LMFDB - Embedded newform 8015.2.a.i.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.22552 q^{2} -2.22296 q^{3} -0.498095 q^{4} +1.00000 q^{5} +2.72428 q^{6} -1.00000 q^{7} +3.06147 q^{8} +1.94153 q^{9} +O(q^{10})$	\(q-1.22552 q^{2} -2.22296 q^{3} -0.498095 q^{4} +1.00000 q^{5} +2.72428 q^{6} -1.00000 q^{7} +3.06147 q^{8} +1.94153 q^{9} -1.22552 q^{10} -3.57846 q^{11} +1.10724 q^{12} +4.39402 q^{13} +1.22552 q^{14} -2.22296 q^{15} -2.75571 q^{16} -3.48536 q^{17} -2.37939 q^{18} +6.31350 q^{19} -0.498095 q^{20} +2.22296 q^{21} +4.38548 q^{22} +1.03420 q^{23} -6.80551 q^{24} +1.00000 q^{25} -5.38497 q^{26} +2.35293 q^{27} +0.498095 q^{28} -6.03735 q^{29} +2.72428 q^{30} +1.01486 q^{31} -2.74576 q^{32} +7.95475 q^{33} +4.27138 q^{34} -1.00000 q^{35} -0.967066 q^{36} -10.4082 q^{37} -7.73734 q^{38} -9.76772 q^{39} +3.06147 q^{40} +8.00728 q^{41} -2.72428 q^{42} -2.32001 q^{43} +1.78241 q^{44} +1.94153 q^{45} -1.26744 q^{46} -4.51629 q^{47} +6.12582 q^{48} +1.00000 q^{49} -1.22552 q^{50} +7.74780 q^{51} -2.18864 q^{52} +2.95301 q^{53} -2.88357 q^{54} -3.57846 q^{55} -3.06147 q^{56} -14.0346 q^{57} +7.39891 q^{58} +0.525228 q^{59} +1.10724 q^{60} -4.82222 q^{61} -1.24374 q^{62} -1.94153 q^{63} +8.87641 q^{64} +4.39402 q^{65} -9.74872 q^{66} -0.272062 q^{67} +1.73604 q^{68} -2.29898 q^{69} +1.22552 q^{70} -3.99489 q^{71} +5.94394 q^{72} +5.63889 q^{73} +12.7555 q^{74} -2.22296 q^{75} -3.14472 q^{76} +3.57846 q^{77} +11.9706 q^{78} -4.92567 q^{79} -2.75571 q^{80} -11.0551 q^{81} -9.81310 q^{82} +11.3355 q^{83} -1.10724 q^{84} -3.48536 q^{85} +2.84323 q^{86} +13.4208 q^{87} -10.9553 q^{88} +11.3697 q^{89} -2.37939 q^{90} -4.39402 q^{91} -0.515130 q^{92} -2.25599 q^{93} +5.53482 q^{94} +6.31350 q^{95} +6.10369 q^{96} -6.01260 q^{97} -1.22552 q^{98} -6.94768 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) $ 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.22552	−0.866575	−0.433288	−	0.901256i	$-0.642647\pi$
$2$	−1.22552	−0.866575	−0.433288	+	0.901256i	$0.642647\pi$
$3$	−2.22296	−1.28342	−0.641712	−	0.766946i	$-0.721776\pi$
$3$	−2.22296	−1.28342	−0.641712	+	0.766946i	$0.721776\pi$
$4$	−0.498095	−0.249047
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.72428	1.11218
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.06147	1.08239
$9$	1.94153	0.647177
$10$	−1.22552	−0.387544
$11$	−3.57846	−1.07894	−0.539472	−	0.842003i	$-0.681376\pi$
$11$	−3.57846	−1.07894	−0.539472	+	0.842003i	$0.681376\pi$
$12$	1.10724	0.319633
$13$	4.39402	1.21868	0.609341	−	0.792908i	$-0.291434\pi$
$13$	4.39402	1.21868	0.609341	+	0.792908i	$0.291434\pi$
$14$	1.22552	0.327535
$15$	−2.22296	−0.573965
$16$	−2.75571	−0.688928
$17$	−3.48536	−0.845324	−0.422662	−	0.906287i	$-0.638904\pi$
$17$	−3.48536	−0.845324	−0.422662	+	0.906287i	$0.638904\pi$
$18$	−2.37939	−0.560828
$19$	6.31350	1.44842	0.724208	−	0.689581i	$-0.242205\pi$
$19$	6.31350	1.44842	0.724208	+	0.689581i	$0.242205\pi$
$20$	−0.498095	−0.111377
$21$	2.22296	0.485089
$22$	4.38548	0.934987
$23$	1.03420	0.215646	0.107823	−	0.994170i	$-0.465612\pi$
$23$	1.03420	0.215646	0.107823	+	0.994170i	$0.465612\pi$
$24$	−6.80551	−1.38917
$25$	1.00000	0.200000
$26$	−5.38497	−1.05608
$27$	2.35293	0.452822
$28$	0.498095	0.0941311
$29$	−6.03735	−1.12111	−0.560554	−	0.828118i	$-0.689412\pi$
$29$	−6.03735	−1.12111	−0.560554	+	0.828118i	$0.689412\pi$
$30$	2.72428	0.497384
$31$	1.01486	0.182275	0.0911373	−	0.995838i	$-0.470950\pi$
$31$	1.01486	0.182275	0.0911373	+	0.995838i	$0.470950\pi$
$32$	−2.74576	−0.485386
$33$	7.95475	1.38474
$34$	4.27138	0.732536
$35$	−1.00000	−0.169031
$36$	−0.967066	−0.161178
$37$	−10.4082	−1.71110	−0.855549	−	0.517722i	$-0.826780\pi$
$37$	−10.4082	−1.71110	−0.855549	+	0.517722i	$0.826780\pi$
$38$	−7.73734	−1.25516
$39$	−9.76772	−1.56409
$40$	3.06147	0.484061
$41$	8.00728	1.25053	0.625263	−	0.780414i	$-0.284992\pi$
$41$	8.00728	1.25053	0.625263	+	0.780414i	$0.284992\pi$
$42$	−2.72428	−0.420366
$43$	−2.32001	−0.353799	−0.176899	−	0.984229i	$-0.556607\pi$
$43$	−2.32001	−0.353799	−0.176899	+	0.984229i	$0.556607\pi$
$44$	1.78241	0.268708
$45$	1.94153	0.289426
$46$	−1.26744	−0.186873
$47$	−4.51629	−0.658769	−0.329385	−	0.944196i	$-0.606841\pi$
$47$	−4.51629	−0.658769	−0.329385	+	0.944196i	$0.606841\pi$
$48$	6.12582	0.884187
$49$	1.00000	0.142857
$50$	−1.22552	−0.173315
$51$	7.74780	1.08491
$52$	−2.18864	−0.303510
$53$	2.95301	0.405627	0.202813	−	0.979217i	$-0.434992\pi$
$53$	2.95301	0.405627	0.202813	+	0.979217i	$0.434992\pi$
$54$	−2.88357	−0.392404
$55$	−3.57846	−0.482519
$56$	−3.06147	−0.409106
$57$	−14.0346	−1.85893
$58$	7.39891	0.971524
$59$	0.525228	0.0683789	0.0341894	−	0.999415i	$-0.489115\pi$
$59$	0.525228	0.0683789	0.0341894	+	0.999415i	$0.489115\pi$
$60$	1.10724	0.142944
$61$	−4.82222	−0.617422	−0.308711	−	0.951156i	$-0.599898\pi$
$61$	−4.82222	−0.617422	−0.308711	+	0.951156i	$0.599898\pi$
$62$	−1.24374	−0.157955
$63$	−1.94153	−0.244610
$64$	8.87641	1.10955
$65$	4.39402	0.545011
$66$	−9.74872	−1.19998
$67$	−0.272062	−0.0332376	−0.0166188	−	0.999862i	$-0.505290\pi$
$67$	−0.272062	−0.0332376	−0.0166188	+	0.999862i	$0.505290\pi$
$68$	1.73604	0.210526
$69$	−2.29898	−0.276765
$70$	1.22552	0.146478
$71$	−3.99489	−0.474106	−0.237053	−	0.971497i	$-0.576181\pi$
$71$	−3.99489	−0.474106	−0.237053	+	0.971497i	$0.576181\pi$
$72$	5.94394	0.700500
$73$	5.63889	0.659982	0.329991	−	0.943984i	$-0.392954\pi$
$73$	5.63889	0.659982	0.329991	+	0.943984i	$0.392954\pi$
$74$	12.7555	1.48280
$75$	−2.22296	−0.256685
$76$	−3.14472	−0.360724
$77$	3.57846	0.407803
$78$	11.9706	1.35540
$79$	−4.92567	−0.554181	−0.277090	−	0.960844i	$-0.589370\pi$
$79$	−4.92567	−0.554181	−0.277090	+	0.960844i	$0.589370\pi$
$80$	−2.75571	−0.308098
$81$	−11.0551	−1.22834
$82$	−9.81310	−1.08368
