LMFDB - Embedded newform 8041.2.a.i.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} +O(q^{10})$	\(q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} -4.40747 q^{10} +1.00000 q^{11} +2.74675 q^{12} +2.82188 q^{13} +5.11310 q^{14} +7.75599 q^{15} -4.99266 q^{16} -1.00000 q^{17} -10.2851 q^{18} -4.52884 q^{19} +2.36060 q^{20} -8.99771 q^{21} -1.70714 q^{22} +8.03274 q^{23} +5.56781 q^{24} +1.66562 q^{25} -4.81735 q^{26} +9.08665 q^{27} -2.73853 q^{28} -1.93883 q^{29} -13.2406 q^{30} -4.01354 q^{31} +4.81639 q^{32} +3.00412 q^{33} +1.70714 q^{34} -7.73277 q^{35} +5.50859 q^{36} +3.59747 q^{37} +7.73136 q^{38} +8.47727 q^{39} +4.78506 q^{40} -3.41107 q^{41} +15.3604 q^{42} -1.00000 q^{43} +0.914329 q^{44} +15.5546 q^{45} -13.7130 q^{46} +5.66303 q^{47} -14.9985 q^{48} +1.97077 q^{49} -2.84345 q^{50} -3.00412 q^{51} +2.58013 q^{52} -3.29387 q^{53} -15.5122 q^{54} +2.58179 q^{55} -5.55114 q^{56} -13.6052 q^{57} +3.30986 q^{58} +3.03259 q^{59} +7.09153 q^{60} +7.35064 q^{61} +6.85167 q^{62} -18.0448 q^{63} +1.76307 q^{64} +7.28549 q^{65} -5.12845 q^{66} +12.8738 q^{67} -0.914329 q^{68} +24.1313 q^{69} +13.2009 q^{70} -1.74265 q^{71} +11.1662 q^{72} +9.72601 q^{73} -6.14138 q^{74} +5.00372 q^{75} -4.14085 q^{76} -2.99512 q^{77} -14.4719 q^{78} +10.1543 q^{79} -12.8900 q^{80} +9.22319 q^{81} +5.82318 q^{82} -0.743214 q^{83} -8.22687 q^{84} -2.58179 q^{85} +1.70714 q^{86} -5.82449 q^{87} +1.85339 q^{88} +2.14243 q^{89} -26.5538 q^{90} -8.45189 q^{91} +7.34457 q^{92} -12.0571 q^{93} -9.66759 q^{94} -11.6925 q^{95} +14.4690 q^{96} +7.44229 q^{97} -3.36438 q^{98} +6.02473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * 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 $

$2$	−1.70714	−1.20713	−0.603565	−	0.797314i	$-0.706254\pi$
$2$	−1.70714	−1.20713	−0.603565	+	0.797314i	$0.706254\pi$
$3$	3.00412	1.73443	0.867214	−	0.497935i	$-0.165908\pi$
$3$	3.00412	1.73443	0.867214	+	0.497935i	$0.165908\pi$
$4$	0.914329	0.457165
$5$	2.58179	1.15461	0.577305	−	0.816529i	$-0.304104\pi$
$5$	2.58179	1.15461	0.577305	+	0.816529i	$0.304104\pi$
$6$	−5.12845	−2.09368
$7$	−2.99512	−1.13205	−0.566025	−	0.824388i	$-0.691520\pi$
$7$	−2.99512	−1.13205	−0.566025	+	0.824388i	$0.691520\pi$
$8$	1.85339	0.655273
$9$	6.02473	2.00824
$10$	−4.40747	−1.39377
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.74675	0.792920
$13$	2.82188	0.782649	0.391325	−	0.920253i	$-0.372017\pi$
$13$	2.82188	0.782649	0.391325	+	0.920253i	$0.372017\pi$
$14$	5.11310	1.36653
$15$	7.75599	2.00259
$16$	−4.99266	−1.24817
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−10.2851	−2.42421
$19$	−4.52884	−1.03899	−0.519493	−	0.854475i	$-0.673879\pi$
$19$	−4.52884	−1.03899	−0.519493	+	0.854475i	$0.673879\pi$
$20$	2.36060	0.527847
$21$	−8.99771	−1.96346
$22$	−1.70714	−0.363964
$23$	8.03274	1.67494	0.837471	−	0.546482i	$-0.184033\pi$
$23$	8.03274	1.67494	0.837471	+	0.546482i	$0.184033\pi$
$24$	5.56781	1.13652
$25$	1.66562	0.333124
$26$	−4.81735	−0.944760
$27$	9.08665	1.74873
$28$	−2.73853	−0.517534
$29$	−1.93883	−0.360032	−0.180016	−	0.983664i	$-0.557615\pi$
$29$	−1.93883	−0.360032	−0.180016	+	0.983664i	$0.557615\pi$
$30$	−13.2406	−2.41739
$31$	−4.01354	−0.720852	−0.360426	−	0.932788i	$-0.617369\pi$
$31$	−4.01354	−0.720852	−0.360426	+	0.932788i	$0.617369\pi$
$32$	4.81639	0.851425
$33$	3.00412	0.522950
$34$	1.70714	0.292772
$35$	−7.73277	−1.30708
$36$	5.50859	0.918098
$37$	3.59747	0.591420	0.295710	−	0.955278i	$-0.404444\pi$
$37$	3.59747	0.591420	0.295710	+	0.955278i	$0.404444\pi$
$38$	7.73136	1.25419
$39$	8.47727	1.35745
$40$	4.78506	0.756585
$41$	−3.41107	−0.532720	−0.266360	−	0.963874i	$-0.585821\pi$
$41$	−3.41107	−0.532720	−0.266360	+	0.963874i	$0.585821\pi$
$42$	15.3604	2.37015
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	0.914329	0.137840
$45$	15.5546	2.31874
$46$	−13.7130	−2.02187
$47$	5.66303	0.826038	0.413019	−	0.910722i	$-0.364474\pi$
$47$	5.66303	0.826038	0.413019	+	0.910722i	$0.364474\pi$
$48$	−14.9985	−2.16485
$49$	1.97077	0.281538
$50$	−2.84345	−0.402124
$51$	−3.00412	−0.420661
$52$	2.58013	0.357800
$53$	−3.29387	−0.452448	−0.226224	−	0.974075i	$-0.572638\pi$
$53$	−3.29387	−0.452448	−0.226224	+	0.974075i	$0.572638\pi$
$54$	−15.5122	−2.11094
$55$	2.58179	0.348128
$56$	−5.55114	−0.741802
$57$	−13.6052	−1.80205
$58$	3.30986	0.434606
$59$	3.03259	0.394809	0.197405	−	0.980322i	$-0.436749\pi$
$59$	3.03259	0.394809	0.197405	+	0.980322i	$0.436749\pi$
$60$	7.09153	0.915513
$61$	7.35064	0.941153	0.470576	−	0.882359i	$-0.344046\pi$
$61$	7.35064	0.941153	0.470576	+	0.882359i	$0.344046\pi$
$62$	6.85167	0.870163
$63$	−18.0448	−2.27343
$64$	1.76307	0.220383
$65$	7.28549	0.903654
$66$	−5.12845	−0.631269
$67$	12.8738	1.57279	0.786393	−	0.617726i	$-0.211946\pi$
$67$	12.8738	1.57279	0.786393	+	0.617726i	$0.211946\pi$
$68$	−0.914329	−0.110879
$69$	24.1313	2.90507
$70$	13.2009	1.57781
$71$	−1.74265	−0.206814	−0.103407	−	0.994639i	$-0.532974\pi$
$71$	−1.74265	−0.206814	−0.103407	+	0.994639i	$0.532974\pi$
$72$	11.1662	1.31595
$73$	9.72601	1.13834	0.569172	−	0.822219i	$-0.307264\pi$
$73$	9.72601	1.13834	0.569172	+	0.822219i	$0.307264\pi$
$74$	−6.14138	−0.713921
$75$	5.00372	0.577780
$76$	−4.14085	−0.474988
$77$	−2.99512	−0.341326
$78$	−14.4719	−1.63862
$79$	10.1543	1.14245	0.571224	−	0.820794i	$-0.306469\pi$
$79$	10.1543	1.14245	0.571224	+	0.820794i	$0.306469\pi$
$80$	−12.8900	−1.44114
$81$	9.22319	1.02480
$82$	5.82318	0.643063
