LMFDB - Embedded newform 4017.2.a.k.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.166477 q^{2} +1.00000 q^{3} -1.97229 q^{4} +3.74884 q^{5} -0.166477 q^{6} -0.361248 q^{7} +0.661293 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.166477 q^{2} +1.00000 q^{3} -1.97229 q^{4} +3.74884 q^{5} -0.166477 q^{6} -0.361248 q^{7} +0.661293 q^{8} +1.00000 q^{9} -0.624094 q^{10} -0.314428 q^{11} -1.97229 q^{12} +1.00000 q^{13} +0.0601394 q^{14} +3.74884 q^{15} +3.83448 q^{16} +5.97290 q^{17} -0.166477 q^{18} -4.10553 q^{19} -7.39378 q^{20} -0.361248 q^{21} +0.0523449 q^{22} +6.88687 q^{23} +0.661293 q^{24} +9.05379 q^{25} -0.166477 q^{26} +1.00000 q^{27} +0.712484 q^{28} -1.86549 q^{29} -0.624094 q^{30} +3.17415 q^{31} -1.96094 q^{32} -0.314428 q^{33} -0.994348 q^{34} -1.35426 q^{35} -1.97229 q^{36} -4.32128 q^{37} +0.683475 q^{38} +1.00000 q^{39} +2.47908 q^{40} -6.48641 q^{41} +0.0601394 q^{42} -5.66524 q^{43} +0.620142 q^{44} +3.74884 q^{45} -1.14650 q^{46} +10.8680 q^{47} +3.83448 q^{48} -6.86950 q^{49} -1.50724 q^{50} +5.97290 q^{51} -1.97229 q^{52} +1.73694 q^{53} -0.166477 q^{54} -1.17874 q^{55} -0.238891 q^{56} -4.10553 q^{57} +0.310561 q^{58} +5.25857 q^{59} -7.39378 q^{60} -7.01064 q^{61} -0.528422 q^{62} -0.361248 q^{63} -7.34251 q^{64} +3.74884 q^{65} +0.0523449 q^{66} +0.855530 q^{67} -11.7803 q^{68} +6.88687 q^{69} +0.225453 q^{70} +9.35294 q^{71} +0.661293 q^{72} +5.63766 q^{73} +0.719392 q^{74} +9.05379 q^{75} +8.09728 q^{76} +0.113586 q^{77} -0.166477 q^{78} +0.529364 q^{79} +14.3749 q^{80} +1.00000 q^{81} +1.07984 q^{82} -0.539733 q^{83} +0.712484 q^{84} +22.3914 q^{85} +0.943130 q^{86} -1.86549 q^{87} -0.207929 q^{88} +15.2855 q^{89} -0.624094 q^{90} -0.361248 q^{91} -13.5829 q^{92} +3.17415 q^{93} -1.80926 q^{94} -15.3910 q^{95} -1.96094 q^{96} -4.76394 q^{97} +1.14361 q^{98} -0.314428 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * 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 $

$2$	−0.166477	−0.117717	−0.0588584	−	0.998266i	$-0.518746\pi$
$2$	−0.166477	−0.117717	−0.0588584	+	0.998266i	$0.518746\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.97229	−0.986143
$5$	3.74884	1.67653	0.838266	−	0.545262i	$-0.183570\pi$
$5$	3.74884	1.67653	0.838266	+	0.545262i	$0.183570\pi$
$6$	−0.166477	−0.0679638
$7$	−0.361248	−0.136539	−0.0682695	−	0.997667i	$-0.521748\pi$
$7$	−0.361248	−0.136539	−0.0682695	+	0.997667i	$0.521748\pi$
$8$	0.661293	0.233802
$9$	1.00000	0.333333
$10$	−0.624094	−0.197356
$11$	−0.314428	−0.0948036	−0.0474018	−	0.998876i	$-0.515094\pi$
$11$	−0.314428	−0.0948036	−0.0474018	+	0.998876i	$0.515094\pi$
$12$	−1.97229	−0.569350
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	0.0601394	0.0160729
$15$	3.74884	0.967946
$16$	3.83448	0.958620
$17$	5.97290	1.44864	0.724320	−	0.689464i	$-0.242154\pi$
$17$	5.97290	1.44864	0.724320	+	0.689464i	$0.242154\pi$
$18$	−0.166477	−0.0392389
$19$	−4.10553	−0.941873	−0.470937	−	0.882167i	$-0.656084\pi$
$19$	−4.10553	−0.941873	−0.470937	+	0.882167i	$0.656084\pi$
$20$	−7.39378	−1.65330
$21$	−0.361248	−0.0788308
$22$	0.0523449	0.0111600
$23$	6.88687	1.43601	0.718006	−	0.696037i	$-0.245055\pi$
$23$	6.88687	1.43601	0.718006	+	0.696037i	$0.245055\pi$
$24$	0.661293	0.134986
$25$	9.05379	1.81076
$26$	−0.166477	−0.0326488
$27$	1.00000	0.192450
$28$	0.712484	0.134647
$29$	−1.86549	−0.346413	−0.173207	−	0.984886i	$-0.555413\pi$
$29$	−1.86549	−0.346413	−0.173207	+	0.984886i	$0.555413\pi$
$30$	−0.624094	−0.113943
$31$	3.17415	0.570095	0.285047	−	0.958513i	$-0.407991\pi$
$31$	3.17415	0.570095	0.285047	+	0.958513i	$0.407991\pi$
$32$	−1.96094	−0.346648
$33$	−0.314428	−0.0547349
$34$	−0.994348	−0.170529
$35$	−1.35426	−0.228912
$36$	−1.97229	−0.328714
$37$	−4.32128	−0.710414	−0.355207	−	0.934788i	$-0.615590\pi$
$37$	−4.32128	−0.710414	−0.355207	+	0.934788i	$0.615590\pi$
$38$	0.683475	0.110874
$39$	1.00000	0.160128
$40$	2.47908	0.391977
$41$	−6.48641	−1.01301	−0.506504	−	0.862238i	$-0.669062\pi$
$41$	−6.48641	−1.01301	−0.506504	+	0.862238i	$0.669062\pi$
$42$	0.0601394	0.00927971
$43$	−5.66524	−0.863941	−0.431971	−	0.901888i	$-0.642182\pi$
$43$	−5.66524	−0.863941	−0.431971	+	0.901888i	$0.642182\pi$
$44$	0.620142	0.0934899
$45$	3.74884	0.558844
$46$	−1.14650	−0.169043
$47$	10.8680	1.58525	0.792627	−	0.609707i	$-0.208713\pi$
$47$	10.8680	1.58525	0.792627	+	0.609707i	$0.208713\pi$
$48$	3.83448	0.553460
$49$	−6.86950	−0.981357
$50$	−1.50724	−0.213157
$51$	5.97290	0.836373
$52$	−1.97229	−0.273507
$53$	1.73694	0.238587	0.119293	−	0.992859i	$-0.461937\pi$
$53$	1.73694	0.238587	0.119293	+	0.992859i	$0.461937\pi$
$54$	−0.166477	−0.0226546
$55$	−1.17874	−0.158941
$56$	−0.238891	−0.0319231
$57$	−4.10553	−0.543791
$58$	0.310561	0.0407787
$59$	5.25857	0.684608	0.342304	−	0.939589i	$-0.388793\pi$
$59$	5.25857	0.684608	0.342304	+	0.939589i	$0.388793\pi$
$60$	−7.39378	−0.954533
$61$	−7.01064	−0.897621	−0.448810	−	0.893627i	$-0.648152\pi$
$61$	−7.01064	−0.897621	−0.448810	+	0.893627i	$0.648152\pi$
$62$	−0.528422	−0.0671097
$63$	−0.361248	−0.0455130
$64$	−7.34251	−0.917814
$65$	3.74884	0.464986
$66$	0.0523449	0.00644321
$67$	0.855530	0.104520	0.0522598	−	0.998634i	$-0.483358\pi$
$67$	0.855530	0.104520	0.0522598	+	0.998634i	$0.483358\pi$
$68$	−11.7803	−1.42857
$69$	6.88687	0.829082
$70$	0.225453	0.0269468
$71$	9.35294	1.10999	0.554995	−	0.831854i	$-0.312720\pi$
$71$	9.35294	1.10999	0.554995	+	0.831854i	$0.312720\pi$
$72$	0.661293	0.0779341
$73$	5.63766	0.659838	0.329919	−	0.944009i	$-0.392978\pi$
$73$	5.63766	0.659838	0.329919	+	0.944009i	$0.392978\pi$
$74$	0.719392	0.0836277
$75$	9.05379	1.04544
$76$	8.09728	0.928821
$77$	0.113586	0.0129444
$78$	−0.166477	−0.0188498
$79$	0.529364	0.0595581	0.0297790	−	0.999557i	$-0.490520\pi$
$79$	0.529364	0.0595581	0.0297790	+	0.999557i	$0.490520\pi$
$80$	14.3749	1.60716
$81$	1.00000	0.111111
$82$	1.07984	0.119248
