LMFDB - Embedded newform 983.2.a.a.1.20

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			1.20
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.912923 q^{2} -2.89686 q^{3} -1.16657 q^{4} -1.17872 q^{5} -2.64461 q^{6} +3.45815 q^{7} -2.89084 q^{8} +5.39181 q^{9} +O(q^{10})$	\(q+0.912923 q^{2} -2.89686 q^{3} -1.16657 q^{4} -1.17872 q^{5} -2.64461 q^{6} +3.45815 q^{7} -2.89084 q^{8} +5.39181 q^{9} -1.07608 q^{10} +1.56665 q^{11} +3.37940 q^{12} +1.13134 q^{13} +3.15703 q^{14} +3.41459 q^{15} -0.305970 q^{16} -0.0116973 q^{17} +4.92231 q^{18} +2.31580 q^{19} +1.37506 q^{20} -10.0178 q^{21} +1.43024 q^{22} -7.71643 q^{23} +8.37436 q^{24} -3.61062 q^{25} +1.03283 q^{26} -6.92875 q^{27} -4.03418 q^{28} +2.15267 q^{29} +3.11726 q^{30} -8.15054 q^{31} +5.50235 q^{32} -4.53838 q^{33} -0.0106787 q^{34} -4.07619 q^{35} -6.28993 q^{36} -8.91976 q^{37} +2.11414 q^{38} -3.27734 q^{39} +3.40748 q^{40} -1.72063 q^{41} -9.14547 q^{42} -4.59687 q^{43} -1.82761 q^{44} -6.35543 q^{45} -7.04451 q^{46} +3.42907 q^{47} +0.886354 q^{48} +4.95880 q^{49} -3.29622 q^{50} +0.0338854 q^{51} -1.31979 q^{52} +2.09122 q^{53} -6.32542 q^{54} -1.84665 q^{55} -9.99695 q^{56} -6.70854 q^{57} +1.96523 q^{58} +4.77995 q^{59} -3.98336 q^{60} -5.07785 q^{61} -7.44082 q^{62} +18.6457 q^{63} +5.63516 q^{64} -1.33353 q^{65} -4.14320 q^{66} +3.58751 q^{67} +0.0136457 q^{68} +22.3534 q^{69} -3.72125 q^{70} +4.24949 q^{71} -15.5868 q^{72} -14.4027 q^{73} -8.14306 q^{74} +10.4595 q^{75} -2.70154 q^{76} +5.41773 q^{77} -2.99196 q^{78} -11.5440 q^{79} +0.360653 q^{80} +3.89620 q^{81} -1.57080 q^{82} +12.0979 q^{83} +11.6865 q^{84} +0.0137878 q^{85} -4.19659 q^{86} -6.23600 q^{87} -4.52894 q^{88} -3.42826 q^{89} -5.80202 q^{90} +3.91234 q^{91} +9.00176 q^{92} +23.6110 q^{93} +3.13048 q^{94} -2.72967 q^{95} -15.9395 q^{96} -14.6754 q^{97} +4.52701 q^{98} +8.44711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	0.912923	0.645534	0.322767	−	0.946478i	$-0.395387\pi$
$2$	0.912923	0.645534	0.322767	+	0.946478i	$0.395387\pi$
$3$	−2.89686	−1.67250	−0.836252	−	0.548345i	$-0.815258\pi$
$3$	−2.89686	−1.67250	−0.836252	+	0.548345i	$0.815258\pi$
$4$	−1.16657	−0.583285
$5$	−1.17872	−0.527139	−0.263570	−	0.964640i	$-0.584900\pi$
$5$	−1.17872	−0.527139	−0.263570	+	0.964640i	$0.584900\pi$
$6$	−2.64461	−1.07966
$7$	3.45815	1.30706	0.653529	−	0.756902i	$-0.273288\pi$
$7$	3.45815	1.30706	0.653529	+	0.756902i	$0.273288\pi$
$8$	−2.89084	−1.02207
$9$	5.39181	1.79727
$10$	−1.07608	−0.340286
$11$	1.56665	0.472364	0.236182	−	0.971709i	$-0.424104\pi$
$11$	1.56665	0.472364	0.236182	+	0.971709i	$0.424104\pi$
$12$	3.37940	0.975547
$13$	1.13134	0.313777	0.156889	−	0.987616i	$-0.449854\pi$
$13$	1.13134	0.313777	0.156889	+	0.987616i	$0.449854\pi$
$14$	3.15703	0.843751
$15$	3.41459	0.881642
$16$	−0.305970	−0.0764926
$17$	−0.0116973	−0.00283701	−0.00141850	−	0.999999i	$-0.500452\pi$
$17$	−0.0116973	−0.00283701	−0.00141850	+	0.999999i	$0.500452\pi$
$18$	4.92231	1.16020
$19$	2.31580	0.531280	0.265640	−	0.964072i	$-0.414417\pi$
$19$	2.31580	0.531280	0.265640	+	0.964072i	$0.414417\pi$
$20$	1.37506	0.307473
$21$	−10.0178	−2.18606
$22$	1.43024	0.304927
$23$	−7.71643	−1.60899	−0.804494	−	0.593961i	$-0.797563\pi$
$23$	−7.71643	−1.60899	−0.804494	+	0.593961i	$0.797563\pi$
$24$	8.37436	1.70941
$25$	−3.61062	−0.722124
$26$	1.03283	0.202554
$27$	−6.92875	−1.33344
$28$	−4.03418	−0.762388
$29$	2.15267	0.399742	0.199871	−	0.979822i	$-0.435948\pi$
$29$	2.15267	0.399742	0.199871	+	0.979822i	$0.435948\pi$
$30$	3.11726	0.569130
$31$	−8.15054	−1.46388	−0.731941	−	0.681369i	$-0.761385\pi$
$31$	−8.15054	−1.46388	−0.731941	+	0.681369i	$0.761385\pi$
$32$	5.50235	0.972686
$33$	−4.53838	−0.790031
$34$	−0.0106787	−0.00183139
$35$	−4.07619	−0.689001
$36$	−6.28993	−1.04832
$37$	−8.91976	−1.46640	−0.733200	−	0.680013i	$-0.761974\pi$
$37$	−8.91976	−1.46640	−0.733200	+	0.680013i	$0.761974\pi$
$38$	2.11414	0.342959
$39$	−3.27734	−0.524794
$40$	3.40748	0.538770
$41$	−1.72063	−0.268717	−0.134358	−	0.990933i	$-0.542897\pi$
$41$	−1.72063	−0.268717	−0.134358	+	0.990933i	$0.542897\pi$
$42$	−9.14547	−1.41118
$43$	−4.59687	−0.701016	−0.350508	−	0.936560i	$-0.613991\pi$
$43$	−4.59687	−0.701016	−0.350508	+	0.936560i	$0.613991\pi$
$44$	−1.82761	−0.275523
$45$	−6.35543	−0.947412
$46$	−7.04451	−1.03866
$47$	3.42907	0.500181	0.250090	−	0.968222i	$-0.419540\pi$
$47$	3.42907	0.500181	0.250090	+	0.968222i	$0.419540\pi$
$48$	0.886354	0.127934
$49$	4.95880	0.708400
$50$	−3.29622	−0.466156
$51$	0.0338854	0.00474491
$52$	−1.31979	−0.183022
$53$	2.09122	0.287251	0.143626	−	0.989632i	$-0.454124\pi$
$53$	2.09122	0.287251	0.143626	+	0.989632i	$0.454124\pi$
$54$	−6.32542	−0.860780
$55$	−1.84665	−0.249002
$56$	−9.99695	−1.33590
$57$	−6.70854	−0.888568
$58$	1.96523	0.258047
$59$	4.77995	0.622296	0.311148	−	0.950361i	$-0.399287\pi$
$59$	4.77995	0.622296	0.311148	+	0.950361i	$0.399287\pi$
$60$	−3.98336	−0.514249
$61$	−5.07785	−0.650152	−0.325076	−	0.945688i	$-0.605390\pi$
$61$	−5.07785	−0.650152	−0.325076	+	0.945688i	$0.605390\pi$
$62$	−7.44082	−0.944985
$63$	18.6457	2.34914
$64$	5.63516	0.704395
$65$	−1.33353	−0.165404
$66$	−4.14320	−0.509992
$67$	3.58751	0.438284	0.219142	−	0.975693i	$-0.429674\pi$
$67$	3.58751	0.438284	0.219142	+	0.975693i	$0.429674\pi$
$68$	0.0136457	0.00165479
$69$	22.3534	2.69104
$70$	−3.72125	−0.444774
$71$	4.24949	0.504322	0.252161	−	0.967685i	$-0.418859\pi$
$71$	4.24949	0.504322	0.252161	+	0.967685i	$0.418859\pi$
$72$	−15.5868	−1.83693
$73$	−14.4027	−1.68571	−0.842856	−	0.538139i	$-0.819128\pi$
