LMFDB - Embedded newform 983.2.a.a.1.13

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:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-0.468024 q^{2} -2.30825 q^{3} -1.78095 q^{4} -2.20940 q^{5} +1.08031 q^{6} +0.238349 q^{7} +1.76958 q^{8} +2.32800 q^{9} +O(q^{10})$	\(q-0.468024 q^{2} -2.30825 q^{3} -1.78095 q^{4} -2.20940 q^{5} +1.08031 q^{6} +0.238349 q^{7} +1.76958 q^{8} +2.32800 q^{9} +1.03405 q^{10} +1.21267 q^{11} +4.11088 q^{12} +2.76897 q^{13} -0.111553 q^{14} +5.09984 q^{15} +2.73370 q^{16} +2.28408 q^{17} -1.08956 q^{18} -0.497826 q^{19} +3.93484 q^{20} -0.550169 q^{21} -0.567561 q^{22} +5.41163 q^{23} -4.08462 q^{24} -0.118544 q^{25} -1.29594 q^{26} +1.55115 q^{27} -0.424489 q^{28} -8.34976 q^{29} -2.38685 q^{30} -9.40529 q^{31} -4.81859 q^{32} -2.79915 q^{33} -1.06901 q^{34} -0.526609 q^{35} -4.14605 q^{36} +3.68928 q^{37} +0.232995 q^{38} -6.39145 q^{39} -3.90971 q^{40} +7.06937 q^{41} +0.257492 q^{42} +8.60786 q^{43} -2.15972 q^{44} -5.14348 q^{45} -2.53277 q^{46} -9.59458 q^{47} -6.31005 q^{48} -6.94319 q^{49} +0.0554817 q^{50} -5.27222 q^{51} -4.93140 q^{52} -1.29976 q^{53} -0.725976 q^{54} -2.67929 q^{55} +0.421778 q^{56} +1.14911 q^{57} +3.90789 q^{58} +13.9187 q^{59} -9.08258 q^{60} +4.87995 q^{61} +4.40190 q^{62} +0.554876 q^{63} -3.21218 q^{64} -6.11776 q^{65} +1.31007 q^{66} -13.3779 q^{67} -4.06784 q^{68} -12.4914 q^{69} +0.246466 q^{70} -2.00007 q^{71} +4.11957 q^{72} -5.70775 q^{73} -1.72667 q^{74} +0.273630 q^{75} +0.886606 q^{76} +0.289040 q^{77} +2.99136 q^{78} +1.55684 q^{79} -6.03984 q^{80} -10.5644 q^{81} -3.30864 q^{82} -8.35646 q^{83} +0.979825 q^{84} -5.04645 q^{85} -4.02869 q^{86} +19.2733 q^{87} +2.14592 q^{88} +6.40922 q^{89} +2.40727 q^{90} +0.659981 q^{91} -9.63785 q^{92} +21.7097 q^{93} +4.49050 q^{94} +1.09990 q^{95} +11.1225 q^{96} -18.2762 q^{97} +3.24958 q^{98} +2.82310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * 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 $

$2$	−0.468024	−0.330943	−0.165472	−	0.986215i	$-0.552915\pi$
$2$	−0.468024	−0.330943	−0.165472	+	0.986215i	$0.552915\pi$
$3$	−2.30825	−1.33267	−0.666333	−	0.745654i	$-0.732137\pi$
$3$	−2.30825	−1.33267	−0.666333	+	0.745654i	$0.732137\pi$
$4$	−1.78095	−0.890477
$5$	−2.20940	−0.988074	−0.494037	−	0.869441i	$-0.664479\pi$
$5$	−2.20940	−0.988074	−0.494037	+	0.869441i	$0.664479\pi$
$6$	1.08031	0.441037
$7$	0.238349	0.0900876	0.0450438	−	0.998985i	$-0.485657\pi$
$7$	0.238349	0.0900876	0.0450438	+	0.998985i	$0.485657\pi$
$8$	1.76958	0.625640
$9$	2.32800	0.775999
$10$	1.03405	0.326996
$11$	1.21267	0.365635	0.182818	−	0.983147i	$-0.441478\pi$
$11$	1.21267	0.365635	0.182818	+	0.983147i	$0.441478\pi$
$12$	4.11088	1.18671
$13$	2.76897	0.767973	0.383987	−	0.923339i	$-0.374551\pi$
$13$	2.76897	0.767973	0.383987	+	0.923339i	$0.374551\pi$
$14$	−0.111553	−0.0298139
$15$	5.09984	1.31677
$16$	2.73370	0.683425
$17$	2.28408	0.553971	0.276986	−	0.960874i	$-0.410665\pi$
$17$	2.28408	0.553971	0.276986	+	0.960874i	$0.410665\pi$
$18$	−1.08956	−0.256811
$19$	−0.497826	−0.114209	−0.0571046	−	0.998368i	$-0.518187\pi$
$19$	−0.497826	−0.114209	−0.0571046	+	0.998368i	$0.518187\pi$
$20$	3.93484	0.879857
$21$	−0.550169	−0.120057
$22$	−0.567561	−0.121004
$23$	5.41163	1.12840	0.564201	−	0.825637i	$-0.309184\pi$
$23$	5.41163	1.12840	0.564201	+	0.825637i	$0.309184\pi$
$24$	−4.08462	−0.833769
$25$	−0.118544	−0.0237089
$26$	−1.29594	−0.254155
$27$	1.55115	0.298519
$28$	−0.424489	−0.0802209
$29$	−8.34976	−1.55051	−0.775256	−	0.631647i	$-0.782379\pi$
$29$	−8.34976	−1.55051	−0.775256	+	0.631647i	$0.782379\pi$
$30$	−2.38685	−0.435777
$31$	−9.40529	−1.68924	−0.844620	−	0.535366i	$-0.820174\pi$
$31$	−9.40529	−1.68924	−0.844620	+	0.535366i	$0.820174\pi$
$32$	−4.81859	−0.851815
$33$	−2.79915	−0.487270
$34$	−1.06901	−0.183333
$35$	−0.526609	−0.0890132
$36$	−4.14605	−0.691009
$37$	3.68928	0.606514	0.303257	−	0.952909i	$-0.401926\pi$
$37$	3.68928	0.606514	0.303257	+	0.952909i	$0.401926\pi$
$38$	0.232995	0.0377967
$39$	−6.39145	−1.02345
$40$	−3.90971	−0.618179
$41$	7.06937	1.10405	0.552025	−	0.833827i	$-0.313855\pi$
$41$	7.06937	1.10405	0.552025	+	0.833827i	$0.313855\pi$
$42$	0.257492	0.0397319
$43$	8.60786	1.31269	0.656343	−	0.754463i	$-0.272102\pi$
$43$	8.60786	1.31269	0.656343	+	0.754463i	$0.272102\pi$
$44$	−2.15972	−0.325590
$45$	−5.14348	−0.766744
$46$	−2.53277	−0.373437
$47$	−9.59458	−1.39951	−0.699757	−	0.714381i	$-0.746708\pi$
$47$	−9.59458	−1.39951	−0.699757	+	0.714381i	$0.746708\pi$
$48$	−6.31005	−0.910778
$49$	−6.94319	−0.991884
$50$	0.0554817	0.00784629
$51$	−5.27222	−0.738258
$52$	−4.93140	−0.683862
$53$	−1.29976	−0.178536	−0.0892679	−	0.996008i	$-0.528453\pi$
$53$	−1.29976	−0.178536	−0.0892679	+	0.996008i	$0.528453\pi$
$54$	−0.725976	−0.0987928
$55$	−2.67929	−0.361275
$56$	0.421778	0.0563624
$57$	1.14911	0.152203
$58$	3.90789	0.513131
$59$	13.9187	1.81206	0.906030	−	0.423214i	$-0.139098\pi$
$59$	13.9187	1.81206	0.906030	+	0.423214i	$0.139098\pi$
$60$	−9.08258	−1.17256
$61$	4.87995	0.624813	0.312407	−	0.949948i	$-0.398865\pi$
$61$	4.87995	0.624813	0.312407	+	0.949948i	$0.398865\pi$
$62$	4.40190	0.559042
$63$	0.554876	0.0699078
$64$	−3.21218	−0.401523
$65$	−6.11776	−0.758815
$66$	1.31007	0.161258
$67$	−13.3779	−1.63437	−0.817183	−	0.576379i	$-0.804465\pi$
$67$	−13.3779	−1.63437	−0.817183	+	0.576379i	$0.804465\pi$
$68$	−4.06784	−0.493298
$69$	−12.4914	−1.50378
$70$	0.246466	0.0294583
$71$	−2.00007	−0.237364	−0.118682	−	0.992932i	$-0.537867\pi$
$71$	−2.00007	−0.237364	−0.118682	+	0.992932i	$0.537867\pi$
