LMFDB - Embedded newform 8015.2.a.j.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:	$45$
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)

$f(q)$	$=$	$q-1.27565 q^{2} -2.40768 q^{3} -0.372716 q^{4} -1.00000 q^{5} +3.07136 q^{6} +1.00000 q^{7} +3.02676 q^{8} +2.79693 q^{9} +O(q^{10})$	\(q-1.27565 q^{2} -2.40768 q^{3} -0.372716 q^{4} -1.00000 q^{5} +3.07136 q^{6} +1.00000 q^{7} +3.02676 q^{8} +2.79693 q^{9} +1.27565 q^{10} +3.46344 q^{11} +0.897382 q^{12} +3.32992 q^{13} -1.27565 q^{14} +2.40768 q^{15} -3.11565 q^{16} +1.57706 q^{17} -3.56790 q^{18} -3.81767 q^{19} +0.372716 q^{20} -2.40768 q^{21} -4.41814 q^{22} +7.52512 q^{23} -7.28746 q^{24} +1.00000 q^{25} -4.24781 q^{26} +0.488936 q^{27} -0.372716 q^{28} -6.34232 q^{29} -3.07136 q^{30} +5.51593 q^{31} -2.07903 q^{32} -8.33886 q^{33} -2.01178 q^{34} -1.00000 q^{35} -1.04246 q^{36} -0.599204 q^{37} +4.87001 q^{38} -8.01738 q^{39} -3.02676 q^{40} +10.2048 q^{41} +3.07136 q^{42} -4.41362 q^{43} -1.29088 q^{44} -2.79693 q^{45} -9.59942 q^{46} -11.0158 q^{47} +7.50149 q^{48} +1.00000 q^{49} -1.27565 q^{50} -3.79706 q^{51} -1.24111 q^{52} -11.4200 q^{53} -0.623711 q^{54} -3.46344 q^{55} +3.02676 q^{56} +9.19172 q^{57} +8.09058 q^{58} +0.322037 q^{59} -0.897382 q^{60} -2.75849 q^{61} -7.03640 q^{62} +2.79693 q^{63} +8.88342 q^{64} -3.32992 q^{65} +10.6375 q^{66} +7.46330 q^{67} -0.587797 q^{68} -18.1181 q^{69} +1.27565 q^{70} -11.9904 q^{71} +8.46562 q^{72} -3.40488 q^{73} +0.764375 q^{74} -2.40768 q^{75} +1.42291 q^{76} +3.46344 q^{77} +10.2274 q^{78} -11.5295 q^{79} +3.11565 q^{80} -9.56798 q^{81} -13.0178 q^{82} -8.83360 q^{83} +0.897382 q^{84} -1.57706 q^{85} +5.63024 q^{86} +15.2703 q^{87} +10.4830 q^{88} -12.1626 q^{89} +3.56790 q^{90} +3.32992 q^{91} -2.80474 q^{92} -13.2806 q^{93} +14.0523 q^{94} +3.81767 q^{95} +5.00565 q^{96} -11.7996 q^{97} -1.27565 q^{98} +9.68698 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) $ 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * 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 $

$2$	−1.27565	−0.902021	−0.451010	−	0.892519i	$-0.648936\pi$
$2$	−1.27565	−0.902021	−0.451010	+	0.892519i	$0.648936\pi$
$3$	−2.40768	−1.39008	−0.695038	−	0.718973i	$-0.744612\pi$
$3$	−2.40768	−1.39008	−0.695038	+	0.718973i	$0.744612\pi$
$4$	−0.372716	−0.186358
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.07136	1.25388
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	3.02676	1.07012
$9$	2.79693	0.932309
$10$	1.27565	0.403396
$11$	3.46344	1.04427	0.522133	−	0.852864i	$-0.325136\pi$
$11$	3.46344	1.04427	0.522133	+	0.852864i	$0.325136\pi$
$12$	0.897382	0.259052
$13$	3.32992	0.923553	0.461776	−	0.886996i	$-0.347212\pi$
$13$	3.32992	0.923553	0.461776	+	0.886996i	$0.347212\pi$
$14$	−1.27565	−0.340932
$15$	2.40768	0.621660
$16$	−3.11565	−0.778912
$17$	1.57706	0.382494	0.191247	−	0.981542i	$-0.438747\pi$
$17$	1.57706	0.382494	0.191247	+	0.981542i	$0.438747\pi$
$18$	−3.56790	−0.840962
$19$	−3.81767	−0.875833	−0.437916	−	0.899016i	$-0.644283\pi$
$19$	−3.81767	−0.875833	−0.437916	+	0.899016i	$0.644283\pi$
$20$	0.372716	0.0833419
$21$	−2.40768	−0.525399
$22$	−4.41814	−0.941950
$23$	7.52512	1.56910	0.784548	−	0.620068i	$-0.212895\pi$
$23$	7.52512	1.56910	0.784548	+	0.620068i	$0.212895\pi$
$24$	−7.28746	−1.48755
$25$	1.00000	0.200000
$26$	−4.24781	−0.833064
$27$	0.488936	0.0940958
$28$	−0.372716	−0.0704368
$29$	−6.34232	−1.17774	−0.588869	−	0.808228i	$-0.700427\pi$
$29$	−6.34232	−1.17774	−0.588869	+	0.808228i	$0.700427\pi$
$30$	−3.07136	−0.560751
$31$	5.51593	0.990690	0.495345	−	0.868696i	$-0.335042\pi$
$31$	5.51593	0.990690	0.495345	+	0.868696i	$0.335042\pi$
$32$	−2.07903	−0.367525
$33$	−8.33886	−1.45161
$34$	−2.01178	−0.345017
$35$	−1.00000	−0.169031
$36$	−1.04246	−0.173743
$37$	−0.599204	−0.0985086	−0.0492543	−	0.998786i	$-0.515684\pi$
$37$	−0.599204	−0.0985086	−0.0492543	+	0.998786i	$0.515684\pi$
$38$	4.87001	0.790019
$39$	−8.01738	−1.28381
$40$	−3.02676	−0.478572
$41$	10.2048	1.59372	0.796861	−	0.604162i	$-0.206492\pi$
$41$	10.2048	1.59372	0.796861	+	0.604162i	$0.206492\pi$
$42$	3.07136	0.473921
$43$	−4.41362	−0.673071	−0.336535	−	0.941671i	$-0.609255\pi$
$43$	−4.41362	−0.673071	−0.336535	+	0.941671i	$0.609255\pi$
$44$	−1.29088	−0.194608
$45$	−2.79693	−0.416941
$46$	−9.59942	−1.41536
$47$	−11.0158	−1.60682	−0.803408	−	0.595429i	$-0.796982\pi$
$47$	−11.0158	−1.60682	−0.803408	+	0.595429i	$0.796982\pi$
$48$	7.50149	1.08275
$49$	1.00000	0.142857
$50$	−1.27565	−0.180404
$51$	−3.79706	−0.531695
$52$	−1.24111	−0.172112
$53$	−11.4200	−1.56866	−0.784329	−	0.620345i	$-0.786993\pi$
$53$	−11.4200	−1.56866	−0.784329	+	0.620345i	$0.786993\pi$
$54$	−0.623711	−0.0848763
$55$	−3.46344	−0.467010
$56$	3.02676	0.404467
$57$	9.19172	1.21747
$58$	8.09058	1.06235
$59$	0.322037	0.0419257	0.0209629	−	0.999780i	$-0.493327\pi$
$59$	0.322037	0.0419257	0.0209629	+	0.999780i	$0.493327\pi$
$60$	−0.897382	−0.115852
$61$	−2.75849	−0.353189	−0.176594	−	0.984284i	$-0.556508\pi$
$61$	−2.75849	−0.353189	−0.176594	+	0.984284i	$0.556508\pi$
$62$	−7.03640	−0.893623
$63$	2.79693	0.352380
$64$	8.88342	1.11043
$65$	−3.32992	−0.413025
$66$	10.6375	1.30938
$67$	7.46330	0.911788	0.455894	−	0.890034i	$-0.349320\pi$
$67$	7.46330	0.911788	0.455894	+	0.890034i	$0.349320\pi$
$68$	−0.587797	−0.0712809
$69$	−18.1181	−2.18116
$70$	1.27565	0.152469
$71$	−11.9904	−1.42300	−0.711498	−	0.702688i	$-0.751983\pi$
$71$	−11.9904	−1.42300	−0.711498	+	0.702688i	$0.751983\pi$
$72$	8.46562	0.997682
$73$	−3.40488	−0.398511	−0.199255	−	0.979948i	$-0.563852\pi$
$73$	−3.40488	−0.398511	−0.199255	+	0.979948i	$0.563852\pi$
$74$	0.764375	0.0888568
$75$	−2.40768	−0.278015
$76$	1.42291	0.163219
$77$	3.46344	0.394696
$78$	10.2274	1.15802
$79$	−11.5295	−1.29717	−0.648585	−	0.761143i	$-0.724639\pi$
