LMFDB - Embedded newform 8015.2.a.j.1.14

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			1.14
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)

$f(q)$	$=$	$q-1.48089 q^{2} -0.908664 q^{3} +0.193023 q^{4} -1.00000 q^{5} +1.34563 q^{6} +1.00000 q^{7} +2.67593 q^{8} -2.17433 q^{9} +O(q^{10})$	\(q-1.48089 q^{2} -0.908664 q^{3} +0.193023 q^{4} -1.00000 q^{5} +1.34563 q^{6} +1.00000 q^{7} +2.67593 q^{8} -2.17433 q^{9} +1.48089 q^{10} +1.26459 q^{11} -0.175393 q^{12} -3.08009 q^{13} -1.48089 q^{14} +0.908664 q^{15} -4.34879 q^{16} -6.58840 q^{17} +3.21994 q^{18} +3.71997 q^{19} -0.193023 q^{20} -0.908664 q^{21} -1.87272 q^{22} +0.121133 q^{23} -2.43152 q^{24} +1.00000 q^{25} +4.56127 q^{26} +4.70173 q^{27} +0.193023 q^{28} +4.27143 q^{29} -1.34563 q^{30} +1.00271 q^{31} +1.08821 q^{32} -1.14909 q^{33} +9.75667 q^{34} -1.00000 q^{35} -0.419696 q^{36} +5.21747 q^{37} -5.50885 q^{38} +2.79877 q^{39} -2.67593 q^{40} -8.09518 q^{41} +1.34563 q^{42} -4.26309 q^{43} +0.244096 q^{44} +2.17433 q^{45} -0.179384 q^{46} -0.858936 q^{47} +3.95159 q^{48} +1.00000 q^{49} -1.48089 q^{50} +5.98664 q^{51} -0.594529 q^{52} +4.22077 q^{53} -6.96272 q^{54} -1.26459 q^{55} +2.67593 q^{56} -3.38020 q^{57} -6.32550 q^{58} +9.23760 q^{59} +0.175393 q^{60} -5.74414 q^{61} -1.48490 q^{62} -2.17433 q^{63} +7.08607 q^{64} +3.08009 q^{65} +1.70167 q^{66} -3.27324 q^{67} -1.27171 q^{68} -0.110069 q^{69} +1.48089 q^{70} +7.93689 q^{71} -5.81835 q^{72} -1.88764 q^{73} -7.72648 q^{74} -0.908664 q^{75} +0.718040 q^{76} +1.26459 q^{77} -4.14466 q^{78} -10.1503 q^{79} +4.34879 q^{80} +2.25070 q^{81} +11.9880 q^{82} -0.109044 q^{83} -0.175393 q^{84} +6.58840 q^{85} +6.31314 q^{86} -3.88130 q^{87} +3.38396 q^{88} +9.21888 q^{89} -3.21994 q^{90} -3.08009 q^{91} +0.0233814 q^{92} -0.911126 q^{93} +1.27199 q^{94} -3.71997 q^{95} -0.988813 q^{96} +14.7217 q^{97} -1.48089 q^{98} -2.74964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.48089	−1.04714	−0.523572	−	0.851981i	$-0.675401\pi$
$2$	−1.48089	−1.04714	−0.523572	+	0.851981i	$0.675401\pi$
$3$	−0.908664	−0.524617	−0.262309	−	0.964984i	$-0.584484\pi$
$3$	−0.908664	−0.524617	−0.262309	+	0.964984i	$0.584484\pi$
$4$	0.193023	0.0965116
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.34563	0.549350
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.67593	0.946083
$9$	−2.17433	−0.724777
$10$	1.48089	0.468297
$11$	1.26459	0.381289	0.190645	−	0.981659i	$-0.438942\pi$
$11$	1.26459	0.381289	0.190645	+	0.981659i	$0.438942\pi$
$12$	−0.175393	−0.0506316
$13$	−3.08009	−0.854264	−0.427132	−	0.904189i	$-0.640476\pi$
$13$	−3.08009	−0.854264	−0.427132	+	0.904189i	$0.640476\pi$
$14$	−1.48089	−0.395783
$15$	0.908664	0.234616
$16$	−4.34879	−1.08720
$17$	−6.58840	−1.59792	−0.798961	−	0.601382i	$-0.794617\pi$
$17$	−6.58840	−1.59792	−0.798961	+	0.601382i	$0.794617\pi$
$18$	3.21994	0.758946
$19$	3.71997	0.853419	0.426709	−	0.904389i	$-0.359673\pi$
$19$	3.71997	0.853419	0.426709	+	0.904389i	$0.359673\pi$
$20$	−0.193023	−0.0431613
$21$	−0.908664	−0.198287
$22$	−1.87272	−0.399265
$23$	0.121133	0.0252579	0.0126289	−	0.999920i	$-0.495980\pi$
$23$	0.121133	0.0252579	0.0126289	+	0.999920i	$0.495980\pi$
$24$	−2.43152	−0.496331
$25$	1.00000	0.200000
$26$	4.56127	0.894538
$27$	4.70173	0.904848
$28$	0.193023	0.0364779
$29$	4.27143	0.793185	0.396593	−	0.917995i	$-0.370193\pi$
$29$	4.27143	0.793185	0.396593	+	0.917995i	$0.370193\pi$
$30$	−1.34563	−0.245677
$31$	1.00271	0.180092	0.0900460	−	0.995938i	$-0.471299\pi$
$31$	1.00271	0.180092	0.0900460	+	0.995938i	$0.471299\pi$
$32$	1.08821	0.192370
$33$	−1.14909	−0.200031
$34$	9.75667	1.67326
$35$	−1.00000	−0.169031
$36$	−0.419696	−0.0699493
$37$	5.21747	0.857747	0.428873	−	0.903365i	$-0.358911\pi$
$37$	5.21747	0.857747	0.428873	+	0.903365i	$0.358911\pi$
$38$	−5.50885	−0.893653
$39$	2.79877	0.448162
$40$	−2.67593	−0.423101
$41$	−8.09518	−1.26426	−0.632128	−	0.774864i	$-0.717818\pi$
$41$	−8.09518	−1.26426	−0.632128	+	0.774864i	$0.717818\pi$
$42$	1.34563	0.207635
$43$	−4.26309	−0.650115	−0.325057	−	0.945694i	$-0.605384\pi$
$43$	−4.26309	−0.650115	−0.325057	+	0.945694i	$0.605384\pi$
$44$	0.244096	0.0367988
$45$	2.17433	0.324130
$46$	−0.179384	−0.0264487
$47$	−0.858936	−0.125289	−0.0626443	−	0.998036i	$-0.519953\pi$
$47$	−0.858936	−0.125289	−0.0626443	+	0.998036i	$0.519953\pi$
$48$	3.95159	0.570362
$49$	1.00000	0.142857
$50$	−1.48089	−0.209429
$51$	5.98664	0.838298
$52$	−0.594529	−0.0824464
$53$	4.22077	0.579767	0.289883	−	0.957062i	$-0.406383\pi$
$53$	4.22077	0.579767	0.289883	+	0.957062i	$0.406383\pi$
$54$	−6.96272	−0.947506
$55$	−1.26459	−0.170518
$56$	2.67593	0.357586
$57$	−3.38020	−0.447718
$58$	−6.32550	−0.830579
$59$	9.23760	1.20263	0.601317	−	0.799011i	$-0.294643\pi$
$59$	9.23760	1.20263	0.601317	+	0.799011i	$0.294643\pi$
$60$	0.175393	0.0226432
$61$	−5.74414	−0.735462	−0.367731	−	0.929932i	$-0.619865\pi$
$61$	−5.74414	−0.735462	−0.367731	+	0.929932i	$0.619865\pi$
$62$	−1.48490	−0.188582
$63$	−2.17433	−0.273940
$64$	7.08607	0.885758
$65$	3.08009	0.382039
$66$	1.70167	0.209461
$67$	−3.27324	−0.399890	−0.199945	−	0.979807i	$-0.564076\pi$
$67$	−3.27324	−0.399890	−0.199945	+	0.979807i	$0.564076\pi$
$68$	−1.27171	−0.154218
$69$	−0.110069	−0.0132507
$70$	1.48089	0.177000
$71$	7.93689	0.941935	0.470968	−	0.882151i	$-0.343905\pi$
$71$	7.93689	0.941935	0.470968	+	0.882151i	$0.343905\pi$
$72$	−5.81835	−0.685699
$73$	−1.88764	−0.220932	−0.110466	−	0.993880i	$-0.535234\pi$
$73$	−1.88764	−0.220932	−0.110466	+	0.993880i	$0.535234\pi$
$74$	−7.72648	−0.898185
$75$	−0.908664	−0.104923