$83$	11.3355	1.24424	0.622119	−	0.782923i	$-0.286272\pi$
$83$	11.3355	1.24424	0.622119	+	0.782923i	$0.286272\pi$
$84$	−1.10724	−0.120810
$85$	−3.48536	−0.378040
$86$	2.84323	0.306593
$87$	13.4208	1.43886
$88$	−10.9553	−1.16784
$89$	11.3697	1.20519	0.602593	−	0.798048i	$-0.294134\pi$
$89$	11.3697	1.20519	0.602593	+	0.798048i	$0.294134\pi$
$90$	−2.37939	−0.250810
$91$	−4.39402	−0.460619
$92$	−0.515130	−0.0537061
$93$	−2.25599	−0.233936
$94$	5.53482	0.570873
$95$	6.31350	0.647752
$96$	6.10369	0.622955
$97$	−6.01260	−0.610487	−0.305244	−	0.952274i	$-0.598738\pi$
$97$	−6.01260	−0.610487	−0.305244	+	0.952274i	$0.598738\pi$
$98$	−1.22552	−0.123796
$99$	−6.94768	−0.698268
$100$	−0.498095	−0.0498095
$101$	−11.4080	−1.13514	−0.567570	−	0.823325i	$-0.692116\pi$
$101$	−11.4080	−1.13514	−0.567570	+	0.823325i	$0.692116\pi$
$102$	−9.49510	−0.940155
$103$	−5.59496	−0.551288	−0.275644	−	0.961260i	$-0.588891\pi$
$103$	−5.59496	−0.551288	−0.275644	+	0.961260i	$0.588891\pi$
$104$	13.4522	1.31909
$105$	2.22296	0.216938
$106$	−3.61898	−0.351506
$107$	18.2430	1.76362	0.881808	−	0.471609i	$-0.156327\pi$
$107$	18.2430	1.76362	0.881808	+	0.471609i	$0.156327\pi$
$108$	−1.17198	−0.112774
$109$	−14.5475	−1.39340	−0.696699	−	0.717363i	$-0.745349\pi$
$109$	−14.5475	−1.39340	−0.696699	+	0.717363i	$0.745349\pi$
$110$	4.38548	0.418139
$111$	23.1370	2.19606
$112$	2.75571	0.260390
$113$	3.97025	0.373490	0.186745	−	0.982408i	$-0.440206\pi$
$113$	3.97025	0.373490	0.186745	+	0.982408i	$0.440206\pi$
$114$	17.1998	1.61090
$115$	1.03420	0.0964398
$116$	3.00717	0.279209
$117$	8.53113	0.788703
$118$	−0.643679	−0.0592554
$119$	3.48536	0.319502
$120$	−6.80551	−0.621256
$121$	1.80534	0.164122
$122$	5.90974	0.535043
$123$	−17.7998	−1.60496
$124$	−0.505498	−0.0453950
$125$	1.00000	0.0894427
$126$	2.37939	0.211973
$127$	−7.79726	−0.691895	−0.345948	−	0.938254i	$-0.612443\pi$
$127$	−7.79726	−0.691895	−0.345948	+	0.938254i	$0.612443\pi$
$128$	−5.38673	−0.476124
$129$	5.15728	0.454074
$130$	−5.38497	−0.472293
$131$	10.9882	0.960039	0.480020	−	0.877258i	$-0.340629\pi$
$131$	10.9882	0.960039	0.480020	+	0.877258i	$0.340629\pi$
$132$	−3.96222	−0.344867
$133$	−6.31350	−0.547450
$134$	0.333418	0.0288029
$135$	2.35293	0.202508
$136$	−10.6703	−0.914973
$137$	−2.50533	−0.214044	−0.107022	−	0.994257i	$-0.534132\pi$
$137$	−2.50533	−0.214044	−0.107022	+	0.994257i	$0.534132\pi$
$138$	2.81746	0.239838
$139$	−2.43241	−0.206314	−0.103157	−	0.994665i	$-0.532894\pi$
$139$	−2.43241	−0.206314	−0.103157	+	0.994665i	$0.532894\pi$
$140$	0.498095	0.0420967
$141$	10.0395	0.845480
$142$	4.89582	0.410848
$143$	−15.7238	−1.31489
$144$	−5.35030	−0.445858
$145$	−6.03735	−0.501374
$146$	−6.91058	−0.571924
$147$	−2.22296	−0.183346
$148$	5.18427	0.426145
$149$	−9.24880	−0.757691	−0.378846	−	0.925460i	$-0.623679\pi$
$149$	−9.24880	−0.757691	−0.378846	+	0.925460i	$0.623679\pi$
$150$	2.72428	0.222437
$151$	−12.7979	−1.04148	−0.520738	−	0.853717i	$-0.674343\pi$
$151$	−12.7979	−1.04148	−0.520738	+	0.853717i	$0.674343\pi$
$152$	19.3286	1.56776
$153$	−6.76693	−0.547074
$154$	−4.38548	−0.353392
$155$	1.01486	0.0815157
$156$	4.86525	0.389532
$157$	7.14828	0.570495	0.285247	−	0.958454i	$-0.407924\pi$
$157$	7.14828	0.570495	0.285247	+	0.958454i	$0.407924\pi$
$158$	6.03651	0.480239
$159$	−6.56440	−0.520591
$160$	−2.74576	−0.217071
$161$	−1.03420	−0.0815065
$162$	13.5482	1.06445
$163$	13.2193	1.03542	0.517708	−	0.855557i	$-0.326785\pi$
$163$	13.2193	1.03542	0.517708	+	0.855557i	$0.326785\pi$
$164$	−3.98838	−0.311440
$165$	7.95475	0.619276
$166$	−13.8920	−1.07823
$167$	24.3528	1.88447	0.942237	−	0.334947i	$-0.108719\pi$
$167$	24.3528	1.88447	0.942237	+	0.334947i	$0.108719\pi$
$168$	6.80551	0.525057
$169$	6.30744	0.485188
$170$	4.27138	0.327600
$171$	12.2579	0.937382
$172$	1.15559	0.0881126
$173$	13.8296	1.05144	0.525722	−	0.850657i	$-0.323795\pi$
$173$	13.8296	1.05144	0.525722	+	0.850657i	$0.323795\pi$
$174$	−16.4474	−1.24688
$175$	−1.00000	−0.0755929
$176$	9.86119	0.743315
$177$	−1.16756	−0.0877591
$178$	−13.9338	−1.04439
$179$	−2.73489	−0.204415	−0.102208	−	0.994763i	$-0.532591\pi$
$179$	−2.73489	−0.204415	−0.102208	+	0.994763i	$0.532591\pi$
$180$	−0.967066	−0.0720809
$181$	15.0260	1.11687	0.558437	−	0.829547i	$-0.311401\pi$
$181$	15.0260	1.11687	0.558437	+	0.829547i	$0.311401\pi$
$182$	5.38497	0.399161
$183$	10.7196	0.792415
$184$	3.16618	0.233414
$185$	−10.4082	−0.765226
$186$	2.76477	0.202723
$187$	12.4722	0.912058
$188$	2.24954	0.164065
$189$	−2.35293	−0.171150
$190$	−7.73734	−0.561325
$191$	8.24345	0.596475	0.298238	−	0.954492i	$-0.403601\pi$
$191$	8.24345	0.596475	0.298238	+	0.954492i	$0.403601\pi$
$192$	−19.7319	−1.42402
$193$	−21.3764	−1.53871	−0.769355	−	0.638822i	$-0.779422\pi$
$193$	−21.3764	−1.53871	−0.769355	+	0.638822i	$0.779422\pi$
$194$	7.36858	0.529033
$195$	−9.76772	−0.699481
$196$	−0.498095	−0.0355782
$197$	−14.4125	−1.02685	−0.513424	−	0.858135i	$-0.671623\pi$
$197$	−14.4125	−1.02685	−0.513424	+	0.858135i	$0.671623\pi$
$198$	8.51454	0.605102
$199$	16.3915	1.16197	0.580983	−	0.813916i	$-0.302668\pi$
$199$	16.3915	1.16197	0.580983	+	0.813916i	$0.302668\pi$
$200$	3.06147	0.216479
$201$	0.604781	0.0426580
$202$	13.9808	0.983685
$203$	6.03735	0.423739
$204$	−3.85914	−0.270194
$205$	8.00728	0.559253
$206$	6.85675	0.477732
$207$	2.00793	0.139561
$208$	−12.1087	−0.839585
$209$	−22.5926	−1.56276
$210$	−2.72428	−0.187993
$211$	4.52500	0.311514	0.155757	−	0.987795i	$-0.450218\pi$
$211$	4.52500	0.311514	0.155757	+	0.987795i	$0.450218\pi$
$212$	−1.47088	−0.101020
$213$	8.88045	0.608479
$214$	−22.3572	−1.52831
$215$	−2.32001	−0.158224
$216$	7.20343	0.490131
$217$	−1.01486	−0.0688933
$218$	17.8283	1.20748
$219$	−12.5350	−0.847036
$220$	1.78241	0.120170
$221$	−15.3147	−1.03018
$222$	−28.3549	−1.90305