$73$	−14.4027	−1.68571	−0.842856	+	0.538139i	$0.819128\pi$
$74$	−8.14306	−0.946611
$75$	10.4595	1.20776
$76$	−2.70154	−0.309888
$77$	5.41773	0.617407
$78$	−2.99196	−0.338772
$79$	−11.5440	−1.29880	−0.649401	−	0.760446i	$-0.724980\pi$
$79$	−11.5440	−1.29880	−0.649401	+	0.760446i	$0.724980\pi$
$80$	0.360653	0.0403222
$81$	3.89620	0.432911
$82$	−1.57080	−0.173466
$83$	12.0979	1.32792	0.663961	−	0.747767i	$-0.268874\pi$
$83$	12.0979	1.32792	0.663961	+	0.747767i	$0.268874\pi$
$84$	11.6865	1.27510
$85$	0.0137878	0.00149550
$86$	−4.19659	−0.452530
$87$	−6.23600	−0.668570
$88$	−4.52894	−0.482787
$89$	−3.42826	−0.363394	−0.181697	−	0.983355i	$-0.558159\pi$
$89$	−3.42826	−0.363394	−0.181697	+	0.983355i	$0.558159\pi$
$90$	−5.80202	−0.611587
$91$	3.91234	0.410125
$92$	9.00176	0.938499
$93$	23.6110	2.44835
$94$	3.13048	0.322884
$95$	−2.72967	−0.280058
$96$	−15.9395	−1.62682
$97$	−14.6754	−1.49006	−0.745028	−	0.667033i	$-0.767564\pi$
$97$	−14.6754	−1.49006	−0.745028	+	0.667033i	$0.767564\pi$
$98$	4.52701	0.457297
$99$	8.44711	0.848966
$100$	4.21205	0.421205
$101$	−4.63421	−0.461121	−0.230560	−	0.973058i	$-0.574056\pi$
$101$	−4.63421	−0.461121	−0.230560	+	0.973058i	$0.574056\pi$
$102$	0.0309348	0.00306300
$103$	−11.7442	−1.15719	−0.578596	−	0.815614i	$-0.696399\pi$
$103$	−11.7442	−1.15719	−0.578596	+	0.815614i	$0.696399\pi$
$104$	−3.27052	−0.320701
$105$	11.8082	1.15236
$106$	1.90912	0.185431
$107$	−13.9762	−1.35113	−0.675567	−	0.737298i	$-0.736101\pi$
$107$	−13.9762	−1.35113	−0.675567	+	0.737298i	$0.736101\pi$
$108$	8.08288	0.777775
$109$	4.31011	0.412834	0.206417	−	0.978464i	$-0.433820\pi$
$109$	4.31011	0.412834	0.206417	+	0.978464i	$0.433820\pi$
$110$	−1.68585	−0.160739
$111$	25.8393	2.45256
$112$	−1.05809	−0.0999803
$113$	−2.59692	−0.244298	−0.122149	−	0.992512i	$-0.538979\pi$
$113$	−2.59692	−0.244298	−0.122149	+	0.992512i	$0.538979\pi$
$114$	−6.12438	−0.573601
$115$	9.09550	0.848160
$116$	−2.51125	−0.233163
$117$	6.09997	0.563943
$118$	4.36372	0.401713
$119$	−0.0404510	−0.00370813
$120$	−9.87101	−0.901096
$121$	−8.54559	−0.776872
$122$	−4.63569	−0.419695
$123$	4.98442	0.449430
$124$	9.50819	0.853861
$125$	10.1495	0.907799
$126$	17.0221	1.51645
$127$	−3.05689	−0.271255	−0.135628	−	0.990760i	$-0.543305\pi$
$127$	−3.05689	−0.271255	−0.135628	+	0.990760i	$0.543305\pi$
$128$	−5.86022	−0.517975
$129$	13.3165	1.17245
$130$	−1.21741	−0.106774
$131$	9.78119	0.854587	0.427293	−	0.904113i	$-0.359467\pi$
$131$	9.78119	0.854587	0.427293	+	0.904113i	$0.359467\pi$
$132$	5.29434	0.460814
$133$	8.00837	0.694414
$134$	3.27512	0.282927
$135$	8.16705	0.702908
$136$	0.0338149	0.00289961
$137$	−1.69275	−0.144621	−0.0723106	−	0.997382i	$-0.523037\pi$
$137$	−1.69275	−0.144621	−0.0723106	+	0.997382i	$0.523037\pi$
$138$	20.4070	1.73716
$139$	0.210599	0.0178628	0.00893141	−	0.999960i	$-0.497157\pi$
$139$	0.210599	0.0178628	0.00893141	+	0.999960i	$0.497157\pi$
$140$	4.75516	0.401884
$141$	−9.93354	−0.836555
$142$	3.87946	0.325557
$143$	1.77242	0.148217
$144$	−1.64974	−0.137478
$145$	−2.53740	−0.210719
$146$	−13.1486	−1.08819
$147$	−14.3650	−1.18480
$148$	10.4055	0.855330
$149$	−4.64956	−0.380907	−0.190454	−	0.981696i	$-0.560996\pi$
$149$	−4.64956	−0.380907	−0.190454	+	0.981696i	$0.560996\pi$
$150$	9.54870	0.779648
$151$	4.05735	0.330183	0.165091	−	0.986278i	$-0.447208\pi$
$151$	4.05735	0.330183	0.165091	+	0.986278i	$0.447208\pi$
$152$	−6.69459	−0.543003
$153$	−0.0630695	−0.00509887
$154$	4.94597	0.398558
$155$	9.60720	0.771669
$156$	3.82324	0.306105
$157$	13.5504	1.08144	0.540720	−	0.841203i	$-0.318152\pi$
$157$	13.5504	1.08144	0.540720	+	0.841203i	$0.318152\pi$
$158$	−10.5388	−0.838422
$159$	−6.05798	−0.480429
$160$	−6.48572	−0.512741
$161$	−26.6846	−2.10304
$162$	3.55693	0.279459
$163$	−24.4802	−1.91744	−0.958719	−	0.284356i	$-0.908220\pi$
$163$	−24.4802	−1.91744	−0.958719	+	0.284356i	$0.908220\pi$
$164$	2.00723	0.156739
$165$	5.34948	0.416456
$166$	11.0445	0.857219
$167$	14.1666	1.09624	0.548122	−	0.836398i	$-0.315343\pi$
$167$	14.1666	1.09624	0.548122	+	0.836398i	$0.315343\pi$
$168$	28.9598	2.23430
$169$	−11.7201	−0.901544
$170$	0.0125872	0.000965395 0
$171$	12.4863	0.954854
$172$	5.36258	0.408893
$173$	−11.4102	−0.867502	−0.433751	−	0.901033i	$-0.642810\pi$
$173$	−11.4102	−0.867502	−0.433751	+	0.901033i	$0.642810\pi$
$174$	−5.69299	−0.431585
$175$	−12.4861	−0.943858
$176$	−0.479350	−0.0361324
$177$	−13.8468	−1.04079
$178$	−3.12974	−0.234584
$179$	15.3156	1.14474	0.572370	−	0.819996i	$-0.306024\pi$
$179$	15.3156	1.14474	0.572370	+	0.819996i	$0.306024\pi$
$180$	7.41406	0.552611
$181$	15.1319	1.12475	0.562374	−	0.826883i	$-0.309888\pi$
$181$	15.1319	1.12475	0.562374	+	0.826883i	$0.309888\pi$
$182$	3.57167	0.264750
$183$	14.7098	1.08738
$184$	22.3069	1.64449
$185$	10.5139	0.772997
$186$	21.5550	1.58049
$187$	−0.0183256	−0.00134010
$188$	−4.00025	−0.291748
$189$	−23.9607	−1.74288
$190$	−2.49198	−0.180787
$191$	−10.0153	−0.724681	−0.362341	−	0.932046i	$-0.618022\pi$
$191$	−10.0153	−0.724681	−0.362341	+	0.932046i	$0.618022\pi$
$192$	−16.3243	−1.17810
$193$	12.9628	0.933080	0.466540	−	0.884500i	$-0.345500\pi$
$193$	12.9628	0.933080	0.466540	+	0.884500i	$0.345500\pi$
$194$	−13.3975	−0.961883
$195$	3.86306	0.276639
$196$	−5.78479	−0.413200
$197$	8.22992	0.586358	0.293179	−	0.956058i	$-0.405287\pi$
$197$	8.22992	0.586358	0.293179	+	0.956058i	$0.405287\pi$
$198$	7.71156	0.548037
$199$	−6.40798	−0.454250	−0.227125	−	0.973866i	$-0.572933\pi$
$199$	−6.40798	−0.454250	−0.227125	+	0.973866i	$0.572933\pi$