$76$	0.718040	0.0823648
$77$	1.26459	0.144114
$78$	−4.14466	−0.469290
$79$	−10.1503	−1.14199	−0.570997	−	0.820952i	$-0.693443\pi$
$79$	−10.1503	−1.14199	−0.570997	+	0.820952i	$0.693443\pi$
$80$	4.34879	0.486209
$81$	2.25070	0.250078
$82$	11.9880	1.32386
$83$	−0.109044	−0.0119691	−0.00598457	−	0.999982i	$-0.501905\pi$
$83$	−0.109044	−0.0119691	−0.00598457	+	0.999982i	$0.501905\pi$
$84$	−0.175393	−0.0191370
$85$	6.58840	0.714613
$86$	6.31314	0.680764
$87$	−3.88130	−0.416119
$88$	3.38396	0.360731
$89$	9.21888	0.977199	0.488600	−	0.872508i	$-0.337508\pi$
$89$	9.21888	0.977199	0.488600	+	0.872508i	$0.337508\pi$
$90$	−3.21994	−0.339411
$91$	−3.08009	−0.322881
$92$	0.0233814	0.00243768
$93$	−0.911126	−0.0944794
$94$	1.27199	0.131195
$95$	−3.71997	−0.381661
$96$	−0.988813	−0.100920
$97$	14.7217	1.49477	0.747383	−	0.664393i	$-0.231310\pi$
$97$	14.7217	1.49477	0.747383	+	0.664393i	$0.231310\pi$
$98$	−1.48089	−0.149592
$99$	−2.74964	−0.276350
$100$	0.193023	0.0193023
$101$	13.4033	1.33368	0.666841	−	0.745200i	$-0.267646\pi$
$101$	13.4033	1.33368	0.666841	+	0.745200i	$0.267646\pi$
$102$	−8.86554	−0.877819
$103$	1.15416	0.113723	0.0568614	−	0.998382i	$-0.481891\pi$
$103$	1.15416	0.113723	0.0568614	+	0.998382i	$0.481891\pi$
$104$	−8.24210	−0.808205
$105$	0.908664	0.0886765
$106$	−6.25047	−0.607100
$107$	−15.9474	−1.54170	−0.770848	−	0.637020i	$-0.780167\pi$
$107$	−15.9474	−1.54170	−0.770848	+	0.637020i	$0.780167\pi$
$108$	0.907542	0.0873283
$109$	−10.6736	−1.02234	−0.511171	−	0.859479i	$-0.670788\pi$
$109$	−10.6736	−1.02234	−0.511171	+	0.859479i	$0.670788\pi$
$110$	1.87272	0.178557
$111$	−4.74092	−0.449989
$112$	−4.34879	−0.410922
$113$	−5.31280	−0.499786	−0.249893	−	0.968273i	$-0.580395\pi$
$113$	−5.31280	−0.499786	−0.249893	+	0.968273i	$0.580395\pi$
$114$	5.00569	0.468826
$115$	−0.121133	−0.0112957
$116$	0.824485	0.0765515
$117$	6.69714	0.619151
$118$	−13.6798	−1.25933
$119$	−6.58840	−0.603958
$120$	2.43152	0.221966
$121$	−9.40080	−0.854618
$122$	8.50642	0.770135
$123$	7.35580	0.663250
$124$	0.193546	0.0173810
$125$	−1.00000	−0.0894427
$126$	3.21994	0.286855
$127$	2.62275	0.232731	0.116366	−	0.993206i	$-0.462876\pi$
$127$	2.62275	0.232731	0.116366	+	0.993206i	$0.462876\pi$
$128$	−12.6701	−1.11989
$129$	3.87371	0.341061
$130$	−4.56127	−0.400050
$131$	9.01699	0.787818	0.393909	−	0.919149i	$-0.371122\pi$
$131$	9.01699	0.787818	0.393909	+	0.919149i	$0.371122\pi$
$132$	−0.221801	−0.0193053
$133$	3.71997	0.322562
$134$	4.84729	0.418742
$135$	−4.70173	−0.404660
$136$	−17.6301	−1.51177
$137$	17.3217	1.47989	0.739947	−	0.672666i	$-0.234851\pi$
$137$	17.3217	1.47989	0.739947	+	0.672666i	$0.234851\pi$
$138$	0.162999	0.0138754
$139$	1.83465	0.155613	0.0778065	−	0.996968i	$-0.475208\pi$
$139$	1.83465	0.155613	0.0778065	+	0.996968i	$0.475208\pi$
$140$	−0.193023	−0.0163134
$141$	0.780484	0.0657286
$142$	−11.7536	−0.986342
$143$	−3.89507	−0.325722
$144$	9.45570	0.787975
$145$	−4.27143	−0.354723
$146$	2.79538	0.231347
$147$	−0.908664	−0.0749453
$148$	1.00709	0.0827825
$149$	−21.3788	−1.75142	−0.875710	−	0.482837i	$-0.839606\pi$
$149$	−21.3788	−1.75142	−0.875710	+	0.482837i	$0.839606\pi$
$150$	1.34563	0.109870
$151$	−0.690853	−0.0562209	−0.0281104	−	0.999605i	$-0.508949\pi$
$151$	−0.690853	−0.0562209	−0.0281104	+	0.999605i	$0.508949\pi$
$152$	9.95436	0.807405
$153$	14.3254	1.15814
$154$	−1.87272	−0.150908
$155$	−1.00271	−0.0805396
$156$	0.540227	0.0432528
$157$	4.21068	0.336049	0.168024	−	0.985783i	$-0.446261\pi$
$157$	4.21068	0.336049	0.168024	+	0.985783i	$0.446261\pi$
$158$	15.0314	1.19583
$159$	−3.83526	−0.304156
$160$	−1.08821	−0.0860303
$161$	0.121133	0.00954659
$162$	−3.33304	−0.261868
$163$	−20.4550	−1.60216	−0.801079	−	0.598558i	$-0.795741\pi$
$163$	−20.4550	−1.60216	−0.801079	+	0.598558i	$0.795741\pi$
$164$	−1.56256	−0.122015
$165$	1.14909	0.0894566
$166$	0.161482	0.0125334
$167$	12.2814	0.950362	0.475181	−	0.879888i	$-0.342383\pi$
$167$	12.2814	0.950362	0.475181	+	0.879888i	$0.342383\pi$
$168$	−2.43152	−0.187596
$169$	−3.51303	−0.270233
$170$	−9.75667	−0.748303
$171$	−8.08844	−0.618538
$172$	−0.822874	−0.0627436
$173$	8.56962	0.651537	0.325768	−	0.945450i	$-0.394377\pi$
$173$	8.56962	0.651537	0.325768	+	0.945450i	$0.394377\pi$
$174$	5.74776	0.435736
$175$	1.00000	0.0755929
$176$	−5.49945	−0.414537
$177$	−8.39387	−0.630922
$178$	−13.6521	−1.02327
$179$	−18.2257	−1.36226	−0.681128	−	0.732165i	$-0.738510\pi$
$179$	−18.2257	−1.36226	−0.681128	+	0.732165i	$0.738510\pi$
$180$	0.419696	0.0312823
$181$	9.58654	0.712562	0.356281	−	0.934379i	$-0.384045\pi$
$181$	9.58654	0.712562	0.356281	+	0.934379i	$0.384045\pi$
$182$	4.56127	0.338104
$183$	5.21949	0.385836
$184$	0.324142	0.0238961
$185$	−5.21747	−0.383596
$186$	1.34927	0.0989336
$187$	−8.33165	−0.609271
$188$	−0.165794	−0.0120918
$189$	4.70173	0.342000
$190$	5.50885	0.399654
$191$	16.7243	1.21013	0.605063	−	0.796178i	$-0.293148\pi$
$191$	16.7243	1.21013	0.605063	+	0.796178i	$0.293148\pi$
$192$	−6.43885	−0.464684
$193$	20.0937	1.44637	0.723186	−	0.690653i	$-0.242677\pi$
$193$	20.0937	1.44637	0.723186	+	0.690653i	$0.242677\pi$
$194$	−21.8012	−1.56524
$195$	−2.79877	−0.200424
$196$	0.193023	0.0137874
$197$	12.2323	0.871517	0.435758	−	0.900064i	$-0.356480\pi$
$197$	12.2323	0.871517	0.435758	+	0.900064i	$0.356480\pi$
$198$	4.07191	0.289378
$199$	8.14350	0.577278	0.288639	−	0.957438i	$-0.406797\pi$
$199$	8.14350	0.577278	0.288639	+	0.957438i	$0.406797\pi$
$200$	2.67593	0.189217
$201$	2.97427	0.209789
$202$	−19.8488	−1.39656
$203$	4.27143	0.299796
$204$	1.15556	0.0809054
$205$	8.09518	0.565392
$206$	−1.70918	−0.119084