$79$	−11.5295	−1.29717	−0.648585	+	0.761143i	$0.724639\pi$
$80$	3.11565	0.348340
$81$	−9.56798	−1.06311
$82$	−13.0178	−1.43757
$83$	−8.83360	−0.969614	−0.484807	−	0.874621i	$-0.661110\pi$
$83$	−8.83360	−0.969614	−0.484807	+	0.874621i	$0.661110\pi$
$84$	0.897382	0.0979124
$85$	−1.57706	−0.171056
$86$	5.63024	0.607124
$87$	15.2703	1.63715
$88$	10.4830	1.11749
$89$	−12.1626	−1.28923	−0.644615	−	0.764507i	$-0.722982\pi$
$89$	−12.1626	−1.28923	−0.644615	+	0.764507i	$0.722982\pi$
$90$	3.56790	0.376090
$91$	3.32992	0.349070
$92$	−2.80474	−0.292414
$93$	−13.2806	−1.37713
$94$	14.0523	1.44938
$95$	3.81767	0.391684
$96$	5.00565	0.510887
$97$	−11.7996	−1.19807	−0.599035	−	0.800723i	$-0.704449\pi$
$97$	−11.7996	−1.19807	−0.599035	+	0.800723i	$0.704449\pi$
$98$	−1.27565	−0.128860
$99$	9.68698	0.973579
$100$	−0.372716	−0.0372716
$101$	11.9347	1.18754	0.593772	−	0.804633i	$-0.297638\pi$
$101$	11.9347	1.18754	0.593772	+	0.804633i	$0.297638\pi$
$102$	4.84372	0.479600
$103$	−0.983469	−0.0969041	−0.0484520	−	0.998826i	$-0.515429\pi$
$103$	−0.983469	−0.0969041	−0.0484520	+	0.998826i	$0.515429\pi$
$104$	10.0788	0.988312
$105$	2.40768	0.234966
$106$	14.5679	1.41496
$107$	−3.67183	−0.354969	−0.177485	−	0.984124i	$-0.556796\pi$
$107$	−3.67183	−0.354969	−0.177485	+	0.984124i	$0.556796\pi$
$108$	−0.182234	−0.0175355
$109$	2.36787	0.226800	0.113400	−	0.993549i	$-0.463826\pi$
$109$	2.36787	0.226800	0.113400	+	0.993549i	$0.463826\pi$
$110$	4.41814	0.421253
$111$	1.44269	0.136934
$112$	−3.11565	−0.294401
$113$	13.6135	1.28065	0.640325	−	0.768104i	$-0.278800\pi$
$113$	13.6135	1.28065	0.640325	+	0.768104i	$0.278800\pi$
$114$	−11.7254	−1.09819
$115$	−7.52512	−0.701721
$116$	2.36389	0.219481
$117$	9.31353	0.861036
$118$	−0.410807	−0.0378179
$119$	1.57706	0.144569
$120$	7.28746	0.665251
$121$	0.995409	0.0904918
$122$	3.51887	0.318584
$123$	−24.5699	−2.21539
$124$	−2.05588	−0.184623
$125$	−1.00000	−0.0894427
$126$	−3.56790	−0.317854
$127$	−5.92167	−0.525464	−0.262732	−	0.964869i	$-0.584623\pi$
$127$	−5.92167	−0.525464	−0.262732	+	0.964869i	$0.584623\pi$
$128$	−7.17407	−0.634104
$129$	10.6266	0.935619
$130$	4.24781	0.372557
$131$	3.43217	0.299870	0.149935	−	0.988696i	$-0.452094\pi$
$131$	3.43217	0.299870	0.149935	+	0.988696i	$0.452094\pi$
$132$	3.10803	0.270519
$133$	−3.81767	−0.331034
$134$	−9.52057	−0.822452
$135$	−0.488936	−0.0420809
$136$	4.77338	0.409314
$137$	18.1143	1.54761	0.773806	−	0.633422i	$-0.218350\pi$
$137$	18.1143	1.54761	0.773806	+	0.633422i	$0.218350\pi$
$138$	23.1123	1.96745
$139$	17.6240	1.49485	0.747424	−	0.664347i	$-0.231290\pi$
$139$	17.6240	1.49485	0.747424	+	0.664347i	$0.231290\pi$
$140$	0.372716	0.0315003
$141$	26.5225	2.23359
$142$	15.2955	1.28357
$143$	11.5330	0.964435
$144$	−8.71424	−0.726187
$145$	6.34232	0.526701
$146$	4.34343	0.359465
$147$	−2.40768	−0.198582
$148$	0.223333	0.0183579
$149$	−10.1652	−0.832764	−0.416382	−	0.909190i	$-0.636702\pi$
$149$	−10.1652	−0.832764	−0.416382	+	0.909190i	$0.636702\pi$
$150$	3.07136	0.250775
$151$	−19.1139	−1.55547	−0.777734	−	0.628594i	$-0.783631\pi$
$151$	−19.1139	−1.55547	−0.777734	+	0.628594i	$0.783631\pi$
$152$	−11.5551	−0.937246
$153$	4.41093	0.356602
$154$	−4.41814	−0.356024
$155$	−5.51593	−0.443050
$156$	2.98821	0.239248
$157$	5.26296	0.420030	0.210015	−	0.977698i	$-0.432649\pi$
$157$	5.26296	0.420030	0.210015	+	0.977698i	$0.432649\pi$
$158$	14.7076	1.17007
$159$	27.4957	2.18055
$160$	2.07903	0.164362
$161$	7.52512	0.593063
$162$	12.2054	0.958947
$163$	−5.03639	−0.394480	−0.197240	−	0.980355i	$-0.563198\pi$
$163$	−5.03639	−0.394480	−0.197240	+	0.980355i	$0.563198\pi$
$164$	−3.80350	−0.297003
$165$	8.33886	0.649179
$166$	11.2686	0.874612
$167$	−22.3372	−1.72850	−0.864251	−	0.503061i	$-0.832207\pi$
$167$	−22.3372	−1.72850	−0.864251	+	0.503061i	$0.832207\pi$
$168$	−7.28746	−0.562240
$169$	−1.91166	−0.147051
$170$	2.01178	0.154296
$171$	−10.6777	−0.816547
$172$	1.64503	0.125432
$173$	−2.60664	−0.198179	−0.0990896	−	0.995079i	$-0.531593\pi$
$173$	−2.60664	−0.198179	−0.0990896	+	0.995079i	$0.531593\pi$
$174$	−19.4795	−1.47674
$175$	1.00000	0.0755929
$176$	−10.7909	−0.813392
$177$	−0.775363	−0.0582799
$178$	15.5152	1.16291
$179$	10.5042	0.785122	0.392561	−	0.919726i	$-0.371589\pi$
$179$	10.5042	0.785122	0.392561	+	0.919726i	$0.371589\pi$
$180$	1.04246	0.0777004
$181$	17.7050	1.31600	0.658002	−	0.753016i	$-0.271402\pi$
$181$	17.7050	1.31600	0.658002	+	0.753016i	$0.271402\pi$
$182$	−4.24781	−0.314869
$183$	6.64157	0.490959
$184$	22.7767	1.67912
$185$	0.599204	0.0440544
$186$	16.9414	1.24220
$187$	5.46206	0.399425
$188$	4.10576	0.299443
$189$	0.488936	0.0355649
$190$	−4.87001	−0.353307
$191$	18.5079	1.33918	0.669592	−	0.742729i	$-0.266469\pi$
$191$	18.5079	1.33918	0.669592	+	0.742729i	$0.266469\pi$
$192$	−21.3884	−1.54358
$193$	8.96210	0.645106	0.322553	−	0.946551i	$-0.395459\pi$
$193$	8.96210	0.645106	0.322553	+	0.946551i	$0.395459\pi$
$194$	15.0522	1.08068
$195$	8.01738	0.574136
$196$	−0.372716	−0.0266226
$197$	−6.13210	−0.436894	−0.218447	−	0.975849i	$-0.570099\pi$
$197$	−6.13210	−0.436894	−0.218447	+	0.975849i	$0.570099\pi$
$198$	−12.3572	−0.878188
$199$	22.5278	1.59695	0.798477	−	0.602025i	$-0.205639\pi$
$199$	22.5278	1.59695	0.798477	+	0.602025i	$0.205639\pi$
$200$	3.02676	0.214024
$201$	−17.9693	−1.26745
$202$	−15.2245	−1.07119
$203$	−6.34232	−0.445143
$204$	1.41523	0.0990858
$205$	−10.2048	−0.712734
$206$	1.25456	0.0874095
$207$	21.0472	1.46288
$208$	−10.3749	−0.719367
$209$	−13.2223	−0.914602
$210$	−3.07136	−0.211944
$211$	20.3376	1.40010	0.700050	−	0.714093i	$-0.253161\pi$
$211$	20.3376	1.40010	0.700050	+	0.714093i	$0.253161\pi$
$212$	4.25642	0.292332
$213$	28.8690	1.97807
$214$	4.68397	0.320190
$215$	4.41362	0.301006
$216$	1.47989	0.100694
$217$	5.51593	0.374446
$218$	−3.02057	−0.204579