$200$	10.4377	0.738058
$201$	−10.3925	−0.733032
$202$	−4.23068	−0.297669
$203$	7.44427	0.522485
$204$	−0.0395297	−0.00276764
$205$	2.02813	0.141651
$206$	−10.7216	−0.747007
$207$	−41.6055	−2.89179
$208$	−0.346157	−0.0240016
$209$	3.62805	0.250958
$210$	10.7799	0.743886
$211$	−0.523963	−0.0360711	−0.0180355	−	0.999837i	$-0.505741\pi$
$211$	−0.523963	−0.0360711	−0.0180355	+	0.999837i	$0.505741\pi$
$212$	−2.43956	−0.167549
$213$	−12.3102	−0.843480
$214$	−12.7592	−0.872204
$215$	5.41842	0.369533
$216$	20.0299	1.36286
$217$	−28.1858	−1.91338
$218$	3.93480	0.266498
$219$	41.7227	2.81936
$220$	2.15424	0.145239
$221$	−0.0132336	−0.000890188 0
$222$	23.5893	1.58321
$223$	21.4972	1.43956	0.719780	−	0.694202i	$-0.244243\pi$
$223$	21.4972	1.43956	0.719780	+	0.694202i	$0.244243\pi$
$224$	19.0279	1.27136
$225$	−19.4678	−1.29785
$226$	−2.37079	−0.157703
$227$	2.98400	0.198055	0.0990275	−	0.995085i	$-0.468427\pi$
$227$	2.98400	0.198055	0.0990275	+	0.995085i	$0.468427\pi$
$228$	7.82599	0.518289
$229$	−15.1667	−1.00225	−0.501123	−	0.865376i	$-0.667080\pi$
$229$	−15.1667	−1.00225	−0.501123	+	0.865376i	$0.667080\pi$
$230$	8.30350	0.547516
$231$	−15.6944	−1.03262
$232$	−6.22303	−0.408562
$233$	−22.7236	−1.48867	−0.744335	−	0.667807i	$-0.767233\pi$
$233$	−22.7236	−1.48867	−0.744335	+	0.667807i	$0.767233\pi$
$234$	5.56881	0.364044
$235$	−4.04191	−0.263665
$236$	−5.57615	−0.362976
$237$	33.4414	2.17225
$238$	−0.0369286	−0.00239373
$239$	15.7446	1.01844	0.509218	−	0.860638i	$-0.329935\pi$
$239$	15.7446	1.01844	0.509218	+	0.860638i	$0.329935\pi$
$240$	−1.04476	−0.0674391
$241$	2.92341	0.188314	0.0941568	−	0.995557i	$-0.469984\pi$
$241$	2.92341	0.188314	0.0941568	+	0.995557i	$0.469984\pi$
$242$	−7.80147	−0.501498
$243$	9.49949	0.609393
$244$	5.92367	0.379224
$245$	−5.84503	−0.373426
$246$	4.55039	0.290122
$247$	2.61995	0.166704
$248$	23.5619	1.49618
$249$	−35.0461	−2.22095
$250$	9.26572	0.586015
$251$	5.41430	0.341747	0.170874	−	0.985293i	$-0.445341\pi$
$251$	5.41430	0.341747	0.170874	+	0.985293i	$0.445341\pi$
$252$	−21.7515	−1.37022
$253$	−12.0890	−0.760028
$254$	−2.79071	−0.175105
$255$	−0.0399414	−0.00250123
$256$	−16.6203	−1.03877
$257$	−5.42898	−0.338650	−0.169325	−	0.985560i	$-0.554159\pi$
$257$	−5.42898	−0.338650	−0.169325	+	0.985560i	$0.554159\pi$
$258$	12.1569	0.756859
$259$	−30.8459	−1.91667
$260$	1.55566	0.0964779
$261$	11.6068	0.718444
$262$	8.92948	0.551665
$263$	−8.27358	−0.510171	−0.255085	−	0.966919i	$-0.582104\pi$
$263$	−8.27358	−0.510171	−0.255085	+	0.966919i	$0.582104\pi$
$264$	13.1197	0.807463
$265$	−2.46496	−0.151421
$266$	7.31103	0.448268
$267$	9.93119	0.607779
$268$	−4.18508	−0.255645
$269$	3.94216	0.240358	0.120179	−	0.992752i	$-0.461653\pi$
$269$	3.94216	0.240358	0.120179	+	0.992752i	$0.461653\pi$
$270$	7.45589	0.453751
$271$	19.8719	1.20713	0.603567	−	0.797312i	$-0.293746\pi$
$271$	19.8719	1.20713	0.603567	+	0.797312i	$0.293746\pi$
$272$	0.00357902	0.000217010 0
$273$	−11.3335	−0.685936
$274$	−1.54535	−0.0933579
$275$	−5.65660	−0.341106
$276$	−26.0769	−1.56964
$277$	−28.4935	−1.71201	−0.856004	−	0.516970i	$-0.827060\pi$
$277$	−28.4935	−1.71201	−0.856004	+	0.516970i	$0.827060\pi$
$278$	0.192261	0.0115311
$279$	−43.9462	−2.63099
$280$	11.7836	0.704204
$281$	−31.0192	−1.85045	−0.925225	−	0.379419i	$-0.876124\pi$
$281$	−31.0192	−1.85045	−0.925225	+	0.379419i	$0.876124\pi$
$282$	−9.06856	−0.540025
$283$	31.5173	1.87351	0.936753	−	0.349991i	$-0.113815\pi$
$283$	31.5173	1.87351	0.936753	+	0.349991i	$0.113815\pi$
$284$	−4.95733	−0.294163
$285$	7.90748	0.468399
$286$	1.61808	0.0956792
$287$	−5.95018	−0.351228
$288$	29.6676	1.74818
$289$	−16.9999	−0.999992
$290$	−2.31645	−0.136027
$291$	42.5125	2.49213
$292$	16.8018	0.983252
$293$	−10.8195	−0.632079	−0.316040	−	0.948746i	$-0.602353\pi$
$293$	−10.8195	−0.632079	−0.316040	+	0.948746i	$0.602353\pi$
$294$	−13.1141	−0.764831
$295$	−5.63421	−0.328037
$296$	25.7856	1.49876
$297$	−10.8550	−0.629869
$298$	−4.24469	−0.245889
$299$	−8.72991	−0.504863
$300$	−12.2017	−0.704467
$301$	−15.8967	−0.916269
$302$	3.70405	0.213144
$303$	13.4247	0.771227
$304$	−0.708565	−0.0406390
$305$	5.98536	0.342720
$306$	−0.0575777	−0.00329150
$307$	−17.3475	−0.990072	−0.495036	−	0.868872i	$-0.664845\pi$
$307$	−17.3475	−0.990072	−0.495036	+	0.868872i	$0.664845\pi$
$308$	−6.32016	−0.360125
$309$	34.0214	1.93541
$310$	8.77064	0.498139
$311$	−8.78677	−0.498252	−0.249126	−	0.968471i	$-0.580143\pi$
$311$	−8.78677	−0.498252	−0.249126	+	0.968471i	$0.580143\pi$
$312$	9.47424	0.536373
$313$	29.5409	1.66975	0.834876	−	0.550439i	$-0.185539\pi$
$313$	29.5409	1.66975	0.834876	+	0.550439i	$0.185539\pi$
$314$	12.3705	0.698106
$315$	−21.9780	−1.23832
$316$	13.4669	0.757573
$317$	−18.5919	−1.04422	−0.522112	−	0.852877i	$-0.674856\pi$
$317$	−18.5919	−1.04422	−0.522112	+	0.852877i	$0.674856\pi$
$318$	−5.53047	−0.310133
$319$	3.37250	0.188824
$320$	−6.64227	−0.371314
$321$	40.4873	2.25978
$322$	−24.3610	−1.35758
$323$	−0.0270885	−0.00150724
$324$	−4.54519	−0.252511
$325$	−4.08484	−0.226586
$326$	−22.3486	−1.23777
$327$	−12.4858	−0.690466
$328$	4.97405	0.274646
$329$	11.8582	0.653765
$330$	4.88366	0.268837
$331$	−3.35828	−0.184588	−0.0922938	−	0.995732i	$-0.529420\pi$
$331$	−3.35828	−0.184588	−0.0922938	+	0.995732i	$0.529420\pi$
$332$	−14.1131	−0.774557
$333$	−48.0937	−2.63552
$334$	12.9330	0.707663
$335$	−4.22867	−0.231037
$336$	3.06515	0.167217
$337$	17.2033	0.937125	0.468562	−	0.883430i	$-0.344772\pi$
$337$	17.2033	0.937125	0.468562	+	0.883430i	$0.344772\pi$
$338$	−10.6995	−0.581977