$83$	−0.743214	−0.0815784	−0.0407892	−	0.999168i	$-0.512987\pi$
$83$	−0.743214	−0.0815784	−0.0407892	+	0.999168i	$0.512987\pi$
$84$	−8.22687	−0.897625
$85$	−2.58179	−0.280034
$86$	1.70714	0.184086
$87$	−5.82449	−0.624451
$88$	1.85339	0.197572
$89$	2.14243	0.227097	0.113549	−	0.993532i	$-0.463778\pi$
$89$	2.14243	0.227097	0.113549	+	0.993532i	$0.463778\pi$
$90$	−26.5538	−2.79902
$91$	−8.45189	−0.885998
$92$	7.34457	0.765724
$93$	−12.0571	−1.25027
$94$	−9.66759	−0.997136
$95$	−11.6925	−1.19962
$96$	14.4690	1.47674
$97$	7.44229	0.755650	0.377825	−	0.925877i	$-0.376672\pi$
$97$	7.44229	0.755650	0.377825	+	0.925877i	$0.376672\pi$
$98$	−3.36438	−0.339854
$99$	6.02473	0.605508
$100$	1.52293	0.152293
$101$	−9.81951	−0.977078	−0.488539	−	0.872542i	$-0.662470\pi$
$101$	−9.81951	−0.977078	−0.488539	+	0.872542i	$0.662470\pi$
$102$	5.12845	0.507793
$103$	8.89443	0.876394	0.438197	−	0.898879i	$-0.355617\pi$
$103$	8.89443	0.876394	0.438197	+	0.898879i	$0.355617\pi$
$104$	5.23005	0.512849
$105$	−23.2302	−2.26703
$106$	5.62311	0.546164
$107$	19.4655	1.88180	0.940900	−	0.338685i	$-0.109982\pi$
$107$	19.4655	1.88180	0.940900	+	0.338685i	$0.109982\pi$
$108$	8.30819	0.799456
$109$	9.31212	0.891940	0.445970	−	0.895048i	$-0.352859\pi$
$109$	9.31212	0.891940	0.445970	+	0.895048i	$0.352859\pi$
$110$	−4.40747	−0.420236
$111$	10.8072	1.02578
$112$	14.9536	1.41299
$113$	12.0389	1.13253	0.566263	−	0.824224i	$-0.308389\pi$
$113$	12.0389	1.13253	0.566263	+	0.824224i	$0.308389\pi$
$114$	23.2259	2.17531
$115$	20.7388	1.93390
$116$	−1.77273	−0.164594
$117$	17.0011	1.57175
$118$	−5.17705	−0.476586
$119$	2.99512	0.274563
$120$	14.3749	1.31224
$121$	1.00000	0.0909091
$122$	−12.5486	−1.13609
$123$	−10.2473	−0.923965
$124$	−3.66969	−0.329548
$125$	−8.60866	−0.769982
$126$	30.8050	2.74433
$127$	−15.4638	−1.37219	−0.686096	−	0.727511i	$-0.740677\pi$
$127$	−15.4638	−1.37219	−0.686096	+	0.727511i	$0.740677\pi$
$128$	−12.6426	−1.11746
$129$	−3.00412	−0.264498
$130$	−12.4374	−1.09083
$131$	3.00229	0.262312	0.131156	−	0.991362i	$-0.458131\pi$
$131$	3.00229	0.262312	0.131156	+	0.991362i	$0.458131\pi$
$132$	2.74675	0.239074
$133$	13.5644	1.17619
$134$	−21.9774	−1.89856
$135$	23.4598	2.01910
$136$	−1.85339	−0.158927
$137$	−5.04309	−0.430860	−0.215430	−	0.976519i	$-0.569115\pi$
$137$	−5.04309	−0.430860	−0.215430	+	0.976519i	$0.569115\pi$
$138$	−41.1955	−3.50680
$139$	6.41950	0.544495	0.272248	−	0.962227i	$-0.412233\pi$
$139$	6.41950	0.544495	0.272248	+	0.962227i	$0.412233\pi$
$140$	−7.07030	−0.597549
$141$	17.0124	1.43270
$142$	2.97495	0.249652
$143$	2.82188	0.235978
$144$	−30.0794	−2.50662
$145$	−5.00565	−0.415697
$146$	−16.6037	−1.37413
$147$	5.92043	0.488308
$148$	3.28927	0.270376
$149$	3.09057	0.253189	0.126595	−	0.991955i	$-0.459595\pi$
$149$	3.09057	0.253189	0.126595	+	0.991955i	$0.459595\pi$
$150$	−8.54206	−0.697456
$151$	1.88358	0.153283	0.0766417	−	0.997059i	$-0.475580\pi$
$151$	1.88358	0.153283	0.0766417	+	0.997059i	$0.475580\pi$
$152$	−8.39371	−0.680820
$153$	−6.02473	−0.487071
$154$	5.11310	0.412025
$155$	−10.3621	−0.832303
$156$	7.75101	0.620578
$157$	13.8893	1.10849	0.554245	−	0.832354i	$-0.313007\pi$
$157$	13.8893	1.10849	0.554245	+	0.832354i	$0.313007\pi$
$158$	−17.3348	−1.37908
$159$	−9.89519	−0.784739
$160$	12.4349	0.983064
$161$	−24.0591	−1.89612
$162$	−15.7453	−1.23707
$163$	17.6830	1.38504	0.692522	−	0.721397i	$-0.256500\pi$
$163$	17.6830	1.38504	0.692522	+	0.721397i	$0.256500\pi$
$164$	−3.11884	−0.243541
$165$	7.75599	0.603803
$166$	1.26877	0.0984757
$167$	−6.84736	−0.529865	−0.264932	−	0.964267i	$-0.585350\pi$
$167$	−6.84736	−0.529865	−0.264932	+	0.964267i	$0.585350\pi$
$168$	−16.6763	−1.28660
$169$	−5.03699	−0.387460
$170$	4.40747	0.338038
$171$	−27.2850	−2.08654
$172$	−0.914329	−0.0697170
$173$	1.26214	0.0959585	0.0479792	−	0.998848i	$-0.484722\pi$
$173$	1.26214	0.0959585	0.0479792	+	0.998848i	$0.484722\pi$
$174$	9.94322	0.753794
$175$	−4.98874	−0.377113
$176$	−4.99266	−0.376336
$177$	9.11025	0.684769
$178$	−3.65743	−0.274136
$179$	8.56192	0.639948	0.319974	−	0.947426i	$-0.396326\pi$
$179$	8.56192	0.639948	0.319974	+	0.947426i	$0.396326\pi$
$180$	14.2220	1.06005
$181$	−17.1931	−1.27795	−0.638977	−	0.769226i	$-0.720642\pi$
$181$	−17.1931	−1.27795	−0.638977	+	0.769226i	$0.720642\pi$
$182$	14.4286	1.06952
$183$	22.0822	1.63236
$184$	14.8878	1.09754
$185$	9.28789	0.682859
$186$	20.5832	1.50924
$187$	−1.00000	−0.0731272
$188$	5.17788	0.377635
$189$	−27.2157	−1.97965
$190$	19.9607	1.44810
$191$	−17.3556	−1.25581	−0.627905	−	0.778290i	$-0.716087\pi$
$191$	−17.3556	−1.25581	−0.627905	+	0.778290i	$0.716087\pi$
$192$	5.29646	0.382239
$193$	−6.21215	−0.447161	−0.223580	−	0.974686i	$-0.571774\pi$
$193$	−6.21215	−0.447161	−0.223580	+	0.974686i	$0.571774\pi$
$194$	−12.7050	−0.912168
$195$	21.8865	1.56732
$196$	1.80193	0.128709
$197$	2.56523	0.182765	0.0913824	−	0.995816i	$-0.470871\pi$
$197$	2.56523	0.182765	0.0913824	+	0.995816i	$0.470871\pi$
$198$	−10.2851	−0.730928
$199$	−14.6875	−1.04117	−0.520586	−	0.853809i	$-0.674286\pi$
$199$	−14.6875	−1.04117	−0.520586	+	0.853809i	$0.674286\pi$
$200$	3.08705	0.218287
$201$	38.6745	2.72789
$202$	16.7633	1.17946
$203$	5.80705	0.407575
$204$	−2.74675	−0.192311
$205$	−8.80666	−0.615084
$206$	−15.1840	−1.05792
$207$	48.3951	3.36369
$208$	−14.0887	−0.976875
$209$	−4.52884	−0.313266
$210$	39.6572	2.73660
$211$	−16.3647	−1.12659	−0.563296	−	0.826255i	$-0.690467\pi$