$207$	−0.263382	−0.0183063
$208$	13.3947	0.928753
$209$	4.70425	0.325399
$210$	−1.34563	−0.0928571
$211$	18.5402	1.27636	0.638179	−	0.769888i	$-0.279688\pi$
$211$	18.5402	1.27636	0.638179	+	0.769888i	$0.279688\pi$
$212$	0.814705	0.0559542
$213$	−7.21196	−0.494155
$214$	23.6163	1.61438
$215$	4.26309	0.290740
$216$	12.5815	0.856061
$217$	1.00271	0.0680684
$218$	15.8063	1.07054
$219$	1.71523	0.115905
$220$	−0.244096	−0.0164569
$221$	20.2929	1.36505
$222$	7.02077	0.471203
$223$	−9.07597	−0.607772	−0.303886	−	0.952708i	$-0.598284\pi$
$223$	−9.07597	−0.607772	−0.303886	+	0.952708i	$0.598284\pi$
$224$	1.08821	0.0727088
$225$	−2.17433	−0.144955
$226$	7.86765	0.523348
$227$	−22.1560	−1.47054	−0.735272	−	0.677772i	$-0.762946\pi$
$227$	−22.1560	−1.47054	−0.735272	+	0.677772i	$0.762946\pi$
$228$	−0.652457	−0.0432100
$229$	1.00000	0.0660819
$229$	1.00000	0.0660819
$230$	0.179384	0.0118282
$231$	−1.14909	−0.0756046
$232$	11.4300	0.750419
$233$	−2.22469	−0.145744	−0.0728721	−	0.997341i	$-0.523216\pi$
$233$	−2.22469	−0.145744	−0.0728721	+	0.997341i	$0.523216\pi$
$234$	−9.91770	−0.648340
$235$	0.858936	0.0560308
$236$	1.78307	0.116068
$237$	9.22318	0.599110
$238$	9.75667	0.632431
$239$	−5.56664	−0.360076	−0.180038	−	0.983660i	$-0.557622\pi$
$239$	−5.56664	−0.360076	−0.180038	+	0.983660i	$0.557622\pi$
$240$	−3.95159	−0.255074
$241$	22.0821	1.42243	0.711217	−	0.702972i	$-0.248144\pi$
$241$	22.0821	1.42243	0.711217	+	0.702972i	$0.248144\pi$
$242$	13.9215	0.894909
$243$	−16.1503	−1.03604
$244$	−1.10875	−0.0709806
$245$	−1.00000	−0.0638877
$246$	−10.8931	−0.694519
$247$	−11.4578	−0.729045
$248$	2.68318	0.170382
$249$	0.0990843	0.00627921
$250$	1.48089	0.0936594
$251$	27.8765	1.75955	0.879776	−	0.475388i	$-0.157692\pi$
$251$	27.8765	1.75955	0.879776	+	0.475388i	$0.157692\pi$
$252$	−0.419696	−0.0264384
$253$	0.153184	0.00963057
$254$	−3.88399	−0.243703
$255$	−5.98664	−0.374898
$256$	4.59079	0.286925
$257$	15.9904	0.997453	0.498726	−	0.866760i	$-0.333801\pi$
$257$	15.9904	0.997453	0.498726	+	0.866760i	$0.333801\pi$
$258$	−5.73653	−0.357140
$259$	5.21747	0.324198
$260$	0.594529	0.0368711
$261$	−9.28751	−0.574882
$262$	−13.3531	−0.824960
$263$	−13.6486	−0.841611	−0.420805	−	0.907151i	$-0.638252\pi$
$263$	−13.6486	−0.841611	−0.420805	+	0.907151i	$0.638252\pi$
$264$	−3.07488	−0.189246
$265$	−4.22077	−0.259280
$266$	−5.50885	−0.337769
$267$	−8.37686	−0.512655
$268$	−0.631811	−0.0385940
$269$	−16.8088	−1.02485	−0.512425	−	0.858732i	$-0.671253\pi$
$269$	−16.8088	−1.02485	−0.512425	+	0.858732i	$0.671253\pi$
$270$	6.96272	0.423738
$271$	25.4088	1.54348	0.771739	−	0.635940i	$-0.219387\pi$
$271$	25.4088	1.54348	0.771739	+	0.635940i	$0.219387\pi$
$272$	28.6516	1.73726
$273$	2.79877	0.169389
$274$	−25.6515	−1.54966
$275$	1.26459	0.0762579
$276$	−0.0212458	−0.00127885
$277$	−20.3656	−1.22365	−0.611825	−	0.790993i	$-0.709564\pi$
$277$	−20.3656	−1.22365	−0.611825	+	0.790993i	$0.709564\pi$
$278$	−2.71691	−0.162949
$279$	−2.18022	−0.130527
$280$	−2.67593	−0.159917
$281$	19.2944	1.15101	0.575505	−	0.817798i	$-0.304806\pi$
$281$	19.2944	1.15101	0.575505	+	0.817798i	$0.304806\pi$
$282$	−1.15581	−0.0688273
$283$	0.414663	0.0246492	0.0123246	−	0.999924i	$-0.496077\pi$
$283$	0.414663	0.0246492	0.0123246	+	0.999924i	$0.496077\pi$
$284$	1.53200	0.0909076
$285$	3.38020	0.200226
$286$	5.76815	0.341078
$287$	−8.09518	−0.477844
$288$	−2.36612	−0.139425
$289$	26.4071	1.55336
$290$	6.32550	0.371446
$291$	−13.3771	−0.784180
$292$	−0.364358	−0.0213225
$293$	8.70038	0.508282	0.254141	−	0.967167i	$-0.418207\pi$
$293$	8.70038	0.508282	0.254141	+	0.967167i	$0.418207\pi$
$294$	1.34563	0.0784786
$295$	−9.23760	−0.537834
$296$	13.9616	0.811499
$297$	5.94577	0.345009
$298$	31.6596	1.83399
$299$	−0.373100	−0.0215769
$300$	−0.175393	−0.0101263
$301$	−4.26309	−0.245720
$302$	1.02308	0.0588714
$303$	−12.1791	−0.699673
$304$	−16.1773	−0.927835
$305$	5.74414	0.328909
$306$	−21.2142	−1.21274
$307$	−13.4240	−0.766150	−0.383075	−	0.923717i	$-0.625135\pi$
$307$	−13.4240	−0.766150	−0.383075	+	0.923717i	$0.625135\pi$
$308$	0.244096	0.0139087
$309$	−1.04874	−0.0596610
$310$	1.48490	0.0843366
$311$	0.508260	0.0288208	0.0144104	−	0.999896i	$-0.495413\pi$
$311$	0.508260	0.0288208	0.0144104	+	0.999896i	$0.495413\pi$
$312$	7.48930	0.423998
$313$	−21.2710	−1.20231	−0.601153	−	0.799134i	$-0.705292\pi$
$313$	−21.2710	−1.20231	−0.601153	+	0.799134i	$0.705292\pi$
$314$	−6.23554	−0.351892
$315$	2.17433	0.122510
$316$	−1.95924	−0.110216
$317$	−18.0703	−1.01493	−0.507465	−	0.861672i	$-0.669417\pi$
$317$	−18.0703	−1.01493	−0.507465	+	0.861672i	$0.669417\pi$
$318$	5.67958	0.318495
$319$	5.40163	0.302433
$320$	−7.08607	−0.396123
$321$	14.4908	0.808800
$322$	−0.179384	−0.00999666
$323$	−24.5086	−1.36370
$324$	0.434438	0.0241354
$325$	−3.08009	−0.170853
$326$	30.2915	1.67769
$327$	9.69868	0.536338
$328$	−21.6621	−1.19609
$329$	−0.858936	−0.0473547
$330$	−1.70167	−0.0936739
$331$	32.0642	1.76241	0.881205	−	0.472734i	$-0.156733\pi$
$331$	32.0642	1.76241	0.881205	+	0.472734i	$0.156733\pi$
$332$	−0.0210480	−0.00115516
$333$	−11.3445	−0.621675
$334$	−18.1873	−0.995166
$335$	3.27324	0.178836
$336$	3.95159	0.215577
$337$	30.2299	1.64673	0.823363	−	0.567514i	$-0.192095\pi$
$337$	30.2299	1.64673	0.823363	+	0.567514i	$0.192095\pi$
$338$	5.20239	0.282973
$339$	4.82755	0.262196
$340$	1.27171	0.0689684
$341$	1.26802	0.0686672
$342$	11.9781	0.647699
$343$	1.00000	0.0539949
$344$	−11.4077	−0.615062
$345$	0.110069	0.00592591
$346$	−12.6906	−0.682253
$347$	19.4801	1.04575	0.522873	−	0.852411i	$-0.324860\pi$
