LMFDB - Embedded newform 731.2.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.899791 q^{2} +0.468379 q^{3} -1.19038 q^{4} -0.603312 q^{5} -0.421443 q^{6} -2.56518 q^{7} +2.87067 q^{8} -2.78062 q^{9} +O(q^{10})$	\(q-0.899791 q^{2} +0.468379 q^{3} -1.19038 q^{4} -0.603312 q^{5} -0.421443 q^{6} -2.56518 q^{7} +2.87067 q^{8} -2.78062 q^{9} +0.542854 q^{10} +6.21613 q^{11} -0.557548 q^{12} -4.20204 q^{13} +2.30813 q^{14} -0.282579 q^{15} -0.202249 q^{16} -1.00000 q^{17} +2.50198 q^{18} +2.10920 q^{19} +0.718168 q^{20} -1.20148 q^{21} -5.59322 q^{22} +5.22842 q^{23} +1.34456 q^{24} -4.63601 q^{25} +3.78096 q^{26} -2.70752 q^{27} +3.05354 q^{28} +8.03061 q^{29} +0.254262 q^{30} +8.32533 q^{31} -5.55936 q^{32} +2.91151 q^{33} +0.899791 q^{34} +1.54761 q^{35} +3.30999 q^{36} +5.76809 q^{37} -1.89784 q^{38} -1.96815 q^{39} -1.73191 q^{40} +5.53414 q^{41} +1.08108 q^{42} +1.00000 q^{43} -7.39954 q^{44} +1.67758 q^{45} -4.70448 q^{46} +6.12834 q^{47} -0.0947292 q^{48} -0.419833 q^{49} +4.17144 q^{50} -0.468379 q^{51} +5.00202 q^{52} -11.1970 q^{53} +2.43620 q^{54} -3.75027 q^{55} -7.36380 q^{56} +0.987904 q^{57} -7.22586 q^{58} +10.9898 q^{59} +0.336375 q^{60} +7.69221 q^{61} -7.49106 q^{62} +7.13280 q^{63} +5.40676 q^{64} +2.53514 q^{65} -2.61975 q^{66} -5.36562 q^{67} +1.19038 q^{68} +2.44888 q^{69} -1.39252 q^{70} +6.37948 q^{71} -7.98225 q^{72} +2.92158 q^{73} -5.19007 q^{74} -2.17141 q^{75} -2.51074 q^{76} -15.9455 q^{77} +1.77092 q^{78} -0.365215 q^{79} +0.122019 q^{80} +7.07372 q^{81} -4.97957 q^{82} +12.2784 q^{83} +1.43021 q^{84} +0.603312 q^{85} -0.899791 q^{86} +3.76137 q^{87} +17.8445 q^{88} -17.0849 q^{89} -1.50947 q^{90} +10.7790 q^{91} -6.22379 q^{92} +3.89941 q^{93} -5.51422 q^{94} -1.27250 q^{95} -2.60389 q^{96} -0.788712 q^{97} +0.377762 q^{98} -17.2847 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) $ 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * 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 $

$2$	−0.899791	−0.636248	−0.318124	−	0.948049i	$-0.603053\pi$
$2$	−0.899791	−0.636248	−0.318124	+	0.948049i	$0.603053\pi$
$3$	0.468379	0.270419	0.135209	−	0.990817i	$-0.456829\pi$
$3$	0.468379	0.270419	0.135209	+	0.990817i	$0.456829\pi$
$4$	−1.19038	−0.595188
$5$	−0.603312	−0.269809	−0.134905	−	0.990859i	$-0.543073\pi$
$5$	−0.603312	−0.269809	−0.134905	+	0.990859i	$0.543073\pi$
$6$	−0.421443	−0.172053
$7$	−2.56518	−0.969548	−0.484774	−	0.874639i	$-0.661098\pi$
$7$	−2.56518	−0.969548	−0.484774	+	0.874639i	$0.661098\pi$
$8$	2.87067	1.01494
$9$	−2.78062	−0.926874
$10$	0.542854	0.171666
$11$	6.21613	1.87424	0.937118	−	0.349014i	$-0.113483\pi$
$11$	6.21613	1.87424	0.937118	+	0.349014i	$0.113483\pi$
$12$	−0.557548	−0.160950
$13$	−4.20204	−1.16544	−0.582719	−	0.812674i	$-0.698011\pi$
$13$	−4.20204	−1.16544	−0.582719	+	0.812674i	$0.698011\pi$
$14$	2.30813	0.616873
$15$	−0.282579	−0.0729615
$16$	−0.202249	−0.0505623
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	2.50198	0.589722
$19$	2.10920	0.483883	0.241942	−	0.970291i	$-0.422216\pi$
$19$	2.10920	0.483883	0.241942	+	0.970291i	$0.422216\pi$
$20$	0.718168	0.160587
$21$	−1.20148	−0.262184
$22$	−5.59322	−1.19248
$23$	5.22842	1.09020	0.545100	−	0.838371i	$-0.316492\pi$
$23$	5.22842	1.09020	0.545100	+	0.838371i	$0.316492\pi$
$24$	1.34456	0.274458
$25$	−4.63601	−0.927203
$26$	3.78096	0.741507
$27$	−2.70752	−0.521063
$28$	3.05354	0.577064
$29$	8.03061	1.49125	0.745623	−	0.666368i	$-0.232152\pi$
$29$	8.03061	1.49125	0.745623	+	0.666368i	$0.232152\pi$
$30$	0.254262	0.0464216
$31$	8.32533	1.49527	0.747637	−	0.664108i	$-0.231188\pi$
$31$	8.32533	1.49527	0.747637	+	0.664108i	$0.231188\pi$
$32$	−5.55936	−0.982765
$33$	2.91151	0.506828
$34$	0.899791	0.154313
$35$	1.54761	0.261593
$36$	3.30999	0.551665
$37$	5.76809	0.948268	0.474134	−	0.880453i	$-0.342761\pi$
$37$	5.76809	0.948268	0.474134	+	0.880453i	$0.342761\pi$
$38$	−1.89784	−0.307870
$39$	−1.96815	−0.315156
$40$	−1.73191	−0.273839
$41$	5.53414	0.864288	0.432144	−	0.901805i	$-0.357757\pi$
$41$	5.53414	0.864288	0.432144	+	0.901805i	$0.357757\pi$
$42$	1.08108	0.166814
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−7.39954	−1.11552
$45$	1.67758	0.250079
$46$	−4.70448	−0.693638
$47$	6.12834	0.893910	0.446955	−	0.894556i	$-0.352508\pi$
$47$	6.12834	0.893910	0.446955	+	0.894556i	$0.352508\pi$
$48$	−0.0947292	−0.0136730
$49$	−0.419833	−0.0599762
$50$	4.17144	0.589931
$51$	−0.468379	−0.0655862
$52$	5.00202	0.693655
$53$	−11.1970	−1.53803	−0.769013	−	0.639233i	$-0.779252\pi$
$53$	−11.1970	−1.53803	−0.769013	+	0.639233i	$0.779252\pi$
$54$	2.43620	0.331525
$55$	−3.75027	−0.505686
$56$	−7.36380	−0.984029
$57$	0.987904	0.130851
$58$	−7.22586	−0.948802
$59$	10.9898	1.43075	0.715375	−	0.698741i	$-0.246256\pi$
$59$	10.9898	1.43075	0.715375	+	0.698741i	$0.246256\pi$
$60$	0.336375	0.0434258
$61$	7.69221	0.984886	0.492443	−	0.870345i	$-0.336104\pi$
$61$	7.69221	0.984886	0.492443	+	0.870345i	$0.336104\pi$
$62$	−7.49106	−0.951365
$63$	7.13280	0.898649
$64$	5.40676	0.675845
$65$	2.53514	0.314446
$66$	−2.61975	−0.322469
$67$	−5.36562	−0.655514	−0.327757	−	0.944762i	$-0.606293\pi$
$67$	−5.36562	−0.655514	−0.327757	+	0.944762i	$0.606293\pi$
$68$	1.19038	0.144354
$69$	2.44888	0.294811
$70$	−1.39252	−0.166438
$71$	6.37948	0.757105	0.378553	−	0.925580i	$-0.376422\pi$
$71$	6.37948	0.757105	0.378553	+	0.925580i	$0.376422\pi$
$72$	−7.98225	−0.940717
$73$	2.92158	0.341945	0.170972	−	0.985276i	$-0.445309\pi$
$73$	2.92158	0.341945	0.170972	+	0.985276i	$0.445309\pi$
$74$	−5.19007	−0.603334
$75$	−2.17141	−0.250733
$76$	−2.51074	−0.288002
$77$	−15.9455	−1.81716
$78$	1.77092	0.200518
$79$	−0.365215	−0.0410898	−0.0205449	−	0.999789i	$-0.506540\pi$
$79$	−0.365215	−0.0410898	−0.0205449	+	0.999789i	$0.506540\pi$
$80$	0.122019	0.0136422
$81$	7.07372	0.785969
$82$	−4.97957	−0.549901