$72$	4.11957	0.485496
$73$	−5.70775	−0.668041	−0.334021	−	0.942566i	$-0.608406\pi$
$73$	−5.70775	−0.668041	−0.334021	+	0.942566i	$0.608406\pi$
$74$	−1.72667	−0.200722
$75$	0.273630	0.0315960
$76$	0.886606	0.101701
$77$	0.289040	0.0329392
$78$	2.99136	0.338704
$79$	1.55684	0.175158	0.0875792	−	0.996158i	$-0.472087\pi$
$79$	1.55684	0.175158	0.0875792	+	0.996158i	$0.472087\pi$
$80$	−6.03984	−0.675275
$81$	−10.5644	−1.17382
$82$	−3.30864	−0.365378
$83$	−8.35646	−0.917241	−0.458621	−	0.888632i	$-0.651656\pi$
$83$	−8.35646	−0.917241	−0.458621	+	0.888632i	$0.651656\pi$
$84$	0.979825	0.106908
$85$	−5.04645	−0.547365
$86$	−4.02869	−0.434424
$87$	19.2733	2.06631
$88$	2.14592	0.228756
$89$	6.40922	0.679376	0.339688	−	0.940538i	$-0.389678\pi$
$89$	6.40922	0.679376	0.339688	+	0.940538i	$0.389678\pi$
$90$	2.40727	0.253749
$91$	0.659981	0.0691849
$92$	−9.63785	−1.00482
$93$	21.7097	2.25119
$94$	4.49050	0.463159
$95$	1.09990	0.112847
$96$	11.1225	1.13519
$97$	−18.2762	−1.85567	−0.927836	−	0.372989i	$-0.878333\pi$
$97$	−18.2762	−1.85567	−0.927836	+	0.372989i	$0.878333\pi$
$98$	3.24958	0.328257
$99$	2.82310	0.283732
$100$	0.211122	0.0211122
$101$	17.3829	1.72966	0.864830	−	0.502064i	$-0.167426\pi$
$101$	17.3829	1.72966	0.864830	+	0.502064i	$0.167426\pi$
$102$	2.46753	0.244322
$103$	17.8958	1.76332	0.881661	−	0.471883i	$-0.156426\pi$
$103$	17.8958	1.76332	0.881661	+	0.471883i	$0.156426\pi$
$104$	4.89990	0.480475
$105$	1.21554	0.118625
$106$	0.608319	0.0590852
$107$	−8.28777	−0.801209	−0.400604	−	0.916251i	$-0.631200\pi$
$107$	−8.28777	−0.801209	−0.400604	+	0.916251i	$0.631200\pi$
$108$	−2.76253	−0.265824
$109$	−12.2784	−1.17606	−0.588029	−	0.808840i	$-0.700096\pi$
$109$	−12.2784	−1.17606	−0.588029	+	0.808840i	$0.700096\pi$
$110$	1.25397	0.119561
$111$	−8.51577	−0.808281
$112$	0.651576	0.0615681
$113$	−7.84656	−0.738142	−0.369071	−	0.929401i	$-0.620324\pi$
$113$	−7.84656	−0.738142	−0.369071	+	0.929401i	$0.620324\pi$
$114$	−0.537809	−0.0503704
$115$	−11.9565	−1.11495
$116$	14.8705	1.38069
$117$	6.44614	0.595946
$118$	−6.51428	−0.599688
$119$	0.544409	0.0499059
$120$	9.02456	0.823826
$121$	−9.52942	−0.866311
$122$	−2.28393	−0.206778
$123$	−16.3178	−1.47133
$124$	16.7504	1.50423
$125$	11.3089	1.01150
$126$	−0.259696	−0.0231355
$127$	1.64455	0.145930	0.0729649	−	0.997335i	$-0.476754\pi$
$127$	1.64455	0.145930	0.0729649	+	0.997335i	$0.476754\pi$
$128$	11.1406	0.984696
$129$	−19.8690	−1.74937
$130$	2.86326	0.251124
$131$	−9.46007	−0.826530	−0.413265	−	0.910611i	$-0.635612\pi$
$131$	−9.46007	−0.826530	−0.413265	+	0.910611i	$0.635612\pi$
$132$	4.98516	0.433902
$133$	−0.118657	−0.0102888
$134$	6.26116	0.540882
$135$	−3.42711	−0.294959
$136$	4.04186	0.346587
$137$	−19.6057	−1.67502	−0.837512	−	0.546418i	$-0.815991\pi$
$137$	−19.6057	−1.67502	−0.837512	+	0.546418i	$0.815991\pi$
$138$	5.84626	0.497667
$139$	3.47373	0.294638	0.147319	−	0.989089i	$-0.452936\pi$
$139$	3.47373	0.294638	0.147319	+	0.989089i	$0.452936\pi$
$140$	0.937867	0.0792642
$141$	22.1466	1.86508
$142$	0.936080	0.0785541
$143$	3.35786	0.280798
$144$	6.36405	0.530337
$145$	18.4480	1.53202
$146$	2.67136	0.221084
$147$	16.0266	1.32185
$148$	−6.57044	−0.540087
$149$	10.9387	0.896136	0.448068	−	0.894000i	$-0.352112\pi$
$149$	10.9387	0.896136	0.448068	+	0.894000i	$0.352112\pi$
$150$	−0.128065	−0.0104565
$151$	−4.75935	−0.387311	−0.193655	−	0.981070i	$-0.562034\pi$
$151$	−4.75935	−0.387311	−0.193655	+	0.981070i	$0.562034\pi$
$152$	−0.880942	−0.0714539
$153$	5.31733	0.429881
$154$	−0.135278	−0.0109010
$155$	20.7801	1.66909
$156$	11.3829	0.911360
$157$	−6.82792	−0.544927	−0.272464	−	0.962166i	$-0.587838\pi$
$157$	−6.82792	−0.544927	−0.272464	+	0.962166i	$0.587838\pi$
$158$	−0.728639	−0.0579674
$159$	3.00017	0.237929
$160$	10.6462	0.841657
$161$	1.28986	0.101655
$162$	4.94441	0.388469
$163$	6.67688	0.522973	0.261487	−	0.965207i	$-0.415787\pi$
$163$	6.67688	0.522973	0.261487	+	0.965207i	$0.415787\pi$
$164$	−12.5902	−0.983131
$165$	6.18445	0.481459
$166$	3.91103	0.303555
$167$	18.5256	1.43355	0.716777	−	0.697302i	$-0.245617\pi$
$167$	18.5256	1.43355	0.716777	+	0.697302i	$0.245617\pi$
$168$	−0.973566	−0.0751123
$169$	−5.33282	−0.410217
$170$	2.36186	0.181147
$171$	−1.15894	−0.0886262
$172$	−15.3302	−1.16892
$173$	−16.6992	−1.26962	−0.634809	−	0.772669i	$-0.718921\pi$
$173$	−16.6992	−1.26962	−0.634809	+	0.772669i	$0.718921\pi$
$174$	−9.02037	−0.683832
$175$	−0.0282550	−0.00213588
$176$	3.31509	0.249884
$177$	−32.1278	−2.41487
$178$	−2.99967	−0.224835
$179$	13.8952	1.03858	0.519289	−	0.854599i	$-0.326197\pi$
$179$	13.8952	1.03858	0.519289	+	0.854599i	$0.326197\pi$
$180$	9.16029	0.682768
$181$	−11.8853	−0.883430	−0.441715	−	0.897156i	$-0.645630\pi$
$181$	−11.8853	−0.883430	−0.441715	+	0.897156i	$0.645630\pi$
$182$	−0.308887	−0.0228962
$183$	−11.2641	−0.832667
$184$	9.57629	0.705974
$185$	−8.15110	−0.599281
$186$	−10.1607	−0.745017
$187$	2.76985	0.202551
$188$	17.0875	1.24623
$189$	0.369716	0.0268929
$190$	−0.514779	−0.0373460
$191$	−1.91160	−0.138318	−0.0691591	−	0.997606i	$-0.522032\pi$
$191$	−1.91160	−0.138318	−0.0691591	+	0.997606i	$0.522032\pi$
$192$	7.41451	0.535096
$193$	−23.3705	−1.68224	−0.841121	−	0.540847i	$-0.818104\pi$
$193$	−23.3705	−1.68224	−0.841121	+	0.540847i	$0.818104\pi$
$194$	8.55372	0.614122
$195$	14.1213	1.01125
$196$	12.3655	0.883250
$197$	−16.6109	−1.18348	−0.591738	−	0.806130i	$-0.701558\pi$
$197$	−16.6109	−1.18348	−0.591738	+	0.806130i	$0.701558\pi$
$198$	−1.32128	−0.0938993
$199$	13.5050	0.957346	0.478673	−	0.877993i	$-0.341118\pi$
$199$	13.5050	0.957346	0.478673	+	0.877993i	$0.341118\pi$