$347$	19.4801	1.04575	0.522873	+	0.852411i	$0.324860\pi$
$348$	−0.749180	−0.0401603
$349$	28.5711	1.52938	0.764689	−	0.644399i	$-0.222893\pi$
$349$	28.5711	1.52938	0.764689	+	0.644399i	$0.222893\pi$
$350$	−1.48089	−0.0791567
$351$	−14.4818	−0.772979
$352$	1.37614	0.0733484
$353$	12.9892	0.691348	0.345674	−	0.938355i	$-0.387650\pi$
$353$	12.9892	0.691348	0.345674	+	0.938355i	$0.387650\pi$
$354$	12.4304	0.660667
$355$	−7.93689	−0.421246
$356$	1.77946	0.0943110
$357$	5.98664	0.316847
$358$	26.9902	1.42648
$359$	−22.4807	−1.18649	−0.593243	−	0.805023i	$-0.702153\pi$
$359$	−22.4807	−1.18649	−0.593243	+	0.805023i	$0.702153\pi$
$360$	5.81835	0.306654
$361$	−5.16185	−0.271676
$362$	−14.1966	−0.746155
$363$	8.54217	0.448348
$364$	−0.594529	−0.0311618
$365$	1.88764	0.0988036
$366$	−7.72948	−0.404026
$367$	−31.7833	−1.65908	−0.829538	−	0.558450i	$-0.811396\pi$
$367$	−31.7833	−1.65908	−0.829538	+	0.558450i	$0.811396\pi$
$368$	−0.526780	−0.0274603
$369$	17.6016	0.916303
$370$	7.72648	0.401680
$371$	4.22077	0.219131
$372$	−0.175868	−0.00911835
$373$	12.1658	0.629919	0.314960	−	0.949105i	$-0.398009\pi$
$373$	12.1658	0.629919	0.314960	+	0.949105i	$0.398009\pi$
$374$	12.3382	0.637995
$375$	0.908664	0.0469232
$376$	−2.29845	−0.118533
$377$	−13.1564	−0.677590
$378$	−6.96272	−0.358124
$379$	−11.1033	−0.570336	−0.285168	−	0.958478i	$-0.592049\pi$
$379$	−11.1033	−0.570336	−0.285168	+	0.958478i	$0.592049\pi$
$380$	−0.718040	−0.0368347
$381$	−2.38320	−0.122095
$382$	−24.7667	−1.26718
$383$	−17.6090	−0.899779	−0.449889	−	0.893084i	$-0.648537\pi$
$383$	−17.6090	−0.899779	−0.449889	+	0.893084i	$0.648537\pi$
$384$	11.5128	0.587512
$385$	−1.26459	−0.0644497
$386$	−29.7564	−1.51456
$387$	9.26936	0.471188
$388$	2.84164	0.144262
$389$	−36.0753	−1.82909	−0.914545	−	0.404484i	$-0.867451\pi$
$389$	−36.0753	−1.82909	−0.914545	+	0.404484i	$0.867451\pi$
$390$	4.14466	0.209873
$391$	−0.798071	−0.0403602
$392$	2.67593	0.135155
$393$	−8.19341	−0.413303
$394$	−18.1147	−0.912604
$395$	10.1503	0.510716
$396$	−0.530745	−0.0266709
$397$	−34.2229	−1.71760	−0.858799	−	0.512312i	$-0.828789\pi$
$397$	−34.2229	−1.71760	−0.858799	+	0.512312i	$0.828789\pi$
$398$	−12.0596	−0.604493
$399$	−3.38020	−0.169222
$400$	−4.34879	−0.217439
$401$	−26.6146	−1.32907	−0.664534	−	0.747258i	$-0.731370\pi$
$401$	−26.6146	−1.32907	−0.664534	+	0.747258i	$0.731370\pi$
$402$	−4.40456	−0.219679
$403$	−3.08844	−0.153846
$404$	2.58716	0.128716
$405$	−2.25070	−0.111838
$406$	−6.32550	−0.313930
$407$	6.59798	0.327050
$408$	16.0198	0.793099
$409$	−28.7870	−1.42342	−0.711712	−	0.702471i	$-0.752080\pi$
$409$	−28.7870	−1.42342	−0.711712	+	0.702471i	$0.752080\pi$
$410$	−11.9880	−0.592047
$411$	−15.7396	−0.776378
$412$	0.222780	0.0109756
$413$	9.23760	0.454553
$414$	0.390039	0.0191694
$415$	0.109044	0.00535276
$416$	−3.35178	−0.164334
$417$	−1.66708	−0.0816373
$418$	−6.96645	−0.340740
$419$	−18.7711	−0.917026	−0.458513	−	0.888688i	$-0.651618\pi$
$419$	−18.7711	−0.917026	−0.458513	+	0.888688i	$0.651618\pi$
$420$	0.175393	0.00855831
$421$	5.93469	0.289239	0.144620	−	0.989487i	$-0.453804\pi$
$421$	5.93469	0.289239	0.144620	+	0.989487i	$0.453804\pi$
$422$	−27.4559	−1.33653
$423$	1.86761	0.0908063
$424$	11.2945	0.548507
$425$	−6.58840	−0.319585
$426$	10.6801	0.517452
$427$	−5.74414	−0.277979
$428$	−3.07822	−0.148791
$429$	3.53930	0.170879
$430$	−6.31314	−0.304447
$431$	−19.6343	−0.945753	−0.472876	−	0.881129i	$-0.656784\pi$
$431$	−19.6343	−0.945753	−0.472876	+	0.881129i	$0.656784\pi$
$432$	−20.4468	−0.983748
$433$	−0.541987	−0.0260462	−0.0130231	−	0.999915i	$-0.504146\pi$
$433$	−0.541987	−0.0260462	−0.0130231	+	0.999915i	$0.504146\pi$
$434$	−1.48490	−0.0712774
$435$	3.88130	0.186094
$436$	−2.06024	−0.0986678
$437$	0.450609	0.0215556
$438$	−2.54006	−0.121369
$439$	23.1578	1.10526	0.552631	−	0.833426i	$-0.313624\pi$
$439$	23.1578	1.10526	0.552631	+	0.833426i	$0.313624\pi$
$440$	−3.38396	−0.161324
$441$	−2.17433	−0.103540
$442$	−30.0515	−1.42940
$443$	−32.3456	−1.53678	−0.768392	−	0.639980i	$-0.778943\pi$
$443$	−32.3456	−1.53678	−0.768392	+	0.639980i	$0.778943\pi$
$444$	−0.915108	−0.0434291
$445$	−9.21888	−0.437017
$446$	13.4405	0.636425
$447$	19.4261	0.918825
$448$	7.08607	0.334785
$449$	27.8761	1.31555	0.657777	−	0.753212i	$-0.271497\pi$
$449$	27.8761	1.31555	0.657777	+	0.753212i	$0.271497\pi$
$450$	3.21994	0.151789
$451$	−10.2371	−0.482047
$452$	−1.02549	−0.0482351
$453$	0.627753	0.0294944
$454$	32.8105	1.53987
$455$	3.08009	0.144397
$456$	−9.04516	−0.423579
$457$	−19.5810	−0.915959	−0.457980	−	0.888963i	$-0.651427\pi$
$457$	−19.5810	−0.915959	−0.457980	+	0.888963i	$0.651427\pi$
$458$	−1.48089	−0.0691973
$459$	−30.9769	−1.44588
$460$	−0.0233814	−0.00109016
$461$	29.6448	1.38070	0.690349	−	0.723477i	$-0.257457\pi$
$461$	29.6448	1.38070	0.690349	+	0.723477i	$0.257457\pi$
$462$	1.70167	0.0791689
$463$	−35.7165	−1.65989	−0.829944	−	0.557847i	$-0.811628\pi$
$463$	−35.7165	−1.65989	−0.829944	+	0.557847i	$0.811628\pi$
$464$	−18.5756	−0.862349
$465$	0.911126	0.0422525
$466$	3.29451	0.152615
$467$	−2.13538	−0.0988136	−0.0494068	−	0.998779i	$-0.515733\pi$
$467$	−2.13538	−0.0988136	−0.0494068	+	0.998779i	$0.515733\pi$
$468$	1.29270	0.0597552
$469$	−3.27324	−0.151144
$470$	−1.27199	−0.0586723
$471$	−3.82609	−0.176297
$472$	24.7191	1.13779
$473$	−5.39107	−0.247882
$474$	−13.6585	−0.627355
$475$	3.71997	0.170684
$476$	−1.27171	−0.0582889
$477$	−9.17734	−0.420201
$478$	8.24356	0.377052
$479$	29.7519	1.35940	0.679700	−	0.733490i	$-0.262110\pi$
$479$	29.7519	1.35940	0.679700	+	0.733490i	$0.262110\pi$
$480$	0.988813	0.0451330
