LMFDB - Embedded newform 6034.2.a.n.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +1.52105 q^{3} +1.00000 q^{4} -3.19164 q^{5} -1.52105 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.686407 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.52105 q^{3} +1.00000 q^{4} -3.19164 q^{5} -1.52105 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.686407 q^{9} +3.19164 q^{10} -1.28860 q^{11} +1.52105 q^{12} +1.34956 q^{13} +1.00000 q^{14} -4.85464 q^{15} +1.00000 q^{16} +5.77216 q^{17} +0.686407 q^{18} -7.04424 q^{19} -3.19164 q^{20} -1.52105 q^{21} +1.28860 q^{22} -5.21023 q^{23} -1.52105 q^{24} +5.18656 q^{25} -1.34956 q^{26} -5.60721 q^{27} -1.00000 q^{28} -2.06455 q^{29} +4.85464 q^{30} -1.05869 q^{31} -1.00000 q^{32} -1.96003 q^{33} -5.77216 q^{34} +3.19164 q^{35} -0.686407 q^{36} +0.620197 q^{37} +7.04424 q^{38} +2.05275 q^{39} +3.19164 q^{40} -6.09301 q^{41} +1.52105 q^{42} -9.64795 q^{43} -1.28860 q^{44} +2.19076 q^{45} +5.21023 q^{46} +11.2768 q^{47} +1.52105 q^{48} +1.00000 q^{49} -5.18656 q^{50} +8.77974 q^{51} +1.34956 q^{52} +11.5691 q^{53} +5.60721 q^{54} +4.11276 q^{55} +1.00000 q^{56} -10.7146 q^{57} +2.06455 q^{58} -2.46795 q^{59} -4.85464 q^{60} -9.99054 q^{61} +1.05869 q^{62} +0.686407 q^{63} +1.00000 q^{64} -4.30731 q^{65} +1.96003 q^{66} +15.7014 q^{67} +5.77216 q^{68} -7.92502 q^{69} -3.19164 q^{70} +7.43814 q^{71} +0.686407 q^{72} +5.84106 q^{73} -0.620197 q^{74} +7.88902 q^{75} -7.04424 q^{76} +1.28860 q^{77} -2.05275 q^{78} -2.91941 q^{79} -3.19164 q^{80} -6.46962 q^{81} +6.09301 q^{82} -2.31837 q^{83} -1.52105 q^{84} -18.4226 q^{85} +9.64795 q^{86} -3.14028 q^{87} +1.28860 q^{88} +14.5030 q^{89} -2.19076 q^{90} -1.34956 q^{91} -5.21023 q^{92} -1.61032 q^{93} -11.2768 q^{94} +22.4827 q^{95} -1.52105 q^{96} +9.65031 q^{97} -1.00000 q^{98} +0.884507 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * 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
$3$	1.52105	0.878179	0.439089	−	0.898443i	$-0.355301\pi$
$3$	1.52105	0.878179	0.439089	+	0.898443i	$0.355301\pi$
$4$	1.00000	0.500000
$5$	−3.19164	−1.42734	−0.713672	−	0.700480i	$-0.752969\pi$
$5$	−3.19164	−1.42734	−0.713672	+	0.700480i	$0.752969\pi$
$6$	−1.52105	−0.620966
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−0.686407	−0.228802
$10$	3.19164	1.00928
$11$	−1.28860	−0.388529	−0.194264	−	0.980949i	$-0.562232\pi$
$11$	−1.28860	−0.388529	−0.194264	+	0.980949i	$0.562232\pi$
$12$	1.52105	0.439089
$13$	1.34956	0.374301	0.187150	−	0.982331i	$-0.440075\pi$
$13$	1.34956	0.374301	0.187150	+	0.982331i	$0.440075\pi$
$14$	1.00000	0.267261
$15$	−4.85464	−1.25346
$16$	1.00000	0.250000
$17$	5.77216	1.39995	0.699977	−	0.714165i	$-0.253194\pi$
$17$	5.77216	1.39995	0.699977	+	0.714165i	$0.253194\pi$
$18$	0.686407	0.161788
$19$	−7.04424	−1.61606	−0.808029	−	0.589142i	$-0.799466\pi$
$19$	−7.04424	−1.61606	−0.808029	+	0.589142i	$0.799466\pi$
$20$	−3.19164	−0.713672
$21$	−1.52105	−0.331920
$22$	1.28860	0.274731
$23$	−5.21023	−1.08641	−0.543204	−	0.839601i	$-0.682789\pi$
$23$	−5.21023	−1.08641	−0.543204	+	0.839601i	$0.682789\pi$
$24$	−1.52105	−0.310483
$25$	5.18656	1.03731
$26$	−1.34956	−0.264671
$27$	−5.60721	−1.07911
$28$	−1.00000	−0.188982
$29$	−2.06455	−0.383377	−0.191689	−	0.981456i	$-0.561396\pi$
$29$	−2.06455	−0.383377	−0.191689	+	0.981456i	$0.561396\pi$
$30$	4.85464	0.886332
$31$	−1.05869	−0.190146	−0.0950730	−	0.995470i	$-0.530308\pi$
$31$	−1.05869	−0.190146	−0.0950730	+	0.995470i	$0.530308\pi$
$32$	−1.00000	−0.176777
$33$	−1.96003	−0.341197
$34$	−5.77216	−0.989917
$35$	3.19164	0.539485
$36$	−0.686407	−0.114401
$37$	0.620197	0.101960	0.0509799	−	0.998700i	$-0.483766\pi$
$37$	0.620197	0.101960	0.0509799	+	0.998700i	$0.483766\pi$
$38$	7.04424	1.14273
$39$	2.05275	0.328703
$40$	3.19164	0.504642
$41$	−6.09301	−0.951569	−0.475784	−	0.879562i	$-0.657836\pi$
$41$	−6.09301	−0.951569	−0.475784	+	0.879562i	$0.657836\pi$
$42$	1.52105	0.234703
$43$	−9.64795	−1.47130	−0.735649	−	0.677363i	$-0.763123\pi$
$43$	−9.64795	−1.47130	−0.735649	+	0.677363i	$0.763123\pi$
$44$	−1.28860	−0.194264
$45$	2.19076	0.326580
$46$	5.21023	0.768207
$47$	11.2768	1.64489	0.822445	−	0.568844i	$-0.192609\pi$
$47$	11.2768	1.64489	0.822445	+	0.568844i	$0.192609\pi$
$48$	1.52105	0.219545
$49$	1.00000	0.142857
$50$	−5.18656	−0.733490
$51$	8.77974	1.22941
$52$	1.34956	0.187150
$53$	11.5691	1.58914	0.794571	−	0.607172i	$-0.207696\pi$
$53$	11.5691	1.58914	0.794571	+	0.607172i	$0.207696\pi$
$54$	5.60721	0.763045
$55$	4.11276	0.554564
$56$	1.00000	0.133631
$57$	−10.7146	−1.41919
$58$	2.06455	0.271089
$59$	−2.46795	−0.321299	−0.160650	−	0.987011i	$-0.551359\pi$
$59$	−2.46795	−0.321299	−0.160650	+	0.987011i	$0.551359\pi$
$60$	−4.85464	−0.626732
$61$	−9.99054	−1.27916	−0.639579	−	0.768726i	$-0.720891\pi$
$61$	−9.99054	−1.27916	−0.639579	+	0.768726i	$0.720891\pi$
$62$	1.05869	0.134454
$63$	0.686407	0.0864792
$64$	1.00000	0.125000
$65$	−4.30731	−0.534256
$66$	1.96003	0.241263
$67$	15.7014	1.91823	0.959114	−	0.283019i	$-0.0913361\pi$
$67$	15.7014	1.91823	0.959114	+	0.283019i	$0.0913361\pi$
$68$	5.77216	0.699977
$69$	−7.92502	−0.954060
$70$	−3.19164	−0.381474
$71$	7.43814	0.882745	0.441373	−	0.897324i	$-0.354492\pi$
$71$	7.43814	0.882745	0.441373	+	0.897324i	$0.354492\pi$
$72$	0.686407	0.0808939
$73$	5.84106	0.683645	0.341822	−	0.939765i	$-0.388956\pi$
$73$	5.84106	0.683645	0.341822	+	0.939765i	$0.388956\pi$
$74$	−0.620197	−0.0720964
$75$	7.88902	0.910945
$76$	−7.04424	−0.808029
$77$	1.28860	0.146850
$78$	−2.05275	−0.232428
$79$	−2.91941	−0.328459	−0.164229	−	0.986422i	$-0.552514\pi$
$79$	−2.91941	−0.328459	−0.164229	+	0.986422i	$0.552514\pi$
$80$	−3.19164	−0.356836
$81$	−6.46962	−0.718847
$82$	6.09301	0.672861
$83$	−2.31837	−0.254475	−0.127237	−	0.991872i	$-0.540611\pi$
