LMFDB - Embedded newform 983.2.a.a.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.64741 q^{2} -0.803598 q^{3} +0.713964 q^{4} +2.48769 q^{5} +1.32386 q^{6} +2.09423 q^{7} +2.11863 q^{8} -2.35423 q^{9} +O(q^{10})$	\(q-1.64741 q^{2} -0.803598 q^{3} +0.713964 q^{4} +2.48769 q^{5} +1.32386 q^{6} +2.09423 q^{7} +2.11863 q^{8} -2.35423 q^{9} -4.09824 q^{10} -3.82694 q^{11} -0.573740 q^{12} +1.12633 q^{13} -3.45006 q^{14} -1.99910 q^{15} -4.91818 q^{16} -4.62036 q^{17} +3.87838 q^{18} -6.43778 q^{19} +1.77612 q^{20} -1.68292 q^{21} +6.30454 q^{22} +5.61922 q^{23} -1.70253 q^{24} +1.18858 q^{25} -1.85552 q^{26} +4.30265 q^{27} +1.49520 q^{28} +0.357349 q^{29} +3.29334 q^{30} -1.45175 q^{31} +3.86501 q^{32} +3.07532 q^{33} +7.61163 q^{34} +5.20979 q^{35} -1.68083 q^{36} +3.29798 q^{37} +10.6057 q^{38} -0.905113 q^{39} +5.27049 q^{40} -8.09625 q^{41} +2.77246 q^{42} -7.25204 q^{43} -2.73230 q^{44} -5.85658 q^{45} -9.25716 q^{46} +9.45901 q^{47} +3.95224 q^{48} -2.61420 q^{49} -1.95808 q^{50} +3.71291 q^{51} +0.804155 q^{52} -9.44411 q^{53} -7.08823 q^{54} -9.52023 q^{55} +4.43690 q^{56} +5.17339 q^{57} -0.588701 q^{58} +4.05412 q^{59} -1.42728 q^{60} -1.85363 q^{61} +2.39163 q^{62} -4.93030 q^{63} +3.46911 q^{64} +2.80194 q^{65} -5.06632 q^{66} +7.83695 q^{67} -3.29877 q^{68} -4.51559 q^{69} -8.58266 q^{70} -7.40491 q^{71} -4.98774 q^{72} -6.72027 q^{73} -5.43313 q^{74} -0.955142 q^{75} -4.59634 q^{76} -8.01449 q^{77} +1.49109 q^{78} -10.5786 q^{79} -12.2349 q^{80} +3.60509 q^{81} +13.3379 q^{82} -14.6847 q^{83} -1.20154 q^{84} -11.4940 q^{85} +11.9471 q^{86} -0.287165 q^{87} -8.10787 q^{88} +0.605361 q^{89} +9.64820 q^{90} +2.35878 q^{91} +4.01192 q^{92} +1.16662 q^{93} -15.5829 q^{94} -16.0152 q^{95} -3.10591 q^{96} -18.9734 q^{97} +4.30666 q^{98} +9.00950 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.64741	−1.16490	−0.582448	−	0.812868i	$-0.697905\pi$
$2$	−1.64741	−1.16490	−0.582448	+	0.812868i	$0.697905\pi$
$3$	−0.803598	−0.463958	−0.231979	−	0.972721i	$-0.574520\pi$
$3$	−0.803598	−0.463958	−0.231979	+	0.972721i	$0.574520\pi$
$4$	0.713964	0.356982
$5$	2.48769	1.11253	0.556263	−	0.831006i	$-0.312235\pi$
$5$	2.48769	1.11253	0.556263	+	0.831006i	$0.312235\pi$
$6$	1.32386	0.540462
$7$	2.09423	0.791545	0.395772	−	0.918349i	$-0.370477\pi$
$7$	2.09423	0.791545	0.395772	+	0.918349i	$0.370477\pi$
$8$	2.11863	0.749049
$9$	−2.35423	−0.784743
$10$	−4.09824	−1.29598
$11$	−3.82694	−1.15387	−0.576933	−	0.816792i	$-0.695751\pi$
$11$	−3.82694	−1.15387	−0.576933	+	0.816792i	$0.695751\pi$
$12$	−0.573740	−0.165624
$13$	1.12633	0.312386	0.156193	−	0.987727i	$-0.450078\pi$
$13$	1.12633	0.312386	0.156193	+	0.987727i	$0.450078\pi$
$14$	−3.45006	−0.922067
$15$	−1.99910	−0.516165
$16$	−4.91818	−1.22955
$17$	−4.62036	−1.12060	−0.560301	−	0.828289i	$-0.689315\pi$
$17$	−4.62036	−1.12060	−0.560301	+	0.828289i	$0.689315\pi$
$18$	3.87838	0.914144
$19$	−6.43778	−1.47693	−0.738464	−	0.674293i	$-0.764449\pi$
$19$	−6.43778	−1.47693	−0.738464	+	0.674293i	$0.764449\pi$
$20$	1.77612	0.397152
$21$	−1.68292	−0.367243
$22$	6.30454	1.34413
$23$	5.61922	1.17169	0.585844	−	0.810424i	$-0.300763\pi$
$23$	5.61922	1.17169	0.585844	+	0.810424i	$0.300763\pi$
$24$	−1.70253	−0.347527
$25$	1.18858	0.237716
$26$	−1.85552	−0.363898
$27$	4.30265	0.828045
$28$	1.49520	0.282567
$29$	0.357349	0.0663581	0.0331790	−	0.999449i	$-0.489437\pi$
$29$	0.357349	0.0663581	0.0331790	+	0.999449i	$0.489437\pi$
$30$	3.29334	0.601279
$31$	−1.45175	−0.260742	−0.130371	−	0.991465i	$-0.541617\pi$
$31$	−1.45175	−0.260742	−0.130371	+	0.991465i	$0.541617\pi$
$32$	3.86501	0.683244
$33$	3.07532	0.535345
$34$	7.61163	1.30538
$35$	5.20979	0.880615
$36$	−1.68083	−0.280139
$37$	3.29798	0.542184	0.271092	−	0.962553i	$-0.412615\pi$
$37$	3.29798	0.542184	0.271092	+	0.962553i	$0.412615\pi$
$38$	10.6057	1.72047
$39$	−0.905113	−0.144934
$40$	5.27049	0.833337
$41$	−8.09625	−1.26442	−0.632211	−	0.774796i	$-0.717853\pi$
$41$	−8.09625	−1.26442	−0.632211	+	0.774796i	$0.717853\pi$
$42$	2.77246	0.427800
$43$	−7.25204	−1.10593	−0.552963	−	0.833206i	$-0.686503\pi$
$43$	−7.25204	−1.10593	−0.552963	+	0.833206i	$0.686503\pi$
$44$	−2.73230	−0.411909
$45$	−5.85658	−0.873048
$46$	−9.25716	−1.36489
$47$	9.45901	1.37974	0.689870	−	0.723934i	$-0.257668\pi$
$47$	9.45901	1.37974	0.689870	+	0.723934i	$0.257668\pi$
$48$	3.95224	0.570457
$49$	−2.61420	−0.373457
$50$	−1.95808	−0.276915
$51$	3.71291	0.519912
$52$	0.804155	0.111516
$53$	−9.44411	−1.29725	−0.648624	−	0.761109i	$-0.724655\pi$
$53$	−9.44411	−1.29725	−0.648624	+	0.761109i	$0.724655\pi$
$54$	−7.08823	−0.964586
$55$	−9.52023	−1.28371
$56$	4.43690	0.592906
$57$	5.17339	0.685232
$58$	−0.588701	−0.0773002
$59$	4.05412	0.527801	0.263901	−	0.964550i	$-0.414991\pi$
$59$	4.05412	0.527801	0.263901	+	0.964550i	$0.414991\pi$
$60$	−1.42728	−0.184262
$61$	−1.85363	−0.237333	−0.118667	−	0.992934i	$-0.537862\pi$
$61$	−1.85363	−0.237333	−0.118667	+	0.992934i	$0.537862\pi$
$62$	2.39163	0.303737
$63$	−4.93030	−0.621159
$64$	3.46911	0.433638
$65$	2.80194	0.347538
$66$	−5.06632	−0.623621
$67$	7.83695	0.957436	0.478718	−	0.877969i	$-0.341102\pi$
$67$	7.83695	0.957436	0.478718	+	0.877969i	$0.341102\pi$
$68$	−3.29877	−0.400035
$69$	−4.51559	−0.543613
$70$	−8.58266	−1.02582
$71$	−7.40491	−0.878801	−0.439401	−	0.898291i	$-0.644809\pi$
$71$	−7.40491	−0.878801	−0.439401	+	0.898291i	$0.644809\pi$
$72$	−4.98774	−0.587811
$73$	−6.72027	−0.786548	−0.393274	−	0.919421i	$-0.628658\pi$
$73$	−6.72027	−0.786548	−0.393274	+	0.919421i	$0.628658\pi$
