LMFDB - Embedded newform 4015.2.a.f.1.16

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:	$31$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
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)

$f(q)$	$=$	$q-0.485073 q^{2} -0.214641 q^{3} -1.76470 q^{4} -1.00000 q^{5} +0.104117 q^{6} +3.34739 q^{7} +1.82616 q^{8} -2.95393 q^{9} +O(q^{10})$	\(q-0.485073 q^{2} -0.214641 q^{3} -1.76470 q^{4} -1.00000 q^{5} +0.104117 q^{6} +3.34739 q^{7} +1.82616 q^{8} -2.95393 q^{9} +0.485073 q^{10} +1.00000 q^{11} +0.378778 q^{12} +5.34868 q^{13} -1.62373 q^{14} +0.214641 q^{15} +2.64359 q^{16} -7.63283 q^{17} +1.43287 q^{18} -5.15261 q^{19} +1.76470 q^{20} -0.718487 q^{21} -0.485073 q^{22} -1.25741 q^{23} -0.391968 q^{24} +1.00000 q^{25} -2.59450 q^{26} +1.27796 q^{27} -5.90715 q^{28} -3.65158 q^{29} -0.104117 q^{30} +7.44817 q^{31} -4.93465 q^{32} -0.214641 q^{33} +3.70248 q^{34} -3.34739 q^{35} +5.21281 q^{36} +11.7124 q^{37} +2.49939 q^{38} -1.14805 q^{39} -1.82616 q^{40} -11.6926 q^{41} +0.348519 q^{42} -1.02945 q^{43} -1.76470 q^{44} +2.95393 q^{45} +0.609933 q^{46} +9.09942 q^{47} -0.567423 q^{48} +4.20500 q^{49} -0.485073 q^{50} +1.63832 q^{51} -9.43884 q^{52} -0.0737022 q^{53} -0.619903 q^{54} -1.00000 q^{55} +6.11285 q^{56} +1.10596 q^{57} +1.77128 q^{58} -12.5976 q^{59} -0.378778 q^{60} +0.307979 q^{61} -3.61290 q^{62} -9.88794 q^{63} -2.89352 q^{64} -5.34868 q^{65} +0.104117 q^{66} +2.23434 q^{67} +13.4697 q^{68} +0.269891 q^{69} +1.62373 q^{70} -13.1123 q^{71} -5.39433 q^{72} +1.00000 q^{73} -5.68139 q^{74} -0.214641 q^{75} +9.09284 q^{76} +3.34739 q^{77} +0.556887 q^{78} -1.94585 q^{79} -2.64359 q^{80} +8.58749 q^{81} +5.67176 q^{82} +11.2555 q^{83} +1.26792 q^{84} +7.63283 q^{85} +0.499359 q^{86} +0.783779 q^{87} +1.82616 q^{88} -1.89737 q^{89} -1.43287 q^{90} +17.9041 q^{91} +2.21895 q^{92} -1.59868 q^{93} -4.41388 q^{94} +5.15261 q^{95} +1.05918 q^{96} +13.1615 q^{97} -2.03973 q^{98} -2.95393 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * 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 $

$2$	−0.485073	−0.342998	−0.171499	−	0.985184i	$-0.554861\pi$
$2$	−0.485073	−0.342998	−0.171499	+	0.985184i	$0.554861\pi$
$3$	−0.214641	−0.123923	−0.0619616	−	0.998079i	$-0.519736\pi$
$3$	−0.214641	−0.123923	−0.0619616	+	0.998079i	$0.519736\pi$
$4$	−1.76470	−0.882352
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	0.104117	0.0425054
$7$	3.34739	1.26519	0.632597	−	0.774481i	$-0.281989\pi$
$7$	3.34739	1.26519	0.632597	+	0.774481i	$0.281989\pi$
$8$	1.82616	0.645644
$9$	−2.95393	−0.984643
$10$	0.485073	0.153393
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.378778	0.109344
$13$	5.34868	1.48346	0.741729	−	0.670700i	$-0.234006\pi$
$13$	5.34868	1.48346	0.741729	+	0.670700i	$0.234006\pi$
$14$	−1.62373	−0.433959
$15$	0.214641	0.0554201
$16$	2.64359	0.660898
$17$	−7.63283	−1.85123	−0.925616	−	0.378463i	$-0.876453\pi$
$17$	−7.63283	−1.85123	−0.925616	+	0.378463i	$0.876453\pi$
$18$	1.43287	0.337731
$19$	−5.15261	−1.18209	−0.591045	−	0.806638i	$-0.701285\pi$
$19$	−5.15261	−1.18209	−0.591045	+	0.806638i	$0.701285\pi$
$20$	1.76470	0.394600
$21$	−0.718487	−0.156787
$22$	−0.485073	−0.103418
$23$	−1.25741	−0.262187	−0.131094	−	0.991370i	$-0.541849\pi$
$23$	−1.25741	−0.262187	−0.131094	+	0.991370i	$0.541849\pi$
$24$	−0.391968	−0.0800102
$25$	1.00000	0.200000
$26$	−2.59450	−0.508823
$27$	1.27796	0.245943
$28$	−5.90715	−1.11635
$29$	−3.65158	−0.678081	−0.339041	−	0.940772i	$-0.610102\pi$
$29$	−3.65158	−0.678081	−0.339041	+	0.940772i	$0.610102\pi$
$30$	−0.104117	−0.0190090
$31$	7.44817	1.33773	0.668865	−	0.743384i	$-0.266780\pi$
$31$	7.44817	1.33773	0.668865	+	0.743384i	$0.266780\pi$
$32$	−4.93465	−0.872330
$33$	−0.214641	−0.0373642
$34$	3.70248	0.634970
$35$	−3.34739	−0.565812
$36$	5.21281	0.868802
$37$	11.7124	1.92551	0.962757	−	0.270367i	$-0.0871451\pi$
$37$	11.7124	1.92551	0.962757	+	0.270367i	$0.0871451\pi$
$38$	2.49939	0.405455
$39$	−1.14805	−0.183835
$40$	−1.82616	−0.288741
$41$	−11.6926	−1.82608	−0.913038	−	0.407875i	$-0.866270\pi$
$41$	−11.6926	−1.82608	−0.913038	+	0.407875i	$0.866270\pi$
$42$	0.348519	0.0537776
$43$	−1.02945	−0.156990	−0.0784949	−	0.996915i	$-0.525011\pi$
$43$	−1.02945	−0.156990	−0.0784949	+	0.996915i	$0.525011\pi$
$44$	−1.76470	−0.266039
$45$	2.95393	0.440346
$46$	0.609933	0.0899298
$47$	9.09942	1.32729	0.663643	−	0.748049i	$-0.269009\pi$
$47$	9.09942	1.32729	0.663643	+	0.748049i	$0.269009\pi$
$48$	−0.567423	−0.0819005
$49$	4.20500	0.600714
$50$	−0.485073	−0.0685997
$51$	1.63832	0.229411
$52$	−9.43884	−1.30893
$53$	−0.0737022	−0.0101238	−0.00506189	−	0.999987i	$-0.501611\pi$
$53$	−0.0737022	−0.0101238	−0.00506189	+	0.999987i	$0.501611\pi$
$54$	−0.619903	−0.0843581
$55$	−1.00000	−0.134840
$56$	6.11285	0.816864
$57$	1.10596	0.146488
$58$	1.77128	0.232581
$59$	−12.5976	−1.64006	−0.820032	−	0.572318i	$-0.806044\pi$
$59$	−12.5976	−1.64006	−0.820032	+	0.572318i	$0.806044\pi$
$60$	−0.378778	−0.0489001
$61$	0.307979	0.0394327	0.0197163	−	0.999806i	$-0.493724\pi$
$61$	0.307979	0.0394327	0.0197163	+	0.999806i	$0.493724\pi$
$62$	−3.61290	−0.458839
$63$	−9.88794	−1.24576
$64$	−2.89352	−0.361690
$65$	−5.34868	−0.663422
$66$	0.104117	0.0128159
$67$	2.23434	0.272968	0.136484	−	0.990642i	$-0.456420\pi$
$67$	2.23434	0.272968	0.136484	+	0.990642i	$0.456420\pi$
$68$	13.4697	1.63344
$69$	0.269891	0.0324911
$70$	1.62373	0.194072
$71$	−13.1123	−1.55614	−0.778072	−	0.628176i	$-0.783802\pi$
$71$	−13.1123	−1.55614	−0.778072	+	0.628176i	$0.783802\pi$
$72$	−5.39433	−0.635728
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	−5.68139	−0.660448
$75$	−0.214641	−0.0247846
$76$	9.09284	1.04302
$77$	3.34739	0.381470
$78$	0.556887	0.0630550
$79$	−1.94585	−0.218925	−0.109463	−	0.993991i	$-0.534913\pi$
$79$	−1.94585	−0.218925	−0.109463	+	0.993991i	$0.534913\pi$
$80$	−2.64359	−0.295562
