LMFDB - Embedded newform 8022.2.a.w.1.13

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:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 39 x^{11} + 67 x^{10} + 588 x^{9} - 823 x^{8} - 4265 x^{7} + 4419 x^{6} + 14926 x^{5} + \cdots - 984 $ x^13 - 2x^12 - 39x^11 + 67x^10 + 588x^9 - 823x^8 - 4265x^7 + 4419x^6 + 14926x^5 - 9090x^4 - 21330x^3 + 2178x^2 + 5892x - 984
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$-3.35344$ of defining polynomial
Character	$\chi$	$=$	8022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.35344 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.35344 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.35344 q^{10} -4.97051 q^{11} +1.00000 q^{12} +4.24592 q^{13} +1.00000 q^{14} +3.35344 q^{15} +1.00000 q^{16} -4.37776 q^{17} -1.00000 q^{18} -1.85037 q^{19} +3.35344 q^{20} -1.00000 q^{21} +4.97051 q^{22} +3.23003 q^{23} -1.00000 q^{24} +6.24556 q^{25} -4.24592 q^{26} +1.00000 q^{27} -1.00000 q^{28} +7.23952 q^{29} -3.35344 q^{30} +1.55659 q^{31} -1.00000 q^{32} -4.97051 q^{33} +4.37776 q^{34} -3.35344 q^{35} +1.00000 q^{36} +4.92819 q^{37} +1.85037 q^{38} +4.24592 q^{39} -3.35344 q^{40} +3.33098 q^{41} +1.00000 q^{42} +1.36529 q^{43} -4.97051 q^{44} +3.35344 q^{45} -3.23003 q^{46} -3.65068 q^{47} +1.00000 q^{48} +1.00000 q^{49} -6.24556 q^{50} -4.37776 q^{51} +4.24592 q^{52} +5.41989 q^{53} -1.00000 q^{54} -16.6683 q^{55} +1.00000 q^{56} -1.85037 q^{57} -7.23952 q^{58} -9.62729 q^{59} +3.35344 q^{60} +11.9716 q^{61} -1.55659 q^{62} -1.00000 q^{63} +1.00000 q^{64} +14.2385 q^{65} +4.97051 q^{66} +6.35600 q^{67} -4.37776 q^{68} +3.23003 q^{69} +3.35344 q^{70} -11.8152 q^{71} -1.00000 q^{72} +6.38145 q^{73} -4.92819 q^{74} +6.24556 q^{75} -1.85037 q^{76} +4.97051 q^{77} -4.24592 q^{78} +5.23644 q^{79} +3.35344 q^{80} +1.00000 q^{81} -3.33098 q^{82} -15.0799 q^{83} -1.00000 q^{84} -14.6806 q^{85} -1.36529 q^{86} +7.23952 q^{87} +4.97051 q^{88} -0.840213 q^{89} -3.35344 q^{90} -4.24592 q^{91} +3.23003 q^{92} +1.55659 q^{93} +3.65068 q^{94} -6.20512 q^{95} -1.00000 q^{96} -19.0193 q^{97} -1.00000 q^{98} -4.97051 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	3.35344	1.49970	0.749852	−	0.661606i	$-0.230125\pi$
$5$	3.35344	1.49970	0.749852	+	0.661606i	$0.230125\pi$
$6$	−1.00000	−0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.35344	−1.06045
$11$	−4.97051	−1.49867	−0.749333	−	0.662193i	$-0.769626\pi$
$11$	−4.97051	−1.49867	−0.749333	+	0.662193i	$0.769626\pi$
$12$	1.00000	0.288675
$13$	4.24592	1.17761	0.588804	−	0.808276i	$-0.299599\pi$
$13$	4.24592	1.17761	0.588804	+	0.808276i	$0.299599\pi$
$14$	1.00000	0.267261
$15$	3.35344	0.865855
$16$	1.00000	0.250000
$17$	−4.37776	−1.06176	−0.530882	−	0.847446i	$-0.678139\pi$
$17$	−4.37776	−1.06176	−0.530882	+	0.847446i	$0.678139\pi$
$18$	−1.00000	−0.235702
$19$	−1.85037	−0.424505	−0.212252	−	0.977215i	$-0.568080\pi$
$19$	−1.85037	−0.424505	−0.212252	+	0.977215i	$0.568080\pi$
$20$	3.35344	0.749852
$21$	−1.00000	−0.218218
$22$	4.97051	1.05972
$23$	3.23003	0.673507	0.336754	−	0.941593i	$-0.390671\pi$
$23$	3.23003	0.673507	0.336754	+	0.941593i	$0.390671\pi$
$24$	−1.00000	−0.204124
$25$	6.24556	1.24911
$26$	−4.24592	−0.832694
$27$	1.00000	0.192450
$28$	−1.00000	−0.188982
$29$	7.23952	1.34434	0.672172	−	0.740395i	$-0.265361\pi$
$29$	7.23952	1.34434	0.672172	+	0.740395i	$0.265361\pi$
$30$	−3.35344	−0.612252
$31$	1.55659	0.279572	0.139786	−	0.990182i	$-0.455359\pi$
$31$	1.55659	0.279572	0.139786	+	0.990182i	$0.455359\pi$
$32$	−1.00000	−0.176777
$33$	−4.97051	−0.865255
$34$	4.37776	0.750780
$35$	−3.35344	−0.566835
$36$	1.00000	0.166667
$37$	4.92819	0.810189	0.405095	−	0.914275i	$-0.367239\pi$
$37$	4.92819	0.810189	0.405095	+	0.914275i	$0.367239\pi$
$38$	1.85037	0.300170
$39$	4.24592	0.679892
$40$	−3.35344	−0.530225
$41$	3.33098	0.520211	0.260106	−	0.965580i	$-0.416243\pi$
$41$	3.33098	0.520211	0.260106	+	0.965580i	$0.416243\pi$
$42$	1.00000	0.154303
$43$	1.36529	0.208204	0.104102	−	0.994567i	$-0.466803\pi$
$43$	1.36529	0.208204	0.104102	+	0.994567i	$0.466803\pi$
$44$	−4.97051	−0.749333
$45$	3.35344	0.499901
$46$	−3.23003	−0.476242
$47$	−3.65068	−0.532507	−0.266253	−	0.963903i	$-0.585786\pi$
$47$	−3.65068	−0.532507	−0.266253	+	0.963903i	$0.585786\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	−6.24556	−0.883256
$51$	−4.37776	−0.613009
$52$	4.24592	0.588804
$53$	5.41989	0.744479	0.372240	−	0.928137i	$-0.378590\pi$
$53$	5.41989	0.744479	0.372240	+	0.928137i	$0.378590\pi$
$54$	−1.00000	−0.136083
$55$	−16.6683	−2.24756
$56$	1.00000	0.133631
$57$	−1.85037	−0.245088
$58$	−7.23952	−0.950595
$59$	−9.62729	−1.25337	−0.626683	−	0.779274i	$-0.715588\pi$
$59$	−9.62729	−1.25337	−0.626683	+	0.779274i	$0.715588\pi$
$60$	3.35344	0.432927
$61$	11.9716	1.53281	0.766404	−	0.642359i	$-0.222044\pi$
$61$	11.9716	1.53281	0.766404	+	0.642359i	$0.222044\pi$
$62$	−1.55659	−0.197687
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	14.2385	1.76606
$66$	4.97051	0.611828
$67$	6.35600	0.776509	0.388255	−	0.921552i	$-0.373078\pi$
$67$	6.35600	0.776509	0.388255	+	0.921552i	$0.373078\pi$
$68$	−4.37776	−0.530882
$69$	3.23003	0.388850
$70$	3.35344	0.400813
$71$	−11.8152	−1.40220	−0.701101	−	0.713062i	$-0.747308\pi$
$71$	−11.8152	−1.40220	−0.701101	+	0.713062i	$0.747308\pi$
$72$	−1.00000	−0.117851
$73$	6.38145	0.746892	0.373446	−	0.927652i	$-0.378176\pi$
$73$	6.38145	0.746892	0.373446	+	0.927652i	$0.378176\pi$
$74$	−4.92819	−0.572890
$75$	6.24556	0.721175
$76$	−1.85037	−0.212252
$77$	4.97051	0.566443
$78$	−4.24592	−0.480756
$79$	5.23644	0.589146	0.294573	−	0.955629i	$-0.404823\pi$
$79$	5.23644	0.589146	0.294573	+	0.955629i	$0.404823\pi$
$80$	3.35344	0.374926
$81$	1.00000	0.111111
$82$	−3.33098	−0.367845
$83$	−15.0799	−1.65524	−0.827618	−	0.561291i	$-0.810305\pi$