$211$	−16.3647	−1.12659	−0.563296	+	0.826255i	$0.690467\pi$
$212$	−3.01169	−0.206843
$213$	−5.23512	−0.358705
$214$	−33.2303	−2.27158
$215$	−2.58179	−0.176076
$216$	16.8411	1.14589
$217$	12.0210	0.816041
$218$	−15.8971	−1.07669
$219$	29.2181	1.97438
$220$	2.36060	0.159152
$221$	−2.82188	−0.189820
$222$	−18.4494	−1.23825
$223$	2.55653	0.171198	0.0855990	−	0.996330i	$-0.472720\pi$
$223$	2.55653	0.171198	0.0855990	+	0.996330i	$0.472720\pi$
$224$	−14.4257	−0.963857
$225$	10.0349	0.668994
$226$	−20.5521	−1.36711
$227$	6.98626	0.463695	0.231847	−	0.972752i	$-0.425523\pi$
$227$	6.98626	0.463695	0.231847	+	0.972752i	$0.425523\pi$
$228$	−12.4396	−0.823833
$229$	7.62415	0.503818	0.251909	−	0.967751i	$-0.418942\pi$
$229$	7.62415	0.503818	0.251909	+	0.967751i	$0.418942\pi$
$230$	−35.4041	−2.33448
$231$	−8.99771	−0.592006
$232$	−3.59342	−0.235920
$233$	−18.9266	−1.23992	−0.619960	−	0.784633i	$-0.712851\pi$
$233$	−18.9266	−1.23992	−0.619960	+	0.784633i	$0.712851\pi$
$234$	−29.0232	−1.89731
$235$	14.6207	0.953752
$236$	2.77278	0.180493
$237$	30.5047	1.98149
$238$	−5.11310	−0.331433
$239$	1.97805	0.127950	0.0639748	−	0.997952i	$-0.479622\pi$
$239$	1.97805	0.127950	0.0639748	+	0.997952i	$0.479622\pi$
$240$	−38.7230	−2.49956
$241$	5.15695	0.332189	0.166094	−	0.986110i	$-0.446884\pi$
$241$	5.15695	0.332189	0.166094	+	0.986110i	$0.446884\pi$
$242$	−1.70714	−0.109739
$243$	0.447607	0.0287140
$244$	6.72091	0.430262
$245$	5.08811	0.325067
$246$	17.4935	1.11535
$247$	−12.7798	−0.813162
$248$	−7.43866	−0.472355
$249$	−2.23270	−0.141492
$250$	14.6962	0.929468
$251$	24.0312	1.51683	0.758417	−	0.651769i	$-0.225973\pi$
$251$	24.0312	1.51683	0.758417	+	0.651769i	$0.225973\pi$
$252$	−16.4989	−1.03933
$253$	8.03274	0.505014
$254$	26.3989	1.65641
$255$	−7.75599	−0.485699
$256$	18.0565	1.12853
$257$	−5.40174	−0.336951	−0.168476	−	0.985706i	$-0.553884\pi$
$257$	−5.40174	−0.336951	−0.168476	+	0.985706i	$0.553884\pi$
$258$	5.12845	0.319284
$259$	−10.7749	−0.669517
$260$	6.66134	0.413119
$261$	−11.6810	−0.723033
$262$	−5.12534	−0.316645
$263$	9.40836	0.580144	0.290072	−	0.957005i	$-0.406321\pi$
$263$	9.40836	0.580144	0.290072	+	0.957005i	$0.406321\pi$
$264$	5.56781	0.342675
$265$	−8.50408	−0.522401
$266$	−23.1564	−1.41981
$267$	6.43612	0.393884
$268$	11.7709	0.719022
$269$	−8.71453	−0.531334	−0.265667	−	0.964065i	$-0.585592\pi$
$269$	−8.71453	−0.531334	−0.265667	+	0.964065i	$0.585592\pi$
$270$	−40.0492	−2.43731
$271$	−19.2783	−1.17107	−0.585536	−	0.810646i	$-0.699116\pi$
$271$	−19.2783	−1.17107	−0.585536	+	0.810646i	$0.699116\pi$
$272$	4.99266	0.302725
$273$	−25.3905	−1.53670
$274$	8.60927	0.520105
$275$	1.66562	0.100441
$276$	22.0640	1.32809
$277$	28.6412	1.72088	0.860441	−	0.509550i	$-0.170188\pi$
$277$	28.6412	1.72088	0.860441	+	0.509550i	$0.170188\pi$
$278$	−10.9590	−0.657277
$279$	−24.1805	−1.44765
$280$	−14.3319	−0.856492
$281$	−3.53038	−0.210605	−0.105302	−	0.994440i	$-0.533581\pi$
$281$	−3.53038	−0.210605	−0.105302	+	0.994440i	$0.533581\pi$
$282$	−29.0426	−1.72946
$283$	−28.9441	−1.72055	−0.860275	−	0.509831i	$-0.829708\pi$
$283$	−28.9441	−1.72055	−0.860275	+	0.509831i	$0.829708\pi$
$284$	−1.59335	−0.0945482
$285$	−35.1256	−2.08066
$286$	−4.81735	−0.284856
$287$	10.2166	0.603066
$288$	29.0174	1.70987
$289$	1.00000	0.0588235
$290$	8.54536	0.501801
$291$	22.3575	1.31062
$292$	8.89277	0.520410
$293$	19.8993	1.16253	0.581266	−	0.813714i	$-0.302558\pi$
$293$	19.8993	1.16253	0.581266	+	0.813714i	$0.302558\pi$
$294$	−10.1070	−0.589452
$295$	7.82949	0.455851
$296$	6.66752	0.387542
$297$	9.08665	0.527261
$298$	−5.27603	−0.305632
$299$	22.6674	1.31089
$300$	4.57505	0.264141
$301$	2.99512	0.172636
$302$	−3.21553	−0.185033
$303$	−29.4990	−1.69467
$304$	22.6109	1.29683
$305$	18.9778	1.08666
$306$	10.2851	0.587958
$307$	26.2441	1.49783	0.748914	−	0.662667i	$-0.230575\pi$
$307$	26.2441	1.49783	0.748914	+	0.662667i	$0.230575\pi$
$308$	−2.73853	−0.156042
$309$	26.7199	1.52004
$310$	17.6895	1.00470
$311$	3.43363	0.194703	0.0973515	−	0.995250i	$-0.468963\pi$
$311$	3.43363	0.194703	0.0973515	+	0.995250i	$0.468963\pi$
$312$	15.7117	0.889500
$313$	16.7662	0.947684	0.473842	−	0.880610i	$-0.342867\pi$
$313$	16.7662	0.947684	0.473842	+	0.880610i	$0.342867\pi$
$314$	−23.7110	−1.33809
$315$	−46.5879	−2.62493
$316$	9.28437	0.522287
$317$	5.20653	0.292428	0.146214	−	0.989253i	$-0.453291\pi$
$317$	5.20653	0.292428	0.146214	+	0.989253i	$0.453291\pi$
$318$	16.8925	0.947283
$319$	−1.93883	−0.108554
$320$	4.55186	0.254457
$321$	58.4766	3.26385
$322$	41.0722	2.28886
$323$	4.52884	0.251991
$324$	8.43303	0.468502
$325$	4.70018	0.260719
$326$	−30.1875	−1.67193
$327$	27.9747	1.54701
$328$	−6.32206	−0.349077
$329$	−16.9615	−0.935117
$330$	−13.2406	−0.728869
$331$	−0.264100	−0.0145162	−0.00725811	−	0.999974i	$-0.502310\pi$
$331$	−0.264100	−0.0145162	−0.00725811	+	0.999974i	$0.502310\pi$
$332$	−0.679543	−0.0372947
$333$	21.6738	1.18772
$334$	11.6894	0.639616
$335$	33.2374	1.81595
$336$	44.9225	2.45072
$337$	4.95839	0.270101	0.135050	−	0.990839i	$-0.456880\pi$
$337$	4.95839	0.270101	0.135050	+	0.990839i	$0.456880\pi$
$338$	8.59884	0.467715
$339$	36.1664	1.96429
$340$	−2.36060	−0.128022
$341$	−4.01354	−0.217345
$342$	46.5794	2.51872
$343$	15.0632	0.813335
$344$	−1.85339	−0.0999282
$345$	62.3019	3.35422
$346$	−2.15465	−0.115834
$347$	−4.37562	−0.234896	−0.117448	−	0.993079i	$-0.537471\pi$
$347$	−4.37562	−0.234896	−0.117448	+	0.993079i	$0.537471\pi$
