LMFDB - Embedded newform 8015.2.a.i.1.16

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			1.16
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)

$f(q)$	$=$	$q-1.03648 q^{2} -2.16444 q^{3} -0.925705 q^{4} +1.00000 q^{5} +2.24341 q^{6} -1.00000 q^{7} +3.03244 q^{8} +1.68482 q^{9} +O(q^{10})$	\(q-1.03648 q^{2} -2.16444 q^{3} -0.925705 q^{4} +1.00000 q^{5} +2.24341 q^{6} -1.00000 q^{7} +3.03244 q^{8} +1.68482 q^{9} -1.03648 q^{10} +5.93714 q^{11} +2.00364 q^{12} +3.60183 q^{13} +1.03648 q^{14} -2.16444 q^{15} -1.29166 q^{16} -3.86602 q^{17} -1.74629 q^{18} +1.24749 q^{19} -0.925705 q^{20} +2.16444 q^{21} -6.15374 q^{22} +3.21202 q^{23} -6.56355 q^{24} +1.00000 q^{25} -3.73323 q^{26} +2.84663 q^{27} +0.925705 q^{28} +4.70067 q^{29} +2.24341 q^{30} -9.46888 q^{31} -4.72610 q^{32} -12.8506 q^{33} +4.00706 q^{34} -1.00000 q^{35} -1.55965 q^{36} +4.84592 q^{37} -1.29300 q^{38} -7.79596 q^{39} +3.03244 q^{40} -6.71634 q^{41} -2.24341 q^{42} -5.88457 q^{43} -5.49604 q^{44} +1.68482 q^{45} -3.32920 q^{46} +1.31075 q^{47} +2.79573 q^{48} +1.00000 q^{49} -1.03648 q^{50} +8.36779 q^{51} -3.33423 q^{52} -0.324777 q^{53} -2.95048 q^{54} +5.93714 q^{55} -3.03244 q^{56} -2.70012 q^{57} -4.87216 q^{58} +0.398226 q^{59} +2.00364 q^{60} -11.7151 q^{61} +9.81432 q^{62} -1.68482 q^{63} +7.48184 q^{64} +3.60183 q^{65} +13.3194 q^{66} +8.24809 q^{67} +3.57880 q^{68} -6.95223 q^{69} +1.03648 q^{70} -11.3664 q^{71} +5.10912 q^{72} -15.4385 q^{73} -5.02270 q^{74} -2.16444 q^{75} -1.15481 q^{76} -5.93714 q^{77} +8.08037 q^{78} -11.5049 q^{79} -1.29166 q^{80} -11.2158 q^{81} +6.96136 q^{82} -6.19861 q^{83} -2.00364 q^{84} -3.86602 q^{85} +6.09925 q^{86} -10.1743 q^{87} +18.0040 q^{88} +4.89407 q^{89} -1.74629 q^{90} -3.60183 q^{91} -2.97338 q^{92} +20.4949 q^{93} -1.35857 q^{94} +1.24749 q^{95} +10.2294 q^{96} +12.3345 q^{97} -1.03648 q^{98} +10.0030 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.03648	−0.732903	−0.366452	−	0.930437i	$-0.619428\pi$
$2$	−1.03648	−0.732903	−0.366452	+	0.930437i	$0.619428\pi$
$3$	−2.16444	−1.24964	−0.624821	−	0.780768i	$-0.714828\pi$
$3$	−2.16444	−1.24964	−0.624821	+	0.780768i	$0.714828\pi$
$4$	−0.925705	−0.462853
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.24341	0.915868
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.03244	1.07213
$9$	1.68482	0.561607
$10$	−1.03648	−0.327764
$11$	5.93714	1.79012	0.895058	−	0.445950i	$-0.147134\pi$
$11$	5.93714	1.79012	0.895058	+	0.445950i	$0.147134\pi$
$12$	2.00364	0.578400
$13$	3.60183	0.998967	0.499484	−	0.866323i	$-0.333523\pi$
$13$	3.60183	0.998967	0.499484	+	0.866323i	$0.333523\pi$
$14$	1.03648	0.277011
$15$	−2.16444	−0.558857
$16$	−1.29166	−0.322915
$17$	−3.86602	−0.937648	−0.468824	−	0.883292i	$-0.655322\pi$
$17$	−3.86602	−0.937648	−0.468824	+	0.883292i	$0.655322\pi$
$18$	−1.74629	−0.411604
$19$	1.24749	0.286194	0.143097	−	0.989709i	$-0.454294\pi$
$19$	1.24749	0.286194	0.143097	+	0.989709i	$0.454294\pi$
$20$	−0.925705	−0.206994
$21$	2.16444	0.472321
$22$	−6.15374	−1.31198
$23$	3.21202	0.669752	0.334876	−	0.942262i	$-0.391306\pi$
$23$	3.21202	0.669752	0.334876	+	0.942262i	$0.391306\pi$
$24$	−6.56355	−1.33978
$25$	1.00000	0.200000
$26$	−3.73323	−0.732146
$27$	2.84663	0.547834
$28$	0.925705	0.174942
$29$	4.70067	0.872892	0.436446	−	0.899730i	$-0.356237\pi$
$29$	4.70067	0.872892	0.436446	+	0.899730i	$0.356237\pi$
$30$	2.24341	0.409588
$31$	−9.46888	−1.70066	−0.850330	−	0.526250i	$-0.823598\pi$
$31$	−9.46888	−1.70066	−0.850330	+	0.526250i	$0.823598\pi$
$32$	−4.72610	−0.835464
$33$	−12.8506	−2.23700
$34$	4.00706	0.687205
$35$	−1.00000	−0.169031
$36$	−1.55965	−0.259941
$37$	4.84592	0.796664	0.398332	−	0.917241i	$-0.369589\pi$
$37$	4.84592	0.796664	0.398332	+	0.917241i	$0.369589\pi$
$38$	−1.29300	−0.209752
$39$	−7.79596	−1.24835
$40$	3.03244	0.479471
$41$	−6.71634	−1.04892	−0.524458	−	0.851437i	$-0.675732\pi$
$41$	−6.71634	−1.04892	−0.524458	+	0.851437i	$0.675732\pi$
$42$	−2.24341	−0.346165
$43$	−5.88457	−0.897388	−0.448694	−	0.893685i	$-0.648111\pi$
$43$	−5.88457	−0.897388	−0.448694	+	0.893685i	$0.648111\pi$
$44$	−5.49604	−0.828559
$45$	1.68482	0.251158
$46$	−3.32920	−0.490863
$47$	1.31075	0.191193	0.0955964	−	0.995420i	$-0.469524\pi$
$47$	1.31075	0.191193	0.0955964	+	0.995420i	$0.469524\pi$
$48$	2.79573	0.403528
$49$	1.00000	0.142857
$50$	−1.03648	−0.146581
$51$	8.36779	1.17172
$52$	−3.33423	−0.462374
$53$	−0.324777	−0.0446116	−0.0223058	−	0.999751i	$-0.507101\pi$
$53$	−0.324777	−0.0446116	−0.0223058	+	0.999751i	$0.507101\pi$
$54$	−2.95048	−0.401510
$55$	5.93714	0.800564
$56$	−3.03244	−0.405227
$57$	−2.70012	−0.357640
$58$	−4.87216	−0.639746
$59$	0.398226	0.0518446	0.0259223	−	0.999664i	$-0.491748\pi$
$59$	0.398226	0.0518446	0.0259223	+	0.999664i	$0.491748\pi$
$60$	2.00364	0.258669
$61$	−11.7151	−1.49997	−0.749984	−	0.661455i	$-0.769939\pi$
$61$	−11.7151	−1.49997	−0.749984	+	0.661455i	$0.769939\pi$
$62$	9.81432	1.24642
$63$	−1.68482	−0.212268
$64$	7.48184	0.935230
$65$	3.60183	0.446752
$66$	13.3194	1.63951
$67$	8.24809	1.00767	0.503833	−	0.863801i	$-0.331923\pi$
$67$	8.24809	1.00767	0.503833	+	0.863801i	$0.331923\pi$
$68$	3.57880	0.433993
$69$	−6.95223	−0.836950
$70$	1.03648	0.123883
$71$	−11.3664	−1.34894	−0.674471	−	0.738301i	$-0.735628\pi$
$71$	−11.3664	−1.34894	−0.674471	+	0.738301i	$0.735628\pi$
$72$	5.10912	0.602116
$73$	−15.4385	−1.80694	−0.903472	−	0.428647i	$-0.858990\pi$
$73$	−15.4385	−1.80694	−0.903472	+	0.428647i	$0.858990\pi$
$74$	−5.02270	−0.583877
$75$	−2.16444	−0.249929
$76$	−1.15481	−0.132465
