LMFDB - Embedded newform 6045.2.a.bh.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6045,2,Mod(1,6045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6045, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6045.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6045 = 3 \cdot 5 \cdot 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6045.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:	$48.2695680219$
Analytic rank:	$0$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 25 x^{15} + 47 x^{14} + 252 x^{13} - 437 x^{12} - 1319 x^{11} + 2056 x^{10} + \cdots + 8 $ x^17 - 2x^16 - 25x^15 + 47x^14 + 252x^13 - 437x^12 - 1319x^11 + 2056x^10 + 3854x^9 - 5201x^8 - 6304x^7 + 6915x^6 + 5469x^5 - 4238x^4 - 2198x^3 + 760x^2 + 306x + 8
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-0.565863$ of defining polynomial
Character	$\chi$	$=$	6045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.565863 q^{2} -1.00000 q^{3} -1.67980 q^{4} +1.00000 q^{5} +0.565863 q^{6} -3.78718 q^{7} +2.08226 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.565863 q^{2} -1.00000 q^{3} -1.67980 q^{4} +1.00000 q^{5} +0.565863 q^{6} -3.78718 q^{7} +2.08226 q^{8} +1.00000 q^{9} -0.565863 q^{10} +0.609111 q^{11} +1.67980 q^{12} +1.00000 q^{13} +2.14303 q^{14} -1.00000 q^{15} +2.18132 q^{16} -3.76728 q^{17} -0.565863 q^{18} -5.88030 q^{19} -1.67980 q^{20} +3.78718 q^{21} -0.344674 q^{22} +7.17920 q^{23} -2.08226 q^{24} +1.00000 q^{25} -0.565863 q^{26} -1.00000 q^{27} +6.36171 q^{28} -1.74208 q^{29} +0.565863 q^{30} +1.00000 q^{31} -5.39885 q^{32} -0.609111 q^{33} +2.13177 q^{34} -3.78718 q^{35} -1.67980 q^{36} -8.08226 q^{37} +3.32744 q^{38} -1.00000 q^{39} +2.08226 q^{40} +0.325748 q^{41} -2.14303 q^{42} -9.08260 q^{43} -1.02318 q^{44} +1.00000 q^{45} -4.06245 q^{46} +10.8335 q^{47} -2.18132 q^{48} +7.34275 q^{49} -0.565863 q^{50} +3.76728 q^{51} -1.67980 q^{52} +6.89871 q^{53} +0.565863 q^{54} +0.609111 q^{55} -7.88591 q^{56} +5.88030 q^{57} +0.985778 q^{58} -2.39707 q^{59} +1.67980 q^{60} -8.50012 q^{61} -0.565863 q^{62} -3.78718 q^{63} -1.30763 q^{64} +1.00000 q^{65} +0.344674 q^{66} +3.28924 q^{67} +6.32828 q^{68} -7.17920 q^{69} +2.14303 q^{70} +3.63026 q^{71} +2.08226 q^{72} +0.542012 q^{73} +4.57345 q^{74} -1.00000 q^{75} +9.87772 q^{76} -2.30682 q^{77} +0.565863 q^{78} -12.3602 q^{79} +2.18132 q^{80} +1.00000 q^{81} -0.184329 q^{82} -6.16365 q^{83} -6.36171 q^{84} -3.76728 q^{85} +5.13951 q^{86} +1.74208 q^{87} +1.26833 q^{88} -13.9194 q^{89} -0.565863 q^{90} -3.78718 q^{91} -12.0596 q^{92} -1.00000 q^{93} -6.13025 q^{94} -5.88030 q^{95} +5.39885 q^{96} -12.5776 q^{97} -4.15499 q^{98} +0.609111 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) $ 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * 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 $

$2$	−0.565863	−0.400126	−0.200063	−	0.979783i	$-0.564115\pi$
$2$	−0.565863	−0.400126	−0.200063	+	0.979783i	$0.564115\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.67980	−0.839899
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.565863	0.231013
$7$	−3.78718	−1.43142	−0.715710	−	0.698397i	$-0.753897\pi$
$7$	−3.78718	−1.43142	−0.715710	+	0.698397i	$0.753897\pi$
$8$	2.08226	0.736191
$9$	1.00000	0.333333
$10$	−0.565863	−0.178942
$11$	0.609111	0.183654	0.0918270	−	0.995775i	$-0.470729\pi$
$11$	0.609111	0.183654	0.0918270	+	0.995775i	$0.470729\pi$
$12$	1.67980	0.484916
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	2.14303	0.572748
$15$	−1.00000	−0.258199
$16$	2.18132	0.545331
$17$	−3.76728	−0.913700	−0.456850	−	0.889544i	$-0.651022\pi$
$17$	−3.76728	−0.913700	−0.456850	+	0.889544i	$0.651022\pi$
$18$	−0.565863	−0.133375
$19$	−5.88030	−1.34903	−0.674517	−	0.738260i	$-0.735648\pi$
$19$	−5.88030	−1.34903	−0.674517	+	0.738260i	$0.735648\pi$
$20$	−1.67980	−0.375614
$21$	3.78718	0.826431
$22$	−0.344674	−0.0734847
$23$	7.17920	1.49697	0.748484	−	0.663153i	$-0.230782\pi$
$23$	7.17920	1.49697	0.748484	+	0.663153i	$0.230782\pi$
$24$	−2.08226	−0.425040
$25$	1.00000	0.200000
$26$	−0.565863	−0.110975
$27$	−1.00000	−0.192450
$28$	6.36171	1.20225
$29$	−1.74208	−0.323496	−0.161748	−	0.986832i	$-0.551713\pi$
$29$	−1.74208	−0.323496	−0.161748	+	0.986832i	$0.551713\pi$
$30$	0.565863	0.103312
$31$	1.00000	0.179605
$31$	1.00000	0.179605
$32$	−5.39885	−0.954392
$33$	−0.609111	−0.106033
$34$	2.13177	0.365595
$35$	−3.78718	−0.640151
$36$	−1.67980	−0.279966
$37$	−8.08226	−1.32871	−0.664357	−	0.747415i	$-0.731295\pi$
$37$	−8.08226	−1.32871	−0.664357	+	0.747415i	$0.731295\pi$
$38$	3.32744	0.539783
$39$	−1.00000	−0.160128
$40$	2.08226	0.329235
$41$	0.325748	0.0508733	0.0254366	−	0.999676i	$-0.491902\pi$
$41$	0.325748	0.0508733	0.0254366	+	0.999676i	$0.491902\pi$
$42$	−2.14303	−0.330676
$43$	−9.08260	−1.38508	−0.692542	−	0.721378i	$-0.743509\pi$
$43$	−9.08260	−1.38508	−0.692542	+	0.721378i	$0.743509\pi$
$44$	−1.02318	−0.154251
$45$	1.00000	0.149071
$46$	−4.06245	−0.598975
$47$	10.8335	1.58022	0.790111	−	0.612964i	$-0.210023\pi$
$47$	10.8335	1.58022	0.790111	+	0.612964i	$0.210023\pi$
$48$	−2.18132	−0.314847
$49$	7.34275	1.04896
$50$	−0.565863	−0.0800251
$51$	3.76728	0.527525
$52$	−1.67980	−0.232946
$53$	6.89871	0.947611	0.473806	−	0.880629i	$-0.342880\pi$
$53$	6.89871	0.947611	0.473806	+	0.880629i	$0.342880\pi$
$54$	0.565863	0.0770042
$55$	0.609111	0.0821325
$56$	−7.88591	−1.05380
$57$	5.88030	0.778865
$58$	0.985778	0.129439
$59$	−2.39707	−0.312072	−0.156036	−	0.987751i	$-0.549872\pi$
$59$	−2.39707	−0.312072	−0.156036	+	0.987751i	$0.549872\pi$
$60$	1.67980	0.216861
$61$	−8.50012	−1.08833	−0.544165	−	0.838979i	$-0.683153\pi$
$61$	−8.50012	−1.08833	−0.544165	+	0.838979i	$0.683153\pi$
$62$	−0.565863	−0.0718647
$63$	−3.78718	−0.477140
$64$	−1.30763	−0.163454
$65$	1.00000	0.124035
$66$	0.344674	0.0424264
$67$	3.28924	0.401845	0.200922	−	0.979607i	$-0.435606\pi$
$67$	3.28924	0.401845	0.200922	+	0.979607i	$0.435606\pi$
$68$	6.32828	0.767416
