LMFDB - Embedded newform 983.2.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.42034 q^{2} -0.187530 q^{3} +3.85806 q^{4} -0.842553 q^{5} +0.453886 q^{6} -4.42798 q^{7} -4.49714 q^{8} -2.96483 q^{9} +O(q^{10})$	\(q-2.42034 q^{2} -0.187530 q^{3} +3.85806 q^{4} -0.842553 q^{5} +0.453886 q^{6} -4.42798 q^{7} -4.49714 q^{8} -2.96483 q^{9} +2.03927 q^{10} +3.24563 q^{11} -0.723501 q^{12} +5.55746 q^{13} +10.7172 q^{14} +0.158004 q^{15} +3.16851 q^{16} +4.25842 q^{17} +7.17591 q^{18} +3.08612 q^{19} -3.25062 q^{20} +0.830378 q^{21} -7.85554 q^{22} -3.57761 q^{23} +0.843348 q^{24} -4.29010 q^{25} -13.4510 q^{26} +1.11858 q^{27} -17.0834 q^{28} +6.29431 q^{29} -0.382423 q^{30} -1.87267 q^{31} +1.32541 q^{32} -0.608652 q^{33} -10.3068 q^{34} +3.73081 q^{35} -11.4385 q^{36} -9.28267 q^{37} -7.46946 q^{38} -1.04219 q^{39} +3.78908 q^{40} -6.75571 q^{41} -2.00980 q^{42} +1.44805 q^{43} +12.5218 q^{44} +2.49803 q^{45} +8.65904 q^{46} +6.92600 q^{47} -0.594189 q^{48} +12.6070 q^{49} +10.3835 q^{50} -0.798579 q^{51} +21.4410 q^{52} -11.3718 q^{53} -2.70735 q^{54} -2.73462 q^{55} +19.9133 q^{56} -0.578739 q^{57} -15.2344 q^{58} +7.61241 q^{59} +0.609588 q^{60} -13.5032 q^{61} +4.53249 q^{62} +13.1282 q^{63} -9.54497 q^{64} -4.68245 q^{65} +1.47315 q^{66} -6.99442 q^{67} +16.4292 q^{68} +0.670908 q^{69} -9.02984 q^{70} +9.15452 q^{71} +13.3333 q^{72} -15.6930 q^{73} +22.4672 q^{74} +0.804522 q^{75} +11.9064 q^{76} -14.3716 q^{77} +2.52245 q^{78} +8.88430 q^{79} -2.66963 q^{80} +8.68473 q^{81} +16.3511 q^{82} -14.7643 q^{83} +3.20365 q^{84} -3.58794 q^{85} -3.50477 q^{86} -1.18037 q^{87} -14.5961 q^{88} -6.86351 q^{89} -6.04609 q^{90} -24.6083 q^{91} -13.8026 q^{92} +0.351180 q^{93} -16.7633 q^{94} -2.60022 q^{95} -0.248554 q^{96} -16.3322 q^{97} -30.5133 q^{98} -9.62275 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.42034	−1.71144	−0.855720	−	0.517438i	$-0.826886\pi$
$2$	−2.42034	−1.71144	−0.855720	+	0.517438i	$0.826886\pi$
$3$	−0.187530	−0.108270	−0.0541352	−	0.998534i	$-0.517240\pi$
$3$	−0.187530	−0.108270	−0.0541352	+	0.998534i	$0.517240\pi$
$4$	3.85806	1.92903
$5$	−0.842553	−0.376801	−0.188401	−	0.982092i	$-0.560330\pi$
$5$	−0.842553	−0.376801	−0.188401	+	0.982092i	$0.560330\pi$
$6$	0.453886	0.185298
$7$	−4.42798	−1.67362	−0.836810	−	0.547494i	$-0.815582\pi$
$7$	−4.42798	−1.67362	−0.836810	+	0.547494i	$0.815582\pi$
$8$	−4.49714	−1.58998
$9$	−2.96483	−0.988278
$10$	2.03927	0.644873
$11$	3.24563	0.978594	0.489297	−	0.872117i	$-0.337253\pi$
$11$	3.24563	0.978594	0.489297	+	0.872117i	$0.337253\pi$
$12$	−0.723501	−0.208857
$13$	5.55746	1.54136	0.770681	−	0.637221i	$-0.219916\pi$
$13$	5.55746	1.54136	0.770681	+	0.637221i	$0.219916\pi$
$14$	10.7172	2.86430
$15$	0.158004	0.0407964
$16$	3.16851	0.792126
$17$	4.25842	1.03282	0.516409	−	0.856342i	$-0.327269\pi$
$17$	4.25842	1.03282	0.516409	+	0.856342i	$0.327269\pi$
$18$	7.17591	1.69138
$19$	3.08612	0.708004	0.354002	−	0.935245i	$-0.384821\pi$
$19$	3.08612	0.708004	0.354002	+	0.935245i	$0.384821\pi$
$20$	−3.25062	−0.726861
$21$	0.830378	0.181203
$22$	−7.85554	−1.67481
$23$	−3.57761	−0.745983	−0.372992	−	0.927835i	$-0.621668\pi$
$23$	−3.57761	−0.745983	−0.372992	+	0.927835i	$0.621668\pi$
$24$	0.843348	0.172148
$25$	−4.29010	−0.858021
$26$	−13.4510	−2.63795
$27$	1.11858	0.215271
$28$	−17.0834	−3.22846
$29$	6.29431	1.16882	0.584412	−	0.811457i	$-0.301325\pi$
$29$	6.29431	1.16882	0.584412	+	0.811457i	$0.301325\pi$
$30$	−0.382423	−0.0698206
$31$	−1.87267	−0.336341	−0.168170	−	0.985758i	$-0.553786\pi$
$31$	−1.87267	−0.336341	−0.168170	+	0.985758i	$0.553786\pi$
$32$	1.32541	0.234302
$33$	−0.608652	−0.105953
$34$	−10.3068	−1.76761
$35$	3.73081	0.630622
$36$	−11.4385	−1.90642
$37$	−9.28267	−1.52606	−0.763031	−	0.646362i	$-0.776289\pi$
$37$	−9.28267	−1.52606	−0.763031	+	0.646362i	$0.776289\pi$
$38$	−7.46946	−1.21171
$39$	−1.04219	−0.166884
$40$	3.78908	0.599106
$41$	−6.75571	−1.05506	−0.527532	−	0.849535i	$-0.676883\pi$
$41$	−6.75571	−1.05506	−0.527532	+	0.849535i	$0.676883\pi$
$42$	−2.00980	−0.310119
$43$	1.44805	0.220825	0.110413	−	0.993886i	$-0.464783\pi$
$43$	1.44805	0.220825	0.110413	+	0.993886i	$0.464783\pi$
$44$	12.5218	1.88774
$45$	2.49803	0.372384
$46$	8.65904	1.27671
$47$	6.92600	1.01026	0.505130	−	0.863043i	$-0.331444\pi$
$47$	6.92600	1.01026	0.505130	+	0.863043i	$0.331444\pi$
$48$	−0.594189	−0.0857638
$49$	12.6070	1.80100
$50$	10.3835	1.46845
$51$	−0.798579	−0.111823
$52$	21.4410	2.97333
$53$	−11.3718	−1.56204	−0.781021	−	0.624505i	$-0.785301\pi$
$53$	−11.3718	−1.56204	−0.781021	+	0.624505i	$0.785301\pi$
$54$	−2.70735	−0.368424
$55$	−2.73462	−0.368736
$56$	19.9133	2.66102
$57$	−0.578739	−0.0766558
$58$	−15.2344	−2.00037
$59$	7.61241	0.991051	0.495525	−	0.868593i	$-0.334976\pi$
$59$	7.61241	0.991051	0.495525	+	0.868593i	$0.334976\pi$
$60$	0.609588	0.0786975
$61$	−13.5032	−1.72891	−0.864455	−	0.502710i	$-0.832336\pi$
$61$	−13.5032	−1.72891	−0.864455	+	0.502710i	$0.832336\pi$
$62$	4.53249	0.575627
$63$	13.1282	1.65400
$64$	−9.54497	−1.19312
$65$	−4.68245	−0.580787
$66$	1.47315	0.181332
$67$	−6.99442	−0.854505	−0.427252	−	0.904132i	$-0.640518\pi$
$67$	−6.99442	−0.854505	−0.427252	+	0.904132i	$0.640518\pi$
$68$	16.4292	1.99234
$69$	0.670908	0.0807678
$70$	−9.02984	−1.07927
$71$	9.15452	1.08644	0.543221	−	0.839590i	$-0.317205\pi$
$71$	9.15452	1.08644	0.543221	+	0.839590i	$0.317205\pi$
$72$	13.3333	1.57134
$73$	−15.6930	−1.83673	−0.918364	−	0.395738i	$-0.870489\pi$
$73$	−15.6930	−1.83673	−0.918364	+	0.395738i	$0.870489\pi$
