LMFDB - Embedded newform 4015.2.a.g.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.472050 q^{2} -2.02631 q^{3} -1.77717 q^{4} -1.00000 q^{5} -0.956522 q^{6} -4.07098 q^{7} -1.78301 q^{8} +1.10595 q^{9} +O(q^{10})$	\(q+0.472050 q^{2} -2.02631 q^{3} -1.77717 q^{4} -1.00000 q^{5} -0.956522 q^{6} -4.07098 q^{7} -1.78301 q^{8} +1.10595 q^{9} -0.472050 q^{10} -1.00000 q^{11} +3.60110 q^{12} -4.33553 q^{13} -1.92171 q^{14} +2.02631 q^{15} +2.71267 q^{16} +3.91699 q^{17} +0.522064 q^{18} +3.80342 q^{19} +1.77717 q^{20} +8.24909 q^{21} -0.472050 q^{22} +5.26232 q^{23} +3.61295 q^{24} +1.00000 q^{25} -2.04659 q^{26} +3.83794 q^{27} +7.23482 q^{28} +8.29204 q^{29} +0.956522 q^{30} -1.25617 q^{31} +4.84654 q^{32} +2.02631 q^{33} +1.84901 q^{34} +4.07098 q^{35} -1.96546 q^{36} -8.07142 q^{37} +1.79541 q^{38} +8.78514 q^{39} +1.78301 q^{40} -8.57425 q^{41} +3.89398 q^{42} +1.45905 q^{43} +1.77717 q^{44} -1.10595 q^{45} +2.48408 q^{46} -7.22712 q^{47} -5.49671 q^{48} +9.57290 q^{49} +0.472050 q^{50} -7.93705 q^{51} +7.70497 q^{52} +12.2485 q^{53} +1.81170 q^{54} +1.00000 q^{55} +7.25861 q^{56} -7.70693 q^{57} +3.91426 q^{58} -2.63918 q^{59} -3.60110 q^{60} -4.25130 q^{61} -0.592973 q^{62} -4.50231 q^{63} -3.13752 q^{64} +4.33553 q^{65} +0.956522 q^{66} -0.607298 q^{67} -6.96115 q^{68} -10.6631 q^{69} +1.92171 q^{70} +15.6313 q^{71} -1.97192 q^{72} -1.00000 q^{73} -3.81011 q^{74} -2.02631 q^{75} -6.75932 q^{76} +4.07098 q^{77} +4.14703 q^{78} +6.62809 q^{79} -2.71267 q^{80} -11.0947 q^{81} -4.04748 q^{82} -12.6498 q^{83} -14.6600 q^{84} -3.91699 q^{85} +0.688745 q^{86} -16.8023 q^{87} +1.78301 q^{88} -4.38106 q^{89} -0.522064 q^{90} +17.6499 q^{91} -9.35203 q^{92} +2.54539 q^{93} -3.41156 q^{94} -3.80342 q^{95} -9.82062 q^{96} -15.9437 q^{97} +4.51889 q^{98} -1.10595 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.472050	0.333790	0.166895	−	0.985975i	$-0.446626\pi$
$2$	0.472050	0.333790	0.166895	+	0.985975i	$0.446626\pi$
$3$	−2.02631	−1.16989	−0.584947	−	0.811072i	$-0.698885\pi$
$3$	−2.02631	−1.16989	−0.584947	+	0.811072i	$0.698885\pi$
$4$	−1.77717	−0.888584
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.956522	−0.390499
$7$	−4.07098	−1.53869	−0.769343	−	0.638836i	$-0.779416\pi$
$7$	−4.07098	−1.53869	−0.769343	+	0.638836i	$0.779416\pi$
$8$	−1.78301	−0.630390
$9$	1.10595	0.368650
$10$	−0.472050	−0.149275
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	3.60110	1.03955
$13$	−4.33553	−1.20246	−0.601230	−	0.799076i	$-0.705322\pi$
$13$	−4.33553	−1.20246	−0.601230	+	0.799076i	$0.705322\pi$
$14$	−1.92171	−0.513598
$15$	2.02631	0.523192
$16$	2.71267	0.678166
$17$	3.91699	0.950009	0.475005	−	0.879983i	$-0.342446\pi$
$17$	3.91699	0.950009	0.475005	+	0.879983i	$0.342446\pi$
$18$	0.522064	0.123052
$19$	3.80342	0.872565	0.436282	−	0.899810i	$-0.356295\pi$
$19$	3.80342	0.872565	0.436282	+	0.899810i	$0.356295\pi$
$20$	1.77717	0.397387
$21$	8.24909	1.80010
$22$	−0.472050	−0.100641
$23$	5.26232	1.09727	0.548635	−	0.836062i	$-0.315148\pi$
$23$	5.26232	1.09727	0.548635	+	0.836062i	$0.315148\pi$
$24$	3.61295	0.737489
$25$	1.00000	0.200000
$26$	−2.04659	−0.401369
$27$	3.83794	0.738612
$28$	7.23482	1.36725
$29$	8.29204	1.53979	0.769897	−	0.638168i	$-0.220308\pi$
$29$	8.29204	1.53979	0.769897	+	0.638168i	$0.220308\pi$
$30$	0.956522	0.174636
$31$	−1.25617	−0.225614	−0.112807	−	0.993617i	$-0.535984\pi$
$31$	−1.25617	−0.225614	−0.112807	+	0.993617i	$0.535984\pi$
$32$	4.84654	0.856755
$33$	2.02631	0.352736
$34$	1.84901	0.317103
$35$	4.07098	0.688122
$36$	−1.96546	−0.327577
$37$	−8.07142	−1.32693	−0.663466	−	0.748206i	$-0.730915\pi$
$37$	−8.07142	−1.32693	−0.663466	+	0.748206i	$0.730915\pi$
$38$	1.79541	0.291253
$39$	8.78514	1.40675
$40$	1.78301	0.281919
$41$	−8.57425	−1.33907	−0.669536	−	0.742779i	$-0.733507\pi$
$41$	−8.57425	−1.33907	−0.669536	+	0.742779i	$0.733507\pi$
$42$	3.89398	0.600855
$43$	1.45905	0.222503	0.111252	−	0.993792i	$-0.464514\pi$
$43$	1.45905	0.222503	0.111252	+	0.993792i	$0.464514\pi$
$44$	1.77717	0.267918
$45$	−1.10595	−0.164865
$46$	2.48408	0.366257
$47$	−7.22712	−1.05418	−0.527092	−	0.849809i	$-0.676718\pi$
$47$	−7.22712	−1.05418	−0.527092	+	0.849809i	$0.676718\pi$
$48$	−5.49671	−0.793382
$49$	9.57290	1.36756
$50$	0.472050	0.0667580
$51$	−7.93705	−1.11141
$52$	7.70497	1.06849
$53$	12.2485	1.68246	0.841228	−	0.540681i	$-0.181834\pi$
$53$	12.2485	1.68246	0.841228	+	0.540681i	$0.181834\pi$
$54$	1.81170	0.246541
$55$	1.00000	0.134840
$56$	7.25861	0.969973
$57$	−7.70693	−1.02081
$58$	3.91426	0.513968
$59$	−2.63918	−0.343592	−0.171796	−	0.985133i	$-0.554957\pi$
$59$	−2.63918	−0.343592	−0.171796	+	0.985133i	$0.554957\pi$
$60$	−3.60110	−0.464900
$61$	−4.25130	−0.544323	−0.272161	−	0.962252i	$-0.587738\pi$
$61$	−4.25130	−0.544323	−0.272161	+	0.962252i	$0.587738\pi$
$62$	−0.592973	−0.0753077
$63$	−4.50231	−0.567237
$64$	−3.13752	−0.392190
$65$	4.33553	0.537756
$66$	0.956522	0.117740
$67$	−0.607298	−0.0741932	−0.0370966	−	0.999312i	$-0.511811\pi$
$67$	−0.607298	−0.0741932	−0.0370966	+	0.999312i	$0.511811\pi$
$68$	−6.96115	−0.844163
$69$	−10.6631	−1.28369
$70$	1.92171	0.229688
$71$	15.6313	1.85510	0.927548	−	0.373704i	$-0.121913\pi$
$71$	15.6313	1.85510	0.927548	+	0.373704i	$0.121913\pi$
$72$	−1.97192	−0.232394
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−3.81011	−0.442917
$75$	−2.02631	−0.233979
$76$	−6.75932	−0.775348
$77$	4.07098	0.463931
$78$	4.14703	0.469559
$79$	6.62809	0.745719	0.372859	−	0.927888i	$-0.378377\pi$
$79$	6.62809	0.745719	0.372859	+	0.927888i	$0.378377\pi$
$80$	−2.71267	−0.303285
$81$	−11.0947	−1.23275
$82$	−4.04748	−0.446969
$83$	−12.6498	−1.38850	−0.694249	−	0.719735i	$-0.744263\pi$
$83$	−12.6498	−1.38850	−0.694249	+	0.719735i	$0.744263\pi$
$84$	−14.6600	−1.59954
$85$	−3.91699	−0.424857
