LMFDB - Embedded newform 6015.2.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31182 q^{2} +1.00000 q^{3} +3.34451 q^{4} -1.00000 q^{5} -2.31182 q^{6} -2.77511 q^{7} -3.10826 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.31182 q^{2} +1.00000 q^{3} +3.34451 q^{4} -1.00000 q^{5} -2.31182 q^{6} -2.77511 q^{7} -3.10826 q^{8} +1.00000 q^{9} +2.31182 q^{10} +5.86685 q^{11} +3.34451 q^{12} +7.05291 q^{13} +6.41556 q^{14} -1.00000 q^{15} +0.496716 q^{16} -4.28168 q^{17} -2.31182 q^{18} -1.98057 q^{19} -3.34451 q^{20} -2.77511 q^{21} -13.5631 q^{22} -2.46375 q^{23} -3.10826 q^{24} +1.00000 q^{25} -16.3051 q^{26} +1.00000 q^{27} -9.28139 q^{28} +9.29296 q^{29} +2.31182 q^{30} -1.49528 q^{31} +5.06820 q^{32} +5.86685 q^{33} +9.89847 q^{34} +2.77511 q^{35} +3.34451 q^{36} -10.6535 q^{37} +4.57872 q^{38} +7.05291 q^{39} +3.10826 q^{40} -12.2894 q^{41} +6.41556 q^{42} -11.5923 q^{43} +19.6217 q^{44} -1.00000 q^{45} +5.69574 q^{46} +2.28064 q^{47} +0.496716 q^{48} +0.701257 q^{49} -2.31182 q^{50} -4.28168 q^{51} +23.5885 q^{52} -12.1035 q^{53} -2.31182 q^{54} -5.86685 q^{55} +8.62577 q^{56} -1.98057 q^{57} -21.4836 q^{58} -1.21429 q^{59} -3.34451 q^{60} +4.42619 q^{61} +3.45681 q^{62} -2.77511 q^{63} -12.7102 q^{64} -7.05291 q^{65} -13.5631 q^{66} +5.84241 q^{67} -14.3201 q^{68} -2.46375 q^{69} -6.41556 q^{70} -8.56362 q^{71} -3.10826 q^{72} -1.25965 q^{73} +24.6290 q^{74} +1.00000 q^{75} -6.62403 q^{76} -16.2812 q^{77} -16.3051 q^{78} -9.35475 q^{79} -0.496716 q^{80} +1.00000 q^{81} +28.4109 q^{82} +10.7937 q^{83} -9.28139 q^{84} +4.28168 q^{85} +26.7993 q^{86} +9.29296 q^{87} -18.2357 q^{88} +12.3512 q^{89} +2.31182 q^{90} -19.5726 q^{91} -8.24002 q^{92} -1.49528 q^{93} -5.27243 q^{94} +1.98057 q^{95} +5.06820 q^{96} -9.45070 q^{97} -1.62118 q^{98} +5.86685 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) $ 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.31182	−1.63470	−0.817351	−	0.576139i	$-0.804559\pi$
$2$	−2.31182	−1.63470	−0.817351	+	0.576139i	$0.804559\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	3.34451	1.67225
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.31182	−0.943796
$7$	−2.77511	−1.04889	−0.524447	−	0.851443i	$-0.675728\pi$
$7$	−2.77511	−1.04889	−0.524447	+	0.851443i	$0.675728\pi$
$8$	−3.10826	−1.09894
$9$	1.00000	0.333333
$10$	2.31182	0.731061
$11$	5.86685	1.76892	0.884461	−	0.466615i	$-0.154527\pi$
$11$	5.86685	1.76892	0.884461	+	0.466615i	$0.154527\pi$
$12$	3.34451	0.965476
$13$	7.05291	1.95613	0.978063	−	0.208310i	$-0.0667962\pi$
$13$	7.05291	1.95613	0.978063	+	0.208310i	$0.0667962\pi$
$14$	6.41556	1.71463
$15$	−1.00000	−0.258199
$16$	0.496716	0.124179
$17$	−4.28168	−1.03846	−0.519230	−	0.854634i	$-0.673781\pi$
$17$	−4.28168	−1.03846	−0.519230	+	0.854634i	$0.673781\pi$
$18$	−2.31182	−0.544901
$19$	−1.98057	−0.454374	−0.227187	−	0.973851i	$-0.572953\pi$
$19$	−1.98057	−0.454374	−0.227187	+	0.973851i	$0.572953\pi$
$20$	−3.34451	−0.747855
$21$	−2.77511	−0.605580
$22$	−13.5631	−2.89166
$23$	−2.46375	−0.513727	−0.256863	−	0.966448i	$-0.582689\pi$
$23$	−2.46375	−0.513727	−0.256863	+	0.966448i	$0.582689\pi$
$24$	−3.10826	−0.634471
$25$	1.00000	0.200000
$26$	−16.3051	−3.19768
$27$	1.00000	0.192450
$28$	−9.28139	−1.75402
$29$	9.29296	1.72566	0.862830	−	0.505495i	$-0.168690\pi$
$29$	9.29296	1.72566	0.862830	+	0.505495i	$0.168690\pi$
$30$	2.31182	0.422078
$31$	−1.49528	−0.268560	−0.134280	−	0.990943i	$-0.542872\pi$
$31$	−1.49528	−0.268560	−0.134280	+	0.990943i	$0.542872\pi$
$32$	5.06820	0.895940
$33$	5.86685	1.02129
$34$	9.89847	1.69757
$35$	2.77511	0.469080
$36$	3.34451	0.557418
$37$	−10.6535	−1.75143	−0.875714	−	0.482830i	$-0.839609\pi$
$37$	−10.6535	−1.75143	−0.875714	+	0.482830i	$0.839609\pi$
$38$	4.57872	0.742767
$39$	7.05291	1.12937
$40$	3.10826	0.491459
$41$	−12.2894	−1.91928	−0.959641	−	0.281229i	$-0.909258\pi$
$41$	−12.2894	−1.91928	−0.959641	+	0.281229i	$0.909258\pi$
$42$	6.41556	0.989943
$43$	−11.5923	−1.76781	−0.883906	−	0.467664i	$-0.845096\pi$
$43$	−11.5923	−1.76781	−0.883906	+	0.467664i	$0.845096\pi$
$44$	19.6217	2.95809
$45$	−1.00000	−0.149071
$46$	5.69574	0.839791
$47$	2.28064	0.332666	0.166333	−	0.986070i	$-0.446807\pi$
$47$	2.28064	0.332666	0.166333	+	0.986070i	$0.446807\pi$
$48$	0.496716	0.0716948
$49$	0.701257	0.100180
$50$	−2.31182	−0.326941
$51$	−4.28168	−0.599555
$52$	23.5885	3.27114
$53$	−12.1035	−1.66255	−0.831273	−	0.555865i	$-0.812387\pi$
$53$	−12.1035	−1.66255	−0.831273	+	0.555865i	$0.812387\pi$
$54$	−2.31182	−0.314599
$55$	−5.86685	−0.791086
$56$	8.62577	1.15267
$57$	−1.98057	−0.262333
$58$	−21.4836	−2.82094
$59$	−1.21429	−0.158086	−0.0790432	−	0.996871i	$-0.525187\pi$
$59$	−1.21429	−0.158086	−0.0790432	+	0.996871i	$0.525187\pi$
$60$	−3.34451	−0.431774
$61$	4.42619	0.566715	0.283358	−	0.959014i	$-0.408552\pi$
$61$	4.42619	0.566715	0.283358	+	0.959014i	$0.408552\pi$
$62$	3.45681	0.439016
$63$	−2.77511	−0.349631
$64$	−12.7102	−1.58877
$65$	−7.05291	−0.874806
$66$	−13.5631	−1.66950
$67$	5.84241	0.713764	0.356882	−	0.934150i	$-0.383840\pi$
$67$	5.84241	0.713764	0.356882	+	0.934150i	$0.383840\pi$
$68$	−14.3201	−1.73657
$69$	−2.46375	−0.296600
$70$	−6.41556	−0.766806
$71$	−8.56362	−1.01631	−0.508157	−	0.861264i	$-0.669673\pi$
$71$	−8.56362	−1.01631	−0.508157	+	0.861264i	$0.669673\pi$
$72$	−3.10826	−0.366312
$73$	−1.25965	−0.147431	−0.0737155	−	0.997279i	$-0.523486\pi$
$73$	−1.25965	−0.147431	−0.0737155	+	0.997279i	$0.523486\pi$
$74$	24.6290	2.86307
$75$	1.00000	0.115470
$76$	−6.62403	−0.759829
$77$	−16.2812	−1.85541
$78$	−16.3051	−1.84618
$79$	−9.35475	−1.05249	−0.526246	−	0.850332i	$-0.676401\pi$
$79$	−9.35475	−1.05249	−0.526246	+	0.850332i	$0.676401\pi$
$80$	−0.496716	−0.0555345
$81$	1.00000	0.111111
$82$	28.4109	3.13745
