LMFDB - Embedded newform 787.2.a.b.1.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [787,2,Mod(1,787)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("787.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(787, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 787 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	787.a (trivial)

Newform invariants

comment:select newform

sage:traces = [37] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$6.28422663907$
Analytic rank:	$0$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	787.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.00817556 q^{2} -0.445090 q^{3} -1.99993 q^{4} -3.45726 q^{5} -0.00363886 q^{6} -1.06207 q^{7} -0.0327017 q^{8} -2.80189 q^{9} -0.0282650 q^{10} +1.20144 q^{11} +0.890150 q^{12} +1.53086 q^{13} -0.00868301 q^{14} +1.53879 q^{15} +3.99960 q^{16} +0.0987406 q^{17} -0.0229071 q^{18} -6.08964 q^{19} +6.91429 q^{20} +0.472717 q^{21} +0.00982243 q^{22} +0.357250 q^{23} +0.0145552 q^{24} +6.95263 q^{25} +0.0125156 q^{26} +2.58237 q^{27} +2.12407 q^{28} +5.47618 q^{29} +0.0125805 q^{30} +5.07703 q^{31} +0.0981023 q^{32} -0.534748 q^{33} +0.000807260 q^{34} +3.67185 q^{35} +5.60360 q^{36} -4.20663 q^{37} -0.0497862 q^{38} -0.681370 q^{39} +0.113058 q^{40} +4.10036 q^{41} +0.00386472 q^{42} +10.5737 q^{43} -2.40280 q^{44} +9.68687 q^{45} +0.00292072 q^{46} -2.20326 q^{47} -1.78018 q^{48} -5.87201 q^{49} +0.0568417 q^{50} -0.0439485 q^{51} -3.06161 q^{52} +1.17618 q^{53} +0.0211123 q^{54} -4.15368 q^{55} +0.0347315 q^{56} +2.71044 q^{57} +0.0447709 q^{58} +4.07464 q^{59} -3.07748 q^{60} +0.772561 q^{61} +0.0415076 q^{62} +2.97581 q^{63} -7.99840 q^{64} -5.29257 q^{65} -0.00437187 q^{66} +0.401418 q^{67} -0.197475 q^{68} -0.159008 q^{69} +0.0300194 q^{70} +3.57752 q^{71} +0.0916267 q^{72} -10.6826 q^{73} -0.0343915 q^{74} -3.09455 q^{75} +12.1789 q^{76} -1.27601 q^{77} -0.00557058 q^{78} -4.24327 q^{79} -13.8276 q^{80} +7.25630 q^{81} +0.0335228 q^{82} +2.80800 q^{83} -0.945402 q^{84} -0.341372 q^{85} +0.0864456 q^{86} -2.43740 q^{87} -0.0392891 q^{88} +12.4928 q^{89} +0.0791956 q^{90} -1.62588 q^{91} -0.714476 q^{92} -2.25974 q^{93} -0.0180129 q^{94} +21.0535 q^{95} -0.0436644 q^{96} -5.02154 q^{97} -0.0480070 q^{98} -3.36630 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) $ 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

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 $

$2$	0.00817556	0.00578099	0.00289050	−	0.999996i	$-0.499080\pi$
$2$	0.00817556	0.00578099	0.00289050	+	0.999996i	$0.499080\pi$
$3$	−0.445090	−0.256973	−0.128486	−	0.991711i	$-0.541012\pi$
$3$	−0.445090	−0.256973	−0.128486	+	0.991711i	$0.541012\pi$
$4$	−1.99993	−0.999967
$5$	−3.45726	−1.54613	−0.773066	−	0.634325i	$-0.781278\pi$
$5$	−3.45726	−1.54613	−0.773066	+	0.634325i	$0.781278\pi$
$6$	−0.00363886	−0.00148556
$7$	−1.06207	−0.401424	−0.200712	−	0.979650i	$-0.564326\pi$
$7$	−1.06207	−0.401424	−0.200712	+	0.979650i	$0.564326\pi$
$8$	−0.0327017	−0.0115618
$9$	−2.80189	−0.933965
$10$	−0.0282650	−0.00893818
$11$	1.20144	0.362247	0.181124	−	0.983460i	$-0.442027\pi$
$11$	1.20144	0.362247	0.181124	+	0.983460i	$0.442027\pi$
$12$	0.890150	0.256964
$13$	1.53086	0.424584	0.212292	−	0.977206i	$-0.431907\pi$
$13$	1.53086	0.424584	0.212292	+	0.977206i	$0.431907\pi$
$14$	−0.00868301	−0.00232063
$15$	1.53879	0.397314
$16$	3.99960	0.999900
$17$	0.0987406	0.0239481	0.0119741	−	0.999928i	$-0.496188\pi$
$17$	0.0987406	0.0239481	0.0119741	+	0.999928i	$0.496188\pi$
$18$	−0.0229071	−0.00539924
$19$	−6.08964	−1.39706	−0.698530	−	0.715581i	$-0.746162\pi$
$19$	−6.08964	−1.39706	−0.698530	+	0.715581i	$0.746162\pi$
$20$	6.91429	1.54608
$21$	0.472717	0.103155
$22$	0.00982243	0.00209415
$23$	0.357250	0.0744918	0.0372459	−	0.999306i	$-0.488142\pi$
$23$	0.357250	0.0744918	0.0372459	+	0.999306i	$0.488142\pi$
$24$	0.0145552	0.00297107
$25$	6.95263	1.39053
$26$	0.0125156	0.00245452
$27$	2.58237	0.496977
$28$	2.12407	0.401411
$29$	5.47618	1.01690	0.508451	−	0.861091i	$-0.330218\pi$
$29$	5.47618	1.01690	0.508451	+	0.861091i	$0.330218\pi$
$30$	0.0125805	0.00229687
$31$	5.07703	0.911862	0.455931	−	0.890015i	$-0.349306\pi$
$31$	5.07703	0.911862	0.455931	+	0.890015i	$0.349306\pi$
$32$	0.0981023	0.0173422
$33$	−0.534748	−0.0930877
$34$	0.000807260 0	0.000138444 0
$35$	3.67185	0.620656
$36$	5.60360	0.933934
$37$	−4.20663	−0.691565	−0.345783	−	0.938315i	$-0.612387\pi$
$37$	−4.20663	−0.691565	−0.345783	+	0.938315i	$0.612387\pi$
$38$	−0.0497862	−0.00807640
$39$	−0.681370	−0.109106
$40$	0.113058	0.0178761
$41$	4.10036	0.640369	0.320185	−	0.947355i	$-0.396255\pi$
$41$	4.10036	0.640369	0.320185	+	0.947355i	$0.396255\pi$
$42$	0.00386472	0.000596340 0
$43$	10.5737	1.61247	0.806235	−	0.591596i	$-0.201502\pi$
$43$	10.5737	1.61247	0.806235	+	0.591596i	$0.201502\pi$
$44$	−2.40280	−0.362235
$45$	9.68687	1.44403
$46$	0.00292072	0.000430636 0
$47$	−2.20326	−0.321379	−0.160689	−	0.987005i	$-0.551372\pi$
$47$	−2.20326	−0.321379	−0.160689	+	0.987005i	$0.551372\pi$
$48$	−1.78018	−0.256947
$49$	−5.87201	−0.838858
$50$	0.0568417	0.00803863
$51$	−0.0439485	−0.00615402
$52$	−3.06161	−0.424570
$53$	1.17618	0.161561	0.0807805	−	0.996732i	$-0.474259\pi$
$53$	1.17618	0.161561	0.0807805	+	0.996732i	$0.474259\pi$
$54$	0.0211123	0.00287302
$55$	−4.15368	−0.560082
$56$	0.0347315	0.00464119
$57$	2.71044	0.359007
$58$	0.0447709	0.00587870
$59$	4.07464	0.530472	0.265236	−	0.964183i	$-0.414550\pi$
$59$	4.07464	0.530472	0.265236	+	0.964183i	$0.414550\pi$
$60$	−3.07748	−0.397301
$61$	0.772561	0.0989163	0.0494581	−	0.998776i	$-0.484251\pi$
$61$	0.772561	0.0989163	0.0494581	+	0.998776i	$0.484251\pi$
$62$	0.0415076	0.00527147
$63$	2.97581	0.374916
$64$	−7.99840	−0.999799
$65$	−5.29257	−0.656463
$66$	−0.00437187	−0.000538139 0
$67$	0.401418	0.0490410	0.0245205	−	0.999699i	$-0.492194\pi$
$67$	0.401418	0.0490410	0.0245205	+	0.999699i	$0.492194\pi$
$68$	−0.197475	−0.0239473
$69$	−0.159008	−0.0191424
$70$	0.0300194	0.00358801
