LMFDB - Embedded newform 8049.2.a.c.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8049,2,Mod(1,8049)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8049, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8049.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8049 = 3 \cdot 2683 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8049.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:	$64.2715885869$
Analytic rank:	$0$
Dimension:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8049.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.25432 q^{2} -1.00000 q^{3} +3.08196 q^{4} -2.79786 q^{5} +2.25432 q^{6} -0.509718 q^{7} -2.43909 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.25432 q^{2} -1.00000 q^{3} +3.08196 q^{4} -2.79786 q^{5} +2.25432 q^{6} -0.509718 q^{7} -2.43909 q^{8} +1.00000 q^{9} +6.30728 q^{10} +4.69145 q^{11} -3.08196 q^{12} -1.22895 q^{13} +1.14907 q^{14} +2.79786 q^{15} -0.665441 q^{16} -2.26817 q^{17} -2.25432 q^{18} -2.30560 q^{19} -8.62290 q^{20} +0.509718 q^{21} -10.5760 q^{22} -5.83375 q^{23} +2.43909 q^{24} +2.82803 q^{25} +2.77044 q^{26} -1.00000 q^{27} -1.57093 q^{28} +9.55431 q^{29} -6.30728 q^{30} -0.959245 q^{31} +6.37829 q^{32} -4.69145 q^{33} +5.11318 q^{34} +1.42612 q^{35} +3.08196 q^{36} -7.44845 q^{37} +5.19756 q^{38} +1.22895 q^{39} +6.82422 q^{40} -6.11701 q^{41} -1.14907 q^{42} +4.46433 q^{43} +14.4589 q^{44} -2.79786 q^{45} +13.1511 q^{46} -8.14355 q^{47} +0.665441 q^{48} -6.74019 q^{49} -6.37528 q^{50} +2.26817 q^{51} -3.78756 q^{52} +3.82099 q^{53} +2.25432 q^{54} -13.1260 q^{55} +1.24325 q^{56} +2.30560 q^{57} -21.5385 q^{58} +9.24264 q^{59} +8.62290 q^{60} +12.3693 q^{61} +2.16245 q^{62} -0.509718 q^{63} -13.0478 q^{64} +3.43842 q^{65} +10.5760 q^{66} -1.88285 q^{67} -6.99040 q^{68} +5.83375 q^{69} -3.21493 q^{70} +5.91066 q^{71} -2.43909 q^{72} -1.46526 q^{73} +16.7912 q^{74} -2.82803 q^{75} -7.10577 q^{76} -2.39132 q^{77} -2.77044 q^{78} -3.20889 q^{79} +1.86181 q^{80} +1.00000 q^{81} +13.7897 q^{82} +2.14774 q^{83} +1.57093 q^{84} +6.34602 q^{85} -10.0640 q^{86} -9.55431 q^{87} -11.4428 q^{88} +7.28802 q^{89} +6.30728 q^{90} +0.626416 q^{91} -17.9794 q^{92} +0.959245 q^{93} +18.3582 q^{94} +6.45075 q^{95} -6.37829 q^{96} -8.21187 q^{97} +15.1945 q^{98} +4.69145 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) $ 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * 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 $

$2$	−2.25432	−1.59405	−0.797023	−	0.603949i	$-0.793593\pi$
$2$	−2.25432	−1.59405	−0.797023	+	0.603949i	$0.793593\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	3.08196	1.54098
$5$	−2.79786	−1.25124	−0.625621	−	0.780127i	$-0.715154\pi$
$5$	−2.79786	−1.25124	−0.625621	+	0.780127i	$0.715154\pi$
$6$	2.25432	0.920322
$7$	−0.509718	−0.192655	−0.0963277	−	0.995350i	$-0.530710\pi$
$7$	−0.509718	−0.192655	−0.0963277	+	0.995350i	$0.530710\pi$
$8$	−2.43909	−0.862347
$9$	1.00000	0.333333
$10$	6.30728	1.99454
$11$	4.69145	1.41453	0.707263	−	0.706951i	$-0.249930\pi$
$11$	4.69145	1.41453	0.707263	+	0.706951i	$0.249930\pi$
$12$	−3.08196	−0.889685
$13$	−1.22895	−0.340848	−0.170424	−	0.985371i	$-0.554514\pi$
$13$	−1.22895	−0.340848	−0.170424	+	0.985371i	$0.554514\pi$
$14$	1.14907	0.307101
$15$	2.79786	0.722405
$16$	−0.665441	−0.166360
$17$	−2.26817	−0.550112	−0.275056	−	0.961428i	$-0.588696\pi$
$17$	−2.26817	−0.550112	−0.275056	+	0.961428i	$0.588696\pi$
$18$	−2.25432	−0.531348
$19$	−2.30560	−0.528941	−0.264470	−	0.964394i	$-0.585197\pi$
$19$	−2.30560	−0.528941	−0.264470	+	0.964394i	$0.585197\pi$
$20$	−8.62290	−1.92814
$21$	0.509718	0.111230
$22$	−10.5760	−2.25482
$23$	−5.83375	−1.21642	−0.608210	−	0.793776i	$-0.708112\pi$
$23$	−5.83375	−1.21642	−0.608210	+	0.793776i	$0.708112\pi$
$24$	2.43909	0.497876
$25$	2.82803	0.565606
$26$	2.77044	0.543328
$27$	−1.00000	−0.192450
$28$	−1.57093	−0.296878
$29$	9.55431	1.77419	0.887095	−	0.461586i	$-0.152719\pi$
$29$	9.55431	1.77419	0.887095	+	0.461586i	$0.152719\pi$
$30$	−6.30728	−1.15155
$31$	−0.959245	−0.172285	−0.0861427	−	0.996283i	$-0.527454\pi$
$31$	−0.959245	−0.172285	−0.0861427	+	0.996283i	$0.527454\pi$
$32$	6.37829	1.12753
$33$	−4.69145	−0.816677
$34$	5.11318	0.876903
$35$	1.42612	0.241058
$36$	3.08196	0.513660
$37$	−7.44845	−1.22452	−0.612259	−	0.790658i	$-0.709739\pi$
$37$	−7.44845	−1.22452	−0.612259	+	0.790658i	$0.709739\pi$
$38$	5.19756	0.843155
$39$	1.22895	0.196789
$40$	6.82422	1.07900
$41$	−6.11701	−0.955316	−0.477658	−	0.878546i	$-0.658514\pi$
$41$	−6.11701	−0.955316	−0.477658	+	0.878546i	$0.658514\pi$
$42$	−1.14907	−0.177305
$43$	4.46433	0.680805	0.340402	−	0.940280i	$-0.389437\pi$
$43$	4.46433	0.680805	0.340402	+	0.940280i	$0.389437\pi$
$44$	14.4589	2.17976
$45$	−2.79786	−0.417081
$46$	13.1511	1.93903
$47$	−8.14355	−1.18786	−0.593930	−	0.804517i	$-0.702424\pi$
$47$	−8.14355	−1.18786	−0.593930	+	0.804517i	$0.702424\pi$
$48$	0.665441	0.0960481
$49$	−6.74019	−0.962884
$50$	−6.37528	−0.901601
$51$	2.26817	0.317607
$52$	−3.78756	−0.525241
$53$	3.82099	0.524854	0.262427	−	0.964952i	$-0.415477\pi$
$53$	3.82099	0.524854	0.262427	+	0.964952i	$0.415477\pi$
$54$	2.25432	0.306774
$55$	−13.1260	−1.76991
$56$	1.24325	0.166136
$57$	2.30560	0.305384
$58$	−21.5385	−2.82814
$59$	9.24264	1.20329	0.601644	−	0.798764i	$-0.294512\pi$
$59$	9.24264	1.20329	0.601644	+	0.798764i	$0.294512\pi$
$60$	8.62290	1.11321
$61$	12.3693	1.58373	0.791866	−	0.610695i	$-0.209110\pi$
$61$	12.3693	1.58373	0.791866	+	0.610695i	$0.209110\pi$
$62$	2.16245	0.274631
$63$	−0.509718	−0.0642185
$64$	−13.0478	−1.63098
$65$	3.43842	0.426484
$66$	10.5760	1.30182
$67$	−1.88285	−0.230027	−0.115013	−	0.993364i	$-0.536691\pi$
$67$	−1.88285	−0.230027	−0.115013	+	0.993364i	$0.536691\pi$
$68$	−6.99040	−0.847711
$69$	5.83375	0.702301
$70$	−3.21493	−0.384258
$71$	5.91066	0.701466	0.350733	−	0.936475i	$-0.385932\pi$
$71$	5.91066	0.701466	0.350733	+	0.936475i	$0.385932\pi$
