LMFDB - Embedded newform 6010.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.50288 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.50288 q^{6} +1.45988 q^{7} -1.00000 q^{8} +3.26441 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.50288 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.50288 q^{6} +1.45988 q^{7} -1.00000 q^{8} +3.26441 q^{9} +1.00000 q^{10} +3.62407 q^{11} +2.50288 q^{12} -1.42101 q^{13} -1.45988 q^{14} -2.50288 q^{15} +1.00000 q^{16} -4.15023 q^{17} -3.26441 q^{18} +4.87121 q^{19} -1.00000 q^{20} +3.65389 q^{21} -3.62407 q^{22} -2.49752 q^{23} -2.50288 q^{24} +1.00000 q^{25} +1.42101 q^{26} +0.661791 q^{27} +1.45988 q^{28} +0.964607 q^{29} +2.50288 q^{30} -6.39289 q^{31} -1.00000 q^{32} +9.07061 q^{33} +4.15023 q^{34} -1.45988 q^{35} +3.26441 q^{36} +3.87562 q^{37} -4.87121 q^{38} -3.55663 q^{39} +1.00000 q^{40} +8.19184 q^{41} -3.65389 q^{42} +1.59279 q^{43} +3.62407 q^{44} -3.26441 q^{45} +2.49752 q^{46} +9.87702 q^{47} +2.50288 q^{48} -4.86876 q^{49} -1.00000 q^{50} -10.3875 q^{51} -1.42101 q^{52} +6.92443 q^{53} -0.661791 q^{54} -3.62407 q^{55} -1.45988 q^{56} +12.1921 q^{57} -0.964607 q^{58} +1.30205 q^{59} -2.50288 q^{60} -6.74790 q^{61} +6.39289 q^{62} +4.76563 q^{63} +1.00000 q^{64} +1.42101 q^{65} -9.07061 q^{66} +11.8383 q^{67} -4.15023 q^{68} -6.25099 q^{69} +1.45988 q^{70} +13.3229 q^{71} -3.26441 q^{72} +9.01835 q^{73} -3.87562 q^{74} +2.50288 q^{75} +4.87121 q^{76} +5.29069 q^{77} +3.55663 q^{78} +1.79814 q^{79} -1.00000 q^{80} -8.13685 q^{81} -8.19184 q^{82} +15.3380 q^{83} +3.65389 q^{84} +4.15023 q^{85} -1.59279 q^{86} +2.41430 q^{87} -3.62407 q^{88} +3.42410 q^{89} +3.26441 q^{90} -2.07450 q^{91} -2.49752 q^{92} -16.0007 q^{93} -9.87702 q^{94} -4.87121 q^{95} -2.50288 q^{96} +4.28518 q^{97} +4.86876 q^{98} +11.8304 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9}+O(q^{10}) $ 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9} + 21 q^{10} + 8 q^{11} + 8 q^{12} + 2 q^{13} - 8 q^{15} + 21 q^{16} + 25 q^{17} - 15 q^{18} - 11 q^{19} - 21 q^{20} - 8 q^{21} - 8 q^{22} + 15 q^{23} - 8 q^{24} + 21 q^{25} - 2 q^{26} + 29 q^{27} + 3 q^{29} + 8 q^{30} - 19 q^{31} - 21 q^{32} + 11 q^{33} - 25 q^{34} + 15 q^{36} - 8 q^{37} + 11 q^{38} - 2 q^{39} + 21 q^{40} + 15 q^{41} + 8 q^{42} + 19 q^{43} + 8 q^{44} - 15 q^{45} - 15 q^{46} + 19 q^{47} + 8 q^{48} - 15 q^{49} - 21 q^{50} + 13 q^{51} + 2 q^{52} + 45 q^{53} - 29 q^{54} - 8 q^{55} + 22 q^{57} - 3 q^{58} + 34 q^{59} - 8 q^{60} - 26 q^{61} + 19 q^{62} + 5 q^{63} + 21 q^{64} - 2 q^{65} - 11 q^{66} + 19 q^{67} + 25 q^{68} - 3 q^{69} + 10 q^{71} - 15 q^{72} - 17 q^{73} + 8 q^{74} + 8 q^{75} - 11 q^{76} + 42 q^{77} + 2 q^{78} - 42 q^{79} - 21 q^{80} + q^{81} - 15 q^{82} + 76 q^{83} - 8 q^{84} - 25 q^{85} - 19 q^{86} + 6 q^{87} - 8 q^{88} + 14 q^{89} + 15 q^{90} - 19 q^{91} + 15 q^{92} + 2 q^{93} - 19 q^{94} + 11 q^{95} - 8 q^{96} - 9 q^{97} + 15 q^{98} + 21 q^{99}+O(q^{100}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9 + 21 * q^10 + 8 * q^11 + 8 * q^12 + 2 * q^13 - 8 * q^15 + 21 * q^16 + 25 * q^17 - 15 * q^18 - 11 * q^19 - 21 * q^20 - 8 * q^21 - 8 * q^22 + 15 * q^23 - 8 * q^24 + 21 * q^25 - 2 * q^26 + 29 * q^27 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 21 * q^32 + 11 * q^33 - 25 * q^34 + 15 * q^36 - 8 * q^37 + 11 * q^38 - 2 * q^39 + 21 * q^40 + 15 * q^41 + 8 * q^42 + 19 * q^43 + 8 * q^44 - 15 * q^45 - 15 * q^46 + 19 * q^47 + 8 * q^48 - 15 * q^49 - 21 * q^50 + 13 * q^51 + 2 * q^52 + 45 * q^53 - 29 * q^54 - 8 * q^55 + 22 * q^57 - 3 * q^58 + 34 * q^59 - 8 * q^60 - 26 * q^61 + 19 * q^62 + 5 * q^63 + 21 * q^64 - 2 * q^65 - 11 * q^66 + 19 * q^67 + 25 * q^68 - 3 * q^69 + 10 * q^71 - 15 * q^72 - 17 * q^73 + 8 * q^74 + 8 * q^75 - 11 * q^76 + 42 * q^77 + 2 * q^78 - 42 * q^79 - 21 * q^80 + q^81 - 15 * q^82 + 76 * q^83 - 8 * q^84 - 25 * q^85 - 19 * q^86 + 6 * q^87 - 8 * q^88 + 14 * q^89 + 15 * q^90 - 19 * q^91 + 15 * q^92 + 2 * q^93 - 19 * q^94 + 11 * q^95 - 8 * q^96 - 9 * q^97 + 15 * q^98 + 21 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.50288	1.44504	0.722519	−	0.691351i	$-0.242984\pi$
$3$	2.50288	1.44504	0.722519	+	0.691351i	$0.242984\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.50288	−1.02180
$7$	1.45988	0.551781	0.275890	−	0.961189i	$-0.411027\pi$
$7$	1.45988	0.551781	0.275890	+	0.961189i	$0.411027\pi$
$8$	−1.00000	−0.353553
$9$	3.26441	1.08814
$10$	1.00000	0.316228
$11$	3.62407	1.09270	0.546349	−	0.837558i	$-0.316017\pi$
$11$	3.62407	1.09270	0.546349	+	0.837558i	$0.316017\pi$
$12$	2.50288	0.722519
$13$	−1.42101	−0.394119	−0.197059	−	0.980392i	$-0.563139\pi$
$13$	−1.42101	−0.394119	−0.197059	+	0.980392i	$0.563139\pi$
$14$	−1.45988	−0.390168
$15$	−2.50288	−0.646241
$16$	1.00000	0.250000
$17$	−4.15023	−1.00658	−0.503289	−	0.864118i	$-0.667877\pi$
$17$	−4.15023	−1.00658	−0.503289	+	0.864118i	$0.667877\pi$
$18$	−3.26441	−0.769429
$19$	4.87121	1.11753	0.558766	−	0.829325i	$-0.311275\pi$
$19$	4.87121	1.11753	0.558766	+	0.829325i	$0.311275\pi$
$20$	−1.00000	−0.223607
$21$	3.65389	0.797345
$22$	−3.62407	−0.772654
$23$	−2.49752	−0.520768	−0.260384	−	0.965505i	$-0.583849\pi$
$23$	−2.49752	−0.520768	−0.260384	+	0.965505i	$0.583849\pi$
$24$	−2.50288	−0.510898
$25$	1.00000	0.200000
$26$	1.42101	0.278684
$27$	0.661791	0.127362
$28$	1.45988	0.275890
$29$	0.964607	0.179123	0.0895615	−	0.995981i	$-0.471453\pi$
$29$	0.964607	0.179123	0.0895615	+	0.995981i	$0.471453\pi$
$30$	2.50288	0.456961
$31$	−6.39289	−1.14820	−0.574099	−	0.818786i	$-0.694647\pi$
$31$	−6.39289	−1.14820	−0.574099	+	0.818786i	$0.694647\pi$
$32$	−1.00000	−0.176777
$33$	9.07061	1.57899
$34$	4.15023	0.711759
$35$	−1.45988	−0.246764
$36$	3.26441	0.544069
$37$	3.87562	0.637148	0.318574	−	0.947898i	$-0.396796\pi$
$37$	3.87562	0.637148	0.318574	+	0.947898i	$0.396796\pi$
$38$	−4.87121	−0.790215
$39$	−3.55663	−0.569517
$40$	1.00000	0.158114
$41$	8.19184	1.27935	0.639675	−	0.768645i	$-0.279069\pi$
$41$	8.19184	1.27935	0.639675	+	0.768645i	$0.279069\pi$
$42$	−3.65389	−0.563808