$339$	7.52293	0.408590
$340$	−0.0160845	−0.000872302 0
$341$	−12.7691	−0.691485
$342$	11.3991	0.616391
$343$	−7.05877	−0.381138
$344$	13.2888	0.716484
$345$	−26.3484	−1.41855
$346$	−10.4166	−0.560002
$347$	−32.8198	−1.76186	−0.880929	−	0.473249i	$-0.843081\pi$
$347$	−32.8198	−1.76186	−0.880929	+	0.473249i	$0.843081\pi$
$348$	7.27474	0.389967
$349$	−2.65295	−0.142009	−0.0710046	−	0.997476i	$-0.522620\pi$
$349$	−2.65295	−0.142009	−0.0710046	+	0.997476i	$0.522620\pi$
$350$	−11.3988	−0.609293
$351$	−7.83877	−0.418403
$352$	8.62027	0.459462
$353$	−20.7549	−1.10467	−0.552335	−	0.833622i	$-0.686263\pi$
$353$	−20.7549	−1.10467	−0.552335	+	0.833622i	$0.686263\pi$
$354$	−12.6411	−0.671867
$355$	−5.00895	−0.265848
$356$	3.99930	0.211963
$357$	0.117181	0.00620187
$358$	13.9819	0.738969
$359$	24.1576	1.27499	0.637495	−	0.770455i	$-0.279971\pi$
$359$	24.1576	1.27499	0.637495	+	0.770455i	$0.279971\pi$
$360$	18.3725	0.968316
$361$	−13.6371	−0.717742
$362$	13.8143	0.726064
$363$	24.7554	1.29932
$364$	−4.56403	−0.239220
$365$	16.9768	0.888605
$366$	13.4289	0.701942
$367$	29.2563	1.52716	0.763582	−	0.645711i	$-0.223439\pi$
$367$	29.2563	1.52716	0.763582	+	0.645711i	$0.223439\pi$
$368$	2.36100	0.123076
$369$	−9.27729	−0.482957
$370$	9.59838	0.498996
$371$	7.23176	0.375454
$372$	−27.5439	−1.42809
$373$	5.06956	0.262492	0.131246	−	0.991350i	$-0.458102\pi$
$373$	5.06956	0.262492	0.131246	+	0.991350i	$0.458102\pi$
$374$	−0.0167299	−0.000865081 0
$375$	−29.4017	−1.51830
$376$	−9.91287	−0.511217
$377$	2.43541	0.125430
$378$	−21.8742	−1.12509
$379$	7.03123	0.361170	0.180585	−	0.983559i	$-0.442201\pi$
$379$	7.03123	0.361170	0.180585	+	0.983559i	$0.442201\pi$
$380$	3.18436	0.163354
$381$	8.85539	0.453676
$382$	−9.14320	−0.467807
$383$	20.2528	1.03487	0.517436	−	0.855722i	$-0.326887\pi$
$383$	20.2528	1.03487	0.517436	+	0.855722i	$0.326887\pi$
$384$	16.9763	0.866316
$385$	−6.38598	−0.325459
$386$	11.8340	0.602335
$387$	−24.7855	−1.25992
$388$	17.1198	0.869129
$389$	−19.6476	−0.996174	−0.498087	−	0.867127i	$-0.665964\pi$
$389$	−19.6476	−0.996174	−0.498087	+	0.867127i	$0.665964\pi$
$390$	3.52668	0.178580
$391$	0.0902613	0.00456471
$392$	−14.3351	−0.724031
$393$	−28.3348	−1.42930
$394$	7.51329	0.378514
$395$	13.6071	0.684650
$396$	−9.85415	−0.495190
$397$	2.23294	0.112068	0.0560341	−	0.998429i	$-0.482154\pi$
$397$	2.23294	0.112068	0.0560341	+	0.998429i	$0.482154\pi$
$398$	−5.84999	−0.293234
$399$	−23.1991	−1.16141
$400$	1.10474	0.0552372
$401$	25.4677	1.27180	0.635899	−	0.771772i	$-0.280629\pi$
$401$	25.4677	1.27180	0.635899	+	0.771772i	$0.280629\pi$
$402$	−9.48758	−0.473197
$403$	−9.22104	−0.459333
$404$	5.40613	0.268965
$405$	−4.59253	−0.228204
$406$	6.79605	0.337282
$407$	−13.9742	−0.692675
$408$	−0.0979572	−0.00484960
$409$	30.1656	1.49159	0.745796	−	0.666174i	$-0.232069\pi$
$409$	30.1656	1.49159	0.745796	+	0.666174i	$0.232069\pi$
$410$	1.85153	0.0914406
$411$	4.90366	0.241880
$412$	13.7005	0.674973
$413$	16.5298	0.813377
$414$	−37.9827	−1.86675
$415$	−14.2601	−0.700000
$416$	6.22502	0.305207
$417$	−0.610078	−0.0298756
$418$	3.31213	0.162002
$419$	−28.7548	−1.40476	−0.702382	−	0.711801i	$-0.747880\pi$
$419$	−28.7548	−1.40476	−0.702382	+	0.711801i	$0.747880\pi$
$420$	−13.7750	−0.672154
$421$	−13.4270	−0.654393	−0.327197	−	0.944956i	$-0.606104\pi$
$421$	−13.4270	−0.654393	−0.327197	+	0.944956i	$0.606104\pi$
$422$	−0.478338	−0.0232851
$423$	18.4889	0.898960
$424$	−6.04538	−0.293589
$425$	0.0422345	0.00204867
$426$	−11.2383	−0.544495
$427$	−17.5600	−0.849786
$428$	16.3043	0.788097
$429$	−5.13445	−0.247894
$430$	4.94660	0.238546
$431$	28.6125	1.37822	0.689108	−	0.724658i	$-0.258002\pi$
$431$	28.6125	1.37822	0.689108	+	0.724658i	$0.258002\pi$
$432$	2.11999	0.101998
$433$	−14.8232	−0.712355	−0.356178	−	0.934418i	$-0.615920\pi$
$433$	−14.8232	−0.712355	−0.356178	+	0.934418i	$0.615920\pi$
$434$	−25.7315	−1.23515
$435$	7.35049	0.352429
$436$	−5.02805	−0.240800
$437$	−17.8697	−0.854822
$438$	38.0897	1.81999
$439$	−1.35916	−0.0648694	−0.0324347	−	0.999474i	$-0.510326\pi$
$439$	−1.35916	−0.0648694	−0.0324347	+	0.999474i	$0.510326\pi$
$440$	5.33835	0.254496
$441$	26.7369	1.27319
$442$	−0.0120813	−0.000574647 0
$443$	7.08781	0.336752	0.168376	−	0.985723i	$-0.446148\pi$
$443$	7.08781	0.336752	0.168376	+	0.985723i	$0.446148\pi$
$444$	−30.1434	−1.43054
$445$	4.04095	0.191559
$446$	19.6253	0.929286
$447$	13.4691	0.637069
$448$	19.4872	0.920685
$449$	24.2354	1.14374	0.571869	−	0.820345i	$-0.306218\pi$
$449$	24.2354	1.14374	0.571869	+	0.820345i	$0.306218\pi$
$450$	−17.7726	−0.837809
$451$	−2.69563	−0.126932
$452$	3.02950	0.142495
$453$	−11.7536	−0.552232
$454$	2.72416	0.127851
$455$	−4.61155	−0.216193
$456$	19.3933	0.908174
$457$	−21.6697	−1.01366	−0.506832	−	0.862045i	$-0.669184\pi$
$457$	−21.6697	−1.01366	−0.506832	+	0.862045i	$0.669184\pi$
$458$	−13.8461	−0.646985
$459$	0.0810475	0.00378298
$460$	−10.6105	−0.494719
$461$	36.9294	1.71997	0.859986	−	0.510318i	$-0.170472\pi$
$461$	36.9294	1.71997	0.859986	+	0.510318i	$0.170472\pi$
$462$	−14.3278	−0.666589
$463$	23.4486	1.08975	0.544875	−	0.838517i	$-0.316577\pi$
$463$	23.4486	1.08975	0.544875	+	0.838517i	$0.316577\pi$
$464$	−0.658655	−0.0305773
$465$	−27.8307	−1.29062
$466$	−20.7449	−0.960987
$467$	3.89784	0.180371	0.0901853	−	0.995925i	$-0.471254\pi$
$467$	3.89784	0.180371	0.0901853	+	0.995925i	$0.471254\pi$
$468$	−7.11605	−0.328940
$469$	12.4061	0.572863
$470$	−3.68995	−0.170205
$471$	−39.2536	−1.80871
$472$	−13.8180	−0.636027
$473$	−7.20171	−0.331135
$474$	30.5294	1.40226