$83$	−2.31837	−0.254475	−0.127237	+	0.991872i	$0.540611\pi$
$84$	−1.52105	−0.165960
$85$	−18.4226	−1.99822
$86$	9.64795	1.04037
$87$	−3.14028	−0.336674
$88$	1.28860	0.137366
$89$	14.5030	1.53732	0.768658	−	0.639660i	$-0.220925\pi$
$89$	14.5030	1.53732	0.768658	+	0.639660i	$0.220925\pi$
$90$	−2.19076	−0.230927
$91$	−1.34956	−0.141472
$92$	−5.21023	−0.543204
$93$	−1.61032	−0.166982
$94$	−11.2768	−1.16311
$95$	22.4827	2.30667
$96$	−1.52105	−0.155242
$97$	9.65031	0.979840	0.489920	−	0.871767i	$-0.337026\pi$
$97$	9.65031	0.979840	0.489920	+	0.871767i	$0.337026\pi$
$98$	−1.00000	−0.101015
$99$	0.884507	0.0888963
$100$	5.18656	0.518656
$101$	−17.2580	−1.71724	−0.858620	−	0.512613i	$-0.828678\pi$
$101$	−17.2580	−1.71724	−0.858620	+	0.512613i	$0.828678\pi$
$102$	−8.77974	−0.869324
$103$	8.12280	0.800364	0.400182	−	0.916436i	$-0.368947\pi$
$103$	8.12280	0.800364	0.400182	+	0.916436i	$0.368947\pi$
$104$	−1.34956	−0.132335
$105$	4.85464	0.473765
$106$	−11.5691	−1.12369
$107$	−7.61685	−0.736349	−0.368174	−	0.929757i	$-0.620017\pi$
$107$	−7.61685	−0.736349	−0.368174	+	0.929757i	$0.620017\pi$
$108$	−5.60721	−0.539554
$109$	−14.9452	−1.43150	−0.715748	−	0.698359i	$-0.753914\pi$
$109$	−14.9452	−1.43150	−0.715748	+	0.698359i	$0.753914\pi$
$110$	−4.11276	−0.392136
$111$	0.943351	0.0895389
$112$	−1.00000	−0.0944911
$113$	5.90534	0.555528	0.277764	−	0.960649i	$-0.410407\pi$
$113$	5.90534	0.555528	0.277764	+	0.960649i	$0.410407\pi$
$114$	10.7146	1.00352
$115$	16.6292	1.55068
$116$	−2.06455	−0.191689
$117$	−0.926348	−0.0856409
$118$	2.46795	0.227193
$119$	−5.77216	−0.529133
$120$	4.85464	0.443166
$121$	−9.33950	−0.849046
$122$	9.99054	0.904501
$123$	−9.26778	−0.835647
$124$	−1.05869	−0.0950730
$125$	−0.595431	−0.0532570
$126$	−0.686407	−0.0611500
$127$	5.92583	0.525833	0.262916	−	0.964819i	$-0.415316\pi$
$127$	5.92583	0.525833	0.262916	+	0.964819i	$0.415316\pi$
$128$	−1.00000	−0.0883883
$129$	−14.6750	−1.29206
$130$	4.30731	0.377776
$131$	−7.13803	−0.623653	−0.311826	−	0.950139i	$-0.600941\pi$
$131$	−7.13803	−0.623653	−0.311826	+	0.950139i	$0.600941\pi$
$132$	−1.96003	−0.170599
$133$	7.04424	0.610813
$134$	−15.7014	−1.35639
$135$	17.8962	1.54026
$136$	−5.77216	−0.494958
$137$	8.51425	0.727421	0.363711	−	0.931512i	$-0.381510\pi$
$137$	8.51425	0.727421	0.363711	+	0.931512i	$0.381510\pi$
$138$	7.92502	0.674623
$139$	−8.10576	−0.687522	−0.343761	−	0.939057i	$-0.611701\pi$
$139$	−8.10576	−0.687522	−0.343761	+	0.939057i	$0.611701\pi$
$140$	3.19164	0.269743
$141$	17.1526	1.44451
$142$	−7.43814	−0.624195
$143$	−1.73905	−0.145426
$144$	−0.686407	−0.0572006
$145$	6.58930	0.547211
$146$	−5.84106	−0.483410
$147$	1.52105	0.125454
$148$	0.620197	0.0509799
$149$	−13.2557	−1.08595	−0.542973	−	0.839750i	$-0.682701\pi$
$149$	−13.2557	−1.08595	−0.542973	+	0.839750i	$0.682701\pi$
$150$	−7.88902	−0.644135
$151$	11.8253	0.962331	0.481165	−	0.876630i	$-0.340214\pi$
$151$	11.8253	0.962331	0.481165	+	0.876630i	$0.340214\pi$
$152$	7.04424	0.571363
$153$	−3.96205	−0.320313
$154$	−1.28860	−0.103839
$155$	3.37895	0.271404
$156$	2.05275	0.164351
$157$	−10.4632	−0.835057	−0.417529	−	0.908664i	$-0.637104\pi$
$157$	−10.4632	−0.835057	−0.417529	+	0.908664i	$0.637104\pi$
$158$	2.91941	0.232256
$159$	17.5972	1.39555
$160$	3.19164	0.252321
$161$	5.21023	0.410624
$162$	6.46962	0.508302
$163$	2.15221	0.168574	0.0842870	−	0.996442i	$-0.473139\pi$
$163$	2.15221	0.168574	0.0842870	+	0.996442i	$0.473139\pi$
$164$	−6.09301	−0.475784
$165$	6.25571	0.487006
$166$	2.31837	0.179941
$167$	22.9023	1.77224	0.886118	−	0.463461i	$-0.153392\pi$
$167$	22.9023	1.77224	0.886118	+	0.463461i	$0.153392\pi$
$168$	1.52105	0.117352
$169$	−11.1787	−0.859899
$170$	18.4226	1.41295
$171$	4.83522	0.369758
$172$	−9.64795	−0.735649
$173$	3.05284	0.232103	0.116051	−	0.993243i	$-0.462976\pi$
$173$	3.05284	0.232103	0.116051	+	0.993243i	$0.462976\pi$
$174$	3.14028	0.238064
$175$	−5.18656	−0.392067
$176$	−1.28860	−0.0971321
$177$	−3.75387	−0.282158
$178$	−14.5030	−1.08705
$179$	10.9370	0.817466	0.408733	−	0.912654i	$-0.365971\pi$
$179$	10.9370	0.817466	0.408733	+	0.912654i	$0.365971\pi$
$180$	2.19076	0.163290
$181$	−7.20674	−0.535673	−0.267836	−	0.963464i	$-0.586309\pi$
$181$	−7.20674	−0.535673	−0.267836	+	0.963464i	$0.586309\pi$
$182$	1.34956	0.100036
$183$	−15.1961	−1.12333
$184$	5.21023	0.384103
$185$	−1.97944	−0.145532
$186$	1.61032	0.118074
$187$	−7.43802	−0.543922
$188$	11.2768	0.822445
$189$	5.60721	0.407864
$190$	−22.4827	−1.63106
$191$	4.94052	0.357483	0.178742	−	0.983896i	$-0.442797\pi$
$191$	4.94052	0.357483	0.178742	+	0.983896i	$0.442797\pi$
$192$	1.52105	0.109772
$193$	0.189080	0.0136102	0.00680512	−	0.999977i	$-0.497834\pi$
$193$	0.189080	0.0136102	0.00680512	+	0.999977i	$0.497834\pi$
$194$	−9.65031	−0.692852
$195$	−6.55163	−0.469172
$196$	1.00000	0.0714286
$197$	−2.30403	−0.164155	−0.0820776	−	0.996626i	$-0.526156\pi$
$197$	−2.30403	−0.164155	−0.0820776	+	0.996626i	$0.526156\pi$
$198$	−0.884507	−0.0628592
$199$	22.6764	1.60749	0.803744	−	0.594975i	$-0.202838\pi$
$199$	22.6764	1.60749	0.803744	+	0.594975i	$0.202838\pi$
$200$	−5.18656	−0.366745
$201$	23.8826	1.68455
$202$	17.2580	1.21427
$203$	2.06455	0.144903
$204$	8.77974	0.614705
$205$	19.4467	1.35822
$206$	−8.12280	−0.565943
$207$	3.57634	0.248573
$208$	1.34956	0.0935752
$209$	9.07723	0.627885
$210$	−4.85464	−0.335002
$211$	12.5303	0.862620	0.431310	−	0.902204i	$-0.358052\pi$
$211$	12.5303	0.862620	0.431310	+	0.902204i	$0.358052\pi$
$212$	11.5691	0.794571
$213$	11.3138	0.775208
$214$	7.61685	0.520677
$215$	30.7928	2.10005
$216$	5.60721	0.381522
$217$	1.05869	0.0718684
$218$	14.9452	1.01222
$219$	8.88455	0.600362
$220$	4.11276	0.277282
$221$	7.78987	0.524004
$222$	−0.943351	−0.0633135
$223$	−12.9727	−0.868717	−0.434359	−	0.900740i	$-0.643025\pi$
$223$	−12.9727	−0.868717	−0.434359	+	0.900740i	$0.643025\pi$