$71$	3.57752	0.424574	0.212287	−	0.977207i	$-0.431909\pi$
$71$	3.57752	0.424574	0.212287	+	0.977207i	$0.431909\pi$
$72$	0.0916267	0.0107983
$73$	−10.6826	−1.25031	−0.625154	−	0.780501i	$-0.714964\pi$
$73$	−10.6826	−1.25031	−0.625154	+	0.780501i	$0.714964\pi$
$74$	−0.0343915	−0.00399793
$75$	−3.09455	−0.357328
$76$	12.1789	1.39701
$77$	−1.27601	−0.145415
$78$	−0.00557058	−0.000630744 0
$79$	−4.24327	−0.477405	−0.238703	−	0.971093i	$-0.576722\pi$
$79$	−4.24327	−0.477405	−0.238703	+	0.971093i	$0.576722\pi$
$80$	−13.8276	−1.54598
$81$	7.25630	0.806255
$82$	0.0335228	0.00370197
$83$	2.80800	0.308218	0.154109	−	0.988054i	$-0.450749\pi$
$83$	2.80800	0.308218	0.154109	+	0.988054i	$0.450749\pi$
$84$	−0.945402	−0.103152
$85$	−0.341372	−0.0370270
$86$	0.0864456	0.00932167
$87$	−2.43740	−0.261316
$88$	−0.0392891	−0.00418823
$89$	12.4928	1.32424	0.662118	−	0.749399i	$-0.269658\pi$
$89$	12.4928	1.32424	0.662118	+	0.749399i	$0.269658\pi$
$90$	0.0791956	0.00834795
$91$	−1.62588	−0.170438
$92$	−0.714476	−0.0744893
$93$	−2.25974	−0.234324
$94$	−0.0180129	−0.00185789
$95$	21.0535	2.16004
$96$	−0.0436644	−0.00445648
$97$	−5.02154	−0.509860	−0.254930	−	0.966959i	$-0.582052\pi$
$97$	−5.02154	−0.509860	−0.254930	+	0.966959i	$0.582052\pi$
$98$	−0.0480070	−0.00484943
$99$	−3.36630	−0.338326
$100$	−13.9048	−1.39048
$101$	−15.8086	−1.57301	−0.786506	−	0.617583i	$-0.788112\pi$
$101$	−15.8086	−1.57301	−0.786506	+	0.617583i	$0.788112\pi$
$102$	−0.000359303 0	−3.55763e−5 0
$103$	1.35382	0.133396	0.0666978	−	0.997773i	$-0.478754\pi$
$103$	1.35382	0.133396	0.0666978	+	0.997773i	$0.478754\pi$
$104$	−0.0500617	−0.00490895
$105$	−1.63430	−0.159492
$106$	0.00961594	0.000933983 0
$107$	−15.5524	−1.50351	−0.751753	−	0.659444i	$-0.770792\pi$
$107$	−15.5524	−1.50351	−0.751753	+	0.659444i	$0.770792\pi$
$108$	−5.16456	−0.496960
$109$	2.96104	0.283616	0.141808	−	0.989894i	$-0.454708\pi$
$109$	2.96104	0.283616	0.141808	+	0.989894i	$0.454708\pi$
$110$	−0.0339587	−0.00323783
$111$	1.87233	0.177714
$112$	−4.24785	−0.401384
$113$	10.1785	0.957515	0.478758	−	0.877947i	$-0.341087\pi$
$113$	10.1785	0.957515	0.478758	+	0.877947i	$0.341087\pi$
$114$	0.0221594	0.00207541
$115$	−1.23511	−0.115174
$116$	−10.9520	−1.01687
$117$	−4.28930	−0.396546
$118$	0.0333124	0.00306666
$119$	−0.104869	−0.00961336
$120$	−0.0503211	−0.00459366
$121$	−9.55655	−0.868777
$122$	0.00631612	0.000571834 0
$123$	−1.82503	−0.164558
$124$	−10.1537	−0.911832
$125$	−6.75076	−0.603806
$126$	0.0243289	0.00216739
$127$	10.4941	0.931197	0.465598	−	0.884996i	$-0.345839\pi$
$127$	10.4941	0.931197	0.465598	+	0.884996i	$0.345839\pi$
$128$	−0.261596	−0.0231220
$129$	−4.70623	−0.414361
$130$	−0.0432697	−0.00379501
$131$	16.4972	1.44136	0.720682	−	0.693265i	$-0.243829\pi$
$131$	16.4972	1.44136	0.720682	+	0.693265i	$0.243829\pi$
$132$	1.06946	0.0930846
$133$	6.46763	0.560814
$134$	0.00328181	0.000283506 0
$135$	−8.92791	−0.768392
$136$	−0.00322899	−0.000276883 0
$137$	13.8765	1.18555	0.592773	−	0.805370i	$-0.298033\pi$
$137$	13.8765	1.18555	0.592773	+	0.805370i	$0.298033\pi$
$138$	−0.00129998	−0.000110662 0
$139$	−1.41673	−0.120165	−0.0600827	−	0.998193i	$-0.519136\pi$
$139$	−1.41673	−0.120165	−0.0600827	+	0.998193i	$0.519136\pi$
$140$	−7.34345	−0.620635
$141$	0.980650	0.0825856
$142$	0.0292482	0.00245446
$143$	1.83923	0.153804
$144$	−11.2065	−0.933871
$145$	−18.9326	−1.57227
$146$	−0.0873366	−0.00722803
$147$	2.61357	0.215564
$148$	8.41298	0.691542
$149$	17.1937	1.40856	0.704282	−	0.709921i	$-0.251269\pi$
$149$	17.1937	1.40856	0.704282	+	0.709921i	$0.251269\pi$
$150$	−0.0252997	−0.00206571
$151$	9.62322	0.783127	0.391563	−	0.920151i	$-0.371934\pi$
$151$	9.62322	0.783127	0.391563	+	0.920151i	$0.371934\pi$
$152$	0.199142	0.0161525
$153$	−0.276661	−0.0223667
$154$	−0.0104321	−0.000840643 0
$155$	−17.5526	−1.40986
$156$	1.36269	0.109103
$157$	5.65446	0.451275	0.225638	−	0.974211i	$-0.427553\pi$
$157$	5.65446	0.451275	0.225638	+	0.974211i	$0.427553\pi$
$158$	−0.0346911	−0.00275988
$159$	−0.523507	−0.0415168
$160$	−0.339165	−0.0268134
$161$	−0.379424	−0.0299028
$162$	0.0593243	0.00466096
$163$	13.8775	1.08697	0.543484	−	0.839420i	$-0.317105\pi$
$163$	13.8775	1.08697	0.543484	+	0.839420i	$0.317105\pi$
$164$	−8.20045	−0.640348
$165$	1.84876	0.143926
$166$	0.0229569	0.00178180
$167$	−2.63502	−0.203904	−0.101952	−	0.994789i	$-0.532509\pi$
$167$	−2.63502	−0.203904	−0.101952	+	0.994789i	$0.532509\pi$
$168$	−0.0154586	−0.00119266
$169$	−10.6565	−0.819729
$170$	−0.00279091	−0.000214053 0
$171$	17.0625	1.30481
$172$	−21.1466	−1.61242
$173$	−7.77204	−0.590897	−0.295449	−	0.955359i	$-0.595469\pi$
$173$	−7.77204	−0.590897	−0.295449	+	0.955359i	$0.595469\pi$
$174$	−0.0199271	−0.00151067
$175$	−7.38418	−0.558192
$176$	4.80527	0.362211
$177$	−1.81358	−0.136317
$178$	0.102136	0.00765540
$179$	8.89091	0.664537	0.332269	−	0.943185i	$-0.392186\pi$
$179$	8.89091	0.664537	0.332269	+	0.943185i	$0.392186\pi$
$180$	−19.3731	−1.44399
$181$	22.3928	1.66445	0.832223	−	0.554441i	$-0.187068\pi$
$181$	22.3928	1.66445	0.832223	+	0.554441i	$0.187068\pi$
$182$	−0.0132925	−0.000985303 0
$183$	−0.343859	−0.0254188
$184$	−0.0116827	−0.000861258 0
$185$	14.5434	1.06925
$186$	−0.0184746	−0.00135462
$187$	0.118631	0.00867514
$188$	4.40637	0.321368
$189$	−2.74265	−0.199499
$190$	0.172124	0.0124872
$191$	5.16308	0.373587	0.186794	−	0.982399i	$-0.440190\pi$
$191$	5.16308	0.373587	0.186794	+	0.982399i	$0.440190\pi$
$192$	3.56001	0.256921
$193$	14.1283	1.01698	0.508490	−	0.861068i	$-0.330204\pi$
$193$	14.1283	1.01698	0.508490	+	0.861068i	$0.330204\pi$
$194$	−0.0410539	−0.00294750
$195$	2.35567	0.168693
$196$	11.7436	0.838830
$197$	−0.696614	−0.0496317	−0.0248159	−	0.999692i	$-0.507900\pi$
$197$	−0.696614	−0.0496317	−0.0248159	+	0.999692i	$0.507900\pi$
$198$	−0.0275214	−0.00195586
$199$	−14.3219	−1.01526	−0.507628	−	0.861577i	$-0.669477\pi$
$199$	−14.3219	−1.01526	−0.507628	+	0.861577i	$0.669477\pi$
$200$	−0.227363	−0.0160770