$81$	8.58749	0.954165
$82$	5.67176	0.626341
$83$	11.2555	1.23545	0.617727	−	0.786392i	$-0.288054\pi$
$83$	11.2555	1.23545	0.617727	+	0.786392i	$0.288054\pi$
$84$	1.26792	0.138341
$85$	7.63283	0.827897
$86$	0.499359	0.0538472
$87$	0.783779	0.0840300
$88$	1.82616	0.194669
$89$	−1.89737	−0.201121	−0.100560	−	0.994931i	$-0.532064\pi$
$89$	−1.89737	−0.201121	−0.100560	+	0.994931i	$0.532064\pi$
$90$	−1.43287	−0.151038
$91$	17.9041	1.87686
$92$	2.21895	0.231341
$93$	−1.59868	−0.165776
$94$	−4.41388	−0.455257
$95$	5.15261	0.528647
$96$	1.05918	0.108102
$97$	13.1615	1.33635	0.668174	−	0.744005i	$-0.267076\pi$
$97$	13.1615	1.33635	0.668174	+	0.744005i	$0.267076\pi$
$98$	−2.03973	−0.206044
$99$	−2.95393	−0.296881
$100$	−1.76470	−0.176470
$101$	5.62455	0.559664	0.279832	−	0.960049i	$-0.409721\pi$
$101$	5.62455	0.559664	0.279832	+	0.960049i	$0.409721\pi$
$102$	−0.794704	−0.0786874
$103$	10.4343	1.02813	0.514063	−	0.857752i	$-0.328140\pi$
$103$	10.4343	1.02813	0.514063	+	0.857752i	$0.328140\pi$
$104$	9.76753	0.957785
$105$	0.718487	0.0701171
$106$	0.0357510	0.00347244
$107$	−0.314041	−0.0303595	−0.0151797	−	0.999885i	$-0.504832\pi$
$107$	−0.314041	−0.0303595	−0.0151797	+	0.999885i	$0.504832\pi$
$108$	−2.25522	−0.217009
$109$	−2.94316	−0.281904	−0.140952	−	0.990016i	$-0.545016\pi$
$109$	−2.94316	−0.281904	−0.140952	+	0.990016i	$0.545016\pi$
$110$	0.485073	0.0462499
$111$	−2.51397	−0.238616
$112$	8.84912	0.836163
$113$	−14.8754	−1.39936	−0.699682	−	0.714454i	$-0.746675\pi$
$113$	−14.8754	−1.39936	−0.699682	+	0.714454i	$0.746675\pi$
$114$	−0.536472	−0.0502452
$115$	1.25741	0.117254
$116$	6.44396	0.598307
$117$	−15.7996	−1.46068
$118$	6.11074	0.562539
$119$	−25.5500	−2.34217
$120$	0.391968	0.0357816
$121$	1.00000	0.0909091
$122$	−0.149392	−0.0135253
$123$	2.50971	0.226293
$124$	−13.1438	−1.18035
$125$	−1.00000	−0.0894427
$126$	4.79637	0.427295
$127$	−11.5766	−1.02726	−0.513629	−	0.858012i	$-0.671699\pi$
$127$	−11.5766	−1.02726	−0.513629	+	0.858012i	$0.671699\pi$
$128$	11.2729	0.996389
$129$	0.220962	0.0194547
$130$	2.59450	0.227553
$131$	−3.51437	−0.307052	−0.153526	−	0.988145i	$-0.549063\pi$
$131$	−3.51437	−0.307052	−0.153526	+	0.988145i	$0.549063\pi$
$132$	0.378778	0.0329684
$133$	−17.2478	−1.49557
$134$	−1.08382	−0.0936276
$135$	−1.27796	−0.109989
$136$	−13.9387	−1.19524
$137$	17.7846	1.51945	0.759723	−	0.650247i	$-0.225335\pi$
$137$	17.7846	1.51945	0.759723	+	0.650247i	$0.225335\pi$
$138$	−0.130917	−0.0111444
$139$	−8.02527	−0.680694	−0.340347	−	0.940300i	$-0.610545\pi$
$139$	−8.02527	−0.680694	−0.340347	+	0.940300i	$0.610545\pi$
$140$	5.90715	0.499245
$141$	−1.95311	−0.164482
$142$	6.36042	0.533754
$143$	5.34868	0.447279
$144$	−7.80898	−0.650748
$145$	3.65158	0.303247
$146$	−0.485073	−0.0401449
$147$	−0.902565	−0.0744423
$148$	−20.6690	−1.69898
$149$	−15.7115	−1.28714	−0.643569	−	0.765388i	$-0.722547\pi$
$149$	−15.7115	−1.28714	−0.643569	+	0.765388i	$0.722547\pi$
$150$	0.104117	0.00850108
$151$	−23.9840	−1.95179	−0.975894	−	0.218245i	$-0.929967\pi$
$151$	−23.9840	−1.95179	−0.975894	+	0.218245i	$0.929967\pi$
$152$	−9.40947	−0.763209
$153$	22.5468	1.82280
$154$	−1.62373	−0.130844
$155$	−7.44817	−0.598251
$156$	2.02596	0.162207
$157$	−15.7423	−1.25638	−0.628188	−	0.778062i	$-0.716203\pi$
$157$	−15.7423	−1.25638	−0.628188	+	0.778062i	$0.716203\pi$
$158$	0.943880	0.0750910
$159$	0.0158195	0.00125457
$160$	4.93465	0.390118
$161$	−4.20902	−0.331718
$162$	−4.16556	−0.327277
$163$	−6.55961	−0.513788	−0.256894	−	0.966440i	$-0.582699\pi$
$163$	−6.55961	−0.513788	−0.256894	+	0.966440i	$0.582699\pi$
$164$	20.6340	1.61124
$165$	0.214641	0.0167098
$166$	−5.45975	−0.423759
$167$	−3.21521	−0.248801	−0.124400	−	0.992232i	$-0.539701\pi$
$167$	−3.21521	−0.248801	−0.124400	+	0.992232i	$0.539701\pi$
$168$	−1.31207	−0.101228
$169$	15.6084	1.20065
$170$	−3.70248	−0.283967
$171$	15.2205	1.16394
$172$	1.81668	0.138520
$173$	8.30873	0.631701	0.315851	−	0.948809i	$-0.397710\pi$
$173$	8.30873	0.631701	0.315851	+	0.948809i	$0.397710\pi$
$174$	−0.380190	−0.0288221
$175$	3.34739	0.253039
$176$	2.64359	0.199268
$177$	2.70396	0.203242
$178$	0.920362	0.0689840
$179$	−20.0252	−1.49676	−0.748378	−	0.663272i	$-0.769167\pi$
$179$	−20.0252	−1.49676	−0.748378	+	0.663272i	$0.769167\pi$
$180$	−5.21281	−0.388540
$181$	−2.35798	−0.175268	−0.0876338	−	0.996153i	$-0.527931\pi$
$181$	−2.35798	−0.175268	−0.0876338	+	0.996153i	$0.527931\pi$
$182$	−8.68480	−0.643760
$183$	−0.0661050	−0.00488662
$184$	−2.29622	−0.169280
$185$	−11.7124	−0.861116
$186$	0.775478	0.0568608
$187$	−7.63283	−0.558168
$188$	−16.0578	−1.17113
$189$	4.27782	0.311166
$190$	−2.49939	−0.181325
$191$	8.92286	0.645635	0.322818	−	0.946461i	$-0.395370\pi$
$191$	8.92286	0.645635	0.322818	+	0.946461i	$0.395370\pi$
$192$	0.621068	0.0448217
$193$	−15.6049	−1.12326	−0.561631	−	0.827388i	$-0.689826\pi$
$193$	−15.6049	−1.12326	−0.561631	+	0.827388i	$0.689826\pi$
$194$	−6.38429	−0.458365
$195$	1.14805	0.0822134
$196$	−7.42058	−0.530041
$197$	−8.32907	−0.593421	−0.296711	−	0.954967i	$-0.595890\pi$
$197$	−8.32907	−0.593421	−0.296711	+	0.954967i	$0.595890\pi$
$198$	1.43287	0.101830
$199$	13.7048	0.971505	0.485752	−	0.874096i	$-0.338546\pi$
$199$	13.7048	0.971505	0.485752	+	0.874096i	$0.338546\pi$
$200$	1.82616	0.129129
$201$	−0.479581	−0.0338271
$202$	−2.72832	−0.191964
$203$	−12.2232	−0.857904
$204$	−2.89115	−0.202421
$205$	11.6926	0.816646
$206$	−5.06142	−0.352646
$207$	3.71429	0.258161
$208$	14.1397	0.980414
$209$	−5.15261	−0.356414
$210$	−0.348519	−0.0240501
$211$	−14.7481	−1.01530	−0.507650	−	0.861563i	$-0.669486\pi$
$211$	−14.7481	−1.01530	−0.507650	+	0.861563i	$0.669486\pi$
$212$	0.130063	0.00893274
$213$	2.81444	0.192842
$214$	0.152333	0.0104132
$215$	1.02945	0.0702080
$216$	2.33375	0.158792
$217$	24.9319	1.69249
$218$	1.42765	0.0966926
$219$	−0.214641	−0.0145041
$220$	1.76470	0.118976
$221$	−40.8256	−2.74623