$224$	1.00000	0.0668153
$225$	−3.56009	−0.237339
$226$	−5.90534	−0.392817
$227$	7.24109	0.480608	0.240304	−	0.970698i	$-0.422753\pi$
$227$	7.24109	0.480608	0.240304	+	0.970698i	$0.422753\pi$
$228$	−10.7146	−0.709594
$229$	3.79306	0.250653	0.125326	−	0.992116i	$-0.460002\pi$
$229$	3.79306	0.250653	0.125326	+	0.992116i	$0.460002\pi$
$230$	−16.6292	−1.09650
$231$	1.96003	0.128961
$232$	2.06455	0.135544
$233$	14.4348	0.945656	0.472828	−	0.881155i	$-0.343233\pi$
$233$	14.4348	0.945656	0.472828	+	0.881155i	$0.343233\pi$
$234$	0.926348	0.0605573
$235$	−35.9915	−2.34783
$236$	−2.46795	−0.160650
$237$	−4.44056	−0.288446
$238$	5.77216	0.374153
$239$	18.6684	1.20756	0.603779	−	0.797151i	$-0.293661\pi$
$239$	18.6684	1.20756	0.603779	+	0.797151i	$0.293661\pi$
$240$	−4.85464	−0.313366
$241$	−28.5089	−1.83642	−0.918209	−	0.396097i	$-0.870364\pi$
$241$	−28.5089	−1.83642	−0.918209	+	0.396097i	$0.870364\pi$
$242$	9.33950	0.600366
$243$	6.98101	0.447832
$244$	−9.99054	−0.639579
$245$	−3.19164	−0.203906
$246$	9.26778	0.590892
$247$	−9.50662	−0.604892
$248$	1.05869	0.0672268
$249$	−3.52636	−0.223474
$250$	0.595431	0.0376584
$251$	26.8629	1.69557	0.847786	−	0.530339i	$-0.177935\pi$
$251$	26.8629	1.69557	0.847786	+	0.530339i	$0.177935\pi$
$252$	0.686407	0.0432396
$253$	6.71392	0.422101
$254$	−5.92583	−0.371820
$255$	−28.0218	−1.75479
$256$	1.00000	0.0625000
$257$	−10.6919	−0.666943	−0.333472	−	0.942760i	$-0.608220\pi$
$257$	−10.6919	−0.666943	−0.333472	+	0.942760i	$0.608220\pi$
$258$	14.6750	0.913627
$259$	−0.620197	−0.0385372
$260$	−4.30731	−0.267128
$261$	1.41712	0.0877176
$262$	7.13803	0.440989
$263$	12.9105	0.796094	0.398047	−	0.917365i	$-0.369688\pi$
$263$	12.9105	0.796094	0.398047	+	0.917365i	$0.369688\pi$
$264$	1.96003	0.120632
$265$	−36.9245	−2.26825
$266$	−7.04424	−0.431910
$267$	22.0598	1.35004
$268$	15.7014	0.959114
$269$	12.8847	0.785596	0.392798	−	0.919625i	$-0.371507\pi$
$269$	12.8847	0.785596	0.392798	+	0.919625i	$0.371507\pi$
$270$	−17.8962	−1.08913
$271$	−6.74674	−0.409835	−0.204918	−	0.978779i	$-0.565693\pi$
$271$	−6.74674	−0.409835	−0.204918	+	0.978779i	$0.565693\pi$
$272$	5.77216	0.349988
$273$	−2.05275	−0.124238
$274$	−8.51425	−0.514365
$275$	−6.68342	−0.403025
$276$	−7.92502	−0.477030
$277$	6.70796	0.403042	0.201521	−	0.979484i	$-0.435412\pi$
$277$	6.70796	0.403042	0.201521	+	0.979484i	$0.435412\pi$
$278$	8.10576	0.486151
$279$	0.726691	0.0435059
$280$	−3.19164	−0.190737
$281$	23.7571	1.41723	0.708616	−	0.705594i	$-0.249320\pi$
$281$	23.7571	1.41723	0.708616	+	0.705594i	$0.249320\pi$
$282$	−17.1526	−1.02142
$283$	0.277722	0.0165089	0.00825444	−	0.999966i	$-0.497373\pi$
$283$	0.277722	0.0165089	0.00825444	+	0.999966i	$0.497373\pi$
$284$	7.43814	0.441373
$285$	34.1973	2.02567
$286$	1.73905	0.102832
$287$	6.09301	0.359659
$288$	0.686407	0.0404469
$289$	16.3178	0.959871
$290$	−6.58930	−0.386937
$291$	14.6786	0.860475
$292$	5.84106	0.341822
$293$	2.33289	0.136289	0.0681443	−	0.997675i	$-0.478292\pi$
$293$	2.33289	0.136289	0.0681443	+	0.997675i	$0.478292\pi$
$294$	−1.52105	−0.0887094
$295$	7.87680	0.458605
$296$	−0.620197	−0.0360482
$297$	7.22547	0.419264
$298$	13.2557	0.767880
$299$	−7.03152	−0.406643
$300$	7.88902	0.455473
$301$	9.64795	0.556099
$302$	−11.8253	−0.680471
$303$	−26.2503	−1.50804
$304$	−7.04424	−0.404015
$305$	31.8862	1.82580
$306$	3.96205	0.226495
$307$	11.9231	0.680488	0.340244	−	0.940337i	$-0.389490\pi$
$307$	11.9231	0.680488	0.340244	+	0.940337i	$0.389490\pi$
$308$	1.28860	0.0734250
$309$	12.3552	0.702862
$310$	−3.37895	−0.191912
$311$	13.8823	0.787196	0.393598	−	0.919283i	$-0.371230\pi$
$311$	13.8823	0.787196	0.393598	+	0.919283i	$0.371230\pi$
$312$	−2.05275	−0.116214
$313$	−0.493548	−0.0278970	−0.0139485	−	0.999903i	$-0.504440\pi$
$313$	−0.493548	−0.0278970	−0.0139485	+	0.999903i	$0.504440\pi$
$314$	10.4632	0.590475
$315$	−2.19076	−0.123436
$316$	−2.91941	−0.164229
$317$	5.58340	0.313595	0.156798	−	0.987631i	$-0.449883\pi$
$317$	5.58340	0.313595	0.156798	+	0.987631i	$0.449883\pi$
$318$	−17.5972	−0.986803
$319$	2.66039	0.148953
$320$	−3.19164	−0.178418
$321$	−11.5856	−0.646646
$322$	−5.21023	−0.290355
$323$	−40.6604	−2.26241
$324$	−6.46962	−0.359424
$325$	6.99957	0.388267
$326$	−2.15221	−0.119200
$327$	−22.7325	−1.25711
$328$	6.09301	0.336430
$329$	−11.2768	−0.621710
$330$	−6.25571	−0.344365
$331$	20.1655	1.10840	0.554198	−	0.832385i	$-0.313025\pi$
$331$	20.1655	1.10840	0.554198	+	0.832385i	$0.313025\pi$
$332$	−2.31837	−0.127237
$333$	−0.425708	−0.0233286
$334$	−22.9023	−1.25316
$335$	−50.1131	−2.73797
$336$	−1.52105	−0.0829801
$337$	−12.4429	−0.677809	−0.338904	−	0.940821i	$-0.610056\pi$
$337$	−12.4429	−0.677809	−0.338904	+	0.940821i	$0.610056\pi$
$338$	11.1787	0.608040
$339$	8.98232	0.487852
$340$	−18.4226	−0.999108
$341$	1.36423	0.0738772
$342$	−4.83522	−0.261459
$343$	−1.00000	−0.0539949
$344$	9.64795	0.520183
$345$	25.2938	1.36177
$346$	−3.05284	−0.164122
$347$	−4.20130	−0.225537	−0.112769	−	0.993621i	$-0.535972\pi$
$347$	−4.20130	−0.225537	−0.112769	+	0.993621i	$0.535972\pi$
$348$	−3.14028	−0.168337
$349$	33.7381	1.80596	0.902981	−	0.429681i	$-0.141374\pi$
$349$	33.7381	1.80596	0.902981	+	0.429681i	$0.141374\pi$
$350$	5.18656	0.277233
$351$	−7.56727	−0.403911
$352$	1.28860	0.0686828
$353$	25.2469	1.34376	0.671880	−	0.740660i	$-0.265487\pi$
$353$	25.2469	1.34376	0.671880	+	0.740660i	$0.265487\pi$
$354$	3.75387	0.199516
$355$	−23.7399	−1.25998
$356$	14.5030	0.768658
$357$	−8.77974	−0.464673
$358$	−10.9370	−0.578036
$359$	−9.59978	−0.506657	−0.253328	−	0.967380i	$-0.581525\pi$
$359$	−9.59978	−0.506657	−0.253328	+	0.967380i	$0.581525\pi$
$360$	−2.19076	−0.115463
$361$	30.6213	1.61165
$362$	7.20674	0.378778
$363$	−14.2058	−0.745614
$364$	−1.34956	−0.0707362
$365$	−18.6426	−0.975797
