781	0.194709
$206$	5.53494	0.385637
$207$	7.77024	0.540069
$208$	5.18258	0.359347
$209$	0	0
$210$	−1.99768	−0.137853
$211$	12.7127	0.875181	0.437591	−	0.899174i	$-0.355832\pi$
$211$	12.7127	0.875181	0.437591	+	0.899174i	$0.355832\pi$
$212$	−4.78039	−0.328319
$213$	31.3783	2.15001
$214$	−10.8363	−0.740755
$215$	2.79625	0.190703
$216$	4.22982	0.287803
$217$	6.05852	0.411279
$218$	−1.70640	−0.115572
$219$	−13.4781	−0.910766
$220$	−0.342083	−0.0230632
$221$	−6.33965	−0.426451
$222$	1.80126	0.120893
$223$	18.6221	1.24703	0.623514	−	0.781812i	$-0.285704\pi$
$223$	18.6221	1.24703	0.623514	+	0.781812i	$0.285704\pi$
$224$	−2.97928	−0.199061
$225$	−4.11176	−0.274117
$226$	7.25202	0.482397
$227$	5.06203	0.335979	0.167989	−	0.985789i	$-0.446273\pi$
$227$	5.06203	0.335979	0.167989	+	0.985789i	$0.446273\pi$
$228$	0	0
$229$	−9.87119	−0.652307	−0.326153	−	0.945317i	$-0.605753\pi$
$229$	−9.87119	−0.652307	−0.326153	+	0.945317i	$0.605753\pi$
$230$	−3.15663	−0.208142
$231$	−5.83974	−0.384226
$232$	−2.96691	−0.194787
$233$	−8.22624	−0.538919	−0.269459	−	0.963012i	$-0.586845\pi$
$233$	−8.22624	−0.538919	−0.269459	+	0.963012i	$0.586845\pi$
$234$	−4.36404	−0.285286
$235$	0.0168684	0.00110037
$236$	−3.40757	−0.221814
$237$	6.56774	0.426620
$238$	3.64444	0.236234
$239$	17.1638	1.11023	0.555115	−	0.831773i	$-0.312674\pi$
$239$	17.1638	1.11023	0.555115	+	0.831773i	$0.312674\pi$
$240$	0.670523	0.0432821
$241$	16.7992	1.08213	0.541065	−	0.840981i	$-0.318021\pi$
$241$	16.7992	1.08213	0.541065	+	0.840981i	$0.318021\pi$
$242$	−1.00000	−0.0642824
$243$	−8.51336	−0.546133
$244$	−12.4651	−0.797994
$245$	0.641783	0.0410020
$246$	−15.9740	−1.01846
$247$	0	0
$248$	−2.03355	−0.129131
$249$	30.0962	1.90727
$250$	3.38080	0.213821
$251$	0.292558	0.0184661	0.00923304	−	0.999957i	$-0.497061\pi$
$251$	0.292558	0.0184661	0.00923304	+	0.999957i	$0.497061\pi$
$252$	2.50873	0.158035
$253$	−9.22765	−0.580138
$254$	7.99969	0.501946
$255$	−0.820225	−0.0513645
$256$	1.00000	0.0625000
$257$	1.72479	0.107590	0.0537948	−	0.998552i	$-0.482868\pi$
$257$	1.72479	0.107590	0.0537948	+	0.998552i	$0.482868\pi$
$258$	−16.0223	−0.997508
$259$	−2.73783	−0.170120
$260$	1.77287	0.109949
$261$	2.49832	0.154642
$262$	−3.63042	−0.224288
$263$	−23.8585	−1.47118	−0.735589	−	0.677428i	$-0.763094\pi$
$263$	−23.8585	−1.47118	−0.735589	+	0.677428i	$0.763094\pi$
$264$	1.96012	0.120637
$265$	−1.63529	−0.100455
$266$	0	0
$267$	13.3069	0.814366
$268$	−3.70377	−0.226244
$269$	16.5753	1.01061	0.505306	−	0.862940i	$-0.331380\pi$
$269$	16.5753	1.01061	0.505306	+	0.862940i	$0.331380\pi$
$270$	1.44695	0.0880585
$271$	−16.2076	−0.984544	−0.492272	−	0.870442i	$-0.663833\pi$
$271$	−16.2076	−0.984544	−0.492272	+	0.870442i	$0.663833\pi$
$272$	−1.22326	−0.0741711
$273$	30.2649	1.83172
$274$	−2.45225	−0.148146
$275$	4.88298	0.294455
$276$	18.0873	1.08873
$277$	−10.8091	−0.649455	−0.324728	−	0.945808i	$-0.605273\pi$
$277$	−10.8091	−0.649455	−0.324728	+	0.945808i	$0.605273\pi$
$278$	19.2371	1.15376
$279$	1.71237	0.102517
$280$	−1.01916	−0.0609065
$281$	−7.27459	−0.433965	−0.216983	−	0.976175i	$-0.569622\pi$
$281$	−7.27459	−0.433965	−0.216983	+	0.976175i	$0.569622\pi$
$282$	−0.0966548	−0.00575571
$283$	27.1163	1.61189	0.805947	−	0.591988i	$-0.201657\pi$
$283$	27.1163	1.61189	0.805947	+	0.591988i	$0.201657\pi$
$284$	16.0084	0.949924
$285$	0	0
$286$	5.18258	0.306453
$287$	24.2796	1.43318
$288$	−0.842060	−0.0496188
$289$	−15.5036	−0.911978
$290$	−1.01493	−0.0595988
$291$	22.7603	1.33423
$292$	−6.87618	−0.402398
$293$	−9.46921	−0.553197	−0.276599	−	0.960986i	$-0.589207\pi$
$293$	−9.46921	−0.553197	−0.276599	+	0.960986i	$0.589207\pi$
$294$	−3.67738	−0.214469
$295$	−1.16567	−0.0678681
$296$	0.918957	0.0534133
$297$	4.22982	0.245439
$298$	−7.52808	−0.436090
$299$	47.8231	2.76568
$300$	−9.57121	−0.552594
$301$	24.3531	1.40369
$302$	14.0329	0.807505
$303$	−37.3487	−2.14563
$304$	0	0
$305$	−4.26409	−0.244161
$306$	1.03006	0.0588846
$307$	−5.26742	−0.300628	−0.150314	−	0.988638i	$-0.548028\pi$
$307$	−5.26742	−0.300628	−0.150314	+	0.988638i	$0.548028\pi$
$308$	−2.97928	−0.169760
$309$	−10.8491	−0.617185
$310$	−0.695644	−0.0395100
$311$	−11.0327	−0.625609	−0.312804	−	0.949818i	$-0.601268\pi$
$311$	−11.0327	−0.625609	−0.312804	+	0.949818i	$0.601268\pi$
$312$	−10.1585	−0.575110
$313$	−24.7950	−1.40150	−0.700748	−	0.713409i	$-0.747150\pi$