$201$	−0.178667	−0.0126022
$202$	−0.129244	−0.00909357
$203$	−5.81609	−0.408209
$204$	0.0878940	0.00615381
$205$	−14.1760	−0.990096
$206$	0.0110682	0.000771159 0
$207$	−1.00098	−0.0695727
$208$	6.12282	0.424541
$209$	−7.31633	−0.506081
$210$	−0.0133613	−0.000922020 0
$211$	−12.7184	−0.875569	−0.437784	−	0.899080i	$-0.644237\pi$
$211$	−12.7184	−0.875569	−0.437784	+	0.899080i	$0.644237\pi$
$212$	−2.35228	−0.161556
$213$	−1.59232	−0.109104
$214$	−0.127150	−0.00869176
$215$	−36.5559	−2.49309
$216$	−0.0844477	−0.00574594
$217$	−5.39216	−0.366044
$218$	0.0242081	0.00163958
$219$	4.75474	0.321295
$220$	8.30709	0.560064
$221$	0.151158	0.0101680
$222$	0.0153073	0.00102736
$223$	−16.4361	−1.10064	−0.550322	−	0.834952i	$-0.685495\pi$
$223$	−16.4361	−1.10064	−0.550322	+	0.834952i	$0.685495\pi$
$224$	−0.104191	−0.00696159
$225$	−19.4805	−1.29870
$226$	0.0832151	0.00553539
$227$	22.1057	1.46721	0.733603	−	0.679579i	$-0.237837\pi$
$227$	22.1057	1.46721	0.733603	+	0.679579i	$0.237837\pi$
$228$	−5.42070	−0.358995
$229$	16.9268	1.11856	0.559278	−	0.828980i	$-0.311079\pi$
$229$	16.9268	1.11856	0.559278	+	0.828980i	$0.311079\pi$
$230$	−0.0100977	−0.000665821 0
$231$	0.567940	0.0373677
$232$	−0.179080	−0.0117572
$233$	13.4921	0.883897	0.441948	−	0.897040i	$-0.354287\pi$
$233$	13.4921	0.883897	0.441948	+	0.897040i	$0.354287\pi$
$234$	−0.0350675	−0.00229243
$235$	7.61724	0.496894
$236$	−8.14900	−0.530455
$237$	1.88864	0.122680
$238$	−0.000857366 0	−5.55748e−5 0
$239$	3.21795	0.208152	0.104076	−	0.994569i	$-0.466812\pi$
$239$	3.21795	0.208152	0.104076	+	0.994569i	$0.466812\pi$
$240$	6.15455	0.397274
$241$	−25.2127	−1.62409	−0.812047	−	0.583592i	$-0.801647\pi$
$241$	−25.2127	−1.62409	−0.812047	+	0.583592i	$0.801647\pi$
$242$	−0.0781301	−0.00502239
$243$	−10.9768	−0.704162
$244$	−1.54507	−0.0989130
$245$	20.3011	1.29699
$246$	−0.0149206	−0.000951306 0
$247$	−9.32238	−0.593169
$248$	−0.166028	−0.0105428
$249$	−1.24981	−0.0792036
$250$	−0.0551912	−0.00349060
$251$	−13.1820	−0.832039	−0.416019	−	0.909356i	$-0.636575\pi$
$251$	−13.1820	−0.832039	−0.416019	+	0.909356i	$0.636575\pi$
$252$	−5.95141	−0.374904
$253$	0.429214	0.0269844
$254$	0.0857948	0.00538324
$255$	0.151941	0.00951493
$256$	15.9947	0.999666
$257$	−2.07497	−0.129433	−0.0647164	−	0.997904i	$-0.520614\pi$
$257$	−2.07497	−0.129433	−0.0647164	+	0.997904i	$0.520614\pi$
$258$	−0.0384761	−0.00239542
$259$	4.46773	0.277611
$260$	10.5848	0.656441
$261$	−15.3437	−0.949751
$262$	0.134874	0.00833252
$263$	−24.5387	−1.51312	−0.756560	−	0.653925i	$-0.773121\pi$
$263$	−24.5387	−1.51312	−0.756560	+	0.653925i	$0.773121\pi$
$264$	0.0174872	0.00107626
$265$	−4.06636	−0.249795
$266$	0.0528764	0.00324206
$267$	−5.56043	−0.340293
$268$	−0.802809	−0.0490394
$269$	17.7604	1.08287	0.541435	−	0.840743i	$-0.317881\pi$
$269$	17.7604	1.08287	0.541435	+	0.840743i	$0.317881\pi$
$270$	−0.0729906	−0.00444207
$271$	1.58281	0.0961488	0.0480744	−	0.998844i	$-0.484692\pi$
$271$	1.58281	0.0961488	0.0480744	+	0.998844i	$0.484692\pi$
$272$	0.394923	0.0239457
$273$	0.723662	0.0437980
$274$	0.113448	0.00685363
$275$	8.35316	0.503714
$276$	0.318006	0.0191417
$277$	11.4746	0.689442	0.344721	−	0.938705i	$-0.387974\pi$
$277$	11.4746	0.689442	0.344721	+	0.938705i	$0.387974\pi$
$278$	−0.0115826	−0.000694675 0
$279$	−14.2253	−0.851647
$280$	−0.120076	−0.00717589
$281$	12.2204	0.729009	0.364504	−	0.931202i	$-0.381238\pi$
$281$	12.2204	0.729009	0.364504	+	0.931202i	$0.381238\pi$
$282$	0.00801736	0.000477427 0
$283$	−28.8609	−1.71560	−0.857800	−	0.513983i	$-0.828169\pi$
$283$	−28.8609	−1.71560	−0.857800	+	0.513983i	$0.828169\pi$
$284$	−7.15481	−0.424560
$285$	−9.37069	−0.555072
$286$	0.0150367	0.000889141 0
$287$	−4.35487	−0.257060
$288$	−0.274872	−0.0161970
$289$	−16.9903	−0.999426
$290$	−0.154784	−0.00908926
$291$	2.23504	0.131020
$292$	21.3646	1.25027
$293$	21.0437	1.22939	0.614693	−	0.788766i	$-0.289280\pi$
$293$	21.0437	1.22939	0.614693	+	0.788766i	$0.289280\pi$
$294$	0.0213674	0.00124617
$295$	−14.0871	−0.820181
$296$	0.137564	0.00799574
$297$	3.10255	0.180028
$298$	0.140568	0.00814290
$299$	0.546899	0.0316280
$300$	6.18889	0.357316
$301$	−11.2300	−0.647285
$302$	0.0786752	0.00452725
$303$	7.03624	0.404221
$304$	−24.3561	−1.39692
$305$	−2.67094	−0.152938
$306$	−0.00226186	−0.000129302 0
$307$	16.6024	0.947547	0.473773	−	0.880647i	$-0.342892\pi$
$307$	16.6024	0.947547	0.473773	+	0.880647i	$0.342892\pi$
$308$	2.55194	0.145410
$309$	−0.602570	−0.0342790
$310$	−0.143502	−0.00815039
$311$	5.46022	0.309621	0.154810	−	0.987944i	$-0.450523\pi$
$311$	5.46022	0.309621	0.154810	+	0.987944i	$0.450523\pi$
$312$	0.0222819	0.00126147
$313$	24.4129	1.37990	0.689948	−	0.723859i	$-0.257633\pi$
$313$	24.4129	1.37990	0.689948	+	0.723859i	$0.257633\pi$
$314$	0.0462284	0.00260882
$315$	−10.2881	−0.579671
$316$	8.48625	0.477389
$317$	20.1109	1.12954	0.564769	−	0.825249i	$-0.308965\pi$
$317$	20.1109	1.12954	0.564769	+	0.825249i	$0.308965\pi$
$318$	−0.00427996	−0.000240008 0
$319$	6.57930	0.368370
$320$	27.6525	1.54582
$321$	6.92222	0.386360
$322$	−0.00310200	−0.000172868 0
$323$	−0.601295	−0.0334570
$324$	−14.5121	−0.806228
$325$	10.6435	0.590395
$326$	0.113456	0.00628375
$327$	−1.31793	−0.0728816
$328$	−0.134089	−0.00740382
$329$	2.34002	0.129009
$330$	0.0151147	0.000832035 0
$331$	−12.6556	−0.695613	−0.347806	−	0.937566i	$-0.613073\pi$
$331$	−12.6556	−0.695613	−0.347806	+	0.937566i	$0.613073\pi$
$332$	−5.61580	−0.308207
$333$	11.7865	0.645898
$334$	−0.0215427	−0.00117877
$335$	−1.38780	−0.0758239
$336$	1.89068	0.103145
$337$	−4.96487	−0.270453	−0.135227	−	0.990815i	$-0.543176\pi$
$337$	−4.96487	−0.270453	−0.135227	+	0.990815i	$0.543176\pi$
$338$	−0.0871226	−0.00473885
$339$	−4.53036	−0.246055
$340$	0.682721	0.0370257
$341$	6.09974	0.330320
$342$	0.139496	0.00754307
$343$	13.6710	0.738163
$344$	−0.345777	−0.0186430
$345$	0.549733	0.0295966
$346$	−0.0635408	−0.00341597
$347$	−0.321669	−0.0172681	−0.00863406	−	0.999963i	$-0.502748\pi$