$74$	−5.43313	−0.631588
$75$	−0.955142	−0.110290
$76$	−4.59634	−0.527237
$77$	−8.01449	−0.913336
$78$	1.49109	0.168833
$79$	−10.5786	−1.19018	−0.595091	−	0.803659i	$-0.702884\pi$
$79$	−10.5786	−1.19018	−0.595091	+	0.803659i	$0.702884\pi$
$80$	−12.2349	−1.36790
$81$	3.60509	0.400565
$82$	13.3379	1.47292
$83$	−14.6847	−1.61185	−0.805926	−	0.592016i	$-0.798332\pi$
$83$	−14.6847	−1.61185	−0.805926	+	0.592016i	$0.798332\pi$
$84$	−1.20154	−0.131099
$85$	−11.4940	−1.24670
$86$	11.9471	1.28829
$87$	−0.287165	−0.0307873
$88$	−8.10787	−0.864302
$89$	0.605361	0.0641681	0.0320841	−	0.999485i	$-0.489786\pi$
$89$	0.605361	0.0641681	0.0320841	+	0.999485i	$0.489786\pi$
$90$	9.64820	1.01701
$91$	2.35878	0.247268
$92$	4.01192	0.418271
$93$	1.16662	0.120973
$94$	−15.5829	−1.60725
$95$	−16.0152	−1.64312
$96$	−3.10591	−0.316996
$97$	−18.9734	−1.92646	−0.963230	−	0.268679i	$-0.913413\pi$
$97$	−18.9734	−1.92646	−0.963230	+	0.268679i	$0.913413\pi$
$98$	4.30666	0.435039
$99$	9.00950	0.905489
$100$	0.848604	0.0848604
$101$	10.9486	1.08943	0.544713	−	0.838622i	$-0.316639\pi$
$101$	10.9486	1.08943	0.544713	+	0.838622i	$0.316639\pi$
$102$	−6.11670	−0.605643
$103$	19.9941	1.97008	0.985039	−	0.172333i	$-0.0551304\pi$
$103$	19.9941	1.97008	0.985039	+	0.172333i	$0.0551304\pi$
$104$	2.38627	0.233993
$105$	−4.18658	−0.408568
$106$	15.5583	1.51116
$107$	−1.70199	−0.164538	−0.0822690	−	0.996610i	$-0.526217\pi$
$107$	−1.70199	−0.164538	−0.0822690	+	0.996610i	$0.526217\pi$
$108$	3.07194	0.295597
$109$	−13.6117	−1.30377	−0.651884	−	0.758319i	$-0.726021\pi$
$109$	−13.6117	−1.30377	−0.651884	+	0.758319i	$0.726021\pi$
$110$	15.6837	1.49538
$111$	−2.65025	−0.251551
$112$	−10.2998	−0.973240
$113$	−11.2598	−1.05923	−0.529616	−	0.848237i	$-0.677664\pi$
$113$	−11.2598	−1.05923	−0.529616	+	0.848237i	$0.677664\pi$
$114$	−8.52270	−0.798224
$115$	13.9788	1.30353
$116$	0.255134	0.0236886
$117$	−2.65163	−0.245143
$118$	−6.67880	−0.614834
$119$	−9.67610	−0.887007
$120$	−4.23535	−0.386633
$121$	3.64547	0.331407
$122$	3.05370	0.276469
$123$	6.50614	0.586638
$124$	−1.03650	−0.0930802
$125$	−9.48161	−0.848061
$126$	8.12223	0.723586
$127$	−1.20699	−0.107103	−0.0535515	−	0.998565i	$-0.517054\pi$
$127$	−1.20699	−0.107103	−0.0535515	+	0.998565i	$0.517054\pi$
$128$	−13.4451	−1.18839
$129$	5.82772	0.513102
$130$	−4.61595	−0.404846
$131$	22.4280	1.95954	0.979770	−	0.200126i	$-0.0641352\pi$
$131$	22.4280	1.95954	0.979770	+	0.200126i	$0.0641352\pi$
$132$	2.19567	0.191108
$133$	−13.4822	−1.16905
$134$	−12.9107	−1.11531
$135$	10.7036	0.921223
$136$	−9.78884	−0.839386
$137$	19.1034	1.63211	0.816056	−	0.577973i	$-0.196156\pi$
$137$	19.1034	1.63211	0.816056	+	0.577973i	$0.196156\pi$
$138$	7.43904	0.633253
$139$	−11.5452	−0.979251	−0.489626	−	0.871933i	$-0.662867\pi$
$139$	−11.5452	−0.979251	−0.489626	+	0.871933i	$0.662867\pi$
$140$	3.71960	0.314364
$141$	−7.60125	−0.640140
$142$	12.1989	1.02371
$143$	−4.31038	−0.360452
$144$	11.5785	0.964878
$145$	0.888973	0.0738252
$146$	11.0710	0.916246
$147$	2.10077	0.173268
$148$	2.35464	0.193550
$149$	9.25889	0.758518	0.379259	−	0.925291i	$-0.376179\pi$
$149$	9.25889	0.758518	0.379259	+	0.925291i	$0.376179\pi$
$150$	1.57351	0.128477
$151$	−3.42940	−0.279080	−0.139540	−	0.990216i	$-0.544562\pi$
$151$	−3.42940	−0.279080	−0.139540	+	0.990216i	$0.544562\pi$
$152$	−13.6393	−1.10629
$153$	10.8774	0.879385
$154$	13.2032	1.06394
$155$	−3.61150	−0.290083
$156$	−0.646218	−0.0517388
$157$	−7.40914	−0.591313	−0.295657	−	0.955294i	$-0.595538\pi$
$157$	−7.40914	−0.591313	−0.295657	+	0.955294i	$0.595538\pi$
$158$	17.4272	1.38644
$159$	7.58927	0.601868
$160$	9.61493	0.760127
$161$	11.7679	0.927443
$162$	−5.93906	−0.466617
$163$	−7.93473	−0.621496	−0.310748	−	0.950492i	$-0.600580\pi$
$163$	−7.93473	−0.621496	−0.310748	+	0.950492i	$0.600580\pi$
$164$	−5.78043	−0.451376
$165$	7.65044	0.595586
$166$	24.1917	1.87764
$167$	−10.9998	−0.851191	−0.425596	−	0.904913i	$-0.639935\pi$
$167$	−10.9998	−0.851191	−0.425596	+	0.904913i	$0.639935\pi$
$168$	−3.56549	−0.275083
$169$	−11.7314	−0.902415
$170$	18.9354	1.45228
$171$	15.1560	1.15901
$172$	−5.17769	−0.394795
$173$	3.41641	0.259745	0.129872	−	0.991531i	$-0.458543\pi$
$173$	3.41641	0.259745	0.129872	+	0.991531i	$0.458543\pi$
$174$	0.473079	0.0358640
$175$	2.48916	0.188163
$176$	18.8216	1.41873
$177$	−3.25788	−0.244877
$178$	−0.997279	−0.0747492
$179$	19.6560	1.46916	0.734578	−	0.678524i	$-0.237380\pi$
$179$	19.6560	1.46916	0.734578	+	0.678524i	$0.237380\pi$
$180$	−4.18139	−0.311662
$181$	−6.99208	−0.519717	−0.259858	−	0.965647i	$-0.583676\pi$
$181$	−6.99208	−0.519717	−0.259858	+	0.965647i	$0.583676\pi$
$182$	−3.88589	−0.288041
$183$	1.48958	0.110113
$184$	11.9050	0.877652
$185$	8.20434	0.603195
$186$	−1.92191	−0.140921
$187$	17.6818	1.29302
$188$	6.75339	0.492542
$189$	9.01074	0.655435
$190$	26.3836	1.91407
$191$	−9.58053	−0.693223	−0.346611	−	0.938009i	$-0.612668\pi$
$191$	−9.58053	−0.693223	−0.346611	+	0.938009i	$0.612668\pi$
$192$	−2.78777	−0.201190
$193$	−21.2065	−1.52648	−0.763238	−	0.646118i	$-0.776392\pi$
$193$	−21.2065	−1.52648	−0.763238	+	0.646118i	$0.776392\pi$
$194$	31.2570	2.24412
$195$	−2.25164	−0.161243
$196$	−1.86644	−0.133317
$197$	11.2511	0.801606	0.400803	−	0.916164i	$-0.368731\pi$
$197$	11.2511	0.801606	0.400803	+	0.916164i	$0.368731\pi$
$198$	−14.8423	−1.05480
$199$	−20.5355	−1.45573	−0.727863	−	0.685723i	$-0.759486\pi$
$199$	−20.5355	−1.45573	−0.727863	+	0.685723i	$0.759486\pi$
$200$	2.51816	0.178061
$201$	−6.29776	−0.444210
$202$	−18.0368	−1.26907