$72$	−2.43909	−0.287449
$73$	−1.46526	−0.171496	−0.0857478	−	0.996317i	$-0.527328\pi$
$73$	−1.46526	−0.171496	−0.0857478	+	0.996317i	$0.527328\pi$
$74$	16.7912	1.95194
$75$	−2.82803	−0.326553
$76$	−7.10577	−0.815087
$77$	−2.39132	−0.272516
$78$	−2.77044	−0.313690
$79$	−3.20889	−0.361029	−0.180514	−	0.983572i	$-0.557776\pi$
$79$	−3.20889	−0.361029	−0.180514	+	0.983572i	$0.557776\pi$
$80$	1.86181	0.208157
$81$	1.00000	0.111111
$82$	13.7897	1.52282
$83$	2.14774	0.235746	0.117873	−	0.993029i	$-0.462393\pi$
$83$	2.14774	0.235746	0.117873	+	0.993029i	$0.462393\pi$
$84$	1.57093	0.171403
$85$	6.34602	0.688322
$86$	−10.0640	−1.08523
$87$	−9.55431	−1.02433
$88$	−11.4428	−1.21981
$89$	7.28802	0.772529	0.386265	−	0.922388i	$-0.373765\pi$
$89$	7.28802	0.772529	0.386265	+	0.922388i	$0.373765\pi$
$90$	6.30728	0.664845
$91$	0.626416	0.0656663
$92$	−17.9794	−1.87448
$93$	0.959245	0.0994691
$94$	18.3582	1.89350
$95$	6.45075	0.661833
$96$	−6.37829	−0.650981
$97$	−8.21187	−0.833789	−0.416894	−	0.908955i	$-0.636882\pi$
$97$	−8.21187	−0.833789	−0.416894	+	0.908955i	$0.636882\pi$
$98$	15.1945	1.53488
$99$	4.69145	0.471509
$100$	8.71587	0.871587
$101$	−5.66913	−0.564099	−0.282050	−	0.959400i	$-0.591014\pi$
$101$	−5.66913	−0.564099	−0.282050	+	0.959400i	$0.591014\pi$
$102$	−5.11318	−0.506280
$103$	−8.20371	−0.808336	−0.404168	−	0.914685i	$-0.632439\pi$
$103$	−8.20371	−0.808336	−0.404168	+	0.914685i	$0.632439\pi$
$104$	2.99750	0.293930
$105$	−1.42612	−0.139175
$106$	−8.61374	−0.836640
$107$	9.52657	0.920968	0.460484	−	0.887668i	$-0.347676\pi$
$107$	9.52657	0.920968	0.460484	+	0.887668i	$0.347676\pi$
$108$	−3.08196	−0.296562
$109$	6.43404	0.616269	0.308135	−	0.951343i	$-0.400295\pi$
$109$	6.43404	0.616269	0.308135	+	0.951343i	$0.400295\pi$
$110$	29.5903	2.82132
$111$	7.44845	0.706975
$112$	0.339187	0.0320502
$113$	−15.1282	−1.42314	−0.711570	−	0.702615i	$-0.752016\pi$
$113$	−15.1282	−1.42314	−0.711570	+	0.702615i	$0.752016\pi$
$114$	−5.19756	−0.486796
$115$	16.3220	1.52204
$116$	29.4460	2.73399
$117$	−1.22895	−0.113616
$118$	−20.8359	−1.91810
$119$	1.15613	0.105982
$120$	−6.82422	−0.622963
$121$	11.0097	1.00088
$122$	−27.8845	−2.52454
$123$	6.11701	0.551552
$124$	−2.95635	−0.265489
$125$	6.07688	0.543532
$126$	1.14907	0.102367
$127$	2.84814	0.252732	0.126366	−	0.991984i	$-0.459669\pi$
$127$	2.84814	0.252732	0.126366	+	0.991984i	$0.459669\pi$
$128$	16.6574	1.47232
$129$	−4.46433	−0.393063
$130$	−7.75130	−0.679834
$131$	12.1595	1.06238	0.531189	−	0.847253i	$-0.321745\pi$
$131$	12.1595	1.06238	0.531189	+	0.847253i	$0.321745\pi$
$132$	−14.4589	−1.25848
$133$	1.17521	0.101903
$134$	4.24455	0.366673
$135$	2.79786	0.240802
$136$	5.53226	0.474387
$137$	4.40863	0.376655	0.188327	−	0.982106i	$-0.439693\pi$
$137$	4.40863	0.376655	0.188327	+	0.982106i	$0.439693\pi$
$138$	−13.1511	−1.11950
$139$	−14.7298	−1.24937	−0.624685	−	0.780877i	$-0.714772\pi$
$139$	−14.7298	−1.24937	−0.624685	+	0.780877i	$0.714772\pi$
$140$	4.39525	0.371466
$141$	8.14355	0.685811
$142$	−13.3245	−1.11817
$143$	−5.76554	−0.482139
$144$	−0.665441	−0.0554534
$145$	−26.7316	−2.21994
$146$	3.30316	0.273372
$147$	6.74019	0.555921
$148$	−22.9558	−1.88696
$149$	−8.32049	−0.681641	−0.340821	−	0.940128i	$-0.610705\pi$
$149$	−8.32049	−0.681641	−0.340821	+	0.940128i	$0.610705\pi$
$150$	6.37528	0.520540
$151$	−10.8106	−0.879751	−0.439875	−	0.898059i	$-0.644977\pi$
$151$	−10.8106	−0.879751	−0.439875	+	0.898059i	$0.644977\pi$
$152$	5.62355	0.456130
$153$	−2.26817	−0.183371
$154$	5.39080	0.434403
$155$	2.68383	0.215571
$156$	3.78756	0.303248
$157$	−15.4029	−1.22929	−0.614643	−	0.788805i	$-0.710700\pi$
$157$	−15.4029	−1.22929	−0.614643	+	0.788805i	$0.710700\pi$
$158$	7.23388	0.575496
$159$	−3.82099	−0.303024
$160$	−17.8456	−1.41082
$161$	2.97357	0.234350
$162$	−2.25432	−0.177116
$163$	−0.716254	−0.0561014	−0.0280507	−	0.999607i	$-0.508930\pi$
$163$	−0.716254	−0.0561014	−0.0280507	+	0.999607i	$0.508930\pi$
$164$	−18.8524	−1.47212
$165$	13.1260	1.02186
$166$	−4.84170	−0.375789
$167$	−13.7761	−1.06603	−0.533014	−	0.846106i	$-0.678941\pi$
$167$	−13.7761	−1.06603	−0.533014	+	0.846106i	$0.678941\pi$
$168$	−1.24325	−0.0959185
$169$	−11.4897	−0.883822
$170$	−14.3060	−1.09722
$171$	−2.30560	−0.176314
$172$	13.7589	1.04911
$173$	13.0520	0.992326	0.496163	−	0.868229i	$-0.334742\pi$
$173$	13.0520	0.992326	0.496163	+	0.868229i	$0.334742\pi$
$174$	21.5385	1.63283
$175$	−1.44150	−0.108967
$176$	−3.12188	−0.235321
$177$	−9.24264	−0.694719
$178$	−16.4295	−1.23145
$179$	10.2654	0.767275	0.383637	−	0.923484i	$-0.374671\pi$
$179$	10.2654	0.767275	0.383637	+	0.923484i	$0.374671\pi$
$180$	−8.62290	−0.642713
$181$	−8.32057	−0.618463	−0.309232	−	0.950987i	$-0.600072\pi$
$181$	−8.32057	−0.618463	−0.309232	+	0.950987i	$0.600072\pi$
$182$	−1.41214	−0.104675
$183$	−12.3693	−0.914368
$184$	14.2290	1.04898
$185$	20.8397	1.53217
$186$	−2.16245	−0.158558
$187$	−10.6410	−0.778147
$188$	−25.0981	−1.83047
$189$	0.509718	0.0370765
$190$	−14.5421	−1.05499
$191$	−11.6734	−0.844658	−0.422329	−	0.906443i	$-0.638787\pi$
$191$	−11.6734	−0.844658	−0.422329	+	0.906443i	$0.638787\pi$
$192$	13.0478	0.941645
$193$	−18.5449	−1.33489	−0.667444	−	0.744660i	$-0.732612\pi$
$193$	−18.5449	−1.33489	−0.667444	+	0.744660i	$0.732612\pi$
$194$	18.5122	1.32910
$195$	−3.43842	−0.246230
$196$	−20.7730	−1.48379
$197$	8.59787	0.612573	0.306286	−	0.951939i	$-0.400913\pi$
$197$	8.59787	0.612573	0.306286	+	0.951939i	$0.400913\pi$
$198$	−10.5760	−0.751606
$199$	1.77907	0.126115	0.0630575	−	0.998010i	$-0.479915\pi$
$199$	1.77907	0.126115	0.0630575	+	0.998010i	$0.479915\pi$
$200$	−6.89780	−0.487748
$201$	1.88285	0.132806
$202$	12.7800	0.899200
$203$	−4.87001	−0.341807
$204$	6.99040	0.489426
$205$	17.1145	1.19533
$206$	18.4938	1.28852
$207$	−5.83375	−0.405474
$208$	0.817791	0.0567036
$209$	−10.8166	−0.748200
$210$	3.21493	0.221851