$74$	22.4672	2.61176
$75$	0.804522	0.0928982
$76$	11.9064	1.36576
$77$	−14.3716	−1.63779
$78$	2.52245	0.285612
$79$	8.88430	0.999562	0.499781	−	0.866152i	$-0.333414\pi$
$79$	8.88430	0.999562	0.499781	+	0.866152i	$0.333414\pi$
$80$	−2.66963	−0.298474
$81$	8.68473	0.964970
$82$	16.3511	1.80568
$83$	−14.7643	−1.62060	−0.810299	−	0.586017i	$-0.800695\pi$
$83$	−14.7643	−1.62060	−0.810299	+	0.586017i	$0.800695\pi$
$84$	3.20365	0.349547
$85$	−3.58794	−0.389167
$86$	−3.50477	−0.377929
$87$	−1.18037	−0.126549
$88$	−14.5961	−1.55595
$89$	−6.86351	−0.727530	−0.363765	−	0.931491i	$-0.618509\pi$
$89$	−6.86351	−0.727530	−0.363765	+	0.931491i	$0.618509\pi$
$90$	−6.04609	−0.637314
$91$	−24.6083	−2.57965
$92$	−13.8026	−1.43902
$93$	0.351180	0.0364157
$94$	−16.7633	−1.72900
$95$	−2.60022	−0.266777
$96$	−0.248554	−0.0253680
$97$	−16.3322	−1.65828	−0.829141	−	0.559040i	$-0.811170\pi$
$97$	−16.3322	−1.65828	−0.829141	+	0.559040i	$0.811170\pi$
$98$	−30.5133	−3.08231
$99$	−9.62275	−0.967123
$100$	−16.5515	−1.65515
$101$	16.2321	1.61515	0.807575	−	0.589765i	$-0.200780\pi$
$101$	16.2321	1.61515	0.807575	+	0.589765i	$0.200780\pi$
$102$	1.93284	0.191379
$103$	−0.576777	−0.0568316	−0.0284158	−	0.999596i	$-0.509046\pi$
$103$	−0.576777	−0.0568316	−0.0284158	+	0.999596i	$0.509046\pi$
$104$	−24.9927	−2.45073
$105$	−0.699637	−0.0682776
$106$	27.5238	2.67334
$107$	−12.4230	−1.20097	−0.600487	−	0.799634i	$-0.705027\pi$
$107$	−12.4230	−1.20097	−0.600487	+	0.799634i	$0.705027\pi$
$108$	4.31556	0.415265
$109$	−0.652056	−0.0624557	−0.0312278	−	0.999512i	$-0.509942\pi$
$109$	−0.652056	−0.0624557	−0.0312278	+	0.999512i	$0.509942\pi$
$110$	6.61871	0.631069
$111$	1.74078	0.165227
$112$	−14.0301	−1.32572
$113$	−0.369455	−0.0347554	−0.0173777	−	0.999849i	$-0.505532\pi$
$113$	−0.369455	−0.0347554	−0.0173777	+	0.999849i	$0.505532\pi$
$114$	1.40075	0.131192
$115$	3.01433	0.281087
$116$	24.2838	2.25470
$117$	−16.4769	−1.52329
$118$	−18.4246	−1.69613
$119$	−18.8562	−1.72854
$120$	−0.710565	−0.0648654
$121$	−0.465887	−0.0423534
$122$	32.6824	2.95893
$123$	1.26690	0.114232
$124$	−7.22486	−0.648811
$125$	7.82741	0.700105
$126$	−31.7748	−2.83072
$127$	9.86038	0.874967	0.437484	−	0.899226i	$-0.355870\pi$
$127$	9.86038	0.874967	0.437484	+	0.899226i	$0.355870\pi$
$128$	20.4513	1.80765
$129$	−0.271552	−0.0239088
$130$	11.3331	0.993983
$131$	−7.58473	−0.662681	−0.331340	−	0.943511i	$-0.607501\pi$
$131$	−7.58473	−0.662681	−0.331340	+	0.943511i	$0.607501\pi$
$132$	−2.34822	−0.204386
$133$	−13.6653	−1.18493
$134$	16.9289	1.46243
$135$	−0.942466	−0.0811145
$136$	−19.1507	−1.64216
$137$	7.93738	0.678136	0.339068	−	0.940762i	$-0.389888\pi$
$137$	7.93738	0.678136	0.339068	+	0.940762i	$0.389888\pi$
$138$	−1.62383	−0.138229
$139$	−20.9745	−1.77903	−0.889516	−	0.456905i	$-0.848958\pi$
$139$	−20.9745	−1.77903	−0.889516	+	0.456905i	$0.848958\pi$
$140$	14.3937	1.21649
$141$	−1.29883	−0.109381
$142$	−22.1571	−1.85938
$143$	18.0375	1.50837
$144$	−9.39409	−0.782841
$145$	−5.30329	−0.440414
$146$	37.9824	3.14345
$147$	−2.36419	−0.194995
$148$	−35.8131	−2.94382
$149$	4.31184	0.353240	0.176620	−	0.984279i	$-0.443484\pi$
$149$	4.31184	0.353240	0.176620	+	0.984279i	$0.443484\pi$
$150$	−1.94722	−0.158990
$151$	5.61411	0.456870	0.228435	−	0.973559i	$-0.426639\pi$
$151$	5.61411	0.456870	0.228435	+	0.973559i	$0.426639\pi$
$152$	−13.8787	−1.12571
$153$	−12.6255	−1.02071
$154$	34.7842	2.80299
$155$	1.57782	0.126734
$156$	−4.02083	−0.321924
$157$	21.6852	1.73067	0.865333	−	0.501198i	$-0.167107\pi$
$157$	21.6852	1.73067	0.865333	+	0.501198i	$0.167107\pi$
$158$	−21.5031	−1.71069
$159$	2.13256	0.169123
$160$	−1.11673	−0.0882853
$161$	15.8416	1.24849
$162$	−21.0200	−1.65149
$163$	−9.87632	−0.773573	−0.386787	−	0.922169i	$-0.626415\pi$
$163$	−9.87632	−0.773573	−0.386787	+	0.922169i	$0.626415\pi$
$164$	−26.0639	−2.03525
$165$	0.512822	0.0399231
$166$	35.7348	2.77356
$167$	−14.1679	−1.09635	−0.548173	−	0.836365i	$-0.684676\pi$
$167$	−14.1679	−1.09635	−0.548173	+	0.836365i	$0.684676\pi$
$168$	−3.73433	−0.288110
$169$	17.8853	1.37580
$170$	8.68405	0.666036
$171$	−9.14982	−0.699705
$172$	5.58665	0.425978
$173$	−16.0746	−1.22213	−0.611066	−	0.791579i	$-0.709259\pi$
$173$	−16.0746	−1.22213	−0.611066	+	0.791579i	$0.709259\pi$
$174$	2.85690	0.216581
$175$	18.9965	1.43600
$176$	10.2838	0.775170
$177$	−1.42755	−0.107301
$178$	16.6120	1.24512
$179$	−14.3135	−1.06984	−0.534921	−	0.844902i	$-0.679659\pi$
$179$	−14.3135	−1.06984	−0.534921	+	0.844902i	$0.679659\pi$
$180$	9.63755	0.718340
$181$	−20.4483	−1.51991	−0.759956	−	0.649975i	$-0.774779\pi$
$181$	−20.4483	−1.51991	−0.759956	+	0.649975i	$0.774779\pi$
$182$	59.5606	4.41492
$183$	2.53225	0.187190
$184$	16.0890	1.18610
$185$	7.82114	0.575022
$186$	−0.849977	−0.0623233
$187$	13.8212	1.01071
$188$	26.7209	1.94882
$189$	−4.95306	−0.360282
$190$	6.29342	0.456573
$191$	6.55568	0.474352	0.237176	−	0.971467i	$-0.423778\pi$
$191$	6.55568	0.474352	0.237176	+	0.971467i	$0.423778\pi$
$192$	1.78996	0.129180
$193$	−18.6618	−1.34330	−0.671651	−	0.740867i	$-0.734415\pi$
$193$	−18.6618	−1.34330	−0.671651	+	0.740867i	$0.734415\pi$
$194$	39.5295	2.83805
$195$	0.878099	0.0628820
$196$	48.6386	3.47419
$197$	−21.1911	−1.50980	−0.754901	−	0.655839i	$-0.772315\pi$
$197$	−21.1911	−1.50980	−0.754901	+	0.655839i	$0.772315\pi$
$198$	23.2904	1.65517
$199$	1.84812	0.131010	0.0655050	−	0.997852i	$-0.479134\pi$
$199$	1.84812	0.131010	0.0655050	+	0.997852i	$0.479134\pi$
$200$	19.2932	1.36424
$201$	1.31166	0.0925175
$202$	−39.2871	−2.76423