$83$	12.2784	1.34773	0.673864	−	0.738856i	$-0.264633\pi$
$83$	12.2784	1.34773	0.673864	+	0.738856i	$0.264633\pi$
$84$	1.43021	0.156049
$85$	0.603312	0.0654383
$86$	−0.899791	−0.0970269
$87$	3.76137	0.403261
$88$	17.8445	1.90223
$89$	−17.0849	−1.81100	−0.905498	−	0.424350i	$-0.860503\pi$
$89$	−17.0849	−1.81100	−0.905498	+	0.424350i	$0.860503\pi$
$90$	−1.50947	−0.159112
$91$	10.7790	1.12995
$92$	−6.22379	−0.648875
$93$	3.89941	0.404350
$94$	−5.51422	−0.568749
$95$	−1.27250	−0.130556
$96$	−2.60389	−0.265758
$97$	−0.788712	−0.0800816	−0.0400408	−	0.999198i	$-0.512749\pi$
$97$	−0.788712	−0.0800816	−0.0400408	+	0.999198i	$0.512749\pi$
$98$	0.377762	0.0381597
$99$	−17.2847	−1.73718
$100$	5.51861	0.551861
$101$	−13.4577	−1.33909	−0.669547	−	0.742770i	$-0.733512\pi$
$101$	−13.4577	−1.33909	−0.669547	+	0.742770i	$0.733512\pi$
$102$	0.421443	0.0417291
$103$	10.3452	1.01934	0.509670	−	0.860370i	$-0.329767\pi$
$103$	10.3452	1.01934	0.509670	+	0.860370i	$0.329767\pi$
$104$	−12.0627	−1.18284
$105$	0.724866	0.0707397
$106$	10.0750	0.978566
$107$	−9.33149	−0.902109	−0.451055	−	0.892496i	$-0.648952\pi$
$107$	−9.33149	−0.902109	−0.451055	+	0.892496i	$0.648952\pi$
$108$	3.22297	0.310131
$109$	14.1271	1.35313	0.676566	−	0.736382i	$-0.263467\pi$
$109$	14.1271	1.35313	0.676566	+	0.736382i	$0.263467\pi$
$110$	3.37445	0.321742
$111$	2.70165	0.256430
$112$	0.518806	0.0490226
$113$	15.0383	1.41469	0.707344	−	0.706870i	$-0.249893\pi$
$113$	15.0383	1.41469	0.707344	+	0.706870i	$0.249893\pi$
$114$	−0.888907	−0.0832538
$115$	−3.15436	−0.294146
$116$	−9.55945	−0.887572
$117$	11.6843	1.08021
$118$	−9.88851	−0.910311
$119$	2.56518	0.235150
$120$	−0.811190	−0.0740512
$121$	27.6403	2.51276
$122$	−6.92138	−0.626632
$123$	2.59208	0.233720
$124$	−9.91028	−0.889970
$125$	5.81352	0.519977
$126$	−6.41803	−0.571764
$127$	−7.89369	−0.700452	−0.350226	−	0.936665i	$-0.613895\pi$
$127$	−7.89369	−0.700452	−0.350226	+	0.936665i	$0.613895\pi$
$128$	6.25377	0.552760
$129$	0.468379	0.0412385
$130$	−2.28110	−0.200066
$131$	−16.4768	−1.43959	−0.719794	−	0.694188i	$-0.755764\pi$
$131$	−16.4768	−1.43959	−0.719794	+	0.694188i	$0.755764\pi$
$132$	−3.46579	−0.301658
$133$	−5.41048	−0.469148
$134$	4.82793	0.417070
$135$	1.63348	0.140588
$136$	−2.87067	−0.246158
$137$	−3.62060	−0.309328	−0.154664	−	0.987967i	$-0.549430\pi$
$137$	−3.62060	−0.309328	−0.154664	+	0.987967i	$0.549430\pi$
$138$	−2.20348	−0.187573
$139$	−7.25212	−0.615117	−0.307558	−	0.951529i	$-0.599512\pi$
$139$	−7.25212	−0.615117	−0.307558	+	0.951529i	$0.599512\pi$
$140$	−1.84223	−0.155697
$141$	2.87039	0.241730
$142$	−5.74020	−0.481707
$143$	−26.1205	−2.18430
$144$	0.562378	0.0468648
$145$	−4.84496	−0.402352
$146$	−2.62881	−0.217562
$147$	−0.196641	−0.0162187
$148$	−6.86620	−0.564398
$149$	20.7770	1.70212	0.851059	−	0.525071i	$-0.175961\pi$
$149$	20.7770	1.70212	0.851059	+	0.525071i	$0.175961\pi$
$150$	1.95382	0.159528
$151$	−8.49000	−0.690906	−0.345453	−	0.938436i	$-0.612275\pi$
$151$	−8.49000	−0.690906	−0.345453	+	0.938436i	$0.612275\pi$
$152$	6.05482	0.491110
$153$	2.78062	0.224800
$154$	14.3476	1.15617
$155$	−5.02277	−0.403439
$156$	2.34284	0.187577
$157$	−5.64493	−0.450514	−0.225257	−	0.974299i	$-0.572322\pi$
$157$	−5.64493	−0.450514	−0.225257	+	0.974299i	$0.572322\pi$
$158$	0.328617	0.0261433
$159$	−5.24444	−0.415911
$160$	3.35403	0.265159
$161$	−13.4118	−1.05700
$162$	−6.36486	−0.500071
$163$	−8.25314	−0.646436	−0.323218	−	0.946325i	$-0.604765\pi$
$163$	−8.25314	−0.646436	−0.323218	+	0.946325i	$0.604765\pi$
$164$	−6.58771	−0.514414
$165$	−1.75655	−0.136747
$166$	−11.0480	−0.857489
$167$	8.69946	0.673185	0.336592	−	0.941650i	$-0.390726\pi$
$167$	8.69946	0.673185	0.336592	+	0.941650i	$0.390726\pi$
$168$	−3.44905	−0.266100
$169$	4.65718	0.358245
$170$	−0.542854	−0.0416350
$171$	−5.86488	−0.448499
$172$	−1.19038	−0.0907654
$173$	−21.6653	−1.64718	−0.823591	−	0.567184i	$-0.808033\pi$
$173$	−21.6653	−1.64718	−0.823591	+	0.567184i	$0.808033\pi$
$174$	−3.38444	−0.256574
$175$	11.8922	0.898968
$176$	−1.25721	−0.0947656
$177$	5.14739	0.386901
$178$	15.3728	1.15224
$179$	−17.4547	−1.30462	−0.652312	−	0.757950i	$-0.726201\pi$
$179$	−17.4547	−1.30462	−0.652312	+	0.757950i	$0.726201\pi$
$180$	−1.99695	−0.148844
$181$	0.910425	0.0676713	0.0338357	−	0.999427i	$-0.489228\pi$
$181$	0.910425	0.0676713	0.0338357	+	0.999427i	$0.489228\pi$
$182$	−9.69886	−0.718927
$183$	3.60287	0.266332
$184$	15.0091	1.10648
$185$	−3.47996	−0.255852
$186$	−3.50865	−0.257267
$187$	−6.21613	−0.454569
$188$	−7.29503	−0.532045
$189$	6.94529	0.505196
$190$	1.14499	0.0830661
$191$	3.54507	0.256513	0.128256	−	0.991741i	$-0.459062\pi$
$191$	3.54507	0.256513	0.128256	+	0.991741i	$0.459062\pi$
$192$	2.53241	0.182761
$193$	6.11055	0.439847	0.219923	−	0.975517i	$-0.429419\pi$
$193$	6.11055	0.439847	0.219923	+	0.975517i	$0.429419\pi$
$194$	0.709676	0.0509518
$195$	1.18741	0.0850320
$196$	0.499760	0.0356971
$197$	21.4196	1.52609	0.763043	−	0.646348i	$-0.223705\pi$
$197$	21.4196	1.52609	0.763043	+	0.646348i	$0.223705\pi$
$198$	15.5526	1.10528
$199$	−6.91961	−0.490518	−0.245259	−	0.969458i	$-0.578873\pi$
$199$	−6.91961	−0.490518	−0.245259	+	0.969458i	$0.578873\pi$
$200$	−13.3085	−0.941051
$201$	−2.51314	−0.177263
$202$	12.1091	0.851996
$203$	−20.6000	−1.44583
$204$	0.557548	0.0390361
$205$	−3.33881	−0.233193
$206$	−9.30849	−0.648553
$207$	−14.5382	−1.01048
$208$	0.849860	0.0589272
$209$	13.1111	0.906911
$210$	−0.652228	−0.0450080
$211$	8.09449	0.557248	0.278624	−	0.960400i	$-0.410122\pi$
$211$	8.09449	0.557248	0.278624	+	0.960400i	$0.410122\pi$
$212$	13.3287	0.915416
$213$	2.98802	0.204735
$214$	8.39639	0.573965
$215$	−0.603312	−0.0411455
$216$	−7.77240	−0.528845
$217$	−21.3560	−1.44974
$218$	−12.7115	−0.860928
$219$	1.36841	0.0924683
$220$	4.46423	0.300978
$221$	4.20204	0.282660
$222$	−2.43092	−0.163153