$69$	−7.17920	−0.864275
$70$	2.14303	0.256141
$71$	3.63026	0.430833	0.215416	−	0.976522i	$-0.430889\pi$
$71$	3.63026	0.430833	0.215416	+	0.976522i	$0.430889\pi$
$72$	2.08226	0.245397
$73$	0.542012	0.0634377	0.0317189	−	0.999497i	$-0.489902\pi$
$73$	0.542012	0.0634377	0.0317189	+	0.999497i	$0.489902\pi$
$74$	4.57345	0.531653
$75$	−1.00000	−0.115470
$76$	9.87772	1.13305
$77$	−2.30682	−0.262886
$78$	0.565863	0.0640714
$79$	−12.3602	−1.39063	−0.695315	−	0.718705i	$-0.744735\pi$
$79$	−12.3602	−1.39063	−0.695315	+	0.718705i	$0.744735\pi$
$80$	2.18132	0.243879
$81$	1.00000	0.111111
$82$	−0.184329	−0.0203557
$83$	−6.16365	−0.676549	−0.338274	−	0.941048i	$-0.609843\pi$
$83$	−6.16365	−0.676549	−0.338274	+	0.941048i	$0.609843\pi$
$84$	−6.36171	−0.694119
$85$	−3.76728	−0.408619
$86$	5.13951	0.554207
$87$	1.74208	0.186770
$88$	1.26833	0.135204
$89$	−13.9194	−1.47545	−0.737727	−	0.675099i	$-0.764101\pi$
$89$	−13.9194	−1.47545	−0.737727	+	0.675099i	$0.764101\pi$
$90$	−0.565863	−0.0596472
$91$	−3.78718	−0.397005
$92$	−12.0596	−1.25730
$93$	−1.00000	−0.103695
$94$	−6.13025	−0.632287
$95$	−5.88030	−0.603306
$96$	5.39885	0.551018
$97$	−12.5776	−1.27707	−0.638533	−	0.769595i	$-0.720458\pi$
$97$	−12.5776	−1.27707	−0.638533	+	0.769595i	$0.720458\pi$
$98$	−4.15499	−0.419718
$99$	0.609111	0.0612180
$100$	−1.67980	−0.167980
$101$	10.7773	1.07238	0.536192	−	0.844096i	$-0.319862\pi$
$101$	10.7773	1.07238	0.536192	+	0.844096i	$0.319862\pi$
$102$	−2.13177	−0.211076
$103$	15.3597	1.51343	0.756717	−	0.653743i	$-0.226802\pi$
$103$	15.3597	1.51343	0.756717	+	0.653743i	$0.226802\pi$
$104$	2.08226	0.204183
$105$	3.78718	0.369591
$106$	−3.90373	−0.379164
$107$	1.03700	0.100251	0.0501253	−	0.998743i	$-0.484038\pi$
$107$	1.03700	0.100251	0.0501253	+	0.998743i	$0.484038\pi$
$108$	1.67980	0.161639
$109$	−12.5833	−1.20526	−0.602629	−	0.798021i	$-0.705880\pi$
$109$	−12.5833	−1.20526	−0.602629	+	0.798021i	$0.705880\pi$
$110$	−0.344674	−0.0328633
$111$	8.08226	0.767134
$112$	−8.26107	−0.780597
$113$	−6.96065	−0.654803	−0.327402	−	0.944885i	$-0.606173\pi$
$113$	−6.96065	−0.654803	−0.327402	+	0.944885i	$0.606173\pi$
$114$	−3.32744	−0.311644
$115$	7.17920	0.669464
$116$	2.92634	0.271704
$117$	1.00000	0.0924500
$118$	1.35642	0.124868
$119$	14.2674	1.30789
$120$	−2.08226	−0.190084
$121$	−10.6290	−0.966271
$122$	4.80991	0.435468
$123$	−0.325748	−0.0293717
$124$	−1.67980	−0.150850
$125$	1.00000	0.0894427
$126$	2.14303	0.190916
$127$	−7.97288	−0.707478	−0.353739	−	0.935344i	$-0.615090\pi$
$127$	−7.97288	−0.707478	−0.353739	+	0.935344i	$0.615090\pi$
$128$	11.5377	1.01979
$129$	9.08260	0.799678
$130$	−0.565863	−0.0496295
$131$	12.0917	1.05646	0.528230	−	0.849101i	$-0.322856\pi$
$131$	12.0917	1.05646	0.528230	+	0.849101i	$0.322856\pi$
$132$	1.02318	0.0890568
$133$	22.2698	1.93103
$134$	−1.86126	−0.160788
$135$	−1.00000	−0.0860663
$136$	−7.84447	−0.672658
$137$	−13.5905	−1.16111	−0.580556	−	0.814220i	$-0.697165\pi$
$137$	−13.5905	−1.16111	−0.580556	+	0.814220i	$0.697165\pi$
$138$	4.06245	0.345818
$139$	−16.4443	−1.39479	−0.697394	−	0.716688i	$-0.745657\pi$
$139$	−16.4443	−1.39479	−0.697394	+	0.716688i	$0.745657\pi$
$140$	6.36171	0.537662
$141$	−10.8335	−0.912341
$142$	−2.05423	−0.172387
$143$	0.609111	0.0509364
$144$	2.18132	0.181777
$145$	−1.74208	−0.144672
$146$	−0.306705	−0.0253831
$147$	−7.34275	−0.605620
$148$	13.5766	1.11599
$149$	21.5236	1.76328	0.881642	−	0.471919i	$-0.156438\pi$
$149$	21.5236	1.76328	0.881642	+	0.471919i	$0.156438\pi$
$150$	0.565863	0.0462025
$151$	12.2550	0.997297	0.498649	−	0.866804i	$-0.333830\pi$
$151$	12.2550	0.997297	0.498649	+	0.866804i	$0.333830\pi$
$152$	−12.2443	−0.993146
$153$	−3.76728	−0.304567
$154$	1.30534	0.105187
$155$	1.00000	0.0803219
$156$	1.67980	0.134492
$157$	0.0856834	0.00683828	0.00341914	−	0.999994i	$-0.498912\pi$
$157$	0.0856834	0.00683828	0.00341914	+	0.999994i	$0.498912\pi$
$158$	6.99418	0.556427
$159$	−6.89871	−0.547104
$160$	−5.39885	−0.426817
$161$	−27.1890	−2.14279
$162$	−0.565863	−0.0444584
$163$	23.6599	1.85319	0.926594	−	0.376062i	$-0.122722\pi$
$163$	23.6599	1.85319	0.926594	+	0.376062i	$0.122722\pi$
$164$	−0.547191	−0.0427284
$165$	−0.609111	−0.0474192
$166$	3.48778	0.270704
$167$	23.3514	1.80698	0.903492	−	0.428606i	$-0.140995\pi$
$167$	23.3514	1.80698	0.903492	+	0.428606i	$0.140995\pi$
$168$	7.88591	0.608411
$169$	1.00000	0.0769231
$170$	2.13177	0.163499
$171$	−5.88030	−0.449678
$172$	15.2569	1.16333
$173$	6.35415	0.483097	0.241548	−	0.970389i	$-0.422345\pi$
$173$	6.35415	0.483097	0.241548	+	0.970389i	$0.422345\pi$
$174$	−0.985778	−0.0747316
$175$	−3.78718	−0.286284
$176$	1.32867	0.100152
$177$	2.39707	0.180175
$178$	7.87648	0.590367
$179$	−14.1761	−1.05957	−0.529784	−	0.848133i	$-0.677727\pi$
$179$	−14.1761	−1.05957	−0.529784	+	0.848133i	$0.677727\pi$
$180$	−1.67980	−0.125205
$181$	−24.0322	−1.78630	−0.893150	−	0.449760i	$-0.851510\pi$
$181$	−24.0322	−1.78630	−0.893150	+	0.449760i	$0.851510\pi$
$182$	2.14303	0.158852
$183$	8.50012	0.628347
$184$	14.9490	1.10205
$185$	−8.08226	−0.594219
$186$	0.565863	0.0414911
$187$	−2.29469	−0.167805
$188$	−18.1980	−1.32723
$189$	3.78718	0.275477
$190$	3.32744	0.241398
$191$	18.2237	1.31862	0.659311	−	0.751870i	$-0.270848\pi$
$191$	18.2237	1.31862	0.659311	+	0.751870i	$0.270848\pi$
$192$	1.30763	0.0943702
$193$	−5.95783	−0.428854	−0.214427	−	0.976740i	$-0.568788\pi$
$193$	−5.95783	−0.428854	−0.214427	+	0.976740i	$0.568788\pi$
$194$	7.11722	0.510987
$195$	−1.00000	−0.0716115
$196$	−12.3343	−0.881025
$197$	17.3011	1.23265	0.616327	−	0.787490i	$-0.288620\pi$
$197$	17.3011	1.23265	0.616327	+	0.787490i	$0.288620\pi$
$198$	−0.344674	−0.0244949
$199$	−9.81797	−0.695977	−0.347989	−	0.937499i	$-0.613135\pi$
$199$	−9.81797	−0.695977	−0.347989	+	0.937499i	$0.613135\pi$
$200$	2.08226	0.147238
$201$	−3.28924	−0.232005
$202$	−6.09849	−0.429088
$203$	6.59757	0.463059
$204$	−6.32828	−0.443068
$205$	0.325748	0.0227512
$206$	−8.69147	−0.605564
