LMFDB - Embedded newform 4015.2.a.h.1.18

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:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
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)

$f(q)$	$=$	$q-0.199490 q^{2} -3.23393 q^{3} -1.96020 q^{4} +1.00000 q^{5} +0.645135 q^{6} -5.08849 q^{7} +0.790020 q^{8} +7.45829 q^{9} +O(q^{10})$	\(q-0.199490 q^{2} -3.23393 q^{3} -1.96020 q^{4} +1.00000 q^{5} +0.645135 q^{6} -5.08849 q^{7} +0.790020 q^{8} +7.45829 q^{9} -0.199490 q^{10} +1.00000 q^{11} +6.33916 q^{12} +1.81391 q^{13} +1.01510 q^{14} -3.23393 q^{15} +3.76281 q^{16} +2.44895 q^{17} -1.48785 q^{18} -3.81160 q^{19} -1.96020 q^{20} +16.4558 q^{21} -0.199490 q^{22} +1.59753 q^{23} -2.55487 q^{24} +1.00000 q^{25} -0.361857 q^{26} -14.4178 q^{27} +9.97449 q^{28} -0.667100 q^{29} +0.645135 q^{30} -0.936457 q^{31} -2.33068 q^{32} -3.23393 q^{33} -0.488540 q^{34} -5.08849 q^{35} -14.6198 q^{36} -9.86168 q^{37} +0.760375 q^{38} -5.86606 q^{39} +0.790020 q^{40} +1.75199 q^{41} -3.28277 q^{42} -1.98661 q^{43} -1.96020 q^{44} +7.45829 q^{45} -0.318690 q^{46} +8.88010 q^{47} -12.1686 q^{48} +18.8928 q^{49} -0.199490 q^{50} -7.91971 q^{51} -3.55564 q^{52} -7.64714 q^{53} +2.87620 q^{54} +1.00000 q^{55} -4.02001 q^{56} +12.3264 q^{57} +0.133080 q^{58} -11.6715 q^{59} +6.33916 q^{60} -4.97347 q^{61} +0.186814 q^{62} -37.9514 q^{63} -7.06067 q^{64} +1.81391 q^{65} +0.645135 q^{66} -13.1510 q^{67} -4.80043 q^{68} -5.16628 q^{69} +1.01510 q^{70} +7.86330 q^{71} +5.89220 q^{72} +1.00000 q^{73} +1.96730 q^{74} -3.23393 q^{75} +7.47151 q^{76} -5.08849 q^{77} +1.17022 q^{78} -3.69416 q^{79} +3.76281 q^{80} +24.2512 q^{81} -0.349504 q^{82} -15.6546 q^{83} -32.2568 q^{84} +2.44895 q^{85} +0.396308 q^{86} +2.15735 q^{87} +0.790020 q^{88} +1.50523 q^{89} -1.48785 q^{90} -9.23009 q^{91} -3.13148 q^{92} +3.02843 q^{93} -1.77149 q^{94} -3.81160 q^{95} +7.53726 q^{96} -2.22058 q^{97} -3.76891 q^{98} +7.45829 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) $ 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * 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 $

$2$	−0.199490	−0.141061	−0.0705303	−	0.997510i	$-0.522469\pi$
$2$	−0.199490	−0.141061	−0.0705303	+	0.997510i	$0.522469\pi$
$3$	−3.23393	−1.86711	−0.933554	−	0.358436i	$-0.883310\pi$
$3$	−3.23393	−1.86711	−0.933554	+	0.358436i	$0.883310\pi$
$4$	−1.96020	−0.980102
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.645135	0.263375
$7$	−5.08849	−1.92327	−0.961635	−	0.274332i	$-0.911543\pi$
$7$	−5.08849	−1.92327	−0.961635	+	0.274332i	$0.911543\pi$
$8$	0.790020	0.279314
$9$	7.45829	2.48610
$10$	−0.199490	−0.0630842
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	6.33916	1.82996
$13$	1.81391	0.503089	0.251545	−	0.967846i	$-0.419062\pi$
$13$	1.81391	0.503089	0.251545	+	0.967846i	$0.419062\pi$
$14$	1.01510	0.271298
$15$	−3.23393	−0.834996
$16$	3.76281	0.940702
$17$	2.44895	0.593957	0.296978	−	0.954884i	$-0.404021\pi$
$17$	2.44895	0.593957	0.296978	+	0.954884i	$0.404021\pi$
$18$	−1.48785	−0.350690
$19$	−3.81160	−0.874441	−0.437220	−	0.899354i	$-0.644037\pi$
$19$	−3.81160	−0.874441	−0.437220	+	0.899354i	$0.644037\pi$
$20$	−1.96020	−0.438315
$21$	16.4558	3.59095
$22$	−0.199490	−0.0425314
$23$	1.59753	0.333107	0.166554	−	0.986032i	$-0.446736\pi$
$23$	1.59753	0.333107	0.166554	+	0.986032i	$0.446736\pi$
$24$	−2.55487	−0.521510
$25$	1.00000	0.200000
$26$	−0.361857	−0.0709660
$27$	−14.4178	−2.77470
$28$	9.97449	1.88500
$29$	−0.667100	−0.123877	−0.0619387	−	0.998080i	$-0.519728\pi$
$29$	−0.667100	−0.123877	−0.0619387	+	0.998080i	$0.519728\pi$
$30$	0.645135	0.117785
$31$	−0.936457	−0.168193	−0.0840963	−	0.996458i	$-0.526800\pi$
$31$	−0.936457	−0.168193	−0.0840963	+	0.996458i	$0.526800\pi$
$32$	−2.33068	−0.412010
$33$	−3.23393	−0.562955
$34$	−0.488540	−0.0837838
$35$	−5.08849	−0.860112
$36$	−14.6198	−2.43663
$37$	−9.86168	−1.62125	−0.810625	−	0.585565i	$-0.800873\pi$
$37$	−9.86168	−1.62125	−0.810625	+	0.585565i	$0.800873\pi$
$38$	0.760375	0.123349
$39$	−5.86606	−0.939322
$40$	0.790020	0.124913
$41$	1.75199	0.273615	0.136807	−	0.990598i	$-0.456316\pi$
$41$	1.75199	0.273615	0.136807	+	0.990598i	$0.456316\pi$
$42$	−3.28277	−0.506542
$43$	−1.98661	−0.302955	−0.151478	−	0.988461i	$-0.548403\pi$
$43$	−1.98661	−0.302955	−0.151478	+	0.988461i	$0.548403\pi$
$44$	−1.96020	−0.295512
$45$	7.45829	1.11182
$46$	−0.318690	−0.0469883
$47$	8.88010	1.29530	0.647648	−	0.761940i	$-0.275753\pi$
$47$	8.88010	1.29530	0.647648	+	0.761940i	$0.275753\pi$
$48$	−12.1686	−1.75639
$49$	18.8928	2.69897
$50$	−0.199490	−0.0282121
$51$	−7.91971	−1.10898
$52$	−3.55564	−0.493079
$53$	−7.64714	−1.05041	−0.525207	−	0.850974i	$-0.676012\pi$
$53$	−7.64714	−1.05041	−0.525207	+	0.850974i	$0.676012\pi$
$54$	2.87620	0.391401
$55$	1.00000	0.134840
$56$	−4.02001	−0.537197
$57$	12.3264	1.63268
$58$	0.133080	0.0174742
$59$	−11.6715	−1.51950	−0.759749	−	0.650216i	$-0.774678\pi$
$59$	−11.6715	−1.51950	−0.759749	+	0.650216i	$0.774678\pi$
$60$	6.33916	0.818382
$61$	−4.97347	−0.636787	−0.318394	−	0.947959i	$-0.603143\pi$
$61$	−4.97347	−0.636787	−0.318394	+	0.947959i	$0.603143\pi$
$62$	0.186814	0.0237253
$63$	−37.9514	−4.78143
$64$	−7.06067	−0.882583
$65$	1.81391	0.224988
$66$	0.645135	0.0794107
$67$	−13.1510	−1.60665	−0.803323	−	0.595543i	$-0.796937\pi$
$67$	−13.1510	−1.60665	−0.803323	+	0.595543i	$0.796937\pi$
$68$	−4.80043	−0.582138
$69$	−5.16628	−0.621947
$70$	1.01510	0.121328
$71$	7.86330	0.933202	0.466601	−	0.884468i	$-0.345478\pi$
$71$	7.86330	0.933202	0.466601	+	0.884468i	$0.345478\pi$
$72$	5.89220	0.694402
$73$	1.00000	0.117041
$73$	1.00000	0.117041
$74$	1.96730	0.228694
$75$	−3.23393	−0.373422
$76$	7.47151	0.857041
$77$	−5.08849	−0.579888
$78$	1.17022	0.132501
$79$	−3.69416	−0.415626	−0.207813	−	0.978169i	$-0.566635\pi$
$79$	−3.69416	−0.415626	−0.207813	+	0.978169i	$0.566635\pi$
