LMFDB - Embedded newform 6035.2.a.g.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$58$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17363 q^{2} +0.623249 q^{3} +2.72466 q^{4} +1.00000 q^{5} -1.35471 q^{6} -4.14588 q^{7} -1.57514 q^{8} -2.61156 q^{9} +O(q^{10})$	\(q-2.17363 q^{2} +0.623249 q^{3} +2.72466 q^{4} +1.00000 q^{5} -1.35471 q^{6} -4.14588 q^{7} -1.57514 q^{8} -2.61156 q^{9} -2.17363 q^{10} -0.484054 q^{11} +1.69814 q^{12} +6.08377 q^{13} +9.01161 q^{14} +0.623249 q^{15} -2.02554 q^{16} +1.00000 q^{17} +5.67656 q^{18} -5.61637 q^{19} +2.72466 q^{20} -2.58392 q^{21} +1.05215 q^{22} -9.11107 q^{23} -0.981706 q^{24} +1.00000 q^{25} -13.2239 q^{26} -3.49740 q^{27} -11.2961 q^{28} -10.0176 q^{29} -1.35471 q^{30} +1.89987 q^{31} +7.55307 q^{32} -0.301686 q^{33} -2.17363 q^{34} -4.14588 q^{35} -7.11562 q^{36} +0.815587 q^{37} +12.2079 q^{38} +3.79170 q^{39} -1.57514 q^{40} +12.5244 q^{41} +5.61648 q^{42} -9.48333 q^{43} -1.31888 q^{44} -2.61156 q^{45} +19.8041 q^{46} +7.46382 q^{47} -1.26242 q^{48} +10.1884 q^{49} -2.17363 q^{50} +0.623249 q^{51} +16.5762 q^{52} -13.5062 q^{53} +7.60205 q^{54} -0.484054 q^{55} +6.53036 q^{56} -3.50039 q^{57} +21.7745 q^{58} +3.09384 q^{59} +1.69814 q^{60} +6.03286 q^{61} -4.12961 q^{62} +10.8272 q^{63} -12.3665 q^{64} +6.08377 q^{65} +0.655753 q^{66} -2.09075 q^{67} +2.72466 q^{68} -5.67846 q^{69} +9.01161 q^{70} +1.00000 q^{71} +4.11358 q^{72} +1.70923 q^{73} -1.77278 q^{74} +0.623249 q^{75} -15.3027 q^{76} +2.00683 q^{77} -8.24175 q^{78} -11.0615 q^{79} -2.02554 q^{80} +5.65493 q^{81} -27.2235 q^{82} +10.6439 q^{83} -7.04030 q^{84} +1.00000 q^{85} +20.6132 q^{86} -6.24345 q^{87} +0.762454 q^{88} -8.57626 q^{89} +5.67656 q^{90} -25.2226 q^{91} -24.8246 q^{92} +1.18409 q^{93} -16.2236 q^{94} -5.61637 q^{95} +4.70744 q^{96} +5.45446 q^{97} -22.1457 q^{98} +1.26414 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) $ 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * 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 $

$2$	−2.17363	−1.53699	−0.768494	−	0.639857i	$-0.778993\pi$
$2$	−2.17363	−1.53699	−0.768494	+	0.639857i	$0.778993\pi$
$3$	0.623249	0.359833	0.179916	−	0.983682i	$-0.442417\pi$
$3$	0.623249	0.359833	0.179916	+	0.983682i	$0.442417\pi$
$4$	2.72466	1.36233
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.35471	−0.553059
$7$	−4.14588	−1.56700	−0.783498	−	0.621394i	$-0.786567\pi$
$7$	−4.14588	−1.56700	−0.783498	+	0.621394i	$0.786567\pi$
$8$	−1.57514	−0.556897
$9$	−2.61156	−0.870520
$10$	−2.17363	−0.687362
$11$	−0.484054	−0.145948	−0.0729739	−	0.997334i	$-0.523249\pi$
$11$	−0.484054	−0.145948	−0.0729739	+	0.997334i	$0.523249\pi$
$12$	1.69814	0.490211
$13$	6.08377	1.68733	0.843667	−	0.536867i	$-0.180392\pi$
$13$	6.08377	1.68733	0.843667	+	0.536867i	$0.180392\pi$
$14$	9.01161	2.40845
$15$	0.623249	0.160922
$16$	−2.02554	−0.506386
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.67656	1.33798
$19$	−5.61637	−1.28848	−0.644242	−	0.764822i	$-0.722827\pi$
$19$	−5.61637	−1.28848	−0.644242	+	0.764822i	$0.722827\pi$
$20$	2.72466	0.609253
$21$	−2.58392	−0.563857
$22$	1.05215	0.224320
$23$	−9.11107	−1.89979	−0.949895	−	0.312570i	$-0.898810\pi$
$23$	−9.11107	−1.89979	−0.949895	+	0.312570i	$0.898810\pi$
$24$	−0.981706	−0.200390
$25$	1.00000	0.200000
$26$	−13.2239	−2.59341
$27$	−3.49740	−0.673075
$28$	−11.2961	−2.13477
$29$	−10.0176	−1.86022	−0.930109	−	0.367283i	$-0.880288\pi$
$29$	−10.0176	−1.86022	−0.930109	+	0.367283i	$0.880288\pi$
$30$	−1.35471	−0.247335
$31$	1.89987	0.341227	0.170613	−	0.985338i	$-0.445425\pi$
$31$	1.89987	0.341227	0.170613	+	0.985338i	$0.445425\pi$
$32$	7.55307	1.33521
$33$	−0.301686	−0.0525168
$34$	−2.17363	−0.372774
$35$	−4.14588	−0.700782
$36$	−7.11562	−1.18594
$37$	0.815587	0.134082	0.0670408	−	0.997750i	$-0.478644\pi$
$37$	0.815587	0.134082	0.0670408	+	0.997750i	$0.478644\pi$
$38$	12.2079	1.98038
$39$	3.79170	0.607158
$40$	−1.57514	−0.249052
$41$	12.5244	1.95599	0.977994	−	0.208632i	$-0.0669010\pi$
$41$	12.5244	1.95599	0.977994	+	0.208632i	$0.0669010\pi$
$42$	5.61648	0.866641
$43$	−9.48333	−1.44619	−0.723097	−	0.690746i	$-0.757282\pi$
$43$	−9.48333	−1.44619	−0.723097	+	0.690746i	$0.757282\pi$
$44$	−1.31888	−0.198829
$45$	−2.61156	−0.389308
$46$	19.8041	2.91995
$47$	7.46382	1.08871	0.544355	−	0.838855i	$-0.316774\pi$
$47$	7.46382	1.08871	0.544355	+	0.838855i	$0.316774\pi$
$48$	−1.26242	−0.182214
$49$	10.1884	1.45548
$50$	−2.17363	−0.307397
$51$	0.623249	0.0872723
$52$	16.5762	2.29871
$53$	−13.5062	−1.85523	−0.927613	−	0.373543i	$-0.878143\pi$
$53$	−13.5062	−1.85523	−0.927613	+	0.373543i	$0.878143\pi$
$54$	7.60205	1.03451
$55$	−0.484054	−0.0652698
$56$	6.53036	0.872656
$57$	−3.50039	−0.463639
$58$	21.7745	2.85913
$59$	3.09384	0.402783	0.201392	−	0.979511i	$-0.435454\pi$
$59$	3.09384	0.402783	0.201392	+	0.979511i	$0.435454\pi$
$60$	1.69814	0.219229
$61$	6.03286	0.772428	0.386214	−	0.922409i	$-0.373783\pi$
$61$	6.03286	0.772428	0.386214	+	0.922409i	$0.373783\pi$
$62$	−4.12961	−0.524461
$63$	10.8272	1.36410
$64$	−12.3665	−1.54581
$65$	6.08377	0.754599
$66$	0.655753	0.0807177
$67$	−2.09075	−0.255426	−0.127713	−	0.991811i	$-0.540764\pi$
$67$	−2.09075	−0.255426	−0.127713	+	0.991811i	$0.540764\pi$
$68$	2.72466	0.330414
$69$	−5.67846	−0.683607
$70$	9.01161	1.07709
$71$	1.00000	0.118678
$71$	1.00000	0.118678
$72$	4.11358	0.484790
$73$	1.70923	0.200051	0.100025	−	0.994985i	$-0.468108\pi$
$73$	1.70923	0.200051	0.100025	+	0.994985i	$0.468108\pi$
$74$	−1.77278	−0.206082
$75$	0.623249	0.0719666
$76$	−15.3027	−1.75534
$77$	2.00683	0.228700
$78$	−8.24175	−0.933195
$79$	−11.0615	−1.24452	−0.622260	−	0.782811i	$-0.713785\pi$
$79$	−11.0615	−1.24452	−0.622260	+	0.782811i	$0.713785\pi$
$80$	−2.02554	−0.226463
$81$	5.65493	0.628326
$82$	−27.2235	−3.00633