$223$	18.5618	1.24299	0.621496	−	0.783418i	$-0.286525\pi$
$223$	18.5618	1.24299	0.621496	+	0.783418i	$0.286525\pi$
$224$	14.2608	0.952838
$225$	12.8910	0.859400
$226$	−13.5313	−0.900092
$227$	−10.5424	−0.699726	−0.349863	−	0.936801i	$-0.613772\pi$
$227$	−10.5424	−0.699726	−0.349863	+	0.936801i	$0.613772\pi$
$228$	−1.17598	−0.0778811
$229$	−26.8994	−1.77756	−0.888781	−	0.458332i	$-0.848447\pi$
$229$	−26.8994	−1.77756	−0.888781	+	0.458332i	$0.848447\pi$
$230$	2.83827	0.187150
$231$	−7.46855	−0.491395
$232$	23.0532	1.51352
$233$	−29.2284	−1.91482	−0.957409	−	0.288736i	$-0.906765\pi$
$233$	−29.2284	−1.91482	−0.957409	+	0.288736i	$0.906765\pi$
$234$	−10.5134	−0.687284
$235$	−3.69730	−0.241185
$236$	−13.0820	−0.851565
$237$	−0.171059	−0.0111115
$238$	−2.30813	−0.149614
$239$	11.9675	0.774112	0.387056	−	0.922056i	$-0.373492\pi$
$239$	11.9675	0.774112	0.387056	+	0.922056i	$0.373492\pi$
$240$	0.0571513	0.00368910
$241$	4.07148	0.262267	0.131133	−	0.991365i	$-0.458138\pi$
$241$	4.07148	0.262267	0.131133	+	0.991365i	$0.458138\pi$
$242$	−24.8705	−1.59874
$243$	11.4357	0.733603
$244$	−9.15663	−0.586193
$245$	0.253290	0.0161821
$246$	−2.33233	−0.148704
$247$	−8.86295	−0.563936
$248$	23.8993	1.51761
$249$	5.75094	0.364451
$250$	−5.23095	−0.330834
$251$	2.50188	0.157917	0.0789587	−	0.996878i	$-0.474840\pi$
$251$	2.50188	0.157917	0.0789587	+	0.996878i	$0.474840\pi$
$252$	−8.49072	−0.534865
$253$	32.5005	2.04329
$254$	7.10267	0.445661
$255$	0.282579	0.0176958
$256$	−16.4406	−1.02754
$257$	−2.28258	−0.142384	−0.0711918	−	0.997463i	$-0.522680\pi$
$257$	−2.28258	−0.142384	−0.0711918	+	0.997463i	$0.522680\pi$
$258$	−0.421443	−0.0262379
$259$	−14.7962	−0.919392
$260$	−3.01778	−0.187154
$261$	−22.3301	−1.38220
$262$	14.8257	0.915935
$263$	9.38135	0.578479	0.289240	−	0.957257i	$-0.406598\pi$
$263$	9.38135	0.578479	0.289240	+	0.957257i	$0.406598\pi$
$264$	8.35798	0.514398
$265$	6.75528	0.414974
$266$	4.86830	0.298495
$267$	−8.00221	−0.489727
$268$	6.38711	0.390155
$269$	0.475565	0.0289957	0.0144979	−	0.999895i	$-0.495385\pi$
$269$	0.475565	0.0289957	0.0144979	+	0.999895i	$0.495385\pi$
$270$	−1.46979	−0.0894485
$271$	14.3466	0.871495	0.435748	−	0.900069i	$-0.356484\pi$
$271$	14.3466	0.871495	0.435748	+	0.900069i	$0.356484\pi$
$272$	0.202249	0.0122632
$273$	5.04867	0.305559
$274$	3.25778	0.196810
$275$	−28.8181	−1.73780
$276$	−2.91509	−0.175468
$277$	13.0970	0.786923	0.393462	−	0.919341i	$-0.371277\pi$
$277$	13.0970	0.786923	0.393462	+	0.919341i	$0.371277\pi$
$278$	6.52539	0.391367
$279$	−23.1496	−1.38593
$280$	4.44267	0.265500
$281$	6.79813	0.405542	0.202771	−	0.979226i	$-0.435005\pi$
$281$	6.79813	0.405542	0.202771	+	0.979226i	$0.435005\pi$
$282$	−2.58275	−0.153800
$283$	14.8230	0.881133	0.440567	−	0.897720i	$-0.354778\pi$
$283$	14.8230	0.881133	0.440567	+	0.897720i	$0.354778\pi$
$284$	−7.59399	−0.450620
$285$	−0.596014	−0.0353048
$286$	23.5030	1.38976
$287$	−14.1961	−0.837968
$288$	15.4585	0.910899
$289$	1.00000	0.0588235
$290$	4.35945	0.255996
$291$	−0.369416	−0.0216556
$292$	−3.47778	−0.203522
$293$	23.3490	1.36406	0.682032	−	0.731323i	$-0.261097\pi$
$293$	23.3490	1.36406	0.682032	+	0.731323i	$0.261097\pi$
$294$	0.176936	0.0103191
$295$	−6.63027	−0.386029
$296$	16.5583	0.962431
$297$	−16.8303	−0.976594
$298$	−18.6949	−1.08297
$299$	−21.9700	−1.27056
$300$	2.58480	0.149233
$301$	−2.56518	−0.147855
$302$	7.63922	0.439588
$303$	−6.30332	−0.362116
$304$	−0.426584	−0.0244662
$305$	−4.64080	−0.265731
$306$	−2.50198	−0.143028
$307$	−22.5586	−1.28749	−0.643744	−	0.765241i	$-0.722620\pi$
$307$	−22.5586	−1.28749	−0.643744	+	0.765241i	$0.722620\pi$
$308$	18.9812	1.08155
$309$	4.84546	0.275649
$310$	4.51944	0.256687
$311$	17.1638	0.973271	0.486636	−	0.873605i	$-0.338224\pi$
$311$	17.1638	0.973271	0.486636	+	0.873605i	$0.338224\pi$
$312$	−5.64991	−0.319863
$313$	10.2877	0.581497	0.290749	−	0.956799i	$-0.406096\pi$
$313$	10.2877	0.581497	0.290749	+	0.956799i	$0.406096\pi$
$314$	5.07925	0.286639
$315$	−4.30330	−0.242464
$316$	0.434743	0.0244562
$317$	14.0744	0.790495	0.395247	−	0.918575i	$-0.370659\pi$
$317$	14.0744	0.790495	0.395247	+	0.918575i	$0.370659\pi$
$318$	4.71890	0.264623
$319$	49.9193	2.79495
$320$	−3.26196	−0.182349
$321$	−4.37067	−0.243947
$322$	12.0679	0.672515
$323$	−2.10920	−0.117359
$324$	−8.42039	−0.467799
$325$	19.4807	1.08060
$326$	7.42610	0.411294
$327$	6.61685	0.365913
$328$	15.8867	0.877196
$329$	−15.7203	−0.866689
$330$	1.58052	0.0870050
$331$	9.17228	0.504154	0.252077	−	0.967707i	$-0.418886\pi$
$331$	9.17228	0.504154	0.252077	+	0.967707i	$0.418886\pi$
$332$	−14.6159	−0.802152
$333$	−16.0389	−0.878925
$334$	−7.82769	−0.428312
$335$	3.23714	0.176864
$336$	0.242998	0.0132566
$337$	4.76633	0.259639	0.129819	−	0.991538i	$-0.458560\pi$
$337$	4.76633	0.259639	0.129819	+	0.991538i	$0.458560\pi$
$338$	−4.19049	−0.227933
$339$	7.04364	0.382558
$340$	−0.718168	−0.0389481
$341$	51.7514	2.80250
$342$	5.27717	0.285356
$343$	19.0332	1.02770
$344$	2.87067	0.154776
$345$	−1.47744	−0.0795426
$346$	19.4942	1.04802
$347$	23.1212	1.24121	0.620604	−	0.784124i	$-0.286887\pi$
$347$	23.1212	1.24121	0.620604	+	0.784124i	$0.286887\pi$
$348$	−4.47744	−0.240016
$349$	−17.2777	−0.924853	−0.462426	−	0.886658i	$-0.653021\pi$
$349$	−17.2777	−0.924853	−0.462426	+	0.886658i	$0.653021\pi$
$350$	−10.7005	−0.571967
$351$	11.3771	0.607266
$352$	−34.5577	−1.84193
$353$	−0.556093	−0.0295979	−0.0147989	−	0.999890i	$-0.504711\pi$
$353$	−0.556093	−0.0295979	−0.0147989	+	0.999890i	$0.504711\pi$
$354$	−4.63157	−0.246165
$355$	−3.84882	−0.204274
$356$	20.3375	1.07788
$357$	1.20148	0.0635890
$358$	15.7056	0.830065
$359$	−3.71330	−0.195981	−0.0979903	−	0.995187i	$-0.531241\pi$
$359$	−3.71330	−0.195981	−0.0979903	+	0.995187i	$0.531241\pi$
$360$	4.81578	0.253814
$361$	−14.5513	−0.765857
$362$	−0.819191	−0.0430557
$363$	12.9462	0.679497
$364$	−12.8311	−0.672532