$80$	3.76281	0.420695
$81$	24.2512	2.69458
$82$	−0.349504	−0.0385962
$83$	−15.6546	−1.71831	−0.859157	−	0.511712i	$-0.829011\pi$
$83$	−15.6546	−1.71831	−0.859157	+	0.511712i	$0.829011\pi$
$84$	−32.2568	−3.51950
$85$	2.44895	0.265625
$86$	0.396308	0.0427350
$87$	2.15735	0.231293
$88$	0.790020	0.0842164
$89$	1.50523	0.159554	0.0797772	−	0.996813i	$-0.474579\pi$
$89$	1.50523	0.159554	0.0797772	+	0.996813i	$0.474579\pi$
$90$	−1.48785	−0.156833
$91$	−9.23009	−0.967576
$92$	−3.13148	−0.326479
$93$	3.02843	0.314034
$94$	−1.77149	−0.182715
$95$	−3.81160	−0.391062
$96$	7.53726	0.769268
$97$	−2.22058	−0.225465	−0.112733	−	0.993625i	$-0.535960\pi$
$97$	−2.22058	−0.225465	−0.112733	+	0.993625i	$0.535960\pi$
$98$	−3.76891	−0.380718
$99$	7.45829	0.749586
$100$	−1.96020	−0.196020
$101$	−12.3903	−1.23289	−0.616443	−	0.787400i	$-0.711427\pi$
$101$	−12.3903	−1.23289	−0.616443	+	0.787400i	$0.711427\pi$
$102$	1.57990	0.156434
$103$	10.5134	1.03592	0.517959	−	0.855405i	$-0.326692\pi$
$103$	10.5134	1.03592	0.517959	+	0.855405i	$0.326692\pi$
$104$	1.43303	0.140520
$105$	16.4558	1.60592
$106$	1.52553	0.148172
$107$	−0.303178	−0.0293093	−0.0146546	−	0.999893i	$-0.504665\pi$
$107$	−0.303178	−0.0293093	−0.0146546	+	0.999893i	$0.504665\pi$
$108$	28.2618	2.71949
$109$	16.3308	1.56421	0.782104	−	0.623148i	$-0.214146\pi$
$109$	16.3308	1.56421	0.782104	+	0.623148i	$0.214146\pi$
$110$	−0.199490	−0.0190206
$111$	31.8920	3.02705
$112$	−19.1470	−1.80922
$113$	6.10228	0.574054	0.287027	−	0.957922i	$-0.407333\pi$
$113$	6.10228	0.574054	0.287027	+	0.957922i	$0.407333\pi$
$114$	−2.45900	−0.230306
$115$	1.59753	0.148970
$116$	1.30765	0.121412
$117$	13.5287	1.25073
$118$	2.32834	0.214341
$119$	−12.4614	−1.14234
$120$	−2.55487	−0.233226
$121$	1.00000	0.0909091
$122$	0.992155	0.0898255
$123$	−5.66580	−0.510868
$124$	1.83565	0.164846
$125$	1.00000	0.0894427
$126$	7.57093	0.674472
$127$	−17.9997	−1.59722	−0.798608	−	0.601851i	$-0.794430\pi$
$127$	−17.9997	−1.59722	−0.798608	+	0.601851i	$0.794430\pi$
$128$	6.06989	0.536508
$129$	6.42455	0.565650
$130$	−0.361857	−0.0317370
$131$	4.98491	0.435534	0.217767	−	0.976001i	$-0.430123\pi$
$131$	4.98491	0.435534	0.217767	+	0.976001i	$0.430123\pi$
$132$	6.33916	0.551753
$133$	19.3953	1.68179
$134$	2.62348	0.226635
$135$	−14.4178	−1.24088
$136$	1.93472	0.165901
$137$	−8.45540	−0.722394	−0.361197	−	0.932490i	$-0.617632\pi$
$137$	−8.45540	−0.722394	−0.361197	+	0.932490i	$0.617632\pi$
$138$	1.03062	0.0877322
$139$	19.4886	1.65301	0.826503	−	0.562933i	$-0.190327\pi$
$139$	19.4886	1.65301	0.826503	+	0.562933i	$0.190327\pi$
$140$	9.97449	0.842998
$141$	−28.7176	−2.41846
$142$	−1.56865	−0.131638
$143$	1.81391	0.151687
$144$	28.0641	2.33867
$145$	−0.667100	−0.0553996
$146$	−0.199490	−0.0165099
$147$	−61.0979	−5.03927
$148$	19.3309	1.58899
$149$	17.9370	1.46946	0.734728	−	0.678362i	$-0.237310\pi$
$149$	17.9370	1.46946	0.734728	+	0.678362i	$0.237310\pi$
$150$	0.645135	0.0526751
$151$	19.1038	1.55464	0.777322	−	0.629103i	$-0.216578\pi$
$151$	19.1038	1.55464	0.777322	+	0.629103i	$0.216578\pi$
$152$	−3.01124	−0.244244
$153$	18.2649	1.47663
$154$	1.01510	0.0817993
$155$	−0.936457	−0.0752180
$156$	11.4987	0.920631
$157$	−9.88667	−0.789042	−0.394521	−	0.918887i	$-0.629089\pi$
$157$	−9.88667	−0.789042	−0.394521	+	0.918887i	$0.629089\pi$
$158$	0.736947	0.0586284
$159$	24.7303	1.96124
$160$	−2.33068	−0.184257
$161$	−8.12900	−0.640655
$162$	−4.83786	−0.380098
$163$	6.03179	0.472447	0.236223	−	0.971699i	$-0.424090\pi$
$163$	6.03179	0.472447	0.236223	+	0.971699i	$0.424090\pi$
$164$	−3.43425	−0.268170
$165$	−3.23393	−0.251761
$166$	3.12293	0.242386
$167$	−7.84550	−0.607103	−0.303551	−	0.952815i	$-0.598172\pi$
$167$	−7.84550	−0.607103	−0.303551	+	0.952815i	$0.598172\pi$
$168$	13.0004	1.00300
$169$	−9.70972	−0.746901
$170$	−0.488540	−0.0374693
$171$	−28.4280	−2.17394
$172$	3.89416	0.296927
$173$	−5.16279	−0.392520	−0.196260	−	0.980552i	$-0.562880\pi$
$173$	−5.16279	−0.392520	−0.196260	+	0.980552i	$0.562880\pi$
$174$	−0.430370	−0.0326263
$175$	−5.08849	−0.384654
$176$	3.76281	0.283632
$177$	37.7448	2.83707
$178$	−0.300278	−0.0225068
$179$	−19.1713	−1.43293	−0.716467	−	0.697621i	$-0.754242\pi$
$179$	−19.1713	−1.43293	−0.716467	+	0.697621i	$0.754242\pi$
$180$	−14.6198	−1.08969
$181$	−8.14103	−0.605118	−0.302559	−	0.953131i	$-0.597841\pi$
$181$	−8.14103	−0.605118	−0.302559	+	0.953131i	$0.597841\pi$
$182$	1.84131	0.136487
$183$	16.0838	1.18895
$184$	1.26208	0.0930416
$185$	−9.86168	−0.725045
$186$	−0.604141	−0.0442978
$187$	2.44895	0.179085
$188$	−17.4068	−1.26952
$189$	73.3648	5.33650
$190$	0.760375	0.0551634
$191$	3.40543	0.246408	0.123204	−	0.992381i	$-0.460683\pi$
$191$	3.40543	0.246408	0.123204	+	0.992381i	$0.460683\pi$
$192$	22.8337	1.64788
$193$	−13.0471	−0.939148	−0.469574	−	0.882893i	$-0.655592\pi$
$193$	−13.0471	−0.939148	−0.469574	+	0.882893i	$0.655592\pi$
$194$	0.442982	0.0318043
$195$	−5.86606	−0.420078
$196$	−37.0337	−2.64526
$197$	−21.8240	−1.55490	−0.777449	−	0.628946i	$-0.783487\pi$
$197$	−21.8240	−1.55490	−0.777449	+	0.628946i	$0.783487\pi$
$198$	−1.48785	−0.105737
$199$	13.8430	0.981303	0.490651	−	0.871356i	$-0.336759\pi$
$199$	13.8430	0.981303	0.490651	+	0.871356i	$0.336759\pi$
$200$	0.790020	0.0558629
$201$	42.5293	2.99978
$202$	2.47175	0.173911
$203$	3.39453	0.238250
$204$	15.5242	1.08691
$205$	1.75199	0.122364
$206$	−2.09732	−0.146127
$207$	11.9148	0.828136
$208$	6.82541	0.473257
$209$	−3.81160	−0.263654
$210$	−3.28277	−0.226532
$211$	5.68107	0.391101	0.195551	−	0.980694i	$-0.437351\pi$
$211$	5.68107	0.391101	0.195551	+	0.980694i	$0.437351\pi$
$212$	14.9899	1.02951
$213$	−25.4293	−1.74239
$214$	0.0604808	0.00413438
$215$	−1.98661	−0.135486
$216$	−11.3903	−0.775014
$217$	4.76515	0.323480
$218$	−3.25783	−0.220648
$219$	−3.23393	−0.218529
$220$	−1.96020	−0.132157