$223$	5.74633	0.384803	0.192401	−	0.981316i	$-0.438372\pi$
$223$	5.74633	0.384803	0.192401	+	0.981316i	$0.438372\pi$
$224$	2.74576	0.183459
$225$	1.94153	0.129435
$226$	−4.86563	−0.323657
$227$	−0.0222199	−0.00147479	−0.000737393	−	1.00000i	$-0.500235\pi$
$227$	−0.0222199	−0.00147479	−0.000737393		1.00000i	$0.500235\pi$
$228$	6.99058	0.462962
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−1.26744	−0.0835723
$231$	−7.95475	−0.523384
$232$	−18.4832	−1.21348
$233$	15.8892	1.04094	0.520468	−	0.853881i	$-0.325757\pi$
$233$	15.8892	1.04094	0.520468	+	0.853881i	$0.325757\pi$
$234$	−10.4551	−0.683471
$235$	−4.51629	−0.294611
$236$	−0.261613	−0.0170296
$237$	10.9495	0.711249
$238$	−4.27138	−0.276873
$239$	9.45634	0.611680	0.305840	−	0.952083i	$-0.401063\pi$
$239$	9.45634	0.611680	0.305840	+	0.952083i	$0.401063\pi$
$240$	6.12582	0.395420
$241$	4.35471	0.280511	0.140256	−	0.990115i	$-0.455208\pi$
$241$	4.35471	0.280511	0.140256	+	0.990115i	$0.455208\pi$
$242$	−2.21249	−0.142224
$243$	17.5161	1.12366
$244$	2.40192	0.153767
$245$	1.00000	0.0638877
$246$	21.8141	1.39081
$247$	27.7417	1.76516
$248$	3.10697	0.197293
$249$	−25.1984	−1.59688
$250$	−1.22552	−0.0775088
$251$	−12.2239	−0.771565	−0.385782	−	0.922590i	$-0.626068\pi$
$251$	−12.2239	−0.771565	−0.385782	+	0.922590i	$0.626068\pi$
$252$	0.967066	0.0609195
$253$	−3.70084	−0.232670
$254$	9.55572	0.599579
$255$	7.74780	0.485186
$256$	−11.1513	−0.696954
$257$	3.17217	0.197875	0.0989373	−	0.995094i	$-0.468456\pi$
$257$	3.17217	0.197875	0.0989373	+	0.995094i	$0.468456\pi$
$258$	−6.32037	−0.393489
$259$	10.4082	0.646734
$260$	−2.18864	−0.135734
$261$	−11.7217	−0.725555
$262$	−13.4662	−0.831946
$263$	−9.91043	−0.611103	−0.305552	−	0.952176i	$-0.598841\pi$
$263$	−9.91043	−0.611103	−0.305552	+	0.952176i	$0.598841\pi$
$264$	24.3532	1.49884
$265$	2.95301	0.181402
$266$	7.73734	0.474407
$267$	−25.2744	−1.54677
$268$	0.135513	0.00827775
$269$	12.0674	0.735764	0.367882	−	0.929873i	$-0.380083\pi$
$269$	12.0674	0.735764	0.367882	+	0.929873i	$0.380083\pi$
$270$	−2.88357	−0.175488
$271$	19.8008	1.20282	0.601408	−	0.798942i	$-0.294607\pi$
$271$	19.8008	1.20282	0.601408	+	0.798942i	$0.294607\pi$
$272$	9.60464	0.582367
$273$	9.76772	0.591169
$274$	3.07033	0.185486
$275$	−3.57846	−0.215789
$276$	1.14511	0.0689276
$277$	11.8083	0.709493	0.354747	−	0.934962i	$-0.384567\pi$
$277$	11.8083	0.709493	0.354747	+	0.934962i	$0.384567\pi$
$278$	2.98097	0.178787
$279$	1.97039	0.117964
$280$	−3.06147	−0.182958
$281$	4.85152	0.289417	0.144709	−	0.989474i	$-0.453775\pi$
$281$	4.85152	0.289417	0.144709	+	0.989474i	$0.453775\pi$
$282$	−12.3037	−0.732672
$283$	9.46492	0.562631	0.281316	−	0.959615i	$-0.409229\pi$
$283$	9.46492	0.562631	0.281316	+	0.959615i	$0.409229\pi$
$284$	1.98983	0.118075
$285$	−14.0346	−0.831340
$286$	19.2699	1.13945
$287$	−8.00728	−0.472655
$288$	−5.33097	−0.314130
$289$	−4.85228	−0.285428
$290$	7.39891	0.434479
$291$	13.3657	0.783514
$292$	−2.80870	−0.164367
$293$	17.4305	1.01830	0.509149	−	0.860678i	$-0.329960\pi$
$293$	17.4305	1.01830	0.509149	+	0.860678i	$0.329960\pi$
$294$	2.72428	0.158883
$295$	0.525228	0.0305800
$296$	−31.8644	−1.85208
$297$	−8.41985	−0.488569
$298$	11.3346	0.656596
$299$	4.54431	0.262804
$300$	1.10724	0.0639267
$301$	2.32001	0.133723
$302$	15.6841	0.902517
$303$	25.3595	1.45687
$304$	−17.3982	−0.997855
$305$	−4.82222	−0.276120
$306$	8.29303	0.474081
$307$	−5.79954	−0.330997	−0.165499	−	0.986210i	$-0.552923\pi$
$307$	−5.79954	−0.330997	−0.165499	+	0.986210i	$0.552923\pi$
$308$	−1.78241	−0.101562
$309$	12.4373	0.707536
$310$	−1.24374	−0.0706395
$311$	−14.8100	−0.839798	−0.419899	−	0.907571i	$-0.637935\pi$
$311$	−14.8100	−0.839798	−0.419899	+	0.907571i	$0.637935\pi$
$312$	−29.9036	−1.69296
$313$	10.3764	0.586508	0.293254	−	0.956035i	$-0.405262\pi$
$313$	10.3764	0.586508	0.293254	+	0.956035i	$0.405262\pi$
$314$	−8.76037	−0.494376
$315$	−1.94153	−0.109393
$316$	2.45345	0.138017
$317$	23.8350	1.33871	0.669353	−	0.742945i	$-0.266572\pi$
$317$	23.8350	1.33871	0.669353	+	0.742945i	$0.266572\pi$
$318$	8.04482	0.451131
$319$	21.6044	1.20961
$320$	8.87641	0.496206
$321$	−40.5533	−2.26347
$322$	1.26744	0.0706315
$323$	−22.0048	−1.22438
$324$	5.50646	0.305915
$325$	4.39402	0.243737
$326$	−16.2006	−0.897266
$327$	32.3385	1.78832
$328$	24.5140	1.35356
$329$	4.51629	0.248991
$330$	−9.74872	−0.536649
$331$	−25.4139	−1.39687	−0.698437	−	0.715672i	$-0.746121\pi$
$331$	−25.4139	−1.39687	−0.698437	+	0.715672i	$0.746121\pi$
$332$	−5.64618	−0.309874
$333$	−20.2078	−1.10738
$334$	−29.8449	−1.63304
$335$	−0.272062	−0.0148643
$336$	−6.12582	−0.334191
$337$	6.71707	0.365902	0.182951	−	0.983122i	$-0.441435\pi$
$337$	6.71707	0.365902	0.182951	+	0.983122i	$0.441435\pi$
$338$	−7.72991	−0.420452
$339$	−8.82569	−0.479346
$340$	1.73604	0.0941499
$341$	−3.63164	−0.196664
$342$	−15.0223	−0.812312
$343$	−1.00000	−0.0539949
$344$	−7.10265	−0.382949
$345$	−2.29898	−0.123773
$346$	−16.9485	−0.911155
$347$	19.2850	1.03527	0.517636	−	0.855601i	$-0.326812\pi$
$347$	19.2850	1.03527	0.517636	+	0.855601i	$0.326812\pi$
$348$	−6.68481	−0.358343
$349$	−12.1842	−0.652206	−0.326103	−	0.945334i	$-0.605736\pi$
$349$	−12.1842	−0.652206	−0.326103	+	0.945334i	$0.605736\pi$
$350$	1.22552	0.0655069
$351$	10.3388	0.551846
$352$	9.82556	0.523704
$353$	−23.7398	−1.26354	−0.631770	−	0.775156i	$-0.717671\pi$
$353$	−23.7398	−1.26354	−0.631770	+	0.775156i	$0.717671\pi$
$354$	1.43087	0.0760498
$355$	−3.99489	−0.212027
$356$	−5.66319	−0.300149
$357$	−7.74780	−0.410057
$358$	3.35167	0.177141
$359$	2.27237	0.119931	0.0599655	−	0.998200i	$-0.480901\pi$
$359$	2.27237	0.119931	0.0599655	+	0.998200i	$0.480901\pi$
$360$	5.94394	0.313273
$361$	20.8603	1.09791
$362$	−18.4147	−0.967855
$363$	−4.01320	−0.210638
$364$	2.18864	0.114716
