LMFDB - Embedded newform 983.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$0$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79902 q^{2} -1.37741 q^{3} +5.83449 q^{4} -1.52700 q^{5} +3.85540 q^{6} +4.50391 q^{7} -10.7328 q^{8} -1.10273 q^{9} +O(q^{10})$	\(q-2.79902 q^{2} -1.37741 q^{3} +5.83449 q^{4} -1.52700 q^{5} +3.85540 q^{6} +4.50391 q^{7} -10.7328 q^{8} -1.10273 q^{9} +4.27409 q^{10} -1.30593 q^{11} -8.03651 q^{12} -1.85242 q^{13} -12.6065 q^{14} +2.10331 q^{15} +18.3723 q^{16} +8.03336 q^{17} +3.08657 q^{18} +2.29452 q^{19} -8.90925 q^{20} -6.20374 q^{21} +3.65531 q^{22} +2.02125 q^{23} +14.7835 q^{24} -2.66828 q^{25} +5.18495 q^{26} +5.65116 q^{27} +26.2780 q^{28} -3.32591 q^{29} -5.88719 q^{30} -5.30862 q^{31} -29.9588 q^{32} +1.79880 q^{33} -22.4855 q^{34} -6.87745 q^{35} -6.43388 q^{36} -2.11110 q^{37} -6.42239 q^{38} +2.55155 q^{39} +16.3890 q^{40} -2.33673 q^{41} +17.3644 q^{42} -2.47526 q^{43} -7.61943 q^{44} +1.68387 q^{45} -5.65752 q^{46} +9.20445 q^{47} -25.3063 q^{48} +13.2852 q^{49} +7.46856 q^{50} -11.0653 q^{51} -10.8079 q^{52} -10.8871 q^{53} -15.8177 q^{54} +1.99415 q^{55} -48.3396 q^{56} -3.16050 q^{57} +9.30927 q^{58} +9.66147 q^{59} +12.2717 q^{60} -5.60130 q^{61} +14.8589 q^{62} -4.96660 q^{63} +47.1106 q^{64} +2.82864 q^{65} -5.03488 q^{66} +9.62480 q^{67} +46.8706 q^{68} -2.78410 q^{69} +19.2501 q^{70} -10.8910 q^{71} +11.8354 q^{72} +7.26176 q^{73} +5.90901 q^{74} +3.67533 q^{75} +13.3873 q^{76} -5.88178 q^{77} -7.14182 q^{78} +2.19748 q^{79} -28.0545 q^{80} -4.47579 q^{81} +6.54054 q^{82} +3.37238 q^{83} -36.1957 q^{84} -12.2669 q^{85} +6.92830 q^{86} +4.58115 q^{87} +14.0163 q^{88} +12.5738 q^{89} -4.71317 q^{90} -8.34312 q^{91} +11.7930 q^{92} +7.31217 q^{93} -25.7634 q^{94} -3.50372 q^{95} +41.2657 q^{96} +4.00627 q^{97} -37.1854 q^{98} +1.44009 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) $ 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * 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 $

$2$	−2.79902	−1.97920	−0.989602	−	0.143834i	$-0.954057\pi$
$2$	−2.79902	−1.97920	−0.989602	+	0.143834i	$0.954057\pi$
$3$	−1.37741	−0.795250	−0.397625	−	0.917548i	$-0.630166\pi$
$3$	−1.37741	−0.795250	−0.397625	+	0.917548i	$0.630166\pi$
$4$	5.83449	2.91725
$5$	−1.52700	−0.682894	−0.341447	−	0.939901i	$-0.610917\pi$
$5$	−1.52700	−0.682894	−0.341447	+	0.939901i	$0.610917\pi$
$6$	3.85540	1.57396
$7$	4.50391	1.70232	0.851158	−	0.524909i	$-0.175901\pi$
$7$	4.50391	1.70232	0.851158	+	0.524909i	$0.175901\pi$
$8$	−10.7328	−3.79462
$9$	−1.10273	−0.367577
$10$	4.27409	1.35159
$11$	−1.30593	−0.393752	−0.196876	−	0.980428i	$-0.563080\pi$
$11$	−1.30593	−0.393752	−0.196876	+	0.980428i	$0.563080\pi$
$12$	−8.03651	−2.31994
$13$	−1.85242	−0.513769	−0.256884	−	0.966442i	$-0.582696\pi$
$13$	−1.85242	−0.513769	−0.256884	+	0.966442i	$0.582696\pi$
$14$	−12.6065	−3.36923
$15$	2.10331	0.543071
$16$	18.3723	4.59308
$17$	8.03336	1.94838	0.974189	−	0.225736i	$-0.0724787\pi$
$17$	8.03336	1.94838	0.974189	+	0.225736i	$0.0724787\pi$
$18$	3.08657	0.727510
$19$	2.29452	0.526398	0.263199	−	0.964742i	$-0.415222\pi$
$19$	2.29452	0.526398	0.263199	+	0.964742i	$0.415222\pi$
$20$	−8.90925	−1.99217
$21$	−6.20374	−1.35377
$22$	3.65531	0.779315
$23$	2.02125	0.421460	0.210730	−	0.977544i	$-0.432416\pi$
$23$	2.02125	0.421460	0.210730	+	0.977544i	$0.432416\pi$
$24$	14.7835	3.01767
$25$	−2.66828	−0.533656
$26$	5.18495	1.01685
$27$	5.65116	1.08757
$28$	26.2780	4.96608
$29$	−3.32591	−0.617605	−0.308803	−	0.951126i	$-0.599928\pi$
$29$	−3.32591	−0.617605	−0.308803	+	0.951126i	$0.599928\pi$
$30$	−5.88719	−1.07485
$31$	−5.30862	−0.953457	−0.476728	−	0.879051i	$-0.658177\pi$
$31$	−5.30862	−0.953457	−0.476728	+	0.879051i	$0.658177\pi$
$32$	−29.9588	−5.29603
$33$	1.79880	0.313131
$34$	−22.4855	−3.85623
$35$	−6.87745	−1.16250
$36$	−6.43388	−1.07231
$37$	−2.11110	−0.347063	−0.173532	−	0.984828i	$-0.555518\pi$
$37$	−2.11110	−0.347063	−0.173532	+	0.984828i	$0.555518\pi$
$38$	−6.42239	−1.04185
$39$	2.55155	0.408575
$40$	16.3890	2.59132
$41$	−2.33673	−0.364935	−0.182468	−	0.983212i	$-0.558409\pi$
$41$	−2.33673	−0.364935	−0.182468	+	0.983212i	$0.558409\pi$
$42$	17.3644	2.67938
$43$	−2.47526	−0.377474	−0.188737	−	0.982028i	$-0.560439\pi$
$43$	−2.47526	−0.377474	−0.188737	+	0.982028i	$0.560439\pi$
$44$	−7.61943	−1.14867
$45$	1.68387	0.251016
$46$	−5.65752	−0.834156
$47$	9.20445	1.34261	0.671303	−	0.741183i	$-0.265735\pi$
$47$	9.20445	1.34261	0.671303	+	0.741183i	$0.265735\pi$
$48$	−25.3063	−3.65265
$49$	13.2852	1.89788
$50$	7.46856	1.05621
$51$	−11.0653	−1.54945
$52$	−10.8079	−1.49879
$53$	−10.8871	−1.49546	−0.747728	−	0.664005i	$-0.768855\pi$
$53$	−10.8871	−1.49546	−0.747728	+	0.664005i	$0.768855\pi$
$54$	−15.8177	−2.15251
$55$	1.99415	0.268891
$56$	−48.3396	−6.45965
$57$	−3.16050	−0.418618
$58$	9.30927	1.22237
$59$	9.66147	1.25782	0.628908	−	0.777480i	$-0.283502\pi$
$59$	9.66147	1.25782	0.628908	+	0.777480i	$0.283502\pi$
$60$	12.2717	1.58427
$61$	−5.60130	−0.717173	−0.358587	−	0.933496i	$-0.616741\pi$
$61$	−5.60130	−0.717173	−0.358587	+	0.933496i	$0.616741\pi$
$62$	14.8589	1.88708
$63$	−4.96660	−0.625733
$64$	47.1106	5.88883
$65$	2.82864	0.350849
$66$	−5.03488	−0.619751
$67$	9.62480	1.17586	0.587929	−	0.808913i	$-0.299944\pi$
$67$	9.62480	1.17586	0.587929	+	0.808913i	$0.299944\pi$
$68$	46.8706	5.68390
$69$	−2.78410	−0.335166
$70$	19.2501	2.30083
$71$	−10.8910	−1.29252	−0.646259	−	0.763118i	$-0.723668\pi$
$71$	−10.8910	−1.29252	−0.646259	+	0.763118i	$0.723668\pi$
$72$	11.8354	1.39482
$73$	7.26176	0.849924	0.424962	−	0.905211i	$-0.360287\pi$
$73$	7.26176	0.849924	0.424962	+	0.905211i	$0.360287\pi$
$74$	5.90901	0.686908
$75$	3.67533	0.424390
$76$	13.3873	1.53563
$77$	−5.88178	−0.670291
$78$	−7.14182	−0.808652
$79$	2.19748	0.247235	0.123618	−	0.992330i	$-0.460550\pi$