$83$	−0.539733	−0.0592434	−0.0296217	−	0.999561i	$-0.509430\pi$
$83$	−0.539733	−0.0592434	−0.0296217	+	0.999561i	$0.509430\pi$
$84$	0.712484	0.0777384
$85$	22.3914	2.42869
$86$	0.943130	0.101700
$87$	−1.86549	−0.200002
$88$	−0.207929	−0.0221653
$89$	15.2855	1.62026	0.810128	−	0.586252i	$-0.199397\pi$
$89$	15.2855	1.62026	0.810128	+	0.586252i	$0.199397\pi$
$90$	−0.624094	−0.0657853
$91$	−0.361248	−0.0378691
$92$	−13.5829	−1.41611
$93$	3.17415	0.329144
$94$	−1.80926	−0.186611
$95$	−15.3910	−1.57908
$96$	−1.96094	−0.200137
$97$	−4.76394	−0.483705	−0.241853	−	0.970313i	$-0.577755\pi$
$97$	−4.76394	−0.483705	−0.241853	+	0.970313i	$0.577755\pi$
$98$	1.14361	0.115522
$99$	−0.314428	−0.0316012
$100$	−17.8567	−1.78567
$101$	17.0482	1.69636	0.848178	−	0.529712i	$-0.177700\pi$
$101$	17.0482	1.69636	0.848178	+	0.529712i	$0.177700\pi$
$102$	−0.994348	−0.0984551
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	0.661293	0.0648451
$105$	−1.35426	−0.132162
$106$	−0.289159	−0.0280856
$107$	9.23482	0.892763	0.446382	−	0.894843i	$-0.352712\pi$
$107$	9.23482	0.892763	0.446382	+	0.894843i	$0.352712\pi$
$108$	−1.97229	−0.189783
$109$	−15.8067	−1.51401	−0.757004	−	0.653410i	$-0.773338\pi$
$109$	−15.8067	−1.51401	−0.757004	+	0.653410i	$0.773338\pi$
$110$	0.196233	0.0187100
$111$	−4.32128	−0.410158
$112$	−1.38520	−0.130889
$113$	−15.0621	−1.41692	−0.708461	−	0.705750i	$-0.750610\pi$
$113$	−15.0621	−1.41692	−0.708461	+	0.705750i	$0.750610\pi$
$114$	0.683475	0.0640133
$115$	25.8178	2.40752
$116$	3.67928	0.341613
$117$	1.00000	0.0924500
$118$	−0.875429	−0.0805898
$119$	−2.15770	−0.197796
$120$	2.47908	0.226308
$121$	−10.9011	−0.991012
$122$	1.16711	0.105665
$123$	−6.48641	−0.584860
$124$	−6.26034	−0.562195
$125$	15.1970	1.35926
$126$	0.0601394	0.00535764
$127$	−10.1689	−0.902347	−0.451174	−	0.892436i	$-0.648994\pi$
$127$	−10.1689	−0.902347	−0.451174	+	0.892436i	$0.648994\pi$
$128$	5.14423	0.454690
$129$	−5.66524	−0.498797
$130$	−0.624094	−0.0547367
$131$	20.7086	1.80932	0.904660	−	0.426134i	$-0.140125\pi$
$131$	20.7086	1.80932	0.904660	+	0.426134i	$0.140125\pi$
$132$	0.620142	0.0539764
$133$	1.48311	0.128602
$134$	−0.142426	−0.0123037
$135$	3.74884	0.322649
$136$	3.94983	0.338695
$137$	15.8581	1.35485	0.677423	−	0.735594i	$-0.263097\pi$
$137$	15.8581	1.35485	0.677423	+	0.735594i	$0.263097\pi$
$138$	−1.14650	−0.0975969
$139$	−3.51808	−0.298400	−0.149200	−	0.988807i	$-0.547670\pi$
$139$	−3.51808	−0.298400	−0.149200	+	0.988807i	$0.547670\pi$
$140$	2.67099	0.225740
$141$	10.8680	0.915247
$142$	−1.55705	−0.130664
$143$	−0.314428	−0.0262938
$144$	3.83448	0.319540
$145$	−6.99343	−0.580773
$146$	−0.938539	−0.0776741
$147$	−6.86950	−0.566587
$148$	8.52280	0.700570
$149$	3.19950	0.262113	0.131056	−	0.991375i	$-0.458163\pi$
$149$	3.19950	0.262113	0.131056	+	0.991375i	$0.458163\pi$
$150$	−1.50724	−0.123066
$151$	−7.82717	−0.636966	−0.318483	−	0.947929i	$-0.603173\pi$
$151$	−7.82717	−0.636966	−0.318483	+	0.947929i	$0.603173\pi$
$152$	−2.71496	−0.220212
$153$	5.97290	0.482880
$154$	−0.0189095	−0.00152377
$155$	11.8994	0.955782
$156$	−1.97229	−0.157909
$157$	8.04146	0.641778	0.320889	−	0.947117i	$-0.396018\pi$
$157$	8.04146	0.641778	0.320889	+	0.947117i	$0.396018\pi$
$158$	−0.0881267	−0.00701098
$159$	1.73694	0.137748
$160$	−7.35124	−0.581166
$161$	−2.48787	−0.196072
$162$	−0.166477	−0.0130796
$163$	0.823581	0.0645078	0.0322539	−	0.999480i	$-0.489731\pi$
$163$	0.823581	0.0645078	0.0322539	+	0.999480i	$0.489731\pi$
$164$	12.7931	0.998970
$165$	−1.17874	−0.0917647
$166$	0.0898530	0.00697395
$167$	−4.72436	−0.365582	−0.182791	−	0.983152i	$-0.558513\pi$
$167$	−4.72436	−0.365582	−0.182791	+	0.983152i	$0.558513\pi$
$168$	−0.238891	−0.0184308
$169$	1.00000	0.0769231
$170$	−3.72765	−0.285898
$171$	−4.10553	−0.313958
$172$	11.1735	0.851969
$173$	−21.5670	−1.63971	−0.819854	−	0.572573i	$-0.805945\pi$
$173$	−21.5670	−1.63971	−0.819854	+	0.572573i	$0.805945\pi$
$174$	0.310561	0.0235436
$175$	−3.27066	−0.247239
$176$	−1.20567	−0.0908806
$177$	5.25857	0.395258
$178$	−2.54467	−0.190731
$179$	−9.71731	−0.726305	−0.363153	−	0.931730i	$-0.618300\pi$
$179$	−9.71731	−0.726305	−0.363153	+	0.931730i	$0.618300\pi$
$180$	−7.39378	−0.551100
$181$	7.57316	0.562909	0.281454	−	0.959575i	$-0.409183\pi$
$181$	7.57316	0.562909	0.281454	+	0.959575i	$0.409183\pi$
$182$	0.0601394	0.00445783
$183$	−7.01064	−0.518242
$184$	4.55424	0.335743
$185$	−16.1998	−1.19103
$186$	−0.528422	−0.0387458
$187$	−1.87805	−0.137336
$188$	−21.4347	−1.56329
$189$	−0.361248	−0.0262769
$190$	2.56224	0.185884
$191$	5.41443	0.391774	0.195887	−	0.980626i	$-0.437241\pi$
$191$	5.41443	0.391774	0.195887	+	0.980626i	$0.437241\pi$
$192$	−7.34251	−0.529900
$193$	9.67435	0.696375	0.348187	−	0.937425i	$-0.386797\pi$
$193$	9.67435	0.696375	0.348187	+	0.937425i	$0.386797\pi$
$194$	0.793086	0.0569402
$195$	3.74884	0.268460
$196$	13.5486	0.967758
$197$	−21.9164	−1.56148	−0.780738	−	0.624859i	$-0.785156\pi$
$197$	−21.9164	−1.56148	−0.780738	+	0.624859i	$0.785156\pi$
$198$	0.0523449	0.00371999
$199$	21.2087	1.50344	0.751721	−	0.659481i	$-0.229224\pi$
$199$	21.2087	1.50344	0.751721	+	0.659481i	$0.229224\pi$
$200$	5.98721	0.423359
$201$	0.855530	0.0603444
$202$	−2.83812	−0.199690
$203$	0.673906	0.0472989
$204$	−11.7803	−0.824783
$205$	−24.3165	−1.69834
$206$	−0.166477	−0.0115990
$207$	6.88687	0.478671
$208$	3.83448	0.265873
$209$	1.29089	0.0892929
$210$	0.225453	0.0155577
$211$	0.193342	0.0133102	0.00665511	−	0.999978i	$-0.497882\pi$
$211$	0.193342	0.0133102	0.00665511	+	0.999978i	$0.497882\pi$
$212$	−3.42573	−0.235280
$213$	9.35294	0.640853
$214$	−1.53738	−0.105093
$215$	−21.2381	−1.44842
$216$	0.661293	0.0449953
$217$	−1.14666	−0.0778401
$218$	2.63145	0.178224
$219$	5.63766	0.380958
$220$	2.32481	0.156739
$221$	5.97290	0.401780
$222$	0.719392	0.0482824
$223$	−3.26888	−0.218900	−0.109450	−	0.993992i	$-0.534909\pi$
