LMFDB - Embedded newform 4015.2.a.i.1.30

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:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.30
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)

$f(q)$	$=$	$q+1.85144 q^{2} -2.11353 q^{3} +1.42784 q^{4} +1.00000 q^{5} -3.91307 q^{6} -4.74538 q^{7} -1.05933 q^{8} +1.46699 q^{9} +O(q^{10})$	\(q+1.85144 q^{2} -2.11353 q^{3} +1.42784 q^{4} +1.00000 q^{5} -3.91307 q^{6} -4.74538 q^{7} -1.05933 q^{8} +1.46699 q^{9} +1.85144 q^{10} -1.00000 q^{11} -3.01777 q^{12} +3.70564 q^{13} -8.78579 q^{14} -2.11353 q^{15} -4.81696 q^{16} -5.22623 q^{17} +2.71604 q^{18} -4.97207 q^{19} +1.42784 q^{20} +10.0295 q^{21} -1.85144 q^{22} +5.98552 q^{23} +2.23892 q^{24} +1.00000 q^{25} +6.86078 q^{26} +3.24006 q^{27} -6.77562 q^{28} -1.29899 q^{29} -3.91307 q^{30} -1.51745 q^{31} -6.79965 q^{32} +2.11353 q^{33} -9.67606 q^{34} -4.74538 q^{35} +2.09462 q^{36} +0.300464 q^{37} -9.20550 q^{38} -7.83197 q^{39} -1.05933 q^{40} +8.90508 q^{41} +18.5690 q^{42} -1.23169 q^{43} -1.42784 q^{44} +1.46699 q^{45} +11.0818 q^{46} -4.65677 q^{47} +10.1808 q^{48} +15.5186 q^{49} +1.85144 q^{50} +11.0458 q^{51} +5.29105 q^{52} +1.98478 q^{53} +5.99878 q^{54} -1.00000 q^{55} +5.02692 q^{56} +10.5086 q^{57} -2.40500 q^{58} +5.51788 q^{59} -3.01777 q^{60} +0.0688587 q^{61} -2.80948 q^{62} -6.96142 q^{63} -2.95525 q^{64} +3.70564 q^{65} +3.91307 q^{66} +4.54302 q^{67} -7.46220 q^{68} -12.6505 q^{69} -8.78579 q^{70} -4.59896 q^{71} -1.55403 q^{72} -1.00000 q^{73} +0.556292 q^{74} -2.11353 q^{75} -7.09930 q^{76} +4.74538 q^{77} -14.5004 q^{78} +8.84232 q^{79} -4.81696 q^{80} -11.2489 q^{81} +16.4872 q^{82} -11.2807 q^{83} +14.3204 q^{84} -5.22623 q^{85} -2.28041 q^{86} +2.74544 q^{87} +1.05933 q^{88} +13.4014 q^{89} +2.71604 q^{90} -17.5847 q^{91} +8.54634 q^{92} +3.20718 q^{93} -8.62173 q^{94} -4.97207 q^{95} +14.3712 q^{96} +5.11814 q^{97} +28.7318 q^{98} -1.46699 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) $ 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * 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 $

$2$	1.85144	1.30917	0.654583	−	0.755990i	$-0.272844\pi$
$2$	1.85144	1.30917	0.654583	+	0.755990i	$0.272844\pi$
$3$	−2.11353	−1.22024	−0.610122	−	0.792307i	$-0.708880\pi$
$3$	−2.11353	−1.22024	−0.610122	+	0.792307i	$0.708880\pi$
$4$	1.42784	0.713918
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−3.91307	−1.59750
$7$	−4.74538	−1.79358	−0.896792	−	0.442452i	$-0.854109\pi$
$7$	−4.74538	−1.79358	−0.896792	+	0.442452i	$0.854109\pi$
$8$	−1.05933	−0.374530
$9$	1.46699	0.488996
$10$	1.85144	0.585477
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.01777	−0.871154
$13$	3.70564	1.02776	0.513880	−	0.857862i	$-0.328208\pi$
$13$	3.70564	1.02776	0.513880	+	0.857862i	$0.328208\pi$
$14$	−8.78579	−2.34810
$15$	−2.11353	−0.545710
$16$	−4.81696	−1.20424
$17$	−5.22623	−1.26755	−0.633774	−	0.773519i	$-0.718495\pi$
$17$	−5.22623	−1.26755	−0.633774	+	0.773519i	$0.718495\pi$
$18$	2.71604	0.640178
$19$	−4.97207	−1.14067	−0.570336	−	0.821412i	$-0.693187\pi$
$19$	−4.97207	−1.14067	−0.570336	+	0.821412i	$0.693187\pi$
$20$	1.42784	0.319274
$21$	10.0295	2.18861
$22$	−1.85144	−0.394729
$23$	5.98552	1.24807	0.624034	−	0.781397i	$-0.285493\pi$
$23$	5.98552	1.24807	0.624034	+	0.781397i	$0.285493\pi$
$24$	2.23892	0.457018
$25$	1.00000	0.200000
$26$	6.86078	1.34551
$27$	3.24006	0.623549
$28$	−6.77562	−1.28047
$29$	−1.29899	−0.241216	−0.120608	−	0.992700i	$-0.538484\pi$
$29$	−1.29899	−0.241216	−0.120608	+	0.992700i	$0.538484\pi$
$30$	−3.91307	−0.714425
$31$	−1.51745	−0.272543	−0.136271	−	0.990672i	$-0.543512\pi$
$31$	−1.51745	−0.272543	−0.136271	+	0.990672i	$0.543512\pi$
$32$	−6.79965	−1.20202
$33$	2.11353	0.367918
$34$	−9.67606	−1.65943
$35$	−4.74538	−0.802115
$36$	2.09462	0.349103
$37$	0.300464	0.0493960	0.0246980	−	0.999695i	$-0.492138\pi$
$37$	0.300464	0.0493960	0.0246980	+	0.999695i	$0.492138\pi$
$38$	−9.20550	−1.49333
$39$	−7.83197	−1.25412
$40$	−1.05933	−0.167495
$41$	8.90508	1.39074	0.695370	−	0.718652i	$-0.255241\pi$
$41$	8.90508	1.39074	0.695370	+	0.718652i	$0.255241\pi$
$42$	18.5690	2.86526
$43$	−1.23169	−0.187831	−0.0939157	−	0.995580i	$-0.529938\pi$
$43$	−1.23169	−0.187831	−0.0939157	+	0.995580i	$0.529938\pi$
$44$	−1.42784	−0.215254
$45$	1.46699	0.218686
$46$	11.0818	1.63393
$47$	−4.65677	−0.679259	−0.339630	−	0.940559i	$-0.610302\pi$
$47$	−4.65677	−0.679259	−0.339630	+	0.940559i	$0.610302\pi$
$48$	10.1808	1.46947
$49$	15.5186	2.21694
$50$	1.85144	0.261833
$51$	11.0458	1.54672
$52$	5.29105	0.733736
$53$	1.98478	0.272630	0.136315	−	0.990666i	$-0.456474\pi$
$53$	1.98478	0.272630	0.136315	+	0.990666i	$0.456474\pi$
$54$	5.99878	0.816330
$55$	−1.00000	−0.134840
$56$	5.02692	0.671750
$57$	10.5086	1.39190
$58$	−2.40500	−0.315792
$59$	5.51788	0.718367	0.359184	−	0.933267i	$-0.383055\pi$
$59$	5.51788	0.718367	0.359184	+	0.933267i	$0.383055\pi$
$60$	−3.01777	−0.389592
$61$	0.0688587	0.00881645	0.00440823	−	0.999990i	$-0.498597\pi$
$61$	0.0688587	0.00881645	0.00440823	+	0.999990i	$0.498597\pi$
$62$	−2.80948	−0.356804
$63$	−6.96142	−0.877056
$64$	−2.95525	−0.369406
$65$	3.70564	0.459628
$66$	3.91307	0.481665
$67$	4.54302	0.555018	0.277509	−	0.960723i	$-0.410491\pi$
$67$	4.54302	0.555018	0.277509	+	0.960723i	$0.410491\pi$
$68$	−7.46220	−0.904924
$69$	−12.6505	−1.52295
$70$	−8.78579	−1.05010
$71$	−4.59896	−0.545796	−0.272898	−	0.962043i	$-0.587982\pi$
$71$	−4.59896	−0.545796	−0.272898	+	0.962043i	$0.587982\pi$
$72$	−1.55403	−0.183144
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	0.556292	0.0646676
$75$	−2.11353	−0.244049
$76$	−7.09930	−0.814345
$77$	4.74538	0.540786
$78$	−14.5004	−1.64185
$79$	8.84232	0.994839	0.497419	−	0.867510i	$-0.334281\pi$
$79$	8.84232	0.994839	0.497419	+	0.867510i	$0.334281\pi$
$80$	−4.81696	−0.538552