$203$	−27.8711	−1.95617
$204$	−3.08097	−0.215711
$205$	5.69204	0.397549
$206$	1.39600	0.0972638
$207$	10.6070	0.737238
$208$	17.6088	1.22095
$209$	10.0164	0.692849
$210$	1.69336	0.116853
$211$	19.6598	1.35344	0.676719	−	0.736242i	$-0.263401\pi$
$211$	19.6598	1.35344	0.676719	+	0.736242i	$0.263401\pi$
$212$	−43.8732	−3.01323
$213$	−1.71674	−0.117629
$214$	30.0679	2.05540
$215$	−1.22006	−0.0832072
$216$	−5.03043	−0.342277
$217$	8.29213	0.562906
$218$	1.57820	0.106889
$219$	2.94290	0.198863
$220$	−10.5503	−0.711302
$221$	23.6660	1.59195
$222$	−4.21327	−0.282776
$223$	−3.83266	−0.256654	−0.128327	−	0.991732i	$-0.540961\pi$
$223$	−3.83266	−0.256654	−0.128327	+	0.991732i	$0.540961\pi$
$224$	−5.86890	−0.392133
$225$	12.7194	0.847963
$226$	0.894209	0.0594819
$227$	11.4565	0.760395	0.380197	−	0.924905i	$-0.375856\pi$
$227$	11.4565	0.760395	0.380197	+	0.924905i	$0.375856\pi$
$228$	−2.23281	−0.147871
$229$	−1.93524	−0.127884	−0.0639421	−	0.997954i	$-0.520367\pi$
$229$	−1.93524	−0.127884	−0.0639421	+	0.997954i	$0.520367\pi$
$230$	−7.29570	−0.481064
$231$	2.69510	0.177324
$232$	−28.3064	−1.85841
$233$	−9.87647	−0.647029	−0.323514	−	0.946223i	$-0.604864\pi$
$233$	−9.87647	−0.647029	−0.323514	+	0.946223i	$0.604864\pi$
$234$	39.8798	2.60703
$235$	−5.83552	−0.380667
$236$	29.3691	1.91177
$237$	−1.66607	−0.108223
$238$	45.6384	2.95830
$239$	14.5313	0.939954	0.469977	−	0.882679i	$-0.344262\pi$
$239$	14.5313	0.939954	0.469977	+	0.882679i	$0.344262\pi$
$240$	0.500636	0.0323159
$241$	−23.5796	−1.51890	−0.759448	−	0.650568i	$-0.774531\pi$
$241$	−23.5796	−1.51890	−0.759448	+	0.650568i	$0.774531\pi$
$242$	1.12761	0.0724853
$243$	−4.98439	−0.319749
$244$	−52.0962	−3.33512
$245$	−10.6221	−0.678620
$246$	−3.06632	−0.195502
$247$	17.1510	1.09129
$248$	8.42164	0.534775
$249$	2.76875	0.175463
$250$	−18.9450	−1.19819
$251$	8.86810	0.559750	0.279875	−	0.960037i	$-0.409707\pi$
$251$	8.86810	0.559750	0.279875	+	0.960037i	$0.409707\pi$
$252$	50.6495	3.19062
$253$	−11.6116	−0.730015
$254$	−23.8655	−1.49745
$255$	0.672845	0.0421352
$256$	−30.4091	−1.90057
$257$	5.06423	0.315898	0.157949	−	0.987447i	$-0.449512\pi$
$257$	5.06423	0.315898	0.157949	+	0.987447i	$0.449512\pi$
$258$	0.657249	0.0409185
$259$	41.1035	2.55405
$260$	−18.0652	−1.12036
$261$	−18.6616	−1.15512
$262$	18.3576	1.13414
$263$	19.2130	1.18473	0.592363	−	0.805671i	$-0.298195\pi$
$263$	19.2130	1.18473	0.592363	+	0.805671i	$0.298195\pi$
$264$	2.73719	0.168463
$265$	9.58138	0.588580
$266$	33.0746	2.02794
$267$	1.28711	0.0787699
$268$	−26.9849	−1.64837
$269$	16.5456	1.00880	0.504402	−	0.863469i	$-0.331713\pi$
$269$	16.5456	1.00880	0.504402	+	0.863469i	$0.331713\pi$
$270$	2.28109	0.138823
$271$	−22.4974	−1.36662	−0.683311	−	0.730128i	$-0.739461\pi$
$271$	−22.4974	−1.36662	−0.683311	+	0.730128i	$0.739461\pi$
$272$	13.4928	0.818122
$273$	4.61479	0.279300
$274$	−19.2112	−1.16059
$275$	−13.9241	−0.839654
$276$	2.58840	0.155804
$277$	4.38557	0.263503	0.131752	−	0.991283i	$-0.457940\pi$
$277$	4.38557	0.263503	0.131752	+	0.991283i	$0.457940\pi$
$278$	50.7654	3.04471
$279$	5.55214	0.332398
$280$	−16.7780	−1.00268
$281$	3.02717	0.180586	0.0902929	−	0.995915i	$-0.471220\pi$
$281$	3.02717	0.180586	0.0902929	+	0.995915i	$0.471220\pi$
$282$	3.14361	0.187200
$283$	−8.87827	−0.527759	−0.263879	−	0.964556i	$-0.585002\pi$
$283$	−8.87827	−0.527759	−0.263879	+	0.964556i	$0.585002\pi$
$284$	35.3187	2.09578
$285$	0.487618	0.0288840
$286$	−43.6568	−2.58148
$287$	29.9141	1.76578
$288$	−3.92963	−0.231556
$289$	1.13410	0.0667117
$290$	12.8358	0.753743
$291$	3.06277	0.179543
$292$	−60.5445	−3.54310
$293$	3.05817	0.178660	0.0893301	−	0.996002i	$-0.471527\pi$
$293$	3.05817	0.178660	0.0893301	+	0.996002i	$0.471527\pi$
$294$	5.72215	0.333722
$295$	−6.41386	−0.373429
$296$	41.7455	2.42641
$297$	3.63051	0.210663
$298$	−10.4361	−0.604550
$299$	−19.8824	−1.14983
$300$	3.10389	0.179203
$301$	−6.41193	−0.369577
$302$	−13.5881	−0.781906
$303$	−3.04399	−0.174873
$304$	9.77838	0.560829
$305$	11.3772	0.651455
$306$	30.5580	1.74689
$307$	13.9198	0.794447	0.397223	−	0.917722i	$-0.369974\pi$
$307$	13.9198	0.794447	0.397223	+	0.917722i	$0.369974\pi$
$308$	−55.4464	−3.15935
$309$	0.108163	0.00615317
$310$	−3.81887	−0.216897
$311$	−24.1164	−1.36751	−0.683757	−	0.729709i	$-0.739655\pi$
$311$	−24.1164	−1.36751	−0.683757	+	0.729709i	$0.739655\pi$
$312$	4.68687	0.265342
$313$	15.4271	0.871992	0.435996	−	0.899949i	$-0.356396\pi$
$313$	15.4271	0.871992	0.435996	+	0.899949i	$0.356396\pi$
$314$	−52.4856	−2.96193
$315$	−11.0612	−0.623229
$316$	34.2762	1.92818
$317$	−14.5232	−0.815705	−0.407852	−	0.913048i	$-0.633722\pi$
$317$	−14.5232	−0.815705	−0.407852	+	0.913048i	$0.633722\pi$
$318$	−5.16152	−0.289444
$319$	20.4290	1.14380
$320$	8.04214	0.449569
$321$	2.32968	0.130030
$322$	−38.3421	−2.13672
$323$	13.1420	0.731239
$324$	33.5062	1.86146
$325$	−23.8421	−1.32252
$326$	23.9041	1.32392
$327$	0.122280	0.00676209
$328$	30.3814	1.67753
$329$	−30.6682	−1.69079
$330$	−1.24120	−0.0683260
$331$	−14.0269	−0.770989	−0.385495	−	0.922710i	$-0.625969\pi$
$331$	−14.0269	−0.770989	−0.385495	+	0.922710i	$0.625969\pi$
$332$	−56.9617	−3.12618
$333$	27.5216	1.50817
$334$	34.2912	1.87633
$335$	5.89317	0.321978
$336$	2.63106	0.143536
$337$	20.4606	1.11456	0.557279	−	0.830325i	$-0.311845\pi$
$337$	20.4606	1.11456	0.557279	+	0.830325i	$0.311845\pi$
$338$	−43.2887	−2.35459
$339$	0.0692838	0.00376298
$340$	−13.8425	−0.750715
$341$	−6.07798	−0.329141
$342$	22.1457	1.19750
$343$	−24.8277	−1.34057