$83$	10.6439	1.16832	0.584161	−	0.811638i	$-0.301424\pi$
$83$	10.6439	1.16832	0.584161	+	0.811638i	$0.301424\pi$
$84$	−7.04030	−0.768160
$85$	1.00000	0.108465
$86$	20.6132	2.22278
$87$	−6.24345	−0.669368
$88$	0.762454	0.0812779
$89$	−8.57626	−0.909082	−0.454541	−	0.890726i	$-0.650197\pi$
$89$	−8.57626	−0.909082	−0.454541	+	0.890726i	$0.650197\pi$
$90$	5.67656	0.598362
$91$	−25.2226	−2.64405
$92$	−24.8246	−2.58814
$93$	1.18409	0.122785
$94$	−16.2236	−1.67333
$95$	−5.61637	−0.576227
$96$	4.70744	0.480451
$97$	5.45446	0.553817	0.276908	−	0.960896i	$-0.410690\pi$
$97$	5.45446	0.553817	0.276908	+	0.960896i	$0.410690\pi$
$98$	−22.1457	−2.23705
$99$	1.26414	0.127050
$100$	2.72466	0.272466
$101$	3.91207	0.389266	0.194633	−	0.980876i	$-0.437648\pi$
$101$	3.91207	0.389266	0.194633	+	0.980876i	$0.437648\pi$
$102$	−1.35471	−0.134136
$103$	11.8778	1.17035	0.585176	−	0.810906i	$-0.301025\pi$
$103$	11.8778	1.17035	0.585176	+	0.810906i	$0.301025\pi$
$104$	−9.58281	−0.939672
$105$	−2.58392	−0.252165
$106$	29.3576	2.85146
$107$	−5.70234	−0.551266	−0.275633	−	0.961263i	$-0.588887\pi$
$107$	−5.70234	−0.551266	−0.275633	+	0.961263i	$0.588887\pi$
$108$	−9.52923	−0.916950
$109$	13.8141	1.32315	0.661575	−	0.749879i	$-0.269888\pi$
$109$	13.8141	1.32315	0.661575	+	0.749879i	$0.269888\pi$
$110$	1.05215	0.100319
$111$	0.508314	0.0482470
$112$	8.39767	0.793506
$113$	2.07251	0.194965	0.0974826	−	0.995237i	$-0.468921\pi$
$113$	2.07251	0.194965	0.0974826	+	0.995237i	$0.468921\pi$
$114$	7.60856	0.712607
$115$	−9.11107	−0.849612
$116$	−27.2945	−2.53423
$117$	−15.8881	−1.46886
$118$	−6.72485	−0.619073
$119$	−4.14588	−0.380053
$120$	−0.981706	−0.0896171
$121$	−10.7657	−0.978699
$122$	−13.1132	−1.18721
$123$	7.80584	0.703829
$124$	5.17650	0.464863
$125$	1.00000	0.0894427
$126$	−23.5344	−2.09661
$127$	−22.0329	−1.95510	−0.977550	−	0.210702i	$-0.932425\pi$
$127$	−22.0329	−1.95510	−0.977550	+	0.210702i	$0.932425\pi$
$128$	11.7740	1.04068
$129$	−5.91047	−0.520388
$130$	−13.2239	−1.15981
$131$	7.64169	0.667657	0.333829	−	0.942634i	$-0.391659\pi$
$131$	7.64169	0.667657	0.333829	+	0.942634i	$0.391659\pi$
$132$	−0.821992	−0.0715452
$133$	23.2848	2.01905
$134$	4.54452	0.392586
$135$	−3.49740	−0.301008
$136$	−1.57514	−0.135067
$137$	−15.5724	−1.33044	−0.665218	−	0.746649i	$-0.731661\pi$
$137$	−15.5724	−1.33044	−0.665218	+	0.746649i	$0.731661\pi$
$138$	12.3429	1.05070
$139$	−3.54150	−0.300386	−0.150193	−	0.988657i	$-0.547990\pi$
$139$	−3.54150	−0.300386	−0.150193	+	0.988657i	$0.547990\pi$
$140$	−11.2961	−0.954697
$141$	4.65182	0.391754
$142$	−2.17363	−0.182407
$143$	−2.94487	−0.246263
$144$	5.28983	0.440819
$145$	−10.0176	−0.831915
$146$	−3.71524	−0.307475
$147$	6.34988	0.523729
$148$	2.22220	0.182664
$149$	14.5350	1.19076	0.595378	−	0.803446i	$-0.297002\pi$
$149$	14.5350	1.19076	0.595378	+	0.803446i	$0.297002\pi$
$150$	−1.35471	−0.110612
$151$	10.8442	0.882492	0.441246	−	0.897386i	$-0.354537\pi$
$151$	10.8442	0.882492	0.441246	+	0.897386i	$0.354537\pi$
$152$	8.84658	0.717553
$153$	−2.61156	−0.211132
$154$	−4.36211	−0.351509
$155$	1.89987	0.152601
$156$	10.3311	0.827150
$157$	9.53386	0.760885	0.380442	−	0.924805i	$-0.375772\pi$
$157$	9.53386	0.760885	0.380442	+	0.924805i	$0.375772\pi$
$158$	24.0437	1.91281
$159$	−8.41775	−0.667571
$160$	7.55307	0.597123
$161$	37.7734	2.97696
$162$	−12.2917	−0.965729
$163$	4.33471	0.339520	0.169760	−	0.985485i	$-0.445701\pi$
$163$	4.33471	0.339520	0.169760	+	0.985485i	$0.445701\pi$
$164$	34.1248	2.66470
$165$	−0.301686	−0.0234862
$166$	−23.1359	−1.79570
$167$	−3.03076	−0.234527	−0.117264	−	0.993101i	$-0.537412\pi$
$167$	−3.03076	−0.234527	−0.117264	+	0.993101i	$0.537412\pi$
$168$	4.07004	0.314011
$169$	24.0123	1.84710
$170$	−2.17363	−0.166710
$171$	14.6675	1.12165
$172$	−25.8389	−1.97019
$173$	11.1387	0.846857	0.423428	−	0.905930i	$-0.360827\pi$
$173$	11.1387	0.846857	0.423428	+	0.905930i	$0.360827\pi$
$174$	13.5709	1.02881
$175$	−4.14588	−0.313399
$176$	0.980473	0.0739059
$177$	1.92823	0.144935
$178$	18.6416	1.39725
$179$	−1.13472	−0.0848126	−0.0424063	−	0.999100i	$-0.513502\pi$
$179$	−1.13472	−0.0848126	−0.0424063	+	0.999100i	$0.513502\pi$
$180$	−7.11562	−0.530367
$181$	−3.22047	−0.239376	−0.119688	−	0.992812i	$-0.538189\pi$
$181$	−3.22047	−0.239376	−0.119688	+	0.992812i	$0.538189\pi$
$182$	54.8246	4.06387
$183$	3.75997	0.277945
$184$	14.3512	1.05799
$185$	0.815587	0.0599631
$186$	−2.57378	−0.188718
$187$	−0.484054	−0.0353975
$188$	20.3364	1.48318
$189$	14.4998	1.05471
$190$	12.2079	0.885654
$191$	22.3406	1.61651	0.808253	−	0.588835i	$-0.200413\pi$
$191$	22.3406	1.61651	0.808253	+	0.588835i	$0.200413\pi$
$192$	−7.70739	−0.556233
$193$	−8.26759	−0.595114	−0.297557	−	0.954704i	$-0.596172\pi$
$193$	−8.26759	−0.595114	−0.297557	+	0.954704i	$0.596172\pi$
$194$	−11.8560	−0.851210
$195$	3.79170	0.271529
$196$	27.7598	1.98284
$197$	−17.9229	−1.27695	−0.638476	−	0.769642i	$-0.720435\pi$
$197$	−17.9229	−1.27695	−0.638476	+	0.769642i	$0.720435\pi$
$198$	−2.74776	−0.195275
$199$	22.5467	1.59829	0.799147	−	0.601136i	$-0.205285\pi$
$199$	22.5467	1.59829	0.799147	+	0.601136i	$0.205285\pi$
$200$	−1.57514	−0.111379
$201$	−1.30306	−0.0919107
$202$	−8.50339	−0.598297
$203$	41.5317	2.91496
$204$	1.69814	0.118894
$205$	12.5244	0.874745
$206$	−25.8179	−1.79882
$207$	23.7941	1.65381
$208$	−12.3229	−0.854443
$209$	2.71862	0.188051
$210$	5.61648	0.387574
$211$	0.648343	0.0446338	0.0223169	−	0.999751i	$-0.492896\pi$
$211$	0.648343	0.0446338	0.0223169	+	0.999751i	$0.492896\pi$
$212$	−36.7999	−2.52743
$213$	0.623249	0.0427043
$214$	12.3948	0.847289
$215$	−9.48333	−0.646758
$216$	5.50891	0.374834
$217$	−7.87664	−0.534701
$218$	−30.0267	−2.03366
$219$	1.06528	0.0719848
$220$	−1.31888	−0.0889191
$221$	6.08377	0.409239
$222$	−1.10489	−0.0741550
$223$	−25.9813	−1.73984	−0.869919	−	0.493195i	$-0.835829\pi$