$222$	1.21946	0.0818448
$223$	0.877910	0.0587892	0.0293946	−	0.999568i	$-0.490642\pi$
$223$	0.877910	0.0587892	0.0293946	+	0.999568i	$0.490642\pi$
$224$	−16.5182	−1.10367
$225$	−2.95393	−0.196929
$226$	7.21567	0.479979
$227$	−21.7738	−1.44518	−0.722590	−	0.691276i	$-0.757049\pi$
$227$	−21.7738	−1.44518	−0.722590	+	0.691276i	$0.757049\pi$
$228$	−1.95170	−0.129254
$229$	−17.4371	−1.15227	−0.576137	−	0.817353i	$-0.695441\pi$
$229$	−17.4371	−1.15227	−0.576137	+	0.817353i	$0.695441\pi$
$230$	−0.609933	−0.0402178
$231$	−0.718487	−0.0472730
$232$	−6.66835	−0.437799
$233$	12.2601	0.803188	0.401594	−	0.915818i	$-0.368456\pi$
$233$	12.2601	0.803188	0.401594	+	0.915818i	$0.368456\pi$
$234$	7.66397	0.501009
$235$	−9.09942	−0.593581
$236$	22.2310	1.44711
$237$	0.417660	0.0271299
$238$	12.3936	0.803359
$239$	−9.32257	−0.603027	−0.301513	−	0.953462i	$-0.597492\pi$
$239$	−9.32257	−0.603027	−0.301513	+	0.953462i	$0.597492\pi$
$240$	0.567423	0.0366270
$241$	−23.0089	−1.48214	−0.741068	−	0.671430i	$-0.765680\pi$
$241$	−23.0089	−1.48214	−0.741068	+	0.671430i	$0.765680\pi$
$242$	−0.485073	−0.0311817
$243$	−5.67710	−0.364186
$244$	−0.543492	−0.0347935
$245$	−4.20500	−0.268647
$246$	−1.21739	−0.0776181
$247$	−27.5597	−1.75358
$248$	13.6015	0.863697
$249$	−2.41590	−0.153101
$250$	0.485073	0.0306787
$251$	−18.6065	−1.17443	−0.587215	−	0.809431i	$-0.699776\pi$
$251$	−18.6065	−1.17443	−0.587215	+	0.809431i	$0.699776\pi$
$252$	17.4493	1.09920
$253$	−1.25741	−0.0790524
$254$	5.61550	0.352348
$255$	−1.63832	−0.102596
$256$	0.318879	0.0199299
$257$	−24.5176	−1.52937	−0.764684	−	0.644406i	$-0.777105\pi$
$257$	−24.5176	−1.52937	−0.764684	+	0.644406i	$0.777105\pi$
$258$	−0.107183	−0.00667292
$259$	39.2061	2.43615
$260$	9.43884	0.585372
$261$	10.7865	0.667668
$262$	1.70472	0.105318
$263$	7.04304	0.434293	0.217146	−	0.976139i	$-0.430325\pi$
$263$	7.04304	0.434293	0.217146	+	0.976139i	$0.430325\pi$
$264$	−0.391968	−0.0241240
$265$	0.0737022	0.00452749
$266$	8.36643	0.512979
$267$	0.407253	0.0249235
$268$	−3.94295	−0.240854
$269$	−12.2196	−0.745041	−0.372521	−	0.928024i	$-0.621506\pi$
$269$	−12.2196	−0.745041	−0.372521	+	0.928024i	$0.621506\pi$
$270$	0.619903	0.0377261
$271$	−7.11042	−0.431927	−0.215964	−	0.976401i	$-0.569289\pi$
$271$	−7.11042	−0.431927	−0.215964	+	0.976401i	$0.569289\pi$
$272$	−20.1781	−1.22348
$273$	−3.84296	−0.232586
$274$	−8.62685	−0.521167
$275$	1.00000	0.0603023
$276$	−0.476278	−0.0286686
$277$	2.95470	0.177530	0.0887652	−	0.996053i	$-0.471708\pi$
$277$	2.95470	0.177530	0.0887652	+	0.996053i	$0.471708\pi$
$278$	3.89284	0.233477
$279$	−22.0014	−1.31719
$280$	−6.11285	−0.365313
$281$	17.5735	1.04835	0.524175	−	0.851611i	$-0.324374\pi$
$281$	17.5735	1.04835	0.524175	+	0.851611i	$0.324374\pi$
$282$	0.947401	0.0564169
$283$	−15.7328	−0.935215	−0.467608	−	0.883936i	$-0.654884\pi$
$283$	−15.7328	−0.935215	−0.467608	+	0.883936i	$0.654884\pi$
$284$	23.1393	1.37307
$285$	−1.10596	−0.0655116
$286$	−2.59450	−0.153416
$287$	−39.1396	−2.31034
$288$	14.5766	0.858934
$289$	41.2601	2.42706
$290$	−1.77128	−0.104013
$291$	−2.82500	−0.165605
$292$	−1.76470	−0.103272
$293$	11.5625	0.675489	0.337744	−	0.941238i	$-0.390336\pi$
$293$	11.5625	0.675489	0.337744	+	0.941238i	$0.390336\pi$
$294$	0.437810	0.0255336
$295$	12.5976	0.733459
$296$	21.3888	1.24320
$297$	1.27796	0.0741547
$298$	7.62123	0.441486
$299$	−6.72547	−0.388944
$300$	0.378778	0.0218688
$301$	−3.44597	−0.198622
$302$	11.6340	0.669460
$303$	−1.20726	−0.0693553
$304$	−13.6214	−0.781241
$305$	−0.307979	−0.0176348
$306$	−10.9369	−0.625219
$307$	−17.8124	−1.01661	−0.508304	−	0.861178i	$-0.669727\pi$
$307$	−17.8124	−1.01661	−0.508304	+	0.861178i	$0.669727\pi$
$308$	−5.90715	−0.336591
$309$	−2.23964	−0.127409
$310$	3.61290	0.205199
$311$	−17.7841	−1.00845	−0.504223	−	0.863573i	$-0.668221\pi$
$311$	−17.7841	−1.00845	−0.504223	+	0.863573i	$0.668221\pi$
$312$	−2.09651	−0.118692
$313$	−7.82712	−0.442415	−0.221208	−	0.975227i	$-0.571000\pi$
$313$	−7.82712	−0.442415	−0.221208	+	0.975227i	$0.571000\pi$
$314$	7.63618	0.430935
$315$	9.88794	0.557122
$316$	3.43385	0.193169
$317$	−22.4077	−1.25854	−0.629272	−	0.777185i	$-0.716647\pi$
$317$	−22.4077	−1.25854	−0.629272	+	0.777185i	$0.716647\pi$
$318$	−0.00767363	−0.000430316 0
$319$	−3.65158	−0.204449
$320$	2.89352	0.161753
$321$	0.0674061	0.00376224
$322$	2.04168	0.113779
$323$	39.3290	2.18832
$324$	−15.1544	−0.841910
$325$	5.34868	0.296692
$326$	3.18189	0.176229
$327$	0.631724	0.0349344
$328$	−21.3525	−1.17899
$329$	30.4593	1.67927
$330$	−0.104117	−0.00573143
$331$	4.21092	0.231453	0.115726	−	0.993281i	$-0.463080\pi$
$331$	4.21092	0.231453	0.115726	+	0.993281i	$0.463080\pi$
$332$	−19.8627	−1.09011
$333$	−34.5977	−1.89594
$334$	1.55961	0.0853382
$335$	−2.23434	−0.122075
$336$	−1.89939	−0.103620
$337$	16.4824	0.897853	0.448927	−	0.893569i	$-0.351806\pi$
$337$	16.4824	0.897853	0.448927	+	0.893569i	$0.351806\pi$
$338$	−7.57121	−0.411820
$339$	3.19288	0.173414
$340$	−13.4697	−0.730496
$341$	7.44817	0.403341
$342$	−7.38303	−0.399228
$343$	−9.35596	−0.505174
$344$	−1.87994	−0.101359
$345$	−0.269891	−0.0145304
$346$	−4.03034	−0.216673
$347$	−5.07977	−0.272696	−0.136348	−	0.990661i	$-0.543537\pi$
$347$	−5.07977	−0.272696	−0.136348	+	0.990661i	$0.543537\pi$
$348$	−1.38314	−0.0741440
$349$	−27.7222	−1.48393	−0.741967	−	0.670437i	$-0.766107\pi$
$349$	−27.7222	−1.48393	−0.741967	+	0.670437i	$0.766107\pi$
$350$	−1.62373	−0.0867918
$351$	6.83539	0.364846
$352$	−4.93465	−0.263017
$353$	17.5031	0.931596	0.465798	−	0.884891i	$-0.345767\pi$
$353$	17.5031	0.931596	0.465798	+	0.884891i	$0.345767\pi$
$354$	−1.31162	−0.0697116
$355$	13.1123	0.695928
$356$	3.34829	0.177459
$357$	5.48409	0.290249
$358$	9.71370	0.513385
$359$	28.4790	1.50307	0.751533	−	0.659696i	$-0.229315\pi$
$359$	28.4790	1.50307	0.751533	+	0.659696i	$0.229315\pi$
$360$	5.39433	0.284306