$86$	0.688745	0.0742693
$87$	−16.8023	−1.80139
$88$	1.78301	0.190070
$89$	−4.38106	−0.464392	−0.232196	−	0.972669i	$-0.574591\pi$
$89$	−4.38106	−0.464392	−0.232196	+	0.972669i	$0.574591\pi$
$90$	−0.522064	−0.0550304
$91$	17.6499	1.85021
$92$	−9.35203	−0.975016
$93$	2.54539	0.263944
$94$	−3.41156	−0.351876
$95$	−3.80342	−0.390223
$96$	−9.82062	−1.00231
$97$	−15.9437	−1.61884	−0.809418	−	0.587232i	$-0.800217\pi$
$97$	−15.9437	−1.61884	−0.809418	+	0.587232i	$0.800217\pi$
$98$	4.51889	0.456477
$99$	−1.10595	−0.111152
$100$	−1.77717	−0.177717
$101$	15.0667	1.49919	0.749597	−	0.661895i	$-0.230247\pi$
$101$	15.0667	1.49919	0.749597	+	0.661895i	$0.230247\pi$
$102$	−3.74669	−0.370977
$103$	0.966689	0.0952507	0.0476253	−	0.998865i	$-0.484835\pi$
$103$	0.966689	0.0952507	0.0476253	+	0.998865i	$0.484835\pi$
$104$	7.73030	0.758019
$105$	−8.24909	−0.805029
$106$	5.78189	0.561586
$107$	−11.4927	−1.11104	−0.555522	−	0.831502i	$-0.687482\pi$
$107$	−11.4927	−1.11104	−0.555522	+	0.831502i	$0.687482\pi$
$108$	−6.82067	−0.656319
$109$	−17.4384	−1.67029	−0.835147	−	0.550026i	$-0.814618\pi$
$109$	−17.4384	−1.67029	−0.835147	+	0.550026i	$0.814618\pi$
$110$	0.472050	0.0450082
$111$	16.3552	1.55237
$112$	−11.0432	−1.04349
$113$	7.19190	0.676557	0.338279	−	0.941046i	$-0.390155\pi$
$113$	7.19190	0.676557	0.338279	+	0.941046i	$0.390155\pi$
$114$	−3.63806	−0.340735
$115$	−5.26232	−0.490714
$116$	−14.7364	−1.36824
$117$	−4.79488	−0.443287
$118$	−1.24583	−0.114688
$119$	−15.9460	−1.46177
$120$	−3.61295	−0.329815
$121$	1.00000	0.0909091
$122$	−2.00682	−0.181689
$123$	17.3741	1.56657
$124$	2.23242	0.200477
$125$	−1.00000	−0.0894427
$126$	−2.12531	−0.189338
$127$	−9.82935	−0.872213	−0.436107	−	0.899895i	$-0.643643\pi$
$127$	−9.82935	−0.872213	−0.436107	+	0.899895i	$0.643643\pi$
$128$	−11.1741	−0.987665
$129$	−2.95649	−0.260305
$130$	2.04659	0.179498
$131$	21.5337	1.88141	0.940703	−	0.339232i	$-0.110167\pi$
$131$	21.5337	1.88141	0.940703	+	0.339232i	$0.110167\pi$
$132$	−3.60110	−0.313436
$133$	−15.4837	−1.34260
$134$	−0.286675	−0.0247650
$135$	−3.83794	−0.330317
$136$	−6.98404	−0.598877
$137$	18.3565	1.56830	0.784149	−	0.620573i	$-0.213100\pi$
$137$	18.3565	1.56830	0.784149	+	0.620573i	$0.213100\pi$
$138$	−5.03352	−0.428482
$139$	2.78214	0.235978	0.117989	−	0.993015i	$-0.462355\pi$
$139$	2.78214	0.235978	0.117989	+	0.993015i	$0.462355\pi$
$140$	−7.23482	−0.611454
$141$	14.6444	1.23328
$142$	7.37876	0.619212
$143$	4.33553	0.362555
$144$	3.00007	0.250006
$145$	−8.29204	−0.688617
$146$	−0.472050	−0.0390672
$147$	−19.3977	−1.59990
$148$	14.3443	1.17909
$149$	20.2604	1.65979	0.829897	−	0.557916i	$-0.188399\pi$
$149$	20.2604	1.65979	0.829897	+	0.557916i	$0.188399\pi$
$150$	−0.956522	−0.0780997
$151$	7.78469	0.633509	0.316755	−	0.948508i	$-0.397407\pi$
$151$	7.78469	0.633509	0.316755	+	0.948508i	$0.397407\pi$
$152$	−6.78155	−0.550057
$153$	4.33200	0.350221
$154$	1.92171	0.154856
$155$	1.25617	0.100898
$156$	−15.6127	−1.25002
$157$	−0.851755	−0.0679774	−0.0339887	−	0.999422i	$-0.510821\pi$
$157$	−0.851755	−0.0679774	−0.0339887	+	0.999422i	$0.510821\pi$
$158$	3.12879	0.248913
$159$	−24.8192	−1.96829
$160$	−4.84654	−0.383153
$161$	−21.4228	−1.68835
$162$	−5.23727	−0.411479
$163$	−0.791719	−0.0620122	−0.0310061	−	0.999519i	$-0.509871\pi$
$163$	−0.791719	−0.0620122	−0.0310061	+	0.999519i	$0.509871\pi$
$164$	15.2379	1.18988
$165$	−2.02631	−0.157748
$166$	−5.97135	−0.463466
$167$	4.82897	0.373677	0.186838	−	0.982391i	$-0.440176\pi$
$167$	4.82897	0.373677	0.186838	+	0.982391i	$0.440176\pi$
$168$	−14.7082	−1.13477
$169$	5.79681	0.445908
$170$	−1.84901	−0.141813
$171$	4.20640	0.321671
$172$	−2.59298	−0.197713
$173$	26.0876	1.98340	0.991700	−	0.128573i	$-0.0410397\pi$
$173$	26.0876	1.98340	0.991700	+	0.128573i	$0.0410397\pi$
$174$	−7.93152	−0.601287
$175$	−4.07098	−0.307737
$176$	−2.71267	−0.204475
$177$	5.34781	0.401966
$178$	−2.06808	−0.155009
$179$	8.68242	0.648955	0.324477	−	0.945893i	$-0.394812\pi$
$179$	8.68242	0.648955	0.324477	+	0.945893i	$0.394812\pi$
$180$	1.96546	0.146497
$181$	−17.7003	−1.31566	−0.657828	−	0.753169i	$-0.728524\pi$
$181$	−17.7003	−1.31566	−0.657828	+	0.753169i	$0.728524\pi$
$182$	8.33162	0.617581
$183$	8.61446	0.636799
$184$	−9.38278	−0.691708
$185$	8.07142	0.593422
$186$	1.20155	0.0881020
$187$	−3.91699	−0.286439
$188$	12.8438	0.936731
$189$	−15.6242	−1.13649
$190$	−1.79541	−0.130252
$191$	7.73724	0.559847	0.279924	−	0.960022i	$-0.409691\pi$
$191$	7.73724	0.559847	0.279924	+	0.960022i	$0.409691\pi$
$192$	6.35760	0.458821
$193$	4.13300	0.297500	0.148750	−	0.988875i	$-0.452475\pi$
$193$	4.13300	0.297500	0.148750	+	0.988875i	$0.452475\pi$
$194$	−7.52622	−0.540351
$195$	−8.78514	−0.629117
$196$	−17.0127	−1.21519
$197$	−20.2866	−1.44536	−0.722680	−	0.691183i	$-0.757090\pi$
$197$	−20.2866	−1.44536	−0.722680	+	0.691183i	$0.757090\pi$
$198$	−0.522064	−0.0371015
$199$	17.7947	1.26143	0.630716	−	0.776014i	$-0.282761\pi$
$199$	17.7947	1.26143	0.630716	+	0.776014i	$0.282761\pi$
$200$	−1.78301	−0.126078
$201$	1.23058	0.0867982
$202$	7.11224	0.500416
$203$	−33.7568	−2.36926
$204$	14.1055	0.987581
$205$	8.57425	0.598851
$206$	0.456326	0.0317937
$207$	5.81986	0.404508
$208$	−11.7608	−0.815467
$209$	−3.80342	−0.263088
$210$	−3.89398	−0.268710
$211$	24.5193	1.68798	0.843989	−	0.536360i	$-0.180201\pi$
$211$	24.5193	1.68798	0.843989	+	0.536360i	$0.180201\pi$
$212$	−21.7676	−1.49500
$213$	−31.6740	−2.17026
$214$	−5.42514	−0.370855
$215$	−1.45905	−0.0995064
$216$	−6.84310	−0.465614
$217$	5.11383	0.347149
$218$	−8.23180	−0.557528
$219$	2.02631	0.136926
$220$	−1.77717	−0.119817
$221$	−16.9822	−1.14235
$222$	7.72049	0.518165
$223$	8.86536	0.593668	0.296834	−	0.954929i	$-0.404069\pi$
$223$	8.86536	0.593668	0.296834	+	0.954929i	$0.404069\pi$
$224$	−19.7302	−1.31828