$313$	−24.7950	−1.40150	−0.700748	+	0.713409i	$0.747150\pi$
$314$	−21.9511	−1.23877
$315$	0.858195	0.0483538
$316$	3.35069	0.188491
$317$	19.6311	1.10259	0.551295	−	0.834310i	$-0.314134\pi$
$317$	19.6311	1.10259	0.551295	+	0.834310i	$0.314134\pi$
$318$	9.37013	0.525451
$319$	−2.96691	−0.166115
$320$	0.342083	0.0191230
$321$	21.2405	1.18553
$322$	−27.4918	−1.53206
$323$	0	0
$324$	−10.8171	−0.600951
$325$	−25.3064	−1.40375
$326$	5.45282	0.302004
$327$	3.34475	0.184965
$328$	−8.14950	−0.449981
$329$	0.146910	0.00809943
$330$	0.670523	0.0369111
$331$	10.2142	0.561425	0.280713	−	0.959792i	$-0.409429\pi$
$331$	10.2142	0.561425	0.280713	+	0.959792i	$0.409429\pi$
$332$	15.3543	0.842676
$333$	−0.773817	−0.0424049
$334$	−16.0782	−0.879759
$335$	−1.26700	−0.0692234
$336$	5.83974	0.318584
$337$	21.5170	1.17211	0.586053	−	0.810273i	$-0.300681\pi$
$337$	21.5170	1.17211	0.586053	+	0.810273i	$0.300681\pi$
$338$	−13.8592	−0.753839
$339$	−14.2148	−0.772043
$340$	−0.418457	−0.0226940
$341$	−2.03355	−0.110123
$342$	0	0
$343$	−15.2655	−0.824261
$344$	−8.17418	−0.440722
$345$	6.18736	0.333116
$346$	12.0015	0.645207
$347$	−14.8913	−0.799409	−0.399704	−	0.916644i	$-0.630887\pi$
$347$	−14.8913	−0.799409	−0.399704	+	0.916644i	$0.630887\pi$
$348$	5.81550	0.311743
$349$	5.67467	0.303758	0.151879	−	0.988399i	$-0.451468\pi$
$349$	5.67467	0.303758	0.151879	+	0.988399i	$0.451468\pi$
$350$	14.5478	0.777610
$351$	−21.9214	−1.17008
$352$	1.00000	0.0533002
$353$	−14.3649	−0.764567	−0.382283	−	0.924045i	$-0.624862\pi$
$353$	−14.3649	−0.764567	−0.382283	+	0.924045i	$0.624862\pi$
$354$	6.67923	0.354997
$355$	5.47620	0.290647
$356$	6.78881	0.359806
$357$	−7.14352	−0.378075
$358$	−23.2730	−1.23002
$359$	18.2815	0.964860	0.482430	−	0.875935i	$-0.339754\pi$
$359$	18.2815	0.964860	0.482430	+	0.875935i	$0.339754\pi$
$360$	−0.288054	−0.0151818
$361$	0	0
$362$	2.00003	0.105119
$363$	1.96012	0.102879
$364$	15.4404	0.809295
$365$	−2.35222	−0.123121
$366$	24.4330	1.27713
$367$	27.2781	1.42391	0.711953	−	0.702227i	$-0.247811\pi$
$367$	27.2781	1.42391	0.711953	+	0.702227i	$0.247811\pi$
$368$	9.22765	0.481025
$369$	6.86237	0.357241
$370$	0.314360	0.0163428
$371$	−14.2421	−0.739414
$372$	3.98600	0.206665
$373$	−24.5991	−1.27369	−0.636846	−	0.770991i	$-0.719761\pi$
$373$	−24.5991	−1.27369	−0.636846	+	0.770991i	$0.719761\pi$
$374$	−1.22326	−0.0632533
$375$	−6.62677	−0.342205
$376$	−0.0493107	−0.00254301
$377$	15.3763	0.791918
$378$	12.6018	0.648167
$379$	15.7917	0.811165	0.405583	−	0.914058i	$-0.367069\pi$
$379$	15.7917	0.811165	0.405583	+	0.914058i	$0.367069\pi$
$380$	0	0
$381$	−15.6803	−0.803328
$382$	5.19018	0.265553
$383$	7.35935	0.376045	0.188023	−	0.982165i	$-0.439792\pi$
$383$	7.35935	0.376045	0.188023	+	0.982165i	$0.439792\pi$
$384$	−1.96012	−0.100027
$385$	−1.01916	−0.0519413
$386$	12.5071	0.636592
$387$	6.88314	0.349890
$388$	11.6117	0.589495
$389$	−0.147387	−0.00747280	−0.00373640	−	0.999993i	$-0.501189\pi$
$389$	−0.147387	−0.00747280	−0.00373640	+	0.999993i	$0.501189\pi$
$390$	−3.47504	−0.175966
$391$	−11.2878	−0.570850
$392$	−1.87610	−0.0947574
$393$	7.11604	0.358957
$394$	−19.5451	−0.984666
$395$	1.14621	0.0576723
$396$	−0.842060	−0.0423151
$397$	−30.7479	−1.54320	−0.771598	−	0.636111i	$-0.780542\pi$
$397$	−30.7479	−1.54320	−0.771598	+	0.636111i	$0.780542\pi$
$398$	13.2151	0.662414
$399$	0	0
$400$	−4.88298	−0.244149
$401$	27.2145	1.35903	0.679514	−	0.733663i	$-0.262191\pi$
$401$	27.2145	1.35903	0.679514	+	0.733663i	$0.262191\pi$
$402$	7.25982	0.362087
$403$	10.5391	0.524988
$404$	−19.0543	−0.947988
$405$	−3.70035	−0.183872
$406$	−8.83926	−0.438685
$407$	0.918957	0.0455510
$408$	2.39774	0.118706
$409$	−11.8165	−0.584291	−0.292145	−	0.956374i	$-0.594369\pi$
$409$	−11.8165	−0.584291	−0.292145	+	0.956374i	$0.594369\pi$
$410$	−2.78781	−0.137680
$411$	4.80670	0.237097
$412$	−5.53494	−0.272687
$413$	−10.1521	−0.499552
$414$	−7.77024	−0.381886
$415$	5.25245	0.257832
$416$	−5.18258	−0.254097
$417$	−37.7069	−1.84652
$418$	0	0
$419$	27.2073	1.32916	0.664581	−	0.747216i	$-0.268610\pi$
$419$	27.2073	1.32916	0.664581	+	0.747216i	$0.268610\pi$
$420$	1.99768	0.0974766
$421$	20.4229	0.995351	0.497675	−	0.867363i	$-0.334187\pi$
$421$	20.4229	0.995351	0.497675	+	0.867363i	$0.334187\pi$
$422$	−12.7127	−0.618846
$423$	0.0415226	0.00201890
$424$	4.78039	0.232156
$425$	5.97316	0.289741
$426$	−31.3783	−1.52029