$79$	2.19748	0.247235	0.123618	+	0.992330i	$0.460550\pi$
$80$	−28.0545	−3.13659
$81$	−4.47579	−0.497310
$82$	6.54054	0.722282
$83$	3.37238	0.370167	0.185083	−	0.982723i	$-0.440744\pi$
$83$	3.37238	0.370167	0.185083	+	0.982723i	$0.440744\pi$
$84$	−36.1957	−3.94927
$85$	−12.2669	−1.33053
$86$	6.92830	0.747098
$87$	4.58115	0.491151
$88$	14.0163	1.49414
$89$	12.5738	1.33282	0.666409	−	0.745586i	$-0.267830\pi$
$89$	12.5738	1.33282	0.666409	+	0.745586i	$0.267830\pi$
$90$	−4.71317	−0.496812
$91$	−8.34312	−0.874597
$92$	11.7930	1.22950
$93$	7.31217	0.758236
$94$	−25.7634	−2.65729
$95$	−3.50372	−0.359474
$96$	41.2657	4.21166
$97$	4.00627	0.406775	0.203388	−	0.979098i	$-0.434805\pi$
$97$	4.00627	0.406775	0.203388	+	0.979098i	$0.434805\pi$
$98$	−37.1854	−3.75630
$99$	1.44009	0.144734
$100$	−15.5681	−1.55681
$101$	−3.25395	−0.323780	−0.161890	−	0.986809i	$-0.551759\pi$
$101$	−3.25395	−0.323780	−0.161890	+	0.986809i	$0.551759\pi$
$102$	30.9719	3.06667
$103$	9.05996	0.892704	0.446352	−	0.894857i	$-0.352723\pi$
$103$	9.05996	0.892704	0.446352	+	0.894857i	$0.352723\pi$
$104$	19.8817	1.94956
$105$	9.47309	0.924479
$106$	30.4731	2.95981
$107$	2.29204	0.221580	0.110790	−	0.993844i	$-0.464662\pi$
$107$	2.29204	0.221580	0.110790	+	0.993844i	$0.464662\pi$
$108$	32.9717	3.17270
$109$	−0.454463	−0.0435296	−0.0217648	−	0.999763i	$-0.506929\pi$
$109$	−0.454463	−0.0435296	−0.0217648	+	0.999763i	$0.506929\pi$
$110$	−5.58165	−0.532189
$111$	2.90786	0.276002
$112$	82.7473	7.81888
$113$	15.7957	1.48593	0.742966	−	0.669330i	$-0.233419\pi$
$113$	15.7957	1.48593	0.742966	+	0.669330i	$0.233419\pi$
$114$	8.84628	0.828530
$115$	−3.08645	−0.287813
$116$	−19.4050	−1.80171
$117$	2.04272	0.188850
$118$	−27.0426	−2.48947
$119$	36.1815	3.31675
$120$	−22.5744	−2.06075
$121$	−9.29455	−0.844959
$122$	15.6781	1.41943
$123$	3.21864	0.290215
$124$	−30.9731	−2.78147
$125$	11.7094	1.04732
$126$	13.9016	1.23845
$127$	−4.50072	−0.399375	−0.199687	−	0.979860i	$-0.563993\pi$
$127$	−4.50072	−0.399375	−0.199687	+	0.979860i	$0.563993\pi$
$128$	−71.9458	−6.35917
$129$	3.40946	0.300186
$130$	−7.91740	−0.694402
$131$	10.9250	0.954519	0.477259	−	0.878762i	$-0.341630\pi$
$131$	10.9250	0.954519	0.477259	+	0.878762i	$0.341630\pi$
$132$	10.4951	0.913481
$133$	10.3343	0.896096
$134$	−26.9400	−2.32726
$135$	−8.62930	−0.742692
$136$	−86.2206	−7.39336
$137$	22.7391	1.94274	0.971368	−	0.237579i	$-0.0763538\pi$
$137$	22.7391	1.94274	0.971368	+	0.237579i	$0.0763538\pi$
$138$	7.79275	0.663363
$139$	−1.54242	−0.130827	−0.0654133	−	0.997858i	$-0.520837\pi$
$139$	−1.54242	−0.130827	−0.0654133	+	0.997858i	$0.520837\pi$
$140$	−40.1264	−3.39130
$141$	−12.6783	−1.06771
$142$	30.4840	2.55816
$143$	2.41913	0.202297
$144$	−20.2598	−1.68831
$145$	5.07865	0.421759
$146$	−20.3258	−1.68217
$147$	−18.2992	−1.50929
$148$	−12.3172	−1.01247
$149$	12.5265	1.02621	0.513105	−	0.858326i	$-0.328495\pi$
$149$	12.5265	1.02621	0.513105	+	0.858326i	$0.328495\pi$
$150$	−10.2873	−0.839955
$151$	2.15158	0.175093	0.0875465	−	0.996160i	$-0.472097\pi$
$151$	2.15158	0.175093	0.0875465	+	0.996160i	$0.472097\pi$
$152$	−24.6266	−1.99748
$153$	−8.85865	−0.716179
$154$	16.4632	1.32664
$155$	8.10625	0.651109
$156$	14.8870	1.19191
$157$	−3.23073	−0.257840	−0.128920	−	0.991655i	$-0.541151\pi$
$157$	−3.23073	−0.257840	−0.128920	+	0.991655i	$0.541151\pi$
$158$	−6.15077	−0.489329
$159$	14.9960	1.18926
$160$	45.7470	3.61662
$161$	9.10354	0.717459
$162$	12.5278	0.984277
$163$	14.1928	1.11166	0.555832	−	0.831295i	$-0.312400\pi$
$163$	14.1928	1.11166	0.555832	+	0.831295i	$0.312400\pi$
$164$	−13.6336	−1.06461
$165$	−2.74676	−0.213835
$166$	−9.43935	−0.732636
$167$	25.4820	1.97186	0.985929	−	0.167166i	$-0.0534614\pi$
$167$	25.4820	1.97186	0.985929	+	0.167166i	$0.0534614\pi$
$168$	66.5836	5.13704
$169$	−9.56854	−0.736042
$170$	34.3353	2.63340
$171$	−2.53024	−0.193492
$172$	−14.4419	−1.10118
$173$	−0.585351	−0.0445034	−0.0222517	−	0.999752i	$-0.507084\pi$
$173$	−0.585351	−0.0445034	−0.0222517	+	0.999752i	$0.507084\pi$
$174$	−12.8227	−0.972087
$175$	−12.0177	−0.908452
$176$	−23.9929	−1.80854
$177$	−13.3078	−1.00028
$178$	−35.1942	−2.63792
$179$	−18.5478	−1.38633	−0.693164	−	0.720779i	$-0.743784\pi$
$179$	−18.5478	−1.38633	−0.693164	+	0.720779i	$0.743784\pi$
$180$	9.82452	0.732276
$181$	21.3204	1.58473	0.792367	−	0.610044i	$-0.208848\pi$
$181$	21.3204	1.58473	0.792367	+	0.610044i	$0.208848\pi$
$182$	23.3525	1.73101
$183$	7.71531	0.570332
$184$	−21.6937	−1.59928
$185$	3.22365	0.237007
$186$	−20.4669	−1.50070
$187$	−10.4910	−0.767177
$188$	53.7033	3.91672
$189$	25.4523	1.85138
$190$	9.80696	0.711472
$191$	−12.6802	−0.917504	−0.458752	−	0.888564i	$-0.651703\pi$
$191$	−12.6802	−0.917504	−0.458752	+	0.888564i	$0.651703\pi$
$192$	−64.8908	−4.68309
$193$	8.11720	0.584289	0.292144	−	0.956374i	$-0.405631\pi$
$193$	8.11720	0.584289	0.292144	+	0.956374i	$0.405631\pi$
$194$	−11.2136	−0.805091
$195$	−3.89620	−0.279013
$196$	77.5123	5.53659
$197$	18.3776	1.30935	0.654674	−	0.755911i	$-0.272806\pi$
$197$	18.3776	1.30935	0.654674	+	0.755911i	$0.272806\pi$
$198$	−4.03083	−0.286459
$199$	−5.51891	−0.391225	−0.195612	−	0.980681i	$-0.562669\pi$
$199$	−5.51891	−0.391225	−0.195612	+	0.980681i	$0.562669\pi$
$200$	28.6382	2.02502
$201$	−13.2573	−0.935100
$202$	9.10785	0.640826
$203$	−14.9796	−1.05136
$204$	−64.5602	−4.52012
$205$	3.56817	0.249212
$206$	−25.3590	−1.76684
$207$	−2.22890	−0.154919
$208$	−34.0333	−2.35978
$209$	−2.99647	−0.207270
$210$	−26.5153	−1.82973
$211$	21.0288	1.44768	0.723840	−	0.689968i	$-0.242376\pi$
$211$	21.0288	1.44768	0.723840	+	0.689968i	$0.242376\pi$
$212$	−63.5206	−4.36261
$213$	15.0014	1.02788
$214$	−6.41545	−0.438551
$215$	3.77972	0.257775
$216$	−60.6528	−4.12690
$217$	−23.9095	−1.62309
$218$	1.27205	0.0861540