$81$	−11.2489	−1.24988
$82$	16.4872	1.82071
$83$	−11.2807	−1.23822	−0.619111	−	0.785303i	$-0.712507\pi$
$83$	−11.2807	−1.23822	−0.619111	+	0.785303i	$0.712507\pi$
$84$	14.3204	1.56249
$85$	−5.22623	−0.566864
$86$	−2.28041	−0.245903
$87$	2.74544	0.294342
$88$	1.05933	0.112925
$89$	13.4014	1.42054	0.710272	−	0.703928i	$-0.248572\pi$
$89$	13.4014	1.42054	0.710272	+	0.703928i	$0.248572\pi$
$90$	2.71604	0.286296
$91$	−17.5847	−1.84337
$92$	8.54634	0.891017
$93$	3.20718	0.332569
$94$	−8.62173	−0.889264
$95$	−4.97207	−0.510124
$96$	14.3712	1.46676
$97$	5.11814	0.519668	0.259834	−	0.965653i	$-0.416332\pi$
$97$	5.11814	0.519668	0.259834	+	0.965653i	$0.416332\pi$
$98$	28.7318	2.90235
$99$	−1.46699	−0.147438
$100$	1.42784	0.142784
$101$	12.1645	1.21041	0.605206	−	0.796069i	$-0.293091\pi$
$101$	12.1645	1.21041	0.605206	+	0.796069i	$0.293091\pi$
$102$	20.4506	2.02491
$103$	18.3203	1.80516	0.902579	−	0.430525i	$-0.141672\pi$
$103$	18.3203	1.80516	0.902579	+	0.430525i	$0.141672\pi$
$104$	−3.92550	−0.384927
$105$	10.0295	0.978776
$106$	3.67470	0.356918
$107$	−2.38183	−0.230260	−0.115130	−	0.993350i	$-0.536729\pi$
$107$	−2.38183	−0.230260	−0.115130	+	0.993350i	$0.536729\pi$
$108$	4.62627	0.445163
$109$	−10.0778	−0.965277	−0.482638	−	0.875820i	$-0.660321\pi$
$109$	−10.0778	−0.965277	−0.482638	+	0.875820i	$0.660321\pi$
$110$	−1.85144	−0.176528
$111$	−0.635039	−0.0602752
$112$	22.8583	2.15990
$113$	4.63819	0.436324	0.218162	−	0.975913i	$-0.429994\pi$
$113$	4.63819	0.436324	0.218162	+	0.975913i	$0.429994\pi$
$114$	19.4561	1.82223
$115$	5.98552	0.558153
$116$	−1.85474	−0.172208
$117$	5.43614	0.502571
$118$	10.2160	0.940462
$119$	24.8004	2.27345
$120$	2.23892	0.204385
$121$	1.00000	0.0909091
$122$	0.127488	0.0115422
$123$	−18.8211	−1.69704
$124$	−2.16667	−0.194573
$125$	1.00000	0.0894427
$126$	−12.8887	−1.14821
$127$	−2.34206	−0.207824	−0.103912	−	0.994586i	$-0.533136\pi$
$127$	−2.34206	−0.207824	−0.103912	+	0.994586i	$0.533136\pi$
$128$	8.12784	0.718407
$129$	2.60321	0.229200
$130$	6.86078	0.601730
$131$	−19.6239	−1.71455	−0.857273	−	0.514863i	$-0.827843\pi$
$131$	−19.6239	−1.71455	−0.857273	+	0.514863i	$0.827843\pi$
$132$	3.01777	0.262663
$133$	23.5944	2.04589
$134$	8.41113	0.726611
$135$	3.24006	0.278860
$136$	5.53630	0.474734
$137$	5.25760	0.449187	0.224593	−	0.974453i	$-0.427895\pi$
$137$	5.25760	0.449187	0.224593	+	0.974453i	$0.427895\pi$
$138$	−23.4217	−1.99379
$139$	15.4807	1.31305	0.656527	−	0.754302i	$-0.272025\pi$
$139$	15.4807	1.31305	0.656527	+	0.754302i	$0.272025\pi$
$140$	−6.77562	−0.572644
$141$	9.84219	0.828862
$142$	−8.51470	−0.714537
$143$	−3.70564	−0.309881
$144$	−7.06642	−0.588869
$145$	−1.29899	−0.107875
$146$	−1.85144	−0.153226
$147$	−32.7990	−2.70521
$148$	0.429013	0.0352647
$149$	22.5365	1.84626	0.923129	−	0.384490i	$-0.125623\pi$
$149$	22.5365	1.84626	0.923129	+	0.384490i	$0.125623\pi$
$150$	−3.91307	−0.319501
$151$	5.34904	0.435299	0.217649	−	0.976027i	$-0.430161\pi$
$151$	5.34904	0.435299	0.217649	+	0.976027i	$0.430161\pi$
$152$	5.26706	0.427215
$153$	−7.66682	−0.619826
$154$	8.78579	0.707979
$155$	−1.51745	−0.121885
$156$	−11.1828	−0.895338
$157$	−18.3444	−1.46404	−0.732022	−	0.681281i	$-0.761423\pi$
$157$	−18.3444	−1.46404	−0.732022	+	0.681281i	$0.761423\pi$
$158$	16.3710	1.30241
$159$	−4.19487	−0.332675
$160$	−6.79965	−0.537560
$161$	−28.4036	−2.23851
$162$	−20.8267	−1.63630
$163$	−14.4827	−1.13437	−0.567185	−	0.823590i	$-0.691968\pi$
$163$	−14.4827	−1.13437	−0.567185	+	0.823590i	$0.691968\pi$
$164$	12.7150	0.992873
$165$	2.11353	0.164538
$166$	−20.8856	−1.62104
$167$	−13.4299	−1.03924	−0.519618	−	0.854399i	$-0.673926\pi$
$167$	−13.4299	−1.03924	−0.519618	+	0.854399i	$0.673926\pi$
$168$	−10.6245	−0.819700
$169$	0.731792	0.0562917
$170$	−9.67606	−0.742120
$171$	−7.29397	−0.557784
$172$	−1.75865	−0.134096
$173$	−3.58728	−0.272736	−0.136368	−	0.990658i	$-0.543543\pi$
$173$	−3.58728	−0.272736	−0.136368	+	0.990658i	$0.543543\pi$
$174$	5.08303	0.385343
$175$	−4.74538	−0.358717
$176$	4.81696	0.363092
$177$	−11.6622	−0.876583
$178$	24.8119	1.85973
$179$	15.0028	1.12137	0.560683	−	0.828031i	$-0.310539\pi$
$179$	15.0028	1.12137	0.560683	+	0.828031i	$0.310539\pi$
$180$	2.09462	0.156124
$181$	14.0489	1.04425	0.522123	−	0.852870i	$-0.325140\pi$
$181$	14.0489	1.04425	0.522123	+	0.852870i	$0.325140\pi$
$182$	−32.5570	−2.41328
$183$	−0.145535	−0.0107582
$184$	−6.34064	−0.467438
$185$	0.300464	0.0220906
$186$	5.93790	0.435388
$187$	5.22623	0.382180
$188$	−6.64909	−0.484935
$189$	−15.3753	−1.11839
$190$	−9.20550	−0.667837
$191$	−16.0243	−1.15947	−0.579737	−	0.814803i	$-0.696845\pi$
$191$	−16.0243	−1.15947	−0.579737	+	0.814803i	$0.696845\pi$
$192$	6.24599	0.450765
$193$	−11.2281	−0.808219	−0.404110	−	0.914711i	$-0.632419\pi$
$193$	−11.2281	−0.808219	−0.404110	+	0.914711i	$0.632419\pi$
$194$	9.47593	0.680332
$195$	−7.83197	−0.560859
$196$	22.1580	1.58271
$197$	13.3709	0.952638	0.476319	−	0.879272i	$-0.341971\pi$
$197$	13.3709	0.952638	0.476319	+	0.879272i	$0.341971\pi$
$198$	−2.71604	−0.193021
$199$	−2.20134	−0.156049	−0.0780246	−	0.996951i	$-0.524861\pi$
$199$	−2.20134	−0.156049	−0.0780246	+	0.996951i	$0.524861\pi$
$200$	−1.05933	−0.0749059
$201$	−9.60178	−0.677257
$202$	22.5218	1.58463
$203$	6.16419	0.432641
$204$	15.7715	1.10423
$205$	8.90508	0.621958
$206$	33.9190	2.36325
$207$	8.78069	0.610300
$208$	−17.8499	−1.23767
$209$	4.97207	0.343925
$210$	18.5690	1.28138
$211$	21.2776	1.46481	0.732407	−	0.680867i	$-0.238397\pi$
$211$	21.2776	1.46481	0.732407	+	0.680867i	$0.238397\pi$
$212$	2.83393	0.194635
$213$	9.72001	0.666004
$214$	−4.40982	−0.301449
$215$	−1.23169	−0.0840007
$216$	−3.43229	−0.233538
$217$	7.20089	0.488828
$218$	−18.6584	−1.26371
$219$	2.11353	0.142819
$220$	−1.42784	−0.0962646
$221$	−19.3666	−1.30274
$222$	−1.17574	−0.0789103