$83$	10.7937	1.18477	0.592384	−	0.805656i	$-0.298187\pi$
$83$	10.7937	1.18477	0.592384	+	0.805656i	$0.298187\pi$
$84$	−9.28139	−1.01268
$85$	4.28168	0.464414
$86$	26.7993	2.88985
$87$	9.29296	0.996310
$88$	−18.2357	−1.94393
$89$	12.3512	1.30923	0.654613	−	0.755964i	$-0.272831\pi$
$89$	12.3512	1.30923	0.654613	+	0.755964i	$0.272831\pi$
$90$	2.31182	0.243687
$91$	−19.5726	−2.05177
$92$	−8.24002	−0.859082
$93$	−1.49528	−0.155053
$94$	−5.27243	−0.543810
$95$	1.98057	0.203202
$96$	5.06820	0.517271
$97$	−9.45070	−0.959574	−0.479787	−	0.877385i	$-0.659286\pi$
$97$	−9.45070	−0.959574	−0.479787	+	0.877385i	$0.659286\pi$
$98$	−1.62118	−0.163764
$99$	5.86685	0.589640
$100$	3.34451	0.334451
$101$	13.7066	1.36386	0.681931	−	0.731417i	$-0.261140\pi$
$101$	13.7066	1.36386	0.681931	+	0.731417i	$0.261140\pi$
$102$	9.89847	0.980095
$103$	−12.2425	−1.20629	−0.603147	−	0.797630i	$-0.706087\pi$
$103$	−12.2425	−1.20629	−0.603147	+	0.797630i	$0.706087\pi$
$104$	−21.9223	−2.14966
$105$	2.77511	0.270823
$106$	27.9811	2.71777
$107$	12.9996	1.25672	0.628361	−	0.777922i	$-0.283726\pi$
$107$	12.9996	1.25672	0.628361	+	0.777922i	$0.283726\pi$
$108$	3.34451	0.321825
$109$	−4.15687	−0.398156	−0.199078	−	0.979984i	$-0.563795\pi$
$109$	−4.15687	−0.398156	−0.199078	+	0.979984i	$0.563795\pi$
$110$	13.5631	1.29319
$111$	−10.6535	−1.01119
$112$	−1.37844	−0.130251
$113$	−6.09155	−0.573045	−0.286523	−	0.958073i	$-0.592499\pi$
$113$	−6.09155	−0.573045	−0.286523	+	0.958073i	$0.592499\pi$
$114$	4.57872	0.428837
$115$	2.46375	0.229746
$116$	31.0804	2.88574
$117$	7.05291	0.652042
$118$	2.80721	0.258424
$119$	11.8822	1.08924
$120$	3.10826	0.283744
$121$	23.4199	2.12908
$122$	−10.2325	−0.926411
$123$	−12.2894	−1.10810
$124$	−5.00097	−0.449100
$125$	−1.00000	−0.0894427
$126$	6.41556	0.571544
$127$	5.79022	0.513799	0.256899	−	0.966438i	$-0.417299\pi$
$127$	5.79022	0.513799	0.256899	+	0.966438i	$0.417299\pi$
$128$	19.2473	1.70123
$129$	−11.5923	−1.02065
$130$	16.3051	1.43005
$131$	1.48020	0.129326	0.0646629	−	0.997907i	$-0.479403\pi$
$131$	1.48020	0.129326	0.0646629	+	0.997907i	$0.479403\pi$
$132$	19.6217	1.70785
$133$	5.49631	0.476590
$134$	−13.5066	−1.16679
$135$	−1.00000	−0.0860663
$136$	13.3086	1.14120
$137$	−6.34340	−0.541953	−0.270976	−	0.962586i	$-0.587347\pi$
$137$	−6.34340	−0.541953	−0.270976	+	0.962586i	$0.587347\pi$
$138$	5.69574	0.484853
$139$	−14.3017	−1.21305	−0.606526	−	0.795063i	$-0.707438\pi$
$139$	−14.3017	−1.21305	−0.606526	+	0.795063i	$0.707438\pi$
$140$	9.28139	0.784421
$141$	2.28064	0.192065
$142$	19.7975	1.66137
$143$	41.3784	3.46023
$144$	0.496716	0.0413930
$145$	−9.29296	−0.771738
$146$	2.91208	0.241006
$147$	0.701257	0.0578387
$148$	−35.6308	−2.92883
$149$	12.8000	1.04862	0.524308	−	0.851529i	$-0.324324\pi$
$149$	12.8000	1.04862	0.524308	+	0.851529i	$0.324324\pi$
$150$	−2.31182	−0.188759
$151$	−11.7748	−0.958220	−0.479110	−	0.877755i	$-0.659040\pi$
$151$	−11.7748	−0.958220	−0.479110	+	0.877755i	$0.659040\pi$
$152$	6.15613	0.499328
$153$	−4.28168	−0.346153
$154$	37.6391	3.03305
$155$	1.49528	0.120104
$156$	23.5885	1.88859
$157$	10.8829	0.868553	0.434277	−	0.900780i	$-0.357004\pi$
$157$	10.8829	0.868553	0.434277	+	0.900780i	$0.357004\pi$
$158$	21.6265	1.72051
$159$	−12.1035	−0.959871
$160$	−5.06820	−0.400676
$161$	6.83718	0.538845
$162$	−2.31182	−0.181634
$163$	22.9571	1.79814	0.899070	−	0.437804i	$-0.144244\pi$
$163$	22.9571	1.79814	0.899070	+	0.437804i	$0.144244\pi$
$164$	−41.1020	−3.20953
$165$	−5.86685	−0.456733
$166$	−24.9532	−1.93674
$167$	−18.0927	−1.40005	−0.700027	−	0.714116i	$-0.746829\pi$
$167$	−18.0927	−1.40005	−0.700027	+	0.714116i	$0.746829\pi$
$168$	8.62577	0.665493
$169$	36.7436	2.82643
$170$	−9.89847	−0.759178
$171$	−1.98057	−0.151458
$172$	−38.7706	−2.95623
$173$	−14.7996	−1.12520	−0.562598	−	0.826730i	$-0.690198\pi$
$173$	−14.7996	−1.12520	−0.562598	+	0.826730i	$0.690198\pi$
$174$	−21.4836	−1.62867
$175$	−2.77511	−0.209779
$176$	2.91416	0.219663
$177$	−1.21429	−0.0912713
$178$	−28.5538	−2.14020
$179$	14.3208	1.07038	0.535192	−	0.844730i	$-0.320239\pi$
$179$	14.3208	1.07038	0.535192	+	0.844730i	$0.320239\pi$
$180$	−3.34451	−0.249285
$181$	−14.6983	−1.09252	−0.546259	−	0.837616i	$-0.683949\pi$
$181$	−14.6983	−1.09252	−0.546259	+	0.837616i	$0.683949\pi$
$182$	45.2484	3.35403
$183$	4.42619	0.327193
$184$	7.65796	0.564552
$185$	10.6535	0.783263
$186$	3.45681	0.253466
$187$	−25.1200	−1.83695
$188$	7.62762	0.556302
$189$	−2.77511	−0.201860
$190$	−4.57872	−0.332175
$191$	13.2147	0.956182	0.478091	−	0.878310i	$-0.341329\pi$
$191$	13.2147	0.956182	0.478091	+	0.878310i	$0.341329\pi$
$192$	−12.7102	−0.917279
$193$	−21.7211	−1.56352	−0.781759	−	0.623581i	$-0.785677\pi$
$193$	−21.7211	−1.56352	−0.781759	+	0.623581i	$0.785677\pi$
$194$	21.8483	1.56862
$195$	−7.05291	−0.505070
$196$	2.34536	0.167526
$197$	3.79125	0.270115	0.135058	−	0.990838i	$-0.456878\pi$
$197$	3.79125	0.270115	0.135058	+	0.990838i	$0.456878\pi$
$198$	−13.5631	−0.963887
$199$	−9.17474	−0.650380	−0.325190	−	0.945649i	$-0.605428\pi$
$199$	−9.17474	−0.650380	−0.325190	+	0.945649i	$0.605428\pi$
$200$	−3.10826	−0.219787
$201$	5.84241	0.412092
$202$	−31.6873	−2.22951
$203$	−25.7890	−1.81003
$204$	−14.3201	−1.00261
$205$	12.2894	0.858329
$206$	28.3025	1.97193
$207$	−2.46375	−0.171242
$208$	3.50329	0.242910
$209$	−11.6197	−0.803752
$210$	−6.41556	−0.442716
$211$	−13.6439	−0.939287	−0.469643	−	0.882856i	$-0.655617\pi$
$211$	−13.6439	−0.939287	−0.469643	+	0.882856i	$0.655617\pi$
$212$	−40.4803	−2.78020
$213$	−8.56362	−0.586770
$214$	−30.0528	−2.05437
$215$	11.5923	0.790590
$216$	−3.10826	−0.211490
$217$	4.14957	0.281691
$218$	9.60994	0.650867
$219$	−1.25965	−0.0851193
$220$	−19.6217	−1.32290
$221$	−30.1983	−2.03136
$222$	24.6290	1.65299
$223$	−22.4133	−1.50091	−0.750453	−	0.660923i	$-0.770165\pi$