$366$	15.1961	0.794313
$367$	11.8428	0.618192	0.309096	−	0.951031i	$-0.399974\pi$
$367$	11.8428	0.618192	0.309096	+	0.951031i	$0.399974\pi$
$368$	−5.21023	−0.271602
$369$	4.18229	0.217721
$370$	1.97944	0.102906
$371$	−11.5691	−0.600639
$372$	−1.61032	−0.0834911
$373$	24.7385	1.28091	0.640456	−	0.767995i	$-0.278745\pi$
$373$	24.7385	1.28091	0.640456	+	0.767995i	$0.278745\pi$
$374$	7.43802	0.384611
$375$	−0.905681	−0.0467692
$376$	−11.2768	−0.581557
$377$	−2.78623	−0.143498
$378$	−5.60721	−0.288404
$379$	8.42862	0.432949	0.216475	−	0.976288i	$-0.430544\pi$
$379$	8.42862	0.432949	0.216475	+	0.976288i	$0.430544\pi$
$380$	22.4827	1.15334
$381$	9.01349	0.461775
$382$	−4.94052	−0.252779
$383$	22.2967	1.13931	0.569653	−	0.821885i	$-0.307078\pi$
$383$	22.2967	1.13931	0.569653	+	0.821885i	$0.307078\pi$
$384$	−1.52105	−0.0776208
$385$	−4.11276	−0.209606
$386$	−0.189080	−0.00962390
$387$	6.62242	0.336637
$388$	9.65031	0.489920
$389$	6.43268	0.326150	0.163075	−	0.986614i	$-0.447859\pi$
$389$	6.43268	0.326150	0.163075	+	0.986614i	$0.447859\pi$
$390$	6.55163	0.331755
$391$	−30.0743	−1.52092
$392$	−1.00000	−0.0505076
$393$	−10.8573	−0.547678
$394$	2.30403	0.116075
$395$	9.31769	0.468824
$396$	0.884507	0.0444481
$397$	18.5004	0.928509	0.464254	−	0.885702i	$-0.346322\pi$
$397$	18.5004	0.928509	0.464254	+	0.885702i	$0.346322\pi$
$398$	−22.6764	−1.13667
$399$	10.7146	0.536403
$400$	5.18656	0.259328
$401$	−9.81363	−0.490069	−0.245035	−	0.969514i	$-0.578799\pi$
$401$	−9.81363	−0.490069	−0.245035	+	0.969514i	$0.578799\pi$
$402$	−23.8826	−1.19115
$403$	−1.42876	−0.0711718
$404$	−17.2580	−0.858620
$405$	20.6487	1.02604
$406$	−2.06455	−0.102462
$407$	−0.799188	−0.0396143
$408$	−8.77974	−0.434662
$409$	−21.6181	−1.06895	−0.534474	−	0.845185i	$-0.679490\pi$
$409$	−21.6181	−1.06895	−0.534474	+	0.845185i	$0.679490\pi$
$410$	−19.4467	−0.960404
$411$	12.9506	0.638806
$412$	8.12280	0.400182
$413$	2.46795	0.121440
$414$	−3.57634	−0.175768
$415$	7.39941	0.363223
$416$	−1.34956	−0.0661676
$417$	−12.3293	−0.603767
$418$	−9.07723	−0.443982
$419$	13.3692	0.653126	0.326563	−	0.945175i	$-0.394109\pi$
$419$	13.3692	0.653126	0.326563	+	0.945175i	$0.394109\pi$
$420$	4.85464	0.236882
$421$	8.21394	0.400323	0.200162	−	0.979763i	$-0.435853\pi$
$421$	8.21394	0.400323	0.200162	+	0.979763i	$0.435853\pi$
$422$	−12.5303	−0.609964
$423$	−7.74048	−0.376355
$424$	−11.5691	−0.561846
$425$	29.9376	1.45219
$426$	−11.3138	−0.548155
$427$	9.99054	0.483476
$428$	−7.61685	−0.368174
$429$	−2.64518	−0.127710
$430$	−30.7928	−1.48496
$431$	1.00000	0.0481683
$431$	1.00000	0.0481683
$432$	−5.60721	−0.269777
$433$	−7.69393	−0.369747	−0.184873	−	0.982762i	$-0.559187\pi$
$433$	−7.69393	−0.369747	−0.184873	+	0.982762i	$0.559187\pi$
$434$	−1.05869	−0.0508187
$435$	10.0226	0.480549
$436$	−14.9452	−0.715748
$437$	36.7021	1.75570
$438$	−8.88455	−0.424520
$439$	−13.8335	−0.660236	−0.330118	−	0.943940i	$-0.607089\pi$
$439$	−13.8335	−0.660236	−0.330118	+	0.943940i	$0.607089\pi$
$440$	−4.11276	−0.196068
$441$	−0.686407	−0.0326861
$442$	−7.78987	−0.370526
$443$	−16.9069	−0.803271	−0.401636	−	0.915800i	$-0.631558\pi$
$443$	−16.9069	−0.803271	−0.401636	+	0.915800i	$0.631558\pi$
$444$	0.943351	0.0447694
$445$	−46.2884	−2.19428
$446$	12.9727	0.614276
$447$	−20.1625	−0.953655
$448$	−1.00000	−0.0472456
$449$	−20.4743	−0.966244	−0.483122	−	0.875553i	$-0.660497\pi$
$449$	−20.4743	−0.966244	−0.483122	+	0.875553i	$0.660497\pi$
$450$	3.56009	0.167824
$451$	7.85148	0.369712
$452$	5.90534	0.277764
$453$	17.9869	0.845098
$454$	−7.24109	−0.339841
$455$	4.30731	0.201930
$456$	10.7146	0.501759
$457$	8.32894	0.389611	0.194806	−	0.980842i	$-0.437592\pi$
$457$	8.32894	0.389611	0.194806	+	0.980842i	$0.437592\pi$
$458$	−3.79306	−0.177238
$459$	−32.3657	−1.51070
$460$	16.6292	0.775339
$461$	−30.3206	−1.41217	−0.706084	−	0.708128i	$-0.749540\pi$
$461$	−30.3206	−1.41217	−0.706084	+	0.708128i	$0.749540\pi$
$462$	−1.96003	−0.0911888
$463$	12.7482	0.592461	0.296230	−	0.955117i	$-0.404270\pi$
$463$	12.7482	0.592461	0.296230	+	0.955117i	$0.404270\pi$
$464$	−2.06455	−0.0958443
$465$	5.13955	0.238341
$466$	−14.4348	−0.668680
$467$	19.7315	0.913065	0.456533	−	0.889707i	$-0.349091\pi$
$467$	19.7315	0.913065	0.456533	+	0.889707i	$0.349091\pi$
$468$	−0.926348	−0.0428204
$469$	−15.7014	−0.725022
$470$	35.9915	1.66016
$471$	−15.9151	−0.733330
$472$	2.46795	0.113596
$473$	12.4324	0.571642
$474$	4.44056	0.203962
$475$	−36.5354	−1.67636
$476$	−5.77216	−0.264566
$477$	−7.94113	−0.363599
$478$	−18.6684	−0.853873
$479$	−30.1114	−1.37583	−0.687913	−	0.725793i	$-0.741473\pi$
$479$	−30.1114	−1.37583	−0.687913	+	0.725793i	$0.741473\pi$
$480$	4.85464	0.221583
$481$	0.836993	0.0381636
$482$	28.5089	1.29854
$483$	7.92502	0.360601
$484$	−9.33950	−0.424523
$485$	−30.8003	−1.39857
$486$	−6.98101	−0.316665
$487$	−1.44157	−0.0653236	−0.0326618	−	0.999466i	$-0.510398\pi$
$487$	−1.44157	−0.0653236	−0.0326618	+	0.999466i	$0.510398\pi$
$488$	9.99054	0.452250
$489$	3.27362	0.148038
$490$	3.19164	0.144184
$491$	−8.76940	−0.395757	−0.197879	−	0.980227i	$-0.563405\pi$
$491$	−8.76940	−0.395757	−0.197879	+	0.980227i	$0.563405\pi$
$492$	−9.26778	−0.417824
$493$	−11.9169	−0.536710
$494$	9.50662	0.427723
$495$	−2.82303	−0.126886
$496$	−1.05869	−0.0475365
$497$	−7.43814	−0.333646
$498$	3.52636	0.158020
$499$	−9.82796	−0.439960	−0.219980	−	0.975504i	$-0.570599\pi$
$499$	−9.82796	−0.439960	−0.219980	+	0.975504i	$0.570599\pi$
$500$	−0.595431	−0.0266285
$501$	34.8356	1.55634
$502$	−26.8629	−1.19895
$503$	4.66012	0.207785	0.103892	−	0.994589i	$-0.466870\pi$
$503$	4.66012	0.207785	0.103892	+	0.994589i	$0.466870\pi$
$504$	−0.686407	−0.0305750
$505$	55.0814	2.45109
$506$	−6.71392	−0.298470
$507$	−17.0033	−0.755145
$508$	5.92583	0.262916
$509$	13.4419	0.595801	0.297900	−	0.954597i	$-0.403714\pi$