$83$	−15.0799	−1.65524	−0.827618	+	0.561291i	$0.810305\pi$
$84$	−1.00000	−0.109109
$85$	−14.6806	−1.59233
$86$	−1.36529	−0.147223
$87$	7.23952	0.776158
$88$	4.97051	0.529858
$89$	−0.840213	−0.0890624	−0.0445312	−	0.999008i	$-0.514179\pi$
$89$	−0.840213	−0.0890624	−0.0445312	+	0.999008i	$0.514179\pi$
$90$	−3.35344	−0.353484
$91$	−4.24592	−0.445094
$92$	3.23003	0.336754
$93$	1.55659	0.161411
$94$	3.65068	0.376539
$95$	−6.20512	−0.636632
$96$	−1.00000	−0.102062
$97$	−19.0193	−1.93111	−0.965556	−	0.260194i	$-0.916214\pi$
$97$	−19.0193	−1.93111	−0.965556	+	0.260194i	$0.916214\pi$
$98$	−1.00000	−0.101015
$99$	−4.97051	−0.499555
$100$	6.24556	0.624556
$101$	15.8625	1.57837	0.789187	−	0.614153i	$-0.210502\pi$
$101$	15.8625	1.57837	0.789187	+	0.614153i	$0.210502\pi$
$102$	4.37776	0.433463
$103$	4.77972	0.470960	0.235480	−	0.971879i	$-0.424334\pi$
$103$	4.77972	0.470960	0.235480	+	0.971879i	$0.424334\pi$
$104$	−4.24592	−0.416347
$105$	−3.35344	−0.327262
$106$	−5.41989	−0.526426
$107$	12.4517	1.20375	0.601874	−	0.798591i	$-0.294421\pi$
$107$	12.4517	1.20375	0.601874	+	0.798591i	$0.294421\pi$
$108$	1.00000	0.0962250
$109$	4.95724	0.474817	0.237409	−	0.971410i	$-0.423702\pi$
$109$	4.95724	0.474817	0.237409	+	0.971410i	$0.423702\pi$
$110$	16.6683	1.58926
$111$	4.92819	0.467763
$112$	−1.00000	−0.0944911
$113$	11.7943	1.10951	0.554757	−	0.832012i	$-0.312811\pi$
$113$	11.7943	1.10951	0.554757	+	0.832012i	$0.312811\pi$
$114$	1.85037	0.173303
$115$	10.8317	1.01006
$116$	7.23952	0.672172
$117$	4.24592	0.392536
$118$	9.62729	0.886264
$119$	4.37776	0.401309
$120$	−3.35344	−0.306126
$121$	13.7060	1.24600
$122$	−11.9716	−1.08386
$123$	3.33098	0.300344
$124$	1.55659	0.139786
$125$	4.17692	0.373595
$126$	1.00000	0.0890871
$127$	−5.38048	−0.477440	−0.238720	−	0.971088i	$-0.576728\pi$
$127$	−5.38048	−0.477440	−0.238720	+	0.971088i	$0.576728\pi$
$128$	−1.00000	−0.0883883
$129$	1.36529	0.120207
$130$	−14.2385	−1.24880
$131$	−0.609748	−0.0532740	−0.0266370	−	0.999645i	$-0.508480\pi$
$131$	−0.609748	−0.0532740	−0.0266370	+	0.999645i	$0.508480\pi$
$132$	−4.97051	−0.432628
$133$	1.85037	0.160448
$134$	−6.35600	−0.549075
$135$	3.35344	0.288618
$136$	4.37776	0.375390
$137$	21.1658	1.80832	0.904159	−	0.427195i	$-0.140498\pi$
$137$	21.1658	1.80832	0.904159	+	0.427195i	$0.140498\pi$
$138$	−3.23003	−0.274958
$139$	−3.40416	−0.288737	−0.144369	−	0.989524i	$-0.546115\pi$
$139$	−3.40416	−0.288737	−0.144369	+	0.989524i	$0.546115\pi$
$140$	−3.35344	−0.283417
$141$	−3.65068	−0.307443
$142$	11.8152	0.991507
$143$	−21.1044	−1.76484
$144$	1.00000	0.0833333
$145$	24.2773	2.01612
$146$	−6.38145	−0.528133
$147$	1.00000	0.0824786
$148$	4.92819	0.405095
$149$	−2.19296	−0.179654	−0.0898271	−	0.995957i	$-0.528631\pi$
$149$	−2.19296	−0.179654	−0.0898271	+	0.995957i	$0.528631\pi$
$150$	−6.24556	−0.509948
$151$	1.64838	0.134143	0.0670716	−	0.997748i	$-0.478634\pi$
$151$	1.64838	0.134143	0.0670716	+	0.997748i	$0.478634\pi$
$152$	1.85037	0.150085
$153$	−4.37776	−0.353921
$154$	−4.97051	−0.400535
$155$	5.21993	0.419275
$156$	4.24592	0.339946
$157$	−23.8935	−1.90691	−0.953455	−	0.301535i	$-0.902501\pi$
$157$	−23.8935	−1.90691	−0.953455	+	0.301535i	$0.902501\pi$
$158$	−5.23644	−0.416589
$159$	5.41989	0.429825
$160$	−3.35344	−0.265113
$161$	−3.23003	−0.254562
$162$	−1.00000	−0.0785674
$163$	10.9412	0.856979	0.428489	−	0.903547i	$-0.359046\pi$
$163$	10.9412	0.856979	0.428489	+	0.903547i	$0.359046\pi$
$164$	3.33098	0.260106
$165$	−16.6683	−1.29763
$166$	15.0799	1.17043
$167$	5.53717	0.428479	0.214239	−	0.976781i	$-0.431273\pi$
$167$	5.53717	0.428479	0.214239	+	0.976781i	$0.431273\pi$
$168$	1.00000	0.0771517
$169$	5.02787	0.386760
$170$	14.6806	1.12595
$171$	−1.85037	−0.141502
$172$	1.36529	0.104102
$173$	5.35744	0.407319	0.203659	−	0.979042i	$-0.434717\pi$
$173$	5.35744	0.407319	0.203659	+	0.979042i	$0.434717\pi$
$174$	−7.23952	−0.548826
$175$	−6.24556	−0.472120
$176$	−4.97051	−0.374667
$177$	−9.62729	−0.723632
$178$	0.840213	0.0629766
$179$	19.2452	1.43845	0.719226	−	0.694776i	$-0.244496\pi$
$179$	19.2452	1.43845	0.719226	+	0.694776i	$0.244496\pi$
$180$	3.35344	0.249951
$181$	−22.7018	−1.68741	−0.843706	−	0.536806i	$-0.819631\pi$
$181$	−22.7018	−1.68741	−0.843706	+	0.536806i	$0.819631\pi$
$182$	4.24592	0.314729
$183$	11.9716	0.884967
$184$	−3.23003	−0.238121
$185$	16.5264	1.21504
$186$	−1.55659	−0.114135
$187$	21.7597	1.59123
$188$	−3.65068	−0.266253
$189$	−1.00000	−0.0727393
$190$	6.20512	0.450167
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	1.00000	0.0721688
$193$	21.3213	1.53474	0.767372	−	0.641202i	$-0.221564\pi$
$193$	21.3213	1.53474	0.767372	+	0.641202i	$0.221564\pi$
$194$	19.0193	1.36550
$195$	14.2385	1.01964
$196$	1.00000	0.0714286
$197$	2.85335	0.203293	0.101647	−	0.994821i	$-0.467589\pi$
$197$	2.85335	0.203293	0.101647	+	0.994821i	$0.467589\pi$
$198$	4.97051	0.353239
$199$	20.2417	1.43489	0.717447	−	0.696613i	$-0.245310\pi$
$199$	20.2417	1.43489	0.717447	+	0.696613i	$0.245310\pi$
$200$	−6.24556	−0.441628
$201$	6.35600	0.448318
$202$	−15.8625	−1.11608
$203$	−7.23952	−0.508115
$204$	−4.37776	−0.306505
$205$	11.1702	0.780163
$206$	−4.77972	−0.333019
$207$	3.23003	0.224502
$208$	4.24592	0.294402
$209$	9.19731	0.636191
$210$	3.35344	0.231409
$211$	22.4839	1.54786	0.773928	−	0.633273i	$-0.218289\pi$
$211$	22.4839	1.54786	0.773928	+	0.633273i	$0.218289\pi$
$212$	5.41989	0.372240
$213$	−11.8152	−0.809562
$214$	−12.4517	−0.851178
$215$	4.57840	0.312245
$216$	−1.00000	−0.0680414
$217$	−1.55659	−0.105668
$218$	−4.95724	−0.335747
$219$	6.38145	0.431218
$220$	−16.6683	−1.12378
$221$	−18.5877	−1.25034
$222$	−4.92819	−0.330758
$223$	4.45592	0.298391	0.149195	−	0.988808i	$-0.452332\pi$
$223$	4.45592	0.298391	0.149195	+	0.988808i	$0.452332\pi$