$219$	−10.0024	−0.675902
$220$	11.6348	0.784421
$221$	−14.8812	−1.00102
$222$	−8.13915	−0.546264
$223$	15.2177	1.01905	0.509527	−	0.860454i	$-0.329820\pi$
$223$	15.2177	1.01905	0.509527	+	0.860454i	$0.329820\pi$
$224$	−134.932	−9.01551
$225$	2.94240	0.196160
$226$	−44.2123	−2.94096
$227$	−25.3139	−1.68014	−0.840072	−	0.542475i	$-0.817487\pi$
$227$	−25.3139	−1.68014	−0.840072	+	0.542475i	$0.817487\pi$
$228$	−18.4399	−1.22121
$229$	4.65764	0.307786	0.153893	−	0.988088i	$-0.450819\pi$
$229$	4.65764	0.307786	0.153893	+	0.988088i	$0.450819\pi$
$230$	8.63902	0.569640
$231$	8.10164	0.533049
$232$	35.6963	2.34358
$233$	21.8394	1.43074	0.715372	−	0.698744i	$-0.246257\pi$
$233$	21.8394	1.43074	0.715372	+	0.698744i	$0.246257\pi$
$234$	−5.71761	−0.373772
$235$	−14.0552	−0.916858
$236$	56.3698	3.66936
$237$	−3.02683	−0.196614
$238$	−101.273	−6.56453
$239$	−26.5706	−1.71871	−0.859353	−	0.511382i	$-0.829134\pi$
$239$	−26.5706	−1.71871	−0.859353	+	0.511382i	$0.829134\pi$
$240$	38.6426	2.49437
$241$	−6.78378	−0.436982	−0.218491	−	0.975839i	$-0.570113\pi$
$241$	−6.78378	−0.436982	−0.218491	+	0.975839i	$0.570113\pi$
$242$	26.0156	1.67235
$243$	−10.7885	−0.692080
$244$	−32.6808	−2.09217
$245$	−20.2864	−1.29605
$246$	−9.00902	−0.574394
$247$	−4.25040	−0.270447
$248$	56.9764	3.61801
$249$	−4.64516	−0.294375
$250$	−32.7749	−2.07287
$251$	25.4061	1.60362	0.801808	−	0.597582i	$-0.203872\pi$
$251$	25.4061	1.60362	0.801808	+	0.597582i	$0.203872\pi$
$252$	−28.9776	−1.82542
$253$	−2.63961	−0.165951
$254$	12.5976	0.790444
$255$	16.8966	1.05811
$256$	107.156	6.69726
$257$	−5.58112	−0.348141	−0.174071	−	0.984733i	$-0.555692\pi$
$257$	−5.58112	−0.348141	−0.174071	+	0.984733i	$0.555692\pi$
$258$	−9.54313	−0.594130
$259$	−9.50821	−0.590811
$260$	16.5037	1.02351
$261$	3.66758	0.227018
$262$	−30.5792	−1.88919
$263$	−3.24635	−0.200179	−0.100089	−	0.994978i	$-0.531913\pi$
$263$	−3.24635	−0.200179	−0.100089	+	0.994978i	$0.531913\pi$
$264$	−19.3062	−1.18822
$265$	16.6245	1.02124
$266$	−28.9258	−1.77356
$267$	−17.3193	−1.05992
$268$	56.1559	3.43027
$269$	−17.2729	−1.05315	−0.526574	−	0.850129i	$-0.676524\pi$
$269$	−17.2729	−1.05315	−0.526574	+	0.850129i	$0.676524\pi$
$270$	24.1536	1.46994
$271$	−0.359838	−0.0218586	−0.0109293	−	0.999940i	$-0.503479\pi$
$271$	−0.359838	−0.0218586	−0.0109293	+	0.999940i	$0.503479\pi$
$272$	147.592	8.94906
$273$	11.4919	0.695523
$274$	−63.6473	−3.84507
$275$	3.48458	0.210128
$276$	−16.2438	−0.977763
$277$	1.34422	0.0807662	0.0403831	−	0.999184i	$-0.487142\pi$
$277$	1.34422	0.0807662	0.0403831	+	0.999184i	$0.487142\pi$
$278$	4.31726	0.258932
$279$	5.85399	0.350469
$280$	73.8144	4.41125
$281$	11.7062	0.698330	0.349165	−	0.937061i	$-0.386465\pi$
$281$	11.7062	0.698330	0.349165	+	0.937061i	$0.386465\pi$
$282$	35.4869	2.11321
$283$	−29.4200	−1.74884	−0.874419	−	0.485172i	$-0.838757\pi$
$283$	−29.4200	−1.74884	−0.874419	+	0.485172i	$0.838757\pi$
$284$	−63.5432	−3.77060
$285$	4.82607	0.285872
$286$	−6.77117	−0.400388
$287$	−10.5244	−0.621236
$288$	33.0366	1.94670
$289$	47.5349	2.79617
$290$	−14.2152	−0.834747
$291$	−5.51830	−0.323488
$292$	42.3687	2.47944
$293$	−23.9768	−1.40074	−0.700370	−	0.713780i	$-0.746982\pi$
$293$	−23.9768	−1.40074	−0.700370	+	0.713780i	$0.746982\pi$
$294$	51.2197	2.98719
$295$	−14.7530	−0.858954
$296$	22.6581	1.31697
$297$	−7.38000	−0.428231
$298$	−35.0618	−2.03108
$299$	−3.74421	−0.216533
$300$	21.4437	1.23805
$301$	−11.1483	−0.642580
$302$	−6.02231	−0.346545
$303$	4.48203	0.257486
$304$	42.1556	2.41779
$305$	8.55317	0.489753
$306$	24.7955	1.41746
$307$	10.3336	0.589769	0.294884	−	0.955533i	$-0.404719\pi$
$307$	10.3336	0.589769	0.294884	+	0.955533i	$0.404719\pi$
$308$	−34.3172	−1.95540
$309$	−12.4793	−0.709923
$310$	−22.6895	−1.28868
$311$	15.2586	0.865233	0.432617	−	0.901578i	$-0.357590\pi$
$311$	15.2586	0.865233	0.432617	+	0.901578i	$0.357590\pi$
$312$	−27.3853	−1.55039
$313$	−20.5826	−1.16340	−0.581700	−	0.813404i	$-0.697612\pi$
$313$	−20.5826	−1.16340	−0.581700	+	0.813404i	$0.697612\pi$
$314$	9.04287	0.510319
$315$	7.58398	0.427309
$316$	12.8212	0.721247
$317$	−2.76889	−0.155516	−0.0777582	−	0.996972i	$-0.524776\pi$
$317$	−2.76889	−0.155516	−0.0777582	+	0.996972i	$0.524776\pi$
$318$	−41.9741	−2.35379
$319$	4.34339	0.243183
$320$	−71.9378	−4.02144
$321$	−3.15708	−0.176211
$322$	−25.4809	−1.42000
$323$	18.4327	1.02562
$324$	−26.1139	−1.45077
$325$	4.94278	0.274176
$326$	−39.7258	−2.20021
$327$	0.625983	0.0346169
$328$	25.0797	1.38479
$329$	41.4560	2.28554
$330$	7.68824	0.423224
$331$	29.6949	1.63218	0.816091	−	0.577924i	$-0.196137\pi$
$331$	29.6949	1.63218	0.816091	+	0.577924i	$0.196137\pi$
$332$	19.6761	1.07987
$333$	2.32798	0.127572
$334$	−71.3246	−3.90271
$335$	−14.6970	−0.802985
$336$	−113.977	−6.21797
$337$	29.4015	1.60160	0.800802	−	0.598929i	$-0.204407\pi$
$337$	29.4015	1.60160	0.800802	+	0.598929i	$0.204407\pi$
$338$	26.7825	1.45678
$339$	−21.7572	−1.18169
$340$	−71.5713	−3.88150
$341$	6.93268	0.375425
$342$	7.08217	0.382960
$343$	28.3079	1.52848
$344$	26.5665	1.43237
$345$	4.25131	0.228883
$346$	1.63841	0.0880814
$347$	3.61741	0.194193	0.0970964	−	0.995275i	$-0.469044\pi$
$347$	3.61741	0.194193	0.0970964	+	0.995275i	$0.469044\pi$
$348$	26.7287	1.43281
$349$	−20.8918	−1.11831	−0.559157	−	0.829062i	$-0.688875\pi$
$349$	−20.8918	−1.11831	−0.559157	+	0.829062i	$0.688875\pi$
$350$	33.6377	1.79801
$351$	−10.4683	−0.558757
$352$	39.1241	2.08532
$353$	1.10234	0.0586716	0.0293358	−	0.999570i	$-0.490661\pi$
$353$	1.10234	0.0586716	0.0293358	+	0.999570i	$0.490661\pi$
$354$	37.2489	1.97975
$355$	16.6305	0.882653
$356$	73.3617	3.88816
$357$	−49.8369	−2.63765
$358$	51.9156	2.74383
$359$	30.0597	1.58649	0.793245	−	0.608902i	$-0.208390\pi$
$359$	30.0597	1.58649	0.793245	+	0.608902i	$0.208390\pi$
$360$	−18.0726	−0.952512
$361$	−13.7352	−0.722905