$223$	−25.9813	−1.73984	−0.869919	+	0.493195i	$0.835829\pi$
$224$	−31.3142	−2.09226
$225$	−2.61156	−0.174104
$226$	−4.50486	−0.299659
$227$	−4.03960	−0.268117	−0.134059	−	0.990973i	$-0.542801\pi$
$227$	−4.03960	−0.268117	−0.134059	+	0.990973i	$0.542801\pi$
$228$	−9.53739	−0.631629
$229$	9.83525	0.649932	0.324966	−	0.945726i	$-0.394647\pi$
$229$	9.83525	0.649932	0.324966	+	0.945726i	$0.394647\pi$
$230$	19.8041	1.30584
$231$	1.25076	0.0822937
$232$	15.7791	1.03595
$233$	7.44200	0.487542	0.243771	−	0.969833i	$-0.421616\pi$
$233$	7.44200	0.487542	0.243771	+	0.969833i	$0.421616\pi$
$234$	34.5349	2.25762
$235$	7.46382	0.486886
$236$	8.42966	0.548724
$237$	−6.89409	−0.447819
$238$	9.01161	0.584136
$239$	−20.5881	−1.33173	−0.665866	−	0.746071i	$-0.731938\pi$
$239$	−20.5881	−1.33173	−0.665866	+	0.746071i	$0.731938\pi$
$240$	−1.26242	−0.0814888
$241$	13.4213	0.864540	0.432270	−	0.901744i	$-0.357713\pi$
$241$	13.4213	0.864540	0.432270	+	0.901744i	$0.357713\pi$
$242$	23.4006	1.50425
$243$	14.0166	0.899167
$244$	16.4375	1.05230
$245$	10.1884	0.650910
$246$	−16.9670	−1.08178
$247$	−34.1687	−2.17410
$248$	−2.99257	−0.190028
$249$	6.63381	0.420400
$250$	−2.17363	−0.137472
$251$	−14.9698	−0.944888	−0.472444	−	0.881361i	$-0.656628\pi$
$251$	−14.9698	−0.944888	−0.472444	+	0.881361i	$0.656628\pi$
$252$	29.5005	1.85836
$253$	4.41025	0.277270
$254$	47.8913	3.00496
$255$	0.623249	0.0390294
$256$	−0.859322	−0.0537076
$257$	2.59367	0.161788	0.0808942	−	0.996723i	$-0.474222\pi$
$257$	2.59367	0.161788	0.0808942	+	0.996723i	$0.474222\pi$
$258$	12.8472	0.799830
$259$	−3.38133	−0.210106
$260$	16.5762	1.02801
$261$	26.1615	1.61936
$262$	−16.6102	−1.02618
$263$	10.0671	0.620767	0.310383	−	0.950611i	$-0.399543\pi$
$263$	10.0671	0.620767	0.310383	+	0.950611i	$0.399543\pi$
$264$	0.475199	0.0292465
$265$	−13.5062	−0.829682
$266$	−50.6125	−3.10325
$267$	−5.34514	−0.327118
$268$	−5.69659	−0.347975
$269$	−0.194466	−0.0118568	−0.00592839	−	0.999982i	$-0.501887\pi$
$269$	−0.194466	−0.0118568	−0.00592839	+	0.999982i	$0.501887\pi$
$270$	7.60205	0.462646
$271$	20.8764	1.26815	0.634075	−	0.773271i	$-0.281381\pi$
$271$	20.8764	1.26815	0.634075	+	0.773271i	$0.281381\pi$
$272$	−2.02554	−0.122817
$273$	−15.7200	−0.951415
$274$	33.8485	2.04486
$275$	−0.484054	−0.0291896
$276$	−15.4719	−0.931298
$277$	−15.9225	−0.956691	−0.478345	−	0.878172i	$-0.658763\pi$
$277$	−15.9225	−0.956691	−0.478345	+	0.878172i	$0.658763\pi$
$278$	7.69791	0.461690
$279$	−4.96162	−0.297045
$280$	6.53036	0.390264
$281$	−13.4210	−0.800632	−0.400316	−	0.916377i	$-0.631100\pi$
$281$	−13.4210	−0.800632	−0.400316	+	0.916377i	$0.631100\pi$
$282$	−10.1113	−0.602121
$283$	−7.54518	−0.448514	−0.224257	−	0.974530i	$-0.571996\pi$
$283$	−7.54518	−0.448514	−0.224257	+	0.974530i	$0.571996\pi$
$284$	2.72466	0.161679
$285$	−3.50039	−0.207346
$286$	6.40106	0.378503
$287$	−51.9249	−3.06503
$288$	−19.7253	−1.16232
$289$	1.00000	0.0588235
$290$	21.7745	1.27864
$291$	3.39949	0.199282
$292$	4.65708	0.272535
$293$	4.10272	0.239684	0.119842	−	0.992793i	$-0.461761\pi$
$293$	4.10272	0.239684	0.119842	+	0.992793i	$0.461761\pi$
$294$	−13.8023	−0.804966
$295$	3.09384	0.180130
$296$	−1.28467	−0.0746697
$297$	1.69293	0.0982338
$298$	−31.5938	−1.83018
$299$	−55.4297	−3.20558
$300$	1.69814	0.0980423
$301$	39.3168	2.26618
$302$	−23.5714	−1.35638
$303$	2.43820	0.140071
$304$	11.3762	0.652470
$305$	6.03286	0.345440
$306$	5.67656	0.324508
$307$	8.59628	0.490616	0.245308	−	0.969445i	$-0.421111\pi$
$307$	8.59628	0.490616	0.245308	+	0.969445i	$0.421111\pi$
$308$	5.46794	0.311565
$309$	7.40281	0.421131
$310$	−4.12961	−0.234546
$311$	−13.1829	−0.747532	−0.373766	−	0.927523i	$-0.621934\pi$
$311$	−13.1829	−0.747532	−0.373766	+	0.927523i	$0.621934\pi$
$312$	−5.97248	−0.338125
$313$	8.33233	0.470971	0.235486	−	0.971878i	$-0.424332\pi$
$313$	8.33233	0.470971	0.235486	+	0.971878i	$0.424332\pi$
$314$	−20.7231	−1.16947
$315$	10.8272	0.610045
$316$	−30.1389	−1.69545
$317$	26.6788	1.49843	0.749214	−	0.662328i	$-0.230431\pi$
$317$	26.6788	1.49843	0.749214	+	0.662328i	$0.230431\pi$
$318$	18.2971	1.02605
$319$	4.84905	0.271495
$320$	−12.3665	−0.691307
$321$	−3.55398	−0.198364
$322$	−82.1054	−4.57556
$323$	−5.61637	−0.312503
$324$	15.4078	0.855987
$325$	6.08377	0.337467
$326$	−9.42204	−0.521838
$327$	8.60962	0.476113
$328$	−19.7278	−1.08928
$329$	−30.9441	−1.70601
$330$	0.655753	0.0360980
$331$	30.2118	1.66059	0.830296	−	0.557323i	$-0.188171\pi$
$331$	30.2118	1.66059	0.830296	+	0.557323i	$0.188171\pi$
$332$	29.0011	1.59164
$333$	−2.12995	−0.116721
$334$	6.58774	0.360465
$335$	−2.09075	−0.114230
$336$	5.23384	0.285529
$337$	−0.457732	−0.0249343	−0.0124671	−	0.999922i	$-0.503969\pi$
$337$	−0.457732	−0.0249343	−0.0124671	+	0.999922i	$0.503969\pi$
$338$	−52.1937	−2.83896
$339$	1.29169	0.0701549
$340$	2.72466	0.147765
$341$	−0.919639	−0.0498013
$342$	−31.8817	−1.72396
$343$	−13.2186	−0.713735
$344$	14.9376	0.805382
$345$	−5.67846	−0.305718
$346$	−24.2113	−1.30161
$347$	−13.1323	−0.704981	−0.352490	−	0.935815i	$-0.614665\pi$
$347$	−13.1323	−0.704981	−0.352490	+	0.935815i	$0.614665\pi$
$348$	−17.0113	−0.911900
$349$	8.96873	0.480085	0.240043	−	0.970762i	$-0.422839\pi$
$349$	8.96873	0.480085	0.240043	+	0.970762i	$0.422839\pi$
$350$	9.01161	0.481691
$351$	−21.2774	−1.13570
$352$	−3.65609	−0.194870
$353$	−23.7181	−1.26239	−0.631195	−	0.775624i	$-0.717435\pi$
$353$	−23.7181	−1.26239	−0.631195	+	0.775624i	$0.717435\pi$
$354$	−4.19126	−0.222763
$355$	1.00000	0.0530745
$356$	−23.3674	−1.23847
$357$	−2.58392	−0.136755
$358$	2.46645	0.130356
$359$	13.2611	0.699896	0.349948	−	0.936769i	$-0.386199\pi$
$359$	13.2611	0.699896	0.349948	+	0.936769i	$0.386199\pi$
$360$	4.11358	0.216805
$361$	12.5436	0.660189
$362$	7.00010	0.367917
$363$	−6.70971	−0.352168
$364$	−68.7230	−3.60207