$200$	−0.209774	−0.0148332
$201$	30.8794	2.17806
$202$	−8.13561	−0.572419
$203$	−1.99016	−0.139682
$204$	9.38958	0.657402
$205$	−15.6191	−1.09088
$206$	−8.37565	−0.583559
$207$	12.5982	0.875638
$208$	7.56953	0.524852
$209$	−0.603701	−0.0417589
$210$	−0.568904	−0.0392581
$211$	6.44791	0.443892	0.221946	−	0.975059i	$-0.428759\pi$
$211$	6.44791	0.443892	0.221946	+	0.975059i	$0.428759\pi$
$212$	2.31481	0.158982
$213$	4.61664	0.316327
$214$	3.87888	0.265154
$215$	−19.0182	−1.29703
$216$	2.74488	0.186765
$217$	−2.24174	−0.152180
$218$	5.74659	0.389208
$219$	13.1749	0.890276
$220$	4.77168	0.321707
$221$	6.32454	0.425435
$222$	3.98558	0.267495
$223$	−8.70331	−0.582816	−0.291408	−	0.956599i	$-0.594124\pi$
$223$	−8.70331	−0.582816	−0.291408	+	0.956599i	$0.594124\pi$
$224$	−1.14851	−0.0767380
$225$	−0.275971	−0.0183981
$226$	3.67238	0.244283
$227$	−28.7047	−1.90520	−0.952598	−	0.304233i	$-0.901600\pi$
$227$	−28.7047	−1.90520	−0.952598	+	0.304233i	$0.901600\pi$
$228$	−2.04650	−0.135533
$229$	−15.5843	−1.02984	−0.514919	−	0.857239i	$-0.672178\pi$
$229$	−15.5843	−1.02984	−0.514919	+	0.857239i	$0.672178\pi$
$230$	5.59591	0.368983
$231$	−0.667176	−0.0438969
$232$	−14.7756	−0.970063
$233$	11.0436	0.723490	0.361745	−	0.932277i	$-0.382181\pi$
$233$	11.0436	0.723490	0.361745	+	0.932277i	$0.382181\pi$
$234$	−3.01695	−0.197224
$235$	21.1983	1.38282
$236$	−24.7885	−1.61360
$237$	−3.59357	−0.233428
$238$	−0.254797	−0.0165160
$239$	−15.3393	−0.992217	−0.496108	−	0.868261i	$-0.665238\pi$
$239$	−15.3393	−0.992217	−0.496108	+	0.868261i	$0.665238\pi$
$240$	13.9414	0.899916
$241$	−0.946183	−0.0609490	−0.0304745	−	0.999536i	$-0.509702\pi$
$241$	−0.946183	−0.0609490	−0.0304745	+	0.999536i	$0.509702\pi$
$242$	4.46000	0.286700
$243$	19.7318	1.26580
$244$	−8.69096	−0.556381
$245$	15.3403	0.980055
$246$	7.63715	0.486927
$247$	−1.37846	−0.0877096
$248$	−16.6434	−1.05686
$249$	19.2888	1.22238
$250$	−5.29285	−0.334749
$251$	10.7951	0.681381	0.340690	−	0.940176i	$-0.389339\pi$
$251$	10.7951	0.681381	0.340690	+	0.940176i	$0.389339\pi$
$252$	−0.988209	−0.0622513
$253$	6.56254	0.412583
$254$	−0.769687	−0.0482945
$255$	11.6484	0.729454
$256$	1.21031	0.0756446
$257$	−16.8218	−1.04932	−0.524659	−	0.851313i	$-0.675807\pi$
$257$	−16.8218	−1.04932	−0.524659	+	0.851313i	$0.675807\pi$
$258$	9.29919	0.578943
$259$	0.879338	0.0546394
$260$	10.8954	0.675707
$261$	−19.4382	−1.20320
$262$	4.42754	0.273534
$263$	−4.19381	−0.258602	−0.129301	−	0.991605i	$-0.541273\pi$
$263$	−4.19381	−0.258602	−0.129301	+	0.991605i	$0.541273\pi$
$264$	−4.95331	−0.304855
$265$	2.87169	0.176407
$266$	0.0555342	0.00340502
$267$	−14.7941	−0.905382
$268$	23.8253	1.45536
$269$	17.3488	1.05778	0.528889	−	0.848691i	$-0.322609\pi$
$269$	17.3488	1.05778	0.528889	+	0.848691i	$0.322609\pi$
$270$	1.60397	0.0976146
$271$	−14.2546	−0.865903	−0.432951	−	0.901417i	$-0.642528\pi$
$271$	−14.2546	−0.865903	−0.432951	+	0.901417i	$0.642528\pi$
$272$	6.24400	0.378598
$273$	−1.52340	−0.0922003
$274$	9.17592	0.554338
$275$	−0.143756	−0.00866880
$276$	22.2465	1.33908
$277$	−17.0285	−1.02314	−0.511572	−	0.859240i	$-0.670937\pi$
$277$	−17.0285	−1.02314	−0.511572	+	0.859240i	$0.670937\pi$
$278$	−1.62579	−0.0975085
$279$	−21.8955	−1.31085
$280$	−0.931876	−0.0556903
$281$	30.4673	1.81753	0.908764	−	0.417311i	$-0.137027\pi$
$281$	30.4673	1.81753	0.908764	+	0.417311i	$0.137027\pi$
$282$	−10.3652	−0.617237
$283$	1.10336	0.0655878	0.0327939	−	0.999462i	$-0.489560\pi$
$283$	1.10336	0.0655878	0.0327939	+	0.999462i	$0.489560\pi$
$284$	3.56203	0.211367
$285$	−2.53884	−0.150388
$286$	−1.57156	−0.0929282
$287$	1.68498	0.0994613
$288$	−11.2177	−0.661007
$289$	−11.7830	−0.693116
$290$	−8.63410	−0.507012
$291$	42.1860	2.47299
$292$	10.1652	0.594875
$293$	7.05519	0.412169	0.206084	−	0.978534i	$-0.433928\pi$
$293$	7.05519	0.412169	0.206084	+	0.978534i	$0.433928\pi$
$294$	−7.50083	−0.437457
$295$	−30.7520	−1.79045
$296$	6.52847	0.379460
$297$	1.88104	0.109149
$298$	−5.11959	−0.296570
$299$	14.9846	0.866583
$300$	−0.487322	−0.0281355
$301$	2.05168	0.118257
$302$	2.22749	0.128178
$303$	−40.1239	−2.30506
$304$	−1.36091	−0.0780535
$305$	−10.7818	−0.617362
$306$	−2.48864	−0.142266
$307$	23.0145	1.31351	0.656754	−	0.754105i	$-0.271929\pi$
$307$	23.0145	1.31351	0.656754	+	0.754105i	$0.271929\pi$
$308$	−0.514767	−0.0293316
$309$	−41.3078	−2.34992
$310$	−9.72557	−0.552375
$311$	−4.17522	−0.236755	−0.118378	−	0.992969i	$-0.537769\pi$
$311$	−4.17522	−0.236755	−0.118378	+	0.992969i	$0.537769\pi$
$312$	−11.3102	−0.640313
$313$	−14.5653	−0.823280	−0.411640	−	0.911346i	$-0.635044\pi$
$313$	−14.5653	−0.823280	−0.411640	+	0.911346i	$0.635044\pi$
$314$	3.19563	0.180340
$315$	−1.22594	−0.0690742
$316$	−2.77266	−0.155974
$317$	20.5128	1.15211	0.576056	−	0.817410i	$-0.304591\pi$
$317$	20.5128	1.15211	0.576056	+	0.817410i	$0.304591\pi$
$318$	−1.40415	−0.0787408
$319$	−10.1255	−0.566922
$320$	7.09701	0.396735
$321$	19.1302	1.06774
$322$	−0.603685	−0.0336420
$323$	−1.13708	−0.0632686
$324$	18.8147	1.04526
$325$	−0.328246	−0.0182078
$326$	−3.12494	−0.173074
$327$	28.3416	1.56729
$328$	12.5098	0.690739
$329$	−2.28686	−0.126079
$330$	−2.89447	−0.159335
$331$	−16.1356	−0.886894	−0.443447	−	0.896301i	$-0.646245\pi$
$331$	−16.1356	−0.886894	−0.443447	+	0.896301i	$0.646245\pi$
$332$	14.8825	0.816782
$333$	8.58863	0.470654
$334$	−8.67043	−0.474425
$335$	29.5571	1.61487
$336$	−1.50400	−0.0820498
$337$	−21.0168	−1.14486	−0.572430	−	0.819953i	$-0.693999\pi$
$337$	−21.0168	−1.14486	−0.572430	+	0.819953i	$0.693999\pi$
$338$	2.49589	0.135759