$344$	−6.51208	−0.351108
$345$	−0.565276	−0.0304334
$346$	38.9062	2.09161
$347$	−1.37079	−0.0735876	−0.0367938	−	0.999323i	$-0.511714\pi$
$347$	−1.37079	−0.0735876	−0.0367938	+	0.999323i	$0.511714\pi$
$348$	−4.55393	−0.244117
$349$	6.48611	0.347194	0.173597	−	0.984817i	$-0.444461\pi$
$349$	6.48611	0.347194	0.173597	+	0.984817i	$0.444461\pi$
$350$	−45.9780	−2.45763
$351$	6.21648	0.331811
$352$	4.30180	0.229287
$353$	−6.11117	−0.325265	−0.162632	−	0.986687i	$-0.551998\pi$
$353$	−6.11117	−0.325265	−0.162632	+	0.986687i	$0.551998\pi$
$354$	3.45517	0.183640
$355$	−7.71317	−0.409372
$356$	−26.4798	−1.40343
$357$	3.53609	0.187150
$358$	34.6436	1.83097
$359$	4.45960	0.235369	0.117684	−	0.993051i	$-0.462453\pi$
$359$	4.45960	0.235369	0.117684	+	0.993051i	$0.462453\pi$
$360$	−11.2340	−0.592083
$361$	−9.47587	−0.498730
$362$	49.4919	2.60124
$363$	0.0873676	0.00458561
$364$	−94.9404	−4.97623
$365$	13.2222	0.692081
$366$	−6.12892	−0.320364
$367$	33.1949	1.73276	0.866381	−	0.499384i	$-0.166440\pi$
$367$	33.1949	1.73276	0.866381	+	0.499384i	$0.166440\pi$
$368$	−11.3357	−0.590913
$369$	20.0295	1.04270
$370$	−18.9298	−0.984116
$371$	50.3543	2.61426
$372$	1.35487	0.0702470
$373$	11.7723	0.609544	0.304772	−	0.952425i	$-0.401420\pi$
$373$	11.7723	0.609544	0.304772	+	0.952425i	$0.401420\pi$
$374$	−33.4521	−1.72977
$375$	−1.46787	−0.0758005
$376$	−31.1472	−1.60629
$377$	34.9803	1.80158
$378$	11.9881	0.616602
$379$	16.8212	0.864047	0.432023	−	0.901862i	$-0.357800\pi$
$379$	16.8212	0.864047	0.432023	+	0.901862i	$0.357800\pi$
$380$	−10.0318	−0.514620
$381$	−1.84911	−0.0947330
$382$	−15.8670	−0.811826
$383$	−7.85728	−0.401488	−0.200744	−	0.979644i	$-0.564336\pi$
$383$	−7.85728	−0.401488	−0.200744	+	0.979644i	$0.564336\pi$
$384$	−3.83522	−0.195715
$385$	12.1088	0.617123
$386$	45.1679	2.29898
$387$	−4.29322	−0.218237
$388$	−63.0105	−3.19887
$389$	11.5145	0.583809	0.291905	−	0.956447i	$-0.405711\pi$
$389$	11.5145	0.583809	0.291905	+	0.956447i	$0.405711\pi$
$390$	−2.12530	−0.107619
$391$	−15.2349	−0.770464
$392$	−56.6955	−2.86356
$393$	1.42236	0.0717486
$394$	51.2897	2.58394
$395$	−7.48549	−0.376636
$396$	−37.1251	−1.86561
$397$	−27.0481	−1.35750	−0.678752	−	0.734367i	$-0.737479\pi$
$397$	−27.0481	−1.35750	−0.678752	+	0.734367i	$0.737479\pi$
$398$	−4.47309	−0.224216
$399$	2.56264	0.128293
$400$	−13.5932	−0.679661
$401$	−11.4561	−0.572092	−0.286046	−	0.958216i	$-0.592341\pi$
$401$	−11.4561	−0.572092	−0.286046	+	0.958216i	$0.592341\pi$
$402$	−3.17467	−0.158338
$403$	−10.4073	−0.518423
$404$	62.6242	3.11567
$405$	−7.31735	−0.363602
$406$	67.4575	3.34786
$407$	−30.1281	−1.49339
$408$	3.59132	0.177797
$409$	−5.61725	−0.277755	−0.138878	−	0.990310i	$-0.544349\pi$
$409$	−5.61725	−0.277755	−0.138878	+	0.990310i	$0.544349\pi$
$410$	−13.7767	−0.680382
$411$	−1.48849	−0.0734220
$412$	−2.22524	−0.109630
$413$	−33.7076	−1.65864
$414$	−25.6726	−1.26174
$415$	12.4397	0.610643
$416$	7.36593	0.361144
$417$	3.93334	0.192616
$418$	−24.2431	−1.18577
$419$	−18.6606	−0.911632	−0.455816	−	0.890074i	$-0.650652\pi$
$419$	−18.6606	−0.911632	−0.455816	+	0.890074i	$0.650652\pi$
$420$	−2.69924	−0.131710
$421$	6.71202	0.327124	0.163562	−	0.986533i	$-0.447702\pi$
$421$	6.71202	0.327124	0.163562	+	0.986533i	$0.447702\pi$
$422$	−47.5835	−2.31633
$423$	−20.5344	−0.998418
$424$	51.1408	2.48362
$425$	−18.2690	−0.886179
$426$	4.15511	0.201316
$427$	59.7920	2.89354
$428$	−47.9286	−2.31672
$429$	−3.38256	−0.163311
$430$	2.95296	0.142404
$431$	−27.5586	−1.32745	−0.663727	−	0.747975i	$-0.731026\pi$
$431$	−27.5586	−1.32745	−0.663727	+	0.747975i	$0.731026\pi$
$432$	3.54424	0.170522
$433$	5.29353	0.254391	0.127195	−	0.991878i	$-0.459402\pi$
$433$	5.29353	0.254391	0.127195	+	0.991878i	$0.459402\pi$
$434$	−20.0698	−0.963381
$435$	0.994524	0.0476838
$436$	−2.51567	−0.120479
$437$	−11.0409	−0.528159
$438$	−7.12284	−0.340342
$439$	12.2827	0.586220	0.293110	−	0.956079i	$-0.405310\pi$
$439$	12.2827	0.586220	0.293110	+	0.956079i	$0.405310\pi$
$440$	12.2980	0.586282
$441$	−37.3777	−1.77989
$442$	−57.2798	−2.72452
$443$	26.2268	1.24607	0.623037	−	0.782192i	$-0.285899\pi$
$443$	26.2268	1.24607	0.623037	+	0.782192i	$0.285899\pi$
$444$	6.71602	0.318728
$445$	5.78287	0.274134
$446$	9.27634	0.439248
$447$	−0.808599	−0.0382454
$448$	42.2649	1.99683
$449$	−21.8904	−1.03307	−0.516537	−	0.856265i	$-0.672779\pi$
$449$	−21.8904	−1.03307	−0.516537	+	0.856265i	$0.672779\pi$
$450$	−30.7854	−1.45124
$451$	−21.9265	−1.03248
$452$	−1.42538	−0.0670443
$453$	−1.05281	−0.0494654
$454$	−27.7287	−1.30137
$455$	20.7338	0.972016
$456$	2.60267	0.121881
$457$	3.92519	0.183613	0.0918064	−	0.995777i	$-0.470736\pi$
$457$	3.92519	0.183613	0.0918064	+	0.995777i	$0.470736\pi$
$458$	4.68394	0.218866
$459$	4.76339	0.222336
$460$	11.6294	0.542226
$461$	−28.5499	−1.32970	−0.664851	−	0.746976i	$-0.731505\pi$
$461$	−28.5499	−1.32970	−0.664851	+	0.746976i	$0.731505\pi$
$462$	−6.52306	−0.303480
$463$	23.9755	1.11424	0.557119	−	0.830433i	$-0.311907\pi$
$463$	23.9755	1.11424	0.557119	+	0.830433i	$0.311907\pi$
$464$	19.9435	0.925856
$465$	−0.295888	−0.0137215
$466$	23.9044	1.10735
$467$	−7.57913	−0.350720	−0.175360	−	0.984504i	$-0.556109\pi$
$467$	−7.57913	−0.350720	−0.175360	+	0.984504i	$0.556109\pi$
$468$	−63.5690	−2.93848
$469$	30.9712	1.43012
$470$	14.1240	0.651490
$471$	−4.06661	−0.187380
$472$	−34.2341	−1.57575
$473$	4.69983	0.216098
$474$	4.03246	0.185217
$475$	−13.2398	−0.607482
$476$	−72.7483	−3.33441
$477$	33.7156	1.54373
$478$	−35.1708	−1.60868