$348$	−5.32550	−0.285477
$349$	−19.2040	−1.02796	−0.513982	−	0.857801i	$-0.671830\pi$
$349$	−19.2040	−1.02796	−0.513982	+	0.857801i	$0.671830\pi$
$350$	8.51648	0.455225
$351$	25.6415	1.36864
$352$	4.81639	0.256714
$353$	27.3704	1.45678	0.728390	−	0.685162i	$-0.240269\pi$
$353$	27.3704	1.45678	0.728390	+	0.685162i	$0.240269\pi$
$354$	−15.5525	−0.826605
$355$	−4.49915	−0.238790
$356$	1.95889	0.103821
$357$	8.99771	0.476209
$358$	−14.6164	−0.772501
$359$	−13.1360	−0.693293	−0.346646	−	0.937996i	$-0.612680\pi$
$359$	−13.1360	−0.693293	−0.346646	+	0.937996i	$0.612680\pi$
$360$	28.8287	1.51941
$361$	1.51036	0.0794926
$362$	29.3511	1.54266
$363$	3.00412	0.157675
$364$	−7.72781	−0.405047
$365$	25.1105	1.31434
$366$	−37.6974	−1.97048
$367$	4.30071	0.224495	0.112248	−	0.993680i	$-0.464195\pi$
$367$	4.30071	0.224495	0.112248	+	0.993680i	$0.464195\pi$
$368$	−40.1047	−2.09060
$369$	−20.5508	−1.06983
$370$	−15.8557	−0.824300
$371$	9.86556	0.512194
$372$	−11.0242	−0.571578
$373$	11.7573	0.608771	0.304385	−	0.952549i	$-0.401549\pi$
$373$	11.7573	0.608771	0.304385	+	0.952549i	$0.401549\pi$
$374$	1.70714	0.0882741
$375$	−25.8614	−1.33548
$376$	10.4958	0.541281
$377$	−5.47116	−0.281779
$378$	46.4609	2.38969
$379$	−20.9215	−1.07466	−0.537332	−	0.843371i	$-0.680568\pi$
$379$	−20.9215	−1.07466	−0.537332	+	0.843371i	$0.680568\pi$
$380$	−10.6908	−0.548426
$381$	−46.4551	−2.37997
$382$	29.6285	1.51593
$383$	0.294128	0.0150293	0.00751463	−	0.999972i	$-0.497608\pi$
$383$	0.294128	0.0150293	0.00751463	+	0.999972i	$0.497608\pi$
$384$	−37.9798	−1.93815
$385$	−7.73277	−0.394098
$386$	10.6050	0.539781
$387$	−6.02473	−0.306254
$388$	6.80470	0.345457
$389$	8.77705	0.445014	0.222507	−	0.974931i	$-0.428576\pi$
$389$	8.77705	0.445014	0.222507	+	0.974931i	$0.428576\pi$
$390$	−37.3633	−1.89197
$391$	−8.03274	−0.406233
$392$	3.65261	0.184485
$393$	9.01925	0.454961
$394$	−4.37920	−0.220621
$395$	26.2162	1.31908
$396$	5.50859	0.276817
$397$	25.2836	1.26895	0.634473	−	0.772945i	$-0.281217\pi$
$397$	25.2836	1.26895	0.634473	+	0.772945i	$0.281217\pi$
$398$	25.0737	1.25683
$399$	40.7492	2.04001
$400$	−8.31588	−0.415794
$401$	−22.5865	−1.12792	−0.563959	−	0.825803i	$-0.690722\pi$
$401$	−22.5865	−1.12792	−0.563959	+	0.825803i	$0.690722\pi$
$402$	−66.0228	−3.29292
$403$	−11.3257	−0.564174
$404$	−8.97827	−0.446686
$405$	23.8123	1.18324
$406$	−9.91345	−0.491996
$407$	3.59747	0.178320
$408$	−5.56781	−0.275648
$409$	2.30505	0.113977	0.0569887	−	0.998375i	$-0.481850\pi$
$409$	2.30505	0.113977	0.0569887	+	0.998375i	$0.481850\pi$
$410$	15.0342	0.742487
$411$	−15.1501	−0.747297
$412$	8.13244	0.400657
$413$	−9.08298	−0.446944
$414$	−82.6172	−4.06042
$415$	−1.91882	−0.0941912
$416$	13.5913	0.666367
$417$	19.2850	0.944388
$418$	7.73136	0.378153
$419$	−32.3226	−1.57906	−0.789531	−	0.613711i	$-0.789676\pi$
$419$	−32.3226	−1.57906	−0.789531	+	0.613711i	$0.789676\pi$
$420$	−21.2400	−1.03641
$421$	3.05398	0.148842	0.0744210	−	0.997227i	$-0.476289\pi$
$421$	3.05398	0.148842	0.0744210	+	0.997227i	$0.476289\pi$
$422$	27.9368	1.35994
$423$	34.1182	1.65889
$424$	−6.10484	−0.296477
$425$	−1.66562	−0.0807945
$426$	8.93709	0.433004
$427$	−22.0161	−1.06543
$428$	17.7979	0.860292
$429$	8.47727	0.409286
$430$	4.40747	0.212547
$431$	−34.4829	−1.66098	−0.830491	−	0.557032i	$-0.811940\pi$
$431$	−34.4829	−1.66098	−0.830491	+	0.557032i	$0.811940\pi$
$432$	−45.3666	−2.18270
$433$	−28.2661	−1.35838	−0.679192	−	0.733961i	$-0.737669\pi$
$433$	−28.2661	−1.35838	−0.679192	+	0.733961i	$0.737669\pi$
$434$	−20.5216	−0.985068
$435$	−15.0376	−0.720997
$436$	8.51435	0.407763
$437$	−36.3790	−1.74024
$438$	−49.8794	−2.38333
$439$	−2.85011	−0.136028	−0.0680141	−	0.997684i	$-0.521666\pi$
$439$	−2.85011	−0.136028	−0.0680141	+	0.997684i	$0.521666\pi$
$440$	4.78506	0.228119
$441$	11.8734	0.565398
$442$	4.81735	0.229138
$443$	−37.9460	−1.80287	−0.901435	−	0.432914i	$-0.857485\pi$
$443$	−37.9460	−1.80287	−0.901435	+	0.432914i	$0.857485\pi$
$444$	9.88136	0.468948
$445$	5.53130	0.262209
$446$	−4.36436	−0.206658
$447$	9.28443	0.439139
$448$	−5.28061	−0.249485
$449$	−1.63603	−0.0772090	−0.0386045	−	0.999255i	$-0.512291\pi$
$449$	−1.63603	−0.0772090	−0.0386045	+	0.999255i	$0.512291\pi$
$450$	−17.1310	−0.807564
$451$	−3.41107	−0.160621
$452$	11.0075	0.517751
$453$	5.65849	0.265859
$454$	−11.9265	−0.559740
$455$	−21.8210	−1.02298
$456$	−25.2157	−1.18083
$457$	−6.96222	−0.325679	−0.162839	−	0.986653i	$-0.552065\pi$
$457$	−6.96222	−0.325679	−0.162839	+	0.986653i	$0.552065\pi$
$458$	−13.0155	−0.608174
$459$	−9.08665	−0.424129
$460$	18.9621	0.884113
$461$	−1.33882	−0.0623550	−0.0311775	−	0.999514i	$-0.509926\pi$
$461$	−1.33882	−0.0623550	−0.0311775	+	0.999514i	$0.509926\pi$
$462$	15.3604	0.714628
$463$	14.5799	0.677584	0.338792	−	0.940861i	$-0.389982\pi$
$463$	14.5799	0.677584	0.338792	+	0.940861i	$0.389982\pi$
$464$	9.67994	0.449380
$465$	−31.1290	−1.44357
$466$	32.3103	1.49675
$467$	33.4252	1.54674	0.773368	−	0.633958i	$-0.218571\pi$
$467$	33.4252	1.54674	0.773368	+	0.633958i	$0.218571\pi$
$468$	15.5446	0.718549
$469$	−38.5587	−1.78047
$470$	−24.9597	−1.15130
$471$	41.7252	1.92260
$472$	5.62057	0.258708
$473$	−1.00000	−0.0459800
$474$	−52.0759	−2.39192
$475$	−7.54332	−0.346111
$476$	2.73853	0.125520
$477$	−19.8447	−0.908627
$478$	−3.37681	−0.154452
$479$	−5.30744	−0.242503	−0.121252	−	0.992622i	$-0.538691\pi$
$479$	−5.30744	−0.242503	−0.121252	+	0.992622i	$0.538691\pi$
$480$	37.3559	1.70505