$365$	1.70923	0.0894654
$366$	−8.17278	−0.427198
$367$	−1.50834	−0.0787349	−0.0393674	−	0.999225i	$-0.512534\pi$
$367$	−1.50834	−0.0787349	−0.0393674	+	0.999225i	$0.512534\pi$
$368$	18.4549	0.962027
$369$	−32.7083	−1.70273
$370$	−1.77278	−0.0921626
$371$	55.9953	2.90713
$372$	3.22625	0.167273
$373$	−3.93566	−0.203781	−0.101890	−	0.994796i	$-0.532489\pi$
$373$	−3.93566	−0.203781	−0.101890	+	0.994796i	$0.532489\pi$
$374$	1.05215	0.0544056
$375$	0.623249	0.0321844
$376$	−11.7566	−0.606300
$377$	−60.9447	−3.13881
$378$	−31.5172	−1.62107
$379$	−23.5172	−1.20800	−0.603999	−	0.796985i	$-0.706427\pi$
$379$	−23.5172	−1.20800	−0.603999	+	0.796985i	$0.706427\pi$
$380$	−15.3027	−0.785012
$381$	−13.7320	−0.703510
$382$	−48.5601	−2.48455
$383$	−14.9780	−0.765339	−0.382670	−	0.923885i	$-0.624995\pi$
$383$	−14.9780	−0.765339	−0.382670	+	0.923885i	$0.624995\pi$
$384$	7.33813	0.374472
$385$	2.00683	0.102278
$386$	17.9707	0.914683
$387$	24.7663	1.25894
$388$	14.8616	0.754482
$389$	14.6690	0.743746	0.371873	−	0.928284i	$-0.378716\pi$
$389$	14.6690	0.743746	0.371873	+	0.928284i	$0.378716\pi$
$390$	−8.24175	−0.417337
$391$	−9.11107	−0.460767
$392$	−16.0481	−0.810553
$393$	4.76267	0.240245
$394$	38.9577	1.96266
$395$	−11.0615	−0.556566
$396$	3.44434	0.173085
$397$	29.5303	1.48208	0.741041	−	0.671460i	$-0.234332\pi$
$397$	29.5303	1.48208	0.741041	+	0.671460i	$0.234332\pi$
$398$	−49.0082	−2.45656
$399$	14.5122	0.726520
$400$	−2.02554	−0.101277
$401$	31.3238	1.56424	0.782118	−	0.623130i	$-0.214139\pi$
$401$	31.3238	1.56424	0.782118	+	0.623130i	$0.214139\pi$
$402$	2.83237	0.141266
$403$	11.5584	0.575763
$404$	10.6591	0.530309
$405$	5.65493	0.280996
$406$	−90.2746	−4.48025
$407$	−0.394788	−0.0195689
$408$	−0.981706	−0.0486017
$409$	30.1893	1.49276	0.746382	−	0.665517i	$-0.231789\pi$
$409$	30.1893	1.49276	0.746382	+	0.665517i	$0.231789\pi$
$410$	−27.2235	−1.34447
$411$	−9.70546	−0.478735
$412$	32.3629	1.59441
$413$	−12.8267	−0.631160
$414$	−51.7196	−2.54188
$415$	10.6439	0.522489
$416$	45.9511	2.25294
$417$	−2.20724	−0.108089
$418$	−5.90928	−0.289032
$419$	22.2669	1.08781	0.543904	−	0.839148i	$-0.316946\pi$
$419$	22.2669	1.08781	0.543904	+	0.839148i	$0.316946\pi$
$420$	−7.04030	−0.343531
$421$	18.2862	0.891215	0.445608	−	0.895228i	$-0.352988\pi$
$421$	18.2862	0.891215	0.445608	+	0.895228i	$0.352988\pi$
$422$	−1.40926	−0.0686015
$423$	−19.4922	−0.947744
$424$	21.2743	1.03317
$425$	1.00000	0.0485071
$426$	−1.35471	−0.0656360
$427$	−25.0115	−1.21039
$428$	−15.5369	−0.751006
$429$	−1.83539	−0.0886134
$430$	20.6132	0.994059
$431$	37.3138	1.79734	0.898672	−	0.438620i	$-0.144533\pi$
$431$	37.3138	1.79734	0.898672	+	0.438620i	$0.144533\pi$
$432$	7.08414	0.340836
$433$	30.4590	1.46377	0.731883	−	0.681431i	$-0.238642\pi$
$433$	30.4590	1.46377	0.731883	+	0.681431i	$0.238642\pi$
$434$	17.1209	0.821829
$435$	−6.24345	−0.299350
$436$	37.6387	1.80257
$437$	51.1711	2.44785
$438$	−2.31552	−0.110640
$439$	24.0339	1.14708	0.573538	−	0.819179i	$-0.305571\pi$
$439$	24.0339	1.14708	0.573538	+	0.819179i	$0.305571\pi$
$440$	0.762454	0.0363486
$441$	−26.6075	−1.26702
$442$	−13.2239	−0.628995
$443$	−18.4631	−0.877209	−0.438604	−	0.898680i	$-0.644527\pi$
$443$	−18.4631	−0.877209	−0.438604	+	0.898680i	$0.644527\pi$
$444$	1.38498	0.0657283
$445$	−8.57626	−0.406554
$446$	56.4737	2.67411
$447$	9.05895	0.428473
$448$	51.2700	2.42228
$449$	−12.5394	−0.591771	−0.295886	−	0.955223i	$-0.595615\pi$
$449$	−12.5394	−0.591771	−0.295886	+	0.955223i	$0.595615\pi$
$450$	5.67656	0.267596
$451$	−6.06250	−0.285472
$452$	5.64688	0.265607
$453$	6.75867	0.317550
$454$	8.78058	0.412093
$455$	−25.2226	−1.18245
$456$	5.51362	0.258199
$457$	23.9909	1.12225	0.561123	−	0.827732i	$-0.310369\pi$
$457$	23.9909	1.12225	0.561123	+	0.827732i	$0.310369\pi$
$458$	−21.3782	−0.998937
$459$	−3.49740	−0.163245
$460$	−24.8246	−1.15745
$461$	−32.3011	−1.50441	−0.752207	−	0.658927i	$-0.771010\pi$
$461$	−32.3011	−1.50441	−0.752207	+	0.658927i	$0.771010\pi$
$462$	−2.71868	−0.126484
$463$	−34.5109	−1.60386	−0.801930	−	0.597418i	$-0.796193\pi$
$463$	−34.5109	−1.60386	−0.801930	+	0.597418i	$0.796193\pi$
$464$	20.2911	0.941989
$465$	1.18409	0.0549109
$466$	−16.1761	−0.749346
$467$	−27.0493	−1.25169	−0.625847	−	0.779946i	$-0.715247\pi$
$467$	−27.0493	−1.25169	−0.625847	+	0.779946i	$0.715247\pi$
$468$	−43.2898	−2.00107
$469$	8.66801	0.400252
$470$	−16.2236	−0.748338
$471$	5.94197	0.273791
$472$	−4.87324	−0.224309
$473$	4.59044	0.211069
$474$	14.9852	0.688292
$475$	−5.61637	−0.257697
$476$	−11.2961	−0.517757
$477$	35.2724	1.61501
$478$	44.7508	2.04686
$479$	−4.57741	−0.209147	−0.104574	−	0.994517i	$-0.533348\pi$
$479$	−4.57741	−0.209147	−0.104574	+	0.994517i	$0.533348\pi$
$480$	4.70744	0.214864
$481$	4.96184	0.226241
$482$	−29.1728	−1.32879
$483$	23.5423	1.07121
$484$	−29.3329	−1.33331
$485$	5.45446	0.247674
$486$	−30.4669	−1.38201
$487$	−16.7384	−0.758491	−0.379245	−	0.925296i	$-0.623816\pi$
$487$	−16.7384	−0.758491	−0.379245	+	0.925296i	$0.623816\pi$
$488$	−9.50262	−0.430163
$489$	2.70160	0.122171
$490$	−22.1457	−1.00044
$491$	10.9413	0.493772	0.246886	−	0.969044i	$-0.420593\pi$
$491$	10.9413	0.493772	0.246886	+	0.969044i	$0.420593\pi$
$492$	21.2683	0.958848
$493$	−10.0176	−0.451169
$494$	74.2700	3.34157
$495$	1.26414	0.0568187
$496$	−3.84827	−0.172792
$497$	−4.14588	−0.185968
$498$	−14.4194	−0.646150
$499$	3.83244	0.171564	0.0857818	−	0.996314i	$-0.472661\pi$
$499$	3.83244	0.171564	0.0857818	+	0.996314i	$0.472661\pi$
$500$	2.72466	0.121851
$501$	−1.88892	−0.0843905
$502$	32.5389	1.45228
$503$	24.4412	1.08978	0.544890	−	0.838508i	$-0.316571\pi$
$503$	24.4412	1.08978	0.544890	+	0.838508i	$0.316571\pi$
$504$	−17.0544	−0.759665
$505$	3.91207	0.174085
$506$	−9.58624	−0.426161
$507$	14.9656	0.664646
$508$	−60.0321	−2.66349
$509$	−24.1418	−1.07006	−0.535032	−	0.844832i	$-0.679701\pi$