$207$	7.17920	0.498989
$208$	2.18132	0.151247
$209$	−3.58176	−0.247755
$210$	−2.14303	−0.147883
$211$	−8.47824	−0.583666	−0.291833	−	0.956469i	$-0.594265\pi$
$211$	−8.47824	−0.583666	−0.291833	+	0.956469i	$0.594265\pi$
$212$	−11.5885	−0.795898
$213$	−3.63026	−0.248742
$214$	−0.586800	−0.0401128
$215$	−9.08260	−0.619428
$216$	−2.08226	−0.141680
$217$	−3.78718	−0.257091
$218$	7.12041	0.482255
$219$	−0.542012	−0.0366258
$220$	−1.02318	−0.0689831
$221$	−3.76728	−0.253415
$222$	−4.57345	−0.306950
$223$	−8.80661	−0.589734	−0.294867	−	0.955538i	$-0.595275\pi$
$223$	−8.80661	−0.589734	−0.294867	+	0.955538i	$0.595275\pi$
$224$	20.4464	1.36614
$225$	1.00000	0.0666667
$226$	3.93878	0.262004
$227$	9.49855	0.630441	0.315221	−	0.949018i	$-0.397922\pi$
$227$	9.49855	0.630441	0.315221	+	0.949018i	$0.397922\pi$
$228$	−9.87772	−0.654168
$229$	−6.03394	−0.398734	−0.199367	−	0.979925i	$-0.563889\pi$
$229$	−6.03394	−0.398734	−0.199367	+	0.979925i	$0.563889\pi$
$230$	−4.06245	−0.267870
$231$	2.30682	0.151777
$232$	−3.62746	−0.238155
$233$	0.540554	0.0354129	0.0177064	−	0.999843i	$-0.494364\pi$
$233$	0.540554	0.0354129	0.0177064	+	0.999843i	$0.494364\pi$
$234$	−0.565863	−0.0369916
$235$	10.8335	0.706697
$236$	4.02660	0.262109
$237$	12.3602	0.802881
$238$	−8.07339	−0.523320
$239$	19.4290	1.25676	0.628379	−	0.777907i	$-0.283719\pi$
$239$	19.4290	1.25676	0.628379	+	0.777907i	$0.283719\pi$
$240$	−2.18132	−0.140804
$241$	7.73058	0.497970	0.248985	−	0.968507i	$-0.419903\pi$
$241$	7.73058	0.497970	0.248985	+	0.968507i	$0.419903\pi$
$242$	6.01455	0.386630
$243$	−1.00000	−0.0641500
$244$	14.2785	0.914087
$245$	7.34275	0.469111
$246$	0.184329	0.0117524
$247$	−5.88030	−0.374154
$248$	2.08226	0.132224
$249$	6.16365	0.390606
$250$	−0.565863	−0.0357883
$251$	15.3868	0.971205	0.485603	−	0.874180i	$-0.338600\pi$
$251$	15.3868	0.971205	0.485603	+	0.874180i	$0.338600\pi$
$252$	6.36171	0.400750
$253$	4.37293	0.274924
$254$	4.51156	0.283080
$255$	3.76728	0.235916
$256$	−3.91347	−0.244592
$257$	−15.4309	−0.962553	−0.481276	−	0.876569i	$-0.659827\pi$
$257$	−15.4309	−0.962553	−0.481276	+	0.876569i	$0.659827\pi$
$258$	−5.13951	−0.319972
$259$	30.6090	1.90195
$260$	−1.67980	−0.104177
$261$	−1.74208	−0.107832
$262$	−6.84227	−0.422717
$263$	−21.1762	−1.30578	−0.652891	−	0.757452i	$-0.726444\pi$
$263$	−21.1762	−1.30578	−0.652891	+	0.757452i	$0.726444\pi$
$264$	−1.26833	−0.0780603
$265$	6.89871	0.423785
$266$	−12.6016	−0.772656
$267$	13.9194	0.851854
$268$	−5.52527	−0.337509
$269$	21.9665	1.33932	0.669662	−	0.742666i	$-0.266439\pi$
$269$	21.9665	1.33932	0.669662	+	0.742666i	$0.266439\pi$
$270$	0.565863	0.0344373
$271$	20.4845	1.24434	0.622172	−	0.782880i	$-0.286250\pi$
$271$	20.4845	1.24434	0.622172	+	0.782880i	$0.286250\pi$
$272$	−8.21766	−0.498269
$273$	3.78718	0.229211
$274$	7.69035	0.464591
$275$	0.609111	0.0367308
$276$	12.0596	0.725904
$277$	7.59685	0.456451	0.228225	−	0.973608i	$-0.426708\pi$
$277$	7.59685	0.456451	0.228225	+	0.973608i	$0.426708\pi$
$278$	9.30522	0.558090
$279$	1.00000	0.0598684
$280$	−7.88591	−0.471273
$281$	−14.7355	−0.879046	−0.439523	−	0.898231i	$-0.644853\pi$
$281$	−14.7355	−0.879046	−0.439523	+	0.898231i	$0.644853\pi$
$282$	6.13025	0.365051
$283$	−7.34018	−0.436328	−0.218164	−	0.975912i	$-0.570007\pi$
$283$	−7.34018	−0.436328	−0.218164	+	0.975912i	$0.570007\pi$
$284$	−6.09811	−0.361856
$285$	5.88030	0.348319
$286$	−0.344674	−0.0203810
$287$	−1.23367	−0.0728210
$288$	−5.39885	−0.318131
$289$	−2.80758	−0.165152
$290$	0.985778	0.0578869
$291$	12.5776	0.737314
$292$	−0.910471	−0.0532813
$293$	8.87482	0.518472	0.259236	−	0.965814i	$-0.416529\pi$
$293$	8.87482	0.518472	0.259236	+	0.965814i	$0.416529\pi$
$294$	4.15499	0.242324
$295$	−2.39707	−0.139563
$296$	−16.8294	−0.978188
$297$	−0.609111	−0.0353442
$298$	−12.1794	−0.705535
$299$	7.17920	0.415184
$300$	1.67980	0.0969832
$301$	34.3975	1.98264
$302$	−6.93465	−0.399044
$303$	−10.7773	−0.619141
$304$	−12.8268	−0.735669
$305$	−8.50012	−0.486716
$306$	2.13177	0.121865
$307$	24.7010	1.40976	0.704881	−	0.709325i	$-0.251000\pi$
$307$	24.7010	1.40976	0.704881	+	0.709325i	$0.251000\pi$
$308$	3.87499	0.220798
$309$	−15.3597	−0.873781
$310$	−0.565863	−0.0321389
$311$	−33.4451	−1.89650	−0.948248	−	0.317530i	$-0.897147\pi$
$311$	−33.4451	−1.89650	−0.948248	+	0.317530i	$0.897147\pi$
$312$	−2.08226	−0.117885
$313$	27.4739	1.55292	0.776459	−	0.630168i	$-0.217014\pi$
$313$	27.4739	1.55292	0.776459	+	0.630168i	$0.217014\pi$
$314$	−0.0484851	−0.00273617
$315$	−3.78718	−0.213384
$316$	20.7626	1.16799
$317$	21.8618	1.22788	0.613941	−	0.789352i	$-0.289583\pi$
$317$	21.8618	1.22788	0.613941	+	0.789352i	$0.289583\pi$
$318$	3.90373	0.218910
$319$	−1.06112	−0.0594113
$320$	−1.30763	−0.0730989
$321$	−1.03700	−0.0578797
$322$	15.3852	0.857385
$323$	22.1527	1.23261
$324$	−1.67980	−0.0933222
$325$	1.00000	0.0554700
$326$	−13.3883	−0.741508
$327$	12.5833	0.695856
$328$	0.678292	0.0374524
$329$	−41.0283	−2.26196
$330$	0.344674	0.0189737
$331$	13.6960	0.752801	0.376400	−	0.926457i	$-0.377162\pi$
$331$	13.6960	0.752801	0.376400	+	0.926457i	$0.377162\pi$
$332$	10.3537	0.568233
$333$	−8.08226	−0.442905
$334$	−13.2137	−0.723020
$335$	3.28924	0.179711
$336$	8.26107	0.450678
$337$	23.1806	1.26273	0.631365	−	0.775486i	$-0.282495\pi$
$337$	23.1806	1.26273	0.631365	+	0.775486i	$0.282495\pi$
$338$	−0.565863	−0.0307789
$339$	6.96065	0.378051
$340$	6.32828	0.343199
$341$	0.609111	0.0329852
$342$	3.32744	0.179928
$343$	−1.29806	−0.0700887
$344$	−18.9124	−1.01969
$345$	−7.17920	−0.386515
$346$	−3.59558	−0.193299
$347$	34.7175	1.86373	0.931866	−	0.362802i	$-0.118180\pi$
$347$	34.7175	1.86373	0.931866	+	0.362802i	$0.118180\pi$
$348$	−2.92634	−0.156868
$349$	27.0454	1.44771	0.723855	−	0.689952i	$-0.242369\pi$
$349$	27.0454	1.44771	0.723855	+	0.689952i	$0.242369\pi$
$350$	2.14303	0.114550
$351$	−1.00000	−0.0533761
$352$	−3.28850	−0.175278
$353$	−23.0486	−1.22675	−0.613377	−	0.789790i	$-0.710189\pi$