$219$	8.19786	0.553960
$220$	1.29088	0.0870312
$221$	5.25149	0.353253
$222$	−1.84037	−0.123518
$223$	−24.0981	−1.61373	−0.806866	−	0.590735i	$-0.798838\pi$
$223$	−24.0981	−1.61373	−0.806866	+	0.590735i	$0.798838\pi$
$224$	−2.07903	−0.138911
$225$	2.79693	0.186462
$226$	−17.3661	−1.15517
$227$	−19.0487	−1.26431	−0.632155	−	0.774842i	$-0.717829\pi$
$227$	−19.0487	−1.26431	−0.632155	+	0.774842i	$0.717829\pi$
$228$	−3.42591	−0.226886
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	9.59942	0.632967
$231$	−8.33886	−0.548656
$232$	−19.1967	−1.26032
$233$	−7.72947	−0.506374	−0.253187	−	0.967417i	$-0.581479\pi$
$233$	−7.72947	−0.506374	−0.253187	+	0.967417i	$0.581479\pi$
$234$	−11.8808	−0.776673
$235$	11.0158	0.718590
$236$	−0.120029	−0.00781320
$237$	27.7593	1.80316
$238$	−2.01178	−0.130404
$239$	−14.7095	−0.951480	−0.475740	−	0.879586i	$-0.657820\pi$
$239$	−14.7095	−0.951480	−0.475740	+	0.879586i	$0.657820\pi$
$240$	−7.50149	−0.484219
$241$	−20.5798	−1.32566	−0.662830	−	0.748770i	$-0.730645\pi$
$241$	−20.5798	−1.32566	−0.662830	+	0.748770i	$0.730645\pi$
$242$	−1.26979	−0.0816255
$243$	21.5698	1.38371
$244$	1.02814	0.0658197
$245$	−1.00000	−0.0638877
$246$	31.3426	1.99833
$247$	−12.7125	−0.808878
$248$	16.6954	1.06016
$249$	21.2685	1.34784
$250$	1.27565	0.0806792
$251$	20.6396	1.30276	0.651379	−	0.758753i	$-0.274191\pi$
$251$	20.6396	1.30276	0.651379	+	0.758753i	$0.274191\pi$
$252$	−1.04246	−0.0656688
$253$	26.0628	1.63855
$254$	7.55399	0.473979
$255$	3.79706	0.237781
$256$	−8.61524	−0.538452
$257$	−23.5574	−1.46947	−0.734734	−	0.678355i	$-0.762693\pi$
$257$	−23.5574	−1.46947	−0.734734	+	0.678355i	$0.762693\pi$
$258$	−13.5558	−0.843948
$259$	−0.599204	−0.0372327
$260$	1.24111	0.0769707
$261$	−17.7390	−1.09802
$262$	−4.37825	−0.270489
$263$	−20.4501	−1.26101	−0.630504	−	0.776186i	$-0.717152\pi$
$263$	−20.4501	−1.26101	−0.630504	+	0.776186i	$0.717152\pi$
$264$	−25.2397	−1.55340
$265$	11.4200	0.701525
$266$	4.87001	0.298599
$267$	29.2836	1.79213
$268$	−2.78170	−0.169919
$269$	28.9572	1.76555	0.882776	−	0.469795i	$-0.155672\pi$
$269$	28.9572	1.76555	0.882776	+	0.469795i	$0.155672\pi$
$270$	0.623711	0.0379579
$271$	25.3716	1.54122	0.770608	−	0.637309i	$-0.219953\pi$
$271$	25.3716	1.54122	0.770608	+	0.637309i	$0.219953\pi$
$272$	−4.91357	−0.297929
$273$	−8.01738	−0.485234
$274$	−23.1076	−1.39598
$275$	3.46344	0.208853
$276$	6.75291	0.406477
$277$	11.5239	0.692407	0.346203	−	0.938159i	$-0.387471\pi$
$277$	11.5239	0.692407	0.346203	+	0.938159i	$0.387471\pi$
$278$	−22.4821	−1.34838
$279$	15.4276	0.923629
$280$	−3.02676	−0.180883
$281$	−23.0313	−1.37393	−0.686965	−	0.726691i	$-0.741057\pi$
$281$	−23.0313	−1.37393	−0.686965	+	0.726691i	$0.741057\pi$
$282$	−33.8334	−2.01475
$283$	−22.8957	−1.36101	−0.680503	−	0.732745i	$-0.738239\pi$
$283$	−22.8957	−1.36101	−0.680503	+	0.732745i	$0.738239\pi$
$284$	4.46901	0.265187
$285$	−9.19172	−0.544471
$286$	−14.7120	−0.869940
$287$	10.2048	0.602371
$288$	−5.81490	−0.342647
$289$	−14.5129	−0.853698
$290$	−8.09058	−0.475095
$291$	28.4097	1.66541
$292$	1.26905	0.0742657
$293$	30.5721	1.78604	0.893021	−	0.450015i	$-0.148581\pi$
$293$	30.5721	1.78604	0.893021	+	0.450015i	$0.148581\pi$
$294$	3.07136	0.179125
$295$	−0.322037	−0.0187497
$296$	−1.81365	−0.105416
$297$	1.69340	0.0982610
$298$	12.9672	0.751171
$299$	25.0580	1.44914
$300$	0.897382	0.0518104
$301$	−4.41362	−0.254397
$302$	24.3827	1.40306
$303$	−28.7349	−1.65078
$304$	11.8945	0.682197
$305$	2.75849	0.157951
$306$	−5.62680	−0.321663
$307$	17.0754	0.974545	0.487273	−	0.873250i	$-0.337992\pi$
$307$	17.0754	0.974545	0.487273	+	0.873250i	$0.337992\pi$
$308$	−1.29088	−0.0735548
$309$	2.36788	0.134704
$310$	7.03640	0.399640
$311$	−20.9191	−1.18621	−0.593106	−	0.805124i	$-0.702099\pi$
$311$	−20.9191	−1.18621	−0.593106	+	0.805124i	$0.702099\pi$
$312$	−24.2666	−1.37383
$313$	−4.98446	−0.281738	−0.140869	−	0.990028i	$-0.544990\pi$
$313$	−4.98446	−0.281738	−0.140869	+	0.990028i	$0.544990\pi$
$314$	−6.71370	−0.378876
$315$	−2.79693	−0.157589
$316$	4.29723	0.241738
$317$	−11.7998	−0.662744	−0.331372	−	0.943500i	$-0.607512\pi$
$317$	−11.7998	−0.662744	−0.331372	+	0.943500i	$0.607512\pi$
$318$	−35.0749	−1.96690
$319$	−21.9662	−1.22987
$320$	−8.88342	−0.496598
$321$	8.84060	0.493434
$322$	−9.59942	−0.534955
$323$	−6.02070	−0.335001
$324$	3.56614	0.198119
$325$	3.32992	0.184711
$326$	6.42467	0.355829
$327$	−5.70106	−0.315270
$328$	30.8875	1.70547
$329$	−11.0158	−0.607319
$330$	−10.6375	−0.585573
$331$	−17.2683	−0.949151	−0.474575	−	0.880215i	$-0.657398\pi$
$331$	−17.2683	−0.949151	−0.474575	+	0.880215i	$0.657398\pi$
$332$	3.29243	0.180696
$333$	−1.67593	−0.0918404
$334$	28.4944	1.55914
$335$	−7.46330	−0.407764
$336$	7.50149	0.409240
$337$	−14.5187	−0.790883	−0.395441	−	0.918491i	$-0.629408\pi$
$337$	−14.5187	−0.790883	−0.395441	+	0.918491i	$0.629408\pi$
$338$	2.43861	0.132643
$339$	−32.7769	−1.78020
$340$	0.587797	0.0318778
$341$	19.1041	1.03454
$342$	13.6211	0.736542
$343$	1.00000	0.0539949
$344$	−13.3590	−0.720267
$345$	18.1181	0.975445
$346$	3.32516	0.178762
$347$	−9.44217	−0.506882	−0.253441	−	0.967351i	$-0.581562\pi$
$347$	−9.44217	−0.506882	−0.253441	+	0.967351i	$0.581562\pi$
$348$	−5.69148	−0.305096
$349$	11.4791	0.614464	0.307232	−	0.951635i	$-0.400597\pi$
$349$	11.4791	0.614464	0.307232	+	0.951635i	$0.400597\pi$
$350$	−1.27565	−0.0681864
$351$	1.62812	0.0869024
$352$	−7.20061	−0.383794
$353$	−4.65283	−0.247645	−0.123823	−	0.992304i	$-0.539515\pi$
$353$	−4.65283	−0.247645	−0.123823	+	0.992304i	$0.539515\pi$
$354$	0.989092	0.0525697
$355$	11.9904	0.636384
$356$	4.53319	0.240259
$357$	−3.79706	−0.200962
$358$	−13.3997	−0.708196
$359$	−4.76250	−0.251355	−0.125678	−	0.992071i	$-0.540110\pi$
$359$	−4.76250	−0.251355	−0.125678	+	0.992071i	$0.540110\pi$