$509$	−24.1418	−1.07006	−0.535032	+	0.844832i	$0.679701\pi$
$510$	−1.35471	−0.0599876
$511$	−7.08629	−0.313479
$512$	−21.6801	−0.958135
$513$	19.6427	0.867245
$514$	−5.63766	−0.248667
$515$	11.8778	0.523397
$516$	−16.1040	−0.708941
$517$	−3.61289	−0.158895
$518$	7.34975	0.322930
$519$	6.94216	0.304727
$520$	−9.58281	−0.420234
$521$	23.7897	1.04225	0.521123	−	0.853481i	$-0.325513\pi$
$521$	23.7897	1.04225	0.521123	+	0.853481i	$0.325513\pi$
$522$	−56.8654	−2.48893
$523$	−17.2801	−0.755607	−0.377803	−	0.925886i	$-0.623320\pi$
$523$	−17.2801	−0.755607	−0.377803	+	0.925886i	$0.623320\pi$
$524$	20.8210	0.909570
$525$	−2.58392	−0.112771
$526$	−21.8822	−0.954111
$527$	1.89987	0.0827596
$528$	0.611079	0.0265938
$529$	60.0116	2.60920
$530$	29.3576	1.27521
$531$	−8.07974	−0.350631
$532$	63.4432	2.75061
$533$	76.1958	3.30041
$534$	11.6184	0.502776
$535$	−5.70234	−0.246534
$536$	3.29323	0.142246
$537$	−0.707210	−0.0305184
$538$	0.422696	0.0182237
$539$	−4.93171	−0.212424
$540$	−9.52923	−0.410073
$541$	4.95903	0.213205	0.106603	−	0.994302i	$-0.466003\pi$
$541$	4.95903	0.213205	0.106603	+	0.994302i	$0.466003\pi$
$542$	−45.3775	−1.94913
$543$	−2.00715	−0.0861352
$544$	7.55307	0.323835
$545$	13.8141	0.591731
$546$	34.1694	1.46231
$547$	41.5233	1.77541	0.887705	−	0.460413i	$-0.152299\pi$
$547$	41.5233	1.77541	0.887705	+	0.460413i	$0.152299\pi$
$548$	−42.4294	−1.81249
$549$	−15.7552	−0.672415
$550$	1.05215	0.0448640
$551$	56.2624	2.39686
$552$	8.94440	0.380699
$553$	45.8598	1.95016
$554$	34.6096	1.47042
$555$	0.508314	0.0215767
$556$	−9.64940	−0.409226
$557$	28.9685	1.22744	0.613718	−	0.789525i	$-0.289673\pi$
$557$	28.9685	1.22744	0.613718	+	0.789525i	$0.289673\pi$
$558$	10.7847	0.456554
$559$	−57.6944	−2.44021
$560$	8.39767	0.354867
$561$	−0.301686	−0.0127372
$562$	29.1723	1.23056
$563$	0.128876	0.00543148	0.00271574	−	0.999996i	$-0.499136\pi$
$563$	0.128876	0.00543148	0.00271574	+	0.999996i	$0.499136\pi$
$564$	12.6746	0.533698
$565$	2.07251	0.0871911
$566$	16.4004	0.689361
$567$	−23.4447	−0.984585
$568$	−1.57514	−0.0660916
$569$	−20.2725	−0.849868	−0.424934	−	0.905224i	$-0.639703\pi$
$569$	−20.2725	−0.849868	−0.424934	+	0.905224i	$0.639703\pi$
$570$	7.60856	0.318687
$571$	14.5617	0.609389	0.304694	−	0.952450i	$-0.401446\pi$
$571$	14.5617	0.609389	0.304694	+	0.952450i	$0.401446\pi$
$572$	−8.02378	−0.335491
$573$	13.9237	0.581672
$574$	112.865	4.71091
$575$	−9.11107	−0.379958
$576$	32.2958	1.34566
$577$	18.3558	0.764162	0.382081	−	0.924129i	$-0.375208\pi$
$577$	18.3558	0.764162	0.382081	+	0.924129i	$0.375208\pi$
$578$	−2.17363	−0.0904110
$579$	−5.15277	−0.214142
$580$	−27.2945	−1.13334
$581$	−44.1284	−1.83076
$582$	−7.38923	−0.306293
$583$	6.53775	0.270766
$584$	−2.69229	−0.111408
$585$	−15.8881	−0.656893
$586$	−8.91779	−0.368391
$587$	−9.40696	−0.388267	−0.194133	−	0.980975i	$-0.562189\pi$
$587$	−9.40696	−0.388267	−0.194133	+	0.980975i	$0.562189\pi$
$588$	17.3013	0.713493
$589$	−10.6704	−0.439665
$590$	−6.72485	−0.276858
$591$	−11.1704	−0.459489
$592$	−1.65201	−0.0678971
$593$	−2.37207	−0.0974093	−0.0487046	−	0.998813i	$-0.515509\pi$
$593$	−2.37207	−0.0974093	−0.0487046	+	0.998813i	$0.515509\pi$
$594$	−3.67980	−0.150984
$595$	−4.14588	−0.169965
$596$	39.6030	1.62220
$597$	14.0522	0.575119
$598$	120.483	4.92694
$599$	−27.4175	−1.12025	−0.560124	−	0.828408i	$-0.689247\pi$
$599$	−27.4175	−1.12025	−0.560124	+	0.828408i	$0.689247\pi$
$600$	−0.981706	−0.0400780
$601$	−39.9738	−1.63056	−0.815282	−	0.579064i	$-0.803418\pi$
$601$	−39.9738	−1.63056	−0.815282	+	0.579064i	$0.803418\pi$
$602$	−85.4601	−3.48309
$603$	5.46012	0.222353
$604$	29.5469	1.20225
$605$	−10.7657	−0.437688
$606$	−5.29973	−0.215287
$607$	1.66517	0.0675872	0.0337936	−	0.999429i	$-0.489241\pi$
$607$	1.66517	0.0675872	0.0337936	+	0.999429i	$0.489241\pi$
$608$	−42.4208	−1.72039
$609$	25.8846	1.04890
$610$	−13.1132	−0.530938
$611$	45.4082	1.83702
$612$	−7.11562	−0.287632
$613$	18.4277	0.744289	0.372145	−	0.928175i	$-0.378623\pi$
$613$	18.4277	0.744289	0.372145	+	0.928175i	$0.378623\pi$
$614$	−18.6851	−0.754070
$615$	7.80584	0.314762
$616$	−3.16105	−0.127362
$617$	48.1342	1.93781	0.968905	−	0.247432i	$-0.0795867\pi$
$617$	48.1342	1.93781	0.968905	+	0.247432i	$0.0795867\pi$
$618$	−16.0910	−0.647273
$619$	29.9817	1.20507	0.602534	−	0.798093i	$-0.294158\pi$
$619$	29.9817	1.20507	0.602534	+	0.798093i	$0.294158\pi$
$620$	5.17650	0.207893
$621$	31.8651	1.27870
$622$	28.6547	1.14895
$623$	35.5562	1.42453
$624$	−7.68026	−0.307457
$625$	1.00000	0.0400000
$626$	−18.1114	−0.723877
$627$	1.69438	0.0676670
$628$	25.9765	1.03658
$629$	0.815587	0.0325196
$630$	−23.5344	−0.937632
$631$	−13.0746	−0.520493	−0.260247	−	0.965542i	$-0.583804\pi$
$631$	−13.0746	−0.520493	−0.260247	+	0.965542i	$0.583804\pi$
$632$	17.4235	0.693070
$633$	0.404079	0.0160607
$634$	−57.9897	−2.30307
$635$	−22.0329	−0.874348
$636$	−22.9355	−0.909453
$637$	61.9836	2.45588
$638$	−10.5400	−0.417284
$639$	−2.61156	−0.103312
$640$	11.7740	0.465408
$641$	−41.0473	−1.62127	−0.810635	−	0.585552i	$-0.800878\pi$
$641$	−41.0473	−1.62127	−0.810635	+	0.585552i	$0.800878\pi$
$642$	7.72502	0.304882
$643$	−3.65698	−0.144217	−0.0721086	−	0.997397i	$-0.522973\pi$
$643$	−3.65698	−0.144217	−0.0721086	+	0.997397i	$0.522973\pi$
$644$	102.920	4.05561
$645$	−5.91047	−0.232725
$646$	12.2079	0.480313
$647$	−31.7262	−1.24729	−0.623643	−	0.781709i	$-0.714348\pi$
$647$	−31.7262	−1.24729	−0.623643	+	0.781709i	$0.714348\pi$
$648$	−8.90733	−0.349913
$649$	−1.49758	−0.0587853
$650$	−13.2239	−0.518682
$651$	−4.90911	−0.192403
$652$	11.8106	0.462539
$653$	−17.3735	−0.679876	−0.339938	−	0.940448i	$-0.610406\pi$
$653$	−17.3735	−0.679876	−0.339938	+	0.940448i	$0.610406\pi$
$654$	−18.7141	−0.731780
$655$	7.64169	0.298585
$656$	−25.3688	−0.990486
$657$	−4.46377	−0.174148