$353$	−23.0486	−1.22675	−0.613377	+	0.789790i	$0.710189\pi$
$354$	−1.35642	−0.0720927
$355$	3.63026	0.192674
$356$	23.3818	1.23923
$357$	−14.2674	−0.755110
$358$	8.02171	0.423960
$359$	−11.4011	−0.601725	−0.300863	−	0.953668i	$-0.597275\pi$
$359$	−11.4011	−0.601725	−0.300863	+	0.953668i	$0.597275\pi$
$360$	2.08226	0.109745
$361$	15.5779	0.819890
$362$	13.5989	0.714744
$363$	10.6290	0.557877
$364$	6.36171	0.333444
$365$	0.542012	0.0283702
$366$	−4.80991	−0.251418
$367$	29.1330	1.52073	0.760365	−	0.649496i	$-0.225020\pi$
$367$	29.1330	1.52073	0.760365	+	0.649496i	$0.225020\pi$
$368$	15.6602	0.816342
$369$	0.325748	0.0169578
$370$	4.57345	0.237762
$371$	−26.1267	−1.35643
$372$	1.67980	0.0870935
$373$	24.2359	1.25489	0.627444	−	0.778662i	$-0.284101\pi$
$373$	24.2359	1.25489	0.627444	+	0.778662i	$0.284101\pi$
$374$	1.29848	0.0671430
$375$	−1.00000	−0.0516398
$376$	22.5581	1.16334
$377$	−1.74208	−0.0897216
$378$	−2.14303	−0.110225
$379$	−2.55277	−0.131127	−0.0655635	−	0.997848i	$-0.520884\pi$
$379$	−2.55277	−0.131127	−0.0655635	+	0.997848i	$0.520884\pi$
$380$	9.87772	0.506716
$381$	7.97288	0.408463
$382$	−10.3121	−0.527615
$383$	29.4294	1.50377	0.751885	−	0.659294i	$-0.229145\pi$
$383$	29.4294	1.50377	0.751885	+	0.659294i	$0.229145\pi$
$384$	−11.5377	−0.588778
$385$	−2.30682	−0.117566
$386$	3.37131	0.171595
$387$	−9.08260	−0.461694
$388$	21.1279	1.07261
$389$	35.7792	1.81408	0.907040	−	0.421045i	$-0.138337\pi$
$389$	35.7792	1.81408	0.907040	+	0.421045i	$0.138337\pi$
$390$	0.565863	0.0286536
$391$	−27.0461	−1.36778
$392$	15.2895	0.772238
$393$	−12.0917	−0.609948
$394$	−9.79007	−0.493217
$395$	−12.3602	−0.621909
$396$	−1.02318	−0.0514170
$397$	3.31954	0.166603	0.0833014	−	0.996524i	$-0.473454\pi$
$397$	3.31954	0.166603	0.0833014	+	0.996524i	$0.473454\pi$
$398$	5.55562	0.278478
$399$	−22.2698	−1.11488
$400$	2.18132	0.109066
$401$	−36.0449	−1.80000	−0.899998	−	0.435895i	$-0.856432\pi$
$401$	−36.0449	−1.80000	−0.899998	+	0.435895i	$0.856432\pi$
$402$	1.86126	0.0928313
$403$	1.00000	0.0498135
$404$	−18.1037	−0.900694
$405$	1.00000	0.0496904
$406$	−3.73332	−0.185282
$407$	−4.92299	−0.244024
$408$	7.84447	0.388359
$409$	31.8014	1.57248	0.786238	−	0.617924i	$-0.212026\pi$
$409$	31.8014	1.57248	0.786238	+	0.617924i	$0.212026\pi$
$410$	−0.184329	−0.00910334
$411$	13.5905	0.670369
$412$	−25.8012	−1.27113
$413$	9.07815	0.446707
$414$	−4.06245	−0.199658
$415$	−6.16365	−0.302562
$416$	−5.39885	−0.264701
$417$	16.4443	0.805281
$418$	2.02678	0.0991332
$419$	27.7624	1.35628	0.678140	−	0.734933i	$-0.262786\pi$
$419$	27.7624	1.35628	0.678140	+	0.734933i	$0.262786\pi$
$420$	−6.36171	−0.310419
$421$	−3.49721	−0.170444	−0.0852218	−	0.996362i	$-0.527160\pi$
$421$	−3.49721	−0.170444	−0.0852218	+	0.996362i	$0.527160\pi$
$422$	4.79752	0.233540
$423$	10.8335	0.526741
$424$	14.3649	0.697623
$425$	−3.76728	−0.182740
$426$	2.05423	0.0995279
$427$	32.1915	1.55786
$428$	−1.74195	−0.0842004
$429$	−0.609111	−0.0294082
$430$	5.13951	0.247849
$431$	−5.92169	−0.285238	−0.142619	−	0.989778i	$-0.545552\pi$
$431$	−5.92169	−0.285238	−0.142619	+	0.989778i	$0.545552\pi$
$432$	−2.18132	−0.104949
$433$	−8.17614	−0.392920	−0.196460	−	0.980512i	$-0.562945\pi$
$433$	−8.17614	−0.392920	−0.196460	+	0.980512i	$0.562945\pi$
$434$	2.14303	0.102869
$435$	1.74208	0.0835263
$436$	21.1374	1.01230
$437$	−42.2159	−2.01946
$438$	0.306705	0.0146549
$439$	−31.9965	−1.52711	−0.763556	−	0.645742i	$-0.776548\pi$
$439$	−31.9965	−1.52711	−0.763556	+	0.645742i	$0.776548\pi$
$440$	1.26833	0.0604652
$441$	7.34275	0.349655
$442$	2.13177	0.101398
$443$	2.81439	0.133716	0.0668578	−	0.997763i	$-0.478703\pi$
$443$	2.81439	0.133716	0.0668578	+	0.997763i	$0.478703\pi$
$444$	−13.5766	−0.644315
$445$	−13.9194	−0.659843
$446$	4.98333	0.235968
$447$	−21.5236	−1.01803
$448$	4.95224	0.233971
$449$	22.0365	1.03997	0.519984	−	0.854176i	$-0.325938\pi$
$449$	22.0365	1.03997	0.519984	+	0.854176i	$0.325938\pi$
$450$	−0.565863	−0.0266750
$451$	0.198417	0.00934308
$452$	11.6925	0.549969
$453$	−12.2550	−0.575790
$454$	−5.37488	−0.252256
$455$	−3.78718	−0.177546
$456$	12.2443	0.573393
$457$	−33.6344	−1.57335	−0.786674	−	0.617368i	$-0.788199\pi$
$457$	−33.6344	−1.57335	−0.786674	+	0.617368i	$0.788199\pi$
$458$	3.41439	0.159544
$459$	3.76728	0.175842
$460$	−12.0596	−0.562283
$461$	−25.3187	−1.17921	−0.589606	−	0.807691i	$-0.700717\pi$
$461$	−25.3187	−1.17921	−0.589606	+	0.807691i	$0.700717\pi$
$462$	−1.30534	−0.0607300
$463$	35.4263	1.64640	0.823199	−	0.567753i	$-0.192187\pi$
$463$	35.4263	1.64640	0.823199	+	0.567753i	$0.192187\pi$
$464$	−3.80003	−0.176412
$465$	−1.00000	−0.0463739
$466$	−0.305880	−0.0141696
$467$	−5.44381	−0.251909	−0.125955	−	0.992036i	$-0.540199\pi$
$467$	−5.44381	−0.251909	−0.125955	+	0.992036i	$0.540199\pi$
$468$	−1.67980	−0.0776487
$469$	−12.4570	−0.575209
$470$	−6.13025	−0.282767
$471$	−0.0856834	−0.00394808
$472$	−4.99133	−0.229745
$473$	−5.53231	−0.254376
$474$	−6.99418	−0.321253
$475$	−5.88030	−0.269807
$476$	−23.9663	−1.09850
$477$	6.89871	0.315870
$478$	−10.9942	−0.502861
$479$	40.9768	1.87228	0.936140	−	0.351628i	$-0.114372\pi$
$479$	40.9768	1.87228	0.936140	+	0.351628i	$0.114372\pi$
$480$	5.39885	0.246423
$481$	−8.08226	−0.368519
$482$	−4.37445	−0.199251
$483$	27.1890	1.23714
$484$	17.8546	0.811571
$485$	−12.5776	−0.571121
$486$	0.565863	0.0256681
$487$	−21.1566	−0.958699	−0.479349	−	0.877624i	$-0.659127\pi$
$487$	−21.1566	−0.958699	−0.479349	+	0.877624i	$0.659127\pi$
$488$	−17.6995	−0.801218
$489$	−23.6599	−1.06994
$490$	−4.15499	−0.187703
$491$	−29.2502	−1.32004	−0.660022	−	0.751246i	$-0.729453\pi$
$491$	−29.2502	−1.32004	−0.660022	+	0.751246i	$0.729453\pi$
$492$	0.547191	0.0246693
$493$	6.56290	0.295578
$494$	3.32744	0.149709
$495$	0.609111	0.0273775
$496$	2.18132	0.0979443
$497$	−13.7485	−0.616703
$498$	−3.48778	−0.156291
$499$	6.32148	0.282988	0.141494	−	0.989939i	$-0.454809\pi$
$499$	6.32148	0.282988	0.141494	+	0.989939i	$0.454809\pi$