$203$	0.748372	0.0525254
$204$	2.65089	0.185599
$205$	−20.1409	−1.40670
$206$	−32.9385	−2.29493
$207$	−13.2289	−0.919474
$208$	−5.53947	−0.384093
$209$	24.6370	1.70418
$210$	6.89701	0.475939
$211$	−15.7184	−1.08210	−0.541051	−	0.840990i	$-0.681973\pi$
$211$	−15.7184	−1.08210	−0.541051	+	0.840990i	$0.681973\pi$
$212$	−6.74275	−0.463094
$213$	5.95057	0.407727
$214$	2.80388	0.191670
$215$	−18.0408	−1.23037
$216$	9.11572	0.620246
$217$	−3.04030	−0.206389
$218$	22.4241	1.51875
$219$	5.40040	0.364925
$220$	−6.79710	−0.458260
$221$	−5.20403	−0.350061
$222$	4.36605	0.293030
$223$	8.89122	0.595400	0.297700	−	0.954660i	$-0.403781\pi$
$223$	8.89122	0.595400	0.297700	+	0.954660i	$0.403781\pi$
$224$	8.09422	0.540818
$225$	−2.79819	−0.186546
$226$	18.5495	1.23390
$227$	−16.7819	−1.11385	−0.556927	−	0.830562i	$-0.688020\pi$
$227$	−16.7819	−1.11385	−0.556927	+	0.830562i	$0.688020\pi$
$228$	3.69361	0.244615
$229$	−12.5058	−0.826408	−0.413204	−	0.910639i	$-0.635590\pi$
$229$	−12.5058	−0.826408	−0.413204	+	0.910639i	$0.635590\pi$
$230$	−23.0289	−1.51848
$231$	6.44043	0.423749
$232$	0.757091	0.0497055
$233$	−4.70840	−0.308458	−0.154229	−	0.988035i	$-0.549289\pi$
$233$	−4.70840	−0.308458	−0.154229	+	0.988035i	$0.549289\pi$
$234$	4.36832	0.285566
$235$	23.5311	1.53500
$236$	2.89449	0.188416
$237$	8.50091	0.552194
$238$	15.9405	1.03327
$239$	18.3777	1.18875	0.594377	−	0.804187i	$-0.297399\pi$
$239$	18.3777	1.18875	0.594377	+	0.804187i	$0.297399\pi$
$240$	9.83194	0.634649
$241$	25.3003	1.62974	0.814868	−	0.579647i	$-0.196809\pi$
$241$	25.3003	1.62974	0.814868	+	0.579647i	$0.196809\pi$
$242$	−6.00559	−0.386054
$243$	−15.8050	−1.01389
$244$	−1.32343	−0.0847238
$245$	−6.50331	−0.415481
$246$	−10.7183	−0.683373
$247$	−7.25103	−0.461372
$248$	−3.07572	−0.195309
$249$	11.8006	0.747831
$250$	15.6201	0.987903
$251$	12.7355	0.803856	0.401928	−	0.915671i	$-0.368340\pi$
$251$	12.7355	0.803856	0.401928	+	0.915671i	$0.368340\pi$
$252$	−3.52006	−0.221743
$253$	−21.5044	−1.35197
$254$	1.98841	0.124764
$255$	9.23656	0.578416
$256$	15.2113	0.950709
$257$	17.7058	1.10446	0.552228	−	0.833693i	$-0.313778\pi$
$257$	17.7058	1.10446	0.552228	+	0.833693i	$0.313778\pi$
$258$	−9.60066	−0.597711
$259$	6.90673	0.429163
$260$	2.00049	0.124065
$261$	−0.841282	−0.0520741
$262$	−36.9481	−2.28266
$263$	25.6296	1.58039	0.790194	−	0.612857i	$-0.209980\pi$
$263$	25.6296	1.58039	0.790194	+	0.612857i	$0.209980\pi$
$264$	6.51547	0.401000
$265$	−23.4940	−1.44322
$266$	22.2107	1.36183
$267$	−0.486467	−0.0297713
$268$	5.59530	0.341787
$269$	−16.5762	−1.01067	−0.505335	−	0.862923i	$-0.668631\pi$
$269$	−16.5762	−1.01067	−0.505335	+	0.862923i	$0.668631\pi$
$270$	−17.6333	−1.07313
$271$	3.52683	0.214239	0.107120	−	0.994246i	$-0.465837\pi$
$271$	3.52683	0.214239	0.107120	+	0.994246i	$0.465837\pi$
$272$	22.7238	1.37783
$273$	−1.89551	−0.114722
$274$	−31.4711	−1.90124
$275$	−4.54863	−0.274293
$276$	−3.22397	−0.194060
$277$	13.5417	0.813644	0.406822	−	0.913507i	$-0.366637\pi$
$277$	13.5417	0.813644	0.406822	+	0.913507i	$0.366637\pi$
$278$	19.0197	1.14073
$279$	3.41775	0.204616
$280$	11.0376	0.659624
$281$	9.66925	0.576819	0.288409	−	0.957507i	$-0.406874\pi$
$281$	9.66925	0.576819	0.288409	+	0.957507i	$0.406874\pi$
$282$	12.5224	0.745697
$283$	26.1422	1.55399	0.776996	−	0.629506i	$-0.216742\pi$
$283$	26.1422	1.55399	0.776996	+	0.629506i	$0.216742\pi$
$284$	−5.28684	−0.313716
$285$	12.8698	0.762339
$286$	7.10097	0.419889
$287$	−16.9554	−1.00085
$288$	−9.09912	−0.536171
$289$	4.34773	0.255749
$290$	−1.46450	−0.0859986
$291$	15.2470	0.893796
$292$	−4.79803	−0.280783
$293$	12.3557	0.721827	0.360913	−	0.932599i	$-0.382465\pi$
$293$	12.3557	0.721827	0.360913	+	0.932599i	$0.382465\pi$
$294$	−3.46083	−0.201839
$295$	10.0854	0.587193
$296$	6.98720	0.406123
$297$	−16.4660	−0.955453
$298$	−15.2532	−0.883594
$299$	6.32907	0.366019
$300$	−0.681937	−0.0393716
$301$	−15.1874	−0.875389
$302$	5.64963	0.325099
$303$	−8.79827	−0.505448
$304$	31.6622	1.81595
$305$	−4.61126	−0.264040
$306$	−17.9195	−1.02439
$307$	28.1026	1.60390	0.801951	−	0.597389i	$-0.203795\pi$
$307$	28.1026	1.60390	0.801951	+	0.597389i	$0.203795\pi$
$308$	−5.72206	−0.326045
$309$	−16.0672	−0.914033
$310$	5.94962	0.337916
$311$	−20.9161	−1.18604	−0.593020	−	0.805188i	$-0.702065\pi$
$311$	−20.9161	−1.18604	−0.593020	+	0.805188i	$0.702065\pi$
$312$	−1.91760	−0.108563
$313$	11.7534	0.664341	0.332171	−	0.943219i	$-0.392219\pi$
$313$	11.7534	0.664341	0.332171	+	0.943219i	$0.392219\pi$
$314$	12.2059	0.688818
$315$	−12.2650	−0.691057
$316$	−7.55271	−0.424873
$317$	7.71046	0.433063	0.216531	−	0.976276i	$-0.430526\pi$
$317$	7.71046	0.433063	0.216531	+	0.976276i	$0.430526\pi$
$318$	−12.5026	−0.701114
$319$	−1.36755	−0.0765683
$320$	8.63005	0.482434
$321$	1.36772	0.0763386
$322$	−19.3866	−1.08037
$323$	29.7449	1.65505
$324$	2.57390	0.142995
$325$	1.33873	0.0742593
$326$	13.0718	0.723978
$327$	10.9384	0.604893
$328$	−17.1530	−0.947114
$329$	19.8094	1.09213
$330$	−12.6034	−0.693795
$331$	17.0722	0.938372	0.469186	−	0.883099i	$-0.344547\pi$
$331$	17.0722	0.938372	0.469186	+	0.883099i	$0.344547\pi$
$332$	−10.4843	−0.575402
$333$	−7.76420	−0.425476
$334$	18.1212	0.991549
$335$	19.4959	1.06517
$336$	8.27691	0.451542
$337$	−15.1710	−0.826418	−0.413209	−	0.910636i	$-0.635592\pi$
$337$	−15.1710	−0.826418	−0.413209	+	0.910636i	$0.635592\pi$
$338$	19.3264	1.05122
$339$	9.04835	0.491439
$340$	−8.20630	−0.445049
$341$	5.55576	0.300861
$342$	−24.9682	−1.35013
$343$	−20.1343	−1.08715
$344$	−15.3644	−0.828392