$77$	−5.93714	−0.676600
$78$	8.08037	0.914921
$79$	−11.5049	−1.29441	−0.647203	−	0.762318i	$-0.724061\pi$
$79$	−11.5049	−1.29441	−0.647203	+	0.762318i	$0.724061\pi$
$80$	−1.29166	−0.144412
$81$	−11.2158	−1.24620
$82$	6.96136	0.768754
$83$	−6.19861	−0.680386	−0.340193	−	0.940356i	$-0.610492\pi$
$83$	−6.19861	−0.680386	−0.340193	+	0.940356i	$0.610492\pi$
$84$	−2.00364	−0.218615
$85$	−3.86602	−0.419329
$86$	6.09925	0.657699
$87$	−10.1743	−1.09080
$88$	18.0040	1.91924
$89$	4.89407	0.518770	0.259385	−	0.965774i	$-0.416480\pi$
$89$	4.89407	0.518770	0.259385	+	0.965774i	$0.416480\pi$
$90$	−1.74629	−0.184075
$91$	−3.60183	−0.377574
$92$	−2.97338	−0.309996
$93$	20.4949	2.12522
$94$	−1.35857	−0.140126
$95$	1.24749	0.127990
$96$	10.2294	1.04403
$97$	12.3345	1.25238	0.626191	−	0.779670i	$-0.284613\pi$
$97$	12.3345	1.25238	0.626191	+	0.779670i	$0.284613\pi$
$98$	−1.03648	−0.104700
$99$	10.0030	1.00534
$100$	−0.925705	−0.0925705
$101$	−15.8572	−1.57785	−0.788924	−	0.614491i	$-0.789361\pi$
$101$	−15.8572	−1.57785	−0.788924	+	0.614491i	$0.789361\pi$
$102$	−8.67306	−0.858761
$103$	10.5465	1.03918	0.519591	−	0.854415i	$-0.326084\pi$
$103$	10.5465	1.03918	0.519591	+	0.854415i	$0.326084\pi$
$104$	10.9223	1.07102
$105$	2.16444	0.211228
$106$	0.336626	0.0326960
$107$	−6.81264	−0.658603	−0.329302	−	0.944225i	$-0.606813\pi$
$107$	−6.81264	−0.658603	−0.329302	+	0.944225i	$0.606813\pi$
$108$	−2.63514	−0.253567
$109$	−2.79703	−0.267906	−0.133953	−	0.990988i	$-0.542767\pi$
$109$	−2.79703	−0.267906	−0.133953	+	0.990988i	$0.542767\pi$
$110$	−6.15374	−0.586736
$111$	−10.4887	−0.995545
$112$	1.29166	0.122050
$113$	2.46520	0.231907	0.115953	−	0.993255i	$-0.463008\pi$
$113$	2.46520	0.231907	0.115953	+	0.993255i	$0.463008\pi$
$114$	2.79863	0.262115
$115$	3.21202	0.299522
$116$	−4.35143	−0.404020
$117$	6.06844	0.561027
$118$	−0.412754	−0.0379971
$119$	3.86602	0.354398
$120$	−6.56355	−0.599167
$121$	24.2496	2.20451
$122$	12.1425	1.09933
$123$	14.5371	1.31077
$124$	8.76539	0.787155
$125$	1.00000	0.0894427
$126$	1.74629	0.155572
$127$	5.90011	0.523550	0.261775	−	0.965129i	$-0.415692\pi$
$127$	5.90011	0.523550	0.261775	+	0.965129i	$0.415692\pi$
$128$	1.69741	0.150031
$129$	12.7368	1.12141
$130$	−3.73323	−0.327426
$131$	−18.5971	−1.62484	−0.812418	−	0.583076i	$-0.801849\pi$
$131$	−18.5971	−1.62484	−0.812418	+	0.583076i	$0.801849\pi$
$132$	11.8959	1.03540
$133$	−1.24749	−0.108171
$134$	−8.54900	−0.738521
$135$	2.84663	0.244999
$136$	−11.7235	−1.00528
$137$	2.72142	0.232506	0.116253	−	0.993220i	$-0.462912\pi$
$137$	2.72142	0.232506	0.116253	+	0.993220i	$0.462912\pi$
$138$	7.20586	0.613404
$139$	−2.55205	−0.216462	−0.108231	−	0.994126i	$-0.534519\pi$
$139$	−2.55205	−0.216462	−0.108231	+	0.994126i	$0.534519\pi$
$140$	0.925705	0.0782364
$141$	−2.83705	−0.238923
$142$	11.7811	0.988645
$143$	21.3846	1.78827
$144$	−2.17622	−0.181351
$145$	4.70067	0.390369
$146$	16.0018	1.32432
$147$	−2.16444	−0.178520
$148$	−4.48589	−0.368738
$149$	9.29067	0.761121	0.380561	−	0.924756i	$-0.375731\pi$
$149$	9.29067	0.761121	0.380561	+	0.924756i	$0.375731\pi$
$150$	2.24341	0.183174
$151$	9.12287	0.742409	0.371204	−	0.928551i	$-0.378945\pi$
$151$	9.12287	0.742409	0.371204	+	0.928551i	$0.378945\pi$
$152$	3.78294	0.306837
$153$	−6.51356	−0.526590
$154$	6.15374	0.495882
$155$	−9.46888	−0.760558
$156$	7.21676	0.577803
$157$	−24.6852	−1.97009	−0.985047	−	0.172284i	$-0.944885\pi$
$157$	−24.6852	−1.97009	−0.985047	+	0.172284i	$0.944885\pi$
$158$	11.9247	0.948675
$159$	0.702963	0.0557486
$160$	−4.72610	−0.373631
$161$	−3.21202	−0.253142
$162$	11.6250	0.913348
$163$	12.2236	0.957430	0.478715	−	0.877970i	$-0.341103\pi$
$163$	12.2236	0.957430	0.478715	+	0.877970i	$0.341103\pi$
$164$	6.21735	0.485493
$165$	−12.8506	−1.00042
$166$	6.42475	0.498657
$167$	−6.57431	−0.508735	−0.254368	−	0.967108i	$-0.581867\pi$
$167$	−6.57431	−0.508735	−0.254368	+	0.967108i	$0.581867\pi$
$168$	6.56355	0.506389
$169$	−0.0268430	−0.00206485
$170$	4.00706	0.307328
$171$	2.10180	0.160728
$172$	5.44738	0.415359
$173$	12.8033	0.973414	0.486707	−	0.873565i	$-0.338198\pi$
$173$	12.8033	0.973414	0.486707	+	0.873565i	$0.338198\pi$
$174$	10.5455	0.799454
$175$	−1.00000	−0.0755929
$176$	−7.66877	−0.578055
$177$	−0.861939	−0.0647873
$178$	−5.07261	−0.380208
$179$	1.31114	0.0979989	0.0489995	−	0.998799i	$-0.484397\pi$
$179$	1.31114	0.0979989	0.0489995	+	0.998799i	$0.484397\pi$
$180$	−1.55965	−0.116249
$181$	3.56102	0.264689	0.132344	−	0.991204i	$-0.457750\pi$
$181$	3.56102	0.264689	0.132344	+	0.991204i	$0.457750\pi$
$182$	3.73323	0.276725
$183$	25.3568	1.87443
$184$	9.74025	0.718061
$185$	4.84592	0.356279
$186$	−21.2426	−1.55758
$187$	−22.9531	−1.67850
$188$	−1.21337	−0.0884941
$189$	−2.84663	−0.207062
$190$	−1.29300	−0.0938041
$191$	−6.80017	−0.492043	−0.246021	−	0.969264i	$-0.579123\pi$
$191$	−6.80017	−0.492043	−0.246021	+	0.969264i	$0.579123\pi$
$192$	−16.1940	−1.16870
$193$	4.97441	0.358066	0.179033	−	0.983843i	$-0.442703\pi$
$193$	4.97441	0.358066	0.179033	+	0.983843i	$0.442703\pi$
$194$	−12.7845	−0.917875
$195$	−7.79596	−0.558280
$196$	−0.925705	−0.0661218
$197$	4.10238	0.292282	0.146141	−	0.989264i	$-0.453315\pi$
$197$	4.10238	0.292282	0.146141	+	0.989264i	$0.453315\pi$
$198$	−10.3680	−0.736818
$199$	20.7838	1.47332	0.736662	−	0.676261i	$-0.236401\pi$
$199$	20.7838	1.47332	0.736662	+	0.676261i	$0.236401\pi$
$200$	3.03244	0.214426
$201$	−17.8525	−1.25922
$202$	16.4357	1.15641
$203$	−4.70067	−0.329922
$204$	−7.74610	−0.542336
$205$	−6.71634	−0.469089
$206$	−10.9313	−0.761620