$500$	−1.67980	−0.0751229
$501$	−23.3514	−1.04326
$502$	−8.70681	−0.388604
$503$	6.51807	0.290626	0.145313	−	0.989386i	$-0.453581\pi$
$503$	6.51807	0.290626	0.145313	+	0.989386i	$0.453581\pi$
$504$	−7.88591	−0.351266
$505$	10.7773	0.479585
$506$	−2.47448	−0.110004
$507$	−1.00000	−0.0444116
$508$	13.3928	0.594211
$509$	−25.2674	−1.11996	−0.559978	−	0.828507i	$-0.689191\pi$
$509$	−25.2674	−1.11996	−0.559978	+	0.828507i	$0.689191\pi$
$510$	−2.13177	−0.0943962
$511$	−2.05270	−0.0908060
$512$	−20.8608	−0.921926
$513$	5.88030	0.259622
$514$	8.73178	0.385142
$515$	15.3597	0.676828
$516$	−15.2569	−0.671649
$517$	6.59878	0.290214
$518$	−17.3205	−0.761019
$519$	−6.35415	−0.278916
$520$	2.08226	0.0913132
$521$	12.2104	0.534946	0.267473	−	0.963565i	$-0.413811\pi$
$521$	12.2104	0.534946	0.267473	+	0.963565i	$0.413811\pi$
$522$	0.985778	0.0431463
$523$	−2.91732	−0.127566	−0.0637828	−	0.997964i	$-0.520316\pi$
$523$	−2.91732	−0.127566	−0.0637828	+	0.997964i	$0.520316\pi$
$524$	−20.3117	−0.887320
$525$	3.78718	0.165286
$526$	11.9828	0.522477
$527$	−3.76728	−0.164105
$528$	−1.32867	−0.0578229
$529$	28.5410	1.24091
$530$	−3.90373	−0.169567
$531$	−2.39707	−0.104024
$532$	−37.4087	−1.62187
$533$	0.325748	0.0141097
$534$	−7.87648	−0.340849
$535$	1.03700	0.0448334
$536$	6.84907	0.295835
$537$	14.1761	0.611742
$538$	−12.4301	−0.535898
$539$	4.47255	0.192646
$540$	1.67980	0.0722870
$541$	−20.4470	−0.879086	−0.439543	−	0.898221i	$-0.644860\pi$
$541$	−20.4470	−0.879086	−0.439543	+	0.898221i	$0.644860\pi$
$542$	−11.5914	−0.497894
$543$	24.0322	1.03132
$544$	20.3390	0.872028
$545$	−12.5833	−0.539008
$546$	−2.14303	−0.0917131
$547$	−34.1423	−1.45982	−0.729910	−	0.683543i	$-0.760438\pi$
$547$	−34.1423	−1.45982	−0.729910	+	0.683543i	$0.760438\pi$
$548$	22.8293	0.975218
$549$	−8.50012	−0.362776
$550$	−0.344674	−0.0146969
$551$	10.2439	0.436407
$552$	−14.9490	−0.636271
$553$	46.8103	1.99058
$554$	−4.29878	−0.182638
$555$	8.08226	0.343073
$556$	27.6231	1.17148
$557$	1.74464	0.0739228	0.0369614	−	0.999317i	$-0.488232\pi$
$557$	1.74464	0.0739228	0.0369614	+	0.999317i	$0.488232\pi$
$558$	−0.565863	−0.0239549
$559$	−9.08260	−0.384153
$560$	−8.26107	−0.349094
$561$	2.29469	0.0968821
$562$	8.33828	0.351729
$563$	−6.04577	−0.254799	−0.127399	−	0.991851i	$-0.540663\pi$
$563$	−6.04577	−0.254799	−0.127399	+	0.991851i	$0.540663\pi$
$564$	18.1980	0.766275
$565$	−6.96065	−0.292837
$566$	4.15354	0.174586
$567$	−3.78718	−0.159047
$568$	7.55916	0.317175
$569$	−18.6287	−0.780954	−0.390477	−	0.920613i	$-0.627690\pi$
$569$	−18.6287	−0.780954	−0.390477	+	0.920613i	$0.627690\pi$
$570$	−3.32744	−0.139371
$571$	32.9661	1.37959	0.689795	−	0.724005i	$-0.257701\pi$
$571$	32.9661	1.37959	0.689795	+	0.724005i	$0.257701\pi$
$572$	−1.02318	−0.0427815
$573$	−18.2237	−0.761307
$574$	0.698086	0.0291376
$575$	7.17920	0.299394
$576$	−1.30763	−0.0544847
$577$	37.1261	1.54558	0.772789	−	0.634663i	$-0.218861\pi$
$577$	37.1261	1.54558	0.772789	+	0.634663i	$0.218861\pi$
$578$	1.58871	0.0660815
$579$	5.95783	0.247599
$580$	2.92634	0.121510
$581$	23.3429	0.968425
$582$	−7.11722	−0.295018
$583$	4.20208	0.174033
$584$	1.12861	0.0467023
$585$	1.00000	0.0413449
$586$	−5.02193	−0.207454
$587$	−5.87309	−0.242409	−0.121204	−	0.992628i	$-0.538676\pi$
$587$	−5.87309	−0.242409	−0.121204	+	0.992628i	$0.538676\pi$
$588$	12.3343	0.508660
$589$	−5.88030	−0.242293
$590$	1.35642	0.0558427
$591$	−17.3011	−0.711673
$592$	−17.6300	−0.724589
$593$	−4.66247	−0.191465	−0.0957323	−	0.995407i	$-0.530519\pi$
$593$	−4.66247	−0.191465	−0.0957323	+	0.995407i	$0.530519\pi$
$594$	0.344674	0.0141421
$595$	14.2674	0.584906
$596$	−36.1554	−1.48098
$597$	9.81797	0.401823
$598$	−4.06245	−0.166126
$599$	−24.4118	−0.997441	−0.498720	−	0.866763i	$-0.666197\pi$
$599$	−24.4118	−0.997441	−0.498720	+	0.866763i	$0.666197\pi$
$600$	−2.08226	−0.0850080
$601$	30.6027	1.24831	0.624156	−	0.781300i	$-0.285443\pi$
$601$	30.6027	1.24831	0.624156	+	0.781300i	$0.285443\pi$
$602$	−19.4643	−0.793304
$603$	3.28924	0.133948
$604$	−20.5859	−0.837629
$605$	−10.6290	−0.432130
$606$	6.09849	0.247734
$607$	37.8979	1.53823	0.769113	−	0.639112i	$-0.220698\pi$
$607$	37.8979	1.53823	0.769113	+	0.639112i	$0.220698\pi$
$608$	31.7469	1.28751
$609$	−6.59757	−0.267347
$610$	4.80991	0.194747
$611$	10.8335	0.438275
$612$	6.32828	0.255805
$613$	−2.55809	−0.103320	−0.0516601	−	0.998665i	$-0.516451\pi$
$613$	−2.55809	−0.103320	−0.0516601	+	0.998665i	$0.516451\pi$
$614$	−13.9774	−0.564082
$615$	−0.325748	−0.0131354
$616$	−4.80340	−0.193534
$617$	17.6325	0.709857	0.354928	−	0.934893i	$-0.384505\pi$
$617$	17.6325	0.709857	0.354928	+	0.934893i	$0.384505\pi$
$618$	8.69147	0.349622
$619$	22.1953	0.892105	0.446053	−	0.895007i	$-0.352829\pi$
$619$	22.1953	0.892105	0.446053	+	0.895007i	$0.352829\pi$
$620$	−1.67980	−0.0674623
$621$	−7.17920	−0.288092
$622$	18.9253	0.758837
$623$	52.7154	2.11200
$624$	−2.18132	−0.0873228
$625$	1.00000	0.0400000
$626$	−15.5465	−0.621362
$627$	3.58176	0.143042
$628$	−0.143931	−0.00574347
$629$	30.4481	1.21405
$630$	2.14303	0.0853802
$631$	−15.5709	−0.619868	−0.309934	−	0.950758i	$-0.600307\pi$
$631$	−15.5709	−0.619868	−0.309934	+	0.950758i	$0.600307\pi$
$632$	−25.7372	−1.02377
$633$	8.47824	0.336980
$634$	−12.3708	−0.491307
$635$	−7.97288	−0.316394
$636$	11.5885	0.459512
$637$	7.34275	0.290930
$638$	0.600448	0.0237720
$639$	3.63026	0.143611
$640$	11.5377	0.456066
$641$	2.70762	0.106945	0.0534723	−	0.998569i	$-0.482971\pi$
$641$	2.70762	0.106945	0.0534723	+	0.998569i	$0.482971\pi$
$642$	0.586800	0.0231591
$643$	5.16755	0.203788	0.101894	−	0.994795i	$-0.467510\pi$
$643$	5.16755	0.203788	0.101894	+	0.994795i	$0.467510\pi$
$644$	45.6720	1.79973
$645$	9.08260	0.357627
$646$	−12.5354	−0.493200
$647$	33.5205	1.31783	0.658914	−	0.752218i	$-0.271016\pi$
$647$	33.5205	1.31783	0.658914	+	0.752218i	$0.271016\pi$
$648$	2.08226	0.0817990
$649$	−1.46008	−0.0573133
$650$	−0.565863	−0.0221950
$651$	3.78718	0.148431