$365$	−1.76262	−0.0922599
$366$	−3.24183	−0.169453
$367$	23.1837	1.21018	0.605090	−	0.796157i	$-0.293137\pi$
$367$	23.1837	1.21018	0.605090	+	0.796157i	$0.293137\pi$
$368$	−1.05744	−0.0551230
$369$	−15.3883	−0.801085
$370$	3.13123	0.162785
$371$	28.7224	1.49119
$372$	−4.64177	−0.240665
$373$	−18.4374	−0.954654	−0.477327	−	0.878726i	$-0.658394\pi$
$373$	−18.4374	−0.954654	−0.477327	+	0.878726i	$0.658394\pi$
$374$	5.59322	0.289219
$375$	2.72293	0.140612
$376$	17.5924	0.907261
$377$	−33.7450	−1.73795
$378$	−6.24931	−0.321430
$379$	5.13885	0.263965	0.131982	−	0.991252i	$-0.457866\pi$
$379$	5.13885	0.263965	0.131982	+	0.991252i	$0.457866\pi$
$380$	1.51476	0.0777055
$381$	−3.69724	−0.189415
$382$	−3.18982	−0.163206
$383$	−17.9421	−0.916800	−0.458400	−	0.888746i	$-0.651577\pi$
$383$	−17.9421	−0.916800	−0.458400	+	0.888746i	$0.651577\pi$
$384$	2.92914	0.149477
$385$	9.62012	0.490287
$386$	−5.49821	−0.279852
$387$	−2.78062	−0.141347
$388$	0.938865	0.0476636
$389$	30.8756	1.56546	0.782728	−	0.622364i	$-0.213828\pi$
$389$	30.8756	1.56546	0.782728	+	0.622364i	$0.213828\pi$
$390$	−1.06842	−0.0541015
$391$	−5.22842	−0.264412
$392$	−1.20520	−0.0608720
$393$	−7.71741	−0.389292
$394$	−19.2732	−0.970969
$395$	0.220338	0.0110864
$396$	20.5753	1.03395
$397$	21.6562	1.08689	0.543446	−	0.839444i	$-0.317119\pi$
$397$	21.6562	1.08689	0.543446	+	0.839444i	$0.317119\pi$
$398$	6.22620	0.312091
$399$	−2.53416	−0.126866
$400$	0.937630	0.0468815
$401$	23.6236	1.17971	0.589853	−	0.807511i	$-0.299186\pi$
$401$	23.6236	1.17971	0.589853	+	0.807511i	$0.299186\pi$
$402$	2.26130	0.112783
$403$	−34.9834	−1.74265
$404$	16.0198	0.797013
$405$	−4.26766	−0.212062
$406$	18.5357	0.919910
$407$	35.8552	1.77728
$408$	−1.34456	−0.0665657
$409$	39.0487	1.93083	0.965417	−	0.260710i	$-0.0839568\pi$
$409$	39.0487	1.93083	0.965417	+	0.260710i	$0.0839568\pi$
$410$	3.00423	0.148368
$411$	−1.69581	−0.0836482
$412$	−12.3147	−0.606700
$413$	−28.1908	−1.38718
$414$	13.0814	0.642915
$415$	−7.40769	−0.363629
$416$	23.3607	1.14535
$417$	−3.39674	−0.166339
$418$	−11.7972	−0.577020
$419$	−20.9759	−1.02474	−0.512370	−	0.858765i	$-0.671232\pi$
$419$	−20.9759	−1.02474	−0.512370	+	0.858765i	$0.671232\pi$
$420$	−0.862864	−0.0421034
$421$	−1.36150	−0.0663555	−0.0331777	−	0.999449i	$-0.510563\pi$
$421$	−1.36150	−0.0663555	−0.0331777	+	0.999449i	$0.510563\pi$
$422$	−7.28334	−0.354548
$423$	−17.0406	−0.828542
$424$	−32.1429	−1.56100
$425$	4.63601	0.224880
$426$	−2.68859	−0.130263
$427$	−19.7319	−0.954895
$428$	11.1080	0.536925
$429$	−12.2343	−0.590677
$430$	0.542854	0.0261788
$431$	19.2809	0.928730	0.464365	−	0.885644i	$-0.346283\pi$
$431$	19.2809	0.928730	0.464365	+	0.885644i	$0.346283\pi$
$432$	0.547594	0.0263461
$433$	3.60205	0.173103	0.0865517	−	0.996247i	$-0.472415\pi$
$433$	3.60205	0.173103	0.0865517	+	0.996247i	$0.472415\pi$
$434$	19.2159	0.922394
$435$	−2.26928	−0.108804
$436$	−16.8166	−0.805369
$437$	11.0278	0.527530
$438$	−1.23128	−0.0588328
$439$	19.0990	0.911544	0.455772	−	0.890097i	$-0.349363\pi$
$439$	19.0990	0.911544	0.455772	+	0.890097i	$0.349363\pi$
$440$	−10.7658	−0.513239
$441$	1.16740	0.0555904
$442$	−3.78096	−0.179842
$443$	−3.60414	−0.171238	−0.0856190	−	0.996328i	$-0.527287\pi$
$443$	−3.60414	−0.171238	−0.0856190	+	0.996328i	$0.527287\pi$
$444$	−3.21599	−0.152624
$445$	10.3075	0.488623
$446$	−16.7018	−0.790851
$447$	9.73151	0.460284
$448$	−13.8693	−0.655264
$449$	30.4965	1.43922	0.719609	−	0.694380i	$-0.244321\pi$
$449$	30.4965	1.43922	0.719609	+	0.694380i	$0.244321\pi$
$450$	−11.5992	−0.546792
$451$	34.4010	1.61988
$452$	−17.9013	−0.842005
$453$	−3.97654	−0.186834
$454$	9.48598	0.445199
$455$	−6.50311	−0.304870
$456$	2.83595	0.132805
$457$	3.91657	0.183209	0.0916046	−	0.995795i	$-0.470800\pi$
$457$	3.91657	0.183209	0.0916046	+	0.995795i	$0.470800\pi$
$458$	24.2038	1.13097
$459$	2.70752	0.126376
$460$	3.75488	0.175072
$461$	6.16278	0.287029	0.143515	−	0.989648i	$-0.454160\pi$
$461$	6.16278	0.287029	0.143515	+	0.989648i	$0.454160\pi$
$462$	6.72013	0.312649
$463$	−7.71580	−0.358583	−0.179292	−	0.983796i	$-0.557381\pi$
$463$	−7.71580	−0.358583	−0.179292	+	0.983796i	$0.557381\pi$
$464$	−1.62418	−0.0754008
$465$	−2.35256	−0.109097
$466$	26.2995	1.21830
$467$	−11.1930	−0.517948	−0.258974	−	0.965884i	$-0.583384\pi$
$467$	−11.1930	−0.517948	−0.258974	+	0.965884i	$0.583384\pi$
$468$	−13.9087	−0.642931
$469$	13.7638	0.635553
$470$	3.32679	0.153454
$471$	−2.64397	−0.121828
$472$	31.5481	1.45212
$473$	6.21613	0.285818
$474$	0.153917	0.00706965
$475$	−9.77828	−0.448658
$476$	−3.05354	−0.139959
$477$	31.1346	1.42556
$478$	−10.7682	−0.492527
$479$	−12.0769	−0.551806	−0.275903	−	0.961186i	$-0.588977\pi$
$479$	−12.0769	−0.551806	−0.275903	+	0.961186i	$0.588977\pi$
$480$	1.57096	0.0717040
$481$	−24.2378	−1.10515
$482$	−3.66348	−0.166867
$483$	−6.28183	−0.285833
$484$	−32.9024	−1.49556
$485$	0.475839	0.0216068
$486$	−10.2898	−0.466754
$487$	−18.4956	−0.838117	−0.419059	−	0.907959i	$-0.637640\pi$
$487$	−18.4956	−0.838117	−0.419059	+	0.907959i	$0.637640\pi$
$488$	22.0818	0.999596
$489$	−3.86560	−0.174808
$490$	−0.227908	−0.0102958
$491$	−12.2261	−0.551757	−0.275879	−	0.961192i	$-0.588969\pi$
$491$	−12.2261	−0.551757	−0.275879	+	0.961192i	$0.588969\pi$
$492$	−3.08555	−0.139107
$493$	−8.03061	−0.361680
$494$	7.97480	0.358803
$495$	10.4281	0.468707
$496$	−1.68379	−0.0756045
$497$	−16.3645	−0.734050
$498$	−5.17464	−0.231881
$499$	17.8790	0.800374	0.400187	−	0.916434i	$-0.368945\pi$
$499$	17.8790	0.800374	0.400187	+	0.916434i	$0.368945\pi$
$500$	−6.92028	−0.309484
$501$	4.07465	0.182042
$502$	−2.25117	−0.100475
$503$	−6.34356	−0.282845	−0.141423	−	0.989949i	$-0.545168\pi$
$503$	−6.34356	−0.282845	−0.141423	+	0.989949i	$0.545168\pi$
$504$	20.4759	0.912071
$505$	8.11920	0.361300
$506$	−29.2437	−1.30004
$507$	2.18133	0.0968761
$508$	9.39647	0.416901