$207$	5.41167	0.376137
$208$	−4.65234	−0.322581
$209$	7.40652	0.512320
$210$	−2.24341	−0.154810
$211$	−7.36957	−0.507342	−0.253671	−	0.967291i	$-0.581638\pi$
$211$	−7.36957	−0.507342	−0.253671	+	0.967291i	$0.581638\pi$
$212$	0.300648	0.0206486
$213$	24.6019	1.68570
$214$	7.06118	0.482692
$215$	−5.88457	−0.401324
$216$	8.63224	0.587350
$217$	9.46888	0.642789
$218$	2.89907	0.196350
$219$	33.4159	2.25803
$220$	−5.49604	−0.370543
$221$	−13.9247	−0.936679
$222$	10.8714	0.729638
$223$	−13.2317	−0.886062	−0.443031	−	0.896506i	$-0.646097\pi$
$223$	−13.2317	−0.886062	−0.443031	+	0.896506i	$0.646097\pi$
$224$	4.72610	0.315776
$225$	1.68482	0.112321
$226$	−2.55514	−0.169965
$227$	4.49631	0.298431	0.149215	−	0.988805i	$-0.452325\pi$
$227$	4.49631	0.298431	0.149215	+	0.988805i	$0.452325\pi$
$228$	2.49952	0.165534
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	−3.32920	−0.219521
$231$	12.8506	0.845508
$232$	14.2545	0.935854
$233$	−27.9016	−1.82789	−0.913946	−	0.405835i	$-0.866981\pi$
$233$	−27.9016	−1.82789	−0.913946	+	0.405835i	$0.866981\pi$
$234$	−6.28982	−0.411179
$235$	1.31075	0.0855040
$236$	−0.368640	−0.0239964
$237$	24.9018	1.61755
$238$	−4.00706	−0.259739
$239$	9.82388	0.635454	0.317727	−	0.948182i	$-0.397080\pi$
$239$	9.82388	0.635454	0.317727	+	0.948182i	$0.397080\pi$
$240$	2.79573	0.180463
$241$	2.59142	0.166928	0.0834639	−	0.996511i	$-0.473402\pi$
$241$	2.59142	0.166928	0.0834639	+	0.996511i	$0.473402\pi$
$242$	−25.1343	−1.61570
$243$	15.7362	1.00948
$244$	10.8448	0.694264
$245$	1.00000	0.0638877
$246$	−15.0675	−0.960668
$247$	4.49324	0.285898
$248$	−28.7138	−1.82333
$249$	13.4166	0.850240
$250$	−1.03648	−0.0655529
$251$	1.77739	0.112188	0.0560938	−	0.998426i	$-0.482135\pi$
$251$	1.77739	0.112188	0.0560938	+	0.998426i	$0.482135\pi$
$252$	1.55965	0.0982486
$253$	19.0702	1.19893
$254$	−6.11536	−0.383712
$255$	8.36779	0.524011
$256$	−16.7230	−1.04519
$257$	−14.9705	−0.933837	−0.466918	−	0.884300i	$-0.654636\pi$
$257$	−14.9705	−0.933837	−0.466918	+	0.884300i	$0.654636\pi$
$258$	−13.2015	−0.821889
$259$	−4.84592	−0.301111
$260$	−3.33423	−0.206780
$261$	7.91979	0.490223
$262$	19.2756	1.19085
$263$	−11.4175	−0.704035	−0.352017	−	0.935993i	$-0.614504\pi$
$263$	−11.4175	−0.704035	−0.352017	+	0.935993i	$0.614504\pi$
$264$	−38.9687	−2.39836
$265$	−0.324777	−0.0199509
$266$	1.29300	0.0792789
$267$	−10.5929	−0.648277
$268$	−7.63530	−0.466400
$269$	−23.6649	−1.44288	−0.721438	−	0.692479i	$-0.756518\pi$
$269$	−23.6649	−1.44288	−0.721438	+	0.692479i	$0.756518\pi$
$270$	−2.95048	−0.179561
$271$	−11.3613	−0.690150	−0.345075	−	0.938575i	$-0.612147\pi$
$271$	−11.3613	−0.690150	−0.345075	+	0.938575i	$0.612147\pi$
$272$	4.99358	0.302781
$273$	7.79596	0.471833
$274$	−2.82070	−0.170405
$275$	5.93714	0.358023
$276$	6.43572	0.387385
$277$	−1.73995	−0.104543	−0.0522717	−	0.998633i	$-0.516646\pi$
$277$	−1.73995	−0.104543	−0.0522717	+	0.998633i	$0.516646\pi$
$278$	2.64516	0.158646
$279$	−15.9534	−0.955103
$280$	−3.03244	−0.181223
$281$	32.3877	1.93209	0.966043	−	0.258381i	$-0.0831891\pi$
$281$	32.3877	1.93209	0.966043	+	0.258381i	$0.0831891\pi$
$282$	2.94055	0.175107
$283$	13.8759	0.824837	0.412418	−	0.910995i	$-0.364684\pi$
$283$	13.8759	0.824837	0.412418	+	0.910995i	$0.364684\pi$
$284$	10.5219	0.624362
$285$	−2.70012	−0.159941
$286$	−22.1647	−1.31063
$287$	6.71634	0.396453
$288$	−7.96263	−0.469203
$289$	−2.05388	−0.120817
$290$	−4.87216	−0.286103
$291$	−26.6974	−1.56503
$292$	14.2915	0.836349
$293$	13.5273	0.790271	0.395136	−	0.918623i	$-0.370698\pi$
$293$	13.5273	0.790271	0.395136	+	0.918623i	$0.370698\pi$
$294$	2.24341	0.130838
$295$	0.398226	0.0231856
$296$	14.6949	0.854127
$297$	16.9009	0.980687
$298$	−9.62961	−0.557828
$299$	11.5691	0.669060
$300$	2.00364	0.115680
$301$	5.88457	0.339181
$302$	−9.45569	−0.544114
$303$	34.3220	1.97175
$304$	−1.61133	−0.0924162
$305$	−11.7151	−0.670806
$306$	6.75118	0.385939
$307$	8.59738	0.490678	0.245339	−	0.969437i	$-0.421101\pi$
$307$	8.59738	0.490678	0.245339	+	0.969437i	$0.421101\pi$
$308$	5.49604	0.313166
$309$	−22.8274	−1.29861
$310$	9.81432	0.557416
$311$	−14.9387	−0.847096	−0.423548	−	0.905874i	$-0.639215\pi$
$311$	−14.9387	−0.847096	−0.423548	+	0.905874i	$0.639215\pi$
$312$	−23.6408	−1.33840
$313$	−4.18752	−0.236693	−0.118346	−	0.992972i	$-0.537759\pi$
$313$	−4.18752	−0.236693	−0.118346	+	0.992972i	$0.537759\pi$
$314$	25.5858	1.44389
$315$	−1.68482	−0.0949289
$316$	10.6502	0.599119
$317$	20.6650	1.16066	0.580330	−	0.814381i	$-0.302924\pi$
$317$	20.6650	1.16066	0.580330	+	0.814381i	$0.302924\pi$
$318$	−0.728608	−0.0408583
$319$	27.9085	1.56258
$320$	7.48184	0.418247
$321$	14.7456	0.823019
$322$	3.32920	0.185529
$323$	−4.82282	−0.268349
$324$	10.3826	0.576809
$325$	3.60183	0.199793
$326$	−12.6696	−0.701704
$327$	6.05401	0.334787
$328$	−20.3669	−1.12457
$329$	−1.31075	−0.0722641
$330$	13.3194	0.733211
$331$	8.15073	0.448005	0.224002	−	0.974589i	$-0.428088\pi$
$331$	8.15073	0.448005	0.224002	+	0.974589i	$0.428088\pi$
$332$	5.73809	0.314919
$333$	8.16450	0.447412
$334$	6.81415	0.372854
$335$	8.24809	0.450642
$336$	−2.79573	−0.152519
$337$	−12.5523	−0.683766	−0.341883	−	0.939742i	$-0.611065\pi$
$337$	−12.5523	−0.683766	−0.341883	+	0.939742i	$0.611065\pi$
$338$	0.0278223	0.00151333
$339$	−5.33580	−0.289801
$340$	3.57880	0.194087
$341$	−56.2181	−3.04438
$342$	−2.17847	−0.117798
$343$	−1.00000	−0.0539949
$344$	−17.8446	−0.962117
$345$	−6.95223	−0.374296
$346$	−13.2703	−0.713418
$347$	−24.2941	−1.30418	−0.652088	−	0.758143i	$-0.726107\pi$