$475$	−8.36146	−0.383650
$476$	0.0471889	0.00216290
$477$	11.2755	0.516268
$478$	14.3736	0.657435
$479$	−10.4410	−0.477061	−0.238531	−	0.971135i	$-0.576666\pi$
$479$	−10.4410	−0.477061	−0.238531	+	0.971135i	$0.576666\pi$
$480$	18.7882	0.857562
$481$	−10.0913	−0.460123
$482$	2.66885	0.121563
$483$	77.3015	3.51734
$484$	9.96904	0.453138
$485$	17.2981	0.785467
$486$	8.67231	0.393384
$487$	11.8844	0.538532	0.269266	−	0.963066i	$-0.413219\pi$
$487$	11.8844	0.538532	0.269266	+	0.963066i	$0.413219\pi$
$488$	14.6792	0.664497
$489$	70.9158	3.20692
$490$	−5.33607	−0.241059
$491$	27.4571	1.23912	0.619562	−	0.784948i	$-0.287310\pi$
$491$	27.4571	1.23912	0.619562	+	0.784948i	$0.287310\pi$
$492$	−5.81468	−0.262146
$493$	−0.0251804	−0.00113407
$494$	2.39181	0.107613
$495$	−9.95676	−0.447523
$496$	2.49383	0.111976
$497$	14.6954	0.659178
$498$	−31.9944	−1.43370
$499$	36.5142	1.63460	0.817299	−	0.576214i	$-0.195470\pi$
$499$	36.5142	1.63460	0.817299	+	0.576214i	$0.195470\pi$
$500$	−11.8401	−0.529506
$501$	−41.0387	−1.83347
$502$	4.94284	0.220610
$503$	−0.442602	−0.0197347	−0.00986733	−	0.999951i	$-0.503141\pi$
$503$	−0.442602	−0.0197347	−0.00986733	+	0.999951i	$0.503141\pi$
$504$	−53.9017	−2.40097
$505$	5.46243	0.243075
$506$	−11.0363	−0.490624
$507$	33.9514	1.50784
$508$	3.56608	0.158219
$509$	31.8700	1.41261	0.706307	−	0.707906i	$-0.250360\pi$
$509$	31.8700	1.41261	0.706307	+	0.707906i	$0.250360\pi$
$510$	−0.0364634	−0.00161463
$511$	−49.8068	−2.20332
$512$	−3.45258	−0.152584
$513$	−16.0456	−0.708429
$514$	−4.95624	−0.218610
$515$	13.8431	0.610001
$516$	−15.5346	−0.683875
$517$	5.37216	0.236267
$518$	−28.1599	−1.23728
$519$	33.0538	1.45090
$520$	3.85502	0.169054
$521$	13.0585	0.572103	0.286051	−	0.958214i	$-0.407657\pi$
$521$	13.0585	0.572103	0.286051	+	0.958214i	$0.407657\pi$
$522$	10.5961	0.463780
$523$	−2.04070	−0.0892336	−0.0446168	−	0.999004i	$-0.514207\pi$
$523$	−2.04070	−0.0892336	−0.0446168	+	0.999004i	$0.514207\pi$
$524$	−11.4105	−0.498468
$525$	36.1704	1.57861
$526$	−7.55314	−0.329333
$527$	0.0953392	0.00415304
$528$	1.38861	0.0604315
$529$	36.5433	1.58884
$530$	−2.25032	−0.0977477
$531$	25.7726	1.11843
$532$	−9.34233	−0.405041
$533$	−1.94661	−0.0843172
$534$	9.06641	0.392342
$535$	16.4741	0.712236
$536$	−10.3709	−0.447955
$537$	−44.3671	−1.91458
$538$	3.59889	0.155159
$539$	7.76873	0.334623
$540$	−9.52744	−0.409996
$541$	−32.4849	−1.39663	−0.698317	−	0.715788i	$-0.746067\pi$
$541$	−32.4849	−1.39663	−0.698317	+	0.715788i	$0.746067\pi$
$542$	18.1416	0.779247
$543$	−43.8352	−1.88115
$544$	−0.0643625	−0.00275952
$545$	−5.08041	−0.217621
$546$	−10.3466	−0.442795
$547$	−5.77433	−0.246892	−0.123446	−	0.992351i	$-0.539395\pi$
$547$	−5.77433	−0.246892	−0.123446	+	0.992351i	$0.539395\pi$
$548$	1.97471	0.0843554
$549$	−27.3788	−1.16850
$550$	−5.16404	−0.220195
$551$	4.98515	0.212375
$552$	−64.6201	−2.75042
$553$	−39.9209	−1.69761
$554$	−26.0124	−1.10516
$555$	−30.4573	−1.29284
$556$	−0.245679	−0.0104191
$557$	−22.4130	−0.949670	−0.474835	−	0.880075i	$-0.657492\pi$
$557$	−22.4130	−0.949670	−0.474835	+	0.880075i	$0.657492\pi$
$558$	−40.1195	−1.69839
$559$	−5.20062	−0.219963
$560$	1.24719	0.0527035
$561$	0.0530867	0.00224132
$562$	−28.3181	−1.19453
$563$	−2.24085	−0.0944407	−0.0472203	−	0.998884i	$-0.515036\pi$
$563$	−2.24085	−0.0944407	−0.0472203	+	0.998884i	$0.515036\pi$
$564$	11.5882	0.487950
$565$	3.06104	0.128779
$566$	28.7728	1.20941
$567$	13.4736	0.565840
$568$	−12.2846	−0.515450
$569$	3.11655	0.130653	0.0653264	−	0.997864i	$-0.479191\pi$
$569$	3.11655	0.130653	0.0653264	+	0.997864i	$0.479191\pi$
$570$	7.21893	0.302368
$571$	38.2090	1.59900	0.799499	−	0.600667i	$-0.205098\pi$
$571$	38.2090	1.59900	0.799499	+	0.600667i	$0.205098\pi$
$572$	−2.06765	−0.0864529
$573$	29.0129	1.21203
$574$	−5.43206	−0.226730
$575$	27.8611	1.16189
$576$	30.3837	1.26599
$577$	−33.9440	−1.41311	−0.706554	−	0.707659i	$-0.749751\pi$
$577$	−33.9440	−1.41311	−0.706554	+	0.707659i	$0.749751\pi$
$578$	−15.5196	−0.645529
$579$	−37.5513	−1.56058
$580$	2.96005	0.122910
$581$	41.8365	1.73567
$582$	38.8107	1.60875
$583$	3.27622	0.135687
$584$	41.6359	1.72291
$585$	−7.19015	−0.297276
$586$	−9.87733	−0.408029
$587$	40.5865	1.67518	0.837592	−	0.546296i	$-0.183962\pi$
$587$	40.5865	1.67518	0.837592	+	0.546296i	$0.183962\pi$
$588$	16.7578	0.691078
$589$	−18.8750	−0.777731
$590$	−5.14360	−0.211759
$591$	−23.8410	−0.980686
$592$	2.72918	0.112169
$593$	−25.5035	−1.04730	−0.523652	−	0.851932i	$-0.675431\pi$
$593$	−25.5035	−1.04730	−0.523652	+	0.851932i	$0.675431\pi$
$594$	−9.90974	−0.406602
$595$	0.0476803	0.00195470
$596$	5.42404	0.222178
$597$	18.5630	0.759734
$598$	−7.96974	−0.325907
$599$	−13.4331	−0.548861	−0.274430	−	0.961607i	$-0.588489\pi$
$599$	−13.4331	−0.548861	−0.274430	+	0.961607i	$0.588489\pi$
$600$	−30.2366	−1.23441
$601$	−6.16983	−0.251673	−0.125836	−	0.992051i	$-0.540161\pi$
$601$	−6.16983	−0.251673	−0.125836	+	0.992051i	$0.540161\pi$
$602$	−14.5124	−0.591483
$603$	19.3432	0.787715
$604$	−4.73319	−0.192591
$605$	10.0729	0.409520
$606$	12.2557	0.497853
$607$	−1.75135	−0.0710849	−0.0355425	−	0.999368i	$-0.511316\pi$
$607$	−1.75135	−0.0710849	−0.0355425	+	0.999368i	$0.511316\pi$
$608$	12.7423	0.516769
$609$	−21.5650	−0.873859
$610$	5.46417	0.221238
$611$	3.87944	0.156945
$612$	0.0735751	0.00297410
$613$	−9.24279	−0.373313	−0.186656	−	0.982425i	$-0.559765\pi$
$613$	−9.24279	−0.373313	−0.186656	+	0.982425i	$0.559765\pi$
$614$	−15.8369	−0.639126
$615$	−5.87523	−0.236912
$616$	−15.6618	−0.631030