$509$	−32.9265	−1.45944	−0.729721	−	0.683745i	$-0.760350\pi$
$509$	−32.9265	−1.45944	−0.729721	+	0.683745i	$0.760350\pi$
$510$	−0.254262	−0.0112589
$511$	−7.49438	−0.331532
$512$	2.28556	0.101008
$513$	−5.71070	−0.252134
$514$	2.05385	0.0905913
$515$	−6.24137	−0.275027
$516$	−0.557548	−0.0245447
$517$	38.0946	1.67540
$518$	13.3135	0.584961
$519$	−10.1476	−0.445429
$520$	7.27756	0.319142
$521$	−31.6272	−1.38561	−0.692806	−	0.721124i	$-0.743626\pi$
$521$	−31.6272	−1.38561	−0.692806	+	0.721124i	$0.743626\pi$
$522$	20.0924	0.879420
$523$	−9.98506	−0.436616	−0.218308	−	0.975880i	$-0.570054\pi$
$523$	−9.98506	−0.436616	−0.218308	+	0.975880i	$0.570054\pi$
$524$	19.6136	0.856826
$525$	5.57007	0.243098
$526$	−8.44125	−0.368056
$527$	−8.32533	−0.362657
$528$	−0.588850	−0.0256264
$529$	4.33634	0.188536
$530$	−6.07834	−0.264026
$531$	−30.5584	−1.32612
$532$	6.44051	0.279232
$533$	−23.2547	−1.00727
$534$	7.20031	0.311588
$535$	5.62980	0.243397
$536$	−15.4029	−0.665305
$537$	−8.17541	−0.352795
$538$	−0.427909	−0.0184485
$539$	−2.60974	−0.112409
$540$	−1.94446	−0.0836761
$541$	10.8334	0.465766	0.232883	−	0.972505i	$-0.425184\pi$
$541$	10.8334	0.465766	0.232883	+	0.972505i	$0.425184\pi$
$542$	−12.9090	−0.554487
$543$	0.426424	0.0182996
$544$	5.55936	0.238356
$545$	−8.52306	−0.365088
$546$	−4.54274	−0.194411
$547$	−15.7250	−0.672353	−0.336176	−	0.941799i	$-0.609134\pi$
$547$	−15.7250	−0.672353	−0.336176	+	0.941799i	$0.609134\pi$
$548$	4.30987	0.184109
$549$	−21.3891	−0.912865
$550$	25.9303	1.10567
$551$	16.9381	0.721589
$552$	7.02993	0.299214
$553$	0.936842	0.0398386
$554$	−11.7846	−0.500678
$555$	−1.62994	−0.0691871
$556$	8.63276	0.366110
$557$	31.5813	1.33814	0.669071	−	0.743199i	$-0.266692\pi$
$557$	31.5813	1.33814	0.669071	+	0.743199i	$0.266692\pi$
$558$	20.8298	0.881795
$559$	−4.20204	−0.177728
$560$	−0.313002	−0.0132267
$561$	−2.91151	−0.122924
$562$	−6.11689	−0.258026
$563$	−3.18431	−0.134203	−0.0671013	−	0.997746i	$-0.521375\pi$
$563$	−3.18431	−0.134203	−0.0671013	+	0.997746i	$0.521375\pi$
$564$	−3.41684	−0.143875
$565$	−9.07280	−0.381696
$566$	−13.3376	−0.560619
$567$	−18.1454	−0.762034
$568$	18.3134	0.768413
$569$	−38.3936	−1.60954	−0.804772	−	0.593584i	$-0.797712\pi$
$569$	−38.3936	−1.60954	−0.804772	+	0.593584i	$0.797712\pi$
$570$	0.536288	0.0224626
$571$	−2.22902	−0.0932815	−0.0466408	−	0.998912i	$-0.514852\pi$
$571$	−2.22902	−0.0932815	−0.0466408	+	0.998912i	$0.514852\pi$
$572$	31.0932	1.30007
$573$	1.66044	0.0693658
$574$	12.7735	0.533156
$575$	−24.2390	−1.01084
$576$	−15.0341	−0.626423
$577$	−29.9480	−1.24675	−0.623376	−	0.781922i	$-0.714239\pi$
$577$	−29.9480	−1.24675	−0.623376	+	0.781922i	$0.714239\pi$
$578$	−0.899791	−0.0374264
$579$	2.86205	0.118943
$580$	5.76733	0.239475
$581$	−31.4963	−1.30669
$582$	0.332397	0.0137783
$583$	−69.6021	−2.88262
$584$	8.38689	0.347052
$585$	−7.04927	−0.291452
$586$	−21.0092	−0.867883
$587$	−36.7323	−1.51610	−0.758052	−	0.652194i	$-0.773849\pi$
$587$	−36.7323	−1.51610	−0.758052	+	0.652194i	$0.773849\pi$
$588$	0.234077	0.00965318
$589$	17.5598	0.723538
$590$	5.96585	0.245610
$591$	10.0325	0.412682
$592$	−1.16659	−0.0479466
$593$	−37.6960	−1.54799	−0.773995	−	0.633191i	$-0.781745\pi$
$593$	−37.6960	−1.54799	−0.773995	+	0.633191i	$0.781745\pi$
$594$	15.1438	0.621356
$595$	−1.54761	−0.0634456
$596$	−24.7324	−1.01308
$597$	−3.24100	−0.132645
$598$	19.7684	0.808391
$599$	7.45269	0.304509	0.152254	−	0.988341i	$-0.451347\pi$
$599$	7.45269	0.304509	0.152254	+	0.988341i	$0.451347\pi$
$600$	−6.23341	−0.254478
$601$	4.13008	0.168469	0.0842347	−	0.996446i	$-0.473155\pi$
$601$	4.13008	0.168469	0.0842347	+	0.996446i	$0.473155\pi$
$602$	2.30813	0.0940723
$603$	14.9197	0.607579
$604$	10.1063	0.411220
$605$	−16.6757	−0.677965
$606$	5.67167	0.230396
$607$	−39.3716	−1.59805	−0.799023	−	0.601301i	$-0.794649\pi$
$607$	−39.3716	−1.59805	−0.799023	+	0.601301i	$0.794649\pi$
$608$	−11.7258	−0.475544
$609$	−9.64860	−0.390981
$610$	4.17575	0.169071
$611$	−25.7516	−1.04180
$612$	−3.30999	−0.133798
$613$	−39.4807	−1.59461	−0.797304	−	0.603577i	$-0.793741\pi$
$613$	−39.4807	−1.59461	−0.797304	+	0.603577i	$0.793741\pi$
$614$	20.2980	0.819162
$615$	−1.56383	−0.0630597
$616$	−45.7744	−1.84430
$617$	10.1314	0.407874	0.203937	−	0.978984i	$-0.434626\pi$
$617$	10.1314	0.407874	0.203937	+	0.978984i	$0.434626\pi$
$618$	−4.35990	−0.175381
$619$	−10.9041	−0.438271	−0.219135	−	0.975694i	$-0.570324\pi$
$619$	−10.9041	−0.438271	−0.219135	+	0.975694i	$0.570324\pi$
$620$	5.97899	0.240122
$621$	−14.1561	−0.568063
$622$	−15.4438	−0.619242
$623$	43.8259	1.75585
$624$	0.398057	0.0159350
$625$	19.6727	0.786908
$626$	−9.25681	−0.369976
$627$	6.14095	0.245246
$628$	6.71959	0.268141
$629$	−5.76809	−0.229989
$630$	3.87207	0.154267
$631$	−2.68469	−0.106876	−0.0534380	−	0.998571i	$-0.517018\pi$
$631$	−2.68469	−0.106876	−0.0534380	+	0.998571i	$0.517018\pi$
$632$	−1.04841	−0.0417035
$633$	3.79129	0.150690
$634$	−12.6640	−0.502951
$635$	4.76236	0.188988
$636$	6.24286	0.247546
$637$	1.76416	0.0698985
$638$	−44.9169	−1.77828
$639$	−17.7389	−0.701741
$640$	−3.77297	−0.149140
$641$	−28.5058	−1.12591	−0.562956	−	0.826487i	$-0.690336\pi$
$641$	−28.5058	−1.12591	−0.562956	+	0.826487i	$0.690336\pi$
$642$	3.93269	0.155211
$643$	−0.216509	−0.00853830	−0.00426915	−	0.999991i	$-0.501359\pi$
$643$	−0.216509	−0.00853830	−0.00426915	+	0.999991i	$0.501359\pi$
$644$	15.9652	0.629115
$645$	−0.282579	−0.0111265
$646$	1.89784	0.0746694
$647$	−10.8914	−0.428186	−0.214093	−	0.976813i	$-0.568680\pi$
$647$	−10.8914	−0.428186	−0.214093	+	0.976813i	$0.568680\pi$
$648$	20.3063	0.797707
$649$	68.3140	2.68156
$650$	−17.5286	−0.687528
$651$	−10.0027	−0.392037
$652$	9.82435	0.384751
$653$	−30.6188	−1.19820	−0.599102	−	0.800672i	$-0.704476\pi$
$653$	−30.6188	−1.19820	−0.599102	+	0.800672i	$0.704476\pi$
$654$	−5.95378	−0.232811