$221$	4.44218	0.298813
$222$	−6.36212	−0.426998
$223$	15.6168	1.04578	0.522889	−	0.852401i	$-0.324854\pi$
$223$	15.6168	1.04578	0.522889	+	0.852401i	$0.324854\pi$
$224$	11.8597	0.792407
$225$	7.45829	0.497219
$226$	−1.21734	−0.0809764
$227$	17.6442	1.17109	0.585543	−	0.810641i	$-0.300881\pi$
$227$	17.6442	1.17109	0.585543	+	0.810641i	$0.300881\pi$
$228$	−24.1623	−1.60019
$229$	1.85113	0.122326	0.0611631	−	0.998128i	$-0.480519\pi$
$229$	1.85113	0.122326	0.0611631	+	0.998128i	$0.480519\pi$
$230$	−0.318690	−0.0210138
$231$	16.4558	1.08271
$232$	−0.527022	−0.0346007
$233$	17.6958	1.15929	0.579644	−	0.814870i	$-0.303192\pi$
$233$	17.6958	1.15929	0.579644	+	0.814870i	$0.303192\pi$
$234$	−2.69883	−0.176428
$235$	8.88010	0.579274
$236$	22.8785	1.48926
$237$	11.9467	0.776018
$238$	2.48593	0.161139
$239$	−13.3055	−0.860663	−0.430331	−	0.902671i	$-0.641603\pi$
$239$	−13.3055	−0.860663	−0.430331	+	0.902671i	$0.641603\pi$
$240$	−12.1686	−0.785483
$241$	17.2767	1.11289	0.556446	−	0.830884i	$-0.312165\pi$
$241$	17.2767	1.11289	0.556446	+	0.830884i	$0.312165\pi$
$242$	−0.199490	−0.0128237
$243$	−35.1732	−2.25636
$244$	9.74901	0.624116
$245$	18.8928	1.20701
$246$	1.13027	0.0720634
$247$	−6.91391	−0.439922
$248$	−0.739820	−0.0469786
$249$	50.6258	3.20828
$250$	−0.199490	−0.0126168
$251$	−16.6467	−1.05073	−0.525367	−	0.850876i	$-0.676072\pi$
$251$	−16.6467	−1.05073	−0.525367	+	0.850876i	$0.676072\pi$
$252$	74.3926	4.68629
$253$	1.59753	0.100436
$254$	3.59076	0.225304
$255$	−7.91971	−0.495952
$256$	12.9105	0.806903
$257$	−20.2119	−1.26078	−0.630392	−	0.776277i	$-0.717106\pi$
$257$	−20.2119	−1.26078	−0.630392	+	0.776277i	$0.717106\pi$
$258$	−1.28163	−0.0797910
$259$	50.1811	3.11810
$260$	−3.55564	−0.220511
$261$	−4.97542	−0.307971
$262$	−0.994439	−0.0614366
$263$	2.81916	0.173837	0.0869183	−	0.996215i	$-0.472298\pi$
$263$	2.81916	0.173837	0.0869183	+	0.996215i	$0.472298\pi$
$264$	−2.55487	−0.157241
$265$	−7.64714	−0.469760
$266$	−3.86916	−0.237234
$267$	−4.86781	−0.297905
$268$	25.7786	1.57468
$269$	−7.89372	−0.481289	−0.240644	−	0.970613i	$-0.577359\pi$
$269$	−7.89372	−0.481289	−0.240644	+	0.970613i	$0.577359\pi$
$270$	2.87620	0.175040
$271$	−5.05602	−0.307131	−0.153566	−	0.988138i	$-0.549076\pi$
$271$	−5.05602	−0.307131	−0.153566	+	0.988138i	$0.549076\pi$
$272$	9.21491	0.558736
$273$	29.8494	1.80657
$274$	1.68677	0.101901
$275$	1.00000	0.0603023
$276$	10.1270	0.609572
$277$	9.11389	0.547601	0.273800	−	0.961787i	$-0.411719\pi$
$277$	9.11389	0.547601	0.273800	+	0.961787i	$0.411719\pi$
$278$	−3.88779	−0.233174
$279$	−6.98436	−0.418143
$280$	−4.02001	−0.240242
$281$	15.1470	0.903597	0.451798	−	0.892120i	$-0.350783\pi$
$281$	15.1470	0.903597	0.451798	+	0.892120i	$0.350783\pi$
$282$	5.72887	0.341149
$283$	11.3872	0.676901	0.338450	−	0.940984i	$-0.390097\pi$
$283$	11.3872	0.676901	0.338450	+	0.940984i	$0.390097\pi$
$284$	−15.4137	−0.914633
$285$	12.3264	0.730155
$286$	−0.361857	−0.0213971
$287$	−8.91498	−0.526235
$288$	−17.3829	−1.02430
$289$	−11.0027	−0.647216
$290$	0.133080	0.00781470
$291$	7.18118	0.420968
$292$	−1.96020	−0.114712
$293$	24.6240	1.43855	0.719275	−	0.694725i	$-0.244474\pi$
$293$	24.6240	1.43855	0.719275	+	0.694725i	$0.244474\pi$
$294$	12.1884	0.710842
$295$	−11.6715	−0.679540
$296$	−7.79093	−0.452838
$297$	−14.4178	−0.836604
$298$	−3.57825	−0.207282
$299$	2.89777	0.167583
$300$	6.33916	0.365991
$301$	10.1089	0.582665
$302$	−3.81101	−0.219299
$303$	40.0695	2.30193
$304$	−14.3423	−0.822588
$305$	−4.97347	−0.284780
$306$	−3.64367	−0.208295
$307$	6.02662	0.343958	0.171979	−	0.985101i	$-0.444984\pi$
$307$	6.02662	0.343958	0.171979	+	0.985101i	$0.444984\pi$
$308$	9.97449	0.568349
$309$	−33.9997	−1.93417
$310$	0.186814	0.0106103
$311$	−32.9998	−1.87125	−0.935624	−	0.352998i	$-0.885162\pi$
$311$	−32.9998	−1.87125	−0.935624	+	0.352998i	$0.885162\pi$
$312$	−4.63431	−0.262366
$313$	−7.42152	−0.419489	−0.209745	−	0.977756i	$-0.567263\pi$
$313$	−7.42152	−0.419489	−0.209745	+	0.977756i	$0.567263\pi$
$314$	1.97229	0.111303
$315$	−37.9514	−2.13832
$316$	7.24131	0.407356
$317$	−17.6516	−0.991415	−0.495707	−	0.868490i	$-0.665091\pi$
$317$	−17.6516	−0.991415	−0.495707	+	0.868490i	$0.665091\pi$
$318$	−4.93344	−0.276653
$319$	−0.667100	−0.0373504
$320$	−7.06067	−0.394703
$321$	0.980454	0.0547236
$322$	1.62165	0.0903712
$323$	−9.33440	−0.519380
$324$	−47.5373	−2.64096
$325$	1.81391	0.100618
$326$	−1.20328	−0.0666436
$327$	−52.8127	−2.92055
$328$	1.38411	0.0764245
$329$	−45.1863	−2.49120
$330$	0.645135	0.0355135
$331$	35.4038	1.94597	0.972986	−	0.230865i	$-0.0741557\pi$
$331$	35.4038	1.94597	0.972986	+	0.230865i	$0.0741557\pi$
$332$	30.6862	1.68412
$333$	−73.5512	−4.03058
$334$	1.56510	0.0856382
$335$	−13.1510	−0.718514
$336$	61.9201	3.37802
$337$	3.52978	0.192279	0.0961396	−	0.995368i	$-0.469350\pi$
$337$	3.52978	0.192279	0.0961396	+	0.995368i	$0.469350\pi$
$338$	1.93699	0.105358
$339$	−19.7343	−1.07182
$340$	−4.80043	−0.260340
$341$	−0.936457	−0.0507120
$342$	5.67109	0.306658
$343$	−60.5163	−3.26757
$344$	−1.56946	−0.0846197
$345$	−5.16628	−0.278143
$346$	1.02992	0.0553690
$347$	15.2212	0.817118	0.408559	−	0.912732i	$-0.366031\pi$
$347$	15.2212	0.817118	0.408559	+	0.912732i	$0.366031\pi$
$348$	−4.22885	−0.226690
$349$	−15.8857	−0.850341	−0.425171	−	0.905113i	$-0.639786\pi$
$349$	−15.8857	−0.850341	−0.425171	+	0.905113i	$0.639786\pi$
$350$	1.01510	0.0542595
$351$	−26.1526	−1.39592
$352$	−2.33068	−0.124226
$353$	14.0821	0.749517	0.374758	−	0.927122i	$-0.377726\pi$
$353$	14.0821	0.749517	0.374758	+	0.927122i	$0.377726\pi$
$354$	−7.52969	−0.400199
$355$	7.86330	0.417341
$356$	−2.95056	−0.156379
$357$	40.2994	2.13287
$358$	3.82449	0.202130
$359$	8.88663	0.469018	0.234509	−	0.972114i	$-0.424652\pi$
$359$	8.88663	0.469018	0.234509	+	0.972114i	$0.424652\pi$
$360$	5.89220	0.310546
$361$	−4.47172	−0.235353