$481$	10.1516	0.462874
$482$	−8.80365	−0.400995
$483$	−72.2763	−3.28868
$484$	0.914329	0.0415604
$485$	19.2144	0.872481
$486$	−0.764129	−0.0346616
$487$	−32.8945	−1.49059	−0.745295	−	0.666734i	$-0.767692\pi$
$487$	−32.8945	−1.49059	−0.745295	+	0.666734i	$0.767692\pi$
$488$	13.6236	0.616712
$489$	53.1220	2.40226
$490$	−8.68611	−0.392399
$491$	−1.94836	−0.0879283	−0.0439641	−	0.999033i	$-0.513999\pi$
$491$	−1.94836	−0.0879283	−0.0439641	+	0.999033i	$0.513999\pi$
$492$	−9.36938	−0.422404
$493$	1.93883	0.0873207
$494$	21.8170	0.981593
$495$	15.5546	0.699126
$496$	20.0382	0.899743
$497$	5.21945	0.234124
$498$	3.81154	0.170799
$499$	25.4596	1.13973	0.569863	−	0.821740i	$-0.306996\pi$
$499$	25.4596	1.13973	0.569863	+	0.821740i	$0.306996\pi$
$500$	−7.87115	−0.352008
$501$	−20.5703	−0.919013
$502$	−41.0246	−1.83102
$503$	−29.9609	−1.33589	−0.667945	−	0.744211i	$-0.732826\pi$
$503$	−29.9609	−1.33589	−0.667945	+	0.744211i	$0.732826\pi$
$504$	−33.4441	−1.48972
$505$	−25.3519	−1.12814
$506$	−13.7130	−0.609618
$507$	−15.1317	−0.672023
$508$	−14.1390	−0.627318
$509$	−23.3208	−1.03368	−0.516838	−	0.856083i	$-0.672891\pi$
$509$	−23.3208	−1.03368	−0.516838	+	0.856083i	$0.672891\pi$
$510$	13.2406	0.586302
$511$	−29.1306	−1.28866
$512$	−5.53988	−0.244830
$513$	−41.1520	−1.81690
$514$	9.22152	0.406744
$515$	22.9635	1.01189
$516$	−2.74675	−0.120919
$517$	5.66303	0.249060
$518$	18.3942	0.808195
$519$	3.79161	0.166433
$520$	13.5029	0.592140
$521$	−40.1913	−1.76081	−0.880407	−	0.474218i	$-0.842731\pi$
$521$	−40.1913	−1.76081	−0.880407	+	0.474218i	$0.842731\pi$
$522$	19.9410	0.872795
$523$	28.2217	1.23405	0.617024	−	0.786944i	$-0.288338\pi$
$523$	28.2217	1.23405	0.617024	+	0.786944i	$0.288338\pi$
$524$	2.74509	0.119920
$525$	−14.9868	−0.654076
$526$	−16.0614	−0.700310
$527$	4.01354	0.174832
$528$	−14.9985	−0.652728
$529$	41.5249	1.80543
$530$	14.5177	0.630607
$531$	18.2705	0.792873
$532$	12.4024	0.537710
$533$	−9.62564	−0.416933
$534$	−10.9874	−0.475470
$535$	50.2557	2.17274
$536$	23.8602	1.03060
$537$	25.7210	1.10994
$538$	14.8769	0.641390
$539$	1.97077	0.0848870
$540$	21.4500	0.923060
$541$	−18.5299	−0.796663	−0.398331	−	0.917242i	$-0.630411\pi$
$541$	−18.5299	−0.796663	−0.398331	+	0.917242i	$0.630411\pi$
$542$	32.9107	1.41364
$543$	−51.6502	−2.21652
$544$	−4.81639	−0.206501
$545$	24.0419	1.02984
$546$	43.3451	1.85500
$547$	12.0252	0.514158	0.257079	−	0.966390i	$-0.417240\pi$
$547$	12.0252	0.514158	0.257079	+	0.966390i	$0.417240\pi$
$548$	−4.61105	−0.196974
$549$	44.2856	1.89006
$550$	−2.84345	−0.121245
$551$	8.78066	0.374069
$552$	44.7248	1.90361
$553$	−30.4134	−1.29331
$554$	−48.8945	−2.07733
$555$	27.9019	1.18437
$556$	5.86954	0.248924
$557$	16.9330	0.717472	0.358736	−	0.933439i	$-0.383208\pi$
$557$	16.9330	0.717472	0.358736	+	0.933439i	$0.383208\pi$
$558$	41.2795	1.74750
$559$	−2.82188	−0.119353
$560$	38.6071	1.63145
$561$	−3.00412	−0.126834
$562$	6.02686	0.254228
$563$	38.2466	1.61190	0.805952	−	0.591981i	$-0.201654\pi$
$563$	38.2466	1.61190	0.805952	+	0.591981i	$0.201654\pi$
$564$	15.5550	0.654982
$565$	31.0819	1.30763
$566$	49.4117	2.07693
$567$	−27.6246	−1.16012
$568$	−3.22981	−0.135520
$569$	−13.3812	−0.560969	−0.280485	−	0.959859i	$-0.590495\pi$
$569$	−13.3812	−0.560969	−0.280485	+	0.959859i	$0.590495\pi$
$570$	59.9644	2.51163
$571$	−8.54519	−0.357605	−0.178802	−	0.983885i	$-0.557222\pi$
$571$	−8.54519	−0.357605	−0.178802	+	0.983885i	$0.557222\pi$
$572$	2.58013	0.107881
$573$	−52.1384	−2.17811
$574$	−17.4411	−0.727979
$575$	13.3795	0.557963
$576$	10.6220	0.442584
$577$	−15.5254	−0.646332	−0.323166	−	0.946342i	$-0.604747\pi$
$577$	−15.5254	−0.646332	−0.323166	+	0.946342i	$0.604747\pi$
$578$	−1.70714	−0.0710077
$579$	−18.6621	−0.775568
$580$	−4.57682	−0.190042
$581$	2.22602	0.0923508
$582$	−38.1674	−1.58209
$583$	−3.29387	−0.136418
$584$	18.0261	0.745926
$585$	43.8931	1.81476
$586$	−33.9710	−1.40333
$587$	−13.9457	−0.575601	−0.287801	−	0.957690i	$-0.592924\pi$
$587$	−13.9457	−0.575601	−0.287801	+	0.957690i	$0.592924\pi$
$588$	5.41322	0.223237
$589$	18.1766	0.748956
$590$	−13.3660	−0.550271
$591$	7.70625	0.316993
$592$	−17.9609	−0.738190
$593$	1.69391	0.0695604	0.0347802	−	0.999395i	$-0.488927\pi$
$593$	1.69391	0.0695604	0.0347802	+	0.999395i	$0.488927\pi$
$594$	−15.5122	−0.636473
$595$	7.73277	0.317013
$596$	2.82580	0.115749
$597$	−44.1231	−1.80584
$598$	−38.6965	−1.58242
$599$	−17.0080	−0.694930	−0.347465	−	0.937693i	$-0.612957\pi$
$599$	−17.0080	−0.694930	−0.347465	+	0.937693i	$0.612957\pi$
$600$	9.27386	0.378604
$601$	−22.6958	−0.925782	−0.462891	−	0.886415i	$-0.653188\pi$
$601$	−22.6958	−0.925782	−0.462891	+	0.886415i	$0.653188\pi$
$602$	−5.11310	−0.208394
$603$	77.5613	3.15854
$604$	1.72221	0.0700758
$605$	2.58179	0.104965
$606$	50.3589	2.04569
$607$	−9.84320	−0.399523	−0.199762	−	0.979845i	$-0.564017\pi$
$607$	−9.84320	−0.399523	−0.199762	+	0.979845i	$0.564017\pi$
$608$	−21.8126	−0.884619
$609$	17.4451	0.706910
$610$	−32.3977	−1.31175
$611$	15.9804	0.646498
$612$	−5.50859	−0.222672
$613$	−32.3597	−1.30700	−0.653498	−	0.756928i	$-0.726699\pi$
$613$	−32.3597	−1.30700	−0.653498	+	0.756928i	$0.726699\pi$
$614$	−44.8023	−1.80807
$615$	−26.4563	−1.06682
$616$	−5.55114	−0.223662
$617$	−28.0622	−1.12974	−0.564872	−	0.825179i	$-0.691074\pi$
$617$	−28.0622	−1.12974	−0.564872	+	0.825179i	$0.691074\pi$
$618$	−45.6147	−1.83489
$619$	28.0533	1.12756	0.563778	−	0.825926i	$-0.309347\pi$