$347$	−0.321669	−0.0172681	−0.00863406	+	0.999963i	$0.502748\pi$
$348$	4.87463	0.261307
$349$	−5.61439	−0.300531	−0.150266	−	0.988646i	$-0.548013\pi$
$349$	−5.61439	−0.300531	−0.150266	+	0.988646i	$0.548013\pi$
$350$	−0.0603698	−0.00322690
$351$	3.95324	0.211008
$352$	0.117864	0.00628217
$353$	35.7761	1.90417	0.952085	−	0.305832i	$-0.0989347\pi$
$353$	35.7761	1.90417	0.952085	+	0.305832i	$0.0989347\pi$
$354$	−0.0148270	−0.000788048 0
$355$	−12.3684	−0.656447
$356$	−24.9848	−1.32419
$357$	0.0466763	0.00247037
$358$	0.0726881	0.00384169
$359$	5.32816	0.281209	0.140605	−	0.990066i	$-0.455095\pi$
$359$	5.32816	0.281209	0.140605	+	0.990066i	$0.455095\pi$
$360$	−0.316777	−0.0166956
$361$	18.0838	0.951778
$362$	0.183074	0.00962215
$363$	4.25352	0.223252
$364$	3.25165	0.170433
$365$	36.9326	1.93314
$366$	−0.00281124	−0.000146946 0
$367$	12.9212	0.674482	0.337241	−	0.941418i	$-0.390506\pi$
$367$	12.9212	0.674482	0.337241	+	0.941418i	$0.390506\pi$
$368$	1.42886	0.0744843
$369$	−11.4888	−0.598082
$370$	0.118900	0.00618134
$371$	−1.24919	−0.0648545
$372$	4.51932	0.234316
$373$	16.5779	0.858369	0.429185	−	0.903217i	$-0.358801\pi$
$373$	16.5779	0.858369	0.429185	+	0.903217i	$0.358801\pi$
$374$	0.000969873 0	5.01509e−5 0
$375$	3.00470	0.155162
$376$	0.0720504	0.00371571
$377$	8.38326	0.431760
$378$	−0.0224227	−0.00115330
$379$	8.50362	0.436801	0.218401	−	0.975859i	$-0.429916\pi$
$379$	8.50362	0.436801	0.218401	+	0.975859i	$0.429916\pi$
$380$	−42.1055	−2.15997
$381$	−4.67080	−0.239292
$382$	0.0422111	0.00215971
$383$	21.9089	1.11949	0.559746	−	0.828664i	$-0.310899\pi$
$383$	21.9089	1.11949	0.559746	+	0.828664i	$0.310899\pi$
$384$	0.116434	0.00594174
$385$	4.41150	0.224831
$386$	0.115507	0.00587916
$387$	−29.6263	−1.50599
$388$	10.0427	0.509843
$389$	33.1119	1.67884	0.839420	−	0.543483i	$-0.182895\pi$
$389$	33.1119	1.67884	0.839420	+	0.543483i	$0.182895\pi$
$390$	0.0192589	0.000975214 0
$391$	0.0352751	0.00178394
$392$	0.192025	0.00969871
$393$	−7.34273	−0.370392
$394$	−0.00569521	−0.000286921 0
$395$	14.6701	0.738132
$396$	6.73238	0.338315
$397$	19.6035	0.983873	0.491936	−	0.870631i	$-0.336289\pi$
$397$	19.6035	0.983873	0.491936	+	0.870631i	$0.336289\pi$
$398$	−0.117090	−0.00586918
$399$	−2.87868	−0.144114
$400$	27.8077	1.39039
$401$	−0.544957	−0.0272138	−0.0136069	−	0.999907i	$-0.504331\pi$
$401$	−0.544957	−0.0272138	−0.0136069	+	0.999907i	$0.504331\pi$
$402$	−0.00146070	−7.28533e−5 0
$403$	7.77222	0.387162
$404$	31.6161	1.57296
$405$	−25.0869	−1.24658
$406$	−0.0475498	−0.00235986
$407$	−5.05400	−0.250518
$408$	0.00143719	7.11515e−5 0
$409$	−2.71481	−0.134239	−0.0671193	−	0.997745i	$-0.521381\pi$
$409$	−2.71481	−0.134239	−0.0671193	+	0.997745i	$0.521381\pi$
$410$	−0.115897	−0.00572374
$411$	−6.17627	−0.304653
$412$	−2.70754	−0.133391
$413$	−4.32755	−0.212945
$414$	−0.00818354	−0.000402199 0
$415$	−9.70797	−0.476545
$416$	0.150181	0.00736322
$417$	0.630572	0.0308793
$418$	−0.0598151	−0.00292565
$419$	−36.0326	−1.76031	−0.880155	−	0.474687i	$-0.842561\pi$
$419$	−36.0326	−1.76031	−0.880155	+	0.474687i	$0.842561\pi$
$420$	3.26850	0.159486
$421$	2.98907	0.145678	0.0728391	−	0.997344i	$-0.476794\pi$
$421$	2.98907	0.145678	0.0728391	+	0.997344i	$0.476794\pi$
$422$	−0.103980	−0.00506166
$423$	6.17331	0.300156
$424$	−0.0384631	−0.00186793
$425$	0.686508	0.0333005
$426$	−0.0130181	−0.000630729 0
$427$	−0.820513	−0.0397074
$428$	31.1037	1.50346
$429$	−0.818624	−0.0395235
$430$	−0.298865	−0.0144125
$431$	−4.83216	−0.232757	−0.116379	−	0.993205i	$-0.537129\pi$
$431$	−4.83216	−0.232757	−0.116379	+	0.993205i	$0.537129\pi$
$432$	10.3284	0.496927
$433$	−17.9097	−0.860685	−0.430343	−	0.902666i	$-0.641607\pi$
$433$	−17.9097	−0.860685	−0.430343	+	0.902666i	$0.641607\pi$
$434$	−0.0440839	−0.00211610
$435$	8.42671	0.404030
$436$	−5.92188	−0.283607
$437$	−2.17553	−0.104069
$438$	0.0388726	0.00185741
$439$	−16.5856	−0.791588	−0.395794	−	0.918339i	$-0.629531\pi$
$439$	−16.5856	−0.791588	−0.395794	+	0.918339i	$0.629531\pi$
$440$	0.135832	0.00647556
$441$	16.4528	0.783464
$442$	0.00123580	5.87810e−5 0
$443$	−16.2470	−0.771919	−0.385959	−	0.922516i	$-0.626129\pi$
$443$	−16.2470	−0.771919	−0.385959	+	0.922516i	$0.626129\pi$
$444$	−3.74453	−0.177708
$445$	−43.1909	−2.04745
$446$	−0.134375	−0.00636282
$447$	−7.65275	−0.361963
$448$	8.49485	0.401344
$449$	17.0533	0.804793	0.402396	−	0.915466i	$-0.368177\pi$
$449$	17.0533	0.804793	0.402396	+	0.915466i	$0.368177\pi$
$450$	−0.159264	−0.00750779
$451$	4.92633	0.231972
$452$	−20.3564	−0.957483
$453$	−4.28320	−0.201242
$454$	0.180726	0.00848190
$455$	5.62108	0.263520
$456$	−0.0886360	−0.00415076
$457$	−16.1782	−0.756786	−0.378393	−	0.925645i	$-0.623523\pi$
$457$	−16.1782	−0.756786	−0.378393	+	0.925645i	$0.623523\pi$
$458$	0.138386	0.00646636
$459$	0.254984	0.0119017
$460$	2.47013	0.115170
$461$	9.86052	0.459250	0.229625	−	0.973279i	$-0.426250\pi$
$461$	9.86052	0.459250	0.229625	+	0.973279i	$0.426250\pi$
$462$	0.00464322	0.000216022 0
$463$	−5.45892	−0.253698	−0.126849	−	0.991922i	$-0.540486\pi$
$463$	−5.45892	−0.253698	−0.126849	+	0.991922i	$0.540486\pi$
$464$	21.9025	1.01680
$465$	7.81250	0.362296
$466$	0.110305	0.00510980
$467$	−22.3321	−1.03340	−0.516702	−	0.856165i	$-0.672841\pi$
$467$	−22.3321	−1.03340	−0.516702	+	0.856165i	$0.672841\pi$
$468$	8.57832	0.396533
$469$	−0.426334	−0.0196863
$470$	0.0622752	0.00287254
$471$	−2.51675	−0.115966
$472$	−0.133247	−0.00613321
$473$	12.7036	0.584112
$474$	0.0154407	0.000709213 0
$475$	−42.3391	−1.94265
$476$	0.209732	0.00961304
$477$	−3.29554	−0.150892
$478$	0.0263085	0.00120332
$479$	1.27952	0.0584627	0.0292313	−	0.999573i	$-0.490694\pi$
$479$	1.27952	0.0584627	0.0292313	+	0.999573i	$0.490694\pi$
$480$	0.150959	0.00689031
$481$	−6.43975	−0.293627
$482$	−0.206128	−0.00938888
$483$	0.168878	0.00768421
$484$	19.1125	0.868748
$485$	17.3608	0.788311
$486$	−0.0897415	−0.00407076
$487$	−23.4380	−1.06208	−0.531039	−	0.847347i	$-0.678198\pi$
$487$	−23.4380	−1.06208	−0.531039	+	0.847347i	$0.678198\pi$