$223$	−17.0741	−1.14337	−0.571683	−	0.820474i	$-0.693709\pi$
$223$	−17.0741	−1.14337	−0.571683	+	0.820474i	$0.693709\pi$
$224$	32.2669	2.15592
$225$	1.46699	0.0977993
$226$	8.58733	0.571221
$227$	16.0316	1.06405	0.532027	−	0.846727i	$-0.321430\pi$
$227$	16.0316	1.06405	0.532027	+	0.846727i	$0.321430\pi$
$228$	15.0045	0.993700
$229$	25.6623	1.69581	0.847907	−	0.530145i	$-0.177863\pi$
$229$	25.6623	1.69581	0.847907	+	0.530145i	$0.177863\pi$
$230$	11.0818	0.730715
$231$	−10.0295	−0.659891
$232$	1.37606	0.0903425
$233$	2.14455	0.140494	0.0702471	−	0.997530i	$-0.477621\pi$
$233$	2.14455	0.140494	0.0702471	+	0.997530i	$0.477621\pi$
$234$	10.0647	0.657949
$235$	−4.65677	−0.303774
$236$	7.87863	0.512855
$237$	−18.6885	−1.21395
$238$	45.9166	2.97633
$239$	−8.19183	−0.529886	−0.264943	−	0.964264i	$-0.585353\pi$
$239$	−8.19183	−0.529886	−0.264943	+	0.964264i	$0.585353\pi$
$240$	10.1808	0.657165
$241$	17.3384	1.11687	0.558433	−	0.829550i	$-0.311403\pi$
$241$	17.3384	1.11687	0.558433	+	0.829550i	$0.311403\pi$
$242$	1.85144	0.119015
$243$	14.0547	0.901608
$244$	0.0983189	0.00629422
$245$	15.5186	0.991447
$246$	−34.8462	−2.22171
$247$	−18.4247	−1.17234
$248$	1.60748	0.102075
$249$	23.8421	1.51093
$250$	1.85144	0.117095
$251$	−8.26940	−0.521960	−0.260980	−	0.965344i	$-0.584046\pi$
$251$	−8.26940	−0.521960	−0.260980	+	0.965344i	$0.584046\pi$
$252$	−9.93975	−0.626146
$253$	−5.98552	−0.376306
$254$	−4.33618	−0.272076
$255$	11.0458	0.691713
$256$	20.9587	1.30992
$257$	5.29405	0.330234	0.165117	−	0.986274i	$-0.447200\pi$
$257$	5.29405	0.330234	0.165117	+	0.986274i	$0.447200\pi$
$258$	4.81970	0.300061
$259$	−1.42582	−0.0885959
$260$	5.29105	0.328137
$261$	−1.90560	−0.117954
$262$	−36.3324	−2.24463
$263$	18.4671	1.13873	0.569365	−	0.822085i	$-0.307189\pi$
$263$	18.4671	1.13873	0.569365	+	0.822085i	$0.307189\pi$
$264$	−2.23892	−0.137796
$265$	1.98478	0.121924
$266$	43.6836	2.67841
$267$	−28.3242	−1.73341
$268$	6.48668	0.396237
$269$	11.5544	0.704483	0.352242	−	0.935909i	$-0.385420\pi$
$269$	11.5544	0.704483	0.352242	+	0.935909i	$0.385420\pi$
$270$	5.99878	0.365074
$271$	−6.45743	−0.392261	−0.196131	−	0.980578i	$-0.562838\pi$
$271$	−6.45743	−0.392261	−0.196131	+	0.980578i	$0.562838\pi$
$272$	25.1745	1.52643
$273$	37.1657	2.24937
$274$	9.73414	0.588061
$275$	−1.00000	−0.0603023
$276$	−18.0629	−1.08726
$277$	−16.8146	−1.01029	−0.505147	−	0.863033i	$-0.668562\pi$
$277$	−16.8146	−1.01029	−0.505147	+	0.863033i	$0.668562\pi$
$278$	28.6616	1.71901
$279$	−2.22609	−0.133272
$280$	5.02692	0.300416
$281$	−8.25429	−0.492409	−0.246205	−	0.969218i	$-0.579184\pi$
$281$	−8.25429	−0.492409	−0.246205	+	0.969218i	$0.579184\pi$
$282$	18.2222	1.08512
$283$	4.27995	0.254417	0.127208	−	0.991876i	$-0.459398\pi$
$283$	4.27995	0.254417	0.127208	+	0.991876i	$0.459398\pi$
$284$	−6.56655	−0.389653
$285$	10.5086	0.622476
$286$	−6.86078	−0.405686
$287$	−42.2579	−2.49441
$288$	−9.97502	−0.587784
$289$	10.3135	0.606676
$290$	−2.40500	−0.141226
$291$	−10.8173	−0.634122
$292$	−1.42784	−0.0835577
$293$	−25.8284	−1.50891	−0.754456	−	0.656351i	$-0.772099\pi$
$293$	−25.8284	−1.50891	−0.754456	+	0.656351i	$0.772099\pi$
$294$	−60.7253	−3.54157
$295$	5.51788	0.321264
$296$	−0.318291	−0.0185003
$297$	−3.24006	−0.188007
$298$	41.7249	2.41706
$299$	22.1802	1.28271
$300$	−3.01777	−0.174231
$301$	5.84485	0.336891
$302$	9.90344	0.569879
$303$	−25.7100	−1.47700
$304$	23.9503	1.37364
$305$	0.0688587	0.00394284
$306$	−14.1947	−0.811456
$307$	−15.7725	−0.900185	−0.450092	−	0.892982i	$-0.648609\pi$
$307$	−15.7725	−0.900185	−0.450092	+	0.892982i	$0.648609\pi$
$308$	6.77562	0.386077
$309$	−38.7205	−2.20273
$310$	−2.80948	−0.159568
$311$	6.49112	0.368077	0.184039	−	0.982919i	$-0.441083\pi$
$311$	6.49112	0.368077	0.184039	+	0.982919i	$0.441083\pi$
$312$	8.29664	0.469705
$313$	19.4373	1.09866	0.549330	−	0.835605i	$-0.314883\pi$
$313$	19.4373	1.09866	0.549330	+	0.835605i	$0.314883\pi$
$314$	−33.9636	−1.91668
$315$	−6.96142	−0.392231
$316$	12.6254	0.710233
$317$	1.17632	0.0660689	0.0330344	−	0.999454i	$-0.489483\pi$
$317$	1.17632	0.0660689	0.0330344	+	0.999454i	$0.489483\pi$
$318$	−7.76656	−0.435527
$319$	1.29899	0.0727293
$320$	−2.95525	−0.165203
$321$	5.03406	0.280974
$322$	−52.5875	−2.93059
$323$	25.9852	1.44585
$324$	−16.0616	−0.892310
$325$	3.70564	0.205552
$326$	−26.8138	−1.48508
$327$	21.2997	1.17787
$328$	−9.43341	−0.520873
$329$	22.0981	1.21831
$330$	3.91307	0.215407
$331$	−15.5617	−0.855347	−0.427674	−	0.903933i	$-0.640667\pi$
$331$	−15.5617	−0.855347	−0.427674	+	0.903933i	$0.640667\pi$
$332$	−16.1070	−0.883989
$333$	0.440778	0.0241545
$334$	−24.8647	−1.36053
$335$	4.54302	0.248211
$336$	−48.3115	−2.63561
$337$	−33.3009	−1.81402	−0.907008	−	0.421113i	$-0.861640\pi$
$337$	−33.3009	−1.81402	−0.907008	+	0.421113i	$0.861640\pi$
$338$	1.35487	0.0736952
$339$	−9.80292	−0.532422
$340$	−7.46220	−0.404694
$341$	1.51745	0.0821747
$342$	−13.5044	−0.730232
$343$	−40.4240	−2.18269
$344$	1.30477	0.0703484
$345$	−12.6505	−0.681083
$346$	−6.64164	−0.357057
$347$	−0.446398	−0.0239639	−0.0119819	−	0.999928i	$-0.503814\pi$
$347$	−0.446398	−0.0239639	−0.0119819	+	0.999928i	$0.503814\pi$
$348$	3.92004	0.210136
$349$	31.8312	1.70389	0.851943	−	0.523634i	$-0.175424\pi$
$349$	31.8312	1.70389	0.851943	+	0.523634i	$0.175424\pi$
$350$	−8.78579	−0.469620
$351$	12.0065	0.640859
$352$	6.79965	0.362423
$353$	−26.6662	−1.41930	−0.709648	−	0.704556i	$-0.751146\pi$
$353$	−26.6662	−1.41930	−0.709648	+	0.704556i	$0.751146\pi$
$354$	−21.5918	−1.14759
$355$	−4.59896	−0.244087
$356$	19.1350	1.01415
$357$	−52.4164	−2.77417
$358$	27.7769	1.46805
$359$	17.3431	0.915334	0.457667	−	0.889124i	$-0.348685\pi$
$359$	17.3431	0.915334	0.457667	+	0.889124i	$0.348685\pi$
$360$	−1.55403	−0.0819043
$361$	5.72149	0.301131
$362$	26.0107	1.36709
$363$	−2.11353	−0.110931