$427$	−37.1369	−1.79718
$428$	10.8363	0.523793
$429$	−10.1585	−0.490456
$430$	−2.79625	−0.134847
$431$	−33.7220	−1.62433	−0.812165	−	0.583428i	$-0.801711\pi$
$431$	−33.7220	−1.62433	−0.812165	+	0.583428i	$0.801711\pi$
$432$	−4.22982	−0.203507
$433$	6.32601	0.304009	0.152004	−	0.988380i	$-0.451427\pi$
$433$	6.32601	0.304009	0.152004	+	0.988380i	$0.451427\pi$
$434$	−6.05852	−0.290818
$435$	1.98938	0.0953837
$436$	1.70640	0.0817218
$437$	0	0
$438$	13.4781	0.644009
$439$	−0.649985	−0.0310221	−0.0155111	−	0.999880i	$-0.504938\pi$
$439$	−0.649985	−0.0310221	−0.0155111	+	0.999880i	$0.504938\pi$
$440$	0.342083	0.0163082
$441$	1.57979	0.0752280
$442$	6.33965	0.301547
$443$	−7.66671	−0.364256	−0.182128	−	0.983275i	$-0.558299\pi$
$443$	−7.66671	−0.364256	−0.182128	+	0.983275i	$0.558299\pi$
$444$	−1.80126	−0.0854842
$445$	2.32234	0.110089
$446$	−18.6221	−0.881782
$447$	14.7559	0.697931
$448$	2.97928	0.140758
$449$	−38.0684	−1.79656	−0.898280	−	0.439424i	$-0.855183\pi$
$449$	−38.0684	−1.79656	−0.898280	+	0.439424i	$0.855183\pi$
$450$	4.11176	0.193830
$451$	−8.14950	−0.383745
$452$	−7.25202	−0.341106
$453$	−27.5062	−1.29235
$454$	−5.06203	−0.237573
$455$	5.28189	0.247619
$456$	0	0
$457$	−37.3691	−1.74805	−0.874026	−	0.485879i	$-0.838500\pi$
$457$	−37.3691	−1.74805	−0.874026	+	0.485879i	$0.838500\pi$
$458$	9.87119	0.461250
$459$	5.17417	0.241510
$460$	3.15663	0.147178
$461$	8.95491	0.417072	0.208536	−	0.978015i	$-0.433130\pi$
$461$	8.95491	0.417072	0.208536	+	0.978015i	$0.433130\pi$
$462$	5.83974	0.271689
$463$	−36.2926	−1.68666	−0.843330	−	0.537396i	$-0.819408\pi$
$463$	−36.2926	−1.68666	−0.843330	+	0.537396i	$0.819408\pi$
$464$	2.96691	0.137735
$465$	1.36354	0.0632329
$466$	8.22624	0.381073
$467$	21.6548	1.00207	0.501033	−	0.865428i	$-0.332954\pi$
$467$	21.6548	1.00207	0.501033	+	0.865428i	$0.332954\pi$
$468$	4.36404	0.201728
$469$	−11.0346	−0.509529
$470$	−0.0168684	−0.000778080 0
$471$	43.0268	1.98257
$472$	3.40757	0.156846
$473$	−8.17418	−0.375849
$474$	−6.56774	−0.301666
$475$	0	0
$476$	−3.64444	−0.167042
$477$	−4.02538	−0.184309
$478$	−17.1638	−0.785052
$479$	13.0122	0.594541	0.297271	−	0.954793i	$-0.403924\pi$
$479$	13.0122	0.594541	0.297271	+	0.954793i	$0.403924\pi$
$480$	−0.670523	−0.0306051
$481$	−4.76257	−0.217155
$482$	−16.7992	−0.765182
$483$	53.8871	2.45195
$484$	1.00000	0.0454545
$485$	3.97217	0.180367
$486$	8.51336	0.386174
$487$	22.9784	1.04125	0.520624	−	0.853786i	$-0.325699\pi$
$487$	22.9784	1.04125	0.520624	+	0.853786i	$0.325699\pi$
$488$	12.4651	0.564267
$489$	−10.6882	−0.483335
$490$	−0.641783	−0.0289928
$491$	35.8954	1.61994	0.809969	−	0.586473i	$-0.199484\pi$
$491$	35.8954	1.61994	0.809969	+	0.586473i	$0.199484\pi$
$492$	15.9740	0.720163
$493$	−3.62931	−0.163456
$494$	0	0
$495$	−0.288054	−0.0129471
$496$	2.03355	0.0913092
$497$	47.6935	2.13934
$498$	−30.0962	−1.34864
$499$	−33.7253	−1.50975	−0.754876	−	0.655868i	$-0.772303\pi$
$499$	−33.7253	−1.50975	−0.754876	+	0.655868i	$0.772303\pi$
$500$	−3.38080	−0.151194
$501$	31.5151	1.40799
$502$	−0.292558	−0.0130575
$503$	−14.2335	−0.634641	−0.317321	−	0.948318i	$-0.602783\pi$
$503$	−14.2335	−0.634641	−0.317321	+	0.948318i	$0.602783\pi$
$504$	−2.50873	−0.111748
$505$	−6.51816	−0.290054
$506$	9.22765	0.410219
$507$	27.1656	1.20647
$508$	−7.99969	−0.354929
$509$	23.3624	1.03552	0.517761	−	0.855525i	$-0.326766\pi$
$509$	23.3624	1.03552	0.517761	+	0.855525i	$0.326766\pi$
$510$	0.820225	0.0363202
$511$	−20.4860	−0.906249
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−1.72479	−0.0760773
$515$	−1.89341	−0.0834336
$516$	16.0223	0.705344
$517$	−0.0493107	−0.00216868
$518$	2.73783	0.120293
$519$	−23.5244	−1.03261
$520$	−1.77287	−0.0777457
$521$	0.250523	0.0109756	0.00548781	−	0.999985i	$-0.498253\pi$
$521$	0.250523	0.0109756	0.00548781	+	0.999985i	$0.498253\pi$
$522$	−2.49832	−0.109348
$523$	−7.76111	−0.339370	−0.169685	−	0.985498i	$-0.554275\pi$
$523$	−7.76111	−0.339370	−0.169685	+	0.985498i	$0.554275\pi$
$524$	3.63042	0.158595
$525$	−28.5153	−1.24451
$526$	23.8585	1.04028
$527$	−2.48757	−0.108360
$528$	−1.96012	−0.0853032
$529$	62.1496	2.70216
$530$	1.63529	0.0710326
$531$	−2.86938	−0.124520
$532$	0	0
$533$	42.2355	1.82942
$534$	−13.3069	−0.575844
$535$	3.70692	0.160264
$536$	3.70377	0.159978
$537$	45.6178	1.96856
$538$	−16.5753	−0.714611
$539$	−1.87610	−0.0808094