$361$	7.54941	0.397337
$362$	1.14379	0.0601165
$363$	−0.214641	−0.0112657
$364$	−31.5955	−1.65605
$365$	−1.00000	−0.0523424
$366$	0.0320657	0.00167610
$367$	−12.4063	−0.647606	−0.323803	−	0.946125i	$-0.604961\pi$
$367$	−12.4063	−0.647606	−0.323803	+	0.946125i	$0.604961\pi$
$368$	−3.32407	−0.173279
$369$	34.5391	1.79803
$370$	5.68139	0.295361
$371$	−0.246710	−0.0128085
$372$	2.82120	0.146273
$373$	−35.0301	−1.81379	−0.906896	−	0.421355i	$-0.861555\pi$
$373$	−35.0301	−1.81379	−0.906896	+	0.421355i	$0.861555\pi$
$374$	3.70248	0.191451
$375$	0.214641	0.0110840
$376$	16.6170	0.856954
$377$	−19.5311	−1.00590
$378$	−2.07505	−0.106729
$379$	0.0453024	0.00232703	0.00116351	−	0.999999i	$-0.499630\pi$
$379$	0.0453024	0.00232703	0.00116351	+	0.999999i	$0.499630\pi$
$380$	−9.09284	−0.466453
$381$	2.48482	0.127301
$382$	−4.32823	−0.221452
$383$	8.47735	0.433172	0.216586	−	0.976263i	$-0.430508\pi$
$383$	8.47735	0.433172	0.216586	+	0.976263i	$0.430508\pi$
$384$	−2.41962	−0.123476
$385$	−3.34739	−0.170599
$386$	7.56949	0.385277
$387$	3.04092	0.154579
$388$	−23.2262	−1.17913
$389$	29.4673	1.49405	0.747026	−	0.664795i	$-0.231481\pi$
$389$	29.4673	1.49405	0.747026	+	0.664795i	$0.231481\pi$
$390$	−0.556887	−0.0281991
$391$	9.59756	0.485370
$392$	7.67898	0.387847
$393$	0.754328	0.0380508
$394$	4.04020	0.203543
$395$	1.94585	0.0979064
$396$	5.21281	0.261954
$397$	−12.0430	−0.604418	−0.302209	−	0.953242i	$-0.597724\pi$
$397$	−12.0430	−0.604418	−0.302209	+	0.953242i	$0.597724\pi$
$398$	−6.64781	−0.333225
$399$	3.70208	0.185336
$400$	2.64359	0.132180
$401$	7.91628	0.395320	0.197660	−	0.980271i	$-0.436666\pi$
$401$	7.91628	0.395320	0.197660	+	0.980271i	$0.436666\pi$
$402$	0.232632	0.0116026
$403$	39.8379	1.98447
$404$	−9.92567	−0.493820
$405$	−8.58749	−0.426716
$406$	5.92917	0.294260
$407$	11.7124	0.580564
$408$	2.99183	0.148117
$409$	−17.2913	−0.854998	−0.427499	−	0.904016i	$-0.640605\pi$
$409$	−17.2913	−0.854998	−0.427499	+	0.904016i	$0.640605\pi$
$410$	−5.67176	−0.280108
$411$	−3.81732	−0.188294
$412$	−18.4135	−0.907170
$413$	−42.1689	−2.07500
$414$	−1.80170	−0.0885487
$415$	−11.2555	−0.552512
$416$	−26.3939	−1.29407
$417$	1.72255	0.0843538
$418$	2.49939	0.122249
$419$	2.87299	0.140355	0.0701774	−	0.997535i	$-0.477643\pi$
$419$	2.87299	0.140355	0.0701774	+	0.997535i	$0.477643\pi$
$420$	−1.26792	−0.0618680
$421$	29.9650	1.46040	0.730202	−	0.683231i	$-0.239426\pi$
$421$	29.9650	1.46040	0.730202	+	0.683231i	$0.239426\pi$
$422$	7.15390	0.348246
$423$	−26.8790	−1.30690
$424$	−0.134592	−0.00653635
$425$	−7.63283	−0.370247
$426$	−1.36521	−0.0661445
$427$	1.03093	0.0498900
$428$	0.554189	0.0267877
$429$	−1.14805	−0.0554283
$430$	−0.499359	−0.0240812
$431$	12.5236	0.603239	0.301620	−	0.953428i	$-0.402473\pi$
$431$	12.5236	0.603239	0.301620	+	0.953428i	$0.402473\pi$
$432$	3.37840	0.162543
$433$	15.1339	0.727289	0.363645	−	0.931538i	$-0.381532\pi$
$433$	15.1339	0.727289	0.363645	+	0.931538i	$0.381532\pi$
$434$	−12.0938	−0.580520
$435$	−0.783779	−0.0375793
$436$	5.19381	0.248739
$437$	6.47892	0.309929
$438$	0.104117	0.00497488
$439$	−19.5660	−0.933834	−0.466917	−	0.884301i	$-0.654635\pi$
$439$	−19.5660	−0.933834	−0.466917	+	0.884301i	$0.654635\pi$
$440$	−1.82616	−0.0870586
$441$	−12.4213	−0.591489
$442$	19.8034	0.941951
$443$	26.8395	1.27518	0.637590	−	0.770375i	$-0.279931\pi$
$443$	26.8395	1.27518	0.637590	+	0.770375i	$0.279931\pi$
$444$	4.43642	0.210543
$445$	1.89737	0.0899439
$446$	−0.425850	−0.0201646
$447$	3.37234	0.159506
$448$	−9.68572	−0.457607
$449$	−14.0532	−0.663212	−0.331606	−	0.943418i	$-0.607590\pi$
$449$	−14.0532	−0.663212	−0.331606	+	0.943418i	$0.607590\pi$
$450$	1.43287	0.0675462
$451$	−11.6926	−0.550582
$452$	26.2508	1.23473
$453$	5.14795	0.241872
$454$	10.5619	0.495695
$455$	−17.9041	−0.839358
$456$	2.01966	0.0945793
$457$	40.4533	1.89233	0.946163	−	0.323691i	$-0.104924\pi$
$457$	40.4533	1.89233	0.946163	+	0.323691i	$0.104924\pi$
$458$	8.45825	0.395228
$459$	−9.75444	−0.455298
$460$	−2.21895	−0.103459
$461$	1.42206	0.0662321	0.0331161	−	0.999452i	$-0.489457\pi$
$461$	1.42206	0.0662321	0.0331161	+	0.999452i	$0.489457\pi$
$462$	0.348519	0.0162145
$463$	−8.47014	−0.393641	−0.196820	−	0.980440i	$-0.563062\pi$
$463$	−8.47014	−0.393641	−0.196820	+	0.980440i	$0.563062\pi$
$464$	−9.65328	−0.448142
$465$	1.59868	0.0741372
$466$	−5.94705	−0.275492
$467$	16.9135	0.782663	0.391331	−	0.920250i	$-0.372015\pi$
$467$	16.9135	0.782663	0.391331	+	0.920250i	$0.372015\pi$
$468$	27.8817	1.28883
$469$	7.47920	0.345357
$470$	4.41388	0.203597
$471$	3.37895	0.155694
$472$	−23.0051	−1.05890
$473$	−1.02945	−0.0473342
$474$	−0.202595	−0.00930552
$475$	−5.15261	−0.236418
$476$	45.0882	2.06662
$477$	0.217711	0.00996831
$478$	4.52212	0.206837
$479$	39.6594	1.81208	0.906042	−	0.423188i	$-0.139089\pi$
$479$	39.6594	1.81208	0.906042	+	0.423188i	$0.139089\pi$
$480$	−1.05918	−0.0483446
$481$	62.6462	2.85642
$482$	11.1610	0.508370
$483$	0.903430	0.0411075
$484$	−1.76470	−0.0802138
$485$	−13.1615	−0.597633
$486$	2.75381	0.124915
$487$	−21.1860	−0.960031	−0.480016	−	0.877260i	$-0.659369\pi$
$487$	−21.1860	−0.960031	−0.480016	+	0.877260i	$0.659369\pi$
$488$	0.562418	0.0254595
$489$	1.40796	0.0636703
$490$	2.03973	0.0921456
$491$	−3.99430	−0.180260	−0.0901300	−	0.995930i	$-0.528728\pi$
$491$	−3.99430	−0.180260	−0.0901300	+	0.995930i	$0.528728\pi$
$492$	−4.42890	−0.199670
$493$	27.8719	1.25529
$494$	13.3685	0.601475
$495$	2.95393	0.132769
$496$	19.6899	0.884103
$497$	−43.8919	−1.96882
$498$	1.17189	0.0525135
$499$	−23.9370	−1.07157	−0.535785	−	0.844355i	$-0.679984\pi$
$499$	−23.9370	−1.07157	−0.535785	+	0.844355i	$0.679984\pi$
$500$	1.76470	0.0789200
$501$	0.690117	0.0308322
$502$	9.02549	0.402827
$503$	−33.4608	−1.49194	−0.745972	−	0.665978i	$-0.768015\pi$
$503$	−33.4608	−1.49194	−0.745972	+	0.665978i	$0.768015\pi$
$504$	−18.0569	−0.804319
$505$	−5.62455	−0.250289