$339$	18.1118	0.983697
$340$	8.98750	0.487415
$341$	−11.4056	−0.617645
$342$	0.542411	0.0293302
$343$	−3.32335	−0.179444
$344$	15.2323	0.821269
$345$	27.5984	1.48585
$346$	7.81564	0.420172
$347$	−11.6037	−0.622921	−0.311461	−	0.950259i	$-0.600818\pi$
$347$	−11.6037	−0.622921	−0.311461	+	0.950259i	$0.600818\pi$
$348$	−34.3248	−1.84000
$349$	−24.7779	−1.32633	−0.663165	−	0.748474i	$-0.730787\pi$
$349$	−24.7779	−1.32633	−0.663165	+	0.748474i	$0.730787\pi$
$350$	0.0132240	0.000706853 0
$351$	4.29508	0.229255
$352$	−5.84339	−0.311454
$353$	−18.9511	−1.00866	−0.504331	−	0.863510i	$-0.668261\pi$
$353$	−18.9511	−1.00866	−0.504331	+	0.863510i	$0.668261\pi$
$354$	15.0366	0.799184
$355$	4.41895	0.234534
$356$	−11.4145	−0.604969
$357$	−1.25663	−0.0665079
$358$	−6.50330	−0.343710
$359$	−20.0268	−1.05697	−0.528487	−	0.848941i	$-0.677240\pi$
$359$	−20.0268	−1.05697	−0.528487	+	0.848941i	$0.677240\pi$
$360$	−9.10178	−0.479706
$361$	−18.7522	−0.986956
$362$	5.56262	0.292365
$363$	21.9962	1.15450
$364$	−1.17540	−0.0616075
$365$	12.6107	0.660075
$366$	5.27188	0.275565
$367$	−18.1144	−0.945563	−0.472781	−	0.881180i	$-0.656750\pi$
$367$	−18.1144	−0.945563	−0.472781	+	0.881180i	$0.656750\pi$
$368$	14.7938	0.771179
$369$	16.4575	0.856742
$370$	3.81491	0.198328
$371$	−0.309797	−0.0160839
$372$	−38.6640	−2.00463
$373$	15.1847	0.786235	0.393118	−	0.919488i	$-0.371397\pi$
$373$	15.1847	0.786235	0.393118	+	0.919488i	$0.371397\pi$
$374$	−1.29636	−0.0670329
$375$	−26.1038	−1.34799
$376$	−16.9784	−0.875592
$377$	−23.1202	−1.19075
$378$	−0.173036	−0.00890000
$379$	13.2679	0.681524	0.340762	−	0.940150i	$-0.389315\pi$
$379$	13.2679	0.681524	0.340762	+	0.940150i	$0.389315\pi$
$380$	−1.95887	−0.100488
$381$	−3.79601	−0.194476
$382$	0.894673	0.0457755
$383$	−4.12422	−0.210738	−0.105369	−	0.994433i	$-0.533602\pi$
$383$	−4.12422	−0.210738	−0.105369	+	0.994433i	$0.533602\pi$
$384$	−25.7152	−1.31227
$385$	−0.638606	−0.0325464
$386$	10.9379	0.556727
$387$	20.0391	1.01864
$388$	32.5491	1.65243
$389$	23.4766	1.19031	0.595155	−	0.803611i	$-0.297091\pi$
$389$	23.4766	1.19031	0.595155	+	0.803611i	$0.297091\pi$
$390$	−6.60911	−0.334665
$391$	12.3606	0.625102
$392$	−12.2865	−0.620563
$393$	21.8362	1.10149
$394$	7.77429	0.391663
$395$	−3.43969	−0.173069
$396$	−5.02781	−0.252657
$397$	18.3573	0.921325	0.460663	−	0.887575i	$-0.347612\pi$
$397$	18.3573	0.921325	0.460663	+	0.887575i	$0.347612\pi$
$398$	−6.32068	−0.316827
$399$	0.273889	0.0137116
$400$	−0.324065	−0.0162033
$401$	13.8280	0.690537	0.345268	−	0.938504i	$-0.387788\pi$
$401$	13.8280	0.690537	0.345268	+	0.938504i	$0.387788\pi$
$402$	−14.4523	−0.720815
$403$	−26.0429	−1.29729
$404$	−30.9581	−1.54022
$405$	23.3411	1.15983
$406$	0.931443	0.0462267
$407$	4.47390	0.221763
$408$	−9.32960	−0.461884
$409$	−38.2442	−1.89106	−0.945528	−	0.325542i	$-0.894453\pi$
$409$	−38.2442	−1.89106	−0.945528	+	0.325542i	$0.894453\pi$
$410$	7.31011	0.361021
$411$	45.2547	2.23225
$412$	−31.8715	−1.57020
$413$	3.31751	0.163244
$414$	−5.89628	−0.289786
$415$	18.4628	0.906303
$416$	−13.3425	−0.654171
$417$	−8.01823	−0.392654
$418$	0.282547	0.0138198
$419$	4.95014	0.241830	0.120915	−	0.992663i	$-0.461417\pi$
$419$	4.95014	0.241830	0.120915	+	0.992663i	$0.461417\pi$
$420$	−2.16483	−0.105633
$421$	−36.2494	−1.76669	−0.883344	−	0.468725i	$-0.844713\pi$
$421$	−36.2494	−1.76669	−0.883344	+	0.468725i	$0.844713\pi$
$422$	−3.01778	−0.146903
$423$	−22.3361	−1.08602
$424$	−2.30003	−0.111699
$425$	−0.270765	−0.0131340
$426$	−2.16070	−0.104686
$427$	1.16313	0.0562879
$428$	14.7601	0.713458
$429$	−7.75075	−0.374210
$430$	8.90098	0.429244
$431$	5.87239	0.282863	0.141432	−	0.989948i	$-0.454829\pi$
$431$	5.87239	0.282863	0.141432	+	0.989948i	$0.454829\pi$
$432$	4.24038	0.204015
$433$	8.99660	0.432349	0.216175	−	0.976355i	$-0.430642\pi$
$433$	8.99660	0.432349	0.216175	+	0.976355i	$0.430642\pi$
$434$	1.04919	0.0503628
$435$	−42.5825	−2.04167
$436$	21.8673	1.04725
$437$	−2.69405	−0.128874
$438$	−6.16616	−0.294631
$439$	5.26286	0.251183	0.125591	−	0.992082i	$-0.459917\pi$
$439$	5.26286	0.251183	0.125591	+	0.992082i	$0.459917\pi$
$440$	−4.74120	−0.226028
$441$	−16.1637	−0.769701
$442$	−2.96004	−0.140795
$443$	16.9510	0.805369	0.402684	−	0.915339i	$-0.368077\pi$
$443$	16.9510	0.805369	0.402684	+	0.915339i	$0.368077\pi$
$444$	15.1662	0.719755
$445$	−14.1605	−0.671274
$446$	4.07336	0.192879
$447$	−25.2493	−1.19425
$448$	−0.765622	−0.0361722
$449$	−8.85560	−0.417921	−0.208961	−	0.977924i	$-0.567008\pi$
$449$	−8.85560	−0.417921	−0.208961	+	0.977924i	$0.567008\pi$
$450$	0.129161	0.00608871
$451$	8.57285	0.403680
$452$	13.9744	0.657299
$453$	10.9858	0.516156
$454$	13.4345	0.630511
$455$	−1.45816	−0.0683598
$456$	2.03343	0.0952241
$457$	19.3062	0.903107	0.451554	−	0.892244i	$-0.350870\pi$
$457$	19.3062	0.903107	0.451554	+	0.892244i	$0.350870\pi$
$458$	7.29382	0.340818
$459$	3.54295	0.165371
$460$	21.2939	0.992833
$461$	20.7094	0.964531	0.482265	−	0.876025i	$-0.339814\pi$
$461$	20.7094	0.964531	0.482265	+	0.876025i	$0.339814\pi$
$462$	0.312254	0.0145274
$463$	−25.7597	−1.19716	−0.598578	−	0.801065i	$-0.704267\pi$
$463$	−25.7597	−1.19716	−0.598578	+	0.801065i	$0.704267\pi$
$464$	−22.8258	−1.05966
$465$	−47.9655	−2.22435
$466$	−5.16867	−0.239434
$467$	17.8891	0.827810	0.413905	−	0.910320i	$-0.364164\pi$
$467$	17.8891	0.827810	0.413905	+	0.910320i	$0.364164\pi$
$468$	−11.4803	−0.530676
$469$	−3.18860	−0.147236
$470$	−9.92131	−0.457636
$471$	15.7605	0.726206
$472$	24.6302	1.13370
$473$	10.4385	0.479964
$474$	1.68188	0.0772512
$475$	0.0590145	0.00270777