$540$	−1.44695	−0.0622668
$541$	−10.3162	−0.443528	−0.221764	−	0.975100i	$-0.571181\pi$
$541$	−10.3162	−0.443528	−0.221764	+	0.975100i	$0.571181\pi$
$542$	16.2076	0.696178
$543$	−3.92030	−0.168236
$544$	1.22326	0.0524469
$545$	0.583731	0.0250043
$546$	−30.2649	−1.29522
$547$	−24.4560	−1.04566	−0.522832	−	0.852436i	$-0.675125\pi$
$547$	−24.4560	−1.04566	−0.522832	+	0.852436i	$0.675125\pi$
$548$	2.45225	0.104755
$549$	−10.4963	−0.447972
$550$	−4.88298	−0.208211
$551$	0	0
$552$	−18.0873	−0.769846
$553$	9.98263	0.424504
$554$	10.8091	0.459234
$555$	−0.616182	−0.0261555
$556$	−19.2371	−0.815834
$557$	−7.49363	−0.317515	−0.158758	−	0.987318i	$-0.550749\pi$
$557$	−7.49363	−0.317515	−0.158758	+	0.987318i	$0.550749\pi$
$558$	−1.71237	−0.0724905
$559$	42.3633	1.79178
$560$	1.01916	0.0430674
$561$	2.39774	0.101232
$562$	7.27459	0.306860
$563$	−1.19409	−0.0503249	−0.0251624	−	0.999683i	$-0.508010\pi$
$563$	−1.19409	−0.0503249	−0.0251624	+	0.999683i	$0.508010\pi$
$564$	0.0966548	0.00406990
$565$	−2.48080	−0.104368
$566$	−27.1163	−1.13978
$567$	−32.2272	−1.35342
$568$	−16.0084	−0.671697
$569$	15.3486	0.643449	0.321724	−	0.946833i	$-0.395738\pi$
$569$	15.3486	0.643449	0.321724	+	0.946833i	$0.395738\pi$
$570$	0	0
$571$	26.7527	1.11956	0.559782	−	0.828640i	$-0.310885\pi$
$571$	26.7527	1.11956	0.559782	+	0.828640i	$0.310885\pi$
$572$	−5.18258	−0.216695
$573$	−10.1734	−0.424998
$574$	−24.2796	−1.01341
$575$	−45.0584	−1.87907
$576$	0.842060	0.0350858
$577$	42.2863	1.76040	0.880202	−	0.474600i	$-0.157407\pi$
$577$	42.2863	1.76040	0.880202	+	0.474600i	$0.157407\pi$
$578$	15.5036	0.644866
$579$	−24.5153	−1.01882
$580$	1.01493	0.0421427
$581$	45.7447	1.89781
$582$	−22.7603	−0.943444
$583$	4.78039	0.197984
$584$	6.87618	0.284538
$585$	1.49287	0.0617224
$586$	9.46921	0.391170
$587$	−30.1010	−1.24240	−0.621200	−	0.783652i	$-0.713355\pi$
$587$	−30.1010	−1.24240	−0.621200	+	0.783652i	$0.713355\pi$
$588$	3.67738	0.151652
$589$	0	0
$590$	1.16567	0.0479900
$591$	38.3106	1.57589
$592$	−0.918957	−0.0377689
$593$	−17.0212	−0.698979	−0.349489	−	0.936940i	$-0.613645\pi$
$593$	−17.0212	−0.698979	−0.349489	+	0.936940i	$0.613645\pi$
$594$	−4.22982	−0.173551
$595$	−1.24670	−0.0511097
$596$	7.52808	0.308362
$597$	−25.9032	−1.06015
$598$	−47.8231	−1.95563
$599$	−3.38621	−0.138357	−0.0691783	−	0.997604i	$-0.522038\pi$
$599$	−3.38621	−0.138357	−0.0691783	+	0.997604i	$0.522038\pi$
$600$	9.57121	0.390743
$601$	−11.2444	−0.458671	−0.229335	−	0.973347i	$-0.573655\pi$
$601$	−11.2444	−0.458671	−0.229335	+	0.973347i	$0.573655\pi$
$602$	−24.3531	−0.992560
$603$	−3.11879	−0.127007
$604$	−14.0329	−0.570992
$605$	0.342083	0.0139077
$606$	37.3487	1.51719
$607$	−23.3824	−0.949062	−0.474531	−	0.880239i	$-0.657382\pi$
$607$	−23.3824	−0.949062	−0.474531	+	0.880239i	$0.657382\pi$
$608$	0	0
$609$	17.3260	0.702084
$610$	4.26409	0.172648
$611$	0.255557	0.0103387
$612$	−1.03006	−0.0416377
$613$	−5.35125	−0.216135	−0.108068	−	0.994144i	$-0.534466\pi$
$613$	−5.35125	−0.216135	−0.108068	+	0.994144i	$0.534466\pi$
$614$	5.26742	0.212576
$615$	5.46443	0.220347
$616$	2.97928	0.120039
$617$	−27.2246	−1.09602	−0.548010	−	0.836472i	$-0.684614\pi$
$617$	−27.2246	−1.09602	−0.548010	+	0.836472i	$0.684614\pi$
$618$	10.8491	0.436416
$619$	2.97398	0.119534	0.0597672	−	0.998212i	$-0.480964\pi$
$619$	2.97398	0.119534	0.0597672	+	0.998212i	$0.480964\pi$
$620$	0.695644	0.0279378
$621$	−39.0313	−1.56627
$622$	11.0327	0.442372
$623$	20.2257	0.810327
$624$	10.1585	0.406664
$625$	23.2584	0.930335
$626$	24.7950	0.991008
$627$	0	0
$628$	21.9511	0.875945
$629$	1.12412	0.0448218
$630$	−0.858195	−0.0341913
$631$	19.2188	0.765087	0.382543	−	0.923938i	$-0.375048\pi$
$631$	19.2188	0.765087	0.382543	+	0.923938i	$0.375048\pi$
$632$	−3.35069	−0.133283
$633$	24.9185	0.990420
$634$	−19.6311	−0.779649
$635$	−2.73656	−0.108597
$636$	−9.37013	−0.371550
$637$	9.72305	0.385241
$638$	2.96691	0.117461
$639$	13.4800	0.533262
$640$	−0.342083	−0.0135220
$641$	32.0821	1.26717	0.633583	−	0.773675i	$-0.281583\pi$
$641$	32.0821	1.26717	0.633583	+	0.773675i	$0.281583\pi$
$642$	−21.2405	−0.838294
$643$	26.2122	1.03371	0.516853	−	0.856074i	$-0.327103\pi$
$643$	26.2122	1.03371	0.516853	+	0.856074i	$0.327103\pi$
$644$	27.4918	1.08333
$645$	5.48098	0.215813
$646$	0	0
$647$	−40.4393	−1.58983	−0.794916	−	0.606719i	$-0.792485\pi$
$647$	−40.4393	−1.58983	−0.794916	+	0.606719i	$0.792485\pi$