$655$	9.94067	0.388414
$656$	−1.11927	−0.0437003
$657$	−8.12380	−0.316940
$658$	14.1450	0.551429
$659$	26.2748	1.02352	0.511760	−	0.859128i	$-0.328994\pi$
$659$	26.2748	1.02352	0.511760	+	0.859128i	$0.328994\pi$
$660$	2.09095	0.0813902
$661$	33.4642	1.30161	0.650804	−	0.759246i	$-0.274432\pi$
$661$	33.4642	1.30161	0.650804	+	0.759246i	$0.274432\pi$
$662$	−8.25313	−0.320767
$663$	1.96815	0.0764366
$664$	35.2472	1.36786
$665$	3.26421	0.126581
$666$	14.4316	0.559214
$667$	41.9873	1.62576
$668$	−10.3556	−0.400672
$669$	8.69397	0.336128
$670$	−2.91275	−0.112529
$671$	47.8158	1.84591
$672$	6.67945	0.257665
$673$	24.6520	0.950263	0.475131	−	0.879915i	$-0.342400\pi$
$673$	24.6520	0.950263	0.475131	+	0.879915i	$0.342400\pi$
$674$	−4.28870	−0.165195
$675$	12.5521	0.483131
$676$	−5.54380	−0.213223
$677$	−18.5249	−0.711971	−0.355985	−	0.934492i	$-0.615855\pi$
$677$	−18.5249	−0.711971	−0.355985	+	0.934492i	$0.615855\pi$
$678$	−6.33780	−0.243402
$679$	2.02319	0.0776430
$680$	1.73191	0.0664157
$681$	−4.93785	−0.189219
$682$	−46.5654	−1.78308
$683$	40.3970	1.54575	0.772875	−	0.634559i	$-0.218818\pi$
$683$	40.3970	1.54575	0.772875	+	0.634559i	$0.218818\pi$
$684$	6.98142	0.266941
$685$	2.18435	0.0834596
$686$	−17.1259	−0.653871
$687$	−12.5991	−0.480686
$688$	−0.202249	−0.00771067
$689$	47.0503	1.79247
$690$	1.32939	0.0506088
$691$	49.6341	1.88817	0.944085	−	0.329703i	$-0.106949\pi$
$691$	49.6341	1.88817	0.944085	+	0.329703i	$0.106949\pi$
$692$	25.7899	0.980384
$693$	44.3385	1.68428
$694$	−20.8042	−0.789717
$695$	4.37529	0.165964
$696$	10.7976	0.409284
$697$	−5.53414	−0.209621
$698$	15.5463	0.588436
$699$	−13.6900	−0.517803
$700$	−14.1562	−0.535055
$701$	8.95917	0.338383	0.169192	−	0.985583i	$-0.445884\pi$
$701$	8.95917	0.338383	0.169192	+	0.985583i	$0.445884\pi$
$702$	−10.2370	−0.386372
$703$	12.1661	0.458851
$704$	33.6091	1.26669
$705$	−1.73174	−0.0652210
$706$	0.500367	0.0188316
$707$	34.5215	1.29832
$708$	−6.12733	−0.230279
$709$	−29.8369	−1.12055	−0.560273	−	0.828308i	$-0.689304\pi$
$709$	−29.8369	−1.12055	−0.560273	+	0.828308i	$0.689304\pi$
$710$	3.46313	0.129969
$711$	1.01552	0.0380851
$712$	−49.0451	−1.83804
$713$	43.5283	1.63015
$714$	−1.08108	−0.0404584
$715$	15.7588	0.589345
$716$	20.7777	0.776497
$717$	5.60532	0.209335
$718$	3.34120	0.124692
$719$	18.5873	0.693188	0.346594	−	0.938015i	$-0.387338\pi$
$719$	18.5873	0.693188	0.346594	+	0.938015i	$0.387338\pi$
$720$	−0.339289	−0.0126446
$721$	−26.5373	−0.988300
$722$	13.0931	0.487275
$723$	1.90699	0.0709219
$724$	−1.08375	−0.0402772
$725$	−37.2300	−1.38269
$726$	−11.6488	−0.432329
$727$	−51.2013	−1.89895	−0.949476	−	0.313840i	$-0.898384\pi$
$727$	−51.2013	−1.89895	−0.949476	+	0.313840i	$0.898384\pi$
$728$	30.9430	1.14682
$729$	−15.8649	−0.587588
$730$	1.58599	0.0587002
$731$	−1.00000	−0.0369863
$732$	−4.28877	−0.158518
$733$	−13.5700	−0.501218	−0.250609	−	0.968088i	$-0.580631\pi$
$733$	−13.5700	−0.501218	−0.250609	+	0.968088i	$0.580631\pi$
$734$	−20.8605	−0.769974
$735$	0.118636	0.00437595
$736$	−29.0667	−1.07141
$737$	−33.3534	−1.22859
$738$	13.8463	0.509689
$739$	15.3522	0.564738	0.282369	−	0.959306i	$-0.408880\pi$
$739$	15.3522	0.564738	0.282369	+	0.959306i	$0.408880\pi$
$740$	4.14246	0.152280
$741$	−4.15122	−0.152499
$742$	−25.8441	−0.948767
$743$	−3.62439	−0.132966	−0.0664830	−	0.997788i	$-0.521178\pi$
$743$	−3.62439	−0.132966	−0.0664830	+	0.997788i	$0.521178\pi$
$744$	11.1939	0.410389
$745$	−12.5350	−0.459247
$746$	16.5898	0.607397
$747$	−34.1415	−1.24917
$748$	7.39954	0.270554
$749$	23.9370	0.874638
$750$	−2.45007	−0.0894638
$751$	−19.9373	−0.727521	−0.363760	−	0.931493i	$-0.618507\pi$
$751$	−19.9373	−0.727521	−0.363760	+	0.931493i	$0.618507\pi$
$752$	−1.23945	−0.0451981
$753$	1.17183	0.0427038
$754$	30.3634	1.10577
$755$	5.12212	0.186413
$756$	−8.26751	−0.300687
$757$	43.2983	1.57370	0.786852	−	0.617141i	$-0.211709\pi$
$757$	43.2983	1.57370	0.786852	+	0.617141i	$0.211709\pi$
$758$	−4.62389	−0.167947
$759$	15.2226	0.552544
$760$	−3.65294	−0.132506
$761$	−0.915446	−0.0331849	−0.0165925	−	0.999862i	$-0.505282\pi$
$761$	−0.915446	−0.0331849	−0.0165925	+	0.999862i	$0.505282\pi$
$762$	3.32674	0.120515
$763$	−36.2387	−1.31193
$764$	−4.21997	−0.152673
$765$	−1.67758	−0.0606531
$766$	16.1442	0.583312
$767$	−46.1796	−1.66745
$768$	−7.70043	−0.277865
$769$	−7.91608	−0.285461	−0.142731	−	0.989762i	$-0.545588\pi$
$769$	−7.91608	−0.285461	−0.142731	+	0.989762i	$0.545588\pi$
$770$	−8.65610	−0.311944
$771$	−1.06911	−0.0385032
$772$	−7.27385	−0.261792
$773$	−11.9035	−0.428137	−0.214069	−	0.976819i	$-0.568672\pi$
$773$	−11.9035	−0.428137	−0.214069	+	0.976819i	$0.568672\pi$
$774$	2.50198	0.0899317
$775$	−38.5964	−1.38642
$776$	−2.26413	−0.0812777
$777$	−6.93024	−0.248621
$778$	−27.7816	−0.996018
$779$	11.6726	0.418214
$780$	−1.41346	−0.0506101
$781$	39.6557	1.41899
$782$	4.70448	0.168232
$783$	−21.7430	−0.777033
$784$	0.0849109	0.00303253
$785$	3.40565	0.121553
$786$	6.94405	0.247686
$787$	−6.91253	−0.246405	−0.123202	−	0.992382i	$-0.539316\pi$
$787$	−6.91253	−0.246405	−0.123202	+	0.992382i	$0.539316\pi$
$788$	−25.4974	−0.908308
$789$	4.39403	0.156432
$790$	−0.198258	−0.00705371
$791$	−38.5761	−1.37161
$792$	−49.6187	−1.76312
$793$	−32.3230	−1.14782
$794$	−19.4860	−0.691533
$795$	3.16403	0.112217
$796$	8.23694	0.291951
$797$	27.6800	0.980477	0.490239	−	0.871588i	$-0.336910\pi$
$797$	27.6800	0.980477	0.490239	+	0.871588i	$0.336910\pi$
$798$	2.28021	0.0807186
$799$	−6.12834	−0.216805
$800$	25.7733	0.911223
$801$	47.5066	1.67856
$802$	−21.2563	−0.750586
$803$	18.1609	0.640885
$804$	2.99159	0.105505
$805$	8.09152	0.285189
$806$	31.4778	1.10876
$807$	0.222745	0.00784098
$808$	−38.6327	−1.35909
$809$	37.3017	1.31146	0.655729	−	0.754996i	$-0.272361\pi$
$809$	37.3017	1.31146	0.655729	+	0.754996i	$0.272361\pi$
$810$	3.84000	0.134924