$223$	−22.4133	−1.50091	−0.750453	+	0.660923i	$0.770165\pi$
$224$	−14.0648	−0.939746
$225$	1.00000	0.0666667
$226$	14.0826	0.936759
$227$	−4.96339	−0.329431	−0.164716	−	0.986341i	$-0.552671\pi$
$227$	−4.96339	−0.329431	−0.164716	+	0.986341i	$0.552671\pi$
$228$	−6.62403	−0.438687
$229$	3.85618	0.254824	0.127412	−	0.991850i	$-0.459333\pi$
$229$	3.85618	0.254824	0.127412	+	0.991850i	$0.459333\pi$
$230$	−5.69574	−0.375566
$231$	−16.2812	−1.07122
$232$	−28.8849	−1.89639
$233$	−30.0629	−1.96948	−0.984742	−	0.174023i	$-0.944323\pi$
$233$	−30.0629	−1.96948	−0.984742	+	0.174023i	$0.944323\pi$
$234$	−16.3051	−1.06589
$235$	−2.28064	−0.148773
$236$	−4.06119	−0.264361
$237$	−9.35475	−0.607656
$238$	−27.4694	−1.78058
$239$	18.9476	1.22562	0.612808	−	0.790232i	$-0.290040\pi$
$239$	18.9476	1.22562	0.612808	+	0.790232i	$0.290040\pi$
$240$	−0.496716	−0.0320629
$241$	−17.5093	−1.12787	−0.563937	−	0.825818i	$-0.690714\pi$
$241$	−17.5093	−1.12787	−0.563937	+	0.825818i	$0.690714\pi$
$242$	−54.1426	−3.48042
$243$	1.00000	0.0641500
$244$	14.8034	0.947692
$245$	−0.701257	−0.0448017
$246$	28.4109	1.81141
$247$	−13.9688	−0.888813
$248$	4.64771	0.295130
$249$	10.7937	0.684026
$250$	2.31182	0.146212
$251$	−14.7697	−0.932257	−0.466129	−	0.884717i	$-0.654352\pi$
$251$	−14.7697	−0.932257	−0.466129	+	0.884717i	$0.654352\pi$
$252$	−9.28139	−0.584673
$253$	−14.4544	−0.908742
$254$	−13.3859	−0.839908
$255$	4.28168	0.268129
$256$	−19.0758	−1.19224
$257$	−1.99221	−0.124271	−0.0621353	−	0.998068i	$-0.519791\pi$
$257$	−1.99221	−0.124271	−0.0621353	+	0.998068i	$0.519791\pi$
$258$	26.7993	1.66845
$259$	29.5647	1.83706
$260$	−23.5885	−1.46290
$261$	9.29296	0.575220
$262$	−3.42196	−0.211409
$263$	16.0238	0.988071	0.494035	−	0.869442i	$-0.335521\pi$
$263$	16.0238	0.988071	0.494035	+	0.869442i	$0.335521\pi$
$264$	−18.2357	−1.12233
$265$	12.1035	0.743513
$266$	−12.7065	−0.779084
$267$	12.3512	0.755882
$268$	19.5400	1.19359
$269$	4.36037	0.265857	0.132928	−	0.991126i	$-0.457562\pi$
$269$	4.36037	0.265857	0.132928	+	0.991126i	$0.457562\pi$
$270$	2.31182	0.140693
$271$	−0.268065	−0.0162838	−0.00814191	−	0.999967i	$-0.502592\pi$
$271$	−0.268065	−0.0162838	−0.00814191	+	0.999967i	$0.502592\pi$
$272$	−2.12678	−0.128955
$273$	−19.5726	−1.18459
$274$	14.6648	0.885932
$275$	5.86685	0.353784
$276$	−8.24002	−0.495991
$277$	17.1570	1.03087	0.515433	−	0.856930i	$-0.327631\pi$
$277$	17.1570	1.03087	0.515433	+	0.856930i	$0.327631\pi$
$278$	33.0629	1.98298
$279$	−1.49528	−0.0895200
$280$	−8.62577	−0.515488
$281$	3.82317	0.228071	0.114036	−	0.993477i	$-0.463622\pi$
$281$	3.82317	0.228071	0.114036	+	0.993477i	$0.463622\pi$
$282$	−5.27243	−0.313969
$283$	2.68130	0.159387	0.0796935	−	0.996819i	$-0.474606\pi$
$283$	2.68130	0.159387	0.0796935	+	0.996819i	$0.474606\pi$
$284$	−28.6411	−1.69954
$285$	1.98057	0.117319
$286$	−95.6593	−5.65645
$287$	34.1045	2.01312
$288$	5.06820	0.298647
$289$	1.33280	0.0784001
$290$	21.4836	1.26156
$291$	−9.45070	−0.554010
$292$	−4.21291	−0.246542
$293$	1.92255	0.112317	0.0561584	−	0.998422i	$-0.482115\pi$
$293$	1.92255	0.112317	0.0561584	+	0.998422i	$0.482115\pi$
$294$	−1.62118	−0.0945491
$295$	1.21429	0.0706984
$296$	33.1139	1.92471
$297$	5.86685	0.340429
$298$	−29.5912	−1.71417
$299$	−17.3766	−1.00491
$300$	3.34451	0.193095
$301$	32.1700	1.85425
$302$	27.2212	1.56641
$303$	13.7066	0.787426
$304$	−0.983781	−0.0564237
$305$	−4.42619	−0.253443
$306$	9.89847	0.565858
$307$	−13.8335	−0.789520	−0.394760	−	0.918784i	$-0.629172\pi$
$307$	−13.8335	−0.789520	−0.394760	+	0.918784i	$0.629172\pi$
$308$	−54.4525	−3.10272
$309$	−12.2425	−0.696454
$310$	−3.45681	−0.196334
$311$	−7.13820	−0.404770	−0.202385	−	0.979306i	$-0.564869\pi$
$311$	−7.13820	−0.404770	−0.202385	+	0.979306i	$0.564869\pi$
$312$	−21.9223	−1.24110
$313$	−16.5718	−0.936694	−0.468347	−	0.883545i	$-0.655150\pi$
$313$	−16.5718	−0.936694	−0.468347	+	0.883545i	$0.655150\pi$
$314$	−25.1594	−1.41983
$315$	2.77511	0.156360
$316$	−31.2870	−1.76003
$317$	−15.7786	−0.886214	−0.443107	−	0.896469i	$-0.646124\pi$
$317$	−15.7786	−0.886214	−0.443107	+	0.896469i	$0.646124\pi$
$318$	27.9811	1.56910
$319$	54.5204	3.05256
$320$	12.7102	0.710521
$321$	12.9996	0.725569
$322$	−15.8063	−0.880852
$323$	8.48017	0.471849
$324$	3.34451	0.185806
$325$	7.05291	0.391225
$326$	−53.0727	−2.93943
$327$	−4.15687	−0.229876
$328$	38.1986	2.10917
$329$	−6.32904	−0.348931
$330$	13.5631	0.746624
$331$	13.1599	0.723334	0.361667	−	0.932307i	$-0.382208\pi$
$331$	13.1599	0.723334	0.361667	+	0.932307i	$0.382208\pi$
$332$	36.0998	1.98123
$333$	−10.6535	−0.583810
$334$	41.8270	2.28867
$335$	−5.84241	−0.319205
$336$	−1.37844	−0.0752002
$337$	−22.4607	−1.22351	−0.611755	−	0.791047i	$-0.709536\pi$
$337$	−22.4607	−1.22351	−0.611755	+	0.791047i	$0.709536\pi$
$338$	−84.9445	−4.62037
$339$	−6.09155	−0.330848
$340$	14.3201	0.776617
$341$	−8.77257	−0.475061
$342$	4.57872	0.247589
$343$	17.4797	0.943817
$344$	36.0319	1.94271
$345$	2.46375	0.132644
$346$	34.2141	1.83936
$347$	−24.0419	−1.29063	−0.645317	−	0.763915i	$-0.723275\pi$
$347$	−24.0419	−1.29063	−0.645317	+	0.763915i	$0.723275\pi$
$348$	31.0804	1.66608
$349$	−29.5431	−1.58141	−0.790704	−	0.612199i	$-0.790285\pi$
$349$	−29.5431	−1.58141	−0.790704	+	0.612199i	$0.790285\pi$
$350$	6.41556	0.342926
$351$	7.05291	0.376457
$352$	29.7344	1.58485
$353$	10.3182	0.549182	0.274591	−	0.961561i	$-0.411458\pi$
$353$	10.3182	0.549182	0.274591	+	0.961561i	$0.411458\pi$
$354$	2.80721	0.149201
$355$	8.56362	0.454510
$356$	41.3088	2.18936
$357$	11.8822	0.628870
$358$	−33.1070	−1.74976
$359$	20.8743	1.10170	0.550851	−	0.834604i	$-0.314303\pi$
$359$	20.8743	1.10170	0.550851	+	0.834604i	$0.314303\pi$
$360$	3.10826	0.163820
$361$	−15.0773	−0.793544
$362$	33.9799	1.78594