$43$	1.59279	0.242898	0.121449	−	0.992598i	$-0.461246\pi$
$43$	1.59279	0.242898	0.121449	+	0.992598i	$0.461246\pi$
$44$	3.62407	0.546349
$45$	−3.26441	−0.486630
$46$	2.49752	0.368239
$47$	9.87702	1.44071	0.720356	−	0.693605i	$-0.243979\pi$
$47$	9.87702	1.44071	0.720356	+	0.693605i	$0.243979\pi$
$48$	2.50288	0.361260
$49$	−4.86876	−0.695538
$50$	−1.00000	−0.141421
$51$	−10.3875	−1.45455
$52$	−1.42101	−0.197059
$53$	6.92443	0.951144	0.475572	−	0.879677i	$-0.342241\pi$
$53$	6.92443	0.951144	0.475572	+	0.879677i	$0.342241\pi$
$54$	−0.661791	−0.0900583
$55$	−3.62407	−0.488669
$56$	−1.45988	−0.195084
$57$	12.1921	1.61488
$58$	−0.964607	−0.126659
$59$	1.30205	0.169512	0.0847562	−	0.996402i	$-0.472989\pi$
$59$	1.30205	0.169512	0.0847562	+	0.996402i	$0.472989\pi$
$60$	−2.50288	−0.323121
$61$	−6.74790	−0.863981	−0.431990	−	0.901878i	$-0.642189\pi$
$61$	−6.74790	−0.863981	−0.431990	+	0.901878i	$0.642189\pi$
$62$	6.39289	0.811898
$63$	4.76563	0.600413
$64$	1.00000	0.125000
$65$	1.42101	0.176255
$66$	−9.07061	−1.11651
$67$	11.8383	1.44628	0.723140	−	0.690702i	$-0.242698\pi$
$67$	11.8383	1.44628	0.723140	+	0.690702i	$0.242698\pi$
$68$	−4.15023	−0.503289
$69$	−6.25099	−0.752531
$70$	1.45988	0.174488
$71$	13.3229	1.58114	0.790571	−	0.612371i	$-0.209784\pi$
$71$	13.3229	1.58114	0.790571	+	0.612371i	$0.209784\pi$
$72$	−3.26441	−0.384715
$73$	9.01835	1.05552	0.527759	−	0.849394i	$-0.323032\pi$
$73$	9.01835	1.05552	0.527759	+	0.849394i	$0.323032\pi$
$74$	−3.87562	−0.450531
$75$	2.50288	0.289008
$76$	4.87121	0.558766
$77$	5.29069	0.602930
$78$	3.55663	0.402709
$79$	1.79814	0.202306	0.101153	−	0.994871i	$-0.467747\pi$
$79$	1.79814	0.202306	0.101153	+	0.994871i	$0.467747\pi$
$80$	−1.00000	−0.111803
$81$	−8.13685	−0.904095
$82$	−8.19184	−0.904638
$83$	15.3380	1.68357	0.841784	−	0.539814i	$-0.181506\pi$
$83$	15.3380	1.68357	0.841784	+	0.539814i	$0.181506\pi$
$84$	3.65389	0.398672
$85$	4.15023	0.450156
$86$	−1.59279	−0.171755
$87$	2.41430	0.258840
$88$	−3.62407	−0.386327
$89$	3.42410	0.362954	0.181477	−	0.983395i	$-0.441912\pi$
$89$	3.42410	0.362954	0.181477	+	0.983395i	$0.441912\pi$
$90$	3.26441	0.344099
$91$	−2.07450	−0.217467
$92$	−2.49752	−0.260384
$93$	−16.0007	−1.65919
$94$	−9.87702	−1.01874
$95$	−4.87121	−0.499776
$96$	−2.50288	−0.255449
$97$	4.28518	0.435094	0.217547	−	0.976050i	$-0.430194\pi$
$97$	4.28518	0.435094	0.217547	+	0.976050i	$0.430194\pi$
$98$	4.86876	0.491820
$99$	11.8304	1.18900
$100$	1.00000	0.100000
$101$	−9.86042	−0.981148	−0.490574	−	0.871400i	$-0.663213\pi$
$101$	−9.86042	−0.981148	−0.490574	+	0.871400i	$0.663213\pi$
$102$	10.3875	1.02852
$103$	7.01387	0.691097	0.345548	−	0.938401i	$-0.387693\pi$
$103$	7.01387	0.691097	0.345548	+	0.938401i	$0.387693\pi$
$104$	1.42101	0.139342
$105$	−3.65389	−0.356583
$106$	−6.92443	−0.672561
$107$	8.71122	0.842146	0.421073	−	0.907027i	$-0.361654\pi$
$107$	8.71122	0.842146	0.421073	+	0.907027i	$0.361654\pi$
$108$	0.661791	0.0636808
$109$	−9.60949	−0.920422	−0.460211	−	0.887809i	$-0.652226\pi$
$109$	−9.60949	−0.920422	−0.460211	+	0.887809i	$0.652226\pi$
$110$	3.62407	0.345541
$111$	9.70021	0.920703
$112$	1.45988	0.137945
$113$	−8.71121	−0.819482	−0.409741	−	0.912202i	$-0.634381\pi$
$113$	−8.71121	−0.819482	−0.409741	+	0.912202i	$0.634381\pi$
$114$	−12.1921	−1.14189
$115$	2.49752	0.232895
$116$	0.964607	0.0895615
$117$	−4.63878	−0.428855
$118$	−1.30205	−0.119863
$119$	−6.05882	−0.555411
$120$	2.50288	0.228481
$121$	2.13387	0.193988
$122$	6.74790	0.610927
$123$	20.5032	1.84871
$124$	−6.39289	−0.574099
$125$	−1.00000	−0.0894427
$126$	−4.76563	−0.424556
$127$	−7.85251	−0.696798	−0.348399	−	0.937346i	$-0.613275\pi$
$127$	−7.85251	−0.696798	−0.348399	+	0.937346i	$0.613275\pi$
$128$	−1.00000	−0.0883883
$129$	3.98657	0.350998
$130$	−1.42101	−0.124631
$131$	−3.35094	−0.292773	−0.146387	−	0.989227i	$-0.546764\pi$
$131$	−3.35094	−0.292773	−0.146387	+	0.989227i	$0.546764\pi$
$132$	9.07061	0.789495
$133$	7.11136	0.616633
$134$	−11.8383	−1.02267
$135$	−0.661791	−0.0569579
$136$	4.15023	0.355879
$137$	22.2239	1.89871	0.949356	−	0.314201i	$-0.101737\pi$
$137$	22.2239	1.89871	0.949356	+	0.314201i	$0.101737\pi$
$138$	6.25099	0.532120
$139$	−4.36415	−0.370162	−0.185081	−	0.982723i	$-0.559255\pi$
$139$	−4.36415	−0.370162	−0.185081	+	0.982723i	$0.559255\pi$
$140$	−1.45988	−0.123382
$141$	24.7210	2.08188
$142$	−13.3229	−1.11804
$143$	−5.14985	−0.430652
$144$	3.26441	0.272034
$145$	−0.964607	−0.0801063
$146$	−9.01835	−0.746364
$147$	−12.1859	−1.00508
$148$	3.87562	0.318574
$149$	15.1342	1.23984	0.619922	−	0.784664i	$-0.287164\pi$
$149$	15.1342	1.23984	0.619922	+	0.784664i	$0.287164\pi$
$150$	−2.50288	−0.204359
$151$	−0.933954	−0.0760041	−0.0380020	−	0.999278i	$-0.512099\pi$
$151$	−0.933954	−0.0760041	−0.0380020	+	0.999278i	$0.512099\pi$
$152$	−4.87121	−0.395108
$153$	−13.5481	−1.09530
$154$	−5.29069	−0.426336
$155$	6.39289	0.513490
$156$	−3.55663	−0.284758
$157$	−4.29207	−0.342544	−0.171272	−	0.985224i	$-0.554788\pi$
$157$	−4.29207	−0.342544	−0.171272	+	0.985224i	$0.554788\pi$
$158$	−1.79814	−0.143052
$159$	17.3310	1.37444
$160$	1.00000	0.0790569
$161$	−3.64606	−0.287350
$162$	8.13685	0.639291
$163$	−18.2818	−1.43194	−0.715972	−	0.698129i	$-0.754016\pi$
$163$	−18.2818	−1.43194	−0.715972	+	0.698129i	$0.754016\pi$
$164$	8.19184	0.639675
$165$	−9.07061	−0.706146
$166$	−15.3380	−1.19046
$167$	−15.8094	−1.22337	−0.611684	−	0.791102i	$-0.709508\pi$
$167$	−15.8094	−1.22337	−0.611684	+	0.791102i	$0.709508\pi$
$168$	−3.65389	−0.281904
$169$	−10.9807	−0.844671
$170$	−4.15023	−0.318308
$171$	15.9016	1.21603
$172$	1.59279	0.121449
$173$	−3.34199	−0.254087	−0.127043	−	0.991897i	$-0.540549\pi$
$173$	−3.34199	−0.254087	−0.127043	+	0.991897i	$0.540549\pi$
$174$	−2.41430	−0.183027
$175$	1.45988	0.110356
$176$	3.62407	0.273174
$177$	3.25888	0.244952
$178$	−3.42410	−0.256647
$179$	4.28918	0.320588	0.160294	−	0.987069i	$-0.448756\pi$
$179$	4.28918	0.320588	0.160294	+	0.987069i	$0.448756\pi$
$180$	−3.26441	−0.243315
$181$	−13.8245	−1.02757	−0.513785	−	0.857919i	$-0.671757\pi$