$479$	25.4169	1.16133	0.580663	−	0.814144i	$-0.302793\pi$
$479$	25.4169	1.16133	0.580663	+	0.814144i	$0.302793\pi$
$480$	0.209420	0.00955868
$481$	−51.5880	−2.35221
$482$	57.0707	2.59950
$483$	−2.97077	−0.135175
$484$	−1.79742	−0.0817009
$485$	13.7607	0.624843
$486$	12.0639	0.547232
$487$	−36.0554	−1.63383	−0.816913	−	0.576761i	$-0.804317\pi$
$487$	−36.0554	−1.63383	−0.816913	+	0.576761i	$0.804317\pi$
$488$	60.7259	2.74893
$489$	1.85210	0.0837550
$490$	25.7091	1.16142
$491$	−18.4521	−0.832733	−0.416366	−	0.909197i	$-0.636697\pi$
$491$	−18.4521	−0.832733	−0.416366	+	0.909197i	$0.636697\pi$
$492$	4.88776	0.220357
$493$	26.8038	1.20718
$494$	−41.5112	−1.86768
$495$	8.10768	0.364413
$496$	−5.93355	−0.266424
$497$	−40.5360	−1.81829
$498$	−6.70133	−0.300294
$499$	36.9628	1.65468	0.827341	−	0.561700i	$-0.189852\pi$
$499$	36.9628	1.65468	0.827341	+	0.561700i	$0.189852\pi$
$500$	30.1986	1.35052
$501$	2.65690	0.118702
$502$	−21.4638	−0.957978
$503$	7.28082	0.324636	0.162318	−	0.986739i	$-0.448103\pi$
$503$	7.28082	0.324636	0.162318	+	0.986739i	$0.448103\pi$
$504$	−59.0395	−2.62983
$505$	−13.6764	−0.608591
$506$	28.1040	1.24938
$507$	−3.35403	−0.148958
$508$	38.0419	1.68784
$509$	−13.7729	−0.610475	−0.305237	−	0.952276i	$-0.598736\pi$
$509$	−13.7729	−0.610475	−0.305237	+	0.952276i	$0.598736\pi$
$510$	−1.62852	−0.0721119
$511$	69.4883	3.07398
$512$	32.6980	1.44506
$513$	3.45208	0.152413
$514$	−12.2572	−0.540640
$515$	0.485966	0.0214142
$516$	−1.04766	−0.0461208
$517$	22.4792	0.988635
$518$	−99.4845	−4.37110
$519$	3.01447	0.132321
$520$	21.0577	0.923440
$521$	−16.0759	−0.704299	−0.352150	−	0.935944i	$-0.614549\pi$
$521$	−16.0759	−0.704299	−0.352150	+	0.935944i	$0.614549\pi$
$522$	45.1674	1.97692
$523$	−2.54111	−0.111115	−0.0555574	−	0.998455i	$-0.517694\pi$
$523$	−2.54111	−0.111115	−0.0555574	+	0.998455i	$0.517694\pi$
$524$	−29.2623	−1.27833
$525$	−3.56241	−0.155476
$526$	−46.5021	−2.02759
$527$	−7.97459	−0.347379
$528$	−1.92852	−0.0839279
$529$	−10.2007	−0.443509
$530$	−23.1902	−1.00732
$531$	−22.5695	−0.979433
$532$	−52.7214	−2.28576
$533$	−37.5446	−1.62624
$534$	−3.11525	−0.134810
$535$	10.4670	0.452529
$536$	31.4549	1.35865
$537$	2.68421	0.115832
$538$	−40.0461	−1.72651
$539$	40.9177	1.76245
$540$	−3.63609	−0.156472
$541$	−33.5867	−1.44401	−0.722003	−	0.691890i	$-0.756778\pi$
$541$	−33.5867	−1.44401	−0.722003	+	0.691890i	$0.756778\pi$
$542$	54.4515	2.33889
$543$	3.83467	0.164561
$544$	5.64416	0.241991
$545$	0.549392	0.0235334
$546$	−11.1694	−0.478005
$547$	−10.7557	−0.459879	−0.229939	−	0.973205i	$-0.573853\pi$
$547$	−10.7557	−0.459879	−0.229939	+	0.973205i	$0.573853\pi$
$548$	30.6229	1.30814
$549$	40.0348	1.70864
$550$	33.7011	1.43702
$551$	19.4250	0.827532
$552$	−3.01717	−0.128419
$553$	−39.3395	−1.67289
$554$	−10.6146	−0.450970
$555$	−1.46670	−0.0622578
$556$	−80.9208	−3.43180
$557$	28.2376	1.19647	0.598233	−	0.801322i	$-0.295870\pi$
$557$	28.2376	1.19647	0.598233	+	0.801322i	$0.295870\pi$
$558$	−13.4381	−0.568879
$559$	8.04747	0.340372
$560$	11.8211	0.499532
$561$	−2.59189	−0.109430
$562$	−7.32679	−0.309062
$563$	−22.6965	−0.956542	−0.478271	−	0.878212i	$-0.658736\pi$
$563$	−22.6965	−0.956542	−0.478271	+	0.878212i	$0.658736\pi$
$564$	−5.01096	−0.211000
$565$	0.311286	0.0130959
$566$	21.4885	0.903228
$567$	−38.4558	−1.61499
$568$	−41.1692	−1.72742
$569$	−27.1127	−1.13662	−0.568312	−	0.822813i	$-0.692403\pi$
$569$	−27.1127	−1.13662	−0.568312	+	0.822813i	$0.692403\pi$
$570$	−1.18020	−0.0494333
$571$	33.7362	1.41182	0.705908	−	0.708304i	$-0.250539\pi$
$571$	33.7362	1.41182	0.705908	+	0.708304i	$0.250539\pi$
$572$	69.5896	2.90969
$573$	−1.22938	−0.0513583
$574$	−72.4025	−3.02202
$575$	15.3483	0.640069
$576$	28.2992	1.17913
$577$	14.7649	0.614670	0.307335	−	0.951601i	$-0.400563\pi$
$577$	14.7649	0.614670	0.307335	+	0.951601i	$0.400563\pi$
$578$	−2.74491	−0.114173
$579$	3.49963	0.145440
$580$	−20.4604	−0.849572
$581$	65.3762	2.71226
$582$	−7.41295	−0.307277
$583$	−36.9088	−1.52861
$584$	70.5737	2.92036
$585$	13.8827	0.573979
$586$	−7.40182	−0.305766
$587$	−0.401796	−0.0165839	−0.00829195	−	0.999966i	$-0.502639\pi$
$587$	−0.401796	−0.0165839	−0.00829195	+	0.999966i	$0.502639\pi$
$588$	−9.12118	−0.376151
$589$	−5.77927	−0.238131
$590$	15.5237	0.639102
$591$	3.97396	0.163467
$592$	−29.4122	−1.20883
$593$	−14.0179	−0.575648	−0.287824	−	0.957683i	$-0.592932\pi$
$593$	−14.0179	−0.575648	−0.287824	+	0.957683i	$0.592932\pi$
$594$	−8.78707	−0.360538
$595$	15.8873	0.651317
$596$	16.6354	0.681411
$597$	−0.346578	−0.0141845
$598$	48.1223	1.96787
$599$	−46.8732	−1.91519	−0.957594	−	0.288122i	$-0.906969\pi$
$599$	−46.8732	−1.91519	−0.957594	+	0.288122i	$0.906969\pi$
$600$	−3.61805	−0.147706
$601$	10.2768	0.419199	0.209600	−	0.977787i	$-0.432784\pi$
$601$	10.2768	0.419199	0.209600	+	0.977787i	$0.432784\pi$
$602$	15.5191	0.632510
$603$	20.7373	0.844488
$604$	21.6596	0.881315
$605$	0.392534	0.0159588
$606$	7.36750	0.299284
$607$	−10.3849	−0.421511	−0.210755	−	0.977539i	$-0.567592\pi$
$607$	−10.3849	−0.421511	−0.210755	+	0.977539i	$0.567592\pi$
$608$	4.09038	0.165887
$609$	5.22665	0.211795
$610$	−27.5367	−1.11493
$611$	38.4909	1.55718
$612$	−48.7099	−1.96898
$613$	−9.07015	−0.366340	−0.183170	−	0.983081i	$-0.558636\pi$
$613$	−9.07015	−0.366340	−0.183170	+	0.983081i	$0.558636\pi$
$614$	−33.6908	−1.35965
$615$	−1.06743	−0.0430428
$616$	64.6311	2.60406
$617$	3.90322	0.157138	0.0785688	−	0.996909i	$-0.474965\pi$
$617$	3.90322	0.157138	0.0785688	+	0.996909i	$0.474965\pi$
$618$	−0.261791	−0.0105308