$365$	5.63889	0.295153
$366$	−13.1371	−0.686687
$367$	16.6032	0.866681	0.433340	−	0.901230i	$-0.357335\pi$
$367$	16.6032	0.866681	0.433340	+	0.901230i	$0.357335\pi$
$368$	−2.84996	−0.148565
$369$	15.5464	0.809312
$370$	12.7555	0.663126
$371$	−2.95301	−0.153312
$372$	1.12370	0.0582611
$373$	18.5841	0.962251	0.481125	−	0.876652i	$-0.340228\pi$
$373$	18.5841	0.962251	0.481125	+	0.876652i	$0.340228\pi$
$374$	−15.2850	−0.790366
$375$	−2.22296	−0.114793
$376$	−13.8265	−0.713047
$377$	−26.5282	−1.36627
$378$	2.88357	0.148315
$379$	−16.6492	−0.855214	−0.427607	−	0.903965i	$-0.640643\pi$
$379$	−16.6492	−0.855214	−0.427607	+	0.903965i	$0.640643\pi$
$380$	−3.14472	−0.161321
$381$	17.3330	0.887995
$382$	−10.1025	−0.516891
$383$	1.11645	0.0570478	0.0285239	−	0.999593i	$-0.490919\pi$
$383$	1.11645	0.0570478	0.0285239	+	0.999593i	$0.490919\pi$
$384$	11.9745	0.611069
$385$	3.57846	0.182375
$386$	26.1973	1.33341
$387$	−4.50438	−0.228970
$388$	2.99484	0.152040
$389$	−9.44331	−0.478795	−0.239398	−	0.970922i	$-0.576950\pi$
$389$	−9.44331	−0.478795	−0.239398	+	0.970922i	$0.576950\pi$
$390$	11.9706	0.606153
$391$	−3.60456	−0.182291
$392$	3.06147	0.154628
$393$	−24.4262	−1.23214
$394$	17.6628	0.889840
$395$	−4.92567	−0.247837
$396$	3.46060	0.173902
$397$	−25.3917	−1.27437	−0.637185	−	0.770711i	$-0.719901\pi$
$397$	−25.3917	−1.27437	−0.637185	+	0.770711i	$0.719901\pi$
$398$	−20.0882	−1.00693
$399$	14.0346	0.702610
$400$	−2.75571	−0.137786
$401$	−29.1178	−1.45407	−0.727037	−	0.686598i	$-0.759103\pi$
$401$	−29.1178	−1.45407	−0.727037	+	0.686598i	$0.759103\pi$
$402$	−0.741173	−0.0369664
$403$	4.45933	0.222135
$404$	5.68228	0.282704
$405$	−11.0551	−0.549330
$406$	−7.39891	−0.367202
$407$	37.2453	1.84618
$408$	23.7197	1.17430
$409$	15.2621	0.754664	0.377332	−	0.926078i	$-0.376841\pi$
$409$	15.2621	0.754664	0.377332	+	0.926078i	$0.376841\pi$
$410$	−9.81310	−0.484634
$411$	5.56923	0.274710
$412$	2.78682	0.137297
$413$	−0.525228	−0.0258448
$414$	−2.46077	−0.120940
$415$	11.3355	0.556440
$416$	−12.0649	−0.591531
$417$	5.40714	0.264789
$418$	27.6877	1.35425
$419$	−0.0371277	−0.00181381	−0.000906903	−	1.00000i	$-0.500289\pi$
$419$	−0.0371277	−0.00181381	−0.000906903		1.00000i	$0.500289\pi$
$420$	−1.10724	−0.0540279
$421$	−35.3220	−1.72149	−0.860744	−	0.509038i	$-0.830001\pi$
$421$	−35.3220	−1.72149	−0.860744	+	0.509038i	$0.830001\pi$
$422$	−5.54549	−0.269950
$423$	−8.76852	−0.426340
$424$	9.04055	0.439048
$425$	−3.48536	−0.169065
$426$	−10.8832	−0.527293
$427$	4.82222	0.233364
$428$	−9.08673	−0.439224
$429$	34.9533	1.68756
$430$	2.84323	0.137113
$431$	34.6131	1.66725	0.833626	−	0.552329i	$-0.186261\pi$
$431$	34.6131	1.66725	0.833626	+	0.552329i	$0.186261\pi$
$432$	−6.48400	−0.311961
$433$	−20.5205	−0.986152	−0.493076	−	0.869986i	$-0.664128\pi$
$433$	−20.5205	−0.986152	−0.493076	+	0.869986i	$0.664128\pi$
$434$	1.24374	0.0597013
$435$	13.4208	0.643476
$436$	7.24604	0.347022
$437$	6.52943	0.312345
$438$	15.3619	0.734021
$439$	−24.7549	−1.18148	−0.590742	−	0.806860i	$-0.701165\pi$
$439$	−24.7549	−1.18148	−0.590742	+	0.806860i	$0.701165\pi$
$440$	−10.9553	−0.522275
$441$	1.94153	0.0924539
$442$	18.7686	0.892730
$443$	−28.2895	−1.34407	−0.672037	−	0.740518i	$-0.734580\pi$
$443$	−28.2895	−1.34407	−0.672037	+	0.740518i	$0.734580\pi$
$444$	−11.5244	−0.546924
$445$	11.3697	0.538976
$446$	−7.04225	−0.333460
$447$	20.5597	0.972439
$448$	−8.87641	−0.419371
$449$	−9.27520	−0.437724	−0.218862	−	0.975756i	$-0.570234\pi$
$449$	−9.27520	−0.437724	−0.218862	+	0.975756i	$0.570234\pi$
$450$	−2.37939	−0.112166
$451$	−28.6537	−1.34925
$452$	−1.97756	−0.0930167
$453$	28.4491	1.33665
$454$	0.0272310	0.00127801
$455$	−4.39402	−0.205995
$456$	−42.9666	−2.01210
$457$	0.921945	0.0431268	0.0215634	−	0.999767i	$-0.493136\pi$
$457$	0.921945	0.0431268	0.0215634	+	0.999767i	$0.493136\pi$
$458$	−1.22552	−0.0572649
$459$	−8.20080	−0.382781
$460$	−0.515130	−0.0240181
$461$	−37.7939	−1.76024	−0.880119	−	0.474752i	$-0.842538\pi$
$461$	−37.7939	−1.76024	−0.880119	+	0.474752i	$0.842538\pi$
$462$	9.74872	0.453552
$463$	6.82106	0.317002	0.158501	−	0.987359i	$-0.449334\pi$
$463$	6.82106	0.317002	0.158501	+	0.987359i	$0.449334\pi$
$464$	16.6372	0.772362
$465$	−2.25599	−0.104619
$466$	−19.4726	−0.902049
$467$	5.83080	0.269817	0.134909	−	0.990858i	$-0.456926\pi$
$467$	5.83080	0.269817	0.134909	+	0.990858i	$0.456926\pi$
$468$	−4.24931	−0.196425
$469$	0.272062	0.0125627
$470$	5.53482	0.255302
$471$	−15.8903	−0.732186
$472$	1.60797	0.0740128
$473$	8.30206	0.381729
$474$	−13.4189	−0.616351
$475$	6.31350	0.289683
$476$	−1.73604	−0.0795712
$477$	5.73335	0.262512
$478$	−11.5890	−0.530067
$479$	−12.5537	−0.573592	−0.286796	−	0.957992i	$-0.592590\pi$
$479$	−12.5537	−0.573592	−0.286796	+	0.957992i	$0.592590\pi$
$480$	6.10369	0.278594
$481$	−45.7339	−2.08529
$482$	−5.33679	−0.243084
$483$	2.29898	0.104607
$484$	−0.899232	−0.0408742
$485$	−6.01260	−0.273018
$486$	−21.4664	−0.973734
$487$	21.3609	0.967954	0.483977	−	0.875081i	$-0.339192\pi$
$487$	21.3609	0.967954	0.483977	+	0.875081i	$0.339192\pi$
$488$	−14.7631	−0.668294
$489$	−29.3859	−1.32888
$490$	−1.22552	−0.0553635
$491$	−37.0869	−1.67371	−0.836855	−	0.547425i	$-0.815608\pi$
$491$	−37.0869	−1.67371	−0.836855	+	0.547425i	$0.815608\pi$
$492$	8.86600	0.399710
$493$	21.0423	0.947699
$494$	−33.9980	−1.52964
$495$	−6.94768	−0.312275
$496$	−2.79667	−0.125574
$497$	3.99489	0.179195
$498$	30.8812	1.38382
$499$	−0.865557	−0.0387477	−0.0193738	−	0.999812i	$-0.506167\pi$
$499$	−0.865557	−0.0387477	−0.0193738	+	0.999812i	$0.506167\pi$
$500$	−0.498095	−0.0222755
$501$	−54.1351	−2.41858
$502$	14.9806	0.668619
$503$	−18.2576	−0.814067	−0.407034	−	0.913413i	$-0.633437\pi$
$503$	−18.2576	−0.814067	−0.407034	+	0.913413i	$0.633437\pi$
$504$	−5.94394	−0.264764