$225$	1.10595	0.0737300
$226$	3.39494	0.225828
$227$	−3.37628	−0.224092	−0.112046	−	0.993703i	$-0.535740\pi$
$227$	−3.37628	−0.224092	−0.112046	+	0.993703i	$0.535740\pi$
$228$	13.6965	0.907074
$229$	−7.67757	−0.507348	−0.253674	−	0.967290i	$-0.581639\pi$
$229$	−7.67757	−0.507348	−0.253674	+	0.967290i	$0.581639\pi$
$230$	−2.48408	−0.163795
$231$	−8.24909	−0.542750
$232$	−14.7848	−0.970671
$233$	4.46715	0.292653	0.146326	−	0.989236i	$-0.453255\pi$
$233$	4.46715	0.292653	0.146326	+	0.989236i	$0.453255\pi$
$234$	−2.26342	−0.147965
$235$	7.22712	0.471445
$236$	4.69027	0.305311
$237$	−13.4306	−0.872411
$238$	−7.52731	−0.487923
$239$	13.7074	0.886656	0.443328	−	0.896360i	$-0.353798\pi$
$239$	13.7074	0.886656	0.443328	+	0.896360i	$0.353798\pi$
$240$	5.49671	0.354811
$241$	−2.99691	−0.193048	−0.0965241	−	0.995331i	$-0.530772\pi$
$241$	−2.99691	−0.193048	−0.0965241	+	0.995331i	$0.530772\pi$
$242$	0.472050	0.0303445
$243$	10.9676	0.703571
$244$	7.55527	0.483677
$245$	−9.57290	−0.611590
$246$	8.20146	0.522906
$247$	−16.4898	−1.04922
$248$	2.23976	0.142225
$249$	25.6325	1.62439
$250$	−0.472050	−0.0298551
$251$	−14.3609	−0.906455	−0.453227	−	0.891395i	$-0.649727\pi$
$251$	−14.3609	−0.906455	−0.453227	+	0.891395i	$0.649727\pi$
$252$	8.00136	0.504038
$253$	−5.26232	−0.330839
$254$	−4.63994	−0.291136
$255$	7.93705	0.497037
$256$	1.00028	0.0625177
$257$	14.4425	0.900900	0.450450	−	0.892802i	$-0.351264\pi$
$257$	14.4425	0.900900	0.450450	+	0.892802i	$0.351264\pi$
$258$	−1.39561	−0.0868871
$259$	32.8586	2.04173
$260$	−7.70497	−0.477842
$261$	9.17059	0.567645
$262$	10.1650	0.627994
$263$	−14.1336	−0.871517	−0.435759	−	0.900064i	$-0.643520\pi$
$263$	−14.1336	−0.871517	−0.435759	+	0.900064i	$0.643520\pi$
$264$	−3.61295	−0.222361
$265$	−12.2485	−0.752417
$266$	−7.30907	−0.448148
$267$	8.87741	0.543289
$268$	1.07927	0.0659269
$269$	−28.7022	−1.75001	−0.875003	−	0.484118i	$-0.839141\pi$
$269$	−28.7022	−1.75001	−0.875003	+	0.484118i	$0.839141\pi$
$270$	−1.81170	−0.110257
$271$	−12.8239	−0.778998	−0.389499	−	0.921027i	$-0.627352\pi$
$271$	−12.8239	−0.778998	−0.389499	+	0.921027i	$0.627352\pi$
$272$	10.6255	0.644264
$273$	−35.7642	−2.16455
$274$	8.66517	0.523482
$275$	−1.00000	−0.0603023
$276$	18.9501	1.14066
$277$	−26.0447	−1.56488	−0.782438	−	0.622728i	$-0.786024\pi$
$277$	−26.0447	−1.56488	−0.782438	+	0.622728i	$0.786024\pi$
$278$	1.31331	0.0787670
$279$	−1.38926	−0.0831727
$280$	−7.25861	−0.433785
$281$	−8.38301	−0.500089	−0.250044	−	0.968234i	$-0.580445\pi$
$281$	−8.38301	−0.500089	−0.250044	+	0.968234i	$0.580445\pi$
$282$	6.91290	0.411657
$283$	−1.62956	−0.0968671	−0.0484336	−	0.998826i	$-0.515423\pi$
$283$	−1.62956	−0.0968671	−0.0484336	+	0.998826i	$0.515423\pi$
$284$	−27.7795	−1.64841
$285$	7.70693	0.456519
$286$	2.04659	0.121017
$287$	34.9056	2.06041
$288$	5.36003	0.315843
$289$	−1.65721	−0.0974827
$290$	−3.91426	−0.229853
$291$	32.3069	1.89387
$292$	1.77717	0.104001
$293$	9.52112	0.556230	0.278115	−	0.960548i	$-0.410290\pi$
$293$	9.52112	0.556230	0.278115	+	0.960548i	$0.410290\pi$
$294$	−9.15669	−0.534029
$295$	2.63918	0.153659
$296$	14.3914	0.836486
$297$	−3.83794	−0.222700
$298$	9.56391	0.554023
$299$	−22.8149	−1.31942
$300$	3.60110	0.207910
$301$	−5.93977	−0.342363
$302$	3.67476	0.211459
$303$	−30.5299	−1.75390
$304$	10.3174	0.591744
$305$	4.25130	0.243428
$306$	2.04492	0.116900
$307$	−15.9296	−0.909149	−0.454574	−	0.890709i	$-0.650209\pi$
$307$	−15.9296	−0.909149	−0.454574	+	0.890709i	$0.650209\pi$
$308$	−7.23482	−0.412242
$309$	−1.95882	−0.111433
$310$	0.592973	0.0336786
$311$	−7.20310	−0.408451	−0.204225	−	0.978924i	$-0.565468\pi$
$311$	−7.20310	−0.408451	−0.204225	+	0.978924i	$0.565468\pi$
$312$	−15.6640	−0.886801
$313$	−22.8610	−1.29218	−0.646089	−	0.763262i	$-0.723597\pi$
$313$	−22.8610	−1.29218	−0.646089	+	0.763262i	$0.723597\pi$
$314$	−0.402071	−0.0226902
$315$	4.50231	0.253676
$316$	−11.7792	−0.662634
$317$	−25.6571	−1.44105	−0.720523	−	0.693431i	$-0.756098\pi$
$317$	−25.6571	−1.44105	−0.720523	+	0.693431i	$0.756098\pi$
$318$	−11.7159	−0.656996
$319$	−8.29204	−0.464265
$320$	3.13752	0.175393
$321$	23.2879	1.29980
$322$	−10.1126	−0.563555
$323$	14.8980	0.828945
$324$	19.7172	1.09540
$325$	−4.33553	−0.240492
$326$	−0.373731	−0.0206991
$327$	35.3357	1.95407
$328$	15.2880	0.844138
$329$	29.4215	1.62206
$330$	−0.956522	−0.0526548
$331$	−25.8894	−1.42301	−0.711504	−	0.702682i	$-0.751986\pi$
$331$	−25.8894	−1.42301	−0.711504	+	0.702682i	$0.751986\pi$
$332$	22.4808	1.23380
$333$	−8.92659	−0.489174
$334$	2.27951	0.124729
$335$	0.607298	0.0331802
$336$	22.3770	1.22077
$337$	−10.8049	−0.588581	−0.294290	−	0.955716i	$-0.595083\pi$
$337$	−10.8049	−0.588581	−0.294290	+	0.955716i	$0.595083\pi$
$338$	2.73638	0.148840
$339$	−14.5731	−0.791500
$340$	6.96115	0.377521
$341$	1.25617	0.0680252
$342$	1.98563	0.107371
$343$	−10.4742	−0.565555
$344$	−2.60151	−0.140264
$345$	10.6631	0.574083
$346$	12.3146	0.662039
$347$	17.9074	0.961321	0.480661	−	0.876907i	$-0.340397\pi$
$347$	17.9074	0.961321	0.480661	+	0.876907i	$0.340397\pi$
$348$	29.8605	1.60069
$349$	20.3754	1.09067	0.545336	−	0.838218i	$-0.316402\pi$
$349$	20.3754	1.09067	0.545336	+	0.838218i	$0.316402\pi$
$350$	−1.92171	−0.102720
$351$	−16.6395	−0.888151
$352$	−4.84654	−0.258321
$353$	35.8211	1.90657	0.953283	−	0.302077i	$-0.0976801\pi$
$353$	35.8211	1.90657	0.953283	+	0.302077i	$0.0976801\pi$
$354$	2.52444	0.134172
$355$	−15.6313	−0.829624
$356$	7.78589	0.412651
$357$	32.3116	1.71011
$358$	4.09854	0.216615
$359$	−8.22526	−0.434113	−0.217056	−	0.976159i	$-0.569646\pi$
$359$	−8.22526	−0.434113	−0.217056	+	0.976159i	$0.569646\pi$
$360$	1.97192	0.103930
$361$	−4.53398	−0.238630
$362$	−8.35544	−0.439152
$363$	−2.02631	−0.106354
$364$	−31.3668	−1.64407
$365$	1.00000	0.0523424