$223$	−3.26888	−0.218900	−0.109450	+	0.993992i	$0.534909\pi$
$224$	0.708385	0.0473309
$225$	9.05379	0.603586
$226$	2.50749	0.166795
$227$	26.8351	1.78111	0.890553	−	0.454879i	$-0.150317\pi$
$227$	26.8351	1.78111	0.890553	+	0.454879i	$0.150317\pi$
$228$	8.09728	0.536255
$229$	−0.648942	−0.0428833	−0.0214417	−	0.999770i	$-0.506826\pi$
$229$	−0.648942	−0.0428833	−0.0214417	+	0.999770i	$0.506826\pi$
$230$	−4.29806	−0.283406
$231$	0.113586	0.00747344
$232$	−1.23364	−0.0809922
$233$	−8.96100	−0.587055	−0.293527	−	0.955951i	$-0.594829\pi$
$233$	−8.96100	−0.587055	−0.293527	+	0.955951i	$0.594829\pi$
$234$	−0.166477	−0.0108829
$235$	40.7422	2.65773
$236$	−10.3714	−0.675121
$237$	0.529364	0.0343859
$238$	0.359206	0.0232839
$239$	10.8437	0.701420	0.350710	−	0.936484i	$-0.385940\pi$
$239$	10.8437	0.701420	0.350710	+	0.936484i	$0.385940\pi$
$240$	14.3749	0.927893
$241$	−1.67614	−0.107970	−0.0539849	−	0.998542i	$-0.517192\pi$
$241$	−1.67614	−0.107970	−0.0539849	+	0.998542i	$0.517192\pi$
$242$	1.81478	0.116659
$243$	1.00000	0.0641500
$244$	13.8270	0.885182
$245$	−25.7526	−1.64528
$246$	1.07984	0.0688478
$247$	−4.10553	−0.261229
$248$	2.09905	0.133289
$249$	−0.539733	−0.0342042
$250$	−2.52995	−0.160008
$251$	8.75124	0.552373	0.276187	−	0.961104i	$-0.410929\pi$
$251$	8.75124	0.552373	0.276187	+	0.961104i	$0.410929\pi$
$252$	0.712484	0.0448823
$253$	−2.16543	−0.136139
$254$	1.69289	0.106221
$255$	22.3914	1.40221
$256$	13.8286	0.864289
$257$	1.14675	0.0715320	0.0357660	−	0.999360i	$-0.488613\pi$
$257$	1.14675	0.0715320	0.0357660	+	0.999360i	$0.488613\pi$
$258$	0.943130	0.0587167
$259$	1.56105	0.0969992
$260$	−7.39378	−0.458543
$261$	−1.86549	−0.115471
$262$	−3.44750	−0.212987
$263$	19.5990	1.20853	0.604263	−	0.796785i	$-0.293468\pi$
$263$	19.5990	1.20853	0.604263	+	0.796785i	$0.293468\pi$
$264$	−0.207929	−0.0127971
$265$	6.51149	0.399998
$266$	−0.246904	−0.0151387
$267$	15.2855	0.935456
$268$	−1.68735	−0.103071
$269$	−20.8614	−1.27194	−0.635970	−	0.771714i	$-0.719400\pi$
$269$	−20.8614	−1.27194	−0.635970	+	0.771714i	$0.719400\pi$
$270$	−0.624094	−0.0379812
$271$	1.90314	0.115607	0.0578037	−	0.998328i	$-0.481590\pi$
$271$	1.90314	0.115607	0.0578037	+	0.998328i	$0.481590\pi$
$272$	22.9030	1.38870
$273$	−0.361248	−0.0218637
$274$	−2.64000	−0.159488
$275$	−2.84676	−0.171666
$276$	−13.5829	−0.817593
$277$	−21.2874	−1.27903	−0.639517	−	0.768777i	$-0.720865\pi$
$277$	−21.2874	−1.27903	−0.639517	+	0.768777i	$0.720865\pi$
$278$	0.585678	0.0351267
$279$	3.17415	0.190032
$280$	−0.895563	−0.0535201
$281$	28.9794	1.72877	0.864384	−	0.502833i	$-0.167709\pi$
$281$	28.9794	1.72877	0.864384	+	0.502833i	$0.167709\pi$
$282$	−1.80926	−0.107740
$283$	−14.5853	−0.867006	−0.433503	−	0.901152i	$-0.642723\pi$
$283$	−14.5853	−0.867006	−0.433503	+	0.901152i	$0.642723\pi$
$284$	−18.4467	−1.09461
$285$	−15.3910	−0.911682
$286$	0.0523449	0.00309522
$287$	2.34320	0.138315
$288$	−1.96094	−0.115549
$289$	18.6755	1.09856
$290$	1.16424	0.0683667
$291$	−4.76394	−0.279267
$292$	−11.1191	−0.650695
$293$	−22.4552	−1.31184	−0.655922	−	0.754829i	$-0.727720\pi$
$293$	−22.4552	−1.31184	−0.655922	+	0.754829i	$0.727720\pi$
$294$	1.14361	0.0666968
$295$	19.7135	1.14777
$296$	−2.85763	−0.166096
$297$	−0.314428	−0.0182450
$298$	−0.532641	−0.0308551
$299$	6.88687	0.398278
$300$	−17.8567	−1.03095
$301$	2.04656	0.117962
$302$	1.30304	0.0749816
$303$	17.0482	0.979391
$304$	−15.7426	−0.902899
$305$	−26.2818	−1.50489
$306$	−0.994348	−0.0568431
$307$	−23.5826	−1.34593	−0.672965	−	0.739674i	$-0.734980\pi$
$307$	−23.5826	−1.34593	−0.672965	+	0.739674i	$0.734980\pi$
$308$	−0.224025	−0.0127650
$309$	1.00000	0.0568880
$310$	−1.98097	−0.112512
$311$	27.4057	1.55404	0.777018	−	0.629479i	$-0.216732\pi$
$311$	27.4057	1.55404	0.777018	+	0.629479i	$0.216732\pi$
$312$	0.661293	0.0374383
$313$	23.9273	1.35245	0.676226	−	0.736694i	$-0.263614\pi$
$313$	23.9273	1.35245	0.676226	+	0.736694i	$0.263614\pi$
$314$	−1.33871	−0.0755480
$315$	−1.35426	−0.0763039
$316$	−1.04406	−0.0587327
$317$	−13.7886	−0.774447	−0.387223	−	0.921986i	$-0.626566\pi$
$317$	−13.7886	−0.774447	−0.387223	+	0.921986i	$0.626566\pi$
$318$	−0.289159	−0.0162152
$319$	0.586563	0.0328412
$320$	−27.5259	−1.53874
$321$	9.23482	0.515437
$322$	0.414172	0.0230809
$323$	−24.5219	−1.36444
$324$	−1.97229	−0.109571
$325$	9.05379	0.502214
$326$	−0.137107	−0.00759365
$327$	−15.8067	−0.874113
$328$	−4.28942	−0.236843
$329$	−3.92603	−0.216449
$330$	0.196233	0.0108022
$331$	2.67099	0.146811	0.0734053	−	0.997302i	$-0.476613\pi$
$331$	2.67099	0.146811	0.0734053	+	0.997302i	$0.476613\pi$
$332$	1.06451	0.0584225
$333$	−4.32128	−0.236805
$334$	0.786496	0.0430352
$335$	3.20724	0.175230
$336$	−1.38520	−0.0755688
$337$	3.95465	0.215423	0.107712	−	0.994182i	$-0.465648\pi$
$337$	3.95465	0.215423	0.107712	+	0.994182i	$0.465648\pi$
$338$	−0.166477	−0.00905514
$339$	−15.0621	−0.818060
$340$	−44.1623	−2.39504
$341$	−0.998042	−0.0540470
$342$	0.683475	0.0369581
$343$	5.01033	0.270532
$344$	−3.74638	−0.201991
$345$	25.8178	1.38998
$346$	3.59040	0.193021
$347$	11.8006	0.633491	0.316745	−	0.948511i	$-0.397410\pi$
$347$	11.8006	0.633491	0.316745	+	0.948511i	$0.397410\pi$
$348$	3.67928	0.197230
$349$	23.9194	1.28038	0.640189	−	0.768218i	$-0.278856\pi$
$349$	23.9194	1.28038	0.640189	+	0.768218i	$0.278856\pi$
$350$	0.544489	0.0291042
$351$	1.00000	0.0533761
$352$	0.616573	0.0328635
$353$	12.2097	0.649859	0.324929	−	0.945738i	$-0.394659\pi$
$353$	12.2097	0.649859	0.324929	+	0.945738i	$0.394659\pi$
$354$	−0.875429	−0.0465285
$355$	35.0627	1.86093
$356$	−30.1473	−1.59780
$357$	−2.15770	−0.114197
$358$	1.61770	0.0854983
$359$	26.9964	1.42482	0.712408	−	0.701765i	$-0.247605\pi$
$359$	26.9964	1.42482	0.712408	+	0.701765i	$0.247605\pi$
$360$	2.47908	0.130659
$361$	−2.14463	−0.112875
$362$	−1.26075	−0.0662638
$363$	−10.9011	−0.572161
$364$	0.712484	0.0373443
$365$	21.1347	1.10624