$211$	−11.0014	−0.757368	−0.378684	−	0.925526i	$-0.623623\pi$
$211$	−11.0014	−0.757368	−0.378684	+	0.925526i	$0.623623\pi$
$212$	11.7761	0.808789
$213$	−5.91066	−0.404992
$214$	−21.4759	−1.46807
$215$	−12.4906	−0.851851
$216$	2.43909	0.165959
$217$	0.488945	0.0331917
$218$	−14.5044	−0.982361
$219$	1.46526	0.0990131
$220$	−40.4539	−2.72740
$221$	2.78746	0.187505
$222$	−16.7912	−1.12695
$223$	8.25977	0.553115	0.276558	−	0.960997i	$-0.410806\pi$
$223$	8.25977	0.553115	0.276558	+	0.960997i	$0.410806\pi$
$224$	−3.25113	−0.217225
$225$	2.82803	0.188535
$226$	34.1038	2.26855
$227$	−3.78396	−0.251150	−0.125575	−	0.992084i	$-0.540078\pi$
$227$	−3.78396	−0.251150	−0.125575	+	0.992084i	$0.540078\pi$
$228$	7.10577	0.470591
$229$	22.8953	1.51296	0.756482	−	0.654015i	$-0.226917\pi$
$229$	22.8953	1.51296	0.756482	+	0.654015i	$0.226917\pi$
$230$	−36.7951	−2.42619
$231$	2.39132	0.157337
$232$	−23.3038	−1.52997
$233$	17.4013	1.14000	0.569999	−	0.821646i	$-0.306944\pi$
$233$	17.4013	1.14000	0.569999	+	0.821646i	$0.306944\pi$
$234$	2.77044	0.181109
$235$	22.7845	1.48630
$236$	28.4854	1.85424
$237$	3.20889	0.208440
$238$	−2.60628	−0.168940
$239$	−14.2459	−0.921493	−0.460746	−	0.887532i	$-0.652418\pi$
$239$	−14.2459	−0.921493	−0.460746	+	0.887532i	$0.652418\pi$
$240$	−1.86181	−0.120179
$241$	−15.7863	−1.01689	−0.508443	−	0.861096i	$-0.669779\pi$
$241$	−15.7863	−1.01689	−0.508443	+	0.861096i	$0.669779\pi$
$242$	−24.8194	−1.59545
$243$	−1.00000	−0.0641500
$244$	38.1218	2.44050
$245$	18.8581	1.20480
$246$	−13.7897	−0.879199
$247$	2.83346	0.180289
$248$	2.33968	0.148570
$249$	−2.14774	−0.136108
$250$	−13.6992	−0.866415
$251$	−26.3390	−1.66251	−0.831253	−	0.555895i	$-0.812376\pi$
$251$	−26.3390	−1.66251	−0.831253	+	0.555895i	$0.812376\pi$
$252$	−1.57093	−0.0989594
$253$	−27.3687	−1.72066
$254$	−6.42062	−0.402866
$255$	−6.34602	−0.397403
$256$	−11.4555	−0.715966
$257$	−26.3021	−1.64068	−0.820339	−	0.571878i	$-0.806215\pi$
$257$	−26.3021	−1.64068	−0.820339	+	0.571878i	$0.806215\pi$
$258$	10.0640	0.626560
$259$	3.79661	0.235910
$260$	10.5971	0.657203
$261$	9.55431	0.591397
$262$	−27.4113	−1.69348
$263$	6.20843	0.382828	0.191414	−	0.981509i	$-0.438693\pi$
$263$	6.20843	0.382828	0.191414	+	0.981509i	$0.438693\pi$
$264$	11.4428	0.704259
$265$	−10.6906	−0.656719
$266$	−2.64929	−0.162438
$267$	−7.28802	−0.446020
$268$	−5.80287	−0.354466
$269$	−5.79052	−0.353054	−0.176527	−	0.984296i	$-0.556486\pi$
$269$	−5.79052	−0.353054	−0.176527	+	0.984296i	$0.556486\pi$
$270$	−6.30728	−0.383849
$271$	8.67528	0.526986	0.263493	−	0.964661i	$-0.415125\pi$
$271$	8.67528	0.526986	0.263493	+	0.964661i	$0.415125\pi$
$272$	1.50933	0.0915167
$273$	−0.626416	−0.0379124
$274$	−9.93846	−0.600405
$275$	13.2676	0.800064
$276$	17.9794	1.08223
$277$	8.78594	0.527896	0.263948	−	0.964537i	$-0.414975\pi$
$277$	8.78594	0.527896	0.263948	+	0.964537i	$0.414975\pi$
$278$	33.2058	1.99155
$279$	−0.959245	−0.0574285
$280$	−3.47843	−0.207876
$281$	9.03767	0.539142	0.269571	−	0.962980i	$-0.413118\pi$
$281$	9.03767	0.539142	0.269571	+	0.962980i	$0.413118\pi$
$282$	−18.3582	−1.09321
$283$	4.50650	0.267884	0.133942	−	0.990989i	$-0.457236\pi$
$283$	4.50650	0.267884	0.133942	+	0.990989i	$0.457236\pi$
$284$	18.2164	1.08095
$285$	−6.45075	−0.382109
$286$	12.9974	0.768551
$287$	3.11795	0.184047
$288$	6.37829	0.375844
$289$	−11.8554	−0.697377
$290$	60.2617	3.53869
$291$	8.21187	0.481388
$292$	−4.51587	−0.264271
$293$	6.21529	0.363101	0.181551	−	0.983382i	$-0.441888\pi$
$293$	6.21529	0.363101	0.181551	+	0.983382i	$0.441888\pi$
$294$	−15.1945	−0.886164
$295$	−25.8596	−1.50561
$296$	18.1674	1.05596
$297$	−4.69145	−0.272226
$298$	18.7570	1.08657
$299$	7.16936	0.414615
$300$	−8.71587	−0.503211
$301$	−2.27555	−0.131161
$302$	24.3705	1.40236
$303$	5.66913	0.325683
$304$	1.53424	0.0879947
$305$	−34.6077	−1.98163
$306$	5.11318	0.292301
$307$	−2.10290	−0.120019	−0.0600093	−	0.998198i	$-0.519113\pi$
$307$	−2.10290	−0.120019	−0.0600093	+	0.998198i	$0.519113\pi$
$308$	−7.36995	−0.419942
$309$	8.20371	0.466693
$310$	−6.05022	−0.343630
$311$	−33.7769	−1.91531	−0.957657	−	0.287913i	$-0.907039\pi$
$311$	−33.7769	−1.91531	−0.957657	+	0.287913i	$0.907039\pi$
$312$	−2.99750	−0.169700
$313$	−20.4097	−1.15362	−0.576811	−	0.816878i	$-0.695703\pi$
$313$	−20.4097	−1.15362	−0.576811	+	0.816878i	$0.695703\pi$
$314$	34.7231	1.95954
$315$	1.42612	0.0803528
$316$	−9.88969	−0.556338
$317$	4.33807	0.243650	0.121825	−	0.992552i	$-0.461125\pi$
$317$	4.33807	0.243650	0.121825	+	0.992552i	$0.461125\pi$
$318$	8.61374	0.483035
$319$	44.8236	2.50964
$320$	36.5060	2.04075
$321$	−9.52657	−0.531721
$322$	−6.70337	−0.373564
$323$	5.22949	0.290976
$324$	3.08196	0.171220
$325$	−3.47549	−0.192786
$326$	1.61467	0.0894281
$327$	−6.43404	−0.355803
$328$	14.9199	0.823814
$329$	4.15092	0.228847
$330$	−29.5903	−1.62889
$331$	8.71901	0.479240	0.239620	−	0.970867i	$-0.422977\pi$
$331$	8.71901	0.479240	0.239620	+	0.970867i	$0.422977\pi$
$332$	6.61926	0.363279
$333$	−7.44845	−0.408172
$334$	31.0558	1.69930
$335$	5.26795	0.287819
$336$	−0.339187	−0.0185042
$337$	26.3134	1.43338	0.716691	−	0.697391i	$-0.245656\pi$
$337$	26.3134	1.43338	0.716691	+	0.697391i	$0.245656\pi$
$338$	25.9014	1.40885
$339$	15.1282	0.821650
$340$	19.5582	1.06069
$341$	−4.50025	−0.243702
$342$	5.19756	0.281052
$343$	7.00362	0.378160
$344$	−10.8889	−0.587090
$345$	−16.3220	−0.878748
$346$	−29.4234	−1.58181
$347$	21.2663	1.14163	0.570817	−	0.821077i	$-0.306626\pi$
$347$	21.2663	1.14163	0.570817	+	0.821077i	$0.306626\pi$
$348$	−29.4460	−1.57847
$349$	30.2743	1.62054	0.810272	−	0.586054i	$-0.199319\pi$
$349$	30.2743	1.62054	0.810272	+	0.586054i	$0.199319\pi$
$350$	3.24960	0.173698
$351$	1.22895	0.0655963
$352$	29.9234	1.59492
$353$	27.9750	1.48896	0.744478	−	0.667647i	$-0.232698\pi$
$353$	27.9750	1.48896	0.744478	+	0.667647i	$0.232698\pi$
$354$	20.8359	1.10741
$355$	−16.5372	−0.877704
$356$	22.4614	1.19045