$619$	18.1176	0.728208	0.364104	−	0.931358i	$-0.381375\pi$
$619$	18.1176	0.728208	0.364104	+	0.931358i	$0.381375\pi$
$620$	6.08733	0.244473
$621$	−4.00185	−0.160589
$622$	58.3699	2.34042
$623$	30.3915	1.21761
$624$	−3.30218	−0.132193
$625$	14.8555	0.594221
$626$	−37.3389	−1.49236
$627$	−1.87837	−0.0750149
$628$	83.6627	3.33851
$629$	−39.5295	−1.57614
$630$	26.7720	1.06662
$631$	−31.7485	−1.26389	−0.631944	−	0.775014i	$-0.717743\pi$
$631$	−31.7485	−1.26389	−0.631944	+	0.775014i	$0.717743\pi$
$632$	−39.9540	−1.58928
$633$	−3.68680	−0.146537
$634$	35.1512	1.39603
$635$	−8.30790	−0.329689
$636$	8.22753	0.326243
$637$	70.0629	2.77599
$638$	−49.4452	−1.95755
$639$	−27.1416	−1.07371
$640$	−17.2313	−0.681126
$641$	46.0192	1.81765	0.908824	−	0.417179i	$-0.136981\pi$
$641$	46.0192	1.81765	0.908824	+	0.417179i	$0.136981\pi$
$642$	−5.63862	−0.222538
$643$	2.85638	0.112644	0.0563222	−	0.998413i	$-0.482063\pi$
$643$	2.85638	0.112644	0.0563222	+	0.998413i	$0.482063\pi$
$644$	61.1178	2.40838
$645$	0.228797	0.00900887
$646$	−31.8081	−1.25147
$647$	1.31276	0.0516099	0.0258049	−	0.999667i	$-0.491785\pi$
$647$	1.31276	0.0516099	0.0258049	+	0.999667i	$0.491785\pi$
$648$	−39.0565	−1.53428
$649$	24.7071	0.969837
$650$	57.7060	2.26342
$651$	−1.55502	−0.0609460
$652$	−38.1034	−1.49225
$653$	41.5275	1.62510	0.812548	−	0.582894i	$-0.198080\pi$
$653$	41.5275	1.62510	0.812548	+	0.582894i	$0.198080\pi$
$654$	−0.295959	−0.0115729
$655$	6.39054	0.249699
$656$	−21.4055	−0.835744
$657$	46.5271	1.81520
$658$	74.2275	2.89369
$659$	−36.0957	−1.40609	−0.703045	−	0.711146i	$-0.748177\pi$
$659$	−36.0957	−1.40609	−0.703045	+	0.711146i	$0.748177\pi$
$660$	1.97850	0.0770129
$661$	11.7795	0.458171	0.229085	−	0.973406i	$-0.426426\pi$
$661$	11.7795	0.458171	0.229085	+	0.973406i	$0.426426\pi$
$662$	33.9499	1.31950
$663$	−4.43807	−0.172360
$664$	66.3973	2.57672
$665$	11.5137	0.446483
$666$	−66.6116	−2.58115
$667$	−22.5186	−0.871922
$668$	−54.6606	−2.11488
$669$	0.718737	0.0277880
$670$	−14.2635	−0.551047
$671$	−43.8264	−1.69190
$672$	1.10059	0.0424563
$673$	−38.9571	−1.50169	−0.750843	−	0.660480i	$-0.770353\pi$
$673$	−38.9571	−1.50169	−0.750843	+	0.660480i	$0.770353\pi$
$674$	−49.5216	−1.90750
$675$	−4.79884	−0.184707
$676$	69.0027	2.65395
$677$	18.4804	0.710260	0.355130	−	0.934817i	$-0.384437\pi$
$677$	18.4804	0.710260	0.355130	+	0.934817i	$0.384437\pi$
$678$	−0.167691	−0.00644012
$679$	72.3186	2.77533
$680$	16.1355	0.618767
$681$	−2.14843	−0.0823282
$682$	14.7108	0.563305
$683$	2.74844	0.105166	0.0525830	−	0.998617i	$-0.483255\pi$
$683$	2.74844	0.105166	0.0525830	+	0.998617i	$0.483255\pi$
$684$	−35.3006	−1.34975
$685$	−6.68766	−0.255522
$686$	60.0916	2.29431
$687$	0.362915	0.0138461
$688$	4.58815	0.174921
$689$	−63.1985	−2.40767
$690$	1.36816	0.0520850
$691$	34.4220	1.30947	0.654736	−	0.755857i	$-0.272780\pi$
$691$	34.4220	1.30947	0.654736	+	0.755857i	$0.272780\pi$
$692$	−62.0169	−2.35753
$693$	42.6093	1.61860
$694$	3.31777	0.125941
$695$	17.6721	0.670341
$696$	5.30829	0.201210
$697$	−28.7686	−1.08969
$698$	−15.6986	−0.594201
$699$	1.85213	0.0700540
$700$	73.2896	2.77009
$701$	−41.6294	−1.57232	−0.786160	−	0.618023i	$-0.787934\pi$
$701$	−41.6294	−1.57232	−0.786160	+	0.618023i	$0.787934\pi$
$702$	−15.0460	−0.567875
$703$	−28.6474	−1.08046
$704$	−30.9794	−1.16758
$705$	1.09433	0.0412150
$706$	14.7911	0.556671
$707$	−71.8752	−2.70315
$708$	−5.50758	−0.206988
$709$	−30.6256	−1.15017	−0.575084	−	0.818094i	$-0.695031\pi$
$709$	−30.6256	−1.15017	−0.575084	+	0.818094i	$0.695031\pi$
$710$	18.6685	0.700617
$711$	−26.3405	−0.987844
$712$	30.8662	1.15676
$713$	6.69967	0.250904
$714$	−8.55856	−0.320296
$715$	−15.1975	−0.568355
$716$	−55.2224	−2.06376
$717$	−2.72506	−0.101769
$718$	−10.7938	−0.402820
$719$	29.8824	1.11443	0.557214	−	0.830369i	$-0.311870\pi$
$719$	29.8824	1.11443	0.557214	+	0.830369i	$0.311870\pi$
$720$	7.91502	0.294975
$721$	2.55396	0.0951144
$722$	22.9349	0.853547
$723$	4.42187	0.164451
$724$	−78.8908	−2.93195
$725$	−27.0032	−1.00287
$726$	−0.211460	−0.00784800
$727$	42.3525	1.57077	0.785384	−	0.619009i	$-0.212466\pi$
$727$	42.3525	1.57077	0.785384	+	0.619009i	$0.212466\pi$
$728$	110.667	4.10160
$729$	−25.1195	−0.930351
$730$	−32.0022	−1.18446
$731$	6.16639	0.228072
$732$	9.76959	0.361094
$733$	24.0340	0.887716	0.443858	−	0.896097i	$-0.353609\pi$
$733$	24.0340	0.887716	0.443858	+	0.896097i	$0.353609\pi$
$734$	−80.3431	−2.96552
$735$	1.99195	0.0734743
$736$	−4.74181	−0.174785
$737$	−22.7013	−0.836213
$738$	−48.4784	−1.78451
$739$	−26.9585	−0.991683	−0.495841	−	0.868413i	$-0.665140\pi$
$739$	−26.9585	−0.991683	−0.495841	+	0.868413i	$0.665140\pi$
$740$	30.1744	1.10923
$741$	−3.21632	−0.118154
$742$	−121.875	−4.47416
$743$	35.1199	1.28842	0.644212	−	0.764847i	$-0.277185\pi$
$743$	35.1199	1.28842	0.644212	+	0.764847i	$0.277185\pi$
$744$	−1.57931	−0.0579002
$745$	−3.63296	−0.133101
$746$	−28.4929	−1.04320
$747$	43.7738	1.60160
$748$	53.3232	1.94969
$749$	55.0087	2.00997
$750$	3.55275	0.129728
$751$	40.7342	1.48641	0.743206	−	0.669063i	$-0.233304\pi$
$751$	40.7342	1.48641	0.743206	+	0.669063i	$0.233304\pi$
$752$	21.9451	0.800254
$753$	−1.66303	−0.0606043
$754$	−84.6644	−3.08330
$755$	−4.73019	−0.172149
$756$	−19.1092	−0.694995
$757$	−1.73072	−0.0629042	−0.0314521	−	0.999505i	$-0.510013\pi$
$757$	−1.73072	−0.0629042	−0.0314521	+	0.999505i	$0.510013\pi$
$758$	−40.7131	−1.47876
$759$	2.17752	0.0790389
$760$	11.6936	0.424170
$761$	6.68151	0.242205	0.121102	−	0.992640i	$-0.461357\pi$
$761$	6.68151	0.242205	0.121102	+	0.992640i	$0.461357\pi$