$362$	1.62405	0.0853583
$363$	−3.23393	−0.169737
$364$	18.0929	0.948323
$365$	1.00000	0.0523424
$366$	−3.20856	−0.167714
$367$	23.6621	1.23515	0.617575	−	0.786512i	$-0.288115\pi$
$367$	23.6621	1.23515	0.617575	+	0.786512i	$0.288115\pi$
$368$	6.01118	0.313354
$369$	13.0668	0.680232
$370$	1.96730	0.102275
$371$	38.9124	2.02023
$372$	−5.93635	−0.307785
$373$	24.0619	1.24588	0.622939	−	0.782271i	$-0.285939\pi$
$373$	24.0619	1.24588	0.622939	+	0.782271i	$0.285939\pi$
$374$	−0.488540	−0.0252618
$375$	−3.23393	−0.166999
$376$	7.01546	0.361795
$377$	−1.21006	−0.0623213
$378$	−14.6355	−0.752770
$379$	−26.9520	−1.38443	−0.692215	−	0.721692i	$-0.743365\pi$
$379$	−26.9520	−1.38443	−0.692215	+	0.721692i	$0.743365\pi$
$380$	7.47151	0.383280
$381$	58.2098	2.98218
$382$	−0.679348	−0.0347585
$383$	6.83061	0.349028	0.174514	−	0.984655i	$-0.444165\pi$
$383$	6.83061	0.349028	0.174514	+	0.984655i	$0.444165\pi$
$384$	−19.6296	−1.00172
$385$	−5.08849	−0.259334
$386$	2.60275	0.132477
$387$	−14.8167	−0.753176
$388$	4.35278	0.220979
$389$	17.9698	0.911104	0.455552	−	0.890209i	$-0.349442\pi$
$389$	17.9698	0.911104	0.455552	+	0.890209i	$0.349442\pi$
$390$	1.17022	0.0592564
$391$	3.91225	0.197851
$392$	14.9257	0.753860
$393$	−16.1208	−0.813189
$394$	4.35367	0.219335
$395$	−3.69416	−0.185873
$396$	−14.6198	−0.734671
$397$	7.53954	0.378399	0.189199	−	0.981939i	$-0.439411\pi$
$397$	7.53954	0.378399	0.189199	+	0.981939i	$0.439411\pi$
$398$	−2.76153	−0.138423
$399$	−62.7230	−3.14008
$400$	3.76281	0.188140
$401$	12.6850	0.633459	0.316730	−	0.948516i	$-0.397415\pi$
$401$	12.6850	0.633459	0.316730	+	0.948516i	$0.397415\pi$
$402$	−8.48416	−0.423151
$403$	−1.69865	−0.0846159
$404$	24.2876	1.20835
$405$	24.2512	1.20505
$406$	−0.677175	−0.0336076
$407$	−9.86168	−0.488825
$408$	−6.25673	−0.309754
$409$	34.1896	1.69057	0.845283	−	0.534319i	$-0.179432\pi$
$409$	34.1896	1.69057	0.845283	+	0.534319i	$0.179432\pi$
$410$	−0.349504	−0.0172608
$411$	27.3442	1.34879
$412$	−20.6085	−1.01531
$413$	59.3903	2.92241
$414$	−2.37688	−0.116817
$415$	−15.6546	−0.768453
$416$	−4.22765	−0.207278
$417$	−63.0249	−3.08634
$418$	0.760375	0.0371912
$419$	−4.80104	−0.234546	−0.117273	−	0.993100i	$-0.537415\pi$
$419$	−4.80104	−0.234546	−0.117273	+	0.993100i	$0.537415\pi$
$420$	−32.2568	−1.57397
$421$	−1.52853	−0.0744961	−0.0372481	−	0.999306i	$-0.511859\pi$
$421$	−1.52853	−0.0744961	−0.0372481	+	0.999306i	$0.511859\pi$
$422$	−1.13332	−0.0551690
$423$	66.2303	3.22023
$424$	−6.04139	−0.293396
$425$	2.44895	0.118791
$426$	5.07289	0.245783
$427$	25.3075	1.22471
$428$	0.594290	0.0287261
$429$	−5.86606	−0.283216
$430$	0.396308	0.0191117
$431$	2.87906	0.138679	0.0693396	−	0.997593i	$-0.477911\pi$
$431$	2.87906	0.138679	0.0693396	+	0.997593i	$0.477911\pi$
$432$	−54.2513	−2.61017
$433$	7.12162	0.342243	0.171122	−	0.985250i	$-0.445261\pi$
$433$	7.12162	0.342243	0.171122	+	0.985250i	$0.445261\pi$
$434$	−0.950600	−0.0456302
$435$	2.15735	0.103437
$436$	−32.0117	−1.53308
$437$	−6.08913	−0.291282
$438$	0.645135	0.0308258
$439$	27.2069	1.29851	0.649257	−	0.760569i	$-0.275080\pi$
$439$	27.2069	1.29851	0.649257	+	0.760569i	$0.275080\pi$
$440$	0.790020	0.0376627
$441$	140.908	6.70989
$442$	−0.886168	−0.0421507
$443$	−28.6887	−1.36304	−0.681521	−	0.731798i	$-0.738681\pi$
$443$	−28.6887	−1.36304	−0.681521	+	0.731798i	$0.738681\pi$
$444$	−62.5147	−2.96682
$445$	1.50523	0.0713549
$446$	−3.11539	−0.147518
$447$	−58.0069	−2.74363
$448$	35.9282	1.69745
$449$	9.30793	0.439268	0.219634	−	0.975582i	$-0.429514\pi$
$449$	9.30793	0.439268	0.219634	+	0.975582i	$0.429514\pi$
$450$	−1.48785	−0.0701380
$451$	1.75199	0.0824979
$452$	−11.9617	−0.562632
$453$	−61.7803	−2.90269
$454$	−3.51984	−0.165194
$455$	−9.23009	−0.432713
$456$	9.73813	0.456030
$457$	−29.0463	−1.35873	−0.679365	−	0.733801i	$-0.737745\pi$
$457$	−29.0463	−1.35873	−0.679365	+	0.733801i	$0.737745\pi$
$458$	−0.369282	−0.0172554
$459$	−35.3083	−1.64805
$460$	−3.13148	−0.146006
$461$	−0.818568	−0.0381245	−0.0190623	−	0.999818i	$-0.506068\pi$
$461$	−0.818568	−0.0381245	−0.0190623	+	0.999818i	$0.506068\pi$
$462$	−3.28277	−0.152728
$463$	15.8732	0.737691	0.368845	−	0.929491i	$-0.379753\pi$
$463$	15.8732	0.737691	0.368845	+	0.929491i	$0.379753\pi$
$464$	−2.51017	−0.116532
$465$	3.02843	0.140440
$466$	−3.53012	−0.163530
$467$	11.5405	0.534032	0.267016	−	0.963692i	$-0.413962\pi$
$467$	11.5405	0.534032	0.267016	+	0.963692i	$0.413962\pi$
$468$	−26.5190	−1.22584
$469$	66.9186	3.09002
$470$	−1.77149	−0.0817127
$471$	31.9728	1.47323
$472$	−9.22071	−0.424418
$473$	−1.98661	−0.0913444
$474$	−2.38323	−0.109466
$475$	−3.81160	−0.174888
$476$	24.4270	1.11961
$477$	−57.0345	−2.61143
$478$	2.65432	0.121406
$479$	−26.6661	−1.21841	−0.609203	−	0.793015i	$-0.708510\pi$
$479$	−26.6661	−1.21841	−0.609203	+	0.793015i	$0.708510\pi$
$480$	7.53726	0.344027
$481$	−17.8882	−0.815633
$482$	−3.44653	−0.156985
$483$	26.2886	1.19617
$484$	−1.96020	−0.0891002
$485$	−2.22058	−0.100831
$486$	7.01670	0.318284
$487$	30.7891	1.39519	0.697595	−	0.716493i	$-0.254254\pi$
$487$	30.7891	1.39519	0.697595	+	0.716493i	$0.254254\pi$
$488$	−3.92914	−0.177864
$489$	−19.5064	−0.882109
$490$	−3.76891	−0.170262
$491$	−35.6631	−1.60945	−0.804726	−	0.593647i	$-0.797688\pi$
$491$	−35.6631	−1.60945	−0.804726	+	0.593647i	$0.797688\pi$
$492$	11.1061	0.500703
$493$	−1.63369	−0.0735778
$494$	1.37925	0.0620556
$495$	7.45829	0.335225
$496$	−3.52371	−0.158219
$497$	−40.0124	−1.79480
$498$	−10.0993	−0.452562
$499$	−34.7460	−1.55544	−0.777722	−	0.628609i	$-0.783625\pi$
$499$	−34.7460	−1.55544	−0.777722	+	0.628609i	$0.783625\pi$
$500$	−1.96020	−0.0876630
$501$	25.3718	1.13353
$502$	3.32086	0.148217
$503$	−19.7827	−0.882065	−0.441032	−	0.897491i	$-0.645388\pi$
$503$	−19.7827	−0.882065	−0.441032	+	0.897491i	$0.645388\pi$
$504$	−29.9824	−1.33552
$505$	−12.3903	−0.551363