$619$	28.0533	1.12756	0.563778	+	0.825926i	$0.309347\pi$
$620$	−9.47436	−0.380500
$621$	72.9907	2.92902
$622$	−5.86168	−0.235032
$623$	−6.41685	−0.257086
$624$	−42.3241	−1.69432
$625$	−30.5538	−1.22215
$626$	−28.6223	−1.14398
$627$	−13.6052	−0.543338
$628$	12.6994	0.506762
$629$	−3.59747	−0.143440
$630$	79.5320	3.16863
$631$	−13.5333	−0.538752	−0.269376	−	0.963035i	$-0.586817\pi$
$631$	−13.5333	−0.538752	−0.269376	+	0.963035i	$0.586817\pi$
$632$	18.8199	0.748616
$633$	−49.1615	−1.95399
$634$	−8.88829	−0.352999
$635$	−39.9243	−1.58435
$636$	−9.04746	−0.358755
$637$	5.56128	0.220346
$638$	3.30986	0.131039
$639$	−10.4990	−0.415334
$640$	−32.6404	−1.29023
$641$	2.21452	0.0874683	0.0437341	−	0.999043i	$-0.486075\pi$
$641$	2.21452	0.0874683	0.0437341	+	0.999043i	$0.486075\pi$
$642$	−99.8278	−3.93989
$643$	−4.55377	−0.179583	−0.0897916	−	0.995961i	$-0.528620\pi$
$643$	−4.55377	−0.179583	−0.0897916	+	0.995961i	$0.528620\pi$
$644$	−21.9979	−0.866839
$645$	−7.75599	−0.305392
$646$	−7.73136	−0.304186
$647$	15.8632	0.623647	0.311824	−	0.950140i	$-0.399060\pi$
$647$	15.8632	0.623647	0.311824	+	0.950140i	$0.399060\pi$
$648$	17.0942	0.671523
$649$	3.03259	0.119039
$650$	−8.02387	−0.314722
$651$	36.1126	1.41537
$652$	16.1681	0.633193
$653$	−21.9593	−0.859332	−0.429666	−	0.902988i	$-0.641369\pi$
$653$	−21.9593	−0.859332	−0.429666	+	0.902988i	$0.641369\pi$
$654$	−47.7568	−1.86744
$655$	7.75128	0.302868
$656$	17.0303	0.664922
$657$	58.5966	2.28607
$658$	28.9556	1.12881
$659$	−9.64737	−0.375808	−0.187904	−	0.982187i	$-0.560169\pi$
$659$	−9.64737	−0.375808	−0.187904	+	0.982187i	$0.560169\pi$
$660$	7.09153	0.276038
$661$	30.9915	1.20543	0.602715	−	0.797957i	$-0.294086\pi$
$661$	30.9915	1.20543	0.602715	+	0.797957i	$0.294086\pi$
$662$	0.450855	0.0175230
$663$	−8.47727	−0.329230
$664$	−1.37747	−0.0534561
$665$	35.0205	1.35803
$666$	−37.0002	−1.43373
$667$	−15.5741	−0.603033
$668$	−6.26075	−0.242236
$669$	7.68012	0.296931
$670$	−56.7410	−2.19210
$671$	7.35064	0.283768
$672$	−43.3365	−1.67174
$673$	8.15023	0.314168	0.157084	−	0.987585i	$-0.449791\pi$
$673$	8.15023	0.314168	0.157084	+	0.987585i	$0.449791\pi$
$674$	−8.46467	−0.326047
$675$	15.1349	0.582543
$676$	−4.60546	−0.177133
$677$	18.3783	0.706337	0.353168	−	0.935560i	$-0.385104\pi$
$677$	18.3783	0.706337	0.353168	+	0.935560i	$0.385104\pi$
$678$	−61.7411	−2.37115
$679$	−22.2906	−0.855434
$680$	−4.78506	−0.183499
$681$	20.9876	0.804245
$682$	6.85167	0.262364
$683$	19.3461	0.740260	0.370130	−	0.928980i	$-0.379313\pi$
$683$	19.3461	0.740260	0.370130	+	0.928980i	$0.379313\pi$
$684$	−24.9475	−0.953891
$685$	−13.0202	−0.497476
$686$	−25.7150	−0.981801
$687$	22.9038	0.873836
$688$	4.99266	0.190343
$689$	−9.29492	−0.354108
$690$	−106.358	−4.04898
$691$	−22.1628	−0.843115	−0.421557	−	0.906802i	$-0.638516\pi$
$691$	−22.1628	−0.843115	−0.421557	+	0.906802i	$0.638516\pi$
$692$	1.15401	0.0438688
$693$	−18.0448	−0.685466
$694$	7.46981	0.283550
$695$	16.5738	0.628679
$696$	−10.7951	−0.409186
$697$	3.41107	0.129204
$698$	32.7839	1.24089
$699$	−56.8577	−2.15055
$700$	−4.56135	−0.172403
$701$	−1.91078	−0.0721691	−0.0360846	−	0.999349i	$-0.511489\pi$
$701$	−1.91078	−0.0721691	−0.0360846	+	0.999349i	$0.511489\pi$
$702$	−43.7736	−1.65213
$703$	−16.2923	−0.614477
$704$	1.76307	0.0664481
$705$	43.9224	1.65421
$706$	−46.7252	−1.75853
$707$	29.4107	1.10610
$708$	8.32977	0.313052
$709$	−37.6792	−1.41507	−0.707537	−	0.706676i	$-0.750194\pi$
$709$	−37.6792	−1.41507	−0.707537	+	0.706676i	$0.750194\pi$
$710$	7.68067	0.288251
$711$	61.1769	2.29431
$712$	3.97077	0.148811
$713$	−32.2397	−1.20739
$714$	−15.3604	−0.574847
$715$	7.28549	0.272462
$716$	7.82841	0.292562
$717$	5.94230	0.221919
$718$	22.4250	0.836895
$719$	9.48956	0.353901	0.176950	−	0.984220i	$-0.443377\pi$
$719$	9.48956	0.353901	0.176950	+	0.984220i	$0.443377\pi$
$720$	−77.6587	−2.89417
$721$	−26.6399	−0.992123
$722$	−2.57840	−0.0959580
$723$	15.4921	0.576158
$724$	−15.7202	−0.584235
$725$	−3.22936	−0.119935
$726$	−5.12845	−0.190335
$727$	13.3855	0.496439	0.248220	−	0.968704i	$-0.420155\pi$
$727$	13.3855	0.496439	0.248220	+	0.968704i	$0.420155\pi$
$728$	−15.6647	−0.580571
$729$	−26.3249	−0.974997
$730$	−42.8671	−1.58658
$731$	1.00000	0.0369863
$732$	20.1904	0.746259
$733$	50.9164	1.88064	0.940320	−	0.340293i	$-0.110526\pi$
$733$	50.9164	1.88064	0.940320	+	0.340293i	$0.110526\pi$
$734$	−7.34192	−0.270995
$735$	15.2853	0.563806
$736$	38.6888	1.42609
$737$	12.8738	0.474213
$738$	35.0831	1.29143
$739$	17.6718	0.650068	0.325034	−	0.945702i	$-0.394624\pi$
$739$	17.6718	0.650068	0.325034	+	0.945702i	$0.394624\pi$
$740$	8.49219	0.312179
$741$	−38.3922	−1.41037
$742$	−16.8419	−0.618286
$743$	35.6520	1.30795	0.653973	−	0.756518i	$-0.273101\pi$
$743$	35.6520	1.30795	0.653973	+	0.756518i	$0.273101\pi$
$744$	−22.3466	−0.819266
$745$	7.97919	0.292335
$746$	−20.0714	−0.734866
$747$	−4.47767	−0.163829
$748$	−0.914329	−0.0334312
$749$	−58.3015	−2.13029
$750$	44.1491	1.61210
$751$	−8.38924	−0.306128	−0.153064	−	0.988216i	$-0.548914\pi$
$751$	−8.38924	−0.306128	−0.153064	+	0.988216i	$0.548914\pi$
$752$	−28.2736	−1.03103
$753$	72.1925	2.63084
$754$	9.34004	0.340144
$755$	4.86300	0.176983
$756$	−24.8841	−0.905025
$757$	−38.2639	−1.39073	−0.695363	−	0.718659i	$-0.744756\pi$
$757$	−38.2639	−1.39073	−0.695363	+	0.718659i	$0.744756\pi$
$758$	35.7159	1.29726
$759$	24.1313	0.875911
$760$	−21.6708	−0.786081
$761$	28.0751	1.01772	0.508860	−	0.860849i	$-0.330067\pi$