$362$	−59.6762	−3.13651
$363$	12.8024	0.671954
$364$	−48.6779	−2.55142
$365$	−11.0887	−0.580408
$366$	−21.5953	−1.12880
$367$	−10.8475	−0.566234	−0.283117	−	0.959085i	$-0.591368\pi$
$367$	−10.8475	−0.566234	−0.283117	+	0.959085i	$0.591368\pi$
$368$	37.1351	1.93580
$369$	2.57678	0.134142
$370$	−9.02304	−0.469085
$371$	−49.0344	−2.54574
$372$	42.6628	2.21196
$373$	19.5805	1.01384	0.506920	−	0.861993i	$-0.330784\pi$
$373$	19.5805	1.01384	0.506920	+	0.861993i	$0.330784\pi$
$374$	29.3645	1.51840
$375$	−16.1287	−0.832885
$376$	−98.7896	−5.09469
$377$	6.16097	0.317306
$378$	−71.2414	−3.66426
$379$	−5.26680	−0.270537	−0.135269	−	0.990809i	$-0.543190\pi$
$379$	−5.26680	−0.270537	−0.135269	+	0.990809i	$0.543190\pi$
$380$	−20.4424	−1.04867
$381$	6.19936	0.317603
$382$	35.4920	1.81593
$383$	−36.6002	−1.87019	−0.935093	−	0.354403i	$-0.884684\pi$
$383$	−36.6002	−1.87019	−0.935093	+	0.354403i	$0.884684\pi$
$384$	99.0991	5.05713
$385$	8.98145	0.457737
$386$	−22.7202	−1.15643
$387$	2.72955	0.138751
$388$	23.3746	1.18666
$389$	34.5320	1.75084	0.875422	−	0.483359i	$-0.160583\pi$
$389$	34.5320	1.75084	0.875422	+	0.483359i	$0.160583\pi$
$390$	10.9055	0.552223
$391$	16.2375	0.821164
$392$	−142.587	−7.20175
$393$	−15.0482	−0.759081
$394$	−51.4391	−2.59147
$395$	−3.35554	−0.168835
$396$	8.40219	0.422226
$397$	4.13514	0.207536	0.103768	−	0.994602i	$-0.466910\pi$
$397$	4.13514	0.207536	0.103768	+	0.994602i	$0.466910\pi$
$398$	15.4475	0.774314
$399$	−14.2346	−0.712620
$400$	−49.0226	−2.45113
$401$	1.54729	0.0772682	0.0386341	−	0.999253i	$-0.487699\pi$
$401$	1.54729	0.0772682	0.0386341	+	0.999253i	$0.487699\pi$
$402$	37.1075	1.85075
$403$	9.83379	0.489856
$404$	−18.9851	−0.944546
$405$	6.83451	0.339610
$406$	41.9281	2.08086
$407$	2.75695	0.136657
$408$	118.761	5.87957
$409$	9.63604	0.476472	0.238236	−	0.971207i	$-0.423431\pi$
$409$	9.63604	0.476472	0.238236	+	0.971207i	$0.423431\pi$
$410$	−9.98738	−0.493241
$411$	−31.3212	−1.54496
$412$	52.8603	2.60424
$413$	43.5144	2.14120
$414$	6.23873	0.306617
$415$	−5.14961	−0.252785
$416$	55.4963	2.72093
$417$	2.12455	0.104040
$418$	8.38717	0.410230
$419$	−22.6237	−1.10524	−0.552619	−	0.833434i	$-0.686372\pi$
$419$	−22.6237	−1.10524	−0.552619	+	0.833434i	$0.686372\pi$
$420$	55.2707	2.69693
$421$	−5.49975	−0.268042	−0.134021	−	0.990979i	$-0.542789\pi$
$421$	−5.49975	−0.268042	−0.134021	+	0.990979i	$0.542789\pi$
$422$	−58.8598	−2.86525
$423$	−10.1500	−0.493512
$424$	116.849	5.67469
$425$	−21.4353	−1.03976
$426$	−41.9890	−2.03438
$427$	−25.2277	−1.22086
$428$	13.3729	0.646402
$429$	−3.33214	−0.160877
$430$	−10.5795	−0.510188
$431$	23.7658	1.14476	0.572378	−	0.819990i	$-0.306021\pi$
$431$	23.7658	1.14476	0.572378	+	0.819990i	$0.306021\pi$
$432$	103.825	4.99528
$433$	7.70845	0.370444	0.185222	−	0.982697i	$-0.440700\pi$
$433$	7.70845	0.370444	0.185222	+	0.982697i	$0.440700\pi$
$434$	66.9232	3.21242
$435$	−6.99540	−0.335404
$436$	−2.65156	−0.126987
$437$	4.63780	0.221856
$438$	27.9970	1.33775
$439$	37.5278	1.79110	0.895551	−	0.444959i	$-0.146782\pi$
$439$	37.5278	1.79110	0.895551	+	0.444959i	$0.146782\pi$
$440$	−21.4028	−1.02034
$441$	−14.6500	−0.697619
$442$	41.6526	1.98121
$443$	−15.1660	−0.720557	−0.360278	−	0.932845i	$-0.617318\pi$
$443$	−15.1660	−0.720557	−0.360278	+	0.932845i	$0.617318\pi$
$444$	16.9659	0.805166
$445$	−19.2001	−0.910173
$446$	−42.5947	−2.01692
$447$	−17.2541	−0.816093
$448$	212.182	10.0247
$449$	−10.3302	−0.487515	−0.243757	−	0.969836i	$-0.578380\pi$
$449$	−10.3302	−0.487515	−0.243757	+	0.969836i	$0.578380\pi$
$450$	−8.23582	−0.388241
$451$	3.05160	0.143694
$452$	92.1597	4.33483
$453$	−2.96361	−0.139243
$454$	70.8541	3.32535
$455$	12.7399	0.597257
$456$	33.9210	1.58850
$457$	−11.3674	−0.531744	−0.265872	−	0.964008i	$-0.585660\pi$
$457$	−11.3674	−0.531744	−0.265872	+	0.964008i	$0.585660\pi$
$458$	−13.0368	−0.609171
$459$	45.3978	2.11899
$460$	−18.0079	−0.839621
$461$	13.8496	0.645040	0.322520	−	0.946563i	$-0.395470\pi$
$461$	13.8496	0.645040	0.322520	+	0.946563i	$0.395470\pi$
$462$	−22.6766	−1.05501
$463$	−28.2640	−1.31354	−0.656769	−	0.754092i	$-0.728077\pi$
$463$	−28.2640	−1.31354	−0.656769	+	0.754092i	$0.728077\pi$
$464$	−61.1047	−2.83671
$465$	−11.1657	−0.517795
$466$	−61.1287	−2.83173
$467$	−36.9647	−1.71052	−0.855261	−	0.518198i	$-0.826603\pi$
$467$	−36.9647	−1.71052	−0.855261	+	0.518198i	$0.826603\pi$
$468$	11.9182	0.550921
$469$	43.3492	2.00168
$470$	39.3406	1.81465
$471$	4.45005	0.205048
$472$	−103.695	−4.77294
$473$	3.23251	0.148631
$474$	8.47216	0.389139
$475$	−6.12241	−0.280916
$476$	211.101	9.67579
$477$	12.0055	0.549696
$478$	74.3714	3.40167
$479$	−21.2570	−0.971256	−0.485628	−	0.874166i	$-0.661409\pi$
$479$	−21.2570	−0.971256	−0.485628	+	0.874166i	$0.661409\pi$
$480$	−63.0126	−2.87612
$481$	3.91065	0.178310
$482$	18.9879	0.864876
$483$	−12.5393	−0.570559
$484$	−54.2290	−2.46496
$485$	−6.11757	−0.277784
$486$	30.1971	1.36977
$487$	−27.0672	−1.22653	−0.613267	−	0.789876i	$-0.710145\pi$
$487$	−27.0672	−1.22653	−0.613267	+	0.789876i	$0.710145\pi$
$488$	60.1177	2.72140
$489$	−19.5493	−0.884051
$490$	56.7820	2.56515
$491$	−2.88867	−0.130364	−0.0651820	−	0.997873i	$-0.520763\pi$
$491$	−2.88867	−0.130364	−0.0651820	+	0.997873i	$0.520763\pi$
$492$	18.7791	0.846629
$493$	−26.7182	−1.20333
$494$	11.8970	0.535269
$495$	−2.19901	−0.0988381
$496$	−97.5318	−4.37931
$497$	−49.0519	−2.20028
$498$	13.0019	0.582629
$499$	−13.2103	−0.591376	−0.295688	−	0.955285i	$-0.595549\pi$
$499$	−13.2103	−0.591376	−0.295688	+	0.955285i	$0.595549\pi$
$500$	68.3187	3.05530
$501$	−35.0993	−1.56812
$502$	−71.1120	−3.17388
$503$	−27.3368	−1.21889	−0.609443	−	0.792830i	$-0.708607\pi$
$503$	−27.3368	−1.21889	−0.609443	+	0.792830i	$0.708607\pi$
$504$	53.3056	2.37442
$505$	4.96876	0.221107
$506$	7.38831	0.328451