$366$	1.16711	0.0610057
$367$	11.6433	0.607775	0.303887	−	0.952708i	$-0.401715\pi$
$367$	11.6433	0.607775	0.303887	+	0.952708i	$0.401715\pi$
$368$	26.4076	1.37659
$369$	−6.48641	−0.337669
$370$	2.69689	0.140204
$371$	−0.627465	−0.0325763
$372$	−6.26034	−0.324583
$373$	−38.0280	−1.96901	−0.984507	−	0.175347i	$-0.943895\pi$
$373$	−38.0280	−1.96901	−0.984507	+	0.175347i	$0.943895\pi$
$374$	0.312651	0.0161668
$375$	15.1970	0.784770
$376$	7.18690	0.370636
$377$	−1.86549	−0.0960778
$378$	0.0601394	0.00309324
$379$	7.25163	0.372491	0.186245	−	0.982503i	$-0.440368\pi$
$379$	7.25163	0.372491	0.186245	+	0.982503i	$0.440368\pi$
$380$	30.3554	1.55720
$381$	−10.1689	−0.520970
$382$	−0.901376	−0.0461184
$383$	6.11040	0.312227	0.156113	−	0.987739i	$-0.450103\pi$
$383$	6.11040	0.312227	0.156113	+	0.987739i	$0.450103\pi$
$384$	5.14423	0.262515
$385$	0.425817	0.0217017
$386$	−1.61055	−0.0819750
$387$	−5.66524	−0.287980
$388$	9.39586	0.477002
$389$	−18.2973	−0.927711	−0.463856	−	0.885911i	$-0.653534\pi$
$389$	−18.2973	−0.927711	−0.463856	+	0.885911i	$0.653534\pi$
$390$	−0.624094	−0.0316022
$391$	41.1346	2.08027
$392$	−4.54275	−0.229444
$393$	20.7086	1.04461
$394$	3.64856	0.183812
$395$	1.98450	0.0998509
$396$	0.620142	0.0311633
$397$	−6.52213	−0.327336	−0.163668	−	0.986515i	$-0.552333\pi$
$397$	−6.52213	−0.327336	−0.163668	+	0.986515i	$0.552333\pi$
$398$	−3.53075	−0.176980
$399$	1.48311	0.0742486
$400$	34.7166	1.73583
$401$	9.85100	0.491936	0.245968	−	0.969278i	$-0.420894\pi$
$401$	9.85100	0.491936	0.245968	+	0.969278i	$0.420894\pi$
$402$	−0.142426	−0.00710355
$403$	3.17415	0.158116
$404$	−33.6238	−1.67285
$405$	3.74884	0.186281
$406$	−0.112190	−0.00556787
$407$	1.35873	0.0673498
$408$	3.94983	0.195546
$409$	8.33266	0.412024	0.206012	−	0.978549i	$-0.433951\pi$
$409$	8.33266	0.412024	0.206012	+	0.978549i	$0.433951\pi$
$410$	4.04813	0.199923
$411$	15.8581	0.782221
$412$	−1.97229	−0.0971675
$413$	−1.89965	−0.0934756
$414$	−1.14650	−0.0563476
$415$	−2.02337	−0.0993235
$416$	−1.96094	−0.0961429
$417$	−3.51808	−0.172281
$418$	−0.214904	−0.0105113
$419$	−10.2207	−0.499313	−0.249656	−	0.968334i	$-0.580318\pi$
$419$	−10.2207	−0.499313	−0.249656	+	0.968334i	$0.580318\pi$
$420$	2.67099	0.130331
$421$	0.0781706	0.00380980	0.00190490	−	0.999998i	$-0.499394\pi$
$421$	0.0781706	0.00380980	0.00190490	+	0.999998i	$0.499394\pi$
$422$	−0.0321869	−0.00156684
$423$	10.8680	0.528418
$424$	1.14862	0.0557821
$425$	54.0773	2.62314
$426$	−1.55705	−0.0754391
$427$	2.53258	0.122560
$428$	−18.2137	−0.880392
$429$	−0.314428	−0.0151807
$430$	3.53564	0.170504
$431$	0.998603	0.0481010	0.0240505	−	0.999711i	$-0.492344\pi$
$431$	0.998603	0.0481010	0.0240505	+	0.999711i	$0.492344\pi$
$432$	3.83448	0.184487
$433$	−14.7923	−0.710871	−0.355436	−	0.934701i	$-0.615668\pi$
$433$	−14.7923	−0.710871	−0.355436	+	0.934701i	$0.615668\pi$
$434$	0.190892	0.00916309
$435$	−6.99343	−0.335309
$436$	31.1754	1.49303
$437$	−28.2743	−1.35254
$438$	−0.938539	−0.0448451
$439$	−17.3224	−0.826751	−0.413376	−	0.910561i	$-0.635650\pi$
$439$	−17.3224	−0.826751	−0.413376	+	0.910561i	$0.635650\pi$
$440$	−0.779492	−0.0371608
$441$	−6.86950	−0.327119
$442$	−0.994348	−0.0472963
$443$	−9.24492	−0.439239	−0.219620	−	0.975586i	$-0.570482\pi$
$443$	−9.24492	−0.439239	−0.219620	+	0.975586i	$0.570482\pi$
$444$	8.52280	0.404474
$445$	57.3028	2.71641
$446$	0.544192	0.0257682
$447$	3.19950	0.151331
$448$	2.65247	0.125317
$449$	−38.7279	−1.82768	−0.913840	−	0.406074i	$-0.866898\pi$
$449$	−38.7279	−1.82768	−0.913840	+	0.406074i	$0.866898\pi$
$450$	−1.50724	−0.0710522
$451$	2.03951	0.0960367
$452$	29.7067	1.39729
$453$	−7.82717	−0.367753
$454$	−4.46741	−0.209666
$455$	−1.35426	−0.0634887
$456$	−2.71496	−0.127140
$457$	4.33376	0.202725	0.101362	−	0.994850i	$-0.467680\pi$
$457$	4.33376	0.202725	0.101362	+	0.994850i	$0.467680\pi$
$458$	0.108034	0.00504809
$459$	5.97290	0.278791
$460$	−50.9200	−2.37416
$461$	−4.89898	−0.228168	−0.114084	−	0.993471i	$-0.536393\pi$
$461$	−4.89898	−0.228168	−0.114084	+	0.993471i	$0.536393\pi$
$462$	−0.0189095	−0.000879749 0
$463$	5.71979	0.265821	0.132911	−	0.991128i	$-0.457568\pi$
$463$	5.71979	0.265821	0.132911	+	0.991128i	$0.457568\pi$
$464$	−7.15320	−0.332079
$465$	11.8994	0.551821
$466$	1.49180	0.0691062
$467$	34.7776	1.60931	0.804657	−	0.593739i	$-0.202349\pi$
$467$	34.7776	1.60931	0.804657	+	0.593739i	$0.202349\pi$
$468$	−1.97229	−0.0911689
$469$	−0.309059	−0.0142710
$470$	−6.78262	−0.312859
$471$	8.04146	0.370531
$472$	3.47746	0.160063
$473$	1.78131	0.0819047
$474$	−0.0881267	−0.00404779
$475$	−37.1706	−1.70550
$476$	4.25559	0.195055
$477$	1.73694	0.0795288
$478$	−1.80522	−0.0825689
$479$	−18.8519	−0.861363	−0.430682	−	0.902504i	$-0.641727\pi$
$479$	−18.8519	−0.861363	−0.430682	+	0.902504i	$0.641727\pi$
$480$	−7.35124	−0.335537
$481$	−4.32128	−0.197033
$482$	0.279039	0.0127099
$483$	−2.48787	−0.113202
$484$	21.5002	0.977280
$485$	−17.8593	−0.810947
$486$	−0.166477	−0.00755154
$487$	14.7120	0.666662	0.333331	−	0.942810i	$-0.391827\pi$
$487$	14.7120	0.666662	0.333331	+	0.942810i	$0.391827\pi$
$488$	−4.63609	−0.209866
$489$	0.823581	0.0372436
$490$	4.28721	0.193677
$491$	−37.0612	−1.67255	−0.836275	−	0.548310i	$-0.815271\pi$
$491$	−37.0612	−1.67255	−0.836275	+	0.548310i	$0.815271\pi$
$492$	12.7931	0.576755
$493$	−11.1424	−0.501828
$494$	0.683475	0.0307510
$495$	−1.17874	−0.0529804
$496$	12.1712	0.546504
$497$	−3.37873	−0.151557
$498$	0.0898530	0.00402641
$499$	−1.18162	−0.0528964	−0.0264482	−	0.999650i	$-0.508420\pi$
$499$	−1.18162	−0.0528964	−0.0264482	+	0.999650i	$0.508420\pi$
$500$	−29.9728	−1.34043
$501$	−4.72436	−0.211069
$502$	−1.45688	−0.0650236
$503$	1.16484	0.0519375	0.0259688	−	0.999663i	$-0.491733\pi$
$503$	1.16484	0.0519375	0.0259688	+	0.999663i	$0.491733\pi$
$504$	−0.238891	−0.0106410
$505$	63.9108	2.84399
$506$	0.360493	0.0160259
$507$	1.00000	0.0444116