$224$	1.00000	0.0668153
$225$	6.24556	0.416371
$226$	−11.7943	−0.784546
$227$	6.50418	0.431697	0.215849	−	0.976427i	$-0.430748\pi$
$227$	6.50418	0.431697	0.215849	+	0.976427i	$0.430748\pi$
$228$	−1.85037	−0.122544
$229$	15.4925	1.02378	0.511888	−	0.859052i	$-0.328946\pi$
$229$	15.4925	1.02378	0.511888	+	0.859052i	$0.328946\pi$
$230$	−10.8317	−0.714222
$231$	4.97051	0.327036
$232$	−7.23952	−0.475298
$233$	−1.02413	−0.0670928	−0.0335464	−	0.999437i	$-0.510680\pi$
$233$	−1.02413	−0.0670928	−0.0335464	+	0.999437i	$0.510680\pi$
$234$	−4.24592	−0.277565
$235$	−12.2423	−0.798603
$236$	−9.62729	−0.626683
$237$	5.23644	0.340143
$238$	−4.37776	−0.283768
$239$	14.9459	0.966770	0.483385	−	0.875408i	$-0.339407\pi$
$239$	14.9459	0.966770	0.483385	+	0.875408i	$0.339407\pi$
$240$	3.35344	0.216464
$241$	12.8377	0.826947	0.413474	−	0.910516i	$-0.364315\pi$
$241$	12.8377	0.826947	0.413474	+	0.910516i	$0.364315\pi$
$242$	−13.7060	−0.881055
$243$	1.00000	0.0641500
$244$	11.9716	0.766404
$245$	3.35344	0.214243
$246$	−3.33098	−0.212375
$247$	−7.85655	−0.499900
$248$	−1.55659	−0.0988436
$249$	−15.0799	−0.955651
$250$	−4.17692	−0.264172
$251$	−0.296714	−0.0187284	−0.00936420	−	0.999956i	$-0.502981\pi$
$251$	−0.296714	−0.0187284	−0.00936420	+	0.999956i	$0.502981\pi$
$252$	−1.00000	−0.0629941
$253$	−16.0549	−1.00936
$254$	5.38048	0.337601
$255$	−14.6806	−0.919333
$256$	1.00000	0.0625000
$257$	−27.7161	−1.72888	−0.864441	−	0.502734i	$-0.832328\pi$
$257$	−27.7161	−1.72888	−0.864441	+	0.502734i	$0.832328\pi$
$258$	−1.36529	−0.0849990
$259$	−4.92819	−0.306223
$260$	14.2385	0.883031
$261$	7.23952	0.448115
$262$	0.609748	0.0376704
$263$	11.3514	0.699960	0.349980	−	0.936757i	$-0.386188\pi$
$263$	11.3514	0.699960	0.349980	+	0.936757i	$0.386188\pi$
$264$	4.97051	0.305914
$265$	18.1753	1.11650
$266$	−1.85037	−0.113454
$267$	−0.840213	−0.0514202
$268$	6.35600	0.388255
$269$	9.43494	0.575258	0.287629	−	0.957742i	$-0.407133\pi$
$269$	9.43494	0.575258	0.287629	+	0.957742i	$0.407133\pi$
$270$	−3.35344	−0.204084
$271$	−14.2556	−0.865968	−0.432984	−	0.901402i	$-0.642539\pi$
$271$	−14.2556	−0.865968	−0.432984	+	0.901402i	$0.642539\pi$
$272$	−4.37776	−0.265441
$273$	−4.24592	−0.256975
$274$	−21.1658	−1.27867
$275$	−31.0436	−1.87200
$276$	3.23003	0.194425
$277$	7.93063	0.476506	0.238253	−	0.971203i	$-0.423425\pi$
$277$	7.93063	0.476506	0.238253	+	0.971203i	$0.423425\pi$
$278$	3.40416	0.204168
$279$	1.55659	0.0931906
$280$	3.35344	0.200406
$281$	3.06779	0.183009	0.0915046	−	0.995805i	$-0.470832\pi$
$281$	3.06779	0.183009	0.0915046	+	0.995805i	$0.470832\pi$
$282$	3.65068	0.217395
$283$	−22.2343	−1.32169	−0.660847	−	0.750521i	$-0.729803\pi$
$283$	−22.2343	−1.32169	−0.660847	+	0.750521i	$0.729803\pi$
$284$	−11.8152	−0.701101
$285$	−6.20512	−0.367559
$286$	21.1044	1.24793
$287$	−3.33098	−0.196621
$288$	−1.00000	−0.0589256
$289$	2.16481	0.127342
$290$	−24.2773	−1.42561
$291$	−19.0193	−1.11493
$292$	6.38145	0.373446
$293$	−28.5551	−1.66821	−0.834104	−	0.551607i	$-0.814015\pi$
$293$	−28.5551	−1.66821	−0.834104	+	0.551607i	$0.814015\pi$
$294$	−1.00000	−0.0583212
$295$	−32.2846	−1.87968
$296$	−4.92819	−0.286445
$297$	−4.97051	−0.288418
$298$	2.19296	0.127035
$299$	13.7145	0.793127
$300$	6.24556	0.360588
$301$	−1.36529	−0.0786937
$302$	−1.64838	−0.0948536
$303$	15.8625	0.911275
$304$	−1.85037	−0.106126
$305$	40.1461	2.29876
$306$	4.37776	0.250260
$307$	1.08266	0.0617910	0.0308955	−	0.999523i	$-0.490164\pi$
$307$	1.08266	0.0617910	0.0308955	+	0.999523i	$0.490164\pi$
$308$	4.97051	0.283221
$309$	4.77972	0.271909
$310$	−5.21993	−0.296472
$311$	26.3032	1.49152	0.745758	−	0.666217i	$-0.232088\pi$
$311$	26.3032	1.49152	0.745758	+	0.666217i	$0.232088\pi$
$312$	−4.24592	−0.240378
$313$	28.4263	1.60675	0.803376	−	0.595472i	$-0.203035\pi$
$313$	28.4263	1.60675	0.803376	+	0.595472i	$0.203035\pi$
$314$	23.8935	1.34839
$315$	−3.35344	−0.188945
$316$	5.23644	0.294573
$317$	−7.16299	−0.402314	−0.201157	−	0.979559i	$-0.564470\pi$
$317$	−7.16299	−0.402314	−0.201157	+	0.979559i	$0.564470\pi$
$318$	−5.41989	−0.303932
$319$	−35.9841	−2.01472
$320$	3.35344	0.187463
$321$	12.4517	0.694984
$322$	3.23003	0.180002
$323$	8.10050	0.450724
$324$	1.00000	0.0555556
$325$	26.5182	1.47096
$326$	−10.9412	−0.605975
$327$	4.95724	0.274136
$328$	−3.33098	−0.183923
$329$	3.65068	0.201269
$330$	16.6683	0.917561
$331$	3.74664	0.205934	0.102967	−	0.994685i	$-0.467166\pi$
$331$	3.74664	0.205934	0.102967	+	0.994685i	$0.467166\pi$
$332$	−15.0799	−0.827618
$333$	4.92819	0.270063
$334$	−5.53717	−0.302980
$335$	21.3145	1.16453
$336$	−1.00000	−0.0545545
$337$	20.2763	1.10452	0.552261	−	0.833671i	$-0.313765\pi$
$337$	20.2763	1.10452	0.552261	+	0.833671i	$0.313765\pi$
$338$	−5.02787	−0.273480
$339$	11.7943	0.640579
$340$	−14.6806	−0.796166
$341$	−7.73705	−0.418985
$342$	1.85037	0.100057
$343$	−1.00000	−0.0539949
$344$	−1.36529	−0.0736113
$345$	10.8317	0.583159
$346$	−5.35744	−0.288018
$347$	11.6413	0.624939	0.312469	−	0.949928i	$-0.398844\pi$
$347$	11.6413	0.624939	0.312469	+	0.949928i	$0.398844\pi$
$348$	7.23952	0.388079
$349$	29.0629	1.55570	0.777851	−	0.628448i	$-0.216310\pi$
$349$	29.0629	1.55570	0.777851	+	0.628448i	$0.216310\pi$
$350$	6.24556	0.333839
$351$	4.24592	0.226631
$352$	4.97051	0.264929
$353$	−32.4715	−1.72829	−0.864143	−	0.503247i	$-0.832139\pi$
$353$	−32.4715	−1.72829	−0.864143	+	0.503247i	$0.832139\pi$
$354$	9.62729	0.511685
$355$	−39.6215	−2.10289
$356$	−0.840213	−0.0445312
$357$	4.37776	0.231696
$358$	−19.2452	−1.01714
$359$	−27.0548	−1.42790	−0.713948	−	0.700199i	$-0.753095\pi$
$359$	−27.0548	−1.42790	−0.713948	+	0.700199i	$0.753095\pi$
$360$	−3.35344	−0.176742
$361$	−15.5761	−0.819796
$362$	22.7018	1.19318
$363$	13.7060	0.719379
$364$	−4.24592	−0.222547
$365$	21.3998	1.12012