$345$	−11.2334	−0.604785
$346$	−5.62823	−0.302575
$347$	−13.7233	−0.736704	−0.368352	−	0.929686i	$-0.620078\pi$
$347$	−13.7233	−0.736704	−0.368352	+	0.929686i	$0.620078\pi$
$348$	−0.205026	−0.0109905
$349$	−10.0767	−0.539395	−0.269697	−	0.962945i	$-0.586924\pi$
$349$	−10.0767	−0.539395	−0.269697	+	0.962945i	$0.586924\pi$
$350$	−4.10067	−0.219190
$351$	4.84618	0.258670
$352$	−14.7912	−0.788371
$353$	−34.6590	−1.84471	−0.922357	−	0.386339i	$-0.873739\pi$
$353$	−34.6590	−1.84471	−0.922357	+	0.386339i	$0.873739\pi$
$354$	5.36707	0.285257
$355$	−18.4211	−0.977690
$356$	0.432206	0.0229069
$357$	7.77570	0.411533
$358$	−32.3815	−1.71141
$359$	13.4631	0.710556	0.355278	−	0.934761i	$-0.384386\pi$
$359$	13.4631	0.710556	0.355278	+	0.934761i	$0.384386\pi$
$360$	−12.4079	−0.653956
$361$	22.4450	1.18132
$362$	11.5188	0.605416
$363$	−2.92949	−0.153759
$364$	1.68409	0.0882701
$365$	−16.7179	−0.875056
$366$	−2.45395	−0.128270
$367$	−12.9865	−0.677892	−0.338946	−	0.940806i	$-0.610070\pi$
$367$	−12.9865	−0.677892	−0.338946	+	0.940806i	$0.610070\pi$
$368$	−27.6363	−1.44064
$369$	19.0604	0.992247
$370$	−13.5159	−0.702659
$371$	−19.7781	−1.02683
$372$	0.832927	0.0431853
$373$	−35.7591	−1.85154	−0.925768	−	0.378093i	$-0.876580\pi$
$373$	−35.7591	−1.85154	−0.925768	+	0.378093i	$0.876580\pi$
$374$	−29.1293	−1.50624
$375$	7.61941	0.393464
$376$	20.0402	1.03349
$377$	0.402491	0.0207294
$378$	−14.8444	−0.763513
$379$	−2.56674	−0.131844	−0.0659222	−	0.997825i	$-0.520999\pi$
$379$	−2.56674	−0.131844	−0.0659222	+	0.997825i	$0.520999\pi$
$380$	−11.4343	−0.586565
$381$	0.969934	0.0496912
$382$	15.7831	0.807532
$383$	37.9016	1.93668	0.968341	−	0.249631i	$-0.0803092\pi$
$383$	37.9016	1.93668	0.968341	+	0.249631i	$0.0803092\pi$
$384$	10.8044	0.551361
$385$	−19.9375	−1.01611
$386$	34.9358	1.77819
$387$	17.0730	0.867867
$388$	−13.5463	−0.687711
$389$	−6.33221	−0.321056	−0.160528	−	0.987031i	$-0.551320\pi$
$389$	−6.33221	−0.321056	−0.160528	+	0.987031i	$0.551320\pi$
$390$	3.70937	0.187831
$391$	−25.9628	−1.31300
$392$	−5.53852	−0.279738
$393$	−18.0231	−0.909144
$394$	−18.5351	−0.933787
$395$	−26.3161	−1.32411
$396$	6.43245	0.323243
$397$	2.05163	0.102968	0.0514841	−	0.998674i	$-0.483605\pi$
$397$	2.05163	0.102968	0.0514841	+	0.998674i	$0.483605\pi$
$398$	33.8305	1.69577
$399$	10.8343	0.542392
$400$	−5.84566	−0.292283
$401$	8.17393	0.408187	0.204093	−	0.978951i	$-0.434575\pi$
$401$	8.17393	0.408187	0.204093	+	0.978951i	$0.434575\pi$
$402$	10.3750	0.517458
$403$	−1.63514	−0.0814523
$404$	7.81690	0.388905
$405$	8.96833	0.445640
$406$	−1.23288	−0.0611866
$407$	−12.6212	−0.625608
$408$	7.86629	0.389439
$409$	−22.0069	−1.08817	−0.544085	−	0.839030i	$-0.683123\pi$
$409$	−22.0069	−1.08817	−0.544085	+	0.839030i	$0.683123\pi$
$410$	33.1804	1.63866
$411$	−15.3514	−0.757231
$412$	14.2751	0.703282
$413$	8.49026	0.417778
$414$	21.7935	1.07109
$415$	−36.5309	−1.79323
$416$	4.35326	0.213436
$417$	9.27770	0.454331
$418$	−40.5873	−1.98519
$419$	3.15085	0.153929	0.0769646	−	0.997034i	$-0.475477\pi$
$419$	3.15085	0.153929	0.0769646	+	0.997034i	$0.475477\pi$
$420$	−2.98906	−0.145851
$421$	13.1086	0.638875	0.319438	−	0.947607i	$-0.396506\pi$
$421$	13.1086	0.638875	0.319438	+	0.947607i	$0.396506\pi$
$422$	25.8947	1.26053
$423$	−22.2687	−1.08274
$424$	−20.0086	−0.971703
$425$	−5.49167	−0.266385
$426$	−9.80304	−0.474959
$427$	−3.88194	−0.187860
$428$	−1.21516	−0.0587371
$429$	3.46381	0.167234
$430$	29.7206	1.43325
$431$	−11.6037	−0.558932	−0.279466	−	0.960156i	$-0.590157\pi$
$431$	−11.6037	−0.558932	−0.279466	+	0.960156i	$0.590157\pi$
$432$	−21.1612	−1.01812
$433$	−2.01228	−0.0967038	−0.0483519	−	0.998830i	$-0.515397\pi$
$433$	−2.01228	−0.0967038	−0.0483519	+	0.998830i	$0.515397\pi$
$434$	5.00862	0.240422
$435$	−0.714377	−0.0342517
$436$	−9.71828	−0.465421
$437$	−36.1753	−1.73050
$438$	−8.89667	−0.425100
$439$	−22.5931	−1.07831	−0.539155	−	0.842207i	$-0.681256\pi$
$439$	−22.5931	−1.07831	−0.539155	+	0.842207i	$0.681256\pi$
$440$	−20.1698	−0.961559
$441$	6.15443	0.293068
$442$	8.57317	0.407784
$443$	−2.75685	−0.130982	−0.0654909	−	0.997853i	$-0.520861\pi$
$443$	−2.75685	−0.130982	−0.0654909	+	0.997853i	$0.520861\pi$
$444$	−1.89218	−0.0897990
$445$	1.50595	0.0713888
$446$	−14.6475	−0.693579
$447$	−7.44043	−0.351920
$448$	7.26511	0.343244
$449$	−1.90135	−0.0897305	−0.0448652	−	0.998993i	$-0.514286\pi$
$449$	−1.90135	−0.0897305	−0.0448652	+	0.998993i	$0.514286\pi$
$450$	4.60978	0.217307
$451$	30.9839	1.45897
$452$	−8.03909	−0.378127
$453$	2.75586	0.129481
$454$	27.6467	1.29752
$455$	5.86791	0.275092
$456$	10.9605	0.513272
$457$	−14.0492	−0.657192	−0.328596	−	0.944471i	$-0.606575\pi$
$457$	−14.0492	−0.657192	−0.328596	+	0.944471i	$0.606575\pi$
$458$	20.6022	0.962679
$459$	−19.8798	−0.927909
$460$	9.98039	0.465338
$461$	0.101756	0.00473924	0.00236962	−	0.999997i	$-0.499246\pi$
$461$	0.101756	0.00473924	0.00236962	+	0.999997i	$0.499246\pi$
$462$	−10.6100	−0.493624
$463$	36.7663	1.70867	0.854337	−	0.519720i	$-0.173964\pi$
$463$	36.7663	1.70867	0.854337	+	0.519720i	$0.173964\pi$
$464$	−1.75751	−0.0815903
$465$	2.90219	0.134586
$466$	7.75668	0.359321
$467$	−25.9733	−1.20190	−0.600951	−	0.799286i	$-0.705211\pi$
$467$	−25.9733	−1.20190	−0.600951	+	0.799286i	$0.705211\pi$
$468$	−1.89317	−0.0875117
$469$	16.4124	0.757854
$470$	−38.7653	−1.78811
$471$	5.95397	0.274344
$472$	8.58918	0.395349
$473$	27.7531	1.27609
$474$	−14.0045	−0.643248
$475$	−7.65183	−0.351090
$476$	−6.90838	−0.316645
$477$	22.2336	1.01801
$478$	−30.2756	−1.38477