$658$	67.2611	2.62211
$659$	−9.53555	−0.371452	−0.185726	−	0.982602i	$-0.559464\pi$
$659$	−9.53555	−0.371452	−0.185726	+	0.982602i	$0.559464\pi$
$660$	−0.821992	−0.0319960
$661$	31.4354	1.22270	0.611348	−	0.791362i	$-0.290627\pi$
$661$	31.4354	1.22270	0.611348	+	0.791362i	$0.290627\pi$
$662$	−65.6693	−2.55231
$663$	3.79170	0.147258
$664$	−16.7657	−0.650635
$665$	23.2848	0.902946
$666$	4.62973	0.179398
$667$	91.2709	3.53402
$668$	−8.25778	−0.319503
$669$	−16.1928	−0.626051
$670$	4.54452	0.175570
$671$	−2.92023	−0.112734
$672$	−19.5165	−0.752866
$673$	−4.83573	−0.186404	−0.0932018	−	0.995647i	$-0.529710\pi$
$673$	−4.83573	−0.186404	−0.0932018	+	0.995647i	$0.529710\pi$
$674$	0.994940	0.0383236
$675$	−3.49740	−0.134615
$676$	65.4252	2.51636
$677$	−22.1723	−0.852150	−0.426075	−	0.904688i	$-0.640104\pi$
$677$	−22.1723	−0.852150	−0.426075	+	0.904688i	$0.640104\pi$
$678$	−2.80765	−0.107827
$679$	−22.6136	−0.867830
$680$	−1.57514	−0.0604040
$681$	−2.51767	−0.0964775
$682$	1.99895	0.0765439
$683$	29.3832	1.12432	0.562158	−	0.827030i	$-0.309971\pi$
$683$	29.3832	1.12432	0.562158	+	0.827030i	$0.309971\pi$
$684$	39.9639	1.52806
$685$	−15.5724	−0.594989
$686$	28.7322	1.09700
$687$	6.12981	0.233867
$688$	19.2089	0.732333
$689$	−82.1689	−3.13039
$690$	12.3429	0.469885
$691$	−12.4518	−0.473688	−0.236844	−	0.971548i	$-0.576113\pi$
$691$	−12.4518	−0.473688	−0.236844	+	0.971548i	$0.576113\pi$
$692$	30.3491	1.15370
$693$	−5.24096	−0.199088
$694$	28.5448	1.08355
$695$	−3.54150	−0.134337
$696$	9.83433	0.372769
$697$	12.5244	0.474397
$698$	−19.4947	−0.737885
$699$	4.63822	0.175434
$700$	−11.2961	−0.426954
$701$	−46.1647	−1.74362	−0.871808	−	0.489848i	$-0.837052\pi$
$701$	−46.1647	−1.74362	−0.871808	+	0.489848i	$0.837052\pi$
$702$	46.2491	1.74556
$703$	−4.58064	−0.172762
$704$	5.98604	0.225607
$705$	4.65182	0.175198
$706$	51.5544	1.94028
$707$	−16.2190	−0.609978
$708$	5.25378	0.197449
$709$	−2.11079	−0.0792724	−0.0396362	−	0.999214i	$-0.512620\pi$
$709$	−2.11079	−0.0792724	−0.0396362	+	0.999214i	$0.512620\pi$
$710$	−2.17363	−0.0815748
$711$	28.8879	1.08338
$712$	13.5088	0.506265
$713$	−17.3098	−0.648259
$714$	5.61648	0.210191
$715$	−2.94487	−0.110132
$716$	−3.09172	−0.115543
$717$	−12.8315	−0.479201
$718$	−28.8248	−1.07573
$719$	35.1424	1.31059	0.655295	−	0.755373i	$-0.272544\pi$
$719$	35.1424	1.31059	0.655295	+	0.755373i	$0.272544\pi$
$720$	5.28983	0.197140
$721$	−49.2439	−1.83394
$722$	−27.2651	−1.01470
$723$	8.36479	0.311090
$724$	−8.77469	−0.326109
$725$	−10.0176	−0.372044
$726$	14.5844	0.541278
$727$	22.7686	0.844442	0.422221	−	0.906493i	$-0.361251\pi$
$727$	22.7686	0.844442	0.422221	+	0.906493i	$0.361251\pi$
$728$	39.7292	1.47246
$729$	−8.22895	−0.304776
$730$	−3.71524	−0.137507
$731$	−9.48333	−0.350754
$732$	10.2446	0.378653
$733$	38.0960	1.40711	0.703554	−	0.710642i	$-0.251595\pi$
$733$	38.0960	1.40711	0.703554	+	0.710642i	$0.251595\pi$
$734$	3.27858	0.121014
$735$	6.34988	0.234219
$736$	−68.8165	−2.53661
$737$	1.01204	0.0372788
$738$	71.0958	2.61707
$739$	33.8765	1.24617	0.623084	−	0.782155i	$-0.285880\pi$
$739$	33.8765	1.24617	0.623084	+	0.782155i	$0.285880\pi$
$740$	2.22220	0.0816896
$741$	−21.2956	−0.782313
$742$	−121.713	−4.46823
$743$	21.5897	0.792049	0.396024	−	0.918240i	$-0.370390\pi$
$743$	21.5897	0.792049	0.396024	+	0.918240i	$0.370390\pi$
$744$	−1.86511	−0.0683784
$745$	14.5350	0.532523
$746$	8.55467	0.313209
$747$	−27.7972	−1.01705
$748$	−1.31888	−0.0482231
$749$	23.6412	0.863832
$750$	−1.35471	−0.0494671
$751$	49.3660	1.80139	0.900695	−	0.434452i	$-0.143058\pi$
$751$	49.3660	1.80139	0.900695	+	0.434452i	$0.143058\pi$
$752$	−15.1183	−0.551308
$753$	−9.32994	−0.340002
$754$	132.471	4.82431
$755$	10.8442	0.394663
$756$	39.5071	1.43686
$757$	−18.1945	−0.661292	−0.330646	−	0.943755i	$-0.607267\pi$
$757$	−18.1945	−0.661292	−0.330646	+	0.943755i	$0.607267\pi$
$758$	51.1177	1.85668
$759$	2.74868	0.0997709
$760$	8.84658	0.320899
$761$	4.44280	0.161051	0.0805256	−	0.996753i	$-0.474340\pi$
$761$	4.44280	0.161051	0.0805256	+	0.996753i	$0.474340\pi$
$762$	29.8482	1.08129
$763$	−57.2716	−2.07337
$764$	60.8705	2.20222
$765$	−2.61156	−0.0944212
$766$	32.5566	1.17632
$767$	18.8222	0.679630
$768$	−0.535572	−0.0193258
$769$	0.0870389	0.00313870	0.00156935	−	0.999999i	$-0.499500\pi$
$769$	0.0870389	0.00313870	0.00156935	+	0.999999i	$0.499500\pi$
$770$	−4.36211	−0.157199
$771$	1.61650	0.0582168
$772$	−22.5264	−0.810743
$773$	−10.6451	−0.382878	−0.191439	−	0.981504i	$-0.561315\pi$
$773$	−10.6451	−0.382878	−0.191439	+	0.981504i	$0.561315\pi$
$774$	−53.8327	−1.93498
$775$	1.89987	0.0682453
$776$	−8.59156	−0.308419
$777$	−2.10741	−0.0756029
$778$	−31.8849	−1.14313
$779$	−70.3418	−2.52026
$780$	10.3311	0.369913
$781$	−0.484054	−0.0173208
$782$	19.8041	0.708193
$783$	35.0355	1.25207
$784$	−20.6370	−0.737035
$785$	9.53386	0.340278
$786$	−10.3523	−0.369254
$787$	41.9088	1.49389	0.746944	−	0.664887i	$-0.231520\pi$
$787$	41.9088	1.49389	0.746944	+	0.664887i	$0.231520\pi$
$788$	−48.8338	−1.73963
$789$	6.27434	0.223372
$790$	24.0437	0.855435
$791$	−8.59238	−0.305510
$792$	−1.99120	−0.0707541
$793$	36.7025	1.30334
$794$	−64.1878	−2.27794
$795$	−8.41775	−0.298547
$796$	61.4321	2.17740
$797$	3.26677	0.115715	0.0578575	−	0.998325i	$-0.481573\pi$
$797$	3.26677	0.115715	0.0578575	+	0.998325i	$0.481573\pi$
$798$	−31.5442	−1.11665
$799$	7.46382	0.264051
$800$	7.55307	0.267041
$801$	22.3974	0.791374
$802$	−68.0863	−2.40421
$803$	−0.827362	−0.0291970
$804$	−3.55039	−0.125213
$805$	37.7734	1.33134
$806$	−25.1236	−0.884941
$807$	−0.121200	−0.00426646
$808$	−6.16208	−0.216781
$809$	−15.8859	−0.558520	−0.279260	−	0.960216i	$-0.590089\pi$
$809$	−15.8859	−0.558520	−0.279260	+	0.960216i	$0.590089\pi$
$810$	−12.2917	−0.431887
$811$	−22.2866	−0.782589	−0.391294	−	0.920266i	$-0.627973\pi$