$347$	−24.2941	−1.30418	−0.652088	+	0.758143i	$0.726107\pi$
$348$	9.41844	0.504881
$349$	−17.3416	−0.928276	−0.464138	−	0.885763i	$-0.653636\pi$
$349$	−17.3416	−0.928276	−0.464138	+	0.885763i	$0.653636\pi$
$350$	1.03648	0.0554023
$351$	10.2531	0.547269
$352$	−28.0595	−1.49558
$353$	−14.5089	−0.772231	−0.386116	−	0.922450i	$-0.626183\pi$
$353$	−14.5089	−0.772231	−0.386116	+	0.922450i	$0.626183\pi$
$354$	0.893384	0.0474828
$355$	−11.3664	−0.603265
$356$	−4.53046	−0.240114
$357$	−8.36779	−0.442870
$358$	−1.35897	−0.0718237
$359$	23.5524	1.24305	0.621523	−	0.783396i	$-0.286514\pi$
$359$	23.5524	1.24305	0.621523	+	0.783396i	$0.286514\pi$
$360$	5.10912	0.269274
$361$	−17.4438	−0.918093
$362$	−3.69093	−0.193991
$363$	−52.4870	−2.75485
$364$	3.33423	0.174761
$365$	−15.4385	−0.808090
$366$	−26.2818	−1.37377
$367$	35.3181	1.84359	0.921795	−	0.387678i	$-0.126723\pi$
$367$	35.3181	1.84359	0.921795	+	0.387678i	$0.126723\pi$
$368$	−4.14883	−0.216273
$369$	−11.3158	−0.589078
$370$	−5.02270	−0.261118
$371$	0.324777	0.0168616
$372$	−18.9722	−0.983663
$373$	0.165741	0.00858176	0.00429088	−	0.999991i	$-0.498634\pi$
$373$	0.165741	0.00858176	0.00429088	+	0.999991i	$0.498634\pi$
$374$	23.7905	1.23018
$375$	−2.16444	−0.111771
$376$	3.97478	0.204983
$377$	16.9310	0.871991
$378$	2.95048	0.151756
$379$	−31.4169	−1.61378	−0.806890	−	0.590702i	$-0.798851\pi$
$379$	−31.4169	−1.61378	−0.806890	+	0.590702i	$0.798851\pi$
$380$	−1.15481	−0.0592403
$381$	−12.7705	−0.654251
$382$	7.04825	0.360620
$383$	−25.0113	−1.27802	−0.639010	−	0.769199i	$-0.720656\pi$
$383$	−25.0113	−1.27802	−0.639010	+	0.769199i	$0.720656\pi$
$384$	−3.67395	−0.187485
$385$	−5.93714	−0.302585
$386$	−5.15589	−0.262428
$387$	−9.91445	−0.503980
$388$	−11.4181	−0.579668
$389$	−25.8640	−1.31136	−0.655678	−	0.755040i	$-0.727617\pi$
$389$	−25.8640	−1.31136	−0.655678	+	0.755040i	$0.727617\pi$
$390$	8.08037	0.409165
$391$	−12.4177	−0.627991
$392$	3.03244	0.153161
$393$	40.2524	2.03046
$394$	−4.25204	−0.214215
$395$	−11.5049	−0.578876
$396$	−9.25985	−0.465325
$397$	16.0075	0.803392	0.401696	−	0.915773i	$-0.368421\pi$
$397$	16.0075	0.803392	0.401696	+	0.915773i	$0.368421\pi$
$398$	−21.5420	−1.07980
$399$	2.70012	0.135175
$400$	−1.29166	−0.0645830
$401$	15.0948	0.753801	0.376900	−	0.926254i	$-0.376990\pi$
$401$	15.0948	0.753801	0.376900	+	0.926254i	$0.376990\pi$
$402$	18.5038	0.922888
$403$	−34.1053	−1.69890
$404$	14.6791	0.730311
$405$	−11.2158	−0.557320
$406$	4.87216	0.241801
$407$	28.7709	1.42612
$408$	25.3748	1.25624
$409$	−9.02063	−0.446041	−0.223021	−	0.974814i	$-0.571592\pi$
$409$	−9.02063	−0.446041	−0.223021	+	0.974814i	$0.571592\pi$
$410$	6.96136	0.343797
$411$	−5.89036	−0.290550
$412$	−9.76299	−0.480988
$413$	−0.398226	−0.0195954
$414$	−5.60910	−0.275672
$415$	−6.19861	−0.304278
$416$	−17.0226	−0.834601
$417$	5.52378	0.270501
$418$	−7.67672	−0.375481
$419$	−18.0375	−0.881190	−0.440595	−	0.897706i	$-0.645232\pi$
$419$	−18.0375	−0.881190	−0.440595	+	0.897706i	$0.645232\pi$
$420$	−2.00364	−0.0977675
$421$	−34.9524	−1.70347	−0.851737	−	0.523970i	$-0.824451\pi$
$421$	−34.9524	−1.70347	−0.851737	+	0.523970i	$0.824451\pi$
$422$	7.63842	0.371833
$423$	2.20838	0.107375
$424$	−0.984868	−0.0478294
$425$	−3.86602	−0.187530
$426$	−25.4995	−1.23545
$427$	11.7151	0.566935
$428$	6.30650	0.304836
$429$	−46.2857	−2.23469
$430$	6.09925	0.294132
$431$	−24.5441	−1.18225	−0.591124	−	0.806581i	$-0.701316\pi$
$431$	−24.5441	−1.18225	−0.591124	+	0.806581i	$0.701316\pi$
$432$	−3.67688	−0.176904
$433$	12.7137	0.610982	0.305491	−	0.952195i	$-0.401179\pi$
$433$	12.7137	0.610982	0.305491	+	0.952195i	$0.401179\pi$
$434$	−9.81432	−0.471102
$435$	−10.1743	−0.487822
$436$	2.58922	0.124001
$437$	4.00695	0.191679
$438$	−34.6349	−1.65492
$439$	29.8616	1.42522	0.712608	−	0.701562i	$-0.247514\pi$
$439$	29.8616	1.42522	0.712608	+	0.701562i	$0.247514\pi$
$440$	18.0040	0.858308
$441$	1.68482	0.0802296
$442$	14.4327	0.686495
$443$	−1.61566	−0.0767623	−0.0383811	−	0.999263i	$-0.512220\pi$
$443$	−1.61566	−0.0767623	−0.0383811	+	0.999263i	$0.512220\pi$
$444$	9.70946	0.460790
$445$	4.89407	0.232001
$446$	13.7144	0.649398
$447$	−20.1091	−0.951130
$448$	−7.48184	−0.353484
$449$	2.73813	0.129220	0.0646102	−	0.997911i	$-0.479420\pi$
$449$	2.73813	0.129220	0.0646102	+	0.997911i	$0.479420\pi$
$450$	−1.74629	−0.0823208
$451$	−39.8758	−1.87768
$452$	−2.28205	−0.107339
$453$	−19.7460	−0.927746
$454$	−4.66035	−0.218721
$455$	−3.60183	−0.168856
$456$	−8.18796	−0.383436
$457$	−14.1700	−0.662843	−0.331422	−	0.943483i	$-0.607528\pi$
$457$	−14.1700	−0.662843	−0.331422	+	0.943483i	$0.607528\pi$
$458$	−1.03648	−0.0484316
$459$	−11.0051	−0.513676
$460$	−2.97338	−0.138635
$461$	−21.4496	−0.999009	−0.499504	−	0.866311i	$-0.666484\pi$
$461$	−21.4496	−0.999009	−0.499504	+	0.866311i	$0.666484\pi$
$462$	−13.3194	−0.619676
$463$	−27.0925	−1.25909	−0.629547	−	0.776962i	$-0.716760\pi$
$463$	−27.0925	−1.25909	−0.629547	+	0.776962i	$0.716760\pi$
$464$	−6.07167	−0.281870
$465$	20.4949	0.950426
$466$	28.9195	1.33967
$467$	−10.4183	−0.482101	−0.241050	−	0.970513i	$-0.577492\pi$
$467$	−10.4183	−0.482101	−0.241050	+	0.970513i	$0.577492\pi$
$468$	−5.61758	−0.259673
$469$	−8.24809	−0.380862
$470$	−1.35857	−0.0626662
$471$	53.4298	2.46191
$472$	1.20760	0.0555842
$473$	−34.9375	−1.60643
$474$	−25.8103	−1.18550
$475$	1.24749	0.0572387
$476$	−3.57880	−0.164034
$477$	−0.547192	−0.0250542
$478$	−10.1823	−0.465727
$479$	34.0283	1.55479	0.777395	−	0.629012i	$-0.216541\pi$
$479$	34.0283	1.55479	0.777395	+	0.629012i	$0.216541\pi$
$480$	10.2294	0.466905