$364$	−25.1080	−1.31602
$365$	−1.00000	−0.0523424
$366$	−0.269449	−0.0140843
$367$	0.0766897	0.00400317	0.00200158	−	0.999998i	$-0.499363\pi$
$367$	0.0766897	0.00400317	0.00200158	+	0.999998i	$0.499363\pi$
$368$	−28.8320	−1.50297
$369$	13.0637	0.680066
$370$	0.556292	0.0289202
$371$	−9.41851	−0.488985
$372$	4.57932	0.237427
$373$	−20.0921	−1.04033	−0.520164	−	0.854066i	$-0.674129\pi$
$373$	−20.0921	−1.04033	−0.520164	+	0.854066i	$0.674129\pi$
$374$	9.67606	0.500337
$375$	−2.11353	−0.109142
$376$	4.93305	0.254403
$377$	−4.81358	−0.247912
$378$	−28.4665	−1.46416
$379$	11.2562	0.578195	0.289097	−	0.957300i	$-0.406645\pi$
$379$	11.2562	0.578195	0.289097	+	0.957300i	$0.406645\pi$
$380$	−7.09930	−0.364186
$381$	4.95000	0.253596
$382$	−29.6680	−1.51795
$383$	10.1022	0.516199	0.258099	−	0.966118i	$-0.416904\pi$
$383$	10.1022	0.516199	0.258099	+	0.966118i	$0.416904\pi$
$384$	−17.1784	−0.876632
$385$	4.74538	0.241847
$386$	−20.7882	−1.05809
$387$	−1.80688	−0.0918488
$388$	7.30785	0.371000
$389$	9.75839	0.494770	0.247385	−	0.968917i	$-0.420429\pi$
$389$	9.75839	0.494770	0.247385	+	0.968917i	$0.420429\pi$
$390$	−14.5004	−0.734258
$391$	−31.2817	−1.58198
$392$	−16.4393	−0.830311
$393$	41.4755	2.09216
$394$	24.7555	1.24716
$395$	8.84232	0.444905
$396$	−2.09462	−0.105259
$397$	17.2054	0.863512	0.431756	−	0.901990i	$-0.357894\pi$
$397$	17.2054	0.863512	0.431756	+	0.901990i	$0.357894\pi$
$398$	−4.07566	−0.204294
$399$	−49.8673	−2.49649
$400$	−4.81696	−0.240848
$401$	20.2688	1.01218	0.506088	−	0.862482i	$-0.331091\pi$
$401$	20.2688	1.01218	0.506088	+	0.862482i	$0.331091\pi$
$402$	−17.7771	−0.886643
$403$	−5.62314	−0.280109
$404$	17.3689	0.864134
$405$	−11.2489	−0.558963
$406$	11.4126	0.566399
$407$	−0.300464	−0.0148935
$408$	−11.7011	−0.579292
$409$	1.37266	0.0678735	0.0339368	−	0.999424i	$-0.489196\pi$
$409$	1.37266	0.0678735	0.0339368	+	0.999424i	$0.489196\pi$
$410$	16.4872	0.814246
$411$	−11.1121	−0.548118
$412$	26.1584	1.28873
$413$	−26.1844	−1.28845
$414$	16.2569	0.798985
$415$	−11.2807	−0.553750
$416$	−25.1971	−1.23539
$417$	−32.7188	−1.60225
$418$	9.20550	0.450256
$419$	16.3088	0.796738	0.398369	−	0.917225i	$-0.369576\pi$
$419$	16.3088	0.796738	0.398369	+	0.917225i	$0.369576\pi$
$420$	14.3204	0.698766
$421$	31.3159	1.52624	0.763122	−	0.646254i	$-0.223665\pi$
$421$	31.3159	1.52624	0.763122	+	0.646254i	$0.223665\pi$
$422$	39.3943	1.91769
$423$	−6.83143	−0.332155
$424$	−2.10253	−0.102108
$425$	−5.22623	−0.253509
$426$	17.9960	0.871910
$427$	−0.326760	−0.0158130
$428$	−3.40086	−0.164387
$429$	7.83197	0.378131
$430$	−2.28041	−0.109971
$431$	−2.48064	−0.119488	−0.0597441	−	0.998214i	$-0.519028\pi$
$431$	−2.48064	−0.119488	−0.0597441	+	0.998214i	$0.519028\pi$
$432$	−15.6072	−0.750903
$433$	−23.7385	−1.14080	−0.570400	−	0.821367i	$-0.693212\pi$
$433$	−23.7385	−1.14080	−0.570400	+	0.821367i	$0.693212\pi$
$434$	13.3320	0.639958
$435$	2.74544	0.131634
$436$	−14.3894	−0.689128
$437$	−29.7604	−1.42363
$438$	3.91307	0.186974
$439$	10.8851	0.519516	0.259758	−	0.965674i	$-0.416357\pi$
$439$	10.8851	0.519516	0.259758	+	0.965674i	$0.416357\pi$
$440$	1.05933	0.0505016
$441$	22.7656	1.08408
$442$	−35.8560	−1.70550
$443$	23.9920	1.13990	0.569948	−	0.821681i	$-0.306963\pi$
$443$	23.9920	1.13990	0.569948	+	0.821681i	$0.306963\pi$
$444$	−0.906730	−0.0430315
$445$	13.4014	0.635286
$446$	−31.6117	−1.49686
$447$	−47.6314	−2.25289
$448$	14.0238	0.662560
$449$	19.4859	0.919594	0.459797	−	0.888024i	$-0.347922\pi$
$449$	19.4859	0.919594	0.459797	+	0.888024i	$0.347922\pi$
$450$	2.71604	0.128036
$451$	−8.90508	−0.419324
$452$	6.62256	0.311499
$453$	−11.3053	−0.531171
$454$	29.6816	1.39302
$455$	−17.5847	−0.824382
$456$	−11.1321	−0.521307
$457$	9.61603	0.449819	0.224909	−	0.974380i	$-0.427791\pi$
$457$	9.61603	0.449819	0.224909	+	0.974380i	$0.427791\pi$
$458$	47.5123	2.22010
$459$	−16.9333	−0.790378
$460$	8.54634	0.398475
$461$	−6.51856	−0.303600	−0.151800	−	0.988411i	$-0.548507\pi$
$461$	−6.51856	−0.303600	−0.151800	+	0.988411i	$0.548507\pi$
$462$	−18.5690	−0.863907
$463$	5.85728	0.272211	0.136105	−	0.990694i	$-0.456541\pi$
$463$	5.85728	0.272211	0.136105	+	0.990694i	$0.456541\pi$
$464$	6.25717	0.290482
$465$	3.20718	0.148729
$466$	3.97051	0.183930
$467$	−32.3744	−1.49811	−0.749055	−	0.662508i	$-0.769492\pi$
$467$	−32.3744	−1.49811	−0.749055	+	0.662508i	$0.769492\pi$
$468$	7.76191	0.358794
$469$	−21.5583	−0.995471
$470$	−8.62173	−0.397691
$471$	38.7714	1.78649
$472$	−5.84526	−0.269050
$473$	1.23169	0.0566333
$474$	−34.6006	−1.58926
$475$	−4.97207	−0.228134
$476$	35.4109	1.62306
$477$	2.91164	0.133315
$478$	−15.1667	−0.693709
$479$	−22.6402	−1.03446	−0.517228	−	0.855848i	$-0.673036\pi$
$479$	−22.6402	−1.03446	−0.517228	+	0.855848i	$0.673036\pi$
$480$	14.3712	0.655954
$481$	1.11341	0.0507673
$482$	32.1011	1.46216
$483$	60.0316	2.73153
$484$	1.42784	0.0649016
$485$	5.11814	0.232403
$486$	26.0214	1.18036
$487$	8.63879	0.391461	0.195730	−	0.980658i	$-0.437292\pi$
$487$	8.63879	0.391461	0.195730	+	0.980658i	$0.437292\pi$
$488$	−0.0729441	−0.00330202
$489$	30.6095	1.38421
$490$	28.7318	1.29797
$491$	−34.8650	−1.57343	−0.786717	−	0.617313i	$-0.788221\pi$
$491$	−34.8650	−1.57343	−0.786717	+	0.617313i	$0.788221\pi$
$492$	−26.8734	−1.21155
$493$	6.78881	0.305753
$494$	−34.1123	−1.53478
$495$	−1.46699	−0.0659363
$496$	7.30951	0.328207
$497$	21.8238	0.978930
$498$	44.1423	1.97806
$499$	−14.7683	−0.661122	−0.330561	−	0.943785i	$-0.607238\pi$
$499$	−14.7683	−0.661122	−0.330561	+	0.943785i	$0.607238\pi$
$500$	1.42784	0.0638547
$501$	28.3844	1.26812
$502$	−15.3103	−0.683332
$503$	−4.31534	−0.192411	−0.0962057	−	0.995361i	$-0.530671\pi$
$503$	−4.31534	−0.192411	−0.0962057	+	0.995361i	$0.530671\pi$
$504$	7.37444	0.328483
$505$	12.1645	0.541313
$506$	−11.0818	−0.492648
$507$	−1.54666	−0.0686896