$481$	−16.0703	−0.732742
$482$	−32.7011	−1.48949
$483$	−0.110069	−0.00500830
$484$	−1.81457	−0.0824806
$485$	−14.7217	−0.668480
$486$	23.9168	1.08489
$487$	−21.5976	−0.978681	−0.489341	−	0.872093i	$-0.662762\pi$
$487$	−21.5976	−0.978681	−0.489341	+	0.872093i	$0.662762\pi$
$488$	−15.3709	−0.695808
$489$	18.5867	0.840520
$490$	1.48089	0.0668996
$491$	−22.0121	−0.993392	−0.496696	−	0.867924i	$-0.665454\pi$
$491$	−22.0121	−0.993392	−0.496696	+	0.867924i	$0.665454\pi$
$492$	1.41984	0.0640113
$493$	−28.1419	−1.26745
$494$	16.9678	0.763416
$495$	2.74964	0.123587
$496$	−4.36057	−0.195796
$497$	7.93689	0.356018
$498$	−0.146733	−0.00657524
$499$	−36.4030	−1.62962	−0.814810	−	0.579728i	$-0.803159\pi$
$499$	−36.4030	−1.62962	−0.814810	+	0.579728i	$0.803159\pi$
$500$	−0.193023	−0.00863226
$501$	−11.1596	−0.498576
$502$	−41.2820	−1.84251
$503$	4.80711	0.214338	0.107169	−	0.994241i	$-0.465821\pi$
$503$	4.80711	0.214338	0.107169	+	0.994241i	$0.465821\pi$
$504$	−5.81835	−0.259170
$505$	−13.4033	−0.596441
$506$	−0.226847	−0.0100846
$507$	3.19216	0.141769
$508$	0.506251	0.0224613
$509$	−4.23213	−0.187586	−0.0937930	−	0.995592i	$-0.529899\pi$
$509$	−4.23213	−0.187586	−0.0937930	+	0.995592i	$0.529899\pi$
$510$	8.86554	0.392573
$511$	−1.88764	−0.0835043
$512$	18.5417	0.819435
$513$	17.4903	0.772214
$514$	−23.6799	−1.04448
$515$	−1.15416	−0.0508584
$516$	0.747716	0.0329164
$517$	−1.08620	−0.0477712
$518$	−7.72648	−0.339482
$519$	−7.78691	−0.341807
$520$	8.24210	0.361440
$521$	−3.64812	−0.159827	−0.0799135	−	0.996802i	$-0.525464\pi$
$521$	−3.64812	−0.159827	−0.0799135	+	0.996802i	$0.525464\pi$
$522$	13.7537	0.601985
$523$	−34.4711	−1.50732	−0.753659	−	0.657266i	$-0.771713\pi$
$523$	−34.4711	−1.50732	−0.753659	+	0.657266i	$0.771713\pi$
$524$	1.74049	0.0760336
$525$	−0.908664	−0.0396573
$526$	20.2121	0.881288
$527$	−6.60626	−0.287773
$528$	4.99715	0.217473
$529$	−22.9853	−0.999362
$530$	6.25047	0.271503
$531$	−20.0856	−0.871641
$532$	0.718040	0.0311310
$533$	24.9339	1.08001
$534$	12.4052	0.536824
$535$	15.9474	0.689467
$536$	−8.75894	−0.378329
$537$	16.5611	0.714662
$538$	24.8919	1.07317
$539$	1.26459	0.0544699
$540$	−0.907542	−0.0390544
$541$	−6.84770	−0.294406	−0.147203	−	0.989106i	$-0.547027\pi$
$541$	−6.84770	−0.294406	−0.147203	+	0.989106i	$0.547027\pi$
$542$	−37.6276	−1.61624
$543$	−8.71094	−0.373822
$544$	−7.16954	−0.307392
$545$	10.6736	0.457205
$546$	−4.14466	−0.177375
$547$	26.2231	1.12122	0.560610	−	0.828080i	$-0.310567\pi$
$547$	26.2231	1.12122	0.560610	+	0.828080i	$0.310567\pi$
$548$	3.34349	0.142827
$549$	12.4897	0.533046
$550$	−1.87272	−0.0798530
$551$	15.8896	0.676919
$552$	−0.294536	−0.0125363
$553$	−10.1503	−0.431634
$554$	30.1591	1.28134
$555$	4.74092	0.201241
$556$	0.354130	0.0150185
$557$	21.3096	0.902918	0.451459	−	0.892292i	$-0.350904\pi$
$557$	21.3096	0.902918	0.451459	+	0.892292i	$0.350904\pi$
$558$	3.22866	0.136680
$559$	13.1307	0.555370
$560$	4.34879	0.183770
$561$	7.57067	0.319634
$562$	−28.5729	−1.20527
$563$	4.57240	0.192704	0.0963519	−	0.995347i	$-0.469283\pi$
$563$	4.57240	0.192704	0.0963519	+	0.995347i	$0.469283\pi$
$564$	0.150651	0.00634357
$565$	5.31280	0.223511
$566$	−0.614069	−0.0258112
$567$	2.25070	0.0945207
$568$	21.2385	0.891149
$569$	16.9136	0.709055	0.354528	−	0.935046i	$-0.384642\pi$
$569$	16.9136	0.709055	0.354528	+	0.935046i	$0.384642\pi$
$570$	−5.00569	−0.209665
$571$	−11.1908	−0.468322	−0.234161	−	0.972198i	$-0.575234\pi$
$571$	−11.1908	−0.468322	−0.234161	+	0.972198i	$0.575234\pi$
$572$	−0.751838	−0.0314359
$573$	−15.1967	−0.634853
$574$	11.9880	0.500371
$575$	0.121133	0.00505158
$576$	−15.4075	−0.641977
$577$	−23.4748	−0.977267	−0.488633	−	0.872489i	$-0.662504\pi$
$577$	−23.4748	−0.977267	−0.488633	+	0.872489i	$0.662504\pi$
$578$	−39.1059	−1.62659
$579$	−18.2584	−0.758792
$580$	−0.824485	−0.0342349
$581$	−0.109044	−0.00452391
$582$	19.8100	0.821150
$583$	5.33755	0.221059
$584$	−5.05119	−0.209020
$585$	−6.69714	−0.276893
$586$	−12.8843	−0.532244
$587$	−15.1466	−0.625167	−0.312584	−	0.949890i	$-0.601194\pi$
$587$	−15.1466	−0.625167	−0.312584	+	0.949890i	$0.601194\pi$
$588$	−0.175393	−0.00723309
$589$	3.73005	0.153694
$590$	13.6798	0.563190
$591$	−11.1151	−0.457213
$592$	−22.6897	−0.932539
$593$	10.0608	0.413146	0.206573	−	0.978431i	$-0.433769\pi$
$593$	10.0608	0.413146	0.206573	+	0.978431i	$0.433769\pi$
$594$	−8.80501	−0.361274
$595$	6.58840	0.270098
$596$	−4.12660	−0.169032
$597$	−7.39971	−0.302850
$598$	0.552518	0.0225941
$599$	14.8573	0.607053	0.303526	−	0.952823i	$-0.401836\pi$
$599$	14.8573	0.607053	0.303526	+	0.952823i	$0.401836\pi$
$600$	−2.43152	−0.0992663
$601$	4.68715	0.191193	0.0955963	−	0.995420i	$-0.469524\pi$
$601$	4.68715	0.191193	0.0955963	+	0.995420i	$0.469524\pi$
$602$	6.31314	0.257305
$603$	7.11710	0.289831
$604$	−0.133351	−0.00542596
$605$	9.40080	0.382197
$606$	18.0359	0.732659
$607$	−7.63750	−0.309996	−0.154998	−	0.987915i	$-0.549537\pi$
$607$	−7.63750	−0.309996	−0.154998	+	0.987915i	$0.549537\pi$
$608$	4.04809	0.164172
$609$	−3.88130	−0.157278
$610$	−8.50642	−0.344415
$611$	2.64560	0.107030
$612$	2.76513	0.111774
$613$	−49.1668	−1.98583	−0.992914	−	0.118835i	$-0.962084\pi$
$613$	−49.1668	−1.98583	−0.992914	+	0.118835i	$0.962084\pi$
$614$	19.8795	0.802270
$615$	−7.35580	−0.296615
$616$	3.38396	0.136344
$617$	−0.973552	−0.0391937	−0.0195969	−	0.999808i	$-0.506238\pi$
$617$	−0.973552	−0.0391937	−0.0195969	+	0.999808i	$0.506238\pi$
$618$	1.55307	0.0624737
$619$	5.42060	0.217872	0.108936	−	0.994049i	$-0.465256\pi$
$619$	5.42060	0.217872	0.108936	+	0.994049i	$0.465256\pi$