$476$	−0.969567	−0.0444401
$477$	−3.02584	−0.138544
$478$	7.17916	0.328367
$479$	−1.64596	−0.0752060	−0.0376030	−	0.999293i	$-0.511972\pi$
$479$	−1.64596	−0.0752060	−0.0376030	+	0.999293i	$0.511972\pi$
$480$	−24.5741	−1.12165
$481$	10.2155	0.465787
$482$	0.442837	0.0201707
$483$	−2.97731	−0.135472
$484$	16.9715	0.771430
$485$	40.3796	1.83354
$486$	−9.23497	−0.418907
$487$	−8.07315	−0.365829	−0.182915	−	0.983129i	$-0.558553\pi$
$487$	−8.07315	−0.365829	−0.182915	+	0.983129i	$0.558553\pi$
$488$	8.63544	0.390908
$489$	−15.4119	−0.696949
$490$	−7.17963	−0.324343
$491$	5.56200	0.251010	0.125505	−	0.992093i	$-0.459945\pi$
$491$	5.56200	0.251010	0.125505	+	0.992093i	$0.459945\pi$
$492$	29.0613	1.31019
$493$	−19.0715	−0.858939
$494$	0.645155	0.0290269
$495$	−6.23736	−0.280349
$496$	−25.7113	−1.15447
$497$	−0.476715	−0.0213836
$498$	−9.02761	−0.404537
$499$	−41.0131	−1.83600	−0.918000	−	0.396580i	$-0.870197\pi$
$499$	−41.0131	−1.83600	−0.918000	+	0.396580i	$0.870197\pi$
$500$	−20.1407	−0.900718
$501$	−42.7616	−1.91045
$502$	−5.05237	−0.225498
$503$	6.00501	0.267750	0.133875	−	0.990998i	$-0.457258\pi$
$503$	6.00501	0.267750	0.133875	+	0.990998i	$0.457258\pi$
$504$	0.981897	0.0437372
$505$	−38.4058	−1.70903
$506$	−3.07143	−0.136542
$507$	12.3095	0.546682
$508$	−2.92886	−0.129947
$509$	−2.33621	−0.103551	−0.0517755	−	0.998659i	$-0.516488\pi$
$509$	−2.33621	−0.103551	−0.0517755	+	0.998659i	$0.516488\pi$
$510$	−5.45176	−0.241408
$511$	−1.36044	−0.0601822
$512$	−22.8476	−1.00973
$513$	−0.772203	−0.0340936
$514$	7.87303	0.347264
$515$	−39.5389	−1.74229
$516$	35.3858	1.55777
$517$	−11.6351	−0.511711
$518$	−0.411551	−0.0180825
$519$	38.5459	1.69198
$520$	−10.8259	−0.474745
$521$	−33.7196	−1.47728	−0.738642	−	0.674098i	$-0.764532\pi$
$521$	−33.7196	−1.47728	−0.738642	+	0.674098i	$0.764532\pi$
$522$	9.09755	0.398189
$523$	17.0287	0.744612	0.372306	−	0.928110i	$-0.378567\pi$
$523$	17.0287	0.744612	0.372306	+	0.928110i	$0.378567\pi$
$524$	16.8479	0.736006
$525$	0.0652194	0.00284641
$526$	1.96281	0.0855824
$527$	−21.4824	−0.935790
$528$	−7.65204	−0.333012
$529$	6.28570	0.273291
$530$	−1.34402	−0.0583806
$531$	32.4027	1.40616
$532$	0.211322	0.00916196
$533$	19.5749	0.847881
$534$	6.92398	0.299630
$535$	18.3110	0.791654
$536$	−23.6732	−1.02252
$537$	−32.0736	−1.38408
$538$	−8.11968	−0.350064
$539$	−8.41983	−0.362668
$540$	6.10353	0.262654
$541$	1.18488	0.0509420	0.0254710	−	0.999676i	$-0.491891\pi$
$541$	1.18488	0.0509420	0.0254710	+	0.999676i	$0.491891\pi$
$542$	6.67148	0.286565
$543$	27.4343	1.17732
$544$	−11.0061	−0.471881
$545$	27.1279	1.16203
$546$	0.712988	0.0305131
$547$	−3.83164	−0.163829	−0.0819146	−	0.996639i	$-0.526103\pi$
$547$	−3.83164	−0.163829	−0.0819146	+	0.996639i	$0.526103\pi$
$548$	34.9168	1.49157
$549$	11.3605	0.484854
$550$	0.0672812	0.00286888
$551$	4.15673	0.177083
$552$	−22.1044	−0.940827
$553$	0.371072	0.0157796
$554$	7.96975	0.338602
$555$	18.8147	0.798641
$556$	−6.18656	−0.262368
$557$	13.1533	0.557322	0.278661	−	0.960389i	$-0.410109\pi$
$557$	13.1533	0.557322	0.278661	+	0.960389i	$0.410109\pi$
$558$	10.2476	0.433816
$559$	23.8349	1.00811
$560$	−1.43959	−0.0608339
$561$	−6.39349	−0.269933
$562$	−14.2594	−0.601498
$563$	0.787806	0.0332020	0.0166010	−	0.999862i	$-0.494715\pi$
$563$	0.787806	0.0332020	0.0166010	+	0.999862i	$0.494715\pi$
$564$	−39.4421	−1.66081
$565$	17.3362	0.729340
$566$	−0.516398	−0.0217058
$567$	−2.51802	−0.105747
$568$	−3.53927	−0.148505
$569$	−30.9077	−1.29572	−0.647860	−	0.761759i	$-0.724336\pi$
$569$	−30.9077	−1.29572	−0.647860	+	0.761759i	$0.724336\pi$
$570$	1.18824	0.0497697
$571$	39.9807	1.67314	0.836570	−	0.547860i	$-0.184557\pi$
$571$	39.9807	1.67314	0.836570	+	0.547860i	$0.184557\pi$
$572$	−5.98018	−0.250044
$573$	4.41243	0.184332
$574$	−0.788612	−0.0329160
$575$	−0.641518	−0.0267532
$576$	−7.47795	−0.311581
$577$	−6.95723	−0.289633	−0.144817	−	0.989459i	$-0.546259\pi$
$577$	−6.95723	−0.289633	−0.144817	+	0.989459i	$0.546259\pi$
$578$	5.51472	0.229382
$579$	53.9448	2.24187
$580$	−32.8550	−1.36423
$581$	−1.99176	−0.0826320
$582$	−19.7441	−0.818419
$583$	−1.57619	−0.0652790
$584$	−10.1003	−0.417954
$585$	−14.2421	−0.588839
$586$	−3.30200	−0.136404
$587$	−34.8205	−1.43720	−0.718598	−	0.695426i	$-0.755216\pi$
$587$	−34.8205	−1.43720	−0.718598	+	0.695426i	$0.755216\pi$
$588$	−28.5426	−1.17708
$589$	4.68220	0.192927
$590$	14.3927	0.592537
$591$	38.3420	1.57718
$592$	10.0854	0.414507
$593$	43.9613	1.80528	0.902638	−	0.430400i	$-0.141628\pi$
$593$	43.9613	1.80528	0.902638	+	0.430400i	$0.141628\pi$
$594$	−0.880372	−0.0361221
$595$	−1.20282	−0.0493108
$596$	−19.4814	−0.797988
$597$	−31.1729	−1.27582
$598$	−7.01316	−0.286789
$599$	4.35206	0.177820	0.0889102	−	0.996040i	$-0.471662\pi$
$599$	4.35206	0.177820	0.0889102	+	0.996040i	$0.471662\pi$
$600$	0.484209	0.0197677
$601$	40.9550	1.67059	0.835295	−	0.549802i	$-0.185297\pi$
$601$	40.9550	1.67059	0.835295	+	0.549802i	$0.185297\pi$
$602$	−0.960235	−0.0391362
$603$	−31.1436	−1.26827
$604$	8.47619	0.344891
$605$	21.0543	0.855980
$606$	18.7790	0.762844
$607$	27.2967	1.10794	0.553970	−	0.832537i	$-0.313112\pi$
$607$	27.2967	1.10794	0.553970	+	0.832537i	$0.313112\pi$
$608$	2.39882	0.0972851
$609$	4.59378	0.186149
$610$	5.04613	0.204312
$611$	−26.5671	−1.07479
$612$	−9.46992	−0.382799
$613$	−44.8745	−1.81246	−0.906231	−	0.422782i	$-0.861054\pi$
$613$	−44.8745	−1.81246	−0.906231	+	0.422782i	$0.861054\pi$
$614$	−10.7714	−0.434697
$615$	36.0527	1.45378
$616$	0.511479	0.0206081
$617$	−36.6220	−1.47435	−0.737173	−	0.675704i	$-0.763840\pi$