$652$	−39.7439	−1.55649
$653$	−7.00382	−0.274081	−0.137040	−	0.990565i	$-0.543759\pi$
$653$	−7.00382	−0.274081	−0.137040	+	0.990565i	$0.543759\pi$
$654$	−7.12041	−0.278430
$655$	12.0917	0.472463
$656$	0.710561	0.0277427
$657$	0.542012	0.0211459
$658$	23.2164	0.905069
$659$	20.5705	0.801313	0.400657	−	0.916228i	$-0.368782\pi$
$659$	20.5705	0.801313	0.400657	+	0.916228i	$0.368782\pi$
$660$	1.02318	0.0398274
$661$	40.5129	1.57577	0.787885	−	0.615822i	$-0.211176\pi$
$661$	40.5129	1.57577	0.787885	+	0.615822i	$0.211176\pi$
$662$	−7.75007	−0.301215
$663$	3.76728	0.146309
$664$	−12.8343	−0.498069
$665$	22.2698	0.863584
$666$	4.57345	0.177218
$667$	−12.5067	−0.484263
$668$	−39.2256	−1.51768
$669$	8.80661	0.340483
$670$	−1.86126	−0.0719068
$671$	−5.17752	−0.199876
$672$	−20.4464	−0.788739
$673$	−9.70267	−0.374011	−0.187005	−	0.982359i	$-0.559878\pi$
$673$	−9.70267	−0.374011	−0.187005	+	0.982359i	$0.559878\pi$
$674$	−13.1171	−0.505251
$675$	−1.00000	−0.0384900
$676$	−1.67980	−0.0646077
$677$	−20.6756	−0.794628	−0.397314	−	0.917683i	$-0.630058\pi$
$677$	−20.6756	−0.794628	−0.397314	+	0.917683i	$0.630058\pi$
$678$	−3.93878	−0.151268
$679$	47.6338	1.82802
$680$	−7.84447	−0.300822
$681$	−9.49855	−0.363985
$682$	−0.344674	−0.0131982
$683$	−4.35104	−0.166488	−0.0832440	−	0.996529i	$-0.526528\pi$
$683$	−4.35104	−0.166488	−0.0832440	+	0.996529i	$0.526528\pi$
$684$	9.87772	0.377684
$685$	−13.5905	−0.519265
$686$	0.734524	0.0280443
$687$	6.03394	0.230209
$688$	−19.8121	−0.755328
$689$	6.89871	0.262820
$690$	4.06245	0.154655
$691$	5.27961	0.200846	0.100423	−	0.994945i	$-0.467980\pi$
$691$	5.27961	0.200846	0.100423	+	0.994945i	$0.467980\pi$
$692$	−10.6737	−0.405753
$693$	−2.30682	−0.0876287
$694$	−19.6453	−0.745727
$695$	−16.4443	−0.623768
$696$	3.62746	0.137499
$697$	−1.22718	−0.0464829
$698$	−15.3040	−0.579266
$699$	−0.540554	−0.0204456
$700$	6.36171	0.240450
$701$	10.3054	0.389228	0.194614	−	0.980880i	$-0.437655\pi$
$701$	10.3054	0.389228	0.194614	+	0.980880i	$0.437655\pi$
$702$	0.565863	0.0213571
$703$	47.5261	1.79248
$704$	−0.796493	−0.0300190
$705$	−10.8335	−0.408011
$706$	13.0424	0.490856
$707$	−40.8157	−1.53503
$708$	−4.02660	−0.151329
$709$	37.9289	1.42445	0.712225	−	0.701951i	$-0.247687\pi$
$709$	37.9289	1.42445	0.712225	+	0.701951i	$0.247687\pi$
$710$	−2.05423	−0.0770940
$711$	−12.3602	−0.463544
$712$	−28.9839	−1.08622
$713$	7.17920	0.268863
$714$	8.07339	0.302139
$715$	0.609111	0.0227795
$716$	23.8129	0.889931
$717$	−19.4290	−0.725590
$718$	6.45144	0.240766
$719$	21.3022	0.794436	0.397218	−	0.917724i	$-0.369976\pi$
$719$	21.3022	0.794436	0.397218	+	0.917724i	$0.369976\pi$
$720$	2.18132	0.0812931
$721$	−58.1699	−2.16636
$722$	−8.81497	−0.328059
$723$	−7.73058	−0.287503
$724$	40.3693	1.50031
$725$	−1.74208	−0.0646992
$726$	−6.01455	−0.223221
$727$	18.1299	0.672400	0.336200	−	0.941791i	$-0.390858\pi$
$727$	18.1299	0.672400	0.336200	+	0.941791i	$0.390858\pi$
$728$	−7.88591	−0.292271
$729$	1.00000	0.0370370
$730$	−0.306705	−0.0113516
$731$	34.2167	1.26555
$732$	−14.2785	−0.527748
$733$	−11.8569	−0.437943	−0.218971	−	0.975731i	$-0.570270\pi$
$733$	−11.8569	−0.437943	−0.218971	+	0.975731i	$0.570270\pi$
$734$	−16.4853	−0.608483
$735$	−7.34275	−0.270841
$736$	−38.7595	−1.42869
$737$	2.00351	0.0738004
$738$	−0.184329	−0.00678523
$739$	−31.3886	−1.15465	−0.577324	−	0.816515i	$-0.695903\pi$
$739$	−31.3886	−1.15465	−0.577324	+	0.816515i	$0.695903\pi$
$740$	13.5766	0.499084
$741$	5.88030	0.216018
$742$	14.7841	0.542742
$743$	13.6010	0.498971	0.249486	−	0.968378i	$-0.419738\pi$
$743$	13.6010	0.498971	0.249486	+	0.968378i	$0.419738\pi$
$744$	−2.08226	−0.0763394
$745$	21.5236	0.788565
$746$	−13.7142	−0.502113
$747$	−6.16365	−0.225516
$748$	3.85463	0.140939
$749$	−3.92731	−0.143501
$750$	0.565863	0.0206624
$751$	−9.37987	−0.342276	−0.171138	−	0.985247i	$-0.554744\pi$
$751$	−9.37987	−0.342276	−0.171138	+	0.985247i	$0.554744\pi$
$752$	23.6313	0.861743
$753$	−15.3868	−0.560725
$754$	0.985778	0.0358999
$755$	12.2550	0.446005
$756$	−6.36171	−0.231373
$757$	44.5038	1.61752	0.808759	−	0.588140i	$-0.200140\pi$
$757$	44.5038	1.61752	0.808759	+	0.588140i	$0.200140\pi$
$758$	1.44452	0.0524673
$759$	−4.37293	−0.158727
$760$	−12.2443	−0.444148
$761$	−44.0150	−1.59554	−0.797770	−	0.602961i	$-0.793987\pi$
$761$	−44.0150	−1.59554	−0.797770	+	0.602961i	$0.793987\pi$
$762$	−4.51156	−0.163436
$763$	47.6551	1.72523
$764$	−30.6122	−1.10751
$765$	−3.76728	−0.136206
$766$	−16.6530	−0.601697
$767$	−2.39707	−0.0865533
$768$	3.91347	0.141215
$769$	−12.5798	−0.453638	−0.226819	−	0.973937i	$-0.572833\pi$
$769$	−12.5798	−0.453638	−0.226819	+	0.973937i	$0.572833\pi$
$770$	1.30534	0.0470413
$771$	15.4309	0.555730
$772$	10.0080	0.360194
$773$	−42.8342	−1.54064	−0.770320	−	0.637658i	$-0.779903\pi$
$773$	−42.8342	−1.54064	−0.770320	+	0.637658i	$0.779903\pi$
$774$	5.13951	0.184736
$775$	1.00000	0.0359211
$776$	−26.1899	−0.940164
$777$	−30.6090	−1.09809
$778$	−20.2462	−0.725860
$779$	−1.91549	−0.0686297
$780$	1.67980	0.0601465
$781$	2.21123	0.0791242
$782$	15.3044	0.547284
$783$	1.74208	0.0622568
$784$	16.0169	0.572032
$785$	0.0856834	0.00305817
$786$	6.84227	0.244056
$787$	12.5340	0.446787	0.223394	−	0.974728i	$-0.428286\pi$
$787$	12.5340	0.446787	0.223394	+	0.974728i	$0.428286\pi$
$788$	−29.0624	−1.03531
$789$	21.1762	0.753893
$790$	6.99418	0.248842
$791$	26.3613	0.937299
$792$	1.26833	0.0450681
$793$	−8.50012	−0.301848
$794$	−1.87840	−0.0666620
$795$	−6.89871	−0.244672
$796$	16.4922	0.584551
$797$	−40.3521	−1.42934	−0.714672	−	0.699460i	$-0.753424\pi$
$797$	−40.3521	−1.42934	−0.714672	+	0.699460i	$0.753424\pi$
$798$	12.6016	0.446093
$799$	−40.8127	−1.44385
$800$	−5.39885	−0.190878
$801$	−13.9194	−0.491818
$802$	20.3965	0.720224
$803$	0.330146	0.0116506
$804$	5.52527	0.194861
$805$	−27.1890	−0.958285
$806$	−0.565863	−0.0199317
$807$	−21.9665	−0.773259
$808$	22.4412	0.789479
$809$	28.2272	0.992414	0.496207	−	0.868204i	$-0.334726\pi$