$620$	−0.193546	−0.00777300
$621$	0.569532	0.0228545
$622$	−0.752675	−0.0301795
$623$	9.21888	0.369347
$624$	−12.1713	−0.487240
$625$	1.00000	0.0400000
$626$	31.4999	1.25899
$627$	−4.27458	−0.170710
$628$	0.812759	0.0324326
$629$	−34.3748	−1.37061
$630$	−3.21994	−0.128285
$631$	26.5796	1.05812	0.529058	−	0.848586i	$-0.322545\pi$
$631$	26.5796	1.05812	0.529058	+	0.848586i	$0.322545\pi$
$632$	−27.1614	−1.08042
$633$	−16.8468	−0.669600
$634$	26.7601	1.06278
$635$	−2.62275	−0.104081
$636$	−0.740293	−0.0293545
$637$	−3.08009	−0.122038
$638$	−7.99919	−0.316691
$639$	−17.2574	−0.682693
$640$	12.6701	0.500828
$641$	−6.48452	−0.256123	−0.128062	−	0.991766i	$-0.540876\pi$
$641$	−6.48452	−0.256123	−0.128062	+	0.991766i	$0.540876\pi$
$642$	−21.4593	−0.846930
$643$	43.8148	1.72789	0.863944	−	0.503588i	$-0.167987\pi$
$643$	43.8148	1.72789	0.863944	+	0.503588i	$0.167987\pi$
$644$	0.0233814	0.000921356 0
$645$	−3.87371	−0.152527
$646$	36.2945	1.42799
$647$	−35.2900	−1.38739	−0.693697	−	0.720267i	$-0.744019\pi$
$647$	−35.2900	−1.38739	−0.693697	+	0.720267i	$0.744019\pi$
$648$	6.02272	0.236595
$649$	11.6818	0.458551
$650$	4.56127	0.178908
$651$	−0.911126	−0.0357099
$652$	−3.94829	−0.154627
$653$	−35.5686	−1.39191	−0.695953	−	0.718087i	$-0.745018\pi$
$653$	−35.5686	−1.39191	−0.695953	+	0.718087i	$0.745018\pi$
$654$	−14.3626	−0.561623
$655$	−9.01699	−0.352323
$656$	35.2042	1.37449
$657$	4.10435	0.160126
$658$	1.27199	0.0495872
$659$	−17.5123	−0.682183	−0.341091	−	0.940030i	$-0.610797\pi$
$659$	−17.5123	−0.682183	−0.341091	+	0.940030i	$0.610797\pi$
$660$	0.221801	0.00863359
$661$	−31.8802	−1.24000	−0.619998	−	0.784603i	$-0.712867\pi$
$661$	−31.8802	−1.24000	−0.619998	+	0.784603i	$0.712867\pi$
$662$	−47.4835	−1.84550
$663$	−18.4394	−0.716128
$664$	−0.291794	−0.0113238
$665$	−3.71997	−0.144254
$666$	16.7999	0.650983
$667$	0.517410	0.0200342
$668$	2.37059	0.0917209
$669$	8.24701	0.318848
$670$	−4.84729	−0.187267
$671$	−7.26401	−0.280424
$672$	−0.988813	−0.0381443
$673$	−33.9855	−1.31005	−0.655023	−	0.755609i	$-0.727341\pi$
$673$	−33.9855	−1.31005	−0.655023	+	0.755609i	$0.727341\pi$
$674$	−44.7670	−1.72436
$675$	4.70173	0.180970
$676$	−0.678096	−0.0260806
$677$	−12.9405	−0.497345	−0.248672	−	0.968588i	$-0.579994\pi$
$677$	−12.9405	−0.497345	−0.248672	+	0.968588i	$0.579994\pi$
$678$	−7.14905	−0.274557
$679$	14.7217	0.564968
$680$	17.6301	0.676083
$681$	20.1323	0.771473
$682$	−1.87779	−0.0719045
$683$	37.5931	1.43846	0.719230	−	0.694772i	$-0.244495\pi$
$683$	37.5931	1.43846	0.719230	+	0.694772i	$0.244495\pi$
$684$	−1.56126	−0.0596961
$685$	−17.3217	−0.661828
$686$	−1.48089	−0.0565405
$687$	−0.908664	−0.0346677
$688$	18.5393	0.706803
$689$	−13.0004	−0.495274
$690$	−0.162999	−0.00620528
$691$	−43.4245	−1.65195	−0.825973	−	0.563709i	$-0.809374\pi$
$691$	−43.4245	−1.65195	−0.825973	+	0.563709i	$0.809374\pi$
$692$	1.65414	0.0628808
$693$	−2.74964	−0.104450
$694$	−28.8478	−1.09505
$695$	−1.83465	−0.0695923
$696$	−10.3861	−0.393683
$697$	53.3343	2.02018
$698$	−42.3106	−1.60148
$699$	2.02149	0.0764599
$700$	0.193023	0.00729559
$701$	−29.2128	−1.10335	−0.551676	−	0.834058i	$-0.686012\pi$
$701$	−29.2128	−1.10335	−0.551676	+	0.834058i	$0.686012\pi$
$702$	21.4458	0.809420
$703$	19.4088	0.732017
$704$	8.96100	0.337730
$705$	−0.780484	−0.0293947
$706$	−19.2356	−0.723941
$707$	13.4033	0.504085
$708$	−1.62021	−0.0608913
$709$	49.0898	1.84361	0.921804	−	0.387657i	$-0.126715\pi$
$709$	49.0898	1.84361	0.921804	+	0.387657i	$0.126715\pi$
$710$	11.7536	0.441106
$711$	22.0700	0.827691
$712$	24.6690	0.924511
$713$	0.121461	0.00454875
$714$	−8.86554	−0.331784
$715$	3.89507	0.145667
$716$	−3.51799	−0.131473
$717$	5.05821	0.188902
$718$	33.2914	1.24242
$719$	−8.63824	−0.322152	−0.161076	−	0.986942i	$-0.551496\pi$
$719$	−8.63824	−0.322152	−0.161076	+	0.986942i	$0.551496\pi$
$720$	−9.45570	−0.352393
$721$	1.15416	0.0429832
$722$	7.64411	0.284484
$723$	−20.0652	−0.746234
$724$	1.85042	0.0687704
$725$	4.27143	0.158637
$726$	−12.6500	−0.469485
$727$	−28.3378	−1.05099	−0.525496	−	0.850796i	$-0.676120\pi$
$727$	−28.3378	−1.05099	−0.525496	+	0.850796i	$0.676120\pi$
$728$	−8.24210	−0.305473
$729$	7.92309	0.293448
$730$	−2.79538	−0.103462
$731$	28.0869	1.03883
$732$	1.00748	0.0372376
$733$	−19.0676	−0.704279	−0.352139	−	0.935948i	$-0.614546\pi$
$733$	−19.0676	−0.704279	−0.352139	+	0.935948i	$0.614546\pi$
$734$	47.0675	1.73729
$735$	0.908664	0.0335166
$736$	0.131817	0.00485885
$737$	−4.13932	−0.152474
$738$	−26.0660	−0.959502
$739$	−29.2468	−1.07586	−0.537930	−	0.842990i	$-0.680793\pi$
$739$	−29.2468	−1.07586	−0.537930	+	0.842990i	$0.680793\pi$
$740$	−1.00709	−0.0370214
$741$	10.4113	0.382470
$742$	−6.25047	−0.229462
$743$	−11.0510	−0.405423	−0.202712	−	0.979238i	$-0.564975\pi$
$743$	−11.0510	−0.405423	−0.202712	+	0.979238i	$0.564975\pi$
$744$	−2.43811	−0.0893853
$745$	21.3788	0.783259
$746$	−18.0161	−0.659616
$747$	0.237098	0.00867495
$748$	−1.60820	−0.0588017
$749$	−15.9474	−0.582706
$750$	−1.34563	−0.0491354
$751$	−42.0616	−1.53485	−0.767425	−	0.641139i	$-0.778462\pi$
$751$	−42.0616	−1.53485	−0.767425	+	0.641139i	$0.778462\pi$
$752$	3.73533	0.136213
$753$	−25.3304	−0.923091
$754$	19.4831	0.709534
$755$	0.690853	0.0251427
$756$	0.907542	0.0330070
$757$	−38.2188	−1.38909	−0.694543	−	0.719451i	$-0.744393\pi$
$757$	−38.2188	−1.38909	−0.694543	+	0.719451i	$0.744393\pi$
$758$	16.4427	0.597224
$759$	−0.139192	−0.00505236
$760$	−9.95436	−0.361083
$761$	26.6530	0.966171	0.483086	−	0.875573i	$-0.339516\pi$
$761$	26.6530	0.966171	0.483086	+	0.875573i	$0.339516\pi$
$762$	3.52924	0.127851