$360$	−8.46562	−0.446177
$361$	−4.42543	−0.232917
$362$	−22.5854	−1.18706
$363$	−2.39663	−0.125790
$364$	−1.24111	−0.0650521
$365$	3.40488	0.178219
$366$	−8.47232	−0.442856
$367$	−0.900754	−0.0470190	−0.0235095	−	0.999724i	$-0.507484\pi$
$367$	−0.900754	−0.0470190	−0.0235095	+	0.999724i	$0.507484\pi$
$368$	−23.4456	−1.22219
$369$	28.5421	1.48584
$370$	−0.764375	−0.0397380
$371$	−11.4200	−0.592897
$372$	4.94990	0.256640
$373$	−18.7508	−0.970881	−0.485440	−	0.874270i	$-0.661341\pi$
$373$	−18.7508	−0.970881	−0.485440	+	0.874270i	$0.661341\pi$
$374$	−6.96768	−0.360290
$375$	2.40768	0.124332
$376$	−33.3421	−1.71949
$377$	−21.1194	−1.08770
$378$	−0.623711	−0.0320802
$379$	−25.4128	−1.30537	−0.652685	−	0.757629i	$-0.726357\pi$
$379$	−25.4128	−1.30537	−0.652685	+	0.757629i	$0.726357\pi$
$380$	−1.42291	−0.0729936
$381$	14.2575	0.730434
$382$	−23.6096	−1.20797
$383$	3.24418	0.165770	0.0828849	−	0.996559i	$-0.473587\pi$
$383$	3.24418	0.165770	0.0828849	+	0.996559i	$0.473587\pi$
$384$	17.2729	0.881452
$385$	−3.46344	−0.176513
$386$	−11.4325	−0.581899
$387$	−12.3446	−0.627510
$388$	4.39792	0.223270
$389$	−1.93162	−0.0979368	−0.0489684	−	0.998800i	$-0.515593\pi$
$389$	−1.93162	−0.0979368	−0.0489684	+	0.998800i	$0.515593\pi$
$390$	−10.2274	−0.517883
$391$	11.8676	0.600169
$392$	3.02676	0.152874
$393$	−8.26358	−0.416842
$394$	7.82242	0.394088
$395$	11.5295	0.580112
$396$	−3.61050	−0.181434
$397$	−28.8883	−1.44986	−0.724930	−	0.688822i	$-0.758128\pi$
$397$	−28.8883	−1.44986	−0.724930	+	0.688822i	$0.758128\pi$
$398$	−28.7376	−1.44049
$399$	9.19172	0.460162
$400$	−3.11565	−0.155782
$401$	−9.09703	−0.454284	−0.227142	−	0.973862i	$-0.572938\pi$
$401$	−9.09703	−0.454284	−0.227142	+	0.973862i	$0.572938\pi$
$402$	22.9225	1.14327
$403$	18.3676	0.914954
$404$	−4.44825	−0.221309
$405$	9.56798	0.475437
$406$	8.09058	0.401529
$407$	−2.07531	−0.102869
$408$	−11.4928	−0.568978
$409$	−14.9829	−0.740859	−0.370430	−	0.928861i	$-0.620790\pi$
$409$	−14.9829	−0.740859	−0.370430	+	0.928861i	$0.620790\pi$
$410$	13.0178	0.642901
$411$	−43.6135	−2.15130
$412$	0.366555	0.0180589
$413$	0.322037	0.0158464
$414$	−26.8489	−1.31955
$415$	8.83360	0.433625
$416$	−6.92301	−0.339428
$417$	−42.4330	−2.07795
$418$	16.8670	0.824991
$419$	3.99284	0.195063	0.0975314	−	0.995232i	$-0.468905\pi$
$419$	3.99284	0.195063	0.0975314	+	0.995232i	$0.468905\pi$
$420$	−0.897382	−0.0437878
$421$	12.4820	0.608337	0.304168	−	0.952618i	$-0.401621\pi$
$421$	12.4820	0.608337	0.304168	+	0.952618i	$0.401621\pi$
$422$	−25.9437	−1.26292
$423$	−30.8103	−1.49805
$424$	−34.5656	−1.67865
$425$	1.57706	0.0764988
$426$	−36.8268	−1.78426
$427$	−2.75849	−0.133493
$428$	1.36855	0.0661514
$429$	−27.7677	−1.34064
$430$	−5.63024	−0.271514
$431$	7.98702	0.384721	0.192361	−	0.981324i	$-0.438386\pi$
$431$	7.98702	0.384721	0.192361	+	0.981324i	$0.438386\pi$
$432$	−1.52335	−0.0732924
$433$	−27.4216	−1.31780	−0.658900	−	0.752230i	$-0.728978\pi$
$433$	−27.4216	−1.31780	−0.658900	+	0.752230i	$0.728978\pi$
$434$	−7.03640	−0.337758
$435$	−15.2703	−0.732154
$436$	−0.882543	−0.0422661
$437$	−28.7284	−1.37427
$438$	−10.4576	−0.499683
$439$	15.1431	0.722739	0.361369	−	0.932423i	$-0.382309\pi$
$439$	15.1431	0.722739	0.361369	+	0.932423i	$0.382309\pi$
$440$	−10.4830	−0.499757
$441$	2.79693	0.133187
$442$	−6.69906	−0.318642
$443$	13.9963	0.664984	0.332492	−	0.943106i	$-0.392111\pi$
$443$	13.9963	0.664984	0.332492	+	0.943106i	$0.392111\pi$
$444$	−0.537715	−0.0255188
$445$	12.1626	0.576561
$446$	30.7408	1.45562
$447$	24.4745	1.15760
$448$	8.88342	0.419702
$449$	−34.2859	−1.61805	−0.809027	−	0.587772i	$-0.800005\pi$
$449$	−34.2859	−1.61805	−0.809027	+	0.587772i	$0.800005\pi$
$450$	−3.56790	−0.168192
$451$	35.3437	1.66427
$452$	−5.07397	−0.238660
$453$	46.0202	2.16222
$454$	24.2995	1.14043
$455$	−3.32992	−0.156109
$456$	27.8211	1.30284
$457$	−36.7085	−1.71715	−0.858576	−	0.512686i	$-0.828650\pi$
$457$	−36.7085	−1.71715	−0.858576	+	0.512686i	$0.828650\pi$
$458$	−1.27565	−0.0596072
$459$	0.771082	0.0359910
$460$	2.80474	0.130771
$461$	−6.35733	−0.296091	−0.148045	−	0.988981i	$-0.547298\pi$
$461$	−6.35733	−0.296091	−0.148045	+	0.988981i	$0.547298\pi$
$462$	10.6375	0.494900
$463$	−29.7247	−1.38142	−0.690711	−	0.723131i	$-0.742702\pi$
$463$	−29.7247	−1.38142	−0.690711	+	0.723131i	$0.742702\pi$
$464$	19.7604	0.917355
$465$	13.2806	0.615873
$466$	9.86010	0.456760
$467$	9.48696	0.439004	0.219502	−	0.975612i	$-0.429557\pi$
$467$	9.48696	0.439004	0.219502	+	0.975612i	$0.429557\pi$
$468$	−3.47131	−0.160461
$469$	7.46330	0.344623
$470$	−14.0523	−0.648183
$471$	−12.6715	−0.583874
$472$	0.974729	0.0448655
$473$	−15.2863	−0.702865
$474$	−35.4112	−1.62649
$475$	−3.81767	−0.175167
$476$	−0.587797	−0.0269416
$477$	−31.9409	−1.46247
$478$	18.7642	0.858255
$479$	18.9277	0.864830	0.432415	−	0.901675i	$-0.357662\pi$
$479$	18.9277	0.864830	0.432415	+	0.901675i	$0.357662\pi$
$480$	−5.00565	−0.228476
$481$	−1.99530	−0.0909779
$482$	26.2526	1.19577
$483$	−18.1181	−0.824401
$484$	−0.371005	−0.0168639
$485$	11.7996	0.535794
$486$	−27.5156	−1.24813
$487$	−8.28672	−0.375507	−0.187754	−	0.982216i	$-0.560121\pi$
$487$	−8.28672	−0.375507	−0.187754	+	0.982216i	$0.560121\pi$
$488$	−8.34929	−0.377955
$489$	12.1260	0.548357
$490$	1.27565	0.0576280
$491$	32.7380	1.47745	0.738724	−	0.674008i	$-0.235429\pi$
$491$	32.7380	1.47745	0.738724	+	0.674008i	$0.235429\pi$
$492$	9.15761	0.412857
$493$	−10.0022	−0.450478
$494$	16.2167	0.729624
$495$	−9.68698	−0.435398
$496$	−17.1857	−0.771661
$497$	−11.9904	−0.537842
$498$	−27.1312	−1.21578
$499$	−6.53246	−0.292433	−0.146216	−	0.989253i	$-0.546710\pi$
$499$	−6.53246	−0.292433	−0.146216	+	0.989253i	$0.546710\pi$
$500$	0.372716	0.0166684
$501$	53.7808	2.40275
$502$	−26.3289	−1.17511
$503$	37.5364	1.67367	0.836833	−	0.547458i	$-0.184404\pi$