$762$	4.47549	0.162130
$763$	2.88729	0.104527
$764$	25.2922	0.915040
$765$	10.6376	0.384605
$766$	19.0173	0.687124
$767$	42.3056	1.52757
$768$	5.70262	0.205775
$769$	3.14457	0.113396	0.0566981	−	0.998391i	$-0.481943\pi$
$769$	3.14457	0.113396	0.0566981	+	0.998391i	$0.481943\pi$
$770$	−29.3075	−1.05617
$771$	−0.949693	−0.0342023
$772$	−71.9982	−2.59127
$773$	−17.5615	−0.631644	−0.315822	−	0.948818i	$-0.602280\pi$
$773$	−17.5615	−0.631644	−0.315822	+	0.948818i	$0.602280\pi$
$774$	10.3911	0.373499
$775$	8.03393	0.288587
$776$	73.4481	2.63663
$777$	−7.70812	−0.276527
$778$	−27.8691	−0.999155
$779$	−20.8489	−0.746990
$780$	3.38776	0.121301
$781$	29.7122	1.06319
$782$	36.8738	1.31860
$783$	7.04070	0.251614
$784$	39.9454	1.42662
$785$	−18.2709	−0.652117
$786$	−3.44260	−0.122794
$787$	−24.1128	−0.859528	−0.429764	−	0.902941i	$-0.641403\pi$
$787$	−24.1128	−0.859528	−0.429764	+	0.902941i	$0.641403\pi$
$788$	−81.7565	−2.91245
$789$	−3.60301	−0.128271
$790$	18.1175	0.644590
$791$	1.63594	0.0581674
$792$	43.2749	1.53771
$793$	−75.0436	−2.66488
$794$	65.4656	2.32329
$795$	−1.79679	−0.0637257
$796$	7.13017	0.252722
$797$	4.07133	0.144214	0.0721070	−	0.997397i	$-0.477028\pi$
$797$	4.07133	0.144214	0.0721070	+	0.997397i	$0.477028\pi$
$798$	−6.20248	−0.219565
$799$	29.4938	1.04341
$800$	−5.68616	−0.201036
$801$	20.3491	0.719002
$802$	27.7278	0.979102
$803$	−50.9337	−1.79741
$804$	5.06047	0.178469
$805$	−13.3474	−0.470433
$806$	25.1891	0.887250
$807$	−3.10279	−0.109224
$808$	−72.9979	−2.56806
$809$	−1.03878	−0.0365215	−0.0182608	−	0.999833i	$-0.505813\pi$
$809$	−1.03878	−0.0365215	−0.0182608	+	0.999833i	$0.505813\pi$
$810$	17.7105	0.622283
$811$	−16.2295	−0.569893	−0.284947	−	0.958543i	$-0.591976\pi$
$811$	−16.2295	−0.569893	−0.284947	+	0.958543i	$0.591976\pi$
$812$	−107.528	−3.77350
$813$	4.21894	0.147965
$814$	72.9203	2.55586
$815$	8.32133	0.291483
$816$	−2.53030	−0.0885783
$817$	4.46885	0.156345
$818$	13.5957	0.475361
$819$	72.9595	2.54941
$820$	21.9602	0.766885
$821$	12.8850	0.449690	0.224845	−	0.974395i	$-0.427812\pi$
$821$	12.8850	0.449690	0.224845	+	0.974395i	$0.427812\pi$
$822$	3.60267	0.125657
$823$	−29.5561	−1.03026	−0.515131	−	0.857112i	$-0.672257\pi$
$823$	−29.5561	−1.03026	−0.515131	+	0.857112i	$0.672257\pi$
$824$	2.59385	0.0903610
$825$	2.61118	0.0909096
$826$	81.5839	2.83867
$827$	26.1460	0.909184	0.454592	−	0.890700i	$-0.349785\pi$
$827$	26.1460	0.909184	0.454592	+	0.890700i	$0.349785\pi$
$828$	40.9225	1.42215
$829$	19.9517	0.692952	0.346476	−	0.938059i	$-0.387378\pi$
$829$	19.9517	0.692952	0.346476	+	0.938059i	$0.387378\pi$
$830$	−30.1084	−1.04508
$831$	−0.822425	−0.0285296
$832$	−53.0458	−1.83903
$833$	53.6859	1.86011
$834$	−9.52002	−0.329651
$835$	11.9372	0.413104
$836$	38.6439	1.33653
$837$	−2.09473	−0.0724045
$838$	45.1651	1.56020
$839$	−6.23998	−0.215428	−0.107714	−	0.994182i	$-0.534353\pi$
$839$	−6.23998	−0.215428	−0.107714	+	0.994182i	$0.534353\pi$
$840$	3.14637	0.108560
$841$	10.6183	0.366148
$842$	−16.2454	−0.559853
$843$	−0.567684	−0.0195521
$844$	75.8487	2.61082
$845$	−15.0694	−0.518402
$846$	49.7004	1.70873
$847$	2.06294	0.0708834
$848$	−36.0317	−1.23734
$849$	1.66494	0.0571406
$850$	44.2174	1.51664
$851$	33.2098	1.13842
$852$	−6.62330	−0.226910
$853$	−36.1883	−1.23907	−0.619533	−	0.784971i	$-0.712678\pi$
$853$	−36.1883	−1.23907	−0.619533	+	0.784971i	$0.712678\pi$
$854$	−144.717	−4.95212
$855$	7.70921	0.263650
$856$	55.8679	1.90953
$857$	16.6823	0.569857	0.284929	−	0.958549i	$-0.408030\pi$
$857$	16.6823	0.569857	0.284929	+	0.958549i	$0.408030\pi$
$858$	8.18695	0.279498
$859$	4.92086	0.167897	0.0839487	−	0.996470i	$-0.473247\pi$
$859$	4.92086	0.167897	0.0839487	+	0.996470i	$0.473247\pi$
$860$	−4.70705	−0.160509
$861$	−5.60979	−0.191181
$862$	66.7014	2.27186
$863$	−36.4254	−1.23994	−0.619968	−	0.784627i	$-0.712854\pi$
$863$	−36.4254	−1.23994	−0.619968	+	0.784627i	$0.712854\pi$
$864$	1.48258	0.0504386
$865$	13.5437	0.460501
$866$	−12.8121	−0.435375
$867$	−0.212677	−0.00722290
$868$	31.9915	1.08586
$869$	28.8351	0.978165
$870$	−2.40709	−0.0816080
$871$	−38.8712	−1.31710
$872$	2.93239	0.0993033
$873$	48.4222	1.63884
$874$	26.7228	0.903913
$875$	−34.6596	−1.17171
$876$	11.3539	0.383613
$877$	−19.0043	−0.641729	−0.320865	−	0.947125i	$-0.603973\pi$
$877$	−19.0043	−0.641729	−0.320865	+	0.947125i	$0.603973\pi$
$878$	−29.7283	−1.00328
$879$	−0.573498	−0.0193436
$880$	−8.66465	−0.292085
$881$	7.86773	0.265070	0.132535	−	0.991178i	$-0.457688\pi$
$881$	7.86773	0.265070	0.132535	+	0.991178i	$0.457688\pi$
$882$	90.4668	3.04617
$883$	−40.9733	−1.37886	−0.689431	−	0.724352i	$-0.742139\pi$
$883$	−40.9733	−1.37886	−0.689431	+	0.724352i	$0.742139\pi$
$884$	91.3047	3.07091
$885$	1.20279	0.0404313
$886$	−63.4779	−2.13258
$887$	43.5396	1.46192	0.730959	−	0.682421i	$-0.239073\pi$
$887$	43.5396	1.46192	0.730959	+	0.682421i	$0.239073\pi$
$888$	−7.82852	−0.262708
$889$	−43.6616	−1.46436
$890$	−13.9965	−0.469165
$891$	28.1874	0.944314
$892$	−14.7866	−0.495093
$893$	21.3744	0.715269
$894$	1.95709	0.0654548
$895$	12.0599	0.403118
$896$	−90.5578	−3.02532
$897$	3.72854	0.124492
$898$	52.9823	1.76804
$899$	−11.7871	−0.393123
$900$	49.0724	1.63575
$901$	−48.4260	−1.61330
$902$	53.0697	1.76703
$903$	1.20243	0.0400143
$904$	1.66149	0.0552604
$905$	17.2288	0.572705
$906$	2.54817	0.0846572
$907$	−17.1389	−0.569086	−0.284543	−	0.958663i	$-0.591842\pi$
$907$	−17.1389	−0.569086	−0.284543	+	0.958663i	$0.591842\pi$
$908$	44.1999	1.46682
$909$	−48.1253	−1.59622