$363$	23.4199	1.22923
$364$	−65.4608	−3.43108
$365$	1.25965	0.0659331
$366$	−10.2325	−0.534864
$367$	31.9816	1.66942	0.834712	−	0.550687i	$-0.185634\pi$
$367$	31.9816	1.66942	0.834712	+	0.550687i	$0.185634\pi$
$368$	−1.22378	−0.0637941
$369$	−12.2894	−0.639760
$370$	−24.6290	−1.28040
$371$	33.5886	1.74383
$372$	−5.00097	−0.259288
$373$	−27.5998	−1.42906	−0.714532	−	0.699603i	$-0.753360\pi$
$373$	−27.5998	−1.42906	−0.714532	+	0.699603i	$0.753360\pi$
$374$	58.0728	3.00288
$375$	−1.00000	−0.0516398
$376$	−7.08882	−0.365578
$377$	65.5424	3.37561
$378$	6.41556	0.329981
$379$	−20.0849	−1.03169	−0.515847	−	0.856681i	$-0.672523\pi$
$379$	−20.0849	−1.03169	−0.515847	+	0.856681i	$0.672523\pi$
$380$	6.62403	0.339806
$381$	5.79022	0.296642
$382$	−30.5500	−1.56307
$383$	−20.1025	−1.02719	−0.513596	−	0.858032i	$-0.671687\pi$
$383$	−20.1025	−1.02719	−0.513596	+	0.858032i	$0.671687\pi$
$384$	19.2473	0.982208
$385$	16.2812	0.829765
$386$	50.2152	2.55589
$387$	−11.5923	−0.589271
$388$	−31.6080	−1.60465
$389$	−27.6842	−1.40365	−0.701824	−	0.712351i	$-0.747631\pi$
$389$	−27.6842	−1.40365	−0.701824	+	0.712351i	$0.747631\pi$
$390$	16.3051	0.825639
$391$	10.5490	0.533485
$392$	−2.17969	−0.110091
$393$	1.48020	0.0746663
$394$	−8.76468	−0.441558
$395$	9.35475	0.470689
$396$	19.6217	0.986028
$397$	13.4700	0.676038	0.338019	−	0.941139i	$-0.390243\pi$
$397$	13.4700	0.676038	0.338019	+	0.941139i	$0.390243\pi$
$398$	21.2103	1.06318
$399$	5.49631	0.275160
$400$	0.496716	0.0248358
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−13.5066	−0.673648
$403$	−10.5461	−0.525337
$404$	45.8420	2.28072
$405$	−1.00000	−0.0496904
$406$	59.6196	2.95887
$407$	−62.5026	−3.09814
$408$	13.3086	0.658873
$409$	20.3241	1.00496	0.502480	−	0.864589i	$-0.332421\pi$
$409$	20.3241	1.00496	0.502480	+	0.864589i	$0.332421\pi$
$410$	−28.4109	−1.40311
$411$	−6.34340	−0.312897
$412$	−40.9453	−2.01723
$413$	3.36978	0.165816
$414$	5.69574	0.279930
$415$	−10.7937	−0.529844
$416$	35.7456	1.75257
$417$	−14.3017	−0.700356
$418$	26.8627	1.31390
$419$	13.6491	0.666802	0.333401	−	0.942785i	$-0.391804\pi$
$419$	13.6491	0.666802	0.333401	+	0.942785i	$0.391804\pi$
$420$	9.28139	0.452885
$421$	−12.5037	−0.609392	−0.304696	−	0.952450i	$-0.598555\pi$
$421$	−12.5037	−0.609392	−0.304696	+	0.952450i	$0.598555\pi$
$422$	31.5423	1.53545
$423$	2.28064	0.110889
$424$	37.6208	1.82703
$425$	−4.28168	−0.207692
$426$	19.7975	0.959194
$427$	−12.2832	−0.594425
$428$	43.4774	2.10156
$429$	41.3784	1.99777
$430$	−26.7993	−1.29238
$431$	−22.1918	−1.06894	−0.534471	−	0.845187i	$-0.679489\pi$
$431$	−22.1918	−1.06894	−0.534471	+	0.845187i	$0.679489\pi$
$432$	0.496716	0.0238983
$433$	9.65970	0.464215	0.232108	−	0.972690i	$-0.425438\pi$
$433$	9.65970	0.464215	0.232108	+	0.972690i	$0.425438\pi$
$434$	−9.59305	−0.460481
$435$	−9.29296	−0.445563
$436$	−13.9027	−0.665818
$437$	4.87962	0.233424
$438$	2.91208	0.139145
$439$	17.8339	0.851168	0.425584	−	0.904919i	$-0.360069\pi$
$439$	17.8339	0.851168	0.425584	+	0.904919i	$0.360069\pi$
$440$	18.2357	0.869352
$441$	0.701257	0.0333932
$442$	69.8131	3.32067
$443$	2.69762	0.128168	0.0640839	−	0.997945i	$-0.479587\pi$
$443$	2.69762	0.128168	0.0640839	+	0.997945i	$0.479587\pi$
$444$	−35.6308	−1.69096
$445$	−12.3512	−0.585504
$446$	51.8155	2.45354
$447$	12.8000	0.605418
$448$	35.2722	1.66646
$449$	21.4777	1.01360	0.506798	−	0.862065i	$-0.330829\pi$
$449$	21.4777	1.01360	0.506798	+	0.862065i	$0.330829\pi$
$450$	−2.31182	−0.108980
$451$	−72.1000	−3.39506
$452$	−20.3732	−0.958277
$453$	−11.7748	−0.553229
$454$	11.4744	0.538523
$455$	19.5726	0.917579
$456$	6.15613	0.288287
$457$	31.5801	1.47726	0.738628	−	0.674113i	$-0.235474\pi$
$457$	31.5801	1.47726	0.738628	+	0.674113i	$0.235474\pi$
$458$	−8.91479	−0.416561
$459$	−4.28168	−0.199852
$460$	8.24002	0.384193
$461$	16.9261	0.788327	0.394164	−	0.919040i	$-0.371034\pi$
$461$	16.9261	0.788327	0.394164	+	0.919040i	$0.371034\pi$
$462$	37.6391	1.75113
$463$	32.0398	1.48902	0.744509	−	0.667613i	$-0.232684\pi$
$463$	32.0398	1.48902	0.744509	+	0.667613i	$0.232684\pi$
$464$	4.61596	0.214291
$465$	1.49528	0.0693419
$466$	69.4999	3.21952
$467$	−15.8465	−0.733290	−0.366645	−	0.930361i	$-0.619494\pi$
$467$	−15.8465	−0.733290	−0.366645	+	0.930361i	$0.619494\pi$
$468$	23.5885	1.09038
$469$	−16.2133	−0.748663
$470$	5.27243	0.243199
$471$	10.8829	0.501459
$472$	3.77431	0.173727
$473$	−68.0104	−3.12712
$474$	21.6265	0.993338
$475$	−1.98057	−0.0908748
$476$	39.7400	1.82148
$477$	−12.1035	−0.554182
$478$	−43.8033	−2.00352
$479$	−6.79748	−0.310585	−0.155292	−	0.987869i	$-0.549632\pi$
$479$	−6.79748	−0.310585	−0.155292	+	0.987869i	$0.549632\pi$
$480$	−5.06820	−0.231331
$481$	−75.1384	−3.42601
$482$	40.4784	1.84374
$483$	6.83718	0.311102
$484$	78.3280	3.56037
$485$	9.45070	0.429134
$486$	−2.31182	−0.104866
$487$	−8.21951	−0.372462	−0.186231	−	0.982506i	$-0.559627\pi$
$487$	−8.21951	−0.372462	−0.186231	+	0.982506i	$0.559627\pi$
$488$	−13.7577	−0.622784
$489$	22.9571	1.03816
$490$	1.62118	0.0732375
$491$	−5.53606	−0.249839	−0.124919	−	0.992167i	$-0.539867\pi$
$491$	−5.53606	−0.249839	−0.124919	+	0.992167i	$0.539867\pi$
$492$	−41.1020	−1.85302
$493$	−39.7895	−1.79203
$494$	32.2933	1.45294
$495$	−5.86685	−0.263695
$496$	−0.742729	−0.0333495
$497$	23.7650	1.06601
$498$	−24.9532	−1.11818
$499$	−3.65481	−0.163612	−0.0818058	−	0.996648i	$-0.526069\pi$
$499$	−3.65481	−0.163612	−0.0818058	+	0.996648i	$0.526069\pi$
$500$	−3.34451	−0.149571
$501$	−18.0927	−0.808322
$502$	34.1450	1.52396
$503$	12.7322	0.567699	0.283849	−	0.958869i	$-0.408388\pi$
$503$	12.7322	0.567699	0.283849	+	0.958869i	$0.408388\pi$
$504$	8.62577	0.384222
$505$	−13.7066	−0.609938
$506$	33.4160	1.48552
$507$	36.7436	1.63184
$508$	19.3654	0.859202