$481$	17.4541	0.795841
$482$	−2.68596	−0.122342
$483$	6.95223	0.316338
$484$	−22.4480	−1.02036
$485$	12.3345	0.560082
$486$	−16.3103	−0.739849
$487$	7.78221	0.352646	0.176323	−	0.984332i	$-0.443580\pi$
$487$	7.78221	0.352646	0.176323	+	0.984332i	$0.443580\pi$
$488$	−35.5254	−1.60816
$489$	−26.4574	−1.19645
$490$	−1.03648	−0.0468235
$491$	−4.97386	−0.224467	−0.112234	−	0.993682i	$-0.535800\pi$
$491$	−4.97386	−0.224467	−0.112234	+	0.993682i	$0.535800\pi$
$492$	−13.4571	−0.606693
$493$	−18.1729	−0.818465
$494$	−4.65716	−0.209536
$495$	10.0030	0.449602
$496$	12.2306	0.549169
$497$	11.3664	0.509852
$498$	−13.9060	−0.623144
$499$	5.45419	0.244163	0.122082	−	0.992520i	$-0.461043\pi$
$499$	5.45419	0.244163	0.122082	+	0.992520i	$0.461043\pi$
$500$	−0.925705	−0.0413988
$501$	14.2297	0.635737
$502$	−1.84223	−0.0822227
$503$	0.333537	0.0148717	0.00743584	−	0.999972i	$-0.497633\pi$
$503$	0.333537	0.0148717	0.00743584	+	0.999972i	$0.497633\pi$
$504$	−5.10912	−0.227578
$505$	−15.8572	−0.705635
$506$	−19.7659	−0.878702
$507$	0.0581002	0.00258032
$508$	−5.46176	−0.242327
$509$	−8.18186	−0.362654	−0.181327	−	0.983423i	$-0.558039\pi$
$509$	−8.18186	−0.362654	−0.181327	+	0.983423i	$0.558039\pi$
$510$	−8.67306	−0.384050
$511$	15.4385	0.682961
$512$	13.9383	0.615991
$513$	3.55114	0.156787
$514$	15.5167	0.684412
$515$	10.5465	0.464736
$516$	−11.7905	−0.519050
$517$	7.78212	0.342257
$518$	5.02270	0.220685
$519$	−27.7119	−1.21642
$520$	10.9223	0.478976
$521$	−21.6216	−0.947261	−0.473630	−	0.880724i	$-0.657057\pi$
$521$	−21.6216	−0.947261	−0.473630	+	0.880724i	$0.657057\pi$
$522$	−8.20872	−0.359286
$523$	40.7040	1.77986	0.889930	−	0.456097i	$-0.150753\pi$
$523$	40.7040	1.77986	0.889930	+	0.456097i	$0.150753\pi$
$524$	17.2154	0.752059
$525$	2.16444	0.0944641
$526$	11.8341	0.515990
$527$	36.6069	1.59462
$528$	16.5986	0.722362
$529$	−12.6830	−0.551433
$530$	0.336626	0.0146221
$531$	0.670940	0.0291163
$532$	1.15481	0.0500672
$533$	−24.1911	−1.04783
$534$	10.9794	0.475125
$535$	−6.81264	−0.294536
$536$	25.0119	1.08035
$537$	−2.83788	−0.122464
$538$	24.5283	1.05749
$539$	5.93714	0.255731
$540$	−2.63514	−0.113398
$541$	−33.5443	−1.44218	−0.721092	−	0.692840i	$-0.756359\pi$
$541$	−33.5443	−1.44218	−0.721092	+	0.692840i	$0.756359\pi$
$542$	11.7758	0.505813
$543$	−7.70764	−0.330766
$544$	18.2712	0.783371
$545$	−2.79703	−0.119811
$546$	−8.08037	−0.345808
$547$	35.5035	1.51802	0.759009	−	0.651080i	$-0.225684\pi$
$547$	35.5035	1.51802	0.759009	+	0.651080i	$0.225684\pi$
$548$	−2.51923	−0.107616
$549$	−19.7379	−0.842393
$550$	−6.15374	−0.262396
$551$	5.86403	0.249816
$552$	−21.0822	−0.897319
$553$	11.5049	0.489240
$554$	1.80343	0.0766202
$555$	−10.4887	−0.445221
$556$	2.36245	0.100190
$557$	30.6682	1.29946	0.649728	−	0.760167i	$-0.274883\pi$
$557$	30.6682	1.29946	0.649728	+	0.760167i	$0.274883\pi$
$558$	16.5354	0.699998
$559$	−21.1952	−0.896461
$560$	1.29166	0.0545826
$561$	49.6807	2.09752
$562$	−33.5692	−1.41603
$563$	10.7973	0.455053	0.227526	−	0.973772i	$-0.426936\pi$
$563$	10.7973	0.455053	0.227526	+	0.973772i	$0.426936\pi$
$564$	2.62627	0.110586
$565$	2.46520	0.103712
$566$	−14.3821	−0.604526
$567$	11.2158	0.471021
$568$	−34.4679	−1.44624
$569$	−19.7804	−0.829239	−0.414620	−	0.909995i	$-0.636085\pi$
$569$	−19.7804	−0.829239	−0.414620	+	0.909995i	$0.636085\pi$
$570$	2.79863	0.117222
$571$	12.0468	0.504144	0.252072	−	0.967708i	$-0.418888\pi$
$571$	12.0468	0.504144	0.252072	+	0.967708i	$0.418888\pi$
$572$	−19.7958	−0.827704
$573$	14.7186	0.614878
$574$	−6.96136	−0.290562
$575$	3.21202	0.133950
$576$	12.6056	0.525232
$577$	−20.4040	−0.849428	−0.424714	−	0.905327i	$-0.639625\pi$
$577$	−20.4040	−0.849428	−0.424714	+	0.905327i	$0.639625\pi$
$578$	2.12881	0.0885469
$579$	−10.7668	−0.447455
$580$	−4.35143	−0.180683
$581$	6.19861	0.257162
$582$	27.6714	1.14702
$583$	−1.92825	−0.0798599
$584$	−46.8165	−1.93728
$585$	6.06844	0.250899
$586$	−14.0208	−0.579192
$587$	1.03684	0.0427951	0.0213976	−	0.999771i	$-0.493188\pi$
$587$	1.03684	0.0427951	0.0213976	+	0.999771i	$0.493188\pi$
$588$	2.00364	0.0826286
$589$	−11.8123	−0.486718
$590$	−0.412754	−0.0169928
$591$	−8.87937	−0.365249
$592$	−6.25927	−0.257255
$593$	27.2238	1.11795	0.558974	−	0.829185i	$-0.311195\pi$
$593$	27.2238	1.11795	0.558974	+	0.829185i	$0.311195\pi$
$594$	−17.5174	−0.718749
$595$	3.86602	0.158491
$596$	−8.60042	−0.352287
$597$	−44.9854	−1.84113
$598$	−11.9912	−0.490356
$599$	−1.47086	−0.0600977	−0.0300489	−	0.999548i	$-0.509566\pi$
$599$	−1.47086	−0.0600977	−0.0300489	+	0.999548i	$0.509566\pi$
$600$	−6.56355	−0.267956
$601$	20.9267	0.853617	0.426808	−	0.904342i	$-0.359638\pi$
$601$	20.9267	0.853617	0.426808	+	0.904342i	$0.359638\pi$
$602$	−6.09925	−0.248587
$603$	13.8966	0.565912
$604$	−8.44509	−0.343626
$605$	24.2496	0.985888
$606$	−35.5741	−1.44510
$607$	37.0050	1.50199	0.750994	−	0.660309i	$-0.229575\pi$
$607$	37.0050	1.50199	0.750994	+	0.660309i	$0.229575\pi$
$608$	−5.89576	−0.239104
$609$	10.1743	0.412285
$610$	12.1425	0.491636
$611$	4.72110	0.190995
$612$	6.02963	0.243733
$613$	19.2450	0.777299	0.388649	−	0.921386i	$-0.372942\pi$
$613$	19.2450	0.777299	0.388649	+	0.921386i	$0.372942\pi$
$614$	−8.91103	−0.359620
$615$	14.5371	0.586194
$616$	−18.0040	−0.725403
$617$	−29.9282	−1.20486	−0.602431	−	0.798171i	$-0.705801\pi$
$617$	−29.9282	−1.20486	−0.602431	+	0.798171i	$0.705801\pi$
$618$	23.6602	0.951753
$619$	−30.2948	−1.21765	−0.608825	−	0.793304i	$-0.708359\pi$
$619$	−30.2948	−1.21765	−0.608825	+	0.793304i	$0.708359\pi$
$620$	8.76539	0.352026