$509$	13.4419	0.595801	0.297900	+	0.954597i	$0.403714\pi$
$510$	28.0218	1.24082
$511$	−5.84106	−0.258393
$512$	−1.00000	−0.0441942
$513$	39.4985	1.74390
$514$	10.6919	0.471600
$515$	−25.9251	−1.14239
$516$	−14.6750	−0.646032
$517$	−14.5313	−0.639087
$518$	0.620197	0.0272499
$519$	4.64352	0.203828
$520$	4.30731	0.188888
$521$	−26.6330	−1.16681	−0.583407	−	0.812180i	$-0.698281\pi$
$521$	−26.6330	−1.16681	−0.583407	+	0.812180i	$0.698281\pi$
$522$	−1.41712	−0.0620257
$523$	−26.6902	−1.16708	−0.583540	−	0.812085i	$-0.698333\pi$
$523$	−26.6902	−1.16708	−0.583540	+	0.812085i	$0.698333\pi$
$524$	−7.13803	−0.311826
$525$	−7.88902	−0.344305
$526$	−12.9105	−0.562923
$527$	−6.11092	−0.266196
$528$	−1.96003	−0.0852994
$529$	4.14650	0.180283
$530$	36.9245	1.60390
$531$	1.69402	0.0735141
$532$	7.04424	0.305406
$533$	−8.22289	−0.356173
$534$	−22.0598	−0.954621
$535$	24.3102	1.05102
$536$	−15.7014	−0.678196
$537$	16.6356	0.717881
$538$	−12.8847	−0.555500
$539$	−1.28860	−0.0555041
$540$	17.8962	0.770129
$541$	0.262978	0.0113063	0.00565316	−	0.999984i	$-0.498201\pi$
$541$	0.262978	0.0113063	0.00565316	+	0.999984i	$0.498201\pi$
$542$	6.74674	0.289797
$543$	−10.9618	−0.470416
$544$	−5.77216	−0.247479
$545$	47.6998	2.04324
$546$	2.05275	0.0878495
$547$	−15.6346	−0.668488	−0.334244	−	0.942487i	$-0.608481\pi$
$547$	−15.6346	−0.668488	−0.334244	+	0.942487i	$0.608481\pi$
$548$	8.51425	0.363711
$549$	6.85758	0.292674
$550$	6.68342	0.284982
$551$	14.5432	0.619560
$552$	7.92502	0.337311
$553$	2.91941	0.124146
$554$	−6.70796	−0.284994
$555$	−3.01083	−0.127803
$556$	−8.10576	−0.343761
$557$	33.9298	1.43765	0.718826	−	0.695190i	$-0.244680\pi$
$557$	33.9298	1.43765	0.718826	+	0.695190i	$0.244680\pi$
$558$	−0.726691	−0.0307633
$559$	−13.0205	−0.550708
$560$	3.19164	0.134871
$561$	−11.3136	−0.477661
$562$	−23.7571	−1.00213
$563$	−12.5560	−0.529172	−0.264586	−	0.964362i	$-0.585235\pi$
$563$	−12.5560	−0.529172	−0.264586	+	0.964362i	$0.585235\pi$
$564$	17.1526	0.722254
$565$	−18.8477	−0.792929
$566$	−0.277722	−0.0116735
$567$	6.46962	0.271699
$568$	−7.43814	−0.312098
$569$	−6.75825	−0.283321	−0.141660	−	0.989915i	$-0.545244\pi$
$569$	−6.75825	−0.283321	−0.141660	+	0.989915i	$0.545244\pi$
$570$	−34.1973	−1.43237
$571$	−11.7875	−0.493292	−0.246646	−	0.969106i	$-0.579329\pi$
$571$	−11.7875	−0.493292	−0.246646	+	0.969106i	$0.579329\pi$
$572$	−1.73905	−0.0727132
$573$	7.51478	0.313934
$574$	−6.09301	−0.254317
$575$	−27.0232	−1.12694
$576$	−0.686407	−0.0286003
$577$	−1.79260	−0.0746270	−0.0373135	−	0.999304i	$-0.511880\pi$
$577$	−1.79260	−0.0746270	−0.0373135	+	0.999304i	$0.511880\pi$
$578$	−16.3178	−0.678731
$579$	0.287599	0.0119522
$580$	6.58930	0.273606
$581$	2.31837	0.0961824
$582$	−14.6786	−0.608447
$583$	−14.9080	−0.617427
$584$	−5.84106	−0.241705
$585$	2.95657	0.122239
$586$	−2.33289	−0.0963706
$587$	−22.3933	−0.924271	−0.462136	−	0.886809i	$-0.652917\pi$
$587$	−22.3933	−0.924271	−0.462136	+	0.886809i	$0.652917\pi$
$588$	1.52105	0.0627270
$589$	7.45765	0.307287
$590$	−7.87680	−0.324283
$591$	−3.50454	−0.144158
$592$	0.620197	0.0254899
$593$	41.3315	1.69728	0.848641	−	0.528969i	$-0.177421\pi$
$593$	41.3315	1.69728	0.848641	+	0.528969i	$0.177421\pi$
$594$	−7.22547	−0.296465
$595$	18.4226	0.755255
$596$	−13.2557	−0.542973
$597$	34.4920	1.41166
$598$	7.03152	0.287540
$599$	8.37665	0.342261	0.171130	−	0.985248i	$-0.445258\pi$
$599$	8.37665	0.342261	0.171130	+	0.985248i	$0.445258\pi$
$600$	−7.88902	−0.322068
$601$	−5.47057	−0.223149	−0.111575	−	0.993756i	$-0.535589\pi$
$601$	−5.47057	−0.223149	−0.111575	+	0.993756i	$0.535589\pi$
$602$	−9.64795	−0.393221
$603$	−10.7775	−0.438895
$604$	11.8253	0.481165
$605$	29.8083	1.21188
$606$	26.2503	1.06635
$607$	−0.587193	−0.0238334	−0.0119167	−	0.999929i	$-0.503793\pi$
$607$	−0.587193	−0.0238334	−0.0119167	+	0.999929i	$0.503793\pi$
$608$	7.04424	0.285682
$609$	3.14028	0.127251
$610$	−31.8862	−1.29103
$611$	15.2187	0.615684
$612$	−3.96205	−0.160156
$613$	−11.6822	−0.471841	−0.235920	−	0.971772i	$-0.575810\pi$
$613$	−11.6822	−0.471841	−0.235920	+	0.971772i	$0.575810\pi$
$614$	−11.9231	−0.481177
$615$	29.5794	1.19276
$616$	−1.28860	−0.0519193
$617$	−21.9608	−0.884108	−0.442054	−	0.896988i	$-0.645750\pi$
$617$	−21.9608	−0.884108	−0.442054	+	0.896988i	$0.645750\pi$
$618$	−12.3552	−0.496999
$619$	−12.8998	−0.518485	−0.259242	−	0.965812i	$-0.583473\pi$
$619$	−12.8998	−0.518485	−0.259242	+	0.965812i	$0.583473\pi$
$620$	3.37895	0.135702
$621$	29.2149	1.17235
$622$	−13.8823	−0.556631
$623$	−14.5030	−0.581051
$624$	2.05275	0.0821757
$625$	−24.0324	−0.961296
$626$	0.493548	0.0197261
$627$	13.8069	0.551395
$628$	−10.4632	−0.417529
$629$	3.57987	0.142739
$630$	2.19076	0.0872821
$631$	45.0367	1.79288	0.896442	−	0.443161i	$-0.146143\pi$
$631$	45.0367	1.79288	0.896442	+	0.443161i	$0.146143\pi$
$632$	2.91941	0.116128
$633$	19.0592	0.757534
$634$	−5.58340	−0.221745
$635$	−18.9131	−0.750544
$636$	17.5972	0.697775
$637$	1.34956	0.0534715
$638$	−2.66039	−0.105326
$639$	−5.10560	−0.201974
$640$	3.19164	0.126161
$641$	12.6284	0.498794	0.249397	−	0.968401i	$-0.419768\pi$
$641$	12.6284	0.498794	0.249397	+	0.968401i	$0.419768\pi$
$642$	11.5856	0.457248
$643$	25.7783	1.01660	0.508299	−	0.861181i	$-0.330274\pi$
$643$	25.7783	1.01660	0.508299	+	0.861181i	$0.330274\pi$
$644$	5.21023	0.205312
$645$	46.8374	1.84422
$646$	40.6604	1.59976
$647$	21.2392	0.835000	0.417500	−	0.908677i	$-0.362906\pi$
$647$	21.2392	0.835000	0.417500	+	0.908677i	$0.362906\pi$
$648$	6.46962	0.254151
$649$	3.18021	0.124834
$650$	−6.99957	−0.274546
$651$	1.61032	0.0631133
$652$	2.15221	0.0842870
$653$	−22.1599	−0.867182	−0.433591	−	0.901110i	$-0.642754\pi$
$653$	−22.1599	−0.867182	−0.433591	+	0.901110i	$0.642754\pi$
$654$	22.7325	0.888910
$655$	22.7820	0.890167
$656$	−6.09301	−0.237892