$479$	−9.66084	−0.441415	−0.220708	−	0.975340i	$-0.570837\pi$
$479$	−9.66084	−0.441415	−0.220708	+	0.975340i	$0.570837\pi$
$480$	−7.72654	−0.352667
$481$	3.71460	0.169371
$482$	−41.6800	−1.89847
$483$	−9.45669	−0.430294
$484$	2.60274	0.118306
$485$	−47.1999	−2.14324
$486$	26.0373	1.18108
$487$	16.6033	0.752366	0.376183	−	0.926545i	$-0.377236\pi$
$487$	16.6033	0.752366	0.376183	+	0.926545i	$0.377236\pi$
$488$	−3.92717	−0.177774
$489$	6.37633	0.288348
$490$	10.7136	0.483992
$491$	18.5424	0.836805	0.418403	−	0.908262i	$-0.362590\pi$
$491$	18.5424	0.836805	0.418403	+	0.908262i	$0.362590\pi$
$492$	4.64514	0.209419
$493$	−1.65108	−0.0743610
$494$	11.9454	0.537451
$495$	22.4128	1.00738
$496$	7.13997	0.320594
$497$	−15.5076	−0.695610
$498$	−19.4404	−0.871145
$499$	28.5148	1.27650	0.638248	−	0.769831i	$-0.279659\pi$
$499$	28.5148	1.27650	0.638248	+	0.769831i	$0.279659\pi$
$500$	−6.76953	−0.302743
$501$	8.83943	0.394917
$502$	−20.9806	−0.936408
$503$	25.0045	1.11490	0.557448	−	0.830212i	$-0.311781\pi$
$503$	25.0045	1.11490	0.557448	+	0.830212i	$0.311781\pi$
$504$	−10.4455	−0.465279
$505$	27.2367	1.21202
$506$	35.4266	1.57490
$507$	9.42733	0.418682
$508$	−0.861746	−0.0382338
$509$	1.78975	0.0793291	0.0396646	−	0.999213i	$-0.487371\pi$
$509$	1.78975	0.0793291	0.0396646	+	0.999213i	$0.487371\pi$
$510$	−15.2164	−0.673794
$511$	−14.0738	−0.622588
$512$	1.83080	0.0809108
$513$	−27.6995	−1.22296
$514$	−29.1687	−1.28658
$515$	49.7391	2.19176
$516$	4.16078	0.183168
$517$	−36.1991	−1.59203
$518$	−11.3782	−0.499930
$519$	−2.74542	−0.120511
$520$	5.93628	0.260323
$521$	23.7365	1.03991	0.519957	−	0.854193i	$-0.325948\pi$
$521$	23.7365	1.03991	0.519957	+	0.854193i	$0.325948\pi$
$522$	1.38594	0.0606609
$523$	−15.2695	−0.667689	−0.333845	−	0.942628i	$-0.608346\pi$
$523$	−15.2695	−0.667689	−0.333845	+	0.942628i	$0.608346\pi$
$524$	16.0128	0.699520
$525$	−2.00029	−0.0872997
$526$	−42.2224	−1.84099
$527$	6.70761	0.292188
$528$	−15.1250	−0.658231
$529$	8.57560	0.372852
$530$	38.7042	1.68121
$531$	−9.54433	−0.414189
$532$	−9.62580	−0.417331
$533$	−9.11901	−0.394988
$534$	0.801411	0.0346805
$535$	−4.23403	−0.183053
$536$	16.6036	0.717167
$537$	−15.7955	−0.681626
$538$	27.3078	1.17732
$539$	10.0044	0.430919
$540$	7.64201	0.328860
$541$	16.2069	0.696791	0.348395	−	0.937348i	$-0.386727\pi$
$541$	16.2069	0.696791	0.348395	+	0.937348i	$0.386727\pi$
$542$	−5.81013	−0.249567
$543$	5.61882	0.241127
$544$	−17.8577	−0.765644
$545$	−33.8617	−1.45048
$546$	3.12269	0.133639
$547$	21.6434	0.925404	0.462702	−	0.886514i	$-0.346880\pi$
$547$	21.6434	0.925404	0.462702	+	0.886514i	$0.346880\pi$
$548$	13.6391	0.582635
$549$	4.36388	0.186246
$550$	7.49346	0.319522
$551$	−2.30054	−0.0980061
$552$	−9.56687	−0.407193
$553$	−22.1539	−0.942082
$554$	−22.3088	−0.947810
$555$	−6.59299	−0.279857
$556$	−8.24286	−0.349575
$557$	8.57423	0.363302	0.181651	−	0.983363i	$-0.441856\pi$
$557$	8.57423	0.363302	0.181651	+	0.983363i	$0.441856\pi$
$558$	−5.63045	−0.238356
$559$	−8.16815	−0.345476
$560$	−25.6227	−1.08276
$561$	−14.2091	−0.599909
$562$	−15.9292	−0.671934
$563$	−2.70217	−0.113883	−0.0569415	−	0.998378i	$-0.518135\pi$
$563$	−2.70217	−0.113883	−0.0569415	+	0.998378i	$0.518135\pi$
$564$	−5.42701	−0.228519
$565$	−28.0108	−1.17842
$566$	−43.0669	−1.81024
$567$	7.54989	0.317065
$568$	−15.6883	−0.658265
$569$	−5.31348	−0.222753	−0.111376	−	0.993778i	$-0.535526\pi$
$569$	−5.31348	−0.222753	−0.111376	+	0.993778i	$0.535526\pi$
$570$	−21.2018	−0.888046
$571$	−16.3022	−0.682226	−0.341113	−	0.940022i	$-0.610804\pi$
$571$	−16.3022	−0.682226	−0.341113	+	0.940022i	$0.610804\pi$
$572$	−3.07745	−0.128675
$573$	7.69889	0.321626
$574$	27.9326	1.16588
$575$	6.67890	0.278529
$576$	−8.16708	−0.340295
$577$	12.6109	0.524999	0.262499	−	0.964932i	$-0.415453\pi$
$577$	12.6109	0.524999	0.262499	+	0.964932i	$0.415453\pi$
$578$	−7.16250	−0.297921
$579$	17.0415	0.708220
$580$	0.634694	0.0263542
$581$	−30.7531	−1.27585
$582$	−25.1181	−1.04118
$583$	36.1420	1.49685
$584$	−14.2378	−0.589163
$585$	−6.59642	−0.272728
$586$	−20.3549	−0.840853
$587$	17.1964	0.709770	0.354885	−	0.934910i	$-0.384520\pi$
$587$	17.1964	0.709770	0.354885	+	0.934910i	$0.384520\pi$
$588$	1.49987	0.0618536
$589$	9.34605	0.385097
$590$	−16.6148	−0.684019
$591$	−9.04134	−0.371911
$592$	−16.2201	−0.666641
$593$	−23.3684	−0.959625	−0.479812	−	0.877371i	$-0.659295\pi$
$593$	−23.3684	−0.959625	−0.479812	+	0.877371i	$0.659295\pi$
$594$	27.1262	1.11300
$595$	−24.0711	−0.986819
$596$	6.61051	0.270777
$597$	16.5023	0.675395
$598$	−10.4266	−0.426374
$599$	11.3508	0.463782	0.231891	−	0.972742i	$-0.425509\pi$
$599$	11.3508	0.463782	0.231891	+	0.972742i	$0.425509\pi$
$600$	−2.02359	−0.0826128
$601$	37.1783	1.51653	0.758267	−	0.651944i	$-0.226046\pi$
$601$	37.1783	1.51653	0.758267	+	0.651944i	$0.226046\pi$
$602$	25.0200	1.01974
$603$	−18.4500	−0.751342
$604$	−2.44846	−0.0996266
$605$	9.06879	0.368699
$606$	14.4944	0.588794
$607$	−1.75515	−0.0712394	−0.0356197	−	0.999365i	$-0.511340\pi$
$607$	−1.75515	−0.0712394	−0.0356197	+	0.999365i	$0.511340\pi$
$608$	−24.8821	−1.00910
$609$	−0.601390	−0.0243696
$610$	7.59664	0.307579
$611$	10.6539	0.431012
$612$	7.76606	0.313925
$613$	36.2285	1.46326	0.731628	−	0.681704i	$-0.238761\pi$
$613$	36.2285	1.46326	0.731628	+	0.681704i	$0.238761\pi$
$614$	−46.2966	−1.86838
$615$	16.1852	0.652651
$616$	−16.9798	−0.684134
$617$	−0.638819	−0.0257179	−0.0128589	−	0.999917i	$-0.504093\pi$
$617$	−0.638819	−0.0257179	−0.0128589	+	0.999917i	$0.504093\pi$
$618$	26.4693	1.06475