$509$	33.0963	1.46697	0.733483	−	0.679708i	$-0.237894\pi$
$509$	33.0963	1.46697	0.733483	+	0.679708i	$0.237894\pi$
$510$	−9.89847	−0.438312
$511$	3.49567	0.154639
$512$	5.60530	0.247721
$513$	−1.98057	−0.0874443
$514$	4.60563	0.203145
$515$	12.2425	0.539471
$516$	−38.7706	−1.70678
$517$	13.3802	0.588460
$518$	−68.3483	−3.00305
$519$	−14.7996	−0.649632
$520$	21.9223	0.961355
$521$	−16.8931	−0.740101	−0.370050	−	0.929012i	$-0.620660\pi$
$521$	−16.8931	−0.740101	−0.370050	+	0.929012i	$0.620660\pi$
$522$	−21.4836	−0.940313
$523$	−18.7162	−0.818403	−0.409201	−	0.912444i	$-0.634193\pi$
$523$	−18.7162	−0.818403	−0.409201	+	0.912444i	$0.634193\pi$
$524$	4.95055	0.216266
$525$	−2.77511	−0.121116
$526$	−37.0442	−1.61520
$527$	6.40231	0.278889
$528$	2.91416	0.126822
$529$	−16.9300	−0.736085
$530$	−27.9811	−1.21542
$531$	−1.21429	−0.0526955
$532$	18.3824	0.796980
$533$	−86.6760	−3.75436
$534$	−28.5538	−1.23564
$535$	−12.9996	−0.562023
$536$	−18.1597	−0.784380
$537$	14.3208	0.617987
$538$	−10.0804	−0.434596
$539$	4.11417	0.177210
$540$	−3.34451	−0.143925
$541$	30.7161	1.32059	0.660295	−	0.751006i	$-0.270431\pi$
$541$	30.7161	1.32059	0.660295	+	0.751006i	$0.270431\pi$
$542$	0.619719	0.0266192
$543$	−14.6983	−0.630766
$544$	−21.7004	−0.930398
$545$	4.15687	0.178061
$546$	45.2484	1.93645
$547$	−6.43713	−0.275232	−0.137616	−	0.990486i	$-0.543944\pi$
$547$	−6.43713	−0.275232	−0.137616	+	0.990486i	$0.543944\pi$
$548$	−21.2155	−0.906283
$549$	4.42619	0.188905
$550$	−13.5631	−0.578332
$551$	−18.4054	−0.784095
$552$	7.65796	0.325945
$553$	25.9605	1.10395
$554$	−39.6639	−1.68516
$555$	10.6535	0.452217
$556$	−47.8321	−2.02853
$557$	12.1351	0.514182	0.257091	−	0.966387i	$-0.417236\pi$
$557$	12.1351	0.514182	0.257091	+	0.966387i	$0.417236\pi$
$558$	3.45681	0.146339
$559$	−81.7596	−3.45806
$560$	1.37844	0.0582499
$561$	−25.1200	−1.06057
$562$	−8.83848	−0.372829
$563$	16.3837	0.690493	0.345246	−	0.938512i	$-0.387795\pi$
$563$	16.3837	0.690493	0.345246	+	0.938512i	$0.387795\pi$
$564$	7.62762	0.321181
$565$	6.09155	0.256274
$566$	−6.19869	−0.260550
$567$	−2.77511	−0.116544
$568$	26.6179	1.11686
$569$	2.97701	0.124803	0.0624013	−	0.998051i	$-0.480124\pi$
$569$	2.97701	0.124803	0.0624013	+	0.998051i	$0.480124\pi$
$570$	−4.57872	−0.191782
$571$	−11.7117	−0.490117	−0.245059	−	0.969508i	$-0.578807\pi$
$571$	−11.7117	−0.490117	−0.245059	+	0.969508i	$0.578807\pi$
$572$	138.390	5.78639
$573$	13.2147	0.552052
$574$	−78.8434	−3.29086
$575$	−2.46375	−0.102745
$576$	−12.7102	−0.529591
$577$	−45.7526	−1.90470	−0.952352	−	0.305000i	$-0.901344\pi$
$577$	−45.7526	−1.90470	−0.952352	+	0.305000i	$0.901344\pi$
$578$	−3.08120	−0.128161
$579$	−21.7211	−0.902697
$580$	−31.0804	−1.29054
$581$	−29.9539	−1.24270
$582$	21.8483	0.905642
$583$	−71.0095	−2.94091
$584$	3.91532	0.162017
$585$	−7.05291	−0.291602
$586$	−4.44459	−0.183604
$587$	−29.2900	−1.20893	−0.604464	−	0.796632i	$-0.706613\pi$
$587$	−29.2900	−1.20893	−0.604464	+	0.796632i	$0.706613\pi$
$588$	2.34536	0.0967210
$589$	2.96151	0.122027
$590$	−2.80721	−0.115571
$591$	3.79125	0.155951
$592$	−5.29177	−0.217491
$593$	−1.09051	−0.0447821	−0.0223910	−	0.999749i	$-0.507128\pi$
$593$	−1.09051	−0.0447821	−0.0223910	+	0.999749i	$0.507128\pi$
$594$	−13.5631	−0.556500
$595$	−11.8822	−0.487121
$596$	42.8096	1.75355
$597$	−9.17474	−0.375497
$598$	40.1715	1.64274
$599$	38.3944	1.56875	0.784377	−	0.620285i	$-0.212983\pi$
$599$	38.3944	1.56875	0.784377	+	0.620285i	$0.212983\pi$
$600$	−3.10826	−0.126894
$601$	−24.4622	−0.997834	−0.498917	−	0.866650i	$-0.666269\pi$
$601$	−24.4622	−0.997834	−0.498917	+	0.866650i	$0.666269\pi$
$602$	−74.3712	−3.03115
$603$	5.84241	0.237921
$604$	−39.3809	−1.60239
$605$	−23.4199	−0.952154
$606$	−31.6873	−1.28721
$607$	3.18713	0.129362	0.0646809	−	0.997906i	$-0.479397\pi$
$607$	3.18713	0.129362	0.0646809	+	0.997906i	$0.479397\pi$
$608$	−10.0379	−0.407092
$609$	−25.7890	−1.04502
$610$	10.2325	0.414304
$611$	16.0852	0.650736
$612$	−14.3201	−0.578856
$613$	−5.46749	−0.220830	−0.110415	−	0.993886i	$-0.535218\pi$
$613$	−5.46749	−0.220830	−0.110415	+	0.993886i	$0.535218\pi$
$614$	31.9806	1.29063
$615$	12.2894	0.495556
$616$	50.6061	2.03898
$617$	−15.2303	−0.613149	−0.306574	−	0.951847i	$-0.599183\pi$
$617$	−15.2303	−0.613149	−0.306574	+	0.951847i	$0.599183\pi$
$618$	28.3025	1.13850
$619$	34.8601	1.40115	0.700573	−	0.713581i	$-0.252928\pi$
$619$	34.8601	1.40115	0.700573	+	0.713581i	$0.252928\pi$
$620$	5.00097	0.200844
$621$	−2.46375	−0.0988668
$622$	16.5022	0.661679
$623$	−34.2760	−1.37324
$624$	3.50329	0.140244
$625$	1.00000	0.0400000
$626$	38.3110	1.53122
$627$	−11.6197	−0.464046
$628$	36.3981	1.45244
$629$	45.6150	1.81879
$630$	−6.41556	−0.255602
$631$	−30.1830	−1.20157	−0.600783	−	0.799412i	$-0.705144\pi$
$631$	−30.1830	−1.20157	−0.600783	+	0.799412i	$0.705144\pi$
$632$	29.0770	1.15662
$633$	−13.6439	−0.542297
$634$	36.4772	1.44870
$635$	−5.79022	−0.229778
$636$	−40.4803	−1.60515
$637$	4.94591	0.195964
$638$	−126.041	−4.99002
$639$	−8.56362	−0.338772
$640$	−19.2473	−0.760815
$641$	−24.0786	−0.951048	−0.475524	−	0.879703i	$-0.657742\pi$
$641$	−24.0786	−0.951048	−0.475524	+	0.879703i	$0.657742\pi$
$642$	−30.0528	−1.18609
$643$	13.4134	0.528973	0.264486	−	0.964389i	$-0.414798\pi$
$643$	13.4134	0.528973	0.264486	+	0.964389i	$0.414798\pi$
$644$	22.8670	0.901086
$645$	11.5923	0.456447
$646$	−19.6046	−0.771334
$647$	−19.0967	−0.750767	−0.375383	−	0.926870i	$-0.622489\pi$
$647$	−19.0967	−0.750767	−0.375383	+	0.926870i	$0.622489\pi$
$648$	−3.10826	−0.122104
$649$	−7.12403	−0.279642
$650$	−16.3051	−0.639537
$651$	4.14957	0.162634
$652$	76.7803	3.00695
$653$	3.78774	0.148226	0.0741128	−	0.997250i	$-0.476388\pi$
$653$	3.78774	0.148226	0.0741128	+	0.997250i	$0.476388\pi$
$654$	9.60994	0.375778
$655$	−1.48020	−0.0578363