$181$	−13.8245	−1.02757	−0.513785	+	0.857919i	$0.671757\pi$
$182$	2.07450	0.153772
$183$	−16.8892	−1.24849
$184$	2.49752	0.184119
$185$	−3.87562	−0.284941
$186$	16.0007	1.17322
$187$	−15.0407	−1.09989
$188$	9.87702	0.720356
$189$	0.966132	0.0702757
$190$	4.87121	0.353395
$191$	−20.6331	−1.49296	−0.746478	−	0.665410i	$-0.768257\pi$
$191$	−20.6331	−1.49296	−0.746478	+	0.665410i	$0.768257\pi$
$192$	2.50288	0.180630
$193$	5.57987	0.401648	0.200824	−	0.979627i	$-0.435638\pi$
$193$	5.57987	0.401648	0.200824	+	0.979627i	$0.435638\pi$
$194$	−4.28518	−0.307658
$195$	3.55663	0.254696
$196$	−4.86876	−0.347769
$197$	14.7812	1.05312	0.526560	−	0.850138i	$-0.323482\pi$
$197$	14.7812	1.05312	0.526560	+	0.850138i	$0.323482\pi$
$198$	−11.8304	−0.840753
$199$	17.0653	1.20973	0.604865	−	0.796328i	$-0.293227\pi$
$199$	17.0653	1.20973	0.604865	+	0.796328i	$0.293227\pi$
$200$	−1.00000	−0.0707107
$201$	29.6299	2.08993
$202$	9.86042	0.693776
$203$	1.40821	0.0988367
$204$	−10.3875	−0.727273
$205$	−8.19184	−0.572143
$206$	−7.01387	−0.488679
$207$	−8.15293	−0.566668
$208$	−1.42101	−0.0985296
$209$	17.6536	1.22113
$210$	3.65389	0.252143
$211$	−9.86249	−0.678962	−0.339481	−	0.940613i	$-0.610251\pi$
$211$	−9.86249	−0.678962	−0.339481	+	0.940613i	$0.610251\pi$
$212$	6.92443	0.475572
$213$	33.3457	2.28481
$214$	−8.71122	−0.595487
$215$	−1.59279	−0.108627
$216$	−0.661791	−0.0450292
$217$	−9.33283	−0.633554
$218$	9.60949	0.650837
$219$	22.5719	1.52527
$220$	−3.62407	−0.244335
$221$	5.89754	0.396711
$222$	−9.70021	−0.651035
$223$	−26.4470	−1.77102	−0.885512	−	0.464616i	$-0.846192\pi$
$223$	−26.4470	−1.77102	−0.885512	+	0.464616i	$0.846192\pi$
$224$	−1.45988	−0.0975420
$225$	3.26441	0.217627
$226$	8.71121	0.579461
$227$	26.4452	1.75523	0.877616	−	0.479365i	$-0.159133\pi$
$227$	26.4452	1.75523	0.877616	+	0.479365i	$0.159133\pi$
$228$	12.1921	0.807439
$229$	22.2621	1.47112	0.735560	−	0.677459i	$-0.236919\pi$
$229$	22.2621	1.47112	0.735560	+	0.677459i	$0.236919\pi$
$230$	−2.49752	−0.164681
$231$	13.2420	0.871257
$232$	−0.964607	−0.0633296
$233$	−11.5468	−0.756458	−0.378229	−	0.925712i	$-0.623467\pi$
$233$	−11.5468	−0.756458	−0.378229	+	0.925712i	$0.623467\pi$
$234$	4.63878	0.303246
$235$	−9.87702	−0.644306
$236$	1.30205	0.0847562
$237$	4.50052	0.292340
$238$	6.05882	0.392735
$239$	−15.8773	−1.02702	−0.513508	−	0.858085i	$-0.671654\pi$
$239$	−15.8773	−1.02702	−0.513508	+	0.858085i	$0.671654\pi$
$240$	−2.50288	−0.161560
$241$	24.4025	1.57190	0.785951	−	0.618289i	$-0.212174\pi$
$241$	24.4025	1.57190	0.785951	+	0.618289i	$0.212174\pi$
$242$	−2.13387	−0.137170
$243$	−22.3509	−1.43381
$244$	−6.74790	−0.431990
$245$	4.86876	0.311054
$246$	−20.5032	−1.30724
$247$	−6.92207	−0.440441
$248$	6.39289	0.405949
$249$	38.3893	2.43282
$250$	1.00000	0.0632456
$251$	−26.7577	−1.68893	−0.844464	−	0.535612i	$-0.820081\pi$
$251$	−26.7577	−1.68893	−0.844464	+	0.535612i	$0.820081\pi$
$252$	4.76563	0.300207
$253$	−9.05117	−0.569042
$254$	7.85251	0.492710
$255$	10.3875	0.650492
$256$	1.00000	0.0625000
$257$	27.9035	1.74057	0.870287	−	0.492545i	$-0.163933\pi$
$257$	27.9035	1.74057	0.870287	+	0.492545i	$0.163933\pi$
$258$	−3.98657	−0.248193
$259$	5.65792	0.351566
$260$	1.42101	0.0881276
$261$	3.14887	0.194910
$262$	3.35094	0.207022
$263$	26.9364	1.66097	0.830486	−	0.557040i	$-0.188063\pi$
$263$	26.9364	1.66097	0.830486	+	0.557040i	$0.188063\pi$
$264$	−9.07061	−0.558257
$265$	−6.92443	−0.425365
$266$	−7.11136	−0.436026
$267$	8.57011	0.524482
$268$	11.8383	0.723140
$269$	−1.10622	−0.0674475	−0.0337237	−	0.999431i	$-0.510737\pi$
$269$	−1.10622	−0.0674475	−0.0337237	+	0.999431i	$0.510737\pi$
$270$	0.661791	0.0402753
$271$	18.6195	1.13106	0.565528	−	0.824729i	$-0.308673\pi$
$271$	18.6195	1.13106	0.565528	+	0.824729i	$0.308673\pi$
$272$	−4.15023	−0.251645
$273$	−5.19224	−0.314248
$274$	−22.2239	−1.34259
$275$	3.62407	0.218539
$276$	−6.25099	−0.376265
$277$	−1.03604	−0.0622499	−0.0311250	−	0.999516i	$-0.509909\pi$
$277$	−1.03604	−0.0622499	−0.0311250	+	0.999516i	$0.509909\pi$
$278$	4.36415	0.261744
$279$	−20.8690	−1.24940
$280$	1.45988	0.0872442
$281$	5.32081	0.317413	0.158706	−	0.987326i	$-0.449268\pi$
$281$	5.32081	0.317413	0.158706	+	0.987326i	$0.449268\pi$
$282$	−24.7210	−1.47211
$283$	14.4603	0.859577	0.429789	−	0.902930i	$-0.358588\pi$
$283$	14.4603	0.859577	0.429789	+	0.902930i	$0.358588\pi$
$284$	13.3229	0.790571
$285$	−12.1921	−0.722196
$286$	5.14985	0.304517
$287$	11.9591	0.705921
$288$	−3.26441	−0.192357
$289$	0.224412	0.0132007
$290$	0.964607	0.0566437
$291$	10.7253	0.628728
$292$	9.01835	0.527759
$293$	14.7166	0.859753	0.429876	−	0.902888i	$-0.358557\pi$
$293$	14.7166	0.859753	0.429876	+	0.902888i	$0.358557\pi$
$294$	12.1859	0.710698
$295$	−1.30205	−0.0758083
$296$	−3.87562	−0.225266
$297$	2.39837	0.139168
$298$	−15.1342	−0.876702
$299$	3.54901	0.205245
$300$	2.50288	0.144504
$301$	2.32528	0.134027
$302$	0.933954	0.0537430
$303$	−24.6794	−1.41780
$304$	4.87121	0.279383
$305$	6.74790	0.386384
$306$	13.5481	0.774491
$307$	−24.8100	−1.41598	−0.707992	−	0.706221i	$-0.750399\pi$
$307$	−24.8100	−1.41598	−0.707992	+	0.706221i	$0.750399\pi$
$308$	5.29069	0.301465
$309$	17.5549	0.998662
$310$	−6.39289	−0.363092
$311$	12.9279	0.733073	0.366536	−	0.930404i	$-0.380544\pi$
$311$	12.9279	0.733073	0.366536	+	0.930404i	$0.380544\pi$
$312$	3.55663	0.201355
$313$	−0.850777	−0.0480888	−0.0240444	−	0.999711i	$-0.507654\pi$
$313$	−0.850777	−0.0480888	−0.0240444	+	0.999711i	$0.507654\pi$
$314$	4.29207	0.242215
$315$	−4.76563	−0.268513
$316$	1.79814	0.101153
$317$	1.94700	0.109354	0.0546772	−	0.998504i	$-0.482587\pi$
$317$	1.94700	0.109354	0.0546772	+	0.998504i	$0.482587\pi$
$318$	−17.3310	−0.971876
$319$	3.49580	0.195727
$320$	−1.00000	−0.0559017
$321$	21.8031	1.21693
$322$	3.64606	0.203187
$323$	−20.2167	−1.12488
$324$	−8.13685	−0.452047
$325$	−1.42101	−0.0788237
$326$	18.2818	1.01254
$327$	−24.0514	−1.33005
$328$	−8.19184	−0.452319
$329$	14.4192	0.794957
$330$	9.07061	0.499321
$331$	8.02766	0.441240	0.220620	−	0.975360i	$-0.429192\pi$