$621$	9.14343	0.366913
$622$	15.4837	0.620839
$623$	−4.89407	−0.196077
$624$	10.0697	0.403112
$625$	1.00000	0.0400000
$626$	4.34029	0.173473
$627$	−16.0310	−0.640216
$628$	22.8512	0.911863
$629$	−18.7344	−0.746990
$630$	1.74629	0.0695737
$631$	34.2702	1.36427	0.682137	−	0.731225i	$-0.261051\pi$
$631$	34.2702	1.36427	0.682137	+	0.731225i	$0.261051\pi$
$632$	−34.8880	−1.38777
$633$	15.9510	0.633996
$634$	−21.4189	−0.850652
$635$	5.90011	0.234139
$636$	−0.650736	−0.0258034
$637$	3.60183	0.142710
$638$	−28.9267	−1.14522
$639$	−19.1503	−0.757576
$640$	1.69741	0.0670960
$641$	−38.1749	−1.50782	−0.753909	−	0.656979i	$-0.771834\pi$
$641$	−38.1749	−1.50782	−0.753909	+	0.656979i	$0.771834\pi$
$642$	−15.2835	−0.603193
$643$	20.6834	0.815674	0.407837	−	0.913055i	$-0.366283\pi$
$643$	20.6834	0.815674	0.407837	+	0.913055i	$0.366283\pi$
$644$	2.97338	0.117168
$645$	12.7368	0.501512
$646$	4.99876	0.196674
$647$	−29.5374	−1.16123	−0.580617	−	0.814177i	$-0.697189\pi$
$647$	−29.5374	−1.16123	−0.580617	+	0.814177i	$0.697189\pi$
$648$	−34.0114	−1.33609
$649$	2.36433	0.0928079
$650$	−3.73323	−0.146429
$651$	−20.4949	−0.803257
$652$	−11.3155	−0.443149
$653$	−9.97644	−0.390408	−0.195204	−	0.980763i	$-0.562537\pi$
$653$	−9.97644	−0.390408	−0.195204	+	0.980763i	$0.562537\pi$
$654$	−6.27487	−0.245367
$655$	−18.5971	−0.726648
$656$	8.67522	0.338710
$657$	−26.0112	−1.01479
$658$	1.35857	0.0529626
$659$	33.9713	1.32333	0.661667	−	0.749798i	$-0.269849\pi$
$659$	33.9713	1.32333	0.661667	+	0.749798i	$0.269849\pi$
$660$	11.8959	0.463046
$661$	12.5063	0.486438	0.243219	−	0.969971i	$-0.421797\pi$
$661$	12.5063	0.486438	0.243219	+	0.969971i	$0.421797\pi$
$662$	−8.44809	−0.328344
$663$	30.1393	1.17051
$664$	−18.7969	−0.729462
$665$	−1.24749	−0.0483755
$666$	−8.46236	−0.327910
$667$	15.0986	0.584621
$668$	6.08587	0.235469
$669$	28.6393	1.10726
$670$	−8.54900	−0.330277
$671$	−69.5544	−2.68512
$672$	−10.2294	−0.394607
$673$	−35.0898	−1.35261	−0.676307	−	0.736620i	$-0.736421\pi$
$673$	−35.0898	−1.35261	−0.676307	+	0.736620i	$0.736421\pi$
$674$	13.0102	0.501135
$675$	2.84663	0.109567
$676$	0.0248487	0.000955719 0
$677$	−21.1238	−0.811854	−0.405927	−	0.913905i	$-0.633051\pi$
$677$	−21.1238	−0.811854	−0.405927	+	0.913905i	$0.633051\pi$
$678$	5.53046	0.212396
$679$	−12.3345	−0.473356
$680$	−11.7235	−0.449575
$681$	−9.73202	−0.372932
$682$	58.2690	2.23124
$683$	−28.5160	−1.09113	−0.545567	−	0.838067i	$-0.683686\pi$
$683$	−28.5160	−1.09113	−0.545567	+	0.838067i	$0.683686\pi$
$684$	−1.94564	−0.0743935
$685$	2.72142	0.103980
$686$	1.03648	0.0395731
$687$	−2.16444	−0.0825787
$688$	7.60086	0.289780
$689$	−1.16979	−0.0445655
$690$	7.20586	0.274323
$691$	−18.5339	−0.705063	−0.352532	−	0.935800i	$-0.614679\pi$
$691$	−18.5339	−0.705063	−0.352532	+	0.935800i	$0.614679\pi$
$692$	−11.8520	−0.450547
$693$	−10.0030	−0.379983
$694$	25.1804	0.955835
$695$	−2.55205	−0.0968049
$696$	−30.8531	−1.16948
$697$	25.9655	0.983513
$698$	17.9743	0.680337
$699$	60.3914	2.28421
$700$	0.925705	0.0349884
$701$	−26.5370	−1.00229	−0.501143	−	0.865364i	$-0.667087\pi$
$701$	−26.5370	−1.00229	−0.501143	+	0.865364i	$0.667087\pi$
$702$	−10.6271	−0.401095
$703$	6.04523	0.228000
$704$	44.4207	1.67417
$705$	−2.83705	−0.106849
$706$	15.0382	0.565971
$707$	15.8572	0.596370
$708$	0.797901	0.0299870
$709$	17.7991	0.668460	0.334230	−	0.942492i	$-0.391524\pi$
$709$	17.7991	0.668460	0.334230	+	0.942492i	$0.391524\pi$
$710$	11.7811	0.442135
$711$	−19.3838	−0.726948
$712$	14.8410	0.556189
$713$	−30.4142	−1.13902
$714$	8.67306	0.324581
$715$	21.3846	0.799737
$716$	−1.21373	−0.0453590
$717$	−21.2633	−0.794091
$718$	−24.4116	−0.911033
$719$	27.5888	1.02889	0.514445	−	0.857524i	$-0.327998\pi$
$719$	27.5888	1.02889	0.514445	+	0.857524i	$0.327998\pi$
$720$	−2.17622	−0.0811028
$721$	−10.5465	−0.392774
$722$	18.0802	0.672874
$723$	−5.60898	−0.208600
$724$	−3.29646	−0.122512
$725$	4.70067	0.174578
$726$	54.4019	2.01904
$727$	−21.2177	−0.786922	−0.393461	−	0.919341i	$-0.628722\pi$
$727$	−21.2177	−0.786922	−0.393461	+	0.919341i	$0.628722\pi$
$728$	−10.9223	−0.404808
$729$	−0.412562	−0.0152801
$730$	16.0018	0.592252
$731$	22.7499	0.841434
$732$	−23.4729	−0.867583
$733$	36.9866	1.36613	0.683066	−	0.730356i	$-0.260646\pi$
$733$	36.9866	1.36613	0.683066	+	0.730356i	$0.260646\pi$
$734$	−36.6066	−1.35117
$735$	−2.16444	−0.0798368
$736$	−15.1803	−0.559554
$737$	48.9701	1.80384
$738$	11.7287	0.431738
$739$	−1.52448	−0.0560788	−0.0280394	−	0.999607i	$-0.508926\pi$
$739$	−1.52448	−0.0560788	−0.0280394	+	0.999607i	$0.508926\pi$
$740$	−4.48589	−0.164905
$741$	−9.72537	−0.357270
$742$	−0.336626	−0.0123579
$743$	−17.8457	−0.654695	−0.327347	−	0.944904i	$-0.606155\pi$
$743$	−17.8457	−0.654695	−0.327347	+	0.944904i	$0.606155\pi$
$744$	62.1494	2.27851
$745$	9.29067	0.340384
$746$	−0.171788	−0.00628960
$747$	−10.4436	−0.382110
$748$	21.2478	0.776897
$749$	6.81264	0.248929
$750$	2.24341	0.0819177
$751$	32.5847	1.18903	0.594517	−	0.804083i	$-0.297343\pi$
$751$	32.5847	1.18903	0.594517	+	0.804083i	$0.297343\pi$
$752$	−1.69305	−0.0617390
$753$	−3.84706	−0.140195
$754$	−17.5487	−0.639085
$755$	9.12287	0.332015
$756$	2.63514	0.0958391
$757$	−19.0936	−0.693970	−0.346985	−	0.937871i	$-0.612795\pi$
$757$	−19.0936	−0.693970	−0.346985	+	0.937871i	$0.612795\pi$
$758$	32.5631	1.18274
$759$	−41.2764	−1.49824
$760$	3.78294	0.137222
$761$	29.5703	1.07192	0.535962	−	0.844242i	$-0.319949\pi$
$761$	29.5703	1.07192	0.535962	+	0.844242i	$0.319949\pi$
$762$	13.2364	0.479503
$763$	2.79703	0.101259
$764$	6.29495	0.227743