$617$	−36.6220	−1.47435	−0.737173	+	0.675704i	$0.763840\pi$
$618$	19.3331	0.777690
$619$	−16.5839	−0.666564	−0.333282	−	0.942827i	$-0.608156\pi$
$619$	−16.5839	−0.666564	−0.333282	+	0.942827i	$0.608156\pi$
$620$	−37.0083	−1.48629
$621$	8.39424	0.336849
$622$	1.95410	0.0783524
$623$	1.52763	0.0612034
$624$	−17.4723	−0.699453
$625$	−24.3932	−0.975729
$626$	6.81692	0.272459
$627$	1.39349	0.0556507
$628$	12.1602	0.485245
$629$	8.42662	0.335991
$630$	0.573772	0.0228596
$631$	−3.75778	−0.149595	−0.0747975	−	0.997199i	$-0.523831\pi$
$631$	−3.75778	−0.149595	−0.0747975	+	0.997199i	$0.523831\pi$
$632$	2.75495	0.109586
$633$	−14.8834	−0.591560
$634$	−9.60047	−0.381283
$635$	−3.63346	−0.144190
$636$	−5.34315	−0.211870
$637$	−19.2255	−0.761741
$638$	4.73900	0.187619
$639$	−4.65615	−0.184194
$640$	−24.6140	−0.972953
$641$	−21.6669	−0.855792	−0.427896	−	0.903828i	$-0.640745\pi$
$641$	−21.6669	−0.855792	−0.427896	+	0.903828i	$0.640745\pi$
$642$	−8.95340	−0.353362
$643$	−23.5594	−0.929091	−0.464546	−	0.885549i	$-0.653782\pi$
$643$	−23.5594	−0.929091	−0.464546	+	0.885549i	$0.653782\pi$
$644$	−2.29718	−0.0905214
$645$	43.8987	1.72851
$646$	0.532179	0.0209383
$647$	18.1689	0.714292	0.357146	−	0.934049i	$-0.383750\pi$
$647$	18.1689	0.714292	0.357146	+	0.934049i	$0.383750\pi$
$648$	−18.6946	−0.734392
$649$	16.8788	0.662553
$650$	0.153627	0.00602574
$651$	5.17450	0.202805
$652$	−11.8912	−0.465695
$653$	−19.5229	−0.763989	−0.381994	−	0.924165i	$-0.624763\pi$
$653$	−19.5229	−0.763989	−0.381994	+	0.924165i	$0.624763\pi$
$654$	−13.2645	−0.518684
$655$	20.9011	0.816673
$656$	19.3256	0.754536
$657$	−13.2876	−0.518399
$658$	1.07031	0.0417249
$659$	20.0714	0.781872	0.390936	−	0.920418i	$-0.372151\pi$
$659$	20.0714	0.781872	0.390936	+	0.920418i	$0.372151\pi$
$660$	−11.0142	−0.428728
$661$	10.4414	0.406123	0.203061	−	0.979166i	$-0.434911\pi$
$661$	10.4414	0.406123	0.203061	+	0.979166i	$0.434911\pi$
$662$	7.55186	0.293511
$663$	−14.5986	−0.566963
$664$	−14.7874	−0.573863
$665$	0.262160	0.0101661
$666$	−4.01969	−0.155760
$667$	−45.1858	−1.74960
$668$	−32.9932	−1.27655
$669$	20.0894	0.776700
$670$	−13.8334	−0.534432
$671$	5.91779	0.228454
$672$	2.65104	0.102266
$673$	9.41315	0.362850	0.181425	−	0.983405i	$-0.441929\pi$
$673$	9.41315	0.362850	0.181425	+	0.983405i	$0.441929\pi$
$674$	9.83639	0.378884
$675$	−0.183880	−0.00707755
$676$	9.49751	0.365289
$677$	−19.4006	−0.745627	−0.372814	−	0.927906i	$-0.621607\pi$
$677$	−19.4006	−0.745627	−0.372814	+	0.927906i	$0.621607\pi$
$678$	−8.47676	−0.325548
$679$	−4.35613	−0.167173
$680$	−8.93009	−0.342453
$681$	66.2574	2.53899
$682$	5.33808	0.204405
$683$	5.94941	0.227648	0.113824	−	0.993501i	$-0.463690\pi$
$683$	5.94941	0.227648	0.113824	+	0.993501i	$0.463690\pi$
$684$	2.06401	0.0789196
$685$	43.3168	1.65505
$686$	1.55541	0.0593858
$687$	35.9723	1.37243
$688$	23.5313	0.897123
$689$	−3.59899	−0.137111
$690$	−12.9167	−0.491732
$691$	32.7362	1.24534	0.622671	−	0.782483i	$-0.286047\pi$
$691$	32.7362	1.24534	0.622671	+	0.782483i	$0.286047\pi$
$692$	29.7405	1.13057
$693$	0.672884	0.0255608
$694$	5.43083	0.206151
$695$	−7.67487	−0.291124
$696$	34.1056	1.29277
$697$	16.1470	0.611612
$698$	11.5966	0.438940
$699$	−25.4913	−0.964171
$700$	0.0503208	0.00190195
$701$	−18.8732	−0.712832	−0.356416	−	0.934327i	$-0.616001\pi$
$701$	−18.8732	−0.712832	−0.356416	+	0.934327i	$0.616001\pi$
$702$	−2.01020	−0.0758702
$703$	−1.83662	−0.0692695
$704$	−3.89533	−0.146811
$705$	−48.9308	−1.84284
$706$	8.86955	0.333810
$707$	4.14320	0.155821
$708$	57.2180	2.15039
$709$	−4.71421	−0.177046	−0.0885229	−	0.996074i	$-0.528215\pi$
$709$	−4.71421	−0.177046	−0.0885229	+	0.996074i	$0.528215\pi$
$710$	−2.06818	−0.0776173
$711$	3.62432	0.135923
$712$	11.3416	0.425045
$713$	−50.8979	−1.90614
$714$	0.588133	0.0220103
$715$	−7.41885	−0.277449
$716$	−24.7467	−0.924829
$717$	35.4069	1.32229
$718$	9.37302	0.349798
$719$	14.9828	0.558763	0.279382	−	0.960180i	$-0.409871\pi$
$719$	14.9828	0.558763	0.279382	+	0.960180i	$0.409871\pi$
$720$	−14.0607	−0.524013
$721$	4.26544	0.158853
$722$	8.77647	0.326626
$723$	2.18402	0.0812247
$724$	21.1672	0.786673
$725$	0.989818	0.0367609
$726$	−10.2948	−0.382075
$727$	16.7993	0.623053	0.311526	−	0.950237i	$-0.399160\pi$
$727$	16.7993	0.623053	0.311526	+	0.950237i	$0.399160\pi$
$728$	1.16789	0.0432848
$729$	−13.8526	−0.513060
$730$	−5.90212	−0.218447
$731$	19.6610	0.727190
$732$	20.0609	0.741471
$733$	−50.5451	−1.86693	−0.933464	−	0.358672i	$-0.883230\pi$
$733$	−50.5451	−1.86693	−0.933464	+	0.358672i	$0.883230\pi$
$734$	8.47797	0.312927
$735$	−35.4092	−1.30609
$736$	−26.0764	−0.961190
$737$	−16.2230	−0.597581
$738$	−7.70250	−0.283533
$739$	2.17207	0.0799008	0.0399504	−	0.999202i	$-0.487280\pi$
$739$	2.17207	0.0799008	0.0399504	+	0.999202i	$0.487280\pi$
$740$	14.5167	0.533646
$741$	3.18183	0.116888
$742$	0.144992	0.00532284
$743$	42.1896	1.54779	0.773894	−	0.633316i	$-0.218306\pi$
$743$	42.1896	1.54779	0.773894	+	0.633316i	$0.218306\pi$
$744$	38.4170	1.40844
$745$	−24.1680	−0.885449
$746$	−7.10682	−0.260199
$747$	−19.4538	−0.711778
$748$	−4.93297	−0.180367
$749$	−1.97538	−0.0721790
$750$	12.2172	0.446109
$751$	2.41896	0.0882690	0.0441345	−	0.999026i	$-0.485947\pi$
$751$	2.41896	0.0882690	0.0441345	+	0.999026i	$0.485947\pi$
$752$	−26.2287	−0.956463
$753$	−24.9177	−0.908053
$754$	10.8208	0.394071
$755$	10.5153	0.382692
$756$	−0.658446	−0.0239475
$757$	−26.1201	−0.949350	−0.474675	−	0.880161i	$-0.657434\pi$
$757$	−26.1201	−0.949350	−0.474675	+	0.880161i	$0.657434\pi$
$758$	−6.20968	−0.225546
$759$	−15.1480	−0.549836
$760$	1.94636	0.0706017