$366$	4.06646	0.212557
$367$	−24.0507	−1.25544	−0.627719	−	0.778440i	$-0.716011\pi$
$367$	−24.0507	−1.25544	−0.627719	+	0.778440i	$0.716011\pi$
$368$	14.2749	0.744131
$369$	−9.48269	−0.493649
$370$	3.81011	0.198078
$371$	−49.8633	−2.58877
$372$	−4.52358	−0.234537
$373$	−9.62634	−0.498433	−0.249217	−	0.968448i	$-0.580173\pi$
$373$	−9.62634	−0.498433	−0.249217	+	0.968448i	$0.580173\pi$
$374$	−1.84901	−0.0956103
$375$	2.02631	0.104638
$376$	12.8860	0.664547
$377$	−35.9504	−1.85154
$378$	−7.37540	−0.379350
$379$	6.07620	0.312114	0.156057	−	0.987748i	$-0.450122\pi$
$379$	6.07620	0.312114	0.156057	+	0.987748i	$0.450122\pi$
$380$	6.75932	0.346746
$381$	19.9173	1.02040
$382$	3.65237	0.186871
$383$	−17.9309	−0.916228	−0.458114	−	0.888894i	$-0.651475\pi$
$383$	−17.9309	−0.916228	−0.458114	+	0.888894i	$0.651475\pi$
$384$	22.6423	1.15546
$385$	−4.07098	−0.207476
$386$	1.95098	0.0993024
$387$	1.61364	0.0820258
$388$	28.3346	1.43847
$389$	−34.5304	−1.75076	−0.875380	−	0.483435i	$-0.839389\pi$
$389$	−34.5304	−1.75076	−0.875380	+	0.483435i	$0.839389\pi$
$390$	−4.14703	−0.209993
$391$	20.6124	1.04242
$392$	−17.0686	−0.862095
$393$	−43.6340	−2.20104
$394$	−9.57629	−0.482447
$395$	−6.62809	−0.333496
$396$	1.96546	0.0987681
$397$	3.86503	0.193981	0.0969903	−	0.995285i	$-0.469078\pi$
$397$	3.86503	0.193981	0.0969903	+	0.995285i	$0.469078\pi$
$398$	8.39999	0.421053
$399$	31.3748	1.57070
$400$	2.71267	0.135633
$401$	3.45323	0.172446	0.0862231	−	0.996276i	$-0.472520\pi$
$401$	3.45323	0.172446	0.0862231	+	0.996276i	$0.472520\pi$
$402$	0.580894	0.0289723
$403$	5.44614	0.271292
$404$	−26.7761	−1.33216
$405$	11.0947	0.551301
$406$	−15.9349	−0.790835
$407$	8.07142	0.400085
$408$	14.1519	0.700622
$409$	−9.95086	−0.492038	−0.246019	−	0.969265i	$-0.579123\pi$
$409$	−9.95086	−0.492038	−0.246019	+	0.969265i	$0.579123\pi$
$410$	4.04748	0.199891
$411$	−37.1960	−1.83474
$412$	−1.71797	−0.0846383
$413$	10.7441	0.528681
$414$	2.74727	0.135021
$415$	12.6498	0.620955
$416$	−21.0123	−1.03021
$417$	−5.63749	−0.276069
$418$	−1.79541	−0.0878162
$419$	25.9474	1.26761	0.633807	−	0.773491i	$-0.281491\pi$
$419$	25.9474	1.26761	0.633807	+	0.773491i	$0.281491\pi$
$420$	14.6600	0.715336
$421$	25.9093	1.26274	0.631372	−	0.775480i	$-0.282492\pi$
$421$	25.9093	1.26274	0.631372	+	0.775480i	$0.282492\pi$
$422$	11.5743	0.563430
$423$	−7.99283	−0.388625
$424$	−21.8392	−1.06060
$425$	3.91699	0.190002
$426$	−14.9517	−0.724412
$427$	17.3069	0.837542
$428$	20.4245	0.987256
$429$	−8.78514	−0.424151
$430$	−0.688745	−0.0332142
$431$	5.27201	0.253944	0.126972	−	0.991906i	$-0.459474\pi$
$431$	5.27201	0.253944	0.126972	+	0.991906i	$0.459474\pi$
$432$	10.4110	0.500902
$433$	−19.9856	−0.960447	−0.480224	−	0.877146i	$-0.659445\pi$
$433$	−19.9856	−0.960447	−0.480224	+	0.877146i	$0.659445\pi$
$434$	2.41398	0.115875
$435$	16.8023	0.805608
$436$	30.9910	1.48420
$437$	20.0148	0.957438
$438$	0.956522	0.0457044
$439$	14.1608	0.675859	0.337930	−	0.941171i	$-0.390273\pi$
$439$	14.1608	0.675859	0.337930	+	0.941171i	$0.390273\pi$
$440$	−1.78301	−0.0850018
$441$	10.5872	0.504150
$442$	−8.01646	−0.381304
$443$	6.62835	0.314922	0.157461	−	0.987525i	$-0.449669\pi$
$443$	6.62835	0.314922	0.157461	+	0.987525i	$0.449669\pi$
$444$	−29.0660	−1.37941
$445$	4.38106	0.207682
$446$	4.18489	0.198161
$447$	−41.0539	−1.94178
$448$	12.7728	0.603458
$449$	−4.06785	−0.191974	−0.0959869	−	0.995383i	$-0.530601\pi$
$449$	−4.06785	−0.191974	−0.0959869	+	0.995383i	$0.530601\pi$
$450$	0.522064	0.0246103
$451$	8.57425	0.403746
$452$	−12.7812	−0.601178
$453$	−15.7742	−0.741138
$454$	−1.59378	−0.0747996
$455$	−17.6499	−0.827438
$456$	13.7416	0.643507
$457$	−33.8994	−1.58575	−0.792874	−	0.609385i	$-0.791416\pi$
$457$	−33.8994	−1.58575	−0.792874	+	0.609385i	$0.791416\pi$
$458$	−3.62420	−0.169348
$459$	15.0332	0.701688
$460$	9.35203	0.436040
$461$	26.2869	1.22430	0.612150	−	0.790741i	$-0.290305\pi$
$461$	26.2869	1.22430	0.612150	+	0.790741i	$0.290305\pi$
$462$	−3.89398	−0.181165
$463$	27.1873	1.26350	0.631750	−	0.775173i	$-0.282337\pi$
$463$	27.1873	1.26350	0.631750	+	0.775173i	$0.282337\pi$
$464$	22.4935	1.04424
$465$	−2.54539	−0.118040
$466$	2.10872	0.0976846
$467$	−5.39825	−0.249801	−0.124901	−	0.992169i	$-0.539861\pi$
$467$	−5.39825	−0.249801	−0.124901	+	0.992169i	$0.539861\pi$
$468$	8.52131	0.393898
$469$	2.47230	0.114160
$470$	3.41156	0.157364
$471$	1.72592	0.0795263
$472$	4.70570	0.216597
$473$	−1.45905	−0.0670872
$474$	−6.33992	−0.291202
$475$	3.80342	0.174513
$476$	28.3387	1.29890
$477$	13.5462	0.620237
$478$	6.47056	0.295957
$479$	12.7322	0.581748	0.290874	−	0.956761i	$-0.406054\pi$
$479$	12.7322	0.581748	0.290874	+	0.956761i	$0.406054\pi$
$480$	9.82062	0.448248
$481$	34.9939	1.59558
$482$	−1.41469	−0.0644375
$483$	43.4093	1.97519
$484$	−1.77717	−0.0807804
$485$	15.9437	0.723966
$486$	5.17725	0.234845
$487$	−1.89096	−0.0856875	−0.0428437	−	0.999082i	$-0.513642\pi$
$487$	−1.89096	−0.0856875	−0.0428437	+	0.999082i	$0.513642\pi$
$488$	7.58012	0.343136
$489$	1.60427	0.0725477
$490$	−4.51889	−0.204143
$491$	32.4443	1.46419	0.732095	−	0.681203i	$-0.238543\pi$
$491$	32.4443	1.46419	0.732095	+	0.681203i	$0.238543\pi$
$492$	−30.8767	−1.39203
$493$	32.4798	1.46282
$494$	−7.78403	−0.350220
$495$	1.10595	0.0497088
$496$	−3.40756	−0.153004
$497$	−63.6348	−2.85441
$498$	12.0998	0.542206
$499$	25.2125	1.12867	0.564334	−	0.825547i	$-0.309133\pi$
$499$	25.2125	1.12867	0.564334	+	0.825547i	$0.309133\pi$
$500$	1.77717	0.0794774
$501$	−9.78501	−0.437162
$502$	−6.77909	−0.302565
$503$	−20.8480	−0.929567	−0.464784	−	0.885424i	$-0.653868\pi$
$503$	−20.8480	−0.929567	−0.464784	+	0.885424i	$0.653868\pi$
$504$	8.02767	0.357581
$505$	−15.0667	−0.670460
$506$	−2.48408	−0.110431
$507$	−11.7462	−0.521665
$508$	17.4684	0.775035