$761$	28.0751	1.01772	0.508860	+	0.860849i	$0.330067\pi$
$762$	79.3055	2.87293
$763$	−27.8910	−1.00972
$764$	−15.8688	−0.574112
$765$	−15.5546	−0.562377
$766$	−0.502119	−0.0181423
$767$	8.55760	0.308997
$768$	54.2440	1.95736
$769$	−23.6111	−0.851439	−0.425719	−	0.904855i	$-0.639979\pi$
$769$	−23.6111	−0.851439	−0.425719	+	0.904855i	$0.639979\pi$
$770$	13.2009	0.475728
$771$	−16.2275	−0.584418
$772$	−5.67996	−0.204426
$773$	4.89139	0.175931	0.0879655	−	0.996124i	$-0.471963\pi$
$773$	4.89139	0.175931	0.0879655	+	0.996124i	$0.471963\pi$
$774$	10.2851	0.369689
$775$	−6.68503	−0.240133
$776$	13.7935	0.495157
$777$	−32.3690	−1.16123
$778$	−14.9837	−0.537190
$779$	15.4482	0.553489
$780$	20.0115	0.716525
$781$	−1.74265	−0.0623569
$782$	13.7130	0.490376
$783$	−17.6175	−0.629598
$784$	−9.83938	−0.351406
$785$	35.8593	1.27987
$786$	−15.3971	−0.549197
$787$	−36.6731	−1.30726	−0.653628	−	0.756816i	$-0.726754\pi$
$787$	−36.6731	−1.30726	−0.653628	+	0.756816i	$0.726754\pi$
$788$	2.34546	0.0835536
$789$	28.2638	1.00622
$790$	−44.7548	−1.59230
$791$	−36.0581	−1.28208
$792$	11.1662	0.396773
$793$	20.7426	0.736592
$794$	−43.1626	−1.53178
$795$	−25.5473	−0.906068
$796$	−13.4292	−0.475987
$797$	16.1462	0.571926	0.285963	−	0.958241i	$-0.407686\pi$
$797$	16.1462	0.571926	0.285963	+	0.958241i	$0.407686\pi$
$798$	−69.5645	−2.46256
$799$	−5.66303	−0.200344
$800$	8.02228	0.283630
$801$	12.9076	0.456067
$802$	38.5584	1.36154
$803$	9.72601	0.343223
$804$	35.3612	1.24709
$805$	−62.1153	−2.18928
$806$	19.3346	0.681032
$807$	−26.1795	−0.921561
$808$	−18.1994	−0.640253
$809$	23.7534	0.835125	0.417563	−	0.908648i	$-0.362884\pi$
$809$	23.7534	0.835125	0.417563	+	0.908648i	$0.362884\pi$
$810$	−40.6510	−1.42833
$811$	41.4907	1.45693	0.728467	−	0.685081i	$-0.240233\pi$
$811$	41.4907	1.45693	0.728467	+	0.685081i	$0.240233\pi$
$812$	5.30956	0.186329
$813$	−57.9143	−2.03114
$814$	−6.14138	−0.215255
$815$	45.6539	1.59918
$816$	14.9985	0.525054
$817$	4.52884	0.158444
$818$	−3.93504	−0.137586
$819$	−50.9203	−1.77930
$820$	−8.05219	−0.281195
$821$	21.6232	0.754655	0.377327	−	0.926080i	$-0.376843\pi$
$821$	21.6232	0.754655	0.377327	+	0.926080i	$0.376843\pi$
$822$	25.8633	0.902085
$823$	40.3891	1.40787	0.703937	−	0.710262i	$-0.251424\pi$
$823$	40.3891	1.40787	0.703937	+	0.710262i	$0.251424\pi$
$824$	16.4849	0.574278
$825$	5.00372	0.174207
$826$	15.5059	0.539520
$827$	−54.7476	−1.90376	−0.951880	−	0.306472i	$-0.900851\pi$
$827$	−54.7476	−1.90376	−0.951880	+	0.306472i	$0.900851\pi$
$828$	44.2491	1.53776
$829$	−0.207335	−0.00720105	−0.00360053	−	0.999994i	$-0.501146\pi$
$829$	−0.207335	−0.00720105	−0.00360053	+	0.999994i	$0.501146\pi$
$830$	3.27570	0.113701
$831$	86.0416	2.98475
$832$	4.97517	0.172483
$833$	−1.97077	−0.0682831
$834$	−32.9221	−1.14000
$835$	−17.6784	−0.611787
$836$	−4.14085	−0.143214
$837$	−36.4696	−1.26057
$838$	55.1792	1.90613
$839$	21.6296	0.746738	0.373369	−	0.927683i	$-0.378203\pi$
$839$	21.6296	0.746738	0.373369	+	0.927683i	$0.378203\pi$
$840$	−43.0546	−1.48553
$841$	−25.2409	−0.870377
$842$	−5.21358	−0.179672
$843$	−10.6057	−0.365279
$844$	−14.9627	−0.515038
$845$	−13.0044	−0.447366
$846$	−58.2446	−2.00249
$847$	−2.99512	−0.102914
$848$	16.4452	0.564730
$849$	−86.9516	−2.98417
$850$	2.84345	0.0975295
$851$	28.8975	0.990594
$852$	−4.78663	−0.163987
$853$	30.0205	1.02788	0.513941	−	0.857826i	$-0.328185\pi$
$853$	30.0205	1.02788	0.513941	+	0.857826i	$0.328185\pi$
$854$	37.5845	1.28612
$855$	−70.4441	−2.40914
$856$	36.0772	1.23309
$857$	29.4546	1.00615	0.503074	−	0.864243i	$-0.332202\pi$
$857$	29.4546	1.00615	0.503074	+	0.864243i	$0.332202\pi$
$858$	−14.4719	−0.494062
$859$	0.816990	0.0278753	0.0139377	−	0.999903i	$-0.495563\pi$
$859$	0.816990	0.0278753	0.0139377	+	0.999903i	$0.495563\pi$
$860$	−2.36060	−0.0804959
$861$	30.6918	1.04597
$862$	58.8671	2.00502
$863$	−35.6036	−1.21196	−0.605980	−	0.795480i	$-0.707219\pi$
$863$	−35.6036	−1.21196	−0.605980	+	0.795480i	$0.707219\pi$
$864$	43.7649	1.48891
$865$	3.25857	0.110795
$866$	48.2542	1.63975
$867$	3.00412	0.102025
$868$	10.9912	0.373065
$869$	10.1543	0.344461
$870$	25.6713	0.870338
$871$	36.3284	1.23094
$872$	17.2590	0.584464
$873$	44.8378	1.51753
$874$	62.1040	2.10070
$875$	25.7840	0.871658
$876$	26.7150	0.902615
$877$	−38.9840	−1.31639	−0.658197	−	0.752845i	$-0.728681\pi$
$877$	−38.9840	−1.31639	−0.658197	+	0.752845i	$0.728681\pi$
$878$	4.86553	0.164204
$879$	59.7800	2.01633
$880$	−12.8900	−0.434521
$881$	−48.4968	−1.63390	−0.816949	−	0.576709i	$-0.804337\pi$
$881$	−48.4968	−1.63390	−0.816949	+	0.576709i	$0.804337\pi$
$882$	−20.2695	−0.682509
$883$	−43.2022	−1.45387	−0.726935	−	0.686707i	$-0.759056\pi$
$883$	−43.2022	−1.45387	−0.726935	+	0.686707i	$0.759056\pi$
$884$	−2.58013	−0.0867791
$885$	23.5207	0.790641
$886$	64.7792	2.17630
$887$	1.97748	0.0663972	0.0331986	−	0.999449i	$-0.489431\pi$
$887$	1.97748	0.0663972	0.0331986	+	0.999449i	$0.489431\pi$
$888$	20.0300	0.672163
$889$	46.3160	1.55339
$890$	−9.44271	−0.316520
$891$	9.22319	0.308989
$892$	2.33751	0.0782656
$893$	−25.6469	−0.858242
$894$	−15.8498	−0.530098
$895$	22.1050	0.738890
$896$	37.8661	1.26502
$897$	68.0957	2.27365
$898$	2.79293	0.0932013
$899$	7.78158	0.259530
$900$	9.17522	0.305841
$901$	3.29387	0.109735
$902$	5.82318	0.193891
$903$	8.99771	0.299425
$904$	22.3128	0.742114
$905$	−44.3889	−1.47554
$906$	−9.65985	−0.320927
$907$	−47.8605	−1.58918	−0.794590	−	0.607146i	$-0.792314\pi$