$765$	−6.51356	−0.235498
$766$	25.9238	0.936665
$767$	1.43434	0.0517911
$768$	36.1960	1.30611
$769$	−53.8859	−1.94318	−0.971588	−	0.236677i	$-0.923942\pi$
$769$	−53.8859	−1.94318	−0.971588	+	0.236677i	$0.923942\pi$
$770$	6.15374	0.221765
$771$	32.4029	1.16696
$772$	−4.60484	−0.165732
$773$	−37.3186	−1.34226	−0.671129	−	0.741341i	$-0.734190\pi$
$773$	−37.3186	−1.34226	−0.671129	+	0.741341i	$0.734190\pi$
$774$	10.2761	0.369369
$775$	−9.46888	−0.340132
$776$	37.4037	1.34272
$777$	10.4887	0.376281
$778$	26.8076	0.961098
$779$	−8.37855	−0.300193
$780$	7.21676	0.258401
$781$	−67.4839	−2.41476
$782$	12.8707	0.460257
$783$	13.3811	0.478200
$784$	−1.29166	−0.0461307
$785$	−24.6852	−0.881053
$786$	−41.7209	−1.48813
$787$	26.2849	0.936955	0.468478	−	0.883475i	$-0.344803\pi$
$787$	26.2849	0.936955	0.468478	+	0.883475i	$0.344803\pi$
$788$	−3.79759	−0.135284
$789$	24.7126	0.879792
$790$	11.9247	0.424260
$791$	−2.46520	−0.0876526
$792$	30.3336	1.07786
$793$	−42.1959	−1.49842
$794$	−16.5915	−0.588809
$795$	0.702963	0.0249315
$796$	−19.2397	−0.681932
$797$	−24.1062	−0.853886	−0.426943	−	0.904279i	$-0.640409\pi$
$797$	−24.1062	−0.853886	−0.426943	+	0.904279i	$0.640409\pi$
$798$	−2.79863	−0.0990703
$799$	−5.06739	−0.179272
$800$	−4.72610	−0.167093
$801$	8.24563	0.291345
$802$	−15.6455	−0.552463
$803$	−91.6608	−3.23464
$804$	16.5262	0.582834
$805$	−3.21202	−0.113209
$806$	35.3495	1.24513
$807$	51.2214	1.80308
$808$	−48.0859	−1.69166
$809$	24.8824	0.874820	0.437410	−	0.899262i	$-0.355896\pi$
$809$	24.8824	0.874820	0.437410	+	0.899262i	$0.355896\pi$
$810$	11.6250	0.408461
$811$	−41.7100	−1.46463	−0.732317	−	0.680963i	$-0.761561\pi$
$811$	−41.7100	−1.46463	−0.732317	+	0.680963i	$0.761561\pi$
$812$	4.35143	0.152705
$813$	24.5909	0.862441
$814$	−29.8205	−1.04521
$815$	12.2236	0.428176
$816$	−10.8083	−0.378368
$817$	−7.34093	−0.256827
$818$	9.34972	0.326905
$819$	−6.06844	−0.212048
$820$	6.21735	0.217119
$821$	−2.79066	−0.0973946	−0.0486973	−	0.998814i	$-0.515507\pi$
$821$	−2.79066	−0.0973946	−0.0486973	+	0.998814i	$0.515507\pi$
$822$	6.10525	0.212945
$823$	5.86779	0.204538	0.102269	−	0.994757i	$-0.467390\pi$
$823$	5.86779	0.204538	0.102269	+	0.994757i	$0.467390\pi$
$824$	31.9818	1.11414
$825$	−12.8506	−0.447401
$826$	0.412754	0.0143616
$827$	35.6791	1.24069	0.620343	−	0.784331i	$-0.286994\pi$
$827$	35.6791	1.24069	0.620343	+	0.784331i	$0.286994\pi$
$828$	−5.00961	−0.174096
$829$	−35.8012	−1.24343	−0.621714	−	0.783244i	$-0.713563\pi$
$829$	−35.8012	−1.24343	−0.621714	+	0.783244i	$0.713563\pi$
$830$	6.42475	0.223006
$831$	3.76602	0.130642
$832$	26.9483	0.934264
$833$	−3.86602	−0.133950
$834$	−5.72530	−0.198251
$835$	−6.57431	−0.227513
$836$	−6.85625	−0.237128
$837$	−26.9544	−0.931680
$838$	18.6955	0.645827
$839$	11.5319	0.398127	0.199063	−	0.979987i	$-0.436210\pi$
$839$	11.5319	0.398127	0.199063	+	0.979987i	$0.436210\pi$
$840$	6.56355	0.226464
$841$	−6.90372	−0.238059
$842$	36.2275	1.24848
$843$	−70.1013	−2.41442
$844$	6.82205	0.234825
$845$	−0.0268430	−0.000923427 0
$846$	−2.28895	−0.0786957
$847$	−24.2496	−0.833228
$848$	0.419502	0.0144058
$849$	−30.0336	−1.03075
$850$	4.00706	0.137441
$851$	15.5652	0.533567
$852$	−22.7741	−0.780229
$853$	26.7252	0.915054	0.457527	−	0.889196i	$-0.348735\pi$
$853$	26.7252	0.915054	0.457527	+	0.889196i	$0.348735\pi$
$854$	−12.1425	−0.415509
$855$	2.10180	0.0718799
$856$	−20.6589	−0.706108
$857$	6.76667	0.231145	0.115573	−	0.993299i	$-0.463130\pi$
$857$	6.76667	0.231145	0.115573	+	0.993299i	$0.463130\pi$
$858$	47.9743	1.63782
$859$	−39.5974	−1.35105	−0.675523	−	0.737339i	$-0.736082\pi$
$859$	−39.5974	−1.35105	−0.675523	+	0.737339i	$0.736082\pi$
$860$	5.44738	0.185754
$861$	−14.5371	−0.495424
$862$	25.4395	0.866474
$863$	46.8124	1.59351	0.796756	−	0.604301i	$-0.206547\pi$
$863$	46.8124	1.59351	0.796756	+	0.604301i	$0.206547\pi$
$864$	−13.4535	−0.457696
$865$	12.8033	0.435324
$866$	−13.1775	−0.447790
$867$	4.44552	0.150978
$868$	−8.76539	−0.297517
$869$	−68.3064	−2.31714
$870$	10.5455	0.357527
$871$	29.7082	1.00662
$872$	−8.48181	−0.287230
$873$	20.7815	0.703346
$874$	−4.15314	−0.140482
$875$	−1.00000	−0.0338062
$876$	−30.9332	−1.04514
$877$	−3.47582	−0.117370	−0.0586851	−	0.998277i	$-0.518691\pi$
$877$	−3.47582	−0.117370	−0.0586851	+	0.998277i	$0.518691\pi$
$878$	−30.9510	−1.04455
$879$	−29.2790	−0.987557
$880$	−7.66877	−0.258514
$881$	8.56510	0.288565	0.144283	−	0.989537i	$-0.453913\pi$
$881$	8.56510	0.288565	0.144283	+	0.989537i	$0.453913\pi$
$882$	−1.74629	−0.0588005
$883$	−23.8354	−0.802125	−0.401062	−	0.916051i	$-0.631359\pi$
$883$	−23.8354	−0.802125	−0.401062	+	0.916051i	$0.631359\pi$
$884$	12.8902	0.433544
$885$	−0.861939	−0.0289737
$886$	1.67460	0.0562593
$887$	−32.1431	−1.07926	−0.539629	−	0.841903i	$-0.681436\pi$
$887$	−32.1431	−1.07926	−0.539629	+	0.841903i	$0.681436\pi$
$888$	−31.8064	−1.06735
$889$	−5.90011	−0.197883
$890$	−5.07261	−0.170034
$891$	−66.5900	−2.23085
$892$	12.2487	0.410116
$893$	1.63515	0.0547182
$894$	20.8428	0.697086
$895$	1.31114	0.0438265
$896$	−1.69741	−0.0567065
$897$	−25.0407	−0.836086
$898$	−2.83802	−0.0947061
$899$	−44.5100	−1.48449
$900$	−1.55965	−0.0519883
$901$	1.25560	0.0418300
$902$	41.3306	1.37616
$903$	−12.7368	−0.423855
$904$	7.47559	0.248634
$905$	3.56102	0.118372
$906$	20.4663	0.679948
$907$	−42.8710	−1.42351	−0.711754	−	0.702429i	$-0.752099\pi$
$907$	−42.8710	−1.42351	−0.711754	+	0.702429i	$0.752099\pi$
$908$	−4.16226	−0.138129
$909$	−26.7165	−0.886130
$910$	3.73323	0.123755
$911$	5.33383	0.176718	0.0883588	−	0.996089i	$-0.471838\pi$