$505$	−11.4080	−0.507650
$506$	4.53547	0.201626
$507$	−14.0212	−0.622701
$508$	3.88378	0.172315
$509$	−25.6696	−1.13778	−0.568892	−	0.822413i	$-0.692628\pi$
$509$	−25.6696	−1.13778	−0.568892	+	0.822413i	$0.692628\pi$
$510$	−9.49510	−0.420450
$511$	−5.63889	−0.249450
$512$	24.4396	1.08009
$513$	14.8552	0.655874
$514$	−3.88757	−0.171473
$515$	−5.59496	−0.246543
$516$	−2.56882	−0.113086
$517$	16.1614	0.710776
$518$	−12.7555	−0.560444
$519$	−30.7425	−1.34945
$520$	13.4522	0.589917
$521$	−10.9370	−0.479157	−0.239579	−	0.970877i	$-0.577009\pi$
$521$	−10.9370	−0.479157	−0.239579	+	0.970877i	$0.577009\pi$
$522$	14.3652	0.628748
$523$	−27.0502	−1.18282	−0.591411	−	0.806370i	$-0.701429\pi$
$523$	−27.0502	−1.18282	−0.591411	+	0.806370i	$0.701429\pi$
$524$	−5.47314	−0.239095
$525$	2.22296	0.0970177
$526$	12.1455	0.529567
$527$	−3.53716	−0.154081
$528$	−21.9210	−0.953989
$529$	−21.9304	−0.953497
$530$	−3.61898	−0.157198
$531$	1.01975	0.0442532
$532$	3.14472	0.136341
$533$	35.1842	1.52400
$534$	30.9743	1.34039
$535$	18.2430	0.788713
$536$	−0.832910	−0.0359762
$537$	6.07954	0.262352
$538$	−14.7889	−0.637595
$539$	−3.57846	−0.154135
$540$	−1.17198	−0.0504341
$541$	−21.0328	−0.904271	−0.452136	−	0.891949i	$-0.649338\pi$
$541$	−21.0328	−0.904271	−0.452136	+	0.891949i	$0.649338\pi$
$542$	−24.2664	−1.04233
$543$	−33.4021	−1.43342
$544$	9.56994	0.410308
$545$	−14.5475	−0.623147
$546$	−11.9706	−0.512293
$547$	−7.52224	−0.321628	−0.160814	−	0.986985i	$-0.551412\pi$
$547$	−7.52224	−0.321628	−0.160814	+	0.986985i	$0.551412\pi$
$548$	1.24789	0.0533072
$549$	−9.36249	−0.399581
$550$	4.38548	0.186997
$551$	−38.1168	−1.62383
$552$	−7.03827	−0.299569
$553$	4.92567	0.209461
$554$	−14.4714	−0.614829
$555$	23.1370	0.982110
$556$	1.21157	0.0513821
$557$	7.72299	0.327234	0.163617	−	0.986524i	$-0.447684\pi$
$557$	7.72299	0.327234	0.163617	+	0.986524i	$0.447684\pi$
$558$	−2.41475	−0.102225
$559$	−10.1942	−0.431168
$560$	2.75571	0.116450
$561$	−27.7251	−1.17056
$562$	−5.94565	−0.250802
$563$	3.34567	0.141003	0.0705016	−	0.997512i	$-0.477540\pi$
$563$	3.34567	0.141003	0.0705016	+	0.997512i	$0.477540\pi$
$564$	−5.00063	−0.210565
$565$	3.97025	0.167030
$566$	−11.5995	−0.487562
$567$	11.0551	0.464268
$568$	−12.2302	−0.513169
$569$	19.4393	0.814940	0.407470	−	0.913219i	$-0.366411\pi$
$569$	19.4393	0.814940	0.407470	+	0.913219i	$0.366411\pi$
$570$	17.1998	0.720418
$571$	−24.3437	−1.01875	−0.509377	−	0.860544i	$-0.670124\pi$
$571$	−24.3437	−1.01875	−0.509377	+	0.860544i	$0.670124\pi$
$572$	7.83195	0.327470
$573$	−18.3248	−0.765530
$574$	9.81310	0.409591
$575$	1.03420	0.0431292
$576$	17.2338	0.718076
$577$	−25.9528	−1.08043	−0.540215	−	0.841527i	$-0.681657\pi$
$577$	−25.9528	−1.08043	−0.540215	+	0.841527i	$0.681657\pi$
$578$	5.94657	0.247345
$579$	47.5189	1.97482
$580$	3.00717	0.124866
$581$	−11.3355	−0.470278
$582$	−16.3800	−0.678974
$583$	−10.5672	−0.437649
$584$	17.2633	0.714360
$585$	8.53113	0.352719
$586$	−21.3614	−0.882432
$587$	36.2464	1.49605	0.748024	−	0.663672i	$-0.231003\pi$
$587$	36.2464	1.49605	0.748024	+	0.663672i	$0.231003\pi$
$588$	1.10724	0.0456619
$589$	6.40733	0.264010
$590$	−0.643679	−0.0264998
$591$	32.0383	1.31788
$592$	28.6820	1.17882
$593$	0.269061	0.0110490	0.00552450	−	0.999985i	$-0.498241\pi$
$593$	0.269061	0.0110490	0.00552450	+	0.999985i	$0.498241\pi$
$594$	10.3187	0.423382
$595$	3.48536	0.142886
$596$	4.60678	0.188701
$597$	−36.4377	−1.49129
$598$	−5.56915	−0.227739
$599$	12.5862	0.514256	0.257128	−	0.966377i	$-0.417224\pi$
$599$	12.5862	0.514256	0.257128	+	0.966377i	$0.417224\pi$
$600$	−6.80551	−0.277834
$601$	−25.1687	−1.02665	−0.513327	−	0.858193i	$-0.671587\pi$
$601$	−25.1687	−1.02665	−0.513327	+	0.858193i	$0.671587\pi$
$602$	−2.84323	−0.115881
$603$	−0.528217	−0.0215106
$604$	6.37455	0.259377
$605$	1.80534	0.0733976
$606$	−31.0787	−1.26248
$607$	−18.2464	−0.740600	−0.370300	−	0.928912i	$-0.620745\pi$
$607$	−18.2464	−0.740600	−0.370300	+	0.928912i	$0.620745\pi$
$608$	−17.3353	−0.703040
$609$	−13.4208	−0.543836
$610$	5.90974	0.239278
$611$	−19.8447	−0.802831
$612$	3.37057	0.136247
$613$	−43.9632	−1.77566	−0.887828	−	0.460175i	$-0.847787\pi$
$613$	−43.9632	−1.77566	−0.887828	+	0.460175i	$0.847787\pi$
$614$	7.10747	0.286834
$615$	−17.7998	−0.717758
$616$	10.9553	0.441403
$617$	−9.61475	−0.387075	−0.193538	−	0.981093i	$-0.561996\pi$
$617$	−9.61475	−0.387075	−0.193538	+	0.981093i	$0.561996\pi$
$618$	−15.2422	−0.613133
$619$	14.2329	0.572069	0.286034	−	0.958219i	$-0.407663\pi$
$619$	14.2329	0.572069	0.286034	+	0.958219i	$0.407663\pi$
$620$	−0.505498	−0.0203013
$621$	2.43340	0.0976491
$622$	18.1500	0.727748
$623$	−11.3697	−0.455518
$624$	26.9170	1.07754
$625$	1.00000	0.0400000
$626$	−12.7165	−0.508253
$627$	50.2223	2.00569
$628$	−3.56052	−0.142080
$629$	36.2763	1.44643
$630$	2.37939	0.0947972
$631$	−7.45389	−0.296735	−0.148367	−	0.988932i	$-0.547402\pi$
$631$	−7.45389	−0.296735	−0.148367	+	0.988932i	$0.547402\pi$
$632$	−15.0798	−0.599842
$633$	−10.0589	−0.399804
$634$	−29.2103	−1.16009
$635$	−7.79726	−0.309425
$636$	3.26969	0.129652
$637$	4.39402	0.174098
$638$	−26.4767	−1.04822
$639$	−7.75620	−0.306830
$640$	−5.38673	−0.212929
$641$	−7.08580	−0.279872	−0.139936	−	0.990161i	$-0.544690\pi$
$641$	−7.08580	−0.279872	−0.139936	+	0.990161i	$0.544690\pi$
$642$	49.6990	1.96146
$643$	39.7341	1.56696	0.783481	−	0.621416i	$-0.213442\pi$
$643$	39.7341	1.56696	0.783481	+	0.621416i	$0.213442\pi$
$644$	0.515130	0.0202990
$645$	5.15728	0.203068
$646$	26.9674	1.06102
$647$	4.32886	0.170185	0.0850925	−	0.996373i	$-0.472881\pi$
$647$	4.32886	0.170185	0.0850925	+	0.996373i	$0.472881\pi$
$648$	−33.8447	−1.32955
$649$	−1.87950	−0.0737770
$650$	−5.38497	−0.211216
$651$	2.25599	0.0884194
$652$	−6.58447	−0.257868
$653$	47.1074	1.84346	0.921728	−	0.387838i	$-0.126778\pi$