$809$	28.2272	0.992414	0.496207	+	0.868204i	$0.334726\pi$
$810$	−0.565863	−0.0198824
$811$	36.0682	1.26652	0.633262	−	0.773937i	$-0.281715\pi$
$811$	36.0682	1.26652	0.633262	+	0.773937i	$0.281715\pi$
$812$	−11.0826	−0.388923
$813$	−20.4845	−0.718423
$814$	2.78574	0.0976402
$815$	23.6599	0.828771
$816$	8.21766	0.287676
$817$	53.4084	1.86852
$818$	−17.9952	−0.629188
$819$	−3.78718	−0.132335
$820$	−0.547191	−0.0191087
$821$	17.8237	0.622051	0.311026	−	0.950402i	$-0.399327\pi$
$821$	17.8237	0.622051	0.311026	+	0.950402i	$0.399327\pi$
$822$	−7.69035	−0.268232
$823$	27.6398	0.963462	0.481731	−	0.876319i	$-0.340008\pi$
$823$	27.6398	0.963462	0.481731	+	0.876319i	$0.340008\pi$
$824$	31.9829	1.11418
$825$	−0.609111	−0.0212065
$826$	−5.13699	−0.178739
$827$	27.0893	0.941988	0.470994	−	0.882136i	$-0.343895\pi$
$827$	27.0893	0.941988	0.470994	+	0.882136i	$0.343895\pi$
$828$	−12.0596	−0.419101
$829$	7.55412	0.262365	0.131183	−	0.991358i	$-0.458123\pi$
$829$	7.55412	0.262365	0.131183	+	0.991358i	$0.458123\pi$
$830$	3.48778	0.121063
$831$	−7.59685	−0.263532
$832$	−1.30763	−0.0453340
$833$	−27.6622	−0.958439
$834$	−9.30522	−0.322213
$835$	23.3514	0.808107
$836$	6.01663	0.208090
$837$	−1.00000	−0.0345651
$838$	−15.7097	−0.542683
$839$	11.4143	0.394065	0.197032	−	0.980397i	$-0.436870\pi$
$839$	11.4143	0.394065	0.197032	+	0.980397i	$0.436870\pi$
$840$	7.88591	0.272090
$841$	−25.9652	−0.895350
$842$	1.97894	0.0681989
$843$	14.7355	0.507518
$844$	14.2417	0.490221
$845$	1.00000	0.0344010
$846$	−6.13025	−0.210762
$847$	40.2539	1.38314
$848$	15.0483	0.516761
$849$	7.34018	0.251914
$850$	2.13177	0.0731190
$851$	−58.0242	−1.98904
$852$	6.09811	0.208918
$853$	49.1902	1.68424	0.842119	−	0.539291i	$-0.181308\pi$
$853$	49.1902	1.68424	0.842119	+	0.539291i	$0.181308\pi$
$854$	−18.2160	−0.623338
$855$	−5.88030	−0.201102
$856$	2.15931	0.0738035
$857$	−1.53454	−0.0524187	−0.0262094	−	0.999656i	$-0.508344\pi$
$857$	−1.53454	−0.0524187	−0.0262094	+	0.999656i	$0.508344\pi$
$858$	0.344674	0.0117670
$859$	−10.2417	−0.349442	−0.174721	−	0.984618i	$-0.555902\pi$
$859$	−10.2417	−0.349442	−0.174721	+	0.984618i	$0.555902\pi$
$860$	15.2569	0.520257
$861$	1.23367	0.0420432
$862$	3.35087	0.114131
$863$	5.19066	0.176692	0.0883461	−	0.996090i	$-0.471842\pi$
$863$	5.19066	0.176692	0.0883461	+	0.996090i	$0.471842\pi$
$864$	5.39885	0.183673
$865$	6.35415	0.216048
$866$	4.62658	0.157218
$867$	2.80758	0.0953504
$868$	6.36171	0.215930
$869$	−7.52874	−0.255395
$870$	−0.985778	−0.0334210
$871$	3.28924	0.111452
$872$	−26.2017	−0.887300
$873$	−12.5776	−0.425689
$874$	23.8884	0.808037
$875$	−3.78718	−0.128030
$876$	0.910471	0.0307620
$877$	−12.6715	−0.427887	−0.213944	−	0.976846i	$-0.568631\pi$
$877$	−12.6715	−0.427887	−0.213944	+	0.976846i	$0.568631\pi$
$878$	18.1057	0.611036
$879$	−8.87482	−0.299340
$880$	1.32867	0.0447894
$881$	6.66233	0.224460	0.112230	−	0.993682i	$-0.464201\pi$
$881$	6.66233	0.224460	0.112230	+	0.993682i	$0.464201\pi$
$882$	−4.15499	−0.139906
$883$	−29.7612	−1.00154	−0.500772	−	0.865579i	$-0.666950\pi$
$883$	−29.7612	−1.00154	−0.500772	+	0.865579i	$0.666950\pi$
$884$	6.32828	0.212843
$885$	2.39707	0.0805767
$886$	−1.59256	−0.0535030
$887$	−0.297918	−0.0100031	−0.00500156	−	0.999987i	$-0.501592\pi$
$887$	−0.297918	−0.0100031	−0.00500156	+	0.999987i	$0.501592\pi$
$888$	16.8294	0.564757
$889$	30.1947	1.01270
$890$	7.87648	0.264020
$891$	0.609111	0.0204060
$892$	14.7933	0.495317
$893$	−63.7039	−2.13177
$894$	12.1794	0.407341
$895$	−14.1761	−0.473853
$896$	−43.6952	−1.45975
$897$	−7.17920	−0.239707
$898$	−12.4697	−0.416118
$899$	−1.74208	−0.0581016
$900$	−1.67980	−0.0559933
$901$	−25.9894	−0.865833
$902$	−0.112277	−0.00373840
$903$	−34.3975	−1.14468
$904$	−14.4939	−0.482060
$905$	−24.0322	−0.798857
$906$	6.93465	0.230388
$907$	−18.6722	−0.620000	−0.310000	−	0.950736i	$-0.600329\pi$
$907$	−18.6722	−0.620000	−0.310000	+	0.950736i	$0.600329\pi$
$908$	−15.9557	−0.529507
$909$	10.7773	0.357461
$910$	2.14303	0.0710406
$911$	−26.9860	−0.894088	−0.447044	−	0.894512i	$-0.647523\pi$
$911$	−26.9860	−0.894088	−0.447044	+	0.894512i	$0.647523\pi$
$912$	12.8268	0.424739
$913$	−3.75435	−0.124251
$914$	19.0324	0.629537
$915$	8.50012	0.281005
$916$	10.1358	0.334897
$917$	−45.7936	−1.51224
$918$	−2.13177	−0.0703588
$919$	−17.1857	−0.566904	−0.283452	−	0.958986i	$-0.591480\pi$
$919$	−17.1857	−0.566904	−0.283452	+	0.958986i	$0.591480\pi$
$920$	14.9490	0.492854
$921$	−24.7010	−0.813927
$922$	14.3269	0.471833
$923$	3.63026	0.119492
$924$	−3.87499	−0.127478
$925$	−8.08226	−0.265743
$926$	−20.0464	−0.658766
$927$	15.3597	0.504478
$928$	9.40523	0.308742
$929$	−27.3799	−0.898305	−0.449152	−	0.893455i	$-0.648274\pi$
$929$	−27.3799	−0.898305	−0.449152	+	0.893455i	$0.648274\pi$
$930$	0.565863	0.0185554
$931$	−43.1776	−1.41509
$932$	−0.908022	−0.0297432
$933$	33.4451	1.09494
$934$	3.08045	0.100795
$935$	−2.29469	−0.0750445
$936$	2.08226	0.0680609
$937$	−22.3531	−0.730244	−0.365122	−	0.930960i	$-0.618973\pi$
$937$	−22.3531	−0.730244	−0.365122	+	0.930960i	$0.618973\pi$
$938$	7.04893	0.230156
$939$	−27.4739	−0.896577
$940$	−18.1980	−0.593554
$941$	−27.7275	−0.903892	−0.451946	−	0.892045i	$-0.649270\pi$
$941$	−27.7275	−0.903892	−0.451946	+	0.892045i	$0.649270\pi$
$942$	0.0484851	0.00157973
$943$	2.33861	0.0761556
$944$	−5.22879	−0.170183
$945$	3.78718	0.123197
$946$	3.13053	0.101782
$947$	−1.61806	−0.0525800	−0.0262900	−	0.999654i	$-0.508369\pi$
$947$	−1.61806	−0.0525800	−0.0262900	+	0.999654i	$0.508369\pi$
$948$	−20.7626	−0.674339
$949$	0.542012	0.0175945
$950$	3.32744	0.107957
$951$	−21.8618	−0.708918
$952$	29.7084	0.962856
$953$	−1.32592	−0.0429507	−0.0214754	−	0.999769i	$-0.506836\pi$
$953$	−1.32592	−0.0429507	−0.0214754	+	0.999769i	$0.506836\pi$
$954$	−3.90373	−0.126388
$955$	18.2237	0.589706
$956$	−32.6368	−1.05555
$957$	1.06112	0.0343011
$958$	−23.1873	−0.749147
$959$	51.4696	1.66204
$960$	1.30763	0.0422036
$961$	1.00000	0.0322581
$962$	4.57345	0.147454