$648$	10.8171	0.424936
$649$	3.40757	0.133759
$650$	25.3064	0.992600
$651$	11.8754	0.465434
$652$	−5.45282	−0.213549
$653$	−47.2852	−1.85041	−0.925207	−	0.379464i	$-0.876109\pi$
$653$	−47.2852	−1.85041	−0.925207	+	0.379464i	$0.876109\pi$
$654$	−3.34475	−0.130790
$655$	1.24190	0.0485252
$656$	8.14950	0.318185
$657$	−5.79015	−0.225895
$658$	−0.146910	−0.00572716
$659$	−10.8196	−0.421472	−0.210736	−	0.977543i	$-0.567586\pi$
$659$	−10.8196	−0.421472	−0.210736	+	0.977543i	$0.567586\pi$
$660$	−0.670523	−0.0261001
$661$	20.8644	0.811529	0.405765	−	0.913978i	$-0.367005\pi$
$661$	20.8644	0.811529	0.405765	+	0.913978i	$0.367005\pi$
$662$	−10.2142	−0.396988
$663$	−12.4265	−0.482604
$664$	−15.3543	−0.595862
$665$	0	0
$666$	0.773817	0.0299848
$667$	27.3776	1.06007
$668$	16.0782	0.622083
$669$	36.5015	1.41123
$670$	1.26700	0.0489484
$671$	12.4651	0.481208
$672$	−5.83974	−0.225273
$673$	−11.5899	−0.446759	−0.223380	−	0.974732i	$-0.571709\pi$
$673$	−11.5899	−0.446759	−0.223380	+	0.974732i	$0.571709\pi$
$674$	−21.5170	−0.828804
$675$	20.6541	0.794977
$676$	13.8592	0.533045
$677$	11.0572	0.424965	0.212482	−	0.977165i	$-0.431845\pi$
$677$	11.0572	0.424965	0.212482	+	0.977165i	$0.431845\pi$
$678$	14.2148	0.545917
$679$	34.5945	1.32761
$680$	0.418457	0.0160471
$681$	9.92217	0.380218
$682$	2.03355	0.0778688
$683$	25.9782	0.994029	0.497014	−	0.867742i	$-0.334430\pi$
$683$	25.9782	0.994029	0.497014	+	0.867742i	$0.334430\pi$
$684$	0	0
$685$	0.838874	0.0320517
$686$	15.2655	0.582840
$687$	−19.3487	−0.738198
$688$	8.17418	0.311638
$689$	−24.7748	−0.943844
$690$	−6.18736	−0.235549
$691$	8.72761	0.332014	0.166007	−	0.986125i	$-0.446913\pi$
$691$	8.72761	0.332014	0.166007	+	0.986125i	$0.446913\pi$
$692$	−12.0015	−0.456230
$693$	−2.50873	−0.0952988
$694$	14.8913	0.565267
$695$	−6.58068	−0.249620
$696$	−5.81550	−0.220436
$697$	−9.96897	−0.377602
$698$	−5.67467	−0.214789
$699$	−16.1244	−0.609880
$700$	−14.5478	−0.549853
$701$	−52.5635	−1.98530	−0.992648	−	0.121034i	$-0.961379\pi$
$701$	−52.5635	−1.98530	−0.992648	+	0.121034i	$0.961379\pi$
$702$	21.9214	0.827369
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	0.0330640	0.00124526
$706$	14.3649	0.540630
$707$	−56.7681	−2.13498
$708$	−6.67923	−0.251021
$709$	20.4248	0.767069	0.383535	−	0.923527i	$-0.374707\pi$
$709$	20.4248	0.767069	0.383535	+	0.923527i	$0.374707\pi$
$710$	−5.47620	−0.205518
$711$	2.82148	0.105814
$712$	−6.78881	−0.254421
$713$	18.7649	0.702752
$714$	7.14352	0.267340
$715$	−1.77287	−0.0663018
$716$	23.2730	0.869754
$717$	33.6430	1.25642
$718$	−18.2815	−0.682259
$719$	−3.34079	−0.124590	−0.0622952	−	0.998058i	$-0.519842\pi$
$719$	−3.34079	−0.124590	−0.0622952	+	0.998058i	$0.519842\pi$
$720$	0.288054	0.0107352
$721$	−16.4901	−0.614124
$722$	0	0
$723$	32.9284	1.22462
$724$	−2.00003	−0.0743306
$725$	−14.4874	−0.538047
$726$	−1.96012	−0.0727468
$727$	40.6020	1.50584	0.752922	−	0.658110i	$-0.228644\pi$
$727$	40.6020	1.50584	0.752922	+	0.658110i	$0.228644\pi$
$728$	−15.4404	−0.572258
$729$	15.7642	0.583857
$730$	2.35222	0.0870597
$731$	−9.99915	−0.369832
$732$	−24.4330	−0.903069
$733$	−38.0560	−1.40563	−0.702814	−	0.711373i	$-0.748074\pi$
$733$	−38.0560	−1.40563	−0.702814	+	0.711373i	$0.748074\pi$
$734$	−27.2781	−1.00685
$735$	1.25797	0.0464009
$736$	−9.22765	−0.340136
$737$	3.70377	0.136430
$738$	−6.86237	−0.252607
$739$	−31.1226	−1.14486	−0.572432	−	0.819952i	$-0.694000\pi$
$739$	−31.1226	−1.14486	−0.572432	+	0.819952i	$0.694000\pi$
$740$	−0.314360	−0.0115561
$741$	0	0
$742$	14.2421	0.522845
$743$	−15.6136	−0.572808	−0.286404	−	0.958109i	$-0.592460\pi$
$743$	−15.6136	−0.572808	−0.286404	+	0.958109i	$0.592460\pi$
$744$	−3.98600	−0.146134
$745$	2.57523	0.0943491
$746$	24.5991	0.900636
$747$	12.9292	0.473056
$748$	1.22326	0.0447269
$749$	32.2844	1.17965
$750$	6.62677	0.241975
$751$	−22.8193	−0.832689	−0.416344	−	0.909207i	$-0.636689\pi$
$751$	−22.8193	−0.832689	−0.416344	+	0.909207i	$0.636689\pi$
$752$	0.0493107	0.00179818
$753$	0.573447	0.0208976
$754$	−15.3763	−0.559971
$755$	−4.80044	−0.174706
$756$	−12.6018	−0.458323
$757$	6.61868	0.240560	0.120280	−	0.992740i	$-0.461621\pi$
$757$	6.61868	0.240560	0.120280	+	0.992740i	$0.461621\pi$
$758$	−15.7917	−0.573581
$759$	−18.0873	−0.656527
$760$	0	0
$761$	−38.8244	−1.40738	−0.703691	−	0.710506i	$-0.748466\pi$
$761$	−38.8244	−1.40738	−0.703691	+	0.710506i	$0.748466\pi$