$331$	8.02766	0.441240	0.220620	+	0.975360i	$0.429192\pi$
$332$	15.3380	0.841784
$333$	12.6516	0.693304
$334$	15.8094	0.865052
$335$	−11.8383	−0.646796
$336$	3.65389	0.199336
$337$	33.3021	1.81408	0.907040	−	0.421045i	$-0.138337\pi$
$337$	33.3021	1.81408	0.907040	+	0.421045i	$0.138337\pi$
$338$	10.9807	0.597272
$339$	−21.8031	−1.18418
$340$	4.15023	0.225078
$341$	−23.1683	−1.25463
$342$	−15.9016	−0.859863
$343$	−17.3269	−0.935565
$344$	−1.59279	−0.0858776
$345$	6.25099	0.336542
$346$	3.34199	0.179666
$347$	6.89786	0.370297	0.185148	−	0.982711i	$-0.440723\pi$
$347$	6.89786	0.370297	0.185148	+	0.982711i	$0.440723\pi$
$348$	2.41430	0.129420
$349$	8.97859	0.480613	0.240306	−	0.970697i	$-0.422752\pi$
$349$	8.97859	0.480613	0.240306	+	0.970697i	$0.422752\pi$
$350$	−1.45988	−0.0780336
$351$	−0.940414	−0.0501956
$352$	−3.62407	−0.193163
$353$	−5.05680	−0.269146	−0.134573	−	0.990904i	$-0.542966\pi$
$353$	−5.05680	−0.269146	−0.134573	+	0.990904i	$0.542966\pi$
$354$	−3.25888	−0.173207
$355$	−13.3229	−0.707108
$356$	3.42410	0.181477
$357$	−15.1645	−0.802590
$358$	−4.28918	−0.226690
$359$	−27.4300	−1.44770	−0.723849	−	0.689958i	$-0.757629\pi$
$359$	−27.4300	−1.44770	−0.723849	+	0.689958i	$0.757629\pi$
$360$	3.26441	0.172050
$361$	4.72872	0.248880
$362$	13.8245	0.726601
$363$	5.34081	0.280320
$364$	−2.07450	−0.108734
$365$	−9.01835	−0.472042
$366$	16.8892	0.882813
$367$	−6.69666	−0.349563	−0.174781	−	0.984607i	$-0.555922\pi$
$367$	−6.69666	−0.349563	−0.174781	+	0.984607i	$0.555922\pi$
$368$	−2.49752	−0.130192
$369$	26.7415	1.39211
$370$	3.87562	0.201484
$371$	10.1088	0.524823
$372$	−16.0007	−0.829595
$373$	−11.0981	−0.574640	−0.287320	−	0.957835i	$-0.592764\pi$
$373$	−11.0981	−0.574640	−0.287320	+	0.957835i	$0.592764\pi$
$374$	15.0407	0.777737
$375$	−2.50288	−0.129248
$376$	−9.87702	−0.509368
$377$	−1.37072	−0.0705957
$378$	−0.966132	−0.0496925
$379$	−17.5076	−0.899305	−0.449653	−	0.893203i	$-0.648452\pi$
$379$	−17.5076	−0.899305	−0.449653	+	0.893203i	$0.648452\pi$
$380$	−4.87121	−0.249888
$381$	−19.6539	−1.00690
$382$	20.6331	1.05568
$383$	−6.50842	−0.332565	−0.166282	−	0.986078i	$-0.553176\pi$
$383$	−6.50842	−0.332565	−0.166282	+	0.986078i	$0.553176\pi$
$384$	−2.50288	−0.127725
$385$	−5.29069	−0.269638
$386$	−5.57987	−0.284008
$387$	5.19953	0.264307
$388$	4.28518	0.217547
$389$	11.8293	0.599769	0.299885	−	0.953975i	$-0.403052\pi$
$389$	11.8293	0.599769	0.299885	+	0.953975i	$0.403052\pi$
$390$	−3.55663	−0.180097
$391$	10.3653	0.524194
$392$	4.86876	0.245910
$393$	−8.38701	−0.423069
$394$	−14.7812	−0.744668
$395$	−1.79814	−0.0904741
$396$	11.8304	0.594502
$397$	21.0204	1.05499	0.527493	−	0.849559i	$-0.323132\pi$
$397$	21.0204	1.05499	0.527493	+	0.849559i	$0.323132\pi$
$398$	−17.0653	−0.855408
$399$	17.7989	0.891059
$400$	1.00000	0.0500000
$401$	−1.27292	−0.0635664	−0.0317832	−	0.999495i	$-0.510119\pi$
$401$	−1.27292	−0.0635664	−0.0317832	+	0.999495i	$0.510119\pi$
$402$	−29.6299	−1.47780
$403$	9.08440	0.452526
$404$	−9.86042	−0.490574
$405$	8.13685	0.404323
$406$	−1.40821	−0.0698881
$407$	14.0455	0.696210
$408$	10.3875	0.514259
$409$	−37.1597	−1.83743	−0.918714	−	0.394922i	$-0.870771\pi$
$409$	−37.1597	−1.83743	−0.918714	+	0.394922i	$0.870771\pi$
$410$	8.19184	0.404566
$411$	55.6237	2.74371
$412$	7.01387	0.345548
$413$	1.90083	0.0935337
$414$	8.15293	0.400694
$415$	−15.3380	−0.752915
$416$	1.42101	0.0696710
$417$	−10.9229	−0.534898
$418$	−17.6536	−0.863466
$419$	31.6665	1.54701	0.773505	−	0.633790i	$-0.218502\pi$
$419$	31.6665	1.54701	0.773505	+	0.633790i	$0.218502\pi$
$420$	−3.65389	−0.178292
$421$	21.8135	1.06313	0.531563	−	0.847019i	$-0.321605\pi$
$421$	21.8135	1.06313	0.531563	+	0.847019i	$0.321605\pi$
$422$	9.86249	0.480099
$423$	32.2427	1.56769
$424$	−6.92443	−0.336280
$425$	−4.15023	−0.201316
$426$	−33.3457	−1.61561
$427$	−9.85110	−0.476728
$428$	8.71122	0.421073
$429$	−12.8895	−0.622309
$430$	1.59279	0.0768112
$431$	−11.5173	−0.554769	−0.277385	−	0.960759i	$-0.589468\pi$
$431$	−11.5173	−0.554769	−0.277385	+	0.960759i	$0.589468\pi$
$432$	0.661791	0.0318404
$433$	−19.3088	−0.927923	−0.463961	−	0.885855i	$-0.653572\pi$
$433$	−19.3088	−0.927923	−0.463961	+	0.885855i	$0.653572\pi$
$434$	9.33283	0.447990
$435$	−2.41430	−0.115757
$436$	−9.60949	−0.460211
$437$	−12.1659	−0.581976
$438$	−22.5719	−1.07853
$439$	2.21608	0.105768	0.0528839	−	0.998601i	$-0.483159\pi$
$439$	2.21608	0.105768	0.0528839	+	0.998601i	$0.483159\pi$
$440$	3.62407	0.172771
$441$	−15.8937	−0.756841
$442$	−5.89754	−0.280517
$443$	−38.9970	−1.85280	−0.926402	−	0.376537i	$-0.877115\pi$
$443$	−38.9970	−1.85280	−0.926402	+	0.376537i	$0.877115\pi$
$444$	9.70021	0.460351
$445$	−3.42410	−0.162318
$446$	26.4470	1.25230
$447$	37.8791	1.79162
$448$	1.45988	0.0689726
$449$	−1.34429	−0.0634410	−0.0317205	−	0.999497i	$-0.510099\pi$
$449$	−1.34429	−0.0634410	−0.0317205	+	0.999497i	$0.510099\pi$
$450$	−3.26441	−0.153886
$451$	29.6878	1.39794
$452$	−8.71121	−0.409741
$453$	−2.33757	−0.109829
$454$	−26.4452	−1.24114
$455$	2.07450	0.0972542
$456$	−12.1921	−0.570946
$457$	18.6175	0.870890	0.435445	−	0.900215i	$-0.356591\pi$
$457$	18.6175	0.870890	0.435445	+	0.900215i	$0.356591\pi$
$458$	−22.2621	−1.04024
$459$	−2.74658	−0.128200
$460$	2.49752	0.116447
$461$	−32.8053	−1.52790	−0.763948	−	0.645278i	$-0.776742\pi$
$461$	−32.8053	−1.52790	−0.763948	+	0.645278i	$0.776742\pi$
$462$	−13.2420	−0.616072
$463$	4.29192	0.199462	0.0997311	−	0.995014i	$-0.468202\pi$
$463$	4.29192	0.199462	0.0997311	+	0.995014i	$0.468202\pi$
$464$	0.964607	0.0447808
$465$	16.0007	0.742012
$466$	11.5468	0.534897
$467$	0.926198	0.0428593	0.0214297	−	0.999770i	$-0.493178\pi$
$467$	0.926198	0.0428593	0.0214297	+	0.999770i	$0.493178\pi$
$468$	−4.63878	−0.214428
$469$	17.2824	0.798029
$470$	9.87702	0.455593
$471$	−10.7425	−0.494990
$472$	−1.30205	−0.0599317
$473$	5.77238	0.265415
$474$	−4.50052	−0.206716
$475$	4.87121	0.223507
$476$	−6.05882	−0.277705
$477$	22.6042	1.03498
$478$	15.8773	0.726210
$479$	−24.2633	−1.10862	−0.554309	−	0.832311i	$-0.687018\pi$
$479$	−24.2633	−1.10862	−0.554309	+	0.832311i	$0.687018\pi$