$656$	−6.10434	−0.238334
$657$	−1.25965	−0.0491436
$658$	14.6316	0.570399
$659$	24.4395	0.952028	0.476014	−	0.879438i	$-0.342081\pi$
$659$	24.4395	0.952028	0.476014	+	0.879438i	$0.342081\pi$
$660$	−19.6217	−0.763774
$661$	4.22613	0.164377	0.0821887	−	0.996617i	$-0.473809\pi$
$661$	4.22613	0.164377	0.0821887	+	0.996617i	$0.473809\pi$
$662$	−30.4233	−1.18244
$663$	−30.1983	−1.17281
$664$	−33.5497	−1.30198
$665$	−5.49631	−0.213138
$666$	24.6290	0.954355
$667$	−22.8955	−0.886517
$668$	−60.5111	−2.34125
$669$	−22.4133	−0.866549
$670$	13.5066	0.521805
$671$	25.9678	1.00247
$672$	−14.0648	−0.542563
$673$	15.3709	0.592506	0.296253	−	0.955109i	$-0.404263\pi$
$673$	15.3709	0.592506	0.296253	+	0.955109i	$0.404263\pi$
$674$	51.9250	2.00008
$675$	1.00000	0.0384900
$676$	122.889	4.72651
$677$	−25.5699	−0.982730	−0.491365	−	0.870954i	$-0.663502\pi$
$677$	−25.5699	−0.982730	−0.491365	+	0.870954i	$0.663502\pi$
$678$	14.0826	0.540838
$679$	26.2268	1.00649
$680$	−13.3086	−0.510361
$681$	−4.96339	−0.190197
$682$	20.2806	0.776584
$683$	11.0389	0.422392	0.211196	−	0.977444i	$-0.432264\pi$
$683$	11.0389	0.422392	0.211196	+	0.977444i	$0.432264\pi$
$684$	−6.62403	−0.253276
$685$	6.34340	0.242369
$686$	−40.4100	−1.54286
$687$	3.85618	0.147122
$688$	−5.75809	−0.219525
$689$	−85.3650	−3.25215
$690$	−5.69574	−0.216833
$691$	−26.7314	−1.01691	−0.508455	−	0.861088i	$-0.669783\pi$
$691$	−26.7314	−1.01691	−0.508455	+	0.861088i	$0.669783\pi$
$692$	−49.4975	−1.88161
$693$	−16.2812	−0.618471
$694$	55.5804	2.10980
$695$	14.3017	0.542494
$696$	−28.8849	−1.09488
$697$	52.6193	1.99310
$698$	68.2984	2.58513
$699$	−30.0629	−1.13708
$700$	−9.28139	−0.350804
$701$	−17.2979	−0.653331	−0.326665	−	0.945140i	$-0.605925\pi$
$701$	−17.2979	−0.653331	−0.326665	+	0.945140i	$0.605925\pi$
$702$	−16.3051	−0.615395
$703$	21.1001	0.795804
$704$	−74.5688	−2.81042
$705$	−2.28064	−0.0858939
$706$	−23.8538	−0.897749
$707$	−38.0375	−1.43055
$708$	−4.06119	−0.152629
$709$	−37.6896	−1.41546	−0.707731	−	0.706482i	$-0.750281\pi$
$709$	−37.6896	−1.41546	−0.707731	+	0.706482i	$0.750281\pi$
$710$	−19.7975	−0.742989
$711$	−9.35475	−0.350831
$712$	−38.3908	−1.43876
$713$	3.68399	0.137966
$714$	−27.4694	−1.02802
$715$	−41.3784	−1.54746
$716$	47.8959	1.78995
$717$	18.9476	0.707609
$718$	−48.2575	−1.80096
$719$	−1.85227	−0.0690779	−0.0345389	−	0.999403i	$-0.510996\pi$
$719$	−1.85227	−0.0690779	−0.0345389	+	0.999403i	$0.510996\pi$
$720$	−0.496716	−0.0185115
$721$	33.9744	1.26527
$722$	34.8561	1.29721
$723$	−17.5093	−0.651178
$724$	−49.1587	−1.82697
$725$	9.29296	0.345132
$726$	−54.1426	−2.00942
$727$	27.3250	1.01343	0.506715	−	0.862114i	$-0.330860\pi$
$727$	27.3250	1.01343	0.506715	+	0.862114i	$0.330860\pi$
$728$	60.8368	2.25476
$729$	1.00000	0.0370370
$730$	−2.91208	−0.107781
$731$	49.6346	1.83580
$732$	14.8034	0.547150
$733$	9.67672	0.357418	0.178709	−	0.983902i	$-0.442808\pi$
$733$	9.67672	0.357418	0.178709	+	0.983902i	$0.442808\pi$
$734$	−73.9356	−2.72901
$735$	−0.701257	−0.0258663
$736$	−12.4868	−0.460268
$737$	34.2765	1.26259
$738$	28.4109	1.04582
$739$	−3.28499	−0.120840	−0.0604202	−	0.998173i	$-0.519244\pi$
$739$	−3.28499	−0.120840	−0.0604202	+	0.998173i	$0.519244\pi$
$740$	35.6308	1.30981
$741$	−13.9688	−0.513156
$742$	−77.6508	−2.85065
$743$	−33.8393	−1.24144	−0.620721	−	0.784032i	$-0.713160\pi$
$743$	−33.8393	−1.24144	−0.620721	+	0.784032i	$0.713160\pi$
$744$	4.64771	0.170393
$745$	−12.8000	−0.468955
$746$	63.8058	2.33610
$747$	10.7937	0.394922
$748$	−84.0140	−3.07185
$749$	−36.0755	−1.31817
$750$	2.31182	0.0844157
$751$	43.0652	1.57147	0.785736	−	0.618562i	$-0.212284\pi$
$751$	43.0652	1.57147	0.785736	+	0.618562i	$0.212284\pi$
$752$	1.13283	0.0413101
$753$	−14.7697	−0.538239
$754$	−151.522	−5.51811
$755$	11.7748	0.428529
$756$	−9.28139	−0.337561
$757$	−12.4562	−0.452729	−0.226364	−	0.974043i	$-0.572684\pi$
$757$	−12.4562	−0.452729	−0.226364	+	0.974043i	$0.572684\pi$
$758$	46.4328	1.68651
$759$	−14.4544	−0.524663
$760$	−6.15613	−0.223306
$761$	41.9726	1.52151	0.760754	−	0.649041i	$-0.224830\pi$
$761$	41.9726	1.52151	0.760754	+	0.649041i	$0.224830\pi$
$762$	−13.3859	−0.484921
$763$	11.5358	0.417624
$764$	44.1967	1.59898
$765$	4.28168	0.154805
$766$	46.4734	1.67915
$767$	−8.56425	−0.309237
$768$	−19.0758	−0.688339
$769$	−19.1679	−0.691212	−0.345606	−	0.938380i	$-0.612327\pi$
$769$	−19.1679	−0.691212	−0.345606	+	0.938380i	$0.612327\pi$
$770$	−37.6391	−1.35642
$771$	−1.99221	−0.0717476
$772$	−72.6463	−2.61460
$773$	22.9660	0.826031	0.413016	−	0.910724i	$-0.364475\pi$
$773$	22.9660	0.826031	0.413016	+	0.910724i	$0.364475\pi$
$774$	26.7993	0.963283
$775$	−1.49528	−0.0537120
$776$	29.3752	1.05451
$777$	29.5647	1.06063
$778$	64.0010	2.29455
$779$	24.3400	0.872072
$780$	−23.5885	−0.844604
$781$	−50.2415	−1.79778
$782$	−24.3873	−0.872089
$783$	9.29296	0.332103
$784$	0.348326	0.0124402
$785$	−10.8829	−0.388429
$786$	−3.42196	−0.122057
$787$	13.4409	0.479117	0.239558	−	0.970882i	$-0.422997\pi$
$787$	13.4409	0.479117	0.239558	+	0.970882i	$0.422997\pi$
$788$	12.6799	0.451701
$789$	16.0238	0.570463
$790$	−21.6265	−0.769436
$791$	16.9048	0.601064
$792$	−18.2357	−0.647977
$793$	31.2175	1.10857
$794$	−31.1401	−1.10512
$795$	12.1035	0.429267
$796$	−30.6850	−1.08760
$797$	−13.5443	−0.479765	−0.239882	−	0.970802i	$-0.577109\pi$
$797$	−13.5443	−0.479765	−0.239882	+	0.970802i	$0.577109\pi$
$798$	−12.7065	−0.449804
$799$	−9.76498	−0.345460
$800$	5.06820	0.179188
$801$	12.3512	0.436409
$802$	−2.31182	−0.0816332
$803$	−7.39018	−0.260794
$804$	19.5400	0.689122
$805$	−6.83718	−0.240979
$806$	24.3806	0.858770
$807$	4.36037	0.153492
$808$	−42.6038	−1.49880
$809$	−35.1829	−1.23696	−0.618482	−	0.785799i	$-0.712252\pi$
$809$	−35.1829	−1.23696	−0.618482	+	0.785799i	$0.712252\pi$