$507$	13.1798	0.585337
$508$	−26.2594	−1.16507
$509$	27.3631	1.21285	0.606425	−	0.795141i	$-0.292603\pi$
$509$	27.3631	1.21285	0.606425	+	0.795141i	$0.292603\pi$
$510$	−47.2939	−2.09421
$511$	32.7063	1.44684
$512$	−156.040	−6.89607
$513$	12.9667	0.572492
$514$	15.6217	0.689042
$515$	−13.8345	−0.609622
$516$	19.8925	0.875717
$517$	−12.0203	−0.528654
$518$	26.6136	1.16934
$519$	0.806271	0.0353914
$520$	−30.3592	−1.33134
$521$	30.3181	1.32826	0.664130	−	0.747617i	$-0.268802\pi$
$521$	30.3181	1.32826	0.664130	+	0.747617i	$0.268802\pi$
$522$	−10.2656	−0.449314
$523$	−23.8459	−1.04271	−0.521354	−	0.853340i	$-0.674573\pi$
$523$	−23.8459	−1.04271	−0.521354	+	0.853340i	$0.674573\pi$
$524$	63.7417	2.78457
$525$	16.5533	0.722447
$526$	9.08659	0.396194
$527$	−42.6461	−1.85769
$528$	33.0482	1.43824
$529$	−18.9145	−0.822371
$530$	−46.5323	−2.02124
$531$	−10.6540	−0.462345
$532$	60.2953	2.61413
$533$	4.32860	0.187492
$534$	48.4770	2.09781
$535$	−3.49993	−0.151315
$536$	−103.301	−4.46193
$537$	25.5480	1.10248
$538$	48.3472	2.08439
$539$	−17.3495	−0.747295
$540$	−50.3476	−2.16662
$541$	−16.3969	−0.704958	−0.352479	−	0.935820i	$-0.614661\pi$
$541$	−16.3969	−0.704958	−0.352479	+	0.935820i	$0.614661\pi$
$542$	1.00719	0.0432626
$543$	−29.3670	−1.26026
$544$	−240.670	−10.3187
$545$	0.693963	0.0297261
$546$	−32.1661	−1.37658
$547$	−12.0870	−0.516805	−0.258402	−	0.966037i	$-0.583196\pi$
$547$	−12.0870	−0.516805	−0.258402	+	0.966037i	$0.583196\pi$
$548$	132.671	5.66744
$549$	6.17673	0.263617
$550$	−9.75340	−0.415887
$551$	−7.63134	−0.325106
$552$	29.8812	1.27183
$553$	9.89723	0.420873
$554$	−3.76249	−0.159853
$555$	−4.44029	−0.188480
$556$	−8.99925	−0.381653
$557$	−17.4547	−0.739580	−0.369790	−	0.929115i	$-0.620570\pi$
$557$	−17.4547	−0.739580	−0.369790	+	0.929115i	$0.620570\pi$
$558$	−16.3854	−0.693650
$559$	4.58522	0.193934
$560$	−126.355	−5.33947
$561$	14.4504	0.610098
$562$	−32.7657	−1.38214
$563$	−23.0561	−0.971700	−0.485850	−	0.874042i	$-0.661490\pi$
$563$	−23.0561	−0.971700	−0.485850	+	0.874042i	$0.661490\pi$
$564$	−73.9716	−3.11477
$565$	−24.1199	−1.01473
$566$	82.3471	3.46131
$567$	−20.1585	−0.846578
$568$	116.891	4.90462
$569$	15.9841	0.670087	0.335043	−	0.942203i	$-0.391249\pi$
$569$	15.9841	0.670087	0.335043	+	0.942203i	$0.391249\pi$
$570$	−13.5082	−0.565798
$571$	25.1562	1.05275	0.526377	−	0.850252i	$-0.323550\pi$
$571$	25.1562	1.05275	0.526377	+	0.850252i	$0.323550\pi$
$572$	14.1144	0.590152
$573$	17.4658	0.729645
$574$	29.4580	1.22955
$575$	−5.39327	−0.224915
$576$	−51.9504	−2.16460
$577$	23.1646	0.964354	0.482177	−	0.876074i	$-0.339846\pi$
$577$	23.1646	0.964354	0.482177	+	0.876074i	$0.339846\pi$
$578$	−133.051	−5.53420
$579$	−11.1807	−0.464656
$580$	29.6313	1.23037
$581$	15.1889	0.630141
$582$	15.4458	0.640249
$583$	14.2177	0.588839
$584$	−77.9391	−3.22514
$585$	−3.11923	−0.128964
$586$	67.1115	2.77235
$587$	−15.7671	−0.650776	−0.325388	−	0.945581i	$-0.605495\pi$
$587$	−15.7671	−0.650776	−0.325388	+	0.945581i	$0.605495\pi$
$588$	−106.766	−4.40298
$589$	−12.1807	−0.501898
$590$	41.2940	1.70005
$591$	−25.3135	−1.04126
$592$	−38.7859	−1.59409
$593$	24.4968	1.00596	0.502982	−	0.864297i	$-0.332236\pi$
$593$	24.4968	1.00596	0.502982	+	0.864297i	$0.332236\pi$
$594$	20.6568	0.847557
$595$	−55.2491	−2.26499
$596$	73.0857	2.99371
$597$	7.60181	0.311122
$598$	10.4801	0.428563
$599$	−23.1067	−0.944113	−0.472057	−	0.881568i	$-0.656488\pi$
$599$	−23.1067	−0.944113	−0.472057	+	0.881568i	$0.656488\pi$
$600$	−39.4466	−1.61040
$601$	6.31189	0.257467	0.128734	−	0.991679i	$-0.458909\pi$
$601$	6.31189	0.257467	0.128734	+	0.991679i	$0.458909\pi$
$602$	31.2044	1.27180
$603$	−10.6136	−0.432218
$604$	12.5534	0.510790
$605$	14.1928	0.577017
$606$	−12.5453	−0.509617
$607$	4.57481	0.185686	0.0928429	−	0.995681i	$-0.470405\pi$
$607$	4.57481	0.185686	0.0928429	+	0.995681i	$0.470405\pi$
$608$	−68.7410	−2.78782
$609$	20.6331	0.836094
$610$	−23.9405	−0.969321
$611$	−17.0505	−0.689789
$612$	−51.6857	−2.08927
$613$	35.1882	1.42124	0.710618	−	0.703578i	$-0.248415\pi$
$613$	35.1882	1.42124	0.710618	+	0.703578i	$0.248415\pi$
$614$	−28.9239	−1.16727
$615$	−4.91485	−0.198186
$616$	63.1280	2.54350
$617$	29.9656	1.20637	0.603185	−	0.797601i	$-0.293898\pi$
$617$	29.9656	1.20637	0.603185	+	0.797601i	$0.293898\pi$
$618$	34.9298	1.40508
$619$	−21.3234	−0.857062	−0.428531	−	0.903527i	$-0.640969\pi$
$619$	−21.3234	−0.857062	−0.428531	+	0.903527i	$0.640969\pi$
$620$	47.2959	1.89945
$621$	11.4224	0.458366
$622$	−42.7090	−1.71247
$623$	56.6312	2.26888
$624$	46.8779	1.87662
$625$	−4.53887	−0.181555
$626$	57.6112	2.30260
$627$	4.12738	0.164832
$628$	−18.8497	−0.752184
$629$	−16.9592	−0.676210
$630$	−21.2277	−0.845732
$631$	−14.9928	−0.596853	−0.298426	−	0.954433i	$-0.596462\pi$
$631$	−14.9928	−0.596853	−0.298426	+	0.954433i	$0.596462\pi$
$632$	−23.5851	−0.938165
$633$	−28.9653	−1.15127
$634$	7.75017	0.307799
$635$	6.87259	0.272730
$636$	87.4941	3.46937
$637$	−24.6097	−0.975073
$638$	−12.1572	−0.481309
$639$	12.0098	0.475101
$640$	109.861	4.34263
$641$	−27.1731	−1.07327	−0.536636	−	0.843814i	$-0.680305\pi$
$641$	−27.1731	−1.07327	−0.536636	+	0.843814i	$0.680305\pi$
$642$	8.83673	0.348758
$643$	−0.860257	−0.0339252	−0.0169626	−	0.999856i	$-0.505400\pi$
$643$	−0.860257	−0.0339252	−0.0169626	+	0.999856i	$0.505400\pi$
$644$	53.1145	2.09301
$645$	−5.20623	−0.204995
$646$	−51.5934	−2.02991
$647$	−19.1313	−0.752128	−0.376064	−	0.926594i	$-0.622723\pi$
$647$	−19.1313	−0.752128	−0.376064	+	0.926594i	$0.622723\pi$
$648$	48.0378	1.88710
$649$	−12.6172	−0.495268
$650$	−13.8349	−0.542650
$651$	32.9333	1.29076
$652$	82.8077	3.24300
$653$	−9.73557	−0.380982	−0.190491	−	0.981689i	$-0.561008\pi$
$653$	−9.73557	−0.380982	−0.190491	+	0.981689i	$0.561008\pi$
$654$	−1.75214	−0.0685140
$655$	−16.6824	−0.651835
$656$	−42.9311	−1.67618