$357$	−1.15613	−0.0611887
$358$	−23.1416	−1.22307
$359$	20.2919	1.07096	0.535482	−	0.844546i	$-0.320130\pi$
$359$	20.2919	1.07096	0.535482	+	0.844546i	$0.320130\pi$
$360$	6.82422	0.359668
$361$	−13.6842	−0.720222
$362$	18.7572	0.985858
$363$	−11.0097	−0.577860
$364$	1.93059	0.101190
$365$	4.09959	0.214583
$366$	27.8845	1.45754
$367$	7.90453	0.412613	0.206307	−	0.978487i	$-0.433856\pi$
$367$	7.90453	0.412613	0.206307	+	0.978487i	$0.433856\pi$
$368$	3.88202	0.202364
$369$	−6.11701	−0.318439
$370$	−46.9794	−2.44234
$371$	−1.94763	−0.101116
$372$	2.95635	0.153280
$373$	7.43036	0.384730	0.192365	−	0.981323i	$-0.438384\pi$
$373$	7.43036	0.384730	0.192365	+	0.981323i	$0.438384\pi$
$374$	23.9882	1.24040
$375$	−6.07688	−0.313808
$376$	19.8628	1.02435
$377$	−11.7417	−0.604730
$378$	−1.14907	−0.0591017
$379$	−35.2452	−1.81042	−0.905212	−	0.424960i	$-0.860288\pi$
$379$	−35.2452	−1.81042	−0.905212	+	0.424960i	$0.860288\pi$
$380$	19.8809	1.01987
$381$	−2.84814	−0.145915
$382$	26.3156	1.34642
$383$	23.2426	1.18764	0.593822	−	0.804597i	$-0.297618\pi$
$383$	23.2426	1.18764	0.593822	+	0.804597i	$0.297618\pi$
$384$	−16.6574	−0.850044
$385$	6.69057	0.340983
$386$	41.8060	2.12787
$387$	4.46433	0.226935
$388$	−25.3086	−1.28485
$389$	15.7793	0.800043	0.400021	−	0.916506i	$-0.369003\pi$
$389$	15.7793	0.800043	0.400021	+	0.916506i	$0.369003\pi$
$390$	7.75130	0.392502
$391$	13.2319	0.669167
$392$	16.4399	0.830340
$393$	−12.1595	−0.613364
$394$	−19.3824	−0.976469
$395$	8.97804	0.451734
$396$	14.4589	0.726585
$397$	12.3564	0.620151	0.310076	−	0.950712i	$-0.399646\pi$
$397$	12.3564	0.620151	0.310076	+	0.950712i	$0.399646\pi$
$398$	−4.01059	−0.201033
$399$	−1.17521	−0.0588339
$400$	−1.88189	−0.0940943
$401$	23.8032	1.18867	0.594336	−	0.804217i	$-0.297415\pi$
$401$	23.8032	1.18867	0.594336	+	0.804217i	$0.297415\pi$
$402$	−4.24455	−0.211699
$403$	1.17886	0.0587232
$404$	−17.4720	−0.869266
$405$	−2.79786	−0.139027
$406$	10.9786	0.544856
$407$	−34.9440	−1.73211
$408$	−5.53226	−0.273887
$409$	−19.7732	−0.977724	−0.488862	−	0.872361i	$-0.662588\pi$
$409$	−19.7732	−0.977724	−0.488862	+	0.872361i	$0.662588\pi$
$410$	−38.5817	−1.90541
$411$	−4.40863	−0.217462
$412$	−25.2835	−1.24563
$413$	−4.71114	−0.231820
$414$	13.1511	0.646343
$415$	−6.00909	−0.294975
$416$	−7.83857	−0.384318
$417$	14.7298	0.721324
$418$	24.3841	1.19266
$419$	−16.4084	−0.801605	−0.400802	−	0.916165i	$-0.631269\pi$
$419$	−16.4084	−0.801605	−0.400802	+	0.916165i	$0.631269\pi$
$420$	−4.39525	−0.214466
$421$	−15.0344	−0.732730	−0.366365	−	0.930471i	$-0.619398\pi$
$421$	−15.0344	−0.732730	−0.366365	+	0.930471i	$0.619398\pi$
$422$	24.8007	1.20728
$423$	−8.14355	−0.395953
$424$	−9.31972	−0.452606
$425$	−6.41444	−0.311146
$426$	13.3245	0.645575
$427$	−6.30488	−0.305115
$428$	29.3605	1.41919
$429$	5.76554	0.278363
$430$	28.1578	1.35789
$431$	21.2398	1.02309	0.511544	−	0.859257i	$-0.329074\pi$
$431$	21.2398	1.02309	0.511544	+	0.859257i	$0.329074\pi$
$432$	0.665441	0.0320160
$433$	−7.32579	−0.352055	−0.176027	−	0.984385i	$-0.556325\pi$
$433$	−7.32579	−0.352055	−0.176027	+	0.984385i	$0.556325\pi$
$434$	−1.10224	−0.0529091
$435$	26.7316	1.28168
$436$	19.8295	0.949659
$437$	13.4503	0.643415
$438$	−3.30316	−0.157831
$439$	28.4786	1.35921	0.679606	−	0.733577i	$-0.262151\pi$
$439$	28.4786	1.35921	0.679606	+	0.733577i	$0.262151\pi$
$440$	32.0155	1.52628
$441$	−6.74019	−0.320961
$442$	−6.28382	−0.298891
$443$	−28.7644	−1.36664	−0.683318	−	0.730121i	$-0.739464\pi$
$443$	−28.7644	−1.36664	−0.683318	+	0.730121i	$0.739464\pi$
$444$	22.9558	1.08944
$445$	−20.3909	−0.966621
$446$	−18.6202	−0.881691
$447$	8.32049	0.393546
$448$	6.65071	0.314217
$449$	13.9978	0.660598	0.330299	−	0.943876i	$-0.392850\pi$
$449$	13.9978	0.660598	0.330299	+	0.943876i	$0.392850\pi$
$450$	−6.37528	−0.300534
$451$	−28.6976	−1.35132
$452$	−46.6245	−2.19303
$453$	10.8106	0.507924
$454$	8.53025	0.400344
$455$	−1.75263	−0.0821644
$456$	−5.62355	−0.263347
$457$	−14.2216	−0.665256	−0.332628	−	0.943058i	$-0.607935\pi$
$457$	−14.2216	−0.665256	−0.332628	+	0.943058i	$0.607935\pi$
$458$	−51.6133	−2.41173
$459$	2.26817	0.105869
$460$	50.3038	2.34543
$461$	−11.8123	−0.550154	−0.275077	−	0.961422i	$-0.588703\pi$
$461$	−11.8123	−0.550154	−0.275077	+	0.961422i	$0.588703\pi$
$462$	−5.39080	−0.250803
$463$	−10.0521	−0.467159	−0.233580	−	0.972338i	$-0.575044\pi$
$463$	−10.0521	−0.467159	−0.233580	+	0.972338i	$0.575044\pi$
$464$	−6.35783	−0.295155
$465$	−2.68383	−0.124460
$466$	−39.2281	−1.81721
$467$	−24.2781	−1.12346	−0.561729	−	0.827322i	$-0.689863\pi$
$467$	−24.2781	−1.12346	−0.561729	+	0.827322i	$0.689863\pi$
$468$	−3.78756	−0.175080
$469$	0.959722	0.0443159
$470$	−51.3636	−2.36923
$471$	15.4029	0.709729
$472$	−22.5436	−1.03765
$473$	20.9442	0.963015
$474$	−7.23388	−0.332263
$475$	−6.52030	−0.299172
$476$	3.56314	0.163316
$477$	3.82099	0.174951
$478$	32.1149	1.46890
$479$	0.222711	0.0101759	0.00508796	−	0.999987i	$-0.498380\pi$
$479$	0.222711	0.0101759	0.00508796	+	0.999987i	$0.498380\pi$
$480$	17.8456	0.814535
$481$	9.15374	0.417375
$482$	35.5874	1.62096
$483$	−2.97357	−0.135302
$484$	33.9315	1.54234
$485$	22.9757	1.04327
$486$	2.25432	0.102258
$487$	−11.8667	−0.537732	−0.268866	−	0.963178i	$-0.586649\pi$
$487$	−11.8667	−0.537732	−0.268866	+	0.963178i	$0.586649\pi$
$488$	−30.1699	−1.36573
$489$	0.716254	0.0323901
$490$	−42.5122	−1.92051
$491$	19.5658	0.882994	0.441497	−	0.897263i	$-0.354448\pi$
$491$	19.5658	0.882994	0.441497	+	0.897263i	$0.354448\pi$
$492$	18.8524	0.849931
$493$	−21.6708	−0.976003
$494$	−6.38752	−0.287388
$495$	−13.1260	−0.589971
$496$	0.638321	0.0286615
$497$	−3.01277	−0.135141
$498$	4.84170	0.216962
$499$	−33.0055	−1.47753	−0.738765	−	0.673963i	$-0.764591\pi$
$499$	−33.0055	−1.47753	−0.738765	+	0.673963i	$0.764591\pi$
$500$	18.7287	0.837572
$501$	13.7761	0.615472
$502$	59.3766	2.65011
$503$	−25.3123	−1.12862	−0.564309	−	0.825563i	$-0.690857\pi$