$503$	37.5364	1.67367	0.836833	+	0.547458i	$0.184404\pi$
$504$	8.46562	0.377088
$505$	−11.9347	−0.531086
$506$	−33.2470	−1.47801
$507$	4.60266	0.204411
$508$	2.20711	0.0979245
$509$	30.5332	1.35336	0.676680	−	0.736277i	$-0.263418\pi$
$509$	30.5332	1.35336	0.676680	+	0.736277i	$0.263418\pi$
$510$	−4.84372	−0.214484
$511$	−3.40488	−0.150623
$512$	25.3382	1.11980
$513$	−1.86659	−0.0824121
$514$	30.0510	1.32549
$515$	0.983469	0.0433368
$516$	−3.96070	−0.174360
$517$	−38.1525	−1.67794
$518$	0.764375	0.0335847
$519$	6.27596	0.275484
$520$	−10.0788	−0.441987
$521$	13.5177	0.592220	0.296110	−	0.955154i	$-0.404310\pi$
$521$	13.5177	0.592220	0.296110	+	0.955154i	$0.404310\pi$
$522$	22.6288	0.990434
$523$	16.8186	0.735427	0.367714	−	0.929939i	$-0.380141\pi$
$523$	16.8186	0.735427	0.367714	+	0.929939i	$0.380141\pi$
$524$	−1.27923	−0.0558833
$525$	−2.40768	−0.105080
$526$	26.0872	1.13746
$527$	8.69896	0.378933
$528$	25.9810	1.13068
$529$	33.6274	1.46206
$530$	−14.5679	−0.632790
$531$	0.900715	0.0390877
$532$	1.42291	0.0616908
$533$	33.9811	1.47189
$534$	−37.3556	−1.61654
$535$	3.67183	0.158747
$536$	22.5896	0.975722
$537$	−25.2908	−1.09138
$538$	−36.9393	−1.59256
$539$	3.46344	0.149181
$540$	0.182234	0.00784212
$541$	−5.62832	−0.241980	−0.120990	−	0.992654i	$-0.538607\pi$
$541$	−5.62832	−0.241980	−0.120990	+	0.992654i	$0.538607\pi$
$542$	−32.3653	−1.39021
$543$	−42.6281	−1.82935
$544$	−3.27877	−0.140576
$545$	−2.36787	−0.101428
$546$	10.2274	0.437691
$547$	−23.7565	−1.01575	−0.507877	−	0.861430i	$-0.669569\pi$
$547$	−23.7565	−1.01575	−0.507877	+	0.861430i	$0.669569\pi$
$548$	−6.75151	−0.288410
$549$	−7.71531	−0.329281
$550$	−4.41814	−0.188390
$551$	24.2129	1.03150
$552$	−54.8390	−2.33410
$553$	−11.5295	−0.490284
$554$	−14.7005	−0.624565
$555$	−1.44269	−0.0612389
$556$	−6.56876	−0.278577
$557$	−6.21211	−0.263216	−0.131608	−	0.991302i	$-0.542014\pi$
$557$	−6.21211	−0.263216	−0.131608	+	0.991302i	$0.542014\pi$
$558$	−19.6803	−0.833133
$559$	−14.6970	−0.621616
$560$	3.11565	0.131660
$561$	−13.1509	−0.555231
$562$	29.3798	1.23931
$563$	31.6685	1.33467	0.667335	−	0.744758i	$-0.267435\pi$
$563$	31.6685	1.33467	0.667335	+	0.744758i	$0.267435\pi$
$564$	−9.88536	−0.416249
$565$	−13.6135	−0.572724
$566$	29.2069	1.22766
$567$	−9.56798	−0.401817
$568$	−36.2920	−1.52278
$569$	9.11332	0.382050	0.191025	−	0.981585i	$-0.438819\pi$
$569$	9.11332	0.382050	0.191025	+	0.981585i	$0.438819\pi$
$570$	11.7254	0.491124
$571$	10.9925	0.460022	0.230011	−	0.973188i	$-0.426124\pi$
$571$	10.9925	0.460022	0.230011	+	0.973188i	$0.426124\pi$
$572$	−4.29852	−0.179730
$573$	−44.5611	−1.86157
$574$	−13.0178	−0.543351
$575$	7.52512	0.313819
$576$	24.8463	1.03526
$577$	−14.3282	−0.596492	−0.298246	−	0.954489i	$-0.596402\pi$
$577$	−14.3282	−0.596492	−0.298246	+	0.954489i	$0.596402\pi$
$578$	18.5134	0.770054
$579$	−21.5779	−0.896745
$580$	−2.36389	−0.0981550
$581$	−8.83360	−0.366480
$582$	−36.2409	−1.50223
$583$	−39.5525	−1.63810
$584$	−10.3057	−0.426454
$585$	−9.31353	−0.385067
$586$	−38.9993	−1.61105
$587$	−4.37787	−0.180694	−0.0903471	−	0.995910i	$-0.528798\pi$
$587$	−4.37787	−0.180694	−0.0903471	+	0.995910i	$0.528798\pi$
$588$	0.897382	0.0370074
$589$	−21.0580	−0.867679
$590$	0.410807	0.0169127
$591$	14.7642	0.607316
$592$	1.86691	0.0767296
$593$	−13.1441	−0.539762	−0.269881	−	0.962894i	$-0.586984\pi$
$593$	−13.1441	−0.539762	−0.269881	+	0.962894i	$0.586984\pi$
$594$	−2.16019	−0.0886335
$595$	−1.57706	−0.0646533
$596$	3.78873	0.155192
$597$	−54.2398	−2.21989
$598$	−31.9653	−1.30716
$599$	30.5624	1.24874	0.624372	−	0.781127i	$-0.285355\pi$
$599$	30.5624	1.24874	0.624372	+	0.781127i	$0.285355\pi$
$600$	−7.28746	−0.297509
$601$	−32.6744	−1.33282	−0.666408	−	0.745587i	$-0.732169\pi$
$601$	−32.6744	−1.33282	−0.666408	+	0.745587i	$0.732169\pi$
$602$	5.63024	0.229471
$603$	20.8743	0.850068
$604$	7.12407	0.289874
$605$	−0.995409	−0.0404691
$606$	36.6556	1.48903
$607$	−27.5200	−1.11700	−0.558501	−	0.829504i	$-0.688623\pi$
$607$	−27.5200	−1.11700	−0.558501	+	0.829504i	$0.688623\pi$
$608$	7.93706	0.321890
$609$	15.2703	0.618783
$610$	−3.51887	−0.142475
$611$	−36.6816	−1.48398
$612$	−1.64403	−0.0664558
$613$	−12.1670	−0.491420	−0.245710	−	0.969343i	$-0.579021\pi$
$613$	−12.1670	−0.491420	−0.245710	+	0.969343i	$0.579021\pi$
$614$	−21.7823	−0.879060
$615$	24.5699	0.990754
$616$	10.4830	0.422372
$617$	−5.27152	−0.212223	−0.106112	−	0.994354i	$-0.533840\pi$
$617$	−5.27152	−0.212223	−0.106112	+	0.994354i	$0.533840\pi$
$618$	−3.02059	−0.121506
$619$	−24.5529	−0.986865	−0.493433	−	0.869784i	$-0.664258\pi$
$619$	−24.5529	−0.986865	−0.493433	+	0.869784i	$0.664258\pi$
$620$	2.05588	0.0825660
$621$	3.67930	0.147645
$622$	26.6854	1.06999
$623$	−12.1626	−0.487283
$624$	24.9793	0.999974
$625$	1.00000	0.0400000
$626$	6.35843	0.254134
$627$	31.8350	1.27137
$628$	−1.96159	−0.0782761
$629$	−0.944983	−0.0376789
$630$	3.56790	0.142149
$631$	31.7054	1.26217	0.631087	−	0.775712i	$-0.282609\pi$
$631$	31.7054	1.26217	0.631087	+	0.775712i	$0.282609\pi$
$632$	−34.8970	−1.38813
$633$	−48.9665	−1.94625
$634$	15.0525	0.597809
$635$	5.92167	0.234994
$636$	−10.2481	−0.406364
$637$	3.32992	0.131936
$638$	28.0212	1.10937
$639$	−33.5362	−1.32667
$640$	7.17407	0.283580
$641$	−3.90013	−0.154046	−0.0770229	−	0.997029i	$-0.524541\pi$
$641$	−3.90013	−0.154046	−0.0770229	+	0.997029i	$0.524541\pi$
$642$	−11.2775	−0.445088
$643$	21.5503	0.849861	0.424930	−	0.905226i	$-0.360299\pi$
$643$	21.5503	0.849861	0.424930	+	0.905226i	$0.360299\pi$
$644$	−2.80474	−0.110522
$645$	−10.6266	−0.418422
$646$	7.68030	0.302178
$647$	41.5081	1.63185	0.815926	−	0.578156i	$-0.196228\pi$
$647$	41.5081	1.63185	0.815926	+	0.578156i	$0.196228\pi$
$648$	−28.9599	−1.13765
$649$	1.11536	0.0437816
$650$	−4.24781	−0.166613
$651$	−13.2806	−0.520508
$652$	1.87714	0.0735147