$762$	15.6803	0.568039
$763$	5.08384	0.184048
$764$	−5.19018	−0.187774
$765$	−0.352366	−0.0127398
$766$	−7.35935	−0.265904
$767$	−17.6600	−0.637666
$768$	1.96012	0.0707296
$769$	−18.1405	−0.654165	−0.327082	−	0.944996i	$-0.606065\pi$
$769$	−18.1405	−0.654165	−0.327082	+	0.944996i	$0.606065\pi$
$770$	1.01916	0.0367280
$771$	3.38079	0.121756
$772$	−12.5071	−0.450139
$773$	−22.6562	−0.814888	−0.407444	−	0.913230i	$-0.633580\pi$
$773$	−22.6562	−0.814888	−0.407444	+	0.913230i	$0.633580\pi$
$774$	−6.88314	−0.247409
$775$	−9.92980	−0.356689
$776$	−11.6117	−0.416836
$777$	−5.36647	−0.192521
$778$	0.147387	0.00528406
$779$	0	0
$780$	3.47504	0.124426
$781$	−16.0084	−0.572825
$782$	11.2878	0.403652
$783$	−12.5495	−0.448482
$784$	1.87610	0.0670036
$785$	7.50911	0.268012
$786$	−7.11604	−0.253821
$787$	−34.8975	−1.24396	−0.621980	−	0.783033i	$-0.713672\pi$
$787$	−34.8975	−1.24396	−0.621980	+	0.783033i	$0.713672\pi$
$788$	19.5451	0.696264
$789$	−46.7654	−1.66489
$790$	−1.14621	−0.0407804
$791$	−21.6058	−0.768214
$792$	0.842060	0.0299213
$793$	−64.6012	−2.29406
$794$	30.7479	1.09120
$795$	−3.20536	−0.113683
$796$	−13.2151	−0.468397
$797$	−24.9733	−0.884598	−0.442299	−	0.896868i	$-0.645837\pi$
$797$	−24.9733	−0.884598	−0.442299	+	0.896868i	$0.645837\pi$
$798$	0	0
$799$	−0.0603199	−0.00213396
$800$	4.88298	0.172639
$801$	5.71658	0.201985
$802$	−27.2145	−0.960978
$803$	6.87618	0.242655
$804$	−7.25982	−0.256034
$805$	9.40447	0.331464
$806$	−10.5391	−0.371222
$807$	32.4895	1.14368
$808$	19.0543	0.670329
$809$	0.270051	0.00949448	0.00474724	−	0.999989i	$-0.498489\pi$
$809$	0.270051	0.00949448	0.00474724	+	0.999989i	$0.498489\pi$
$810$	3.70035	0.130017
$811$	−9.56304	−0.335804	−0.167902	−	0.985804i	$-0.553699\pi$
$811$	−9.56304	−0.335804	−0.167902	+	0.985804i	$0.553699\pi$
$812$	8.83926	0.310197
$813$	−31.7689	−1.11418
$814$	−0.918957	−0.0322094
$815$	−1.86532	−0.0653392
$816$	−2.39774	−0.0839375
$817$	0	0
$818$	11.8165	0.413156
$819$	13.0017	0.454316
$820$	2.78781	0.0973545
$821$	53.7067	1.87438	0.937188	−	0.348824i	$-0.113419\pi$
$821$	53.7067	1.87438	0.937188	+	0.348824i	$0.113419\pi$
$822$	−4.80670	−0.167653
$823$	−0.678061	−0.0236357	−0.0118179	−	0.999930i	$-0.503762\pi$
$823$	−0.678061	−0.0236357	−0.0118179	+	0.999930i	$0.503762\pi$
$824$	5.53494	0.192819
$825$	9.57121	0.333227
$826$	10.1521	0.353237
$827$	−23.5323	−0.818298	−0.409149	−	0.912468i	$-0.634174\pi$
$827$	−23.5323	−0.818298	−0.409149	+	0.912468i	$0.634174\pi$
$828$	7.77024	0.270034
$829$	−11.1934	−0.388762	−0.194381	−	0.980926i	$-0.562270\pi$
$829$	−11.1934	−0.388762	−0.194381	+	0.980926i	$0.562270\pi$
$830$	−5.25245	−0.182315
$831$	−21.1871	−0.734972
$832$	5.18258	0.179674
$833$	−2.29496	−0.0795157
$834$	37.7069	1.30568
$835$	5.50007	0.190338
$836$	0	0
$837$	−8.60156	−0.297313
$838$	−27.2073	−0.939860
$839$	35.0122	1.20875	0.604377	−	0.796698i	$-0.293422\pi$
$839$	35.0122	1.20875	0.604377	+	0.796698i	$0.293422\pi$
$840$	−1.99768	−0.0689264
$841$	−20.1974	−0.696463
$842$	−20.4229	−0.703819
$843$	−14.2590	−0.491108
$844$	12.7127	0.437591
$845$	4.74099	0.163095
$846$	−0.0415226	−0.00142757
$847$	2.97928	0.102369
$848$	−4.78039	−0.164159
$849$	53.1510	1.82414
$850$	−5.97316	−0.204878
$851$	−8.47982	−0.290684
$852$	31.3783	1.07500
$853$	−5.53439	−0.189494	−0.0947469	−	0.995501i	$-0.530204\pi$
$853$	−5.53439	−0.189494	−0.0947469	+	0.995501i	$0.530204\pi$
$854$	37.1369	1.27080
$855$	0	0
$856$	−10.8363	−0.370378
$857$	−13.6508	−0.466302	−0.233151	−	0.972441i	$-0.574904\pi$
$857$	−13.6508	−0.466302	−0.233151	+	0.972441i	$0.574904\pi$
$858$	10.1585	0.346804
$859$	52.3106	1.78482	0.892408	−	0.451230i	$-0.149015\pi$
$859$	52.3106	1.78482	0.892408	+	0.451230i	$0.149015\pi$
$860$	2.79625	0.0953513
$861$	47.5909	1.62189
$862$	33.7220	1.14857
$863$	20.0987	0.684167	0.342083	−	0.939670i	$-0.388867\pi$
$863$	20.0987	0.684167	0.342083	+	0.939670i	$0.388867\pi$
$864$	4.22982	0.143901
$865$	−4.10552	−0.139592
$866$	−6.32601	−0.214967
$867$	−30.3889	−1.03206
$868$	6.05852	0.205640
$869$	−3.35069	−0.113664
$870$	−1.98938	−0.0674464
$871$	−19.1951	−0.650401
$872$	−1.70640	−0.0577860
$873$	9.77774	0.330926
$874$	0	0
$875$	−10.0723	−0.340508
$876$	−13.4781	−0.455383
$877$	−16.6518	−0.562293	−0.281147	−	0.959665i	$-0.590715\pi$
$877$	−16.6518	−0.562293	−0.281147	+	0.959665i	$0.590715\pi$