$506$	0.609933	0.0271148
$507$	−3.35021	−0.148788
$508$	20.4293	0.906404
$509$	29.2251	1.29538	0.647689	−	0.761905i	$-0.275736\pi$
$509$	29.2251	1.29538	0.647689	+	0.761905i	$0.275736\pi$
$510$	0.794704	0.0351901
$511$	3.34739	0.148080
$512$	−22.7004	−1.00323
$513$	−6.58482	−0.290727
$514$	11.8928	0.524571
$515$	−10.4343	−0.459792
$516$	−0.389933	−0.0171659
$517$	9.09942	0.400192
$518$	−19.0178	−0.835595
$519$	−1.78340	−0.0782824
$520$	−9.76753	−0.428334
$521$	−0.273741	−0.0119928	−0.00599641	−	0.999982i	$-0.501909\pi$
$521$	−0.273741	−0.0119928	−0.00599641	+	0.999982i	$0.501909\pi$
$522$	−5.23224	−0.229009
$523$	−11.2393	−0.491460	−0.245730	−	0.969338i	$-0.579028\pi$
$523$	−11.2393	−0.491460	−0.245730	+	0.969338i	$0.579028\pi$
$524$	6.20182	0.270928
$525$	−0.718487	−0.0313573
$526$	−3.41639	−0.148962
$527$	−56.8506	−2.47645
$528$	−0.567423	−0.0246939
$529$	−21.4189	−0.931258
$530$	−0.0357510	−0.00155292
$531$	37.2123	1.61488
$532$	30.4372	1.31962
$533$	−62.5399	−2.70891
$534$	−0.197548	−0.00854872
$535$	0.314041	0.0135772
$536$	4.08025	0.176240
$537$	4.29824	0.185483
$538$	5.92739	0.255548
$539$	4.20500	0.181122
$540$	2.25522	0.0970492
$541$	−14.5658	−0.626231	−0.313115	−	0.949715i	$-0.601373\pi$
$541$	−14.5658	−0.626231	−0.313115	+	0.949715i	$0.601373\pi$
$542$	3.44907	0.148150
$543$	0.506120	0.0217197
$544$	37.6653	1.61489
$545$	2.94316	0.126071
$546$	1.86411	0.0797768
$547$	−16.2857	−0.696327	−0.348164	−	0.937434i	$-0.613195\pi$
$547$	−16.2857	−0.696327	−0.348164	+	0.937434i	$0.613195\pi$
$548$	−31.3846	−1.34069
$549$	−0.909748	−0.0388271
$550$	−0.485073	−0.0206836
$551$	18.8152	0.801553
$552$	0.492863	0.0209776
$553$	−6.51352	−0.276983
$554$	−1.43324	−0.0608926
$555$	2.51397	0.106712
$556$	14.1622	0.600612
$557$	2.08326	0.0882704	0.0441352	−	0.999026i	$-0.485947\pi$
$557$	2.08326	0.0882704	0.0441352	+	0.999026i	$0.485947\pi$
$558$	10.6723	0.451793
$559$	−5.50621	−0.232888
$560$	−8.84912	−0.373943
$561$	1.63832	0.0691699
$562$	−8.52444	−0.359582
$563$	−28.7505	−1.21169	−0.605844	−	0.795584i	$-0.707164\pi$
$563$	−28.7505	−1.21169	−0.605844	+	0.795584i	$0.707164\pi$
$564$	3.44666	0.145131
$565$	14.8754	0.625815
$566$	7.63153	0.320777
$567$	28.7456	1.20720
$568$	−23.9451	−1.00471
$569$	6.86605	0.287840	0.143920	−	0.989589i	$-0.454029\pi$
$569$	6.86605	0.287840	0.143920	+	0.989589i	$0.454029\pi$
$570$	0.536472	0.0224704
$571$	33.4424	1.39952	0.699760	−	0.714378i	$-0.253290\pi$
$571$	33.4424	1.39952	0.699760	+	0.714378i	$0.253290\pi$
$572$	−9.43884	−0.394658
$573$	−1.91521	−0.0800091
$574$	18.9856	0.792442
$575$	−1.25741	−0.0524374
$576$	8.54725	0.356135
$577$	35.3269	1.47068	0.735339	−	0.677699i	$-0.237023\pi$
$577$	35.3269	1.47068	0.735339	+	0.677699i	$0.237023\pi$
$578$	−20.0141	−0.832479
$579$	3.34944	0.139198
$580$	−6.44396	−0.267571
$581$	37.6766	1.56309
$582$	1.37033	0.0568021
$583$	−0.0737022	−0.00305243
$584$	1.82616	0.0755669
$585$	15.7996	0.653234
$586$	−5.60866	−0.231692
$587$	32.0277	1.32192	0.660962	−	0.750419i	$-0.270148\pi$
$587$	32.0277	1.32192	0.660962	+	0.750419i	$0.270148\pi$
$588$	1.59276	0.0656844
$589$	−38.3775	−1.58132
$590$	−6.11074	−0.251575
$591$	1.78776	0.0735386
$592$	30.9629	1.27257
$593$	1.19004	0.0488690	0.0244345	−	0.999701i	$-0.492221\pi$
$593$	1.19004	0.0488690	0.0244345	+	0.999701i	$0.492221\pi$
$594$	−0.619903	−0.0254349
$595$	25.5500	1.04745
$596$	27.7262	1.13571
$597$	−2.94161	−0.120392
$598$	3.26234	0.133407
$599$	−15.7567	−0.643803	−0.321902	−	0.946773i	$-0.604322\pi$
$599$	−15.7567	−0.643803	−0.321902	+	0.946773i	$0.604322\pi$
$600$	−0.391968	−0.0160020
$601$	−34.2587	−1.39744	−0.698721	−	0.715395i	$-0.746247\pi$
$601$	−34.2587	−1.39744	−0.698721	+	0.715395i	$0.746247\pi$
$602$	1.67155	0.0681271
$603$	−6.60008	−0.268776
$604$	42.3246	1.72216
$605$	−1.00000	−0.0406558
$606$	0.585609	0.0237887
$607$	−23.0434	−0.935301	−0.467651	−	0.883913i	$-0.654899\pi$
$607$	−23.0434	−0.935301	−0.467651	+	0.883913i	$0.654899\pi$
$608$	25.4263	1.03117
$609$	2.62361	0.106314
$610$	0.149392	0.00604872
$611$	48.6699	1.96897
$612$	−39.7885	−1.60835
$613$	−20.1573	−0.814144	−0.407072	−	0.913396i	$-0.633450\pi$
$613$	−20.1573	−0.814144	−0.407072	+	0.913396i	$0.633450\pi$
$614$	8.64032	0.348695
$615$	−2.50971	−0.101201
$616$	6.11285	0.246294
$617$	−24.1088	−0.970585	−0.485292	−	0.874352i	$-0.661287\pi$
$617$	−24.1088	−0.970585	−0.485292	+	0.874352i	$0.661287\pi$
$618$	1.08639	0.0437010
$619$	19.8035	0.795972	0.397986	−	0.917392i	$-0.369709\pi$
$619$	19.8035	0.795972	0.397986	+	0.917392i	$0.369709\pi$
$620$	13.1438	0.527868
$621$	−1.60691	−0.0644832
$622$	8.62660	0.345895
$623$	−6.35122	−0.254456
$624$	−3.03497	−0.121496
$625$	1.00000	0.0400000
$626$	3.79673	0.151748
$627$	1.10596	0.0441679
$628$	27.7806	1.10857
$629$	−89.3991	−3.56458
$630$	−4.79637	−0.191092
$631$	−21.8917	−0.871494	−0.435747	−	0.900069i	$-0.643516\pi$
$631$	−21.8917	−0.871494	−0.435747	+	0.900069i	$0.643516\pi$
$632$	−3.55343	−0.141348
$633$	3.16555	0.125819
$634$	10.8694	0.431679
$635$	11.5766	0.459404
$636$	−0.0279168	−0.00110697
$637$	22.4912	0.891134
$638$	1.77128	0.0701257
$639$	38.7328	1.53225
$640$	−11.2729	−0.445599
$641$	−2.64321	−0.104401	−0.0522003	−	0.998637i	$-0.516623\pi$
$641$	−2.64321	−0.104401	−0.0522003	+	0.998637i	$0.516623\pi$
$642$	−0.0326968	−0.00129044
$643$	42.0276	1.65741	0.828704	−	0.559687i	$-0.189079\pi$
$643$	42.0276	1.65741	0.828704	+	0.559687i	$0.189079\pi$
$644$	7.42768	0.292692
$645$	−0.220962	−0.00870039
$646$	−19.0774	−0.750592
$647$	16.8199	0.661257	0.330628	−	0.943761i	$-0.392739\pi$
$647$	16.8199	0.661257	0.330628	+	0.943761i	$0.392739\pi$
$648$	15.6821	0.616050
$649$	−12.5976	−0.494498
$650$	−2.59450	−0.101765
$651$	−5.35141	−0.209738
$652$	11.5758	0.453342
$653$	−4.86942	−0.190555	−0.0952776	−	0.995451i	$-0.530374\pi$
$653$	−4.86942	−0.190555	−0.0952776	+	0.995451i	$0.530374\pi$