$653$	−20.4228	−0.799206	−0.399603	−	0.916688i	$-0.630852\pi$
$653$	−20.4228	−0.799206	−0.399603	+	0.916688i	$0.630852\pi$
$654$	7.27256	0.284380
$655$	−3.43217	−0.134106
$656$	−31.7946	−1.24137
$657$	−9.52319	−0.371535
$658$	14.0523	0.547815
$659$	11.0577	0.430746	0.215373	−	0.976532i	$-0.430903\pi$
$659$	11.0577	0.430746	0.215373	+	0.976532i	$0.430903\pi$
$660$	−3.10803	−0.120980
$661$	48.6699	1.89304	0.946520	−	0.322645i	$-0.104572\pi$
$661$	48.6699	1.89304	0.946520	+	0.322645i	$0.104572\pi$
$662$	22.0283	0.856154
$663$	−12.6439	−0.491048
$664$	−26.7372	−1.03760
$665$	3.81767	0.148043
$666$	2.13790	0.0828420
$667$	−47.7267	−1.84799
$668$	8.32543	0.322121
$669$	58.0207	2.24321
$670$	9.52057	0.367812
$671$	−9.55388	−0.368823
$672$	5.00565	0.193097
$673$	14.9100	0.574740	0.287370	−	0.957820i	$-0.407219\pi$
$673$	14.9100	0.574740	0.287370	+	0.957820i	$0.407219\pi$
$674$	18.5208	0.713393
$675$	0.488936	0.0188192
$676$	0.712506	0.0274041
$677$	−16.8993	−0.649492	−0.324746	−	0.945801i	$-0.605279\pi$
$677$	−16.8993	−0.649492	−0.324746	+	0.945801i	$0.605279\pi$
$678$	41.8119	1.60578
$679$	−11.7996	−0.452828
$680$	−4.77338	−0.183051
$681$	45.8633	1.75748
$682$	−24.3701	−0.933180
$683$	7.50468	0.287158	0.143579	−	0.989639i	$-0.454139\pi$
$683$	7.50468	0.287158	0.143579	+	0.989639i	$0.454139\pi$
$684$	3.97977	0.152170
$685$	−18.1143	−0.692113
$686$	−1.27565	−0.0487046
$687$	−2.40768	−0.0918588
$688$	13.7513	0.524263
$689$	−38.0277	−1.44874
$690$	−23.1123	−0.879872
$691$	−31.2028	−1.18701	−0.593505	−	0.804830i	$-0.702256\pi$
$691$	−31.2028	−1.18701	−0.593505	+	0.804830i	$0.702256\pi$
$692$	0.971538	0.0369323
$693$	9.68698	0.367978
$694$	12.0449	0.457218
$695$	−17.6240	−0.668517
$696$	46.2194	1.75194
$697$	16.0936	0.609589
$698$	−14.6434	−0.554260
$699$	18.6101	0.703899
$700$	−0.372716	−0.0140874
$701$	22.3693	0.844877	0.422439	−	0.906392i	$-0.361174\pi$
$701$	22.3693	0.844877	0.422439	+	0.906392i	$0.361174\pi$
$702$	−2.07691	−0.0783878
$703$	2.28756	0.0862770
$704$	30.7672	1.15958
$705$	−26.5225	−0.998894
$706$	5.93539	0.223381
$707$	11.9347	0.448849
$708$	0.288991	0.0108609
$709$	−24.3196	−0.913343	−0.456671	−	0.889635i	$-0.650958\pi$
$709$	−24.3196	−0.913343	−0.456671	+	0.889635i	$0.650958\pi$
$710$	−15.2955	−0.574031
$711$	−32.2471	−1.20936
$712$	−36.8131	−1.37963
$713$	41.5080	1.55449
$714$	4.84372	0.181272
$715$	−11.5330	−0.431308
$716$	−3.91509	−0.146314
$717$	35.4158	1.32263
$718$	6.07529	0.226728
$719$	−25.8589	−0.964375	−0.482187	−	0.876068i	$-0.660158\pi$
$719$	−25.8589	−0.964375	−0.482187	+	0.876068i	$0.660158\pi$
$720$	8.71424	0.324761
$721$	−0.983469	−0.0366263
$722$	5.64529	0.210096
$723$	49.5495	1.84277
$724$	−6.59896	−0.245248
$725$	−6.34232	−0.235548
$726$	3.05726	0.113466
$727$	−30.2062	−1.12028	−0.560142	−	0.828396i	$-0.689254\pi$
$727$	−30.2062	−1.12028	−0.560142	+	0.828396i	$0.689254\pi$
$728$	10.0788	0.373547
$729$	−23.2293	−0.860346
$730$	−4.34343	−0.160758
$731$	−6.96055	−0.257445
$732$	−2.47542	−0.0914943
$733$	16.7830	0.619894	0.309947	−	0.950754i	$-0.399689\pi$
$733$	16.7830	0.619894	0.309947	+	0.950754i	$0.399689\pi$
$734$	1.14905	0.0424121
$735$	2.40768	0.0888086
$736$	−15.6450	−0.576681
$737$	25.8487	0.952149
$738$	−36.4097	−1.34026
$739$	6.56970	0.241670	0.120835	−	0.992673i	$-0.461443\pi$
$739$	6.56970	0.241670	0.120835	+	0.992673i	$0.461443\pi$
$740$	−0.223333	−0.00820990
$741$	30.6077	1.12440
$742$	14.5679	0.534806
$743$	−22.2069	−0.814691	−0.407345	−	0.913274i	$-0.633545\pi$
$743$	−22.2069	−0.814691	−0.407345	+	0.913274i	$0.633545\pi$
$744$	−40.1971	−1.47370
$745$	10.1652	0.372424
$746$	23.9195	0.875755
$747$	−24.7069	−0.903980
$748$	−2.03580	−0.0744362
$749$	−3.67183	−0.134166
$750$	−3.07136	−0.112150
$751$	23.5510	0.859386	0.429693	−	0.902975i	$-0.358622\pi$
$751$	23.5510	0.859386	0.429693	+	0.902975i	$0.358622\pi$
$752$	34.3213	1.25157
$753$	−49.6935	−1.81093
$754$	26.9410	0.981132
$755$	19.1139	0.695626
$756$	−0.182234	−0.00662780
$757$	32.3565	1.17602	0.588009	−	0.808855i	$-0.299912\pi$
$757$	32.3565	1.17602	0.588009	+	0.808855i	$0.299912\pi$
$758$	32.4179	1.17747
$759$	−62.7509	−2.27771
$760$	11.5551	0.419149
$761$	51.0195	1.84945	0.924727	−	0.380630i	$-0.124293\pi$
$761$	51.0195	1.84945	0.924727	+	0.380630i	$0.124293\pi$
$762$	−18.1876	−0.658867
$763$	2.36787	0.0857225
$764$	−6.89820	−0.249568
$765$	−4.41093	−0.159477
$766$	−4.13844	−0.149528
$767$	1.07236	0.0387206
$768$	20.7427	0.748489
$769$	−16.1222	−0.581381	−0.290690	−	0.956817i	$-0.593885\pi$
$769$	−16.1222	−0.581381	−0.290690	+	0.956817i	$0.593885\pi$
$770$	4.41814	0.159219
$771$	56.7186	2.04267
$772$	−3.34032	−0.120221
$773$	−0.308333	−0.0110900	−0.00554498	−	0.999985i	$-0.501765\pi$
$773$	−0.308333	−0.0110900	−0.00554498	+	0.999985i	$0.501765\pi$
$774$	15.7474	0.566027
$775$	5.51593	0.198138
$776$	−35.7146	−1.28208
$777$	1.44269	0.0517563
$778$	2.46407	0.0883411
$779$	−38.9585	−1.39583
$780$	−2.98821	−0.106995
$781$	−41.5280	−1.48599
$782$	−15.1389	−0.541365
$783$	−3.10099	−0.110820
$784$	−3.11565	−0.111273
$785$	−5.26296	−0.187843
$786$	10.5414	0.376000
$787$	−17.5779	−0.626583	−0.313292	−	0.949657i	$-0.601432\pi$
$787$	−17.5779	−0.626583	−0.313292	+	0.949657i	$0.601432\pi$
$788$	2.28554	0.0814189
$789$	49.2373	1.75290
$790$	−14.7076	−0.523273
$791$	13.6135	0.484040
$792$	29.3201	1.04185
$793$	−9.18555	−0.326189
$794$	36.8513	1.30780
$795$	−27.4957	−0.975173
$796$	−8.39649	−0.297606
$797$	17.6643	0.625703	0.312851	−	0.949802i	$-0.398716\pi$
$797$	17.6643	0.625703	0.312851	+	0.949802i	$0.398716\pi$
$798$	−11.7254	−0.415075
$799$	−17.3726	−0.614597
$800$	−2.07903	−0.0735049
$801$	−34.0178	−1.20196
$802$	11.6046	0.409774
$803$	−11.7926	−0.416151
$804$	6.69744	0.236200
$805$	−7.52512	−0.265226
$806$	−23.4306	−0.825308