$878$	0.649985	0.0219359
$879$	−18.5608	−0.626039
$880$	−0.342083	−0.0115316
$881$	30.0317	1.01179	0.505897	−	0.862594i	$-0.331162\pi$
$881$	30.0317	1.01179	0.505897	+	0.862594i	$0.331162\pi$
$882$	−1.57979	−0.0531942
$883$	45.7852	1.54080	0.770398	−	0.637564i	$-0.220058\pi$
$883$	45.7852	1.54080	0.770398	+	0.637564i	$0.220058\pi$
$884$	−6.33965	−0.213226
$885$	−2.28485	−0.0768045
$886$	7.66671	0.257568
$887$	32.5339	1.09238	0.546192	−	0.837660i	$-0.316077\pi$
$887$	32.5339	1.09238	0.546192	+	0.837660i	$0.316077\pi$
$888$	1.80126	0.0604465
$889$	−23.8333	−0.799344
$890$	−2.32234	−0.0778449
$891$	10.8171	0.362387
$892$	18.6221	0.623514
$893$	0	0
$894$	−14.7559	−0.493512
$895$	7.96131	0.266117
$896$	−2.97928	−0.0995307
$897$	93.7388	3.12985
$898$	38.0684	1.27036
$899$	6.03337	0.201224
$900$	−4.11176	−0.137059
$901$	5.84767	0.194814
$902$	8.14950	0.271349
$903$	47.7350	1.58852
$904$	7.25202	0.241199
$905$	−0.684177	−0.0227428
$906$	27.5062	0.913833
$907$	−44.2176	−1.46822	−0.734110	−	0.679030i	$-0.762400\pi$
$907$	−44.2176	−1.46822	−0.734110	+	0.679030i	$0.762400\pi$
$908$	5.06203	0.167989
$909$	−16.0449	−0.532175
$910$	−5.28189	−0.175093
$911$	29.2992	0.970725	0.485363	−	0.874313i	$-0.338688\pi$
$911$	29.2992	0.970725	0.485363	+	0.874313i	$0.338688\pi$
$912$	0	0
$913$	−15.3543	−0.508153
$914$	37.3691	1.23606
$915$	−8.35811	−0.276311
$916$	−9.87119	−0.326153
$917$	10.8160	0.357176
$918$	−5.17417	−0.170773
$919$	−33.6293	−1.10933	−0.554664	−	0.832074i	$-0.687153\pi$
$919$	−33.6293	−1.10933	−0.554664	+	0.832074i	$0.687153\pi$
$920$	−3.15663	−0.104071
$921$	−10.3248	−0.340212
$922$	−8.95491	−0.294914
$923$	82.9648	2.73082
$924$	−5.83974	−0.192113
$925$	4.48725	0.147540
$926$	36.2926	1.19265
$927$	−4.66075	−0.153079
$928$	−2.96691	−0.0973937
$929$	7.37638	0.242011	0.121006	−	0.992652i	$-0.461388\pi$
$929$	7.37638	0.242011	0.121006	+	0.992652i	$0.461388\pi$
$930$	−1.36354	−0.0447124
$931$	0	0
$932$	−8.22624	−0.269459
$933$	−21.6254	−0.707985
$934$	−21.6548	−0.708567
$935$	0.418457	0.0136850
$936$	−4.36404	−0.142643
$937$	12.2990	0.401790	0.200895	−	0.979613i	$-0.435615\pi$
$937$	12.2990	0.401790	0.200895	+	0.979613i	$0.435615\pi$
$938$	11.0346	0.360291
$939$	−48.6011	−1.58604
$940$	0.0168684	0.000550185 0
$941$	−19.6959	−0.642069	−0.321034	−	0.947068i	$-0.604031\pi$
$941$	−19.6959	−0.642069	−0.321034	+	0.947068i	$0.604031\pi$
$942$	−43.0268	−1.40189
$943$	75.2008	2.44887
$944$	−3.40757	−0.110907
$945$	−4.31086	−0.140232
$946$	8.17418	0.265765
$947$	−3.24316	−0.105389	−0.0526943	−	0.998611i	$-0.516781\pi$
$947$	−3.24316	−0.105389	−0.0526943	+	0.998611i	$0.516781\pi$
$948$	6.56774	0.213310
$949$	−35.6363	−1.15680
$950$	0	0
$951$	38.4792	1.24777
$952$	3.64444	0.118117
$953$	−24.4153	−0.790890	−0.395445	−	0.918490i	$-0.629410\pi$
$953$	−24.4153	−0.790890	−0.395445	+	0.918490i	$0.629410\pi$
$954$	4.02538	0.130326
$955$	−1.77547	−0.0574529
$956$	17.1638	0.555115
$957$	−5.81550	−0.187988
$958$	−13.0122	−0.420404
$959$	7.30594	0.235921
$960$	0.670523	0.0216410
$961$	−26.8647	−0.866602
$962$	4.76257	0.153551
$963$	9.12483	0.294043
$964$	16.7992	0.541065
$965$	−4.27845	−0.137728
$966$	−53.8871	−1.73379
$967$	40.7330	1.30989	0.654943	−	0.755678i	$-0.272693\pi$
$967$	40.7330	1.30989	0.654943	+	0.755678i	$0.272693\pi$
$968$	−1.00000	−0.0321412
$969$	0	0
$970$	−3.97217	−0.127539
$971$	34.5938	1.11017	0.555085	−	0.831794i	$-0.312686\pi$
$971$	34.5938	1.11017	0.555085	+	0.831794i	$0.312686\pi$
$972$	−8.51336	−0.273066
$973$	−57.3126	−1.83736
$974$	−22.9784	−0.736274
$975$	−49.6036	−1.58859
$976$	−12.4651	−0.398997
$977$	6.57795	0.210447	0.105224	−	0.994449i	$-0.466444\pi$
$977$	6.57795	0.210447	0.105224	+	0.994449i	$0.466444\pi$
$978$	10.6882	0.341770
$979$	−6.78881	−0.216971
$980$	0.641783	0.0205010
$981$	1.43689	0.0458764
$982$	−35.8954	−1.14547
$983$	−9.60959	−0.306498	−0.153249	−	0.988188i	$-0.548974\pi$
$983$	−9.60959	−0.306498	−0.153249	+	0.988188i	$0.548974\pi$
$984$	−15.9740	−0.509232
$985$	6.68604	0.213035
$986$	3.62931	0.115581
$987$	0.287961	0.00916591
$988$	0	0
$989$	75.4285	2.39849
$990$	0.288054	0.00915497
$991$	−43.9400	−1.39580	−0.697900	−	0.716195i	$-0.745882\pi$
$991$	−43.9400	−1.39580	−0.697900	+	0.716195i	$0.745882\pi$
$992$	−2.03355	−0.0645654
$993$	20.0211	0.635351
$994$	−47.6935	−1.51275
$995$	−4.52067	−0.143315
$996$	30.0962	0.953635