$366$	−11.9716	−0.625766
$367$	29.6117	1.54572	0.772858	−	0.634578i	$-0.218826\pi$
$367$	29.6117	1.54572	0.772858	+	0.634578i	$0.218826\pi$
$368$	3.23003	0.168377
$369$	3.33098	0.173404
$370$	−16.5264	−0.859166
$371$	−5.41989	−0.281387
$372$	1.55659	0.0807054
$373$	−25.9629	−1.34431	−0.672153	−	0.740412i	$-0.734630\pi$
$373$	−25.9629	−1.34431	−0.672153	+	0.740412i	$0.734630\pi$
$374$	−21.7597	−1.12517
$375$	4.17692	0.215695
$376$	3.65068	0.188270
$377$	30.7384	1.58311
$378$	1.00000	0.0514344
$379$	22.6779	1.16489	0.582444	−	0.812871i	$-0.302097\pi$
$379$	22.6779	1.16489	0.582444	+	0.812871i	$0.302097\pi$
$380$	−6.20512	−0.318316
$381$	−5.38048	−0.275650
$382$	1.00000	0.0511645
$383$	3.48864	0.178261	0.0891307	−	0.996020i	$-0.471591\pi$
$383$	3.48864	0.178261	0.0891307	+	0.996020i	$0.471591\pi$
$384$	−1.00000	−0.0510310
$385$	16.6683	0.849496
$386$	−21.3213	−1.08523
$387$	1.36529	0.0694014
$388$	−19.0193	−0.965556
$389$	2.19381	0.111231	0.0556153	−	0.998452i	$-0.482288\pi$
$389$	2.19381	0.111231	0.0556153	+	0.998452i	$0.482288\pi$
$390$	−14.2385	−0.720992
$391$	−14.1403	−0.715106
$392$	−1.00000	−0.0505076
$393$	−0.609748	−0.0307577
$394$	−2.85335	−0.143750
$395$	17.5601	0.883544
$396$	−4.97051	−0.249778
$397$	0.200605	0.0100681	0.00503403	−	0.999987i	$-0.498398\pi$
$397$	0.200605	0.0100681	0.00503403	+	0.999987i	$0.498398\pi$
$398$	−20.2417	−1.01462
$399$	1.85037	0.0926345
$400$	6.24556	0.312278
$401$	−12.0194	−0.600218	−0.300109	−	0.953905i	$-0.597023\pi$
$401$	−12.0194	−0.600218	−0.300109	+	0.953905i	$0.597023\pi$
$402$	−6.35600	−0.317009
$403$	6.60916	0.329226
$404$	15.8625	0.789187
$405$	3.35344	0.166634
$406$	7.23952	0.359291
$407$	−24.4956	−1.21420
$408$	4.37776	0.216732
$409$	−12.6656	−0.626274	−0.313137	−	0.949708i	$-0.601380\pi$
$409$	−12.6656	−0.626274	−0.313137	+	0.949708i	$0.601380\pi$
$410$	−11.1702	−0.551659
$411$	21.1658	1.04403
$412$	4.77972	0.235480
$413$	9.62729	0.473728
$414$	−3.23003	−0.158747
$415$	−50.5696	−2.48237
$416$	−4.24592	−0.208174
$417$	−3.40416	−0.166703
$418$	−9.19731	−0.449855
$419$	−23.2170	−1.13423	−0.567113	−	0.823640i	$-0.691940\pi$
$419$	−23.2170	−1.13423	−0.567113	+	0.823640i	$0.691940\pi$
$420$	−3.35344	−0.163631
$421$	−20.4654	−0.997421	−0.498710	−	0.866769i	$-0.666193\pi$
$421$	−20.4654	−0.997421	−0.498710	+	0.866769i	$0.666193\pi$
$422$	−22.4839	−1.09450
$423$	−3.65068	−0.177502
$424$	−5.41989	−0.263213
$425$	−27.3416	−1.32626
$426$	11.8152	0.572447
$427$	−11.9716	−0.579347
$428$	12.4517	0.601874
$429$	−21.1044	−1.01893
$430$	−4.57840	−0.220790
$431$	−8.69175	−0.418667	−0.209333	−	0.977844i	$-0.567129\pi$
$431$	−8.69175	−0.418667	−0.209333	+	0.977844i	$0.567129\pi$
$432$	1.00000	0.0481125
$433$	37.3757	1.79616	0.898082	−	0.439828i	$-0.144961\pi$
$433$	37.3757	1.79616	0.898082	+	0.439828i	$0.144961\pi$
$434$	1.55659	0.0747187
$435$	24.2773	1.16401
$436$	4.95724	0.237409
$437$	−5.97676	−0.285907
$438$	−6.38145	−0.304917
$439$	34.0355	1.62443	0.812213	−	0.583361i	$-0.198263\pi$
$439$	34.0355	1.62443	0.812213	+	0.583361i	$0.198263\pi$
$440$	16.6683	0.794631
$441$	1.00000	0.0476190
$442$	18.5877	0.884124
$443$	−7.99004	−0.379618	−0.189809	−	0.981821i	$-0.560787\pi$
$443$	−7.99004	−0.379618	−0.189809	+	0.981821i	$0.560787\pi$
$444$	4.92819	0.233881
$445$	−2.81760	−0.133567
$446$	−4.45592	−0.210994
$447$	−2.19296	−0.103723
$448$	−1.00000	−0.0472456
$449$	−5.85443	−0.276288	−0.138144	−	0.990412i	$-0.544114\pi$
$449$	−5.85443	−0.276288	−0.138144	+	0.990412i	$0.544114\pi$
$450$	−6.24556	−0.294419
$451$	−16.5567	−0.779623
$452$	11.7943	0.554757
$453$	1.64838	0.0774476
$454$	−6.50418	−0.305256
$455$	−14.2385	−0.667509
$456$	1.85037	0.0866517
$457$	−0.101023	−0.00472564	−0.00236282	−	0.999997i	$-0.500752\pi$
$457$	−0.101023	−0.00472564	−0.00236282	+	0.999997i	$0.500752\pi$
$458$	−15.4925	−0.723918
$459$	−4.37776	−0.204336
$460$	10.8317	0.505031
$461$	−25.6480	−1.19455	−0.597273	−	0.802038i	$-0.703749\pi$
$461$	−25.6480	−1.19455	−0.597273	+	0.802038i	$0.703749\pi$
$462$	−4.97051	−0.231249
$463$	−36.1720	−1.68106	−0.840528	−	0.541768i	$-0.817755\pi$
$463$	−36.1720	−1.68106	−0.840528	+	0.541768i	$0.817755\pi$
$464$	7.23952	0.336086
$465$	5.21993	0.242069
$466$	1.02413	0.0474418
$467$	35.1121	1.62480	0.812398	−	0.583104i	$-0.198162\pi$
$467$	35.1121	1.62480	0.812398	+	0.583104i	$0.198162\pi$
$468$	4.24592	0.196268
$469$	−6.35600	−0.293493
$470$	12.2423	0.564697
$471$	−23.8935	−1.10096
$472$	9.62729	0.443132
$473$	−6.78617	−0.312028
$474$	−5.23644	−0.240518
$475$	−11.5566	−0.530254
$476$	4.37776	0.200654
$477$	5.41989	0.248160
$478$	−14.9459	−0.683610
$479$	−40.2128	−1.83737	−0.918686	−	0.394989i	$-0.870748\pi$
$479$	−40.2128	−1.83737	−0.918686	+	0.394989i	$0.870748\pi$
$480$	−3.35344	−0.153063
$481$	20.9247	0.954085
$482$	−12.8377	−0.584740
$483$	−3.23003	−0.146971
$484$	13.7060	0.623000
$485$	−63.7799	−2.89610
$486$	−1.00000	−0.0453609
$487$	−16.0932	−0.729251	−0.364626	−	0.931154i	$-0.618803\pi$
$487$	−16.0932	−0.729251	−0.364626	+	0.931154i	$0.618803\pi$
$488$	−11.9716	−0.541929
$489$	10.9412	0.494777
$490$	−3.35344	−0.151493
$491$	−26.5619	−1.19872	−0.599361	−	0.800479i	$-0.704579\pi$
$491$	−26.5619	−1.19872	−0.599361	+	0.800479i	$0.704579\pi$
$492$	3.33098	0.150172
$493$	−31.6929	−1.42738
$494$	7.85655	0.353483
$495$	−16.6683	−0.749185
$496$	1.55659	0.0698930
$497$	11.8152	0.529983
$498$	15.0799	0.675748
$499$	35.7123	1.59870	0.799351	−	0.600865i	$-0.205177\pi$
$499$	35.7123	1.59870	0.799351	+	0.600865i	$0.205177\pi$
$500$	4.17692	0.186797
$501$	5.53717	0.247382
$502$	0.296714	0.0132430
$503$	−21.4681	−0.957214	−0.478607	−	0.878029i	$-0.658858\pi$
$503$	−21.4681	−0.957214	−0.478607	+	0.878029i	$0.658858\pi$
$504$	1.00000	0.0445435
$505$	53.1938	2.36710
$506$	16.0549	0.713727