$508$	20.0560	0.889843
$509$	−37.0512	−1.64227	−0.821133	−	0.570737i	$-0.806658\pi$
$509$	−37.0512	−1.64227	−0.821133	+	0.570737i	$0.806658\pi$
$510$	−3.72765	−0.165063
$511$	−2.03659	−0.0900936
$512$	−12.5906	−0.556432
$513$	−4.10553	−0.181264
$514$	−0.190906	−0.00842052
$515$	3.74884	0.165194
$516$	11.1735	0.491885
$517$	−3.41719	−0.150288
$518$	−0.259879	−0.0114184
$519$	−21.5670	−0.946686
$520$	2.47908	0.108715
$521$	−21.4410	−0.939348	−0.469674	−	0.882840i	$-0.655629\pi$
$521$	−21.4410	−0.939348	−0.469674	+	0.882840i	$0.655629\pi$
$522$	0.310561	0.0135929
$523$	23.5525	1.02988	0.514939	−	0.857227i	$-0.327814\pi$
$523$	23.5525	1.02988	0.514939	+	0.857227i	$0.327814\pi$
$524$	−40.8433	−1.78425
$525$	−3.27066	−0.142743
$526$	−3.26278	−0.142264
$527$	18.9589	0.825862
$528$	−1.20567	−0.0524700
$529$	24.4290	1.06213
$530$	−1.08401	−0.0470865
$531$	5.25857	0.228203
$532$	−2.92513	−0.126820
$533$	−6.48641	−0.280958
$534$	−2.54467	−0.110119
$535$	34.6198	1.49675
$536$	0.565756	0.0244369
$537$	−9.71731	−0.419333
$538$	3.47293	0.149729
$539$	2.15996	0.0930362
$540$	−7.39378	−0.318178
$541$	4.20733	0.180887	0.0904436	−	0.995902i	$-0.471172\pi$
$541$	4.20733	0.180887	0.0904436	+	0.995902i	$0.471172\pi$
$542$	−0.316828	−0.0136089
$543$	7.57316	0.324995
$544$	−11.7125	−0.502168
$545$	−59.2568	−2.53828
$546$	0.0601394	0.00257373
$547$	−17.0496	−0.728990	−0.364495	−	0.931205i	$-0.618758\pi$
$547$	−17.0496	−0.728990	−0.364495	+	0.931205i	$0.618758\pi$
$548$	−31.2766	−1.33607
$549$	−7.01064	−0.299207
$550$	0.473920	0.0202080
$551$	7.65884	0.326277
$552$	4.55424	0.193841
$553$	−0.191232	−0.00813199
$554$	3.54385	0.150564
$555$	−16.1998	−0.687642
$556$	6.93866	0.294265
$557$	33.4562	1.41758	0.708791	−	0.705418i	$-0.249241\pi$
$557$	33.4562	1.41758	0.708791	+	0.705418i	$0.249241\pi$
$558$	−0.528422	−0.0223699
$559$	−5.66524	−0.239614
$560$	−5.19289	−0.219440
$561$	−1.87805	−0.0792911
$562$	−4.82440	−0.203505
$563$	−33.2305	−1.40050	−0.700250	−	0.713898i	$-0.746928\pi$
$563$	−33.2305	−1.40050	−0.700250	+	0.713898i	$0.746928\pi$
$564$	−21.4347	−0.902564
$565$	−56.4653	−2.37551
$566$	2.42811	0.102061
$567$	−0.361248	−0.0151710
$568$	6.18503	0.259518
$569$	25.1014	1.05230	0.526152	−	0.850391i	$-0.323634\pi$
$569$	25.1014	1.05230	0.526152	+	0.850391i	$0.323634\pi$
$570$	2.56224	0.107320
$571$	−28.7656	−1.20380	−0.601900	−	0.798571i	$-0.705590\pi$
$571$	−28.7656	−1.20380	−0.601900	+	0.798571i	$0.705590\pi$
$572$	0.620142	0.0259294
$573$	5.41443	0.226191
$574$	−0.390089	−0.0162820
$575$	62.3523	2.60027
$576$	−7.34251	−0.305938
$577$	−23.6164	−0.983163	−0.491581	−	0.870832i	$-0.663581\pi$
$577$	−23.6164	−0.983163	−0.491581	+	0.870832i	$0.663581\pi$
$578$	−3.10903	−0.129319
$579$	9.67435	0.402052
$580$	13.7930	0.572725
$581$	0.194978	0.00808904
$582$	0.793086	0.0328745
$583$	−0.546141	−0.0226189
$584$	3.72815	0.154272
$585$	3.74884	0.154995
$586$	3.73826	0.154426
$587$	−39.4313	−1.62750	−0.813752	−	0.581213i	$-0.802578\pi$
$587$	−39.4313	−1.62750	−0.813752	+	0.581213i	$0.802578\pi$
$588$	13.5486	0.558735
$589$	−13.0316	−0.536957
$590$	−3.28184	−0.135111
$591$	−21.9164	−0.901518
$592$	−16.5699	−0.681017
$593$	11.0600	0.454181	0.227091	−	0.973874i	$-0.427079\pi$
$593$	11.0600	0.454181	0.227091	+	0.973874i	$0.427079\pi$
$594$	0.0523449	0.00214774
$595$	−8.08886	−0.331611
$596$	−6.31032	−0.258481
$597$	21.2087	0.868013
$598$	−1.14650	−0.0468840
$599$	−30.0994	−1.22983	−0.614915	−	0.788593i	$-0.710810\pi$
$599$	−30.0994	−1.22983	−0.614915	+	0.788593i	$0.710810\pi$
$600$	5.98721	0.244427
$601$	1.92541	0.0785392	0.0392696	−	0.999229i	$-0.487497\pi$
$601$	1.92541	0.0785392	0.0392696	+	0.999229i	$0.487497\pi$
$602$	−0.340704	−0.0138861
$603$	0.855530	0.0348399
$604$	15.4374	0.628139
$605$	−40.8666	−1.66146
$606$	−2.83812	−0.115291
$607$	−24.7650	−1.00518	−0.502590	−	0.864525i	$-0.667619\pi$
$607$	−24.7650	−1.00518	−0.502590	+	0.864525i	$0.667619\pi$
$608$	8.05069	0.326498
$609$	0.673906	0.0273080
$610$	4.37530	0.177151
$611$	10.8680	0.439670
$612$	−11.7803	−0.476189
$613$	−39.7584	−1.60583	−0.802913	−	0.596096i	$-0.796718\pi$
$613$	−39.7584	−1.60583	−0.802913	+	0.596096i	$0.796718\pi$
$614$	3.92596	0.158439
$615$	−24.3165	−0.980536
$616$	0.0751139	0.00302643
$617$	−27.3382	−1.10060	−0.550298	−	0.834969i	$-0.685486\pi$
$617$	−27.3382	−1.10060	−0.550298	+	0.834969i	$0.685486\pi$
$618$	−0.166477	−0.00669667
$619$	24.0967	0.968529	0.484264	−	0.874922i	$-0.339087\pi$
$619$	24.0967	0.968529	0.484264	+	0.874922i	$0.339087\pi$
$620$	−23.4690	−0.942537
$621$	6.88687	0.276361
$622$	−4.56241	−0.182936
$623$	−5.52185	−0.221228
$624$	3.83448	0.153502
$625$	11.7022	0.468086
$626$	−3.98334	−0.159206
$627$	1.29089	0.0515533
$628$	−15.8600	−0.632885
$629$	−25.8106	−1.02913
$630$	0.225453	0.00898225
$631$	−0.451923	−0.0179908	−0.00899539	−	0.999960i	$-0.502863\pi$
$631$	−0.451923	−0.0179908	−0.00899539	+	0.999960i	$0.502863\pi$
$632$	0.350064	0.0139248
$633$	0.193342	0.00768466
$634$	2.29549	0.0911654
$635$	−38.1217	−1.51281
$636$	−3.42573	−0.135839
$637$	−6.86950	−0.272179
$638$	−0.0976491	−0.00386596
$639$	9.35294	0.369997
$640$	19.2849	0.762302
$641$	12.9483	0.511428	0.255714	−	0.966753i	$-0.417690\pi$
$641$	12.9483	0.511428	0.255714	+	0.966753i	$0.417690\pi$
$642$	−1.53738	−0.0606756
$643$	−19.6116	−0.773408	−0.386704	−	0.922204i	$-0.626386\pi$
$643$	−19.6116	−0.773408	−0.386704	+	0.922204i	$0.626386\pi$
$644$	4.90679	0.193355
$645$	−21.2381	−0.836248
$646$	4.08232	0.160617
$647$	−15.5449	−0.611133	−0.305567	−	0.952171i	$-0.598846\pi$
$647$	−15.5449	−0.611133	−0.305567	+	0.952171i	$0.598846\pi$
$648$	0.661293	0.0259780
$649$	−1.65344	−0.0649033
$650$	−1.50724	−0.0591190
$651$	−1.14666	−0.0449410
$652$	−1.62434	−0.0636139
$653$	19.6911	0.770571	0.385286	−	0.922797i	$-0.374103\pi$
$653$	19.6911	0.770571	0.385286	+	0.922797i	$0.374103\pi$
$654$	2.63145	0.102898