$617$	35.7600	1.43964	0.719822	−	0.694159i	$-0.244223\pi$
$617$	35.7600	1.43964	0.719822	+	0.694159i	$0.244223\pi$
$618$	31.0589	1.24937
$619$	−24.1365	−0.970128	−0.485064	−	0.874479i	$-0.661204\pi$
$619$	−24.1365	−0.970128	−0.485064	+	0.874479i	$0.661204\pi$
$620$	−11.2075	−0.450103
$621$	53.4652	2.14549
$622$	−8.02164	−0.321639
$623$	−11.8554	−0.474978
$624$	1.00277	0.0401428
$625$	6.08970	0.243588
$626$	26.9686	1.07788
$627$	−10.5100	−0.419728
$628$	−15.8075	−0.630788
$629$	0.104337	0.00416019
$630$	−20.0643	−0.799379
$631$	−19.4991	−0.776247	−0.388123	−	0.921607i	$-0.626877\pi$
$631$	−19.4991	−0.776247	−0.388123	+	0.921607i	$0.626877\pi$
$632$	33.3718	1.32746
$633$	1.51785	0.0603290
$634$	−16.9730	−0.674082
$635$	3.60322	0.142989
$636$	7.06706	0.280227
$637$	5.61009	0.222280
$638$	3.07883	0.121892
$639$	22.9124	0.906402
$640$	6.90755	0.273045
$641$	−29.3032	−1.15741	−0.578703	−	0.815538i	$-0.696441\pi$
$641$	−29.3032	−1.15741	−0.578703	+	0.815538i	$0.696441\pi$
$642$	36.9618	1.45876
$643$	−33.5527	−1.32319	−0.661594	−	0.749862i	$-0.730120\pi$
$643$	−33.5527	−1.32319	−0.661594	+	0.749862i	$0.730120\pi$
$644$	31.1295	1.22667
$645$	−15.6964	−0.618046
$646$	−0.0247297	−0.000972978 0
$647$	−7.93160	−0.311824	−0.155912	−	0.987771i	$-0.549832\pi$
$647$	−7.93160	−0.311824	−0.155912	+	0.987771i	$0.549832\pi$
$648$	−11.2633	−0.442463
$649$	7.48852	0.293950
$650$	−3.72915	−0.146269
$651$	81.6504	3.20013
$652$	28.5579	1.11841
$653$	2.14051	0.0837645	0.0418822	−	0.999123i	$-0.486665\pi$
$653$	2.14051	0.0837645	0.0418822	+	0.999123i	$0.486665\pi$
$654$	−11.3986	−0.445720
$655$	−11.5293	−0.450486
$656$	0.526461	0.0205548
$657$	−77.6568	−3.02968
$658$	10.8257	0.422028
$659$	48.2328	1.87888	0.939442	−	0.342708i	$-0.111344\pi$
$659$	48.2328	1.87888	0.939442	+	0.342708i	$0.111344\pi$
$660$	−6.24054	−0.242913
$661$	30.0091	1.16722	0.583609	−	0.812035i	$-0.301640\pi$
$661$	30.0091	1.16722	0.583609	+	0.812035i	$0.301640\pi$
$662$	−3.06585	−0.119158
$663$	0.0383359	0.00148884
$664$	−34.9732	−1.35722
$665$	−9.43961	−0.366053
$666$	−43.9058	−1.70132
$667$	−16.6110	−0.643179
$668$	−16.5263	−0.639423
$669$	−62.2745	−2.40767
$670$	−3.86045	−0.149142
$671$	−7.95523	−0.307108
$672$	−55.1213	−2.12635
$673$	−28.5885	−1.10201	−0.551003	−	0.834503i	$-0.685755\pi$
$673$	−28.5885	−1.10201	−0.551003	+	0.834503i	$0.685755\pi$
$674$	15.7053	0.604946
$675$	25.0171	0.962908
$676$	13.6723	0.525857
$677$	6.82078	0.262144	0.131072	−	0.991373i	$-0.458158\pi$
$677$	6.82078	0.262144	0.131072	+	0.991373i	$0.458158\pi$
$678$	6.86786	0.263759
$679$	−50.7496	−1.94759
$680$	−0.0398583	−0.00152850
$681$	−8.64423	−0.331248
$682$	−11.6572	−0.446377
$683$	−10.8759	−0.416157	−0.208078	−	0.978112i	$-0.566721\pi$
$683$	−10.8759	−0.416157	−0.208078	+	0.978112i	$0.566721\pi$
$684$	−14.5662	−0.556952
$685$	1.99527	0.0762355
$686$	−6.44411	−0.246037
$687$	43.9360	1.67626
$688$	1.40651	0.0536226
$689$	2.36588	0.0901329
$690$	−24.0541	−0.915724
$691$	1.74582	0.0664141	0.0332070	−	0.999448i	$-0.489428\pi$
$691$	1.74582	0.0664141	0.0332070	+	0.999448i	$0.489428\pi$
$692$	13.3108	0.506001
$693$	29.2114	1.10965
$694$	−29.9619	−1.13734
$695$	−0.248238	−0.00941619
$696$	18.0273	0.683322
$697$	0.0201267	0.000762351 0
$698$	−2.42194	−0.0916718
$699$	65.8270	2.48981
$700$	14.5659	0.550539
$701$	−14.3245	−0.541029	−0.270514	−	0.962716i	$-0.587194\pi$
$701$	−14.3245	−0.541029	−0.270514	+	0.962716i	$0.587194\pi$
$702$	−7.15620	−0.270093
$703$	−20.6563	−0.779069
$704$	8.82835	0.332731
$705$	11.7088	0.440981
$706$	−18.9476	−0.713103
$707$	−16.0258	−0.602712
$708$	16.1533	0.607079
$709$	21.3801	0.802945	0.401472	−	0.915871i	$-0.368499\pi$
$709$	21.3801	0.802945	0.401472	+	0.915871i	$0.368499\pi$
$710$	−4.57279	−0.171614
$711$	−62.2431	−2.33430
$712$	9.91053	0.371413
$713$	62.8931	2.35537
$714$	0.106977	0.00400352
$715$	−2.08918	−0.0781310
$716$	−17.8667	−0.667710
$717$	−45.6100	−1.70334
$718$	22.0540	0.823050
$719$	−41.8105	−1.55927	−0.779634	−	0.626235i	$-0.784595\pi$
$719$	−41.8105	−1.55927	−0.779634	+	0.626235i	$0.784595\pi$
$720$	1.94457	0.0724700
$721$	−40.6133	−1.51252
$722$	−12.4496	−0.463327
$723$	−8.46873	−0.314955
$724$	−17.6525	−0.656050
$725$	−7.77249	−0.288663
$726$	22.5998	0.838757
$727$	−26.7352	−0.991554	−0.495777	−	0.868450i	$-0.665117\pi$
$727$	−26.7352	−0.991554	−0.495777	+	0.868450i	$0.665117\pi$
$728$	−11.3099	−0.419174
$729$	−39.2073	−1.45212
$730$	15.4985	0.573625
$731$	0.0537709	0.00198879
$732$	−17.1601	−0.634254
$733$	13.5766	0.501462	0.250731	−	0.968057i	$-0.419329\pi$
$733$	13.5766	0.501462	0.250731	+	0.968057i	$0.419329\pi$
$734$	26.7087	0.985837
$735$	16.9323	0.624556
$736$	−42.4585	−1.56504
$737$	5.62039	0.207030
$738$	−8.46946	−0.311765
$739$	−32.9194	−1.21096	−0.605481	−	0.795860i	$-0.707019\pi$
$739$	−32.9194	−1.21096	−0.605481	+	0.795860i	$0.707019\pi$
$740$	−12.2652	−0.450878
$741$	−7.58964	−0.278812
$742$	6.60204	0.242368
$743$	−29.9445	−1.09856	−0.549278	−	0.835640i	$-0.685097\pi$
$743$	−29.9445	−1.09856	−0.549278	+	0.835640i	$0.685097\pi$
$744$	−68.2556	−2.50237
$745$	5.48053	0.200791
$746$	4.62812	0.169447
$747$	65.2298	2.38663
$748$	0.0213781	0.000781661 0
$749$	−48.3319	−1.76601
$750$	−26.8415	−0.980113
$751$	−7.68814	−0.280544	−0.140272	−	0.990113i	$-0.544798\pi$
$751$	−7.68814	−0.280544	−0.140272	+	0.990113i	$0.544798\pi$
$752$	−1.04919	−0.0382601
$753$	−15.6845	−0.571574
$754$	2.22334	0.0809692
$755$	−4.78248	−0.174052
$756$	27.9518	1.01660
$757$	−19.4003	−0.705116	−0.352558	−	0.935790i	$-0.614688\pi$