$507$	5.02787	0.223296
$508$	−5.38048	−0.238720
$509$	−24.6610	−1.09308	−0.546539	−	0.837434i	$-0.684055\pi$
$509$	−24.6610	−1.09308	−0.546539	+	0.837434i	$0.684055\pi$
$510$	14.6806	0.650066
$511$	−6.38145	−0.282299
$512$	−1.00000	−0.0441942
$513$	−1.85037	−0.0816960
$514$	27.7161	1.22250
$515$	16.0285	0.706301
$516$	1.36529	0.0601033
$517$	18.1458	0.798050
$518$	4.92819	0.216532
$519$	5.35744	0.235166
$520$	−14.2385	−0.624398
$521$	−14.1285	−0.618979	−0.309489	−	0.950903i	$-0.600158\pi$
$521$	−14.1285	−0.618979	−0.309489	+	0.950903i	$0.600158\pi$
$522$	−7.23952	−0.316865
$523$	20.5299	0.897708	0.448854	−	0.893605i	$-0.351832\pi$
$523$	20.5299	0.897708	0.448854	+	0.893605i	$0.351832\pi$
$524$	−0.609748	−0.0266370
$525$	−6.24556	−0.272579
$526$	−11.3514	−0.494946
$527$	−6.81438	−0.296839
$528$	−4.97051	−0.216314
$529$	−12.5669	−0.546388
$530$	−18.1753	−0.789484
$531$	−9.62729	−0.417789
$532$	1.85037	0.0802239
$533$	14.1431	0.612605
$534$	0.840213	0.0363596
$535$	41.7559	1.80527
$536$	−6.35600	−0.274538
$537$	19.2452	0.830491
$538$	−9.43494	−0.406769
$539$	−4.97051	−0.214095
$540$	3.35344	0.144309
$541$	−19.2896	−0.829326	−0.414663	−	0.909975i	$-0.636100\pi$
$541$	−19.2896	−0.829326	−0.414663	+	0.909975i	$0.636100\pi$
$542$	14.2556	0.612332
$543$	−22.7018	−0.974227
$544$	4.37776	0.187695
$545$	16.6238	0.712085
$546$	4.24592	0.181709
$547$	12.7576	0.545474	0.272737	−	0.962089i	$-0.412071\pi$
$547$	12.7576	0.545474	0.272737	+	0.962089i	$0.412071\pi$
$548$	21.1658	0.904159
$549$	11.9716	0.510936
$550$	31.0436	1.32371
$551$	−13.3958	−0.570681
$552$	−3.23003	−0.137479
$553$	−5.23644	−0.222676
$554$	−7.93063	−0.336940
$555$	16.5264	0.701506
$556$	−3.40416	−0.144369
$557$	8.53260	0.361538	0.180769	−	0.983526i	$-0.442141\pi$
$557$	8.53260	0.361538	0.180769	+	0.983526i	$0.442141\pi$
$558$	−1.55659	−0.0658957
$559$	5.79690	0.245183
$560$	−3.35344	−0.141709
$561$	21.7597	0.918697
$562$	−3.06779	−0.129407
$563$	−16.0042	−0.674497	−0.337248	−	0.941416i	$-0.609496\pi$
$563$	−16.0042	−0.674497	−0.337248	+	0.941416i	$0.609496\pi$
$564$	−3.65068	−0.153721
$565$	39.5515	1.66394
$566$	22.2343	0.934578
$567$	−1.00000	−0.0419961
$568$	11.8152	0.495754
$569$	−2.27256	−0.0952709	−0.0476354	−	0.998865i	$-0.515169\pi$
$569$	−2.27256	−0.0952709	−0.0476354	+	0.998865i	$0.515169\pi$
$570$	6.20512	0.259904
$571$	−7.13656	−0.298656	−0.149328	−	0.988788i	$-0.547711\pi$
$571$	−7.13656	−0.298656	−0.149328	+	0.988788i	$0.547711\pi$
$572$	−21.1044	−0.882420
$573$	−1.00000	−0.0417756
$574$	3.33098	0.139032
$575$	20.1733	0.841286
$576$	1.00000	0.0416667
$577$	3.39713	0.141424	0.0707121	−	0.997497i	$-0.477473\pi$
$577$	3.39713	0.141424	0.0707121	+	0.997497i	$0.477473\pi$
$578$	−2.16481	−0.0900443
$579$	21.3213	0.886085
$580$	24.2773	1.00806
$581$	15.0799	0.625621
$582$	19.0193	0.788374
$583$	−26.9396	−1.11573
$584$	−6.38145	−0.264066
$585$	14.2385	0.588688
$586$	28.5551	1.17960
$587$	−28.9818	−1.19621	−0.598103	−	0.801419i	$-0.704079\pi$
$587$	−28.9818	−1.19621	−0.598103	+	0.801419i	$0.704079\pi$
$588$	1.00000	0.0412393
$589$	−2.88027	−0.118680
$590$	32.2846	1.32913
$591$	2.85335	0.117371
$592$	4.92819	0.202547
$593$	23.3637	0.959434	0.479717	−	0.877423i	$-0.340739\pi$
$593$	23.3637	0.959434	0.479717	+	0.877423i	$0.340739\pi$
$594$	4.97051	0.203943
$595$	14.6806	0.601845
$596$	−2.19296	−0.0898271
$597$	20.2417	0.828437
$598$	−13.7145	−0.560826
$599$	−14.6319	−0.597843	−0.298922	−	0.954278i	$-0.596627\pi$
$599$	−14.6319	−0.597843	−0.298922	+	0.954278i	$0.596627\pi$
$600$	−6.24556	−0.254974
$601$	1.82658	0.0745079	0.0372540	−	0.999306i	$-0.488139\pi$
$601$	1.82658	0.0745079	0.0372540	+	0.999306i	$0.488139\pi$
$602$	1.36529	0.0556449
$603$	6.35600	0.258836
$604$	1.64838	0.0670716
$605$	45.9623	1.86863
$606$	−15.8625	−0.644369
$607$	−4.61217	−0.187202	−0.0936011	−	0.995610i	$-0.529838\pi$
$607$	−4.61217	−0.187202	−0.0936011	+	0.995610i	$0.529838\pi$
$608$	1.85037	0.0750426
$609$	−7.23952	−0.293360
$610$	−40.1461	−1.62547
$611$	−15.5005	−0.627084
$612$	−4.37776	−0.176961
$613$	2.56905	0.103763	0.0518814	−	0.998653i	$-0.483478\pi$
$613$	2.56905	0.103763	0.0518814	+	0.998653i	$0.483478\pi$
$614$	−1.08266	−0.0436928
$615$	11.1702	0.450427
$616$	−4.97051	−0.200268
$617$	−41.2895	−1.66225	−0.831127	−	0.556083i	$-0.812304\pi$
$617$	−41.2895	−1.66225	−0.831127	+	0.556083i	$0.812304\pi$
$618$	−4.77972	−0.192269
$619$	8.71342	0.350222	0.175111	−	0.984549i	$-0.443972\pi$
$619$	8.71342	0.350222	0.175111	+	0.984549i	$0.443972\pi$
$620$	5.21993	0.209637
$621$	3.23003	0.129617
$622$	−26.3032	−1.05466
$623$	0.840213	0.0336624
$624$	4.24592	0.169973
$625$	−17.2208	−0.688831
$626$	−28.4263	−1.13614
$627$	9.19731	0.367305
$628$	−23.8935	−0.953455
$629$	−21.5744	−0.860229
$630$	3.35344	0.133604
$631$	−7.42012	−0.295390	−0.147695	−	0.989033i	$-0.547185\pi$
$631$	−7.42012	−0.295390	−0.147695	+	0.989033i	$0.547185\pi$
$632$	−5.23644	−0.208294
$633$	22.4839	0.893655
$634$	7.16299	0.284479
$635$	−18.0431	−0.716019
$636$	5.41989	0.214913
$637$	4.24592	0.168230
$638$	35.9841	1.42462
$639$	−11.8152	−0.467401
$640$	−3.35344	−0.132556
$641$	30.2582	1.19513	0.597564	−	0.801821i	$-0.296135\pi$
$641$	30.2582	1.19513	0.597564	+	0.801821i	$0.296135\pi$
$642$	−12.4517	−0.491428
$643$	−40.7770	−1.60809	−0.804044	−	0.594569i	$-0.797323\pi$
$643$	−40.7770	−1.60809	−0.804044	+	0.594569i	$0.797323\pi$
$644$	−3.23003	−0.127281
$645$	4.57840	0.180274
$646$	−8.10050	−0.318710
$647$	12.1956	0.479458	0.239729	−	0.970840i	$-0.422941\pi$
$647$	12.1956	0.479458	0.239729	+	0.970840i	$0.422941\pi$
$648$	−1.00000	−0.0392837
$649$	47.8526	1.87838
$650$	−26.5182	−1.04013
$651$	−1.55659	−0.0610076
$652$	10.9412	0.428489
$653$	−48.4396	−1.89559	−0.947794	−	0.318883i	$-0.896692\pi$