$488$	−0.0252640	−0.00114365
$489$	−6.17673	−0.279321
$490$	0.165972	0.00749787
$491$	16.9198	0.763582	0.381791	−	0.924249i	$-0.375307\pi$
$491$	16.9198	0.763582	0.381791	+	0.924249i	$0.375307\pi$
$492$	3.64994	0.164552
$493$	0.540722	0.0243529
$494$	−0.0762157	−0.00342911
$495$	11.6382	0.523097
$496$	20.3061	0.911771
$497$	−3.79958	−0.170434
$498$	−0.0102179	−0.000457875 0
$499$	2.14471	0.0960103	0.0480051	−	0.998847i	$-0.484714\pi$
$499$	2.14471	0.0960103	0.0480051	+	0.998847i	$0.484714\pi$
$500$	13.5011	0.603786
$501$	1.17282	0.0523977
$502$	−0.107770	−0.00481001
$503$	33.0397	1.47317	0.736583	−	0.676347i	$-0.236438\pi$
$503$	33.0397	1.47317	0.736583	+	0.676347i	$0.236438\pi$
$504$	−0.0973139	−0.00433471
$505$	54.6543	2.43208
$506$	0.00350906	0.000155997 0
$507$	4.74309	0.210648
$508$	−20.9874	−0.931166
$509$	−14.2329	−0.630862	−0.315431	−	0.948948i	$-0.602149\pi$
$509$	−14.2329	−0.630862	−0.315431	+	0.948948i	$0.602149\pi$
$510$	0.00124220	5.50057e−5 0
$511$	11.3457	0.501904
$512$	0.653957	0.0289011
$513$	−15.7257	−0.694306
$514$	−0.0169640	−0.000748250 0
$515$	−4.68049	−0.206247
$516$	9.41215	0.414347
$517$	−2.64708	−0.116419
$518$	0.0365262	0.00160487
$519$	3.45926	0.151845
$520$	0.173076	0.00758989
$521$	−15.3143	−0.670931	−0.335465	−	0.942053i	$-0.608894\pi$
$521$	−15.3143	−0.670931	−0.335465	+	0.942053i	$0.608894\pi$
$522$	−0.125443	−0.00549050
$523$	9.16522	0.400767	0.200384	−	0.979718i	$-0.435781\pi$
$523$	9.16522	0.400767	0.200384	+	0.979718i	$0.435781\pi$
$524$	−32.9932	−1.44132
$525$	3.28663	0.143440
$526$	−0.200617	−0.00874733
$527$	0.501310	0.0218374
$528$	−2.13878	−0.0930784
$529$	−22.8724	−0.994451
$530$	−0.0332448	−0.00144406
$531$	−11.4167	−0.495443
$532$	−12.9348	−0.560795
$533$	6.27708	0.271890
$534$	−0.0454596	−0.00196723
$535$	53.7686	2.32462
$536$	−0.0131270	−0.000567002 0
$537$	−3.95725	−0.170768
$538$	0.145201	0.00626006
$539$	−7.05485	−0.303874
$540$	17.8552	0.768366
$541$	−0.910723	−0.0391550	−0.0195775	−	0.999808i	$-0.506232\pi$
$541$	−0.910723	−0.0391550	−0.0195775	+	0.999808i	$0.506232\pi$
$542$	0.0129403	0.000555836 0
$543$	−9.96683	−0.427717
$544$	0.00968669	0.000415313 0
$545$	−10.2371	−0.438508
$546$	0.00591634	0.000253196 0
$547$	42.1417	1.80185	0.900924	−	0.433978i	$-0.142890\pi$
$547$	42.1417	1.80185	0.900924	+	0.433978i	$0.142890\pi$
$548$	−27.7520	−1.18551
$549$	−2.16463	−0.0923843
$550$	0.0682917	0.00291197
$551$	−33.3480	−1.42067
$552$	0.00519984	0.000221320 0
$553$	4.50665	0.191642
$554$	0.0938112	0.00398566
$555$	−6.47312	−0.274769
$556$	2.83336	0.120161
$557$	42.2744	1.79122	0.895611	−	0.444838i	$-0.146739\pi$
$557$	42.2744	1.79122	0.895611	+	0.444838i	$0.146739\pi$
$558$	−0.116300	−0.00492337
$559$	16.1868	0.684628
$560$	14.6859	0.620593
$561$	−0.0528014	−0.00222928
$562$	0.0999087	0.00421439
$563$	−32.2915	−1.36093	−0.680463	−	0.732782i	$-0.738221\pi$
$563$	−32.2915	−1.36093	−0.680463	+	0.732782i	$0.738221\pi$
$564$	−1.96123	−0.0825828
$565$	−35.1898	−1.48045
$566$	−0.235954	−0.00991787
$567$	−7.70669	−0.323651
$568$	−0.116991	−0.00490883
$569$	−23.1732	−0.971469	−0.485735	−	0.874106i	$-0.661448\pi$
$569$	−23.1732	−0.971469	−0.485735	+	0.874106i	$0.661448\pi$
$570$	−0.0766107	−0.00320887
$571$	−11.2243	−0.469723	−0.234862	−	0.972029i	$-0.575464\pi$
$571$	−11.2243	−0.469723	−0.234862	+	0.972029i	$0.575464\pi$
$572$	−3.67834	−0.153799
$573$	−2.29804	−0.0960018
$574$	−0.0356035	−0.00148606
$575$	2.48383	0.103583
$576$	22.4107	0.933778
$577$	5.55603	0.231300	0.115650	−	0.993290i	$-0.463105\pi$
$577$	5.55603	0.231300	0.115650	+	0.993290i	$0.463105\pi$
$578$	−0.138905	−0.00577768
$579$	−6.28838	−0.261336
$580$	37.8639	1.57221
$581$	−2.98229	−0.123726
$582$	0.0182727	0.000757427 0
$583$	1.41311	0.0585250
$584$	0.349340	0.0144558
$585$	14.8292	0.613113
$586$	0.172044	0.00710707
$587$	−13.5097	−0.557603	−0.278802	−	0.960349i	$-0.589937\pi$
$587$	−13.5097	−0.557603	−0.278802	+	0.960349i	$0.589937\pi$
$588$	−5.22697	−0.215557
$589$	−30.9173	−1.27393
$590$	−0.115170	−0.00474146
$591$	0.310056	0.0127540
$592$	−16.8248	−0.691496
$593$	0.742475	0.0304898	0.0152449	−	0.999884i	$-0.495147\pi$
$593$	0.742475	0.0304898	0.0152449	+	0.999884i	$0.495147\pi$
$594$	0.0253651	0.00104074
$595$	0.362561	0.0148635
$596$	−34.3863	−1.40852
$597$	6.37455	0.260893
$598$	0.00447120	0.000182841 0
$599$	33.2242	1.35751	0.678753	−	0.734367i	$-0.262521\pi$
$599$	33.2242	1.35751	0.678753	+	0.734367i	$0.262521\pi$
$600$	0.101197	0.00413135
$601$	−14.3262	−0.584378	−0.292189	−	0.956361i	$-0.594384\pi$
$601$	−14.3262	−0.584378	−0.292189	+	0.956361i	$0.594384\pi$
$602$	−0.0918113	−0.00374195
$603$	−1.12473	−0.0458026
$604$	−19.2458	−0.783100
$605$	33.0394	1.34324
$606$	0.0575252	0.00233680
$607$	30.9448	1.25601	0.628004	−	0.778210i	$-0.283872\pi$
$607$	30.9448	1.25601	0.628004	+	0.778210i	$0.283872\pi$
$608$	−0.597408	−0.0242281
$609$	2.58868	0.104899
$610$	−0.0218364	−0.000884132 0
$611$	−3.37288	−0.136452
$612$	0.553303	0.0223660
$613$	−16.2656	−0.656960	−0.328480	−	0.944511i	$-0.606536\pi$
$613$	−16.2656	−0.656960	−0.328480	+	0.944511i	$0.606536\pi$
$614$	0.135734	0.00547776
$615$	6.30960	0.254428
$616$	0.0417277	0.00168126
$617$	−24.0958	−0.970059	−0.485029	−	0.874498i	$-0.661191\pi$
$617$	−24.0958	−0.970059	−0.485029	+	0.874498i	$0.661191\pi$
$618$	−0.00492635	−0.000198167 0
$619$	−30.3476	−1.21977	−0.609886	−	0.792489i	$-0.708785\pi$
$619$	−30.3476	−1.21977	−0.609886	+	0.792489i	$0.708785\pi$
$620$	35.1041	1.40981
$621$	0.922550	0.0370207
$622$	0.0446403	0.00178991
$623$	−13.2682	−0.531581
$624$	−2.72521	−0.109096
$625$	−11.4240	−0.456962
$626$	0.199589	0.00797717
$627$	3.25643	0.130049
$628$	−11.3085	−0.451260
$629$	−0.415365	−0.0165617
$630$	−0.0841112	−0.00335107
$631$	−4.93910	−0.196623	−0.0983113	−	0.995156i	$-0.531344\pi$
$631$	−4.93910	−0.196623	−0.0983113	+	0.995156i	$0.531344\pi$
$632$	0.138762	0.00551966
$633$	5.66082	0.224997
$634$	0.164418	0.00652986
$635$	−36.2807	−1.43975