$503$	−25.3123	−1.12862	−0.564309	+	0.825563i	$0.690857\pi$
$504$	1.24325	0.0553786
$505$	15.8614	0.705825
$506$	61.6979	2.74281
$507$	11.4897	0.510275
$508$	8.77786	0.389455
$509$	−11.7533	−0.520954	−0.260477	−	0.965480i	$-0.583880\pi$
$509$	−11.7533	−0.520954	−0.260477	+	0.965480i	$0.583880\pi$
$510$	14.3060	0.633479
$511$	0.746869	0.0330396
$512$	−7.49051	−0.331037
$513$	2.30560	0.101795
$514$	59.2933	2.61531
$515$	22.9529	1.01142
$516$	−13.7589	−0.605702
$517$	−38.2051	−1.68026
$518$	−8.55877	−0.376051
$519$	−13.0520	−0.572920
$520$	−8.38660	−0.367777
$521$	18.2159	0.798052	0.399026	−	0.916940i	$-0.369348\pi$
$521$	18.2159	0.798052	0.399026	+	0.916940i	$0.369348\pi$
$522$	−21.5385	−0.942713
$523$	5.70995	0.249679	0.124839	−	0.992177i	$-0.460158\pi$
$523$	5.70995	0.249679	0.124839	+	0.992177i	$0.460158\pi$
$524$	37.4750	1.63710
$525$	1.44150	0.0629121
$526$	−13.9958	−0.610246
$527$	2.17573	0.0947762
$528$	3.12188	0.135863
$529$	11.0326	0.479680
$530$	24.1000	1.04684
$531$	9.24264	0.401096
$532$	3.62194	0.157031
$533$	7.51747	0.325618
$534$	16.4295	0.710976
$535$	−26.6540	−1.15235
$536$	4.59243	0.198363
$537$	−10.2654	−0.442986
$538$	13.0537	0.562784
$539$	−31.6213	−1.36202
$540$	8.62290	0.371070
$541$	−17.1045	−0.735380	−0.367690	−	0.929948i	$-0.619851\pi$
$541$	−17.1045	−0.735380	−0.367690	+	0.929948i	$0.619851\pi$
$542$	−19.5569	−0.840039
$543$	8.32057	0.357070
$544$	−14.4670	−0.620269
$545$	−18.0015	−0.771102
$546$	1.41214	0.0604341
$547$	−22.0588	−0.943164	−0.471582	−	0.881822i	$-0.656317\pi$
$547$	−22.0588	−0.943164	−0.471582	+	0.881822i	$0.656317\pi$
$548$	13.5872	0.580417
$549$	12.3693	0.527911
$550$	−29.9093	−1.27534
$551$	−22.0284	−0.938442
$552$	−14.2290	−0.605627
$553$	1.63563	0.0695541
$554$	−19.8063	−0.841490
$555$	−20.8397	−0.884597
$556$	−45.3968	−1.92525
$557$	−30.6624	−1.29921	−0.649603	−	0.760274i	$-0.725065\pi$
$557$	−30.6624	−1.29921	−0.649603	+	0.760274i	$0.725065\pi$
$558$	2.16245	0.0915436
$559$	−5.48643	−0.232051
$560$	−0.948999	−0.0401025
$561$	10.6410	0.449263
$562$	−20.3738	−0.859417
$563$	−22.5761	−0.951470	−0.475735	−	0.879589i	$-0.657818\pi$
$563$	−22.5761	−0.951470	−0.475735	+	0.879589i	$0.657818\pi$
$564$	25.0981	1.05682
$565$	42.3266	1.78069
$566$	−10.1591	−0.427019
$567$	−0.509718	−0.0214062
$568$	−14.4166	−0.604907
$569$	26.0282	1.09116	0.545579	−	0.838060i	$-0.316310\pi$
$569$	26.0282	1.09116	0.545579	+	0.838060i	$0.316310\pi$
$570$	14.5421	0.609099
$571$	42.2683	1.76887	0.884436	−	0.466662i	$-0.154544\pi$
$571$	42.2683	1.76887	0.884436	+	0.466662i	$0.154544\pi$
$572$	−17.7692	−0.742966
$573$	11.6734	0.487663
$574$	−7.02886	−0.293379
$575$	−16.4980	−0.688015
$576$	−13.0478	−0.543659
$577$	40.0803	1.66856	0.834282	−	0.551338i	$-0.185882\pi$
$577$	40.0803	1.66856	0.834282	+	0.551338i	$0.185882\pi$
$578$	26.7259	1.11165
$579$	18.5449	0.770698
$580$	−82.3858	−3.42089
$581$	−1.09474	−0.0454176
$582$	−18.5122	−0.767354
$583$	17.9260	0.742419
$584$	3.57389	0.147889
$585$	3.43842	0.142161
$586$	−14.0113	−0.578800
$587$	−37.9657	−1.56701	−0.783506	−	0.621385i	$-0.786570\pi$
$587$	−37.9657	−1.56701	−0.783506	+	0.621385i	$0.786570\pi$
$588$	20.7730	0.856664
$589$	2.21163	0.0911288
$590$	58.2959	2.40000
$591$	−8.59787	−0.353669
$592$	4.95650	0.203711
$593$	9.54629	0.392019	0.196010	−	0.980602i	$-0.437202\pi$
$593$	9.54629	0.392019	0.196010	+	0.980602i	$0.437202\pi$
$594$	10.5760	0.433940
$595$	−3.23468	−0.132609
$596$	−25.6434	−1.05040
$597$	−1.77907	−0.0728125
$598$	−16.1620	−0.660915
$599$	−0.310651	−0.0126929	−0.00634643	−	0.999980i	$-0.502020\pi$
$599$	−0.310651	−0.0126929	−0.00634643	+	0.999980i	$0.502020\pi$
$600$	6.89780	0.281602
$601$	8.07084	0.329217	0.164608	−	0.986359i	$-0.447364\pi$
$601$	8.07084	0.329217	0.164608	+	0.986359i	$0.447364\pi$
$602$	5.12982	0.209076
$603$	−1.88285	−0.0766755
$604$	−33.3177	−1.35568
$605$	−30.8036	−1.25235
$606$	−12.7800	−0.519153
$607$	32.1391	1.30448	0.652242	−	0.758010i	$-0.273828\pi$
$607$	32.1391	1.30448	0.652242	+	0.758010i	$0.273828\pi$
$608$	−14.7058	−0.596398
$609$	4.87001	0.197343
$610$	78.0169	3.15881
$611$	10.0080	0.404880
$612$	−6.99040	−0.282570
$613$	44.6318	1.80266	0.901331	−	0.433130i	$-0.142591\pi$
$613$	44.6318	1.80266	0.901331	+	0.433130i	$0.142591\pi$
$614$	4.74060	0.191315
$615$	−17.1145	−0.690125
$616$	5.83263	0.235003
$617$	−17.2218	−0.693324	−0.346662	−	0.937990i	$-0.612685\pi$
$617$	−17.2218	−0.693324	−0.346662	+	0.937990i	$0.612685\pi$
$618$	−18.4938	−0.743930
$619$	3.99502	0.160573	0.0802867	−	0.996772i	$-0.474416\pi$
$619$	3.99502	0.160573	0.0802867	+	0.996772i	$0.474416\pi$
$620$	8.27147	0.332190
$621$	5.83375	0.234100
$622$	76.1440	3.05310
$623$	−3.71484	−0.148832
$624$	−0.817791	−0.0327378
$625$	−31.1424	−1.24570
$626$	46.0099	1.83893
$627$	10.8166	0.431974
$628$	−47.4712	−1.89431
$629$	16.8943	0.673621
$630$	−3.21493	−0.128086
$631$	26.7893	1.06647	0.533233	−	0.845969i	$-0.320977\pi$
$631$	26.7893	1.06647	0.533233	+	0.845969i	$0.320977\pi$
$632$	7.82677	0.311332
$633$	11.0014	0.437267
$634$	−9.77939	−0.388389
$635$	−7.96871	−0.316228
$636$	−11.7761	−0.466955
$637$	8.28333	0.328197
$638$	−101.047	−4.00048
$639$	5.91066	0.233822
$640$	−46.6051	−1.84223
$641$	−1.41329	−0.0558215	−0.0279108	−	0.999610i	$-0.508885\pi$
$641$	−1.41329	−0.0558215	−0.0279108	+	0.999610i	$0.508885\pi$
$642$	21.4759	0.847588
$643$	0.535950	0.0211358	0.0105679	−	0.999944i	$-0.496636\pi$
$643$	0.535950	0.0211358	0.0105679	+	0.999944i	$0.496636\pi$
$644$	9.16442	0.361129
$645$	12.4906	0.491816
$646$	−11.7889	−0.463830
$647$	−2.69628	−0.106002	−0.0530008	−	0.998594i	$-0.516879\pi$
$647$	−2.69628	−0.106002	−0.0530008	+	0.998594i	$0.516879\pi$
$648$	−2.43909	−0.0958163
$649$	43.3614	1.70208
$650$	7.83488	0.307309
$651$	−0.488945	−0.0191632
$652$	−2.20747	−0.0864511
$653$	−28.0558	−1.09791	−0.548954	−	0.835852i	$-0.684974\pi$
$653$	−28.0558	−1.09791	−0.548954	+	0.835852i	$0.684974\pi$