$508$	−3.34407	−0.148369
$509$	−9.51241	−0.421630	−0.210815	−	0.977526i	$-0.567612\pi$
$509$	−9.51241	−0.421630	−0.210815	+	0.977526i	$0.567612\pi$
$510$	20.4506	0.905568
$511$	4.74538	0.209923
$512$	22.5481	0.996497
$513$	−16.1098	−0.711265
$514$	9.80162	0.432331
$515$	18.3203	0.807291
$516$	3.71696	0.163630
$517$	4.65677	0.204804
$518$	−2.63981	−0.115987
$519$	7.58181	0.332805
$520$	−3.92550	−0.172145
$521$	−20.7610	−0.909556	−0.454778	−	0.890605i	$-0.650281\pi$
$521$	−20.7610	−0.909556	−0.454778	+	0.890605i	$0.650281\pi$
$522$	−3.52811	−0.154421
$523$	17.6491	0.771743	0.385871	−	0.922553i	$-0.373901\pi$
$523$	17.6491	0.771743	0.385871	+	0.922553i	$0.373901\pi$
$524$	−28.0196	−1.22404
$525$	10.0295	0.437722
$526$	34.1908	1.49079
$527$	7.93057	0.345461
$528$	−10.1808	−0.443061
$529$	12.8265	0.557672
$530$	3.67470	0.159619
$531$	8.09467	0.351279
$532$	33.6888	1.46060
$533$	32.9990	1.42935
$534$	−52.4405	−2.26932
$535$	−2.38183	−0.102976
$536$	−4.81255	−0.207871
$537$	−31.7089	−1.36834
$538$	21.3923	0.922286
$539$	−15.5186	−0.668434
$540$	4.62627	0.199083
$541$	−28.1961	−1.21224	−0.606122	−	0.795372i	$-0.707276\pi$
$541$	−28.1961	−1.21224	−0.606122	+	0.795372i	$0.707276\pi$
$542$	−11.9556	−0.513535
$543$	−29.6927	−1.27424
$544$	35.5366	1.52362
$545$	−10.0778	−0.431685
$546$	68.8100	2.94480
$547$	0.705338	0.0301581	0.0150790	−	0.999886i	$-0.495200\pi$
$547$	0.705338	0.0301581	0.0150790	+	0.999886i	$0.495200\pi$
$548$	7.50698	0.320682
$549$	0.101015	0.00431121
$550$	−1.85144	−0.0789457
$551$	6.45866	0.275148
$552$	13.4011	0.570389
$553$	−41.9601	−1.78433
$554$	−31.1313	−1.32264
$555$	−0.635039	−0.0269559
$556$	22.1039	0.937413
$557$	−36.9608	−1.56608	−0.783040	−	0.621971i	$-0.786332\pi$
$557$	−36.9608	−1.56608	−0.783040	+	0.621971i	$0.786332\pi$
$558$	−4.12147	−0.174476
$559$	−4.56421	−0.193046
$560$	22.8583	0.965939
$561$	−11.0458	−0.466353
$562$	−15.2823	−0.644646
$563$	15.6385	0.659086	0.329543	−	0.944141i	$-0.393105\pi$
$563$	15.6385	0.659086	0.329543	+	0.944141i	$0.393105\pi$
$564$	14.0530	0.591739
$565$	4.63819	0.195130
$566$	7.92408	0.333074
$567$	53.3803	2.24176
$568$	4.87181	0.204417
$569$	−37.6887	−1.57999	−0.789996	−	0.613113i	$-0.789917\pi$
$569$	−37.6887	−1.57999	−0.789996	+	0.613113i	$0.789917\pi$
$570$	19.4561	0.814924
$571$	44.0096	1.84174	0.920872	−	0.389866i	$-0.127479\pi$
$571$	44.0096	1.84174	0.920872	+	0.389866i	$0.127479\pi$
$572$	−5.29105	−0.221230
$573$	33.8677	1.41484
$574$	−78.2381	−3.26560
$575$	5.98552	0.249613
$576$	−4.33531	−0.180638
$577$	20.1025	0.836880	0.418440	−	0.908244i	$-0.362577\pi$
$577$	20.1025	0.836880	0.418440	+	0.908244i	$0.362577\pi$
$578$	19.0948	0.794240
$579$	23.7310	0.986225
$580$	−1.85474	−0.0770139
$581$	53.5314	2.22086
$582$	−20.0276	−0.830171
$583$	−1.98478	−0.0822010
$584$	1.05933	0.0438354
$585$	5.43614	0.224757
$586$	−47.8198	−1.97542
$587$	7.11423	0.293636	0.146818	−	0.989164i	$-0.453097\pi$
$587$	7.11423	0.293636	0.146818	+	0.989164i	$0.453097\pi$
$588$	−46.8315	−1.93130
$589$	7.54489	0.310882
$590$	10.2160	0.420588
$591$	−28.2598	−1.16245
$592$	−1.44732	−0.0594846
$593$	−13.7938	−0.566442	−0.283221	−	0.959055i	$-0.591403\pi$
$593$	−13.7938	−0.566442	−0.283221	+	0.959055i	$0.591403\pi$
$594$	−5.99878	−0.246133
$595$	24.8004	1.01672
$596$	32.1783	1.31808
$597$	4.65260	0.190418
$598$	41.0653	1.67929
$599$	−40.1446	−1.64026	−0.820131	−	0.572175i	$-0.806100\pi$
$599$	−40.1446	−1.64026	−0.820131	+	0.572175i	$0.806100\pi$
$600$	2.23892	0.0914035
$601$	−9.36754	−0.382110	−0.191055	−	0.981579i	$-0.561191\pi$
$601$	−9.36754	−0.382110	−0.191055	+	0.981579i	$0.561191\pi$
$602$	10.8214	0.441047
$603$	6.66455	0.271402
$604$	7.63755	0.310768
$605$	1.00000	0.0406558
$606$	−47.6005	−1.93364
$607$	27.1870	1.10349	0.551744	−	0.834014i	$-0.313963\pi$
$607$	27.1870	1.10349	0.551744	+	0.834014i	$0.313963\pi$
$608$	33.8084	1.37111
$609$	−13.0282	−0.527928
$610$	0.127488	0.00516183
$611$	−17.2563	−0.698116
$612$	−10.9470	−0.442505
$613$	−14.9377	−0.603329	−0.301664	−	0.953414i	$-0.597542\pi$
$613$	−14.9377	−0.603329	−0.301664	+	0.953414i	$0.597542\pi$
$614$	−29.2019	−1.17849
$615$	−18.8211	−0.758940
$616$	−5.02692	−0.202540
$617$	38.2307	1.53911	0.769554	−	0.638581i	$-0.220478\pi$
$617$	38.2307	1.53911	0.769554	+	0.638581i	$0.220478\pi$
$618$	−71.6888	−2.88374
$619$	2.39282	0.0961757	0.0480878	−	0.998843i	$-0.484687\pi$
$619$	2.39282	0.0961757	0.0480878	+	0.998843i	$0.484687\pi$
$620$	−2.16667	−0.0870157
$621$	19.3934	0.778232
$622$	12.0179	0.481875
$623$	−63.5946	−2.54786
$624$	37.7263	1.51026
$625$	1.00000	0.0400000
$626$	35.9870	1.43833
$627$	−10.5086	−0.419673
$628$	−26.1928	−1.04521
$629$	−1.57030	−0.0626118
$630$	−12.8887	−0.513496
$631$	−5.02701	−0.200122	−0.100061	−	0.994981i	$-0.531904\pi$
$631$	−5.02701	−0.200122	−0.100061	+	0.994981i	$0.531904\pi$
$632$	−9.36693	−0.372597
$633$	−44.9708	−1.78743
$634$	2.17789	0.0864952
$635$	−2.34206	−0.0929417
$636$	−5.98959	−0.237503
$637$	57.5064	2.27849
$638$	2.40500	0.0952148
$639$	−6.74662	−0.266892
$640$	8.12784	0.321281
$641$	0.0586460	0.00231638	0.00115819	−	0.999999i	$-0.499631\pi$
$641$	0.0586460	0.00231638	0.00115819	+	0.999999i	$0.499631\pi$
$642$	9.32027	0.367842
$643$	44.4996	1.75489	0.877446	−	0.479675i	$-0.159245\pi$
$643$	44.4996	1.75489	0.877446	+	0.479675i	$0.159245\pi$
$644$	−40.5556	−1.59811
$645$	2.60321	0.102501
$646$	48.1101	1.89287
$647$	−18.7149	−0.735759	−0.367880	−	0.929873i	$-0.619916\pi$
$647$	−18.7149	−0.735759	−0.367880	+	0.929873i	$0.619916\pi$
$648$	11.9163	0.468117
$649$	−5.51788	−0.216596
$650$	6.86078	0.269102
$651$	−15.2193	−0.596490
$652$	−20.6789	−0.809847
$653$	11.2892	0.441781	0.220891	−	0.975299i	$-0.429104\pi$
$653$	11.2892	0.441781	0.220891	+	0.975299i	$0.429104\pi$
$654$	39.4351	1.54203
$655$	−19.6239	−0.766768