$480$	2.50288	0.114240
$481$	−5.50731	−0.251112
$482$	−24.4025	−1.11150
$483$	−9.12566	−0.415232
$484$	2.13387	0.0969939
$485$	−4.28518	−0.194580
$486$	22.3509	1.01386
$487$	−21.0090	−0.952009	−0.476004	−	0.879443i	$-0.657915\pi$
$487$	−21.0090	−0.952009	−0.476004	+	0.879443i	$0.657915\pi$
$488$	6.74790	0.305463
$489$	−45.7573	−2.06922
$490$	−4.86876	−0.219948
$491$	−19.7574	−0.891639	−0.445820	−	0.895123i	$-0.647088\pi$
$491$	−19.7574	−0.891639	−0.445820	+	0.895123i	$0.647088\pi$
$492$	20.5032	0.924356
$493$	−4.00334	−0.180301
$494$	6.92207	0.311438
$495$	−11.8304	−0.531739
$496$	−6.39289	−0.287049
$497$	19.4498	0.872444
$498$	−38.3893	−1.72026
$499$	13.9288	0.623538	0.311769	−	0.950158i	$-0.399079\pi$
$499$	13.9288	0.623538	0.311769	+	0.950158i	$0.399079\pi$
$500$	−1.00000	−0.0447214
$501$	−39.5691	−1.76782
$502$	26.7577	1.19425
$503$	28.8130	1.28471	0.642355	−	0.766408i	$-0.277958\pi$
$503$	28.8130	1.28471	0.642355	+	0.766408i	$0.277958\pi$
$504$	−4.76563	−0.212278
$505$	9.86042	0.438783
$506$	9.05117	0.402374
$507$	−27.4834	−1.22058
$508$	−7.85251	−0.348399
$509$	−26.0970	−1.15673	−0.578364	−	0.815779i	$-0.696309\pi$
$509$	−26.0970	−1.15673	−0.578364	+	0.815779i	$0.696309\pi$
$510$	−10.3875	−0.459968
$511$	13.1657	0.582415
$512$	−1.00000	−0.0441942
$513$	3.22372	0.142331
$514$	−27.9035	−1.23077
$515$	−7.01387	−0.309068
$516$	3.98657	0.175499
$517$	35.7950	1.57426
$518$	−5.65792	−0.248595
$519$	−8.36459	−0.367165
$520$	−1.42101	−0.0623156
$521$	28.4470	1.24629	0.623143	−	0.782108i	$-0.285855\pi$
$521$	28.4470	1.24629	0.623143	+	0.782108i	$0.285855\pi$
$522$	−3.14887	−0.137822
$523$	−4.29719	−0.187903	−0.0939515	−	0.995577i	$-0.529950\pi$
$523$	−4.29719	−0.187903	−0.0939515	+	0.995577i	$0.529950\pi$
$524$	−3.35094	−0.146387
$525$	3.65389	0.159469
$526$	−26.9364	−1.17448
$527$	26.5320	1.15575
$528$	9.07061	0.394748
$529$	−16.7624	−0.728800
$530$	6.92443	0.300778
$531$	4.25043	0.184453
$532$	7.11136	0.308317
$533$	−11.6407	−0.504216
$534$	−8.57011	−0.370865
$535$	−8.71122	−0.376619
$536$	−11.8383	−0.511337
$537$	10.7353	0.463263
$538$	1.10622	0.0476926
$539$	−17.6447	−0.760012
$540$	−0.661791	−0.0284789
$541$	−41.2418	−1.77312	−0.886562	−	0.462610i	$-0.846913\pi$
$541$	−41.2418	−1.77312	−0.886562	+	0.462610i	$0.846913\pi$
$542$	−18.6195	−0.799777
$543$	−34.6012	−1.48488
$544$	4.15023	0.177940
$545$	9.60949	0.411625
$546$	5.19224	0.222207
$547$	21.1611	0.904782	0.452391	−	0.891820i	$-0.350571\pi$
$547$	21.1611	0.904782	0.452391	+	0.891820i	$0.350571\pi$
$548$	22.2239	0.949356
$549$	−22.0279	−0.940129
$550$	−3.62407	−0.154531
$551$	4.69881	0.200176
$552$	6.25099	0.266060
$553$	2.62506	0.111629
$554$	1.03604	0.0440173
$555$	−9.70021	−0.411751
$556$	−4.36415	−0.185081
$557$	19.7841	0.838281	0.419140	−	0.907921i	$-0.362332\pi$
$557$	19.7841	0.838281	0.419140	+	0.907921i	$0.362332\pi$
$558$	20.8690	0.883457
$559$	−2.26338	−0.0957308
$560$	−1.45988	−0.0616910
$561$	−37.6451	−1.58938
$562$	−5.32081	−0.224445
$563$	−43.0649	−1.81497	−0.907484	−	0.420087i	$-0.862000\pi$
$563$	−43.0649	−1.81497	−0.907484	+	0.420087i	$0.862000\pi$
$564$	24.7210	1.04094
$565$	8.71121	0.366483
$566$	−14.4603	−0.607813
$567$	−11.8788	−0.498862
$568$	−13.3229	−0.559018
$569$	11.3687	0.476602	0.238301	−	0.971191i	$-0.423409\pi$
$569$	11.3687	0.476602	0.238301	+	0.971191i	$0.423409\pi$
$570$	12.1921	0.510669
$571$	44.2538	1.85197	0.925983	−	0.377566i	$-0.123239\pi$
$571$	44.2538	1.85197	0.925983	+	0.377566i	$0.123239\pi$
$572$	−5.14985	−0.215326
$573$	−51.6421	−2.15738
$574$	−11.9591	−0.499162
$575$	−2.49752	−0.104154
$576$	3.26441	0.136017
$577$	5.57589	0.232128	0.116064	−	0.993242i	$-0.462972\pi$
$577$	5.57589	0.232128	0.116064	+	0.993242i	$0.462972\pi$
$578$	−0.224412	−0.00933429
$579$	13.9658	0.580397
$580$	−0.964607	−0.0400531
$581$	22.3916	0.928961
$582$	−10.7253	−0.444578
$583$	25.0946	1.03931
$584$	−9.01835	−0.373182
$585$	4.63878	0.191790
$586$	−14.7166	−0.607937
$587$	−11.2218	−0.463172	−0.231586	−	0.972814i	$-0.574392\pi$
$587$	−11.2218	−0.463172	−0.231586	+	0.972814i	$0.574392\pi$
$588$	−12.1859	−0.502540
$589$	−31.1412	−1.28315
$590$	1.30205	0.0536045
$591$	36.9957	1.52180
$592$	3.87562	0.159287
$593$	21.4350	0.880230	0.440115	−	0.897941i	$-0.354938\pi$
$593$	21.4350	0.880230	0.440115	+	0.897941i	$0.354938\pi$
$594$	−2.39837	−0.0984065
$595$	6.05882	0.248387
$596$	15.1342	0.619922
$597$	42.7125	1.74811
$598$	−3.54901	−0.145130
$599$	20.6413	0.843381	0.421690	−	0.906740i	$-0.361437\pi$
$599$	20.6413	0.843381	0.421690	+	0.906740i	$0.361437\pi$
$600$	−2.50288	−0.102180
$601$	1.00000	0.0407909
$601$	1.00000	0.0407909
$602$	−2.32528	−0.0947712
$603$	38.6451	1.57375
$604$	−0.933954	−0.0380020
$605$	−2.13387	−0.0867540
$606$	24.6794	1.00253
$607$	−31.1541	−1.26451	−0.632253	−	0.774762i	$-0.717870\pi$
$607$	−31.1541	−1.26451	−0.632253	+	0.774762i	$0.717870\pi$
$608$	−4.87121	−0.197554
$609$	3.52457	0.142823
$610$	−6.74790	−0.273215
$611$	−14.0354	−0.567811
$612$	−13.5481	−0.547648
$613$	−43.9651	−1.77573	−0.887866	−	0.460102i	$-0.847813\pi$
$613$	−43.9651	−1.77573	−0.887866	+	0.460102i	$0.847813\pi$
$614$	24.8100	1.00125
$615$	−20.5032	−0.826769
$616$	−5.29069	−0.213168
$617$	0.532113	0.0214221	0.0107110	−	0.999943i	$-0.496591\pi$
$617$	0.532113	0.0214221	0.0107110	+	0.999943i	$0.496591\pi$
$618$	−17.5549	−0.706160
$619$	−49.3134	−1.98207	−0.991036	−	0.133599i	$-0.957347\pi$
$619$	−49.3134	−1.98207	−0.991036	+	0.133599i	$0.957347\pi$
$620$	6.39289	0.256745
$621$	−1.65283	−0.0663260
$622$	−12.9279	−0.518361
$623$	4.99875	0.200271
$624$	−3.55663	−0.142379
$625$	1.00000	0.0400000
$626$	0.850777	0.0340039
$627$	44.1849	1.76457
$628$	−4.29207	−0.171272
$629$	−16.0847	−0.641339
$630$	4.76563	0.189867
$631$	−23.4112	−0.931985	−0.465993	−	0.884789i	$-0.654303\pi$
$631$	−23.4112	−0.931985	−0.465993	+	0.884789i	$0.654303\pi$
$632$	−1.79814	−0.0715261
$633$	−24.6846	−0.981126
$634$	−1.94700	−0.0773252
$635$	7.85251	0.311617
$636$	17.3310	0.687220
$637$	6.91859	0.274124
$638$	−3.49580	−0.138400