$657$	−4.00935	−0.156420
$658$	11.2768	0.439616
$659$	32.5969	1.26979	0.634897	−	0.772597i	$-0.281043\pi$
$659$	32.5969	1.26979	0.634897	+	0.772597i	$0.281043\pi$
$660$	6.25571	0.243503
$661$	−28.1812	−1.09612	−0.548062	−	0.836438i	$-0.684634\pi$
$661$	−28.1812	−1.09612	−0.548062	+	0.836438i	$0.684634\pi$
$662$	−20.1655	−0.783754
$663$	11.8488	0.460169
$664$	2.31837	0.0899704
$665$	−22.4827	−0.871840
$666$	0.425708	0.0164958
$667$	10.7568	0.416504
$668$	22.9023	0.886118
$669$	−19.7321	−0.762889
$670$	50.1131	1.93604
$671$	12.8738	0.496989
$672$	1.52105	0.0586758
$673$	−28.0463	−1.08110	−0.540552	−	0.841311i	$-0.681785\pi$
$673$	−28.0463	−1.08110	−0.540552	+	0.841311i	$0.681785\pi$
$674$	12.4429	0.479283
$675$	−29.0821	−1.11937
$676$	−11.1787	−0.429950
$677$	34.7563	1.33579	0.667896	−	0.744255i	$-0.267195\pi$
$677$	34.7563	1.33579	0.667896	+	0.744255i	$0.267195\pi$
$678$	−8.98232	−0.344964
$679$	−9.65031	−0.370345
$680$	18.4226	0.706476
$681$	11.0141	0.422060
$682$	−1.36423	−0.0522390
$683$	3.41569	0.130698	0.0653488	−	0.997862i	$-0.479184\pi$
$683$	3.41569	0.130698	0.0653488	+	0.997862i	$0.479184\pi$
$684$	4.83522	0.184879
$685$	−27.1744	−1.03828
$686$	1.00000	0.0381802
$687$	5.76944	0.220118
$688$	−9.64795	−0.367825
$689$	15.6132	0.594817
$690$	−25.2938	−0.962919
$691$	−11.6477	−0.443100	−0.221550	−	0.975149i	$-0.571112\pi$
$691$	−11.6477	−0.443100	−0.221550	+	0.975149i	$0.571112\pi$
$692$	3.05284	0.116051
$693$	−0.884507	−0.0335996
$694$	4.20130	0.159479
$695$	25.8707	0.981330
$696$	3.14028	0.119032
$697$	−35.1698	−1.33215
$698$	−33.7381	−1.27701
$699$	21.9561	0.830455
$700$	−5.18656	−0.196034
$701$	−32.4282	−1.22480	−0.612398	−	0.790550i	$-0.709795\pi$
$701$	−32.4282	−1.22480	−0.612398	+	0.790550i	$0.709795\pi$
$702$	7.56727	0.285608
$703$	−4.36881	−0.164773
$704$	−1.28860	−0.0485661
$705$	−54.7448	−2.06181
$706$	−25.2469	−0.950181
$707$	17.2580	0.649056
$708$	−3.75387	−0.141079
$709$	−39.0374	−1.46608	−0.733040	−	0.680186i	$-0.761899\pi$
$709$	−39.0374	−1.46608	−0.733040	+	0.680186i	$0.761899\pi$
$710$	23.7399	0.890942
$711$	2.00390	0.0751522
$712$	−14.5030	−0.543523
$713$	5.51601	0.206576
$714$	8.77974	0.328573
$715$	5.55041	0.207574
$716$	10.9370	0.408733
$717$	28.3956	1.06045
$718$	9.59978	0.358261
$719$	6.43215	0.239879	0.119939	−	0.992781i	$-0.461730\pi$
$719$	6.43215	0.239879	0.119939	+	0.992781i	$0.461730\pi$
$720$	2.19076	0.0816450
$721$	−8.12280	−0.302509
$722$	−30.6213	−1.13961
$723$	−43.3634	−1.61270
$724$	−7.20674	−0.267836
$725$	−10.7079	−0.397682
$726$	14.2058	0.527228
$727$	−20.2201	−0.749920	−0.374960	−	0.927041i	$-0.622344\pi$
$727$	−20.2201	−0.749920	−0.374960	+	0.927041i	$0.622344\pi$
$728$	1.34956	0.0500180
$729$	30.0273	1.11212
$730$	18.6426	0.689992
$731$	−55.6895	−2.05975
$732$	−15.1961	−0.561664
$733$	4.53382	0.167460	0.0837302	−	0.996488i	$-0.473317\pi$
$733$	4.53382	0.167460	0.0837302	+	0.996488i	$0.473317\pi$
$734$	−11.8428	−0.437128
$735$	−4.85464	−0.179066
$736$	5.21023	0.192052
$737$	−20.2328	−0.745286
$738$	−4.18229	−0.153952
$739$	−31.3707	−1.15399	−0.576996	−	0.816747i	$-0.695775\pi$
$739$	−31.3707	−1.15399	−0.576996	+	0.816747i	$0.695775\pi$
$740$	−1.97944	−0.0727658
$741$	−14.4600	−0.531203
$742$	11.5691	0.424716
$743$	46.7592	1.71543	0.857714	−	0.514127i	$-0.171884\pi$
$743$	46.7592	1.71543	0.857714	+	0.514127i	$0.171884\pi$
$744$	1.61032	0.0590371
$745$	42.3073	1.55002
$746$	−24.7385	−0.905742
$747$	1.59135	0.0582244
$748$	−7.43802	−0.271961
$749$	7.61685	0.278314
$750$	0.905681	0.0330708
$751$	−33.0895	−1.20745	−0.603727	−	0.797191i	$-0.706318\pi$
$751$	−33.0895	−1.20745	−0.603727	+	0.797191i	$0.706318\pi$
$752$	11.2768	0.411223
$753$	40.8598	1.48901
$754$	2.78623	0.101469
$755$	−37.7421	−1.37358
$756$	5.60721	0.203932
$757$	−34.1041	−1.23954	−0.619768	−	0.784785i	$-0.712773\pi$
$757$	−34.1041	−1.23954	−0.619768	+	0.784785i	$0.712773\pi$
$758$	−8.42862	−0.306141
$759$	10.2122	0.370680
$760$	−22.4827	−0.815532
$761$	44.9328	1.62881	0.814406	−	0.580296i	$-0.197063\pi$
$761$	44.9328	1.62881	0.814406	+	0.580296i	$0.197063\pi$
$762$	−9.01349	−0.326524
$763$	14.9452	0.541054
$764$	4.94052	0.178742
$765$	12.6454	0.457197
$766$	−22.2967	−0.805611
$767$	−3.33064	−0.120263
$768$	1.52105	0.0548862
$769$	−27.4737	−0.990728	−0.495364	−	0.868686i	$-0.664965\pi$
$769$	−27.4737	−0.990728	−0.495364	+	0.868686i	$0.664965\pi$
$770$	4.11276	0.148213
$771$	−16.2629	−0.585695
$772$	0.189080	0.00680512
$773$	32.8340	1.18096	0.590479	−	0.807053i	$-0.298939\pi$
$773$	32.8340	1.18096	0.590479	+	0.807053i	$0.298939\pi$
$774$	−6.62242	−0.238038
$775$	−5.49095	−0.197241
$776$	−9.65031	−0.346426
$777$	−0.943351	−0.0338425
$778$	−6.43268	−0.230623
$779$	42.9206	1.53779
$780$	−6.55163	−0.234586
$781$	−9.58482	−0.342972
$782$	30.0743	1.07545
$783$	11.5764	0.413705
$784$	1.00000	0.0357143
$785$	33.3949	1.19191
$786$	10.8573	0.387267
$787$	31.2988	1.11568	0.557841	−	0.829948i	$-0.311630\pi$
$787$	31.2988	1.11568	0.557841	+	0.829948i	$0.311630\pi$
$788$	−2.30403	−0.0820776
$789$	19.6375	0.699112
$790$	−9.31769	−0.331509
$791$	−5.90534	−0.209970
$792$	−0.884507	−0.0314296
$793$	−13.4828	−0.478789
$794$	−18.5004	−0.656555
$795$	−56.1640	−1.99193
$796$	22.6764	0.803744
$797$	46.1067	1.63318	0.816591	−	0.577217i	$-0.195861\pi$
$797$	46.1067	1.63318	0.816591	+	0.577217i	$0.195861\pi$
$798$	−10.7146	−0.379294
$799$	65.0915	2.30277
$800$	−5.18656	−0.183373
$801$	−9.95497	−0.351742
$802$	9.81363	0.346531
$803$	−7.52682	−0.265616
$804$	23.8826	0.842274
$805$	−16.6292	−0.586101
$806$	1.42876	0.0503261
$807$	19.5983	0.689894
$808$	17.2580	0.607136
$809$	−35.4448	−1.24617	−0.623087	−	0.782153i	$-0.714122\pi$
$809$	−35.4448	−1.24617	−0.623087	+	0.782153i	$0.714122\pi$
$810$	−20.6487	−0.725521
$811$	0.677435	0.0237880	0.0118940	−	0.999929i	$-0.496214\pi$