$653$	47.1074	1.84346	0.921728	+	0.387838i	$0.126778\pi$
$654$	−39.6315	−1.54972
$655$	10.9882	0.429343
$656$	−22.0658	−0.861523
$657$	10.9481	0.427125
$658$	−5.53482	−0.215770
$659$	−33.4731	−1.30393	−0.651963	−	0.758251i	$-0.726054\pi$
$659$	−33.4731	−1.30393	−0.651963	+	0.758251i	$0.726054\pi$
$660$	−3.96222	−0.154229
$661$	1.76974	0.0688349	0.0344175	−	0.999408i	$-0.489042\pi$
$661$	1.76974	0.0688349	0.0344175	+	0.999408i	$0.489042\pi$
$662$	31.1453	1.21050
$663$	34.0440	1.32216
$664$	34.7035	1.34676
$665$	−6.31350	−0.244827
$666$	24.7652	0.959631
$667$	−6.24384	−0.241762
$668$	−12.1300	−0.469323
$669$	−12.7738	−0.493865
$670$	0.333418	0.0128811
$671$	17.2561	0.666165
$672$	−6.10369	−0.235455
$673$	−19.6425	−0.757164	−0.378582	−	0.925568i	$-0.623588\pi$
$673$	−19.6425	−0.757164	−0.378582	+	0.925568i	$0.623588\pi$
$674$	−8.23192	−0.317082
$675$	2.35293	0.0905643
$676$	−3.14170	−0.120835
$677$	−42.7819	−1.64424	−0.822121	−	0.569313i	$-0.807209\pi$
$677$	−42.7819	−1.64424	−0.822121	+	0.569313i	$0.807209\pi$
$678$	10.8161	0.415389
$679$	6.01260	0.230742
$680$	−10.6703	−0.409188
$681$	0.0493938	0.00189278
$682$	4.45066	0.170424
$683$	−22.7920	−0.872112	−0.436056	−	0.899920i	$-0.643625\pi$
$683$	−22.7920	−0.872112	−0.436056	+	0.899920i	$0.643625\pi$
$684$	−6.10557	−0.233452
$685$	−2.50533	−0.0957236
$686$	1.22552	0.0467907
$687$	−2.22296	−0.0848110
$688$	6.39329	0.243742
$689$	12.9756	0.494330
$690$	2.81746	0.107259
$691$	−37.0597	−1.40982	−0.704908	−	0.709299i	$-0.749012\pi$
$691$	−37.0597	−1.40982	−0.704908	+	0.709299i	$0.749012\pi$
$692$	−6.88844	−0.261859
$693$	6.94768	0.263921
$694$	−23.6342	−0.897142
$695$	−2.43241	−0.0922666
$696$	41.0873	1.55741
$697$	−27.9082	−1.05710
$698$	14.9320	0.565185
$699$	−35.3210	−1.33596
$700$	0.498095	0.0188262
$701$	19.9250	0.752556	0.376278	−	0.926507i	$-0.377204\pi$
$701$	19.9250	0.752556	0.376278	+	0.926507i	$0.377204\pi$
$702$	−12.6705	−0.478216
$703$	−65.7122	−2.47838
$704$	−31.7638	−1.19714
$705$	10.0395	0.378110
$706$	29.0936	1.09495
$707$	11.4080	0.429043
$708$	0.581555	0.0218562
$709$	−30.2532	−1.13618	−0.568092	−	0.822965i	$-0.692318\pi$
$709$	−30.2532	−1.13618	−0.568092	+	0.822965i	$0.692318\pi$
$710$	4.89582	0.183737
$711$	−9.56333	−0.358653
$712$	34.8080	1.30449
$713$	1.04957	0.0393068
$714$	9.49510	0.355345
$715$	−15.7238	−0.588037
$716$	1.36223	0.0509091
$717$	−21.0210	−0.785044
$718$	−2.78484	−0.103929
$719$	24.3465	0.907972	0.453986	−	0.891009i	$-0.350002\pi$
$719$	24.3465	0.907972	0.453986	+	0.891009i	$0.350002\pi$
$720$	−5.35030	−0.199394
$721$	5.59496	0.208367
$722$	−25.5648	−0.951422
$723$	−9.68032	−0.360015
$724$	−7.48437	−0.278154
$725$	−6.03735	−0.224221
$726$	4.91826	0.182534
$727$	17.2525	0.639859	0.319930	−	0.947441i	$-0.396341\pi$
$727$	17.2525	0.639859	0.319930	+	0.947441i	$0.396341\pi$
$728$	−13.4522	−0.498571
$729$	−5.77235	−0.213791
$730$	−6.91058	−0.255772
$731$	8.08608	0.299074
$732$	−5.33937	−0.197349
$733$	−22.3677	−0.826170	−0.413085	−	0.910693i	$-0.635549\pi$
$733$	−22.3677	−0.826170	−0.413085	+	0.910693i	$0.635549\pi$
$734$	−20.3476	−0.751044
$735$	−2.22296	−0.0819949
$736$	−2.83966	−0.104671
$737$	0.973561	0.0358616
$738$	−19.0524	−0.701330
$739$	−8.86055	−0.325940	−0.162970	−	0.986631i	$-0.552107\pi$
$739$	−8.86055	−0.325940	−0.162970	+	0.986631i	$0.552107\pi$
$740$	5.18427	0.190578
$741$	−61.6685	−2.26545
$742$	3.61898	0.132857
$743$	21.4308	0.786219	0.393110	−	0.919492i	$-0.371399\pi$
$743$	21.4308	0.786219	0.393110	+	0.919492i	$0.371399\pi$
$744$	−6.90666	−0.253210
$745$	−9.24880	−0.338850
$746$	−22.7753	−0.833863
$747$	22.0083	0.805242
$748$	−6.21234	−0.227146
$749$	−18.2430	−0.666584
$750$	2.72428	0.0994767
$751$	−45.1463	−1.64741	−0.823706	−	0.567018i	$-0.808097\pi$
$751$	−45.1463	−1.64741	−0.823706	+	0.567018i	$0.808097\pi$
$752$	12.4456	0.453844
$753$	27.1731	0.990245
$754$	32.5110	1.18398
$755$	−12.7979	−0.465762
$756$	1.17198	0.0426246
$757$	14.1905	0.515762	0.257881	−	0.966177i	$-0.416976\pi$
$757$	14.1905	0.515762	0.257881	+	0.966177i	$0.416976\pi$
$758$	20.4040	0.741107
$759$	8.22681	0.298614
$760$	19.3286	0.701122
$761$	−9.73028	−0.352722	−0.176361	−	0.984326i	$-0.556433\pi$
$761$	−9.73028	−0.352722	−0.176361	+	0.984326i	$0.556433\pi$
$762$	−21.2419	−0.769514
$763$	14.5475	0.526655
$764$	−4.10602	−0.148551
$765$	−6.76693	−0.244659
$766$	−1.36823	−0.0494363
$767$	2.30786	0.0833321
$768$	24.7888	0.894487
$769$	0.334898	0.0120767	0.00603836	−	0.999982i	$-0.498078\pi$
$769$	0.334898	0.0120767	0.00603836	+	0.999982i	$0.498078\pi$
$770$	−4.38548	−0.158042
$771$	−7.05160	−0.253957
$772$	10.6475	0.383212
$773$	8.23417	0.296163	0.148081	−	0.988975i	$-0.452690\pi$
$773$	8.23417	0.296163	0.148081	+	0.988975i	$0.452690\pi$
$774$	5.52021	0.198420
$775$	1.01486	0.0364549
$776$	−18.4074	−0.660787
$777$	−23.1370	−0.830034
$778$	11.5730	0.414912
$779$	50.5540	1.81128
$780$	4.86525	0.174204
$781$	14.2955	0.511534
$782$	4.41747	0.157969
$783$	−14.2055	−0.507662
$784$	−2.75571	−0.0984183
$785$	7.14828	0.255133
$786$	29.9348	1.06774
$787$	−51.8277	−1.84746	−0.923728	−	0.383048i	$-0.874874\pi$
$787$	−51.8277	−1.84746	−0.923728	+	0.383048i	$0.874874\pi$
$788$	7.17879	0.255734
$789$	22.0304	0.784305
$790$	6.03651	0.214770
$791$	−3.97025	−0.141166
$792$	−21.2701	−0.755801
$793$	−21.1890	−0.752442
$794$	31.1180	1.10434
$795$	−6.56440	−0.232815
$796$	−8.16454	−0.289385
$797$	26.4836	0.938096	0.469048	−	0.883173i	$-0.344597\pi$
$797$	26.4836	0.938096	0.469048	+	0.883173i	$0.344597\pi$
$798$	−17.1998	−0.608865
$799$	15.7409	0.556873
$800$	−2.74576	−0.0970771
$801$	22.0746	0.779969
$802$	35.6845	1.26006
$803$	−20.1785	−0.712084
$804$	−0.301238	−0.0106239
$805$	−1.03420	−0.0364508
$806$	−5.46501	−0.192497
$807$	−26.8253	−0.944297