$653$	−48.4396	−1.89559	−0.947794	+	0.318883i	$0.896692\pi$
$654$	−4.95724	−0.193843
$655$	−2.04476	−0.0798952
$656$	3.33098	0.130053
$657$	6.38145	0.248964
$658$	−3.65068	−0.142318
$659$	−2.06549	−0.0804601	−0.0402301	−	0.999190i	$-0.512809\pi$
$659$	−2.06549	−0.0804601	−0.0402301	+	0.999190i	$0.512809\pi$
$660$	−16.6683	−0.648813
$661$	9.74819	0.379161	0.189580	−	0.981865i	$-0.439287\pi$
$661$	9.74819	0.379161	0.189580	+	0.981865i	$0.439287\pi$
$662$	−3.74664	−0.145617
$663$	−18.5877	−0.721885
$664$	15.0799	0.585215
$665$	6.20512	0.240624
$666$	−4.92819	−0.190963
$667$	23.3838	0.905426
$668$	5.53717	0.214239
$669$	4.45592	0.172276
$670$	−21.3145	−0.823450
$671$	−59.5051	−2.29717
$672$	1.00000	0.0385758
$673$	−37.1257	−1.43109	−0.715546	−	0.698566i	$-0.753822\pi$
$673$	−37.1257	−1.43109	−0.715546	+	0.698566i	$0.753822\pi$
$674$	−20.2763	−0.781016
$675$	6.24556	0.240392
$676$	5.02787	0.193380
$677$	45.3215	1.74185	0.870923	−	0.491419i	$-0.163522\pi$
$677$	45.3215	1.74185	0.870923	+	0.491419i	$0.163522\pi$
$678$	−11.7943	−0.452958
$679$	19.0193	0.729892
$680$	14.6806	0.562974
$681$	6.50418	0.249241
$682$	7.73705	0.296267
$683$	5.78208	0.221245	0.110623	−	0.993862i	$-0.464716\pi$
$683$	5.78208	0.221245	0.110623	+	0.993862i	$0.464716\pi$
$684$	−1.85037	−0.0707508
$685$	70.9783	2.71194
$686$	1.00000	0.0381802
$687$	15.4925	0.591077
$688$	1.36529	0.0520510
$689$	23.0125	0.876705
$690$	−10.8317	−0.412356
$691$	−17.7501	−0.675244	−0.337622	−	0.941282i	$-0.609623\pi$
$691$	−17.7501	−0.675244	−0.337622	+	0.941282i	$0.609623\pi$
$692$	5.35744	0.203659
$693$	4.97051	0.188814
$694$	−11.6413	−0.441899
$695$	−11.4157	−0.433021
$696$	−7.23952	−0.274413
$697$	−14.5822	−0.552342
$698$	−29.0629	−1.10005
$699$	−1.02413	−0.0387360
$700$	−6.24556	−0.236060
$701$	46.2163	1.74556	0.872782	−	0.488110i	$-0.162313\pi$
$701$	46.2163	1.74556	0.872782	+	0.488110i	$0.162313\pi$
$702$	−4.24592	−0.160252
$703$	−9.11899	−0.343929
$704$	−4.97051	−0.187333
$705$	−12.2423	−0.461073
$706$	32.4715	1.22208
$707$	−15.8625	−0.596570
$708$	−9.62729	−0.361816
$709$	45.2447	1.69920	0.849600	−	0.527427i	$-0.176843\pi$
$709$	45.2447	1.69920	0.849600	+	0.527427i	$0.176843\pi$
$710$	39.6215	1.48697
$711$	5.23644	0.196382
$712$	0.840213	0.0314883
$713$	5.02783	0.188294
$714$	−4.37776	−0.163834
$715$	−70.7724	−2.64674
$716$	19.2452	0.719226
$717$	14.9459	0.558165
$718$	27.0548	1.00968
$719$	22.3006	0.831672	0.415836	−	0.909440i	$-0.363489\pi$
$719$	22.3006	0.831672	0.415836	+	0.909440i	$0.363489\pi$
$720$	3.35344	0.124975
$721$	−4.77972	−0.178006
$722$	15.5761	0.579683
$723$	12.8377	0.477438
$724$	−22.7018	−0.843706
$725$	45.2149	1.67924
$726$	−13.7060	−0.508677
$727$	38.3731	1.42318	0.711589	−	0.702596i	$-0.247976\pi$
$727$	38.3731	1.42318	0.711589	+	0.702596i	$0.247976\pi$
$728$	4.24592	0.157364
$729$	1.00000	0.0370370
$730$	−21.3998	−0.792043
$731$	−5.97690	−0.221064
$732$	11.9716	0.442483
$733$	−11.6263	−0.429426	−0.214713	−	0.976677i	$-0.568882\pi$
$733$	−11.6263	−0.429426	−0.214713	+	0.976677i	$0.568882\pi$
$734$	−29.6117	−1.09299
$735$	3.35344	0.123694
$736$	−3.23003	−0.119060
$737$	−31.5926	−1.16373
$738$	−3.33098	−0.122615
$739$	6.07951	0.223638	0.111819	−	0.993729i	$-0.464332\pi$
$739$	6.07951	0.223638	0.111819	+	0.993729i	$0.464332\pi$
$740$	16.5264	0.607522
$741$	−7.85655	−0.288617
$742$	5.41989	0.198970
$743$	49.4948	1.81579	0.907894	−	0.419200i	$-0.137689\pi$
$743$	49.4948	1.81579	0.907894	+	0.419200i	$0.137689\pi$
$744$	−1.55659	−0.0570674
$745$	−7.35395	−0.269428
$746$	25.9629	0.950568
$747$	−15.0799	−0.551746
$748$	21.7597	0.795615
$749$	−12.4517	−0.454974
$750$	−4.17692	−0.152520
$751$	−31.4122	−1.14625	−0.573124	−	0.819469i	$-0.694269\pi$
$751$	−31.4122	−1.14625	−0.573124	+	0.819469i	$0.694269\pi$
$752$	−3.65068	−0.133127
$753$	−0.296714	−0.0108128
$754$	−30.7384	−1.11943
$755$	5.52774	0.201175
$756$	−1.00000	−0.0363696
$757$	−9.56798	−0.347754	−0.173877	−	0.984767i	$-0.555630\pi$
$757$	−9.56798	−0.347754	−0.173877	+	0.984767i	$0.555630\pi$
$758$	−22.6779	−0.823700
$759$	−16.0549	−0.582756
$760$	6.20512	0.225083
$761$	23.1573	0.839451	0.419726	−	0.907651i	$-0.362126\pi$
$761$	23.1573	0.839451	0.419726	+	0.907651i	$0.362126\pi$
$762$	5.38048	0.194914
$763$	−4.95724	−0.179464
$764$	−1.00000	−0.0361787
$765$	−14.6806	−0.530777
$766$	−3.48864	−0.126050
$767$	−40.8768	−1.47597
$768$	1.00000	0.0360844
$769$	19.3811	0.698900	0.349450	−	0.936955i	$-0.386368\pi$
$769$	19.3811	0.698900	0.349450	+	0.936955i	$0.386368\pi$
$770$	−16.6683	−0.600685
$771$	−27.7161	−0.998171
$772$	21.3213	0.767372
$773$	5.32256	0.191439	0.0957197	−	0.995408i	$-0.469485\pi$
$773$	5.32256	0.191439	0.0957197	+	0.995408i	$0.469485\pi$
$774$	−1.36529	−0.0490742
$775$	9.72178	0.349217
$776$	19.0193	0.682752
$777$	−4.92819	−0.176798
$778$	−2.19381	−0.0786519
$779$	−6.16355	−0.220832
$780$	14.2385	0.509818
$781$	58.7275	2.10143
$782$	14.1403	0.505656
$783$	7.23952	0.258719
$784$	1.00000	0.0357143
$785$	−80.1255	−2.85980
$786$	0.609748	0.0217490
$787$	44.5263	1.58719	0.793596	−	0.608445i	$-0.208206\pi$
$787$	44.5263	1.58719	0.793596	+	0.608445i	$0.208206\pi$
$788$	2.85335	0.101647
$789$	11.3514	0.404122
$790$	−17.5601	−0.624760
$791$	−11.7943	−0.419357
$792$	4.97051	0.176619
$793$	50.8306	1.80505
$794$	−0.200605	−0.00711919
$795$	18.1753	0.644611
$796$	20.2417	0.717447
$797$	−20.8977	−0.740236	−0.370118	−	0.928985i	$-0.620683\pi$
$797$	−20.8977	−0.740236	−0.370118	+	0.928985i	$0.620683\pi$
$798$	−1.85037	−0.0655025
$799$	15.9818	0.565396
$800$	−6.24556	−0.220814
$801$	−0.840213	−0.0296875
$802$	12.0194	0.424418
$803$	−31.7191	−1.11934
$804$	6.35600	0.224159
$805$	−10.8317	−0.381767
$806$	−6.60916	−0.232798
$807$	9.43494	0.332125
$808$	−15.8625	−0.558040