$811$	0.677435	0.0237880	0.0118940	+	0.999929i	$0.496214\pi$
$812$	2.06455	0.0724515
$813$	−10.2621	−0.359908
$814$	0.799188	0.0280115
$815$	−6.86908	−0.240613
$816$	8.77974	0.307352
$817$	67.9625	2.37771
$818$	21.6181	0.755860
$819$	0.926348	0.0323692
$820$	19.4467	0.679108
$821$	−52.8303	−1.84379	−0.921896	−	0.387438i	$-0.873360\pi$
$821$	−52.8303	−1.84379	−0.921896	+	0.387438i	$0.873360\pi$
$822$	−12.9506	−0.451704
$823$	−12.5107	−0.436097	−0.218048	−	0.975938i	$-0.569969\pi$
$823$	−12.5107	−0.436097	−0.218048	+	0.975938i	$0.569969\pi$
$824$	−8.12280	−0.282971
$825$	−10.1658	−0.353928
$826$	−2.46795	−0.0858709
$827$	−44.5300	−1.54846	−0.774229	−	0.632905i	$-0.781862\pi$
$827$	−44.5300	−1.54846	−0.774229	+	0.632905i	$0.781862\pi$
$828$	3.57634	0.124286
$829$	10.3978	0.361130	0.180565	−	0.983563i	$-0.442207\pi$
$829$	10.3978	0.361130	0.180565	+	0.983563i	$0.442207\pi$
$830$	−7.39941	−0.256837
$831$	10.2031	0.353943
$832$	1.34956	0.0467876
$833$	5.77216	0.199993
$834$	12.3293	0.426928
$835$	−73.0960	−2.52959
$836$	9.07723	0.313942
$837$	5.93629	0.205188
$838$	−13.3692	−0.461830
$839$	25.4430	0.878391	0.439195	−	0.898392i	$-0.355264\pi$
$839$	25.4430	0.878391	0.439195	+	0.898392i	$0.355264\pi$
$840$	−4.85464	−0.167501
$841$	−24.7376	−0.853022
$842$	−8.21394	−0.283071
$843$	36.1358	1.24458
$844$	12.5303	0.431310
$845$	35.6783	1.22737
$846$	7.74048	0.266123
$847$	9.33950	0.320909
$848$	11.5691	0.397285
$849$	0.422429	0.0144977
$850$	−29.9376	−1.02685
$851$	−3.23137	−0.110770
$852$	11.3138	0.387604
$853$	20.1321	0.689309	0.344655	−	0.938730i	$-0.387996\pi$
$853$	20.1321	0.689309	0.344655	+	0.938730i	$0.387996\pi$
$854$	−9.99054	−0.341869
$855$	−15.4323	−0.527772
$856$	7.61685	0.260339
$857$	−9.58377	−0.327375	−0.163688	−	0.986512i	$-0.552339\pi$
$857$	−9.58377	−0.327375	−0.163688	+	0.986512i	$0.552339\pi$
$858$	2.64518	0.0903049
$859$	38.3394	1.30812	0.654061	−	0.756442i	$-0.273064\pi$
$859$	38.3394	1.30812	0.654061	+	0.756442i	$0.273064\pi$
$860$	30.7928	1.05003
$861$	9.26778	0.315845
$862$	−1.00000	−0.0340601
$863$	−20.0896	−0.683856	−0.341928	−	0.939726i	$-0.611080\pi$
$863$	−20.0896	−0.683856	−0.341928	+	0.939726i	$0.611080\pi$
$864$	5.60721	0.190761
$865$	−9.74355	−0.331291
$866$	7.69393	0.261450
$867$	24.8202	0.842938
$868$	1.05869	0.0359342
$869$	3.76196	0.127616
$870$	−10.0226	−0.339800
$871$	21.1900	0.717994
$872$	14.9452	0.506110
$873$	−6.62404	−0.224190
$874$	−36.7021	−1.24147
$875$	0.595431	0.0201293
$876$	8.88455	0.300181
$877$	3.62986	0.122572	0.0612859	−	0.998120i	$-0.480480\pi$
$877$	3.62986	0.122572	0.0612859	+	0.998120i	$0.480480\pi$
$878$	13.8335	0.466857
$879$	3.54844	0.119686
$880$	4.11276	0.138641
$881$	−12.2916	−0.414115	−0.207057	−	0.978329i	$-0.566389\pi$
$881$	−12.2916	−0.414115	−0.207057	+	0.978329i	$0.566389\pi$
$882$	0.686407	0.0231125
$883$	−15.3722	−0.517316	−0.258658	−	0.965969i	$-0.583280\pi$
$883$	−15.3722	−0.517316	−0.258658	+	0.965969i	$0.583280\pi$
$884$	7.78987	0.262002
$885$	11.9810	0.402737
$886$	16.9069	0.567999
$887$	42.0265	1.41111	0.705556	−	0.708654i	$-0.250697\pi$
$887$	42.0265	1.41111	0.705556	+	0.708654i	$0.250697\pi$
$888$	−0.943351	−0.0316568
$889$	−5.92583	−0.198746
$890$	46.2884	1.55159
$891$	8.33678	0.279293
$892$	−12.9727	−0.434359
$893$	−79.4365	−2.65824
$894$	20.1625	0.674336
$895$	−34.9068	−1.16681
$896$	1.00000	0.0334077
$897$	−10.6953	−0.357105
$898$	20.4743	0.683238
$899$	2.18571	0.0728977
$900$	−3.56009	−0.118670
$901$	66.7788	2.22472
$902$	−7.85148	−0.261426
$903$	14.6750	0.488354
$904$	−5.90534	−0.196409
$905$	23.0013	0.764589
$906$	−17.9869	−0.597575
$907$	−2.58213	−0.0857381	−0.0428690	−	0.999081i	$-0.513650\pi$
$907$	−2.58213	−0.0857381	−0.0428690	+	0.999081i	$0.513650\pi$
$908$	7.24109	0.240304
$909$	11.8460	0.392909
$910$	−4.30731	−0.142786
$911$	−27.9289	−0.925327	−0.462663	−	0.886534i	$-0.653106\pi$
$911$	−27.9289	−0.925327	−0.462663	+	0.886534i	$0.653106\pi$
$912$	−10.7146	−0.354797
$913$	2.98747	0.0988707
$914$	−8.32894	−0.275497
$915$	48.5005	1.60338
$916$	3.79306	0.125326
$917$	7.13803	0.235719
$918$	32.3657	1.06823
$919$	42.6513	1.40694	0.703469	−	0.710726i	$-0.251634\pi$
$919$	42.6513	1.40694	0.703469	+	0.710726i	$0.251634\pi$
$920$	−16.6292	−0.548248
$921$	18.1356	0.597590
$922$	30.3206	0.998554
$923$	10.0382	0.330412
$924$	1.96003	0.0644803
$925$	3.21669	0.105764
$926$	−12.7482	−0.418933
$927$	−5.57555	−0.183125
$928$	2.06455	0.0677722
$929$	23.5682	0.773248	0.386624	−	0.922237i	$-0.373641\pi$
$929$	23.5682	0.773248	0.386624	+	0.922237i	$0.373641\pi$
$930$	−5.13955	−0.168533
$931$	−7.04424	−0.230866
$932$	14.4348	0.472828
$933$	21.1157	0.691298
$934$	−19.7315	−0.645635
$935$	23.7395	0.776364
$936$	0.926348	0.0302786
$937$	−35.2042	−1.15007	−0.575036	−	0.818128i	$-0.695012\pi$
$937$	−35.2042	−1.15007	−0.575036	+	0.818128i	$0.695012\pi$
$938$	15.7014	0.512668
$939$	−0.750711	−0.0244985
$940$	−35.9915	−1.17391
$941$	4.75056	0.154864	0.0774319	−	0.996998i	$-0.475328\pi$
$941$	4.75056	0.154864	0.0774319	+	0.996998i	$0.475328\pi$
$942$	15.9151	0.518542
$943$	31.7460	1.03379
$944$	−2.46795	−0.0803248
$945$	−17.8962	−0.582163
$946$	−12.4324	−0.404212
$947$	2.56404	0.0833202	0.0416601	−	0.999132i	$-0.486735\pi$
$947$	2.56404	0.0833202	0.0416601	+	0.999132i	$0.486735\pi$
$948$	−4.44056	−0.144223
$949$	7.88287	0.255889
$950$	36.5354	1.18536
$951$	8.49263	0.275392
$952$	5.77216	0.187077
$953$	45.1337	1.46202	0.731012	−	0.682365i	$-0.239048\pi$
$953$	45.1337	1.46202	0.731012	+	0.682365i	$0.239048\pi$
$954$	7.94113	0.257104
$955$	−15.7684	−0.510252
$956$	18.6684	0.603779
$957$	4.04658	0.130807
$958$	30.1114	0.972856
$959$	−8.51425	−0.274939
$960$	−4.85464	−0.156683
$961$	−29.8792	−0.963844
$962$	−0.836993	−0.0269857
$963$	5.22826	0.168478