$636$	1.04698	0.0415154
$637$	−8.98921	−0.356166
$638$	0.0537894	0.00212954
$639$	−10.0238	−0.396537
$640$	0.904405	0.0357497
$641$	2.25217	0.0889553	0.0444776	−	0.999010i	$-0.485838\pi$
$641$	2.25217	0.0889553	0.0444776	+	0.999010i	$0.485838\pi$
$642$	0.0565930	0.00223355
$643$	3.80037	0.149872	0.0749361	−	0.997188i	$-0.476125\pi$
$643$	3.80037	0.149872	0.0749361	+	0.997188i	$0.476125\pi$
$644$	0.758823	0.0299018
$645$	16.2707	0.640657
$646$	−0.00491593	−0.000193415 0
$647$	−44.4910	−1.74912	−0.874561	−	0.484915i	$-0.838850\pi$
$647$	−44.4910	−1.74912	−0.874561	+	0.484915i	$0.838850\pi$
$648$	−0.237293	−0.00932176
$649$	4.89542	0.192162
$650$	0.0870165	0.00341307
$651$	2.40000	0.0940633
$652$	−27.7540	−1.08693
$653$	11.2191	0.439039	0.219519	−	0.975608i	$-0.429551\pi$
$653$	11.2191	0.439039	0.219519	+	0.975608i	$0.429551\pi$
$654$	−0.0107748	−0.000421328 0
$655$	−57.0350	−2.22854
$656$	16.3998	0.640305
$657$	29.9316	1.16774
$658$	0.0191309	0.000745802 0
$659$	22.3612	0.871068	0.435534	−	0.900172i	$-0.356560\pi$
$659$	22.3612	0.871068	0.435534	+	0.900172i	$0.356560\pi$
$660$	−3.69740	−0.143921
$661$	43.4338	1.68938	0.844690	−	0.535255i	$-0.179785\pi$
$661$	43.4338	1.68938	0.844690	+	0.535255i	$0.179785\pi$
$662$	−0.103466	−0.00402133
$663$	−0.0672789	−0.00261290
$664$	−0.0918262	−0.00356355
$665$	−22.3602	−0.867093
$666$	0.0963615	0.00373393
$667$	1.95637	0.0757508
$668$	5.26985	0.203897
$669$	7.31556	0.282836
$670$	−0.0113461	−0.000438337 0
$671$	0.928184	0.0358321
$672$	0.0463746	0.00178894
$673$	−23.7814	−0.916706	−0.458353	−	0.888770i	$-0.651561\pi$
$673$	−23.7814	−0.916706	−0.458353	+	0.888770i	$0.651561\pi$
$674$	−0.0405905	−0.00156349
$675$	17.9542	0.691059
$676$	21.3122	0.819701
$677$	−5.41410	−0.208081	−0.104040	−	0.994573i	$-0.533177\pi$
$677$	−5.41410	−0.208081	−0.104040	+	0.994573i	$0.533177\pi$
$678$	−0.0370382	−0.00142244
$679$	5.33322	0.204670
$680$	0.0111634	0.000428098 0
$681$	−9.83902	−0.377032
$682$	0.0498688	0.00190957
$683$	34.0531	1.30301	0.651504	−	0.758646i	$-0.274139\pi$
$683$	34.0531	1.30301	0.651504	+	0.758646i	$0.274139\pi$
$684$	−34.1239	−1.30476
$685$	−47.9745	−1.83301
$686$	0.111768	0.00426731
$687$	−7.53396	−0.287438
$688$	42.2904	1.61231
$689$	1.80057	0.0685961
$690$	0.00449438	0.000171098 0
$691$	−28.0278	−1.06623	−0.533114	−	0.846043i	$-0.678978\pi$
$691$	−28.0278	−1.06623	−0.533114	+	0.846043i	$0.678978\pi$
$692$	15.5436	0.590878
$693$	3.57525	0.135812
$694$	−0.00262983	−9.98269e−5 0
$695$	4.89800	0.185792
$696$	0.0797069	0.00302128
$697$	0.404872	0.0153356
$698$	−0.0459008	−0.00173737
$699$	−6.00520	−0.227138
$700$	14.7679	0.558173
$701$	39.4442	1.48979	0.744894	−	0.667183i	$-0.232500\pi$
$701$	39.4442	1.48979	0.744894	+	0.667183i	$0.232500\pi$
$702$	0.0323199	0.00121984
$703$	25.6169	0.966159
$704$	−9.60958	−0.362175
$705$	−3.39036	−0.127688
$706$	0.292490	0.0110080
$707$	16.7898	0.631445
$708$	3.62704	0.136312
$709$	16.0468	0.602652	0.301326	−	0.953521i	$-0.402571\pi$
$709$	16.0468	0.602652	0.301326	+	0.953521i	$0.402571\pi$
$710$	−0.101119	−0.00379492
$711$	11.8892	0.445880
$712$	−0.408536	−0.0153105
$713$	1.81377	0.0679262
$714$	0.000381605 0	1.42812e−5 0
$715$	−6.35870	−0.237802
$716$	−17.7812	−0.664515
$717$	−1.43228	−0.0534893
$718$	0.0435607	0.00162567
$719$	−22.4529	−0.837350	−0.418675	−	0.908136i	$-0.637505\pi$
$719$	−22.4529	−0.837350	−0.418675	+	0.908136i	$0.637505\pi$
$720$	38.7436	1.44389
$721$	−1.43785	−0.0535482
$722$	0.147845	0.00550222
$723$	11.2219	0.417348
$724$	−44.7842	−1.66439
$725$	38.0739	1.41403
$726$	0.0347749	0.00129062
$727$	−32.1296	−1.19162	−0.595810	−	0.803125i	$-0.703169\pi$
$727$	−32.1296	−1.19162	−0.595810	+	0.803125i	$0.703169\pi$
$728$	0.0531689	0.00197057
$729$	−16.8832	−0.625305
$730$	0.301945	0.0111755
$731$	1.04405	0.0386156
$732$	0.687695	0.0254179
$733$	−0.354611	−0.0130979	−0.00654893	−	0.999979i	$-0.502085\pi$
$733$	−0.354611	−0.0130979	−0.00654893	+	0.999979i	$0.502085\pi$
$734$	0.105638	0.00389917
$735$	−9.03580	−0.333290
$736$	0.0350471	0.00129185
$737$	0.482279	0.0177650
$738$	−0.0939273	−0.00345751
$739$	−27.4002	−1.00793	−0.503966	−	0.863723i	$-0.668126\pi$
$739$	−27.4002	−1.00793	−0.503966	+	0.863723i	$0.668126\pi$
$740$	−29.0858	−1.06922
$741$	4.14930	0.152428
$742$	−0.0102128	−0.000374923 0
$743$	−13.7534	−0.504562	−0.252281	−	0.967654i	$-0.581181\pi$
$743$	−13.7534	−0.504562	−0.252281	+	0.967654i	$0.581181\pi$
$744$	0.0738972	0.00270920
$745$	−59.4431	−2.17783
$746$	0.135533	0.00496223
$747$	−7.86771	−0.287864
$748$	−0.237254	−0.00867485
$749$	16.5177	0.603544
$750$	0.0245651	0.000896990 0
$751$	−32.6482	−1.19135	−0.595674	−	0.803226i	$-0.703115\pi$
$751$	−32.6482	−1.19135	−0.595674	+	0.803226i	$0.703115\pi$
$752$	−8.81216	−0.321346
$753$	5.86716	0.213811
$754$	0.0685379	0.00249600
$755$	−33.2700	−1.21082
$756$	5.48512	0.199492
$757$	18.5037	0.672530	0.336265	−	0.941767i	$-0.390836\pi$
$757$	18.5037	0.672530	0.336265	+	0.941767i	$0.390836\pi$
$758$	0.0695218	0.00252515
$759$	−0.191039	−0.00693427
$760$	−0.688484	−0.0249739
$761$	24.3396	0.882311	0.441155	−	0.897431i	$-0.354569\pi$
$761$	24.3396	0.882311	0.441155	+	0.897431i	$0.354569\pi$
$762$	−0.0381864	−0.00138335
$763$	−3.14483	−0.113850
$764$	−10.3258	−0.373575
$765$	0.956488	0.0345819
$766$	0.179117	0.00647177
$767$	6.23769	0.225230
$768$	−7.11906	−0.256887
$769$	−52.7307	−1.90152	−0.950758	−	0.309934i	$-0.899693\pi$
$769$	−52.7307	−1.90152	−0.950758	+	0.309934i	$0.899693\pi$
$770$	0.0360665	0.00129975
$771$	0.923547	0.0332607
$772$	−28.2557	−1.01695
$773$	12.2488	0.440558	0.220279	−	0.975437i	$-0.429303\pi$
$773$	12.2488	0.440558	0.220279	+	0.975437i	$0.429303\pi$
$774$	−0.242212	−0.00870612
$775$	35.2988	1.26797
$776$	0.164213	0.00589490
$777$	−1.98854	−0.0713386
$778$	0.270708	0.00970536
$779$	−24.9698	−0.894634
$780$	−4.71119	−0.168688
$781$	4.29817	0.153801
$782$	0.000288394 0	1.03129e−5 0
$783$	14.1415	0.505376
$784$	−23.4857	−0.838774
$785$	−19.5489	−0.697732