$509$	−35.7846	−1.58612	−0.793061	−	0.609142i	$-0.791514\pi$
$509$	−35.7846	−1.58612	−0.793061	+	0.609142i	$0.791514\pi$
$510$	3.74669	0.165906
$511$	4.07098	0.180090
$512$	22.8205	1.00853
$513$	14.5973	0.644487
$514$	6.81760	0.300711
$515$	−0.966689	−0.0425974
$516$	5.25419	0.231303
$517$	7.22712	0.317848
$518$	15.5109	0.681510
$519$	−52.8616	−2.32037
$520$	−7.73030	−0.338996
$521$	−8.86153	−0.388231	−0.194115	−	0.980979i	$-0.562184\pi$
$521$	−8.86153	−0.388231	−0.194115	+	0.980979i	$0.562184\pi$
$522$	4.32898	0.189474
$523$	0.552037	0.0241389	0.0120694	−	0.999927i	$-0.496158\pi$
$523$	0.552037	0.0241389	0.0120694	+	0.999927i	$0.496158\pi$
$524$	−38.2690	−1.67179
$525$	8.24909	0.360020
$526$	−6.67179	−0.290904
$527$	−4.92039	−0.214335
$528$	5.49671	0.239214
$529$	4.69198	0.203999
$530$	−5.78189	−0.251149
$531$	−2.91880	−0.126665
$532$	27.5171	1.19302
$533$	37.1739	1.61018
$534$	4.19059	0.181344
$535$	11.4927	0.496874
$536$	1.08282	0.0467707
$537$	−17.5933	−0.759208
$538$	−13.5489	−0.584134
$539$	−9.57290	−0.412334
$540$	6.82067	0.293515
$541$	−36.6817	−1.57707	−0.788535	−	0.614990i	$-0.789160\pi$
$541$	−36.6817	−1.57707	−0.788535	+	0.614990i	$0.789160\pi$
$542$	−6.05353	−0.260022
$543$	35.8664	1.53918
$544$	18.9838	0.813925
$545$	17.4384	0.746979
$546$	−16.8825	−0.722503
$547$	−6.64800	−0.284248	−0.142124	−	0.989849i	$-0.545393\pi$
$547$	−6.64800	−0.284248	−0.142124	+	0.989849i	$0.545393\pi$
$548$	−32.6225	−1.39356
$549$	−4.70172	−0.200665
$550$	−0.472050	−0.0201283
$551$	31.5381	1.34357
$552$	19.0125	0.809224
$553$	−26.9829	−1.14743
$554$	−12.2944	−0.522340
$555$	−16.3552	−0.694241
$556$	−4.94433	−0.209686
$557$	−1.53614	−0.0650885	−0.0325442	−	0.999470i	$-0.510361\pi$
$557$	−1.53614	−0.0650885	−0.0325442	+	0.999470i	$0.510361\pi$
$558$	−0.655799	−0.0277622
$559$	−6.32575	−0.267551
$560$	11.0432	0.466661
$561$	7.93705	0.335102
$562$	−3.95720	−0.166925
$563$	−4.39608	−0.185273	−0.0926364	−	0.995700i	$-0.529529\pi$
$563$	−4.39608	−0.185273	−0.0926364	+	0.995700i	$0.529529\pi$
$564$	−26.0256	−1.09587
$565$	−7.19190	−0.302566
$566$	−0.769233	−0.0323333
$567$	45.1664	1.89681
$568$	−27.8708	−1.16943
$569$	−13.9851	−0.586286	−0.293143	−	0.956069i	$-0.594701\pi$
$569$	−13.9851	−0.586286	−0.293143	+	0.956069i	$0.594701\pi$
$570$	3.63806	0.152381
$571$	0.805917	0.0337266	0.0168633	−	0.999858i	$-0.494632\pi$
$571$	0.805917	0.0337266	0.0168633	+	0.999858i	$0.494632\pi$
$572$	−7.70497	−0.322161
$573$	−15.6781	−0.654961
$574$	16.4772	0.687745
$575$	5.26232	0.219454
$576$	−3.46994	−0.144581
$577$	−8.30876	−0.345898	−0.172949	−	0.984931i	$-0.555330\pi$
$577$	−8.30876	−0.345898	−0.172949	+	0.984931i	$0.555330\pi$
$578$	−0.782284	−0.0325387
$579$	−8.37475	−0.348043
$580$	14.7364	0.611894
$581$	51.4972	2.13646
$582$	15.2505	0.632153
$583$	−12.2485	−0.507279
$584$	1.78301	0.0737816
$585$	4.79488	0.198244
$586$	4.49445	0.185664
$587$	34.6415	1.42981	0.714904	−	0.699222i	$-0.246470\pi$
$587$	34.6415	1.42981	0.714904	+	0.699222i	$0.246470\pi$
$588$	34.4730	1.42164
$589$	−4.77773	−0.196863
$590$	1.24583	0.0512899
$591$	41.1070	1.69092
$592$	−21.8951	−0.899881
$593$	−45.6745	−1.87563	−0.937813	−	0.347142i	$-0.887152\pi$
$593$	−45.6745	−1.87563	−0.937813	+	0.347142i	$0.887152\pi$
$594$	−1.81170	−0.0743350
$595$	15.9460	0.653722
$596$	−36.0061	−1.47487
$597$	−36.0576	−1.47574
$598$	−10.7698	−0.440409
$599$	9.43719	0.385593	0.192797	−	0.981239i	$-0.438244\pi$
$599$	9.43719	0.385593	0.192797	+	0.981239i	$0.438244\pi$
$600$	3.61295	0.147498
$601$	−28.7165	−1.17137	−0.585684	−	0.810539i	$-0.699174\pi$
$601$	−28.7165	−1.17137	−0.585684	+	0.810539i	$0.699174\pi$
$602$	−2.80387	−0.114277
$603$	−0.671641	−0.0273514
$604$	−13.8347	−0.562926
$605$	−1.00000	−0.0406558
$606$	−14.4116	−0.585433
$607$	0.740362	0.0300504	0.0150252	−	0.999887i	$-0.495217\pi$
$607$	0.740362	0.0300504	0.0150252	+	0.999887i	$0.495217\pi$
$608$	18.4334	0.747575
$609$	68.4018	2.77178
$610$	2.00682	0.0812540
$611$	31.3334	1.26761
$612$	−7.69869	−0.311201
$613$	−36.1538	−1.46024	−0.730119	−	0.683320i	$-0.760535\pi$
$613$	−36.1538	−1.46024	−0.730119	+	0.683320i	$0.760535\pi$
$614$	−7.51956	−0.303465
$615$	−17.3741	−0.700592
$616$	−7.25861	−0.292458
$617$	−30.2603	−1.21824	−0.609118	−	0.793080i	$-0.708476\pi$
$617$	−30.2603	−1.21824	−0.609118	+	0.793080i	$0.708476\pi$
$618$	−0.924659	−0.0371953
$619$	−8.30579	−0.333838	−0.166919	−	0.985971i	$-0.553382\pi$
$619$	−8.30579	−0.333838	−0.166919	+	0.985971i	$0.553382\pi$
$620$	−2.23242	−0.0896561
$621$	20.1965	0.810456
$622$	−3.40023	−0.136337
$623$	17.8352	0.714554
$624$	23.8312	0.954010
$625$	1.00000	0.0400000
$626$	−10.7915	−0.431316
$627$	7.70693	0.307785
$628$	1.51371	0.0604037
$629$	−31.6156	−1.26060
$630$	2.12531	0.0846745
$631$	−31.2449	−1.24384	−0.621919	−	0.783081i	$-0.713647\pi$
$631$	−31.2449	−1.24384	−0.621919	+	0.783081i	$0.713647\pi$
$632$	−11.8180	−0.470094
$633$	−49.6838	−1.97475
$634$	−12.1114	−0.481007
$635$	9.82935	0.390066
$636$	44.1080	1.74899
$637$	−41.5036	−1.64443
$638$	−3.91426	−0.154967
$639$	17.2875	0.683881
$640$	11.1741	0.441697
$641$	−12.5219	−0.494584	−0.247292	−	0.968941i	$-0.579541\pi$
$641$	−12.5219	−0.494584	−0.247292	+	0.968941i	$0.579541\pi$
$642$	10.9930	0.433861
$643$	−7.83390	−0.308939	−0.154469	−	0.987998i	$-0.549367\pi$
$643$	−7.83390	−0.308939	−0.154469	+	0.987998i	$0.549367\pi$
$644$	38.0719	1.50024
$645$	2.95649	0.116412
$646$	7.03258	0.276693
$647$	−4.76009	−0.187138	−0.0935692	−	0.995613i	$-0.529828\pi$
$647$	−4.76009	−0.187138	−0.0935692	+	0.995613i	$0.529828\pi$
$648$	19.7820	0.777112
$649$	2.63918	0.103597
$650$	−2.04659	−0.0802737
$651$	−10.3622	−0.406128
$652$	1.40702	0.0551031
$653$	43.7903	1.71365	0.856824	−	0.515609i	$-0.172434\pi$
$653$	43.7903	1.71365	0.856824	+	0.515609i	$0.172434\pi$