$811$	−22.2866	−0.782589	−0.391294	+	0.920266i	$0.627973\pi$
$812$	113.160	3.97113
$813$	13.0112	0.456322
$814$	0.858123	0.0300772
$815$	4.33471	0.151838
$816$	−1.26242	−0.0441935
$817$	53.2619	1.86340
$818$	−65.6203	−2.29436
$819$	65.8704	2.30170
$820$	34.1248	1.19169
$821$	26.7625	0.934018	0.467009	−	0.884252i	$-0.345331\pi$
$821$	26.7625	0.934018	0.467009	+	0.884252i	$0.345331\pi$
$822$	21.0961	0.735809
$823$	33.4888	1.16735	0.583673	−	0.811989i	$-0.301615\pi$
$823$	33.4888	1.16735	0.583673	+	0.811989i	$0.301615\pi$
$824$	−18.7092	−0.651766
$825$	−0.301686	−0.0105034
$826$	27.8805	0.970085
$827$	55.1384	1.91735	0.958675	−	0.284503i	$-0.0918286\pi$
$827$	55.1384	1.91735	0.958675	+	0.284503i	$0.0918286\pi$
$828$	64.8309	2.25303
$829$	34.9963	1.21547	0.607735	−	0.794140i	$-0.292078\pi$
$829$	34.9963	1.21547	0.607735	+	0.794140i	$0.292078\pi$
$830$	−23.1359	−0.803059
$831$	−9.92369	−0.344249
$832$	−75.2348	−2.60830
$833$	10.1884	0.353006
$834$	4.79772	0.166131
$835$	−3.03076	−0.104884
$836$	7.40733	0.256188
$837$	−6.64460	−0.229671
$838$	−48.3999	−1.67195
$839$	−8.88454	−0.306728	−0.153364	−	0.988170i	$-0.549011\pi$
$839$	−8.88454	−0.306728	−0.153364	+	0.988170i	$0.549011\pi$
$840$	4.07004	0.140430
$841$	71.3519	2.46041
$842$	−39.7474	−1.36979
$843$	−8.36464	−0.288094
$844$	1.76651	0.0608059
$845$	24.0123	0.826047
$846$	42.3689	1.45667
$847$	44.6333	1.53362
$848$	27.3575	0.939461
$849$	−4.70252	−0.161390
$850$	−2.17363	−0.0745548
$851$	−7.43087	−0.254727
$852$	1.69814	0.0581774
$853$	−48.1963	−1.65021	−0.825105	−	0.564980i	$-0.808884\pi$
$853$	−48.1963	−1.65021	−0.825105	+	0.564980i	$0.808884\pi$
$854$	54.3658	1.86036
$855$	14.6675	0.501617
$856$	8.98200	0.306998
$857$	−36.8557	−1.25897	−0.629483	−	0.777014i	$-0.716733\pi$
$857$	−36.8557	−1.25897	−0.629483	+	0.777014i	$0.716733\pi$
$858$	3.98945	0.136198
$859$	28.6856	0.978740	0.489370	−	0.872076i	$-0.337227\pi$
$859$	28.6856	0.978740	0.489370	+	0.872076i	$0.337227\pi$
$860$	−25.8389	−0.881098
$861$	−32.3621	−1.10290
$862$	−81.1064	−2.76250
$863$	25.6425	0.872879	0.436440	−	0.899733i	$-0.356239\pi$
$863$	25.6425	0.872879	0.436440	+	0.899733i	$0.356239\pi$
$864$	−26.4161	−0.898694
$865$	11.1387	0.378726
$866$	−66.2065	−2.24979
$867$	0.623249	0.0211666
$868$	−21.4612	−0.728440
$869$	5.35438	0.181635
$870$	13.5709	0.460098
$871$	−12.7196	−0.430989
$872$	−21.7592	−0.736859
$873$	−14.2447	−0.482109
$874$	−111.227	−3.76231
$875$	−4.14588	−0.140156
$876$	2.90252	0.0980671
$877$	7.08929	0.239388	0.119694	−	0.992811i	$-0.461809\pi$
$877$	7.08929	0.239388	0.119694	+	0.992811i	$0.461809\pi$
$878$	−52.2408	−1.76304
$879$	2.55702	0.0862460
$880$	0.980473	0.0330517
$881$	−35.5349	−1.19720	−0.598601	−	0.801047i	$-0.704276\pi$
$881$	−35.5349	−1.19720	−0.598601	+	0.801047i	$0.704276\pi$
$882$	57.8348	1.94740
$883$	22.4293	0.754805	0.377403	−	0.926049i	$-0.376817\pi$
$883$	22.4293	0.754805	0.377403	+	0.926049i	$0.376817\pi$
$884$	16.5762	0.557518
$885$	1.92823	0.0648168
$886$	40.1319	1.34826
$887$	−44.0103	−1.47772	−0.738861	−	0.673858i	$-0.764636\pi$
$887$	−44.0103	−1.47772	−0.738861	+	0.673858i	$0.764636\pi$
$888$	−0.800667	−0.0268686
$889$	91.3457	3.06364
$890$	18.6416	0.624868
$891$	−2.73729	−0.0917027
$892$	−70.7903	−2.37023
$893$	−41.9196	−1.40278
$894$	−19.6908	−0.658558
$895$	−1.13472	−0.0379294
$896$	−48.8136	−1.63075
$897$	−34.5465	−1.15347
$898$	27.2560	0.909545
$899$	−19.0321	−0.634756
$900$	−7.11562	−0.237187
$901$	−13.5062	−0.449958
$902$	13.1776	0.438767
$903$	24.5041	0.815447
$904$	−3.26450	−0.108576
$905$	−3.22047	−0.107052
$906$	−14.6908	−0.488070
$907$	−25.0197	−0.830766	−0.415383	−	0.909647i	$-0.636352\pi$
$907$	−25.0197	−0.830766	−0.415383	+	0.909647i	$0.636352\pi$
$908$	−11.0065	−0.365264
$909$	−10.2166	−0.338864
$910$	54.8246	1.81742
$911$	40.0784	1.32786	0.663928	−	0.747796i	$-0.268888\pi$
$911$	40.0784	1.32786	0.663928	+	0.747796i	$0.268888\pi$
$912$	7.09021	0.234780
$913$	−5.15223	−0.170514
$914$	−52.1473	−1.72488
$915$	3.75997	0.124301
$916$	26.7977	0.885421
$917$	−31.6815	−1.04622
$918$	7.60205	0.250905
$919$	−40.3938	−1.33247	−0.666234	−	0.745743i	$-0.732095\pi$
$919$	−40.3938	−1.33247	−0.666234	+	0.745743i	$0.732095\pi$
$920$	14.3512	0.473146
$921$	5.35762	0.176540
$922$	70.2106	2.31226
$923$	6.08377	0.200250
$924$	3.40788	0.112111
$925$	0.815587	0.0268163
$926$	75.0140	2.46511
$927$	−31.0195	−1.01881
$928$	−75.6635	−2.48378
$929$	39.6032	1.29934	0.649670	−	0.760216i	$-0.274907\pi$
$929$	39.6032	1.29934	0.649670	+	0.760216i	$0.274907\pi$
$930$	−2.57378	−0.0843974
$931$	−57.2216	−1.87536
$932$	20.2769	0.664193
$933$	−8.21621	−0.268987
$934$	58.7952	1.92384
$935$	−0.484054	−0.0158303
$936$	25.0261	0.818003
$937$	15.6513	0.511305	0.255652	−	0.966769i	$-0.417710\pi$
$937$	15.6513	0.511305	0.255652	+	0.966769i	$0.417710\pi$
$938$	−18.8410	−0.615182
$939$	5.19312	0.169471
$940$	20.3364	0.663300
$941$	−2.21899	−0.0723370	−0.0361685	−	0.999346i	$-0.511515\pi$
$941$	−2.21899	−0.0723370	−0.0361685	+	0.999346i	$0.511515\pi$
$942$	−12.9156	−0.420814
$943$	−114.111	−3.71597
$944$	−6.26671	−0.203964
$945$	14.4998	0.471679
$946$	−9.97792	−0.324410
$947$	−22.2367	−0.722594	−0.361297	−	0.932451i	$-0.617666\pi$
$947$	−22.2367	−0.722594	−0.361297	+	0.932451i	$0.617666\pi$
$948$	−18.7841	−0.610078
$949$	10.3986	0.337552
$950$	12.2079	0.396076
$951$	16.6275	0.539184
$952$	6.53036	0.211650
$953$	−23.7992	−0.770933	−0.385467	−	0.922722i	$-0.625959\pi$
$953$	−23.7992	−0.770933	−0.385467	+	0.922722i	$0.625959\pi$
$954$	−76.6691	−2.48225
$955$	22.3406	0.722924
$956$	−56.0956	−1.81426
$957$	3.02217	0.0976927
$958$	9.94960	0.321457
$959$	64.5612	2.08479
$960$	−7.70739	−0.248755
$961$	−27.3905	−0.883564
$962$	−10.7852	−0.347729
$963$	14.8920	0.479888
$964$	36.5684	1.17779
$965$	−8.26759	−0.266143