$964$	−28.5089	−0.918209
$965$	−0.603474	−0.0194265
$966$	−7.92502	−0.254983
$967$	−2.08878	−0.0671706	−0.0335853	−	0.999436i	$-0.510693\pi$
$967$	−2.08878	−0.0671706	−0.0335853	+	0.999436i	$0.510693\pi$
$968$	9.33950	0.300183
$969$	−61.8466	−1.98680
$970$	30.8003	0.988938
$971$	−39.2254	−1.25880	−0.629401	−	0.777081i	$-0.716700\pi$
$971$	−39.2254	−1.25880	−0.629401	+	0.777081i	$0.716700\pi$
$972$	6.98101	0.223916
$973$	8.10576	0.259859
$974$	1.44157	0.0461907
$975$	10.6467	0.340967
$976$	−9.99054	−0.319789
$977$	−49.1802	−1.57341	−0.786706	−	0.617328i	$-0.788215\pi$
$977$	−49.1802	−1.57341	−0.786706	+	0.617328i	$0.788215\pi$
$978$	−3.27362	−0.104679
$979$	−18.6886	−0.597291
$980$	−3.19164	−0.101953
$981$	10.2585	0.327530
$982$	8.76940	0.279843
$983$	−25.9768	−0.828530	−0.414265	−	0.910156i	$-0.635961\pi$
$983$	−25.9768	−0.828530	−0.414265	+	0.910156i	$0.635961\pi$
$984$	9.26778	0.295446
$985$	7.35362	0.234306
$986$	11.9169	0.379512
$987$	−17.1526	−0.545973
$988$	−9.50662	−0.302446
$989$	50.2681	1.59843
$990$	2.82303	0.0897217
$991$	30.5926	0.971805	0.485903	−	0.874013i	$-0.338491\pi$
$991$	30.5926	0.971805	0.485903	+	0.874013i	$0.338491\pi$
$992$	1.05869	0.0336134
$993$	30.6727	0.973370
$994$	7.43814	0.235924
$995$	−72.3750	−2.29444
$996$	−3.52636	−0.111737
$997$	46.7080	1.47926	0.739628	−	0.673016i	$-0.235001\pi$
$997$	46.7080	1.47926	0.739628	+	0.673016i	$0.235001\pi$
$998$	9.82796	0.311099
$999$	−3.47757	−0.110026

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.n.1.17	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.n.1.17	✓	24	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.52105 q^{3} +1.00000 q^{4} -3.19164 q^{5} -1.52105 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.686407 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.52105 q^{3} +1.00000 q^{4} -3.19164 q^{5} -1.52105 q^{6} -1.00000 q^{7} -1.00000 q^{8} -0.686407 q^{9} +3.19164 q^{10} -1.28860 q^{11} +1.52105 q^{12} +1.34956 q^{13} +1.00000 q^{14} -4.85464 q^{15} +1.00000 q^{16} +5.77216 q^{17} +0.686407 q^{18} -7.04424 q^{19} -3.19164 q^{20} -1.52105 q^{21} +1.28860 q^{22} -5.21023 q^{23} -1.52105 q^{24} +5.18656 q^{25} -1.34956 q^{26} -5.60721 q^{27} -1.00000 q^{28} -2.06455 q^{29} +4.85464 q^{30} -1.05869 q^{31} -1.00000 q^{32} -1.96003 q^{33} -5.77216 q^{34} +3.19164 q^{35} -0.686407 q^{36} +0.620197 q^{37} +7.04424 q^{38} +2.05275 q^{39} +3.19164 q^{40} -6.09301 q^{41} +1.52105 q^{42} -9.64795 q^{43} -1.28860 q^{44} +2.19076 q^{45} +5.21023 q^{46} +11.2768 q^{47} +1.52105 q^{48} +1.00000 q^{49} -5.18656 q^{50} +8.77974 q^{51} +1.34956 q^{52} +11.5691 q^{53} +5.60721 q^{54} +4.11276 q^{55} +1.00000 q^{56} -10.7146 q^{57} +2.06455 q^{58} -2.46795 q^{59} -4.85464 q^{60} -9.99054 q^{61} +1.05869 q^{62} +0.686407 q^{63} +1.00000 q^{64} -4.30731 q^{65} +1.96003 q^{66} +15.7014 q^{67} +5.77216 q^{68} -7.92502 q^{69} -3.19164 q^{70} +7.43814 q^{71} +0.686407 q^{72} +5.84106 q^{73} -0.620197 q^{74} +7.88902 q^{75} -7.04424 q^{76} +1.28860 q^{77} -2.05275 q^{78} -2.91941 q^{79} -3.19164 q^{80} -6.46962 q^{81} +6.09301 q^{82} -2.31837 q^{83} -1.52105 q^{84} -18.4226 q^{85} +9.64795 q^{86} -3.14028 q^{87} +1.28860 q^{88} +14.5030 q^{89} -2.19076 q^{90} -1.34956 q^{91} -5.21023 q^{92} -1.61032 q^{93} -11.2768 q^{94} +22.4827 q^{95} -1.52105 q^{96} +9.65031 q^{97} -1.00000 q^{98} +0.884507 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9	\( 24 q - 24 q^{2} + 7 q^{3} + 24 q^{4} + 8 q^{5} - 7 q^{6} - 24 q^{7} - 24 q^{8} + 19 q^{9} - 8 q^{10} + 15 q^{11} + 7 q^{12} - 7 q^{13} + 24 q^{14} + 13 q^{15} + 24 q^{16} - 5 q^{17} - 19 q^{18} + 6 q^{19} + 8 q^{20} - 7 q^{21} - 15 q^{22} + 3 q^{23} - 7 q^{24} + 12 q^{25} + 7 q^{26} + 22 q^{27} - 24 q^{28} + 5 q^{29} - 13 q^{30} + 13 q^{31} - 24 q^{32} - 8 q^{33} + 5 q^{34} - 8 q^{35} + 19 q^{36} + 2 q^{37} - 6 q^{38} + 7 q^{39} - 8 q^{40} + 25 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 41 q^{45} - 3 q^{46} + 35 q^{47} + 7 q^{48} + 24 q^{49} - 12 q^{50} + 31 q^{51} - 7 q^{52} + 2 q^{53} - 22 q^{54} + 14 q^{55} + 24 q^{56} - 13 q^{57} - 5 q^{58} + 35 q^{59} + 13 q^{60} - 7 q^{61} - 13 q^{62} - 19 q^{63} + 24 q^{64} - 4 q^{65} + 8 q^{66} + 10 q^{67} - 5 q^{68} + 6 q^{69} + 8 q^{70} + 58 q^{71} - 19 q^{72} + 9 q^{73} - 2 q^{74} + 7 q^{75} + 6 q^{76} - 15 q^{77} - 7 q^{78} + 31 q^{79} + 8 q^{80} + 16 q^{81} - 25 q^{82} - q^{83} - 7 q^{84} - 4 q^{85} + 15 q^{86} + 30 q^{87} - 15 q^{88} + 45 q^{89} - 41 q^{90} + 7 q^{91} + 3 q^{92} + 25 q^{93} - 35 q^{94} - 10 q^{95} - 7 q^{96} - 9 q^{97} - 24 q^{98} + 64 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 + 7 * q^3 + 24 * q^4 + 8 * q^5 - 7 * q^6 - 24 * q^7 - 24 * q^8 + 19 * q^9 - 8 * q^10 + 15 * q^11 + 7 * q^12 - 7 * q^13 + 24 * q^14 + 13 * q^15 + 24 * q^16 - 5 * q^17 - 19 * q^18 + 6 * q^19 + 8 * q^20 - 7 * q^21 - 15 * q^22 + 3 * q^23 - 7 * q^24 + 12 * q^25 + 7 * q^26 + 22 * q^27 - 24 * q^28 + 5 * q^29 - 13 * q^30 + 13 * q^31 - 24 * q^32 - 8 * q^33 + 5 * q^34 - 8 * q^35 + 19 * q^36 + 2 * q^37 - 6 * q^38 + 7 * q^39 - 8 * q^40 + 25 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 41 * q^45 - 3 * q^46 + 35 * q^47 + 7 * q^48 + 24 * q^49 - 12 * q^50 + 31 * q^51 - 7 * q^52 + 2 * q^53 - 22 * q^54 + 14 * q^55 + 24 * q^56 - 13 * q^57 - 5 * q^58 + 35 * q^59 + 13 * q^60 - 7 * q^61 - 13 * q^62 - 19 * q^63 + 24 * q^64 - 4 * q^65 + 8 * q^66 + 10 * q^67 - 5 * q^68 + 6 * q^69 + 8 * q^70 + 58 * q^71 - 19 * q^72 + 9 * q^73 - 2 * q^74 + 7 * q^75 + 6 * q^76 - 15 * q^77 - 7 * q^78 + 31 * q^79 + 8 * q^80 + 16 * q^81 - 25 * q^82 - q^83 - 7 * q^84 - 4 * q^85 + 15 * q^86 + 30 * q^87 - 15 * q^88 + 45 * q^89 - 41 * q^90 + 7 * q^91 + 3 * q^92 + 25 * q^93 - 35 * q^94 - 10 * q^95 - 7 * q^96 - 9 * q^97 - 24 * q^98 + 64 * q^99

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