$654$	16.6802	0.652248
$655$	−21.5337	−0.841390
$656$	−23.2591	−0.908114
$657$	−1.10595	−0.0431472
$658$	13.8884	0.541426
$659$	6.81881	0.265623	0.132812	−	0.991141i	$-0.457599\pi$
$659$	6.81881	0.265623	0.132812	+	0.991141i	$0.457599\pi$
$660$	3.60110	0.140173
$661$	21.4245	0.833315	0.416658	−	0.909064i	$-0.363201\pi$
$661$	21.4245	0.833315	0.416658	+	0.909064i	$0.363201\pi$
$662$	−12.2211	−0.474986
$663$	34.4113	1.33642
$664$	22.5548	0.875295
$665$	15.4837	0.600431
$666$	−4.21380	−0.163281
$667$	43.6354	1.68957
$668$	−8.58189	−0.332043
$669$	−17.9640	−0.694529
$670$	0.286675	0.0110752
$671$	4.25130	0.164119
$672$	39.9796	1.54224
$673$	37.4669	1.44424	0.722122	−	0.691766i	$-0.243167\pi$
$673$	37.4669	1.44424	0.722122	+	0.691766i	$0.243167\pi$
$674$	−5.10046	−0.196462
$675$	3.83794	0.147722
$676$	−10.3019	−0.396227
$677$	44.0398	1.69259	0.846294	−	0.532717i	$-0.178829\pi$
$677$	44.0398	1.69259	0.846294	+	0.532717i	$0.178829\pi$
$678$	−6.87922	−0.264195
$679$	64.9065	2.49088
$680$	6.98404	0.267826
$681$	6.84141	0.262163
$682$	0.592973	0.0227061
$683$	49.1287	1.87986	0.939929	−	0.341370i	$-0.110891\pi$
$683$	49.1287	1.87986	0.939929	+	0.341370i	$0.110891\pi$
$684$	−7.47548	−0.285832
$685$	−18.3565	−0.701364
$686$	−4.94436	−0.188776
$687$	15.5572	0.593543
$688$	3.95792	0.150894
$689$	−53.1035	−2.02308
$690$	5.03352	0.191623
$691$	−32.8093	−1.24812	−0.624062	−	0.781375i	$-0.714519\pi$
$691$	−32.8093	−1.24812	−0.624062	+	0.781375i	$0.714519\pi$
$692$	−46.3620	−1.76242
$693$	4.50231	0.171028
$694$	8.45321	0.320879
$695$	−2.78214	−0.105533
$696$	29.9587	1.13558
$697$	−33.5852	−1.27213
$698$	9.61822	0.364055
$699$	−9.05186	−0.342373
$700$	7.23482	0.273451
$701$	34.5689	1.30565	0.652825	−	0.757509i	$-0.273584\pi$
$701$	34.5689	1.30565	0.652825	+	0.757509i	$0.273584\pi$
$702$	−7.85468	−0.296456
$703$	−30.6990	−1.15783
$704$	3.13752	0.118250
$705$	−14.6444	−0.551540
$706$	16.9094	0.636393
$707$	−61.3363	−2.30679
$708$	−9.50397	−0.357181
$709$	11.2891	0.423972	0.211986	−	0.977273i	$-0.432007\pi$
$709$	11.2891	0.423972	0.211986	+	0.977273i	$0.432007\pi$
$710$	−7.37876	−0.276920
$711$	7.33034	0.274909
$712$	7.81150	0.292748
$713$	−6.61034	−0.247559
$714$	15.2527	0.570818
$715$	−4.33553	−0.162140
$716$	−15.4301	−0.576651
$717$	−27.7754	−1.03729
$718$	−3.88274	−0.144902
$719$	−16.2952	−0.607710	−0.303855	−	0.952718i	$-0.598274\pi$
$719$	−16.2952	−0.607710	−0.303855	+	0.952718i	$0.598274\pi$
$720$	−3.00007	−0.111806
$721$	−3.93537	−0.146561
$722$	−2.14026	−0.0796524
$723$	6.07269	0.225846
$724$	31.4565	1.16907
$725$	8.29204	0.307959
$726$	−0.956522	−0.0354999
$727$	−12.1134	−0.449260	−0.224630	−	0.974444i	$-0.572117\pi$
$727$	−12.1134	−0.449260	−0.224630	+	0.974444i	$0.572117\pi$
$728$	−31.4699	−1.16635
$729$	11.0604	0.409645
$730$	0.472050	0.0174714
$731$	5.71508	0.211380
$732$	−15.3094	−0.565850
$733$	5.72510	0.211461	0.105731	−	0.994395i	$-0.466282\pi$
$733$	5.72510	0.211461	0.105731	+	0.994395i	$0.466282\pi$
$734$	−11.3531	−0.419052
$735$	19.3977	0.715495
$736$	25.5040	0.940091
$737$	0.607298	0.0223701
$738$	−4.47631	−0.164775
$739$	−12.7789	−0.470079	−0.235039	−	0.971986i	$-0.575522\pi$
$739$	−12.7789	−0.470079	−0.235039	+	0.971986i	$0.575522\pi$
$740$	−14.3443	−0.527306
$741$	33.4136	1.22748
$742$	−23.5380	−0.864106
$743$	−15.7598	−0.578171	−0.289085	−	0.957303i	$-0.593351\pi$
$743$	−15.7598	−0.578171	−0.289085	+	0.957303i	$0.593351\pi$
$744$	−4.53846	−0.166388
$745$	−20.2604	−0.742283
$746$	−4.54412	−0.166372
$747$	−13.9901	−0.511870
$748$	6.96115	0.254525
$749$	46.7867	1.70955
$750$	0.956522	0.0349273
$751$	−29.2215	−1.06631	−0.533154	−	0.846018i	$-0.678993\pi$
$751$	−29.2215	−1.06631	−0.533154	+	0.846018i	$0.678993\pi$
$752$	−19.6047	−0.714912
$753$	29.0998	1.06046
$754$	−16.9704	−0.618025
$755$	−7.78469	−0.283314
$756$	27.7668	1.00987
$757$	7.16496	0.260415	0.130207	−	0.991487i	$-0.458436\pi$
$757$	7.16496	0.260415	0.130207	+	0.991487i	$0.458436\pi$
$758$	2.86827	0.104180
$759$	10.6631	0.387046
$760$	6.78155	0.245993
$761$	22.7221	0.823674	0.411837	−	0.911258i	$-0.364887\pi$
$761$	22.7221	0.823674	0.411837	+	0.911258i	$0.364887\pi$
$762$	9.40199	0.340598
$763$	70.9914	2.57006
$764$	−13.7504	−0.497471
$765$	−4.33200	−0.156624
$766$	−8.46430	−0.305827
$767$	11.4422	0.413156
$768$	−2.02689	−0.0731390
$769$	51.2078	1.84660	0.923300	−	0.384079i	$-0.125481\pi$
$769$	51.2078	1.84660	0.923300	+	0.384079i	$0.125481\pi$
$770$	−1.92171	−0.0692535
$771$	−29.2651	−1.05396
$772$	−7.34503	−0.264354
$773$	17.1242	0.615913	0.307956	−	0.951400i	$-0.400355\pi$
$773$	17.1242	0.615913	0.307956	+	0.951400i	$0.400355\pi$
$774$	0.761718	0.0273794
$775$	−1.25617	−0.0451228
$776$	28.4278	1.02050
$777$	−66.5818	−2.38861
$778$	−16.3001	−0.584386
$779$	−32.6115	−1.16843
$780$	15.6127	0.559024
$781$	−15.6313	−0.559332
$782$	9.73010	0.347948
$783$	31.8244	1.13731
$784$	25.9681	0.927431
$785$	0.851755	0.0304004
$786$	−20.5974	−0.734686
$787$	−53.9445	−1.92291	−0.961457	−	0.274954i	$-0.911337\pi$
$787$	−53.9445	−1.92291	−0.961457	+	0.274954i	$0.911337\pi$
$788$	36.0527	1.28432
$789$	28.6392	1.01958
$790$	−3.12879	−0.111317
$791$	−29.2781	−1.04101
$792$	1.97192	0.0700693
$793$	18.4316	0.654526
$794$	1.82449	0.0647487
$795$	24.8192	0.880247
$796$	−31.6242	−1.12089
$797$	12.2084	0.432444	0.216222	−	0.976344i	$-0.430627\pi$
$797$	12.2084	0.432444	0.216222	+	0.976344i	$0.430627\pi$
$798$	14.8105	0.524285
$799$	−28.3085	−1.00148
$800$	4.84654	0.171351
$801$	−4.84524	−0.171198
$802$	1.63010	0.0575608
$803$	1.00000	0.0352892
$804$	−2.18694	−0.0771275
$805$	21.4228	0.755054
$806$	2.57085	0.0905544
$807$	58.1597	2.04732
$808$	−26.8641	−0.945077
$809$	−44.8882	−1.57819	−0.789093	−	0.614273i	$-0.789449\pi$
$809$	−44.8882	−1.57819	−0.789093	+	0.614273i	$0.789449\pi$