$656$	−42.8954	−1.67478
$657$	−1.46699	−0.0572327
$658$	40.9134	1.59497
$659$	−23.0026	−0.896054	−0.448027	−	0.894020i	$-0.647873\pi$
$659$	−23.0026	−0.896054	−0.448027	+	0.894020i	$0.647873\pi$
$660$	3.01777	0.117466
$661$	46.8224	1.82118	0.910590	−	0.413312i	$-0.135628\pi$
$661$	46.8224	1.82118	0.910590	+	0.413312i	$0.135628\pi$
$662$	−28.8115	−1.11979
$663$	40.9317	1.58966
$664$	11.9500	0.463751
$665$	23.5944	0.914950
$666$	0.816074	0.0316222
$667$	−7.77512	−0.301054
$668$	−19.1757	−0.741929
$669$	36.0865	1.39519
$670$	8.41113	0.324950
$671$	−0.0688587	−0.00265826
$672$	−68.1970	−2.63075
$673$	48.1775	1.85711	0.928553	−	0.371200i	$-0.121054\pi$
$673$	48.1775	1.85711	0.928553	+	0.371200i	$0.121054\pi$
$674$	−61.6547	−2.37485
$675$	3.24006	0.124710
$676$	1.04488	0.0401876
$677$	37.6054	1.44529	0.722646	−	0.691219i	$-0.242926\pi$
$677$	37.6054	1.44529	0.722646	+	0.691219i	$0.242926\pi$
$678$	−18.1495	−0.697029
$679$	−24.2875	−0.932068
$680$	5.53630	0.212308
$681$	−33.8832	−1.29841
$682$	2.80948	0.107580
$683$	−26.4852	−1.01343	−0.506714	−	0.862114i	$-0.669140\pi$
$683$	−26.4852	−1.01343	−0.506714	+	0.862114i	$0.669140\pi$
$684$	−10.4146	−0.398212
$685$	5.25760	0.200883
$686$	−74.8426	−2.85750
$687$	−54.2380	−2.06931
$688$	5.93301	0.226194
$689$	7.35487	0.280198
$690$	−23.4217	−0.891651
$691$	28.6161	1.08861	0.544304	−	0.838888i	$-0.316794\pi$
$691$	28.6161	1.08861	0.544304	+	0.838888i	$0.316794\pi$
$692$	−5.12205	−0.194711
$693$	6.96142	0.264442
$694$	−0.826479	−0.0313727
$695$	15.4807	0.587216
$696$	−2.90833	−0.110240
$697$	−46.5400	−1.76283
$698$	58.9337	2.23067
$699$	−4.53256	−0.171437
$700$	−6.77562	−0.256094
$701$	32.5503	1.22941	0.614704	−	0.788758i	$-0.289276\pi$
$701$	32.5503	1.22941	0.614704	+	0.788758i	$0.289276\pi$
$702$	22.2293	0.838992
$703$	−1.49393	−0.0563446
$704$	2.95525	0.111380
$705$	9.84219	0.370678
$706$	−49.3708	−1.85810
$707$	−57.7251	−2.17098
$708$	−16.6517	−0.625808
$709$	48.9999	1.84023	0.920116	−	0.391647i	$-0.128095\pi$
$709$	48.9999	1.84023	0.920116	+	0.391647i	$0.128095\pi$
$710$	−8.51470	−0.319551
$711$	12.9716	0.486472
$712$	−14.1965	−0.532036
$713$	−9.08275	−0.340152
$714$	−97.0458	−3.63185
$715$	−3.70564	−0.138583
$716$	21.4216	0.800562
$717$	17.3136	0.646590
$718$	32.1097	1.19832
$719$	0.644831	0.0240481	0.0120241	−	0.999928i	$-0.496173\pi$
$719$	0.644831	0.0240481	0.0120241	+	0.999928i	$0.496173\pi$
$720$	−7.06642	−0.263350
$721$	−86.9370	−3.23770
$722$	10.5930	0.394231
$723$	−36.6452	−1.36285
$724$	20.0595	0.745506
$725$	−1.29899	−0.0482432
$726$	−3.91307	−0.145228
$727$	−3.48306	−0.129179	−0.0645897	−	0.997912i	$-0.520574\pi$
$727$	−3.48306	−0.129179	−0.0645897	+	0.997912i	$0.520574\pi$
$728$	18.6280	0.690399
$729$	4.04180	0.149696
$730$	−1.85144	−0.0685249
$731$	6.43711	0.238085
$732$	−0.207799	−0.00768049
$733$	50.7533	1.87462	0.937308	−	0.348503i	$-0.113310\pi$
$733$	50.7533	1.87462	0.937308	+	0.348503i	$0.113310\pi$
$734$	0.141986	0.00524081
$735$	−32.7990	−1.20981
$736$	−40.6995	−1.50020
$737$	−4.54302	−0.167344
$738$	24.1866	0.890320
$739$	−41.3906	−1.52258	−0.761290	−	0.648412i	$-0.775433\pi$
$739$	−41.3906	−1.52258	−0.761290	+	0.648412i	$0.775433\pi$
$740$	0.429013	0.0157708
$741$	38.9411	1.43054
$742$	−17.4378	−0.640163
$743$	−41.3206	−1.51591	−0.757953	−	0.652309i	$-0.773800\pi$
$743$	−41.3206	−1.51591	−0.757953	+	0.652309i	$0.773800\pi$
$744$	−3.39746	−0.124557
$745$	22.5365	0.825672
$746$	−37.1993	−1.36196
$747$	−16.5487	−0.605486
$748$	7.46220	0.272845
$749$	11.3027	0.412991
$750$	−3.91307	−0.142885
$751$	47.4793	1.73255	0.866273	−	0.499571i	$-0.166509\pi$
$751$	47.4793	1.73255	0.866273	+	0.499571i	$0.166509\pi$
$752$	22.4314	0.817991
$753$	17.4776	0.636918
$754$	−8.91207	−0.324558
$755$	5.34904	0.194672
$756$	−21.9534	−0.798437
$757$	−31.0766	−1.12950	−0.564750	−	0.825262i	$-0.691027\pi$
$757$	−31.0766	−1.12950	−0.564750	+	0.825262i	$0.691027\pi$
$758$	20.8403	0.756953
$759$	12.6505	0.459186
$760$	5.26706	0.191056
$761$	13.4511	0.487601	0.243801	−	0.969825i	$-0.421606\pi$
$761$	13.4511	0.487601	0.243801	+	0.969825i	$0.421606\pi$
$762$	9.16463	0.332000
$763$	47.8229	1.73130
$764$	−22.8800	−0.827769
$765$	−7.66682	−0.277195
$766$	18.7036	0.675790
$767$	20.4473	0.738309
$768$	−44.2968	−1.59842
$769$	42.0341	1.51579	0.757895	−	0.652377i	$-0.226228\pi$
$769$	42.0341	1.51579	0.757895	+	0.652377i	$0.226228\pi$
$770$	8.78579	0.316618
$771$	−11.1891	−0.402966
$772$	−16.0319	−0.577002
$773$	26.5511	0.954977	0.477489	−	0.878638i	$-0.341547\pi$
$773$	26.5511	0.954977	0.477489	+	0.878638i	$0.341547\pi$
$774$	−3.34533	−0.120245
$775$	−1.51745	−0.0545086
$776$	−5.42179	−0.194631
$777$	3.01350	0.108109
$778$	18.0671	0.647737
$779$	−44.2767	−1.58638
$780$	−11.1828	−0.400407
$781$	4.59896	0.164564
$782$	−57.9163	−2.07108
$783$	−4.20879	−0.150410
$784$	−74.7524	−2.66973
$785$	−18.3444	−0.654740
$786$	76.7895	2.73899
$787$	−13.3318	−0.475227	−0.237613	−	0.971360i	$-0.576365\pi$
$787$	−13.3318	−0.475227	−0.237613	+	0.971360i	$0.576365\pi$
$788$	19.0915	0.680105
$789$	−39.0307	−1.38953
$790$	16.3710	0.582455
$791$	−22.0099	−0.782583
$792$	1.55403	0.0552199
$793$	0.255166	0.00906120
$794$	31.8547	1.13048
$795$	−4.19487	−0.148777
$796$	−3.14316	−0.111406
$797$	−30.3116	−1.07369	−0.536846	−	0.843681i	$-0.680384\pi$
$797$	−30.3116	−1.07369	−0.536846	+	0.843681i	$0.680384\pi$
$798$	−92.3263	−3.26832
$799$	24.3373	0.860993
$800$	−6.79965	−0.240404
$801$	19.6597	0.694640
$802$	37.5265	1.32511
$803$	1.00000	0.0352892
$804$	−13.7098	−0.483506
$805$	−28.4036	−1.00109
$806$	−10.4109	−0.366709
$807$	−24.4205	−0.859642
$808$	−12.8862	−0.453335
$809$	30.0347	1.05596	0.527982	−	0.849256i	$-0.322949\pi$
$809$	30.0347	1.05596	0.527982	+	0.849256i	$0.322949\pi$
$810$	−20.8267	−0.731776
$811$	−19.8172	−0.695875	−0.347938	−	0.937518i	$-0.613118\pi$