$506$	−0.318690	−0.0141675
$507$	31.4005	1.39455
$508$	35.2831	1.56544
$509$	27.4381	1.21617	0.608087	−	0.793871i	$-0.291937\pi$
$509$	27.4381	1.21617	0.608087	+	0.793871i	$0.291937\pi$
$510$	1.57990	0.0699592
$511$	−5.08849	−0.225102
$512$	−14.7153	−0.650330
$513$	54.9548	2.42631
$514$	4.03207	0.177847
$515$	10.5134	0.463277
$516$	−12.5934	−0.554395
$517$	8.88010	0.390546
$518$	−10.0106	−0.439841
$519$	16.6961	0.732877
$520$	1.43303	0.0628424
$521$	18.5762	0.813837	0.406918	−	0.913465i	$-0.366603\pi$
$521$	18.5762	0.813837	0.406918	+	0.913465i	$0.366603\pi$
$522$	0.992546	0.0434426
$523$	41.3607	1.80858	0.904289	−	0.426921i	$-0.140402\pi$
$523$	41.3607	1.80858	0.904289	+	0.426921i	$0.140402\pi$
$524$	−9.77144	−0.426867
$525$	16.4558	0.718191
$526$	−0.562393	−0.0245215
$527$	−2.29333	−0.0998991
$528$	−12.1686	−0.529572
$529$	−20.4479	−0.889040
$530$	1.52553	0.0662646
$531$	−87.0493	−3.77762
$532$	−38.0187	−1.64832
$533$	3.17796	0.137653
$534$	0.971079	0.0420227
$535$	−0.303178	−0.0131075
$536$	−10.3895	−0.448759
$537$	61.9987	2.67544
$538$	1.57472	0.0678908
$539$	18.8928	0.813769
$540$	28.2618	1.21619
$541$	8.82640	0.379477	0.189738	−	0.981835i	$-0.439236\pi$
$541$	8.82640	0.379477	0.189738	+	0.981835i	$0.439236\pi$
$542$	1.00862	0.0433241
$543$	26.3275	1.12982
$544$	−5.70771	−0.244716
$545$	16.3308	0.699535
$546$	−5.95466	−0.254836
$547$	−17.8087	−0.761443	−0.380722	−	0.924690i	$-0.624324\pi$
$547$	−17.8087	−0.761443	−0.380722	+	0.924690i	$0.624324\pi$
$548$	16.5743	0.708019
$549$	−37.0935	−1.58311
$550$	−0.199490	−0.00850627
$551$	2.54272	0.108323
$552$	−4.08147	−0.173719
$553$	18.7977	0.799360
$554$	−1.81813	−0.0772449
$555$	31.8920	1.35374
$556$	−38.2017	−1.62011
$557$	24.5953	1.04214	0.521069	−	0.853515i	$-0.325534\pi$
$557$	24.5953	1.04214	0.521069	+	0.853515i	$0.325534\pi$
$558$	1.39331	0.0589835
$559$	−3.60354	−0.152413
$560$	−19.1470	−0.809109
$561$	−7.91971	−0.334370
$562$	−3.02168	−0.127462
$563$	44.0996	1.85858	0.929288	−	0.369356i	$-0.120422\pi$
$563$	44.0996	1.85858	0.929288	+	0.369356i	$0.120422\pi$
$564$	56.2924	2.37034
$565$	6.10228	0.256725
$566$	−2.27164	−0.0954840
$567$	−123.402	−5.18240
$568$	6.21217	0.260657
$569$	32.8125	1.37557	0.687785	−	0.725915i	$-0.258583\pi$
$569$	32.8125	1.37557	0.687785	+	0.725915i	$0.258583\pi$
$570$	−2.45900	−0.102996
$571$	−41.2285	−1.72536	−0.862679	−	0.505752i	$-0.831215\pi$
$571$	−41.2285	−1.72536	−0.862679	+	0.505752i	$0.831215\pi$
$572$	−3.55564	−0.148669
$573$	−11.0129	−0.460071
$574$	1.77845	0.0742310
$575$	1.59753	0.0666214
$576$	−52.6605	−2.19419
$577$	−21.2172	−0.883282	−0.441641	−	0.897192i	$-0.645604\pi$
$577$	−21.2172	−0.883282	−0.441641	+	0.897192i	$0.645604\pi$
$578$	2.19492	0.0912966
$579$	42.1932	1.75349
$580$	1.30765	0.0542973
$581$	79.6582	3.30478
$582$	−1.43257	−0.0593820
$583$	−7.64714	−0.316712
$584$	0.790020	0.0326913
$585$	13.5287	0.559342
$586$	−4.91224	−0.202923
$587$	20.4094	0.842388	0.421194	−	0.906971i	$-0.361611\pi$
$587$	20.4094	0.842388	0.421194	+	0.906971i	$0.361611\pi$
$588$	119.764	4.93899
$589$	3.56940	0.147074
$590$	2.32834	0.0958564
$591$	70.5774	2.90316
$592$	−37.1076	−1.52511
$593$	3.96830	0.162959	0.0814793	−	0.996675i	$-0.474036\pi$
$593$	3.96830	0.162959	0.0814793	+	0.996675i	$0.474036\pi$
$594$	2.87620	0.118012
$595$	−12.4614	−0.510869
$596$	−35.1602	−1.44022
$597$	−44.7672	−1.83220
$598$	−0.578076	−0.0236393
$599$	−38.4890	−1.57262	−0.786310	−	0.617833i	$-0.788011\pi$
$599$	−38.4890	−1.57262	−0.786310	+	0.617833i	$0.788011\pi$
$600$	−2.55487	−0.104302
$601$	2.95147	0.120393	0.0601965	−	0.998187i	$-0.480827\pi$
$601$	2.95147	0.120393	0.0601965	+	0.998187i	$0.480827\pi$
$602$	−2.01661	−0.0821910
$603$	−98.0837	−3.99428
$604$	−37.4473	−1.52371
$605$	1.00000	0.0406558
$606$	−7.99345	−0.324712
$607$	31.0687	1.26104	0.630521	−	0.776173i	$-0.282841\pi$
$607$	31.0687	1.26104	0.630521	+	0.776173i	$0.282841\pi$
$608$	8.88362	0.360278
$609$	−10.9777	−0.444838
$610$	0.992155	0.0401712
$611$	16.1077	0.651649
$612$	−35.8030	−1.44725
$613$	−24.5415	−0.991224	−0.495612	−	0.868544i	$-0.665056\pi$
$613$	−24.5415	−0.991224	−0.495612	+	0.868544i	$0.665056\pi$
$614$	−1.20225	−0.0485189
$615$	−5.66580	−0.228467
$616$	−4.02001	−0.161971
$617$	−23.0002	−0.925955	−0.462977	−	0.886370i	$-0.653219\pi$
$617$	−23.0002	−0.925955	−0.462977	+	0.886370i	$0.653219\pi$
$618$	6.78259	0.272836
$619$	23.6831	0.951905	0.475952	−	0.879471i	$-0.342103\pi$
$619$	23.6831	0.951905	0.475952	+	0.879471i	$0.342103\pi$
$620$	1.83565	0.0737213
$621$	−23.0328	−0.924273
$622$	6.58313	0.263959
$623$	−7.65937	−0.306866
$624$	−22.0729	−0.883622
$625$	1.00000	0.0400000
$626$	1.48052	0.0591734
$627$	12.3264	0.492270
$628$	19.3799	0.773341
$629$	−24.1507	−0.962952
$630$	7.57093	0.301633
$631$	26.1281	1.04014	0.520071	−	0.854123i	$-0.325905\pi$
$631$	26.1281	1.04014	0.520071	+	0.854123i	$0.325905\pi$
$632$	−2.91846	−0.116090
$633$	−18.3722	−0.730229
$634$	3.52132	0.139850
$635$	−17.9997	−0.714297
$636$	−48.4764	−1.92221
$637$	34.2699	1.35782
$638$	0.133080	0.00526867
$639$	58.6468	2.32003
$640$	6.06989	0.239934
$641$	−5.61450	−0.221759	−0.110880	−	0.993834i	$-0.535367\pi$
$641$	−5.61450	−0.221759	−0.110880	+	0.993834i	$0.535367\pi$
$642$	−0.195591	−0.00771934
$643$	−39.9459	−1.57531	−0.787655	−	0.616116i	$-0.788705\pi$
$643$	−39.9459	−1.57531	−0.787655	+	0.616116i	$0.788705\pi$
$644$	15.9345	0.627907
$645$	6.42455	0.252967
$646$	1.86212	0.0732640
$647$	−25.0996	−0.986768	−0.493384	−	0.869811i	$-0.664240\pi$
$647$	−25.0996	−0.986768	−0.493384	+	0.869811i	$0.664240\pi$
$648$	19.1589	0.752634
$649$	−11.6715	−0.458146
$650$	−0.361857	−0.0141932
$651$	−15.4102	−0.603972
$652$	−11.8235	−0.463046
$653$	22.6910	0.887966	0.443983	−	0.896035i	$-0.353565\pi$
$653$	22.6910	0.887966	0.443983	+	0.896035i	$0.353565\pi$
$654$	10.5356	0.411974
$655$	4.98491	0.194777