$810$	2.31182	0.0812290
$811$	−2.77258	−0.0973586	−0.0486793	−	0.998814i	$-0.515501\pi$
$811$	−2.77258	−0.0973586	−0.0486793	+	0.998814i	$0.515501\pi$
$812$	−86.2516	−3.02684
$813$	−0.268065	−0.00940147
$814$	144.495	5.06454
$815$	−22.9571	−0.804153
$816$	−2.12678	−0.0744522
$817$	22.9594	0.803248
$818$	−46.9856	−1.64281
$819$	−19.5726	−0.683923
$820$	41.1020	1.43534
$821$	−52.0724	−1.81734	−0.908669	−	0.417517i	$-0.862900\pi$
$821$	−52.0724	−1.81734	−0.908669	+	0.417517i	$0.862900\pi$
$822$	14.6648	0.511493
$823$	37.2947	1.30001	0.650005	−	0.759930i	$-0.274767\pi$
$823$	37.2947	1.30001	0.650005	+	0.759930i	$0.274767\pi$
$824$	38.0530	1.32564
$825$	5.86685	0.204257
$826$	−7.79032	−0.271060
$827$	−38.1578	−1.32688	−0.663439	−	0.748230i	$-0.730904\pi$
$827$	−38.1578	−1.32688	−0.663439	+	0.748230i	$0.730904\pi$
$828$	−8.24002	−0.286361
$829$	43.1670	1.49925	0.749626	−	0.661862i	$-0.230234\pi$
$829$	43.1670	1.49925	0.749626	+	0.661862i	$0.230234\pi$
$830$	24.9532	0.866138
$831$	17.1570	0.595170
$832$	−89.6439	−3.10784
$833$	−3.00256	−0.104033
$834$	33.0629	1.14487
$835$	18.0927	0.626123
$836$	−38.8622	−1.34408
$837$	−1.49528	−0.0516844
$838$	−31.5542	−1.09002
$839$	12.0334	0.415439	0.207719	−	0.978188i	$-0.433396\pi$
$839$	12.0334	0.415439	0.207719	+	0.978188i	$0.433396\pi$
$840$	−8.62577	−0.297617
$841$	57.3591	1.97790
$842$	28.9062	0.996174
$843$	3.82317	0.131677
$844$	−45.6322	−1.57073
$845$	−36.7436	−1.26402
$846$	−5.27243	−0.181270
$847$	−64.9929	−2.23318
$848$	−6.01201	−0.206453
$849$	2.68130	0.0920221
$850$	9.89847	0.339515
$851$	26.2476	0.899756
$852$	−28.6411	−0.981228
$853$	−1.36147	−0.0466160	−0.0233080	−	0.999728i	$-0.507420\pi$
$853$	−1.36147	−0.0466160	−0.0233080	+	0.999728i	$0.507420\pi$
$854$	28.3965	0.971708
$855$	1.98057	0.0677341
$856$	−40.4062	−1.38106
$857$	0.367264	0.0125455	0.00627274	−	0.999980i	$-0.498003\pi$
$857$	0.367264	0.0125455	0.00627274	+	0.999980i	$0.498003\pi$
$858$	−95.6593	−3.26575
$859$	−41.2939	−1.40893	−0.704465	−	0.709739i	$-0.748813\pi$
$859$	−41.2939	−1.40893	−0.704465	+	0.709739i	$0.748813\pi$
$860$	38.7706	1.32207
$861$	34.1045	1.16228
$862$	51.3034	1.74740
$863$	−14.1945	−0.483186	−0.241593	−	0.970378i	$-0.577670\pi$
$863$	−14.1945	−0.483186	−0.241593	+	0.970378i	$0.577670\pi$
$864$	5.06820	0.172424
$865$	14.7996	0.503203
$866$	−22.3315	−0.758854
$867$	1.33280	0.0452643
$868$	13.8783	0.471059
$869$	−54.8829	−1.86177
$870$	21.4836	0.728364
$871$	41.2060	1.39621
$872$	12.9206	0.437548
$873$	−9.45070	−0.319858
$874$	−11.2808	−0.381579
$875$	2.77511	0.0938160
$876$	−4.21291	−0.142341
$877$	46.4541	1.56864	0.784322	−	0.620354i	$-0.213011\pi$
$877$	46.4541	1.56864	0.784322	+	0.620354i	$0.213011\pi$
$878$	−41.2289	−1.39141
$879$	1.92255	0.0648461
$880$	−2.91416	−0.0982362
$881$	15.3021	0.515541	0.257771	−	0.966206i	$-0.417012\pi$
$881$	15.3021	0.515541	0.257771	+	0.966206i	$0.417012\pi$
$882$	−1.62118	−0.0545880
$883$	−3.55237	−0.119547	−0.0597734	−	0.998212i	$-0.519038\pi$
$883$	−3.55237	−0.119547	−0.0597734	+	0.998212i	$0.519038\pi$
$884$	−100.999	−3.39695
$885$	1.21429	0.0408178
$886$	−6.23641	−0.209516
$887$	−4.71624	−0.158356	−0.0791778	−	0.996861i	$-0.525230\pi$
$887$	−4.71624	−0.158356	−0.0791778	+	0.996861i	$0.525230\pi$
$888$	33.1139	1.11123
$889$	−16.0685	−0.538921
$890$	28.5538	0.957125
$891$	5.86685	0.196547
$892$	−74.9615	−2.50990
$893$	−4.51697	−0.151155
$894$	−29.5912	−0.989679
$895$	−14.3208	−0.478691
$896$	−53.4134	−1.78441
$897$	−17.3766	−0.580187
$898$	−49.6526	−1.65693
$899$	−13.8956	−0.463443
$900$	3.34451	0.111484
$901$	51.8234	1.72649
$902$	166.682	5.54991
$903$	32.1700	1.07055
$904$	18.9341	0.629740
$905$	14.6983	0.488589
$906$	27.2212	0.904364
$907$	−28.9234	−0.960387	−0.480193	−	0.877163i	$-0.659433\pi$
$907$	−28.9234	−0.960387	−0.480193	+	0.877163i	$0.659433\pi$
$908$	−16.6001	−0.550893
$909$	13.7066	0.454621
$910$	−45.2484	−1.49997
$911$	−25.2160	−0.835442	−0.417721	−	0.908575i	$-0.637171\pi$
$911$	−25.2160	−0.835442	−0.417721	+	0.908575i	$0.637171\pi$
$912$	−0.983781	−0.0325762
$913$	63.3253	2.09576
$914$	−73.0075	−2.41487
$915$	−4.42619	−0.146325
$916$	12.8970	0.426130
$917$	−4.10773	−0.135649
$918$	9.89847	0.326698
$919$	−25.7068	−0.847989	−0.423994	−	0.905665i	$-0.639372\pi$
$919$	−25.7068	−0.847989	−0.423994	+	0.905665i	$0.639372\pi$
$920$	−7.65796	−0.252476
$921$	−13.8335	−0.455830
$922$	−39.1301	−1.28868
$923$	−60.3985	−1.98804
$924$	−54.4525	−1.79136
$925$	−10.6535	−0.350286
$926$	−74.0703	−2.43410
$927$	−12.2425	−0.402098
$928$	47.0986	1.54609
$929$	26.0984	0.856260	0.428130	−	0.903717i	$-0.359172\pi$
$929$	26.0984	0.856260	0.428130	+	0.903717i	$0.359172\pi$
$930$	−3.45681	−0.113353
$931$	−1.38889	−0.0455190
$932$	−100.545	−3.29348
$933$	−7.13820	−0.233694
$934$	36.6343	1.19871
$935$	25.1200	0.821511
$936$	−21.9223	−0.716552
$937$	5.93177	0.193782	0.0968912	−	0.995295i	$-0.469110\pi$
$937$	5.93177	0.193782	0.0968912	+	0.995295i	$0.469110\pi$
$938$	37.4823	1.22384
$939$	−16.5718	−0.540801
$940$	−7.62762	−0.248786
$941$	5.16212	0.168280	0.0841402	−	0.996454i	$-0.473186\pi$
$941$	5.16212	0.168280	0.0841402	+	0.996454i	$0.473186\pi$
$942$	−25.1594	−0.819737
$943$	30.2780	0.985986
$944$	−0.603155	−0.0196310
$945$	2.77511	0.0902745
$946$	157.228	5.11191
$947$	−15.3571	−0.499038	−0.249519	−	0.968370i	$-0.580272\pi$
$947$	−15.3571	−0.499038	−0.249519	+	0.968370i	$0.580272\pi$
$948$	−31.2870	−1.01616
$949$	−8.88420	−0.288393
$950$	4.57872	0.148553
$951$	−15.7786	−0.511656
$952$	−36.9328	−1.19700
$953$	−15.7986	−0.511766	−0.255883	−	0.966708i	$-0.582366\pi$
$953$	−15.7986	−0.511766	−0.255883	+	0.966708i	$0.582366\pi$
$954$	27.9811	0.905923
$955$	−13.2147	−0.427618
$956$	63.3702	2.04954
$957$	54.5204	1.76239
$958$	15.7146	0.507714
$959$	17.6036	0.568451