$811$	−19.8172	−0.695875	−0.347938	+	0.937518i	$0.613118\pi$
$812$	8.80144	0.308870
$813$	13.6480	0.478655
$814$	−0.556292	−0.0194980
$815$	−14.4827	−0.507306
$816$	−53.2070	−1.86262
$817$	6.12406	0.214254
$818$	2.54139	0.0888578
$819$	−25.7965	−0.901403
$820$	12.7150	0.444026
$821$	−7.69038	−0.268396	−0.134198	−	0.990955i	$-0.542846\pi$
$821$	−7.69038	−0.268396	−0.134198	+	0.990955i	$0.542846\pi$
$822$	−20.5733	−0.717578
$823$	−46.0169	−1.60405	−0.802024	−	0.597291i	$-0.796244\pi$
$823$	−46.0169	−1.60405	−0.802024	+	0.597291i	$0.796244\pi$
$824$	−19.4073	−0.676085
$825$	2.11353	0.0735835
$826$	−48.4789	−1.68680
$827$	−4.26433	−0.148285	−0.0741427	−	0.997248i	$-0.523622\pi$
$827$	−4.26433	−0.148285	−0.0741427	+	0.997248i	$0.523622\pi$
$828$	12.5374	0.435704
$829$	−4.66437	−0.162000	−0.0810002	−	0.996714i	$-0.525811\pi$
$829$	−4.66437	−0.162000	−0.0810002	+	0.996714i	$0.525811\pi$
$830$	−20.8856	−0.724951
$831$	35.5382	1.23281
$832$	−10.9511	−0.379661
$833$	−81.1038	−2.81008
$834$	−60.5770	−2.09761
$835$	−13.4299	−0.464761
$836$	7.09930	0.245534
$837$	−4.91664	−0.169944
$838$	30.1948	1.04306
$839$	21.3860	0.738326	0.369163	−	0.929365i	$-0.379644\pi$
$839$	21.3860	0.738326	0.369163	+	0.929365i	$0.379644\pi$
$840$	−10.6245	−0.366581
$841$	−27.3126	−0.941815
$842$	57.9796	1.99811
$843$	17.4456	0.600860
$844$	30.3810	1.04576
$845$	0.731792	0.0251744
$846$	−12.6480	−0.434847
$847$	−4.74538	−0.163053
$848$	−9.56058	−0.328312
$849$	−9.04579	−0.310451
$850$	−9.67606	−0.331886
$851$	1.79843	0.0616495
$852$	13.8786	0.475472
$853$	−6.05154	−0.207201	−0.103600	−	0.994619i	$-0.533036\pi$
$853$	−6.05154	−0.207201	−0.103600	+	0.994619i	$0.533036\pi$
$854$	−0.604978	−0.0207019
$855$	−7.29397	−0.249449
$856$	2.52314	0.0862393
$857$	21.0306	0.718392	0.359196	−	0.933262i	$-0.383051\pi$
$857$	21.0306	0.718392	0.359196	+	0.933262i	$0.383051\pi$
$858$	14.5004	0.495037
$859$	27.0428	0.922688	0.461344	−	0.887221i	$-0.347367\pi$
$859$	27.0428	0.922688	0.461344	+	0.887221i	$0.347367\pi$
$860$	−1.75865	−0.0599696
$861$	89.3132	3.04379
$862$	−4.59276	−0.156430
$863$	13.8561	0.471666	0.235833	−	0.971794i	$-0.424218\pi$
$863$	13.8561	0.471666	0.235833	+	0.971794i	$0.424218\pi$
$864$	−22.0313	−0.749519
$865$	−3.58728	−0.121971
$866$	−43.9505	−1.49350
$867$	−21.7978	−0.740293
$868$	10.2817	0.348983
$869$	−8.84232	−0.299955
$870$	5.08303	0.172331
$871$	16.8348	0.570425
$872$	10.6757	0.361525
$873$	7.50825	0.254116
$874$	−55.0997	−1.86378
$875$	−4.74538	−0.160423
$876$	3.01777	0.101961
$877$	−18.2195	−0.615229	−0.307614	−	0.951511i	$-0.599531\pi$
$877$	−18.2195	−0.615229	−0.307614	+	0.951511i	$0.599531\pi$
$878$	20.1530	0.680132
$879$	54.5890	1.84124
$880$	4.81696	0.162380
$881$	−14.8185	−0.499248	−0.249624	−	0.968343i	$-0.580307\pi$
$881$	−14.8185	−0.499248	−0.249624	+	0.968343i	$0.580307\pi$
$882$	42.1492	1.41924
$883$	45.0723	1.51680	0.758401	−	0.651788i	$-0.225981\pi$
$883$	45.0723	1.51680	0.758401	+	0.651788i	$0.225981\pi$
$884$	−27.6522	−0.930045
$885$	−11.6622	−0.392020
$886$	44.4198	1.49231
$887$	47.6663	1.60048	0.800238	−	0.599682i	$-0.204706\pi$
$887$	47.6663	1.60048	0.800238	+	0.599682i	$0.204706\pi$
$888$	0.672715	0.0225748
$889$	11.1139	0.372750
$890$	24.8119	0.831696
$891$	11.2489	0.376853
$892$	−24.3790	−0.816269
$893$	23.1538	0.774812
$894$	−88.1867	−2.94940
$895$	15.0028	0.501490
$896$	−38.5697	−1.28852
$897$	−46.8784	−1.56522
$898$	36.0769	1.20390
$899$	1.97115	0.0657417
$900$	2.09462	0.0698206
$901$	−10.3729	−0.345571
$902$	−16.4872	−0.548965
$903$	−12.3532	−0.411090
$904$	−4.91337	−0.163416
$905$	14.0489	0.467001
$906$	−20.9312	−0.695392
$907$	−6.44122	−0.213877	−0.106939	−	0.994266i	$-0.534105\pi$
$907$	−6.44122	−0.213877	−0.106939	+	0.994266i	$0.534105\pi$
$908$	22.8905	0.759647
$909$	17.8452	0.591887
$910$	−32.5570	−1.07925
$911$	−43.3258	−1.43545	−0.717724	−	0.696328i	$-0.754816\pi$
$911$	−43.3258	−1.43545	−0.717724	+	0.696328i	$0.754816\pi$
$912$	−50.6195	−1.67618
$913$	11.2807	0.373338
$914$	17.8035	0.588888
$915$	−0.145535	−0.00481123
$916$	36.6416	1.21067
$917$	93.1226	3.07518
$918$	−31.3510	−1.03474
$919$	20.6204	0.680205	0.340103	−	0.940388i	$-0.389538\pi$
$919$	20.6204	0.680205	0.340103	+	0.940388i	$0.389538\pi$
$920$	−6.34064	−0.209045
$921$	33.3356	1.09845
$922$	−12.0687	−0.397463
$923$	−17.0421	−0.560947
$924$	−14.3204	−0.471108
$925$	0.300464	0.00987920
$926$	10.8444	0.356369
$927$	26.8757	0.882715
$928$	8.83267	0.289946
$929$	25.0930	0.823274	0.411637	−	0.911348i	$-0.364957\pi$
$929$	25.0930	0.823274	0.411637	+	0.911348i	$0.364957\pi$
$930$	5.93790	0.194711
$931$	−77.1596	−2.52880
$932$	3.06207	0.100301
$933$	−13.7191	−0.449144
$934$	−59.9394	−1.96128
$935$	5.22623	0.170916
$936$	−5.75866	−0.188228
$937$	−54.3177	−1.77448	−0.887242	−	0.461305i	$-0.847381\pi$
$937$	−54.3177	−1.77448	−0.887242	+	0.461305i	$0.847381\pi$
$938$	−39.9140	−1.30324
$939$	−41.0812	−1.34063
$940$	−6.64909	−0.216870
$941$	10.1491	0.330851	0.165425	−	0.986222i	$-0.447100\pi$
$941$	10.1491	0.330851	0.165425	+	0.986222i	$0.447100\pi$
$942$	71.7830	2.33881
$943$	53.3015	1.73574
$944$	−26.5794	−0.865086
$945$	−15.3753	−0.500158
$946$	2.28041	0.0741424
$947$	−21.8285	−0.709332	−0.354666	−	0.934993i	$-0.615405\pi$
$947$	−21.8285	−0.709332	−0.354666	+	0.934993i	$0.615405\pi$
$948$	−26.6840	−0.866658
$949$	−3.70564	−0.120290
$950$	−9.20550	−0.298666
$951$	−2.48619	−0.0806202
$952$	−26.2718	−0.851475
$953$	16.2976	0.527933	0.263966	−	0.964532i	$-0.414969\pi$
$953$	16.2976	0.527933	0.263966	+	0.964532i	$0.414969\pi$
$954$	5.39074	0.174532
$955$	−16.0243	−0.518533
$956$	−11.6966	−0.378295
$957$	−2.74544	−0.0887476
$958$	−41.9169	−1.35427
$959$	−24.9493	−0.805655
$960$	6.24599	0.201588
$961$	−28.6973	−0.925720
$962$	2.06142	0.0664628
$963$	−3.49412	−0.112596