$757$	−19.4003	−0.705116	−0.352558	+	0.935790i	$0.614688\pi$
$758$	6.41897	0.233148
$759$	35.0201	1.27115
$760$	7.89104	0.286238
$761$	38.8358	1.40780	0.703899	−	0.710300i	$-0.251441\pi$
$761$	38.8358	1.40780	0.703899	+	0.710300i	$0.251441\pi$
$762$	8.08430	0.292863
$763$	14.9050	0.539598
$764$	11.6836	0.422696
$765$	0.0743413	0.00268781
$766$	18.4893	0.668046
$767$	5.40774	0.195262
$768$	48.1466	1.73734
$769$	−4.94505	−0.178323	−0.0891616	−	0.996017i	$-0.528419\pi$
$769$	−4.94505	−0.178323	−0.0891616	+	0.996017i	$0.528419\pi$
$770$	−5.82991	−0.210095
$771$	15.7270	0.566394
$772$	−15.1220	−0.544252
$773$	−13.1002	−0.471183	−0.235592	−	0.971852i	$-0.575703\pi$
$773$	−13.1002	−0.471183	−0.235592	+	0.971852i	$0.575703\pi$
$774$	−22.6272	−0.813319
$775$	29.4285	1.05710
$776$	42.4241	1.52294
$777$	89.3563	3.20564
$778$	−17.9368	−0.643064
$779$	−3.98462	−0.142764
$780$	−4.50653	−0.161360
$781$	6.65748	0.238223
$782$	0.0824016	0.00294668
$783$	−14.9153	−0.533031
$784$	−1.51725	−0.0541874
$785$	−15.9721	−0.570069
$786$	−25.8675	−0.922662
$787$	−28.6833	−1.02245	−0.511224	−	0.859447i	$-0.670808\pi$
$787$	−28.6833	−1.02245	−0.511224	+	0.859447i	$0.670808\pi$
$788$	−9.60079	−0.342014
$789$	23.9674	0.853263
$790$	12.4223	0.441965
$791$	−8.98055	−0.319312
$792$	−24.4192	−0.867699
$793$	−5.74477	−0.204003
$794$	2.03851	0.0723439
$795$	7.14065	0.253253
$796$	7.47536	0.264957
$797$	−14.3201	−0.507242	−0.253621	−	0.967304i	$-0.581622\pi$
$797$	−14.3201	−0.507242	−0.253621	+	0.967304i	$0.581622\pi$
$798$	−21.1790	−0.749730
$799$	−0.0401108	−0.00141902
$800$	−19.8669	−0.702401
$801$	−18.4845	−0.653118
$802$	23.2501	0.820989
$803$	−22.5641	−0.796270
$804$	12.1236	0.427567
$805$	31.4536	1.10859
$806$	−8.41810	−0.296515
$807$	−11.4199	−0.402000
$808$	13.3967	0.471296
$809$	14.6335	0.514486	0.257243	−	0.966347i	$-0.417186\pi$
$809$	14.6335	0.514486	0.257243	+	0.966347i	$0.417186\pi$
$810$	−4.19262	−0.147314
$811$	−5.35024	−0.187872	−0.0939362	−	0.995578i	$-0.529945\pi$
$811$	−5.35024	−0.187872	−0.0939362	+	0.995578i	$0.529945\pi$
$812$	−8.68427	−0.304758
$813$	−57.5663	−2.01894
$814$	−12.7574	−0.447145
$815$	28.8553	1.01076
$816$	−0.0103679	−0.000362950 0
$817$	−10.6454	−0.372436
$818$	27.5389	0.962874
$819$	21.0946	0.737106
$820$	−2.36596	−0.0826230
$821$	−7.30505	−0.254948	−0.127474	−	0.991842i	$-0.540687\pi$
$821$	−7.30505	−0.254948	−0.127474	+	0.991842i	$0.540687\pi$
$822$	4.47666	0.156142
$823$	−19.2893	−0.672383	−0.336192	−	0.941794i	$-0.609139\pi$
$823$	−19.2893	−0.672383	−0.336192	+	0.941794i	$0.609139\pi$
$824$	33.9506	1.18273
$825$	16.3864	0.570501
$826$	15.0904	0.525063
$827$	7.82472	0.272092	0.136046	−	0.990703i	$-0.456561\pi$
$827$	7.82472	0.272092	0.136046	+	0.990703i	$0.456561\pi$
$828$	48.5358	1.68674
$829$	26.6166	0.924432	0.462216	−	0.886767i	$-0.347054\pi$
$829$	26.6166	0.924432	0.462216	+	0.886767i	$0.347054\pi$
$830$	−13.0184	−0.451874
$831$	82.5417	2.86334
$832$	6.37528	0.221023
$833$	−0.0580045	−0.00200974
$834$	−0.556954	−0.0192857
$835$	−16.6984	−0.577873
$836$	−4.23238	−0.146380
$837$	56.4731	1.95200
$838$	−26.2509	−0.906823
$839$	48.8846	1.68768	0.843842	−	0.536591i	$-0.180288\pi$
$839$	48.8846	1.68768	0.843842	+	0.536591i	$0.180288\pi$
$840$	−34.1354	−1.17778
$841$	−24.3660	−0.840207
$842$	−12.2579	−0.422433
$843$	89.8583	3.09489
$844$	0.611240	0.0210397
$845$	13.8147	0.475239
$846$	16.8789	0.580310
$847$	−29.5519	−1.01542
$848$	−0.639852	−0.0219726
$849$	−91.3011	−3.13345
$850$	0.0385568	0.00132249
$851$	68.8287	2.35942
$852$	14.3607	0.491990
$853$	10.6286	0.363915	0.181957	−	0.983306i	$-0.441757\pi$
$853$	10.6286	0.363915	0.181957	+	0.983306i	$0.441757\pi$
$854$	−16.0309	−0.548566
$855$	−14.7179	−0.503341
$856$	40.4030	1.38095
$857$	−8.99177	−0.307153	−0.153577	−	0.988137i	$-0.549079\pi$
$857$	−8.99177	−0.307153	−0.153577	+	0.988137i	$0.549079\pi$
$858$	−4.68736	−0.160024
$859$	23.6253	0.806086	0.403043	−	0.915181i	$-0.367953\pi$
$859$	23.6253	0.806086	0.403043	+	0.915181i	$0.367953\pi$
$860$	−6.32097	−0.215543
$861$	17.2369	0.587431
$862$	26.1210	0.889686
$863$	34.7106	1.18156	0.590781	−	0.806832i	$-0.298820\pi$
$863$	34.7106	1.18156	0.590781	+	0.806832i	$0.298820\pi$
$864$	−38.1244	−1.29702
$865$	13.4494	0.457294
$866$	−13.5324	−0.459850
$867$	49.2463	1.67249
$868$	32.8807	1.11605
$869$	−18.0855	−0.613508
$870$	6.71044	0.227505
$871$	4.05869	0.137524
$872$	−12.4598	−0.421943
$873$	−79.1268	−2.67804
$874$	−16.3136	−0.551817
$875$	35.0985	1.18655
$876$	−48.6725	−1.64449
$877$	34.6146	1.16885	0.584426	−	0.811447i	$-0.301320\pi$
$877$	34.6146	1.16885	0.584426	+	0.811447i	$0.301320\pi$
$878$	−1.24081	−0.0418754
$879$	31.3425	1.05716
$880$	0.565019	0.0190468
$881$	6.82337	0.229885	0.114943	−	0.993372i	$-0.463332\pi$
$881$	6.82337	0.229885	0.114943	+	0.993372i	$0.463332\pi$
$882$	24.4088	0.821886
$883$	38.3041	1.28904	0.644519	−	0.764589i	$-0.277058\pi$
$883$	38.3041	1.28904	0.644519	+	0.764589i	$0.277058\pi$
$884$	0.0154379	0.000519234 0
$885$	16.3215	0.548643
$886$	6.47063	0.217385
$887$	−31.7409	−1.06575	−0.532877	−	0.846193i	$-0.678889\pi$
$887$	−31.7409	−1.06575	−0.532877	+	0.846193i	$0.678889\pi$
$888$	−74.6973	−2.50668
$889$	−10.5712	−0.354546
$890$	3.68908	0.123658
$891$	6.10400	0.204492
$892$	−25.0780	−0.839675
$893$	7.94102	0.265736
$894$	12.2963	0.411250
$895$	−18.0528	−0.603437
$896$	−20.2655	−0.677024
$897$	25.2893	0.844386
$898$	22.1251	0.738323
$899$	−17.5455	−0.585174
$900$	22.7106	0.757019
$901$	−0.0244616	−0.000814934 0
$902$	−2.46090	−0.0819390
$903$	46.0505	1.53246