$960$	12.7102	0.410220
$961$	−28.7641	−0.927876
$962$	173.706	5.60052
$963$	12.9996	0.418907
$964$	−58.5600	−1.88609
$965$	21.7211	0.699226
$966$	−15.8063	−0.508560
$967$	−2.39213	−0.0769256	−0.0384628	−	0.999260i	$-0.512246\pi$
$967$	−2.39213	−0.0769256	−0.0384628	+	0.999260i	$0.512246\pi$
$968$	−72.7951	−2.33972
$969$	8.48017	0.272422
$970$	−21.8483	−0.701507
$971$	−24.0134	−0.770627	−0.385313	−	0.922786i	$-0.625907\pi$
$971$	−24.0134	−0.770627	−0.385313	+	0.922786i	$0.625907\pi$
$972$	3.34451	0.107275
$973$	39.6888	1.27236
$974$	19.0020	0.608864
$975$	7.05291	0.225874
$976$	2.19856	0.0703741
$977$	9.54485	0.305367	0.152683	−	0.988275i	$-0.451209\pi$
$977$	9.54485	0.305367	0.152683	+	0.988275i	$0.451209\pi$
$978$	−53.0727	−1.69708
$979$	72.4627	2.31592
$980$	−2.34536	−0.0749198
$981$	−4.15687	−0.132719
$982$	12.7984	0.408412
$983$	2.93086	0.0934800	0.0467400	−	0.998907i	$-0.485117\pi$
$983$	2.93086	0.0934800	0.0467400	+	0.998907i	$0.485117\pi$
$984$	38.1986	1.21773
$985$	−3.79125	−0.120799
$986$	91.9861	2.92944
$987$	−6.32904	−0.201456
$988$	−46.7187	−1.48632
$989$	28.5605	0.908172
$990$	13.5631	0.431063
$991$	12.8674	0.408746	0.204373	−	0.978893i	$-0.434485\pi$
$991$	12.8674	0.408746	0.204373	+	0.978893i	$0.434485\pi$
$992$	−7.57837	−0.240614
$993$	13.1599	0.417617
$994$	−54.9404	−1.74260
$995$	9.17474	0.290859
$996$	36.0998	1.14386
$997$	−40.3033	−1.27642	−0.638209	−	0.769863i	$-0.720324\pi$
$997$	−40.3033	−1.27642	−0.638209	+	0.769863i	$0.720324\pi$
$998$	8.44925	0.267456
$999$	−10.6535	−0.337063

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.c.1.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.c.1.3	✓	28	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31182 q^{2} +1.00000 q^{3} +3.34451 q^{4} -1.00000 q^{5} -2.31182 q^{6} -2.77511 q^{7} -3.10826 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.31182 q^{2} +1.00000 q^{3} +3.34451 q^{4} -1.00000 q^{5} -2.31182 q^{6} -2.77511 q^{7} -3.10826 q^{8} +1.00000 q^{9} +2.31182 q^{10} +5.86685 q^{11} +3.34451 q^{12} +7.05291 q^{13} +6.41556 q^{14} -1.00000 q^{15} +0.496716 q^{16} -4.28168 q^{17} -2.31182 q^{18} -1.98057 q^{19} -3.34451 q^{20} -2.77511 q^{21} -13.5631 q^{22} -2.46375 q^{23} -3.10826 q^{24} +1.00000 q^{25} -16.3051 q^{26} +1.00000 q^{27} -9.28139 q^{28} +9.29296 q^{29} +2.31182 q^{30} -1.49528 q^{31} +5.06820 q^{32} +5.86685 q^{33} +9.89847 q^{34} +2.77511 q^{35} +3.34451 q^{36} -10.6535 q^{37} +4.57872 q^{38} +7.05291 q^{39} +3.10826 q^{40} -12.2894 q^{41} +6.41556 q^{42} -11.5923 q^{43} +19.6217 q^{44} -1.00000 q^{45} +5.69574 q^{46} +2.28064 q^{47} +0.496716 q^{48} +0.701257 q^{49} -2.31182 q^{50} -4.28168 q^{51} +23.5885 q^{52} -12.1035 q^{53} -2.31182 q^{54} -5.86685 q^{55} +8.62577 q^{56} -1.98057 q^{57} -21.4836 q^{58} -1.21429 q^{59} -3.34451 q^{60} +4.42619 q^{61} +3.45681 q^{62} -2.77511 q^{63} -12.7102 q^{64} -7.05291 q^{65} -13.5631 q^{66} +5.84241 q^{67} -14.3201 q^{68} -2.46375 q^{69} -6.41556 q^{70} -8.56362 q^{71} -3.10826 q^{72} -1.25965 q^{73} +24.6290 q^{74} +1.00000 q^{75} -6.62403 q^{76} -16.2812 q^{77} -16.3051 q^{78} -9.35475 q^{79} -0.496716 q^{80} +1.00000 q^{81} +28.4109 q^{82} +10.7937 q^{83} -9.28139 q^{84} +4.28168 q^{85} +26.7993 q^{86} +9.29296 q^{87} -18.2357 q^{88} +12.3512 q^{89} +2.31182 q^{90} -19.5726 q^{91} -8.24002 q^{92} -1.49528 q^{93} -5.27243 q^{94} +1.98057 q^{95} +5.06820 q^{96} -9.45070 q^{97} -1.62118 q^{98} +5.86685 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9}+O(q^{10}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9	\( 28 q - q^{2} + 28 q^{3} + 21 q^{4} - 28 q^{5} - q^{6} - 20 q^{7} + 28 q^{9} + q^{10} - q^{11} + 21 q^{12} - 18 q^{13} - 4 q^{14} - 28 q^{15} - q^{16} - 28 q^{17} - q^{18} - 19 q^{19} - 21 q^{20} - 20 q^{21} - 35 q^{22} + 2 q^{23} + 28 q^{25} - 20 q^{26} + 28 q^{27} - 54 q^{28} + 9 q^{29} + q^{30} - 19 q^{31} - 6 q^{32} - q^{33} - 16 q^{34} + 20 q^{35} + 21 q^{36} - 32 q^{37} - 2 q^{38} - 18 q^{39} - 27 q^{41} - 4 q^{42} - 77 q^{43} + q^{44} - 28 q^{45} - 19 q^{46} + 10 q^{47} - q^{48} - 4 q^{49} - q^{50} - 28 q^{51} - 34 q^{52} - 21 q^{53} - q^{54} + q^{55} - 9 q^{56} - 19 q^{57} - 46 q^{58} - 7 q^{59} - 21 q^{60} - 31 q^{61} - 7 q^{62} - 20 q^{63} - 46 q^{64} + 18 q^{65} - 35 q^{66} - 50 q^{67} - 68 q^{68} + 2 q^{69} + 4 q^{70} - 4 q^{71} - 87 q^{73} + 4 q^{74} + 28 q^{75} - 40 q^{76} - 8 q^{77} - 20 q^{78} - 65 q^{79} + q^{80} + 28 q^{81} - 41 q^{82} + 13 q^{83} - 54 q^{84} + 28 q^{85} - 17 q^{86} + 9 q^{87} - 117 q^{88} - 33 q^{89} + q^{90} - 33 q^{91} + 3 q^{92} - 19 q^{93} - 60 q^{94} + 19 q^{95} - 6 q^{96} - 75 q^{97} - 18 q^{98} - q^{99}+O(q^{100}) \) 28 * q - q^2 + 28 * q^3 + 21 * q^4 - 28 * q^5 - q^6 - 20 * q^7 + 28 * q^9 + q^10 - q^11 + 21 * q^12 - 18 * q^13 - 4 * q^14 - 28 * q^15 - q^16 - 28 * q^17 - q^18 - 19 * q^19 - 21 * q^20 - 20 * q^21 - 35 * q^22 + 2 * q^23 + 28 * q^25 - 20 * q^26 + 28 * q^27 - 54 * q^28 + 9 * q^29 + q^30 - 19 * q^31 - 6 * q^32 - q^33 - 16 * q^34 + 20 * q^35 + 21 * q^36 - 32 * q^37 - 2 * q^38 - 18 * q^39 - 27 * q^41 - 4 * q^42 - 77 * q^43 + q^44 - 28 * q^45 - 19 * q^46 + 10 * q^47 - q^48 - 4 * q^49 - q^50 - 28 * q^51 - 34 * q^52 - 21 * q^53 - q^54 + q^55 - 9 * q^56 - 19 * q^57 - 46 * q^58 - 7 * q^59 - 21 * q^60 - 31 * q^61 - 7 * q^62 - 20 * q^63 - 46 * q^64 + 18 * q^65 - 35 * q^66 - 50 * q^67 - 68 * q^68 + 2 * q^69 + 4 * q^70 - 4 * q^71 - 87 * q^73 + 4 * q^74 + 28 * q^75 - 40 * q^76 - 8 * q^77 - 20 * q^78 - 65 * q^79 + q^80 + 28 * q^81 - 41 * q^82 + 13 * q^83 - 54 * q^84 + 28 * q^85 - 17 * q^86 + 9 * q^87 - 117 * q^88 - 33 * q^89 + q^90 - 33 * q^91 + 3 * q^92 - 19 * q^93 - 60 * q^94 + 19 * q^95 - 6 * q^96 - 75 * q^97 - 18 * q^98 - q^99

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