$639$	43.4915	1.72050
$640$	1.00000	0.0395285
$641$	6.07140	0.239806	0.119903	−	0.992786i	$-0.461742\pi$
$641$	6.07140	0.239806	0.119903	+	0.992786i	$0.461742\pi$
$642$	−21.8031	−0.860502
$643$	27.2047	1.07285	0.536425	−	0.843948i	$-0.319774\pi$
$643$	27.2047	1.07285	0.536425	+	0.843948i	$0.319774\pi$
$644$	−3.64606	−0.143675
$645$	−3.98657	−0.156971
$646$	20.2167	0.795414
$647$	40.3520	1.58640	0.793201	−	0.608959i	$-0.208413\pi$
$647$	40.3520	1.58640	0.793201	+	0.608959i	$0.208413\pi$
$648$	8.13685	0.319646
$649$	4.71872	0.185226
$650$	1.42101	0.0557368
$651$	−23.3590	−0.915510
$652$	−18.2818	−0.715972
$653$	−21.2795	−0.832731	−0.416366	−	0.909197i	$-0.636696\pi$
$653$	−21.2795	−0.832731	−0.416366	+	0.909197i	$0.636696\pi$
$654$	24.0514	0.940485
$655$	3.35094	0.130932
$656$	8.19184	0.319838
$657$	29.4396	1.14855
$658$	−14.4192	−0.562119
$659$	−45.2749	−1.76366	−0.881830	−	0.471568i	$-0.843688\pi$
$659$	−45.2749	−1.76366	−0.881830	+	0.471568i	$0.843688\pi$
$660$	−9.07061	−0.353073
$661$	29.6056	1.15152	0.575762	−	0.817617i	$-0.304705\pi$
$661$	29.6056	1.15152	0.575762	+	0.817617i	$0.304705\pi$
$662$	−8.02766	−0.312004
$663$	14.7608	0.573263
$664$	−15.3380	−0.595231
$665$	−7.11136	−0.275767
$666$	−12.6516	−0.490240
$667$	−2.40912	−0.0932816
$668$	−15.8094	−0.611684
$669$	−66.1938	−2.55920
$670$	11.8383	0.457354
$671$	−24.4549	−0.944069
$672$	−3.65389	−0.140952
$673$	31.4918	1.21392	0.606959	−	0.794733i	$-0.292389\pi$
$673$	31.4918	1.21392	0.606959	+	0.794733i	$0.292389\pi$
$674$	−33.3021	−1.28275
$675$	0.661791	0.0254723
$676$	−10.9807	−0.422335
$677$	−5.95719	−0.228954	−0.114477	−	0.993426i	$-0.536519\pi$
$677$	−5.95719	−0.228954	−0.114477	+	0.993426i	$0.536519\pi$
$678$	21.8031	0.837344
$679$	6.25583	0.240077
$680$	−4.15023	−0.159154
$681$	66.1893	2.53638
$682$	23.1683	0.887159
$683$	−48.7891	−1.86686	−0.933432	−	0.358755i	$-0.883201\pi$
$683$	−48.7891	−1.86686	−0.933432	+	0.358755i	$0.883201\pi$
$684$	15.9016	0.608015
$685$	−22.2239	−0.849130
$686$	17.3269	0.661545
$687$	55.7194	2.12583
$688$	1.59279	0.0607246
$689$	−9.83972	−0.374864
$690$	−6.25099	−0.237971
$691$	−10.6791	−0.406252	−0.203126	−	0.979153i	$-0.565110\pi$
$691$	−10.6791	−0.406252	−0.203126	+	0.979153i	$0.565110\pi$
$692$	−3.34199	−0.127043
$693$	17.2710	0.656070
$694$	−6.89786	−0.261839
$695$	4.36415	0.165541
$696$	−2.41430	−0.0915137
$697$	−33.9980	−1.28777
$698$	−8.97859	−0.339845
$699$	−28.9004	−1.09311
$700$	1.45988	0.0551781
$701$	−37.8483	−1.42951	−0.714754	−	0.699376i	$-0.753462\pi$
$701$	−37.8483	−1.42951	−0.714754	+	0.699376i	$0.753462\pi$
$702$	0.940414	0.0354937
$703$	18.8790	0.712033
$704$	3.62407	0.136587
$705$	−24.7210	−0.931047
$706$	5.05680	0.190315
$707$	−14.3950	−0.541379
$708$	3.25888	0.122476
$709$	10.8070	0.405865	0.202933	−	0.979193i	$-0.434953\pi$
$709$	10.8070	0.405865	0.202933	+	0.979193i	$0.434953\pi$
$710$	13.3229	0.500001
$711$	5.86986	0.220137
$712$	−3.42410	−0.128323
$713$	15.9664	0.597945
$714$	15.1645	0.567517
$715$	5.14985	0.192594
$716$	4.28918	0.160294
$717$	−39.7390	−1.48408
$718$	27.4300	1.02368
$719$	30.1591	1.12474	0.562372	−	0.826885i	$-0.309889\pi$
$719$	30.1591	1.12474	0.562372	+	0.826885i	$0.309889\pi$
$720$	−3.26441	−0.121657
$721$	10.2394	0.381334
$722$	−4.72872	−0.175985
$723$	61.0765	2.27146
$724$	−13.8245	−0.513785
$725$	0.964607	0.0358246
$726$	−5.34081	−0.198216
$727$	6.50203	0.241147	0.120573	−	0.992704i	$-0.461527\pi$
$727$	6.50203	0.241147	0.120573	+	0.992704i	$0.461527\pi$
$728$	2.07450	0.0768862
$729$	−31.5312	−1.16782
$730$	9.01835	0.333784
$731$	−6.61045	−0.244496
$732$	−16.8892	−0.624243
$733$	−20.5328	−0.758395	−0.379198	−	0.925316i	$-0.623800\pi$
$733$	−20.5328	−0.758395	−0.379198	+	0.925316i	$0.623800\pi$
$734$	6.69666	0.247178
$735$	12.1859	0.449485
$736$	2.49752	0.0920597
$737$	42.9028	1.58035
$738$	−26.7415	−0.984370
$739$	−37.3991	−1.37575	−0.687874	−	0.725830i	$-0.741456\pi$
$739$	−37.3991	−1.37575	−0.687874	+	0.725830i	$0.741456\pi$
$740$	−3.87562	−0.142471
$741$	−17.3251	−0.636454
$742$	−10.1088	−0.371106
$743$	0.385348	0.0141370	0.00706852	−	0.999975i	$-0.497750\pi$
$743$	0.385348	0.0141370	0.00706852	+	0.999975i	$0.497750\pi$
$744$	16.0007	0.586612
$745$	−15.1342	−0.554475
$746$	11.0981	0.406332
$747$	50.0697	1.83195
$748$	−15.0407	−0.549943
$749$	12.7173	0.464680
$750$	2.50288	0.0913923
$751$	12.6191	0.460479	0.230240	−	0.973134i	$-0.426049\pi$
$751$	12.6191	0.460479	0.230240	+	0.973134i	$0.426049\pi$
$752$	9.87702	0.360178
$753$	−66.9712	−2.44057
$754$	1.37072	0.0499187
$755$	0.933954	0.0339901
$756$	0.966132	0.0351379
$757$	−6.95996	−0.252964	−0.126482	−	0.991969i	$-0.540369\pi$
$757$	−6.95996	−0.252964	−0.126482	+	0.991969i	$0.540369\pi$
$758$	17.5076	0.635905
$759$	−22.6540	−0.822288
$760$	4.87121	0.176697
$761$	53.3876	1.93530	0.967649	−	0.252298i	$-0.0811864\pi$
$761$	53.3876	1.93530	0.967649	+	0.252298i	$0.0811864\pi$
$762$	19.6539	0.711986
$763$	−14.0287	−0.507871
$764$	−20.6331	−0.746478
$765$	13.5481	0.489831
$766$	6.50842	0.235159
$767$	−1.85023	−0.0668080
$768$	2.50288	0.0903149
$769$	32.6397	1.17702	0.588509	−	0.808491i	$-0.299715\pi$
$769$	32.6397	1.17702	0.588509	+	0.808491i	$0.299715\pi$
$770$	5.29069	0.190663
$771$	69.8392	2.51520
$772$	5.57987	0.200824
$773$	23.0517	0.829112	0.414556	−	0.910024i	$-0.363937\pi$
$773$	23.0517	0.829112	0.414556	+	0.910024i	$0.363937\pi$
$774$	−5.19953	−0.186893
$775$	−6.39289	−0.229640
$776$	−4.28518	−0.153829
$777$	14.1611	0.508026
$778$	−11.8293	−0.424101
$779$	39.9042	1.42972
$780$	3.55663	0.127348
$781$	48.2832	1.72771
$782$	−10.3653	−0.370661
$783$	0.638368	0.0228134
$784$	−4.86876	−0.173884
$785$	4.29207	0.153190
$786$	8.38701	0.299155
$787$	−38.3086	−1.36555	−0.682776	−	0.730628i	$-0.739228\pi$
$787$	−38.3086	−1.36555	−0.682776	+	0.730628i	$0.739228\pi$
$788$	14.7812	0.526560
$789$	67.4187	2.40017
$790$	1.79814	0.0639749
$791$	−12.7173	−0.452174
$792$	−11.8304	−0.420377
$793$	9.58887	0.340511
$794$	−21.0204	−0.745988
$795$	−17.3310	−0.614668
$796$	17.0653	0.604865