$907$	−47.8605	−1.58918	−0.794590	+	0.607146i	$0.792314\pi$
$908$	6.38775	0.211985
$909$	−59.1599	−1.96221
$910$	37.2515	1.23487
$911$	18.5057	0.613122	0.306561	−	0.951851i	$-0.400822\pi$
$911$	18.5057	0.613122	0.306561	+	0.951851i	$0.400822\pi$
$912$	67.9260	2.24925
$913$	−0.743214	−0.0245968
$914$	11.8855	0.393137
$915$	57.0115	1.88474
$916$	6.97098	0.230328
$917$	−8.99225	−0.296950
$918$	15.5122	0.511979
$919$	−0.473425	−0.0156168	−0.00780842	−	0.999970i	$-0.502486\pi$
$919$	−0.473425	−0.0156168	−0.00780842	+	0.999970i	$0.502486\pi$
$920$	38.4372	1.26724
$921$	78.8403	2.59788
$922$	2.28555	0.0752706
$923$	−4.91755	−0.161863
$924$	−8.22687	−0.270644
$925$	5.99201	0.197016
$926$	−24.8899	−0.817932
$927$	53.5866	1.76001
$928$	−9.33818	−0.306541
$929$	24.9772	0.819477	0.409738	−	0.912203i	$-0.365620\pi$
$929$	24.9772	0.819477	0.409738	+	0.912203i	$0.365620\pi$
$930$	53.1415	1.74258
$931$	−8.92529	−0.292515
$932$	−17.3051	−0.566848
$933$	10.3150	0.337699
$934$	−57.0616	−1.86711
$935$	−2.58179	−0.0844334
$936$	31.5097	1.02993
$937$	−37.5992	−1.22831	−0.614155	−	0.789185i	$-0.710503\pi$
$937$	−37.5992	−1.22831	−0.614155	+	0.789185i	$0.710503\pi$
$938$	65.8251	2.14926
$939$	50.3678	1.64369
$940$	13.3682	0.436022
$941$	−50.1251	−1.63403	−0.817016	−	0.576615i	$-0.804373\pi$
$941$	−50.1251	−1.63403	−0.817016	+	0.576615i	$0.804373\pi$
$942$	−71.2308	−2.32082
$943$	−27.4003	−0.892275
$944$	−15.1407	−0.492787
$945$	−70.2650	−2.28572
$946$	1.70714	0.0555039
$947$	−4.46578	−0.145118	−0.0725592	−	0.997364i	$-0.523117\pi$
$947$	−4.46578	−0.145118	−0.0725592	+	0.997364i	$0.523117\pi$
$948$	27.8914	0.905869
$949$	27.4456	0.890923
$950$	12.8775	0.417802
$951$	15.6410	0.507196
$952$	5.55114	0.179914
$953$	−25.1351	−0.814206	−0.407103	−	0.913382i	$-0.633461\pi$
$953$	−25.1351	−0.814206	−0.407103	+	0.913382i	$0.633461\pi$
$954$	33.8777	1.09683
$955$	−44.8086	−1.44997
$956$	1.80859	0.0584940
$957$	−5.82449	−0.188279
$958$	9.06055	0.292733
$959$	15.1047	0.487756
$960$	13.6743	0.441337
$961$	−14.8915	−0.480372
$962$	−17.3302	−0.558750
$963$	117.274	3.77911
$964$	4.71516	0.151865
$965$	−16.0385	−0.516296
$966$	123.386	3.96987
$967$	26.5789	0.854720	0.427360	−	0.904082i	$-0.359444\pi$
$967$	26.5789	0.854720	0.427360	+	0.904082i	$0.359444\pi$
$968$	1.85339	0.0595703
$969$	13.6052	0.437061
$970$	−32.8017	−1.05320
$971$	−12.3495	−0.396314	−0.198157	−	0.980170i	$-0.563496\pi$
$971$	−12.3495	−0.396314	−0.198157	+	0.980170i	$0.563496\pi$
$972$	0.409261	0.0131270
$973$	−19.2272	−0.616396
$974$	56.1555	1.79934
$975$	14.1199	0.452199
$976$	−36.6992	−1.17471
$977$	−0.773179	−0.0247362	−0.0123681	−	0.999924i	$-0.503937\pi$
$977$	−0.773179	−0.0247362	−0.0123681	+	0.999924i	$0.503937\pi$
$978$	−90.6867	−2.89984
$979$	2.14243	0.0684724
$980$	4.65220	0.148609
$981$	56.1030	1.79123
$982$	3.32613	0.106141
$983$	44.2292	1.41069	0.705347	−	0.708863i	$-0.250791\pi$
$983$	44.2292	1.41069	0.705347	+	0.708863i	$0.250791\pi$
$984$	−18.9922	−0.605449
$985$	6.62287	0.211022
$986$	−3.30986	−0.105407
$987$	−50.9543	−1.62189
$988$	−11.6850	−0.371749
$989$	−8.03274	−0.255426
$990$	−26.5538	−0.843936
$991$	41.3435	1.31332	0.656659	−	0.754187i	$-0.271969\pi$
$991$	41.3435	1.31332	0.656659	+	0.754187i	$0.271969\pi$
$992$	−19.3307	−0.613752
$993$	−0.793386	−0.0251774
$994$	−8.91033	−0.282619
$995$	−37.9201	−1.20215
$996$	−2.04143	−0.0646851
$997$	−7.19869	−0.227985	−0.113992	−	0.993482i	$-0.536364\pi$
$997$	−7.19869	−0.227985	−0.113992	+	0.993482i	$0.536364\pi$
$998$	−43.4631	−1.37580
$999$	32.6889	1.03423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.18	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.18	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} +O(q^{10})\)	\(q-1.70714 q^{2} +3.00412 q^{3} +0.914329 q^{4} +2.58179 q^{5} -5.12845 q^{6} -2.99512 q^{7} +1.85339 q^{8} +6.02473 q^{9} -4.40747 q^{10} +1.00000 q^{11} +2.74675 q^{12} +2.82188 q^{13} +5.11310 q^{14} +7.75599 q^{15} -4.99266 q^{16} -1.00000 q^{17} -10.2851 q^{18} -4.52884 q^{19} +2.36060 q^{20} -8.99771 q^{21} -1.70714 q^{22} +8.03274 q^{23} +5.56781 q^{24} +1.66562 q^{25} -4.81735 q^{26} +9.08665 q^{27} -2.73853 q^{28} -1.93883 q^{29} -13.2406 q^{30} -4.01354 q^{31} +4.81639 q^{32} +3.00412 q^{33} +1.70714 q^{34} -7.73277 q^{35} +5.50859 q^{36} +3.59747 q^{37} +7.73136 q^{38} +8.47727 q^{39} +4.78506 q^{40} -3.41107 q^{41} +15.3604 q^{42} -1.00000 q^{43} +0.914329 q^{44} +15.5546 q^{45} -13.7130 q^{46} +5.66303 q^{47} -14.9985 q^{48} +1.97077 q^{49} -2.84345 q^{50} -3.00412 q^{51} +2.58013 q^{52} -3.29387 q^{53} -15.5122 q^{54} +2.58179 q^{55} -5.55114 q^{56} -13.6052 q^{57} +3.30986 q^{58} +3.03259 q^{59} +7.09153 q^{60} +7.35064 q^{61} +6.85167 q^{62} -18.0448 q^{63} +1.76307 q^{64} +7.28549 q^{65} -5.12845 q^{66} +12.8738 q^{67} -0.914329 q^{68} +24.1313 q^{69} +13.2009 q^{70} -1.74265 q^{71} +11.1662 q^{72} +9.72601 q^{73} -6.14138 q^{74} +5.00372 q^{75} -4.14085 q^{76} -2.99512 q^{77} -14.4719 q^{78} +10.1543 q^{79} -12.8900 q^{80} +9.22319 q^{81} +5.82318 q^{82} -0.743214 q^{83} -8.22687 q^{84} -2.58179 q^{85} +1.70714 q^{86} -5.82449 q^{87} +1.85339 q^{88} +2.14243 q^{89} -26.5538 q^{90} -8.45189 q^{91} +7.34457 q^{92} -12.0571 q^{93} -9.66759 q^{94} -11.6925 q^{95} +14.4690 q^{96} +7.44229 q^{97} -3.36438 q^{98} +6.02473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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