$808$	−34.9253	−1.22867
$809$	−19.6271	−0.690051	−0.345025	−	0.938593i	$-0.612130\pi$
$809$	−19.6271	−0.690051	−0.345025	+	0.938593i	$0.612130\pi$
$810$	13.5482	0.476036
$811$	52.8592	1.85614	0.928068	−	0.372411i	$-0.121469\pi$
$811$	52.8592	1.85614	0.928068	+	0.372411i	$0.121469\pi$
$812$	−3.00717	−0.105531
$813$	−44.0164	−1.54372
$814$	−45.6449	−1.59985
$815$	13.2193	0.463052
$816$	−21.3507	−0.747424
$817$	−14.6474	−0.512448
$818$	−18.7041	−0.653974
$819$	−8.53113	−0.298102
$820$	−3.98838	−0.139280
$821$	−51.1540	−1.78529	−0.892644	−	0.450763i	$-0.851152\pi$
$821$	−51.1540	−1.78529	−0.892644	+	0.450763i	$0.851152\pi$
$822$	−6.82521	−0.238057
$823$	−23.8430	−0.831114	−0.415557	−	0.909567i	$-0.636413\pi$
$823$	−23.8430	−0.831114	−0.415557	+	0.909567i	$0.636413\pi$
$824$	−17.1288	−0.596710
$825$	7.95475	0.276949
$826$	0.643679	0.0223964
$827$	40.8669	1.42108	0.710541	−	0.703656i	$-0.248450\pi$
$827$	40.8669	1.42108	0.710541	+	0.703656i	$0.248450\pi$
$828$	−1.00014	−0.0347573
$829$	34.4057	1.19496	0.597479	−	0.801884i	$-0.296169\pi$
$829$	34.4057	1.19496	0.597479	+	0.801884i	$0.296169\pi$
$830$	−13.8920	−0.482197
$831$	−26.2494	−0.910581
$832$	39.0031	1.35219
$833$	−3.48536	−0.120761
$834$	−6.62657	−0.229459
$835$	24.3528	0.842762
$836$	11.2532	0.389202
$837$	2.38790	0.0825379
$838$	0.0455008	0.00157180
$839$	4.61519	0.159334	0.0796671	−	0.996822i	$-0.474614\pi$
$839$	4.61519	0.159334	0.0796671	+	0.996822i	$0.474614\pi$
$840$	6.80551	0.234813
$841$	7.44957	0.256882
$842$	43.2879	1.49180
$843$	−10.7847	−0.371445
$844$	−2.25388	−0.0775817
$845$	6.30744	0.216982
$846$	10.7460	0.369456
$847$	−1.80534	−0.0620323
$848$	−8.13764	−0.279448
$849$	−21.0401	−0.722094
$850$	4.27138	0.146507
$851$	−10.7642	−0.368991
$852$	−4.42331	−0.151540
$853$	−25.5038	−0.873234	−0.436617	−	0.899648i	$-0.643823\pi$
$853$	−25.5038	−0.873234	−0.436617	+	0.899648i	$0.643823\pi$
$854$	−5.90974	−0.202227
$855$	12.2579	0.419210
$856$	55.8504	1.90893
$857$	−25.8599	−0.883356	−0.441678	−	0.897174i	$-0.645617\pi$
$857$	−25.8599	−0.883356	−0.441678	+	0.897174i	$0.645617\pi$
$858$	−42.8361	−1.46240
$859$	28.0556	0.957243	0.478622	−	0.878021i	$-0.341137\pi$
$859$	28.0556	0.957243	0.478622	+	0.878021i	$0.341137\pi$
$860$	1.15559	0.0394052
$861$	17.7998	0.606616
$862$	−42.4191	−1.44480
$863$	30.5234	1.03903	0.519514	−	0.854462i	$-0.326113\pi$
$863$	30.5234	1.03903	0.519514	+	0.854462i	$0.326113\pi$
$864$	−6.46057	−0.219793
$865$	13.8296	0.470220
$866$	25.1483	0.854575
$867$	10.7864	0.366325
$868$	0.505498	0.0171577
$869$	17.6263	0.597931
$870$	−16.4474	−0.557620
$871$	−1.19545	−0.0405061
$872$	−44.5368	−1.50821
$873$	−11.6736	−0.395093
$874$	−8.00197	−0.270671
$875$	−1.00000	−0.0338062
$876$	6.24362	0.210952
$877$	21.1210	0.713206	0.356603	−	0.934256i	$-0.383935\pi$
$877$	21.1210	0.713206	0.356603	+	0.934256i	$0.383935\pi$
$878$	30.3376	1.02385
$879$	−38.7472	−1.30691
$880$	9.86119	0.332421
$881$	−43.7953	−1.47550	−0.737751	−	0.675073i	$-0.764112\pi$
$881$	−43.7953	−1.47550	−0.737751	+	0.675073i	$0.764112\pi$
$882$	−2.37939	−0.0801182
$883$	−45.3757	−1.52702	−0.763508	−	0.645799i	$-0.776524\pi$
$883$	−45.3757	−1.52702	−0.763508	+	0.645799i	$0.776524\pi$
$884$	7.62819	0.256564
$885$	−1.16756	−0.0392470
$886$	34.6694	1.16474
$887$	−41.0064	−1.37686	−0.688430	−	0.725302i	$-0.741700\pi$
$887$	−41.0064	−1.37686	−0.688430	+	0.725302i	$0.741700\pi$
$888$	70.8332	2.37701
$889$	7.79726	0.261512
$890$	−13.9338	−0.467063
$891$	39.5600	1.32531
$892$	−2.86222	−0.0958341
$893$	−28.5136	−0.954172
$894$	−25.1963	−0.842692
$895$	−2.73489	−0.0914173
$896$	5.38673	0.179958
$897$	−10.1018	−0.337289
$898$	11.3670	0.379321
$899$	−6.12708	−0.204349
$900$	−0.967066	−0.0322355
$901$	−10.2923	−0.342886
$902$	35.1157	1.16923
$903$	−5.15728	−0.171624
$904$	12.1548	0.404263
$905$	15.0260	0.499481
$906$	−34.8650	−1.15831
$907$	−24.1856	−0.803070	−0.401535	−	0.915844i	$-0.631523\pi$
$907$	−24.1856	−0.803070	−0.401535	+	0.915844i	$0.631523\pi$
$908$	0.0110676	0.000367292 0
$909$	−22.1490	−0.734637
$910$	5.38497	0.178510
$911$	21.9404	0.726919	0.363460	−	0.931610i	$-0.381595\pi$
$911$	21.9404	0.726919	0.363460	+	0.931610i	$0.381595\pi$
$912$	38.6754	1.28067
$913$	−40.5637	−1.34246
$914$	−1.12986	−0.0373726
$915$	10.7196	0.354379
$916$	−0.498095	−0.0164575
$917$	−10.9882	−0.362861
$918$	10.0503	0.331708
$919$	14.6744	0.484064	0.242032	−	0.970268i	$-0.422186\pi$
$919$	14.6744	0.484064	0.242032	+	0.970268i	$0.422186\pi$
$920$	3.16618	0.104386
$921$	12.8921	0.424810
$922$	46.3173	1.52538
$923$	−17.5536	−0.577785
$924$	3.96222	0.130347
$925$	−10.4082	−0.342220
$926$	−8.35936	−0.274706
$927$	−10.8628	−0.356781
$928$	16.5771	0.544169
$929$	25.7785	0.845766	0.422883	−	0.906184i	$-0.361018\pi$
$929$	25.7785	0.845766	0.422883	+	0.906184i	$0.361018\pi$
$930$	2.76477	0.0906604
$931$	6.31350	0.206917
$932$	−7.91433	−0.259242
$933$	32.9220	1.07782
$934$	−7.14578	−0.233817
$935$	12.4722	0.407885
$936$	26.1178	0.853687
$937$	−37.2419	−1.21664	−0.608321	−	0.793691i	$-0.708156\pi$
$937$	−37.2419	−1.21664	−0.608321	+	0.793691i	$0.708156\pi$
$938$	−0.333418	−0.0108865
$939$	−23.0662	−0.752738
$940$	2.24954	0.0733720
$941$	56.5135	1.84229	0.921143	−	0.389224i	$-0.127257\pi$
$941$	56.5135	1.84229	0.921143	+	0.389224i	$0.127257\pi$
$942$	19.4739	0.634495
$943$	8.28114	0.269671
$944$	−1.44738	−0.0471081
$945$	−2.35293	−0.0765408
$946$	−10.1744	−0.330797
$947$	−9.60248	−0.312039	−0.156019	−	0.987754i	$-0.549866\pi$
$947$	−9.60248	−0.312039	−0.156019	+	0.987754i	$0.549866\pi$
$948$	−5.45391	−0.177135
$949$	24.7774	0.804308
$950$	−7.73734	−0.251032
$951$	−52.9841	−1.71813
$952$	10.6703	0.345827
$953$	26.5667	0.860581	0.430290	−	0.902691i	$-0.358411\pi$
$953$	26.5667	0.860581	0.430290	+	0.902691i	$0.358411\pi$