$655$	77.6333	3.03338
$656$	−24.8720	−0.971089
$657$	5.63766	0.219946
$658$	0.653592	0.0254797
$659$	−29.6509	−1.15504	−0.577518	−	0.816378i	$-0.695979\pi$
$659$	−29.6509	−1.15504	−0.577518	+	0.816378i	$0.695979\pi$
$660$	2.32481	0.0904931
$661$	11.3706	0.442267	0.221133	−	0.975244i	$-0.429024\pi$
$661$	11.3706	0.442267	0.221133	+	0.975244i	$0.429024\pi$
$662$	−0.444657	−0.0172821
$663$	5.97290	0.231968
$664$	−0.356922	−0.0138513
$665$	5.55996	0.215606
$666$	0.719392	0.0278759
$667$	−12.8474	−0.497454
$668$	9.31780	0.360516
$669$	−3.26888	−0.126382
$670$	−0.533931	−0.0206276
$671$	2.20434	0.0850977
$672$	0.708385	0.0273265
$673$	−2.58789	−0.0997558	−0.0498779	−	0.998755i	$-0.515883\pi$
$673$	−2.58789	−0.0997558	−0.0498779	+	0.998755i	$0.515883\pi$
$674$	−0.658357	−0.0253590
$675$	9.05379	0.348481
$676$	−1.97229	−0.0758571
$677$	−19.0000	−0.730230	−0.365115	−	0.930962i	$-0.618970\pi$
$677$	−19.0000	−0.730230	−0.365115	+	0.930962i	$0.618970\pi$
$678$	2.50749	0.0962994
$679$	1.72097	0.0660446
$680$	14.8073	0.567834
$681$	26.8351	1.02832
$682$	0.166151	0.00636224
$683$	−3.62110	−0.138557	−0.0692787	−	0.997597i	$-0.522070\pi$
$683$	−3.62110	−0.138557	−0.0692787	+	0.997597i	$0.522070\pi$
$684$	8.09728	0.309607
$685$	59.4493	2.27144
$686$	−0.834103	−0.0318462
$687$	−0.648942	−0.0247587
$688$	−21.7233	−0.828192
$689$	1.73694	0.0661720
$690$	−4.29806	−0.163624
$691$	7.17285	0.272868	0.136434	−	0.990649i	$-0.456436\pi$
$691$	7.17285	0.272868	0.136434	+	0.990649i	$0.456436\pi$
$692$	42.5363	1.61699
$693$	0.113586	0.00431479
$694$	−1.96453	−0.0745725
$695$	−13.1887	−0.500276
$696$	−1.23364	−0.0467609
$697$	−38.7427	−1.46748
$698$	−3.98202	−0.150722
$699$	−8.96100	−0.338936
$700$	6.45068	0.243813
$701$	−48.0236	−1.81383	−0.906913	−	0.421317i	$-0.861568\pi$
$701$	−48.0236	−1.81383	−0.906913	+	0.421317i	$0.861568\pi$
$702$	−0.166477	−0.00628326
$703$	17.7411	0.669120
$704$	2.30869	0.0870121
$705$	40.7422	1.53444
$706$	−2.03264	−0.0764993
$707$	−6.15861	−0.231619
$708$	−10.3714	−0.389781
$709$	−29.7355	−1.11674	−0.558370	−	0.829592i	$-0.688573\pi$
$709$	−29.7355	−1.11674	−0.558370	+	0.829592i	$0.688573\pi$
$710$	−5.83711	−0.219063
$711$	0.529364	0.0198527
$712$	10.1082	0.378820
$713$	21.8600	0.818663
$714$	0.359206	0.0134430
$715$	−1.17874	−0.0440824
$716$	19.1653	0.716241
$717$	10.8437	0.404965
$718$	−4.49427	−0.167725
$719$	−40.4886	−1.50997	−0.754985	−	0.655742i	$-0.772356\pi$
$719$	−40.4886	−1.50997	−0.754985	+	0.655742i	$0.772356\pi$
$720$	14.3749	0.535719
$721$	−0.361248	−0.0134536
$722$	0.357031	0.0132873
$723$	−1.67614	−0.0623364
$724$	−14.9364	−0.555108
$725$	−16.8898	−0.627271
$726$	1.81478	0.0673530
$727$	9.19297	0.340949	0.170474	−	0.985362i	$-0.445470\pi$
$727$	9.19297	0.340949	0.170474	+	0.985362i	$0.445470\pi$
$728$	−0.238891	−0.00885388
$729$	1.00000	0.0370370
$730$	−3.51843	−0.130223
$731$	−33.8379	−1.25154
$732$	13.8270	0.511060
$733$	3.69814	0.136594	0.0682970	−	0.997665i	$-0.478243\pi$
$733$	3.69814	0.136594	0.0682970	+	0.997665i	$0.478243\pi$
$734$	−1.93834	−0.0715453
$735$	−25.7526	−0.949901
$736$	−13.5047	−0.497791
$737$	−0.269003	−0.00990884
$738$	1.07984	0.0397493
$739$	−25.9758	−0.955535	−0.477768	−	0.878486i	$-0.658554\pi$
$739$	−25.9758	−0.955535	−0.477768	+	0.878486i	$0.658554\pi$
$740$	31.9506	1.17453
$741$	−4.10553	−0.150820
$742$	0.104458	0.00383478
$743$	−42.9559	−1.57590	−0.787950	−	0.615740i	$-0.788857\pi$
$743$	−42.9559	−1.57590	−0.787950	+	0.615740i	$0.788857\pi$
$744$	2.09905	0.0769547
$745$	11.9944	0.439441
$746$	6.33077	0.231786
$747$	−0.539733	−0.0197478
$748$	3.70404	0.135433
$749$	−3.33606	−0.121897
$750$	−2.52995	−0.0923806
$751$	4.12812	0.150637	0.0753186	−	0.997160i	$-0.476003\pi$
$751$	4.12812	0.150637	0.0753186	+	0.997160i	$0.476003\pi$
$752$	41.6730	1.51966
$753$	8.75124	0.318913
$754$	0.310561	0.0113100
$755$	−29.3428	−1.06789
$756$	0.712484	0.0259128
$757$	52.2233	1.89809	0.949044	−	0.315144i	$-0.102053\pi$
$757$	52.2233	1.89809	0.949044	+	0.315144i	$0.102053\pi$
$758$	−1.20723	−0.0438484
$759$	−2.16543	−0.0786000
$760$	−10.1779	−0.369193
$761$	−32.0995	−1.16361	−0.581804	−	0.813329i	$-0.697653\pi$
$761$	−32.0995	−1.16361	−0.581804	+	0.813329i	$0.697653\pi$
$762$	1.69289	0.0613270
$763$	5.71014	0.206721
$764$	−10.6788	−0.386345
$765$	22.3914	0.809564
$766$	−1.01724	−0.0367543
$767$	5.25857	0.189876
$768$	13.8286	0.498998
$769$	−8.59328	−0.309882	−0.154941	−	0.987924i	$-0.549519\pi$
$769$	−8.59328	−0.309882	−0.154941	+	0.987924i	$0.549519\pi$
$770$	−0.0708886	−0.00255465
$771$	1.14675	0.0412990
$772$	−19.0806	−0.686725
$773$	31.8775	1.14655	0.573276	−	0.819362i	$-0.305672\pi$
$773$	31.8775	1.14655	0.573276	+	0.819362i	$0.305672\pi$
$774$	0.943130	0.0339001
$775$	28.7381	1.03230
$776$	−3.15036	−0.113091
$777$	1.56105	0.0560025
$778$	3.04608	0.109207
$779$	26.6301	0.954124
$780$	−7.39378	−0.264740
$781$	−2.94083	−0.105231
$782$	−6.84795	−0.244882
$783$	−1.86549	−0.0666673
$784$	−26.3410	−0.940749
$785$	30.1461	1.07596
$786$	−3.44750	−0.122968
$787$	14.6031	0.520545	0.260272	−	0.965535i	$-0.416188\pi$
$787$	14.6031	0.520545	0.260272	+	0.965535i	$0.416188\pi$
$788$	43.2253	1.53984
$789$	19.5990	0.697743
$790$	−0.330373	−0.0117541
$791$	5.44115	0.193465
$792$	−0.207929	−0.00738843
$793$	−7.01064	−0.248955
$794$	1.08578	0.0385330
$795$	6.51149	0.230939
$796$	−41.8295	−1.48261
$797$	42.5834	1.50838	0.754191	−	0.656655i	$-0.228029\pi$
$797$	42.5834	1.50838	0.754191	+	0.656655i	$0.228029\pi$
$798$	−0.246904	−0.00874030
$799$	64.9131	2.29646
$800$	−17.7539	−0.627696
$801$	15.2855	0.540086
$802$	−1.63996	−0.0579091
$803$	−1.77264	−0.0625550
$804$	−1.68735	−0.0595082
$805$	−9.32662	−0.328720
$806$	−0.528422	−0.0186129
$807$	−20.8614	−0.734355
$808$	11.2738	0.396612
$809$	−10.3025	−0.362218	−0.181109	−	0.983463i	$-0.557969\pi$
$809$	−10.3025	−0.362218	−0.181109	+	0.983463i	$0.557969\pi$