$619$	−7.20840	−0.289730	−0.144865	−	0.989451i	$-0.546275\pi$
$619$	−7.20840	−0.289730	−0.144865	+	0.989451i	$0.546275\pi$
$620$	−2.57848	−0.103554
$621$	24.1775	0.970211
$622$	34.4573	1.38161
$623$	1.26777	0.0507920
$624$	4.45151	0.178203
$625$	−29.5302	−1.18121
$626$	−19.3627	−0.773888
$627$	−19.7983	−0.790666
$628$	−5.28985	−0.211088
$629$	−15.2379	−0.607573
$630$	20.2056	0.805009
$631$	39.3649	1.56709	0.783547	−	0.621333i	$-0.213408\pi$
$631$	39.3649	1.56709	0.783547	+	0.621333i	$0.213408\pi$
$632$	−22.4121	−0.891504
$633$	12.6313	0.502049
$634$	−12.7023	−0.504473
$635$	−3.00261	−0.119155
$636$	5.41846	0.214856
$637$	−2.94444	−0.116663
$638$	2.25292	0.0891941
$639$	17.4329	0.689633
$640$	−33.4471	−1.32211
$641$	−6.38766	−0.252297	−0.126149	−	0.992011i	$-0.540262\pi$
$641$	−6.38766	−0.252297	−0.126149	+	0.992011i	$0.540262\pi$
$642$	−2.25320	−0.0889265
$643$	−24.7774	−0.977126	−0.488563	−	0.872529i	$-0.662479\pi$
$643$	−24.7774	−0.977126	−0.488563	+	0.872529i	$0.662479\pi$
$644$	8.40188	0.331080
$645$	14.4975	0.570840
$646$	−49.0020	−1.92796
$647$	−37.2673	−1.46513	−0.732565	−	0.680697i	$-0.761677\pi$
$647$	−37.2673	−1.46513	−0.732565	+	0.680697i	$0.761677\pi$
$648$	7.63785	0.300043
$649$	−15.5149	−0.609012
$650$	−2.20544	−0.0865043
$651$	2.44318	0.0957557
$652$	−5.66511	−0.221863
$653$	0.174941	0.00684599	0.00342299	−	0.999994i	$-0.498910\pi$
$653$	0.174941	0.00684599	0.00342299	+	0.999994i	$0.498910\pi$
$654$	−18.0200	−0.704637
$655$	55.7937	2.18004
$656$	39.8189	1.55467
$657$	15.8211	0.617238
$658$	−32.6342	−1.27221
$659$	16.8015	0.654494	0.327247	−	0.944939i	$-0.393879\pi$
$659$	16.8015	0.654494	0.327247	+	0.944939i	$0.393879\pi$
$660$	5.46213	0.212613
$661$	31.4781	1.22436	0.612178	−	0.790720i	$-0.290294\pi$
$661$	31.4781	1.22436	0.612178	+	0.790720i	$0.290294\pi$
$662$	−28.1249	−1.09311
$663$	4.18195	0.162413
$664$	−31.1114	−1.20736
$665$	−33.5395	−1.30060
$666$	12.7908	0.495635
$667$	2.00802	0.0777510
$668$	−7.85347	−0.303860
$669$	−7.14496	−0.276240
$670$	−32.1177	−1.24082
$671$	7.09375	0.273851
$672$	−6.50450	−0.250917
$673$	15.9762	0.615837	0.307919	−	0.951413i	$-0.400368\pi$
$673$	15.9762	0.615837	0.307919	+	0.951413i	$0.400368\pi$
$674$	24.9929	0.962691
$675$	5.11405	0.196840
$676$	−8.37579	−0.322146
$677$	18.4699	0.709856	0.354928	−	0.934894i	$-0.384505\pi$
$677$	18.4699	0.709856	0.354928	+	0.934894i	$0.384505\pi$
$678$	−14.9064	−0.572475
$679$	−39.7347	−1.52488
$680$	−24.3516	−0.933839
$681$	13.4859	0.516781
$682$	−9.15262	−0.350472
$683$	34.6722	1.32670	0.663348	−	0.748311i	$-0.269135\pi$
$683$	34.6722	1.32670	0.663348	+	0.748311i	$0.269135\pi$
$684$	10.8208	0.413745
$685$	47.5232	1.81577
$686$	33.1696	1.26642
$687$	10.0497	0.383418
$688$	35.6668	1.35979
$689$	−10.6371	−0.405243
$690$	18.5060	0.704511
$691$	48.9944	1.86383	0.931917	−	0.362672i	$-0.118136\pi$
$691$	48.9944	1.86383	0.931917	+	0.362672i	$0.118136\pi$
$692$	2.43919	0.0927241
$693$	18.8680	0.716735
$694$	22.6079	0.858183
$695$	−28.7208	−1.08944
$696$	−0.608397	−0.0230612
$697$	37.4076	1.41691
$698$	16.6005	0.628339
$699$	3.78366	0.143111
$700$	1.77717	0.0671708
$701$	−28.5131	−1.07692	−0.538462	−	0.842650i	$-0.680994\pi$
$701$	−28.5131	−1.07692	−0.538462	+	0.842650i	$0.680994\pi$
$702$	−7.98365	−0.301324
$703$	−21.2317	−0.800767
$704$	−13.2761	−0.500361
$705$	−18.9095	−0.712174
$706$	57.0977	2.14890
$707$	22.9289	0.862330
$708$	−2.32601	−0.0874168
$709$	22.2537	0.835754	0.417877	−	0.908504i	$-0.362774\pi$
$709$	22.2537	0.835754	0.417877	+	0.908504i	$0.362774\pi$
$710$	30.3471	1.13891
$711$	24.9044	0.933987
$712$	1.28254	0.0480651
$713$	−8.15770	−0.305508
$714$	−12.8098	−0.479394
$715$	−10.7229	−0.401013
$716$	14.0336	0.524462
$717$	−14.7683	−0.551531
$718$	−22.1793	−0.827723
$719$	−24.7281	−0.922202	−0.461101	−	0.887348i	$-0.652545\pi$
$719$	−24.7281	−0.922202	−0.461101	+	0.887348i	$0.652545\pi$
$720$	28.8038	1.07345
$721$	41.8723	1.55940
$722$	−36.9762	−1.37611
$723$	−20.3313	−0.756128
$724$	−4.99209	−0.185530
$725$	0.424739	0.0157744
$726$	4.82608	0.179113
$727$	19.3636	0.718157	0.359079	−	0.933307i	$-0.383091\pi$
$727$	19.3636	0.718157	0.359079	+	0.933307i	$0.383091\pi$
$728$	4.99739	0.185216
$729$	1.88560	0.0698369
$730$	27.5413	1.01935
$731$	33.5070	1.23930
$732$	1.06350	0.0393082
$733$	−45.2847	−1.67263	−0.836315	−	0.548250i	$-0.815294\pi$
$733$	−45.2847	−1.67263	−0.836315	+	0.548250i	$0.815294\pi$
$734$	21.3942	0.789674
$735$	5.22605	0.192766
$736$	21.7183	0.800548
$737$	−29.9916	−1.10475
$738$	−31.4004	−1.15586
$739$	7.91117	0.291017	0.145509	−	0.989357i	$-0.453518\pi$
$739$	7.91117	0.291017	0.145509	+	0.989357i	$0.453518\pi$
$740$	5.85760	0.215330
$741$	5.82692	0.214057
$742$	32.5827	1.19615
$743$	−26.5830	−0.975234	−0.487617	−	0.873058i	$-0.662134\pi$
$743$	−26.5830	−0.975234	−0.487617	+	0.873058i	$0.662134\pi$
$744$	2.47164	0.0906149
$745$	23.0332	0.843872
$746$	58.9099	2.15685
$747$	34.5711	1.26489
$748$	12.6242	0.461586
$749$	−3.56437	−0.130239
$750$	−12.5523	−0.458345
$751$	47.1479	1.72045	0.860225	−	0.509915i	$-0.170323\pi$
$751$	47.1479	1.72045	0.860225	+	0.509915i	$0.170323\pi$
$752$	−46.5212	−1.69645
$753$	−10.2342	−0.372955
$754$	−0.663069	−0.0241475
$755$	−8.53126	−0.310484
$756$	6.43334	0.233978
$757$	20.1188	0.731232	0.365616	−	0.930766i	$-0.380858\pi$
$757$	20.1188	0.731232	0.365616	+	0.930766i	$0.380858\pi$
$758$	4.22847	0.153585
$759$	17.2809	0.627257
$760$	−33.9302	−1.23078
$761$	−13.3028	−0.482227	−0.241114	−	0.970497i	$-0.577513\pi$
$761$	−13.3028	−0.482227	−0.241114	+	0.970497i	$0.577513\pi$