$807$	−69.7197	−2.45425
$808$	36.1233	1.27081
$809$	−16.2913	−0.572771	−0.286386	−	0.958114i	$-0.592454\pi$
$809$	−16.2913	−0.572771	−0.286386	+	0.958114i	$0.592454\pi$
$810$	−12.2054	−0.428854
$811$	−53.1935	−1.86787	−0.933937	−	0.357437i	$-0.883651\pi$
$811$	−53.1935	−1.86787	−0.933937	+	0.357437i	$0.883651\pi$
$812$	2.36389	0.0829561
$813$	−61.0868	−2.14241
$814$	2.64737	0.0927902
$815$	5.03639	0.176417
$816$	11.8303	0.414144
$817$	16.8497	0.589497
$818$	19.1130	0.668271
$819$	9.31353	0.325441
$820$	3.80350	0.132824
$821$	1.50267	0.0524434	0.0262217	−	0.999656i	$-0.491652\pi$
$821$	1.50267	0.0524434	0.0262217	+	0.999656i	$0.491652\pi$
$822$	55.6356	1.94052
$823$	48.7807	1.70039	0.850194	−	0.526469i	$-0.176484\pi$
$823$	48.7807	1.70039	0.850194	+	0.526469i	$0.176484\pi$
$824$	−2.97672	−0.103699
$825$	−8.33886	−0.290322
$826$	−0.410807	−0.0142938
$827$	27.9654	0.972452	0.486226	−	0.873833i	$-0.338373\pi$
$827$	27.9654	0.972452	0.486226	+	0.873833i	$0.338373\pi$
$828$	−7.84464	−0.272620
$829$	−39.7456	−1.38042	−0.690210	−	0.723609i	$-0.742482\pi$
$829$	−39.7456	−1.38042	−0.690210	+	0.723609i	$0.742482\pi$
$830$	−11.2686	−0.391138
$831$	−27.7460	−0.962497
$832$	29.5810	1.02554
$833$	1.57706	0.0546420
$834$	54.1296	1.87436
$835$	22.3372	0.773010
$836$	4.92815	0.170444
$837$	2.69694	0.0932197
$838$	−5.09346	−0.175951
$839$	−37.8220	−1.30576	−0.652880	−	0.757461i	$-0.726439\pi$
$839$	−37.8220	−1.30576	−0.652880	+	0.757461i	$0.726439\pi$
$840$	7.28746	0.251441
$841$	11.2250	0.387069
$842$	−15.9227	−0.548733
$843$	55.4519	1.90987
$844$	−7.58017	−0.260920
$845$	1.91166	0.0657630
$846$	39.3032	1.35127
$847$	0.995409	0.0342027
$848$	35.5807	1.22185
$849$	55.1255	1.89190
$850$	−2.01178	−0.0690035
$851$	−4.50908	−0.154569
$852$	−10.7600	−0.368630
$853$	5.50243	0.188400	0.0941998	−	0.995553i	$-0.469971\pi$
$853$	5.50243	0.188400	0.0941998	+	0.995553i	$0.469971\pi$
$854$	3.51887	0.120413
$855$	10.6777	0.365171
$856$	−11.1137	−0.379860
$857$	34.5947	1.18173	0.590865	−	0.806770i	$-0.298786\pi$
$857$	34.5947	1.18173	0.590865	+	0.806770i	$0.298786\pi$
$858$	35.4219	1.20928
$859$	−19.5621	−0.667451	−0.333725	−	0.942670i	$-0.608306\pi$
$859$	−19.5621	−0.667451	−0.333725	+	0.942670i	$0.608306\pi$
$860$	−1.64503	−0.0560950
$861$	−24.5699	−0.837340
$862$	−10.1886	−0.347026
$863$	−38.9630	−1.32632	−0.663158	−	0.748479i	$-0.730784\pi$
$863$	−38.9630	−1.32632	−0.663158	+	0.748479i	$0.730784\pi$
$864$	−1.01651	−0.0345825
$865$	2.60664	0.0886285
$866$	34.9804	1.18868
$867$	34.9424	1.18671
$868$	−2.05588	−0.0697810
$869$	−39.9317	−1.35459
$870$	19.4795	0.660418
$871$	24.8522	0.842084
$872$	7.16695	0.242704
$873$	−33.0027	−1.11697
$874$	36.6474	1.23962
$875$	−1.00000	−0.0338062
$876$	−3.05548	−0.103235
$877$	−45.0831	−1.52235	−0.761174	−	0.648547i	$-0.775377\pi$
$877$	−45.0831	−1.52235	−0.761174	+	0.648547i	$0.775377\pi$
$878$	−19.3172	−0.651925
$879$	−73.6079	−2.48273
$880$	10.7909	0.363760
$881$	3.83355	0.129155	0.0645777	−	0.997913i	$-0.479430\pi$
$881$	3.83355	0.129155	0.0645777	+	0.997913i	$0.479430\pi$
$882$	−3.56790	−0.120137
$883$	35.5077	1.19493	0.597464	−	0.801896i	$-0.296175\pi$
$883$	35.5077	1.19493	0.597464	+	0.801896i	$0.296175\pi$
$884$	−1.95732	−0.0658316
$885$	0.775363	0.0260636
$886$	−17.8544	−0.599829
$887$	54.9492	1.84501	0.922507	−	0.385979i	$-0.126136\pi$
$887$	54.9492	1.84501	0.922507	+	0.385979i	$0.126136\pi$
$888$	4.36668	0.146536
$889$	−5.92167	−0.198607
$890$	−15.5152	−0.520070
$891$	−33.1381	−1.11017
$892$	8.98178	0.300732
$893$	42.0546	1.40730
$894$	−31.2209	−1.04418
$895$	−10.5042	−0.351117
$896$	−7.17407	−0.239669
$897$	−60.3317	−2.01442
$898$	43.7369	1.45952
$899$	−34.9838	−1.16677
$900$	−1.04246	−0.0347487
$901$	−18.0101	−0.600002
$902$	−45.0862	−1.50121
$903$	10.6266	0.353631
$904$	41.2047	1.37045
$905$	−17.7050	−0.588535
$906$	−58.7057	−1.95036
$907$	−45.7420	−1.51884	−0.759419	−	0.650602i	$-0.774517\pi$
$907$	−45.7420	−1.51884	−0.759419	+	0.650602i	$0.774517\pi$
$908$	7.09978	0.235614
$909$	33.3804	1.10716
$910$	4.24781	0.140813
$911$	46.6157	1.54445	0.772223	−	0.635352i	$-0.219145\pi$
$911$	46.6157	1.54445	0.772223	+	0.635352i	$0.219145\pi$
$912$	−28.6382	−0.948305
$913$	−30.5946	−1.01253
$914$	46.8272	1.54891
$915$	−6.64157	−0.219564
$916$	−0.372716	−0.0123149
$917$	3.43217	0.113340
$918$	−0.983631	−0.0324647
$919$	−10.4196	−0.343712	−0.171856	−	0.985122i	$-0.554976\pi$
$919$	−10.4196	−0.343712	−0.171856	+	0.985122i	$0.554976\pi$
$920$	−22.7767	−0.750926
$921$	−41.1121	−1.35469
$922$	8.10973	0.267080
$923$	−39.9270	−1.31421
$924$	3.10803	0.102247
$925$	−0.599204	−0.0197017
$926$	37.9183	1.24607
$927$	−2.75069	−0.0903445
$928$	13.1859	0.432848
$929$	11.5642	0.379410	0.189705	−	0.981841i	$-0.439247\pi$
$929$	11.5642	0.379410	0.189705	+	0.981841i	$0.439247\pi$
$930$	−16.9414	−0.555530
$931$	−3.81767	−0.125119
$932$	2.88090	0.0943670
$933$	50.3665	1.64893
$934$	−12.1020	−0.395991
$935$	−5.46206	−0.178628
$936$	28.1898	0.921412
$937$	21.8335	0.713269	0.356634	−	0.934244i	$-0.383924\pi$
$937$	21.8335	0.713269	0.356634	+	0.934244i	$0.383924\pi$
$938$	−9.52057	−0.310857
$939$	12.0010	0.391637
$940$	−4.10576	−0.133915
$941$	−22.0150	−0.717668	−0.358834	−	0.933401i	$-0.616826\pi$
$941$	−22.0150	−0.717668	−0.358834	+	0.933401i	$0.616826\pi$
$942$	16.1645	0.526666
$943$	76.7924	2.50070
$944$	−1.00336	−0.0326565
$945$	−0.488936	−0.0159051
$946$	19.5000	0.633999
$947$	−31.6242	−1.02765	−0.513824	−	0.857896i	$-0.671772\pi$
$947$	−31.6242	−1.02765	−0.513824	+	0.857896i	$0.671772\pi$
$948$	−10.3464	−0.336034
$949$	−11.3380	−0.368046
$950$	4.87001	0.158004
$951$	28.4102	0.921265
$952$	4.77338	0.154706
$953$	−26.3316	−0.852963	−0.426482	−	0.904496i	$-0.640247\pi$
$953$	−26.3316	−0.852963	−0.426482	+	0.904496i	$0.640247\pi$
$954$	40.7454	1.31918