$811$	−47.0940	−1.65369	−0.826847	−	0.562426i	$-0.809868\pi$
$811$	−47.0940	−1.65369	−0.826847	+	0.562426i	$0.809868\pi$
$812$	24.5217	0.860544
$813$	6.71966	0.235669
$814$	−32.2622	−1.13079
$815$	4.97922	0.174414
$816$	0.0947292	0.00331619
$817$	2.10920	0.0737915
$818$	−35.1357	−1.22849
$819$	−29.9724	−1.04732
$820$	3.97444	0.138794
$821$	−46.7919	−1.63305	−0.816525	−	0.577310i	$-0.804102\pi$
$821$	−46.7919	−1.63305	−0.816525	+	0.577310i	$0.804102\pi$
$822$	1.52587	0.0532210
$823$	−36.0724	−1.25741	−0.628703	−	0.777645i	$-0.716414\pi$
$823$	−36.0724	−1.25741	−0.628703	+	0.777645i	$0.716414\pi$
$824$	29.6976	1.03456
$825$	−13.4978	−0.469933
$826$	25.3658	0.882591
$827$	11.3508	0.394705	0.197353	−	0.980333i	$-0.436766\pi$
$827$	11.3508	0.394705	0.197353	+	0.980333i	$0.436766\pi$
$828$	17.3060	0.601425
$829$	38.2043	1.32689	0.663446	−	0.748224i	$-0.269093\pi$
$829$	38.2043	1.32689	0.663446	+	0.748224i	$0.269093\pi$
$830$	6.66537	0.231358
$831$	6.13437	0.212799
$832$	−22.7194	−0.787655
$833$	0.419833	0.0145464
$834$	3.05636	0.105833
$835$	−5.24849	−0.181631
$836$	−15.6071	−0.539783
$837$	−22.5410	−0.779132
$838$	18.8739	0.651989
$839$	−34.4576	−1.18961	−0.594804	−	0.803870i	$-0.702771\pi$
$839$	−34.4576	−1.18961	−0.594804	+	0.803870i	$0.702771\pi$
$840$	2.08085	0.0717962
$841$	35.4906	1.22381
$842$	1.22507	0.0422185
$843$	3.18410	0.109666
$844$	−9.63549	−0.331667
$845$	−2.80973	−0.0966577
$846$	15.3330	0.527158
$847$	−70.9025	−2.43624
$848$	2.26458	0.0777661
$849$	6.94276	0.238275
$850$	−4.17144	−0.143079
$851$	30.1580	1.03380
$852$	−3.55686	−0.121856
$853$	−7.52702	−0.257720	−0.128860	−	0.991663i	$-0.541132\pi$
$853$	−7.52702	−0.257720	−0.128860	+	0.991663i	$0.541132\pi$
$854$	17.7546	0.607550
$855$	3.53835	0.121009
$856$	−26.7876	−0.915583
$857$	−8.57048	−0.292762	−0.146381	−	0.989228i	$-0.546763\pi$
$857$	−8.57048	−0.292762	−0.146381	+	0.989228i	$0.546763\pi$
$858$	11.0083	0.375817
$859$	17.0292	0.581030	0.290515	−	0.956870i	$-0.406173\pi$
$859$	17.0292	0.581030	0.290515	+	0.956870i	$0.406173\pi$
$860$	0.718168	0.0244893
$861$	−6.64915	−0.226602
$862$	−17.3488	−0.590903
$863$	40.8745	1.39139	0.695693	−	0.718340i	$-0.255098\pi$
$863$	40.8745	1.39139	0.695693	+	0.718340i	$0.255098\pi$
$864$	15.0521	0.512082
$865$	13.0709	0.444425
$866$	−3.24109	−0.110137
$867$	0.468379	0.0159070
$868$	25.4217	0.862869
$869$	−2.27022	−0.0770120
$870$	2.04187	0.0692260
$871$	22.5466	0.763961
$872$	40.5543	1.37334
$873$	2.19311	0.0742255
$874$	−9.92268	−0.335640
$875$	−14.9127	−0.504143
$876$	−1.62892	−0.0550361
$877$	21.2026	0.715960	0.357980	−	0.933729i	$-0.383466\pi$
$877$	21.2026	0.715960	0.357980	+	0.933729i	$0.383466\pi$
$878$	−17.1851	−0.579968
$879$	10.9362	0.368868
$880$	0.758488	0.0255686
$881$	−17.7196	−0.596990	−0.298495	−	0.954411i	$-0.596485\pi$
$881$	−17.7196	−0.596990	−0.298495	+	0.954411i	$0.596485\pi$
$882$	−1.05041	−0.0353693
$883$	−46.6628	−1.57033	−0.785164	−	0.619288i	$-0.787421\pi$
$883$	−46.6628	−1.57033	−0.785164	+	0.619288i	$0.787421\pi$
$884$	−5.00202	−0.168236
$885$	−3.10548	−0.104390
$886$	3.24297	0.108950
$887$	−17.5521	−0.589341	−0.294670	−	0.955599i	$-0.595210\pi$
$887$	−17.5521	−0.589341	−0.294670	+	0.955599i	$0.595210\pi$
$888$	7.75556	0.260259
$889$	20.2488	0.679122
$890$	−9.27461	−0.310886
$891$	43.9712	1.47309
$892$	−22.0956	−0.739814
$893$	12.9259	0.432548
$894$	−8.75632	−0.292855
$895$	10.5306	0.352000
$896$	−16.0421	−0.535928
$897$	−10.2903	−0.343583
$898$	−27.4404	−0.915699
$899$	66.8575	2.22982
$900$	−15.3451	−0.511505
$901$	11.1970	0.373026
$902$	−30.9537	−1.03064
$903$	−1.20148	−0.0399827
$904$	43.1701	1.43582
$905$	−0.549270	−0.0182583
$906$	3.57805	0.118873
$907$	8.65585	0.287413	0.143706	−	0.989620i	$-0.454098\pi$
$907$	8.65585	0.287413	0.143706	+	0.989620i	$0.454098\pi$
$908$	12.5495	0.416469
$909$	37.4208	1.24117
$910$	5.85143	0.193973
$911$	11.7089	0.387932	0.193966	−	0.981008i	$-0.437865\pi$
$911$	11.7089	0.387932	0.193966	+	0.981008i	$0.437865\pi$
$912$	−0.199803	−0.00661613
$913$	76.3241	2.52596
$914$	−3.52409	−0.116567
$915$	−2.17365	−0.0718588
$916$	32.0204	1.05798
$917$	42.2661	1.39575
$918$	−2.43620	−0.0804067
$919$	17.1531	0.565830	0.282915	−	0.959145i	$-0.408699\pi$
$919$	17.1531	0.565830	0.282915	+	0.959145i	$0.408699\pi$
$920$	−9.05514	−0.298539
$921$	−10.5660	−0.348161
$922$	−5.54521	−0.182622
$923$	−26.8069	−0.882359
$924$	8.89039	0.292472
$925$	−26.7410	−0.879237
$926$	6.94260	0.228148
$927$	−28.7660	−0.944800
$928$	−44.6450	−1.46554
$929$	28.9387	0.949447	0.474724	−	0.880135i	$-0.342548\pi$
$929$	28.9387	0.949447	0.474724	+	0.880135i	$0.342548\pi$
$930$	2.11681	0.0694130
$931$	−0.885512	−0.0290215
$932$	34.7928	1.13968
$933$	8.03917	0.263191
$934$	10.0713	0.329544
$935$	3.75027	0.122647
$936$	33.5418	1.09635
$937$	−5.36789	−0.175361	−0.0876806	−	0.996149i	$-0.527945\pi$
$937$	−5.36789	−0.175361	−0.0876806	+	0.996149i	$0.527945\pi$
$938$	−12.3845	−0.404369
$939$	4.81856	0.157248
$940$	4.40118	0.143551
$941$	−20.2908	−0.661460	−0.330730	−	0.943725i	$-0.607295\pi$
$941$	−20.2908	−0.661460	−0.330730	+	0.943725i	$0.607295\pi$
$942$	2.37902	0.0775125
$943$	28.9348	0.942246
$944$	−2.22268	−0.0723419
$945$	−4.19018	−0.136306
$946$	−5.59322	−0.181851
$947$	−26.6728	−0.866749	−0.433375	−	0.901214i	$-0.642677\pi$
$947$	−26.6728	−0.866749	−0.433375	+	0.901214i	$0.642677\pi$
$948$	0.203625	0.00661342
$949$	−12.2766	−0.398515
$950$	8.79840	0.285458
$951$	6.59213	0.213765
$952$	7.36380	0.238662
$953$	−56.6738	−1.83584	−0.917922	−	0.396760i	$-0.870134\pi$
$953$	−56.6738	−1.83584	−0.917922	+	0.396760i	$0.870134\pi$
$954$	−28.0146	−0.907007
$955$	−2.13878	−0.0692094
$956$	−14.2458	−0.460743
$957$	23.3812	0.755806
$958$	10.8666	0.351085
$959$	9.28749	0.299909
$960$	−1.52783	−0.0493106
$961$	38.3112	1.23584
$962$	21.8089	0.703148
$963$	25.9473	0.836141
$964$	−4.84659	−0.156098