$904$	7.50728	0.249689
$905$	−17.8363	−0.592899
$906$	−10.7301	−0.356485
$907$	28.6943	0.952778	0.476389	−	0.879235i	$-0.341945\pi$
$907$	28.6943	0.952778	0.476389	+	0.879235i	$0.341945\pi$
$908$	−3.48105	−0.115523
$909$	−24.9868	−0.828759
$910$	−4.20999	−0.139560
$911$	−16.6615	−0.552019	−0.276010	−	0.961155i	$-0.589012\pi$
$911$	−16.6615	−0.552019	−0.276010	+	0.961155i	$0.589012\pi$
$912$	2.05262	0.0679689
$913$	18.9533	0.627263
$914$	−19.7828	−0.654355
$915$	−17.3388	−0.573201
$916$	17.6931	0.584596
$917$	33.8248	1.11699
$918$	0.0739902	0.00244204
$919$	51.3529	1.69398	0.846989	−	0.531611i	$-0.178413\pi$
$919$	51.3529	1.69398	0.846989	+	0.531611i	$0.178413\pi$
$920$	−26.2936	−0.866875
$921$	50.2532	1.65590
$922$	33.7137	1.11030
$923$	4.80762	0.158245
$924$	18.3086	0.602310
$925$	32.2059	1.05892
$926$	21.4068	0.703471
$927$	−63.3226	−2.07979
$928$	11.8448	0.388823
$929$	−25.9849	−0.852536	−0.426268	−	0.904597i	$-0.640172\pi$
$929$	−25.9849	−0.852536	−0.426268	+	0.904597i	$0.640172\pi$
$930$	−25.4073	−0.833139
$931$	11.4836	0.376359
$932$	26.5086	0.868319
$933$	25.4541	0.833328
$934$	3.55843	0.116435
$935$	0.0216007	0.000706419 0
$936$	−17.6340	−0.576386
$937$	33.1421	1.08271	0.541353	−	0.840795i	$-0.317912\pi$
$937$	33.1421	1.08271	0.541353	+	0.840795i	$0.317912\pi$
$938$	11.3259	0.369802
$939$	−85.5760	−2.79267
$940$	4.71517	0.153792
$941$	59.0258	1.92419	0.962093	−	0.272722i	$-0.0879239\pi$
$941$	59.0258	1.92419	0.962093	+	0.272722i	$0.0879239\pi$
$942$	−35.8356	−1.16759
$943$	13.2771	0.432362
$944$	−1.46252	−0.0476010
$945$	28.2429	0.918741
$946$	−6.57461	−0.213759
$947$	−56.3189	−1.83012	−0.915059	−	0.403321i	$-0.867856\pi$
$947$	−56.3189	−1.83012	−0.915059	+	0.403321i	$0.867856\pi$
$948$	−39.0118	−1.26704
$949$	−16.2944	−0.528938
$950$	−7.63337	−0.247659
$951$	53.8581	1.74647
$952$	0.116937	0.00378995
$953$	−36.9075	−1.19555	−0.597775	−	0.801664i	$-0.703948\pi$
$953$	−36.9075	−1.19555	−0.597775	+	0.801664i	$0.703948\pi$
$954$	10.2936	0.333269
$955$	11.8052	0.382008
$956$	−18.3672	−0.594039
$957$	−9.76966	−0.315808
$958$	−9.53183	−0.307959
$959$	−5.85378	−0.189028
$960$	19.2417	0.621025
$961$	35.4314	1.14295
$962$	−9.21257	−0.297025
$963$	−75.3573	−2.42835
$964$	−3.41037	−0.109841
$965$	−15.2794	−0.491863
$966$	70.5704	2.27057
$967$	51.5376	1.65734	0.828669	−	0.559739i	$-0.189098\pi$
$967$	51.5376	1.65734	0.828669	+	0.559739i	$0.189098\pi$
$968$	24.7039	0.794014
$969$	0.0784717	0.00252087
$970$	15.7919	0.507046
$971$	7.44496	0.238920	0.119460	−	0.992839i	$-0.461884\pi$
$971$	7.44496	0.238920	0.119460	+	0.992839i	$0.461884\pi$
$972$	−11.0818	−0.355450
$973$	0.728284	0.0233477
$974$	10.8495	0.347641
$975$	11.8332	0.378966
$976$	1.55367	0.0497318
$977$	54.1913	1.73373	0.866866	−	0.498541i	$-0.166131\pi$
$977$	54.1913	1.73373	0.866866	+	0.498541i	$0.166131\pi$
$978$	64.7407	2.07018
$979$	−5.37089	−0.171654
$980$	6.81865	0.217814
$981$	23.2393	0.741974
$982$	25.0663	0.799897
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	−14.4091	−0.459347
$985$	−9.70077	−0.309092
$986$	−0.0229878	−0.000732081 0
$987$	−34.3517	−1.09343
$988$	−3.05636	−0.0972357
$989$	35.4714	1.12793
$990$	−9.08976	−0.288892
$991$	−8.62792	−0.274075	−0.137037	−	0.990566i	$-0.543758\pi$
$991$	−8.62792	−0.274075	−0.137037	+	0.990566i	$0.543758\pi$
$992$	−44.8471	−1.42390
$993$	9.72846	0.308723
$994$	13.4157	0.425522
$995$	7.55321	0.239453
$996$	40.8837	1.29545
$997$	−48.3754	−1.53206	−0.766032	−	0.642802i	$-0.777772\pi$
$997$	−48.3754	−1.53206	−0.766032	+	0.642802i	$0.777772\pi$
$998$	33.3346	1.05519
$999$	61.8028	1.95535

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+0.912923 q^{2} -2.89686 q^{3} -1.16657 q^{4} -1.17872 q^{5} -2.64461 q^{6} +3.45815 q^{7} -2.89084 q^{8} +5.39181 q^{9} +O(q^{10})\)	\(q+0.912923 q^{2} -2.89686 q^{3} -1.16657 q^{4} -1.17872 q^{5} -2.64461 q^{6} +3.45815 q^{7} -2.89084 q^{8} +5.39181 q^{9} -1.07608 q^{10} +1.56665 q^{11} +3.37940 q^{12} +1.13134 q^{13} +3.15703 q^{14} +3.41459 q^{15} -0.305970 q^{16} -0.0116973 q^{17} +4.92231 q^{18} +2.31580 q^{19} +1.37506 q^{20} -10.0178 q^{21} +1.43024 q^{22} -7.71643 q^{23} +8.37436 q^{24} -3.61062 q^{25} +1.03283 q^{26} -6.92875 q^{27} -4.03418 q^{28} +2.15267 q^{29} +3.11726 q^{30} -8.15054 q^{31} +5.50235 q^{32} -4.53838 q^{33} -0.0106787 q^{34} -4.07619 q^{35} -6.28993 q^{36} -8.91976 q^{37} +2.11414 q^{38} -3.27734 q^{39} +3.40748 q^{40} -1.72063 q^{41} -9.14547 q^{42} -4.59687 q^{43} -1.82761 q^{44} -6.35543 q^{45} -7.04451 q^{46} +3.42907 q^{47} +0.886354 q^{48} +4.95880 q^{49} -3.29622 q^{50} +0.0338854 q^{51} -1.31979 q^{52} +2.09122 q^{53} -6.32542 q^{54} -1.84665 q^{55} -9.99695 q^{56} -6.70854 q^{57} +1.96523 q^{58} +4.77995 q^{59} -3.98336 q^{60} -5.07785 q^{61} -7.44082 q^{62} +18.6457 q^{63} +5.63516 q^{64} -1.33353 q^{65} -4.14320 q^{66} +3.58751 q^{67} +0.0136457 q^{68} +22.3534 q^{69} -3.72125 q^{70} +4.24949 q^{71} -15.5868 q^{72} -14.4027 q^{73} -8.14306 q^{74} +10.4595 q^{75} -2.70154 q^{76} +5.41773 q^{77} -2.99196 q^{78} -11.5440 q^{79} +0.360653 q^{80} +3.89620 q^{81} -1.57080 q^{82} +12.0979 q^{83} +11.6865 q^{84} +0.0137878 q^{85} -4.19659 q^{86} -6.23600 q^{87} -4.52894 q^{88} -3.42826 q^{89} -5.80202 q^{90} +3.91234 q^{91} +9.00176 q^{92} +23.6110 q^{93} +3.13048 q^{94} -2.72967 q^{95} -15.9395 q^{96} -14.6754 q^{97} +4.52701 q^{98} +8.44711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 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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