$810$	−0.624094	−0.0219284
$811$	32.4326	1.13886	0.569431	−	0.822039i	$-0.307164\pi$
$811$	32.4326	1.13886	0.569431	+	0.822039i	$0.307164\pi$
$812$	−1.32913	−0.0466435
$813$	1.90314	0.0667459
$814$	−0.226197	−0.00792820
$815$	3.08747	0.108149
$816$	22.9030	0.801764
$817$	23.2588	0.813723
$818$	−1.38719	−0.0485021
$819$	−0.361248	−0.0126230
$820$	47.9591	1.67480
$821$	14.3641	0.501311	0.250655	−	0.968076i	$-0.419354\pi$
$821$	14.3641	0.501311	0.250655	+	0.968076i	$0.419354\pi$
$822$	−2.64000	−0.0920805
$823$	−46.4322	−1.61852	−0.809262	−	0.587448i	$-0.800133\pi$
$823$	−46.4322	−1.61852	−0.809262	+	0.587448i	$0.800133\pi$
$824$	0.661293	0.0230372
$825$	−2.84676	−0.0991116
$826$	0.316247	0.0110036
$827$	15.0860	0.524593	0.262296	−	0.964987i	$-0.415520\pi$
$827$	15.0860	0.524593	0.262296	+	0.964987i	$0.415520\pi$
$828$	−13.5829	−0.472038
$829$	5.68456	0.197433	0.0987165	−	0.995116i	$-0.468526\pi$
$829$	5.68456	0.197433	0.0987165	+	0.995116i	$0.468526\pi$
$830$	0.336845	0.0116920
$831$	−21.2874	−0.738450
$832$	−7.34251	−0.254556
$833$	−41.0308	−1.42163
$834$	0.585678	0.0202804
$835$	−17.7109	−0.612910
$836$	−2.54601	−0.0880556
$837$	3.17415	0.109715
$838$	1.70150	0.0587775
$839$	17.9887	0.621038	0.310519	−	0.950567i	$-0.399497\pi$
$839$	17.9887	0.621038	0.310519	+	0.950567i	$0.399497\pi$
$840$	−0.895563	−0.0308999
$841$	−25.5199	−0.879998
$842$	−0.0130136	−0.000448478 0
$843$	28.9794	0.998104
$844$	−0.381326	−0.0131258
$845$	3.74884	0.128964
$846$	−1.80926	−0.0622037
$847$	3.93801	0.135312
$848$	6.66025	0.228714
$849$	−14.5853	−0.500566
$850$	−9.00262	−0.308787
$851$	−29.7601	−1.02016
$852$	−18.4467	−0.631972
$853$	40.6950	1.39337	0.696685	−	0.717377i	$-0.254658\pi$
$853$	40.6950	1.39337	0.696685	+	0.717377i	$0.254658\pi$
$854$	−0.421616	−0.0144274
$855$	−15.3910	−0.526360
$856$	6.10692	0.208730
$857$	34.9039	1.19229	0.596147	−	0.802876i	$-0.296698\pi$
$857$	34.9039	1.19229	0.596147	+	0.802876i	$0.296698\pi$
$858$	0.0523449	0.00178703
$859$	−1.41651	−0.0483306	−0.0241653	−	0.999708i	$-0.507693\pi$
$859$	−1.41651	−0.0483306	−0.0241653	+	0.999708i	$0.507693\pi$
$860$	41.8875	1.42835
$861$	2.34320	0.0798561
$862$	−0.166244	−0.00566230
$863$	−11.6842	−0.397736	−0.198868	−	0.980026i	$-0.563726\pi$
$863$	−11.6842	−0.397736	−0.198868	+	0.980026i	$0.563726\pi$
$864$	−1.96094	−0.0667124
$865$	−80.8511	−2.74902
$866$	2.46257	0.0836815
$867$	18.6755	0.634253
$868$	2.26153	0.0767615
$869$	−0.166447	−0.00564632
$870$	1.16424	0.0394715
$871$	0.855530	0.0289885
$872$	−10.4529	−0.353979
$873$	−4.76394	−0.161235
$874$	4.70701	0.159217
$875$	−5.48989	−0.185592
$876$	−11.1191	−0.375679
$877$	38.2811	1.29266	0.646331	−	0.763057i	$-0.276302\pi$
$877$	38.2811	1.29266	0.646331	+	0.763057i	$0.276302\pi$
$878$	2.88377	0.0973225
$879$	−22.4552	−0.757393
$880$	−4.51985	−0.152364
$881$	47.7835	1.60987	0.804933	−	0.593366i	$-0.202201\pi$
$881$	47.7835	1.60987	0.804933	+	0.593366i	$0.202201\pi$
$882$	1.14361	0.0385074
$883$	4.72950	0.159160	0.0795801	−	0.996828i	$-0.474642\pi$
$883$	4.72950	0.159160	0.0795801	+	0.996828i	$0.474642\pi$
$884$	−11.7803	−0.396213
$885$	19.7135	0.662663
$886$	1.53906	0.0517058
$887$	−45.7550	−1.53630	−0.768152	−	0.640268i	$-0.778823\pi$
$887$	−45.7550	−1.53630	−0.768152	+	0.640268i	$0.778823\pi$
$888$	−2.85763	−0.0958958
$889$	3.67351	0.123206
$890$	−9.53957	−0.319767
$891$	−0.314428	−0.0105337
$892$	6.44716	0.215867
$893$	−44.6187	−1.49311
$894$	−0.532641	−0.0178142
$895$	−36.4286	−1.21767
$896$	−1.85834	−0.0620829
$897$	6.88687	0.229946
$898$	6.44729	0.215149
$899$	−5.92136	−0.197488
$900$	−17.8567	−0.595222
$901$	10.3745	0.345626
$902$	−0.339531	−0.0113051
$903$	2.04656	0.0681052
$904$	−9.96045	−0.331280
$905$	28.3906	0.943734
$906$	1.30304	0.0432906
$907$	−16.5259	−0.548733	−0.274367	−	0.961625i	$-0.588468\pi$
$907$	−16.5259	−0.548733	−0.274367	+	0.961625i	$0.588468\pi$
$908$	−52.9264	−1.75643
$909$	17.0482	0.565452
$910$	0.225453	0.00747369
$911$	−24.5202	−0.812392	−0.406196	−	0.913786i	$-0.633145\pi$
$911$	−24.5202	−0.812392	−0.406196	+	0.913786i	$0.633145\pi$
$912$	−15.7426	−0.521289
$913$	0.169707	0.00561649
$914$	−0.721471	−0.0238641
$915$	−26.2818	−0.868848
$916$	1.27990	0.0422891
$917$	−7.48095	−0.247043
$918$	−0.994348	−0.0328184
$919$	29.4531	0.971568	0.485784	−	0.874079i	$-0.338534\pi$
$919$	29.4531	0.971568	0.485784	+	0.874079i	$0.338534\pi$
$920$	17.0731	0.562884
$921$	−23.5826	−0.777074
$922$	0.815565	0.0268592
$923$	9.35294	0.307856
$924$	−0.224025	−0.00736988
$925$	−39.1240	−1.28639
$926$	−0.952212	−0.0312916
$927$	1.00000	0.0328443
$928$	3.65811	0.120083
$929$	−8.99095	−0.294984	−0.147492	−	0.989063i	$-0.547120\pi$
$929$	−8.99095	−0.294984	−0.147492	+	0.989063i	$0.547120\pi$
$930$	−1.98097	−0.0649586
$931$	28.2029	0.924314
$932$	17.6737	0.578920
$933$	27.4057	0.897223
$934$	−5.78966	−0.189443
$935$	−7.04049	−0.230249
$936$	0.661293	0.0216150
$937$	−40.1484	−1.31159	−0.655796	−	0.754938i	$-0.727667\pi$
$937$	−40.1484	−1.31159	−0.655796	+	0.754938i	$0.727667\pi$
$938$	0.0514510	0.00167994
$939$	23.9273	0.780839
$940$	−80.3552	−2.62090
$941$	−13.6418	−0.444708	−0.222354	−	0.974966i	$-0.571374\pi$
$941$	−13.6418	−0.444708	−0.222354	+	0.974966i	$0.571374\pi$
$942$	−1.33871	−0.0436177
$943$	−44.6711	−1.45469
$944$	20.1639	0.656279
$945$	−1.35426	−0.0440541
$946$	−0.296547	−0.00964156
$947$	19.3313	0.628181	0.314091	−	0.949393i	$-0.398300\pi$
$947$	19.3313	0.628181	0.314091	+	0.949393i	$0.398300\pi$
$948$	−1.04406	−0.0339094
$949$	5.63766	0.183006
$950$	6.18804	0.200766
$951$	−13.7886	−0.447127
$952$	−1.42687	−0.0462451
$953$	34.0328	1.10243	0.551216	−	0.834363i	$-0.314164\pi$
$953$	34.0328	1.10243	0.551216	+	0.834363i	$0.314164\pi$
$954$	−0.289159	−0.00936188
$955$	20.2978	0.656822
$956$	−21.3869	−0.691700
$957$	0.586563	0.0189609
$958$	3.13840	0.101397
$959$	−5.72869	−0.184989