$762$	−1.59788	−0.0578851
$763$	−28.5061	−1.03199
$764$	−6.84015	−0.247468
$765$	27.0595	0.978339
$766$	−62.4396	−2.25603
$767$	4.56626	0.164878
$768$	−12.2238	−0.441088
$769$	−25.4017	−0.916009	−0.458005	−	0.888950i	$-0.651436\pi$
$769$	−25.4017	−0.916009	−0.458005	+	0.888950i	$0.651436\pi$
$770$	32.8453	1.18366
$771$	−14.2283	−0.512421
$772$	−15.1407	−0.544924
$773$	−38.5881	−1.38792	−0.693959	−	0.720015i	$-0.744135\pi$
$773$	−38.5881	−1.38792	−0.693959	+	0.720015i	$0.744135\pi$
$774$	−28.1262	−1.01098
$775$	−1.72552	−0.0619826
$776$	−40.1977	−1.44301
$777$	−5.55023	−0.199114
$778$	10.4318	0.373997
$779$	52.1219	1.86746
$780$	−1.60759	−0.0575608
$781$	28.3382	1.01402
$782$	42.7714	1.52950
$783$	1.53755	0.0549475
$784$	12.8571	0.459183
$785$	−18.4316	−0.657852
$786$	29.6914	1.05906
$787$	−5.58006	−0.198908	−0.0994538	−	0.995042i	$-0.531710\pi$
$787$	−5.58006	−0.198908	−0.0994538	+	0.995042i	$0.531710\pi$
$788$	8.03286	0.286159
$789$	−20.5959	−0.733233
$790$	43.3535	1.54245
$791$	−23.5806	−0.838430
$792$	19.0878	0.678255
$793$	−2.08779	−0.0741398
$794$	−3.37988	−0.119947
$795$	18.8797	0.669595
$796$	−14.6616	−0.519668
$797$	−18.9854	−0.672499	−0.336249	−	0.941773i	$-0.609159\pi$
$797$	−18.9854	−0.672499	−0.336249	+	0.941773i	$0.609159\pi$
$798$	−17.8485	−0.631830
$799$	−43.7041	−1.54614
$800$	4.59388	0.162418
$801$	−1.42516	−0.0503555
$802$	−13.4658	−0.475495
$803$	25.7181	0.907571
$804$	−4.49637	−0.158575
$805$	29.2749	1.03181
$806$	2.69375	0.0948834
$807$	13.3206	0.468908
$808$	23.1960	0.816034
$809$	−46.5379	−1.63618	−0.818092	−	0.575087i	$-0.804968\pi$
$809$	−46.5379	−1.63618	−0.818092	+	0.575087i	$0.804968\pi$
$810$	−14.7745	−0.519124
$811$	−28.8818	−1.01418	−0.507089	−	0.861894i	$-0.669278\pi$
$811$	−28.8818	−1.01418	−0.507089	+	0.861894i	$0.669278\pi$
$812$	0.534310	0.0187506
$813$	−2.83415	−0.0993980
$814$	20.7923	0.728768
$815$	−19.7391	−0.691431
$816$	−18.2608	−0.639255
$817$	46.6870	1.63337
$818$	36.2544	1.26761
$819$	−5.55312	−0.194042
$820$	−14.3799	−0.502168
$821$	−1.48857	−0.0519514	−0.0259757	−	0.999663i	$-0.508269\pi$
$821$	−1.48857	−0.0519514	−0.0259757	+	0.999663i	$0.508269\pi$
$822$	25.2901	0.882095
$823$	−14.5821	−0.508299	−0.254149	−	0.967165i	$-0.581796\pi$
$823$	−14.5821	−0.508299	−0.254149	+	0.967165i	$0.581796\pi$
$824$	42.3601	1.47568
$825$	3.65527	0.127260
$826$	−13.9869	−0.486668
$827$	27.6321	0.960863	0.480431	−	0.877032i	$-0.340480\pi$
$827$	27.6321	0.960863	0.480431	+	0.877032i	$0.340480\pi$
$828$	−9.44498	−0.328236
$829$	18.9100	0.656770	0.328385	−	0.944544i	$-0.393496\pi$
$829$	18.9100	0.656770	0.328385	+	0.944544i	$0.393496\pi$
$830$	60.1814	2.08893
$831$	−10.8821	−0.377496
$832$	3.90734	0.135463
$833$	12.0785	0.418497
$834$	−15.2842	−0.529248
$835$	−27.3641	−0.946973
$836$	17.5899	0.608360
$837$	−6.24637	−0.215906
$838$	−5.19075	−0.179311
$839$	−1.33745	−0.0461741	−0.0230870	−	0.999733i	$-0.507349\pi$
$839$	−1.33745	−0.0461741	−0.0230870	+	0.999733i	$0.507349\pi$
$840$	−8.86981	−0.306037
$841$	−28.8723	−0.995597
$842$	−21.5953	−0.744223
$843$	−7.77019	−0.267620
$844$	−11.2224	−0.386290
$845$	−29.1840	−1.00396
$846$	36.6857	1.26128
$847$	7.63446	0.262323
$848$	46.4479	1.59503
$849$	−21.0078	−0.720986
$850$	9.04704	0.310311
$851$	18.5321	0.635271
$852$	4.24849	0.145551
$853$	−30.4764	−1.04349	−0.521746	−	0.853101i	$-0.674719\pi$
$853$	−30.4764	−1.04349	−0.521746	+	0.853101i	$0.674719\pi$
$854$	6.39515	0.218837
$855$	37.7034	1.28943
$856$	−3.60590	−0.123247
$857$	49.1448	1.67876	0.839378	−	0.543549i	$-0.182920\pi$
$857$	49.1448	1.67876	0.839378	+	0.543549i	$0.182920\pi$
$858$	−5.70632	−0.194811
$859$	−17.5805	−0.599839	−0.299919	−	0.953965i	$-0.596960\pi$
$859$	−17.5805	−0.599839	−0.299919	+	0.953965i	$0.596960\pi$
$860$	−12.8805	−0.439220
$861$	13.6253	0.464351
$862$	19.1161	0.651097
$863$	−11.8568	−0.403611	−0.201805	−	0.979426i	$-0.564681\pi$
$863$	−11.8568	−0.403611	−0.201805	+	0.979426i	$0.564681\pi$
$864$	16.6298	0.565757
$865$	8.49895	0.288973
$866$	3.31504	0.112650
$867$	−3.49383	−0.118657
$868$	−2.17066	−0.0736771
$869$	40.4835	1.37331
$870$	1.17687	0.0398997
$871$	8.82696	0.299090
$872$	−28.8382	−0.976586
$873$	44.6678	1.51178
$874$	59.5956	2.01585
$875$	−19.8567	−0.671278
$876$	3.85569	0.130272
$877$	21.1843	0.715342	0.357671	−	0.933848i	$-0.383571\pi$
$877$	21.1843	0.715342	0.357671	+	0.933848i	$0.383571\pi$
$878$	37.2201	1.25612
$879$	−9.92900	−0.334897
$880$	46.8222	1.57838
$881$	−39.7746	−1.34004	−0.670020	−	0.742343i	$-0.733714\pi$
$881$	−39.7746	−1.34004	−0.670020	+	0.742343i	$0.733714\pi$
$882$	−10.1389	−0.341394
$883$	4.41111	0.148446	0.0742228	−	0.997242i	$-0.476352\pi$
$883$	4.41111	0.148446	0.0742228	+	0.997242i	$0.476352\pi$
$884$	−3.71549	−0.124965
$885$	−8.10459	−0.272433
$886$	4.54166	0.152580
$887$	19.9120	0.668578	0.334289	−	0.942471i	$-0.391504\pi$
$887$	19.9120	0.668578	0.334289	+	0.942471i	$0.391504\pi$
$888$	−5.61490	−0.188424
$889$	−2.52771	−0.0847768
$890$	−2.48092	−0.0831605
$891$	−13.7965	−0.462199
$892$	6.34801	0.212547
$893$	−60.8951	−2.03778
$894$	12.2574	0.409950
$895$	48.8979	1.63448
$896$	−28.1571	−0.940661
$897$	−5.08603	−0.169817
$898$	3.13231	0.104527
$899$	−0.518782	−0.0173023
$900$	−1.99781	−0.0665936
$901$	43.6352	1.45370
$902$	−51.0432	−1.69955
$903$	12.2046	0.406144
$904$	−23.8553	−0.793417
$905$	−17.3941	−0.578199
$906$	−4.54003	−0.150832
$907$	3.05945	0.101587	0.0507936	−	0.998709i	$-0.483825\pi$
$907$	3.05945	0.101587	0.0507936	+	0.998709i	$0.483825\pi$