$997$	20.1903	0.639432	0.319716	−	0.947513i	$-0.396412\pi$
$997$	20.1903	0.639432	0.319716	+	0.947513i	$0.396412\pi$
$998$	33.7253	1.06756
$999$	3.88702	0.122980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bo.1.6	✓	8
19.18	odd	2		7942.2.a.bp.1.3	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7942.2.a.bo.1.6	✓	8	1.1	even	1	trivial
7942.2.a.bp.1.3	yes	8	19.18	odd	2

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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.96012 q^{3} +1.00000 q^{4} +0.342083 q^{5} -1.96012 q^{6} +2.97928 q^{7} -1.00000 q^{8} +0.842060 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.96012 q^{3} +1.00000 q^{4} +0.342083 q^{5} -1.96012 q^{6} +2.97928 q^{7} -1.00000 q^{8} +0.842060 q^{9} -0.342083 q^{10} -1.00000 q^{11} +1.96012 q^{12} +5.18258 q^{13} -2.97928 q^{14} +0.670523 q^{15} +1.00000 q^{16} -1.22326 q^{17} -0.842060 q^{18} +0.342083 q^{20} +5.83974 q^{21} +1.00000 q^{22} +9.22765 q^{23} -1.96012 q^{24} -4.88298 q^{25} -5.18258 q^{26} -4.22982 q^{27} +2.97928 q^{28} +2.96691 q^{29} -0.670523 q^{30} +2.03355 q^{31} -1.00000 q^{32} -1.96012 q^{33} +1.22326 q^{34} +1.01916 q^{35} +0.842060 q^{36} -0.918957 q^{37} +10.1585 q^{39} -0.342083 q^{40} +8.14950 q^{41} -5.83974 q^{42} +8.17418 q^{43} -1.00000 q^{44} +0.288054 q^{45} -9.22765 q^{46} +0.0493107 q^{47} +1.96012 q^{48} +1.87610 q^{49} +4.88298 q^{50} -2.39774 q^{51} +5.18258 q^{52} -4.78039 q^{53} +4.22982 q^{54} -0.342083 q^{55} -2.97928 q^{56} -2.96691 q^{58} -3.40757 q^{59} +0.670523 q^{60} -12.4651 q^{61} -2.03355 q^{62} +2.50873 q^{63} +1.00000 q^{64} +1.77287 q^{65} +1.96012 q^{66} -3.70377 q^{67} -1.22326 q^{68} +18.0873 q^{69} -1.01916 q^{70} +16.0084 q^{71} -0.842060 q^{72} -6.87618 q^{73} +0.918957 q^{74} -9.57121 q^{75} -2.97928 q^{77} -10.1585 q^{78} +3.35069 q^{79} +0.342083 q^{80} -10.8171 q^{81} -8.14950 q^{82} +15.3543 q^{83} +5.83974 q^{84} -0.418457 q^{85} -8.17418 q^{86} +5.81550 q^{87} +1.00000 q^{88} +6.78881 q^{89} -0.288054 q^{90} +15.4404 q^{91} +9.22765 q^{92} +3.98600 q^{93} -0.0493107 q^{94} -1.96012 q^{96} +11.6117 q^{97} -1.87610 q^{98} -0.842060 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9}+O(q^{10}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9	\( 8 q - 8 q^{2} + 5 q^{3} + 8 q^{4} + q^{5} - 5 q^{6} - 4 q^{7} - 8 q^{8} + 15 q^{9} - q^{10} - 8 q^{11} + 5 q^{12} + 3 q^{13} + 4 q^{14} + 34 q^{15} + 8 q^{16} - 6 q^{17} - 15 q^{18} + q^{20} - 11 q^{21} + 8 q^{22} + 9 q^{23} - 5 q^{24} + q^{25} - 3 q^{26} + 14 q^{27} - 4 q^{28} + 4 q^{29} - 34 q^{30} + 11 q^{31} - 8 q^{32} - 5 q^{33} + 6 q^{34} - 9 q^{35} + 15 q^{36} - 10 q^{37} + 2 q^{39} - q^{40} + 29 q^{41} + 11 q^{42} + 2 q^{43} - 8 q^{44} + 19 q^{45} - 9 q^{46} + 5 q^{48} - 8 q^{49} - q^{50} + 2 q^{51} + 3 q^{52} + 59 q^{53} - 14 q^{54} - q^{55} + 4 q^{56} - 4 q^{58} + 23 q^{59} + 34 q^{60} - 2 q^{61} - 11 q^{62} - 51 q^{63} + 8 q^{64} + 8 q^{65} + 5 q^{66} - 3 q^{67} - 6 q^{68} + 20 q^{69} + 9 q^{70} + q^{71} - 15 q^{72} - 6 q^{73} + 10 q^{74} - 15 q^{75} + 4 q^{77} - 2 q^{78} + q^{80} + 48 q^{81} - 29 q^{82} + 15 q^{83} - 11 q^{84} - 10 q^{85} - 2 q^{86} - 15 q^{87} + 8 q^{88} + 4 q^{89} - 19 q^{90} + 47 q^{91} + 9 q^{92} + 31 q^{93} - 5 q^{96} + 62 q^{97} + 8 q^{98} - 15 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 + 5 * q^3 + 8 * q^4 + q^5 - 5 * q^6 - 4 * q^7 - 8 * q^8 + 15 * q^9 - q^10 - 8 * q^11 + 5 * q^12 + 3 * q^13 + 4 * q^14 + 34 * q^15 + 8 * q^16 - 6 * q^17 - 15 * q^18 + q^20 - 11 * q^21 + 8 * q^22 + 9 * q^23 - 5 * q^24 + q^25 - 3 * q^26 + 14 * q^27 - 4 * q^28 + 4 * q^29 - 34 * q^30 + 11 * q^31 - 8 * q^32 - 5 * q^33 + 6 * q^34 - 9 * q^35 + 15 * q^36 - 10 * q^37 + 2 * q^39 - q^40 + 29 * q^41 + 11 * q^42 + 2 * q^43 - 8 * q^44 + 19 * q^45 - 9 * q^46 + 5 * q^48 - 8 * q^49 - q^50 + 2 * q^51 + 3 * q^52 + 59 * q^53 - 14 * q^54 - q^55 + 4 * q^56 - 4 * q^58 + 23 * q^59 + 34 * q^60 - 2 * q^61 - 11 * q^62 - 51 * q^63 + 8 * q^64 + 8 * q^65 + 5 * q^66 - 3 * q^67 - 6 * q^68 + 20 * q^69 + 9 * q^70 + q^71 - 15 * q^72 - 6 * q^73 + 10 * q^74 - 15 * q^75 + 4 * q^77 - 2 * q^78 + q^80 + 48 * q^81 - 29 * q^82 + 15 * q^83 - 11 * q^84 - 10 * q^85 - 2 * q^86 - 15 * q^87 + 8 * q^88 + 4 * q^89 - 19 * q^90 + 47 * q^91 + 9 * q^92 + 31 * q^93 - 5 * q^96 + 62 * q^97 + 8 * q^98 - 15 * q^99

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