$911$	5.33383	0.176718	0.0883588	+	0.996089i	$0.471838\pi$
$912$	3.48764	0.115487
$913$	−36.8020	−1.21797
$914$	14.6869	0.485800
$915$	25.3568	0.838268
$916$	−0.925705	−0.0305862
$917$	18.5971	0.614130
$918$	11.4066	0.376475
$919$	−23.7730	−0.784198	−0.392099	−	0.919923i	$-0.628251\pi$
$919$	−23.7730	−0.784198	−0.392099	+	0.919923i	$0.628251\pi$
$920$	9.74025	0.321127
$921$	−18.6086	−0.613173
$922$	22.2321	0.732177
$923$	−40.9398	−1.34755
$924$	−11.8959	−0.391346
$925$	4.84592	0.159333
$926$	28.0809	0.922795
$927$	17.7691	0.583612
$928$	−22.2158	−0.729270
$929$	35.1666	1.15378	0.576889	−	0.816822i	$-0.304266\pi$
$929$	35.1666	1.15378	0.576889	+	0.816822i	$0.304266\pi$
$930$	−21.2426	−0.696571
$931$	1.24749	0.0408848
$932$	25.8286	0.846045
$933$	32.3340	1.05857
$934$	10.7984	0.353333
$935$	−22.9531	−0.750647
$936$	18.4022	0.601494
$937$	30.3513	0.991533	0.495767	−	0.868456i	$-0.334887\pi$
$937$	30.3513	0.991533	0.495767	+	0.868456i	$0.334887\pi$
$938$	8.54900	0.279135
$939$	9.06367	0.295782
$940$	−1.21337	−0.0395758
$941$	−34.3100	−1.11848	−0.559238	−	0.829007i	$-0.688906\pi$
$941$	−34.3100	−1.11848	−0.559238	+	0.829007i	$0.688906\pi$
$942$	−55.3790	−1.80435
$943$	−21.5730	−0.702513
$944$	−0.514373	−0.0167414
$945$	−2.84663	−0.0926009
$946$	36.2121	1.17736
$947$	18.9186	0.614773	0.307386	−	0.951585i	$-0.400546\pi$
$947$	18.9186	0.614773	0.307386	+	0.951585i	$0.400546\pi$
$948$	−23.0517	−0.748685
$949$	−55.6069	−1.80508
$950$	−1.29300	−0.0419505
$951$	−44.7282	−1.45041
$952$	11.7235	0.379960
$953$	39.6120	1.28316	0.641579	−	0.767057i	$-0.278280\pi$
$953$	39.6120	1.28316	0.641579	+	0.767057i	$0.278280\pi$
$954$	0.567155	0.0183623
$955$	−6.80017	−0.220048
$956$	−9.09402	−0.294122
$957$	−60.4065	−1.95266
$958$	−35.2697	−1.13951
$959$	−2.72142	−0.0878792
$960$	−16.1940	−0.522660
$961$	58.6596	1.89225
$962$	−18.0909	−0.583274
$963$	−11.4781	−0.369876
$964$	−2.39889	−0.0772630
$965$	4.97441	0.160132
$966$	−7.20586	−0.231845
$967$	12.5914	0.404911	0.202455	−	0.979291i	$-0.435108\pi$
$967$	12.5914	0.404911	0.202455	+	0.979291i	$0.435108\pi$
$968$	73.5356	2.36352
$969$	10.4387	0.335340
$970$	−12.7845	−0.410486
$971$	−31.3932	−1.00746	−0.503728	−	0.863862i	$-0.668039\pi$
$971$	−31.3932	−1.00746	−0.503728	+	0.863862i	$0.668039\pi$
$972$	−14.5671	−0.467239
$973$	2.55205	0.0818151
$974$	−8.06612	−0.258455
$975$	−7.79596	−0.249670
$976$	15.1320	0.484362
$977$	−1.15618	−0.0369896	−0.0184948	−	0.999829i	$-0.505887\pi$
$977$	−1.15618	−0.0369896	−0.0184948	+	0.999829i	$0.505887\pi$
$978$	27.4226	0.876879
$979$	29.0568	0.928658
$980$	−0.925705	−0.0295706
$981$	−4.71249	−0.150458
$982$	5.15532	0.164513
$983$	−0.169844	−0.00541717	−0.00270859	−	0.999996i	$-0.500862\pi$
$983$	−0.169844	−0.00541717	−0.00270859	+	0.999996i	$0.500862\pi$
$984$	44.0830	1.40531
$985$	4.10238	0.130713
$986$	18.8359	0.599856
$987$	2.83705	0.0903043
$988$	−4.15941	−0.132329
$989$	−18.9013	−0.601027
$990$	−10.3680	−0.329515
$991$	−11.7124	−0.372057	−0.186029	−	0.982544i	$-0.559562\pi$
$991$	−11.7124	−0.372057	−0.186029	+	0.982544i	$0.559562\pi$
$992$	44.7508	1.42084
$993$	−17.6418	−0.559846
$994$	−11.7811	−0.373673
$995$	20.7838	0.658891
$996$	−12.4198	−0.393536
$997$	−53.4210	−1.69186	−0.845930	−	0.533294i	$-0.820954\pi$
$997$	−53.4210	−1.69186	−0.845930	+	0.533294i	$0.820954\pi$
$998$	−5.65317	−0.178948
$999$	13.7945	0.436440

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.i.1.16	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.i.1.16	✓	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)

\(f(q)\)	\(=\)	\(q-1.03648 q^{2} -2.16444 q^{3} -0.925705 q^{4} +1.00000 q^{5} +2.24341 q^{6} -1.00000 q^{7} +3.03244 q^{8} +1.68482 q^{9} +O(q^{10})\)	\(q-1.03648 q^{2} -2.16444 q^{3} -0.925705 q^{4} +1.00000 q^{5} +2.24341 q^{6} -1.00000 q^{7} +3.03244 q^{8} +1.68482 q^{9} -1.03648 q^{10} +5.93714 q^{11} +2.00364 q^{12} +3.60183 q^{13} +1.03648 q^{14} -2.16444 q^{15} -1.29166 q^{16} -3.86602 q^{17} -1.74629 q^{18} +1.24749 q^{19} -0.925705 q^{20} +2.16444 q^{21} -6.15374 q^{22} +3.21202 q^{23} -6.56355 q^{24} +1.00000 q^{25} -3.73323 q^{26} +2.84663 q^{27} +0.925705 q^{28} +4.70067 q^{29} +2.24341 q^{30} -9.46888 q^{31} -4.72610 q^{32} -12.8506 q^{33} +4.00706 q^{34} -1.00000 q^{35} -1.55965 q^{36} +4.84592 q^{37} -1.29300 q^{38} -7.79596 q^{39} +3.03244 q^{40} -6.71634 q^{41} -2.24341 q^{42} -5.88457 q^{43} -5.49604 q^{44} +1.68482 q^{45} -3.32920 q^{46} +1.31075 q^{47} +2.79573 q^{48} +1.00000 q^{49} -1.03648 q^{50} +8.36779 q^{51} -3.33423 q^{52} -0.324777 q^{53} -2.95048 q^{54} +5.93714 q^{55} -3.03244 q^{56} -2.70012 q^{57} -4.87216 q^{58} +0.398226 q^{59} +2.00364 q^{60} -11.7151 q^{61} +9.81432 q^{62} -1.68482 q^{63} +7.48184 q^{64} +3.60183 q^{65} +13.3194 q^{66} +8.24809 q^{67} +3.57880 q^{68} -6.95223 q^{69} +1.03648 q^{70} -11.3664 q^{71} +5.10912 q^{72} -15.4385 q^{73} -5.02270 q^{74} -2.16444 q^{75} -1.15481 q^{76} -5.93714 q^{77} +8.08037 q^{78} -11.5049 q^{79} -1.29166 q^{80} -11.2158 q^{81} +6.96136 q^{82} -6.19861 q^{83} -2.00364 q^{84} -3.86602 q^{85} +6.09925 q^{86} -10.1743 q^{87} +18.0040 q^{88} +4.89407 q^{89} -1.74629 q^{90} -3.60183 q^{91} -2.97338 q^{92} +20.4949 q^{93} -1.35857 q^{94} +1.24749 q^{95} +10.2294 q^{96} +12.3345 q^{97} -1.03648 q^{98} +10.0030 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{2} + 30 q^{4} + 44 q^{5} - 7 q^{6} - 44 q^{7} - 3 q^{8} + 16 q^{9}+O(q^{10}) \) 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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