$965$	−3.68656	−0.118675
$966$	5.65233	0.181861
$967$	42.3608	1.36223	0.681116	−	0.732176i	$-0.261495\pi$
$967$	42.3608	1.36223	0.681116	+	0.732176i	$0.261495\pi$
$968$	79.3463	2.55029
$969$	−0.987904	−0.0317361
$970$	−0.428156	−0.0137473
$971$	7.82788	0.251209	0.125604	−	0.992080i	$-0.459913\pi$
$971$	7.82788	0.251209	0.125604	+	0.992080i	$0.459913\pi$
$972$	−13.6128	−0.436632
$973$	18.6030	0.596386
$974$	16.6422	0.533250
$975$	9.12437	0.292214
$976$	−1.55574	−0.0497981
$977$	11.8805	0.380091	0.190045	−	0.981775i	$-0.439137\pi$
$977$	11.8805	0.380091	0.190045	+	0.981775i	$0.439137\pi$
$978$	3.47823	0.111222
$979$	−106.202	−3.39423
$980$	−0.301511	−0.00963142
$981$	−39.2822	−1.25418
$982$	11.0010	0.351054
$983$	−14.8090	−0.472333	−0.236166	−	0.971713i	$-0.575891\pi$
$983$	−14.8090	−0.472333	−0.236166	+	0.971713i	$0.575891\pi$
$984$	7.44100	0.237210
$985$	−12.9227	−0.411752
$986$	7.22586	0.230118
$987$	−7.36307	−0.234369
$988$	10.5502	0.335648
$989$	5.22842	0.166254
$990$	−9.38308	−0.298214
$991$	−58.2731	−1.85111	−0.925554	−	0.378617i	$-0.876400\pi$
$991$	−58.2731	−1.85111	−0.925554	+	0.378617i	$0.876400\pi$
$992$	−46.2835	−1.46950
$993$	4.29610	0.136333
$994$	14.7247	0.467038
$995$	4.17468	0.132346
$996$	−6.84578	−0.216917
$997$	36.7618	1.16426	0.582128	−	0.813097i	$-0.302220\pi$
$997$	36.7618	1.16426	0.582128	+	0.813097i	$0.302220\pi$
$998$	−16.0874	−0.509236
$999$	−15.6172	−0.494107

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.f.1.8	✓	21
3.2	odd	2		6579.2.a.u.1.14		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.f.1.8	✓	21	1.1	even	1	trivial
6579.2.a.u.1.14		21	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q-0.899791 q^{2} +0.468379 q^{3} -1.19038 q^{4} -0.603312 q^{5} -0.421443 q^{6} -2.56518 q^{7} +2.87067 q^{8} -2.78062 q^{9} +O(q^{10})\)	\(q-0.899791 q^{2} +0.468379 q^{3} -1.19038 q^{4} -0.603312 q^{5} -0.421443 q^{6} -2.56518 q^{7} +2.87067 q^{8} -2.78062 q^{9} +0.542854 q^{10} +6.21613 q^{11} -0.557548 q^{12} -4.20204 q^{13} +2.30813 q^{14} -0.282579 q^{15} -0.202249 q^{16} -1.00000 q^{17} +2.50198 q^{18} +2.10920 q^{19} +0.718168 q^{20} -1.20148 q^{21} -5.59322 q^{22} +5.22842 q^{23} +1.34456 q^{24} -4.63601 q^{25} +3.78096 q^{26} -2.70752 q^{27} +3.05354 q^{28} +8.03061 q^{29} +0.254262 q^{30} +8.32533 q^{31} -5.55936 q^{32} +2.91151 q^{33} +0.899791 q^{34} +1.54761 q^{35} +3.30999 q^{36} +5.76809 q^{37} -1.89784 q^{38} -1.96815 q^{39} -1.73191 q^{40} +5.53414 q^{41} +1.08108 q^{42} +1.00000 q^{43} -7.39954 q^{44} +1.67758 q^{45} -4.70448 q^{46} +6.12834 q^{47} -0.0947292 q^{48} -0.419833 q^{49} +4.17144 q^{50} -0.468379 q^{51} +5.00202 q^{52} -11.1970 q^{53} +2.43620 q^{54} -3.75027 q^{55} -7.36380 q^{56} +0.987904 q^{57} -7.22586 q^{58} +10.9898 q^{59} +0.336375 q^{60} +7.69221 q^{61} -7.49106 q^{62} +7.13280 q^{63} +5.40676 q^{64} +2.53514 q^{65} -2.61975 q^{66} -5.36562 q^{67} +1.19038 q^{68} +2.44888 q^{69} -1.39252 q^{70} +6.37948 q^{71} -7.98225 q^{72} +2.92158 q^{73} -5.19007 q^{74} -2.17141 q^{75} -2.51074 q^{76} -15.9455 q^{77} +1.77092 q^{78} -0.365215 q^{79} +0.122019 q^{80} +7.07372 q^{81} -4.97957 q^{82} +12.2784 q^{83} +1.43021 q^{84} +0.603312 q^{85} -0.899791 q^{86} +3.76137 q^{87} +17.8445 q^{88} -17.0849 q^{89} -1.50947 q^{90} +10.7790 q^{91} -6.22379 q^{92} +3.89941 q^{93} -5.51422 q^{94} -1.27250 q^{95} -2.60389 q^{96} -0.788712 q^{97} +0.377762 q^{98} -17.2847 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9}+O(q^{10}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9	\( 21 q + 2 q^{2} - q^{3} + 32 q^{4} - 3 q^{5} + q^{6} + 5 q^{7} + 6 q^{8} + 34 q^{9} + 12 q^{10} + 2 q^{11} - 5 q^{12} + 26 q^{13} - 3 q^{14} + 5 q^{15} + 62 q^{16} - 21 q^{17} - 10 q^{18} + 16 q^{19} - 27 q^{20} + 36 q^{21} - 14 q^{22} - q^{23} + 15 q^{24} + 40 q^{25} - 3 q^{26} - 16 q^{27} + 25 q^{28} + 15 q^{29} + 38 q^{30} + 18 q^{31} + 14 q^{32} + 14 q^{33} - 2 q^{34} - 5 q^{35} + 73 q^{36} + 12 q^{37} + 19 q^{38} - 11 q^{39} + 41 q^{40} - 45 q^{42} + 21 q^{43} - 34 q^{44} - 18 q^{45} + 28 q^{46} - q^{47} - 36 q^{48} + 40 q^{49} + 24 q^{50} + q^{51} + 23 q^{52} + 39 q^{53} - 83 q^{54} - 2 q^{55} - 10 q^{56} + 3 q^{57} + 19 q^{58} + 4 q^{59} - 35 q^{60} + 50 q^{61} + 5 q^{62} - 37 q^{63} + 120 q^{64} - 8 q^{65} - 37 q^{66} + 16 q^{67} - 32 q^{68} + 33 q^{69} - q^{70} + q^{71} - 54 q^{72} + 15 q^{73} + 52 q^{74} + 11 q^{75} - 15 q^{76} + 13 q^{77} - 100 q^{78} + 56 q^{79} - 100 q^{80} + 97 q^{81} - 11 q^{82} + 61 q^{84} + 3 q^{85} + 2 q^{86} - 8 q^{87} - 56 q^{88} + 5 q^{89} - 69 q^{90} - 4 q^{91} - 27 q^{92} + 17 q^{93} - 47 q^{94} - 9 q^{95} + 81 q^{96} - 28 q^{97} + 18 q^{98} - 19 q^{99}+O(q^{100}) \) 21 * q + 2 * q^2 - q^3 + 32 * q^4 - 3 * q^5 + q^6 + 5 * q^7 + 6 * q^8 + 34 * q^9 + 12 * q^10 + 2 * q^11 - 5 * q^12 + 26 * q^13 - 3 * q^14 + 5 * q^15 + 62 * q^16 - 21 * q^17 - 10 * q^18 + 16 * q^19 - 27 * q^20 + 36 * q^21 - 14 * q^22 - q^23 + 15 * q^24 + 40 * q^25 - 3 * q^26 - 16 * q^27 + 25 * q^28 + 15 * q^29 + 38 * q^30 + 18 * q^31 + 14 * q^32 + 14 * q^33 - 2 * q^34 - 5 * q^35 + 73 * q^36 + 12 * q^37 + 19 * q^38 - 11 * q^39 + 41 * q^40 - 45 * q^42 + 21 * q^43 - 34 * q^44 - 18 * q^45 + 28 * q^46 - q^47 - 36 * q^48 + 40 * q^49 + 24 * q^50 + q^51 + 23 * q^52 + 39 * q^53 - 83 * q^54 - 2 * q^55 - 10 * q^56 + 3 * q^57 + 19 * q^58 + 4 * q^59 - 35 * q^60 + 50 * q^61 + 5 * q^62 - 37 * q^63 + 120 * q^64 - 8 * q^65 - 37 * q^66 + 16 * q^67 - 32 * q^68 + 33 * q^69 - q^70 + q^71 - 54 * q^72 + 15 * q^73 + 52 * q^74 + 11 * q^75 - 15 * q^76 + 13 * q^77 - 100 * q^78 + 56 * q^79 - 100 * q^80 + 97 * q^81 - 11 * q^82 + 61 * q^84 + 3 * q^85 + 2 * q^86 - 8 * q^87 - 56 * q^88 + 5 * q^89 - 69 * q^90 - 4 * q^91 - 27 * q^92 + 17 * q^93 - 47 * q^94 - 9 * q^95 + 81 * q^96 - 28 * q^97 + 18 * q^98 - 19 * q^99

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