$761$	37.4242	1.35663	0.678313	−	0.734773i	$-0.262712\pi$
$761$	37.4242	1.35663	0.678313	+	0.734773i	$0.262712\pi$
$762$	1.77663	0.0643604
$763$	−2.92655	−0.105948
$764$	3.40446	0.123169
$765$	−11.7481	−0.424754
$766$	1.93023	0.0697422
$767$	38.5404	1.39161
$768$	−2.79370	−0.100809
$769$	17.1452	0.618272	0.309136	−	0.951018i	$-0.399960\pi$
$769$	17.1452	0.618272	0.309136	+	0.951018i	$0.399960\pi$
$770$	0.298883	0.0107710
$771$	38.8289	1.39839
$772$	41.6217	1.49800
$773$	8.69849	0.312863	0.156431	−	0.987689i	$-0.450001\pi$
$773$	8.69849	0.312863	0.156431	+	0.987689i	$0.450001\pi$
$774$	−9.37876	−0.337113
$775$	1.11494	0.0400500
$776$	−32.3412	−1.16098
$777$	−2.02973	−0.0728161
$778$	−10.9876	−0.393925
$779$	−3.51932	−0.126093
$780$	−25.1494	−0.900491
$781$	−2.42543	−0.0867887
$782$	−5.78506	−0.206873
$783$	−12.9517	−0.462857
$784$	−18.9806	−0.677879
$785$	15.0856	0.538429
$786$	−10.2199	−0.364530
$787$	13.0154	0.463951	0.231975	−	0.972722i	$-0.425481\pi$
$787$	13.0154	0.463951	0.231975	+	0.972722i	$0.425481\pi$
$788$	29.5832	1.05386
$789$	9.68035	0.344630
$790$	1.60986	0.0572761
$791$	−1.87022	−0.0664975
$792$	4.99570	0.177514
$793$	13.5124	0.479840
$794$	−8.59165	−0.304906
$795$	−6.62857	−0.235091
$796$	−24.0518	−0.852494
$797$	−24.2704	−0.859701	−0.429851	−	0.902900i	$-0.641434\pi$
$797$	−24.2704	−0.859701	−0.429851	+	0.902900i	$0.641434\pi$
$798$	−0.128186	−0.00453775
$799$	−21.9148	−0.775290
$800$	0.571217	0.0201956
$801$	14.9206	0.527195
$802$	−6.47183	−0.228528
$803$	−6.92164	−0.244259
$804$	−54.9947	−1.93951
$805$	−2.84981	−0.100443
$806$	12.1887	0.429329
$807$	−40.0454	−1.40966
$808$	30.7603	1.08215
$809$	−12.4933	−0.439240	−0.219620	−	0.975586i	$-0.570482\pi$
$809$	−12.4933	−0.439240	−0.219620	+	0.975586i	$0.570482\pi$
$810$	−10.9242	−0.383836
$811$	40.7415	1.43063	0.715313	−	0.698804i	$-0.246284\pi$
$811$	40.7415	1.43063	0.715313	+	0.698804i	$0.246284\pi$
$812$	3.54438	0.124383
$813$	32.9030	1.15396
$814$	−2.09389	−0.0733909
$815$	−14.7519	−0.516737
$816$	−14.4127	−0.504544
$817$	−4.28522	−0.149921
$818$	17.8992	0.625832
$819$	1.53643	0.0536874
$820$	27.8169	0.971407
$821$	5.36259	0.187156	0.0935778	−	0.995612i	$-0.470170\pi$
$821$	5.36259	0.187156	0.0935778	+	0.995612i	$0.470170\pi$
$822$	−21.1803	−0.738747
$823$	37.0594	1.29181	0.645904	−	0.763419i	$-0.276481\pi$
$823$	37.0594	1.29181	0.645904	+	0.763419i	$0.276481\pi$
$824$	31.6679	1.10321
$825$	0.331824	0.0115526
$826$	−1.55268	−0.0540245
$827$	26.8175	0.932536	0.466268	−	0.884643i	$-0.345598\pi$
$827$	26.8175	0.932536	0.466268	+	0.884643i	$0.345598\pi$
$828$	−22.4369	−0.779736
$829$	23.2374	0.807069	0.403534	−	0.914965i	$-0.367782\pi$
$829$	23.2374	0.807069	0.403534	+	0.914965i	$0.367782\pi$
$830$	−8.64103	−0.299935
$831$	39.3060	1.36351
$832$	−8.89443	−0.308359
$833$	−15.8588	−0.549475
$834$	3.75272	0.129946
$835$	−40.9305	−1.41646
$836$	1.07516	0.0371853
$837$	−14.5890	−0.504270
$838$	−2.31678	−0.0800320
$839$	−24.3371	−0.840209	−0.420104	−	0.907476i	$-0.638007\pi$
$839$	−24.3371	−0.840209	−0.420104	+	0.907476i	$0.638007\pi$
$840$	2.15100	0.0742165
$841$	40.7185	1.40409
$842$	16.9656	0.584673
$843$	−70.3260	−2.42216
$844$	−11.4834	−0.395276
$845$	11.7823	0.405325
$846$	10.4539	0.359411
$847$	−2.27133	−0.0780439
$848$	−3.55316	−0.122016
$849$	−2.54682	−0.0874066
$850$	0.126725	0.00434662
$851$	19.9650	0.684392
$852$	−8.22203	−0.281682
$853$	4.96649	0.170049	0.0850247	−	0.996379i	$-0.472903\pi$
$853$	4.96649	0.170049	0.0850247	+	0.996379i	$0.472903\pi$
$854$	−0.544374	−0.0186281
$855$	2.56056	0.0875693
$856$	−14.6658	−0.501268
$857$	4.70246	0.160633	0.0803165	−	0.996769i	$-0.474407\pi$
$857$	4.70246	0.160633	0.0803165	+	0.996769i	$0.474407\pi$
$858$	3.62754	0.123842
$859$	−4.07672	−0.139096	−0.0695479	−	0.997579i	$-0.522156\pi$
$859$	−4.07672	−0.139096	−0.0695479	+	0.997579i	$0.522156\pi$
$860$	33.8706	1.15498
$861$	−3.88935	−0.132549
$862$	−2.74842	−0.0936116
$863$	56.7979	1.93342	0.966711	−	0.255870i	$-0.0823619\pi$
$863$	56.7979	1.93342	0.966711	+	0.255870i	$0.0823619\pi$
$864$	−7.47436	−0.254283
$865$	36.8953	1.25448
$866$	−4.21063	−0.143083
$867$	27.1980	0.923692
$868$	3.99244	0.135512
$869$	1.88794	0.0640440
$870$	19.9296	0.675677
$871$	−37.0428	−1.25515
$872$	−21.7276	−0.735789
$873$	−42.5470	−1.44000
$874$	1.26088	0.0426499
$875$	2.69547	0.0911236
$876$	−23.4638	−0.792770
$877$	−17.8297	−0.602065	−0.301032	−	0.953614i	$-0.597331\pi$
$877$	−17.8297	−0.602065	−0.301032	+	0.953614i	$0.597331\pi$
$878$	−2.46315	−0.0831271
$879$	−16.2851	−0.549283
$880$	−7.32437	−0.246904
$881$	2.40619	0.0810667	0.0405334	−	0.999178i	$-0.487094\pi$
$881$	2.40619	0.0810667	0.0405334	+	0.999178i	$0.487094\pi$
$882$	7.56501	0.254727
$883$	−23.8286	−0.801898	−0.400949	−	0.916100i	$-0.631320\pi$
$883$	−23.8286	−0.801898	−0.400949	+	0.916100i	$0.631320\pi$
$884$	−11.2637	−0.378840
$885$	70.9831	2.38607
$886$	−7.93350	−0.266531
$887$	−30.1484	−1.01228	−0.506142	−	0.862450i	$-0.668929\pi$
$887$	−30.1484	−1.01228	−0.506142	+	0.862450i	$0.668929\pi$
$888$	−15.0693	−0.505693
$889$	0.391976	0.0131465
$890$	6.62748	0.222154
$891$	−12.8112	−0.429192
$892$	15.5002	0.518984
$893$	4.77643	0.159837
$894$	11.8173	0.395229
$895$	−30.7001	−1.02619
$896$	2.65535	0.0887089
$897$	−34.5882	−1.15487
$898$	4.14463	0.138308
$899$	78.5319	2.61919
$900$	0.491491	0.0163830
$901$	−2.96876	−0.0989037
$902$	−4.01230	−0.133595
$903$	−4.73577	−0.157597
$904$	−13.8851	−0.461812
$905$	26.2595	0.872894
$906$	−5.14160	−0.170818
$907$	−28.0234	−0.930501	−0.465250	−	0.885179i	$-0.654036\pi$