$908$	−11.9817	−0.397626
$909$	−25.7755	−0.854920
$910$	−9.66687	−0.320454
$911$	−34.7765	−1.15220	−0.576099	−	0.817380i	$-0.695426\pi$
$911$	−34.7765	−1.15220	−0.576099	+	0.817380i	$0.695426\pi$
$912$	−25.4437	−0.842524
$913$	56.1974	1.85986
$914$	23.1447	0.765560
$915$	3.70560	0.122503
$916$	−8.92870	−0.295013
$917$	46.9693	1.55106
$918$	32.7502	1.08092
$919$	−56.2686	−1.85613	−0.928065	−	0.372419i	$-0.878528\pi$
$919$	−56.2686	−1.85613	−0.928065	+	0.372419i	$0.878528\pi$
$920$	29.6160	0.976411
$921$	−22.5832	−0.744143
$922$	−0.167634	−0.00552072
$923$	−8.34034	−0.274526
$924$	4.59824	0.151271
$925$	3.91992	0.128886
$926$	−60.5692	−1.99043
$927$	−47.0707	−1.54601
$928$	1.38116	0.0453387
$929$	57.0122	1.87051	0.935255	−	0.353974i	$-0.115170\pi$
$929$	57.0122	1.87051	0.935255	+	0.353974i	$0.115170\pi$
$930$	−4.78111	−0.156779
$931$	16.8296	0.551569
$932$	−3.36163	−0.110114
$933$	16.8081	0.550273
$934$	42.7887	1.40009
$935$	43.9869	1.43852
$936$	−5.61782	−0.183624
$937$	2.07924	0.0679257	0.0339629	−	0.999423i	$-0.489187\pi$
$937$	2.07924	0.0679257	0.0339629	+	0.999423i	$0.489187\pi$
$938$	−27.0380	−0.882820
$939$	−9.44501	−0.308226
$940$	16.8003	0.547966
$941$	51.0676	1.66476	0.832379	−	0.554207i	$-0.186978\pi$
$941$	51.0676	1.66476	0.832379	+	0.554207i	$0.186978\pi$
$942$	−9.80863	−0.319583
$943$	−45.4946	−1.48151
$944$	−19.9389	−0.648956
$945$	22.4159	0.729189
$946$	−45.7208	−1.48651
$947$	−40.2743	−1.30874	−0.654370	−	0.756175i	$-0.727066\pi$
$947$	−40.2743	−1.30874	−0.654370	+	0.756175i	$0.727066\pi$
$948$	6.06935	0.197123
$949$	−7.56921	−0.245707
$950$	12.6057	0.408983
$951$	−6.19611	−0.200923
$952$	−20.5001	−0.664411
$953$	54.4421	1.76355	0.881777	−	0.471667i	$-0.156348\pi$
$953$	54.4421	1.76355	0.881777	+	0.471667i	$0.156348\pi$
$954$	−36.6279	−1.18587
$955$	−23.8333	−0.771229
$956$	13.1210	0.424363
$957$	1.09896	0.0355245
$958$	15.9154	0.514203
$959$	40.0069	1.29189
$960$	−6.93509	−0.223829
$961$	−28.8924	−0.932014
$962$	−6.11947	−0.197300
$963$	4.00688	0.129120
$964$	18.0635	0.581786
$965$	−52.7551	−1.69825
$966$	15.5791	0.501248
$967$	27.2309	0.875686	0.437843	−	0.899051i	$-0.355743\pi$
$967$	27.2309	0.875686	0.437843	+	0.899051i	$0.355743\pi$
$968$	7.72341	0.248240
$969$	−23.9029	−0.767873
$970$	77.7577	2.49665
$971$	36.4762	1.17058	0.585288	−	0.810825i	$-0.300981\pi$
$971$	36.4762	1.17058	0.585288	+	0.810825i	$0.300981\pi$
$972$	−11.2842	−0.361941
$973$	−24.1783	−0.775121
$974$	−27.3524	−0.876428
$975$	−1.07580	−0.0344532
$976$	9.11651	0.291812
$977$	5.47206	0.175067	0.0875333	−	0.996162i	$-0.472102\pi$
$977$	5.47206	0.175067	0.0875333	+	0.996162i	$0.472102\pi$
$978$	−10.5044	−0.335895
$979$	−2.31668	−0.0740414
$980$	−4.64313	−0.148319
$981$	32.0451	1.02312
$982$	−30.5469	−0.974791
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	13.7841	0.439421
$985$	27.9891	0.891808
$986$	2.72001	0.0866228
$987$	−15.9188	−0.506700
$988$	−5.17698	−0.164702
$989$	−40.7508	−1.29580
$990$	−36.9231	−1.17349
$991$	13.3629	0.424488	0.212244	−	0.977217i	$-0.431923\pi$
$991$	13.3629	0.424488	0.212244	+	0.977217i	$0.431923\pi$
$992$	−5.61103	−0.178150
$993$	−13.7192	−0.435365
$994$	25.5474	0.810314
$995$	−51.0860	−1.61953
$996$	8.42519	0.266962
$997$	32.2796	1.02231	0.511153	−	0.859490i	$-0.329218\pi$
$997$	32.2796	1.02231	0.511153	+	0.859490i	$0.329218\pi$
$998$	−46.9755	−1.48698
$999$	14.1900	0.448953

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.9	✓	28
3.2	odd	2		8847.2.a.b.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.9	✓	28	1.1	even	1	trivial
8847.2.a.b.1.20		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)

\(f(q)\)	\(=\)	\(q-1.64741 q^{2} -0.803598 q^{3} +0.713964 q^{4} +2.48769 q^{5} +1.32386 q^{6} +2.09423 q^{7} +2.11863 q^{8} -2.35423 q^{9} +O(q^{10})\)	\(q-1.64741 q^{2} -0.803598 q^{3} +0.713964 q^{4} +2.48769 q^{5} +1.32386 q^{6} +2.09423 q^{7} +2.11863 q^{8} -2.35423 q^{9} -4.09824 q^{10} -3.82694 q^{11} -0.573740 q^{12} +1.12633 q^{13} -3.45006 q^{14} -1.99910 q^{15} -4.91818 q^{16} -4.62036 q^{17} +3.87838 q^{18} -6.43778 q^{19} +1.77612 q^{20} -1.68292 q^{21} +6.30454 q^{22} +5.61922 q^{23} -1.70253 q^{24} +1.18858 q^{25} -1.85552 q^{26} +4.30265 q^{27} +1.49520 q^{28} +0.357349 q^{29} +3.29334 q^{30} -1.45175 q^{31} +3.86501 q^{32} +3.07532 q^{33} +7.61163 q^{34} +5.20979 q^{35} -1.68083 q^{36} +3.29798 q^{37} +10.6057 q^{38} -0.905113 q^{39} +5.27049 q^{40} -8.09625 q^{41} +2.77246 q^{42} -7.25204 q^{43} -2.73230 q^{44} -5.85658 q^{45} -9.25716 q^{46} +9.45901 q^{47} +3.95224 q^{48} -2.61420 q^{49} -1.95808 q^{50} +3.71291 q^{51} +0.804155 q^{52} -9.44411 q^{53} -7.08823 q^{54} -9.52023 q^{55} +4.43690 q^{56} +5.17339 q^{57} -0.588701 q^{58} +4.05412 q^{59} -1.42728 q^{60} -1.85363 q^{61} +2.39163 q^{62} -4.93030 q^{63} +3.46911 q^{64} +2.80194 q^{65} -5.06632 q^{66} +7.83695 q^{67} -3.29877 q^{68} -4.51559 q^{69} -8.58266 q^{70} -7.40491 q^{71} -4.98774 q^{72} -6.72027 q^{73} -5.43313 q^{74} -0.955142 q^{75} -4.59634 q^{76} -8.01449 q^{77} +1.49109 q^{78} -10.5786 q^{79} -12.2349 q^{80} +3.60509 q^{81} +13.3379 q^{82} -14.6847 q^{83} -1.20154 q^{84} -11.4940 q^{85} +11.9471 q^{86} -0.287165 q^{87} -8.10787 q^{88} +0.605361 q^{89} +9.64820 q^{90} +2.35878 q^{91} +4.01192 q^{92} +1.16662 q^{93} -15.5829 q^{94} -16.0152 q^{95} -3.10591 q^{96} -18.9734 q^{97} +4.30666 q^{98} +9.00950 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 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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