$654$	14.5044	0.567166
$655$	−34.0205	−1.32929
$656$	4.07051	0.158927
$657$	−1.46526	−0.0571652
$658$	−9.35750	−0.364793
$659$	4.83446	0.188324	0.0941618	−	0.995557i	$-0.469983\pi$
$659$	4.83446	0.188324	0.0941618	+	0.995557i	$0.469983\pi$
$660$	40.4539	1.57467
$661$	25.0803	0.975510	0.487755	−	0.872981i	$-0.337816\pi$
$661$	25.0803	0.975510	0.487755	+	0.872981i	$0.337816\pi$
$662$	−19.6555	−0.763931
$663$	−2.78746	−0.108256
$664$	−5.23853	−0.203294
$665$	−3.28806	−0.127506
$666$	16.7912	0.650645
$667$	−55.7374	−2.15816
$668$	−42.4575	−1.64273
$669$	−8.25977	−0.319341
$670$	−11.8756	−0.458796
$671$	58.0302	2.24023
$672$	3.25113	0.125415
$673$	41.4207	1.59665	0.798326	−	0.602226i	$-0.205719\pi$
$673$	41.4207	1.59665	0.798326	+	0.602226i	$0.205719\pi$
$674$	−59.3188	−2.28487
$675$	−2.82803	−0.108851
$676$	−35.4108	−1.36195
$677$	37.5276	1.44230	0.721151	−	0.692778i	$-0.243613\pi$
$677$	37.5276	1.44230	0.721151	+	0.692778i	$0.243613\pi$
$678$	−34.1038	−1.30975
$679$	4.18574	0.160634
$680$	−15.4785	−0.593573
$681$	3.78396	0.145002
$682$	10.1450	0.388472
$683$	15.0695	0.576620	0.288310	−	0.957537i	$-0.406907\pi$
$683$	15.0695	0.576620	0.288310	+	0.957537i	$0.406907\pi$
$684$	−7.10577	−0.271696
$685$	−12.3347	−0.471286
$686$	−15.7884	−0.602804
$687$	−22.8953	−0.873510
$688$	−2.97075	−0.113259
$689$	−4.69579	−0.178895
$690$	36.7951	1.40076
$691$	27.3431	1.04018	0.520089	−	0.854112i	$-0.325899\pi$
$691$	27.3431	1.04018	0.520089	+	0.854112i	$0.325899\pi$
$692$	40.2258	1.52916
$693$	−2.39132	−0.0908386
$694$	−47.9411	−1.81982
$695$	41.2121	1.56326
$696$	23.3038	0.883327
$697$	13.8744	0.525530
$698$	−68.2479	−2.58322
$699$	−17.4013	−0.658178
$700$	−4.44264	−0.167916
$701$	14.2642	0.538753	0.269377	−	0.963035i	$-0.413182\pi$
$701$	14.2642	0.538753	0.269377	+	0.963035i	$0.413182\pi$
$702$	−2.77044	−0.104563
$703$	17.1731	0.647697
$704$	−61.2132	−2.30706
$705$	−22.7845	−0.858115
$706$	−63.0645	−2.37346
$707$	2.88966	0.108677
$708$	−28.4854	−1.07055
$709$	17.7238	0.665630	0.332815	−	0.942992i	$-0.392002\pi$
$709$	17.7238	0.665630	0.332815	+	0.942992i	$0.392002\pi$
$710$	37.2802	1.39910
$711$	−3.20889	−0.120343
$712$	−17.7761	−0.666188
$713$	5.59599	0.209572
$714$	2.60628	0.0975376
$715$	16.1312	0.603272
$716$	31.6377	1.18235
$717$	14.2459	0.532024
$718$	−45.7444	−1.70717
$719$	19.1561	0.714403	0.357202	−	0.934027i	$-0.383731\pi$
$719$	19.1561	0.714403	0.357202	+	0.934027i	$0.383731\pi$
$720$	1.86181	0.0693856
$721$	4.18158	0.155730
$722$	30.8486	1.14807
$723$	15.7863	0.587099
$724$	−25.6437	−0.953040
$725$	27.0199	1.00349
$726$	24.8194	0.921135
$727$	36.3806	1.34928	0.674641	−	0.738146i	$-0.264298\pi$
$727$	36.3806	1.34928	0.674641	+	0.738146i	$0.264298\pi$
$728$	−1.52788	−0.0566271
$729$	1.00000	0.0370370
$730$	−9.24180	−0.342054
$731$	−10.1259	−0.374518
$732$	−38.1218	−1.40902
$733$	−26.5834	−0.981880	−0.490940	−	0.871193i	$-0.663347\pi$
$733$	−26.5834	−0.981880	−0.490940	+	0.871193i	$0.663347\pi$
$734$	−17.8193	−0.657724
$735$	−18.8581	−0.695592
$736$	−37.2093	−1.37155
$737$	−8.83329	−0.325379
$738$	13.7897	0.507606
$739$	11.7203	0.431137	0.215569	−	0.976489i	$-0.430840\pi$
$739$	11.7203	0.431137	0.215569	+	0.976489i	$0.430840\pi$
$740$	64.2272	2.36104
$741$	−2.83346	−0.104090
$742$	4.39058	0.161183
$743$	44.5759	1.63533	0.817666	−	0.575693i	$-0.195268\pi$
$743$	44.5759	1.63533	0.817666	+	0.575693i	$0.195268\pi$
$744$	−2.33968	−0.0857768
$745$	23.2796	0.852898
$746$	−16.7504	−0.613276
$747$	2.14774	0.0785818
$748$	−32.7951	−1.19911
$749$	−4.85587	−0.177429
$750$	13.6992	0.500225
$751$	8.26641	0.301646	0.150823	−	0.988561i	$-0.451808\pi$
$751$	8.26641	0.301646	0.150823	+	0.988561i	$0.451808\pi$
$752$	5.41905	0.197613
$753$	26.3390	0.959848
$754$	26.4696	0.963967
$755$	30.2464	1.10078
$756$	1.57093	0.0571342
$757$	−0.570848	−0.0207478	−0.0103739	−	0.999946i	$-0.503302\pi$
$757$	−0.570848	−0.0207478	−0.0103739	+	0.999946i	$0.503302\pi$
$758$	79.4540	2.88590
$759$	27.3687	0.993423
$760$	−15.7339	−0.570729
$761$	0.505663	0.0183303	0.00916513	−	0.999958i	$-0.497083\pi$
$761$	0.505663	0.0183303	0.00916513	+	0.999958i	$0.497083\pi$
$762$	6.42062	0.232595
$763$	−3.27955	−0.118728
$764$	−35.9770	−1.30160
$765$	6.34602	0.229441
$766$	−52.3963	−1.89316
$767$	−11.3587	−0.410139
$768$	11.4555	0.413363
$769$	−26.9994	−0.973622	−0.486811	−	0.873507i	$-0.661840\pi$
$769$	−26.9994	−0.973622	−0.486811	+	0.873507i	$0.661840\pi$
$770$	−15.0827	−0.543543
$771$	26.3021	0.947246
$772$	−57.1545	−2.05704
$773$	−32.5707	−1.17149	−0.585744	−	0.810496i	$-0.699198\pi$
$773$	−32.5707	−1.17149	−0.585744	+	0.810496i	$0.699198\pi$
$774$	−10.0640	−0.361744
$775$	−2.71277	−0.0974456
$776$	20.0294	0.719015
$777$	−3.79661	−0.136203
$778$	−35.5716	−1.27530
$779$	14.1034	0.505306
$780$	−10.5971	−0.379436
$781$	27.7296	0.992242
$782$	−29.8290	−1.06668
$783$	−9.55431	−0.341443
$784$	4.48520	0.160186
$785$	43.0952	1.53813
$786$	27.4113	0.977730
$787$	36.6611	1.30683	0.653414	−	0.757001i	$-0.273336\pi$
$787$	36.6611	1.30683	0.653414	+	0.757001i	$0.273336\pi$
$788$	26.4983	0.943963
$789$	−6.20843	−0.221026
$790$	−20.2394	−0.720085
$791$	7.71111	0.274176
$792$	−11.4428	−0.406604
$793$	−15.2013	−0.539813
$794$	−27.8553	−0.988549
$795$	10.6906	0.379157
$796$	5.48302	0.194341
$797$	7.63416	0.270416	0.135208	−	0.990817i	$-0.456830\pi$
$797$	7.63416	0.270416	0.135208	+	0.990817i	$0.456830\pi$
$798$	2.64929	0.0937839
$799$	18.4709	0.653455
$800$	18.0380	0.637739
$801$	7.28802	0.257510
$802$	−53.6599	−1.89480
$803$	−6.87419	−0.242585
$804$	5.80287	0.204651
$805$	−8.31963	−0.293228
$806$	−2.65753	−0.0936075
$807$	5.79052	0.203836
$808$	13.8275	0.486449
$809$	31.8167	1.11861	0.559307	−	0.828960i	$-0.311067\pi$
$809$	31.8167	1.11861	0.559307	+	0.828960i	$0.311067\pi$
$810$	6.30728	0.221615
$811$	−24.5822	−0.863196	−0.431598	−	0.902066i	$-0.642050\pi$