$657$	−8.00777	−0.312413
$658$	−116.036	−4.52355
$659$	−15.1480	−0.590081	−0.295041	−	0.955485i	$-0.595333\pi$
$659$	−15.1480	−0.590081	−0.295041	+	0.955485i	$0.595333\pi$
$660$	−16.0260	−0.623811
$661$	27.1840	1.05734	0.528668	−	0.848829i	$-0.322692\pi$
$661$	27.1840	1.05734	0.528668	+	0.848829i	$0.322692\pi$
$662$	−83.1166	−3.23042
$663$	20.4975	0.796057
$664$	−36.1951	−1.40464
$665$	−15.7804	−0.611938
$666$	−6.51605	−0.252492
$667$	−6.72250	−0.260296
$668$	148.675	5.75240
$669$	−20.9611	−0.810403
$670$	41.1373	1.58927
$671$	7.31489	0.282388
$672$	185.857	7.16959
$673$	−17.3019	−0.666939	−0.333470	−	0.942761i	$-0.608219\pi$
$673$	−17.3019	−0.666939	−0.333470	+	0.942761i	$0.608219\pi$
$674$	−82.2954	−3.16990
$675$	−15.0789	−0.580386
$676$	−55.8276	−2.14722
$677$	−26.1729	−1.00590	−0.502952	−	0.864314i	$-0.667753\pi$
$677$	−26.1729	−1.00590	−0.502952	+	0.864314i	$0.667753\pi$
$678$	60.8987	2.33880
$679$	18.0439	0.692461
$680$	131.659	5.04887
$681$	34.8677	1.33613
$682$	−19.4047	−0.743043
$683$	9.22868	0.353125	0.176563	−	0.984289i	$-0.443502\pi$
$683$	9.22868	0.353125	0.176563	+	0.984289i	$0.443502\pi$
$684$	−14.7626	−0.564464
$685$	−34.7226	−1.32668
$686$	−79.2342	−3.02517
$687$	−6.41550	−0.244767
$688$	−45.4763	−1.73377
$689$	20.1674	0.768318
$690$	−11.8995	−0.453006
$691$	−14.0326	−0.533824	−0.266912	−	0.963721i	$-0.586003\pi$
$691$	−14.0326	−0.533824	−0.266912	+	0.963721i	$0.586003\pi$
$692$	−3.41523	−0.129828
$693$	6.48602	0.246384
$694$	−10.1252	−0.384347
$695$	2.35527	0.0893406
$696$	−49.1686	−1.86373
$697$	−18.7718	−0.711032
$698$	58.4766	2.21337
$699$	−30.0818	−1.13780
$700$	−70.1172	−2.65018
$701$	−6.12091	−0.231184	−0.115592	−	0.993297i	$-0.536876\pi$
$701$	−6.12091	−0.231184	−0.115592	+	0.993297i	$0.536876\pi$
$702$	29.3010	1.10589
$703$	−4.84396	−0.182693
$704$	−61.5231	−2.31874
$705$	19.3598	0.729131
$706$	−3.08547	−0.116123
$707$	−14.6555	−0.551176
$708$	−77.6445	−2.91806
$709$	−2.82404	−0.106059	−0.0530295	−	0.998593i	$-0.516888\pi$
$709$	−2.82404	−0.106059	−0.0530295	+	0.998593i	$0.516888\pi$
$710$	−46.5489	−1.74695
$711$	−2.42323	−0.0908781
$712$	−134.952	−5.05754
$713$	−10.7301	−0.401844
$714$	139.494	5.22045
$715$	−3.69400	−0.138148
$716$	−108.217	−4.04426
$717$	36.5986	1.36680
$718$	−84.1376	−3.13999
$719$	32.7148	1.22005	0.610027	−	0.792380i	$-0.291158\pi$
$719$	32.7148	1.22005	0.610027	+	0.792380i	$0.291158\pi$
$720$	30.9366	1.15294
$721$	40.8052	1.51967
$722$	38.4451	1.43078
$723$	9.34407	0.347510
$724$	124.394	4.62306
$725$	8.87446	0.329589
$726$	−35.8343	−1.32993
$727$	37.0115	1.37268	0.686340	−	0.727281i	$-0.259216\pi$
$727$	37.0115	1.37268	0.686340	+	0.727281i	$0.259216\pi$
$728$	89.5452	3.31877
$729$	28.2875	1.04769
$730$	31.0374	1.14875
$731$	−19.8847	−0.735461
$732$	45.0149	1.66380
$733$	36.7810	1.35854	0.679268	−	0.733890i	$-0.262297\pi$
$733$	36.7810	1.35854	0.679268	+	0.733890i	$0.262297\pi$
$734$	30.3623	1.12069
$735$	27.9428	1.03069
$736$	−60.5544	−2.23207
$737$	−12.5693	−0.462996
$738$	−7.21246	−0.265494
$739$	24.2353	0.891511	0.445755	−	0.895155i	$-0.352935\pi$
$739$	24.2353	0.891511	0.445755	+	0.895155i	$0.352935\pi$
$740$	18.8083	0.691408
$741$	5.85456	0.215073
$742$	137.248	5.03854
$743$	−5.58084	−0.204741	−0.102370	−	0.994746i	$-0.532643\pi$
$743$	−5.58084	−0.204741	−0.102370	+	0.994746i	$0.532643\pi$
$744$	−78.4801	−2.87722
$745$	−19.1279	−0.700792
$746$	−54.8062	−2.00660
$747$	−3.71883	−0.136065
$748$	−61.2096	−2.23805
$749$	10.3231	0.377199
$750$	45.1446	1.64845
$751$	12.1859	0.444671	0.222336	−	0.974970i	$-0.428632\pi$
$751$	12.1859	0.444671	0.222336	+	0.974970i	$0.428632\pi$
$752$	169.107	6.16670
$753$	−34.9947	−1.27528
$754$	−17.2447	−0.628014
$755$	−3.28545	−0.119570
$756$	148.501	5.40094
$757$	−26.7300	−0.971517	−0.485759	−	0.874093i	$-0.661457\pi$
$757$	−26.7300	−0.971517	−0.485759	+	0.874093i	$0.661457\pi$
$758$	14.7418	0.535448
$759$	3.63583	0.131972
$760$	37.6047	1.36407
$761$	−19.3292	−0.700683	−0.350341	−	0.936622i	$-0.613934\pi$
$761$	−19.3292	−0.700683	−0.350341	+	0.936622i	$0.613934\pi$
$762$	−17.3521	−0.628600
$763$	−2.04686	−0.0741012
$764$	−73.9823	−2.67659
$765$	13.5271	0.489074
$766$	102.445	3.70148
$767$	−17.8971	−0.646226
$768$	−147.598	−5.32599
$769$	22.7325	0.819755	0.409878	−	0.912140i	$-0.365571\pi$
$769$	22.7325	0.819755	0.409878	+	0.912140i	$0.365571\pi$
$770$	−25.1392	−0.905955
$771$	7.68752	0.276859
$772$	47.3598	1.70452
$773$	17.3972	0.625734	0.312867	−	0.949797i	$-0.398711\pi$
$773$	17.3972	0.625734	0.312867	+	0.949797i	$0.398711\pi$
$774$	−7.64006	−0.274616
$775$	14.1649	0.508818
$776$	−42.9986	−1.54356
$777$	13.0967	0.469843
$778$	−96.6558	−3.46528
$779$	−5.36166	−0.192101
$780$	−22.7324	−0.813950
$781$	14.2228	0.508932
$782$	−45.4489	−1.62525
$783$	−18.7952	−0.671687
$784$	244.080	8.71713
$785$	4.93332	0.176078
$786$	42.1202	1.50238
$787$	23.6273	0.842223	0.421111	−	0.907009i	$-0.361640\pi$
$787$	23.6273	0.842223	0.421111	+	0.907009i	$0.361640\pi$
$788$	107.224	3.81969
$789$	4.47157	0.159192
$790$	9.39221	0.334160
$791$	71.1422	2.52953
$792$	−15.4562	−0.549212
$793$	10.3760	0.368461
$794$	−11.5743	−0.410757
$795$	−22.8989	−0.812139
$796$	−32.2000	−1.14130
$797$	20.1366	0.713275	0.356637	−	0.934243i	$-0.383923\pi$
$797$	20.1366	0.713275	0.356637	+	0.934243i	$0.383923\pi$
$798$	39.8428	1.41042
$799$	73.9427	2.61590
$800$	79.9386	2.82626
$801$	−13.8655	−0.489914
$802$	−4.33090	−0.152929
$803$	−9.48333	−0.334659
$804$	−77.3499	−2.72792
$805$	−13.9011	−0.489948
$806$	−27.5250	−0.969525
$807$	23.7919	0.837516
$808$	34.9240	1.22862
$809$	−1.25701	−0.0441942	−0.0220971	−	0.999756i	$-0.507034\pi$
$809$	−1.25701	−0.0441942	−0.0220971	+	0.999756i	$0.507034\pi$
$810$	−19.1299	−0.672156
$811$	−21.1998	−0.744424	−0.372212	−	0.928148i	$-0.621401\pi$