$656$	6.59239	0.257390
$657$	7.45829	0.290975
$658$	9.01421	0.351411
$659$	−38.9264	−1.51636	−0.758178	−	0.652047i	$-0.773910\pi$
$659$	−38.9264	−1.51636	−0.758178	+	0.652047i	$0.773910\pi$
$660$	6.33916	0.246751
$661$	−1.79011	−0.0696274	−0.0348137	−	0.999394i	$-0.511084\pi$
$661$	−1.79011	−0.0696274	−0.0348137	+	0.999394i	$0.511084\pi$
$662$	−7.06271	−0.274500
$663$	−14.3657	−0.557916
$664$	−12.3674	−0.479950
$665$	19.3953	0.752117
$666$	14.6727	0.568556
$667$	−1.06571	−0.0412644
$668$	15.3788	0.595023
$669$	−50.5036	−1.95258
$670$	2.62348	0.101354
$671$	−4.97347	−0.191999
$672$	−38.3533	−1.47951
$673$	15.7767	0.608148	0.304074	−	0.952648i	$-0.401653\pi$
$673$	15.7767	0.608148	0.304074	+	0.952648i	$0.401653\pi$
$674$	−0.704154	−0.0271230
$675$	−14.4178	−0.554940
$676$	19.0330	0.732039
$677$	−23.8678	−0.917314	−0.458657	−	0.888614i	$-0.651669\pi$
$677$	−23.8678	−0.917314	−0.458657	+	0.888614i	$0.651669\pi$
$678$	3.93680	0.151192
$679$	11.2994	0.433631
$680$	1.93472	0.0741930
$681$	−57.0600	−2.18655
$682$	0.186814	0.00715346
$683$	20.2845	0.776165	0.388083	−	0.921625i	$-0.373137\pi$
$683$	20.2845	0.776165	0.388083	+	0.921625i	$0.373137\pi$
$684$	55.7247	2.13069
$685$	−8.45540	−0.323064
$686$	12.0724	0.460926
$687$	−5.98642	−0.228396
$688$	−7.47523	−0.284990
$689$	−13.8712	−0.528452
$690$	1.03062	0.0392351
$691$	9.55265	0.363400	0.181700	−	0.983354i	$-0.441840\pi$
$691$	9.55265	0.363400	0.181700	+	0.983354i	$0.441840\pi$
$692$	10.1201	0.384709
$693$	−37.9514	−1.44166
$694$	−3.03648	−0.115263
$695$	19.4886	0.739246
$696$	1.70435	0.0646033
$697$	4.29052	0.162515
$698$	3.16903	0.119950
$699$	−57.2268	−2.16452
$700$	9.97449	0.377000
$701$	32.7484	1.23689	0.618445	−	0.785828i	$-0.287763\pi$
$701$	32.7484	1.23689	0.618445	+	0.785828i	$0.287763\pi$
$702$	5.21718	0.196910
$703$	37.5888	1.41769
$704$	−7.06067	−0.266109
$705$	−28.7176	−1.08157
$706$	−2.80924	−0.105727
$707$	63.0482	2.37117
$708$	−73.9874	−2.78062
$709$	−28.6857	−1.07732	−0.538658	−	0.842525i	$-0.681068\pi$
$709$	−28.6857	−1.07732	−0.538658	+	0.842525i	$0.681068\pi$
$710$	−1.56865	−0.0588703
$711$	−27.5521	−1.03329
$712$	1.18916	0.0445658
$713$	−1.49601	−0.0560262
$714$	−8.03932	−0.300864
$715$	1.81391	0.0678365
$716$	37.5797	1.40442
$717$	43.0291	1.60695
$718$	−1.77279	−0.0661600
$719$	−27.9305	−1.04163	−0.520816	−	0.853669i	$-0.674372\pi$
$719$	−27.9305	−1.04163	−0.520816	+	0.853669i	$0.674372\pi$
$720$	28.0641	1.04589
$721$	−53.4975	−1.99235
$722$	0.892062	0.0331991
$723$	−55.8717	−2.07789
$724$	15.9581	0.593077
$725$	−0.667100	−0.0247755
$726$	0.645135	0.0239432
$727$	43.8990	1.62812	0.814062	−	0.580778i	$-0.197252\pi$
$727$	43.8990	1.62812	0.814062	+	0.580778i	$0.197252\pi$
$728$	−7.29196	−0.270258
$729$	40.9941	1.51830
$730$	−0.199490	−0.00738345
$731$	−4.86510	−0.179942
$732$	−31.5276	−1.16529
$733$	11.5712	0.427391	0.213696	−	0.976900i	$-0.431450\pi$
$733$	11.5712	0.427391	0.213696	+	0.976900i	$0.431450\pi$
$734$	−4.72034	−0.174231
$735$	−61.0979	−2.25363
$736$	−3.72332	−0.137244
$737$	−13.1510	−0.484422
$738$	−2.60670	−0.0959539
$739$	7.11325	0.261665	0.130833	−	0.991404i	$-0.458235\pi$
$739$	7.11325	0.261665	0.130833	+	0.991404i	$0.458235\pi$
$740$	19.3309	0.710618
$741$	22.3591	0.821381
$742$	−7.76263	−0.284975
$743$	33.9716	1.24630	0.623148	−	0.782104i	$-0.285853\pi$
$743$	33.9716	1.24630	0.623148	+	0.782104i	$0.285853\pi$
$744$	2.39252	0.0877142
$745$	17.9370	0.657160
$746$	−4.80010	−0.175744
$747$	−116.756	−4.27189
$748$	−4.80043	−0.175521
$749$	1.54272	0.0563697
$750$	0.645135	0.0235570
$751$	−14.1515	−0.516396	−0.258198	−	0.966092i	$-0.583129\pi$
$751$	−14.1515	−0.516396	−0.258198	+	0.966092i	$0.583129\pi$
$752$	33.4141	1.21849
$753$	53.8344	1.96183
$754$	0.241395	0.00879108
$755$	19.1038	0.695258
$756$	−143.810	−5.23032
$757$	−28.2459	−1.02661	−0.513307	−	0.858205i	$-0.671580\pi$
$757$	−28.2459	−1.02661	−0.513307	+	0.858205i	$0.671580\pi$
$758$	5.37664	0.195288
$759$	−5.16628	−0.187524
$760$	−3.01124	−0.109229
$761$	−40.9436	−1.48420	−0.742101	−	0.670288i	$-0.766171\pi$
$761$	−40.9436	−1.48420	−0.742101	+	0.670288i	$0.766171\pi$
$762$	−11.6123	−0.420668
$763$	−83.0993	−3.00839
$764$	−6.67534	−0.241505
$765$	18.2649	0.660370
$766$	−1.36264	−0.0492340
$767$	−21.1711	−0.764443
$768$	−41.7515	−1.50658
$769$	−24.0881	−0.868641	−0.434320	−	0.900758i	$-0.643011\pi$
$769$	−24.0881	−0.868641	−0.434320	+	0.900758i	$0.643011\pi$
$770$	1.01510	0.0365818
$771$	65.3638	2.35402
$772$	25.5749	0.920460
$773$	25.0757	0.901912	0.450956	−	0.892546i	$-0.351083\pi$
$773$	25.0757	0.901912	0.450956	+	0.892546i	$0.351083\pi$
$774$	2.95578	0.106243
$775$	−0.936457	−0.0336385
$776$	−1.75430	−0.0629757
$777$	−162.282	−5.82184
$778$	−3.58479	−0.128521
$779$	−6.67788	−0.239260
$780$	11.4987	0.411719
$781$	7.86330	0.281371
$782$	−0.780455	−0.0279090
$783$	9.61810	0.343723
$784$	71.0899	2.53892
$785$	−9.88667	−0.352870
$786$	3.21594	0.114709
$787$	−26.3223	−0.938289	−0.469145	−	0.883121i	$-0.655438\pi$
$787$	−26.3223	−0.938289	−0.469145	+	0.883121i	$0.655438\pi$
$788$	42.7796	1.52396
$789$	−9.11695	−0.324572
$790$	0.736947	0.0262194
$791$	−31.0514	−1.10406
$792$	5.89220	0.209370
$793$	−9.02144	−0.320361
$794$	−1.50406	−0.0533771
$795$	24.7303	0.877093
$796$	−27.1351	−0.961777
$797$	−8.78817	−0.311293	−0.155647	−	0.987813i	$-0.549746\pi$
$797$	−8.78817	−0.311293	−0.155647	+	0.987813i	$0.549746\pi$
$798$	12.5126	0.442941
$799$	21.7469	0.769350
$800$	−2.33068	−0.0824020
$801$	11.2265	0.396667
$802$	−2.53053	−0.0893561
$803$	1.00000	0.0352892
$804$	−83.3661	−2.94009
$805$	−8.12900	−0.286510
$806$	0.338864	0.0119360
$807$	25.5277	0.898618
$808$	−9.78862	−0.344362
$809$	10.8460	0.381324	0.190662	−	0.981656i	$-0.438936\pi$
$809$	10.8460	0.381324	0.190662	+	0.981656i	$0.438936\pi$
$810$	−4.83786	−0.169985