$811$	−24.5822	−0.863196	−0.431598	+	0.902066i	$0.642050\pi$
$812$	−15.0092	−0.526718
$813$	−8.67528	−0.304255
$814$	78.7750	2.76106
$815$	2.00398	0.0701964
$816$	−1.50933	−0.0528372
$817$	−10.2930	−0.360105
$818$	44.5752	1.55854
$819$	0.626416	0.0218888
$820$	52.7463	1.84198
$821$	23.9215	0.834866	0.417433	−	0.908708i	$-0.362930\pi$
$821$	23.9215	0.834866	0.417433	+	0.908708i	$0.362930\pi$
$822$	9.93846	0.346644
$823$	−12.3004	−0.428765	−0.214382	−	0.976750i	$-0.568774\pi$
$823$	−12.3004	−0.428765	−0.214382	+	0.976750i	$0.568774\pi$
$824$	20.0096	0.697066
$825$	−13.2676	−0.461917
$826$	10.6204	0.369532
$827$	7.06031	0.245511	0.122756	−	0.992437i	$-0.460827\pi$
$827$	7.06031	0.245511	0.122756	+	0.992437i	$0.460827\pi$
$828$	−17.9794	−0.624827
$829$	39.5453	1.37346	0.686732	−	0.726911i	$-0.259045\pi$
$829$	39.5453	1.37346	0.686732	+	0.726911i	$0.259045\pi$
$830$	13.5464	0.470203
$831$	−8.78594	−0.304781
$832$	16.0351	0.555916
$833$	15.2879	0.529694
$834$	−33.2058	−1.14982
$835$	38.5437	1.33386
$836$	−33.3363	−1.15296
$837$	0.959245	0.0331564
$838$	36.9899	1.27779
$839$	−23.7483	−0.819883	−0.409941	−	0.912112i	$-0.634451\pi$
$839$	−23.7483	−0.819883	−0.409941	+	0.912112i	$0.634451\pi$
$840$	3.47843	0.120017
$841$	62.2848	2.14775
$842$	33.8923	1.16800
$843$	−9.03767	−0.311274
$844$	−33.9059	−1.16709
$845$	32.1466	1.10588
$846$	18.3582	0.631167
$847$	−5.61185	−0.192825
$848$	−2.54264	−0.0873148
$849$	−4.50650	−0.154663
$850$	14.4602	0.495981
$851$	43.4524	1.48953
$852$	−18.2164	−0.624084
$853$	6.64694	0.227587	0.113793	−	0.993504i	$-0.463700\pi$
$853$	6.64694	0.227587	0.113793	+	0.993504i	$0.463700\pi$
$854$	14.2132	0.486366
$855$	6.45075	0.220611
$856$	−23.2361	−0.794194
$857$	−14.6501	−0.500436	−0.250218	−	0.968189i	$-0.580502\pi$
$857$	−14.6501	−0.500436	−0.250218	+	0.968189i	$0.580502\pi$
$858$	−12.9974	−0.443723
$859$	38.0796	1.29926	0.649629	−	0.760251i	$-0.274924\pi$
$859$	38.0796	1.29926	0.649629	+	0.760251i	$0.274924\pi$
$860$	−38.4955	−1.31269
$861$	−3.11795	−0.106259
$862$	−47.8814	−1.63085
$863$	20.8632	0.710192	0.355096	−	0.934830i	$-0.384448\pi$
$863$	20.8632	0.710192	0.355096	+	0.934830i	$0.384448\pi$
$864$	−6.37829	−0.216994
$865$	−36.5177	−1.24164
$866$	16.5147	0.561191
$867$	11.8554	0.402631
$868$	1.50691	0.0511478
$869$	−15.0544	−0.510684
$870$	−60.2617	−2.04306
$871$	2.31392	0.0784042
$872$	−15.6932	−0.531438
$873$	−8.21187	−0.277930
$874$	−30.3213	−1.02563
$875$	−3.09749	−0.104714
$876$	4.51587	0.152577
$877$	29.4650	0.994962	0.497481	−	0.867475i	$-0.334259\pi$
$877$	29.4650	0.994962	0.497481	+	0.867475i	$0.334259\pi$
$878$	−64.2000	−2.16664
$879$	−6.21529	−0.209637
$880$	8.73460	0.294443
$881$	−46.9657	−1.58232	−0.791158	−	0.611612i	$-0.790521\pi$
$881$	−46.9657	−1.58232	−0.791158	+	0.611612i	$0.790521\pi$
$882$	15.1945	0.511627
$883$	−28.1144	−0.946124	−0.473062	−	0.881029i	$-0.656851\pi$
$883$	−28.1144	−0.946124	−0.473062	+	0.881029i	$0.656851\pi$
$884$	8.59083	0.288941
$885$	25.8596	0.869262
$886$	64.8441	2.17848
$887$	29.5588	0.992488	0.496244	−	0.868183i	$-0.334712\pi$
$887$	29.5588	0.992488	0.496244	+	0.868183i	$0.334712\pi$
$888$	−18.1674	−0.609658
$889$	−1.45175	−0.0486901
$890$	45.9676	1.54084
$891$	4.69145	0.157170
$892$	25.4563	0.852339
$893$	18.7758	0.628307
$894$	−18.7570	−0.627330
$895$	−28.7213	−0.960046
$896$	−8.49058	−0.283650
$897$	−7.16936	−0.239378
$898$	−31.5556	−1.05302
$899$	−9.16492	−0.305667
$900$	8.71587	0.290529
$901$	−8.66665	−0.288728
$902$	64.6937	2.15406
$903$	2.27555	0.0757256
$904$	36.8989	1.22724
$905$	23.2798	0.773847
$906$	−24.3705	−0.809654
$907$	41.9719	1.39365	0.696827	−	0.717239i	$-0.254594\pi$
$907$	41.9719	1.39365	0.696827	+	0.717239i	$0.254594\pi$
$908$	−11.6620	−0.387017
$909$	−5.66913	−0.188033
$910$	3.95098	0.130974
$911$	16.3899	0.543020	0.271510	−	0.962436i	$-0.412477\pi$
$911$	16.3899	0.543020	0.271510	+	0.962436i	$0.412477\pi$
$912$	−1.53424	−0.0508038
$913$	10.0760	0.333468
$914$	32.0599	1.06045
$915$	34.6077	1.14410
$916$	70.5624	2.33145
$917$	−6.19790	−0.204673
$918$	−5.11318	−0.168760
$919$	11.1807	0.368816	0.184408	−	0.982850i	$-0.440963\pi$
$919$	11.1807	0.368816	0.184408	+	0.982850i	$0.440963\pi$
$920$	−39.8108	−1.31252
$921$	2.10290	0.0692928
$922$	26.6287	0.876971
$923$	−7.26388	−0.239094
$924$	7.36995	0.242453
$925$	−21.0644	−0.692594
$926$	22.6606	0.744673
$927$	−8.20371	−0.269445
$928$	60.9401	2.00046
$929$	−28.8593	−0.946842	−0.473421	−	0.880836i	$-0.656981\pi$
$929$	−28.8593	−0.946842	−0.473421	+	0.880836i	$0.656981\pi$
$930$	6.05022	0.198395
$931$	15.5402	0.509309
$932$	53.6301	1.75671
$933$	33.7769	1.10581
$934$	54.7306	1.79084
$935$	29.7720	0.973650
$936$	2.99750	0.0979765
$937$	19.2893	0.630153	0.315077	−	0.949066i	$-0.397970\pi$
$937$	19.2893	0.630153	0.315077	+	0.949066i	$0.397970\pi$
$938$	−2.16352	−0.0706415
$939$	20.4097	0.666044
$940$	70.2210	2.29036
$941$	10.7299	0.349785	0.174892	−	0.984588i	$-0.444042\pi$
$941$	10.7299	0.349785	0.174892	+	0.984588i	$0.444042\pi$
$942$	−34.7231	−1.13134
$943$	35.6851	1.16207
$944$	−6.15043	−0.200179
$945$	−1.42612	−0.0463917
$946$	−47.2149	−1.53509
$947$	−9.19051	−0.298652	−0.149326	−	0.988788i	$-0.547710\pi$
$947$	−9.19051	−0.298652	−0.149326	+	0.988788i	$0.547710\pi$
$948$	9.88969	0.321202
$949$	1.80073	0.0584540
$950$	14.6988	0.476894
$951$	−4.33807	−0.140671
$952$	−2.81989	−0.0913932
$953$	8.97638	0.290773	0.145387	−	0.989375i	$-0.453557\pi$
$953$	8.97638	0.290773	0.145387	+	0.989375i	$0.453557\pi$
$954$	−8.61374	−0.278880
$955$	32.6606	1.05687
$956$	−43.9054	−1.42000
$957$	−44.8236	−1.44894
$958$	−0.502062	−0.0162209
$959$	−2.24716	−0.0725645
$960$	−36.5060	−1.17823
$961$	−30.0798	−0.970318
$962$	−20.6355	−0.665314
$963$	9.52657	0.306989
$964$	−48.6528	−1.56700
$965$	51.8859	1.67027
$966$	6.70337	0.215678
$967$	−6.97021	−0.224147	−0.112073	−	0.993700i	$-0.535749\pi$
$967$	−6.97021	−0.224147	−0.112073	+	0.993700i	$0.535749\pi$