$811$	−21.1998	−0.744424	−0.372212	+	0.928148i	$0.621401\pi$
$812$	−87.3982	−3.06708
$813$	0.495646	0.0173831
$814$	−7.71674	−0.270472
$815$	−21.6723	−0.759148
$816$	−203.295	−7.11674
$817$	−5.67953	−0.198701
$818$	−26.9714	−0.943035
$819$	9.20023	0.321482
$820$	20.8185	0.727013
$821$	−0.590951	−0.0206243	−0.0103122	−	0.999947i	$-0.503283\pi$
$821$	−0.590951	−0.0206243	−0.0103122	+	0.999947i	$0.503283\pi$
$822$	87.6686	3.05779
$823$	−2.60021	−0.0906375	−0.0453188	−	0.998973i	$-0.514430\pi$
$823$	−2.60021	−0.0906375	−0.0453188	+	0.998973i	$0.514430\pi$
$824$	−97.2389	−3.38748
$825$	−4.79971	−0.167104
$826$	−121.797	−4.23787
$827$	20.5773	0.715543	0.357772	−	0.933809i	$-0.383537\pi$
$827$	20.5773	0.715543	0.357772	+	0.933809i	$0.383537\pi$
$828$	−13.0045	−0.451938
$829$	−5.91518	−0.205443	−0.102721	−	0.994710i	$-0.532755\pi$
$829$	−5.91518	−0.205443	−0.102721	+	0.994710i	$0.532755\pi$
$830$	14.4139	0.500312
$831$	−1.85154	−0.0642293
$832$	−87.2686	−3.02550
$833$	106.725	3.69779
$834$	−5.94666	−0.205916
$835$	−38.9110	−1.34657
$836$	−17.4829	−0.604658
$837$	−29.9999	−1.03695
$838$	63.3240	2.18749
$839$	−4.29194	−0.148174	−0.0740872	−	0.997252i	$-0.523604\pi$
$839$	−4.29194	−0.148174	−0.0740872	+	0.997252i	$0.523604\pi$
$840$	−101.673	−3.50805
$841$	−17.9383	−0.618564
$842$	15.3939	0.530509
$843$	−16.1242	−0.555347
$844$	122.692	4.22324
$845$	14.6111	0.502638
$846$	28.4101	0.976760
$847$	−41.8618	−1.43839
$848$	−200.021	−6.86875
$849$	40.5235	1.39076
$850$	59.9977	2.05790
$851$	−4.26707	−0.146273
$852$	87.5253	2.99857
$853$	27.1932	0.931078	0.465539	−	0.885027i	$-0.345861\pi$
$853$	27.1932	0.931078	0.465539	+	0.885027i	$0.345861\pi$
$854$	70.6129	2.41632
$855$	3.86366	0.132134
$856$	−24.6000	−0.840811
$857$	−36.3710	−1.24241	−0.621204	−	0.783649i	$-0.713356\pi$
$857$	−36.3710	−1.24241	−0.621204	+	0.783649i	$0.713356\pi$
$858$	9.32670	0.318408
$859$	−8.28294	−0.282610	−0.141305	−	0.989966i	$-0.545130\pi$
$859$	−8.28294	−0.282610	−0.141305	+	0.989966i	$0.545130\pi$
$860$	22.0527	0.751992
$861$	14.4965	0.494038
$862$	−66.5208	−2.26571
$863$	20.1964	0.687493	0.343746	−	0.939063i	$-0.388304\pi$
$863$	20.1964	0.687493	0.343746	+	0.939063i	$0.388304\pi$
$864$	−169.302	−5.75978
$865$	0.893830	0.0303911
$866$	−21.5761	−0.733185
$867$	−65.4753	−2.22366
$868$	−139.500	−4.73494
$869$	−2.86975	−0.0973494
$870$	19.5802	0.663832
$871$	−17.8292	−0.604119
$872$	4.87766	0.165178
$873$	−4.41785	−0.149521
$874$	−12.9813	−0.439098
$875$	52.7382	1.78288
$876$	−58.3592	−1.97177
$877$	41.5884	1.40434	0.702171	−	0.712009i	$-0.252214\pi$
$877$	41.5884	1.40434	0.702171	+	0.712009i	$0.252214\pi$
$878$	−105.041	−3.54496
$879$	33.0260	1.11394
$880$	36.6371	1.23504
$881$	25.1692	0.847973	0.423986	−	0.905669i	$-0.360630\pi$
$881$	25.1692	0.847973	0.423986	+	0.905669i	$0.360630\pi$
$882$	41.0056	1.38073
$883$	16.4821	0.554666	0.277333	−	0.960774i	$-0.410549\pi$
$883$	16.4821	0.554666	0.277333	+	0.960774i	$0.410549\pi$
$884$	−86.8240	−2.92021
$885$	20.3210	0.683084
$886$	42.4498	1.42613
$887$	33.5342	1.12597	0.562983	−	0.826468i	$-0.309654\pi$
$887$	33.5342	1.12597	0.562983	+	0.826468i	$0.309654\pi$
$888$	−31.2095	−1.04732
$889$	−20.2708	−0.679862
$890$	53.7415	1.80142
$891$	5.84505	0.195817
$892$	88.7878	2.97283
$893$	21.1197	0.706745
$894$	48.2946	1.61521
$895$	28.3225	0.946715
$896$	−324.037	−10.8253
$897$	5.15732	0.172198
$898$	28.9145	0.964891
$899$	17.6560	0.588860
$900$	17.1674	0.572247
$901$	−87.4599	−2.91371
$902$	−8.54147	−0.284400
$903$	15.3559	0.511012
$904$	−169.532	−5.63855
$905$	−32.5562	−1.08221
$906$	8.29521	0.275590
$907$	47.4720	1.57628	0.788142	−	0.615494i	$-0.211044\pi$
$907$	47.4720	1.57628	0.788142	+	0.615494i	$0.211044\pi$
$908$	−147.694	−4.90139
$909$	3.58823	0.119014
$910$	−35.6593	−1.18209
$911$	−52.7328	−1.74712	−0.873558	−	0.486721i	$-0.838193\pi$
$911$	−52.7328	−1.74712	−0.873558	+	0.486721i	$0.838193\pi$
$912$	−58.0657	−1.92275
$913$	−4.40408	−0.145754
$914$	31.8175	1.05243
$915$	−11.7812	−0.389476
$916$	27.1750	0.897887
$917$	49.2050	1.62489
$918$	−127.069	−4.19391
$919$	−57.6225	−1.90079	−0.950396	−	0.311042i	$-0.899322\pi$
$919$	−57.6225	−1.90079	−0.950396	+	0.311042i	$0.899322\pi$
$920$	33.1263	1.09214
$921$	−14.2336	−0.469014
$922$	−38.7653	−1.27667
$923$	20.1746	0.664056
$924$	47.2690	1.55503
$925$	5.63301	0.185212
$926$	79.1113	2.59976
$927$	−9.99071	−0.328138
$928$	99.6403	3.27085
$929$	−20.6427	−0.677267	−0.338633	−	0.940918i	$-0.609965\pi$
$929$	−20.6427	−0.677267	−0.338633	+	0.940918i	$0.609965\pi$
$930$	31.2529	1.02482
$931$	30.4830	0.999041
$932$	127.422	4.17383
$933$	−21.0173	−0.688077
$934$	103.465	3.38547
$935$	16.0197	0.523900
$936$	−21.9242	−0.716613
$937$	25.4176	0.830356	0.415178	−	0.909740i	$-0.363719\pi$
$937$	25.4176	0.830356	0.415178	+	0.909740i	$0.363719\pi$
$938$	−121.335	−3.96173
$939$	28.3508	0.925194
$940$	−82.0047	−2.67470
$941$	−13.7286	−0.447541	−0.223770	−	0.974642i	$-0.571837\pi$
$941$	−13.7286	−0.447541	−0.223770	+	0.974642i	$0.571837\pi$
$942$	−12.4558	−0.405831
$943$	−4.72312	−0.153806
$944$	177.504	5.77725
$945$	−38.8656	−1.26430
$946$	−9.04786	−0.294171
$947$	−22.3583	−0.726546	−0.363273	−	0.931683i	$-0.618341\pi$
$947$	−22.3583	−0.726546	−0.363273	+	0.931683i	$0.618341\pi$
$948$	−17.6600	−0.573572
$949$	−13.4518	−0.436665
$950$	17.1367	0.555989
$951$	3.81391	0.123674
$952$	−388.330	−12.5858
$953$	23.9630	0.776239	0.388120	−	0.921609i	$-0.373125\pi$
$953$	23.9630	0.776239	0.388120	+	0.921609i	$0.373125\pi$
$954$	−33.6037	−1.08796
$955$	19.3626	0.626558
$956$	−155.026	−5.01389
$957$	−5.98265	−0.193392
$958$	59.4986	1.92231
$959$	102.415	3.30715
$960$	99.0881	3.19805
$961$	−2.81854	−0.0909205
$962$	−10.9460	−0.352912
$963$	−2.52750	−0.0814476
$964$	−39.5799	−1.27478
$965$	−12.3949	−0.399007
$966$	35.0978	1.12925