$907$	−28.0234	−0.930501	−0.465250	+	0.885179i	$0.654036\pi$
$908$	51.1217	1.69653
$909$	40.4673	1.34221
$910$	0.682456	0.0226232
$911$	−12.4842	−0.413620	−0.206810	−	0.978381i	$-0.566308\pi$
$911$	−12.4842	−0.413620	−0.206810	+	0.978381i	$0.566308\pi$
$912$	3.14131	0.104019
$913$	−10.1337	−0.335376
$914$	−9.03578	−0.298877
$915$	24.8869	0.822737
$916$	27.7549	0.917047
$917$	−2.25480	−0.0744601
$918$	−1.65819	−0.0547283
$919$	34.9133	1.15168	0.575842	−	0.817561i	$-0.304674\pi$
$919$	34.9133	1.15168	0.575842	+	0.817561i	$0.304674\pi$
$920$	−21.1579	−0.697555
$921$	−53.1232	−1.75047
$922$	−9.69248	−0.319205
$923$	−5.53812	−0.182289
$924$	1.18821	0.0390892
$925$	−0.437344	−0.0143798
$926$	12.0562	0.396190
$927$	41.6613	1.36834
$928$	40.2341	1.32075
$929$	−2.52020	−0.0826851	−0.0413425	−	0.999145i	$-0.513163\pi$
$929$	−2.52020	−0.0826851	−0.0413425	+	0.999145i	$0.513163\pi$
$930$	22.4490	0.736132
$931$	3.45650	0.113282
$932$	−19.6681	−0.644251
$933$	9.63743	0.315515
$934$	−8.37255	−0.273958
$935$	−6.11970	−0.200136
$936$	11.4070	0.372848
$937$	15.6053	0.509802	0.254901	−	0.966967i	$-0.417957\pi$
$937$	15.6053	0.509802	0.254901	+	0.966967i	$0.417957\pi$
$938$	1.49234	0.0487267
$939$	33.6203	1.09716
$940$	−37.7531	−1.23137
$941$	43.2596	1.41022	0.705111	−	0.709097i	$-0.250897\pi$
$941$	43.2596	1.41022	0.705111	+	0.709097i	$0.250897\pi$
$942$	−7.37630	−0.240333
$943$	38.2568	1.24581
$944$	38.0495	1.23841
$945$	−0.816850	−0.0265721
$946$	−4.88548	−0.158841
$947$	5.06125	0.164468	0.0822342	−	0.996613i	$-0.473794\pi$
$947$	5.06125	0.164468	0.0822342	+	0.996613i	$0.473794\pi$
$948$	6.39998	0.207862
$949$	−15.8046	−0.513038
$950$	−0.0276202	−0.000896119 0
$951$	−47.3485	−1.53538
$952$	0.963374	0.0312231
$953$	−18.4874	−0.598865	−0.299433	−	0.954117i	$-0.596797\pi$
$953$	−18.4874	−0.598865	−0.299433	+	0.954117i	$0.596797\pi$
$954$	1.41616	0.0458500
$955$	4.22348	0.136669
$956$	27.3186	0.883546
$957$	23.3722	0.755517
$958$	0.770350	0.0248889
$959$	−4.67300	−0.150899
$960$	−16.3816	−0.528715
$961$	57.4595	1.85353
$962$	−4.78110	−0.154149
$963$	−19.2939	−0.621737
$964$	1.68511	0.0542737
$965$	51.6347	1.66218
$966$	1.39345	0.0448336
$967$	30.1517	0.969612	0.484806	−	0.874622i	$-0.338890\pi$
$967$	30.1517	0.969612	0.484806	+	0.874622i	$0.338890\pi$
$968$	−16.8630	−0.541999
$969$	2.62465	0.0843159
$970$	−18.8986	−0.606798
$971$	56.2443	1.80497	0.902483	−	0.430726i	$-0.141742\pi$
$971$	56.2443	1.80497	0.902483	+	0.430726i	$0.141742\pi$
$972$	−35.1415	−1.12716
$973$	0.827962	0.0265432
$974$	3.77843	0.121069
$975$	0.757671	0.0242649
$976$	13.3403	0.427013
$977$	19.7620	0.632244	0.316122	−	0.948719i	$-0.397619\pi$
$977$	19.7620	0.632244	0.316122	+	0.948719i	$0.397619\pi$
$978$	7.21313	0.230650
$979$	7.77230	0.248404
$980$	−27.3203	−0.872717
$981$	−28.5841	−0.912619
$982$	−2.60315	−0.0830699
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	−28.8757	−0.920524
$985$	36.7001	1.16936
$986$	8.92594	0.284260
$987$	5.27864	0.168021
$988$	2.45498	0.0781034
$989$	46.5825	1.48124
$990$	2.91924	0.0927795
$991$	−35.8741	−1.13958	−0.569789	−	0.821791i	$-0.692975\pi$
$991$	−35.8741	−1.13958	−0.569789	+	0.821791i	$0.692975\pi$
$992$	45.3203	1.43892
$993$	37.2450	1.18193
$994$	0.223114	0.00707675
$995$	−29.8380	−0.945929
$996$	−34.3524	−1.08850
$997$	12.5497	0.397452	0.198726	−	0.980055i	$-0.436320\pi$
$997$	12.5497	0.397452	0.198726	+	0.980055i	$0.436320\pi$
$998$	19.1951	0.607612
$999$	5.72263	0.181056

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.13	✓	28
3.2	odd	2		8847.2.a.b.1.16		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.13	✓	28	1.1	even	1	trivial
8847.2.a.b.1.16		28	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)

\(f(q)\)	\(=\)	\(q-0.468024 q^{2} -2.30825 q^{3} -1.78095 q^{4} -2.20940 q^{5} +1.08031 q^{6} +0.238349 q^{7} +1.76958 q^{8} +2.32800 q^{9} +O(q^{10})\)	\(q-0.468024 q^{2} -2.30825 q^{3} -1.78095 q^{4} -2.20940 q^{5} +1.08031 q^{6} +0.238349 q^{7} +1.76958 q^{8} +2.32800 q^{9} +1.03405 q^{10} +1.21267 q^{11} +4.11088 q^{12} +2.76897 q^{13} -0.111553 q^{14} +5.09984 q^{15} +2.73370 q^{16} +2.28408 q^{17} -1.08956 q^{18} -0.497826 q^{19} +3.93484 q^{20} -0.550169 q^{21} -0.567561 q^{22} +5.41163 q^{23} -4.08462 q^{24} -0.118544 q^{25} -1.29594 q^{26} +1.55115 q^{27} -0.424489 q^{28} -8.34976 q^{29} -2.38685 q^{30} -9.40529 q^{31} -4.81859 q^{32} -2.79915 q^{33} -1.06901 q^{34} -0.526609 q^{35} -4.14605 q^{36} +3.68928 q^{37} +0.232995 q^{38} -6.39145 q^{39} -3.90971 q^{40} +7.06937 q^{41} +0.257492 q^{42} +8.60786 q^{43} -2.15972 q^{44} -5.14348 q^{45} -2.53277 q^{46} -9.59458 q^{47} -6.31005 q^{48} -6.94319 q^{49} +0.0554817 q^{50} -5.27222 q^{51} -4.93140 q^{52} -1.29976 q^{53} -0.725976 q^{54} -2.67929 q^{55} +0.421778 q^{56} +1.14911 q^{57} +3.90789 q^{58} +13.9187 q^{59} -9.08258 q^{60} +4.87995 q^{61} +4.40190 q^{62} +0.554876 q^{63} -3.21218 q^{64} -6.11776 q^{65} +1.31007 q^{66} -13.3779 q^{67} -4.06784 q^{68} -12.4914 q^{69} +0.246466 q^{70} -2.00007 q^{71} +4.11957 q^{72} -5.70775 q^{73} -1.72667 q^{74} +0.273630 q^{75} +0.886606 q^{76} +0.289040 q^{77} +2.99136 q^{78} +1.55684 q^{79} -6.03984 q^{80} -10.5644 q^{81} -3.30864 q^{82} -8.35646 q^{83} +0.979825 q^{84} -5.04645 q^{85} -4.02869 q^{86} +19.2733 q^{87} +2.14592 q^{88} +6.40922 q^{89} +2.40727 q^{90} +0.659981 q^{91} -9.63785 q^{92} +21.7097 q^{93} +4.49050 q^{94} +1.09990 q^{95} +11.1225 q^{96} -18.2762 q^{97} +3.24958 q^{98} +2.82310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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