$763$	−10.6736	−0.386409
$764$	3.22817	0.116791
$765$	−14.3254	−0.517935
$766$	26.0769	0.942198
$767$	−28.4527	−1.02737
$768$	−4.17149	−0.150526
$769$	−17.5032	−0.631181	−0.315590	−	0.948896i	$-0.602203\pi$
$769$	−17.5032	−0.631181	−0.315590	+	0.948896i	$0.602203\pi$
$770$	1.87272	0.0674881
$771$	−14.5299	−0.523281
$772$	3.87854	0.139592
$773$	−9.55268	−0.343586	−0.171793	−	0.985133i	$-0.554956\pi$
$773$	−9.55268	−0.343586	−0.171793	+	0.985133i	$0.554956\pi$
$774$	−13.7269	−0.493402
$775$	1.00271	0.0360184
$776$	39.3943	1.41417
$777$	−4.74092	−0.170080
$778$	53.4234	1.91532
$779$	−30.1138	−1.07894
$780$	−0.540227	−0.0193432
$781$	10.0369	0.359150
$782$	1.18185	0.0422629
$783$	20.0831	0.717712
$784$	−4.34879	−0.155314
$785$	−4.21068	−0.150286
$786$	12.1335	0.432788
$787$	−7.64270	−0.272433	−0.136216	−	0.990679i	$-0.543494\pi$
$787$	−7.64270	−0.272433	−0.136216	+	0.990679i	$0.543494\pi$
$788$	2.36112	0.0841114
$789$	12.4020	0.441524
$790$	−15.0314	−0.534793
$791$	−5.31280	−0.188901
$792$	−7.35785	−0.261450
$793$	17.6925	0.628279
$794$	50.6802	1.79857
$795$	3.83526	0.136023
$796$	1.57188	0.0557140
$797$	−11.6368	−0.412197	−0.206099	−	0.978531i	$-0.566077\pi$
$797$	−11.6368	−0.412197	−0.206099	+	0.978531i	$0.566077\pi$
$798$	5.00569	0.177199
$799$	5.65902	0.200202
$800$	1.08821	0.0384739
$801$	−20.0449	−0.708251
$802$	39.4132	1.39173
$803$	−2.38710	−0.0842389
$804$	0.574103	0.0202471
$805$	−0.121133	−0.00426936
$806$	4.57363	0.161099
$807$	15.2735	0.537654
$808$	35.8664	1.26177
$809$	−40.4614	−1.42255	−0.711274	−	0.702915i	$-0.751882\pi$
$809$	−40.4614	−1.42255	−0.711274	+	0.702915i	$0.751882\pi$
$810$	3.33304	0.117111
$811$	9.71556	0.341159	0.170580	−	0.985344i	$-0.445436\pi$
$811$	9.71556	0.341159	0.170580	+	0.985344i	$0.445436\pi$
$812$	0.824485	0.0289338
$813$	−23.0881	−0.809735
$814$	−9.77085	−0.342468
$815$	20.4550	0.716507
$816$	−26.0346	−0.911395
$817$	−15.8585	−0.554820
$818$	42.6302	1.49053
$819$	6.69714	0.234017
$820$	1.56256	0.0545669
$821$	46.5823	1.62573	0.812867	−	0.582450i	$-0.197906\pi$
$821$	46.5823	1.62573	0.812867	+	0.582450i	$0.197906\pi$
$822$	23.3086	0.812979
$823$	−23.8058	−0.829818	−0.414909	−	0.909863i	$-0.636187\pi$
$823$	−23.8058	−0.829818	−0.414909	+	0.909863i	$0.636187\pi$
$824$	3.08845	0.107591
$825$	−1.14909	−0.0400062
$826$	−13.6798	−0.475982
$827$	−1.62328	−0.0564470	−0.0282235	−	0.999602i	$-0.508985\pi$
$827$	−1.62328	−0.0564470	−0.0282235	+	0.999602i	$0.508985\pi$
$828$	−0.0508389	−0.00176677
$829$	−11.5537	−0.401277	−0.200639	−	0.979665i	$-0.564302\pi$
$829$	−11.5537	−0.401277	−0.200639	+	0.979665i	$0.564302\pi$
$830$	−0.161482	−0.00560511
$831$	18.5055	0.641948
$832$	−21.8257	−0.756672
$833$	−6.58840	−0.228275
$834$	2.46876	0.0854861
$835$	−12.2814	−0.425015
$836$	0.908028	0.0314048
$837$	4.71447	0.162956
$838$	27.7978	0.960259
$839$	36.7848	1.26995	0.634977	−	0.772531i	$-0.281010\pi$
$839$	36.7848	1.26995	0.634977	+	0.772531i	$0.281010\pi$
$840$	2.43152	0.0838953
$841$	−10.7549	−0.370857
$842$	−8.78860	−0.302875
$843$	−17.5322	−0.603839
$844$	3.57868	0.123183
$845$	3.51303	0.120852
$846$	−2.76572	−0.0950873
$847$	−9.40080	−0.323015
$848$	−18.3552	−0.630321
$849$	−0.376789	−0.0129314
$850$	9.75667	0.334651
$851$	0.632006	0.0216649
$852$	−1.39208	−0.0476917
$853$	−37.7828	−1.29366	−0.646829	−	0.762635i	$-0.723905\pi$
$853$	−37.7828	−1.29366	−0.646829	+	0.762635i	$0.723905\pi$
$854$	8.50642	0.291084
$855$	8.08844	0.276619
$856$	−42.6741	−1.45857
$857$	0.676733	0.0231167	0.0115584	−	0.999933i	$-0.496321\pi$
$857$	0.676733	0.0231167	0.0115584	+	0.999933i	$0.496321\pi$
$858$	−5.24131	−0.178935
$859$	40.3114	1.37541	0.687703	−	0.725992i	$-0.258619\pi$
$859$	40.3114	1.37541	0.687703	+	0.725992i	$0.258619\pi$
$860$	0.822874	0.0280598
$861$	7.35580	0.250685
$862$	29.0762	0.990340
$863$	19.0319	0.647855	0.323927	−	0.946082i	$-0.394997\pi$
$863$	19.0319	0.647855	0.323927	+	0.946082i	$0.394997\pi$
$864$	5.11645	0.174065
$865$	−8.56962	−0.291376
$866$	0.802621	0.0272742
$867$	−23.9951	−0.814918
$868$	0.193546	0.00656939
$869$	−12.8360	−0.435430
$870$	−5.74776	−0.194867
$871$	10.0819	0.341611
$872$	−28.5617	−0.967220
$873$	−32.0099	−1.08337
$874$	−0.667301	−0.0225718
$875$	−1.00000	−0.0338062
$876$	0.331079	0.0111861
$877$	−20.8777	−0.704991	−0.352496	−	0.935813i	$-0.614667\pi$
$877$	−20.8777	−0.704991	−0.352496	+	0.935813i	$0.614667\pi$
$878$	−34.2941	−1.15737
$879$	−7.90572	−0.266653
$880$	5.49945	0.185386
$881$	19.2999	0.650231	0.325115	−	0.945674i	$-0.394597\pi$
$881$	19.2999	0.650231	0.325115	+	0.945674i	$0.394597\pi$
$882$	3.21994	0.108421
$883$	−42.4145	−1.42736	−0.713681	−	0.700470i	$-0.752974\pi$
$883$	−42.4145	−1.42736	−0.713681	+	0.700470i	$0.752974\pi$
$884$	3.91700	0.131743
$885$	8.39387	0.282157
$886$	47.9001	1.60923
$887$	−40.3775	−1.35574	−0.677872	−	0.735180i	$-0.737098\pi$
$887$	−40.3775	−1.35574	−0.677872	+	0.735180i	$0.737098\pi$
$888$	−12.6864	−0.425727
$889$	2.62275	0.0879641
$890$	13.6521	0.457620
$891$	2.84623	0.0953521
$892$	−1.75187	−0.0586570
$893$	−3.19521	−0.106924
$894$	−28.7679	−0.962143
$895$	18.2257	0.609219
$896$	−12.6701	−0.423277
$897$	0.339022	0.0113196
$898$	−41.2813	−1.37758
$899$	4.28301	0.142846
$900$	−0.419696	−0.0139899
$901$	−27.8081	−0.926422
$902$	15.1600	0.504773
$903$	3.87371	0.128909
$904$	−14.2167	−0.472839
$905$	−9.58654	−0.318667
$906$	−0.929631	−0.0308849
$907$	6.70983	0.222796	0.111398	−	0.993776i	$-0.464467\pi$
$907$	6.70983	0.222796	0.111398	+	0.993776i	$0.464467\pi$
$908$	−4.27662	−0.141925
$909$	−29.1433	−0.966622
$910$	−4.56127	−0.151205