$654$	−0.306432	−0.0119824
$655$	3.51437	0.137318
$656$	−30.9104	−1.20685
$657$	−2.95393	−0.115244
$658$	−14.7750	−0.575988
$659$	9.00734	0.350876	0.175438	−	0.984490i	$-0.443866\pi$
$659$	9.00734	0.350876	0.175438	+	0.984490i	$0.443866\pi$
$660$	−0.378778	−0.0147439
$661$	−19.8134	−0.770651	−0.385326	−	0.922781i	$-0.625911\pi$
$661$	−19.8134	−0.770651	−0.385326	+	0.922781i	$0.625911\pi$
$662$	−2.04260	−0.0793879
$663$	8.76285	0.340321
$664$	20.5543	0.797663
$665$	17.2478	0.668840
$666$	16.7824	0.650306
$667$	4.59152	0.177784
$668$	5.67390	0.219530
$669$	−0.188436	−0.00728534
$670$	1.08382	0.0418715
$671$	0.307979	0.0118894
$672$	3.54548	0.136770
$673$	−4.72050	−0.181962	−0.0909810	−	0.995853i	$-0.529000\pi$
$673$	−4.72050	−0.181962	−0.0909810	+	0.995853i	$0.529000\pi$
$674$	−7.99516	−0.307962
$675$	1.27796	0.0491886
$676$	−27.5442	−1.05939
$677$	47.5025	1.82567	0.912834	−	0.408331i	$-0.133889\pi$
$677$	47.5025	1.82567	0.912834	+	0.408331i	$0.133889\pi$
$678$	−1.54878	−0.0594806
$679$	44.0567	1.69074
$680$	13.9387	0.534526
$681$	4.67356	0.179091
$682$	−3.61290	−0.138345
$683$	18.4065	0.704306	0.352153	−	0.935942i	$-0.385450\pi$
$683$	18.4065	0.704306	0.352153	+	0.935942i	$0.385450\pi$
$684$	−26.8596	−1.02700
$685$	−17.7846	−0.679517
$686$	4.53832	0.173274
$687$	3.74272	0.142793
$688$	−2.72145	−0.103754
$689$	−0.394210	−0.0150182
$690$	0.130917	0.00498392
$691$	50.3836	1.91668	0.958342	−	0.285623i	$-0.0922004\pi$
$691$	50.3836	1.91668	0.958342	+	0.285623i	$0.0922004\pi$
$692$	−14.6625	−0.557383
$693$	−9.88794	−0.375612
$694$	2.46406	0.0935344
$695$	8.02527	0.304416
$696$	1.43130	0.0542534
$697$	89.2475	3.38049
$698$	13.4473	0.508987
$699$	−2.63153	−0.0995335
$700$	−5.90715	−0.223269
$701$	10.8530	0.409912	0.204956	−	0.978771i	$-0.434295\pi$
$701$	10.8530	0.409912	0.204956	+	0.978771i	$0.434295\pi$
$702$	−3.31566	−0.125142
$703$	−60.3497	−2.27613
$704$	−2.89352	−0.109054
$705$	1.95311	0.0735584
$706$	−8.49028	−0.319536
$707$	18.8275	0.708082
$708$	−4.77168	−0.179331
$709$	18.2373	0.684916	0.342458	−	0.939533i	$-0.388741\pi$
$709$	18.2373	0.684916	0.342458	+	0.939533i	$0.388741\pi$
$710$	−6.36042	−0.238702
$711$	5.74791	0.215563
$712$	−3.46489	−0.129852
$713$	−9.36537	−0.350736
$714$	−2.66018	−0.0995548
$715$	−5.34868	−0.200029
$716$	35.3386	1.32067
$717$	2.00101	0.0747290
$718$	−13.8144	−0.515549
$719$	18.4949	0.689742	0.344871	−	0.938650i	$-0.387923\pi$
$719$	18.4949	0.689742	0.344871	+	0.938650i	$0.387923\pi$
$720$	7.80898	0.291023
$721$	34.9278	1.30078
$722$	−3.66201	−0.136286
$723$	4.93867	0.183671
$724$	4.16114	0.154648
$725$	−3.65158	−0.135616
$726$	0.104117	0.00386413
$727$	−6.94524	−0.257585	−0.128792	−	0.991672i	$-0.541110\pi$
$727$	−6.94524	−0.257585	−0.128792	+	0.991672i	$0.541110\pi$
$728$	32.6957	1.21178
$729$	−24.5439	−0.909034
$730$	0.485073	0.0179534
$731$	7.85762	0.290625
$732$	0.116656	0.00431172
$733$	26.6945	0.985985	0.492993	−	0.870034i	$-0.335903\pi$
$733$	26.6945	0.985985	0.492993	+	0.870034i	$0.335903\pi$
$734$	6.01798	0.222128
$735$	0.902565	0.0332916
$736$	6.20485	0.228714
$737$	2.23434	0.0823030
$738$	−16.7540	−0.616722
$739$	−29.8063	−1.09644	−0.548222	−	0.836333i	$-0.684695\pi$
$739$	−29.8063	−1.09644	−0.548222	+	0.836333i	$0.684695\pi$
$740$	20.6690	0.759808
$741$	5.91544	0.217309
$742$	0.119672	0.00439331
$743$	18.1365	0.665365	0.332682	−	0.943039i	$-0.392046\pi$
$743$	18.1365	0.665365	0.332682	+	0.943039i	$0.392046\pi$
$744$	−2.91945	−0.107032
$745$	15.7115	0.575625
$746$	16.9922	0.622128
$747$	−33.2480	−1.21648
$748$	13.4697	0.492501
$749$	−1.05122	−0.0384106
$750$	−0.104117	−0.00380180
$751$	−11.9038	−0.434376	−0.217188	−	0.976130i	$-0.569689\pi$
$751$	−11.9038	−0.434376	−0.217188	+	0.976130i	$0.569689\pi$
$752$	24.0551	0.877200
$753$	3.99371	0.145539
$754$	9.47403	0.345024
$755$	23.9840	0.872866
$756$	−7.54909	−0.274558
$757$	21.8204	0.793077	0.396539	−	0.918018i	$-0.370211\pi$
$757$	21.8204	0.793077	0.396539	+	0.918018i	$0.370211\pi$
$758$	−0.0219750	−0.000798167 0
$759$	0.269891	0.00979642
$760$	9.40947	0.341317
$761$	0.235698	0.00854403	0.00427202	−	0.999991i	$-0.498640\pi$
$761$	0.235698	0.00854403	0.00427202	+	0.999991i	$0.498640\pi$
$762$	−1.20532	−0.0436641
$763$	−9.85191	−0.356663
$764$	−15.7462	−0.569678
$765$	−22.5468	−0.815183
$766$	−4.11213	−0.148577
$767$	−67.3804	−2.43297
$768$	−0.0684446	−0.00246978
$769$	−28.8498	−1.04035	−0.520176	−	0.854059i	$-0.674134\pi$
$769$	−28.8498	−1.04035	−0.520176	+	0.854059i	$0.674134\pi$
$770$	1.62373	0.0585150
$771$	5.26249	0.189524
$772$	27.5380	0.991113
$773$	−17.5045	−0.629593	−0.314796	−	0.949159i	$-0.601936\pi$
$773$	−17.5045	−0.629593	−0.314796	+	0.949159i	$0.601936\pi$
$774$	−1.47507	−0.0530203
$775$	7.44817	0.267546
$776$	24.0350	0.862805
$777$	−8.41524	−0.301895
$778$	−14.2938	−0.512457
$779$	60.2474	2.15859
$780$	−2.02596	−0.0725412
$781$	−13.1123	−0.469195
$782$	−4.65552	−0.166481
$783$	−4.66657	−0.166769
$784$	11.1163	0.397010
$785$	15.7423	0.561868
$786$	−0.365904	−0.0130514
$787$	−30.6164	−1.09136	−0.545679	−	0.837994i	$-0.683728\pi$
$787$	−30.6164	−1.09136	−0.545679	+	0.837994i	$0.683728\pi$
$788$	14.6983	0.523607
$789$	−1.51173	−0.0538189
$790$	−0.943880	−0.0335817
$791$	−49.7939	−1.77047
$792$	−5.39433	−0.191679
$793$	1.64728	0.0584967
$794$	5.84171	0.207314
$795$	−0.0158195	−0.000561061 0
$796$	−24.1849	−0.857209
$797$	−41.9715	−1.48671	−0.743354	−	0.668899i	$-0.766766\pi$
$797$	−41.9715	−1.48671	−0.743354	+	0.668899i	$0.766766\pi$
$798$	−1.79578	−0.0635699
$799$	−69.4543	−2.45712
$800$	−4.93465	−0.174466
$801$	5.60469	0.198032
$802$	−3.83997	−0.135594
$803$	1.00000	0.0352892
$804$	0.846319	0.0298474
$805$	4.20902	0.148349
$806$	−19.3243	−0.680669
$807$	2.62283	0.0923278
$808$	10.2713	0.361343
$809$	19.4629	0.684279	0.342139	−	0.939649i	$-0.388849\pi$