$809$	25.5704	0.899007	0.449503	−	0.893279i	$-0.351601\pi$
$809$	25.5704	0.899007	0.449503	+	0.893279i	$0.351601\pi$
$810$	−3.35344	−0.117828
$811$	6.93627	0.243565	0.121783	−	0.992557i	$-0.461139\pi$
$811$	6.93627	0.243565	0.121783	+	0.992557i	$0.461139\pi$
$812$	−7.23952	−0.254057
$813$	−14.2556	−0.499967
$814$	24.4956	0.858571
$815$	36.6906	1.28521
$816$	−4.37776	−0.153252
$817$	−2.52629	−0.0883836
$818$	12.6656	0.442843
$819$	−4.24592	−0.148365
$820$	11.1702	0.390082
$821$	−9.82905	−0.343036	−0.171518	−	0.985181i	$-0.554867\pi$
$821$	−9.82905	−0.343036	−0.171518	+	0.985181i	$0.554867\pi$
$822$	−21.1658	−0.738243
$823$	39.6386	1.38171	0.690857	−	0.722991i	$-0.257233\pi$
$823$	39.6386	1.38171	0.690857	+	0.722991i	$0.257233\pi$
$824$	−4.77972	−0.166509
$825$	−31.0436	−1.08080
$826$	−9.62729	−0.334976
$827$	−0.993198	−0.0345369	−0.0172684	−	0.999851i	$-0.505497\pi$
$827$	−0.993198	−0.0345369	−0.0172684	+	0.999851i	$0.505497\pi$
$828$	3.23003	0.112251
$829$	20.5340	0.713176	0.356588	−	0.934262i	$-0.383940\pi$
$829$	20.5340	0.713176	0.356588	+	0.934262i	$0.383940\pi$
$830$	50.5696	1.75530
$831$	7.93063	0.275111
$832$	4.24592	0.147201
$833$	−4.37776	−0.151681
$834$	3.40416	0.117877
$835$	18.5686	0.642592
$836$	9.19731	0.318095
$837$	1.55659	0.0538036
$838$	23.2170	0.802019
$839$	0.0949686	0.00327868	0.00163934	−	0.999999i	$-0.499478\pi$
$839$	0.0949686	0.00327868	0.00163934	+	0.999999i	$0.499478\pi$
$840$	3.35344	0.115705
$841$	23.4106	0.807263
$842$	20.4654	0.705283
$843$	3.06779	0.105660
$844$	22.4839	0.773928
$845$	16.8607	0.580025
$846$	3.65068	0.125513
$847$	−13.7060	−0.470944
$848$	5.41989	0.186120
$849$	−22.2343	−0.763080
$850$	27.3416	0.937809
$851$	15.9182	0.545668
$852$	−11.8152	−0.404781
$853$	−27.9828	−0.958113	−0.479057	−	0.877784i	$-0.659021\pi$
$853$	−27.9828	−0.958113	−0.479057	+	0.877784i	$0.659021\pi$
$854$	11.9716	0.409660
$855$	−6.20512	−0.212211
$856$	−12.4517	−0.425589
$857$	−33.8965	−1.15788	−0.578941	−	0.815370i	$-0.696534\pi$
$857$	−33.8965	−1.15788	−0.578941	+	0.815370i	$0.696534\pi$
$858$	21.1044	0.720493
$859$	38.4006	1.31021	0.655105	−	0.755538i	$-0.272624\pi$
$859$	38.4006	1.31021	0.655105	+	0.755538i	$0.272624\pi$
$860$	4.57840	0.156122
$861$	−3.33098	−0.113519
$862$	8.69175	0.296042
$863$	−49.8947	−1.69843	−0.849217	−	0.528044i	$-0.822926\pi$
$863$	−49.8947	−1.69843	−0.849217	+	0.528044i	$0.822926\pi$
$864$	−1.00000	−0.0340207
$865$	17.9659	0.610858
$866$	−37.3757	−1.27008
$867$	2.16481	0.0735208
$868$	−1.55659	−0.0528341
$869$	−26.0278	−0.882933
$870$	−24.2773	−0.823077
$871$	26.9871	0.914423
$872$	−4.95724	−0.167873
$873$	−19.0193	−0.643704
$874$	5.97676	0.202167
$875$	−4.17692	−0.141206
$876$	6.38145	0.215609
$877$	−6.56416	−0.221656	−0.110828	−	0.993840i	$-0.535350\pi$
$877$	−6.56416	−0.221656	−0.110828	+	0.993840i	$0.535350\pi$
$878$	−34.0355	−1.14864
$879$	−28.5551	−0.963141
$880$	−16.6683	−0.561889
$881$	46.5755	1.56917	0.784583	−	0.620023i	$-0.212877\pi$
$881$	46.5755	1.56917	0.784583	+	0.620023i	$0.212877\pi$
$882$	−1.00000	−0.0336718
$883$	1.99434	0.0671147	0.0335574	−	0.999437i	$-0.489316\pi$
$883$	1.99434	0.0671147	0.0335574	+	0.999437i	$0.489316\pi$
$884$	−18.5877	−0.625170
$885$	−32.2846	−1.08523
$886$	7.99004	0.268431
$887$	24.6248	0.826818	0.413409	−	0.910545i	$-0.364338\pi$
$887$	24.6248	0.826818	0.413409	+	0.910545i	$0.364338\pi$
$888$	−4.92819	−0.165379
$889$	5.38048	0.180455
$890$	2.81760	0.0944463
$891$	−4.97051	−0.166518
$892$	4.45592	0.149195
$893$	6.75513	0.226052
$894$	2.19296	0.0733435
$895$	64.5376	2.15725
$896$	1.00000	0.0334077
$897$	13.7145	0.457912
$898$	5.85443	0.195365
$899$	11.2690	0.375841
$900$	6.24556	0.208185
$901$	−23.7270	−0.790461
$902$	16.5567	0.551277
$903$	−1.36529	−0.0454339
$904$	−11.7943	−0.392273
$905$	−76.1291	−2.53062
$906$	−1.64838	−0.0547637
$907$	−2.86919	−0.0952700	−0.0476350	−	0.998865i	$-0.515168\pi$
$907$	−2.86919	−0.0952700	−0.0476350	+	0.998865i	$0.515168\pi$
$908$	6.50418	0.215849
$909$	15.8625	0.526125
$910$	14.2385	0.472000
$911$	30.4348	1.00835	0.504174	−	0.863602i	$-0.331797\pi$
$911$	30.4348	1.00835	0.504174	+	0.863602i	$0.331797\pi$
$912$	−1.85037	−0.0612720
$913$	74.9550	2.48065
$914$	0.101023	0.00334153
$915$	40.1461	1.32719
$916$	15.4925	0.511888
$917$	0.609748	0.0201357
$918$	4.37776	0.144488
$919$	2.08588	0.0688067	0.0344034	−	0.999408i	$-0.489047\pi$
$919$	2.08588	0.0688067	0.0344034	+	0.999408i	$0.489047\pi$
$920$	−10.8317	−0.357111
$921$	1.08266	0.0356750
$922$	25.6480	0.844671
$923$	−50.1663	−1.65124
$924$	4.97051	0.163518
$925$	30.7793	1.01202
$926$	36.1720	1.18869
$927$	4.77972	0.156987
$928$	−7.23952	−0.237649
$929$	−5.00712	−0.164278	−0.0821391	−	0.996621i	$-0.526175\pi$
$929$	−5.00712	−0.164278	−0.0821391	+	0.996621i	$0.526175\pi$
$930$	−5.21993	−0.171168
$931$	−1.85037	−0.0606435
$932$	−1.02413	−0.0335464
$933$	26.3032	0.861127
$934$	−35.1121	−1.14890
$935$	72.9700	2.38637
$936$	−4.24592	−0.138782
$937$	5.38022	0.175764	0.0878821	−	0.996131i	$-0.471990\pi$
$937$	5.38022	0.175764	0.0878821	+	0.996131i	$0.471990\pi$
$938$	6.35600	0.207531
$939$	28.4263	0.927658
$940$	−12.2423	−0.399301
$941$	14.9081	0.485991	0.242996	−	0.970027i	$-0.421870\pi$
$941$	14.9081	0.485991	0.242996	+	0.970027i	$0.421870\pi$
$942$	23.8935	0.778493
$943$	10.7592	0.350366
$944$	−9.62729	−0.313342
$945$	−3.35344	−0.109087
$946$	6.78617	0.220637
$947$	−12.3588	−0.401608	−0.200804	−	0.979631i	$-0.564355\pi$
$947$	−12.3588	−0.401608	−0.200804	+	0.979631i	$0.564355\pi$
$948$	5.23644	0.170072
$949$	27.0952	0.879546
$950$	11.5566	0.374946
$951$	−7.16299	−0.232276
$952$	−4.37776	−0.141884
$953$	15.5858	0.504874	0.252437	−	0.967613i	$-0.418768\pi$
$953$	15.5858	0.504874	0.252437	+	0.967613i	$0.418768\pi$
$954$	−5.41989	−0.175475
$955$	−3.35344	−0.108515