$810$	5.23727	0.184019
$811$	16.3171	0.572970	0.286485	−	0.958085i	$-0.407513\pi$
$811$	16.3171	0.572970	0.286485	+	0.958085i	$0.407513\pi$
$812$	59.9915	2.10529
$813$	25.9853	0.911344
$814$	3.81011	0.133544
$815$	0.791719	0.0277327
$816$	−21.5306	−0.753720
$817$	5.54938	0.194148
$818$	−4.69730	−0.164237
$819$	19.5199	0.682080
$820$	−15.2379	−0.532130
$821$	−39.9548	−1.39443	−0.697215	−	0.716862i	$-0.745578\pi$
$821$	−39.9548	−1.39443	−0.697215	+	0.716862i	$0.745578\pi$
$822$	−17.5584	−0.612418
$823$	28.5147	0.993960	0.496980	−	0.867762i	$-0.334442\pi$
$823$	28.5147	0.993960	0.496980	+	0.867762i	$0.334442\pi$
$824$	−1.72362	−0.0600451
$825$	2.02631	0.0705472
$826$	5.07174	0.176468
$827$	12.4591	0.433245	0.216623	−	0.976255i	$-0.430496\pi$
$827$	12.4591	0.433245	0.216623	+	0.976255i	$0.430496\pi$
$828$	−10.3429	−0.359440
$829$	−20.7925	−0.722153	−0.361077	−	0.932536i	$-0.617591\pi$
$829$	−20.7925	−0.722153	−0.361077	+	0.932536i	$0.617591\pi$
$830$	5.97135	0.207268
$831$	52.7748	1.83074
$832$	13.6028	0.471593
$833$	37.4969	1.29919
$834$	−2.66118	−0.0921490
$835$	−4.82897	−0.167113
$836$	6.75932	0.233776
$837$	−4.82109	−0.166641
$838$	12.2485	0.423117
$839$	54.5974	1.88491	0.942455	−	0.334332i	$-0.108511\pi$
$839$	54.5974	1.88491	0.942455	+	0.334332i	$0.108511\pi$
$840$	14.7082	0.507482
$841$	39.7580	1.37096
$842$	12.2305	0.421491
$843$	16.9866	0.585050
$844$	−43.5749	−1.49991
$845$	−5.79681	−0.199416
$846$	−3.77302	−0.129719
$847$	−4.07098	−0.139881
$848$	33.2260	1.14098
$849$	3.30200	0.113324
$850$	1.84901	0.0634207
$851$	−42.4744	−1.45600
$852$	56.2900	1.92846
$853$	29.5475	1.01169	0.505843	−	0.862626i	$-0.331182\pi$
$853$	29.5475	1.01169	0.505843	+	0.862626i	$0.331182\pi$
$854$	8.16975	0.279563
$855$	−4.20640	−0.143856
$856$	20.4917	0.700391
$857$	−3.61826	−0.123597	−0.0617987	−	0.998089i	$-0.519684\pi$
$857$	−3.61826	−0.123597	−0.0617987	+	0.998089i	$0.519684\pi$
$858$	−4.14703	−0.141577
$859$	53.1745	1.81429	0.907146	−	0.420816i	$-0.138256\pi$
$859$	53.1745	1.81429	0.907146	+	0.420816i	$0.138256\pi$
$860$	2.59298	0.0884198
$861$	−70.7297	−2.41046
$862$	2.48865	0.0847638
$863$	−22.7423	−0.774158	−0.387079	−	0.922047i	$-0.626516\pi$
$863$	−22.7423	−0.774158	−0.387079	+	0.922047i	$0.626516\pi$
$864$	18.6007	0.632810
$865$	−26.0876	−0.887003
$866$	−9.43421	−0.320588
$867$	3.35802	0.114044
$868$	−9.08814	−0.308471
$869$	−6.62809	−0.224843
$870$	7.93152	0.268904
$871$	2.63296	0.0892143
$872$	31.0929	1.05294
$873$	−17.6329	−0.596784
$874$	9.44800	0.319583
$875$	4.07098	0.137624
$876$	−3.60110	−0.121670
$877$	−8.32917	−0.281256	−0.140628	−	0.990062i	$-0.544912\pi$
$877$	−8.32917	−0.281256	−0.140628	+	0.990062i	$0.544912\pi$
$878$	6.68462	0.225595
$879$	−19.2928	−0.650729
$880$	2.71267	0.0914439
$881$	−8.81777	−0.297078	−0.148539	−	0.988907i	$-0.547457\pi$
$881$	−8.81777	−0.297078	−0.148539	+	0.988907i	$0.547457\pi$
$882$	4.99767	0.168280
$883$	−4.41768	−0.148667	−0.0743333	−	0.997233i	$-0.523683\pi$
$883$	−4.41768	−0.148667	−0.0743333	+	0.997233i	$0.523683\pi$
$884$	30.1803	1.01507
$885$	−5.34781	−0.179765
$886$	3.12891	0.105118
$887$	34.0871	1.14453	0.572266	−	0.820068i	$-0.306064\pi$
$887$	34.0871	1.14453	0.572266	+	0.820068i	$0.306064\pi$
$888$	−29.1616	−0.978599
$889$	40.0151	1.34206
$890$	2.06808	0.0693223
$891$	11.0947	0.371687
$892$	−15.7552	−0.527524
$893$	−27.4878	−0.919843
$894$	−19.3795	−0.648147
$895$	−8.68242	−0.290221
$896$	45.4898	1.51971
$897$	46.2302	1.54358
$898$	−1.92023	−0.0640789
$899$	−10.4162	−0.347399
$900$	−1.96546	−0.0655154
$901$	47.9771	1.59835
$902$	4.04748	0.134766
$903$	12.0358	0.400528
$904$	−12.8233	−0.426495
$905$	17.7003	0.588379
$906$	−7.44623	−0.247384
$907$	−19.7801	−0.656786	−0.328393	−	0.944541i	$-0.606507\pi$
$907$	−19.7801	−0.656786	−0.328393	+	0.944541i	$0.606507\pi$
$908$	6.00022	0.199124
$909$	16.6630	0.552678
$910$	−8.33162	−0.276190
$911$	17.8359	0.590930	0.295465	−	0.955354i	$-0.404525\pi$
$911$	17.8359	0.590930	0.295465	+	0.955354i	$0.404525\pi$
$912$	−20.9063	−0.692278
$913$	12.6498	0.418648
$914$	−16.0022	−0.529307
$915$	−8.61446	−0.284785
$916$	13.6443	0.450822
$917$	−87.6632	−2.89489
$918$	7.09641	0.234216
$919$	−39.2620	−1.29513	−0.647567	−	0.762008i	$-0.724214\pi$
$919$	−39.2620	−1.29513	−0.647567	+	0.762008i	$0.724214\pi$
$920$	9.38278	0.309341
$921$	32.2783	1.06361
$922$	12.4087	0.408659
$923$	−67.7700	−2.23068
$924$	14.6600	0.482279
$925$	−8.07142	−0.265387
$926$	12.8338	0.421743
$927$	1.06911	0.0351142
$928$	40.1877	1.31923
$929$	−25.2521	−0.828495	−0.414248	−	0.910164i	$-0.635955\pi$
$929$	−25.2521	−0.828495	−0.414248	+	0.910164i	$0.635955\pi$
$930$	−1.20155	−0.0394004
$931$	36.4098	1.19328
$932$	−7.93888	−0.260047
$933$	14.5958	0.477844
$934$	−2.54824	−0.0833811
$935$	3.91699	0.128099
$936$	8.54933	0.279444
$937$	15.4819	0.505770	0.252885	−	0.967496i	$-0.418621\pi$
$937$	15.4819	0.505770	0.252885	+	0.967496i	$0.418621\pi$
$938$	1.16705	0.0381055
$939$	46.3235	1.51171
$940$	−12.8438	−0.418919
$941$	−57.9268	−1.88836	−0.944179	−	0.329433i	$-0.893143\pi$
$941$	−57.9268	−1.88836	−0.944179	+	0.329433i	$0.893143\pi$
$942$	0.814722	0.0265451
$943$	−45.1204	−1.46932
$944$	−7.15922	−0.233013
$945$	15.6242	0.508255
$946$	−0.688745	−0.0223930
$947$	35.1050	1.14076	0.570379	−	0.821382i	$-0.306796\pi$
$947$	35.1050	1.14076	0.570379	+	0.821382i	$0.306796\pi$
$948$	23.8684	0.775211
$949$	4.33553	0.140737
$950$	1.79541	0.0582507
$951$	51.9894	1.68587
$952$	28.4319	0.921483
$953$	−52.9922	−1.71659	−0.858293	−	0.513161i	$-0.828475\pi$
$953$	−52.9922	−1.71659	−0.858293	+	0.513161i	$0.828475\pi$
$954$	6.39448	0.207029
$955$	−7.73724	−0.250371
$956$	−24.3603	−0.787868
$957$	16.8023	0.543141
$958$	6.01023	0.194182
$959$	−74.7288	−2.41312
$960$	−6.35760	−0.205191
$961$	−29.4220	−0.949098