$968$	−26.8536	−0.863108
$969$	−5.22949	−0.167995
$970$	−51.7945	−1.66302
$971$	35.8455	1.15034	0.575169	−	0.818035i	$-0.304936\pi$
$971$	35.8455	1.15034	0.575169	+	0.818035i	$0.304936\pi$
$972$	−3.08196	−0.0988539
$973$	7.50807	0.240698
$974$	26.7514	0.857170
$975$	3.47549	0.111305
$976$	−8.23107	−0.263470
$977$	52.4919	1.67936	0.839682	−	0.543078i	$-0.182741\pi$
$977$	52.4919	1.67936	0.839682	+	0.543078i	$0.182741\pi$
$978$	−1.61467	−0.0516313
$979$	34.1914	1.09276
$980$	58.1199	1.85657
$981$	6.43404	0.205423
$982$	−44.1077	−1.40753
$983$	4.95732	0.158114	0.0790570	−	0.996870i	$-0.474809\pi$
$983$	4.95732	0.158114	0.0790570	+	0.996870i	$0.474809\pi$
$984$	−14.9199	−0.475629
$985$	−24.0556	−0.766477
$986$	48.8529	1.55579
$987$	−4.15092	−0.132125
$988$	8.73260	0.277821
$989$	−26.0438	−0.828145
$990$	29.5903	0.940441
$991$	−35.2593	−1.12005	−0.560024	−	0.828476i	$-0.689208\pi$
$991$	−35.2593	−1.12005	−0.560024	+	0.828476i	$0.689208\pi$
$992$	−6.11834	−0.194258
$993$	−8.71901	−0.276690
$994$	6.79175	0.215421
$995$	−4.97759	−0.157800
$996$	−6.61926	−0.209739
$997$	42.7161	1.35283	0.676416	−	0.736520i	$-0.263532\pi$
$997$	42.7161	1.35283	0.676416	+	0.736520i	$0.263532\pi$
$998$	74.4050	2.35525
$999$	7.44845	0.235658

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8049.2.a.c.1.15	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8049.2.a.c.1.15	✓	119	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:	\( N \)	\(=\)	\( 8049 = 3 \cdot 2683 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8049.a (trivial)

\(f(q)\)	\(=\)	\(q-2.25432 q^{2} -1.00000 q^{3} +3.08196 q^{4} -2.79786 q^{5} +2.25432 q^{6} -0.509718 q^{7} -2.43909 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.25432 q^{2} -1.00000 q^{3} +3.08196 q^{4} -2.79786 q^{5} +2.25432 q^{6} -0.509718 q^{7} -2.43909 q^{8} +1.00000 q^{9} +6.30728 q^{10} +4.69145 q^{11} -3.08196 q^{12} -1.22895 q^{13} +1.14907 q^{14} +2.79786 q^{15} -0.665441 q^{16} -2.26817 q^{17} -2.25432 q^{18} -2.30560 q^{19} -8.62290 q^{20} +0.509718 q^{21} -10.5760 q^{22} -5.83375 q^{23} +2.43909 q^{24} +2.82803 q^{25} +2.77044 q^{26} -1.00000 q^{27} -1.57093 q^{28} +9.55431 q^{29} -6.30728 q^{30} -0.959245 q^{31} +6.37829 q^{32} -4.69145 q^{33} +5.11318 q^{34} +1.42612 q^{35} +3.08196 q^{36} -7.44845 q^{37} +5.19756 q^{38} +1.22895 q^{39} +6.82422 q^{40} -6.11701 q^{41} -1.14907 q^{42} +4.46433 q^{43} +14.4589 q^{44} -2.79786 q^{45} +13.1511 q^{46} -8.14355 q^{47} +0.665441 q^{48} -6.74019 q^{49} -6.37528 q^{50} +2.26817 q^{51} -3.78756 q^{52} +3.82099 q^{53} +2.25432 q^{54} -13.1260 q^{55} +1.24325 q^{56} +2.30560 q^{57} -21.5385 q^{58} +9.24264 q^{59} +8.62290 q^{60} +12.3693 q^{61} +2.16245 q^{62} -0.509718 q^{63} -13.0478 q^{64} +3.43842 q^{65} +10.5760 q^{66} -1.88285 q^{67} -6.99040 q^{68} +5.83375 q^{69} -3.21493 q^{70} +5.91066 q^{71} -2.43909 q^{72} -1.46526 q^{73} +16.7912 q^{74} -2.82803 q^{75} -7.10577 q^{76} -2.39132 q^{77} -2.77044 q^{78} -3.20889 q^{79} +1.86181 q^{80} +1.00000 q^{81} +13.7897 q^{82} +2.14774 q^{83} +1.57093 q^{84} +6.34602 q^{85} -10.0640 q^{86} -9.55431 q^{87} -11.4428 q^{88} +7.28802 q^{89} +6.30728 q^{90} +0.626416 q^{91} -17.9794 q^{92} +0.959245 q^{93} +18.3582 q^{94} +6.45075 q^{95} -6.37829 q^{96} -8.21187 q^{97} +15.1945 q^{98} +4.69145 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9}+O(q^{10}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9	\( 119 q + 11 q^{2} - 119 q^{3} + 137 q^{4} + 17 q^{5} - 11 q^{6} + 10 q^{7} + 33 q^{8} + 119 q^{9} - 10 q^{10} + 56 q^{11} - 137 q^{12} - 37 q^{13} + 31 q^{14} - 17 q^{15} + 173 q^{16} + 17 q^{17} + 11 q^{18} + 16 q^{19} + 61 q^{20} - 10 q^{21} - 3 q^{22} + 76 q^{23} - 33 q^{24} + 134 q^{25} + 47 q^{26} - 119 q^{27} - q^{28} + 47 q^{29} + 10 q^{30} + 51 q^{31} + 87 q^{32} - 56 q^{33} + 13 q^{34} + 58 q^{35} + 137 q^{36} - 67 q^{37} + 35 q^{38} + 37 q^{39} - 40 q^{40} + 47 q^{41} - 31 q^{42} + 12 q^{43} + 148 q^{44} + 17 q^{45} + 26 q^{46} + 107 q^{47} - 173 q^{48} + 163 q^{49} + 76 q^{50} - 17 q^{51} - 57 q^{52} + 64 q^{53} - 11 q^{54} + 71 q^{55} + 91 q^{56} - 16 q^{57} + 12 q^{58} + 98 q^{59} - 61 q^{60} - 50 q^{61} + 40 q^{62} + 10 q^{63} + 245 q^{64} + 40 q^{65} + 3 q^{66} + 12 q^{67} + 75 q^{68} - 76 q^{69} - 9 q^{70} + 194 q^{71} + 33 q^{72} - 79 q^{73} + 72 q^{74} - 134 q^{75} + 12 q^{76} + 71 q^{77} - 47 q^{78} + 127 q^{79} + 148 q^{80} + 119 q^{81} - 54 q^{82} + 77 q^{83} + q^{84} - 25 q^{85} + 142 q^{86} - 47 q^{87} + q^{88} + 93 q^{89} - 10 q^{90} + 61 q^{91} + 156 q^{92} - 51 q^{93} + 16 q^{94} + 138 q^{95} - 87 q^{96} - 110 q^{97} + 96 q^{98} + 56 q^{99}+O(q^{100}) \) 119 * q + 11 * q^2 - 119 * q^3 + 137 * q^4 + 17 * q^5 - 11 * q^6 + 10 * q^7 + 33 * q^8 + 119 * q^9 - 10 * q^10 + 56 * q^11 - 137 * q^12 - 37 * q^13 + 31 * q^14 - 17 * q^15 + 173 * q^16 + 17 * q^17 + 11 * q^18 + 16 * q^19 + 61 * q^20 - 10 * q^21 - 3 * q^22 + 76 * q^23 - 33 * q^24 + 134 * q^25 + 47 * q^26 - 119 * q^27 - q^28 + 47 * q^29 + 10 * q^30 + 51 * q^31 + 87 * q^32 - 56 * q^33 + 13 * q^34 + 58 * q^35 + 137 * q^36 - 67 * q^37 + 35 * q^38 + 37 * q^39 - 40 * q^40 + 47 * q^41 - 31 * q^42 + 12 * q^43 + 148 * q^44 + 17 * q^45 + 26 * q^46 + 107 * q^47 - 173 * q^48 + 163 * q^49 + 76 * q^50 - 17 * q^51 - 57 * q^52 + 64 * q^53 - 11 * q^54 + 71 * q^55 + 91 * q^56 - 16 * q^57 + 12 * q^58 + 98 * q^59 - 61 * q^60 - 50 * q^61 + 40 * q^62 + 10 * q^63 + 245 * q^64 + 40 * q^65 + 3 * q^66 + 12 * q^67 + 75 * q^68 - 76 * q^69 - 9 * q^70 + 194 * q^71 + 33 * q^72 - 79 * q^73 + 72 * q^74 - 134 * q^75 + 12 * q^76 + 71 * q^77 - 47 * q^78 + 127 * q^79 + 148 * q^80 + 119 * q^81 - 54 * q^82 + 77 * q^83 + q^84 - 25 * q^85 + 142 * q^86 - 47 * q^87 + q^88 + 93 * q^89 - 10 * q^90 + 61 * q^91 + 156 * q^92 - 51 * q^93 + 16 * q^94 + 138 * q^95 - 87 * q^96 - 110 * q^97 + 96 * q^98 + 56 * q^99

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