$809$	19.4629	0.684279	0.342139	+	0.939649i	$0.388849\pi$
$810$	4.16556	0.146363
$811$	10.5166	0.369287	0.184644	−	0.982806i	$-0.440887\pi$
$811$	10.5166	0.369287	0.184644	+	0.982806i	$0.440887\pi$
$812$	21.5704	0.756973
$813$	1.52619	0.0535258
$814$	−5.68139	−0.199133
$815$	6.55961	0.229773
$816$	4.33104	0.151617
$817$	5.30436	0.185576
$818$	8.38753	0.293263
$819$	−52.8875	−1.84804
$820$	−20.6340	−0.720569
$821$	34.2468	1.19522	0.597610	−	0.801787i	$-0.296117\pi$
$821$	34.2468	1.19522	0.597610	+	0.801787i	$0.296117\pi$
$822$	1.85168	0.0645847
$823$	−31.6479	−1.10318	−0.551589	−	0.834116i	$-0.685978\pi$
$823$	−31.6479	−1.10318	−0.551589	+	0.834116i	$0.685978\pi$
$824$	19.0547	0.663803
$825$	−0.214641	−0.00747285
$826$	20.4550	0.711721
$827$	−9.65956	−0.335896	−0.167948	−	0.985796i	$-0.553714\pi$
$827$	−9.65956	−0.335896	−0.167948	+	0.985796i	$0.553714\pi$
$828$	−6.55462	−0.227789
$829$	−28.3755	−0.985520	−0.492760	−	0.870165i	$-0.664012\pi$
$829$	−28.3755	−0.985520	−0.492760	+	0.870165i	$0.664012\pi$
$830$	5.45975	0.189511
$831$	−0.634199	−0.0220001
$832$	−15.4765	−0.536551
$833$	−32.0960	−1.11206
$834$	−0.835564	−0.0289332
$835$	3.21521	0.111267
$836$	9.09284	0.314482
$837$	9.51845	0.329006
$838$	−1.39361	−0.0481415
$839$	−42.4286	−1.46480	−0.732400	−	0.680875i	$-0.761600\pi$
$839$	−42.4286	−1.46480	−0.732400	+	0.680875i	$0.761600\pi$
$840$	1.31207	0.0452707
$841$	−15.6660	−0.540206
$842$	−14.5352	−0.500916
$843$	−3.77200	−0.129915
$844$	26.0260	0.895852
$845$	−15.6084	−0.536946
$846$	13.0383	0.448266
$847$	3.34739	0.115018
$848$	−0.194839	−0.00669078
$849$	3.37690	0.115895
$850$	3.70248	0.126994
$851$	−14.7273	−0.504845
$852$	−4.96665	−0.170155
$853$	−1.85110	−0.0633804	−0.0316902	−	0.999498i	$-0.510089\pi$
$853$	−1.85110	−0.0633804	−0.0316902	+	0.999498i	$0.510089\pi$
$854$	−0.500074	−0.0171122
$855$	−15.2205	−0.520528
$856$	−0.573487	−0.0196014
$857$	12.2471	0.418353	0.209176	−	0.977878i	$-0.432922\pi$
$857$	12.2471	0.418353	0.209176	+	0.977878i	$0.432922\pi$
$858$	0.556887	0.0190118
$859$	−10.4320	−0.355934	−0.177967	−	0.984036i	$-0.556952\pi$
$859$	−10.4320	−0.355934	−0.177967	+	0.984036i	$0.556952\pi$
$860$	−1.81668	−0.0619481
$861$	8.40097	0.286304
$862$	−6.07485	−0.206910
$863$	−51.8786	−1.76597	−0.882984	−	0.469403i	$-0.844469\pi$
$863$	−51.8786	−1.76597	−0.882984	+	0.469403i	$0.844469\pi$
$864$	−6.30627	−0.214544
$865$	−8.30873	−0.282505
$866$	−7.34105	−0.249459
$867$	−8.85611	−0.300769
$868$	−43.9974	−1.49337
$869$	−1.94585	−0.0660085
$870$	0.380190	0.0128897
$871$	11.9508	0.404937
$872$	−5.37468	−0.182009
$873$	−38.8782	−1.31583
$874$	−3.14275	−0.106305
$875$	−3.34739	−0.113162
$876$	0.378778	0.0127977
$877$	44.8291	1.51377	0.756886	−	0.653547i	$-0.226720\pi$
$877$	44.8291	1.51377	0.756886	+	0.653547i	$0.226720\pi$
$878$	9.49093	0.320303
$879$	−2.48179	−0.0837087
$880$	−2.64359	−0.0891154
$881$	−47.4095	−1.59727	−0.798633	−	0.601819i	$-0.794443\pi$
$881$	−47.4095	−1.59727	−0.798633	+	0.601819i	$0.794443\pi$
$882$	6.02522	0.202880
$883$	15.0997	0.508144	0.254072	−	0.967185i	$-0.418230\pi$
$883$	15.0997	0.508144	0.254072	+	0.967185i	$0.418230\pi$
$884$	72.0451	2.42314
$885$	−2.70396	−0.0908925
$886$	−13.0191	−0.437385
$887$	−19.2410	−0.646050	−0.323025	−	0.946390i	$-0.604700\pi$
$887$	−19.2410	−0.646050	−0.323025	+	0.946390i	$0.604700\pi$
$888$	−4.59091	−0.154061
$889$	−38.7514	−1.29968
$890$	−0.920362	−0.0308506
$891$	8.58749	0.287692
$892$	−1.54925	−0.0518728
$893$	−46.8858	−1.56897
$894$	−1.63583	−0.0547103
$895$	20.0252	0.669370
$896$	37.7346	1.26062
$897$	1.44356	0.0481991
$898$	6.81683	0.227480
$899$	−27.1976	−0.907090
$900$	5.21281	0.173760
$901$	0.562557	0.0187415
$902$	5.67176	0.188849
$903$	0.739647	0.0246139
$904$	−27.1649	−0.903490
$905$	2.35798	0.0783820
$906$	−2.49713	−0.0829616
$907$	−3.21899	−0.106885	−0.0534423	−	0.998571i	$-0.517019\pi$
$907$	−3.21899	−0.106885	−0.0534423	+	0.998571i	$0.517019\pi$
$908$	38.4244	1.27516
$909$	−16.6145	−0.551069
$910$	8.68480	0.287898
$911$	−8.36848	−0.277260	−0.138630	−	0.990344i	$-0.544270\pi$
$911$	−8.36848	−0.277260	−0.138630	+	0.990344i	$0.544270\pi$
$912$	2.92371	0.0968138
$913$	11.2555	0.372504
$914$	−19.6228	−0.649065
$915$	0.0661050	0.00218536
$916$	30.7713	1.01671
$917$	−11.7640	−0.388480
$918$	4.73161	0.156166
$919$	24.3763	0.804098	0.402049	−	0.915618i	$-0.368298\pi$
$919$	24.3763	0.804098	0.402049	+	0.915618i	$0.368298\pi$
$920$	2.29622	0.0757041
$921$	3.82328	0.125981
$922$	−0.689805	−0.0227175
$923$	−70.1335	−2.30847
$924$	1.26792	0.0417114
$925$	11.7124	0.385103
$926$	4.10863	0.135018
$927$	−30.8223	−1.01234
$928$	18.0193	0.591511
$929$	−29.2274	−0.958921	−0.479461	−	0.877563i	$-0.659168\pi$
$929$	−29.2274	−0.958921	−0.479461	+	0.877563i	$0.659168\pi$
$930$	−0.775478	−0.0254289
$931$	−21.6667	−0.710098
$932$	−21.6355	−0.708694
$933$	3.81721	0.124970
$934$	−8.20427	−0.268452
$935$	7.63283	0.249620
$936$	−28.8526	−0.943076
$937$	34.0272	1.11162	0.555811	−	0.831309i	$-0.312408\pi$
$937$	34.0272	1.11162	0.555811	+	0.831309i	$0.312408\pi$
$938$	−3.62796	−0.118457
$939$	1.68002	0.0548255
$940$	16.0578	0.523747
$941$	22.0364	0.718367	0.359183	−	0.933267i	$-0.383055\pi$
$941$	22.0364	0.718367	0.359183	+	0.933267i	$0.383055\pi$
$942$	−1.63904	−0.0534028
$943$	14.7023	0.478774
$944$	−33.3028	−1.08391
$945$	−4.27782	−0.139158
$946$	0.499359	0.0162355
$947$	−14.2137	−0.461883	−0.230941	−	0.972968i	$-0.574181\pi$
$947$	−14.2137	−0.461883	−0.230941	+	0.972968i	$0.574181\pi$
$948$	−0.737046	−0.0239381
$949$	5.34868	0.173626
$950$	2.49939	0.0810910
$951$	4.80962	0.155963
$952$	−46.6583	−1.51221
$953$	−4.46843	−0.144747	−0.0723733	−	0.997378i	$-0.523057\pi$
$953$	−4.46843	−0.144747	−0.0723733	+	0.997378i	$0.523057\pi$
$954$	−0.105606	−0.00341911
$955$	−8.92286	−0.288737
$956$	16.4516	0.532082
$957$	0.783779	0.0253360
$958$	−19.2377	−0.621542
$959$	59.5321	1.92239