$963$	1.03700	0.0334168
$964$	−12.9858	−0.418245
$965$	−5.95783	−0.191789
$966$	−15.3852	−0.495012
$967$	−49.0307	−1.57672	−0.788360	−	0.615214i	$-0.789070\pi$
$967$	−49.0307	−1.57672	−0.788360	+	0.615214i	$0.789070\pi$
$968$	−22.1323	−0.711360
$969$	−22.1527	−0.711649
$970$	7.11722	0.228520
$971$	39.8690	1.27946	0.639728	−	0.768601i	$-0.279047\pi$
$971$	39.8690	1.27946	0.639728	+	0.768601i	$0.279047\pi$
$972$	1.67980	0.0538796
$973$	62.2776	1.99653
$974$	11.9718	0.383600
$975$	−1.00000	−0.0320256
$976$	−18.5415	−0.593499
$977$	−47.4563	−1.51826	−0.759130	−	0.650939i	$-0.774375\pi$
$977$	−47.4563	−1.51826	−0.759130	+	0.650939i	$0.774375\pi$
$978$	13.3883	0.428110
$979$	−8.47847	−0.270973
$980$	−12.3343	−0.394006
$981$	−12.5833	−0.401753
$982$	16.5516	0.528184
$983$	30.0248	0.957641	0.478820	−	0.877913i	$-0.341064\pi$
$983$	30.0248	0.957641	0.478820	+	0.877913i	$0.341064\pi$
$984$	−0.678292	−0.0216232
$985$	17.3011	0.551260
$986$	−3.71370	−0.118268
$987$	41.0283	1.30594
$988$	9.87772	0.314252
$989$	−65.2058	−2.07342
$990$	−0.344674	−0.0109544
$991$	33.0341	1.04936	0.524682	−	0.851298i	$-0.324184\pi$
$991$	33.0341	1.04936	0.524682	+	0.851298i	$0.324184\pi$
$992$	−5.39885	−0.171414
$993$	−13.6960	−0.434630
$994$	7.77975	0.246759
$995$	−9.81797	−0.311250
$996$	−10.3537	−0.328069
$997$	−32.7365	−1.03678	−0.518388	−	0.855145i	$-0.673468\pi$
$997$	−32.7365	−1.03678	−0.518388	+	0.855145i	$0.673468\pi$
$998$	−3.57709	−0.113231
$999$	8.08226	0.255711

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6045.2.a.bh.1.7	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6045.2.a.bh.1.7	✓	17	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:	\( N \)	\(=\)	\( 6045 = 3 \cdot 5 \cdot 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6045.a (trivial)

\(f(q)\)	\(=\)	\(q-0.565863 q^{2} -1.00000 q^{3} -1.67980 q^{4} +1.00000 q^{5} +0.565863 q^{6} -3.78718 q^{7} +2.08226 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.565863 q^{2} -1.00000 q^{3} -1.67980 q^{4} +1.00000 q^{5} +0.565863 q^{6} -3.78718 q^{7} +2.08226 q^{8} +1.00000 q^{9} -0.565863 q^{10} +0.609111 q^{11} +1.67980 q^{12} +1.00000 q^{13} +2.14303 q^{14} -1.00000 q^{15} +2.18132 q^{16} -3.76728 q^{17} -0.565863 q^{18} -5.88030 q^{19} -1.67980 q^{20} +3.78718 q^{21} -0.344674 q^{22} +7.17920 q^{23} -2.08226 q^{24} +1.00000 q^{25} -0.565863 q^{26} -1.00000 q^{27} +6.36171 q^{28} -1.74208 q^{29} +0.565863 q^{30} +1.00000 q^{31} -5.39885 q^{32} -0.609111 q^{33} +2.13177 q^{34} -3.78718 q^{35} -1.67980 q^{36} -8.08226 q^{37} +3.32744 q^{38} -1.00000 q^{39} +2.08226 q^{40} +0.325748 q^{41} -2.14303 q^{42} -9.08260 q^{43} -1.02318 q^{44} +1.00000 q^{45} -4.06245 q^{46} +10.8335 q^{47} -2.18132 q^{48} +7.34275 q^{49} -0.565863 q^{50} +3.76728 q^{51} -1.67980 q^{52} +6.89871 q^{53} +0.565863 q^{54} +0.609111 q^{55} -7.88591 q^{56} +5.88030 q^{57} +0.985778 q^{58} -2.39707 q^{59} +1.67980 q^{60} -8.50012 q^{61} -0.565863 q^{62} -3.78718 q^{63} -1.30763 q^{64} +1.00000 q^{65} +0.344674 q^{66} +3.28924 q^{67} +6.32828 q^{68} -7.17920 q^{69} +2.14303 q^{70} +3.63026 q^{71} +2.08226 q^{72} +0.542012 q^{73} +4.57345 q^{74} -1.00000 q^{75} +9.87772 q^{76} -2.30682 q^{77} +0.565863 q^{78} -12.3602 q^{79} +2.18132 q^{80} +1.00000 q^{81} -0.184329 q^{82} -6.16365 q^{83} -6.36171 q^{84} -3.76728 q^{85} +5.13951 q^{86} +1.74208 q^{87} +1.26833 q^{88} -13.9194 q^{89} -0.565863 q^{90} -3.78718 q^{91} -12.0596 q^{92} -1.00000 q^{93} -6.13025 q^{94} -5.88030 q^{95} +5.39885 q^{96} -12.5776 q^{97} -4.15499 q^{98} +0.609111 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9}+O(q^{10}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9	\( 17 q + 2 q^{2} - 17 q^{3} + 20 q^{4} + 17 q^{5} - 2 q^{6} + 18 q^{7} + 9 q^{8} + 17 q^{9} + 2 q^{10} + 3 q^{11} - 20 q^{12} + 17 q^{13} + q^{14} - 17 q^{15} + 26 q^{16} + 2 q^{18} + 10 q^{19} + 20 q^{20} - 18 q^{21} + 5 q^{22} + 16 q^{23} - 9 q^{24} + 17 q^{25} + 2 q^{26} - 17 q^{27} + 36 q^{28} - 3 q^{29} - 2 q^{30} + 17 q^{31} + 20 q^{32} - 3 q^{33} + q^{34} + 18 q^{35} + 20 q^{36} + 14 q^{37} + 22 q^{38} - 17 q^{39} + 9 q^{40} - 6 q^{41} - q^{42} + 24 q^{43} - 15 q^{44} + 17 q^{45} + 6 q^{46} + 25 q^{47} - 26 q^{48} + 31 q^{49} + 2 q^{50} + 20 q^{52} - 15 q^{53} - 2 q^{54} + 3 q^{55} + 31 q^{56} - 10 q^{57} + 44 q^{58} + 16 q^{59} - 20 q^{60} - 5 q^{61} + 2 q^{62} + 18 q^{63} + 35 q^{64} + 17 q^{65} - 5 q^{66} + 50 q^{67} + 13 q^{68} - 16 q^{69} + q^{70} + 16 q^{71} + 9 q^{72} + 33 q^{73} + 2 q^{74} - 17 q^{75} + 9 q^{77} - 2 q^{78} - 10 q^{79} + 26 q^{80} + 17 q^{81} + 61 q^{82} + 27 q^{83} - 36 q^{84} - 12 q^{86} + 3 q^{87} + 23 q^{88} - 24 q^{89} + 2 q^{90} + 18 q^{91} - 21 q^{92} - 17 q^{93} + 6 q^{94} + 10 q^{95} - 20 q^{96} + 48 q^{97} + 14 q^{98} + 3 q^{99}+O(q^{100}) \) 17 * q + 2 * q^2 - 17 * q^3 + 20 * q^4 + 17 * q^5 - 2 * q^6 + 18 * q^7 + 9 * q^8 + 17 * q^9 + 2 * q^10 + 3 * q^11 - 20 * q^12 + 17 * q^13 + q^14 - 17 * q^15 + 26 * q^16 + 2 * q^18 + 10 * q^19 + 20 * q^20 - 18 * q^21 + 5 * q^22 + 16 * q^23 - 9 * q^24 + 17 * q^25 + 2 * q^26 - 17 * q^27 + 36 * q^28 - 3 * q^29 - 2 * q^30 + 17 * q^31 + 20 * q^32 - 3 * q^33 + q^34 + 18 * q^35 + 20 * q^36 + 14 * q^37 + 22 * q^38 - 17 * q^39 + 9 * q^40 - 6 * q^41 - q^42 + 24 * q^43 - 15 * q^44 + 17 * q^45 + 6 * q^46 + 25 * q^47 - 26 * q^48 + 31 * q^49 + 2 * q^50 + 20 * q^52 - 15 * q^53 - 2 * q^54 + 3 * q^55 + 31 * q^56 - 10 * q^57 + 44 * q^58 + 16 * q^59 - 20 * q^60 - 5 * q^61 + 2 * q^62 + 18 * q^63 + 35 * q^64 + 17 * q^65 - 5 * q^66 + 50 * q^67 + 13 * q^68 - 16 * q^69 + q^70 + 16 * q^71 + 9 * q^72 + 33 * q^73 + 2 * q^74 - 17 * q^75 + 9 * q^77 - 2 * q^78 - 10 * q^79 + 26 * q^80 + 17 * q^81 + 61 * q^82 + 27 * q^83 - 36 * q^84 - 12 * q^86 + 3 * q^87 + 23 * q^88 - 24 * q^89 + 2 * q^90 + 18 * q^91 - 21 * q^92 - 17 * q^93 + 6 * q^94 + 10 * q^95 - 20 * q^96 + 48 * q^97 + 14 * q^98 + 3 * q^99

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