$811$	17.3101	0.607839	0.303920	−	0.952698i	$-0.401705\pi$
$811$	17.3101	0.607839	0.303920	+	0.952698i	$0.401705\pi$
$812$	−6.65398	−0.233509
$813$	16.3508	0.573448
$814$	1.96730	0.0689540
$815$	6.03179	0.211285
$816$	−29.8003	−1.04322
$817$	7.57216	0.264916
$818$	−6.82047	−0.238472
$819$	−68.8406	−2.40549
$820$	−3.43425	−0.119929
$821$	12.7795	0.446009	0.223005	−	0.974817i	$-0.428414\pi$
$821$	12.7795	0.446009	0.223005	+	0.974817i	$0.428414\pi$
$822$	−5.45488	−0.190261
$823$	22.4386	0.782159	0.391079	−	0.920357i	$-0.372102\pi$
$823$	22.4386	0.782159	0.391079	+	0.920357i	$0.372102\pi$
$824$	8.30582	0.289347
$825$	−3.23393	−0.112591
$826$	−11.8478	−0.412236
$827$	36.2568	1.26077	0.630386	−	0.776282i	$-0.282897\pi$
$827$	36.2568	1.26077	0.630386	+	0.776282i	$0.282897\pi$
$828$	−23.3554	−0.811658
$829$	4.80574	0.166910	0.0834550	−	0.996512i	$-0.473404\pi$
$829$	4.80574	0.166910	0.0834550	+	0.996512i	$0.473404\pi$
$830$	3.12293	0.108398
$831$	−29.4737	−1.02243
$832$	−12.8074	−0.444018
$833$	46.2674	1.60307
$834$	12.5728	0.435361
$835$	−7.84550	−0.271505
$836$	7.47151	0.258408
$837$	13.5016	0.466684
$838$	0.957758	0.0330852
$839$	−28.0417	−0.968108	−0.484054	−	0.875038i	$-0.660836\pi$
$839$	−28.0417	−0.968108	−0.484054	+	0.875038i	$0.660836\pi$
$840$	13.0004	0.448557
$841$	−28.5550	−0.984654
$842$	0.304927	0.0105085
$843$	−48.9844	−1.68711
$844$	−11.1361	−0.383319
$845$	−9.70972	−0.334024
$846$	−13.2123	−0.454247
$847$	−5.08849	−0.174843
$848$	−28.7747	−0.988127
$849$	−36.8255	−1.26385
$850$	−0.488540	−0.0167568
$851$	−15.7543	−0.540050
$852$	49.8467	1.70772
$853$	−53.9392	−1.84684	−0.923422	−	0.383786i	$-0.874620\pi$
$853$	−53.9392	−1.84684	−0.923422	+	0.383786i	$0.874620\pi$
$854$	−5.04858	−0.172759
$855$	−28.4280	−0.972217
$856$	−0.239516	−0.00818650
$857$	−0.740933	−0.0253098	−0.0126549	−	0.999920i	$-0.504028\pi$
$857$	−0.740933	−0.0253098	−0.0126549	+	0.999920i	$0.504028\pi$
$858$	1.17022	0.0399506
$859$	6.44786	0.219998	0.109999	−	0.993932i	$-0.464915\pi$
$859$	6.44786	0.219998	0.109999	+	0.993932i	$0.464915\pi$
$860$	3.89416	0.132790
$861$	28.8304	0.982538
$862$	−0.574342	−0.0195622
$863$	17.6608	0.601182	0.300591	−	0.953753i	$-0.402816\pi$
$863$	17.6608	0.601182	0.300591	+	0.953753i	$0.402816\pi$
$864$	33.6032	1.14321
$865$	−5.16279	−0.175540
$866$	−1.42069	−0.0482770
$867$	35.5818	1.20842
$868$	−9.34067	−0.317043
$869$	−3.69416	−0.125316
$870$	−0.430370	−0.0145909
$871$	−23.8547	−0.808287
$872$	12.9017	0.436906
$873$	−16.5617	−0.560528
$874$	1.21472	0.0410885
$875$	−5.08849	−0.172022
$876$	6.33916	0.214180
$877$	−27.5285	−0.929571	−0.464785	−	0.885423i	$-0.653869\pi$
$877$	−27.5285	−0.929571	−0.464785	+	0.885423i	$0.653869\pi$
$878$	−5.42749	−0.183169
$879$	−79.6323	−2.68593
$880$	3.76281	0.126844
$881$	−9.19379	−0.309747	−0.154873	−	0.987934i	$-0.549497\pi$
$881$	−9.19379	−0.309747	−0.154873	+	0.987934i	$0.549497\pi$
$882$	−28.1096	−0.946501
$883$	56.0149	1.88505	0.942526	−	0.334133i	$-0.108444\pi$
$883$	56.0149	1.88505	0.942526	+	0.334133i	$0.108444\pi$
$884$	−8.70757	−0.292867
$885$	37.7448	1.26878
$886$	5.72311	0.192272
$887$	−18.4238	−0.618610	−0.309305	−	0.950963i	$-0.600096\pi$
$887$	−18.4238	−0.618610	−0.309305	+	0.950963i	$0.600096\pi$
$888$	25.1953	0.845499
$889$	91.5915	3.07188
$890$	−0.300278	−0.0100654
$891$	24.2512	0.812445
$892$	−30.6121	−1.02497
$893$	−33.8474	−1.13266
$894$	11.5718	0.387018
$895$	−19.1713	−0.640827
$896$	−30.8866	−1.03185
$897$	−9.37119	−0.312895
$898$	−1.85684	−0.0619634
$899$	0.624710	0.0208353
$900$	−14.6198	−0.487325
$901$	−18.7274	−0.623901
$902$	−0.349504	−0.0116372
$903$	−32.6913	−1.08790
$904$	4.82092	0.160342
$905$	−8.14103	−0.270617
$906$	12.3245	0.409455
$907$	34.6290	1.14984	0.574918	−	0.818211i	$-0.305034\pi$
$907$	34.6290	1.14984	0.574918	+	0.818211i	$0.305034\pi$
$908$	−34.5862	−1.14778
$909$	−92.4107	−3.06507
$910$	1.84131	0.0610388
$911$	39.7520	1.31704	0.658521	−	0.752562i	$-0.271182\pi$
$911$	39.7520	1.31704	0.658521	+	0.752562i	$0.271182\pi$
$912$	46.3820	1.53586
$913$	−15.6546	−0.518091
$914$	5.79444	0.191663
$915$	16.0838	0.531715
$916$	−3.62859	−0.119892
$917$	−25.3657	−0.837649
$918$	7.04365	0.232475
$919$	1.88632	0.0622240	0.0311120	−	0.999516i	$-0.490095\pi$
$919$	1.88632	0.0622240	0.0311120	+	0.999516i	$0.490095\pi$
$920$	1.26208	0.0416095
$921$	−19.4897	−0.642206
$922$	0.163296	0.00537787
$923$	14.2633	0.469484
$924$	−32.2568	−1.06117
$925$	−9.86168	−0.324250
$926$	−3.16654	−0.104059
$927$	78.4122	2.57539
$928$	1.55480	0.0510387
$929$	58.5796	1.92193	0.960967	−	0.276665i	$-0.0892291\pi$
$929$	58.5796	1.92193	0.960967	+	0.276665i	$0.0892291\pi$
$930$	−0.604141	−0.0198106
$931$	−72.0117	−2.36009
$932$	−34.6873	−1.13622
$933$	106.719	3.49382
$934$	−2.30222	−0.0753309
$935$	2.44895	0.0800891
$936$	10.6879	0.349346
$937$	40.7269	1.33049	0.665244	−	0.746626i	$-0.268327\pi$
$937$	40.7269	1.33049	0.665244	+	0.746626i	$0.268327\pi$
$938$	−13.3496	−0.435879
$939$	24.0007	0.783232
$940$	−17.4068	−0.567748
$941$	8.81728	0.287435	0.143717	−	0.989619i	$-0.454094\pi$
$941$	8.81728	0.287435	0.143717	+	0.989619i	$0.454094\pi$
$942$	−6.37824	−0.207814
$943$	2.79885	0.0911430
$944$	−43.9176	−1.42940
$945$	73.3648	2.38656
$946$	0.396308	0.0128851
$947$	7.72028	0.250875	0.125438	−	0.992102i	$-0.459966\pi$
$947$	7.72028	0.250875	0.125438	+	0.992102i	$0.459966\pi$
$948$	−23.4179	−0.760577
$949$	1.81391	0.0588821
$950$	0.760375	0.0246698
$951$	57.0841	1.85108
$952$	−9.84479	−0.319072
$953$	−43.5999	−1.41234	−0.706170	−	0.708042i	$-0.749579\pi$
$953$	−43.5999	−1.41234	−0.706170	+	0.708042i	$0.749579\pi$
$954$	11.3778	0.368370
$955$	3.40543	0.110197
$956$	26.0815	0.843537
$957$	2.15735	0.0697373
$958$	5.31961	0.171869
$959$	43.0253	1.38936
$960$	22.8337	0.736954
$961$	−30.1230	−0.971711
$962$	3.56852	0.115054
$963$	−2.26118	−0.0728657
$964$	−33.8659	−1.09075