$955$	−18.5079	−0.598902
$956$	5.48248	0.177316
$957$	52.8877	1.70962
$958$	−24.1452	−0.780095
$959$	18.1143	0.584943
$960$	21.3884	0.690309
$961$	−0.574524	−0.0185330
$962$	2.54531	0.0820639
$963$	−10.2698	−0.330941
$964$	7.67042	0.247048
$965$	−8.96210	−0.288500
$966$	23.1123	0.743627
$967$	31.8927	1.02560	0.512800	−	0.858508i	$-0.328608\pi$
$967$	31.8927	1.02560	0.512800	+	0.858508i	$0.328608\pi$
$968$	3.01286	0.0968370
$969$	14.4959	0.465676
$970$	−15.0522	−0.483297
$971$	4.07583	0.130800	0.0653998	−	0.997859i	$-0.479168\pi$
$971$	4.07583	0.130800	0.0653998	+	0.997859i	$0.479168\pi$
$972$	−8.03943	−0.257865
$973$	17.6240	0.565000
$974$	10.5710	0.338715
$975$	−8.01738	−0.256762
$976$	8.59450	0.275103
$977$	−32.7306	−1.04714	−0.523572	−	0.851981i	$-0.675401\pi$
$977$	−32.7306	−1.04714	−0.523572	+	0.851981i	$0.675401\pi$
$978$	−15.4686	−0.494630
$979$	−42.1243	−1.34630
$980$	0.372716	0.0119060
$981$	6.62275	0.211448
$982$	−41.7623	−1.33269
$983$	−23.9228	−0.763019	−0.381509	−	0.924365i	$-0.624596\pi$
$983$	−23.9228	−0.763019	−0.381509	+	0.924365i	$0.624596\pi$
$984$	−74.3671	−2.37074
$985$	6.13210	0.195385
$986$	12.7593	0.406340
$987$	26.5225	0.844219
$988$	4.73816	0.150741
$989$	−33.2130	−1.05611
$990$	12.3572	0.392738
$991$	22.9319	0.728454	0.364227	−	0.931310i	$-0.381333\pi$
$991$	22.9319	0.728454	0.364227	+	0.931310i	$0.381333\pi$
$992$	−11.4678	−0.364103
$993$	41.5765	1.31939
$994$	15.2955	0.485145
$995$	−22.5278	−0.714180
$996$	−7.92712	−0.251180
$997$	14.5138	0.459656	0.229828	−	0.973231i	$-0.426184\pi$
$997$	14.5138	0.459656	0.229828	+	0.973231i	$0.426184\pi$
$998$	8.33313	0.263781
$999$	−0.292973	−0.00926924

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.15	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.15	✓	45	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)

\(f(q)\)	\(=\)	\(q-1.27565 q^{2} -2.40768 q^{3} -0.372716 q^{4} -1.00000 q^{5} +3.07136 q^{6} +1.00000 q^{7} +3.02676 q^{8} +2.79693 q^{9} +O(q^{10})\)	\(q-1.27565 q^{2} -2.40768 q^{3} -0.372716 q^{4} -1.00000 q^{5} +3.07136 q^{6} +1.00000 q^{7} +3.02676 q^{8} +2.79693 q^{9} +1.27565 q^{10} +3.46344 q^{11} +0.897382 q^{12} +3.32992 q^{13} -1.27565 q^{14} +2.40768 q^{15} -3.11565 q^{16} +1.57706 q^{17} -3.56790 q^{18} -3.81767 q^{19} +0.372716 q^{20} -2.40768 q^{21} -4.41814 q^{22} +7.52512 q^{23} -7.28746 q^{24} +1.00000 q^{25} -4.24781 q^{26} +0.488936 q^{27} -0.372716 q^{28} -6.34232 q^{29} -3.07136 q^{30} +5.51593 q^{31} -2.07903 q^{32} -8.33886 q^{33} -2.01178 q^{34} -1.00000 q^{35} -1.04246 q^{36} -0.599204 q^{37} +4.87001 q^{38} -8.01738 q^{39} -3.02676 q^{40} +10.2048 q^{41} +3.07136 q^{42} -4.41362 q^{43} -1.29088 q^{44} -2.79693 q^{45} -9.59942 q^{46} -11.0158 q^{47} +7.50149 q^{48} +1.00000 q^{49} -1.27565 q^{50} -3.79706 q^{51} -1.24111 q^{52} -11.4200 q^{53} -0.623711 q^{54} -3.46344 q^{55} +3.02676 q^{56} +9.19172 q^{57} +8.09058 q^{58} +0.322037 q^{59} -0.897382 q^{60} -2.75849 q^{61} -7.03640 q^{62} +2.79693 q^{63} +8.88342 q^{64} -3.32992 q^{65} +10.6375 q^{66} +7.46330 q^{67} -0.587797 q^{68} -18.1181 q^{69} +1.27565 q^{70} -11.9904 q^{71} +8.46562 q^{72} -3.40488 q^{73} +0.764375 q^{74} -2.40768 q^{75} +1.42291 q^{76} +3.46344 q^{77} +10.2274 q^{78} -11.5295 q^{79} +3.11565 q^{80} -9.56798 q^{81} -13.0178 q^{82} -8.83360 q^{83} +0.897382 q^{84} -1.57706 q^{85} +5.63024 q^{86} +15.2703 q^{87} +10.4830 q^{88} -12.1626 q^{89} +3.56790 q^{90} +3.32992 q^{91} -2.80474 q^{92} -13.2806 q^{93} +14.0523 q^{94} +3.81767 q^{95} +5.00565 q^{96} -11.7996 q^{97} -1.27565 q^{98} +9.68698 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9} + 6 q^{10} - q^{11} - 3 q^{12} - 21 q^{13} - 6 q^{14} + 8 q^{16} - 7 q^{17} - 36 q^{18} - 20 q^{19} - 34 q^{20} - 34 q^{22} - 22 q^{23} - 11 q^{24} + 45 q^{25} - q^{26} + 12 q^{27} + 34 q^{28} + 10 q^{29} - q^{30} - 27 q^{31} - 26 q^{32} - 39 q^{33} - 13 q^{34} - 45 q^{35} - 3 q^{36} - 72 q^{37} + 2 q^{38} - 37 q^{39} + 15 q^{40} - 4 q^{41} + q^{42} - 49 q^{43} + 5 q^{44} - 29 q^{45} - 67 q^{46} + 2 q^{47} + 8 q^{48} + 45 q^{49} - 6 q^{50} - 49 q^{51} - 47 q^{52} - 35 q^{53} - 12 q^{54} + q^{55} - 15 q^{56} - 77 q^{57} - 50 q^{58} + 4 q^{59} + 3 q^{60} - 36 q^{61} + 17 q^{62} + 29 q^{63} + 5 q^{64} + 21 q^{65} - 8 q^{66} - 80 q^{67} + 27 q^{68} + 9 q^{69} + 6 q^{70} - 12 q^{71} - 97 q^{72} - 55 q^{73} + 32 q^{74} - 37 q^{76} - q^{77} + 20 q^{78} - 94 q^{79} - 8 q^{80} - 19 q^{81} - 36 q^{82} + 24 q^{83} - 3 q^{84} + 7 q^{85} - 3 q^{86} - 4 q^{87} - 95 q^{88} + q^{89} + 36 q^{90} - 21 q^{91} - 65 q^{92} - 71 q^{93} - 53 q^{94} + 20 q^{95} - 13 q^{96} - 110 q^{97} - 6 q^{98} - 27 q^{99}+O(q^{100}) \) 45 * q - 6 * q^2 + 34 * q^4 - 45 * q^5 + q^6 + 45 * q^7 - 15 * q^8 + 29 * q^9 + 6 * q^10 - q^11 - 3 * q^12 - 21 * q^13 - 6 * q^14 + 8 * q^16 - 7 * q^17 - 36 * q^18 - 20 * q^19 - 34 * q^20 - 34 * q^22 - 22 * q^23 - 11 * q^24 + 45 * q^25 - q^26 + 12 * q^27 + 34 * q^28 + 10 * q^29 - q^30 - 27 * q^31 - 26 * q^32 - 39 * q^33 - 13 * q^34 - 45 * q^35 - 3 * q^36 - 72 * q^37 + 2 * q^38 - 37 * q^39 + 15 * q^40 - 4 * q^41 + q^42 - 49 * q^43 + 5 * q^44 - 29 * q^45 - 67 * q^46 + 2 * q^47 + 8 * q^48 + 45 * q^49 - 6 * q^50 - 49 * q^51 - 47 * q^52 - 35 * q^53 - 12 * q^54 + q^55 - 15 * q^56 - 77 * q^57 - 50 * q^58 + 4 * q^59 + 3 * q^60 - 36 * q^61 + 17 * q^62 + 29 * q^63 + 5 * q^64 + 21 * q^65 - 8 * q^66 - 80 * q^67 + 27 * q^68 + 9 * q^69 + 6 * q^70 - 12 * q^71 - 97 * q^72 - 55 * q^73 + 32 * q^74 - 37 * q^76 - q^77 + 20 * q^78 - 94 * q^79 - 8 * q^80 - 19 * q^81 - 36 * q^82 + 24 * q^83 - 3 * q^84 + 7 * q^85 - 3 * q^86 - 4 * q^87 - 95 * q^88 + q^89 + 36 * q^90 - 21 * q^91 - 65 * q^92 - 71 * q^93 - 53 * q^94 + 20 * q^95 - 13 * q^96 - 110 * q^97 - 6 * q^98 - 27 * q^99

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