$797$	−20.5876	−0.729251	−0.364626	−	0.931154i	$-0.618803\pi$
$797$	−20.5876	−0.729251	−0.364626	+	0.931154i	$0.618803\pi$
$798$	−17.7989	−0.630074
$799$	−40.9919	−1.45019
$800$	−1.00000	−0.0353553
$801$	11.1777	0.394943
$802$	1.27292	0.0449483
$803$	32.6831	1.15336
$804$	29.6299	1.04496
$805$	3.64606	0.128507
$806$	−9.08440	−0.319984
$807$	−2.76874	−0.0974643
$808$	9.86042	0.346888
$809$	12.9569	0.455540	0.227770	−	0.973715i	$-0.426857\pi$
$809$	12.9569	0.455540	0.227770	+	0.973715i	$0.426857\pi$
$810$	−8.13685	−0.285900
$811$	16.4047	0.576047	0.288023	−	0.957623i	$-0.407002\pi$
$811$	16.4047	0.576047	0.288023	+	0.957623i	$0.407002\pi$
$812$	1.40821	0.0494183
$813$	46.6024	1.63442
$814$	−14.0455	−0.492294
$815$	18.2818	0.640385
$816$	−10.3875	−0.363636
$817$	7.75883	0.271447
$818$	37.1597	1.29926
$819$	−6.77203	−0.236634
$820$	−8.19184	−0.286072
$821$	4.37795	0.152792	0.0763958	−	0.997078i	$-0.475659\pi$
$821$	4.37795	0.152792	0.0763958	+	0.997078i	$0.475659\pi$
$822$	−55.6237	−1.94010
$823$	−21.0567	−0.733991	−0.366996	−	0.930223i	$-0.619614\pi$
$823$	−21.0567	−0.733991	−0.366996	+	0.930223i	$0.619614\pi$
$824$	−7.01387	−0.244340
$825$	9.07061	0.315798
$826$	−1.90083	−0.0661383
$827$	45.0822	1.56766	0.783830	−	0.620975i	$-0.213263\pi$
$827$	45.0822	1.56766	0.783830	+	0.620975i	$0.213263\pi$
$828$	−8.15293	−0.283334
$829$	−39.3052	−1.36512	−0.682562	−	0.730827i	$-0.739134\pi$
$829$	−39.3052	−1.36512	−0.682562	+	0.730827i	$0.739134\pi$
$830$	15.3380	0.532391
$831$	−2.59310	−0.0899535
$832$	−1.42101	−0.0492648
$833$	20.2065	0.700114
$834$	10.9229	0.378230
$835$	15.8094	0.547107
$836$	17.6536	0.610563
$837$	−4.23076	−0.146236
$838$	−31.6665	−1.09390
$839$	−23.7804	−0.820991	−0.410496	−	0.911863i	$-0.634644\pi$
$839$	−23.7804	−0.820991	−0.410496	+	0.911863i	$0.634644\pi$
$840$	3.65389	0.126071
$841$	−28.0695	−0.967915
$842$	−21.8135	−0.751743
$843$	13.3174	0.458674
$844$	−9.86249	−0.339481
$845$	10.9807	0.377748
$846$	−32.2427	−1.10853
$847$	3.11518	0.107039
$848$	6.92443	0.237786
$849$	36.1925	1.24212
$850$	4.15023	0.142352
$851$	−9.67942	−0.331806
$852$	33.3457	1.14241
$853$	4.03297	0.138086	0.0690431	−	0.997614i	$-0.478005\pi$
$853$	4.03297	0.138086	0.0690431	+	0.997614i	$0.478005\pi$
$854$	9.85110	0.337098
$855$	−15.9016	−0.543825
$856$	−8.71122	−0.297743
$857$	20.5968	0.703573	0.351787	−	0.936080i	$-0.385574\pi$
$857$	20.5968	0.703573	0.351787	+	0.936080i	$0.385574\pi$
$858$	12.8895	0.440039
$859$	22.6953	0.774354	0.387177	−	0.922005i	$-0.373450\pi$
$859$	22.6953	0.774354	0.387177	+	0.922005i	$0.373450\pi$
$860$	−1.59279	−0.0543137
$861$	29.9321	1.02008
$862$	11.5173	0.392281
$863$	−30.3666	−1.03369	−0.516845	−	0.856079i	$-0.672894\pi$
$863$	−30.3666	−1.03369	−0.516845	+	0.856079i	$0.672894\pi$
$864$	−0.661791	−0.0225146
$865$	3.34199	0.113631
$866$	19.3088	0.656140
$867$	0.561676	0.0190755
$868$	−9.33283	−0.316777
$869$	6.51657	0.221060
$870$	2.41430	0.0818523
$871$	−16.8224	−0.570006
$872$	9.60949	0.325418
$873$	13.9886	0.473442
$874$	12.1659	0.411519
$875$	−1.45988	−0.0493528
$876$	22.5719	0.762633
$877$	21.6300	0.730394	0.365197	−	0.930930i	$-0.381002\pi$
$877$	21.6300	0.730394	0.365197	+	0.930930i	$0.381002\pi$
$878$	−2.21608	−0.0747891
$879$	36.8339	1.24238
$880$	−3.62407	−0.122167
$881$	16.9900	0.572407	0.286204	−	0.958169i	$-0.407607\pi$
$881$	16.9900	0.572407	0.286204	+	0.958169i	$0.407607\pi$
$882$	15.8937	0.535167
$883$	9.89751	0.333078	0.166539	−	0.986035i	$-0.446741\pi$
$883$	9.89751	0.333078	0.166539	+	0.986035i	$0.446741\pi$
$884$	5.89754	0.198356
$885$	−3.25888	−0.109546
$886$	38.9970	1.31013
$887$	−0.707080	−0.0237414	−0.0118707	−	0.999930i	$-0.503779\pi$
$887$	−0.707080	−0.0237414	−0.0118707	+	0.999930i	$0.503779\pi$
$888$	−9.70021	−0.325518
$889$	−11.4637	−0.384480
$890$	3.42410	0.114776
$891$	−29.4885	−0.987902
$892$	−26.4470	−0.885512
$893$	48.1131	1.61004
$894$	−37.8791	−1.26687
$895$	−4.28918	−0.143371
$896$	−1.45988	−0.0487710
$897$	8.88275	0.296586
$898$	1.34429	0.0448595
$899$	−6.16663	−0.205669
$900$	3.26441	0.108814
$901$	−28.7380	−0.957401
$902$	−29.6878	−0.988495
$903$	5.81989	0.193674
$904$	8.71121	0.289731
$905$	13.8245	0.459543
$906$	2.33757	0.0776607
$907$	−16.4093	−0.544863	−0.272432	−	0.962175i	$-0.587828\pi$
$907$	−16.4093	−0.544863	−0.272432	+	0.962175i	$0.587828\pi$
$908$	26.4452	0.877616
$909$	−32.1885	−1.06762
$910$	−2.07450	−0.0687691
$911$	−24.8884	−0.824589	−0.412294	−	0.911051i	$-0.635272\pi$
$911$	−24.8884	−0.824589	−0.412294	+	0.911051i	$0.635272\pi$
$912$	12.1921	0.403720
$913$	55.5861	1.83963
$914$	−18.6175	−0.615812
$915$	16.8892	0.558340
$916$	22.2621	0.735560
$917$	−4.89196	−0.161547
$918$	2.74658	0.0906508
$919$	9.47765	0.312639	0.156319	−	0.987707i	$-0.450037\pi$
$919$	9.47765	0.312639	0.156319	+	0.987707i	$0.450037\pi$
$920$	−2.49752	−0.0823407
$921$	−62.0965	−2.04615
$922$	32.8053	1.08039
$923$	−18.9321	−0.623157
$924$	13.2420	0.435628
$925$	3.87562	0.127430
$926$	−4.29192	−0.141041
$927$	22.8961	0.752008
$928$	−0.964607	−0.0316648
$929$	−50.7007	−1.66344	−0.831718	−	0.555198i	$-0.812642\pi$
$929$	−50.7007	−1.66344	−0.831718	+	0.555198i	$0.812642\pi$
$930$	−16.0007	−0.524682
$931$	−23.7168	−0.777286
$932$	−11.5468	−0.378229
$933$	32.3569	1.05932
$934$	−0.926198	−0.0303061
$935$	15.0407	0.491884
$936$	4.63878	0.151623
$937$	46.8146	1.52937	0.764684	−	0.644406i	$-0.222895\pi$
$937$	46.8146	1.52937	0.764684	+	0.644406i	$0.222895\pi$
$938$	−17.2824	−0.564292
$939$	−2.12939	−0.0694901
$940$	−9.87702	−0.322153
$941$	−51.9784	−1.69445	−0.847224	−	0.531236i	$-0.821728\pi$
$941$	−51.9784	−1.69445	−0.847224	+	0.531236i	$0.821728\pi$
$942$	10.7425	0.350011
$943$	−20.4593	−0.666246
$944$	1.30205	0.0423781
$945$	−0.966132	−0.0314283
$946$	−5.77238	−0.187676
$947$	9.47139	0.307779	0.153889	−	0.988088i	$-0.450820\pi$
$947$	9.47139	0.307779	0.153889	+	0.988088i	$0.450820\pi$
$948$	4.50052	0.146170
$949$	−12.8152	−0.415999
$950$	−4.87121	−0.158043
$951$	4.87311	0.158021
$952$	6.05882	0.196367