$956$	14.9459	0.483385
$957$	−35.9841	−1.16320
$958$	40.2128	1.29922
$959$	−21.1658	−0.683480
$960$	3.35344	0.108232
$961$	−28.5770	−0.921840
$962$	−20.9247	−0.674640
$963$	12.4517	0.401249
$964$	12.8377	0.413474
$965$	71.4998	2.30166
$966$	3.23003	0.103924
$967$	37.5119	1.20630	0.603151	−	0.797627i	$-0.293912\pi$
$967$	37.5119	1.20630	0.603151	+	0.797627i	$0.293912\pi$
$968$	−13.7060	−0.440528
$969$	8.10050	0.260225
$970$	63.7799	2.04785
$971$	−53.1861	−1.70682	−0.853411	−	0.521239i	$-0.825470\pi$
$971$	−53.1861	−1.70682	−0.853411	+	0.521239i	$0.825470\pi$
$972$	1.00000	0.0320750
$973$	3.40416	0.109132
$974$	16.0932	0.515658
$975$	26.5182	0.849262
$976$	11.9716	0.383202
$977$	−30.9185	−0.989169	−0.494585	−	0.869129i	$-0.664680\pi$
$977$	−30.9185	−0.989169	−0.494585	+	0.869129i	$0.664680\pi$
$978$	−10.9412	−0.349860
$979$	4.17629	0.133475
$980$	3.35344	0.107122
$981$	4.95724	0.158272
$982$	26.5619	0.847625
$983$	−46.3026	−1.47682	−0.738412	−	0.674350i	$-0.764424\pi$
$983$	−46.3026	−1.47682	−0.738412	+	0.674350i	$0.764424\pi$
$984$	−3.33098	−0.106188
$985$	9.56855	0.304879
$986$	31.6929	1.00931
$987$	3.65068	0.116202
$988$	−7.85655	−0.249950
$989$	4.40991	0.140227
$990$	16.6683	0.529754
$991$	−37.0121	−1.17573	−0.587865	−	0.808959i	$-0.700031\pi$
$991$	−37.0121	−1.17573	−0.587865	+	0.808959i	$0.700031\pi$
$992$	−1.55659	−0.0494218
$993$	3.74664	0.118896
$994$	−11.8152	−0.374754
$995$	67.8793	2.15192
$996$	−15.0799	−0.477826
$997$	2.04501	0.0647663	0.0323831	−	0.999476i	$-0.489690\pi$
$997$	2.04501	0.0647663	0.0323831	+	0.999476i	$0.489690\pi$
$998$	−35.7123	−1.13045
$999$	4.92819	0.155921

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8022.2.a.w.1.13	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8022.2.a.w.1.13	✓	13	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8022 = 2 \cdot 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8022.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.35344 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.35344 q^{5} -1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.35344 q^{10} -4.97051 q^{11} +1.00000 q^{12} +4.24592 q^{13} +1.00000 q^{14} +3.35344 q^{15} +1.00000 q^{16} -4.37776 q^{17} -1.00000 q^{18} -1.85037 q^{19} +3.35344 q^{20} -1.00000 q^{21} +4.97051 q^{22} +3.23003 q^{23} -1.00000 q^{24} +6.24556 q^{25} -4.24592 q^{26} +1.00000 q^{27} -1.00000 q^{28} +7.23952 q^{29} -3.35344 q^{30} +1.55659 q^{31} -1.00000 q^{32} -4.97051 q^{33} +4.37776 q^{34} -3.35344 q^{35} +1.00000 q^{36} +4.92819 q^{37} +1.85037 q^{38} +4.24592 q^{39} -3.35344 q^{40} +3.33098 q^{41} +1.00000 q^{42} +1.36529 q^{43} -4.97051 q^{44} +3.35344 q^{45} -3.23003 q^{46} -3.65068 q^{47} +1.00000 q^{48} +1.00000 q^{49} -6.24556 q^{50} -4.37776 q^{51} +4.24592 q^{52} +5.41989 q^{53} -1.00000 q^{54} -16.6683 q^{55} +1.00000 q^{56} -1.85037 q^{57} -7.23952 q^{58} -9.62729 q^{59} +3.35344 q^{60} +11.9716 q^{61} -1.55659 q^{62} -1.00000 q^{63} +1.00000 q^{64} +14.2385 q^{65} +4.97051 q^{66} +6.35600 q^{67} -4.37776 q^{68} +3.23003 q^{69} +3.35344 q^{70} -11.8152 q^{71} -1.00000 q^{72} +6.38145 q^{73} -4.92819 q^{74} +6.24556 q^{75} -1.85037 q^{76} +4.97051 q^{77} -4.24592 q^{78} +5.23644 q^{79} +3.35344 q^{80} +1.00000 q^{81} -3.33098 q^{82} -15.0799 q^{83} -1.00000 q^{84} -14.6806 q^{85} -1.36529 q^{86} +7.23952 q^{87} +4.97051 q^{88} -0.840213 q^{89} -3.35344 q^{90} -4.24592 q^{91} +3.23003 q^{92} +1.55659 q^{93} +3.65068 q^{94} -6.20512 q^{95} -1.00000 q^{96} -19.0193 q^{97} -1.00000 q^{98} -4.97051 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} - 2 q^{5} - 13 q^{6} - 13 q^{7} - 13 q^{8} + 13 q^{9} + 2 q^{10} - q^{11} + 13 q^{12} + 14 q^{13} + 13 q^{14} - 2 q^{15} + 13 q^{16} + 7 q^{17} - 13 q^{18} - 2 q^{20} - 13 q^{21} + q^{22} + 11 q^{23} - 13 q^{24} + 17 q^{25} - 14 q^{26} + 13 q^{27} - 13 q^{28} + 5 q^{29} + 2 q^{30} - 7 q^{31} - 13 q^{32} - q^{33} - 7 q^{34} + 2 q^{35} + 13 q^{36} + 15 q^{37} + 14 q^{39} + 2 q^{40} - 10 q^{41} + 13 q^{42} + 15 q^{43} - q^{44} - 2 q^{45} - 11 q^{46} - 7 q^{47} + 13 q^{48} + 13 q^{49} - 17 q^{50} + 7 q^{51} + 14 q^{52} + 14 q^{53} - 13 q^{54} + 19 q^{55} + 13 q^{56} - 5 q^{58} - 18 q^{59} - 2 q^{60} + 27 q^{61} + 7 q^{62} - 13 q^{63} + 13 q^{64} + 18 q^{65} + q^{66} + 7 q^{67} + 7 q^{68} + 11 q^{69} - 2 q^{70} - 4 q^{71} - 13 q^{72} + 26 q^{73} - 15 q^{74} + 17 q^{75} + q^{77} - 14 q^{78} + 20 q^{79} - 2 q^{80} + 13 q^{81} + 10 q^{82} + q^{83} - 13 q^{84} + 34 q^{85} - 15 q^{86} + 5 q^{87} + q^{88} - 15 q^{89} + 2 q^{90} - 14 q^{91} + 11 q^{92} - 7 q^{93} + 7 q^{94} + 24 q^{95} - 13 q^{96} + 18 q^{97} - 13 q^{98} - q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 - 2 * q^5 - 13 * q^6 - 13 * q^7 - 13 * q^8 + 13 * q^9 + 2 * q^10 - q^11 + 13 * q^12 + 14 * q^13 + 13 * q^14 - 2 * q^15 + 13 * q^16 + 7 * q^17 - 13 * q^18 - 2 * q^20 - 13 * q^21 + q^22 + 11 * q^23 - 13 * q^24 + 17 * q^25 - 14 * q^26 + 13 * q^27 - 13 * q^28 + 5 * q^29 + 2 * q^30 - 7 * q^31 - 13 * q^32 - q^33 - 7 * q^34 + 2 * q^35 + 13 * q^36 + 15 * q^37 + 14 * q^39 + 2 * q^40 - 10 * q^41 + 13 * q^42 + 15 * q^43 - q^44 - 2 * q^45 - 11 * q^46 - 7 * q^47 + 13 * q^48 + 13 * q^49 - 17 * q^50 + 7 * q^51 + 14 * q^52 + 14 * q^53 - 13 * q^54 + 19 * q^55 + 13 * q^56 - 5 * q^58 - 18 * q^59 - 2 * q^60 + 27 * q^61 + 7 * q^62 - 13 * q^63 + 13 * q^64 + 18 * q^65 + q^66 + 7 * q^67 + 7 * q^68 + 11 * q^69 - 2 * q^70 - 4 * q^71 - 13 * q^72 + 26 * q^73 - 15 * q^74 + 17 * q^75 + q^77 - 14 * q^78 + 20 * q^79 - 2 * q^80 + 13 * q^81 + 10 * q^82 + q^83 - 13 * q^84 + 34 * q^85 - 15 * q^86 + 5 * q^87 + q^88 - 15 * q^89 + 2 * q^90 - 14 * q^91 + 11 * q^92 - 7 * q^93 + 7 * q^94 + 24 * q^95 - 13 * q^96 + 18 * q^97 - 13 * q^98 - q^99

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