$954$	−7.02635	−0.227487
$955$	8.24345	0.266752
$956$	−4.71015	−0.152337
$957$	−48.0256	−1.55245
$958$	15.3848	0.497061
$959$	2.50533	0.0809012
$960$	−19.7319	−0.636843
$961$	−29.9701	−0.966776
$962$	56.0479	1.80706
$963$	35.4193	1.14137
$964$	−2.16906	−0.0698606
$965$	−21.3764	−0.688132
$966$	−2.81746	−0.0906502
$967$	28.4948	0.916331	0.458165	−	0.888867i	$-0.348507\pi$
$967$	28.4948	0.916331	0.458165	+	0.888867i	$0.348507\pi$
$968$	5.52701	0.177645
$969$	48.9157	1.57140
$970$	7.36858	0.236591
$971$	9.63888	0.309326	0.154663	−	0.987967i	$-0.450571\pi$
$971$	9.63888	0.309326	0.154663	+	0.987967i	$0.450571\pi$
$972$	−8.72468	−0.279844
$973$	2.43241	0.0779795
$974$	−26.1782	−0.838805
$975$	−9.76772	−0.312817
$976$	13.2887	0.425360
$977$	−31.7347	−1.01528	−0.507641	−	0.861569i	$-0.669482\pi$
$977$	−31.7347	−1.01528	−0.507641	+	0.861569i	$0.669482\pi$
$978$	36.0131	1.15157
$979$	−40.6860	−1.30033
$980$	−0.498095	−0.0159111
$981$	−28.2444	−0.901776
$982$	45.4509	1.45040
$983$	43.6485	1.39217	0.696085	−	0.717959i	$-0.254923\pi$
$983$	43.6485	1.39217	0.696085	+	0.717959i	$0.254923\pi$
$984$	−54.4936	−1.73719
$985$	−14.4125	−0.459220
$986$	−25.7878	−0.821252
$987$	−10.0395	−0.319561
$988$	−13.8180	−0.439609
$989$	−2.39936	−0.0762952
$990$	8.51454	0.270610
$991$	18.3812	0.583897	0.291949	−	0.956434i	$-0.405696\pi$
$991$	18.3812	0.583897	0.291949	+	0.956434i	$0.405696\pi$
$992$	−2.78656	−0.0884735
$993$	56.4939	1.79278
$994$	−4.89582	−0.155286
$995$	16.3915	0.519647
$996$	12.5512	0.397700
$997$	56.8936	1.80184	0.900919	−	0.433988i	$-0.142894\pi$
$997$	56.8936	1.80184	0.900919	+	0.433988i	$0.142894\pi$
$998$	1.06076	0.0335778
$999$	−24.4898	−0.774822

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.15	✓	44	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-1.22552 q^{2} -2.22296 q^{3} -0.498095 q^{4} +1.00000 q^{5} +2.72428 q^{6} -1.00000 q^{7} +3.06147 q^{8} +1.94153 q^{9} +O(q^{10})\)	\(q-1.22552 q^{2} -2.22296 q^{3} -0.498095 q^{4} +1.00000 q^{5} +2.72428 q^{6} -1.00000 q^{7} +3.06147 q^{8} +1.94153 q^{9} -1.22552 q^{10} -3.57846 q^{11} +1.10724 q^{12} +4.39402 q^{13} +1.22552 q^{14} -2.22296 q^{15} -2.75571 q^{16} -3.48536 q^{17} -2.37939 q^{18} +6.31350 q^{19} -0.498095 q^{20} +2.22296 q^{21} +4.38548 q^{22} +1.03420 q^{23} -6.80551 q^{24} +1.00000 q^{25} -5.38497 q^{26} +2.35293 q^{27} +0.498095 q^{28} -6.03735 q^{29} +2.72428 q^{30} +1.01486 q^{31} -2.74576 q^{32} +7.95475 q^{33} +4.27138 q^{34} -1.00000 q^{35} -0.967066 q^{36} -10.4082 q^{37} -7.73734 q^{38} -9.76772 q^{39} +3.06147 q^{40} +8.00728 q^{41} -2.72428 q^{42} -2.32001 q^{43} +1.78241 q^{44} +1.94153 q^{45} -1.26744 q^{46} -4.51629 q^{47} +6.12582 q^{48} +1.00000 q^{49} -1.22552 q^{50} +7.74780 q^{51} -2.18864 q^{52} +2.95301 q^{53} -2.88357 q^{54} -3.57846 q^{55} -3.06147 q^{56} -14.0346 q^{57} +7.39891 q^{58} +0.525228 q^{59} +1.10724 q^{60} -4.82222 q^{61} -1.24374 q^{62} -1.94153 q^{63} +8.87641 q^{64} +4.39402 q^{65} -9.74872 q^{66} -0.272062 q^{67} +1.73604 q^{68} -2.29898 q^{69} +1.22552 q^{70} -3.99489 q^{71} +5.94394 q^{72} +5.63889 q^{73} +12.7555 q^{74} -2.22296 q^{75} -3.14472 q^{76} +3.57846 q^{77} +11.9706 q^{78} -4.92567 q^{79} -2.75571 q^{80} -11.0551 q^{81} -9.81310 q^{82} +11.3355 q^{83} -1.10724 q^{84} -3.48536 q^{85} +2.84323 q^{86} +13.4208 q^{87} -10.9553 q^{88} +11.3697 q^{89} -2.37939 q^{90} -4.39402 q^{91} -0.515130 q^{92} -2.25599 q^{93} +5.53482 q^{94} +6.31350 q^{95} +6.10369 q^{96} -6.01260 q^{97} -1.22552 q^{98} -6.94768 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9} - 2 q^{10} - 15 q^{11} - 3 q^{12} - 17 q^{13} + 2 q^{14} + 10 q^{16} - 7 q^{17} - 16 q^{18} - 32 q^{19} + 30 q^{20} - 14 q^{22} + 8 q^{23} - 35 q^{24} + 44 q^{25} - 27 q^{26} + 6 q^{27} - 30 q^{28} - 42 q^{29} - 7 q^{30} - 43 q^{31} - 8 q^{32} - 33 q^{33} - 33 q^{34} - 44 q^{35} - 11 q^{36} - 44 q^{37} + 4 q^{38} + 3 q^{39} - 3 q^{40} - 62 q^{41} + 7 q^{42} - 7 q^{43} - 45 q^{44} + 16 q^{45} - 15 q^{46} + 2 q^{47} - 26 q^{48} + 44 q^{49} - 2 q^{50} - 25 q^{51} - 35 q^{52} - 25 q^{53} - 76 q^{54} - 15 q^{55} + 3 q^{56} - 7 q^{57} - 2 q^{58} - 35 q^{59} - 3 q^{60} - 86 q^{61} - 23 q^{62} - 16 q^{63} - 5 q^{64} - 17 q^{65} - 6 q^{66} + 2 q^{67} - q^{68} - 75 q^{69} + 2 q^{70} - 54 q^{71} - 3 q^{72} - 52 q^{73} - 22 q^{74} - 77 q^{76} + 15 q^{77} + 2 q^{78} + 46 q^{79} + 10 q^{80} - 72 q^{81} - 16 q^{82} + 26 q^{83} + 3 q^{84} - 7 q^{85} - 33 q^{86} - 8 q^{87} - 23 q^{88} - 105 q^{89} - 16 q^{90} + 17 q^{91} - 41 q^{92} - 11 q^{93} - 47 q^{94} - 32 q^{95} - 39 q^{96} - 80 q^{97} - 2 q^{98} - 53 q^{99}+O(q^{100}) \) 44 * q - 2 * q^2 + 30 * q^4 + 44 * q^5 - 7 * q^6 - 44 * q^7 - 3 * q^8 + 16 * q^9 - 2 * q^10 - 15 * q^11 - 3 * q^12 - 17 * q^13 + 2 * q^14 + 10 * q^16 - 7 * q^17 - 16 * q^18 - 32 * q^19 + 30 * q^20 - 14 * q^22 + 8 * q^23 - 35 * q^24 + 44 * q^25 - 27 * q^26 + 6 * q^27 - 30 * q^28 - 42 * q^29 - 7 * q^30 - 43 * q^31 - 8 * q^32 - 33 * q^33 - 33 * q^34 - 44 * q^35 - 11 * q^36 - 44 * q^37 + 4 * q^38 + 3 * q^39 - 3 * q^40 - 62 * q^41 + 7 * q^42 - 7 * q^43 - 45 * q^44 + 16 * q^45 - 15 * q^46 + 2 * q^47 - 26 * q^48 + 44 * q^49 - 2 * q^50 - 25 * q^51 - 35 * q^52 - 25 * q^53 - 76 * q^54 - 15 * q^55 + 3 * q^56 - 7 * q^57 - 2 * q^58 - 35 * q^59 - 3 * q^60 - 86 * q^61 - 23 * q^62 - 16 * q^63 - 5 * q^64 - 17 * q^65 - 6 * q^66 + 2 * q^67 - q^68 - 75 * q^69 + 2 * q^70 - 54 * q^71 - 3 * q^72 - 52 * q^73 - 22 * q^74 - 77 * q^76 + 15 * q^77 + 2 * q^78 + 46 * q^79 + 10 * q^80 - 72 * q^81 - 16 * q^82 + 26 * q^83 + 3 * q^84 - 7 * q^85 - 33 * q^86 - 8 * q^87 - 23 * q^88 - 105 * q^89 - 16 * q^90 + 17 * q^91 - 41 * q^92 - 11 * q^93 - 47 * q^94 - 32 * q^95 - 39 * q^96 - 80 * q^97 - 2 * q^98 - 53 * q^99

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