$953$	53.4932	1.73281	0.866407	−	0.499339i	$-0.166424\pi$
$953$	53.4932	1.73281	0.866407	+	0.499339i	$0.166424\pi$
$954$	−22.6042	−0.731838
$955$	20.6331	0.667670
$956$	−15.8773	−0.513508
$957$	8.74957	0.282834
$958$	24.2633	0.783912
$959$	32.4441	1.04767
$960$	−2.50288	−0.0807801
$961$	9.86910	0.318358
$962$	5.50731	0.177563
$963$	28.4370	0.916370
$964$	24.4025	0.785951
$965$	−5.57987	−0.179622
$966$	9.12566	0.293613
$967$	−7.71674	−0.248154	−0.124077	−	0.992273i	$-0.539597\pi$
$967$	−7.71674	−0.248154	−0.124077	+	0.992273i	$0.539597\pi$
$968$	−2.13387	−0.0685850
$969$	−50.5999	−1.62550
$970$	4.28518	0.137589
$971$	27.4954	0.882370	0.441185	−	0.897416i	$-0.354558\pi$
$971$	27.4954	0.882370	0.441185	+	0.897416i	$0.354558\pi$
$972$	−22.3509	−0.716907
$973$	−6.37111	−0.204248
$974$	21.0090	0.673172
$975$	−3.55663	−0.113903
$976$	−6.74790	−0.215995
$977$	11.3008	0.361545	0.180773	−	0.983525i	$-0.442140\pi$
$977$	11.3008	0.361545	0.180773	+	0.983525i	$0.442140\pi$
$978$	45.7573	1.46316
$979$	12.4092	0.396598
$980$	4.86876	0.155527
$981$	−31.3693	−1.00155
$982$	19.7574	0.630484
$983$	40.9616	1.30647	0.653237	−	0.757154i	$-0.273411\pi$
$983$	40.9616	1.30647	0.653237	+	0.757154i	$0.273411\pi$
$984$	−20.5032	−0.653618
$985$	−14.7812	−0.470970
$986$	4.00334	0.127492
$987$	36.0896	1.14874
$988$	−6.92207	−0.220220
$989$	−3.97803	−0.126494
$990$	11.8304	0.375996
$991$	−11.9915	−0.380924	−0.190462	−	0.981695i	$-0.560999\pi$
$991$	−11.9915	−0.380924	−0.190462	+	0.981695i	$0.560999\pi$
$992$	6.39289	0.202975
$993$	20.0923	0.637609
$994$	−19.4498	−0.616911
$995$	−17.0653	−0.541007
$996$	38.3893	1.21641
$997$	20.2904	0.642604	0.321302	−	0.946977i	$-0.395880\pi$
$997$	20.2904	0.642604	0.321302	+	0.946977i	$0.395880\pi$
$998$	−13.9288	−0.440908
$999$	2.56485	0.0811482

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.e.1.17	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.e.1.17	✓	21	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.50288 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.50288 q^{6} +1.45988 q^{7} -1.00000 q^{8} +3.26441 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.50288 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.50288 q^{6} +1.45988 q^{7} -1.00000 q^{8} +3.26441 q^{9} +1.00000 q^{10} +3.62407 q^{11} +2.50288 q^{12} -1.42101 q^{13} -1.45988 q^{14} -2.50288 q^{15} +1.00000 q^{16} -4.15023 q^{17} -3.26441 q^{18} +4.87121 q^{19} -1.00000 q^{20} +3.65389 q^{21} -3.62407 q^{22} -2.49752 q^{23} -2.50288 q^{24} +1.00000 q^{25} +1.42101 q^{26} +0.661791 q^{27} +1.45988 q^{28} +0.964607 q^{29} +2.50288 q^{30} -6.39289 q^{31} -1.00000 q^{32} +9.07061 q^{33} +4.15023 q^{34} -1.45988 q^{35} +3.26441 q^{36} +3.87562 q^{37} -4.87121 q^{38} -3.55663 q^{39} +1.00000 q^{40} +8.19184 q^{41} -3.65389 q^{42} +1.59279 q^{43} +3.62407 q^{44} -3.26441 q^{45} +2.49752 q^{46} +9.87702 q^{47} +2.50288 q^{48} -4.86876 q^{49} -1.00000 q^{50} -10.3875 q^{51} -1.42101 q^{52} +6.92443 q^{53} -0.661791 q^{54} -3.62407 q^{55} -1.45988 q^{56} +12.1921 q^{57} -0.964607 q^{58} +1.30205 q^{59} -2.50288 q^{60} -6.74790 q^{61} +6.39289 q^{62} +4.76563 q^{63} +1.00000 q^{64} +1.42101 q^{65} -9.07061 q^{66} +11.8383 q^{67} -4.15023 q^{68} -6.25099 q^{69} +1.45988 q^{70} +13.3229 q^{71} -3.26441 q^{72} +9.01835 q^{73} -3.87562 q^{74} +2.50288 q^{75} +4.87121 q^{76} +5.29069 q^{77} +3.55663 q^{78} +1.79814 q^{79} -1.00000 q^{80} -8.13685 q^{81} -8.19184 q^{82} +15.3380 q^{83} +3.65389 q^{84} +4.15023 q^{85} -1.59279 q^{86} +2.41430 q^{87} -3.62407 q^{88} +3.42410 q^{89} +3.26441 q^{90} -2.07450 q^{91} -2.49752 q^{92} -16.0007 q^{93} -9.87702 q^{94} -4.87121 q^{95} -2.50288 q^{96} +4.28518 q^{97} +4.86876 q^{98} +11.8304 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9}+O(q^{10}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9	\( 21 q - 21 q^{2} + 8 q^{3} + 21 q^{4} - 21 q^{5} - 8 q^{6} - 21 q^{8} + 15 q^{9} + 21 q^{10} + 8 q^{11} + 8 q^{12} + 2 q^{13} - 8 q^{15} + 21 q^{16} + 25 q^{17} - 15 q^{18} - 11 q^{19} - 21 q^{20} - 8 q^{21} - 8 q^{22} + 15 q^{23} - 8 q^{24} + 21 q^{25} - 2 q^{26} + 29 q^{27} + 3 q^{29} + 8 q^{30} - 19 q^{31} - 21 q^{32} + 11 q^{33} - 25 q^{34} + 15 q^{36} - 8 q^{37} + 11 q^{38} - 2 q^{39} + 21 q^{40} + 15 q^{41} + 8 q^{42} + 19 q^{43} + 8 q^{44} - 15 q^{45} - 15 q^{46} + 19 q^{47} + 8 q^{48} - 15 q^{49} - 21 q^{50} + 13 q^{51} + 2 q^{52} + 45 q^{53} - 29 q^{54} - 8 q^{55} + 22 q^{57} - 3 q^{58} + 34 q^{59} - 8 q^{60} - 26 q^{61} + 19 q^{62} + 5 q^{63} + 21 q^{64} - 2 q^{65} - 11 q^{66} + 19 q^{67} + 25 q^{68} - 3 q^{69} + 10 q^{71} - 15 q^{72} - 17 q^{73} + 8 q^{74} + 8 q^{75} - 11 q^{76} + 42 q^{77} + 2 q^{78} - 42 q^{79} - 21 q^{80} + q^{81} - 15 q^{82} + 76 q^{83} - 8 q^{84} - 25 q^{85} - 19 q^{86} + 6 q^{87} - 8 q^{88} + 14 q^{89} + 15 q^{90} - 19 q^{91} + 15 q^{92} + 2 q^{93} - 19 q^{94} + 11 q^{95} - 8 q^{96} - 9 q^{97} + 15 q^{98} + 21 q^{99}+O(q^{100}) \) 21 * q - 21 * q^2 + 8 * q^3 + 21 * q^4 - 21 * q^5 - 8 * q^6 - 21 * q^8 + 15 * q^9 + 21 * q^10 + 8 * q^11 + 8 * q^12 + 2 * q^13 - 8 * q^15 + 21 * q^16 + 25 * q^17 - 15 * q^18 - 11 * q^19 - 21 * q^20 - 8 * q^21 - 8 * q^22 + 15 * q^23 - 8 * q^24 + 21 * q^25 - 2 * q^26 + 29 * q^27 + 3 * q^29 + 8 * q^30 - 19 * q^31 - 21 * q^32 + 11 * q^33 - 25 * q^34 + 15 * q^36 - 8 * q^37 + 11 * q^38 - 2 * q^39 + 21 * q^40 + 15 * q^41 + 8 * q^42 + 19 * q^43 + 8 * q^44 - 15 * q^45 - 15 * q^46 + 19 * q^47 + 8 * q^48 - 15 * q^49 - 21 * q^50 + 13 * q^51 + 2 * q^52 + 45 * q^53 - 29 * q^54 - 8 * q^55 + 22 * q^57 - 3 * q^58 + 34 * q^59 - 8 * q^60 - 26 * q^61 + 19 * q^62 + 5 * q^63 + 21 * q^64 - 2 * q^65 - 11 * q^66 + 19 * q^67 + 25 * q^68 - 3 * q^69 + 10 * q^71 - 15 * q^72 - 17 * q^73 + 8 * q^74 + 8 * q^75 - 11 * q^76 + 42 * q^77 + 2 * q^78 - 42 * q^79 - 21 * q^80 + q^81 - 15 * q^82 + 76 * q^83 - 8 * q^84 - 25 * q^85 - 19 * q^86 + 6 * q^87 - 8 * q^88 + 14 * q^89 + 15 * q^90 - 19 * q^91 + 15 * q^92 + 2 * q^93 - 19 * q^94 + 11 * q^95 - 8 * q^96 - 9 * q^97 + 15 * q^98 + 21 * q^99

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