$910$	−50.1829	−1.66355
$911$	4.40934	0.146088	0.0730439	−	0.997329i	$-0.476729\pi$
$911$	4.40934	0.146088	0.0730439	+	0.997329i	$0.476729\pi$
$912$	−1.83374	−0.0607211
$913$	−47.9196	−1.58591
$914$	−9.50031	−0.314242
$915$	−2.13356	−0.0705333
$916$	−7.46627	−0.246692
$917$	33.5850	1.10908
$918$	−11.5290	−0.380515
$919$	29.4113	0.970188	0.485094	−	0.874462i	$-0.338785\pi$
$919$	29.4113	0.970188	0.485094	+	0.874462i	$0.338785\pi$
$920$	−13.5559	−0.446923
$921$	−2.61038	−0.0860150
$922$	69.1006	2.27571
$923$	50.8758	1.67460
$924$	10.3979	0.342064
$925$	39.8236	1.30939
$926$	−58.0290	−1.90695
$927$	1.71005	0.0561654
$928$	8.34256	0.273858
$929$	−31.7919	−1.04306	−0.521529	−	0.853234i	$-0.674638\pi$
$929$	−31.7919	−1.04306	−0.521529	+	0.853234i	$0.674638\pi$
$930$	0.716151	0.0234835
$931$	38.9067	1.27512
$932$	−38.1040	−1.24814
$933$	4.52254	0.148061
$934$	18.3441	0.600237
$935$	−11.6451	−0.380836
$936$	74.0991	2.42201
$937$	10.7649	0.351675	0.175837	−	0.984419i	$-0.443737\pi$
$937$	10.7649	0.351675	0.175837	+	0.984419i	$0.443737\pi$
$938$	−74.9608	−2.44756
$939$	−2.89304	−0.0944108
$940$	−22.5138	−0.734319
$941$	−53.8870	−1.75667	−0.878333	−	0.478049i	$-0.841344\pi$
$941$	−53.8870	−1.75667	−0.878333	+	0.478049i	$0.841344\pi$
$942$	9.84260	0.320689
$943$	24.1693	0.787060
$944$	24.1200	0.785038
$945$	4.17322	0.135755
$946$	−11.3752	−0.369839
$947$	4.85983	0.157923	0.0789616	−	0.996878i	$-0.474840\pi$
$947$	4.85983	0.157923	0.0789616	+	0.996878i	$0.474840\pi$
$948$	−6.42780	−0.208765
$949$	−87.2132	−2.83106
$950$	32.0448	1.03967
$951$	2.72353	0.0883166
$952$	84.7989	2.74835
$953$	−11.7990	−0.382207	−0.191103	−	0.981570i	$-0.561207\pi$
$953$	−11.7990	−0.382207	−0.191103	+	0.981570i	$0.561207\pi$
$954$	−81.6033	−2.64200
$955$	−5.52351	−0.178737
$956$	56.0628	1.81320
$957$	−3.83104	−0.123840
$958$	−61.5175	−1.98754
$959$	−35.1466	−1.13494
$960$	−1.50814	−0.0486750
$961$	−27.4931	−0.886875
$962$	124.861	4.02567
$963$	36.8321	1.18690
$964$	−90.9715	−2.92999
$965$	15.7235	0.506158
$966$	7.19027	0.231343
$967$	−41.7145	−1.34145	−0.670724	−	0.741707i	$-0.734017\pi$
$967$	−41.7145	−1.34145	−0.670724	+	0.741707i	$0.734017\pi$
$968$	2.09516	0.0673410
$969$	−2.46451	−0.0791715
$970$	−33.3057	−1.06938
$971$	32.1723	1.03246	0.516229	−	0.856451i	$-0.327335\pi$
$971$	32.1723	1.03246	0.516229	+	0.856451i	$0.327335\pi$
$972$	−19.2301	−0.616805
$973$	92.8745	2.97742
$974$	87.2664	2.79620
$975$	4.47110	0.143190
$976$	−42.7850	−1.36952
$977$	47.7575	1.52790	0.763948	−	0.645277i	$-0.223258\pi$
$977$	47.7575	1.52790	0.763948	+	0.645277i	$0.223258\pi$
$978$	−4.48273	−0.143342
$979$	−22.2764	−0.711957
$980$	−40.9806	−1.30908
$981$	1.93324	0.0617235
$982$	44.6605	1.42517
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	−5.69741	−0.181627
$985$	17.8546	0.568895
$986$	−64.8743	−2.06602
$987$	5.75119	0.183063
$988$	66.1695	2.10513
$989$	−5.18055	−0.164732
$990$	−19.6234	−0.623671
$991$	−3.13215	−0.0994960	−0.0497480	−	0.998762i	$-0.515842\pi$
$991$	−3.13215	−0.0994960	−0.0497480	+	0.998762i	$0.515842\pi$
$992$	−2.48206	−0.0788053
$993$	2.63046	0.0834752
$994$	98.1111	3.11189
$995$	−1.55714	−0.0493647
$996$	10.6820	0.338472
$997$	−39.6968	−1.25721	−0.628606	−	0.777724i	$-0.716374\pi$
$997$	−39.6968	−1.25721	−0.628606	+	0.777724i	$0.716374\pi$
$998$	−89.4626	−2.83189
$999$	−10.3834	−0.328517

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.3	✓	28
3.2	odd	2		8847.2.a.b.1.26		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.3	✓	28	1.1	even	1	trivial
8847.2.a.b.1.26		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)

\(f(q)\)	\(=\)	\(q-2.42034 q^{2} -0.187530 q^{3} +3.85806 q^{4} -0.842553 q^{5} +0.453886 q^{6} -4.42798 q^{7} -4.49714 q^{8} -2.96483 q^{9} +O(q^{10})\)	\(q-2.42034 q^{2} -0.187530 q^{3} +3.85806 q^{4} -0.842553 q^{5} +0.453886 q^{6} -4.42798 q^{7} -4.49714 q^{8} -2.96483 q^{9} +2.03927 q^{10} +3.24563 q^{11} -0.723501 q^{12} +5.55746 q^{13} +10.7172 q^{14} +0.158004 q^{15} +3.16851 q^{16} +4.25842 q^{17} +7.17591 q^{18} +3.08612 q^{19} -3.25062 q^{20} +0.830378 q^{21} -7.85554 q^{22} -3.57761 q^{23} +0.843348 q^{24} -4.29010 q^{25} -13.4510 q^{26} +1.11858 q^{27} -17.0834 q^{28} +6.29431 q^{29} -0.382423 q^{30} -1.87267 q^{31} +1.32541 q^{32} -0.608652 q^{33} -10.3068 q^{34} +3.73081 q^{35} -11.4385 q^{36} -9.28267 q^{37} -7.46946 q^{38} -1.04219 q^{39} +3.78908 q^{40} -6.75571 q^{41} -2.00980 q^{42} +1.44805 q^{43} +12.5218 q^{44} +2.49803 q^{45} +8.65904 q^{46} +6.92600 q^{47} -0.594189 q^{48} +12.6070 q^{49} +10.3835 q^{50} -0.798579 q^{51} +21.4410 q^{52} -11.3718 q^{53} -2.70735 q^{54} -2.73462 q^{55} +19.9133 q^{56} -0.578739 q^{57} -15.2344 q^{58} +7.61241 q^{59} +0.609588 q^{60} -13.5032 q^{61} +4.53249 q^{62} +13.1282 q^{63} -9.54497 q^{64} -4.68245 q^{65} +1.47315 q^{66} -6.99442 q^{67} +16.4292 q^{68} +0.670908 q^{69} -9.02984 q^{70} +9.15452 q^{71} +13.3333 q^{72} -15.6930 q^{73} +22.4672 q^{74} +0.804522 q^{75} +11.9064 q^{76} -14.3716 q^{77} +2.52245 q^{78} +8.88430 q^{79} -2.66963 q^{80} +8.68473 q^{81} +16.3511 q^{82} -14.7643 q^{83} +3.20365 q^{84} -3.58794 q^{85} -3.50477 q^{86} -1.18037 q^{87} -14.5961 q^{88} -6.86351 q^{89} -6.04609 q^{90} -24.6083 q^{91} -13.8026 q^{92} +0.351180 q^{93} -16.7633 q^{94} -2.60022 q^{95} -0.248554 q^{96} -16.3322 q^{97} -30.5133 q^{98} -9.62275 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 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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