$965$	−13.0471	−0.420000
$966$	−5.24431	−0.168733
$967$	17.4798	0.562114	0.281057	−	0.959691i	$-0.409315\pi$
$967$	17.4798	0.562114	0.281057	+	0.959691i	$0.409315\pi$
$968$	0.790020	0.0253922
$969$	30.1868	0.969739
$970$	0.442982	0.0142233
$971$	44.3467	1.42315	0.711577	−	0.702609i	$-0.247981\pi$
$971$	44.3467	1.42315	0.711577	+	0.702609i	$0.247981\pi$
$972$	68.9467	2.21147
$973$	−99.1679	−3.17918
$974$	−6.14212	−0.196806
$975$	−5.86606	−0.187864
$976$	−18.7142	−0.599027
$977$	23.2598	0.744147	0.372074	−	0.928203i	$-0.378647\pi$
$977$	23.2598	0.744147	0.372074	+	0.928203i	$0.378647\pi$
$978$	3.89132	0.124431
$979$	1.50523	0.0481074
$980$	−37.0337	−1.18300
$981$	121.800	3.88877
$982$	7.11442	0.227030
$983$	29.9241	0.954431	0.477216	−	0.878786i	$-0.341646\pi$
$983$	29.9241	0.954431	0.477216	+	0.878786i	$0.341646\pi$
$984$	−4.47610	−0.142693
$985$	−21.8240	−0.695372
$986$	0.325905	0.0103789
$987$	146.129	4.65135
$988$	13.5527	0.431168
$989$	−3.17366	−0.100917
$990$	−1.48785	−0.0472870
$991$	47.1723	1.49848	0.749239	−	0.662300i	$-0.230420\pi$
$991$	47.1723	1.49848	0.749239	+	0.662300i	$0.230420\pi$
$992$	2.18258	0.0692971
$993$	−114.493	−3.63334
$994$	7.98206	0.253175
$995$	13.8430	0.438852
$996$	−99.2369	−3.14444
$997$	35.5594	1.12618	0.563089	−	0.826396i	$-0.309613\pi$
$997$	35.5594	1.12618	0.563089	+	0.826396i	$0.309613\pi$
$998$	6.93147	0.219412
$999$	142.184	4.49849

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.h.1.18	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.h.1.18	✓	37	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)

\(f(q)\)	\(=\)	\(q-0.199490 q^{2} -3.23393 q^{3} -1.96020 q^{4} +1.00000 q^{5} +0.645135 q^{6} -5.08849 q^{7} +0.790020 q^{8} +7.45829 q^{9} +O(q^{10})\)	\(q-0.199490 q^{2} -3.23393 q^{3} -1.96020 q^{4} +1.00000 q^{5} +0.645135 q^{6} -5.08849 q^{7} +0.790020 q^{8} +7.45829 q^{9} -0.199490 q^{10} +1.00000 q^{11} +6.33916 q^{12} +1.81391 q^{13} +1.01510 q^{14} -3.23393 q^{15} +3.76281 q^{16} +2.44895 q^{17} -1.48785 q^{18} -3.81160 q^{19} -1.96020 q^{20} +16.4558 q^{21} -0.199490 q^{22} +1.59753 q^{23} -2.55487 q^{24} +1.00000 q^{25} -0.361857 q^{26} -14.4178 q^{27} +9.97449 q^{28} -0.667100 q^{29} +0.645135 q^{30} -0.936457 q^{31} -2.33068 q^{32} -3.23393 q^{33} -0.488540 q^{34} -5.08849 q^{35} -14.6198 q^{36} -9.86168 q^{37} +0.760375 q^{38} -5.86606 q^{39} +0.790020 q^{40} +1.75199 q^{41} -3.28277 q^{42} -1.98661 q^{43} -1.96020 q^{44} +7.45829 q^{45} -0.318690 q^{46} +8.88010 q^{47} -12.1686 q^{48} +18.8928 q^{49} -0.199490 q^{50} -7.91971 q^{51} -3.55564 q^{52} -7.64714 q^{53} +2.87620 q^{54} +1.00000 q^{55} -4.02001 q^{56} +12.3264 q^{57} +0.133080 q^{58} -11.6715 q^{59} +6.33916 q^{60} -4.97347 q^{61} +0.186814 q^{62} -37.9514 q^{63} -7.06067 q^{64} +1.81391 q^{65} +0.645135 q^{66} -13.1510 q^{67} -4.80043 q^{68} -5.16628 q^{69} +1.01510 q^{70} +7.86330 q^{71} +5.89220 q^{72} +1.00000 q^{73} +1.96730 q^{74} -3.23393 q^{75} +7.47151 q^{76} -5.08849 q^{77} +1.17022 q^{78} -3.69416 q^{79} +3.76281 q^{80} +24.2512 q^{81} -0.349504 q^{82} -15.6546 q^{83} -32.2568 q^{84} +2.44895 q^{85} +0.396308 q^{86} +2.15735 q^{87} +0.790020 q^{88} +1.50523 q^{89} -1.48785 q^{90} -9.23009 q^{91} -3.13148 q^{92} +3.02843 q^{93} -1.77149 q^{94} -3.81160 q^{95} +7.53726 q^{96} -2.22058 q^{97} -3.76891 q^{98} +7.45829 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9}+O(q^{10}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9	\( 37 q + 5 q^{2} + 3 q^{3} + 43 q^{4} + 37 q^{5} + 9 q^{6} + 6 q^{7} + 12 q^{8} + 50 q^{9} + 5 q^{10} + 37 q^{11} + 6 q^{12} + 11 q^{13} + 11 q^{14} + 3 q^{15} + 43 q^{16} + 38 q^{17} + 11 q^{18} + 34 q^{19} + 43 q^{20} + 39 q^{21} + 5 q^{22} + 4 q^{23} + 25 q^{24} + 37 q^{25} - 9 q^{26} + 3 q^{27} + 14 q^{28} + 58 q^{29} + 9 q^{30} + 8 q^{31} + 14 q^{32} + 3 q^{33} + 8 q^{34} + 6 q^{35} + 20 q^{36} + 2 q^{37} + 15 q^{38} + 14 q^{39} + 12 q^{40} + 62 q^{41} - 13 q^{42} + 30 q^{43} + 43 q^{44} + 50 q^{45} + 31 q^{46} + 5 q^{47} - 25 q^{48} + 59 q^{49} + 5 q^{50} + 23 q^{51} - q^{52} + 18 q^{53} + 13 q^{54} + 37 q^{55} + 22 q^{56} + 5 q^{57} - 40 q^{58} + 15 q^{59} + 6 q^{60} + 57 q^{61} + 20 q^{62} - 29 q^{63} + 10 q^{64} + 11 q^{65} + 9 q^{66} - 14 q^{67} + 53 q^{68} + 24 q^{69} + 11 q^{70} + 8 q^{71} + 15 q^{72} + 37 q^{73} + 7 q^{74} + 3 q^{75} + 59 q^{76} + 6 q^{77} + q^{78} + 42 q^{79} + 43 q^{80} + 61 q^{81} - 22 q^{82} + 44 q^{83} + 66 q^{84} + 38 q^{85} - q^{86} - 26 q^{87} + 12 q^{88} + 69 q^{89} + 11 q^{90} - 10 q^{91} - 21 q^{92} - 26 q^{93} + 29 q^{94} + 34 q^{95} - 9 q^{96} + 37 q^{97} - 15 q^{98} + 50 q^{99}+O(q^{100}) \) 37 * q + 5 * q^2 + 3 * q^3 + 43 * q^4 + 37 * q^5 + 9 * q^6 + 6 * q^7 + 12 * q^8 + 50 * q^9 + 5 * q^10 + 37 * q^11 + 6 * q^12 + 11 * q^13 + 11 * q^14 + 3 * q^15 + 43 * q^16 + 38 * q^17 + 11 * q^18 + 34 * q^19 + 43 * q^20 + 39 * q^21 + 5 * q^22 + 4 * q^23 + 25 * q^24 + 37 * q^25 - 9 * q^26 + 3 * q^27 + 14 * q^28 + 58 * q^29 + 9 * q^30 + 8 * q^31 + 14 * q^32 + 3 * q^33 + 8 * q^34 + 6 * q^35 + 20 * q^36 + 2 * q^37 + 15 * q^38 + 14 * q^39 + 12 * q^40 + 62 * q^41 - 13 * q^42 + 30 * q^43 + 43 * q^44 + 50 * q^45 + 31 * q^46 + 5 * q^47 - 25 * q^48 + 59 * q^49 + 5 * q^50 + 23 * q^51 - q^52 + 18 * q^53 + 13 * q^54 + 37 * q^55 + 22 * q^56 + 5 * q^57 - 40 * q^58 + 15 * q^59 + 6 * q^60 + 57 * q^61 + 20 * q^62 - 29 * q^63 + 10 * q^64 + 11 * q^65 + 9 * q^66 - 14 * q^67 + 53 * q^68 + 24 * q^69 + 11 * q^70 + 8 * q^71 + 15 * q^72 + 37 * q^73 + 7 * q^74 + 3 * q^75 + 59 * q^76 + 6 * q^77 + q^78 + 42 * q^79 + 43 * q^80 + 61 * q^81 - 22 * q^82 + 44 * q^83 + 66 * q^84 + 38 * q^85 - q^86 - 26 * q^87 + 12 * q^88 + 69 * q^89 + 11 * q^90 - 10 * q^91 - 21 * q^92 - 26 * q^93 + 29 * q^94 + 34 * q^95 - 9 * q^96 + 37 * q^97 - 15 * q^98 + 50 * q^99

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