$966$	−51.1721	−1.64644
$967$	−26.4947	−0.852012	−0.426006	−	0.904720i	$-0.640080\pi$
$967$	−26.4947	−0.852012	−0.426006	+	0.904720i	$0.640080\pi$
$968$	16.9575	0.545035
$969$	−3.50039	−0.112449
$970$	−11.8560	−0.380673
$971$	10.4063	0.333953	0.166977	−	0.985961i	$-0.446600\pi$
$971$	10.4063	0.333953	0.166977	+	0.985961i	$0.446600\pi$
$972$	38.1906	1.22496
$973$	14.6827	0.470705
$974$	36.3831	1.16579
$975$	3.79170	0.121432
$976$	−12.2198	−0.391147
$977$	−28.9131	−0.925010	−0.462505	−	0.886617i	$-0.653049\pi$
$977$	−28.9131	−0.925010	−0.462505	+	0.886617i	$0.653049\pi$
$978$	−5.87228	−0.187775
$979$	4.15137	0.132678
$980$	27.7598	0.886755
$981$	−36.0763	−1.15183
$982$	−23.7822	−0.758922
$983$	−53.7573	−1.71459	−0.857297	−	0.514823i	$-0.827858\pi$
$983$	−53.7573	−1.71459	−0.857297	+	0.514823i	$0.827858\pi$
$984$	−12.2953	−0.391961
$985$	−17.9229	−0.571070
$986$	21.7745	0.693441
$987$	−19.2859	−0.613877
$988$	−93.0981	−2.96184
$989$	86.4033	2.74746
$990$	−2.74776	−0.0873296
$991$	−12.3977	−0.393827	−0.196913	−	0.980421i	$-0.563092\pi$
$991$	−12.3977	−0.393827	−0.196913	+	0.980421i	$0.563092\pi$
$992$	14.3498	0.455608
$993$	18.8295	0.597536
$994$	9.01161	0.285831
$995$	22.5467	0.714779
$996$	18.0749	0.572724
$997$	59.4088	1.88150	0.940748	−	0.339105i	$-0.110124\pi$
$997$	59.4088	1.88150	0.940748	+	0.339105i	$0.110124\pi$
$998$	−8.33030	−0.263691
$999$	−2.85243	−0.0902470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.g.1.9	✓	58

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.g.1.9	✓	58	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17363 q^{2} +0.623249 q^{3} +2.72466 q^{4} +1.00000 q^{5} -1.35471 q^{6} -4.14588 q^{7} -1.57514 q^{8} -2.61156 q^{9} +O(q^{10})\)	\(q-2.17363 q^{2} +0.623249 q^{3} +2.72466 q^{4} +1.00000 q^{5} -1.35471 q^{6} -4.14588 q^{7} -1.57514 q^{8} -2.61156 q^{9} -2.17363 q^{10} -0.484054 q^{11} +1.69814 q^{12} +6.08377 q^{13} +9.01161 q^{14} +0.623249 q^{15} -2.02554 q^{16} +1.00000 q^{17} +5.67656 q^{18} -5.61637 q^{19} +2.72466 q^{20} -2.58392 q^{21} +1.05215 q^{22} -9.11107 q^{23} -0.981706 q^{24} +1.00000 q^{25} -13.2239 q^{26} -3.49740 q^{27} -11.2961 q^{28} -10.0176 q^{29} -1.35471 q^{30} +1.89987 q^{31} +7.55307 q^{32} -0.301686 q^{33} -2.17363 q^{34} -4.14588 q^{35} -7.11562 q^{36} +0.815587 q^{37} +12.2079 q^{38} +3.79170 q^{39} -1.57514 q^{40} +12.5244 q^{41} +5.61648 q^{42} -9.48333 q^{43} -1.31888 q^{44} -2.61156 q^{45} +19.8041 q^{46} +7.46382 q^{47} -1.26242 q^{48} +10.1884 q^{49} -2.17363 q^{50} +0.623249 q^{51} +16.5762 q^{52} -13.5062 q^{53} +7.60205 q^{54} -0.484054 q^{55} +6.53036 q^{56} -3.50039 q^{57} +21.7745 q^{58} +3.09384 q^{59} +1.69814 q^{60} +6.03286 q^{61} -4.12961 q^{62} +10.8272 q^{63} -12.3665 q^{64} +6.08377 q^{65} +0.655753 q^{66} -2.09075 q^{67} +2.72466 q^{68} -5.67846 q^{69} +9.01161 q^{70} +1.00000 q^{71} +4.11358 q^{72} +1.70923 q^{73} -1.77278 q^{74} +0.623249 q^{75} -15.3027 q^{76} +2.00683 q^{77} -8.24175 q^{78} -11.0615 q^{79} -2.02554 q^{80} +5.65493 q^{81} -27.2235 q^{82} +10.6439 q^{83} -7.04030 q^{84} +1.00000 q^{85} +20.6132 q^{86} -6.24345 q^{87} +0.762454 q^{88} -8.57626 q^{89} +5.67656 q^{90} -25.2226 q^{91} -24.8246 q^{92} +1.18409 q^{93} -16.2236 q^{94} -5.61637 q^{95} +4.70744 q^{96} +5.45446 q^{97} -22.1457 q^{98} +1.26414 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9}+O(q^{10}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9	\( 58 q + q^{2} + 6 q^{3} + 69 q^{4} + 58 q^{5} + 10 q^{6} + 13 q^{7} - 3 q^{8} + 84 q^{9} + q^{10} + 28 q^{11} + 18 q^{12} + 37 q^{13} + 28 q^{14} + 6 q^{15} + 83 q^{16} + 58 q^{17} - 12 q^{18} + 19 q^{19} + 69 q^{20} + 31 q^{21} + 13 q^{22} + 14 q^{23} + 13 q^{24} + 58 q^{25} + 18 q^{26} + 9 q^{27} + 8 q^{28} + 60 q^{29} + 10 q^{30} + 39 q^{31} - 30 q^{32} + 13 q^{33} + q^{34} + 13 q^{35} + 113 q^{36} + 60 q^{37} - q^{38} + 41 q^{39} - 3 q^{40} + 65 q^{41} - 30 q^{42} + 17 q^{43} + 69 q^{44} + 84 q^{45} + 24 q^{46} + 16 q^{47} + 14 q^{48} + 117 q^{49} + q^{50} + 6 q^{51} + 61 q^{52} + 5 q^{53} + 24 q^{54} + 28 q^{55} + 105 q^{56} + 8 q^{57} - 34 q^{58} + 22 q^{59} + 18 q^{60} + 113 q^{61} - 19 q^{62} + 8 q^{63} + 89 q^{64} + 37 q^{65} - 37 q^{66} + 19 q^{67} + 69 q^{68} + 75 q^{69} + 28 q^{70} + 58 q^{71} - 17 q^{72} + 49 q^{73} + 29 q^{74} + 6 q^{75} - 6 q^{76} + 17 q^{77} - 12 q^{78} + 7 q^{79} + 83 q^{80} + 134 q^{81} + 7 q^{82} - 12 q^{83} - 18 q^{84} + 58 q^{85} + 23 q^{86} - 36 q^{87} - 33 q^{88} + 52 q^{89} - 12 q^{90} + 31 q^{91} + 80 q^{92} - 37 q^{93} + 4 q^{94} + 19 q^{95} - 35 q^{96} + 26 q^{97} - 33 q^{98} + 57 q^{99}+O(q^{100}) \) 58 * q + q^2 + 6 * q^3 + 69 * q^4 + 58 * q^5 + 10 * q^6 + 13 * q^7 - 3 * q^8 + 84 * q^9 + q^10 + 28 * q^11 + 18 * q^12 + 37 * q^13 + 28 * q^14 + 6 * q^15 + 83 * q^16 + 58 * q^17 - 12 * q^18 + 19 * q^19 + 69 * q^20 + 31 * q^21 + 13 * q^22 + 14 * q^23 + 13 * q^24 + 58 * q^25 + 18 * q^26 + 9 * q^27 + 8 * q^28 + 60 * q^29 + 10 * q^30 + 39 * q^31 - 30 * q^32 + 13 * q^33 + q^34 + 13 * q^35 + 113 * q^36 + 60 * q^37 - q^38 + 41 * q^39 - 3 * q^40 + 65 * q^41 - 30 * q^42 + 17 * q^43 + 69 * q^44 + 84 * q^45 + 24 * q^46 + 16 * q^47 + 14 * q^48 + 117 * q^49 + q^50 + 6 * q^51 + 61 * q^52 + 5 * q^53 + 24 * q^54 + 28 * q^55 + 105 * q^56 + 8 * q^57 - 34 * q^58 + 22 * q^59 + 18 * q^60 + 113 * q^61 - 19 * q^62 + 8 * q^63 + 89 * q^64 + 37 * q^65 - 37 * q^66 + 19 * q^67 + 69 * q^68 + 75 * q^69 + 28 * q^70 + 58 * q^71 - 17 * q^72 + 49 * q^73 + 29 * q^74 + 6 * q^75 - 6 * q^76 + 17 * q^77 - 12 * q^78 + 7 * q^79 + 83 * q^80 + 134 * q^81 + 7 * q^82 - 12 * q^83 - 18 * q^84 + 58 * q^85 + 23 * q^86 - 36 * q^87 - 33 * q^88 + 52 * q^89 - 12 * q^90 + 31 * q^91 + 80 * q^92 - 37 * q^93 + 4 * q^94 + 19 * q^95 - 35 * q^96 + 26 * q^97 - 33 * q^98 + 57 * q^99

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