$786$	−0.0600309	−0.00214123
$787$	1.00000	0.0356462
$787$	1.00000	0.0356462
$788$	1.39318	0.0496301
$789$	10.9219	0.388831
$790$	0.119936	0.00426713
$791$	−10.8103	−0.384370
$792$	0.110084	0.00391166
$793$	1.18268	0.0419982
$794$	0.160270	0.00568776
$795$	1.80990	0.0641905
$796$	28.6429	1.01522
$797$	47.5818	1.68543	0.842716	−	0.538358i	$-0.180955\pi$
$797$	47.5818	1.68543	0.842716	+	0.538358i	$0.180955\pi$
$798$	−0.0235348	−0.000833122 0
$799$	−0.217551	−0.00769641
$800$	0.682070	0.0241148
$801$	−35.0036	−1.23679
$802$	−0.00445533	−0.000157323 0
$803$	−12.8345	−0.452921
$804$	0.357322	0.0126018
$805$	1.31177	0.0462337
$806$	0.0635422	0.00223818
$807$	−7.90497	−0.278268
$808$	0.516967	0.0181868
$809$	−20.0143	−0.703667	−0.351833	−	0.936063i	$-0.614442\pi$
$809$	−20.0143	−0.703667	−0.351833	+	0.936063i	$0.614442\pi$
$810$	−0.205099	−0.00720646
$811$	−47.4322	−1.66557	−0.832784	−	0.553597i	$-0.813255\pi$
$811$	−47.4322	−1.66557	−0.832784	+	0.553597i	$0.813255\pi$
$812$	11.6318	0.408196
$813$	−0.704493	−0.0247076
$814$	−0.0413193	−0.00144824
$815$	−47.9780	−1.68060
$816$	−0.175776	−0.00615340
$817$	−64.3899	−2.25272
$818$	−0.0221951	−0.000776033 0
$819$	4.55554	0.159183
$820$	28.3511	0.990063
$821$	7.58759	0.264809	0.132404	−	0.991196i	$-0.457730\pi$
$821$	7.58759	0.264809	0.132404	+	0.991196i	$0.457730\pi$
$822$	−0.0504945	−0.00176120
$823$	45.8737	1.59906	0.799528	−	0.600629i	$-0.205083\pi$
$823$	45.8737	1.59906	0.799528	+	0.600629i	$0.205083\pi$
$824$	−0.0442721	−0.00154229
$825$	−3.71791	−0.129441
$826$	−0.0353801	−0.00123103
$827$	10.8138	0.376033	0.188017	−	0.982166i	$-0.439794\pi$
$827$	10.8138	0.376033	0.188017	+	0.982166i	$0.439794\pi$
$828$	2.00189	0.0695704
$829$	−31.5870	−1.09706	−0.548531	−	0.836130i	$-0.684813\pi$
$829$	−31.5870	−1.09706	−0.548531	+	0.836130i	$0.684813\pi$
$830$	−0.0793680	−0.00275491
$831$	−5.10723	−0.177168
$832$	−12.2444	−0.424499
$833$	−0.579806	−0.0200891
$834$	0.00515528	0.000178513 0
$835$	9.10993	0.315262
$836$	14.6322	0.506064
$837$	13.1108	0.453174
$838$	−0.294587	−0.0101763
$839$	−42.7629	−1.47634	−0.738170	−	0.674615i	$-0.764310\pi$
$839$	−42.7629	−1.47634	−0.738170	+	0.674615i	$0.764310\pi$
$840$	0.0534445	0.00184401
$841$	0.988594	0.0340895
$842$	0.0244373	0.000842165 0
$843$	−5.43918	−0.187335
$844$	25.4359	0.875540
$845$	36.8422	1.26741
$846$	0.0504702	0.00173520
$847$	10.1497	0.348748
$848$	4.70425	0.161545
$849$	12.8457	0.440863
$850$	0.00561258	0.000192510 0
$851$	−1.50282	−0.0515159
$852$	3.18453	0.109100
$853$	−13.5092	−0.462545	−0.231272	−	0.972889i	$-0.574289\pi$
$853$	−13.5092	−0.462545	−0.231272	+	0.972889i	$0.574289\pi$
$854$	−0.00670815	−0.000229548 0
$855$	−58.9896	−2.01740
$856$	0.508590	0.0173832
$857$	38.3745	1.31085	0.655424	−	0.755261i	$-0.272490\pi$
$857$	38.3745	1.31085	0.655424	+	0.755261i	$0.272490\pi$
$858$	−0.00669271	−0.000228485 0
$859$	−2.64915	−0.0903877	−0.0451938	−	0.998978i	$-0.514391\pi$
$859$	−2.64915	−0.0903877	−0.0451938	+	0.998978i	$0.514391\pi$
$860$	73.1093	2.49301
$861$	1.93831	0.0660574
$862$	−0.0395056	−0.00134557
$863$	−27.0771	−0.921714	−0.460857	−	0.887475i	$-0.652458\pi$
$863$	−27.0771	−0.921714	−0.460857	+	0.887475i	$0.652458\pi$
$864$	0.253336	0.00861867
$865$	26.8700	0.913606
$866$	−0.146422	−0.00497562
$867$	7.56219	0.256826
$868$	10.7840	0.366032
$869$	−5.09803	−0.172939
$870$	0.0688930	0.00233569
$871$	0.614514	0.0208220
$872$	−0.0968310	−0.00327911
$873$	14.0698	0.476191
$874$	−0.0177861	−0.000601625 0
$875$	7.16978	0.242383
$876$	−9.50916	−0.321285
$877$	26.6275	0.899145	0.449573	−	0.893244i	$-0.351576\pi$
$877$	26.6275	0.899145	0.449573	+	0.893244i	$0.351576\pi$
$878$	−0.135597	−0.00457616
$879$	−9.36635	−0.315919
$880$	−16.6131	−0.560026
$881$	−25.2361	−0.850225	−0.425112	−	0.905141i	$-0.639765\pi$
$881$	−25.2361	−0.850225	−0.425112	+	0.905141i	$0.639765\pi$
$882$	0.134510	0.00452920
$883$	10.6676	0.358992	0.179496	−	0.983759i	$-0.442553\pi$
$883$	10.6676	0.358992	0.179496	+	0.983759i	$0.442553\pi$
$884$	−0.302306	−0.0101676
$885$	6.27001	0.210764
$886$	−0.132828	−0.00446246
$887$	6.48531	0.217755	0.108878	−	0.994055i	$-0.465274\pi$
$887$	6.48531	0.217755	0.108878	+	0.994055i	$0.465274\pi$
$888$	−0.0612283	−0.00205469
$889$	−11.1454	−0.373805
$890$	−0.353110	−0.0118363
$891$	8.71799	0.292064
$892$	32.8712	1.10061
$893$	13.4171	0.448985
$894$	−0.0625655	−0.00209250
$895$	−30.7382	−1.02746
$896$	0.277833	0.00928175
$897$	−0.243419	−0.00812753
$898$	0.139420	0.00465250
$899$	27.8028	0.927274
$900$	38.9598	1.29866
$901$	0.116137	0.00386908
$902$	0.0402755	0.00134103
$903$	4.99835	0.166335
$904$	−0.332855	−0.0110706
$905$	−77.4178	−2.57345
$906$	−0.0350176	−0.00116338
$907$	−42.0834	−1.39736	−0.698678	−	0.715437i	$-0.746228\pi$
$907$	−42.0834	−1.39736	−0.698678	+	0.715437i	$0.746228\pi$
$908$	−44.2099	−1.46716
$909$	44.2940	1.46914
$910$	0.0459555	0.00152341
$911$	2.60814	0.0864117	0.0432058	−	0.999066i	$-0.486243\pi$
$911$	2.60814	0.0864117	0.0432058	+	0.999066i	$0.486243\pi$
$912$	10.8407	0.358971
$913$	3.37363	0.111651
$914$	−0.132266	−0.00437498
$915$	1.18881	0.0393008
$916$	−33.8525	−1.11852
$917$	−17.5211	−0.578599
$918$	0.00208464	6.88034e−5 0
$919$	22.2966	0.735498	0.367749	−	0.929925i	$-0.380128\pi$
$919$	22.2966	0.735498	0.367749	+	0.929925i	$0.380128\pi$
$920$	0.0403900	0.00133162
$921$	−7.38955	−0.243494
$922$	0.0806153	0.00265492
$923$	5.47668	0.180267
$924$	−1.13584	−0.0373664
$925$	−29.2471	−0.961640
$926$	−0.0446297	−0.00146662
$927$	−3.79325	−0.124587
$928$	0.537226	0.0176353
$929$	−1.75658	−0.0576316	−0.0288158	−	0.999585i	$-0.509174\pi$
$929$	−1.75658	−0.0576316	−0.0288158	+	0.999585i	$0.509174\pi$
$930$	0.0638715	0.00209443
$931$	35.7584	1.17194
$932$	−26.9833	−0.883867
$933$	−2.43029	−0.0795641
$934$	−0.182577	−0.00597411
$935$	−0.410137	−0.0134129
$936$	0.140267	0.00458479
$937$	15.7354	0.514054	0.257027	−	0.966404i	$-0.417257\pi$
$937$	15.7354	0.514054	0.257027	+	0.966404i	$0.417257\pi$