$911$	42.5416	1.40946	0.704732	−	0.709473i	$-0.251067\pi$
$911$	42.5416	1.40946	0.704732	+	0.709473i	$0.251067\pi$
$912$	14.6998	0.486758
$913$	−0.137896	−0.00456370
$914$	28.9972	0.959142
$915$	−5.21949	−0.172551
$916$	0.193023	0.00637766
$917$	9.01699	0.297767
$918$	45.8732	1.51404
$919$	0.470339	0.0155150	0.00775752	−	0.999970i	$-0.497531\pi$
$919$	0.470339	0.0155150	0.00775752	+	0.999970i	$0.497531\pi$
$920$	−0.324142	−0.0106866
$921$	12.1979	0.401935
$922$	−43.9006	−1.44579
$923$	−24.4463	−0.804661
$924$	−0.221801	−0.00729672
$925$	5.21747	0.171549
$926$	52.8921	1.73814
$927$	−2.50953	−0.0824237
$928$	4.64820	0.152585
$929$	49.4857	1.62357	0.811786	−	0.583955i	$-0.198496\pi$
$929$	49.4857	1.62357	0.811786	+	0.583955i	$0.198496\pi$
$930$	−1.34927	−0.0442444
$931$	3.71997	0.121917
$932$	−0.429416	−0.0140660
$933$	−0.461837	−0.0151199
$934$	3.16226	0.103472
$935$	8.33165	0.272474
$936$	17.9211	0.585768
$937$	−59.5526	−1.94550	−0.972749	−	0.231862i	$-0.925518\pi$
$937$	−59.5526	−1.94550	−0.972749	+	0.231862i	$0.925518\pi$
$938$	4.84729	0.158270
$939$	19.3281	0.630750
$940$	0.165794	0.00540762
$941$	13.9237	0.453900	0.226950	−	0.973906i	$-0.427125\pi$
$941$	13.9237	0.453900	0.226950	+	0.973906i	$0.427125\pi$
$942$	5.66601	0.184608
$943$	−0.980591	−0.0319324
$944$	−40.1724	−1.30750
$945$	−4.70173	−0.152947
$946$	7.98356	0.259568
$947$	25.7713	0.837455	0.418728	−	0.908112i	$-0.362476\pi$
$947$	25.7713	0.837455	0.418728	+	0.908112i	$0.362476\pi$
$948$	1.78029	0.0578211
$949$	5.81411	0.188734
$950$	−5.50885	−0.178731
$951$	16.4199	0.532450
$952$	−17.6301	−0.571394
$953$	−33.0814	−1.07161	−0.535805	−	0.844341i	$-0.679992\pi$
$953$	−33.0814	−1.07161	−0.535805	+	0.844341i	$0.679992\pi$
$954$	13.5906	0.440012
$955$	−16.7243	−0.541185
$956$	−1.07449	−0.0347515
$957$	−4.90826	−0.158662
$958$	−44.0592	−1.42349
$959$	17.3217	0.559347
$960$	6.43885	0.207813
$961$	−29.9946	−0.967567
$962$	23.7983	0.767287
$963$	34.6750	1.11738
$964$	4.26236	0.137281
$965$	−20.0937	−0.646838
$966$	0.162999	0.00524442
$967$	−26.4214	−0.849655	−0.424828	−	0.905274i	$-0.639665\pi$
$967$	−26.4214	−0.849655	−0.424828	+	0.905274i	$0.639665\pi$
$968$	−25.1559	−0.808540
$969$	22.2701	0.715419
$970$	21.8012	0.699995
$971$	−31.2219	−1.00196	−0.500980	−	0.865459i	$-0.667027\pi$
$971$	−31.2219	−1.00196	−0.500980	+	0.865459i	$0.667027\pi$
$972$	−3.11738	−0.0999901
$973$	1.83465	0.0588162
$974$	31.9836	1.02482
$975$	2.79877	0.0896323
$976$	24.9801	0.799592
$977$	45.3914	1.45220	0.726100	−	0.687590i	$-0.241331\pi$
$977$	45.3914	1.45220	0.726100	+	0.687590i	$0.241331\pi$
$978$	−27.5248	−0.880146
$979$	11.6581	0.372596
$980$	−0.193023	−0.00616590
$981$	23.2078	0.740969
$982$	32.5974	1.04023
$983$	−16.0537	−0.512032	−0.256016	−	0.966672i	$-0.582410\pi$
$983$	−16.0537	−0.512032	−0.256016	+	0.966672i	$0.582410\pi$
$984$	19.6836	0.627490
$985$	−12.2323	−0.389754
$986$	41.6750	1.32720
$987$	0.780484	0.0248431
$988$	−2.21163	−0.0703613
$989$	−0.516399	−0.0164205
$990$	−4.07191	−0.129414
$991$	48.4393	1.53872	0.769362	−	0.638813i	$-0.220574\pi$
$991$	48.4393	1.53872	0.769362	+	0.638813i	$0.220574\pi$
$992$	1.09116	0.0346442
$993$	−29.1356	−0.924591
$994$	−11.7536	−0.372802
$995$	−8.14350	−0.258166
$996$	0.0191256	0.000606017 0
$997$	31.5490	0.999167	0.499584	−	0.866266i	$-0.333486\pi$
$997$	31.5490	0.999167	0.499584	+	0.866266i	$0.333486\pi$
$998$	53.9086	1.70645
$999$	24.5311	0.776130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.j.1.14	✓	45

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.j.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-1.48089 q^{2} -0.908664 q^{3} +0.193023 q^{4} -1.00000 q^{5} +1.34563 q^{6} +1.00000 q^{7} +2.67593 q^{8} -2.17433 q^{9} +O(q^{10})\)	\(q-1.48089 q^{2} -0.908664 q^{3} +0.193023 q^{4} -1.00000 q^{5} +1.34563 q^{6} +1.00000 q^{7} +2.67593 q^{8} -2.17433 q^{9} +1.48089 q^{10} +1.26459 q^{11} -0.175393 q^{12} -3.08009 q^{13} -1.48089 q^{14} +0.908664 q^{15} -4.34879 q^{16} -6.58840 q^{17} +3.21994 q^{18} +3.71997 q^{19} -0.193023 q^{20} -0.908664 q^{21} -1.87272 q^{22} +0.121133 q^{23} -2.43152 q^{24} +1.00000 q^{25} +4.56127 q^{26} +4.70173 q^{27} +0.193023 q^{28} +4.27143 q^{29} -1.34563 q^{30} +1.00271 q^{31} +1.08821 q^{32} -1.14909 q^{33} +9.75667 q^{34} -1.00000 q^{35} -0.419696 q^{36} +5.21747 q^{37} -5.50885 q^{38} +2.79877 q^{39} -2.67593 q^{40} -8.09518 q^{41} +1.34563 q^{42} -4.26309 q^{43} +0.244096 q^{44} +2.17433 q^{45} -0.179384 q^{46} -0.858936 q^{47} +3.95159 q^{48} +1.00000 q^{49} -1.48089 q^{50} +5.98664 q^{51} -0.594529 q^{52} +4.22077 q^{53} -6.96272 q^{54} -1.26459 q^{55} +2.67593 q^{56} -3.38020 q^{57} -6.32550 q^{58} +9.23760 q^{59} +0.175393 q^{60} -5.74414 q^{61} -1.48490 q^{62} -2.17433 q^{63} +7.08607 q^{64} +3.08009 q^{65} +1.70167 q^{66} -3.27324 q^{67} -1.27171 q^{68} -0.110069 q^{69} +1.48089 q^{70} +7.93689 q^{71} -5.81835 q^{72} -1.88764 q^{73} -7.72648 q^{74} -0.908664 q^{75} +0.718040 q^{76} +1.26459 q^{77} -4.14466 q^{78} -10.1503 q^{79} +4.34879 q^{80} +2.25070 q^{81} +11.9880 q^{82} -0.109044 q^{83} -0.175393 q^{84} +6.58840 q^{85} +6.31314 q^{86} -3.88130 q^{87} +3.38396 q^{88} +9.21888 q^{89} -3.21994 q^{90} -3.08009 q^{91} +0.0233814 q^{92} -0.911126 q^{93} +1.27199 q^{94} -3.71997 q^{95} -0.988813 q^{96} +14.7217 q^{97} -1.48089 q^{98} -2.74964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 45 q - 6 q^{2} + 34 q^{4} - 45 q^{5} + q^{6} + 45 q^{7} - 15 q^{8} + 29 q^{9}+O(q^{10}) \) 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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