$964$	24.7564	0.797350
$965$	−11.2281	−0.361447
$966$	111.145	3.57603
$967$	25.4724	0.819138	0.409569	−	0.912279i	$-0.365679\pi$
$967$	25.4724	0.819138	0.409569	+	0.912279i	$0.365679\pi$
$968$	−1.05933	−0.0340482
$969$	−54.9204	−1.76430
$970$	9.47593	0.304254
$971$	9.61468	0.308550	0.154275	−	0.988028i	$-0.450696\pi$
$971$	9.61468	0.308550	0.154275	+	0.988028i	$0.450696\pi$
$972$	20.0678	0.643674
$973$	−73.4617	−2.35507
$974$	15.9942	0.512487
$975$	−7.83197	−0.250824
$976$	−0.331689	−0.0106171
$977$	−6.71380	−0.214793	−0.107397	−	0.994216i	$-0.534252\pi$
$977$	−6.71380	−0.214793	−0.107397	+	0.994216i	$0.534252\pi$
$978$	56.6717	1.81216
$979$	−13.4014	−0.428310
$980$	22.1580	0.707811
$981$	−14.7840	−0.472017
$982$	−64.5505	−2.05989
$983$	12.8927	0.411214	0.205607	−	0.978635i	$-0.434083\pi$
$983$	12.8927	0.411214	0.205607	+	0.978635i	$0.434083\pi$
$984$	19.9378	0.635593
$985$	13.3709	0.426033
$986$	12.5691	0.400281
$987$	−46.7049	−1.48663
$988$	−26.3075	−0.836952
$989$	−7.37232	−0.234426
$990$	−2.71604	−0.0863215
$991$	30.2723	0.961631	0.480816	−	0.876822i	$-0.340341\pi$
$991$	30.2723	0.961631	0.480816	+	0.876822i	$0.340341\pi$
$992$	10.3182	0.327602
$993$	32.8900	1.04373
$994$	40.4054	1.28158
$995$	−2.20134	−0.0697873
$996$	34.0426	1.07868
$997$	−18.7778	−0.594700	−0.297350	−	0.954769i	$-0.596103\pi$
$997$	−18.7778	−0.594700	−0.297350	+	0.954769i	$0.596103\pi$
$998$	−27.3427	−0.865519
$999$	0.973521	0.0308008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.i.1.30	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.i.1.30	✓	38	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)

\(f(q)\)	\(=\)	\(q+1.85144 q^{2} -2.11353 q^{3} +1.42784 q^{4} +1.00000 q^{5} -3.91307 q^{6} -4.74538 q^{7} -1.05933 q^{8} +1.46699 q^{9} +O(q^{10})\)	\(q+1.85144 q^{2} -2.11353 q^{3} +1.42784 q^{4} +1.00000 q^{5} -3.91307 q^{6} -4.74538 q^{7} -1.05933 q^{8} +1.46699 q^{9} +1.85144 q^{10} -1.00000 q^{11} -3.01777 q^{12} +3.70564 q^{13} -8.78579 q^{14} -2.11353 q^{15} -4.81696 q^{16} -5.22623 q^{17} +2.71604 q^{18} -4.97207 q^{19} +1.42784 q^{20} +10.0295 q^{21} -1.85144 q^{22} +5.98552 q^{23} +2.23892 q^{24} +1.00000 q^{25} +6.86078 q^{26} +3.24006 q^{27} -6.77562 q^{28} -1.29899 q^{29} -3.91307 q^{30} -1.51745 q^{31} -6.79965 q^{32} +2.11353 q^{33} -9.67606 q^{34} -4.74538 q^{35} +2.09462 q^{36} +0.300464 q^{37} -9.20550 q^{38} -7.83197 q^{39} -1.05933 q^{40} +8.90508 q^{41} +18.5690 q^{42} -1.23169 q^{43} -1.42784 q^{44} +1.46699 q^{45} +11.0818 q^{46} -4.65677 q^{47} +10.1808 q^{48} +15.5186 q^{49} +1.85144 q^{50} +11.0458 q^{51} +5.29105 q^{52} +1.98478 q^{53} +5.99878 q^{54} -1.00000 q^{55} +5.02692 q^{56} +10.5086 q^{57} -2.40500 q^{58} +5.51788 q^{59} -3.01777 q^{60} +0.0688587 q^{61} -2.80948 q^{62} -6.96142 q^{63} -2.95525 q^{64} +3.70564 q^{65} +3.91307 q^{66} +4.54302 q^{67} -7.46220 q^{68} -12.6505 q^{69} -8.78579 q^{70} -4.59896 q^{71} -1.55403 q^{72} -1.00000 q^{73} +0.556292 q^{74} -2.11353 q^{75} -7.09930 q^{76} +4.74538 q^{77} -14.5004 q^{78} +8.84232 q^{79} -4.81696 q^{80} -11.2489 q^{81} +16.4872 q^{82} -11.2807 q^{83} +14.3204 q^{84} -5.22623 q^{85} -2.28041 q^{86} +2.74544 q^{87} +1.05933 q^{88} +13.4014 q^{89} +2.71604 q^{90} -17.5847 q^{91} +8.54634 q^{92} +3.20718 q^{93} -8.62173 q^{94} -4.97207 q^{95} +14.3712 q^{96} +5.11814 q^{97} +28.7318 q^{98} -1.46699 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9}+O(q^{10}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9	\( 38 q + 4 q^{2} + 5 q^{3} + 50 q^{4} + 38 q^{5} + 11 q^{6} + 15 q^{8} + 63 q^{9} + 4 q^{10} - 38 q^{11} + 12 q^{12} - q^{13} + 23 q^{14} + 5 q^{15} + 74 q^{16} + 26 q^{17} + 16 q^{18} - 10 q^{19} + 50 q^{20} + 21 q^{21} - 4 q^{22} + 10 q^{23} + 41 q^{24} + 38 q^{25} + 25 q^{26} + 5 q^{27} + 2 q^{28} + 28 q^{29} + 11 q^{30} + 24 q^{31} + 39 q^{32} - 5 q^{33} + 38 q^{34} + 111 q^{36} + 12 q^{37} + 19 q^{38} - 18 q^{39} + 15 q^{40} + 62 q^{41} - 17 q^{42} - 32 q^{43} - 50 q^{44} + 63 q^{45} - 9 q^{46} + 31 q^{47} + 53 q^{48} + 88 q^{49} + 4 q^{50} - 3 q^{51} - 21 q^{52} + 30 q^{53} + 49 q^{54} - 38 q^{55} + 32 q^{56} + 49 q^{57} + 12 q^{58} + 31 q^{59} + 12 q^{60} + 25 q^{61} + 12 q^{62} + 15 q^{63} + 137 q^{64} - q^{65} - 11 q^{66} + 20 q^{67} + 75 q^{68} + 92 q^{69} + 23 q^{70} + 32 q^{71} + 6 q^{72} - 38 q^{73} + 55 q^{74} + 5 q^{75} - 57 q^{76} - 17 q^{78} - 2 q^{79} + 74 q^{80} + 118 q^{81} + 14 q^{82} + 4 q^{83} + 22 q^{84} + 26 q^{85} + 5 q^{86} + 24 q^{87} - 15 q^{88} + 143 q^{89} + 16 q^{90} + 66 q^{91} + 29 q^{92} - 8 q^{93} - 7 q^{94} - 10 q^{95} + 59 q^{96} + 41 q^{97} - 10 q^{98} - 63 q^{99}+O(q^{100}) \) 38 * q + 4 * q^2 + 5 * q^3 + 50 * q^4 + 38 * q^5 + 11 * q^6 + 15 * q^8 + 63 * q^9 + 4 * q^10 - 38 * q^11 + 12 * q^12 - q^13 + 23 * q^14 + 5 * q^15 + 74 * q^16 + 26 * q^17 + 16 * q^18 - 10 * q^19 + 50 * q^20 + 21 * q^21 - 4 * q^22 + 10 * q^23 + 41 * q^24 + 38 * q^25 + 25 * q^26 + 5 * q^27 + 2 * q^28 + 28 * q^29 + 11 * q^30 + 24 * q^31 + 39 * q^32 - 5 * q^33 + 38 * q^34 + 111 * q^36 + 12 * q^37 + 19 * q^38 - 18 * q^39 + 15 * q^40 + 62 * q^41 - 17 * q^42 - 32 * q^43 - 50 * q^44 + 63 * q^45 - 9 * q^46 + 31 * q^47 + 53 * q^48 + 88 * q^49 + 4 * q^50 - 3 * q^51 - 21 * q^52 + 30 * q^53 + 49 * q^54 - 38 * q^55 + 32 * q^56 + 49 * q^57 + 12 * q^58 + 31 * q^59 + 12 * q^60 + 25 * q^61 + 12 * q^62 + 15 * q^63 + 137 * q^64 - q^65 - 11 * q^66 + 20 * q^67 + 75 * q^68 + 92 * q^69 + 23 * q^70 + 32 * q^71 + 6 * q^72 - 38 * q^73 + 55 * q^74 + 5 * q^75 - 57 * q^76 - 17 * q^78 - 2 * q^79 + 74 * q^80 + 118 * q^81 + 14 * q^82 + 4 * q^83 + 22 * q^84 + 26 * q^85 + 5 * q^86 + 24 * q^87 - 15 * q^88 + 143 * q^89 + 16 * q^90 + 66 * q^91 + 29 * q^92 - 8 * q^93 - 7 * q^94 - 10 * q^95 + 59 * q^96 + 41 * q^97 - 10 * q^98 - 63 * q^99

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