$962$	16.5189	0.532589
$963$	−12.7104	−0.409587
$964$	5.32602	0.171540
$965$	−4.13300	−0.133046
$966$	20.4914	0.659299
$967$	−28.8749	−0.928554	−0.464277	−	0.885690i	$-0.653686\pi$
$967$	−28.8749	−0.928554	−0.464277	+	0.885690i	$0.653686\pi$
$968$	−1.78301	−0.0573082
$969$	−30.1880	−0.969777
$970$	7.52622	0.241652
$971$	39.2072	1.25822	0.629109	−	0.777317i	$-0.283420\pi$
$971$	39.2072	1.25822	0.629109	+	0.777317i	$0.283420\pi$
$972$	−19.4912	−0.625182
$973$	−11.3260	−0.363096
$974$	−0.892627	−0.0286016
$975$	8.78514	0.281350
$976$	−11.5323	−0.369141
$977$	−38.8208	−1.24199	−0.620993	−	0.783816i	$-0.713270\pi$
$977$	−38.8208	−1.24199	−0.620993	+	0.783816i	$0.713270\pi$
$978$	0.757297	0.0242157
$979$	4.38106	0.140019
$980$	17.0127	0.543449
$981$	−19.2860	−0.615755
$982$	15.3153	0.488732
$983$	30.2449	0.964663	0.482331	−	0.875989i	$-0.339790\pi$
$983$	30.2449	0.964663	0.482331	+	0.875989i	$0.339790\pi$
$984$	−30.9783	−0.987552
$985$	20.2866	0.646385
$986$	15.3321	0.488274
$987$	−59.6171	−1.89763
$988$	29.3052	0.932324
$989$	7.67798	0.244146
$990$	0.522064	0.0165923
$991$	43.6851	1.38770	0.693852	−	0.720118i	$-0.255912\pi$
$991$	43.6851	1.38770	0.693852	+	0.720118i	$0.255912\pi$
$992$	−6.08806	−0.193296
$993$	52.4600	1.66477
$994$	−30.0388	−0.952774
$995$	−17.7947	−0.564130
$996$	−45.5533	−1.44341
$997$	−25.0310	−0.792739	−0.396370	−	0.918091i	$-0.629730\pi$
$997$	−25.0310	−0.792739	−0.396370	+	0.918091i	$0.629730\pi$
$998$	11.9016	0.376738
$999$	−30.9776	−0.980088

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.g.1.20	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.g.1.20	✓	32	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.472050 q^{2} -2.02631 q^{3} -1.77717 q^{4} -1.00000 q^{5} -0.956522 q^{6} -4.07098 q^{7} -1.78301 q^{8} +1.10595 q^{9} +O(q^{10})\)	\(q+0.472050 q^{2} -2.02631 q^{3} -1.77717 q^{4} -1.00000 q^{5} -0.956522 q^{6} -4.07098 q^{7} -1.78301 q^{8} +1.10595 q^{9} -0.472050 q^{10} -1.00000 q^{11} +3.60110 q^{12} -4.33553 q^{13} -1.92171 q^{14} +2.02631 q^{15} +2.71267 q^{16} +3.91699 q^{17} +0.522064 q^{18} +3.80342 q^{19} +1.77717 q^{20} +8.24909 q^{21} -0.472050 q^{22} +5.26232 q^{23} +3.61295 q^{24} +1.00000 q^{25} -2.04659 q^{26} +3.83794 q^{27} +7.23482 q^{28} +8.29204 q^{29} +0.956522 q^{30} -1.25617 q^{31} +4.84654 q^{32} +2.02631 q^{33} +1.84901 q^{34} +4.07098 q^{35} -1.96546 q^{36} -8.07142 q^{37} +1.79541 q^{38} +8.78514 q^{39} +1.78301 q^{40} -8.57425 q^{41} +3.89398 q^{42} +1.45905 q^{43} +1.77717 q^{44} -1.10595 q^{45} +2.48408 q^{46} -7.22712 q^{47} -5.49671 q^{48} +9.57290 q^{49} +0.472050 q^{50} -7.93705 q^{51} +7.70497 q^{52} +12.2485 q^{53} +1.81170 q^{54} +1.00000 q^{55} +7.25861 q^{56} -7.70693 q^{57} +3.91426 q^{58} -2.63918 q^{59} -3.60110 q^{60} -4.25130 q^{61} -0.592973 q^{62} -4.50231 q^{63} -3.13752 q^{64} +4.33553 q^{65} +0.956522 q^{66} -0.607298 q^{67} -6.96115 q^{68} -10.6631 q^{69} +1.92171 q^{70} +15.6313 q^{71} -1.97192 q^{72} -1.00000 q^{73} -3.81011 q^{74} -2.02631 q^{75} -6.75932 q^{76} +4.07098 q^{77} +4.14703 q^{78} +6.62809 q^{79} -2.71267 q^{80} -11.0947 q^{81} -4.04748 q^{82} -12.6498 q^{83} -14.6600 q^{84} -3.91699 q^{85} +0.688745 q^{86} -16.8023 q^{87} +1.78301 q^{88} -4.38106 q^{89} -0.522064 q^{90} +17.6499 q^{91} -9.35203 q^{92} +2.54539 q^{93} -3.41156 q^{94} -3.80342 q^{95} -9.82062 q^{96} -15.9437 q^{97} +4.51889 q^{98} -1.10595 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9	\( 32 q - 5 q^{2} - 7 q^{3} + 37 q^{4} - 32 q^{5} - 3 q^{6} - 18 q^{8} + 29 q^{9} + 5 q^{10} - 32 q^{11} - 24 q^{12} - q^{13} - 5 q^{14} + 7 q^{15} + 47 q^{16} - 30 q^{17} - 11 q^{18} + 16 q^{19} - 37 q^{20} + q^{21} + 5 q^{22} - 26 q^{23} - 21 q^{24} + 32 q^{25} - q^{26} - 31 q^{27} - 24 q^{28} - 10 q^{29} + 3 q^{30} - 2 q^{31} - 31 q^{32} + 7 q^{33} - 14 q^{34} + 38 q^{36} - 28 q^{37} - 63 q^{38} - 2 q^{39} + 18 q^{40} - 62 q^{41} - 9 q^{42} + 8 q^{43} - 37 q^{44} - 29 q^{45} + 19 q^{46} - 21 q^{47} - 79 q^{48} + 34 q^{49} - 5 q^{50} + 17 q^{51} + 15 q^{52} - 32 q^{53} + 5 q^{54} + 32 q^{55} - 52 q^{56} - 57 q^{57} + 4 q^{58} - 37 q^{59} + 24 q^{60} + 15 q^{61} - 22 q^{62} + 5 q^{63} + 70 q^{64} + q^{65} + 3 q^{66} - 42 q^{67} - 81 q^{68} - 8 q^{69} + 5 q^{70} - 40 q^{71} - 27 q^{72} - 32 q^{73} - 17 q^{74} - 7 q^{75} + 21 q^{76} - 105 q^{78} + 18 q^{79} - 47 q^{80} + 12 q^{81} - 70 q^{82} - 26 q^{83} + 22 q^{84} + 30 q^{85} - 45 q^{86} - 18 q^{87} + 18 q^{88} - 83 q^{89} + 11 q^{90} - 18 q^{91} - 73 q^{92} - 68 q^{93} + 56 q^{94} - 16 q^{95} - 35 q^{96} - 99 q^{97} - 61 q^{98} - 29 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 7 * q^3 + 37 * q^4 - 32 * q^5 - 3 * q^6 - 18 * q^8 + 29 * q^9 + 5 * q^10 - 32 * q^11 - 24 * q^12 - q^13 - 5 * q^14 + 7 * q^15 + 47 * q^16 - 30 * q^17 - 11 * q^18 + 16 * q^19 - 37 * q^20 + q^21 + 5 * q^22 - 26 * q^23 - 21 * q^24 + 32 * q^25 - q^26 - 31 * q^27 - 24 * q^28 - 10 * q^29 + 3 * q^30 - 2 * q^31 - 31 * q^32 + 7 * q^33 - 14 * q^34 + 38 * q^36 - 28 * q^37 - 63 * q^38 - 2 * q^39 + 18 * q^40 - 62 * q^41 - 9 * q^42 + 8 * q^43 - 37 * q^44 - 29 * q^45 + 19 * q^46 - 21 * q^47 - 79 * q^48 + 34 * q^49 - 5 * q^50 + 17 * q^51 + 15 * q^52 - 32 * q^53 + 5 * q^54 + 32 * q^55 - 52 * q^56 - 57 * q^57 + 4 * q^58 - 37 * q^59 + 24 * q^60 + 15 * q^61 - 22 * q^62 + 5 * q^63 + 70 * q^64 + q^65 + 3 * q^66 - 42 * q^67 - 81 * q^68 - 8 * q^69 + 5 * q^70 - 40 * q^71 - 27 * q^72 - 32 * q^73 - 17 * q^74 - 7 * q^75 + 21 * q^76 - 105 * q^78 + 18 * q^79 - 47 * q^80 + 12 * q^81 - 70 * q^82 - 26 * q^83 + 22 * q^84 + 30 * q^85 - 45 * q^86 - 18 * q^87 + 18 * q^88 - 83 * q^89 + 11 * q^90 - 18 * q^91 - 73 * q^92 - 68 * q^93 + 56 * q^94 - 16 * q^95 - 35 * q^96 - 99 * q^97 - 61 * q^98 - 29 * q^99

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