$960$	−0.621068	−0.0200449
$961$	24.4752	0.789523
$962$	−30.3880	−0.979747
$963$	0.927654	0.0298932
$964$	40.6040	1.30777
$965$	15.6049	0.502338
$966$	−0.438229	−0.0140998
$967$	15.7804	0.507462	0.253731	−	0.967275i	$-0.418342\pi$
$967$	15.7804	0.507462	0.253731	+	0.967275i	$0.418342\pi$
$968$	1.82616	0.0586949
$969$	−8.44162	−0.271184
$970$	6.38429	0.204987
$971$	43.1053	1.38331	0.691657	−	0.722226i	$-0.256881\pi$
$971$	43.1053	1.38331	0.691657	+	0.722226i	$0.256881\pi$
$972$	10.0184	0.321341
$973$	−26.8637	−0.861210
$974$	10.2768	0.329289
$975$	−1.14805	−0.0367669
$976$	0.814170	0.0260610
$977$	22.1620	0.709025	0.354513	−	0.935051i	$-0.384647\pi$
$977$	22.1620	0.709025	0.354513	+	0.935051i	$0.384647\pi$
$978$	−0.682964	−0.0218388
$979$	−1.89737	−0.0606401
$980$	7.42058	0.237042
$981$	8.69390	0.277575
$982$	1.93752	0.0618289
$983$	41.3458	1.31872	0.659362	−	0.751825i	$-0.270826\pi$
$983$	41.3458	1.31872	0.659362	+	0.751825i	$0.270826\pi$
$984$	4.58312	0.146105
$985$	8.32907	0.265386
$986$	−13.5199	−0.430561
$987$	−6.53781	−0.208101
$988$	48.6347	1.54728
$989$	1.29444	0.0411607
$990$	−1.43287	−0.0455396
$991$	−61.8424	−1.96449	−0.982244	−	0.187610i	$-0.939926\pi$
$991$	−61.8424	−1.96449	−0.982244	+	0.187610i	$0.939926\pi$
$992$	−36.7541	−1.16694
$993$	−0.903836	−0.0286824
$994$	21.2908	0.675302
$995$	−13.7048	−0.434470
$996$	4.26335	0.135089
$997$	29.1924	0.924533	0.462267	−	0.886741i	$-0.347036\pi$
$997$	29.1924	0.924533	0.462267	+	0.886741i	$0.347036\pi$
$998$	11.6112	0.367546
$999$	14.9680	0.473567

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.f.1.16	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.f.1.16	✓	31	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)

\(f(q)\)	\(=\)	\(q-0.485073 q^{2} -0.214641 q^{3} -1.76470 q^{4} -1.00000 q^{5} +0.104117 q^{6} +3.34739 q^{7} +1.82616 q^{8} -2.95393 q^{9} +O(q^{10})\)	\(q-0.485073 q^{2} -0.214641 q^{3} -1.76470 q^{4} -1.00000 q^{5} +0.104117 q^{6} +3.34739 q^{7} +1.82616 q^{8} -2.95393 q^{9} +0.485073 q^{10} +1.00000 q^{11} +0.378778 q^{12} +5.34868 q^{13} -1.62373 q^{14} +0.214641 q^{15} +2.64359 q^{16} -7.63283 q^{17} +1.43287 q^{18} -5.15261 q^{19} +1.76470 q^{20} -0.718487 q^{21} -0.485073 q^{22} -1.25741 q^{23} -0.391968 q^{24} +1.00000 q^{25} -2.59450 q^{26} +1.27796 q^{27} -5.90715 q^{28} -3.65158 q^{29} -0.104117 q^{30} +7.44817 q^{31} -4.93465 q^{32} -0.214641 q^{33} +3.70248 q^{34} -3.34739 q^{35} +5.21281 q^{36} +11.7124 q^{37} +2.49939 q^{38} -1.14805 q^{39} -1.82616 q^{40} -11.6926 q^{41} +0.348519 q^{42} -1.02945 q^{43} -1.76470 q^{44} +2.95393 q^{45} +0.609933 q^{46} +9.09942 q^{47} -0.567423 q^{48} +4.20500 q^{49} -0.485073 q^{50} +1.63832 q^{51} -9.43884 q^{52} -0.0737022 q^{53} -0.619903 q^{54} -1.00000 q^{55} +6.11285 q^{56} +1.10596 q^{57} +1.77128 q^{58} -12.5976 q^{59} -0.378778 q^{60} +0.307979 q^{61} -3.61290 q^{62} -9.88794 q^{63} -2.89352 q^{64} -5.34868 q^{65} +0.104117 q^{66} +2.23434 q^{67} +13.4697 q^{68} +0.269891 q^{69} +1.62373 q^{70} -13.1123 q^{71} -5.39433 q^{72} +1.00000 q^{73} -5.68139 q^{74} -0.214641 q^{75} +9.09284 q^{76} +3.34739 q^{77} +0.556887 q^{78} -1.94585 q^{79} -2.64359 q^{80} +8.58749 q^{81} +5.67176 q^{82} +11.2555 q^{83} +1.26792 q^{84} +7.63283 q^{85} +0.499359 q^{86} +0.783779 q^{87} +1.82616 q^{88} -1.89737 q^{89} -1.43287 q^{90} +17.9041 q^{91} +2.21895 q^{92} -1.59868 q^{93} -4.41388 q^{94} +5.15261 q^{95} +1.05918 q^{96} +13.1615 q^{97} -2.03973 q^{98} -2.95393 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9	\( 31 q - 7 q^{2} - 4 q^{3} + 39 q^{4} - 31 q^{5} - 5 q^{6} - 11 q^{7} - 24 q^{8} + 31 q^{9} + 7 q^{10} + 31 q^{11} - 4 q^{12} - 24 q^{13} - 9 q^{14} + 4 q^{15} + 43 q^{16} - 49 q^{17} - 35 q^{18} - 22 q^{19} - 39 q^{20} - 8 q^{21} - 7 q^{22} - q^{23} - 13 q^{24} + 31 q^{25} - 9 q^{26} - 22 q^{27} - 34 q^{28} - 12 q^{29} + 5 q^{30} + 4 q^{31} - 45 q^{32} - 4 q^{33} + 2 q^{34} + 11 q^{35} + 34 q^{36} - 18 q^{37} - 7 q^{38} - q^{39} + 24 q^{40} - 58 q^{41} - 21 q^{42} - 41 q^{43} + 39 q^{44} - 31 q^{45} + 23 q^{46} - 31 q^{47} - 29 q^{48} + 44 q^{49} - 7 q^{50} + 8 q^{51} - 89 q^{52} - 46 q^{53} - 47 q^{54} - 31 q^{55} + 10 q^{56} - 47 q^{57} - 34 q^{58} - 9 q^{59} + 4 q^{60} - 5 q^{61} - 50 q^{62} - 61 q^{63} + 78 q^{64} + 24 q^{65} - 5 q^{66} + q^{67} - 115 q^{68} - 19 q^{69} + 9 q^{70} - 8 q^{71} - 93 q^{72} + 31 q^{73} - 19 q^{74} - 4 q^{75} - 7 q^{76} - 11 q^{77} + 57 q^{78} - 43 q^{80} + 43 q^{81} + 20 q^{82} - 29 q^{83} - 32 q^{84} + 49 q^{85} + 25 q^{86} - 62 q^{87} - 24 q^{88} - 77 q^{89} + 35 q^{90} - 11 q^{91} - 25 q^{92} - 38 q^{94} + 22 q^{95} - 23 q^{96} - 39 q^{97} - 65 q^{98} + 31 q^{99}+O(q^{100}) \) 31 * q - 7 * q^2 - 4 * q^3 + 39 * q^4 - 31 * q^5 - 5 * q^6 - 11 * q^7 - 24 * q^8 + 31 * q^9 + 7 * q^10 + 31 * q^11 - 4 * q^12 - 24 * q^13 - 9 * q^14 + 4 * q^15 + 43 * q^16 - 49 * q^17 - 35 * q^18 - 22 * q^19 - 39 * q^20 - 8 * q^21 - 7 * q^22 - q^23 - 13 * q^24 + 31 * q^25 - 9 * q^26 - 22 * q^27 - 34 * q^28 - 12 * q^29 + 5 * q^30 + 4 * q^31 - 45 * q^32 - 4 * q^33 + 2 * q^34 + 11 * q^35 + 34 * q^36 - 18 * q^37 - 7 * q^38 - q^39 + 24 * q^40 - 58 * q^41 - 21 * q^42 - 41 * q^43 + 39 * q^44 - 31 * q^45 + 23 * q^46 - 31 * q^47 - 29 * q^48 + 44 * q^49 - 7 * q^50 + 8 * q^51 - 89 * q^52 - 46 * q^53 - 47 * q^54 - 31 * q^55 + 10 * q^56 - 47 * q^57 - 34 * q^58 - 9 * q^59 + 4 * q^60 - 5 * q^61 - 50 * q^62 - 61 * q^63 + 78 * q^64 + 24 * q^65 - 5 * q^66 + q^67 - 115 * q^68 - 19 * q^69 + 9 * q^70 - 8 * q^71 - 93 * q^72 + 31 * q^73 - 19 * q^74 - 4 * q^75 - 7 * q^76 - 11 * q^77 + 57 * q^78 - 43 * q^80 + 43 * q^81 + 20 * q^82 - 29 * q^83 - 32 * q^84 + 49 * q^85 + 25 * q^86 - 62 * q^87 - 24 * q^88 - 77 * q^89 + 35 * q^90 - 11 * q^91 - 25 * q^92 - 38 * q^94 + 22 * q^95 - 23 * q^96 - 39 * q^97 - 65 * q^98 + 31 * q^99

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