$960$	−27.5259	−0.888394
$961$	−20.9248	−0.674992
$962$	0.719392	0.0231941
$963$	9.23482	0.297588
$964$	3.30583	0.106474
$965$	36.2676	1.16749
$966$	0.414172	0.0133258
$967$	−33.2951	−1.07070	−0.535349	−	0.844631i	$-0.679820\pi$
$967$	−33.2951	−1.07070	−0.535349	+	0.844631i	$0.679820\pi$
$968$	−7.20884	−0.231701
$969$	−24.5219	−0.787757
$970$	2.97315	0.0954621
$971$	−18.3037	−0.587393	−0.293696	−	0.955899i	$-0.594885\pi$
$971$	−18.3037	−0.587393	−0.293696	+	0.955899i	$0.594885\pi$
$972$	−1.97229	−0.0632611
$973$	1.27090	0.0407432
$974$	−2.44920	−0.0784773
$975$	9.05379	0.289953
$976$	−26.8822	−0.860477
$977$	−56.8319	−1.81821	−0.909107	−	0.416562i	$-0.863235\pi$
$977$	−56.8319	−1.81821	−0.909107	+	0.416562i	$0.863235\pi$
$978$	−0.137107	−0.00438420
$979$	−4.80618	−0.153606
$980$	50.7916	1.62248
$981$	−15.8067	−0.504669
$982$	6.16983	0.196887
$983$	−27.3211	−0.871409	−0.435704	−	0.900090i	$-0.643501\pi$
$983$	−27.3211	−0.871409	−0.435704	+	0.900090i	$0.643501\pi$
$984$	−4.28942	−0.136742
$985$	−82.1609	−2.61786
$986$	1.85495	0.0590736
$987$	−3.92603	−0.124967
$988$	8.09728	0.257609
$989$	−39.0158	−1.24063
$990$	0.196233	0.00623668
$991$	41.5609	1.32023	0.660113	−	0.751166i	$-0.270508\pi$
$991$	41.5609	1.32023	0.660113	+	0.751166i	$0.270508\pi$
$992$	−6.22432	−0.197622
$993$	2.67099	0.0847612
$994$	0.562480	0.0178408
$995$	79.5079	2.52057
$996$	1.06451	0.0337302
$997$	−57.4662	−1.81997	−0.909986	−	0.414638i	$-0.863908\pi$
$997$	−57.4662	−1.81997	−0.909986	+	0.414638i	$0.863908\pi$
$998$	0.196712	0.00622680
$999$	−4.32128	−0.136719

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.k.1.14	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.k.1.14	✓	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-0.166477 q^{2} +1.00000 q^{3} -1.97229 q^{4} +3.74884 q^{5} -0.166477 q^{6} -0.361248 q^{7} +0.661293 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.166477 q^{2} +1.00000 q^{3} -1.97229 q^{4} +3.74884 q^{5} -0.166477 q^{6} -0.361248 q^{7} +0.661293 q^{8} +1.00000 q^{9} -0.624094 q^{10} -0.314428 q^{11} -1.97229 q^{12} +1.00000 q^{13} +0.0601394 q^{14} +3.74884 q^{15} +3.83448 q^{16} +5.97290 q^{17} -0.166477 q^{18} -4.10553 q^{19} -7.39378 q^{20} -0.361248 q^{21} +0.0523449 q^{22} +6.88687 q^{23} +0.661293 q^{24} +9.05379 q^{25} -0.166477 q^{26} +1.00000 q^{27} +0.712484 q^{28} -1.86549 q^{29} -0.624094 q^{30} +3.17415 q^{31} -1.96094 q^{32} -0.314428 q^{33} -0.994348 q^{34} -1.35426 q^{35} -1.97229 q^{36} -4.32128 q^{37} +0.683475 q^{38} +1.00000 q^{39} +2.47908 q^{40} -6.48641 q^{41} +0.0601394 q^{42} -5.66524 q^{43} +0.620142 q^{44} +3.74884 q^{45} -1.14650 q^{46} +10.8680 q^{47} +3.83448 q^{48} -6.86950 q^{49} -1.50724 q^{50} +5.97290 q^{51} -1.97229 q^{52} +1.73694 q^{53} -0.166477 q^{54} -1.17874 q^{55} -0.238891 q^{56} -4.10553 q^{57} +0.310561 q^{58} +5.25857 q^{59} -7.39378 q^{60} -7.01064 q^{61} -0.528422 q^{62} -0.361248 q^{63} -7.34251 q^{64} +3.74884 q^{65} +0.0523449 q^{66} +0.855530 q^{67} -11.7803 q^{68} +6.88687 q^{69} +0.225453 q^{70} +9.35294 q^{71} +0.661293 q^{72} +5.63766 q^{73} +0.719392 q^{74} +9.05379 q^{75} +8.09728 q^{76} +0.113586 q^{77} -0.166477 q^{78} +0.529364 q^{79} +14.3749 q^{80} +1.00000 q^{81} +1.07984 q^{82} -0.539733 q^{83} +0.712484 q^{84} +22.3914 q^{85} +0.943130 q^{86} -1.86549 q^{87} -0.207929 q^{88} +15.2855 q^{89} -0.624094 q^{90} -0.361248 q^{91} -13.5829 q^{92} +3.17415 q^{93} -1.80926 q^{94} -15.3910 q^{95} -1.96094 q^{96} -4.76394 q^{97} +1.14361 q^{98} -0.314428 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 41 q^{4} + 7 q^{5} + 5 q^{6} + 25 q^{7} + 12 q^{8} + 32 q^{9} + 2 q^{10} + 17 q^{11} + 41 q^{12} + 32 q^{13} - 10 q^{14} + 7 q^{15} + 51 q^{16} + 2 q^{17} + 5 q^{18} + 36 q^{19} - 2 q^{20} + 25 q^{21} - 3 q^{22} + 37 q^{23} + 12 q^{24} + 43 q^{25} + 5 q^{26} + 32 q^{27} + 54 q^{28} + 2 q^{29} + 2 q^{30} + 44 q^{31} + 19 q^{32} + 17 q^{33} + 27 q^{34} - 10 q^{35} + 41 q^{36} + 46 q^{37} - 6 q^{38} + 32 q^{39} - 6 q^{40} + 5 q^{41} - 10 q^{42} + 19 q^{43} + 37 q^{44} + 7 q^{45} + 23 q^{46} + 50 q^{47} + 51 q^{48} + 67 q^{49} - 4 q^{50} + 2 q^{51} + 41 q^{52} + 5 q^{54} + 18 q^{55} - 54 q^{56} + 36 q^{57} + 27 q^{58} + 26 q^{59} - 2 q^{60} + 23 q^{61} + 27 q^{62} + 25 q^{63} + 70 q^{64} + 7 q^{65} - 3 q^{66} + 30 q^{67} - 22 q^{68} + 37 q^{69} + 59 q^{70} + 34 q^{71} + 12 q^{72} + 54 q^{73} + 18 q^{74} + 43 q^{75} + 40 q^{76} - 5 q^{77} + 5 q^{78} + 35 q^{79} - 46 q^{80} + 32 q^{81} + 23 q^{83} + 54 q^{84} + 59 q^{85} - 5 q^{86} + 2 q^{87} - 13 q^{88} + 16 q^{89} + 2 q^{90} + 25 q^{91} + 101 q^{92} + 44 q^{93} - 16 q^{94} - q^{95} + 19 q^{96} + 44 q^{97} - 44 q^{98} + 17 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 41 * q^4 + 7 * q^5 + 5 * q^6 + 25 * q^7 + 12 * q^8 + 32 * q^9 + 2 * q^10 + 17 * q^11 + 41 * q^12 + 32 * q^13 - 10 * q^14 + 7 * q^15 + 51 * q^16 + 2 * q^17 + 5 * q^18 + 36 * q^19 - 2 * q^20 + 25 * q^21 - 3 * q^22 + 37 * q^23 + 12 * q^24 + 43 * q^25 + 5 * q^26 + 32 * q^27 + 54 * q^28 + 2 * q^29 + 2 * q^30 + 44 * q^31 + 19 * q^32 + 17 * q^33 + 27 * q^34 - 10 * q^35 + 41 * q^36 + 46 * q^37 - 6 * q^38 + 32 * q^39 - 6 * q^40 + 5 * q^41 - 10 * q^42 + 19 * q^43 + 37 * q^44 + 7 * q^45 + 23 * q^46 + 50 * q^47 + 51 * q^48 + 67 * q^49 - 4 * q^50 + 2 * q^51 + 41 * q^52 + 5 * q^54 + 18 * q^55 - 54 * q^56 + 36 * q^57 + 27 * q^58 + 26 * q^59 - 2 * q^60 + 23 * q^61 + 27 * q^62 + 25 * q^63 + 70 * q^64 + 7 * q^65 - 3 * q^66 + 30 * q^67 - 22 * q^68 + 37 * q^69 + 59 * q^70 + 34 * q^71 + 12 * q^72 + 54 * q^73 + 18 * q^74 + 43 * q^75 + 40 * q^76 - 5 * q^77 + 5 * q^78 + 35 * q^79 - 46 * q^80 + 32 * q^81 + 23 * q^83 + 54 * q^84 + 59 * q^85 - 5 * q^86 + 2 * q^87 - 13 * q^88 + 16 * q^89 + 2 * q^90 + 25 * q^91 + 101 * q^92 + 44 * q^93 - 16 * q^94 - q^95 + 19 * q^96 + 44 * q^97 - 44 * q^98 + 17 * q^99

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