$938$	−0.00348551	−0.000113806 0
$939$	−10.8659	−0.354596
$940$	−15.2340	−0.496877
$941$	−33.2873	−1.08514	−0.542568	−	0.840012i	$-0.682548\pi$
$941$	−33.2873	−1.08514	−0.542568	+	0.840012i	$0.682548\pi$
$942$	−0.0205758	−0.000670396 0
$943$	1.46485	0.0477022
$944$	16.2969	0.530419
$945$	9.48206	0.308451
$946$	0.103859	0.00337675
$947$	41.2345	1.33994	0.669970	−	0.742388i	$-0.266307\pi$
$947$	41.2345	1.33994	0.669970	+	0.742388i	$0.266307\pi$
$948$	−3.77715	−0.122676
$949$	−16.3536	−0.530861
$950$	−0.346146	−0.0112304
$951$	−8.95115	−0.290261
$952$	0.00342941	0.000111148 0
$953$	−6.56705	−0.212728	−0.106364	−	0.994327i	$-0.533921\pi$
$953$	−6.56705	−0.212728	−0.106364	+	0.994327i	$0.533921\pi$
$954$	−0.0269429	−0.000872307 0
$955$	−17.8501	−0.577616
$956$	−6.43568	−0.208145
$957$	−2.92838	−0.0946611
$958$	0.0104608	0.000337972 0
$959$	−14.7378	−0.475907
$960$	−12.3079	−0.397235
$961$	−5.22373	−0.168507
$962$	−0.0526486	−0.00169746
$963$	43.5762	1.40422
$964$	50.4238	1.62404
$965$	−48.8453	−1.57239
$966$	0.00138067	4.44224e−5 0
$967$	46.9509	1.50984	0.754920	−	0.655817i	$-0.227676\pi$
$967$	46.9509	1.50984	0.754920	+	0.655817i	$0.227676\pi$
$968$	0.312515	0.0100446
$969$	0.267631	0.00859753
$970$	0.141934	0.00455722
$971$	−33.0339	−1.06011	−0.530054	−	0.847964i	$-0.677828\pi$
$971$	−33.0339	−1.06011	−0.530054	+	0.847964i	$0.677828\pi$
$972$	21.9529	0.704139
$973$	1.50466	0.0482373
$974$	−0.191619	−0.00613986
$975$	−4.73732	−0.151716
$976$	3.08993	0.0989063
$977$	6.26226	0.200348	0.100174	−	0.994970i	$-0.468060\pi$
$977$	6.26226	0.200348	0.100174	+	0.994970i	$0.468060\pi$
$978$	−0.0504982	−0.00161475
$979$	15.0094	0.479701
$980$	−40.6007	−1.29694
$981$	−8.29652	−0.264887
$982$	0.138329	0.00441426
$983$	−13.2316	−0.422023	−0.211011	−	0.977484i	$-0.567676\pi$
$983$	−13.2316	−0.422023	−0.211011	+	0.977484i	$0.567676\pi$
$984$	0.0596816	0.00190258
$985$	2.40838	0.0767372
$986$	0.00442070	0.000140784 0
$987$	−1.04152	−0.0331519
$988$	18.6441	0.593149
$989$	3.77744	0.120116
$990$	0.0951486	0.00302402
$991$	27.8792	0.885612	0.442806	−	0.896617i	$-0.353983\pi$
$991$	27.8792	0.885612	0.442806	+	0.896617i	$0.353983\pi$
$992$	0.498069	0.0158137
$993$	5.63287	0.178754
$994$	−0.0310637	−0.000985280 0
$995$	49.5146	1.56972
$996$	2.49954	0.0792009
$997$	13.4478	0.425896	0.212948	−	0.977063i	$-0.431693\pi$
$997$	13.4478	0.425896	0.212948	+	0.977063i	$0.431693\pi$
$998$	0.0175342	0.000555035 0
$999$	−10.8631	−0.343692

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	787.2.a.b.1.17	✓	37
3.2	odd	2		7083.2.a.g.1.21		37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
787.2.a.b.1.17	✓	37	1.1	even	1	trivial
7083.2.a.g.1.21		37	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 787 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	787.a (trivial)

\(f(q)\)	\(=\)	\(q+0.00817556 q^{2} -0.445090 q^{3} -1.99993 q^{4} -3.45726 q^{5} -0.00363886 q^{6} -1.06207 q^{7} -0.0327017 q^{8} -2.80189 q^{9} -0.0282650 q^{10} +1.20144 q^{11} +0.890150 q^{12} +1.53086 q^{13} -0.00868301 q^{14} +1.53879 q^{15} +3.99960 q^{16} +0.0987406 q^{17} -0.0229071 q^{18} -6.08964 q^{19} +6.91429 q^{20} +0.472717 q^{21} +0.00982243 q^{22} +0.357250 q^{23} +0.0145552 q^{24} +6.95263 q^{25} +0.0125156 q^{26} +2.58237 q^{27} +2.12407 q^{28} +5.47618 q^{29} +0.0125805 q^{30} +5.07703 q^{31} +0.0981023 q^{32} -0.534748 q^{33} +0.000807260 q^{34} +3.67185 q^{35} +5.60360 q^{36} -4.20663 q^{37} -0.0497862 q^{38} -0.681370 q^{39} +0.113058 q^{40} +4.10036 q^{41} +0.00386472 q^{42} +10.5737 q^{43} -2.40280 q^{44} +9.68687 q^{45} +0.00292072 q^{46} -2.20326 q^{47} -1.78018 q^{48} -5.87201 q^{49} +0.0568417 q^{50} -0.0439485 q^{51} -3.06161 q^{52} +1.17618 q^{53} +0.0211123 q^{54} -4.15368 q^{55} +0.0347315 q^{56} +2.71044 q^{57} +0.0447709 q^{58} +4.07464 q^{59} -3.07748 q^{60} +0.772561 q^{61} +0.0415076 q^{62} +2.97581 q^{63} -7.99840 q^{64} -5.29257 q^{65} -0.00437187 q^{66} +0.401418 q^{67} -0.197475 q^{68} -0.159008 q^{69} +0.0300194 q^{70} +3.57752 q^{71} +0.0916267 q^{72} -10.6826 q^{73} -0.0343915 q^{74} -3.09455 q^{75} +12.1789 q^{76} -1.27601 q^{77} -0.00557058 q^{78} -4.24327 q^{79} -13.8276 q^{80} +7.25630 q^{81} +0.0335228 q^{82} +2.80800 q^{83} -0.945402 q^{84} -0.341372 q^{85} +0.0864456 q^{86} -2.43740 q^{87} -0.0392891 q^{88} +12.4928 q^{89} +0.0791956 q^{90} -1.62588 q^{91} -0.714476 q^{92} -2.25974 q^{93} -0.0180129 q^{94} +21.0535 q^{95} -0.0436644 q^{96} -5.02154 q^{97} -0.0480070 q^{98} -3.36630 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q + 12 q^{2} + 6 q^{3} + 42 q^{4} + 31 q^{5} + 4 q^{6} + 9 q^{7} + 36 q^{8} + 47 q^{9} + 4 q^{10} + 18 q^{11} + 15 q^{12} + 13 q^{13} + 8 q^{14} + 3 q^{15} + 48 q^{16} + 18 q^{17} + 17 q^{18} + 40 q^{20}+ \cdots - 35 q^{99}+O(q^{100}) \) 37 * q + 12 * q^2 + 6 * q^3 + 42 * q^4 + 31 * q^5 + 4 * q^6 + 9 * q^7 + 36 * q^8 + 47 * q^9 + 4 * q^10 + 18 * q^11 + 15 * q^12 + 13 * q^13 + 8 * q^14 + 3 * q^15 + 48 * q^16 + 18 * q^17 + 17 * q^18 + 40 * q^20 - 4 * q^21 - 4 * q^22 + 42 * q^23 - 10 * q^24 + 56 * q^25 - 4 * q^26 + 18 * q^27 + 3 * q^28 + 45 * q^29 - 32 * q^30 - 3 * q^31 + 59 * q^32 + 14 * q^33 - 22 * q^34 + 16 * q^35 + 28 * q^36 + 52 * q^37 - 5 * q^38 - 13 * q^39 - 11 * q^40 + 23 * q^41 - 16 * q^42 + 4 * q^43 + 23 * q^44 + 69 * q^45 - 5 * q^46 + 45 * q^47 - 5 * q^48 + 30 * q^49 + 13 * q^50 - 7 * q^51 + 3 * q^52 + 103 * q^53 - 23 * q^54 - 9 * q^55 + 4 * q^56 + 9 * q^57 + 8 * q^58 + 2 * q^59 - 47 * q^60 - 6 * q^61 + 20 * q^62 + 5 * q^63 + 28 * q^64 + 51 * q^65 - 48 * q^66 + 24 * q^67 - 9 * q^68 - 52 * q^70 + 32 * q^71 + 42 * q^72 + 5 * q^73 + 4 * q^74 - 35 * q^75 - 34 * q^76 + 97 * q^77 - 31 * q^78 - 27 * q^79 + 47 * q^80 + 29 * q^81 - q^82 + 23 * q^83 - 93 * q^84 + 27 * q^85 + 10 * q^86 - 46 * q^87 - 45 * q^88 + 9 * q^89 - 70 * q^90 - 48 * q^91 + 67 * q^92 + 72 * q^93 - 52 * q^94 - 20 * q^95 - 89 * q^96 - 7 * q^97 - 12 * q^98 - 35 * q^99

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