$967$	19.6775	0.632786	0.316393	−	0.948628i	$-0.397528\pi$
$967$	19.6775	0.632786	0.316393	+	0.948628i	$0.397528\pi$
$968$	99.7567	3.20630
$969$	−25.3894	−0.815626
$970$	17.1232	0.549792
$971$	7.83478	0.251430	0.125715	−	0.992066i	$-0.459878\pi$
$971$	7.83478	0.251430	0.125715	+	0.992066i	$0.459878\pi$
$972$	−62.9452	−2.01897
$973$	−6.94692	−0.222708
$974$	75.7617	2.42756
$975$	−6.80825	−0.218038
$976$	−102.909	−3.29404
$977$	−46.9659	−1.50257	−0.751287	−	0.659976i	$-0.770566\pi$
$977$	−46.9659	−1.50257	−0.751287	+	0.659976i	$0.770566\pi$
$978$	54.7189	1.74972
$979$	−16.4205	−0.524800
$980$	−118.361	−3.78090
$981$	0.501150	0.0160005
$982$	8.08544	0.258017
$983$	1.00000	0.0318950
$983$	1.00000	0.0318950
$984$	−34.5451	−1.10126
$985$	−28.0625	−0.894145
$986$	74.7847	2.38163
$987$	−57.1020	−1.81758
$988$	−24.7990	−0.788960
$989$	−5.00313	−0.159090
$990$	6.15506	0.195621
$991$	−3.39709	−0.107912	−0.0539560	−	0.998543i	$-0.517183\pi$
$991$	−3.39709	−0.107912	−0.0539560	+	0.998543i	$0.517183\pi$
$992$	159.040	5.04953
$993$	−40.9022	−1.29799
$994$	137.297	4.35480
$995$	8.42735	0.267165
$996$	−27.1022	−0.858765
$997$	−47.7282	−1.51157	−0.755783	−	0.654822i	$-0.772744\pi$
$997$	−47.7282	−1.51157	−0.755783	+	0.654822i	$0.772744\pi$
$998$	36.9759	1.17045
$999$	−11.9302	−0.377454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.b.1.1	✓	54
3.2	odd	2		8847.2.a.g.1.54		54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.b.1.1	✓	54	1.1	even	1	trivial
8847.2.a.g.1.54		54	3.2	odd	2

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79902 q^{2} -1.37741 q^{3} +5.83449 q^{4} -1.52700 q^{5} +3.85540 q^{6} +4.50391 q^{7} -10.7328 q^{8} -1.10273 q^{9} +O(q^{10})\)	\(q-2.79902 q^{2} -1.37741 q^{3} +5.83449 q^{4} -1.52700 q^{5} +3.85540 q^{6} +4.50391 q^{7} -10.7328 q^{8} -1.10273 q^{9} +4.27409 q^{10} -1.30593 q^{11} -8.03651 q^{12} -1.85242 q^{13} -12.6065 q^{14} +2.10331 q^{15} +18.3723 q^{16} +8.03336 q^{17} +3.08657 q^{18} +2.29452 q^{19} -8.90925 q^{20} -6.20374 q^{21} +3.65531 q^{22} +2.02125 q^{23} +14.7835 q^{24} -2.66828 q^{25} +5.18495 q^{26} +5.65116 q^{27} +26.2780 q^{28} -3.32591 q^{29} -5.88719 q^{30} -5.30862 q^{31} -29.9588 q^{32} +1.79880 q^{33} -22.4855 q^{34} -6.87745 q^{35} -6.43388 q^{36} -2.11110 q^{37} -6.42239 q^{38} +2.55155 q^{39} +16.3890 q^{40} -2.33673 q^{41} +17.3644 q^{42} -2.47526 q^{43} -7.61943 q^{44} +1.68387 q^{45} -5.65752 q^{46} +9.20445 q^{47} -25.3063 q^{48} +13.2852 q^{49} +7.46856 q^{50} -11.0653 q^{51} -10.8079 q^{52} -10.8871 q^{53} -15.8177 q^{54} +1.99415 q^{55} -48.3396 q^{56} -3.16050 q^{57} +9.30927 q^{58} +9.66147 q^{59} +12.2717 q^{60} -5.60130 q^{61} +14.8589 q^{62} -4.96660 q^{63} +47.1106 q^{64} +2.82864 q^{65} -5.03488 q^{66} +9.62480 q^{67} +46.8706 q^{68} -2.78410 q^{69} +19.2501 q^{70} -10.8910 q^{71} +11.8354 q^{72} +7.26176 q^{73} +5.90901 q^{74} +3.67533 q^{75} +13.3873 q^{76} -5.88178 q^{77} -7.14182 q^{78} +2.19748 q^{79} -28.0545 q^{80} -4.47579 q^{81} +6.54054 q^{82} +3.37238 q^{83} -36.1957 q^{84} -12.2669 q^{85} +6.92830 q^{86} +4.58115 q^{87} +14.0163 q^{88} +12.5738 q^{89} -4.71317 q^{90} -8.34312 q^{91} +11.7930 q^{92} +7.31217 q^{93} -25.7634 q^{94} -3.50372 q^{95} +41.2657 q^{96} +4.00627 q^{97} -37.1854 q^{98} +1.44009 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9}+O(q^{10}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9	\( 54 q + 8 q^{2} + 6 q^{3} + 64 q^{4} + 7 q^{5} + 5 q^{6} + 31 q^{7} + 24 q^{8} + 74 q^{9} + 15 q^{10} + 8 q^{11} + 10 q^{12} + 34 q^{13} + q^{14} + 3 q^{15} + 80 q^{16} + 32 q^{17} + 28 q^{18} + 15 q^{19} + 4 q^{20} + 11 q^{21} + 25 q^{22} + 15 q^{23} - 7 q^{24} + 125 q^{25} - 14 q^{26} + 12 q^{27} + 78 q^{28} + 8 q^{29} - 32 q^{30} + 16 q^{31} + 36 q^{32} + 38 q^{33} - 8 q^{34} - 2 q^{35} + 65 q^{36} + 80 q^{37} - 14 q^{38} + 16 q^{39} + 36 q^{40} + 30 q^{41} - 10 q^{42} + 53 q^{43} + 6 q^{44} + 3 q^{45} + 24 q^{46} + 22 q^{47} + 7 q^{48} + 111 q^{49} + 14 q^{50} - 10 q^{51} + 45 q^{52} + 10 q^{53} - 8 q^{54} + 12 q^{55} - 30 q^{56} + 106 q^{57} + 61 q^{58} - 4 q^{59} - 61 q^{60} + 24 q^{61} - 12 q^{62} + 73 q^{63} + 86 q^{64} + 32 q^{65} - 43 q^{66} + 54 q^{67} + 33 q^{68} - 30 q^{69} - 21 q^{70} - 6 q^{71} + 60 q^{72} + 172 q^{73} - 32 q^{74} - 36 q^{75} + 7 q^{76} - 12 q^{77} - 3 q^{78} + 28 q^{79} - 66 q^{80} + 86 q^{81} + 4 q^{82} + 14 q^{83} - 58 q^{84} + 99 q^{85} - 31 q^{86} - 27 q^{87} + 5 q^{88} - 5 q^{89} - 45 q^{90} - 11 q^{91} + 20 q^{92} + 27 q^{93} - 39 q^{94} + 5 q^{95} - 87 q^{96} + 127 q^{97} - 29 q^{98} - 21 q^{99}+O(q^{100}) \) 54 * q + 8 * q^2 + 6 * q^3 + 64 * q^4 + 7 * q^5 + 5 * q^6 + 31 * q^7 + 24 * q^8 + 74 * q^9 + 15 * q^10 + 8 * q^11 + 10 * q^12 + 34 * q^13 + q^14 + 3 * q^15 + 80 * q^16 + 32 * q^17 + 28 * q^18 + 15 * q^19 + 4 * q^20 + 11 * q^21 + 25 * q^22 + 15 * q^23 - 7 * q^24 + 125 * q^25 - 14 * q^26 + 12 * q^27 + 78 * q^28 + 8 * q^29 - 32 * q^30 + 16 * q^31 + 36 * q^32 + 38 * q^33 - 8 * q^34 - 2 * q^35 + 65 * q^36 + 80 * q^37 - 14 * q^38 + 16 * q^39 + 36 * q^40 + 30 * q^41 - 10 * q^42 + 53 * q^43 + 6 * q^44 + 3 * q^45 + 24 * q^46 + 22 * q^47 + 7 * q^48 + 111 * q^49 + 14 * q^50 - 10 * q^51 + 45 * q^52 + 10 * q^53 - 8 * q^54 + 12 * q^55 - 30 * q^56 + 106 * q^57 + 61 * q^58 - 4 * q^59 - 61 * q^60 + 24 * q^61 - 12 * q^62 + 73 * q^63 + 86 * q^64 + 32 * q^65 - 43 * q^66 + 54 * q^67 + 33 * q^68 - 30 * q^69 - 21 * q^70 - 6 * q^71 + 60 * q^72 + 172 * q^73 - 32 * q^74 - 36 * q^75 + 7 * q^76 - 12 * q^77 - 3 * q^78 + 28 * q^79 - 66 * q^80 + 86 * q^81 + 4 * q^82 + 14 * q^83 - 58 * q^84 + 99 * q^85 - 31 * q^86 - 27 * q^87 + 5 * q^88 - 5 * q^89 - 45 * q^90 - 11 * q^91 + 20 * q^92 + 27 * q^93 - 39 * q^94 + 5 * q^95 - 87 * q^96 + 127 * q^97 - 29 * q^98 - 21 * q^99

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